<?xml version="1.0" encoding="ISO-8859-1"?>

<!DOCTYPE proofs SYSTEM "proof3.dtd">

<?xml-stylesheet type="text/xsl" href="proof3.xsl"?>

<proofs number_of_proofs="1">

<source>nslm_to_aa1.out</source>

<heading><![CDATA[
Prover9 (64) version 2026-3T, March 2026.
Process 372825 was started by veroff on b146-03,
Wed May 13 07:07:44 2026
The command was "prover9 -f nslm_to_aa1.in".
]]></heading>

<proof number="1" length="43892" max_count="86">

<comments><![CDATA[
% Proof 1 at 24148.13 (+ 0.57) seconds: "aa1".
% Length of proof: 43892 (0 new hints)
% Level of proof: 1282
% Maximum clause weight: 86.000
% Given clauses in run: 44541
% Given clauses in proof: 43874 (0 new hints)
]]></comments>

  <clause id="1" type="assumption">
    <literal><![CDATA[
      a(x,y,z) = 1 -> L(z,y,x) = z
    ]]></literal>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="2" type="assumption">
    <literal><![CDATA[
      L(x,y,z) = x -> a(z,y,x) = 1
    ]]></literal>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="3" type="assumption">
    <literal><![CDATA[
      T(x,y) = x -> T(y,x) = y
    ]]></literal>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="4" type="assumption">
    <literal><![CDATA[
      T(x,y) = x -> K(x,y) = 1
    ]]></literal>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="5" type="assumption">
    <literal><![CDATA[
      K(x,y) = 1 -> T(x,y) = x
    ]]></literal>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="6" type="goal">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("aa1")
    ]]></attribute>
    <attribute><![CDATA[
      label(non_clause)
    ]]></attribute>
    <attribute><![CDATA[
      label(goal)
    ]]></attribute>
    <justification jstring="[goal].">
      <j1 rule="goal"/>
    </justification>
  </clause>

  <clause id="7" type="assumption">
    <literal><![CDATA[
      1 * x = x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="8" type="assumption">
    <literal><![CDATA[
      x * 1 = x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="9" type="assumption">
    <literal><![CDATA[
      x \ (x * y) = y
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="10" type="assumption">
    <literal><![CDATA[
      x * (x \ y) = y
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="11" type="assumption">
    <literal><![CDATA[
      (x * y) / y = x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="12" type="assumption">
    <literal><![CDATA[
      (x / y) * y = x
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="13" type="assumption">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,y,z)
    ]]></literal>
    <attribute><![CDATA[
      label("associator")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="14">
    <literal><![CDATA[
      a(x,y,z) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[copy(13),flip(a)].">
      <j1 rule="copy" parents="13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15" type="assumption">
    <literal><![CDATA[
      (x * y) \ (y * x) = K(y,x)
    ]]></literal>
    <attribute><![CDATA[
      label("commutator")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="16">
    <literal><![CDATA[
      K(x,y) = (y * x) \ (x * y)
    ]]></literal>
    <justification jstring="[copy(15),flip(a)].">
      <j1 rule="copy" parents="15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17" type="assumption">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="18">
    <literal><![CDATA[
      L(x,y,z) = (z * y) \ (z * (y * x))
    ]]></literal>
    <justification jstring="[copy(17),flip(a)].">
      <j1 rule="copy" parents="17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19" type="assumption">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="20">
    <literal><![CDATA[
      R(x,y,z) = ((x * y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[copy(19),flip(a)].">
      <j1 rule="copy" parents="19"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21" type="assumption">
    <literal><![CDATA[
      x \ (y * x) = T(y,x)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="22">
    <literal><![CDATA[
      T(x,y) = y \ (x * y)
    ]]></literal>
    <justification jstring="[copy(21),flip(a)].">
      <j1 rule="copy" parents="21"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23" type="assumption">
    <literal><![CDATA[
      T(T(x,y),z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="24" type="assumption">
    <literal><![CDATA[
      T(L(x,y,z),u) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="25">
    <literal><![CDATA[
      L(T(x,y),z,u) = T(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[copy(24),flip(a)].">
      <j1 rule="copy" parents="24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26" type="assumption">
    <literal><![CDATA[
      T(R(x,y,z),u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="27">
    <literal><![CDATA[
      R(T(x,y),z,u) = T(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[copy(26),flip(a)].">
      <j1 rule="copy" parents="26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28" type="assumption">
    <literal><![CDATA[
      L(R(x,y,z),u,w) = R(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="29">
    <literal><![CDATA[
      R(L(x,y,z),u,w) = L(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[copy(28),flip(a)].">
      <j1 rule="copy" parents="28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30" type="assumption">
    <literal><![CDATA[
      L(L(x,y,z),u,w) = L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="31" type="assumption">
    <literal><![CDATA[
      R(R(x,y,z),u,w) = R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="32" type="assumption">
    <literal><![CDATA[
      (x * x) * (y * z) = ((x * x) * y) * z
    ]]></literal>
    <attribute><![CDATA[
      label("NucSq_l")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="33">
    <literal><![CDATA[
      ((x * x) * y) * z = (x * x) * (y * z)
    ]]></literal>
    <justification jstring="[copy(32),flip(a)].">
      <j1 rule="copy" parents="32"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34" type="assumption">
    <literal><![CDATA[
      (x * (y * y)) * z = x * ((y * y) * z)
    ]]></literal>
    <attribute><![CDATA[
      label("NucSq_m")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="35" type="assumption">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x * u != z
    ]]></literal>
    <literal><![CDATA[
      y = u
    ]]></literal>
    <attribute><![CDATA[
      label("*-Cancellation 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="36" type="assumption">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      u * y != z
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <attribute><![CDATA[
      label("*-Cancellation 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="37" type="assumption">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      x / u != z
    ]]></literal>
    <literal><![CDATA[
      y = u
    ]]></literal>
    <attribute><![CDATA[
      label("/-Cancellation 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="38" type="assumption">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      u / y != z
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <attribute><![CDATA[
      label("/-Cancellation 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="39" type="assumption">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      x \ u != z
    ]]></literal>
    <literal><![CDATA[
      y = u
    ]]></literal>
    <attribute><![CDATA[
      label("\-Cancellation 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="40" type="assumption">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      u \ y != z
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <attribute><![CDATA[
      label("\-Cancellation 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="41" type="assumption">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(u,y) != z
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <attribute><![CDATA[
      label("T-Cancellation 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="42" type="assumption">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(w,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <attribute><![CDATA[
      label("L-Cancellation 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="43" type="assumption">
    <literal><![CDATA[
      R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(w,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <attribute><![CDATA[
      label("R-Cancellation 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="44" type="assumption">
    <literal><![CDATA[
      x * y != x * z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <attribute><![CDATA[
      label("*-Cancellation 3")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="45" type="assumption">
    <literal><![CDATA[
      x * y != z * y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <attribute><![CDATA[
      label("*-Cancellation 4")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="46" type="assumption">
    <literal><![CDATA[
      x / y != x / z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <attribute><![CDATA[
      label("/-Cancellation 3")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="47" type="assumption">
    <literal><![CDATA[
      x / y != z / y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <attribute><![CDATA[
      label("/-Cancellation 4")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="48" type="assumption">
    <literal><![CDATA[
      x \ y != x \ z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <attribute><![CDATA[
      label("\-Cancellation 3")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="49" type="assumption">
    <literal><![CDATA[
      x \ y != z \ y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <attribute><![CDATA[
      label("\-Cancellation 4")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="50" type="assumption">
    <literal><![CDATA[
      T(x,y) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <attribute><![CDATA[
      label("T-Cancellation 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="51" type="assumption">
    <literal><![CDATA[
      L(x,y,z) != L(u,y,z)
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <attribute><![CDATA[
      label("L-Cancellation 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="52" type="assumption">
    <literal><![CDATA[
      R(x,y,z) != R(u,y,z)
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <attribute><![CDATA[
      label("R-Cancellation 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="53" type="clausify">
    <literal><![CDATA[
      a(x,y,z) != 1
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = z
    ]]></literal>
    <justification jstring="[clausify(1)].">
      <j1 rule="clausify" parents="1"/>
    </justification>
  </clause>

  <clause id="54" type="clausify">
    <literal><![CDATA[
      L(x,y,z) != x
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = 1
    ]]></literal>
    <justification jstring="[clausify(2)].">
      <j1 rule="clausify" parents="2"/>
    </justification>
  </clause>

  <clause id="55" type="clausify">
    <literal><![CDATA[
      T(x,y) != x
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = y
    ]]></literal>
    <justification jstring="[clausify(3)].">
      <j1 rule="clausify" parents="3"/>
    </justification>
  </clause>

  <clause id="56" type="clausify">
    <literal><![CDATA[
      T(x,y) != x
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = 1
    ]]></literal>
    <justification jstring="[clausify(4)].">
      <j1 rule="clausify" parents="4"/>
    </justification>
  </clause>

  <clause id="57" type="clausify">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = x
    ]]></literal>
    <justification jstring="[clausify(5)].">
      <j1 rule="clausify" parents="5"/>
    </justification>
  </clause>

  <clause id="58" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x * z = y * z
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 1")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="59" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * x = z * y
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 2")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="60" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x / z = y / z
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 3")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="61" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z / x = z / y
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 4")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="62" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x \ z = y \ z
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 5")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="63" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ x = z \ y
    ]]></literal>
    <attribute><![CDATA[
      label("Aux 6")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="64" type="assumption">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <attribute><![CDATA[
      label("Transitivity =")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="65" type="deny">
    <literal><![CDATA[
      a(a(c1,c2,c3),c4,c5) != 1
    ]]></literal>
    <attribute><![CDATA[
      label("aa1")
    ]]></attribute>
    <attribute><![CDATA[
      answer("aa1")
    ]]></attribute>
    <justification jstring="[deny(6)].">
      <j1 rule="deny" parents="6"/>
    </justification>
  </clause>

  <clause id="66">
    <literal><![CDATA[
      1 \ x = x
    ]]></literal>
    <justification jstring="[para(7(a,1),9(a,1,2))].">
      <j1 rule="para" parents="7 9"/>
    </justification>
  </clause>

  <clause id="68">
    <literal><![CDATA[
      x \ x = 1
    ]]></literal>
    <justification jstring="[para(8(a,1),9(a,1,2))].">
      <j1 rule="para" parents="8 9"/>
    </justification>
  </clause>

  <clause id="69">
    <literal><![CDATA[
      x \ (y \ (y * (x * z))) = z
    ]]></literal>
    <justification jstring="[para(9(a,2),9(a,1,2))].">
      <j1 rule="para" parents="9 9"/>
    </justification>
  </clause>

  <clause id="70">
    <literal><![CDATA[
      x \ (x * (y \ (y * z))) = z
    ]]></literal>
    <justification jstring="[para(9(a,2),9(a,1))].">
      <j1 rule="para" parents="9 9"/>
    </justification>
  </clause>

  <clause id="71">
    <literal><![CDATA[
      (x * (x \ 1)) * y = y
    ]]></literal>
    <justification jstring="[para(10(a,2),7(a,1,1))].">
      <j1 rule="para" parents="10 7"/>
    </justification>
  </clause>

  <clause id="72">
    <literal><![CDATA[
      x * (y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10(a,2),8(a,1,2))].">
      <j1 rule="para" parents="10 8"/>
    </justification>
  </clause>

  <clause id="73">
    <literal><![CDATA[
      x \ (y * (y \ (x * z))) = z
    ]]></literal>
    <justification jstring="[para(10(a,2),9(a,1,2))].">
      <j1 rule="para" parents="10 9"/>
    </justification>
  </clause>

  <clause id="74">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) = z
    ]]></literal>
    <justification jstring="[para(9(a,2),10(a,1,2))].">
      <j1 rule="para" parents="9 10"/>
    </justification>
  </clause>

  <clause id="75">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) = z
    ]]></literal>
    <justification jstring="[para(10(a,2),10(a,1,2))].">
      <j1 rule="para" parents="10 10"/>
    </justification>
  </clause>

  <clause id="76">
    <literal><![CDATA[
      x / x = 1
    ]]></literal>
    <justification jstring="[para(7(a,1),11(a,1,1))].">
      <j1 rule="para" parents="7 11"/>
    </justification>
  </clause>

  <clause id="77">
    <literal><![CDATA[
      x / 1 = x
    ]]></literal>
    <justification jstring="[para(8(a,1),11(a,1,1))].">
      <j1 rule="para" parents="8 11"/>
    </justification>
  </clause>

  <clause id="78">
    <literal><![CDATA[
      x * (((x \ y) * z) / z) = y
    ]]></literal>
    <justification jstring="[para(11(a,2),10(a,1,2))].">
      <j1 rule="para" parents="11 10"/>
    </justification>
  </clause>

  <clause id="79">
    <literal><![CDATA[
      x / (y \ x) = y
    ]]></literal>
    <justification jstring="[para(10(a,1),11(a,1,1))].">
      <j1 rule="para" parents="10 11"/>
    </justification>
  </clause>

  <clause id="80">
    <literal><![CDATA[
      ((1 / x) * x) * y = y
    ]]></literal>
    <justification jstring="[para(12(a,2),7(a,1,1))].">
      <j1 rule="para" parents="12 7"/>
    </justification>
  </clause>

  <clause id="81">
    <literal><![CDATA[
      x * ((1 / y) * y) = x
    ]]></literal>
    <justification jstring="[para(12(a,2),8(a,1,2))].">
      <j1 rule="para" parents="12 8"/>
    </justification>
  </clause>

  <clause id="82">
    <literal><![CDATA[
      (x / y) \ x = y
    ]]></literal>
    <justification jstring="[para(12(a,1),9(a,1,2))].">
      <j1 rule="para" parents="12 9"/>
    </justification>
  </clause>

  <clause id="84">
    <literal><![CDATA[
      (x \ (x * (y / z))) * z = y
    ]]></literal>
    <justification jstring="[para(9(a,2),12(a,1,1))].">
      <j1 rule="para" parents="9 12"/>
    </justification>
  </clause>

  <clause id="85">
    <literal><![CDATA[
      ((x * (x \ y)) / z) * z = y
    ]]></literal>
    <justification jstring="[para(12(a,2),10(a,1))].">
      <j1 rule="para" parents="12 10"/>
    </justification>
  </clause>

  <clause id="86">
    <literal><![CDATA[
      (((x * y) / z) * z) / y = x
    ]]></literal>
    <justification jstring="[para(12(a,2),11(a,1,1))].">
      <j1 rule="para" parents="12 11"/>
    </justification>
  </clause>

  <clause id="87">
    <literal><![CDATA[
      (((x / y) / z) * z) * y = x
    ]]></literal>
    <justification jstring="[para(12(a,2),12(a,1,1))].">
      <j1 rule="para" parents="12 12"/>
    </justification>
  </clause>

  <clause id="88">
    <literal><![CDATA[
      (x * (y * z)) * a(x,y,z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(14(a,2),10(a,1,2))].">
      <j1 rule="para" parents="14 10"/>
    </justification>
  </clause>

  <clause id="89">
    <literal><![CDATA[
      (x * y) \ ((x * z) * (z \ y)) = a(x,z,z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="90">
    <literal><![CDATA[
      (x * ((x \ y) * z)) \ (y * z) = a(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="91">
    <literal><![CDATA[
      (x * (y * ((x * y) \ z))) \ z = a(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="92">
    <literal><![CDATA[
      (x * y) \ ((x * (y / z)) * z) = a(x,y / z,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="93">
    <literal><![CDATA[
      ((x / y) * (y * z)) \ (x * z) = a(x / y,y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="94">
    <literal><![CDATA[
      (x * y) * K(y,x) = y * x
    ]]></literal>
    <justification jstring="[para(16(a,2),10(a,1,2))].">
      <j1 rule="para" parents="16 10"/>
    </justification>
  </clause>

  <clause id="95">
    <literal><![CDATA[
      x \ ((y \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="96">
    <literal><![CDATA[
      ((x \ y) * x) \ y = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),16(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="97">
    <literal><![CDATA[
      x \ (y * (x / y)) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="98">
    <literal><![CDATA[
      K(x * x,x) = a(x,x,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),14(a,2)),flip(a)].">
      <j1 rule="para" parents="16 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="99">
    <literal><![CDATA[
      (x * y) \ (x * y) = L(1,y,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="100">
    <literal><![CDATA[
      (x * y) * L(z,y,x) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(18(a,2),10(a,1,2))].">
      <j1 rule="para" parents="18 10"/>
    </justification>
  </clause>

  <clause id="101">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) = L(z,y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="102">
    <literal><![CDATA[
      L(x \ y,x,z) = (z * x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="10 18"/>
    </justification>
  </clause>

  <clause id="103">
    <literal><![CDATA[
      x \ ((x / y) * (y * z)) = L(z,y,x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="104">
    <literal><![CDATA[
      L(x,y / x,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="12 18"/>
    </justification>
  </clause>

  <clause id="105">
    <literal><![CDATA[
      L(x,y,z / (y * x)) = ((z / (y * x)) * y) \ z
    ]]></literal>
    <justification jstring="[para(12(a,1),18(a,2,2))].">
      <j1 rule="para" parents="12 18"/>
    </justification>
  </clause>

  <clause id="106">
    <literal><![CDATA[
      (x * y) / (x * y) = R(1,x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="107">
    <literal><![CDATA[
      (x * y) / (y * 1) = R(x,y,1)
    ]]></literal>
    <justification jstring="[para(8(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="108">
    <literal><![CDATA[
      R(x,x \ y,z) = (y * z) / ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),20(a,2,1,1))].">
      <j1 rule="para" parents="10 20"/>
    </justification>
  </clause>

  <clause id="109">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) = z / (y * ((x * y) \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),20(a,2,1))].">
      <j1 rule="para" parents="10 20"/>
    </justification>
  </clause>

  <clause id="110">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / z = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="111">
    <literal><![CDATA[
      R(x,y,z) * (y * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(20(a,2),12(a,1,1))].">
      <j1 rule="para" parents="20 12"/>
    </justification>
  </clause>

  <clause id="112">
    <literal><![CDATA[
      R(x / y,y,z) = (x * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(12(a,1),20(a,2,1,1))].">
      <j1 rule="para" parents="12 20"/>
    </justification>
  </clause>

  <clause id="113">
    <literal><![CDATA[
      ((x * (y / z)) * z) / y = R(x,y / z,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="114">
    <literal><![CDATA[
      T(x,x) = x
    ]]></literal>
    <justification jstring="[para(22(a,2),9(a,1))].">
      <j1 rule="para" parents="22 9"/>
    </justification>
  </clause>

  <clause id="115">
    <literal><![CDATA[
      x * T(y,x) = y * x
    ]]></literal>
    <justification jstring="[para(22(a,2),10(a,1,2))].">
      <j1 rule="para" parents="22 10"/>
    </justification>
  </clause>

  <clause id="116">
    <literal><![CDATA[
      T(x,x \ y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),22(a,2,2))].">
      <j1 rule="para" parents="10 22"/>
    </justification>
  </clause>

  <clause id="117">
    <literal><![CDATA[
      T(x / y,y) = y \ x
    ]]></literal>
    <justification jstring="[para(12(a,1),22(a,2,2))].">
      <j1 rule="para" parents="12 22"/>
    </justification>
  </clause>

  <clause id="118">
    <literal><![CDATA[
      T(x,x * x) = L(x,x,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),18(a,2)),flip(a)].">
      <j1 rule="para" parents="22 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="119">
    <literal><![CDATA[
      x \ (T(y,z) * x) = T(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(23(a,1),22(a,1)),flip(a)].">
      <j1 rule="para" parents="23 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="120">
    <literal><![CDATA[
      T(T(T(x,y),z),u) = T(T(T(x,u),y),z)
    ]]></literal>
    <justification jstring="[para(23(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="121">
    <literal><![CDATA[
      x \ (L(y,z,u) * x) = L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),22(a,1)),flip(a)].">
      <j1 rule="para" parents="25 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="122">
    <literal><![CDATA[
      x \ (R(y,z,u) * x) = R(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(27(a,2),22(a,1)),flip(a)].">
      <j1 rule="para" parents="27 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="123">
    <literal><![CDATA[
      T(T(R(x,y,z),u),w) = T(R(T(x,w),y,z),u)
    ]]></literal>
    <justification jstring="[para(27(a,2),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="124">
    <literal><![CDATA[
      L(L(L(x,y,z),u,w),v5,v6) = L(L(L(x,v5,v6),y,z),u,w)
    ]]></literal>
    <justification jstring="[para(30(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="125">
    <literal><![CDATA[
      ((x * x) * y) \ ((x * x) * (y * z)) = z
    ]]></literal>
    <justification jstring="[para(33(a,1),9(a,1,2))].">
      <j1 rule="para" parents="33 9"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      (x * x) * (((x * x) \ y) * z) = y * z
    ]]></literal>
    <justification jstring="[para(10(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="127">
    <literal><![CDATA[
      ((x * x) * (y * z)) / z = (x * x) * y
    ]]></literal>
    <justification jstring="[para(33(a,1),11(a,1,1))].">
      <j1 rule="para" parents="33 11"/>
    </justification>
  </clause>

  <clause id="128">
    <literal><![CDATA[
      (x * ((y * y) * (z * u))) \ ((x * ((y * y) * z)) * u) = a(x,(y * y) * z,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="33 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="129">
    <literal><![CDATA[
      (x * ((y * y) * z)) \ (x * ((y * y) * (z * u))) = L(u,(y * y) * z,x)
    ]]></literal>
    <justification jstring="[para(33(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="33 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="130">
    <literal><![CDATA[
      (((x * x) * (y * z)) * u) / (z * u) = R((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="33 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="133">
    <literal><![CDATA[
      (x * ((y * y) * z)) / z = x * (y * y)
    ]]></literal>
    <justification jstring="[para(34(a,1),11(a,1,1))].">
      <j1 rule="para" parents="34 11"/>
    </justification>
  </clause>

  <clause id="134">
    <literal><![CDATA[
      (x * ((y * y) * (z * u))) \ (((x * (y * y)) * z) * u) = a(x * (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(34(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="34 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="135">
    <literal><![CDATA[
      (x * ((y * y) * z)) \ ((x * (y * y)) * (z * u)) = L(u,z,x * (y * y))
    ]]></literal>
    <justification jstring="[para(34(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="34 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="136">
    <literal><![CDATA[
      (x * ((y * y) * (z * z))) * u = (x * (y * y)) * ((z * z) * u)
    ]]></literal>
    <justification jstring="[para(34(a,1),34(a,1,1))].">
      <j1 rule="para" parents="34 34"/>
    </justification>
  </clause>

  <clause id="137">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),35(b,1))].">
      <j1 rule="para" parents="7 35"/>
    </justification>
  </clause>

  <clause id="138">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x * z != y
    ]]></literal>
    <literal><![CDATA[
      1 = z
    ]]></literal>
    <justification jstring="[para(8(a,1),35(a,1))].">
      <j1 rule="para" parents="8 35"/>
    </justification>
  </clause>

  <clause id="139">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(10(a,1),35(a,1))].">
      <j1 rule="para" parents="10 35"/>
    </justification>
  </clause>

  <clause id="140">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * x != y
    ]]></literal>
    <literal><![CDATA[
      1 = z
    ]]></literal>
    <justification jstring="[para(7(a,1),36(a,1))].">
      <j1 rule="para" parents="7 36"/>
    </justification>
  </clause>

  <clause id="141">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(8(a,1),36(b,1))].">
      <j1 rule="para" parents="8 36"/>
    </justification>
  </clause>

  <clause id="142">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(12(a,1),36(a,1))].">
      <j1 rule="para" parents="12 36"/>
    </justification>
  </clause>

  <clause id="143">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      (x * z) / u != y
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(11(a,1),37(a,1))].">
      <j1 rule="para" parents="11 37"/>
    </justification>
  </clause>

  <clause id="144">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z / u != y
    ]]></literal>
    <literal><![CDATA[
      x * u = z
    ]]></literal>
    <justification jstring="[para(11(a,1),38(a,1))].">
      <j1 rule="para" parents="11 38"/>
    </justification>
  </clause>

  <clause id="145">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      z * x = u
    ]]></literal>
    <justification jstring="[para(9(a,1),39(a,1))].">
      <j1 rule="para" parents="9 39"/>
    </justification>
  </clause>

  <clause id="146">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(7(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="7 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="147">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(7(a,1),44(a,2))].">
      <j1 rule="para" parents="7 44"/>
    </justification>
  </clause>

  <clause id="148">
    <literal><![CDATA[
      x * y != x
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(8(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="8 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="149">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x \ z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="10 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="150">
    <literal><![CDATA[
      (x / y) * z != x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(12(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="12 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="151">
    <literal><![CDATA[
      x * y != y
    ]]></literal>
    <literal><![CDATA[
      1 = x
    ]]></literal>
    <justification jstring="[para(7(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="7 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="152">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(8(a,1),45(a,2))].">
      <j1 rule="para" parents="8 45"/>
    </justification>
  </clause>

  <clause id="153">
    <literal><![CDATA[
      x * (y \ z) != z
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(10(a,1),45(a,2))].">
      <j1 rule="para" parents="10 45"/>
    </justification>
  </clause>

  <clause id="154">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(12(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="12 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="156">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(11(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="11 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="157">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(9(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="9 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="158">
    <literal><![CDATA[
      T(x,y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(22(a,2),48(a,1))].">
      <j1 rule="para" parents="22 48"/>
    </justification>
  </clause>

  <clause id="159">
    <literal><![CDATA[
      x \ (y * z) != z
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(9(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="9 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="160">
    <literal><![CDATA[
      x \ ((y * z) * u) != a(y,z,u)
    ]]></literal>
    <literal><![CDATA[
      y * (z * u) = x
    ]]></literal>
    <justification jstring="[para(14(a,2),49(a,1)),flip(a)].">
      <j1 rule="para" parents="14 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="161">
    <literal><![CDATA[
      x \ (y * (z * u)) != L(u,z,y)
    ]]></literal>
    <literal><![CDATA[
      y * z = x
    ]]></literal>
    <justification jstring="[para(18(a,2),49(a,1)),flip(a)].">
      <j1 rule="para" parents="18 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="162">
    <literal><![CDATA[
      T(x,y) != L(T(z,y),u,w)
    ]]></literal>
    <literal><![CDATA[
      L(z,u,w) = x
    ]]></literal>
    <justification jstring="[para(25(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="25 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="163">
    <literal><![CDATA[
      T(x,y) != R(T(z,y),u,w)
    ]]></literal>
    <literal><![CDATA[
      R(z,u,w) = x
    ]]></literal>
    <justification jstring="[para(27(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="27 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="164">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * v5 = L(L(x,u,w),y,z) * v5
    ]]></literal>
    <justification jstring="[hyper(58,a,30,a)].">
      <j1 rule="hyper" parents="58 30"/>
    </justification>
  </clause>

  <clause id="166">
    <literal><![CDATA[
      ((x / y) * y) * z = x * z
    ]]></literal>
    <justification jstring="[hyper(58,a,12,a)].">
      <j1 rule="hyper" parents="58 12"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      (x * (x \ y)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(58,a,10,a)].">
      <j1 rule="hyper" parents="58 10"/>
    </justification>
  </clause>

  <clause id="168">
    <literal><![CDATA[
      x * (y * (y \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(59,a,10,a)].">
      <j1 rule="hyper" parents="59 10"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      x * (y \ (y * z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(59,a,9,a)].">
      <j1 rule="hyper" parents="59 9"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      ((x / y) * y) / z = x / z
    ]]></literal>
    <justification jstring="[hyper(60,a,12,a)].">
      <j1 rule="hyper" parents="60 12"/>
    </justification>
  </clause>

  <clause id="171">
    <literal><![CDATA[
      (x * (x \ y)) / z = y / z
    ]]></literal>
    <justification jstring="[hyper(60,a,10,a)].">
      <j1 rule="hyper" parents="60 10"/>
    </justification>
  </clause>

  <clause id="172">
    <literal><![CDATA[
      (1 * x) / y = x / y
    ]]></literal>
    <justification jstring="[hyper(60,a,7,a)].">
      <j1 rule="hyper" parents="60 7"/>
    </justification>
  </clause>

  <clause id="173">
    <literal><![CDATA[
      R(R(x,y,z),u,w) \ v5 = R(R(x,u,w),y,z) \ v5
    ]]></literal>
    <justification jstring="[hyper(62,a,31,a)].">
      <j1 rule="hyper" parents="62 31"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      (x * (x \ y)) \ z = y \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,10,a)].">
      <j1 rule="hyper" parents="62 10"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      x \ L(L(y,z,u),w,v5) = x \ L(L(y,w,v5),z,u)
    ]]></literal>
    <justification jstring="[hyper(63,a,30,a)].">
      <j1 rule="hyper" parents="63 30"/>
    </justification>
  </clause>

  <clause id="176">
    <literal><![CDATA[
      x \ T(T(y,z),u) = x \ T(T(y,u),z)
    ]]></literal>
    <justification jstring="[hyper(63,a,23,a)].">
      <j1 rule="hyper" parents="63 23"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      x \ (y * 1) = x \ y
    ]]></literal>
    <justification jstring="[hyper(63,a,8,a)].">
      <j1 rule="hyper" parents="63 8"/>
    </justification>
  </clause>

  <clause id="178">
    <literal><![CDATA[
      (x * y) / y = (x / z) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,12,a,b,11,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="64 12 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      (x / y) * y = z * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="64 12 10"/>
    </justification>
  </clause>

  <clause id="180">
    <literal><![CDATA[
      (x / y) * y = 1 * x
    ]]></literal>
    <justification jstring="[hyper(64,a,12,a,b,7,a(flip))].">
      <j1 rule="hyper" parents="64 12 7"/>
    </justification>
  </clause>

  <clause id="181">
    <literal><![CDATA[
      (x * y) / y = 1 * x
    ]]></literal>
    <justification jstring="[hyper(64,a,11,a,b,7,a(flip))].">
      <j1 rule="hyper" parents="64 11 7"/>
    </justification>
  </clause>

  <clause id="182">
    <literal><![CDATA[
      x \ (x * y) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10,a,b,9,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="64 10 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      x * (x \ y) = y * 1
    ]]></literal>
    <justification jstring="[hyper(64,a,10,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="64 10 8"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      x * (x \ y) = 1 * y
    ]]></literal>
    <justification jstring="[hyper(64,a,10,a,b,7,a(flip))].">
      <j1 rule="hyper" parents="64 10 7"/>
    </justification>
  </clause>

  <clause id="185">
    <literal><![CDATA[
      (x * (x \ 1)) \ y = y
    ]]></literal>
    <justification jstring="[para(10(a,2),66(a,1,1))].">
      <j1 rule="para" parents="10 66"/>
    </justification>
  </clause>

  <clause id="186">
    <literal><![CDATA[
      ((1 / x) * x) \ y = y
    ]]></literal>
    <justification jstring="[para(12(a,2),66(a,1,1))].">
      <j1 rule="para" parents="12 66"/>
    </justification>
  </clause>

  <clause id="187">
    <literal><![CDATA[
      1 \ x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(66(a,1),48(a,2))].">
      <j1 rule="para" parents="66 48"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      K(x,x) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,16,a,b,68,a)].">
      <j1 rule="hyper" parents="64 16 68"/>
    </justification>
  </clause>

  <clause id="189">
    <literal><![CDATA[
      x \ x = 1 * 1
    ]]></literal>
    <justification jstring="[hyper(64,a,68,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="64 68 8"/>
    </justification>
  </clause>

  <clause id="190">
    <literal><![CDATA[
      (x \ x) * y = y
    ]]></literal>
    <justification jstring="[para(68(a,2),7(a,1,1))].">
      <j1 rule="para" parents="68 7"/>
    </justification>
  </clause>

  <clause id="191">
    <literal><![CDATA[
      x * (y \ y) = x
    ]]></literal>
    <justification jstring="[para(68(a,2),8(a,1,2))].">
      <j1 rule="para" parents="68 8"/>
    </justification>
  </clause>

  <clause id="192">
    <literal><![CDATA[
      (x / x) * y = y
    ]]></literal>
    <justification jstring="[para(76(a,2),7(a,1,1))].">
      <j1 rule="para" parents="76 7"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      x * (y / y) = x
    ]]></literal>
    <justification jstring="[para(76(a,2),8(a,1,2))].">
      <j1 rule="para" parents="76 8"/>
    </justification>
  </clause>

  <clause id="194">
    <literal><![CDATA[
      x / (y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10(a,2),77(a,1,2))].">
      <j1 rule="para" parents="10 77"/>
    </justification>
  </clause>

  <clause id="195">
    <literal><![CDATA[
      x / ((1 / y) * y) = x
    ]]></literal>
    <justification jstring="[para(12(a,2),77(a,1,2))].">
      <j1 rule="para" parents="12 77"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      x / 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(77(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="77 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="197">
    <literal><![CDATA[
      T(x,R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,27,a,b,114,a(flip))].">
      <j1 rule="hyper" parents="43 27 114"/>
    </justification>
  </clause>

  <clause id="198">
    <literal><![CDATA[
      T(x,L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,25,a,b,114,a(flip))].">
      <j1 rule="hyper" parents="42 25 114"/>
    </justification>
  </clause>

  <clause id="199">
    <literal><![CDATA[
      T(x,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,23,a,b,114,a(flip))].">
      <j1 rule="hyper" parents="41 23 114"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      T(T(x,y),x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(114(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="114 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="201">
    <literal><![CDATA[
      T(L(x,y,z),x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(114(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="114 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="202">
    <literal><![CDATA[
      T(R(x,y,z),x) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(114(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="114 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="203">
    <literal><![CDATA[
      T(x,y) != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(114(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="114 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="204">
    <literal><![CDATA[
      x * K(y,y) = x
    ]]></literal>
    <justification jstring="[para(188(a,2),8(a,1,2))].">
      <j1 rule="para" parents="188 8"/>
    </justification>
  </clause>

  <clause id="205">
    <literal><![CDATA[
      (x * y) / y = z / (x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,79,a,b,11,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="64 79 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      x / (y \ x) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,79,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="64 79 10"/>
    </justification>
  </clause>

  <clause id="207">
    <literal><![CDATA[
      (x / (y \ x)) \ z = y \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,79,a)].">
      <j1 rule="hyper" parents="62 79"/>
    </justification>
  </clause>

  <clause id="208">
    <literal><![CDATA[
      x * (y / (z \ y)) = x * z
    ]]></literal>
    <justification jstring="[hyper(59,a,79,a)].">
      <j1 rule="hyper" parents="59 79"/>
    </justification>
  </clause>

  <clause id="209">
    <literal><![CDATA[
      (x / (y \ x)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(58,a,79,a)].">
      <j1 rule="hyper" parents="58 79"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(37,a,20,a(flip),b,79,a),flip(a)].">
      <j1 rule="hyper" parents="37 20 79"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      x \ (y / ((x * z) \ y)) = z
    ]]></literal>
    <justification jstring="[hyper(35,a,10,a,b,79,a(flip))].">
      <j1 rule="hyper" parents="35 10 79"/>
    </justification>
  </clause>

  <clause id="212">
    <literal><![CDATA[
      ((x * y) * z) / a(x,y,z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(14(a,2),79(a,1,2))].">
      <j1 rule="para" parents="14 79"/>
    </justification>
  </clause>

  <clause id="213">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) = x * y
    ]]></literal>
    <justification jstring="[para(18(a,2),79(a,1,2))].">
      <j1 rule="para" parents="18 79"/>
    </justification>
  </clause>

  <clause id="214">
    <literal><![CDATA[
      (x * y) / T(x,y) = y
    ]]></literal>
    <justification jstring="[para(22(a,2),79(a,1,2))].">
      <j1 rule="para" parents="22 79"/>
    </justification>
  </clause>

  <clause id="215">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z \ x = y
    ]]></literal>
    <justification jstring="[para(79(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="79 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="216">
    <literal><![CDATA[
      x / (y / ((z \ x) \ y)) = z
    ]]></literal>
    <justification jstring="[para(79(a,2),79(a,1,2))].">
      <j1 rule="para" parents="79 79"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      (x / y) \ x = y / 1
    ]]></literal>
    <justification jstring="[hyper(64,a,82,a,b,77,a(flip))].">
      <j1 rule="hyper" parents="64 82 77"/>
    </justification>
  </clause>

  <clause id="218">
    <literal><![CDATA[
      (x / y) \ x = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,82,a,b,10,a(flip))].">
      <j1 rule="hyper" parents="64 82 10"/>
    </justification>
  </clause>

  <clause id="219">
    <literal><![CDATA[
      ((x / y) \ x) \ z = y \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,82,a)].">
      <j1 rule="hyper" parents="62 82"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      x * ((y / z) \ y) = x * z
    ]]></literal>
    <justification jstring="[hyper(59,a,82,a)].">
      <j1 rule="hyper" parents="59 82"/>
    </justification>
  </clause>

  <clause id="221">
    <literal><![CDATA[
      ((x / y) \ x) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(58,a,82,a)].">
      <j1 rule="hyper" parents="58 82"/>
    </justification>
  </clause>

  <clause id="223">
    <literal><![CDATA[
      ((x / (y / z)) \ x) * z = y
    ]]></literal>
    <justification jstring="[hyper(38,a,11,a,b,82,a(flip))].">
      <j1 rule="hyper" parents="38 11 82"/>
    </justification>
  </clause>

  <clause id="224">
    <literal><![CDATA[
      ((x / (y / z)) \ x) \ y = z
    ]]></literal>
    <justification jstring="[hyper(37,a,79,a,b,82,a(flip))].">
      <j1 rule="hyper" parents="37 79 82"/>
    </justification>
  </clause>

  <clause id="225">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      u / x = z
    ]]></literal>
    <justification jstring="[para(82(a,1),40(a,1))].">
      <j1 rule="para" parents="82 40"/>
    </justification>
  </clause>

  <clause id="226">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      y / z = x
    ]]></literal>
    <justification jstring="[para(82(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="82 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      L(x,y,z) != (u \ u) * L(w,y,z)
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(190(a,2),51(a,1)),flip(a)].">
      <j1 rule="para" parents="190 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="228">
    <literal><![CDATA[
      x * (y \ y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(191(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="191 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="229">
    <literal><![CDATA[
      x * (y \ y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(191(a,1),45(a,2))].">
      <j1 rule="para" parents="191 45"/>
    </justification>
  </clause>

  <clause id="230">
    <literal><![CDATA[
      K(x,T(x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,199,a)].">
      <j1 rule="hyper" parents="56 199"/>
    </justification>
  </clause>

  <clause id="231">
    <literal><![CDATA[
      T(x,T(T(x,y),z)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,23,a,b,199,a(flip))].">
      <j1 rule="hyper" parents="41 23 199"/>
    </justification>
  </clause>

  <clause id="232">
    <literal><![CDATA[
      x \ x != y
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(189(a,2),146(a,1)),flip(b)].">
      <j1 rule="para" parents="189 146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="233">
    <literal><![CDATA[
      (x * (x \ 1)) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(10(a,2),147(a,1,1))].">
      <j1 rule="para" parents="10 147"/>
    </justification>
  </clause>

  <clause id="234">
    <literal><![CDATA[
      ((1 / x) * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(12(a,2),147(a,1,1))].">
      <j1 rule="para" parents="12 147"/>
    </justification>
  </clause>

  <clause id="235">
    <literal><![CDATA[
      x / x != y
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(192(a,1),148(a,1)),flip(a)].">
      <j1 rule="para" parents="192 148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="236">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(10(a,2),152(a,1,2))].">
      <j1 rule="para" parents="10 152"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      T(x,R(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,23,a,b,197,a(flip))].">
      <j1 rule="hyper" parents="41 23 197"/>
    </justification>
  </clause>

  <clause id="238">
    <literal><![CDATA[
      (x * ((x \ 1) * y)) \ y = a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(71(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="71 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="239">
    <literal><![CDATA[
      R(x,x \ 1,y) = y / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(71(a,1),20(a,2,1))].">
      <j1 rule="para" parents="71 20"/>
    </justification>
  </clause>

  <clause id="240">
    <literal><![CDATA[
      x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="72 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="241">
    <literal><![CDATA[
      L(x \ 1,x,y) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),18(a,2,2))].">
      <j1 rule="para" parents="72 18"/>
    </justification>
  </clause>

  <clause id="242">
    <literal><![CDATA[
      (x / y) * y = ((1 / z) * z) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,80,a,b,12,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="64 80 12"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      (((1 / x) * x) * y) / z = y / z
    ]]></literal>
    <justification jstring="[hyper(60,a,80,a)].">
      <j1 rule="hyper" parents="60 80"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      R(1 / x,x,y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(80(a,1),20(a,2,1))].">
      <j1 rule="para" parents="80 20"/>
    </justification>
  </clause>

  <clause id="245">
    <literal><![CDATA[
      (x * x) * (1 / x) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,33,a,b,81,a(flip))].">
      <j1 rule="hyper" parents="36 33 81"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      L(x,1 / x,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(81(a,1),18(a,2,2))].">
      <j1 rule="para" parents="81 18"/>
    </justification>
  </clause>

  <clause id="247">
    <literal><![CDATA[
      x * T(y / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(64,a,115,a,b,12,a)].">
      <j1 rule="hyper" parents="64 115 12"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      (x \ y) * T(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(64,a,115,a,b,10,a)].">
      <j1 rule="hyper" parents="64 115 10"/>
    </justification>
  </clause>

  <clause id="249">
    <literal><![CDATA[
      x \ (y * T(z,y)) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(63,a,115,a)].">
      <j1 rule="hyper" parents="63 115"/>
    </justification>
  </clause>

  <clause id="250">
    <literal><![CDATA[
      (x * T(y,x)) / z = (y * x) / z
    ]]></literal>
    <justification jstring="[hyper(60,a,115,a)].">
      <j1 rule="hyper" parents="60 115"/>
    </justification>
  </clause>

  <clause id="251">
    <literal><![CDATA[
      x * (y * T(z,y)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(59,a,115,a)].">
      <j1 rule="hyper" parents="59 115"/>
    </justification>
  </clause>

  <clause id="252">
    <literal><![CDATA[
      (x * T(y,x)) * z = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,115,a)].">
      <j1 rule="hyper" parents="58 115"/>
    </justification>
  </clause>

  <clause id="253">
    <literal><![CDATA[
      T(x * (y * y),x) = (y * y) * x
    ]]></literal>
    <justification jstring="[hyper(35,a,34,a(flip),b,115,a),flip(a)].">
      <j1 rule="hyper" parents="35 34 115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      T((x * x) * y,x * x) = y * (x * x)
    ]]></literal>
    <justification jstring="[hyper(35,a,33,a(flip),b,115,a),flip(a)].">
      <j1 rule="hyper" parents="35 33 115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      T((x * y) / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(35,a,12,a(flip),b,115,a),flip(a)].">
      <j1 rule="hyper" parents="35 12 115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      (x * T(y,x)) / x = y
    ]]></literal>
    <justification jstring="[hyper(36,a,12,a,b,115,a(flip))].">
      <j1 rule="hyper" parents="36 12 115"/>
    </justification>
  </clause>

  <clause id="257">
    <literal><![CDATA[
      x \ (y * T(x,y)) = y
    ]]></literal>
    <justification jstring="[hyper(35,a,10,a,b,115,a(flip))].">
      <j1 rule="hyper" parents="35 10 115"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      x * (y * (y \ T(z,x))) = z * x
    ]]></literal>
    <justification jstring="[para(10(a,2),115(a,1,2))].">
      <j1 rule="para" parents="10 115"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(115(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="115 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      (x * (y * T(z,x * y))) \ (z * (x * y)) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(115(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="115 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(115(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="115 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[para(115(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="115 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      ((x * y) * z) / (T(x,y) * z) = R(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(115(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="115 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="264">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (z * y) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[para(115(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="115 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="265">
    <literal><![CDATA[
      x * T(T(y,x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),115(a,1,2))].">
      <j1 rule="para" parents="23 115"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      x * L(T(y,x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),115(a,1,2))].">
      <j1 rule="para" parents="25 115"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      x * R(T(y,x),z,u) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(27(a,2),115(a,1,2))].">
      <j1 rule="para" parents="27 115"/>
    </justification>
  </clause>

  <clause id="268">
    <literal><![CDATA[
      (x * x) * (T(y,x * x) * z) = (y * (x * x)) * z
    ]]></literal>
    <justification jstring="[para(115(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="115 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="269">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * u != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(115(a,1),35(a,1))].">
      <j1 rule="para" parents="115 35"/>
    </justification>
  </clause>

  <clause id="270">
    <literal><![CDATA[
      x * y != z * x
    ]]></literal>
    <literal><![CDATA[
      T(z,x) = y
    ]]></literal>
    <justification jstring="[para(115(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="115 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="271">
    <literal><![CDATA[
      x * T(y,x) != y * z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(115(a,2),44(a,2)),flip(a)].">
      <j1 rule="para" parents="115 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="272">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(115(a,2),45(a,2)),flip(a)].">
      <j1 rule="para" parents="115 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      T(x,y) * x = x * T(x,y)
    ]]></literal>
    <justification jstring="[para(199(a,1),115(a,1,2))].">
      <j1 rule="para" parents="199 115"/>
    </justification>
  </clause>

  <clause id="274">
    <literal><![CDATA[
      R(x,y,z) * x = x * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(197(a,1),115(a,1,2))].">
      <j1 rule="para" parents="197 115"/>
    </justification>
  </clause>

  <clause id="275">
    <literal><![CDATA[
      L(x,y,z) * x = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(198(a,1),115(a,1,2))].">
      <j1 rule="para" parents="198 115"/>
    </justification>
  </clause>

  <clause id="276">
    <literal><![CDATA[
      T(x / (x / y),x / y) = y
    ]]></literal>
    <justification jstring="[hyper(64,a,117,a,b,82,a)].">
      <j1 rule="hyper" parents="64 117 82"/>
    </justification>
  </clause>

  <clause id="277">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y)
    ]]></literal>
    <justification jstring="[para(20(a,2),117(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      T(T(x / y,z),y) = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(117(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="117 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="279">
    <literal><![CDATA[
      T(L(x / y,z,u),y) = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(117(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="117 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      T(R(x / y,z,u),y) = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(117(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="117 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="281">
    <literal><![CDATA[
      T(x,y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(117(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="117 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="282">
    <literal><![CDATA[
      T(x / y,y \ x) = x / y
    ]]></literal>
    <justification jstring="[para(117(a,1),199(a,1,2))].">
      <j1 rule="para" parents="117 199"/>
    </justification>
  </clause>

  <clause id="283">
    <literal><![CDATA[
      K(x / y,y \ x) = 1
    ]]></literal>
    <justification jstring="[para(117(a,1),230(a,1,2))].">
      <j1 rule="para" parents="117 230"/>
    </justification>
  </clause>

  <clause id="284">
    <literal><![CDATA[
      T(x / y,y) = y \ (x * 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,177,a,b,117,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="64 177 117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="285">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(180(a,2),146(a,1))].">
      <j1 rule="para" parents="180 146"/>
    </justification>
  </clause>

  <clause id="286">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(180(a,2),147(a,1))].">
      <j1 rule="para" parents="180 147"/>
    </justification>
  </clause>

  <clause id="287">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(181(a,2),146(a,1))].">
      <j1 rule="para" parents="181 146"/>
    </justification>
  </clause>

  <clause id="288">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(181(a,2),147(a,1))].">
      <j1 rule="para" parents="181 147"/>
    </justification>
  </clause>

  <clause id="289">
    <literal><![CDATA[
      x \ (y * (y \ x)) = 1
    ]]></literal>
    <justification jstring="[hyper(35,a,10,a,b,183,a(flip))].">
      <j1 rule="hyper" parents="35 10 183"/>
    </justification>
  </clause>

  <clause id="290">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(183(a,2),152(a,1))].">
      <j1 rule="para" parents="183 152"/>
    </justification>
  </clause>

  <clause id="291">
    <literal><![CDATA[
      1 * x != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(184(a,1),44(a,1))].">
      <j1 rule="para" parents="184 44"/>
    </justification>
  </clause>

  <clause id="292">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(184(a,2),146(a,1))].">
      <j1 rule="para" parents="184 146"/>
    </justification>
  </clause>

  <clause id="293">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18,a,b,185,a),flip(a)].">
      <j1 rule="hyper" parents="64 18 185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      K(x \ 1,x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,16,a,b,185,a)].">
      <j1 rule="hyper" parents="64 16 185"/>
    </justification>
  </clause>

  <clause id="295">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18,a,b,186,a),flip(a)].">
      <j1 rule="hyper" parents="64 18 186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="296">
    <literal><![CDATA[
      K(x,1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,16,a,b,186,a)].">
      <j1 rule="hyper" parents="64 16 186"/>
    </justification>
  </clause>

  <clause id="297">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,20,a,b,194,a),flip(a)].">
      <j1 rule="hyper" parents="64 20 194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="298">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,20,a,b,195,a),flip(a)].">
      <j1 rule="hyper" parents="64 20 195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="299">
    <literal><![CDATA[
      K(T(x,y),x) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,200,a)].">
      <j1 rule="hyper" parents="56 200"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      T(T(T(x,y),z),x) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(200(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="200 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="301">
    <literal><![CDATA[
      x / T(y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),214(a,1,1))].">
      <j1 rule="para" parents="10 214"/>
    </justification>
  </clause>

  <clause id="302">
    <literal><![CDATA[
      (T(x,y) * z) / T(T(x,z),y) = z
    ]]></literal>
    <justification jstring="[para(23(a,1),214(a,1,2))].">
      <j1 rule="para" parents="23 214"/>
    </justification>
  </clause>

  <clause id="303">
    <literal><![CDATA[
      (x * y) / z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(214(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="214 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="304">
    <literal><![CDATA[
      (x * T(x,y)) / x = T(x,y)
    ]]></literal>
    <justification jstring="[para(199(a,1),214(a,1,2))].">
      <j1 rule="para" parents="199 214"/>
    </justification>
  </clause>

  <clause id="305">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(217(a,2),196(a,1))].">
      <j1 rule="para" parents="217 196"/>
    </justification>
  </clause>

  <clause id="306">
    <literal><![CDATA[
      T(T(x,y),z) * x = x * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(231(a,1),115(a,1,2))].">
      <j1 rule="para" parents="231 115"/>
    </justification>
  </clause>

  <clause id="307">
    <literal><![CDATA[
      T(x / y,T(y \ x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(117(a,1),231(a,1,2,1))].">
      <j1 rule="para" parents="117 231"/>
    </justification>
  </clause>

  <clause id="308">
    <literal><![CDATA[
      x / (1 / x) = x * x
    ]]></literal>
    <justification jstring="[hyper(36,a,12,a,b,245,a)].">
      <j1 rule="hyper" parents="36 12 245"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      (x * x) \ x = 1 / x
    ]]></literal>
    <justification jstring="[hyper(35,a,10,a,b,245,a)].">
      <j1 rule="hyper" parents="35 10 245"/>
    </justification>
  </clause>

  <clause id="310">
    <literal><![CDATA[
      (x * x) * ((1 / x) * y) = x * y
    ]]></literal>
    <justification jstring="[para(245(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="245 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="312">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(255(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="255 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="313">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * z) / y = x
    ]]></literal>
    <justification jstring="[para(255(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="255 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="314">
    <literal><![CDATA[
      T((x * y) / x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(255(a,1),199(a,1,2))].">
      <j1 rule="para" parents="255 199"/>
    </justification>
  </clause>

  <clause id="315">
    <literal><![CDATA[
      K(x,(y * x) / y) = 1
    ]]></literal>
    <justification jstring="[para(255(a,1),299(a,1,1))].">
      <j1 rule="para" parents="255 299"/>
    </justification>
  </clause>

  <clause id="316">
    <literal><![CDATA[
      L(x,y,z) \ (u * L(T(x,u),y,z)) = u
    ]]></literal>
    <justification jstring="[para(25(a,2),257(a,1,2,2))].">
      <j1 rule="para" parents="25 257"/>
    </justification>
  </clause>

  <clause id="317">
    <literal><![CDATA[
      (x \ 1) * (x \ 1) = (x \ 1) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="318">
    <literal><![CDATA[
      T(x,(y * x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,315,a)].">
      <j1 rule="hyper" parents="57 315"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      T(x \ y,y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),318(a,1,2,1))].">
      <j1 rule="para" parents="10 318"/>
    </justification>
  </clause>

  <clause id="321">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = y \ z
    ]]></literal>
    <justification jstring="[para(115(a,1),149(a,1)),flip(b)].">
      <j1 rule="para" parents="115 149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      x * y != x * z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(11(a,1),150(a,1,1))].">
      <j1 rule="para" parents="11 150"/>
    </justification>
  </clause>

  <clause id="325">
    <literal><![CDATA[
      x \ y != z \ y
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(10(a,1),159(a,1,2))].">
      <j1 rule="para" parents="10 159"/>
    </justification>
  </clause>

  <clause id="326">
    <literal><![CDATA[
      R(T(x,y),z,u) * x = x * R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(237(a,1),115(a,1,2))].">
      <j1 rule="para" parents="237 115"/>
    </justification>
  </clause>

  <clause id="327">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(20(a,2),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="20 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="328">
    <literal><![CDATA[
      x * T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(214(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="214 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="329">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(256(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="256 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(10(a,1),287(a,1,1))].">
      <j1 rule="para" parents="10 287"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(115(a,2),287(a,1,1))].">
      <j1 rule="para" parents="115 287"/>
    </justification>
  </clause>

  <clause id="332">
    <literal><![CDATA[
      (1 * x) / y != z
    ]]></literal>
    <literal><![CDATA[
      x / y = z
    ]]></literal>
    <justification jstring="[para(180(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="180 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="334">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(18(a,2),290(a,1,2))].">
      <j1 rule="para" parents="18 290"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(11(a,1),305(a,1,1))].">
      <j1 rule="para" parents="11 305"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      x \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(214(a,1),305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="214 305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="337">
    <literal><![CDATA[
      x \ (y * T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(256(a,1),305(a,1,1))].">
      <j1 rule="para" parents="256 305"/>
    </justification>
  </clause>

  <clause id="338">
    <literal><![CDATA[
      (x * x) \ x != y
    ]]></literal>
    <literal><![CDATA[
      1 / x = y
    ]]></literal>
    <justification jstring="[para(308(a,1),305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="308 305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      T(x,x) != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(22(a,2),335(a,1))].">
      <j1 rule="para" parents="22 335"/>
    </justification>
  </clause>

  <clause id="340">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(117(a,2),335(a,1))].">
      <j1 rule="para" parents="117 335"/>
    </justification>
  </clause>

  <clause id="341">
    <literal><![CDATA[
      x \ (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(183(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="183 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="342">
    <literal><![CDATA[
      x \ (1 * y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(184(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="184 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="343">
    <literal><![CDATA[
      (x / y) \ (z * (z \ x)) = y
    ]]></literal>
    <justification jstring="[para(12(a,1),73(a,1,2,2,2))].">
      <j1 rule="para" parents="12 73"/>
    </justification>
  </clause>

  <clause id="344">
    <literal><![CDATA[
      x \ ((x * y) * L(z,y,x)) = y * z
    ]]></literal>
    <justification jstring="[para(18(a,2),73(a,1,2,2))].">
      <j1 rule="para" parents="18 73"/>
    </justification>
  </clause>

  <clause id="345">
    <literal><![CDATA[
      x \ ((y * z) * (z \ (y \ x))) = a(y,z,z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(75(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="75 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="346">
    <literal><![CDATA[
      L(x \ (y \ z),x,y) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(75(a,1),18(a,2,2))].">
      <j1 rule="para" parents="75 18"/>
    </justification>
  </clause>

  <clause id="349">
    <literal><![CDATA[
      ((x * (x \ y)) / z) \ y = z
    ]]></literal>
    <justification jstring="[hyper(149,a,85,a)].">
      <j1 rule="hyper" parents="149 85"/>
    </justification>
  </clause>

  <clause id="350">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z = x * y
    ]]></literal>
    <justification jstring="[para(20(a,2),86(a,1,1,1))].">
      <j1 rule="para" parents="20 86"/>
    </justification>
  </clause>

  <clause id="351">
    <literal><![CDATA[
      R((x / y) / z,z,y) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(87(a,1),20(a,2,1))].">
      <j1 rule="para" parents="87 20"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      ((x \ y) * x) * K(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(64,a,94,a,b,10,a)].">
      <j1 rule="hyper" parents="64 94 10"/>
    </justification>
  </clause>

  <clause id="354">
    <literal><![CDATA[
      x * K(y \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(10(a,1),94(a,1,1))].">
      <j1 rule="para" parents="10 94"/>
    </justification>
  </clause>

  <clause id="355">
    <literal><![CDATA[
      x * K(y,x / y) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),94(a,1,1))].">
      <j1 rule="para" parents="12 94"/>
    </justification>
  </clause>

  <clause id="356">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(94(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="94 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="357">
    <literal><![CDATA[
      (x * y) / (x * K(x,y)) = R(y,x,K(x,y))
    ]]></literal>
    <justification jstring="[para(94(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="94 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="358">
    <literal><![CDATA[
      (x * y) * z != y * x
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(94(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="94 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="359">
    <literal><![CDATA[
      (x * y) \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(94(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="94 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      (x \ y) \ y = z * (z \ T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,10,a,b,116,a),flip(a)].">
      <j1 rule="hyper" parents="64 10 116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="361">
    <literal><![CDATA[
      x \ T(y,y \ z) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(63,a,116,a)].">
      <j1 rule="hyper" parents="63 116"/>
    </justification>
  </clause>

  <clause id="362">
    <literal><![CDATA[
      T(x,x \ y) \ z = ((x \ y) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,116,a)].">
      <j1 rule="hyper" parents="62 116"/>
    </justification>
  </clause>

  <clause id="363">
    <literal><![CDATA[
      x / T(y,y \ z) = x / ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(61,a,116,a)].">
      <j1 rule="hyper" parents="61 116"/>
    </justification>
  </clause>

  <clause id="364">
    <literal><![CDATA[
      x * T(y,y \ z) = x * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(59,a,116,a)].">
      <j1 rule="hyper" parents="59 116"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      T(x,x \ y) * z = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,116,a)].">
      <j1 rule="hyper" parents="58 116"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      T(x,y) = (x \ (x * y)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),116(a,1,2))].">
      <j1 rule="para" parents="9 116"/>
    </justification>
  </clause>

  <clause id="367">
    <literal><![CDATA[
      T(T(x,y),x \ z) = T((x \ z) \ z,y)
    ]]></literal>
    <justification jstring="[para(116(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="116 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="368">
    <literal><![CDATA[
      T(L(x,y,z),x \ u) = L((x \ u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(116(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="116 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="370">
    <literal><![CDATA[
      T(x,(x \ y) \ y) = x
    ]]></literal>
    <justification jstring="[para(116(a,1),199(a,1,2))].">
      <j1 rule="para" parents="116 199"/>
    </justification>
  </clause>

  <clause id="371">
    <literal><![CDATA[
      ((x \ y) \ y) * x = x * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(370(a,1),115(a,1,2))].">
      <j1 rule="para" parents="370 115"/>
    </justification>
  </clause>

  <clause id="372">
    <literal><![CDATA[
      T(x,1) = x
    ]]></literal>
    <justification jstring="[hyper(137,a,115,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="137 115 8"/>
    </justification>
  </clause>

  <clause id="373">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(7(a,1),137(a,1))].">
      <j1 rule="para" parents="7 137"/>
    </justification>
  </clause>

  <clause id="374">
    <literal><![CDATA[
      T(T(x,1),1) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,372,a,b,372,a)].">
      <j1 rule="hyper" parents="64 372 372"/>
    </justification>
  </clause>

  <clause id="375">
    <literal><![CDATA[
      K(x,1) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,372,a)].">
      <j1 rule="hyper" parents="56 372"/>
    </justification>
  </clause>

  <clause id="376">
    <literal><![CDATA[
      T(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(55,a,372,a)].">
      <j1 rule="hyper" parents="55 372"/>
    </justification>
  </clause>

  <clause id="377">
    <literal><![CDATA[
      T(x,y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(10(a,2),372(a,1,2))].">
      <j1 rule="para" parents="10 372"/>
    </justification>
  </clause>

  <clause id="378">
    <literal><![CDATA[
      T(x,1) != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(372(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="372 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="379">
    <literal><![CDATA[
      T(x,y \ y) = x
    ]]></literal>
    <justification jstring="[para(68(a,2),372(a,1,2))].">
      <j1 rule="para" parents="68 372"/>
    </justification>
  </clause>

  <clause id="380">
    <literal><![CDATA[
      K(x,1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(375(a,2),147(a,1,1))].">
      <j1 rule="para" parents="375 147"/>
    </justification>
  </clause>

  <clause id="381">
    <literal><![CDATA[
      K(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,376,a)].">
      <j1 rule="hyper" parents="56 376"/>
    </justification>
  </clause>

  <clause id="382">
    <literal><![CDATA[
      T(1,x) * y = y
    ]]></literal>
    <justification jstring="[para(376(a,2),7(a,1,1))].">
      <j1 rule="para" parents="376 7"/>
    </justification>
  </clause>

  <clause id="384">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x \ u = z
    ]]></literal>
    <justification jstring="[para(166(a,2),149(a,1))].">
      <j1 rule="para" parents="166 149"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      (x / (y * (y \ z))) * z = x
    ]]></literal>
    <justification jstring="[hyper(286,a,168,a),flip(a)].">
      <j1 rule="hyper" parents="286 168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="386">
    <literal><![CDATA[
      x / (y \ ((x / z) * z)) = y
    ]]></literal>
    <justification jstring="[hyper(330,a,170,a)].">
      <j1 rule="hyper" parents="330 170"/>
    </justification>
  </clause>

  <clause id="387">
    <literal><![CDATA[
      (((x / y) * y) / z) \ x = z
    ]]></literal>
    <justification jstring="[hyper(37,a,79,a(flip),b,170,a),flip(a)].">
      <j1 rule="hyper" parents="37 79 170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="388">
    <literal><![CDATA[
      x / (y \ ((x * z) / z)) = y
    ]]></literal>
    <justification jstring="[hyper(153,a,178,a(flip))].">
      <j1 rule="hyper" parents="153 178"/>
    </justification>
  </clause>

  <clause id="389">
    <literal><![CDATA[
      x / y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(178(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="178 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="390">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(178(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="178 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="391">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(179(a,2),44(a,1))].">
      <j1 rule="para" parents="179 44"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(179(a,1),45(a,1))].">
      <j1 rule="para" parents="179 45"/>
    </justification>
  </clause>

  <clause id="393">
    <literal><![CDATA[
      (x * (x \ y)) / z != u
    ]]></literal>
    <literal><![CDATA[
      y / z = u
    ]]></literal>
    <justification jstring="[para(179(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="179 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="394">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(182(a,2),44(a,1))].">
      <j1 rule="para" parents="182 44"/>
    </justification>
  </clause>

  <clause id="395">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(182(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="182 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="396">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(182(a,2),229(a,1))].">
      <j1 rule="para" parents="182 229"/>
    </justification>
  </clause>

  <clause id="397">
    <literal><![CDATA[
      x * (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(182(a,1),290(a,1,2))].">
      <j1 rule="para" parents="182 290"/>
    </justification>
  </clause>

  <clause id="398">
    <literal><![CDATA[
      x \ (y * (y \ (x * z))) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(10(a,2),396(a,1,2))].">
      <j1 rule="para" parents="10 396"/>
    </justification>
  </clause>

  <clause id="399">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(117(a,2),396(a,1))].">
      <j1 rule="para" parents="117 396"/>
    </justification>
  </clause>

  <clause id="400">
    <literal><![CDATA[
      (x / (y \ x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(205(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="205 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="401">
    <literal><![CDATA[
      x / y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      u \ x = y
    ]]></literal>
    <justification jstring="[para(206(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="206 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="402">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(206(a,1),305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="206 305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="403">
    <literal><![CDATA[
      ((x * (y * z)) / L(z,y,x)) * u = (x * y) * u
    ]]></literal>
    <justification jstring="[para(18(a,2),209(a,1,1,2))].">
      <j1 rule="para" parents="18 209"/>
    </justification>
  </clause>

  <clause id="404">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      y / u = x
    ]]></literal>
    <justification jstring="[para(218(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="218 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="405">
    <literal><![CDATA[
      ((x / y) \ x) * (y \ z) = z
    ]]></literal>
    <justification jstring="[hyper(157,a,219,a)].">
      <j1 rule="hyper" parents="157 219"/>
    </justification>
  </clause>

  <clause id="406">
    <literal><![CDATA[
      (x / y) * ((z / y) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,12,a(flip),b,220,a),flip(a)].">
      <j1 rule="hyper" parents="373 12 220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="407">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      u / z = x
    ]]></literal>
    <justification jstring="[para(220(a,2),154(a,1))].">
      <j1 rule="para" parents="220 154"/>
    </justification>
  </clause>

  <clause id="408">
    <literal><![CDATA[
      T(x / (x / y),y) = x / (x / y)
    ]]></literal>
    <justification jstring="[para(224(a,1),370(a,1,2))].">
      <j1 rule="para" parents="224 370"/>
    </justification>
  </clause>

  <clause id="409">
    <literal><![CDATA[
      L(T(x,x \ y),x \ y,z) = (z * (x \ y)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(248(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="248 18"/>
    </justification>
  </clause>

  <clause id="410">
    <literal><![CDATA[
      (x \ y) * z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(248(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="248 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="411">
    <literal><![CDATA[
      ((x * T(y,z)) * y) / (y * T(y,z)) = R(x,T(y,z),y)
    ]]></literal>
    <justification jstring="[para(273(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="273 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="412">
    <literal><![CDATA[
      T(x / (x / y),(z / (x / y)) \ z) = y
    ]]></literal>
    <justification jstring="[para(82(a,2),276(a,1,2))].">
      <j1 rule="para" parents="82 276"/>
    </justification>
  </clause>

  <clause id="413">
    <literal><![CDATA[
      (x / y) * (y \ x) = (y \ x) * (x / y)
    ]]></literal>
    <justification jstring="[para(282(a,1),115(a,1,2)),flip(a)].">
      <j1 rule="para" parents="282 115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="414">
    <literal><![CDATA[
      x * T(x \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,115,a,b,294,a)].">
      <j1 rule="hyper" parents="373 115 294"/>
    </justification>
  </clause>

  <clause id="415">
    <literal><![CDATA[
      K(x \ 1,x) / x = x \ 1
    ]]></literal>
    <justification jstring="[hyper(154,a,294,a(flip))].">
      <j1 rule="hyper" parents="154 294"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      (x \ 1) \ K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(149,a,294,a(flip))].">
      <j1 rule="hyper" parents="149 294"/>
    </justification>
  </clause>

  <clause id="417">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(294(a,2),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="294 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      K(x,1 / x) / (1 / x) = x
    ]]></literal>
    <justification jstring="[hyper(154,a,296,a(flip))].">
      <j1 rule="hyper" parents="154 296"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      x / L(T(y,L(y,z,u) \ x),z,u) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(25(a,2),301(a,1,2))].">
      <j1 rule="para" parents="25 301"/>
    </justification>
  </clause>

  <clause id="420">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(20(a,2),349(a,1,1))].">
      <j1 rule="para" parents="20 349"/>
    </justification>
  </clause>

  <clause id="421">
    <literal><![CDATA[
      R(x,y,y \ z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(20(a,2),385(a,1,1))].">
      <j1 rule="para" parents="20 385"/>
    </justification>
  </clause>

  <clause id="422">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[para(301(a,1),405(a,1,1,1))].">
      <j1 rule="para" parents="301 405"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      (x / T(y,y \ z)) * ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[para(301(a,1),406(a,1,2,1))].">
      <j1 rule="para" parents="301 406"/>
    </justification>
  </clause>

  <clause id="424">
    <literal><![CDATA[
      (x \ 1) * x != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(415(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="415 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="425">
    <literal><![CDATA[
      L(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(232,a,99,a),flip(a)].">
      <j1 rule="hyper" parents="232 99"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="427">
    <literal><![CDATA[
      a(x,y,1) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,425,a)].">
      <j1 rule="hyper" parents="54 425"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      R(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(235,a,106,a),flip(a)].">
      <j1 rule="hyper" parents="235 106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="430">
    <literal><![CDATA[
      (x * y) / y = R(x,y,1)
    ]]></literal>
    <justification jstring="[para(8(a,1),107(a,1,2))].">
      <j1 rule="para" parents="8 107"/>
    </justification>
  </clause>

  <clause id="431">
    <literal><![CDATA[
      R(x,y,1) = x
    ]]></literal>
    <justification jstring="[hyper(288,a,430,a),flip(a)].">
      <j1 rule="hyper" parents="288 430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="432">
    <literal><![CDATA[
      R(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(430(a,1),287(a,1))].">
      <j1 rule="para" parents="430 287"/>
    </justification>
  </clause>

  <clause id="434">
    <literal><![CDATA[
      L(x \ 1,x,x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(373,a,309,a(flip),b,241,a),flip(a)].">
      <j1 rule="hyper" parents="373 309 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="435">
    <literal><![CDATA[
      L(x \ 1,x,1 / x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(373,a,186,a(flip),b,241,a),flip(a)].">
      <j1 rule="hyper" parents="373 186 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="436">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,174,a(flip),b,241,a),flip(a)].">
      <j1 rule="hyper" parents="373 174 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="437">
    <literal><![CDATA[
      L(x \ 1,x,y) \ z = ((y * x) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,241,a)].">
      <j1 rule="hyper" parents="62 241"/>
    </justification>
  </clause>

  <clause id="438">
    <literal><![CDATA[
      x / L(y \ 1,y,z) = x / ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(61,a,241,a)].">
      <j1 rule="hyper" parents="61 241"/>
    </justification>
  </clause>

  <clause id="439">
    <literal><![CDATA[
      x * L(y \ 1,y,z) = x * ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(59,a,241,a)].">
      <j1 rule="hyper" parents="59 241"/>
    </justification>
  </clause>

  <clause id="440">
    <literal><![CDATA[
      L(x \ 1,x,y) * z = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,241,a)].">
      <j1 rule="hyper" parents="58 241"/>
    </justification>
  </clause>

  <clause id="441">
    <literal><![CDATA[
      x / L(y \ 1,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(226,a,241,a(flip))].">
      <j1 rule="hyper" parents="226 241"/>
    </justification>
  </clause>

  <clause id="442">
    <literal><![CDATA[
      (x * y) * L(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(157,a,241,a(flip))].">
      <j1 rule="hyper" parents="157 241"/>
    </justification>
  </clause>

  <clause id="443">
    <literal><![CDATA[
      L(x \ 1,x,y / x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),241(a,2,1))].">
      <j1 rule="para" parents="12 241"/>
    </justification>
  </clause>

  <clause id="444">
    <literal><![CDATA[
      T((x * y) \ x,z) = L(T(y \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(241(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="241 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="445">
    <literal><![CDATA[
      R((x * y) \ x,z,u) = L(R(y \ 1,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(241(a,1),29(a,1,1))].">
      <j1 rule="para" parents="241 29"/>
    </justification>
  </clause>

  <clause id="446">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(241(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="241 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="447">
    <literal><![CDATA[
      L(T(x,x \ 1),x \ 1,y) = (y * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(116(a,2),241(a,1,1))].">
      <j1 rule="para" parents="116 241"/>
    </justification>
  </clause>

  <clause id="448">
    <literal><![CDATA[
      x \ (x / L(y \ 1,y,x)) = y
    ]]></literal>
    <justification jstring="[para(241(a,2),211(a,1,2,2))].">
      <j1 rule="para" parents="241 211"/>
    </justification>
  </clause>

  <clause id="449">
    <literal><![CDATA[
      R(1 / x,x,y) \ z = (y / (x * y)) \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,244,a)].">
      <j1 rule="hyper" parents="62 244"/>
    </justification>
  </clause>

  <clause id="450">
    <literal><![CDATA[
      x * R(1 / y,y,z) = x * (z / (y * z))
    ]]></literal>
    <justification jstring="[hyper(59,a,244,a)].">
      <j1 rule="hyper" parents="59 244"/>
    </justification>
  </clause>

  <clause id="451">
    <literal><![CDATA[
      R(1 / x,x,y) * z = (y / (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,244,a)].">
      <j1 rule="hyper" parents="58 244"/>
    </justification>
  </clause>

  <clause id="452">
    <literal><![CDATA[
      R(1 / x,x,y) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(215,a,244,a(flip))].">
      <j1 rule="hyper" parents="215 244"/>
    </justification>
  </clause>

  <clause id="453">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(10(a,1),244(a,2,2))].">
      <j1 rule="para" parents="10 244"/>
    </justification>
  </clause>

  <clause id="454">
    <literal><![CDATA[
      R(1 / (x / y),x / y,y) = y / x
    ]]></literal>
    <justification jstring="[para(12(a,1),244(a,2,2))].">
      <j1 rule="para" parents="12 244"/>
    </justification>
  </clause>

  <clause id="455">
    <literal><![CDATA[
      T(x / (y * x),z) = R(T(1 / y,z),y,x)
    ]]></literal>
    <justification jstring="[para(244(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="244 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="456">
    <literal><![CDATA[
      R(R(1 / x,y,z),x,u) = R(u / (x * u),y,z)
    ]]></literal>
    <justification jstring="[para(244(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="244 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="458">
    <literal><![CDATA[
      (x * (x \ 1)) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(10(a,2),291(a,1,1))].">
      <j1 rule="para" parents="10 291"/>
    </justification>
  </clause>

  <clause id="459">
    <literal><![CDATA[
      (x / x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(76(a,2),291(a,1,1))].">
      <j1 rule="para" parents="76 291"/>
    </justification>
  </clause>

  <clause id="460">
    <literal><![CDATA[
      x \ x != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ 1 = z
    ]]></literal>
    <justification jstring="[para(189(a,2),291(a,1))].">
      <j1 rule="para" parents="189 291"/>
    </justification>
  </clause>

  <clause id="461">
    <literal><![CDATA[
      (x * y) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(181(a,2),291(a,1))].">
      <j1 rule="para" parents="181 291"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(184(a,2),291(a,1))].">
      <j1 rule="para" parents="184 291"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      x * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(23(a,1),328(a,1,2))].">
      <j1 rule="para" parents="23 328"/>
    </justification>
  </clause>

  <clause id="464">
    <literal><![CDATA[
      x * L(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(25(a,2),328(a,1,2))].">
      <j1 rule="para" parents="25 328"/>
    </justification>
  </clause>

  <clause id="465">
    <literal><![CDATA[
      x * R(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(27(a,2),328(a,1,2))].">
      <j1 rule="para" parents="27 328"/>
    </justification>
  </clause>

  <clause id="466">
    <literal><![CDATA[
      ((x / y) * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / z = u
    ]]></literal>
    <justification jstring="[para(180(a,2),332(a,1,1))].">
      <j1 rule="para" parents="180 332"/>
    </justification>
  </clause>

  <clause id="467">
    <literal><![CDATA[
      T(x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(10(a,1),340(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="10 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="468">
    <literal><![CDATA[
      T(T(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(304(a,1),340(a,1,1)),flip(b)].">
      <j1 rule="para" parents="304 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="469">
    <literal><![CDATA[
      L(T(x \ 1,y),x,1 / x) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(435(a,1),25(a,2,1))].">
      <j1 rule="para" parents="435 25"/>
    </justification>
  </clause>

  <clause id="470">
    <literal><![CDATA[
      x / L(y,1 / y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(82(a,1),441(a,1,2,1))].">
      <j1 rule="para" parents="82 441"/>
    </justification>
  </clause>

  <clause id="471">
    <literal><![CDATA[
      (x * y) * z != x
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(441(a,1),150(a,1,1))].">
      <j1 rule="para" parents="441 150"/>
    </justification>
  </clause>

  <clause id="472">
    <literal><![CDATA[
      (x * y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(441(a,1),305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="441 305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="473">
    <literal><![CDATA[
      ((x * y) \ x) * (L(y \ 1,y,x) \ z) = z
    ]]></literal>
    <justification jstring="[para(441(a,1),405(a,1,1,1))].">
      <j1 rule="para" parents="441 405"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      L(L(x \ 1,x,y),y * x,z) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(442(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="442 18"/>
    </justification>
  </clause>

  <clause id="475">
    <literal><![CDATA[
      R(x,x \ 1,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(79(a,1),452(a,1,1,1))].">
      <j1 rule="para" parents="79 452"/>
    </justification>
  </clause>

  <clause id="476">
    <literal><![CDATA[
      x / (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,x) = z
    ]]></literal>
    <justification jstring="[para(452(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="452 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="477">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ (x * y) = z
    ]]></literal>
    <justification jstring="[para(11(a,1),467(a,1,1))].">
      <j1 rule="para" parents="11 467"/>
    </justification>
  </clause>

  <clause id="478">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(79(a,1),467(a,1,1))].">
      <j1 rule="para" parents="79 467"/>
    </justification>
  </clause>

  <clause id="479">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(294(a,2),96(a,1,1))].">
      <j1 rule="para" parents="294 96"/>
    </justification>
  </clause>

  <clause id="480">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(97(a,1),187(a,1))].">
      <j1 rule="para" parents="97 187"/>
    </justification>
  </clause>

  <clause id="481">
    <literal><![CDATA[
      T(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(119(a,1),336(a,1))].">
      <j1 rule="para" parents="119 336"/>
    </justification>
  </clause>

  <clause id="482">
    <literal><![CDATA[
      (x * y) \ R(x,y,y \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,20,a,b,194,a(flip))].">
      <j1 rule="hyper" parents="139 20 194"/>
    </justification>
  </clause>

  <clause id="484">
    <literal><![CDATA[
      (x * x) \ (y * z) = ((x * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,167,a(flip),b,33,a(flip))].">
      <j1 rule="hyper" parents="139 167 33"/>
    </justification>
  </clause>

  <clause id="485">
    <literal><![CDATA[
      ((x * x) * (1 / y)) \ (x * x) = y
    ]]></literal>
    <justification jstring="[hyper(139,a,81,a(flip),b,33,a)].">
      <j1 rule="hyper" parents="139 81 33"/>
    </justification>
  </clause>

  <clause id="486">
    <literal><![CDATA[
      (x * (y * y)) \ z = (y * y) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,75,a(flip),b,34,a)].">
      <j1 rule="hyper" parents="139 75 34"/>
    </justification>
  </clause>

  <clause id="487">
    <literal><![CDATA[
      ((x * x) * y) \ z = y \ ((x * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,75,a(flip),b,33,a)].">
      <j1 rule="hyper" parents="139 75 33"/>
    </justification>
  </clause>

  <clause id="488">
    <literal><![CDATA[
      (x * (y * y)) \ x = (y * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,72,a(flip),b,34,a)].">
      <j1 rule="hyper" parents="139 72 34"/>
    </justification>
  </clause>

  <clause id="489">
    <literal><![CDATA[
      ((x * x) * y) \ (x * x) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,72,a(flip),b,33,a)].">
      <j1 rule="hyper" parents="139 72 33"/>
    </justification>
  </clause>

  <clause id="490">
    <literal><![CDATA[
      ((x * x) \ 1) * y = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,71,a(flip),b,33,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 71 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="491">
    <literal><![CDATA[
      (x * x) * ((y * (x * x)) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,34,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 10 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="492">
    <literal><![CDATA[
      x * (((y * y) * x) \ z) = (y * y) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,33,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 10 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="493">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      T(z,u) = u \ x
    ]]></literal>
    <justification jstring="[para(115(a,1),139(b,1)),flip(c)].">
      <j1 rule="para" parents="115 139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="494">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(142,a,20,a,b,194,a(flip))].">
      <j1 rule="hyper" parents="142 20 194"/>
    </justification>
  </clause>

  <clause id="495">
    <literal><![CDATA[
      (x * y) / ((z * z) * y) = x / (z * z)
    ]]></literal>
    <justification jstring="[hyper(142,a,166,a(flip),b,34,a(flip))].">
      <j1 rule="hyper" parents="142 166 34"/>
    </justification>
  </clause>

  <clause id="496">
    <literal><![CDATA[
      (x / y) / (z * z) = x / ((z * z) * y)
    ]]></literal>
    <justification jstring="[hyper(142,a,87,a(flip),b,34,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="142 87 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="497">
    <literal><![CDATA[
      (x * x) * (1 / y) = (x * x) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,81,a(flip),b,33,a),flip(a)].">
      <j1 rule="hyper" parents="142 81 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="498">
    <literal><![CDATA[
      x / ((y * y) \ 1) = x * (y * y)
    ]]></literal>
    <justification jstring="[hyper(142,a,72,a(flip),b,34,a)].">
      <j1 rule="hyper" parents="142 72 34"/>
    </justification>
  </clause>

  <clause id="499">
    <literal><![CDATA[
      (x * x) / (y \ 1) = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(142,a,72,a(flip),b,33,a)].">
      <j1 rule="hyper" parents="142 72 33"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      (x / ((y * y) * z)) * (y * y) = x / z
    ]]></literal>
    <justification jstring="[hyper(142,a,12,a(flip),b,34,a),flip(a)].">
      <j1 rule="hyper" parents="142 12 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="501">
    <literal><![CDATA[
      ((x \ y) \ y) \ (T(x,x \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(143,a,116,a,b,79,a),flip(a)].">
      <j1 rule="hyper" parents="143 116 79"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="502">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (((y * x) \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(143,a,241,a(flip),b,79,a),flip(a)].">
      <j1 rule="hyper" parents="143 241 79"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="503">
    <literal><![CDATA[
      T(x,x \ y) \ (((x \ y) \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(143,a,116,a(flip),b,79,a),flip(a)].">
      <j1 rule="hyper" parents="143 116 79"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="504">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = z
    ]]></literal>
    <justification jstring="[para(214(a,1),143(b,1)),flip(c)].">
      <j1 rule="para" parents="214 143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="505">
    <literal><![CDATA[
      T(x,x \ y) * (((x \ y) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(144,a,116,a,b,79,a)].">
      <j1 rule="hyper" parents="144 116 79"/>
    </justification>
  </clause>

  <clause id="506">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,31,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="144 31 20"/>
    </justification>
  </clause>

  <clause id="507">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (L(L(x,u,w),y,z) \ v5) = v5
    ]]></literal>
    <justification jstring="[hyper(144,a,30,a,b,79,a)].">
      <j1 rule="hyper" parents="144 30 79"/>
    </justification>
  </clause>

  <clause id="508">
    <literal><![CDATA[
      (x / (y * x)) * (R(1 / y,y,x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(144,a,244,a(flip),b,79,a)].">
      <j1 rule="hyper" parents="144 244 79"/>
    </justification>
  </clause>

  <clause id="509">
    <literal><![CDATA[
      ((x \ y) \ y) * T(z,T(x,x \ y)) = z * T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(144,a,116,a(flip),b,214,a)].">
      <j1 rule="hyper" parents="144 116 214"/>
    </justification>
  </clause>

  <clause id="510">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,29,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 29 20"/>
    </justification>
  </clause>

  <clause id="511">
    <literal><![CDATA[
      T(R(x,y,z),u) * (y * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,27,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 27 20"/>
    </justification>
  </clause>

  <clause id="512">
    <literal><![CDATA[
      (x / ((y \ z) \ z)) * T(y,y \ z) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,116,a,b,82,a)].">
      <j1 rule="hyper" parents="145 116 82"/>
    </justification>
  </clause>

  <clause id="513">
    <literal><![CDATA[
      (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,30,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="145 30 18"/>
    </justification>
  </clause>

  <clause id="514">
    <literal><![CDATA[
      (x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,29,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="145 29 18"/>
    </justification>
  </clause>

  <clause id="515">
    <literal><![CDATA[
      x * L(y,z \ x,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,18,a,b,174,a(flip))].">
      <j1 rule="hyper" parents="145 18 174"/>
    </justification>
  </clause>

  <clause id="517">
    <literal><![CDATA[
      (x * y) * T(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,25,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 25 18"/>
    </justification>
  </clause>

  <clause id="518">
    <literal><![CDATA[
      (x * T(y,y \ z)) / ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(225,a,116,a(flip),b,9,a)].">
      <j1 rule="hyper" parents="225 116 9"/>
    </justification>
  </clause>

  <clause id="519">
    <literal><![CDATA[
      ((1 / x) * x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(242(a,1),45(a,1))].">
      <j1 rule="para" parents="242 45"/>
    </justification>
  </clause>

  <clause id="520">
    <literal><![CDATA[
      x * (y * L(T(z,y),u,w)) = x * (L(z,u,w) * y)
    ]]></literal>
    <justification jstring="[para(25(a,2),251(a,1,2,2))].">
      <j1 rule="para" parents="25 251"/>
    </justification>
  </clause>

  <clause id="521">
    <literal><![CDATA[
      L(x \ T(y,z),x,z) = (z * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(258(a,1),18(a,2,2))].">
      <j1 rule="para" parents="258 18"/>
    </justification>
  </clause>

  <clause id="522">
    <literal><![CDATA[
      x * T(x \ (y * x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(22(a,1),265(a,1,2,1))].">
      <j1 rule="para" parents="22 265"/>
    </justification>
  </clause>

  <clause id="523">
    <literal><![CDATA[
      x * T(T(T(y,x),z),u) = T(T(y,z),u) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),265(a,1,2,1))].">
      <j1 rule="para" parents="23 265"/>
    </justification>
  </clause>

  <clause id="524">
    <literal><![CDATA[
      T(x,y) * R(x,z,u) = R(x,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(197(a,1),265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="197 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="525">
    <literal><![CDATA[
      T(x / y,z) * y = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(117(a,1),265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="117 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      T((x * y) / x,z) * x = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(255(a,1),265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="255 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="527">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(116(a,1),265(a,1,2,1))].">
      <j1 rule="para" parents="116 265"/>
    </justification>
  </clause>

  <clause id="528">
    <literal><![CDATA[
      (x * (y * R(y,z,u))) \ ((x * R(y,z,u)) * y) = a(x,R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(274(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="274 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="529">
    <literal><![CDATA[
      (L(x,y,z) * (x * u)) \ ((x * L(x,y,z)) * u) = a(L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(275(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="275 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="530">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (L(x,y,z) * (x * u)) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(275(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="275 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="531">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x = T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(313,a,278,a)].">
      <j1 rule="hyper" parents="313 278"/>
    </justification>
  </clause>

  <clause id="532">
    <literal><![CDATA[
      x * T(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) * x = u
    ]]></literal>
    <justification jstring="[para(278(a,1),328(a,1,2))].">
      <j1 rule="para" parents="278 328"/>
    </justification>
  </clause>

  <clause id="533">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(278(a,1),331(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="278 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="534">
    <literal><![CDATA[
      T(T((x \ y) \ y,z),x) = T(T(x,x \ y),z)
    ]]></literal>
    <justification jstring="[para(116(a,1),300(a,1,1,1))].">
      <j1 rule="para" parents="116 300"/>
    </justification>
  </clause>

  <clause id="535">
    <literal><![CDATA[
      (x * x) \ (x * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(149,a,310,a)].">
      <j1 rule="hyper" parents="149 310"/>
    </justification>
  </clause>

  <clause id="536">
    <literal><![CDATA[
      (1 / x) * (x \ y) = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,310,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="537">
    <literal><![CDATA[
      (x * x) * (y * (1 / x)) = x * T(y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,251,a(flip),b,310,a)].">
      <j1 rule="hyper" parents="64 251 310"/>
    </justification>
  </clause>

  <clause id="538">
    <literal><![CDATA[
      x * ((1 / x) \ y) = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,168,a(flip),b,310,a),flip(a)].">
      <j1 rule="hyper" parents="64 168 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="539">
    <literal><![CDATA[
      x \ ((x * x) * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,310,a(flip))].">
      <j1 rule="hyper" parents="139 168 310"/>
    </justification>
  </clause>

  <clause id="540">
    <literal><![CDATA[
      (1 / x) \ ((x * x) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,75,a(flip),b,310,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 75 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="541">
    <literal><![CDATA[
      (x * T(y,z)) / x = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(313,a,312,a)].">
      <j1 rule="hyper" parents="313 312"/>
    </justification>
  </clause>

  <clause id="542">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T((y * z) / y,u) = x
    ]]></literal>
    <justification jstring="[para(312(a,1),50(a,2)),flip(b)].">
      <j1 rule="para" parents="312 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="543">
    <literal><![CDATA[
      T((((x * y) / x) \ z) \ z,x) = T(y,((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[para(116(a,1),312(a,1,1))].">
      <j1 rule="para" parents="116 312"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      x \ ((y \ x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(354(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="354 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="546">
    <literal><![CDATA[
      K(x \ y,x) * z != (x \ y) * x
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x \ y,x)) = z
    ]]></literal>
    <justification jstring="[para(354(a,1),270(a,2))].">
      <j1 rule="para" parents="354 270"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(355(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="355 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="548">
    <literal><![CDATA[
      (x * x) \ ((x * x) / y) = 1 / y
    ]]></literal>
    <justification jstring="[para(485(a,1),211(a,1,2,2))].">
      <j1 rule="para" parents="485 211"/>
    </justification>
  </clause>

  <clause id="549">
    <literal><![CDATA[
      1 / (x * x) = (x * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(338,a,488,a)].">
      <j1 rule="hyper" parents="338 488"/>
    </justification>
  </clause>

  <clause id="550">
    <literal><![CDATA[
      ((x * x) \ y) \ 1 = y \ (x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,174,a(flip),b,489,a),flip(a)].">
      <j1 rule="hyper" parents="64 174 489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="551">
    <literal><![CDATA[
      1 / (x \ (y * y)) = (y * y) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,174,a(flip),b,489,a(flip))].">
      <j1 rule="hyper" parents="225 174 489"/>
    </justification>
  </clause>

  <clause id="552">
    <literal><![CDATA[
      ((1 / x) * y) \ 1 = (x * y) \ (x * x)
    ]]></literal>
    <justification jstring="[para(310(a,1),489(a,1,1)),flip(a)].">
      <j1 rule="para" parents="310 489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="553">
    <literal><![CDATA[
      (1 / x) / x = (x * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(142,a,309,a(flip),b,490,a)].">
      <j1 rule="hyper" parents="142 309 490"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      ((x * x) \ 1) \ y = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,9,a(flip),b,490,a)].">
      <j1 rule="hyper" parents="139 9 490"/>
    </justification>
  </clause>

  <clause id="555">
    <literal><![CDATA[
      T((x * x) \ 1,x) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[para(553(a,1),117(a,1,1))].">
      <j1 rule="para" parents="553 117"/>
    </justification>
  </clause>

  <clause id="556">
    <literal><![CDATA[
      (x * x) * ((1 / y) * z) = ((x * x) / y) * z
    ]]></literal>
    <justification jstring="[para(497(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="497 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="557">
    <literal><![CDATA[
      x * ((y * y) \ 1) = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,12,a(flip),b,498,a)].">
      <j1 rule="hyper" parents="144 12 498"/>
    </justification>
  </clause>

  <clause id="558">
    <literal><![CDATA[
      T((x * x) * y,y \ 1) = (y \ 1) \ (x * x)
    ]]></literal>
    <justification jstring="[para(499(a,1),117(a,1,1))].">
      <j1 rule="para" parents="499 117"/>
    </justification>
  </clause>

  <clause id="559">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18,a,b,535,a),flip(a)].">
      <j1 rule="hyper" parents="64 18 535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="560">
    <literal><![CDATA[
      L(x,y,y) / (y * x) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(142,a,18,a,b,535,a(flip))].">
      <j1 rule="hyper" parents="142 18 535"/>
    </justification>
  </clause>

  <clause id="561">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(139,a,18,a,b,535,a(flip))].">
      <j1 rule="hyper" parents="139 18 535"/>
    </justification>
  </clause>

  <clause id="562">
    <literal><![CDATA[
      T(x * x,x) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,257,a(flip),b,535,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 257 535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="563">
    <literal><![CDATA[
      x / T(y * y,y) = x / ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[hyper(225,a,562,a,b,82,a)].">
      <j1 rule="hyper" parents="225 562 82"/>
    </justification>
  </clause>

  <clause id="564">
    <literal><![CDATA[
      T(x * x,x) \ y = ((1 / x) \ x) \ y
    ]]></literal>
    <justification jstring="[hyper(62,a,562,a)].">
      <j1 rule="hyper" parents="62 562"/>
    </justification>
  </clause>

  <clause id="565">
    <literal><![CDATA[
      (x * y) \ L(y,x,x) = T(1 / x,x * y)
    ]]></literal>
    <justification jstring="[hyper(321,a,559,a),flip(a)].">
      <j1 rule="hyper" parents="321 559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="566">
    <literal><![CDATA[
      (1 / x) \ L(L(y,x,x),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,30,a,b,559,a)].">
      <j1 rule="hyper" parents="139 30 559"/>
    </justification>
  </clause>

  <clause id="567">
    <literal><![CDATA[
      L(T(x,y),y,y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,251,a(flip),b,559,a),flip(a)].">
      <j1 rule="hyper" parents="64 251 559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      L(x,y \ 1,y \ 1) = y * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,209,a(flip),b,559,a),flip(a)].">
      <j1 rule="hyper" parents="64 209 559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      L(x \ y,x,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,168,a(flip),b,559,a),flip(a)].">
      <j1 rule="hyper" parents="64 168 559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="570">
    <literal><![CDATA[
      L(x,y / x,y / x) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[para(12(a,1),559(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="571">
    <literal><![CDATA[
      (1 / x) * ((x * x) * y) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[para(559(a,1),34(a,1,1)),flip(a)].">
      <j1 rule="para" parents="559 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="572">
    <literal><![CDATA[
      ((x * x) \ x) * (x * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[para(309(a,2),559(a,1,1))].">
      <j1 rule="para" parents="309 559"/>
    </justification>
  </clause>

  <clause id="573">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x) = z
    ]]></literal>
    <justification jstring="[para(560(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="560 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      L(x,y,y) / (((z / y) \ z) * x) = 1 / y
    ]]></literal>
    <justification jstring="[para(221(a,2),560(a,1,2))].">
      <j1 rule="para" parents="221 560"/>
    </justification>
  </clause>

  <clause id="575">
    <literal><![CDATA[
      T(1 / x,x * y) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ L(y,x,x) = z
    ]]></literal>
    <justification jstring="[para(560(a,1),467(a,1,1))].">
      <j1 rule="para" parents="560 467"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(373,a,209,a(flip),b,569,a),flip(a)].">
      <j1 rule="hyper" parents="373 209 569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      L(L(x,y,z),z * y,z * y) = (1 / (z * y)) * (z * (y * x))
    ]]></literal>
    <justification jstring="[para(18(a,2),569(a,1,1))].">
      <j1 rule="para" parents="18 569"/>
    </justification>
  </clause>

  <clause id="578">
    <literal><![CDATA[
      L(T(x \ y,z),x,x) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(569(a,1),25(a,2,1))].">
      <j1 rule="para" parents="569 25"/>
    </justification>
  </clause>

  <clause id="579">
    <literal><![CDATA[
      L(R(x \ y,z,u),x,x) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(569(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="569 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="580">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,x) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(569(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="569 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="581">
    <literal><![CDATA[
      ((x * x) \ x) * y = L(x \ y,x,x)
    ]]></literal>
    <justification jstring="[para(309(a,2),569(a,2,1)),flip(a)].">
      <j1 rule="para" parents="309 569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) \ y = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,209,a(flip),b,536,a),flip(a)].">
      <j1 rule="hyper" parents="64 209 536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="583">
    <literal><![CDATA[
      (x * y) \ (x * ((y * y) * z)) = L((1 / y) \ z,y,x)
    ]]></literal>
    <justification jstring="[para(538(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="538 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="584">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) * y = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),538(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="585">
    <literal><![CDATA[
      (x * (x * y)) \ (x * x) = L(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[para(18(a,2),550(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="586">
    <literal><![CDATA[
      (x * y) \ (x * (y / (z * z))) = L((z * z) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(557(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="557 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="587">
    <literal><![CDATA[
      x * (1 / (y * y)) = x / (y * y)
    ]]></literal>
    <justification jstring="[para(549(a,2),557(a,1,2))].">
      <j1 rule="para" parents="549 557"/>
    </justification>
  </clause>

  <clause id="588">
    <literal><![CDATA[
      (x * y) * L(T(z,y),y,x) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,251,a(flip),b,100,a),flip(a)].">
      <j1 rule="hyper" parents="373 251 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(321,a,100,a),flip(a)].">
      <j1 rule="hyper" parents="321 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      (x * (y * z)) / L(T(y,z),z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(142,a,251,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="142 251 100"/>
    </justification>
  </clause>

  <clause id="591">
    <literal><![CDATA[
      (x * y) / L(z \ y,z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(142,a,168,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="142 168 100"/>
    </justification>
  </clause>

  <clause id="592">
    <literal><![CDATA[
      x * L(y,z,x / z) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,166,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="64 166 100"/>
    </justification>
  </clause>

  <clause id="593">
    <literal><![CDATA[
      L(x,y * y,z) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,34,a,b,100,a),flip(a)].">
      <j1 rule="hyper" parents="35 34 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="594">
    <literal><![CDATA[
      L(x,y,z * z) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,33,a,b,100,a),flip(a)].">
      <j1 rule="hyper" parents="35 33 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="595">
    <literal><![CDATA[
      L(x \ T(y * x,y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(35,a,258,a(flip),b,100,a),flip(a)].">
      <j1 rule="hyper" parents="35 258 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="596">
    <literal><![CDATA[
      L(x \ (y \ ((y * x) * z)),x,y) = z
    ]]></literal>
    <justification jstring="[hyper(35,a,75,a(flip),b,100,a),flip(a)].">
      <j1 rule="hyper" parents="35 75 100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="597">
    <literal><![CDATA[
      (x * (y * z)) / T(x * y,L(z,y,x)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,100,a(flip),b,115,a)].">
      <j1 rule="hyper" parents="142 100 115"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      x \ (y * L(z,x \ y,x)) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,167,a(flip),b,100,a(flip))].">
      <j1 rule="hyper" parents="139 167 100"/>
    </justification>
  </clause>

  <clause id="599">
    <literal><![CDATA[
      (x * (y * (z * u))) \ ((x * (y * z)) * L(u,z,y)) = a(x,y * z,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(100(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="100 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      (x * (y * L(z,y,x))) \ (x * (y * z)) = a(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(100(a,1),14(a,2,2)),flip(a)].">
      <j1 rule="para" parents="100 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="601">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(100(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="100 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="602">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(100(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="100 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="603">
    <literal><![CDATA[
      ((x * (y * z)) * u) / (L(z,y,x) * u) = R(x * y,L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(100(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="100 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      (x * (y * z)) / (y * L(z,y,x)) = R(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(100(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="100 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="605">
    <literal><![CDATA[
      (x * x) * (L(y,x,x) * z) = (x * (x * y)) * z
    ]]></literal>
    <justification jstring="[para(100(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="100 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="606">
    <literal><![CDATA[
      (x * y) * z != x * (y * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(100(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="100 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="607">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != x * u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(100(a,2),44(a,1))].">
      <j1 rule="para" parents="100 44"/>
    </justification>
  </clause>

  <clause id="608">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(100(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="100 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="609">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(100(a,1),94(a,1,1))].">
      <j1 rule="para" parents="100 94"/>
    </justification>
  </clause>

  <clause id="610">
    <literal><![CDATA[
      K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(294(a,2),100(a,1,1))].">
      <j1 rule="para" parents="294 100"/>
    </justification>
  </clause>

  <clause id="611">
    <literal><![CDATA[
      x * ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(100(a,1),233(a,1))].">
      <j1 rule="para" parents="100 233"/>
    </justification>
  </clause>

  <clause id="612">
    <literal><![CDATA[
      x * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,L(z,y,x)) = L(z,y,x) \ u
    ]]></literal>
    <justification jstring="[para(100(a,1),321(a,1))].">
      <j1 rule="para" parents="100 321"/>
    </justification>
  </clause>

  <clause id="613">
    <literal><![CDATA[
      (x * y) * L(K(z \ y,z),y,x) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(354(a,1),100(a,2,2))].">
      <j1 rule="para" parents="354 100"/>
    </justification>
  </clause>

  <clause id="614">
    <literal><![CDATA[
      L(x,y * y,z) = L(x,u * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,593,a,b,593,a)].">
      <j1 rule="hyper" parents="373 593 593"/>
    </justification>
  </clause>

  <clause id="615">
    <literal><![CDATA[
      L(x,1,y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),593(a,1,2))].">
      <j1 rule="para" parents="7 593"/>
    </justification>
  </clause>

  <clause id="616">
    <literal><![CDATA[
      L(x,y * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(593(a,1),51(a,2))].">
      <j1 rule="para" parents="593 51"/>
    </justification>
  </clause>

  <clause id="617">
    <literal><![CDATA[
      L(x,1,y) = z \ (z * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,9,a,b,615,a),flip(a)].">
      <j1 rule="hyper" parents="373 9 615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="618">
    <literal><![CDATA[
      a(x,1,y) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,615,a)].">
      <j1 rule="hyper" parents="54 615"/>
    </justification>
  </clause>

  <clause id="620">
    <literal><![CDATA[
      a(x * x,y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,594,a)].">
      <j1 rule="hyper" parents="54 594"/>
    </justification>
  </clause>

  <clause id="621">
    <literal><![CDATA[
      L(x,y,1) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),594(a,1,3))].">
      <j1 rule="para" parents="7 594"/>
    </justification>
  </clause>

  <clause id="622">
    <literal><![CDATA[
      L(x,y,z * z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(594(a,1),51(a,2))].">
      <j1 rule="para" parents="594 51"/>
    </justification>
  </clause>

  <clause id="623">
    <literal><![CDATA[
      L(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(621(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="621 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="624">
    <literal><![CDATA[
      L(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(621(a,1),51(a,2))].">
      <j1 rule="para" parents="621 51"/>
    </justification>
  </clause>

  <clause id="625">
    <literal><![CDATA[
      L(x,a(y * y,z,u),w) = x
    ]]></literal>
    <justification jstring="[para(620(a,2),615(a,1,2))].">
      <j1 rule="para" parents="620 615"/>
    </justification>
  </clause>

  <clause id="626">
    <literal><![CDATA[
      L(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(z * y,z) = x
    ]]></literal>
    <justification jstring="[para(595(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="595 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="627">
    <literal><![CDATA[
      L(x \ (y * x),x,y) = T(y,y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,22,a,b,102,a),flip(a)].">
      <j1 rule="hyper" parents="373 22 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="628">
    <literal><![CDATA[
      L(x \ y,x,1 / x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,186,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="373 186 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="629">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(373,a,185,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="373 185 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="630">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,174,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="373 174 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="631">
    <literal><![CDATA[
      ((x * y) * (x * y)) \ (x * z) = (1 / (x * y)) * L(y \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,102,a,b,540,a),flip(a)].">
      <j1 rule="hyper" parents="145 102 540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="632">
    <literal><![CDATA[
      x * L(y \ z,y,u) = x * ((u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(145,a,102,a,b,9,a)].">
      <j1 rule="hyper" parents="145 102 9"/>
    </justification>
  </clause>

  <clause id="633">
    <literal><![CDATA[
      L(x \ y,x,z / x) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),102(a,2,1))].">
      <j1 rule="para" parents="12 102"/>
    </justification>
  </clause>

  <clause id="634">
    <literal><![CDATA[
      L(x \ y,x,z / y) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[para(12(a,1),102(a,2,2))].">
      <j1 rule="para" parents="12 102"/>
    </justification>
  </clause>

  <clause id="635">
    <literal><![CDATA[
      (x * (y * (z * u))) \ (x * ((y * z) * u)) = L(a(y,z,u),y * (z * u),x)
    ]]></literal>
    <justification jstring="[para(14(a,2),102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="636">
    <literal><![CDATA[
      T((x * y) \ (x * z),u) = L(T(y \ z,u),y,x)
    ]]></literal>
    <justification jstring="[para(102(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="102 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="637">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,w) = L((w * x) \ (w * y),z,u)
    ]]></literal>
    <justification jstring="[para(102(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="102 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="638">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(115(a,1),102(a,2,1))].">
      <j1 rule="para" parents="115 102"/>
    </justification>
  </clause>

  <clause id="639">
    <literal><![CDATA[
      L(x \ K(y,z),x,z * y) = ((z * y) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(94(a,1),102(a,2,2))].">
      <j1 rule="para" parents="94 102"/>
    </justification>
  </clause>

  <clause id="640">
    <literal><![CDATA[
      (x * T(x,y)) \ (T(x,y) * z) = L(x \ z,x,T(x,y))
    ]]></literal>
    <justification jstring="[para(273(a,1),102(a,2,1)),flip(a)].">
      <j1 rule="para" parents="273 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="641">
    <literal><![CDATA[
      L(x \ (1 / y),x,y) = (y * x) \ K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(296(a,2),102(a,2,2))].">
      <j1 rule="para" parents="296 102"/>
    </justification>
  </clause>

  <clause id="642">
    <literal><![CDATA[
      L(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ y = z
    ]]></literal>
    <justification jstring="[para(102(a,2),341(a,1))].">
      <j1 rule="para" parents="102 341"/>
    </justification>
  </clause>

  <clause id="643">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (L(x,y,z) * u) = L(x \ u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(275(a,1),102(a,2,1)),flip(a)].">
      <j1 rule="para" parents="275 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="644">
    <literal><![CDATA[
      L(L(x \ y,x,z),z * x,z * x) = (1 / (z * x)) * (z * y)
    ]]></literal>
    <justification jstring="[para(102(a,2),569(a,1,1))].">
      <j1 rule="para" parents="102 569"/>
    </justification>
  </clause>

  <clause id="645">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * u)
    ]]></literal>
    <justification jstring="[para(100(a,1),102(a,2,1))].">
      <j1 rule="para" parents="100 102"/>
    </justification>
  </clause>

  <clause id="646">
    <literal><![CDATA[
      L(x \ L(y,z,u),x,u * z) = ((u * z) * x) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(100(a,1),102(a,2,2))].">
      <j1 rule="para" parents="100 102"/>
    </justification>
  </clause>

  <clause id="647">
    <literal><![CDATA[
      L(L(x \ y,x,z),z * x,u) = (u * (z * x)) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(102(a,2),102(a,1,1))].">
      <j1 rule="para" parents="102 102"/>
    </justification>
  </clause>

  <clause id="648">
    <literal><![CDATA[
      R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,252,a(flip),b,111,a)].">
      <j1 rule="hyper" parents="139 252 111"/>
    </justification>
  </clause>

  <clause id="649">
    <literal><![CDATA[
      R(x,x \ y,z) \ (y * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,167,a(flip),b,111,a)].">
      <j1 rule="hyper" parents="139 167 111"/>
    </justification>
  </clause>

  <clause id="650">
    <literal><![CDATA[
      R(x / y,y,z) \ (x * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(139,a,166,a(flip),b,111,a)].">
      <j1 rule="hyper" parents="139 166 111"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      R(x,y,L(z,y,x)) \ (x * (y * z)) = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,100,a(flip),b,111,a)].">
      <j1 rule="hyper" parents="139 100 111"/>
    </justification>
  </clause>

  <clause id="652">
    <literal><![CDATA[
      R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,251,a(flip),b,111,a)].">
      <j1 rule="hyper" parents="64 251 111"/>
    </justification>
  </clause>

  <clause id="654">
    <literal><![CDATA[
      R(x,y * y,z) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,34,a(flip),b,111,a),flip(a)].">
      <j1 rule="hyper" parents="36 34 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="655">
    <literal><![CDATA[
      R(x * x,y,z) = x * x
    ]]></literal>
    <justification jstring="[hyper(36,a,33,a(flip),b,111,a),flip(a)].">
      <j1 rule="hyper" parents="36 33 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="656">
    <literal><![CDATA[
      (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,111,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="139 111 100"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      R(x,y / z,z) * y = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(12(a,1),111(a,1,2))].">
      <j1 rule="para" parents="12 111"/>
    </justification>
  </clause>

  <clause id="658">
    <literal><![CDATA[
      ((x * y) * z) \ ((R(x,y,z) * y) * z) = a(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(111(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="111 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="659">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * z) * R(x,y,z)) = K(y * z,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(111(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="111 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="660">
    <literal><![CDATA[
      (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u)
    ]]></literal>
    <justification jstring="[para(111(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="111 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="661">
    <literal><![CDATA[
      ((x * R(y,z,u)) * (z * u)) / ((y * z) * u) = R(x,R(y,z,u),z * u)
    ]]></literal>
    <justification jstring="[para(111(a,1),20(a,2,2)),flip(a)].">
      <j1 rule="para" parents="111 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="662">
    <literal><![CDATA[
      R(x,y,y) * ((y * y) * z) = ((x * y) * y) * z
    ]]></literal>
    <justification jstring="[para(111(a,1),34(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 34"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="663">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != (x * y) * u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(111(a,2),44(a,1))].">
      <j1 rule="para" parents="111 44"/>
    </justification>
  </clause>

  <clause id="664">
    <literal><![CDATA[
      (x * y) * z != u * (y * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(111(a,1),45(a,1))].">
      <j1 rule="para" parents="111 45"/>
    </justification>
  </clause>

  <clause id="665">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u * z
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(111(a,2),45(a,1))].">
      <j1 rule="para" parents="111 45"/>
    </justification>
  </clause>

  <clause id="666">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(111(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="111 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="667">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z != u
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(111(a,2),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="111 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="668">
    <literal><![CDATA[
      R(x,y \ 1,y) * K(y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(294(a,2),111(a,1,2))].">
      <j1 rule="para" parents="294 111"/>
    </justification>
  </clause>

  <clause id="669">
    <literal><![CDATA[
      (x * y) * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(111(a,1),236(a,1))].">
      <j1 rule="para" parents="111 236"/>
    </justification>
  </clause>

  <clause id="670">
    <literal><![CDATA[
      R(x,R(y,z,u),y) * (y * R(y,z,u)) = (x * R(y,z,u)) * y
    ]]></literal>
    <justification jstring="[para(274(a,1),111(a,1,2))].">
      <j1 rule="para" parents="274 111"/>
    </justification>
  </clause>

  <clause id="671">
    <literal><![CDATA[
      R(x,1,y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),654(a,1,2))].">
      <j1 rule="para" parents="7 654"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      R(x,y * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(654(a,1),52(a,2))].">
      <j1 rule="para" parents="654 52"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      R(T(x * x,y),z,u) = T(x * x,y)
    ]]></literal>
    <justification jstring="[para(655(a,1),27(a,2,1))].">
      <j1 rule="para" parents="655 27"/>
    </justification>
  </clause>

  <clause id="674">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(373,a,195,a(flip),b,112,a),flip(a)].">
      <j1 rule="hyper" parents="373 195 112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      R(x / y,y,y \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,194,a(flip),b,112,a),flip(a)].">
      <j1 rule="hyper" parents="373 194 112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      R(x / y,y,x \ z) = z / (y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,171,a(flip),b,112,a),flip(a)].">
      <j1 rule="hyper" parents="373 171 112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="677">
    <literal><![CDATA[
      R(x / y,y,y \ z) = (x * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),112(a,2,2))].">
      <j1 rule="para" parents="10 112"/>
    </justification>
  </clause>

  <clause id="678">
    <literal><![CDATA[
      R(x / (y / z),y / z,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),112(a,2,2))].">
      <j1 rule="para" parents="12 112"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      T((x * y) / (z * y),u) = R(T(x / z,u),z,y)
    ]]></literal>
    <justification jstring="[para(112(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="112 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      R(x / y,y,T(z,y)) = (x * T(z,y)) / (z * y)
    ]]></literal>
    <justification jstring="[para(115(a,1),112(a,2,2))].">
      <j1 rule="para" parents="115 112"/>
    </justification>
  </clause>

  <clause id="681">
    <literal><![CDATA[
      T(R(x / y,y,z),y * z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[para(112(a,2),117(a,1,1))].">
      <j1 rule="para" parents="112 117"/>
    </justification>
  </clause>

  <clause id="682">
    <literal><![CDATA[
      R((x * x) / y,y,1 / x) = x / (y * (1 / x))
    ]]></literal>
    <justification jstring="[para(245(a,1),112(a,2,1))].">
      <j1 rule="para" parents="245 112"/>
    </justification>
  </clause>

  <clause id="683">
    <literal><![CDATA[
      (x * (1 / y)) / K(y,1 / y) = R(x / y,y,1 / y)
    ]]></literal>
    <justification jstring="[para(296(a,2),112(a,2,2)),flip(a)].">
      <j1 rule="para" parents="296 112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="684">
    <literal><![CDATA[
      R(x / y,y,x \ z) \ z = y * (x \ z)
    ]]></literal>
    <justification jstring="[para(112(a,2),349(a,1,1))].">
      <j1 rule="para" parents="112 349"/>
    </justification>
  </clause>

  <clause id="685">
    <literal><![CDATA[
      R(R(1 / x,x,y),x * y,z) = (y * z) / ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(244(a,2),112(a,1,1))].">
      <j1 rule="para" parents="244 112"/>
    </justification>
  </clause>

  <clause id="686">
    <literal><![CDATA[
      R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z))
    ]]></literal>
    <justification jstring="[para(111(a,1),112(a,2,1))].">
      <j1 rule="para" parents="111 112"/>
    </justification>
  </clause>

  <clause id="687">
    <literal><![CDATA[
      R(x / R(y,z,u),R(y,z,u),z * u) = (x * (z * u)) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(111(a,1),112(a,2,2))].">
      <j1 rule="para" parents="111 112"/>
    </justification>
  </clause>

  <clause id="688">
    <literal><![CDATA[
      R(R(x / y,y,z),y * z,u) = ((x * z) * u) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(112(a,2),112(a,1,1))].">
      <j1 rule="para" parents="112 112"/>
    </justification>
  </clause>

  <clause id="689">
    <literal><![CDATA[
      R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(94(a,1),210(a,1,2,1))].">
      <j1 rule="para" parents="94 210"/>
    </justification>
  </clause>

  <clause id="690">
    <literal><![CDATA[
      R(x,K(y \ x,y),z) \ (((y \ x) * y) * z) = K(y \ x,y) * z
    ]]></literal>
    <justification jstring="[para(354(a,1),210(a,1,2,1))].">
      <j1 rule="para" parents="354 210"/>
    </justification>
  </clause>

  <clause id="691">
    <literal><![CDATA[
      R(x * y,L(z,y,x),u) \ ((x * (y * z)) * u) = L(z,y,x) * u
    ]]></literal>
    <justification jstring="[para(100(a,1),210(a,1,2,1))].">
      <j1 rule="para" parents="100 210"/>
    </justification>
  </clause>

  <clause id="692">
    <literal><![CDATA[
      (x * y) / L(z,y / z,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),213(a,1,1,2))].">
      <j1 rule="para" parents="12 213"/>
    </justification>
  </clause>

  <clause id="693">
    <literal><![CDATA[
      (x * ((y * z) * u)) / L(z * u,R(y,z,u),x) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(111(a,1),213(a,1,1,2))].">
      <j1 rule="para" parents="111 213"/>
    </justification>
  </clause>

  <clause id="694">
    <literal><![CDATA[
      x \ L(L(y,x \ 1,x),z,u) = (x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,30,a,b,293,a)].">
      <j1 rule="hyper" parents="139 30 293"/>
    </justification>
  </clause>

  <clause id="695">
    <literal><![CDATA[
      L(T(x,y \ 1),y \ 1,y) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,251,a(flip),b,293,a),flip(a)].">
      <j1 rule="hyper" parents="64 251 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="696">
    <literal><![CDATA[
      (x * y) \ (x * L(z,y \ 1,y)) = L((y \ 1) * z,y,x)
    ]]></literal>
    <justification jstring="[para(293(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="293 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="697">
    <literal><![CDATA[
      (1 / x) \ L(L(y,x,1 / x),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,30,a,b,295,a)].">
      <j1 rule="hyper" parents="139 30 295"/>
    </justification>
  </clause>

  <clause id="698">
    <literal><![CDATA[
      (x \ 1) \ R(y,x,x \ 1) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(321,a,297,a),flip(a)].">
      <j1 rule="hyper" parents="321 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="699">
    <literal><![CDATA[
      L(R(x,y,y \ 1),z,u) / (y \ 1) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(142,a,29,a(flip),b,297,a)].">
      <j1 rule="hyper" parents="142 29 297"/>
    </justification>
  </clause>

  <clause id="700">
    <literal><![CDATA[
      T(R(x,y,y \ 1),z) / (y \ 1) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(142,a,27,a(flip),b,297,a)].">
      <j1 rule="hyper" parents="142 27 297"/>
    </justification>
  </clause>

  <clause id="701">
    <literal><![CDATA[
      R(x,x \ y,(x \ y) \ 1) = y * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,167,a(flip),b,297,a),flip(a)].">
      <j1 rule="hyper" parents="64 167 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="702">
    <literal><![CDATA[
      (x * x) * ((x \ 1) * y) = R(x,x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(297(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="297 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="703">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(297(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="297 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="704">
    <literal><![CDATA[
      L(R(x,1 / y,y),z,u) / y = L(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(142,a,29,a(flip),b,298,a)].">
      <j1 rule="hyper" parents="142 29 298"/>
    </justification>
  </clause>

  <clause id="705">
    <literal><![CDATA[
      T(R(x,1 / y,y),z) / y = T(x,z) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(142,a,27,a(flip),b,298,a)].">
      <j1 rule="hyper" parents="142 27 298"/>
    </justification>
  </clause>

  <clause id="706">
    <literal><![CDATA[
      K(x,1 / x) * x = R(x,1 / x,x)
    ]]></literal>
    <justification jstring="[para(296(a,2),298(a,1,1))].">
      <j1 rule="para" parents="296 298"/>
    </justification>
  </clause>

  <clause id="708">
    <literal><![CDATA[
      L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(346(a,1),25(a,2,1))].">
      <j1 rule="para" parents="346 25"/>
    </justification>
  </clause>

  <clause id="709">
    <literal><![CDATA[
      L(L(x \ (y \ z),u,w),x,y) = L((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(346(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="346 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="710">
    <literal><![CDATA[
      L(x,y,z) != (z * y) \ u
    ]]></literal>
    <literal><![CDATA[
      y \ (z \ u) = x
    ]]></literal>
    <justification jstring="[para(346(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="346 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="711">
    <literal><![CDATA[
      L(x,(y \ z) / x,y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[para(82(a,1),346(a,1,1))].">
      <j1 rule="para" parents="82 346"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      (x * (y * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      (y * y) \ (x \ z) = u
    ]]></literal>
    <justification jstring="[para(346(a,1),616(a,1))].">
      <j1 rule="para" parents="346 616"/>
    </justification>
  </clause>

  <clause id="713">
    <literal><![CDATA[
      L(x \ L(y \ z,y,u),x,u * y) = ((u * y) * x) \ (u * z)
    ]]></literal>
    <justification jstring="[para(102(a,2),346(a,1,1,2))].">
      <j1 rule="para" parents="102 346"/>
    </justification>
  </clause>

  <clause id="714">
    <literal><![CDATA[
      R(T((x / y) / z,u),z,y) = T(x / (z * y),u)
    ]]></literal>
    <justification jstring="[para(351(a,1),27(a,2,1))].">
      <j1 rule="para" parents="351 27"/>
    </justification>
  </clause>

  <clause id="715">
    <literal><![CDATA[
      R(x,x \ (y / z),z) = y / ((x \ (y / z)) * z)
    ]]></literal>
    <justification jstring="[para(79(a,1),351(a,1,1))].">
      <j1 rule="para" parents="79 351"/>
    </justification>
  </clause>

  <clause id="717">
    <literal><![CDATA[
      (x * (x \ y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(79(a,1),390(a,1,1,1))].">
      <j1 rule="para" parents="79 390"/>
    </justification>
  </clause>

  <clause id="718">
    <literal><![CDATA[
      (x * T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * z = u
    ]]></literal>
    <justification jstring="[para(214(a,1),390(a,1,1,1))].">
      <j1 rule="para" parents="214 390"/>
    </justification>
  </clause>

  <clause id="719">
    <literal><![CDATA[
      R(x / y,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(297(a,1),390(a,1))].">
      <j1 rule="para" parents="297 390"/>
    </justification>
  </clause>

  <clause id="720">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (x * y) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),391(a,1,1))].">
      <j1 rule="para" parents="11 391"/>
    </justification>
  </clause>

  <clause id="721">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(194(a,1),391(a,1,1))].">
      <j1 rule="para" parents="194 391"/>
    </justification>
  </clause>

  <clause id="723">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(178(a,1),391(a,1,1))].">
      <j1 rule="para" parents="178 391"/>
    </justification>
  </clause>

  <clause id="724">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      (x * y) / u = z
    ]]></literal>
    <justification jstring="[para(9(a,1),392(a,1,2))].">
      <j1 rule="para" parents="9 392"/>
    </justification>
  </clause>

  <clause id="727">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(82(a,1),392(a,1,2))].">
      <j1 rule="para" parents="82 392"/>
    </justification>
  </clause>

  <clause id="728">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(182(a,1),392(a,1,2))].">
      <j1 rule="para" parents="182 392"/>
    </justification>
  </clause>

  <clause id="729">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(182(a,2),392(a,1))].">
      <j1 rule="para" parents="182 392"/>
    </justification>
  </clause>

  <clause id="730">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z / (x \ z) = y
    ]]></literal>
    <justification jstring="[para(11(a,1),393(a,1))].">
      <j1 rule="para" parents="11 393"/>
    </justification>
  </clause>

  <clause id="731">
    <literal><![CDATA[
      x \ (y * (y \ (x * z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(10(a,2),394(a,1,2))].">
      <j1 rule="para" parents="10 394"/>
    </justification>
  </clause>

  <clause id="732">
    <literal><![CDATA[
      x \ (y * x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(y,x) = u
    ]]></literal>
    <justification jstring="[para(115(a,1),394(a,1,2))].">
      <j1 rule="para" parents="115 394"/>
    </justification>
  </clause>

  <clause id="733">
    <literal><![CDATA[
      x \ y != z * (u \ (u * (z \ w)))
    ]]></literal>
    <literal><![CDATA[
      x * w = y
    ]]></literal>
    <justification jstring="[para(9(a,2),395(a,2,2))].">
      <j1 rule="para" parents="9 395"/>
    </justification>
  </clause>

  <clause id="734">
    <literal><![CDATA[
      x \ y != z * 1
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(68(a,1),395(a,2,2))].">
      <j1 rule="para" parents="68 395"/>
    </justification>
  </clause>

  <clause id="736">
    <literal><![CDATA[
      x \ (x * y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * y = u
    ]]></literal>
    <justification jstring="[para(182(a,2),395(a,2)),flip(a)].">
      <j1 rule="para" parents="182 395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="737">
    <literal><![CDATA[
      x * (y * T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),397(a,1,2,2))].">
      <j1 rule="para" parents="22 397"/>
    </justification>
  </clause>

  <clause id="738">
    <literal><![CDATA[
      x * (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(68(a,1),397(a,1,2,2))].">
      <j1 rule="para" parents="68 397"/>
    </justification>
  </clause>

  <clause id="739">
    <literal><![CDATA[
      x * (y \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(182(a,2),397(a,1,2))].">
      <j1 rule="para" parents="182 397"/>
    </justification>
  </clause>

  <clause id="740">
    <literal><![CDATA[
      x * (y / (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(206(a,2),397(a,1,2))].">
      <j1 rule="para" parents="206 397"/>
    </justification>
  </clause>

  <clause id="741">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(218(a,2),397(a,1,2))].">
      <j1 rule="para" parents="218 397"/>
    </justification>
  </clause>

  <clause id="742">
    <literal><![CDATA[
      L(x \ y,x,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * y = z
    ]]></literal>
    <justification jstring="[para(559(a,1),397(a,1))].">
      <j1 rule="para" parents="559 397"/>
    </justification>
  </clause>

  <clause id="743">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(102(a,2),402(a,1))].">
      <j1 rule="para" parents="102 402"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      x \ y != z * (u * (u \ (z \ w)))
    ]]></literal>
    <literal><![CDATA[
      y / w = x
    ]]></literal>
    <justification jstring="[para(10(a,2),404(a,2,2))].">
      <j1 rule="para" parents="10 404"/>
    </justification>
  </clause>

  <clause id="746">
    <literal><![CDATA[
      T((x \ y) \ 1,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(436(a,1),198(a,1,2))].">
      <j1 rule="para" parents="436 198"/>
    </justification>
  </clause>

  <clause id="747">
    <literal><![CDATA[
      T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y)
    ]]></literal>
    <justification jstring="[para(443(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="443 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="748">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u / x) = L(u \ (u / x),y,z)
    ]]></literal>
    <justification jstring="[para(443(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="443 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="749">
    <literal><![CDATA[
      L(x \ 1,x,y / x) * y = (y / x) * K(y \ (y / x),y)
    ]]></literal>
    <justification jstring="[para(443(a,2),354(a,2,1)),flip(a)].">
      <j1 rule="para" parents="443 354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="750">
    <literal><![CDATA[
      ((x \ y) / y) * (R(1 / x,x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(144,a,453,a(flip),b,79,a)].">
      <j1 rule="hyper" parents="144 453 79"/>
    </justification>
  </clause>

  <clause id="751">
    <literal><![CDATA[
      R(L(1 / x,y,z),x,x \ u) = L((x \ u) / u,y,z)
    ]]></literal>
    <justification jstring="[para(453(a,1),29(a,2,1))].">
      <j1 rule="para" parents="453 29"/>
    </justification>
  </clause>

  <clause id="752">
    <literal><![CDATA[
      T(1 / (x / y),y / x) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(454(a,1),197(a,1,2))].">
      <j1 rule="para" parents="454 197"/>
    </justification>
  </clause>

  <clause id="753">
    <literal><![CDATA[
      x / x != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ 1 = z
    ]]></literal>
    <justification jstring="[para(8(a,1),459(a,1))].">
      <j1 rule="para" parents="8 459"/>
    </justification>
  </clause>

  <clause id="755">
    <literal><![CDATA[
      (x * (x \ y)) / z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y / z) = w
    ]]></literal>
    <justification jstring="[para(179(a,1),461(a,1,1))].">
      <j1 rule="para" parents="179 461"/>
    </justification>
  </clause>

  <clause id="756">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(9(a,2),462(a,1,2))].">
      <j1 rule="para" parents="9 462"/>
    </justification>
  </clause>

  <clause id="757">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(10(a,2),462(a,1,2))].">
      <j1 rule="para" parents="10 462"/>
    </justification>
  </clause>

  <clause id="758">
    <literal><![CDATA[
      (x * (y * z)) * a(x,y,z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ ((x * y) * z) = w
    ]]></literal>
    <justification jstring="[para(14(a,2),462(a,1,2))].">
      <j1 rule="para" parents="14 462"/>
    </justification>
  </clause>

  <clause id="759">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(182(a,1),462(a,1,2))].">
      <j1 rule="para" parents="182 462"/>
    </justification>
  </clause>

  <clause id="760">
    <literal><![CDATA[
      R((x / y) / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * y) = u
    ]]></literal>
    <justification jstring="[para(112(a,2),466(a,1))].">
      <j1 rule="para" parents="112 466"/>
    </justification>
  </clause>

  <clause id="761">
    <literal><![CDATA[
      x / ((y \ 1) * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(y,y \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(475(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="475 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="762">
    <literal><![CDATA[
      R(T(x,R(x,y,z) \ u),y,z) != w
    ]]></literal>
    <literal><![CDATA[
      (R(x,y,z) \ u) \ u = w
    ]]></literal>
    <justification jstring="[para(27(a,2),478(a,1))].">
      <j1 rule="para" parents="27 478"/>
    </justification>
  </clause>

  <clause id="763">
    <literal><![CDATA[
      (((x * x) \ x) * y) * L(z,y,(x * x) \ x) = L(x \ (y * z),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,100,a,b,581,a)].">
      <j1 rule="hyper" parents="64 100 581"/>
    </justification>
  </clause>

  <clause id="764">
    <literal><![CDATA[
      (x * y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ z,y,x) = u
    ]]></literal>
    <justification jstring="[para(591(a,1),305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="591 305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="765">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(22(a,2),627(a,1,1))].">
      <j1 rule="para" parents="22 627"/>
    </justification>
  </clause>

  <clause id="766">
    <literal><![CDATA[
      T(x,x * (y * y)) = T(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(616,a,765,a),flip(a)].">
      <j1 rule="hyper" parents="616 765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="767">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,25,a(flip),b,765,a)].">
      <j1 rule="hyper" parents="64 25 765"/>
    </justification>
  </clause>

  <clause id="768">
    <literal><![CDATA[
      L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(765(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="765 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      (x * T(y,y * x)) / x = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(313,a,767,a)].">
      <j1 rule="hyper" parents="313 767"/>
    </justification>
  </clause>

  <clause id="770">
    <literal><![CDATA[
      T((x * y) / x,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,312,a,b,767,a)].">
      <j1 rule="hyper" parents="41 312 767"/>
    </justification>
  </clause>

  <clause id="771">
    <literal><![CDATA[
      x * T(y,y * x) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,767,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 767 22"/>
    </justification>
  </clause>

  <clause id="772">
    <literal><![CDATA[
      x * T(y,y * x) != z * x
    ]]></literal>
    <literal><![CDATA[
      L(y,x,y) = z
    ]]></literal>
    <justification jstring="[para(767(a,1),272(a,1,2)),flip(b)].">
      <j1 rule="para" parents="767 272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="773">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,1 / x) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(628(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="628 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="774">
    <literal><![CDATA[
      L(T((x \ 1) \ y,z),x \ 1,x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(629(a,1),25(a,2,1))].">
      <j1 rule="para" parents="629 25"/>
    </justification>
  </clause>

  <clause id="775">
    <literal><![CDATA[
      T((x \ 1) \ y,x * y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(629(a,1),198(a,1,2))].">
      <j1 rule="para" parents="629 198"/>
    </justification>
  </clause>

  <clause id="776">
    <literal><![CDATA[
      (x * y) / (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x / z,z,y) = u
    ]]></literal>
    <justification jstring="[para(650(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="650 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="777">
    <literal><![CDATA[
      (T(x * x,y) * z) * u = T(x * x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,673,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 673 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="778">
    <literal><![CDATA[
      (T(x * x,y) \ 1) * z = T(x * x,y) \ z
    ]]></literal>
    <justification jstring="[para(673(a,1),475(a,1,1)),flip(a)].">
      <j1 rule="para" parents="673 475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="779">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(675(a,1),27(a,2,1))].">
      <j1 rule="para" parents="675 27"/>
    </justification>
  </clause>

  <clause id="780">
    <literal><![CDATA[
      R(L(x / y,z,u),y,y \ 1) = L(x * (y \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(675(a,1),29(a,2,1))].">
      <j1 rule="para" parents="675 29"/>
    </justification>
  </clause>

  <clause id="781">
    <literal><![CDATA[
      R(R(x / y,z,u),y,y \ 1) = R(x * (y \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(675(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="675 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="782">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(218(a,2),717(a,1,1))].">
      <j1 rule="para" parents="218 717"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      (x * (x \ y)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(167(a,2),720(a,1))].">
      <j1 rule="para" parents="167 720"/>
    </justification>
  </clause>

  <clause id="784">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(166(a,2),724(a,1))].">
      <j1 rule="para" parents="166 724"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      x * (y \ (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(169(a,2),724(a,1))].">
      <j1 rule="para" parents="169 724"/>
    </justification>
  </clause>

  <clause id="786">
    <literal><![CDATA[
      (((x / y) / z) * z) * y != u * w
    ]]></literal>
    <literal><![CDATA[
      x / w = u
    ]]></literal>
    <justification jstring="[para(12(a,2),727(a,1,1))].">
      <j1 rule="para" parents="12 727"/>
    </justification>
  </clause>

  <clause id="787">
    <literal><![CDATA[
      x \ (y \ (y * (x * z))) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * z = w
    ]]></literal>
    <justification jstring="[para(9(a,2),736(a,1,2))].">
      <j1 rule="para" parents="9 736"/>
    </justification>
  </clause>

  <clause id="788">
    <literal><![CDATA[
      (x * y) \ x != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * L(y \ 1,y,x) = u
    ]]></literal>
    <justification jstring="[para(442(a,1),736(a,1,2))].">
      <j1 rule="para" parents="442 736"/>
    </justification>
  </clause>

  <clause id="789">
    <literal><![CDATA[
      T(L(x,y,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(769(a,1),340(a,1,1)),flip(b)].">
      <j1 rule="para" parents="769 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="790">
    <literal><![CDATA[
      ((x * y) / x) * (y * x) = (y * x) * L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,770,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 770 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="791">
    <literal><![CDATA[
      T(((x \ y) * x) / (x \ y),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),770(a,1,2))].">
      <j1 rule="para" parents="10 770"/>
    </justification>
  </clause>

  <clause id="792">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,567,a(flip),b,121,a)].">
      <j1 rule="hyper" parents="145 567 121"/>
    </justification>
  </clause>

  <clause id="793">
    <literal><![CDATA[
      x * (y * T(z,x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(39,a,18,a(flip),b,121,a)].">
      <j1 rule="hyper" parents="39 18 121"/>
    </justification>
  </clause>

  <clause id="794">
    <literal><![CDATA[
      L(T(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      T(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(121(a,1),336(a,1))].">
      <j1 rule="para" parents="121 336"/>
    </justification>
  </clause>

  <clause id="795">
    <literal><![CDATA[
      R(T(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      T(R(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(122(a,1),336(a,1))].">
      <j1 rule="para" parents="122 336"/>
    </justification>
  </clause>

  <clause id="796">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(111(a,1),122(a,1,2))].">
      <j1 rule="para" parents="111 122"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      L(x \ R(T(y,z),u,w),x,z) = (z * x) \ (R(y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(122(a,1),346(a,1,1,2))].">
      <j1 rule="para" parents="122 346"/>
    </justification>
  </clause>

  <clause id="798">
    <literal><![CDATA[
      ((x * x) \ y) * (x * x) = T(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(270,a,126,a),flip(a)].">
      <j1 rule="hyper" parents="270 126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="799">
    <literal><![CDATA[
      ((x * x) \ y) * T(z,y) = (x * x) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,115,a(flip),b,126,a),flip(a)].">
      <j1 rule="hyper" parents="139 115 126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      ((x * x) \ (y * z)) * L(u,z,y) = (x * x) \ (y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(139,a,100,a(flip),b,126,a),flip(a)].">
      <j1 rule="hyper" parents="139 100 126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="801">
    <literal><![CDATA[
      ((x * x) \ (y / z)) * z = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,12,a(flip),b,126,a),flip(a)].">
      <j1 rule="hyper" parents="139 12 126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="802">
    <literal><![CDATA[
      ((x * x) \ y) * (y \ z) = (x * x) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,126,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="804">
    <literal><![CDATA[
      ((x * x) \ y) \ z = y \ ((x * x) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,126,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 168 126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      (x * x) * ((((x * x) \ y) * z) * u) = (y * z) * u
    ]]></literal>
    <justification jstring="[para(126(a,1),33(a,1,1)),flip(a)].">
      <j1 rule="para" parents="126 33"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="806">
    <literal><![CDATA[
      (x * x) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      ((x * x) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(126(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="126 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="807">
    <literal><![CDATA[
      ((x * x) * y) / z = (x * x) * (y / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),127(a,1,1,2))].">
      <j1 rule="para" parents="12 127"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      (x * y) / (1 / y) = x * (y * y)
    ]]></literal>
    <justification jstring="[para(245(a,1),133(a,1,1,2))].">
      <j1 rule="para" parents="245 133"/>
    </justification>
  </clause>

  <clause id="809">
    <literal><![CDATA[
      (x / y) * (y * y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(466,a,808,a),flip(a)].">
      <j1 rule="hyper" parents="466 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="810">
    <literal><![CDATA[
      x * ((x \ y) * (x \ y)) = y / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(393,a,808,a),flip(a)].">
      <j1 rule="hyper" parents="393 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="811">
    <literal><![CDATA[
      (x / (y * y)) * y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(389,a,808,a),flip(a)].">
      <j1 rule="hyper" parents="389 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      ((x * y) * y) * (1 / y) = R(x,y,y) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,111,a(flip),b,808,a)].">
      <j1 rule="hyper" parents="144 111 808"/>
    </justification>
  </clause>

  <clause id="813">
    <literal><![CDATA[
      (x * (1 / y)) / y = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(142,a,86,a(flip),b,808,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="142 86 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      (x / y) \ (x / (1 / y)) = y * y
    ]]></literal>
    <justification jstring="[hyper(139,a,170,a(flip),b,808,a(flip))].">
      <j1 rule="hyper" parents="139 170 808"/>
    </justification>
  </clause>

  <clause id="815">
    <literal><![CDATA[
      x * ((y \ 1) * (y \ 1)) = (x * (y \ 1)) / y
    ]]></literal>
    <justification jstring="[para(79(a,1),808(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      K(x \ 1,x) / (1 / x) = (x \ 1) * (x * x)
    ]]></literal>
    <justification jstring="[para(294(a,2),808(a,1,1))].">
      <j1 rule="para" parents="294 808"/>
    </justification>
  </clause>

  <clause id="817">
    <literal><![CDATA[
      (x * x) \ (y / (1 / x)) = T(y / x,x * x)
    ]]></literal>
    <justification jstring="[hyper(321,a,809,a),flip(a)].">
      <j1 rule="hyper" parents="321 809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="818">
    <literal><![CDATA[
      L(x,x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,559,a(flip),b,809,a)].">
      <j1 rule="hyper" parents="64 559 809"/>
    </justification>
  </clause>

  <clause id="819">
    <literal><![CDATA[
      (x / y) * ((y * y) * z) = (x / (1 / y)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,809,a(flip),b,133,a),flip(a)].">
      <j1 rule="hyper" parents="144 809 133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="820">
    <literal><![CDATA[
      (x / (1 / y)) \ (x / y) = (y * y) \ 1
    ]]></literal>
    <justification jstring="[para(809(a,1),488(a,1,1))].">
      <j1 rule="para" parents="809 488"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      x / L(y,y,y) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(225,a,818,a,b,82,a)].">
      <j1 rule="hyper" parents="225 818 82"/>
    </justification>
  </clause>

  <clause id="822">
    <literal><![CDATA[
      L(x,x,x) \ 1 = 1 / x
    ]]></literal>
    <justification jstring="[hyper(143,a,818,a,b,171,a)].">
      <j1 rule="hyper" parents="143 818 171"/>
    </justification>
  </clause>

  <clause id="823">
    <literal><![CDATA[
      L(x,x,x) \ y = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(62,a,818,a)].">
      <j1 rule="hyper" parents="62 818"/>
    </justification>
  </clause>

  <clause id="824">
    <literal><![CDATA[
      T(1 / (1 / x),y) = L(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[para(818(a,1),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="818 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="825">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) = L(R(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(818(a,1),29(a,1,1))].">
      <j1 rule="para" parents="818 29"/>
    </justification>
  </clause>

  <clause id="826">
    <literal><![CDATA[
      R(x / (y * y),y,y \ 1) = (x * (1 / y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,811,a(flip),b,494,a),flip(a)].">
      <j1 rule="hyper" parents="144 811 494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      T(1 / (1 / x),x \ y) = L((x \ y) \ y,x,x)
    ]]></literal>
    <justification jstring="[para(116(a,1),824(a,2,1))].">
      <j1 rule="para" parents="116 824"/>
    </justification>
  </clause>

  <clause id="828">
    <literal><![CDATA[
      x * (y \ T(T(z,u),w)) = x * (y \ T(T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(145,a,176,a,b,9,a)].">
      <j1 rule="hyper" parents="145 176 9"/>
    </justification>
  </clause>

  <clause id="829">
    <literal><![CDATA[
      T((x * x) / y,x * x) = (1 / y) * (x * x)
    ]]></literal>
    <justification jstring="[para(497(a,1),254(a,1,1))].">
      <j1 rule="para" parents="497 254"/>
    </justification>
  </clause>

  <clause id="830">
    <literal><![CDATA[
      (((x * x) \ y) * z) * (x * x) = T(y * z,x * x)
    ]]></literal>
    <justification jstring="[para(126(a,1),254(a,1,1)),flip(a)].">
      <j1 rule="para" parents="126 254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="831">
    <literal><![CDATA[
      x \ (L(y,z,x) * (x * z)) = z * T(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,266,a(flip),b,100,a(flip))].">
      <j1 rule="hyper" parents="139 266 100"/>
    </justification>
  </clause>

  <clause id="832">
    <literal><![CDATA[
      (x * (L(y,z,u) * w)) \ ((x * w) * L(T(y,w),z,u)) = a(x,w,L(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[para(266(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="266 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      x * L(x \ (y * x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(22(a,1),266(a,1,2,1))].">
      <j1 rule="para" parents="22 266"/>
    </justification>
  </clause>

  <clause id="834">
    <literal><![CDATA[
      x * L(L(T(y,x),z,u),w,v5) = L(L(y,z,u),w,v5) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),266(a,1,2,1))].">
      <j1 rule="para" parents="25 266"/>
    </justification>
  </clause>

  <clause id="835">
    <literal><![CDATA[
      x * L(R(T(y,x),z,u),w,v5) = L(R(y,z,u),w,v5) * x
    ]]></literal>
    <justification jstring="[para(27(a,2),266(a,1,2,1))].">
      <j1 rule="para" parents="27 266"/>
    </justification>
  </clause>

  <clause id="836">
    <literal><![CDATA[
      L(x / y,z,u) * y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(117(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="117 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="837">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(255(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="255 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="838">
    <literal><![CDATA[
      (x * x) * L(L(x,x,x),y,z) = L(x,y,z) * (x * x)
    ]]></literal>
    <justification jstring="[para(118(a,1),266(a,1,2,1))].">
      <j1 rule="para" parents="118 266"/>
    </justification>
  </clause>

  <clause id="839">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(116(a,1),266(a,1,2,1))].">
      <j1 rule="para" parents="116 266"/>
    </justification>
  </clause>

  <clause id="840">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * x = x * L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(202(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="202 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="841">
    <literal><![CDATA[
      (x * y) * R(T(z,x * y),x,y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,111,a(flip),b,267,a),flip(a)].">
      <j1 rule="hyper" parents="373 111 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      x * R(T(T(y,x),z),u,w) = R(T(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),267(a,1,2,1))].">
      <j1 rule="para" parents="23 267"/>
    </justification>
  </clause>

  <clause id="843">
    <literal><![CDATA[
      R(x / y,z,u) * y = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(117(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="117 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="844">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(255(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="255 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="845">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(116(a,1),267(a,1,2,1))].">
      <j1 rule="para" parents="116 267"/>
    </justification>
  </clause>

  <clause id="846">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * x = x * R(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(202(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="202 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      (x * y) * R(L(T(x,y),y,x),z,u) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(765(a,2),267(a,1,2,1))].">
      <j1 rule="para" parents="765 267"/>
    </justification>
  </clause>

  <clause id="848">
    <literal><![CDATA[
      T(x / y,(z / y) \ z) = y \ x
    ]]></literal>
    <justification jstring="[hyper(269,a,406,a,b,405,a)].">
      <j1 rule="hyper" parents="269 406 405"/>
    </justification>
  </clause>

  <clause id="849">
    <literal><![CDATA[
      T(x / (y \ x),z) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(269,a,209,a,b,115,a)].">
      <j1 rule="hyper" parents="269 209 115"/>
    </justification>
  </clause>

  <clause id="850">
    <literal><![CDATA[
      ((x * x) \ y) \ y = T(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(269,a,168,a(flip),b,126,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 168 126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      L(T(x * x,y),(x * x) \ y,z) = (z * ((x * x) \ y)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(850(a,1),102(a,1,1))].">
      <j1 rule="para" parents="850 102"/>
    </justification>
  </clause>

  <clause id="852">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / x = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(313,a,279,a)].">
      <j1 rule="hyper" parents="313 279"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) / x = R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(313,a,280,a)].">
      <j1 rule="hyper" parents="313 280"/>
    </justification>
  </clause>

  <clause id="854">
    <literal><![CDATA[
      T(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(244(a,1),280(a,1,1))].">
      <j1 rule="para" parents="244 280"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      T((x * y) / (z * y),z) = R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[para(112(a,1),280(a,1,1))].">
      <j1 rule="para" parents="112 280"/>
    </justification>
  </clause>

  <clause id="856">
    <literal><![CDATA[
      R(x \ (y / z),x,z) = T(y / (x * z),x)
    ]]></literal>
    <justification jstring="[para(351(a,1),280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="351 280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="857">
    <literal><![CDATA[
      R((x / y) \ 1,x / y,y) = T(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(454(a,1),280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="454 280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      R(x \ y,x,x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[para(675(a,1),280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="675 280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="859">
    <literal><![CDATA[
      (x / (y * x)) * y = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,854,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 854 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="861">
    <literal><![CDATA[
      T(R(x \ 1,x,y),x * y) = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(854(a,1),278(a,1,1))].">
      <j1 rule="para" parents="854 278"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      x * (y \ T(z,z \ u)) = x * (y \ ((z \ u) \ u))
    ]]></literal>
    <justification jstring="[para(360(a,2),169(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="360 169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="863">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ ((y \ z) \ z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(504,a,361,a,b,xx)].">
      <j1 rule="hyper" parents="504 361"/>
    </justification>
  </clause>

  <clause id="864">
    <literal><![CDATA[
      x \ ((y \ z) \ z) != x \ u
    ]]></literal>
    <literal><![CDATA[
      T(y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(361(a,1),48(a,1))].">
      <j1 rule="para" parents="361 48"/>
    </justification>
  </clause>

  <clause id="865">
    <literal><![CDATA[
      ((x \ y) \ y) / T(z,z \ T(x,x \ y)) = z \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(361(a,2),301(a,1,2,2))].">
      <j1 rule="para" parents="361 301"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      T(T(x,x \ y),z) = T((x \ y) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(269,a,365,a,b,115,a)].">
      <j1 rule="hyper" parents="269 365 115"/>
    </justification>
  </clause>

  <clause id="868">
    <literal><![CDATA[
      (x \ 1) * (1 / x) = (x * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,536,a(flip),b,413,a),flip(a)].">
      <j1 rule="hyper" parents="64 536 413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      T(x,x \ y) * z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(422(a,1),739(a,1))].">
      <j1 rule="para" parents="422 739"/>
    </justification>
  </clause>

  <clause id="870">
    <literal><![CDATA[
      T(x,y) / (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(115(a,1),476(a,1,2))].">
      <j1 rule="para" parents="115 476"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      (((x * y) * (x * y)) \ ((x * y) * x)) * y = a(x * y,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14,a,b,484,a),flip(a)].">
      <j1 rule="hyper" parents="64 14 484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="872">
    <literal><![CDATA[
      T(x,y * y) / (y * y) = (y * y) \ x
    ]]></literal>
    <justification jstring="[hyper(142,a,22,a,b,484,a(flip))].">
      <j1 rule="hyper" parents="142 22 484"/>
    </justification>
  </clause>

  <clause id="873">
    <literal><![CDATA[
      ((x * y) * (x * y)) \ x = (1 / (x * y)) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,309,a(flip),b,484,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="142 309 484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      (x * x) \ (y \ ((y * x) * x)) = a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,14,a,b,486,a),flip(a)].">
      <j1 rule="hyper" parents="64 14 486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="875">
    <literal><![CDATA[
      (x * x) \ (R(y,x,x) \ z) = ((y * x) * x) \ z
    ]]></literal>
    <justification jstring="[para(111(a,1),486(a,1,1)),flip(a)].">
      <j1 rule="para" parents="111 486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="876">
    <literal><![CDATA[
      (x * x) \ ((y / x) \ z) = (y / (1 / x)) \ z
    ]]></literal>
    <justification jstring="[para(809(a,1),486(a,1,1)),flip(a)].">
      <j1 rule="para" parents="809 486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="877">
    <literal><![CDATA[
      T(x,y * y) \ ((y * y) \ z) = (x * (y * y)) \ z
    ]]></literal>
    <justification jstring="[para(115(a,1),487(a,1,1)),flip(a)].">
      <j1 rule="para" parents="115 487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="878">
    <literal><![CDATA[
      ((x * x) * y) \ x = y \ (1 / x)
    ]]></literal>
    <justification jstring="[para(309(a,1),487(a,2,2))].">
      <j1 rule="para" parents="309 487"/>
    </justification>
  </clause>

  <clause id="879">
    <literal><![CDATA[
      (1 / x) \ ((y * y) \ z) = ((y * y) / x) \ z
    ]]></literal>
    <justification jstring="[para(497(a,1),487(a,1,1)),flip(a)].">
      <j1 rule="para" parents="497 487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="880">
    <literal><![CDATA[
      ((x * x) / (y \ 1)) \ z = y \ ((x * x) \ z)
    ]]></literal>
    <justification jstring="[para(499(a,2),487(a,1,1))].">
      <j1 rule="para" parents="499 487"/>
    </justification>
  </clause>

  <clause id="881">
    <literal><![CDATA[
      L(x,y,y) \ ((y * y) \ z) = (y * (y * x)) \ z
    ]]></literal>
    <justification jstring="[para(100(a,1),487(a,1,1)),flip(a)].">
      <j1 rule="para" parents="100 487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="883">
    <literal><![CDATA[
      (x * x) * ((1 / x) / y) = x / y
    ]]></literal>
    <justification jstring="[hyper(225,a,82,a(flip),b,878,a),flip(a)].">
      <j1 rule="hyper" parents="225 82 878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="884">
    <literal><![CDATA[
      (1 / x) / (y \ x) = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(225,a,174,a(flip),b,878,a(flip))].">
      <j1 rule="hyper" parents="225 174 878"/>
    </justification>
  </clause>

  <clause id="885">
    <literal><![CDATA[
      ((1 / x) * y) \ (1 / x) = (x * y) \ x
    ]]></literal>
    <justification jstring="[para(310(a,1),878(a,1,1)),flip(a)].">
      <j1 rule="para" parents="310 878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="886">
    <literal><![CDATA[
      L(x,y,y) \ (1 / y) = (y * (y * x)) \ y
    ]]></literal>
    <justification jstring="[para(100(a,1),878(a,1,1)),flip(a)].">
      <j1 rule="para" parents="100 878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="887">
    <literal><![CDATA[
      (x * x) \ (x / y) = (1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(149,a,883,a)].">
      <j1 rule="hyper" parents="149 883"/>
    </justification>
  </clause>

  <clause id="888">
    <literal><![CDATA[
      (1 / x) \ ((1 / x) / y) = x \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,883,a(flip),b,538,a),flip(a)].">
      <j1 rule="hyper" parents="139 883 538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="889">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) * (x / y) = (x \ 1) / y
    ]]></literal>
    <justification jstring="[para(79(a,1),883(a,1,2,1))].">
      <j1 rule="para" parents="79 883"/>
    </justification>
  </clause>

  <clause id="890">
    <literal><![CDATA[
      (x / (y * y)) \ z = (y * y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(12(a,1),491(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="891">
    <literal><![CDATA[
      (x * x) * ((y / (1 / x)) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[para(809(a,1),491(a,1,2,1))].">
      <j1 rule="para" parents="809 491"/>
    </justification>
  </clause>

  <clause id="892">
    <literal><![CDATA[
      ((1 / x) * y) * ((x * y) \ z) = (x * x) \ z
    ]]></literal>
    <justification jstring="[para(310(a,1),492(a,1,2,1))].">
      <j1 rule="para" parents="310 492"/>
    </justification>
  </clause>

  <clause id="893">
    <literal><![CDATA[
      T(x / ((y * y) * z),y * y) = (y * y) \ (x / z)
    ]]></literal>
    <justification jstring="[hyper(493,a,170,a(flip),b,133,a(flip))].">
      <j1 rule="hyper" parents="493 170 133"/>
    </justification>
  </clause>

  <clause id="894">
    <literal><![CDATA[
      x \ ((y * z) * (z \ x)) = T(R(y,z,z \ x),x)
    ]]></literal>
    <justification jstring="[hyper(493,a,111,a(flip),b,168,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="493 111 168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="895">
    <literal><![CDATA[
      x / ((y * y) * (z \ x)) = z / (y * y)
    ]]></literal>
    <justification jstring="[hyper(393,a,495,a)].">
      <j1 rule="hyper" parents="393 495"/>
    </justification>
  </clause>

  <clause id="896">
    <literal><![CDATA[
      (x * ((y * y) \ z)) / z = x / (y * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),495(a,1,2))].">
      <j1 rule="para" parents="10 495"/>
    </justification>
  </clause>

  <clause id="897">
    <literal><![CDATA[
      (x / (y * y)) * z = x * ((y * y) \ z)
    ]]></literal>
    <justification jstring="[para(495(a,1),385(a,1,1))].">
      <j1 rule="para" parents="495 385"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      ((x * y) * z) / ((u * u) * (y * z)) = R(x,y,z) / (u * u)
    ]]></literal>
    <justification jstring="[para(111(a,1),495(a,1,1))].">
      <j1 rule="para" parents="111 495"/>
    </justification>
  </clause>

  <clause id="899">
    <literal><![CDATA[
      R(x / (y * y),(y * y) * z,u) = ((x * z) * u) / (((y * y) * z) * u)
    ]]></literal>
    <justification jstring="[para(495(a,1),112(a,1,1))].">
      <j1 rule="para" parents="495 112"/>
    </justification>
  </clause>

  <clause id="900">
    <literal><![CDATA[
      x / ((y * y) \ z) = (x / z) * (y * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),500(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="901">
    <literal><![CDATA[
      (x / (y * z)) * (y * y) = x / ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(310(a,1),500(a,1,1,2))].">
      <j1 rule="para" parents="310 500"/>
    </justification>
  </clause>

  <clause id="902">
    <literal><![CDATA[
      (x / ((y * y) / z)) * (y * y) = x / (1 / z)
    ]]></literal>
    <justification jstring="[para(497(a,1),500(a,1,1,2))].">
      <j1 rule="para" parents="497 500"/>
    </justification>
  </clause>

  <clause id="904">
    <literal><![CDATA[
      (x / (y / z)) * (y * y) = x / ((1 / y) / z)
    ]]></literal>
    <justification jstring="[para(883(a,1),500(a,1,1,2))].">
      <j1 rule="para" parents="883 500"/>
    </justification>
  </clause>

  <clause id="905">
    <literal><![CDATA[
      (x / ((y * y) * z)) \ u = (y * y) * ((x / z) \ u)
    ]]></literal>
    <justification jstring="[para(500(a,1),491(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="500 491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="906">
    <literal><![CDATA[
      T(x,x \ y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ z = u
    ]]></literal>
    <justification jstring="[para(505(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="505 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      x / T(y,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x / ((y \ z) \ z) = u
    ]]></literal>
    <justification jstring="[para(512(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="512 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ (y * x),z) = T(y * (x * x),z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(808(a,1),525(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="808 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="909">
    <literal><![CDATA[
      ((((x * y) / x) \ z) \ z) * x = x * T(y,((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,365,a(flip),b,526,a)].">
      <j1 rule="hyper" parents="64 365 526"/>
    </justification>
  </clause>

  <clause id="910">
    <literal><![CDATA[
      ((x * y) * T(L(z,y,x),u)) / (x * y) = T((x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(18(a,2),531(a,1,1,2,1))].">
      <j1 rule="para" parents="18 531"/>
    </justification>
  </clause>

  <clause id="911">
    <literal><![CDATA[
      ((x / y) * T(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(82(a,1),531(a,1,1,2,1))].">
      <j1 rule="para" parents="82 531"/>
    </justification>
  </clause>

  <clause id="912">
    <literal><![CDATA[
      T(x / y,z) * y != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(531(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="531 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="913">
    <literal><![CDATA[
      T(T(x / y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(531(a,1),340(a,1,1)),flip(b)].">
      <j1 rule="para" parents="531 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="914">
    <literal><![CDATA[
      T((x * (y / z)) / x,z) = (x * (z \ y)) / x
    ]]></literal>
    <justification jstring="[para(117(a,1),541(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="117 541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="915">
    <literal><![CDATA[
      T((x * y) / x,z) * x != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(541(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="541 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="916">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(541(a,1),340(a,1,1)),flip(b)].">
      <j1 rule="para" parents="541 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="917">
    <literal><![CDATA[
      L(x \ y,x,y) = ((1 / y) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,102,a,b,552,a)].">
      <j1 rule="hyper" parents="373 102 552"/>
    </justification>
  </clause>

  <clause id="918">
    <literal><![CDATA[
      L(x,y,y * x) = ((1 / (y * x)) * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,18,a,b,552,a)].">
      <j1 rule="hyper" parents="373 18 552"/>
    </justification>
  </clause>

  <clause id="919">
    <literal><![CDATA[
      1 / L(x \ y,x,y) = (1 / y) * x
    ]]></literal>
    <justification jstring="[hyper(225,a,102,a,b,552,a)].">
      <j1 rule="hyper" parents="225 102 552"/>
    </justification>
  </clause>

  <clause id="920">
    <literal><![CDATA[
      1 / L(x,y,y * x) = (1 / (y * x)) * y
    ]]></literal>
    <justification jstring="[hyper(225,a,18,a,b,552,a)].">
      <j1 rule="hyper" parents="225 18 552"/>
    </justification>
  </clause>

  <clause id="921">
    <literal><![CDATA[
      L(T(x,x \ y),x \ y,y) = ((1 / y) * (x \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(116(a,2),917(a,1,1))].">
      <j1 rule="para" parents="116 917"/>
    </justification>
  </clause>

  <clause id="922">
    <literal><![CDATA[
      L(x,1 / x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * (1 / x)) \ y = z
    ]]></literal>
    <justification jstring="[para(82(a,1),642(a,1,1))].">
      <j1 rule="para" parents="82 642"/>
    </justification>
  </clause>

  <clause id="923">
    <literal><![CDATA[
      L(x,y,y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (y * x) = z
    ]]></literal>
    <justification jstring="[para(9(a,1),742(a,1,1))].">
      <j1 rule="para" parents="9 742"/>
    </justification>
  </clause>

  <clause id="924">
    <literal><![CDATA[
      K((x \ y) \ 1,y \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,746,a)].">
      <j1 rule="hyper" parents="56 746"/>
    </justification>
  </clause>

  <clause id="925">
    <literal><![CDATA[
      ((x \ y) \ 1) * (y \ x) = (y \ x) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,746,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 746 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="926">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,y) = ((x * y) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),746(a,1,2))].">
      <j1 rule="para" parents="9 746"/>
    </justification>
  </clause>

  <clause id="927">
    <literal><![CDATA[
      T((x \ (x / y)) \ 1,y) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),746(a,1,2))].">
      <j1 rule="para" parents="82 746"/>
    </justification>
  </clause>

  <clause id="928">
    <literal><![CDATA[
      T(x * y,(x \ 1) \ y) = x * y
    ]]></literal>
    <justification jstring="[hyper(55,a,775,a)].">
      <j1 rule="hyper" parents="55 775"/>
    </justification>
  </clause>

  <clause id="929">
    <literal><![CDATA[
      T(x,y * y) * (1 / y) = ((y * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,798,a(flip),b,808,a)].">
      <j1 rule="hyper" parents="144 798 808"/>
    </justification>
  </clause>

  <clause id="930">
    <literal><![CDATA[
      ((x * x) \ y) * ((x * x) * z) = T(y,x * x) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,798,a(flip),b,133,a),flip(a)].">
      <j1 rule="hyper" parents="144 798 133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="931">
    <literal><![CDATA[
      (x * x) \ (((x * x) \ y) \ z) = T(y,x * x) \ z
    ]]></literal>
    <justification jstring="[para(798(a,1),486(a,1,1)),flip(a)].">
      <j1 rule="para" parents="798 486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="932">
    <literal><![CDATA[
      T((x * x) \ (y / z),z) = z \ ((x * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(493,a,xx,b,801,a)].">
      <j1 rule="hyper" parents="493 801"/>
    </justification>
  </clause>

  <clause id="933">
    <literal><![CDATA[
      ((x * x) \ y) / z = (x * x) \ (y / z)
    ]]></literal>
    <justification jstring="[hyper(154,a,801,a)].">
      <j1 rule="hyper" parents="154 801"/>
    </justification>
  </clause>

  <clause id="934">
    <literal><![CDATA[
      (x * x) \ ((y * (x * x)) / z) = T(y,x * x) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,22,a,b,801,a),flip(a)].">
      <j1 rule="hyper" parents="142 22 801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="935">
    <literal><![CDATA[
      (x * x) \ ((x / y) / z) = ((1 / x) / y) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,887,a(flip),b,801,a),flip(a)].">
      <j1 rule="hyper" parents="142 887 801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="936">
    <literal><![CDATA[
      (x * x) \ (((x * x) / y) / z) = (1 / y) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,548,a(flip),b,801,a),flip(a)].">
      <j1 rule="hyper" parents="142 548 801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="937">
    <literal><![CDATA[
      (x * x) \ ((x * y) / z) = ((1 / x) * y) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,535,a(flip),b,801,a),flip(a)].">
      <j1 rule="hyper" parents="142 535 801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="938">
    <literal><![CDATA[
      (((x * x) \ y) * z) / u = (x * x) \ ((y * z) / u)
    ]]></literal>
    <justification jstring="[hyper(142,a,484,a(flip),b,801,a)].">
      <j1 rule="hyper" parents="142 484 801"/>
    </justification>
  </clause>

  <clause id="939">
    <literal><![CDATA[
      ((x * x) \ (y * (z * u))) * a(y,z,u) = (x * x) \ ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(14(a,2),802(a,1,2))].">
      <j1 rule="para" parents="14 802"/>
    </justification>
  </clause>

  <clause id="940">
    <literal><![CDATA[
      (x * (y * y)) \ ((y * y) * z) = T(x,y * y) \ z
    ]]></literal>
    <justification jstring="[para(22(a,2),804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22 804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="941">
    <literal><![CDATA[
      (x * y) \ ((x * x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(535(a,1),804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="535 804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="942">
    <literal><![CDATA[
      (((x * x) \ y) * z) \ u = (y * z) \ ((x * x) * u)
    ]]></literal>
    <justification jstring="[para(484(a,1),804(a,1,1))].">
      <j1 rule="para" parents="484 804"/>
    </justification>
  </clause>

  <clause id="943">
    <literal><![CDATA[
      (x / y) \ ((x * x) * z) = ((1 / x) / y) \ z
    ]]></literal>
    <justification jstring="[para(887(a,1),804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="887 804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="944">
    <literal><![CDATA[
      (x * x) * (y / (x * y)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,20,a,b,807,a),flip(a)].">
      <j1 rule="hyper" parents="64 20 807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="946">
    <literal><![CDATA[
      T((x * x) * (y / z),z) = z \ ((x * x) * y)
    ]]></literal>
    <justification jstring="[para(807(a,1),117(a,1,1))].">
      <j1 rule="para" parents="807 117"/>
    </justification>
  </clause>

  <clause id="947">
    <literal><![CDATA[
      (x * x) * (L(y,x,x) / z) = (x * (x * y)) / z
    ]]></literal>
    <justification jstring="[para(100(a,1),807(a,1,1)),flip(a)].">
      <j1 rule="para" parents="100 807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="948">
    <literal><![CDATA[
      (x * x) * ((y * x) \ z) = R(y / x,x,x) \ z
    ]]></literal>
    <justification jstring="[para(112(a,2),890(a,1,1)),flip(a)].">
      <j1 rule="para" parents="112 890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="949">
    <literal><![CDATA[
      (x * ((y * y) \ 1)) * z = x * ((y * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(144,a,557,a,b,896,a)].">
      <j1 rule="hyper" parents="144 557 896"/>
    </justification>
  </clause>

  <clause id="950">
    <literal><![CDATA[
      R(1 / x,x,x) * y = x * ((x * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(144,a,244,a,b,896,a)].">
      <j1 rule="hyper" parents="144 244 896"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      (x * y) * ((y * y) \ z) = R(x / y,y,y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,112,a,b,896,a),flip(a)].">
      <j1 rule="hyper" parents="144 112 896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="952">
    <literal><![CDATA[
      T(x,y * y) * ((y * y) \ z) = ((y * y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,872,a(flip),b,896,a),flip(a)].">
      <j1 rule="hyper" parents="144 872 896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="953">
    <literal><![CDATA[
      (x / ((y * y) * z)) * u = (x / z) * ((y * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(144,a,496,a(flip),b,896,a)].">
      <j1 rule="hyper" parents="144 496 896"/>
    </justification>
  </clause>

  <clause id="954">
    <literal><![CDATA[
      (x * y) / a(z,z \ x,y) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(142,a,167,a(flip),b,88,a)].">
      <j1 rule="hyper" parents="142 167 88"/>
    </justification>
  </clause>

  <clause id="955">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(142,a,166,a(flip),b,88,a)].">
      <j1 rule="hyper" parents="142 166 88"/>
    </justification>
  </clause>

  <clause id="956">
    <literal><![CDATA[
      ((x * y) * z) / ((y * z) * a(x,y,z)) = R(x,y * z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(142,a,88,a(flip),b,111,a)].">
      <j1 rule="hyper" parents="142 88 111"/>
    </justification>
  </clause>

  <clause id="957">
    <literal><![CDATA[
      (x * y) * a(x,z,z \ y) = (x * z) * (z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),88(a,1,1,2))].">
      <j1 rule="para" parents="10 88"/>
    </justification>
  </clause>

  <clause id="958">
    <literal><![CDATA[
      (x * y) * a(x,y / z,z) = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(12(a,1),88(a,1,1,2))].">
      <j1 rule="para" parents="12 88"/>
    </justification>
  </clause>

  <clause id="959">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(88(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="88 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="960">
    <literal><![CDATA[
      x * a(y,z,z \ (y \ x)) = (y * z) * (z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(75(a,1),88(a,1,1))].">
      <j1 rule="para" parents="75 88"/>
    </justification>
  </clause>

  <clause id="961">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),x * (y * z)) = ((x * y) * z) \ ((x * (y * z)) * u)
    ]]></literal>
    <justification jstring="[para(88(a,1),102(a,2,1))].">
      <j1 rule="para" parents="88 102"/>
    </justification>
  </clause>

  <clause id="962">
    <literal><![CDATA[
      ((x * y) * z) * a(R(x,y,z),y,z) = (R(x,y,z) * y) * z
    ]]></literal>
    <justification jstring="[para(111(a,1),88(a,1,1))].">
      <j1 rule="para" parents="111 88"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      x * L(L(y,z \ x,z),u,w) = z * ((z \ x) * L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,30,a,b,101,a)].">
      <j1 rule="hyper" parents="145 30 101"/>
    </justification>
  </clause>

  <clause id="964">
    <literal><![CDATA[
      x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y
    ]]></literal>
    <justification jstring="[hyper(39,a,121,a,b,101,a),flip(a)].">
      <j1 rule="hyper" parents="39 121 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="965">
    <literal><![CDATA[
      (x * x) \ (y * ((y \ x) * z)) = (1 / x) * L(z,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,101,a(flip),b,540,a),flip(a)].">
      <j1 rule="hyper" parents="145 101 540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="967">
    <literal><![CDATA[
      L(T(x,y \ z),y \ z,y) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[para(115(a,1),101(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="115 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="968">
    <literal><![CDATA[
      x * R(L(y,z,x / z),u,w) = (x / z) * (z * R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,29,a,b,103,a)].">
      <j1 rule="hyper" parents="145 29 103"/>
    </justification>
  </clause>

  <clause id="969">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,x / y) * x
    ]]></literal>
    <justification jstring="[hyper(39,a,121,a,b,103,a),flip(a)].">
      <j1 rule="hyper" parents="39 121 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="970">
    <literal><![CDATA[
      L(x,y,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (y * x) = z
    ]]></literal>
    <justification jstring="[para(103(a,1),187(a,1))].">
      <j1 rule="para" parents="103 187"/>
    </justification>
  </clause>

  <clause id="971">
    <literal><![CDATA[
      L(T(x,y),y,z / y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(115(a,1),103(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="115 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="972">
    <literal><![CDATA[
      L(L(x,y,z),z * y,u / (z * y)) = u \ ((u / (z * y)) * (z * (y * x)))
    ]]></literal>
    <justification jstring="[para(100(a,1),103(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="100 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="973">
    <literal><![CDATA[
      R(x,x \ y,(x \ y) \ z) = (y * ((x \ y) \ z)) / z
    ]]></literal>
    <justification jstring="[para(10(a,1),108(a,2,2))].">
      <j1 rule="para" parents="10 108"/>
    </justification>
  </clause>

  <clause id="974">
    <literal><![CDATA[
      R(x,x \ y,y \ z) \ z = (x \ y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(108(a,2),349(a,1,1))].">
      <j1 rule="para" parents="108 349"/>
    </justification>
  </clause>

  <clause id="975">
    <literal><![CDATA[
      R(x,x \ (y / z),z) \ y = (x \ (y / z)) * z
    ]]></literal>
    <justification jstring="[para(108(a,2),387(a,1,1))].">
      <j1 rule="para" parents="108 387"/>
    </justification>
  </clause>

  <clause id="976">
    <literal><![CDATA[
      L(R(x,y,y \ z),u,w) * z = (L(x,u,w) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(144,a,29,a(flip),b,110,a)].">
      <j1 rule="hyper" parents="144 29 110"/>
    </justification>
  </clause>

  <clause id="977">
    <literal><![CDATA[
      R(x,y,y \ z) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(110(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="110 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="978">
    <literal><![CDATA[
      R(R(x,y / z,z),u,w) * y = (R(x,u,w) * (y / z)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,31,a,b,113,a)].">
      <j1 rule="hyper" parents="144 31 113"/>
    </justification>
  </clause>

  <clause id="979">
    <literal><![CDATA[
      L(x,y \ 1,y) \ x = a(y,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(293(a,1),238(a,1,1))].">
      <j1 rule="para" parents="293 238"/>
    </justification>
  </clause>

  <clause id="980">
    <literal><![CDATA[
      a(x,x \ y,(x \ y) \ 1) = x \ (y * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(10(a,1),240(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="981">
    <literal><![CDATA[
      a((x / (y \ 1)) / y,y,y \ 1) = ((x / (y \ 1)) / y) \ x
    ]]></literal>
    <justification jstring="[para(87(a,1),240(a,1,2)),flip(a)].">
      <j1 rule="para" parents="87 240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="982">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(297(a,1),240(a,1,2))].">
      <j1 rule="para" parents="297 240"/>
    </justification>
  </clause>

  <clause id="983">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(157,a,982,a)].">
      <j1 rule="hyper" parents="157 982"/>
    </justification>
  </clause>

  <clause id="984">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,u \ 1),y,z) = a(L(x,y,z),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(29(a,1),982(a,1,2))].">
      <j1 rule="para" parents="29 982"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      L(x \ a(y,z,z \ 1),x,y) = (y * x) \ R(y,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(982(a,1),346(a,1,1,2))].">
      <j1 rule="para" parents="982 346"/>
    </justification>
  </clause>

  <clause id="986">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(983(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="983 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="987">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,25,a(flip),b,262,a),flip(a)].">
      <j1 rule="hyper" parents="373 25 262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="988">
    <literal><![CDATA[
      (x * y) * T(L(z,y,x),y) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,25,a(flip),b,262,a)].">
      <j1 rule="hyper" parents="145 25 262"/>
    </justification>
  </clause>

  <clause id="989">
    <literal><![CDATA[
      x * ((y * x) \ (y * (z * x))) = L(z,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,262,a,b,121,a)].">
      <j1 rule="hyper" parents="145 262 121"/>
    </justification>
  </clause>

  <clause id="990">
    <literal><![CDATA[
      (R(x,y,z) * z) \ ((x * y) * z) = L(T(y,z),z,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(111(a,1),262(a,1,2))].">
      <j1 rule="para" parents="111 262"/>
    </justification>
  </clause>

  <clause id="991">
    <literal><![CDATA[
      L(T(x,y \ z),y \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      z \ (y * (x * (y \ z))) = u
    ]]></literal>
    <justification jstring="[para(262(a,1),402(a,1))].">
      <j1 rule="para" parents="262 402"/>
    </justification>
  </clause>

  <clause id="992">
    <literal><![CDATA[
      (x * K(x,y)) * T((x * K(x,y)) \ (x * y),z) = T(R(y,x,K(x,y)),z) * (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(357(a,1),525(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="357 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="993">
    <literal><![CDATA[
      T(R(x / y,y,y \ z),z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(493,a,166,a(flip),b,421,a)].">
      <j1 rule="hyper" parents="493 166 421"/>
    </justification>
  </clause>

  <clause id="994">
    <literal><![CDATA[
      x * R(T(y,x),z,z \ x) = (y * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,267,a,b,421,a)].">
      <j1 rule="hyper" parents="64 267 421"/>
    </justification>
  </clause>

  <clause id="995">
    <literal><![CDATA[
      x * R(x,y,y \ x) = (x * y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,274,a(flip),b,421,a)].">
      <j1 rule="hyper" parents="64 274 421"/>
    </justification>
  </clause>

  <clause id="996">
    <literal><![CDATA[
      x \ ((y * z) * (z \ x)) = R(T(y,x),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,421,a(flip),b,267,a)].">
      <j1 rule="hyper" parents="139 421 267"/>
    </justification>
  </clause>

  <clause id="997">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (z * ((y * x) \ y)) = T(z,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,22,a,b,437,a),flip(a)].">
      <j1 rule="hyper" parents="373 22 437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="998">
    <literal><![CDATA[
      L(x \ 1,x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      ((y * x) \ y) * u = z
    ]]></literal>
    <justification jstring="[para(437(a,2),157(a,1))].">
      <j1 rule="para" parents="437 157"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      x * (y * L(z \ 1,z,u)) = x * (y * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(145,a,439,a,b,9,a)].">
      <j1 rule="hyper" parents="145 439 9"/>
    </justification>
  </clause>

  <clause id="1000">
    <literal><![CDATA[
      x * (L(y \ 1,y,z) * u) = x * (((z * y) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,440,a,b,9,a)].">
      <j1 rule="hyper" parents="145 440 9"/>
    </justification>
  </clause>

  <clause id="1001">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,444,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="145 444 18"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      R(T(1 / x,x * y),x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(467,a,455,a),flip(a)].">
      <j1 rule="hyper" parents="467 455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      T((x \ y) / (x * (x \ y)),z) * y = (T(1 / x,z) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(144,a,455,a,b,110,a)].">
      <j1 rule="hyper" parents="144 455 110"/>
    </justification>
  </clause>

  <clause id="1004">
    <literal><![CDATA[
      R(T(1 / x,y),x,x \ 1) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(194(a,1),455(a,1,1)),flip(a)].">
      <j1 rule="para" parents="194 455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1005">
    <literal><![CDATA[
      x * T(x \ (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(22(a,1),463(a,1,2,1))].">
      <j1 rule="para" parents="22 463"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      L(T(x \ 1,x),x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,117,a(flip),b,469,a),flip(a)].">
      <j1 rule="hyper" parents="373 117 469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      (1 / x) \ T(1 / x,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,469,a(flip),b,295,a)].">
      <j1 rule="hyper" parents="139 469 295"/>
    </justification>
  </clause>

  <clause id="1008">
    <literal><![CDATA[
      ((x * y) \ x) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(473(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="473 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      (x * ((x \ y) * y)) / y = L(y,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,515,a(flip),b,275,a)].">
      <j1 rule="hyper" parents="142 515 275"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,266,a(flip),b,515,a(flip))].">
      <j1 rule="hyper" parents="139 266 515"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      x * ((x \ y) * z) != y * u
    ]]></literal>
    <literal><![CDATA[
      L(z,x \ y,x) = u
    ]]></literal>
    <justification jstring="[para(515(a,1),44(a,1))].">
      <j1 rule="para" parents="515 44"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y \ x,y) = u
    ]]></literal>
    <justification jstring="[para(515(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="515 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1013">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,16,a,b,521,a)].">
      <j1 rule="hyper" parents="373 16 521"/>
    </justification>
  </clause>

  <clause id="1014">
    <literal><![CDATA[
      L(x \ T(y,x),x,x) = ((x * x) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,484,a(flip),b,521,a),flip(a)].">
      <j1 rule="hyper" parents="373 484 521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      L(T(x \ T(y,z),u),x,z) = T((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(521(a,1),25(a,2,1))].">
      <j1 rule="para" parents="521 25"/>
    </justification>
  </clause>

  <clause id="1016">
    <literal><![CDATA[
      L((1 / x) \ T(y,x \ 1),1 / x,x \ 1) = ((x * x) \ 1) \ (y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(868(a,1),521(a,2,1))].">
      <j1 rule="para" parents="868 521"/>
    </justification>
  </clause>

  <clause id="1017">
    <literal><![CDATA[
      L(R(x,y,z),u / x,u / x) = R((1 / (u / x)) * u,y,z)
    ]]></literal>
    <justification jstring="[para(570(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="570 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1018">
    <literal><![CDATA[
      L(x \ ((x * x) * y),x,x) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,569,a,b,571,a)].">
      <j1 rule="hyper" parents="64 569 571"/>
    </justification>
  </clause>

  <clause id="1019">
    <literal><![CDATA[
      (1 / x) * ((x \ y) * x) = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,567,a(flip),b,578,a)].">
      <j1 rule="hyper" parents="64 567 578"/>
    </justification>
  </clause>

  <clause id="1020">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,z) = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,578,a(flip),b,559,a)].">
      <j1 rule="hyper" parents="139 578 559"/>
    </justification>
  </clause>

  <clause id="1021">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,x) = u
    ]]></literal>
    <justification jstring="[para(588(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="588 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1022">
    <literal><![CDATA[
      L(x \ y,x,y / x) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(269,a,168,a(flip),b,592,a),flip(a)].">
      <j1 rule="hyper" parents="269 168 592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1023">
    <literal><![CDATA[
      (x / y) \ (L(z,y,x / y) * x) = y * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,266,a(flip),b,592,a(flip))].">
      <j1 rule="hyper" parents="139 266 592"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(630(a,1),25(a,2,1))].">
      <j1 rule="para" parents="630 25"/>
    </justification>
  </clause>

  <clause id="1025">
    <literal><![CDATA[
      L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(630(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="630 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1026">
    <literal><![CDATA[
      L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(630(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="630 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1028">
    <literal><![CDATA[
      L(R(x,L(x,y,z) \ u,w),y,z) \ (u * w) = (L(x,y,z) \ u) * w
    ]]></literal>
    <justification jstring="[para(29(a,1),649(a,1,1))].">
      <j1 rule="para" parents="29 649"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      (x * y) / ((z \ x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(z,z \ x,y) = u
    ]]></literal>
    <justification jstring="[para(649(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="649 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      x \ ((y * (x / z)) * z) = R(T(y,x),x / z,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,657,a(flip),b,267,a)].">
      <j1 rule="hyper" parents="139 657 267"/>
    </justification>
  </clause>

  <clause id="1031">
    <literal><![CDATA[
      T(x / (y * (z \ x)),u) = R(T(z / y,u),y,z \ x)
    ]]></literal>
    <justification jstring="[para(676(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="676 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1032">
    <literal><![CDATA[
      T((x * (y \ z)) / z,y) = R(y \ x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(677(a,1),280(a,1,1))].">
      <j1 rule="para" parents="677 280"/>
    </justification>
  </clause>

  <clause id="1033">
    <literal><![CDATA[
      R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(678(a,1),27(a,2,1))].">
      <j1 rule="para" parents="678 27"/>
    </justification>
  </clause>

  <clause id="1034">
    <literal><![CDATA[
      R(x / R(1 / y,y,z),z / (y * z),y * z) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(244(a,2),678(a,1,1,2))].">
      <j1 rule="para" parents="244 678"/>
    </justification>
  </clause>

  <clause id="1035">
    <literal><![CDATA[
      R((x / y) \ z,x / y,y) = T((z * y) / x,x / y)
    ]]></literal>
    <justification jstring="[para(678(a,1),280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="678 280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      T(x,y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),732(a,1))].">
      <j1 rule="para" parents="22 732"/>
    </justification>
  </clause>

  <clause id="1037">
    <literal><![CDATA[
      L(R(x,1 / x,y),x,x) = y / ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,244,a(flip),b,825,a),flip(a)].">
      <j1 rule="hyper" parents="64 244 825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1038">
    <literal><![CDATA[
      ((x * y) / (z * y)) * z = z * R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,855,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 855 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1039">
    <literal><![CDATA[
      R(x,y,z) = T(((y * x) * z) / (y * z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),855(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9 855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      T((x * (1 / y)) / ((y * y) \ 1),y \ 1) = R((y \ 1) \ x,y \ 1,1 / y)
    ]]></literal>
    <justification jstring="[para(868(a,1),855(a,1,1,2))].">
      <j1 rule="para" parents="868 855"/>
    </justification>
  </clause>

  <clause id="1041">
    <literal><![CDATA[
      (x \ 1) \ T(y * (x \ 1),x) = T((x \ y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(493,a,858,a(flip),b,297,a),flip(a)].">
      <j1 rule="hyper" parents="493 858 297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1042">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),858(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1043">
    <literal><![CDATA[
      R(x \ 1,x,x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(35,a,811,a(flip),b,859,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 811 859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1044">
    <literal><![CDATA[
      R(R(x \ 1,y,z),x,x) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1043(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1043 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1045">
    <literal><![CDATA[
      T(x \ ((x * y) * y),y * y) = a(x,y,y) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,874,a(flip),b,872,a),flip(a)].">
      <j1 rule="hyper" parents="144 874 872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1046">
    <literal><![CDATA[
      x \ (y \ ((y * x) * x)) = (1 / x) \ a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,874,a(flip),b,536,a),flip(a)].">
      <j1 rule="hyper" parents="139 874 536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1047">
    <literal><![CDATA[
      (x \ ((x * y) * y)) \ ((y * y) * z) = a(x,y,y) \ z
    ]]></literal>
    <justification jstring="[para(874(a,1),804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="874 804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1048">
    <literal><![CDATA[
      L(L(x,y,y),z,u) \ (1 / y) = (y * (y * L(x,z,u))) \ y
    ]]></literal>
    <justification jstring="[para(30(a,1),886(a,1,1))].">
      <j1 rule="para" parents="30 886"/>
    </justification>
  </clause>

  <clause id="1049">
    <literal><![CDATA[
      T(L(x,y \ z,y),y \ z) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(402,a,987,a),flip(a)].">
      <j1 rule="hyper" parents="402 987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      ((x * y) * (L(y \ 1,y,x) * x)) / x = L(x,(x * y) \ x,x * y)
    ]]></literal>
    <justification jstring="[para(241(a,2),1009(a,1,1,2,1))].">
      <j1 rule="para" parents="241 1009"/>
    </justification>
  </clause>

  <clause id="1051">
    <literal><![CDATA[
      ((x * x) \ y) * x = (1 / x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(742,a,1014,a),flip(a)].">
      <j1 rule="hyper" parents="742 1014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1052">
    <literal><![CDATA[
      (1 / x) * T(x * y,x) = ((1 / x) * y) * x
    ]]></literal>
    <justification jstring="[para(535(a,1),1051(a,1,1)),flip(a)].">
      <j1 rule="para" parents="535 1051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1053">
    <literal><![CDATA[
      (((x * y) * z) / (x * z)) * x = x * R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1039,a,b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 1039 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1054">
    <literal><![CDATA[
      T(x,y) != R(z,y,u)
    ]]></literal>
    <literal><![CDATA[
      ((y * z) * u) / (y * u) = x
    ]]></literal>
    <justification jstring="[para(1039(a,2),50(a,1)),flip(a)].">
      <j1 rule="para" parents="1039 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1055">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = T(R(z,x,y),x * y)
    ]]></literal>
    <justification jstring="[para(1039(a,2),278(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1039 278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1056">
    <literal><![CDATA[
      T(R(x,y,x),y * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1039(a,2),312(a,1,1))].">
      <j1 rule="para" parents="1039 312"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      R(T(x,y * x),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,1056,a)].">
      <j1 rule="hyper" parents="64 27 1056"/>
    </justification>
  </clause>

  <clause id="1058">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (y * x) = (y * x) * L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(1056(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1056 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1059">
    <literal><![CDATA[
      R(R(x,y,x),z,u) * (y * x) = (y * x) * R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(1056(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1056 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      ((x * T(y,x * y)) * y) / (x * y) = y
    ]]></literal>
    <justification jstring="[hyper(41,a,1039,a(flip),b,1057,a(flip))].">
      <j1 rule="hyper" parents="41 1039 1057"/>
    </justification>
  </clause>

  <clause id="1061">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),1057(a,1,1,2))].">
      <j1 rule="para" parents="12 1057"/>
    </justification>
  </clause>

  <clause id="1062">
    <literal><![CDATA[
      R(x,y,z) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,y * z) = x
    ]]></literal>
    <justification jstring="[para(1057(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="1057 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1063">
    <literal><![CDATA[
      R(x,y / z,z) != T(z,y / z)
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = x
    ]]></literal>
    <justification jstring="[para(1061(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="1061 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1064">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(372(a,1),1061(a,1,1))].">
      <j1 rule="para" parents="372 1061"/>
    </justification>
  </clause>

  <clause id="1065">
    <literal><![CDATA[
      T(x * T(y,x * y),y) = x * y
    ]]></literal>
    <justification jstring="[hyper(303,a,1060,a)].">
      <j1 rule="hyper" parents="303 1060"/>
    </justification>
  </clause>

  <clause id="1066">
    <literal><![CDATA[
      (x * (y * x)) / x = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(1060(a,1),86(a,1,1,1))].">
      <j1 rule="para" parents="1060 86"/>
    </justification>
  </clause>

  <clause id="1067">
    <literal><![CDATA[
      (x * R(y,x,x \ 1)) / x = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(313,a,1042,a)].">
      <j1 rule="hyper" parents="313 1042"/>
    </justification>
  </clause>

  <clause id="1068">
    <literal><![CDATA[
      R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,27,a,b,123,a)].">
      <j1 rule="hyper" parents="373 27 123"/>
    </justification>
  </clause>

  <clause id="1070">
    <literal><![CDATA[
      (x * y) * R(L(z,y,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * R(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(29(a,2),334(a,1,2))].">
      <j1 rule="para" parents="29 334"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      L(T(x,x \ y),z,u) = L((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25,a,b,368,a)].">
      <j1 rule="hyper" parents="64 25 368"/>
    </justification>
  </clause>

  <clause id="1072">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) * (x \ y) = w
    ]]></literal>
    <justification jstring="[para(368(a,1),328(a,1,2))].">
      <j1 rule="para" parents="368 328"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      T(x * T(y,1 / x),x * x) = (y * (1 / x)) * (x * x)
    ]]></literal>
    <justification jstring="[para(537(a,1),254(a,1,1))].">
      <j1 rule="para" parents="537 254"/>
    </justification>
  </clause>

  <clause id="1074">
    <literal><![CDATA[
      (x * x) * (((1 / y) * z) * u) = (((x * x) / y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,556,a(flip),b,127,a),flip(a)].">
      <j1 rule="hyper" parents="144 556 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1075">
    <literal><![CDATA[
      (((x * x) / y) * z) \ (x * x) = ((1 / y) * z) \ 1
    ]]></literal>
    <justification jstring="[para(556(a,1),489(a,1,1))].">
      <j1 rule="para" parents="556 489"/>
    </justification>
  </clause>

  <clause id="1076">
    <literal><![CDATA[
      ((x * x) / y) * (y * z) = (x * x) * L(z,y,y)
    ]]></literal>
    <justification jstring="[para(559(a,1),556(a,1,2)),flip(a)].">
      <j1 rule="para" parents="559 556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) != (y * x) * u
    ]]></literal>
    <literal><![CDATA[
      L(z,K(y,x),x * y) = u
    ]]></literal>
    <justification jstring="[para(94(a,1),606(a,1,1)),flip(a)].">
      <j1 rule="para" parents="94 606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1080">
    <literal><![CDATA[
      (x * y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ (x \ z),y,x) = u
    ]]></literal>
    <justification jstring="[para(75(a,1),608(a,1,2))].">
      <j1 rule="para" parents="75 608"/>
    </justification>
  </clause>

  <clause id="1081">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(L(u,z,y),y * z,x) = w
    ]]></literal>
    <justification jstring="[para(100(a,1),608(a,1,2,2))].">
      <j1 rule="para" parents="100 608"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      (x * (y * (z * u))) \ (x * ((y * z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(a(y,z,u),y * (z * u),x) = w
    ]]></literal>
    <justification jstring="[para(88(a,1),608(a,1,2,2))].">
      <j1 rule="para" parents="88 608"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) != u * (z * y)
    ]]></literal>
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(94(a,1),664(a,2,2))].">
      <j1 rule="para" parents="94 664"/>
    </justification>
  </clause>

  <clause id="1084">
    <literal><![CDATA[
      R(x / y,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) / (y * z) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),760(a,1,1,1))].">
      <j1 rule="para" parents="11 760"/>
    </justification>
  </clause>

  <clause id="1085">
    <literal><![CDATA[
      1 / T(x * x,y) = T(x * x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(142,a,68,a(flip),b,778,a)].">
      <j1 rule="hyper" parents="142 68 778"/>
    </justification>
  </clause>

  <clause id="1086">
    <literal><![CDATA[
      T(x * x,x) \ 1 = 1 / ((1 / x) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,563,a(flip),b,1085,a),flip(a)].">
      <j1 rule="hyper" parents="64 563 1085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      ((x * x) \ y) * T(z,y) = ((x * x) \ z) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,484,a(flip),b,799,a),flip(a)].">
      <j1 rule="hyper" parents="373 484 799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      x * (((x \ y) * (x \ y)) * z) = (y / (1 / (x \ y))) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,810,a(flip),b,133,a),flip(a)].">
      <j1 rule="hyper" parents="144 810 133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1089">
    <literal><![CDATA[
      ((x \ y) * (x \ y)) \ (x \ z) = (y / (1 / (x \ y))) \ z
    ]]></literal>
    <justification jstring="[para(810(a,1),486(a,1,1)),flip(a)].">
      <j1 rule="para" parents="810 486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1090">
    <literal><![CDATA[
      (x \ 1) * (x \ 1) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(139,a,171,a(flip),b,815,a),flip(a)].">
      <j1 rule="hyper" parents="139 171 815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1091">
    <literal><![CDATA[
      (x \ 1) \ (x \ (1 / x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(149,a,1090,a)].">
      <j1 rule="hyper" parents="149 1090"/>
    </justification>
  </clause>

  <clause id="1092">
    <literal><![CDATA[
      (x \ (1 / x)) * x = x \ 1
    ]]></literal>
    <justification jstring="[hyper(144,a,1090,a(flip),b,317,a(flip))].">
      <j1 rule="hyper" parents="144 1090 317"/>
    </justification>
  </clause>

  <clause id="1093">
    <literal><![CDATA[
      L(x,y \ (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(1090(a,1),593(a,1,2))].">
      <j1 rule="para" parents="1090 593"/>
    </justification>
  </clause>

  <clause id="1094">
    <literal><![CDATA[
      L(x,y,z \ (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(1090(a,1),594(a,1,3))].">
      <j1 rule="para" parents="1090 594"/>
    </justification>
  </clause>

  <clause id="1095">
    <literal><![CDATA[
      L(x,y \ (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(1090(a,1),616(a,1,2))].">
      <j1 rule="para" parents="1090 616"/>
    </justification>
  </clause>

  <clause id="1096">
    <literal><![CDATA[
      R(x,y \ (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(1090(a,1),654(a,1,2))].">
      <j1 rule="para" parents="1090 654"/>
    </justification>
  </clause>

  <clause id="1097">
    <literal><![CDATA[
      (x \ (1 / x)) \ y = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(1090(a,1),582(a,1,1))].">
      <j1 rule="para" parents="1090 582"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      (x \ (1 / x)) * y = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[para(1090(a,1),584(a,1,1))].">
      <j1 rule="para" parents="1090 584"/>
    </justification>
  </clause>

  <clause id="1099">
    <literal><![CDATA[
      (x * (y \ 1)) / y = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[para(1090(a,1),815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1090 815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1100">
    <literal><![CDATA[
      (x * (y \ (1 / y))) \ z = (y \ (1 / y)) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(710,a,1093,a),flip(a)].">
      <j1 rule="hyper" parents="710 1093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      (x \ (1 / x)) \ y = (1 / x) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,630,a(flip),b,1093,a),flip(a)].">
      <j1 rule="hyper" parents="64 630 1093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      1 / ((1 / x) \ x) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(225,a,436,a(flip),b,1093,a(flip))].">
      <j1 rule="hyper" parents="225 436 1093"/>
    </justification>
  </clause>

  <clause id="1103">
    <literal><![CDATA[
      T(x * (y \ (1 / y)),x) = (y \ (1 / y)) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,595,a(flip),b,1093,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 595 1093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1104">
    <literal><![CDATA[
      x * ((x \ (1 / x)) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,1093,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 1093 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      (x * (y \ (1 / y))) * z = x * ((y \ (1 / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1093,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 1093 18"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      L(x,(y \ 1) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),1093(a,1,2,2))].">
      <j1 rule="para" parents="79 1093"/>
    </justification>
  </clause>

  <clause id="1107">
    <literal><![CDATA[
      x \ ((1 / x) * y) = (x \ (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1093(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="1093 598"/>
    </justification>
  </clause>

  <clause id="1108">
    <literal><![CDATA[
      ((x \ (1 / x)) * y) * z = (x \ (1 / x)) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1094,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 1094 18"/>
    </justification>
  </clause>

  <clause id="1109">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ z) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),1094(a,1,3,2))].">
      <j1 rule="para" parents="79 1094"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      (x / y) / (z \ (1 / z)) = x / ((z \ (1 / z)) * y)
    ]]></literal>
    <justification jstring="[hyper(760,a,1096,a),flip(a)].">
      <j1 rule="hyper" parents="760 1096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1111">
    <literal><![CDATA[
      (x * ((y \ (1 / y)) \ z)) / z = x / (y \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,677,a(flip),b,1096,a)].">
      <j1 rule="hyper" parents="64 677 1096"/>
    </justification>
  </clause>

  <clause id="1112">
    <literal><![CDATA[
      R(x,(y \ 1) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),1096(a,1,2,2))].">
      <j1 rule="para" parents="79 1096"/>
    </justification>
  </clause>

  <clause id="1113">
    <literal><![CDATA[
      (x * ((y \ 1) \ y)) \ z = ((y \ 1) \ y) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(710,a,1106,a),flip(a)].">
      <j1 rule="hyper" parents="710 1106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1114">
    <literal><![CDATA[
      (x * ((y \ 1) \ y)) * z = x * (((y \ 1) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1106,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 1106 18"/>
    </justification>
  </clause>

  <clause id="1115">
    <literal><![CDATA[
      (x \ 1) \ (x * y) = ((x \ 1) \ x) * y
    ]]></literal>
    <justification jstring="[para(1106(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="1106 598"/>
    </justification>
  </clause>

  <clause id="1116">
    <literal><![CDATA[
      (((x \ 1) \ x) \ y) \ z = y \ (((x \ 1) \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,630,a(flip),b,1109,a),flip(a)].">
      <j1 rule="hyper" parents="64 630 1109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1117">
    <literal><![CDATA[
      (((x \ 1) \ x) * y) / z = ((x \ 1) \ x) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(225,a,1109,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="225 1109 104"/>
    </justification>
  </clause>

  <clause id="1118">
    <literal><![CDATA[
      x * ((((y \ 1) \ y) * x) \ z) = ((y \ 1) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(145,a,346,a(flip),b,1109,a(flip))].">
      <j1 rule="hyper" parents="145 346 1109"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      (((x \ 1) \ x) * y) * z = ((x \ 1) \ x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1109,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 1109 18"/>
    </justification>
  </clause>

  <clause id="1120">
    <literal><![CDATA[
      (x / y) / ((z \ 1) \ z) = x / (((z \ 1) \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(760,a,1112,a),flip(a)].">
      <j1 rule="hyper" parents="760 1112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1121">
    <literal><![CDATA[
      T(x * x,x) \ 1 = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1086,a,b,1102,a)].">
      <j1 rule="hyper" parents="64 1086 1102"/>
    </justification>
  </clause>

  <clause id="1122">
    <literal><![CDATA[
      T(x * x,x) \ y = (x \ (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1121(a,1),778(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1121 778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1123">
    <literal><![CDATA[
      (x * (y \ (1 / y))) * y = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(156,a,1099,a)].">
      <j1 rule="hyper" parents="156 1099"/>
    </justification>
  </clause>

  <clause id="1124">
    <literal><![CDATA[
      (1 / x) \ (x * y) = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1097,a(flip),b,1101,a),flip(a)].">
      <j1 rule="hyper" parents="64 1097 1101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      (1 / x) * (x * ((x \ 1) \ y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(145,a,1097,a(flip),b,1101,a(flip))].">
      <j1 rule="hyper" parents="145 1097 1101"/>
    </justification>
  </clause>

  <clause id="1126">
    <literal><![CDATA[
      (x \ (1 / x)) * ((1 / x) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,1104,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 1104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1127">
    <literal><![CDATA[
      x * ((x \ 1) * (x \ y)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(1098(a,1),1104(a,1,2))].">
      <j1 rule="para" parents="1098 1104"/>
    </justification>
  </clause>

  <clause id="1128">
    <literal><![CDATA[
      x \ ((1 / x) * y) = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1098,a(flip),b,1107,a),flip(a)].">
      <j1 rule="hyper" parents="373 1098 1107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1129">
    <literal><![CDATA[
      ((x \ 1) \ x) * T(y,x) = (x \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,1115,a),flip(a)].">
      <j1 rule="hyper" parents="64 249 1115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1130">
    <literal><![CDATA[
      ((x \ 1) \ x) \ x = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,257,a(flip),b,1115,a(flip))].">
      <j1 rule="hyper" parents="139 257 1115"/>
    </justification>
  </clause>

  <clause id="1131">
    <literal><![CDATA[
      ((x \ 1) \ x) * (x \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),1115(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1132">
    <literal><![CDATA[
      T(x * x,x) \ y = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1098,a(flip),b,1122,a),flip(a)].">
      <j1 rule="hyper" parents="373 1098 1122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1133">
    <literal><![CDATA[
      ((1 / x) \ x) \ y = (x \ (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,564,a(flip),b,1122,a)].">
      <j1 rule="hyper" parents="64 564 1122"/>
    </justification>
  </clause>

  <clause id="1134">
    <literal><![CDATA[
      x * ((x \ 1) \ 1) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(341,a,1124,a),flip(a)].">
      <j1 rule="hyper" parents="341 1124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1135">
    <literal><![CDATA[
      (1 / x) * (x * y) = x * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,169,a(flip),b,1124,a)].">
      <j1 rule="hyper" parents="145 169 1124"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      x * ((x \ 1) \ T(y,x)) = (1 / x) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,1124,a),flip(a)].">
      <j1 rule="hyper" parents="64 249 1124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1137">
    <literal><![CDATA[
      L((x \ 1) \ y,x,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(39,a,561,a,b,1124,a)].">
      <j1 rule="hyper" parents="39 561 1124"/>
    </justification>
  </clause>

  <clause id="1138">
    <literal><![CDATA[
      x * ((x \ 1) \ (x \ y)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),1124(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1139">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      L(T(x,y \ 1),y,y) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(22(a,2),1137(a,1,1))].">
      <j1 rule="para" parents="22 1137"/>
    </justification>
  </clause>

  <clause id="1141">
    <literal><![CDATA[
      L(T((x \ 1) \ y,z),x,x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(1137(a,1),25(a,2,1))].">
      <j1 rule="para" parents="1137 25"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      L(R((x \ 1) \ y,z,u),x,x) = R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(1137(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1137 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1143">
    <literal><![CDATA[
      L(L((x \ 1) \ y,z,u),x,x) = L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(1137(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1137 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1144">
    <literal><![CDATA[
      L(((x \ 1) \ x) * y,x,x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(1115(a,1),1137(a,1,1))].">
      <j1 rule="para" parents="1115 1137"/>
    </justification>
  </clause>

  <clause id="1145">
    <literal><![CDATA[
      L(x,y \ 1,y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(611,a,1139,a)].">
      <j1 rule="hyper" parents="611 1139"/>
    </justification>
  </clause>

  <clause id="1146">
    <literal><![CDATA[
      (x \ 1) * (x \ T(y,x)) = T((x * x) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(269,a,1014,a(flip),b,1139,a),flip(a)].">
      <j1 rule="hyper" parents="269 1014 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1147">
    <literal><![CDATA[
      L(x,y,y) / ((y \ 1) * x) = y
    ]]></literal>
    <justification jstring="[hyper(154,a,1139,a)].">
      <j1 rule="hyper" parents="154 1139"/>
    </justification>
  </clause>

  <clause id="1148">
    <literal><![CDATA[
      x \ L(y,x,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(149,a,1139,a)].">
      <j1 rule="hyper" parents="149 1139"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      x \ L(L(y,x,x),z,u) = (x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,30,a,b,1139,a)].">
      <j1 rule="hyper" parents="139 30 1139"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      x \ (1 / (1 / x)) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,818,a(flip),b,1139,a)].">
      <j1 rule="hyper" parents="139 818 1139"/>
    </justification>
  </clause>

  <clause id="1151">
    <literal><![CDATA[
      L(x,y \ 1,y \ 1) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,568,a,b,1139,a)].">
      <j1 rule="hyper" parents="64 568 1139"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      L((x \ 1) * y,x,x) = (1 / x) * L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,1139,a(flip),b,561,a),flip(a)].">
      <j1 rule="hyper" parents="145 1139 561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1153">
    <literal><![CDATA[
      R(x,y,(y \ 1) * z) * L(z,y,y) = (x * y) * ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1139,a(flip),b,210,a)].">
      <j1 rule="hyper" parents="145 1139 210"/>
    </justification>
  </clause>

  <clause id="1155">
    <literal><![CDATA[
      L((x \ 1) \ y,x,x) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(1139(a,1),397(a,1))].">
      <j1 rule="para" parents="1139 397"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,559,a,b,1145,a)].">
      <j1 rule="hyper" parents="373 559 1145"/>
    </justification>
  </clause>

  <clause id="1157">
    <literal><![CDATA[
      L(x,x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,818,a(flip),b,1145,a),flip(a)].">
      <j1 rule="hyper" parents="373 818 1145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      L(x,1 / y,1 / y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(38,a,574,a,b,1147,a),flip(a)].">
      <j1 rule="hyper" parents="38 574 1147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1159">
    <literal><![CDATA[
      T(L(x,T(x,y) \ 1,T(x,y)),y) = 1 / (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(794,a,1157,a)].">
      <j1 rule="hyper" parents="794 1157"/>
    </justification>
  </clause>

  <clause id="1160">
    <literal><![CDATA[
      x * T(x,x \ 1) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,364,a,b,1134,a)].">
      <j1 rule="hyper" parents="64 364 1134"/>
    </justification>
  </clause>

  <clause id="1161">
    <literal><![CDATA[
      x \ (1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,294,a,b,1150,a),flip(a)].">
      <j1 rule="hyper" parents="373 294 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1162">
    <literal><![CDATA[
      x * K(x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,294,a,b,1150,a)].">
      <j1 rule="hyper" parents="145 294 1150"/>
    </justification>
  </clause>

  <clause id="1163">
    <literal><![CDATA[
      (x \ 1) \ L(y,x,x) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,1151,a(flip),b,1139,a)].">
      <j1 rule="hyper" parents="139 1151 1139"/>
    </justification>
  </clause>

  <clause id="1165">
    <literal><![CDATA[
      (x \ 1) * (x \ ((1 / x) \ y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,1098,a(flip),b,1126,a)].">
      <j1 rule="hyper" parents="64 1098 1126"/>
    </justification>
  </clause>

  <clause id="1166">
    <literal><![CDATA[
      (x \ 1) \ (x \ y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,1126,a(flip),b,1098,a(flip))].">
      <j1 rule="hyper" parents="139 1126 1098"/>
    </justification>
  </clause>

  <clause id="1167">
    <literal><![CDATA[
      x \ (T(x * x,x) * y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(394,a,1132,a),flip(a)].">
      <j1 rule="hyper" parents="394 1132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1168">
    <literal><![CDATA[
      ((1 / x) \ x) \ y = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,564,a(flip),b,1132,a)].">
      <j1 rule="hyper" parents="64 564 1132"/>
    </justification>
  </clause>

  <clause id="1169">
    <literal><![CDATA[
      (x \ (1 / x)) \ y = ((1 / x) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(395,a,1133,a),flip(a)].">
      <j1 rule="hyper" parents="395 1133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1170">
    <literal><![CDATA[
      x / (x \ 1) = (1 / x) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,1092,a(flip),b,1133,a)].">
      <j1 rule="hyper" parents="225 1092 1133"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      T((1 / x) \ x,x \ 1) = (x \ 1) \ x
    ]]></literal>
    <justification jstring="[para(1170(a,1),117(a,1,1))].">
      <j1 rule="para" parents="1170 117"/>
    </justification>
  </clause>

  <clause id="1172">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,295,a(flip),b,1135,a),flip(a)].">
      <j1 rule="hyper" parents="64 295 1135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1173">
    <literal><![CDATA[
      L(x,y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y * ((y \ 1) * x) = z
    ]]></literal>
    <justification jstring="[para(9(a,1),1155(a,1,1))].">
      <j1 rule="para" parents="9 1155"/>
    </justification>
  </clause>

  <clause id="1174">
    <literal><![CDATA[
      L(((x \ 1) \ 1) \ y,x,x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(1151(a,1),1155(a,1))].">
      <j1 rule="para" parents="1151 1155"/>
    </justification>
  </clause>

  <clause id="1175">
    <literal><![CDATA[
      ((1 / x) \ x) * y = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,74,a(flip),b,1168,a)].">
      <j1 rule="hyper" parents="145 74 1168"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      T(T(x * x,x),x \ 1) = (x \ 1) \ x
    ]]></literal>
    <justification jstring="[para(562(a,2),1171(a,1,1))].">
      <j1 rule="para" parents="562 1171"/>
    </justification>
  </clause>

  <clause id="1177">
    <literal><![CDATA[
      (x / (x \ 1)) * y = x * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(1170(a,2),1175(a,1,1))].">
      <j1 rule="para" parents="1170 1175"/>
    </justification>
  </clause>

  <clause id="1178">
    <literal><![CDATA[
      T(L(x,y,y),y \ 1) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(794,a,1140,a)].">
      <j1 rule="hyper" parents="794 1140"/>
    </justification>
  </clause>

  <clause id="1179">
    <literal><![CDATA[
      (x * x) * (x * (y * (x \ 1))) = x * (x * T(y,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(145,a,1140,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 1140 18"/>
    </justification>
  </clause>

  <clause id="1180">
    <literal><![CDATA[
      L(L(T(x,y \ 1),z,u),y,y) = L(y * (x * (y \ 1)),z,u)
    ]]></literal>
    <justification jstring="[para(1140(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1140 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1181">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (x \ 1)) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,1140,a(flip),b,1141,a)].">
      <j1 rule="hyper" parents="64 1140 1141"/>
    </justification>
  </clause>

  <clause id="1182">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,1141,a(flip),b,1139,a),flip(a)].">
      <j1 rule="hyper" parents="139 1141 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1183">
    <literal><![CDATA[
      (1 / x) \ T(x * y,z) = x * T((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,1141,a(flip),b,559,a)].">
      <j1 rule="hyper" parents="139 1141 559"/>
    </justification>
  </clause>

  <clause id="1184">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,1141,a(flip),b,1140,a(flip))].">
      <j1 rule="hyper" parents="139 1141 1140"/>
    </justification>
  </clause>

  <clause id="1185">
    <literal><![CDATA[
      T(x / y,y * y) \ 1 = (x / (1 / y)) \ (y * y)
    ]]></literal>
    <justification jstring="[para(817(a,1),550(a,1,1))].">
      <j1 rule="para" parents="817 550"/>
    </justification>
  </clause>

  <clause id="1186">
    <literal><![CDATA[
      (x / (y / (1 / z))) * (z * z) = x / T(y / z,z * z)
    ]]></literal>
    <justification jstring="[para(817(a,1),900(a,1,2)),flip(a)].">
      <j1 rule="para" parents="817 900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1187">
    <literal><![CDATA[
      (x / (1 / y)) \ ((x / y) * z) = (y * y) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,819,a(flip))].">
      <j1 rule="hyper" parents="139 168 819"/>
    </justification>
  </clause>

  <clause id="1188">
    <literal><![CDATA[
      x * L(x \ ((y * y) \ x),z,u) = L((y * y) \ 1,z,u) * x
    ]]></literal>
    <justification jstring="[para(490(a,1),833(a,1,2,1,2))].">
      <j1 rule="para" parents="490 833"/>
    </justification>
  </clause>

  <clause id="1189">
    <literal><![CDATA[
      (x * ((x \ y) * (y \ z))) / y = L(z / y,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,515,a(flip),b,836,a)].">
      <j1 rule="hyper" parents="142 515 836"/>
    </justification>
  </clause>

  <clause id="1190">
    <literal><![CDATA[
      (x * ((y * x) \ y)) / x = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,439,a(flip),b,836,a)].">
      <j1 rule="hyper" parents="142 439 836"/>
    </justification>
  </clause>

  <clause id="1191">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * (x \ y) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(436(a,1),836(a,2,2))].">
      <j1 rule="para" parents="436 836"/>
    </justification>
  </clause>

  <clause id="1192">
    <literal><![CDATA[
      L(1 / x,x,x) = x / (x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,896,a(flip),b,1190,a),flip(a)].">
      <j1 rule="hyper" parents="64 896 1190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1193">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) / (x \ y) = L(1 / (x \ y),x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),1190(a,1,1,2,1))].">
      <j1 rule="para" parents="10 1190"/>
    </justification>
  </clause>

  <clause id="1194">
    <literal><![CDATA[
      L((x * y) / x,z,u) = (x * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(154,a,837,a),flip(a)].">
      <j1 rule="hyper" parents="154 837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1195">
    <literal><![CDATA[
      L(((x * y) * T(z,y)) / (x * y),y,x) = (x * (z * y)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(142,a,588,a(flip),b,837,a),flip(a)].">
      <j1 rule="hyper" parents="142 588 837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1196">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(142,a,100,a(flip),b,837,a),flip(a)].">
      <j1 rule="hyper" parents="142 100 837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,x,y) = ((z / (x * y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(327,a,843,a),flip(a)].">
      <j1 rule="hyper" parents="327 843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1198">
    <literal><![CDATA[
      x * R(x \ y,z,z \ x) = ((y / x) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,421,a(flip),b,843,a),flip(a)].">
      <j1 rule="hyper" parents="64 421 843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1199">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) \ R(y / x,z,u) = L(x \ 1,x,R(y / x,z,u))
    ]]></literal>
    <justification jstring="[para(843(a,1),241(a,2,1)),flip(a)].">
      <j1 rule="para" parents="843 241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1200">
    <literal><![CDATA[
      R((x * x) \ (y / z),u,w) * z = z * R(z \ ((x * x) \ y),u,w)
    ]]></literal>
    <justification jstring="[para(933(a,1),843(a,1,1,1))].">
      <j1 rule="para" parents="933 843"/>
    </justification>
  </clause>

  <clause id="1201">
    <literal><![CDATA[
      (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = R(R(y,x,K(x,y)),z,u) * (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(357(a,1),843(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="357 843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1202">
    <literal><![CDATA[
      ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(327,a,844,a)].">
      <j1 rule="hyper" parents="327 844"/>
    </justification>
  </clause>

  <clause id="1203">
    <literal><![CDATA[
      R((x * y) / x,z,u) = (x * R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(154,a,844,a),flip(a)].">
      <j1 rule="hyper" parents="154 844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1204">
    <literal><![CDATA[
      ((x * y) * R(z,x,y)) / y = (((x * y) * z) / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(142,a,844,a(flip),b,111,a(flip))].">
      <j1 rule="hyper" parents="142 844 111"/>
    </justification>
  </clause>

  <clause id="1205">
    <literal><![CDATA[
      R(x / (x * x),y,z) * x = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(813(a,1),844(a,1,1,1))].">
      <j1 rule="para" parents="813 844"/>
    </justification>
  </clause>

  <clause id="1206">
    <literal><![CDATA[
      (x * ((1 / x) * y)) / x = L(y / x,x,x)
    ]]></literal>
    <justification jstring="[para(569(a,1),852(a,1,1,2))].">
      <j1 rule="para" parents="569 852"/>
    </justification>
  </clause>

  <clause id="1207">
    <literal><![CDATA[
      (x * ((y * x) \ (y * z))) / x = L(z / x,x,y)
    ]]></literal>
    <justification jstring="[para(102(a,1),852(a,1,1,2))].">
      <j1 rule="para" parents="102 852"/>
    </justification>
  </clause>

  <clause id="1208">
    <literal><![CDATA[
      L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z
    ]]></literal>
    <justification jstring="[para(346(a,1),852(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="346 852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1209">
    <literal><![CDATA[
      (x * ((1 / x) * y)) / x = L(y / x,x,1 / x)
    ]]></literal>
    <justification jstring="[para(628(a,1),852(a,1,1,2))].">
      <j1 rule="para" parents="628 852"/>
    </justification>
  </clause>

  <clause id="1210">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[para(1013(a,2),852(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1013 852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1211">
    <literal><![CDATA[
      L(((1 / x) \ y) / x,x,x) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(10(a,1),1206(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 1206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      ((x * y) * R(L(z,y,x),u,w)) / (x * y) = R((x * (y * z)) / (x * y),u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),853(a,1,1,2,1))].">
      <j1 rule="para" parents="18 853"/>
    </justification>
  </clause>

  <clause id="1213">
    <literal><![CDATA[
      R(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * R(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(853(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="853 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1214">
    <literal><![CDATA[
      (x \ 1) * (x \ (x / y)) = (x \ 1) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,584,a(flip),b,889,a)].">
      <j1 rule="hyper" parents="64 584 889"/>
    </justification>
  </clause>

  <clause id="1215">
    <literal><![CDATA[
      (x \ 1) \ ((x \ 1) / y) = x \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,889,a(flip),b,584,a(flip))].">
      <j1 rule="hyper" parents="139 889 584"/>
    </justification>
  </clause>

  <clause id="1217">
    <literal><![CDATA[
      (1 / x) * (x / y) = x * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,1214,a(flip),b,1128,a),flip(a)].">
      <j1 rule="hyper" parents="145 1214 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1218">
    <literal><![CDATA[
      (x \ 1) / (y \ x) = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),1214(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 1214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1219">
    <literal><![CDATA[
      (x \ 1) / L(y \ 1,y,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(448(a,1),1214(a,1,2)),flip(a)].">
      <j1 rule="para" parents="448 1214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1221">
    <literal><![CDATA[
      (x * y) * (((x * y) \ 1) / y) = (1 / (x * y)) * x
    ]]></literal>
    <justification jstring="[para(11(a,1),1217(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 1217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1222">
    <literal><![CDATA[
      L(x \ 1,x,y) = ((y \ 1) * x) \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(215,a,1219,a),flip(a)].">
      <j1 rule="hyper" parents="215 1219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1223">
    <literal><![CDATA[
      L(x \ 1,x,y \ 1) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,441,a,b,1219,a)].">
      <j1 rule="hyper" parents="37 441 1219"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(434(a,1),1219(a,1,2))].">
      <j1 rule="para" parents="434 1219"/>
    </justification>
  </clause>

  <clause id="1225">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(144,a,294,a,b,1224,a)].">
      <j1 rule="hyper" parents="144 294 1224"/>
    </justification>
  </clause>

  <clause id="1226">
    <literal><![CDATA[
      (x \ 1) / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1224(a,2),424(a,1))].">
      <j1 rule="para" parents="1224 424"/>
    </justification>
  </clause>

  <clause id="1227">
    <literal><![CDATA[
      R(x,K(y \ 1,y),1 / y) * (y \ 1) = (x * K(y \ 1,y)) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,1225,a(flip),b,210,a)].">
      <j1 rule="hyper" parents="145 1225 210"/>
    </justification>
  </clause>

  <clause id="1228">
    <literal><![CDATA[
      ((x \ 1) * y) \ (x \ 1) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(642,a,1222,a),flip(a)].">
      <j1 rule="hyper" parents="642 1222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1229">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) \ x = y \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(402,a,1228,a),flip(a)].">
      <j1 rule="hyper" parents="402 1228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1230">
    <literal><![CDATA[
      ((1 / x) \ y) \ x = (x \ y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(1138(a,1),1229(a,1,1))].">
      <j1 rule="para" parents="1138 1229"/>
    </justification>
  </clause>

  <clause id="1231">
    <literal><![CDATA[
      (x \ ((y * y) \ z)) \ (x \ 1) = (((y * y) / x) \ z) \ x
    ]]></literal>
    <justification jstring="[para(879(a,1),1230(a,1,1)),flip(a)].">
      <j1 rule="para" parents="879 1230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1232">
    <literal><![CDATA[
      (x / (1 / y)) * ((z / (1 / y)) \ u) = (x / y) * ((z / y) \ u)
    ]]></literal>
    <justification jstring="[para(891(a,1),819(a,1,2)),flip(a)].">
      <j1 rule="para" parents="891 819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1233">
    <literal><![CDATA[
      (x / ((1 / y) * z)) * (1 / y) = (x / (y * z)) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,901,a(flip),b,808,a)].">
      <j1 rule="hyper" parents="144 901 808"/>
    </justification>
  </clause>

  <clause id="1234">
    <literal><![CDATA[
      (x * x) \ (y / ((1 / x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / (x * z),x * x) = u
    ]]></literal>
    <justification jstring="[para(901(a,1),336(a,1,2))].">
      <j1 rule="para" parents="901 336"/>
    </justification>
  </clause>

  <clause id="1235">
    <literal><![CDATA[
      (x * x) * ((y / (1 / z)) \ u) = (y / ((x * x) / z)) \ u
    ]]></literal>
    <justification jstring="[para(902(a,1),491(a,1,2,1))].">
      <j1 rule="para" parents="902 491"/>
    </justification>
  </clause>

  <clause id="1236">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / x = (y * (z / x)) / y
    ]]></literal>
    <justification jstring="[hyper(313,a,914,a)].">
      <j1 rule="hyper" parents="313 914"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,914,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 914 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1238">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) * y = y * (((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,926,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 926 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1239">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) * y = y * ((x \ (x / y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,927,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 927 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1240">
    <literal><![CDATA[
      ((x * y) / z) \ ((x * x) * u) = (((1 / x) * y) / z) \ u
    ]]></literal>
    <justification jstring="[para(937(a,1),804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="937 804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1241">
    <literal><![CDATA[
      (x / ((y * z) / u)) * (y * y) = x / (((1 / y) * z) / u)
    ]]></literal>
    <justification jstring="[para(937(a,1),900(a,1,2)),flip(a)].">
      <j1 rule="para" parents="937 900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1242">
    <literal><![CDATA[
      ((1 / x) * (x * y)) \ y = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14,a,b,941,a),flip(a)].">
      <j1 rule="hyper" parents="64 14 941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1243">
    <literal><![CDATA[
      L(x,y,y) \ x = a(y,y,x)
    ]]></literal>
    <justification jstring="[para(559(a,1),1242(a,1,1))].">
      <j1 rule="para" parents="559 1242"/>
    </justification>
  </clause>

  <clause id="1244">
    <literal><![CDATA[
      a(x,x,(x \ 1) \ y) = (x * y) \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(1125(a,1),1242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1125 1242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1245">
    <literal><![CDATA[
      L(x,y,y) * a(y,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(157,a,1243,a)].">
      <j1 rule="hyper" parents="157 1243"/>
    </justification>
  </clause>

  <clause id="1246">
    <literal><![CDATA[
      L(L(x,y,y),z,u) \ L(x,z,u) = a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(30(a,1),1243(a,1,1))].">
      <j1 rule="para" parents="30 1243"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      L(a(x,x,y),L(y,x,x),z) = (z * L(y,x,x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(1243(a,1),102(a,1,1))].">
      <j1 rule="para" parents="1243 102"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      x * L(y,a(z,z,x),L(x,z,z)) = L(x,z,z) * (a(z,z,x) * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,1245,a(flip),b,213,a)].">
      <j1 rule="hyper" parents="144 1245 213"/>
    </justification>
  </clause>

  <clause id="1249">
    <literal><![CDATA[
      ((x * x) \ y) * a(x,x,x \ (x \ y)) = x \ (x \ y)
    ]]></literal>
    <justification jstring="[para(346(a,1),1245(a,1,1))].">
      <j1 rule="para" parents="346 1245"/>
    </justification>
  </clause>

  <clause id="1250">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = T(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,115,a(flip),b,1007,a)].">
      <j1 rule="hyper" parents="145 115 1007"/>
    </justification>
  </clause>

  <clause id="1251">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,117,a(flip),b,1250,a),flip(a)].">
      <j1 rule="hyper" parents="373 117 1250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1252">
    <literal><![CDATA[
      (1 / x) \ (x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,117,a(flip),b,1250,a)].">
      <j1 rule="hyper" parents="139 117 1250"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(294(a,2),1251(a,1,2))].">
      <j1 rule="para" parents="294 1251"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      (1 / x) \ (x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,294,a,b,1252,a),flip(a)].">
      <j1 rule="hyper" parents="373 294 1252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1255">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = x \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,1253,a(flip),b,209,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 1253 209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1256">
    <literal><![CDATA[
      L((1 / x) \ y,x,x) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[para(539(a,1),1018(a,1,1))].">
      <j1 rule="para" parents="539 1018"/>
    </justification>
  </clause>

  <clause id="1257">
    <literal><![CDATA[
      L(x,x,x) * L(y,x,x) = L(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(344(a,1),1018(a,1,1)),flip(a)].">
      <j1 rule="para" parents="344 1018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1258">
    <literal><![CDATA[
      L(x,x,x) * ((1 / x) * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      L(x,x,x) * (L(x,x,x) * y) = L((x * x) * y,x,x)
    ]]></literal>
    <justification jstring="[para(571(a,1),1258(a,1,2))].">
      <j1 rule="para" parents="571 1258"/>
    </justification>
  </clause>

  <clause id="1260">
    <literal><![CDATA[
      (1 / (1 / x)) * L(y,x,x) = L(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(818(a,1),1257(a,1,1))].">
      <j1 rule="para" parents="818 1257"/>
    </justification>
  </clause>

  <clause id="1262">
    <literal><![CDATA[
      ((1 / x) * T(y,x)) * x = (1 / x) * T(y * x,x)
    ]]></literal>
    <justification jstring="[para(115(a,1),1052(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="115 1052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      T(T(R(x / y,z,u),w),y) = R(T(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(117(a,1),1068(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="117 1068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      R(x,x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) / ((x \ y) * z) = u
    ]]></literal>
    <justification jstring="[para(79(a,1),1084(a,1,1))].">
      <j1 rule="para" parents="79 1084"/>
    </justification>
  </clause>

  <clause id="1265">
    <literal><![CDATA[
      ((x * x) \ y) * ((x * x) * z) = z * T(y,(x * x) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1087(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      ((x * x) \ y) * L(T(z,y),u,w) = ((x * x) \ L(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(25(a,2),1087(a,1,2))].">
      <j1 rule="para" parents="25 1087"/>
    </justification>
  </clause>

  <clause id="1267">
    <literal><![CDATA[
      ((x * x) \ L(y,z,u)) * y = ((x * x) \ y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(198(a,1),1087(a,1,2))].">
      <j1 rule="para" parents="198 1087"/>
    </justification>
  </clause>

  <clause id="1268">
    <literal><![CDATA[
      ((x * x) \ R(y / z,u,w)) * z = ((x * x) \ z) * R(z \ y,u,w)
    ]]></literal>
    <justification jstring="[para(280(a,1),1087(a,1,2)),flip(a)].">
      <j1 rule="para" parents="280 1087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1269">
    <literal><![CDATA[
      T(x * (y \ (1 / y)),x) = (y \ 1) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1098,a(flip),b,1103,a),flip(a)].">
      <j1 rule="hyper" parents="373 1098 1103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      (x / y) * (z \ ((z * y) * y)) = (x / (1 / y)) * a(z,y,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,874,a(flip),b,1187,a),flip(a)].">
      <j1 rule="hyper" parents="145 874 1187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      (x * y) * ((z * L(u,y,x)) / z) = x * (y * ((z * u) / z))
    ]]></literal>
    <justification jstring="[hyper(145,a,1194,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 1194 18"/>
    </justification>
  </clause>

  <clause id="1272">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(1194(a,2),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1194 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1273">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x
    ]]></literal>
    <justification jstring="[para(443(a,1),1194(a,2,1,2))].">
      <j1 rule="para" parents="443 1194"/>
    </justification>
  </clause>

  <clause id="1274">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,1 / y) = (x * ((1 / y) * z)) / x
    ]]></literal>
    <justification jstring="[para(628(a,1),1194(a,2,1,2))].">
      <j1 rule="para" parents="628 1194"/>
    </justification>
  </clause>

  <clause id="1275">
    <literal><![CDATA[
      L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x
    ]]></literal>
    <justification jstring="[para(630(a,1),1194(a,2,1,2))].">
      <j1 rule="para" parents="630 1194"/>
    </justification>
  </clause>

  <clause id="1276">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) = (((x * y) / x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,1203,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 1203 20"/>
    </justification>
  </clause>

  <clause id="1277">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * R(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(1203(a,2),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1203 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x
    ]]></literal>
    <justification jstring="[para(351(a,1),1203(a,2,1,2))].">
      <j1 rule="para" parents="351 1203"/>
    </justification>
  </clause>

  <clause id="1279">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x
    ]]></literal>
    <justification jstring="[para(675(a,1),1203(a,2,1,2))].">
      <j1 rule="para" parents="675 1203"/>
    </justification>
  </clause>

  <clause id="1280">
    <literal><![CDATA[
      (1 / x) * (x \ ((x * y) * (y \ x))) = a(x,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,536,a,b,89,a)].">
      <j1 rule="hyper" parents="64 536 89"/>
    </justification>
  </clause>

  <clause id="1281">
    <literal><![CDATA[
      ((x * x) \ (x * y)) * (y \ x) = a(x,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,484,a(flip),b,89,a)].">
      <j1 rule="hyper" parents="64 484 89"/>
    </justification>
  </clause>

  <clause id="1282">
    <literal><![CDATA[
      (x * y) * (y \ (x \ 1)) = a(x,y,y \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,185,a(flip),b,89,a)].">
      <j1 rule="hyper" parents="64 185 89"/>
    </justification>
  </clause>

  <clause id="1283">
    <literal><![CDATA[
      a(x,y,y \ (x \ 1)) / (y \ (x \ 1)) = x * y
    ]]></literal>
    <justification jstring="[hyper(142,a,89,a(flip),b,185,a(flip))].">
      <j1 rule="hyper" parents="142 89 185"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      (x * y) \ a(x,y,y \ (x \ 1)) = y \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,89,a(flip),b,185,a(flip))].">
      <j1 rule="hyper" parents="139 89 185"/>
    </justification>
  </clause>

  <clause id="1285">
    <literal><![CDATA[
      x \ (((x / y) * z) * (z \ y)) = a(x / y,z,z \ y)
    ]]></literal>
    <justification jstring="[para(12(a,1),89(a,1,1))].">
      <j1 rule="para" parents="12 89"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      a(x / y,y,y \ z) = ((x / y) * z) \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[para(12(a,1),89(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 89"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1287">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = z * ((z \ y) * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(225,a,90,a(flip),b,249,a(flip))].">
      <j1 rule="hyper" parents="225 90 249"/>
    </justification>
  </clause>

  <clause id="1288">
    <literal><![CDATA[
      ((x * x) \ (x * (x / y))) * y = a(x,x / y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,484,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="64 484 92"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      x \ (((x / y) * (y / z)) * z) = a(x / y,y / z,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),92(a,1,1))].">
      <j1 rule="para" parents="12 92"/>
    </justification>
  </clause>

  <clause id="1290">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(93(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="93 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1291">
    <literal><![CDATA[
      (((x \ 1) / y) * (y * x)) \ K(x \ 1,x) = a((x \ 1) / y,y,x)
    ]]></literal>
    <justification jstring="[para(294(a,2),93(a,1,2))].">
      <j1 rule="para" parents="294 93"/>
    </justification>
  </clause>

  <clause id="1292">
    <literal><![CDATA[
      x / L(y,z,x / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x / (z * y)) * z = u
    ]]></literal>
    <justification jstring="[para(105(a,2),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="105 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1293">
    <literal><![CDATA[
      x / T((x / (y * z)) * y,L(z,y,x / (y * z))) = ((x / (y * z)) * y) \ x
    ]]></literal>
    <justification jstring="[para(105(a,2),301(a,1,2,2))].">
      <j1 rule="para" parents="105 301"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      (x * y) * T((y * T(x,y)) \ y,z) = y * (T(x,y) * T(T(x,y) \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,444,a,b,261,a)].">
      <j1 rule="hyper" parents="145 444 261"/>
    </justification>
  </clause>

  <clause id="1295">
    <literal><![CDATA[
      (x * y) * L(L(z,T(x,y),y),u,w) = y * (T(x,y) * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,30,a,b,261,a)].">
      <j1 rule="hyper" parents="145 30 261"/>
    </justification>
  </clause>

  <clause id="1296">
    <literal><![CDATA[
      (x * y) * T(y,x) = (y * x) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,1056,a(flip),b,277,a)].">
      <j1 rule="hyper" parents="145 1056 277"/>
    </justification>
  </clause>

  <clause id="1297">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ y) = y * T(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(717,a,1296,a),flip(a)].">
      <j1 rule="hyper" parents="717 1296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1298">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(390,a,1296,a),flip(a)].">
      <j1 rule="hyper" parents="390 1296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1299">
    <literal><![CDATA[
      (x * y) * R((y * T(x,y)) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,445,a,b,261,a)].">
      <j1 rule="hyper" parents="145 445 261"/>
    </justification>
  </clause>

  <clause id="1300">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,445,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="145 445 18"/>
    </justification>
  </clause>

  <clause id="1301">
    <literal><![CDATA[
      L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,102,a(flip),b,446,a),flip(a)].">
      <j1 rule="hyper" parents="373 102 446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1302">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,446,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 446 18"/>
    </justification>
  </clause>

  <clause id="1303">
    <literal><![CDATA[
      L((x * (y \ z)) \ x,y \ z,y) = L(z \ y,y \ z,x)
    ]]></literal>
    <justification jstring="[para(436(a,1),446(a,1,1)),flip(a)].">
      <j1 rule="para" parents="436 446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1304">
    <literal><![CDATA[
      R(x / (y * x),z,u) * (y * x) = (R(1 / y,z,u) * y) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,456,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 456 20"/>
    </justification>
  </clause>

  <clause id="1305">
    <literal><![CDATA[
      R(x / (y * x),y,y \ 1) = R(1 * (y \ 1),y,x)
    ]]></literal>
    <justification jstring="[para(675(a,1),456(a,1,1)),flip(a)].">
      <j1 rule="para" parents="675 456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1306">
    <literal><![CDATA[
      x * L(x \ (y * x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(22(a,1),464(a,1,2,1))].">
      <j1 rule="para" parents="22 464"/>
    </justification>
  </clause>

  <clause id="1307">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(102(a,1),517(a,1,2,1))].">
      <j1 rule="para" parents="102 517"/>
    </justification>
  </clause>

  <clause id="1308">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u))
    ]]></literal>
    <justification jstring="[para(346(a,1),517(a,1,2,1))].">
      <j1 rule="para" parents="346 517"/>
    </justification>
  </clause>

  <clause id="1309">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(434(a,1),566(a,1,2,1))].">
      <j1 rule="para" parents="434 566"/>
    </justification>
  </clause>

  <clause id="1310">
    <literal><![CDATA[
      (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(569(a,1),566(a,1,2,1))].">
      <j1 rule="para" parents="569 566"/>
    </justification>
  </clause>

  <clause id="1311">
    <literal><![CDATA[
      (1 / x) * (x * R(x \ y,z,u)) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(923,a,579,a)].">
      <j1 rule="hyper" parents="923 579"/>
    </justification>
  </clause>

  <clause id="1312">
    <literal><![CDATA[
      x \ R((1 / x) * y,z,u) = (x \ 1) * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,579,a(flip),b,1139,a)].">
      <j1 rule="hyper" parents="139 579 1139"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      L((x * y) \ (x * z),y,y) = L((1 / y) * z,y,x)
    ]]></literal>
    <justification jstring="[para(102(a,1),580(a,1,1))].">
      <j1 rule="para" parents="102 580"/>
    </justification>
  </clause>

  <clause id="1314">
    <literal><![CDATA[
      (x * x) * ((L(y,x,x) * z) * u) = ((x * (x * y)) * z) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,605,a(flip),b,127,a),flip(a)].">
      <j1 rule="hyper" parents="144 605 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1315">
    <literal><![CDATA[
      L(T(T(x,y) \ z,u),T(x,y),y) = T((x * y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(115(a,1),636(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="115 636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1316">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * T(y \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(636(a,2),334(a,1,2))].">
      <j1 rule="para" parents="636 334"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      L(R(T(x,y) \ z,u,w),T(x,y),y) = R((x * y) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(638(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="638 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1318">
    <literal><![CDATA[
      R(x,T(y,x),T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,648,a)].">
      <j1 rule="hyper" parents="64 249 648"/>
    </justification>
  </clause>

  <clause id="1319">
    <literal><![CDATA[
      T(R(x / y,y,T(z,y)),z * y) = (z * y) \ (x * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(493,a,166,a(flip),b,652,a)].">
      <j1 rule="hyper" parents="493 166 652"/>
    </justification>
  </clause>

  <clause id="1320">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,267,a,b,652,a(flip))].">
      <j1 rule="hyper" parents="35 267 652"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      (T(x,x * y) * y) * T(x,y) = T(x,y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,1320,a(flip),b,264,a),flip(a)].">
      <j1 rule="hyper" parents="144 1320 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1322">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,x \ y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1320(a,1,1,2))].">
      <j1 rule="para" parents="10 1320"/>
    </justification>
  </clause>

  <clause id="1323">
    <literal><![CDATA[
      R(x,y,T(z,y)) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,z * y) = x
    ]]></literal>
    <justification jstring="[para(1320(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="1320 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1324">
    <literal><![CDATA[
      R(x,y,y) * ((y * y) * (y \ 1)) = R(x * y,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,297,a(flip),b,662,a),flip(a)].">
      <j1 rule="hyper" parents="373 297 662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1325">
    <literal><![CDATA[
      R(x,y,y) * ((y * y) / z) = ((x * y) * y) * (1 / z)
    ]]></literal>
    <justification jstring="[para(497(a,1),662(a,1,2))].">
      <j1 rule="para" parents="497 662"/>
    </justification>
  </clause>

  <clause id="1326">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(467,a,679,a),flip(a)].">
      <j1 rule="hyper" parents="467 679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1327">
    <literal><![CDATA[
      R(T((x * y) / x,x * y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(399,a,679,a),flip(a)].">
      <j1 rule="hyper" parents="399 679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1328">
    <literal><![CDATA[
      R(T(x / y,z),y,u) * (y * u) = (y * u) * T((y * u) \ (x * u),z)
    ]]></literal>
    <justification jstring="[hyper(144,a,679,a(flip),b,531,a)].">
      <j1 rule="hyper" parents="144 679 531"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(679(a,1),467(a,1))].">
      <j1 rule="para" parents="679 467"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = T(x / y,z) * y
    ]]></literal>
    <justification jstring="[para(675(a,1),700(a,1,1,1))].">
      <j1 rule="para" parents="675 700"/>
    </justification>
  </clause>

  <clause id="1331">
    <literal><![CDATA[
      T(x,y * ((x \ y) \ 1)) = x
    ]]></literal>
    <justification jstring="[para(701(a,1),197(a,1,2))].">
      <j1 rule="para" parents="701 197"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      T(x / (1 / y),z) * (1 / y) = T(x * y,z) / y
    ]]></literal>
    <justification jstring="[para(674(a,1),705(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="674 705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1334">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),u)) = w
    ]]></literal>
    <justification jstring="[para(708(a,1),334(a,1,2))].">
      <j1 rule="para" parents="708 334"/>
    </justification>
  </clause>

  <clause id="1335">
    <literal><![CDATA[
      x \ y != z * (u \ (u * w))
    ]]></literal>
    <literal><![CDATA[
      x * (z * w) = y
    ]]></literal>
    <justification jstring="[para(9(a,1),733(a,2,2,2,2))].">
      <j1 rule="para" parents="9 733"/>
    </justification>
  </clause>

  <clause id="1336">
    <literal><![CDATA[
      (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,747,a,b,103,a),flip(a)].">
      <j1 rule="hyper" parents="145 747 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1337">
    <literal><![CDATA[
      x * (y \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(191(a,1),756(a,1,2,2))].">
      <j1 rule="para" parents="191 756"/>
    </justification>
  </clause>

  <clause id="1338">
    <literal><![CDATA[
      L(T(R(x,y,z),u),u,x) = R(T(x,x * u),y,z)
    ]]></literal>
    <justification jstring="[para(27(a,1),768(a,1,1))].">
      <j1 rule="para" parents="27 768"/>
    </justification>
  </clause>

  <clause id="1339">
    <literal><![CDATA[
      L(((x * y) * x) / (x * y),y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(36,a,837,a,b,790,a)].">
      <j1 rule="hyper" parents="36 837 790"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * (y * T(y \ 1,x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,440,a(flip),b,793,a)].">
      <j1 rule="hyper" parents="373 440 793"/>
    </justification>
  </clause>

  <clause id="1341">
    <literal><![CDATA[
      (1 / x) * (L(y,z,x) * (x * z)) = L(z * T(y,x * z),x,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,793,a(flip),b,561,a)].">
      <j1 rule="hyper" parents="145 793 561"/>
    </justification>
  </clause>

  <clause id="1342">
    <literal><![CDATA[
      R(T(x,x * y),x,y) = ((1 / x) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,941,a(flip),b,796,a),flip(a)].">
      <j1 rule="hyper" parents="64 941 796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1343">
    <literal><![CDATA[
      ((x * x) \ (y * x)) * x = R(T(y,x * x),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,484,a(flip),b,796,a)].">
      <j1 rule="hyper" parents="64 484 796"/>
    </justification>
  </clause>

  <clause id="1344">
    <literal><![CDATA[
      ((x * y) * y) \ ((y * y) * z) = R(T(x,y * y),y,y) \ z
    ]]></literal>
    <justification jstring="[para(796(a,1),804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="796 804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1345">
    <literal><![CDATA[
      R(T(x,(y * z) * a(x,y,z)),y * z,a(x,y,z)) = ((y * z) * a(x,y,z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(88(a,1),796(a,1,2)),flip(a)].">
      <j1 rule="para" parents="88 796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1346">
    <literal><![CDATA[
      R(T(L((x * y) / x,z,u),x * w),x,w) = (x * w) \ ((x * L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(837(a,1),796(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="837 796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1347">
    <literal><![CDATA[
      T(1 / (1 / x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(141,a,1137,a(flip),b,827,a),flip(a)].">
      <j1 rule="hyper" parents="141 1137 827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      T(T(1 / (1 / x),y),x \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1347(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1347 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      T(x,y \ 1) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      T(1 / (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(1348(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="1348 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1350">
    <literal><![CDATA[
      T(x,1 / x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(276(a,1),1348(a,1,1)),flip(a)].">
      <j1 rule="para" parents="276 1348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1351">
    <literal><![CDATA[
      T(1 / x,1 / (1 / x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,848,a(flip),b,1350,a),flip(a)].">
      <j1 rule="hyper" parents="373 848 1350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1352">
    <literal><![CDATA[
      T(x,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,116,a(flip),b,1350,a),flip(a)].">
      <j1 rule="hyper" parents="373 116 1350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1353">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,1064,a,b,1350,a)].">
      <j1 rule="hyper" parents="64 1064 1350"/>
    </justification>
  </clause>

  <clause id="1354">
    <literal><![CDATA[
      T(x \ 1,x) = ((x \ 1) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),1352(a,1,2))].">
      <j1 rule="para" parents="79 1352"/>
    </justification>
  </clause>

  <clause id="1355">
    <literal><![CDATA[
      K(x,1 / x) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,706,a,b,1353,a)].">
      <j1 rule="hyper" parents="64 706 1353"/>
    </justification>
  </clause>

  <clause id="1356">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(142,a,1353,a(flip),b,706,a)].">
      <j1 rule="hyper" parents="142 1353 706"/>
    </justification>
  </clause>

  <clause id="1357">
    <literal><![CDATA[
      T(x,x \ 1) / x = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(142,a,1353,a(flip),b,298,a)].">
      <j1 rule="hyper" parents="142 1353 298"/>
    </justification>
  </clause>

  <clause id="1358">
    <literal><![CDATA[
      T(x,x \ 1) \ 1 = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,362,a,b,1354,a)].">
      <j1 rule="hyper" parents="373 362 1354"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = (x \ 1) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(142,a,848,a(flip),b,1355,a),flip(a)].">
      <j1 rule="hyper" parents="142 848 1355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1360">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(142,a,116,a(flip),b,1355,a)].">
      <j1 rule="hyper" parents="142 116 1355"/>
    </justification>
  </clause>

  <clause id="1361">
    <literal><![CDATA[
      T(x,x \ 1) / x != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(1356(a,2),480(a,1))].">
      <j1 rule="para" parents="1356 480"/>
    </justification>
  </clause>

  <clause id="1362">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1359(a,2),1226(a,1))].">
      <j1 rule="para" parents="1359 1226"/>
    </justification>
  </clause>

  <clause id="1363">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y / x) * (x / y) = z
    ]]></literal>
    <justification jstring="[para(857(a,2),328(a,1,2))].">
      <j1 rule="para" parents="857 328"/>
    </justification>
  </clause>

  <clause id="1364">
    <literal><![CDATA[
      R(T(x \ 1,x * y),x,y) = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,861,a)].">
      <j1 rule="hyper" parents="64 27 861"/>
    </justification>
  </clause>

  <clause id="1365">
    <literal><![CDATA[
      (x * (x * y)) \ (x * (x * z)) = L(y,x,x) \ L(z,x,x)
    ]]></literal>
    <justification jstring="[para(18(a,2),881(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1366">
    <literal><![CDATA[
      L(x,y,y) \ ((1 / y) * z) = (y * (y * x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(535(a,1),881(a,1,2))].">
      <j1 rule="para" parents="535 881"/>
    </justification>
  </clause>

  <clause id="1367">
    <literal><![CDATA[
      L(x,y,y) \ (((y * y) \ z) * u) = (y * (y * x)) \ (z * u)
    ]]></literal>
    <justification jstring="[para(484(a,1),881(a,1,2))].">
      <j1 rule="para" parents="484 881"/>
    </justification>
  </clause>

  <clause id="1368">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * T((x \ z) \ z,y) = u
    ]]></literal>
    <justification jstring="[para(79(a,1),912(a,1,1,1))].">
      <j1 rule="para" parents="79 912"/>
    </justification>
  </clause>

  <clause id="1369">
    <literal><![CDATA[
      T(x / (x / y),z) * (x / y) != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),915(a,1,1,1,1))].">
      <j1 rule="para" parents="12 915"/>
    </justification>
  </clause>

  <clause id="1370">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(791(a,1),915(a,1,1))].">
      <j1 rule="para" parents="791 915"/>
    </justification>
  </clause>

  <clause id="1371">
    <literal><![CDATA[
      R(x / (y \ 1),y \ 1,y \ 1) \ z = (y \ 1) * (y \ ((x * (y \ 1)) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,584,a(flip),b,948,a),flip(a)].">
      <j1 rule="hyper" parents="64 584 948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1372">
    <literal><![CDATA[
      (x * x) * (((y * x) \ z) * u) = (R(y / x,x,x) \ z) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,948,a(flip),b,127,a),flip(a)].">
      <j1 rule="hyper" parents="144 948 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1373">
    <literal><![CDATA[
      x \ (R(y / x,x,x) \ z) = (1 / x) \ ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,948,a(flip),b,538,a)].">
      <j1 rule="hyper" parents="139 948 538"/>
    </justification>
  </clause>

  <clause id="1374">
    <literal><![CDATA[
      ((x * y) \ z) \ ((y * y) \ u) = (R(x / y,y,y) \ z) \ u
    ]]></literal>
    <justification jstring="[para(948(a,1),487(a,1,1)),flip(a)].">
      <j1 rule="para" parents="948 487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1375">
    <literal><![CDATA[
      (x * T(y,(x / z) * z)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,x / z) * ((x / z) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,793,a(flip),b,955,a),flip(a)].">
      <j1 rule="hyper" parents="373 793 955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1376">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / T(x * z,a(x,y,y \ z)) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(142,a,957,a(flip),b,115,a)].">
      <j1 rule="hyper" parents="142 957 115"/>
    </justification>
  </clause>

  <clause id="1377">
    <literal><![CDATA[
      T(((x / y) * y) \ ((x / y) * z),y) = x \ ((x / y) * ((y \ z) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,636,a,b,971,a)].">
      <j1 rule="hyper" parents="64 636 971"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      (x / y) * ((y \ 1) * y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(145,a,747,a,b,971,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 747 971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,993,a)].">
      <j1 rule="hyper" parents="64 27 993"/>
    </justification>
  </clause>

  <clause id="1380">
    <literal><![CDATA[
      R(T(1 / x,y),x,x \ y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,80,a(flip),b,994,a),flip(a)].">
      <j1 rule="hyper" parents="139 80 994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1381">
    <literal><![CDATA[
      R(T(x / y,x),y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(35,a,166,a(flip),b,994,a),flip(a)].">
      <j1 rule="hyper" parents="35 166 994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1382">
    <literal><![CDATA[
      R(x,y,y \ z) != y \ z
    ]]></literal>
    <literal><![CDATA[
      T(z / y,z) = x
    ]]></literal>
    <justification jstring="[para(1381(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="1381 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1383">
    <literal><![CDATA[
      R(L(T(x,y),x,x),1 / x,(1 / x) \ y) = y \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(824(a,1),1380(a,1,1))].">
      <j1 rule="para" parents="824 1380"/>
    </justification>
  </clause>

  <clause id="1384">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(436(a,1),1010(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="436 1010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1385">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[para(630(a,1),1010(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="630 1010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1386">
    <literal><![CDATA[
      x * R(x \ y,x,x) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,811,a(flip),b,1038,a),flip(a)].">
      <j1 rule="hyper" parents="64 811 1038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1387">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,1142,a(flip),b,1139,a),flip(a)].">
      <j1 rule="hyper" parents="139 1142 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1388">
    <literal><![CDATA[
      L(L(((x \ 1) \ 1) \ y,z,u),x,x) = L((x \ 1) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1151,a(flip),b,1143,a)].">
      <j1 rule="hyper" parents="64 1151 1143"/>
    </justification>
  </clause>

  <clause id="1389">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,1143,a(flip),b,1139,a),flip(a)].">
      <j1 rule="hyper" parents="139 1143 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1390">
    <literal><![CDATA[
      L((x * (y \ 1)) \ (x * z),y,y) = L(y * z,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(102(a,1),1143(a,1,1))].">
      <j1 rule="para" parents="102 1143"/>
    </justification>
  </clause>

  <clause id="1391">
    <literal><![CDATA[
      (x \ 1) * L(x \ 1,y,z) = x \ L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(434(a,1),1149(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="434 1149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1392">
    <literal><![CDATA[
      L(((x / y) \ z) / y,y,x / y) = (y * (x \ z)) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),1208(a,2,1,2,1))].">
      <j1 rule="para" parents="12 1208"/>
    </justification>
  </clause>

  <clause id="1393">
    <literal><![CDATA[
      ((1 / x) * y) * (y \ x) = a(x,y,y \ x)
    ]]></literal>
    <justification jstring="[para(535(a,1),1281(a,1,1))].">
      <j1 rule="para" parents="535 1281"/>
    </justification>
  </clause>

  <clause id="1394">
    <literal><![CDATA[
      L(x \ (x / y),x,x) * y = a(x,x / y,y)
    ]]></literal>
    <justification jstring="[para(102(a,2),1288(a,1,1))].">
      <j1 rule="para" parents="102 1288"/>
    </justification>
  </clause>

  <clause id="1395">
    <literal><![CDATA[
      R(T(x / (x * y),(x * y) * y),x * y,y) = L(y \ 1,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,241,a,b,1326,a),flip(a)].">
      <j1 rule="hyper" parents="373 241 1326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1396">
    <literal><![CDATA[
      L(((x * y) * x) / (x * y),y,x) * y = y * x
    ]]></literal>
    <justification jstring="[hyper(144,a,1339,a,b,xx)].">
      <j1 rule="hyper" parents="144 1339"/>
    </justification>
  </clause>

  <clause id="1397">
    <literal><![CDATA[
      (((x * x) \ y) * x) * x = R(T(y,x * x),x,x)
    ]]></literal>
    <justification jstring="[para(484(a,1),1343(a,1,1))].">
      <j1 rule="para" parents="484 1343"/>
    </justification>
  </clause>

  <clause id="1398">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(144,a,1379,a(flip),b,110,a)].">
      <j1 rule="hyper" parents="144 1379 110"/>
    </justification>
  </clause>

  <clause id="1399">
    <literal><![CDATA[
      (x * y) \ (x * ((((x * y) * x) / (x * y)) * y)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,989,a,b,1396,a(flip))].">
      <j1 rule="hyper" parents="35 989 1396"/>
    </justification>
  </clause>

  <clause id="1400">
    <literal><![CDATA[
      x \ R(T(y,x * x),x,x) = T(((x * x) \ y) * x,x)
    ]]></literal>
    <justification jstring="[hyper(493,a,xx,b,1397,a),flip(a)].">
      <j1 rule="hyper" parents="493 1397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1401">
    <literal><![CDATA[
      R(T((x * x) * y,x * x),x,x) = (y * x) * x
    ]]></literal>
    <justification jstring="[para(9(a,1),1397(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 1397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1402">
    <literal><![CDATA[
      T(R((x * x) * y,x,x),x * x) = (y * x) * x
    ]]></literal>
    <justification jstring="[hyper(795,a,1401,a)].">
      <j1 rule="hyper" parents="795 1401"/>
    </justification>
  </clause>

  <clause id="1403">
    <literal><![CDATA[
      R(x * (y * y),y,y) = (x * y) * y
    ]]></literal>
    <justification jstring="[para(254(a,1),1401(a,1,1))].">
      <j1 rule="para" parents="254 1401"/>
    </justification>
  </clause>

  <clause id="1404">
    <literal><![CDATA[
      ((x / (y * y)) * y) * y = R(x,y,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),1403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1405">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y,y)
    ]]></literal>
    <justification jstring="[para(811(a,1),1404(a,1,1))].">
      <j1 rule="para" parents="811 1404"/>
    </justification>
  </clause>

  <clause id="1406">
    <literal><![CDATA[
      T(x * (1 / y),y) = y \ R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(493,a,xx,b,1405,a)].">
      <j1 rule="hyper" parents="493 1405"/>
    </justification>
  </clause>

  <clause id="1407">
    <literal><![CDATA[
      R(x / (1 / y),y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(390,a,1405,a),flip(a)].">
      <j1 rule="hyper" parents="390 1405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1408">
    <literal><![CDATA[
      R(x,y,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(154,a,1405,a)].">
      <j1 rule="hyper" parents="154 1405"/>
    </justification>
  </clause>

  <clause id="1409">
    <literal><![CDATA[
      (x * (1 / y)) \ R(x,y,y) = y
    ]]></literal>
    <justification jstring="[hyper(149,a,1405,a)].">
      <j1 rule="hyper" parents="149 1405"/>
    </justification>
  </clause>

  <clause id="1410">
    <literal><![CDATA[
      L(R(x,y,y),z,u) / y = L(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(142,a,29,a(flip),b,1405,a)].">
      <j1 rule="hyper" parents="142 29 1405"/>
    </justification>
  </clause>

  <clause id="1411">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) * (x * y) = R(1 / x,x,x) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,1405,a(flip),b,127,a),flip(a)].">
      <j1 rule="hyper" parents="144 1405 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1412">
    <literal><![CDATA[
      (x * ((y * y) * (1 / z))) * z = R(x * (y * y),z,z)
    ]]></literal>
    <justification jstring="[para(34(a,1),1405(a,1,1))].">
      <j1 rule="para" parents="34 1405"/>
    </justification>
  </clause>

  <clause id="1413">
    <literal><![CDATA[
      (x * (1 / y)) * (y * y) = R(x,y,y) / (1 / y)
    ]]></literal>
    <justification jstring="[para(1405(a,1),808(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1405 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      R(T(x / (1 / y),z),y,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(1407(a,1),27(a,2,1))].">
      <j1 rule="para" parents="1407 27"/>
    </justification>
  </clause>

  <clause id="1415">
    <literal><![CDATA[
      R(R(x / (1 / y),z,u),y,y) = R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(1407(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1407 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      ((x * y) * (y * y)) / y = (x / (1 / y)) * y
    ]]></literal>
    <justification jstring="[para(1407(a,1),350(a,1,1,1))].">
      <j1 rule="para" parents="1407 350"/>
    </justification>
  </clause>

  <clause id="1417">
    <literal><![CDATA[
      T(x,x \ 1) = R(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(38,a,1357,a,b,1408,a)].">
      <j1 rule="hyper" parents="38 1357 1408"/>
    </justification>
  </clause>

  <clause id="1418">
    <literal><![CDATA[
      R(x,x,x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(478,a,1417,a),flip(a)].">
      <j1 rule="hyper" parents="478 1417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1419">
    <literal><![CDATA[
      T(x,x \ 1) \ y = R(x,x,x) \ y
    ]]></literal>
    <justification jstring="[hyper(62,a,1417,a)].">
      <j1 rule="hyper" parents="62 1417"/>
    </justification>
  </clause>

  <clause id="1420">
    <literal><![CDATA[
      1 / R(x,x,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(225,a,1417,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 1417 116"/>
    </justification>
  </clause>

  <clause id="1421">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = R(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[para(1417(a,2),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1417 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1422">
    <literal><![CDATA[
      R(R(x,x,x),y,z) * x = x * R(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1417(a,1),326(a,1,1,1))].">
      <j1 rule="para" parents="1417 326"/>
    </justification>
  </clause>

  <clause id="1423">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = R(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[para(1418(a,1),27(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1418 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1424">
    <literal><![CDATA[
      R(R(x,y,z),x,x) = R((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1418(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1418 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1425">
    <literal><![CDATA[
      R((x * x) \ y,(x * x) \ y,(x * x) \ y) = (y \ (x * x)) \ 1
    ]]></literal>
    <justification jstring="[para(550(a,1),1418(a,2,1))].">
      <j1 rule="para" parents="550 1418"/>
    </justification>
  </clause>

  <clause id="1426">
    <literal><![CDATA[
      (x * y) \ R(x,y \ 1,y \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),1409(a,1,1,2))].">
      <j1 rule="para" parents="79 1409"/>
    </justification>
  </clause>

  <clause id="1427">
    <literal><![CDATA[
      1 / L(x,y * (1 / x),R(y,x,x)) = (1 / R(y,x,x)) * (y * (1 / x))
    ]]></literal>
    <justification jstring="[para(1409(a,1),919(a,1,2,1))].">
      <j1 rule="para" parents="1409 919"/>
    </justification>
  </clause>

  <clause id="1428">
    <literal><![CDATA[
      R(x,y \ 1,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,482,a,b,1426,a),flip(a)].">
      <j1 rule="hyper" parents="39 482 1426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1429">
    <literal><![CDATA[
      R(x,y \ 1,y \ 1) = x * a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,983,a,b,1428,a),flip(a)].">
      <j1 rule="hyper" parents="373 983 1428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1430">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1418(a,1),1410(a,1,1,1))].">
      <j1 rule="para" parents="1418 1410"/>
    </justification>
  </clause>

  <clause id="1431">
    <literal><![CDATA[
      R(x / (1 / y),z,u) * (1 / y) = R(x * y,z,u) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,1415,a(flip),b,1405,a),flip(a)].">
      <j1 rule="hyper" parents="142 1415 1405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1432">
    <literal><![CDATA[
      a(x,y,z) != 1
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[para(68(a,1),160(a,1)),flip(a),flip(b)].">
      <j1 rule="para" parents="68 160"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1433">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * v5 != v6
    ]]></literal>
    <literal><![CDATA[
      L(L(x,u,w),y,z) \ v6 = v5
    ]]></literal>
    <justification jstring="[para(164(a,1),149(a,1))].">
      <j1 rule="para" parents="164 149"/>
    </justification>
  </clause>

  <clause id="1434">
    <literal><![CDATA[
      (x * x) * (T(y,x * x) * z) = y * ((x * x) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,34,a(flip),b,268,a),flip(a)].">
      <j1 rule="hyper" parents="373 34 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1435">
    <literal><![CDATA[
      L(L(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(L(x,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(507(a,1),228(a,1)),flip(b)].">
      <j1 rule="para" parents="507 228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1436">
    <literal><![CDATA[
      L(x,y,T(z * z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(606,a,777,a)].">
      <j1 rule="hyper" parents="606 777"/>
    </justification>
  </clause>

  <clause id="1437">
    <literal><![CDATA[
      (T(x * x,y) \ z) \ u = z \ (T(x * x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(743,a,1436,a),flip(a)].">
      <j1 rule="hyper" parents="743 1436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1438">
    <literal><![CDATA[
      L(x,y,T(z * z,u)) = L(x,w,v5 * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,594,a,b,1436,a),flip(a)].">
      <j1 rule="hyper" parents="373 594 1436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1439">
    <literal><![CDATA[
      (T(x * x,y) * z) / u = T(x * x,y) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(225,a,1436,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="225 1436 104"/>
    </justification>
  </clause>

  <clause id="1440">
    <literal><![CDATA[
      L(x,y,(1 / z) \ z) = x
    ]]></literal>
    <justification jstring="[para(562(a,1),1436(a,1,3))].">
      <j1 rule="para" parents="562 1436"/>
    </justification>
  </clause>

  <clause id="1441">
    <literal><![CDATA[
      (((1 / x) \ x) * y) \ z = y \ (((1 / x) \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(710,a,1440,a),flip(a)].">
      <j1 rule="hyper" parents="710 1440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1442">
    <literal><![CDATA[
      ((1 / x) \ x) * (1 / y) = ((1 / x) \ x) / y
    ]]></literal>
    <justification jstring="[hyper(225,a,1440,a(flip),b,246,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 1440 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1443">
    <literal><![CDATA[
      (((1 / x) \ x) * y) * z = ((1 / x) \ x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1440,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 1440 18"/>
    </justification>
  </clause>

  <clause id="1444">
    <literal><![CDATA[
      L(x,y,z \ (z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),1440(a,1,3,1))].">
      <j1 rule="para" parents="79 1440"/>
    </justification>
  </clause>

  <clause id="1445">
    <literal><![CDATA[
      L(x,y,(z * z) \ 1) = x
    ]]></literal>
    <justification jstring="[para(820(a,1),1440(a,1,3))].">
      <j1 rule="para" parents="820 1440"/>
    </justification>
  </clause>

  <clause id="1446">
    <literal><![CDATA[
      (x * (y \ (y \ 1))) \ ((y \ (y \ 1)) * z) = T(x,y \ (y \ 1)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,638,a(flip),b,1444,a)].">
      <j1 rule="hyper" parents="64 638 1444"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      ((x \ (x \ 1)) * y) * z = (x \ (x \ 1)) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1444,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 1444 18"/>
    </justification>
  </clause>

  <clause id="1448">
    <literal><![CDATA[
      x * ((x \ 1) \ (1 / y)) = ((1 / x) \ x) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,1175,a(flip),b,1442,a)].">
      <j1 rule="hyper" parents="64 1175 1442"/>
    </justification>
  </clause>

  <clause id="1449">
    <literal><![CDATA[
      R(x,x \ y,z \ T(T(u,w),v5)) \ (y * (z \ T(T(u,w),v5))) = (x \ y) * (z \ T(T(u,v5),w))
    ]]></literal>
    <justification jstring="[hyper(373,a,649,a,b,828,a)].">
      <j1 rule="hyper" parents="373 649 828"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      (L(R(x,y,z),u,w) * (x * v5)) \ ((x * L(R(x,y,z),u,w)) * v5) = a(L(R(x,y,z),u,w),x,v5)
    ]]></literal>
    <justification jstring="[para(840(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="840 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1451">
    <literal><![CDATA[
      (x * L(R(x,y,z),u,w)) \ (L(R(x,y,z),u,w) * (x * v5)) = L(v5,x,L(R(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(840(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="840 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1452">
    <literal><![CDATA[
      T(x,y * y) \ ((y * y) \ z) = (y * y) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,486,a(flip),b,877,a),flip(a)].">
      <j1 rule="hyper" parents="373 486 877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1454">
    <literal><![CDATA[
      T(x,y * y) * ((1 / y) * z) = ((y * y) \ x) * (y * z)
    ]]></literal>
    <justification jstring="[para(310(a,1),930(a,1,2)),flip(a)].">
      <j1 rule="para" parents="310 930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      (x * x) * ((T(y,x * x) * z) * u) = (y * ((x * x) * z)) * u
    ]]></literal>
    <justification jstring="[para(930(a,1),805(a,1,2,1))].">
      <j1 rule="para" parents="930 805"/>
    </justification>
  </clause>

  <clause id="1456">
    <literal><![CDATA[
      (x * x) \ (((1 / x) * y) \ z) = T(x * y,x * x) \ z
    ]]></literal>
    <justification jstring="[para(535(a,1),931(a,1,2,1))].">
      <j1 rule="para" parents="535 931"/>
    </justification>
  </clause>

  <clause id="1457">
    <literal><![CDATA[
      (x * x) \ (y \ (x * x)) = T(y,x * x) \ 1
    ]]></literal>
    <justification jstring="[para(550(a,1),931(a,1,2))].">
      <j1 rule="para" parents="550 931"/>
    </justification>
  </clause>

  <clause id="1458">
    <literal><![CDATA[
      (x * x) \ (y \ ((x * x) * z)) = T(y,x * x) \ z
    ]]></literal>
    <justification jstring="[para(804(a,1),931(a,1,2))].">
      <j1 rule="para" parents="804 931"/>
    </justification>
  </clause>

  <clause id="1459">
    <literal><![CDATA[
      (x * x) * ((T(y,x * x) / z) * u) = ((y * (x * x)) / z) * u
    ]]></literal>
    <justification jstring="[para(934(a,1),126(a,1,2,1))].">
      <j1 rule="para" parents="934 126"/>
    </justification>
  </clause>

  <clause id="1460">
    <literal><![CDATA[
      (x * x) * (T(y,x * x) \ z) = y \ ((x * x) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,940,a(flip),b,486,a(flip))].">
      <j1 rule="hyper" parents="145 940 486"/>
    </justification>
  </clause>

  <clause id="1461">
    <literal><![CDATA[
      T((x * x) \ y,x * x) \ z = T(y,x * x) \ ((x * x) * z)
    ]]></literal>
    <justification jstring="[para(798(a,1),940(a,1,1)),flip(a)].">
      <j1 rule="para" parents="798 940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      ((x * y) * z) \ ((x * x) * u) = (((1 / x) * y) * z) \ u
    ]]></literal>
    <justification jstring="[para(535(a,1),942(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="535 942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1463">
    <literal><![CDATA[
      (x * ((y * y) * z)) \ ((y * y) * u) = (T(x,y * y) * z) \ u
    ]]></literal>
    <justification jstring="[para(930(a,1),942(a,1,1)),flip(a)].">
      <j1 rule="para" parents="930 942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1464">
    <literal><![CDATA[
      (x / (1 / y)) * ((z * z) \ u) = (x / ((z * z) / y)) * u
    ]]></literal>
    <justification jstring="[para(497(a,1),953(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="497 953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1465">
    <literal><![CDATA[
      (x / (y \ 1)) * ((y * y) \ z) = (x / R(y,y,y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(297(a,1),953(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="297 953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1466">
    <literal><![CDATA[
      (x * ((y * y) * (z * u))) \ ((x * ((y * y) * z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,(y * y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(33(a,1),959(a,1,1,2))].">
      <j1 rule="para" parents="33 959"/>
    </justification>
  </clause>

  <clause id="1468">
    <literal><![CDATA[
      T((1 / x) * (y * x),z) = (1 / x) * (T(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,522,a(flip),b,1020,a),flip(a)].">
      <j1 rule="hyper" parents="145 522 1020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      x * T(x \ ((1 / x) \ y),z) = (1 / x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1020(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1470">
    <literal><![CDATA[
      (x * (y \ (1 / y))) \ z = ((1 / y) \ y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1169,a(flip),b,1100,a),flip(a)].">
      <j1 rule="hyper" parents="373 1169 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1471">
    <literal><![CDATA[
      (x * (y \ (1 / y))) \ z = y * ((y \ 1) \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,1097,a(flip),b,1100,a),flip(a)].">
      <j1 rule="hyper" parents="373 1097 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1472">
    <literal><![CDATA[
      (x * (y \ (1 / y))) * z = x * ((y \ 1) * (y \ z))
    ]]></literal>
    <justification jstring="[para(1098(a,1),1105(a,2,2))].">
      <j1 rule="para" parents="1098 1105"/>
    </justification>
  </clause>

  <clause id="1473">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) * z = (x \ (1 / x)) * (y * z)
    ]]></literal>
    <justification jstring="[para(1098(a,1),1108(a,1,1))].">
      <j1 rule="para" parents="1098 1108"/>
    </justification>
  </clause>

  <clause id="1474">
    <literal><![CDATA[
      (x * (((1 / y) \ y) * z)) / z = x / (y \ (1 / y))
    ]]></literal>
    <justification jstring="[para(1169(a,1),1111(a,1,1,2))].">
      <j1 rule="para" parents="1169 1111"/>
    </justification>
  </clause>

  <clause id="1475">
    <literal><![CDATA[
      x \ (((x \ 1) \ x) * y) = T(x \ 1,x) \ y
    ]]></literal>
    <justification jstring="[para(1130(a,1),1116(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1130 1116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1476">
    <literal><![CDATA[
      x * (T(x \ 1,x) \ 1) = (x \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,1475,a(flip),b,177,a(flip))].">
      <j1 rule="hyper" parents="145 1475 177"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      T(x \ 1,x) \ T(y,x) = x \ ((x \ 1) \ (y * x))
    ]]></literal>
    <justification jstring="[para(1129(a,1),1475(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1129 1475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1478">
    <literal><![CDATA[
      ((x \ 1) \ x) * ((x \ y) / z) = ((x \ 1) \ y) / z
    ]]></literal>
    <justification jstring="[para(1131(a,1),1117(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1131 1117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1479">
    <literal><![CDATA[
      (x * (T(x \ 1,x) \ 1)) * (y / z) = (((x \ 1) \ x) * y) / z
    ]]></literal>
    <justification jstring="[para(1476(a,2),1117(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1476 1117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1480">
    <literal><![CDATA[
      ((x \ 1) \ x) * ((x \ y) * z) = ((x \ 1) \ y) * z
    ]]></literal>
    <justification jstring="[para(1131(a,1),1119(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1131 1119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1481">
    <literal><![CDATA[
      T(x * y,x \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1181(a,1),44(a,1))].">
      <j1 rule="para" parents="1181 44"/>
    </justification>
  </clause>

  <clause id="1482">
    <literal><![CDATA[
      x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1005,a,1182,a),flip(a)].">
      <j1 rule="hyper" parents="1005 1182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1483">
    <literal><![CDATA[
      (x \ 1) \ (x \ T(x * y,z)) = T((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,1182,a)].">
      <j1 rule="hyper" parents="149 1182"/>
    </justification>
  </clause>

  <clause id="1484">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),1182(a,2,2,1))].">
      <j1 rule="para" parents="8 1182"/>
    </justification>
  </clause>

  <clause id="1485">
    <literal><![CDATA[
      x \ T(x * ((x \ 1) * y),z) = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1182(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1486">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1182(a,2,2,1))].">
      <j1 rule="para" parents="10 1182"/>
    </justification>
  </clause>

  <clause id="1487">
    <literal><![CDATA[
      T(x,y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,527,a(flip),b,1484,a)].">
      <j1 rule="hyper" parents="64 527 1484"/>
    </justification>
  </clause>

  <clause id="1490">
    <literal><![CDATA[
      x * T((x \ 1) \ 1,y) = (1 / x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),1183(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8 1183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1491">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = (((x / y) \ 1) \ y) * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(12(a,1),1184(a,1,2,1))].">
      <j1 rule="para" parents="12 1184"/>
    </justification>
  </clause>

  <clause id="1492">
    <literal><![CDATA[
      (x * ((y * z) / y)) / x = (y * ((x * z) / x)) / y
    ]]></literal>
    <justification jstring="[para(9(a,1),1236(a,1,1,2,1,2))].">
      <j1 rule="para" parents="9 1236"/>
    </justification>
  </clause>

  <clause id="1493">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x * (z \ y)) / x) = u
    ]]></literal>
    <justification jstring="[para(1236(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1236 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1494">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,494,a,b,1237,a)].">
      <j1 rule="hyper" parents="64 494 1237"/>
    </justification>
  </clause>

  <clause id="1495">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),1237(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 1237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1496">
    <literal><![CDATA[
      ((x * R(y / z,z,u)) / x) * (z * u) = (z * u) * ((x * ((z * u) \ (y * u))) / x)
    ]]></literal>
    <justification jstring="[para(112(a,2),1237(a,1,1,1,2))].">
      <j1 rule="para" parents="112 1237"/>
    </justification>
  </clause>

  <clause id="1497">
    <literal><![CDATA[
      T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y)
    ]]></literal>
    <justification jstring="[para(112(a,1),1263(a,1,1,1))].">
      <j1 rule="para" parents="112 1263"/>
    </justification>
  </clause>

  <clause id="1498">
    <literal><![CDATA[
      R(T(x \ y,z),x,x \ z) = T(z \ (y * (x \ z)),x)
    ]]></literal>
    <justification jstring="[para(993(a,1),1263(a,1,1)),flip(a)].">
      <j1 rule="para" parents="993 1263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1499">
    <literal><![CDATA[
      R(x / (y * x),y,y \ 1) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1305(a,2,1))].">
      <j1 rule="para" parents="7 1305"/>
    </justification>
  </clause>

  <clause id="1500">
    <literal><![CDATA[
      R(x / y,y / x,(y / x) \ 1) = R((y / x) \ 1,y / x,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),1499(a,1,1,2))].">
      <j1 rule="para" parents="12 1499"/>
    </justification>
  </clause>

  <clause id="1501">
    <literal><![CDATA[
      T(T(x,x * y) * y,T(x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(269,a,1321,a,b,xx)].">
      <j1 rule="hyper" parents="269 1321"/>
    </justification>
  </clause>

  <clause id="1502">
    <literal><![CDATA[
      T(T(x / y,(x / y) * y) * y,T(x / y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,12,a(flip),b,1501,a),flip(a)].">
      <j1 rule="hyper" parents="373 12 1501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1503">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,525,a(flip),b,1330,a),flip(a)].">
      <j1 rule="hyper" parents="373 525 1330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1504">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (x \ 1) = T(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(144,a,525,a(flip),b,1330,a)].">
      <j1 rule="hyper" parents="144 525 1330"/>
    </justification>
  </clause>

  <clause id="1505">
    <literal><![CDATA[
      T(((1 / x) * y) * x,z) / x = (1 / x) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(915,a,1332,a),flip(a)].">
      <j1 rule="hyper" parents="915 1332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1506">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(912,a,1332,a)].">
      <j1 rule="hyper" parents="912 1332"/>
    </justification>
  </clause>

  <clause id="1507">
    <literal><![CDATA[
      T(((1 / x) * y) * x,z) = ((1 / x) * T(y,z)) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,526,a(flip),b,1332,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 526 1332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1508">
    <literal><![CDATA[
      T(1 / (1 / x),y) * (1 / x) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1332(a,2,1,1))].">
      <j1 rule="para" parents="7 1332"/>
    </justification>
  </clause>

  <clause id="1509">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(912,a,1508,a)].">
      <j1 rule="hyper" parents="912 1508"/>
    </justification>
  </clause>

  <clause id="1510">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1508(a,1),912(a,1))].">
      <j1 rule="para" parents="1508 912"/>
    </justification>
  </clause>

  <clause id="1511">
    <literal><![CDATA[
      (1 / x) * T(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(82(a,1),1509(a,1,2,1))].">
      <j1 rule="para" parents="82 1509"/>
    </justification>
  </clause>

  <clause id="1512">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(493,a,xx,b,1511,a),flip(a)].">
      <j1 rule="hyper" parents="493 1511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1513">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(400,a,1511,a),flip(a)].">
      <j1 rule="hyper" parents="400 1511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1514">
    <literal><![CDATA[
      (T(x,y) / x) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(154,a,1511,a)].">
      <j1 rule="hyper" parents="154 1511"/>
    </justification>
  </clause>

  <clause id="1515">
    <literal><![CDATA[
      (1 / x) \ (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(149,a,1511,a)].">
      <j1 rule="hyper" parents="149 1511"/>
    </justification>
  </clause>

  <clause id="1516">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1511(a,1),400(a,1))].">
      <j1 rule="para" parents="1511 400"/>
    </justification>
  </clause>

  <clause id="1517">
    <literal><![CDATA[
      T((T(x,y) * (1 / x)) / T(x,y),T(x,y) / x) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1511(a,1),770(a,1,2))].">
      <j1 rule="para" parents="1511 770"/>
    </justification>
  </clause>

  <clause id="1518">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(294(a,2),1378(a,1,2))].">
      <j1 rule="para" parents="294 1378"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      (x \ y) \ K(y \ x,y) = T((x \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,95,a(flip),b,1384,a)].">
      <j1 rule="hyper" parents="139 95 1384"/>
    </justification>
  </clause>

  <clause id="1520">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),1519(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 1519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1521">
    <literal><![CDATA[
      x * ((((x * y) * x) / (x * y)) * y) = (x * y) * x
    ]]></literal>
    <justification jstring="[hyper(157,a,1399,a),flip(a)].">
      <j1 rule="hyper" parents="157 1399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1522">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) != u
    ]]></literal>
    <literal><![CDATA[
      x \ L((x \ 1) \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(1430(a,1),467(a,1,1))].">
      <j1 rule="para" parents="1430 467"/>
    </justification>
  </clause>

  <clause id="1523">
    <literal><![CDATA[
      (x * x) * ((T(y,x * x) * z) / u) = (y * ((x * x) * z)) / u
    ]]></literal>
    <justification jstring="[para(1434(a,1),807(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1434 807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1524">
    <literal><![CDATA[
      (((1 / x) \ x) * y) \ z = y \ ((x \ (1 / x)) * z)
    ]]></literal>
    <justification jstring="[para(1133(a,1),1441(a,2,2))].">
      <j1 rule="para" parents="1133 1441"/>
    </justification>
  </clause>

  <clause id="1525">
    <literal><![CDATA[
      ((1 / x) \ x) \ ((y * ((1 / x) \ x)) * z) = T(y,(1 / x) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,252,a(flip),b,1443,a(flip))].">
      <j1 rule="hyper" parents="139 252 1443"/>
    </justification>
  </clause>

  <clause id="1526">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) * z = ((1 / x) \ x) * (y * z)
    ]]></literal>
    <justification jstring="[para(1175(a,1),1443(a,1,1))].">
      <j1 rule="para" parents="1175 1443"/>
    </justification>
  </clause>

  <clause id="1527">
    <literal><![CDATA[
      T(x,y * y) \ (1 / y) = (y * y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(309(a,1),1452(a,1,2))].">
      <j1 rule="para" parents="309 1452"/>
    </justification>
  </clause>

  <clause id="1528">
    <literal><![CDATA[
      T(x,y * y) \ ((1 / y) * z) = (y * y) \ (x \ (y * z))
    ]]></literal>
    <justification jstring="[para(535(a,1),1452(a,1,2))].">
      <j1 rule="para" parents="535 1452"/>
    </justification>
  </clause>

  <clause id="1529">
    <literal><![CDATA[
      (x * x) \ ((y \ ((x * x) * z)) / u) = (T(y,x * x) \ z) / u
    ]]></literal>
    <justification jstring="[hyper(142,a,1458,a(flip),b,801,a),flip(a)].">
      <j1 rule="hyper" parents="142 1458 801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1530">
    <literal><![CDATA[
      (x * x) \ R(T(x,y),x,x \ y) = T(y,x * x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(996(a,1),1458(a,1,2))].">
      <j1 rule="para" parents="996 1458"/>
    </justification>
  </clause>

  <clause id="1531">
    <literal><![CDATA[
      (x * x) * (T(x * y,x * x) \ y) = R(T(x,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,796,a(flip),b,1460,a),flip(a)].">
      <j1 rule="hyper" parents="373 796 1460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1532">
    <literal><![CDATA[
      T(x \ ((1 / x) \ y),z) = x \ ((1 / x) \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(149,a,1469,a),flip(a)].">
      <j1 rule="hyper" parents="149 1469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1533">
    <literal><![CDATA[
      x / ((1 / y) \ y) = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(225,a,191,a(flip),b,1470,a)].">
      <j1 rule="hyper" parents="225 191 1470"/>
    </justification>
  </clause>

  <clause id="1534">
    <literal><![CDATA[
      x / (y \ (1 / y)) = x * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[hyper(389,a,1533,a),flip(a)].">
      <j1 rule="hyper" parents="389 1533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1535">
    <literal><![CDATA[
      x / T(y * y,y) = x * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,563,a,b,1533,a)].">
      <j1 rule="hyper" parents="64 563 1533"/>
    </justification>
  </clause>

  <clause id="1536">
    <literal><![CDATA[
      x / ((y \ (1 / y)) * z) = (x / z) * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1110,a(flip),b,1534,a)].">
      <j1 rule="hyper" parents="64 1110 1534"/>
    </justification>
  </clause>

  <clause id="1537">
    <literal><![CDATA[
      (x * (y \ (1 / y))) * (y * z) = x * ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1472(a,2,2,2))].">
      <j1 rule="para" parents="9 1472"/>
    </justification>
  </clause>

  <clause id="1538">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) * z = (x \ 1) * (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,1098,a(flip),b,1473,a),flip(a)].">
      <j1 rule="hyper" parents="373 1098 1473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1539">
    <literal><![CDATA[
      (x \ 1) * (x \ (1 / y)) = (x \ (1 / x)) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,81,a(flip),b,1473,a),flip(a)].">
      <j1 rule="hyper" parents="142 81 1473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1540">
    <literal><![CDATA[
      (x \ 1) \ (((x \ 1) * (x \ y)) * z) = x \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,1473,a,b,1098,a(flip))].">
      <j1 rule="hyper" parents="139 1473 1098"/>
    </justification>
  </clause>

  <clause id="1541">
    <literal><![CDATA[
      (x \ (1 / x)) * ((x * y) * z) = ((x \ 1) * y) * z
    ]]></literal>
    <justification jstring="[para(9(a,1),1473(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1542">
    <literal><![CDATA[
      (x * (((1 / y) \ y) * z)) / z = x * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1534,a(flip),b,1474,a),flip(a)].">
      <j1 rule="hyper" parents="373 1534 1474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1543">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) * z = x * (((1 / y) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,1534,a(flip),b,1474,a)].">
      <j1 rule="hyper" parents="144 1534 1474"/>
    </justification>
  </clause>

  <clause id="1544">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (((x \ 1) \ x) * z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(759,a,1480,a)].">
      <j1 rule="hyper" parents="759 1480"/>
    </justification>
  </clause>

  <clause id="1545">
    <literal><![CDATA[
      ((x \ 1) \ x) * ((x \ (x \ 1)) * y) = y
    ]]></literal>
    <justification jstring="[hyper(373,a,190,a(flip),b,1480,a),flip(a)].">
      <j1 rule="hyper" parents="373 190 1480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      ((x \ 1) \ x) \ y = (x \ (x \ 1)) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,190,a(flip),b,1480,a)].">
      <j1 rule="hyper" parents="139 190 1480"/>
    </justification>
  </clause>

  <clause id="1547">
    <literal><![CDATA[
      (x \ 1) * (((x \ 1) \ y) * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1480,a(flip),b,1115,a)].">
      <j1 rule="hyper" parents="145 1480 1115"/>
    </justification>
  </clause>

  <clause id="1548">
    <literal><![CDATA[
      (((x / y) \ 1) \ (x / y)) * (y * z) = (((x / y) \ 1) \ x) * z
    ]]></literal>
    <justification jstring="[para(82(a,1),1480(a,1,2,1))].">
      <j1 rule="para" parents="82 1480"/>
    </justification>
  </clause>

  <clause id="1549">
    <literal><![CDATA[
      (x \ (x \ 1)) \ y = ((x \ 1) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(397,a,1545,a),flip(a)].">
      <j1 rule="hyper" parents="397 1545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1550">
    <literal><![CDATA[
      (x \ (x \ 1)) * (((x \ 1) \ y) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(35,a,1480,a,b,1545,a),flip(a)].">
      <j1 rule="hyper" parents="35 1480 1545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1551">
    <literal><![CDATA[
      (x \ (x \ 1)) * ((x \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,1131,a,b,1545,a),flip(a)].">
      <j1 rule="hyper" parents="35 1131 1545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1552">
    <literal><![CDATA[
      x * ((x \ (x \ 1)) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,1545,a(flip),b,1115,a),flip(a)].">
      <j1 rule="hyper" parents="145 1545 1115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1553">
    <literal><![CDATA[
      x * ((((y \ 1) \ y) * x) \ z) = (y \ (y \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,1118,a,b,1546,a)].">
      <j1 rule="hyper" parents="64 1118 1546"/>
    </justification>
  </clause>

  <clause id="1554">
    <literal><![CDATA[
      (x * ((y \ 1) \ y)) \ z = (y \ (y \ 1)) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1113,a,b,1546,a)].">
      <j1 rule="hyper" parents="64 1113 1546"/>
    </justification>
  </clause>

  <clause id="1555">
    <literal><![CDATA[
      (x \ (x \ 1)) * x = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1130,a(flip),b,1546,a),flip(a)].">
      <j1 rule="hyper" parents="64 1130 1546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1556">
    <literal><![CDATA[
      (((x \ 1) \ x) * y) \ z = y \ ((x \ (x \ 1)) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,1546,a(flip),b,1118,a),flip(a)].">
      <j1 rule="hyper" parents="139 1546 1118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1557">
    <literal><![CDATA[
      x \ ((x \ 1) * y) = (x \ (x \ 1)) * y
    ]]></literal>
    <justification jstring="[hyper(739,a,1551,a),flip(a)].">
      <j1 rule="hyper" parents="739 1551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1558">
    <literal><![CDATA[
      (x \ (x \ 1)) * T(x,x \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,364,a,b,1551,a)].">
      <j1 rule="hyper" parents="64 364 1551"/>
    </justification>
  </clause>

  <clause id="1559">
    <literal><![CDATA[
      (x \ (x \ 1)) * T((x \ 1) \ y,z) = x \ (x \ T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,1182,a(flip),b,1552,a),flip(a)].">
      <j1 rule="hyper" parents="139 1182 1552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1560">
    <literal><![CDATA[
      T(x,x \ (x \ 1)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(410,a,1558,a)].">
      <j1 rule="hyper" parents="410 1558"/>
    </justification>
  </clause>

  <clause id="1561">
    <literal><![CDATA[
      T(x,x \ (x \ 1)) = R(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1417,a(flip),b,1560,a),flip(a)].">
      <j1 rule="hyper" parents="373 1417 1560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1562">
    <literal><![CDATA[
      (1 / x) * T(x * (y * (x \ 1)),z) = L(T(y,z) * (x \ 1),x,x)
    ]]></literal>
    <justification jstring="[para(1482(a,1),569(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1482 569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1563">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(1483(a,1),290(a,1,2))].">
      <j1 rule="para" parents="1483 290"/>
    </justification>
  </clause>

  <clause id="1564">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ 1) = T((x \ y) / (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(142,a,1486,a(flip),b,525,a)].">
      <j1 rule="hyper" parents="142 1486 525"/>
    </justification>
  </clause>

  <clause id="1565">
    <literal><![CDATA[
      T(x * y,1 / y) / y != z
    ]]></literal>
    <literal><![CDATA[
      ((1 / y) \ x) * (1 / y) = z
    ]]></literal>
    <justification jstring="[para(1506(a,1),328(a,1))].">
      <j1 rule="para" parents="1506 328"/>
    </justification>
  </clause>

  <clause id="1566">
    <literal><![CDATA[
      T(((1 / x) * y) * x,x) = (1 / x) * T(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1262,a(flip),b,1507,a),flip(a)].">
      <j1 rule="hyper" parents="373 1262 1507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,1520,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="145 1520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1568">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,1519,a,b,1520,a(flip))].">
      <j1 rule="hyper" parents="39 1519 1520"/>
    </justification>
  </clause>

  <clause id="1569">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) \ K(y,x) = z
    ]]></literal>
    <justification jstring="[para(1520(a,2),1008(a,1))].">
      <j1 rule="para" parents="1520 1008"/>
    </justification>
  </clause>

  <clause id="1570">
    <literal><![CDATA[
      (((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = ((x * y) \ x) * T(((x * y) \ x) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1520(a,1),1513(a,1,1))].">
      <j1 rule="para" parents="1520 1513"/>
    </justification>
  </clause>

  <clause id="1571">
    <literal><![CDATA[
      K(x \ (x * y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(70(a,1),1568(a,1,1)),flip(a)].">
      <j1 rule="para" parents="70 1568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1572">
    <literal><![CDATA[
      K((x / y) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),1571(a,1,1,2))].">
      <j1 rule="para" parents="12 1571"/>
    </justification>
  </clause>

  <clause id="1573">
    <literal><![CDATA[
      (((x * y) * x) / (x * y)) * y = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(270,a,1521,a),flip(a)].">
      <j1 rule="hyper" parents="270 1521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1574">
    <literal><![CDATA[
      ((x * y) * x) / (x * y) = T(x * y,x) / y
    ]]></literal>
    <justification jstring="[hyper(154,a,1573,a),flip(a)].">
      <j1 rule="hyper" parents="154 1573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1575">
    <literal><![CDATA[
      T(T(x * y,x) / y,x * y) = x
    ]]></literal>
    <justification jstring="[para(1574(a,1),255(a,1,1))].">
      <j1 rule="para" parents="1574 255"/>
    </justification>
  </clause>

  <clause id="1576">
    <literal><![CDATA[
      T(T(x,x / y) / y,(x / y) * y) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),1575(a,1,1,1,1))].">
      <j1 rule="para" parents="12 1575"/>
    </justification>
  </clause>

  <clause id="1577">
    <literal><![CDATA[
      T(T(x,x / y) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(12(a,1),1576(a,1,2))].">
      <j1 rule="para" parents="12 1576"/>
    </justification>
  </clause>

  <clause id="1578">
    <literal><![CDATA[
      T(x,x / y) / y = (x * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(313,a,1577,a),flip(a)].">
      <j1 rule="hyper" parents="313 1577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1579">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y = T(x,x / y)
    ]]></literal>
    <justification jstring="[hyper(156,a,1578,a)].">
      <j1 rule="hyper" parents="156 1578"/>
    </justification>
  </clause>

  <clause id="1580">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,y / x)
    ]]></literal>
    <justification jstring="[hyper(38,a,1236,a,b,1578,a)].">
      <j1 rule="hyper" parents="38 1236 1578"/>
    </justification>
  </clause>

  <clause id="1581">
    <literal><![CDATA[
      x \ T(y,y / x) = (y * (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(139,a,1579,a(flip),b,1237,a(flip))].">
      <j1 rule="hyper" parents="139 1579 1237"/>
    </justification>
  </clause>

  <clause id="1582">
    <literal><![CDATA[
      (x / y) * ((x * y) / x) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[para(82(a,1),1580(a,1,2,1,2))].">
      <j1 rule="para" parents="82 1580"/>
    </justification>
  </clause>

  <clause id="1583">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(y,y / x) = u
    ]]></literal>
    <justification jstring="[para(1580(a,2),1036(a,1))].">
      <j1 rule="para" parents="1580 1036"/>
    </justification>
  </clause>

  <clause id="1584">
    <literal><![CDATA[
      (x * y) * L((x \ y) / y,y,x) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[para(1208(a,2),1580(a,1,2))].">
      <j1 rule="para" parents="1208 1580"/>
    </justification>
  </clause>

  <clause id="1585">
    <literal><![CDATA[
      T(x \ T(y,y / x),y) = x \ y
    ]]></literal>
    <justification jstring="[para(1581(a,2),255(a,1,1))].">
      <j1 rule="para" parents="1581 255"/>
    </justification>
  </clause>

  <clause id="1586">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[para(79(a,1),1585(a,1,1,2,2))].">
      <j1 rule="para" parents="79 1585"/>
    </justification>
  </clause>

  <clause id="1587">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(256(a,1),1582(a,1,2)),flip(a)].">
      <j1 rule="para" parents="256 1582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1588">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) \ z = y \ ((x \ (1 / x)) * z)
    ]]></literal>
    <justification jstring="[para(1175(a,1),1524(a,1,1))].">
      <j1 rule="para" parents="1175 1524"/>
    </justification>
  </clause>

  <clause id="1589">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) * z = x * ((x \ 1) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,1175,a(flip),b,1526,a),flip(a)].">
      <j1 rule="hyper" parents="373 1175 1526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1590">
    <literal><![CDATA[
      (x / y) * ((1 / y) \ y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(1092(a,1),1536(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1092 1536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1591">
    <literal><![CDATA[
      x / ((y \ 1) * (y \ z)) = (x / z) * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[para(1098(a,1),1536(a,1,2))].">
      <j1 rule="para" parents="1098 1536"/>
    </justification>
  </clause>

  <clause id="1592">
    <literal><![CDATA[
      (x * y) / (y \ 1) = x * ((1 / y) \ y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1590(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1593">
    <literal><![CDATA[
      T(x * ((1 / y) \ y),y \ 1) = (y \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1592(a,1),117(a,1,1))].">
      <j1 rule="para" parents="1592 117"/>
    </justification>
  </clause>

  <clause id="1594">
    <literal><![CDATA[
      (x / ((y \ 1) * z)) * (y \ (1 / y)) = x / (y * z)
    ]]></literal>
    <justification jstring="[hyper(142,a,12,a(flip),b,1537,a),flip(a)].">
      <j1 rule="hyper" parents="142 12 1537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1595">
    <literal><![CDATA[
      ((x * (y \ 1)) / y) * (y * z) = x * ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(1099(a,2),1537(a,1,1))].">
      <j1 rule="para" parents="1099 1537"/>
    </justification>
  </clause>

  <clause id="1596">
    <literal><![CDATA[
      (x \ 1) * (x \ ((x * y) * z)) = ((x \ 1) * y) * z
    ]]></literal>
    <justification jstring="[para(9(a,1),1538(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 1538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1597">
    <literal><![CDATA[
      (x \ 1) * (x \ ((y * x) * z)) = ((x \ 1) * T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(22(a,2),1538(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1598">
    <literal><![CDATA[
      (x \ 1) * (x \ (((1 / x) \ y) * z)) = (x \ y) * z
    ]]></literal>
    <justification jstring="[para(1165(a,1),1538(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1165 1538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1599">
    <literal><![CDATA[
      (x \ 1) * (x \ ((x / y) * z)) = ((x \ 1) / y) * z
    ]]></literal>
    <justification jstring="[para(1214(a,1),1538(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1214 1538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1600">
    <literal><![CDATA[
      (x \ 1) \ (((x \ 1) * y) * z) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1540(a,1,2,1,2))].">
      <j1 rule="para" parents="9 1540"/>
    </justification>
  </clause>

  <clause id="1601">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) * z) = x \ (((1 / x) \ y) * z)
    ]]></literal>
    <justification jstring="[para(1165(a,1),1540(a,1,2,1))].">
      <j1 rule="para" parents="1165 1540"/>
    </justification>
  </clause>

  <clause id="1602">
    <literal><![CDATA[
      T((x \ 1) * y,x \ (1 / x)) = (x * y) * (x \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(270,a,1541,a)].">
      <j1 rule="hyper" parents="270 1541"/>
    </justification>
  </clause>

  <clause id="1603">
    <literal><![CDATA[
      (1 / x) * ((x * y) * z) = x * (((x \ 1) * y) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1541,a(flip),b,1107,a),flip(a)].">
      <j1 rule="hyper" parents="145 1541 1107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1604">
    <literal><![CDATA[
      L(x,(1 / y) \ y,z) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,213,a,b,1542,a)].">
      <j1 rule="hyper" parents="37 213 1542"/>
    </justification>
  </clause>

  <clause id="1605">
    <literal><![CDATA[
      R(x,(1 / y) \ y,z) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,350,a(flip),b,1542,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 350 1542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1606">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) \ z = ((1 / y) \ y) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(710,a,1604,a),flip(a)].">
      <j1 rule="hyper" parents="710 1604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1607">
    <literal><![CDATA[
      L(x,y \ (y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),1604(a,1,2,1))].">
      <j1 rule="para" parents="79 1604"/>
    </justification>
  </clause>

  <clause id="1608">
    <literal><![CDATA[
      R(x,(y * y) \ 1,z) = x
    ]]></literal>
    <justification jstring="[para(820(a,1),1605(a,1,2))].">
      <j1 rule="para" parents="820 1605"/>
    </justification>
  </clause>

  <clause id="1609">
    <literal><![CDATA[
      (x * (y \ (y \ 1))) \ z = (y \ (y \ 1)) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(710,a,1607,a),flip(a)].">
      <j1 rule="hyper" parents="710 1607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1610">
    <literal><![CDATA[
      (x * (y \ (y \ 1))) * z = x * ((y \ (y \ 1)) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1607,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 1607 18"/>
    </justification>
  </clause>

  <clause id="1611">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) * z = x * (y * ((y \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(1175(a,1),1543(a,2,2))].">
      <j1 rule="para" parents="1175 1543"/>
    </justification>
  </clause>

  <clause id="1612">
    <literal><![CDATA[
      ((x \ 1) \ y) \ ((x \ 1) \ z) = (x \ y) \ (x \ z)
    ]]></literal>
    <justification jstring="[para(1131(a,1),1544(a,1,2))].">
      <j1 rule="para" parents="1131 1544"/>
    </justification>
  </clause>

  <clause id="1613">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (((x \ 1) \ z) / u) = (x \ y) \ ((x \ z) / u)
    ]]></literal>
    <justification jstring="[para(1478(a,1),1544(a,1,2))].">
      <j1 rule="para" parents="1478 1544"/>
    </justification>
  </clause>

  <clause id="1614">
    <literal><![CDATA[
      (x \ 1) \ (L(y,x \ z,x) * z) = ((x \ 1) \ z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,964,a(flip),b,1547,a)].">
      <j1 rule="hyper" parents="139 964 1547"/>
    </justification>
  </clause>

  <clause id="1615">
    <literal><![CDATA[
      (x \ y) * (((x \ 1) \ y) \ z) = (x \ (x \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(397,a,1550,a),flip(a)].">
      <j1 rule="hyper" parents="397 1550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1616">
    <literal><![CDATA[
      (x \ (x \ 1)) * ((((x \ 1) \ y) * z) * u) = ((x \ y) * z) * u
    ]]></literal>
    <justification jstring="[para(1550(a,1),1447(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1550 1447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1617">
    <literal><![CDATA[
      x / (y \ (y \ 1)) = x * ((y \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(225,a,191,a(flip),b,1554,a)].">
      <j1 rule="hyper" parents="225 191 1554"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      x / ((y \ 1) \ y) = x * (y \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(389,a,1617,a),flip(a)].">
      <j1 rule="hyper" parents="389 1617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1619">
    <literal><![CDATA[
      x / (((y \ 1) \ y) * z) = (x / z) * (y \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,1120,a(flip),b,1618,a)].">
      <j1 rule="hyper" parents="64 1120 1618"/>
    </justification>
  </clause>

  <clause id="1620">
    <literal><![CDATA[
      T(((1 / x) * (y * x)) * x,x) = T(((1 / x) * y) * x,x) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,1566,a,b,1505,a),flip(a)].">
      <j1 rule="hyper" parents="144 1566 1505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1621">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) \ z = y \ ((x \ 1) * (x \ z))
    ]]></literal>
    <justification jstring="[para(1098(a,1),1588(a,2,2))].">
      <j1 rule="para" parents="1098 1588"/>
    </justification>
  </clause>

  <clause id="1622">
    <literal><![CDATA[
      (x \ y) \ ((x \ (1 / x)) * z) = ((1 / x) \ y) \ z
    ]]></literal>
    <justification jstring="[para(1138(a,1),1588(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1138 1588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1623">
    <literal><![CDATA[
      (x / y) * ((1 / (y / z)) \ (y / z)) = x / (((y / z) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(82(a,1),1591(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 1591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1624">
    <literal><![CDATA[
      (x / ((y \ 1) * z)) * (y \ 1) = (x / (y * z)) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,1594,a(flip),b,1099,a),flip(a)].">
      <j1 rule="hyper" parents="144 1594 1099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1625">
    <literal><![CDATA[
      (x / (y * (z \ 1))) * (z \ (1 / z)) = x / (z * T(y,z \ 1))
    ]]></literal>
    <justification jstring="[para(115(a,1),1594(a,1,1,2))].">
      <j1 rule="para" parents="115 1594"/>
    </justification>
  </clause>

  <clause id="1626">
    <literal><![CDATA[
      x * ((x \ 1) \ ((y / ((x \ 1) * z)) \ u)) = (y / (x * z)) \ u
    ]]></literal>
    <justification jstring="[para(1594(a,1),1471(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1594 1471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1627">
    <literal><![CDATA[
      (x / (y \ 1)) * ((y \ 1) * z) = (x / y) * (y * z)
    ]]></literal>
    <justification jstring="[para(12(a,1),1595(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1628">
    <literal><![CDATA[
      ((x \ 1) * y) * ((x * y) \ z) = (x \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),1596(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 1596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1629">
    <literal><![CDATA[
      (x \ 1) * T(x * y,x) = ((x \ 1) * y) * x
    ]]></literal>
    <justification jstring="[para(22(a,2),1596(a,1,2))].">
      <j1 rule="para" parents="22 1596"/>
    </justification>
  </clause>

  <clause id="1630">
    <literal><![CDATA[
      ((x \ 1) * y) * L(z,y,x) = (x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[para(344(a,1),1596(a,1,2)),flip(a)].">
      <j1 rule="para" parents="344 1596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1631">
    <literal><![CDATA[
      L(x,y,z \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(606,a,1630,a)].">
      <j1 rule="hyper" parents="606 1630"/>
    </justification>
  </clause>

  <clause id="1632">
    <literal><![CDATA[
      L(x \ y,x,z) = ((z \ 1) * x) \ ((z \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,1630,a),flip(a)].">
      <j1 rule="hyper" parents="139 168 1630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1633">
    <literal><![CDATA[
      L(x \ ((y \ 1) \ z),x,y) = ((y \ 1) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,75,a(flip),b,1630,a),flip(a)].">
      <j1 rule="hyper" parents="139 75 1630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1634">
    <literal><![CDATA[
      ((x \ 1) * (y * z)) / (y * L(z,y,x)) = R(x \ 1,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(142,a,1630,a(flip),b,111,a)].">
      <j1 rule="hyper" parents="142 1630 111"/>
    </justification>
  </clause>

  <clause id="1635">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,559,a,b,1631,a)].">
      <j1 rule="hyper" parents="373 559 1631"/>
    </justification>
  </clause>

  <clause id="1636">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1631,a(flip),b,1631,a),flip(a)].">
      <j1 rule="hyper" parents="373 1631 1631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1637">
    <literal><![CDATA[
      L((x \ 1) \ y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(373,a,1137,a(flip),b,1631,a),flip(a)].">
      <j1 rule="hyper" parents="373 1137 1631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1638">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,569,a(flip),b,1631,a),flip(a)].">
      <j1 rule="hyper" parents="373 569 1631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1639">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,567,a(flip),b,1631,a),flip(a)].">
      <j1 rule="hyper" parents="373 567 1631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1640">
    <literal><![CDATA[
      x \ L(y,x,x \ 1) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,1631,a,b,1139,a)].">
      <j1 rule="hyper" parents="139 1631 1139"/>
    </justification>
  </clause>

  <clause id="1641">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(139,a,1631,a,b,559,a)].">
      <j1 rule="hyper" parents="139 1631 559"/>
    </justification>
  </clause>

  <clause id="1642">
    <literal><![CDATA[
      L(((x \ 1) \ 1) \ y,x,x \ 1) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(1174,a,1631,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1174 1631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1643">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),1631(a,1,3)),flip(a)].">
      <j1 rule="para" parents="82 1631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1644">
    <literal><![CDATA[
      L(x,y,(z * z) \ u) = L(x,y,u \ (z * z))
    ]]></literal>
    <justification jstring="[para(550(a,1),1631(a,1,3)),flip(a)].">
      <j1 rule="para" parents="550 1631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1646">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1631(a,2),792(a,2,1))].">
      <j1 rule="para" parents="1631 792"/>
    </justification>
  </clause>

  <clause id="1647">
    <literal><![CDATA[
      x * L(y \ z,y,u \ 1) = x * ((u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[para(1631(a,2),632(a,1,2))].">
      <j1 rule="para" parents="1631 632"/>
    </justification>
  </clause>

  <clause id="1648">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,1631,a,b,1643,a),flip(a)].">
      <j1 rule="hyper" parents="373 1631 1643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1649">
    <literal><![CDATA[
      L(x,1 / y,y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1158,a(flip),b,1643,a),flip(a)].">
      <j1 rule="hyper" parents="64 1158 1643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1650">
    <literal><![CDATA[
      L(x \ ((1 / y) \ z),x,y) = ((1 / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,346,a(flip),b,1643,a),flip(a)].">
      <j1 rule="hyper" parents="64 346 1643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1651">
    <literal><![CDATA[
      ((1 / x) * y) * L(z,y,x) = (1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1643,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 1643 18"/>
    </justification>
  </clause>

  <clause id="1652">
    <literal><![CDATA[
      L(x,1 / x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(141,a,570,a(flip),b,1643,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="141 570 1643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      L(x,1 / y,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1145,a,b,1649,a),flip(a)].">
      <j1 rule="hyper" parents="373 1145 1649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1655">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      1 / x = y
    ]]></literal>
    <justification jstring="[para(1635(a,1),236(a,1))].">
      <j1 rule="para" parents="1635 236"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      L((x \ 1) * y,x,x \ 1) = (1 / x) * L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(293(a,1),1635(a,1,2)),flip(a)].">
      <j1 rule="para" parents="293 1635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1657">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1641(a,1),290(a,1,2))].">
      <j1 rule="para" parents="1641 290"/>
    </justification>
  </clause>

  <clause id="1658">
    <literal><![CDATA[
      ((x \ 1) * y) \ ((x \ 1) * z) = (x * y) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,1632,a),flip(a)].">
      <j1 rule="hyper" parents="64 102 1632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1659">
    <literal><![CDATA[
      ((x \ 1) * y) / (z \ (x * y)) = (x \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(225,a,630,a(flip),b,1632,a(flip))].">
      <j1 rule="hyper" parents="225 630 1632"/>
    </justification>
  </clause>

  <clause id="1660">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) \ z = y \ (x * ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(743,a,1633,a),flip(a)].">
      <j1 rule="hyper" parents="743 1633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1661">
    <literal><![CDATA[
      (x \ 1) * (T(x,x \ 1) * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(501(a,1),1642(a,1,1)),flip(a)].">
      <j1 rule="para" parents="501 1642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      L(x \ ((1 / y) \ L(x,1 / y,1 / y)),x,y) = T(1 / (1 / y),(1 / y) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,565,a(flip),b,1650,a),flip(a)].">
      <j1 rule="hyper" parents="373 565 1650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1663">
    <literal><![CDATA[
      L(x,y,y) * L(z,y * x,y) = (1 / y) * ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(559(a,1),1651(a,1,1))].">
      <j1 rule="para" parents="559 1651"/>
    </justification>
  </clause>

  <clause id="1664">
    <literal><![CDATA[
      (x \ 1) * (R(x,x,x) * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1417(a,1),1661(a,1,2,1))].">
      <j1 rule="para" parents="1417 1661"/>
    </justification>
  </clause>

  <clause id="1665">
    <literal><![CDATA[
      (x \ 1) * (R(x,x,x) * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1631,a(flip),b,1664,a),flip(a)].">
      <j1 rule="hyper" parents="373 1631 1664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1666">
    <literal><![CDATA[
      (1 / x) * (((1 / x) \ y) * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1598,a(flip),b,1128,a),flip(a)].">
      <j1 rule="hyper" parents="145 1598 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      (x \ 1) \ (((x \ y) * z) * u) = x \ ((((1 / x) \ y) * z) * u)
    ]]></literal>
    <justification jstring="[para(1598(a,1),1540(a,1,2,1))].">
      <j1 rule="para" parents="1598 1540"/>
    </justification>
  </clause>

  <clause id="1668">
    <literal><![CDATA[
      (1 / x) * ((x / y) * z) = x * (((x \ 1) / y) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1599,a(flip),b,1128,a),flip(a)].">
      <j1 rule="hyper" parents="145 1599 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1670">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (((x \ 1) * y) * z)) = T(1 / x,(x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(493,a,xx,b,1603,a),flip(a)].">
      <j1 rule="hyper" parents="493 1603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      (1 / x) * ((x * (x \ 1)) * (T(y,(x \ 1) * (x \ 1)) \ z)) = x * (y \ (((x \ 1) * (x \ 1)) * z))
    ]]></literal>
    <justification jstring="[para(1460(a,1),1603(a,2,2))].">
      <j1 rule="para" parents="1460 1603"/>
    </justification>
  </clause>

  <clause id="1672">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) \ z = (y \ 1) * (y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,1168,a(flip),b,1606,a),flip(a)].">
      <j1 rule="hyper" parents="373 1168 1606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1673">
    <literal><![CDATA[
      (x * (y \ (y \ 1))) \ z = ((y \ 1) \ y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1549,a(flip),b,1609,a),flip(a)].">
      <j1 rule="hyper" parents="373 1549 1609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1674">
    <literal><![CDATA[
      (x / y) * (y * ((y \ 1) \ z)) = (x / (y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(1590(a,1),1611(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1590 1611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ ((x \ 1) \ y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1166,a(flip),b,1612,a),flip(a)].">
      <j1 rule="hyper" parents="373 1166 1612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1676">
    <literal><![CDATA[
      (x / (y \ z)) * (y \ (y \ 1)) = x / ((y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(1131(a,1),1619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1131 1619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      (x * (y \ 1)) \ ((y \ 1) * (y \ z)) = (y * T(x,y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(22(a,2),1621(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="22 1621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1678">
    <literal><![CDATA[
      (x \ y) \ ((x \ 1) * (x \ z)) = ((1 / x) \ y) \ z
    ]]></literal>
    <justification jstring="[para(1138(a,1),1621(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1138 1621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1679">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ z) = (x \ y) \ (x \ z)
    ]]></literal>
    <justification jstring="[para(1126(a,1),1622(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1126 1622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1680">
    <literal><![CDATA[
      (x \ 1) * (x \ ((y / x) \ z)) = (y / (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,75,a(flip),b,1627,a),flip(a)].">
      <j1 rule="hyper" parents="139 75 1627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1681">
    <literal><![CDATA[
      ((x \ 1) * y) \ ((x \ z) * u) = (x * y) \ (((1 / x) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,1598,a(flip),b,1628,a)].">
      <j1 rule="hyper" parents="139 1598 1628"/>
    </justification>
  </clause>

  <clause id="1682">
    <literal><![CDATA[
      ((x \ 1) * y) \ (x \ z) = (x * y) \ ((1 / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,1165,a(flip),b,1628,a)].">
      <j1 rule="hyper" parents="139 1165 1628"/>
    </justification>
  </clause>

  <clause id="1683">
    <literal><![CDATA[
      (x * (R(x,x,x) * y)) \ (x * z) = L(y,x,x) \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(1665(a,1),1658(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1665 1658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1685">
    <literal><![CDATA[
      ((x \ 1) * T(y,x)) / x = (x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[para(257(a,1),1659(a,1,2))].">
      <j1 rule="para" parents="257 1659"/>
    </justification>
  </clause>

  <clause id="1686">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) / z = (x \ 1) * (x \ (y / z))
    ]]></literal>
    <justification jstring="[para(343(a,1),1659(a,1,2))].">
      <j1 rule="para" parents="343 1659"/>
    </justification>
  </clause>

  <clause id="1687">
    <literal><![CDATA[
      ((x \ (1 / x)) * y) \ z = y \ (x * ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(1098(a,2),1660(a,1,1))].">
      <j1 rule="para" parents="1098 1660"/>
    </justification>
  </clause>

  <clause id="1689">
    <literal><![CDATA[
      (x / (y \ 1)) * (y \ z) = (x / y) * ((1 / y) \ z)
    ]]></literal>
    <justification jstring="[para(1138(a,1),1674(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1138 1674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1690">
    <literal><![CDATA[
      R(x,x,x) \ ((x \ 1) \ y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(1418(a,2),1675(a,1,1))].">
      <j1 rule="para" parents="1418 1675"/>
    </justification>
  </clause>

  <clause id="1691">
    <literal><![CDATA[
      x / T(y \ 1,y \ x) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,22,a,b,1678,a(flip))].">
      <j1 rule="hyper" parents="225 22 1678"/>
    </justification>
  </clause>

  <clause id="1692">
    <literal><![CDATA[
      ((1 / x) \ y) \ (x * z) = (x \ y) \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),1678(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 1678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1693">
    <literal><![CDATA[
      (1 / x) * ((y / x) \ z) = x * ((y / (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1680,a(flip),b,1128,a),flip(a)].">
      <j1 rule="hyper" parents="145 1680 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1694">
    <literal><![CDATA[
      x * ((R(y,x,x) / (x \ 1)) \ z) = (1 / x) * ((y * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[para(1408(a,1),1693(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1408 1693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1695">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y)
    ]]></literal>
    <justification jstring="[para(1635(a,1),356(a,1,1))].">
      <j1 rule="para" parents="1635 356"/>
    </justification>
  </clause>

  <clause id="1696">
    <literal><![CDATA[
      R(R(x,y \ 1,y),z,u) * K(y \ 1,y) = (R(x,z,u) * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(294(a,2),506(a,1,2))].">
      <j1 rule="para" parents="294 506"/>
    </justification>
  </clause>

  <clause id="1697">
    <literal><![CDATA[
      R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y
    ]]></literal>
    <justification jstring="[para(112(a,1),506(a,1,1,1))].">
      <j1 rule="para" parents="112 506"/>
    </justification>
  </clause>

  <clause id="1698">
    <literal><![CDATA[
      (R((x / y) / z,u,w) * z) * y = R(x / (z * y),u,w) * (z * y)
    ]]></literal>
    <justification jstring="[para(351(a,1),506(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="351 506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1699">
    <literal><![CDATA[
      x \ ((L(y,z,x) * x) * z) = z * T(R(y,x,z),x * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,510,a(flip),b,793,a)].">
      <j1 rule="hyper" parents="139 510 793"/>
    </justification>
  </clause>

  <clause id="1700">
    <literal><![CDATA[
      L(x / (y * x),z,u) * (y * x) = (L(1 / y,z,u) * y) * x
    ]]></literal>
    <justification jstring="[para(244(a,1),510(a,1,1,1))].">
      <j1 rule="para" parents="244 510"/>
    </justification>
  </clause>

  <clause id="1701">
    <literal><![CDATA[
      (L(x * x,y,z) * u) * w = L(x * x,y,z) * (u * w)
    ]]></literal>
    <justification jstring="[para(655(a,1),510(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="655 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1702">
    <literal><![CDATA[
      L((x * y) / (z * y),u,w) * (z * y) = (L(x / z,u,w) * z) * y
    ]]></literal>
    <justification jstring="[para(112(a,1),510(a,1,1,1))].">
      <j1 rule="para" parents="112 510"/>
    </justification>
  </clause>

  <clause id="1703">
    <literal><![CDATA[
      (L(x \ 1,y,z) * x) * x = L(1 / x,y,z) * (x * x)
    ]]></literal>
    <justification jstring="[para(1043(a,1),510(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1043 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1704">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (x * z),u,w) = x * (y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(102(a,1),513(a,1,2,1))].">
      <j1 rule="para" parents="102 513"/>
    </justification>
  </clause>

  <clause id="1705">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(346(a,1),513(a,1,2,1))].">
      <j1 rule="para" parents="346 513"/>
    </justification>
  </clause>

  <clause id="1706">
    <literal><![CDATA[
      (x * y) * L(T(x,x * y),z,u) = x * (y * L(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(765(a,1),513(a,1,2,1))].">
      <j1 rule="para" parents="765 513"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      (x * y) * L(R(T(x,x * y),z,u),w,v5) = x * (y * L(R(T(x,y),z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(768(a,1),513(a,1,2,1))].">
      <j1 rule="para" parents="768 513"/>
    </justification>
  </clause>

  <clause id="1708">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(102(a,1),514(a,1,2,1))].">
      <j1 rule="para" parents="102 514"/>
    </justification>
  </clause>

  <clause id="1709">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(346(a,1),514(a,1,2,1))].">
      <j1 rule="para" parents="346 514"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      K(x \ 1,x) * T(((x \ 1) * x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z))
    ]]></literal>
    <justification jstring="[para(708(a,1),610(a,1,2))].">
      <j1 rule="para" parents="708 610"/>
    </justification>
  </clause>

  <clause id="1711">
    <literal><![CDATA[
      L(L(L(x,y,z) \ u,w,v5),L(x,y,z),z * y) = L((z * (y * x)) \ ((z * y) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(100(a,1),637(a,2,1,1))].">
      <j1 rule="para" parents="100 637"/>
    </justification>
  </clause>

  <clause id="1712">
    <literal><![CDATA[
      R(x \ T(x,y),K(x \ 1,T(x,y)),z) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(1487(a,1),689(a,1,1,1))].">
      <j1 rule="para" parents="1487 689"/>
    </justification>
  </clause>

  <clause id="1713">
    <literal><![CDATA[
      (1 / x) \ L(x \ 1,y,z) = x * L(T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(1006(a,1),697(a,1,2,1))].">
      <j1 rule="para" parents="1006 697"/>
    </justification>
  </clause>

  <clause id="1714">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = L(x / y,z,u) * y
    ]]></literal>
    <justification jstring="[para(675(a,1),699(a,1,1,1))].">
      <j1 rule="para" parents="675 699"/>
    </justification>
  </clause>

  <clause id="1715">
    <literal><![CDATA[
      L(R(x / (1 / y),1 / y,y),z,u) / y = (1 / y) * L((1 / y) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,836,a(flip),b,704,a),flip(a)].">
      <j1 rule="hyper" parents="373 836 704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1716">
    <literal><![CDATA[
      L(T(x / ((1 / x) * x),y),z,u) / x = L(T(1 / (1 / x),y),z,u) * (1 / x)
    ]]></literal>
    <justification jstring="[para(455(a,2),704(a,1,1,1))].">
      <j1 rule="para" parents="455 704"/>
    </justification>
  </clause>

  <clause id="1717">
    <literal><![CDATA[
      L(L(x \ ((y / x) \ z),u,w),x,y / x) = L(y \ z,u,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),709(a,2,1,1))].">
      <j1 rule="para" parents="12 709"/>
    </justification>
  </clause>

  <clause id="1718">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * L(y \ (x \ z),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(709(a,1),334(a,1,2))].">
      <j1 rule="para" parents="709 334"/>
    </justification>
  </clause>

  <clause id="1719">
    <literal><![CDATA[
      (x / y) * (y * L(y \ 1,z,u)) = x * L(x \ (x / y),z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,748,a(flip),b,103,a),flip(a)].">
      <j1 rule="hyper" parents="145 748 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1720">
    <literal><![CDATA[
      R(x / (x * x),x,x \ y) = L((x \ y) / y,x,x)
    ]]></literal>
    <justification jstring="[para(1192(a,1),751(a,1,1))].">
      <j1 rule="para" parents="1192 751"/>
    </justification>
  </clause>

  <clause id="1721">
    <literal><![CDATA[
      L((1 / x) * T(x,y),x,y) = L(K(x,y),x,1 / x)
    ]]></literal>
    <justification jstring="[para(1013(a,2),773(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1013 773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1722">
    <literal><![CDATA[
      L(K(x,y),x,1 / x) = L(T(x,y) / x,x,y)
    ]]></literal>
    <justification jstring="[para(1511(a,1),1721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1511 1721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1723">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(42,a,1648,a,b,1722,a)].">
      <j1 rule="hyper" parents="42 1648 1722"/>
    </justification>
  </clause>

  <clause id="1724">
    <literal><![CDATA[
      K(x,x \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1361,a,1723,a),flip(a)].">
      <j1 rule="hyper" parents="1361 1723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1725">
    <literal><![CDATA[
      K(x,x \ 1) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(156,a,1723,a)].">
      <j1 rule="hyper" parents="156 1723"/>
    </justification>
  </clause>

  <clause id="1726">
    <literal><![CDATA[
      K(x,1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,1356,a(flip),b,1723,a)].">
      <j1 rule="hyper" parents="64 1356 1723"/>
    </justification>
  </clause>

  <clause id="1727">
    <literal><![CDATA[
      x \ K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(139,a,1723,a(flip),b,1357,a(flip))].">
      <j1 rule="hyper" parents="139 1723 1357"/>
    </justification>
  </clause>

  <clause id="1728">
    <literal><![CDATA[
      K(x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(1723(a,1),1361(a,1))].">
      <j1 rule="para" parents="1723 1361"/>
    </justification>
  </clause>

  <clause id="1729">
    <literal><![CDATA[
      K(x,x \ 1) / x = x / (x * x)
    ]]></literal>
    <justification jstring="[hyper(142,a,1724,a,b,811,a)].">
      <j1 rule="hyper" parents="142 1724 811"/>
    </justification>
  </clause>

  <clause id="1730">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * y) * (1 / y)) = a(x,y,1 / y)
    ]]></literal>
    <justification jstring="[para(1724(a,2),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1724 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1731">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1362,a,1726,a),flip(a)].">
      <j1 rule="hyper" parents="1362 1726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1732">
    <literal><![CDATA[
      K(x \ 1,x) * K(x,1 / x) = 1
    ]]></literal>
    <justification jstring="[hyper(145,a,1726,a,b,479,a)].">
      <j1 rule="hyper" parents="145 1726 479"/>
    </justification>
  </clause>

  <clause id="1733">
    <literal><![CDATA[
      K(x,x \ 1) * x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(144,a,1726,a(flip),b,1360,a)].">
      <j1 rule="hyper" parents="144 1726 1360"/>
    </justification>
  </clause>

  <clause id="1734">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),1726(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 1726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1735">
    <literal><![CDATA[
      x * (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1727(a,1),290(a,1,2))].">
      <j1 rule="para" parents="1727 290"/>
    </justification>
  </clause>

  <clause id="1736">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(296(a,2),1735(a,1))].">
      <j1 rule="para" parents="296 1735"/>
    </justification>
  </clause>

  <clause id="1737">
    <literal><![CDATA[
      K(1 / x,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),1731(a,1,2))].">
      <j1 rule="para" parents="82 1731"/>
    </justification>
  </clause>

  <clause id="1738">
    <literal><![CDATA[
      x * K(1 / x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,1737,a,b,1161,a)].">
      <j1 rule="hyper" parents="145 1737 1161"/>
    </justification>
  </clause>

  <clause id="1739">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),1737(a,1,1)),flip(a)].">
      <j1 rule="para" parents="79 1737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1740">
    <literal><![CDATA[
      x * K(x,x \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(145,a,1739,a(flip),b,1255,a(flip))].">
      <j1 rule="hyper" parents="145 1739 1255"/>
    </justification>
  </clause>

  <clause id="1741">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ K(x,x \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,1739,a(flip),b,294,a(flip))].">
      <j1 rule="hyper" parents="139 1739 294"/>
    </justification>
  </clause>

  <clause id="1742">
    <literal><![CDATA[
      x * K(x,x \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,116,a,b,1740,a),flip(a)].">
      <j1 rule="hyper" parents="373 116 1740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1743">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) != z * ((y \ 1) \ 1)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,K(y,y \ 1)) = z
    ]]></literal>
    <justification jstring="[para(1740(a,1),664(a,2,2))].">
      <j1 rule="para" parents="1740 664"/>
    </justification>
  </clause>

  <clause id="1744">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / T(y,y \ 1) = R(x / y,y,K(y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(225,a,1742,a(flip),b,650,a)].">
      <j1 rule="hyper" parents="225 1742 650"/>
    </justification>
  </clause>

  <clause id="1745">
    <literal><![CDATA[
      (T(x,x \ 1) * y) / (K(x,x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,K(x,x \ 1),y) = z
    ]]></literal>
    <justification jstring="[para(1742(a,1),666(a,1,1,1))].">
      <j1 rule="para" parents="1742 666"/>
    </justification>
  </clause>

  <clause id="1746">
    <literal><![CDATA[
      x * (x * (1 / x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1724(a,1),1742(a,1,2))].">
      <j1 rule="para" parents="1724 1742"/>
    </justification>
  </clause>

  <clause id="1747">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(139,a,116,a(flip),b,1746,a)].">
      <j1 rule="hyper" parents="139 116 1746"/>
    </justification>
  </clause>

  <clause id="1748">
    <literal><![CDATA[
      (R(x / y,z,u) * y) * (y \ 1) = R(x * (y \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,297,a,b,781,a)].">
      <j1 rule="hyper" parents="64 297 781"/>
    </justification>
  </clause>

  <clause id="1749">
    <literal><![CDATA[
      L(x,y,z) * (x * x) = x * (x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,513,a(flip),b,838,a),flip(a)].">
      <j1 rule="hyper" parents="64 513 838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1750">
    <literal><![CDATA[
      (x * (x * L(x,y,z))) * u = L(x,y,z) * ((x * x) * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,1749,a(flip),b,133,a)].">
      <j1 rule="hyper" parents="144 1749 133"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      x \ (y * (((y \ x) \ z) * (y \ x))) = T(x \ (y * z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,967,a(flip),b,1024,a)].">
      <j1 rule="hyper" parents="64 967 1024"/>
    </justification>
  </clause>

  <clause id="1752">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(145,a,1024,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 1024 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1753">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,1033,a(flip),b,113,a),flip(a)].">
      <j1 rule="hyper" parents="144 1033 113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1754">
    <literal><![CDATA[
      T(((x * y) * y) / x,a(x,y,y) * (y * y)) = ((x * y) * y) / x
    ]]></literal>
    <justification jstring="[para(1045(a,1),307(a,1,2))].">
      <j1 rule="para" parents="1045 307"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = (x * y) \ ((z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,277,a,b,1055,a),flip(a)].">
      <j1 rule="hyper" parents="373 277 1055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1756">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,27,a,b,1055,a),flip(a)].">
      <j1 rule="hyper" parents="373 27 1055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1757">
    <literal><![CDATA[
      (x * (T(y,x) * ((y * x) \ z))) / (y * x) = L(z / (y * x),x \ (y * x),x)
    ]]></literal>
    <justification jstring="[para(22(a,2),1189(a,1,1,2,1))].">
      <j1 rule="para" parents="22 1189"/>
    </justification>
  </clause>

  <clause id="1758">
    <literal><![CDATA[
      L(T(x / y,z),u,w) * y != v5
    ]]></literal>
    <literal><![CDATA[
      y * L(T(y \ x,z),u,w) = v5
    ]]></literal>
    <justification jstring="[para(531(a,1),1272(a,1,1,1))].">
      <j1 rule="para" parents="531 1272"/>
    </justification>
  </clause>

  <clause id="1759">
    <literal><![CDATA[
      (1 / x) * R(T(x,x),y,y \ x) = a(x,y,y \ x)
    ]]></literal>
    <justification jstring="[para(996(a,1),1280(a,1,2))].">
      <j1 rule="para" parents="996 1280"/>
    </justification>
  </clause>

  <clause id="1760">
    <literal><![CDATA[
      (1 / x) * R(x,y,y \ x) = a(x,y,y \ x)
    ]]></literal>
    <justification jstring="[para(114(a,1),1759(a,1,2,1))].">
      <j1 rule="para" parents="114 1759"/>
    </justification>
  </clause>

  <clause id="1761">
    <literal><![CDATA[
      ((1 / x) * (1 / x)) * (x * y) = x * ((x * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,950,a(flip),b,1411,a),flip(a)].">
      <j1 rule="hyper" parents="373 950 1411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1762">
    <literal><![CDATA[
      (x * ((y * y) / z)) * z = R(x * (y * y),z,z)
    ]]></literal>
    <justification jstring="[para(497(a,1),1412(a,1,1,2))].">
      <j1 rule="para" parents="497 1412"/>
    </justification>
  </clause>

  <clause id="1763">
    <literal><![CDATA[
      x * R(T(x,x \ 1),y,z) = x * R(R(x,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,846,a(flip),b,1422,a),flip(a)].">
      <j1 rule="hyper" parents="64 846 1422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1764">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ z) = z * T(z \ (y * (x \ z)),x)
    ]]></literal>
    <justification jstring="[hyper(145,a,1498,a(flip),b,996,a),flip(a)].">
      <j1 rule="hyper" parents="145 1498 996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1765">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(334,a,1584,a)].">
      <j1 rule="hyper" parents="334 1584"/>
    </justification>
  </clause>

  <clause id="1766">
    <literal><![CDATA[
      T(x,x / (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * ((y \ x) / x)) = z
    ]]></literal>
    <justification jstring="[para(1584(a,1),334(a,1))].">
      <j1 rule="para" parents="1584 334"/>
    </justification>
  </clause>

  <clause id="1767">
    <literal><![CDATA[
      L(L(L(T(x,y),z,u),w,v5),y,x) = L(L(T(x,x * y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(765(a,1),124(a,2,1,1))].">
      <j1 rule="para" parents="765 124"/>
    </justification>
  </clause>

  <clause id="1768">
    <literal><![CDATA[
      T(x,x \ 1) \ (x * L(y,(x * (1 / x)) \ 1,x * (1 / x))) = L(((x * (1 / x)) \ 1) * y,x * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(1746(a,1),696(a,1,1))].">
      <j1 rule="para" parents="1746 696"/>
    </justification>
  </clause>

  <clause id="1769">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = R((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,267,a,b,845,a)].">
      <j1 rule="hyper" parents="35 267 845"/>
    </justification>
  </clause>

  <clause id="1770">
    <literal><![CDATA[
      T(x,x \ y) \ R(T(z,z \ u),w,v5) = ((x \ y) \ y) \ R((z \ u) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(139,a,1769,a,b,505,a)].">
      <j1 rule="hyper" parents="139 1769 505"/>
    </justification>
  </clause>

  <clause id="1771">
    <literal><![CDATA[
      (x * (y * z)) * T(((x * y) * L(z,y,x)) \ (x * y),u) = (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u))
    ]]></literal>
    <justification jstring="[para(100(a,1),1001(a,1,1))].">
      <j1 rule="para" parents="100 1001"/>
    </justification>
  </clause>

  <clause id="1772">
    <literal><![CDATA[
      T(x * T(y,1 / x),x * x) = R(y,x,x) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1413,a(flip),b,1073,a),flip(a)].">
      <j1 rule="hyper" parents="373 1413 1073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1773">
    <literal><![CDATA[
      T(T(x,y * y),z) = T(x,(y * y) * z)
    ]]></literal>
    <justification jstring="[hyper(269,a,930,a(flip),b,1265,a(flip))].">
      <j1 rule="hyper" parents="269 930 1265"/>
    </justification>
  </clause>

  <clause id="1775">
    <literal><![CDATA[
      T(T(x,y),z * z) = T(x,(z * z) * y)
    ]]></literal>
    <justification jstring="[hyper(481,a,1773,a)].">
      <j1 rule="hyper" parents="481 1773"/>
    </justification>
  </clause>

  <clause id="1776">
    <literal><![CDATA[
      T(x,(y * y) * z) \ ((y * y) \ u) = (y * y) \ (T(x,z) \ u)
    ]]></literal>
    <justification jstring="[para(1775(a,1),1452(a,1,1))].">
      <j1 rule="para" parents="1775 1452"/>
    </justification>
  </clause>

  <clause id="1777">
    <literal><![CDATA[
      L(x \ y,y \ x,1 / (y \ x)) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[para(186(a,1),1303(a,1,1)),flip(a)].">
      <j1 rule="para" parents="186 1303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1778">
    <literal><![CDATA[
      x \ (y * L(y \ x,x \ y,z)) = (x \ y) * ((z * (x \ y)) \ z)
    ]]></literal>
    <justification jstring="[para(1303(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="1303 598"/>
    </justification>
  </clause>

  <clause id="1779">
    <literal><![CDATA[
      x * L(x \ ((1 / x) \ y),z,u) = (1 / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1310(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1780">
    <literal><![CDATA[
      (1 / x) * (x * R(x \ 1,y,z)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),1311(a,2,1))].">
      <j1 rule="para" parents="8 1311"/>
    </justification>
  </clause>

  <clause id="1781">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,1780,a)].">
      <j1 rule="hyper" parents="149 1780"/>
    </justification>
  </clause>

  <clause id="1782">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (1 / (x / y)) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(139,a,454,a(flip),b,1780,a),flip(a)].">
      <j1 rule="hyper" parents="139 454 1780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1783">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) = a(1 / x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,983,a,b,1780,a),flip(a)].">
      <j1 rule="hyper" parents="35 983 1780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1784">
    <literal><![CDATA[
      (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(859(a,2),1780(a,1,2))].">
      <j1 rule="para" parents="859 1780"/>
    </justification>
  </clause>

  <clause id="1785">
    <literal><![CDATA[
      (1 / x) * ((y / (x * y)) * x) = y / (x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,244,a(flip),b,1784,a),flip(a)].">
      <j1 rule="hyper" parents="373 244 1784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1786">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,x,y) = (y / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(149,a,1784,a)].">
      <j1 rule="hyper" parents="149 1784"/>
    </justification>
  </clause>

  <clause id="1787">
    <literal><![CDATA[
      (x / ((y \ 1) * x)) * (y \ 1) = y \ (x / ((y \ 1) * x))
    ]]></literal>
    <justification jstring="[hyper(139,a,1785,a(flip),b,209,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 1785 209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1788">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(1 / x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1781(a,1),986(a,1))].">
      <j1 rule="para" parents="1781 986"/>
    </justification>
  </clause>

  <clause id="1789">
    <literal><![CDATA[
      (x \ 1) * R(x \ ((1 / x) \ y),z,u) = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1312(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1790">
    <literal><![CDATA[
      R(x,y,y) * R(y,y,y \ 1) = R(x * y,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(297(a,1),1324(a,1,2))].">
      <j1 rule="para" parents="297 1324"/>
    </justification>
  </clause>

  <clause id="1791">
    <literal><![CDATA[
      (x / y) \ (x * T(x \ (x / y),z)) = y * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,1336,a)].">
      <j1 rule="hyper" parents="149 1336"/>
    </justification>
  </clause>

  <clause id="1792">
    <literal><![CDATA[
      R(x / (y \ 1),z,u) * (y \ 1) = y \ R(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,843,a,b,1387,a)].">
      <j1 rule="hyper" parents="64 843 1387"/>
    </justification>
  </clause>

  <clause id="1793">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),1387(a,2,2,1))].">
      <j1 rule="para" parents="8 1387"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,845,a(flip),b,1793,a)].">
      <j1 rule="hyper" parents="64 845 1793"/>
    </justification>
  </clause>

  <clause id="1795">
    <literal><![CDATA[
      x * (R(x,y,z) * (x \ 1)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,845,a(flip),b,1793,a(flip))].">
      <j1 rule="hyper" parents="145 845 1793"/>
    </justification>
  </clause>

  <clause id="1796">
    <literal><![CDATA[
      R(x,y,z) \ (x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,1793,a(flip),b,845,a(flip))].">
      <j1 rule="hyper" parents="139 1793 845"/>
    </justification>
  </clause>

  <clause id="1797">
    <literal><![CDATA[
      (x \ R(x,y,z)) / R(T(x,x \ 1),y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(142,a,1794,a(flip),b,267,a)].">
      <j1 rule="hyper" parents="142 1794 267"/>
    </justification>
  </clause>

  <clause id="1798">
    <literal><![CDATA[
      R(x,y,z) * R(R(x,y,z) \ 1,R(x,y,z),x \ 1) = ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1794(a,1),859(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1794 859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1799">
    <literal><![CDATA[
      (x / (1 / y)) \ R(x / (1 / y),y,y) = (x * y) * ((x / (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(1407(a,1),1794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1407 1794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1800">
    <literal><![CDATA[
      x \ L(x * (y * (x \ 1)),z,u) = L(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1306,a,1389,a),flip(a)].">
      <j1 rule="hyper" parents="1306 1389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1801">
    <literal><![CDATA[
      L(x / (y \ 1),z,u) * (y \ 1) = y \ L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,836,a,b,1389,a)].">
      <j1 rule="hyper" parents="64 836 1389"/>
    </justification>
  </clause>

  <clause id="1802">
    <literal><![CDATA[
      L(x * (y * (x \ 1)),z,u) = x * (L(y,z,u) * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(145,a,833,a(flip),b,1389,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 833 1389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1803">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) / (x \ 1) = L(y / (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(142,a,1389,a(flip),b,836,a)].">
      <j1 rule="hyper" parents="142 1389 836"/>
    </justification>
  </clause>

  <clause id="1804">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),1389(a,2,2,1))].">
      <j1 rule="para" parents="8 1389"/>
    </justification>
  </clause>

  <clause id="1805">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ (x \ y),z,u) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1389(a,2,2,1))].">
      <j1 rule="para" parents="10 1389"/>
    </justification>
  </clause>

  <clause id="1806">
    <literal><![CDATA[
      x \ L(x * (y \ z),x \ 1,y) = (x \ 1) * ((y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(346(a,1),1389(a,1,2)),flip(a)].">
      <j1 rule="para" parents="346 1389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1807">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,839,a(flip),b,1804,a)].">
      <j1 rule="hyper" parents="64 839 1804"/>
    </justification>
  </clause>

  <clause id="1808">
    <literal><![CDATA[
      L(x,y,z) \ (x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,1804,a(flip),b,839,a(flip))].">
      <j1 rule="hyper" parents="139 1804 839"/>
    </justification>
  </clause>

  <clause id="1809">
    <literal><![CDATA[
      (x \ 1) * L(R(x,x,x),y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1418(a,2),1804(a,1,2,1))].">
      <j1 rule="para" parents="1418 1804"/>
    </justification>
  </clause>

  <clause id="1810">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ u = (x \ L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(62,a,1807,a)].">
      <j1 rule="hyper" parents="62 1807"/>
    </justification>
  </clause>

  <clause id="1811">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,x,x) = ((1 / x) * y) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(569(a,1),1807(a,1,1)),flip(a)].">
      <j1 rule="para" parents="569 1807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1812">
    <literal><![CDATA[
      L(x,y,z) * R(L(x,y,z) \ 1,L(x,y,z),x \ 1) = ((x \ 1) / (x \ L(x,y,z))) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1807(a,1),859(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1807 859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1813">
    <literal><![CDATA[
      ((x \ 1) \ y) \ L((x \ 1) \ y,x,x) = (x * y) * (((x \ 1) \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1137(a,1),1807(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1137 1807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1814">
    <literal><![CDATA[
      x \ T(x * (x \ L(x,y,z)),u) = T(L(x,y,z),u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1807(a,1),1482(a,1,2,1,2))].">
      <j1 rule="para" parents="1807 1482"/>
    </justification>
  </clause>

  <clause id="1815">
    <literal><![CDATA[
      (x \ y) \ (((y \ x) \ 1) \ L((y \ x) \ 1,y \ x,y)) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(436(a,1),1808(a,1,1))].">
      <j1 rule="para" parents="436 1808"/>
    </justification>
  </clause>

  <clause id="1816">
    <literal><![CDATA[
      T(L(x,y,z),(x \ L(x,y,z)) * (x \ L(x,y,z))) \ (1 / (x \ L(x,y,z))) = ((x \ L(x,y,z)) * (x \ L(x,y,z))) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(1808(a,1),1527(a,2,2))].">
      <j1 rule="para" parents="1808 1527"/>
    </justification>
  </clause>

  <clause id="1817">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[para(525(a,1),1398(a,2,1))].">
      <j1 rule="para" parents="525 1398"/>
    </justification>
  </clause>

  <clause id="1818">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ y,z,u) = R(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(1213,a,1431,a)].">
      <j1 rule="hyper" parents="1213 1431"/>
    </justification>
  </clause>

  <clause id="1819">
    <literal><![CDATA[
      R(((1 / x) * y) * x,z,u) = ((1 / x) * R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,844,a(flip),b,1431,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 844 1431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1820">
    <literal><![CDATA[
      L(x,y,y) * L(z,y * x,y) = y * (((y \ 1) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1603,a(flip),b,1663,a),flip(a)].">
      <j1 rule="hyper" parents="373 1603 1663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1821">
    <literal><![CDATA[
      x \ ((L(y,z,x) * x) * z) = z * R(T(y,x * z),x,z)
    ]]></literal>
    <justification jstring="[para(27(a,2),1699(a,2,2))].">
      <j1 rule="para" parents="27 1699"/>
    </justification>
  </clause>

  <clause id="1822">
    <literal><![CDATA[
      L(x * x,y,z) \ (u * w) = (L(x * x,y,z) \ u) * w
    ]]></literal>
    <justification jstring="[hyper(783,a,1701,a)].">
      <j1 rule="hyper" parents="783 1701"/>
    </justification>
  </clause>

  <clause id="1823">
    <literal><![CDATA[
      L(x,y,L(z * z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(606,a,1701,a)].">
      <j1 rule="hyper" parents="606 1701"/>
    </justification>
  </clause>

  <clause id="1824">
    <literal><![CDATA[
      (L(x * x,y,z) \ 1) * u = L(x * x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(458,a,1701,a),flip(a)].">
      <j1 rule="hyper" parents="458 1701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1825">
    <literal><![CDATA[
      a(L(x * x,y,z),u,w) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,1701,a(flip),b,88,a),flip(a)].">
      <j1 rule="hyper" parents="138 1701 88"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1826">
    <literal><![CDATA[
      (L(x * x,y,z) * (u * (w * v5))) \ (((L(x * x,y,z) * u) * w) * v5) = a(L(x * x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(1701(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1701 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1827">
    <literal><![CDATA[
      (L(x * x,y,z) \ u) \ 1 = u \ L(x * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,436,a(flip),b,1823,a),flip(a)].">
      <j1 rule="hyper" parents="64 436 1823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1828">
    <literal><![CDATA[
      (1 / x) \ L(x \ 1,y,z) = L(x \ 1,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,266,a(flip),b,1713,a),flip(a)].">
      <j1 rule="hyper" parents="373 266 1713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1829">
    <literal><![CDATA[
      (1 / x) * (L(x \ 1,y,z) * x) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,266,a(flip),b,1713,a)].">
      <j1 rule="hyper" parents="145 266 1713"/>
    </justification>
  </clause>

  <clause id="1830">
    <literal><![CDATA[
      (x * x) * L(x \ 1,y,z) = x * (L(x \ 1,y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,1828,a(flip),b,539,a),flip(a)].">
      <j1 rule="hyper" parents="145 1828 539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1832">
    <literal><![CDATA[
      (x * y) \ x = (1 / y) * (L(y \ 1,y,x) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,241,a(flip),b,1829,a)].">
      <j1 rule="hyper" parents="373 241 1829"/>
    </justification>
  </clause>

  <clause id="1833">
    <literal><![CDATA[
      (1 / x) * (((y * x) \ y) * x) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,1000,a(flip),b,1832,a)].">
      <j1 rule="hyper" parents="373 1000 1832"/>
    </justification>
  </clause>

  <clause id="1834">
    <literal><![CDATA[
      x * L(x \ (((y * x) \ y) * x),z,u) = (1 / x) \ L((y * x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1833(a,1),1310(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1833 1310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1835">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,836,a(flip),b,1714,a),flip(a)].">
      <j1 rule="hyper" parents="373 836 1714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1836">
    <literal><![CDATA[
      L((x * y) * (x \ 1),z,u) = (x * L(y,z,u)) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,837,a(flip),b,1714,a),flip(a)].">
      <j1 rule="hyper" parents="144 837 1714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1837">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) * (x \ 1) = R(y * (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(843(a,1),1748(a,1,1))].">
      <j1 rule="para" parents="843 1748"/>
    </justification>
  </clause>

  <clause id="1838">
    <literal><![CDATA[
      ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1764(a,2,2,1,2))].">
      <j1 rule="para" parents="7 1764"/>
    </justification>
  </clause>

  <clause id="1839">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(294(a,2),1838(a,1,1))].">
      <j1 rule="para" parents="294 1838"/>
    </justification>
  </clause>

  <clause id="1840">
    <literal><![CDATA[
      L(x \ ((1 / x) \ y),z,u) = x \ ((1 / x) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(149,a,1779,a),flip(a)].">
      <j1 rule="hyper" parents="149 1779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1841">
    <literal><![CDATA[
      x * L((x \ 1) \ (x \ y),z,u) = (1 / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(1166(a,2),1779(a,1,2,1))].">
      <j1 rule="para" parents="1166 1779"/>
    </justification>
  </clause>

  <clause id="1842">
    <literal><![CDATA[
      x \ (y / ((x \ 1) * y)) = (y / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,1624,a(flip),b,1787,a),flip(a)].">
      <j1 rule="hyper" parents="64 1624 1787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1843">
    <literal><![CDATA[
      x \ R(x * (y * (x \ 1)),z,u) = R(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),1792(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 1792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1844">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (x \ 1) = x \ L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1795(a,1),1800(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1795 1800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1845">
    <literal><![CDATA[
      L(x,y,z) * (x * (L(x,y,z) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,72,a(flip),b,1802,a),flip(a)].">
      <j1 rule="hyper" parents="42 72 1802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1846">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(149,a,1845,a),flip(a)].">
      <j1 rule="hyper" parents="149 1845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1847">
    <literal><![CDATA[
      x * (L(x,y,y) \ 1) = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1245,a,b,1845,a),flip(a)].">
      <j1 rule="hyper" parents="35 1245 1845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1848">
    <literal><![CDATA[
      x \ (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1845(a,1),69(a,1,2,2))].">
      <j1 rule="para" parents="1845 69"/>
    </justification>
  </clause>

  <clause id="1849">
    <literal><![CDATA[
      T(x,y) * (L(x,z,u) \ 1) = L(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(1845(a,1),1482(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1845 1482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1850">
    <literal><![CDATA[
      L(x,y,z) * (L(x,u,w) \ 1) = L(x,u,w) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1845(a,1),1800(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1845 1800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1851">
    <literal><![CDATA[
      L(x,y,y) \ 1 = x \ a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(149,a,1847,a),flip(a)].">
      <j1 rule="hyper" parents="149 1847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1852">
    <literal><![CDATA[
      a(x,x,x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[para(822(a,1),1847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="822 1847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1853">
    <literal><![CDATA[
      K(x,x \ 1) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1724,a,b,1852,a)].">
      <j1 rule="hyper" parents="373 1724 1852"/>
    </justification>
  </clause>

  <clause id="1854">
    <literal><![CDATA[
      a(x,x,x) / x = x / (x * x)
    ]]></literal>
    <justification jstring="[hyper(142,a,1852,a,b,811,a)].">
      <j1 rule="hyper" parents="142 1852 811"/>
    </justification>
  </clause>

  <clause id="1856">
    <literal><![CDATA[
      1 / (x \ a(y,y,x)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(226,a,1851,a)].">
      <j1 rule="hyper" parents="226 1851"/>
    </justification>
  </clause>

  <clause id="1857">
    <literal><![CDATA[
      (x \ 1) \ (((y * x) \ y) \ (x \ 1)) = L(x \ 1,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,437,a(flip),b,1846,a)].">
      <j1 rule="hyper" parents="139 437 1846"/>
    </justification>
  </clause>

  <clause id="1858">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((L(x,y,z) \ 1) * x) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1846(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1846 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1859">
    <literal><![CDATA[
      (x * y) \ (x * (L(y,z,u) \ y)) = L(L(y,z,u) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1846(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1846 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      L(x,y,z) \ x != x * u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ 1 = u
    ]]></literal>
    <justification jstring="[para(1846(a,1),44(a,1))].">
      <j1 rule="para" parents="1846 44"/>
    </justification>
  </clause>

  <clause id="1861">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,1 / x) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(1846(a,1),295(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1846 295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1862">
    <literal><![CDATA[
      T((1 / x) * (L(x,y,z) \ x),x) = (1 / x) * ((L(x,y,z) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1848(a,1),1019(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1848 1019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1863">
    <literal><![CDATA[
      (x \ 1) * L(x \ ((1 / x) \ y),z,u) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(1166(a,1),1805(a,1,2,1))].">
      <j1 rule="para" parents="1166 1805"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      (x \ (y \ x)) * x = (y * T(y \ 1,x)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1817(a,1,1,2))].">
      <j1 rule="para" parents="7 1817"/>
    </justification>
  </clause>

  <clause id="1865">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(269,a,1864,a(flip),b,354,a)].">
      <j1 rule="hyper" parents="269 1864 354"/>
    </justification>
  </clause>

  <clause id="1866">
    <literal><![CDATA[
      T(L(x,y,z) * T(L(x,y,z) \ 1,x),x * (L(x,y,z) \ 1)) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[para(1846(a,2),1865(a,1,2))].">
      <j1 rule="para" parents="1846 1865"/>
    </justification>
  </clause>

  <clause id="1867">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1818(a,2,1,1))].">
      <j1 rule="para" parents="7 1818"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(82(a,1),1867(a,1,2,1))].">
      <j1 rule="para" parents="82 1867"/>
    </justification>
  </clause>

  <clause id="1870">
    <literal><![CDATA[
      L(((x \ 1) * y) \ z,x * y,x) = L(y,x,x) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,1820,a),flip(a)].">
      <j1 rule="hyper" parents="139 168 1820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1871">
    <literal><![CDATA[
      x \ (L(y,x * z,x) * L(z,x,x)) = ((x \ 1) * z) * T(y,L(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(139,a,266,a(flip),b,1820,a(flip))].">
      <j1 rule="hyper" parents="139 266 1820"/>
    </justification>
  </clause>

  <clause id="1872">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ 1) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(71(a,1),1836(a,1,1)),flip(a)].">
      <j1 rule="para" parents="71 1836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1873">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * (x \ 1) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(241(a,1),1872(a,1,1,2))].">
      <j1 rule="para" parents="241 1872"/>
    </justification>
  </clause>

  <clause id="1874">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ L(x \ 1,x,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(149,a,1873,a)].">
      <j1 rule="hyper" parents="149 1873"/>
    </justification>
  </clause>

  <clause id="1875">
    <literal><![CDATA[
      ((x * y) \ x) / (y \ 1) = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(142,a,241,a(flip),b,1873,a)].">
      <j1 rule="hyper" parents="142 241 1873"/>
    </justification>
  </clause>

  <clause id="1876">
    <literal><![CDATA[
      L(x \ 1,x,y) \ ((x \ 1) * (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(1873(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1873 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1877">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ L((x \ y) \ 1,x \ y,x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),1874(a,1,1,2,1))].">
      <j1 rule="para" parents="10 1874"/>
    </justification>
  </clause>

  <clause id="1878">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (x \ 1) = x \ R(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(1795(a,1),1843(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1795 1843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1879">
    <literal><![CDATA[
      R(x,y,z) * (L(x,u,w) \ 1) = L(x,u,w) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1845(a,1),1843(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1845 1843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1880">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,u,w) \ x)) = L(x,u,w) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1848(a,2),1850(a,1,2))].">
      <j1 rule="para" parents="1848 1850"/>
    </justification>
  </clause>

  <clause id="1881">
    <literal><![CDATA[
      R(x,y,z) * (x \ a(u,u,x)) = L(x,u,u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1851(a,1),1879(a,1,2))].">
      <j1 rule="para" parents="1851 1879"/>
    </justification>
  </clause>

  <clause id="1882">
    <literal><![CDATA[
      ((x * x) * ((y * z) * u)) / (z * u) = R((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),130(a,1,1))].">
      <j1 rule="para" parents="33 130"/>
    </justification>
  </clause>

  <clause id="1883">
    <literal><![CDATA[
      K(x \ (x / y),x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,969,a,b,749,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 969 749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1884">
    <literal><![CDATA[
      K(x \ (x / (1 / y)),x) = T(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,1509,a(flip),b,1883,a),flip(a)].">
      <j1 rule="hyper" parents="373 1509 1883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1885">
    <literal><![CDATA[
      K(x \ (x / (y \ 1)),x) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1484,a(flip),b,1883,a),flip(a)].">
      <j1 rule="hyper" parents="373 1484 1883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1886">
    <literal><![CDATA[
      T(x,y) = K(y \ (y / (1 / x)),y) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,1883,a,b,1509,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 1883 1509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1887">
    <literal><![CDATA[
      K(x \ (x / y),x) / y = T(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,1883,a,b,525,a)].">
      <j1 rule="hyper" parents="142 1883 525"/>
    </justification>
  </clause>

  <clause id="1888">
    <literal><![CDATA[
      K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(448(a,1),1883(a,1,1))].">
      <j1 rule="para" parents="448 1883"/>
    </justification>
  </clause>

  <clause id="1889">
    <literal><![CDATA[
      K(T(1 / x,T(x,y)),T(x,y)) = x * T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1512(a,1),1883(a,1,1))].">
      <j1 rule="para" parents="1512 1883"/>
    </justification>
  </clause>

  <clause id="1890">
    <literal><![CDATA[
      K(x \ (x / (1 / (y / (x * y)))),x) = R(x \ 1,x,y) / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(854(a,1),1884(a,2,1))].">
      <j1 rule="para" parents="854 1884"/>
    </justification>
  </clause>

  <clause id="1891">
    <literal><![CDATA[
      K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[para(255(a,1),1885(a,2,2))].">
      <j1 rule="para" parents="255 1885"/>
    </justification>
  </clause>

  <clause id="1892">
    <literal><![CDATA[
      K((x * y) \ x,x * y) / y = T(1 / y,x * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),1887(a,1,1,1,2))].">
      <j1 rule="para" parents="11 1887"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      T((x * y) / x,K(x \ (x / (((x * y) / x) \ 1)),x)) != z
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(1891(a,2),478(a,1,2))].">
      <j1 rule="para" parents="1891 478"/>
    </justification>
  </clause>

  <clause id="1894">
    <literal><![CDATA[
      K((x / y) \ ((x / y) / (T(x / (x / y),z) \ 1)),x / y) = (((x / y) * T(y,z)) / (x / y)) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(911(a,1),1891(a,1,1,2,2,1))].">
      <j1 rule="para" parents="911 1891"/>
    </justification>
  </clause>

  <clause id="1895">
    <literal><![CDATA[
      ((x * x) \ (y * z)) * L(u,z,y) = ((x * x) \ y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,484,a(flip),b,800,a),flip(a)].">
      <j1 rule="hyper" parents="373 484 800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1896">
    <literal><![CDATA[
      x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,514,a(flip),b,847,a)].">
      <j1 rule="hyper" parents="64 514 847"/>
    </justification>
  </clause>

  <clause id="1897">
    <literal><![CDATA[
      R(x,y,z) * (x * u) = x * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(267(a,1),1896(a,1,2)),flip(a)].">
      <j1 rule="para" parents="267 1896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(759,a,1897,a)].">
      <j1 rule="hyper" parents="759 1897"/>
    </justification>
  </clause>

  <clause id="1899">
    <literal><![CDATA[
      R(x,y,z) * (x \ (R(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(757,a,1897,a),flip(a)].">
      <j1 rule="hyper" parents="757 1897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1900">
    <literal><![CDATA[
      x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(737,a,1897,a),flip(a)].">
      <j1 rule="hyper" parents="737 1897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1901">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(x,y,z) * (x \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(728,a,1897,a)].">
      <j1 rule="hyper" parents="728 1897"/>
    </justification>
  </clause>

  <clause id="1902">
    <literal><![CDATA[
      x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(397,a,1897,a),flip(a)].">
      <j1 rule="hyper" parents="397 1897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1903">
    <literal><![CDATA[
      x * (R(x,x,y) * y) = (x * x) * y
    ]]></literal>
    <justification jstring="[hyper(327,a,1897,a),flip(a)].">
      <j1 rule="hyper" parents="327 1897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1904">
    <literal><![CDATA[
      (x * (R(x,y,z) * u)) / (x * u) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(154,a,1897,a)].">
      <j1 rule="hyper" parents="154 1897"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      R(x,y,z) \ (x * (R(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(149,a,1897,a)].">
      <j1 rule="hyper" parents="149 1897"/>
    </justification>
  </clause>

  <clause id="1906">
    <literal><![CDATA[
      (x * y) / (x * (R(x,z,u) \ y)) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(142,a,168,a(flip),b,1897,a)].">
      <j1 rule="hyper" parents="142 168 1897"/>
    </justification>
  </clause>

  <clause id="1907">
    <literal><![CDATA[
      R(x,y,z) \ (x * u) = x * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,1897,a)].">
      <j1 rule="hyper" parents="139 168 1897"/>
    </justification>
  </clause>

  <clause id="1908">
    <literal><![CDATA[
      x * (R(x,y,z) \ (x \ u)) = R(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(139,a,75,a(flip),b,1897,a),flip(a)].">
      <j1 rule="hyper" parents="139 75 1897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1909">
    <literal><![CDATA[
      x * (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,72,a(flip),b,1897,a),flip(a)].">
      <j1 rule="hyper" parents="139 72 1897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1910">
    <literal><![CDATA[
      (R(x,y,z) * (x \ u)) \ (R(x,y,z) * u) = T(x,R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(493,a,168,a(flip),b,1897,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="493 168 1897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1911">
    <literal><![CDATA[
      (R(x,y,z) * x) \ (x * (R(x,y,z) * u)) = L(u,x,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,1897,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="139 1897 100"/>
    </justification>
  </clause>

  <clause id="1912">
    <literal><![CDATA[
      x * (R(x,y,z) * ((x \ 1) * u)) = R(x,y,z) * L(u,x,x)
    ]]></literal>
    <justification jstring="[para(1139(a,1),1897(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1139 1897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1913">
    <literal><![CDATA[
      R(x,x,y) * y = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,538,a,b,1903,a),flip(a)].">
      <j1 rule="hyper" parents="35 538 1903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1914">
    <literal><![CDATA[
      x * R(T(y,x),y,x) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,267,a,b,1913,a)].">
      <j1 rule="hyper" parents="64 267 1913"/>
    </justification>
  </clause>

  <clause id="1915">
    <literal><![CDATA[
      R(x,x,y) * (z \ (z * y)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,169,a,b,1913,a)].">
      <j1 rule="hyper" parents="64 169 1913"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      ((1 / x) \ y) * L(z,y,R(x,x,y)) = R(x,x,y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,1913,a(flip),b,213,a)].">
      <j1 rule="hyper" parents="144 1913 213"/>
    </justification>
  </clause>

  <clause id="1917">
    <literal><![CDATA[
      R(T(x,y),x,y) = y \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,1913,a(flip),b,267,a),flip(a)].">
      <j1 rule="hyper" parents="139 1913 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1918">
    <literal><![CDATA[
      (x * R(y,y,z)) \ (x * ((1 / y) \ z)) = L(z,R(y,y,z),x)
    ]]></literal>
    <justification jstring="[para(1913(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1913 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1919">
    <literal><![CDATA[
      L(R(x,L(x,y,z),u),y,z) * u = (1 / L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(29(a,1),1913(a,1,1))].">
      <j1 rule="para" parents="29 1913"/>
    </justification>
  </clause>

  <clause id="1920">
    <literal><![CDATA[
      (R(x,x,y) * R(x,x,y)) * (y / ((1 / x) \ y)) = R(R(x,x,y),R(x,x,y),y)
    ]]></literal>
    <justification jstring="[para(1913(a,1),944(a,1,2,2))].">
      <j1 rule="para" parents="1913 944"/>
    </justification>
  </clause>

  <clause id="1921">
    <literal><![CDATA[
      R(T(x \ 1,y),x \ 1,y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,207,a(flip),b,1914,a),flip(a)].">
      <j1 rule="hyper" parents="139 207 1914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1922">
    <literal><![CDATA[
      x \ R(T(y,z),y,z) = x \ (z \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[hyper(139,a,1917,a,b,10,a)].">
      <j1 rule="hyper" parents="139 1917 10"/>
    </justification>
  </clause>

  <clause id="1923">
    <literal><![CDATA[
      R(T(x,y),x,y) \ z = (y \ ((1 / x) \ y)) \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,1917,a)].">
      <j1 rule="hyper" parents="62 1917"/>
    </justification>
  </clause>

  <clause id="1924">
    <literal><![CDATA[
      R(R(T(x,y),z,u),R(x,z,u),y) = y \ ((1 / R(x,z,u)) \ y)
    ]]></literal>
    <justification jstring="[para(27(a,2),1917(a,1,1))].">
      <j1 rule="para" parents="27 1917"/>
    </justification>
  </clause>

  <clause id="1925">
    <literal><![CDATA[
      L(R(x,y,z) \ 1,x,1 / x) = (1 / x) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(1909(a,1),295(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1909 295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1926">
    <literal><![CDATA[
      R(x,y,z) \ T(R(x,y,z) * (R(x,y,z) \ x),u) = T(x,u) * (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1909(a,1),1482(a,1,2,1,2))].">
      <j1 rule="para" parents="1909 1482"/>
    </justification>
  </clause>

  <clause id="1927">
    <literal><![CDATA[
      T(x \ 1,y \ (x \ y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1921(a,1),237(a,1,2))].">
      <j1 rule="para" parents="1921 237"/>
    </justification>
  </clause>

  <clause id="1928">
    <literal><![CDATA[
      (x \ (y \ x)) * (y \ 1) = (y \ 1) * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(145,a,1927,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 1927 22"/>
    </justification>
  </clause>

  <clause id="1929">
    <literal><![CDATA[
      x \ (R(x,y,z) \ (x * u)) = R(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(731,a,1898,a),flip(a)].">
      <j1 rule="hyper" parents="731 1898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1930">
    <literal><![CDATA[
      R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(111(a,1),1898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="111 1898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1931">
    <literal><![CDATA[
      x \ (y * R(T(x,y),z,u)) = R(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(267(a,2),1898(a,1,2))].">
      <j1 rule="para" parents="267 1898"/>
    </justification>
  </clause>

  <clause id="1932">
    <literal><![CDATA[
      R(x,y,y \ z) * (x \ z) = x \ ((x * y) * (y \ z))
    ]]></literal>
    <justification jstring="[para(421(a,1),1898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="421 1898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1933">
    <literal><![CDATA[
      R(x,x,y) * (x \ y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(1913(a,1),1898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1913 1898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1934">
    <literal><![CDATA[
      R(x,x,y) * (x \ y) = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1166,a,b,1933,a),flip(a)].">
      <j1 rule="hyper" parents="373 1166 1933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1935">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ y,x,y) = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,845,a,b,1934,a)].">
      <j1 rule="hyper" parents="64 845 1934"/>
    </justification>
  </clause>

  <clause id="1936">
    <literal><![CDATA[
      x \ (R(x,y,z) \ ((x * x) * u)) = R(x,y,z) \ ((1 / x) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,539,a(flip),b,1899,a),flip(a)].">
      <j1 rule="hyper" parents="139 539 1899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1937">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(1901(a,1),305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1901 305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1938">
    <literal><![CDATA[
      x * (R(x,y,L(z,y,x)) \ (y * z)) = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,604,a,b,1906,a),flip(a)].">
      <j1 rule="hyper" parents="37 604 1906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1939">
    <literal><![CDATA[
      R(x,y,z) = (x \ ((x * y) * z)) / (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(154,a,1930,a),flip(a)].">
      <j1 rule="hyper" parents="154 1930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1940">
    <literal><![CDATA[
      R(x,y,x) * T(y,x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(269,a,111,a(flip),b,1900,a),flip(a)].">
      <j1 rule="hyper" parents="269 111 1900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1941">
    <literal><![CDATA[
      R(x,y,x) \ T(x * y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(149,a,1940,a)].">
      <j1 rule="hyper" parents="149 1940"/>
    </justification>
  </clause>

  <clause id="1942">
    <literal><![CDATA[
      x \ T(y * z,y) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) = x
    ]]></literal>
    <justification jstring="[para(1940(a,1),159(a,1,2))].">
      <j1 rule="para" parents="1940 159"/>
    </justification>
  </clause>

  <clause id="1943">
    <literal><![CDATA[
      K(x \ (y \ x),y \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,1928,a(flip),b,94,a),flip(a)].">
      <j1 rule="hyper" parents="138 1928 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1944">
    <literal><![CDATA[
      K((x * y) \ y,x \ 1) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),1943(a,1,1,2))].">
      <j1 rule="para" parents="9 1943"/>
    </justification>
  </clause>

  <clause id="1945">
    <literal><![CDATA[
      T((x * y) \ y,x \ 1) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(57,a,1944,a)].">
      <j1 rule="hyper" parents="57 1944"/>
    </justification>
  </clause>

  <clause id="1946">
    <literal><![CDATA[
      ((x * y) \ y) * (x \ 1) = (x \ 1) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,1945,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 1945 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1947">
    <literal><![CDATA[
      x \ ((x * (x \ y)) * ((x \ y) \ z)) = ((y * ((x \ y) \ z)) / z) * (x \ z)
    ]]></literal>
    <justification jstring="[para(973(a,1),1932(a,1,1)),flip(a)].">
      <j1 rule="para" parents="973 1932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1949">
    <literal><![CDATA[
      ((1 / (x * y)) * x) * y = a(x * y,x,y)
    ]]></literal>
    <justification jstring="[para(535(a,1),871(a,1,1))].">
      <j1 rule="para" parents="535 871"/>
    </justification>
  </clause>

  <clause id="1950">
    <literal><![CDATA[
      ((x * y) * z) * a(R(y,T(x,y),z),T(x,y),z) = (R(y,T(x,y),z) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(115(a,1),962(a,1,1,1))].">
      <j1 rule="para" parents="115 962"/>
    </justification>
  </clause>

  <clause id="1951">
    <literal><![CDATA[
      x * ((x \ y) * L((x \ y) \ 1,z,u)) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(436(a,1),963(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="436 963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1952">
    <literal><![CDATA[
      (x / y) * (y * R(y \ 1,z,u)) = x * R(x \ (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(443(a,1),968(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="443 968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1953">
    <literal><![CDATA[
      x * L(R(T(y,x),z,z \ x),u,w) = (L(y,u,w) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,835,a,b,976,a)].">
      <j1 rule="hyper" parents="64 835 976"/>
    </justification>
  </clause>

  <clause id="1954">
    <literal><![CDATA[
      (R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * y
    ]]></literal>
    <justification jstring="[para(678(a,1),978(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="678 978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1955">
    <literal><![CDATA[
      x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,1025,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 1025 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1956">
    <literal><![CDATA[
      x \ (y * R(y \ (x * z),u,w)) = (x \ y) * R((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(1025(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="1025 598"/>
    </justification>
  </clause>

  <clause id="1957">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(1026(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="1026 598"/>
    </justification>
  </clause>

  <clause id="1958">
    <literal><![CDATA[
      (x * y) * L(T(y,x),z,u) = (L(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,510,a(flip),b,1058,a),flip(a)].">
      <j1 rule="hyper" parents="64 510 1058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1959">
    <literal><![CDATA[
      (x * y) * R(T(y,x),z,u) = (R(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,506,a(flip),b,1059,a),flip(a)].">
      <j1 rule="hyper" parents="64 506 1059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1960">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) != u / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(1196(a,2),47(a,1))].">
      <j1 rule="para" parents="1196 47"/>
    </justification>
  </clause>

  <clause id="1961">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[para(241(a,1),1271(a,1,2,1,2))].">
      <j1 rule="para" parents="241 1271"/>
    </justification>
  </clause>

  <clause id="1962">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(102(a,1),1271(a,1,2,1,2))].">
      <j1 rule="para" parents="102 1271"/>
    </justification>
  </clause>

  <clause id="1963">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z))
    ]]></literal>
    <justification jstring="[para(346(a,1),1271(a,1,2,1,2))].">
      <j1 rule="para" parents="346 1271"/>
    </justification>
  </clause>

  <clause id="1964">
    <literal><![CDATA[
      (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1273,a(flip),b,103,a),flip(a)].">
      <j1 rule="hyper" parents="145 1273 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1965">
    <literal><![CDATA[
      (1 / x) \ ((y * ((1 / x) * z)) / y) = x * ((y * (x \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,1274,a(flip),b,295,a)].">
      <j1 rule="hyper" parents="139 1274 295"/>
    </justification>
  </clause>

  <clause id="1966">
    <literal><![CDATA[
      ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y
    ]]></literal>
    <justification jstring="[para(244(a,1),1276(a,1,1,1,2))].">
      <j1 rule="para" parents="244 1276"/>
    </justification>
  </clause>

  <clause id="1967">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = L(x,z \ y,z) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,964,a(flip),b,1287,a),flip(a)].">
      <j1 rule="hyper" parents="373 964 1287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1968">
    <literal><![CDATA[
      (L(x,y \ z,y) * z) \ (x * z) = a(y,y \ z,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(215,a,1967,a)].">
      <j1 rule="hyper" parents="215 1967"/>
    </justification>
  </clause>

  <clause id="1969">
    <literal><![CDATA[
      (x * x) * ((R((x * x) \ x,y,z) * u) * w) = ((x * (x * R(x \ 1,y,z))) * u) * w
    ]]></literal>
    <justification jstring="[para(445(a,2),1314(a,1,2,1,1))].">
      <j1 rule="para" parents="445 1314"/>
    </justification>
  </clause>

  <clause id="1970">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * z),u) = y * (T(x,y) * T(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,1315,a(flip),b,261,a)].">
      <j1 rule="hyper" parents="145 1315 261"/>
    </justification>
  </clause>

  <clause id="1971">
    <literal><![CDATA[
      R(T(x / y,z * y),y,T(z,y)) = (z * y) \ (x * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,1319,a)].">
      <j1 rule="hyper" parents="64 27 1319"/>
    </justification>
  </clause>

  <clause id="1972">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1508(a,1),1369(a,1))].">
      <j1 rule="para" parents="1508 1369"/>
    </justification>
  </clause>

  <clause id="1973">
    <literal><![CDATA[
      (R(x / y,y,y) \ z) \ (y * u) = ((x * y) \ z) \ ((1 / y) * u)
    ]]></literal>
    <justification jstring="[para(535(a,1),1374(a,1,2)),flip(a)].">
      <j1 rule="para" parents="535 1374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1974">
    <literal><![CDATA[
      ((x * y) * K(y,y \ 1)) \ (R(x,y,y) * y) = a(x * y,y,1 / y)
    ]]></literal>
    <justification jstring="[para(812(a,1),1730(a,1,2))].">
      <j1 rule="para" parents="812 1730"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      ((1 / x) * y) * ((x \ y) \ 1) = (x \ y) \ ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(569(a,1),1811(a,1,2)),flip(a)].">
      <j1 rule="para" parents="569 1811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1976">
    <literal><![CDATA[
      ((1 / x) \ 1) * ((1 / x) \ ((x \ y) \ ((1 / x) * y))) = (((1 / x) \ 1) * y) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1975(a,1),1596(a,1,2,2))].">
      <j1 rule="para" parents="1975 1596"/>
    </justification>
  </clause>

  <clause id="1977">
    <literal><![CDATA[
      (x * x) * (((y * z) * u) / (z * u)) = R((x * x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,807,a(flip),b,1882,a)].">
      <j1 rule="hyper" parents="64 807 1882"/>
    </justification>
  </clause>

  <clause id="1978">
    <literal><![CDATA[
      ((x * x) \ ((y * y) * z)) * u = ((x * x) \ (y * y)) * (z * u)
    ]]></literal>
    <justification jstring="[para(594(a,1),1895(a,1,2))].">
      <j1 rule="para" parents="594 1895"/>
    </justification>
  </clause>

  <clause id="1979">
    <literal><![CDATA[
      (((x * x) \ y) * z) * L(u,z,y) = ((x * x) \ y) * (z * u)
    ]]></literal>
    <justification jstring="[para(484(a,1),1895(a,1,1))].">
      <j1 rule="para" parents="484 1895"/>
    </justification>
  </clause>

  <clause id="1980">
    <literal><![CDATA[
      R(T((x * y) / x,y * x),x,T(y,x)) = (y * x) \ ((y * x) * y)
    ]]></literal>
    <justification jstring="[para(1296(a,1),1971(a,2,2))].">
      <j1 rule="para" parents="1296 1971"/>
    </justification>
  </clause>

  <clause id="1981">
    <literal><![CDATA[
      R((x * x) * y,z,u) = (x * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(20(a,2),1977(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 1977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1982">
    <literal><![CDATA[
      x \ R((x * x) * y,z,u) = (1 / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,1981,a,b,538,a)].">
      <j1 rule="hyper" parents="139 1981 538"/>
    </justification>
  </clause>

  <clause id="1983">
    <literal><![CDATA[
      (x * x) * R(T(y,x * x),z,u) = R(y * (x * x),z,u)
    ]]></literal>
    <justification jstring="[para(115(a,1),1981(a,1,1)),flip(a)].">
      <j1 rule="para" parents="115 1981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1984">
    <literal><![CDATA[
      (1 / x) \ R((x * x) \ y,z,u) = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1982(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1985">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(245(a,1),1982(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="245 1982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1986">
    <literal><![CDATA[
      x \ R(x,x,y) = (y / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,1786,a(flip),b,1985,a),flip(a)].">
      <j1 rule="hyper" parents="64 1786 1985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1987">
    <literal><![CDATA[
      x * R(x \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1781,a(flip),b,1985,a)].">
      <j1 rule="hyper" parents="64 1781 1985"/>
    </justification>
  </clause>

  <clause id="1988">
    <literal><![CDATA[
      x * (x * R(x \ 1,y,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1781,a(flip),b,1985,a(flip))].">
      <j1 rule="hyper" parents="145 1781 1985"/>
    </justification>
  </clause>

  <clause id="1989">
    <literal><![CDATA[
      (x / (y * x)) \ (y \ R(y,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(139,a,1985,a(flip),b,1786,a(flip))].">
      <j1 rule="hyper" parents="139 1985 1786"/>
    </justification>
  </clause>

  <clause id="1990">
    <literal><![CDATA[
      x \ (x \ R(x,y,z)) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,1985,a(flip),b,1781,a(flip))].">
      <j1 rule="hyper" parents="139 1985 1781"/>
    </justification>
  </clause>

  <clause id="1991">
    <literal><![CDATA[
      R(x,x,y) = y / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(39,a,1842,a,b,1986,a),flip(a)].">
      <j1 rule="hyper" parents="39 1842 1986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1992">
    <literal><![CDATA[
      x \ R(x,x,x \ y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),1986(a,2,1,2))].">
      <j1 rule="para" parents="10 1986"/>
    </justification>
  </clause>

  <clause id="1993">
    <literal><![CDATA[
      R(T(x / (y * x),z),y,y \ z) = z \ ((y \ R(y,y,x)) * (y \ z))
    ]]></literal>
    <justification jstring="[para(1986(a,2),996(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1986 996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1994">
    <literal><![CDATA[
      R(x,x \ 1,y) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,239,a,b,1991,a)].">
      <j1 rule="hyper" parents="373 239 1991"/>
    </justification>
  </clause>

  <clause id="1995">
    <literal><![CDATA[
      ((x \ y) / y) * ((1 / x) \ x) = R(x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1591,a(flip),b,1991,a)].">
      <j1 rule="hyper" parents="373 1591 1991"/>
    </justification>
  </clause>

  <clause id="1996">
    <literal><![CDATA[
      R(x,x,y) * ((x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[hyper(144,a,1991,a,b,xx)].">
      <j1 rule="hyper" parents="144 1991"/>
    </justification>
  </clause>

  <clause id="1997">
    <literal><![CDATA[
      R(x,x,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(143,a,1991,a,b,171,a)].">
      <j1 rule="hyper" parents="143 1991 171"/>
    </justification>
  </clause>

  <clause id="1998">
    <literal><![CDATA[
      R(x,x,(x \ 1) \ y) * y = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(1991(a,2),385(a,1,1))].">
      <j1 rule="para" parents="1991 385"/>
    </justification>
  </clause>

  <clause id="1999">
    <literal><![CDATA[
      (x / ((y \ 1) * x)) * x = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(1991(a,1),1913(a,1,1))].">
      <j1 rule="para" parents="1991 1913"/>
    </justification>
  </clause>

  <clause id="2000">
    <literal><![CDATA[
      R(x,x \ 1,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,1417,a,b,1994,a),flip(a)].">
      <j1 rule="hyper" parents="373 1417 1994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2001">
    <literal><![CDATA[
      R(x,x,y) * L(y,x,x) = x * y
    ]]></literal>
    <justification jstring="[para(1996(a,1),1912(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1996 1912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2003">
    <literal><![CDATA[
      T(x,(x \ 1) * x) = x
    ]]></literal>
    <justification jstring="[hyper(1062,a,2000,a)].">
      <j1 rule="hyper" parents="1062 2000"/>
    </justification>
  </clause>

  <clause id="2004">
    <literal><![CDATA[
      T(x,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[para(294(a,2),2003(a,1,2))].">
      <j1 rule="para" parents="294 2003"/>
    </justification>
  </clause>

  <clause id="2005">
    <literal><![CDATA[
      R(x,x,x \ y) \ y = L(x \ y,x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,2001,a)].">
      <j1 rule="hyper" parents="139 10 2001"/>
    </justification>
  </clause>

  <clause id="2006">
    <literal><![CDATA[
      R(x,x,y) \ (x * (x * y)) = x * L(y,x,x)
    ]]></literal>
    <justification jstring="[para(2001(a,1),1905(a,1,2,2))].">
      <j1 rule="para" parents="2001 1905"/>
    </justification>
  </clause>

  <clause id="2007">
    <literal><![CDATA[
      R(1 / x,y,z) * x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,843,a,b,1987,a)].">
      <j1 rule="hyper" parents="64 843 1987"/>
    </justification>
  </clause>

  <clause id="2008">
    <literal><![CDATA[
      (x / y) * ((y * y) * R((x / (1 / y)) \ 1,z,u)) = (x / (1 / y)) \ R(x / (1 / y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,819,a,b,1987,a)].">
      <j1 rule="hyper" parents="64 819 1987"/>
    </justification>
  </clause>

  <clause id="2009">
    <literal><![CDATA[
      (x \ 1) \ R(x \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1793,a(flip),b,1987,a),flip(a)].">
      <j1 rule="hyper" parents="64 1793 1987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2010">
    <literal><![CDATA[
      x * (R(x,y,z) * R(x \ 1,u,w)) = R(x,y,z) * (x \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,1987,a(flip),b,1905,a),flip(a)].">
      <j1 rule="hyper" parents="145 1987 1905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2011">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(u,R(x \ 1,y,z),x) = x * (R(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,1987,a(flip),b,213,a)].">
      <j1 rule="hyper" parents="144 1987 213"/>
    </justification>
  </clause>

  <clause id="2012">
    <literal><![CDATA[
      R(x \ 1,x \ y,(x \ y) \ 1) = x \ (x \ (y * ((x \ y) \ 1)))
    ]]></literal>
    <justification jstring="[para(701(a,1),1990(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="701 1990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2013">
    <literal><![CDATA[
      x / (((y \ 1) \ 1) * x) = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,207,a(flip),b,1999,a),flip(a)].">
      <j1 rule="hyper" parents="142 207 1999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2014">
    <literal><![CDATA[
      (1 / (1 / x)) \ y = (y / (x * y)) * y
    ]]></literal>
    <justification jstring="[para(82(a,1),1999(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 1999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2015">
    <literal><![CDATA[
      (1 / (1 / (x / y))) \ y = (y / x) * y
    ]]></literal>
    <justification jstring="[para(223(a,1),1999(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="223 1999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2016">
    <literal><![CDATA[
      R(x,x,x \ y) \ y = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,569,a(flip),b,2005,a),flip(a)].">
      <j1 rule="hyper" parents="373 569 2005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2017">
    <literal><![CDATA[
      R(x,x,x \ y) = y / ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(225,a,569,a(flip),b,2005,a),flip(a)].">
      <j1 rule="hyper" parents="225 569 2005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2018">
    <literal><![CDATA[
      R(x,x,x \ 1) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(225,a,434,a(flip),b,2005,a),flip(a)].">
      <j1 rule="hyper" parents="225 434 2005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2020">
    <literal><![CDATA[
      (x * x) * ((x \ 1) * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(2018(a,1),702(a,2,1))].">
      <j1 rule="para" parents="2018 702"/>
    </justification>
  </clause>

  <clause id="2021">
    <literal><![CDATA[
      R(x,y,y) * (1 / (1 / y)) = R(x * y,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2018(a,1),1790(a,1,2))].">
      <j1 rule="para" parents="2018 1790"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      (x / (y \ 1)) * ((y * y) \ z) = (x / (1 / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(2018(a,1),1465(a,2,1,2))].">
      <j1 rule="para" parents="2018 1465"/>
    </justification>
  </clause>

  <clause id="2024">
    <literal><![CDATA[
      L(x,x,x) \ y = (y / (x * y)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,823,a,b,2014,a)].">
      <j1 rule="hyper" parents="64 823 2014"/>
    </justification>
  </clause>

  <clause id="2025">
    <literal><![CDATA[
      (L(x,x,x) \ y) / y = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,2024,a,b,451,a)].">
      <j1 rule="hyper" parents="142 2024 451"/>
    </justification>
  </clause>

  <clause id="2026">
    <literal><![CDATA[
      1 / (1 / (x / y)) = y / ((y / x) * y)
    ]]></literal>
    <justification jstring="[hyper(226,a,2015,a),flip(a)].">
      <j1 rule="hyper" parents="226 2015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2027">
    <literal><![CDATA[
      1 / (1 / ((x \ y) / y)) = y / (x * y)
    ]]></literal>
    <justification jstring="[hyper(225,a,209,a(flip),b,2015,a),flip(a)].">
      <j1 rule="hyper" parents="225 209 2015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      (x / ((x / y) * x)) \ 1 = 1 / (y / x)
    ]]></literal>
    <justification jstring="[hyper(215,a,2026,a)].">
      <j1 rule="hyper" parents="215 2026"/>
    </justification>
  </clause>

  <clause id="2029">
    <literal><![CDATA[
      1 / (1 / (1 / x)) = x / (x * x)
    ]]></literal>
    <justification jstring="[para(77(a,1),2026(a,2,2,1))].">
      <j1 rule="para" parents="77 2026"/>
    </justification>
  </clause>

  <clause id="2030">
    <literal><![CDATA[
      (1 / (1 / (1 / x))) * y = x * ((x * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(144,a,2029,a,b,896,a)].">
      <j1 rule="hyper" parents="144 2029 896"/>
    </justification>
  </clause>

  <clause id="2031">
    <literal><![CDATA[
      (1 / (1 / (1 / x))) \ y = (x * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(2029(a,2),890(a,1,1))].">
      <j1 rule="para" parents="2029 890"/>
    </justification>
  </clause>

  <clause id="2032">
    <literal><![CDATA[
      1 / ((x \ y) / y) = (y / (x * y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,2027,a),flip(a)].">
      <j1 rule="hyper" parents="215 2027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2033">
    <literal><![CDATA[
      ((x / (y * x)) \ 1) \ 1 = (y \ x) / x
    ]]></literal>
    <justification jstring="[para(2027(a,1),224(a,1,1,1))].">
      <j1 rule="para" parents="2027 224"/>
    </justification>
  </clause>

  <clause id="2034">
    <literal><![CDATA[
      (x / (((y \ z) / z) * x)) * x = (z / (y * z)) \ x
    ]]></literal>
    <justification jstring="[para(2027(a,1),2014(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2027 2014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2035">
    <literal><![CDATA[
      (1 / (1 / ((x \ y) / y))) * y = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(2027(a,2),2014(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2027 2014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2036">
    <literal><![CDATA[
      ((1 * x) / ((x / y) * x)) \ 1 = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(172(a,2),2028(a,1,1))].">
      <j1 rule="para" parents="172 2028"/>
    </justification>
  </clause>

  <clause id="2037">
    <literal><![CDATA[
      ((x / y) \ 1) \ 1 = ((y / x) \ x) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),2033(a,1,1,1,2))].">
      <j1 rule="para" parents="12 2033"/>
    </justification>
  </clause>

  <clause id="2038">
    <literal><![CDATA[
      (1 / (x / (y * x))) \ (x / (y * x)) = (x / (y * x)) * ((y \ x) / x)
    ]]></literal>
    <justification jstring="[para(2033(a,1),1134(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2033 1134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2039">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) / y = (((x \ y) / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2013(a,1),2033(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2013 2033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2040">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) * x = (y / x) \ x
    ]]></literal>
    <justification jstring="[hyper(144,a,2037,a,b,xx)].">
      <j1 rule="hyper" parents="144 2037"/>
    </justification>
  </clause>

  <clause id="2041">
    <literal><![CDATA[
      (((x \ y) / y) \ y) / y = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),2037(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 2037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2042">
    <literal><![CDATA[
      R(x,x,L(y,x,x)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,651,a,b,2006,a)].">
      <j1 rule="hyper" parents="40 651 2006"/>
    </justification>
  </clause>

  <clause id="2043">
    <literal><![CDATA[
      R(x,x,(x \ 1) \ y) = R(x,x,x * y)
    ]]></literal>
    <justification jstring="[para(1137(a,1),2042(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1137 2042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2044">
    <literal><![CDATA[
      R(x,x,x * y) * y = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(2043(a,1),1998(a,1,1))].">
      <j1 rule="para" parents="2043 1998"/>
    </justification>
  </clause>

  <clause id="2045">
    <literal><![CDATA[
      R(R(x,(x \ 1) \ 1,((x \ 1) \ 1) * y),x,x) * y = (((x \ 1) \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(1424(a,2),2044(a,1,1))].">
      <j1 rule="para" parents="1424 2044"/>
    </justification>
  </clause>

  <clause id="2046">
    <literal><![CDATA[
      (x \ 1) \ R(x \ 1,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1987,a,b,2009,a),flip(a)].">
      <j1 rule="hyper" parents="373 1987 2009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2047">
    <literal><![CDATA[
      (x \ 1) * (x * R(x \ 1,y,z)) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1987,a,b,2009,a)].">
      <j1 rule="hyper" parents="145 1987 2009"/>
    </justification>
  </clause>

  <clause id="2049">
    <literal><![CDATA[
      ((1 / x) * y) \ ((x \ 1) * z) = (x * y) \ ((1 / (1 / x)) * z)
    ]]></literal>
    <justification jstring="[para(2020(a,1),941(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2020 941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2050">
    <literal><![CDATA[
      (x * x) \ (y \ ((1 / (1 / x)) * z)) = T(y,x * x) \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2020(a,1),1458(a,1,2,2))].">
      <j1 rule="para" parents="2020 1458"/>
    </justification>
  </clause>

  <clause id="2051">
    <literal><![CDATA[
      R((x * x) \ y,z,u) = (x * x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,540,a,b,1984,a),flip(a)].">
      <j1 rule="hyper" parents="39 540 1984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2052">
    <literal><![CDATA[
      R((x * x) \ T(x,y),x,x \ y) = T(y,x * x) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1530,a(flip),b,2051,a),flip(a)].">
      <j1 rule="hyper" parents="373 1530 2051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2053">
    <literal><![CDATA[
      R((x * x) \ y,z,u) / w = (x * x) \ (R(y,z,u) / w)
    ]]></literal>
    <justification jstring="[hyper(142,a,2051,a,b,801,a)].">
      <j1 rule="hyper" parents="142 2051 801"/>
    </justification>
  </clause>

  <clause id="2054">
    <literal><![CDATA[
      R((x * x) \ y,z,u) * (R(y,z,u) \ w) = (x * x) \ w
    ]]></literal>
    <justification jstring="[para(2051(a,2),802(a,1,1))].">
      <j1 rule="para" parents="2051 802"/>
    </justification>
  </clause>

  <clause id="2055">
    <literal><![CDATA[
      R((x * x) \ y,z,u) \ w = R(y,z,u) \ ((x * x) * w)
    ]]></literal>
    <justification jstring="[para(2051(a,2),804(a,1,1))].">
      <j1 rule="para" parents="2051 804"/>
    </justification>
  </clause>

  <clause id="2056">
    <literal><![CDATA[
      T(x,R(x \ 1,y,z)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(269,a,2046,a(flip),b,1794,a)].">
      <j1 rule="hyper" parents="269 2046 1794"/>
    </justification>
  </clause>

  <clause id="2057">
    <literal><![CDATA[
      T(1 / x,R((1 / x) \ 1,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,219,a(flip),b,2056,a),flip(a)].">
      <j1 rule="hyper" parents="373 219 2056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      T(1 / x,R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),2057(a,1,2,1))].">
      <j1 rule="para" parents="82 2057"/>
    </justification>
  </clause>

  <clause id="2059">
    <literal><![CDATA[
      x * T(x \ 1,R((1 / x) \ 1,y,z)) = (1 / x) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2057(a,1),1007(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2057 1007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2060">
    <literal><![CDATA[
      T(1 / (1 / x),R(1 / x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,82,a(flip),b,2058,a),flip(a)].">
      <j1 rule="hyper" parents="373 82 2058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2061">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = (1 / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,2058,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 2058 22"/>
    </justification>
  </clause>

  <clause id="2062">
    <literal><![CDATA[
      T(1 / (1 / x),y / (x * y)) = x
    ]]></literal>
    <justification jstring="[para(244(a,1),2060(a,1,2))].">
      <j1 rule="para" parents="244 2060"/>
    </justification>
  </clause>

  <clause id="2063">
    <literal><![CDATA[
      T(1 / (1 / (x / y)),y / x) = x / y
    ]]></literal>
    <justification jstring="[para(454(a,1),2060(a,1,2))].">
      <j1 rule="para" parents="454 2060"/>
    </justification>
  </clause>

  <clause id="2064">
    <literal><![CDATA[
      T(x,y / (x * y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2062(a,1),1348(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2062 1348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2065">
    <literal><![CDATA[
      (1 / (1 / (x / y))) * (y / x) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,2063,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 2063 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2066">
    <literal><![CDATA[
      (R(x,y,z) * (x \ 1)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,2061,a,b,1868,a(flip))].">
      <j1 rule="hyper" parents="144 2061 1868"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1794,a(flip),b,2061,a),flip(a)].">
      <j1 rule="hyper" parents="64 1794 2061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2069">
    <literal><![CDATA[
      (x \ R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1794(a,1),2066(a,1,1))].">
      <j1 rule="para" parents="1794 2066"/>
    </justification>
  </clause>

  <clause id="2070">
    <literal><![CDATA[
      T(x,x \ R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(410,a,2069,a)].">
      <j1 rule="hyper" parents="410 2069"/>
    </justification>
  </clause>

  <clause id="2071">
    <literal><![CDATA[
      R(x,y,z) / x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(154,a,2069,a)].">
      <j1 rule="hyper" parents="154 2069"/>
    </justification>
  </clause>

  <clause id="2072">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(149,a,2069,a)].">
      <j1 rule="hyper" parents="149 2069"/>
    </justification>
  </clause>

  <clause id="2073">
    <literal><![CDATA[
      L(R(x,y,z),u,w) / L(x,u,w) = L(x,u,w) \ R(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,29,a(flip),b,2069,a)].">
      <j1 rule="hyper" parents="142 29 2069"/>
    </justification>
  </clause>

  <clause id="2074">
    <literal><![CDATA[
      ((x * (y \ R(y,z,u))) * y) / R(y,z,u) = R(x,y \ R(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(225,a,2069,a(flip),b,210,a)].">
      <j1 rule="hyper" parents="225 2069 210"/>
    </justification>
  </clause>

  <clause id="2075">
    <literal><![CDATA[
      R(x,y,z) \ ((x \ R(x,y,z)) * (x * u)) = L(u,x,x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(2069(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2069 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2076">
    <literal><![CDATA[
      x * (R(x,y,z) / x) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2069(a,1),78(a,1,2,1))].">
      <j1 rule="para" parents="2069 78"/>
    </justification>
  </clause>

  <clause id="2077">
    <literal><![CDATA[
      L(x \ y,x,x \ R(x,z,u)) = R(x,z,u) \ ((x \ R(x,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(2069(a,1),102(a,2,1))].">
      <j1 rule="para" parents="2069 102"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      R((x \ R(x,y,z)) / u,u,x) = R(x,y,z) / (u * x)
    ]]></literal>
    <justification jstring="[para(2069(a,1),112(a,2,1))].">
      <j1 rule="para" parents="2069 112"/>
    </justification>
  </clause>

  <clause id="2080">
    <literal><![CDATA[
      a(x,y,y \ 1) * x = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(982(a,1),2069(a,1,1))].">
      <j1 rule="para" parents="982 2069"/>
    </justification>
  </clause>

  <clause id="2081">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (1 / x) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1781(a,1),2069(a,1,1))].">
      <j1 rule="para" parents="1781 2069"/>
    </justification>
  </clause>

  <clause id="2082">
    <literal><![CDATA[
      ((x / (y * x)) * y) * y = R(y,y,x)
    ]]></literal>
    <justification jstring="[para(1986(a,1),2069(a,1,1))].">
      <j1 rule="para" parents="1986 2069"/>
    </justification>
  </clause>

  <clause id="2083">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (x \ 1) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2009(a,1),2069(a,1,1))].">
      <j1 rule="para" parents="2009 2069"/>
    </justification>
  </clause>

  <clause id="2084">
    <literal><![CDATA[
      T(x \ 1,x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(2009(a,1),2070(a,1,2))].">
      <j1 rule="para" parents="2009 2070"/>
    </justification>
  </clause>

  <clause id="2085">
    <literal><![CDATA[
      R(x,y,z) / (R(x,y,z) / x) = x
    ]]></literal>
    <justification jstring="[hyper(225,a,2071,a,b,xx)].">
      <j1 rule="hyper" parents="225 2071"/>
    </justification>
  </clause>

  <clause id="2086">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) \ R(1 / x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[para(1781(a,1),2072(a,1,1))].">
      <j1 rule="para" parents="1781 2072"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      x \ R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) / x = u
    ]]></literal>
    <justification jstring="[para(2076(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2076 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2088">
    <literal><![CDATA[
      T(T(x \ 1,y),x \ R(x,z,u)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2084(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2084 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2089">
    <literal><![CDATA[
      T(x \ 1,R(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1794(a,2),2084(a,1,2))].">
      <j1 rule="para" parents="1794 2084"/>
    </justification>
  </clause>

  <clause id="2090">
    <literal><![CDATA[
      x \ R(x,y,y \ x) = a(x,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1760,a(flip),b,2067,a),flip(a)].">
      <j1 rule="hyper" parents="64 1760 2067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2091">
    <literal><![CDATA[
      x * a(x,y,y \ x) = R(x,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,1760,a(flip),b,2067,a(flip))].">
      <j1 rule="hyper" parents="145 1760 2067"/>
    </justification>
  </clause>

  <clause id="2093">
    <literal><![CDATA[
      R(x \ 1,x,y) / (y / (x * y)) = a(y / (x * y),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(142,a,1499,a(flip),b,2080,a)].">
      <j1 rule="hyper" parents="142 1499 2080"/>
    </justification>
  </clause>

  <clause id="2094">
    <literal><![CDATA[
      R((x \ 1) / (x * (x \ 1)),y,z) / R(1 / x,y,z) = a(R(1 / x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(142,a,456,a(flip),b,2080,a)].">
      <j1 rule="hyper" parents="142 456 2080"/>
    </justification>
  </clause>

  <clause id="2095">
    <literal><![CDATA[
      a(x \ 1,x,x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(36,a,297,a,b,2080,a),flip(a)].">
      <j1 rule="hyper" parents="36 297 2080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      a(x \ 1,x,x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,294,a,b,2095,a),flip(a)].">
      <j1 rule="hyper" parents="373 294 2095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2098">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,u \ L(x,y,z)),y,z) = a(L(x,y,z),u,u \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(29(a,1),2090(a,1,2))].">
      <j1 rule="para" parents="29 2090"/>
    </justification>
  </clause>

  <clause id="2099">
    <literal><![CDATA[
      R(x \ 1,R(x,y,z),x \ 1) = T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(2089(a,1),1057(a,1,1))].">
      <j1 rule="para" parents="2089 1057"/>
    </justification>
  </clause>

  <clause id="2102">
    <literal><![CDATA[
      R(x * (y * y),z,u) = R(x,z,u) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(465,a,1983,a),flip(a)].">
      <j1 rule="hyper" parents="465 1983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2103">
    <literal><![CDATA[
      x \ R(x * (y * y),z,u) = R(x,z,u) * (x \ (y * y))
    ]]></literal>
    <justification jstring="[para(1983(a,1),1931(a,1,2))].">
      <j1 rule="para" parents="1983 1931"/>
    </justification>
  </clause>

  <clause id="2104">
    <literal><![CDATA[
      R(R(x,y,y) * (y * y),z,u) = (R(x,z,u) * y) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,506,a(flip),b,2102,a),flip(a)].">
      <j1 rule="hyper" parents="373 506 2102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2105">
    <literal><![CDATA[
      R(x * (y * y),z,u) \ w = (y * y) \ (R(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(2102(a,2),486(a,1,1))].">
      <j1 rule="para" parents="2102 486"/>
    </justification>
  </clause>

  <clause id="2106">
    <literal><![CDATA[
      R((x * y) * y,z,u) = (R(x,z,u) * y) * y
    ]]></literal>
    <justification jstring="[para(111(a,1),2104(a,1,1))].">
      <j1 rule="para" parents="111 2104"/>
    </justification>
  </clause>

  <clause id="2107">
    <literal><![CDATA[
      x * R(x \ (y * (x \ 1)),z,u) = R(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,1837,a,b,2106,a(flip))].">
      <j1 rule="hyper" parents="36 1837 2106"/>
    </justification>
  </clause>

  <clause id="2108">
    <literal><![CDATA[
      (R(x / y,z,u) * y) * y = R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),2106(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 2106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2109">
    <literal><![CDATA[
      R(x / (y \ 1),z,u) * (y \ 1) = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(36,a,1837,a,b,2108,a),flip(a)].">
      <j1 rule="hyper" parents="36 1837 2108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2110">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) * x = R(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(843(a,1),2108(a,1,1))].">
      <j1 rule="para" parents="843 2108"/>
    </justification>
  </clause>

  <clause id="2111">
    <literal><![CDATA[
      R(x * y,z,u) / y = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(154,a,2110,a)].">
      <j1 rule="hyper" parents="154 2110"/>
    </justification>
  </clause>

  <clause id="2112">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(36,a,1837,a,b,2110,a),flip(a)].">
      <j1 rule="hyper" parents="36 1837 2110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2113">
    <literal><![CDATA[
      x * R(x \ ((1 / x) * y),z,u) = (1 / x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(36,a,1819,a(flip),b,2110,a),flip(a)].">
      <j1 rule="hyper" parents="36 1819 2110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2114">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ x,z,u) = R(y,z,u) / (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),2111(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 2111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2115">
    <literal><![CDATA[
      x * R(x \ (y / x),z,u) = R(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),2111(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 2111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2116">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ (1 / x),z,u) = R((x * x) \ y,z,u) / (x \ y)
    ]]></literal>
    <justification jstring="[para(536(a,1),2111(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="536 2111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2117">
    <literal><![CDATA[
      R((x * x) \ y,z,u) \ L(w,x,x) = R(y,z,u) \ (x * (x * w))
    ]]></literal>
    <justification jstring="[hyper(139,a,18,a,b,2054,a)].">
      <j1 rule="hyper" parents="139 18 2054"/>
    </justification>
  </clause>

  <clause id="2118">
    <literal><![CDATA[
      R(x,y,z) \ ((x * x) * u) = R(1 / x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(309(a,1),2055(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="309 2055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2119">
    <literal><![CDATA[
      R(x,y,z) * (R(1 / x,y,z) \ u) = (x * x) * u
    ]]></literal>
    <justification jstring="[hyper(157,a,2118,a)].">
      <j1 rule="hyper" parents="157 2118"/>
    </justification>
  </clause>

  <clause id="2120">
    <literal><![CDATA[
      R(x,y,z) / R(1 / x,y,z) = x * x
    ]]></literal>
    <justification jstring="[hyper(142,a,191,a(flip),b,2119,a(flip))].">
      <j1 rule="hyper" parents="142 191 2119"/>
    </justification>
  </clause>

  <clause id="2121">
    <literal><![CDATA[
      (x * x) \ (R(y / x,z,u) \ w) = R(y / (1 / x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(809(a,1),2105(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="809 2105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2123">
    <literal><![CDATA[
      x * R(x \ ((x \ 1) * y),z,u) = (x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(1277,a,2109,a),flip(a)].">
      <j1 rule="hyper" parents="1277 2109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2124">
    <literal><![CDATA[
      x \ R(x * y,z,u) = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1792,a(flip),b,2109,a)].">
      <j1 rule="hyper" parents="64 1792 2109"/>
    </justification>
  </clause>

  <clause id="2125">
    <literal><![CDATA[
      x * (x * R(x \ y,z,u)) = R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,2109,a(flip),b,1792,a(flip))].">
      <j1 rule="hyper" parents="145 2109 1792"/>
    </justification>
  </clause>

  <clause id="2126">
    <literal><![CDATA[
      x \ R(x * y,z,u) = R(y / x,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,843,a,b,2124,a),flip(a)].">
      <j1 rule="hyper" parents="373 843 2124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2127">
    <literal><![CDATA[
      x \ R(x * (y / x),z,u) = R(y,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,2115,a(flip),b,2124,a),flip(a)].">
      <j1 rule="hyper" parents="373 2115 2124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2128">
    <literal><![CDATA[
      x * (R(y / x,z,u) * x) = R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,843,a,b,2124,a)].">
      <j1 rule="hyper" parents="145 843 2124"/>
    </justification>
  </clause>

  <clause id="2129">
    <literal><![CDATA[
      R(x * (y / x),z,u) = x * (R(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,2115,a(flip),b,2124,a),flip(a)].">
      <j1 rule="hyper" parents="145 2115 2124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2130">
    <literal><![CDATA[
      x * ((y * x) * (1 / x)) = R(x * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,1386,a(flip),b,2124,a)].">
      <j1 rule="hyper" parents="145 1386 2124"/>
    </justification>
  </clause>

  <clause id="2131">
    <literal><![CDATA[
      (x \ R(x * y,z,u)) * x = R(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,2124,a,b,2111,a)].">
      <j1 rule="hyper" parents="144 2124 2111"/>
    </justification>
  </clause>

  <clause id="2132">
    <literal><![CDATA[
      R(x,y,z) * (x \ (u * u)) = x * R(x \ (u * u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2103,a(flip),b,2124,a)].">
      <j1 rule="hyper" parents="64 2103 2124"/>
    </justification>
  </clause>

  <clause id="2133">
    <literal><![CDATA[
      x * R(x \ (x \ y),z,u) = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),2124(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2134">
    <literal><![CDATA[
      L(x \ (y * R(y \ z,u,w)),x,y) = (y * x) \ R(y * z,u,w)
    ]]></literal>
    <justification jstring="[para(2124(a,1),346(a,1,1,2))].">
      <j1 rule="para" parents="2124 346"/>
    </justification>
  </clause>

  <clause id="2135">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(269,a,1405,a,b,2130,a)].">
      <j1 rule="hyper" parents="269 1405 2130"/>
    </justification>
  </clause>

  <clause id="2136">
    <literal><![CDATA[
      R((x \ y) * x,x \ y,x \ y) = (x \ y) * (y * (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[para(10(a,1),2130(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2137">
    <literal><![CDATA[
      R(x * (x * y),z,u) = x * (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),2125(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2138">
    <literal><![CDATA[
      (x \ 1) * (x * R(x \ y,z,u)) = R((x \ 1) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,2109,a(flip),b,2126,a)].">
      <j1 rule="hyper" parents="145 2109 2126"/>
    </justification>
  </clause>

  <clause id="2139">
    <literal><![CDATA[
      x \ R(x * (y * x),z,u) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(11(a,1),2126(a,2,1,1))].">
      <j1 rule="para" parents="11 2126"/>
    </justification>
  </clause>

  <clause id="2140">
    <literal><![CDATA[
      R(x * (y * x),z,u) = x * (R(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),2128(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="11 2128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2141">
    <literal><![CDATA[
      R(x * (y \ R(y,z,u)),x,y) = x * ((R(y,z,u) / (x * y)) * x)
    ]]></literal>
    <justification jstring="[para(2078(a,1),2128(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2078 2128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2142">
    <literal><![CDATA[
      R(x / (y * y),z,u) = R(x,z,u) / (y * y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1981,a(flip),b,2129,a(flip))].">
      <j1 rule="hyper" parents="35 1981 2129"/>
    </justification>
  </clause>

  <clause id="2143">
    <literal><![CDATA[
      R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),2131(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2144">
    <literal><![CDATA[
      R(x \ (x \ y),z,u) = x \ (x \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(149,a,2133,a),flip(a)].">
      <j1 rule="hyper" parents="149 2133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2145">
    <literal><![CDATA[
      (((x \ y) * z) / (x * z)) * x = x \ R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1038,a,b,2133,a)].">
      <j1 rule="hyper" parents="64 1038 2133"/>
    </justification>
  </clause>

  <clause id="2146">
    <literal><![CDATA[
      R(x * ((x \ 1) \ y),z,u) = x * ((x \ 1) \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,2133,a(flip),b,1387,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 2133 1387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2147">
    <literal><![CDATA[
      R((x \ y) / x,z,u) = (x \ R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,2133,a(flip),b,843,a),flip(a)].">
      <j1 rule="hyper" parents="142 2133 843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2148">
    <literal><![CDATA[
      ((x \ y) * x) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(10(a,1),2135(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 2135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2149">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) != z * (1 / x)
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(2135(a,2),45(a,1))].">
      <j1 rule="para" parents="2135 45"/>
    </justification>
  </clause>

  <clause id="2150">
    <literal><![CDATA[
      x * (x * R(1 / x,y,z)) = R(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1746(a,1),2137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1746 2137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2151">
    <literal><![CDATA[
      R(x * (y * x),z,u) / T(x,R(y,z,u) * x) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(142,a,2140,a,b,115,a)].">
      <j1 rule="hyper" parents="142 2140 115"/>
    </justification>
  </clause>

  <clause id="2152">
    <literal><![CDATA[
      R(x / (y * y),z,u) * w = R(x,z,u) * ((y * y) \ w)
    ]]></literal>
    <justification jstring="[hyper(144,a,2142,a,b,896,a)].">
      <j1 rule="hyper" parents="144 2142 896"/>
    </justification>
  </clause>

  <clause id="2153">
    <literal><![CDATA[
      R(x / (y * y),z,u) \ w = (y * y) * (R(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(2142(a,2),890(a,1,1))].">
      <j1 rule="para" parents="2142 890"/>
    </justification>
  </clause>

  <clause id="2154">
    <literal><![CDATA[
      (R(x,y,z) \ x) * R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,190,a(flip),b,2143,a),flip(a)].">
      <j1 rule="hyper" parents="43 190 2143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2155">
    <literal><![CDATA[
      R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x
    ]]></literal>
    <justification jstring="[para(675(a,1),2143(a,2,1,2))].">
      <j1 rule="para" parents="675 2143"/>
    </justification>
  </clause>

  <clause id="2156">
    <literal><![CDATA[
      x / R(x,y,z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(154,a,2154,a)].">
      <j1 rule="hyper" parents="154 2154"/>
    </justification>
  </clause>

  <clause id="2157">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,2154,a)].">
      <j1 rule="hyper" parents="149 2154"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ x = R(x,x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(974(a,1),2157(a,1,1))].">
      <j1 rule="para" parents="974 2157"/>
    </justification>
  </clause>

  <clause id="2159">
    <literal><![CDATA[
      T(x * (1 / y),y) != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * y = z
    ]]></literal>
    <justification jstring="[para(2148(a,1),45(a,1))].">
      <j1 rule="para" parents="2148 45"/>
    </justification>
  </clause>

  <clause id="2160">
    <literal><![CDATA[
      x \ R(T(x,x \ 1),y,z) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,2150,a)].">
      <j1 rule="hyper" parents="149 2150"/>
    </justification>
  </clause>

  <clause id="2161">
    <literal><![CDATA[
      R(x \ ((x \ 1) \ y),z,u) = x \ ((x \ 1) \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,2133,a(flip),b,2112,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 2133 2112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2162">
    <literal><![CDATA[
      x * R((x \ 1) * (x \ y),z,u) = (1 / x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(1128(a,1),2113(a,1,2,1))].">
      <j1 rule="para" parents="1128 2113"/>
    </justification>
  </clause>

  <clause id="2163">
    <literal><![CDATA[
      x * R((x \ (x \ 1)) * y,z,u) = (x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(1557(a,1),2123(a,1,2,1))].">
      <j1 rule="para" parents="1557 2123"/>
    </justification>
  </clause>

  <clause id="2164">
    <literal><![CDATA[
      R((x \ 1) * (x * y),z,u) = (x \ 1) * (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),2138(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2165">
    <literal><![CDATA[
      L(x \ (y * R(y \ z,u,w)),x,y) = ((y \ 1) * x) \ R((y \ 1) * z,u,w)
    ]]></literal>
    <justification jstring="[para(2138(a,1),1632(a,2,2))].">
      <j1 rule="para" parents="2138 1632"/>
    </justification>
  </clause>

  <clause id="2166">
    <literal><![CDATA[
      R((x \ 1) * (x \ y),z,u) = (x \ 1) * (x \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(2133(a,1),2138(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2133 2138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2167">
    <literal><![CDATA[
      R(x / (y * y),x,z) * ((y * y) * z) = (1 / x) \ z
    ]]></literal>
    <justification jstring="[hyper(373,a,1915,a(flip),b,2152,a),flip(a)].">
      <j1 rule="hyper" parents="373 1915 2152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2168">
    <literal><![CDATA[
      R(x,y,z) * ((x * x) \ x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1205,a(flip),b,2152,a),flip(a)].">
      <j1 rule="hyper" parents="64 1205 2152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2169">
    <literal><![CDATA[
      R(x,y,z) * (1 / x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(309(a,1),2168(a,1,2))].">
      <j1 rule="para" parents="309 2168"/>
    </justification>
  </clause>

  <clause id="2170">
    <literal><![CDATA[
      (1 / x) * R(x * y,z,u) = x * R((x \ 1) * y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),2162(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 2162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2171">
    <literal><![CDATA[
      R((x \ (x \ 1)) * y,z,u) = (x \ (x \ 1)) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,1552,a,b,2163,a),flip(a)].">
      <j1 rule="hyper" parents="35 1552 2163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2172">
    <literal><![CDATA[
      (x \ 1) * R((x \ (x \ 1)) \ y,z,u) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),2163(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2173">
    <literal><![CDATA[
      R((x \ (1 / x)) * y,z,u) = (x \ 1) * (x \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(1098(a,2),2166(a,1,1))].">
      <j1 rule="para" parents="1098 2166"/>
    </justification>
  </clause>

  <clause id="2174">
    <literal><![CDATA[
      (x \ y) \ R((x \ 1) * (x \ z),u,w) = ((1 / x) \ y) \ R(z,u,w)
    ]]></literal>
    <justification jstring="[para(2166(a,2),1678(a,1,2))].">
      <j1 rule="para" parents="2166 1678"/>
    </justification>
  </clause>

  <clause id="2175">
    <literal><![CDATA[
      (x \ (x \ 1)) * R(x,y,z) = R(T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(1555(a,1),2171(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1555 2171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2176">
    <literal><![CDATA[
      (x \ (x \ 1)) * (R(x,y,z) * u) = R(T(x \ 1,x),y,z) * u
    ]]></literal>
    <justification jstring="[para(2175(a,1),1447(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2175 1447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2177">
    <literal><![CDATA[
      (x \ 1) * R(((x \ 1) \ x) * y,z,u) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(1549(a,1),2172(a,1,2,1))].">
      <j1 rule="para" parents="1549 2172"/>
    </justification>
  </clause>

  <clause id="2178">
    <literal><![CDATA[
      R((x \ (1 / x)) * y,z,u) = (x \ (1 / x)) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,1098,a,b,2173,a),flip(a)].">
      <j1 rule="hyper" parents="373 1098 2173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2179">
    <literal><![CDATA[
      L(R(((x \ 1) \ x) * y,z,u),x,x) = x * (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,2177,a(flip),b,1148,a),flip(a)].">
      <j1 rule="hyper" parents="145 2177 1148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2180">
    <literal><![CDATA[
      R(x * (y \ (1 / y)),z,u) = R(x,z,u) * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(35,a,2140,a(flip),b,2178,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 2140 2178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2181">
    <literal><![CDATA[
      L(x,y,(z * z) \ u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(606,a,1979,a)].">
      <j1 rule="hyper" parents="606 1979"/>
    </justification>
  </clause>

  <clause id="2182">
    <literal><![CDATA[
      L(L(x,y,z),u,(w * w) \ 1) = L(x,y,(v5 * v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1445,a,b,2181,a)].">
      <j1 rule="hyper" parents="373 1445 2181"/>
    </justification>
  </clause>

  <clause id="2183">
    <literal><![CDATA[
      L(x,y,z \ (u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1644,a(flip),b,2181,a)].">
      <j1 rule="hyper" parents="64 1644 2181"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      L(x,y,(z * z) * u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),2181(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 2181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2185">
    <literal><![CDATA[
      L(x,y,z * (z * u)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(18(a,2),2181(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18 2181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2186">
    <literal><![CDATA[
      L(x,y,(1 / z) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(535(a,1),2181(a,1,3))].">
      <j1 rule="para" parents="535 2181"/>
    </justification>
  </clause>

  <clause id="2187">
    <literal><![CDATA[
      L(x,y,L(z \ u,z,z)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(102(a,2),2181(a,1,3))].">
      <j1 rule="para" parents="102 2181"/>
    </justification>
  </clause>

  <clause id="2188">
    <literal><![CDATA[
      L(x,y,((z * z) \ u) * w) = L(x,y,u * w)
    ]]></literal>
    <justification jstring="[para(484(a,1),2181(a,1,3))].">
      <j1 rule="para" parents="484 2181"/>
    </justification>
  </clause>

  <clause id="2189">
    <literal><![CDATA[
      L(x,y,L(T(z,u),u,u)) = L(x,y,u * (z * u))
    ]]></literal>
    <justification jstring="[para(262(a,1),2181(a,1,3))].">
      <j1 rule="para" parents="262 2181"/>
    </justification>
  </clause>

  <clause id="2190">
    <literal><![CDATA[
      L(x,y,z \ ((z * u) * u)) = L(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(874(a,1),2181(a,1,3)),flip(a)].">
      <j1 rule="para" parents="874 2181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2191">
    <literal><![CDATA[
      L(x,y,z * ((z \ 1) \ u)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(582(a,1),2181(a,1,3))].">
      <j1 rule="para" parents="582 2181"/>
    </justification>
  </clause>

  <clause id="2192">
    <literal><![CDATA[
      L(x,y,(z / (1 / u)) \ w) = L(x,y,(z / u) \ w)
    ]]></literal>
    <justification jstring="[para(876(a,1),2181(a,1,3))].">
      <j1 rule="para" parents="876 2181"/>
    </justification>
  </clause>

  <clause id="2193">
    <literal><![CDATA[
      L(x,y,(z * u) * (u \ z)) = L(x,y,a(z,u,u \ z))
    ]]></literal>
    <justification jstring="[para(89(a,1),2181(a,1,3)),flip(a)].">
      <j1 rule="para" parents="89 2181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2194">
    <literal><![CDATA[
      L(x,y,((z * u) * u) \ w) = L(x,y,R(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[para(875(a,1),2181(a,1,3))].">
      <j1 rule="para" parents="875 2181"/>
    </justification>
  </clause>

  <clause id="2195">
    <literal><![CDATA[
      L(x,y,R((z * z) \ u,w,v5)) = L(x,y,R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(2051(a,2),2181(a,1,3))].">
      <j1 rule="para" parents="2051 2181"/>
    </justification>
  </clause>

  <clause id="2197">
    <literal><![CDATA[
      L(x,y,(z * z) / u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(82(a,1),2183(a,1,3)),flip(a)].">
      <j1 rule="para" parents="82 2183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2198">
    <literal><![CDATA[
      L(x,y,L(z \ u,z,u)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(102(a,2),2183(a,1,3))].">
      <j1 rule="para" parents="102 2183"/>
    </justification>
  </clause>

  <clause id="2199">
    <literal><![CDATA[
      L(x,y,z * ((z \ u) * u)) = L(x,y,a(z,z \ u,u))
    ]]></literal>
    <justification jstring="[para(90(a,1),2183(a,1,3)),flip(a)].">
      <j1 rule="para" parents="90 2183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2200">
    <literal><![CDATA[
      L(x,y,R(z,u,w) * (z \ R(z,u,w))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1898(a,1),2183(a,1,3))].">
      <j1 rule="para" parents="1898 2183"/>
    </justification>
  </clause>

  <clause id="2201">
    <literal><![CDATA[
      L(x,y,z * (R(z,u,w) \ z)) = L(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[para(1907(a,1),2183(a,1,3))].">
      <j1 rule="para" parents="1907 2183"/>
    </justification>
  </clause>

  <clause id="2202">
    <literal><![CDATA[
      L(x,y,((z * z) * u) * w) = L(x,y,u * w)
    ]]></literal>
    <justification jstring="[para(33(a,2),2184(a,1,3))].">
      <j1 rule="para" parents="33 2184"/>
    </justification>
  </clause>

  <clause id="2203">
    <literal><![CDATA[
      L(x,y,((z * z) / u) * w) = L(x,y,(1 / u) * w)
    ]]></literal>
    <justification jstring="[para(556(a,1),2184(a,1,3))].">
      <j1 rule="para" parents="556 2184"/>
    </justification>
  </clause>

  <clause id="2204">
    <literal><![CDATA[
      L(x,y,(z * (z * u)) * w) = L(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[para(605(a,1),2184(a,1,3))].">
      <j1 rule="para" parents="605 2184"/>
    </justification>
  </clause>

  <clause id="2205">
    <literal><![CDATA[
      L(x,y,(((z * z) \ u) * w) * v5) = L(x,y,(u * w) * v5)
    ]]></literal>
    <justification jstring="[para(805(a,1),2184(a,1,3)),flip(a)].">
      <j1 rule="para" parents="805 2184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2207">
    <literal><![CDATA[
      L(x,y,((z * (z * u)) * w) * v5) = L(x,y,(L(u,z,z) * w) * v5)
    ]]></literal>
    <justification jstring="[para(1314(a,1),2184(a,1,3))].">
      <j1 rule="para" parents="1314 2184"/>
    </justification>
  </clause>

  <clause id="2208">
    <literal><![CDATA[
      L(x,y,R((z * z) * u,w,v5)) = L(x,y,R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1981(a,2),2184(a,1,3))].">
      <j1 rule="para" parents="1981 2184"/>
    </justification>
  </clause>

  <clause id="2209">
    <literal><![CDATA[
      L(x \ (((y * y) / z) \ u),x,z) = (((y * y) / z) * x) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,346,a(flip),b,2197,a),flip(a)].">
      <j1 rule="hyper" parents="64 346 2197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2210">
    <literal><![CDATA[
      L(x,y,z * (1 / z)) = x
    ]]></literal>
    <justification jstring="[hyper(622,a,2186,a),flip(a)].">
      <j1 rule="hyper" parents="622 2186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2211">
    <literal><![CDATA[
      L(x,y,(z \ 1) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),2186(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="79 2186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2212">
    <literal><![CDATA[
      L(x,y,z \ R(z,u,w)) = L(x,y,z * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(2067(a,1),2186(a,1,3))].">
      <j1 rule="para" parents="2067 2186"/>
    </justification>
  </clause>

  <clause id="2213">
    <literal><![CDATA[
      ((x * (1 / x)) \ y) \ z = y \ ((x * (1 / x)) * z)
    ]]></literal>
    <justification jstring="[hyper(743,a,2210,a),flip(a)].">
      <j1 rule="hyper" parents="743 2210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2214">
    <literal><![CDATA[
      ((x * (1 / x)) * y) \ z = y \ ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(710,a,2210,a),flip(a)].">
      <j1 rule="hyper" parents="710 2210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2215">
    <literal><![CDATA[
      ((x * (1 / x)) * y) / z = (x * (1 / x)) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(225,a,2210,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="225 2210 104"/>
    </justification>
  </clause>

  <clause id="2216">
    <literal><![CDATA[
      L(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(296(a,2),2210(a,1,3))].">
      <j1 rule="para" parents="296 2210"/>
    </justification>
  </clause>

  <clause id="2217">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1724(a,2),2210(a,1,3))].">
      <j1 rule="para" parents="1724 2210"/>
    </justification>
  </clause>

  <clause id="2218">
    <literal><![CDATA[
      K(x,1 / x) * (1 / y) = K(x,1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(225,a,2216,a(flip),b,246,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 2216 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2219">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = K(x,1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,2216,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 2216 18"/>
    </justification>
  </clause>

  <clause id="2220">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(79(a,1),2216(a,1,3,2))].">
      <j1 rule="para" parents="79 2216"/>
    </justification>
  </clause>

  <clause id="2221">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) * (y * z) = u
    ]]></literal>
    <justification jstring="[para(2216(a,1),334(a,1,2))].">
      <j1 rule="para" parents="2216 334"/>
    </justification>
  </clause>

  <clause id="2222">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ (K(x,x \ 1) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,2217,a)].">
      <j1 rule="hyper" parents="64 102 2217"/>
    </justification>
  </clause>

  <clause id="2223">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / z = K(x,x \ 1) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(225,a,2217,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="225 2217 104"/>
    </justification>
  </clause>

  <clause id="2224">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = K(x,x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,2217,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 2217 18"/>
    </justification>
  </clause>

  <clause id="2225">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (K(x \ 1,x) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,2220,a)].">
      <j1 rule="hyper" parents="64 102 2220"/>
    </justification>
  </clause>

  <clause id="2226">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(225,a,2220,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="225 2220 104"/>
    </justification>
  </clause>

  <clause id="2227">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,2220,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 2220 18"/>
    </justification>
  </clause>

  <clause id="2228">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(2220(a,1),51(a,2))].">
      <j1 rule="para" parents="2220 51"/>
    </justification>
  </clause>

  <clause id="2229">
    <literal><![CDATA[
      K(x \ 1,x) * y != (K(x \ 1,x) * z) * u
    ]]></literal>
    <literal><![CDATA[
      z * u = y
    ]]></literal>
    <justification jstring="[para(2220(a,1),607(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2220 607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2230">
    <literal><![CDATA[
      L(x,y,(1 / z) \ u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(1138(a,1),2191(a,1,3))].">
      <j1 rule="para" parents="1138 2191"/>
    </justification>
  </clause>

  <clause id="2231">
    <literal><![CDATA[
      L(x,y,(z \ (z \ 1)) * u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(1615(a,1),2191(a,1,3))].">
      <j1 rule="para" parents="1615 2191"/>
    </justification>
  </clause>

  <clause id="2232">
    <literal><![CDATA[
      L(x \ 1,x,(y \ 1) * z) = ((y * z) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,241,a(flip),b,2211,a),flip(a)].">
      <j1 rule="hyper" parents="373 241 2211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2233">
    <literal><![CDATA[
      L(x,y,z \ L(1 / z,u,w)) = L(x,y,z * L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(1391(a,1),2211(a,1,3))].">
      <j1 rule="para" parents="1391 2211"/>
    </justification>
  </clause>

  <clause id="2234">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(79(a,1),2230(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="79 2230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2235">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ u) * w) = L(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[para(1550(a,1),2231(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1550 2231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2236">
    <literal><![CDATA[
      L(x,y,(1 / z) \ u) = L(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2230,a,b,2234,a)].">
      <j1 rule="hyper" parents="373 2230 2234"/>
    </justification>
  </clause>

  <clause id="2237">
    <literal><![CDATA[
      L(x,y,L(z \ u,z,z)) = L(x,y,(z \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2211,a,b,2187,a),flip(a)].">
      <j1 rule="hyper" parents="373 2211 2187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2238">
    <literal><![CDATA[
      L(x,y,((1 / z) * u) * w) = L(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[para(535(a,1),2188(a,1,3,1))].">
      <j1 rule="para" parents="535 2188"/>
    </justification>
  </clause>

  <clause id="2239">
    <literal><![CDATA[
      L(x,y,L(T(z,u),u,u) * w) = L(x,y,(u * (z * u)) * w)
    ]]></literal>
    <justification jstring="[para(262(a,1),2188(a,1,3,1))].">
      <j1 rule="para" parents="262 2188"/>
    </justification>
  </clause>

  <clause id="2240">
    <literal><![CDATA[
      L(x,y,(T(z,u * u) \ w) * v5) = L(x,y,(z \ ((u * u) * w)) * v5)
    ]]></literal>
    <justification jstring="[para(1458(a,1),2188(a,1,3,1))].">
      <j1 rule="para" parents="1458 2188"/>
    </justification>
  </clause>

  <clause id="2241">
    <literal><![CDATA[
      L(x,y,R((z * z) \ u,w,v5) * v6) = L(x,y,R(u,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(2051(a,2),2188(a,1,3,1))].">
      <j1 rule="para" parents="2051 2188"/>
    </justification>
  </clause>

  <clause id="2242">
    <literal><![CDATA[
      x / (1 / (1 / x)) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(142,a,418,a(flip),b,2218,a)].">
      <j1 rule="hyper" parents="142 418 2218"/>
    </justification>
  </clause>

  <clause id="2243">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,1726,a(flip),b,2242,a)].">
      <j1 rule="hyper" parents="144 1726 2242"/>
    </justification>
  </clause>

  <clause id="2244">
    <literal><![CDATA[
      L(x,y,a(z,z \ u,z \ u)) = L(x,y,z \ (u * (z \ u)))
    ]]></literal>
    <justification jstring="[para(10(a,1),2190(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="10 2190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2245">
    <literal><![CDATA[
      L(x,y,R(1 / z,u,w)) = L(x,y,R(z,u,w))
    ]]></literal>
    <justification jstring="[para(309(a,1),2195(a,1,3,1))].">
      <j1 rule="para" parents="309 2195"/>
    </justification>
  </clause>

  <clause id="2246">
    <literal><![CDATA[
      L(x,y,R((z * z) / u,w,v5)) = L(x,y,R(1 / u,w,v5))
    ]]></literal>
    <justification jstring="[para(548(a,1),2195(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="548 2195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2247">
    <literal><![CDATA[
      L(x,y,z * ((z \ u) * (u \ z))) = L(x,y,R(z,z \ u,u \ z))
    ]]></literal>
    <justification jstring="[para(974(a,1),2201(a,1,3,2))].">
      <j1 rule="para" parents="974 2201"/>
    </justification>
  </clause>

  <clause id="2248">
    <literal><![CDATA[
      L(x,y,((z * z) / u) * w) = L(x,y,u * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2186,a(flip),b,2203,a),flip(a)].">
      <j1 rule="hyper" parents="373 2186 2203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2249">
    <literal><![CDATA[
      L(x,y,L(z \ u,z,u) * w) = L(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[para(591(a,1),2248(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="591 2248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2250">
    <literal><![CDATA[
      L(x,y,(R(z,u,w) * (z \ R(z,u,w))) * v5) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(1901(a,1),2248(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1901 2248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2251">
    <literal><![CDATA[
      T(x,x \ 1) \ (K(x,x \ 1) * y) = x \ y
    ]]></literal>
    <justification jstring="[para(1725(a,1),2222(a,1,1))].">
      <j1 rule="para" parents="1725 2222"/>
    </justification>
  </clause>

  <clause id="2252">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = T(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,22,a,b,2251,a),flip(a)].">
      <j1 rule="hyper" parents="145 22 2251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2253">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,9,a(flip),b,2251,a),flip(a)].">
      <j1 rule="hyper" parents="145 9 2251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2254">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,365,a(flip),b,2253,a),flip(a)].">
      <j1 rule="hyper" parents="373 365 2253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2255">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(2253(a,2),869(a,1))].">
      <j1 rule="para" parents="2253 869"/>
    </justification>
  </clause>

  <clause id="2256">
    <literal><![CDATA[
      R(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(664,a,2224,a)].">
      <j1 rule="hyper" parents="664 2224"/>
    </justification>
  </clause>

  <clause id="2257">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y
    ]]></literal>
    <justification jstring="[para(2243(a,1),2224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2243 2224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2258">
    <literal><![CDATA[
      x * ((1 / (1 / x)) \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(397,a,2257,a),flip(a)].">
      <j1 rule="hyper" parents="397 2257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2259">
    <literal><![CDATA[
      (x * y) \ (K(x,x \ 1) * z) = ((1 / (1 / x)) * y) \ z
    ]]></literal>
    <justification jstring="[para(2257(a,1),2222(a,1,1))].">
      <j1 rule="para" parents="2257 2222"/>
    </justification>
  </clause>

  <clause id="2260">
    <literal><![CDATA[
      (x \ 1) \ (K(x \ 1,x) * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(1225(a,1),2225(a,1,1))].">
      <j1 rule="para" parents="1225 2225"/>
    </justification>
  </clause>

  <clause id="2261">
    <literal><![CDATA[
      (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(157,a,2260,a)].">
      <j1 rule="hyper" parents="157 2260"/>
    </justification>
  </clause>

  <clause id="2262">
    <literal><![CDATA[
      K(x \ 1,x) * R(1 / x,y,z) = (x \ 1) * (x * R(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,1781,a(flip),b,2260,a),flip(a)].">
      <j1 rule="hyper" parents="145 1781 2260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2263">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,9,a(flip),b,2260,a),flip(a)].">
      <j1 rule="hyper" parents="145 9 2260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2264">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(2261(a,1),739(a,1))].">
      <j1 rule="para" parents="2261 739"/>
    </justification>
  </clause>

  <clause id="2265">
    <literal><![CDATA[
      ((x * K(y \ 1,y)) * ((1 / y) * z)) / ((y \ 1) * z) = R(x,K(y \ 1,y),(1 / y) * z)
    ]]></literal>
    <justification jstring="[hyper(225,a,2263,a(flip),b,210,a)].">
      <j1 rule="hyper" parents="225 2263 210"/>
    </justification>
  </clause>

  <clause id="2267">
    <literal><![CDATA[
      ((x \ 1) * y) \ (K(x \ 1,x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(2263(a,1),2225(a,1,1))].">
      <j1 rule="para" parents="2263 2225"/>
    </justification>
  </clause>

  <clause id="2268">
    <literal><![CDATA[
      T(K(x \ 1,x) * (y / z),z) = z \ (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(2226(a,1),117(a,1,1))].">
      <j1 rule="para" parents="2226 117"/>
    </justification>
  </clause>

  <clause id="2269">
    <literal><![CDATA[
      ((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(2227(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2227 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2270">
    <literal><![CDATA[
      L(x,y,((1 / z) \ u) * w) = L(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[para(82(a,1),2235(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="82 2235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2271">
    <literal><![CDATA[
      L(x,y,((z \ 1) * u) * w) = L(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[para(79(a,1),2238(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="79 2238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2272">
    <literal><![CDATA[
      L(x,y,(z * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(2182(a,1),616(a,1))].">
      <j1 rule="para" parents="2182 616"/>
    </justification>
  </clause>

  <clause id="2273">
    <literal><![CDATA[
      L(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(309(a,1),2272(a,1,3))].">
      <j1 rule="para" parents="309 2272"/>
    </justification>
  </clause>

  <clause id="2274">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(79(a,1),2273(a,1,3))].">
      <j1 rule="para" parents="79 2273"/>
    </justification>
  </clause>

  <clause id="2275">
    <literal><![CDATA[
      L(x,y,z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1648(a,1),2273(a,1))].">
      <j1 rule="para" parents="1648 2273"/>
    </justification>
  </clause>

  <clause id="2276">
    <literal><![CDATA[
      L(x,y,1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(1643(a,2),2274(a,1))].">
      <j1 rule="para" parents="1643 2274"/>
    </justification>
  </clause>

  <clause id="2277">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,1 / z) = u
    ]]></literal>
    <justification jstring="[para(82(a,1),2275(a,1,3))].">
      <j1 rule="para" parents="82 2275"/>
    </justification>
  </clause>

  <clause id="2278">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * ((1 / x) \ y) = z
    ]]></literal>
    <justification jstring="[para(10(a,1),2264(a,1,2))].">
      <j1 rule="para" parents="10 2264"/>
    </justification>
  </clause>

  <clause id="2279">
    <literal><![CDATA[
      L(x,y,(((1 / z) * u) * w) * v5) = L(x,y,((z * u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(535(a,1),2205(a,1,3,1,1))].">
      <j1 rule="para" parents="535 2205"/>
    </justification>
  </clause>

  <clause id="2280">
    <literal><![CDATA[
      L(x,y,(L(T(z,u),u,u) * w) * v5) = L(x,y,((u * (z * u)) * w) * v5)
    ]]></literal>
    <justification jstring="[para(262(a,1),2205(a,1,3,1,1))].">
      <j1 rule="para" parents="262 2205"/>
    </justification>
  </clause>

  <clause id="2281">
    <literal><![CDATA[
      L(x,y,R((z * z) / u,w,v5)) = L(x,y,R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,2245,a(flip),b,2246,a),flip(a)].">
      <j1 rule="hyper" parents="373 2245 2246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2282">
    <literal><![CDATA[
      L(x,y,R(z \ (u * u),w,v5)) = L(x,y,R(z,w,v5))
    ]]></literal>
    <justification jstring="[para(79(a,1),2281(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="79 2281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2283">
    <literal><![CDATA[
      x * T(x \ 1,R((1 / x) \ 1,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1254,a(flip),b,2059,a),flip(a)].">
      <j1 rule="hyper" parents="373 1254 2059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2284">
    <literal><![CDATA[
      x * T(x \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),2283(a,1,2,2,1))].">
      <j1 rule="para" parents="82 2283"/>
    </justification>
  </clause>

  <clause id="2285">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z
    ]]></literal>
    <justification jstring="[hyper(142,a,2155,a(flip),b,297,a)].">
      <j1 rule="hyper" parents="142 2155 297"/>
    </justification>
  </clause>

  <clause id="2286">
    <literal><![CDATA[
      R(((x \ 1) \ x) * y,z,u) = ((x \ 1) \ x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(42,a,1144,a,b,2179,a),flip(a)].">
      <j1 rule="hyper" parents="42 1144 2179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2287">
    <literal><![CDATA[
      R(x * ((y \ 1) \ y),z,u) = R(x,z,u) * ((y \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,2140,a(flip),b,2286,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 2140 2286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2288">
    <literal><![CDATA[
      R(x * ((y \ 1) \ y),z,u) * w = R(x,z,u) * (((y \ 1) \ y) * w)
    ]]></literal>
    <justification jstring="[para(2287(a,2),1114(a,1,1))].">
      <j1 rule="para" parents="2287 1114"/>
    </justification>
  </clause>

  <clause id="2289">
    <literal><![CDATA[
      (x * ((y * y) * (z * z))) * u = x * ((y * y) * ((z * z) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,34,a(flip),b,136,a),flip(a)].">
      <j1 rule="hyper" parents="373 34 136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2290">
    <literal><![CDATA[
      L(x,y,y) \ L(x * z,y,y) = L(L(z,x,y),y * x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1365,a(flip),b,602,a)].">
      <j1 rule="hyper" parents="64 1365 602"/>
    </justification>
  </clause>

  <clause id="2291">
    <literal><![CDATA[
      L((x * x) \ y,z * (x * x),u) = (u * (z * (x * x))) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(593(a,1),647(a,1,1))].">
      <j1 rule="para" parents="593 647"/>
    </justification>
  </clause>

  <clause id="2292">
    <literal><![CDATA[
      ((x * y) * ((z * z) * u)) / ((y * (z * z)) * u) = R(R(x,y,z * z),y * (z * z),u)
    ]]></literal>
    <justification jstring="[para(34(a,1),660(a,1,1))].">
      <j1 rule="para" parents="34 660"/>
    </justification>
  </clause>

  <clause id="2293">
    <literal><![CDATA[
      ((x * y) * (z * u)) / ((y * z) * L(u,z,x * y)) = R(R(x,y,z),y * z,L(u,z,x * y))
    ]]></literal>
    <justification jstring="[para(100(a,1),660(a,1,1))].">
      <j1 rule="para" parents="100 660"/>
    </justification>
  </clause>

  <clause id="2294">
    <literal><![CDATA[
      ((x * y) * ((z * z) \ u)) / ((y * ((z * z) \ 1)) * u) = R(R(x,y,(z * z) \ 1),y * ((z * z) \ 1),u)
    ]]></literal>
    <justification jstring="[para(949(a,1),660(a,1,1))].">
      <j1 rule="para" parents="949 660"/>
    </justification>
  </clause>

  <clause id="2295">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(2071(a,1),686(a,1,1))].">
      <j1 rule="para" parents="2071 686"/>
    </justification>
  </clause>

  <clause id="2296">
    <literal><![CDATA[
      L((x \ y) \ L(x \ z,x,x),x \ y,x * x) = ((1 / (1 / (1 / x))) \ y) \ (x * z)
    ]]></literal>
    <justification jstring="[para(2031(a,2),713(a,2,1))].">
      <j1 rule="para" parents="2031 713"/>
    </justification>
  </clause>

  <clause id="2297">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (y * R(y \ (x \ z),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(346(a,1),1070(a,1,2,1))].">
      <j1 rule="para" parents="346 1070"/>
    </justification>
  </clause>

  <clause id="2298">
    <literal><![CDATA[
      (x * (y * z)) * R(((x * y) * L(z,y,x)) \ (x * y),u,w) = (x * y) * (L(z,y,x) * R(L(z,y,x) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(100(a,1),1300(a,1,1))].">
      <j1 rule="para" parents="100 1300"/>
    </justification>
  </clause>

  <clause id="2299">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(1987(a,1),1300(a,2,2))].">
      <j1 rule="para" parents="1987 1300"/>
    </justification>
  </clause>

  <clause id="2300">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (R(1 / x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(1213,a,1304,a)].">
      <j1 rule="hyper" parents="1213 1304"/>
    </justification>
  </clause>

  <clause id="2301">
    <literal><![CDATA[
      K(x,x \ 1) * T((x * (1 / x)) \ y,z) = x * ((1 / x) * T((1 / x) \ (x \ y),z))
    ]]></literal>
    <justification jstring="[para(1724(a,2),1308(a,1,1))].">
      <j1 rule="para" parents="1724 1308"/>
    </justification>
  </clause>

  <clause id="2302">
    <literal><![CDATA[
      L(R(T(x,y),1 / x,(1 / x) \ y),x,x) = y \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29,a(flip),b,1383,a)].">
      <j1 rule="hyper" parents="64 29 1383"/>
    </justification>
  </clause>

  <clause id="2304">
    <literal><![CDATA[
      R(x / y,y / x,(y / x) \ 1) = T(x / y,y / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,857,a(flip),b,1500,a),flip(a)].">
      <j1 rule="hyper" parents="373 857 1500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2305">
    <literal><![CDATA[
      ((x / y) * (y / x)) * ((x / y) \ 1) = y / x
    ]]></literal>
    <justification jstring="[hyper(41,a,1042,a,b,2304,a(flip))].">
      <j1 rule="hyper" parents="41 1042 2304"/>
    </justification>
  </clause>

  <clause id="2306">
    <literal><![CDATA[
      (x / y) / ((y / x) \ 1) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(154,a,2305,a)].">
      <j1 rule="hyper" parents="154 2305"/>
    </justification>
  </clause>

  <clause id="2307">
    <literal><![CDATA[
      ((x \ y) / y) * (y / (x \ y)) = x / (((x \ y) / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(142,a,79,a(flip),b,2305,a),flip(a)].">
      <j1 rule="hyper" parents="142 79 2305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2308">
    <literal><![CDATA[
      (x / (y \ x)) * ((y \ x) / x) = ((y \ x) / x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),2306(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 2306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2309">
    <literal><![CDATA[
      x / (((x \ y) / y) \ 1) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(740,a,2307,a),flip(a)].">
      <j1 rule="hyper" parents="740 2307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2311">
    <literal><![CDATA[
      (((x \ y) / y) * x) \ x = ((x \ y) / y) \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,2309,a)].">
      <j1 rule="hyper" parents="215 2309"/>
    </justification>
  </clause>

  <clause id="2312">
    <literal><![CDATA[
      (x * ((x \ y) / y)) * (x \ 1) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(144,a,209,a(flip),b,2308,a(flip))].">
      <j1 rule="hyper" parents="144 209 2308"/>
    </justification>
  </clause>

  <clause id="2313">
    <literal><![CDATA[
      (x * ((x \ y) / y)) * (x \ 1) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,453,a,b,2312,a),flip(a)].">
      <j1 rule="hyper" parents="373 453 2312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2314">
    <literal><![CDATA[
      (x * ((x \ y) / y)) \ ((x \ y) / y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(149,a,2312,a)].">
      <j1 rule="hyper" parents="149 2312"/>
    </justification>
  </clause>

  <clause id="2315">
    <literal><![CDATA[
      (x * x) * ((T(y,x * x) \ R(T(y,x * x),z,u)) / w) = (y * ((x * x) * R(T(y,x * x) \ 1,z,u))) / w
    ]]></literal>
    <justification jstring="[para(1987(a,1),1523(a,1,2,1))].">
      <j1 rule="para" parents="1987 1523"/>
    </justification>
  </clause>

  <clause id="2316">
    <literal><![CDATA[
      L(x,y,(((z \ 1) \ u) * w) * v5) = L(x,y,((z \ u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(1616(a,1),2231(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1616 2231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2317">
    <literal><![CDATA[
      (x \ 1) \ ((y / ((x \ 1) * z)) \ u) = x \ ((y / (x * z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(149,a,1626,a),flip(a)].">
      <j1 rule="hyper" parents="149 1626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2318">
    <literal><![CDATA[
      (x \ 1) \ (((x \ y) * z) * x) = T(((1 / x) \ y) * z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,22,a,b,1667,a),flip(a)].">
      <j1 rule="hyper" parents="373 22 1667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2319">
    <literal><![CDATA[
      (x * (y \ 1)) \ (y \ (1 / y)) = (y * T(x,y \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(1090(a,1),1677(a,1,2))].">
      <j1 rule="para" parents="1090 1677"/>
    </justification>
  </clause>

  <clause id="2320">
    <literal><![CDATA[
      (x * (T(x,x \ 1) * y)) \ (x * z) = L(y,x,x) \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(1417(a,2),1683(a,1,1,2,1))].">
      <j1 rule="para" parents="1417 1683"/>
    </justification>
  </clause>

  <clause id="2321">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (L(1 / x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,836,a(flip),b,1700,a)].">
      <j1 rule="hyper" parents="64 836 1700"/>
    </justification>
  </clause>

  <clause id="2322">
    <literal><![CDATA[
      x * (y * L(T(x,y),z,u)) = L(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(464,a,1706,a),flip(a)].">
      <j1 rule="hyper" parents="464 1706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2323">
    <literal><![CDATA[
      L(x,y,z) * (x * u) = x * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,520,a(flip),b,2322,a),flip(a)].">
      <j1 rule="hyper" parents="64 520 2322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2324">
    <literal><![CDATA[
      L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(139,a,520,a(flip),b,2322,a(flip))].">
      <j1 rule="hyper" parents="139 520 2322"/>
    </justification>
  </clause>

  <clause id="2325">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(759,a,2323,a)].">
      <j1 rule="hyper" parents="759 2323"/>
    </justification>
  </clause>

  <clause id="2326">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(757,a,2323,a),flip(a)].">
      <j1 rule="hyper" parents="757 2323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2327">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(397,a,2323,a),flip(a)].">
      <j1 rule="hyper" parents="397 2323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2328">
    <literal><![CDATA[
      L(x,y,z) * (x * (L(x,y,z) \ u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(373,a,168,a(flip),b,2323,a),flip(a)].">
      <j1 rule="hyper" parents="373 168 2323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2329">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,2323,a)].">
      <j1 rule="hyper" parents="139 168 2323"/>
    </justification>
  </clause>

  <clause id="2330">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x \ u)) = L(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(139,a,75,a(flip),b,2323,a),flip(a)].">
      <j1 rule="hyper" parents="139 75 2323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2331">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) \ (L(x,y,z) * u) = T(x,L(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(493,a,168,a(flip),b,2323,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="493 168 2323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2332">
    <literal><![CDATA[
      L(T(x,y),y,L(x,z,u)) = T(x,L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(269,a,2323,a(flip),b,588,a),flip(a)].">
      <j1 rule="hyper" parents="269 2323 588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2333">
    <literal><![CDATA[
      ((x * y) * L(x,z,u)) \ (x * (L(x,z,u) * y)) = K(L(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,2323,a(flip),b,94,a)].">
      <j1 rule="hyper" parents="139 2323 94"/>
    </justification>
  </clause>

  <clause id="2334">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) * u = w
    ]]></literal>
    <justification jstring="[para(2323(a,1),397(a,1))].">
      <j1 rule="para" parents="2323 397"/>
    </justification>
  </clause>

  <clause id="2335">
    <literal><![CDATA[
      x * (L(x,y,z) * ((x \ 1) * u)) = L(x,y,z) * L(u,x,x)
    ]]></literal>
    <justification jstring="[para(1139(a,1),2323(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1139 2323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2336">
    <literal><![CDATA[
      L(x,y,z) * K(x,x \ 1) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[para(1724(a,2),2323(a,1,2))].">
      <j1 rule="para" parents="1724 2323"/>
    </justification>
  </clause>

  <clause id="2337">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (x * (L(x,y,z) * u)) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2323(a,1),530(a,1,2))].">
      <j1 rule="para" parents="2323 530"/>
    </justification>
  </clause>

  <clause id="2338">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(u,x \ L(x,y,z),x)) = (x \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,598,a(flip),b,2325,a),flip(a)].">
      <j1 rule="hyper" parents="64 598 2325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2339">
    <literal><![CDATA[
      L(x,y,z) \ (x \ u) = x \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(149,a,2326,a)].">
      <j1 rule="hyper" parents="149 2326"/>
    </justification>
  </clause>

  <clause id="2340">
    <literal><![CDATA[
      L(x,y,z) * u != x * w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(2327(a,1),44(a,1))].">
      <j1 rule="para" parents="2327 44"/>
    </justification>
  </clause>

  <clause id="2341">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = x * (L(x,y,z) \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(139,a,1724,a,b,2328,a)].">
      <j1 rule="hyper" parents="139 1724 2328"/>
    </justification>
  </clause>

  <clause id="2342">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(2328(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2328 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2343">
    <literal><![CDATA[
      ((x \ 1) \ y) * (L((x \ 1) \ y,x,x) \ z) = (x * y) \ (((x \ 1) \ y) * z)
    ]]></literal>
    <justification jstring="[para(1137(a,1),2329(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1137 2329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2344">
    <literal><![CDATA[
      x * (L(x,1 / x,x) \ y) = (1 / (1 / x)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1652(a,1),2329(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1652 2329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2345">
    <literal><![CDATA[
      L(x,y,z) \ (T(x * x,x) * u) = x * (L(x,y,z) \ ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(1167(a,1),2330(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1167 2330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2346">
    <literal><![CDATA[
      x * (L(x,y,z) \ (x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ u = w
    ]]></literal>
    <justification jstring="[para(2339(a,2),290(a,1,2))].">
      <j1 rule="para" parents="2339 290"/>
    </justification>
  </clause>

  <clause id="2347">
    <literal><![CDATA[
      (1 / (1 / x)) \ (x * y) = x * ((1 / (1 / x)) \ y)
    ]]></literal>
    <justification jstring="[para(1652(a,1),2344(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1652 2344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2348">
    <literal><![CDATA[
      (1 / (1 / x)) * (K(x,x \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(145,a,2258,a(flip),b,2347,a)].">
      <j1 rule="hyper" parents="145 2258 2347"/>
    </justification>
  </clause>

  <clause id="2349">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,2348,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 2348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2350">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(35,a,179,a,b,2348,a),flip(a)].">
      <j1 rule="hyper" parents="35 179 2348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2351">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2348(a,1),2257(a,1,2))].">
      <j1 rule="para" parents="2348 2257"/>
    </justification>
  </clause>

  <clause id="2352">
    <literal><![CDATA[
      (1 / x) \ (K(x,x \ 1) * y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(2350(a,1),2222(a,1,1))].">
      <j1 rule="para" parents="2350 2222"/>
    </justification>
  </clause>

  <clause id="2353">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) / y) = (1 / x) / y
    ]]></literal>
    <justification jstring="[para(2350(a,1),2223(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2350 2223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2354">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(2350(a,1),2224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2350 2224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2355">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2349(a,2),2258(a,1,2))].">
      <j1 rule="para" parents="2349 2258"/>
    </justification>
  </clause>

  <clause id="2356">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(157,a,2352,a)].">
      <j1 rule="hyper" parents="157 2352"/>
    </justification>
  </clause>

  <clause id="2357">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) = y
    ]]></literal>
    <justification jstring="[hyper(39,a,2260,a(flip),b,2352,a),flip(a)].">
      <j1 rule="hyper" parents="39 2260 2352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2358">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[hyper(39,a,2260,a,b,2352,a(flip))].">
      <j1 rule="hyper" parents="39 2260 2352"/>
    </justification>
  </clause>

  <clause id="2359">
    <literal><![CDATA[
      K(x \ 1,x) \ y = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(397,a,2357,a),flip(a)].">
      <j1 rule="hyper" parents="397 2357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2360">
    <literal><![CDATA[
      K(x,x \ 1) \ y = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(149,a,2357,a)].">
      <j1 rule="hyper" parents="149 2357"/>
    </justification>
  </clause>

  <clause id="2361">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,2257,a,b,2357,a),flip(a)].">
      <j1 rule="hyper" parents="35 2257 2357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(35,a,2254,a,b,2357,a),flip(a)].">
      <j1 rule="hyper" parents="35 2254 2357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2363">
    <literal><![CDATA[
      K(x \ 1,x) * x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(35,a,2243,a,b,2357,a),flip(a)].">
      <j1 rule="hyper" parents="35 2243 2357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2364">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,1733,a,b,2357,a),flip(a)].">
      <j1 rule="hyper" parents="35 1733 2357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2365">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * z = y
    ]]></literal>
    <justification jstring="[para(2357(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2357 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2366">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2357(a,1),2222(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2357 2222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2367">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = y \ (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[para(2357(a,1),2222(a,1,2))].">
      <j1 rule="para" parents="2357 2222"/>
    </justification>
  </clause>

  <clause id="2368">
    <literal><![CDATA[
      x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(2357(a,1),2348(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2357 2348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2369">
    <literal><![CDATA[
      L(x,x \ 1,x) / x = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,1157,a,b,2363,a)].">
      <j1 rule="hyper" parents="142 1157 2363"/>
    </justification>
  </clause>

  <clause id="2370">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) * x = (1 / (1 / (x / y))) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,2363,a(flip),b,2226,a),flip(a)].">
      <j1 rule="hyper" parents="144 2363 2226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2371">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(236,a,2358,a),flip(a)].">
      <j1 rule="hyper" parents="236 2358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2372">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * z = y
    ]]></literal>
    <justification jstring="[para(2358(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2358 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2373">
    <literal><![CDATA[
      a(x,x,x) \ y = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(1853(a,1),2360(a,1,1))].">
      <j1 rule="para" parents="1853 2360"/>
    </justification>
  </clause>

  <clause id="2374">
    <literal><![CDATA[
      (x * ((1 / y) * z)) / L((y \ 1) * z,K(y,y \ 1),x) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2354(a,1),213(a,1,1,2))].">
      <j1 rule="para" parents="2354 213"/>
    </justification>
  </clause>

  <clause id="2375">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (x * ((1 / y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L((y \ 1) * z,K(y,y \ 1),x) = u
    ]]></literal>
    <justification jstring="[para(2354(a,1),608(a,1,2,2))].">
      <j1 rule="para" parents="2354 608"/>
    </justification>
  </clause>

  <clause id="2377">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) * y) * z) = ((1 / x) * y) * z
    ]]></literal>
    <justification jstring="[para(2354(a,1),2224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2354 2224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2378">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * y = z
    ]]></literal>
    <justification jstring="[para(2356(a,1),739(a,1))].">
      <j1 rule="para" parents="2356 739"/>
    </justification>
  </clause>

  <clause id="2379">
    <literal><![CDATA[
      K(x \ 1,x) * (y * x) = (1 / (1 / x)) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(737,a,2361,a)].">
      <j1 rule="hyper" parents="737 2361"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(397,a,2362,a),flip(a)].">
      <j1 rule="hyper" parents="397 2362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2382">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = x * (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,2361,a,b,2368,a)].">
      <j1 rule="hyper" parents="373 2361 2368"/>
    </justification>
  </clause>

  <clause id="2383">
    <literal><![CDATA[
      x * (K(x,x \ 1) * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,2253,a(flip),b,2351,a),flip(a)].">
      <j1 rule="hyper" parents="64 2253 2351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2384">
    <literal><![CDATA[
      (T(x,x \ 1) * y) / (K(x,x \ 1) * y) = x
    ]]></literal>
    <justification jstring="[hyper(142,a,2253,a(flip),b,2351,a(flip))].">
      <j1 rule="hyper" parents="142 2253 2351"/>
    </justification>
  </clause>

  <clause id="2385">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,505,a(flip),b,2383,a),flip(a)].">
      <j1 rule="hyper" parents="139 505 2383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2386">
    <literal><![CDATA[
      K(x,x \ 1) * (T(x,x \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,2383,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 2383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(2365,a,2385,a)].">
      <j1 rule="hyper" parents="2365 2385"/>
    </justification>
  </clause>

  <clause id="2388">
    <literal><![CDATA[
      (x \ y) \ (K(x,x \ 1) * z) = (((x \ 1) \ 1) \ y) \ z
    ]]></literal>
    <justification jstring="[para(2385(a,1),2222(a,1,1))].">
      <j1 rule="para" parents="2385 2222"/>
    </justification>
  </clause>

  <clause id="2389">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (K(x \ 1,x) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(1335,a,2387,a(flip))].">
      <j1 rule="hyper" parents="1335 2387"/>
    </justification>
  </clause>

  <clause id="2390">
    <literal><![CDATA[
      T(x \ (y \ x),y) = x \ (((y \ 1) \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,2387,a(flip),b,1839,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 2387 1839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2391">
    <literal><![CDATA[
      K(x \ 1,x) * y != (((x \ 1) \ 1) \ z) * u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * u = y
    ]]></literal>
    <justification jstring="[para(2387(a,1),2229(a,2,1))].">
      <j1 rule="para" parents="2387 2229"/>
    </justification>
  </clause>

  <clause id="2392">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,x,x) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,2389,a(flip),b,1163,a),flip(a)].">
      <j1 rule="hyper" parents="145 2389 1163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2394">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (x * (K(x \ 1,x) * y)) = L(T(x,y),y,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(139,a,2382,a(flip),b,588,a)].">
      <j1 rule="hyper" parents="139 2382 588"/>
    </justification>
  </clause>

  <clause id="2395">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((((x * y) \ (x * (y * z))) \ z) * ((x * y) \ (x * (y * z))))) = T(a(x,y,z),(x * y) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(14(a,2),1751(a,2,1))].">
      <j1 rule="para" parents="14 1751"/>
    </justification>
  </clause>

  <clause id="2396">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),1752(a,2,2,1,2))].">
      <j1 rule="para" parents="8 1752"/>
    </justification>
  </clause>

  <clause id="2397">
    <literal><![CDATA[
      x * T(x \ (y * x),z) = y * (T(y,z) * (y \ x))
    ]]></literal>
    <justification jstring="[para(527(a,1),1752(a,1,2)),flip(a)].">
      <j1 rule="para" parents="527 1752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2398">
    <literal><![CDATA[
      1 * T(1 \ (x * y),z) = x * (x \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(1182(a,1),1752(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1182 1752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2399">
    <literal><![CDATA[
      x * (T(x,y) * (x \ z)) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(1005,a,2397,a),flip(a)].">
      <j1 rule="hyper" parents="1005 2397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2400">
    <literal><![CDATA[
      (T(x,y) * z) / (T(x,y) * (x \ z)) = x
    ]]></literal>
    <justification jstring="[hyper(142,a,522,a(flip),b,2397,a(flip))].">
      <j1 rule="hyper" parents="142 522 2397"/>
    </justification>
  </clause>

  <clause id="2401">
    <literal><![CDATA[
      x \ (T(x,y) * z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,522,a(flip),b,2397,a(flip))].">
      <j1 rule="hyper" parents="139 522 2397"/>
    </justification>
  </clause>

  <clause id="2402">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) = x \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,2399,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 2399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2403">
    <literal><![CDATA[
      T(x,y) * (x * z) = x * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),2399(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 2399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2404">
    <literal><![CDATA[
      x * (T(x,y) * T(z,x)) = T(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(22(a,2),2399(a,1,2,2))].">
      <j1 rule="para" parents="22 2399"/>
    </justification>
  </clause>

  <clause id="2405">
    <literal><![CDATA[
      (x / y) * (T(x / y,z) * y) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(82(a,1),2399(a,1,2,2))].">
      <j1 rule="para" parents="82 2399"/>
    </justification>
  </clause>

  <clause id="2406">
    <literal><![CDATA[
      (x \ y) \ (x \ (T(x,z) * y)) = T(T(x,z),x \ y)
    ]]></literal>
    <justification jstring="[hyper(493,a,2401,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="493 2401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2407">
    <literal><![CDATA[
      x \ (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,289,a(flip),b,2401,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 289 2401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2408">
    <literal><![CDATA[
      (T(x,y) \ x) / (T(x,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(226,a,2407,a)].">
      <j1 rule="hyper" parents="226 2407"/>
    </justification>
  </clause>

  <clause id="2409">
    <literal><![CDATA[
      x * (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(157,a,2407,a)].">
      <j1 rule="hyper" parents="157 2407"/>
    </justification>
  </clause>

  <clause id="2410">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,117,a,b,2407,a)].">
      <j1 rule="hyper" parents="64 117 2407"/>
    </justification>
  </clause>

  <clause id="2411">
    <literal><![CDATA[
      T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(2407(a,1),1019(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2407 1019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2412">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,x \ 1) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2407(a,1),1638(a,1,1))].">
      <j1 rule="para" parents="2407 1638"/>
    </justification>
  </clause>

  <clause id="2413">
    <literal><![CDATA[
      (T(x,y) * T(T(x,y) \ 1,x)) * (T(x,y) \ x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(2407(a,1),1864(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2407 1864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2414">
    <literal><![CDATA[
      (T(x,y) \ T(x,z)) / (T(x,y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2408(a,1),1564(a,2,1))].">
      <j1 rule="para" parents="2408 1564"/>
    </justification>
  </clause>

  <clause id="2415">
    <literal><![CDATA[
      T(x,y) \ (x \ z) = x \ (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(149,a,2402,a)].">
      <j1 rule="hyper" parents="149 2402"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[para(2402(a,1),74(a,1,2,2))].">
      <j1 rule="para" parents="2402 74"/>
    </justification>
  </clause>

  <clause id="2417">
    <literal><![CDATA[
      (x * y) / (x * (T(x,z) \ y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,168,a(flip),b,2403,a)].">
      <j1 rule="hyper" parents="142 168 2403"/>
    </justification>
  </clause>

  <clause id="2418">
    <literal><![CDATA[
      T(x,y) \ (x * z) = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,2403,a)].">
      <j1 rule="hyper" parents="139 168 2403"/>
    </justification>
  </clause>

  <clause id="2419">
    <literal><![CDATA[
      (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(117(a,1),2403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="117 2403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2420">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = x * (T(x,y) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(1727(a,1),2416(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1727 2416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2421">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,y) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (T(x,y) \ z)) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(2417(a,1),467(a,1,1))].">
      <j1 rule="para" parents="2417 467"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,515,a,b,2404,a),flip(a)].">
      <j1 rule="hyper" parents="35 515 2404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2424">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * x) = x * K(x \ (x / T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(1883(a,2),2404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1883 2404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2425">
    <literal><![CDATA[
      T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(156,a,2414,a)].">
      <j1 rule="hyper" parents="156 2414"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(525(a,1),2405(a,1,2))].">
      <j1 rule="para" parents="525 2405"/>
    </justification>
  </clause>

  <clause id="2427">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ z)) * T((x * (T(x,y) \ z)) \ (x * z),u)) = T((x * z) / (x * (T(x,y) \ z)),u) * (x * z)
    ]]></literal>
    <justification jstring="[para(2417(a,1),2426(a,1,1))].">
      <j1 rule="para" parents="2417 2426"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(149,a,2396,a),flip(a)].">
      <j1 rule="hyper" parents="149 2396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2429">
    <literal><![CDATA[
      x * T(x \ y,y \ x) = y * K((y \ x) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(414(a,1),2396(a,1,2)),flip(a)].">
      <j1 rule="para" parents="414 2396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2430">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z)
    ]]></literal>
    <justification jstring="[para(1883(a,2),2396(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1883 2396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2432">
    <literal><![CDATA[
      T(x * y,z) / y = x * K(z \ (z / (x \ (1 / y))),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1506,a(flip),b,2430,a)].">
      <j1 rule="hyper" parents="64 1506 2430"/>
    </justification>
  </clause>

  <clause id="2433">
    <literal><![CDATA[
      (x \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1486,a(flip),b,2430,a),flip(a)].">
      <j1 rule="hyper" parents="64 1486 2430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2434">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(z \ (z / (x \ (x / y))),z)
    ]]></literal>
    <justification jstring="[para(82(a,1),2430(a,1,2,1))].">
      <j1 rule="para" parents="82 2430"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(117(a,1),2419(a,1,2,1))].">
      <j1 rule="para" parents="117 2419"/>
    </justification>
  </clause>

  <clause id="2437">
    <literal><![CDATA[
      (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(255(a,1),2419(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="255 2419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2438">
    <literal><![CDATA[
      (x \ y) \ ((y / x) * z) = (y / x) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(759,a,2436,a)].">
      <j1 rule="hyper" parents="759 2436"/>
    </justification>
  </clause>

  <clause id="2439">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ ((x / y) \ z)) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[hyper(757,a,2436,a),flip(a)].">
      <j1 rule="hyper" parents="757 2436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2440">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(721,a,2436,a),flip(a)].">
      <j1 rule="hyper" parents="721 2436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2442">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(141,a,2356,a(flip),b,2440,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="141 2356 2440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2443">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1724,a(flip),b,2442,a),flip(a)].">
      <j1 rule="hyper" parents="373 1724 2442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2444">
    <literal><![CDATA[
      (x \ 1) * K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(157,a,2442,a)].">
      <j1 rule="hyper" parents="157 2442"/>
    </justification>
  </clause>

  <clause id="2445">
    <literal><![CDATA[
      R(1 / x,x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(40,a,452,a,b,2443,a)].">
      <j1 rule="hyper" parents="40 452 2443"/>
    </justification>
  </clause>

  <clause id="2446">
    <literal><![CDATA[
      (R(1 / x,y,z) * x) * (1 / x) = R(x \ 1,y,z) * (x * (1 / x))
    ]]></literal>
    <justification jstring="[para(2445(a,1),506(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2445 506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,2356,a(flip),b,2438,a)].">
      <j1 rule="hyper" parents="145 2356 2438"/>
    </justification>
  </clause>

  <clause id="2449">
    <literal><![CDATA[
      (x \ 1) \ (K(x,x \ 1) * y) = K(x,x \ 1) * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,2356,a(flip),b,2448,a)].">
      <j1 rule="hyper" parents="139 2356 2448"/>
    </justification>
  </clause>

  <clause id="2450">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / x) \ y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,2448,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 2448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2451">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,2448,a(flip),b,1148,a),flip(a)].">
      <j1 rule="hyper" parents="145 2448 1148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2452">
    <literal><![CDATA[
      (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2357(a,1),2448(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2357 2448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2453">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(2365,a,2450,a)].">
      <j1 rule="hyper" parents="2365 2450"/>
    </justification>
  </clause>

  <clause id="2454">
    <literal><![CDATA[
      (1 / x) \ ((x \ 1) * y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(149,a,2452,a)].">
      <j1 rule="hyper" parents="149 2452"/>
    </justification>
  </clause>

  <clause id="2455">
    <literal><![CDATA[
      (x / y) \ ((y \ x) \ z) = (y \ x) \ ((x / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(149,a,2439,a)].">
      <j1 rule="hyper" parents="149 2439"/>
    </justification>
  </clause>

  <clause id="2457">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ x) \ 1,(x * y) \ x) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2429(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2458">
    <literal><![CDATA[
      (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),2432(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 2432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2459">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = T((z * y) / x,u) * x
    ]]></literal>
    <justification jstring="[para(525(a,1),1753(a,1,1))].">
      <j1 rule="para" parents="525 1753"/>
    </justification>
  </clause>

  <clause id="2460">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,y \ x,1 / (y \ x)) = L(1 / (y \ x),y \ x,y) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1777(a,1),1807(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1777 1807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2461">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),1814(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2463">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),2461(a,2,2))].">
      <j1 rule="para" parents="25 2461"/>
    </justification>
  </clause>

  <clause id="2464">
    <literal><![CDATA[
      L(T(x,y),z,u) * (x \ 1) = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),2463(a,1,1))].">
      <j1 rule="para" parents="25 2463"/>
    </justification>
  </clause>

  <clause id="2465">
    <literal><![CDATA[
      (x * R(x,y,z)) \ (x * (R(x,y,z) * u)) = L(u,x,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(274(a,1),1911(a,1,1))].">
      <j1 rule="para" parents="274 1911"/>
    </justification>
  </clause>

  <clause id="2466">
    <literal><![CDATA[
      R(x,y,z) \ ((1 / x) \ u) = x \ (R(1 / x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(2118(a,1),1936(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2118 1936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2467">
    <literal><![CDATA[
      x \ (R(1 / x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(82(a,1),2466(a,1,2)),flip(a)].">
      <j1 rule="para" parents="82 2466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2468">
    <literal><![CDATA[
      R(1 / x,y,z) \ 1 = x * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(157,a,2467,a),flip(a)].">
      <j1 rule="hyper" parents="157 2467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2469">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(149,a,1951,a),flip(a)].">
      <j1 rule="hyper" parents="149 1951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2470">
    <literal><![CDATA[
      (x / y) * (y \ R(y,z,u)) = x * R(x \ (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(1987(a,1),1952(a,1,2))].">
      <j1 rule="para" parents="1987 1952"/>
    </justification>
  </clause>

  <clause id="2471">
    <literal><![CDATA[
      (x / y) \ (x * R(x \ (x / y),z,u)) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(149,a,2470,a)].">
      <j1 rule="hyper" parents="149 2470"/>
    </justification>
  </clause>

  <clause id="2472">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * ((1 / x) * z)) / y) = (x \ 1) * (x * ((y * (x \ z)) / y))
    ]]></literal>
    <justification jstring="[hyper(145,a,1965,a(flip),b,2260,a),flip(a)].">
      <j1 rule="hyper" parents="145 1965 2260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2473">
    <literal><![CDATA[
      ((x * x) \ ((y * y) * z)) * u = (((x * x) \ y) * y) * (z * u)
    ]]></literal>
    <justification jstring="[para(484(a,1),1978(a,2,1))].">
      <j1 rule="para" parents="484 1978"/>
    </justification>
  </clause>

  <clause id="2474">
    <literal><![CDATA[
      (x * (x * y)) \ ((1 / (1 / x)) * z) = L(y,x,x) \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(559(a,1),2049(a,1,1)),flip(a)].">
      <j1 rule="para" parents="559 2049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2475">
    <literal><![CDATA[
      (x * x) * (R(y / (1 / x),z,u) \ w) = R(y / x,z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(157,a,2121,a)].">
      <j1 rule="hyper" parents="157 2121"/>
    </justification>
  </clause>

  <clause id="2476">
    <literal><![CDATA[
      ((x \ 1) \ x) * (R(T(x \ 1,x),y,z) * u) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(145,a,2176,a(flip),b,1546,a)].">
      <j1 rule="hyper" parents="145 2176 1546"/>
    </justification>
  </clause>

  <clause id="2477">
    <literal><![CDATA[
      L(x,y,R(1 / z,u,w) * v5) = L(x,y,R(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(309(a,1),2241(a,1,3,1,1))].">
      <j1 rule="para" parents="309 2241"/>
    </justification>
  </clause>

  <clause id="2478">
    <literal><![CDATA[
      L(x,y,(((z \ 1) * u) * w) * v5) = L(x,y,((z * u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),2279(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 2279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2479">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(843(a,1),2300(a,2,1))].">
      <j1 rule="para" parents="843 2300"/>
    </justification>
  </clause>

  <clause id="2480">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x \ R(x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(2007(a,1),2300(a,2,1))].">
      <j1 rule="para" parents="2007 2300"/>
    </justification>
  </clause>

  <clause id="2481">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(836(a,1),2321(a,2,1))].">
      <j1 rule="para" parents="836 2321"/>
    </justification>
  </clause>

  <clause id="2482">
    <literal><![CDATA[
      L(x,L(y,z,u),y) = L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(608,a,2337,a)].">
      <j1 rule="hyper" parents="608 2337"/>
    </justification>
  </clause>

  <clause id="2483">
    <literal><![CDATA[
      ((x \ 1) * L(x,y,z)) * L(u,x,L(x,y,z)) = (x \ 1) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,2337,a(flip),b,1658,a)].">
      <j1 rule="hyper" parents="145 2337 1658"/>
    </justification>
  </clause>

  <clause id="2484">
    <literal><![CDATA[
      L(x,T(x,y) \ 1,T(x,y)) = x * K(x \ (x / T(x,y)),x)
    ]]></literal>
    <justification jstring="[hyper(611,a,2424,a)].">
      <j1 rule="hyper" parents="611 2424"/>
    </justification>
  </clause>

  <clause id="2485">
    <literal><![CDATA[
      ((x * y) / x) * (y * z) = y * (((x * y) / x) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),2437(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2486">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(759,a,2485,a)].">
      <j1 rule="hyper" parents="759 2485"/>
    </justification>
  </clause>

  <clause id="2487">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(721,a,2485,a),flip(a)].">
      <j1 rule="hyper" parents="721 2485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2488">
    <literal><![CDATA[
      x * (((y * x) / y) * (x \ z)) = ((y * x) / y) * z
    ]]></literal>
    <justification jstring="[hyper(397,a,2485,a),flip(a)].">
      <j1 rule="hyper" parents="397 2485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2489">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,2485,a)].">
      <j1 rule="hyper" parents="139 168 2485"/>
    </justification>
  </clause>

  <clause id="2490">
    <literal><![CDATA[
      x * (((y * x) / y) \ 1) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,72,a(flip),b,2485,a),flip(a)].">
      <j1 rule="hyper" parents="139 72 2485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2491">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ 1)) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1495,a,b,2487,a)].">
      <j1 rule="hyper" parents="64 1495 2487"/>
    </justification>
  </clause>

  <clause id="2492">
    <literal><![CDATA[
      (((x / y) * T(y,z)) / (x / y)) \ T(y,z) = T(y,z) * (T(x / (x / y),z) \ 1)
    ]]></literal>
    <justification jstring="[para(911(a,1),2490(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="911 2490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((((x * y) / x) \ y) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(1012,a,2486,a),flip(a)].">
      <j1 rule="hyper" parents="1012 2486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2494">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(269,a,12,a(flip),b,2488,a)].">
      <j1 rule="hyper" parents="269 12 2488"/>
    </justification>
  </clause>

  <clause id="2496">
    <literal><![CDATA[
      T(x,y) / (y \ x) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,2494,a,b,xx)].">
      <j1 rule="hyper" parents="142 2494"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(256(a,1),2494(a,2,1)),flip(a)].">
      <j1 rule="para" parents="256 2494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      ((x * R(1 / y,y,x)) / x) * (y * x) = T(x,R(1 / y,y,x))
    ]]></literal>
    <justification jstring="[para(452(a,1),2494(a,2,2)),flip(a)].">
      <j1 rule="para" parents="452 2494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2500">
    <literal><![CDATA[
      ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x) = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[para(475(a,1),2494(a,2,2)),flip(a)].">
      <j1 rule="para" parents="475 2494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2502">
    <literal><![CDATA[
      T(T(x,y) / (y \ x),x) = y
    ]]></literal>
    <justification jstring="[para(2496(a,2),255(a,1,1))].">
      <j1 rule="para" parents="2496 255"/>
    </justification>
  </clause>

  <clause id="2503">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(482(a,1),2502(a,1,1,2))].">
      <j1 rule="para" parents="482 2502"/>
    </justification>
  </clause>

  <clause id="2506">
    <literal><![CDATA[
      T((1 / x) \ (y / x),z) = (1 / x) \ (T(y,z) / x)
    ]]></literal>
    <justification jstring="[hyper(139,a,2458,a(flip),b,2430,a),flip(a)].">
      <j1 rule="hyper" parents="139 2458 2430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2507">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ x,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,526,a(flip),b,2459,a),flip(a)].">
      <j1 rule="hyper" parents="373 526 2459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2508">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,525,a(flip),b,2459,a),flip(a)].">
      <j1 rule="hyper" parents="373 525 2459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2509">
    <literal><![CDATA[
      (x * T(x \ (y * z),u)) / z = (x / z) * T((x / z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(142,a,525,a(flip),b,2459,a)].">
      <j1 rule="hyper" parents="142 525 2459"/>
    </justification>
  </clause>

  <clause id="2510">
    <literal><![CDATA[
      ((x / y) * T(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),2507(a,1,1,2,1))].">
      <j1 rule="para" parents="82 2507"/>
    </justification>
  </clause>

  <clause id="2511">
    <literal><![CDATA[
      T((x / y) * T(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(493,a,xx,b,2510,a)].">
      <j1 rule="hyper" parents="493 2510"/>
    </justification>
  </clause>

  <clause id="2512">
    <literal><![CDATA[
      (x * T(y,z)) / y = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(154,a,2510,a)].">
      <j1 rule="hyper" parents="154 2510"/>
    </justification>
  </clause>

  <clause id="2513">
    <literal><![CDATA[
      (x / y) * T(y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,115,a(flip),b,2510,a),flip(a)].">
      <j1 rule="hyper" parents="142 115 2510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2514">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(142,a,12,a(flip),b,2510,a),flip(a)].">
      <j1 rule="hyper" parents="142 12 2510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2515">
    <literal><![CDATA[
      (x * T(y,z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),2510(a,1,1,1))].">
      <j1 rule="para" parents="11 2510"/>
    </justification>
  </clause>

  <clause id="2516">
    <literal><![CDATA[
      (x * T(T(y,x),z)) * T(y,x) = (y * x) * T(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(214(a,1),2510(a,1,1,1))].">
      <j1 rule="para" parents="214 2510"/>
    </justification>
  </clause>

  <clause id="2517">
    <literal><![CDATA[
      ((x \ y) * y) / (x \ y) = x * T(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(400,a,2513,a),flip(a)].">
      <j1 rule="hyper" parents="400 2513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2518">
    <literal><![CDATA[
      ((x * y) / x) / T(x,y) = y / x
    ]]></literal>
    <justification jstring="[hyper(154,a,2513,a)].">
      <j1 rule="hyper" parents="154 2513"/>
    </justification>
  </clause>

  <clause id="2519">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,256,a(flip),b,2513,a)].">
      <j1 rule="hyper" parents="139 256 2513"/>
    </justification>
  </clause>

  <clause id="2520">
    <literal><![CDATA[
      K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,2513,a(flip),b,2434,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 2513 2434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2521">
    <literal><![CDATA[
      (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = (y * x) * T(L(x \ 1,x,y),y)
    ]]></literal>
    <justification jstring="[para(441(a,1),2513(a,1,1)),flip(a)].">
      <j1 rule="para" parents="441 2513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2522">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = (y * (1 / x)) * T(L(x,1 / x,y),y)
    ]]></literal>
    <justification jstring="[para(470(a,1),2513(a,1,1)),flip(a)].">
      <j1 rule="para" parents="470 2513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2523">
    <literal><![CDATA[
      (x / (y / z)) * T(y / z,z) = (x * (z \ y)) / (y / z)
    ]]></literal>
    <justification jstring="[para(117(a,1),2512(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="117 2512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2524">
    <literal><![CDATA[
      (x * y) / T(y,z) = (x / T(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(784,a,2515,a)].">
      <j1 rule="hyper" parents="784 2515"/>
    </justification>
  </clause>

  <clause id="2525">
    <literal><![CDATA[
      (1 / T(x,y)) * x = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(519,a,2515,a),flip(a)].">
      <j1 rule="hyper" parents="519 2515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2526">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(149,a,2515,a)].">
      <j1 rule="hyper" parents="149 2515"/>
    </justification>
  </clause>

  <clause id="2527">
    <literal><![CDATA[
      (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(117(a,1),2515(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="117 2515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2528">
    <literal><![CDATA[
      ((x * y) * T(y,z)) / (y * T(y,z)) = R(x,T(y,z),y)
    ]]></literal>
    <justification jstring="[para(2515(a,1),411(a,1,1))].">
      <j1 rule="para" parents="2515 411"/>
    </justification>
  </clause>

  <clause id="2529">
    <literal><![CDATA[
      (1 / T(x,y)) \ (x / T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(149,a,2525,a)].">
      <j1 rule="hyper" parents="149 2525"/>
    </justification>
  </clause>

  <clause id="2530">
    <literal><![CDATA[
      (1 / T(x,y)) * x != z
    ]]></literal>
    <literal><![CDATA[
      x / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2529(a,1),290(a,1,2))].">
      <j1 rule="para" parents="2529 290"/>
    </justification>
  </clause>

  <clause id="2531">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(x,z) / T(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2529(a,1),2506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2529 2506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2532">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(144,a,1587,a,b,2524,a)].">
      <j1 rule="hyper" parents="144 1587 2524"/>
    </justification>
  </clause>

  <clause id="2533">
    <literal><![CDATA[
      T((x / y) / T(y,z),y) = y \ (x / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(493,a,170,a(flip),b,2524,a(flip))].">
      <j1 rule="hyper" parents="493 170 2524"/>
    </justification>
  </clause>

  <clause id="2534">
    <literal><![CDATA[
      (x * y) / T(y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(x / T(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(2524(a,2),270(a,2)),flip(a)].">
      <j1 rule="para" parents="2524 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2535">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2526(a,1),1756(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2526 1756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2536">
    <literal><![CDATA[
      T(x * T(x \ y,y),x \ y) = y
    ]]></literal>
    <justification jstring="[para(2517(a,1),255(a,1,1))].">
      <j1 rule="para" parents="2517 255"/>
    </justification>
  </clause>

  <clause id="2537">
    <literal><![CDATA[
      (T(x,y) / T(x,z)) / T(x,y) = 1 / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(226,a,2531,a)].">
      <j1 rule="hyper" parents="226 2531"/>
    </justification>
  </clause>

  <clause id="2538">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(2532(a,1),2404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2532 2404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2539">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x * (x * y)) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(154,a,2538,a),flip(a)].">
      <j1 rule="hyper" parents="154 2538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2540">
    <literal><![CDATA[
      (x * (x * y)) / (y * x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1587,a(flip),b,2539,a),flip(a)].">
      <j1 rule="hyper" parents="64 1587 2539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2541">
    <literal><![CDATA[
      R(((x * (x * y)) / x) / y,y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,351,a,b,2540,a)].">
      <j1 rule="hyper" parents="64 351 2540"/>
    </justification>
  </clause>

  <clause id="2542">
    <literal><![CDATA[
      R(x,T(y,z),y) = R(x,y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(666,a,2528,a),flip(a)].">
      <j1 rule="hyper" parents="666 2528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2543">
    <literal><![CDATA[
      (T(x,y) * z) * T(x,z) = (x * z) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(265(a,1),2516(a,1,1))].">
      <j1 rule="para" parents="265 2516"/>
    </justification>
  </clause>

  <clause id="2544">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(142,a,71,a(flip),b,2543,a)].">
      <j1 rule="hyper" parents="142 71 2543"/>
    </justification>
  </clause>

  <clause id="2545">
    <literal><![CDATA[
      (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(117(a,1),2523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 2523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2546">
    <literal><![CDATA[
      (x / ((y * z) / y)) * (y \ (y * z)) = (x * z) / ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),2545(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 2545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2547">
    <literal><![CDATA[
      (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(117(a,1),2527(a,1,2))].">
      <j1 rule="para" parents="117 2527"/>
    </justification>
  </clause>

  <clause id="2548">
    <literal><![CDATA[
      (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z
    ]]></literal>
    <justification jstring="[para(255(a,1),2527(a,1,2)),flip(a)].">
      <j1 rule="para" parents="255 2527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2549">
    <literal><![CDATA[
      R(x / (y * y),y,y \ 1) = (x * (y \ 1)) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,826,a,b,2547,a)].">
      <j1 rule="hyper" parents="64 826 2547"/>
    </justification>
  </clause>

  <clause id="2550">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y * y) = (x * (y \ 1)) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2142,a(flip),b,2549,a)].">
      <j1 rule="hyper" parents="64 2142 2549"/>
    </justification>
  </clause>

  <clause id="2551">
    <literal><![CDATA[
      R(x / (y \ 1),y,y \ 1) = (x * (1 / y)) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,166,a(flip),b,2550,a),flip(a)].">
      <j1 rule="hyper" parents="144 166 2550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2552">
    <literal><![CDATA[
      R(x / (y \ 1),y,y \ 1) = R(x,y,y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1413,a(flip),b,2551,a),flip(a)].">
      <j1 rule="hyper" parents="373 1413 2551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2553">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1487,a(flip),b,2544,a),flip(a)].">
      <j1 rule="hyper" parents="373 1487 2544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2554">
    <literal><![CDATA[
      L(x,R(y,z,u),y) = L(x,y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(608,a,2465,a)].">
      <j1 rule="hyper" parents="608 2465"/>
    </justification>
  </clause>

  <clause id="2555">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * L((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * L(((x * y) \ (x * (y * z))) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),2469(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 2469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2556">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,u))) * ((x \ y) \ 1) = L((x \ y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(2469(a,1),1872(a,1,1))].">
      <j1 rule="para" parents="2469 1872"/>
    </justification>
  </clause>

  <clause id="2557">
    <literal><![CDATA[
      (((x * x) \ (y * y)) * z) * u = (((x * x) \ y) * y) * (z * u)
    ]]></literal>
    <justification jstring="[para(484(a,1),2473(a,1,1))].">
      <j1 rule="para" parents="484 2473"/>
    </justification>
  </clause>

  <clause id="2558">
    <literal><![CDATA[
      K(x \ 1,x) * R(((x \ 1) * x) \ x,y,z) = ((x \ 1) * R((x \ 1) \ 1,y,z)) * x
    ]]></literal>
    <justification jstring="[para(294(a,2),2479(a,1,1))].">
      <j1 rule="para" parents="294 2479"/>
    </justification>
  </clause>

  <clause id="2559">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ 1,z,u)) * y = x * L(((x / y) * y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(390,a,2481,a),flip(a)].">
      <j1 rule="hyper" parents="390 2481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2561">
    <literal><![CDATA[
      T(x,x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,1302,a(flip),b,2481,a(flip))].">
      <j1 rule="hyper" parents="269 1302 2481"/>
    </justification>
  </clause>

  <clause id="2562">
    <literal><![CDATA[
      K(x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,2561,a)].">
      <j1 rule="hyper" parents="56 2561"/>
    </justification>
  </clause>

  <clause id="2563">
    <literal><![CDATA[
      T(x,x * ((y * x) \ y)) = x
    ]]></literal>
    <justification jstring="[para(241(a,1),2561(a,1,2,2))].">
      <j1 rule="para" parents="241 2561"/>
    </justification>
  </clause>

  <clause id="2564">
    <literal><![CDATA[
      T(x \ y,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[para(436(a,1),2561(a,1,2,2))].">
      <j1 rule="para" parents="436 2561"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(839(a,1),2561(a,1,2))].">
      <j1 rule="para" parents="839 2561"/>
    </justification>
  </clause>

  <clause id="2566">
    <literal><![CDATA[
      L(T(x,(y * x) \ y),(y * x) \ y,x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,765,a,b,2563,a)].">
      <j1 rule="hyper" parents="64 765 2563"/>
    </justification>
  </clause>

  <clause id="2567">
    <literal><![CDATA[
      T(T(x,y),T(x,y) * ((T(x,y) / x) \ (1 / x))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1511(a,1),2563(a,1,2,2,1))].">
      <j1 rule="para" parents="1511 2563"/>
    </justification>
  </clause>

  <clause id="2568">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) * (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(2564(a,1),771(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2564 771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2569">
    <literal><![CDATA[
      R(x \ 1,L(x,y,z),x \ 1) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2565(a,1),1057(a,1,1))].">
      <j1 rule="para" parents="2565 1057"/>
    </justification>
  </clause>

  <clause id="2570">
    <literal><![CDATA[
      T(T(x,y) * ((T(x,y) / x) \ (1 / x)),T(x,y)) = T(x,y) * ((T(x,y) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(55,a,2567,a)].">
      <j1 rule="hyper" parents="55 2567"/>
    </justification>
  </clause>

  <clause id="2571">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,1191,a,b,2568,a),flip(a)].">
      <j1 rule="hyper" parents="36 1191 2568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2572">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(42,a,1303,a,b,2571,a(flip))].">
      <j1 rule="hyper" parents="42 1303 2571"/>
    </justification>
  </clause>

  <clause id="2573">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),2572(a,1,1,2))].">
      <j1 rule="para" parents="9 2572"/>
    </justification>
  </clause>

  <clause id="2574">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y
    ]]></literal>
    <justification jstring="[para(9(a,1),2573(a,2,2))].">
      <j1 rule="para" parents="9 2573"/>
    </justification>
  </clause>

  <clause id="2575">
    <literal><![CDATA[
      L(x \ 1,x,(y * x) \ y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(472,a,2574,a)].">
      <j1 rule="hyper" parents="472 2574"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      (((x * y) \ x) * y) * (1 / y) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(157,a,2574,a)].">
      <j1 rule="hyper" parents="157 2574"/>
    </justification>
  </clause>

  <clause id="2577">
    <literal><![CDATA[
      L(x \ 1,x,y \ (y / x)) = 1 / x
    ]]></literal>
    <justification jstring="[para(12(a,1),2575(a,1,3,1))].">
      <j1 rule="para" parents="12 2575"/>
    </justification>
  </clause>

  <clause id="2578">
    <literal><![CDATA[
      (x * y) \ x = (L(y \ 1,y,x) * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(241(a,2),2576(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="241 2576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2579">
    <literal><![CDATA[
      L(x \ 1,x,y) / (1 / x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(142,a,241,a,b,2578,a(flip))].">
      <j1 rule="hyper" parents="142 241 2578"/>
    </justification>
  </clause>

  <clause id="2580">
    <literal><![CDATA[
      (((x * (1 / y)) / x) * y) * x = T(x,R(1 / y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,1276,a(flip),b,2499,a)].">
      <j1 rule="hyper" parents="64 1276 2499"/>
    </justification>
  </clause>

  <clause id="2581">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(1 / x,x,y))
    ]]></literal>
    <justification jstring="[para(1237(a,1),2580(a,1,1))].">
      <j1 rule="para" parents="1237 2580"/>
    </justification>
  </clause>

  <clause id="2583">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ (z * u)),w))) / u = ((x * y) / u) * T(((x * y) / u) \ z,w)
    ]]></literal>
    <justification jstring="[hyper(142,a,1308,a(flip),b,2508,a)].">
      <j1 rule="hyper" parents="142 1308 2508"/>
    </justification>
  </clause>

  <clause id="2584">
    <literal><![CDATA[
      (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,115,a(flip),b,2508,a),flip(a)].">
      <j1 rule="hyper" parents="142 115 2508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2586">
    <literal><![CDATA[
      (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),2509(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 2509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2587">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,1883,a,b,2586,a)].">
      <j1 rule="hyper" parents="64 1883 2586"/>
    </justification>
  </clause>

  <clause id="2588">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y)
    ]]></literal>
    <justification jstring="[hyper(144,a,414,a(flip),b,2586,a(flip))].">
      <j1 rule="hyper" parents="144 414 2586"/>
    </justification>
  </clause>

  <clause id="2589">
    <literal><![CDATA[
      K((x * (y / z)) \ x,x * (y / z)) = (y * T(y \ z,x * (y / z))) / z
    ]]></literal>
    <justification jstring="[para(11(a,1),2587(a,1,1,2))].">
      <j1 rule="para" parents="11 2587"/>
    </justification>
  </clause>

  <clause id="2590">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * u) * T(((y * z) * u) \ (z * u),x)) / (z * u)
    ]]></literal>
    <justification jstring="[para(20(a,2),2587(a,1,1,2,2))].">
      <j1 rule="para" parents="20 2587"/>
    </justification>
  </clause>

  <clause id="2591">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,522,a(flip),b,2588,a),flip(a)].">
      <j1 rule="hyper" parents="373 522 2588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2592">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(739,a,2546,a),flip(a)].">
      <j1 rule="hyper" parents="739 2546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2594">
    <literal><![CDATA[
      (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),2548(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 2548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2595">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,80,a(flip),b,2594,a),flip(a)].">
      <j1 rule="hyper" parents="142 80 2594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2597">
    <literal><![CDATA[
      ((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y
    ]]></literal>
    <justification jstring="[para(1582(a,1),2594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1582 2594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2598">
    <literal><![CDATA[
      (1 / x) * ((y * ((z / x) \ z)) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(220(a,2),2595(a,1,2,1))].">
      <j1 rule="para" parents="220 2595"/>
    </justification>
  </clause>

  <clause id="2599">
    <literal><![CDATA[
      T(x,x / (x / y)) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(390,a,2597,a),flip(a)].">
      <j1 rule="hyper" parents="390 2597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2603">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) \ (x * (z * y)) = a(z,y,T(x,z * y))
    ]]></literal>
    <justification jstring="[para(793(a,1),260(a,1,1))].">
      <j1 rule="para" parents="793 260"/>
    </justification>
  </clause>

  <clause id="2606">
    <literal><![CDATA[
      (((x * y) * (x * y)) \ x) * z = (1 / (x * y)) * L(y \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(806,a,631,a)].">
      <j1 rule="hyper" parents="806 631"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      ((x * x) \ (y * (z * u))) * a(y,z,u) = ((x * x) \ (y * z)) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,484,a(flip),b,939,a),flip(a)].">
      <j1 rule="hyper" parents="373 484 939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2608">
    <literal><![CDATA[
      R(x,y * ((x * y) \ z),a(x,y,(x * y) \ z)) \ z = (y * ((x * y) \ z)) * a(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(956(a,1),349(a,1,1))].">
      <j1 rule="para" parents="956 349"/>
    </justification>
  </clause>

  <clause id="2609">
    <literal><![CDATA[
      L(T(((x * y) * z) / (x * y),y),y,x) = (x * (z * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(541(a,1),1195(a,1,1))].">
      <j1 rule="para" parents="541 1195"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      L((x \ 1) \ ((x \ 1) \ (y / ((1 / (x \ 1)) * z))),x \ 1,x) = T(y / ((x \ 1) * z),(x \ 1) * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(1234,a,1633,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1234 1633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2611">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z)
    ]]></literal>
    <justification jstring="[hyper(145,a,1275,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 1275 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2612">
    <literal><![CDATA[
      x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z)
    ]]></literal>
    <justification jstring="[para(1275(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="1275 598"/>
    </justification>
  </clause>

  <clause id="2613">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (y * z),u,w) = y * (T(x,y) * L(T(x,y) \ z,u,w))
    ]]></literal>
    <justification jstring="[para(638(a,1),1295(a,1,2,1))].">
      <j1 rule="para" parents="638 1295"/>
    </justification>
  </clause>

  <clause id="2614">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (y * z),u,w) = y * (T(x,y) * R(T(x,y) \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,1317,a(flip),b,261,a)].">
      <j1 rule="hyper" parents="145 1317 261"/>
    </justification>
  </clause>

  <clause id="2617">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(436(a,1),1877(a,1,2))].">
      <j1 rule="para" parents="436 1877"/>
    </justification>
  </clause>

  <clause id="2618">
    <literal><![CDATA[
      (x \ y) / ((y \ x) \ 1) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(226,a,2617,a)].">
      <j1 rule="hyper" parents="226 2617"/>
    </justification>
  </clause>

  <clause id="2619">
    <literal><![CDATA[
      ((x \ (x / y)) * y) \ ((x / y) \ x) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),2617(a,1,1,2))].">
      <j1 rule="para" parents="82 2617"/>
    </justification>
  </clause>

  <clause id="2620">
    <literal><![CDATA[
      ((x \ (x / y)) * y) \ y = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),2619(a,1,2))].">
      <j1 rule="para" parents="82 2619"/>
    </justification>
  </clause>

  <clause id="2621">
    <literal><![CDATA[
      (L(1 / x,y,z) * x) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(1380(a,1),1953(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1380 1953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2622">
    <literal><![CDATA[
      (L(x / y,z,u) * y) * (y \ w) = w * L(w \ (x * (y \ w)),z,u)
    ]]></literal>
    <justification jstring="[para(1379(a,1),1953(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1379 1953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2623">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(836(a,1),2621(a,1,1))].">
      <j1 rule="para" parents="836 2621"/>
    </justification>
  </clause>

  <clause id="2624">
    <literal><![CDATA[
      (x * L(x \ (y \ x),z,u)) / (y \ x) = y * L(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(154,a,2623,a)].">
      <j1 rule="hyper" parents="154 2623"/>
    </justification>
  </clause>

  <clause id="2625">
    <literal><![CDATA[
      R(L(x,y,x),y,T(x,y)) = (x * y) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[para(770(a,1),1980(a,1,1))].">
      <j1 rule="para" parents="770 1980"/>
    </justification>
  </clause>

  <clause id="2626">
    <literal><![CDATA[
      L(R(x,y,T(x,y)),y,x) = (x * y) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29,a(flip),b,2625,a)].">
      <j1 rule="hyper" parents="64 29 2625"/>
    </justification>
  </clause>

  <clause id="2627">
    <literal><![CDATA[
      L(R(x,y,T(x,y)),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,9,a(flip),b,2626,a),flip(a)].">
      <j1 rule="hyper" parents="373 9 2626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2629">
    <literal><![CDATA[
      L(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      R(z,y,T(z,y)) = x
    ]]></literal>
    <justification jstring="[para(2627(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="2627 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2630">
    <literal><![CDATA[
      R((x * x) \ x,y,z) \ L(u,x,x) = x * (R(x,y,z) \ (x * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,1907,a(flip),b,2117,a),flip(a)].">
      <j1 rule="hyper" parents="373 1907 2117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2631">
    <literal><![CDATA[
      (1 / (x * y)) * L(y \ z,y,x) = ((1 / (x * y)) / y) * z
    ]]></literal>
    <justification jstring="[para(873(a,1),2606(a,1,1)),flip(a)].">
      <j1 rule="para" parents="873 2606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2632">
    <literal><![CDATA[
      (1 / (x \ L(x,y,z))) * L((x \ 1) \ u,x \ 1,L(x,y,z)) = ((1 / (L(x,y,z) * (x \ 1))) / (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(1807(a,1),2631(a,1,1,2))].">
      <j1 rule="para" parents="1807 2631"/>
    </justification>
  </clause>

  <clause id="2633">
    <literal><![CDATA[
      ((x * x) \ (y * (z * u))) * a(y,z,u) = (((x * x) \ y) * z) * u
    ]]></literal>
    <justification jstring="[para(484(a,1),2607(a,2,1))].">
      <j1 rule="para" parents="484 2607"/>
    </justification>
  </clause>

  <clause id="2634">
    <literal><![CDATA[
      R((x * x) \ x,y,z) \ L(u,x,x) = x * (x * (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(1907(a,1),2630(a,2,2))].">
      <j1 rule="para" parents="1907 2630"/>
    </justification>
  </clause>

  <clause id="2635">
    <literal><![CDATA[
      (((x * x) \ y) * (z * u)) * a(y,z,u) = (((x * x) \ y) * z) * u
    ]]></literal>
    <justification jstring="[para(484(a,1),2633(a,1,1))].">
      <j1 rule="para" parents="484 2633"/>
    </justification>
  </clause>

  <clause id="2636">
    <literal><![CDATA[
      R(1 / x,y,z) \ L(u,x,x) = x * (x * (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(309(a,1),2634(a,1,1,1))].">
      <j1 rule="para" parents="309 2634"/>
    </justification>
  </clause>

  <clause id="2637">
    <literal><![CDATA[
      a((x * x) \ y,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,88,a,b,2635,a)].">
      <j1 rule="hyper" parents="35 88 2635"/>
    </justification>
  </clause>

  <clause id="2638">
    <literal><![CDATA[
      a((x * x) \ y,z,u) = (y * (z * u)) \ ((y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,14,a(flip),b,2637,a),flip(a)].">
      <j1 rule="hyper" parents="373 14 2637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2639">
    <literal><![CDATA[
      a((x * x) * y,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),2637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 2637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2640">
    <literal><![CDATA[
      a(x * (x * y),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(18(a,2),2637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 2637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2641">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(309(a,1),2637(a,1,1))].">
      <j1 rule="para" parents="309 2637"/>
    </justification>
  </clause>

  <clause id="2642">
    <literal><![CDATA[
      a((1 / x) * y,z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(535(a,1),2637(a,1,1))].">
      <j1 rule="para" parents="535 2637"/>
    </justification>
  </clause>

  <clause id="2643">
    <literal><![CDATA[
      a((x * x) / y,z,u) = a(1 / y,z,u)
    ]]></literal>
    <justification jstring="[para(548(a,1),2637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="548 2637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2644">
    <literal><![CDATA[
      a(L(x \ y,x,x),z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(102(a,2),2637(a,1,1))].">
      <j1 rule="para" parents="102 2637"/>
    </justification>
  </clause>

  <clause id="2645">
    <literal><![CDATA[
      a(((x * x) \ y) * z,u,w) = a(y * z,u,w)
    ]]></literal>
    <justification jstring="[para(484(a,1),2637(a,1,1))].">
      <j1 rule="para" parents="484 2637"/>
    </justification>
  </clause>

  <clause id="2646">
    <literal><![CDATA[
      a((1 / x) / y,z,u) = a(x / y,z,u)
    ]]></literal>
    <justification jstring="[para(887(a,1),2637(a,1,1))].">
      <j1 rule="para" parents="887 2637"/>
    </justification>
  </clause>

  <clause id="2647">
    <literal><![CDATA[
      a(L(T(x,y),y,y),z,u) = a(y * (x * y),z,u)
    ]]></literal>
    <justification jstring="[para(262(a,1),2637(a,1,1))].">
      <j1 rule="para" parents="262 2637"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      a(x * ((x \ 1) \ y),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(582(a,1),2637(a,1,1))].">
      <j1 rule="para" parents="582 2637"/>
    </justification>
  </clause>

  <clause id="2649">
    <literal><![CDATA[
      a((x * y) * (y \ x),z,u) = a(a(x,y,y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(89(a,1),2637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="89 2637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2650">
    <literal><![CDATA[
      a(R((x * x) \ y,z,u),w,v5) = a(R(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(2051(a,2),2637(a,1,1))].">
      <j1 rule="para" parents="2051 2637"/>
    </justification>
  </clause>

  <clause id="2651">
    <literal><![CDATA[
      a(1 / x,x,y) = L(y,x,x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,1243,a,b,2641,a),flip(a)].">
      <j1 rule="hyper" parents="373 1243 2641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2652">
    <literal><![CDATA[
      ((1 / x) * y) * a(x,z,z \ y) = ((1 / x) * z) * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,2641,a(flip),b,89,a)].">
      <j1 rule="hyper" parents="145 2641 89"/>
    </justification>
  </clause>

  <clause id="2653">
    <literal><![CDATA[
      a(x \ 1,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),2641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="79 2641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2654">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2641,a,b,2653,a)].">
      <j1 rule="hyper" parents="373 2641 2653"/>
    </justification>
  </clause>

  <clause id="2655">
    <literal><![CDATA[
      a(((x * x) * y) * z,u,w) = a(y * z,u,w)
    ]]></literal>
    <justification jstring="[para(33(a,2),2639(a,1,1))].">
      <j1 rule="para" parents="33 2639"/>
    </justification>
  </clause>

  <clause id="2656">
    <literal><![CDATA[
      a(((x * x) / y) * z,u,w) = a((1 / y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(556(a,1),2639(a,1,1))].">
      <j1 rule="para" parents="556 2639"/>
    </justification>
  </clause>

  <clause id="2657">
    <literal><![CDATA[
      a((x * (x * y)) * z,u,w) = a(L(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(605(a,1),2639(a,1,1))].">
      <j1 rule="para" parents="605 2639"/>
    </justification>
  </clause>

  <clause id="2658">
    <literal><![CDATA[
      a((((x * x) \ y) * z) * u,w,v5) = a((y * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(805(a,1),2639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="805 2639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      a(((x * (x * y)) * z) * u,w,v5) = a((L(y,x,x) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(1314(a,1),2639(a,1,1))].">
      <j1 rule="para" parents="1314 2639"/>
    </justification>
  </clause>

  <clause id="2660">
    <literal><![CDATA[
      a((T(x,y * y) * z) * u,w,v5) = a((x * ((y * y) * z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(1455(a,1),2639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1455 2639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2661">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(1631(a,2),2651(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1631 2651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2662">
    <literal><![CDATA[
      a((x \ 1) * y,z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),2642(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 2642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2663">
    <literal><![CDATA[
      a(((x / (y * x)) \ 1) * z,u,w) = a(((y \ x) / x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(2032(a,1),2642(a,1,1,1))].">
      <j1 rule="para" parents="2032 2642"/>
    </justification>
  </clause>

  <clause id="2664">
    <literal><![CDATA[
      a(x \ R(x,y,z),u,w) = a(x * R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(2067(a,1),2642(a,1,1))].">
      <j1 rule="para" parents="2067 2642"/>
    </justification>
  </clause>

  <clause id="2665">
    <literal><![CDATA[
      a((x * x) / y,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2641,a(flip),b,2643,a),flip(a)].">
      <j1 rule="hyper" parents="373 2641 2643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2666">
    <literal><![CDATA[
      a(x \ (y * y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),2665(a,1,1)),flip(a)].">
      <j1 rule="para" parents="79 2665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2667">
    <literal><![CDATA[
      a(L(x \ y,x,y),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(591(a,1),2665(a,1,1)),flip(a)].">
      <j1 rule="para" parents="591 2665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2668">
    <literal><![CDATA[
      a(T(x,x \ y),z,u) = a((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(518(a,1),2665(a,1,1))].">
      <j1 rule="para" parents="518 2665"/>
    </justification>
  </clause>

  <clause id="2669">
    <literal><![CDATA[
      a(L(T(x,y),y,x * y),z,u) = a((x * y) * y,z,u)
    ]]></literal>
    <justification jstring="[para(590(a,1),2665(a,1,1)),flip(a)].">
      <j1 rule="para" parents="590 2665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2670">
    <literal><![CDATA[
      a(R(x,y,z) * (x \ R(x,y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(1901(a,1),2665(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1901 2665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2671">
    <literal><![CDATA[
      a((1 / x) \ y,z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1138(a,1),2648(a,1,1))].">
      <j1 rule="para" parents="1138 2648"/>
    </justification>
  </clause>

  <clause id="2672">
    <literal><![CDATA[
      a(R(x * ((x \ 1) \ y),z,u),w,v5) = a(R(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(2146(a,2),2648(a,1,1))].">
      <j1 rule="para" parents="2146 2648"/>
    </justification>
  </clause>

  <clause id="2673">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2654,a(flip),b,2661,a),flip(a)].">
      <j1 rule="hyper" parents="373 2654 2661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2674">
    <literal><![CDATA[
      L(x,y,y \ 1) * a(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,2654,a(flip),b,2661,a)].">
      <j1 rule="hyper" parents="145 2654 2661"/>
    </justification>
  </clause>

  <clause id="2675">
    <literal><![CDATA[
      a((x \ 1) \ y,z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),2671(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 2671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2676">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x != z
    ]]></literal>
    <literal><![CDATA[
      a(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(2674(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="2674 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2677">
    <literal><![CDATA[
      a(L(((x * x) * y) \ z,(x * x) * y,(x * x) * y),u,w) = a((x * x) * (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(33(a,1),2644(a,2,1))].">
      <j1 rule="para" parents="33 2644"/>
    </justification>
  </clause>

  <clause id="2678">
    <literal><![CDATA[
      a((((x * y) * x) * y) * z,u,w) = a(a(x * y,x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(14(a,2),2645(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14 2645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2679">
    <literal><![CDATA[
      a(((1 / x) * y) * z,u,w) = a((x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(535(a,1),2645(a,1,1,1))].">
      <j1 rule="para" parents="535 2645"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      a(L(x \ y,x,x) * z,u,w) = a((x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(102(a,2),2645(a,1,1,1))].">
      <j1 rule="para" parents="102 2645"/>
    </justification>
  </clause>

  <clause id="2681">
    <literal><![CDATA[
      a(((1 / x) / y) * z,u,w) = a((x / y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(887(a,1),2645(a,1,1,1))].">
      <j1 rule="para" parents="887 2645"/>
    </justification>
  </clause>

  <clause id="2682">
    <literal><![CDATA[
      a(L(T(x,y),y,y) * z,u,w) = a((y * (x * y)) * z,u,w)
    ]]></literal>
    <justification jstring="[para(262(a,1),2645(a,1,1,1))].">
      <j1 rule="para" parents="262 2645"/>
    </justification>
  </clause>

  <clause id="2683">
    <literal><![CDATA[
      a((x \ ((x * y) * y)) * z,u,w) = a(a(x,y,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(874(a,1),2645(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="874 2645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2684">
    <literal><![CDATA[
      a(((x / (1 / y)) \ z) * u,w,v5) = a(((x / y) \ z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(876(a,1),2645(a,1,1,1))].">
      <j1 rule="para" parents="876 2645"/>
    </justification>
  </clause>

  <clause id="2685">
    <literal><![CDATA[
      a((((1 / x) * y) / z) * u,w,v5) = a(((x * y) / z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(937(a,1),2645(a,1,1,1))].">
      <j1 rule="para" parents="937 2645"/>
    </justification>
  </clause>

  <clause id="2686">
    <literal><![CDATA[
      a(R((x * x) \ y,z,u) * w,v5,v6) = a(R(y,z,u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(2051(a,2),2645(a,1,1,1))].">
      <j1 rule="para" parents="2051 2645"/>
    </justification>
  </clause>

  <clause id="2687">
    <literal><![CDATA[
      a(R(((x * x) \ y) * z,u,w),v5,v6) = a(R(y * z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(484(a,1),2650(a,1,1,1))].">
      <j1 rule="para" parents="484 2650"/>
    </justification>
  </clause>

  <clause id="2688">
    <literal><![CDATA[
      a(((x * x) / y) * z,u,w) = a(y * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2642,a(flip),b,2656,a),flip(a)].">
      <j1 rule="hyper" parents="373 2642 2656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2689">
    <literal><![CDATA[
      a((R(x,y,z) * (x \ R(x,y,z))) * u,w,v5) = a(x * u,w,v5)
    ]]></literal>
    <justification jstring="[para(1901(a,1),2688(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1901 2688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2690">
    <literal><![CDATA[
      a(((x \ 1) * y) * z,u,w) = a((x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),2679(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 2679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2691">
    <literal><![CDATA[
      a((L(x * x,y,z) \ u) * w,v5,v6) = a((L(x * x,y,z) * u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(1824(a,1),2690(a,1,1,1))].">
      <j1 rule="para" parents="1824 2690"/>
    </justification>
  </clause>

  <clause id="2692">
    <literal><![CDATA[
      a((x * x) \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(2638(a,2),959(a,1))].">
      <j1 rule="para" parents="2638 959"/>
    </justification>
  </clause>

  <clause id="2693">
    <literal><![CDATA[
      a((1 / x) * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(535(a,1),2692(a,1,1))].">
      <j1 rule="para" parents="535 2692"/>
    </justification>
  </clause>

  <clause id="2694">
    <literal><![CDATA[
      a(L(x \ y,x,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * y,z,u) = w
    ]]></literal>
    <justification jstring="[para(102(a,2),2692(a,1,1))].">
      <j1 rule="para" parents="102 2692"/>
    </justification>
  </clause>

  <clause id="2695">
    <literal><![CDATA[
      a((((1 / x) * y) * z) * u,w,v5) = a(((x * y) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(535(a,1),2658(a,1,1,1,1))].">
      <j1 rule="para" parents="535 2658"/>
    </justification>
  </clause>

  <clause id="2696">
    <literal><![CDATA[
      a(R((x \ 1) * y,z,u),w,v5) = a(R(x * y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),2672(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 2672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2697">
    <literal><![CDATA[
      a(R(x \ 1,y,z),u,w) = a(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(191(a,1),2672(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="191 2672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2698">
    <literal><![CDATA[
      a(R((1 / x) \ y,z,u),w,v5) = a(R(x \ y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(1138(a,1),2672(a,1,1,1))].">
      <j1 rule="para" parents="1138 2672"/>
    </justification>
  </clause>

  <clause id="2699">
    <literal><![CDATA[
      a(R((x \ 1) \ y,z,u),w,v5) = a(R(x \ y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),2698(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 2698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2700">
    <literal><![CDATA[
      a(((x / (y * x)) \ 1) * x,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),2663(a,2,1))].">
      <j1 rule="para" parents="12 2663"/>
    </justification>
  </clause>

  <clause id="2701">
    <literal><![CDATA[
      a((x / (y * x)) * x,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2662,a(flip),b,2700,a)].">
      <j1 rule="hyper" parents="64 2662 2700"/>
    </justification>
  </clause>

  <clause id="2702">
    <literal><![CDATA[
      a((x / y) \ y,z,u) = a((y / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),2701(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 2701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      a(R(1 / x,y,z) * u,w,v5) = a(R(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(309(a,1),2686(a,1,1,1,1))].">
      <j1 rule="para" parents="309 2686"/>
    </justification>
  </clause>

  <clause id="2704">
    <literal><![CDATA[
      a(R((1 / x) * y,z,u) * w,v5,v6) = a(R(x * y,z,u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(535(a,1),2686(a,1,1,1,1))].">
      <j1 rule="para" parents="535 2686"/>
    </justification>
  </clause>

  <clause id="2705">
    <literal><![CDATA[
      a(R(x \ 1,y,z) * u,w,v5) = a(R(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),2703(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 2703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2706">
    <literal><![CDATA[
      a((((x \ 1) * y) * z) * u,w,v5) = a(((x * y) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),2695(a,1,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 2695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2707">
    <literal><![CDATA[
      (x * (L(x,y,z) * u)) \ ((x * L(x,y,z)) * u) = a(L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(2323(a,1),529(a,1,1))].">
      <j1 rule="para" parents="2323 529"/>
    </justification>
  </clause>

  <clause id="2708">
    <literal><![CDATA[
      L(x \ y,x,x) * L(z,y,(x * x) \ x) = L(x \ (y * z),x,x)
    ]]></literal>
    <justification jstring="[para(581(a,1),763(a,1,1))].">
      <j1 rule="para" parents="581 763"/>
    </justification>
  </clause>

  <clause id="2709">
    <literal><![CDATA[
      L(x \ y,x,x) * L(z,y,x) = L(x \ (y * z),x,x)
    ]]></literal>
    <justification jstring="[para(2181(a,1),2708(a,1,2))].">
      <j1 rule="para" parents="2181 2708"/>
    </justification>
  </clause>

  <clause id="2710">
    <literal><![CDATA[
      L(x \ y,x,x) \ L(x \ (y * z),x,x) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(149,a,2709,a)].">
      <j1 rule="hyper" parents="149 2709"/>
    </justification>
  </clause>

  <clause id="2712">
    <literal><![CDATA[
      T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1003(a,1,1,1,2))].">
      <j1 rule="para" parents="10 1003"/>
    </justification>
  </clause>

  <clause id="2713">
    <literal><![CDATA[
      (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(912,a,2712,a),flip(a)].">
      <j1 rule="hyper" parents="912 2712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2714">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(525(a,1),2713(a,1,1))].">
      <j1 rule="para" parents="525 2713"/>
    </justification>
  </clause>

  <clause id="2715">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) = y * T(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(154,a,2714,a)].">
      <j1 rule="hyper" parents="154 2714"/>
    </justification>
  </clause>

  <clause id="2716">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(2714(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2714 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2717">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(1484(a,1),2714(a,1,1))].">
      <j1 rule="para" parents="1484 2714"/>
    </justification>
  </clause>

  <clause id="2718">
    <literal><![CDATA[
      R((x * x) \ (y / z),u,w) * z = ((x * x) \ z) * R(z \ y,u,w)
    ]]></literal>
    <justification jstring="[para(2051(a,2),1268(a,1,1))].">
      <j1 rule="para" parents="2051 1268"/>
    </justification>
  </clause>

  <clause id="2719">
    <literal><![CDATA[
      (1 / (x / y)) \ (y / x) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(1363,a,1782,a),flip(a)].">
      <j1 rule="hyper" parents="1363 1782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2720">
    <literal><![CDATA[
      (x / (y \ x)) * ((y \ x) / x) = (1 / ((y \ x) / x)) \ y
    ]]></literal>
    <justification jstring="[para(79(a,1),2719(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 2719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2721">
    <literal><![CDATA[
      (x / y) * L(z,(x / y) * (y / x),1 / (y / x)) = (1 / (y / x)) * (((1 / (y / x)) \ (x / y)) * z)
    ]]></literal>
    <justification jstring="[para(2719(a,1),515(a,1,2,2))].">
      <j1 rule="para" parents="2719 515"/>
    </justification>
  </clause>

  <clause id="2722">
    <literal><![CDATA[
      (1 / ((x \ y) / y)) * (x * ((x \ y) / y)) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,209,a(flip),b,2720,a(flip))].">
      <j1 rule="hyper" parents="145 209 2720"/>
    </justification>
  </clause>

  <clause id="2723">
    <literal><![CDATA[
      T(1 / ((x \ y) / y),x * ((x \ y) / y)) = (x * ((x \ y) / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(493,a,xx,b,2722,a)].">
      <j1 rule="hyper" parents="493 2722"/>
    </justification>
  </clause>

  <clause id="2724">
    <literal><![CDATA[
      x \ ((x / y) * ((y \ z) * y)) = T(x \ ((x / y) * z),y)
    ]]></literal>
    <justification jstring="[para(12(a,1),1377(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 1377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2725">
    <literal><![CDATA[
      ((x \ 1) \ x) * (y \ ((x \ (x \ 1)) * z)) = T(y,x \ (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,1673,a(flip),b,1446,a)].">
      <j1 rule="hyper" parents="64 1673 1446"/>
    </justification>
  </clause>

  <clause id="2726">
    <literal><![CDATA[
      ((1 / x) \ x) \ (y * (x * ((x \ 1) \ z))) = T(y,(1 / x) \ x) * z
    ]]></literal>
    <justification jstring="[para(1611(a,1),1525(a,1,2))].">
      <j1 rule="para" parents="1611 1525"/>
    </justification>
  </clause>

  <clause id="2727">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1695(a,2),2276(a,1))].">
      <j1 rule="para" parents="1695 2276"/>
    </justification>
  </clause>

  <clause id="2728">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(1213,a,1697,a)].">
      <j1 rule="hyper" parents="1213 1697"/>
    </justification>
  </clause>

  <clause id="2729">
    <literal><![CDATA[
      (R((x / y) / z,u,w) * z) * y = (z * y) * R((z * y) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,843,a(flip),b,1698,a),flip(a)].">
      <j1 rule="hyper" parents="373 843 1698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,836,a(flip),b,1702,a)].">
      <j1 rule="hyper" parents="64 836 1702"/>
    </justification>
  </clause>

  <clause id="2731">
    <literal><![CDATA[
      x * ((x * y) * L((x * y) \ y,z,u)) = (x * L(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2481,a(flip),b,1704,a),flip(a)].">
      <j1 rule="hyper" parents="64 2481 1704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2732">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,2481,a(flip),b,1705,a),flip(a)].">
      <j1 rule="hyper" parents="64 2481 1705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2733">
    <literal><![CDATA[
      x * ((x * y) * R((x * y) \ y,z,u)) = (x \ R(x,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2480,a(flip),b,1708,a),flip(a)].">
      <j1 rule="hyper" parents="64 2480 1708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2734">
    <literal><![CDATA[
      x * ((x * y) * R((x * y) \ y,z,u)) = (x * R(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2479,a(flip),b,1708,a),flip(a)].">
      <j1 rule="hyper" parents="64 2479 1708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2735">
    <literal><![CDATA[
      (((x * y) / (x * z)) * x) * z = x * (z * R(z \ y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1197,a(flip),b,1708,a)].">
      <j1 rule="hyper" parents="64 1197 1708"/>
    </justification>
  </clause>

  <clause id="2736">
    <literal><![CDATA[
      (((x * (y * z)) / (x * y)) * x) * y = x * (y * R(z,x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),2735(a,2,2,2,1))].">
      <j1 rule="para" parents="9 2735"/>
    </justification>
  </clause>

  <clause id="2737">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (z * R(T(y,z),x,z))
    ]]></literal>
    <justification jstring="[para(22(a,2),2735(a,2,2,2,1))].">
      <j1 rule="para" parents="22 2735"/>
    </justification>
  </clause>

  <clause id="2738">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (R(y,x,z) * z)
    ]]></literal>
    <justification jstring="[para(267(a,1),2737(a,2,2))].">
      <j1 rule="para" parents="267 2737"/>
    </justification>
  </clause>

  <clause id="2739">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,2479,a(flip),b,1709,a),flip(a)].">
      <j1 rule="hyper" parents="64 2479 1709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2740">
    <literal><![CDATA[
      x * (y * R(y \ (x \ 1),z,u)) = (x * y) \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1987,a(flip),b,1709,a),flip(a)].">
      <j1 rule="hyper" parents="64 1987 1709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2741">
    <literal><![CDATA[
      (R(x / (y / z),u,w) * (y / z)) * z = y * R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,843,a(flip),b,1954,a),flip(a)].">
      <j1 rule="hyper" parents="373 843 1954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ (y \ 1),z,u) = x \ (R(x,z,u) * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(139,a,2107,a(flip),b,1955,a),flip(a)].">
      <j1 rule="hyper" parents="139 2107 1955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2743">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),1956(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 1956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2744">
    <literal><![CDATA[
      (x \ y) \ R(x \ y,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,1987,a(flip),b,2743,a)].">
      <j1 rule="hyper" parents="64 1987 2743"/>
    </justification>
  </clause>

  <clause id="2745">
    <literal><![CDATA[
      (x \ (y * R(y \ x,z,u))) * (x \ y) = R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,2744,a(flip),b,2071,a)].">
      <j1 rule="hyper" parents="144 2744 2071"/>
    </justification>
  </clause>

  <clause id="2746">
    <literal><![CDATA[
      (x * (x * y)) \ ((x * x) * R((x * x) \ (x * (x * y)),z,u)) = (L(y,x,x) \ 1) \ R((x * (x * y)) \ (x * x),z,u)
    ]]></literal>
    <justification jstring="[para(585(a,1),2744(a,1,1)),flip(a)].">
      <j1 rule="para" parents="585 2744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2747">
    <literal><![CDATA[
      x \ (y * (z * L(z \ (y \ (x * u)),w,v5))) = (x \ (y * z)) * L((x \ (y * z)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(1705(a,1),1957(a,1,2))].">
      <j1 rule="para" parents="1705 1957"/>
    </justification>
  </clause>

  <clause id="2748">
    <literal><![CDATA[
      x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(1583,a,1961,a)].">
      <j1 rule="hyper" parents="1583 1961"/>
    </justification>
  </clause>

  <clause id="2749">
    <literal><![CDATA[
      (x * (y * z)) * ((u * (((x * y) * L(z,y,x)) \ (x * y))) / u) = (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u))
    ]]></literal>
    <justification jstring="[para(100(a,1),1961(a,1,1))].">
      <j1 rule="para" parents="100 1961"/>
    </justification>
  </clause>

  <clause id="2750">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = (x \ T(x,x / (x * y))) * x
    ]]></literal>
    <justification jstring="[para(2748(a,2),2581(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2748 2581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2751">
    <literal><![CDATA[
      (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z)
    ]]></literal>
    <justification jstring="[hyper(149,a,1964,a)].">
      <j1 rule="hyper" parents="149 1964"/>
    </justification>
  </clause>

  <clause id="2752">
    <literal><![CDATA[
      ((x * ((y \ z) / (y * (y \ z)))) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(397,a,1966,a)].">
      <j1 rule="hyper" parents="397 1966"/>
    </justification>
  </clause>

  <clause id="2754">
    <literal><![CDATA[
      ((x * ((y * z) / (R(u,y,z) * (y * z)))) / x) * ((u * y) * z) = (((x * (1 / R(u,y,z))) / x) * R(u,y,z)) * (y * z)
    ]]></literal>
    <justification jstring="[para(111(a,1),1966(a,1,2))].">
      <j1 rule="para" parents="111 1966"/>
    </justification>
  </clause>

  <clause id="2755">
    <literal><![CDATA[
      L(x \ y,x,x * R(x,z,u)) = R(x,z,u) \ ((x \ R(x,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2212,a(flip),b,2077,a)].">
      <j1 rule="hyper" parents="64 2212 2077"/>
    </justification>
  </clause>

  <clause id="2756">
    <literal><![CDATA[
      ((1 / x) \ y) \ R(x,z,u) = (x \ y) \ R(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(191(a,1),2174(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="191 2174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2757">
    <literal><![CDATA[
      R(x \ 1,y,z) / R(1 / x,y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,2047,a(flip),b,2262,a)].">
      <j1 rule="hyper" parents="142 2047 2262"/>
    </justification>
  </clause>

  <clause id="2758">
    <literal><![CDATA[
      R(x \ 1,y,z) * (((x \ 1) \ x) * u) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(10(a,1),2288(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 2288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2759">
    <literal><![CDATA[
      ((x \ 1) \ x) * (R(x,y,z) \ u) = R(x \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,2758,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 2758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2760">
    <literal><![CDATA[
      R(x \ 1,y,z) * ((x \ 1) \ u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(1131(a,1),2758(a,1,2))].">
      <j1 rule="para" parents="1131 2758"/>
    </justification>
  </clause>

  <clause id="2761">
    <literal><![CDATA[
      (x \ 1) * (R(x,y,z) * (x \ u)) = R(x \ 1,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(145,a,2760,a(flip),b,1898,a)].">
      <j1 rule="hyper" parents="145 2760 1898"/>
    </justification>
  </clause>

  <clause id="2762">
    <literal><![CDATA[
      R(x,y,z) \ ((x \ 1) \ u) = x \ (R(x \ 1,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,1899,a(flip),b,2760,a(flip))].">
      <j1 rule="hyper" parents="139 1899 2760"/>
    </justification>
  </clause>

  <clause id="2763">
    <literal><![CDATA[
      R(x \ 1,y,z) * (x * u) = (x \ 1) * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),2761(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 2761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2764">
    <literal><![CDATA[
      (x \ 1) * (R(x,y,z) * T(u,x)) = R(x \ 1,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[para(22(a,2),2761(a,1,2,2))].">
      <j1 rule="para" parents="22 2761"/>
    </justification>
  </clause>

  <clause id="2765">
    <literal><![CDATA[
      R(x \ 1,y,z) * x = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(191(a,1),2761(a,1,2)),flip(a)].">
      <j1 rule="para" parents="191 2761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2766">
    <literal><![CDATA[
      (x \ 1) * (x \ (R(x,y,z) * u)) = R(x \ 1,y,z) * u
    ]]></literal>
    <justification jstring="[para(1898(a,2),2761(a,1,2))].">
      <j1 rule="para" parents="1898 2761"/>
    </justification>
  </clause>

  <clause id="2767">
    <literal><![CDATA[
      R(x \ 1,y,z) * (R(x,y,z) \ u) = (x \ 1) * (x \ u)
    ]]></literal>
    <justification jstring="[para(1899(a,1),2761(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1899 2761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2768">
    <literal><![CDATA[
      R(x,y,z) \ (x * ((x \ 1) \ u)) = R(x \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(39,a,1929,a,b,2762,a(flip))].">
      <j1 rule="hyper" parents="39 1929 2762"/>
    </justification>
  </clause>

  <clause id="2769">
    <literal><![CDATA[
      (1 / x) * (R(x,y,z) * u) = x * (R(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,2766,a(flip),b,1128,a),flip(a)].">
      <j1 rule="hyper" parents="145 2766 1128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2770">
    <literal><![CDATA[
      R(x,y,z) \ (((x \ 1) * (x \ 1)) \ u) = R(x \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[para(582(a,2),2768(a,1,2))].">
      <j1 rule="para" parents="582 2768"/>
    </justification>
  </clause>

  <clause id="2771">
    <literal><![CDATA[
      (R(1 / x,y,z) * x) * (1 / x) = R(x \ 1,y,z) * K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(296(a,2),2446(a,2,2))].">
      <j1 rule="para" parents="296 2446"/>
    </justification>
  </clause>

  <clause id="2772">
    <literal><![CDATA[
      (((x * y) / x) * (y \ 1)) * x = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,1276,a(flip),b,2500,a)].">
      <j1 rule="hyper" parents="64 1276 2500"/>
    </justification>
  </clause>

  <clause id="2773">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * y = T(y,R(x,x \ 1,y))
    ]]></literal>
    <justification jstring="[para(2487(a,1),2772(a,1,1))].">
      <j1 rule="para" parents="2487 2772"/>
    </justification>
  </clause>

  <clause id="2774">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[para(256(a,1),2773(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="256 2773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2775">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) \ 1 = x \ (((T(y,x) \ y) * x) \ x)
    ]]></literal>
    <justification jstring="[para(2774(a,1),2407(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2774 2407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2776">
    <literal><![CDATA[
      T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(700(a,1),2503(a,1,1))].">
      <j1 rule="para" parents="700 2503"/>
    </justification>
  </clause>

  <clause id="2777">
    <literal><![CDATA[
      T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(2776(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2776 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2778">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(1502(a,1),2777(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1502 2777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2779">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(675(a,1),2778(a,2,2))].">
      <j1 rule="para" parents="675 2778"/>
    </justification>
  </clause>

  <clause id="2780">
    <literal><![CDATA[
      T(x,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(12(a,1),2779(a,1,1))].">
      <j1 rule="para" parents="12 2779"/>
    </justification>
  </clause>

  <clause id="2781">
    <literal><![CDATA[
      T(x,x * (y \ 1)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(117(a,1),2780(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 2780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2782">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * (x \ w) = w * L(w \ (y * (x \ w)),z,u)
    ]]></literal>
    <justification jstring="[para(836(a,1),2622(a,1,1))].">
      <j1 rule="para" parents="836 2622"/>
    </justification>
  </clause>

  <clause id="2783">
    <literal><![CDATA[
      a(R((x \ 1) * y,z,u) * w,v5,v6) = a(R(x * y,z,u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(79(a,1),2704(a,1,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 2704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2784">
    <literal><![CDATA[
      a(L(x,y,z),x,u) = a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(959,a,2707,a),flip(a)].">
      <j1 rule="hyper" parents="959 2707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2785">
    <literal><![CDATA[
      a(x \ y,L(x \ y,x,y),z) = a(y * x,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2667,a(flip),b,2784,a),flip(a)].">
      <j1 rule="hyper" parents="64 2667 2784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2786">
    <literal><![CDATA[
      ((x * x) \ y) * R(y \ z,u,w) = y * R(y \ ((x * x) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,1200,a(flip),b,2718,a),flip(a)].">
      <j1 rule="hyper" parents="64 1200 2718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2787">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) \ ((y \ 1) \ z) = ((y \ 1) \ y) * (x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(1551(a,1),2725(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1551 2725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2788">
    <literal><![CDATA[
      (x \ 1) * (x \ (y * (x * ((x \ 1) \ z)))) = T(y,(1 / x) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,1168,a(flip),b,2726,a)].">
      <j1 rule="hyper" parents="64 1168 2726"/>
    </justification>
  </clause>

  <clause id="2789">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(843(a,1),2728(a,2,1))].">
      <j1 rule="para" parents="843 2728"/>
    </justification>
  </clause>

  <clause id="2790">
    <literal><![CDATA[
      (x * y) * R((x * y) \ ((x * z) * y),u,w) = (x * R(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(844(a,1),2728(a,2,1))].">
      <j1 rule="para" parents="844 2728"/>
    </justification>
  </clause>

  <clause id="2791">
    <literal><![CDATA[
      (x * R(x \ (y / z),u,w)) * z = (x * z) * R((x * z) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(843(a,1),2729(a,1,1))].">
      <j1 rule="para" parents="843 2729"/>
    </justification>
  </clause>

  <clause id="2792">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (L(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1705,a(flip),b,2730,a)].">
      <j1 rule="hyper" parents="64 1705 2730"/>
    </justification>
  </clause>

  <clause id="2793">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(836(a,1),2730(a,2,1))].">
      <j1 rule="para" parents="836 2730"/>
    </justification>
  </clause>

  <clause id="2794">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (x * u) = x * ((x \ R(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(2480(a,1),2733(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2480 2733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x * u) = x * ((x \ R(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,2794,a)].">
      <j1 rule="hyper" parents="139 168 2794"/>
    </justification>
  </clause>

  <clause id="2796">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (x * x) = x * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2069(a,1),2794(a,2,2))].">
      <j1 rule="para" parents="2069 2794"/>
    </justification>
  </clause>

  <clause id="2797">
    <literal><![CDATA[
      R(x,y,z) \ (x * ((x \ R(x,y,z)) * u)) = L(u,x,x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(2794(a,1),2075(a,1,2))].">
      <j1 rule="para" parents="2794 2075"/>
    </justification>
  </clause>

  <clause id="2800">
    <literal><![CDATA[
      ((x / y) * R((x / y) \ z,u,w)) * y = x * R(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(843(a,1),2741(a,1,1))].">
      <j1 rule="para" parents="843 2741"/>
    </justification>
  </clause>

  <clause id="2801">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ (y \ 1),z,u) = R(x,z,u) * (x \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,1898,a(flip),b,2742,a),flip(a)].">
      <j1 rule="hyper" parents="373 1898 2742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2802">
    <literal><![CDATA[
      (x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),2751(a,1,2,2,1))].">
      <j1 rule="para" parents="10 2751"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      K(x,(x / y) / x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(547,a,2802,a)].">
      <j1 rule="hyper" parents="547 2802"/>
    </justification>
  </clause>

  <clause id="2804">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,(y / x) / y) = z
    ]]></literal>
    <justification jstring="[para(2802(a,1),547(a,1))].">
      <j1 rule="para" parents="2802 547"/>
    </justification>
  </clause>

  <clause id="2805">
    <literal><![CDATA[
      K(x,(x / (y \ 1)) / x) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2491,a(flip),b,2803,a),flip(a)].">
      <j1 rule="hyper" parents="373 2491 2803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2806">
    <literal><![CDATA[
      (x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(79(a,1),2803(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 2803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2807">
    <literal><![CDATA[
      x * ((T(x,y) * (x \ 1)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1514(a,1),2803(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1514 2803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2808">
    <literal><![CDATA[
      T(x,y) * ((T(x,z) * (T(x,y) \ 1)) / T(x,z)) = K(T(x,z),1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(2537(a,1),2803(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2537 2803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2809">
    <literal><![CDATA[
      K(x,(x / ((T(x,y) \ 1) \ 1)) / x) = (T(x,y) \ 1) \ ((T(x,y) \ x) / x)
    ]]></literal>
    <justification jstring="[para(2409(a,1),2805(a,2,2,1))].">
      <j1 rule="para" parents="2409 2805"/>
    </justification>
  </clause>

  <clause id="2810">
    <literal><![CDATA[
      x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(527(a,2),2807(a,1,2,1))].">
      <j1 rule="para" parents="527 2807"/>
    </justification>
  </clause>

  <clause id="2811">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (1 / x) = R(x \ 1,y,z) * K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(843(a,1),2771(a,1,1))].">
      <j1 rule="para" parents="843 2771"/>
    </justification>
  </clause>

  <clause id="2812">
    <literal><![CDATA[
      ((x * L(x \ y,z,u)) * (x \ w)) / w = L((y * (x \ w)) / w,z,u)
    ]]></literal>
    <justification jstring="[hyper(142,a,2782,a,b,836,a)].">
      <j1 rule="hyper" parents="142 2782 836"/>
    </justification>
  </clause>

  <clause id="2813">
    <literal><![CDATA[
      T(L(x,y,z),x \ (x \ 1)) \ ((x \ 1) \ u) = ((x \ 1) \ x) * (x \ (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(2339(a,1),2787(a,2,2))].">
      <j1 rule="para" parents="2339 2787"/>
    </justification>
  </clause>

  <clause id="2814">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1709,a(flip),b,2789,a)].">
      <j1 rule="hyper" parents="64 1709 2789"/>
    </justification>
  </clause>

  <clause id="2815">
    <literal><![CDATA[
      (x \ (y * x)) * R((x \ (y * x)) \ x,z,u) = T(y * R(y \ x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(269,a,2789,a(flip),b,1955,a),flip(a)].">
      <j1 rule="hyper" parents="269 2789 1955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2816">
    <literal><![CDATA[
      x * R(x \ (x \ (y * x)),z,u) = T(x * R(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(269,a,2789,a(flip),b,1709,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 2789 1709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2817">
    <literal><![CDATA[
      (x \ (y * z)) * R((x \ (y * z)) \ z,u,w) = x \ ((y * R(y \ x,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2789,a(flip),b,1955,a),flip(a)].">
      <j1 rule="hyper" parents="139 2789 1955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2818">
    <literal><![CDATA[
      (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = (R(x,y,z) * z) * R(L(T(y,z),z,R(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(990(a,1),2789(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="990 2789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2819">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),x) = x * R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),2816(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 2816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2820">
    <literal><![CDATA[
      x \ T(x * R(x \ y,z,u),x) = R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(1036,a,2819,a)].">
      <j1 rule="hyper" parents="1036 2819"/>
    </justification>
  </clause>

  <clause id="2821">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),x) / x = R(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(142,a,2819,a,b,843,a)].">
      <j1 rule="hyper" parents="142 2819 843"/>
    </justification>
  </clause>

  <clause id="2822">
    <literal><![CDATA[
      R(T(x * y,x) / x,z,u) = T(x * R(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(9(a,1),2821(a,1,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2823">
    <literal><![CDATA[
      (x * R(y,z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),2790(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2825">
    <literal><![CDATA[
      ((x / R(y,z,u)) * y) * R(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(390,a,2823,a),flip(a)].">
      <j1 rule="hyper" parents="390 2823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2826">
    <literal><![CDATA[
      R(x,y,R(y,z,u)) * (y * R(y,z,u)) = (x * R(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,111,a,b,2823,a)].">
      <j1 rule="hyper" parents="373 111 2823"/>
    </justification>
  </clause>

  <clause id="2827">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(149,a,2823,a)].">
      <j1 rule="hyper" parents="149 2823"/>
    </justification>
  </clause>

  <clause id="2828">
    <literal><![CDATA[
      (x * R(y,z,u)) / y = (x / y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(142,a,166,a(flip),b,2823,a)].">
      <j1 rule="hyper" parents="142 166 2823"/>
    </justification>
  </clause>

  <clause id="2829">
    <literal><![CDATA[
      (x * (y * R(y,z,u))) \ ((x * y) * R(y,z,u)) = a(x,R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(2823(a,1),528(a,1,2))].">
      <j1 rule="para" parents="2823 528"/>
    </justification>
  </clause>

  <clause id="2830">
    <literal><![CDATA[
      (x * y) / R(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / R(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(2825(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2825 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2831">
    <literal><![CDATA[
      T(R(x,y,R(x,z,u)),y * R(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2827(a,1),1055(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2827 1055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2832">
    <literal><![CDATA[
      (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,2831,a(flip),b,277,a)].">
      <j1 rule="hyper" parents="145 2831 277"/>
    </justification>
  </clause>

  <clause id="2833">
    <literal><![CDATA[
      T(x,y * R(z,u,w)) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      R(z,y,R(z,u,w)) = x
    ]]></literal>
    <justification jstring="[para(2831(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="2831 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2834">
    <literal><![CDATA[
      x / R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = u
    ]]></literal>
    <justification jstring="[para(7(a,1),2830(a,1,1))].">
      <j1 rule="para" parents="7 2830"/>
    </justification>
  </clause>

  <clause id="2835">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(2834,a,2156,a)].">
      <j1 rule="hyper" parents="2834 2156"/>
    </justification>
  </clause>

  <clause id="2836">
    <literal><![CDATA[
      (R(x,y,z) \ x) / x = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(154,a,2835,a)].">
      <j1 rule="hyper" parents="154 2835"/>
    </justification>
  </clause>

  <clause id="2837">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * (R(x,y,z) \ x) = R(x,y,z) \ (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,2835,a(flip),b,1127,a),flip(a)].">
      <j1 rule="hyper" parents="139 2835 1127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2838">
    <literal><![CDATA[
      R(x,R(y,z,u),y) = R(x,y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,670,a,b,2826,a)].">
      <j1 rule="hyper" parents="36 670 2826"/>
    </justification>
  </clause>

  <clause id="2839">
    <literal><![CDATA[
      (x * R(x \ (y / z),u,w)) * z = x * (z * R(z \ (x \ y),u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,1709,a(flip),b,2791,a),flip(a)].">
      <j1 rule="hyper" parents="373 1709 2791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2840">
    <literal><![CDATA[
      (x * (y * R(y \ (x \ z),u,w))) / y = x * R(x \ (z / y),u,w)
    ]]></literal>
    <justification jstring="[hyper(142,a,1709,a(flip),b,2791,a)].">
      <j1 rule="hyper" parents="142 1709 2791"/>
    </justification>
  </clause>

  <clause id="2841">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(836(a,1),2792(a,2,1))].">
      <j1 rule="para" parents="836 2792"/>
    </justification>
  </clause>

  <clause id="2842">
    <literal><![CDATA[
      (x * L(x \ y,z,x)) * z = x * (z * ((x * z) \ (y * z)))
    ]]></literal>
    <justification jstring="[hyper(334,a,2793,a),flip(a)].">
      <j1 rule="hyper" parents="334 2793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2843">
    <literal><![CDATA[
      ((x * y) * L((x * y) \ x,z,u)) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,1302,a(flip),b,2793,a),flip(a)].">
      <j1 rule="hyper" parents="64 1302 2793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2844">
    <literal><![CDATA[
      x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(269,a,2793,a(flip),b,1705,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 2793 1705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2845">
    <literal><![CDATA[
      x * (y * ((x * y) \ ((x * z) * y))) = (x * L(z,y,x)) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),2842(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2846">
    <literal><![CDATA[
      (x * L(y,y,x)) * y = x * (y * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),2845(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 2845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2847">
    <literal><![CDATA[
      x \ (y \ ((y * L(z,x,y)) * x)) = (y * x) \ ((y * z) * x)
    ]]></literal>
    <justification jstring="[para(2845(a,1),69(a,1,2,2))].">
      <j1 rule="para" parents="2845 69"/>
    </justification>
  </clause>

  <clause id="2848">
    <literal><![CDATA[
      T(x * L(y,y,x),y) = y \ (x * (y * y))
    ]]></literal>
    <justification jstring="[hyper(493,a,xx,b,2846,a)].">
      <j1 rule="hyper" parents="493 2846"/>
    </justification>
  </clause>

  <clause id="2849">
    <literal><![CDATA[
      (x * (y * y)) / y = x * L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(154,a,2846,a)].">
      <j1 rule="hyper" parents="154 2846"/>
    </justification>
  </clause>

  <clause id="2850">
    <literal><![CDATA[
      (x * y) / L(y,y,R(x,y,y)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,350,a(flip),b,2849,a(flip))].">
      <j1 rule="hyper" parents="142 350 2849"/>
    </justification>
  </clause>

  <clause id="2851">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),x) = x * L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),2844(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 2844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2852">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(1036,a,2851,a)].">
      <j1 rule="hyper" parents="1036 2851"/>
    </justification>
  </clause>

  <clause id="2853">
    <literal><![CDATA[
      T(x * L(x \ y,x,1 / x),x) = x * ((1 / x) * T(y,x))
    ]]></literal>
    <justification jstring="[para(628(a,1),2851(a,2,2))].">
      <j1 rule="para" parents="628 2851"/>
    </justification>
  </clause>

  <clause id="2854">
    <literal><![CDATA[
      L(x \ T(x * y,x),z,u) = x \ T(x * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2852(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2855">
    <literal><![CDATA[
      T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x))
    ]]></literal>
    <justification jstring="[para(628(a,1),2853(a,1,1,2))].">
      <j1 rule="para" parents="628 2853"/>
    </justification>
  </clause>

  <clause id="2856">
    <literal><![CDATA[
      T(x * ((1 / x) * ((1 / x) \ ((1 / (1 / x)) \ y))),x) = x * ((1 / (1 / x)) \ T(y,x))
    ]]></literal>
    <justification jstring="[para(1469(a,1),2855(a,2,2))].">
      <j1 rule="para" parents="1469 2855"/>
    </justification>
  </clause>

  <clause id="2857">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),y) = L(x,y,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(1012,a,2797,a)].">
      <j1 rule="hyper" parents="1012 2797"/>
    </justification>
  </clause>

  <clause id="2858">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),y) = L(x,y,y * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,2212,a(flip),b,2857,a),flip(a)].">
      <j1 rule="hyper" parents="373 2212 2857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2859">
    <literal><![CDATA[
      (x * R(x \ (y * z),u,w)) / z = (x / z) * R((x / z) \ y,u,w)
    ]]></literal>
    <justification jstring="[hyper(154,a,2800,a)].">
      <j1 rule="hyper" parents="154 2800"/>
    </justification>
  </clause>

  <clause id="2860">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (1 / x) = R(x \ 1,y,z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1726(a,1),2811(a,2,2))].">
      <j1 rule="para" parents="1726 2811"/>
    </justification>
  </clause>

  <clause id="2861">
    <literal><![CDATA[
      a(x,R(y,z,u),y) = a(x,y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(959,a,2829,a),flip(a)].">
      <j1 rule="hyper" parents="959 2829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2862">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = x * (z * L(z \ (x \ y),u,w))
    ]]></literal>
    <justification jstring="[para(12(a,1),2841(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 2841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2863">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,z,u) = (x * R(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),2859(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 2859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2864">
    <literal><![CDATA[
      (x / y) * R((x / y) \ (z / y),u,w) = (x * R(x \ z,u,w)) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),2859(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 2859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2865">
    <literal><![CDATA[
      (((x * y) * z) * R(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * R((((x * y) * z) / (y * z)) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),2863(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 2863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2866">
    <literal><![CDATA[
      R(x \ 1,y,z) * K(x,x \ 1) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2081,a(flip),b,2860,a),flip(a)].">
      <j1 rule="hyper" parents="64 2081 2860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2867">
    <literal><![CDATA[
      x \ (y * (x * L(x \ (y \ z),u,w))) = T(y * L(y \ (z / x),u,w),x)
    ]]></literal>
    <justification jstring="[hyper(493,a,xx,b,2862,a),flip(a)].">
      <j1 rule="hyper" parents="493 2862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2868">
    <literal><![CDATA[
      (x * ((y * y) * z)) \ (x * ((y * y) * (z * u))) = L(u,z,x * (y * y))
    ]]></literal>
    <justification jstring="[para(34(a,1),135(a,1,2))].">
      <j1 rule="para" parents="34 135"/>
    </justification>
  </clause>

  <clause id="2869">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,14,a,b,645,a)].">
      <j1 rule="hyper" parents="373 14 645"/>
    </justification>
  </clause>

  <clause id="2870">
    <literal><![CDATA[
      L(R(L(x,y,z) \ x,u,w),L(x,y,z),z * y) = R(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(2869(a,2),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2869 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2871">
    <literal><![CDATA[
      a(x,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x) \ y = z
    ]]></literal>
    <justification jstring="[para(2869(a,2),622(a,1))].">
      <j1 rule="para" parents="2869 622"/>
    </justification>
  </clause>

  <clause id="2872">
    <literal><![CDATA[
      R(x / (y * y),(y * y) * z,u) = ((x * z) * u) / ((y * y) * (z * u))
    ]]></literal>
    <justification jstring="[para(33(a,1),899(a,2,2))].">
      <j1 rule="para" parents="33 899"/>
    </justification>
  </clause>

  <clause id="2873">
    <literal><![CDATA[
      T((x * (y * z)) / (x * y),y) = (x * (z * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(988(a,1),910(a,1,1)),flip(a)].">
      <j1 rule="para" parents="988 910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2874">
    <literal><![CDATA[
      (x * (y * T(z,u))) / (x * y) = T((x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(517(a,1),910(a,1,1))].">
      <j1 rule="para" parents="517 910"/>
    </justification>
  </clause>

  <clause id="2875">
    <literal><![CDATA[
      (x * (y * T(T(z,y),u))) / (x * y) = T((x * (z * y)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(115(a,1),2874(a,2,1,1,2))].">
      <j1 rule="para" parents="115 2874"/>
    </justification>
  </clause>

  <clause id="2876">
    <literal><![CDATA[
      (x * (T(y,z) * u)) / (x * u) = T((x * (y * u)) / (x * u),z)
    ]]></literal>
    <justification jstring="[para(265(a,1),2875(a,1,1,2))].">
      <j1 rule="para" parents="265 2875"/>
    </justification>
  </clause>

  <clause id="2877">
    <literal><![CDATA[
      (x * (T(y \ R(y,z,u),w) * y)) / (x * y) = T((x * R(y,z,u)) / (x * y),w)
    ]]></literal>
    <justification jstring="[para(2069(a,1),2876(a,2,1,1,2))].">
      <j1 rule="para" parents="2069 2876"/>
    </justification>
  </clause>

  <clause id="2878">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(327,a,1328,a),flip(a)].">
      <j1 rule="hyper" parents="327 1328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2879">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (T(1 / x,z) * x) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),2878(a,1,2,1,2))].">
      <j1 rule="para" parents="7 2878"/>
    </justification>
  </clause>

  <clause id="2880">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(525(a,1),2878(a,2,1))].">
      <j1 rule="para" parents="525 2878"/>
    </justification>
  </clause>

  <clause id="2881">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(525(a,1),2879(a,2,1))].">
      <j1 rule="para" parents="525 2879"/>
    </justification>
  </clause>

  <clause id="2882">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1308,a(flip),b,2881,a)].">
      <j1 rule="hyper" parents="64 1308 2881"/>
    </justification>
  </clause>

  <clause id="2883">
    <literal><![CDATA[
      T(x,x * T(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,1001,a(flip),b,2881,a(flip))].">
      <j1 rule="hyper" parents="269 1001 2881"/>
    </justification>
  </clause>

  <clause id="2884">
    <literal><![CDATA[
      R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x)
    ]]></literal>
    <justification jstring="[para(2883(a,1),1061(a,1,1))].">
      <j1 rule="para" parents="2883 1061"/>
    </justification>
  </clause>

  <clause id="2885">
    <literal><![CDATA[
      T(x \ 1,T(x,y) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(527(a,1),2883(a,1,2))].">
      <j1 rule="para" parents="527 2883"/>
    </justification>
  </clause>

  <clause id="2886">
    <literal><![CDATA[
      T(x \ 1,x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1484(a,1),2883(a,1,2))].">
      <j1 rule="para" parents="1484 2883"/>
    </justification>
  </clause>

  <clause id="2887">
    <literal><![CDATA[
      T(1 / x,T(x,y) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1509(a,1),2883(a,1,2))].">
      <j1 rule="para" parents="1509 2883"/>
    </justification>
  </clause>

  <clause id="2888">
    <literal><![CDATA[
      T(x \ T(x,y),x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(55,a,2886,a)].">
      <j1 rule="hyper" parents="55 2886"/>
    </justification>
  </clause>

  <clause id="2889">
    <literal><![CDATA[
      T((x * (1 / y)) / x,T(y,z) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(2887(a,1),541(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2887 541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2890">
    <literal><![CDATA[
      R(x \ 1,T(x,y),x \ 1) = T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(2885(a,1),1057(a,1,1))].">
      <j1 rule="para" parents="2885 1057"/>
    </justification>
  </clause>

  <clause id="2891">
    <literal><![CDATA[
      T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(2888(a,1),1015(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2888 1015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2892">
    <literal><![CDATA[
      K(x,y) = T((y * x) \ (x * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,1013,a,b,2891,a)].">
      <j1 rule="hyper" parents="373 1013 2891"/>
    </justification>
  </clause>

  <clause id="2893">
    <literal><![CDATA[
      T(K(x,y),x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(16(a,2),2892(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16 2892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2894">
    <literal><![CDATA[
      T(x \ 1,K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(55,a,2893,a)].">
      <j1 rule="hyper" parents="55 2893"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = (x \ 1) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,2893,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 2893 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2896">
    <literal><![CDATA[
      T(T(x \ 1,y),K(x,z)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2894(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2894 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2897">
    <literal><![CDATA[
      x * T(x \ 1,K(x,y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      1 / u = z
    ]]></literal>
    <justification jstring="[para(2894(a,2),392(a,1,2))].">
      <j1 rule="para" parents="2894 392"/>
    </justification>
  </clause>

  <clause id="2898">
    <literal><![CDATA[
      T(1 / x,K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(2897,a,525,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="2897 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2899">
    <literal><![CDATA[
      T(x / (y * x),K(y,z)) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(2898(a,1),455(a,2,1))].">
      <j1 rule="para" parents="2898 455"/>
    </justification>
  </clause>

  <clause id="2900">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = R(1 / (y / x),y / x,x)
    ]]></literal>
    <justification jstring="[para(2898(a,1),1033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2898 1033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2901">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y)
    ]]></literal>
    <justification jstring="[hyper(737,a,2882,a),flip(a)].">
      <j1 rule="hyper" parents="737 2882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2903">
    <literal><![CDATA[
      (x \ y) * ((y \ T(x,x \ y)) * y) = ((x \ y) * T((x \ y) \ 1,y)) * y
    ]]></literal>
    <justification jstring="[para(116(a,2),2901(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="116 2901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2904">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[hyper(373,a,454,a(flip),b,2900,a),flip(a)].">
      <j1 rule="hyper" parents="373 454 2900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2905">
    <literal><![CDATA[
      T(x / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(7(a,1),2904(a,1,1,1))].">
      <j1 rule="para" parents="7 2904"/>
    </justification>
  </clause>

  <clause id="2906">
    <literal><![CDATA[
      K(x / y,z) * (y / x) = (y / x) * K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,2905,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 2905 22"/>
    </justification>
  </clause>

  <clause id="2907">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(2905(a,1),278(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2905 278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2908">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,117,a(flip),b,2907,a),flip(a)].">
      <j1 rule="hyper" parents="373 117 2907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2909">
    <literal><![CDATA[
      T((x * y) \ y,K(x,z)) = (x * y) \ y
    ]]></literal>
    <justification jstring="[para(11(a,1),2908(a,1,2,1))].">
      <j1 rule="para" parents="11 2908"/>
    </justification>
  </clause>

  <clause id="2910">
    <literal><![CDATA[
      T(x \ (y \ x),K(y,z)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(79(a,1),2908(a,1,2,1))].">
      <j1 rule="para" parents="79 2908"/>
    </justification>
  </clause>

  <clause id="2911">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1308,a(flip),b,2880,a)].">
      <j1 rule="hyper" parents="64 1308 2880"/>
    </justification>
  </clause>

  <clause id="2912">
    <literal><![CDATA[
      ((x * y) * T((x * y) \ x,z)) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1001,a(flip),b,2880,a),flip(a)].">
      <j1 rule="hyper" parents="64 1001 2880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2913">
    <literal><![CDATA[
      x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(269,a,2880,a(flip),b,1308,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 2880 1308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2914">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) != y * w
    ]]></literal>
    <literal><![CDATA[
      T(x * T(x \ z,u),y) = w
    ]]></literal>
    <justification jstring="[para(2880(a,2),270(a,2)),flip(a)].">
      <j1 rule="para" parents="2880 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2915">
    <literal><![CDATA[
      T(x * T(x \ y,z),x) = x * T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[para(22(a,2),2913(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 2913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2916">
    <literal><![CDATA[
      x \ T(x * T(x \ y,z),x) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(1036,a,2915,a)].">
      <j1 rule="hyper" parents="1036 2915"/>
    </justification>
  </clause>

  <clause id="2917">
    <literal><![CDATA[
      T(x \ T(x * y,x),z) = x \ T(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),2916(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 2916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2918">
    <literal><![CDATA[
      x * ((y \ (x \ (z * y))) * y) = (x * T(x \ z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(737,a,2911,a)].">
      <j1 rule="hyper" parents="737 2911"/>
    </justification>
  </clause>

  <clause id="2919">
    <literal><![CDATA[
      x * ((y \ z) * T((y \ z) \ (x \ z),u)) = (x * T(x \ y,u)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),2911(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="10 2911"/>
    </justification>
  </clause>

  <clause id="2920">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u))
    ]]></literal>
    <justification jstring="[para(12(a,1),2911(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 2911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2922">
    <literal><![CDATA[
      ((x * (y \ z)) * T((x * (y \ z)) \ x,z)) * z = (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z)
    ]]></literal>
    <justification jstring="[para(409(a,2),2918(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="409 2918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2923">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(718,a,2920,a),flip(a)].">
      <j1 rule="hyper" parents="718 2920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2924">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(2920(a,1),718(a,1))].">
      <j1 rule="para" parents="2920 718"/>
    </justification>
  </clause>

  <clause id="2925">
    <literal><![CDATA[
      (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(1182(a,1),2920(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1182 2920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2926">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y))
    ]]></literal>
    <justification jstring="[para(1518(a,2),2920(a,1,1))].">
      <j1 rule="para" parents="1518 2920"/>
    </justification>
  </clause>

  <clause id="2927">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1308,a,b,2923,a)].">
      <j1 rule="hyper" parents="64 1308 2923"/>
    </justification>
  </clause>

  <clause id="2928">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[para(68(a,1),2923(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="68 2923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2929">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z)
    ]]></literal>
    <justification jstring="[para(1506(a,1),2923(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1506 2923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2930">
    <literal><![CDATA[
      x * ((y \ x) * T((y \ x) \ 1,x)) = ((x \ y) * x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(79(a,1),2928(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 2928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2931">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(68(a,1),2926(a,2,2,2,1,2))].">
      <j1 rule="para" parents="68 2926"/>
    </justification>
  </clause>

  <clause id="2932">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * ((y \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,251,a(flip),b,2931,a),flip(a)].">
      <j1 rule="hyper" parents="373 251 2931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2934">
    <literal><![CDATA[
      (R(x,y \ 1,y) / y) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,111,a(flip),b,2932,a),flip(a)].">
      <j1 rule="hyper" parents="36 111 2932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2935">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * (y \ ((x \ y) * x))
    ]]></literal>
    <justification jstring="[para(1384(a,1),2930(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1384 2930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2936">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(95(a,1),2935(a,2,2))].">
      <j1 rule="para" parents="95 2935"/>
    </justification>
  </clause>

  <clause id="2937">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(y \ (y * x),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),2936(a,1,1,1))].">
      <j1 rule="para" parents="9 2936"/>
    </justification>
  </clause>

  <clause id="2938">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),2937(a,2,2,1))].">
      <j1 rule="para" parents="9 2937"/>
    </justification>
  </clause>

  <clause id="2939">
    <literal><![CDATA[
      x \ (y * K(x / y,y)) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(384,a,2938,a)].">
      <j1 rule="hyper" parents="384 2938"/>
    </justification>
  </clause>

  <clause id="2940">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y * x) \ y) = (y \ 1) * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(1228(a,1),2938(a,1,2))].">
      <j1 rule="para" parents="1228 2938"/>
    </justification>
  </clause>

  <clause id="2942">
    <literal><![CDATA[
      T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(531(a,1),2884(a,1,2)),flip(a)].">
      <j1 rule="para" parents="531 2884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2943">
    <literal><![CDATA[
      R(x,T(1 / x,y),x) = T(x,T(1 / x,y))
    ]]></literal>
    <justification jstring="[para(531(a,1),2942(a,1,2)),flip(a)].">
      <j1 rule="para" parents="531 2942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2944">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(T(1 / x,y),x) = T(x * T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(2943(a,1),1940(a,1,1))].">
      <j1 rule="para" parents="2943 1940"/>
    </justification>
  </clause>

  <clause id="2945">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / (y \ 1))) * x) * (y \ 1) = u
    ]]></literal>
    <justification jstring="[para(1182(a,1),2924(a,1,2))].">
      <j1 rule="para" parents="1182 2924"/>
    </justification>
  </clause>

  <clause id="2947">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(1001(a,1),2912(a,1,1))].">
      <j1 rule="para" parents="1001 2912"/>
    </justification>
  </clause>

  <clause id="2948">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = T(x * T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(278(a,1),2944(a,1,2))].">
      <j1 rule="para" parents="278 2944"/>
    </justification>
  </clause>

  <clause id="2949">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[para(1279(a,1),1494(a,1,1))].">
      <j1 rule="para" parents="1279 1494"/>
    </justification>
  </clause>

  <clause id="2950">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ K(x \ 1,x))) / y) = ((y * x) / y) / ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2364(a,1),2949(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2364 2949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2951">
    <literal><![CDATA[
      R(T(x,x \ 1),y,z) * K(x \ 1,x) = (R(x,y,z) * (x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(2000(a,1),1696(a,1,1,1))].">
      <j1 rule="para" parents="2000 1696"/>
    </justification>
  </clause>

  <clause id="2952">
    <literal><![CDATA[
      R(T(x,x \ 1),y,z) * K(x \ 1,x) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2066,a(flip),b,2951,a),flip(a)].">
      <j1 rule="hyper" parents="373 2066 2951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2953">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) * K(x \ 1,x) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(116(a,1),2952(a,1,1,1))].">
      <j1 rule="para" parents="116 2952"/>
    </justification>
  </clause>

  <clause id="2954">
    <literal><![CDATA[
      (x * y) * ((x / (1 / y)) \ 1) = (x / (1 / y)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1407(a,1),1799(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1407 1799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2955">
    <literal><![CDATA[
      (x * y) * (((x \ 1) \ y) \ 1) = ((x \ 1) \ y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1137(a,1),1813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1137 1813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2956">
    <literal><![CDATA[
      K(x \ (x / (1 / (y / (x * y)))),x) = a(y / (x * y),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,2093,a(flip),b,1890,a),flip(a)].">
      <j1 rule="hyper" parents="373 2093 1890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2959">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(2227(a,1),2269(a,1,1))].">
      <j1 rule="para" parents="2227 2269"/>
    </justification>
  </clause>

  <clause id="2960">
    <literal><![CDATA[
      x \ (((T(y,x) \ y) * x) \ x) = ((T(y,x) \ y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(2774(a,1),2775(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2774 2775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2961">
    <literal><![CDATA[
      L(x,(y * y) * z,u) = L(x,z,u * (y * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,129,a(flip),b,2868,a)].">
      <j1 rule="hyper" parents="64 129 2868"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      L(x,T(y,z * z) * u,w * (z * z)) = L(x,y * ((z * z) * u),w)
    ]]></literal>
    <justification jstring="[para(1434(a,1),2961(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1434 2961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2963">
    <literal><![CDATA[
      L(x,T(y,z * z) * u,T(w,z * z)) = L(x,y * ((z * z) * u),(z * z) \ w)
    ]]></literal>
    <justification jstring="[para(798(a,1),2962(a,1,3))].">
      <j1 rule="para" parents="798 2962"/>
    </justification>
  </clause>

  <clause id="2964">
    <literal><![CDATA[
      R(x / (y * y),(y * y) * z,u) = R(x,z,u) / (y * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,898,a(flip),b,2872,a),flip(a)].">
      <j1 rule="hyper" parents="373 898 2872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2965">
    <literal><![CDATA[
      R(x,(y * y) * z,u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(38,a,2142,a(flip),b,2964,a(flip))].">
      <j1 rule="hyper" parents="38 2142 2964"/>
    </justification>
  </clause>

  <clause id="2967">
    <literal><![CDATA[
      R(x,(y * y) \ z,u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),2965(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 2965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2968">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(245(a,1),2965(a,1,2)),flip(a)].">
      <j1 rule="para" parents="245 2965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2969">
    <literal><![CDATA[
      R(x,(1 / y) * z,u) = R(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(310(a,1),2965(a,1,2)),flip(a)].">
      <j1 rule="para" parents="310 2965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2970">
    <literal><![CDATA[
      R(x,y * (y * z),u) = R(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(100(a,1),2965(a,1,2))].">
      <j1 rule="para" parents="100 2965"/>
    </justification>
  </clause>

  <clause id="2971">
    <literal><![CDATA[
      R(x,((y * y) \ z) * u,w) = R(x,z * u,w)
    ]]></literal>
    <justification jstring="[para(126(a,1),2965(a,1,2)),flip(a)].">
      <j1 rule="para" parents="126 2965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2972">
    <literal><![CDATA[
      R(x,(1 / y) / z,u) = R(x,y / z,u)
    ]]></literal>
    <justification jstring="[para(883(a,1),2965(a,1,2)),flip(a)].">
      <j1 rule="para" parents="883 2965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2973">
    <literal><![CDATA[
      R(x,(y * (y * z)) * u,w) = R(x,L(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[para(605(a,1),2965(a,1,2))].">
      <j1 rule="para" parents="605 2965"/>
    </justification>
  </clause>

  <clause id="2975">
    <literal><![CDATA[
      R(x,y \ 1,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),2968(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 2968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2976">
    <literal><![CDATA[
      L(R(x,x,y),x,x) = y / ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(2968(a,1),1037(a,1,1))].">
      <j1 rule="para" parents="2968 1037"/>
    </justification>
  </clause>

  <clause id="2978">
    <literal><![CDATA[
      x \ R(y,x \ 1,x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(493,a,2975,a,b,1405,a),flip(a)].">
      <j1 rule="hyper" parents="493 2975 1405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2979">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2968,a,b,2975,a)].">
      <j1 rule="hyper" parents="373 2968 2975"/>
    </justification>
  </clause>

  <clause id="2980">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1405,a,b,2975,a)].">
      <j1 rule="hyper" parents="373 1405 2975"/>
    </justification>
  </clause>

  <clause id="2981">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2975,a(flip),b,2975,a),flip(a)].">
      <j1 rule="hyper" parents="373 2975 2975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2982">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(373,a,1407,a(flip),b,2975,a),flip(a)].">
      <j1 rule="hyper" parents="373 1407 2975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2983">
    <literal><![CDATA[
      R(x,y \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(142,a,2975,a,b,1405,a)].">
      <j1 rule="hyper" parents="142 2975 1405"/>
    </justification>
  </clause>

  <clause id="2984">
    <literal><![CDATA[
      R(x \ 1,x,y) = y / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1991,a(flip),b,2975,a),flip(a)].">
      <j1 rule="hyper" parents="64 1991 2975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2985">
    <literal><![CDATA[
      R(T(x \ 1,y),x,y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1921,a(flip),b,2975,a),flip(a)].">
      <j1 rule="hyper" parents="64 1921 2975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2986">
    <literal><![CDATA[
      R(x,y,(x * (y \ 1)) \ z) \ z = (y \ 1) * ((x * (y \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(2975(a,1),420(a,1,1))].">
      <j1 rule="para" parents="2975 420"/>
    </justification>
  </clause>

  <clause id="2987">
    <literal><![CDATA[
      R(x \ 1,x,y) \ y = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(2975(a,1),1997(a,1,1))].">
      <j1 rule="para" parents="2975 1997"/>
    </justification>
  </clause>

  <clause id="2988">
    <literal><![CDATA[
      R((x * x) \ y,y,(x * x) \ y) = (y \ (x * x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,1425,a(flip),b,2967,a),flip(a)].">
      <j1 rule="hyper" parents="64 1425 2967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2989">
    <literal><![CDATA[
      R(x,y * ((y \ 1) \ z),u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(582(a,1),2967(a,1,2))].">
      <j1 rule="para" parents="582 2967"/>
    </justification>
  </clause>

  <clause id="2990">
    <literal><![CDATA[
      R(x,R((y * y) \ z,u,w),v5) = R(x,R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(2051(a,2),2967(a,1,2))].">
      <j1 rule="para" parents="2051 2967"/>
    </justification>
  </clause>

  <clause id="2993">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(2982(a,1),2143(a,2,1,2))].">
      <j1 rule="para" parents="2982 2143"/>
    </justification>
  </clause>

  <clause id="2994">
    <literal><![CDATA[
      x / y != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      R(z,y \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(2983(a,1),47(a,1)),flip(a)].">
      <j1 rule="para" parents="2983 47"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2995">
    <literal><![CDATA[
      (x * (1 / y)) * y != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2983(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2983 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2996">
    <literal><![CDATA[
      (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(2983(a,1),2934(a,1,1))].">
      <j1 rule="para" parents="2983 2934"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      T(R(x \ 1,x,y),y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(795,a,2985,a)].">
      <j1 rule="hyper" parents="795 2985"/>
    </justification>
  </clause>

  <clause id="2998">
    <literal><![CDATA[
      R(x \ 1,x,y) * y = x \ y
    ]]></literal>
    <justification jstring="[hyper(39,a,122,a,b,2985,a(flip))].">
      <j1 rule="hyper" parents="39 122 2985"/>
    </justification>
  </clause>

  <clause id="2999">
    <literal><![CDATA[
      R(T(x \ 1,y) * (z * z),x,y) = (y \ (x \ y)) * (z * z)
    ]]></literal>
    <justification jstring="[para(2985(a,1),2102(a,2,1))].">
      <j1 rule="para" parents="2985 2102"/>
    </justification>
  </clause>

  <clause id="3000">
    <literal><![CDATA[
      R(x \ 1,x,(x * x) * y) * ((x * x) * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,539,a(flip),b,2998,a),flip(a)].">
      <j1 rule="hyper" parents="373 539 2998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3001">
    <literal><![CDATA[
      R(x \ 1,x,y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(154,a,2998,a),flip(a)].">
      <j1 rule="hyper" parents="154 2998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3002">
    <literal><![CDATA[
      R((x / y) \ 1,x / y,y) = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,2040,a,b,2998,a),flip(a)].">
      <j1 rule="hyper" parents="36 2040 2998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3003">
    <literal><![CDATA[
      R(x / R(y \ 1,y,z),R(y \ 1,y,z),z) = (x * z) / (y \ z)
    ]]></literal>
    <justification jstring="[hyper(225,a,2998,a(flip),b,650,a),flip(a)].">
      <j1 rule="hyper" parents="225 2998 650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3004">
    <literal><![CDATA[
      R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,2033,a,b,3001,a),flip(a)].">
      <j1 rule="hyper" parents="373 2033 3001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3005">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,453,a,b,3001,a)].">
      <j1 rule="hyper" parents="373 453 3001"/>
    </justification>
  </clause>

  <clause id="3006">
    <literal><![CDATA[
      R(x \ 1,x,y) * z = ((x \ y) / y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,3001,a,b,11,a)].">
      <j1 rule="hyper" parents="144 3001 11"/>
    </justification>
  </clause>

  <clause id="3007">
    <literal><![CDATA[
      T(x / (y * x),y) = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,854,a,b,3001,a)].">
      <j1 rule="hyper" parents="64 854 3001"/>
    </justification>
  </clause>

  <clause id="3008">
    <literal><![CDATA[
      x \ R(x,x,y) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,3001,a(flip),b,1990,a),flip(a)].">
      <j1 rule="hyper" parents="145 3001 1990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3009">
    <literal><![CDATA[
      (x / (y * x)) * y = y * ((y \ x) / x)
    ]]></literal>
    <justification jstring="[para(3001(a,1),859(a,2,2))].">
      <j1 rule="para" parents="3001 859"/>
    </justification>
  </clause>

  <clause id="3010">
    <literal><![CDATA[
      R((1 / x) * 1,x,y) = L((x \ y) / y,x,x)
    ]]></literal>
    <justification jstring="[para(3001(a,1),579(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3001 579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3011">
    <literal><![CDATA[
      L(((x \ y) \ z) / z,x \ y,x) = R(y \ (x * 1),x \ y,z)
    ]]></literal>
    <justification jstring="[para(3001(a,1),1025(a,1,1))].">
      <j1 rule="para" parents="3001 1025"/>
    </justification>
  </clause>

  <clause id="3012">
    <literal><![CDATA[
      x * (x * ((x \ y) / y)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[para(3001(a,1),1988(a,1,2,2))].">
      <j1 rule="para" parents="3001 1988"/>
    </justification>
  </clause>

  <clause id="3013">
    <literal><![CDATA[
      T(x / (y * x),z) * y = y * T((y \ x) / x,z)
    ]]></literal>
    <justification jstring="[para(3007(a,1),265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3007 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3014">
    <literal><![CDATA[
      (x \ R(x,x,y)) * L(z,(x \ y) / y,x) = x * (((x \ y) / y) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,3008,a,b,213,a)].">
      <j1 rule="hyper" parents="144 3008 213"/>
    </justification>
  </clause>

  <clause id="3015">
    <literal><![CDATA[
      x \ R(x,x,x * y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),3008(a,2,2,1))].">
      <j1 rule="para" parents="9 3008"/>
    </justification>
  </clause>

  <clause id="3016">
    <literal><![CDATA[
      T(x,x * ((x \ y) / y)) = x
    ]]></literal>
    <justification jstring="[para(3008(a,1),2070(a,1,2))].">
      <j1 rule="para" parents="3008 2070"/>
    </justification>
  </clause>

  <clause id="3017">
    <literal><![CDATA[
      T((x \ y) \ y,x * ((x \ z) / z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(3016(a,1),367(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3016 367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3018">
    <literal><![CDATA[
      R(x,(y \ 1) * z,u) = R(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),2969(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 2969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3019">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),w) = R(x,y * R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(2067(a,1),2969(a,1,2))].">
      <j1 rule="para" parents="2067 2969"/>
    </justification>
  </clause>

  <clause id="3020">
    <literal><![CDATA[
      L(R(x,x,y),x,x) = R(x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,2017,a,b,2976,a),flip(a)].">
      <j1 rule="hyper" parents="373 2017 2976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3021">
    <literal><![CDATA[
      R(1 / (1 / x),x,y) = R(x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,825,a,b,3020,a)].">
      <j1 rule="hyper" parents="64 825 3020"/>
    </justification>
  </clause>

  <clause id="3022">
    <literal><![CDATA[
      x \ R(x,x,x \ y) = (x \ 1) * R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,3020,a(flip),b,1139,a)].">
      <j1 rule="hyper" parents="139 3020 1139"/>
    </justification>
  </clause>

  <clause id="3023">
    <literal><![CDATA[
      R(x,(1 / y) \ z,u) = R(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(1138(a,1),2989(a,1,2))].">
      <j1 rule="para" parents="1138 2989"/>
    </justification>
  </clause>

  <clause id="3024">
    <literal><![CDATA[
      R(x,(y \ (y \ 1)) * z,u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(1615(a,1),2989(a,1,2))].">
      <j1 rule="para" parents="1615 2989"/>
    </justification>
  </clause>

  <clause id="3025">
    <literal><![CDATA[
      R(x \ 1,x,x * y) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),3005(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 3005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3026">
    <literal><![CDATA[
      (((1 / x) * x) * (x \ y)) \ ((R(x \ 1,x,y) * x) * (x \ y)) = a(R(1 / x,x,x \ y),x,x \ y)
    ]]></literal>
    <justification jstring="[para(3005(a,1),658(a,1,2,1,1))].">
      <j1 rule="para" parents="3005 658"/>
    </justification>
  </clause>

  <clause id="3027">
    <literal><![CDATA[
      (1 / (1 / (x / (y * x)))) \ y = (y / (y * ((y \ x) / x))) * y
    ]]></literal>
    <justification jstring="[para(3009(a,1),2014(a,2,1,2))].">
      <j1 rule="para" parents="3009 2014"/>
    </justification>
  </clause>

  <clause id="3028">
    <literal><![CDATA[
      R(x,(y \ 1) \ z,u) = R(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),3023(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 3023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3029">
    <literal><![CDATA[
      R(x,((y \ 1) \ z) * u,w) = R(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(1550(a,1),3024(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1550 3024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3030">
    <literal><![CDATA[
      R(x,((y \ 1) \ 1) \ z,u) = R(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,3028,a(flip),b,3028,a),flip(a)].">
      <j1 rule="hyper" parents="373 3028 3028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3031">
    <literal><![CDATA[
      T(R(x \ 1,x,y),((x \ 1) \ 1) * y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(2984(a,2),117(a,1,1))].">
      <j1 rule="para" parents="2984 117"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      x / (T(y,y \ 1) * x) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(116(a,2),2984(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="116 2984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3033">
    <literal><![CDATA[
      R(x \ 1,x,y) \ y = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,365,a,b,2987,a),flip(a)].">
      <j1 rule="hyper" parents="373 365 2987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3034">
    <literal><![CDATA[
      R(x,((1 / y) / z) * u,w) = R(x,(y / z) * u,w)
    ]]></literal>
    <justification jstring="[para(887(a,1),2971(a,1,2,1))].">
      <j1 rule="para" parents="887 2971"/>
    </justification>
  </clause>

  <clause id="3035">
    <literal><![CDATA[
      L((x \ y) / y,x,x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(8(a,1),3010(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8 3010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3036">
    <literal><![CDATA[
      R(x / (x * x),x,x \ y) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1720,a,b,3035,a)].">
      <j1 rule="hyper" parents="64 1720 3035"/>
    </justification>
  </clause>

  <clause id="3037">
    <literal><![CDATA[
      R(x / (x * x),x,x \ y) = (L(x,x,x) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,2025,a,b,3036,a),flip(a)].">
      <j1 rule="hyper" parents="373 2025 3036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3039">
    <literal><![CDATA[
      T(x / y,y / x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,857,a(flip),b,3002,a)].">
      <j1 rule="hyper" parents="64 857 3002"/>
    </justification>
  </clause>

  <clause id="3040">
    <literal><![CDATA[
      1 / T(x / y,y / x) = (x / y) \ 1
    ]]></literal>
    <justification jstring="[hyper(225,a,857,a(flip),b,3002,a(flip))].">
      <j1 rule="hyper" parents="225 857 3002"/>
    </justification>
  </clause>

  <clause id="3041">
    <literal><![CDATA[
      ((((x * y) / x) \ 1) \ 1) * x = x * T(y,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(144,a,3039,a(flip),b,541,a)].">
      <j1 rule="hyper" parents="144 3039 541"/>
    </justification>
  </clause>

  <clause id="3042">
    <literal><![CDATA[
      T(((x / y) \ 1) \ 1,y) = T(y \ x,y / x)
    ]]></literal>
    <justification jstring="[para(3039(a,1),278(a,1,1))].">
      <j1 rule="para" parents="3039 278"/>
    </justification>
  </clause>

  <clause id="3043">
    <literal><![CDATA[
      R(x,R(1 / y,z,u),w) = R(x,R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(309(a,1),2990(a,1,2,1))].">
      <j1 rule="para" parents="309 2990"/>
    </justification>
  </clause>

  <clause id="3044">
    <literal><![CDATA[
      R(x,R(y \ 1,z,u),w) = R(x,R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(79(a,1),3043(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 3043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3045">
    <literal><![CDATA[
      R(R(T(x \ 1,y),z,u),R(x,z,u),y) = y \ ((1 / R(x \ 1,z,u)) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1924,a(flip),b,3044,a),flip(a)].">
      <j1 rule="hyper" parents="64 1924 3044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3046">
    <literal><![CDATA[
      R(x,((y \ z) / z) * y,u) = R(x,y * R(y,y,y \ z),u)
    ]]></literal>
    <justification jstring="[para(1992(a,1),3019(a,1,2))].">
      <j1 rule="para" parents="1992 3019"/>
    </justification>
  </clause>

  <clause id="3048">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = T(x,y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(35,a,909,a(flip),b,3041,a(flip))].">
      <j1 rule="hyper" parents="35 909 3041"/>
    </justification>
  </clause>

  <clause id="3049">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,2993,a(flip),b,2980,a),flip(a)].">
      <j1 rule="hyper" parents="142 2993 2980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3050">
    <literal><![CDATA[
      R(x \ 1,x,(x * x) * y) = R(x / (x * x),x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,2167,a,b,3000,a),flip(a)].">
      <j1 rule="hyper" parents="36 2167 3000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3051">
    <literal><![CDATA[
      L(((x \ y) \ z) / z,x \ y,x) = R(y \ x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(8(a,1),3011(a,2,1,2))].">
      <j1 rule="para" parents="8 3011"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,2929,a(flip),b,3049,a)].">
      <j1 rule="hyper" parents="64 2929 3049"/>
    </justification>
  </clause>

  <clause id="3053">
    <literal><![CDATA[
      R(x / R(y \ 1,y,z),R(y,y,z),z) = (x * z) / (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3044,a(flip),b,3003,a)].">
      <j1 rule="hyper" parents="64 3044 3003"/>
    </justification>
  </clause>

  <clause id="3054">
    <literal><![CDATA[
      R(T(x \ 1,((x \ 1) \ 1) * y),x,y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,3031,a)].">
      <j1 rule="hyper" parents="64 27 3031"/>
    </justification>
  </clause>

  <clause id="3055">
    <literal><![CDATA[
      K(x \ 1,x) * (((y * z) * u) / (z * u)) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2226,a(flip),b,2959,a)].">
      <j1 rule="hyper" parents="64 2226 2959"/>
    </justification>
  </clause>

  <clause id="3056">
    <literal><![CDATA[
      R(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(20(a,2),3055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 3055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      (x * R(x \ 1,x,x \ y)) \ R(1 / x,x,x \ y) = L(x \ 1,x,(x \ y) / y)
    ]]></literal>
    <justification jstring="[para(453(a,1),1199(a,2,3))].">
      <j1 rule="para" parents="453 1199"/>
    </justification>
  </clause>

  <clause id="3058">
    <literal><![CDATA[
      x * (T(y,x) * T(T(y,x) \ 1,z)) = (y * x) * T((y * x) \ x,z)
    ]]></literal>
    <justification jstring="[para(115(a,1),1294(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="115 1294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3060">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(269,a,2881,a(flip),b,3058,a),flip(a)].">
      <j1 rule="hyper" parents="269 2881 3058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3061">
    <literal><![CDATA[
      T(x * T(x \ 1,T(x,y)),y) = (T(x,y) \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(328,a,3060,a),flip(a)].">
      <j1 rule="hyper" parents="328 3060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      T(x,y) \ T(x * T(x \ 1,z),y) = T(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,3060,a)].">
      <j1 rule="hyper" parents="149 3060"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1883,a,b,3060,a),flip(a)].">
      <j1 rule="hyper" parents="64 1883 3060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3064">
    <literal><![CDATA[
      T(x * T(x \ 1,x),y) * (T(x,y) \ x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(3060(a,1),2413(a,1,1))].">
      <j1 rule="para" parents="3060 2413"/>
    </justification>
  </clause>

  <clause id="3066">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(414(a,1),3063(a,1,1)),flip(a)].">
      <j1 rule="para" parents="414 3063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3067">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = T(K(x \ (x / y),x),z)
    ]]></literal>
    <justification jstring="[para(1883(a,2),3063(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1883 3063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3068">
    <literal><![CDATA[
      K(x \ (x / T(L(y \ 1,y,x),z)),x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(1888(a,2),3063(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1888 3063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3069">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,z)),x) = T(K(x \ y,x),z)
    ]]></literal>
    <justification jstring="[para(79(a,1),3067(a,2,1,1,2))].">
      <j1 rule="para" parents="79 3067"/>
    </justification>
  </clause>

  <clause id="3070">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ z) = K(x \ (x / (((y \ x) \ z) \ z)),x)
    ]]></literal>
    <justification jstring="[para(116(a,1),3069(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="116 3069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3071">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(x * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(2886(a,1),3062(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2886 3062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3075">
    <literal><![CDATA[
      T(K(x \ 1,x),y) * (T(x,y) \ x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(414(a,1),3064(a,1,1,1))].">
      <j1 rule="para" parents="414 3064"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(1,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3071(a,2,2,1))].">
      <j1 rule="para" parents="10 3071"/>
    </justification>
  </clause>

  <clause id="3078">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(376(a,1),3076(a,2,2))].">
      <j1 rule="para" parents="376 3076"/>
    </justification>
  </clause>

  <clause id="3080">
    <literal><![CDATA[
      R(x,K(x,x \ 1),y) = x
    ]]></literal>
    <justification jstring="[hyper(1745,a,2384,a)].">
      <j1 rule="hyper" parents="1745 2384"/>
    </justification>
  </clause>

  <clause id="3081">
    <literal><![CDATA[
      R(1 / x,K(x \ 1,x),y) = 1 / x
    ]]></literal>
    <justification jstring="[para(1731(a,1),3080(a,1,2))].">
      <j1 rule="para" parents="1731 3080"/>
    </justification>
  </clause>

  <clause id="3082">
    <literal><![CDATA[
      (1 / x) \ L((y * x) \ y,z,u) = L((y * x) \ y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(1306,a,1834,a),flip(a)].">
      <j1 rule="hyper" parents="1306 1834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3083">
    <literal><![CDATA[
      ((x * ((y \ x) \ z)) / z) * (y \ z) = y \ (x * ((y \ x) \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),1947(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3085">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(x * T(x \ y,z),y)
    ]]></literal>
    <justification jstring="[hyper(269,a,2880,a(flip),b,1970,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 2880 1970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3086">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * x),x) = y * L(x,T(x,y) \ x,T(x,y))
    ]]></literal>
    <justification jstring="[para(2422(a,1),1970(a,2,2))].">
      <j1 rule="para" parents="2422 1970"/>
    </justification>
  </clause>

  <clause id="3087">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,T(y,x)) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(16(a,2),3086(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16 3086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3088">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ (1 / x),z,u) = (x * x) \ (R(y,z,u) / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,2053,a(flip),b,2116,a),flip(a)].">
      <j1 rule="hyper" parents="373 2053 2116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3089">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ 1,z,u)) * y = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),2559(a,2,2,1,1))].">
      <j1 rule="para" parents="12 2559"/>
    </justification>
  </clause>

  <clause id="3090">
    <literal><![CDATA[
      (x / y) * L((x / y) \ 1,z,u) = (x * L(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(154,a,3089,a),flip(a)].">
      <j1 rule="hyper" parents="154 3089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3091">
    <literal><![CDATA[
      (((x * y) * z) * L(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * L((((x * y) * z) / (y * z)) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),3090(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20 3090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3092">
    <literal><![CDATA[
      K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = ((x \ y) * T(x,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(3017(a,1),2589(a,2,1,2))].">
      <j1 rule="para" parents="3017 2589"/>
    </justification>
  </clause>

  <clause id="3093">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[para(2064(a,1),2591(a,2,1))].">
      <j1 rule="para" parents="2064 2591"/>
    </justification>
  </clause>

  <clause id="3095">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ 1)) / z) = x \ (y * ((z * (y \ x)) / z))
    ]]></literal>
    <justification jstring="[para(8(a,1),2612(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 2612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3096">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ (x \ u))) / z) = x \ (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),2612(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 2612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3097">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,2803,a,b,3095,a(flip))].">
      <j1 rule="hyper" parents="145 2803 3095"/>
    </justification>
  </clause>

  <clause id="3098">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z)
    ]]></literal>
    <justification jstring="[para(22(a,2),3097(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 3097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3099">
    <literal><![CDATA[
      a((L(x * x,y,z) \ u) * w,v5,v6) = a(L(x * x,y,z) * (u * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(1701(a,1),2691(a,2,1))].">
      <j1 rule="para" parents="1701 2691"/>
    </justification>
  </clause>

  <clause id="3100">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x * u) = x * ((x * L(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(2481(a,1),2731(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2481 2731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3101">
    <literal><![CDATA[
      x \ ((x * L(x \ 1,y,z)) * u) = (x * L(x \ 1,y,z)) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(759,a,3100,a)].">
      <j1 rule="hyper" parents="759 3100"/>
    </justification>
  </clause>

  <clause id="3102">
    <literal><![CDATA[
      (x \ 1) * (((x \ 1) * L((x \ 1) \ 1,y,z)) * u) = (x \ L(x,y,z)) * ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1804(a,1),3100(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1804 3100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3103">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (x * u) = x * ((x * R(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(2479(a,1),2734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2479 2734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      (x \ 1) * (((x \ 1) * R((x \ 1) \ 1,y,z)) * u) = (x \ R(x,y,z)) * ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1793(a,1),3103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1793 3103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3105">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ T(x,z)) / T(x,z)) = K(T(x,z),1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(2425(a,1),2808(a,1,2,1))].">
      <j1 rule="para" parents="2425 2808"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      T(x,y) * R((y \ (x * y)) \ y,z,u) = T(x * R(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),2815(a,1,1))].">
      <j1 rule="para" parents="22 2815"/>
    </justification>
  </clause>

  <clause id="3107">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ y,z,u) = T(x * R(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),3106(a,1,2,1,1))].">
      <j1 rule="para" parents="22 3106"/>
    </justification>
  </clause>

  <clause id="3108">
    <literal><![CDATA[
      T(x,x * y) * R(T(x,x * y) \ (x * y),z,u) = T(x * R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),3107(a,2,1,2,1))].">
      <j1 rule="para" parents="9 3107"/>
    </justification>
  </clause>

  <clause id="3109">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(1302(a,1),2843(a,1,1))].">
      <j1 rule="para" parents="1302 2843"/>
    </justification>
  </clause>

  <clause id="3110">
    <literal><![CDATA[
      (x \ y) * ((y \ T(x,x \ y)) * y) = (x \ ((y \ x) * y)) * y
    ]]></literal>
    <justification jstring="[para(1384(a,1),2903(a,2,1))].">
      <j1 rule="para" parents="1384 2903"/>
    </justification>
  </clause>

  <clause id="3111">
    <literal><![CDATA[
      (x \ y) * ((y \ T(x,x \ y)) * y) = K(y \ x,y) * y
    ]]></literal>
    <justification jstring="[para(95(a,1),3110(a,2,1))].">
      <j1 rule="para" parents="95 3110"/>
    </justification>
  </clause>

  <clause id="3112">
    <literal><![CDATA[
      (x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(737,a,2925,a),flip(a)].">
      <j1 rule="hyper" parents="737 2925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3113">
    <literal><![CDATA[
      (x \ T(x * (y / y),z)) * y = (x \ 1) * ((x \ T(x,z)) * ((x \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(2717(a,2),2925(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2717 2925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3114">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(193(a,1),3113(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="193 3113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3115">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ ((x \ T(x,y)) \ (x \ 1))) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,10,a(flip),b,3114,a),flip(a)].">
      <j1 rule="hyper" parents="138 10 3114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3116">
    <literal><![CDATA[
      (x * ((y * y) * (z * u))) \ ((x * ((y * y) * z)) * u) = a(x * (y * y),z,u)
    ]]></literal>
    <justification jstring="[para(34(a,1),134(a,1,2,1))].">
      <j1 rule="para" parents="34 134"/>
    </justification>
  </clause>

  <clause id="3117">
    <literal><![CDATA[
      T((x * (1 / y)) * (y * y),y \ 1) = R((y \ 1) \ x,y \ 1,1 / y)
    ]]></literal>
    <justification jstring="[para(498(a,1),1040(a,1,1))].">
      <j1 rule="para" parents="498 1040"/>
    </justification>
  </clause>

  <clause id="3118">
    <literal><![CDATA[
      T(R(x,y,y) / (1 / y),y \ 1) = R((y \ 1) \ x,y \ 1,1 / y)
    ]]></literal>
    <justification jstring="[para(1413(a,1),3117(a,1,1))].">
      <j1 rule="para" parents="1413 3117"/>
    </justification>
  </clause>

  <clause id="3119">
    <literal><![CDATA[
      R((x * (y * z)) / (x * y),u,w) = (x * (y * R(z,u,w))) / (x * y)
    ]]></literal>
    <justification jstring="[para(514(a,1),1212(a,1,1)),flip(a)].">
      <j1 rule="para" parents="514 1212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      R(L(T((x * y) / x,x * z),u,w),x,z) = (x * z) \ ((x * L(y,u,w)) * z)
    ]]></literal>
    <justification jstring="[para(25(a,2),1346(a,1,1))].">
      <j1 rule="para" parents="25 1346"/>
    </justification>
  </clause>

  <clause id="3121">
    <literal><![CDATA[
      (x \ 1) * (x \ ((y * (x \ 1)) \ z)) = R(y / (x \ 1),x,x \ 1) \ z
    ]]></literal>
    <justification jstring="[para(1428(a,1),1371(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1428 1371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3122">
    <literal><![CDATA[
      (x \ 1) * (x \ ((y * (x \ 1)) \ z)) = (R(y,x,x) / (1 / x)) \ z
    ]]></literal>
    <justification jstring="[para(2552(a,1),3121(a,2,1))].">
      <j1 rule="para" parents="2552 3121"/>
    </justification>
  </clause>

  <clause id="3123">
    <literal><![CDATA[
      (T(x,y) * (1 / x)) / T(x,y) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2889,a(flip),b,1517,a)].">
      <j1 rule="hyper" parents="64 2889 1517"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      T(L(1 / x,T(x,y),1 / x),x) = (T(x,y) * (x \ 1)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(3123(a,1),914(a,1,1))].">
      <j1 rule="para" parents="3123 914"/>
    </justification>
  </clause>

  <clause id="3126">
    <literal><![CDATA[
      (T(x,y) * (x \ 1)) / T(x,y) = L(x \ 1,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,279,a(flip),b,3125,a),flip(a)].">
      <j1 rule="hyper" parents="64 279 3125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3127">
    <literal><![CDATA[
      x * L(x \ 1,T(x,y),1 / x) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(3126(a,1),2807(a,1,2))].">
      <j1 rule="para" parents="3126 2807"/>
    </justification>
  </clause>

  <clause id="3128">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(674(a,1),1715(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="674 1715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3129">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ 1,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),3128(a,2,1,1))].">
      <j1 rule="para" parents="7 3128"/>
    </justification>
  </clause>

  <clause id="3130">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(82(a,1),3129(a,1,2,1))].">
      <j1 rule="para" parents="82 3129"/>
    </justification>
  </clause>

  <clause id="3131">
    <literal><![CDATA[
      T(1 / x,L(x,y,z) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(3129(a,1),2561(a,1,2))].">
      <j1 rule="para" parents="3129 2561"/>
    </justification>
  </clause>

  <clause id="3132">
    <literal><![CDATA[
      T((x * (1 / y)) / x,L(y,z,u) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(3131(a,1),541(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3131 541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3133">
    <literal><![CDATA[
      (L(x,y,z) / x) / L(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(154,a,3130,a)].">
      <j1 rule="hyper" parents="154 3130"/>
    </justification>
  </clause>

  <clause id="3134">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),1 / x) = (L(x,y,z) / x) \ ((1 / x) * u)
    ]]></literal>
    <justification jstring="[para(3130(a,1),102(a,2,1))].">
      <j1 rule="para" parents="3130 102"/>
    </justification>
  </clause>

  <clause id="3135">
    <literal><![CDATA[
      T((L(x,y,z) * (1 / x)) / L(x,y,z),L(x,y,z) / x) = L(1 / x,L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(3130(a,1),770(a,1,2))].">
      <j1 rule="para" parents="3130 770"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(3133(a,1),2803(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3133 2803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3137">
    <literal><![CDATA[
      (x \ y) \ (((y \ x) \ 1) \ (x \ y)) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(436(a,1),1815(a,1,2,2))].">
      <j1 rule="para" parents="436 1815"/>
    </justification>
  </clause>

  <clause id="3138">
    <literal><![CDATA[
      (x \ y) * (((y \ x) \ 1) \ 1) = ((y \ x) \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(157,a,3137,a)].">
      <j1 rule="hyper" parents="157 3137"/>
    </justification>
  </clause>

  <clause id="3139">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = (((y \ x) * (x \ y)) / (y \ x)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(3138(a,1),1495(a,1,2,1))].">
      <j1 rule="para" parents="3138 1495"/>
    </justification>
  </clause>

  <clause id="3140">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = K(y \ x,((y \ x) / ((x \ y) \ 1)) / (y \ x))
    ]]></literal>
    <justification jstring="[para(3138(a,1),2803(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3138 2803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3141">
    <literal><![CDATA[
      R(R(x,x,y),R(x,x,y),y) = (R(x,x,y) * R(x,x,y)) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(740,a,1920,a),flip(a)].">
      <j1 rule="hyper" parents="740 1920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3143">
    <literal><![CDATA[
      R(R(x,x,y),R(x,x,y),y) = (R(x,x,y) * R(x,x,y)) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,497,a(flip),b,3141,a),flip(a)].">
      <j1 rule="hyper" parents="373 497 3141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3144">
    <literal><![CDATA[
      ((x \ 1) * y) \ R((x \ 1) * z,u,w) = (x * y) \ R(x * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2134,a(flip),b,2165,a),flip(a)].">
      <j1 rule="hyper" parents="64 2134 2165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3145">
    <literal><![CDATA[
      (x * y) \ (((x \ 1) \ y) * z) = ((x \ 1) \ y) * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(1137(a,1),2343(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1137 2343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3146">
    <literal><![CDATA[
      ((x \ 1) \ y) * ((x * y) * z) = (x * y) * (((x \ 1) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(1335,a,3145,a),flip(a)].">
      <j1 rule="hyper" parents="1335 3145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3147">
    <literal><![CDATA[
      ((x \ 1) \ y) \ ((x * y) * z) = (x * y) * (((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,3146,a)].">
      <j1 rule="hyper" parents="139 168 3146"/>
    </justification>
  </clause>

  <clause id="3148">
    <literal><![CDATA[
      L(T(x,y),y,K(x \ 1,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,K(x \ 1,x) * y) = z
    ]]></literal>
    <justification jstring="[para(2394(a,1),336(a,1))].">
      <j1 rule="para" parents="2394 336"/>
    </justification>
  </clause>

  <clause id="3149">
    <literal><![CDATA[
      T(x,K(x \ 1,x) * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3148,a,2220,a)].">
      <j1 rule="hyper" parents="3148 2220"/>
    </justification>
  </clause>

  <clause id="3150">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2263(a,1),3149(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2263 3149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3151">
    <literal><![CDATA[
      T(x \ 1,((x \ 1) \ 1) * y) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(79(a,1),3150(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 3150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3152">
    <literal><![CDATA[
      R(T(x \ 1,x * y),x,y) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(3151(a,1),3054(a,1,1))].">
      <j1 rule="para" parents="3151 3054"/>
    </justification>
  </clause>

  <clause id="3153">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,1364,a(flip),b,3152,a)].">
      <j1 rule="hyper" parents="64 1364 3152"/>
    </justification>
  </clause>

  <clause id="3154">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ y = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(116(a,2),3153(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="116 3153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3155">
    <literal><![CDATA[
      (x * (T(x,x \ 1) * y)) \ (x * y) = T((x * (x * y)) \ (x * y),x)
    ]]></literal>
    <justification jstring="[para(2403(a,1),3154(a,1,1))].">
      <j1 rule="para" parents="2403 3154"/>
    </justification>
  </clause>

  <clause id="3156">
    <literal><![CDATA[
      T((x * (x * y)) \ (x * y),x) = L(y,x,x) \ ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2320,a(flip),b,3155,a),flip(a)].">
      <j1 rule="hyper" parents="64 2320 3155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3157">
    <literal><![CDATA[
      (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,517,a(flip),b,2521,a),flip(a)].">
      <j1 rule="hyper" parents="373 517 2521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3158">
    <literal><![CDATA[
      T(x,x * (y * T(y \ 1,x))) = x
    ]]></literal>
    <justification jstring="[para(3157(a,1),318(a,1,2))].">
      <j1 rule="para" parents="3157 318"/>
    </justification>
  </clause>

  <clause id="3160">
    <literal><![CDATA[
      ((L(x \ 1,x,y) * y) / L(x \ 1,x,y)) / y = (1 / y) * (y * (x * T(x \ 1,y)))
    ]]></literal>
    <justification jstring="[para(3157(a,1),2595(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3157 2595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3161">
    <literal><![CDATA[
      T(x,x * K(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1567(a,2),3158(a,1,2,2))].">
      <j1 rule="para" parents="1567 3158"/>
    </justification>
  </clause>

  <clause id="3162">
    <literal><![CDATA[
      T(x,x * (y \ (z * T(z \ y,x)))) = x
    ]]></literal>
    <justification jstring="[para(2428(a,1),3158(a,1,2,2))].">
      <j1 rule="para" parents="2428 3158"/>
    </justification>
  </clause>

  <clause id="3163">
    <literal><![CDATA[
      T(x * K(y,x),x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(55,a,3161,a)].">
      <j1 rule="hyper" parents="55 3161"/>
    </justification>
  </clause>

  <clause id="3164">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ ((y \ x) * ((y \ x) \ x)))) = x
    ]]></literal>
    <justification jstring="[para(1586(a,1),3162(a,1,2,2,2,2))].">
      <j1 rule="para" parents="1586 3162"/>
    </justification>
  </clause>

  <clause id="3165">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ x)) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),3164(a,1,2,2,2))].">
      <j1 rule="para" parents="10 3164"/>
    </justification>
  </clause>

  <clause id="3166">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,z) \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3165(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3165 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3167">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ (x * x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2421,a,3166,a)].">
      <j1 rule="hyper" parents="2421 3166"/>
    </justification>
  </clause>

  <clause id="3168">
    <literal><![CDATA[
      (x * x) / T(x,y) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(226,a,3167,a)].">
      <j1 rule="hyper" parents="226 3167"/>
    </justification>
  </clause>

  <clause id="3169">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(225,a,3167,a(flip),b,552,a),flip(a)].">
      <j1 rule="hyper" parents="225 3167 552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3170">
    <literal><![CDATA[
      (x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = T(x,R(T(y,x),T(y,x) \ 1,x))
    ]]></literal>
    <justification jstring="[para(2774(a,1),3167(a,1,1,2,1))].">
      <j1 rule="para" parents="2774 3167"/>
    </justification>
  </clause>

  <clause id="3171">
    <literal><![CDATA[
      T(x / T(x,y),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(2534,a,3168,a)].">
      <j1 rule="hyper" parents="2534 3168"/>
    </justification>
  </clause>

  <clause id="3172">
    <literal><![CDATA[
      T(((T(x,y) \ x) * x) / (T(x,y) \ x),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(3168(a,2),770(a,1,2))].">
      <j1 rule="para" parents="3168 770"/>
    </justification>
  </clause>

  <clause id="3173">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,3171,a(flip),b,531,a),flip(a)].">
      <j1 rule="hyper" parents="144 3171 531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3174">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,x \ 1) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2412,a,b,3169,a)].">
      <j1 rule="hyper" parents="64 2412 3169"/>
    </justification>
  </clause>

  <clause id="3175">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2275,a,3174,a)].">
      <j1 rule="hyper" parents="2275 3174"/>
    </justification>
  </clause>

  <clause id="3176">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) != y * w
    ]]></literal>
    <literal><![CDATA[
      T(x * T(x \ (z / y),u),y) = w
    ]]></literal>
    <justification jstring="[para(12(a,1),2914(a,1,2,1,2))].">
      <j1 rule="para" parents="12 2914"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      a(x * (y * y),z,u) = a(x,(y * y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,128,a(flip),b,3116,a),flip(a)].">
      <j1 rule="hyper" parents="64 128 3116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3178">
    <literal><![CDATA[
      L(R(T((x * y) / x,x * z),x,z),u,w) = (x * z) \ ((x * L(y,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29,a(flip),b,3120,a)].">
      <j1 rule="hyper" parents="64 29 3120"/>
    </justification>
  </clause>

  <clause id="3179">
    <literal><![CDATA[
      (x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,2774,a(flip),b,3170,a),flip(a)].">
      <j1 rule="hyper" parents="373 2774 3170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3180">
    <literal><![CDATA[
      T(x * T(x \ ((y * z) / y),u),y) = T(x,y) * T(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(3176,a,1970,a)].">
      <j1 rule="hyper" parents="3176 1970"/>
    </justification>
  </clause>

  <clause id="3181">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ T(z,y),u) = T(x * T(x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(256(a,1),3180(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="256 3180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3182">
    <literal><![CDATA[
      L((x * y) \ ((x * z) * y),u,w) = (x * y) \ ((x * L(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(1326(a,1),3178(a,1,1))].">
      <j1 rule="para" parents="1326 3178"/>
    </justification>
  </clause>

  <clause id="3183">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((x * y) * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(42,a,9,a(flip),b,3182,a),flip(a)].">
      <j1 rule="hyper" parents="42 9 3182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3184">
    <literal><![CDATA[
      (x * L(y,z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(157,a,3183,a)].">
      <j1 rule="hyper" parents="157 3183"/>
    </justification>
  </clause>

  <clause id="3185">
    <literal><![CDATA[
      ((1 / L(x,y,z)) * x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,186,a(flip),b,3183,a)].">
      <j1 rule="hyper" parents="64 186 3183"/>
    </justification>
  </clause>

  <clause id="3186">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = x / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,3183,a(flip),b,186,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="142 3183 186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3187">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[para(12(a,1),3183(a,1,2,1))].">
      <j1 rule="para" parents="12 3183"/>
    </justification>
  </clause>

  <clause id="3188">
    <literal><![CDATA[
      T(R(x,y,L(x,z,u)),y * L(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3183(a,1),1055(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3183 1055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3189">
    <literal><![CDATA[
      x * L(y,z,u) != y
    ]]></literal>
    <literal><![CDATA[
      (1 / L(y,z,u)) * y = x
    ]]></literal>
    <justification jstring="[para(3185(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="3185 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3190">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = (x / L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(784,a,3184,a)].">
      <j1 rule="hyper" parents="784 3184"/>
    </justification>
  </clause>

  <clause id="3191">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(723,a,3184,a)].">
      <j1 rule="hyper" parents="723 3184"/>
    </justification>
  </clause>

  <clause id="3192">
    <literal><![CDATA[
      T((x / y) * L(y,z,u),y) = y \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(493,a,166,a(flip),b,3184,a)].">
      <j1 rule="hyper" parents="493 166 3184"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) * L(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(390,a,3184,a),flip(a)].">
      <j1 rule="hyper" parents="390 3184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3194">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) * y = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,166,a(flip),b,3184,a),flip(a)].">
      <j1 rule="hyper" parents="373 166 3184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3196">
    <literal><![CDATA[
      (x * L(y,z,u)) / y = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(142,a,166,a(flip),b,3184,a)].">
      <j1 rule="hyper" parents="142 166 3184"/>
    </justification>
  </clause>

  <clause id="3197">
    <literal><![CDATA[
      ((x / L(y,z,u)) / y) * L(y,z,u) = x / y
    ]]></literal>
    <justification jstring="[hyper(142,a,87,a(flip),b,3184,a),flip(a)].">
      <j1 rule="hyper" parents="142 87 3184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3198">
    <literal><![CDATA[
      ((x * y) * z) * L(z,y,x) = (x * (y * z)) * z
    ]]></literal>
    <justification jstring="[para(100(a,1),3184(a,1,1)),flip(a)].">
      <j1 rule="para" parents="100 3184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3199">
    <literal><![CDATA[
      ((x * y) * L(y,z,u)) \ (y * (x * L(y,z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,x * L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(3184(a,1),359(a,1,1))].">
      <j1 rule="para" parents="3184 359"/>
    </justification>
  </clause>

  <clause id="3200">
    <literal><![CDATA[
      (x * ((y * y) \ L(z,u,w))) * z = ((x / (y * y)) * z) * L(z,u,w)
    ]]></literal>
    <justification jstring="[para(897(a,1),3184(a,1,1))].">
      <j1 rule="para" parents="897 3184"/>
    </justification>
  </clause>

  <clause id="3201">
    <literal><![CDATA[
      (x / L(y,z,u)) / y = (x / y) / L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(142,a,170,a(flip),b,3190,a(flip))].">
      <j1 rule="hyper" parents="142 170 3190"/>
    </justification>
  </clause>

  <clause id="3202">
    <literal><![CDATA[
      (x * y) / L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / L(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(3191(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3191 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3203">
    <literal><![CDATA[
      L(x,y,z) = ((z * y) * x) \ ((z * (y * x)) * x)
    ]]></literal>
    <justification jstring="[para(213(a,1),3191(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="213 3191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3204">
    <literal><![CDATA[
      R(x / L(y,z,u),y,L(y,z,u)) = (x * y) / (y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(142,a,3193,a(flip),b,111,a),flip(a)].">
      <j1 rule="hyper" parents="142 3193 111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3205">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,100,a(flip),b,3194,a),flip(a)].">
      <j1 rule="hyper" parents="142 100 3194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3206">
    <literal><![CDATA[
      (R(x,L(y,z,u) / y,y) / y) * L(y,z,u) = x * (L(y,z,u) / y)
    ]]></literal>
    <justification jstring="[hyper(36,a,657,a(flip),b,3194,a),flip(a)].">
      <j1 rule="hyper" parents="36 657 3194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3207">
    <literal><![CDATA[
      (x * L(y,z,u)) * T(y,x) = (y * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,3188,a(flip),b,277,a)].">
      <j1 rule="hyper" parents="145 3188 277"/>
    </justification>
  </clause>

  <clause id="3208">
    <literal><![CDATA[
      x \ ((((x / y) / z) * (z * y)) * y) = L(y,z,(x / y) / z)
    ]]></literal>
    <justification jstring="[para(87(a,1),3203(a,2,1)),flip(a)].">
      <j1 rule="para" parents="87 3203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3209">
    <literal><![CDATA[
      L(x,y,z) = ((z * y) / x) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(149,a,3205,a),flip(a)].">
      <j1 rule="hyper" parents="149 3205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3210">
    <literal><![CDATA[
      (x * (y * z)) / z != L(z,y,x) * u
    ]]></literal>
    <literal><![CDATA[
      T((x * y) / z,L(z,y,x)) = u
    ]]></literal>
    <justification jstring="[para(3205(a,1),270(a,2)),flip(a)].">
      <j1 rule="para" parents="3205 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3211">
    <literal><![CDATA[
      L(L(x,y,y) \ (((y * y) / x) \ z),L(x,y,y),x) = ((y * (y * x)) / x) \ z
    ]]></literal>
    <justification jstring="[para(3205(a,1),2209(a,2,1))].">
      <j1 rule="para" parents="3205 2209"/>
    </justification>
  </clause>

  <clause id="3212">
    <literal><![CDATA[
      (x * ((y * y) \ L(z,u,w))) * z = (x * ((y * y) \ z)) * L(z,u,w)
    ]]></literal>
    <justification jstring="[para(897(a,1),3200(a,2,1))].">
      <j1 rule="para" parents="897 3200"/>
    </justification>
  </clause>

  <clause id="3213">
    <literal><![CDATA[
      (R(x,K(y \ 1,y),y) / y) * L(y,y \ 1,y) = x * (L(y,y \ 1,y) / y)
    ]]></literal>
    <justification jstring="[para(2369(a,1),3206(a,1,1,1,2))].">
      <j1 rule="para" parents="2369 3206"/>
    </justification>
  </clause>

  <clause id="3214">
    <literal><![CDATA[
      (L(x,y,z) * u) \ ((x * (x \ u)) * L(T(x,x \ u),y,z)) = a(x,x \ u,L(T(x,x \ u),y,z))
    ]]></literal>
    <justification jstring="[para(2327(a,1),832(a,1,1))].">
      <j1 rule="para" parents="2327 832"/>
    </justification>
  </clause>

  <clause id="3215">
    <literal><![CDATA[
      x * (T(y,x) * R(T(y,x) \ 1,z,u)) = (y * x) * R((y * x) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(115(a,1),1299(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="115 1299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3216">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(269,a,2479,a(flip),b,3215,a),flip(a)].">
      <j1 rule="hyper" parents="269 2479 3215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3217">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),z),y) = (z / (T(x,y) * z)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,859,a,b,3216,a),flip(a)].">
      <j1 rule="hyper" parents="64 859 3216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3219">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),x \ 1),y) = ((x \ 1) / (x \ T(x,y))) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1487(a,1),3217(a,2,1,2))].">
      <j1 rule="para" parents="1487 3217"/>
    </justification>
  </clause>

  <clause id="3220">
    <literal><![CDATA[
      ((x \ 1) / (x \ T(x,y))) * T(x,y) = T(x * T(x \ 1,T(x,y)),y)
    ]]></literal>
    <justification jstring="[para(2890(a,1),3219(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2890 3219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3221">
    <literal><![CDATA[
      (x \ 1) / (x \ T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,3061,a(flip),b,3220,a),flip(a)].">
      <j1 rule="hyper" parents="36 3061 3220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3222">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,y)) = (x \ T(x,y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3221(a,1),117(a,1,1))].">
      <j1 rule="para" parents="3221 117"/>
    </justification>
  </clause>

  <clause id="3223">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,3078,a(flip),b,3222,a),flip(a)].">
      <j1 rule="hyper" parents="64 3078 3222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3225">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ ((1 / x) \ 1) = T(1 / x,y) \ 1
    ]]></literal>
    <justification jstring="[para(1007(a,1),3223(a,1,1))].">
      <j1 rule="para" parents="1007 3223"/>
    </justification>
  </clause>

  <clause id="3226">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ (T(x,y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(3223(a,1),3115(a,1,2,2))].">
      <j1 rule="para" parents="3223 3115"/>
    </justification>
  </clause>

  <clause id="3227">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = (x \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(149,a,3226,a),flip(a)].">
      <j1 rule="hyper" parents="149 3226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3228">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ x = T(1 / x,y) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),3225(a,1,2))].">
      <j1 rule="para" parents="82 3225"/>
    </justification>
  </clause>

  <clause id="3229">
    <literal><![CDATA[
      x / (T(1 / x,y) \ 1) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(226,a,3228,a)].">
      <j1 rule="hyper" parents="226 3228"/>
    </justification>
  </clause>

  <clause id="3230">
    <literal><![CDATA[
      K(x \ (x / y),x) \ y = T(1 / y,x) \ 1
    ]]></literal>
    <justification jstring="[para(1883(a,2),3228(a,1,1))].">
      <j1 rule="para" parents="1883 3228"/>
    </justification>
  </clause>

  <clause id="3231">
    <literal><![CDATA[
      L(x \ ((1 / y) \ L(x,y,y)),x,y) = T(1 / (1 / y),(1 / y) * x)
    ]]></literal>
    <justification jstring="[para(1158(a,1),1662(a,1,1,2,2))].">
      <j1 rule="para" parents="1158 1662"/>
    </justification>
  </clause>

  <clause id="3232">
    <literal><![CDATA[
      T(1 / (1 / x),(1 / x) * y) = L(y \ (x * y),y,x)
    ]]></literal>
    <justification jstring="[para(561(a,1),3231(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="561 3231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3233">
    <literal><![CDATA[
      T(1 / (1 / x),(1 / x) * y) = L(T(x,y),y,x)
    ]]></literal>
    <justification jstring="[para(22(a,2),3232(a,2,1))].">
      <j1 rule="para" parents="22 3232"/>
    </justification>
  </clause>

  <clause id="3234">
    <literal><![CDATA[
      x * (y * L(R(T(x,y),z,u),w,v5)) = L(R(x,z,u),w,v5) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,835,a(flip),b,1707,a),flip(a)].">
      <j1 rule="hyper" parents="64 835 1707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3235">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (x * v5) = x * (L(R(x,y,z),u,w) * v5)
    ]]></literal>
    <justification jstring="[para(835(a,1),3234(a,1,2)),flip(a)].">
      <j1 rule="para" parents="835 3234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3236">
    <literal><![CDATA[
      L(T(1 / (1 / x),y),z,u) * (1 / x) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[para(195(a,1),1716(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="195 1716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3237">
    <literal><![CDATA[
      (1 / x) * L(T((1 / x) \ 1,y),z,u) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[hyper(1758,a,3236,a)].">
      <j1 rule="hyper" parents="1758 3236"/>
    </justification>
  </clause>

  <clause id="3238">
    <literal><![CDATA[
      (1 / x) * L(T(x,y),z,u) = L(T(x,y),z,u) / x
    ]]></literal>
    <justification jstring="[para(82(a,1),3237(a,1,2,1,1))].">
      <j1 rule="para" parents="82 3237"/>
    </justification>
  </clause>

  <clause id="3239">
    <literal><![CDATA[
      T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),1926(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 1926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3240">
    <literal><![CDATA[
      R(x / y,z,u) \ T(x / y,y) = (y \ x) * (R(x / y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(117(a,1),3239(a,1,1)),flip(a)].">
      <j1 rule="para" parents="117 3239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3241">
    <literal><![CDATA[
      (x \ y) * (R(y / x,z,u) \ 1) = R(y / x,z,u) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(117(a,1),3240(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 3240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3242">
    <literal><![CDATA[
      R((x * y) / x,z,u) \ (x \ (x * y)) = y * (R((x * y) / x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),3241(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3243">
    <literal><![CDATA[
      x * (R((y * x) / y,z,u) \ 1) = R((y * x) / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(9(a,1),3242(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 3242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3244">
    <literal><![CDATA[
      T((x \ 1) * (x * ((y * (x \ z)) / y)),y) = y \ (K(x \ 1,x) * (y * ((1 / x) * z)))
    ]]></literal>
    <justification jstring="[para(2472(a,1),2268(a,1,1))].">
      <j1 rule="para" parents="2472 2268"/>
    </justification>
  </clause>

  <clause id="3245">
    <literal><![CDATA[
      T(x,y) * (T(z / (z / x),y) \ 1) = T(z / (z / x),y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(911(a,1),2492(a,1,1)),flip(a)].">
      <j1 rule="para" parents="911 2492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3246">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ y,z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(269,a,2793,a(flip),b,2613,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="269 2793 2613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3247">
    <literal><![CDATA[
      x \ (y * (x * L(x \ (y \ (x * z)),u,w))) = T(y,x) * L(T(y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,1705,a(flip),b,2613,a(flip))].">
      <j1 rule="hyper" parents="139 1705 2613"/>
    </justification>
  </clause>

  <clause id="3248">
    <literal><![CDATA[
      x * (T(y,x) * L(T(y,x) \ 1,z,u)) = (y * x) * L((y * x) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(8(a,1),2613(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8 2613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3250">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(269,a,2481,a(flip),b,3248,a),flip(a)].">
      <j1 rule="hyper" parents="269 2481 3248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3251">
    <literal><![CDATA[
      T(x,y) \ T(x * L(x \ 1,z,u),y) = L(T(x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(149,a,3250,a)].">
      <j1 rule="hyper" parents="149 3250"/>
    </justification>
  </clause>

  <clause id="3252">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),z),y) = T(x,y) * ((z * T(x,y)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,439,a(flip),b,3250,a),flip(a)].">
      <j1 rule="hyper" parents="64 439 3250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3253">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * L(x \ 1,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(3251(a,1),290(a,1,2))].">
      <j1 rule="para" parents="3251 290"/>
    </justification>
  </clause>

  <clause id="3254">
    <literal><![CDATA[
      T(x \ y,z) \ T((x \ y) * (y \ x),z) = L(T(x \ y,z) \ 1,x \ y,x)
    ]]></literal>
    <justification jstring="[para(436(a,1),3251(a,1,2,1,2))].">
      <j1 rule="para" parents="436 3251"/>
    </justification>
  </clause>

  <clause id="3255">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),1 / x),y) = T(x,y) * ((T(x,y) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(1511(a,1),3252(a,2,2,1))].">
      <j1 rule="para" parents="1511 3252"/>
    </justification>
  </clause>

  <clause id="3256">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(3127(a,1),3255(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3127 3255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3257">
    <literal><![CDATA[
      ((x * ((y \ z) / z)) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),2752(a,1,1,1,2,2))].">
      <j1 rule="para" parents="10 2752"/>
    </justification>
  </clause>

  <clause id="3258">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[hyper(727,a,3257,a)].">
      <j1 rule="hyper" parents="727 3257"/>
    </justification>
  </clause>

  <clause id="3259">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1237,a(flip),b,3258,a),flip(a)].">
      <j1 rule="hyper" parents="373 1237 3258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3260">
    <literal><![CDATA[
      (x \ ((y \ x) * z)) * R((x \ ((y \ x) * z)) \ z,u,w) = x \ ((R(y,u,w) * (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(845(a,1),2817(a,2,2,1))].">
      <j1 rule="para" parents="845 2817"/>
    </justification>
  </clause>

  <clause id="3261">
    <literal><![CDATA[
      ((x * y) / x) / ((y \ 1) \ 1) = (y \ 1) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(416(a,1),2950(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="416 2950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3262">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((y * T(x,y)) / y) = x / ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(256(a,1),3261(a,1,1)),flip(a)].">
      <j1 rule="para" parents="256 3261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3263">
    <literal><![CDATA[
      x / ((T(x,y) \ 1) \ 1) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(256(a,1),3262(a,1,2)),flip(a)].">
      <j1 rule="para" parents="256 3262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3264">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,((T(x,y) \ 1) * x) / x)
    ]]></literal>
    <justification jstring="[para(3263(a,1),2809(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3263 2809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3265">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),3264(a,2,2))].">
      <j1 rule="para" parents="11 3264"/>
    </justification>
  </clause>

  <clause id="3266">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,T(x,y) \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(157,a,3265,a)].">
      <j1 rule="hyper" parents="157 3265"/>
    </justification>
  </clause>

  <clause id="3268">
    <literal><![CDATA[
      L(x,T(y,z * z) * u,T(w,z * z)) = L(x,y * ((z * z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2181,a(flip),b,2963,a),flip(a)].">
      <j1 rule="hyper" parents="373 2181 2963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3270">
    <literal><![CDATA[
      L(x,T(1,y * y) * z,T(u,y * y)) = L(x,(y * y) * z,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),3268(a,2,2))].">
      <j1 rule="para" parents="7 3268"/>
    </justification>
  </clause>

  <clause id="3271">
    <literal><![CDATA[
      L(x,(y * y) * z,u) = L(x,z,T(u,y * y))
    ]]></literal>
    <justification jstring="[para(382(a,1),3270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="382 3270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3272">
    <literal><![CDATA[
      K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = y / y
    ]]></literal>
    <justification jstring="[para(248(a,1),3092(a,2,1))].">
      <j1 rule="para" parents="248 3092"/>
    </justification>
  </clause>

  <clause id="3273">
    <literal><![CDATA[
      K((x * ((x \ y) / y)) \ x,x * ((x \ y) / y)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,76,a(flip),b,3272,a),flip(a)].">
      <j1 rule="hyper" parents="373 76 3272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3275">
    <literal><![CDATA[
      T(1 / ((x \ y) / y),x * ((x \ y) / y)) = 1 / ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(3273(a,1),1892(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3273 1892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3276">
    <literal><![CDATA[
      (x * ((x \ y) / y)) \ x = 1 / ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2723,a(flip),b,3275,a)].">
      <j1 rule="hyper" parents="64 2723 3275"/>
    </justification>
  </clause>

  <clause id="3277">
    <literal><![CDATA[
      (x * ((x \ y) / y)) \ x = (y / (x * y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,2032,a(flip),b,3276,a),flip(a)].">
      <j1 rule="hyper" parents="373 2032 3276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3278">
    <literal><![CDATA[
      x / ((y / (x * y)) \ 1) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(225,a,2032,a(flip),b,3276,a)].">
      <j1 rule="hyper" parents="225 2032 3276"/>
    </justification>
  </clause>

  <clause id="3279">
    <literal><![CDATA[
      ((x * ((x \ y) / y)) \ x) \ 1 = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(143,a,3276,a,b,171,a)].">
      <j1 rule="hyper" parents="143 3276 171"/>
    </justification>
  </clause>

  <clause id="3280">
    <literal><![CDATA[
      ((x / (y * x)) * y) \ y = (x / (y * x)) \ 1
    ]]></literal>
    <justification jstring="[para(3009(a,2),3277(a,1,1))].">
      <j1 rule="para" parents="3009 3277"/>
    </justification>
  </clause>

  <clause id="3281">
    <literal><![CDATA[
      ((x / (y * x)) * y) * ((x / (y * x)) \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(144,a,3009,a,b,3278,a)].">
      <j1 rule="hyper" parents="144 3009 3278"/>
    </justification>
  </clause>

  <clause id="3284">
    <literal><![CDATA[
      T(x * L(x \ ((y * z) / y),u,w),y) = T(x,y) * L(T(x,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2867,a(flip),b,3247,a)].">
      <j1 rule="hyper" parents="64 2867 3247"/>
    </justification>
  </clause>

  <clause id="3285">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ T(z,y),u,w) = T(x * L(x \ z,u,w),y)
    ]]></literal>
    <justification jstring="[para(256(a,1),3284(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="256 3284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3286">
    <literal><![CDATA[
      T(x \ L(x * ((y * z) / y),u,w),y) = T(x \ 1,y) * L(T(x \ 1,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(1389(a,1),3284(a,1,1))].">
      <j1 rule="para" parents="1389 3284"/>
    </justification>
  </clause>

  <clause id="3287">
    <literal><![CDATA[
      T(L((x \ 1) * ((1 / x) \ ((y * z) / y)),x,x \ 1),y) = T(1 / x,y) * L(T(1 / x,y) \ z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1656(a,2),3284(a,1,1))].">
      <j1 rule="para" parents="1656 3284"/>
    </justification>
  </clause>

  <clause id="3288">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ T(z,y),u,w) != v5 * v6
    ]]></literal>
    <literal><![CDATA[
      v5 \ T(x * L(x \ z,u,w),y) = v6
    ]]></literal>
    <justification jstring="[para(3285(a,2),1036(a,1))].">
      <j1 rule="para" parents="3285 1036"/>
    </justification>
  </clause>

  <clause id="3289">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1276,a(flip),b,1496,a),flip(a)].">
      <j1 rule="hyper" parents="64 1276 1496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3290">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),3289(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 3289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3291">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[para(1237(a,1),3289(a,2,1))].">
      <j1 rule="para" parents="1237 3289"/>
    </justification>
  </clause>

  <clause id="3292">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(390,a,3290,a),flip(a)].">
      <j1 rule="hyper" parents="390 3290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3293">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * ((z / y) / x)) * y = u
    ]]></literal>
    <justification jstring="[para(3290(a,1),390(a,1))].">
      <j1 rule="para" parents="3290 390"/>
    </justification>
  </clause>

  <clause id="3294">
    <literal><![CDATA[
      x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1963,a(flip),b,3292,a)].">
      <j1 rule="hyper" parents="64 1963 3292"/>
    </justification>
  </clause>

  <clause id="3295">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,1580,a(flip),b,3292,a),flip(a)].">
      <j1 rule="hyper" parents="64 1580 3292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3296">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ z
    ]]></literal>
    <justification jstring="[para(3295(a,1),321(a,1))].">
      <j1 rule="para" parents="3295 321"/>
    </justification>
  </clause>

  <clause id="3297">
    <literal><![CDATA[
      (x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = x * ((z * (y \ u)) * ((x * ((z * (y \ u)) \ (x \ u))) / x))
    ]]></literal>
    <justification jstring="[para(676(a,2),3294(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="676 3294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3298">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = z
    ]]></literal>
    <justification jstring="[para(1580(a,1),3293(a,1))].">
      <j1 rule="para" parents="1580 3293"/>
    </justification>
  </clause>

  <clause id="3299">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[hyper(390,a,3291,a),flip(a)].">
      <j1 rule="hyper" parents="390 3291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3301">
    <literal><![CDATA[
      (x \ (y * x)) * ((z * ((x \ (y * x)) \ x)) / z) = T(y * ((z * (y \ x)) / z),x)
    ]]></literal>
    <justification jstring="[hyper(269,a,3291,a(flip),b,2611,a),flip(a)].">
      <j1 rule="hyper" parents="269 3291 2611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3302">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y
    ]]></literal>
    <justification jstring="[para(7(a,1),3291(a,1,2,1,2,2))].">
      <j1 rule="para" parents="7 3291"/>
    </justification>
  </clause>

  <clause id="3303">
    <literal><![CDATA[
      x * ((x * y) * ((z * ((x * y) \ y)) / z)) = (x * ((z * (x \ 1)) / z)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1962,a(flip),b,3302,a)].">
      <j1 rule="hyper" parents="64 1962 3302"/>
    </justification>
  </clause>

  <clause id="3304">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,1961,a(flip),b,3302,a),flip(a)].">
      <j1 rule="hyper" parents="64 1961 3302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3305">
    <literal><![CDATA[
      T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y)
    ]]></literal>
    <justification jstring="[hyper(269,a,3302,a(flip),b,3098,a(flip))].">
      <j1 rule="hyper" parents="269 3302 3098"/>
    </justification>
  </clause>

  <clause id="3307">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(3302(a,1),3294(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3302 3294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3308">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,2803,a(flip),b,3305,a)].">
      <j1 rule="hyper" parents="373 2803 3305"/>
    </justification>
  </clause>

  <clause id="3309">
    <literal><![CDATA[
      K(x,(x / T(x,y)) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3305(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3310">
    <literal><![CDATA[
      K(x,(x / T(y \ x,z)) / x) = T(K(x,y / x),z)
    ]]></literal>
    <justification jstring="[para(2806(a,1),3305(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2806 3305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3311">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2803,a(flip),b,3309,a)].">
      <j1 rule="hyper" parents="64 2803 3309"/>
    </justification>
  </clause>

  <clause id="3312">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,(x / (y \ x)) / x)
    ]]></literal>
    <justification jstring="[para(2908(a,1),3310(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2908 3310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3313">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(2409(a,1),3311(a,1,2,1))].">
      <j1 rule="para" parents="2409 3311"/>
    </justification>
  </clause>

  <clause id="3314">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1724(a,2),3313(a,2,1))].">
      <j1 rule="para" parents="1724 3313"/>
    </justification>
  </clause>

  <clause id="3315">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),3312(a,2,2,1))].">
      <j1 rule="para" parents="79 3312"/>
    </justification>
  </clause>

  <clause id="3316">
    <literal><![CDATA[
      T(K(x,y),K((y * x) / x,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),3315(a,1,1,2))].">
      <j1 rule="para" parents="11 3315"/>
    </justification>
  </clause>

  <clause id="3317">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),3316(a,1,2,1))].">
      <j1 rule="para" parents="11 3316"/>
    </justification>
  </clause>

  <clause id="3318">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),3317(a,2,2))].">
      <j1 rule="para" parents="11 3317"/>
    </justification>
  </clause>

  <clause id="3319">
    <literal><![CDATA[
      T(K(x,y),K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(55,a,3318,a)].">
      <j1 rule="hyper" parents="55 3318"/>
    </justification>
  </clause>

  <clause id="3320">
    <literal><![CDATA[
      K(x,y) * K(z,x) = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,3318,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 3318 22"/>
    </justification>
  </clause>

  <clause id="3321">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3318(a,1),328(a,1,2))].">
      <j1 rule="para" parents="3318 328"/>
    </justification>
  </clause>

  <clause id="3322">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,w) = K(y,w) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3318(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3318 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3323">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,w) = K(y,w) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3318(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3318 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3324">
    <literal><![CDATA[
      K(x,y) * L(K(z,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(z,x),u,w) * K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(3318(a,1),464(a,1,2,1))].">
      <j1 rule="para" parents="3318 464"/>
    </justification>
  </clause>

  <clause id="3325">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3319(a,1),328(a,1,2))].">
      <j1 rule="para" parents="3319 328"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(w,x) = K(w,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3319(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3319 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3327">
    <literal><![CDATA[
      K(x,y) * R(K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      R(K(y,z),u,w) * K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(3319(a,1),465(a,1,2,1))].">
      <j1 rule="para" parents="3319 465"/>
    </justification>
  </clause>

  <clause id="3328">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(2598(a,1),3304(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2598 3304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3329">
    <literal><![CDATA[
      T(x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)),z) = T(x,z) * ((T(x,y) * (T(x,z) \ 1)) / T(x,y))
    ]]></literal>
    <justification jstring="[para(527(a,2),3308(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="527 3308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3330">
    <literal><![CDATA[
      T(x,y) * ((z * ((y \ (x * y)) \ y)) / z) = T(x * ((z * (x \ y)) / z),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),3301(a,1,1))].">
      <j1 rule="para" parents="22 3301"/>
    </justification>
  </clause>

  <clause id="3331">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ y)) / z) = T(x * ((z * (x \ y)) / z),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),3330(a,1,2,1,2,1))].">
      <j1 rule="para" parents="22 3330"/>
    </justification>
  </clause>

  <clause id="3332">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * (x * z) = x * ((x * ((y * (x \ 1)) / y)) * z)
    ]]></literal>
    <justification jstring="[para(3302(a,1),3303(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3302 3303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3333">
    <literal><![CDATA[
      K(x,(x / y) / x) * (y * z) = y * ((y * ((x * (y \ 1)) / x)) * z)
    ]]></literal>
    <justification jstring="[para(2803(a,2),3332(a,1,1))].">
      <j1 rule="para" parents="2803 3332"/>
    </justification>
  </clause>

  <clause id="3334">
    <literal><![CDATA[
      (((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y)
    ]]></literal>
    <justification jstring="[para(2598(a,1),3328(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2598 3328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3335">
    <literal><![CDATA[
      ((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(154,a,3334,a)].">
      <j1 rule="hyper" parents="154 3334"/>
    </justification>
  </clause>

  <clause id="3337">
    <literal><![CDATA[
      R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(3335(a,1),1278(a,1,1))].">
      <j1 rule="para" parents="3335 1278"/>
    </justification>
  </clause>

  <clause id="3338">
    <literal><![CDATA[
      ((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(760,a,3337,a),flip(a)].">
      <j1 rule="hyper" parents="760 3337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3339">
    <literal><![CDATA[
      T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(3338(a,1),914(a,1,1))].">
      <j1 rule="para" parents="3338 914"/>
    </justification>
  </clause>

  <clause id="3340">
    <literal><![CDATA[
      ((1 / x) * ((x * y) \ (y * x))) / (1 / x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(467,a,3339,a),flip(a)].">
      <j1 rule="hyper" parents="467 3339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3341">
    <literal><![CDATA[
      K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,16,a,b,3340,a)].">
      <j1 rule="hyper" parents="373 16 3340"/>
    </justification>
  </clause>

  <clause id="3342">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) / (1 / x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(16(a,2),3341(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="16 3341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3343">
    <literal><![CDATA[
      T(1 / x,K(y,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(303,a,3342,a)].">
      <j1 rule="hyper" parents="303 3342"/>
    </justification>
  </clause>

  <clause id="3344">
    <literal><![CDATA[
      K(1 / x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,3343,a)].">
      <j1 rule="hyper" parents="56 3343"/>
    </justification>
  </clause>

  <clause id="3345">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = T(1 / x,x)
    ]]></literal>
    <justification jstring="[para(3343(a,1),278(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3343 278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3346">
    <literal><![CDATA[
      K(x,K(y,x \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(79(a,1),3344(a,1,1))].">
      <j1 rule="para" parents="79 3344"/>
    </justification>
  </clause>

  <clause id="3347">
    <literal><![CDATA[
      T(x,K(y,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,3346,a)].">
      <j1 rule="hyper" parents="57 3346"/>
    </justification>
  </clause>

  <clause id="3348">
    <literal><![CDATA[
      K(x,y \ 1) * y = y * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,3347,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 3347 22"/>
    </justification>
  </clause>

  <clause id="3349">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,117,a(flip),b,3345,a),flip(a)].">
      <j1 rule="hyper" parents="373 117 3345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3350">
    <literal><![CDATA[
      T((x * y) \ x,K(z,y)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(3349(a,1),444(a,2,1))].">
      <j1 rule="para" parents="3349 444"/>
    </justification>
  </clause>

  <clause id="3351">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = L((y \ x) \ 1,y \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),3350(a,1,1,1))].">
      <j1 rule="para" parents="10 3350"/>
    </justification>
  </clause>

  <clause id="3352">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,436,a(flip),b,3351,a),flip(a)].">
      <j1 rule="hyper" parents="373 436 3351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3353">
    <literal><![CDATA[
      K(x,y \ z) * (z \ y) = (z \ y) * K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,3352,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 3352 22"/>
    </justification>
  </clause>

  <clause id="3354">
    <literal><![CDATA[
      T(x \ (x / y),K(z,y)) = x \ (x / y)
    ]]></literal>
    <justification jstring="[para(82(a,1),3352(a,1,2,2))].">
      <j1 rule="para" parents="82 3352"/>
    </justification>
  </clause>

  <clause id="3355">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,x,y) \ (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(2342,a,1876,a)].">
      <j1 rule="hyper" parents="2342 1876"/>
    </justification>
  </clause>

  <clause id="3356">
    <literal><![CDATA[
      ((x * y) \ x) * K(y \ 1,y * ((x * y) \ x)) = (y \ 1) * (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(998,a,1876,a)].">
      <j1 rule="hyper" parents="998 1876"/>
    </justification>
  </clause>

  <clause id="3357">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * ((1 / x) * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,517,a(flip),b,2522,a),flip(a)].">
      <j1 rule="hyper" parents="373 517 2522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3358">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1511(a,1),3357(a,2,2))].">
      <j1 rule="para" parents="1511 3357"/>
    </justification>
  </clause>

  <clause id="3359">
    <literal><![CDATA[
      x * (((L(y,1 / y,x) * x) / L(y,1 / y,x)) \ z) = (x * (T(y,x) / y)) \ (x * z)
    ]]></literal>
    <justification jstring="[para(3358(a,1),2489(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3358 2489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3361">
    <literal><![CDATA[
      L(x \ 1,x,(x \ y) / y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(64,a,2086,a(flip),b,3057,a),flip(a)].">
      <j1 rule="hyper" parents="64 2086 3057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3363">
    <literal><![CDATA[
      ((x \ y) / y) / (1 / x) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(225,a,3361,a(flip),b,241,a(flip))].">
      <j1 rule="hyper" parents="225 3361 241"/>
    </justification>
  </clause>

  <clause id="3364">
    <literal><![CDATA[
      L((x / y) \ 1,x / y,y / x) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(82(a,1),3361(a,1,3,1))].">
      <j1 rule="para" parents="82 3361"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[hyper(642,a,3364,a)].">
      <j1 rule="hyper" parents="642 3364"/>
    </justification>
  </clause>

  <clause id="3366">
    <literal><![CDATA[
      ((x * y) / y) * (y / (x * y)) = x / (1 / (y / (x * y)))
    ]]></literal>
    <justification jstring="[para(3365(a,1),388(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3365 388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3367">
    <literal><![CDATA[
      x / (1 / (y / (x * y))) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(11(a,1),3366(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 3366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3368">
    <literal><![CDATA[
      (x * (y / (x * y))) \ x = 1 / (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(215,a,3367,a)].">
      <j1 rule="hyper" parents="215 3367"/>
    </justification>
  </clause>

  <clause id="3369">
    <literal><![CDATA[
      K(x \ (x * (y / (x * y))),x) = a(y / (x * y),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3367(a,1),2956(a,1,1,2))].">
      <j1 rule="para" parents="3367 2956"/>
    </justification>
  </clause>

  <clause id="3370">
    <literal><![CDATA[
      a(x / (y * x),y,y \ 1) = K(x / (y * x),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1571,a(flip),b,3369,a),flip(a)].">
      <j1 rule="hyper" parents="64 1571 3369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3372">
    <literal><![CDATA[
      T(T(x,y) * T(T(x,y) \ x,x),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(2517(a,1),3172(a,1,1))].">
      <j1 rule="para" parents="2517 3172"/>
    </justification>
  </clause>

  <clause id="3373">
    <literal><![CDATA[
      T(L(x,T(x,y) \ x,T(x,y)),(x * x) / T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(2422(a,1),3372(a,1,1))].">
      <j1 rule="para" parents="2422 3372"/>
    </justification>
  </clause>

  <clause id="3374">
    <literal><![CDATA[
      T(L(x,T(x,y) \ x,T(x,y)),x * (T(x,y) \ x)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(3168(a,1),3373(a,1,2))].">
      <j1 rule="para" parents="3168 3373"/>
    </justification>
  </clause>

  <clause id="3375">
    <literal><![CDATA[
      L(T(x,x * (T(x,y) \ x)),T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25,a,b,3374,a)].">
      <j1 rule="hyper" parents="64 25 3374"/>
    </justification>
  </clause>

  <clause id="3376">
    <literal><![CDATA[
      L(x,T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(3165(a,1),3375(a,1,1))].">
      <j1 rule="para" parents="3165 3375"/>
    </justification>
  </clause>

  <clause id="3377">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2422,a,b,3376,a)].">
      <j1 rule="hyper" parents="64 2422 3376"/>
    </justification>
  </clause>

  <clause id="3378">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,y) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(3376(a,1),3087(a,1,2))].">
      <j1 rule="para" parents="3376 3087"/>
    </justification>
  </clause>

  <clause id="3379">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3173,a(flip),b,3377,a),flip(a)].">
      <j1 rule="hyper" parents="64 3173 3377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3380">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = (x \ 1) * T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(997(a,1),3355(a,1,2)),flip(a)].">
      <j1 rule="para" parents="997 3355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3381">
    <literal><![CDATA[
      a(x * (y * y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,(y * y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(3116(a,1),1466(a,1))].">
      <j1 rule="para" parents="3116 1466"/>
    </justification>
  </clause>

  <clause id="3382">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z))
    ]]></literal>
    <justification jstring="[para(294(a,2),1710(a,1,2,1,1))].">
      <j1 rule="para" parents="294 1710"/>
    </justification>
  </clause>

  <clause id="3383">
    <literal><![CDATA[
      ((x * (x * R(x \ 1,y,z))) * u) * w = (x * x) * ((R(1 / x,y,z) * u) * w)
    ]]></literal>
    <justification jstring="[para(309(a,1),1969(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="309 1969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3384">
    <literal><![CDATA[
      (x * x) * ((R(1 / x,y,z) * u) * w) = (R(x,y,z) * u) * w
    ]]></literal>
    <justification jstring="[para(1988(a,1),3383(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1988 3383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3385">
    <literal><![CDATA[
      L(x,y,(R(1 / z,u,w) * v5) * v6) = L(x,y,(R(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(3384(a,1),2184(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3384 2184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3386">
    <literal><![CDATA[
      a((R(1 / x,y,z) * u) * w,v5,v6) = a((R(x,y,z) * u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(3384(a,1),2639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3384 2639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3387">
    <literal><![CDATA[
      a((R(x \ 1,y,z) * u) * w,v5,v6) = a((R(x,y,z) * u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(79(a,1),3386(a,1,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 3386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3388">
    <literal><![CDATA[
      a(R(1 / x,y,z),x,x \ 1) = R(x \ 1,y,z) / R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(194(a,1),2094(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="194 2094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3389">
    <literal><![CDATA[
      a(R(1 / x,y,z),x,x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2757,a(flip),b,3388,a),flip(a)].">
      <j1 rule="hyper" parents="373 2757 3388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3392">
    <literal><![CDATA[
      a(x / (y * x),y,y \ 1) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(244(a,1),3389(a,1,1))].">
      <j1 rule="para" parents="244 3389"/>
    </justification>
  </clause>

  <clause id="3393">
    <literal><![CDATA[
      K(x / (y * x),y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3370,a(flip),b,3392,a)].">
      <j1 rule="hyper" parents="64 3370 3392"/>
    </justification>
  </clause>

  <clause id="3395">
    <literal><![CDATA[
      K((x \ y) / y,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3393(a,1,1,2))].">
      <j1 rule="para" parents="10 3393"/>
    </justification>
  </clause>

  <clause id="3396">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),3393(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 3393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3397">
    <literal><![CDATA[
      K(x / y,y / x) * y = (1 / (1 / (y / x))) * x
    ]]></literal>
    <justification jstring="[para(3396(a,1),2370(a,1,1))].">
      <j1 rule="para" parents="3396 2370"/>
    </justification>
  </clause>

  <clause id="3398">
    <literal><![CDATA[
      K(x / y,y / x) * x = y * T(y \ x,y / x)
    ]]></literal>
    <justification jstring="[para(3396(a,1),2588(a,1,1))].">
      <j1 rule="para" parents="3396 2588"/>
    </justification>
  </clause>

  <clause id="3399">
    <literal><![CDATA[
      K((x * y) / y,y / (x * y)) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(3396(a,1),3093(a,1,1))].">
      <j1 rule="para" parents="3396 3093"/>
    </justification>
  </clause>

  <clause id="3400">
    <literal><![CDATA[
      K((x * y) / y,y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,2253,a,b,3399,a),flip(a)].">
      <j1 rule="hyper" parents="36 2253 3399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3401">
    <literal><![CDATA[
      K(x,y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),3400(a,1,1))].">
      <j1 rule="para" parents="11 3400"/>
    </justification>
  </clause>

  <clause id="3403">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = K(x / y,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),3401(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 3401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3404">
    <literal><![CDATA[
      (x / y) \ K(x / y,y / x) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,3403,a(flip),b,1724,a(flip))].">
      <j1 rule="hyper" parents="139 3403 1724"/>
    </justification>
  </clause>

  <clause id="3405">
    <literal><![CDATA[
      ((x * y) * ((z * z) * u)) / (y * ((z * z) * u)) = R(R(x,y,z * z),y * (z * z),u)
    ]]></literal>
    <justification jstring="[para(34(a,1),2292(a,1,2))].">
      <j1 rule="para" parents="34 2292"/>
    </justification>
  </clause>

  <clause id="3406">
    <literal><![CDATA[
      L((x \ y) \ ((1 / x) * z),x \ y,x * x) = ((1 / (1 / (1 / x))) \ y) \ (x * z)
    ]]></literal>
    <justification jstring="[para(569(a,1),2296(a,1,1,2))].">
      <j1 rule="para" parents="569 2296"/>
    </justification>
  </clause>

  <clause id="3407">
    <literal><![CDATA[
      ((1 / (1 / (1 / x))) \ y) \ (x * z) = (x \ y) \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[hyper(622,a,3406,a),flip(a)].">
      <j1 rule="hyper" parents="622 3406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3409">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * ((1 / x) * T((1 / x) \ (x \ y),z))
    ]]></literal>
    <justification jstring="[para(1724(a,2),2301(a,1,2,1,1))].">
      <j1 rule="para" parents="1724 2301"/>
    </justification>
  </clause>

  <clause id="3410">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x \ 1,x) \ x,y,z) = ((x \ 1) * R((x \ 1) \ 1,y,z)) * x
    ]]></literal>
    <justification jstring="[para(294(a,2),2558(a,1,2,1,1))].">
      <j1 rule="para" parents="294 2558"/>
    </justification>
  </clause>

  <clause id="3411">
    <literal><![CDATA[
      T(T(x,y) * ((T(x,y) / x) \ (1 / x)),T(x,y)) = T(x,y) * (K(y \ (y / (1 / x)),y) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(1884(a,2),2570(a,2,2,1))].">
      <j1 rule="para" parents="1884 2570"/>
    </justification>
  </clause>

  <clause id="3412">
    <literal><![CDATA[
      ((x * y) / x) * T(((x * y) / x) \ z,u) = (x * (y * T(y \ T(z,x),u))) / x
    ]]></literal>
    <justification jstring="[para(22(a,2),2583(a,1,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="22 2583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3413">
    <literal><![CDATA[
      L(T(x,x \ (x \ 1)),y,z) \ ((x \ 1) \ u) = ((x \ 1) \ x) * (x \ (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(25(a,2),2813(a,1,1))].">
      <j1 rule="para" parents="25 2813"/>
    </justification>
  </clause>

  <clause id="3414">
    <literal><![CDATA[
      T(x * ((1 / x) * ((1 / x) \ ((1 / (1 / x)) \ y))),x) = K(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2258,a(flip),b,2856,a),flip(a)].">
      <j1 rule="hyper" parents="373 2258 2856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3415">
    <literal><![CDATA[
      T(x * ((1 / (1 / x)) \ y),x) = K(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),3414(a,1,1,2))].">
      <j1 rule="para" parents="10 3414"/>
    </justification>
  </clause>

  <clause id="3417">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(2258(a,1),3415(a,1,1))].">
      <j1 rule="para" parents="2258 3415"/>
    </justification>
  </clause>

  <clause id="3418">
    <literal><![CDATA[
      T((1 / x) * ((x \ 1) \ y),x) = K(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(2356(a,2),3417(a,1,1))].">
      <j1 rule="para" parents="2356 3417"/>
    </justification>
  </clause>

  <clause id="3419">
    <literal><![CDATA[
      T((1 / x) * ((x \ 1) \ y),x) = (1 / x) * ((x \ 1) \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,2356,a,b,3418,a),flip(a)].">
      <j1 rule="hyper" parents="373 2356 3418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3420">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) * x = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1019,a,b,3419,a(flip))].">
      <j1 rule="hyper" parents="35 1019 3419"/>
    </justification>
  </clause>

  <clause id="3421">
    <literal><![CDATA[
      T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,3420,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="145 3420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3422">
    <literal><![CDATA[
      (x \ 1) \ T((x \ 1) * y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(9(a,1),3420(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 3420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3423">
    <literal><![CDATA[
      T((x \ ((x \ 1) \ y)) * ((1 / x) \ x),x \ 1) = (x \ 1) \ ((x \ 1) \ T(y,x))
    ]]></literal>
    <justification jstring="[para(3420(a,1),1593(a,2,2))].">
      <j1 rule="para" parents="3420 1593"/>
    </justification>
  </clause>

  <clause id="3424">
    <literal><![CDATA[
      x \ T(x * (y / x),x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,3421,a,b,3112,a),flip(a)].">
      <j1 rule="hyper" parents="142 3421 3112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3425">
    <literal><![CDATA[
      (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3421(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 3421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3426">
    <literal><![CDATA[
      T((x \ 1) * (x * y),x) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(69(a,1),3421(a,2,2,1))].">
      <j1 rule="para" parents="69 3421"/>
    </justification>
  </clause>

  <clause id="3428">
    <literal><![CDATA[
      T((x \ y) * x,x) / x = x \ T(y,x)
    ]]></literal>
    <justification jstring="[para(78(a,1),3424(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 3424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3429">
    <literal><![CDATA[
      x \ T(x * L((x * y) / x,z,u),x) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(1194(a,2),3424(a,1,2,1,2))].">
      <j1 rule="para" parents="1194 3424"/>
    </justification>
  </clause>

  <clause id="3430">
    <literal><![CDATA[
      x \ T(x * L(y / x,z,u),x) = L(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[para(3424(a,1),2854(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3424 2854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3431">
    <literal><![CDATA[
      x \ T(x * T(y / x,z),x) = T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[para(3424(a,1),2917(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3424 2917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3433">
    <literal><![CDATA[
      T((x \ y) * x,x) = (x \ T(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(156,a,3428,a),flip(a)].">
      <j1 rule="hyper" parents="156 3428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3434">
    <literal><![CDATA[
      T(((x / y) \ 1) * x,x / y) = ((x / y) \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[hyper(145,a,221,a(flip),b,3422,a),flip(a)].">
      <j1 rule="hyper" parents="145 221 3422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3436">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = L(K(x \ y,x),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,3425,a(flip),b,613,a)].">
      <j1 rule="hyper" parents="139 3425 613"/>
    </justification>
  </clause>

  <clause id="3437">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * (K(y \ x,y) * x)
    ]]></literal>
    <justification jstring="[para(95(a,1),3425(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="95 3425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3438">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = x * ((x \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(145,a,3426,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 3426 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3439">
    <literal><![CDATA[
      T(x * T(y / x,z),x) = x * T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(157,a,3431,a),flip(a)].">
      <j1 rule="hyper" parents="157 3431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3440">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = L(y * x,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1139,a(flip),b,3438,a),flip(a)].">
      <j1 rule="hyper" parents="373 1139 3438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3441">
    <literal><![CDATA[
      L(x * y,y \ 1,y) / y = (y \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(142,a,293,a(flip),b,3438,a)].">
      <j1 rule="hyper" parents="142 293 3438"/>
    </justification>
  </clause>

  <clause id="3442">
    <literal><![CDATA[
      L((x \ y) * x,x,x) = ((x \ 1) * y) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),3440(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 3440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3443">
    <literal><![CDATA[
      (x \ 1) * (x * (y / x)) = L(y,x \ 1,x) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),3441(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 3441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3444">
    <literal><![CDATA[
      (x \ 1) * (x * (y / x)) = L(y,x,x) / x
    ]]></literal>
    <justification jstring="[para(1145(a,1),3443(a,2,1))].">
      <j1 rule="para" parents="1145 3443"/>
    </justification>
  </clause>

  <clause id="3445">
    <literal><![CDATA[
      L(R(x,y,y),y,y) / y = (y \ 1) * (y * (x * (1 / y)))
    ]]></literal>
    <justification jstring="[para(1408(a,1),3444(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1408 3444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3446">
    <literal><![CDATA[
      T(x * T(1 / x,y),x) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(376(a,1),3439(a,2,2,1,1))].">
      <j1 rule="para" parents="376 3439"/>
    </justification>
  </clause>

  <clause id="3447">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2948,a,b,3446,a)].">
      <j1 rule="hyper" parents="64 2948 3446"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      (x \ 1) * (x * (y * (1 / x))) = L(y,x,x) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1410,a(flip),b,3445,a),flip(a)].">
      <j1 rule="hyper" parents="64 1410 3445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3449">
    <literal><![CDATA[
      L(T(x * y,x) / x,z,u) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,3430,a(flip),b,3429,a)].">
      <j1 rule="hyper" parents="64 3430 3429"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1804(a,1),3102(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1804 3102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3451">
    <literal><![CDATA[
      (x \ 1) * ((x \ L(x,y,z)) \ 1) = (x \ L(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,72,a(flip),b,3450,a),flip(a)].">
      <j1 rule="hyper" parents="139 72 3450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3452">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) != (x \ 1) * u
    ]]></literal>
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = u
    ]]></literal>
    <justification jstring="[para(3451(a,1),44(a,1))].">
      <j1 rule="para" parents="3451 44"/>
    </justification>
  </clause>

  <clause id="3453">
    <literal><![CDATA[
      (x \ R(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ R(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1793(a,1),3104(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1793 3104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      (x \ 1) * ((x \ R(x,y,z)) \ 1) = (x \ R(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,72,a(flip),b,3453,a),flip(a)].">
      <j1 rule="hyper" parents="139 72 3453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3455">
    <literal><![CDATA[
      ((L(x \ 1,x,y) * y) / L(x \ 1,x,y)) / y = L(x * T(x \ 1,y),y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,295,a(flip),b,3160,a),flip(a)].">
      <j1 rule="hyper" parents="373 295 3160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3456">
    <literal><![CDATA[
      L(x * T(x \ 1,y),y,1 / y) = (y * (x * T(x \ 1,y))) / y
    ]]></literal>
    <justification jstring="[para(3157(a,1),3455(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3157 3455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3457">
    <literal><![CDATA[
      (x * (((x * y) \ x) * T(((x * y) \ x) \ 1,x))) / x = L(K(y,x),x,1 / x)
    ]]></literal>
    <justification jstring="[para(1567(a,2),3456(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1567 3456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3458">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = (y * K(x,y)) / y
    ]]></literal>
    <justification jstring="[para(1567(a,2),3457(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1567 3457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3459">
    <literal><![CDATA[
      (x \ 1) * (K(x \ 1,(x \ 1) \ 1) * L(T(x \ 1,(x \ 1) \ 1) \ y,z,u)) = T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,2383,a,b,3286,a)].">
      <j1 rule="hyper" parents="373 2383 3286"/>
    </justification>
  </clause>

  <clause id="3460">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),3299(a,2,2,1,2,1))].">
      <j1 rule="para" parents="12 3299"/>
    </justification>
  </clause>

  <clause id="3461">
    <literal><![CDATA[
      (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(154,a,3460,a)].">
      <j1 rule="hyper" parents="154 3460"/>
    </justification>
  </clause>

  <clause id="3462">
    <literal><![CDATA[
      (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),3461(a,1,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 3461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3463">
    <literal><![CDATA[
      (x * (T(y,x) / y)) \ (x * z) = x * ((x * (T(y,x) / y)) \ z)
    ]]></literal>
    <justification jstring="[para(3358(a,1),3359(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3358 3359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3464">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,2925,a(flip),b,3382,a),flip(a)].">
      <j1 rule="hyper" parents="373 2925 3382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3465">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[para(2359(a,1),3464(a,1,2,1))].">
      <j1 rule="para" parents="2359 3464"/>
    </justification>
  </clause>

  <clause id="3466">
    <literal><![CDATA[
      R(R(x,y,z * z),y * (z * z),u) = R(x,y,(z * z) * u)
    ]]></literal>
    <justification jstring="[hyper(666,a,3405,a),flip(a)].">
      <j1 rule="hyper" parents="666 3405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3467">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * (T((x \ y) * x,z) / x)
    ]]></literal>
    <justification jstring="[para(1506(a,1),3409(a,2,2))].">
      <j1 rule="para" parents="1506 3409"/>
    </justification>
  </clause>

  <clause id="3468">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ x,y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(190(a,1),3467(a,2,2,1,1))].">
      <j1 rule="para" parents="190 3467"/>
    </justification>
  </clause>

  <clause id="3469">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * (K(x,x \ 1) \ 1) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(144,a,3468,a(flip),b,1503,a)].">
      <j1 rule="hyper" parents="144 3468 1503"/>
    </justification>
  </clause>

  <clause id="3470">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[para(2371(a,1),3469(a,1,2))].">
      <j1 rule="para" parents="2371 3469"/>
    </justification>
  </clause>

  <clause id="3471">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(2371(a,1),3470(a,2,1,2))].">
      <j1 rule="para" parents="2371 3470"/>
    </justification>
  </clause>

  <clause id="3472">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1162(a,1),3471(a,2,1))].">
      <j1 rule="para" parents="1162 3471"/>
    </justification>
  </clause>

  <clause id="3473">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x \ 1,x) \ x,y,z) = (x \ R(x,y,z)) * x
    ]]></literal>
    <justification jstring="[para(1793(a,1),3410(a,2,1))].">
      <j1 rule="para" parents="1793 3410"/>
    </justification>
  </clause>

  <clause id="3474">
    <literal><![CDATA[
      ((x \ 1) \ x) * (x \ (L(x,y,z) \ u)) = L(R(x,x,x),y,z) \ ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1561(a,1),3413(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1561 3413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3475">
    <literal><![CDATA[
      L(R(x,x,x),y,z) \ ((x \ 1) \ u) = (x \ 1) \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1131,a(flip),b,3474,a),flip(a)].">
      <j1 rule="hyper" parents="64 1131 3474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3476">
    <literal><![CDATA[
      (x * K(x,y)) * T((x * K(x,y)) \ (x * y),z) = (T(y,z) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,511,a(flip),b,992,a),flip(a)].">
      <j1 rule="hyper" parents="373 511 992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3477">
    <literal><![CDATA[
      x * (K(x,y) * T(K(x,y) \ y,z)) = (T(y,z) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1316,a,3476,a)].">
      <j1 rule="hyper" parents="1316 3476"/>
    </justification>
  </clause>

  <clause id="3478">
    <literal><![CDATA[
      (T(x,K(y,x)) * y) * K(y,x) = y * ((K(y,x) \ x) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(737,a,3477,a),flip(a)].">
      <j1 rule="hyper" parents="737 3477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3479">
    <literal><![CDATA[
      (x * L(R(x,y,z),u,w)) \ (x * (L(R(x,y,z),u,w) * v5)) = L(v5,x,L(R(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(3235(a,1),1451(a,1,2))].">
      <j1 rule="para" parents="3235 1451"/>
    </justification>
  </clause>

  <clause id="3480">
    <literal><![CDATA[
      (((x * y) * z) * T(((x * y) * z) \ (y * z),u)) / (y * z) = R(x,y,z) * T(R(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1883,a(flip),b,2590,a),flip(a)].">
      <j1 rule="hyper" parents="64 1883 2590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3481">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(2880(a,1),2590(a,2,1))].">
      <j1 rule="para" parents="2880 2590"/>
    </justification>
  </clause>

  <clause id="3482">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(2881(a,1),3481(a,2,1,1))].">
      <j1 rule="para" parents="2881 3481"/>
    </justification>
  </clause>

  <clause id="3483">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,20,a,b,3482,a)].">
      <j1 rule="hyper" parents="373 20 3482"/>
    </justification>
  </clause>

  <clause id="3484">
    <literal><![CDATA[
      R(x,y,z) * T(R(x,y,z) \ 1,u) = R(x * T(x \ 1,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1883,a(flip),b,3483,a)].">
      <j1 rule="hyper" parents="373 1883 3483"/>
    </justification>
  </clause>

  <clause id="3485">
    <literal><![CDATA[
      R(T(x,x \ 1) * T(T(x,x \ 1) \ 1,x \ R(x,y,z)),y,z) = K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1797(a,1),3483(a,2,1,2))].">
      <j1 rule="para" parents="1797 3483"/>
    </justification>
  </clause>

  <clause id="3486">
    <literal><![CDATA[
      R(x * T(x \ 1,R(x,y,z)),y,z) = (R(x,y,z) \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(328,a,3484,a),flip(a)].">
      <j1 rule="hyper" parents="328 3484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3487">
    <literal><![CDATA[
      R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = (1 / x) * T(R(1 / x,K(x \ 1,x),z) \ 1,y)
    ]]></literal>
    <justification jstring="[para(3081(a,1),3484(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3081 3484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3488">
    <literal><![CDATA[
      a(L(x \ ((y * y) \ z),(y * y) * x,(y * y) * x),u,w) = a((y * y) * (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(487(a,1),2677(a,1,1,1))].">
      <j1 rule="para" parents="487 2677"/>
    </justification>
  </clause>

  <clause id="3489">
    <literal><![CDATA[
      (L(x,y,z) * (1 / x)) / L(x,y,z) = L(1 / x,L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3132,a(flip),b,3135,a)].">
      <j1 rule="hyper" parents="64 3132 3135"/>
    </justification>
  </clause>

  <clause id="3491">
    <literal><![CDATA[
      L(1 / x,L(x,y,z),1 / x) * x != u
    ]]></literal>
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(3489(a,1),1493(a,1,1))].">
      <j1 rule="para" parents="3489 1493"/>
    </justification>
  </clause>

  <clause id="3492">
    <literal><![CDATA[
      L(x,L(R(y,z,u),w,v5),y) = L(x,y,L(R(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(608,a,3479,a)].">
      <j1 rule="hyper" parents="608 3479"/>
    </justification>
  </clause>

  <clause id="3493">
    <literal><![CDATA[
      a(L(x \ ((y * y) \ z),(y * y) * x,x),u,w) = a((y * y) * (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(2184(a,1),3488(a,1,1))].">
      <j1 rule="para" parents="2184 3488"/>
    </justification>
  </clause>

  <clause id="3495">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = x * L(x \ 1,L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(3491,a,836,a)].">
      <j1 rule="hyper" parents="3491 836"/>
    </justification>
  </clause>

  <clause id="3496">
    <literal><![CDATA[
      x * L(x \ 1,L(x,y,z),1 / x) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3136,a(flip),b,3495,a),flip(a)].">
      <j1 rule="hyper" parents="64 3136 3495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3497">
    <literal><![CDATA[
      (((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1567,a,b,1570,a),flip(a)].">
      <j1 rule="hyper" parents="373 1567 1570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3498">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (((y * x) \ y) \ 1) \ (((y * x) \ y) \ K(x,y)) = z
    ]]></literal>
    <justification jstring="[para(3497(a,1),467(a,1,1))].">
      <j1 rule="para" parents="3497 467"/>
    </justification>
  </clause>

  <clause id="3499">
    <literal><![CDATA[
      x * ((1 / x) \ ((x \ y) \ ((1 / x) * y))) = (((1 / x) \ 1) * y) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(782,a,1976,a)].">
      <j1 rule="hyper" parents="782 1976"/>
    </justification>
  </clause>

  <clause id="3501">
    <literal><![CDATA[
      (((1 / x) \ 1) * y) * ((x \ y) \ 1) = (x * x) * ((x \ y) \ ((1 / x) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,538,a(flip),b,3499,a),flip(a)].">
      <j1 rule="hyper" parents="64 538 3499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3502">
    <literal><![CDATA[
      (x / y) * R((y * y) * ((x / (1 / y)) \ 1),z,u) = (x / (1 / y)) \ R(x / (1 / y),z,u)
    ]]></literal>
    <justification jstring="[para(1981(a,2),2008(a,1,2))].">
      <j1 rule="para" parents="1981 2008"/>
    </justification>
  </clause>

  <clause id="3503">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * ((y \ x) \ 1) = (y \ x) \ L(1 / (x \ y),x \ y,x)
    ]]></literal>
    <justification jstring="[para(1777(a,1),2460(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1777 2460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3504">
    <literal><![CDATA[
      K(x \ y,x) * R((y \ ((x \ y) * x)) \ x,z,u) = y \ ((R(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[para(95(a,1),3260(a,1,1))].">
      <j1 rule="para" parents="95 3260"/>
    </justification>
  </clause>

  <clause id="3505">
    <literal><![CDATA[
      K(x \ y,x) * R(K(x \ y,x) \ x,z,u) = y \ ((R(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[para(95(a,1),3504(a,1,2,1,1))].">
      <j1 rule="para" parents="95 3504"/>
    </justification>
  </clause>

  <clause id="3506">
    <literal><![CDATA[
      (x / (1 / y)) \ R(x / (1 / y),z,u) = (x / y) * R((x / y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(891(a,1),3502(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="891 3502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3507">
    <literal><![CDATA[
      (x / (1 / y)) \ R(x / (1 / y),z,u) = (x / y) \ R(x / y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,1987,a(flip),b,3506,a),flip(a)].">
      <j1 rule="hyper" parents="373 1987 3506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3508">
    <literal><![CDATA[
      (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = (R(y,z,u) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,506,a(flip),b,1201,a),flip(a)].">
      <j1 rule="hyper" parents="373 506 1201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3509">
    <literal><![CDATA[
      x * (K(x,y) * R(K(x,y) \ y,z,u)) = (R(y,z,u) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1708,a(flip),b,3508,a)].">
      <j1 rule="hyper" parents="64 1708 3508"/>
    </justification>
  </clause>

  <clause id="3510">
    <literal><![CDATA[
      (R(x,y,z) * (x \ 1)) * K(x \ 1,x) = (x \ 1) * ((x \ R(x,y,z)) * x)
    ]]></literal>
    <justification jstring="[para(3473(a,1),3509(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3473 3509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3511">
    <literal><![CDATA[
      (R(x,y,z) * (x \ 1)) * K(x \ 1,x) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2069(a,1),3510(a,2,2))].">
      <j1 rule="para" parents="2069 3510"/>
    </justification>
  </clause>

  <clause id="3512">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(358,a,3511,a)].">
      <j1 rule="hyper" parents="358 3511"/>
    </justification>
  </clause>

  <clause id="3513">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,x) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1794(a,1),3511(a,1,1))].">
      <j1 rule="para" parents="1794 3511"/>
    </justification>
  </clause>

  <clause id="3514">
    <literal><![CDATA[
      (x * (L(R(x,y,z),u,w) * v5)) \ ((x * L(R(x,y,z),u,w)) * v5) = a(L(R(x,y,z),u,w),x,v5)
    ]]></literal>
    <justification jstring="[para(3235(a,1),1450(a,1,1))].">
      <j1 rule="para" parents="3235 1450"/>
    </justification>
  </clause>

  <clause id="3515">
    <literal><![CDATA[
      a(L(R(x,y,z),u,w),x,v5) = a(x,L(R(x,y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(959,a,3514,a),flip(a)].">
      <j1 rule="hyper" parents="959 3514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3516">
    <literal><![CDATA[
      (1 / x) * (1 * (T(y,(x \ 1) * (x \ 1)) \ z)) = x * (y \ (((x \ 1) * (x \ 1)) * z))
    ]]></literal>
    <justification jstring="[para(10(a,1),1671(a,1,2,1))].">
      <j1 rule="para" parents="10 1671"/>
    </justification>
  </clause>

  <clause id="3518">
    <literal><![CDATA[
      a(x,x \ y,L(T(x,x \ y),z,u)) = (L(x,z,u) * y) \ (y * L(T(x,x \ y),z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),3214(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 3214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3520">
    <literal><![CDATA[
      T(x,y) * (K(y \ (y / (1 / x)),y) \ (1 / x)) = T(x,y) * ((T(x,y) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,2570,a(flip),b,3411,a),flip(a)].">
      <j1 rule="hyper" parents="64 2570 3411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3521">
    <literal><![CDATA[
      T(x,y) * (T(1 / (1 / x),y) \ 1) = T(x,y) * ((T(x,y) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(3230(a,1),3520(a,1,2))].">
      <j1 rule="para" parents="3230 3520"/>
    </justification>
  </clause>

  <clause id="3522">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(1 / (1 / x),y) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3245,a(flip),b,3521,a),flip(a)].">
      <j1 rule="hyper" parents="64 3245 3521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3523">
    <literal><![CDATA[
      ((x * y) * z) * T(((x * y) * z) \ (y * z),R(x,y,z)) = K(R(x,y,z) \ 1,R(x,y,z)) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,414,a(flip),b,3480,a),flip(a)].">
      <j1 rule="hyper" parents="144 414 3480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3526">
    <literal><![CDATA[
      (1 / (x / y)) * (((1 / (x / y)) \ (y / x)) * z) = (y / x) * L(z,(y / x) * (x / y),x / y)
    ]]></literal>
    <justification jstring="[para(1643(a,1),2721(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1643 2721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3527">
    <literal><![CDATA[
      (x \ y) \ ((R(x \ 1,x,y) * x) * (x \ y)) = a(R(1 / x,x,x \ y),x,x \ y)
    ]]></literal>
    <justification jstring="[para(80(a,1),3026(a,1,1))].">
      <j1 rule="para" parents="80 3026"/>
    </justification>
  </clause>

  <clause id="3529">
    <literal><![CDATA[
      (x \ y) \ (((x \ 1) * R(x,x,y)) * (x \ y)) = a(R(1 / x,x,x \ y),x,x \ y)
    ]]></literal>
    <justification jstring="[para(2765(a,1),3527(a,1,2,1))].">
      <j1 rule="para" parents="2765 3527"/>
    </justification>
  </clause>

  <clause id="3530">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = ((x * y) * T((x * y) \ y,R(x,y,z))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,2880,a(flip),b,3523,a),flip(a)].">
      <j1 rule="hyper" parents="64 2880 3523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3531">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = ((x * T(x \ 1,R(x,y,z))) * y) * z
    ]]></literal>
    <justification jstring="[para(2881(a,1),3530(a,2,1))].">
      <j1 rule="para" parents="2881 3530"/>
    </justification>
  </clause>

  <clause id="3532">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) * (y * z) = (K(x \ 1,x) * y) * z
    ]]></literal>
    <justification jstring="[para(2284(a,1),3531(a,2,1,1))].">
      <j1 rule="para" parents="2284 3531"/>
    </justification>
  </clause>

  <clause id="3533">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,2227,a(flip),b,3532,a),flip(a)].">
      <j1 rule="hyper" parents="36 2227 3532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3537">
    <literal><![CDATA[
      (L(x * x,y,z) * (u * (w * v5))) \ ((L(x * x,y,z) * (u * w)) * v5) = a(L(x * x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(1701(a,1),1826(a,1,2,1))].">
      <j1 rule="para" parents="1701 1826"/>
    </justification>
  </clause>

  <clause id="3538">
    <literal><![CDATA[
      K((1 / x) \ ((1 / x) * T((1 / x) \ 1,y)),1 / x) = (((1 / x) * T(x,y)) / (1 / x)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3229(a,1),1894(a,1,1,2))].">
      <j1 rule="para" parents="3229 1894"/>
    </justification>
  </clause>

  <clause id="3539">
    <literal><![CDATA[
      (((1 / x) * T(x,y)) / (1 / x)) \ T(x,y) = K((1 / x) \ (T(x,y) / x),1 / x)
    ]]></literal>
    <justification jstring="[para(1509(a,1),3538(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1509 3538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3540">
    <literal><![CDATA[
      (((1 / x) * T(x,y)) / (1 / x)) \ T(x,y) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1515(a,1),3539(a,2,1))].">
      <j1 rule="para" parents="1515 3539"/>
    </justification>
  </clause>

  <clause id="3541">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ T(x,y) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(911(a,1),3540(a,1,1))].">
      <j1 rule="para" parents="911 3540"/>
    </justification>
  </clause>

  <clause id="3542">
    <literal><![CDATA[
      R(R(x,y,(z * z) \ 1),y * ((z * z) \ 1),u) = ((x * y) * ((z * z) \ u)) / (y * ((z * z) \ u))
    ]]></literal>
    <justification jstring="[para(949(a,1),2294(a,1,2)),flip(a)].">
      <j1 rule="para" parents="949 2294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3543">
    <literal><![CDATA[
      R(R(x,y,(z * z) \ 1),y * ((z * z) \ 1),u) = R(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,20,a,b,3542,a),flip(a)].">
      <j1 rule="hyper" parents="373 20 3542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3544">
    <literal><![CDATA[
      R(R(x,y,(z * z) \ 1),y / (z * z),u) = R(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[para(557(a,1),3543(a,1,2))].">
      <j1 rule="para" parents="557 3543"/>
    </justification>
  </clause>

  <clause id="3545">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = L(1 / (y \ x),y \ x,y) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1193(a,1),3139(a,2,1))].">
      <j1 rule="para" parents="1193 3139"/>
    </justification>
  </clause>

  <clause id="3546">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = (x \ y) \ L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,3503,a(flip),b,3545,a),flip(a)].">
      <j1 rule="hyper" parents="373 3503 3545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3547">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = K(y \ x,((x \ y) * (y \ x)) / (y \ x))
    ]]></literal>
    <justification jstring="[para(2618(a,1),3140(a,2,2,1))].">
      <j1 rule="para" parents="2618 3140"/>
    </justification>
  </clause>

  <clause id="3548">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((((x \ y) \ 1) \ (y \ x)) / (y \ x)) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(11(a,1),3547(a,2,2))].">
      <j1 rule="para" parents="11 3547"/>
    </justification>
  </clause>

  <clause id="3549">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,3548,a(flip),b,3546,a(flip))].">
      <j1 rule="hyper" parents="145 3548 3546"/>
    </justification>
  </clause>

  <clause id="3551">
    <literal><![CDATA[
      T(x * (((x \ 1) * T((x \ 1) \ 1,y)) / T(x,y)),z) = T(x,z) * ((T(x,z) \ T(x,y)) / T(x,y))
    ]]></literal>
    <justification jstring="[para(2425(a,1),3329(a,2,2,1))].">
      <j1 rule="para" parents="2425 3329"/>
    </justification>
  </clause>

  <clause id="3552">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ T(x,z)) / T(x,z)) = T(K(T(x,z),1 / x),y)
    ]]></literal>
    <justification jstring="[para(2810(a,1),3551(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2810 3551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3553">
    <literal><![CDATA[
      K(T(x,y),1 / T(x,z)) = T(K(T(x,y),1 / x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3105,a(flip),b,3552,a)].">
      <j1 rule="hyper" parents="64 3105 3552"/>
    </justification>
  </clause>

  <clause id="3554">
    <literal><![CDATA[
      T(K(T(x,y),1 / x),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3553(a,1),1736(a,1))].">
      <j1 rule="para" parents="3553 1736"/>
    </justification>
  </clause>

  <clause id="3555">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = K(T(x,y),T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3554,a,3256,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3554 3256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3556">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3256(a,2),3554(a,1))].">
      <j1 rule="para" parents="3256 3554"/>
    </justification>
  </clause>

  <clause id="3557">
    <literal><![CDATA[
      (T(x,y) / x) \ (1 / x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1724,a(flip),b,3555,a),flip(a)].">
      <j1 rule="hyper" parents="35 1724 3555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3558">
    <literal><![CDATA[
      (T(T(x,x \ 1),y) / T(x,x \ 1)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(301(a,1),3557(a,1,2))].">
      <j1 rule="para" parents="301 3557"/>
    </justification>
  </clause>

  <clause id="3559">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3522(a,1),3556(a,1))].">
      <j1 rule="para" parents="3522 3556"/>
    </justification>
  </clause>

  <clause id="3560">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(3559,a,3541,a)].">
      <j1 rule="hyper" parents="3559 3541"/>
    </justification>
  </clause>

  <clause id="3561">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(2553(a,1),3558(a,1,1))].">
      <j1 rule="para" parents="2553 3558"/>
    </justification>
  </clause>

  <clause id="3562">
    <literal><![CDATA[
      1 / T(T(x,x \ 1),y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,3223,a(flip),b,3561,a),flip(a)].">
      <j1 rule="hyper" parents="64 3223 3561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3563">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,3562,a),flip(a)].">
      <j1 rule="hyper" parents="215 3562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3565">
    <literal><![CDATA[
      1 / T(x \ 1,y) = T(1 / x,y) \ 1
    ]]></literal>
    <justification jstring="[para(848(a,1),3562(a,1,2,1))].">
      <j1 rule="para" parents="848 3562"/>
    </justification>
  </clause>

  <clause id="3566">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(412(a,1),3562(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="412 3562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      1 / R(T(x,y),x,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(1421(a,1),3562(a,1,2))].">
      <j1 rule="para" parents="1421 3562"/>
    </justification>
  </clause>

  <clause id="3568">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,866,a(flip),b,3563,a)].">
      <j1 rule="hyper" parents="64 866 3563"/>
    </justification>
  </clause>

  <clause id="3569">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ 1 = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(848(a,1),3563(a,1,1)),flip(a)].">
      <j1 rule="para" parents="848 3563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3570">
    <literal><![CDATA[
      1 / (1 / T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(226,a,3566,a)].">
      <j1 rule="hyper" parents="226 3566"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      L(T(x,y),x,x) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(824(a,1),3566(a,1,1))].">
      <j1 rule="para" parents="824 3566"/>
    </justification>
  </clause>

  <clause id="3572">
    <literal><![CDATA[
      T(x / (x * x),y) \ 1 = 1 / T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2029(a,1),3566(a,1,1,1))].">
      <j1 rule="para" parents="2029 3566"/>
    </justification>
  </clause>

  <clause id="3573">
    <literal><![CDATA[
      T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(117(a,1),3568(a,2,1,1))].">
      <j1 rule="para" parents="117 3568"/>
    </justification>
  </clause>

  <clause id="3574">
    <literal><![CDATA[
      x * ((T(y,x) \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      ((y \ 1) \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(3568(a,1),328(a,1,2))].">
      <j1 rule="para" parents="3568 328"/>
    </justification>
  </clause>

  <clause id="3575">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) \ ((T(x,y) \ 1) \ z) = T(x,y) \ ((1 / T(x,y)) \ z)
    ]]></literal>
    <justification jstring="[para(3568(a,2),1675(a,1,1))].">
      <j1 rule="para" parents="3568 1675"/>
    </justification>
  </clause>

  <clause id="3576">
    <literal><![CDATA[
      ((1 / x) * y) \ L(y,1 / x,1 / x) = 1 / (1 / T(x,(1 / x) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,565,a,b,3570,a)].">
      <j1 rule="hyper" parents="373 565 3570"/>
    </justification>
  </clause>

  <clause id="3577">
    <literal><![CDATA[
      L(x,T(x,y) \ 1,T(x,y)) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(41,a,1159,a,b,3570,a(flip))].">
      <j1 rule="hyper" parents="41 1159 3570"/>
    </justification>
  </clause>

  <clause id="3578">
    <literal><![CDATA[
      T(1 / (1 / (x / y)),y) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(117(a,1),3570(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 3570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3579">
    <literal><![CDATA[
      x * K(x \ (x / T(x,y)),x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2484,a(flip),b,3577,a)].">
      <j1 rule="hyper" parents="64 2484 3577"/>
    </justification>
  </clause>

  <clause id="3581">
    <literal><![CDATA[
      (x * (((x \ y) \ 1) \ 1)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(313,a,3573,a)].">
      <j1 rule="hyper" parents="313 3573"/>
    </justification>
  </clause>

  <clause id="3582">
    <literal><![CDATA[
      T(x \ y,x / y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,3042,a(flip),b,3573,a)].">
      <j1 rule="hyper" parents="64 3042 3573"/>
    </justification>
  </clause>

  <clause id="3583">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = ((y \ (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,543,a(flip),b,3573,a)].">
      <j1 rule="hyper" parents="64 543 3573"/>
    </justification>
  </clause>

  <clause id="3584">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x * y) \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(11(a,1),3582(a,1,2))].">
      <j1 rule="para" parents="11 3582"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),3582(a,1,2))].">
      <j1 rule="para" parents="79 3582"/>
    </justification>
  </clause>

  <clause id="3586">
    <literal><![CDATA[
      K(x / y,y / x) * x = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3582(a,1),3398(a,2,2))].">
      <j1 rule="para" parents="3582 3398"/>
    </justification>
  </clause>

  <clause id="3587">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) / x = 1 / (1 / (y / x))
    ]]></literal>
    <justification jstring="[hyper(313,a,3578,a)].">
      <j1 rule="hyper" parents="313 3578"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      (1 / (1 / (x / y))) * y = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(145,a,3578,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 3578 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3590">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1162,a,b,3579,a),flip(a)].">
      <j1 rule="hyper" parents="35 1162 3579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3591">
    <literal><![CDATA[
      T(K(x \ 1,x),y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3066,a(flip),b,3590,a)].">
      <j1 rule="hyper" parents="64 3066 3590"/>
    </justification>
  </clause>

  <clause id="3593">
    <literal><![CDATA[
      (x * K(y \ 1,y)) / x = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(313,a,3591,a)].">
      <j1 rule="hyper" parents="313 3591"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      T(x,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,3591,a)].">
      <j1 rule="hyper" parents="55 3591"/>
    </justification>
  </clause>

  <clause id="3595">
    <literal><![CDATA[
      K(x \ 1,x) * y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,3591,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 3591 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3596">
    <literal><![CDATA[
      T((x \ 1) * x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(294(a,1),3591(a,1,1))].">
      <j1 rule="para" parents="294 3591"/>
    </justification>
  </clause>

  <clause id="3597">
    <literal><![CDATA[
      K(x \ 1,x) * y != z * K(x \ 1,x)
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(3591(a,1),271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3591 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3598">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) * x = z
    ]]></literal>
    <justification jstring="[para(3591(a,1),328(a,1,2))].">
      <j1 rule="para" parents="3591 328"/>
    </justification>
  </clause>

  <clause id="3599">
    <literal><![CDATA[
      x * (K(y \ 1,y) * z) = x * (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(3591(a,1),251(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3591 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3600">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) * (z * y) = z * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(3591(a,1),793(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3591 793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3601">
    <literal><![CDATA[
      K(x \ 1,x) * (T(x,y) \ x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(3591(a,1),3075(a,1,1))].">
      <j1 rule="para" parents="3591 3075"/>
    </justification>
  </clause>

  <clause id="3602">
    <literal><![CDATA[
      T(x,K(y,1 / y)) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),3594(a,1,2,1))].">
      <j1 rule="para" parents="82 3594"/>
    </justification>
  </clause>

  <clause id="3604">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(3594(a,1),328(a,1,2))].">
      <j1 rule="para" parents="3594 328"/>
    </justification>
  </clause>

  <clause id="3605">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1739(a,1),3594(a,1,2))].">
      <j1 rule="para" parents="1739 3594"/>
    </justification>
  </clause>

  <clause id="3606">
    <literal><![CDATA[
      T(x,K(y \ 1,R(y,z,u))) = x
    ]]></literal>
    <justification jstring="[para(3512(a,2),3594(a,1,2))].">
      <j1 rule="para" parents="3512 3594"/>
    </justification>
  </clause>

  <clause id="3607">
    <literal><![CDATA[
      K(x,1 / x) * y = y * K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(2149,a,3602,a),flip(a)].">
      <j1 rule="hyper" parents="2149 3602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3608">
    <literal><![CDATA[
      x / K(y,1 / y) = K(y,1 / y) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,3602,a),flip(a)].">
      <j1 rule="hyper" parents="467 3602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3609">
    <literal><![CDATA[
      T(x,y * (1 / y)) = x
    ]]></literal>
    <justification jstring="[para(296(a,1),3602(a,1,2))].">
      <j1 rule="para" parents="296 3602"/>
    </justification>
  </clause>

  <clause id="3610">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2149,a,3605,a),flip(a)].">
      <j1 rule="hyper" parents="2149 3605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3611">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(55,a,3605,a)].">
      <j1 rule="hyper" parents="55 3605"/>
    </justification>
  </clause>

  <clause id="3612">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3605(a,1),328(a,1,2))].">
      <j1 rule="para" parents="3605 328"/>
    </justification>
  </clause>

  <clause id="3614">
    <literal><![CDATA[
      x / (y * (1 / y)) = (y * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,3609,a),flip(a)].">
      <j1 rule="hyper" parents="467 3609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3615">
    <literal><![CDATA[
      T(K(x \ 1,R(x,y,z)),u) = K(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(55,a,3606,a)].">
      <j1 rule="hyper" parents="55 3606"/>
    </justification>
  </clause>

  <clause id="3616">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(139,a,3611,a(flip),b,3314,a)].">
      <j1 rule="hyper" parents="139 3611 3314"/>
    </justification>
  </clause>

  <clause id="3618">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) * (z * y) = z * (y * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(3611(a,1),793(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3611 793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3619">
    <literal><![CDATA[
      R(1 / x,y,z) * K(x \ 1,x) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,2757,a,b,3593,a),flip(a)].">
      <j1 rule="hyper" parents="38 2757 3593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3620">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(2391,a,3595,a)].">
      <j1 rule="hyper" parents="2391 3595"/>
    </justification>
  </clause>

  <clause id="3621">
    <literal><![CDATA[
      K(x,x \ 1) * (y * K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[hyper(2372,a,3595,a)].">
      <j1 rule="hyper" parents="2372 3595"/>
    </justification>
  </clause>

  <clause id="3622">
    <literal><![CDATA[
      (x \ 1) * ((1 / x) \ y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2278,a,3595,a)].">
      <j1 rule="hyper" parents="2278 3595"/>
    </justification>
  </clause>

  <clause id="3623">
    <literal><![CDATA[
      ((1 / x) * y) * K(x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2264,a,3595,a),flip(a)].">
      <j1 rule="hyper" parents="2264 3595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3624">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) * x = y * T(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,2429,a,b,3595,a),flip(a)].">
      <j1 rule="hyper" parents="373 2429 3595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3625">
    <literal><![CDATA[
      K(x \ 1,x) * (y * (1 / x)) = y * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,2996,a(flip),b,3595,a),flip(a)].">
      <j1 rule="hyper" parents="373 2996 3595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3626">
    <literal><![CDATA[
      R(x / y,y,K(z \ 1,z)) = (x * K(z \ 1,z)) / (K(z \ 1,z) * y)
    ]]></literal>
    <justification jstring="[hyper(225,a,3595,a,b,650,a),flip(a)].">
      <j1 rule="hyper" parents="225 3595 650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3627">
    <literal><![CDATA[
      K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,668,a(flip),b,3595,a)].">
      <j1 rule="hyper" parents="139 668 3595"/>
    </justification>
  </clause>

  <clause id="3628">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2381,a,b,3595,a)].">
      <j1 rule="hyper" parents="64 2381 3595"/>
    </justification>
  </clause>

  <clause id="3629">
    <literal><![CDATA[
      a(x,x,x) \ y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2373,a,b,3595,a)].">
      <j1 rule="hyper" parents="64 2373 3595"/>
    </justification>
  </clause>

  <clause id="3630">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = (y / z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2226,a,b,3595,a)].">
      <j1 rule="hyper" parents="64 2226 3595"/>
    </justification>
  </clause>

  <clause id="3631">
    <literal><![CDATA[
      K(x \ 1,x) * (y * L(z \ 1,z,u)) = (y * ((u * z) \ u)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,999,a,b,3595,a)].">
      <j1 rule="hyper" parents="64 999 3595"/>
    </justification>
  </clause>

  <clause id="3632">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,2453,a(flip),b,3595,a),flip(a)].">
      <j1 rule="hyper" parents="64 2453 3595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3633">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,2361,a(flip),b,3595,a),flip(a)].">
      <j1 rule="hyper" parents="64 2361 3595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3634">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[hyper(64,a,2358,a(flip),b,3595,a),flip(a)].">
      <j1 rule="hyper" parents="64 2358 3595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3636">
    <literal><![CDATA[
      x / K(y \ 1,y) = K(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(142,a,2358,a(flip),b,3595,a(flip))].">
      <j1 rule="hyper" parents="142 2358 3595"/>
    </justification>
  </clause>

  <clause id="3637">
    <literal><![CDATA[
      (x * y) \ ((1 / (1 / x)) * y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,2361,a(flip),b,3595,a(flip))].">
      <j1 rule="hyper" parents="139 2361 3595"/>
    </justification>
  </clause>

  <clause id="3638">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ ((y * (x \ 1)) * x) = a(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3595(a,2),417(a,1,1))].">
      <j1 rule="para" parents="3595 417"/>
    </justification>
  </clause>

  <clause id="3639">
    <literal><![CDATA[
      (x * K(y \ 1,y)) / z = K(y \ 1,y) * (x / z)
    ]]></literal>
    <justification jstring="[para(3595(a,1),2226(a,1,1))].">
      <j1 rule="para" parents="3595 2226"/>
    </justification>
  </clause>

  <clause id="3640">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(3595(a,1),2227(a,1,1))].">
      <j1 rule="para" parents="3595 2227"/>
    </justification>
  </clause>

  <clause id="3641">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * z = x
    ]]></literal>
    <justification jstring="[para(3595(a,1),2372(a,1))].">
      <j1 rule="para" parents="3595 2372"/>
    </justification>
  </clause>

  <clause id="3642">
    <literal><![CDATA[
      L(x * K(y \ 1,y),y,y) = (y \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(3595(a,1),2392(a,1,1))].">
      <j1 rule="para" parents="3595 2392"/>
    </justification>
  </clause>

  <clause id="3643">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3595(a,1),2366(a,1,1))].">
      <j1 rule="para" parents="3595 2366"/>
    </justification>
  </clause>

  <clause id="3644">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = (y * z) * K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2219,a,b,3607,a)].">
      <j1 rule="hyper" parents="64 2219 3607"/>
    </justification>
  </clause>

  <clause id="3645">
    <literal><![CDATA[
      K(x,1 / x) \ (y * (1 / x)) = R(y / x,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,683,a(flip),b,3608,a),flip(a)].">
      <j1 rule="hyper" parents="64 683 3608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3646">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(2378,a,3610,a),flip(a)].">
      <j1 rule="hyper" parents="2378 3610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3647">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(2365,a,3610,a)].">
      <j1 rule="hyper" parents="2365 3610"/>
    </justification>
  </clause>

  <clause id="3648">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2255,a,3610,a),flip(a)].">
      <j1 rule="hyper" parents="2255 3610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3649">
    <literal><![CDATA[
      x * ((1 / (1 / x)) \ y) = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2258,a,b,3610,a)].">
      <j1 rule="hyper" parents="64 2258 3610"/>
    </justification>
  </clause>

  <clause id="3650">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,2450,a(flip),b,3610,a),flip(a)].">
      <j1 rule="hyper" parents="64 2450 3610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3651">
    <literal><![CDATA[
      (((x \ 1) * y) * z) * K(x,x \ 1) = ((1 / x) * y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,2377,a(flip),b,3610,a),flip(a)].">
      <j1 rule="hyper" parents="64 2377 3610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3652">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(64,a,2357,a(flip),b,3610,a),flip(a)].">
      <j1 rule="hyper" parents="64 2357 3610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3654">
    <literal><![CDATA[
      (x \ y) * K(x,x \ 1) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,2349,a(flip),b,3610,a),flip(a)].">
      <j1 rule="hyper" parents="64 2349 3610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3655">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,2253,a(flip),b,3610,a),flip(a)].">
      <j1 rule="hyper" parents="64 2253 3610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3656">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ y = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,2357,a(flip),b,3610,a(flip))].">
      <j1 rule="hyper" parents="139 2357 3610"/>
    </justification>
  </clause>

  <clause id="3657">
    <literal><![CDATA[
      a(x,x,x) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1853(a,1),3610(a,1,1))].">
      <j1 rule="para" parents="1853 3610"/>
    </justification>
  </clause>

  <clause id="3658">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[para(3610(a,1),2223(a,1,1))].">
      <j1 rule="para" parents="3610 2223"/>
    </justification>
  </clause>

  <clause id="3659">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(3610(a,1),2224(a,1,1))].">
      <j1 rule="para" parents="3610 2224"/>
    </justification>
  </clause>

  <clause id="3660">
    <literal><![CDATA[
      (1 / (1 / x)) * (y * K(x,x \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(3610(a,1),2348(a,1,2))].">
      <j1 rule="para" parents="3610 2348"/>
    </justification>
  </clause>

  <clause id="3661">
    <literal><![CDATA[
      x * (y * K(x,x \ 1)) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(3610(a,1),2383(a,1,2))].">
      <j1 rule="para" parents="3610 2383"/>
    </justification>
  </clause>

  <clause id="3662">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (z * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(3610(a,1),2366(a,2,2))].">
      <j1 rule="para" parents="3610 2366"/>
    </justification>
  </clause>

  <clause id="3663">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[para(3610(a,1),2367(a,1,1))].">
      <j1 rule="para" parents="3610 2367"/>
    </justification>
  </clause>

  <clause id="3664">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,3610,a(flip),b,3621,a)].">
      <j1 rule="hyper" parents="64 3610 3621"/>
    </justification>
  </clause>

  <clause id="3665">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ x = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,3621,a(flip),b,3610,a(flip))].">
      <j1 rule="hyper" parents="139 3621 3610"/>
    </justification>
  </clause>

  <clause id="3666">
    <literal><![CDATA[
      x \ (y * K(x \ 1,x)) = T(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(3621(a,1),2251(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3621 2251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3667">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (x \ 1)) = y * (1 / x)
    ]]></literal>
    <justification jstring="[para(2996(a,1),3621(a,1,2))].">
      <j1 rule="para" parents="2996 3621"/>
    </justification>
  </clause>

  <clause id="3668">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(3647(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="3647 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3669">
    <literal><![CDATA[
      R((K(x \ 1,x) * y) / x,x,K(x,x \ 1)) = y / T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3652(a,1),1744(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3652 1744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3670">
    <literal><![CDATA[
      K(R(x,y,z),R(x,y,z) \ 1) = (K(x \ 1,x) * u) \ u
    ]]></literal>
    <justification jstring="[para(3533(a,1),3656(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3533 3656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3671">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y,y \ 1) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(2996(a,1),3664(a,1,1))].">
      <j1 rule="para" parents="2996 3664"/>
    </justification>
  </clause>

  <clause id="3672">
    <literal><![CDATA[
      1 / T(x \ (y \ x),y) = (x \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(225,a,3585,a,b,xx)].">
      <j1 rule="hyper" parents="225 3585"/>
    </justification>
  </clause>

  <clause id="3673">
    <literal><![CDATA[
      ((x \ (y \ x)) \ 1) \ 1 = x \ (((y \ 1) \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2390,a(flip),b,3585,a),flip(a)].">
      <j1 rule="hyper" parents="64 2390 3585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3674">
    <literal><![CDATA[
      x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,3585,a(flip),b,2390,a(flip))].">
      <j1 rule="hyper" parents="145 3585 2390"/>
    </justification>
  </clause>

  <clause id="3675">
    <literal><![CDATA[
      x * (((y \ (x \ y)) \ 1) \ 1) = (y \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,3585,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 3585 22"/>
    </justification>
  </clause>

  <clause id="3676">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3620(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3677">
    <literal><![CDATA[
      L(x,y,y) * K(y \ 1,y) = (y \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(561(a,1),3622(a,1,2)),flip(a)].">
      <j1 rule="para" parents="561 3622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3678">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (z * (x \ 1)) = y \ (z * (1 / x))
    ]]></literal>
    <justification jstring="[para(3625(a,1),2225(a,1,2))].">
      <j1 rule="para" parents="3625 2225"/>
    </justification>
  </clause>

  <clause id="3679">
    <literal><![CDATA[
      (x \ 1) * (x * (y * (1 / x))) = L(y * (x \ 1),x,x)
    ]]></literal>
    <justification jstring="[para(3625(a,1),2392(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3625 2392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3680">
    <literal><![CDATA[
      (1 / (1 / x)) \ L(x,y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(35,a,2336,a(flip),b,3649,a),flip(a)].">
      <j1 rule="hyper" parents="35 2336 3649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3681">
    <literal><![CDATA[
      (x \ y) * K(x,1 / x) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(1726(a,2),3654(a,1,2))].">
      <j1 rule="para" parents="1726 3654"/>
    </justification>
  </clause>

  <clause id="3682">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = x * (y * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,3655,a,b,3661,a)].">
      <j1 rule="hyper" parents="373 3655 3661"/>
    </justification>
  </clause>

  <clause id="3683">
    <literal><![CDATA[
      (1 / x) * (y * K(1 / x,(1 / x) \ 1)) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(848(a,1),3661(a,2,1))].">
      <j1 rule="para" parents="848 3661"/>
    </justification>
  </clause>

  <clause id="3684">
    <literal><![CDATA[
      x * (y * K(x,x \ 1)) = R(x,x,x) * y
    ]]></literal>
    <justification jstring="[para(1417(a,1),3661(a,2,1))].">
      <j1 rule="para" parents="1417 3661"/>
    </justification>
  </clause>

  <clause id="3685">
    <literal><![CDATA[
      x * (a(x,x,x) * y) = R(x,x,x) * y
    ]]></literal>
    <justification jstring="[para(3657(a,2),3684(a,1,2))].">
      <j1 rule="para" parents="3657 3684"/>
    </justification>
  </clause>

  <clause id="3686">
    <literal><![CDATA[
      a(x,x,x) * (x * y) = R(x,x,x) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,1897,a(flip),b,3685,a),flip(a)].">
      <j1 rule="hyper" parents="35 1897 3685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3687">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = K(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[para(12(a,1),3667(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 3667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3688">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(390,a,3671,a),flip(a)].">
      <j1 rule="hyper" parents="390 3671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3689">
    <literal><![CDATA[
      T(1 / (1 / (x \ (y \ x))),y) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(40,a,3566,a,b,3672,a(flip))].">
      <j1 rule="hyper" parents="40 3566 3672"/>
    </justification>
  </clause>

  <clause id="3690">
    <literal><![CDATA[
      L(x * K(y \ 1,y),y,y \ 1) = (y \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(3676(a,1),1642(a,1,1))].">
      <j1 rule="para" parents="3676 1642"/>
    </justification>
  </clause>

  <clause id="3691">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) / (1 / x) = (x \ y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(142,a,2349,a(flip),b,3687,a)].">
      <j1 rule="hyper" parents="142 2349 3687"/>
    </justification>
  </clause>

  <clause id="3692">
    <literal><![CDATA[
      (x * (y \ (x \ y))) / x = 1 / (1 / (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(313,a,3689,a)].">
      <j1 rule="hyper" parents="313 3689"/>
    </justification>
  </clause>

  <clause id="3693">
    <literal><![CDATA[
      a(x,x,x) \ L(y,x,x) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3629,a,b,3677,a)].">
      <j1 rule="hyper" parents="64 3629 3677"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),3583(a,2,1,1))].">
      <j1 rule="para" parents="9 3583"/>
    </justification>
  </clause>

  <clause id="3695">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,116,a,b,3694,a),flip(a)].">
      <j1 rule="hyper" parents="373 116 3694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3696">
    <literal><![CDATA[
      T(x,y / (y * x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3048,a(flip),b,3695,a)].">
      <j1 rule="hyper" parents="64 3048 3695"/>
    </justification>
  </clause>

  <clause id="3698">
    <literal><![CDATA[
      T(1 / (1 / x),y / (y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(1349,a,3696,a(flip))].">
      <j1 rule="hyper" parents="1349 3696"/>
    </justification>
  </clause>

  <clause id="3699">
    <literal><![CDATA[
      T(1 / (1 / x),(y / x) / y) = x
    ]]></literal>
    <justification jstring="[para(12(a,1),3698(a,1,2,2))].">
      <j1 rule="para" parents="12 3698"/>
    </justification>
  </clause>

  <clause id="3700">
    <literal><![CDATA[
      (1 / (1 / x)) \ (((y / x) / y) * x) = (y / x) / y
    ]]></literal>
    <justification jstring="[para(3699(a,1),257(a,1,2,2))].">
      <j1 rule="para" parents="3699 257"/>
    </justification>
  </clause>

  <clause id="3701">
    <literal><![CDATA[
      (x * (1 / (1 / y))) / x = 1 / (1 / ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(9(a,1),3587(a,1,1,2,2,2))].">
      <j1 rule="para" parents="9 3587"/>
    </justification>
  </clause>

  <clause id="3702">
    <literal><![CDATA[
      x \ (K(x / y,y / x) * y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(139,a,3397,a,b,3588,a(flip))].">
      <j1 rule="hyper" parents="139 3397 3588"/>
    </justification>
  </clause>

  <clause id="3703">
    <literal><![CDATA[
      1 / (1 / (x \ (y \ x))) = x \ ((1 / (1 / y)) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,2035,a(flip),b,3588,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 2035 3588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3704">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,3601,a(flip),b,2454,a)].">
      <j1 rule="hyper" parents="145 3601 2454"/>
    </justification>
  </clause>

  <clause id="3707">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * (1 / y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,3625,a(flip),b,3640,a),flip(a)].">
      <j1 rule="hyper" parents="373 3625 3640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3708">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * z)) \ ((y * K(x \ 1,x)) * (z * u)) = L(u,z,y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(3640(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3640 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3709">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * K(z \ 1,z),x) = u
    ]]></literal>
    <justification jstring="[para(3640(a,1),359(a,1,2))].">
      <j1 rule="para" parents="3640 359"/>
    </justification>
  </clause>

  <clause id="3710">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (x * (K(z \ 1,z) * (y * u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,y * K(z \ 1,z),x) = w
    ]]></literal>
    <justification jstring="[para(3640(a,1),608(a,1,2,2))].">
      <j1 rule="para" parents="3640 608"/>
    </justification>
  </clause>

  <clause id="3711">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * ((1 / x) * z))) / ((x \ 1) * z) = R(y,K(x \ 1,x),(1 / x) * z)
    ]]></literal>
    <justification jstring="[para(3640(a,1),2265(a,1,1))].">
      <j1 rule="para" parents="3640 2265"/>
    </justification>
  </clause>

  <clause id="3712">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) * (u * w) = (u * K(x \ 1,x)) * w
    ]]></literal>
    <justification jstring="[para(3512(a,2),3640(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3512 3640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3713">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(142,a,1873,a(flip),b,3707,a),flip(a)].">
      <j1 rule="hyper" parents="142 1873 3707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3714">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(142,a,12,a(flip),b,3707,a),flip(a)].">
      <j1 rule="hyper" parents="142 12 3707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3715">
    <literal><![CDATA[
      R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,3707,a(flip),b,2983,a),flip(a)].">
      <j1 rule="hyper" parents="144 3707 2983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3716">
    <literal><![CDATA[
      R(x,K(y \ 1,y),1 / y) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,1227,a,b,3707,a(flip))].">
      <j1 rule="hyper" parents="36 1227 3707"/>
    </justification>
  </clause>

  <clause id="3717">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3632(a,1),3707(a,1,1))].">
      <j1 rule="para" parents="3632 3707"/>
    </justification>
  </clause>

  <clause id="3718">
    <literal><![CDATA[
      K(x,x \ 1) * (y / (1 / x)) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3641,a,3714,a)].">
      <j1 rule="hyper" parents="3641 3714"/>
    </justification>
  </clause>

  <clause id="3719">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x \ 1)) = y / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(3598,a,3714,a)].">
      <j1 rule="hyper" parents="3598 3714"/>
    </justification>
  </clause>

  <clause id="3720">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (y / (1 / x)) = x * (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(145,a,3714,a(flip),b,3676,a)].">
      <j1 rule="hyper" parents="145 3714 3676"/>
    </justification>
  </clause>

  <clause id="3721">
    <literal><![CDATA[
      (1 / (1 / x)) \ (y / (1 / x)) = x \ (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(139,a,3718,a(flip),b,2258,a),flip(a)].">
      <j1 rule="hyper" parents="139 3718 2258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3723">
    <literal><![CDATA[
      R(x,y,y \ 1) / (1 / y) = K(y \ 1,y) * (x * y)
    ]]></literal>
    <justification jstring="[para(494(a,1),3719(a,1,2)),flip(a)].">
      <j1 rule="para" parents="494 3719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3724">
    <literal><![CDATA[
      (x * K(y,1 / y)) / z = K(y,1 / y) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(142,a,166,a(flip),b,3644,a)].">
      <j1 rule="hyper" parents="142 166 3644"/>
    </justification>
  </clause>

  <clause id="3725">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * z) * K(y,y \ 1)) = z
    ]]></literal>
    <justification jstring="[hyper(139,a,3610,a(flip),b,3659,a)].">
      <j1 rule="hyper" parents="139 3610 3659"/>
    </justification>
  </clause>

  <clause id="3726">
    <literal><![CDATA[
      (x * (1 / y)) \ (z * K(y,y \ 1)) = (x * (y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(3625(a,1),3662(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3625 3662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3727">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (y * z) = x \ ((1 / (1 / y)) * z)
    ]]></literal>
    <justification jstring="[para(2361(a,1),3663(a,2,2))].">
      <j1 rule="para" parents="2361 3663"/>
    </justification>
  </clause>

  <clause id="3728">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * (x * ((1 / y) * z))) != u
    ]]></literal>
    <literal><![CDATA[
      L((y \ 1) * z,K(y,y \ 1),x) = u
    ]]></literal>
    <justification jstring="[para(3663(a,1),2375(a,1))].">
      <j1 rule="para" parents="3663 2375"/>
    </justification>
  </clause>

  <clause id="3729">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) \ x = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(82(a,1),3674(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="82 3674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3730">
    <literal><![CDATA[
      x \ (y * K(x,x \ 1)) = (x \ y) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(783,a,3682,a)].">
      <j1 rule="hyper" parents="783 3682"/>
    </justification>
  </clause>

  <clause id="3731">
    <literal><![CDATA[
      T(x / (1 / (1 / y)),1 / (1 / y)) / (1 / y) = (y \ x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(117(a,2),3691(a,1,1))].">
      <j1 rule="para" parents="117 3691"/>
    </justification>
  </clause>

  <clause id="3732">
    <literal><![CDATA[
      T(1 / (1 / ((x \ y) / y)),y) = (x * (y \ (x \ y))) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,3578,a,b,3692,a)].">
      <j1 rule="hyper" parents="373 3578 3692"/>
    </justification>
  </clause>

  <clause id="3733">
    <literal><![CDATA[
      (x * y) \ (K(x,x \ 1) * y) = 1 / (1 / ((x * y) \ y))
    ]]></literal>
    <justification jstring="[para(3400(a,1),3702(a,1,2,1))].">
      <j1 rule="para" parents="3400 3702"/>
    </justification>
  </clause>

  <clause id="3734">
    <literal><![CDATA[
      L(x \ (y \ x),x \ (y \ x),x \ (y \ x)) = x \ ((1 / (1 / y)) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,818,a,b,3703,a)].">
      <j1 rule="hyper" parents="64 818 3703"/>
    </justification>
  </clause>

  <clause id="3735">
    <literal><![CDATA[
      T(x \ ((1 / (1 / y)) \ x),y) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(3703(a,1),3689(a,1,1))].">
      <j1 rule="para" parents="3703 3689"/>
    </justification>
  </clause>

  <clause id="3736">
    <literal><![CDATA[
      (((x \ 1) \ y) * (x \ 1)) / x = ((1 / x) \ y) / (x * x)
    ]]></literal>
    <justification jstring="[hyper(142,a,3717,a(flip),b,811,a)].">
      <j1 rule="hyper" parents="142 3717 811"/>
    </justification>
  </clause>

  <clause id="3737">
    <literal><![CDATA[
      R(x / (y / K(z,1 / z)),y / K(z,1 / z),K(z,1 / z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,678,a,b,3724,a)].">
      <j1 rule="hyper" parents="64 678 3724"/>
    </justification>
  </clause>

  <clause id="3738">
    <literal><![CDATA[
      R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3725(a,1),1756(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3725 1756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3739">
    <literal><![CDATA[
      x / (x * (((x \ y) \ 1) \ 1)) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(226,a,3729,a)].">
      <j1 rule="hyper" parents="226 3729"/>
    </justification>
  </clause>

  <clause id="3740">
    <literal><![CDATA[
      x \ (y * K(x,x \ 1)) != z * K(x,x \ 1)
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(3730(a,2),45(a,1))].">
      <j1 rule="para" parents="3730 45"/>
    </justification>
  </clause>

  <clause id="3741">
    <literal><![CDATA[
      x / (x * ((y \ 1) \ 1)) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),3739(a,1,2,2,1,1))].">
      <j1 rule="para" parents="9 3739"/>
    </justification>
  </clause>

  <clause id="3742">
    <literal><![CDATA[
      ((x / (x * (1 / y))) \ 1) \ 1 = x / (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(82(a,1),3741(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="82 3741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3743">
    <literal><![CDATA[
      1 / (x / (x * (y \ 1))) = (x / (x * (1 / y))) \ 1
    ]]></literal>
    <justification jstring="[hyper(226,a,3742,a)].">
      <j1 rule="hyper" parents="226 3742"/>
    </justification>
  </clause>

  <clause id="3744">
    <literal><![CDATA[
      (x / (x * (1 / (1 / y)))) \ 1 = 1 / (x / (x * y))
    ]]></literal>
    <justification jstring="[para(82(a,1),3743(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="82 3743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3745">
    <literal><![CDATA[
      (x / (x * (y / (y * y)))) \ 1 = 1 / (x / (x * (1 / y)))
    ]]></literal>
    <justification jstring="[para(2029(a,1),3744(a,1,1,2,2))].">
      <j1 rule="para" parents="2029 3744"/>
    </justification>
  </clause>

  <clause id="3746">
    <literal><![CDATA[
      K(x,x \ 1) \ (y * (1 / x)) = R(y / x,x,1 / x)
    ]]></literal>
    <justification jstring="[para(1726(a,1),3645(a,1,1))].">
      <j1 rule="para" parents="1726 3645"/>
    </justification>
  </clause>

  <clause id="3747">
    <literal><![CDATA[
      L(x * (y \ 1),y,y) = L(x,y,y) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3448,a(flip),b,3679,a),flip(a)].">
      <j1 rule="hyper" parents="64 3448 3679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3748">
    <literal><![CDATA[
      L((x \ 1) * ((1 / x) \ y),x,x \ 1) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(3622(a,2),3690(a,1,1))].">
      <j1 rule="para" parents="3622 3690"/>
    </justification>
  </clause>

  <clause id="3749">
    <literal><![CDATA[
      R(((x \ (x / (y \ 1))) * x) * K(y \ 1,y),y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(2928(a,1),3715(a,2,1))].">
      <j1 rule="para" parents="2928 3715"/>
    </justification>
  </clause>

  <clause id="3750">
    <literal><![CDATA[
      K(x \ 1,x) * (y * (1 / x)) = R(y / x,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2360,a(flip),b,3746,a)].">
      <j1 rule="hyper" parents="64 2360 3746"/>
    </justification>
  </clause>

  <clause id="3751">
    <literal><![CDATA[
      R(x / y,y,1 / y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3625,a(flip),b,3750,a),flip(a)].">
      <j1 rule="hyper" parents="64 3625 3750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3752">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,1 / y)
    ]]></literal>
    <justification jstring="[para(11(a,1),3751(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 3751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3753">
    <literal><![CDATA[
      R(x,y,1 / y) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(154,a,3752,a)].">
      <j1 rule="hyper" parents="154 3752"/>
    </justification>
  </clause>

  <clause id="3754">
    <literal><![CDATA[
      T(R(x,y,1 / y),z) / (y \ 1) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(142,a,27,a(flip),b,3752,a)].">
      <j1 rule="hyper" parents="142 27 3752"/>
    </justification>
  </clause>

  <clause id="3755">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),3752(a,2,3))].">
      <j1 rule="para" parents="79 3752"/>
    </justification>
  </clause>

  <clause id="3756">
    <literal><![CDATA[
      R(x,y \ 1,(y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(669,a,3755,a)].">
      <j1 rule="hyper" parents="669 3755"/>
    </justification>
  </clause>

  <clause id="3757">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,2975,a(flip),b,3755,a),flip(a)].">
      <j1 rule="hyper" parents="373 2975 3755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3758">
    <literal><![CDATA[
      K(R(x,y,z),R(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,3665,a(flip),b,3670,a),flip(a)].">
      <j1 rule="hyper" parents="373 3665 3670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3759">
    <literal><![CDATA[
      R(x,y,z) * (1 / R(x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1728,a,3758,a)].">
      <j1 rule="hyper" parents="1728 3758"/>
    </justification>
  </clause>

  <clause id="3760">
    <literal><![CDATA[
      R(x,y,z) \ K(x,x \ 1) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,3758,a(flip),b,1724,a(flip))].">
      <j1 rule="hyper" parents="139 3758 1724"/>
    </justification>
  </clause>

  <clause id="3761">
    <literal><![CDATA[
      T((1 / x) * (T(x,y) \ x),x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2411,a,b,3704,a)].">
      <j1 rule="hyper" parents="64 2411 3704"/>
    </justification>
  </clause>

  <clause id="3762">
    <literal><![CDATA[
      (x * (1 / y)) \ (1 / y) = (x * (y \ 1)) \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(2444(a,1),3726(a,1,2))].">
      <j1 rule="para" parents="2444 3726"/>
    </justification>
  </clause>

  <clause id="3763">
    <literal><![CDATA[
      (x * (1 / y)) \ ((1 / y) * z) = (x * (y \ 1)) \ ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3646(a,1),3726(a,1,2))].">
      <j1 rule="para" parents="3646 3726"/>
    </justification>
  </clause>

  <clause id="3764">
    <literal><![CDATA[
      (x * ((x \ y) / y)) / x = 1 / (1 / ((x \ y) / y))
    ]]></literal>
    <justification jstring="[hyper(41,a,914,a,b,3732,a)].">
      <j1 rule="hyper" parents="41 914 3732"/>
    </justification>
  </clause>

  <clause id="3765">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,2259,a(flip),b,3733,a),flip(a)].">
      <j1 rule="hyper" parents="64 2259 3733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3766">
    <literal><![CDATA[
      (((1 / (1 / x)) * y) \ y) \ 1 = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(215,a,3765,a)].">
      <j1 rule="hyper" parents="215 3765"/>
    </justification>
  </clause>

  <clause id="3767">
    <literal><![CDATA[
      1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),3766(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 3766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3768">
    <literal><![CDATA[
      ((((1 / x) * y) \ y) \ 1) \ 1 = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(215,a,3767,a)].">
      <j1 rule="hyper" parents="215 3767"/>
    </justification>
  </clause>

  <clause id="3770">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = ((y \ 1) * (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(1635(a,1),3768(a,1,1,1,1))].">
      <j1 rule="para" parents="1635 3768"/>
    </justification>
  </clause>

  <clause id="3771">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ (1 / x)) = ((1 / x) \ y) / (x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1099,a(flip),b,3736,a)].">
      <j1 rule="hyper" parents="64 1099 3736"/>
    </justification>
  </clause>

  <clause id="3772">
    <literal><![CDATA[
      (x \ 1) * (T(x,y) \ x) = T(1 / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(3169(a,1),3761(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3169 3761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3773">
    <literal><![CDATA[
      L(x \ (K(y \ 1,y) \ ((x * (y \ 1)) * y)),x,K(y \ 1,y)) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1080,a,3638,a)].">
      <j1 rule="hyper" parents="1080 3638"/>
    </justification>
  </clause>

  <clause id="3774">
    <literal><![CDATA[
      R(x,T(y,x),T(K(z \ 1,R(z,u,w)),y * x)) \ ((y * K(z \ 1,z)) * x) = T(y,x) * T(K(z \ 1,R(z,u,w)),y * x)
    ]]></literal>
    <justification jstring="[para(3712(a,1),1318(a,1,2))].">
      <j1 rule="para" parents="3712 1318"/>
    </justification>
  </clause>

  <clause id="3775">
    <literal><![CDATA[
      (x * (y \ 1)) \ ((y \ 1) * x) = K(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(359,a,3763,a),flip(a)].">
      <j1 rule="hyper" parents="359 3763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3776">
    <literal><![CDATA[
      K(1 / x,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(359,a,3775,a),flip(a)].">
      <j1 rule="hyper" parents="359 3775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3777">
    <literal><![CDATA[
      K(1 / x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(3775(a,1),359(a,1))].">
      <j1 rule="para" parents="3775 359"/>
    </justification>
  </clause>

  <clause id="3778">
    <literal><![CDATA[
      K(1 / (1 / x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1572,a(flip),b,3776,a),flip(a)].">
      <j1 rule="hyper" parents="373 1572 3776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3779">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),3776(a,1,1)),flip(a)].">
      <j1 rule="para" parents="79 3776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3780">
    <literal><![CDATA[
      K(T(x,x \ 1),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(116(a,2),3779(a,1,1))].">
      <j1 rule="para" parents="116 3779"/>
    </justification>
  </clause>

  <clause id="3782">
    <literal><![CDATA[
      R((x / y) * K(y \ 1,y),y,K(y,y \ 1)) = x / T(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3630(a,1),3669(a,1,1))].">
      <j1 rule="para" parents="3630 3669"/>
    </justification>
  </clause>

  <clause id="3783">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,2579,a(flip),b,3713,a),flip(a)].">
      <j1 rule="hyper" parents="373 2579 3713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3784">
    <literal><![CDATA[
      ((1 / x) * y) \ L(y,x,x) = 1 / (1 / T(x,(1 / x) * y))
    ]]></literal>
    <justification jstring="[para(1158(a,1),3576(a,1,2))].">
      <j1 rule="para" parents="1158 3576"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      R(x / y,y,K(z \ 1,z)) = K(z \ 1,z) * (x / (K(z \ 1,z) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,3639,a(flip),b,3626,a),flip(a)].">
      <j1 rule="hyper" parents="373 3639 3626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3786">
    <literal><![CDATA[
      R((x * y) / y,y,K(z \ 1,z)) = K(z \ 1,z) * R(x / K(z \ 1,z),K(z \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(112(a,2),3785(a,2,2))].">
      <j1 rule="para" parents="112 3785"/>
    </justification>
  </clause>

  <clause id="3787">
    <literal><![CDATA[
      ((x \ 1) * x) * (y * L(z \ 1,z,u)) = (y * ((u * z) \ u)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(294(a,1),3631(a,1,1))].">
      <j1 rule="para" parents="294 3631"/>
    </justification>
  </clause>

  <clause id="3788">
    <literal><![CDATA[
      ((x \ 1) * (x * L(x \ 1,x,y))) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3109,a,b,3787,a)].">
      <j1 rule="hyper" parents="64 3109 3787"/>
    </justification>
  </clause>

  <clause id="3789">
    <literal><![CDATA[
      (x \ 1) * (x * L(x \ 1,x,y)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,3783,a(flip),b,3788,a),flip(a)].">
      <j1 rule="hyper" parents="36 3783 3788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3790">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,999,a(flip),b,3789,a)].">
      <j1 rule="hyper" parents="64 999 3789"/>
    </justification>
  </clause>

  <clause id="3791">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,241,a(flip),b,3790,a),flip(a)].">
      <j1 rule="hyper" parents="373 241 3790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3792">
    <literal><![CDATA[
      ((x * y) \ x) / (y * ((x * y) \ x)) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(142,a,241,a(flip),b,3790,a)].">
      <j1 rule="hyper" parents="142 241 3790"/>
    </justification>
  </clause>

  <clause id="3793">
    <literal><![CDATA[
      (x \ 1) \ ((y * x) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,241,a(flip),b,3790,a)].">
      <j1 rule="hyper" parents="139 241 3790"/>
    </justification>
  </clause>

  <clause id="3794">
    <literal><![CDATA[
      (x * (x * ((y * x) \ y))) \ x = L(x \ 1,x,y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3790(a,1),1228(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3790 1228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3795">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,3791,a(flip),b,3356,a),flip(a)].">
      <j1 rule="hyper" parents="138 3791 3356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3796">
    <literal><![CDATA[
      (x / y) * (y * (y * ((z * y) \ z))) = (x / (y \ 1)) * ((z * y) \ z)
    ]]></literal>
    <justification jstring="[para(3791(a,1),1627(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3791 1627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3797">
    <literal><![CDATA[
      T(x,(y * x) \ y) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,3795,a(flip),b,3380,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 3795 3380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3798">
    <literal><![CDATA[
      T(x,(y * x) \ y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,116,a,b,3797,a),flip(a)].">
      <j1 rule="hyper" parents="373 116 3797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3799">
    <literal><![CDATA[
      T(x \ y,y \ x) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),3797(a,1,2,1))].">
      <j1 rule="para" parents="10 3797"/>
    </justification>
  </clause>

  <clause id="3800">
    <literal><![CDATA[
      T(K(x,y),(x * y) \ (y * x)) = T(K(x,y),K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(94(a,1),3798(a,1,2,1))].">
      <j1 rule="para" parents="94 3798"/>
    </justification>
  </clause>

  <clause id="3801">
    <literal><![CDATA[
      L(T(x,x \ 1),(y * x) \ y,x) = x
    ]]></literal>
    <justification jstring="[para(3798(a,1),2566(a,1,1))].">
      <j1 rule="para" parents="3798 2566"/>
    </justification>
  </clause>

  <clause id="3803">
    <literal><![CDATA[
      1 / T(x \ y,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(225,a,3799,a,b,xx)].">
      <j1 rule="hyper" parents="225 3799"/>
    </justification>
  </clause>

  <clause id="3804">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,x \ y)),x) = T(K(x \ y,x),(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(3799(a,2),3070(a,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3799 3070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3805">
    <literal><![CDATA[
      (x * T(x \ y,y \ x)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(3799(a,2),3581(a,1,1,2))].">
      <j1 rule="para" parents="3799 3581"/>
    </justification>
  </clause>

  <clause id="3806">
    <literal><![CDATA[
      K(x / y,y / x) * x = y * T(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(3799(a,2),3586(a,2,2))].">
      <j1 rule="para" parents="3799 3586"/>
    </justification>
  </clause>

  <clause id="3807">
    <literal><![CDATA[
      1 / T(x \ (x / y),y) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),3803(a,1,2,2))].">
      <j1 rule="para" parents="82 3803"/>
    </justification>
  </clause>

  <clause id="3808">
    <literal><![CDATA[
      R(1 / x,x,(y * x) \ y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(476,a,3792,a)].">
      <j1 rule="hyper" parents="476 3792"/>
    </justification>
  </clause>

  <clause id="3809">
    <literal><![CDATA[
      R(1 / (x \ y),x \ y,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),3808(a,1,3,1))].">
      <j1 rule="para" parents="10 3808"/>
    </justification>
  </clause>

  <clause id="3810">
    <literal><![CDATA[
      R(1 / x,x,y \ (y / x)) = x \ 1
    ]]></literal>
    <justification jstring="[para(12(a,1),3808(a,1,3,1))].">
      <j1 rule="para" parents="12 3808"/>
    </justification>
  </clause>

  <clause id="3811">
    <literal><![CDATA[
      (x \ 1) * (x * (y \ (y / x))) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(144,a,3810,a(flip),b,244,a(flip))].">
      <j1 rule="hyper" parents="144 3810 244"/>
    </justification>
  </clause>

  <clause id="3813">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = ((y * x) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(3793(a,1),346(a,1,1))].">
      <j1 rule="para" parents="3793 346"/>
    </justification>
  </clause>

  <clause id="3814">
    <literal><![CDATA[
      ((x \ y) \ 1) \ (y \ x) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(3809(a,1),452(a,1,1))].">
      <j1 rule="para" parents="3809 452"/>
    </justification>
  </clause>

  <clause id="3815">
    <literal><![CDATA[
      T(x / y,x \ y) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(533,a,3805,a)].">
      <j1 rule="hyper" parents="533 3805"/>
    </justification>
  </clause>

  <clause id="3816">
    <literal><![CDATA[
      1 / T(x / y,x \ y) = (x / y) \ 1
    ]]></literal>
    <justification jstring="[hyper(225,a,531,a(flip),b,3805,a(flip))].">
      <j1 rule="hyper" parents="225 531 3805"/>
    </justification>
  </clause>

  <clause id="3817">
    <literal><![CDATA[
      T(x / y,y / x) = T(x / y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,3039,a,b,3815,a)].">
      <j1 rule="hyper" parents="373 3039 3815"/>
    </justification>
  </clause>

  <clause id="3818">
    <literal><![CDATA[
      T(x / y,x \ y) * x = (y / x) \ x
    ]]></literal>
    <justification jstring="[hyper(144,a,3815,a,b,2037,a(flip))].">
      <j1 rule="hyper" parents="144 3815 2037"/>
    </justification>
  </clause>

  <clause id="3819">
    <literal><![CDATA[
      T(x / (x * y),y) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),3815(a,1,2))].">
      <j1 rule="para" parents="9 3815"/>
    </justification>
  </clause>

  <clause id="3820">
    <literal><![CDATA[
      T(1 / (1 / (x / y)),x \ y) = x / y
    ]]></literal>
    <justification jstring="[hyper(40,a,3566,a,b,3816,a(flip))].">
      <j1 rule="hyper" parents="40 3566 3816"/>
    </justification>
  </clause>

  <clause id="3821">
    <literal><![CDATA[
      T(T(x / y,x),x \ y) = x \ ((y / x) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,3818,a(flip),b,265,a),flip(a)].">
      <j1 rule="hyper" parents="139 3818 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3822">
    <literal><![CDATA[
      (1 / (1 / (x / y))) * (x \ y) = (x \ y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,3820,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 3820 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3823">
    <literal><![CDATA[
      T(1 / (1 / ((x / y) / x)),y) = (x / y) / x
    ]]></literal>
    <justification jstring="[para(82(a,1),3820(a,1,2))].">
      <j1 rule="para" parents="82 3820"/>
    </justification>
  </clause>

  <clause id="3824">
    <literal><![CDATA[
      T(x / (x * y),y) = x / (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,3741,a,b,3819,a),flip(a)].">
      <j1 rule="hyper" parents="373 3741 3819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3825">
    <literal><![CDATA[
      (1 / (1 / ((x / y) / x))) * y = y * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,3823,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 3823 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3826">
    <literal><![CDATA[
      x / (x * R(y,y,y)) = T(x / (x * y),y)
    ]]></literal>
    <justification jstring="[para(1418(a,2),3824(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1418 3824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3827">
    <literal><![CDATA[
      (1 * x) / (x * R(y,y,y)) = T(x / (x * y),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,172,a,b,3826,a)].">
      <j1 rule="hyper" parents="64 172 3826"/>
    </justification>
  </clause>

  <clause id="3828">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(x / y,y / x)
    ]]></literal>
    <justification jstring="[hyper(36,a,3624,a,b,3806,a)].">
      <j1 rule="hyper" parents="36 3624 3806"/>
    </justification>
  </clause>

  <clause id="3829">
    <literal><![CDATA[
      T(K(x,y),K(x,y) \ 1) = T(K(x,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(16(a,2),3800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16 3800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3830">
    <literal><![CDATA[
      T(K(x,y),K(y,x)) = (K(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(478,a,3829,a),flip(a)].">
      <j1 rule="hyper" parents="478 3829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3831">
    <literal><![CDATA[
      (K(x,y) \ 1) \ 1 = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3319,a(flip),b,3830,a),flip(a)].">
      <j1 rule="hyper" parents="64 3319 3830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3835">
    <literal><![CDATA[
      1 / (1 / K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3831(a,1),216(a,1,2,2))].">
      <j1 rule="para" parents="3831 216"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = R(y,x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(297(a,1),3813(a,2,1))].">
      <j1 rule="para" parents="297 3813"/>
    </justification>
  </clause>

  <clause id="3837">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ 1) = T(K(x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3069,a(flip),b,3804,a),flip(a)].">
      <j1 rule="hyper" parents="64 3069 3804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      T(K(x \ (x * y),x),x \ (x * y)) = T(K(y,x),((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),3837(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3839">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),y \ (y * x))
    ]]></literal>
    <justification jstring="[para(9(a,1),3838(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3840">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3839(a,2,2))].">
      <j1 rule="para" parents="9 3839"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      T(K(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      (((y * x) \ y) \ 1) \ (((y * x) \ y) \ K(x,y)) = z
    ]]></literal>
    <justification jstring="[para(3840(a,1),3498(a,1))].">
      <j1 rule="para" parents="3840 3498"/>
    </justification>
  </clause>

  <clause id="3843">
    <literal><![CDATA[
      L(x \ R(x,y \ 1,y),x,K(y \ 1,y)) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3627(a,1),3773(a,1,1,2))].">
      <j1 rule="para" parents="3627 3773"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2228,a,3843,a)].">
      <j1 rule="hyper" parents="2228 3843"/>
    </justification>
  </clause>

  <clause id="3846">
    <literal><![CDATA[
      T((x \ 1) * (x * ((y * (x \ z)) / y)),y) != u
    ]]></literal>
    <literal><![CDATA[
      L((x \ 1) * z,K(x,x \ 1),y) = u
    ]]></literal>
    <justification jstring="[para(3244(a,2),3728(a,1))].">
      <j1 rule="para" parents="3244 3728"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * z)) \ (K(x \ 1,x) * (y * (z * u))) = L(u,z,y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(3640(a,1),3708(a,1,2))].">
      <j1 rule="para" parents="3640 3708"/>
    </justification>
  </clause>

  <clause id="3848">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * ((1 / x) * z)) / ((x \ 1) * z)) = R(y,K(x \ 1,x),(1 / x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2226,a(flip),b,3711,a)].">
      <j1 rule="hyper" parents="64 2226 3711"/>
    </justification>
  </clause>

  <clause id="3849">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u \ 1,u)) = L(x,y,z * K(u \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(1081,a,3847,a)].">
      <j1 rule="hyper" parents="1081 3847"/>
    </justification>
  </clause>

  <clause id="3850">
    <literal><![CDATA[
      L(x,y,z * K(u \ 1,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2228,a,3849,a),flip(a)].">
      <j1 rule="hyper" parents="2228 3849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3852">
    <literal><![CDATA[
      L(x,y,R(1 / z,u,w)) = L(x,y,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3619(a,1),3850(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3619 3850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3853">
    <literal><![CDATA[
      L(x,y,z / (1 / u)) = L(x,y,z / (u \ 1))
    ]]></literal>
    <justification jstring="[para(3714(a,1),3850(a,1,3))].">
      <j1 rule="para" parents="3714 3850"/>
    </justification>
  </clause>

  <clause id="3854">
    <literal><![CDATA[
      K(x \ 1,x) * R(y / K(x \ 1,x),K(x \ 1,x),z) = R(y,z,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(11(a,1),3786(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 3786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3855">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x,x \ 1) * y,K(x \ 1,x),z) = R(y,z,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(3636(a,1),3854(a,1,2,1))].">
      <j1 rule="para" parents="3636 3854"/>
    </justification>
  </clause>

  <clause id="3856">
    <literal><![CDATA[
      R(K(x \ 1,x) * (K(x,x \ 1) * y),K(x \ 1,x),z) = R(y,z,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,3056,a,b,3855,a)].">
      <j1 rule="hyper" parents="64 3056 3855"/>
    </justification>
  </clause>

  <clause id="3857">
    <literal><![CDATA[
      R(x,K(y \ 1,y),z) = R(x,z,K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(2358(a,1),3856(a,1,1))].">
      <j1 rule="para" parents="2358 3856"/>
    </justification>
  </clause>

  <clause id="3858">
    <literal><![CDATA[
      R(x,1 / y,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,3716,a(flip),b,3857,a),flip(a)].">
      <j1 rule="hyper" parents="64 3716 3857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3859">
    <literal><![CDATA[
      (R(x,y,K(y \ 1,y)) / y) * L(y,y \ 1,y) = x * (L(y,y \ 1,y) / y)
    ]]></literal>
    <justification jstring="[para(3857(a,1),3213(a,1,1,1))].">
      <j1 rule="para" parents="3857 3213"/>
    </justification>
  </clause>

  <clause id="3860">
    <literal><![CDATA[
      R(x,y,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,2968,a(flip),b,3858,a)].">
      <j1 rule="hyper" parents="64 2968 3858"/>
    </justification>
  </clause>

  <clause id="3861">
    <literal><![CDATA[
      (R(x,y,K(y \ 1,y)) / y) * (1 / (1 / y)) = x * (L(y,y \ 1,y) / y)
    ]]></literal>
    <justification jstring="[para(1157(a,1),3859(a,1,2))].">
      <j1 rule="para" parents="1157 3859"/>
    </justification>
  </clause>

  <clause id="3862">
    <literal><![CDATA[
      (R(x,y,K(y \ 1,y)) / y) * (1 / (1 / y)) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2369(a,1),3861(a,2,2))].">
      <j1 rule="para" parents="2369 3861"/>
    </justification>
  </clause>

  <clause id="3863">
    <literal><![CDATA[
      (x / y) * (1 / (1 / y)) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3860(a,1),3862(a,1,1,1))].">
      <j1 rule="para" parents="3860 3862"/>
    </justification>
  </clause>

  <clause id="3864">
    <literal><![CDATA[
      (x / y) * (1 / (1 / y)) = K(y \ 1,y) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,3595,a,b,3863,a),flip(a)].">
      <j1 rule="hyper" parents="373 3595 3863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3866">
    <literal><![CDATA[
      K(x \ 1,x) * (y * x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(11(a,1),3864(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 3864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3867">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(3668,a,3866,a)].">
      <j1 rule="hyper" parents="3668 3866"/>
    </justification>
  </clause>

  <clause id="3868">
    <literal><![CDATA[
      R(x,y,y \ 1) / (1 / y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,3723,a,b,3866,a)].">
      <j1 rule="hyper" parents="64 3723 3866"/>
    </justification>
  </clause>

  <clause id="3869">
    <literal><![CDATA[
      T(x,1 / (1 / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(269,a,3866,a(flip),b,2379,a(flip))].">
      <j1 rule="hyper" parents="269 3866 2379"/>
    </justification>
  </clause>

  <clause id="3870">
    <literal><![CDATA[
      T(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),3869(a,1,2,2))].">
      <j1 rule="para" parents="79 3869"/>
    </justification>
  </clause>

  <clause id="3871">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(216(a,1),3869(a,1,2)),flip(a)].">
      <j1 rule="para" parents="216 3869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3872">
    <literal><![CDATA[
      T(x / (1 / y),y \ 1) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,3870,a),flip(a)].">
      <j1 rule="hyper" parents="467 3870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3873">
    <literal><![CDATA[
      (1 / x) * T(y,x \ 1) = y * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,3870,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 3870 22"/>
    </justification>
  </clause>

  <clause id="3874">
    <literal><![CDATA[
      (x * x) * (y * (1 / x)) = x * T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(3870(a,1),537(a,2,2))].">
      <j1 rule="para" parents="3870 537"/>
    </justification>
  </clause>

  <clause id="3875">
    <literal><![CDATA[
      T(x * T(y,x \ 1),x * x) = R(y,x,x) / (1 / x)
    ]]></literal>
    <justification jstring="[para(3870(a,1),1772(a,1,1,2))].">
      <j1 rule="para" parents="3870 1772"/>
    </justification>
  </clause>

  <clause id="3876">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(116(a,2),3871(a,1,2))].">
      <j1 rule="para" parents="116 3871"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      T(x,T(y \ 1,y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(1354(a,2),3871(a,1,2))].">
      <j1 rule="para" parents="1354 3871"/>
    </justification>
  </clause>

  <clause id="3878">
    <literal><![CDATA[
      T(x / T(y,y \ 1),y) = T(y,y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,3876,a),flip(a)].">
      <j1 rule="hyper" parents="467 3876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3879">
    <literal><![CDATA[
      T(x,x \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,3876,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 3876 22"/>
    </justification>
  </clause>

  <clause id="3880">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3876(a,1),509(a,1,2))].">
      <j1 rule="para" parents="3876 509"/>
    </justification>
  </clause>

  <clause id="3881">
    <literal><![CDATA[
      R((x \ 1) \ y,x \ 1,1 / x) = (1 / x) \ R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3118,a(flip),b,3872,a)].">
      <j1 rule="hyper" parents="64 3118 3872"/>
    </justification>
  </clause>

  <clause id="3882">
    <literal><![CDATA[
      R((1 / x) \ y,x,x) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3872(a,1),1414(a,1,1))].">
      <j1 rule="para" parents="3872 1414"/>
    </justification>
  </clause>

  <clause id="3883">
    <literal><![CDATA[
      T(((1 / x) * y) * x,x \ 1) = R(y,x,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),3882(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 3882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3884">
    <literal><![CDATA[
      T(L(x,y,y) * y,y \ 1) = R(y * x,y,y)
    ]]></literal>
    <justification jstring="[para(561(a,1),3882(a,1,1)),flip(a)].">
      <j1 rule="para" parents="561 3882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3885">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (x * y) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[para(3867(a,1),3725(a,1,2))].">
      <j1 rule="para" parents="3867 3725"/>
    </justification>
  </clause>

  <clause id="3886">
    <literal><![CDATA[
      (x * x) * ((y * (1 / x)) * z) = (x * T(y,x \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,3874,a(flip),b,127,a),flip(a)].">
      <j1 rule="hyper" parents="144 3874 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      (x * (1 / y)) \ ((y * y) \ z) = (y * T(x,y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(3874(a,1),487(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3874 487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3888">
    <literal><![CDATA[
      (x * x) * ((y * (1 / x)) / z) = (x * T(y,x \ 1)) / z
    ]]></literal>
    <justification jstring="[para(3874(a,1),807(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3874 807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3889">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2252,a,b,3879,a)].">
      <j1 rule="hyper" parents="64 2252 3879"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      T(x,x \ 1) * (y * x) = x * (y * T(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(3879(a,1),2404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3879 2404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3892">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(3885(a,1),386(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3885 386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3893">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3612,a,3889,a)].">
      <j1 rule="hyper" parents="3612 3889"/>
    </justification>
  </clause>

  <clause id="3894">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,x \ 1)) = y * x
    ]]></literal>
    <justification jstring="[hyper(2365,a,3889,a)].">
      <j1 rule="hyper" parents="2365 3889"/>
    </justification>
  </clause>

  <clause id="3895">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,364,a(flip),b,3889,a),flip(a)].">
      <j1 rule="hyper" parents="373 364 3889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      K(x \ 1,x) \ (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2359,a,b,3889,a)].">
      <j1 rule="hyper" parents="64 2359 3889"/>
    </justification>
  </clause>

  <clause id="3898">
    <literal><![CDATA[
      a(x,x,x) * (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1853(a,1),3889(a,1,1))].">
      <j1 rule="para" parents="1853 3889"/>
    </justification>
  </clause>

  <clause id="3899">
    <literal><![CDATA[
      (x \ 1) * (y * T(x,x \ 1)) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(3889(a,1),2448(a,1,2))].">
      <j1 rule="para" parents="3889 2448"/>
    </justification>
  </clause>

  <clause id="3900">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / (1 / y) = (x / y) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(142,a,3892,a(flip),b,3688,a)].">
      <j1 rule="hyper" parents="142 3892 3688"/>
    </justification>
  </clause>

  <clause id="3901">
    <literal><![CDATA[
      K(x,x \ 1) * ((y / x) / z) = (y / (1 / (1 / x))) / z
    ]]></literal>
    <justification jstring="[para(3892(a,1),3658(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3892 3658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3902">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,364,a(flip),b,3893,a),flip(a)].">
      <j1 rule="hyper" parents="373 364 3893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3903">
    <literal><![CDATA[
      (x * T(y,y \ 1)) \ (R(x,y,y) * y) = a(x * y,y,1 / y)
    ]]></literal>
    <justification jstring="[para(3893(a,1),1974(a,1,1))].">
      <j1 rule="para" parents="3893 1974"/>
    </justification>
  </clause>

  <clause id="3904">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,(z * y) \ z)
    ]]></literal>
    <justification jstring="[para(3798(a,2),3893(a,2,2))].">
      <j1 rule="para" parents="3798 3893"/>
    </justification>
  </clause>

  <clause id="3906">
    <literal><![CDATA[
      x * K(y \ 1,y) != z * y
    ]]></literal>
    <literal><![CDATA[
      z * T(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(3894(a,1),3597(a,1)),flip(a)].">
      <j1 rule="para" parents="3894 3597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3907">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3659,a,b,3895,a)].">
      <j1 rule="hyper" parents="64 3659 3895"/>
    </justification>
  </clause>

  <clause id="3908">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2224,a,b,3895,a)].">
      <j1 rule="hyper" parents="64 2224 3895"/>
    </justification>
  </clause>

  <clause id="3909">
    <literal><![CDATA[
      ((x \ 1) * y) * ((x \ 1) \ 1) = ((1 / x) * y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,2377,a(flip),b,3895,a),flip(a)].">
      <j1 rule="hyper" parents="64 2377 3895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3910">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(35,a,3621,a,b,3895,a)].">
      <j1 rule="hyper" parents="35 3621 3895"/>
    </justification>
  </clause>

  <clause id="3911">
    <literal><![CDATA[
      (x \ 1) * (y * ((x \ 1) \ 1)) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(3895(a,1),2448(a,1,2))].">
      <j1 rule="para" parents="3895 2448"/>
    </justification>
  </clause>

  <clause id="3912">
    <literal><![CDATA[
      L(x * ((y \ 1) \ 1),y,y) = y * ((1 / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(3895(a,1),2451(a,1,1))].">
      <j1 rule="para" parents="3895 2451"/>
    </justification>
  </clause>

  <clause id="3913">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(294(a,1),3896(a,1,1))].">
      <j1 rule="para" parents="294 3896"/>
    </justification>
  </clause>

  <clause id="3914">
    <literal><![CDATA[
      R(x,y,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(1743,a,3902,a)].">
      <j1 rule="hyper" parents="1743 3902"/>
    </justification>
  </clause>

  <clause id="3915">
    <literal><![CDATA[
      (x * y) * K(T(x,y),T(x,y) \ 1) = y * ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(718,a,3902,a)].">
      <j1 rule="hyper" parents="718 3902"/>
    </justification>
  </clause>

  <clause id="3916">
    <literal><![CDATA[
      (x / y) * ((y \ 1) \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(390,a,3902,a),flip(a)].">
      <j1 rule="hyper" parents="390 3902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3917">
    <literal><![CDATA[
      ((x * y) * ((z \ 1) \ 1)) / ((y * z) * K(z,z \ 1)) = R(R(x,y,z),y * z,K(z,z \ 1))
    ]]></literal>
    <justification jstring="[para(3902(a,1),660(a,1,1))].">
      <j1 rule="para" parents="3902 660"/>
    </justification>
  </clause>

  <clause id="3918">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) \ (y * z) = (x * y) \ ((1 / (1 / y)) * z)
    ]]></literal>
    <justification jstring="[para(3902(a,1),3727(a,1,1))].">
      <j1 rule="para" parents="3902 3727"/>
    </justification>
  </clause>

  <clause id="3919">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3782,a(flip),b,3914,a),flip(a)].">
      <j1 rule="hyper" parents="64 3782 3914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3920">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) * x = (x \ y) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3654(a,1),3907(a,1,1))].">
      <j1 rule="para" parents="3654 3907"/>
    </justification>
  </clause>

  <clause id="3921">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(2385(a,1),3908(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2385 3908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3922">
    <literal><![CDATA[
      ((x \ 1) * x) \ y != z * T(x,x \ 1)
    ]]></literal>
    <literal><![CDATA[
      z * x = y
    ]]></literal>
    <justification jstring="[para(3913(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="3913 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3923">
    <literal><![CDATA[
      (((x \ 1) \ 1) * y) / ((x \ 1) \ 1) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,3648,a(flip),b,3916,a)].">
      <j1 rule="hyper" parents="142 3648 3916"/>
    </justification>
  </clause>

  <clause id="3924">
    <literal><![CDATA[
      (x / T(y,z)) * T((y \ 1) \ 1,z) = x * K(T(y,z),T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(3568(a,2),3916(a,1,2))].">
      <j1 rule="para" parents="3568 3916"/>
    </justification>
  </clause>

  <clause id="3925">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,363,a(flip),b,3919,a),flip(a)].">
      <j1 rule="hyper" parents="373 363 3919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3927">
    <literal><![CDATA[
      x \ (x / T(y,y \ 1)) = T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(139,a,3919,a(flip),b,1518,a(flip))].">
      <j1 rule="hyper" parents="139 3919 1518"/>
    </justification>
  </clause>

  <clause id="3929">
    <literal><![CDATA[
      T(x \ (x / y),y) = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(139,a,3925,a(flip),b,1518,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 3925 1518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3930">
    <literal><![CDATA[
      (1 / x) * T(x \ (x / y),y) = (1 / x) / T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,3927,a(flip),b,888,a)].">
      <j1 rule="hyper" parents="145 3927 888"/>
    </justification>
  </clause>

  <clause id="3931">
    <literal><![CDATA[
      1 / (x \ (x / ((y \ 1) \ 1))) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(3929(a,1),3807(a,1,2))].">
      <j1 rule="para" parents="3929 3807"/>
    </justification>
  </clause>

  <clause id="3932">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((x \ 1) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(35,a,3704,a(flip),b,3911,a),flip(a)].">
      <j1 rule="hyper" parents="35 3704 3911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3933">
    <literal><![CDATA[
      (1 / x) * ((y * (x \ 1)) * x) = (x \ 1) * R(y,x,x)
    ]]></literal>
    <justification jstring="[para(3757(a,1),3911(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3757 3911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3934">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,3932,a(flip),b,3907,a),flip(a)].">
      <j1 rule="hyper" parents="142 3932 3907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3935">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(215,a,3931,a)].">
      <j1 rule="hyper" parents="215 3931"/>
    </justification>
  </clause>

  <clause id="3936">
    <literal><![CDATA[
      (x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(224(a,1),3931(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="224 3931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3937">
    <literal><![CDATA[
      K(x,T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,3266,a,b,3934,a)].">
      <j1 rule="hyper" parents="35 3266 3934"/>
    </justification>
  </clause>

  <clause id="3938">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,T(x,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,3611,a,b,3937,a)].">
      <j1 rule="hyper" parents="373 3611 3937"/>
    </justification>
  </clause>

  <clause id="3940">
    <literal><![CDATA[
      K(x,T(x,y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3938(a,1),203(a,1)),flip(b)].">
      <j1 rule="para" parents="3938 203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3941">
    <literal><![CDATA[
      T(K(T(x,y),1 / x),z) = K(T(x,y),T(T(x,y),u) \ 1)
    ]]></literal>
    <justification jstring="[para(3560(a,1),3938(a,1,1))].">
      <j1 rule="para" parents="3560 3938"/>
    </justification>
  </clause>

  <clause id="3942">
    <literal><![CDATA[
      1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(226,a,3936,a)].">
      <j1 rule="hyper" parents="226 3936"/>
    </justification>
  </clause>

  <clause id="3943">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(145,a,3942,a,b,xx)].">
      <j1 rule="hyper" parents="145 3942"/>
    </justification>
  </clause>

  <clause id="3944">
    <literal><![CDATA[
      1 / (1 / (x \ (x / (y \ 1)))) = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(79(a,1),3942(a,2,2,2,2))].">
      <j1 rule="para" parents="79 3942"/>
    </justification>
  </clause>

  <clause id="3945">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x * (1 / (1 / (x \ (x / y))))
    ]]></literal>
    <justification jstring="[hyper(373,a,3892,a,b,3943,a)].">
      <j1 rule="hyper" parents="373 3892 3943"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / x = 1 / (1 / ((x / y) / x))
    ]]></literal>
    <justification jstring="[hyper(142,a,3943,a(flip),b,3588,a)].">
      <j1 rule="hyper" parents="142 3943 3588"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      x / (1 / (1 / ((x * y) \ x))) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(211(a,1),3943(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="211 3943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      1 / (1 / ((x / (y \ 1)) / x)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(79(a,1),3946(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 3946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3949">
    <literal><![CDATA[
      1 / ((x / (y \ 1)) / x) = ((x / (1 / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,3948,a),flip(a)].">
      <j1 rule="hyper" parents="215 3948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3950">
    <literal><![CDATA[
      L(x * ((y \ 1) \ 1),y,y) = L(x,y,y) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,792,a(flip),b,3912,a),flip(a)].">
      <j1 rule="hyper" parents="373 792 3912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3951">
    <literal><![CDATA[
      L(x * T(y,y \ 1),y,y) = L(x,y,y) * y
    ]]></literal>
    <justification jstring="[para(116(a,2),3950(a,1,1,2))].">
      <j1 rule="para" parents="116 3950"/>
    </justification>
  </clause>

  <clause id="3952">
    <literal><![CDATA[
      L(T(x * (y \ 1),y),y,y) = (y \ 1) * R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,567,a,b,3933,a)].">
      <j1 rule="hyper" parents="64 567 3933"/>
    </justification>
  </clause>

  <clause id="3953">
    <literal><![CDATA[
      ((x \ 1) * R(y,x,x)) \ T(y * (x \ 1),x) = a(x,x,T(y * (x \ 1),x))
    ]]></literal>
    <justification jstring="[para(3952(a,1),1243(a,1,1))].">
      <j1 rule="para" parents="3952 1243"/>
    </justification>
  </clause>

  <clause id="3954">
    <literal><![CDATA[
      (x * T(y,x \ 1)) * x = (x * x) * R(y,x,x)
    ]]></literal>
    <justification jstring="[para(1405(a,1),3886(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1405 3886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3955">
    <literal><![CDATA[
      R((x * x) * y,x,x) = (x * T(y,x \ 1)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,1981,a,b,3954,a)].">
      <j1 rule="hyper" parents="373 1981 3954"/>
    </justification>
  </clause>

  <clause id="3956">
    <literal><![CDATA[
      ((x * T(y,x \ 1)) \ 1) \ (((x * T(y,x \ 1)) \ 1) / z) = (y * (1 / x)) \ ((x * x) \ ((x * T(y,x \ 1)) / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,1215,a,b,3887,a)].">
      <j1 rule="hyper" parents="373 1215 3887"/>
    </justification>
  </clause>

  <clause id="3957">
    <literal><![CDATA[
      (1 / (1 / x)) \ ((y / x) / z) = x \ ((y / (1 / (1 / x))) / z)
    ]]></literal>
    <justification jstring="[hyper(139,a,3901,a(flip),b,2258,a),flip(a)].">
      <j1 rule="hyper" parents="139 3901 2258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3958">
    <literal><![CDATA[
      K(T(x,y),T(T(x,y),z) \ 1) = K(T(x,y),1 / T(x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,3553,a,b,3941,a),flip(a)].">
      <j1 rule="hyper" parents="64 3553 3941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3960">
    <literal><![CDATA[
      (x * (y * z)) * (1 / (1 / ((x * (y * z)) \ ((x * (y * z)) / L(z,y,x))))) = (x * y) * K(L(z,y,x),L(z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,403,a(flip),b,3945,a),flip(a)].">
      <j1 rule="hyper" parents="64 403 3945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3961">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / T(x,z))
    ]]></literal>
    <justification jstring="[hyper(3940,a,3958,a)].">
      <j1 rule="hyper" parents="3940 3958"/>
    </justification>
  </clause>

  <clause id="3963">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),x \ 1)
    ]]></literal>
    <justification jstring="[para(301(a,1),3961(a,2,2))].">
      <j1 rule="para" parents="301 3961"/>
    </justification>
  </clause>

  <clause id="3964">
    <literal><![CDATA[
      K(T(x,y),1 / x) = K(T(x,y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3560,a(flip),b,3963,a)].">
      <j1 rule="hyper" parents="64 3560 3963"/>
    </justification>
  </clause>

  <clause id="3965">
    <literal><![CDATA[
      (x * y) * K(T(x,y),1 / x) = y * ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3560(a,1),3915(a,1,2))].">
      <j1 rule="para" parents="3560 3915"/>
    </justification>
  </clause>

  <clause id="3966">
    <literal><![CDATA[
      (x * y) * K(T(x,y),1 / x) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(3574,a,3965,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3574 3965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3967">
    <literal><![CDATA[
      (x * y) * K(T(x,y),x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(3964(a,1),3966(a,1,2))].">
      <j1 rule="para" parents="3964 3966"/>
    </justification>
  </clause>

  <clause id="3968">
    <literal><![CDATA[
      K(T(x,y),x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,3648,a,b,3967,a),flip(a)].">
      <j1 rule="hyper" parents="35 3648 3967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3969">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3963,a,b,3968,a)].">
      <j1 rule="hyper" parents="64 3963 3968"/>
    </justification>
  </clause>

  <clause id="3973">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,x \ 1) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,3969,a(flip),b,2442,a)].">
      <j1 rule="hyper" parents="145 3969 2442"/>
    </justification>
  </clause>

  <clause id="3974">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,3969,a(flip),b,1724,a(flip))].">
      <j1 rule="hyper" parents="139 3969 1724"/>
    </justification>
  </clause>

  <clause id="3975">
    <literal><![CDATA[
      K(x,x \ 1) * (T(x,y) \ z) = (1 / (1 / T(x,y))) \ z
    ]]></literal>
    <justification jstring="[para(3969(a,1),2349(a,1,1))].">
      <j1 rule="para" parents="3969 2349"/>
    </justification>
  </clause>

  <clause id="3976">
    <literal><![CDATA[
      (T(x,y) \ x) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3616,a(flip),b,3974,a)].">
      <j1 rule="hyper" parents="64 3616 3974"/>
    </justification>
  </clause>

  <clause id="3977">
    <literal><![CDATA[
      (1 / T(x,y)) * x = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(144,a,3974,a(flip),b,3616,a(flip))].">
      <j1 rule="hyper" parents="144 3974 3616"/>
    </justification>
  </clause>

  <clause id="3978">
    <literal><![CDATA[
      T(x,y) \ (1 / x) = x \ (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,3974,a(flip),b,2420,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 3974 2420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3979">
    <literal><![CDATA[
      ((T(x,y) \ x) / x) \ 1 = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,3976,a,b,171,a)].">
      <j1 rule="hyper" parents="143 3976 171"/>
    </justification>
  </clause>

  <clause id="3980">
    <literal><![CDATA[
      T(1 / T(x,y),x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(3976(a,1),2410(a,1,1))].">
      <j1 rule="para" parents="3976 2410"/>
    </justification>
  </clause>

  <clause id="3981">
    <literal><![CDATA[
      x / T(x,y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(2530,a,3977,a)].">
      <j1 rule="hyper" parents="2530 3977"/>
    </justification>
  </clause>

  <clause id="3982">
    <literal><![CDATA[
      x / (x / T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(225,a,2525,a(flip),b,3977,a(flip))].">
      <j1 rule="hyper" parents="225 2525 3977"/>
    </justification>
  </clause>

  <clause id="3983">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,3977,a(flip),b,2525,a(flip))].">
      <j1 rule="hyper" parents="144 3977 2525"/>
    </justification>
  </clause>

  <clause id="3984">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      x / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3977(a,1),2530(a,1))].">
      <j1 rule="para" parents="3977 2530"/>
    </justification>
  </clause>

  <clause id="3985">
    <literal><![CDATA[
      (T(x,y) \ x) \ x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(215,a,3981,a)].">
      <j1 rule="hyper" parents="215 3981"/>
    </justification>
  </clause>

  <clause id="3986">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,3379,a,b,3983,a)].">
      <j1 rule="hyper" parents="64 3379 3983"/>
    </justification>
  </clause>

  <clause id="3988">
    <literal><![CDATA[
      (x * y) * T(K(y,x),x) = y * x
    ]]></literal>
    <justification jstring="[para(3986(a,1),3378(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3986 3378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3989">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,3980,a(flip),b,3772,a)].">
      <j1 rule="hyper" parents="139 3980 3772"/>
    </justification>
  </clause>

  <clause id="3990">
    <literal><![CDATA[
      T(1 / T(x,y),z) * x = x * T(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(3980(a,1),265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3980 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3991">
    <literal><![CDATA[
      T(K(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(358,a,3988,a),flip(a)].">
      <j1 rule="hyper" parents="358 3988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3992">
    <literal><![CDATA[
      (x * K(y,x)) / x = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(313,a,3991,a)].">
      <j1 rule="hyper" parents="313 3991"/>
    </justification>
  </clause>

  <clause id="3993">
    <literal><![CDATA[
      T(x,K(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,3991,a)].">
      <j1 rule="hyper" parents="55 3991"/>
    </justification>
  </clause>

  <clause id="3994">
    <literal><![CDATA[
      K(x,y) * y = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,3991,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 3991 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3995">
    <literal><![CDATA[
      L(K(x,y),z,u) * y = y * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3991(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3991 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3996">
    <literal><![CDATA[
      K(x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,3993,a)].">
      <j1 rule="hyper" parents="56 3993"/>
    </justification>
  </clause>

  <clause id="3997">
    <literal><![CDATA[
      T(x,K(y,R(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(43,a,27,a,b,3993,a(flip))].">
      <j1 rule="hyper" parents="43 27 3993"/>
    </justification>
  </clause>

  <clause id="3998">
    <literal><![CDATA[
      T(x,K(y,L(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,25,a,b,3993,a(flip))].">
      <j1 rule="hyper" parents="42 25 3993"/>
    </justification>
  </clause>

  <clause id="3999">
    <literal><![CDATA[
      T(x,K(y,T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,23,a,b,3993,a(flip))].">
      <j1 rule="hyper" parents="41 23 3993"/>
    </justification>
  </clause>

  <clause id="4000">
    <literal><![CDATA[
      T(T(x,y),K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3993(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3993 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4001">
    <literal><![CDATA[
      T(x,y) * K(z,x) = K(z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3993(a,1),265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3993 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4002">
    <literal><![CDATA[
      L(x,y,z) * K(u,x) = K(u,x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3993(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3993 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4003">
    <literal><![CDATA[
      R(x,y,z) * K(u,x) = K(u,x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3993(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3993 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4004">
    <literal><![CDATA[
      K(x,y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3993(a,1),463(a,1,2,1))].">
      <j1 rule="para" parents="3993 463"/>
    </justification>
  </clause>

  <clause id="4005">
    <literal><![CDATA[
      L(x \ y,x,K(z,y)) = (K(z,y) * x) \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(3993(a,1),521(a,1,1,2))].">
      <j1 rule="para" parents="3993 521"/>
    </justification>
  </clause>

  <clause id="4006">
    <literal><![CDATA[
      T(T(x,y),z) * K(u,x) = K(u,x) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3993(a,1),523(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3993 523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4008">
    <literal><![CDATA[
      T(x,y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1885(a,1),3993(a,1,2))].">
      <j1 rule="para" parents="1885 3993"/>
    </justification>
  </clause>

  <clause id="4009">
    <literal><![CDATA[
      T(x,x \ ((y * x) / y)) = x
    ]]></literal>
    <justification jstring="[para(2520(a,1),3993(a,1,2))].">
      <j1 rule="para" parents="2520 3993"/>
    </justification>
  </clause>

  <clause id="4010">
    <literal><![CDATA[
      x * ((K(x,y) \ y) * K(x,y)) = (y * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3993(a,1),3478(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3993 3478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4011">
    <literal><![CDATA[
      K(x,T(y,z)) * y = y * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,3999,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 3999 22"/>
    </justification>
  </clause>

  <clause id="4012">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,u)) = K(z,T(x,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3999(a,1),265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3999 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4013">
    <literal><![CDATA[
      T(x \ T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(55,a,4008,a)].">
      <j1 rule="hyper" parents="55 4008"/>
    </justification>
  </clause>

  <clause id="4014">
    <literal><![CDATA[
      T(T(x,y),K(z,R(x,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3997(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3997 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4015">
    <literal><![CDATA[
      K(x,L(y,z,u)) * y = y * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,3998,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 3998 22"/>
    </justification>
  </clause>

  <clause id="4016">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3458,a,b,3992,a)].">
      <j1 rule="hyper" parents="64 3458 3992"/>
    </justification>
  </clause>

  <clause id="4017">
    <literal><![CDATA[
      T(K(x,y),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3992(a,1),340(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3992 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4018">
    <literal><![CDATA[
      (x \ y) * ((y \ T(x,x \ y)) * y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3111,a,b,3994,a)].">
      <j1 rule="hyper" parents="64 3111 3994"/>
    </justification>
  </clause>

  <clause id="4019">
    <literal><![CDATA[
      (x * (y * K(z,y))) * a(x,K(z,y),y) = (x * K(z,y)) * y
    ]]></literal>
    <justification jstring="[para(3994(a,1),88(a,1,1,2))].">
      <j1 rule="para" parents="3994 88"/>
    </justification>
  </clause>

  <clause id="4020">
    <literal><![CDATA[
      T(K(x,y),T(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(55,a,4000,a)].">
      <j1 rule="hyper" parents="55 4000"/>
    </justification>
  </clause>

  <clause id="4021">
    <literal><![CDATA[
      K(x,y) * T(T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(y,z),u) * K(x,y) = w
    ]]></literal>
    <justification jstring="[para(4000(a,1),463(a,1,2,1))].">
      <j1 rule="para" parents="4000 463"/>
    </justification>
  </clause>

  <clause id="4023">
    <literal><![CDATA[
      ((x * y) / x) / y = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(225,a,4009,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 4009 116"/>
    </justification>
  </clause>

  <clause id="4024">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * x = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(145,a,4009,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="145 4009 116"/>
    </justification>
  </clause>

  <clause id="4025">
    <literal><![CDATA[
      (1 / x) * (x * K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(970,a,4016,a)].">
      <j1 rule="hyper" parents="970 4016"/>
    </justification>
  </clause>

  <clause id="4026">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,4016,a(flip),b,1172,a),flip(a)].">
      <j1 rule="hyper" parents="139 4016 1172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4028">
    <literal><![CDATA[
      x * (y \ T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ T(y,x)) * x = z
    ]]></literal>
    <justification jstring="[para(4013(a,1),328(a,1,2))].">
      <j1 rule="para" parents="4013 328"/>
    </justification>
  </clause>

  <clause id="4029">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,4025,a(flip),b,209,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 4025 209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4030">
    <literal><![CDATA[
      ((x * (y \ 1)) * K(z,y)) / (y \ K(z,y)) = R(x,y \ 1,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(225,a,4026,a(flip),b,210,a)].">
      <j1 rule="hyper" parents="225 4026 210"/>
    </justification>
  </clause>

  <clause id="4031">
    <literal><![CDATA[
      (x \ T(x,y)) \ 1 = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,3227,a(flip),b,3989,a)].">
      <j1 rule="hyper" parents="64 3227 3989"/>
    </justification>
  </clause>

  <clause id="4032">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2595,a,b,4023,a)].">
      <j1 rule="hyper" parents="64 2595 4023"/>
    </justification>
  </clause>

  <clause id="4034">
    <literal><![CDATA[
      (x * y) / x != z * y
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * y) / x) = z
    ]]></literal>
    <justification jstring="[para(4024(a,1),45(a,1))].">
      <j1 rule="para" parents="4024 45"/>
    </justification>
  </clause>

  <clause id="4035">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x \ 1,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,3664,a,b,3973,a)].">
      <j1 rule="hyper" parents="36 3664 3973"/>
    </justification>
  </clause>

  <clause id="4036">
    <literal><![CDATA[
      T(x,L(K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(270,a,3995,a)].">
      <j1 rule="hyper" parents="270 3995"/>
    </justification>
  </clause>

  <clause id="4038">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y * x) \ y) = y \ K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2940,a,b,4029,a)].">
      <j1 rule="hyper" parents="64 2940 4029"/>
    </justification>
  </clause>

  <clause id="4039">
    <literal><![CDATA[
      (x \ 1) \ ((y * (x \ 1)) / y) = x * ((y * (x \ 1)) / y)
    ]]></literal>
    <justification jstring="[hyper(400,a,4032,a),flip(a)].">
      <j1 rule="hyper" parents="400 4032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4040">
    <literal><![CDATA[
      T(1 / x,(y * x) / y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(269,a,4032,a,b,2487,a)].">
      <j1 rule="hyper" parents="269 4032 2487"/>
    </justification>
  </clause>

  <clause id="4042">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1253,a,b,4035,a)].">
      <j1 rule="hyper" parents="35 1253 4035"/>
    </justification>
  </clause>

  <clause id="4043">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1251,a,b,4035,a)].">
      <j1 rule="hyper" parents="35 1251 4035"/>
    </justification>
  </clause>

  <clause id="4044">
    <literal><![CDATA[
      T(x,y) * K(x \ 1,x) = 1 / (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,4042,a(flip),b,1161,a)].">
      <j1 rule="hyper" parents="145 4042 1161"/>
    </justification>
  </clause>

  <clause id="4045">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x,y) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,294,a(flip),b,4043,a),flip(a)].">
      <j1 rule="hyper" parents="373 294 4043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4046">
    <literal><![CDATA[
      T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,3570,a(flip),b,4044,a),flip(a)].">
      <j1 rule="hyper" parents="373 3570 4044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4047">
    <literal><![CDATA[
      x * (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,3472,a,b,4046,a)].">
      <j1 rule="hyper" parents="36 3472 4046"/>
    </justification>
  </clause>

  <clause id="4048">
    <literal><![CDATA[
      T(x,y) / x = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(149,a,4047,a),flip(a)].">
      <j1 rule="hyper" parents="149 4047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4049">
    <literal><![CDATA[
      (x \ T(x,y)) * x = T(x,y)
    ]]></literal>
    <justification jstring="[para(4047(a,1),84(a,1,1,2))].">
      <j1 rule="para" parents="4047 84"/>
    </justification>
  </clause>

  <clause id="4050">
    <literal><![CDATA[
      R(T(x,y),z,u) / x = x \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4047(a,1),2127(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4047 2127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4051">
    <literal><![CDATA[
      (1 / x) * T(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1972,a,4048,a)].">
      <j1 rule="hyper" parents="1972 4048"/>
    </justification>
  </clause>

  <clause id="4052">
    <literal><![CDATA[
      (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1516,a,4048,a),flip(a)].">
      <j1 rule="hyper" parents="1516 4048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4053">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1510,a,4048,a)].">
      <j1 rule="hyper" parents="1510 4048"/>
    </justification>
  </clause>

  <clause id="4054">
    <literal><![CDATA[
      T(x,x \ T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,301,a,b,4048,a)].">
      <j1 rule="hyper" parents="37 301 4048"/>
    </justification>
  </clause>

  <clause id="4055">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = (T(x,y) * z) / (x * z)
    ]]></literal>
    <justification jstring="[para(4048(a,1),112(a,1,1))].">
      <j1 rule="para" parents="4048 112"/>
    </justification>
  </clause>

  <clause id="4056">
    <literal><![CDATA[
      K(x,y) = L(T(x,y) / x,x,y)
    ]]></literal>
    <justification jstring="[para(4048(a,2),1013(a,2,1))].">
      <j1 rule="para" parents="4048 1013"/>
    </justification>
  </clause>

  <clause id="4057">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (T(x / y,z) * y) / x
    ]]></literal>
    <justification jstring="[para(4048(a,1),678(a,1,1))].">
      <j1 rule="para" parents="4048 678"/>
    </justification>
  </clause>

  <clause id="4058">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) = x * ((x * (T(y,x) / y)) \ z)
    ]]></literal>
    <justification jstring="[para(4048(a,1),3463(a,1,1,2))].">
      <j1 rule="para" parents="4048 3463"/>
    </justification>
  </clause>

  <clause id="4059">
    <literal><![CDATA[
      T(x,K(y \ (y / (x \ 1)),y)) = x
    ]]></literal>
    <justification jstring="[para(1885(a,2),4054(a,1,2))].">
      <j1 rule="para" parents="1885 4054"/>
    </justification>
  </clause>

  <clause id="4060">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,2750,a,b,4049,a)].">
      <j1 rule="hyper" parents="64 2750 4049"/>
    </justification>
  </clause>

  <clause id="4062">
    <literal><![CDATA[
      T(x,y) * z != (x \ T(x,y)) * (x * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,x,x \ T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(4049(a,1),606(a,1,1))].">
      <j1 rule="para" parents="4049 606"/>
    </justification>
  </clause>

  <clause id="4063">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = u
    ]]></literal>
    <justification jstring="[para(4049(a,1),666(a,1,1,1))].">
      <j1 rule="para" parents="4049 666"/>
    </justification>
  </clause>

  <clause id="4064">
    <literal><![CDATA[
      L(K(x,y),x,1 / x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1722,a,b,4056,a)].">
      <j1 rule="hyper" parents="373 1722 4056"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      K(x,y) * x = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,4056,a,b,1210,a(flip))].">
      <j1 rule="hyper" parents="144 4056 1210"/>
    </justification>
  </clause>

  <clause id="4067">
    <literal><![CDATA[
      T(x,K(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(270,a,4065,a)].">
      <j1 rule="hyper" parents="270 4065"/>
    </justification>
  </clause>

  <clause id="4068">
    <literal><![CDATA[
      T(K(x,y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(269,a,4065,a,b,xx)].">
      <j1 rule="hyper" parents="269 4065"/>
    </justification>
  </clause>

  <clause id="4069">
    <literal><![CDATA[
      T(x,K(T(x,y),z)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,23,a,b,4067,a(flip))].">
      <j1 rule="hyper" parents="41 23 4067"/>
    </justification>
  </clause>

  <clause id="4070">
    <literal><![CDATA[
      T(T(x,y),K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4067(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4067 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4071">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4067(a,1),328(a,1,2))].">
      <j1 rule="para" parents="4067 328"/>
    </justification>
  </clause>

  <clause id="4072">
    <literal><![CDATA[
      T(x,y) * K(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4067(a,1),265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4067 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4073">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4067(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4067 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4074">
    <literal><![CDATA[
      R(x,y,z) * K(x,u) = K(x,u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4067(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4067 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4075">
    <literal><![CDATA[
      T((x \ y) \ y,K(x,z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4067(a,1),367(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4067 367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4076">
    <literal><![CDATA[
      T((x * y) / x,K(y,z)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(4067(a,1),541(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4067 541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4077">
    <literal><![CDATA[
      T(x,y \ ((x * y) / x)) = x
    ]]></literal>
    <justification jstring="[para(2805(a,1),4067(a,1,2))].">
      <j1 rule="para" parents="2805 4067"/>
    </justification>
  </clause>

  <clause id="4078">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(3842,a,4068,a)].">
      <j1 rule="hyper" parents="3842 4068"/>
    </justification>
  </clause>

  <clause id="4079">
    <literal><![CDATA[
      R(K(x,y),z,u) * x = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4068(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4068 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4081">
    <literal><![CDATA[
      T(x / y,K(y \ x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(117(a,1),4069(a,1,2,1))].">
      <j1 rule="para" parents="117 4069"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      T(K(x,y),T(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(55,a,4070,a)].">
      <j1 rule="hyper" parents="55 4070"/>
    </justification>
  </clause>

  <clause id="4083">
    <literal><![CDATA[
      T(x,T(y,x) \ y) = x
    ]]></literal>
    <justification jstring="[para(256(a,1),4077(a,1,2,2))].">
      <j1 rule="para" parents="256 4077"/>
    </justification>
  </clause>

  <clause id="4084">
    <literal><![CDATA[
      (T(x,y) \ x) * y = y * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,4083,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 4083 22"/>
    </justification>
  </clause>

  <clause id="4085">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(4082(a,1),328(a,1,2))].">
      <j1 rule="para" parents="4082 328"/>
    </justification>
  </clause>

  <clause id="4087">
    <literal><![CDATA[
      (x \ 1) * K(x,y) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,4064,a(flip),b,1172,a),flip(a)].">
      <j1 rule="hyper" parents="139 4064 1172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4088">
    <literal><![CDATA[
      T(1 / x,T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(269,a,4051,a,b,1487,a)].">
      <j1 rule="hyper" parents="269 4051 1487"/>
    </justification>
  </clause>

  <clause id="4089">
    <literal><![CDATA[
      T(x,T(x \ 1,y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,849,a(flip),b,4088,a)].">
      <j1 rule="hyper" parents="64 849 4088"/>
    </justification>
  </clause>

  <clause id="4090">
    <literal><![CDATA[
      T(x \ 1,T(x,y)) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(4088(a,1),278(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4088 278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4091">
    <literal><![CDATA[
      T(x,y) * R(x \ 1,z,u) = R(1 / x,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4088(a,1),267(a,1,2,1))].">
      <j1 rule="para" parents="4088 267"/>
    </justification>
  </clause>

  <clause id="4092">
    <literal><![CDATA[
      T(x / (y * x),T(y,z)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(4088(a,1),455(a,2,1))].">
      <j1 rule="para" parents="4088 455"/>
    </justification>
  </clause>

  <clause id="4093">
    <literal><![CDATA[
      x * T(x \ 1,T(x,y)) = K(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(4088(a,1),1889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4088 1889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4094">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1893,a,4059,a)].">
      <j1 rule="hyper" parents="1893 4059"/>
    </justification>
  </clause>

  <clause id="4096">
    <literal><![CDATA[
      T(K(x \ y,z),y / x) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(55,a,4081,a)].">
      <j1 rule="hyper" parents="55 4081"/>
    </justification>
  </clause>

  <clause id="4097">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2895,a,b,4087,a)].">
      <j1 rule="hyper" parents="64 2895 4087"/>
    </justification>
  </clause>

  <clause id="4098">
    <literal><![CDATA[
      T((1 / x) \ 1,1 / x) = T(x,T(1 / x,y))
    ]]></literal>
    <justification jstring="[para(82(a,1),4090(a,1,1)),flip(a)].">
      <j1 rule="para" parents="82 4090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4099">
    <literal><![CDATA[
      x \ ((x * (T(y,x) \ y)) \ x) = ((T(y,x) \ y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(4084(a,1),2960(a,1,2,1))].">
      <j1 rule="para" parents="4084 2960"/>
    </justification>
  </clause>

  <clause id="4100">
    <literal><![CDATA[
      (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[para(4084(a,1),3179(a,1,1,2,1))].">
      <j1 rule="para" parents="4084 3179"/>
    </justification>
  </clause>

  <clause id="4101">
    <literal><![CDATA[
      (((x * y) / x) \ y) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(157,a,4094,a)].">
      <j1 rule="hyper" parents="157 4094"/>
    </justification>
  </clause>

  <clause id="4102">
    <literal><![CDATA[
      (((L(x,y,y \ 1) * y) / y) \ ((1 / y) * (x * y))) * ((y * ((1 / y) * (x * y))) / y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(1646(a,1),4101(a,1,1,1,1))].">
      <j1 rule="para" parents="1646 4101"/>
    </justification>
  </clause>

  <clause id="4103">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[para(244(a,1),4060(a,1,2))].">
      <j1 rule="para" parents="244 4060"/>
    </justification>
  </clause>

  <clause id="4104">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = T(x \ 1,y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(4052(a,1),4031(a,1,1))].">
      <j1 rule="para" parents="4052 4031"/>
    </justification>
  </clause>

  <clause id="4105">
    <literal><![CDATA[
      T(K(x,y),L(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(270,a,4073,a)].">
      <j1 rule="hyper" parents="270 4073"/>
    </justification>
  </clause>

  <clause id="4106">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) * L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(4105(a,1),328(a,1,2))].">
      <j1 rule="para" parents="4105 328"/>
    </justification>
  </clause>

  <clause id="4107">
    <literal><![CDATA[
      T(K(x,y),R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(270,a,4074,a)].">
      <j1 rule="hyper" parents="270 4074"/>
    </justification>
  </clause>

  <clause id="4108">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,4079,a,b,94,a),flip(a)].">
      <j1 rule="hyper" parents="138 4079 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4110">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = x * T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(4090(a,1),4093(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4090 4093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4111">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,414,a(flip),b,4110,a),flip(a)].">
      <j1 rule="hyper" parents="373 414 4110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      R(x \ T(x,y),K(x \ 1,x),z) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(4111(a,1),1712(a,1,1,2))].">
      <j1 rule="para" parents="4111 1712"/>
    </justification>
  </clause>

  <clause id="4115">
    <literal><![CDATA[
      T(x,T(1 / x,y)) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(82(a,1),4098(a,1,1)),flip(a)].">
      <j1 rule="para" parents="82 4098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4116">
    <literal><![CDATA[
      T(x,T(1 / x,y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,3870,a(flip),b,4115,a),flip(a)].">
      <j1 rule="hyper" parents="373 3870 4115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      T(x,x \ 1) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(4116(a,1),3447(a,1,1))].">
      <j1 rule="para" parents="4116 3447"/>
    </justification>
  </clause>

  <clause id="4118">
    <literal><![CDATA[
      (K(x,y) \ y) * K(x,y) = y
    ]]></literal>
    <justification jstring="[hyper(35,a,94,a(flip),b,4010,a),flip(a)].">
      <j1 rule="hyper" parents="35 94 4010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4119">
    <literal><![CDATA[
      x / K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ x = z
    ]]></literal>
    <justification jstring="[para(4118(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4118 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4120">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(1888(a,2),4104(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1888 4104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4121">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(869,a,4117,a)].">
      <j1 rule="hyper" parents="869 4117"/>
    </justification>
  </clause>

  <clause id="4123">
    <literal><![CDATA[
      (x * T(1 / x,y)) \ (((x \ 1) \ 1) * (T(x \ 1,y) * z)) = L(z,T(x \ 1,y),(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4121(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4121 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4124">
    <literal><![CDATA[
      K(x,x \ 1) * (T(x,y) \ z) = T(1 / (1 / x),y) \ z
    ]]></literal>
    <justification jstring="[para(3570(a,1),3975(a,2,1))].">
      <j1 rule="para" parents="3570 3975"/>
    </justification>
  </clause>

  <clause id="4125">
    <literal><![CDATA[
      x \ ((x * (T(y,x) \ y)) \ x) = (x * (T(y,x) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(4084(a,1),4099(a,2,1))].">
      <j1 rule="para" parents="4084 4099"/>
    </justification>
  </clause>

  <clause id="4126">
    <literal><![CDATA[
      (T(x,y) \ z) * K(x,x \ 1) = T(1 / (1 / x),y) \ z
    ]]></literal>
    <justification jstring="[hyper(3612,a,4124,a)].">
      <j1 rule="hyper" parents="3612 4124"/>
    </justification>
  </clause>

  <clause id="4127">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ (T(x,y) \ z)) = x \ (T(1 / (1 / x),y) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,4124,a(flip),b,2355,a),flip(a)].">
      <j1 rule="hyper" parents="139 4124 2355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4128">
    <literal><![CDATA[
      (T(x \ 1,y) \ z) * K(x \ 1,x) = T(1 / (1 / (x \ 1)),y) \ z
    ]]></literal>
    <justification jstring="[para(1734(a,1),4126(a,1,2))].">
      <j1 rule="para" parents="1734 4126"/>
    </justification>
  </clause>

  <clause id="4129">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) = x * ((x * (y \ T(y,x))) \ z)
    ]]></literal>
    <justification jstring="[para(4048(a,1),4058(a,2,2,1,2))].">
      <j1 rule="para" parents="4048 4058"/>
    </justification>
  </clause>

  <clause id="4130">
    <literal><![CDATA[
      (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4084,a(flip),b,4100,a),flip(a)].">
      <j1 rule="hyper" parents="373 4084 4100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4131">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (y * T(y \ x,z)) / x
    ]]></literal>
    <justification jstring="[para(525(a,1),4057(a,2,1))].">
      <j1 rule="para" parents="525 4057"/>
    </justification>
  </clause>

  <clause id="4132">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = z * T((T(x,z) \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[para(302(a,1),3924(a,1,1)),flip(a)].">
      <j1 rule="para" parents="302 3924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4133">
    <literal><![CDATA[
      (T(x \ 1,y) \ z) * K(x \ 1,x) = T(1 / x,y) \ z
    ]]></literal>
    <justification jstring="[para(79(a,1),4128(a,2,1,1,2))].">
      <j1 rule="para" parents="79 4128"/>
    </justification>
  </clause>

  <clause id="4134">
    <literal><![CDATA[
      K(x,x \ 1) * (T(1 / x,y) \ z) = T(x \ 1,y) \ z
    ]]></literal>
    <justification jstring="[hyper(3641,a,4133,a)].">
      <j1 rule="hyper" parents="3641 4133"/>
    </justification>
  </clause>

  <clause id="4135">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (T(x \ 1,y) \ z) = x \ (T(1 / x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,4133,a(flip),b,3628,a),flip(a)].">
      <j1 rule="hyper" parents="139 4133 3628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4136">
    <literal><![CDATA[
      T(x \ 1,y) \ (T(1 / x,y) * z) = K(x,x \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(739,a,4134,a),flip(a)].">
      <j1 rule="hyper" parents="739 4134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4137">
    <literal><![CDATA[
      T(x \ 1,y) * ((x \ 1) \ (K(x,x \ 1) * z)) = T(1 / x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,2449,a,b,4136,a)].">
      <j1 rule="hyper" parents="145 2449 4136"/>
    </justification>
  </clause>

  <clause id="4138">
    <literal><![CDATA[
      T(1 / x,y) * ((1 / x) \ z) = T(x \ 1,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,2450,a(flip),b,4136,a),flip(a)].">
      <j1 rule="hyper" parents="145 2450 4136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4139">
    <literal><![CDATA[
      (1 / x) * (T(x \ 1,y) * ((x \ 1) \ z)) = T(1 / x,y) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,4138,a(flip),b,2401,a)].">
      <j1 rule="hyper" parents="145 4138 2401"/>
    </justification>
  </clause>

  <clause id="4140">
    <literal><![CDATA[
      (1 / x) * (T(x \ 1,y) * ((x \ 1) \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (T(1 / x,y) * z) / w = u
    ]]></literal>
    <justification jstring="[para(4139(a,2),724(a,1))].">
      <j1 rule="para" parents="4139 724"/>
    </justification>
  </clause>

  <clause id="4141">
    <literal><![CDATA[
      T(x \ 1,y) * ((((x \ 1) \ 1) \ 1) \ z) = T(1 / x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2388(a,1),4137(a,1,2))].">
      <j1 rule="para" parents="2388 4137"/>
    </justification>
  </clause>

  <clause id="4142">
    <literal><![CDATA[
      T(x \ 1,y) * (T(x \ 1,(x \ 1) \ 1) \ z) = T(1 / x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(116(a,2),4141(a,1,2,1))].">
      <j1 rule="para" parents="116 4141"/>
    </justification>
  </clause>

  <clause id="4147">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = z * T(T((x \ 1) \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(3568(a,2),4132(a,2,2,1))].">
      <j1 rule="para" parents="3568 4132"/>
    </justification>
  </clause>

  <clause id="4149">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(T(x,z),y),T(T(x,z),y) \ 1) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,265,a(flip),b,4147,a),flip(a)].">
      <j1 rule="hyper" parents="373 265 4147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4150">
    <literal><![CDATA[
      (T(x,y) * z) * K(T(x,z),T(x,z) \ 1) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(3969(a,1),4149(a,1,2))].">
      <j1 rule="para" parents="3969 4149"/>
    </justification>
  </clause>

  <clause id="4151">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,x \ 1) = T((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(3969(a,1),4150(a,1,2))].">
      <j1 rule="para" parents="3969 4150"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      (1 / x) * (T(((1 / x) \ 1) \ 1,y) * z) = (x \ 1) * (T(1 / x,y) * z)
    ]]></literal>
    <justification jstring="[para(4151(a,1),3683(a,1,2))].">
      <j1 rule="para" parents="4151 3683"/>
    </justification>
  </clause>

  <clause id="4155">
    <literal><![CDATA[
      (1 / x) * (T(x \ 1,y) * z) = (x \ 1) * (T(1 / x,y) * z)
    ]]></literal>
    <justification jstring="[para(82(a,1),4153(a,1,2,1,1,1))].">
      <j1 rule="para" parents="82 4153"/>
    </justification>
  </clause>

  <clause id="4156">
    <literal><![CDATA[
      (T(1 / x,y) * z) / (T(1 / x,y) * ((x \ 1) \ z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(4140,a,4155,a)].">
      <j1 rule="hyper" parents="4140 4155"/>
    </justification>
  </clause>

  <clause id="4157">
    <literal><![CDATA[
      K(x \ 1,x) * (T(1 / x,y) * z) = T(x \ 1,y) * z
    ]]></literal>
    <justification jstring="[hyper(35,a,2452,a,b,4155,a)].">
      <j1 rule="hyper" parents="35 2452 4155"/>
    </justification>
  </clause>

  <clause id="4159">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (T(x \ 1,y) * z) = x * (T(1 / x,y) * z)
    ]]></literal>
    <justification jstring="[para(4157(a,1),2389(a,1,2))].">
      <j1 rule="para" parents="4157 2389"/>
    </justification>
  </clause>

  <clause id="4161">
    <literal><![CDATA[
      R(R(x,y,z),y * z,K(z,z \ 1)) = ((x * y) * ((z \ 1) \ 1)) / (y * ((z \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(3902(a,1),3917(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3902 3917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4162">
    <literal><![CDATA[
      R(R(x,y,z),y * z,K(z,z \ 1)) = R(x,y,(z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,20,a,b,4161,a),flip(a)].">
      <j1 rule="hyper" parents="373 20 4161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4163">
    <literal><![CDATA[
      (x * T(1 / x,y)) \ (x * (T(1 / x,y) * z)) = L(z,T(x \ 1,y),(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(4159(a,1),4123(a,1,2))].">
      <j1 rule="para" parents="4159 4123"/>
    </justification>
  </clause>

  <clause id="4164">
    <literal><![CDATA[
      L(x,T(y \ 1,z),(y \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,T(1 / y,z),y) = u
    ]]></literal>
    <justification jstring="[para(4163(a,1),608(a,1))].">
      <j1 rule="para" parents="4163 608"/>
    </justification>
  </clause>

  <clause id="4165">
    <literal><![CDATA[
      L(x,T(1 / y,z),y) = L(x,T(y \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(4164,a,1636,a)].">
      <j1 rule="hyper" parents="4164 1636"/>
    </justification>
  </clause>

  <clause id="4166">
    <literal><![CDATA[
      L(T(1 / x,y) \ z,T(x \ 1,y),x) = (x * T(1 / x,y)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,4165,a),flip(a)].">
      <j1 rule="hyper" parents="64 102 4165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4171">
    <literal><![CDATA[
      R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = (1 / x) * T((1 / x) \ 1,y)
    ]]></literal>
    <justification jstring="[para(3081(a,1),3487(a,2,2,1,1))].">
      <j1 rule="para" parents="3081 3487"/>
    </justification>
  </clause>

  <clause id="4172">
    <literal><![CDATA[
      R((1 / x) * T((1 / x) \ 1,y),K(x \ 1,x),z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4053,a(flip),b,4171,a),flip(a)].">
      <j1 rule="hyper" parents="373 4053 4171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4174">
    <literal><![CDATA[
      R(x \ T(x,y),K(x \ 1,x),z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4053(a,1),4172(a,1,1))].">
      <j1 rule="para" parents="4053 4172"/>
    </justification>
  </clause>

  <clause id="4175">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(4174(a,1),4114(a,1,1))].">
      <j1 rule="para" parents="4174 4114"/>
    </justification>
  </clause>

  <clause id="4176">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x \ 1) * T(x,y)) * z) = K(x \ 1,x) * z
    ]]></literal>
    <justification jstring="[para(4111(a,1),4175(a,2,1))].">
      <j1 rule="para" parents="4111 4175"/>
    </justification>
  </clause>

  <clause id="4178">
    <literal><![CDATA[
      (x \ T(x,y)) * (z * K(x \ 1,x)) = ((x \ 1) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,3595,a(flip),b,4176,a)].">
      <j1 rule="hyper" parents="145 3595 4176"/>
    </justification>
  </clause>

  <clause id="4180">
    <literal><![CDATA[
      (L(x * x,y,z) * (u * (w * v5))) \ (L(x * x,y,z) * ((u * w) * v5)) = a(L(x * x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(1701(a,1),3537(a,1,2))].">
      <j1 rule="para" parents="1701 3537"/>
    </justification>
  </clause>

  <clause id="4181">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),L(u * u,w,v5)) = a(L(u * u,w,v5) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1082,a,4180,a)].">
      <j1 rule="hyper" parents="1082 4180"/>
    </justification>
  </clause>

  <clause id="4182">
    <literal><![CDATA[
      a(L(x * x,y,z) * u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,1823,a(flip),b,4181,a),flip(a)].">
      <j1 rule="hyper" parents="64 1823 4181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4184">
    <literal><![CDATA[
      a((L(x * x,y,z) \ u) * w,v5,v6) = a(u * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,3099,a,b,4182,a)].">
      <j1 rule="hyper" parents="64 3099 4182"/>
    </justification>
  </clause>

  <clause id="4185">
    <literal><![CDATA[
      a(L(x * x,y,z) \ u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),4182(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 4182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4187">
    <literal><![CDATA[
      (x * (y * z)) * T((x * (y * z)) \ (x * y),u) = (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u))
    ]]></literal>
    <justification jstring="[para(100(a,1),1771(a,1,2,1,1))].">
      <j1 rule="para" parents="100 1771"/>
    </justification>
  </clause>

  <clause id="4188">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)) = x * ((y * z) * T((y * z) \ y,u))
    ]]></literal>
    <justification jstring="[hyper(1316,a,4187,a),flip(a)].">
      <j1 rule="hyper" parents="1316 4187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4189">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * T(L(z,y,x) \ 1,u)) = x * (y * (z * T(z \ 1,u)))
    ]]></literal>
    <justification jstring="[para(1001(a,1),4188(a,2,2))].">
      <j1 rule="para" parents="1001 4188"/>
    </justification>
  </clause>

  <clause id="4190">
    <literal><![CDATA[
      L(x,y,z) * T(L(x,y,z) \ 1,u) = L(x * T(x \ 1,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(606,a,4189,a),flip(a)].">
      <j1 rule="hyper" parents="606 4189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4191">
    <literal><![CDATA[
      L(x * T(x \ 1,L(x,y,z)),y,z) = (L(x,y,z) \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(328,a,4190,a),flip(a)].">
      <j1 rule="hyper" parents="328 4190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4192">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1883,a,b,4190,a),flip(a)].">
      <j1 rule="hyper" parents="64 1883 4190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4193">
    <literal><![CDATA[
      T(L(x * T(x \ 1,x),y,z),x * (L(x,y,z) \ 1)) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[para(4190(a,1),1866(a,1,1))].">
      <j1 rule="para" parents="4190 1866"/>
    </justification>
  </clause>

  <clause id="4194">
    <literal><![CDATA[
      L(x \ T(x,y),z,u) = K(y \ (y / L(x \ 1,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1484(a,1),4192(a,1,1))].">
      <j1 rule="para" parents="1484 4192"/>
    </justification>
  </clause>

  <clause id="4195">
    <literal><![CDATA[
      L(x \ T(x,y * L(x \ 1,z,u)),z,u) = K((y * L(x \ 1,z,u)) \ y,y * L(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),4194(a,2,1,2))].">
      <j1 rule="para" parents="11 4194"/>
    </justification>
  </clause>

  <clause id="4196">
    <literal><![CDATA[
      T(L(K(x \ 1,x),y,z),x * (L(x,y,z) \ 1)) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[para(414(a,1),4193(a,1,1,1))].">
      <j1 rule="para" parents="414 4193"/>
    </justification>
  </clause>

  <clause id="4197">
    <literal><![CDATA[
      T(L(K(x \ 1,x),y,z),L(x,y,z) \ x) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[para(1846(a,1),4196(a,1,2))].">
      <j1 rule="para" parents="1846 4196"/>
    </justification>
  </clause>

  <clause id="4198">
    <literal><![CDATA[
      L(T(K(x \ 1,x),L(x,y,z) \ x),y,z) = K(x \ (L(x,y,z) \ x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25,a,b,4197,a)].">
      <j1 rule="hyper" parents="64 25 4197"/>
    </justification>
  </clause>

  <clause id="4199">
    <literal><![CDATA[
      L(T(K(x \ 1,x),L(x,y,z) \ x),y,z) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1848(a,1),4198(a,2,1))].">
      <j1 rule="para" parents="1848 4198"/>
    </justification>
  </clause>

  <clause id="4200">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(3591(a,1),4199(a,1,1))].">
      <j1 rule="para" parents="3591 4199"/>
    </justification>
  </clause>

  <clause id="4202">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = L(x \ x,y,z)
    ]]></literal>
    <justification jstring="[para(2561(a,1),4195(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2561 4195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4203">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(68(a,1),4202(a,2,1))].">
      <j1 rule="para" parents="68 4202"/>
    </justification>
  </clause>

  <clause id="4204">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,425,a(flip),b,4203,a),flip(a)].">
      <j1 rule="hyper" parents="373 425 4203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4207">
    <literal><![CDATA[
      ((x * L(x \ 1,y,z)) \ x) * (x * L(x \ 1,y,z)) = x * 1
    ]]></literal>
    <justification jstring="[hyper(145,a,4204,a(flip),b,95,a),flip(a)].">
      <j1 rule="hyper" parents="145 4204 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      ((x * L(x \ 1,y,z)) \ x) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a(flip),b,4207,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 4207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4209">
    <literal><![CDATA[
      L((x \ 1) \ ((x \ 1) \ (y / (x * z))),x \ 1,x) = T(y / ((x \ 1) * z),(x \ 1) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(79(a,1),2610(a,1,1,2,2,2,1))].">
      <j1 rule="para" parents="79 2610"/>
    </justification>
  </clause>

  <clause id="4210">
    <literal><![CDATA[
      T(x / ((y \ 1) * z),(y \ 1) * (y \ 1)) = y * ((y \ 1) \ (x / (y * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,629,a(flip),b,4209,a),flip(a)].">
      <j1 rule="hyper" parents="64 629 4209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4212">
    <literal><![CDATA[
      (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = R(x,y,z) * (z * R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,514,a(flip),b,2818,a),flip(a)].">
      <j1 rule="hyper" parents="373 514 2818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4213">
    <literal><![CDATA[
      (R(x,y,z) * R(R(x,y,z) \ (x * y),u,w)) * z = R(x,y,z) * (R(y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(267(a,1),4212(a,2,2))].">
      <j1 rule="para" parents="267 4212"/>
    </justification>
  </clause>

  <clause id="4214">
    <literal><![CDATA[
      (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * ((y \ z) * T((y \ z) \ 1,z))) * z
    ]]></literal>
    <justification jstring="[para(1001(a,1),2922(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1001 2922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4215">
    <literal><![CDATA[
      (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * (y \ ((z \ y) * z))) * z
    ]]></literal>
    <justification jstring="[para(1384(a,1),4214(a,2,1,2))].">
      <j1 rule="para" parents="1384 4214"/>
    </justification>
  </clause>

  <clause id="4216">
    <literal><![CDATA[
      (x * (y \ z)) * ((z \ L(T(y,y \ z),y \ z,x)) * z) = (x * K(z \ y,z)) * z
    ]]></literal>
    <justification jstring="[para(95(a,1),4215(a,2,1,2))].">
      <j1 rule="para" parents="95 4215"/>
    </justification>
  </clause>

  <clause id="4217">
    <literal><![CDATA[
      (L(x,y,y \ 1) \ ((1 / y) * (x * y))) * ((y * ((1 / y) * (x * y))) / y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),4102(a,1,1,1))].">
      <j1 rule="para" parents="11 4102"/>
    </justification>
  </clause>

  <clause id="4219">
    <literal><![CDATA[
      L(((x * (1 / x)) \ 1) * y,x * (1 / x),x) = T(x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(2210(a,1),1768(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2210 1768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4224">
    <literal><![CDATA[
      T((x \ 1) * (x * ((y * z) / y)),y) = T(1 / x,y) * L(T(1 / x,y) \ z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3748(a,1),3287(a,1,1))].">
      <j1 rule="para" parents="3748 3287"/>
    </justification>
  </clause>

  <clause id="4225">
    <literal><![CDATA[
      (x * (y * z)) * R((x * (y * z)) \ (x * y),u,w) = (x * y) * (L(z,y,x) * R(L(z,y,x) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(100(a,1),2298(a,1,2,1,1))].">
      <j1 rule="para" parents="100 2298"/>
    </justification>
  </clause>

  <clause id="4226">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * R(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(720,a,4225,a)].">
      <j1 rule="hyper" parents="720 4225"/>
    </justification>
  </clause>

  <clause id="4227">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * R(L(z,y,x) \ 1,u,w)) = x * ((y * z) * R((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,1708,a(flip),b,4225,a),flip(a)].">
      <j1 rule="hyper" parents="64 1708 4225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * R(L(z,y,x) \ 1,u,w)) = x * (y * (z * R(z \ 1,u,w)))
    ]]></literal>
    <justification jstring="[para(1300(a,1),4227(a,2,2))].">
      <j1 rule="para" parents="1300 4227"/>
    </justification>
  </clause>

  <clause id="4229">
    <literal><![CDATA[
      L(x,y,z) * R(L(x,y,z) \ 1,u,w) = L(x * R(x \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(606,a,4228,a),flip(a)].">
      <j1 rule="hyper" parents="606 4228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4230">
    <literal><![CDATA[
      L(x * R(x \ 1,L(x,y,z),x \ 1),y,z) = ((x \ 1) / (x \ L(x,y,z))) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1812,a(flip),b,4229,a),flip(a)].">
      <j1 rule="hyper" parents="64 1812 4229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4231">
    <literal><![CDATA[
      ((x \ 1) / (x \ L(x,y,z))) * L(x,y,z) = L(x * T(x \ 1,L(x,y,z)),y,z)
    ]]></literal>
    <justification jstring="[para(2569(a,1),4230(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2569 4230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4232">
    <literal><![CDATA[
      (x \ 1) / (x \ L(x,y,z)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,4191,a(flip),b,4231,a),flip(a)].">
      <j1 rule="hyper" parents="36 4191 4231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4233">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(215,a,4232,a)].">
      <j1 rule="hyper" parents="215 4232"/>
    </justification>
  </clause>

  <clause id="4234">
    <literal><![CDATA[
      x / ((1 / x) \ L(1 / x,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),4232(a,1,1))].">
      <j1 rule="para" parents="82 4232"/>
    </justification>
  </clause>

  <clause id="4235">
    <literal><![CDATA[
      x / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1309(a,1),4234(a,1,2))].">
      <j1 rule="para" parents="1309 4234"/>
    </justification>
  </clause>

  <clause id="4236">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(156,a,4235,a)].">
      <j1 rule="hyper" parents="156 4235"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ x = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,4208,a,b,4236,a)].">
      <j1 rule="hyper" parents="36 4208 4236"/>
    </justification>
  </clause>

  <clause id="4238">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = (L(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(3129(a,1),4237(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3129 4237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4239">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) \ R(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,1987,a(flip),b,4226,a),flip(a)].">
      <j1 rule="hyper" parents="373 1987 4226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4240">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * R((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(29(a,1),4239(a,2,2))].">
      <j1 rule="para" parents="29 4239"/>
    </justification>
  </clause>

  <clause id="4241">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * R((y * z) \ y,u,w))) = L(z,y,x) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(1708(a,1),4240(a,1,2))].">
      <j1 rule="para" parents="1708 4240"/>
    </justification>
  </clause>

  <clause id="4242">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z \ R(z,u,w)))) = L(z,y,x) \ L(R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(2299(a,1),4241(a,1,2,2))].">
      <j1 rule="para" parents="2299 4241"/>
    </justification>
  </clause>

  <clause id="4243">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,w),y,z) = L(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(608,a,4242,a),flip(a)].">
      <j1 rule="hyper" parents="608 4242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4244">
    <literal><![CDATA[
      L(x \ R(x,y,y \ 1),z,u) = a(L(x,z,u),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,984,a(flip),b,4243,a),flip(a)].">
      <j1 rule="hyper" parents="64 984 4243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4245">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(L(R(x,v5,v6),y,z),u,w) = L(L(x,y,z) \ R(L(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(29(a,1),4243(a,1,2,1))].">
      <j1 rule="para" parents="29 4243"/>
    </justification>
  </clause>

  <clause id="4246">
    <literal><![CDATA[
      L(x,y,z) \ R(L(x,y,z),u,w) = L(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(29(a,2),4243(a,1,2))].">
      <j1 rule="para" parents="29 4243"/>
    </justification>
  </clause>

  <clause id="4247">
    <literal><![CDATA[
      L((x \ 1) \ R(x \ 1,x,y),z,u) = L(x \ 1,z,u) \ L((x \ y) / y,z,u)
    ]]></literal>
    <justification jstring="[para(3001(a,1),4243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3001 4243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4248">
    <literal><![CDATA[
      a(L(x,y,z),u,u \ 1) = L(a(x,u,u \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(982(a,1),4244(a,1,1)),flip(a)].">
      <j1 rule="para" parents="982 4244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4249">
    <literal><![CDATA[
      (x * y) * a(L(z,y,x),u,u \ 1) = x * (y * a(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(145,a,4248,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="145 4248 18"/>
    </justification>
  </clause>

  <clause id="4250">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) * L(x,u,w) = L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(144,a,4246,a(flip),b,2073,a)].">
      <j1 rule="hyper" parents="144 4246 2073"/>
    </justification>
  </clause>

  <clause id="4251">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) \ L(R(x,y,z),u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(149,a,4250,a)].">
      <j1 rule="hyper" parents="149 4250"/>
    </justification>
  </clause>

  <clause id="4252">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(L(R(x,v5,v6),y,z),u,w) = L(L(x \ R(x,v5,v6),y,z),u,w)
    ]]></literal>
    <justification jstring="[para(4246(a,1),4245(a,2,1))].">
      <j1 rule="para" parents="4246 4245"/>
    </justification>
  </clause>

  <clause id="4253">
    <literal><![CDATA[
      (x * (R(y / z,z,y \ u) / x)) * (z * (y \ u)) = (x * ((u / (z * (y \ u))) / x)) * (z * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,3294,a(flip),b,3297,a),flip(a)].">
      <j1 rule="hyper" parents="373 3294 3297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      R(x * ((y / z) / x),z,y \ u) * (z * (y \ u)) = (x * ((u / (z * (y \ u))) / x)) * (z * (y \ u))
    ]]></literal>
    <justification jstring="[para(2129(a,2),4253(a,1,1))].">
      <j1 rule="para" parents="2129 4253"/>
    </justification>
  </clause>

  <clause id="4255">
    <literal><![CDATA[
      (x * ((y / (z * (u \ y))) / x)) * (z * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      ((x * ((u / z) / x)) * z) * (u \ y) = w
    ]]></literal>
    <justification jstring="[para(4254(a,1),327(a,1))].">
      <j1 rule="para" parents="4254 327"/>
    </justification>
  </clause>

  <clause id="4256">
    <literal><![CDATA[
      R(T(x,x \ 1) * T(T(x \ 1,x),x \ R(x,y,z)),y,z) = K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1358(a,1),3485(a,1,1,2,1))].">
      <j1 rule="para" parents="1358 3485"/>
    </justification>
  </clause>

  <clause id="4257">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(T(x,x \ 1) * T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(2088(a,1),4256(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2088 4256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4259">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R((x \ 1) * T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(3879(a,1),4257(a,2,1))].">
      <j1 rule="para" parents="3879 4257"/>
    </justification>
  </clause>

  <clause id="4260">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(1,y,z)
    ]]></literal>
    <justification jstring="[para(248(a,1),4259(a,2,1))].">
      <j1 rule="para" parents="248 4259"/>
    </justification>
  </clause>

  <clause id="4261">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,428,a(flip),b,4260,a),flip(a)].">
      <j1 rule="hyper" parents="373 428 4260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4264">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = (x \ 1) * 1
    ]]></literal>
    <justification jstring="[hyper(145,a,4261,a(flip),b,95,a),flip(a)].">
      <j1 rule="hyper" parents="145 4261 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4265">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a(flip),b,4264,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 4264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4266">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(4265(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4265 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4267">
    <literal><![CDATA[
      ((x * T(y,x \ 1)) \ 1) \ (((x * T(y,x \ 1)) \ 1) / z) = (y * (1 / x)) \ (((1 / x) * T(y,x \ 1)) / z)
    ]]></literal>
    <justification jstring="[para(937(a,1),3956(a,2,2))].">
      <j1 rule="para" parents="937 3956"/>
    </justification>
  </clause>

  <clause id="4268">
    <literal><![CDATA[
      ((x * T(y,x \ 1)) \ 1) \ (((x * T(y,x \ 1)) \ 1) / z) = (y * (1 / x)) \ ((y * (1 / x)) / z)
    ]]></literal>
    <justification jstring="[para(3873(a,1),4267(a,2,2,1))].">
      <j1 rule="para" parents="3873 4267"/>
    </justification>
  </clause>

  <clause id="4269">
    <literal><![CDATA[
      (x * T(y,x \ 1)) \ ((x * T(y,x \ 1)) / z) = (y * (1 / x)) \ ((y * (1 / x)) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1215,a(flip),b,4268,a)].">
      <j1 rule="hyper" parents="64 1215 4268"/>
    </justification>
  </clause>

  <clause id="4270">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * L((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * L(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),2555(a,2,2,1,1))].">
      <j1 rule="para" parents="18 2555"/>
    </justification>
  </clause>

  <clause id="4271">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L((y * z) \ y,u,w))) = L(z,y,x) * L(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(1704(a,1),4270(a,1,2))].">
      <j1 rule="para" parents="1704 4270"/>
    </justification>
  </clause>

  <clause id="4272">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * L(z \ 1,u,w)))) = L(z,y,x) * L(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(1302(a,1),4271(a,1,2,2))].">
      <j1 rule="para" parents="1302 4271"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ 1,u,w) = L(x * L(x \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(608,a,4272,a),flip(a)].">
      <j1 rule="hyper" parents="608 4272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ 1,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x * L(x \ 1,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(4272(a,1),608(a,1))].">
      <j1 rule="para" parents="4272 608"/>
    </justification>
  </clause>

  <clause id="4275">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ 1,x,1 / x) = L(x * T(1 / x,1),y,z)
    ]]></literal>
    <justification jstring="[para(1022(a,1),4273(a,2,1,2))].">
      <j1 rule="para" parents="1022 4273"/>
    </justification>
  </clause>

  <clause id="4276">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) / x) \ ((1 / x) * 1)) = L(x * L(x \ 1,L(x,y,z),1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(3134(a,1),4273(a,1,2))].">
      <j1 rule="para" parents="3134 4273"/>
    </justification>
  </clause>

  <clause id="4277">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(x * T(1 / x,1),y,z)
    ]]></literal>
    <justification jstring="[para(1861(a,1),4275(a,1,2))].">
      <j1 rule="para" parents="1861 4275"/>
    </justification>
  </clause>

  <clause id="4278">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(372(a,1),4277(a,2,1,2))].">
      <j1 rule="para" parents="372 4277"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1724(a,2),4278(a,2,1))].">
      <j1 rule="para" parents="1724 4278"/>
    </justification>
  </clause>

  <clause id="4280">
    <literal><![CDATA[
      L(x * L(x \ 1,L(x,y,z),1 / x),y,z) = L(x,y,z) * ((L(x,y,z) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(8(a,1),4276(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 4276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) / x) \ (1 / x)) = L(K(L(x,y,z),1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(3496(a,1),4280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3496 4280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      (x * (x * y)) \ ((x * x) * R((x * x) \ (x * (x * y)),z,u)) = (L(y,x,x) \ 1) \ R(L(y,x,x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(585(a,1),2746(a,2,2,1))].">
      <j1 rule="para" parents="585 2746"/>
    </justification>
  </clause>

  <clause id="4283">
    <literal><![CDATA[
      (x * (x * y)) \ ((x * x) * R((x * x) \ (x * (x * y)),z,u)) = L(y,x,x) \ (1 * R(1 \ L(y,x,x),z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,2744,a(flip),b,4282,a),flip(a)].">
      <j1 rule="hyper" parents="373 2744 4282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      (x * (x * y)) \ ((x * x) * R((x * x) \ (x * (x * y)),z,u)) = L(y,x,x) \ (1 * R(L(y,x,x),z,u))
    ]]></literal>
    <justification jstring="[para(66(a,1),4283(a,2,2,2,1))].">
      <j1 rule="para" parents="66 4283"/>
    </justification>
  </clause>

  <clause id="4285">
    <literal><![CDATA[
      (x * (x * y)) \ ((x * x) * R((x * x) \ (x * (x * y)),z,u)) = L(y,x,x) \ (1 * L(R(y,z,u),x,x))
    ]]></literal>
    <justification jstring="[para(29(a,1),4284(a,2,2,2))].">
      <j1 rule="para" parents="29 4284"/>
    </justification>
  </clause>

  <clause id="4286">
    <literal><![CDATA[
      (x * (x * y)) \ ((x * x) * R((x * x) \ (x * (x * y)),z,u)) = L(y,x,x) \ L(R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(342,a,4285,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="342 4285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4287">
    <literal><![CDATA[
      (x * (x * y)) \ ((x * x) * R((x * x) \ (x * (x * y)),z,u)) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,4243,a(flip),b,4286,a),flip(a)].">
      <j1 rule="hyper" parents="373 4243 4286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4288">
    <literal><![CDATA[
      (x * (x * y)) \ ((x * x) * R(L(y,x,x),z,u)) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(18(a,2),4287(a,1,2,2,1))].">
      <j1 rule="para" parents="18 4287"/>
    </justification>
  </clause>

  <clause id="4289">
    <literal><![CDATA[
      (x * (x * y)) \ R((x * x) * L(y,x,x),z,u) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(1981(a,2),4288(a,1,2))].">
      <j1 rule="para" parents="1981 4288"/>
    </justification>
  </clause>

  <clause id="4290">
    <literal><![CDATA[
      (x * (x * y)) \ R(x * (x * y),z,u) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(100(a,1),4289(a,1,2,1))].">
      <j1 rule="para" parents="100 4289"/>
    </justification>
  </clause>

  <clause id="4291">
    <literal><![CDATA[
      (x * (y * z)) * ((u * ((x * (y * z)) \ (x * y))) / u) = (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u))
    ]]></literal>
    <justification jstring="[para(100(a,1),2749(a,1,2,1,2,1))].">
      <j1 rule="para" parents="100 2749"/>
    </justification>
  </clause>

  <clause id="4292">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)) = x * ((y * z) * ((u * ((y * z) \ y)) / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,1962,a(flip),b,4291,a),flip(a)].">
      <j1 rule="hyper" parents="64 1962 4291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4293">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * ((u * (L(z,y,x) \ 1)) / u)) = x * (y * (z * ((u * (z \ 1)) / u)))
    ]]></literal>
    <justification jstring="[para(1961(a,1),4292(a,2,2))].">
      <j1 rule="para" parents="1961 4292"/>
    </justification>
  </clause>

  <clause id="4294">
    <literal><![CDATA[
      L(x,y,z) * ((u * (L(x,y,z) \ 1)) / u) = L(x * ((u * (x \ 1)) / u),y,z)
    ]]></literal>
    <justification jstring="[hyper(606,a,4293,a),flip(a)].">
      <j1 rule="hyper" parents="606 4293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4295">
    <literal><![CDATA[
      L(x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)),y,z) = L(x,y,z) * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),4294(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 4294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4296">
    <literal><![CDATA[
      L(x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)),y,z) = K(L(x,y,z),L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,1724,a,b,4295,a),flip(a)].">
      <j1 rule="hyper" parents="373 1724 4295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4297">
    <literal><![CDATA[
      L(K(L(x,y,z),1 / x),y,z) = K(L(x,y,z),L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(3136(a,1),4296(a,1,1))].">
      <j1 rule="para" parents="3136 4296"/>
    </justification>
  </clause>

  <clause id="4298">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) / x) \ (1 / x)) = K(L(x,y,z),L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,4281,a,b,4297,a)].">
      <j1 rule="hyper" parents="64 4281 4297"/>
    </justification>
  </clause>

  <clause id="4299">
    <literal><![CDATA[
      (L(x,y,z) / x) \ (1 / x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,1724,a(flip),b,4298,a),flip(a)].">
      <j1 rule="hyper" parents="35 1724 4298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4300">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(225,a,4299,a(flip),b,4238,a),flip(a)].">
      <j1 rule="hyper" parents="225 4299 4238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4301">
    <literal><![CDATA[
      1 / (1 / L(x \ 1,y,z)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),4300(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 4300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4302">
    <literal><![CDATA[
      L(1 / (1 / (x \ (y \ z))),x,y) = 1 / (1 / ((y * x) \ z))
    ]]></literal>
    <justification jstring="[para(346(a,1),4300(a,2,2,2))].">
      <j1 rule="para" parents="346 4300"/>
    </justification>
  </clause>

  <clause id="4303">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L((1 / x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(4300(a,1),279(a,1,1))].">
      <j1 rule="para" parents="4300 279"/>
    </justification>
  </clause>

  <clause id="4304">
    <literal><![CDATA[
      L(1 / x,x,y) = 1 / (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(241(a,1),4301(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="241 4301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4305">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(436(a,1),4301(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="436 4301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4306">
    <literal><![CDATA[
      1 / (1 / L(L(x \ 1,y,z),u,w)) = L(L(1 / x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(4301(a,1),4300(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4301 4300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4307">
    <literal><![CDATA[
      L(1 / x,x,y) \ 1 = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(143,a,4304,a,b,171,a)].">
      <j1 rule="hyper" parents="143 4304 171"/>
    </justification>
  </clause>

  <clause id="4308">
    <literal><![CDATA[
      x / L(1 / y,y,x) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(4304(a,2),3947(a,1,2))].">
      <j1 rule="para" parents="4304 3947"/>
    </justification>
  </clause>

  <clause id="4309">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,3549,a,b,4305,a)].">
      <j1 rule="hyper" parents="64 3549 4305"/>
    </justification>
  </clause>

  <clause id="4312">
    <literal><![CDATA[
      L(x,1 / (y \ z),L(1 / (y \ z),y \ z,y)) = L(x,1 / (1 / (z \ y)),1 / (y \ z))
    ]]></literal>
    <justification jstring="[para(4305(a,1),2482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4305 2482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4313">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1162,a,b,4309,a)].">
      <j1 rule="hyper" parents="35 1162 4309"/>
    </justification>
  </clause>

  <clause id="4314">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,(x * y) \ x) = K(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1571,a(flip),b,4313,a),flip(a)].">
      <j1 rule="hyper" parents="373 1571 4313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      K(x / y,y / x) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3828,a(flip),b,4313,a)].">
      <j1 rule="hyper" parents="64 3828 4313"/>
    </justification>
  </clause>

  <clause id="4317">
    <literal><![CDATA[
      ((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,4313,a(flip),b,3637,a)].">
      <j1 rule="hyper" parents="145 4313 3637"/>
    </justification>
  </clause>

  <clause id="4318">
    <literal><![CDATA[
      ((x \ y) \ 1) \ K(y \ x,x \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,4313,a(flip),b,294,a(flip))].">
      <j1 rule="hyper" parents="139 4313 294"/>
    </justification>
  </clause>

  <clause id="4319">
    <literal><![CDATA[
      (x \ y) * (K(y \ x,x \ y) * z) = (1 / (1 / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(4313(a,1),2368(a,1,2,1))].">
      <j1 rule="para" parents="4313 2368"/>
    </justification>
  </clause>

  <clause id="4320">
    <literal><![CDATA[
      K(x \ y,y \ x) * y = x * T(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(4313(a,1),3624(a,1,1))].">
      <j1 rule="para" parents="4313 3624"/>
    </justification>
  </clause>

  <clause id="4321">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3403,a,b,4316,a)].">
      <j1 rule="hyper" parents="64 3403 4316"/>
    </justification>
  </clause>

  <clause id="4322">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3396,a,b,4316,a)].">
      <j1 rule="hyper" parents="64 3396 4316"/>
    </justification>
  </clause>

  <clause id="4323">
    <literal><![CDATA[
      (x / y) \ K(y \ x,x \ y) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(4316(a,1),3404(a,1,2))].">
      <j1 rule="para" parents="4316 3404"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      (1 / (1 / (x / y))) * (z * K(y \ x,x \ y)) = (x / y) * z
    ]]></literal>
    <justification jstring="[para(4321(a,1),3660(a,1,2,2))].">
      <j1 rule="para" parents="4321 3660"/>
    </justification>
  </clause>

  <clause id="4325">
    <literal><![CDATA[
      (x / y) * K(x \ y,y \ x) = 1 / (1 / (x / y))
    ]]></literal>
    <justification jstring="[hyper(145,a,4322,a(flip),b,1161,a)].">
      <j1 rule="hyper" parents="145 4322 1161"/>
    </justification>
  </clause>

  <clause id="4326">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),4303(a,2,1))].">
      <j1 rule="para" parents="82 4303"/>
    </justification>
  </clause>

  <clause id="4327">
    <literal><![CDATA[
      T(T(1 / (1 / L(x,y,z)),u),1 / x) = T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4326(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4326 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4328">
    <literal><![CDATA[
      (x * y) * K(y,(x * y) \ x) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4314(a,1),2457(a,1,2))].">
      <j1 rule="para" parents="4314 2457"/>
    </justification>
  </clause>

  <clause id="4329">
    <literal><![CDATA[
      K(x,(y * x) \ y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,3904,a,b,4328,a),flip(a)].">
      <j1 rule="hyper" parents="35 3904 4328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4330">
    <literal><![CDATA[
      K(x \ (x * y),(z * y) \ z) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,1571,a,b,4329,a)].">
      <j1 rule="hyper" parents="64 1571 4329"/>
    </justification>
  </clause>

  <clause id="4331">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),4329(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 4329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4332">
    <literal><![CDATA[
      K(x,y \ (y / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(12(a,1),4329(a,1,2,1))].">
      <j1 rule="para" parents="12 4329"/>
    </justification>
  </clause>

  <clause id="4333">
    <literal><![CDATA[
      K(x,(y * x) \ y) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(4329(a,2),2371(a,1,1))].">
      <j1 rule="para" parents="4329 2371"/>
    </justification>
  </clause>

  <clause id="4335">
    <literal><![CDATA[
      K((x / y) \ x,z \ (z / y)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,1572,a,b,4332,a)].">
      <j1 rule="hyper" parents="64 1572 4332"/>
    </justification>
  </clause>

  <clause id="4336">
    <literal><![CDATA[
      K((x * y) \ x,((x * y) \ x) \ 1) = K((x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(211(a,1),4332(a,1,2)),flip(a)].">
      <j1 rule="para" parents="211 4332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4337">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * T(y \ (y * x),(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(4330(a,1),4320(a,1,1))].">
      <j1 rule="para" parents="4330 4320"/>
    </justification>
  </clause>

  <clause id="4338">
    <literal><![CDATA[
      (x \ y) * (1 / (x \ y)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(1728,a,4331,a)].">
      <j1 rule="hyper" parents="1728 4331"/>
    </justification>
  </clause>

  <clause id="4339">
    <literal><![CDATA[
      (x \ y) \ K(x \ y,y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,4331,a(flip),b,1724,a(flip))].">
      <j1 rule="hyper" parents="139 4331 1724"/>
    </justification>
  </clause>

  <clause id="4340">
    <literal><![CDATA[
      ((x \ y) \ z) * K(x \ y,y \ x) = (1 / (1 / (x \ y))) \ z
    ]]></literal>
    <justification jstring="[para(4331(a,1),3654(a,1,2))].">
      <j1 rule="para" parents="4331 3654"/>
    </justification>
  </clause>

  <clause id="4341">
    <literal><![CDATA[
      ((x / y) / x) * K(y,y \ 1) = 1 / (1 / ((x / y) / x))
    ]]></literal>
    <justification jstring="[para(4335(a,1),4325(a,1,2))].">
      <j1 rule="para" parents="4335 4325"/>
    </justification>
  </clause>

  <clause id="4342">
    <literal><![CDATA[
      (x * y) * (1 / (1 / ((x * y) \ z))) = x * (y * (1 / (1 / (y \ (x \ z)))))
    ]]></literal>
    <justification jstring="[hyper(145,a,4302,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 4302 18"/>
    </justification>
  </clause>

  <clause id="4343">
    <literal><![CDATA[
      ((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z
    ]]></literal>
    <justification jstring="[para(4335(a,1),4317(a,1,2))].">
      <j1 rule="para" parents="4335 4317"/>
    </justification>
  </clause>

  <clause id="4344">
    <literal><![CDATA[
      (1 / (1 / (x / y))) * (1 / (1 / (y / x))) = (x / y) * (y / x)
    ]]></literal>
    <justification jstring="[para(4325(a,1),4324(a,1,2))].">
      <j1 rule="para" parents="4325 4324"/>
    </justification>
  </clause>

  <clause id="4345">
    <literal><![CDATA[
      x * T(x \ (x * y),(x * y) \ x) = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3889,a(flip),b,4337,a),flip(a)].">
      <j1 rule="hyper" parents="64 3889 4337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4346">
    <literal><![CDATA[
      x * T(x \ (x * y),(x * y) \ x) = x * (y * K(y,y \ 1))
    ]]></literal>
    <justification jstring="[para(1742(a,2),4345(a,2,2))].">
      <j1 rule="para" parents="1742 4345"/>
    </justification>
  </clause>

  <clause id="4347">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) * (y * x) = y * T(y \ (y * x),(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,3618,a,b,4346,a)].">
      <j1 rule="hyper" parents="373 3618 4346"/>
    </justification>
  </clause>

  <clause id="4348">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z
    ]]></literal>
    <justification jstring="[para(1734(a,1),4343(a,1,2))].">
      <j1 rule="para" parents="1734 4343"/>
    </justification>
  </clause>

  <clause id="4349">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(36,a,3624,a,b,4347,a),flip(a)].">
      <j1 rule="hyper" parents="36 3624 4347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4350">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4314,a(flip),b,4349,a),flip(a)].">
      <j1 rule="hyper" parents="373 4314 4349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4351">
    <literal><![CDATA[
      K((x * y) \ x,((x * y) \ x) \ 1) = L(K(y,y \ 1),y,x) \ 1
    ]]></literal>
    <justification jstring="[para(4349(a,2),479(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4349 479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4352">
    <literal><![CDATA[
      K((x * y) \ x,y) = L(K(y,y \ 1),y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,4336,a(flip),b,4351,a)].">
      <j1 rule="hyper" parents="64 4336 4351"/>
    </justification>
  </clause>

  <clause id="4353">
    <literal><![CDATA[
      K(x,(y * x) \ y) \ 1 = K((y * x) \ y,x)
    ]]></literal>
    <justification jstring="[para(4350(a,1),4352(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4350 4352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4354">
    <literal><![CDATA[
      K((x * y) \ x,y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4333,a(flip),b,4353,a),flip(a)].">
      <j1 rule="hyper" parents="64 4333 4353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4356">
    <literal><![CDATA[
      K(x \ (x / y),y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),4354(a,1,1,1))].">
      <j1 rule="para" parents="12 4354"/>
    </justification>
  </clause>

  <clause id="4357">
    <literal><![CDATA[
      K(x \ (x / y),y) = (y \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,294,a(flip),b,4356,a),flip(a)].">
      <j1 rule="hyper" parents="373 294 4356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4358">
    <literal><![CDATA[
      (x * y) * (1 / (1 / ((x * y) \ (x * z)))) = x * (y * (1 / (1 / (y \ z))))
    ]]></literal>
    <justification jstring="[para(9(a,1),4342(a,2,2,2,2,2,2))].">
      <j1 rule="para" parents="9 4342"/>
    </justification>
  </clause>

  <clause id="4359">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(3944(a,1),4348(a,2,1))].">
      <j1 rule="para" parents="3944 4348"/>
    </justification>
  </clause>

  <clause id="4360">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(4359(a,1),3749(a,1,1))].">
      <j1 rule="para" parents="4359 3749"/>
    </justification>
  </clause>

  <clause id="4361">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[para(1484(a,1),4360(a,2,1,2))].">
      <j1 rule="para" parents="1484 4360"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      (x \ (x * y)) * x = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,2993,a(flip),b,4361,a)].">
      <j1 rule="hyper" parents="64 2993 4361"/>
    </justification>
  </clause>

  <clause id="4363">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * y = y * x
    ]]></literal>
    <justification jstring="[para(9(a,1),4362(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 4362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4364">
    <literal><![CDATA[
      x * (y \ T(y,x)) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(154,a,4363,a),flip(a)].">
      <j1 rule="hyper" parents="154 4363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4365">
    <literal><![CDATA[
      (x \ y) * (x \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(142,a,10,a(flip),b,4363,a),flip(a)].">
      <j1 rule="hyper" parents="142 10 4363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4366">
    <literal><![CDATA[
      (x \ T(x,y)) * y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(4028,a,4364,a)].">
      <j1 rule="hyper" parents="4028 4364"/>
    </justification>
  </clause>

  <clause id="4367">
    <literal><![CDATA[
      x \ ((y * x) / y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(149,a,4364,a)].">
      <j1 rule="hyper" parents="149 4364"/>
    </justification>
  </clause>

  <clause id="4368">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,256,a(flip),b,4364,a)].">
      <j1 rule="hyper" parents="139 256 4364"/>
    </justification>
  </clause>

  <clause id="4369">
    <literal><![CDATA[
      (x / y) \ T(x / y,y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(139,a,170,a(flip),b,4364,a),flip(a)].">
      <j1 rule="hyper" parents="139 170 4364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4370">
    <literal><![CDATA[
      ((x * y) / x) / y = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(154,a,4366,a)].">
      <j1 rule="hyper" parents="154 4366"/>
    </justification>
  </clause>

  <clause id="4372">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4366(a,1),210(a,1,2,1))].">
      <j1 rule="para" parents="4366 210"/>
    </justification>
  </clause>

  <clause id="4373">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2487,a,b,4367,a)].">
      <j1 rule="hyper" parents="64 2487 4367"/>
    </justification>
  </clause>

  <clause id="4374">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,4039,a(flip),b,4367,a)].">
      <j1 rule="hyper" parents="64 4039 4367"/>
    </justification>
  </clause>

  <clause id="4375">
    <literal><![CDATA[
      T(x,y) \ x = T(y,T(x,y)) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,4048,a,b,4368,a),flip(a)].">
      <j1 rule="hyper" parents="373 4048 4368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4376">
    <literal><![CDATA[
      x * (T(y,x) \ y) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,4368,a,b,xx)].">
      <j1 rule="hyper" parents="145 4368"/>
    </justification>
  </clause>

  <clause id="4377">
    <literal><![CDATA[
      R(T(x,y) \ x,y,z) = (T(y,T(x,y)) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(4368(a,2),4055(a,1,1))].">
      <j1 rule="para" parents="4368 4055"/>
    </justification>
  </clause>

  <clause id="4378">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[para(4370(a,1),684(a,1,1,1))].">
      <j1 rule="para" parents="4370 684"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      T(x,T(y,x)) / x = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(3984,a,4375,a),flip(a)].">
      <j1 rule="hyper" parents="3984 4375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4381">
    <literal><![CDATA[
      (x \ y) \ (y / x) = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,4365,a(flip),b,862,a(flip))].">
      <j1 rule="hyper" parents="139 4365 862"/>
    </justification>
  </clause>

  <clause id="4383">
    <literal><![CDATA[
      (x / y) \ (y \ x) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[para(117(a,1),4369(a,1,2))].">
      <j1 rule="para" parents="117 4369"/>
    </justification>
  </clause>

  <clause id="4384">
    <literal><![CDATA[
      K(x,(x / y) / x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2804,a,4374,a)].">
      <j1 rule="hyper" parents="2804 4374"/>
    </justification>
  </clause>

  <clause id="4385">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3259,a,b,4374,a)].">
      <j1 rule="hyper" parents="64 3259 4374"/>
    </justification>
  </clause>

  <clause id="4386">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,4294,a(flip),b,4374,a)].">
      <j1 rule="hyper" parents="64 4294 4374"/>
    </justification>
  </clause>

  <clause id="4387">
    <literal><![CDATA[
      x * K(x,(x / y) / x) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,2803,a,b,4374,a(flip))].">
      <j1 rule="hyper" parents="145 2803 4374"/>
    </justification>
  </clause>

  <clause id="4388">
    <literal><![CDATA[
      T(x,x / (x * y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,2748,a,b,4374,a(flip))].">
      <j1 rule="hyper" parents="39 2748 4374"/>
    </justification>
  </clause>

  <clause id="4389">
    <literal><![CDATA[
      x \ T(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(x / y) / x) = z
    ]]></literal>
    <justification jstring="[para(4374(a,1),2804(a,1))].">
      <j1 rule="para" parents="4374 2804"/>
    </justification>
  </clause>

  <clause id="4390">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x)
    ]]></literal>
    <justification jstring="[para(4374(a,1),3305(a,1,1))].">
      <j1 rule="para" parents="4374 3305"/>
    </justification>
  </clause>

  <clause id="4391">
    <literal><![CDATA[
      K(x,(x / y) / x) * (y * z) = y * ((x \ T(x,y \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(4374(a,1),3333(a,2,2,1))].">
      <j1 rule="para" parents="4374 3333"/>
    </justification>
  </clause>

  <clause id="4392">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(4374(a,1),3307(a,2,2,1))].">
      <j1 rule="para" parents="4374 3307"/>
    </justification>
  </clause>

  <clause id="4393">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3298,a,4388,a)].">
      <j1 rule="hyper" parents="3298 4388"/>
    </justification>
  </clause>

  <clause id="4394">
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3296,a,4388,a)].">
      <j1 rule="hyper" parents="3296 4388"/>
    </justification>
  </clause>

  <clause id="4395">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,4103,a,b,4388,a)].">
      <j1 rule="hyper" parents="64 4103 4388"/>
    </justification>
  </clause>

  <clause id="4396">
    <literal><![CDATA[
      T(x,y \ 1) / y = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(142,a,4388,a(flip),b,3295,a)].">
      <j1 rule="hyper" parents="142 4388 3295"/>
    </justification>
  </clause>

  <clause id="4397">
    <literal><![CDATA[
      (x * ((x / y) / x)) \ T(x,y \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(139,a,4388,a(flip),b,3295,a)].">
      <j1 rule="hyper" parents="139 4388 3295"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1766,a,4395,a)].">
      <j1 rule="hyper" parents="1766 4395"/>
    </justification>
  </clause>

  <clause id="4399">
    <literal><![CDATA[
      x \ T(y,x \ 1) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,4395,a(flip),b,1765,a)].">
      <j1 rule="hyper" parents="139 4395 1765"/>
    </justification>
  </clause>

  <clause id="4400">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,(y \ x) / x)
    ]]></literal>
    <justification jstring="[para(301(a,1),4387(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="301 4387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4401">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x * ((x / (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(142,a,3871,a(flip),b,4393,a)].">
      <j1 rule="hyper" parents="142 3871 4393"/>
    </justification>
  </clause>

  <clause id="4402">
    <literal><![CDATA[
      x \ (T(x,y \ 1) / y) = (x / y) / x
    ]]></literal>
    <justification jstring="[hyper(139,a,4396,a,b,xx)].">
      <j1 rule="hyper" parents="139 4396"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),4396(a,2,2,1))].">
      <j1 rule="para" parents="79 4396"/>
    </justification>
  </clause>

  <clause id="4404">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x * ((x / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(82(a,1),4396(a,1,1,2))].">
      <j1 rule="para" parents="82 4396"/>
    </justification>
  </clause>

  <clause id="4405">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[para(4396(a,2),241(a,2,1))].">
      <j1 rule="para" parents="4396 241"/>
    </justification>
  </clause>

  <clause id="4406">
    <literal><![CDATA[
      a(((x * ((x / y) / x)) \ T(x,y \ 1)) \ T(x,y \ 1),z,u) = a(T(x * ((x / y) / x),y),z,u)
    ]]></literal>
    <justification jstring="[para(4397(a,1),2668(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4397 2668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4407">
    <literal><![CDATA[
      (x \ 1) \ T(y,x) = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,3871,a(flip),b,4398,a)].">
      <j1 rule="hyper" parents="139 3871 4398"/>
    </justification>
  </clause>

  <clause id="4408">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),4398(a,1,2,2,1))].">
      <j1 rule="para" parents="9 4398"/>
    </justification>
  </clause>

  <clause id="4409">
    <literal><![CDATA[
      x \ (y \ T(x,y \ 1)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[para(4398(a,1),69(a,1,2,2))].">
      <j1 rule="para" parents="4398 69"/>
    </justification>
  </clause>

  <clause id="4410">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(82(a,1),4399(a,2,2,1))].">
      <j1 rule="para" parents="82 4399"/>
    </justification>
  </clause>

  <clause id="4411">
    <literal><![CDATA[
      x \ (T(x,1 / y) / y) = (x / y) / x
    ]]></literal>
    <justification jstring="[para(3870(a,2),4402(a,1,2,1))].">
      <j1 rule="para" parents="3870 4402"/>
    </justification>
  </clause>

  <clause id="4413">
    <literal><![CDATA[
      (((x / y) \ 1) \ y) * ((x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1491,a(flip),b,4410,a)].">
      <j1 rule="hyper" parents="64 1491 4410"/>
    </justification>
  </clause>

  <clause id="4414">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,4384,a(flip),b,4390,a),flip(a)].">
      <j1 rule="hyper" parents="373 4384 4390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4415">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ x) / x) = z
    ]]></literal>
    <justification jstring="[para(4400(a,2),44(a,1))].">
      <j1 rule="para" parents="4400 44"/>
    </justification>
  </clause>

  <clause id="4416">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(35,a,1181,a,b,4408,a)].">
      <j1 rule="hyper" parents="35 1181 4408"/>
    </justification>
  </clause>

  <clause id="4417">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(((y / x) \ 1) \ x,(y / x) \ 1) = z
    ]]></literal>
    <justification jstring="[para(4413(a,1),545(a,1,2))].">
      <j1 rule="para" parents="4413 545"/>
    </justification>
  </clause>

  <clause id="4418">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = x \ T(x,R(z \ 1,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(4092(a,1),4414(a,2,2,2,1))].">
      <j1 rule="para" parents="4092 4414"/>
    </justification>
  </clause>

  <clause id="4419">
    <literal><![CDATA[
      ((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,3921,a(flip),b,4416,a),flip(a)].">
      <j1 rule="hyper" parents="64 3921 4416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4420">
    <literal><![CDATA[
      ((x \ 1) * y) * R(x,x \ 1,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(239(a,2),4419(a,1,2))].">
      <j1 rule="para" parents="239 4419"/>
    </justification>
  </clause>

  <clause id="4421">
    <literal><![CDATA[
      ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,4420,a(flip),b,1202,a),flip(a)].">
      <j1 rule="hyper" parents="142 4420 1202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4422">
    <literal><![CDATA[
      L((T(x,T(y,x)) * z) / (x * z),T(y,x),x) = R((y * x) \ (x * y),x,z)
    ]]></literal>
    <justification jstring="[para(4377(a,1),1317(a,1,1))].">
      <j1 rule="para" parents="4377 1317"/>
    </justification>
  </clause>

  <clause id="4423">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4374(a,1),4386(a,1,1))].">
      <j1 rule="para" parents="4374 4386"/>
    </justification>
  </clause>

  <clause id="4424">
    <literal><![CDATA[
      (x \ T(x,y \ 1)) * (y * z) = y * ((x \ T(x,y \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(4384(a,1),4391(a,1,1))].">
      <j1 rule="para" parents="4384 4391"/>
    </justification>
  </clause>

  <clause id="4425">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,4373,a(flip),b,4421,a)].">
      <j1 rule="hyper" parents="64 4373 4421"/>
    </justification>
  </clause>

  <clause id="4426">
    <literal><![CDATA[
      L(K(x \ y,x),y,x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,3436,a(flip),b,4425,a)].">
      <j1 rule="hyper" parents="64 3436 4425"/>
    </justification>
  </clause>

  <clause id="4427">
    <literal><![CDATA[
      ((x \ (x * y)) * x) / (x * y) = L(K(y,x),x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),4426(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 4426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4428">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4427(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 4427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4429">
    <literal><![CDATA[
      L((T(x,T(y,x)) * z) / (x * z),T(y,x),x) = R(K(x,y),x,z)
    ]]></literal>
    <justification jstring="[para(16(a,2),4422(a,2,1))].">
      <j1 rule="para" parents="16 4422"/>
    </justification>
  </clause>

  <clause id="4430">
    <literal><![CDATA[
      ((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(4255,a,4392,a)].">
      <j1 rule="hyper" parents="4255 4392"/>
    </justification>
  </clause>

  <clause id="4431">
    <literal><![CDATA[
      x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(4393(a,1),4430(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4393 4430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4432">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z))
    ]]></literal>
    <justification jstring="[para(3871(a,1),4431(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3871 4431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4433">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(3871(a,1),4432(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3871 4432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4434">
    <literal><![CDATA[
      T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),4433(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 4433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4435">
    <literal><![CDATA[
      (T(x,y) * z) / ((x \ T(x,y)) * z) = x
    ]]></literal>
    <justification jstring="[hyper(785,a,4434,a)].">
      <j1 rule="hyper" parents="785 4434"/>
    </justification>
  </clause>

  <clause id="4436">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(739,a,4434,a),flip(a)].">
      <j1 rule="hyper" parents="739 4434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4437">
    <literal><![CDATA[
      R(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(1029,a,4435,a)].">
      <j1 rule="hyper" parents="1029 4435"/>
    </justification>
  </clause>

  <clause id="4438">
    <literal><![CDATA[
      (x \ T(x,y)) * z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(37,a,2400,a,b,4435,a),flip(a)].">
      <j1 rule="hyper" parents="37 2400 4435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4439">
    <literal><![CDATA[
      R(x,T(y,x) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(4368(a,2),4437(a,1,2))].">
      <j1 rule="para" parents="4368 4437"/>
    </justification>
  </clause>

  <clause id="4440">
    <literal><![CDATA[
      R(x,K(y,x) \ 1,z) = x
    ]]></literal>
    <justification jstring="[para(4120(a,1),4439(a,1,2))].">
      <j1 rule="para" parents="4120 4439"/>
    </justification>
  </clause>

  <clause id="4441">
    <literal><![CDATA[
      R(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,2975,a(flip),b,4440,a)].">
      <j1 rule="hyper" parents="64 2975 4440"/>
    </justification>
  </clause>

  <clause id="4442">
    <literal><![CDATA[
      (x * K(y,x)) * z = x * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,4441,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 4441 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4443">
    <literal><![CDATA[
      (T(x,y) * K(z,x)) * u = T(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(4441(a,1),511(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4441 511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4444">
    <literal><![CDATA[
      (R(x,y,z) * K(u,x)) * w = R(x,y,z) * (K(u,x) * w)
    ]]></literal>
    <justification jstring="[para(4441(a,1),506(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4441 506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4445">
    <literal><![CDATA[
      L(x,y \ T(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(1011,a,4436,a)].">
      <j1 rule="hyper" parents="1011 4436"/>
    </justification>
  </clause>

  <clause id="4448">
    <literal><![CDATA[
      (x \ T(x,y)) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(35,a,2403,a(flip),b,4436,a),flip(a)].">
      <j1 rule="hyper" parents="35 2403 4436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4450">
    <literal><![CDATA[
      T(x,y) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(4366(a,1),4436(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4366 4436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4451">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(4368(a,2),4436(a,1,2,1))].">
      <j1 rule="para" parents="4368 4436"/>
    </justification>
  </clause>

  <clause id="4453">
    <literal><![CDATA[
      x \ (T(x,y) * y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(720,a,4450,a)].">
      <j1 rule="hyper" parents="720 4450"/>
    </justification>
  </clause>

  <clause id="4454">
    <literal><![CDATA[
      T(x,x / (x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,2599,a,b,4450,a)].">
      <j1 rule="hyper" parents="36 2599 4450"/>
    </justification>
  </clause>

  <clause id="4455">
    <literal><![CDATA[
      T(x,y) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(35,a,2399,a,b,4450,a(flip))].">
      <j1 rule="hyper" parents="35 2399 4450"/>
    </justification>
  </clause>

  <clause id="4456">
    <literal><![CDATA[
      T(x,x \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),4450(a,2,2,1))].">
      <j1 rule="para" parents="10 4450"/>
    </justification>
  </clause>

  <clause id="4457">
    <literal><![CDATA[
      T(x / y,y) * y = (x / y) * (x / (x / y))
    ]]></literal>
    <justification jstring="[para(12(a,1),4450(a,2,2,1))].">
      <j1 rule="para" parents="12 4450"/>
    </justification>
  </clause>

  <clause id="4458">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,1587,a(flip),b,4454,a)].">
      <j1 rule="hyper" parents="64 1587 4454"/>
    </justification>
  </clause>

  <clause id="4459">
    <literal><![CDATA[
      T(x,T(y,x)) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,4454,a(flip),b,2539,a(flip))].">
      <j1 rule="hyper" parents="144 4454 2539"/>
    </justification>
  </clause>

  <clause id="4460">
    <literal><![CDATA[
      T(x,y) / ((x * y) / x) = x / y
    ]]></literal>
    <justification jstring="[hyper(142,a,4454,a(flip),b,1582,a)].">
      <j1 rule="hyper" parents="142 4454 1582"/>
    </justification>
  </clause>

  <clause id="4461">
    <literal><![CDATA[
      T(x,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(79(a,1),4454(a,1,2,2))].">
      <j1 rule="para" parents="79 4454"/>
    </justification>
  </clause>

  <clause id="4462">
    <literal><![CDATA[
      T(x,(y \ x) \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(216(a,1),4454(a,1,2)),flip(a)].">
      <j1 rule="para" parents="216 4454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4463">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1580,a,b,4461,a)].">
      <j1 rule="hyper" parents="64 1580 4461"/>
    </justification>
  </clause>

  <clause id="4464">
    <literal><![CDATA[
      x \ T(y,x \ y) = (y * (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(139,a,4461,a(flip),b,1580,a)].">
      <j1 rule="hyper" parents="139 4461 1580"/>
    </justification>
  </clause>

  <clause id="4465">
    <literal><![CDATA[
      T(T(x,y \ x) / y,x) = x / y
    ]]></literal>
    <justification jstring="[para(4461(a,1),1577(a,1,1,1))].">
      <j1 rule="para" parents="4461 1577"/>
    </justification>
  </clause>

  <clause id="4466">
    <literal><![CDATA[
      T(x \ T(y,x \ y),y) = x \ y
    ]]></literal>
    <justification jstring="[para(4461(a,1),1585(a,1,1,2))].">
      <j1 rule="para" parents="4461 1585"/>
    </justification>
  </clause>

  <clause id="4467">
    <literal><![CDATA[
      T(x,T(y,y \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(116(a,2),4462(a,1,2))].">
      <j1 rule="para" parents="116 4462"/>
    </justification>
  </clause>

  <clause id="4468">
    <literal><![CDATA[
      T(x * y,T(x,y)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(366(a,2),4462(a,1,2))].">
      <j1 rule="para" parents="366 4462"/>
    </justification>
  </clause>

  <clause id="4469">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,4453,a(flip),b,2401,a(flip))].">
      <j1 rule="hyper" parents="139 4453 2401"/>
    </justification>
  </clause>

  <clause id="4470">
    <literal><![CDATA[
      T(x / y,T(y,x)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(269,a,2513,a,b,4455,a)].">
      <j1 rule="hyper" parents="269 2513 4455"/>
    </justification>
  </clause>

  <clause id="4471">
    <literal><![CDATA[
      T(x,T(y,x * y)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(269,a,1066,a(flip),b,4455,a)].">
      <j1 rule="hyper" parents="269 1066 4455"/>
    </justification>
  </clause>

  <clause id="4472">
    <literal><![CDATA[
      (x / y) / (y \ (y \ x)) = T(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(142,a,171,a(flip),b,4455,a)].">
      <j1 rule="hyper" parents="142 171 4455"/>
    </justification>
  </clause>

  <clause id="4473">
    <literal><![CDATA[
      T(x,x \ y) \ (y / x) = x \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,171,a(flip),b,4455,a)].">
      <j1 rule="hyper" parents="139 171 4455"/>
    </justification>
  </clause>

  <clause id="4474">
    <literal><![CDATA[
      ((x * (x * y)) / x) / y = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(142,a,4455,a(flip),b,169,a(flip))].">
      <j1 rule="hyper" parents="142 4455 169"/>
    </justification>
  </clause>

  <clause id="4475">
    <literal><![CDATA[
      T(T(x,y) * (x \ y),x) = y
    ]]></literal>
    <justification jstring="[para(4455(a,2),255(a,1,1))].">
      <j1 rule="para" parents="4455 255"/>
    </justification>
  </clause>

  <clause id="4476">
    <literal><![CDATA[
      T(T(x / y,z),T(y,x)) = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4470(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4470 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4477">
    <literal><![CDATA[
      T(x / y,z) * T(y,x) = T(y,x) * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4470(a,1),265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4470 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4478">
    <literal><![CDATA[
      T(T(x,x * y) * y,x) = x * y
    ]]></literal>
    <justification jstring="[para(9(a,1),4475(a,1,1,2))].">
      <j1 rule="para" parents="9 4475"/>
    </justification>
  </clause>

  <clause id="4479">
    <literal><![CDATA[
      T(x / T(y,x),y) = T(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(269,a,4458,a,b,2498,a)].">
      <j1 rule="hyper" parents="269 4458 2498"/>
    </justification>
  </clause>

  <clause id="4480">
    <literal><![CDATA[
      ((x * y) * y) / (x * y) = x \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,205,a(flip),b,4460,a),flip(a)].">
      <j1 rule="hyper" parents="37 205 4460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4481">
    <literal><![CDATA[
      T(T(x * y,z),T(x,y)) = T(T(x * y,x),z)
    ]]></literal>
    <justification jstring="[para(4468(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4468 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4482">
    <literal><![CDATA[
      T(T(x,y),x) * L(T(T(x,y),x) \ y,z,u) = T(T(x,y) * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[para(4469(a,1),3284(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4469 3284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4483">
    <literal><![CDATA[
      T(x,T(y,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,22,a,b,4471,a),flip(a)].">
      <j1 rule="hyper" parents="373 22 4471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4484">
    <literal><![CDATA[
      T(T(x / T(y,x),z),y) = T(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[para(4479(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4479 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4485">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,169,a(flip),b,4438,a)].">
      <j1 rule="hyper" parents="142 169 4438"/>
    </justification>
  </clause>

  <clause id="4486">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(139,a,169,a(flip),b,4438,a)].">
      <j1 rule="hyper" parents="139 169 4438"/>
    </justification>
  </clause>

  <clause id="4487">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,74,a(flip),b,4438,a)].">
      <j1 rule="hyper" parents="139 74 4438"/>
    </justification>
  </clause>

  <clause id="4488">
    <literal><![CDATA[
      T(x,y \ 1) * (x \ (y * z)) = y * ((x \ T(x,y \ 1)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4424,a(flip),b,4438,a),flip(a)].">
      <j1 rule="hyper" parents="64 4424 4438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4489">
    <literal><![CDATA[
      T(x,y) * (x \ (z * K(x \ 1,x))) = ((x \ 1) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,4178,a(flip),b,4438,a),flip(a)].">
      <j1 rule="hyper" parents="64 4178 4438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4490">
    <literal><![CDATA[
      L(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(606,a,4442,a)].">
      <j1 rule="hyper" parents="606 4442"/>
    </justification>
  </clause>

  <clause id="4491">
    <literal><![CDATA[
      L(x,K(y,z \ 1),z) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,1630,a,b,4442,a)].">
      <j1 rule="hyper" parents="35 1630 4442"/>
    </justification>
  </clause>

  <clause id="4492">
    <literal><![CDATA[
      ((x \ 1) * K(y,x)) \ z = K(y,x) \ ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1633,a(flip),b,4490,a)].">
      <j1 rule="hyper" parents="64 1633 4490"/>
    </justification>
  </clause>

  <clause id="4493">
    <literal><![CDATA[
      L(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4490(a,1),51(a,2))].">
      <j1 rule="para" parents="4490 51"/>
    </justification>
  </clause>

  <clause id="4494">
    <literal><![CDATA[
      (x * K(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,x) * z) = u
    ]]></literal>
    <justification jstring="[para(4490(a,1),334(a,1,2))].">
      <j1 rule="para" parents="4490 334"/>
    </justification>
  </clause>

  <clause id="4495">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = x * (K(y,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(1960,a,4491,a),flip(a)].">
      <j1 rule="hyper" parents="1960 4491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4496">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,x \ 1) * z) = u
    ]]></literal>
    <justification jstring="[para(4491(a,1),334(a,1,2))].">
      <j1 rule="para" parents="4491 334"/>
    </justification>
  </clause>

  <clause id="4497">
    <literal><![CDATA[
      L(x,K(y,z),1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(1643(a,2),4493(a,1))].">
      <j1 rule="para" parents="1643 4493"/>
    </justification>
  </clause>

  <clause id="4498">
    <literal><![CDATA[
      L(x,y,y \ T(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4062,a,4448,a(flip))].">
      <j1 rule="hyper" parents="4062 4448"/>
    </justification>
  </clause>

  <clause id="4499">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(4448(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4448 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4500">
    <literal><![CDATA[
      L(x,y,T(z,y) \ z) = x
    ]]></literal>
    <justification jstring="[para(4368(a,2),4498(a,1,3))].">
      <j1 rule="para" parents="4368 4498"/>
    </justification>
  </clause>

  <clause id="4501">
    <literal><![CDATA[
      L(x,y,K(z,y) \ 1) = x
    ]]></literal>
    <justification jstring="[para(4120(a,1),4500(a,1,3))].">
      <j1 rule="para" parents="4120 4500"/>
    </justification>
  </clause>

  <clause id="4502">
    <literal><![CDATA[
      L(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(2275,a,4501,a)].">
      <j1 rule="hyper" parents="2275 4501"/>
    </justification>
  </clause>

  <clause id="4503">
    <literal><![CDATA[
      (K(x,y) * y) * z = K(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1960,a,4502,a),flip(a)].">
      <j1 rule="hyper" parents="1960 4502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4504">
    <literal><![CDATA[
      L(x,y,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4502(a,1),51(a,2))].">
      <j1 rule="para" parents="4502 51"/>
    </justification>
  </clause>

  <clause id="4505">
    <literal><![CDATA[
      L(x,y,T(z,y) / z) = x
    ]]></literal>
    <justification jstring="[para(1884(a,1),4502(a,1,3))].">
      <j1 rule="para" parents="1884 4502"/>
    </justification>
  </clause>

  <clause id="4506">
    <literal><![CDATA[
      L(x,T(y,z),y / T(y,z)) = x
    ]]></literal>
    <justification jstring="[para(4379(a,1),4505(a,1,3))].">
      <j1 rule="para" parents="4379 4505"/>
    </justification>
  </clause>

  <clause id="4507">
    <literal><![CDATA[
      ((x \ y) \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(869,a,4456,a)].">
      <j1 rule="hyper" parents="869 4456"/>
    </justification>
  </clause>

  <clause id="4508">
    <literal><![CDATA[
      T(x,x \ (y \ x)) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,4399,a,b,4456,a)].">
      <j1 rule="hyper" parents="139 4399 4456"/>
    </justification>
  </clause>

  <clause id="4509">
    <literal><![CDATA[
      (x \ T(x,x \ y)) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4438,a,b,4456,a)].">
      <j1 rule="hyper" parents="64 4438 4456"/>
    </justification>
  </clause>

  <clause id="4510">
    <literal><![CDATA[
      T(x \ T(y,x \ y),x) = R(x \ y,x,x \ y)
    ]]></literal>
    <justification jstring="[para(4464(a,2),1032(a,1,1))].">
      <j1 rule="para" parents="4464 1032"/>
    </justification>
  </clause>

  <clause id="4511">
    <literal><![CDATA[
      ((x \ y) \ y) \ (y / x) = x \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(906,a,4473,a)].">
      <j1 rule="hyper" parents="906 4473"/>
    </justification>
  </clause>

  <clause id="4512">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(4474(a,1),2541(a,1,1))].">
      <j1 rule="para" parents="4474 2541"/>
    </justification>
  </clause>

  <clause id="4513">
    <literal><![CDATA[
      ((R(x \ 1,x,y) * (x \ y)) / R(x \ 1,x,y)) / y = T(R(x \ 1,x,y),R(x \ 1,x,y) * y)
    ]]></literal>
    <justification jstring="[para(2998(a,1),4474(a,1,1,1,2))].">
      <j1 rule="para" parents="2998 4474"/>
    </justification>
  </clause>

  <clause id="4514">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4063,a,4485,a)].">
      <j1 rule="hyper" parents="4063 4485"/>
    </justification>
  </clause>

  <clause id="4515">
    <literal><![CDATA[
      R(K(x,y),x,z) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4485(a,1),4429(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4485 4429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4517">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = (y / x) \ T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4131,a(flip),b,4514,a)].">
      <j1 rule="hyper" parents="64 4131 4514"/>
    </justification>
  </clause>

  <clause id="4518">
    <literal><![CDATA[
      (x \ T(x,y)) \ y = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,2498,a(flip),b,4487,a),flip(a)].">
      <j1 rule="hyper" parents="373 2498 4487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4519">
    <literal><![CDATA[
      T(x,T(y,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,3985,a,b,4518,a)].">
      <j1 rule="hyper" parents="40 3985 4518"/>
    </justification>
  </clause>

  <clause id="4520">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ y = T(y,T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(4052(a,1),4518(a,1,1))].">
      <j1 rule="para" parents="4052 4518"/>
    </justification>
  </clause>

  <clause id="4521">
    <literal><![CDATA[
      (x * (T(y,x) \ y)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4376(a,2),4519(a,1,1))].">
      <j1 rule="para" parents="4376 4519"/>
    </justification>
  </clause>

  <clause id="4522">
    <literal><![CDATA[
      L(x,T(y,T(z,y)) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(4519(a,2),4445(a,1,2))].">
      <j1 rule="para" parents="4519 4445"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      L(x,T(y,z) \ y,(y * z) / y) = x
    ]]></literal>
    <justification jstring="[para(255(a,1),4522(a,1,2,1,2))].">
      <j1 rule="para" parents="255 4522"/>
    </justification>
  </clause>

  <clause id="4524">
    <literal><![CDATA[
      R(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(664,a,4503,a)].">
      <j1 rule="hyper" parents="664 4503"/>
    </justification>
  </clause>

  <clause id="4525">
    <literal><![CDATA[
      (x * K(y,x)) * z = K(y,x) * (x * z)
    ]]></literal>
    <justification jstring="[para(3994(a,1),4503(a,1,1))].">
      <j1 rule="para" parents="3994 4503"/>
    </justification>
  </clause>

  <clause id="4526">
    <literal><![CDATA[
      R(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2975,a,b,4524,a)].">
      <j1 rule="hyper" parents="64 2975 4524"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      x / (y \ T(y,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(226,a,4521,a)].">
      <j1 rule="hyper" parents="226 4521"/>
    </justification>
  </clause>

  <clause id="4528">
    <literal><![CDATA[
      (x * (T(y,x) \ y)) \ 1 = x \ (y \ T(y,x))
    ]]></literal>
    <justification jstring="[para(4521(a,1),4125(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4521 4125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4529">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * x) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[para(4521(a,1),4130(a,1,1,2))].">
      <j1 rule="para" parents="4521 4130"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      (x * K(y,x)) * (x \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,168,a(flip),b,4525,a),flip(a)].">
      <j1 rule="hyper" parents="373 168 4525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4531">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,1 / x) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,81,a(flip),b,4525,a),flip(a)].">
      <j1 rule="hyper" parents="142 81 4525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4532">
    <literal><![CDATA[
      (x * K(y,x)) \ z = x \ (K(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,75,a(flip),b,4525,a)].">
      <j1 rule="hyper" parents="139 75 4525"/>
    </justification>
  </clause>

  <clause id="4533">
    <literal><![CDATA[
      (x * K(y,x)) \ K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,72,a(flip),b,4525,a)].">
      <j1 rule="hyper" parents="139 72 4525"/>
    </justification>
  </clause>

  <clause id="4534">
    <literal><![CDATA[
      K(x,y) * (y * z) = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4442,a(flip),b,4525,a),flip(a)].">
      <j1 rule="hyper" parents="64 4442 4525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4535">
    <literal><![CDATA[
      (x * K(y,x)) * (x \ 1) != z * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) / u = z
    ]]></literal>
    <justification jstring="[para(4533(a,1),392(a,1,2))].">
      <j1 rule="para" parents="4533 392"/>
    </justification>
  </clause>

  <clause id="4537">
    <literal><![CDATA[
      x / ((((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x))) = x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1))
    ]]></literal>
    <justification jstring="[para(1520(a,1),4527(a,1,2,2))].">
      <j1 rule="para" parents="1520 4527"/>
    </justification>
  </clause>

  <clause id="4539">
    <literal><![CDATA[
      K(x,y) \ (y * z) = y * (K(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,4534,a)].">
      <j1 rule="hyper" parents="139 168 4534"/>
    </justification>
  </clause>

  <clause id="4540">
    <literal><![CDATA[
      R(K(x,y),y * z,u) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,4534,a(flip),b,350,a),flip(a)].">
      <j1 rule="hyper" parents="144 4534 350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4542">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(4534(a,1),397(a,1))].">
      <j1 rule="para" parents="4534 397"/>
    </justification>
  </clause>

  <clause id="4543">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ (K(y,x) * (x * (z * u))) = L(L(u,z,x),x * z,K(y,x))
    ]]></literal>
    <justification jstring="[para(4534(a,1),602(a,1,1))].">
      <j1 rule="para" parents="4534 602"/>
    </justification>
  </clause>

  <clause id="4544">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,4458,a(flip),b,4512,a),flip(a)].">
      <j1 rule="hyper" parents="373 4458 4512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4545">
    <literal><![CDATA[
      (T(x,y) \ x) * (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(35,a,4459,a(flip),b,4451,a),flip(a)].">
      <j1 rule="hyper" parents="35 4459 4451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4546">
    <literal><![CDATA[
      K(x,y) = T(T(y,x) \ y,y * x)
    ]]></literal>
    <justification jstring="[hyper(269,a,4545,a,b,94,a),flip(a)].">
      <j1 rule="hyper" parents="269 4545 94"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4547">
    <literal><![CDATA[
      (x * y) / (y * x) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(154,a,4545,a)].">
      <j1 rule="hyper" parents="154 4545"/>
    </justification>
  </clause>

  <clause id="4548">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = (y * (x / y)) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),4547(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 4547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4549">
    <literal><![CDATA[
      x \ y != (z * y) / (y * z)
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = x
    ]]></literal>
    <justification jstring="[para(4547(a,2),49(a,1)),flip(a)].">
      <j1 rule="para" parents="4547 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4550">
    <literal><![CDATA[
      (x / y) * (x / (x / y)) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(117(a,1),4457(a,1,1)),flip(a)].">
      <j1 rule="para" parents="117 4457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4552">
    <literal><![CDATA[
      T(x \ T(x * y,y),x) = R(y,x,y)
    ]]></literal>
    <justification jstring="[para(4480(a,1),1039(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4480 1039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4553">
    <literal><![CDATA[
      (x * (y / x)) / y = (x \ y) \ (y / x)
    ]]></literal>
    <justification jstring="[para(117(a,1),4548(a,1,1)),flip(a)].">
      <j1 rule="para" parents="117 4548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4554">
    <literal><![CDATA[
      (x * (y / x)) / y = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4381,a(flip),b,4553,a),flip(a)].">
      <j1 rule="hyper" parents="373 4381 4553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4555">
    <literal><![CDATA[
      x \ ((x \ (y \ x)) \ (y \ x)) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,4385,a(flip),b,4554,a),flip(a)].">
      <j1 rule="hyper" parents="64 4385 4554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4556">
    <literal><![CDATA[
      K(x,y) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      y * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(4525(a,1),4494(a,1))].">
      <j1 rule="para" parents="4525 4494"/>
    </justification>
  </clause>

  <clause id="4557">
    <literal><![CDATA[
      (x \ T(x,y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),4499(a,1,2))].">
      <j1 rule="para" parents="10 4499"/>
    </justification>
  </clause>

  <clause id="4558">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * (T(y,x) \ x) = z
    ]]></literal>
    <justification jstring="[para(4518(a,1),4557(a,1))].">
      <j1 rule="para" parents="4518 4557"/>
    </justification>
  </clause>

  <clause id="4559">
    <literal><![CDATA[
      T(x,y) * T(x \ y,x) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(117(a,1),4477(a,1,1)),flip(a)].">
      <j1 rule="para" parents="117 4477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4560">
    <literal><![CDATA[
      K(x,y) \ ((y \ 1) \ z) = (y \ K(x,y)) \ z
    ]]></literal>
    <justification jstring="[para(4026(a,1),4492(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4026 4492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4562">
    <literal><![CDATA[
      L(x \ T(x,T(y,x)),T(y,x),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4515(a,1),432(a,1)),flip(b)].">
      <j1 rule="para" parents="4515 432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4564">
    <literal><![CDATA[
      ((x \ y) / y) \ T((x \ y) / y,z) = x * T(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(2716,a,4517,a),flip(a)].">
      <j1 rule="hyper" parents="2716 4517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4567">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ x = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,4129,a(flip),b,4529,a(flip))].">
      <j1 rule="hyper" parents="35 4129 4529"/>
    </justification>
  </clause>

  <clause id="4568">
    <literal><![CDATA[
      ((x * y) / x) \ y = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(4364(a,1),4567(a,1,1))].">
      <j1 rule="para" parents="4364 4567"/>
    </justification>
  </clause>

  <clause id="4569">
    <literal><![CDATA[
      T(x,x \ y) \ x = (y / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(4365(a,1),4567(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4365 4567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4570">
    <literal><![CDATA[
      (((x * y) / x) * T(((x * y) / x) \ z,y)) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(4568(a,1),1817(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4568 1817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4571">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(4568(a,1),2493(a,1,2,2,1))].">
      <j1 rule="para" parents="4568 2493"/>
    </justification>
  </clause>

  <clause id="4572">
    <literal><![CDATA[
      (T(x,y) \ x) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[para(4568(a,1),4101(a,1,1))].">
      <j1 rule="para" parents="4568 4101"/>
    </justification>
  </clause>

  <clause id="4573">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(36,a,4217,a,b,4572,a)].">
      <j1 rule="hyper" parents="36 4217 4572"/>
    </justification>
  </clause>

  <clause id="4574">
    <literal><![CDATA[
      T(x,x \ y) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,4383,a(flip),b,4569,a),flip(a)].">
      <j1 rule="hyper" parents="373 4383 4569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4575">
    <literal><![CDATA[
      T(x,x \ (y \ x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(864,a,4555,a)].">
      <j1 rule="hyper" parents="864 4555"/>
    </justification>
  </clause>

  <clause id="4576">
    <literal><![CDATA[
      (x \ y) / T(y,x \ 1) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(225,a,4575,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 4575 116"/>
    </justification>
  </clause>

  <clause id="4577">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x,y \ 1) = y \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,4575,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="145 4575 116"/>
    </justification>
  </clause>

  <clause id="4578">
    <literal><![CDATA[
      T(x * y,(x * y) \ y) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),4575(a,1,2,2))].">
      <j1 rule="para" parents="9 4575"/>
    </justification>
  </clause>

  <clause id="4579">
    <literal><![CDATA[
      T(x,(x / y) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(82(a,1),4575(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 4575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4581">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(4575(a,1),4574(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4575 4574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4582">
    <literal><![CDATA[
      (1 / (x / y)) * T(x,x \ y) = x * (1 / (x / y))
    ]]></literal>
    <justification jstring="[para(4579(a,1),3873(a,1,2))].">
      <j1 rule="para" parents="4579 3873"/>
    </justification>
  </clause>

  <clause id="4583">
    <literal><![CDATA[
      (x / y) \ T(x,x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4579(a,1),4410(a,1,2))].">
      <j1 rule="para" parents="4579 4410"/>
    </justification>
  </clause>

  <clause id="4584">
    <literal><![CDATA[
      ((x \ 1) \ y) / T(y,x) = y \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(3871(a,1),4576(a,1,2))].">
      <j1 rule="para" parents="3871 4576"/>
    </justification>
  </clause>

  <clause id="4585">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) \ ((x * y) / x)) = (x \ y) / T((x * y) / x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(4469(a,1),4576(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4469 4576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4586">
    <literal><![CDATA[
      ((x * y) \ (y \ (x * y))) * T(x * y,y \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,22,a,b,4577,a),flip(a)].">
      <j1 rule="hyper" parents="373 22 4577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4587">
    <literal><![CDATA[
      (x \ ((1 / y) \ x)) * T(x,y) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(82(a,1),4577(a,1,2,2))].">
      <j1 rule="para" parents="82 4577"/>
    </justification>
  </clause>

  <clause id="4588">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,x \ (y * x)) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),4583(a,2,2))].">
      <j1 rule="para" parents="11 4583"/>
    </justification>
  </clause>

  <clause id="4589">
    <literal><![CDATA[
      ((x / y) * ((x * (y / x)) / T(x,x \ y))) * ((x / y) \ 1) = R(1 / (x / y),x / y,(x / y) \ T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(4583(a,1),2313(a,1,1,2,1))].">
      <j1 rule="para" parents="4583 2313"/>
    </justification>
  </clause>

  <clause id="4590">
    <literal><![CDATA[
      T(x * y,x \ 1) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(478,a,4578,a),flip(a)].">
      <j1 rule="hyper" parents="478 4578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4591">
    <literal><![CDATA[
      x / T(y * x,y \ 1) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,4578,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 4578 116"/>
    </justification>
  </clause>

  <clause id="4592">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,4408,a,b,4590,a)].">
      <j1 rule="hyper" parents="64 4408 4590"/>
    </justification>
  </clause>

  <clause id="4593">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ 1) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,3871,a(flip),b,4590,a)].">
      <j1 rule="hyper" parents="64 3871 4590"/>
    </justification>
  </clause>

  <clause id="4594">
    <literal><![CDATA[
      x / T((y \ 1) * x,y) = ((y \ 1) * x) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,3871,a(flip),b,4590,a(flip))].">
      <j1 rule="hyper" parents="225 3871 4590"/>
    </justification>
  </clause>

  <clause id="4595">
    <literal><![CDATA[
      (x \ 1) * (((x * y) \ y) \ y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,4590,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 4590 22"/>
    </justification>
  </clause>

  <clause id="4596">
    <literal><![CDATA[
      T((1 / x) * y,x) = (((1 / x) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(82(a,1),4590(a,1,2))].">
      <j1 rule="para" parents="82 4590"/>
    </justification>
  </clause>

  <clause id="4597">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,T(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(22(a,2),4588(a,1,2,2))].">
      <j1 rule="para" parents="22 4588"/>
    </justification>
  </clause>

  <clause id="4598">
    <literal><![CDATA[
      ((((x / y) \ 1) * x) \ x) \ x = ((x / y) \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,3434,a(flip),b,4593,a),flip(a)].">
      <j1 rule="hyper" parents="64 3434 4593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4599">
    <literal><![CDATA[
      R(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4562,a,4515,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4562 4515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4600">
    <literal><![CDATA[
      R(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4515(a,2),4562(a,1))].">
      <j1 rule="para" parents="4515 4562"/>
    </justification>
  </clause>

  <clause id="4601">
    <literal><![CDATA[
      (K(x,y) * x) * z = K(x,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,4599,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 4599 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4602">
    <literal><![CDATA[
      K(x,y) * (1 / x) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,4599,a(flip),b,1405,a),flip(a)].">
      <j1 rule="hyper" parents="142 4599 1405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4603">
    <literal><![CDATA[
      L(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(606,a,4601,a)].">
      <j1 rule="hyper" parents="606 4601"/>
    </justification>
  </clause>

  <clause id="4604">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4603(a,1),51(a,2))].">
      <j1 rule="para" parents="4603 51"/>
    </justification>
  </clause>

  <clause id="4605">
    <literal><![CDATA[
      L(x,1 / y,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3776(a,1),4604(a,1,3))].">
      <j1 rule="para" parents="3776 4604"/>
    </justification>
  </clause>

  <clause id="4606">
    <literal><![CDATA[
      (1 / x) * K(y,x \ 1) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(4535,a,3909,a),flip(a)].">
      <j1 rule="hyper" parents="4535 3909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4607">
    <literal><![CDATA[
      (K(x,y) * R(y,z,u)) * w = R(y,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(4003(a,1),4444(a,1,1))].">
      <j1 rule="para" parents="4003 4444"/>
    </justification>
  </clause>

  <clause id="4608">
    <literal><![CDATA[
      T(x,y \ 1) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(4575(a,1),4508(a,1,1))].">
      <j1 rule="para" parents="4575 4508"/>
    </justification>
  </clause>

  <clause id="4609">
    <literal><![CDATA[
      T(L(x,y,y \ 1),(1 / y) \ 1) \ ((1 / y) \ T(L(x,y,y \ 1),(1 / y) \ 1)) = L(x,y,y \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(1641(a,1),4608(a,2,2))].">
      <j1 rule="para" parents="1641 4608"/>
    </justification>
  </clause>

  <clause id="4610">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4369,a(flip),b,4564,a)].">
      <j1 rule="hyper" parents="64 4369 4564"/>
    </justification>
  </clause>

  <clause id="4611">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = (y * T(y \ 1,x)) \ x
    ]]></literal>
    <justification jstring="[para(4564(a,1),4518(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4564 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4612">
    <literal><![CDATA[
      T(x,y \ 1) \ x = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4581,a(flip),b,4610,a)].">
      <j1 rule="hyper" parents="64 4581 4610"/>
    </justification>
  </clause>

  <clause id="4613">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1484,a(flip),b,4612,a),flip(a)].">
      <j1 rule="hyper" parents="373 1484 4612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4614">
    <literal><![CDATA[
      (T(x,y \ 1) \ x) \ (y * (T(y \ 1,x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,T(y \ 1,x),y) = u
    ]]></literal>
    <justification jstring="[para(4612(a,2),608(a,1,1))].">
      <j1 rule="para" parents="4612 608"/>
    </justification>
  </clause>

  <clause id="4615">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3871(a,1),4613(a,1,1))].">
      <j1 rule="para" parents="3871 4613"/>
    </justification>
  </clause>

  <clause id="4616">
    <literal><![CDATA[
      x \ ((y * x) / y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,4367,a,b,4615,a)].">
      <j1 rule="hyper" parents="373 4367 4615"/>
    </justification>
  </clause>

  <clause id="4618">
    <literal><![CDATA[
      (T(x,y / z) \ x) * y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,4615,a,b,4517,a)].">
      <j1 rule="hyper" parents="144 4615 4517"/>
    </justification>
  </clause>

  <clause id="4619">
    <literal><![CDATA[
      T(x,T(y,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,4519,a,b,4615,a)].">
      <j1 rule="hyper" parents="40 4519 4615"/>
    </justification>
  </clause>

  <clause id="4620">
    <literal><![CDATA[
      x \ (y \ T(y,x)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,4615,a(flip),b,2409,a)].">
      <j1 rule="hyper" parents="139 4615 2409"/>
    </justification>
  </clause>

  <clause id="4621">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4615(a,2),4436(a,1,2,1))].">
      <j1 rule="para" parents="4615 4436"/>
    </justification>
  </clause>

  <clause id="4622">
    <literal><![CDATA[
      T(x,y) * (x \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[para(4615(a,2),4438(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4615 4438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4623">
    <literal><![CDATA[
      K(x,y) = T(x \ T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4615(a,1),4546(a,2,1))].">
      <j1 rule="para" parents="4615 4546"/>
    </justification>
  </clause>

  <clause id="4624">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(4558,a,4619,a)].">
      <j1 rule="hyper" parents="4558 4619"/>
    </justification>
  </clause>

  <clause id="4625">
    <literal><![CDATA[
      T((T(x,y) * y) / T(x,y),x) = y
    ]]></literal>
    <justification jstring="[hyper(542,a,4619,a)].">
      <j1 rule="hyper" parents="542 4619"/>
    </justification>
  </clause>

  <clause id="4626">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4544,a,b,4619,a)].">
      <j1 rule="hyper" parents="64 4544 4619"/>
    </justification>
  </clause>

  <clause id="4627">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4458,a,b,4619,a)].">
      <j1 rule="hyper" parents="64 4458 4619"/>
    </justification>
  </clause>

  <clause id="4628">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2519,a,b,4619,a)].">
      <j1 rule="hyper" parents="64 2519 4619"/>
    </justification>
  </clause>

  <clause id="4629">
    <literal><![CDATA[
      T(x / T(y,x),y) = y \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(493,a,4619,a(flip),b,4458,a)].">
      <j1 rule="hyper" parents="493 4619 4458"/>
    </justification>
  </clause>

  <clause id="4630">
    <literal><![CDATA[
      T(x,y) / y = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(225,a,4619,a(flip),b,2519,a),flip(a)].">
      <j1 rule="hyper" parents="225 4619 2519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4631">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ x) = y
    ]]></literal>
    <justification jstring="[hyper(142,a,4619,a(flip),b,2498,a)].">
      <j1 rule="hyper" parents="142 4619 2498"/>
    </justification>
  </clause>

  <clause id="4632">
    <literal><![CDATA[
      T(x,y) \ y = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,4619,a(flip),b,2498,a),flip(a)].">
      <j1 rule="hyper" parents="139 4619 2498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4633">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4619(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4619 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4634">
    <literal><![CDATA[
      T(L(x,y,z),T(u,x)) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4619(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4619 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4635">
    <literal><![CDATA[
      T(x,L(T(y,x),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),4619(a,1,2))].">
      <j1 rule="para" parents="25 4619"/>
    </justification>
  </clause>

  <clause id="4636">
    <literal><![CDATA[
      T(x,y / x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(117(a,1),4619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 4619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4638">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4619(a,1),265(a,1,2,1))].">
      <j1 rule="para" parents="4619 265"/>
    </justification>
  </clause>

  <clause id="4639">
    <literal><![CDATA[
      L(T(x,y),T(y,x),x) = T(x,x * T(y,x))
    ]]></literal>
    <justification jstring="[para(4619(a,1),765(a,1,1))].">
      <j1 rule="para" parents="4619 765"/>
    </justification>
  </clause>

  <clause id="4640">
    <literal><![CDATA[
      T(x,y) * L(T(y,x),z,u) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4619(a,1),266(a,1,2,1))].">
      <j1 rule="para" parents="4619 266"/>
    </justification>
  </clause>

  <clause id="4641">
    <literal><![CDATA[
      T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4619(a,1),267(a,1,2,1))].">
      <j1 rule="para" parents="4619 267"/>
    </justification>
  </clause>

  <clause id="4642">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(4619(a,1),463(a,1,2,1))].">
      <j1 rule="para" parents="4619 463"/>
    </justification>
  </clause>

  <clause id="4645">
    <literal><![CDATA[
      T(x,y) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(4619(a,1),4459(a,1,1))].">
      <j1 rule="para" parents="4619 4459"/>
    </justification>
  </clause>

  <clause id="4646">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,y) = x * y
    ]]></literal>
    <justification jstring="[para(4619(a,1),4597(a,1,2))].">
      <j1 rule="para" parents="4619 4597"/>
    </justification>
  </clause>

  <clause id="4648">
    <literal><![CDATA[
      T(x,x \ y) \ y = T(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2416,a(flip),b,4624,a)].">
      <j1 rule="hyper" parents="64 2416 4624"/>
    </justification>
  </clause>

  <clause id="4649">
    <literal><![CDATA[
      (x * y) / T(y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(225,a,4624,a(flip),b,2418,a)].">
      <j1 rule="hyper" parents="225 4624 2418"/>
    </justification>
  </clause>

  <clause id="4650">
    <literal><![CDATA[
      T(x,y) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(145,a,4624,a(flip),b,2418,a)].">
      <j1 rule="hyper" parents="145 4624 2418"/>
    </justification>
  </clause>

  <clause id="4651">
    <literal><![CDATA[
      K(T(x,y) \ y,z) = K(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4624(a,1),1571(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4624 1571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4652">
    <literal><![CDATA[
      (x / y) / T(y,x / y) = (y \ x) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,117,a(flip),b,4627,a),flip(a)].">
      <j1 rule="hyper" parents="142 117 4627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4653">
    <literal><![CDATA[
      T(x,y) = (x * (x * y)) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2540,a,b,4627,a),flip(a)].">
      <j1 rule="hyper" parents="64 2540 4627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4654">
    <literal><![CDATA[
      ((x / T(y,x)) * z) \ T(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      L(z \ y,z,x / T(y,x)) = u
    ]]></literal>
    <justification jstring="[para(4627(a,1),764(a,1,2))].">
      <j1 rule="para" parents="4627 764"/>
    </justification>
  </clause>

  <clause id="4655">
    <literal><![CDATA[
      (T(x,y) / y) * z = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(4628(a,1),209(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4628 209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4656">
    <literal><![CDATA[
      (x / T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (T(x,y) / y) * z = u
    ]]></literal>
    <justification jstring="[para(4628(a,1),400(a,1,1,2))].">
      <j1 rule="para" parents="4628 400"/>
    </justification>
  </clause>

  <clause id="4657">
    <literal><![CDATA[
      T(T(x,y) / y,z) = T(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4628(a,1),849(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4628 849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4658">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,4630,a(flip),b,3424,a),flip(a)].">
      <j1 rule="hyper" parents="145 4630 3424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4659">
    <literal><![CDATA[
      T(T(x / T(y,x),z),y) = T(y \ T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4630(a,1),278(a,1,1,1))].">
      <j1 rule="para" parents="4630 278"/>
    </justification>
  </clause>

  <clause id="4660">
    <literal><![CDATA[
      x / (y \ T(x,y)) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(226,a,4632,a)].">
      <j1 rule="hyper" parents="226 4632"/>
    </justification>
  </clause>

  <clause id="4661">
    <literal><![CDATA[
      T((x \ y) * x,x) = (T(x,y) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,4632,a,b,3428,a),flip(a)].">
      <j1 rule="hyper" parents="144 4632 3428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4662">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4632(a,2),95(a,1,2,1))].">
      <j1 rule="para" parents="4632 95"/>
    </justification>
  </clause>

  <clause id="4663">
    <literal><![CDATA[
      (T(x,y) * ((x \ T(y,x)) * z)) \ (y * z) = a(T(x,y),T(x,y) \ y,z)
    ]]></literal>
    <justification jstring="[para(4632(a,1),90(a,1,1,2,1))].">
      <j1 rule="para" parents="4632 90"/>
    </justification>
  </clause>

  <clause id="4664">
    <literal><![CDATA[
      T(x,x * y) * R(x \ T(x * y,x),z,u) = T(x * R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(4632(a,1),3108(a,1,2,1))].">
      <j1 rule="para" parents="4632 3108"/>
    </justification>
  </clause>

  <clause id="4666">
    <literal><![CDATA[
      T(x,y / x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,116,a(flip),b,4636,a),flip(a)].">
      <j1 rule="hyper" parents="373 116 4636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4667">
    <literal><![CDATA[
      (x * (y / x)) / T(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(225,a,4636,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="225 4636 22"/>
    </justification>
  </clause>

  <clause id="4668">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4636(a,1),1298(a,2,2))].">
      <j1 rule="para" parents="4636 1298"/>
    </justification>
  </clause>

  <clause id="4669">
    <literal><![CDATA[
      (T(x,y) * (y * x)) / T(x,y) = T(y,x) * T(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[hyper(144,a,4649,a(flip),b,2518,a),flip(a)].">
      <j1 rule="hyper" parents="144 4649 2518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4670">
    <literal><![CDATA[
      (x * R(y,z,u)) / R(T(y,x),z,u) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(27(a,2),4649(a,1,2))].">
      <j1 rule="para" parents="27 4649"/>
    </justification>
  </clause>

  <clause id="4671">
    <literal><![CDATA[
      R(x,T(y,z),T(z,y)) * (y * z) = (x * T(y,z)) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,4650,a(flip),b,210,a)].">
      <j1 rule="hyper" parents="145 4650 210"/>
    </justification>
  </clause>

  <clause id="4672">
    <literal><![CDATA[
      (x * y) * L(z,T(y,x),T(x,y)) = T(x,y) * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,4650,a(flip),b,213,a)].">
      <j1 rule="hyper" parents="144 4650 213"/>
    </justification>
  </clause>

  <clause id="4673">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * T(y,z)) * T(z,y)) = a(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[para(4650(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4650 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4674">
    <literal><![CDATA[
      (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4650(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4650 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4675">
    <literal><![CDATA[
      (x * y) / T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4650(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4650 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4677">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(T(x,y),T(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(4650(a,1),666(a,1,1,1))].">
      <j1 rule="para" parents="4650 666"/>
    </justification>
  </clause>

  <clause id="4678">
    <literal><![CDATA[
      T(x,y) = (x \ (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),4666(a,1,2))].">
      <j1 rule="para" parents="11 4666"/>
    </justification>
  </clause>

  <clause id="4679">
    <literal><![CDATA[
      T(x \ y,x) = ((x \ y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(79(a,1),4666(a,1,2))].">
      <j1 rule="para" parents="79 4666"/>
    </justification>
  </clause>

  <clause id="4680">
    <literal><![CDATA[
      (x / y) * L((y \ x) \ x,z,u) = L(y,z,u) * (x / y)
    ]]></literal>
    <justification jstring="[para(4666(a,1),266(a,1,2,1))].">
      <j1 rule="para" parents="4666 266"/>
    </justification>
  </clause>

  <clause id="4681">
    <literal><![CDATA[
      (x / y) * R((y \ x) \ x,z,u) = R(y,z,u) * (x / y)
    ]]></literal>
    <justification jstring="[para(4666(a,1),267(a,1,2,1))].">
      <j1 rule="para" parents="4666 267"/>
    </justification>
  </clause>

  <clause id="4682">
    <literal><![CDATA[
      T(x,x * (y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1063,a,4626,a),flip(a)].">
      <j1 rule="hyper" parents="1063 4626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4683">
    <literal><![CDATA[
      T(x,y * x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(1062,a,4626,a)].">
      <j1 rule="hyper" parents="1062 4626"/>
    </justification>
  </clause>

  <clause id="4684">
    <literal><![CDATA[
      T(R(x,y,x),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(795,a,4626,a)].">
      <j1 rule="hyper" parents="795 4626"/>
    </justification>
  </clause>

  <clause id="4685">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),4626(a,1,1,2))].">
      <j1 rule="para" parents="10 4626"/>
    </justification>
  </clause>

  <clause id="4686">
    <literal><![CDATA[
      T(x,y * z) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) = x
    ]]></literal>
    <justification jstring="[para(4626(a,1),163(a,2))].">
      <j1 rule="para" parents="4626 163"/>
    </justification>
  </clause>

  <clause id="4687">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * (y / x),x)) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(144,a,4682,a(flip),b,4660,a)].">
      <j1 rule="hyper" parents="144 4682 4660"/>
    </justification>
  </clause>

  <clause id="4688">
    <literal><![CDATA[
      T(x,(x \ y) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(78(a,1),4682(a,1,2)),flip(a)].">
      <j1 rule="para" parents="78 4682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4689">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,767,a,b,4683,a)].">
      <j1 rule="hyper" parents="373 767 4683"/>
    </justification>
  </clause>

  <clause id="4690">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,765,a,b,4683,a)].">
      <j1 rule="hyper" parents="373 765 4683"/>
    </justification>
  </clause>

  <clause id="4691">
    <literal><![CDATA[
      R(T(x,y * R(x,z,u)),z,u) = T(R(x,z,u),R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,4683,a)].">
      <j1 rule="hyper" parents="64 27 4683"/>
    </justification>
  </clause>

  <clause id="4692">
    <literal><![CDATA[
      T(x / y,y * (x / y)) = T(x / y,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),4683(a,2,2))].">
      <j1 rule="para" parents="12 4683"/>
    </justification>
  </clause>

  <clause id="4693">
    <literal><![CDATA[
      T(T(x,x * y),z) = T(T(x,z),y * x)
    ]]></literal>
    <justification jstring="[para(4683(a,1),23(a,1,1))].">
      <j1 rule="para" parents="4683 23"/>
    </justification>
  </clause>

  <clause id="4694">
    <literal><![CDATA[
      x * T(y,x * y) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(4683(a,2),771(a,1,2))].">
      <j1 rule="para" parents="4683 771"/>
    </justification>
  </clause>

  <clause id="4695">
    <literal><![CDATA[
      T(x * T(y,y * x),y) = x * y
    ]]></literal>
    <justification jstring="[para(4683(a,1),1065(a,1,1,2))].">
      <j1 rule="para" parents="4683 1065"/>
    </justification>
  </clause>

  <clause id="4696">
    <literal><![CDATA[
      x * T(y,x * y) != z * x
    ]]></literal>
    <literal><![CDATA[
      L(y,x,y) = z
    ]]></literal>
    <justification jstring="[para(4683(a,2),772(a,1,2))].">
      <j1 rule="para" parents="4683 772"/>
    </justification>
  </clause>

  <clause id="4697">
    <literal><![CDATA[
      T(T(x,x \ 1),y * x) = R(T(x,x * y),x,x)
    ]]></literal>
    <justification jstring="[para(4683(a,1),1421(a,2,1))].">
      <j1 rule="para" parents="4683 1421"/>
    </justification>
  </clause>

  <clause id="4698">
    <literal><![CDATA[
      R(x * (y * x),z,u) / T(x,x * R(y,z,u)) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(4683(a,1),2151(a,1,2))].">
      <j1 rule="para" parents="4683 2151"/>
    </justification>
  </clause>

  <clause id="4699">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4683(a,1),4483(a,1,2))].">
      <j1 rule="para" parents="4683 4483"/>
    </justification>
  </clause>

  <clause id="4700">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * ((x \ y) * x) = z
    ]]></literal>
    <justification jstring="[para(4688(a,1),328(a,1,2))].">
      <j1 rule="para" parents="4688 328"/>
    </justification>
  </clause>

  <clause id="4701">
    <literal><![CDATA[
      T((x \ y) * T(x,y),x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(4688(a,1),1065(a,1,1,2))].">
      <j1 rule="para" parents="4688 1065"/>
    </justification>
  </clause>

  <clause id="4702">
    <literal><![CDATA[
      (((x \ y) * x) / T(x,y)) * x = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(4688(a,1),4627(a,1,1,2))].">
      <j1 rule="para" parents="4688 4627"/>
    </justification>
  </clause>

  <clause id="4703">
    <literal><![CDATA[
      T(x,x * y) * R(T(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y,z,u) * T(x,x * y) = w
    ]]></literal>
    <justification jstring="[para(4699(a,1),465(a,1,2,1))].">
      <j1 rule="para" parents="4699 465"/>
    </justification>
  </clause>

  <clause id="4704">
    <literal><![CDATA[
      T((x * y) / x,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(542,a,4689,a)].">
      <j1 rule="hyper" parents="542 4689"/>
    </justification>
  </clause>

  <clause id="4705">
    <literal><![CDATA[
      T(x,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(4689(a,1),789(a,1))].">
      <j1 rule="para" parents="4689 789"/>
    </justification>
  </clause>

  <clause id="4706">
    <literal><![CDATA[
      T(1 / (1 / x),(1 / x) * y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3233,a,b,4690,a)].">
      <j1 rule="hyper" parents="64 3233 4690"/>
    </justification>
  </clause>

  <clause id="4707">
    <literal><![CDATA[
      ((x \ y) * x) / (x \ y) = y / (y / x)
    ]]></literal>
    <justification jstring="[hyper(39,a,4574,a(flip),b,4616,a),flip(a)].">
      <j1 rule="hyper" parents="39 4574 4616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4708">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,y) = (y * x) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4620(a,1),346(a,1,1))].">
      <j1 rule="para" parents="4620 346"/>
    </justification>
  </clause>

  <clause id="4709">
    <literal><![CDATA[
      x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,4414,a(flip),b,4623,a)].">
      <j1 rule="hyper" parents="373 4414 4623"/>
    </justification>
  </clause>

  <clause id="4710">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4625(a,1),916(a,1,1))].">
      <j1 rule="para" parents="4625 916"/>
    </justification>
  </clause>

  <clause id="4711">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,23,a,b,4633,a),flip(a)].">
      <j1 rule="hyper" parents="373 23 4633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      T(T(x,y),T(T(z,x),u)) = T(T(x,T(z,u)),y)
    ]]></literal>
    <justification jstring="[para(23(a,1),4633(a,1,2))].">
      <j1 rule="para" parents="23 4633"/>
    </justification>
  </clause>

  <clause id="4713">
    <literal><![CDATA[
      T(T(x,y),L(T(z,x),u,w)) = T(T(x,L(z,u,w)),y)
    ]]></literal>
    <justification jstring="[para(25(a,2),4633(a,1,2))].">
      <j1 rule="para" parents="25 4633"/>
    </justification>
  </clause>

  <clause id="4714">
    <literal><![CDATA[
      T(x,x \ (x \ y)) \ y = (x \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,75,a(flip),b,4645,a)].">
      <j1 rule="hyper" parents="139 75 4645"/>
    </justification>
  </clause>

  <clause id="4715">
    <literal><![CDATA[
      T(x,x \ y) / y = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(404,a,4646,a)].">
      <j1 rule="hyper" parents="404 4646"/>
    </justification>
  </clause>

  <clause id="4716">
    <literal><![CDATA[
      T(x,y) / (x * y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(226,a,4646,a)].">
      <j1 rule="hyper" parents="226 4646"/>
    </justification>
  </clause>

  <clause id="4717">
    <literal><![CDATA[
      R(1 / x,x,y) \ T(y,x) = y * x
    ]]></literal>
    <justification jstring="[hyper(64,a,449,a,b,4646,a)].">
      <j1 rule="hyper" parents="64 449 4646"/>
    </justification>
  </clause>

  <clause id="4718">
    <literal><![CDATA[
      T(x,y) / (x * y) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(225,a,4646,a(flip),b,449,a)].">
      <j1 rule="hyper" parents="225 4646 449"/>
    </justification>
  </clause>

  <clause id="4719">
    <literal><![CDATA[
      T((x / y) \ x,x / y) = (y \ x) \ x
    ]]></literal>
    <justification jstring="[para(848(a,1),4648(a,1,1)),flip(a)].">
      <j1 rule="para" parents="848 4648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4720">
    <literal><![CDATA[
      T(x \ (y \ x),x) = T(x,y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(4575(a,1),4648(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4575 4648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4721">
    <literal><![CDATA[
      T(T(x \ y,z),x) = T(((x \ y) \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(4679(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4679 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4722">
    <literal><![CDATA[
      T(x \ y,x) != z \ y
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(4679(a,2),49(a,1))].">
      <j1 rule="para" parents="4679 49"/>
    </justification>
  </clause>

  <clause id="4723">
    <literal><![CDATA[
      L((((x \ y) \ z) \ z) \ z,x \ y,x) = T(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(4679(a,1),1024(a,1,1))].">
      <j1 rule="para" parents="4679 1024"/>
    </justification>
  </clause>

  <clause id="4724">
    <literal><![CDATA[
      T(L(x,y,x) * y,x) = y * x
    ]]></literal>
    <justification jstring="[para(771(a,1),4695(a,1,1))].">
      <j1 rule="para" parents="771 4695"/>
    </justification>
  </clause>

  <clause id="4725">
    <literal><![CDATA[
      (x * (y * x)) / x = L(x,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(313,a,4724,a)].">
      <j1 rule="hyper" parents="313 4724"/>
    </justification>
  </clause>

  <clause id="4726">
    <literal><![CDATA[
      T(x,y) * T(T(y,z),x) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,4711,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 4711 22"/>
    </justification>
  </clause>

  <clause id="4727">
    <literal><![CDATA[
      T(T(x,y),z / x) = T(T(x,y),x \ z)
    ]]></literal>
    <justification jstring="[para(117(a,1),4711(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 4711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4728">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(4711(a,2),481(a,1))].">
      <j1 rule="para" parents="4711 481"/>
    </justification>
  </clause>

  <clause id="4729">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,116,a(flip),b,4685,a),flip(a)].">
      <j1 rule="hyper" parents="373 116 4685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4730">
    <literal><![CDATA[
      R(L(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[para(4704(a,1),1327(a,1,1))].">
      <j1 rule="para" parents="4704 1327"/>
    </justification>
  </clause>

  <clause id="4731">
    <literal><![CDATA[
      L(x \ y,x,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(1382,a,4730,a),flip(a)].">
      <j1 rule="hyper" parents="1382 4730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4732">
    <literal><![CDATA[
      L(T(x,y),y,T(x,y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(1323,a,4730,a),flip(a)].">
      <j1 rule="hyper" parents="1323 4730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4733">
    <literal><![CDATA[
      L(R(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,29,a(flip),b,4730,a)].">
      <j1 rule="hyper" parents="64 29 4730"/>
    </justification>
  </clause>

  <clause id="4734">
    <literal><![CDATA[
      R(x,y,z) != z
    ]]></literal>
    <literal><![CDATA[
      L(z,y,z) = x
    ]]></literal>
    <justification jstring="[para(4730(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="4730 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4735">
    <literal><![CDATA[
      R(x,y,T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2629,a,4733,a)].">
      <j1 rule="hyper" parents="2629 4733"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(626,a,4733,a)].">
      <j1 rule="hyper" parents="626 4733"/>
    </justification>
  </clause>

  <clause id="4737">
    <literal><![CDATA[
      L(T(R(x,y,x),z),y,x) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4733(a,1),25(a,2,1))].">
      <j1 rule="para" parents="4733 25"/>
    </justification>
  </clause>

  <clause id="4738">
    <literal><![CDATA[
      L(R(R(x,y,x),z,u),y,x) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(4733(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4733 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4739">
    <literal><![CDATA[
      L(L(R(x,y,x),z,u),y,x) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4733(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4733 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4740">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4619(a,1),4735(a,1,3))].">
      <j1 rule="para" parents="4619 4735"/>
    </justification>
  </clause>

  <clause id="4741">
    <literal><![CDATA[
      x * R(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(157,a,4736,a)].">
      <j1 rule="hyper" parents="157 4736"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      (1 / x) * R(y,x,y) = T(y * (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(145,a,2968,a(flip),b,4736,a)].">
      <j1 rule="hyper" parents="145 2968 4736"/>
    </justification>
  </clause>

  <clause id="4743">
    <literal><![CDATA[
      ((x * x) \ y) * R(z,y,z) = T(z * ((x * x) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,2967,a(flip),b,4736,a)].">
      <j1 rule="hyper" parents="145 2967 4736"/>
    </justification>
  </clause>

  <clause id="4744">
    <literal><![CDATA[
      (x * x) * (y * R(z,(x * x) * y,z)) = T(z * ((x * x) * y),z)
    ]]></literal>
    <justification jstring="[hyper(39,a,125,a,b,4736,a)].">
      <j1 rule="hyper" parents="39 125 4736"/>
    </justification>
  </clause>

  <clause id="4745">
    <literal><![CDATA[
      R(x,x \ y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),4736(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 4736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4746">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),4736(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 4736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      T(x,y) \ T(x * y,y) = R(y,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(115(a,1),4736(a,1,2,1))].">
      <j1 rule="para" parents="115 4736"/>
    </justification>
  </clause>

  <clause id="4748">
    <literal><![CDATA[
      (x * y) \ (x * T(z * y,z)) = L(R(z,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(4736(a,1),102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4736 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4749">
    <literal><![CDATA[
      ((x * x) \ y) * R(z,y,z) = (x * x) \ T(z * y,z)
    ]]></literal>
    <justification jstring="[para(4736(a,1),802(a,1,2))].">
      <j1 rule="para" parents="4736 802"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      L(R(x,y,x) \ 1,R(x,y,x),y) = T(x * y,x) \ y
    ]]></literal>
    <justification jstring="[para(4741(a,1),241(a,2,1))].">
      <j1 rule="para" parents="4741 241"/>
    </justification>
  </clause>

  <clause id="4751">
    <literal><![CDATA[
      (x * y) \ (x * T(z * y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(R(z,y,z),y,x) = u
    ]]></literal>
    <justification jstring="[para(4741(a,1),608(a,1,2,2))].">
      <j1 rule="para" parents="4741 608"/>
    </justification>
  </clause>

  <clause id="4752">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4741(a,1),2832(a,1,1))].">
      <j1 rule="para" parents="4741 2832"/>
    </justification>
  </clause>

  <clause id="4753">
    <literal><![CDATA[
      L(x,y,z) * R(L(x,y,z) \ 1,x,x \ 1) = L(T((x \ 1) * x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(4741(a,1),4229(a,2,1))].">
      <j1 rule="para" parents="4741 4229"/>
    </justification>
  </clause>

  <clause id="4754">
    <literal><![CDATA[
      L(R(T(x,y),z,x),z,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(27(a,2),4737(a,1,1))].">
      <j1 rule="para" parents="27 4737"/>
    </justification>
  </clause>

  <clause id="4755">
    <literal><![CDATA[
      R(1 / x,x,T(y,x)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(870,a,4718,a)].">
      <j1 rule="hyper" parents="870 4718"/>
    </justification>
  </clause>

  <clause id="4756">
    <literal><![CDATA[
      T((x * y) / x,L(x,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(3210,a,4725,a)].">
      <j1 rule="hyper" parents="3210 4725"/>
    </justification>
  </clause>

  <clause id="4757">
    <literal><![CDATA[
      ((x * (y * x)) / x) * L(z,y,L(x,y,x)) = L(x,y,x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,4725,a,b,213,a)].">
      <j1 rule="hyper" parents="144 4725 213"/>
    </justification>
  </clause>

  <clause id="4758">
    <literal><![CDATA[
      (x * ((x \ y) * x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4725(a,2),1370(a,1))].">
      <j1 rule="para" parents="4725 1370"/>
    </justification>
  </clause>

  <clause id="4759">
    <literal><![CDATA[
      T(x,L(y,x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4756(a,1),312(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4756 312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4760">
    <literal><![CDATA[
      L(x,y,x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,4759,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 4759 22"/>
    </justification>
  </clause>

  <clause id="4761">
    <literal><![CDATA[
      L(T(x \ y,z),x,x \ y) = T(T(y / x,y),z)
    ]]></literal>
    <justification jstring="[para(4731(a,1),25(a,2,1))].">
      <j1 rule="para" parents="4731 25"/>
    </justification>
  </clause>

  <clause id="4762">
    <literal><![CDATA[
      R(x,x \ (y / x),x) = (x \ (y / x)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(117(a,1),4745(a,2,2))].">
      <j1 rule="para" parents="117 4745"/>
    </justification>
  </clause>

  <clause id="4763">
    <literal><![CDATA[
      (x * (x * (T(x,y) \ y))) / T((x \ y) * x,x) = T(x,T(x,y) \ y)
    ]]></literal>
    <justification jstring="[para(4661(a,2),4653(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4661 4653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4764">
    <literal><![CDATA[
      T(x * (y / x),x) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(493,a,364,a(flip),b,4668,a)].">
      <j1 rule="hyper" parents="493 364 4668"/>
    </justification>
  </clause>

  <clause id="4765">
    <literal><![CDATA[
      (x * y) \ (y * T(x,x \ y)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,4668,a(flip),b,958,a)].">
      <j1 rule="hyper" parents="139 4668 958"/>
    </justification>
  </clause>

  <clause id="4766">
    <literal><![CDATA[
      ((x * (y / x)) * x) * x = (y * x) * T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4668(a,2),2515(a,1,1))].">
      <j1 rule="para" parents="4668 2515"/>
    </justification>
  </clause>

  <clause id="4767">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,(x \ y) * x)
    ]]></literal>
    <justification jstring="[para(4701(a,1),4619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4701 4619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4768">
    <literal><![CDATA[
      (x / (x / y)) * (y \ x) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(156,a,4707,a)].">
      <j1 rule="hyper" parents="156 4707"/>
    </justification>
  </clause>

  <clause id="4769">
    <literal><![CDATA[
      T(x / (x / y),y \ x) = y
    ]]></literal>
    <justification jstring="[para(4707(a,1),255(a,1,1))].">
      <j1 rule="para" parents="4707 255"/>
    </justification>
  </clause>

  <clause id="4771">
    <literal><![CDATA[
      T(x / (x / y),x) = L(y,y \ x,y)
    ]]></literal>
    <justification jstring="[para(4707(a,1),791(a,1,1))].">
      <j1 rule="para" parents="4707 791"/>
    </justification>
  </clause>

  <clause id="4772">
    <literal><![CDATA[
      T(x / (x / (x / y)),y) = x / y
    ]]></literal>
    <justification jstring="[para(82(a,1),4769(a,1,2))].">
      <j1 rule="para" parents="82 4769"/>
    </justification>
  </clause>

  <clause id="4773">
    <literal><![CDATA[
      (x * (y / x)) / x = y / (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(313,a,4772,a)].">
      <j1 rule="hyper" parents="313 4772"/>
    </justification>
  </clause>

  <clause id="4774">
    <literal><![CDATA[
      R(x / y,x / (x / y),x / y) = T((x * (x / y)) / x,y)
    ]]></literal>
    <justification jstring="[para(4772(a,1),1033(a,1,1))].">
      <j1 rule="para" parents="4772 1033"/>
    </justification>
  </clause>

  <clause id="4775">
    <literal><![CDATA[
      x * T(x / (x / y),x) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,4771,a,b,101,a)].">
      <j1 rule="hyper" parents="145 4771 101"/>
    </justification>
  </clause>

  <clause id="4776">
    <literal><![CDATA[
      T(T(x / (x / y),x),z) = L(T(y,z),y \ x,y)
    ]]></literal>
    <justification jstring="[para(4771(a,2),25(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4771 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4777">
    <literal><![CDATA[
      (x * y) / a(T(x,x \ z) / z,(x \ z) * x,y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(4715(a,2),955(a,1,2,1))].">
      <j1 rule="para" parents="4715 955"/>
    </justification>
  </clause>

  <clause id="4778">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = x / ((x \ (y \ x)) * x)
    ]]></literal>
    <justification jstring="[para(4575(a,1),4715(a,1,1))].">
      <j1 rule="para" parents="4575 4715"/>
    </justification>
  </clause>

  <clause id="4779">
    <literal><![CDATA[
      L(L(R(R(x,y,x),z,u),w,v5),y,x) = L(R(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(4738(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4738 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4780">
    <literal><![CDATA[
      x * (y * L(L(R(x,y,x),z,u),w,v5)) = (x * y) * L(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(4739(a,1),513(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4739 513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4781">
    <literal><![CDATA[
      R(1 / x,x,y / x) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(117(a,1),4755(a,1,3)),flip(a)].">
      <j1 rule="para" parents="117 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4782">
    <literal><![CDATA[
      ((x \ y) * x) * (y / x) = y * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(144,a,4768,a(flip),b,2545,a)].">
      <j1 rule="hyper" parents="144 4768 2545"/>
    </justification>
  </clause>

  <clause id="4785">
    <literal><![CDATA[
      (x * (y / x)) * (y / (y / x)) = y * ((y / x) \ y)
    ]]></literal>
    <justification jstring="[para(82(a,1),4782(a,1,1,1))].">
      <j1 rule="para" parents="82 4782"/>
    </justification>
  </clause>

  <clause id="4786">
    <literal><![CDATA[
      L(T(x,y),T(y,x),x) = T(x,y * x)
    ]]></literal>
    <justification jstring="[para(115(a,1),4639(a,2,2))].">
      <j1 rule="para" parents="115 4639"/>
    </justification>
  </clause>

  <clause id="4787">
    <literal><![CDATA[
      T(R(x,T(y,x),x),y * x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,4737,a,b,4786,a)].">
      <j1 rule="hyper" parents="42 4737 4786"/>
    </justification>
  </clause>

  <clause id="4788">
    <literal><![CDATA[
      R(x,T(y,x),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,1056,a,b,4787,a),flip(a)].">
      <j1 rule="hyper" parents="41 1056 4787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4789">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4740,a,b,4788,a)].">
      <j1 rule="hyper" parents="64 4740 4788"/>
    </justification>
  </clause>

  <clause id="4790">
    <literal><![CDATA[
      R(R(x,y,z),T(u,x),T(x,u)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(4789(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4789 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4791">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(4461(a,1),4746(a,2,2))].">
      <j1 rule="para" parents="4461 4746"/>
    </justification>
  </clause>

  <clause id="4792">
    <literal><![CDATA[
      T(x,y) \ T(x * y,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4788,a(flip),b,4747,a),flip(a)].">
      <j1 rule="hyper" parents="373 4788 4747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4793">
    <literal><![CDATA[
      (x \ (y * x)) \ T(y * x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),4792(a,1,1))].">
      <j1 rule="para" parents="22 4792"/>
    </justification>
  </clause>

  <clause id="4794">
    <literal><![CDATA[
      x * K(y \ (y / (x \ z)),y) = (T(y,x / z) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,2430,a(flip),b,4618,a)].">
      <j1 rule="hyper" parents="373 2430 4618"/>
    </justification>
  </clause>

  <clause id="4795">
    <literal><![CDATA[
      (x * y) / T(T(x,y),y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,4650,a(flip),b,4638,a)].">
      <j1 rule="hyper" parents="142 4650 4638"/>
    </justification>
  </clause>

  <clause id="4796">
    <literal><![CDATA[
      T(x,y) \ (y * x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(139,a,4650,a(flip),b,4638,a)].">
      <j1 rule="hyper" parents="139 4650 4638"/>
    </justification>
  </clause>

  <clause id="4797">
    <literal><![CDATA[
      T(T(x,x \ y),x \ y) = T(x \ y,x) \ y
    ]]></literal>
    <justification jstring="[para(4795(a,1),349(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4795 349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4798">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (y * L(x,z,u)) = T(T(y,L(x,z,u)),L(x,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),4796(a,1,1))].">
      <j1 rule="para" parents="25 4796"/>
    </justification>
  </clause>

  <clause id="4799">
    <literal><![CDATA[
      T(T(x,y) \ y,z) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4484,a(flip),b,4659,a)].">
      <j1 rule="hyper" parents="64 4484 4659"/>
    </justification>
  </clause>

  <clause id="4800">
    <literal><![CDATA[
      L(T(x,y),T(z,x),z / T(z,x)) * z = (z / T(z,x)) * (T(x,y) * T(z,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,4726,a(flip),b,1023,a),flip(a)].">
      <j1 rule="hyper" parents="145 4726 1023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4801">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,4658,a(flip),b,4764,a),flip(a)].">
      <j1 rule="hyper" parents="64 4658 4764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4802">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4688,a(flip),b,4767,a),flip(a)].">
      <j1 rule="hyper" parents="373 4688 4767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4803">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4802(a,1),2535(a,1,1))].">
      <j1 rule="para" parents="4802 2535"/>
    </justification>
  </clause>

  <clause id="4804">
    <literal><![CDATA[
      (x / (x / y)) * x = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(328,a,4775,a)].">
      <j1 rule="hyper" parents="328 4775"/>
    </justification>
  </clause>

  <clause id="4805">
    <literal><![CDATA[
      (x * (y * y)) / x = x / (x / (y * y))
    ]]></literal>
    <justification jstring="[hyper(142,a,126,a(flip),b,4804,a)].">
      <j1 rule="hyper" parents="142 126 4804"/>
    </justification>
  </clause>

  <clause id="4806">
    <literal><![CDATA[
      x / (x / (x * x)) = x * L(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2849,a(flip),b,4805,a),flip(a)].">
      <j1 rule="hyper" parents="64 2849 4805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4807">
    <literal><![CDATA[
      R(1 / x,x,x \ y) \ (y / x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4781(a,1),452(a,1,1))].">
      <j1 rule="para" parents="4781 452"/>
    </justification>
  </clause>

  <clause id="4808">
    <literal><![CDATA[
      (x * T(T(x,x \ 1),x \ 1)) * (y / z) = (((x \ 1) \ x) * y) / z
    ]]></literal>
    <justification jstring="[para(4797(a,2),1479(a,1,1,2))].">
      <j1 rule="para" parents="4797 1479"/>
    </justification>
  </clause>

  <clause id="4809">
    <literal><![CDATA[
      L(T(x \ y,z),x,x \ y) = T(T(y / x,z),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,23,a,b,4761,a),flip(a)].">
      <j1 rule="hyper" parents="373 23 4761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4810">
    <literal><![CDATA[
      ((x \ y) / y) * (x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[para(4807(a,1),750(a,1,2))].">
      <j1 rule="para" parents="4807 750"/>
    </justification>
  </clause>

  <clause id="4811">
    <literal><![CDATA[
      (x / y) / (y * (x / y)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(154,a,4810,a)].">
      <j1 rule="hyper" parents="154 4810"/>
    </justification>
  </clause>

  <clause id="4812">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = T(x,T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,4520,a(flip),b,4611,a),flip(a)].">
      <j1 rule="hyper" parents="373 4520 4611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4813">
    <literal><![CDATA[
      T(x,T(y \ 1,x)) = T(x,(y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(4710,a,4812,a),flip(a)].">
      <j1 rule="hyper" parents="4710 4812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4814">
    <literal><![CDATA[
      T(x,(y \ z) / z) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4710,a,4813,a),flip(a)].">
      <j1 rule="hyper" parents="4710 4813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4815">
    <literal><![CDATA[
      T(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(4813(a,1),4710(a,1))].">
      <j1 rule="para" parents="4813 4710"/>
    </justification>
  </clause>

  <clause id="4816">
    <literal><![CDATA[
      ((x \ y) / y) * T(z,x \ 1) = z * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,4814,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 4814 22"/>
    </justification>
  </clause>

  <clause id="4817">
    <literal><![CDATA[
      T(x,y / (z * y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),4814(a,1,2,1))].">
      <j1 rule="para" parents="9 4814"/>
    </justification>
  </clause>

  <clause id="4818">
    <literal><![CDATA[
      T(x,(y / z) \ 1) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(82(a,1),4814(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 4814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4819">
    <literal><![CDATA[
      T(x / (y / (z * y)),z \ 1) = (y / (z * y)) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,4817,a),flip(a)].">
      <j1 rule="hyper" parents="467 4817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4823">
    <literal><![CDATA[
      T(x / (y * x),y \ 1) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(339,a,4817,a)].">
      <j1 rule="hyper" parents="339 4817"/>
    </justification>
  </clause>

  <clause id="4824">
    <literal><![CDATA[
      (x / (y * x)) * T(z,y \ 1) = z * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(145,a,4817,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 4817 22"/>
    </justification>
  </clause>

  <clause id="4825">
    <literal><![CDATA[
      T((x / y) \ 1,y / x) = (x / y) \ 1
    ]]></literal>
    <justification jstring="[hyper(339,a,4818,a)].">
      <j1 rule="hyper" parents="339 4818"/>
    </justification>
  </clause>

  <clause id="4827">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),4818(a,2,2))].">
      <j1 rule="para" parents="79 4818"/>
    </justification>
  </clause>

  <clause id="4828">
    <literal><![CDATA[
      ((x / y) \ 1) * (y / x) = (y / x) * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,4825,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 4825 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4829">
    <literal><![CDATA[
      T(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(82(a,1),4815(a,1,2,1))].">
      <j1 rule="para" parents="82 4815"/>
    </justification>
  </clause>

  <clause id="4830">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = L(y,x,y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(765(a,1),4640(a,1,2))].">
      <j1 rule="para" parents="765 4640"/>
    </justification>
  </clause>

  <clause id="4831">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4760,a(flip),b,4830,a),flip(a)].">
      <j1 rule="hyper" parents="373 4760 4830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4832">
    <literal><![CDATA[
      (x * (R(x,y,z) * T(u,x))) \ ((u * x) * R(T(x,u),y,z)) = a(x,T(u,x),R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(4641(a,1),259(a,1,1,2))].">
      <j1 rule="para" parents="4641 259"/>
    </justification>
  </clause>

  <clause id="4833">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = T(x * y,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4626(a,1),4641(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4626 4641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4834">
    <literal><![CDATA[
      T(x,y) * (T(y,x) / x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3424(a,1),4687(a,1,2))].">
      <j1 rule="para" parents="3424 4687"/>
    </justification>
  </clause>

  <clause id="4835">
    <literal><![CDATA[
      T(x,y) * (y / T(x,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4630(a,1),4834(a,1,2))].">
      <j1 rule="para" parents="4630 4834"/>
    </justification>
  </clause>

  <clause id="4836">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      y / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4835(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4835 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4837">
    <literal><![CDATA[
      ((x \ y) * x) / T(x,y) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,3433,a(flip),b,4702,a),flip(a)].">
      <j1 rule="hyper" parents="36 3433 4702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4838">
    <literal><![CDATA[
      (x \ T(y,x)) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(156,a,4837,a)].">
      <j1 rule="hyper" parents="156 4837"/>
    </justification>
  </clause>

  <clause id="4839">
    <literal><![CDATA[
      R(x,K(x,y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(4709(a,1),4437(a,1,2))].">
      <j1 rule="para" parents="4709 4437"/>
    </justification>
  </clause>

  <clause id="4840">
    <literal><![CDATA[
      R(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),4839(a,1,2,2))].">
      <j1 rule="para" parents="82 4839"/>
    </justification>
  </clause>

  <clause id="4841">
    <literal><![CDATA[
      R(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4840(a,1),27(a,2,1))].">
      <j1 rule="para" parents="4840 27"/>
    </justification>
  </clause>

  <clause id="4842">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) * w = L(x,y,z) * (K(x,u) * w)
    ]]></literal>
    <justification jstring="[para(4840(a,1),510(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4840 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4844">
    <literal><![CDATA[
      (R(T(x,y),z,u) * K(x,w)) * v5 = R(T(x,y),z,u) * (K(x,w) * v5)
    ]]></literal>
    <justification jstring="[para(4841(a,1),506(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4841 506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4845">
    <literal><![CDATA[
      (T(x,y \ 1) / (y \ x)) \ x = (x \ (y \ x)) * x
    ]]></literal>
    <justification jstring="[hyper(143,a,4778,a,b,171,a)].">
      <j1 rule="hyper" parents="143 4778 171"/>
    </justification>
  </clause>

  <clause id="4846">
    <literal><![CDATA[
      (x * (y / x)) * (y / (y / x)) = y * x
    ]]></literal>
    <justification jstring="[hyper(373,a,220,a(flip),b,4785,a),flip(a)].">
      <j1 rule="hyper" parents="373 220 4785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4848">
    <literal><![CDATA[
      (x * y) * ((y * x) / ((y * x) / x)) = (y * x) * x
    ]]></literal>
    <justification jstring="[para(11(a,1),4846(a,1,1,2))].">
      <j1 rule="para" parents="11 4846"/>
    </justification>
  </clause>

  <clause id="4849">
    <literal><![CDATA[
      ((x \ y) / y) * (z / (x * z)) = (z / (x * z)) * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(4823(a,1),4816(a,1,2))].">
      <j1 rule="para" parents="4823 4816"/>
    </justification>
  </clause>

  <clause id="4850">
    <literal><![CDATA[
      (x / (y * x)) * T(z,y \ 1) = z * R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,450,a,b,4824,a),flip(a)].">
      <j1 rule="hyper" parents="373 450 4824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4851">
    <literal><![CDATA[
      a(((x / y) * ((y / x) \ 1)) * z,u,w) = a(((y / x) * (x / y)) * z,u,w)
    ]]></literal>
    <justification jstring="[para(4828(a,1),2690(a,1,1,1))].">
      <j1 rule="para" parents="4828 2690"/>
    </justification>
  </clause>

  <clause id="4852">
    <literal><![CDATA[
      (T(x,y) / ((y \ 1) \ x)) \ x = (x \ ((y \ 1) \ x)) * x
    ]]></literal>
    <justification jstring="[para(3871(a,1),4845(a,1,1,1))].">
      <j1 rule="para" parents="3871 4845"/>
    </justification>
  </clause>

  <clause id="4853">
    <literal><![CDATA[
      (x * y) * ((y * x) / y) = (y * x) * x
    ]]></literal>
    <justification jstring="[para(11(a,1),4848(a,1,2,2))].">
      <j1 rule="para" parents="11 4848"/>
    </justification>
  </clause>

  <clause id="4854">
    <literal><![CDATA[
      x * (((y \ x) * y) / (y \ x)) = ((y \ x) * y) * y
    ]]></literal>
    <justification jstring="[hyper(717,a,4853,a)].">
      <j1 rule="hyper" parents="717 4853"/>
    </justification>
  </clause>

  <clause id="4855">
    <literal><![CDATA[
      (x * y) \ ((y * x) * x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(149,a,4853,a)].">
      <j1 rule="hyper" parents="149 4853"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      ((x \ y) * x) * x = y * (y / (y / x))
    ]]></literal>
    <justification jstring="[para(4707(a,1),4854(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4707 4854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4857">
    <literal><![CDATA[
      ((x \ T(y,x)) * T(x,y)) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4632(a,1),4856(a,1,1,1))].">
      <j1 rule="para" parents="4632 4856"/>
    </justification>
  </clause>

  <clause id="4858">
    <literal><![CDATA[
      (x * R(x * K(y,x),z,u)) / R(x * K(y,x),z,u) = T(x,R(x * K(y,x),z,u))
    ]]></literal>
    <justification jstring="[para(3163(a,1),4670(a,1,2,1))].">
      <j1 rule="para" parents="3163 4670"/>
    </justification>
  </clause>

  <clause id="4859">
    <literal><![CDATA[
      T(x * ((y * y) \ z),x) = (y * y) \ T(x * z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4743,a(flip),b,4749,a)].">
      <j1 rule="hyper" parents="64 4743 4749"/>
    </justification>
  </clause>

  <clause id="4860">
    <literal><![CDATA[
      T(x * ((y * y) \ z),x) \ u = T(x * z,x) \ ((y * y) * u)
    ]]></literal>
    <justification jstring="[para(4859(a,2),804(a,1,1))].">
      <j1 rule="para" parents="4859 804"/>
    </justification>
  </clause>

  <clause id="4861">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,4752,a(flip),b,4833,a),flip(a)].">
      <j1 rule="hyper" parents="373 4752 4833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4862">
    <literal><![CDATA[
      (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) = L(R(x,y,x),y,R(x,y,x))
    ]]></literal>
    <justification jstring="[para(4861(a,1),4748(a,1,2))].">
      <j1 rule="para" parents="4861 4748"/>
    </justification>
  </clause>

  <clause id="4863">
    <literal><![CDATA[
      ((x * y) \ T(x,y)) * T(x * y,y \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(22(a,2),4586(a,1,1,2))].">
      <j1 rule="para" parents="22 4586"/>
    </justification>
  </clause>

  <clause id="4864">
    <literal><![CDATA[
      R(x,y,z) * (K(u,x) * w) != v5 * (R(x,y,z) * w)
    ]]></literal>
    <literal><![CDATA[
      R(K(u,x),R(x,y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(4607(a,1),664(a,1))].">
      <j1 rule="para" parents="4607 664"/>
    </justification>
  </clause>

  <clause id="4865">
    <literal><![CDATA[
      (T(x,(y / z) / (1 / z)) \ x) * (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,2458,a(flip),b,4794,a),flip(a)].">
      <j1 rule="hyper" parents="64 2458 4794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4866">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(606,a,4842,a)].">
      <j1 rule="hyper" parents="606 4842"/>
    </justification>
  </clause>

  <clause id="4867">
    <literal><![CDATA[
      (K(x,y) * L(x,z,u)) * w = L(x,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(4073(a,1),4842(a,1,1))].">
      <j1 rule="para" parents="4073 4842"/>
    </justification>
  </clause>

  <clause id="4868">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(4866(a,1),51(a,2))].">
      <j1 rule="para" parents="4866 51"/>
    </justification>
  </clause>

  <clause id="4869">
    <literal><![CDATA[
      L(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[para(593(a,1),4866(a,1,3))].">
      <j1 rule="para" parents="593 4866"/>
    </justification>
  </clause>

  <clause id="4870">
    <literal><![CDATA[
      L(x,K(y,z),1 / y) = x
    ]]></literal>
    <justification jstring="[hyper(2277,a,4869,a)].">
      <j1 rule="hyper" parents="2277 4869"/>
    </justification>
  </clause>

  <clause id="4872">
    <literal><![CDATA[
      L(x,K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4869(a,1),51(a,2))].">
      <j1 rule="para" parents="4869 51"/>
    </justification>
  </clause>

  <clause id="4873">
    <literal><![CDATA[
      (R(x,y,z) * T(u,x)) * T(x,u) = R(R(x,u,x),y,z) * (u * x)
    ]]></literal>
    <justification jstring="[para(4790(a,1),4671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4790 4671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4874">
    <literal><![CDATA[
      R(x / y,x / (x / y),x / y) = (x * (y \ x)) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,914,a(flip),b,4774,a),flip(a)].">
      <j1 rule="hyper" parents="373 914 4774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4875">
    <literal><![CDATA[
      R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * ((x / y) \ x)) / x
    ]]></literal>
    <justification jstring="[para(4773(a,2),4874(a,1,2))].">
      <j1 rule="para" parents="4773 4874"/>
    </justification>
  </clause>

  <clause id="4876">
    <literal><![CDATA[
      T(x,y \ 1) * (x \ (y * z)) = y * (T(x,y \ 1) * (x \ z))
    ]]></literal>
    <justification jstring="[para(4438(a,1),4488(a,2,2))].">
      <j1 rule="para" parents="4438 4488"/>
    </justification>
  </clause>

  <clause id="4877">
    <literal><![CDATA[
      T(x,y) * (T(x,x \ 1) \ z) = ((x \ 1) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(3666(a,1),4489(a,1,2))].">
      <j1 rule="para" parents="3666 4489"/>
    </justification>
  </clause>

  <clause id="4878">
    <literal><![CDATA[
      (((x \ 1) \ 1) * T(x \ 1,y)) * z = T(1 / x,y) * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4142,a(flip),b,4877,a),flip(a)].">
      <j1 rule="hyper" parents="64 4142 4877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4879">
    <literal><![CDATA[
      (T(x,y) * (y * x)) / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y * x) * T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4669(a,2),4642(a,1))].">
      <j1 rule="para" parents="4669 4642"/>
    </justification>
  </clause>

  <clause id="4880">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4838(a,1),4857(a,1,1))].">
      <j1 rule="para" parents="4838 4857"/>
    </justification>
  </clause>

  <clause id="4881">
    <literal><![CDATA[
      x * (x / (x / T(y,x))) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(4700,a,4880,a),flip(a)].">
      <j1 rule="hyper" parents="4700 4880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4882">
    <literal><![CDATA[
      x / (x / T(y,x)) = T(x / (x / y),x)
    ]]></literal>
    <justification jstring="[hyper(269,a,4804,a,b,4881,a),flip(a)].">
      <j1 rule="hyper" parents="269 4804 4881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4883">
    <literal><![CDATA[
      T(x / (x / y),x) \ x = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(215,a,4882,a)].">
      <j1 rule="hyper" parents="215 4882"/>
    </justification>
  </clause>

  <clause id="4884">
    <literal><![CDATA[
      x / T(y \ x,x) = T(x / y,x) \ x
    ]]></literal>
    <justification jstring="[para(79(a,1),4883(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 4883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4885">
    <literal><![CDATA[
      L(x,x \ y,x) \ y = y / T(x,y)
    ]]></literal>
    <justification jstring="[para(4771(a,1),4883(a,1,1))].">
      <j1 rule="para" parents="4771 4883"/>
    </justification>
  </clause>

  <clause id="4886">
    <literal><![CDATA[
      L(x,x \ y,x) = y / (T(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(225,a,4630,a,b,4885,a),flip(a)].">
      <j1 rule="hyper" parents="225 4630 4885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      (x * x) * (y * R(z,y,z)) = T(z * ((x * x) * y),z)
    ]]></literal>
    <justification jstring="[para(2965(a,1),4744(a,1,2,2))].">
      <j1 rule="para" parents="2965 4744"/>
    </justification>
  </clause>

  <clause id="4889">
    <literal><![CDATA[
      T(x * ((y * y) * z),x) = (y * y) * T(x * z,x)
    ]]></literal>
    <justification jstring="[para(4741(a,1),4887(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4741 4887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4890">
    <literal><![CDATA[
      T(T(x * ((y * y) * z),x),y * y) = T(x * z,x) * (y * y)
    ]]></literal>
    <justification jstring="[para(4889(a,2),254(a,1,1))].">
      <j1 rule="para" parents="4889 254"/>
    </justification>
  </clause>

  <clause id="4891">
    <literal><![CDATA[
      (R(x,y,z) * T(u,x)) * T(x,u) = (R(x,y,z) * u) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,506,a(flip),b,4873,a),flip(a)].">
      <j1 rule="hyper" parents="373 506 4873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4892">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (R(x,y,x) * y) * x
    ]]></literal>
    <justification jstring="[para(1940(a,1),4891(a,1,1))].">
      <j1 rule="para" parents="1940 4891"/>
    </justification>
  </clause>

  <clause id="4893">
    <literal><![CDATA[
      (R(x,y,x) * y) * x = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4752,a(flip),b,4892,a),flip(a)].">
      <j1 rule="hyper" parents="64 4752 4892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4894">
    <literal><![CDATA[
      (R(x,y,x) * y) \ (R(x,y,x) * T(x * y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,4833,a,b,4892,a(flip))].">
      <j1 rule="hyper" parents="139 4833 4892"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(4893(a,1),335(a,1,2))].">
      <j1 rule="para" parents="4893 335"/>
    </justification>
  </clause>

  <clause id="4896">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(4751,a,4894,a)].">
      <j1 rule="hyper" parents="4751 4894"/>
    </justification>
  </clause>

  <clause id="4897">
    <literal><![CDATA[
      (x * T(y,x)) / T((x \ y) * x,x) = T(x,T(x,y) \ y)
    ]]></literal>
    <justification jstring="[para(4624(a,1),4763(a,1,1,2))].">
      <j1 rule="para" parents="4624 4763"/>
    </justification>
  </clause>

  <clause id="4898">
    <literal><![CDATA[
      (x * y) / T((y \ x) * y,y) = T(y,T(y,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,250,a(flip),b,4897,a)].">
      <j1 rule="hyper" parents="64 250 4897"/>
    </justification>
  </clause>

  <clause id="4899">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (y * L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(y,L(x,z,u)),L(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(4798(a,2),481(a,1))].">
      <j1 rule="para" parents="4798 481"/>
    </justification>
  </clause>

  <clause id="4900">
    <literal><![CDATA[
      T(1 / x,y) * ((x \ 1) \ z) = (x * T(1 / x,y)) * z
    ]]></literal>
    <justification jstring="[para(4121(a,1),4878(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4121 4878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4901">
    <literal><![CDATA[
      (T(1 / x,y) * z) / ((x * T(1 / x,y)) * z) = x \ 1
    ]]></literal>
    <justification jstring="[para(4900(a,1),4156(a,1,2))].">
      <j1 rule="para" parents="4900 4156"/>
    </justification>
  </clause>

  <clause id="4902">
    <literal><![CDATA[
      T(1 / x,y) * ((x * T(1 / x,y)) \ z) = (x \ 1) * z
    ]]></literal>
    <justification jstring="[para(4901(a,1),385(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4901 385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4903">
    <literal><![CDATA[
      (x \ 1) \ T(1 / x,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(1337,a,4902,a)].">
      <j1 rule="hyper" parents="1337 4902"/>
    </justification>
  </clause>

  <clause id="4904">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(2727,a,4573,a)].">
      <j1 rule="hyper" parents="2727 4573"/>
    </justification>
  </clause>

  <clause id="4905">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(y \ 1) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(3150(a,1),4904(a,2,1))].">
      <j1 rule="para" parents="3150 4904"/>
    </justification>
  </clause>

  <clause id="4906">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4428,a(flip),b,4905,a),flip(a)].">
      <j1 rule="hyper" parents="64 4428 4905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4907">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4549,a,4906,a),flip(a)].">
      <j1 rule="hyper" parents="4549 4906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4908">
    <literal><![CDATA[
      T(x,T((x \ 1) * y,x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(3425(a,1),4907(a,1,2))].">
      <j1 rule="para" parents="3425 4907"/>
    </justification>
  </clause>

  <clause id="4909">
    <literal><![CDATA[
      T(x,(x \ 1) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(4710,a,4908,a)].">
      <j1 rule="hyper" parents="4710 4908"/>
    </justification>
  </clause>

  <clause id="4910">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3150,a,b,4909,a)].">
      <j1 rule="hyper" parents="64 3150 4909"/>
    </justification>
  </clause>

  <clause id="4912">
    <literal><![CDATA[
      x \ T(x,T(y,y \ x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4909(a,1),4709(a,1,2,2,1))].">
      <j1 rule="para" parents="4909 4709"/>
    </justification>
  </clause>

  <clause id="4913">
    <literal><![CDATA[
      x / T(y,(1 / y) * x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,4910,a,b,116,a(flip))].">
      <j1 rule="hyper" parents="225 4910 116"/>
    </justification>
  </clause>

  <clause id="4914">
    <literal><![CDATA[
      ((1 / x) * y) \ L(y,x,x) = 1 / (1 / T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(4910(a,1),3784(a,2,2,2))].">
      <j1 rule="para" parents="4910 3784"/>
    </justification>
  </clause>

  <clause id="4915">
    <literal><![CDATA[
      x / T(y \ 1,y * x) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(79(a,1),4913(a,1,2,2,1))].">
      <j1 rule="para" parents="79 4913"/>
    </justification>
  </clause>

  <clause id="4916">
    <literal><![CDATA[
      T(x \ 1,x * y) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(215,a,4915,a),flip(a)].">
      <j1 rule="hyper" parents="215 4915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4917">
    <literal><![CDATA[
      T(x \ 1,x * x) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1130,a(flip),b,4916,a),flip(a)].">
      <j1 rule="hyper" parents="373 1130 4916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4918">
    <literal><![CDATA[
      T((x / y) \ 1,x) = (((x / y) \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[para(12(a,1),4916(a,1,2))].">
      <j1 rule="para" parents="12 4916"/>
    </justification>
  </clause>

  <clause id="4919">
    <literal><![CDATA[
      T(((x \ 1) \ y) \ y,K(x,z)) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(4916(a,1),2896(a,1,1))].">
      <j1 rule="para" parents="4916 2896"/>
    </justification>
  </clause>

  <clause id="4920">
    <literal><![CDATA[
      T(1 / x,x * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(41,a,278,a,b,4917,a(flip))].">
      <j1 rule="hyper" parents="41 278 4917"/>
    </justification>
  </clause>

  <clause id="4921">
    <literal><![CDATA[
      (x * x) \ L(x,x,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(575,a,4920,a)].">
      <j1 rule="hyper" parents="575 4920"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      L(1 / x,y,z) * (x * x) = (x * x) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(4920(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4920 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4923">
    <literal><![CDATA[
      ((x * x) \ (1 / x)) * y = (x \ 1) * ((x * x) \ y)
    ]]></literal>
    <justification jstring="[para(4920(a,1),952(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4920 952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4924">
    <literal><![CDATA[
      ((x * x) \ y) * L(x,x,x) = (x \ 1) * T(y,L(x,x,x))
    ]]></literal>
    <justification jstring="[para(4921(a,1),1087(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4921 1087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4925">
    <literal><![CDATA[
      ((x * x) \ y) * L(x,x,x) = T(y,x * x) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(4921(a,1),952(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4921 952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4926">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(157,a,4912,a),flip(a)].">
      <j1 rule="hyper" parents="157 4912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4927">
    <literal><![CDATA[
      K(x,(y \ x) / x) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4415,a,4926,a)].">
      <j1 rule="hyper" parents="4415 4926"/>
    </justification>
  </clause>

  <clause id="4928">
    <literal><![CDATA[
      ((x \ 1) * ((x * x) \ y)) \ z = ((1 / x) * y) \ ((x * x) * z)
    ]]></literal>
    <justification jstring="[para(4923(a,1),942(a,1,1))].">
      <j1 rule="para" parents="4923 942"/>
    </justification>
  </clause>

  <clause id="4929">
    <literal><![CDATA[
      ((1 / x) * y) \ L(y,x,x) = T(1 / (1 / x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,3570,a(flip),b,4914,a),flip(a)].">
      <j1 rule="hyper" parents="373 3570 4914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4930">
    <literal><![CDATA[
      L(1 / x,y,z) * (x * x) = x * (L(x \ 1,y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1830,a(flip),b,4922,a),flip(a)].">
      <j1 rule="hyper" parents="373 1830 4922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4931">
    <literal><![CDATA[
      (L(x \ 1,y,z) * x) * x = x * (L(x \ 1,y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1703,a,b,4930,a)].">
      <j1 rule="hyper" parents="64 1703 4930"/>
    </justification>
  </clause>

  <clause id="4933">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(4862(a,1),4895(a,1))].">
      <j1 rule="para" parents="4862 4895"/>
    </justification>
  </clause>

  <clause id="4934">
    <literal><![CDATA[
      R(x / (x / y),(y * (x / y)) / y,x / (x / y)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(82(a,1),4875(a,2,1,2))].">
      <j1 rule="para" parents="82 4875"/>
    </justification>
  </clause>

  <clause id="4936">
    <literal><![CDATA[
      T(x,y) * L(T(T(x,y),x) \ y,z,u) = T(T(x,y) * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[para(200(a,1),4482(a,1,1))].">
      <j1 rule="para" parents="200 4482"/>
    </justification>
  </clause>

  <clause id="4937">
    <literal><![CDATA[
      T(T(x,y) * L(x \ y,z,u),x) = T(x,y) * L(T(x,y) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(200(a,1),4936(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="200 4936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4938">
    <literal><![CDATA[
      T(T(x,y) * L(x \ y,z,u),x) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,3246,a(flip),b,4937,a),flip(a)].">
      <j1 rule="hyper" parents="373 3246 4937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4939">
    <literal><![CDATA[
      T(x * L(x \ (x * y),z,u),x * y) = T(T(x,x * y) * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),4938(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 4938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4940">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = T(x * L(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),4939(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 4939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4941">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ (x * (K(y,x) * (z * u))) = L(L(u,z,x),x * z,K(y,x))
    ]]></literal>
    <justification jstring="[para(4534(a,1),4543(a,1,2))].">
      <j1 rule="para" parents="4534 4543"/>
    </justification>
  </clause>

  <clause id="4942">
    <literal><![CDATA[
      L(T((x \ 1) * x,x \ 1),y,z) = a(1 / L(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1788,a,4753,a),flip(a)].">
      <j1 rule="hyper" parents="1788 4753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4943">
    <literal><![CDATA[
      a(1 / L(x,y,z),x,x \ 1) = L(K(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(3596(a,1),4942(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3596 4942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4944">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) / R(L(x,y,z) \ 1,x,x \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,4943,a(flip),b,1783,a)].">
      <j1 rule="hyper" parents="142 4943 1783"/>
    </justification>
  </clause>

  <clause id="4946">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) / R(L(x,y,z) \ 1,x,x \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4200(a,1),4944(a,1,1))].">
      <j1 rule="para" parents="4200 4944"/>
    </justification>
  </clause>

  <clause id="4947">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,u) = L(L(x,y,u),u * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(1081,a,4941,a)].">
      <j1 rule="hyper" parents="1081 4941"/>
    </justification>
  </clause>

  <clause id="4948">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,T(x,y) \ x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(4568(a,1),4571(a,2,2))].">
      <j1 rule="para" parents="4568 4571"/>
    </justification>
  </clause>

  <clause id="4949">
    <literal><![CDATA[
      x \ ((T(y,x) \ y) * z) = ((y * x) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,4523,a(flip),b,4948,a),flip(a)].">
      <j1 rule="hyper" parents="139 4523 4948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4950">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(157,a,4949,a)].">
      <j1 rule="hyper" parents="157 4949"/>
    </justification>
  </clause>

  <clause id="4951">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,4622,a,b,4950,a),flip(a)].">
      <j1 rule="hyper" parents="373 4622 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4952">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,4378,a,b,4950,a)].">
      <j1 rule="hyper" parents="64 4378 4950"/>
    </justification>
  </clause>

  <clause id="4953">
    <literal><![CDATA[
      ((x * y) / x) \ x = y \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,4455,a(flip),b,4951,a),flip(a)].">
      <j1 rule="hyper" parents="139 4455 4951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4954">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2489,a,b,4951,a)].">
      <j1 rule="hyper" parents="64 2489 4951"/>
    </justification>
  </clause>

  <clause id="4955">
    <literal><![CDATA[
      (x * y) \ ((x * R(x,y,y \ x)) / (x * y)) = (((y \ x) * (x * y)) / (y \ x)) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(995(a,2),4953(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="995 4953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4956">
    <literal><![CDATA[
      ((x * y) / x) * (T(y,x) * z) = y * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1335,a,4954,a)].">
      <j1 rule="hyper" parents="1335 4954"/>
    </justification>
  </clause>

  <clause id="4957">
    <literal><![CDATA[
      T(x,y) * (T(x,y) * z) = x * (T(T(x,y),y) * z)
    ]]></literal>
    <justification jstring="[para(256(a,1),4956(a,1,1)),flip(a)].">
      <j1 rule="para" parents="256 4956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4958">
    <literal><![CDATA[
      x * (T(T(x,x * x),x * x) * y) = L(x,x,x) * (T(x,x * x) * y)
    ]]></literal>
    <justification jstring="[para(118(a,1),4957(a,1,1)),flip(a)].">
      <j1 rule="para" parents="118 4957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4959">
    <literal><![CDATA[
      x * (T(T(x,x * x),x * x) * y) = L(x,x,x) * (L(x,x,x) * y)
    ]]></literal>
    <justification jstring="[para(118(a,1),4958(a,2,2,1))].">
      <j1 rule="para" parents="118 4958"/>
    </justification>
  </clause>

  <clause id="4960">
    <literal><![CDATA[
      x * (T(T(x,x * x),x * x) * y) = L((x * x) * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1259,a(flip),b,4959,a),flip(a)].">
      <j1 rule="hyper" parents="373 1259 4959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4961">
    <literal><![CDATA[
      T(x,R(x * K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(288,a,4858,a),flip(a)].">
      <j1 rule="hyper" parents="288 4858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4963">
    <literal><![CDATA[
      L(x,1 / (y \ z),L(1 / (y \ z),y \ z,y)) = L(x,1 / (1 / (z \ y)),y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1643,a(flip),b,4312,a),flip(a)].">
      <j1 rule="hyper" parents="373 1643 4312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4964">
    <literal><![CDATA[
      (R(x,y,z) * (u * x)) \ ((u * x) * R(T(x,u),y,z)) = a(x,T(u,x),R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(1900(a,1),4832(a,1,1))].">
      <j1 rule="para" parents="1900 4832"/>
    </justification>
  </clause>

  <clause id="4965">
    <literal><![CDATA[
      (R(x,y,z) * (u * x)) \ ((R(x,y,z) * u) * x) = a(x,T(u,x),R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(1959(a,1),4964(a,1,2))].">
      <j1 rule="para" parents="1959 4964"/>
    </justification>
  </clause>

  <clause id="4966">
    <literal><![CDATA[
      a(x,T(y,x),R(T(x,y),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(R(x,z,u),y,x) = w
    ]]></literal>
    <justification jstring="[para(4965(a,1),959(a,1))].">
      <j1 rule="para" parents="4965 959"/>
    </justification>
  </clause>

  <clause id="4967">
    <literal><![CDATA[
      ((x * (y * T(y \ T(z,x),y))) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(3412(a,1),4570(a,1,1))].">
      <j1 rule="para" parents="3412 4570"/>
    </justification>
  </clause>

  <clause id="4968">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(115(a,1),4967(a,1,1,1,2))].">
      <j1 rule="para" parents="115 4967"/>
    </justification>
  </clause>

  <clause id="4969">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(4568(a,1),4968(a,1,2))].">
      <j1 rule="para" parents="4568 4968"/>
    </justification>
  </clause>

  <clause id="4970">
    <literal><![CDATA[
      x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(4078(a,1),4537(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4078 4537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4971">
    <literal><![CDATA[
      x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(4119,a,4970,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4119 4970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4972">
    <literal><![CDATA[
      x \ ((((x * y) \ x) \ 1) \ T(((x * y) \ x) \ 1,x)) = (K(y,x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(4971(a,1),4528(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4971 4528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4973">
    <literal><![CDATA[
      x \ (((x * y) \ x) * T(((x * y) \ x) \ 1,x)) = (K(y,x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(4052(a,1),4972(a,1,2))].">
      <j1 rule="para" parents="4052 4972"/>
    </justification>
  </clause>

  <clause id="4974">
    <literal><![CDATA[
      (K(x,y) \ y) \ 1 = y \ K(x,y)
    ]]></literal>
    <justification jstring="[para(1567(a,2),4973(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1567 4973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4975">
    <literal><![CDATA[
      1 / (x \ K(y,x)) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(226,a,4974,a)].">
      <j1 rule="hyper" parents="226 4974"/>
    </justification>
  </clause>

  <clause id="4976">
    <literal><![CDATA[
      R(1 / (x / y),x / y,(x / y) \ T(x,x \ y)) = ((x / y) * (y / x)) * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(4667(a,1),4589(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4667 4589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4977">
    <literal><![CDATA[
      R(1 / (x / y),x / y,(x / y) \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(373,a,2305,a(flip),b,4976,a),flip(a)].">
      <j1 rule="hyper" parents="373 2305 4976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4978">
    <literal><![CDATA[
      R(1 / (x / y),x / y,x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[para(4583(a,1),4977(a,1,3))].">
      <j1 rule="para" parents="4583 4977"/>
    </justification>
  </clause>

  <clause id="4979">
    <literal><![CDATA[
      ((x / y) \ (1 / (y / x))) * R(1 / (y / x),y / x,y * (x / y)) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(4978(a,1),2154(a,1,1,1))].">
      <j1 rule="para" parents="4978 2154"/>
    </justification>
  </clause>

  <clause id="4980">
    <literal><![CDATA[
      ((x / y) \ (1 / (y / x))) * (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(4978(a,1),4979(a,1,2))].">
      <j1 rule="para" parents="4978 4979"/>
    </justification>
  </clause>

  <clause id="4981">
    <literal><![CDATA[
      T(x / y,(x / y) \ (1 / (y / x))) = x / y
    ]]></literal>
    <justification jstring="[hyper(410,a,4980,a)].">
      <j1 rule="hyper" parents="410 4980"/>
    </justification>
  </clause>

  <clause id="4982">
    <literal><![CDATA[
      T(L(x,y,y \ 1),y) \ ((1 / y) \ T(L(x,y,y \ 1),(1 / y) \ 1)) = L(x,y,y \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(82(a,1),4609(a,1,1,2))].">
      <j1 rule="para" parents="82 4609"/>
    </justification>
  </clause>

  <clause id="4983">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) \ ((1 / y) \ T(L(x,y,y \ 1),(1 / y) \ 1)) = L(x,y,y \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(25(a,2),4982(a,1,1))].">
      <j1 rule="para" parents="25 4982"/>
    </justification>
  </clause>

  <clause id="4984">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ T(L(y,x,x \ 1),(1 / x) \ 1)) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1639(a,1),4983(a,1,1))].">
      <j1 rule="para" parents="1639 4983"/>
    </justification>
  </clause>

  <clause id="4985">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ T(L(y,x,x \ 1),x)) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(82(a,1),4984(a,1,2,2,2))].">
      <j1 rule="para" parents="82 4984"/>
    </justification>
  </clause>

  <clause id="4986">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ L(T(y,x),x,x \ 1)) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(25(a,2),4985(a,1,2,2))].">
      <j1 rule="para" parents="25 4985"/>
    </justification>
  </clause>

  <clause id="4987">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ ((1 / x) * (y * x))) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1639(a,1),4986(a,1,2,2))].">
      <j1 rule="para" parents="1639 4986"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * x) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),4987(a,1,2))].">
      <j1 rule="para" parents="9 4987"/>
    </justification>
  </clause>

  <clause id="4990">
    <literal><![CDATA[
      (((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((x * ((z * u) / ((y * z) * u))) / x) * ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(111(a,1),2754(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 2754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4991">
    <literal><![CDATA[
      (((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((y * z) * u) * ((x * (((y * z) * u) \ (z * u))) / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1237,a(flip),b,4990,a),flip(a)].">
      <j1 rule="hyper" parents="373 1237 4990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4992">
    <literal><![CDATA[
      (((x * (1 / R(y,z,u))) / x) * R(y,z,u)) * (z * u) = ((y * z) * ((x * ((y * z) \ z)) / x)) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,3291,a(flip),b,4991,a),flip(a)].">
      <j1 rule="hyper" parents="373 3291 4991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4993">
    <literal><![CDATA[
      (R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u)) * (y * z) = ((x * y) * ((u * ((x * y) \ y)) / u)) * z
    ]]></literal>
    <justification jstring="[para(1237(a,1),4992(a,1,1))].">
      <j1 rule="para" parents="1237 4992"/>
    </justification>
  </clause>

  <clause id="4994">
    <literal><![CDATA[
      (R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u)) * (y * z) = ((x * ((u * (x \ 1)) / u)) * y) * z
    ]]></literal>
    <justification jstring="[para(3302(a,1),4993(a,2,1))].">
      <j1 rule="para" parents="3302 4993"/>
    </justification>
  </clause>

  <clause id="4995">
    <literal><![CDATA[
      R(x,y,z) * ((u * (R(x,y,z) \ 1)) / u) = R(x * ((u * (x \ 1)) / u),y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,111,a,b,4994,a),flip(a)].">
      <j1 rule="hyper" parents="36 111 4994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4996">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,(y / R(x,z,u)) / y)
    ]]></literal>
    <justification jstring="[hyper(2804,a,4995,a),flip(a)].">
      <j1 rule="hyper" parents="2804 4995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4997">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = K(x,(x / R(y,z,u)) / x)
    ]]></literal>
    <justification jstring="[para(4374(a,1),4996(a,1,1))].">
      <j1 rule="para" parents="4374 4996"/>
    </justification>
  </clause>

  <clause id="4998">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = x \ T(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,4384,a(flip),b,4997,a),flip(a)].">
      <j1 rule="hyper" parents="373 4384 4997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4999">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,(z \ 1) \ 1),z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4418,a,b,4998,a)].">
      <j1 rule="hyper" parents="373 4418 4998"/>
    </justification>
  </clause>

  <clause id="5000">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,z),z,y)
    ]]></literal>
    <justification jstring="[para(3871(a,1),4999(a,2,1,2))].">
      <j1 rule="para" parents="3871 4999"/>
    </justification>
  </clause>

  <clause id="5001">
    <literal><![CDATA[
      T(x \ T(x,(y * z) / z),T(y,u)) = R(x \ T(x,y),y,z)
    ]]></literal>
    <justification jstring="[para(4818(a,1),5000(a,1,1,2))].">
      <j1 rule="para" parents="4818 5000"/>
    </justification>
  </clause>

  <clause id="5002">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = R(x \ T(x,y),y,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),5001(a,1,1,2,2))].">
      <j1 rule="para" parents="11 5001"/>
    </justification>
  </clause>

  <clause id="5003">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(5002(a,2),432(a,1)),flip(b)].">
      <j1 rule="para" parents="5002 432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5004">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5003,a,5002,a),flip(a)].">
      <j1 rule="hyper" parents="5003 5002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5005">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(5004(a,1),4372(a,1,1))].">
      <j1 rule="para" parents="5004 4372"/>
    </justification>
  </clause>

  <clause id="5006">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[para(5004(a,1),4952(a,1,1))].">
      <j1 rule="para" parents="5004 4952"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      (T(x,y) \ x) * z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(4557,a,5006,a),flip(a)].">
      <j1 rule="hyper" parents="4557 5006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5008">
    <literal><![CDATA[
      (T(x,y) \ x) * (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(4499,a,5006,a),flip(a)].">
      <j1 rule="hyper" parents="4499 5006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5010">
    <literal><![CDATA[
      (T(x,y) \ x) \ z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,74,a(flip),b,5007,a)].">
      <j1 rule="hyper" parents="139 74 5007"/>
    </justification>
  </clause>

  <clause id="5011">
    <literal><![CDATA[
      T(x,y) * (x \ z) = y * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4622,a,b,5007,a)].">
      <j1 rule="hyper" parents="64 4622 5007"/>
    </justification>
  </clause>

  <clause id="5012">
    <literal><![CDATA[
      x * (T(x,(y / z) / (1 / z)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,4865,a(flip),b,5007,a),flip(a)].">
      <j1 rule="hyper" parents="64 4865 5007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5013">
    <literal><![CDATA[
      x * T(x \ y,z) = z * (T(z,y / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4618,a(flip),b,5007,a)].">
      <j1 rule="hyper" parents="64 4618 5007"/>
    </justification>
  </clause>

  <clause id="5014">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(64,a,4622,a,b,5008,a)].">
      <j1 rule="hyper" parents="64 4622 5008"/>
    </justification>
  </clause>

  <clause id="5015">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * z) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,5008,a(flip),b,4950,a),flip(a)].">
      <j1 rule="hyper" parents="139 5008 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5016">
    <literal><![CDATA[
      T(x,y) \ (y * z) = x \ (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,5008,a(flip),b,4622,a)].">
      <j1 rule="hyper" parents="139 5008 4622"/>
    </justification>
  </clause>

  <clause id="5017">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(5008(a,1),4621(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5008 4621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5018">
    <literal><![CDATA[
      T(x,y \ 1) * (x \ (y * (T(y \ 1,x) * z))) = L(z,T(y \ 1,x),y)
    ]]></literal>
    <justification jstring="[hyper(4614,a,5010,a),flip(a)].">
      <j1 rule="hyper" parents="4614 5010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5019">
    <literal><![CDATA[
      T(x,y) \ (T(y,x) \ z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,2416,a(flip),b,5011,a)].">
      <j1 rule="hyper" parents="139 2416 5011"/>
    </justification>
  </clause>

  <clause id="5020">
    <literal><![CDATA[
      x \ (y \ (T(y,x) * z)) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,2401,a,b,5011,a(flip))].">
      <j1 rule="hyper" parents="139 2401 5011"/>
    </justification>
  </clause>

  <clause id="5022">
    <literal><![CDATA[
      ((x * y) / x) * (x * z) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5014,a(flip),b,4954,a)].">
      <j1 rule="hyper" parents="145 5014 4954"/>
    </justification>
  </clause>

  <clause id="5023">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(5014(a,2),720(a,1))].">
      <j1 rule="para" parents="5014 720"/>
    </justification>
  </clause>

  <clause id="5024">
    <literal><![CDATA[
      T(x,y) * ((x \ T(y,x)) * z) = y * L(z,x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(598(a,1),5014(a,1,2))].">
      <j1 rule="para" parents="598 5014"/>
    </justification>
  </clause>

  <clause id="5025">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x \ y,x) * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(869,a,5017,a)].">
      <j1 rule="hyper" parents="869 5017"/>
    </justification>
  </clause>

  <clause id="5026">
    <literal><![CDATA[
      T(x,y) \ (x * (y * z)) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(149,a,5017,a)].">
      <j1 rule="hyper" parents="149 5017"/>
    </justification>
  </clause>

  <clause id="5027">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,5017,a(flip),b,4672,a)].">
      <j1 rule="hyper" parents="139 5017 4672"/>
    </justification>
  </clause>

  <clause id="5028">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(5017(a,1),4674(a,1,1))].">
      <j1 rule="para" parents="5017 4674"/>
    </justification>
  </clause>

  <clause id="5029">
    <literal><![CDATA[
      T(x,y / x) \ ((x \ y) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[para(117(a,1),5019(a,1,2,1))].">
      <j1 rule="para" parents="117 5019"/>
    </justification>
  </clause>

  <clause id="5030">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * z) = L(T(y,x) \ z,y,x)
    ]]></literal>
    <justification jstring="[para(5020(a,1),346(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5020 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5031">
    <literal><![CDATA[
      (x \ T(x,x \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(85(a,1),5005(a,1,2))].">
      <j1 rule="para" parents="85 5005"/>
    </justification>
  </clause>

  <clause id="5033">
    <literal><![CDATA[
      (x \ ((x \ y) \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(116(a,1),5031(a,1,1,2))].">
      <j1 rule="para" parents="116 5031"/>
    </justification>
  </clause>

  <clause id="5035">
    <literal><![CDATA[
      (x * (1 / x)) \ 1 = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1747(a,1),5033(a,1,1))].">
      <j1 rule="para" parents="1747 5033"/>
    </justification>
  </clause>

  <clause id="5037">
    <literal><![CDATA[
      (x * y) / (1 / x) = y * (T(x,y) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,809,a(flip),b,5022,a)].">
      <j1 rule="hyper" parents="64 809 5022"/>
    </justification>
  </clause>

  <clause id="5038">
    <literal><![CDATA[
      (x \ y) * (T(x,x \ y) * z) = (y / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),5022(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5039">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * (T(x,y) * a(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(983(a,1),5022(a,1,2))].">
      <j1 rule="para" parents="983 5022"/>
    </justification>
  </clause>

  <clause id="5040">
    <literal><![CDATA[
      a((x * y) / x,x,z) = (y * (T(x,y) * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(5022(a,1),93(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5022 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5041">
    <literal><![CDATA[
      (x * y) / (1 / x) = y * (x * T(x,y))
    ]]></literal>
    <justification jstring="[para(273(a,1),5037(a,2,2))].">
      <j1 rule="para" parents="273 5037"/>
    </justification>
  </clause>

  <clause id="5042">
    <literal><![CDATA[
      ((x \ y) / y) * (z * T(z,x \ 1)) = (z * ((x \ y) / y)) / (1 / z)
    ]]></literal>
    <justification jstring="[para(4814(a,1),5041(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4814 5041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5043">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(5027(a,1),608(a,1))].">
      <j1 rule="para" parents="5027 608"/>
    </justification>
  </clause>

  <clause id="5044">
    <literal><![CDATA[
      L(x,T(y,y \ z),T((y / z) \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(4579(a,1),5043(a,1,2))].">
      <j1 rule="para" parents="4579 5043"/>
    </justification>
  </clause>

  <clause id="5045">
    <literal><![CDATA[
      T(x,x \ y) \ ((x \ y) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[para(4636(a,1),5029(a,1,1))].">
      <j1 rule="para" parents="4636 5029"/>
    </justification>
  </clause>

  <clause id="5047">
    <literal><![CDATA[
      (x \ (y \ x)) * (T(x,y \ 1) * z) = ((y \ x) / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(4575(a,1),5038(a,1,2,1))].">
      <j1 rule="para" parents="4575 5038"/>
    </justification>
  </clause>

  <clause id="5048">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(959,a,5028,a),flip(a)].">
      <j1 rule="hyper" parents="959 5028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5049">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(5028(a,1),959(a,1))].">
      <j1 rule="para" parents="5028 959"/>
    </justification>
  </clause>

  <clause id="5050">
    <literal><![CDATA[
      a(T(x,T(y,x)),T(T(y,x),x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(4966,a,5048,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4966 5048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5051">
    <literal><![CDATA[
      a(T(x * (y / x),x),T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x * (y / x),x,z) = u
    ]]></literal>
    <justification jstring="[para(4682(a,1),5049(a,1,2))].">
      <j1 rule="para" parents="4682 5049"/>
    </justification>
  </clause>

  <clause id="5052">
    <literal><![CDATA[
      (x * L(y,z \ T(x,z),z)) \ (x * y) = a(T(z,x),T(z,x) \ x,y)
    ]]></literal>
    <justification jstring="[para(5024(a,1),4663(a,1,1))].">
      <j1 rule="para" parents="5024 4663"/>
    </justification>
  </clause>

  <clause id="5053">
    <literal><![CDATA[
      a((x * y) / x,x,z) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,259,a(flip),b,5040,a),flip(a)].">
      <j1 rule="hyper" parents="373 259 5040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5054">
    <literal><![CDATA[
      (x * ((x \ y) / y)) / (1 / x) = ((x \ y) / y) * ((1 / x) \ x)
    ]]></literal>
    <justification jstring="[para(1160(a,1),5042(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1160 5042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5055">
    <literal><![CDATA[
      (x * ((x \ y) / y)) / (1 / x) = R(x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1995,a(flip),b,5054,a),flip(a)].">
      <j1 rule="hyper" parents="373 1995 5054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5056">
    <literal><![CDATA[
      a(T(x,y),T(T(y,x),x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(4619(a,1),5050(a,1,1))].">
      <j1 rule="para" parents="4619 5050"/>
    </justification>
  </clause>

  <clause id="5057">
    <literal><![CDATA[
      x * (T(y,x \ 1) * (y \ (T(x \ 1,y) * z))) = L(z,T(x \ 1,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4876,a(flip),b,5018,a)].">
      <j1 rule="hyper" parents="64 4876 5018"/>
    </justification>
  </clause>

  <clause id="5058">
    <literal><![CDATA[
      L(x,T(y \ 1,z),y) = y * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(5014(a,1),5057(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5014 5057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5059">
    <literal><![CDATA[
      L(x,T(y \ 1,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(5058(a,2),611(a,1))].">
      <j1 rule="para" parents="5058 611"/>
    </justification>
  </clause>

  <clause id="5061">
    <literal><![CDATA[
      L(T(1 / x,y) \ z,x \ 1,x) = (x * T(1 / x,y)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(5059,a,4166,a)].">
      <j1 rule="hyper" parents="5059 4166"/>
    </justification>
  </clause>

  <clause id="5062">
    <literal><![CDATA[
      T((x \ 1) * (x * ((y * z) / y)),y) = T(1 / x,y) * ((x * T(1 / x,y)) \ (x * z))
    ]]></literal>
    <justification jstring="[para(5061(a,1),4224(a,2,2))].">
      <j1 rule="para" parents="5061 4224"/>
    </justification>
  </clause>

  <clause id="5063">
    <literal><![CDATA[
      T((x \ 1) * (x * ((y * z) / y)),y) = (x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,4902,a(flip),b,5062,a),flip(a)].">
      <j1 rule="hyper" parents="373 4902 5062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      L((x \ 1) * y,K(x,x \ 1),z) = (x \ 1) * (x * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(3846,a,5063,a)].">
      <j1 rule="hyper" parents="3846 5063"/>
    </justification>
  </clause>

  <clause id="5066">
    <literal><![CDATA[
      L((x \ 1) * y,K(x,x \ 1),z) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,168,a(flip),b,5064,a),flip(a)].">
      <j1 rule="hyper" parents="373 168 5064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5068">
    <literal><![CDATA[
      (x * ((1 / y) * z)) / ((y \ 1) * z) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(5066(a,1),2374(a,1,2))].">
      <j1 rule="para" parents="5066 2374"/>
    </justification>
  </clause>

  <clause id="5069">
    <literal><![CDATA[
      R(x,K(y \ 1,y),(1 / y) * z) = K(y \ 1,y) * (x * K(y,y \ 1))
    ]]></literal>
    <justification jstring="[para(5068(a,1),3848(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5068 3848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5071">
    <literal><![CDATA[
      R(x,K(y \ 1,y),(1 / y) * z) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,3647,a(flip),b,5069,a),flip(a)].">
      <j1 rule="hyper" parents="373 3647 5069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5075">
    <literal><![CDATA[
      R(x,K(y \ 1,y),z) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),5071(a,1,3))].">
      <j1 rule="para" parents="10 5071"/>
    </justification>
  </clause>

  <clause id="5078">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,3857,a(flip),b,5075,a)].">
      <j1 rule="hyper" parents="64 3857 5075"/>
    </justification>
  </clause>

  <clause id="5079">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = x * (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,5075,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 5075 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5085">
    <literal><![CDATA[
      (x \ 1) * K(y \ 1,y) = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,5078,a(flip),b,3001,a(flip))].">
      <j1 rule="hyper" parents="144 5078 3001"/>
    </justification>
  </clause>

  <clause id="5086">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),5078(a,1,3,1))].">
      <j1 rule="para" parents="82 5078"/>
    </justification>
  </clause>

  <clause id="5087">
    <literal><![CDATA[
      R(x,y,(z \ 1) * z) = x
    ]]></literal>
    <justification jstring="[para(294(a,1),5078(a,1,3))].">
      <j1 rule="para" parents="294 5078"/>
    </justification>
  </clause>

  <clause id="5088">
    <literal><![CDATA[
      R(x,y,K(1 / z,z)) = x
    ]]></literal>
    <justification jstring="[para(1737(a,2),5078(a,1,3))].">
      <j1 rule="para" parents="1737 5078"/>
    </justification>
  </clause>

  <clause id="5089">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1739(a,1),5078(a,1,3))].">
      <j1 rule="para" parents="1739 5078"/>
    </justification>
  </clause>

  <clause id="5090">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * K(u \ 1,u)) = L(z,y,x) * K(u \ 1,u)
    ]]></literal>
    <justification jstring="[para(5078(a,1),691(a,1,1))].">
      <j1 rule="para" parents="5078 691"/>
    </justification>
  </clause>

  <clause id="5091">
    <literal><![CDATA[
      R(x,y,K(z \ 1,R(z,u,w))) = x
    ]]></literal>
    <justification jstring="[para(3512(a,2),5078(a,1,3))].">
      <j1 rule="para" parents="3512 5078"/>
    </justification>
  </clause>

  <clause id="5092">
    <literal><![CDATA[
      R(x,y,z * (1 / z)) = x
    ]]></literal>
    <justification jstring="[para(296(a,1),5086(a,1,3))].">
      <j1 rule="para" parents="296 5086"/>
    </justification>
  </clause>

  <clause id="5093">
    <literal><![CDATA[
      x * K(y,1 / y) != z * (u * K(y,1 / y))
    ]]></literal>
    <literal><![CDATA[
      z * u = x
    ]]></literal>
    <justification jstring="[para(5086(a,1),665(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5086 665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5094">
    <literal><![CDATA[
      R(x,y,(z \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(5087(a,1),52(a,1)),flip(a)].">
      <j1 rule="para" parents="5087 52"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5095">
    <literal><![CDATA[
      (x * y) * K(1 / z,z) = x * (y * K(1 / z,z))
    ]]></literal>
    <justification jstring="[hyper(144,a,5088,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 5088 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5096">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * K(1 / u,u)) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(5088(a,1),691(a,1,1))].">
      <j1 rule="para" parents="5088 691"/>
    </justification>
  </clause>

  <clause id="5098">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4162,a(flip),b,5089,a)].">
      <j1 rule="hyper" parents="64 4162 5089"/>
    </justification>
  </clause>

  <clause id="5099">
    <literal><![CDATA[
      T(x,y * K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3738,a(flip),b,5089,a),flip(a)].">
      <j1 rule="hyper" parents="64 3738 5089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5101">
    <literal><![CDATA[
      (x \ 1) * K(y,y \ 1) = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,5089,a(flip),b,3001,a(flip))].">
      <j1 rule="hyper" parents="144 5089 3001"/>
    </justification>
  </clause>

  <clause id="5104">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u,u \ 1))
    ]]></literal>
    <literal><![CDATA[
      K(u,u \ 1) = z
    ]]></literal>
    <justification jstring="[para(5089(a,1),663(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5089 663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5105">
    <literal><![CDATA[
      (x * (y * (1 / y))) / z = x / (z / (y * (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,678,a(flip),b,5092,a)].">
      <j1 rule="hyper" parents="64 678 5092"/>
    </justification>
  </clause>

  <clause id="5107">
    <literal><![CDATA[
      R(x,y,1 / z) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(82(a,1),5098(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="82 5098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5109">
    <literal><![CDATA[
      T(x,K(y \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3652(a,1),5099(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3652 5099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5110">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3646(a,1),5099(a,1,2))].">
      <j1 rule="para" parents="3646 5099"/>
    </justification>
  </clause>

  <clause id="5112">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3650(a,1),5099(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3650 5099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5113">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(3671(a,1),5099(a,1,2))].">
      <j1 rule="para" parents="3671 5099"/>
    </justification>
  </clause>

  <clause id="5114">
    <literal><![CDATA[
      T(x,((1 / y) * z) * u) = T(x,((y \ 1) * z) * u)
    ]]></literal>
    <justification jstring="[para(3651(a,1),5099(a,1,2))].">
      <j1 rule="para" parents="3651 5099"/>
    </justification>
  </clause>

  <clause id="5115">
    <literal><![CDATA[
      T(x,y * ((z \ 1) \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(3902(a,1),5099(a,1,2))].">
      <j1 rule="para" parents="3902 5099"/>
    </justification>
  </clause>

  <clause id="5116">
    <literal><![CDATA[
      R((x \ 1) \ y,x \ 1,x \ 1) = (1 / x) \ R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3881,a(flip),b,5107,a),flip(a)].">
      <j1 rule="hyper" parents="64 3881 5107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5117">
    <literal><![CDATA[
      R((x * x) / y,y,x \ 1) = x / (y * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,682,a(flip),b,5107,a),flip(a)].">
      <j1 rule="hyper" parents="64 682 5107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5118">
    <literal><![CDATA[
      T(x,(1 / (1 / y)) * z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2361(a,1),5109(a,1,2))].">
      <j1 rule="para" parents="2361 5109"/>
    </justification>
  </clause>

  <clause id="5119">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2387(a,1),5109(a,1,2))].">
      <j1 rule="para" parents="2387 5109"/>
    </justification>
  </clause>

  <clause id="5120">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(3719(a,1),5109(a,1,2))].">
      <j1 rule="para" parents="3719 5109"/>
    </justification>
  </clause>

  <clause id="5121">
    <literal><![CDATA[
      T(x,(1 / y) * K(z,y \ 1)) = T(x,y \ K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(4029(a,1),5110(a,2,2))].">
      <j1 rule="para" parents="4029 5110"/>
    </justification>
  </clause>

  <clause id="5122">
    <literal><![CDATA[
      T(x,L(y,z,u) * (1 / y)) = T(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1807(a,1),5113(a,2,2))].">
      <j1 rule="para" parents="1807 5113"/>
    </justification>
  </clause>

  <clause id="5123">
    <literal><![CDATA[
      T(x,(1 / y) \ y) = T(x,y * y)
    ]]></literal>
    <justification jstring="[para(1134(a,1),5115(a,1,2))].">
      <j1 rule="para" parents="1134 5115"/>
    </justification>
  </clause>

  <clause id="5124">
    <literal><![CDATA[
      T(x,y * T(1 / z,u)) = T(x,y * T(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(3569(a,1),5115(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3569 5115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5125">
    <literal><![CDATA[
      T(x,(y \ (z \ y)) * z) = T(x,z * (y \ (z \ y)))
    ]]></literal>
    <justification jstring="[para(3675(a,1),5115(a,1,2))].">
      <j1 rule="para" parents="3675 5115"/>
    </justification>
  </clause>

  <clause id="5126">
    <literal><![CDATA[
      (x \ 1) * (x \ (y * (x * ((x \ 1) \ z)))) = T(y,x * x) * z
    ]]></literal>
    <justification jstring="[para(5123(a,1),2788(a,2,1))].">
      <j1 rule="para" parents="5123 2788"/>
    </justification>
  </clause>

  <clause id="5127">
    <literal><![CDATA[
      x / T(1 / y,y * x) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(5118(a,1),4913(a,1,2))].">
      <j1 rule="para" parents="5118 4913"/>
    </justification>
  </clause>

  <clause id="5128">
    <literal><![CDATA[
      T((x \ 1) * y,x \ y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,928,a(flip),b,5119,a),flip(a)].">
      <j1 rule="hyper" parents="64 928 5119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5129">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ u) = T(x,(z / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(3004(a,2),5119(a,1,2,1))].">
      <j1 rule="para" parents="3004 5119"/>
    </justification>
  </clause>

  <clause id="5130">
    <literal><![CDATA[
      x * (T(x,(y / z) / (z \ 1)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[para(5120(a,1),5012(a,1,2,1))].">
      <j1 rule="para" parents="5120 5012"/>
    </justification>
  </clause>

  <clause id="5131">
    <literal><![CDATA[
      T(1 / x,x * y) = T(x \ 1,x \ y)
    ]]></literal>
    <justification jstring="[hyper(37,a,1691,a,b,5127,a),flip(a)].">
      <j1 rule="hyper" parents="37 1691 5127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5132">
    <literal><![CDATA[
      (1 / (1 / x)) \ y = y / T(x,y * x)
    ]]></literal>
    <justification jstring="[para(4706(a,1),5127(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4706 5127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5133">
    <literal><![CDATA[
      K((x \ 1) * y,x \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,5128,a)].">
      <j1 rule="hyper" parents="56 5128"/>
    </justification>
  </clause>

  <clause id="5134">
    <literal><![CDATA[
      (x * y) * T(x \ 1,x \ y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,5131,a(flip),b,565,a)].">
      <j1 rule="hyper" parents="145 5131 565"/>
    </justification>
  </clause>

  <clause id="5135">
    <literal><![CDATA[
      T(1 / x,x * (x * y)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),5131(a,2,2))].">
      <j1 rule="para" parents="9 5131"/>
    </justification>
  </clause>

  <clause id="5136">
    <literal><![CDATA[
      R(T(x \ 1,x \ y),x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[para(5131(a,1),1002(a,1,1))].">
      <j1 rule="para" parents="5131 1002"/>
    </justification>
  </clause>

  <clause id="5137">
    <literal><![CDATA[
      x / T((y \ z) / z,x * ((y \ z) / z)) = (z / (y * z)) \ x
    ]]></literal>
    <justification jstring="[para(2027(a,1),5132(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2027 5132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5138">
    <literal><![CDATA[
      x / T(y \ (y / z),x * (y \ (y / z))) = (y \ (y / (1 / (1 / z)))) \ x
    ]]></literal>
    <justification jstring="[para(3942(a,1),5132(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3942 5132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5139">
    <literal><![CDATA[
      (1 / (1 / x)) \ y = y / T(x,x * y)
    ]]></literal>
    <justification jstring="[para(4683(a,1),5132(a,2,2))].">
      <j1 rule="para" parents="4683 5132"/>
    </justification>
  </clause>

  <clause id="5140">
    <literal><![CDATA[
      (1 / (1 / (x / y))) \ y = y / T(x / y,x)
    ]]></literal>
    <justification jstring="[para(4692(a,1),5132(a,2,2))].">
      <j1 rule="para" parents="4692 5132"/>
    </justification>
  </clause>

  <clause id="5141">
    <literal><![CDATA[
      (x \ 1) / T(y,(1 / x) * y) = (1 / (1 / y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(5110(a,2),5132(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5110 5132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5142">
    <literal><![CDATA[
      (1 / (1 / x)) \ (y \ 1) = (y \ 1) / T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(2781(a,1),5139(a,2,2))].">
      <j1 rule="para" parents="2781 5139"/>
    </justification>
  </clause>

  <clause id="5143">
    <literal><![CDATA[
      T(R(x \ 1,x,y),x \ y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(795,a,5136,a)].">
      <j1 rule="hyper" parents="795 5136"/>
    </justification>
  </clause>

  <clause id="5144">
    <literal><![CDATA[
      T((x \ y) / y,x \ y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[para(3001(a,1),5143(a,1,1))].">
      <j1 rule="para" parents="3001 5143"/>
    </justification>
  </clause>

  <clause id="5146">
    <literal><![CDATA[
      (x \ 1) \ (K(y \ 1,y) * z) = (x \ K(y,y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(5101(a,1),3663(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5101 3663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5147">
    <literal><![CDATA[
      x / T(y / x,y) = (x / y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,2015,a(flip),b,5140,a),flip(a)].">
      <j1 rule="hyper" parents="64 2015 5140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5148">
    <literal><![CDATA[
      ((x / y) * x) * T(y / x,y) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,2015,a(flip),b,5140,a(flip))].">
      <j1 rule="hyper" parents="144 2015 5140"/>
    </justification>
  </clause>

  <clause id="5149">
    <literal><![CDATA[
      T(x / y,x) = ((y / x) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(215,a,5147,a),flip(a)].">
      <j1 rule="hyper" parents="215 5147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5150">
    <literal><![CDATA[
      ((x \ y) / y) * (x \ y) = (x \ y) / T(x,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),5147(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 5147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5151">
    <literal><![CDATA[
      x / L(y,x,y) = (x / (x * y)) * x
    ]]></literal>
    <justification jstring="[para(4704(a,1),5147(a,1,2))].">
      <j1 rule="para" parents="4704 5147"/>
    </justification>
  </clause>

  <clause id="5152">
    <literal><![CDATA[
      T(x / y,x) * ((y / x) * y) = y * K(((y / x) * y) \ y,(y / x) * y)
    ]]></literal>
    <justification jstring="[para(5149(a,2),354(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5149 354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5153">
    <literal><![CDATA[
      T((x \ y) / (1 / y),x \ y) = (((y * y) \ x) * (1 / y)) \ (1 / y)
    ]]></literal>
    <justification jstring="[para(884(a,1),5149(a,2,1,1))].">
      <j1 rule="para" parents="884 5149"/>
    </justification>
  </clause>

  <clause id="5154">
    <literal><![CDATA[
      x / L((y * (x \ y)) / y,x,(y * (x \ y)) / y) = (x / T(y,x \ y)) * x
    ]]></literal>
    <justification jstring="[para(4463(a,1),5151(a,2,1,2))].">
      <j1 rule="para" parents="4463 5151"/>
    </justification>
  </clause>

  <clause id="5155">
    <literal><![CDATA[
      R(x \ 1,x,y) * (x \ y) = (x \ y) / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3006,a,b,5150,a)].">
      <j1 rule="hyper" parents="64 3006 5150"/>
    </justification>
  </clause>

  <clause id="5156">
    <literal><![CDATA[
      R(x \ (y * y),x,y \ 1) = T(y / (x * (1 / y)),x)
    ]]></literal>
    <justification jstring="[para(5117(a,1),280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5117 280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5157">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3640,a(flip),b,5079,a)].">
      <j1 rule="hyper" parents="64 3640 5079"/>
    </justification>
  </clause>

  <clause id="5158">
    <literal><![CDATA[
      a(x,K(y \ 1,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,5079,a(flip),b,2635,a),flip(a)].">
      <j1 rule="hyper" parents="138 5079 2635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5159">
    <literal><![CDATA[
      (x * y) * (K(x \ 1,x) * z) = ((1 / (1 / x)) * y) * z
    ]]></literal>
    <justification jstring="[para(3633(a,1),5079(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3633 5079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5160">
    <literal><![CDATA[
      a(x,K(y,1 / y),z) = 1
    ]]></literal>
    <justification jstring="[para(82(a,1),5158(a,1,2,1))].">
      <j1 rule="para" parents="82 5158"/>
    </justification>
  </clause>

  <clause id="5161">
    <literal><![CDATA[
      L(x,K(y,1 / y),z) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,5160,a)].">
      <j1 rule="hyper" parents="53 5160"/>
    </justification>
  </clause>

  <clause id="5162">
    <literal><![CDATA[
      L(x,y * (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(296(a,1),5161(a,1,2))].">
      <j1 rule="para" parents="296 5161"/>
    </justification>
  </clause>

  <clause id="5164">
    <literal><![CDATA[
      (x * (y * (1 / y))) \ z = (y * (1 / y)) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(710,a,5162,a),flip(a)].">
      <j1 rule="hyper" parents="710 5162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5165">
    <literal><![CDATA[
      L(K(1 / x,x),y,z) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(606,a,5095,a)].">
      <j1 rule="hyper" parents="606 5095"/>
    </justification>
  </clause>

  <clause id="5166">
    <literal><![CDATA[
      a(x,y,K(1 / z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,5095,a(flip),b,2635,a),flip(a)].">
      <j1 rule="hyper" parents="138 5095 2635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5167">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(79(a,1),5166(a,1,3,1))].">
      <j1 rule="para" parents="79 5166"/>
    </justification>
  </clause>

  <clause id="5168">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(53,a,5167,a)].">
      <j1 rule="hyper" parents="53 5167"/>
    </justification>
  </clause>

  <clause id="5170">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (z * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(5168(a,1),3618(a,1,1))].">
      <j1 rule="para" parents="5168 3618"/>
    </justification>
  </clause>

  <clause id="5172">
    <literal><![CDATA[
      (x * (y * (1 / y))) / z = x / ((y * (1 / y)) \ z)
    ]]></literal>
    <justification jstring="[para(3614(a,1),5105(a,2,2))].">
      <j1 rule="para" parents="3614 5105"/>
    </justification>
  </clause>

  <clause id="5173">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (K(z \ 1,z) * y)
    ]]></literal>
    <justification jstring="[hyper(3604,a,5157,a)].">
      <j1 rule="hyper" parents="3604 5157"/>
    </justification>
  </clause>

  <clause id="5174">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(2372,a,5157,a)].">
      <j1 rule="hyper" parents="2372 5157"/>
    </justification>
  </clause>

  <clause id="5175">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(759,a,5157,a)].">
      <j1 rule="hyper" parents="759 5157"/>
    </justification>
  </clause>

  <clause id="5176">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,3599,a(flip),b,5157,a),flip(a)].">
      <j1 rule="hyper" parents="373 3599 5157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5178">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(K(z \ 1,z) * u,y,x)
    ]]></literal>
    <justification jstring="[para(5157(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5157 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5179">
    <literal><![CDATA[
      (x * (1 / x)) \ (x \ y) = T(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(1746(a,1),5164(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1746 5164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5180">
    <literal><![CDATA[
      T(x,x \ 1) \ (x * y) = (x * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(9(a,1),5179(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 5179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5181">
    <literal><![CDATA[
      L(((x * (1 / x)) \ 1) * y,x * (1 / x),x) = (x * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,4219,a,b,5180,a)].">
      <j1 rule="hyper" parents="64 4219 5180"/>
    </justification>
  </clause>

  <clause id="5182">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(759,a,5170,a)].">
      <j1 rule="hyper" parents="759 5170"/>
    </justification>
  </clause>

  <clause id="5183">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3610(a,2),5170(a,2,2))].">
      <j1 rule="para" parents="3610 5170"/>
    </justification>
  </clause>

  <clause id="5184">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * K(x \ 1,x))) = y * z
    ]]></literal>
    <justification jstring="[para(3664(a,1),5170(a,2,2))].">
      <j1 rule="para" parents="3664 5170"/>
    </justification>
  </clause>

  <clause id="5185">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((1 / x) \ z)) = y * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3650(a,1),5170(a,2,2))].">
      <j1 rule="para" parents="3650 5170"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * (x \ 1))) = y * (z * (1 / x))
    ]]></literal>
    <justification jstring="[para(3671(a,1),5170(a,2,2))].">
      <j1 rule="para" parents="3671 5170"/>
    </justification>
  </clause>

  <clause id="5188">
    <literal><![CDATA[
      (x * (K(y \ 1,y) * z)) * u = (x * z) * (K(y \ 1,y) * u)
    ]]></literal>
    <justification jstring="[para(5173(a,1),5079(a,1,1))].">
      <j1 rule="para" parents="5173 5079"/>
    </justification>
  </clause>

  <clause id="5189">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z / (1 / x))) = y * (z / (x \ 1))
    ]]></literal>
    <justification jstring="[para(3719(a,1),5174(a,1,2,2))].">
      <j1 rule="para" parents="3719 5174"/>
    </justification>
  </clause>

  <clause id="5190">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = K(x \ 1,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2367,a,b,5175,a)].">
      <j1 rule="hyper" parents="64 2367 5175"/>
    </justification>
  </clause>

  <clause id="5191">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) * y) \ z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,2267,a(flip),b,5175,a),flip(a)].">
      <j1 rule="hyper" parents="64 2267 5175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5192">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ (1 / x)) = y \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(1225(a,1),5175(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1225 5175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5193">
    <literal><![CDATA[
      (x \ (1 / y)) * K(y \ 1,y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3604,a,5192,a)].">
      <j1 rule="hyper" parents="3604 5192"/>
    </justification>
  </clause>

  <clause id="5194">
    <literal><![CDATA[
      (1 / x) \ (y \ (1 / x)) = (x \ 1) \ (y \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(139,a,5192,a(flip),b,2261,a),flip(a)].">
      <j1 rule="hyper" parents="139 5192 2261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5195">
    <literal><![CDATA[
      T(x,y \ (1 / z)) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(5192(a,1),5109(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5192 5109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5196">
    <literal><![CDATA[
      T(x / y,(x / y) \ ((y / x) \ 1)) = x / y
    ]]></literal>
    <justification jstring="[hyper(64,a,4981,a(flip),b,5195,a),flip(a)].">
      <j1 rule="hyper" parents="64 4981 5195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5197">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ 1)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(79(a,1),5195(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 5195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5198">
    <literal><![CDATA[
      (x \ (1 / R(y,z,u))) * K(y \ 1,y) = x \ (R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(3533(a,1),5193(a,1,2))].">
      <j1 rule="para" parents="3533 5193"/>
    </justification>
  </clause>

  <clause id="5199">
    <literal><![CDATA[
      ((x / y) \ ((y / x) \ 1)) * (x / y) = (y / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(145,a,5196,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="145 5196 116"/>
    </justification>
  </clause>

  <clause id="5200">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,3600,a,b,5176,a)].">
      <j1 rule="hyper" parents="36 3600 5176"/>
    </justification>
  </clause>

  <clause id="5201">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * u) = (x * y) \ u
    ]]></literal>
    <justification jstring="[para(5176(a,1),2225(a,1,1))].">
      <j1 rule="para" parents="5176 2225"/>
    </justification>
  </clause>

  <clause id="5202">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(5176(a,1),2366(a,1,1))].">
      <j1 rule="para" parents="5176 2366"/>
    </justification>
  </clause>

  <clause id="5203">
    <literal><![CDATA[
      K(x \ 1,x) * (y * (z \ 1)) = y * (z \ K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(5085(a,1),5176(a,2,2))].">
      <j1 rule="para" parents="5085 5176"/>
    </justification>
  </clause>

  <clause id="5204">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4200,a(flip),b,5200,a)].">
      <j1 rule="hyper" parents="64 4200 5200"/>
    </justification>
  </clause>

  <clause id="5207">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(x \ 1,x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,5204,a(flip),b,1858,a)].">
      <j1 rule="hyper" parents="145 5204 1858"/>
    </justification>
  </clause>

  <clause id="5210">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ z = (x \ z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3643,a,b,5182,a)].">
      <j1 rule="hyper" parents="64 3643 5182"/>
    </justification>
  </clause>

  <clause id="5212">
    <literal><![CDATA[
      (x \ (y \ z)) * K(y,y \ 1) = x \ ((1 / (1 / y)) \ z)
    ]]></literal>
    <justification jstring="[para(2349(a,1),5182(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2349 5182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5213">
    <literal><![CDATA[
      (x * y) * K(z,z \ 1) = x * (K(z,z \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(3612,a,5183,a)].">
      <j1 rule="hyper" parents="3612 5183"/>
    </justification>
  </clause>

  <clause id="5214">
    <literal><![CDATA[
      (x * ((K(y,y \ 1) * z) * u)) \ ((K(y,y \ 1) * (x * z)) * u) = a(x,K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(5183(a,2),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5183 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5215">
    <literal><![CDATA[
      x \ (y * (K(z,z \ 1) * u)) = (x \ (y * u)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(5183(a,1),5182(a,1,2))].">
      <j1 rule="para" parents="5183 5182"/>
    </justification>
  </clause>

  <clause id="5216">
    <literal><![CDATA[
      K(x,x \ 1) * (y * R(x,z,u)) = y * R((x \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(2953(a,1),5184(a,1,2,2))].">
      <j1 rule="para" parents="2953 5184"/>
    </justification>
  </clause>

  <clause id="5217">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = (y \ z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,3595,a(flip),b,5190,a),flip(a)].">
      <j1 rule="hyper" parents="373 3595 5190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5218">
    <literal><![CDATA[
      T(x,(K(y,y \ 1) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(5190(a,2),5109(a,1,2))].">
      <j1 rule="para" parents="5190 5109"/>
    </justification>
  </clause>

  <clause id="5219">
    <literal><![CDATA[
      T(x,((1 / y) * z) \ u) = T(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(2354(a,1),5218(a,1,2,1))].">
      <j1 rule="para" parents="2354 5218"/>
    </justification>
  </clause>

  <clause id="5220">
    <literal><![CDATA[
      T(x,(((y \ 1) \ 1) \ z) \ u) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(2385(a,1),5218(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2385 5218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5221">
    <literal><![CDATA[
      (x \ 1) * (x \ (1 / x)) = (x * x) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,540,a(flip),b,5194,a(flip))].">
      <j1 rule="hyper" parents="145 540 5194"/>
    </justification>
  </clause>

  <clause id="5222">
    <literal><![CDATA[
      x * ((x \ 1) \ (y \ (x \ 1))) = (x * x) * (y \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(145,a,5194,a(flip),b,539,a)].">
      <j1 rule="hyper" parents="145 5194 539"/>
    </justification>
  </clause>

  <clause id="5223">
    <literal><![CDATA[
      (x \ (1 / x)) / x = (x * x) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,1539,a(flip),b,5221,a)].">
      <j1 rule="hyper" parents="64 1539 5221"/>
    </justification>
  </clause>

  <clause id="5224">
    <literal><![CDATA[
      x / (y * K(z,z \ 1)) = (x / y) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,221,a(flip),b,5210,a)].">
      <j1 rule="hyper" parents="225 221 5210"/>
    </justification>
  </clause>

  <clause id="5225">
    <literal><![CDATA[
      (((1 / x) * y) \ z) * K(x,x \ 1) = ((x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(3623(a,1),5210(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3623 5210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5226">
    <literal><![CDATA[
      (((x \ 1) \ y) \ z) * K(x,x \ 1) = ((1 / x) \ y) \ z
    ]]></literal>
    <justification jstring="[para(3632(a,1),5210(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3632 5210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5227">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = K(z,z \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(783,a,5213,a)].">
      <j1 rule="hyper" parents="783 5213"/>
    </justification>
  </clause>

  <clause id="5228">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(5183(a,1),5217(a,1,1))].">
      <j1 rule="para" parents="5183 5217"/>
    </justification>
  </clause>

  <clause id="5229">
    <literal><![CDATA[
      T(x,((y \ 1) * y) \ z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(186(a,1),5219(a,1,2)),flip(a)].">
      <j1 rule="para" parents="186 5219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5230">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ (x \ z)) = y \ ((1 / (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[para(3654(a,1),5227(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3654 5227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5231">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ (x * z)) = y \ (T(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3655(a,1),5227(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3655 5227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5233">
    <literal><![CDATA[
      ((x \ 1) \ y) * a((x \ 1) \ y,x,x \ 1) = (1 / x) \ R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1429,a(flip),b,5116,a)].">
      <j1 rule="hyper" parents="64 1429 5116"/>
    </justification>
  </clause>

  <clause id="5234">
    <literal><![CDATA[
      T(x,K(y,z \ 1) / z) = T(x,z \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[para(4606(a,1),5121(a,1,2))].">
      <j1 rule="para" parents="4606 5121"/>
    </justification>
  </clause>

  <clause id="5235">
    <literal><![CDATA[
      K(x \ 1,x) * ((y \ 1) \ z) = (y \ K(x,x \ 1)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,5175,a(flip),b,5146,a)].">
      <j1 rule="hyper" parents="64 5175 5146"/>
    </justification>
  </clause>

  <clause id="5236">
    <literal><![CDATA[
      ((1 / (1 / x)) * y) * ((1 / x) * z) = (x * y) * ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2263(a,1),5159(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2263 5159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5237">
    <literal><![CDATA[
      (1 / x) * (y * ((1 / x) \ z)) = (x \ 1) * (y * ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(5185(a,1),2448(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5185 2448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5238">
    <literal><![CDATA[
      (1 / x) * (((1 / x) * y) \ z) = (x \ 1) * (((x \ 1) * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5191,a(flip),b,2454,a)].">
      <j1 rule="hyper" parents="145 5191 2454"/>
    </justification>
  </clause>

  <clause id="5239">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (((1 / x) * z) \ u)) = y * (((x \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(5191(a,1),5174(a,1,2,2))].">
      <j1 rule="para" parents="5191 5174"/>
    </justification>
  </clause>

  <clause id="5240">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * T(x,x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(3906,a,5207,a)].">
      <j1 rule="hyper" parents="3906 5207"/>
    </justification>
  </clause>

  <clause id="5241">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ (T(x,y) \ z)) = T(x,y) \ ((1 / (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[para(2415(a,1),5230(a,1,2))].">
      <j1 rule="para" parents="2415 5230"/>
    </justification>
  </clause>

  <clause id="5242">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(5093,a,3644,a(flip))].">
      <j1 rule="hyper" parents="5093 3644"/>
    </justification>
  </clause>

  <clause id="5243">
    <literal><![CDATA[
      K(x,1 / x) * (y * z) = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(2221,a,5242,a)].">
      <j1 rule="hyper" parents="2221 5242"/>
    </justification>
  </clause>

  <clause id="5245">
    <literal><![CDATA[
      T((1 / x) \ y,x * x) * z = (x \ y) * (x * ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1598,a(flip),b,5126,a),flip(a)].">
      <j1 rule="hyper" parents="64 1598 5126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5246">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = (x \ 1) \ (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3632,a(flip),b,5198,a)].">
      <j1 rule="hyper" parents="64 3632 5198"/>
    </justification>
  </clause>

  <clause id="5247">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = (z * x) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(3709,a,5201,a)].">
      <j1 rule="hyper" parents="3709 5201"/>
    </justification>
  </clause>

  <clause id="5248">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,16,a,b,5247,a),flip(a)].">
      <j1 rule="hyper" parents="373 16 5247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5249">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2996(a,1),5248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2996 5248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5250">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(3595(a,2),5248(a,1,1))].">
      <j1 rule="para" parents="3595 5248"/>
    </justification>
  </clause>

  <clause id="5251">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(3634(a,1),5248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3634 5248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5252">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(3620(a,1),5248(a,1,1))].">
      <j1 rule="para" parents="3620 5248"/>
    </justification>
  </clause>

  <clause id="5253">
    <literal><![CDATA[
      K((1 / x) * y,z) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(3623(a,1),5248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3623 5248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5254">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(3632(a,1),5248(a,1,1))].">
      <j1 rule="para" parents="3632 5248"/>
    </justification>
  </clause>

  <clause id="5255">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(3714(a,1),5248(a,1,1))].">
      <j1 rule="para" parents="3714 5248"/>
    </justification>
  </clause>

  <clause id="5256">
    <literal><![CDATA[
      K(x * ((y \ 1) \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3910(a,1),5248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3910 5248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5257">
    <literal><![CDATA[
      K(T(1 / x,y) \ z,u) = K(T(x \ 1,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(4133(a,1),5248(a,1,1))].">
      <j1 rule="para" parents="4133 5248"/>
    </justification>
  </clause>

  <clause id="5258">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3866(a,1),5250(a,1,1))].">
      <j1 rule="para" parents="3866 5250"/>
    </justification>
  </clause>

  <clause id="5259">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) = K(((x \ 1) * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(5191(a,1),5250(a,1,1))].">
      <j1 rule="para" parents="5191 5250"/>
    </justification>
  </clause>

  <clause id="5260">
    <literal><![CDATA[
      K((1 / (1 / x)) \ y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2349(a,1),5251(a,1,1))].">
      <j1 rule="para" parents="2349 5251"/>
    </justification>
  </clause>

  <clause id="5261">
    <literal><![CDATA[
      K(T(x,x \ 1) \ y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2386(a,1),5251(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2386 5251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5262">
    <literal><![CDATA[
      K(x \ (y * K(z,z \ 1)),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(5227(a,2),5251(a,1,1))].">
      <j1 rule="para" parents="5227 5251"/>
    </justification>
  </clause>

  <clause id="5263">
    <literal><![CDATA[
      K(x * T(1 / y,z),u) = K(x * T(y \ 1,z),u)
    ]]></literal>
    <justification jstring="[para(3569(a,1),5256(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3569 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5264">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),u) = K(x * ((y * z) \ z),u)
    ]]></literal>
    <justification jstring="[para(3584(a,2),5256(a,1,1,2))].">
      <j1 rule="para" parents="3584 5256"/>
    </justification>
  </clause>

  <clause id="5265">
    <literal><![CDATA[
      K(x \ R(1 / y,z,u),w) = K(x \ R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(2866(a,1),5262(a,1,1,2))].">
      <j1 rule="para" parents="2866 5262"/>
    </justification>
  </clause>

  <clause id="5266">
    <literal><![CDATA[
      K(x \ (K(y,y \ 1) * z),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(3610(a,2),5262(a,1,1,2))].">
      <j1 rule="para" parents="3610 5262"/>
    </justification>
  </clause>

  <clause id="5267">
    <literal><![CDATA[
      K(x \ (y * (1 / z)),u) = K(x \ (y * (z \ 1)),u)
    ]]></literal>
    <justification jstring="[para(3671(a,1),5262(a,1,1,2))].">
      <j1 rule="para" parents="3671 5262"/>
    </justification>
  </clause>

  <clause id="5268">
    <literal><![CDATA[
      K((((x \ 1) \ 1) \ y) \ z,u) = K((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(2388(a,1),5266(a,1,1))].">
      <j1 rule="para" parents="2388 5266"/>
    </justification>
  </clause>

  <clause id="5269">
    <literal><![CDATA[
      K(((x \ 1) * (x * y)) \ z,u) = K(L(y,x,x \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(1635(a,1),5259(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1635 5259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5270">
    <literal><![CDATA[
      (x * y) \ (K(z,z \ 1) * (x * (K(z \ 1,z) * (y * u)))) = L(u,y * K(z \ 1,z),x)
    ]]></literal>
    <justification jstring="[hyper(3710,a,5202,a),flip(a)].">
      <j1 rule="hyper" parents="3710 5202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5271">
    <literal><![CDATA[
      ((x * (y * (K(z,z \ 1) * u))) \ ((x * y) * u)) * K(z,z \ 1) = a(x,y,K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(959,a,5215,a),flip(a)].">
      <j1 rule="hyper" parents="959 5215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5272">
    <literal><![CDATA[
      L(x * R((y \ 1) \ 1,z,u),y,y) = y * ((1 / y) * (x * R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(5216(a,1),2451(a,1,1))].">
      <j1 rule="para" parents="5216 2451"/>
    </justification>
  </clause>

  <clause id="5273">
    <literal><![CDATA[
      ((1 / (1 / x)) * y) * ((x * x) \ z) = (x * y) * ((x \ 1) * (x \ z))
    ]]></literal>
    <justification jstring="[para(536(a,1),5236(a,1,2))].">
      <j1 rule="para" parents="536 5236"/>
    </justification>
  </clause>

  <clause id="5274">
    <literal><![CDATA[
      ((x / y) * (y / x)) * (((x / y) \ 1) * z) = ((y / x) * (x / y)) * ((1 / (x / y)) * z)
    ]]></literal>
    <justification jstring="[para(2065(a,1),5236(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2065 5236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5275">
    <literal><![CDATA[
      L(((x \ 1) * x) * y,x * (1 / x),x) = (x * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(5035(a,1),5181(a,1,1,1))].">
      <j1 rule="para" parents="5035 5181"/>
    </justification>
  </clause>

  <clause id="5276">
    <literal><![CDATA[
      ((x \ 1) * x) \ ((x * (1 / x)) \ y) = y
    ]]></literal>
    <justification jstring="[hyper(139,a,5275,a(flip),b,5162,a(flip))].">
      <j1 rule="hyper" parents="139 5275 5162"/>
    </justification>
  </clause>

  <clause id="5277">
    <literal><![CDATA[
      (x * (1 / x)) \ (y * T(x,x \ 1)) = y * x
    ]]></literal>
    <justification jstring="[hyper(3922,a,5276,a),flip(a)].">
      <j1 rule="hyper" parents="3922 5276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5278">
    <literal><![CDATA[
      (x * (1 / x)) \ (((x \ 1) * x) \ y) = y
    ]]></literal>
    <justification jstring="[hyper(48,a,5276,a)].">
      <j1 rule="hyper" parents="48 5276"/>
    </justification>
  </clause>

  <clause id="5279">
    <literal><![CDATA[
      ((x \ 1) * x) \ y = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),5276(a,1,2))].">
      <j1 rule="para" parents="9 5276"/>
    </justification>
  </clause>

  <clause id="5280">
    <literal><![CDATA[
      ((x \ 1) * x) \ y = y * (x * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(144,a,5278,a(flip),b,3614,a),flip(a)].">
      <j1 rule="hyper" parents="144 5278 3614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5281">
    <literal><![CDATA[
      (x * (1 / x)) \ y != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) * x) \ z = y
    ]]></literal>
    <justification jstring="[para(5278(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="5278 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5282">
    <literal><![CDATA[
      ((x * (1 / x)) \ y) \ z = y \ (((x \ 1) * x) \ z)
    ]]></literal>
    <justification jstring="[para(5279(a,2),2213(a,2,2))].">
      <j1 rule="para" parents="5279 2213"/>
    </justification>
  </clause>

  <clause id="5283">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) \ z = y \ ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[para(5279(a,2),2214(a,1,1))].">
      <j1 rule="para" parents="5279 2214"/>
    </justification>
  </clause>

  <clause id="5284">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) / z = (x * (1 / x)) * (y / z)
    ]]></literal>
    <justification jstring="[para(5279(a,2),2215(a,1,1))].">
      <j1 rule="para" parents="5279 2215"/>
    </justification>
  </clause>

  <clause id="5285">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) \ z = (x * (1 / x)) \ (y \ z)
    ]]></literal>
    <justification jstring="[para(5280(a,2),5164(a,1,1))].">
      <j1 rule="para" parents="5280 5164"/>
    </justification>
  </clause>

  <clause id="5286">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) / z = y / ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[para(5280(a,2),5172(a,1,1))].">
      <j1 rule="para" parents="5280 5172"/>
    </justification>
  </clause>

  <clause id="5287">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * y = (y * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[para(512(a,1),5277(a,1,2)),flip(a)].">
      <j1 rule="para" parents="512 5277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5288">
    <literal><![CDATA[
      (((x \ 1) * x) \ y) / z = ((x \ 1) * x) \ (y / z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5279,a,b,5284,a),flip(a)].">
      <j1 rule="hyper" parents="373 5279 5284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5289">
    <literal><![CDATA[
      (x * (1 / x)) \ (y \ z) = y \ ((x * (1 / x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5283,a(flip),b,5285,a),flip(a)].">
      <j1 rule="hyper" parents="64 5283 5285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5290">
    <literal><![CDATA[
      (x * y) / ((y * (1 / y)) \ z) = (x * T(y,y \ 1)) / z
    ]]></literal>
    <justification jstring="[para(3913(a,1),5286(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3913 5286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5291">
    <literal><![CDATA[
      ((x \ 1) * x) \ ((y * x) / z) = (y * T(x,x \ 1)) / z
    ]]></literal>
    <justification jstring="[para(3913(a,1),5288(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3913 5288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5292">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y \ ((x * (1 / x)) \ z)) = y \ z
    ]]></literal>
    <justification jstring="[hyper(5281,a,5289,a)].">
      <j1 rule="hyper" parents="5281 5289"/>
    </justification>
  </clause>

  <clause id="5293">
    <literal><![CDATA[
      (x * (1 / x)) \ (y \ 1) = y \ ((x \ 1) * x)
    ]]></literal>
    <justification jstring="[para(5035(a,1),5289(a,2,2))].">
      <j1 rule="para" parents="5035 5289"/>
    </justification>
  </clause>

  <clause id="5294">
    <literal><![CDATA[
      (x \ 1) \ (((y \ 1) * y) \ z) = (x \ ((y \ 1) * y)) \ z
    ]]></literal>
    <justification jstring="[para(5293(a,1),5282(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5293 5282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5295">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y \ z) = y \ (((x \ 1) * x) \ z)
    ]]></literal>
    <justification jstring="[para(5278(a,1),5292(a,1,2,2))].">
      <j1 rule="para" parents="5278 5292"/>
    </justification>
  </clause>

  <clause id="5296">
    <literal><![CDATA[
      x \ (((y \ 1) * y) \ (x * z)) = ((y \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(9(a,1),5295(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 5295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5297">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y * ((x \ 1) * z)) = y * L(x \ z,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,102,a,b,5296,a),flip(a)].">
      <j1 rule="hyper" parents="145 102 5296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5298">
    <literal><![CDATA[
      T(x,(y * T(z,z \ 1)) / u) = T(x,(y * z) / u)
    ]]></literal>
    <justification jstring="[para(5291(a,1),5229(a,1,2))].">
      <j1 rule="para" parents="5291 5229"/>
    </justification>
  </clause>

  <clause id="5299">
    <literal><![CDATA[
      ((x \ 1) * x) \ ((y \ 1) \ z) = (y \ ((x \ 1) * x)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,5295,a,b,5294,a)].">
      <j1 rule="hyper" parents="64 5295 5294"/>
    </justification>
  </clause>

  <clause id="5300">
    <literal><![CDATA[
      ((x \ 1) * x) \ (y * ((x \ 1) * z)) = y * ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(1638(a,1),5297(a,2,2))].">
      <j1 rule="para" parents="1638 5297"/>
    </justification>
  </clause>

  <clause id="5301">
    <literal><![CDATA[
      T(x,y * ((1 / z) * u)) = T(x,y * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(5300(a,1),5229(a,1,2))].">
      <j1 rule="para" parents="5300 5229"/>
    </justification>
  </clause>

  <clause id="5302">
    <literal><![CDATA[
      T((x \ y) / (1 / y),x \ y) = (((y * y) \ x) * (y \ 1)) \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,3762,a(flip),b,5153,a),flip(a)].">
      <j1 rule="hyper" parents="373 3762 5153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5303">
    <literal><![CDATA[
      ((x \ 1) \ y) * a(x \ y,x,x \ 1) = (1 / x) \ R(y,x,x)
    ]]></literal>
    <justification jstring="[para(2675(a,1),5233(a,1,2))].">
      <j1 rule="para" parents="2675 5233"/>
    </justification>
  </clause>

  <clause id="5304">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((((1 / x) \ 1) \ z) * (((1 / x) * z) \ u))) = y * (((x \ 1) * z) \ ((((1 / x) \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[para(3145(a,1),5239(a,1,2,2))].">
      <j1 rule="para" parents="3145 5239"/>
    </justification>
  </clause>

  <clause id="5305">
    <literal><![CDATA[
      T(x,y) \ ((1 / (1 / x)) \ z) = x \ (T(1 / (1 / x),y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4127,a(flip),b,5241,a),flip(a)].">
      <j1 rule="hyper" parents="64 4127 5241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5306">
    <literal><![CDATA[
      T((x \ y) / (1 / y),x \ y) = (x * (y \ 1)) \ ((y * y) * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,942,a(flip),b,5302,a),flip(a)].">
      <j1 rule="hyper" parents="373 942 5302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5307">
    <literal><![CDATA[
      T((x \ y) / (1 / y),x \ y) = (x * (y \ 1)) \ R(y,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(297(a,1),5306(a,2,2))].">
      <j1 rule="para" parents="297 5306"/>
    </justification>
  </clause>

  <clause id="5308">
    <literal><![CDATA[
      T((x \ y) / (1 / y),x \ y) = (x * (y \ 1)) \ (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(2018(a,1),5307(a,2,2))].">
      <j1 rule="para" parents="2018 5307"/>
    </justification>
  </clause>

  <clause id="5309">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u,y,x) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(5173(a,1),5090(a,1,2))].">
      <j1 rule="para" parents="5173 5090"/>
    </justification>
  </clause>

  <clause id="5310">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * K(1 / u,u))) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(5095(a,1),5096(a,1,2))].">
      <j1 rule="para" parents="5095 5096"/>
    </justification>
  </clause>

  <clause id="5311">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = L(y,z,u) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5178,a(flip),b,5309,a)].">
      <j1 rule="hyper" parents="64 5178 5309"/>
    </justification>
  </clause>

  <clause id="5312">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,3595,a,b,5311,a),flip(a)].">
      <j1 rule="hyper" parents="373 3595 5311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5313">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(3647(a,1),5312(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3647 5312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5314">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = K(y,y \ 1) * L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2372,a,5313,a),flip(a)].">
      <j1 rule="hyper" parents="2372 5313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5315">
    <literal><![CDATA[
      x \ L(y * K(z,z \ 1),u,w) = (x \ L(y,u,w)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(5314(a,2),5182(a,1,2))].">
      <j1 rule="para" parents="5314 5182"/>
    </justification>
  </clause>

  <clause id="5316">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * K(1 / u,u)))) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(5095(a,1),5310(a,1,2,2))].">
      <j1 rule="para" parents="5095 5310"/>
    </justification>
  </clause>

  <clause id="5317">
    <literal><![CDATA[
      L(x * K(1 / y,y),z,u) = L(x,z,u) * K(1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(608,a,5316,a)].">
      <j1 rule="hyper" parents="608 5316"/>
    </justification>
  </clause>

  <clause id="5318">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x))
    ]]></literal>
    <justification jstring="[para(5174(a,1),5270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5174 5270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5319">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,18,a,b,5318,a),flip(a)].">
      <j1 rule="hyper" parents="373 18 5318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5321">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(1253(a,1),5319(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1253 5319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5322">
    <literal><![CDATA[
      L(x,y * (1 / z),u) = L(x,y * (z \ 1),u)
    ]]></literal>
    <justification jstring="[para(2996(a,1),5319(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2996 5319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5323">
    <literal><![CDATA[
      L(x,y / ((z \ 1) \ 1),u) = L(x,y / z,u)
    ]]></literal>
    <justification jstring="[para(3925(a,1),5319(a,1,2))].">
      <j1 rule="para" parents="3925 5319"/>
    </justification>
  </clause>

  <clause id="5324">
    <literal><![CDATA[
      L(x,1 / (y \ z),L(1 / (y \ z),y \ z,y)) = L(x,(1 / (z \ y)) \ 1,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4963,a,b,5321,a)].">
      <j1 rule="hyper" parents="64 4963 5321"/>
    </justification>
  </clause>

  <clause id="5325">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),5321(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 5321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5326">
    <literal><![CDATA[
      L(x,(y \ (z * z)) \ 1,u) = L(x,(z * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(551(a,1),5321(a,1,2)),flip(a)].">
      <j1 rule="para" parents="551 5321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5328">
    <literal><![CDATA[
      L(x,1 / (y \ z),L(1 / (y \ z),y \ z,y)) = L(x,z \ y,y \ z)
    ]]></literal>
    <justification jstring="[para(82(a,1),5324(a,2,2))].">
      <j1 rule="para" parents="82 5324"/>
    </justification>
  </clause>

  <clause id="5330">
    <literal><![CDATA[
      L(x,1 / (y \ z),1 / (1 / (z \ y))) = L(x,z \ y,y \ z)
    ]]></literal>
    <justification jstring="[para(4305(a,1),5328(a,1,3))].">
      <j1 rule="para" parents="4305 5328"/>
    </justification>
  </clause>

  <clause id="5331">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * (z * u))) \ ((K(y,y \ 1) * (x * z)) * u) = a(x,K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(2224(a,1),5214(a,1,1,2))].">
      <j1 rule="para" parents="2224 5214"/>
    </justification>
  </clause>

  <clause id="5332">
    <literal><![CDATA[
      ((x * (K(y,y \ 1) * (z * u))) \ ((x * z) * u)) * K(y,y \ 1) = a(x,z,K(y,y \ 1) * u)
    ]]></literal>
    <justification jstring="[para(5183(a,2),5271(a,1,1,1,2))].">
      <j1 rule="para" parents="5183 5271"/>
    </justification>
  </clause>

  <clause id="5333">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * (z * u))) \ (K(y,y \ 1) * ((x * z) * u)) = a(x,K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(2224(a,1),5331(a,1,2))].">
      <j1 rule="para" parents="2224 5331"/>
    </justification>
  </clause>

  <clause id="5334">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) * K(u \ 1,u)) * K(u,u \ 1) = a(x,y,K(u,u \ 1) * z)
    ]]></literal>
    <justification jstring="[para(5228(a,1),5332(a,1,1))].">
      <j1 rule="para" parents="5228 5332"/>
    </justification>
  </clause>

  <clause id="5335">
    <literal><![CDATA[
      ((x * (K(y,y \ 1) * (z * u))) \ ((x * z) * u)) * K(y,y \ 1) = a(x,K(y,y \ 1) * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5182,a(flip),b,5333,a)].">
      <j1 rule="hyper" parents="64 5182 5333"/>
    </justification>
  </clause>

  <clause id="5336">
    <literal><![CDATA[
      (a(x,y,z) * K(u \ 1,u)) * K(u,u \ 1) = a(x,y,K(u,u \ 1) * z)
    ]]></literal>
    <justification jstring="[para(14(a,2),5334(a,1,1,1))].">
      <j1 rule="para" parents="14 5334"/>
    </justification>
  </clause>

  <clause id="5337">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,3664,a(flip),b,5336,a),flip(a)].">
      <j1 rule="hyper" parents="64 3664 5336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5339">
    <literal><![CDATA[
      ((x * (y * (K(z,z \ 1) * u))) \ ((x * y) * u)) * K(z,z \ 1) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5271,a,b,5337,a)].">
      <j1 rule="hyper" parents="64 5271 5337"/>
    </justification>
  </clause>

  <clause id="5340">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1733(a,1),5337(a,1,3))].">
      <j1 rule="para" parents="1733 5337"/>
    </justification>
  </clause>

  <clause id="5341">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ 1) * u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(2254(a,1),5337(a,1,3))].">
      <j1 rule="para" parents="2254 5337"/>
    </justification>
  </clause>

  <clause id="5342">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(2350(a,1),5337(a,1,3))].">
      <j1 rule="para" parents="2350 5337"/>
    </justification>
  </clause>

  <clause id="5343">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ 1) \ u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(2385(a,1),5337(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2385 5337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5344">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u) \ 1) = a(x,y,(1 / u) * z)
    ]]></literal>
    <justification jstring="[para(917(a,2),5340(a,1,3,1))].">
      <j1 rule="para" parents="917 5340"/>
    </justification>
  </clause>

  <clause id="5345">
    <literal><![CDATA[
      (x * T(y,y \ 1)) \ (R(x,y,y) * y) = a(x * y,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3903,a,b,5342,a)].">
      <j1 rule="hyper" parents="64 3903 5342"/>
    </justification>
  </clause>

  <clause id="5346">
    <literal><![CDATA[
      a(x,y,(z / u) \ u) = a(x,y,(u / z) * u)
    ]]></literal>
    <justification jstring="[para(2040(a,1),5341(a,1,3))].">
      <j1 rule="para" parents="2040 5341"/>
    </justification>
  </clause>

  <clause id="5347">
    <literal><![CDATA[
      a(x,y,((z \ (u * u)) \ 1) \ w) = a(x,y,((u * u) \ z) \ w)
    ]]></literal>
    <justification jstring="[para(550(a,1),5343(a,1,3,1,1))].">
      <j1 rule="para" parents="550 5343"/>
    </justification>
  </clause>

  <clause id="5348">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ (z \ u)) = a(x,y,z \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(1612(a,1),5343(a,1,3))].">
      <j1 rule="para" parents="1612 5343"/>
    </justification>
  </clause>

  <clause id="5350">
    <literal><![CDATA[
      ((x * (y * (z * K(u,u \ 1)))) \ ((x * y) * z)) * K(u,u \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(3610(a,1),5339(a,1,1,1,2,2))].">
      <j1 rule="para" parents="3610 5339"/>
    </justification>
  </clause>

  <clause id="5351">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) * K(u \ 1,u)) * K(u,u \ 1) = a(x,K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(5228(a,1),5335(a,1,1))].">
      <j1 rule="para" parents="5228 5335"/>
    </justification>
  </clause>

  <clause id="5352">
    <literal><![CDATA[
      (a(x,y,z) * K(u \ 1,u)) * K(u,u \ 1) = a(x,K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(14(a,2),5351(a,1,1,1))].">
      <j1 rule="para" parents="14 5351"/>
    </justification>
  </clause>

  <clause id="5353">
    <literal><![CDATA[
      a(x,K(y,y \ 1) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,3664,a(flip),b,5352,a),flip(a)].">
      <j1 rule="hyper" parents="64 3664 5352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5355">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(2350(a,1),5353(a,1,2))].">
      <j1 rule="para" parents="2350 5353"/>
    </justification>
  </clause>

  <clause id="5356">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(3610(a,1),5353(a,1,2))].">
      <j1 rule="para" parents="3610 5353"/>
    </justification>
  </clause>

  <clause id="5357">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((x \ z) * (((1 / x) * z) \ u))) = y * (((x \ 1) * z) \ ((((1 / x) \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[para(82(a,1),5304(a,1,2,2,1,1))].">
      <j1 rule="para" parents="82 5304"/>
    </justification>
  </clause>

  <clause id="5359">
    <literal><![CDATA[
      (((x * y) * z) * R(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * R(R(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),2865(a,2,2,1,1))].">
      <j1 rule="para" parents="20 2865"/>
    </justification>
  </clause>

  <clause id="5360">
    <literal><![CDATA[
      (((x * y) * R((x * y) \ y,z,u)) * w) / (y * w) = R(x,y,w) * R(R(x,y,w) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(2789(a,1),5359(a,1,1))].">
      <j1 rule="para" parents="2789 5359"/>
    </justification>
  </clause>

  <clause id="5361">
    <literal><![CDATA[
      (((x * R(x \ 1,y,z)) * u) * w) / (u * w) = R(x,u,w) * R(R(x,u,w) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2479(a,1),5360(a,1,1,1))].">
      <j1 rule="para" parents="2479 5360"/>
    </justification>
  </clause>

  <clause id="5362">
    <literal><![CDATA[
      R(x,y,z) * R(R(x,y,z) \ 1,u,w) = R(x * R(x \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(666,a,5361,a),flip(a)].">
      <j1 rule="hyper" parents="666 5361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5363">
    <literal><![CDATA[
      R(x * R(x \ 1,R(x,y,z),x \ 1),y,z) = ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1798,a(flip),b,5362,a),flip(a)].">
      <j1 rule="hyper" parents="64 1798 5362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5364">
    <literal><![CDATA[
      ((x \ 1) / (x \ R(x,y,z))) * R(x,y,z) = R(x * T(x \ 1,R(x,y,z)),y,z)
    ]]></literal>
    <justification jstring="[para(2099(a,1),5363(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2099 5363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5365">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,3486,a(flip),b,5364,a),flip(a)].">
      <j1 rule="hyper" parents="36 3486 5364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5366">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(4266,a,5365,a)].">
      <j1 rule="hyper" parents="4266 5365"/>
    </justification>
  </clause>

  <clause id="5367">
    <literal><![CDATA[
      ((x / y) \ R(x / y,y,x \ 1)) * (y * (x \ 1)) = (x / y) \ 1
    ]]></literal>
    <justification jstring="[hyper(145,a,684,a(flip),b,5366,a)].">
      <j1 rule="hyper" parents="145 684 5366"/>
    </justification>
  </clause>

  <clause id="5368">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,5366,a(flip),b,3454,a)].">
      <j1 rule="hyper" parents="139 5366 3454"/>
    </justification>
  </clause>

  <clause id="5369">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,5246,a,b,5368,a)].">
      <j1 rule="hyper" parents="64 5246 5368"/>
    </justification>
  </clause>

  <clause id="5370">
    <literal><![CDATA[
      (((x * y) * z) * L(((x * y) * z) \ (y * z),u,w)) / (y * z) = R(x,y,z) * L(R(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),3091(a,2,2,1,1))].">
      <j1 rule="para" parents="20 3091"/>
    </justification>
  </clause>

  <clause id="5371">
    <literal><![CDATA[
      (((x * y) * L((x * y) \ y,z,u)) * w) / (y * w) = R(x,y,w) * L(R(x,y,w) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(2793(a,1),5370(a,1,1))].">
      <j1 rule="para" parents="2793 5370"/>
    </justification>
  </clause>

  <clause id="5372">
    <literal><![CDATA[
      (((x * L(x \ 1,y,z)) * u) * w) / (u * w) = R(x,u,w) * L(R(x,u,w) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2481(a,1),5371(a,1,1,1))].">
      <j1 rule="para" parents="2481 5371"/>
    </justification>
  </clause>

  <clause id="5373">
    <literal><![CDATA[
      R(x,y,z) * L(R(x,y,z) \ 1,u,w) = R(x * L(x \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(666,a,5372,a),flip(a)].">
      <j1 rule="hyper" parents="666 5372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5374">
    <literal><![CDATA[
      R(x,y,z) * L(R(x,y,z) \ 1,x,1 / x) = R(x * T(1 / x,1),y,z)
    ]]></literal>
    <justification jstring="[para(1022(a,1),5373(a,2,1,2))].">
      <j1 rule="para" parents="1022 5373"/>
    </justification>
  </clause>

  <clause id="5375">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(x * T(1 / x,1),y,z)
    ]]></literal>
    <justification jstring="[para(1925(a,1),5374(a,1,2))].">
      <j1 rule="para" parents="1925 5374"/>
    </justification>
  </clause>

  <clause id="5376">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(372(a,1),5375(a,2,1,2))].">
      <j1 rule="para" parents="372 5375"/>
    </justification>
  </clause>

  <clause id="5377">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1724(a,2),5376(a,2,1))].">
      <j1 rule="para" parents="1724 5376"/>
    </justification>
  </clause>

  <clause id="5378">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,2256,a(flip),b,5377,a),flip(a)].">
      <j1 rule="hyper" parents="373 2256 5377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5380">
    <literal><![CDATA[
      (1 / x) * (R(x,y,z) \ x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,3759,a,b,5378,a),flip(a)].">
      <j1 rule="hyper" parents="35 3759 5378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5381">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(149,a,5380,a)].">
      <j1 rule="hyper" parents="149 5380"/>
    </justification>
  </clause>

  <clause id="5382">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,5369,a(flip),b,5381,a)].">
      <j1 rule="hyper" parents="64 5369 5381"/>
    </justification>
  </clause>

  <clause id="5383">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ 1 = x * (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,1909,a,b,5382,a),flip(a)].">
      <j1 rule="hyper" parents="373 1909 5382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5384">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) * u = (R(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,5382,a,b,11,a)].">
      <j1 rule="hyper" parents="144 5382 11"/>
    </justification>
  </clause>

  <clause id="5385">
    <literal><![CDATA[
      R(L(x,y,z),u,w) \ L(x,y,z) = L(x \ R(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(4246(a,1),5382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4246 5382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5386">
    <literal><![CDATA[
      L(R(x,y,z),u,w) \ L(x,u,w) = L(x \ R(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[para(29(a,1),5385(a,1,1))].">
      <j1 rule="para" parents="29 5385"/>
    </justification>
  </clause>

  <clause id="5388">
    <literal><![CDATA[
      (x * (y * z)) * (1 / (1 / ((x * (y * z)) \ (x * y)))) = (x * y) * K(L(z,y,x),L(z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(213(a,1),3960(a,1,2,2,2,2))].">
      <j1 rule="para" parents="213 3960"/>
    </justification>
  </clause>

  <clause id="5389">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * ((y * z) * (1 / (1 / ((y * z) \ y))))
    ]]></literal>
    <justification jstring="[hyper(64,a,4358,a(flip),b,5388,a),flip(a)].">
      <j1 rule="hyper" parents="64 4358 5388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5391">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * (z * (1 / (1 / (z \ (y \ y))))))
    ]]></literal>
    <justification jstring="[para(4342(a,1),5389(a,2,2))].">
      <j1 rule="para" parents="4342 5389"/>
    </justification>
  </clause>

  <clause id="5392">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * (z * (1 / (1 / (z \ 1)))))
    ]]></literal>
    <justification jstring="[para(68(a,1),5391(a,2,2,2,2,2,2,2))].">
      <j1 rule="para" parents="68 5391"/>
    </justification>
  </clause>

  <clause id="5394">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * (z * (1 / z)))
    ]]></literal>
    <justification jstring="[para(79(a,1),5392(a,2,2,2,2,2))].">
      <j1 rule="para" parents="79 5392"/>
    </justification>
  </clause>

  <clause id="5395">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x),L(z,y,x) \ 1) = x * (y * K(z,z \ 1))
    ]]></literal>
    <justification jstring="[para(1724(a,2),5394(a,2,2,2))].">
      <j1 rule="para" parents="1724 5394"/>
    </justification>
  </clause>

  <clause id="5396">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(5104,a,5395,a),flip(a)].">
      <j1 rule="hyper" parents="5104 5395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5398">
    <literal><![CDATA[
      L(x,y,z) * (1 / L(x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1728,a,5396,a)].">
      <j1 rule="hyper" parents="1728 5396"/>
    </justification>
  </clause>

  <clause id="5399">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,5396,a(flip),b,1724,a(flip))].">
      <j1 rule="hyper" parents="139 5396 1724"/>
    </justification>
  </clause>

  <clause id="5400">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ K(L(x,u,w),L(x,u,w) \ 1) = 1 / L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(1433,a,5398,a)].">
      <j1 rule="hyper" parents="1433 5398"/>
    </justification>
  </clause>

  <clause id="5401">
    <literal><![CDATA[
      L(x,y,z) \ (1 / x) = x \ (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,5399,a(flip),b,2341,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 5399 2341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5402">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ K(x,x \ 1) = 1 / L(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(5396(a,1),5400(a,1,2))].">
      <j1 rule="para" parents="5396 5400"/>
    </justification>
  </clause>

  <clause id="5405">
    <literal><![CDATA[
      T(x,y) * (x * ((T(x,y) \ z) * T((T(x,y) \ z) \ z,u))) = T((x * z) / (x * (T(x,y) \ z)),u) * (x * z)
    ]]></literal>
    <justification jstring="[para(1307(a,1),2427(a,1,2))].">
      <j1 rule="para" parents="1307 2427"/>
    </justification>
  </clause>

  <clause id="5406">
    <literal><![CDATA[
      T((x * y) / (x * (T(x,z) \ y)),u) * (x * y) = T(x,z) * (x * (T(T(x,z),u) * (T(x,z) \ y)))
    ]]></literal>
    <justification jstring="[para(527(a,1),5405(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="527 5405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5407">
    <literal><![CDATA[
      T((x * y) / (x * (T(x,z) \ y)),u) * (x * y) = x * (T(x,z) * (T(T(x,z),u) * (T(x,z) \ y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,2403,a(flip),b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="373 2403 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      T((x * y) / (x * (T(x,z) \ y)),u) * (x * y) = x * (T(T(x,z),u) * y)
    ]]></literal>
    <justification jstring="[para(2399(a,1),5407(a,2,2))].">
      <j1 rule="para" parents="2399 5407"/>
    </justification>
  </clause>

  <clause id="5409">
    <literal><![CDATA[
      T(T(x,y),z) * (x * u) = x * (T(T(x,y),z) * u)
    ]]></literal>
    <justification jstring="[para(2417(a,1),5408(a,1,1,1))].">
      <j1 rule="para" parents="2417 5408"/>
    </justification>
  </clause>

  <clause id="5410">
    <literal><![CDATA[
      T(T(x,y),z) \ (x * u) = x * (T(T(x,y),z) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,5409,a)].">
      <j1 rule="hyper" parents="139 168 5409"/>
    </justification>
  </clause>

  <clause id="5412">
    <literal><![CDATA[
      R(x,T(y,x),K(z \ 1,R(z,u,w))) \ ((y * K(z \ 1,z)) * x) = T(y,x) * T(K(z \ 1,R(z,u,w)),y * x)
    ]]></literal>
    <justification jstring="[para(3615(a,1),3774(a,1,1,3))].">
      <j1 rule="para" parents="3615 3774"/>
    </justification>
  </clause>

  <clause id="5414">
    <literal><![CDATA[
      T(x,y) * T(K(z \ 1,R(z,u,w)),x * y) = y \ ((x * K(z \ 1,z)) * y)
    ]]></literal>
    <justification jstring="[para(5091(a,1),5412(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5091 5412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5415">
    <literal><![CDATA[
      T(x,y) * T(K(z \ 1,R(z,u,w)),x * y) = T(x * K(z \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,22,a,b,5414,a),flip(a)].">
      <j1 rule="hyper" parents="373 22 5414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5416">
    <literal><![CDATA[
      T(x,y) * K(z \ 1,R(z,u,w)) = T(x * K(z \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(3615(a,1),5415(a,1,2))].">
      <j1 rule="para" parents="3615 5415"/>
    </justification>
  </clause>

  <clause id="5417">
    <literal><![CDATA[
      T(x * K(y \ 1,y),z) = T(x,z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(431(a,1),5416(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="431 5416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5419">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,z) = T(y,z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3595(a,2),5417(a,1,1))].">
      <j1 rule="para" parents="3595 5417"/>
    </justification>
  </clause>

  <clause id="5421">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,z) = K(x \ 1,x) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,3595,a,b,5419,a),flip(a)].">
      <j1 rule="hyper" parents="373 3595 5419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5422">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[para(2358(a,1),5421(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2358 5421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5423">
    <literal><![CDATA[
      T(x,T(K(y \ 1,y) * z,u)) = T(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(5421(a,2),5109(a,1,2))].">
      <j1 rule="para" parents="5421 5109"/>
    </justification>
  </clause>

  <clause id="5424">
    <literal><![CDATA[
      T(x,T(y * (1 / z),u)) = T(x,T(y * (z \ 1),u))
    ]]></literal>
    <justification jstring="[para(3625(a,1),5423(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3625 5423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5425">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,z) = K(x,x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(2372,a,5422,a),flip(a)].">
      <j1 rule="hyper" parents="2372 5422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5426">
    <literal><![CDATA[
      (x \ T(x * (y / x),z)) * x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3465,a(flip),b,5422,a)].">
      <j1 rule="hyper" parents="64 3465 5422"/>
    </justification>
  </clause>

  <clause id="5427">
    <literal><![CDATA[
      x \ T(x * (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,5422,a(flip),b,3465,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="142 5422 3465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5430">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x = T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5426(a,1,1,2,1,2))].">
      <j1 rule="para" parents="11 5426"/>
    </justification>
  </clause>

  <clause id="5431">
    <literal><![CDATA[
      T(x * (y / x),z) = x * (T(y,z) / x)
    ]]></literal>
    <justification jstring="[para(5426(a,1),78(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5426 78"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5432">
    <literal><![CDATA[
      T((x \ y) * x,z) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(78(a,1),5426(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 5426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5433">
    <literal><![CDATA[
      ((x \ 1) \ (y / x)) * (x \ 1) = T(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,1184,a(flip),b,5427,a)].">
      <j1 rule="hyper" parents="64 1184 5427"/>
    </justification>
  </clause>

  <clause id="5434">
    <literal><![CDATA[
      T(x * y,z) / y = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5427(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 5427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5435">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) = T(y,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),5427(a,1,2,1,2))].">
      <j1 rule="para" parents="79 5427"/>
    </justification>
  </clause>

  <clause id="5436">
    <literal><![CDATA[
      T((x \ y) * x,z) / x = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(78(a,1),5427(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="78 5427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5437">
    <literal><![CDATA[
      x * (y * (T(z,x) / y)) = (y * (z / y)) * x
    ]]></literal>
    <justification jstring="[para(5427(a,1),258(a,1,2,2))].">
      <j1 rule="para" parents="5427 258"/>
    </justification>
  </clause>

  <clause id="5439">
    <literal><![CDATA[
      x \ T(T(x,y) * y,z) = T(x * y,z) / x
    ]]></literal>
    <justification jstring="[para(4450(a,2),5427(a,1,2,1))].">
      <j1 rule="para" parents="4450 5427"/>
    </justification>
  </clause>

  <clause id="5440">
    <literal><![CDATA[
      T(x \ T(x * y,z),x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(493,a,xx,b,5430,a)].">
      <j1 rule="hyper" parents="493 5430"/>
    </justification>
  </clause>

  <clause id="5441">
    <literal><![CDATA[
      (x \ 1) \ T((x \ 1) * y,z) = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,1504,a,b,5430,a),flip(a)].">
      <j1 rule="hyper" parents="36 1504 5430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5443">
    <literal><![CDATA[
      x * (T(y * x,z) / x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(5430(a,1),78(a,1,2,1))].">
      <j1 rule="para" parents="5430 78"/>
    </justification>
  </clause>

  <clause id="5444">
    <literal><![CDATA[
      T((x * (y \ 1)) * y,z) = (T(x,z) * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(1482(a,1),5430(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1482 5430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5445">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(5430(a,1),4688(a,1,2))].">
      <j1 rule="para" parents="5430 4688"/>
    </justification>
  </clause>

  <clause id="5447">
    <literal><![CDATA[
      T(x * ((y / z) / x),z) = x * ((z \ y) / x)
    ]]></literal>
    <justification jstring="[para(117(a,1),5431(a,2,2,1))].">
      <j1 rule="para" parents="117 5431"/>
    </justification>
  </clause>

  <clause id="5449">
    <literal><![CDATA[
      T(x * (y / x),K(y,z)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4067(a,1),5431(a,2,2,1))].">
      <j1 rule="para" parents="4067 5431"/>
    </justification>
  </clause>

  <clause id="5450">
    <literal><![CDATA[
      T(x * (y / x),z / y) = x * (T(y,y \ z) / x)
    ]]></literal>
    <justification jstring="[para(4636(a,1),5431(a,2,2,1))].">
      <j1 rule="para" parents="4636 5431"/>
    </justification>
  </clause>

  <clause id="5452">
    <literal><![CDATA[
      x \ T((x \ y) * x,z) = T(x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(493,a,5432,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="493 5432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5453">
    <literal><![CDATA[
      x * ((y \ T(z,x)) * y) = ((y \ z) * y) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,5432,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 5432 22"/>
    </justification>
  </clause>

  <clause id="5454">
    <literal><![CDATA[
      T((x \ L(y,z,u)) * x,w) = (x \ L(T(y,w),z,u)) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),5432(a,2,1,2))].">
      <j1 rule="para" parents="25 5432"/>
    </justification>
  </clause>

  <clause id="5455">
    <literal><![CDATA[
      T((x \ y) * x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(114(a,1),5432(a,2,1,2))].">
      <j1 rule="para" parents="114 5432"/>
    </justification>
  </clause>

  <clause id="5456">
    <literal><![CDATA[
      T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x
    ]]></literal>
    <justification jstring="[para(117(a,1),5432(a,2,1,2))].">
      <j1 rule="para" parents="117 5432"/>
    </justification>
  </clause>

  <clause id="5457">
    <literal><![CDATA[
      T((x \ y) * x,z) / x != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(5432(a,2),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5432 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5458">
    <literal><![CDATA[
      T((x \ y) * x,K(y,z)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(4067(a,1),5432(a,2,1,2))].">
      <j1 rule="para" parents="4067 5432"/>
    </justification>
  </clause>

  <clause id="5459">
    <literal><![CDATA[
      ((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(5432(a,2),4969(a,1,1,1,2))].">
      <j1 rule="para" parents="5432 4969"/>
    </justification>
  </clause>

  <clause id="5460">
    <literal><![CDATA[
      T(x,(y \ x) * y) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,5455,a)].">
      <j1 rule="hyper" parents="55 5455"/>
    </justification>
  </clause>

  <clause id="5461">
    <literal><![CDATA[
      T(x * y,y * x) = x * y
    ]]></literal>
    <justification jstring="[para(9(a,1),5460(a,1,2,1))].">
      <j1 rule="para" parents="9 5460"/>
    </justification>
  </clause>

  <clause id="5462">
    <literal><![CDATA[
      T(x * y,z) * (y * x) = (y * x) * T(x * y,z)
    ]]></literal>
    <justification jstring="[para(5461(a,1),265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5461 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5463">
    <literal><![CDATA[
      x \ T(x * y,1 / x) = ((1 / x) \ y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1565,a,5434,a),flip(a)].">
      <j1 rule="hyper" parents="1565 5434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5464">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,1182,a,b,5434,a)].">
      <j1 rule="hyper" parents="373 1182 5434"/>
    </justification>
  </clause>

  <clause id="5465">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1506,a,b,5434,a)].">
      <j1 rule="hyper" parents="64 1506 5434"/>
    </justification>
  </clause>

  <clause id="5467">
    <literal><![CDATA[
      x * (T(y * x,z) / x) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ T(x * y,z) = w
    ]]></literal>
    <justification jstring="[para(5434(a,2),462(a,1,2))].">
      <j1 rule="para" parents="5434 462"/>
    </justification>
  </clause>

  <clause id="5468">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(5434(a,1),3052(a,1,2))].">
      <j1 rule="para" parents="5434 3052"/>
    </justification>
  </clause>

  <clause id="5469">
    <literal><![CDATA[
      T(x \ ((x \ 1) \ y),z) = x \ ((x \ 1) \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,5436,a(flip),b,1503,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 5436 1503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5470">
    <literal><![CDATA[
      T(x,y) / R(x,z,u) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2154(a,1),5436(a,1,1,1))].">
      <j1 rule="para" parents="2154 5436"/>
    </justification>
  </clause>

  <clause id="5471">
    <literal><![CDATA[
      T(x,y) / T(x,z) = T(x,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3983(a,1),5436(a,1,1,1))].">
      <j1 rule="para" parents="3983 5436"/>
    </justification>
  </clause>

  <clause id="5472">
    <literal><![CDATA[
      T(K(x,y),z * (x / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(55,a,5449,a)].">
      <j1 rule="hyper" parents="55 5449"/>
    </justification>
  </clause>

  <clause id="5473">
    <literal><![CDATA[
      T(K(x * y,z),y * x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),5472(a,1,2,2))].">
      <j1 rule="para" parents="11 5472"/>
    </justification>
  </clause>

  <clause id="5474">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x))
    ]]></literal>
    <justification jstring="[para(117(a,1),5437(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="117 5437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5475">
    <literal><![CDATA[
      T(((x \ 1) \ y) * (x \ 1),x) = x \ T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1184(a,1),5440(a,1,1))].">
      <j1 rule="para" parents="1184 5440"/>
    </justification>
  </clause>

  <clause id="5476">
    <literal><![CDATA[
      a(((x * ((x / y) / x)) \ T(x,y \ 1)) \ T(x,y \ 1),z,u) = a(x * ((y \ x) / x),z,u)
    ]]></literal>
    <justification jstring="[para(5447(a,1),4406(a,2,1))].">
      <j1 rule="para" parents="5447 4406"/>
    </justification>
  </clause>

  <clause id="5478">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[para(117(a,1),5453(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="117 5453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5479">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) / x = (y \ (z / x)) * y
    ]]></literal>
    <justification jstring="[hyper(313,a,5456,a)].">
      <j1 rule="hyper" parents="313 5456"/>
    </justification>
  </clause>

  <clause id="5484">
    <literal><![CDATA[
      T(x * K(y,y \ 1),z) = K(y,y \ 1) * T(x,z)
    ]]></literal>
    <justification jstring="[para(3610(a,1),5425(a,1,1))].">
      <j1 rule="para" parents="3610 5425"/>
    </justification>
  </clause>

  <clause id="5486">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,2496,a(flip),b,5435,a),flip(a)].">
      <j1 rule="hyper" parents="373 2496 5435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5487">
    <literal><![CDATA[
      T(x * (y / x),z / y) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5431,a,b,5450,a),flip(a)].">
      <j1 rule="hyper" parents="373 5431 5450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5488">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(5464(a,2),5457(a,1))].">
      <j1 rule="para" parents="5464 5457"/>
    </justification>
  </clause>

  <clause id="5489">
    <literal><![CDATA[
      T(x * (y * y),z) * (1 / y) = y \ T(y * (x * y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,908,a(flip),b,5465,a)].">
      <j1 rule="hyper" parents="64 908 5465"/>
    </justification>
  </clause>

  <clause id="5490">
    <literal><![CDATA[
      T(x \ ((x \ 1) \ y),y) = x \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(114(a,1),5469(a,2,2,2))].">
      <j1 rule="para" parents="114 5469"/>
    </justification>
  </clause>

  <clause id="5491">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) * y = y * (x \ ((x \ 1) \ y))
    ]]></literal>
    <justification jstring="[hyper(145,a,5490,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 5490 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5492">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(4255,a,5474,a),flip(a)].">
      <j1 rule="hyper" parents="4255 5474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5493">
    <literal><![CDATA[
      (x * ((y / (y * z)) / x)) * (y * z) = (y * z) * (x * (L(z \ 1,z,y) / x))
    ]]></literal>
    <justification jstring="[para(241(a,2),5474(a,2,2,2,1))].">
      <j1 rule="para" parents="241 5474"/>
    </justification>
  </clause>

  <clause id="5494">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = y * ((x \ (y \ z)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2927,a,b,5478,a)].">
      <j1 rule="hyper" parents="64 2927 5478"/>
    </justification>
  </clause>

  <clause id="5495">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2285,a,b,5478,a)].">
      <j1 rule="hyper" parents="64 2285 5478"/>
    </justification>
  </clause>

  <clause id="5496">
    <literal><![CDATA[
      ((x \ R(1 / y,y,z)) * x) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(244(a,2),5478(a,1,1,1,2))].">
      <j1 rule="para" parents="244 5478"/>
    </justification>
  </clause>

  <clause id="5497">
    <literal><![CDATA[
      (x * ((y \ z) * y)) / x = (y \ ((x * z) / x)) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),5479(a,1,1,2,1,2))].">
      <j1 rule="para" parents="9 5479"/>
    </justification>
  </clause>

  <clause id="5498">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x \ (z \ y)) * x) = u
    ]]></literal>
    <justification jstring="[para(5479(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5479 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5499">
    <literal><![CDATA[
      (x \ ((y * (x * z)) / y)) * x = (y * (z * x)) / y
    ]]></literal>
    <justification jstring="[para(69(a,1),5479(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="69 5479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5500">
    <literal><![CDATA[
      T(x * (y / x),(y / z) \ 1) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(4829,a,5487,a)].">
      <j1 rule="hyper" parents="4829 5487"/>
    </justification>
  </clause>

  <clause id="5501">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (x * (y * (x \ ((x \ 1) \ y)))) = L(y,x \ ((x \ 1) \ y),x)
    ]]></literal>
    <justification jstring="[para(5491(a,1),101(a,1,2,2))].">
      <j1 rule="para" parents="5491 101"/>
    </justification>
  </clause>

  <clause id="5502">
    <literal><![CDATA[
      (x \ ((x * y) / x)) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4758,a,5497,a),flip(a)].">
      <j1 rule="hyper" parents="4758 5497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5503">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(2945,a,5468,a)].">
      <j1 rule="hyper" parents="2945 5468"/>
    </justification>
  </clause>

  <clause id="5504">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x
    ]]></literal>
    <justification jstring="[hyper(5498,a,5503,a)].">
      <j1 rule="hyper" parents="5498 5503"/>
    </justification>
  </clause>

  <clause id="5507">
    <literal><![CDATA[
      (x * y) * (z * (L(y \ 1,y,x) / z)) = (x * y) * (z * (((x * y) \ x) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5474,a(flip),b,5493,a),flip(a)].">
      <j1 rule="hyper" parents="64 5474 5493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5508">
    <literal><![CDATA[
      R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(2143(a,2),5496(a,1,1))].">
      <j1 rule="para" parents="2143 5496"/>
    </justification>
  </clause>

  <clause id="5509">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = (((z \ (1 / x)) * z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(327,a,5508,a),flip(a)].">
      <j1 rule="hyper" parents="327 5508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5510">
    <literal><![CDATA[
      (x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z)
    ]]></literal>
    <justification jstring="[para(256(a,1),5459(a,1,1)),flip(a)].">
      <j1 rule="para" parents="256 5459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5512">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z)
    ]]></literal>
    <justification jstring="[para(5474(a,1),5492(a,2,1))].">
      <j1 rule="para" parents="5474 5492"/>
    </justification>
  </clause>

  <clause id="5513">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * ((z / u) \ z)) \ z) / y))
    ]]></literal>
    <justification jstring="[para(82(a,1),5512(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="82 5512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5514">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[para(82(a,1),5513(a,2,2,2,1,1,2))].">
      <j1 rule="para" parents="82 5513"/>
    </justification>
  </clause>

  <clause id="5515">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(741,a,5514,a)].">
      <j1 rule="hyper" parents="741 5514"/>
    </justification>
  </clause>

  <clause id="5523">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((L(z,y,x) \ z) * ((x * y) \ (x * (y * z))))) = T(a(x,y,z),(x * y) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(18(a,2),2395(a,1,2,2,1,1))].">
      <j1 rule="para" parents="18 2395"/>
    </justification>
  </clause>

  <clause id="5524">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((L(z,y,x) \ z) * L(z,y,x))) = T(a(x,y,z),(x * y) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(18(a,2),5523(a,1,2,2,2))].">
      <j1 rule="para" parents="18 5523"/>
    </justification>
  </clause>

  <clause id="5525">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((L(z,y,x) \ z) * L(z,y,x))) = T(a(x,y,z),L(z,y,x))
    ]]></literal>
    <justification jstring="[para(18(a,2),5524(a,2,2))].">
      <j1 rule="para" parents="18 5524"/>
    </justification>
  </clause>

  <clause id="5526">
    <literal><![CDATA[
      T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * (K(x \ 1,x) * L(T(x \ 1,(x \ 1) \ 1) \ y,z,u))
    ]]></literal>
    <justification jstring="[para(1734(a,1),3459(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1734 3459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5527">
    <literal><![CDATA[
      T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * (K(x \ 1,x) * L((((x \ 1) \ 1) \ 1) \ y,z,u))
    ]]></literal>
    <justification jstring="[para(116(a,1),5526(a,2,2,2,1,1))].">
      <j1 rule="para" parents="116 5526"/>
    </justification>
  </clause>

  <clause id="5528">
    <literal><![CDATA[
      T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * L(K(x \ 1,x) * ((((x \ 1) \ 1) \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(5312(a,2),5527(a,2,2))].">
      <j1 rule="para" parents="5312 5527"/>
    </justification>
  </clause>

  <clause id="5529">
    <literal><![CDATA[
      T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * L((((x \ 1) \ 1) \ K(x,x \ 1)) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(5235(a,1),5528(a,2,2,1))].">
      <j1 rule="para" parents="5235 5528"/>
    </justification>
  </clause>

  <clause id="5530">
    <literal><![CDATA[
      T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = (x \ 1) * L((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1741(a,1),5529(a,2,2,1,1))].">
      <j1 rule="para" parents="1741 5529"/>
    </justification>
  </clause>

  <clause id="5531">
    <literal><![CDATA[
      T(x \ L(x * ((((x \ 1) \ 1) * y) / ((x \ 1) \ 1)),z,u),(x \ 1) \ 1) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,1389,a(flip),b,5530,a),flip(a)].">
      <j1 rule="hyper" parents="373 1389 5530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5532">
    <literal><![CDATA[
      T(x \ L(x * ((x * y) / x),z,u),(x \ 1) \ 1) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(3923(a,1),5531(a,1,1,2,1,2))].">
      <j1 rule="para" parents="3923 5531"/>
    </justification>
  </clause>

  <clause id="5533">
    <literal><![CDATA[
      T(x \ L(x * ((x * y) / x),z,u),x) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,3871,a(flip),b,5532,a)].">
      <j1 rule="hyper" parents="64 3871 5532"/>
    </justification>
  </clause>

  <clause id="5534">
    <literal><![CDATA[
      T(x \ 1,x) * L(T(x \ 1,x) \ y,z,u) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,3286,a(flip),b,5533,a)].">
      <j1 rule="hyper" parents="64 3286 5533"/>
    </justification>
  </clause>

  <clause id="5535">
    <literal><![CDATA[
      T((1 / x) \ 1,1 / x) * L(T((1 / x) \ 1,1 / x) \ y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,1310,a(flip),b,5534,a),flip(a)].">
      <j1 rule="hyper" parents="373 1310 5534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5536">
    <literal><![CDATA[
      T((1 / (1 / x)) \ 1,1 / (1 / x)) * L(T((1 / (1 / x)) \ 1,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,3128,a(flip),b,5535,a),flip(a)].">
      <j1 rule="hyper" parents="373 3128 5535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5537">
    <literal><![CDATA[
      T(1 / x,1 / (1 / x)) * L(T((1 / (1 / x)) \ 1,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(82(a,1),5536(a,1,1,1))].">
      <j1 rule="para" parents="82 5536"/>
    </justification>
  </clause>

  <clause id="5539">
    <literal><![CDATA[
      (x \ 1) * L(T((1 / (1 / x)) \ 1,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(1351(a,1),5537(a,1,1))].">
      <j1 rule="para" parents="1351 5537"/>
    </justification>
  </clause>

  <clause id="5540">
    <literal><![CDATA[
      (x \ 1) * L(T(1 / x,1 / (1 / x)) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(82(a,1),5539(a,1,2,1,1,1))].">
      <j1 rule="para" parents="82 5539"/>
    </justification>
  </clause>

  <clause id="5542">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(1351(a,1),5540(a,1,2,1,1))].">
      <j1 rule="para" parents="1351 5540"/>
    </justification>
  </clause>

  <clause id="5543">
    <literal><![CDATA[
      L(x * y,z,u) / y = y \ L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1389,a(flip),b,5542,a),flip(a)].">
      <j1 rule="hyper" parents="64 1389 5542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5544">
    <literal><![CDATA[
      L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,1805,a(flip),b,5542,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 1805 5542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5545">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,1389,a(flip),b,5542,a(flip))].">
      <j1 rule="hyper" parents="144 1389 5542"/>
    </justification>
  </clause>

  <clause id="5546">
    <literal><![CDATA[
      (x \ 1) \ L((x \ 1) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1835,a(flip),b,5543,a),flip(a)].">
      <j1 rule="hyper" parents="64 1835 5543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5547">
    <literal><![CDATA[
      x \ L(x * (y / x),z,u) = L(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),5543(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 5543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5548">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(227,a,5544,a),flip(a)].">
      <j1 rule="hyper" parents="227 5544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5549">
    <literal><![CDATA[
      (x * y) * ((z \ L(u,y,x)) * z) = x * (y * ((z \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(145,a,5544,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 5544 18"/>
    </justification>
  </clause>

  <clause id="5550">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(190(a,1),5544(a,1,1)),flip(a)].">
      <j1 rule="para" parents="190 5544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5552">
    <literal><![CDATA[
      ((1 / x) \ L(L(y,x,x),z,u)) * (1 / x) = L((x * y) * (1 / x),z,u)
    ]]></literal>
    <justification jstring="[para(561(a,1),5544(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="561 5544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5553">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(629(a,1),5544(a,2,1,2))].">
      <j1 rule="para" parents="629 5544"/>
    </justification>
  </clause>

  <clause id="5556">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(3189,a,5548,a)].">
      <j1 rule="hyper" parents="3189 5548"/>
    </justification>
  </clause>

  <clause id="5557">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(410,a,5548,a)].">
      <j1 rule="hyper" parents="410 5548"/>
    </justification>
  </clause>

  <clause id="5558">
    <literal><![CDATA[
      x / L(x,y,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(154,a,5548,a)].">
      <j1 rule="hyper" parents="154 5548"/>
    </justification>
  </clause>

  <clause id="5559">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,5548,a)].">
      <j1 rule="hyper" parents="149 5548"/>
    </justification>
  </clause>

  <clause id="5560">
    <literal><![CDATA[
      x / L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(5548(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5548 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5561">
    <literal><![CDATA[
      L(x,y,z) * (x / L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[para(5548(a,1),78(a,1,2,1))].">
      <j1 rule="para" parents="5548 78"/>
    </justification>
  </clause>

  <clause id="5562">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) * L(x,y,z)) = x / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5548(a,1),808(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5548 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5563">
    <literal><![CDATA[
      a(x,x,y) * L(y,x,x) = y
    ]]></literal>
    <justification jstring="[para(1243(a,1),5548(a,1,1))].">
      <j1 rule="para" parents="1243 5548"/>
    </justification>
  </clause>

  <clause id="5564">
    <literal><![CDATA[
      a(x \ 1,x,y) * L(y,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(2673(a,1),5548(a,1,1))].">
      <j1 rule="para" parents="2673 5548"/>
    </justification>
  </clause>

  <clause id="5565">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = T(a(x,y,z),L(z,y,x))
    ]]></literal>
    <justification jstring="[para(5548(a,1),5525(a,1,2,2))].">
      <j1 rule="para" parents="5548 5525"/>
    </justification>
  </clause>

  <clause id="5566">
    <literal><![CDATA[
      (L(x,y,z) \ L(x,u,w)) * L(x,y,z) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(5548(a,1),5544(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5548 5544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5567">
    <literal><![CDATA[
      a(x,x,y) \ y = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(149,a,5563,a)].">
      <j1 rule="hyper" parents="149 5563"/>
    </justification>
  </clause>

  <clause id="5568">
    <literal><![CDATA[
      x * L(y,L(x,z,z),a(z,z,x)) = a(z,z,x) * (L(x,z,z) * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,5563,a(flip),b,213,a)].">
      <j1 rule="hyper" parents="144 5563 213"/>
    </justification>
  </clause>

  <clause id="5569">
    <literal><![CDATA[
      T(x,a(y,y,z) * a(y,y,z)) \ ((1 / a(y,y,z)) * L(z,y,y)) = (a(y,y,z) * a(y,y,z)) \ (x \ z)
    ]]></literal>
    <justification jstring="[para(5563(a,1),1528(a,2,2,2))].">
      <j1 rule="para" parents="5563 1528"/>
    </justification>
  </clause>

  <clause id="5570">
    <literal><![CDATA[
      L(x,y \ 1,y) = a(y,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,1145,a,b,5567,a)].">
      <j1 rule="hyper" parents="373 1145 5567"/>
    </justification>
  </clause>

  <clause id="5571">
    <literal><![CDATA[
      T(x,x \ L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(410,a,5550,a)].">
      <j1 rule="hyper" parents="410 5550"/>
    </justification>
  </clause>

  <clause id="5572">
    <literal><![CDATA[
      L(x,y,z) / x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(154,a,5550,a)].">
      <j1 rule="hyper" parents="154 5550"/>
    </justification>
  </clause>

  <clause id="5573">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(149,a,5550,a)].">
      <j1 rule="hyper" parents="149 5550"/>
    </justification>
  </clause>

  <clause id="5574">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,1872,a,b,5550,a),flip(a)].">
      <j1 rule="hyper" parents="36 1872 5550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5575">
    <literal><![CDATA[
      ((x * (y \ L(y,z,u))) * y) / L(y,z,u) = R(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(225,a,5550,a(flip),b,210,a)].">
      <j1 rule="hyper" parents="225 5550 210"/>
    </justification>
  </clause>

  <clause id="5576">
    <literal><![CDATA[
      L(x,y,z) * L(u,x,x \ L(x,y,z)) = (x \ L(x,y,z)) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,5550,a(flip),b,213,a)].">
      <j1 rule="hyper" parents="144 5550 213"/>
    </justification>
  </clause>

  <clause id="5577">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((x * (y \ L(y,z,u))) * y) = a(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(5550(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5550 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5578">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ L(x,y,z)) * (x * u)) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5550(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5550 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5579">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) \ (x * L(y,z,u)) = L(y,y \ L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(5550(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5550 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5580">
    <literal><![CDATA[
      L(x \ 1,x,x \ L(x,y,z)) = L(x,y,z) \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5550(a,1),241(a,2,1))].">
      <j1 rule="para" parents="5550 241"/>
    </justification>
  </clause>

  <clause id="5581">
    <literal><![CDATA[
      L(x \ y,x,x \ L(x,z,u)) = L(x,z,u) \ ((x \ L(x,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(5550(a,1),102(a,2,1))].">
      <j1 rule="para" parents="5550 102"/>
    </justification>
  </clause>

  <clause id="5582">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(5550(a,1),2148(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5550 2148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5583">
    <literal><![CDATA[
      T(x,y) * (x \ L(x,z,u)) = (x \ L(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5571(a,1),265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5571 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5584">
    <literal><![CDATA[
      (L(x,y,z) \ x) / x = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,5558,a(flip),b,3186,a)].">
      <j1 rule="hyper" parents="142 5558 3186"/>
    </justification>
  </clause>

  <clause id="5585">
    <literal><![CDATA[
      L(T(x,x \ y),z,u) \ T(x,x \ y) = T(x,x \ y) / L((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1071(a,1),5558(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1071 5558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5586">
    <literal><![CDATA[
      (((x * y) \ x) \ (y \ 1)) \ (y \ 1) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(241(a,1),5559(a,1,1,1))].">
      <j1 rule="para" parents="241 5559"/>
    </justification>
  </clause>

  <clause id="5587">
    <literal><![CDATA[
      a(x,x \ 1,y) \ y = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(979(a,1),5559(a,1,1))].">
      <j1 rule="para" parents="979 5559"/>
    </justification>
  </clause>

  <clause id="5588">
    <literal><![CDATA[
      a(x \ 1,x,y) \ y = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2673(a,1),5559(a,1,1))].">
      <j1 rule="para" parents="2673 5559"/>
    </justification>
  </clause>

  <clause id="5589">
    <literal><![CDATA[
      R(x,y,z) / L(x,u,w) = L(x,u,w) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5561(a,1),2127(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5561 2127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5590">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3130,a,b,5572,a)].">
      <j1 rule="hyper" parents="64 3130 5572"/>
    </justification>
  </clause>

  <clause id="5591">
    <literal><![CDATA[
      (1 / x) \ (x \ L(x,y,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,5572,a(flip),b,3130,a)].">
      <j1 rule="hyper" parents="139 5572 3130"/>
    </justification>
  </clause>

  <clause id="5592">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ ((x \ L(x,y,z)) \ 1)) * u = x * ((((x \ L(x,y,z)) \ 1) \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(5573(a,1),1615(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5573 1615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5593">
    <literal><![CDATA[
      T(1 / L(x,y,z),x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(269,a,5556,a,b,1846,a)].">
      <j1 rule="hyper" parents="269 5556 1846"/>
    </justification>
  </clause>

  <clause id="5594">
    <literal><![CDATA[
      (1 / L(x,y,y \ 1)) \ a(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,2673,a(flip),b,5556,a)].">
      <j1 rule="hyper" parents="139 2673 5556"/>
    </justification>
  </clause>

  <clause id="5595">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,5556,a(flip),b,1127,a),flip(a)].">
      <j1 rule="hyper" parents="139 5556 1127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5596">
    <literal><![CDATA[
      (1 / L(x,y,z)) * ((1 / x) \ x) = (L(x,y,z) \ x) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(5556(a,1),1592(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5556 1592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5597">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(u,x,L(x,y,z)) = (1 / L(x,y,z)) * (x * u)
    ]]></literal>
    <justification jstring="[para(5556(a,1),1651(a,1,1))].">
      <j1 rule="para" parents="5556 1651"/>
    </justification>
  </clause>

  <clause id="5598">
    <literal><![CDATA[
      a(x,x \ 1,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,5570,a(flip),b,5587,a),flip(a)].">
      <j1 rule="hyper" parents="40 5570 5587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5599">
    <literal><![CDATA[
      a(x \ 1,x \ 1,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2653,a,b,5598,a)].">
      <j1 rule="hyper" parents="64 2653 5598"/>
    </justification>
  </clause>

  <clause id="5600">
    <literal><![CDATA[
      T(1 / x,L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(269,a,5590,a,b,1807,a)].">
      <j1 rule="hyper" parents="269 5590 1807"/>
    </justification>
  </clause>

  <clause id="5602">
    <literal><![CDATA[
      (x * x) * (x \ L(x,y,z)) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5590,a(flip),b,535,a)].">
      <j1 rule="hyper" parents="145 5590 535"/>
    </justification>
  </clause>

  <clause id="5603">
    <literal><![CDATA[
      (x \ 1) * (x \ L(x,y,z)) = x \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,5590,a(flip),b,1127,a),flip(a)].">
      <j1 rule="hyper" parents="139 5590 1127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5604">
    <literal><![CDATA[
      R(x,x,x \ L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,2016,a,b,5590,a(flip))].">
      <j1 rule="hyper" parents="40 2016 5590"/>
    </justification>
  </clause>

  <clause id="5605">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (x * x) = (x \ L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(5590(a,1),552(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5590 552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5606">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,L(x,y,z),x) = (1 / x) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(5590(a,1),1651(a,1,1))].">
      <j1 rule="para" parents="5590 1651"/>
    </justification>
  </clause>

  <clause id="5607">
    <literal><![CDATA[
      (1 / x) \ L(x \ L(x,y,z),u,w) = x * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(5590(a,1),1310(a,1,2,1))].">
      <j1 rule="para" parents="5590 1310"/>
    </justification>
  </clause>

  <clause id="5608">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,w)) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(5590(a,1),2186(a,1,3))].">
      <j1 rule="para" parents="5590 2186"/>
    </justification>
  </clause>

  <clause id="5609">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,w) = a(x * L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(5590(a,1),2642(a,1,1))].">
      <j1 rule="para" parents="5590 2642"/>
    </justification>
  </clause>

  <clause id="5610">
    <literal><![CDATA[
      a((x \ L(x,y,z)) * u,w,v5) = a((x * L(x,y,z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(5590(a,1),2679(a,1,1,1))].">
      <j1 rule="para" parents="5590 2679"/>
    </justification>
  </clause>

  <clause id="5611">
    <literal><![CDATA[
      a(((x \ L(x,y,z)) * u) * w,v5,v6) = a(((x * L(x,y,z)) * u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(5590(a,1),2695(a,1,1,1,1))].">
      <j1 rule="para" parents="5590 2695"/>
    </justification>
  </clause>

  <clause id="5612">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),w) = R(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(5590(a,1),2969(a,1,2))].">
      <j1 rule="para" parents="5590 2969"/>
    </justification>
  </clause>

  <clause id="5613">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(x \ 1,x) = (x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5590(a,1),3623(a,1,1))].">
      <j1 rule="para" parents="5590 3623"/>
    </justification>
  </clause>

  <clause id="5614">
    <literal><![CDATA[
      (L(x,y,z) * x) * (x \ L(x,u,w)) = L(x,y,z) * L(x,u,w)
    ]]></literal>
    <justification jstring="[para(5604(a,1),976(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5604 976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5615">
    <literal><![CDATA[
      T((1 / x) * y,y \ x) = L(y \ x,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(919(a,1),5593(a,1,1))].">
      <j1 rule="para" parents="919 5593"/>
    </justification>
  </clause>

  <clause id="5616">
    <literal><![CDATA[
      T(x,L(x,y,z) \ x) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,25,a,b,5557,a(flip))].">
      <j1 rule="hyper" parents="42 25 5557"/>
    </justification>
  </clause>

  <clause id="5618">
    <literal><![CDATA[
      L(x * (y / x),z,u) = x * (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(157,a,5547,a),flip(a)].">
      <j1 rule="hyper" parents="157 5547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5620">
    <literal><![CDATA[
      L(T(x,y),z,u) / x = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4047(a,1),5547(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4047 5547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5621">
    <literal><![CDATA[
      (x * x) * ((x \ L(x,y,z)) * u) = (x * L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,5602,a(flip),b,127,a),flip(a)].">
      <j1 rule="hyper" parents="144 5602 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5622">
    <literal><![CDATA[
      L(x,y,R(z \ L(z,u,w),v5,v6)) = L(x,y,R(z * L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(5602(a,1),2208(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5602 2208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5623">
    <literal><![CDATA[
      (x * y) * L(z * ((y \ 1) / z),y,x) = (x * y) * (z * (((x * y) \ x) / z))
    ]]></literal>
    <justification jstring="[para(5618(a,2),5507(a,1,2))].">
      <j1 rule="para" parents="5618 5507"/>
    </justification>
  </clause>

  <clause id="5624">
    <literal><![CDATA[
      T(x,x \ L(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,301,a,b,5620,a)].">
      <j1 rule="hyper" parents="37 301 5620"/>
    </justification>
  </clause>

  <clause id="5625">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,x,y) \ 1) = ((1 / y) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,5615,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 5615 22"/>
    </justification>
  </clause>

  <clause id="5626">
    <literal><![CDATA[
      L(L(x * L(x \ 1,y,z),u,w),x,x) = L(x * L(x \ 1,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(5574(a,1),1143(a,1,1,1))].">
      <j1 rule="para" parents="5574 1143"/>
    </justification>
  </clause>

  <clause id="5627">
    <literal><![CDATA[
      x \ L((x \ 1) \ 1,y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1522,a,5582,a)].">
      <j1 rule="hyper" parents="1522 5582"/>
    </justification>
  </clause>

  <clause id="5628">
    <literal><![CDATA[
      (x / L(y,z,u)) * ((1 / y) \ y) = x / (y \ (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(5603(a,1),1591(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5603 1591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5629">
    <literal><![CDATA[
      L(x,y,z) \ (x * ((x \ 1) \ u)) = (x \ (x \ L(x,y,z))) \ u
    ]]></literal>
    <justification jstring="[para(5603(a,1),1660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5603 1660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5630">
    <literal><![CDATA[
      x \ L(T(x,x \ 1),y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(116(a,2),5627(a,1,2,1))].">
      <j1 rule="para" parents="116 5627"/>
    </justification>
  </clause>

  <clause id="5631">
    <literal><![CDATA[
      x * L(x \ ((x \ 1) \ y),z,u) = (x \ 1) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),5546(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 5546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5632">
    <literal><![CDATA[
      L(x * L(x \ y,z,u),x,x) = x * L((x \ 1) * y,z,u)
    ]]></literal>
    <justification jstring="[para(5546(a,1),1137(a,1,1))].">
      <j1 rule="para" parents="5546 1137"/>
    </justification>
  </clause>

  <clause id="5633">
    <literal><![CDATA[
      T(a(x,y,z),L(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(959,a,5565,a),flip(a)].">
      <j1 rule="hyper" parents="959 5565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5634">
    <literal><![CDATA[
      x \ ((x \ L(x,y,z)) * T(x,u)) = T(x,u) * (x \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(139,a,5583,a(flip),b,2399,a)].">
      <j1 rule="hyper" parents="139 5583 2399"/>
    </justification>
  </clause>

  <clause id="5635">
    <literal><![CDATA[
      (x * L(x,y,z)) * ((x \ L(x,y,z)) \ u) = (x * x) * u
    ]]></literal>
    <justification jstring="[hyper(397,a,5621,a),flip(a)].">
      <j1 rule="hyper" parents="397 5621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5636">
    <literal><![CDATA[
      L(x \ ((x \ 1) \ y),z,u) = x \ ((x \ 1) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(149,a,5631,a),flip(a)].">
      <j1 rule="hyper" parents="149 5631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5638">
    <literal><![CDATA[
      x * ((y \ z) * ((z \ T(y,y \ z)) * z)) = (x * K(z \ y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,4216,a(flip),b,5549,a),flip(a)].">
      <j1 rule="hyper" parents="64 4216 5549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5639">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z))
    ]]></literal>
    <justification jstring="[para(346(a,1),5549(a,1,2,1,2))].">
      <j1 rule="para" parents="346 5549"/>
    </justification>
  </clause>

  <clause id="5640">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,5553,a(flip),b,293,a),flip(a)].">
      <j1 rule="hyper" parents="139 5553 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5641">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,x,y) \ 1) = a(y,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1393,a(flip),b,5625,a),flip(a)].">
      <j1 rule="hyper" parents="373 1393 5625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5642">
    <literal><![CDATA[
      L(x \ y,x,y) \ (x \ y) = a(y,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1846,a(flip),b,5641,a)].">
      <j1 rule="hyper" parents="64 1846 5641"/>
    </justification>
  </clause>

  <clause id="5643">
    <literal><![CDATA[
      L(a(x,y,y \ x),L(y \ x,y,x),y) = (y * L(y \ x,y,x)) \ x
    ]]></literal>
    <justification jstring="[para(5642(a,1),346(a,1,1))].">
      <j1 rule="para" parents="5642 346"/>
    </justification>
  </clause>

  <clause id="5644">
    <literal><![CDATA[
      x * L((x \ 1) * (x * y),z,u) = L(x * L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),5632(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 5632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5645">
    <literal><![CDATA[
      L((x \ 1) * (x * y),z,u) = (x \ 1) * (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,1139,a,b,5644,a),flip(a)].">
      <j1 rule="hyper" parents="35 1139 5644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5646">
    <literal><![CDATA[
      L(x \ 1,x,x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,1808,a(flip),b,5580,a),flip(a)].">
      <j1 rule="hyper" parents="373 1808 5580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5648">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ 1) / (x \ 1) = ((x \ L(x,y,z)) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(225,a,5646,a(flip),b,1222,a(flip))].">
      <j1 rule="hyper" parents="225 5646 1222"/>
    </justification>
  </clause>

  <clause id="5649">
    <literal><![CDATA[
      (x * L(x,y,z)) * (x \ L(x,u,w)) = L(x,y,z) * L(x,u,w)
    ]]></literal>
    <justification jstring="[para(275(a,1),5614(a,1,1))].">
      <j1 rule="para" parents="275 5614"/>
    </justification>
  </clause>

  <clause id="5650">
    <literal><![CDATA[
      (L(x,y,z) \ x) / (x \ 1) = 1 / (x \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,5596,a(flip),b,5628,a)].">
      <j1 rule="hyper" parents="64 5596 5628"/>
    </justification>
  </clause>

  <clause id="5651">
    <literal><![CDATA[
      x * (L(x,y,z) \ ((x \ 1) \ u)) = (x \ (x \ L(x,y,z))) \ u
    ]]></literal>
    <justification jstring="[hyper(2342,a,5629,a)].">
      <j1 rule="hyper" parents="2342 5629"/>
    </justification>
  </clause>

  <clause id="5652">
    <literal><![CDATA[
      ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5504,a(flip),b,5640,a)].">
      <j1 rule="hyper" parents="64 5504 5640"/>
    </justification>
  </clause>

  <clause id="5653">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x = (y \ (z * x)) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,5640,a(flip),b,5504,a(flip))].">
      <j1 rule="hyper" parents="144 5640 5504"/>
    </justification>
  </clause>

  <clause id="5654">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (L(x,y,z) * L(x,u,w)) = x \ L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(149,a,5649,a)].">
      <j1 rule="hyper" parents="149 5649"/>
    </justification>
  </clause>

  <clause id="5655">
    <literal><![CDATA[
      L(x,y,z) \ (T(x * x,x) * u) = (x \ (x \ L(x,y,z))) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,2345,a,b,5651,a)].">
      <j1 rule="hyper" parents="64 2345 5651"/>
    </justification>
  </clause>

  <clause id="5656">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,L(x,u,w)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,643,a(flip),b,5654,a)].">
      <j1 rule="hyper" parents="64 643 5654"/>
    </justification>
  </clause>

  <clause id="5657">
    <literal><![CDATA[
      ((1 / L(x,y,z)) * x) \ 1 = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,917,a(flip),b,5656,a)].">
      <j1 rule="hyper" parents="64 917 5656"/>
    </justification>
  </clause>

  <clause id="5658">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ 1 = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5556(a,1),5657(a,1,1))].">
      <j1 rule="para" parents="5556 5657"/>
    </justification>
  </clause>

  <clause id="5659">
    <literal><![CDATA[
      1 / (x \ L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(226,a,5658,a)].">
      <j1 rule="hyper" parents="226 5658"/>
    </justification>
  </clause>

  <clause id="5660">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(225,a,5574,a(flip),b,5658,a)].">
      <j1 rule="hyper" parents="225 5574 5658"/>
    </justification>
  </clause>

  <clause id="5661">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(225,a,1309,a(flip),b,5658,a)].">
      <j1 rule="hyper" parents="225 1309 5658"/>
    </justification>
  </clause>

  <clause id="5662">
    <literal><![CDATA[
      x * ((L(x,y,z) \ x) \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5658,a,b,xx)].">
      <j1 rule="hyper" parents="145 5658"/>
    </justification>
  </clause>

  <clause id="5663">
    <literal><![CDATA[
      (((1 / x) * y) \ (x \ y)) \ 1 = (x \ y) \ L(x \ y,x,x)
    ]]></literal>
    <justification jstring="[para(569(a,1),5658(a,1,1,1))].">
      <j1 rule="para" parents="569 5658"/>
    </justification>
  </clause>

  <clause id="5664">
    <literal><![CDATA[
      ((x \ 1) \ y) \ L((x \ 1) \ y,x,x) = ((x * y) \ ((x \ 1) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(1137(a,1),5658(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1137 5658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5665">
    <literal><![CDATA[
      a(x,x,y) \ 1 = y \ L(y,x,x)
    ]]></literal>
    <justification jstring="[para(1243(a,1),5658(a,1,1))].">
      <j1 rule="para" parents="1243 5658"/>
    </justification>
  </clause>

  <clause id="5666">
    <literal><![CDATA[
      a(x,x,y \ 1) \ 1 = y * L(y \ 1,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5574,a(flip),b,5665,a),flip(a)].">
      <j1 rule="hyper" parents="373 5574 5665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5667">
    <literal><![CDATA[
      x * (a(y,y,z) \ 1) = x * (z \ L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,5665,a,b,9,a)].">
      <j1 rule="hyper" parents="145 5665 9"/>
    </justification>
  </clause>

  <clause id="5668">
    <literal><![CDATA[
      x * (a(y,y,x) \ 1) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,5665,a,b,xx)].">
      <j1 rule="hyper" parents="145 5665"/>
    </justification>
  </clause>

  <clause id="5669">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * y = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,5665,a,b,5572,a)].">
      <j1 rule="hyper" parents="144 5665 5572"/>
    </justification>
  </clause>

  <clause id="5670">
    <literal><![CDATA[
      (a(x,x,y) \ 1) \ z = (y \ L(y,x,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,5665,a)].">
      <j1 rule="hyper" parents="62 5665"/>
    </justification>
  </clause>

  <clause id="5671">
    <literal><![CDATA[
      (x \ L(x,y,y)) * ((a(y,y,x) \ 1) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(144,a,5665,a(flip),b,79,a)].">
      <j1 rule="hyper" parents="144 5665 79"/>
    </justification>
  </clause>

  <clause id="5672">
    <literal><![CDATA[
      (x \ L(x,y,y)) \ (a(y,y,x) * z) = ((a(y,y,x) \ 1) \ a(y,y,x)) * z
    ]]></literal>
    <justification jstring="[para(5665(a,1),1115(a,1,1))].">
      <j1 rule="para" parents="5665 1115"/>
    </justification>
  </clause>

  <clause id="5673">
    <literal><![CDATA[
      L(x,y,(z \ L(z,u,u)) \ w) = L(x,y,a(u,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(5665(a,1),2234(a,1,3,1))].">
      <j1 rule="para" parents="5665 2234"/>
    </justification>
  </clause>

  <clause id="5674">
    <literal><![CDATA[
      a((x \ L(x,y,y)) * z,u,w) = a(a(y,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(5665(a,1),2662(a,1,1,1))].">
      <j1 rule="para" parents="5665 2662"/>
    </justification>
  </clause>

  <clause id="5675">
    <literal><![CDATA[
      L(x,a(y,y,x) \ 1,a(y,y,x)) = 1 \ (a(y,y,x) * L(x,y,y))
    ]]></literal>
    <justification jstring="[para(5669(a,1),101(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5669 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5676">
    <literal><![CDATA[
      L(x,y,y) * L(z,x,a(y,y,x)) = (a(y,y,x) \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(5669(a,1),1630(a,1,1))].">
      <j1 rule="para" parents="5669 1630"/>
    </justification>
  </clause>

  <clause id="5677">
    <literal><![CDATA[
      (a(x,x,y) * a(x,x,y)) * L(y,x,x) = (1 / (1 / a(x,x,y))) * y
    ]]></literal>
    <justification jstring="[para(5669(a,1),2020(a,1,2))].">
      <j1 rule="para" parents="5669 2020"/>
    </justification>
  </clause>

  <clause id="5678">
    <literal><![CDATA[
      a(a(x,x,y) * y,z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(5669(a,1),2662(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5669 2662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5679">
    <literal><![CDATA[
      a((a(x,x,y) * y) * z,u,w) = a(L(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(5669(a,1),2690(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5669 2690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5680">
    <literal><![CDATA[
      R(L(x,y,z) \ x,x \ L(x,y,z),u) = u / ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(5659(a,1),244(a,1,1))].">
      <j1 rule="para" parents="5659 244"/>
    </justification>
  </clause>

  <clause id="5681">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L((x \ 1) \ u,x \ 1,L(x,y,z)) = ((1 / (L(x,y,z) * (x \ 1))) / (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(5659(a,1),2632(a,1,1))].">
      <j1 rule="para" parents="5659 2632"/>
    </justification>
  </clause>

  <clause id="5682">
    <literal><![CDATA[
      x * (y * L(y \ (x \ 1),z,z)) = a(z,z,(x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,1705,a(flip),b,5666,a)].">
      <j1 rule="hyper" parents="373 1705 5666"/>
    </justification>
  </clause>

  <clause id="5683">
    <literal><![CDATA[
      (a(x,x,y \ 1) \ 1) * z = (y * L(y \ 1,x,x)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,5666,a,b,11,a)].">
      <j1 rule="hyper" parents="144 5666 11"/>
    </justification>
  </clause>

  <clause id="5684">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5660,a(flip),b,5661,a),flip(a)].">
      <j1 rule="hyper" parents="64 5660 5661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5685">
    <literal><![CDATA[
      L(x,y,a(z,z,u) \ L(u,z,z)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(5573(a,1),5673(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5573 5673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5686">
    <literal><![CDATA[
      a((x * L(x,y,y)) * z,u,w) = a(a(y,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,5610,a(flip),b,5674,a)].">
      <j1 rule="hyper" parents="64 5610 5674"/>
    </justification>
  </clause>

  <clause id="5687">
    <literal><![CDATA[
      (a(x,x,(y \ z) \ 1) \ 1) * u = (y \ (z * L(z \ y,x,x))) * u
    ]]></literal>
    <justification jstring="[para(2469(a,1),5683(a,2,1))].">
      <j1 rule="para" parents="2469 5683"/>
    </justification>
  </clause>

  <clause id="5688">
    <literal><![CDATA[
      (((1 / x) * y) \ (x \ y)) \ 1 = (x \ y) \ ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(569(a,1),5663(a,2,2))].">
      <j1 rule="para" parents="569 5663"/>
    </justification>
  </clause>

  <clause id="5689">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) \ ((1 / x) * ((1 / x) \ y)) = (y \ (x \ ((1 / x) \ y))) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),5688(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5690">
    <literal><![CDATA[
      L(x,a(y,y,x) \ 1,a(y,y,x)) = 1 \ x
    ]]></literal>
    <justification jstring="[para(5563(a,1),5675(a,2,2))].">
      <j1 rule="para" parents="5563 5675"/>
    </justification>
  </clause>

  <clause id="5691">
    <literal><![CDATA[
      L(x,a(y,y,x) \ 1,a(y,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,66,a(flip),b,5690,a),flip(a)].">
      <j1 rule="hyper" parents="373 66 5690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5692">
    <literal><![CDATA[
      L(x,a(y,y,x),a(y,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,1145,a(flip),b,5691,a)].">
      <j1 rule="hyper" parents="64 1145 5691"/>
    </justification>
  </clause>

  <clause id="5693">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * L(y,z,u) = a(x,x,y) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(5691(a,1),694(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5691 694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5694">
    <literal><![CDATA[
      L(L(x,y,z),a(u,u,x),a(u,u,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5692(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5692 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5695">
    <literal><![CDATA[
      L(x \ y,x,x * L(x,z,u)) = L(x,z,u) \ ((x \ L(x,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5608,a(flip),b,5581,a)].">
      <j1 rule="hyper" parents="64 5608 5581"/>
    </justification>
  </clause>

  <clause id="5696">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(u,L(x,y,z),x) = (1 / L(x,y,z)) * (x * u)
    ]]></literal>
    <justification jstring="[para(2482(a,2),5597(a,1,2))].">
      <j1 rule="para" parents="2482 5597"/>
    </justification>
  </clause>

  <clause id="5697">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(u,x,L(x,y,z)) = (1 / x) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(2482(a,1),5606(a,1,2))].">
      <j1 rule="para" parents="2482 5606"/>
    </justification>
  </clause>

  <clause id="5698">
    <literal><![CDATA[
      (x * K(y \ z,y)) * y = x * (y * K(y \ z,y))
    ]]></literal>
    <justification jstring="[para(4018(a,1),5638(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4018 5638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5699">
    <literal><![CDATA[
      x * (y * K(y \ (y * z),y)) = (x * K(z,y)) * y
    ]]></literal>
    <justification jstring="[para(9(a,1),5698(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 5698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5700">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),5699(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 5699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5701">
    <literal><![CDATA[
      (x * y) / (y * K(z,y)) = x / K(z,y)
    ]]></literal>
    <justification jstring="[hyper(784,a,5700,a)].">
      <j1 rule="hyper" parents="784 5700"/>
    </justification>
  </clause>

  <clause id="5702">
    <literal><![CDATA[
      x \ (y * (x * K(z,x))) = T(y * K(z,x),x)
    ]]></literal>
    <justification jstring="[hyper(493,a,xx,b,5700,a),flip(a)].">
      <j1 rule="hyper" parents="493 5700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5703">
    <literal><![CDATA[
      (x * (y * K(z,y))) / y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(154,a,5700,a)].">
      <j1 rule="hyper" parents="154 5700"/>
    </justification>
  </clause>

  <clause id="5704">
    <literal><![CDATA[
      (1 / x) * K(y,x) = K(y,x) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,4025,a(flip),b,5700,a),flip(a)].">
      <j1 rule="hyper" parents="142 4025 5700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5705">
    <literal><![CDATA[
      a(x,K(y,z),z) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,5700,a(flip),b,4019,a),flip(a)].">
      <j1 rule="hyper" parents="138 5700 4019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5707">
    <literal><![CDATA[
      L(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,5705,a)].">
      <j1 rule="hyper" parents="53 5705"/>
    </justification>
  </clause>

  <clause id="5708">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,u) = x * (K(y,z) * T(z,u))
    ]]></literal>
    <justification jstring="[para(5707(a,1),517(a,1,2,1))].">
      <j1 rule="para" parents="5707 517"/>
    </justification>
  </clause>

  <clause id="5709">
    <literal><![CDATA[
      (x * K(y,z)) * L(z,u,w) = x * (K(y,z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(5707(a,1),513(a,1,2,1))].">
      <j1 rule="para" parents="5707 513"/>
    </justification>
  </clause>

  <clause id="5710">
    <literal><![CDATA[
      (x * K(y,z)) * R(z,u,w) = x * (K(y,z) * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(5707(a,1),514(a,1,2,1))].">
      <j1 rule="para" parents="5707 514"/>
    </justification>
  </clause>

  <clause id="5711">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(664,a,5708,a)].">
      <j1 rule="hyper" parents="664 5708"/>
    </justification>
  </clause>

  <clause id="5712">
    <literal><![CDATA[
      R(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[para(114(a,1),5711(a,1,3))].">
      <j1 rule="para" parents="114 5711"/>
    </justification>
  </clause>

  <clause id="5713">
    <literal><![CDATA[
      R(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5712(a,1),52(a,2))].">
      <j1 rule="para" parents="5712 52"/>
    </justification>
  </clause>

  <clause id="5714">
    <literal><![CDATA[
      (x * y) \ ((y * x) * x) = K(y,x) * x
    ]]></literal>
    <justification jstring="[para(5712(a,1),689(a,1,1))].">
      <j1 rule="para" parents="5712 689"/>
    </justification>
  </clause>

  <clause id="5718">
    <literal><![CDATA[
      (x * y) / x = K(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,4855,a(flip),b,5714,a)].">
      <j1 rule="hyper" parents="64 4855 5714"/>
    </justification>
  </clause>

  <clause id="5719">
    <literal><![CDATA[
      K(x,y) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(4034,a,5718,a),flip(a)].">
      <j1 rule="hyper" parents="4034 5718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5720">
    <literal><![CDATA[
      K(x,x \ y) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(393,a,5718,a),flip(a)].">
      <j1 rule="hyper" parents="393 5718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5721">
    <literal><![CDATA[
      (x * y) / x = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,3994,a(flip),b,5718,a),flip(a)].">
      <j1 rule="hyper" parents="373 3994 5718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5722">
    <literal><![CDATA[
      (x * K(y,x)) * y = y * x
    ]]></literal>
    <justification jstring="[hyper(144,a,3994,a(flip),b,5718,a)].">
      <j1 rule="hyper" parents="144 3994 5718"/>
    </justification>
  </clause>

  <clause id="5723">
    <literal><![CDATA[
      x / (x / y) = K(y \ x,y) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,4707,a(flip),b,5718,a)].">
      <j1 rule="hyper" parents="64 4707 5718"/>
    </justification>
  </clause>

  <clause id="5724">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(y,(x * z) / x)
    ]]></literal>
    <justification jstring="[hyper(142,a,1492,a,b,5718,a(flip))].">
      <j1 rule="hyper" parents="142 1492 5718"/>
    </justification>
  </clause>

  <clause id="5725">
    <literal><![CDATA[
      (x / y) / (y \ x) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(142,a,171,a(flip),b,5718,a(flip))].">
      <j1 rule="hyper" parents="142 171 5718"/>
    </justification>
  </clause>

  <clause id="5726">
    <literal><![CDATA[
      K(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,4366,a,b,5718,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 4366 5718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5727">
    <literal><![CDATA[
      T(K(x,y) * y,x) = y
    ]]></literal>
    <justification jstring="[para(5718(a,1),255(a,1,1))].">
      <j1 rule="para" parents="5718 255"/>
    </justification>
  </clause>

  <clause id="5729">
    <literal><![CDATA[
      K(x,y) * (y * z) = ((x * y) / x) * z
    ]]></literal>
    <justification jstring="[para(5718(a,2),4503(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5718 4503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5730">
    <literal><![CDATA[
      T(T(x,y),x \ 1) = (x \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(493,a,5726,a,b,1487,a)].">
      <j1 rule="hyper" parents="493 5726 1487"/>
    </justification>
  </clause>

  <clause id="5731">
    <literal><![CDATA[
      K(x,y) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,4615,a,b,5726,a),flip(a)].">
      <j1 rule="hyper" parents="373 4615 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5732">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,4517,a,b,5726,a)].">
      <j1 rule="hyper" parents="373 4517 5726"/>
    </justification>
  </clause>

  <clause id="5733">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4485,a,b,5726,a)].">
      <j1 rule="hyper" parents="373 4485 5726"/>
    </justification>
  </clause>

  <clause id="5734">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,4423,a,b,5726,a)].">
      <j1 rule="hyper" parents="373 4423 5726"/>
    </justification>
  </clause>

  <clause id="5736">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,4374,a,b,5726,a)].">
      <j1 rule="hyper" parents="373 4374 5726"/>
    </justification>
  </clause>

  <clause id="5737">
    <literal><![CDATA[
      K(x,T(y,x)) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,4368,a,b,5726,a),flip(a)].">
      <j1 rule="hyper" parents="373 4368 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5738">
    <literal><![CDATA[
      K(x,y) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4051,a,b,5726,a),flip(a)].">
      <j1 rule="hyper" parents="373 4051 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5739">
    <literal><![CDATA[
      K(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,4048,a,b,5726,a),flip(a)].">
      <j1 rule="hyper" parents="373 4048 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5740">
    <literal><![CDATA[
      K(x,y) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,1487,a,b,5726,a),flip(a)].">
      <j1 rule="hyper" parents="373 1487 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5741">
    <literal><![CDATA[
      K(x,y) = (x \ 1) * T((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1484,a,b,5726,a),flip(a)].">
      <j1 rule="hyper" parents="373 1484 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5742">
    <literal><![CDATA[
      T(x,y) \ T(T(x,z),y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,176,a,b,5726,a)].">
      <j1 rule="hyper" parents="373 176 5726"/>
    </justification>
  </clause>

  <clause id="5743">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4052,a(flip),b,5726,a)].">
      <j1 rule="hyper" parents="373 4052 5726"/>
    </justification>
  </clause>

  <clause id="5744">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1007,a(flip),b,5726,a)].">
      <j1 rule="hyper" parents="373 1007 5726"/>
    </justification>
  </clause>

  <clause id="5745">
    <literal><![CDATA[
      x \ ((x \ y) \ y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,361,a(flip),b,5726,a)].">
      <j1 rule="hyper" parents="373 361 5726"/>
    </justification>
  </clause>

  <clause id="5746">
    <literal><![CDATA[
      T(x,y) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(225,a,5726,a,b,4615,a),flip(a)].">
      <j1 rule="hyper" parents="225 5726 4615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5747">
    <literal><![CDATA[
      T(x,y) / K(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(225,a,5726,a,b,xx)].">
      <j1 rule="hyper" parents="225 5726"/>
    </justification>
  </clause>

  <clause id="5748">
    <literal><![CDATA[
      T(x,y) * K(y,x) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,5726,a,b,4615,a)].">
      <j1 rule="hyper" parents="145 5726 4615"/>
    </justification>
  </clause>

  <clause id="5749">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,5726,a,b,4368,a)].">
      <j1 rule="hyper" parents="145 5726 4368"/>
    </justification>
  </clause>

  <clause id="5750">
    <literal><![CDATA[
      (x * x) \ T(x,y) = (1 / x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,5726,a,b,540,a),flip(a)].">
      <j1 rule="hyper" parents="145 5726 540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5751">
    <literal><![CDATA[
      x / (x / y) = y * K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,5726,a,b,4369,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 5726 4369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5752">
    <literal><![CDATA[
      (x \ y) \ y = x * K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,5726,a,b,361,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 5726 361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5753">
    <literal><![CDATA[
      T(x,y) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,5726,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="145 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5754">
    <literal><![CDATA[
      K(x / y,z) * x = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,5726,a,b,4517,a)].">
      <j1 rule="hyper" parents="144 5726 4517"/>
    </justification>
  </clause>

  <clause id="5755">
    <literal><![CDATA[
      K(x,y) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,5726,a,b,4485,a)].">
      <j1 rule="hyper" parents="144 5726 4485"/>
    </justification>
  </clause>

  <clause id="5756">
    <literal><![CDATA[
      T(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,5726,a,b,4048,a),flip(a)].">
      <j1 rule="hyper" parents="144 5726 4048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5757">
    <literal><![CDATA[
      K(x,y) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(142,a,5726,a,b,4051,a)].">
      <j1 rule="hyper" parents="142 5726 4051"/>
    </justification>
  </clause>

  <clause id="5759">
    <literal><![CDATA[
      ((x * y) / x) \ K(x,y) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,5726,a,b,4373,a)].">
      <j1 rule="hyper" parents="139 5726 4373"/>
    </justification>
  </clause>

  <clause id="5760">
    <literal><![CDATA[
      T(x,y) = (1 / x) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,5726,a,b,4051,a),flip(a)].">
      <j1 rule="hyper" parents="139 5726 4051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5761">
    <literal><![CDATA[
      T(x,y) \ K(x,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,5726,a,b,1487,a)].">
      <j1 rule="hyper" parents="139 5726 1487"/>
    </justification>
  </clause>

  <clause id="5762">
    <literal><![CDATA[
      x \ K(x \ 1,y) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,5726,a,b,4052,a(flip))].">
      <j1 rule="hyper" parents="139 5726 4052"/>
    </justification>
  </clause>

  <clause id="5763">
    <literal><![CDATA[
      K(x \ (x * y),z) = y \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1571,a,b,5726,a)].">
      <j1 rule="hyper" parents="64 1571 5726"/>
    </justification>
  </clause>

  <clause id="5764">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,u),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(25(a,2),5726(a,2,2)),flip(a)].">
      <j1 rule="para" parents="25 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5765">
    <literal><![CDATA[
      R(x,y,z) \ R(T(x,u),y,z) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(27(a,2),5726(a,2,2)),flip(a)].">
      <j1 rule="para" parents="27 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5767">
    <literal><![CDATA[
      x * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5726(a,2),290(a,1,2))].">
      <j1 rule="para" parents="5726 290"/>
    </justification>
  </clause>

  <clause id="5768">
    <literal><![CDATA[
      L(x \ K(y,z),x,y) = (y * x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5726(a,2),346(a,1,1,2))].">
      <j1 rule="para" parents="5726 346"/>
    </justification>
  </clause>

  <clause id="5770">
    <literal><![CDATA[
      x * R(x \ K(x,y),z,u) = x \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5726(a,2),2133(a,1,2,1,2))].">
      <j1 rule="para" parents="5726 2133"/>
    </justification>
  </clause>

  <clause id="5771">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = x \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(2781(a,1),5726(a,2,2))].">
      <j1 rule="para" parents="2781 5726"/>
    </justification>
  </clause>

  <clause id="5772">
    <literal><![CDATA[
      (x \ 1) / K(x,y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(5726(a,2),3221(a,1,2))].">
      <j1 rule="para" parents="5726 3221"/>
    </justification>
  </clause>

  <clause id="5773">
    <literal><![CDATA[
      x \ T(x,y \ 1) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(3870(a,1),5726(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3870 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5774">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(5726(a,2),4365(a,1,2))].">
      <j1 rule="para" parents="5726 4365"/>
    </justification>
  </clause>

  <clause id="5776">
    <literal><![CDATA[
      x * (K(x,y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(5726(a,2),4436(a,1,2,1))].">
      <j1 rule="para" parents="5726 4436"/>
    </justification>
  </clause>

  <clause id="5777">
    <literal><![CDATA[
      x \ T(x,y \ x) = K(x,x / y)
    ]]></literal>
    <justification jstring="[para(4461(a,1),5726(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4461 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5778">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(5726(a,2),4438(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5726 4438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5779">
    <literal><![CDATA[
      K(x,y) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[para(5726(a,2),4486(a,1,1))].">
      <j1 rule="para" parents="5726 4486"/>
    </justification>
  </clause>

  <clause id="5780">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(5726(a,2),4487(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5726 4487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5781">
    <literal><![CDATA[
      K(x,x \ y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5726(a,2),4509(a,1,1))].">
      <j1 rule="para" parents="5726 4509"/>
    </justification>
  </clause>

  <clause id="5782">
    <literal><![CDATA[
      x \ T(x,x * y) = K(x,y * x)
    ]]></literal>
    <justification jstring="[para(4683(a,1),5726(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4683 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5783">
    <literal><![CDATA[
      T(x,y) \ 1 = x \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5726(a,2),4620(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5726 4620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5784">
    <literal><![CDATA[
      K(x,x \ y) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(5726(a,2),5031(a,1,1))].">
      <j1 rule="para" parents="5726 5031"/>
    </justification>
  </clause>

  <clause id="5785">
    <literal><![CDATA[
      T(x * K(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(3994(a,1),5727(a,1,1))].">
      <j1 rule="para" parents="3994 5727"/>
    </justification>
  </clause>

  <clause id="5786">
    <literal><![CDATA[
      K(x,y) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,4547,a,b,5731,a),flip(a)].">
      <j1 rule="hyper" parents="373 4547 5731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5787">
    <literal><![CDATA[
      K(x,y) = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,3981,a,b,5731,a),flip(a)].">
      <j1 rule="hyper" parents="373 3981 5731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5788">
    <literal><![CDATA[
      K(x,y) = (1 / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,3977,a,b,5731,a),flip(a)].">
      <j1 rule="hyper" parents="373 3977 5731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5789">
    <literal><![CDATA[
      K(x,y) = y * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,2409,a,b,5731,a),flip(a)].">
      <j1 rule="hyper" parents="373 2409 5731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5790">
    <literal><![CDATA[
      x \ (y / (y / x)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,4574,a(flip),b,5731,a)].">
      <j1 rule="hyper" parents="373 4574 5731"/>
    </justification>
  </clause>

  <clause id="5792">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(145,a,5731,a,b,3989,a)].">
      <j1 rule="hyper" parents="145 5731 3989"/>
    </justification>
  </clause>

  <clause id="5793">
    <literal><![CDATA[
      x / (x / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,5731,a,b,4574,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 5731 4574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5795">
    <literal><![CDATA[
      ((x \ y) \ y) * K(x \ y,x) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,5731,a,b,362,a(flip))].">
      <j1 rule="hyper" parents="145 5731 362"/>
    </justification>
  </clause>

  <clause id="5796">
    <literal><![CDATA[
      K(x,y) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[hyper(144,a,5731,a,b,4547,a)].">
      <j1 rule="hyper" parents="144 5731 4547"/>
    </justification>
  </clause>

  <clause id="5797">
    <literal><![CDATA[
      K(x,y) * T(y,x) = y
    ]]></literal>
    <justification jstring="[hyper(144,a,5731,a,b,3981,a)].">
      <j1 rule="hyper" parents="144 5731 3981"/>
    </justification>
  </clause>

  <clause id="5799">
    <literal><![CDATA[
      K(x,y) / y = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,5731,a,b,3977,a)].">
      <j1 rule="hyper" parents="142 5731 3977"/>
    </justification>
  </clause>

  <clause id="5800">
    <literal><![CDATA[
      T(T(x,y),z) \ T(x,z) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(23(a,1),5731(a,2,1)),flip(a)].">
      <j1 rule="para" parents="23 5731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5801">
    <literal><![CDATA[
      L(T(x,y),z,u) \ L(x,z,u) = K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),5731(a,2,1)),flip(a)].">
      <j1 rule="para" parents="25 5731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5802">
    <literal><![CDATA[
      R(T(x,y),z,u) \ R(x,z,u) = K(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(27(a,2),5731(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27 5731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5803">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = K(y,x) / x
    ]]></literal>
    <justification jstring="[para(5731(a,2),3616(a,2,1))].">
      <j1 rule="para" parents="5731 3616"/>
    </justification>
  </clause>

  <clause id="5804">
    <literal><![CDATA[
      T(x,y) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[para(5731(a,2),3985(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5731 3985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5805">
    <literal><![CDATA[
      T(x,y) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(5731(a,2),3979(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5731 3979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5807">
    <literal><![CDATA[
      K(x,y) * ((y * x) / y) = x
    ]]></literal>
    <justification jstring="[para(5731(a,2),4572(a,1,1))].">
      <j1 rule="para" parents="5731 4572"/>
    </justification>
  </clause>

  <clause id="5809">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(5731(a,2),4950(a,2,1))].">
      <j1 rule="para" parents="5731 4950"/>
    </justification>
  </clause>

  <clause id="5810">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(5731(a,2),5007(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5731 5007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5811">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(5731(a,2),5008(a,1,1))].">
      <j1 rule="para" parents="5731 5008"/>
    </justification>
  </clause>

  <clause id="5812">
    <literal><![CDATA[
      ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x
    ]]></literal>
    <justification jstring="[para(5731(a,2),5510(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5731 5510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5814">
    <literal><![CDATA[
      K(x,y) \ T(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(143,a,5739,a,b,171,a)].">
      <j1 rule="hyper" parents="143 5739 171"/>
    </justification>
  </clause>

  <clause id="5815">
    <literal><![CDATA[
      R(T(x,y),z,u) / R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(27(a,2),5739(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27 5739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5816">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5739(a,2),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5739 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5820">
    <literal><![CDATA[
      T(x \ T(y,x),z) * K(z,T(x,y) \ y) = T(x,y) \ y
    ]]></literal>
    <justification jstring="[hyper(144,a,4799,a(flip),b,5746,a(flip))].">
      <j1 rule="hyper" parents="144 4799 5746"/>
    </justification>
  </clause>

  <clause id="5821">
    <literal><![CDATA[
      ((x \ y) \ y) * K(y / x,x) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,4666,a(flip),b,5746,a(flip))].">
      <j1 rule="hyper" parents="144 4666 5746"/>
    </justification>
  </clause>

  <clause id="5822">
    <literal><![CDATA[
      (x \ y) * K(x,y / x) = y / x
    ]]></literal>
    <justification jstring="[hyper(144,a,117,a(flip),b,5746,a(flip))].">
      <j1 rule="hyper" parents="144 117 5746"/>
    </justification>
  </clause>

  <clause id="5823">
    <literal><![CDATA[
      T(x,y) != x / z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5746(a,2),46(a,1))].">
      <j1 rule="para" parents="5746 46"/>
    </justification>
  </clause>

  <clause id="5824">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5746(a,2),305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5746 305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5825">
    <literal><![CDATA[
      x * (y * K(x,y)) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,5747,a(flip),b,5701,a)].">
      <j1 rule="hyper" parents="144 5747 5701"/>
    </justification>
  </clause>

  <clause id="5826">
    <literal><![CDATA[
      T(x,y) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5747(a,1),150(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5747 150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5827">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5747(a,1),305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5747 305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5828">
    <literal><![CDATA[
      R(x / y,y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) / (y * K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(5747(a,1),760(a,1,1,1))].">
      <j1 rule="para" parents="5747 760"/>
    </justification>
  </clause>

  <clause id="5829">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[para(5748(a,1),4443(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5748 4443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5833">
    <literal><![CDATA[
      x * K(x,y * (z \ 1)) = T(x,y * (1 / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5113,a,b,5753,a),flip(a)].">
      <j1 rule="hyper" parents="64 5113 5753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5834">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ 1) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4827,a,b,5753,a)].">
      <j1 rule="hyper" parents="64 4827 5753"/>
    </justification>
  </clause>

  <clause id="5836">
    <literal><![CDATA[
      (x \ y) \ y = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4666,a(flip),b,5753,a)].">
      <j1 rule="hyper" parents="64 4666 5753"/>
    </justification>
  </clause>

  <clause id="5838">
    <literal><![CDATA[
      (x * y) * z != x * T(y,u)
    ]]></literal>
    <literal><![CDATA[
      L(K(y,u),y,x) = z
    ]]></literal>
    <justification jstring="[para(5753(a,2),606(a,2,2))].">
      <j1 rule="para" parents="5753 606"/>
    </justification>
  </clause>

  <clause id="5839">
    <literal><![CDATA[
      (x * y) * K(y,z) != u * T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5753(a,2),664(a,2,2))].">
      <j1 rule="para" parents="5753 664"/>
    </justification>
  </clause>

  <clause id="5841">
    <literal><![CDATA[
      K(T(x,y),z) * T(x,y) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(481,a,5756,a),flip(a)].">
      <j1 rule="hyper" parents="481 5756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5842">
    <literal><![CDATA[
      (x \ y) \ y = K(x,x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(478,a,5756,a)].">
      <j1 rule="hyper" parents="478 5756"/>
    </justification>
  </clause>

  <clause id="5844">
    <literal><![CDATA[
      T(x,y) / (y \ x) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,5756,a,b,4530,a)].">
      <j1 rule="hyper" parents="142 5756 4530"/>
    </justification>
  </clause>

  <clause id="5845">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) * x = T(x,y) / R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(142,a,5756,a,b,2825,a),flip(a)].">
      <j1 rule="hyper" parents="142 5756 2825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5848">
    <literal><![CDATA[
      x * (K(y,x) * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(145,a,5756,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 5756 22"/>
    </justification>
  </clause>

  <clause id="5849">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5756(a,2),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5756 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5850">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      L(z \ x,z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(5756(a,2),764(a,1,2))].">
      <j1 rule="para" parents="5756 764"/>
    </justification>
  </clause>

  <clause id="5851">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5756(a,2),4071(a,1))].">
      <j1 rule="para" parents="5756 4071"/>
    </justification>
  </clause>

  <clause id="5852">
    <literal><![CDATA[
      T(x,y) * K(y * R(x,z,u),T(x,y)) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(2833,a,5785,a),flip(a)].">
      <j1 rule="hyper" parents="2833 5785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5853">
    <literal><![CDATA[
      T((x * y) / x,z) = T(y,z) * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(542,a,5785,a)].">
      <j1 rule="hyper" parents="542 5785"/>
    </justification>
  </clause>

  <clause id="5854">
    <literal><![CDATA[
      (T(x,y) * y) / T(x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,4625,a,b,5785,a)].">
      <j1 rule="hyper" parents="41 4625 5785"/>
    </justification>
  </clause>

  <clause id="5855">
    <literal><![CDATA[
      T(x,y) * K(y * L(x,z,u),T(x,y)) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,3188,a,b,5785,a),flip(a)].">
      <j1 rule="hyper" parents="41 3188 5785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5856">
    <literal><![CDATA[
      K(x,y * K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,5785,a(flip),b,5746,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="143 5785 5746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5857">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5785(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5785 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5858">
    <literal><![CDATA[
      T(R(x * K(y,x),z,u),y) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(5785(a,1),27(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5785 27"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5859">
    <literal><![CDATA[
      (x * K(y,x)) \ (y * x) = y
    ]]></literal>
    <justification jstring="[para(5785(a,1),257(a,1,2,2))].">
      <j1 rule="para" parents="5785 257"/>
    </justification>
  </clause>

  <clause id="5860">
    <literal><![CDATA[
      T(x * K(y,x),z) * y = y * T(x,z)
    ]]></literal>
    <justification jstring="[para(5785(a,1),265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5785 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5861">
    <literal><![CDATA[
      T(T(T(x * K(y,x),z),u),y) = T(T(x,z),u)
    ]]></literal>
    <justification jstring="[para(5785(a,1),120(a,2,1,1))].">
      <j1 rule="para" parents="5785 120"/>
    </justification>
  </clause>

  <clause id="5862">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * y = y * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5785(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5785 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5863">
    <literal><![CDATA[
      T((x * (y * K(z,y))) / x,z) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(5785(a,1),541(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5785 541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5864">
    <literal><![CDATA[
      R(T(x * K(y,x),z),u,w) * y = y * R(T(x,z),u,w)
    ]]></literal>
    <justification jstring="[para(5785(a,1),842(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5785 842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5865">
    <literal><![CDATA[
      L(T(x * K(y,x),y),z,u) / (x * K(y,x)) = (1 / (x * K(y,x))) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5785(a,1),3238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5785 3238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5866">
    <literal><![CDATA[
      T(x \ K(y,x \ 1),y) = x \ 1
    ]]></literal>
    <justification jstring="[para(4029(a,1),5785(a,1,1))].">
      <j1 rule="para" parents="4029 5785"/>
    </justification>
  </clause>

  <clause id="5867">
    <literal><![CDATA[
      T(x,y * K(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5785(a,1),4619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5785 4619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5868">
    <literal><![CDATA[
      T(x,L(y * K(x,y),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5785(a,1),4635(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5785 4635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5870">
    <literal><![CDATA[
      K(x,y) != y / z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(5787(a,2),46(a,1))].">
      <j1 rule="para" parents="5787 46"/>
    </justification>
  </clause>

  <clause id="5871">
    <literal><![CDATA[
      K(x,y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(5787(a,2),305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5787 305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5872">
    <literal><![CDATA[
      L(T(x,y),T(z,x),z / T(z,x)) * z = K(x,z) * (T(x,y) * T(z,x))
    ]]></literal>
    <justification jstring="[para(5787(a,2),4800(a,2,1))].">
      <j1 rule="para" parents="5787 4800"/>
    </justification>
  </clause>

  <clause id="5873">
    <literal><![CDATA[
      K(x,y / x) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(117(a,1),5797(a,1,2))].">
      <j1 rule="para" parents="117 5797"/>
    </justification>
  </clause>

  <clause id="5874">
    <literal><![CDATA[
      x / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5797(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5797 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5875">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,y) = x * z
    ]]></literal>
    <justification jstring="[para(5797(a,1),5708(a,2,2))].">
      <j1 rule="para" parents="5797 5708"/>
    </justification>
  </clause>

  <clause id="5876">
    <literal><![CDATA[
      K(x,y / x) \ (y / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(467,a,5804,a),flip(a)].">
      <j1 rule="hyper" parents="467 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5877">
    <literal><![CDATA[
      T(x,y) = 1 / (x \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,4975,a,b,5804,a),flip(a)].">
      <j1 rule="hyper" parents="373 4975 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5878">
    <literal><![CDATA[
      K(x \ y,x) * R(T(x,x \ y),z,u) = y \ ((R(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[para(5804(a,2),3505(a,1,2,1))].">
      <j1 rule="para" parents="5804 3505"/>
    </justification>
  </clause>

  <clause id="5879">
    <literal><![CDATA[
      (x \ y) \ (y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),5719(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 5719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5880">
    <literal><![CDATA[
      x * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(5719(a,2),290(a,1,2))].">
      <j1 rule="para" parents="5719 290"/>
    </justification>
  </clause>

  <clause id="5881">
    <literal><![CDATA[
      x * ((y * z) / y) = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(5719(a,2),168(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5719 168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5882">
    <literal><![CDATA[
      x * (y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((z * y) / z) = u
    ]]></literal>
    <justification jstring="[para(5719(a,2),397(a,1,2,2))].">
      <j1 rule="para" parents="5719 397"/>
    </justification>
  </clause>

  <clause id="5883">
    <literal><![CDATA[
      ((x * x) * y) \ (y * (x * x)) = K(y,(x * x) * y)
    ]]></literal>
    <justification jstring="[para(133(a,1),5719(a,2,2)),flip(a)].">
      <j1 rule="para" parents="133 5719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5884">
    <literal><![CDATA[
      T(x \ y,z) \ T(y / x,z) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(531(a,1),5719(a,2,2)),flip(a)].">
      <j1 rule="para" parents="531 5719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5885">
    <literal><![CDATA[
      (x * y) * K(T(y,x),x * y) = T(y,x * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4879,a,5721,a),flip(a)].">
      <j1 rule="hyper" parents="4879 5721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5887">
    <literal><![CDATA[
      (x \ K(y,x \ 1)) * y = y * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,4029,a(flip),b,5721,a)].">
      <j1 rule="hyper" parents="144 4029 5721"/>
    </justification>
  </clause>

  <clause id="5888">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,5721,a,b,2938,a)].">
      <j1 rule="hyper" parents="139 5721 2938"/>
    </justification>
  </clause>

  <clause id="5889">
    <literal><![CDATA[
      x \ ((y * z) / y) = x \ (z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,5721,a,b,10,a)].">
      <j1 rule="hyper" parents="139 5721 10"/>
    </justification>
  </clause>

  <clause id="5890">
    <literal><![CDATA[
      T((x * y) / x,K(y,z)) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4076,a,b,5721,a)].">
      <j1 rule="hyper" parents="64 4076 5721"/>
    </justification>
  </clause>

  <clause id="5892">
    <literal><![CDATA[
      T(x * K(y,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(5721(a,1),340(a,1,1))].">
      <j1 rule="para" parents="5721 340"/>
    </justification>
  </clause>

  <clause id="5893">
    <literal><![CDATA[
      T(x * K(y,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(5721(a,1),399(a,1,1))].">
      <j1 rule="para" parents="5721 399"/>
    </justification>
  </clause>

  <clause id="5894">
    <literal><![CDATA[
      (x * y) * K(1 / x,x * y) = L(y,x,x) / (1 / x)
    ]]></literal>
    <justification jstring="[para(559(a,1),5721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="559 5721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5895">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,(1 / x) \ y) = ((x * x) * y) / x
    ]]></literal>
    <justification jstring="[para(538(a,1),5721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="538 5721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5896">
    <literal><![CDATA[
      ((x * y) * z) / R(x,y,z) = (y * z) * K(R(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[para(111(a,1),5721(a,1,1))].">
      <j1 rule="para" parents="111 5721"/>
    </justification>
  </clause>

  <clause id="5897">
    <literal><![CDATA[
      R(x * K(y,x),y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(5721(a,1),112(a,1,1))].">
      <j1 rule="para" parents="5721 112"/>
    </justification>
  </clause>

  <clause id="5898">
    <literal><![CDATA[
      R(x / y,y,K(z,x)) \ ((z * x) / z) = y * K(z,x)
    ]]></literal>
    <justification jstring="[para(5721(a,2),650(a,1,2))].">
      <j1 rule="para" parents="5721 650"/>
    </justification>
  </clause>

  <clause id="5899">
    <literal><![CDATA[
      T(x * K(y,x),x * y) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(5721(a,1),770(a,1,1))].">
      <j1 rule="para" parents="5721 770"/>
    </justification>
  </clause>

  <clause id="5900">
    <literal><![CDATA[
      T(x * K(y,x),z) = (y * T(x,z)) / y
    ]]></literal>
    <justification jstring="[para(5721(a,1),541(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5721 541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5901">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(5721(a,1),916(a,1,1,1))].">
      <j1 rule="para" parents="5721 916"/>
    </justification>
  </clause>

  <clause id="5902">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5721(a,1),1039(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5721 1039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5903">
    <literal><![CDATA[
      L(x * K(y,x),z,u) = (y * L(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(5721(a,1),1194(a,1,1))].">
      <j1 rule="para" parents="5721 1194"/>
    </justification>
  </clause>

  <clause id="5904">
    <literal><![CDATA[
      R(x * K(y,x),z,u) = (y * R(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(5721(a,1),1203(a,1,1))].">
      <j1 rule="para" parents="5721 1203"/>
    </justification>
  </clause>

  <clause id="5905">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(5721(a,1),791(a,1,1))].">
      <j1 rule="para" parents="5721 791"/>
    </justification>
  </clause>

  <clause id="5906">
    <literal><![CDATA[
      L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z)
    ]]></literal>
    <justification jstring="[para(5721(a,1),1196(a,1,1))].">
      <j1 rule="para" parents="5721 1196"/>
    </justification>
  </clause>

  <clause id="5907">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / (y * K(z,y))) * y
    ]]></literal>
    <justification jstring="[para(5721(a,1),2592(a,2,1,2))].">
      <j1 rule="para" parents="5721 2592"/>
    </justification>
  </clause>

  <clause id="5908">
    <literal><![CDATA[
      L(T(x * K(y * z,x),z),z,y) = (y * (x * z)) / (y * z)
    ]]></literal>
    <justification jstring="[para(5721(a,1),2609(a,1,1,1))].">
      <j1 rule="para" parents="5721 2609"/>
    </justification>
  </clause>

  <clause id="5909">
    <literal><![CDATA[
      ((x * y) * R(y,z,u)) / (x * R(y,z,u)) = y * K(x * R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(2823(a,1),5721(a,1,1))].">
      <j1 rule="para" parents="2823 5721"/>
    </justification>
  </clause>

  <clause id="5910">
    <literal><![CDATA[
      (x * (K(y,x) * z)) \ ((x * K(y,x)) * (L(z,K(y,x),x) * u)) = L(u,L(z,K(y,x),x),(y * x) / y)
    ]]></literal>
    <justification jstring="[para(5721(a,2),601(a,2,3))].">
      <j1 rule="para" parents="5721 601"/>
    </justification>
  </clause>

  <clause id="5911">
    <literal><![CDATA[
      ((x * y) / x) * z = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(5721(a,2),4442(a,1,1))].">
      <j1 rule="para" parents="5721 4442"/>
    </justification>
  </clause>

  <clause id="5912">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(5721(a,2),4530(a,1,1))].">
      <j1 rule="para" parents="5721 4530"/>
    </justification>
  </clause>

  <clause id="5913">
    <literal><![CDATA[
      ((x * y) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(5721(a,2),4494(a,1,1))].">
      <j1 rule="para" parents="5721 4494"/>
    </justification>
  </clause>

  <clause id="5914">
    <literal><![CDATA[
      (T(x,y) * z) * K((y * x) / y,T(x,y) * z) = (x * (x * z)) / ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4956(a,1),5721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4956 5721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5915">
    <literal><![CDATA[
      a(x * K(y,x),y,z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(5721(a,1),5053(a,1,1))].">
      <j1 rule="para" parents="5721 5053"/>
    </justification>
  </clause>

  <clause id="5916">
    <literal><![CDATA[
      (x \ (y * K(x,y))) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5721(a,1),5502(a,1,1,2))].">
      <j1 rule="para" parents="5721 5502"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x / K(z,y)
    ]]></literal>
    <justification jstring="[para(5721(a,2),5701(a,1,2))].">
      <j1 rule="para" parents="5721 5701"/>
    </justification>
  </clause>

  <clause id="5918">
    <literal><![CDATA[
      x \ (y * ((z * x) / z)) = T(y * K(z,x),x)
    ]]></literal>
    <justification jstring="[para(5721(a,2),5702(a,1,2,2))].">
      <j1 rule="para" parents="5721 5702"/>
    </justification>
  </clause>

  <clause id="5919">
    <literal><![CDATA[
      K(x \ y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,4530,a(flip),b,5722,a)].">
      <j1 rule="hyper" parents="64 4530 5722"/>
    </justification>
  </clause>

  <clause id="5921">
    <literal><![CDATA[
      K(x,y) \ (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(139,a,5722,a(flip),b,4525,a(flip))].">
      <j1 rule="hyper" parents="139 5722 4525"/>
    </justification>
  </clause>

  <clause id="5922">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y * K(x,y)) = x * (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(5722(a,1),4646(a,1,1,2))].">
      <j1 rule="para" parents="5722 4646"/>
    </justification>
  </clause>

  <clause id="5923">
    <literal><![CDATA[
      K(x,T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5731,a,b,5737,a),flip(a)].">
      <j1 rule="hyper" parents="373 5731 5737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5924">
    <literal><![CDATA[
      K(x,x \ (y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),5923(a,1,2))].">
      <j1 rule="para" parents="22 5923"/>
    </justification>
  </clause>

  <clause id="5925">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),5923(a,1,2))].">
      <j1 rule="para" parents="25 5923"/>
    </justification>
  </clause>

  <clause id="5926">
    <literal><![CDATA[
      K(x,y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(117(a,1),5923(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 5923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5927">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ y) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(116(a,1),5923(a,1,2))].">
      <j1 rule="para" parents="116 5923"/>
    </justification>
  </clause>

  <clause id="5928">
    <literal><![CDATA[
      K(x,L(y / x,z,u)) = K(x,L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(279(a,1),5923(a,1,2)),flip(a)].">
      <j1 rule="para" parents="279 5923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5929">
    <literal><![CDATA[
      K(x,R(y / x,z,u)) = K(x,R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(280(a,1),5923(a,1,2)),flip(a)].">
      <j1 rule="para" parents="280 5923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5930">
    <literal><![CDATA[
      K(x,y) \ T(y,x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(5923(a,1),5804(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5923 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5931">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T(x \ L(x,y,z),u) = K(x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5659(a,1),5738(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5659 5738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5932">
    <literal><![CDATA[
      K(x,y) = x * (((y * x) / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,4951,a,b,5740,a),flip(a)].">
      <j1 rule="hyper" parents="373 4951 5740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5933">
    <literal><![CDATA[
      K(1 / x,y) / x = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,5740,a,b,220,a(flip))].">
      <j1 rule="hyper" parents="142 5740 220"/>
    </justification>
  </clause>

  <clause id="5934">
    <literal><![CDATA[
      ((x * y) / x) \ 1 = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,5740,a,b,4951,a),flip(a)].">
      <j1 rule="hyper" parents="139 5740 4951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5936">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,T(y,z),x) = u
    ]]></literal>
    <justification jstring="[para(5740(a,2),608(a,1,2,2))].">
      <j1 rule="para" parents="5740 608"/>
    </justification>
  </clause>

  <clause id="5937">
    <literal><![CDATA[
      ((x \ y) \ y) \ 1 = x \ K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(906,a,5783,a)].">
      <j1 rule="hyper" parents="906 5783"/>
    </justification>
  </clause>

  <clause id="5938">
    <literal><![CDATA[
      x * (T(y,z) \ 1) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,5783,a,b,9,a)].">
      <j1 rule="hyper" parents="145 5783 9"/>
    </justification>
  </clause>

  <clause id="5939">
    <literal><![CDATA[
      (T(x,y) \ 1) * z = (x \ K(y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,5783,a,b,11,a)].">
      <j1 rule="hyper" parents="144 5783 11"/>
    </justification>
  </clause>

  <clause id="5940">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x \ 1,x) = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4035,a,b,5783,a)].">
      <j1 rule="hyper" parents="64 4035 5783"/>
    </justification>
  </clause>

  <clause id="5941">
    <literal><![CDATA[
      (x * y) \ (x * K(z,y)) = L(T(y,z) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(5783(a,2),102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5783 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5942">
    <literal><![CDATA[
      L(T(x \ y,z) \ 1,x \ y,x) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[para(5783(a,2),630(a,1,1))].">
      <j1 rule="para" parents="5783 630"/>
    </justification>
  </clause>

  <clause id="5943">
    <literal><![CDATA[
      R(K(x,y) / y,z,u) * y = y * R(T(y,x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(5783(a,2),843(a,2,2,1))].">
      <j1 rule="para" parents="5783 843"/>
    </justification>
  </clause>

  <clause id="5944">
    <literal><![CDATA[
      T(x,y) * L(x \ K(y,x),z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(5783(a,1),3250(a,1,2,1))].">
      <j1 rule="para" parents="5783 3250"/>
    </justification>
  </clause>

  <clause id="5945">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (x \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(5783(a,1),3563(a,2,1))].">
      <j1 rule="para" parents="5783 3563"/>
    </justification>
  </clause>

  <clause id="5946">
    <literal><![CDATA[
      x / ((y \ x) * y) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,171,a(flip),b,5786,a)].">
      <j1 rule="hyper" parents="373 171 5786"/>
    </justification>
  </clause>

  <clause id="5947">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * x) = y
    ]]></literal>
    <justification jstring="[hyper(144,a,5786,a,b,171,a(flip))].">
      <j1 rule="hyper" parents="144 5786 171"/>
    </justification>
  </clause>

  <clause id="5948">
    <literal><![CDATA[
      ((x * (1 / T(y,z))) * y) / K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,1 / T(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(5788(a,2),666(a,1,2))].">
      <j1 rule="para" parents="5788 666"/>
    </justification>
  </clause>

  <clause id="5949">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ K(y,x),z)
    ]]></literal>
    <justification jstring="[para(5789(a,2),1571(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5789 1571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5950">
    <literal><![CDATA[
      T(x * y,K(y,x)) = x * y
    ]]></literal>
    <justification jstring="[hyper(269,a,94,a,b,5796,a)].">
      <j1 rule="hyper" parents="269 94 5796"/>
    </justification>
  </clause>

  <clause id="5952">
    <literal><![CDATA[
      L(T(x,y),x,x) = 1 / (K(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(225,a,5799,a,b,3571,a),flip(a)].">
      <j1 rule="hyper" parents="225 5799 3571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5953">
    <literal><![CDATA[
      T(x,y) * (((T(x,y) \ 1) * z) * u) = (K(y,x) / x) * ((T(x,y) * z) * u)
    ]]></literal>
    <justification jstring="[para(5799(a,2),1603(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5799 1603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5954">
    <literal><![CDATA[
      T((1 / T(x,y)) / T(x,z),x) = x \ (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(5799(a,1),2533(a,1,1,1))].">
      <j1 rule="para" parents="5799 2533"/>
    </justification>
  </clause>

  <clause id="5955">
    <literal><![CDATA[
      K(x,y) \ x = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(149,a,5807,a)].">
      <j1 rule="hyper" parents="149 5807"/>
    </justification>
  </clause>

  <clause id="5956">
    <literal><![CDATA[
      K(x \ y,x) * (y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),5807(a,1,2,1))].">
      <j1 rule="para" parents="10 5807"/>
    </justification>
  </clause>

  <clause id="5958">
    <literal><![CDATA[
      K(a(x,y,z),x * (y * z)) * (((x * y) * z) / (x * (y * z))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(88(a,1),5807(a,1,2,1))].">
      <j1 rule="para" parents="88 5807"/>
    </justification>
  </clause>

  <clause id="5960">
    <literal><![CDATA[
      x * ((y * z) / y) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5859(a,1),740(a,1,2,2))].">
      <j1 rule="para" parents="5859 740"/>
    </justification>
  </clause>

  <clause id="5961">
    <literal><![CDATA[
      x \ (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,97,a,b,5926,a)].">
      <j1 rule="hyper" parents="64 97 5926"/>
    </justification>
  </clause>

  <clause id="5962">
    <literal><![CDATA[
      K(x,x \ (y \ x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,4927,a(flip),b,5926,a),flip(a)].">
      <j1 rule="hyper" parents="64 4927 5926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5963">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,5926,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="145 5926 97"/>
    </justification>
  </clause>

  <clause id="5964">
    <literal><![CDATA[
      T(x * ((y * z) / x),K(z,y)) = x * ((y * z) / x)
    ]]></literal>
    <justification jstring="[para(5950(a,1),5431(a,2,2,1))].">
      <j1 rule="para" parents="5950 5431"/>
    </justification>
  </clause>

  <clause id="5965">
    <literal><![CDATA[
      K(x,y) \ x = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5721,a(flip),b,5955,a),flip(a)].">
      <j1 rule="hyper" parents="373 5721 5955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5966">
    <literal><![CDATA[
      x / (y / (y / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(225,a,4707,a(flip),b,5955,a)].">
      <j1 rule="hyper" parents="225 4707 5955"/>
    </justification>
  </clause>

  <clause id="5968">
    <literal><![CDATA[
      R(K(x,y) \ x,y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(5955(a,2),112(a,1,1))].">
      <j1 rule="para" parents="5955 112"/>
    </justification>
  </clause>

  <clause id="5969">
    <literal><![CDATA[
      K(x \ 1,x) \ ((x \ y) / y) = (x * ((x \ y) / y)) / x
    ]]></literal>
    <justification jstring="[para(3395(a,1),5955(a,1,1))].">
      <j1 rule="para" parents="3395 5955"/>
    </justification>
  </clause>

  <clause id="5970">
    <literal><![CDATA[
      (x * K(y,x)) \ y = x \ (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(5965(a,1),4532(a,2,2))].">
      <j1 rule="para" parents="5965 4532"/>
    </justification>
  </clause>

  <clause id="5971">
    <literal><![CDATA[
      (K(x,y) \ x) \ z = x \ (K(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(5965(a,2),4532(a,1,1))].">
      <j1 rule="para" parents="5965 4532"/>
    </justification>
  </clause>

  <clause id="5972">
    <literal><![CDATA[
      x * K(T(y,x),x) = K(x,y) \ x
    ]]></literal>
    <justification jstring="[para(5923(a,1),5965(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5923 5965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5973">
    <literal><![CDATA[
      T(T(x,y),z) \ T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),5824(a,1,1))].">
      <j1 rule="para" parents="23 5824"/>
    </justification>
  </clause>

  <clause id="5974">
    <literal><![CDATA[
      L(T(x,y),z,u) \ L(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,L(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(25(a,2),5824(a,1,1))].">
      <j1 rule="para" parents="25 5824"/>
    </justification>
  </clause>

  <clause id="5975">
    <literal><![CDATA[
      R(T(x,y),z,u) \ R(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,R(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(27(a,2),5824(a,1,1))].">
      <j1 rule="para" parents="27 5824"/>
    </justification>
  </clause>

  <clause id="5976">
    <literal><![CDATA[
      x * T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(4612(a,1),5824(a,1))].">
      <j1 rule="para" parents="4612 5824"/>
    </justification>
  </clause>

  <clause id="5977">
    <literal><![CDATA[
      K(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5737(a,2),5824(a,1))].">
      <j1 rule="para" parents="5737 5824"/>
    </justification>
  </clause>

  <clause id="5978">
    <literal><![CDATA[
      K(x,x \ (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(22(a,1),5977(a,1,2))].">
      <j1 rule="para" parents="22 5977"/>
    </justification>
  </clause>

  <clause id="5979">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(25(a,2),5977(a,1,2))].">
      <j1 rule="para" parents="25 5977"/>
    </justification>
  </clause>

  <clause id="5980">
    <literal><![CDATA[
      K(x,R(T(y,x),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(27(a,2),5977(a,1,2))].">
      <j1 rule="para" parents="27 5977"/>
    </justification>
  </clause>

  <clause id="5981">
    <literal><![CDATA[
      K(x,R(T(y,x * z),x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(x * z) \ ((x * y) * z)) = u
    ]]></literal>
    <justification jstring="[para(1756(a,1),5977(a,1,2))].">
      <j1 rule="para" parents="1756 5977"/>
    </justification>
  </clause>

  <clause id="5982">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(5720(a,1),4503(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5720 4503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5983">
    <literal><![CDATA[
      x * (y / (y / z)) = x * (K(z \ y,z) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5723,a,b,9,a)].">
      <j1 rule="hyper" parents="145 5723 9"/>
    </justification>
  </clause>

  <clause id="5984">
    <literal><![CDATA[
      K(x \ y,x) * (x * z) = (y / (y / x)) * z
    ]]></literal>
    <justification jstring="[para(5723(a,2),4503(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5723 4503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5985">
    <literal><![CDATA[
      K(x,y) * (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5733(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5733 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5986">
    <literal><![CDATA[
      (T(R(x,y,z),u) * (y * z)) / ((x * y) * z) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(111(a,1),5733(a,1,2))].">
      <j1 rule="para" parents="111 5733"/>
    </justification>
  </clause>

  <clause id="5987">
    <literal><![CDATA[
      (T(x,y) * R(x \ 1,x,z)) / ((z / (x * z)) * x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(859(a,2),5733(a,1,2))].">
      <j1 rule="para" parents="859 5733"/>
    </justification>
  </clause>

  <clause id="5988">
    <literal><![CDATA[
      x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1334,a,5743,a)].">
      <j1 rule="hyper" parents="1334 5743"/>
    </justification>
  </clause>

  <clause id="5989">
    <literal><![CDATA[
      T(1 / x,y) * x = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(532,a,5743,a)].">
      <j1 rule="hyper" parents="532 5743"/>
    </justification>
  </clause>

  <clause id="5990">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3484,a(flip),b,5743,a)].">
      <j1 rule="hyper" parents="64 3484 5743"/>
    </justification>
  </clause>

  <clause id="5991">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(T(x,z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3060,a(flip),b,5743,a)].">
      <j1 rule="hyper" parents="64 3060 5743"/>
    </justification>
  </clause>

  <clause id="5992">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2428,a(flip),b,5743,a)].">
      <j1 rule="hyper" parents="64 2428 5743"/>
    </justification>
  </clause>

  <clause id="5994">
    <literal><![CDATA[
      (x / y) * K(y \ 1,z) = x * T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5743,a(flip),b,1791,a)].">
      <j1 rule="hyper" parents="145 5743 1791"/>
    </justification>
  </clause>

  <clause id="5995">
    <literal><![CDATA[
      L(x \ 1,x,y) * (y * x) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,5743,a(flip),b,831,a),flip(a)].">
      <j1 rule="hyper" parents="145 5743 831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5996">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K((y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5743,a(flip),b,2428,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 5743 2428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5998">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(144,a,5743,a(flip),b,2715,a)].">
      <j1 rule="hyper" parents="144 5743 2715"/>
    </justification>
  </clause>

  <clause id="6000">
    <literal><![CDATA[
      K((x / y) \ 1,z) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,5743,a(flip),b,2586,a(flip))].">
      <j1 rule="hyper" parents="144 5743 2586"/>
    </justification>
  </clause>

  <clause id="6001">
    <literal><![CDATA[
      K(x \ 1,y) / x = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,5743,a(flip),b,525,a)].">
      <j1 rule="hyper" parents="142 5743 525"/>
    </justification>
  </clause>

  <clause id="6002">
    <literal><![CDATA[
      x \ K((x * y) \ 1,z) = y * T(y \ (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(139,a,5743,a(flip),b,1308,a(flip))].">
      <j1 rule="hyper" parents="139 5743 1308"/>
    </justification>
  </clause>

  <clause id="6003">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(5743(a,1),1001(a,2,2))].">
      <j1 rule="para" parents="5743 1001"/>
    </justification>
  </clause>

  <clause id="6004">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * K(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(5743(a,1),1340(a,2,2))].">
      <j1 rule="para" parents="5743 1340"/>
    </justification>
  </clause>

  <clause id="6005">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(5743(a,1),2881(a,2,1))].">
      <j1 rule="para" parents="5743 2881"/>
    </justification>
  </clause>

  <clause id="6006">
    <literal><![CDATA[
      T(x,K(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(5743(a,1),2883(a,1,2))].">
      <j1 rule="para" parents="5743 2883"/>
    </justification>
  </clause>

  <clause id="6007">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(5743(a,1),2882(a,2,1))].">
      <j1 rule="para" parents="5743 2882"/>
    </justification>
  </clause>

  <clause id="6009">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(5743(a,1),2947(a,2,2))].">
      <j1 rule="para" parents="5743 2947"/>
    </justification>
  </clause>

  <clause id="6011">
    <literal><![CDATA[
      T(1 / x,y) \ 1 = K(x \ 1,y) \ x
    ]]></literal>
    <justification jstring="[para(5743(a,1),3228(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5743 3228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6013">
    <literal><![CDATA[
      K(x \ 1,y) * x = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,6006,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 6006 22"/>
    </justification>
  </clause>

  <clause id="6014">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(1 / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2586,a(flip),b,5744,a)].">
      <j1 rule="hyper" parents="64 2586 5744"/>
    </justification>
  </clause>

  <clause id="6016">
    <literal><![CDATA[
      (x * (y / x)) / y = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4554,a,b,5745,a)].">
      <j1 rule="hyper" parents="64 4554 5745"/>
    </justification>
  </clause>

  <clause id="6018">
    <literal><![CDATA[
      (x * (y / x)) \ x = y \ (y / (y / x))
    ]]></literal>
    <justification jstring="[para(5751(a,2),2939(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5751 2939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6020">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(759,a,5755,a)].">
      <j1 rule="hyper" parents="759 5755"/>
    </justification>
  </clause>

  <clause id="6021">
    <literal><![CDATA[
      x \ (K(x,y) \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(757,a,5755,a),flip(a)].">
      <j1 rule="hyper" parents="757 5755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6022">
    <literal><![CDATA[
      K(x,y) * (z * x) = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(737,a,5755,a)].">
      <j1 rule="hyper" parents="737 5755"/>
    </justification>
  </clause>

  <clause id="6023">
    <literal><![CDATA[
      K(x,y) * (x * (T(y,x) * z)) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5017,a(flip),b,5755,a),flip(a)].">
      <j1 rule="hyper" parents="373 5017 5755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6024">
    <literal><![CDATA[
      K(x,y * y) * (x * ((y * y) \ z)) = ((y * y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,952,a(flip),b,5755,a),flip(a)].">
      <j1 rule="hyper" parents="373 952 5755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6025">
    <literal><![CDATA[
      K(x,x \ y) * (x * z) = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,365,a(flip),b,5755,a),flip(a)].">
      <j1 rule="hyper" parents="373 365 5755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6026">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = x * T(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,115,a(flip),b,5755,a)].">
      <j1 rule="hyper" parents="139 115 5755"/>
    </justification>
  </clause>

  <clause id="6027">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * x) = T(x,y) * L(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,520,a(flip),b,5755,a)].">
      <j1 rule="hyper" parents="64 520 5755"/>
    </justification>
  </clause>

  <clause id="6028">
    <literal><![CDATA[
      K(R(x,y,z),u) * (R(x,y,z) * w) = R(T(x,u),y,z) * w
    ]]></literal>
    <justification jstring="[para(27(a,2),5755(a,2,1))].">
      <j1 rule="para" parents="27 5755"/>
    </justification>
  </clause>

  <clause id="6029">
    <literal><![CDATA[
      K(x * y,z) * (x * (y * u)) = T(x * y,z) * L(u,y,x)
    ]]></literal>
    <justification jstring="[para(100(a,1),5755(a,1,2))].">
      <j1 rule="para" parents="100 5755"/>
    </justification>
  </clause>

  <clause id="6030">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5755(a,1),397(a,1))].">
      <j1 rule="para" parents="5755 397"/>
    </justification>
  </clause>

  <clause id="6031">
    <literal><![CDATA[
      K(x,y) * (R(z,u,w) * x) = T(x,y) * R(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(267(a,1),5755(a,1,2))].">
      <j1 rule="para" parents="267 5755"/>
    </justification>
  </clause>

  <clause id="6032">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),x * z,u) = w
    ]]></literal>
    <justification jstring="[para(5755(a,1),666(a,1,1,1))].">
      <j1 rule="para" parents="5755 666"/>
    </justification>
  </clause>

  <clause id="6033">
    <literal><![CDATA[
      T(x,y) * ((x \ 1) * z) = K(x,y) * L(z,x,x)
    ]]></literal>
    <justification jstring="[para(1139(a,1),5755(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1139 5755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6035">
    <literal><![CDATA[
      K(x,y) * a(x,x,x) = T(x,y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1852(a,2),5755(a,1,2))].">
      <j1 rule="para" parents="1852 5755"/>
    </justification>
  </clause>

  <clause id="6036">
    <literal><![CDATA[
      K(x,y) * T(x,z) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5753(a,2),5755(a,1,2))].">
      <j1 rule="para" parents="5753 5755"/>
    </justification>
  </clause>

  <clause id="6037">
    <literal><![CDATA[
      (x / y) \ K(y,y \ x) = (y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),5759(a,1,1,1))].">
      <j1 rule="para" parents="10 5759"/>
    </justification>
  </clause>

  <clause id="6038">
    <literal><![CDATA[
      K(x \ (x * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(5763(a,2),5827(a,1))].">
      <j1 rule="para" parents="5763 5827"/>
    </justification>
  </clause>

  <clause id="6039">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(156,a,5772,a)].">
      <j1 rule="hyper" parents="156 5772"/>
    </justification>
  </clause>

  <clause id="6040">
    <literal><![CDATA[
      x / y != (T(z,u) \ 1) * K(z,u)
    ]]></literal>
    <literal><![CDATA[
      (z \ 1) * y = x
    ]]></literal>
    <justification jstring="[para(5772(a,1),389(a,2,1))].">
      <j1 rule="para" parents="5772 389"/>
    </justification>
  </clause>

  <clause id="6041">
    <literal><![CDATA[
      K(x,1 / y) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5827,a,5773,a),flip(a)].">
      <j1 rule="hyper" parents="5827 5773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6042">
    <literal><![CDATA[
      K(x,(x / y) / x) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(4389,a,5773,a)].">
      <j1 rule="hyper" parents="4389 5773"/>
    </justification>
  </clause>

  <clause id="6044">
    <literal><![CDATA[
      x \ K(y,1 / x) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(139,a,5773,a(flip),b,4374,a)].">
      <j1 rule="hyper" parents="139 5773 4374"/>
    </justification>
  </clause>

  <clause id="6045">
    <literal><![CDATA[
      K(x,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(5773(a,1),5827(a,1))].">
      <j1 rule="para" parents="5773 5827"/>
    </justification>
  </clause>

  <clause id="6047">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),6041(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 6041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6048">
    <literal><![CDATA[
      K(x,1 / (1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(82(a,1),6041(a,2,2))].">
      <j1 rule="para" parents="82 6041"/>
    </justification>
  </clause>

  <clause id="6049">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(6041(a,2),4029(a,2,2))].">
      <j1 rule="para" parents="6041 4029"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(6041(a,1),4531(a,2,1))].">
      <j1 rule="para" parents="6041 4531"/>
    </justification>
  </clause>

  <clause id="6051">
    <literal><![CDATA[
      K(x,T(y,y \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(116(a,2),6047(a,1,2))].">
      <j1 rule="para" parents="116 6047"/>
    </justification>
  </clause>

  <clause id="6052">
    <literal><![CDATA[
      K(x,T(y,1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1352(a,2),6047(a,1,2))].">
      <j1 rule="para" parents="1352 6047"/>
    </justification>
  </clause>

  <clause id="6053">
    <literal><![CDATA[
      K(x,T(y \ 1,y)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(1354(a,2),6047(a,1,2))].">
      <j1 rule="para" parents="1354 6047"/>
    </justification>
  </clause>

  <clause id="6054">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(3039(a,2),6047(a,1,2))].">
      <j1 rule="para" parents="3039 6047"/>
    </justification>
  </clause>

  <clause id="6055">
    <literal><![CDATA[
      K(x,T(1 / y,z)) = K(x,T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(3569(a,1),6047(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3569 6047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6056">
    <literal><![CDATA[
      K(x,((1 / y) * z) \ z) = K(x,((y \ 1) * z) \ z)
    ]]></literal>
    <justification jstring="[para(3768(a,1),6047(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3768 6047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6057">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(3815(a,2),6047(a,1,2))].">
      <j1 rule="para" parents="3815 6047"/>
    </justification>
  </clause>

  <clause id="6059">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) / y) = K(x,(y / z) / y)
    ]]></literal>
    <justification jstring="[para(3946(a,2),6048(a,1,2))].">
      <j1 rule="para" parents="3946 6048"/>
    </justification>
  </clause>

  <clause id="6060">
    <literal><![CDATA[
      K(x,L(L(1 / y,z,u),w,v5)) = K(x,L(L(y \ 1,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(4306(a,1),6048(a,1,2))].">
      <j1 rule="para" parents="4306 6048"/>
    </justification>
  </clause>

  <clause id="6061">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(5774(a,1),4442(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5774 4442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6062">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[para(5774(a,1),4530(a,1,1))].">
      <j1 rule="para" parents="5774 4530"/>
    </justification>
  </clause>

  <clause id="6063">
    <literal><![CDATA[
      T(x \ y,R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[para(5774(a,1),4961(a,1,2,1))].">
      <j1 rule="para" parents="5774 4961"/>
    </justification>
  </clause>

  <clause id="6064">
    <literal><![CDATA[
      (x * K(y,y \ z)) * (y \ z) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(5774(a,1),5700(a,2,2))].">
      <j1 rule="para" parents="5774 5700"/>
    </justification>
  </clause>

  <clause id="6065">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(759,a,5776,a)].">
      <j1 rule="hyper" parents="759 5776"/>
    </justification>
  </clause>

  <clause id="6066">
    <literal><![CDATA[
      K(x,y) \ (x \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(757,a,5776,a),flip(a)].">
      <j1 rule="hyper" parents="757 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6067">
    <literal><![CDATA[
      T(x,y) * (K(x,y) \ z) = x * z
    ]]></literal>
    <justification jstring="[hyper(397,a,5776,a),flip(a)].">
      <j1 rule="hyper" parents="397 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6070">
    <literal><![CDATA[
      ((x \ y) \ y) * z = x * (K(x,x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,365,a(flip),b,5776,a)].">
      <j1 rule="hyper" parents="373 365 5776"/>
    </justification>
  </clause>

  <clause id="6071">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(149,a,5776,a)].">
      <j1 rule="hyper" parents="149 5776"/>
    </justification>
  </clause>

  <clause id="6072">
    <literal><![CDATA[
      x \ ((x * y) / x) = K(x,y) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,4455,a(flip),b,5776,a)].">
      <j1 rule="hyper" parents="139 4455 5776"/>
    </justification>
  </clause>

  <clause id="6073">
    <literal><![CDATA[
      K(x,x \ y) * (((x \ y) \ y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,505,a(flip),b,5776,a),flip(a)].">
      <j1 rule="hyper" parents="139 505 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6074">
    <literal><![CDATA[
      K(x,y) * T(z,T(x,y)) = x \ (z * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,115,a(flip),b,5776,a),flip(a)].">
      <j1 rule="hyper" parents="139 115 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6075">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,5776,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6076">
    <literal><![CDATA[
      K(x,y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,5748,a(flip),b,5776,a),flip(a)].">
      <j1 rule="hyper" parents="138 5748 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6077">
    <literal><![CDATA[
      ((x * y) / x) \ z = K(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(35,a,4951,a,b,5776,a)].">
      <j1 rule="hyper" parents="35 4951 5776"/>
    </justification>
  </clause>

  <clause id="6078">
    <literal><![CDATA[
      K(x,y) * (T(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[hyper(35,a,4957,a(flip),b,5776,a),flip(a)].">
      <j1 rule="hyper" parents="35 4957 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6079">
    <literal><![CDATA[
      K(x,y) * (y / T(x,y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(35,a,4835,a(flip),b,5776,a),flip(a)].">
      <j1 rule="hyper" parents="35 4835 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6080">
    <literal><![CDATA[
      K(x,y) * T(y,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,4831,a(flip),b,5776,a),flip(a)].">
      <j1 rule="hyper" parents="35 4831 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6081">
    <literal><![CDATA[
      K(x * y,x) * T(x,y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,4752,a(flip),b,5776,a),flip(a)].">
      <j1 rule="hyper" parents="35 4752 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6082">
    <literal><![CDATA[
      L(K(x \ 1,y) * z,x,x) = x * (T(x \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5776,a(flip),b,1148,a),flip(a)].">
      <j1 rule="hyper" parents="145 5776 1148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6083">
    <literal><![CDATA[
      L(K(x,y) * z,x,x) = (1 / x) * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5776,a(flip),b,561,a),flip(a)].">
      <j1 rule="hyper" parents="145 5776 561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6084">
    <literal><![CDATA[
      (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5776(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5776 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6085">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5776(a,1),44(a,1))].">
      <j1 rule="para" parents="5776 44"/>
    </justification>
  </clause>

  <clause id="6086">
    <literal><![CDATA[
      x * (K(x,x * x) * y) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[para(118(a,1),5776(a,2,1))].">
      <j1 rule="para" parents="118 5776"/>
    </justification>
  </clause>

  <clause id="6087">
    <literal><![CDATA[
      x \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5776(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5776 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6088">
    <literal><![CDATA[
      x * (K(y,x) * K(x,z)) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(3320(a,1),5776(a,1,2))].">
      <j1 rule="para" parents="3320 5776"/>
    </justification>
  </clause>

  <clause id="6089">
    <literal><![CDATA[
      T(x \ 1,x) * (y / (x \ 1)) = (x \ 1) * (y / (1 / x))
    ]]></literal>
    <justification jstring="[para(3719(a,1),5776(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3719 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6090">
    <literal><![CDATA[
      x * (y * (K(x,y) * z)) = T(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(4534(a,1),5776(a,1,2))].">
      <j1 rule="para" parents="4534 5776"/>
    </justification>
  </clause>

  <clause id="6091">
    <literal><![CDATA[
      1 / K(x,y) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(154,a,6076,a)].">
      <j1 rule="hyper" parents="154 6076"/>
    </justification>
  </clause>

  <clause id="6092">
    <literal><![CDATA[
      K(x,y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(149,a,6076,a)].">
      <j1 rule="hyper" parents="149 6076"/>
    </justification>
  </clause>

  <clause id="6093">
    <literal><![CDATA[
      x * (K(y,z) * K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,6076,a,b,68,a)].">
      <j1 rule="hyper" parents="145 6076 68"/>
    </justification>
  </clause>

  <clause id="6094">
    <literal><![CDATA[
      1 / (x \ K(x,y)) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,6076,a(flip),b,4530,a)].">
      <j1 rule="hyper" parents="142 6076 4530"/>
    </justification>
  </clause>

  <clause id="6095">
    <literal><![CDATA[
      (x * K(y,x)) \ 1 = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,6076,a(flip),b,4530,a)].">
      <j1 rule="hyper" parents="139 6076 4530"/>
    </justification>
  </clause>

  <clause id="6096">
    <literal><![CDATA[
      K(x,y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(6076(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="6076 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6097">
    <literal><![CDATA[
      x * K(y,z) != 1
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(6076(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="6076 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6100">
    <literal><![CDATA[
      1 / K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(6076(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6076 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6101">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(6076(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6076 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6104">
    <literal><![CDATA[
      L(x,y,K(z,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(6091(a,1),1643(a,1,3))].">
      <j1 rule="para" parents="6091 1643"/>
    </justification>
  </clause>

  <clause id="6105">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(6091(a,1),2273(a,1,3))].">
      <j1 rule="para" parents="6091 2273"/>
    </justification>
  </clause>

  <clause id="6106">
    <literal><![CDATA[
      R(x,K(y,z),u) = R(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(6091(a,1),2968(a,1,2))].">
      <j1 rule="para" parents="6091 2968"/>
    </justification>
  </clause>

  <clause id="6108">
    <literal><![CDATA[
      K(x,T(y,x)) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,5923,a,b,6092,a)].">
      <j1 rule="hyper" parents="373 5923 6092"/>
    </justification>
  </clause>

  <clause id="6109">
    <literal><![CDATA[
      T(K(x,y),z) * R(T(K(x,y),z) \ 1,u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(6092(a,1),3216(a,2,1,2,1))].">
      <j1 rule="para" parents="6092 3216"/>
    </justification>
  </clause>

  <clause id="6110">
    <literal><![CDATA[
      (x * K(y,x)) \ x = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,6093,a(flip),b,4442,a)].">
      <j1 rule="hyper" parents="139 6093 4442"/>
    </justification>
  </clause>

  <clause id="6111">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,6092,a,b,6108,a(flip))].">
      <j1 rule="hyper" parents="40 6092 6108"/>
    </justification>
  </clause>

  <clause id="6113">
    <literal><![CDATA[
      T(x,y) * K(x,y) = T(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(145,a,6111,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 6111 5726"/>
    </justification>
  </clause>

  <clause id="6114">
    <literal><![CDATA[
      K(x,y) * T(x,y) = T(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(144,a,6111,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 6111 5739"/>
    </justification>
  </clause>

  <clause id="6115">
    <literal><![CDATA[
      K(x \ (y * x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(22(a,1),6111(a,1,1))].">
      <j1 rule="para" parents="22 6111"/>
    </justification>
  </clause>

  <clause id="6116">
    <literal><![CDATA[
      K(x / y,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(117(a,1),6111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="117 6111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6117">
    <literal><![CDATA[
      K((x * y) / x,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(255(a,1),6111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="255 6111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6118">
    <literal><![CDATA[
      K((x \ y) \ y,x \ y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(116(a,1),6111(a,1,1))].">
      <j1 rule="para" parents="116 6111"/>
    </justification>
  </clause>

  <clause id="6119">
    <literal><![CDATA[
      K(R(x \ y,x,z),x) = K((y * z) / (x * z),x)
    ]]></literal>
    <justification jstring="[para(855(a,1),6111(a,1,1))].">
      <j1 rule="para" parents="855 6111"/>
    </justification>
  </clause>

  <clause id="6120">
    <literal><![CDATA[
      K(R(x,y,x),y * x) = K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(1056(a,1),6111(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1056 6111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6121">
    <literal><![CDATA[
      T(x,y) * (K(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[para(6111(a,1),5776(a,1,2,1))].">
      <j1 rule="para" parents="6111 5776"/>
    </justification>
  </clause>

  <clause id="6122">
    <literal><![CDATA[
      x * K(x / y,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,6116,a,b,95,a)].">
      <j1 rule="hyper" parents="145 6116 95"/>
    </justification>
  </clause>

  <clause id="6123">
    <literal><![CDATA[
      L(x,y / z,K(z \ y,z)) = x
    ]]></literal>
    <justification jstring="[para(6116(a,1),4603(a,1,3))].">
      <j1 rule="para" parents="6116 4603"/>
    </justification>
  </clause>

  <clause id="6125">
    <literal><![CDATA[
      L(x,K(y \ z,y),z / y) = x
    ]]></literal>
    <justification jstring="[para(6116(a,1),4869(a,1,2))].">
      <j1 rule="para" parents="6116 4869"/>
    </justification>
  </clause>

  <clause id="6126">
    <literal><![CDATA[
      K(x,x / y) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(5827,a,5777,a),flip(a)].">
      <j1 rule="hyper" parents="5827 5777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6127">
    <literal><![CDATA[
      (x / y) \ K(x,y \ x) = T(x / y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,6126,a(flip),b,5789,a(flip))].">
      <j1 rule="hyper" parents="139 6126 5789"/>
    </justification>
  </clause>

  <clause id="6128">
    <literal><![CDATA[
      K(x,(y \ x) \ x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),6126(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 6126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6129">
    <literal><![CDATA[
      K(x * y,T(x,y)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(366(a,2),6128(a,1,2))].">
      <j1 rule="para" parents="366 6128"/>
    </justification>
  </clause>

  <clause id="6130">
    <literal><![CDATA[
      K(x * y,T(y,x)) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(4678(a,2),6128(a,1,2))].">
      <j1 rule="para" parents="4678 6128"/>
    </justification>
  </clause>

  <clause id="6131">
    <literal><![CDATA[
      K(x,y) \ (y * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(5023,a,5778,a)].">
      <j1 rule="hyper" parents="5023 5778"/>
    </justification>
  </clause>

  <clause id="6132">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(1368,a,5778,a)].">
      <j1 rule="hyper" parents="1368 5778"/>
    </justification>
  </clause>

  <clause id="6133">
    <literal><![CDATA[
      x * (K(x,y) * (x \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,5776,a,b,5778,a)].">
      <j1 rule="hyper" parents="64 5776 5778"/>
    </justification>
  </clause>

  <clause id="6134">
    <literal><![CDATA[
      T(x * y,z) * L(y \ u,y,x) = K(x * y,z) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,632,a,b,5778,a)].">
      <j1 rule="hyper" parents="64 632 5778"/>
    </justification>
  </clause>

  <clause id="6135">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5583,a(flip),b,5778,a)].">
      <j1 rule="hyper" parents="64 5583 5778"/>
    </justification>
  </clause>

  <clause id="6136">
    <literal><![CDATA[
      (x \ y) / (T(x,z) \ y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,2402,a(flip),b,5778,a(flip))].">
      <j1 rule="hyper" parents="142 2402 5778"/>
    </justification>
  </clause>

  <clause id="6137">
    <literal><![CDATA[
      x \ (K(y,x) * z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,5778,a(flip),b,5011,a(flip))].">
      <j1 rule="hyper" parents="139 5778 5011"/>
    </justification>
  </clause>

  <clause id="6138">
    <literal><![CDATA[
      (T(x,y) \ L(K(x,y) * z,u,w)) / (T(x,y) \ 1) = L((x \ z) / (T(x,y) \ 1),u,w)
    ]]></literal>
    <justification jstring="[para(5778(a,1),1803(a,1,1,2,1))].">
      <j1 rule="para" parents="5778 1803"/>
    </justification>
  </clause>

  <clause id="6139">
    <literal><![CDATA[
      ((x \ y) / y) * ((y / (x * y)) \ z) = K(y / (x * y),x) * z
    ]]></literal>
    <justification jstring="[para(3007(a,1),5778(a,1,1))].">
      <j1 rule="para" parents="3007 5778"/>
    </justification>
  </clause>

  <clause id="6140">
    <literal><![CDATA[
      K(x,y / z) \ y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5013,a,b,5780,a),flip(a)].">
      <j1 rule="hyper" parents="64 5013 5780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6141">
    <literal><![CDATA[
      K(x,y / z) * (z * T(z \ y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(145,a,5013,a,b,5780,a(flip))].">
      <j1 rule="hyper" parents="145 5013 5780"/>
    </justification>
  </clause>

  <clause id="6142">
    <literal><![CDATA[
      K(x,y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5827,a,5782,a),flip(a)].">
      <j1 rule="hyper" parents="5827 5782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6143">
    <literal><![CDATA[
      K(x,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(5782(a,1),5827(a,1))].">
      <j1 rule="para" parents="5782 5827"/>
    </justification>
  </clause>

  <clause id="6144">
    <literal><![CDATA[
      K(x * (y * z),a(x,y,z) * (x * (y * z))) = K(x * (y * z),(x * y) * z)
    ]]></literal>
    <justification jstring="[para(88(a,1),6142(a,2,2))].">
      <j1 rule="para" parents="88 6142"/>
    </justification>
  </clause>

  <clause id="6145">
    <literal><![CDATA[
      x * K(x \ y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y / (y / x) = z
    ]]></literal>
    <justification jstring="[para(5790(a,1),290(a,1,2))].">
      <j1 rule="para" parents="5790 290"/>
    </justification>
  </clause>

  <clause id="6146">
    <literal><![CDATA[
      x * (y / (y / z)) = x * (z * K(z \ y,z))
    ]]></literal>
    <justification jstring="[para(5790(a,1),168(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5790 168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6148">
    <literal><![CDATA[
      (x * K(x \ y,x)) \ y = y / x
    ]]></literal>
    <justification jstring="[hyper(215,a,5793,a)].">
      <j1 rule="hyper" parents="215 5793"/>
    </justification>
  </clause>

  <clause id="6149">
    <literal><![CDATA[
      (x / (x / y)) * z = y * (K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(5793(a,2),4442(a,1,1))].">
      <j1 rule="para" parents="5793 4442"/>
    </justification>
  </clause>

  <clause id="6151">
    <literal><![CDATA[
      (T(x,y) \ z) / ((T(x,y) \ z) / T(y,x)) = T(y,x) * K(y \ (x \ z),T(y,x))
    ]]></literal>
    <justification jstring="[para(5019(a,1),5793(a,2,2,1))].">
      <j1 rule="para" parents="5019 5793"/>
    </justification>
  </clause>

  <clause id="6152">
    <literal><![CDATA[
      (x * (y / (y / z))) / z = x * K(z \ y,z)
    ]]></literal>
    <justification jstring="[para(5793(a,2),5703(a,1,1,2))].">
      <j1 rule="para" parents="5793 5703"/>
    </justification>
  </clause>

  <clause id="6154">
    <literal><![CDATA[
      x * (y * (T(y,z) \ u)) = x * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,5810,a,b,9,a)].">
      <j1 rule="hyper" parents="145 5810 9"/>
    </justification>
  </clause>

  <clause id="6155">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,2418,a,b,5810,a)].">
      <j1 rule="hyper" parents="64 2418 5810"/>
    </justification>
  </clause>

  <clause id="6156">
    <literal><![CDATA[
      K(x,y) \ z = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,5780,a(flip),b,5810,a)].">
      <j1 rule="hyper" parents="64 5780 5810"/>
    </justification>
  </clause>

  <clause id="6157">
    <literal><![CDATA[
      K(x,y) * (y \ z) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,2416,a(flip),b,5810,a),flip(a)].">
      <j1 rule="hyper" parents="64 2416 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6158">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(493,a,5780,a(flip),b,5810,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="493 5780 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6159">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,5810,a(flip),b,2418,a)].">
      <j1 rule="hyper" parents="225 5810 2418"/>
    </justification>
  </clause>

  <clause id="6160">
    <literal><![CDATA[
      x / (K(y,z) * x) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(225,a,5810,a(flip),b,5780,a(flip))].">
      <j1 rule="hyper" parents="225 5810 5780"/>
    </justification>
  </clause>

  <clause id="6161">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = z
    ]]></literal>
    <justification jstring="[hyper(145,a,5810,a(flip),b,5780,a(flip))].">
      <j1 rule="hyper" parents="145 5810 5780"/>
    </justification>
  </clause>

  <clause id="6162">
    <literal><![CDATA[
      (K(x,y) \ z) / z = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,5780,a(flip),b,5810,a(flip))].">
      <j1 rule="hyper" parents="142 5780 5810"/>
    </justification>
  </clause>

  <clause id="6163">
    <literal><![CDATA[
      K((x / y) / (y \ 1),z) = (T(x,z) / y) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(142,a,5130,a(flip),b,5810,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="142 5130 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6164">
    <literal><![CDATA[
      K(x,y) \ (K(y,x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(139,a,5780,a(flip),b,5810,a(flip))].">
      <j1 rule="hyper" parents="139 5780 5810"/>
    </justification>
  </clause>

  <clause id="6165">
    <literal><![CDATA[
      K(x,y) \ (T(y,x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,2416,a(flip),b,5810,a(flip))].">
      <j1 rule="hyper" parents="139 2416 5810"/>
    </justification>
  </clause>

  <clause id="6166">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ z) = K(y,x / y) * z
    ]]></literal>
    <justification jstring="[para(117(a,1),5810(a,1,2,1))].">
      <j1 rule="para" parents="117 5810"/>
    </justification>
  </clause>

  <clause id="6168">
    <literal><![CDATA[
      K(x \ y,x) * (((x \ y) \ y) * z) = x * z
    ]]></literal>
    <justification jstring="[para(503(a,1),5810(a,1,2)),flip(a)].">
      <j1 rule="para" parents="503 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6169">
    <literal><![CDATA[
      x \ (y * (K(z,y \ x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(y \ x,z) \ u,y \ x,y) = w
    ]]></literal>
    <justification jstring="[para(5810(a,1),1012(a,1,2,2))].">
      <j1 rule="para" parents="5810 1012"/>
    </justification>
  </clause>

  <clause id="6170">
    <literal><![CDATA[
      (x \ 1) \ L(K(y,x \ 1) * z,u,w) = x * L(x \ (T(x \ 1,y) \ z),u,w)
    ]]></literal>
    <justification jstring="[para(5810(a,1),5546(a,1,2,1))].">
      <j1 rule="para" parents="5810 5546"/>
    </justification>
  </clause>

  <clause id="6171">
    <literal><![CDATA[
      K(x,y) * T(T(y,x),z) = y * K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(5726(a,2),5810(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5726 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6172">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,z \ 1) = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(986,a,6156,a),flip(a)].">
      <j1 rule="hyper" parents="986 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6173">
    <literal><![CDATA[
      K(x,y) \ T(T(x,z),u) = T(T(x,z),u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,4006,a,b,6156,a),flip(a)].">
      <j1 rule="hyper" parents="373 4006 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6174">
    <literal><![CDATA[
      K(x \ y,x) \ y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5781,a(flip),b,6156,a),flip(a)].">
      <j1 rule="hyper" parents="373 5781 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6175">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(336,a,6156,a),flip(a)].">
      <j1 rule="hyper" parents="336 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6176">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * K(z,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,4001,a,b,6156,a)].">
      <j1 rule="hyper" parents="225 4001 6156"/>
    </justification>
  </clause>

  <clause id="6177">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(225,a,4097,a(flip),b,6156,a)].">
      <j1 rule="hyper" parents="225 4097 6156"/>
    </justification>
  </clause>

  <clause id="6178">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * K(y,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,3320,a,b,6156,a)].">
      <j1 rule="hyper" parents="145 3320 6156"/>
    </justification>
  </clause>

  <clause id="6179">
    <literal><![CDATA[
      K(x \ y,x) * (x * (y / x)) = y
    ]]></literal>
    <justification jstring="[hyper(145,a,5781,a(flip),b,6156,a)].">
      <j1 rule="hyper" parents="145 5781 6156"/>
    </justification>
  </clause>

  <clause id="6180">
    <literal><![CDATA[
      K(x,y) * (y \ K(y,x)) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(145,a,4097,a(flip),b,6156,a)].">
      <j1 rule="hyper" parents="145 4097 6156"/>
    </justification>
  </clause>

  <clause id="6181">
    <literal><![CDATA[
      T(x / K(y,z),K(y,z)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,247,a(flip),b,6156,a),flip(a)].">
      <j1 rule="hyper" parents="145 247 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6182">
    <literal><![CDATA[
      (K(x,y) \ z) * L(u,z,K(y,x)) = K(y,x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,6156,a,b,213,a)].">
      <j1 rule="hyper" parents="144 6156 213"/>
    </justification>
  </clause>

  <clause id="6183">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ z) = (x \ K(y,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,4560,a(flip),b,6156,a),flip(a)].">
      <j1 rule="hyper" parents="64 4560 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6184">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z \ 1,z) = a(K(y,x),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3844,a(flip),b,6156,a),flip(a)].">
      <j1 rule="hyper" parents="64 3844 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6185">
    <literal><![CDATA[
      K(x,x * x) * y = a(x,x,x) \ y
    ]]></literal>
    <justification jstring="[para(98(a,1),6156(a,1,1)),flip(a)].">
      <j1 rule="para" parents="98 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6186">
    <literal><![CDATA[
      x * (K(y,z) * u) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(6156(a,1),153(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6156 153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6187">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(6156(a,1),157(a,1))].">
      <j1 rule="para" parents="6156 157"/>
    </justification>
  </clause>

  <clause id="6188">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(6156(a,1),292(a,1,2))].">
      <j1 rule="para" parents="6156 292"/>
    </justification>
  </clause>

  <clause id="6189">
    <literal><![CDATA[
      x / (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6156(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6156 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6190">
    <literal><![CDATA[
      L(x \ (K(y,z) * u),x,K(z,y)) = (K(z,y) * x) \ u
    ]]></literal>
    <justification jstring="[para(6156(a,1),346(a,1,1,2))].">
      <j1 rule="para" parents="6156 346"/>
    </justification>
  </clause>

  <clause id="6191">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),K(y,x),z) = (z * K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(6156(a,1),346(a,1,1))].">
      <j1 rule="para" parents="6156 346"/>
    </justification>
  </clause>

  <clause id="6194">
    <literal><![CDATA[
      T((x \ K(y,z)) \ 1,K(z,y) * x) = (x \ K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(6156(a,1),746(a,1,2))].">
      <j1 rule="para" parents="6156 746"/>
    </justification>
  </clause>

  <clause id="6195">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(6156(a,1),421(a,1,1,3))].">
      <j1 rule="para" parents="6156 421"/>
    </justification>
  </clause>

  <clause id="6196">
    <literal><![CDATA[
      R(K(x,y) * R(K(y,x),z,u),K(y,x),z * u) = ((K(y,x) * z) * u) / (K(y,x) * (z * u))
    ]]></literal>
    <justification jstring="[para(6156(a,1),2295(a,1,1))].">
      <j1 rule="para" parents="6156 2295"/>
    </justification>
  </clause>

  <clause id="6197">
    <literal><![CDATA[
      x * (K(y,x) \ z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(6156(a,2),5776(a,1,2))].">
      <j1 rule="para" parents="6156 5776"/>
    </justification>
  </clause>

  <clause id="6198">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(6160(a,1),305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6160 305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6199">
    <literal><![CDATA[
      x / y != K(z,u) * (K(u,z) * w)
    ]]></literal>
    <literal><![CDATA[
      w * y = x
    ]]></literal>
    <justification jstring="[para(6160(a,1),389(a,2,1))].">
      <j1 rule="para" parents="6160 389"/>
    </justification>
  </clause>

  <clause id="6200">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,6161,a(flip),b,210,a)].">
      <j1 rule="hyper" parents="145 6161 210"/>
    </justification>
  </clause>

  <clause id="6201">
    <literal><![CDATA[
      x * L(y,K(z,u) * x,K(u,z)) = K(u,z) * ((K(z,u) * x) * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,6161,a(flip),b,213,a)].">
      <j1 rule="hyper" parents="144 6161 213"/>
    </justification>
  </clause>

  <clause id="6202">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (x * K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6161(a,1),737(a,1))].">
      <j1 rule="para" parents="6161 737"/>
    </justification>
  </clause>

  <clause id="6203">
    <literal><![CDATA[
      L(T(x,x \ (K(y,z) * u)),x \ (K(y,z) * u),K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[para(6161(a,1),409(a,2,2))].">
      <j1 rule="para" parents="6161 409"/>
    </justification>
  </clause>

  <clause id="6204">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(u,z)) = y \ (K(u,z) * (K(z,u) * (y * x)))
    ]]></literal>
    <justification jstring="[para(6161(a,1),602(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6161 602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6205">
    <literal><![CDATA[
      K(x,y) != z / u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ u = z
    ]]></literal>
    <justification jstring="[para(6162(a,1),47(a,1))].">
      <j1 rule="para" parents="6162 47"/>
    </justification>
  </clause>

  <clause id="6206">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(6162(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6162 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6208">
    <literal><![CDATA[
      x / y != K(z,u) * w
    ]]></literal>
    <literal><![CDATA[
      (K(u,z) \ w) * y = x
    ]]></literal>
    <justification jstring="[para(6162(a,1),389(a,2,1))].">
      <j1 rule="para" parents="6162 389"/>
    </justification>
  </clause>

  <clause id="6209">
    <literal><![CDATA[
      K(x,y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (K(y,x) \ z) = w
    ]]></literal>
    <justification jstring="[para(6162(a,1),391(a,1,1))].">
      <j1 rule="para" parents="6162 391"/>
    </justification>
  </clause>

  <clause id="6210">
    <literal><![CDATA[
      ((x * y) * z) / (T(R(x,y,z),u) * (y * z)) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(142,a,111,a(flip),b,5811,a)].">
      <j1 rule="hyper" parents="142 111 5811"/>
    </justification>
  </clause>

  <clause id="6211">
    <literal><![CDATA[
      T(x \ y,z) * T(x,x \ y) = K(z,x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,248,a(flip),b,5811,a),flip(a)].">
      <j1 rule="hyper" parents="139 248 5811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6213">
    <literal><![CDATA[
      K(x,y) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5811(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5811 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6215">
    <literal><![CDATA[
      K(x * x,y) * (((x * x) \ y) * z) = y * ((x * x) \ z)
    ]]></literal>
    <justification jstring="[para(952(a,1),5811(a,1,2))].">
      <j1 rule="para" parents="952 5811"/>
    </justification>
  </clause>

  <clause id="6216">
    <literal><![CDATA[
      K(x,y) * (K(z,T(y,x)) * u) = y * (T(T(y,x),z) \ u)
    ]]></literal>
    <justification jstring="[para(5810(a,1),5811(a,1,2))].">
      <j1 rule="para" parents="5810 5811"/>
    </justification>
  </clause>

  <clause id="6217">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) * K(1 / x,x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5821(a,1),5317(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5821 5317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6219">
    <literal><![CDATA[
      K(x,y) * (x / y) = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(4836,a,5829,a),flip(a)].">
      <j1 rule="hyper" parents="4836 5829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6220">
    <literal><![CDATA[
      ((x \ y) \ y) * (K(x \ y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(869,a,5829,a)].">
      <j1 rule="hyper" parents="869 5829"/>
    </justification>
  </clause>

  <clause id="6221">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(759,a,5829,a)].">
      <j1 rule="hyper" parents="759 5829"/>
    </justification>
  </clause>

  <clause id="6222">
    <literal><![CDATA[
      ((x * y) * z) / (K(u,R(x,y,z)) * (y * z)) = T(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(142,a,111,a(flip),b,5829,a)].">
      <j1 rule="hyper" parents="142 111 5829"/>
    </justification>
  </clause>

  <clause id="6223">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,5753,a,b,5829,a)].">
      <j1 rule="hyper" parents="139 5753 5829"/>
    </justification>
  </clause>

  <clause id="6224">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(z,y) * u) = T(T(y,z),x) \ (y * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,5829,a(flip),b,5829,a),flip(a)].">
      <j1 rule="hyper" parents="139 5829 5829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6225">
    <literal><![CDATA[
      K(x,T(y,z)) * K(z,y) = T(T(y,z),x) \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,5748,a(flip),b,5829,a),flip(a)].">
      <j1 rule="hyper" parents="139 5748 5829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6226">
    <literal><![CDATA[
      T(x,y) \ K(x \ 1,z) = K(y,x) * T(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,5743,a(flip),b,5829,a)].">
      <j1 rule="hyper" parents="139 5743 5829"/>
    </justification>
  </clause>

  <clause id="6228">
    <literal><![CDATA[
      T(x * y,z) \ (x * (y * u)) = K(z,x * y) * L(u,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,100,a(flip),b,5829,a)].">
      <j1 rule="hyper" parents="139 100 5829"/>
    </justification>
  </clause>

  <clause id="6229">
    <literal><![CDATA[
      T(x / y,z) \ x = K(z,x / y) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,12,a(flip),b,5829,a)].">
      <j1 rule="hyper" parents="139 12 5829"/>
    </justification>
  </clause>

  <clause id="6230">
    <literal><![CDATA[
      ((x \ y) \ y) \ (x * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[hyper(35,a,505,a,b,5829,a)].">
      <j1 rule="hyper" parents="35 505 5829"/>
    </justification>
  </clause>

  <clause id="6231">
    <literal><![CDATA[
      (x / y) / T(x,y \ 1) = x \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(225,a,4387,a(flip),b,5836,a)].">
      <j1 rule="hyper" parents="225 4387 5836"/>
    </justification>
  </clause>

  <clause id="6232">
    <literal><![CDATA[
      (x \ (x / y)) * T(x,y \ 1) = x / y
    ]]></literal>
    <justification jstring="[hyper(145,a,4387,a(flip),b,5836,a)].">
      <j1 rule="hyper" parents="145 4387 5836"/>
    </justification>
  </clause>

  <clause id="6235">
    <literal><![CDATA[
      T(x * K(x * y,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4686,a,5857,a),flip(a)].">
      <j1 rule="hyper" parents="4686 5857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6236">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(2833,a,5857,a),flip(a)].">
      <j1 rule="hyper" parents="2833 5857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6237">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(41,a,5785,a,b,5857,a)].">
      <j1 rule="hyper" parents="41 5785 5857"/>
    </justification>
  </clause>

  <clause id="6238">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,z) = T(y * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(41,a,5727,a,b,5857,a)].">
      <j1 rule="hyper" parents="41 5727 5857"/>
    </justification>
  </clause>

  <clause id="6239">
    <literal><![CDATA[
      T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,3188,a,b,5857,a),flip(a)].">
      <j1 rule="hyper" parents="41 3188 5857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6240">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(z * K(y,z),u) = x
    ]]></literal>
    <justification jstring="[para(5857(a,1),50(a,2)),flip(b)].">
      <j1 rule="para" parents="5857 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6241">
    <literal><![CDATA[
      K(x,y \ 1) * (x \ (y \ x)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[para(4927(a,1),5873(a,1,1))].">
      <j1 rule="para" parents="4927 5873"/>
    </justification>
  </clause>

  <clause id="6242">
    <literal><![CDATA[
      (x / T(y,z)) / K(z,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(786,a,5875,a),flip(a)].">
      <j1 rule="hyper" parents="786 5875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6243">
    <literal><![CDATA[
      (x * y) / T(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(154,a,5875,a)].">
      <j1 rule="hyper" parents="154 5875"/>
    </justification>
  </clause>

  <clause id="6244">
    <literal><![CDATA[
      R(x \ 1,x,y) * K(z,y) = (x \ y) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,2998,a(flip),b,5875,a),flip(a)].">
      <j1 rule="hyper" parents="142 2998 5875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6245">
    <literal><![CDATA[
      (x / y) * K(z,y) = x / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,12,a(flip),b,5875,a),flip(a)].">
      <j1 rule="hyper" parents="142 12 5875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6246">
    <literal><![CDATA[
      x / T(y \ x,z) = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(142,a,10,a(flip),b,5875,a)].">
      <j1 rule="hyper" parents="142 10 5875"/>
    </justification>
  </clause>

  <clause id="6247">
    <literal><![CDATA[
      (x * K(y,x \ z)) \ z = T(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,5875,a)].">
      <j1 rule="hyper" parents="139 10 5875"/>
    </justification>
  </clause>

  <clause id="6248">
    <literal><![CDATA[
      (x \ y) * K(y,x) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,4838,a,b,5875,a),flip(a)].">
      <j1 rule="hyper" parents="36 4838 5875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6249">
    <literal><![CDATA[
      (x * T(y,z)) * K(z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(36,a,2515,a(flip),b,5875,a),flip(a)].">
      <j1 rule="hyper" parents="36 2515 5875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6250">
    <literal><![CDATA[
      T(x,y) * T(x,y) = x * T(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(5749(a,1),5875(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5749 5875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6251">
    <literal><![CDATA[
      (x / y) * T(y \ x,y) = (y \ x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(5774(a,1),5875(a,1,1))].">
      <j1 rule="para" parents="5774 5875"/>
    </justification>
  </clause>

  <clause id="6252">
    <literal><![CDATA[
      T(x,K(y \ x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(546,a,5919,a)].">
      <j1 rule="hyper" parents="546 5919"/>
    </justification>
  </clause>

  <clause id="6253">
    <literal><![CDATA[
      K((x * x) \ y,x * x) = T(y,x * x) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,798,a(flip),b,5919,a),flip(a)].">
      <j1 rule="hyper" parents="142 798 5919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6254">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(5919(a,1),3437(a,2,2))].">
      <j1 rule="para" parents="5919 3437"/>
    </justification>
  </clause>

  <clause id="6255">
    <literal><![CDATA[
      R(x,y,z) * (x * (((u * R(x,y,z)) / u) \ 1)) = x * K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5932(a,2),1897(a,2,2))].">
      <j1 rule="para" parents="5932 1897"/>
    </justification>
  </clause>

  <clause id="6256">
    <literal><![CDATA[
      (x \ y) \ K(x \ y,x) = (y / x) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),5934(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 5934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6257">
    <literal><![CDATA[
      (x * y) \ K(x * y,y) = (L(y,x,y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(4725(a,1),5934(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4725 5934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6258">
    <literal><![CDATA[
      (x / (x / y)) \ 1 = y \ K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(4707(a,1),5934(a,1,1))].">
      <j1 rule="para" parents="4707 5934"/>
    </justification>
  </clause>

  <clause id="6259">
    <literal><![CDATA[
      T(x,y \ K(y,z)) = T(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(5934(a,1),4818(a,1,2))].">
      <j1 rule="para" parents="5934 4818"/>
    </justification>
  </clause>

  <clause id="6262">
    <literal><![CDATA[
      K(((x / y) \ 1) \ y,(x / y) \ 1) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(4417,a,5961,a)].">
      <j1 rule="hyper" parents="4417 5961"/>
    </justification>
  </clause>

  <clause id="6263">
    <literal><![CDATA[
      T(x,K(y,y \ x)) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,5963,a,b,5781,a)].">
      <j1 rule="hyper" parents="269 5963 5781"/>
    </justification>
  </clause>

  <clause id="6264">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (1 * (x / y))
    ]]></literal>
    <justification jstring="[para(7(a,2),5963(a,2,2))].">
      <j1 rule="para" parents="7 5963"/>
    </justification>
  </clause>

  <clause id="6265">
    <literal><![CDATA[
      (x * (y / x)) \ (y * (K(x,x \ y) * z)) = L(z,K(x,x \ y),y)
    ]]></literal>
    <justification jstring="[para(5963(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5963 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6266">
    <literal><![CDATA[
      x * (y / x) != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(5963(a,1),44(a,1))].">
      <j1 rule="para" parents="5963 44"/>
    </justification>
  </clause>

  <clause id="6267">
    <literal><![CDATA[
      T(x,y) * K(x * y,(x * y) \ T(x,y)) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(4716(a,1),5963(a,2,2))].">
      <j1 rule="para" parents="4716 5963"/>
    </justification>
  </clause>

  <clause id="6268">
    <literal><![CDATA[
      T(1 / (x \ y),y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(142,a,924,a(flip),b,5989,a),flip(a)].">
      <j1 rule="hyper" parents="142 924 5989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6269">
    <literal><![CDATA[
      (K(x \ 1,y) * z) / (x * z) = R(T(1 / x,y),x,z)
    ]]></literal>
    <justification jstring="[para(5989(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5989 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6270">
    <literal><![CDATA[
      K(x,x \ y) * ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(39,a,5045,a,b,6020,a),flip(a)].">
      <j1 rule="hyper" parents="39 5045 6020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6271">
    <literal><![CDATA[
      (T(x,y) \ 1) * y = (x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(6039(a,1),5875(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6039 5875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6272">
    <literal><![CDATA[
      (x / y) * K(x,1 / y) = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,6042,a(flip),b,97,a)].">
      <j1 rule="hyper" parents="145 6042 97"/>
    </justification>
  </clause>

  <clause id="6273">
    <literal><![CDATA[
      K(x,1 / (y \ x)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(79(a,1),6042(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 6042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6274">
    <literal><![CDATA[
      x * K(y,1 / (x \ z)) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(6042(a,1),3097(a,1,2))].">
      <j1 rule="para" parents="6042 3097"/>
    </justification>
  </clause>

  <clause id="6276">
    <literal><![CDATA[
      (T(x,y) * T(K(x,y) \ z,u)) / T(x,y) = T((x * z) / T(x,y),u)
    ]]></literal>
    <justification jstring="[para(6065(a,1),531(a,1,1,2,1))].">
      <j1 rule="para" parents="6065 531"/>
    </justification>
  </clause>

  <clause id="6277">
    <literal><![CDATA[
      K(x,x \ y) * (x \ (x \ y)) = x \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,4473,a(flip),b,6066,a)].">
      <j1 rule="hyper" parents="145 4473 6066"/>
    </justification>
  </clause>

  <clause id="6278">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(6066(a,1),290(a,1,2))].">
      <j1 rule="para" parents="6066 290"/>
    </justification>
  </clause>

  <clause id="6279">
    <literal><![CDATA[
      L(x \ (T(y,z) \ u),x,K(y,z)) = (K(y,z) * x) \ (y \ u)
    ]]></literal>
    <justification jstring="[para(6066(a,1),346(a,1,1,2))].">
      <j1 rule="para" parents="6066 346"/>
    </justification>
  </clause>

  <clause id="6281">
    <literal><![CDATA[
      x * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(6067(a,1),739(a,1))].">
      <j1 rule="para" parents="6067 739"/>
    </justification>
  </clause>

  <clause id="6282">
    <literal><![CDATA[
      K(T(x,y) \ (x * z),u) = K(K(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(6067(a,1),1571(a,1,1,2))].">
      <j1 rule="para" parents="6067 1571"/>
    </justification>
  </clause>

  <clause id="6283">
    <literal><![CDATA[
      K(x / y,y) * ((y \ x) \ z) = (x / y) \ z
    ]]></literal>
    <justification jstring="[para(117(a,1),6075(a,1,2,1))].">
      <j1 rule="para" parents="117 6075"/>
    </justification>
  </clause>

  <clause id="6284">
    <literal><![CDATA[
      T(x,y) * (y \ z) = x * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(6075(a,1),5829(a,1,2))].">
      <j1 rule="para" parents="6075 5829"/>
    </justification>
  </clause>

  <clause id="6285">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,z,K(y,x)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,6104,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="145 6104 18"/>
    </justification>
  </clause>

  <clause id="6286">
    <literal><![CDATA[
      R(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(5713,a,6106,a),flip(a)].">
      <j1 rule="hyper" parents="5713 6106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6289">
    <literal><![CDATA[
      ((x \ 1) * x) \ (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(294(a,1),6131(a,1,1))].">
      <j1 rule="para" parents="294 6131"/>
    </justification>
  </clause>

  <clause id="6290">
    <literal><![CDATA[
      (L(x,y,z) \ u) / (L(T(x,w),y,z) \ u) = K(L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(25(a,2),6136(a,1,2,1))].">
      <j1 rule="para" parents="25 6136"/>
    </justification>
  </clause>

  <clause id="6291">
    <literal><![CDATA[
      ((x \ y) \ y) \ z = x \ (K(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,362,a(flip),b,6137,a)].">
      <j1 rule="hyper" parents="373 362 6137"/>
    </justification>
  </clause>

  <clause id="6292">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[hyper(39,a,5045,a(flip),b,6137,a),flip(a)].">
      <j1 rule="hyper" parents="39 5045 6137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6293">
    <literal><![CDATA[
      K(x,y) * (1 / y) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(39,a,3978,a(flip),b,6137,a),flip(a)].">
      <j1 rule="hyper" parents="39 3978 6137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6294">
    <literal><![CDATA[
      x \ (K(y,T(x,y)) * z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[para(5923(a,2),6137(a,1,2,1))].">
      <j1 rule="para" parents="5923 6137"/>
    </justification>
  </clause>

  <clause id="6295">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (L(x,z,u) * w) = K(y,L(x,z,u)) * w
    ]]></literal>
    <justification jstring="[para(25(a,2),6155(a,1,1))].">
      <j1 rule="para" parents="25 6155"/>
    </justification>
  </clause>

  <clause id="6296">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(6155(a,1),290(a,1,2))].">
      <j1 rule="para" parents="6155 290"/>
    </justification>
  </clause>

  <clause id="6297">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) \ T(y,x)) = x \ ((x \ 1) \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,1477,a(flip),b,6157,a),flip(a)].">
      <j1 rule="hyper" parents="373 1477 6157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6299">
    <literal><![CDATA[
      K(x,y) * (T(y,x) \ z) = T(T(y,x),x) \ z
    ]]></literal>
    <justification jstring="[para(5923(a,1),6157(a,1,1))].">
      <j1 rule="para" parents="5923 6157"/>
    </justification>
  </clause>

  <clause id="6300">
    <literal><![CDATA[
      K(x,y) * (z * R(T(K(y,x),z),u,w)) = (K(x,y) * R(K(x,y) \ 1,u,w)) * z
    ]]></literal>
    <justification jstring="[para(6158(a,1),2739(a,1,2,2,1))].">
      <j1 rule="para" parents="6158 2739"/>
    </justification>
  </clause>

  <clause id="6301">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(6165(a,1),290(a,1,2))].">
      <j1 rule="para" parents="6165 290"/>
    </justification>
  </clause>

  <clause id="6302">
    <literal><![CDATA[
      x \ y != K(z \ u,z) * (z * (u / z))
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(6174(a,1),395(a,2,2))].">
      <j1 rule="para" parents="6174 395"/>
    </justification>
  </clause>

  <clause id="6303">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(6180(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6180 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6304">
    <literal><![CDATA[
      K(x,y) \ T(x,x * y) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,4831,a(flip),b,6197,a),flip(a)].">
      <j1 rule="hyper" parents="35 4831 6197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6305">
    <literal><![CDATA[
      K(x,x * y) \ T(x,y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,4752,a(flip),b,6197,a),flip(a)].">
      <j1 rule="hyper" parents="35 4752 6197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6306">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,x / y,K(x,y)) = K(x,y) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,6219,a(flip),b,213,a)].">
      <j1 rule="hyper" parents="144 6219 213"/>
    </justification>
  </clause>

  <clause id="6307">
    <literal><![CDATA[
      R(K(x,y),x / y,z) \ ((x / T(y,x)) * z) = (x / y) * z
    ]]></literal>
    <justification jstring="[para(6219(a,1),210(a,1,2,1))].">
      <j1 rule="para" parents="6219 210"/>
    </justification>
  </clause>

  <clause id="6308">
    <literal><![CDATA[
      (x / y) \ (x / T(y,z)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(215,a,6242,a)].">
      <j1 rule="hyper" parents="215 6242"/>
    </justification>
  </clause>

  <clause id="6309">
    <literal><![CDATA[
      (x / y) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6242(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6242 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6310">
    <literal><![CDATA[
      R(x * K(y,z),K(u,w),u) = (x * z) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6286,a,b,6243,a)].">
      <j1 rule="hyper" parents="373 6286 6243"/>
    </justification>
  </clause>

  <clause id="6311">
    <literal><![CDATA[
      (x / T(y,z)) * y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2524,a(flip),b,6243,a)].">
      <j1 rule="hyper" parents="64 2524 6243"/>
    </justification>
  </clause>

  <clause id="6312">
    <literal><![CDATA[
      (x * K(y,z)) / z = x / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,6243,a(flip),b,2524,a(flip))].">
      <j1 rule="hyper" parents="142 6243 2524"/>
    </justification>
  </clause>

  <clause id="6313">
    <literal><![CDATA[
      L(x,y,z * K(u,z)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(6243(a,1),2197(a,1,3))].">
      <j1 rule="para" parents="6243 2197"/>
    </justification>
  </clause>

  <clause id="6315">
    <literal><![CDATA[
      (x / y) * K(x,y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,4630,a,b,6245,a),flip(a)].">
      <j1 rule="hyper" parents="373 4630 6245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6316">
    <literal><![CDATA[
      x / ((y \ z) \ z) = (x / y) * K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,363,a(flip),b,6245,a)].">
      <j1 rule="hyper" parents="373 363 6245"/>
    </justification>
  </clause>

  <clause id="6319">
    <literal><![CDATA[
      (x / T(y,z)) * K(z,y) = x / T(T(y,z),z)
    ]]></literal>
    <justification jstring="[para(5923(a,1),6245(a,1,2))].">
      <j1 rule="para" parents="5923 6245"/>
    </justification>
  </clause>

  <clause id="6320">
    <literal><![CDATA[
      x \ T(x * y,x) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),6248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 6248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6321">
    <literal><![CDATA[
      T(x * T(y,z),K(z,y)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(269,a,6249,a,b,6161,a)].">
      <j1 rule="hyper" parents="269 6249 6161"/>
    </justification>
  </clause>

  <clause id="6322">
    <literal><![CDATA[
      (x * y) / K(z,y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(154,a,6249,a)].">
      <j1 rule="hyper" parents="154 6249"/>
    </justification>
  </clause>

  <clause id="6323">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(149,a,6249,a)].">
      <j1 rule="hyper" parents="149 6249"/>
    </justification>
  </clause>

  <clause id="6324">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,6249,a)].">
      <j1 rule="hyper" parents="139 10 6249"/>
    </justification>
  </clause>

  <clause id="6326">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) * K(y \ z,y) = x * y
    ]]></literal>
    <justification jstring="[para(116(a,1),6249(a,1,1,2))].">
      <j1 rule="para" parents="116 6249"/>
    </justification>
  </clause>

  <clause id="6327">
    <literal><![CDATA[
      R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = (((x * y) * T(z,u)) * K(u,z)) / (y * z)
    ]]></literal>
    <justification jstring="[para(6249(a,1),660(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6249 660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6328">
    <literal><![CDATA[
      (x \ (y \ x)) * x = (y \ x) * K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(4577(a,1),6249(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4577 6249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6329">
    <literal><![CDATA[
      (x * y) * K(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[para(4650(a,1),6249(a,1,1))].">
      <j1 rule="para" parents="4650 6249"/>
    </justification>
  </clause>

  <clause id="6330">
    <literal><![CDATA[
      T(x,y) * (1 / y) = x * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,6293,a(flip),b,6071,a),flip(a)].">
      <j1 rule="hyper" parents="145 6293 6071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6331">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      R(x / T(z,y),z,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6311(a,1),669(a,1,1))].">
      <j1 rule="para" parents="6311 669"/>
    </justification>
  </clause>

  <clause id="6332">
    <literal><![CDATA[
      ((1 / x) \ y) * (x \ 1) = y * K(x \ y,x \ 1)
    ]]></literal>
    <justification jstring="[para(1691(a,1),6311(a,1,1))].">
      <j1 rule="para" parents="1691 6311"/>
    </justification>
  </clause>

  <clause id="6333">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(4591(a,1),6311(a,1,1))].">
      <j1 rule="para" parents="4591 6311"/>
    </justification>
  </clause>

  <clause id="6334">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = y * K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4915(a,1),6311(a,1,1))].">
      <j1 rule="para" parents="4915 6311"/>
    </justification>
  </clause>

  <clause id="6335">
    <literal><![CDATA[
      T(T(x * K(y,x),z),x * y) = T(L(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(5899(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5899 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6336">
    <literal><![CDATA[
      K(T(x,y) \ (x * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(6067(a,1),6038(a,1,1,2))].">
      <j1 rule="para" parents="6067 6038"/>
    </justification>
  </clause>

  <clause id="6337">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = z
    ]]></literal>
    <justification jstring="[para(79(a,1),6045(a,1,2))].">
      <j1 rule="para" parents="79 6045"/>
    </justification>
  </clause>

  <clause id="6339">
    <literal><![CDATA[
      T((1 / x) \ y,y * x) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(674(a,1),6063(a,1,2))].">
      <j1 rule="para" parents="674 6063"/>
    </justification>
  </clause>

  <clause id="6340">
    <literal><![CDATA[
      T(x,y) \ T(x,x * y) = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,6080,a(flip),b,5810,a),flip(a)].">
      <j1 rule="hyper" parents="139 6080 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6341">
    <literal><![CDATA[
      K(x,y) = T(y,y * x) \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,6080,a(flip),b,4001,a),flip(a)].">
      <j1 rule="hyper" parents="139 6080 4001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6342">
    <literal><![CDATA[
      T(x,y) * K(x * y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4004,a,6081,a)].">
      <j1 rule="hyper" parents="4004 6081"/>
    </justification>
  </clause>

  <clause id="6343">
    <literal><![CDATA[
      T(x,x * y) \ T(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,6081,a(flip),b,5810,a),flip(a)].">
      <j1 rule="hyper" parents="139 6081 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6344">
    <literal><![CDATA[
      T(x,y) \ R(x,y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,6081,a(flip),b,4001,a)].">
      <j1 rule="hyper" parents="139 6081 4001"/>
    </justification>
  </clause>

  <clause id="6345">
    <literal><![CDATA[
      K(x \ 1,x) = K(x,x * x)
    ]]></literal>
    <justification jstring="[hyper(36,a,3629,a(flip),b,6185,a)].">
      <j1 rule="hyper" parents="36 3629 6185"/>
    </justification>
  </clause>

  <clause id="6346">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(5157(a,1),6188(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5157 6188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6347">
    <literal><![CDATA[
      x \ T(x * y,y) = y * K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,4552,a,b,6235,a)].">
      <j1 rule="hyper" parents="41 4552 6235"/>
    </justification>
  </clause>

  <clause id="6348">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = T(R(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(6235(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6235 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6349">
    <literal><![CDATA[
      K(x,y) \ T(x,y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4683(a,2),6304(a,1,2))].">
      <j1 rule="para" parents="4683 6304"/>
    </justification>
  </clause>

  <clause id="6350">
    <literal><![CDATA[
      K(x,y) \ T(x,x \ y) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),6305(a,1,1,2))].">
      <j1 rule="para" parents="10 6305"/>
    </justification>
  </clause>

  <clause id="6351">
    <literal><![CDATA[
      K(x,x * y) \ (L(K(x,x * y),z,u) * T(x,y)) = L(K(x,x * y),z,u) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(6305(a,1),2325(a,2,2))].">
      <j1 rule="para" parents="6305 2325"/>
    </justification>
  </clause>

  <clause id="6352">
    <literal><![CDATA[
      K(x * ((y * y) \ 1),x) = T(x,(y * y) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,1608,a(flip),b,6342,a),flip(a)].">
      <j1 rule="hyper" parents="139 1608 6342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6353">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,6342,a(flip),b,5776,a),flip(a)].">
      <j1 rule="hyper" parents="139 6342 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6354">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = L(K(y * z,y),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(6342(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6342 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6355">
    <literal><![CDATA[
      T(x,y) * (K(x * y,x) * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(6342(a,1),4443(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6342 4443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6356">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,5729,a(flip),b,4534,a(flip))].">
      <j1 rule="hyper" parents="139 5729 4534"/>
    </justification>
  </clause>

  <clause id="6357">
    <literal><![CDATA[
      x * ((y * T(y \ z,u)) / z) = x * K(z / y,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,5732,a,b,9,a)].">
      <j1 rule="hyper" parents="145 5732 9"/>
    </justification>
  </clause>

  <clause id="6358">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) = K((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5732(a,1,1,2,1))].">
      <j1 rule="para" parents="9 5732"/>
    </justification>
  </clause>

  <clause id="6359">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3462,a(flip),b,5736,a)].">
      <j1 rule="hyper" parents="64 3462 5736"/>
    </justification>
  </clause>

  <clause id="6360">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,5736,a(flip),b,3095,a(flip))].">
      <j1 rule="hyper" parents="145 5736 3095"/>
    </justification>
  </clause>

  <clause id="6361">
    <literal><![CDATA[
      K(x,y \ 1) / y = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,5736,a(flip),b,1237,a)].">
      <j1 rule="hyper" parents="142 5736 1237"/>
    </justification>
  </clause>

  <clause id="6362">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(5736(a,1),1961(a,2,2))].">
      <j1 rule="para" parents="5736 1961"/>
    </justification>
  </clause>

  <clause id="6363">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(5736(a,1),3302(a,2,1))].">
      <j1 rule="para" parents="5736 3302"/>
    </justification>
  </clause>

  <clause id="6364">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) * (z * u) = ((y * z) * ((x * ((y * z) \ z)) / x)) * u
    ]]></literal>
    <justification jstring="[para(5736(a,1),4993(a,1,1))].">
      <j1 rule="para" parents="5736 4993"/>
    </justification>
  </clause>

  <clause id="6365">
    <literal><![CDATA[
      K(x,y) = (x \ 1) * R(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[para(1423(a,1),5741(a,2,2))].">
      <j1 rule="para" parents="1423 5741"/>
    </justification>
  </clause>

  <clause id="6366">
    <literal><![CDATA[
      (x / y) * (y * R(T(y,z),y,y)) = (x / (y \ 1)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6365(a,2),1627(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6365 1627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6367">
    <literal><![CDATA[
      K((x * y) / x,z) * (x * y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),5754(a,2,2,1))].">
      <j1 rule="para" parents="9 5754"/>
    </justification>
  </clause>

  <clause id="6368">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5726,a,b,5771,a),flip(a)].">
      <j1 rule="hyper" parents="373 5726 5771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6369">
    <literal><![CDATA[
      K(x,y) * K(y,y \ 1) = y * (K(x,y) / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,5803,a(flip),b,6137,a),flip(a)].">
      <j1 rule="hyper" parents="145 5803 6137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6370">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),5809(a,1,2,1,1))].">
      <j1 rule="para" parents="10 5809"/>
    </justification>
  </clause>

  <clause id="6371">
    <literal><![CDATA[
      x * ((y / (y / x)) \ z) = K(x,y / x) * z
    ]]></literal>
    <justification jstring="[para(12(a,1),5809(a,1,2,1,1))].">
      <j1 rule="para" parents="12 5809"/>
    </justification>
  </clause>

  <clause id="6372">
    <literal><![CDATA[
      T(x,x * y) * (L(x,y,x) \ z) = K(T(x,x * y),y) * z
    ]]></literal>
    <justification jstring="[para(769(a,1),5809(a,1,2,1))].">
      <j1 rule="para" parents="769 5809"/>
    </justification>
  </clause>

  <clause id="6373">
    <literal><![CDATA[
      x * ((y / (y / x)) \ z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(4707(a,1),5809(a,1,2,1))].">
      <j1 rule="para" parents="4707 5809"/>
    </justification>
  </clause>

  <clause id="6374">
    <literal><![CDATA[
      K(x,((y \ z) / z) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5826,a,5834,a)].">
      <j1 rule="hyper" parents="5826 5834"/>
    </justification>
  </clause>

  <clause id="6375">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(82(a,1),6374(a,1,2,1,1))].">
      <j1 rule="para" parents="82 6374"/>
    </justification>
  </clause>

  <clause id="6376">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y) * 1
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a,b,6375,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 6375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6377">
    <literal><![CDATA[
      K(x,1 / (y / z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6041,a,b,6375,a)].">
      <j1 rule="hyper" parents="64 6041 6375"/>
    </justification>
  </clause>

  <clause id="6378">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),6375(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 6375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6379">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),6375(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 6375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6380">
    <literal><![CDATA[
      T(x / y,K(z,y / x)) = x / y
    ]]></literal>
    <justification jstring="[para(6375(a,1),3347(a,1,2))].">
      <j1 rule="para" parents="6375 3347"/>
    </justification>
  </clause>

  <clause id="6381">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(11(a,1),6377(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 6377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6382">
    <literal><![CDATA[
      K(x * y,x \ 1) * ((x * y) \ y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(6378(a,1),5873(a,1,1))].">
      <j1 rule="para" parents="6378 5873"/>
    </justification>
  </clause>

  <clause id="6384">
    <literal><![CDATA[
      ((x * y) \ y) * K(x * y,1 / x) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(6381(a,1),5822(a,1,2))].">
      <j1 rule="para" parents="6381 5822"/>
    </justification>
  </clause>

  <clause id="6385">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6381(a,2),6045(a,1))].">
      <j1 rule="para" parents="6381 6045"/>
    </justification>
  </clause>

  <clause id="6386">
    <literal><![CDATA[
      T(R(x * K(y,x),x,x),y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,1417,a,b,5858,a),flip(a)].">
      <j1 rule="hyper" parents="373 1417 5858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6387">
    <literal><![CDATA[
      R(x * K(y,x),y,x) = x * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,6235,a,b,5858,a),flip(a)].">
      <j1 rule="hyper" parents="41 6235 5858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6388">
    <literal><![CDATA[
      R(x,y,z) * K(u,R(x,y,z)) = R(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,5785,a,b,5858,a)].">
      <j1 rule="hyper" parents="41 5785 5858"/>
    </justification>
  </clause>

  <clause id="6390">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,241,a,b,5888,a),flip(a)].">
      <j1 rule="hyper" parents="373 241 5888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6391">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z,x),y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,5900,a,b,5721,a(flip))].">
      <j1 rule="hyper" parents="139 5900 5721"/>
    </justification>
  </clause>

  <clause id="6392">
    <literal><![CDATA[
      x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,6315,a(flip),b,5911,a),flip(a)].">
      <j1 rule="hyper" parents="64 6315 5911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6393">
    <literal><![CDATA[
      x * (K(y,x) * K(z,y)) = (y * x) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6245,a(flip),b,5911,a),flip(a)].">
      <j1 rule="hyper" parents="64 6245 5911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6394">
    <literal><![CDATA[
      (x * (K(y * z,x) * y)) * z = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,5911,a(flip),b,1204,a)].">
      <j1 rule="hyper" parents="144 5911 1204"/>
    </justification>
  </clause>

  <clause id="6395">
    <literal><![CDATA[
      K(x,y) * (K((x * y) / x,z) * u) = y \ (T((x * y) / x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,5776,a(flip),b,5911,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 5776 5911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6396">
    <literal><![CDATA[
      (x / y) * (K(y,y \ x) * z) = ((y * (x / y)) / y) * z
    ]]></literal>
    <justification jstring="[para(5926(a,1),5911(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5926 5911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6397">
    <literal><![CDATA[
      ((x * y) / x) * (x / y) = y * (x / T(y,x))
    ]]></literal>
    <justification jstring="[para(6219(a,1),5911(a,2,2))].">
      <j1 rule="para" parents="6219 5911"/>
    </justification>
  </clause>

  <clause id="6398">
    <literal><![CDATA[
      a((x \ y) * K(y / (y / x),x \ y),y / (y / x),z) = a(x \ y,x,z)
    ]]></literal>
    <justification jstring="[para(4769(a,1),5915(a,2,2))].">
      <j1 rule="para" parents="4769 5915"/>
    </justification>
  </clause>

  <clause id="6399">
    <literal><![CDATA[
      (x / ((y * z) / y)) * z = x / K(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2592,a(flip),b,5917,a)].">
      <j1 rule="hyper" parents="64 2592 5917"/>
    </justification>
  </clause>

  <clause id="6400">
    <literal><![CDATA[
      (x / ((y * z) / y)) * K(y,z) = x / z
    ]]></literal>
    <justification jstring="[hyper(144,a,170,a(flip),b,5917,a(flip))].">
      <j1 rule="hyper" parents="144 170 5917"/>
    </justification>
  </clause>

  <clause id="6401">
    <literal><![CDATA[
      x \ (x \ (T(x,y) * z)) = (K(x,y) \ x) \ z
    ]]></literal>
    <justification jstring="[para(6221(a,2),5971(a,2,2)),flip(a)].">
      <j1 rule="para" parents="6221 5971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6402">
    <literal><![CDATA[
      x * ((y * (x / y)) \ y) = x / (x / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,6018,a,b,xx)].">
      <j1 rule="hyper" parents="145 6018"/>
    </justification>
  </clause>

  <clause id="6403">
    <literal><![CDATA[
      x * (K(x,y) * T(z,x)) = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5776,a,b,6022,a)].">
      <j1 rule="hyper" parents="373 5776 6022"/>
    </justification>
  </clause>

  <clause id="6404">
    <literal><![CDATA[
      K(x / y,y) * (z * (x / y)) = (y \ x) * T(z,x / y)
    ]]></literal>
    <justification jstring="[para(117(a,1),6022(a,2,1))].">
      <j1 rule="para" parents="117 6022"/>
    </justification>
  </clause>

  <clause id="6405">
    <literal><![CDATA[
      K(x,y) * T(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4072,a(flip),b,6036,a)].">
      <j1 rule="hyper" parents="373 4072 6036"/>
    </justification>
  </clause>

  <clause id="6406">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) / T(x,y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,4072,a(flip),b,6036,a)].">
      <j1 rule="hyper" parents="142 4072 6036"/>
    </justification>
  </clause>

  <clause id="6407">
    <literal><![CDATA[
      T(x,y) * K(x,z) = T(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4072,a,b,6036,a)].">
      <j1 rule="hyper" parents="64 4072 6036"/>
    </justification>
  </clause>

  <clause id="6408">
    <literal><![CDATA[
      K(x,y) * T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(6036(a,2),4085(a,1))].">
      <j1 rule="para" parents="6036 4085"/>
    </justification>
  </clause>

  <clause id="6409">
    <literal><![CDATA[
      T(x / y,z) * ((y \ x) \ 1) = K(x / y,z) * K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,6037,a(flip),b,6020,a)].">
      <j1 rule="hyper" parents="145 6037 6020"/>
    </justification>
  </clause>

  <clause id="6410">
    <literal><![CDATA[
      x \ (y \ ((y * z) / y)) = x \ (K(y,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(139,a,6072,a,b,10,a)].">
      <j1 rule="hyper" parents="139 6072 10"/>
    </justification>
  </clause>

  <clause id="6411">
    <literal><![CDATA[
      x \ (y * K(x,y)) = K(x,y) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5889,a(flip),b,6072,a)].">
      <j1 rule="hyper" parents="64 5889 6072"/>
    </justification>
  </clause>

  <clause id="6412">
    <literal><![CDATA[
      L(x \ (y \ z),x,K(y,z)) = (K(y,z) * x) \ (y \ ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(6072(a,2),102(a,2,2))].">
      <j1 rule="para" parents="6072 102"/>
    </justification>
  </clause>

  <clause id="6413">
    <literal><![CDATA[
      (x / (x / y)) \ z = K(y,y \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4707(a,1),6077(a,1,1))].">
      <j1 rule="para" parents="4707 6077"/>
    </justification>
  </clause>

  <clause id="6414">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(5721(a,1),6077(a,1,1))].">
      <j1 rule="para" parents="5721 6077"/>
    </justification>
  </clause>

  <clause id="6415">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z * y))
    ]]></literal>
    <justification jstring="[hyper(225,a,5494,a(flip),b,6140,a)].">
      <j1 rule="hyper" parents="225 5494 6140"/>
    </justification>
  </clause>

  <clause id="6416">
    <literal><![CDATA[
      x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z))
    ]]></literal>
    <justification jstring="[hyper(225,a,2584,a(flip),b,6140,a)].">
      <j1 rule="hyper" parents="225 2584 6140"/>
    </justification>
  </clause>

  <clause id="6417">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ 1)) * (y \ T(z,x)) = y \ z
    ]]></literal>
    <justification jstring="[hyper(145,a,1486,a(flip),b,6140,a)].">
      <j1 rule="hyper" parents="145 1486 6140"/>
    </justification>
  </clause>

  <clause id="6418">
    <literal><![CDATA[
      K(x,y / (z \ 1)) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(145,a,1182,a(flip),b,6140,a)].">
      <j1 rule="hyper" parents="145 1182 6140"/>
    </justification>
  </clause>

  <clause id="6420">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * ((y * (u \ z)) * T(L(T(u,u \ z),u \ z,y),x)) = y * z
    ]]></literal>
    <justification jstring="[para(409(a,2),6141(a,1,2,2,1))].">
      <j1 rule="para" parents="409 6141"/>
    </justification>
  </clause>

  <clause id="6421">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) / (T((x \ 1) \ 1,y) * K(z,(x \ 1) \ 1)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,3779,a(flip),b,6176,a),flip(a)].">
      <j1 rule="hyper" parents="373 3779 6176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6422">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,3320,a,b,6223,a),flip(a)].">
      <j1 rule="hyper" parents="373 3320 6223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6423">
    <literal><![CDATA[
      T(x,y) \ T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(6223(a,2),3325(a,1))].">
      <j1 rule="para" parents="6223 3325"/>
    </justification>
  </clause>

  <clause id="6424">
    <literal><![CDATA[
      T(x,y) \ T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ K(x,z) = u
    ]]></literal>
    <justification jstring="[para(6223(a,2),6206(a,1))].">
      <j1 rule="para" parents="6223 6206"/>
    </justification>
  </clause>

  <clause id="6425">
    <literal><![CDATA[
      (x \ (x / y)) * x = (x / y) * K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,6231,a(flip),b,6312,a)].">
      <j1 rule="hyper" parents="144 6231 6312"/>
    </justification>
  </clause>

  <clause id="6426">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * T(x,y) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(3871(a,1),6232(a,1,2))].">
      <j1 rule="para" parents="3871 6232"/>
    </justification>
  </clause>

  <clause id="6427">
    <literal><![CDATA[
      (T(x,x \ 1) * T(x,x \ 1)) * (y / z) = (((x \ 1) \ x) * y) / z
    ]]></literal>
    <justification jstring="[para(6250(a,2),4808(a,1,1))].">
      <j1 rule="para" parents="6250 4808"/>
    </justification>
  </clause>

  <clause id="6428">
    <literal><![CDATA[
      T(x \ y,z) \ K(x \ y,x) = K(z,x \ y) * ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,6256,a(flip),b,6165,a),flip(a)].">
      <j1 rule="hyper" parents="145 6256 6165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6429">
    <literal><![CDATA[
      ((x / (x / y)) \ 1) * z = (y \ K(y,y \ x)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,6258,a,b,11,a)].">
      <j1 rule="hyper" parents="144 6258 11"/>
    </justification>
  </clause>

  <clause id="6430">
    <literal><![CDATA[
      (1 / (x \ y)) * (y \ x) = (y \ x) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(145,a,6268,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 6268 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6431">
    <literal><![CDATA[
      T(x * x,y) * (y \ z) = y \ ((x * x) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1460,a(flip),b,6284,a),flip(a)].">
      <j1 rule="hyper" parents="373 1460 6284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6432">
    <literal><![CDATA[
      T(x,y) \ (1 / T(x,y)) = x \ (1 / T(T(x,y),y))
    ]]></literal>
    <justification jstring="[para(6293(a,1),6294(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6293 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6433">
    <literal><![CDATA[
      L(x,y,(z * u) / z) = L(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[para(5721(a,2),6313(a,1,3))].">
      <j1 rule="para" parents="5721 6313"/>
    </justification>
  </clause>

  <clause id="6435">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ z)) = (y \ T(z,x)) \ (y \ z)
    ]]></literal>
    <justification jstring="[para(1486(a,1),6324(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1486 6324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6436">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(1308(a,1),6324(a,1,1))].">
      <j1 rule="para" parents="1308 6324"/>
    </justification>
  </clause>

  <clause id="6437">
    <literal><![CDATA[
      ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(2880(a,1),6324(a,1,1))].">
      <j1 rule="para" parents="2880 6324"/>
    </justification>
  </clause>

  <clause id="6438">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(2927(a,1),6324(a,1,1))].">
      <j1 rule="para" parents="2927 6324"/>
    </justification>
  </clause>

  <clause id="6439">
    <literal><![CDATA[
      T(x * T(x \ y,z),u) \ T(y,u) = K(z,T(x,u) \ T(y,u))
    ]]></literal>
    <justification jstring="[para(3181(a,1),6324(a,1,1))].">
      <j1 rule="para" parents="3181 6324"/>
    </justification>
  </clause>

  <clause id="6440">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) * R(R(x * T(x \ 1,y),z,u) \ 1,w,v5) = R((x * T(x \ 1,y)) * R(K(y,x \ 1),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(6324(a,1),5362(a,2,1,2,1))].">
      <j1 rule="para" parents="6324 5362"/>
    </justification>
  </clause>

  <clause id="6441">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(5494(a,1),6324(a,1,1))].">
      <j1 rule="para" parents="5494 6324"/>
    </justification>
  </clause>

  <clause id="6442">
    <literal><![CDATA[
      (x \ y) \ ((y / x) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),6356(a,1,2,1,1))].">
      <j1 rule="para" parents="10 6356"/>
    </justification>
  </clause>

  <clause id="6443">
    <literal><![CDATA[
      x \ ((y / (y / x)) * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(4707(a,1),6356(a,1,2,1))].">
      <j1 rule="para" parents="4707 6356"/>
    </justification>
  </clause>

  <clause id="6444">
    <literal><![CDATA[
      T(K(x,y \ 1) / y,x) = 1 / y
    ]]></literal>
    <justification jstring="[para(6361(a,2),255(a,1,1))].">
      <j1 rule="para" parents="6361 255"/>
    </justification>
  </clause>

  <clause id="6445">
    <literal><![CDATA[
      T(K(x * (1 / y),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(6361(a,2),1039(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6361 1039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6446">
    <literal><![CDATA[
      T(K(x,y) / (1 / y),x) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[para(82(a,1),6444(a,1,1,1,2))].">
      <j1 rule="para" parents="82 6444"/>
    </justification>
  </clause>

  <clause id="6447">
    <literal><![CDATA[
      K(x,(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(6376(a,2),152(a,1))].">
      <j1 rule="para" parents="6376 152"/>
    </justification>
  </clause>

  <clause id="6448">
    <literal><![CDATA[
      K(x,y) / x = 1 / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(142,a,6091,a(flip),b,6399,a)].">
      <j1 rule="hyper" parents="142 6091 6399"/>
    </justification>
  </clause>

  <clause id="6449">
    <literal><![CDATA[
      (x * ((y * z) / y)) / K(y,z) = x * z
    ]]></literal>
    <justification jstring="[para(11(a,1),6399(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 6399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6450">
    <literal><![CDATA[
      K(x \ y,x) / (x \ y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),6448(a,2,2,1))].">
      <j1 rule="para" parents="10 6448"/>
    </justification>
  </clause>

  <clause id="6451">
    <literal><![CDATA[
      K(R(x,y,y \ 1),y) / R(x,y,y \ 1) = 1 / ((y * x) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(1067(a,1),6448(a,2,2))].">
      <j1 rule="para" parents="1067 6448"/>
    </justification>
  </clause>

  <clause id="6452">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(5721(a,1),6448(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5721 6448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6453">
    <literal><![CDATA[
      (K(x,y) / x) \ 1 = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(215,a,6452,a)].">
      <j1 rule="hyper" parents="215 6452"/>
    </justification>
  </clause>

  <clause id="6454">
    <literal><![CDATA[
      1 / ((x \ 1) * K(y,x \ 1)) = K(1 / x,y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(3776(a,2),6452(a,2,1))].">
      <j1 rule="para" parents="3776 6452"/>
    </justification>
  </clause>

  <clause id="6455">
    <literal><![CDATA[
      (x / (y / z)) * K(z,z \ y) = x / (z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),6400(a,1,1,2,1))].">
      <j1 rule="para" parents="10 6400"/>
    </justification>
  </clause>

  <clause id="6456">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((((y * z) / y) \ K(y,z)) * ((y * z) / y))) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(6400(a,1),2724(a,2,1,2))].">
      <j1 rule="para" parents="6400 2724"/>
    </justification>
  </clause>

  <clause id="6457">
    <literal><![CDATA[
      (x / ((y * z) / y)) \ T(x / z,1 / (x / ((y * z) / y))) = ((1 / (x / ((y * z) / y))) \ K(y,z)) * (1 / (x / ((y * z) / y)))
    ]]></literal>
    <justification jstring="[para(6400(a,1),5463(a,1,2,1))].">
      <j1 rule="para" parents="6400 5463"/>
    </justification>
  </clause>

  <clause id="6458">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * T(y,x)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(6187,a,6405,a)].">
      <j1 rule="hyper" parents="6187 6405"/>
    </justification>
  </clause>

  <clause id="6459">
    <literal><![CDATA[
      T(x,(x / y) / x) = T(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(143,a,6042,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 6042 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6460">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * T(x,z) = u
    ]]></literal>
    <justification jstring="[para(6407(a,1),4085(a,1))].">
      <j1 rule="para" parents="6407 4085"/>
    </justification>
  </clause>

  <clause id="6461">
    <literal><![CDATA[
      T(x,y) \ T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * K(x,z) = u
    ]]></literal>
    <justification jstring="[para(6422(a,2),3321(a,1))].">
      <j1 rule="para" parents="6422 3321"/>
    </justification>
  </clause>

  <clause id="6462">
    <literal><![CDATA[
      (x / y) * ((z * y) / z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(389,a,6449,a),flip(a)].">
      <j1 rule="hyper" parents="389 6449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6463">
    <literal><![CDATA[
      (x * y) \ (x * ((z * y) / z)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(215,a,6449,a)].">
      <j1 rule="hyper" parents="215 6449"/>
    </justification>
  </clause>

  <clause id="6464">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * ((z * y) / z)
    ]]></literal>
    <justification jstring="[hyper(156,a,6449,a)].">
      <j1 rule="hyper" parents="156 6449"/>
    </justification>
  </clause>

  <clause id="6465">
    <literal><![CDATA[
      x * K(y,z \ x) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(144,a,10,a(flip),b,6449,a)].">
      <j1 rule="hyper" parents="144 10 6449"/>
    </justification>
  </clause>

  <clause id="6466">
    <literal><![CDATA[
      x / (K(y \ z,y) / (y \ z)) = x / (1 / (z / y))
    ]]></literal>
    <justification jstring="[hyper(225,a,6450,a,b,82,a)].">
      <j1 rule="hyper" parents="225 6450 82"/>
    </justification>
  </clause>

  <clause id="6467">
    <literal><![CDATA[
      (x / y) * (y * K(z,y)) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5881,a(flip),b,6462,a)].">
      <j1 rule="hyper" parents="64 5881 6462"/>
    </justification>
  </clause>

  <clause id="6468">
    <literal><![CDATA[
      (x / (y \ z)) * (z / y) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),6462(a,1,2,1))].">
      <j1 rule="para" parents="10 6462"/>
    </justification>
  </clause>

  <clause id="6469">
    <literal><![CDATA[
      (x / y) * (z / (z / y)) = x * K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(4707(a,1),6462(a,1,2))].">
      <j1 rule="para" parents="4707 6462"/>
    </justification>
  </clause>

  <clause id="6470">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,5881,a(flip),b,6464,a),flip(a)].">
      <j1 rule="hyper" parents="373 5881 6464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6471">
    <literal><![CDATA[
      (x * (y \ z)) * K(y,y \ z) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(10(a,1),6464(a,2,2,1))].">
      <j1 rule="para" parents="10 6464"/>
    </justification>
  </clause>

  <clause id="6472">
    <literal><![CDATA[
      (x * y) * K(y \ z,y) = x * (z / (z / y))
    ]]></literal>
    <justification jstring="[para(4707(a,1),6464(a,2,2))].">
      <j1 rule="para" parents="4707 6464"/>
    </justification>
  </clause>

  <clause id="6474">
    <literal><![CDATA[
      R(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(664,a,6470,a)].">
      <j1 rule="hyper" parents="664 6470"/>
    </justification>
  </clause>

  <clause id="6475">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(606,a,6470,a)].">
      <j1 rule="hyper" parents="606 6470"/>
    </justification>
  </clause>

  <clause id="6476">
    <literal><![CDATA[
      a(x,y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,6470,a(flip),b,2635,a),flip(a)].">
      <j1 rule="hyper" parents="138 6470 2635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6477">
    <literal><![CDATA[
      R(x,y \ 1,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,2975,a,b,6474,a)].">
      <j1 rule="hyper" parents="64 2975 6474"/>
    </justification>
  </clause>

  <clause id="6479">
    <literal><![CDATA[
      R(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,2975,a(flip),b,6474,a)].">
      <j1 rule="hyper" parents="64 2975 6474"/>
    </justification>
  </clause>

  <clause id="6480">
    <literal><![CDATA[
      L(K(x,y),y,z) = L(K(x,y),y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6475,a,b,6475,a)].">
      <j1 rule="hyper" parents="373 6475 6475"/>
    </justification>
  </clause>

  <clause id="6483">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,y) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(144,a,6477,a(flip),b,4030,a),flip(a)].">
      <j1 rule="hyper" parents="144 6477 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6485">
    <literal><![CDATA[
      (x * y) * K(z,y \ 1) = x * (y * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(144,a,6479,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 6479 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6487">
    <literal><![CDATA[
      L(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6480(a,1),623(a,1)),flip(b)].">
      <j1 rule="para" parents="6480 623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6488">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u) \ 1,y) = w
    ]]></literal>
    <justification jstring="[para(4190(a,1),5976(a,1))].">
      <j1 rule="para" parents="4190 5976"/>
    </justification>
  </clause>

  <clause id="6489">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),5985(a,1,2))].">
      <j1 rule="para" parents="10 5985"/>
    </justification>
  </clause>

  <clause id="6490">
    <literal><![CDATA[
      K(x,y) * (z * x) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * T(z,x) = u
    ]]></literal>
    <justification jstring="[para(115(a,1),5985(a,1,2))].">
      <j1 rule="para" parents="115 5985"/>
    </justification>
  </clause>

  <clause id="6491">
    <literal><![CDATA[
      K(x,y) * T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * K(x,z) = u
    ]]></literal>
    <justification jstring="[para(5753(a,2),5985(a,1,2))].">
      <j1 rule="para" parents="5753 5985"/>
    </justification>
  </clause>

  <clause id="6492">
    <literal><![CDATA[
      T(x,y) * L(T(z,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * x) = v5
    ]]></literal>
    <justification jstring="[para(121(a,1),6030(a,1,2))].">
      <j1 rule="para" parents="121 6030"/>
    </justification>
  </clause>

  <clause id="6493">
    <literal><![CDATA[
      T(x,y) * (T(x,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = w
    ]]></literal>
    <justification jstring="[para(6137(a,1),6030(a,1,2))].">
      <j1 rule="para" parents="6137 6030"/>
    </justification>
  </clause>

  <clause id="6494">
    <literal><![CDATA[
      x * (a(x,x,x) \ y) = L(x,x,x) * y
    ]]></literal>
    <justification jstring="[para(6185(a,1),6086(a,1,2))].">
      <j1 rule="para" parents="6185 6086"/>
    </justification>
  </clause>

  <clause id="6495">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(6342(a,1),6087(a,1,2))].">
      <j1 rule="para" parents="6342 6087"/>
    </justification>
  </clause>

  <clause id="6496">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(6344(a,1),6278(a,1,2))].">
      <j1 rule="para" parents="6344 6278"/>
    </justification>
  </clause>

  <clause id="6498">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * (y \ x) = u
    ]]></literal>
    <justification jstring="[para(3353(a,1),6296(a,1,2))].">
      <j1 rule="para" parents="3353 6296"/>
    </justification>
  </clause>

  <clause id="6499">
    <literal><![CDATA[
      T(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(6161(a,1),6296(a,1,2))].">
      <j1 rule="para" parents="6161 6296"/>
    </justification>
  </clause>

  <clause id="6500">
    <literal><![CDATA[
      K(x,y / z) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(y / z,x) \ y = u
    ]]></literal>
    <justification jstring="[para(82(a,1),6301(a,1,2))].">
      <j1 rule="para" parents="82 6301"/>
    </justification>
  </clause>

  <clause id="6501">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      (z * x) / T(T(z,x),y) = u
    ]]></literal>
    <justification jstring="[para(214(a,1),6309(a,1,1))].">
      <j1 rule="para" parents="214 6309"/>
    </justification>
  </clause>

  <clause id="6502">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / T(x,z) = u
    ]]></literal>
    <justification jstring="[para(5739(a,2),6309(a,1,1))].">
      <j1 rule="para" parents="5739 6309"/>
    </justification>
  </clause>

  <clause id="6503">
    <literal><![CDATA[
      x * (K(y,x) * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) / T(y,z) = u
    ]]></literal>
    <justification jstring="[para(5911(a,1),6309(a,1))].">
      <j1 rule="para" parents="5911 6309"/>
    </justification>
  </clause>

  <clause id="6504">
    <literal><![CDATA[
      K(x,y) * K(y,y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6223,a(flip),b,6340,a)].">
      <j1 rule="hyper" parents="64 6223 6340"/>
    </justification>
  </clause>

  <clause id="6505">
    <literal><![CDATA[
      x * (K(y,x) * K(x,x * y)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,6223,a(flip),b,6340,a(flip))].">
      <j1 rule="hyper" parents="145 6223 6340"/>
    </justification>
  </clause>

  <clause id="6506">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6223,a(flip),b,6343,a)].">
      <j1 rule="hyper" parents="64 6223 6343"/>
    </justification>
  </clause>

  <clause id="6507">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y),z)) \ (T(K(x,y),z) * T(x,x \ y)) = L(R(x,x \ y,x),K(x,y),T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(6350(a,1),640(a,2,1))].">
      <j1 rule="para" parents="6350 640"/>
    </justification>
  </clause>

  <clause id="6508">
    <literal><![CDATA[
      x \ y != K(x,z) * K(x * z,x)
    ]]></literal>
    <literal><![CDATA[
      R(x,z,x) = y
    ]]></literal>
    <justification jstring="[para(6353(a,2),48(a,1)),flip(a)].">
      <j1 rule="para" parents="6353 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6509">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(6353(a,1),3321(a,1))].">
      <j1 rule="para" parents="6353 3321"/>
    </justification>
  </clause>

  <clause id="6510">
    <literal><![CDATA[
      K(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),6385(a,1,2,2))].">
      <j1 rule="para" parents="10 6385"/>
    </justification>
  </clause>

  <clause id="6511">
    <literal><![CDATA[
      K(x * (y * y),x) = K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,654,a(flip),b,6387,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 654 6387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6512">
    <literal><![CDATA[
      (x * (y \ x)) \ (y \ T(x,y \ x)) = L(x \ 1,x,y \ x)
    ]]></literal>
    <justification jstring="[para(4464(a,2),6390(a,1,2))].">
      <j1 rule="para" parents="4464 6390"/>
    </justification>
  </clause>

  <clause id="6513">
    <literal><![CDATA[
      K(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / y) = z
    ]]></literal>
    <justification jstring="[para(77(a,1),6447(a,1,2,1))].">
      <j1 rule="para" parents="77 6447"/>
    </justification>
  </clause>

  <clause id="6514">
    <literal><![CDATA[
      K(x,R(y / z,z,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * u) / (y * u)) = w
    ]]></literal>
    <justification jstring="[para(112(a,2),6447(a,1,2,1))].">
      <j1 rule="para" parents="112 6447"/>
    </justification>
  </clause>

  <clause id="6515">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / (1 / y)) = z
    ]]></literal>
    <justification jstring="[para(82(a,1),6513(a,1,2))].">
      <j1 rule="para" parents="82 6513"/>
    </justification>
  </clause>

  <clause id="6516">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / (z / y)) = u
    ]]></literal>
    <justification jstring="[para(6375(a,1),6513(a,1))].">
      <j1 rule="para" parents="6375 6513"/>
    </justification>
  </clause>

  <clause id="6517">
    <literal><![CDATA[
      (x * K(y,x)) \ L(x,y,x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,6505,a(flip),b,4442,a)].">
      <j1 rule="hyper" parents="139 6505 4442"/>
    </justification>
  </clause>

  <clause id="6518">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = K(y,x) * K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),6506(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 6506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6519">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(35,a,5753,a(flip),b,5833,a)].">
      <j1 rule="hyper" parents="35 5753 5833"/>
    </justification>
  </clause>

  <clause id="6520">
    <literal><![CDATA[
      K(x,(y / (z \ 1)) * (1 / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),6519(a,2,2))].">
      <j1 rule="para" parents="12 6519"/>
    </justification>
  </clause>

  <clause id="6521">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(79(a,1),6519(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 6519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6522">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3687(a,1),6520(a,1,2))].">
      <j1 rule="para" parents="3687 6520"/>
    </justification>
  </clause>

  <clause id="6523">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3688(a,1),6520(a,1,2))].">
      <j1 rule="para" parents="3688 6520"/>
    </justification>
  </clause>

  <clause id="6524">
    <literal><![CDATA[
      K(x,(1 / (1 / y)) * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2257(a,1),6522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2257 6522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6525">
    <literal><![CDATA[
      K(x,(1 / y) / z) = K(x,(y \ 1) / z)
    ]]></literal>
    <justification jstring="[para(2353(a,1),6522(a,1,2))].">
      <j1 rule="para" parents="2353 6522"/>
    </justification>
  </clause>

  <clause id="6526">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2354(a,1),6522(a,1,2))].">
      <j1 rule="para" parents="2354 6522"/>
    </justification>
  </clause>

  <clause id="6527">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2385(a,1),6522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2385 6522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6528">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2450(a,1),6522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2450 6522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6529">
    <literal><![CDATA[
      K(x,y * K(z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3621(a,1),6522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3621 6522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6530">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(3718(a,1),6522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3718 6522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6532">
    <literal><![CDATA[
      K(x,y * (K(z,z \ 1) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(5183(a,1),6522(a,1,2))].">
      <j1 rule="para" parents="5183 6522"/>
    </justification>
  </clause>

  <clause id="6533">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(5184(a,1),6522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5184 6522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6534">
    <literal><![CDATA[
      K(x,y * ((1 / z) \ u)) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(5185(a,1),6522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5185 6522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6535">
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(5186(a,1),6522(a,1,2))].">
      <j1 rule="para" parents="5186 6522"/>
    </justification>
  </clause>

  <clause id="6536">
    <literal><![CDATA[
      K(x,y * (z / (1 / u))) = K(x,y * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(5189(a,1),6522(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5189 6522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6537">
    <literal><![CDATA[
      K(x,T(y * K(z,z \ 1),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(5484(a,2),6522(a,1,2))].">
      <j1 rule="para" parents="5484 6522"/>
    </justification>
  </clause>

  <clause id="6538">
    <literal><![CDATA[
      K(x,y / (1 / (1 / z))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(3892(a,1),6523(a,1,2))].">
      <j1 rule="para" parents="3892 6523"/>
    </justification>
  </clause>

  <clause id="6539">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ 1) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(5182(a,2),6523(a,1,2))].">
      <j1 rule="para" parents="5182 6523"/>
    </justification>
  </clause>

  <clause id="6541">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[para(3630(a,2),6529(a,1,2))].">
      <j1 rule="para" parents="3630 6529"/>
    </justification>
  </clause>

  <clause id="6542">
    <literal><![CDATA[
      K(x,y \ (1 / z)) = K(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(5193(a,1),6529(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5193 6529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6543">
    <literal><![CDATA[
      K(x,(K(y,y \ 1) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(5217(a,2),6529(a,1,2))].">
      <j1 rule="para" parents="5217 6529"/>
    </justification>
  </clause>

  <clause id="6544">
    <literal><![CDATA[
      K(x,y * T(1 / z,u)) = K(x,y * T(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(3569(a,1),6521(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3569 6521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6545">
    <literal><![CDATA[
      K(x,(y \ 1) * (y * z)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(1635(a,1),6526(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1635 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6546">
    <literal><![CDATA[
      K(x,R(y \ 1,y,z) \ u) = K(x,(z / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(3004(a,2),6527(a,1,2,1))].">
      <j1 rule="para" parents="3004 6527"/>
    </justification>
  </clause>

  <clause id="6547">
    <literal><![CDATA[
      L(x,y,z) * K(u,L(x,y,z)) = L(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,5722,a,b,5862,a)].">
      <j1 rule="hyper" parents="36 5722 5862"/>
    </justification>
  </clause>

  <clause id="6548">
    <literal><![CDATA[
      L(x,y,z) / L(x * K(u,x),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(225,a,5903,a,b,5955,a)].">
      <j1 rule="hyper" parents="225 5903 5955"/>
    </justification>
  </clause>

  <clause id="6549">
    <literal><![CDATA[
      L(x * K(y,x),z,u) / L(x,z,u) = K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(142,a,5903,a,b,5718,a(flip))].">
      <j1 rule="hyper" parents="142 5903 5718"/>
    </justification>
  </clause>

  <clause id="6550">
    <literal><![CDATA[
      R(x,y,z) \ R(x * K(u,x),y,z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,5904,a,b,5721,a(flip))].">
      <j1 rule="hyper" parents="139 5904 5721"/>
    </justification>
  </clause>

  <clause id="6551">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ y = R(x,z,u) \ ((R(x,z,u) * y) / R(x,z,u))
    ]]></literal>
    <justification jstring="[para(5904(a,2),4953(a,1,1))].">
      <j1 rule="para" parents="5904 4953"/>
    </justification>
  </clause>

  <clause id="6552">
    <literal><![CDATA[
      (T(x,y) * R(y,z,u)) / T(x,y) = R(K(y,x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(5972(a,1),5904(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5972 5904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6553">
    <literal><![CDATA[
      K(x \ y,x) * ((y / x) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(6187,a,5982,a)].">
      <j1 rule="hyper" parents="6187 5982"/>
    </justification>
  </clause>

  <clause id="6557">
    <literal><![CDATA[
      K(x,y \ 1) * ((x \ (y \ x)) * z) = ((y \ x) / x) * z
    ]]></literal>
    <justification jstring="[para(5962(a,1),5982(a,1,1))].">
      <j1 rule="para" parents="5962 5982"/>
    </justification>
  </clause>

  <clause id="6560">
    <literal><![CDATA[
      (x / (x / y)) \ (K(y \ x,y) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(759,a,5984,a)].">
      <j1 rule="hyper" parents="759 5984"/>
    </justification>
  </clause>

  <clause id="6563">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(5743(a,1),5991(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5743 5991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6564">
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(5741(a,2),5991(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5741 5991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6565">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(82(a,1),6563(a,2,1,1))].">
      <j1 rule="para" parents="82 6563"/>
    </justification>
  </clause>

  <clause id="6566">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = 1 / T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(225,a,6564,a(flip),b,6092,a),flip(a)].">
      <j1 rule="hyper" parents="225 6564 6092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6567">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((x \ (y / z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2584(a,1),5992(a,1,2))].">
      <j1 rule="para" parents="2584 5992"/>
    </justification>
  </clause>

  <clause id="6568">
    <literal><![CDATA[
      x \ (((y \ (x / z)) * y) * z) = K((x \ (y * z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2927(a,1),5992(a,1,2))].">
      <j1 rule="para" parents="2927 5992"/>
    </justification>
  </clause>

  <clause id="6569">
    <literal><![CDATA[
      (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(5488,a,5996,a),flip(a)].">
      <j1 rule="hyper" parents="5488 5996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6570">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ y) \ 1,z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(1005,a,5996,a),flip(a)].">
      <j1 rule="hyper" parents="1005 5996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6571">
    <literal><![CDATA[
      T(K(x / y,z),x) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(269,a,5754,a,b,5996,a(flip))].">
      <j1 rule="hyper" parents="269 5754 5996"/>
    </justification>
  </clause>

  <clause id="6572">
    <literal><![CDATA[
      x * (y * K((y \ (x \ 1)) \ 1,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5996,a(flip),b,1182,a(flip))].">
      <j1 rule="hyper" parents="145 5996 1182"/>
    </justification>
  </clause>

  <clause id="6573">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,5996,a(flip),b,525,a)].">
      <j1 rule="hyper" parents="142 5996 525"/>
    </justification>
  </clause>

  <clause id="6575">
    <literal><![CDATA[
      K((x \ (y \ x)) \ 1,z) = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(79(a,1),6571(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 6571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6576">
    <literal><![CDATA[
      x * K((x \ (y \ x)) \ 1,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,6575,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="145 6575 22"/>
    </justification>
  </clause>

  <clause id="6577">
    <literal><![CDATA[
      T(x * y,z) / y = K(((1 / y) / x) \ 1,z) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,1506,a(flip),b,6000,a)].">
      <j1 rule="hyper" parents="373 1506 6000"/>
    </justification>
  </clause>

  <clause id="6578">
    <literal><![CDATA[
      K(((x \ 1) / (x \ y)) \ 1,z) * (x \ y) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1486,a(flip),b,6000,a),flip(a)].">
      <j1 rule="hyper" parents="373 1486 6000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6580">
    <literal><![CDATA[
      K((x / y) \ 1,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,5754,a,b,6000,a),flip(a)].">
      <j1 rule="hyper" parents="36 5754 6000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6581">
    <literal><![CDATA[
      K(1 / (x / y),z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3776,a,b,6580,a)].">
      <j1 rule="hyper" parents="64 3776 6580"/>
    </justification>
  </clause>

  <clause id="6582">
    <literal><![CDATA[
      K(x / (y * x),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),6580(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 6580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6583">
    <literal><![CDATA[
      K((x \ y) / y,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),6580(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 6580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6584">
    <literal><![CDATA[
      K(x / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(6581(a,1),3777(a,1))].">
      <j1 rule="para" parents="6581 3777"/>
    </justification>
  </clause>

  <clause id="6585">
    <literal><![CDATA[
      K(x \ (y \ x),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6116,a(flip),b,6583,a)].">
      <j1 rule="hyper" parents="64 6116 6583"/>
    </justification>
  </clause>

  <clause id="6587">
    <literal><![CDATA[
      K(x \ 1,y) / (y \ (x \ y)) = 1 / ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(6585(a,1),6450(a,1,1))].">
      <j1 rule="para" parents="6585 6450"/>
    </justification>
  </clause>

  <clause id="6588">
    <literal><![CDATA[
      K(x \ y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K((x / y) \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(6116(a,1),6584(a,1))].">
      <j1 rule="para" parents="6116 6584"/>
    </justification>
  </clause>

  <clause id="6589">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),z) = (T(y * x,z) / x) / y
    ]]></literal>
    <justification jstring="[para(1506(a,1),6014(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1506 6014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6590">
    <literal><![CDATA[
      K(x,x \ y) * T(z,y / x) = (x \ y) \ (z * (y / x))
    ]]></literal>
    <justification jstring="[hyper(139,a,115,a(flip),b,6061,a),flip(a)].">
      <j1 rule="hyper" parents="139 115 6061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6591">
    <literal><![CDATA[
      (x \ y) * (x * (y / x)) = (y / x) * y
    ]]></literal>
    <justification jstring="[para(5781(a,1),6061(a,1,2))].">
      <j1 rule="para" parents="5781 6061"/>
    </justification>
  </clause>

  <clause id="6592">
    <literal><![CDATA[
      (x / y) * (K(y \ x,y) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(6161(a,1),6061(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6161 6061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6593">
    <literal><![CDATA[
      (x \ y) \ (K(x \ y,x) * z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,6161,a(flip),b,6062,a),flip(a)].">
      <j1 rule="hyper" parents="139 6161 6062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6594">
    <literal><![CDATA[
      (x \ y) \ (x * (T(x \ y,x) * z)) = (y / x) \ (x * ((x \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(139,a,6023,a(flip),b,6062,a),flip(a)].">
      <j1 rule="hyper" parents="139 6023 6062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6596">
    <literal><![CDATA[
      (x / (x / y)) * K(y,y \ x) = y
    ]]></literal>
    <justification jstring="[hyper(36,a,179,a(flip),b,6064,a),flip(a)].">
      <j1 rule="hyper" parents="36 179 6064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6597">
    <literal><![CDATA[
      (x * (y \ 1)) \ (1 / (1 / y)) = (x * (1 / y)) \ y
    ]]></literal>
    <justification jstring="[para(6596(a,1),3726(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6596 3726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6598">
    <literal><![CDATA[
      (T(x,y) * (y * z)) \ ((x * y) * (K(x,y) * z)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(6090(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6090 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6599">
    <literal><![CDATA[
      K(x \ y,x) * ((y / (y / x)) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(462,a,6149,a),flip(a)].">
      <j1 rule="hyper" parents="462 6149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6600">
    <literal><![CDATA[
      K(x \ y,x) * K(z,y / x) = x \ (y / T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,6245,a(flip),b,6149,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 6245 6149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6602">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(4021,a,6171,a)].">
      <j1 rule="hyper" parents="4021 6171"/>
    </justification>
  </clause>

  <clause id="6603">
    <literal><![CDATA[
      (x \ K(y,x)) \ (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(6183(a,1),228(a,1)),flip(b)].">
      <j1 rule="para" parents="6183 228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6604">
    <literal><![CDATA[
      (x \ K(y,x)) \ L((x \ 1) * z,u,w) = K(x,y) * (x * L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(5546(a,1),6183(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5546 6183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6605">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ z) = (T(x,y) \ 1) \ z
    ]]></literal>
    <justification jstring="[para(5783(a,2),6183(a,2,1))].">
      <j1 rule="para" parents="5783 6183"/>
    </justification>
  </clause>

  <clause id="6606">
    <literal><![CDATA[
      T(T(x,y),y) \ x = K(y,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5923(a,1),6225(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5923 6225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6607">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z,x),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,T(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6237(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6237 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6608">
    <literal><![CDATA[
      K((x * x) \ y,x * x) = K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5739,a,b,6253,a),flip(a)].">
      <j1 rule="hyper" parents="373 5739 6253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6609">
    <literal><![CDATA[
      K(x \ y,x) \ ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(6206,a,6270,a)].">
      <j1 rule="hyper" parents="6206 6270"/>
    </justification>
  </clause>

  <clause id="6610">
    <literal><![CDATA[
      ((x \ 1) * x) \ (T(x,y) * z) = T(T(x,y),T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(4045(a,1),6289(a,1,1))].">
      <j1 rule="para" parents="4045 6289"/>
    </justification>
  </clause>

  <clause id="6611">
    <literal><![CDATA[
      (x * y) \ ((x * (1 / x)) \ z) = (T(x,x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(6289(a,1),5283(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6289 5283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6613">
    <literal><![CDATA[
      K(x \ y,x) * T(z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(22(a,2),6292(a,1,2))].">
      <j1 rule="para" parents="22 6292"/>
    </justification>
  </clause>

  <clause id="6614">
    <literal><![CDATA[
      K(x \ y,x) * K(x \ y,z) = (y / x) \ T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5726(a,2),6292(a,1,2))].">
      <j1 rule="para" parents="5726 6292"/>
    </justification>
  </clause>

  <clause id="6615">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ z) = y * ((x / (x / y)) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6166,a,b,6371,a)].">
      <j1 rule="hyper" parents="373 6166 6371"/>
    </justification>
  </clause>

  <clause id="6616">
    <literal><![CDATA[
      (x / (x / y)) \ z = y \ (K(y,y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(149,a,6373,a),flip(a)].">
      <j1 rule="hyper" parents="149 6373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6617">
    <literal><![CDATA[
      (x / (x / y)) \ ((x / y) \ z) = y \ ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,6270,a(flip),b,6373,a),flip(a)].">
      <j1 rule="hyper" parents="139 6270 6373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6618">
    <literal><![CDATA[
      x * (K(R(y,z,u),x) * K(w,R(y,z,u))) = (R(y,z,u) * x) / R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(27(a,2),6393(a,2,2))].">
      <j1 rule="para" parents="27 6393"/>
    </justification>
  </clause>

  <clause id="6619">
    <literal><![CDATA[
      (x \ y) * (y / T(x \ y,y)) = ((y * (x \ y)) / y) * x
    ]]></literal>
    <justification jstring="[hyper(740,a,6397,a),flip(a)].">
      <j1 rule="hyper" parents="740 6397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6620">
    <literal><![CDATA[
      (x / (x / y)) \ (y \ z) = y \ ((x / (x / y)) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,6413,a,b,6373,a),flip(a)].">
      <j1 rule="hyper" parents="139 6413 6373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6621">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = (x / (y \ 1)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(3779(a,1),6425(a,2,2))].">
      <j1 rule="para" parents="3779 6425"/>
    </justification>
  </clause>

  <clause id="6622">
    <literal><![CDATA[
      x \ ((y * y) * (x * z)) = T(y * y,x) * z
    ]]></literal>
    <justification jstring="[hyper(739,a,6431,a),flip(a)].">
      <j1 rule="hyper" parents="739 6431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6623">
    <literal><![CDATA[
      T(x * x,y) \ (y \ (x * x)) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,177,a(flip),b,6431,a)].">
      <j1 rule="hyper" parents="139 177 6431"/>
    </justification>
  </clause>

  <clause id="6624">
    <literal><![CDATA[
      x \ ((y * y) \ (x * z)) = T(y * y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,73,a(flip),b,6431,a),flip(a)].">
      <j1 rule="hyper" parents="139 73 6431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6625">
    <literal><![CDATA[
      x * (T(y * y,x) * z) = (y * y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(1335,a,6431,a(flip))].">
      <j1 rule="hyper" parents="1335 6431"/>
    </justification>
  </clause>

  <clause id="6626">
    <literal><![CDATA[
      K(x,y * y) * (x \ ((y * y) * z)) = (y * y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,6431,a(flip),b,6131,a)].">
      <j1 rule="hyper" parents="145 6431 6131"/>
    </justification>
  </clause>

  <clause id="6627">
    <literal><![CDATA[
      T(x * x,y) * ((y \ z) * u) = (y \ ((x * x) * z)) * u
    ]]></literal>
    <justification jstring="[para(6431(a,1),777(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6431 777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6628">
    <literal><![CDATA[
      T(x * x,y) * ((y \ z) / u) = (y \ ((x * x) * z)) / u
    ]]></literal>
    <justification jstring="[para(6431(a,1),1439(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6431 1439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6629">
    <literal><![CDATA[
      K(x,y * y) * (x \ (y * y)) = (y * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,6623,a(flip),b,6137,a),flip(a)].">
      <j1 rule="hyper" parents="145 6623 6137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6630">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * z = u
    ]]></literal>
    <justification jstring="[para(6442(a,1),290(a,1,2))].">
      <j1 rule="para" parents="6442 290"/>
    </justification>
  </clause>

  <clause id="6631">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,3292,a(flip),b,6465,a)].">
      <j1 rule="hyper" parents="373 3292 6465"/>
    </justification>
  </clause>

  <clause id="6634">
    <literal><![CDATA[
      (x / ((y \ z) \ z)) / (z / (z / y)) = (x / y) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,6316,a,b,6469,a)].">
      <j1 rule="hyper" parents="142 6316 6469"/>
    </justification>
  </clause>

  <clause id="6635">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (u / (u / x)) = R(x,y,z) * K(x \ u,x)
    ]]></literal>
    <justification jstring="[para(2071(a,1),6469(a,1,1))].">
      <j1 rule="para" parents="2071 6469"/>
    </justification>
  </clause>

  <clause id="6636">
    <literal><![CDATA[
      K(x,y * (((1 / z) * u) * w)) = K(x,y * (((z \ 1) * u) * w))
    ]]></literal>
    <justification jstring="[para(2377(a,1),6532(a,1,2,2))].">
      <j1 rule="para" parents="2377 6532"/>
    </justification>
  </clause>

  <clause id="6637">
    <literal><![CDATA[
      K(x,y * (z * ((u \ 1) \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(3895(a,1),6532(a,1,2,2))].">
      <j1 rule="para" parents="3895 6532"/>
    </justification>
  </clause>

  <clause id="6638">
    <literal><![CDATA[
      K(x,y * (z * K(u,1 / u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(82(a,1),6533(a,1,2,2,2,1))].">
      <j1 rule="para" parents="82 6533"/>
    </justification>
  </clause>

  <clause id="6639">
    <literal><![CDATA[
      K(x,T((1 / y) * z,u)) = K(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(3646(a,1),6537(a,1,2,1))].">
      <j1 rule="para" parents="3646 6537"/>
    </justification>
  </clause>

  <clause id="6640">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ 1) * u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(2254(a,1),6539(a,1,2,2))].">
      <j1 rule="para" parents="2254 6539"/>
    </justification>
  </clause>

  <clause id="6641">
    <literal><![CDATA[
      K(x,y \ ((1 / z) * u)) = K(x,y \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(2354(a,1),6539(a,1,2,2))].">
      <j1 rule="para" parents="2354 6539"/>
    </justification>
  </clause>

  <clause id="6642">
    <literal><![CDATA[
      K(x,y \ (z * (1 / u))) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3667(a,1),6539(a,1,2,2))].">
      <j1 rule="para" parents="3667 6539"/>
    </justification>
  </clause>

  <clause id="6643">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / u) \ w))) = K(x,y \ (z * ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[para(5185(a,1),6539(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5185 6539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6644">
    <literal><![CDATA[
      K(x,K(y,1 / y) / z) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(1732(a,1),6541(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1732 6541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6645">
    <literal><![CDATA[
      K(x,((1 / y) * z) / u) = K(x,((y \ 1) * z) / u)
    ]]></literal>
    <justification jstring="[para(2263(a,1),6541(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2263 6541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6646">
    <literal><![CDATA[
      K(x,(y * (1 / z)) \ u) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3667(a,1),6543(a,1,2,1))].">
      <j1 rule="para" parents="3667 6543"/>
    </justification>
  </clause>

  <clause id="6649">
    <literal><![CDATA[
      (x / y) * ((x / (x / y)) * z) = (y \ x) * (y * z)
    ]]></literal>
    <justification jstring="[para(5984(a,1),6592(a,1,2))].">
      <j1 rule="para" parents="5984 6592"/>
    </justification>
  </clause>

  <clause id="6650">
    <literal><![CDATA[
      x * (K(y * y,x) * ((y * y) * z)) = (y * y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5755,a,b,6622,a)].">
      <j1 rule="hyper" parents="145 5755 6622"/>
    </justification>
  </clause>

  <clause id="6651">
    <literal><![CDATA[
      (x * y) \ (x * ((z * z) * (y * u))) = L(T(z * z,y) * u,y,x)
    ]]></literal>
    <justification jstring="[para(6622(a,1),102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6622 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6652">
    <literal><![CDATA[
      T(x * x,y) \ (y \ z) = y \ ((x * x) \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),6624(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 6624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6653">
    <literal><![CDATA[
      L(T(T(x * x,y),z),z,y) = T(x * x,y * z)
    ]]></literal>
    <justification jstring="[hyper(269,a,6625,a(flip),b,588,a),flip(a)].">
      <j1 rule="hyper" parents="269 6625 588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6654">
    <literal><![CDATA[
      (x \ y) \ (T(z * z,x) * u) = (x \ ((z * z) \ y)) \ u
    ]]></literal>
    <justification jstring="[para(6652(a,1),1437(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6652 1437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6655">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = R(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2070(a,1),5765(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2070 5765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6656">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) * ((y * z) / y) = u
    ]]></literal>
    <justification jstring="[para(6467(a,1),5882(a,1))].">
      <j1 rule="para" parents="6467 5882"/>
    </justification>
  </clause>

  <clause id="6657">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(z,K(x * y,x))) = L(T(K(x * y,x),z) \ 1,K(x * y,x),y)
    ]]></literal>
    <justification jstring="[para(6320(a,2),5941(a,1,1))].">
      <j1 rule="para" parents="6320 5941"/>
    </justification>
  </clause>

  <clause id="6658">
    <literal><![CDATA[
      (L(K(x,y) * z,x,x) / u) \ (((1 / x) * ((T(x,y) * z) * u)) / u) = L(u,T(x,y) * z,1 / x)
    ]]></literal>
    <justification jstring="[para(6083(a,2),3209(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6083 3209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6659">
    <literal><![CDATA[
      K(R(x \ (y / z),x,y / (y / z)),x) = K(((z \ y) * z) / (x * (y / (y / z))),x)
    ]]></literal>
    <justification jstring="[para(4550(a,1),6119(a,2,1,1))].">
      <j1 rule="para" parents="4550 6119"/>
    </justification>
  </clause>

  <clause id="6660">
    <literal><![CDATA[
      x / y != K(z,u) * (u \ w)
    ]]></literal>
    <literal><![CDATA[
      (T(u,z) \ w) * y = x
    ]]></literal>
    <justification jstring="[para(6075(a,1),6199(a,2,2))].">
      <j1 rule="para" parents="6075 6199"/>
    </justification>
  </clause>

  <clause id="6661">
    <literal><![CDATA[
      T(T(x * K(y,x),z),x * y) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25,a,b,6335,a),flip(a)].">
      <j1 rule="hyper" parents="373 25 6335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6662">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,27,a,b,6348,a),flip(a)].">
      <j1 rule="hyper" parents="373 27 6348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6663">
    <literal><![CDATA[
      T(x,y) / T(x,z) = K(x,z) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6424,a,5471,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="6424 5471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6664">
    <literal><![CDATA[
      (K(x,y) \ K(x,z)) \ T(x,z) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(215,a,6663,a)].">
      <j1 rule="hyper" parents="215 6663"/>
    </justification>
  </clause>

  <clause id="6665">
    <literal><![CDATA[
      K(x / y,z) \ y != u
    ]]></literal>
    <literal><![CDATA[
      T(x / y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(6156(a,2),6500(a,1))].">
      <j1 rule="para" parents="6156 6500"/>
    </justification>
  </clause>

  <clause id="6666">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(5726(a,2),5734(a,1,1))].">
      <j1 rule="para" parents="5726 5734"/>
    </justification>
  </clause>

  <clause id="6668">
    <literal><![CDATA[
      K(x,L(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5168,a(flip),b,6666,a),flip(a)].">
      <j1 rule="hyper" parents="64 5168 6666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6669">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,y,z) \ 1) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,6666,a(flip),b,4279,a)].">
      <j1 rule="hyper" parents="139 6666 4279"/>
    </justification>
  </clause>

  <clause id="6670">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6047(a,1),6666(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6047 6666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6671">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,u,w) \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,6668,a,b,5398,a)].">
      <j1 rule="hyper" parents="139 6668 5398"/>
    </justification>
  </clause>

  <clause id="6672">
    <literal><![CDATA[
      K(x,L(L(y \ 1,z,u),w,v5) \ 1) = L(L(K(x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(6670(a,1),6666(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6670 6666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6673">
    <literal><![CDATA[
      (K(x,y) / R(x,z,u)) * x = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5470,a(flip),b,5845,a),flip(a)].">
      <j1 rule="hyper" parents="373 5470 5845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6674">
    <literal><![CDATA[
      K(x,(y * y) * x) = K(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(359,a,5883,a),flip(a)].">
      <j1 rule="hyper" parents="359 5883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6675">
    <literal><![CDATA[
      K(x,x * (y * y)) = K(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(6143,a,6674,a)].">
      <j1 rule="hyper" parents="6143 6674"/>
    </justification>
  </clause>

  <clause id="6676">
    <literal><![CDATA[
      T((x / (y * K(z,y))) * y,(z * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      ((z * y) / z) \ (x * y) = u
    ]]></literal>
    <justification jstring="[para(5907(a,1),467(a,1,1))].">
      <j1 rule="para" parents="5907 467"/>
    </justification>
  </clause>

  <clause id="6677">
    <literal><![CDATA[
      x * ((y \ (x \ 1)) * y) = K((x * y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(737,a,5988,a)].">
      <j1 rule="hyper" parents="737 5988"/>
    </justification>
  </clause>

  <clause id="6678">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2919,a(flip),b,5988,a)].">
      <j1 rule="hyper" parents="64 2919 5988"/>
    </justification>
  </clause>

  <clause id="6679">
    <literal><![CDATA[
      x * (y \ T(y * (x \ 1),z)) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(1182(a,1),5988(a,1,2))].">
      <j1 rule="para" parents="1182 5988"/>
    </justification>
  </clause>

  <clause id="6681">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(5743(a,1),5990(a,1,1))].">
      <j1 rule="para" parents="5743 5990"/>
    </justification>
  </clause>

  <clause id="6682">
    <literal><![CDATA[
      K(R(x \ 1,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(5741(a,2),5990(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5741 5990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6683">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4524,a(flip),b,6681,a),flip(a)].">
      <j1 rule="hyper" parents="64 4524 6681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6684">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * (y * z) = (K(x \ 1,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,6681,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 6681 20"/>
    </justification>
  </clause>

  <clause id="6685">
    <literal><![CDATA[
      K(((x * (y * z)) / z) \ 1,z / (y * z)) = K((x / R(1 / y,y,z)) \ 1,z / (y * z))
    ]]></literal>
    <justification jstring="[para(1034(a,1),6683(a,1,1,1))].">
      <j1 rule="para" parents="1034 6683"/>
    </justification>
  </clause>

  <clause id="6686">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) * w = R(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(6682(a,1),6156(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6682 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6688">
    <literal><![CDATA[
      (x / T(y,y \ 1)) * K(y \ 1,z) = x * T(x \ (x / T(y,y \ 1)),z)
    ]]></literal>
    <justification jstring="[para(5261(a,1),5994(a,1,2))].">
      <j1 rule="para" parents="5261 5994"/>
    </justification>
  </clause>

  <clause id="6689">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ R(x,z,u)) = R(x,z,u) * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1796(a,1),5998(a,2,2,1))].">
      <j1 rule="para" parents="1796 5998"/>
    </justification>
  </clause>

  <clause id="6690">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),T(x,z))
    ]]></literal>
    <justification jstring="[para(4111(a,1),5998(a,1,1))].">
      <j1 rule="para" parents="4111 5998"/>
    </justification>
  </clause>

  <clause id="6691">
    <literal><![CDATA[
      x * (y \ K((y * (x \ 1)) \ 1,z)) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,6002,a,b,1182,a(flip))].">
      <j1 rule="hyper" parents="145 6002 1182"/>
    </justification>
  </clause>

  <clause id="6692">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * y) = y * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5494,a(flip),b,6003,a)].">
      <j1 rule="hyper" parents="64 5494 6003"/>
    </justification>
  </clause>

  <clause id="6693">
    <literal><![CDATA[
      (x * K(y \ 1,x)) / L(x,x \ (y \ x),y) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(142,a,6692,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="142 6692 100"/>
    </justification>
  </clause>

  <clause id="6694">
    <literal><![CDATA[
      ((1 / x) * y) * T(((1 / x) * y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[para(82(a,1),6005(a,2,1,1))].">
      <j1 rule="para" parents="82 6005"/>
    </justification>
  </clause>

  <clause id="6695">
    <literal><![CDATA[
      x * (K(x \ 1,y) * (x \ z)) = K(x \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(5998(a,2),6007(a,1,2))].">
      <j1 rule="para" parents="5998 6007"/>
    </justification>
  </clause>

  <clause id="6696">
    <literal><![CDATA[
      K(((x \ 1) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(6584,a,6163,a)].">
      <j1 rule="hyper" parents="6584 6163"/>
    </justification>
  </clause>

  <clause id="6697">
    <literal><![CDATA[
      x \ T(T(y,z),u) != T(T(y,z),u) * K(w,y)
    ]]></literal>
    <literal><![CDATA[
      K(y,w) = x
    ]]></literal>
    <justification jstring="[para(6173(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="6173 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6698">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = K(z,1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(149,a,6274,a)].">
      <j1 rule="hyper" parents="149 6274"/>
    </justification>
  </clause>

  <clause id="6699">
    <literal><![CDATA[
      K(x,1 / (y \ z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,6465,a,b,6274,a),flip(a)].">
      <j1 rule="hyper" parents="35 6465 6274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6700">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(6045,a,6699,a)].">
      <j1 rule="hyper" parents="6045 6699"/>
    </justification>
  </clause>

  <clause id="6701">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ (y * z)) = K(x,1 / L(u,z,y))
    ]]></literal>
    <justification jstring="[para(18(a,2),6699(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18 6699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6702">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(82(a,1),6699(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 6699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6703">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,u) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,6475,a,b,6700,a)].">
      <j1 rule="hyper" parents="373 6475 6700"/>
    </justification>
  </clause>

  <clause id="6704">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(143,a,6700,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 6700 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6705">
    <literal><![CDATA[
      K(x,(y * z) \ y) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),6700(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6706">
    <literal><![CDATA[
      K(x,((y * z) \ y) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6700(a,2,2))].">
      <j1 rule="para" parents="9 6700"/>
    </justification>
  </clause>

  <clause id="6707">
    <literal><![CDATA[
      K(x,((y * z) * u) \ (y * (z * u))) = K(x,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(14(a,2),6700(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14 6700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6708">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[para(22(a,2),6700(a,1,2,1))].">
      <j1 rule="para" parents="22 6700"/>
    </justification>
  </clause>

  <clause id="6709">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(82(a,1),6700(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 6700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6710">
    <literal><![CDATA[
      K(x,(y \ (y / z)) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),6700(a,2,2))].">
      <j1 rule="para" parents="82 6700"/>
    </justification>
  </clause>

  <clause id="6711">
    <literal><![CDATA[
      K(x,L(y \ z,y,u) \ 1) = K(x,(u * z) \ (u * y))
    ]]></literal>
    <justification jstring="[para(102(a,2),6700(a,1,2,1))].">
      <j1 rule="para" parents="102 6700"/>
    </justification>
  </clause>

  <clause id="6712">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ y) = K(x,a(y,z,z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(982(a,1),6700(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="982 6700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6713">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(6156(a,1),6700(a,1,2,1))].">
      <j1 rule="para" parents="6156 6700"/>
    </justification>
  </clause>

  <clause id="6714">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ 1) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(6156(a,1),6700(a,2,2))].">
      <j1 rule="para" parents="6156 6700"/>
    </justification>
  </clause>

  <clause id="6715">
    <literal><![CDATA[
      T((x \ y) \ K(z,y \ x),z) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(6700(a,1),5866(a,1,1,2))].">
      <j1 rule="para" parents="6700 5866"/>
    </justification>
  </clause>

  <clause id="6716">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,(z * u) \ T(z,y))
    ]]></literal>
    <justification jstring="[para(6155(a,1),6700(a,1,2,1))].">
      <j1 rule="para" parents="6155 6700"/>
    </justification>
  </clause>

  <clause id="6717">
    <literal><![CDATA[
      R(x,y \ z,K(u,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(6700(a,1),6479(a,1,3))].">
      <j1 rule="para" parents="6700 6479"/>
    </justification>
  </clause>

  <clause id="6718">
    <literal><![CDATA[
      K(x,y \ z) * K(x * ((z \ y) \ 1),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6700(a,1),6353(a,1,1))].">
      <j1 rule="para" parents="6700 6353"/>
    </justification>
  </clause>

  <clause id="6719">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6700(a,1),6666(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6700 6666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6720">
    <literal><![CDATA[
      T(x \ y,z) * T(x,x \ y) = K(z,(y \ x) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(6700(a,2),6211(a,2,1))].">
      <j1 rule="para" parents="6700 6211"/>
    </justification>
  </clause>

  <clause id="6721">
    <literal><![CDATA[
      x \ (y * K(z,y \ x)) = (x \ y) * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(6717(a,1),649(a,1,1))].">
      <j1 rule="para" parents="6717 649"/>
    </justification>
  </clause>

  <clause id="6722">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,u / (z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,6381,a,b,6702,a),flip(a)].">
      <j1 rule="hyper" parents="373 6381 6702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6724">
    <literal><![CDATA[
      K(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6702(a,2),6045(a,1))].">
      <j1 rule="para" parents="6702 6045"/>
    </justification>
  </clause>

  <clause id="6725">
    <literal><![CDATA[
      T(x / ((y \ z) \ 1),z \ y) = ((y \ z) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,6704,a),flip(a)].">
      <j1 rule="hyper" parents="467 6704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6727">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = K(z \ y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,5804,a(flip),b,6704,a),flip(a)].">
      <j1 rule="hyper" parents="373 5804 6704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6728">
    <literal><![CDATA[
      x / T((y \ z) * x,z \ y) = ((y \ z) * x) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,6704,a(flip),b,4590,a(flip))].">
      <j1 rule="hyper" parents="225 6704 4590"/>
    </justification>
  </clause>

  <clause id="6729">
    <literal><![CDATA[
      T(x,(y * z) \ y) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),6704(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6730">
    <literal><![CDATA[
      T(x,((y * z) \ y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6704(a,2,2))].">
      <j1 rule="para" parents="9 6704"/>
    </justification>
  </clause>

  <clause id="6732">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[para(22(a,2),6704(a,1,2,1))].">
      <j1 rule="para" parents="22 6704"/>
    </justification>
  </clause>

  <clause id="6733">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(82(a,1),6704(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 6704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6734">
    <literal><![CDATA[
      T(x,x \ y) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(6704(a,1),4403(a,1,1))].">
      <j1 rule="para" parents="6704 4403"/>
    </justification>
  </clause>

  <clause id="6735">
    <literal><![CDATA[
      ((x \ y) \ z) / T(z,y \ x) = z \ ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(6704(a,1),4576(a,1,2))].">
      <j1 rule="para" parents="6704 4576"/>
    </justification>
  </clause>

  <clause id="6736">
    <literal><![CDATA[
      T(x,y \ z) / ((z \ y) \ x) = x / ((x \ ((z \ y) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(6704(a,1),4778(a,1,1))].">
      <j1 rule="para" parents="6704 4778"/>
    </justification>
  </clause>

  <clause id="6738">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,6705,a(flip),b,5961,a),flip(a)].">
      <j1 rule="hyper" parents="145 6705 5961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6739">
    <literal><![CDATA[
      K(x * y,y \ 1) * ((x * y) \ x) = x / (x * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,6705,a(flip),b,5725,a)].">
      <j1 rule="hyper" parents="144 6705 5725"/>
    </justification>
  </clause>

  <clause id="6743">
    <literal><![CDATA[
      L(x,K(y,z),u \ (u / z)) = x
    ]]></literal>
    <justification jstring="[para(6710(a,1),4491(a,1,2))].">
      <j1 rule="para" parents="6710 4491"/>
    </justification>
  </clause>

  <clause id="6744">
    <literal><![CDATA[
      L(x,K(y,z),u \ (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6743(a,1),51(a,2))].">
      <j1 rule="para" parents="6743 51"/>
    </justification>
  </clause>

  <clause id="6745">
    <literal><![CDATA[
      T(x * y,y \ 1) = ((x * y) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(478,a,6729,a),flip(a)].">
      <j1 rule="hyper" parents="478 6729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6746">
    <literal><![CDATA[
      T(x / ((y * z) \ y),z \ 1) = ((y * z) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,6729,a),flip(a)].">
      <j1 rule="hyper" parents="467 6729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6747">
    <literal><![CDATA[
      ((x * y) \ x) * T(z,y \ 1) = z * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,6729,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 6729 22"/>
    </justification>
  </clause>

  <clause id="6748">
    <literal><![CDATA[
      ((x * y) \ x) \ T(((x * y) \ x) * z,y) = ((((x * y) \ x) \ 1) \ z) * (((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,6730,a(flip),b,1181,a)].">
      <j1 rule="hyper" parents="139 6730 1181"/>
    </justification>
  </clause>

  <clause id="6750">
    <literal><![CDATA[
      T(x,L(y \ 1,y,z) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(241(a,2),6730(a,1,2,1))].">
      <j1 rule="para" parents="241 6730"/>
    </justification>
  </clause>

  <clause id="6752">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * T(z,y) = z * (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(6730(a,1),3873(a,1,2))].">
      <j1 rule="para" parents="6730 3873"/>
    </justification>
  </clause>

  <clause id="6753">
    <literal><![CDATA[
      T(T(x \ (x / y),z),y \ 1) = T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(468,a,6733,a),flip(a)].">
      <j1 rule="hyper" parents="468 6733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6754">
    <literal><![CDATA[
      T(x / (y \ (y / z)),z \ 1) = (y \ (y / z)) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,6733,a),flip(a)].">
      <j1 rule="hyper" parents="467 6733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6755">
    <literal><![CDATA[
      T((x / y) / x,y \ 1) = (x / y) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,282,a(flip),b,6733,a),flip(a)].">
      <j1 rule="hyper" parents="64 282 6733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6756">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,5804,a(flip),b,6727,a(flip))].">
      <j1 rule="hyper" parents="40 5804 6727"/>
    </justification>
  </clause>

  <clause id="6757">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6727(a,2),5871(a,1))].">
      <j1 rule="para" parents="6727 5871"/>
    </justification>
  </clause>

  <clause id="6758">
    <literal><![CDATA[
      K((x \ (x / y)) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1572,a(flip),b,6756,a),flip(a)].">
      <j1 rule="hyper" parents="373 1572 6756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6759">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1571,a(flip),b,6756,a),flip(a)].">
      <j1 rule="hyper" parents="373 1571 6756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6761">
    <literal><![CDATA[
      T(K(x / y,z),x) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6571,a,b,6756,a)].">
      <j1 rule="hyper" parents="64 6571 6756"/>
    </justification>
  </clause>

  <clause id="6762">
    <literal><![CDATA[
      K((x \ y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6575,a(flip),b,6756,a),flip(a)].">
      <j1 rule="hyper" parents="64 6575 6756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6763">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,6756,a(flip),b,5992,a),flip(a)].">
      <j1 rule="hyper" parents="145 6756 5992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6764">
    <literal><![CDATA[
      K(x \ y,z) * ((y \ x) \ 1) = T((y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,6756,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 6756 5739"/>
    </justification>
  </clause>

  <clause id="6765">
    <literal><![CDATA[
      (x \ y) \ K(y \ x,z) = T((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,6756,a(flip),b,5743,a)].">
      <j1 rule="hyper" parents="139 6756 5743"/>
    </justification>
  </clause>

  <clause id="6766">
    <literal><![CDATA[
      K((x * y) \ x,z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6756(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 6756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6767">
    <literal><![CDATA[
      K(x \ (x / y),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),6756(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 6756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6768">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) = K(z \ K(y,x),u)
    ]]></literal>
    <justification jstring="[para(6156(a,1),6756(a,1,1,1))].">
      <j1 rule="para" parents="6156 6756"/>
    </justification>
  </clause>

  <clause id="6769">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6756(a,2),6038(a,1))].">
      <j1 rule="para" parents="6756 6038"/>
    </justification>
  </clause>

  <clause id="6770">
    <literal><![CDATA[
      (x * K(y \ x,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[para(6756(a,1),6573(a,1,1,2))].">
      <j1 rule="para" parents="6756 6573"/>
    </justification>
  </clause>

  <clause id="6771">
    <literal><![CDATA[
      K(L(x \ 1,x,y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(448(a,1),6758(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="448 6758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6772">
    <literal><![CDATA[
      T(x \ (x / y),K(y,z)) = x \ (x / y)
    ]]></literal>
    <justification jstring="[para(6758(a,1),6006(a,1,2))].">
      <j1 rule="para" parents="6758 6006"/>
    </justification>
  </clause>

  <clause id="6773">
    <literal><![CDATA[
      T(1 / (x \ (x / y)),z) \ 1 = K(y,z) \ (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(6758(a,1),6011(a,2,1))].">
      <j1 rule="para" parents="6758 6011"/>
    </justification>
  </clause>

  <clause id="6774">
    <literal><![CDATA[
      (x * K(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(6758(a,1),6573(a,1,1,2))].">
      <j1 rule="para" parents="6758 6573"/>
    </justification>
  </clause>

  <clause id="6778">
    <literal><![CDATA[
      K(x / y,x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(4017,a,6761,a)].">
      <j1 rule="hyper" parents="4017 6761"/>
    </justification>
  </clause>

  <clause id="6779">
    <literal><![CDATA[
      K(x \ y,z) * K(y,K(x \ y,z)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,5785,a,b,6761,a)].">
      <j1 rule="hyper" parents="41 5785 6761"/>
    </justification>
  </clause>

  <clause id="6780">
    <literal><![CDATA[
      K(x / y,z) * x = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,6761,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 6761 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6781">
    <literal><![CDATA[
      K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(6761(a,1),378(a,1)),flip(b)].">
      <j1 rule="para" parents="6761 378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6783">
    <literal><![CDATA[
      K((x \ y) \ y,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),6778(a,1,1)),flip(a)].">
      <j1 rule="para" parents="79 6778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6784">
    <literal><![CDATA[
      K((x \ y) \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(6762(a,2),4017(a,1))].">
      <j1 rule="para" parents="6762 4017"/>
    </justification>
  </clause>

  <clause id="6785">
    <literal><![CDATA[
      T(K(x,y),z * x) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4678(a,2),6762(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4678 6762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6786">
    <literal><![CDATA[
      K((x * y) \ x,z) = K(1 / y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,3776,a,b,6766,a),flip(a)].">
      <j1 rule="hyper" parents="373 3776 6766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6788">
    <literal><![CDATA[
      K(x \ 1,x * x) = K(x,x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6608,a(flip),b,6766,a),flip(a)].">
      <j1 rule="hyper" parents="64 6608 6766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6789">
    <literal><![CDATA[
      K(x \ 1,y) * ((z * x) \ z) = T((z * x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,6766,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 6766 5739"/>
    </justification>
  </clause>

  <clause id="6790">
    <literal><![CDATA[
      (((x * y) \ x) * z) / T((x * y) \ x,u) = z * (K(y \ 1,z) * K(u,(x * y) \ x))
    ]]></literal>
    <justification jstring="[para(6766(a,1),6393(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6766 6393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6797">
    <literal><![CDATA[
      (x / y) / ((x / y) / x) = x * K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,6767,a(flip),b,5790,a),flip(a)].">
      <j1 rule="hyper" parents="145 6767 5790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6798">
    <literal><![CDATA[
      (x \ (x / y)) * K(y \ 1,z) = T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,6767,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 6767 5726"/>
    </justification>
  </clause>

  <clause id="6802">
    <literal><![CDATA[
      K((x * y) \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(6786(a,2),3777(a,1))].">
      <j1 rule="para" parents="6786 3777"/>
    </justification>
  </clause>

  <clause id="6803">
    <literal><![CDATA[
      K(x / (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / y,z) = u
    ]]></literal>
    <justification jstring="[para(6582(a,2),6781(a,1))].">
      <j1 rule="para" parents="6582 6781"/>
    </justification>
  </clause>

  <clause id="6804">
    <literal><![CDATA[
      T(x,x \ (y * x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),6734(a,2,2))].">
      <j1 rule="para" parents="11 6734"/>
    </justification>
  </clause>

  <clause id="6805">
    <literal><![CDATA[
      (x * (y / x)) * (y \ x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,x \ y) = u
    ]]></literal>
    <justification jstring="[para(6734(a,1),391(a,1,1))].">
      <j1 rule="para" parents="6734 391"/>
    </justification>
  </clause>

  <clause id="6806">
    <literal><![CDATA[
      T(x,y / x) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4636(a,2),6734(a,1,1))].">
      <j1 rule="para" parents="4636 6734"/>
    </justification>
  </clause>

  <clause id="6807">
    <literal><![CDATA[
      L(x \ 1,x,y) \ y = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,437,a,b,6745,a)].">
      <j1 rule="hyper" parents="373 437 6745"/>
    </justification>
  </clause>

  <clause id="6808">
    <literal><![CDATA[
      (x \ 1) * (((y * x) \ y) \ y) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,6745,a(flip),b,698,a)].">
      <j1 rule="hyper" parents="145 6745 698"/>
    </justification>
  </clause>

  <clause id="6809">
    <literal><![CDATA[
      T(x * (1 / y),y) = ((x * (1 / y)) \ x) \ x
    ]]></literal>
    <justification jstring="[para(82(a,1),6745(a,1,2))].">
      <j1 rule="para" parents="82 6745"/>
    </justification>
  </clause>

  <clause id="6810">
    <literal><![CDATA[
      T((x / (y \ 1)) / x,y) = (x / (y \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,3871,a(flip),b,6755,a)].">
      <j1 rule="hyper" parents="64 3871 6755"/>
    </justification>
  </clause>

  <clause id="6811">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(1563,a,6763,a)].">
      <j1 rule="hyper" parents="1563 6763"/>
    </justification>
  </clause>

  <clause id="6812">
    <literal><![CDATA[
      x \ (y * K(x \ y,z)) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,6763,a)].">
      <j1 rule="hyper" parents="149 6763"/>
    </justification>
  </clause>

  <clause id="6814">
    <literal><![CDATA[
      (x \ 1) * (y * K(x \ y,z)) = T((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,6763,a(flip),b,5441,a)].">
      <j1 rule="hyper" parents="145 6763 5441"/>
    </justification>
  </clause>

  <clause id="6815">
    <literal><![CDATA[
      (1 / x) * (y * K(x \ y,z)) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,6763,a(flip),b,1020,a)].">
      <j1 rule="hyper" parents="145 6763 1020"/>
    </justification>
  </clause>

  <clause id="6816">
    <literal><![CDATA[
      x * (y * K((x \ 1) \ y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,6763,a(flip),b,1182,a(flip))].">
      <j1 rule="hyper" parents="145 6763 1182"/>
    </justification>
  </clause>

  <clause id="6817">
    <literal><![CDATA[
      (x * K(y \ x,z)) * (y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(144,a,6763,a(flip),b,1503,a)].">
      <j1 rule="hyper" parents="144 6763 1503"/>
    </justification>
  </clause>

  <clause id="6818">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((y / z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,2584,a(flip),b,6763,a(flip))].">
      <j1 rule="hyper" parents="139 2584 6763"/>
    </justification>
  </clause>

  <clause id="6819">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6763(a,2),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6763 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6820">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(y * K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(6763(a,1),3085(a,2,1))].">
      <j1 rule="para" parents="6763 3085"/>
    </justification>
  </clause>

  <clause id="6821">
    <literal><![CDATA[
      (((x / y) * (y * z)) * K(L(z,y,x / y),u)) / x = T(((x / y) * (y * z)) / x,u)
    ]]></literal>
    <justification jstring="[para(103(a,1),6770(a,1,1,2,1))].">
      <j1 rule="para" parents="103 6770"/>
    </justification>
  </clause>

  <clause id="6822">
    <literal><![CDATA[
      K(L(x,y,z) / u,x) = K(u \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(36,a,4002,a(flip),b,6780,a),flip(a)].">
      <j1 rule="hyper" parents="36 4002 6780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6823">
    <literal><![CDATA[
      K(x / (x / y),z) * x = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),6780(a,2,2,1))].">
      <j1 rule="para" parents="82 6780"/>
    </justification>
  </clause>

  <clause id="6824">
    <literal><![CDATA[
      T(x,(x / y) / x) / ((x / y) \ x) = (x / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6272,a,b,6806,a),flip(a)].">
      <j1 rule="hyper" parents="373 6272 6806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6825">
    <literal><![CDATA[
      K(x,(y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(11(a,1),6724(a,1,2,2))].">
      <j1 rule="para" parents="11 6724"/>
    </justification>
  </clause>

  <clause id="6826">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * z) \ z) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),6757(a,1,2,1))].">
      <j1 rule="para" parents="22 6757"/>
    </justification>
  </clause>

  <clause id="6827">
    <literal><![CDATA[
      K((x \ y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),6769(a,1,1,1,1))].">
      <j1 rule="para" parents="10 6769"/>
    </justification>
  </clause>

  <clause id="6828">
    <literal><![CDATA[
      K(x \ (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),6802(a,1,1,1))].">
      <j1 rule="para" parents="12 6802"/>
    </justification>
  </clause>

  <clause id="6829">
    <literal><![CDATA[
      x / T(x * (y / x),y \ x) = L((y / x) \ 1,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(225,a,5500,a(flip),b,6807,a)].">
      <j1 rule="hyper" parents="225 5500 6807"/>
    </justification>
  </clause>

  <clause id="6830">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,L(y \ 1,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(6807(a,1),4575(a,1,2,2))].">
      <j1 rule="para" parents="6807 4575"/>
    </justification>
  </clause>

  <clause id="6831">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),6827(a,1,1,1))].">
      <j1 rule="para" parents="22 6827"/>
    </justification>
  </clause>

  <clause id="6832">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z \ K(y,x),u) = w
    ]]></literal>
    <justification jstring="[para(6156(a,1),6827(a,1,1,1))].">
      <j1 rule="para" parents="6156 6827"/>
    </justification>
  </clause>

  <clause id="6833">
    <literal><![CDATA[
      T(K(x / y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6571(a,2),6827(a,1))].">
      <j1 rule="para" parents="6571 6827"/>
    </justification>
  </clause>

  <clause id="6835">
    <literal><![CDATA[
      K(x / y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(3991(a,1),6833(a,1))].">
      <j1 rule="para" parents="3991 6833"/>
    </justification>
  </clause>

  <clause id="6836">
    <literal><![CDATA[
      T((x \ y) \ 1,x / y) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(283(a,1),6715(a,1,1,2))].">
      <j1 rule="para" parents="283 6715"/>
    </justification>
  </clause>

  <clause id="6837">
    <literal><![CDATA[
      ((x \ y) \ 1) * (x / y) = (x / y) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,6836,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 6836 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6838">
    <literal><![CDATA[
      K(x \ y,x) * T((x \ y) \ 1,z) = (y / x) \ K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,6765,a(flip),b,6609,a)].">
      <j1 rule="hyper" parents="145 6765 6609"/>
    </justification>
  </clause>

  <clause id="6839">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) \ 1,w) = T(K(z \ K(y,x),w),u)
    ]]></literal>
    <justification jstring="[para(6768(a,1),6563(a,2,1))].">
      <j1 rule="para" parents="6768 6563"/>
    </justification>
  </clause>

  <clause id="6840">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,911,a,b,6774,a)].">
      <j1 rule="hyper" parents="38 911 6774"/>
    </justification>
  </clause>

  <clause id="6841">
    <literal><![CDATA[
      x * K(y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(38,a,3594,a(flip),b,6774,a),flip(a)].">
      <j1 rule="hyper" parents="38 3594 6774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6842">
    <literal><![CDATA[
      T(x,y) \ (z * K(x,y)) = T(z / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(493,a,xx,b,6840,a),flip(a)].">
      <j1 rule="hyper" parents="493 6840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6843">
    <literal><![CDATA[
      ((x / y) / z) * T(z,y) = x / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6245,a(flip),b,6840,a),flip(a)].">
      <j1 rule="hyper" parents="373 6245 6840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6844">
    <literal><![CDATA[
      (x / y) \ (x * K(y,z)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,6840,a)].">
      <j1 rule="hyper" parents="149 6840"/>
    </justification>
  </clause>

  <clause id="6845">
    <literal><![CDATA[
      (T(x,y) / y) / T(x,y) = (x / y) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,6315,a(flip),b,6840,a)].">
      <j1 rule="hyper" parents="142 6315 6840"/>
    </justification>
  </clause>

  <clause id="6846">
    <literal><![CDATA[
      (x * T(y,z)) / z = (x * y) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,6249,a(flip),b,6840,a),flip(a)].">
      <j1 rule="hyper" parents="142 6249 6840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6847">
    <literal><![CDATA[
      (x * T(y,z)) / y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2512,a,b,6840,a)].">
      <j1 rule="hyper" parents="64 2512 6840"/>
    </justification>
  </clause>

  <clause id="6848">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(64,a,2514,a(flip),b,6840,a),flip(a)].">
      <j1 rule="hyper" parents="64 2514 6840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6849">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ z) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,364,a(flip),b,6840,a)].">
      <j1 rule="hyper" parents="64 364 6840"/>
    </justification>
  </clause>

  <clause id="6850">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,6840,a(flip),b,2512,a)].">
      <j1 rule="hyper" parents="144 6840 2512"/>
    </justification>
  </clause>

  <clause id="6851">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * T(L(z,y,x),u)) = K(L(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(139,a,403,a(flip),b,6840,a(flip))].">
      <j1 rule="hyper" parents="139 403 6840"/>
    </justification>
  </clause>

  <clause id="6852">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),6840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 6840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6853">
    <literal><![CDATA[
      T(x * K(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[para(6840(a,1),2511(a,1,1))].">
      <j1 rule="para" parents="6840 2511"/>
    </justification>
  </clause>

  <clause id="6854">
    <literal><![CDATA[
      (x / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6844(a,1),290(a,1,2))].">
      <j1 rule="para" parents="6844 290"/>
    </justification>
  </clause>

  <clause id="6855">
    <literal><![CDATA[
      (x * (y \ z)) * T(y,y \ z) = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,6471,a(flip),b,6847,a),flip(a)].">
      <j1 rule="hyper" parents="144 6471 6847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6856">
    <literal><![CDATA[
      (x * (y * K(z,y))) * z = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,6470,a(flip),b,6847,a)].">
      <j1 rule="hyper" parents="144 6470 6847"/>
    </justification>
  </clause>

  <clause id="6857">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,6464,a(flip),b,6847,a)].">
      <j1 rule="hyper" parents="144 6464 6847"/>
    </justification>
  </clause>

  <clause id="6858">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,6249,a(flip),b,6847,a),flip(a)].">
      <j1 rule="hyper" parents="144 6249 6847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6859">
    <literal><![CDATA[
      (x / T(y,z)) * z = (x / y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,6245,a(flip),b,6847,a)].">
      <j1 rule="hyper" parents="144 6245 6847"/>
    </justification>
  </clause>

  <clause id="6860">
    <literal><![CDATA[
      (x * y) / T(y,z) = x / K(y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,86,a(flip),b,6847,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="142 86 6847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6861">
    <literal><![CDATA[
      T(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6847(a,1),467(a,1,1))].">
      <j1 rule="para" parents="6847 467"/>
    </justification>
  </clause>

  <clause id="6862">
    <literal><![CDATA[
      (1 / x) * K(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(5738(a,2),6847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5738 6847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6863">
    <literal><![CDATA[
      (x * K(y,z)) / y = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6840(a,1),6847(a,1,1))].">
      <j1 rule="para" parents="6840 6847"/>
    </justification>
  </clause>

  <clause id="6864">
    <literal><![CDATA[
      (T(x,y) / y) * K(y,x) = x / y
    ]]></literal>
    <justification jstring="[hyper(4656,a,6848,a)].">
      <j1 rule="hyper" parents="4656 6848"/>
    </justification>
  </clause>

  <clause id="6865">
    <literal><![CDATA[
      T(x / T(y,z),K(y,z)) = K(z,y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(269,a,6848,a,b,6161,a)].">
      <j1 rule="hyper" parents="269 6848 6161"/>
    </justification>
  </clause>

  <clause id="6866">
    <literal><![CDATA[
      (x / T(y,y \ z)) / (y \ z) = (x / y) / (z / y)
    ]]></literal>
    <justification jstring="[hyper(142,a,6848,a(flip),b,6468,a),flip(a)].">
      <j1 rule="hyper" parents="142 6848 6468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6867">
    <literal><![CDATA[
      (x * K(y,x)) * K(y,x) = (T(y,x) * x) / y
    ]]></literal>
    <justification jstring="[para(5854(a,1),6848(a,1,1))].">
      <j1 rule="para" parents="5854 6848"/>
    </justification>
  </clause>

  <clause id="6868">
    <literal><![CDATA[
      (x / T(y,y \ z)) * (z / y) = (x / y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(6848(a,1),6064(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6848 6064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6869">
    <literal><![CDATA[
      (x * K(y,y \ z)) * y = x * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,364,a(flip),b,6850,a),flip(a)].">
      <j1 rule="hyper" parents="373 364 6850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6870">
    <literal><![CDATA[
      ((x * y) * K(L(z,y,x),u)) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,517,a(flip),b,6850,a)].">
      <j1 rule="hyper" parents="139 517 6850"/>
    </justification>
  </clause>

  <clause id="6871">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,5875,a(flip),b,6850,a),flip(a)].">
      <j1 rule="hyper" parents="36 5875 6850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6872">
    <literal><![CDATA[
      (x * (y / z)) * K(y / z,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(36,a,2527,a(flip),b,6850,a),flip(a)].">
      <j1 rule="hyper" parents="36 2527 6850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6874">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ ((x * (y * K(z,u))) * z) = a(x,y * K(z,u),z)
    ]]></literal>
    <justification jstring="[para(6850(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6850 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6875">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = (y * T(x,z)) \ (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(6850(a,1),241(a,2,1))].">
      <j1 rule="para" parents="6850 241"/>
    </justification>
  </clause>

  <clause id="6876">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * (y * T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(z,y * K(z,u),x) = w
    ]]></literal>
    <justification jstring="[para(6850(a,1),608(a,1,2,2))].">
      <j1 rule="para" parents="6850 608"/>
    </justification>
  </clause>

  <clause id="6877">
    <literal><![CDATA[
      (K(x,y) * K(x,y)) * (T(z,K(x,y) * K(x,y)) * x) = z * (K(x,y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(6850(a,1),1434(a,2,2))].">
      <j1 rule="para" parents="6850 1434"/>
    </justification>
  </clause>

  <clause id="6878">
    <literal><![CDATA[
      x / K(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(390,a,6871,a),flip(a)].">
      <j1 rule="hyper" parents="390 6871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6881">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(269,a,6871,a,b,6161,a)].">
      <j1 rule="hyper" parents="269 6871 6161"/>
    </justification>
  </clause>

  <clause id="6882">
    <literal><![CDATA[
      (x * K(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(149,a,6871,a)].">
      <j1 rule="hyper" parents="149 6871"/>
    </justification>
  </clause>

  <clause id="6883">
    <literal><![CDATA[
      (((x \ y) \ y) * K(z,u)) \ T(x,x \ y) = K(u,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,116,a,b,6871,a)].">
      <j1 rule="hyper" parents="139 116 6871"/>
    </justification>
  </clause>

  <clause id="6884">
    <literal><![CDATA[
      (x \ R(x,y,x)) * K(y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,6506,a,b,6871,a),flip(a)].">
      <j1 rule="hyper" parents="36 6506 6871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6886">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(36,a,6471,a,b,6871,a),flip(a)].">
      <j1 rule="hyper" parents="36 6471 6871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6887">
    <literal><![CDATA[
      (x / (y \ z)) * K(y \ z,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[hyper(36,a,6455,a,b,6871,a),flip(a)].">
      <j1 rule="hyper" parents="36 6455 6871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6888">
    <literal><![CDATA[
      x / ((y * z) / y) = (x / z) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,6400,a,b,6871,a)].">
      <j1 rule="hyper" parents="36 6400 6871"/>
    </justification>
  </clause>

  <clause id="6889">
    <literal><![CDATA[
      (x * y) * K(y,y \ z) = x * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(36,a,6326,a,b,6871,a),flip(a)].">
      <j1 rule="hyper" parents="36 6326 6871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6890">
    <literal><![CDATA[
      L(x,y,z) * K(x,1 / x) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,6217,a,b,6871,a),flip(a)].">
      <j1 rule="hyper" parents="36 6217 6871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6891">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * K(y,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,3320,a,b,6871,a),flip(a)].">
      <j1 rule="hyper" parents="36 3320 6871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6892">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(z,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(144,a,6871,a(flip),b,5703,a),flip(a)].">
      <j1 rule="hyper" parents="144 6871 5703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6893">
    <literal><![CDATA[
      x * L(y,K(z,u),x * K(u,z)) = (x * K(u,z)) * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,6871,a(flip),b,213,a)].">
      <j1 rule="hyper" parents="144 6871 213"/>
    </justification>
  </clause>

  <clause id="6894">
    <literal><![CDATA[
      (x * K(y,y \ z)) / y = x / (z / (z / y))
    ]]></literal>
    <justification jstring="[hyper(142,a,6871,a(flip),b,6469,a),flip(a)].">
      <j1 rule="hyper" parents="142 6871 6469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6895">
    <literal><![CDATA[
      (x * K(y \ z,y)) / (y \ z) = x / (z / y)
    ]]></literal>
    <justification jstring="[hyper(142,a,6871,a(flip),b,6468,a),flip(a)].">
      <j1 rule="hyper" parents="142 6871 6468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6896">
    <literal><![CDATA[
      L(K(x,y),z * K(y,x),u) = (u * (z * K(y,x))) \ (u * z)
    ]]></literal>
    <justification jstring="[para(6871(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="6871 18"/>
    </justification>
  </clause>

  <clause id="6897">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(6871(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="6871 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6898">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6871(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6871 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6899">
    <literal><![CDATA[
      (x * K(y,z)) \ x != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6871(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6871 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6900">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * (K(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,K(z,y),x * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6871(a,1),608(a,1,1))].">
      <j1 rule="para" parents="6871 608"/>
    </justification>
  </clause>

  <clause id="6901">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(6871(a,1),959(a,1,1,2))].">
      <j1 rule="para" parents="6871 959"/>
    </justification>
  </clause>

  <clause id="6903">
    <literal><![CDATA[
      (x / T(y,z)) * y = x / K(y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6311,a,b,6878,a)].">
      <j1 rule="hyper" parents="373 6311 6878"/>
    </justification>
  </clause>

  <clause id="6904">
    <literal><![CDATA[
      (x * (y \ z)) / K(y \ z,y) = x * (z / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6471,a(flip),b,6878,a),flip(a)].">
      <j1 rule="hyper" parents="373 6471 6878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6905">
    <literal><![CDATA[
      (x / ((y * z) / y)) * z = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6399,a,b,6878,a)].">
      <j1 rule="hyper" parents="64 6399 6878"/>
    </justification>
  </clause>

  <clause id="6906">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5917,a,b,6878,a)].">
      <j1 rule="hyper" parents="64 5917 6878"/>
    </justification>
  </clause>

  <clause id="6907">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = T(z * x,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(493,a,6322,a(flip),b,6878,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="493 6322 6878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6908">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,6322,a(flip),b,6878,a(flip))].">
      <j1 rule="hyper" parents="139 6322 6878"/>
    </justification>
  </clause>

  <clause id="6909">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(6878(a,1),285(a,1,1))].">
      <j1 rule="para" parents="6878 285"/>
    </justification>
  </clause>

  <clause id="6910">
    <literal><![CDATA[
      R((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(6878(a,1),351(a,1,1))].">
      <j1 rule="para" parents="6878 351"/>
    </justification>
  </clause>

  <clause id="6911">
    <literal><![CDATA[
      x / y != (z * K(u,w)) * K(w,u)
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(6878(a,1),389(a,2,1))].">
      <j1 rule="para" parents="6878 389"/>
    </justification>
  </clause>

  <clause id="6912">
    <literal><![CDATA[
      R((x * K(y,z)) / u,u,K(z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      x / (u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(6878(a,1),760(a,1,1,1))].">
      <j1 rule="para" parents="6878 760"/>
    </justification>
  </clause>

  <clause id="6913">
    <literal><![CDATA[
      R((x / y) * K(z,u),K(u,z),y) != w
    ]]></literal>
    <literal><![CDATA[
      x / (K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(6878(a,1),760(a,1,1))].">
      <j1 rule="para" parents="6878 760"/>
    </justification>
  </clause>

  <clause id="6914">
    <literal><![CDATA[
      R(x / (y * K(1 / z,z)),y / K(z,1 / z),K(z,1 / z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[para(6878(a,1),3737(a,1,1,2))].">
      <j1 rule="para" parents="6878 3737"/>
    </justification>
  </clause>

  <clause id="6915">
    <literal><![CDATA[
      K(x,1 / (K(y,z) / u)) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6878(a,1),6377(a,2,2))].">
      <j1 rule="para" parents="6878 6377"/>
    </justification>
  </clause>

  <clause id="6916">
    <literal><![CDATA[
      (x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6670,a(flip),b,6882,a),flip(a)].">
      <j1 rule="hyper" parents="373 6670 6882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6917">
    <literal><![CDATA[
      x \ y != (z * K(u,w)) * K(w,u)
    ]]></literal>
    <literal><![CDATA[
      y / z = x
    ]]></literal>
    <justification jstring="[para(6882(a,1),404(a,2,2))].">
      <j1 rule="para" parents="6882 404"/>
    </justification>
  </clause>

  <clause id="6918">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5838,a,6852,a)].">
      <j1 rule="hyper" parents="5838 6852"/>
    </justification>
  </clause>

  <clause id="6919">
    <literal><![CDATA[
      ((1 / (x / y)) * x) * K(x,x \ y) = x * (1 / (x / y))
    ]]></literal>
    <justification jstring="[hyper(373,a,4582,a(flip),b,6852,a),flip(a)].">
      <j1 rule="hyper" parents="373 4582 6852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6920">
    <literal><![CDATA[
      K(x,y) * (z * T(y,x)) = T(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(269,a,6852,a,b,6161,a),flip(a)].">
      <j1 rule="hyper" parents="269 6852 6161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6921">
    <literal><![CDATA[
      T((x * y) / T(z,y),z) = z \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(493,a,6852,a(flip),b,6311,a)].">
      <j1 rule="hyper" parents="493 6852 6311"/>
    </justification>
  </clause>

  <clause id="6922">
    <literal><![CDATA[
      ((x * (y * z)) * K(z,u)) / (y * T(z,u)) = R(x,y * z,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(225,a,6852,a(flip),b,210,a)].">
      <j1 rule="hyper" parents="225 6852 210"/>
    </justification>
  </clause>

  <clause id="6923">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * T(z,u))) = L(K(z,u),y * z,x)
    ]]></literal>
    <justification jstring="[para(6852(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6852 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6924">
    <literal><![CDATA[
      (x * y) * K(y,z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6852(a,2),44(a,1))].">
      <j1 rule="para" parents="6852 44"/>
    </justification>
  </clause>

  <clause id="6926">
    <literal><![CDATA[
      ((x * y) * T(z,u)) / ((y * z) * K(z,u)) = R(R(x,y,z),y * z,K(z,u))
    ]]></literal>
    <justification jstring="[para(6852(a,1),660(a,1,1))].">
      <j1 rule="para" parents="6852 660"/>
    </justification>
  </clause>

  <clause id="6931">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,6092,a,b,6918,a),flip(a)].">
      <j1 rule="hyper" parents="373 6092 6918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6933">
    <literal><![CDATA[
      a(x,y,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,6918,a)].">
      <j1 rule="hyper" parents="54 6918"/>
    </justification>
  </clause>

  <clause id="6934">
    <literal><![CDATA[
      (1 / x) \ K(x \ 1,y) = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,6918,a(flip),b,1156,a)].">
      <j1 rule="hyper" parents="139 6918 1156"/>
    </justification>
  </clause>

  <clause id="6935">
    <literal><![CDATA[
      x * a(y,z,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,6933,a,b,68,a)].">
      <j1 rule="hyper" parents="145 6933 68"/>
    </justification>
  </clause>

  <clause id="6936">
    <literal><![CDATA[
      a(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(6935(a,1),151(a,1)),flip(a)].">
      <j1 rule="para" parents="6935 151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6937">
    <literal><![CDATA[
      L(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6931(a,2),6101(a,1))].">
      <j1 rule="para" parents="6931 6101"/>
    </justification>
  </clause>

  <clause id="6938">
    <literal><![CDATA[
      (x * x) \ T(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,5750,a,b,6862,a)].">
      <j1 rule="hyper" parents="64 5750 6862"/>
    </justification>
  </clause>

  <clause id="6939">
    <literal><![CDATA[
      (K(x,y) / x) * L(z,K(x,y),1 / x) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,6862,a(flip),b,213,a)].">
      <j1 rule="hyper" parents="144 6862 213"/>
    </justification>
  </clause>

  <clause id="6940">
    <literal><![CDATA[
      (x * y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6908(a,1),290(a,1,2))].">
      <j1 rule="para" parents="6908 290"/>
    </justification>
  </clause>

  <clause id="6941">
    <literal><![CDATA[
      x \ y != (z * u) * K(u,w)
    ]]></literal>
    <literal><![CDATA[
      y / (z * T(u,w)) = x
    ]]></literal>
    <justification jstring="[para(6908(a,1),404(a,2,2))].">
      <j1 rule="para" parents="6908 404"/>
    </justification>
  </clause>

  <clause id="6943">
    <literal><![CDATA[
      ((x * y) * R((x * y) \ x,z,u)) * T(y,w) = (x * y) * (T(y,w) * R(T(y,w) \ K(y,w),z,u))
    ]]></literal>
    <justification jstring="[para(6908(a,1),2814(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6908 2814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6944">
    <literal><![CDATA[
      R(K(x,y) / x,x,x \ y) = T(y,x * x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(6938(a,1),2052(a,1,1))].">
      <j1 rule="para" parents="6938 2052"/>
    </justification>
  </clause>

  <clause id="6945">
    <literal><![CDATA[
      (((x \ y) \ y) * K(z,u)) \ T(x,x \ y) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,z) = w
    ]]></literal>
    <justification jstring="[para(361(a,2),6899(a,1))].">
      <j1 rule="para" parents="361 6899"/>
    </justification>
  </clause>

  <clause id="6946">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(6763(a,2),6899(a,1,1))].">
      <j1 rule="para" parents="6763 6899"/>
    </justification>
  </clause>

  <clause id="6950">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(139,a,100,a(flip),b,6858,a)].">
      <j1 rule="hyper" parents="139 100 6858"/>
    </justification>
  </clause>

  <clause id="6951">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,T(y,z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(4619(a,2),6858(a,1,2))].">
      <j1 rule="para" parents="4619 6858"/>
    </justification>
  </clause>

  <clause id="6952">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[para(6858(a,1),4673(a,1,2))].">
      <j1 rule="para" parents="6858 4673"/>
    </justification>
  </clause>

  <clause id="6953">
    <literal><![CDATA[
      ((x * x) \ y) * x = (1 / T(x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,1051,a,b,6859,a)].">
      <j1 rule="hyper" parents="373 1051 6859"/>
    </justification>
  </clause>

  <clause id="6954">
    <literal><![CDATA[
      (((x * x) \ y) * x) / y = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,1051,a,b,6859,a)].">
      <j1 rule="hyper" parents="142 1051 6859"/>
    </justification>
  </clause>

  <clause id="6955">
    <literal><![CDATA[
      K(x,(y / (z * K(y,u))) \ 1) = K(x,(z / y) * K(y,u))
    ]]></literal>
    <justification jstring="[para(6863(a,1),6375(a,2,2))].">
      <j1 rule="para" parents="6863 6375"/>
    </justification>
  </clause>

  <clause id="6956">
    <literal><![CDATA[
      L(x * K(y,z),u,w) * K(z,y) = K(z,y) * L(K(y,z) * x,u,w)
    ]]></literal>
    <justification jstring="[para(6881(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6881 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6957">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,y / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),6888(a,1,2,1))].">
      <j1 rule="para" parents="12 6888"/>
    </justification>
  </clause>

  <clause id="6958">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(4707(a,1),6888(a,1,2))].">
      <j1 rule="para" parents="4707 6888"/>
    </justification>
  </clause>

  <clause id="6959">
    <literal><![CDATA[
      x / (y * K(z,y)) = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(5721(a,1),6888(a,1,2))].">
      <j1 rule="para" parents="5721 6888"/>
    </justification>
  </clause>

  <clause id="6960">
    <literal><![CDATA[
      K(x,((y / z) * K(z,u)) \ 1) = K(x,((u * z) / u) / y)
    ]]></literal>
    <justification jstring="[para(6888(a,1),6375(a,1,2,1))].">
      <j1 rule="para" parents="6888 6375"/>
    </justification>
  </clause>

  <clause id="6961">
    <literal><![CDATA[
      K(x,1 / ((y * (1 / z)) / y)) = K(x,z * K(1 / z,y))
    ]]></literal>
    <justification jstring="[para(6888(a,2),6524(a,1,2))].">
      <j1 rule="para" parents="6888 6524"/>
    </justification>
  </clause>

  <clause id="6962">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (y * K(u,y)) = (x * K(z,y)) * K(y,u)
    ]]></literal>
    <justification jstring="[hyper(142,a,5700,a(flip),b,6892,a)].">
      <j1 rule="hyper" parents="142 5700 6892"/>
    </justification>
  </clause>

  <clause id="6963">
    <literal><![CDATA[
      ((x / y) * K(y,z)) \ x = y * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,12,a(flip),b,6892,a)].">
      <j1 rule="hyper" parents="139 12 6892"/>
    </justification>
  </clause>

  <clause id="6965">
    <literal><![CDATA[
      (1 / (1 / ((x / y) / x))) * (y * K(y \ 1,y)) = ((x / y) / x) * y
    ]]></literal>
    <justification jstring="[para(4341(a,1),6892(a,1,1))].">
      <j1 rule="para" parents="4341 6892"/>
    </justification>
  </clause>

  <clause id="6966">
    <literal><![CDATA[
      (x / (y / z)) * (z \ y) = x * K(z \ y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),6905(a,1,1,2,1))].">
      <j1 rule="para" parents="10 6905"/>
    </justification>
  </clause>

  <clause id="6967">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x / ((z * y) / z),y) = y \ u
    ]]></literal>
    <justification jstring="[para(6905(a,1),321(a,1))].">
      <j1 rule="para" parents="6905 321"/>
    </justification>
  </clause>

  <clause id="6968">
    <literal><![CDATA[
      (x / (y * K(z,y))) * y = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(5721(a,1),6905(a,1,1,2))].">
      <j1 rule="para" parents="5721 6905"/>
    </justification>
  </clause>

  <clause id="6969">
    <literal><![CDATA[
      (x \ y) * ((K(x,x \ y) * z) / ((u * z) / u)) = (y / x) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,6906,a,b,6442,a)].">
      <j1 rule="hyper" parents="145 6906 6442"/>
    </justification>
  </clause>

  <clause id="6970">
    <literal><![CDATA[
      (x \ 1) * ((y * x) / y) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,6039,a(flip),b,6906,a)].">
      <j1 rule="hyper" parents="144 6039 6906"/>
    </justification>
  </clause>

  <clause id="6971">
    <literal><![CDATA[
      (x * (y \ z)) / (z / y) = x * K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),6906(a,1,2,1))].">
      <j1 rule="para" parents="10 6906"/>
    </justification>
  </clause>

  <clause id="6972">
    <literal><![CDATA[
      (((x \ y) * (x \ y)) \ (y \ x)) * (x \ y) = ((x \ y) \ 1) * (y \ x)
    ]]></literal>
    <justification jstring="[para(3803(a,1),6953(a,2,1))].">
      <j1 rule="para" parents="3803 6953"/>
    </justification>
  </clause>

  <clause id="6973">
    <literal><![CDATA[
      (x * x) \ ((y * x) / y) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,938,a(flip),b,6954,a)].">
      <j1 rule="hyper" parents="64 938 6954"/>
    </justification>
  </clause>

  <clause id="6974">
    <literal><![CDATA[
      (x / (y * K(z,y))) * u != w
    ]]></literal>
    <literal><![CDATA[
      ((x / y) * K(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(6963(a,1),400(a,1,1,2))].">
      <j1 rule="para" parents="6963 400"/>
    </justification>
  </clause>

  <clause id="6975">
    <literal><![CDATA[
      R(x,y,z) * T(y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,u) = w
    ]]></literal>
    <justification jstring="[para(20(a,2),6854(a,1,1))].">
      <j1 rule="para" parents="20 6854"/>
    </justification>
  </clause>

  <clause id="6977">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * K(x,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(y / x,z,u) * T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(836(a,1),6940(a,1,1))].">
      <j1 rule="para" parents="836 6940"/>
    </justification>
  </clause>

  <clause id="6978">
    <literal><![CDATA[
      T(x,T(y,x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(22(a,2),6804(a,1,1,2))].">
      <j1 rule="para" parents="22 6804"/>
    </justification>
  </clause>

  <clause id="6979">
    <literal><![CDATA[
      T(x,y) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(4619(a,1),6978(a,1,1))].">
      <j1 rule="para" parents="4619 6978"/>
    </justification>
  </clause>

  <clause id="6980">
    <literal><![CDATA[
      ((x \ y) * x) \ x = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(401,a,6979,a),flip(a)].">
      <j1 rule="hyper" parents="401 6979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6981">
    <literal><![CDATA[
      (x * y) \ T(x,y) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(215,a,6979,a)].">
      <j1 rule="hyper" parents="215 6979"/>
    </justification>
  </clause>

  <clause id="6982">
    <literal><![CDATA[
      T(x,y) = (x * y) * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[hyper(156,a,6979,a),flip(a)].">
      <j1 rule="hyper" parents="156 6979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6983">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,4708,a,b,6981,a)].">
      <j1 rule="hyper" parents="64 4708 6981"/>
    </justification>
  </clause>

  <clause id="6984">
    <literal><![CDATA[
      T(x * y,z) * ((y * x) \ x) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,6981,a(flip),b,6020,a)].">
      <j1 rule="hyper" parents="145 6981 6020"/>
    </justification>
  </clause>

  <clause id="6985">
    <literal><![CDATA[
      ((x * y) \ y) * T(y * x,x \ 1) = T(y,x)
    ]]></literal>
    <justification jstring="[para(6981(a,1),4863(a,1,1))].">
      <j1 rule="para" parents="6981 4863"/>
    </justification>
  </clause>

  <clause id="6986">
    <literal><![CDATA[
      R((x \ y) * x,((x \ y) * x) \ x,x \ ((x \ y) * x)) = ((y \ T(x,x \ y)) * (x \ ((x \ y) * x))) \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(6980(a,1),2158(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6980 2158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6987">
    <literal><![CDATA[
      x / T(x * (1 / y),y) = (x * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,6809,a,b,xx)].">
      <j1 rule="hyper" parents="225 6809"/>
    </justification>
  </clause>

  <clause id="6988">
    <literal><![CDATA[
      K((x \ 1) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,6320,a(flip),b,6811,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 6320 6811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6989">
    <literal><![CDATA[
      T(x * K((y \ 1) \ x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6811(a,1),5440(a,1,1))].">
      <j1 rule="para" parents="6811 5440"/>
    </justification>
  </clause>

  <clause id="6990">
    <literal><![CDATA[
      K((1 / x) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5254,a,b,6988,a)].">
      <j1 rule="hyper" parents="64 5254 6988"/>
    </justification>
  </clause>

  <clause id="6991">
    <literal><![CDATA[
      K((x \ 1) * y,x \ 1) = K(x \ y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5252,a(flip),b,6988,a),flip(a)].">
      <j1 rule="hyper" parents="64 5252 6988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6993">
    <literal><![CDATA[
      R(x,(y * z) / y,y) = ((x * z) * T(y,z)) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(142,a,6857,a(flip),b,657,a),flip(a)].">
      <j1 rule="hyper" parents="142 6857 657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6994">
    <literal><![CDATA[
      x * (K(y,x) * K(y,x)) = (T(y,x) * x) / y
    ]]></literal>
    <justification jstring="[hyper(4494,a,6867,a)].">
      <j1 rule="hyper" parents="4494 6867"/>
    </justification>
  </clause>

  <clause id="6995">
    <literal><![CDATA[
      R(T((x / (y \ z)) / u,u * K(y \ z,y)),u,K(y \ z,y)) = (u * K(y \ z,y)) \ (x / (z / y))
    ]]></literal>
    <justification jstring="[para(6887(a,1),1326(a,2,2))].">
      <j1 rule="para" parents="6887 1326"/>
    </justification>
  </clause>

  <clause id="6996">
    <literal><![CDATA[
      (x * K(y \ z,u)) * K(y \ z,y) = (x * T(y \ z,u)) / (z / y)
    ]]></literal>
    <justification jstring="[para(6847(a,1),6887(a,1,1))].">
      <j1 rule="para" parents="6847 6887"/>
    </justification>
  </clause>

  <clause id="6998">
    <literal><![CDATA[
      T(x * y,K(y,z)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6026,a(flip),b,6907,a),flip(a)].">
      <j1 rule="hyper" parents="64 6026 6907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6999">
    <literal><![CDATA[
      x * T(y / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),6998(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 6998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7000">
    <literal><![CDATA[
      T(x * (y / z),K(y / z,z)) = (y / z) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(117(a,1),6998(a,2,2,2))].">
      <j1 rule="para" parents="117 6998"/>
    </justification>
  </clause>

  <clause id="7001">
    <literal><![CDATA[
      T(x / y,T(y,z)) = y \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(149,a,6999,a),flip(a)].">
      <j1 rule="hyper" parents="149 6999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7002">
    <literal><![CDATA[
      K(x,1 / x) * (y / x) = y / (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,3607,a,b,6957,a)].">
      <j1 rule="hyper" parents="373 3607 6957"/>
    </justification>
  </clause>

  <clause id="7004">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,6700,a(flip),b,6991,a)].">
      <j1 rule="hyper" parents="64 6700 6991"/>
    </justification>
  </clause>

  <clause id="7005">
    <literal><![CDATA[
      (x / y) * (z * K(y,1 / y)) = (x / (1 / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(7002(a,1),5242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7002 5242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7006">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = T(K(x,(z \ y) \ 1),u)
    ]]></literal>
    <justification jstring="[para(6703(a,1),25(a,2,1))].">
      <j1 rule="para" parents="6703 25"/>
    </justification>
  </clause>

  <clause id="7007">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6703(a,1),623(a,1)),flip(b)].">
      <j1 rule="para" parents="6703 623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7008">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ z) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),7007(a,1,2,1))].">
      <j1 rule="para" parents="22 7007"/>
    </justification>
  </clause>

  <clause id="7009">
    <literal><![CDATA[
      K(x,L(y \ z,y,u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * z) \ (u * y)) = w
    ]]></literal>
    <justification jstring="[para(102(a,2),7007(a,1,2,1))].">
      <j1 rule="para" parents="102 7007"/>
    </justification>
  </clause>

  <clause id="7010">
    <literal><![CDATA[
      K(x,1 / (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6041(a,2),7007(a,1))].">
      <j1 rule="para" parents="6041 7007"/>
    </justification>
  </clause>

  <clause id="7011">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(6156(a,1),7007(a,1,2,1))].">
      <j1 rule="para" parents="6156 7007"/>
    </justification>
  </clause>

  <clause id="7013">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(1385(a,1),6819(a,1,2))].">
      <j1 rule="para" parents="1385 6819"/>
    </justification>
  </clause>

  <clause id="7014">
    <literal><![CDATA[
      K(((x \ 1) * y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(6831,a,6564,a)].">
      <j1 rule="hyper" parents="6831 6564"/>
    </justification>
  </clause>

  <clause id="7015">
    <literal><![CDATA[
      x / y != (z / u) * K(u,w)
    ]]></literal>
    <literal><![CDATA[
      (z / ((w * u) / w)) * y = x
    ]]></literal>
    <justification jstring="[para(6400(a,1),6911(a,2,1))].">
      <j1 rule="para" parents="6400 6911"/>
    </justification>
  </clause>

  <clause id="7016">
    <literal><![CDATA[
      x \ y != (z \ K(z,u)) * K(u,z)
    ]]></literal>
    <literal><![CDATA[
      y / (z \ 1) = x
    ]]></literal>
    <justification jstring="[para(4087(a,1),6917(a,2,1))].">
      <j1 rule="para" parents="4087 6917"/>
    </justification>
  </clause>

  <clause id="7017">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * y) \ z) = w
    ]]></literal>
    <justification jstring="[para(1308(a,1),6946(a,1,1))].">
      <j1 rule="para" parents="1308 6946"/>
    </justification>
  </clause>

  <clause id="7018">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = z * K(y \ x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(6756(a,1),6333(a,2,2))].">
      <j1 rule="para" parents="6756 6333"/>
    </justification>
  </clause>

  <clause id="7019">
    <literal><![CDATA[
      (((x \ 1) \ y) * (x \ (1 / x))) * x = y * K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,1123,a,b,6334,a)].">
      <j1 rule="hyper" parents="64 1123 6334"/>
    </justification>
  </clause>

  <clause id="7020">
    <literal><![CDATA[
      (x * (y * ((z * (y \ (x \ u))) / z))) / u = K(z,((x * y) / u) \ 1)
    ]]></literal>
    <justification jstring="[para(1963(a,1),6359(a,1,1))].">
      <j1 rule="para" parents="1963 6359"/>
    </justification>
  </clause>

  <clause id="7021">
    <literal><![CDATA[
      T(x * ((y * (x \ z)) / y),z) / z = K(y,(T(x,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(3331(a,1),6359(a,1,1))].">
      <j1 rule="para" parents="3331 6359"/>
    </justification>
  </clause>

  <clause id="7022">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,((z * u) \ u) * K(z * u,1 / z))
    ]]></literal>
    <justification jstring="[para(6384(a,2),6722(a,2,2))].">
      <j1 rule="para" parents="6384 6722"/>
    </justification>
  </clause>

  <clause id="7023">
    <literal><![CDATA[
      x * (y \ R(y,x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[para(6353(a,1),6392(a,1,2))].">
      <j1 rule="para" parents="6353 6392"/>
    </justification>
  </clause>

  <clause id="7024">
    <literal><![CDATA[
      (x \ R(x,y \ 1,x)) / (T(x * (y \ 1),x) / x) != z
    ]]></literal>
    <literal><![CDATA[
      R(y,y \ 1,x \ R(x,y \ 1,x)) = z
    ]]></literal>
    <justification jstring="[para(7023(a,1),761(a,1,2))].">
      <j1 rule="para" parents="7023 761"/>
    </justification>
  </clause>

  <clause id="7025">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(5495(a,1),6416(a,1,2))].">
      <j1 rule="para" parents="5495 6416"/>
    </justification>
  </clause>

  <clause id="7026">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,(x \ 1) \ (x \ y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(145,a,6435,a,b,xx)].">
      <j1 rule="hyper" parents="145 6435"/>
    </justification>
  </clause>

  <clause id="7027">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,(x \ 1) \ (x \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      x \ y = u
    ]]></literal>
    <justification jstring="[para(6435(a,2),290(a,1,2))].">
      <j1 rule="para" parents="6435 290"/>
    </justification>
  </clause>

  <clause id="7028">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * ((1 / u) \ K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(5934(a,2),6534(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5934 6534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7029">
    <literal><![CDATA[
      K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(6092(a,1),6572(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="6092 6572"/>
    </justification>
  </clause>

  <clause id="7030">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) * (y / x) = T(y,z) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),6577(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 6577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7031">
    <literal><![CDATA[
      K(x \ 1,y) / (y \ (x \ y)) = (y / (x * y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,2032,a(flip),b,6587,a),flip(a)].">
      <j1 rule="hyper" parents="373 2032 6587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7032">
    <literal><![CDATA[
      T((x \ y) / (1 / y),x \ y) = (x * (1 / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,5308,a,b,6597,a)].">
      <j1 rule="hyper" parents="64 5308 6597"/>
    </justification>
  </clause>

  <clause id="7033">
    <literal><![CDATA[
      (x \ 1) * (x \ ((x \ 1) \ y)) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,1127,a,b,6615,a(flip))].">
      <j1 rule="hyper" parents="35 1127 6615"/>
    </justification>
  </clause>

  <clause id="7034">
    <literal><![CDATA[
      K(x,y \ (T(1 / z,u) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[para(3569(a,1),6640(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3569 6640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7035">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ L(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(1635(a,1),6641(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1635 6641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7036">
    <literal><![CDATA[
      T(x,y \ (z * (1 / u))) = T(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(143,a,6642,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 6642 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7037">
    <literal><![CDATA[
      (1 / x) * ((1 / ((y * y) / x)) * z) = (x \ 1) * (x * ((y * y) \ z))
    ]]></literal>
    <justification jstring="[para(1464(a,1),6649(a,1,2))].">
      <j1 rule="para" parents="1464 6649"/>
    </justification>
  </clause>

  <clause id="7038">
    <literal><![CDATA[
      K(x \ 1,y) * (x * z) = x * (K(x \ 1,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),6695(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 6695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7039">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K((x \ 1) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(3779(a,1),6695(a,1,2,1))].">
      <j1 rule="para" parents="3779 6695"/>
    </justification>
  </clause>

  <clause id="7040">
    <literal><![CDATA[
      x \ (R(1 / y,y,x) * ((z * (y * x)) / z)) = K(z,1 / (x \ R(1 / y,y,x)))
    ]]></literal>
    <justification jstring="[para(452(a,1),6698(a,1,2,2,1,2))].">
      <j1 rule="para" parents="452 6698"/>
    </justification>
  </clause>

  <clause id="7041">
    <literal><![CDATA[
      K(x,(y * z) \ T(y,u)) = K(x,z \ K(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,6713,a(flip),b,6716,a),flip(a)].">
      <j1 rule="hyper" parents="64 6713 6716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7042">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = (u \ 1) / (u \ K(u,y \ K(x,z)))
    ]]></literal>
    <justification jstring="[para(7041(a,1),6177(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7041 6177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7043">
    <literal><![CDATA[
      T(x,x \ T(y,y \ x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(37,a,865,a,b,6735,a)].">
      <j1 rule="hyper" parents="37 865 6735"/>
    </justification>
  </clause>

  <clause id="7044">
    <literal><![CDATA[
      T(x,x \ y) / T(y,y \ x) = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(225,a,7043,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 7043 116"/>
    </justification>
  </clause>

  <clause id="7045">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(82(a,1),6738(a,2,2,2))].">
      <j1 rule="para" parents="82 6738"/>
    </justification>
  </clause>

  <clause id="7046">
    <literal><![CDATA[
      ((x * y) \ x) * (y \ 1) = (y \ 1) * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(114(a,1),6747(a,1,2))].">
      <j1 rule="para" parents="114 6747"/>
    </justification>
  </clause>

  <clause id="7047">
    <literal><![CDATA[
      ((x * y) \ x) * ((y \ 1) \ z) = (z / (y \ 1)) * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(117(a,1),6747(a,1,2))].">
      <j1 rule="para" parents="117 6747"/>
    </justification>
  </clause>

  <clause id="7048">
    <literal><![CDATA[
      K(x \ 1,y) * ((z * x) \ z) = L(T(x \ 1,y),x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,444,a(flip),b,6789,a),flip(a)].">
      <j1 rule="hyper" parents="373 444 6789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7049">
    <literal><![CDATA[
      (x \ (x / y)) * K(y,y * y) = T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(6345(a,1),6798(a,1,2))].">
      <j1 rule="para" parents="6345 6798"/>
    </justification>
  </clause>

  <clause id="7050">
    <literal><![CDATA[
      (x \ (x / y)) * K(y,y * y) = T(x \ (x / y),y * y)
    ]]></literal>
    <justification jstring="[para(6788(a,1),6798(a,1,2))].">
      <j1 rule="para" parents="6788 6798"/>
    </justification>
  </clause>

  <clause id="7052">
    <literal><![CDATA[
      x * (K(y \ x,x) * (y \ 1)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(4494,a,6817,a)].">
      <j1 rule="hyper" parents="4494 6817"/>
    </justification>
  </clause>

  <clause id="7054">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((z / y) \ x,z)
    ]]></literal>
    <justification jstring="[para(5652(a,1),6818(a,1,2))].">
      <j1 rule="para" parents="5652 6818"/>
    </justification>
  </clause>

  <clause id="7055">
    <literal><![CDATA[
      (1 / T(x,x \ y)) * (y / x) = (x * x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,536,a(flip),b,6868,a),flip(a)].">
      <j1 rule="hyper" parents="373 536 6868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7056">
    <literal><![CDATA[
      K(x,1 / x) * (y * L(x,z,u)) = y * L((x \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(6890(a,1),5243(a,2,2))].">
      <j1 rule="para" parents="6890 5243"/>
    </justification>
  </clause>

  <clause id="7057">
    <literal><![CDATA[
      x \ ((x \ 1) \ (((y / x) / y) * x)) = (x \ 1) \ ((y / x) / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,3700,a(flip),b,7033,a),flip(a)].">
      <j1 rule="hyper" parents="139 3700 7033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7058">
    <literal><![CDATA[
      (x \ 1) * R(x \ ((x \ 1) \ y),z,u) = (1 / (1 / x)) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(2161(a,2),7033(a,1,2))].">
      <j1 rule="para" parents="2161 7033"/>
    </justification>
  </clause>

  <clause id="7059">
    <literal><![CDATA[
      (x \ 1) * L(x \ ((x \ 1) \ y),z,u) = (1 / (1 / x)) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(5636(a,2),7033(a,1,2))].">
      <j1 rule="para" parents="5636 7033"/>
    </justification>
  </clause>

  <clause id="7061">
    <literal><![CDATA[
      T(x,x \ y) / ((y \ x) \ x) = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(907,a,7044,a)].">
      <j1 rule="hyper" parents="907 7044"/>
    </justification>
  </clause>

  <clause id="7062">
    <literal><![CDATA[
      L(K(x \ 1,y) * L(T(z,T(x \ 1,y)),u,w),x,x) = x * (L(z,u,w) * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,520,a(flip),b,6082,a),flip(a)].">
      <j1 rule="hyper" parents="373 520 6082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7063">
    <literal><![CDATA[
      x * (T(x \ 1,x) * y) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2392,a(flip),b,6082,a),flip(a)].">
      <j1 rule="hyper" parents="64 2392 6082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7064">
    <literal><![CDATA[
      (K(x,y) \ (z * u)) / L(u,z,K(y,x)) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(142,a,6156,a,b,6182,a)].">
      <j1 rule="hyper" parents="142 6156 6182"/>
    </justification>
  </clause>

  <clause id="7065">
    <literal><![CDATA[
      (K(x,y) \ z) \ (K(x,y) \ (z * u)) = L(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(139,a,6156,a,b,6182,a)].">
      <j1 rule="hyper" parents="139 6156 6182"/>
    </justification>
  </clause>

  <clause id="7066">
    <literal><![CDATA[
      L(x \ (K(y,z) * u),x,K(y,z)) = (K(z,y) * x) \ u
    ]]></literal>
    <justification jstring="[hyper(6105,a,6190,a)].">
      <j1 rule="hyper" parents="6105 6190"/>
    </justification>
  </clause>

  <clause id="7067">
    <literal><![CDATA[
      L(K(x,y) * (K(z,u) * w),K(y,x),K(u,z)) = (K(u,z) * K(y,x)) \ w
    ]]></literal>
    <justification jstring="[para(6156(a,1),6190(a,1,1))].">
      <j1 rule="para" parents="6156 6190"/>
    </justification>
  </clause>

  <clause id="7068">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) \ w = K(u,x) * (L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(4868,a,6191,a),flip(a)].">
      <j1 rule="hyper" parents="4868 6191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7069">
    <literal><![CDATA[
      (x * K(y,x)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(6191(a,1),4493(a,1))].">
      <j1 rule="para" parents="6191 4493"/>
    </justification>
  </clause>

  <clause id="7070">
    <literal><![CDATA[
      x \ (y * K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ y) = z
    ]]></literal>
    <justification jstring="[para(5970(a,1),7069(a,1))].">
      <j1 rule="para" parents="5970 7069"/>
    </justification>
  </clause>

  <clause id="7071">
    <literal><![CDATA[
      T((1 / x) * K(y * R(1 / x,x,z),1 / x),y) = R(1 / x,y,z / (x * z))
    ]]></literal>
    <justification jstring="[para(244(a,1),6236(a,2,3))].">
      <j1 rule="para" parents="244 6236"/>
    </justification>
  </clause>

  <clause id="7072">
    <literal><![CDATA[
      R(x * K(y,x),y,L(x,z,u)) = x * K(y * L(x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(41,a,5858,a,b,6239,a)].">
      <j1 rule="hyper" parents="41 5858 6239"/>
    </justification>
  </clause>

  <clause id="7073">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(6388(a,1),6110(a,1,1))].">
      <j1 rule="para" parents="6388 6110"/>
    </justification>
  </clause>

  <clause id="7074">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(R(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(6388(a,1),6899(a,1,1))].">
      <j1 rule="para" parents="6388 6899"/>
    </justification>
  </clause>

  <clause id="7075">
    <literal><![CDATA[
      K(1 / x,L(x,y,z)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,5317,a(flip),b,6547,a),flip(a)].">
      <j1 rule="hyper" parents="35 5317 6547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7076">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * (x * z) = u
    ]]></literal>
    <justification jstring="[para(6025(a,1),6630(a,1,2))].">
      <j1 rule="para" parents="6025 6630"/>
    </justification>
  </clause>

  <clause id="7077">
    <literal><![CDATA[
      K(x,L(L(y \ 1,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(474(a,2),6701(a,1,2))].">
      <j1 rule="para" parents="474 6701"/>
    </justification>
  </clause>

  <clause id="7078">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6719,a(flip),b,6711,a)].">
      <j1 rule="hyper" parents="64 6719 6711"/>
    </justification>
  </clause>

  <clause id="7079">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6937,a,7078,a),flip(a)].">
      <j1 rule="hyper" parents="6937 7078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7080">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),7078(a,2,2,1))].">
      <j1 rule="para" parents="10 7078"/>
    </justification>
  </clause>

  <clause id="7081">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),7078(a,2,2,2))].">
      <j1 rule="para" parents="10 7078"/>
    </justification>
  </clause>

  <clause id="7082">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(102(a,2),7078(a,2,2))].">
      <j1 rule="para" parents="102 7078"/>
    </justification>
  </clause>

  <clause id="7083">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),7079(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 7079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7084">
    <literal><![CDATA[
      K(x \ y,(x * z) \ y) = K(x \ y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(10(a,1),7079(a,1,2,2))].">
      <j1 rule="para" parents="10 7079"/>
    </justification>
  </clause>

  <clause id="7085">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ x) = K(x,u \ (K(z,y) * x))
    ]]></literal>
    <justification jstring="[para(6161(a,1),7079(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6161 7079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7086">
    <literal><![CDATA[
      T(x,(y \ z) \ x) = T(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(143,a,7083,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 7083 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7087">
    <literal><![CDATA[
      K(x,((y * K(z,y)) \ u) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(4442(a,1),7083(a,2,2,2))].">
      <j1 rule="para" parents="4442 7083"/>
    </justification>
  </clause>

  <clause id="7088">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7078,a(flip),b,7082,a),flip(a)].">
      <j1 rule="hyper" parents="64 7078 7082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7089">
    <literal><![CDATA[
      L(K(x,y \ z),z,y \ 1) = K(x,(1 / y) * z)
    ]]></literal>
    <justification jstring="[para(1638(a,1),7082(a,2,2))].">
      <j1 rule="para" parents="1638 7082"/>
    </justification>
  </clause>

  <clause id="7090">
    <literal><![CDATA[
      (x * y) * K(z,u \ (x * y)) = x * (y * K(z,(x \ u) \ y))
    ]]></literal>
    <justification jstring="[hyper(145,a,7080,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 7080 18"/>
    </justification>
  </clause>

  <clause id="7091">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = T(K(x,z \ (y * u)),w)
    ]]></literal>
    <justification jstring="[para(7080(a,1),25(a,2,1))].">
      <j1 rule="para" parents="7080 25"/>
    </justification>
  </clause>

  <clause id="7092">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(7080(a,1),4493(a,1))].">
      <j1 rule="para" parents="7080 4493"/>
    </justification>
  </clause>

  <clause id="7093">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ x) = u
    ]]></literal>
    <justification jstring="[para(7080(a,1),6937(a,1))].">
      <j1 rule="para" parents="7080 6937"/>
    </justification>
  </clause>

  <clause id="7094">
    <literal><![CDATA[
      K(x,L(a(y \ 1,y,z) \ u,a(y \ 1,y,z),L(z,y,y \ 1))) = K(x,z \ (L(z,y,y \ 1) * u))
    ]]></literal>
    <justification jstring="[para(2674(a,1),7088(a,2,2,1))].">
      <j1 rule="para" parents="2674 7088"/>
    </justification>
  </clause>

  <clause id="7095">
    <literal><![CDATA[
      K(x,L((((y * z) \ y) \ y) \ u,((y * z) \ y) \ y,z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(6808(a,1),7088(a,2,2,1))].">
      <j1 rule="para" parents="6808 7088"/>
    </justification>
  </clause>

  <clause id="7096">
    <literal><![CDATA[
      L(K(x,y \ z),z,y \ 1) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6526,a(flip),b,7089,a),flip(a)].">
      <j1 rule="hyper" parents="373 6526 7089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7097">
    <literal><![CDATA[
      x / (K(y,z) * T(z,u)) = (x / T(z,u)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5711,a(flip),b,6910,a),flip(a)].">
      <j1 rule="hyper" parents="64 5711 6910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7098">
    <literal><![CDATA[
      x / (K(y \ 1,y) * z) = (x / z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5075,a(flip),b,6910,a),flip(a)].">
      <j1 rule="hyper" parents="64 5075 6910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7099">
    <literal><![CDATA[
      x / (T(y,z) * K(u,y)) = (x / T(y,z)) * K(y,u)
    ]]></literal>
    <justification jstring="[para(4001(a,2),7097(a,1,2))].">
      <j1 rule="para" parents="4001 7097"/>
    </justification>
  </clause>

  <clause id="7100">
    <literal><![CDATA[
      (x / T(y,y * z)) * K(y,z) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(6080(a,1),7097(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6080 7097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7101">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,y * z) = x / R(y,z,y)
    ]]></literal>
    <justification jstring="[para(6081(a,1),7097(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6081 7097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7102">
    <literal><![CDATA[
      K(x,y / (K(z \ 1,z) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(7098(a,2),6523(a,1,2))].">
      <j1 rule="para" parents="7098 6523"/>
    </justification>
  </clause>

  <clause id="7103">
    <literal><![CDATA[
      K(x,y / (K(z,z \ 1) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(1739(a,1),7102(a,1,2,2,1))].">
      <j1 rule="para" parents="1739 7102"/>
    </justification>
  </clause>

  <clause id="7104">
    <literal><![CDATA[
      K(x,y / (((z \ 1) \ 1) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(2362(a,1),7102(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2362 7102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7105">
    <literal><![CDATA[
      K(x,y / (z * (1 / u))) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3625(a,1),7102(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3625 7102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7106">
    <literal><![CDATA[
      K(x,y / (z * (u / (1 / w)))) = K(x,y / (z * (u / (w \ 1))))
    ]]></literal>
    <justification jstring="[para(5189(a,1),7103(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5189 7103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7107">
    <literal><![CDATA[
      a(x,T(y,z),T(z,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(959,a,6952,a),flip(a)].">
      <j1 rule="hyper" parents="959 6952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7108">
    <literal><![CDATA[
      R(x,(y * z) / y,y) = R(x,z,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,264,a(flip),b,6993,a),flip(a)].">
      <j1 rule="hyper" parents="373 264 6993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7109">
    <literal><![CDATA[
      R(x,y \ z,T(y,y \ z)) = R(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),7108(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 7108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7110">
    <literal><![CDATA[
      R(x,y / (y / z),y / z) = R(x,z,T(y / z,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),7108(a,1,2,1))].">
      <j1 rule="para" parents="12 7108"/>
    </justification>
  </clause>

  <clause id="7111">
    <literal><![CDATA[
      R(x,y * K(z,y),z) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[para(5721(a,1),7108(a,1,2))].">
      <j1 rule="para" parents="5721 7108"/>
    </justification>
  </clause>

  <clause id="7112">
    <literal><![CDATA[
      R(x,y / (y / z),y / z) = R(x,z,z \ y)
    ]]></literal>
    <justification jstring="[para(117(a,1),7110(a,2,3))].">
      <j1 rule="para" parents="117 7110"/>
    </justification>
  </clause>

  <clause id="7114">
    <literal><![CDATA[
      R(x / (y / (y / z)),z,z \ y) = (x * (y / z)) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,678,a(flip),b,7112,a),flip(a)].">
      <j1 rule="hyper" parents="64 678 7112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7115">
    <literal><![CDATA[
      K(x,(y * z) \ T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(6716(a,1),7011(a,1))].">
      <j1 rule="para" parents="6716 7011"/>
    </justification>
  </clause>

  <clause id="7116">
    <literal><![CDATA[
      R(x / (y \ K(y,z)),y \ K(y,z),K(z,y)) = (x * K(z,y)) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(7016,a,650,a),flip(a)].">
      <j1 rule="hyper" parents="7016 650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7117">
    <literal><![CDATA[
      (x * y) * L(z,y * x,K(x,y)) = K(y,x) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,5921,a(flip),b,7064,a)].">
      <j1 rule="hyper" parents="144 5921 7064"/>
    </justification>
  </clause>

  <clause id="7118">
    <literal><![CDATA[
      L(x \ y,x,K(z,u)) = (K(u,z) \ x) \ (K(u,z) \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),7065(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 7065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7119">
    <literal><![CDATA[
      (K(x,y) \ (z * u)) \ (K(x,y) \ (z * (u * w))) = L(L(w,u,z),z * u,K(y,x))
    ]]></literal>
    <justification jstring="[para(100(a,1),7065(a,1,2,2))].">
      <j1 rule="para" parents="100 7065"/>
    </justification>
  </clause>

  <clause id="7120">
    <literal><![CDATA[
      L(x,y,K(z,u)) != (K(u,z) * y) \ w
    ]]></literal>
    <literal><![CDATA[
      y \ (K(z,u) * w) = x
    ]]></literal>
    <justification jstring="[para(7066(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="7066 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7121">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(u * K(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(6156(a,1),7081(a,1,1,2))].">
      <j1 rule="para" parents="6156 7081"/>
    </justification>
  </clause>

  <clause id="7122">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(y,z) \ x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(5921(a,1),7118(a,2,2))].">
      <j1 rule="para" parents="5921 7118"/>
    </justification>
  </clause>

  <clause id="7123">
    <literal><![CDATA[
      L(x \ T(y,z),x,K(y,z)) = (K(z,y) \ x) \ T(T(y,z),z)
    ]]></literal>
    <justification jstring="[para(5930(a,1),7118(a,2,2))].">
      <j1 rule="para" parents="5930 7118"/>
    </justification>
  </clause>

  <clause id="7124">
    <literal><![CDATA[
      R(x,K(y,z),L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(664,a,5709,a)].">
      <j1 rule="hyper" parents="664 5709"/>
    </justification>
  </clause>

  <clause id="7125">
    <literal><![CDATA[
      R(x,K(y,z),R(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(664,a,5710,a)].">
      <j1 rule="hyper" parents="664 5710"/>
    </justification>
  </clause>

  <clause id="7126">
    <literal><![CDATA[
      x / (K(y,z) * R(z,u,w)) = (x / R(z,u,w)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6910,a(flip),b,7125,a)].">
      <j1 rule="hyper" parents="64 6910 7125"/>
    </justification>
  </clause>

  <clause id="7127">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5731(a,2),5812(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5731 5812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7128">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = (x \ y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6852,a(flip),b,7127,a),flip(a)].">
      <j1 rule="hyper" parents="373 6852 7127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7129">
    <literal><![CDATA[
      x \ (y * K(x,z)) = (x \ y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,6850,a,b,7128,a),flip(a)].">
      <j1 rule="hyper" parents="36 6850 7128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7130">
    <literal><![CDATA[
      K(x,y) * (x \ y) = (x \ y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7070,a,7129,a)].">
      <j1 rule="hyper" parents="7070 7129"/>
    </justification>
  </clause>

  <clause id="7131">
    <literal><![CDATA[
      x * ((x \ y) * K(x,z)) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(157,a,7129,a)].">
      <j1 rule="hyper" parents="157 7129"/>
    </justification>
  </clause>

  <clause id="7132">
    <literal><![CDATA[
      T(x,y) \ (z * K(x,y)) = T(x \ z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(269,a,7129,a(flip),b,6075,a),flip(a)].">
      <j1 rule="hyper" parents="269 7129 6075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7133">
    <literal><![CDATA[
      T(x \ y,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(269,a,7129,a(flip),b,6411,a(flip))].">
      <j1 rule="hyper" parents="269 7129 6411"/>
    </justification>
  </clause>

  <clause id="7135">
    <literal><![CDATA[
      (x * y) * K(x,z) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),7131(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 7131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7136">
    <literal><![CDATA[
      R(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(664,a,7135,a)].">
      <j1 rule="hyper" parents="664 7135"/>
    </justification>
  </clause>

  <clause id="7137">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(606,a,7135,a)].">
      <j1 rule="hyper" parents="606 7135"/>
    </justification>
  </clause>

  <clause id="7138">
    <literal><![CDATA[
      L(K(x \ 1,y),z,x) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1630,a,b,7135,a)].">
      <j1 rule="hyper" parents="35 1630 7135"/>
    </justification>
  </clause>

  <clause id="7139">
    <literal><![CDATA[
      (x * (y * K(x,z))) * x = (x * y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,7135,a(flip),b,6847,a)].">
      <j1 rule="hyper" parents="144 7135 6847"/>
    </justification>
  </clause>

  <clause id="7140">
    <literal><![CDATA[
      (x * (y * K(x,z))) / T(x,z) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,7135,a(flip),b,6840,a)].">
      <j1 rule="hyper" parents="142 7135 6840"/>
    </justification>
  </clause>

  <clause id="7141">
    <literal><![CDATA[
      a(x,y,K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,7135,a(flip),b,88,a),flip(a)].">
      <j1 rule="hyper" parents="138 7135 88"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7142">
    <literal><![CDATA[
      (x * (y * K(x,z))) / x = ((x * y) / x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(7135(a,1),6863(a,1,1))].">
      <j1 rule="para" parents="7135 6863"/>
    </justification>
  </clause>

  <clause id="7143">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,u) = T(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(7136(a,1),511(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7136 511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7144">
    <literal><![CDATA[
      (R(x,y,z) * u) * K(x,w) = R(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(7136(a,1),506(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7136 506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7145">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(x,w) = L(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(7136(a,1),510(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7136 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7147">
    <literal><![CDATA[
      L(K(x,y),z,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2274,a,7137,a)].">
      <j1 rule="hyper" parents="2274 7137"/>
    </justification>
  </clause>

  <clause id="7148">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7081,a(flip),b,7137,a)].">
      <j1 rule="hyper" parents="64 7081 7137"/>
    </justification>
  </clause>

  <clause id="7149">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7080,a(flip),b,7137,a),flip(a)].">
      <j1 rule="hyper" parents="64 7080 7137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7150">
    <literal><![CDATA[
      K(x,(x \ 1) * y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7096,a(flip),b,7147,a)].">
      <j1 rule="hyper" parents="64 7096 7147"/>
    </justification>
  </clause>

  <clause id="7151">
    <literal><![CDATA[
      K(x,x \ ((x \ 1) \ y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),7150(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 7150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7152">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ y) = x * (((x \ 1) \ y) / x)
    ]]></literal>
    <justification jstring="[hyper(144,a,7151,a(flip),b,6016,a)].">
      <j1 rule="hyper" parents="144 7151 6016"/>
    </justification>
  </clause>

  <clause id="7153">
    <literal><![CDATA[
      (x * y) * K(x \ 1,z) = x * (y * K(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,7138,a(flip),b,5318,a(flip))].">
      <j1 rule="hyper" parents="145 7138 5318"/>
    </justification>
  </clause>

  <clause id="7154">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6438,a,b,7148,a)].">
      <j1 rule="hyper" parents="64 6438 7148"/>
    </justification>
  </clause>

  <clause id="7155">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ (x \ z)) = K(x,L(y,x \ 1,x) \ z)
    ]]></literal>
    <justification jstring="[para(293(a,1),7148(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="293 7148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7156">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(7148(a,1),6631(a,2,2))].">
      <j1 rule="para" parents="7148 6631"/>
    </justification>
  </clause>

  <clause id="7157">
    <literal><![CDATA[
      K(x,(x \ 1) \ y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(66(a,1),7149(a,2,2))].">
      <j1 rule="para" parents="66 7149"/>
    </justification>
  </clause>

  <clause id="7158">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,(y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(7157(a,1),7081(a,1,1))].">
      <j1 rule="para" parents="7157 7081"/>
    </justification>
  </clause>

  <clause id="7159">
    <literal><![CDATA[
      T(x / y,T(y,z)) = T(y \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6842,a(flip),b,7132,a)].">
      <j1 rule="hyper" parents="64 6842 7132"/>
    </justification>
  </clause>

  <clause id="7160">
    <literal><![CDATA[
      T(x \ (y / z),K(x,z)) = T(x,z) \ (y / T(z,x))
    ]]></literal>
    <justification jstring="[para(6245(a,1),7132(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6245 7132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7161">
    <literal><![CDATA[
      T(x \ y,K(x,z)) = x \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7001,a(flip),b,7159,a),flip(a)].">
      <j1 rule="hyper" parents="64 7001 7159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7162">
    <literal><![CDATA[
      T(x / y,K(y,x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(41,a,4476,a,b,7159,a)].">
      <j1 rule="hyper" parents="41 4476 7159"/>
    </justification>
  </clause>

  <clause id="7163">
    <literal><![CDATA[
      K(x,y) * (y / x) = (y / x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,7162,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 7162 22"/>
    </justification>
  </clause>

  <clause id="7164">
    <literal><![CDATA[
      T(R(T(x,x * y),x,y),K((1 / x) * y,z)) = ((1 / x) * y) \ T(y,K((1 / x) * y,z))
    ]]></literal>
    <justification jstring="[para(1342(a,2),7161(a,1,1))].">
      <j1 rule="para" parents="1342 7161"/>
    </justification>
  </clause>

  <clause id="7165">
    <literal><![CDATA[
      x / ((x * y) / x) = K(y,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6888,a,b,7163,a)].">
      <j1 rule="hyper" parents="373 6888 7163"/>
    </justification>
  </clause>

  <clause id="7166">
    <literal><![CDATA[
      (K(x,y) * (y / x)) / y = (y / x) / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,7163,a,b,6311,a)].">
      <j1 rule="hyper" parents="142 7163 6311"/>
    </justification>
  </clause>

  <clause id="7167">
    <literal><![CDATA[
      T((((x * y) \ x) * (z * K((x * y) \ x,u))) / T((x * y) \ x,u),(((x * y) \ x) * z) / L(y \ 1,y,x)) = (((x * y) \ x) * z) / L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(504,a,7140,a,b,438,a)].">
      <j1 rule="hyper" parents="504 7140 438"/>
    </justification>
  </clause>

  <clause id="7168">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(L(x,y,z),w))) / L(T(x,w),y,z) = (L(x,y,z) * u) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),7140(a,1,2))].">
      <j1 rule="para" parents="25 7140"/>
    </justification>
  </clause>

  <clause id="7169">
    <literal><![CDATA[
      (R(x,y,z) * (u * K(R(x,y,z),w))) / R(T(x,w),y,z) = (R(x,y,z) * u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(27(a,2),7140(a,1,2))].">
      <j1 rule="para" parents="27 7140"/>
    </justification>
  </clause>

  <clause id="7170">
    <literal><![CDATA[
      (x * (y * K(z,x))) / x = (x * y) / T(x,z)
    ]]></literal>
    <justification jstring="[para(6871(a,1),7140(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6871 7140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7171">
    <literal><![CDATA[
      (x * y) * K(z,x) = x * (y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(38,a,6312,a,b,7170,a)].">
      <j1 rule="hyper" parents="38 6312 7170"/>
    </justification>
  </clause>

  <clause id="7172">
    <literal><![CDATA[
      T((x * y) / T(x,z),x) = y * K(z,x)
    ]]></literal>
    <justification jstring="[para(7170(a,1),255(a,1,1))].">
      <j1 rule="para" parents="7170 255"/>
    </justification>
  </clause>

  <clause id="7173">
    <literal><![CDATA[
      R(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(664,a,7171,a)].">
      <j1 rule="hyper" parents="664 7171"/>
    </justification>
  </clause>

  <clause id="7174">
    <literal><![CDATA[
      L(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(606,a,7171,a)].">
      <j1 rule="hyper" parents="606 7171"/>
    </justification>
  </clause>

  <clause id="7175">
    <literal><![CDATA[
      (x * (y * K(z,x))) * z = (x * y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,7171,a(flip),b,6847,a)].">
      <j1 rule="hyper" parents="144 7171 6847"/>
    </justification>
  </clause>

  <clause id="7177">
    <literal><![CDATA[
      R(x,y,K(z,T(x,u))) = x
    ]]></literal>
    <justification jstring="[hyper(163,a,7173,a(flip))].">
      <j1 rule="hyper" parents="163 7173"/>
    </justification>
  </clause>

  <clause id="7178">
    <literal><![CDATA[
      R(R(x,y,z),u,K(w,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(7173(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7173 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7179">
    <literal><![CDATA[
      R(x,y,T(K(z,x),u)) = x
    ]]></literal>
    <justification jstring="[para(3068(a,1),7173(a,1,3))].">
      <j1 rule="para" parents="3068 7173"/>
    </justification>
  </clause>

  <clause id="7181">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(w,T(x,v5)) = L(x,y,z) * (u * K(w,T(x,v5)))
    ]]></literal>
    <justification jstring="[para(7177(a,1),510(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7177 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7182">
    <literal><![CDATA[
      x \ (y * T(K(z,x),u)) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7179(a,1),649(a,1,1))].">
      <j1 rule="para" parents="7179 649"/>
    </justification>
  </clause>

  <clause id="7183">
    <literal><![CDATA[
      (((x * K(y,z)) * R(z,u,w)) / (x * K(y,z))) * x = ((x * K(y,z)) * R(z,u,w)) / K(y,z)
    ]]></literal>
    <justification jstring="[para(7178(a,1),1204(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7178 1204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7184">
    <literal><![CDATA[
      T(x / T(y,z),y) = (y \ x) * K(z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),7172(a,1,1,1))].">
      <j1 rule="para" parents="10 7172"/>
    </justification>
  </clause>

  <clause id="7185">
    <literal><![CDATA[
      T(((x * x) * y) / T(x,z),x) = ((1 / x) \ y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(538(a,1),7172(a,1,1,1))].">
      <j1 rule="para" parents="538 7172"/>
    </justification>
  </clause>

  <clause id="7186">
    <literal><![CDATA[
      T(x / T(y,z),y) * y = (y \ x) * (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(144,a,7184,a,b,5703,a)].">
      <j1 rule="hyper" parents="144 7184 5703"/>
    </justification>
  </clause>

  <clause id="7188">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(269,a,7143,a,b,5755,a)].">
      <j1 rule="hyper" parents="269 7143 5755"/>
    </justification>
  </clause>

  <clause id="7189">
    <literal><![CDATA[
      (T(x,y) \ 1) \ y = x * (((x \ 1) \ y) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6605,a(flip),b,7152,a)].">
      <j1 rule="hyper" parents="64 6605 7152"/>
    </justification>
  </clause>

  <clause id="7190">
    <literal><![CDATA[
      R(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(664,a,7153,a)].">
      <j1 rule="hyper" parents="664 7153"/>
    </justification>
  </clause>

  <clause id="7191">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7190(a,1),27(a,2,1))].">
      <j1 rule="para" parents="7190 27"/>
    </justification>
  </clause>

  <clause id="7192">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = y * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(40,a,6882,a,b,7154,a),flip(a)].">
      <j1 rule="hyper" parents="40 6882 7154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7193">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(40,a,6092,a,b,7154,a),flip(a)].">
      <j1 rule="hyper" parents="40 6092 7154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7194">
    <literal><![CDATA[
      (((x \ y) * x) * z) \ (y * z) = K(x,z \ (x \ (y * z)))
    ]]></literal>
    <justification jstring="[para(11(a,1),7154(a,1,1,1,1,2))].">
      <j1 rule="para" parents="11 7154"/>
    </justification>
  </clause>

  <clause id="7195">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = K(x \ (z \ 1),z) * y
    ]]></literal>
    <justification jstring="[para(7193(a,1),5509(a,2,1))].">
      <j1 rule="para" parents="7193 5509"/>
    </justification>
  </clause>

  <clause id="7196">
    <literal><![CDATA[
      x * K(y,z \ (y \ x)) = z * (y * ((z \ x) / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5474,a(flip),b,7156,a),flip(a)].">
      <j1 rule="hyper" parents="64 5474 7156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7197">
    <literal><![CDATA[
      x * (y * ((x \ 1) / y)) = K(y,x \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(137,a,7156,a(flip),b,5474,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 7156 5474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7198">
    <literal><![CDATA[
      T(x / T(y,z),y) * y = (y \ x) * (K(y,z) \ y)
    ]]></literal>
    <justification jstring="[para(5965(a,2),7186(a,2,2))].">
      <j1 rule="para" parents="5965 7186"/>
    </justification>
  </clause>

  <clause id="7199">
    <literal><![CDATA[
      x / T(y,y \ (y \ x)) = (y \ (x / y)) * y
    ]]></literal>
    <justification jstring="[hyper(36,a,6311,a,b,7192,a)].">
      <j1 rule="hyper" parents="36 6311 7192"/>
    </justification>
  </clause>

  <clause id="7200">
    <literal><![CDATA[
      (x * K((y \ 1) \ (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,7192,a(flip),b,5503,a(flip))].">
      <j1 rule="hyper" parents="144 7192 5503"/>
    </justification>
  </clause>

  <clause id="7201">
    <literal><![CDATA[
      (x * y) * K(z,x \ (z \ (x * y))) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(9(a,1),7196(a,2,2,2,1))].">
      <j1 rule="para" parents="9 7196"/>
    </justification>
  </clause>

  <clause id="7202">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) * K(x,y)) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5828,a,6477,a)].">
      <j1 rule="hyper" parents="5828 6477"/>
    </justification>
  </clause>

  <clause id="7203">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(5792(a,1),7202(a,1,2))].">
      <j1 rule="para" parents="5792 7202"/>
    </justification>
  </clause>

  <clause id="7204">
    <literal><![CDATA[
      (x / (y \ 1)) \ T(x,y) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,7203,a)].">
      <j1 rule="hyper" parents="215 7203"/>
    </justification>
  </clause>

  <clause id="7205">
    <literal><![CDATA[
      T(x,y \ 1) / (T(z \ (z / y),x) \ 1) = x / ((z \ (z / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(6733(a,1),7203(a,1,1))].">
      <j1 rule="para" parents="6733 7203"/>
    </justification>
  </clause>

  <clause id="7206">
    <literal><![CDATA[
      R(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5839,a,6852,a)].">
      <j1 rule="hyper" parents="5839 6852"/>
    </justification>
  </clause>

  <clause id="7211">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,(1 / x) \ y) = (x * x) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,807,a(flip),b,5895,a),flip(a)].">
      <j1 rule="hyper" parents="373 807 5895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7212">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = x * (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(5867(a,1),5922(a,1,2))].">
      <j1 rule="para" parents="5867 5922"/>
    </justification>
  </clause>

  <clause id="7213">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,5825,a(flip),b,7212,a),flip(a)].">
      <j1 rule="hyper" parents="373 5825 7212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7214">
    <literal><![CDATA[
      x * R(T(x,y) \ 1,z,u) = x * R(x \ K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(1213,a,5943,a),flip(a)].">
      <j1 rule="hyper" parents="1213 5943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7215">
    <literal><![CDATA[
      K(x \ 1,x) \ ((x \ y) / y) = 1 / (1 / ((x \ y) / y))
    ]]></literal>
    <justification jstring="[hyper(373,a,3764,a(flip),b,5969,a),flip(a)].">
      <j1 rule="hyper" parents="373 3764 5969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7216">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(5743(a,1),6009(a,1,1,2))].">
      <j1 rule="para" parents="5743 6009"/>
    </justification>
  </clause>

  <clause id="7217">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ ((x * y) * K(y \ 1,z)) = y
    ]]></literal>
    <justification jstring="[hyper(149,a,7216,a)].">
      <j1 rule="hyper" parents="149 7216"/>
    </justification>
  </clause>

  <clause id="7218">
    <literal><![CDATA[
      R(T(x,y * K(x \ 1,z)),y,K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7217(a,1),1756(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7217 1756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7219">
    <literal><![CDATA[
      T(x,y * K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7191,a(flip),b,7218,a)].">
      <j1 rule="hyper" parents="64 7191 7218"/>
    </justification>
  </clause>

  <clause id="7221">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,7219,a(flip),b,5753,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 7219 5753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7222">
    <literal><![CDATA[
      T(x \ 1,y * K(x,z)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3779(a,1),7219(a,1,2,2))].">
      <j1 rule="para" parents="3779 7219"/>
    </justification>
  </clause>

  <clause id="7223">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5726,a,b,7221,a),flip(a)].">
      <j1 rule="hyper" parents="373 5726 7221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7224">
    <literal><![CDATA[
      K(x,y * K(z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6871(a,1),7223(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6871 7223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7225">
    <literal><![CDATA[
      K(x \ y,z * K(u,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6700(a,1),7224(a,1,2,2))].">
      <j1 rule="para" parents="6700 7224"/>
    </justification>
  </clause>

  <clause id="7226">
    <literal><![CDATA[
      T(x \ 1,y * x) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(94(a,1),7222(a,1,2)),flip(a)].">
      <j1 rule="para" parents="94 7222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7227">
    <literal><![CDATA[
      T(x \ 1,T(y,x)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(5748(a,1),7222(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5748 7222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7228">
    <literal><![CDATA[
      T(x \ 1,y * (z / x)) = T(x \ 1,y * (x \ z))
    ]]></literal>
    <justification jstring="[para(6471(a,1),7222(a,1,2))].">
      <j1 rule="para" parents="6471 7222"/>
    </justification>
  </clause>

  <clause id="7229">
    <literal><![CDATA[
      T(x \ 1,y * x) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,4916,a(flip),b,7226,a),flip(a)].">
      <j1 rule="hyper" parents="373 4916 7226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7230">
    <literal><![CDATA[
      x / T(y \ 1,x * y) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,7226,a,b,4916,a(flip))].">
      <j1 rule="hyper" parents="225 7226 4916"/>
    </justification>
  </clause>

  <clause id="7231">
    <literal><![CDATA[
      x * T(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,7226,a,b,5762,a)].">
      <j1 rule="hyper" parents="145 7226 5762"/>
    </justification>
  </clause>

  <clause id="7232">
    <literal><![CDATA[
      T((x / y) \ 1,y * (x / y)) = T((x / y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),7226(a,2,2))].">
      <j1 rule="para" parents="12 7226"/>
    </justification>
  </clause>

  <clause id="7233">
    <literal><![CDATA[
      T(x \ 1,y * x) * L(T(x \ 1,x * y) \ 1,z,u) = T((x \ 1) * L((x \ 1) \ 1,z,u),y * x)
    ]]></literal>
    <justification jstring="[para(7226(a,1),3250(a,1,2,1,1))].">
      <j1 rule="para" parents="7226 3250"/>
    </justification>
  </clause>

  <clause id="7234">
    <literal><![CDATA[
      T(x \ 1,y * x) * L(T(x \ 1,x * y) \ 1,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,z,u),x * y) = w
    ]]></literal>
    <justification jstring="[para(7226(a,2),3253(a,1,1))].">
      <j1 rule="para" parents="7226 3253"/>
    </justification>
  </clause>

  <clause id="7235">
    <literal><![CDATA[
      T((x \ y) \ 1,y) = (((x \ y) \ 1) \ x) \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),7229(a,1,2))].">
      <j1 rule="para" parents="10 7229"/>
    </justification>
  </clause>

  <clause id="7236">
    <literal><![CDATA[
      (x / y) / T(y \ 1,x) = (y \ 1) \ (x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),7230(a,1,2,2))].">
      <j1 rule="para" parents="12 7230"/>
    </justification>
  </clause>

  <clause id="7238">
    <literal><![CDATA[
      K(x \ y,(y \ x) * z) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(94(a,1),7225(a,1,2)),flip(a)].">
      <j1 rule="para" parents="94 7225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7239">
    <literal><![CDATA[
      K(x \ y,z * (x / y)) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(6471(a,1),7225(a,1,2))].">
      <j1 rule="para" parents="6471 7225"/>
    </justification>
  </clause>

  <clause id="7240">
    <literal><![CDATA[
      K(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(5976,a,7231,a)].">
      <j1 rule="hyper" parents="5976 7231"/>
    </justification>
  </clause>

  <clause id="7241">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(7240(a,2),6333(a,2,2))].">
      <j1 rule="para" parents="7240 6333"/>
    </justification>
  </clause>

  <clause id="7242">
    <literal><![CDATA[
      K(x \ (x * (y / x)),(y \ (y / (y / x))) * z) = K(x \ (x * (y / x)),z * ((x * (y / x)) \ x))
    ]]></literal>
    <justification jstring="[para(6018(a,1),7238(a,1,2,1))].">
      <j1 rule="para" parents="6018 7238"/>
    </justification>
  </clause>

  <clause id="7243">
    <literal><![CDATA[
      K((x * (y / x)) \ x,(x \ (x * (y / x))) * z) = K(y \ (y / (y / x)),z * (x \ (x * (y / x))))
    ]]></literal>
    <justification jstring="[para(6018(a,1),7238(a,2,1))].">
      <j1 rule="para" parents="6018 7238"/>
    </justification>
  </clause>

  <clause id="7244">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) * x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4640,a(flip),b,6027,a),flip(a)].">
      <j1 rule="hyper" parents="373 4640 6027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7245">
    <literal><![CDATA[
      K(x,x * y) * (R(y,z,u) * x) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(4703,a,6031,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4703 6031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7246">
    <literal><![CDATA[
      R((x / R(K(y,z),u,u \ 1)) * K(y,z),K(z,y),R(K(y,z),u,u \ 1)) = x / a(K(y,z),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(6172(a,1),6910(a,2,2))].">
      <j1 rule="para" parents="6172 6910"/>
    </justification>
  </clause>

  <clause id="7247">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * z) = y * (T(T(y,x),x) \ z)
    ]]></literal>
    <justification jstring="[para(5923(a,1),6216(a,1,2,1))].">
      <j1 rule="para" parents="5923 6216"/>
    </justification>
  </clause>

  <clause id="7248">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * y = (x * y) * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3291,a(flip),b,6362,a)].">
      <j1 rule="hyper" parents="64 3291 6362"/>
    </justification>
  </clause>

  <clause id="7249">
    <literal><![CDATA[
      K(x,y * ((z / u) * (K(u,u \ z) * (1 / w)))) = K(x,y * (((u * (z / u)) / u) * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(6396(a,2),6535(a,1,2,2))].">
      <j1 rule="para" parents="6396 6535"/>
    </justification>
  </clause>

  <clause id="7250">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(115(a,1),6436(a,1,1,2))].">
      <j1 rule="para" parents="115 6436"/>
    </justification>
  </clause>

  <clause id="7251">
    <literal><![CDATA[
      (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(1308(a,1),6436(a,1,1,2))].">
      <j1 rule="para" parents="1308 6436"/>
    </justification>
  </clause>

  <clause id="7252">
    <literal><![CDATA[
      (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z)
    ]]></literal>
    <justification jstring="[para(2584(a,1),6436(a,1,1,2))].">
      <j1 rule="para" parents="2584 6436"/>
    </justification>
  </clause>

  <clause id="7253">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6441,a(flip),b,7250,a),flip(a)].">
      <j1 rule="hyper" parents="64 6441 7250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7254">
    <literal><![CDATA[
      1 / K((x * y) \ z,x) = K(x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6091,a,b,7253,a)].">
      <j1 rule="hyper" parents="373 6091 7253"/>
    </justification>
  </clause>

  <clause id="7255">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7148,a(flip),b,7253,a),flip(a)].">
      <j1 rule="hyper" parents="373 7148 7253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7256">
    <literal><![CDATA[
      K(x,y \ (x \ y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(6825,a,7255,a),flip(a)].">
      <j1 rule="hyper" parents="6825 7255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7257">
    <literal><![CDATA[
      K(x,L(x \ y,x,z)) = K(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7088,a,b,7255,a)].">
      <j1 rule="hyper" parents="64 7088 7255"/>
    </justification>
  </clause>

  <clause id="7258">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (x * z)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(18(a,2),7255(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 7255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7259">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(T(z,x),x,y))
    ]]></literal>
    <justification jstring="[para(262(a,1),7255(a,1,2)),flip(a)].">
      <j1 rule="para" parents="262 7255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7260">
    <literal><![CDATA[
      T(x,y \ (x \ y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(143,a,7256,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 7256 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7261">
    <literal><![CDATA[
      K(x,x \ 1) / (y \ (x \ y)) = 1 / T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(142,a,7256,a(flip),b,5788,a(flip))].">
      <j1 rule="hyper" parents="142 7256 5788"/>
    </justification>
  </clause>

  <clause id="7262">
    <literal><![CDATA[
      R(1 / (x \ (y \ x)),x \ (y \ x),y) \ T(y,y \ 1) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(7260(a,1),4717(a,1,2))].">
      <j1 rule="para" parents="7260 4717"/>
    </justification>
  </clause>

  <clause id="7263">
    <literal><![CDATA[
      K((x * y) \ z,y) = K((y * x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,6091,a,b,7254,a)].">
      <j1 rule="hyper" parents="37 6091 7254"/>
    </justification>
  </clause>

  <clause id="7264">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,(y \ ((1 / z) \ y)) \ (x \ ((1 / z) \ y)))
    ]]></literal>
    <justification jstring="[para(4587(a,1),7257(a,2,2,2,2))].">
      <j1 rule="para" parents="4587 7257"/>
    </justification>
  </clause>

  <clause id="7265">
    <literal><![CDATA[
      K(x,L(L(x \ (y \ (z * x)),u,w),x,y)) = K(x,y \ (x \ ((y * L(y \ z,u,w)) * x)))
    ]]></literal>
    <justification jstring="[para(2841(a,1),7258(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2841 7258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7266">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,5925,a(flip),b,7259,a),flip(a)].">
      <j1 rule="hyper" parents="373 5925 7259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7267">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z,x,y)) = u
    ]]></literal>
    <justification jstring="[para(7259(a,2),5979(a,1))].">
      <j1 rule="para" parents="7259 5979"/>
    </justification>
  </clause>

  <clause id="7268">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = 1 / (x \ K(y,1 / x))
    ]]></literal>
    <justification jstring="[para(6049(a,1),6454(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6049 6454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7269">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = x \ (((y \ (x / z)) * y) * z)
    ]]></literal>
    <justification jstring="[para(2285(a,1),6567(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2285 6567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7270">
    <literal><![CDATA[
      (x \ R(y,z,u)) * K(((x \ R(y,z,u)) \ (x \ 1)) \ 1,w) = x \ R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(27(a,2),6569(a,2,2))].">
      <j1 rule="para" parents="27 6569"/>
    </justification>
  </clause>

  <clause id="7272">
    <literal><![CDATA[
      (T(x \ (x / y),(x \ (x / y)) \ 1) * T(x,y \ 1)) \ z = (x / y) \ (((x \ (x / y)) * (1 / (x \ (x / y)))) \ z)
    ]]></literal>
    <justification jstring="[para(6232(a,1),6611(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6232 6611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7273">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = ((y * ((x \ y) \ y)) / y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(116(a,2),6619(a,1,2,2,1))].">
      <j1 rule="para" parents="116 6619"/>
    </justification>
  </clause>

  <clause id="7274">
    <literal><![CDATA[
      x \ ((x \ ((x * x) * y)) / z) = (x \ 1) \ ((x \ y) / z)
    ]]></literal>
    <justification jstring="[para(6628(a,1),1167(a,1,2))].">
      <j1 rule="para" parents="6628 1167"/>
    </justification>
  </clause>

  <clause id="7275">
    <literal><![CDATA[
      (x \ ((y * y) \ z)) \ (x \ u) = (x \ z) \ (x \ ((y * y) * u))
    ]]></literal>
    <justification jstring="[para(6431(a,1),6654(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6431 6654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7276">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,68,a(flip),b,6655,a),flip(a)].">
      <j1 rule="hyper" parents="373 68 6655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7278">
    <literal><![CDATA[
      K(((1 / x) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(82(a,1),6679(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="82 6679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7279">
    <literal><![CDATA[
      x * T(x \ (y \ x),T(y,z)) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,2387,a(flip),b,6690,a),flip(a)].">
      <j1 rule="hyper" parents="64 2387 6690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7280">
    <literal><![CDATA[
      K(x,((y \ 1) / (z / y)) \ 1) \ (z / y) = T(z,x) / y
    ]]></literal>
    <justification jstring="[hyper(6205,a,6696,a)].">
      <j1 rule="hyper" parents="6205 6696"/>
    </justification>
  </clause>

  <clause id="7281">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),y \ 1,z * y)) = K(x,a(z,y,y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3836(a,2),6712(a,1,2))].">
      <j1 rule="para" parents="3836 6712"/>
    </justification>
  </clause>

  <clause id="7282">
    <literal><![CDATA[
      K(x,((y / z) \ y) \ 1) \ (y / z) = T(y \ (y / z),x) * T(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(6733(a,1),6720(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6733 6720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7283">
    <literal><![CDATA[
      x \ T(x * K(y \ x,z),x) = K(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,6820,a(flip),b,6763,a(flip))].">
      <j1 rule="hyper" parents="139 6820 6763"/>
    </justification>
  </clause>

  <clause id="7284">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = x \ T(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(82(a,1),7283(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 7283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7285">
    <literal><![CDATA[
      T(K(x \ K(x,y),z),y) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(5727(a,1),6839(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5727 6839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7286">
    <literal><![CDATA[
      K(x \ K(x,y),z) * y = y * K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,7285,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 7285 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7287">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25,a,b,6950,a),flip(a)].">
      <j1 rule="hyper" parents="373 25 6950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7288">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(7005(a,1),6638(a,1,2))].">
      <j1 rule="para" parents="7005 6638"/>
    </justification>
  </clause>

  <clause id="7289">
    <literal><![CDATA[
      K(x,y / (x / (z \ 1))) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6415,a(flip),b,7025,a),flip(a)].">
      <j1 rule="hyper" parents="64 6415 7025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7290">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(154,a,7030,a),flip(a)].">
      <j1 rule="hyper" parents="154 7030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7291">
    <literal><![CDATA[
      T(x \ (x / y),y * y) = T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7049,a(flip),b,7050,a),flip(a)].">
      <j1 rule="hyper" parents="64 7049 7050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7294">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(x,w))) \ (L(x,y,z) * u) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,x) = v5
    ]]></literal>
    <justification jstring="[para(7145(a,1),6899(a,1,1))].">
      <j1 rule="para" parents="7145 6899"/>
    </justification>
  </clause>

  <clause id="7295">
    <literal><![CDATA[
      T((x * x) * (y / T(x,z)),x) = ((1 / x) \ y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(807(a,1),7185(a,1,1))].">
      <j1 rule="para" parents="807 7185"/>
    </justification>
  </clause>

  <clause id="7296">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * y))) = ((z * x) * y) \ ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),7194(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 7194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7297">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ y) / y) = 1 / (1 / ((x \ y) / y))
    ]]></literal>
    <justification jstring="[hyper(6198,a,7215,a)].">
      <j1 rule="hyper" parents="6198 7215"/>
    </justification>
  </clause>

  <clause id="7298">
    <literal><![CDATA[
      K(x,x \ 1) / (y \ (x \ y)) = (y \ (x \ y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,3672,a(flip),b,7261,a),flip(a)].">
      <j1 rule="hyper" parents="373 3672 7261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7299">
    <literal><![CDATA[
      (x \ 1) \ ((x \ y) / z) = x \ (((1 / x) \ y) / z)
    ]]></literal>
    <justification jstring="[para(539(a,1),7274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="539 7274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7300">
    <literal><![CDATA[
      (x * T(y,L(z * K(y,z),y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(5785(a,1),7287(a,2,1))].">
      <j1 rule="para" parents="5785 7287"/>
    </justification>
  </clause>

  <clause id="7301">
    <literal><![CDATA[
      ((x \ y) / y) * K(x,x \ 1) = 1 / (1 / ((x \ y) / y))
    ]]></literal>
    <justification jstring="[hyper(3612,a,7297,a)].">
      <j1 rule="hyper" parents="3612 7297"/>
    </justification>
  </clause>

  <clause id="7302">
    <literal><![CDATA[
      T(x \ y,z) \ T((x \ y) * (y \ x),z) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,3254,a,b,5942,a)].">
      <j1 rule="hyper" parents="64 3254 5942"/>
    </justification>
  </clause>

  <clause id="7303">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(5249(a,1),6445(a,1,1,1))].">
      <j1 rule="para" parents="5249 6445"/>
    </justification>
  </clause>

  <clause id="7304">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u) \ 1,y) = w
    ]]></literal>
    <justification jstring="[para(5743(a,1),6488(a,1,1))].">
      <j1 rule="para" parents="5743 6488"/>
    </justification>
  </clause>

  <clause id="7305">
    <literal><![CDATA[
      K(L(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(7304,a,7138,a)].">
      <j1 rule="hyper" parents="7304 7138"/>
    </justification>
  </clause>

  <clause id="7306">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(7304,a,xx),flip(a)].">
      <j1 rule="hyper" parents="7304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7307">
    <literal><![CDATA[
      K(R(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(4896(a,1),7305(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4896 7305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7308">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(2562(a,1),7306(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2562 7306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7309">
    <literal><![CDATA[
      L(K(1 / x,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(3776(a,2),7306(a,1,1))].">
      <j1 rule="para" parents="3776 7306"/>
    </justification>
  </clause>

  <clause id="7310">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3779(a,1),7306(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3779 7306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7311">
    <literal><![CDATA[
      K(L(T(1 / x,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(6565(a,1),7306(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6565 7306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7312">
    <literal><![CDATA[
      L(K(1 / x,y),z,u) = K(1 / L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,3776,a,b,7309,a),flip(a)].">
      <j1 rule="hyper" parents="373 3776 7309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7314">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) * w = L(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(7310(a,1),6156(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7310 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7315">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(7310(a,1),6916(a,1,1,2))].">
      <j1 rule="para" parents="7310 6916"/>
    </justification>
  </clause>

  <clause id="7316">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = L(K(1 / x,x),y,z)
    ]]></literal>
    <justification jstring="[para(7075(a,1),7312(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7075 7312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7317">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(226,a,7315,a)].">
      <j1 rule="hyper" parents="226 7315"/>
    </justification>
  </clause>

  <clause id="7318">
    <literal><![CDATA[
      (x * (y * K(z,u))) * L(K(u,z),y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(161,a,7315,a),flip(a)].">
      <j1 rule="hyper" parents="161 7315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7319">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,489,a(flip),b,7315,a)].">
      <j1 rule="hyper" parents="64 489 7315"/>
    </justification>
  </clause>

  <clause id="7320">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[para(100(a,1),7315(a,1,1))].">
      <j1 rule="para" parents="100 7315"/>
    </justification>
  </clause>

  <clause id="7321">
    <literal><![CDATA[
      (x * ((x \ y) * K(z,u))) \ y = L(K(u,z),x \ y,x)
    ]]></literal>
    <justification jstring="[para(515(a,1),7315(a,1,1))].">
      <j1 rule="para" parents="515 7315"/>
    </justification>
  </clause>

  <clause id="7322">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(u,z),y,x) = w
    ]]></literal>
    <justification jstring="[para(7318(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7318 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7323">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5165,a(flip),b,7316,a),flip(a)].">
      <j1 rule="hyper" parents="373 5165 7316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7325">
    <literal><![CDATA[
      L(x,y,z) * K(1 / x,x) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(7323(a,1),1738(a,1,2))].">
      <j1 rule="para" parents="7323 1738"/>
    </justification>
  </clause>

  <clause id="7326">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(6670(a,1),7314(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6670 7314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7327">
    <literal><![CDATA[
      L(K(x,y),z,u) * (L(K(y,x),z,u) * w) = w
    ]]></literal>
    <justification jstring="[hyper(396,a,7326,a),flip(a)].">
      <j1 rule="hyper" parents="396 7326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7328">
    <literal><![CDATA[
      L(K(x,y),z,u) * w != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) * v5 = w
    ]]></literal>
    <justification jstring="[para(7326(a,1),157(a,1))].">
      <j1 rule="para" parents="7326 157"/>
    </justification>
  </clause>

  <clause id="7329">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) * w = v5
    ]]></literal>
    <justification jstring="[para(7327(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7327 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7331">
    <literal><![CDATA[
      (K(x \ 1,y) * z) * x = K(x \ 1,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(7307(a,1),6684(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7307 6684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7332">
    <literal><![CDATA[
      L(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(606,a,7331,a)].">
      <j1 rule="hyper" parents="606 7331"/>
    </justification>
  </clause>

  <clause id="7333">
    <literal><![CDATA[
      L(x \ 1,y,K(x,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(3779(a,1),7332(a,1,3))].">
      <j1 rule="para" parents="3779 7332"/>
    </justification>
  </clause>

  <clause id="7334">
    <literal><![CDATA[
      (K(x,y) * z) * (x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(145,a,7333,a(flip),b,5318,a(flip))].">
      <j1 rule="hyper" parents="145 7333 5318"/>
    </justification>
  </clause>

  <clause id="7335">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[para(7333(a,1),1301(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7333 1301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7336">
    <literal><![CDATA[
      (x \ 1) * T(K(x,y) * z,x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(329,a,7334,a)].">
      <j1 rule="hyper" parents="329 7334"/>
    </justification>
  </clause>

  <clause id="7337">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,u * z)) = K(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(646(a,2),6707(a,1,2))].">
      <j1 rule="para" parents="646 6707"/>
    </justification>
  </clause>

  <clause id="7338">
    <literal><![CDATA[
      (x \ y) \ T(y,y \ x) = y * (T(x,x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(6805,a,5437,a(flip))].">
      <j1 rule="hyper" parents="6805 5437"/>
    </justification>
  </clause>

  <clause id="7339">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / T(x * ((x / y) / x),y)
    ]]></literal>
    <justification jstring="[para(82(a,1),6829(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 6829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7340">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6750,a(flip),b,6830,a),flip(a)].">
      <j1 rule="hyper" parents="373 6750 6830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7342">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),7340(a,1,2,2,1))].">
      <j1 rule="para" parents="12 7340"/>
    </justification>
  </clause>

  <clause id="7343">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,117,a(flip),b,7342,a),flip(a)].">
      <j1 rule="hyper" parents="373 117 7342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7344">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = (x / y) \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(225,a,7343,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 7343 116"/>
    </justification>
  </clause>

  <clause id="7345">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3871(a,1),7344(a,2,2))].">
      <j1 rule="para" parents="3871 7344"/>
    </justification>
  </clause>

  <clause id="7346">
    <literal><![CDATA[
      L(K(x,y),z * K(y,x),u) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,7320,a(flip),b,6896,a),flip(a)].">
      <j1 rule="hyper" parents="373 7320 6896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7347">
    <literal><![CDATA[
      K((x / y) \ z,x) = K((y \ x) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(7013,a,7054,a),flip(a)].">
      <j1 rule="hyper" parents="7013 7054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7348">
    <literal><![CDATA[
      K((x / y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,x) = u
    ]]></literal>
    <justification jstring="[para(7054(a,1),7013(a,1))].">
      <j1 rule="para" parents="7054 7013"/>
    </justification>
  </clause>

  <clause id="7349">
    <literal><![CDATA[
      (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = (x * (y * K(z * L(y,u,w),y))) / (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(7072(a,1),2828(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7072 2828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7350">
    <literal><![CDATA[
      K(x,y) \ ((x * y) * z) != (y * x) * u
    ]]></literal>
    <literal><![CDATA[
      L(z,x * y,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(7117(a,1),44(a,1))].">
      <j1 rule="para" parents="7117 44"/>
    </justification>
  </clause>

  <clause id="7351">
    <literal><![CDATA[
      L(x \ (y * z),x,K(T(y,y * z) * z,y)) = (K(y,T(y,y * z) * z) \ x) \ T(T(T(y,y * z) * z,y),y)
    ]]></literal>
    <justification jstring="[para(4478(a,1),7123(a,1,1,2))].">
      <j1 rule="para" parents="4478 7123"/>
    </justification>
  </clause>

  <clause id="7352">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,5107,a(flip),b,7303,a),flip(a)].">
      <j1 rule="hyper" parents="373 5107 7303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7353">
    <literal><![CDATA[
      (x * y) * K(R(y,x,y),x * y) = ((y * x) / R(y,x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(2830,a,5896,a),flip(a)].">
      <j1 rule="hyper" parents="2830 5896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7354">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(6875(a,2),5936(a,1))].">
      <j1 rule="para" parents="6875 5936"/>
    </justification>
  </clause>

  <clause id="7355">
    <literal><![CDATA[
      T(x * L(x \ 1,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(x,u) * L(x \ K(u,x),y,z)) = w
    ]]></literal>
    <justification jstring="[para(5944(a,1),6499(a,1))].">
      <j1 rule="para" parents="5944 6499"/>
    </justification>
  </clause>

  <clause id="7356">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(511(a,1),5986(a,1,1))].">
      <j1 rule="para" parents="511 5986"/>
    </justification>
  </clause>

  <clause id="7357">
    <literal><![CDATA[
      K(x,L(L(1 / y,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,7077,a(flip),b,6060,a),flip(a)].">
      <j1 rule="hyper" parents="373 7077 6060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7358">
    <literal><![CDATA[
      ((x \ y) / y) * ((y / (x * y)) \ z) = K(x \ 1,x) * z
    ]]></literal>
    <justification jstring="[para(3393(a,1),6139(a,2,1))].">
      <j1 rule="para" parents="3393 6139"/>
    </justification>
  </clause>

  <clause id="7360">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(511(a,1),6210(a,1,2))].">
      <j1 rule="para" parents="511 6210"/>
    </justification>
  </clause>

  <clause id="7361">
    <literal><![CDATA[
      (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u))
    ]]></literal>
    <justification jstring="[para(82(a,1),6437(a,1,1,1,2,1))].">
      <j1 rule="para" parents="82 6437"/>
    </justification>
  </clause>

  <clause id="7362">
    <literal><![CDATA[
      K(x,T(y \ z,u) \ T(z,u)) = T(K(y,x) * z,u) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(6132(a,1),6439(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6132 6439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7363">
    <literal><![CDATA[
      ((x \ 1) * x) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      ((T(x,y) \ 1) \ 1) * z = u
    ]]></literal>
    <justification jstring="[para(6610(a,2),869(a,1))].">
      <j1 rule="para" parents="6610 869"/>
    </justification>
  </clause>

  <clause id="7364">
    <literal><![CDATA[
      x \ T(y,y \ x) = y / ((y \ ((x \ y) \ y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7061,a(flip),b,6736,a)].">
      <j1 rule="hyper" parents="64 7061 6736"/>
    </justification>
  </clause>

  <clause id="7365">
    <literal><![CDATA[
      T(x,1 / y) / ((x / y) \ x) = (x / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(6459(a,1),6824(a,1,1))].">
      <j1 rule="para" parents="6459 6824"/>
    </justification>
  </clause>

  <clause id="7366">
    <literal><![CDATA[
      (x / y) * K(x,1 / y) = T(x,1 / y) / y
    ]]></literal>
    <justification jstring="[para(82(a,1),7365(a,1,2)),flip(a)].">
      <j1 rule="para" parents="82 7365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7367">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * T(z,u))) = K(L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(517(a,1),6851(a,1,2))].">
      <j1 rule="para" parents="517 6851"/>
    </justification>
  </clause>

  <clause id="7368">
    <literal><![CDATA[
      (x * (y * z)) * K(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(157,a,7367,a)].">
      <j1 rule="hyper" parents="157 7367"/>
    </justification>
  </clause>

  <clause id="7369">
    <literal><![CDATA[
      L(K(x,y),z * x,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6923,a(flip),b,7367,a)].">
      <j1 rule="hyper" parents="64 6923 7367"/>
    </justification>
  </clause>

  <clause id="7370">
    <literal><![CDATA[
      (x * (y * T(z,u))) * K(u,L(z,y,x)) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(40,a,6882,a,b,7367,a)].">
      <j1 rule="hyper" parents="40 6882 7367"/>
    </justification>
  </clause>

  <clause id="7371">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(6487,a,7369,a),flip(a)].">
      <j1 rule="hyper" parents="6487 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7372">
    <literal><![CDATA[
      K(L(x,x,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(616,a,7369,a),flip(a)].">
      <j1 rule="hyper" parents="616 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7373">
    <literal><![CDATA[
      K(L(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7174,a(flip),b,7369,a),flip(a)].">
      <j1 rule="hyper" parents="64 7174 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7374">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7137,a(flip),b,7369,a),flip(a)].">
      <j1 rule="hyper" parents="64 7137 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7375">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K(L(x \ y,x,u),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),7369(a,1,2))].">
      <j1 rule="para" parents="10 7369"/>
    </justification>
  </clause>

  <clause id="7376">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),7369(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7377">
    <literal><![CDATA[
      K(x,L(y,z,x)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(225,a,7373,a(flip),b,6092,a),flip(a)].">
      <j1 rule="hyper" parents="225 7373 6092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7378">
    <literal><![CDATA[
      K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(30(a,1),7373(a,1,1))].">
      <j1 rule="para" parents="30 7373"/>
    </justification>
  </clause>

  <clause id="7379">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(569(a,1),7373(a,1,1))].">
      <j1 rule="para" parents="569 7373"/>
    </justification>
  </clause>

  <clause id="7380">
    <literal><![CDATA[
      K((x * y) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[para(346(a,1),7373(a,1,1))].">
      <j1 rule="para" parents="346 7373"/>
    </justification>
  </clause>

  <clause id="7381">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (x * z),x)
    ]]></literal>
    <justification jstring="[para(630(a,1),7373(a,1,1)),flip(a)].">
      <j1 rule="para" parents="630 7373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7382">
    <literal><![CDATA[
      K(L(x,y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1631(a,2),7373(a,1,1))].">
      <j1 rule="para" parents="1631 7373"/>
    </justification>
  </clause>

  <clause id="7383">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,x)) = x
    ]]></literal>
    <justification jstring="[para(7373(a,1),5785(a,1,1,2))].">
      <j1 rule="para" parents="7373 5785"/>
    </justification>
  </clause>

  <clause id="7384">
    <literal><![CDATA[
      K(L(x,y,z),R(z,u,w)) = R(z,u,w) \ R(z * K(x,z),u,w)
    ]]></literal>
    <justification jstring="[para(7373(a,1),6550(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7373 6550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7385">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(L(x,u,x),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,7137,a,b,7374,a)].">
      <j1 rule="hyper" parents="373 7137 7374"/>
    </justification>
  </clause>

  <clause id="7386">
    <literal><![CDATA[
      L(x,y,x) * K(x,z) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,7374,a(flip),b,5764,a)].">
      <j1 rule="hyper" parents="145 7374 5764"/>
    </justification>
  </clause>

  <clause id="7387">
    <literal><![CDATA[
      K(T(x / y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4731(a,1),7374(a,1,1))].">
      <j1 rule="para" parents="4731 7374"/>
    </justification>
  </clause>

  <clause id="7388">
    <literal><![CDATA[
      K(R(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4896(a,1),7374(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4896 7374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7389">
    <literal><![CDATA[
      x * K(R(x,y,x),z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,7388,a,b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 7388 5726"/>
    </justification>
  </clause>

  <clause id="7390">
    <literal><![CDATA[
      K(x,R(y,z,y)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(225,a,7388,a(flip),b,6092,a),flip(a)].">
      <j1 rule="hyper" parents="225 7388 6092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7391">
    <literal><![CDATA[
      K(x,y) * R(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,7388,a(flip),b,5815,a)].">
      <j1 rule="hyper" parents="144 7388 5815"/>
    </justification>
  </clause>

  <clause id="7392">
    <literal><![CDATA[
      K(T(x,x \ y),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4803(a,1),7388(a,1,1))].">
      <j1 rule="para" parents="4803 7388"/>
    </justification>
  </clause>

  <clause id="7393">
    <literal><![CDATA[
      K(x,y) * (R(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(7388(a,1),6028(a,1,1))].">
      <j1 rule="para" parents="7388 6028"/>
    </justification>
  </clause>

  <clause id="7394">
    <literal><![CDATA[
      K(x,L(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6091,a(flip),b,7377,a),flip(a)].">
      <j1 rule="hyper" parents="373 6091 7377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7395">
    <literal><![CDATA[
      K(x,L(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7377(a,2),6100(a,1))].">
      <j1 rule="para" parents="7377 6100"/>
    </justification>
  </clause>

  <clause id="7396">
    <literal><![CDATA[
      K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),7394(a,1,2))].">
      <j1 rule="para" parents="30 7394"/>
    </justification>
  </clause>

  <clause id="7397">
    <literal><![CDATA[
      K(x \ 1,L(y,z,x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1631(a,1),7394(a,1,2))].">
      <j1 rule="para" parents="1631 7394"/>
    </justification>
  </clause>

  <clause id="7398">
    <literal><![CDATA[
      K(x,L(y,z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1631(a,2),7394(a,1,2))].">
      <j1 rule="para" parents="1631 7394"/>
    </justification>
  </clause>

  <clause id="7399">
    <literal><![CDATA[
      K(x,T((x \ y) \ z,u)) = K(x,T(y \ (x * z),u))
    ]]></literal>
    <justification jstring="[para(1024(a,1),7394(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1024 7394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7400">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(7394(a,1),7369(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7394 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7401">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (z * (x \ 1)),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[para(521(a,1),7382(a,1,1))].">
      <j1 rule="para" parents="521 7382"/>
    </justification>
  </clause>

  <clause id="7402">
    <literal><![CDATA[
      K(x,R(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6091,a(flip),b,7390,a),flip(a)].">
      <j1 rule="hyper" parents="373 6091 7390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7403">
    <literal><![CDATA[
      K(x,R(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7390(a,2),6100(a,1))].">
      <j1 rule="para" parents="7390 6100"/>
    </justification>
  </clause>

  <clause id="7404">
    <literal><![CDATA[
      T(x,R(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,7402,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 7402 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7405">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = R(x,z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,7402,a(flip),b,6550,a),flip(a)].">
      <j1 rule="hyper" parents="145 7402 6550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7406">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4803(a,1),7402(a,1,2))].">
      <j1 rule="para" parents="4803 7402"/>
    </justification>
  </clause>

  <clause id="7407">
    <literal><![CDATA[
      T(x / R(y,z,y),y) = R(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,7404,a),flip(a)].">
      <j1 rule="hyper" parents="467 7404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7408">
    <literal><![CDATA[
      R(x,y,x) * T(z,x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,7404,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 7404 22"/>
    </justification>
  </clause>

  <clause id="7409">
    <literal><![CDATA[
      T(x,(y \ z) \ T(z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4745(a,1),7404(a,1,2))].">
      <j1 rule="para" parents="4745 7404"/>
    </justification>
  </clause>

  <clause id="7410">
    <literal><![CDATA[
      T(x,T(y,y \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4803(a,1),7404(a,1,2))].">
      <j1 rule="para" parents="4803 7404"/>
    </justification>
  </clause>

  <clause id="7411">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,y / (y / z))
    ]]></literal>
    <justification jstring="[para(4934(a,1),7404(a,1,2))].">
      <j1 rule="para" parents="4934 7404"/>
    </justification>
  </clause>

  <clause id="7412">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),7379(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 7379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7413">
    <literal><![CDATA[
      K(L(x,y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7385(a,1),616(a,1))].">
      <j1 rule="para" parents="7385 616"/>
    </justification>
  </clause>

  <clause id="7414">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(79(a,1),7387(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 7387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7416">
    <literal><![CDATA[
      K(x,L(y,z * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(614(a,1),7395(a,1,2))].">
      <j1 rule="para" parents="614 7395"/>
    </justification>
  </clause>

  <clause id="7417">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(346(a,1),7395(a,1,2))].">
      <j1 rule="para" parents="346 7395"/>
    </justification>
  </clause>

  <clause id="7419">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(1418(a,1),7403(a,1,2))].">
      <j1 rule="para" parents="1418 7403"/>
    </justification>
  </clause>

  <clause id="7420">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4803(a,1),7403(a,1,2))].">
      <j1 rule="para" parents="4803 7403"/>
    </justification>
  </clause>

  <clause id="7421">
    <literal><![CDATA[
      K(x,T(y,y * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),7406(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7422">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(116(a,1),7406(a,1,2))].">
      <j1 rule="para" parents="116 7406"/>
    </justification>
  </clause>

  <clause id="7423">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(848(a,1),7406(a,1,2)),flip(a)].">
      <j1 rule="para" parents="848 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7424">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(4575(a,1),7406(a,1,2))].">
      <j1 rule="para" parents="4575 7406"/>
    </justification>
  </clause>

  <clause id="7425">
    <literal><![CDATA[
      K(x,T(y,z / y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4636(a,2),7406(a,1,2))].">
      <j1 rule="para" parents="4636 7406"/>
    </justification>
  </clause>

  <clause id="7426">
    <literal><![CDATA[
      T(x,x \ y) * T(z,T(x,y)) = z * T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,7410,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 7410 22"/>
    </justification>
  </clause>

  <clause id="7427">
    <literal><![CDATA[
      T(x,T(y,y * z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),7410(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 7410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7428">
    <literal><![CDATA[
      T(x,(y \ z) \ z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(116(a,1),7410(a,1,2))].">
      <j1 rule="para" parents="116 7410"/>
    </justification>
  </clause>

  <clause id="7429">
    <literal><![CDATA[
      T(x,T(y / z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(848(a,1),7410(a,1,2)),flip(a)].">
      <j1 rule="para" parents="848 7410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7430">
    <literal><![CDATA[
      K((x / ((1 / x) \ y)) \ 1,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(6588,a,7412,a)].">
      <j1 rule="hyper" parents="6588 7412"/>
    </justification>
  </clause>

  <clause id="7431">
    <literal><![CDATA[
      K(T(x / (x / y),x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(4771(a,2),7413(a,1,1))].">
      <j1 rule="para" parents="4771 7413"/>
    </justification>
  </clause>

  <clause id="7432">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(R(x,u,x),y) = z
    ]]></literal>
    <justification jstring="[para(4896(a,1),7413(a,1,1))].">
      <j1 rule="para" parents="4896 7413"/>
    </justification>
  </clause>

  <clause id="7433">
    <literal><![CDATA[
      K(T(x,y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6762,a(flip),b,7414,a),flip(a)].">
      <j1 rule="hyper" parents="64 6762 7414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7434">
    <literal><![CDATA[
      K(T(x,T(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4020,a(flip),b,7433,a),flip(a)].">
      <j1 rule="hyper" parents="373 4020 7433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7435">
    <literal><![CDATA[
      K(T(x,K(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,3318,a(flip),b,7433,a),flip(a)].">
      <j1 rule="hyper" parents="373 3318 7433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7436">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,7433,a,b,6158,a)].">
      <j1 rule="hyper" parents="145 7433 6158"/>
    </justification>
  </clause>

  <clause id="7437">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,7433,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="145 7433 22"/>
    </justification>
  </clause>

  <clause id="7438">
    <literal><![CDATA[
      T(K(x,y),z) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(144,a,7433,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 7433 5739"/>
    </justification>
  </clause>

  <clause id="7439">
    <literal><![CDATA[
      T(K(x,y),K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4067(a,1),7433(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4067 7433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7440">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7433(a,1),6092(a,1,1))].">
      <j1 rule="para" parents="7433 6092"/>
    </justification>
  </clause>

  <clause id="7441">
    <literal><![CDATA[
      T(x,T(y,z)) * K(x,y) = T(T(x,y),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,7434,a(flip),b,5742,a)].">
      <j1 rule="hyper" parents="145 7434 5742"/>
    </justification>
  </clause>

  <clause id="7442">
    <literal><![CDATA[
      K(x,y) * T(x,K(y,z)) = T(T(x,K(y,z)),y)
    ]]></literal>
    <justification jstring="[hyper(144,a,7435,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 7435 5739"/>
    </justification>
  </clause>

  <clause id="7443">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[para(7435(a,1),6092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7435 6092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7444">
    <literal><![CDATA[
      K(x,y) * K(x,z) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,7439,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 7439 22"/>
    </justification>
  </clause>

  <clause id="7445">
    <literal><![CDATA[
      K(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7439(a,1),328(a,1,2))].">
      <j1 rule="para" parents="7439 328"/>
    </justification>
  </clause>

  <clause id="7446">
    <literal><![CDATA[
      K(x,T(y,z * y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4683(a,2),7421(a,1,2))].">
      <j1 rule="para" parents="4683 7421"/>
    </justification>
  </clause>

  <clause id="7447">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = L(K(x,T(z,u)),u,y)
    ]]></literal>
    <justification jstring="[para(7422(a,1),7078(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7422 7078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7448">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(5144(a,1),7423(a,1,2))].">
      <j1 rule="para" parents="5144 7423"/>
    </justification>
  </clause>

  <clause id="7449">
    <literal><![CDATA[
      T(x,T(y,z * y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4683(a,2),7427(a,1,2))].">
      <j1 rule="para" parents="4683 7427"/>
    </justification>
  </clause>

  <clause id="7450">
    <literal><![CDATA[
      T(x / ((y \ z) \ z),T(y,z)) = ((y \ z) \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,7428,a),flip(a)].">
      <j1 rule="hyper" parents="467 7428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7451">
    <literal><![CDATA[
      T(x,(y \ (z \ y)) \ 1) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6704,a,b,7428,a)].">
      <j1 rule="hyper" parents="64 6704 7428"/>
    </justification>
  </clause>

  <clause id="7452">
    <literal><![CDATA[
      T(T(x,y),x / z) = T(T(x,y),z \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4711,a(flip),b,7429,a)].">
      <j1 rule="hyper" parents="64 4711 7429"/>
    </justification>
  </clause>

  <clause id="7453">
    <literal><![CDATA[
      T(x,(y * z) \ z) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(5144(a,1),7429(a,1,2))].">
      <j1 rule="para" parents="5144 7429"/>
    </justification>
  </clause>

  <clause id="7454">
    <literal><![CDATA[
      K(x,T(y,T(T(x,z),u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6697,a,7436,a(flip))].">
      <j1 rule="hyper" parents="6697 7436"/>
    </justification>
  </clause>

  <clause id="7455">
    <literal><![CDATA[
      (K(x,y) \ z) \ z = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7436(a,1),6882(a,1,1))].">
      <j1 rule="para" parents="7436 6882"/>
    </justification>
  </clause>

  <clause id="7456">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,T(x,z)) = z
    ]]></literal>
    <justification jstring="[hyper(6897,a,7437,a)].">
      <j1 rule="hyper" parents="6897 7437"/>
    </justification>
  </clause>

  <clause id="7457">
    <literal><![CDATA[
      K(x / y,z) * y = y * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(117(a,1),7437(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="117 7437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7459">
    <literal><![CDATA[
      (K(x,y) * z) \ z = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7437(a,1),6882(a,1,1))].">
      <j1 rule="para" parents="7437 6882"/>
    </justification>
  </clause>

  <clause id="7460">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(z,T(y,u)),u,x) = w
    ]]></literal>
    <justification jstring="[para(7437(a,1),7322(a,1,1,2))].">
      <j1 rule="para" parents="7437 7322"/>
    </justification>
  </clause>

  <clause id="7461">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,7440,a(flip),b,5783,a(flip))].">
      <j1 rule="hyper" parents="145 7440 5783"/>
    </justification>
  </clause>

  <clause id="7462">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6092,a(flip),b,7443,a),flip(a)].">
      <j1 rule="hyper" parents="373 6092 7443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7463">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7443(a,2),6101(a,1))].">
      <j1 rule="para" parents="7443 6101"/>
    </justification>
  </clause>

  <clause id="7464">
    <literal><![CDATA[
      K(x,T(y,x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(7446(a,2),5977(a,1))].">
      <j1 rule="para" parents="7446 5977"/>
    </justification>
  </clause>

  <clause id="7465">
    <literal><![CDATA[
      T(x * y,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(7449(a,1),4710(a,1))].">
      <j1 rule="para" parents="7449 4710"/>
    </justification>
  </clause>

  <clause id="7466">
    <literal><![CDATA[
      T(x,T(y,T(T(x,z),u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,7454,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 7454 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7467">
    <literal><![CDATA[
      K(x,T(y,T(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(114(a,1),7454(a,1,2,2,1))].">
      <j1 rule="para" parents="114 7454"/>
    </justification>
  </clause>

  <clause id="7468">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,7467,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 7467 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7470">
    <literal><![CDATA[
      K(x / y,T(z,y \ x)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(117(a,1),7467(a,1,2,2))].">
      <j1 rule="para" parents="117 7467"/>
    </justification>
  </clause>

  <clause id="7471">
    <literal><![CDATA[
      T(x,T(y,z)) * T(y,x) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,7468,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 7468 22"/>
    </justification>
  </clause>

  <clause id="7472">
    <literal><![CDATA[
      T(x / y,T(z,y \ x)) = T(x / y,z)
    ]]></literal>
    <justification jstring="[para(117(a,1),7468(a,1,2,2))].">
      <j1 rule="para" parents="117 7468"/>
    </justification>
  </clause>

  <clause id="7473">
    <literal><![CDATA[
      T(x,y / T(x,z)) = T(x,T(x,z) \ y)
    ]]></literal>
    <justification jstring="[para(117(a,1),7468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 7468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7474">
    <literal><![CDATA[
      T(x / (x / y),T(z,y)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(276(a,1),7468(a,1,2,2))].">
      <j1 rule="para" parents="276 7468"/>
    </justification>
  </clause>

  <clause id="7475">
    <literal><![CDATA[
      K(x,K(y,T(z,x))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7455(a,1),6128(a,1,2))].">
      <j1 rule="para" parents="7455 6128"/>
    </justification>
  </clause>

  <clause id="7476">
    <literal><![CDATA[
      T(x,K(y,x \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7456(a,1),7219(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7456 7219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7477">
    <literal><![CDATA[
      T(x * K(y,x),T(z,T(x,u))) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[para(5785(a,1),7466(a,1,2,2,1))].">
      <j1 rule="para" parents="5785 7466"/>
    </justification>
  </clause>

  <clause id="7478">
    <literal><![CDATA[
      T(x,K(y,1 / x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6041(a,2),7476(a,1,2,1))].">
      <j1 rule="para" parents="6041 7476"/>
    </justification>
  </clause>

  <clause id="7480">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = y / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,7478,a(flip),b,5804,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 7478 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7481">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6142,a(flip),b,7371,a),flip(a)].">
      <j1 rule="hyper" parents="373 6142 7371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7482">
    <literal><![CDATA[
      K(L(x,y,z),y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = u
    ]]></literal>
    <justification jstring="[para(7371(a,2),6143(a,1))].">
      <j1 rule="para" parents="7371 6143"/>
    </justification>
  </clause>

  <clause id="7483">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(3039(a,2),7419(a,1,2))].">
      <j1 rule="para" parents="3039 7419"/>
    </justification>
  </clause>

  <clause id="7484">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(3815(a,2),7419(a,1,2))].">
      <j1 rule="para" parents="3815 7419"/>
    </justification>
  </clause>

  <clause id="7485">
    <literal><![CDATA[
      K(x,K(T(y,K(x,z)),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(7433(a,2),7463(a,1,2))].">
      <j1 rule="para" parents="7433 7463"/>
    </justification>
  </clause>

  <clause id="7486">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = (z * y) \ (z * (y * K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18,a(flip),b,7376,a),flip(a)].">
      <j1 rule="hyper" parents="373 18 7376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7487">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(7376(a,1),6092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7376 6092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7488">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7263,a,b,7380,a)].">
      <j1 rule="hyper" parents="64 7263 7380"/>
    </justification>
  </clause>

  <clause id="7489">
    <literal><![CDATA[
      K((x \ y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),7380(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 7380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7490">
    <literal><![CDATA[
      K(x,y) * L(x,z,x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(4106,a,7386,a)].">
      <j1 rule="hyper" parents="4106 7386"/>
    </justification>
  </clause>

  <clause id="7491">
    <literal><![CDATA[
      K(x,y) * (L(y,z,y) \ u) = L(T(y,x),z,y) \ u
    ]]></literal>
    <justification jstring="[para(7386(a,1),7068(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7386 7068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7492">
    <literal><![CDATA[
      K(x,y) \ R(y,z,y) = R(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(6206,a,7391,a)].">
      <j1 rule="hyper" parents="6206 7391"/>
    </justification>
  </clause>

  <clause id="7493">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,7391,a(flip),b,5778,a)].">
      <j1 rule="hyper" parents="139 7391 5778"/>
    </justification>
  </clause>

  <clause id="7494">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = y * (R(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,7407,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 7407 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7495">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = (z / x) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(117(a,1),7408(a,1,2))].">
      <j1 rule="para" parents="117 7408"/>
    </justification>
  </clause>

  <clause id="7497">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ y)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6704(a,1),7424(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6704 7424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7498">
    <literal><![CDATA[
      K(x \ y,z) * K(x \ y,x) = (y / x) \ T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6614,a(flip),b,7444,a),flip(a)].">
      <j1 rule="hyper" parents="373 6614 7444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7499">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6708,a,b,7448,a)].">
      <j1 rule="hyper" parents="64 6708 7448"/>
    </justification>
  </clause>

  <clause id="7500">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6732,a,b,7453,a)].">
      <j1 rule="hyper" parents="64 6732 7453"/>
    </justification>
  </clause>

  <clause id="7501">
    <literal><![CDATA[
      K(x / y,L(y,z,u)) = K(y \ x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,4015,a,b,7457,a),flip(a)].">
      <j1 rule="hyper" parents="36 4015 7457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7502">
    <literal><![CDATA[
      K(x / (y \ z),z \ y) = K((y \ z) \ x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(36,a,3353,a,b,7457,a),flip(a)].">
      <j1 rule="hyper" parents="36 3353 7457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7503">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6187,a,7461,a)].">
      <j1 rule="hyper" parents="6187 7461"/>
    </justification>
  </clause>

  <clause id="7504">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(7461(a,1),6891(a,1,1))].">
      <j1 rule="para" parents="7461 6891"/>
    </justification>
  </clause>

  <clause id="7505">
    <literal><![CDATA[
      T(x / (x / y),z / y) = T(x / (x / y),y \ z)
    ]]></literal>
    <justification jstring="[para(848(a,1),7472(a,1,2)),flip(a)].">
      <j1 rule="para" parents="848 7472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7506">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5787,a,b,7480,a),flip(a)].">
      <j1 rule="hyper" parents="373 5787 7480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7507">
    <literal><![CDATA[
      K(K(x,y) * z,y \ 1) = K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),7506(a,1,1,1,2))].">
      <j1 rule="para" parents="79 7506"/>
    </justification>
  </clause>

  <clause id="7508">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(5796(a,1),7506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5796 7506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7509">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(6041(a,1),7506(a,1,1,1))].">
      <j1 rule="para" parents="6041 7506"/>
    </justification>
  </clause>

  <clause id="7510">
    <literal><![CDATA[
      K(T(x,1 / y) / z,y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[para(7030(a,1),7506(a,1,1))].">
      <j1 rule="para" parents="7030 7506"/>
    </justification>
  </clause>

  <clause id="7511">
    <literal><![CDATA[
      (K(x,y \ 1) * z) * K(z,y) = T(K(x,y \ 1) * z,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,7509,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 7509 5726"/>
    </justification>
  </clause>

  <clause id="7512">
    <literal><![CDATA[
      K(K(x,x \ y) * z,x / y) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(6262(a,1),7509(a,1,1,1))].">
      <j1 rule="para" parents="6262 7509"/>
    </justification>
  </clause>

  <clause id="7513">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6578(a,1),7509(a,1,1))].">
      <j1 rule="para" parents="6578 7509"/>
    </justification>
  </clause>

  <clause id="7514">
    <literal><![CDATA[
      K(x \ (y \ x),y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(6802,a,7488,a),flip(a)].">
      <j1 rule="hyper" parents="6802 7488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7515">
    <literal><![CDATA[
      L(x * K(y \ (x \ z),x),u,w) / L(x,u,w) = K((y * x) \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(7488(a,1),6549(a,1,1,1,2))].">
      <j1 rule="para" parents="7488 6549"/>
    </justification>
  </clause>

  <clause id="7516">
    <literal><![CDATA[
      (x \ (y \ x)) * K(y \ 1,y) = T(x \ (y \ x),y)
    ]]></literal>
    <justification jstring="[hyper(145,a,7514,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 7514 5726"/>
    </justification>
  </clause>

  <clause id="7517">
    <literal><![CDATA[
      K(x,y \ K(z,y)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(5783(a,1),7499(a,1,2))].">
      <j1 rule="para" parents="5783 7499"/>
    </justification>
  </clause>

  <clause id="7518">
    <literal><![CDATA[
      K(x,K(y,x * y)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,6130,a(flip),b,7503,a),flip(a)].">
      <j1 rule="hyper" parents="138 6130 7503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7519">
    <literal><![CDATA[
      T(x,K(y,x * y)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,7518,a)].">
      <j1 rule="hyper" parents="57 7518"/>
    </justification>
  </clause>

  <clause id="7520">
    <literal><![CDATA[
      K(x * y,y \ 1) = K(y * x,y \ 1)
    ]]></literal>
    <justification jstring="[para(5796(a,1),7507(a,1,1))].">
      <j1 rule="para" parents="5796 7507"/>
    </justification>
  </clause>

  <clause id="7521">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7379,a(flip),b,7508,a),flip(a)].">
      <j1 rule="hyper" parents="64 7379 7508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7522">
    <literal><![CDATA[
      K(x * (y \ 1),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5249,a(flip),b,7521,a)].">
      <j1 rule="hyper" parents="64 5249 7521"/>
    </justification>
  </clause>

  <clause id="7523">
    <literal><![CDATA[
      K(x \ y,x) * (y * (1 / x)) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(144,a,7521,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 7521 5739"/>
    </justification>
  </clause>

  <clause id="7524">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),7521(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 7521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7525">
    <literal><![CDATA[
      K(T(x / (1 / (1 / y)),1 / z) / (1 / y),z) = K((x / y) / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(3900(a,1),7510(a,2,1))].">
      <j1 rule="para" parents="3900 7510"/>
    </justification>
  </clause>

  <clause id="7526">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * (y \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(2325(a,1),7420(a,1,2,2))].">
      <j1 rule="para" parents="2325 7420"/>
    </justification>
  </clause>

  <clause id="7527">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z)
    ]]></literal>
    <justification jstring="[para(102(a,1),7375(a,2,1))].">
      <j1 rule="para" parents="102 7375"/>
    </justification>
  </clause>

  <clause id="7528">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(346(a,1),7375(a,2,1))].">
      <j1 rule="para" parents="346 7375"/>
    </justification>
  </clause>

  <clause id="7529">
    <literal><![CDATA[
      L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(630(a,1),7375(a,2,1))].">
      <j1 rule="para" parents="630 7375"/>
    </justification>
  </clause>

  <clause id="7530">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(1638(a,1),7375(a,2,1))].">
      <j1 rule="para" parents="1638 7375"/>
    </justification>
  </clause>

  <clause id="7531">
    <literal><![CDATA[
      L(K(L(x,y,z) \ x,u),x,z * y) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(2869(a,2),7375(a,2,1))].">
      <j1 rule="para" parents="2869 7375"/>
    </justification>
  </clause>

  <clause id="7532">
    <literal><![CDATA[
      (R(x \ y,z,x \ y) / (x \ y)) * (y / x) = R((x \ y) * K(x,x \ y),z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6468,a,b,7405,a)].">
      <j1 rule="hyper" parents="373 6468 7405"/>
    </justification>
  </clause>

  <clause id="7533">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = K(y,x) * R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,4003,a(flip),b,7405,a),flip(a)].">
      <j1 rule="hyper" parents="373 4003 7405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7534">
    <literal><![CDATA[
      R(x * K(R(y \ 1,z,u) \ 1,x),w,x) = R(x,w,x) * R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(6682(a,1),7405(a,2,2))].">
      <j1 rule="para" parents="6682 7405"/>
    </justification>
  </clause>

  <clause id="7535">
    <literal><![CDATA[
      (x \ T(y,x)) \ (x \ (y * T(x,T(y,z)))) = T(T(x,T(y,z)),x \ T(y,x))
    ]]></literal>
    <justification jstring="[para(7471(a,1),2406(a,1,2,2))].">
      <j1 rule="para" parents="7471 2406"/>
    </justification>
  </clause>

  <clause id="7536">
    <literal><![CDATA[
      T(T(T(x,y) / (T(x,y) / y),x),z) = L(T(y,z),y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(7474(a,1),4776(a,1,1))].">
      <j1 rule="para" parents="7474 4776"/>
    </justification>
  </clause>

  <clause id="7537">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,7319,a(flip),b,7487,a),flip(a)].">
      <j1 rule="hyper" parents="373 7319 7487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7538">
    <literal><![CDATA[
      L(K(x,y),z * y,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),7537(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7539">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) = K(x,L(y,z * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(6847(a,1),7537(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6847 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7540">
    <literal><![CDATA[
      K(x,L(y,y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(616,a,7538,a),flip(a)].">
      <j1 rule="hyper" parents="616 7538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7541">
    <literal><![CDATA[
      K(x,L(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7174,a(flip),b,7538,a),flip(a)].">
      <j1 rule="hyper" parents="64 7174 7538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7542">
    <literal><![CDATA[
      K(x,L(1 / y,y,z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5162,a(flip),b,7538,a),flip(a)].">
      <j1 rule="hyper" parents="64 5162 7538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7544">
    <literal><![CDATA[
      T(x,L(y,y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,7540,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 7540 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7546">
    <literal><![CDATA[
      T(x,L(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,7541,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 7541 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7547">
    <literal><![CDATA[
      T(x,L(y,z,y)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,7541,a(flip),b,5726,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 7541 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7548">
    <literal><![CDATA[
      ((x * x) \ y) * L(x,x,x) = (x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(7544(a,1),4924(a,2,2))].">
      <j1 rule="para" parents="7544 4924"/>
    </justification>
  </clause>

  <clause id="7550">
    <literal><![CDATA[
      x * T(y,L(x,z,x)) = y * x
    ]]></literal>
    <justification jstring="[hyper(145,a,7546,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="145 7546 22"/>
    </justification>
  </clause>

  <clause id="7552">
    <literal><![CDATA[
      T(x,L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(7547(a,2),5767(a,1))].">
      <j1 rule="para" parents="7547 5767"/>
    </justification>
  </clause>

  <clause id="7553">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = y * (L(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[para(117(a,1),7550(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 7550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7554">
    <literal><![CDATA[
      T(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(4731(a,1),7552(a,1,2))].">
      <j1 rule="para" parents="4731 7552"/>
    </justification>
  </clause>

  <clause id="7556">
    <literal><![CDATA[
      T(x,T(y * K(z,y \ u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ u,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(6246(a,1),7554(a,1,2,1))].">
      <j1 rule="para" parents="6246 7554"/>
    </justification>
  </clause>

  <clause id="7557">
    <literal><![CDATA[
      K(x,T(y,z \ (u * y))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(7086(a,1),7497(a,1,2))].">
      <j1 rule="para" parents="7086 7497"/>
    </justification>
  </clause>

  <clause id="7558">
    <literal><![CDATA[
      K((x / y) \ z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[para(6270(a,1),7512(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6270 7512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7559">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,((x * y) \ x) \ 1) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6706,a(flip),b,7524,a),flip(a)].">
      <j1 rule="hyper" parents="373 6706 7524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7560">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = y \ T(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(7524(a,1),6989(a,1,1,2))].">
      <j1 rule="para" parents="7524 6989"/>
    </justification>
  </clause>

  <clause id="7561">
    <literal><![CDATA[
      x / R(y * K(z,y),u,y) = (x / R(y,u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(7533(a,2),7126(a,1,2))].">
      <j1 rule="para" parents="7533 7126"/>
    </justification>
  </clause>

  <clause id="7562">
    <literal><![CDATA[
      L(K(x,y),z * x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(7400(a,1),7416(a,1))].">
      <j1 rule="para" parents="7400 7416"/>
    </justification>
  </clause>

  <clause id="7563">
    <literal><![CDATA[
      K(x,(K(y,z / x) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ z,y) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(6140(a,2),7417(a,1,2,1))].">
      <j1 rule="para" parents="6140 7417"/>
    </justification>
  </clause>

  <clause id="7564">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(6441(a,2),7417(a,1))].">
      <j1 rule="para" parents="6441 7417"/>
    </justification>
  </clause>

  <clause id="7565">
    <literal><![CDATA[
      T(T(x,y),y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * K(y,x) = z
    ]]></literal>
    <justification jstring="[para(6606(a,2),7445(a,1))].">
      <j1 rule="para" parents="6606 7445"/>
    </justification>
  </clause>

  <clause id="7566">
    <literal><![CDATA[
      L(K((K(x,y) * z) \ u,w),u,K(y,x)) = K(z \ (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[para(6161(a,1),7527(a,2,1,1))].">
      <j1 rule="para" parents="6161 7527"/>
    </justification>
  </clause>

  <clause id="7567">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K((z * (x \ 1)) \ (z * y),x)
    ]]></literal>
    <justification jstring="[para(6988(a,1),7527(a,1,1))].">
      <j1 rule="para" parents="6988 7527"/>
    </justification>
  </clause>

  <clause id="7568">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(y \ (x * z),z)
    ]]></literal>
    <justification jstring="[hyper(6487,a,7529,a)].">
      <j1 rule="hyper" parents="6487 7529"/>
    </justification>
  </clause>

  <clause id="7569">
    <literal><![CDATA[
      K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7080,a(flip),b,7529,a)].">
      <j1 rule="hyper" parents="64 7080 7529"/>
    </justification>
  </clause>

  <clause id="7570">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,z) = u
    ]]></literal>
    <justification jstring="[para(7529(a,1),6487(a,1))].">
      <j1 rule="para" parents="7529 6487"/>
    </justification>
  </clause>

  <clause id="7571">
    <literal><![CDATA[
      K((1 / x) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(6487,a,7530,a),flip(a)].">
      <j1 rule="hyper" parents="6487 7530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7572">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5253,a(flip),b,7530,a),flip(a)].">
      <j1 rule="hyper" parents="373 5253 7530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7573">
    <literal><![CDATA[
      K((x \ 1) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5253,a(flip),b,7571,a)].">
      <j1 rule="hyper" parents="64 5253 7571"/>
    </justification>
  </clause>

  <clause id="7574">
    <literal><![CDATA[
      T(x,y * y) * (y \ 1) = (y \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4925,a(flip),b,7548,a)].">
      <j1 rule="hyper" parents="64 4925 7548"/>
    </justification>
  </clause>

  <clause id="7577">
    <literal><![CDATA[
      T(x * K(y \ 1,x),y) = T(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(36,a,5860,a,b,7574,a)].">
      <j1 rule="hyper" parents="36 5860 7574"/>
    </justification>
  </clause>

  <clause id="7578">
    <literal><![CDATA[
      T((x \ 1) \ y,x * x) = T(y / (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(36,a,525,a,b,7574,a),flip(a)].">
      <j1 rule="hyper" parents="36 525 7574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7579">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x \ y) = T(y / x,x * x)
    ]]></literal>
    <justification jstring="[hyper(41,a,278,a,b,7577,a),flip(a)].">
      <j1 rule="hyper" parents="41 278 7577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7580">
    <literal><![CDATA[
      T(x * K(y,x),1 / y) = T(x,(1 / y) * (1 / y))
    ]]></literal>
    <justification jstring="[para(82(a,1),7577(a,1,1,2,1))].">
      <j1 rule="para" parents="82 7577"/>
    </justification>
  </clause>

  <clause id="7581">
    <literal><![CDATA[
      T(x * K(1 / y,x),y) = T(x,y * y)
    ]]></literal>
    <justification jstring="[para(3776(a,2),7577(a,1,1,2))].">
      <j1 rule="para" parents="3776 7577"/>
    </justification>
  </clause>

  <clause id="7582">
    <literal><![CDATA[
      T(x * K(y \ z,x),z \ y) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[para(6756(a,1),7577(a,1,1,2))].">
      <j1 rule="para" parents="6756 7577"/>
    </justification>
  </clause>

  <clause id="7583">
    <literal><![CDATA[
      T((1 / x) \ y,x * x) = T(y / (1 / x),x)
    ]]></literal>
    <justification jstring="[para(5774(a,1),7581(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5774 7581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7584">
    <literal><![CDATA[
      (x \ y) * (x * ((x \ 1) \ z)) = T(y / (1 / x),x) * z
    ]]></literal>
    <justification jstring="[para(7583(a,1),5245(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7583 5245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7585">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),u) = v5
    ]]></literal>
    <justification jstring="[para(7400(a,2),7562(a,1))].">
      <j1 rule="para" parents="7400 7562"/>
    </justification>
  </clause>

  <clause id="7586">
    <literal><![CDATA[
      ((x \ y) \ y) \ (z * T(x,x \ y)) = T(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,505,a,b,7426,a)].">
      <j1 rule="hyper" parents="35 505 7426"/>
    </justification>
  </clause>

  <clause id="7587">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = x * (L(x,z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(145,a,7491,a(flip),b,6155,a)].">
      <j1 rule="hyper" parents="145 7491 6155"/>
    </justification>
  </clause>

  <clause id="7588">
    <literal><![CDATA[
      (x \ 1) \ T(y \ (x \ y),x) = (1 / x) \ (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(139,a,7516,a(flip),b,3622,a)].">
      <j1 rule="hyper" parents="139 7516 3622"/>
    </justification>
  </clause>

  <clause id="7589">
    <literal><![CDATA[
      T(x * K(y,x),y \ 1) = T(x,(1 / y) * (1 / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,3870,a(flip),b,7580,a)].">
      <j1 rule="hyper" parents="64 3870 7580"/>
    </justification>
  </clause>

  <clause id="7590">
    <literal><![CDATA[
      (x * (y * T(T(z,y),u))) \ (x * (z * y)) = K(u,L(T(z,y),y,x))
    ]]></literal>
    <justification jstring="[hyper(139,a,251,a(flip),b,7370,a)].">
      <j1 rule="hyper" parents="139 251 7370"/>
    </justification>
  </clause>

  <clause id="7591">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(115(a,1),7370(a,1,1,2))].">
      <j1 rule="para" parents="115 7370"/>
    </justification>
  </clause>

  <clause id="7592">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * (z * y)) = w
    ]]></literal>
    <justification jstring="[para(7591(a,2),720(a,1))].">
      <j1 rule="para" parents="7591 720"/>
    </justification>
  </clause>

  <clause id="7593">
    <literal><![CDATA[
      L(K(x,T(y,z)),z,L(y,u,w)) = K(x,T(y,L(y,u,w) * (y \ z)))
    ]]></literal>
    <justification jstring="[para(2331(a,1),7447(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2331 7447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7594">
    <literal><![CDATA[
      K(L(x,y / x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(7486(a,2),608(a,1))].">
      <j1 rule="para" parents="7486 608"/>
    </justification>
  </clause>

  <clause id="7595">
    <literal><![CDATA[
      K(L(x \ y,x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x \ y,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(79(a,1),7594(a,1,1,2))].">
      <j1 rule="para" parents="79 7594"/>
    </justification>
  </clause>

  <clause id="7596">
    <literal><![CDATA[
      x * ((x \ y) * K(z \ (x \ y),u)) = y * K((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,7528,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 7528 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7597">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K((y * (x \ 1)) \ z,x)
    ]]></literal>
    <justification jstring="[para(6988(a,1),7528(a,1,1))].">
      <j1 rule="para" parents="6988 7528"/>
    </justification>
  </clause>

  <clause id="7598">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ u),y),z \ u,z) = K((z * (y / x)) \ u,y)
    ]]></literal>
    <justification jstring="[para(7347(a,1),7528(a,1,1))].">
      <j1 rule="para" parents="7347 7528"/>
    </justification>
  </clause>

  <clause id="7599">
    <literal><![CDATA[
      K((x * (y * z)) \ ((x * y) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(L(z,y,x) \ u,w),u,x * y) = v5
    ]]></literal>
    <justification jstring="[para(645(a,1),7595(a,1,1))].">
      <j1 rule="para" parents="645 7595"/>
    </justification>
  </clause>

  <clause id="7600">
    <literal><![CDATA[
      T(K(x,y \ 1) * z,y) = K(x,y \ 1) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6940,a,7511,a),flip(a)].">
      <j1 rule="hyper" parents="6940 7511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7601">
    <literal><![CDATA[
      (x \ y) * ((1 / x) \ x) = T(y / (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(36,a,1611,a,b,7584,a(flip))].">
      <j1 rule="hyper" parents="36 1611 7584"/>
    </justification>
  </clause>

  <clause id="7602">
    <literal><![CDATA[
      (x \ 1) * (x * ((x \ 1) \ y)) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(408(a,1),7584(a,2,1))].">
      <j1 rule="para" parents="408 7584"/>
    </justification>
  </clause>

  <clause id="7603">
    <literal><![CDATA[
      ((x \ 1) \ y) * ((1 / (x \ 1)) \ (x \ 1)) = T(y / x,x \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),7601(a,2,1,2))].">
      <j1 rule="para" parents="79 7601"/>
    </justification>
  </clause>

  <clause id="7604">
    <literal><![CDATA[
      T(T(((x \ 1) \ y) / (1 / x),x),x \ 1) = (x \ 1) \ ((x \ 1) \ T(y,x))
    ]]></literal>
    <justification jstring="[para(7601(a,1),3423(a,1,1))].">
      <j1 rule="para" parents="7601 3423"/>
    </justification>
  </clause>

  <clause id="7605">
    <literal><![CDATA[
      L(x * ((x \ 1) \ y),x,x) = x * ((1 / (1 / x)) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,7602,a(flip),b,1148,a),flip(a)].">
      <j1 rule="hyper" parents="145 7602 1148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7606">
    <literal><![CDATA[
      R(x,x,x * ((1 / (1 / x)) * y)) = R(x,x,x * ((x \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(7605(a,1),2042(a,1,3))].">
      <j1 rule="para" parents="7605 2042"/>
    </justification>
  </clause>

  <clause id="7607">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6700,a(flip),b,7004,a),flip(a)].">
      <j1 rule="hyper" parents="373 6700 7004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7608">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K(z / (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,7502,a,b,7607,a),flip(a)].">
      <j1 rule="hyper" parents="373 7502 7607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7609">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,x \ (x * y)) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),7608(a,2,2))].">
      <j1 rule="para" parents="9 7608"/>
    </justification>
  </clause>

  <clause id="7610">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(6719(a,1),7009(a,1))].">
      <j1 rule="para" parents="6719 7009"/>
    </justification>
  </clause>

  <clause id="7611">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(7082(a,1),7610(a,1))].">
      <j1 rule="para" parents="7082 7610"/>
    </justification>
  </clause>

  <clause id="7612">
    <literal><![CDATA[
      L(K(x,T(y,z)),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * (y \ z)) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(7422(a,1),7610(a,1,1))].">
      <j1 rule="para" parents="7422 7610"/>
    </justification>
  </clause>

  <clause id="7613">
    <literal><![CDATA[
      T(((x * y) / x) * (y \ z),z) / z = K(x,(T(y \ z,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1495(a,1),7021(a,1,1,1))].">
      <j1 rule="para" parents="1495 7021"/>
    </justification>
  </clause>

  <clause id="7614">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5996(a,2),7029(a,1,2))].">
      <j1 rule="para" parents="5996 7029"/>
    </justification>
  </clause>

  <clause id="7615">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,x)),u) = K(x,y) * (T(z,u) * K(y,x))
    ]]></literal>
    <justification jstring="[para(6570(a,1),7029(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6570 7029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7616">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(3779(a,1),7039(a,2,1))].">
      <j1 rule="para" parents="3779 7039"/>
    </justification>
  </clause>

  <clause id="7618">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,5237,a,b,7616,a)].">
      <j1 rule="hyper" parents="64 5237 7616"/>
    </justification>
  </clause>

  <clause id="7619">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ 1) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),7616(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 7616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7620">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * T(z,x \ 1)) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(22(a,2),7616(a,1,2,2))].">
      <j1 rule="para" parents="22 7616"/>
    </justification>
  </clause>

  <clause id="7621">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),7618(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 7618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7622">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ 1) * (K(x,z) * y)) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(225,a,7619,a(flip),b,6156,a)].">
      <j1 rule="hyper" parents="225 7619 6156"/>
    </justification>
  </clause>

  <clause id="7623">
    <literal><![CDATA[
      (K(x,y) * ((1 / x) * z)) / (K(x,y) * z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(724,a,7621,a)].">
      <j1 rule="hyper" parents="724 7621"/>
    </justification>
  </clause>

  <clause id="7624">
    <literal><![CDATA[
      L(T(1 / x,y),y,K(x,z)) = T(1 / x,K(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(269,a,7621,a(flip),b,588,a),flip(a)].">
      <j1 rule="hyper" parents="269 7621 588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7625">
    <literal><![CDATA[
      ((x \ 1) * (K(y,x) * z)) / ((x \ 1) * z) = K(y,x)
    ]]></literal>
    <justification jstring="[para(6161(a,1),7622(a,1,2,2))].">
      <j1 rule="para" parents="6161 7622"/>
    </justification>
  </clause>

  <clause id="7626">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = u
    ]]></literal>
    <justification jstring="[para(7623(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7623 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7627">
    <literal><![CDATA[
      L(T(K(x,y),z),z,K(x,u)) = K(T(1 / x,K(x,u) * z) \ 1,y)
    ]]></literal>
    <justification jstring="[para(7624(a,1),7311(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7624 7311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7628">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = K(y \ K(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6177,a(flip),b,7042,a),flip(a)].">
      <j1 rule="hyper" parents="373 6177 7042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7629">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ K(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(7042(a,2),6303(a,1))].">
      <j1 rule="para" parents="7042 6303"/>
    </justification>
  </clause>

  <clause id="7630">
    <literal><![CDATA[
      K((x \ y) \ K(x,z),u) = K(y \ T(x,z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),7628(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 7628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7631">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ K(y,z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4470(a,2),7630(a,1,1,1))].">
      <j1 rule="para" parents="4470 7630"/>
    </justification>
  </clause>

  <clause id="7632">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(7521(a,1),7045(a,2,2))].">
      <j1 rule="para" parents="7521 7045"/>
    </justification>
  </clause>

  <clause id="7633">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,354,a(flip),b,7632,a),flip(a)].">
      <j1 rule="hyper" parents="373 354 7632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7634">
    <literal><![CDATA[
      K(x,(K(y,z) * (y \ u)) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(6414(a,1),7087(a,1,2,1))].">
      <j1 rule="para" parents="6414 7087"/>
    </justification>
  </clause>

  <clause id="7635">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,u \ (R(x,y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(35,a,7144,a,b,7090,a)].">
      <j1 rule="hyper" parents="35 7144 7090"/>
    </justification>
  </clause>

  <clause id="7636">
    <literal><![CDATA[
      K(x,y / (K((z \ 1) \ u,z \ 1) \ u)) = K(x,y / ((z \ 1) * (u / (1 / z))))
    ]]></literal>
    <justification jstring="[para(6174(a,2),7106(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6174 7106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7637">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = y / (K(z \ (x \ 1),x) * y)
    ]]></literal>
    <justification jstring="[para(7195(a,1),7025(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7195 7025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7638">
    <literal><![CDATA[
      K(R(x,R(y,z,u),x),R(x,R(y,z,u),x) * y) * T(x * R(y,z,u),x) = R(y,z,u) * T(R(x,R(y,z,u),x),R(x,R(y,z,u),x) * y)
    ]]></literal>
    <justification jstring="[para(4741(a,1),7245(a,1,2))].">
      <j1 rule="para" parents="4741 7245"/>
    </justification>
  </clause>

  <clause id="7639">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = K((x \ (y * z)) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6568,a(flip),b,7269,a),flip(a)].">
      <j1 rule="hyper" parents="373 6568 7269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7640">
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = K((y / (z \ 1)) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(6827,a,7639,a),flip(a)].">
      <j1 rule="hyper" parents="6827 7639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7641">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K((x * y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(6827,a,7640,a),flip(a)].">
      <j1 rule="hyper" parents="6827 7640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7642">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,7380,a(flip),b,7641,a),flip(a)].">
      <j1 rule="hyper" parents="373 7380 7641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7643">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(7348,a,7642,a)].">
      <j1 rule="hyper" parents="7348 7642"/>
    </justification>
  </clause>

  <clause id="7644">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) = K((x \ y) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5268,a(flip),b,7643,a),flip(a)].">
      <j1 rule="hyper" parents="64 5268 7643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7645">
    <literal><![CDATA[
      (x * K((y \ z) \ x,z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(7644(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="7644 7200"/>
    </justification>
  </clause>

  <clause id="7646">
    <literal><![CDATA[
      (x \ y) \ (x \ ((z * z) * 1)) = (((z * z) / x) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,1231,a(flip),b,7275,a),flip(a)].">
      <j1 rule="hyper" parents="64 1231 7275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7647">
    <literal><![CDATA[
      (((x * x) / y) \ z) \ y = (y \ z) \ (y \ (x * x))
    ]]></literal>
    <justification jstring="[para(8(a,1),7646(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 7646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7648">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ y,z)) * (y \ 1) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6678,a,b,7278,a)].">
      <j1 rule="hyper" parents="64 6678 7278"/>
    </justification>
  </clause>

  <clause id="7649">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3871(a,1),7345(a,1,1))].">
      <j1 rule="para" parents="3871 7345"/>
    </justification>
  </clause>

  <clause id="7650">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,7204,a(flip),b,7649,a),flip(a)].">
      <j1 rule="hyper" parents="373 7204 7649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7651">
    <literal><![CDATA[
      (x \ ((y \ 1) \ x)) * x = (T(y,x) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(7650(a,1),4852(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7650 4852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7652">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ y = (y \ (x \ y)) * y
    ]]></literal>
    <justification jstring="[para(82(a,1),7651(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 7651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7653">
    <literal><![CDATA[
      x / ((x \ (y \ x)) * x) = T(1 / y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(226,a,7652,a)].">
      <j1 rule="hyper" parents="226 7652"/>
    </justification>
  </clause>

  <clause id="7654">
    <literal><![CDATA[
      T(1 / (x \ y),y) \ 1 = x \ T(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7364,a,b,7653,a),flip(a)].">
      <j1 rule="hyper" parents="64 7364 7653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7655">
    <literal><![CDATA[
      T(1 / (x / y),x) \ 1 = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(82(a,1),7653(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="82 7653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7656">
    <literal><![CDATA[
      (x \ T(y,y \ x)) \ 1 = T((x \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(7654(a,1),3569(a,1,1))].">
      <j1 rule="para" parents="7654 3569"/>
    </justification>
  </clause>

  <clause id="7657">
    <literal><![CDATA[
      (x / ((x \ y) * x)) \ 1 = T((x / y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(7655(a,1),3569(a,1,1))].">
      <j1 rule="para" parents="7655 3569"/>
    </justification>
  </clause>

  <clause id="7658">
    <literal><![CDATA[
      T((x \ (x / y)) \ 1,x / y) = (x \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(848(a,1),7656(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="848 7656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7659">
    <literal><![CDATA[
      (((x \ y) * x) \ x) \ 1 = T((y \ x) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6980(a,2),7656(a,1,1))].">
      <j1 rule="para" parents="6980 7656"/>
    </justification>
  </clause>

  <clause id="7660">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((y * x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),7659(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 7659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7661">
    <literal><![CDATA[
      L(x \ 1,x,y) \ K(x,y) = ((x * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(1569,a,7660,a)].">
      <j1 rule="hyper" parents="1569 7660"/>
    </justification>
  </clause>

  <clause id="7662">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = (y * x) * K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(6120(a,1),7353(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6120 7353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7663">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = T(x,y * x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5885,a(flip),b,7662,a),flip(a)].">
      <j1 rule="hyper" parents="373 5885 7662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7664">
    <literal><![CDATA[
      T(x,(x \ y) * x) * T(x \ y,x) = (y / R(x,x \ y,x)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),7663(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 7663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7665">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x \ z,u) \ T(z,u)) = T(z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,7362,a,b,xx)].">
      <j1 rule="hyper" parents="145 7362"/>
    </justification>
  </clause>

  <clause id="7666">
    <literal><![CDATA[
      K(L(x,y,z),R(z,u,w)) = K(x,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,6550,a(flip),b,7384,a),flip(a)].">
      <j1 rule="hyper" parents="373 6550 7384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7667">
    <literal><![CDATA[
      K((x \ 1) \ y,R(x,z,u)) = K(x * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(629(a,1),7666(a,1,1)),flip(a)].">
      <j1 rule="para" parents="629 7666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7668">
    <literal><![CDATA[
      K((x \ 1) * y,R(x \ 1,z,u)) = K(x \ y,R(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5252,a(flip),b,7667,a),flip(a)].">
      <j1 rule="hyper" parents="64 5252 7667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7669">
    <literal><![CDATA[
      K((x \ 1) \ y,z \ (x * y)) = K(x * y,(x \ z) \ y)
    ]]></literal>
    <justification jstring="[para(66(a,1),7569(a,2,1))].">
      <j1 rule="para" parents="66 7569"/>
    </justification>
  </clause>

  <clause id="7670">
    <literal><![CDATA[
      K((R(x,y,z) \ (R(x,y,z) * (x \ u))) \ u,w \ (R(x,y,z) * u)) = K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u)
    ]]></literal>
    <justification jstring="[para(1910(a,1),7569(a,2,1))].">
      <j1 rule="para" parents="1910 7569"/>
    </justification>
  </clause>

  <clause id="7671">
    <literal><![CDATA[
      (x * ((x \ y) * K(z \ (x \ y),u))) \ y != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * z) \ y) = w
    ]]></literal>
    <justification jstring="[para(7596(a,2),6899(a,1,1))].">
      <j1 rule="para" parents="7596 6899"/>
    </justification>
  </clause>

  <clause id="7672">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ (x \ 1)) = T(y / x,x \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),7603(a,1,2,1))].">
      <j1 rule="para" parents="79 7603"/>
    </justification>
  </clause>

  <clause id="7674">
    <literal><![CDATA[
      ((x \ 1) \ y) * ((x \ (x \ 1)) * z) = T(y / x,x \ 1) * z
    ]]></literal>
    <justification jstring="[para(7672(a,1),1610(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7672 1610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7675">
    <literal><![CDATA[
      K(x,y) \ T(K(x,y) * z,u) = K(y,x) * T(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(149,a,7614,a)].">
      <j1 rule="hyper" parents="149 7614"/>
    </justification>
  </clause>

  <clause id="7676">
    <literal><![CDATA[
      T(K(x,y) * z,x \ 1) = K(x,y) * T(z,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(269,a,7334,a,b,7620,a)].">
      <j1 rule="hyper" parents="269 7334 7620"/>
    </justification>
  </clause>

  <clause id="7677">
    <literal><![CDATA[
      T(K(x,y) * L(z,u,w),x \ 1) = K(x,y) * L(T(z,x \ 1),u,w)
    ]]></literal>
    <justification jstring="[para(25(a,2),7676(a,2,2))].">
      <j1 rule="para" parents="25 7676"/>
    </justification>
  </clause>

  <clause id="7678">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,6160,a(flip),b,7637,a),flip(a)].">
      <j1 rule="hyper" parents="373 6160 7637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7680">
    <literal><![CDATA[
      K(x,y / (x * (z * y))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,7289,a(flip),b,7678,a)].">
      <j1 rule="hyper" parents="64 7289 7678"/>
    </justification>
  </clause>

  <clause id="7681">
    <literal><![CDATA[
      K((x / y) \ z,R((x / y) \ 1,x / y,y)) = K(((x / y) \ 1) * z,T(y / x,x / y))
    ]]></literal>
    <justification jstring="[para(857(a,1),7668(a,1,2)),flip(a)].">
      <j1 rule="para" parents="857 7668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7682">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(144,a,7675,a(flip),b,5434,a)].">
      <j1 rule="hyper" parents="144 7675 5434"/>
    </justification>
  </clause>

  <clause id="7683">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y,x),u) = (K(x,y) * T(z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),7682(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 7682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7684">
    <literal><![CDATA[
      L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(6161(a,1),6265(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6161 6265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7685">
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) \ x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6671,a(flip),b,6669,a),flip(a)].">
      <j1 rule="hyper" parents="64 6671 6669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7687">
    <literal><![CDATA[
      (1 / x) * a(y,y,x) = 1 / L(x,y,y)
    ]]></literal>
    <justification jstring="[para(1243(a,1),7685(a,1,2))].">
      <j1 rule="para" parents="1243 7685"/>
    </justification>
  </clause>

  <clause id="7688">
    <literal><![CDATA[
      (1 / x) * ((L(x,y,z) \ 1) * x) = T(1 / L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(7685(a,1),1862(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7685 1862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7689">
    <literal><![CDATA[
      (x \ 1) \ T(1 / L(x,y,z),x) = (L(x,y,z) \ 1) * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,7688,a(flip),b,3899,a)].">
      <j1 rule="hyper" parents="139 7688 3899"/>
    </justification>
  </clause>

  <clause id="7690">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * z) = (K(x,y) / x) * z
    ]]></literal>
    <justification jstring="[para(4870(a,1),6939(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4870 6939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7691">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (K(x,y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(7626,a,7690,a)].">
      <j1 rule="hyper" parents="7626 7690"/>
    </justification>
  </clause>

  <clause id="7692">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * z)) = (1 / x) * (x * (y * z))
    ]]></literal>
    <justification jstring="[para(6023(a,1),7690(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6023 7690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7693">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y * z,x,x \ 1) = u
    ]]></literal>
    <justification jstring="[para(7692(a,2),1657(a,1))].">
      <j1 rule="para" parents="7692 1657"/>
    </justification>
  </clause>

  <clause id="7694">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(z,(x * (y \ z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(1385(a,1),7017(a,1,1,2))].">
      <j1 rule="para" parents="1385 7017"/>
    </justification>
  </clause>

  <clause id="7695">
    <literal><![CDATA[
      L(K(x,K(y,z \ 1) * (u \ w)),u \ w,u) = K(x,(K(z \ K(z,u),y) * u) \ w)
    ]]></literal>
    <justification jstring="[para(7286(a,2),7121(a,2,2,1))].">
      <j1 rule="para" parents="7286 7121"/>
    </justification>
  </clause>

  <clause id="7696">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7294,a,7320,a),flip(a)].">
      <j1 rule="hyper" parents="7294 7320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7697">
    <literal><![CDATA[
      K(L(x,y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(7562,a,7696,a)].">
      <j1 rule="hyper" parents="7562 7696"/>
    </justification>
  </clause>

  <clause id="7698">
    <literal><![CDATA[
      K(x,L(y,z,L(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7538,a(flip),b,7696,a)].">
      <j1 rule="hyper" parents="64 7538 7696"/>
    </justification>
  </clause>

  <clause id="7699">
    <literal><![CDATA[
      K(T(x \ (L(y,z,u) * w),L(y,z,u) \ x),y) = K((((L(y,z,u) \ x) \ w) \ w) \ w,y)
    ]]></literal>
    <justification jstring="[para(4723(a,1),7697(a,1,1))].">
      <j1 rule="para" parents="4723 7697"/>
    </justification>
  </clause>

  <clause id="7700">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,425,a(flip),b,7308,a),flip(a)].">
      <j1 rule="hyper" parents="373 425 7308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7702">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x \ L(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[para(1804(a,1),7700(a,1,2))].">
      <j1 rule="para" parents="1804 7700"/>
    </justification>
  </clause>

  <clause id="7703">
    <literal><![CDATA[
      T(L(x,y,z) \ 1,x \ L(x,u,w)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(57,a,7702,a)].">
      <j1 rule="hyper" parents="57 7702"/>
    </justification>
  </clause>

  <clause id="7704">
    <literal><![CDATA[
      T(x \ L(x,y,z),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(55,a,7703,a)].">
      <j1 rule="hyper" parents="55 7703"/>
    </justification>
  </clause>

  <clause id="7705">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ 1),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1807(a,2),7704(a,1,1))].">
      <j1 rule="para" parents="1807 7704"/>
    </justification>
  </clause>

  <clause id="7706">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = (x \ 1) / (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(225,a,7705,a(flip),b,4590,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 7705 4590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7707">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,4232,a(flip),b,7706,a),flip(a)].">
      <j1 rule="hyper" parents="373 4232 7706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7708">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,1810,a(flip),b,7707,a)].">
      <j1 rule="hyper" parents="64 1810 7707"/>
    </justification>
  </clause>

  <clause id="7709">
    <literal><![CDATA[
      x / (L(x,y,z) \ 1) = (1 / x) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,7708,a(flip),b,1230,a)].">
      <j1 rule="hyper" parents="225 7708 1230"/>
    </justification>
  </clause>

  <clause id="7710">
    <literal><![CDATA[
      ((T(x,y) \ 1) \ 1) * ((x \ 1) * z) = T(x,y) * ((1 / x) * z)
    ]]></literal>
    <justification jstring="[hyper(7363,a,5300,a)].">
      <j1 rule="hyper" parents="7363 5300"/>
    </justification>
  </clause>

  <clause id="7711">
    <literal><![CDATA[
      (x * (T(y,z) * u)) \ (x * (y * u)) = K(z,L(T(y,u),u,x))
    ]]></literal>
    <justification jstring="[para(265(a,1),7590(a,1,1,2))].">
      <j1 rule="para" parents="265 7590"/>
    </justification>
  </clause>

  <clause id="7712">
    <literal><![CDATA[
      (x * (T(y,z) * u)) \ (x * (y * u)) = K(z,T(L(y,u,x),u))
    ]]></literal>
    <justification jstring="[para(25(a,1),7711(a,2,2))].">
      <j1 rule="para" parents="25 7711"/>
    </justification>
  </clause>

  <clause id="7713">
    <literal><![CDATA[
      K((x * (y / z)) \ u,y) = K((x * (z \ y)) \ u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7528,a(flip),b,7598,a),flip(a)].">
      <j1 rule="hyper" parents="64 7528 7598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7714">
    <literal><![CDATA[
      K((x * (y / x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),7713(a,2,1,1))].">
      <j1 rule="para" parents="10 7713"/>
    </justification>
  </clause>

  <clause id="7715">
    <literal><![CDATA[
      L(T(K(x,y),z),z,K(x,u)) = T(K(x,y),K(x,u) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6565,a(flip),b,7627,a),flip(a)].">
      <j1 rule="hyper" parents="373 6565 7627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7716">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ z) * L(T(K(x,u),K(x,y) \ z),w,v5)) = z * L(T(K(x,u),K(x,y) * (K(x,y) \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(7715(a,1),963(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7715 963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7717">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = T(y,x) * T(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4688(a,1),7664(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4688 7664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7718">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = (y \ x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,4559,a(flip),b,7717,a),flip(a)].">
      <j1 rule="hyper" parents="373 4559 7717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7719">
    <literal><![CDATA[
      x / R(y,y \ x,y) = y \ (x * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,7128,a,b,7718,a),flip(a)].">
      <j1 rule="hyper" parents="36 7128 7718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7720">
    <literal><![CDATA[
      x / R(y,y \ x,y) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,5970,a,b,7719,a),flip(a)].">
      <j1 rule="hyper" parents="373 5970 7719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7721">
    <literal><![CDATA[
      x / R(y,y \ x,y) = K(y,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6411,a(flip),b,7719,a),flip(a)].">
      <j1 rule="hyper" parents="373 6411 7719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7722">
    <literal><![CDATA[
      x / ((y \ x) \ T(x,y)) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[para(4745(a,1),7720(a,1,2))].">
      <j1 rule="para" parents="4745 7720"/>
    </justification>
  </clause>

  <clause id="7723">
    <literal><![CDATA[
      K(x * x,y) * ((x * x) \ y) = y / (x * x)
    ]]></literal>
    <justification jstring="[para(655(a,1),7721(a,1,2)),flip(a)].">
      <j1 rule="para" parents="655 7721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7724">
    <literal><![CDATA[
      T(K(x,y) * (x \ y),x) = R(x,x \ y,x) \ y
    ]]></literal>
    <justification jstring="[para(7721(a,1),7407(a,1,1))].">
      <j1 rule="para" parents="7721 7407"/>
    </justification>
  </clause>

  <clause id="7725">
    <literal><![CDATA[
      ((x * K(y,x)) \ y) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(215,a,7722,a)].">
      <j1 rule="hyper" parents="215 7722"/>
    </justification>
  </clause>

  <clause id="7726">
    <literal><![CDATA[
      K(x * x,(x * x) \ y) = K(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,5720,a,b,7723,a)].">
      <j1 rule="hyper" parents="36 5720 7723"/>
    </justification>
  </clause>

  <clause id="7727">
    <literal><![CDATA[
      K(x * x,y * (x * x)) = K(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(5978,a,7726,a),flip(a)].">
      <j1 rule="hyper" parents="5978 7726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7728">
    <literal><![CDATA[
      K(x * x,(x * x) \ x) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,98,a(flip),b,7726,a),flip(a)].">
      <j1 rule="hyper" parents="373 98 7726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7729">
    <literal><![CDATA[
      K(x * x,x \ 1) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(6825,a,7728,a)].">
      <j1 rule="hyper" parents="6825 7728"/>
    </justification>
  </clause>

  <clause id="7731">
    <literal><![CDATA[
      (x \ (y * K(x,y))) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5970(a,1),7725(a,1,1))].">
      <j1 rule="para" parents="5970 7725"/>
    </justification>
  </clause>

  <clause id="7732">
    <literal><![CDATA[
      (x \ ((x * y) / x)) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5721(a,2),7731(a,1,1,2))].">
      <j1 rule="para" parents="5721 7731"/>
    </justification>
  </clause>

  <clause id="7733">
    <literal><![CDATA[
      K((x * (y / x)) \ (y * z),y) = K(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[para(7684(a,1),7373(a,1,1))].">
      <j1 rule="para" parents="7684 7373"/>
    </justification>
  </clause>

  <clause id="7734">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ (x * z)) = K(x,K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(7684(a,1),7394(a,1,2))].">
      <j1 rule="para" parents="7684 7394"/>
    </justification>
  </clause>

  <clause id="7735">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(K(z \ x,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7714,a(flip),b,7733,a)].">
      <j1 rule="hyper" parents="64 7714 7733"/>
    </justification>
  </clause>

  <clause id="7736">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6038,a,7735,a),flip(a)].">
      <j1 rule="hyper" parents="6038 7735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7738">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(7735(a,1),6038(a,1))].">
      <j1 rule="para" parents="7735 6038"/>
    </justification>
  </clause>

  <clause id="7740">
    <literal><![CDATA[
      (K(x \ y,x) * z) * K(z,y) = T(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,7736,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 7736 5726"/>
    </justification>
  </clause>

  <clause id="7741">
    <literal><![CDATA[
      K(K(x,y) * z,x * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x * y) = u
    ]]></literal>
    <justification jstring="[para(6115(a,1),7738(a,1,1,1))].">
      <j1 rule="para" parents="6115 7738"/>
    </justification>
  </clause>

  <clause id="7742">
    <literal><![CDATA[
      K((x \ y) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) * z,y) = u
    ]]></literal>
    <justification jstring="[para(6553(a,1),7738(a,1,1))].">
      <j1 rule="para" parents="6553 7738"/>
    </justification>
  </clause>

  <clause id="7743">
    <literal><![CDATA[
      T(K(x \ y,x) * z,y) = K(x \ y,x) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6940,a,7740,a),flip(a)].">
      <j1 rule="hyper" parents="6940 7740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7744">
    <literal><![CDATA[
      T(K(x \ (y * x),x) * z,y * x) = K(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(6115(a,1),7743(a,2,1))].">
      <j1 rule="para" parents="6115 7743"/>
    </justification>
  </clause>

  <clause id="7745">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = K(x,y) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(6115(a,1),7744(a,1,1,1))].">
      <j1 rule="para" parents="6115 7744"/>
    </justification>
  </clause>

  <clause id="7746">
    <literal><![CDATA[
      T(x * K(y,z),z * y) = T(x,z * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,7615,a(flip),b,7745,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 7615 7745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7747">
    <literal><![CDATA[
      (x * (y * z)) \ ((y * z) * T(x * K(z,y),y * z)) = L(K(z,y),T(x,y * z),y * z)
    ]]></literal>
    <justification jstring="[para(7746(a,2),261(a,1,2,2))].">
      <j1 rule="para" parents="7746 261"/>
    </justification>
  </clause>

  <clause id="7748">
    <literal><![CDATA[
      (L(x,y,z) \ x) * ((x \ L(x,y,z)) * u) = L(u,x \ L(x,y,z),L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(38,a,604,a,b,5680,a(flip))].">
      <j1 rule="hyper" parents="38 604 5680"/>
    </justification>
  </clause>

  <clause id="7749">
    <literal><![CDATA[
      (x * (L(x,y,z) \ 1)) * L(u,L(x,y,z),x) = (1 / L(x,y,z)) * (x * u)
    ]]></literal>
    <justification jstring="[para(1846(a,2),5696(a,1,1))].">
      <j1 rule="para" parents="1846 5696"/>
    </justification>
  </clause>

  <clause id="7750">
    <literal><![CDATA[
      (a(x,x,y) \ 1) \ ((1 / y) * (L(y,x,x) * z)) = L(z,y,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,5671,a,b,5697,a)].">
      <j1 rule="hyper" parents="35 5671 5697"/>
    </justification>
  </clause>

  <clause id="7751">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * T(y,z) = R(x,1 / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(5948,a,6322,a),flip(a)].">
      <j1 rule="hyper" parents="5948 6322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7752">
    <literal><![CDATA[
      R(x,1 / T(y,z),y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,7751,a(flip),b,6850,a)].">
      <j1 rule="hyper" parents="142 7751 6850"/>
    </justification>
  </clause>

  <clause id="7753">
    <literal><![CDATA[
      R(x,1 / T(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7751(a,1),2995(a,1))].">
      <j1 rule="para" parents="7751 2995"/>
    </justification>
  </clause>

  <clause id="7754">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[para(2979(a,1),7752(a,1,1))].">
      <j1 rule="para" parents="2979 7752"/>
    </justification>
  </clause>

  <clause id="7755">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(2979(a,1),7753(a,1))].">
      <j1 rule="para" parents="2979 7753"/>
    </justification>
  </clause>

  <clause id="7756">
    <literal><![CDATA[
      R(K(x,y),x * z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(6032,a,7356,a)].">
      <j1 rule="hyper" parents="6032 7356"/>
    </justification>
  </clause>

  <clause id="7757">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),7756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 7756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7758">
    <literal><![CDATA[
      K(R(x,K(x,y) * (x \ z),u),w) = R(K(x,w),K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(6133(a,1),7756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6133 7756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7759">
    <literal><![CDATA[
      K(R(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,671,a(flip),b,7757,a),flip(a)].">
      <j1 rule="hyper" parents="373 671 7757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7760">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) * (y * z) = (K(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,7757,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="144 7757 20"/>
    </justification>
  </clause>

  <clause id="7761">
    <literal><![CDATA[
      R(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7388,a(flip),b,7757,a),flip(a)].">
      <j1 rule="hyper" parents="64 7388 7757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7762">
    <literal><![CDATA[
      K((x * y) / ((z \ x) * y),u) = R(K(z,u),x,y)
    ]]></literal>
    <justification jstring="[para(108(a,1),7757(a,1,1))].">
      <j1 rule="para" parents="108 7757"/>
    </justification>
  </clause>

  <clause id="7763">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = (w * R(K(y,x),z,u)) \ w
    ]]></literal>
    <justification jstring="[para(7757(a,1),6882(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7757 6882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7764">
    <literal><![CDATA[
      (K(x,y) * z) * x = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(144,a,7761,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 7761 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7765">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * y = K(y,x) * ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(7761(a,1),4540(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7761 4540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7766">
    <literal><![CDATA[
      K(R(x,x \ 1,y),L(z,u,x \ 1)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,7398,a(flip),b,7759,a),flip(a)].">
      <j1 rule="hyper" parents="373 7398 7759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7767">
    <literal><![CDATA[
      L(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(606,a,7764,a)].">
      <j1 rule="hyper" parents="606 7764"/>
    </justification>
  </clause>

  <clause id="7768">
    <literal><![CDATA[
      (K(x,y) * z) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6022,a(flip),b,7764,a),flip(a)].">
      <j1 rule="hyper" parents="373 6022 7764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7769">
    <literal><![CDATA[
      T(K(x,y) * z,x) = K(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(269,a,7764,a,b,6403,a)].">
      <j1 rule="hyper" parents="269 7764 6403"/>
    </justification>
  </clause>

  <clause id="7770">
    <literal><![CDATA[
      T(K(x \ y,x) * z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(269,a,7764,a,b,6370,a)].">
      <j1 rule="hyper" parents="269 7764 6370"/>
    </justification>
  </clause>

  <clause id="7771">
    <literal><![CDATA[
      ((x * y) / x) \ (z * y) = T(K(y,x) * z,y)
    ]]></literal>
    <justification jstring="[hyper(269,a,7764,a,b,5809,a),flip(a)].">
      <j1 rule="hyper" parents="269 7764 5809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7772">
    <literal><![CDATA[
      L(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,6285,a,b,7764,a)].">
      <j1 rule="hyper" parents="35 6285 7764"/>
    </justification>
  </clause>

  <clause id="7773">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,x,K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(7764(a,1),472(a,1,1))].">
      <j1 rule="para" parents="7764 472"/>
    </justification>
  </clause>

  <clause id="7774">
    <literal><![CDATA[
      (K(x,y) * z) / x = K(x,y) * (z / x)
    ]]></literal>
    <justification jstring="[hyper(225,a,7767,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="225 7767 104"/>
    </justification>
  </clause>

  <clause id="7775">
    <literal><![CDATA[
      L(L(x,y,z),u,K(x,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(7767(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7767 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7776">
    <literal><![CDATA[
      (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w))
    ]]></literal>
    <justification jstring="[para(7767(a,1),514(a,1,2,1))].">
      <j1 rule="para" parents="7767 514"/>
    </justification>
  </clause>

  <clause id="7777">
    <literal><![CDATA[
      (K(x,y) * z) * y = K(x,y) * (z * y)
    ]]></literal>
    <justification jstring="[para(7767(a,1),6285(a,1,2))].">
      <j1 rule="para" parents="7767 6285"/>
    </justification>
  </clause>

  <clause id="7778">
    <literal><![CDATA[
      L(K(x,y),z,K(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7767(a,1),7376(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7767 7376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7779">
    <literal><![CDATA[
      L(L(x,y,z),u,K(w,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(7772(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7772 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7780">
    <literal><![CDATA[
      (K(x,y) * z) * T(y,u) = K(x,y) * (z * T(y,u))
    ]]></literal>
    <justification jstring="[para(7772(a,1),517(a,1,2,1))].">
      <j1 rule="para" parents="7772 517"/>
    </justification>
  </clause>

  <clause id="7781">
    <literal><![CDATA[
      L(K(x,y),z,K(u,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7772(a,1),7376(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7772 7376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7782">
    <literal><![CDATA[
      L(K(x,y),z,K(u,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7772(a,1),7537(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7772 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7783">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,u) = K(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,7778,a(flip),b,5318,a(flip))].">
      <j1 rule="hyper" parents="145 7778 5318"/>
    </justification>
  </clause>

  <clause id="7784">
    <literal><![CDATA[
      L(T(K(x,y),z),u,K(x,w)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7778(a,1),25(a,2,1))].">
      <j1 rule="para" parents="7778 25"/>
    </justification>
  </clause>

  <clause id="7785">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[para(7778(a,1),4724(a,1,1,1))].">
      <j1 rule="para" parents="7778 4724"/>
    </justification>
  </clause>

  <clause id="7786">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,u) = K(x,y) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[para(7778(a,1),6285(a,1,2))].">
      <j1 rule="para" parents="7778 6285"/>
    </justification>
  </clause>

  <clause id="7787">
    <literal><![CDATA[
      K(x,L(y,z,K(u,x))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7538,a(flip),b,7781,a)].">
      <j1 rule="hyper" parents="64 7538 7781"/>
    </justification>
  </clause>

  <clause id="7788">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(7562,a,7782,a)].">
      <j1 rule="hyper" parents="7562 7782"/>
    </justification>
  </clause>

  <clause id="7789">
    <literal><![CDATA[
      T(x,L(y,z,K(u,x))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,7787,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 7787 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7790">
    <literal><![CDATA[
      K(x,L(L(y,z,K(u,x)),w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(30(a,1),7787(a,1,2))].">
      <j1 rule="para" parents="30 7787"/>
    </justification>
  </clause>

  <clause id="7791">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u))
    ]]></literal>
    <justification jstring="[para(6190(a,1),7787(a,1,2))].">
      <j1 rule="para" parents="6190 7787"/>
    </justification>
  </clause>

  <clause id="7792">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ (K(y,x) * u),y)
    ]]></literal>
    <justification jstring="[para(6190(a,1),7788(a,1,1))].">
      <j1 rule="para" parents="6190 7788"/>
    </justification>
  </clause>

  <clause id="7793">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ (K(y,x) * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(102(a,1),7789(a,1,2))].">
      <j1 rule="para" parents="102 7789"/>
    </justification>
  </clause>

  <clause id="7794">
    <literal><![CDATA[
      (T(x,y) * (x \ z)) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(5778(a,2),7768(a,1,1))].">
      <j1 rule="para" parents="5778 7768"/>
    </justification>
  </clause>

  <clause id="7795">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ z,x) = (x \ z) * x
    ]]></literal>
    <justification jstring="[para(6075(a,1),7768(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6075 7768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7796">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,y) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,7614,a,b,7769,a(flip))].">
      <j1 rule="hyper" parents="35 7614 7769"/>
    </justification>
  </clause>

  <clause id="7797">
    <literal><![CDATA[
      T(x * K(y,z),z) = T(x,z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,7615,a(flip),b,7769,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 7615 7769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7798">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,x) = T(z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),7769(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 7769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7799">
    <literal><![CDATA[
      T(K(x,y) * L(z,u,w),x) = K(x,y) * L(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(25(a,2),7769(a,2,2))].">
      <j1 rule="para" parents="25 7769"/>
    </justification>
  </clause>

  <clause id="7802">
    <literal><![CDATA[
      K(x,y) * ((x * z) / x) = (T(x,y) * z) / x
    ]]></literal>
    <justification jstring="[para(5755(a,1),7774(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5755 7774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7803">
    <literal><![CDATA[
      T(K(x,y) * z,y) = T(y,x) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(269,a,7777,a,b,5810,a)].">
      <j1 rule="hyper" parents="269 7777 5810"/>
    </justification>
  </clause>

  <clause id="7804">
    <literal><![CDATA[
      K(x,y) * ((x * z) * y) = (T(x,y) * z) * y
    ]]></literal>
    <justification jstring="[para(5755(a,1),7777(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5755 7777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7805">
    <literal><![CDATA[
      (K(x,y) * T(z * K(y,z),u)) * y = K(x,y) * (y * T(z,u))
    ]]></literal>
    <justification jstring="[para(5860(a,1),7777(a,2,2))].">
      <j1 rule="para" parents="5860 7777"/>
    </justification>
  </clause>

  <clause id="7806">
    <literal><![CDATA[
      (K(x,y) \ z) * K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),7785(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 7785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7807">
    <literal><![CDATA[
      T(T(K(x,y) * z,u),K(x,y)) = T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(7785(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7785 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7808">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(6161(a,1),7785(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6161 7785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7809">
    <literal><![CDATA[
      (T(x,y) \ z) * K(x,y) = T(x \ z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6075(a,1),7785(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6075 7785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7810">
    <literal><![CDATA[
      T((x \ K(y,x)) \ z,K(x,y)) = ((x \ 1) \ z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6183(a,1),7785(a,1,1))].">
      <j1 rule="para" parents="6183 7785"/>
    </justification>
  </clause>

  <clause id="7811">
    <literal><![CDATA[
      T(K(x,y) * z,y) = K(x,y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),7796(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 7796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7812">
    <literal><![CDATA[
      T(x * K(y,z),y) = T(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(7796(a,1),7682(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7796 7682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7813">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = T(u / z,x) * z
    ]]></literal>
    <justification jstring="[para(7798(a,1),2920(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7798 2920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7814">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = (y * T(y \ u,x)) \ u
    ]]></literal>
    <justification jstring="[para(7798(a,1),6436(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7798 6436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7815">
    <literal><![CDATA[
      T(K(x,y \ z) * y,y \ z) = T(y \ z,x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),7803(a,2,2))].">
      <j1 rule="para" parents="10 7803"/>
    </justification>
  </clause>

  <clause id="7816">
    <literal><![CDATA[
      T(K(x,y) * (z / y),y) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[para(12(a,1),7803(a,2,2))].">
      <j1 rule="para" parents="12 7803"/>
    </justification>
  </clause>

  <clause id="7817">
    <literal><![CDATA[
      T(K(x,y) * (z * (1 / y)),y) = T(y,x) \ R(z,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2980(a,1),7803(a,2,2))].">
      <j1 rule="para" parents="2980 7803"/>
    </justification>
  </clause>

  <clause id="7818">
    <literal><![CDATA[
      T(x,K(y,z)) * K(z,y) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(6897,a,7808,a)].">
      <j1 rule="hyper" parents="6897 7808"/>
    </justification>
  </clause>

  <clause id="7819">
    <literal><![CDATA[
      K(x,y) * T(K(x * y,x),y) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(6353(a,1),7811(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6353 7811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7820">
    <literal><![CDATA[
      x \ (y * T(x,z)) = T(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(6861,a,7812,a)].">
      <j1 rule="hyper" parents="6861 7812"/>
    </justification>
  </clause>

  <clause id="7821">
    <literal><![CDATA[
      (T(x,y) / y) * T(y,z) = T(x * K(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6840,a,b,7812,a)].">
      <j1 rule="hyper" parents="373 6840 7812"/>
    </justification>
  </clause>

  <clause id="7822">
    <literal><![CDATA[
      T(x * K(x \ y,z),x \ y) = ((x \ y) \ y) * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,365,a(flip),b,7812,a),flip(a)].">
      <j1 rule="hyper" parents="373 365 7812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7823">
    <literal><![CDATA[
      T((x / y) * K(y,z),y) = (y \ x) * K(y,z)
    ]]></literal>
    <justification jstring="[para(117(a,1),7812(a,2,1))].">
      <j1 rule="para" parents="117 7812"/>
    </justification>
  </clause>

  <clause id="7824">
    <literal><![CDATA[
      x \ T(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7812(a,2),6087(a,1,2))].">
      <j1 rule="para" parents="7812 6087"/>
    </justification>
  </clause>

  <clause id="7825">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,7818,a,b,xx)].">
      <j1 rule="hyper" parents="269 7818"/>
    </justification>
  </clause>

  <clause id="7826">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z / K(x,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,10,a(flip),b,7818,a),flip(a)].">
      <j1 rule="hyper" parents="142 10 7818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7827">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,5722,a,b,7818,a)].">
      <j1 rule="hyper" parents="36 5722 7818"/>
    </justification>
  </clause>

  <clause id="7828">
    <literal><![CDATA[
      K(x,y) * K(z,y) = K(z,y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3318(a,1),7818(a,1,1))].">
      <j1 rule="para" parents="3318 7818"/>
    </justification>
  </clause>

  <clause id="7829">
    <literal><![CDATA[
      T((x * y) \ y,K(z,x)) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(41,a,2909,a,b,7825,a),flip(a)].">
      <j1 rule="hyper" parents="41 2909 7825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7830">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,5753,a(flip),b,7827,a),flip(a)].">
      <j1 rule="hyper" parents="35 5753 7827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7831">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(7827(a,1),5892(a,1,1))].">
      <j1 rule="para" parents="7827 5892"/>
    </justification>
  </clause>

  <clause id="7832">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(7827(a,1),5893(a,1,1))].">
      <j1 rule="para" parents="7827 5893"/>
    </justification>
  </clause>

  <clause id="7833">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,7830,a,b,6871,a),flip(a)].">
      <j1 rule="hyper" parents="140 7830 6871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7834">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,7830,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 7830 5726"/>
    </justification>
  </clause>

  <clause id="7835">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = T(K(z,y),x) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,7830,a(flip),b,5733,a)].">
      <j1 rule="hyper" parents="144 7830 5733"/>
    </justification>
  </clause>

  <clause id="7836">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7830(a,1),6101(a,1,1))].">
      <j1 rule="para" parents="7830 6101"/>
    </justification>
  </clause>

  <clause id="7837">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6881(a,1),7831(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6881 7831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7838">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(7785(a,1),7831(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7785 7831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7840">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(269,a,7820,a(flip),b,6074,a)].">
      <j1 rule="hyper" parents="269 7820 6074"/>
    </justification>
  </clause>

  <clause id="7841">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(481,a,7840,a)].">
      <j1 rule="hyper" parents="481 7840"/>
    </justification>
  </clause>

  <clause id="7842">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,7825,a,b,7840,a)].">
      <j1 rule="hyper" parents="41 7825 7840"/>
    </justification>
  </clause>

  <clause id="7843">
    <literal><![CDATA[
      T(x,K(y,z)) * y = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,7840,a(flip),b,119,a),flip(a)].">
      <j1 rule="hyper" parents="145 7840 119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7844">
    <literal><![CDATA[
      T(T(T(x,y),z),K(y,u)) = T(T(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(7840(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7840 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7845">
    <literal><![CDATA[
      T(T(x,y / z),K(y / z,z)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(117(a,1),7840(a,2,2))].">
      <j1 rule="para" parents="117 7840"/>
    </justification>
  </clause>

  <clause id="7846">
    <literal><![CDATA[
      T(x * K(y,x),T(y,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5785(a,1),7840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5785 7840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7847">
    <literal><![CDATA[
      T(T(x * K(y,x),z),T(y,u)) = T(T(x,z),K(y,u))
    ]]></literal>
    <justification jstring="[para(5857(a,1),7840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5857 7840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7848">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(7840(a,1),7831(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7840 7831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7849">
    <literal><![CDATA[
      K(x,y) * T(x,K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7442,a,b,7841,a)].">
      <j1 rule="hyper" parents="64 7442 7841"/>
    </justification>
  </clause>

  <clause id="7850">
    <literal><![CDATA[
      T(1 / x,T(y,x)) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(3343(a,1),7841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3343 7841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7851">
    <literal><![CDATA[
      T(x * K(y,z),T(z,y)) = T(K(y,z) * x,z)
    ]]></literal>
    <justification jstring="[para(6881(a,1),7841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6881 7841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7852">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,y)) = T(z * K(x,y),x)
    ]]></literal>
    <justification jstring="[para(7785(a,1),7841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7785 7841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7853">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7825(a,1),7841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7825 7841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7854">
    <literal><![CDATA[
      T(T(x,y) \ z,K(y,x)) = T(z / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(117(a,1),7842(a,1,1))].">
      <j1 rule="para" parents="117 7842"/>
    </justification>
  </clause>

  <clause id="7855">
    <literal><![CDATA[
      K(T(x,T(y,z)),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(7842(a,1),7435(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7842 7435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7856">
    <literal><![CDATA[
      K(x,T(y,T(z,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7842(a,1),7462(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7842 7462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7857">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7842(a,1),7831(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7842 7831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7858">
    <literal><![CDATA[
      T(x \ (y \ x),T(z,y)) = T(x \ (y \ x),z)
    ]]></literal>
    <justification jstring="[para(2910(a,1),7853(a,1,1))].">
      <j1 rule="para" parents="2910 7853"/>
    </justification>
  </clause>

  <clause id="7859">
    <literal><![CDATA[
      T(K(x,y),T(z,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3318(a,1),7853(a,1,1))].">
      <j1 rule="para" parents="3318 7853"/>
    </justification>
  </clause>

  <clause id="7860">
    <literal><![CDATA[
      T(x,T(x * y,y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(7519(a,1),7853(a,1,1))].">
      <j1 rule="para" parents="7519 7853"/>
    </justification>
  </clause>

  <clause id="7861">
    <literal><![CDATA[
      K(x,T(y,z / x)) = K(x,T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(117(a,1),7856(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 7856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7862">
    <literal><![CDATA[
      K(x,T(y,x / z)) = K(x,T(y,z \ x))
    ]]></literal>
    <justification jstring="[para(7429(a,1),7856(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7429 7856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7863">
    <literal><![CDATA[
      T(K(x,y \ z),T(y,z)) = T(K(x,y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7410,a(flip),b,7859,a)].">
      <j1 rule="hyper" parents="64 7410 7859"/>
    </justification>
  </clause>

  <clause id="7864">
    <literal><![CDATA[
      K(x,y) \ K(z,x) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(6206,a,7828,a)].">
      <j1 rule="hyper" parents="6206 7828"/>
    </justification>
  </clause>

  <clause id="7866">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,7433,a,b,7834,a),flip(a)].">
      <j1 rule="hyper" parents="373 7433 7834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7867">
    <literal><![CDATA[
      K(x,T(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7503,a(flip),b,7834,a)].">
      <j1 rule="hyper" parents="64 7503 7834"/>
    </justification>
  </clause>

  <clause id="7868">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7834(a,1),6188(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7834 6188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7869">
    <literal><![CDATA[
      K(T(x,y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,7433,a,b,7867,a)].">
      <j1 rule="hyper" parents="373 7433 7867"/>
    </justification>
  </clause>

  <clause id="7870">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[hyper(373,a,7091,a,b,7867,a)].">
      <j1 rule="hyper" parents="373 7091 7867"/>
    </justification>
  </clause>

  <clause id="7871">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,6762,a,b,7867,a)].">
      <j1 rule="hyper" parents="373 6762 7867"/>
    </justification>
  </clause>

  <clause id="7872">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,6563,a,b,7867,a)].">
      <j1 rule="hyper" parents="373 6563 7867"/>
    </justification>
  </clause>

  <clause id="7873">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,6158,a,b,7867,a)].">
      <j1 rule="hyper" parents="373 6158 7867"/>
    </justification>
  </clause>

  <clause id="7874">
    <literal><![CDATA[
      K(x / y,T(z,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6761,a(flip),b,7867,a),flip(a)].">
      <j1 rule="hyper" parents="373 6761 7867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7875">
    <literal><![CDATA[
      K(x * y,T(z,y * x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5473,a(flip),b,7867,a),flip(a)].">
      <j1 rule="hyper" parents="373 5473 7867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7876">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4107,a(flip),b,7867,a),flip(a)].">
      <j1 rule="hyper" parents="373 4107 7867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7877">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4105,a(flip),b,7867,a),flip(a)].">
      <j1 rule="hyper" parents="373 4105 7867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7878">
    <literal><![CDATA[
      x * K(y,T(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(145,a,7867,a,b,9,a)].">
      <j1 rule="hyper" parents="145 7867 9"/>
    </justification>
  </clause>

  <clause id="7879">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,7867,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="145 7867 22"/>
    </justification>
  </clause>

  <clause id="7880">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7440,a,b,7867,a)].">
      <j1 rule="hyper" parents="64 7440 7867"/>
    </justification>
  </clause>

  <clause id="7882">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7406,a,b,7867,a)].">
      <j1 rule="hyper" parents="64 7406 7867"/>
    </justification>
  </clause>

  <clause id="7883">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7446,a(flip),b,7867,a),flip(a)].">
      <j1 rule="hyper" parents="64 7446 7867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7884">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7423,a(flip),b,7867,a),flip(a)].">
      <j1 rule="hyper" parents="64 7423 7867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7885">
    <literal><![CDATA[
      T(K(x,y),y * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7421,a(flip),b,7867,a),flip(a)].">
      <j1 rule="hyper" parents="64 7421 7867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7886">
    <literal><![CDATA[
      T(K(x * y,x),y) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6129,a(flip),b,7867,a),flip(a)].">
      <j1 rule="hyper" parents="64 6129 7867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7887">
    <literal><![CDATA[
      1 / T(K(x,y),z) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(225,a,7867,a(flip),b,7440,a)].">
      <j1 rule="hyper" parents="225 7867 7440"/>
    </justification>
  </clause>

  <clause id="7888">
    <literal><![CDATA[
      x * T(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,7867,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 7867 5726"/>
    </justification>
  </clause>

  <clause id="7889">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(7867(a,2),328(a,1,2))].">
      <j1 rule="para" parents="7867 328"/>
    </justification>
  </clause>

  <clause id="7891">
    <literal><![CDATA[
      x * L(K(y,T(z,x)),u,w) = L(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(7867(a,2),266(a,1,2,1))].">
      <j1 rule="para" parents="7867 266"/>
    </justification>
  </clause>

  <clause id="7893">
    <literal><![CDATA[
      x * (y * K(z,T(u,y))) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(7867(a,2),737(a,1,2,2))].">
      <j1 rule="para" parents="7867 737"/>
    </justification>
  </clause>

  <clause id="7894">
    <literal><![CDATA[
      x * (y * K(z,T(u,x * y))) = L(K(z,u),y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(7867(a,2),793(a,1,2,2))].">
      <j1 rule="para" parents="7867 793"/>
    </justification>
  </clause>

  <clause id="7895">
    <literal><![CDATA[
      L(K(x,T(y,z \ u)),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      u \ (z * (K(x,y) * (z \ u))) = w
    ]]></literal>
    <justification jstring="[para(7867(a,2),991(a,1,1))].">
      <j1 rule="para" parents="7867 991"/>
    </justification>
  </clause>

  <clause id="7896">
    <literal><![CDATA[
      K(x,R(T(K(x,y),z),u,w)) = 1
    ]]></literal>
    <justification jstring="[para(7867(a,1),4108(a,1,2,1))].">
      <j1 rule="para" parents="7867 4108"/>
    </justification>
  </clause>

  <clause id="7897">
    <literal><![CDATA[
      K(x / y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(7867(a,2),6833(a,1))].">
      <j1 rule="para" parents="7867 6833"/>
    </justification>
  </clause>

  <clause id="7898">
    <literal><![CDATA[
      x \ (y * K(z,T(x,u))) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7867(a,2),7182(a,1,2,2))].">
      <j1 rule="para" parents="7867 7182"/>
    </justification>
  </clause>

  <clause id="7899">
    <literal><![CDATA[
      K(x,T(y,z)) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7867(a,2),7440(a,1,1))].">
      <j1 rule="para" parents="7867 7440"/>
    </justification>
  </clause>

  <clause id="7900">
    <literal><![CDATA[
      T(K(x,y) * K(z,u),u) = K(x,T(y,u)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(7867(a,2),7797(a,2,1))].">
      <j1 rule="para" parents="7867 7797"/>
    </justification>
  </clause>

  <clause id="7901">
    <literal><![CDATA[
      K(T(T(x,y),z),u) = K(x,T(T(u,z),y))
    ]]></literal>
    <justification jstring="[hyper(373,a,7869,a(flip),b,7869,a),flip(a)].">
      <j1 rule="hyper" parents="373 7869 7869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7902">
    <literal><![CDATA[
      K(T(x,y),y / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,7423,a(flip),b,7869,a),flip(a)].">
      <j1 rule="hyper" parents="373 7423 7869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7903">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,z),x) = z
    ]]></literal>
    <justification jstring="[hyper(145,a,7869,a,b,7459,a)].">
      <j1 rule="hyper" parents="145 7869 7459"/>
    </justification>
  </clause>

  <clause id="7904">
    <literal><![CDATA[
      x * K(T(y,z),u) = x * K(y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,7869,a,b,9,a)].">
      <j1 rule="hyper" parents="145 7869 9"/>
    </justification>
  </clause>

  <clause id="7905">
    <literal><![CDATA[
      x * K(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,7869,a,b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 7869 5726"/>
    </justification>
  </clause>

  <clause id="7906">
    <literal><![CDATA[
      K(T(x,x \ y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7392,a,b,7869,a)].">
      <j1 rule="hyper" parents="64 7392 7869"/>
    </justification>
  </clause>

  <clause id="7907">
    <literal><![CDATA[
      K(T(x,x * y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7464,a,7869,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7464 7869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7908">
    <literal><![CDATA[
      x / K(y,T(z,u)) = x * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(225,a,7869,a(flip),b,6882,a)].">
      <j1 rule="hyper" parents="225 7869 6882"/>
    </justification>
  </clause>

  <clause id="7909">
    <literal><![CDATA[
      x / K(y,T(x,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(225,a,7869,a(flip),b,5731,a(flip))].">
      <j1 rule="hyper" parents="225 7869 5731"/>
    </justification>
  </clause>

  <clause id="7910">
    <literal><![CDATA[
      (x / y) * K(z,T(y,u)) = x / T(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,7869,a(flip),b,6308,a)].">
      <j1 rule="hyper" parents="145 7869 6308"/>
    </justification>
  </clause>

  <clause id="7911">
    <literal><![CDATA[
      T(x,x * T(y,z)) * K(y,T(x,z)) = L(x,T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(145,a,7869,a(flip),b,6341,a(flip))].">
      <j1 rule="hyper" parents="145 7869 6341"/>
    </justification>
  </clause>

  <clause id="7912">
    <literal><![CDATA[
      T(x,y) * K(x,T(z,y)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,7869,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 7869 5726"/>
    </justification>
  </clause>

  <clause id="7913">
    <literal><![CDATA[
      (T(x,y) * z) / T(x,y) = z * K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,7869,a(flip),b,5719,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 7869 5719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7914">
    <literal><![CDATA[
      K(x,T(y,z)) \ u = K(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,7869,a(flip),b,6162,a),flip(a)].">
      <j1 rule="hyper" parents="144 7869 6162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7915">
    <literal><![CDATA[
      K(T(x,y),T(z,u)) = K(x,T(T(z,y),u))
    ]]></literal>
    <justification jstring="[para(23(a,1),7869(a,2,2))].">
      <j1 rule="para" parents="23 7869"/>
    </justification>
  </clause>

  <clause id="7916">
    <literal><![CDATA[
      K(L(T(x,y),z,u),w) = K(L(x,z,u),T(w,y))
    ]]></literal>
    <justification jstring="[para(25(a,2),7869(a,1,1))].">
      <j1 rule="para" parents="25 7869"/>
    </justification>
  </clause>

  <clause id="7917">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(117(a,1),7869(a,1,1)),flip(a)].">
      <j1 rule="para" parents="117 7869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7918">
    <literal><![CDATA[
      K(T(x,y),z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(117(a,1),7869(a,2,2))].">
      <j1 rule="para" parents="117 7869"/>
    </justification>
  </clause>

  <clause id="7919">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(255(a,1),7869(a,1,1)),flip(a)].">
      <j1 rule="para" parents="255 7869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7920">
    <literal><![CDATA[
      K(L(x,y,z),T(u,x)) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(201(a,1),7869(a,1,1)),flip(a)].">
      <j1 rule="para" parents="201 7869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7921">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),T(w,y * R(x,z,u))) = K(T(x,y),w)
    ]]></literal>
    <justification jstring="[para(2831(a,1),7869(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2831 7869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7922">
    <literal><![CDATA[
      K(T(x,y),K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4068(a,1),7869(a,2,2))].">
      <j1 rule="para" parents="4068 7869"/>
    </justification>
  </clause>

  <clause id="7923">
    <literal><![CDATA[
      (x * y) / (K(z,T(x,u)) * y) = T(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(7869(a,1),6159(a,1,2,1))].">
      <j1 rule="para" parents="7869 6159"/>
    </justification>
  </clause>

  <clause id="7924">
    <literal><![CDATA[
      K(x,T(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7869(a,1),6198(a,1,1))].">
      <j1 rule="para" parents="7869 6198"/>
    </justification>
  </clause>

  <clause id="7925">
    <literal><![CDATA[
      K(x,T(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(7869(a,1),6206(a,1,1))].">
      <j1 rule="para" parents="7869 6206"/>
    </justification>
  </clause>

  <clause id="7926">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,z) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(7869(a,1),5841(a,1,1))].">
      <j1 rule="para" parents="7869 5841"/>
    </justification>
  </clause>

  <clause id="7927">
    <literal><![CDATA[
      R(x,y \ 1,K(z,T(y,u))) = x
    ]]></literal>
    <justification jstring="[para(7869(a,1),6477(a,1,3))].">
      <j1 rule="para" parents="7869 6477"/>
    </justification>
  </clause>

  <clause id="7928">
    <literal><![CDATA[
      K(x,T(y,z)) \ (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7869(a,1),6213(a,1,1))].">
      <j1 rule="para" parents="7869 6213"/>
    </justification>
  </clause>

  <clause id="7929">
    <literal><![CDATA[
      x * K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w * K(z,T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(7869(a,1),6897(a,1,2))].">
      <j1 rule="para" parents="7869 6897"/>
    </justification>
  </clause>

  <clause id="7930">
    <literal><![CDATA[
      x / K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(7869(a,1),6898(a,1,2))].">
      <j1 rule="para" parents="7869 6898"/>
    </justification>
  </clause>

  <clause id="7931">
    <literal><![CDATA[
      T(x / T(y,T(z,u)),y) = (y \ x) * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(7869(a,1),7184(a,2,2))].">
      <j1 rule="para" parents="7869 7184"/>
    </justification>
  </clause>

  <clause id="7932">
    <literal><![CDATA[
      T(x,x * y) * (L(x,y,x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(7907(a,1),6372(a,2,1))].">
      <j1 rule="para" parents="7907 6372"/>
    </justification>
  </clause>

  <clause id="7933">
    <literal><![CDATA[
      K(x,y / R(x,z,u)) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(117(a,1),7876(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 7876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7934">
    <literal><![CDATA[
      R(x,(y * K(z,y)) \ 1,K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(5785(a,1),7927(a,1,3,2))].">
      <j1 rule="para" parents="5785 7927"/>
    </justification>
  </clause>

  <clause id="7935">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(366(a,2),7871(a,1,1)),flip(a)].">
      <j1 rule="para" parents="366 7871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7936">
    <literal><![CDATA[
      K(x,K(y,x / z)) * K(x / z,y) = K(z \ x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7504,a,b,7874,a)].">
      <j1 rule="hyper" parents="64 7504 7874"/>
    </justification>
  </clause>

  <clause id="7937">
    <literal><![CDATA[
      K(x / y,z \ x) = K(y \ x,x / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7423,a(flip),b,7874,a)].">
      <j1 rule="hyper" parents="64 7423 7874"/>
    </justification>
  </clause>

  <clause id="7938">
    <literal><![CDATA[
      K(x / y,x \ z) = K(y \ x,z / x)
    ]]></literal>
    <justification jstring="[para(117(a,1),7874(a,1,2))].">
      <j1 rule="para" parents="117 7874"/>
    </justification>
  </clause>

  <clause id="7944">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * T(y / z,T(u,y)) = w
    ]]></literal>
    <justification jstring="[para(7874(a,1),6940(a,1,2))].">
      <j1 rule="para" parents="7874 6940"/>
    </justification>
  </clause>

  <clause id="7946">
    <literal><![CDATA[
      L(x / y,z,K(y \ x,u)) = x / y
    ]]></literal>
    <justification jstring="[para(7874(a,1),7767(a,1,3))].">
      <j1 rule="para" parents="7874 7767"/>
    </justification>
  </clause>

  <clause id="7947">
    <literal><![CDATA[
      (x * y) / T(T(x,y),z) = K(z,x) * y
    ]]></literal>
    <justification jstring="[hyper(6501,a,7879,a)].">
      <j1 rule="hyper" parents="6501 7879"/>
    </justification>
  </clause>

  <clause id="7948">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,x \ y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,6157,a(flip),b,7879,a),flip(a)].">
      <j1 rule="hyper" parents="373 6157 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7949">
    <literal><![CDATA[
      (x * y) * K(x,T(z,x * y)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,5755,a(flip),b,7879,a),flip(a)].">
      <j1 rule="hyper" parents="373 5755 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7950">
    <literal><![CDATA[
      x * (y * K(x,T(z,y))) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,7879,a,b,6071,a)].">
      <j1 rule="hyper" parents="145 7879 6071"/>
    </justification>
  </clause>

  <clause id="7951">
    <literal><![CDATA[
      x \ (y * K(z,T(x,y))) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,7879,a,b,5810,a)].">
      <j1 rule="hyper" parents="139 7879 5810"/>
    </justification>
  </clause>

  <clause id="7952">
    <literal><![CDATA[
      (K(x,y) * z) / T(y,z) = z / T(T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(142,a,7879,a(flip),b,6311,a)].">
      <j1 rule="hyper" parents="142 7879 6311"/>
    </justification>
  </clause>

  <clause id="7953">
    <literal><![CDATA[
      x * K(y,T(T(z,x),u)) = K(y,T(z,u)) * x
    ]]></literal>
    <justification jstring="[para(23(a,1),7879(a,1,2,2))].">
      <j1 rule="para" parents="23 7879"/>
    </justification>
  </clause>

  <clause id="7954">
    <literal><![CDATA[
      x * K(y,L(T(z,x),u,w)) = K(y,L(z,u,w)) * x
    ]]></literal>
    <justification jstring="[para(25(a,2),7879(a,1,2,2))].">
      <j1 rule="para" parents="25 7879"/>
    </justification>
  </clause>

  <clause id="7955">
    <literal><![CDATA[
      K(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7879(a,1),44(a,1))].">
      <j1 rule="para" parents="7879 44"/>
    </justification>
  </clause>

  <clause id="7956">
    <literal><![CDATA[
      K(x,y / z) * z = z * K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(117(a,1),7879(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7957">
    <literal><![CDATA[
      K(x \ y,z) * K(u,y / x) = K(u,y / x) * K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(4081(a,1),7879(a,1,2,2))].">
      <j1 rule="para" parents="4081 7879"/>
    </justification>
  </clause>

  <clause id="7958">
    <literal><![CDATA[
      T(x,y) * K(z,T(x * y,x)) = K(z,x * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4468(a,1),7879(a,1,2,2))].">
      <j1 rule="para" parents="4468 7879"/>
    </justification>
  </clause>

  <clause id="7959">
    <literal><![CDATA[
      K(x,K(x \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7879(a,1),7223(a,1,2))].">
      <j1 rule="para" parents="7879 7223"/>
    </justification>
  </clause>

  <clause id="7960">
    <literal><![CDATA[
      (x * y) * K(z,T(x,y)) = K(z,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(7421(a,1),7879(a,1,2))].">
      <j1 rule="para" parents="7421 7879"/>
    </justification>
  </clause>

  <clause id="7961">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ x) = K(z,y) * x
    ]]></literal>
    <justification jstring="[para(7459(a,2),7879(a,1,2))].">
      <j1 rule="para" parents="7459 7879"/>
    </justification>
  </clause>

  <clause id="7962">
    <literal><![CDATA[
      x * K(y,K(z,T(u,x))) = K(y,K(z,u)) * x
    ]]></literal>
    <justification jstring="[para(7867(a,2),7879(a,1,2,2))].">
      <j1 rule="para" parents="7867 7879"/>
    </justification>
  </clause>

  <clause id="7963">
    <literal><![CDATA[
      R(x,T(K(y,z),u),T(K(y,z),u) \ 1) = (x * T(K(y,z),u)) * T(K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(145,a,7880,a(flip),b,482,a),flip(a)].">
      <j1 rule="hyper" parents="145 7880 482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7964">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7882(a,1),7420(a,1))].">
      <j1 rule="para" parents="7882 7420"/>
    </justification>
  </clause>

  <clause id="7965">
    <literal><![CDATA[
      T(K(x,y),z * y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,7867,a(flip),b,7883,a),flip(a)].">
      <j1 rule="hyper" parents="373 7867 7883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7966">
    <literal><![CDATA[
      T(x,y) != K(z,u \ y)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(7884(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="7884 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7968">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6566,a,b,7887,a)].">
      <j1 rule="hyper" parents="64 6566 7887"/>
    </justification>
  </clause>

  <clause id="7970">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7899(a,1),6101(a,1))].">
      <j1 rule="para" parents="7899 6101"/>
    </justification>
  </clause>

  <clause id="7971">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(237(a,1),7902(a,1,1))].">
      <j1 rule="para" parents="237 7902"/>
    </justification>
  </clause>

  <clause id="7972">
    <literal><![CDATA[
      T(x / y,K(z,x \ y)) = x / y
    ]]></literal>
    <justification jstring="[para(7902(a,1),6380(a,1,2))].">
      <j1 rule="para" parents="7902 6380"/>
    </justification>
  </clause>

  <clause id="7975">
    <literal><![CDATA[
      (x / y) * K(y \ x,z) = T(x / y,T(z,y))
    ]]></literal>
    <justification jstring="[para(117(a,1),7905(a,1,2,1))].">
      <j1 rule="para" parents="117 7905"/>
    </justification>
  </clause>

  <clause id="7976">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7869,a(flip),b,7906,a)].">
      <j1 rule="hyper" parents="64 7869 7906"/>
    </justification>
  </clause>

  <clause id="7978">
    <literal><![CDATA[
      K(x \ (y \ x),z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,6583,a(flip),b,7917,a),flip(a)].">
      <j1 rule="hyper" parents="64 6583 7917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7979">
    <literal><![CDATA[
      K(x \ y,z) * ((y / x) * u) = T(y / x,T(z,x)) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,7917,a(flip),b,5733,a)].">
      <j1 rule="hyper" parents="144 7917 5733"/>
    </justification>
  </clause>

  <clause id="7980">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) = T(y / x,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(144,a,7917,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 7917 5739"/>
    </justification>
  </clause>

  <clause id="7981">
    <literal><![CDATA[
      K(x / y,y \ z) = K(y \ x,z / y)
    ]]></literal>
    <justification jstring="[para(117(a,1),7917(a,1,2))].">
      <j1 rule="para" parents="117 7917"/>
    </justification>
  </clause>

  <clause id="7982">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7917(a,1),5816(a,1,1))].">
      <j1 rule="para" parents="7917 5816"/>
    </justification>
  </clause>

  <clause id="7983">
    <literal><![CDATA[
      (x / y) * (K(y \ x,z) * u) = T(x / y,T(z,y)) * u
    ]]></literal>
    <justification jstring="[para(7917(a,1),5776(a,1,2,1))].">
      <j1 rule="para" parents="7917 5776"/>
    </justification>
  </clause>

  <clause id="7985">
    <literal><![CDATA[
      T(x * K(y / z,x),z) = K(z \ y,x) * T(x,z)
    ]]></literal>
    <justification jstring="[para(7917(a,1),6238(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7917 6238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7986">
    <literal><![CDATA[
      K(T(x,y),z \ 1) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(6510,a,7918,a)].">
      <j1 rule="hyper" parents="6510 7918"/>
    </justification>
  </clause>

  <clause id="7987">
    <literal><![CDATA[
      (x / (y / z)) * K(u,z \ y) = x / T(y / z,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,7918,a(flip),b,6308,a)].">
      <j1 rule="hyper" parents="145 7918 6308"/>
    </justification>
  </clause>

  <clause id="7989">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(T(x,z),u,w) \ y)
    ]]></literal>
    <justification jstring="[para(237(a,1),7918(a,1,1))].">
      <j1 rule="para" parents="237 7918"/>
    </justification>
  </clause>

  <clause id="7990">
    <literal><![CDATA[
      K(x,y \ z) * ((z / y) \ u) = T(z / y,T(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(7918(a,1),6157(a,1,1))].">
      <j1 rule="para" parents="7918 6157"/>
    </justification>
  </clause>

  <clause id="7991">
    <literal><![CDATA[
      (x / (y / z)) * K(u,z \ y) != w
    ]]></literal>
    <literal><![CDATA[
      x / T(y / z,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(7918(a,1),6309(a,1,2))].">
      <j1 rule="para" parents="7918 6309"/>
    </justification>
  </clause>

  <clause id="7992">
    <literal><![CDATA[
      K(x / y,z) \ y = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(7918(a,1),7436(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7918 7436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7993">
    <literal><![CDATA[
      K(x,y) * (z * x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(144,a,7919,a(flip),b,6358,a)].">
      <j1 rule="hyper" parents="144 7919 6358"/>
    </justification>
  </clause>

  <clause id="7994">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(7919(a,1),4504(a,1,3))].">
      <j1 rule="para" parents="7919 4504"/>
    </justification>
  </clause>

  <clause id="7995">
    <literal><![CDATA[
      R(x,T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(7919(a,1),6474(a,1,3))].">
      <j1 rule="para" parents="7919 6474"/>
    </justification>
  </clause>

  <clause id="7996">
    <literal><![CDATA[
      a(x,T(y,z),K(u,y)) = 1
    ]]></literal>
    <justification jstring="[para(7919(a,1),6476(a,1,3))].">
      <j1 rule="para" parents="7919 6476"/>
    </justification>
  </clause>

  <clause id="7997">
    <literal><![CDATA[
      R(x,K(y,z),L(T(z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(7919(a,1),7124(a,1,2))].">
      <j1 rule="para" parents="7919 7124"/>
    </justification>
  </clause>

  <clause id="7998">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,u) = x / (T(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6912,a,7995,a),flip(a)].">
      <j1 rule="hyper" parents="6912 7995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7999">
    <literal><![CDATA[
      (x * T(y,z)) * K(u,y) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(144,a,7995,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 7995 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8000">
    <literal><![CDATA[
      (1 / T(x,y)) \ K(z,x) = T(x,y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(7995(a,1),452(a,1,1))].">
      <j1 rule="para" parents="7995 452"/>
    </justification>
  </clause>

  <clause id="8001">
    <literal><![CDATA[
      L(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,7996,a)].">
      <j1 rule="hyper" parents="53 7996"/>
    </justification>
  </clause>

  <clause id="8002">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6354,a,b,8001,a)].">
      <j1 rule="hyper" parents="64 6354 8001"/>
    </justification>
  </clause>

  <clause id="8003">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7869,a(flip),b,7935,a),flip(a)].">
      <j1 rule="hyper" parents="373 7869 7935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8004">
    <literal><![CDATA[
      K(x,T(y,x \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6157(a,1),7959(a,1,2))].">
      <j1 rule="para" parents="6157 7959"/>
    </justification>
  </clause>

  <clause id="8005">
    <literal><![CDATA[
      T(x / y,T(x \ y,z)) = T(x / y,x \ y)
    ]]></literal>
    <justification jstring="[para(7972(a,1),7853(a,1,1))].">
      <j1 rule="para" parents="7972 7853"/>
    </justification>
  </clause>

  <clause id="8006">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,7867,a(flip),b,7976,a),flip(a)].">
      <j1 rule="hyper" parents="373 7867 7976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8007">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,7976,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 7976 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8008">
    <literal><![CDATA[
      K(x,R(T(y,x \ z),u,w)) = K(x,T(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[para(27(a,2),7976(a,1,2))].">
      <j1 rule="para" parents="27 7976"/>
    </justification>
  </clause>

  <clause id="8009">
    <literal><![CDATA[
      R(K(x,T(y,z)),x * u,w) = K(R(x,u,w),T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(7976(a,1),7756(a,1,1))].">
      <j1 rule="para" parents="7976 7756"/>
    </justification>
  </clause>

  <clause id="8010">
    <literal><![CDATA[
      x \ (((y \ x) * y) * L(T(y,z),u,w)) = K(y \ x,y) * L(T(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(7997(a,1),690(a,1,1))].">
      <j1 rule="para" parents="7997 690"/>
    </justification>
  </clause>

  <clause id="8011">
    <literal><![CDATA[
      (x * y) * K(x,T(z,y)) = K(x,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(8003(a,1),7879(a,1,2))].">
      <j1 rule="para" parents="8003 7879"/>
    </justification>
  </clause>

  <clause id="8012">
    <literal><![CDATA[
      T(x,T(y,x \ y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(114(a,1),8007(a,2,2))].">
      <j1 rule="para" parents="114 8007"/>
    </justification>
  </clause>

  <clause id="8013">
    <literal><![CDATA[
      T(x / y,T(z,y)) = T(x / y,T(z,x))
    ]]></literal>
    <justification jstring="[para(82(a,1),8007(a,1,2,2))].">
      <j1 rule="para" parents="82 8007"/>
    </justification>
  </clause>

  <clause id="8014">
    <literal><![CDATA[
      T(x,T(y,y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4461(a,2),8012(a,1,2))].">
      <j1 rule="para" parents="4461 8012"/>
    </justification>
  </clause>

  <clause id="8015">
    <literal><![CDATA[
      T(K(x,y) * z,T(z,K(y,x))) = T(K(x,y) * z,z)
    ]]></literal>
    <justification jstring="[para(6160(a,1),8014(a,1,2,2))].">
      <j1 rule="para" parents="6160 8014"/>
    </justification>
  </clause>

  <clause id="8016">
    <literal><![CDATA[
      R(x,y \ K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(6095(a,1),7934(a,1,2))].">
      <j1 rule="para" parents="6095 7934"/>
    </justification>
  </clause>

  <clause id="8017">
    <literal><![CDATA[
      (K(x \ y,z) * u) * (y / x) = K(x \ y,z) * (u * (y / x))
    ]]></literal>
    <justification jstring="[hyper(145,a,7946,a(flip),b,5318,a(flip))].">
      <j1 rule="hyper" parents="145 7946 5318"/>
    </justification>
  </clause>

  <clause id="8018">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6563(a,2),7964(a,1))].">
      <j1 rule="para" parents="6563 7964"/>
    </justification>
  </clause>

  <clause id="8019">
    <literal><![CDATA[
      K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7433(a,2),7964(a,1))].">
      <j1 rule="para" parents="7433 7964"/>
    </justification>
  </clause>

  <clause id="8020">
    <literal><![CDATA[
      T(K(x,y),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7965(a,2),7964(a,1))].">
      <j1 rule="para" parents="7965 7964"/>
    </justification>
  </clause>

  <clause id="8021">
    <literal><![CDATA[
      K(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8006(a,2),7964(a,1))].">
      <j1 rule="para" parents="8006 7964"/>
    </justification>
  </clause>

  <clause id="8022">
    <literal><![CDATA[
      T(K(x,y),z * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6785(a,2),8019(a,1))].">
      <j1 rule="para" parents="6785 8019"/>
    </justification>
  </clause>

  <clause id="8023">
    <literal><![CDATA[
      K(x,T(y,x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7935(a,2),8019(a,1))].">
      <j1 rule="para" parents="7935 8019"/>
    </justification>
  </clause>

  <clause id="8024">
    <literal><![CDATA[
      T(x * y,K(y,z)) / y = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(142,a,6998,a,b,7843,a)].">
      <j1 rule="hyper" parents="142 6998 7843"/>
    </justification>
  </clause>

  <clause id="8027">
    <literal><![CDATA[
      T(x,y) * K(x,K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6491,a,7849,a)].">
      <j1 rule="hyper" parents="6491 7849"/>
    </justification>
  </clause>

  <clause id="8028">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6408,a,7849,a)].">
      <j1 rule="hyper" parents="6408 7849"/>
    </justification>
  </clause>

  <clause id="8029">
    <literal><![CDATA[
      T(x,y) \ T(x,T(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,7849,a(flip),b,6036,a(flip))].">
      <j1 rule="hyper" parents="139 7849 6036"/>
    </justification>
  </clause>

  <clause id="8030">
    <literal><![CDATA[
      K(x,T(y,z / x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7976,a(flip),b,7861,a),flip(a)].">
      <j1 rule="hyper" parents="373 7976 7861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8031">
    <literal><![CDATA[
      K(x,T(y,z * x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),8030(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 8030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8032">
    <literal><![CDATA[
      K(a(x,y,z),T(u,(x * y) * z)) = K(a(x,y,z),T(u,x * (y * z)))
    ]]></literal>
    <justification jstring="[para(212(a,1),8030(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="212 8030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8033">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ x))
    ]]></literal>
    <justification jstring="[para(4814(a,1),8030(a,1,2))].">
      <j1 rule="para" parents="4814 8030"/>
    </justification>
  </clause>

  <clause id="8034">
    <literal><![CDATA[
      (x / y) * K(y,T(z,x)) = K(y,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(8030(a,1),7879(a,1,2))].">
      <j1 rule="para" parents="8030 7879"/>
    </justification>
  </clause>

  <clause id="8036">
    <literal><![CDATA[
      (x / y) * K(x,T(z,y \ x)) = K(x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(7862(a,1),7879(a,1,2))].">
      <j1 rule="para" parents="7862 7879"/>
    </justification>
  </clause>

  <clause id="8037">
    <literal><![CDATA[
      x \ K(y,z) != K(y,z) * K(u,z)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(7864(a,1),49(a,1)),flip(a)].">
      <j1 rule="para" parents="7864 49"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8038">
    <literal><![CDATA[
      K(x,K(K(x,y),z)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,7922,a(flip),b,7866,a),flip(a)].">
      <j1 rule="hyper" parents="138 7922 7866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8039">
    <literal><![CDATA[
      K(x \ K(y,x),z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5949,a(flip),b,7872,a)].">
      <j1 rule="hyper" parents="64 5949 7872"/>
    </justification>
  </clause>

  <clause id="8040">
    <literal><![CDATA[
      K(x \ 1,T(y,L(x,z,u))) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(198(a,1),7872(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="198 7872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8041">
    <literal><![CDATA[
      K(x,y) * T(x,T(z,y)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(6460,a,7912,a)].">
      <j1 rule="hyper" parents="6460 7912"/>
    </justification>
  </clause>

  <clause id="8042">
    <literal><![CDATA[
      K(x,y) \ T(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,7912,a(flip),b,6036,a)].">
      <j1 rule="hyper" parents="139 7912 6036"/>
    </justification>
  </clause>

  <clause id="8043">
    <literal><![CDATA[
      K(x,y) * K(x,T(z,y)) = x \ T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(139,a,7912,a(flip),b,5776,a),flip(a)].">
      <j1 rule="hyper" parents="139 7912 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8044">
    <literal><![CDATA[
      T(x,y) / T(x * K(z,x),y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(225,a,6238,a(flip),b,7914,a)].">
      <j1 rule="hyper" parents="225 6238 7914"/>
    </justification>
  </clause>

  <clause id="8045">
    <literal><![CDATA[
      K(x,y) * T(T(y,z),x) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7926(a,1),6458(a,1,2))].">
      <j1 rule="para" parents="7926 6458"/>
    </justification>
  </clause>

  <clause id="8047">
    <literal><![CDATA[
      (x * y) * K(x,T(z,y)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,7135,a,b,7950,a)].">
      <j1 rule="hyper" parents="64 7135 7950"/>
    </justification>
  </clause>

  <clause id="8048">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,7950,a(flip),b,7135,a)].">
      <j1 rule="hyper" parents="139 7950 7135"/>
    </justification>
  </clause>

  <clause id="8049">
    <literal><![CDATA[
      T(x / y,z) \ x = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(6500,a,7956,a)].">
      <j1 rule="hyper" parents="6500 7956"/>
    </justification>
  </clause>

  <clause id="8050">
    <literal><![CDATA[
      x / (y * K(z,y \ x)) = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,7956,a(flip),b,6229,a)].">
      <j1 rule="hyper" parents="225 7956 6229"/>
    </justification>
  </clause>

  <clause id="8051">
    <literal><![CDATA[
      x \ (T(y / x,z) \ y) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,6229,a,b,7956,a(flip))].">
      <j1 rule="hyper" parents="139 6229 7956"/>
    </justification>
  </clause>

  <clause id="8052">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = K(z,(x * (1 / y)) \ x) * T(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(6987(a,1),7956(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6987 7956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8053">
    <literal><![CDATA[
      K(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      (K(y,x) * z) \ z = u
    ]]></literal>
    <justification jstring="[para(7961(a,1),44(a,1))].">
      <j1 rule="para" parents="7961 44"/>
    </justification>
  </clause>

  <clause id="8054">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(7008,a,7968,a)].">
      <j1 rule="hyper" parents="7008 7968"/>
    </justification>
  </clause>

  <clause id="8055">
    <literal><![CDATA[
      K(R(x,y,(x * y) \ z) \ 1,T(u,z)) = K(z \ (y * ((x * y) \ z)),u)
    ]]></literal>
    <justification jstring="[para(420(a,1),7978(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="420 7978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8056">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(8019,a,7986,a)].">
      <j1 rule="hyper" parents="8019 7986"/>
    </justification>
  </clause>

  <clause id="8057">
    <literal><![CDATA[
      K(T(x,L(y,z,u)),y \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(1808(a,1),7986(a,2,2))].">
      <j1 rule="para" parents="1808 7986"/>
    </justification>
  </clause>

  <clause id="8058">
    <literal><![CDATA[
      K(x,y \ (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ 1,y)) = u
    ]]></literal>
    <justification jstring="[para(7986(a,1),8019(a,1))].">
      <j1 rule="para" parents="7986 8019"/>
    </justification>
  </clause>

  <clause id="8059">
    <literal><![CDATA[
      L((x * y) \ z,x * y,K(y,u)) = (x * T(y,T(u,x))) \ (K(y,u) * z)
    ]]></literal>
    <justification jstring="[para(7993(a,1),102(a,2,1))].">
      <j1 rule="para" parents="7993 102"/>
    </justification>
  </clause>

  <clause id="8060">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * T(y,x \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(8004(a,1),7081(a,1,1))].">
      <j1 rule="para" parents="8004 7081"/>
    </justification>
  </clause>

  <clause id="8061">
    <literal><![CDATA[
      T(x / L(y,z,u),T(y,x)) = T(x / L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(198(a,1),8013(a,1,2)),flip(a)].">
      <j1 rule="para" parents="198 8013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8062">
    <literal><![CDATA[
      T(x * y,K(x,z)) = x * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,8024,a(flip),b,5434,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 8024 5434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8063">
    <literal><![CDATA[
      T(x \ y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8024(a,1),5457(a,1))].">
      <j1 rule="para" parents="8024 5457"/>
    </justification>
  </clause>

  <clause id="8064">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6461,a,8029,a)].">
      <j1 rule="hyper" parents="6461 8029"/>
    </justification>
  </clause>

  <clause id="8065">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6423,a,8029,a)].">
      <j1 rule="hyper" parents="6423 8029"/>
    </justification>
  </clause>

  <clause id="8066">
    <literal><![CDATA[
      (x \ K(y,x)) * K(x \ 1,T(z,y)) = T(x \ K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,8039,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 8039 5726"/>
    </justification>
  </clause>

  <clause id="8067">
    <literal><![CDATA[
      T(x,y) * T(x,T(z,y)) = x * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,8041,a(flip),b,6071,a),flip(a)].">
      <j1 rule="hyper" parents="145 8041 6071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8068">
    <literal><![CDATA[
      K(x,y) * T(x,K(z,T(u,y))) = T(T(x,y),K(z,u))
    ]]></literal>
    <justification jstring="[para(7867(a,2),8041(a,1,2,2))].">
      <j1 rule="para" parents="7867 8041"/>
    </justification>
  </clause>

  <clause id="8069">
    <literal><![CDATA[
      T(K(x,y) * T(y,z),x) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,7769,a,b,8045,a)].">
      <j1 rule="hyper" parents="64 7769 8045"/>
    </justification>
  </clause>

  <clause id="8070">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8047(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8047 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8071">
    <literal><![CDATA[
      x / T(y \ x,z) = T(x / y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,6246,a,b,8049,a)].">
      <j1 rule="hyper" parents="373 6246 8049"/>
    </justification>
  </clause>

  <clause id="8072">
    <literal><![CDATA[
      x / T(y,T(y \ x,z)) = T(x / y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(225,a,7905,a(flip),b,8049,a)].">
      <j1 rule="hyper" parents="225 7905 8049"/>
    </justification>
  </clause>

  <clause id="8073">
    <literal><![CDATA[
      T((x * y) / x,z) \ (x * y) = x * K(z,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),8049(a,2,2,2))].">
      <j1 rule="para" parents="9 8049"/>
    </justification>
  </clause>

  <clause id="8074">
    <literal><![CDATA[
      (T(x / y,z) \ x) \ x = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(8049(a,2),6247(a,1,1))].">
      <j1 rule="para" parents="8049 6247"/>
    </justification>
  </clause>

  <clause id="8075">
    <literal><![CDATA[
      (x * y) / (x * K(z,y)) = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8050(a,1,2,2,2))].">
      <j1 rule="para" parents="9 8050"/>
    </justification>
  </clause>

  <clause id="8076">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),(x * K(y,x \ z)) \ z) = T(T(x * K(y,x \ z),u),T(z / x,y))
    ]]></literal>
    <justification jstring="[para(8050(a,1),4727(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8050 4727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8077">
    <literal><![CDATA[
      x / ((x * y) * K(z,y \ 1)) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(6705(a,1),8050(a,1,2,2))].">
      <j1 rule="para" parents="6705 8050"/>
    </justification>
  </clause>

  <clause id="8078">
    <literal><![CDATA[
      x / (T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x)) = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(6987(a,1),8050(a,2,1))].">
      <j1 rule="para" parents="6987 8050"/>
    </justification>
  </clause>

  <clause id="8079">
    <literal><![CDATA[
      (x * y) \ (T(R(z * K(x,z),x,y),u) \ ((x * z) * y)) = K(u,(x * y) \ ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(5897(a,2),8051(a,1,2,1,1))].">
      <j1 rule="para" parents="5897 8051"/>
    </justification>
  </clause>

  <clause id="8080">
    <literal><![CDATA[
      K(x,((1 / y) * z) \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6056,a,b,8054,a)].">
      <j1 rule="hyper" parents="64 6056 8054"/>
    </justification>
  </clause>

  <clause id="8081">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,7499,a,b,8056,a),flip(a)].">
      <j1 rule="hyper" parents="373 7499 8056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8082">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,7448,a,b,8056,a),flip(a)].">
      <j1 rule="hyper" parents="373 7448 8056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8083">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(143,a,8056,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 8056 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8084">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,y)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(82(a,1),8056(a,2,2,2))].">
      <j1 rule="para" parents="82 8056"/>
    </justification>
  </clause>

  <clause id="8085">
    <literal><![CDATA[
      T(x * R(y,z,u),K(x,w)) = x * R(T(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(27(a,2),8062(a,2,2))].">
      <j1 rule="para" parents="27 8062"/>
    </justification>
  </clause>

  <clause id="8086">
    <literal><![CDATA[
      T(x * T(y,K(x,z)),x) = T(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(8062(a,1),7841(a,1,1))].">
      <j1 rule="para" parents="8062 7841"/>
    </justification>
  </clause>

  <clause id="8087">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6187,a,8064,a)].">
      <j1 rule="hyper" parents="6187 8064"/>
    </justification>
  </clause>

  <clause id="8088">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,7461,a(flip),b,8064,a)].">
      <j1 rule="hyper" parents="64 7461 8064"/>
    </justification>
  </clause>

  <clause id="8089">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8064(a,1),6188(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8064 6188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8092">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7830,a,b,8088,a)].">
      <j1 rule="hyper" parents="373 7830 8088"/>
    </justification>
  </clause>

  <clause id="8093">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,8088,a,b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 8088 5726"/>
    </justification>
  </clause>

  <clause id="8094">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(144,a,8088,a,b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 8088 5739"/>
    </justification>
  </clause>

  <clause id="8095">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(8088(a,1),5804(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8088 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8096">
    <literal><![CDATA[
      a(x,y,K(z,K(u,y))) = 1
    ]]></literal>
    <justification jstring="[para(8088(a,1),6933(a,1,3))].">
      <j1 rule="para" parents="8088 6933"/>
    </justification>
  </clause>

  <clause id="8097">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8088(a,1),7834(a,1,2))].">
      <j1 rule="para" parents="8088 7834"/>
    </justification>
  </clause>

  <clause id="8098">
    <literal><![CDATA[
      K(x,K(y,z)) * T(z,y) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(8088(a,1),8028(a,1,1))].">
      <j1 rule="para" parents="8088 8028"/>
    </justification>
  </clause>

  <clause id="8099">
    <literal><![CDATA[
      K(K(R(x \ 1,y,z) \ 1,u),w) = R(K(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6682,a(flip),b,8092,a),flip(a)].">
      <j1 rule="hyper" parents="373 6682 8092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8100">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,K(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(145,a,8092,a(flip),b,6908,a)].">
      <j1 rule="hyper" parents="145 8092 6908"/>
    </justification>
  </clause>

  <clause id="8102">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(144,a,8092,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 8092 5739"/>
    </justification>
  </clause>

  <clause id="8103">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8092(a,1),5767(a,1,2))].">
      <j1 rule="para" parents="8092 5767"/>
    </justification>
  </clause>

  <clause id="8104">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) \ u = w
    ]]></literal>
    <justification jstring="[para(8092(a,1),6301(a,1,1))].">
      <j1 rule="para" parents="8092 6301"/>
    </justification>
  </clause>

  <clause id="8105">
    <literal><![CDATA[
      T(x * T(K(y,z),u),K(u,K(y,z))) = K(y,K(z,u)) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(8092(a,1),6321(a,2,1))].">
      <j1 rule="para" parents="8092 6321"/>
    </justification>
  </clause>

  <clause id="8106">
    <literal><![CDATA[
      (K(x,y) / z) * K(x,K(y,1 / z)) = T(K(x,y),1 / z) / z
    ]]></literal>
    <justification jstring="[para(8092(a,1),7366(a,1,2))].">
      <j1 rule="para" parents="8092 7366"/>
    </justification>
  </clause>

  <clause id="8107">
    <literal><![CDATA[
      K(x,K(y,z)) * K(K(x,z),y) = 1
    ]]></literal>
    <justification jstring="[para(8092(a,2),7833(a,1,2))].">
      <j1 rule="para" parents="8092 7833"/>
    </justification>
  </clause>

  <clause id="8108">
    <literal><![CDATA[
      K(x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6097,a,8107,a)].">
      <j1 rule="hyper" parents="6097 8107"/>
    </justification>
  </clause>

  <clause id="8109">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8092,a,b,8108,a)].">
      <j1 rule="hyper" parents="373 8092 8108"/>
    </justification>
  </clause>

  <clause id="8110">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8088,a,b,8108,a),flip(a)].">
      <j1 rule="hyper" parents="373 8088 8108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8111">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8064,a,b,8108,a)].">
      <j1 rule="hyper" parents="373 8064 8108"/>
    </justification>
  </clause>

  <clause id="8112">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,7830,a,b,8108,a)].">
      <j1 rule="hyper" parents="373 7830 8108"/>
    </justification>
  </clause>

  <clause id="8113">
    <literal><![CDATA[
      x * K(y,K(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,8108,a,b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 8108 5726"/>
    </justification>
  </clause>

  <clause id="8114">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) = T(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,8108,a,b,5733,a)].">
      <j1 rule="hyper" parents="144 8108 5733"/>
    </justification>
  </clause>

  <clause id="8115">
    <literal><![CDATA[
      K(x,K(y,z)) * y = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(144,a,8108,a,b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 8108 5739"/>
    </justification>
  </clause>

  <clause id="8116">
    <literal><![CDATA[
      x * K(y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8108(a,1),5767(a,1,2))].">
      <j1 rule="para" parents="8108 5767"/>
    </justification>
  </clause>

  <clause id="8117">
    <literal><![CDATA[
      x * (K(y,K(x,z)) * u) = T(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8108(a,1),5776(a,1,2,1))].">
      <j1 rule="para" parents="8108 5776"/>
    </justification>
  </clause>

  <clause id="8118">
    <literal><![CDATA[
      (x * K(y,z)) \ K(y,K(x * K(y,z),z)) = (L(K(y,z),x,K(y,z)) * x) \ 1
    ]]></literal>
    <justification jstring="[para(8108(a,1),6257(a,1,2))].">
      <j1 rule="para" parents="8108 6257"/>
    </justification>
  </clause>

  <clause id="8119">
    <literal><![CDATA[
      T(x / y,K(z,u)) * ((y \ x) \ 1) = K(z,K(x / y,u)) * K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(8108(a,1),6409(a,2,1))].">
      <j1 rule="para" parents="8108 6409"/>
    </justification>
  </clause>

  <clause id="8120">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8108(a,1),7834(a,1,2))].">
      <j1 rule="para" parents="8108 7834"/>
    </justification>
  </clause>

  <clause id="8121">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8108(a,1),8093(a,1,2))].">
      <j1 rule="para" parents="8108 8093"/>
    </justification>
  </clause>

  <clause id="8122">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8108(a,1),8094(a,1,1))].">
      <j1 rule="para" parents="8108 8094"/>
    </justification>
  </clause>

  <clause id="8123">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8088,a,b,8109,a),flip(a)].">
      <j1 rule="hyper" parents="373 8088 8109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8124">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(y,x)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,8109,a(flip),b,5786,a(flip))].">
      <j1 rule="hyper" parents="144 8109 5786"/>
    </justification>
  </clause>

  <clause id="8125">
    <literal><![CDATA[
      K(x,K(R(y \ 1,z,u) \ 1,w)) = K(R(K(y,x),z,u),w)
    ]]></literal>
    <justification jstring="[para(6682(a,1),8109(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6682 8109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8126">
    <literal><![CDATA[
      K(x,K(y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8108,a,b,8110,a)].">
      <j1 rule="hyper" parents="373 8108 8110"/>
    </justification>
  </clause>

  <clause id="8127">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * u) = T(z,K(x,y)) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,8110,a,b,5733,a)].">
      <j1 rule="hyper" parents="144 8110 5733"/>
    </justification>
  </clause>

  <clause id="8128">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) * (u / z) = T(u,K(x,y)) / z
    ]]></literal>
    <justification jstring="[hyper(144,a,8110,a,b,7290,a(flip))].">
      <j1 rule="hyper" parents="144 8110 7290"/>
    </justification>
  </clause>

  <clause id="8129">
    <literal><![CDATA[
      K(x,K(y,z)) * y = T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(144,a,8110,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 8110 5739"/>
    </justification>
  </clause>

  <clause id="8130">
    <literal><![CDATA[
      x * (K(y,K(z,x)) * u) = T(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8110(a,2),5776(a,1,2,1))].">
      <j1 rule="para" parents="8110 5776"/>
    </justification>
  </clause>

  <clause id="8131">
    <literal><![CDATA[
      (x * K(y,K(z,u))) / K(y,z) = x / T(K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8110(a,2),6312(a,1,1,2))].">
      <j1 rule="para" parents="8110 6312"/>
    </justification>
  </clause>

  <clause id="8132">
    <literal><![CDATA[
      x * T(x \ y,K(z,u)) = y * K(z,K(u,x \ y))
    ]]></literal>
    <justification jstring="[para(8110(a,2),6763(a,2,2))].">
      <j1 rule="para" parents="8110 6763"/>
    </justification>
  </clause>

  <clause id="8133">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,(x \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(8110(a,2),6811(a,2,2))].">
      <j1 rule="para" parents="8110 6811"/>
    </justification>
  </clause>

  <clause id="8134">
    <literal><![CDATA[
      x * (y * K(z,K(u,(x \ 1) \ y))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8110(a,2),6816(a,1,2,2))].">
      <j1 rule="para" parents="8110 6816"/>
    </justification>
  </clause>

  <clause id="8136">
    <literal><![CDATA[
      K(x,y) * K(y,K(x,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8110(a,2),7503(a,1,2))].">
      <j1 rule="para" parents="8110 7503"/>
    </justification>
  </clause>

  <clause id="8137">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(8110(a,2),7504(a,1,1))].">
      <j1 rule="para" parents="8110 7504"/>
    </justification>
  </clause>

  <clause id="8138">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(7869(a,1),8110(a,1,2))].">
      <j1 rule="para" parents="7869 8110"/>
    </justification>
  </clause>

  <clause id="8139">
    <literal><![CDATA[
      x * K(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(8110(a,1),8093(a,1,2))].">
      <j1 rule="para" parents="8110 8093"/>
    </justification>
  </clause>

  <clause id="8140">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,8123,a,b,6871,a),flip(a)].">
      <j1 rule="hyper" parents="140 8123 6871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8141">
    <literal><![CDATA[
      x / K(y,K(z,u)) = x * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(225,a,8123,a(flip),b,6882,a)].">
      <j1 rule="hyper" parents="225 8123 6882"/>
    </justification>
  </clause>

  <clause id="8142">
    <literal><![CDATA[
      (x / y) * K(y,K(z,u)) = x / T(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,8123,a(flip),b,6308,a)].">
      <j1 rule="hyper" parents="145 8123 6308"/>
    </justification>
  </clause>

  <clause id="8143">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,8123,a(flip),b,6162,a),flip(a)].">
      <j1 rule="hyper" parents="144 8123 6162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8145">
    <literal><![CDATA[
      T(x,K(y,z)) \ 1 = x \ K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,8123,a(flip),b,5789,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 8123 5789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8146">
    <literal><![CDATA[
      K(x,K(y,z)) \ (x * u) = T(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8123(a,1),6131(a,1,1))].">
      <j1 rule="para" parents="8123 6131"/>
    </justification>
  </clause>

  <clause id="8147">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(8123(a,1),6157(a,1,1))].">
      <j1 rule="para" parents="8123 6157"/>
    </justification>
  </clause>

  <clause id="8148">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * w = u
    ]]></literal>
    <justification jstring="[para(8123(a,1),6187(a,1,1))].">
      <j1 rule="para" parents="8123 6187"/>
    </justification>
  </clause>

  <clause id="8149">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(8123(a,1),6206(a,1,1))].">
      <j1 rule="para" parents="8123 6206"/>
    </justification>
  </clause>

  <clause id="8150">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(8123(a,1),6301(a,1,1))].">
      <j1 rule="para" parents="8123 6301"/>
    </justification>
  </clause>

  <clause id="8151">
    <literal><![CDATA[
      K(x,K(y,T(z,x))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,7475,a,b,8126,a)].">
      <j1 rule="hyper" parents="373 7475 8126"/>
    </justification>
  </clause>

  <clause id="8152">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T(x \ L(x,y,z),K(u,w)) = K(x \ L(x,y,z),K(w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,5931,a,b,8126,a)].">
      <j1 rule="hyper" parents="373 5931 8126"/>
    </justification>
  </clause>

  <clause id="8153">
    <literal><![CDATA[
      T(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(143,a,8126,a,b,6406,a)].">
      <j1 rule="hyper" parents="143 8126 6406"/>
    </justification>
  </clause>

  <clause id="8154">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) = K(x,(T(u,y) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(7290(a,1),8126(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7290 8126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8155">
    <literal><![CDATA[
      K(x,K(y,L(z,z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(7372(a,1),8126(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7372 8126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8156">
    <literal><![CDATA[
      K(x,y) * K(z,K(x,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8126(a,1),7503(a,1,2))].">
      <j1 rule="para" parents="8126 7503"/>
    </justification>
  </clause>

  <clause id="8157">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(7832,a,8153,a),flip(a)].">
      <j1 rule="hyper" parents="7832 8153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8158">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6202,a,8153,a)].">
      <j1 rule="hyper" parents="6202 8153"/>
    </justification>
  </clause>

  <clause id="8159">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(T(x,u),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(481,a,8153,a)].">
      <j1 rule="hyper" parents="481 8153"/>
    </justification>
  </clause>

  <clause id="8160">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,7808,a,b,8153,a)].">
      <j1 rule="hyper" parents="373 7808 8153"/>
    </justification>
  </clause>

  <clause id="8161">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,7842,a(flip),b,8153,a),flip(a)].">
      <j1 rule="hyper" parents="373 7842 8153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8162">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7840,a(flip),b,8153,a),flip(a)].">
      <j1 rule="hyper" parents="373 7840 8153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8163">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,7785,a(flip),b,8153,a),flip(a)].">
      <j1 rule="hyper" parents="373 7785 8153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8164">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,6881,a(flip),b,8153,a),flip(a)].">
      <j1 rule="hyper" parents="373 6881 8153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8165">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6321,a(flip),b,8153,a),flip(a)].">
      <j1 rule="hyper" parents="373 6321 8153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8166">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,8153,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="145 8153 22"/>
    </justification>
  </clause>

  <clause id="8167">
    <literal><![CDATA[
      T(x * y,K(y,z)) = T(x,K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,8153,a,b,8024,a),flip(a)].">
      <j1 rule="hyper" parents="144 8153 8024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8168">
    <literal><![CDATA[
      x \ T(x * (y / x),K(z,u)) = T(y,K(u,z)) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,8153,a,b,5426,a),flip(a)].">
      <j1 rule="hyper" parents="142 8153 5426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8169">
    <literal><![CDATA[
      K(x,y) \ T(z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,8153,a,b,6175,a)].">
      <j1 rule="hyper" parents="139 8153 6175"/>
    </justification>
  </clause>

  <clause id="8170">
    <literal><![CDATA[
      T(T(x,y),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(x,K(u,z)),y) = w
    ]]></literal>
    <justification jstring="[para(8153(a,1),481(a,1))].">
      <j1 rule="para" parents="8153 481"/>
    </justification>
  </clause>

  <clause id="8171">
    <literal><![CDATA[
      K(x,y) * (T(z,K(y,x)) * u) = ((z * K(x,y)) / z) * (z * u)
    ]]></literal>
    <justification jstring="[para(8153(a,1),5022(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8153 5022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8172">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(8153(a,1),7818(a,1,1))].">
      <j1 rule="para" parents="8153 7818"/>
    </justification>
  </clause>

  <clause id="8173">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(8153(a,1),7832(a,1,1))].">
      <j1 rule="para" parents="8153 7832"/>
    </justification>
  </clause>

  <clause id="8174">
    <literal><![CDATA[
      T(T(x,K(y,z)),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(8153(a,1),7841(a,1,1))].">
      <j1 rule="para" parents="8153 7841"/>
    </justification>
  </clause>

  <clause id="8175">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(8153(a,1),7853(a,1,1))].">
      <j1 rule="para" parents="8153 7853"/>
    </justification>
  </clause>

  <clause id="8176">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (K(x,y) * u) = T(R(z,K(x,y),u),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(1054,a,8157,a)].">
      <j1 rule="hyper" parents="1054 8157"/>
    </justification>
  </clause>

  <clause id="8177">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(916,a,8157,a),flip(a)].">
      <j1 rule="hyper" parents="916 8157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8178">
    <literal><![CDATA[
      T(T(T(x,K(y,z)),u),K(y,z)) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,120,a(flip),b,8157,a)].">
      <j1 rule="hyper" parents="64 120 8157"/>
    </justification>
  </clause>

  <clause id="8179">
    <literal><![CDATA[
      T(x * (y * K(x,z)),K(x,z)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(41,a,7188,a,b,8157,a),flip(a)].">
      <j1 rule="hyper" parents="41 7188 8157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8180">
    <literal><![CDATA[
      (x * K(y,z)) / x = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(225,a,8157,a(flip),b,4796,a)].">
      <j1 rule="hyper" parents="225 8157 4796"/>
    </justification>
  </clause>

  <clause id="8181">
    <literal><![CDATA[
      T(K(x,y),z) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,8157,a(flip),b,4796,a)].">
      <j1 rule="hyper" parents="145 8157 4796"/>
    </justification>
  </clause>

  <clause id="8182">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(8157(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="8157 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8183">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8157(a,1),331(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="8157 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8184">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8157(a,1),7831(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8157 7831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8185">
    <literal><![CDATA[
      T(x,K(y,z)) * z = x * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,8122,a(flip),b,6071,a),flip(a)].">
      <j1 rule="hyper" parents="145 8122 6071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8187">
    <literal><![CDATA[
      T(x / T(y,z),K(y,z)) = T(x / (x / (x / T(y,z))),y)
    ]]></literal>
    <justification jstring="[para(4772(a,1),8161(a,1,1))].">
      <j1 rule="para" parents="4772 8161"/>
    </justification>
  </clause>

  <clause id="8188">
    <literal><![CDATA[
      T(x * K(T(y,z),x),y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5785(a,1),8161(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5785 8161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8189">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8161(a,1),7831(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8161 7831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8190">
    <literal><![CDATA[
      T((x * y) / x,T(z,y)) = T(y * K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5890(a,1),8174(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5890 8174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8191">
    <literal><![CDATA[
      T(x,T(y,z)) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(8175(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="8175 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8192">
    <literal><![CDATA[
      (x * K(y,z)) / x = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,7867,a,b,8180,a),flip(a)].">
      <j1 rule="hyper" parents="373 7867 8180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8193">
    <literal><![CDATA[
      K(x,T(y,z)) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,7867,a,b,8180,a)].">
      <j1 rule="hyper" parents="144 7867 8180"/>
    </justification>
  </clause>

  <clause id="8194">
    <literal><![CDATA[
      K(T(x,y),z) * y = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,7433,a,b,8180,a)].">
      <j1 rule="hyper" parents="144 7433 8180"/>
    </justification>
  </clause>

  <clause id="8196">
    <literal><![CDATA[
      K(x \ y,z) * y = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,6761,a(flip),b,8180,a)].">
      <j1 rule="hyper" parents="144 6761 8180"/>
    </justification>
  </clause>

  <clause id="8197">
    <literal><![CDATA[
      T(T(K(x,y),z),z) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8180(a,1),255(a,1,1))].">
      <j1 rule="para" parents="8180 255"/>
    </justification>
  </clause>

  <clause id="8198">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(8180(a,1),7108(a,1,2))].">
      <j1 rule="para" parents="8180 7108"/>
    </justification>
  </clause>

  <clause id="8199">
    <literal><![CDATA[
      T(K(x,y \ z),z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(41,a,7884,a,b,8197,a),flip(a)].">
      <j1 rule="hyper" parents="41 7884 8197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8200">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,7867,a(flip),b,8197,a),flip(a)].">
      <j1 rule="hyper" parents="41 7867 8197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8201">
    <literal><![CDATA[
      T(x,y) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(K(z,u),y) = x
    ]]></literal>
    <justification jstring="[para(8197(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="8197 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8202">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ (z * L(K(x,y),u,w)) = z
    ]]></literal>
    <justification jstring="[para(8197(a,1),316(a,1,2,2,1))].">
      <j1 rule="para" parents="8197 316"/>
    </justification>
  </clause>

  <clause id="8203">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7964,a,8200,a)].">
      <j1 rule="hyper" parents="7964 8200"/>
    </justification>
  </clause>

  <clause id="8204">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6833,a,8200,a)].">
      <j1 rule="hyper" parents="6833 8200"/>
    </justification>
  </clause>

  <clause id="8205">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7433,a,b,8200,a)].">
      <j1 rule="hyper" parents="64 7433 8200"/>
    </justification>
  </clause>

  <clause id="8207">
    <literal><![CDATA[
      K(x,T(y \ z,z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(41,a,7884,a,b,8200,a),flip(a)].">
      <j1 rule="hyper" parents="41 7884 8200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8208">
    <literal><![CDATA[
      x * K(y,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8200(a,1),272(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8200 272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8209">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8200(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8200 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8210">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8200(a,1),841(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8200 841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8211">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8200(a,1),7438(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8200 7438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8212">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(7917(a,1),8200(a,1,1))].">
      <j1 rule="para" parents="7917 8200"/>
    </justification>
  </clause>

  <clause id="8213">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,8203,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 8203 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8214">
    <literal><![CDATA[
      K((x * y) / x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,7919,a(flip),b,8203,a),flip(a)].">
      <j1 rule="hyper" parents="64 7919 8203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8215">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7917,a(flip),b,8203,a)].">
      <j1 rule="hyper" parents="64 7917 8203"/>
    </justification>
  </clause>

  <clause id="8216">
    <literal><![CDATA[
      K(x,T(y \ z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(117(a,1),8203(a,1,2,1))].">
      <j1 rule="para" parents="117 8203"/>
    </justification>
  </clause>

  <clause id="8217">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(255(a,1),8203(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="255 8203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8218">
    <literal><![CDATA[
      K(x,T(T(y \ z,u),y)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(278(a,1),8203(a,1,2,1))].">
      <j1 rule="para" parents="278 8203"/>
    </justification>
  </clause>

  <clause id="8219">
    <literal><![CDATA[
      K(x,T(T(T(y,z),z),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(120(a,2),8203(a,1,2))].">
      <j1 rule="para" parents="120 8203"/>
    </justification>
  </clause>

  <clause id="8220">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5785(a,1),8203(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5785 8203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8221">
    <literal><![CDATA[
      T(x,T(y,z)) * z = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(8203(a,1),7950(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8203 7950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8222">
    <literal><![CDATA[
      K(x / (x / y),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7431,a,8205,a),flip(a)].">
      <j1 rule="hyper" parents="7431 8205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8223">
    <literal><![CDATA[
      x * K(T(x,y),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,8205,a,b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 8205 5726"/>
    </justification>
  </clause>

  <clause id="8224">
    <literal><![CDATA[
      K(x,T(y,z)) \ z = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,8205,a(flip),b,7873,a),flip(a)].">
      <j1 rule="hyper" parents="145 8205 7873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8225">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(25(a,2),8205(a,1,1))].">
      <j1 rule="para" parents="25 8205"/>
    </justification>
  </clause>

  <clause id="8226">
    <literal><![CDATA[
      K(T(x,y),L(T(z,y),u,w)) = K(x,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),8205(a,1,2))].">
      <j1 rule="para" parents="25 8205"/>
    </justification>
  </clause>

  <clause id="8227">
    <literal><![CDATA[
      K(R(T(x,y),z,u),T(w,y)) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(27(a,2),8205(a,1,1))].">
      <j1 rule="para" parents="27 8205"/>
    </justification>
  </clause>

  <clause id="8228">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(117(a,1),8205(a,1,2))].">
      <j1 rule="para" parents="117 8205"/>
    </justification>
  </clause>

  <clause id="8229">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(255(a,1),8205(a,1,2)),flip(a)].">
      <j1 rule="para" parents="255 8205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8230">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * u)) = K(T(x,y),R(z,y,u))
    ]]></literal>
    <justification jstring="[para(1039(a,2),8205(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1039 8205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8231">
    <literal><![CDATA[
      K(x * T(x \ y,y),z) = K(y,T(z,x \ y))
    ]]></literal>
    <justification jstring="[para(2536(a,1),8205(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2536 8205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8233">
    <literal><![CDATA[
      K(T(x,y \ z),y) = K(x,z / (z / y))
    ]]></literal>
    <justification jstring="[para(4769(a,1),8205(a,1,2))].">
      <j1 rule="para" parents="4769 8205"/>
    </justification>
  </clause>

  <clause id="8234">
    <literal><![CDATA[
      K(x * K(y,x),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(5785(a,1),8205(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5785 8205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8235">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8205(a,1),6225(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8205 6225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8236">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(7383(a,1),8205(a,1,1))].">
      <j1 rule="para" parents="7383 8205"/>
    </justification>
  </clause>

  <clause id="8237">
    <literal><![CDATA[
      K(x / (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8205(a,1),7431(a,1))].">
      <j1 rule="para" parents="8205 7431"/>
    </justification>
  </clause>

  <clause id="8238">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) = K(T(x,u),L(T(y,u),z,w))
    ]]></literal>
    <justification jstring="[para(8205(a,1),7538(a,1,1))].">
      <j1 rule="para" parents="8205 7538"/>
    </justification>
  </clause>

  <clause id="8239">
    <literal><![CDATA[
      T(x,y) * (y * K(x,z)) = T(T(x,y),z) * y
    ]]></literal>
    <justification jstring="[para(8205(a,1),7950(a,1,2,2))].">
      <j1 rule="para" parents="8205 7950"/>
    </justification>
  </clause>

  <clause id="8240">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,8213,a(flip),b,8042,a),flip(a)].">
      <j1 rule="hyper" parents="145 8213 8042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8241">
    <literal><![CDATA[
      T(x,T(y \ z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(117(a,1),8213(a,1,2,1))].">
      <j1 rule="para" parents="117 8213"/>
    </justification>
  </clause>

  <clause id="8242">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(255(a,1),8213(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="255 8213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8243">
    <literal><![CDATA[
      T(x,T(T(y \ z,u),y)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(278(a,1),8213(a,1,2,1))].">
      <j1 rule="para" parents="278 8213"/>
    </justification>
  </clause>

  <clause id="8244">
    <literal><![CDATA[
      T(x,T(y * K(z,y),u)) = T(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(5857(a,1),8213(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5857 8213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8245">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[para(8213(a,1),7993(a,2,2))].">
      <j1 rule="para" parents="8213 7993"/>
    </justification>
  </clause>

  <clause id="8246">
    <literal><![CDATA[
      K(x,T(y,z)) * (z / y) = (z / y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,7425,a(flip),b,8192,a)].">
      <j1 rule="hyper" parents="144 7425 8192"/>
    </justification>
  </clause>

  <clause id="8247">
    <literal><![CDATA[
      x * T(x \ y,T(z,y)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,5732,a,b,8192,a)].">
      <j1 rule="hyper" parents="38 5732 8192"/>
    </justification>
  </clause>

  <clause id="8248">
    <literal><![CDATA[
      K(T(x,y),z) * (y * K(z,x)) = y
    ]]></literal>
    <justification jstring="[hyper(37,a,6160,a,b,8192,a)].">
      <j1 rule="hyper" parents="37 6160 8192"/>
    </justification>
  </clause>

  <clause id="8249">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8192(a,1),340(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8192 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8250">
    <literal><![CDATA[
      K(x,T(y,z)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (z * K(x,y)) / w = u
    ]]></literal>
    <justification jstring="[para(8192(a,1),727(a,1,1))].">
      <j1 rule="para" parents="8192 727"/>
    </justification>
  </clause>

  <clause id="8252">
    <literal><![CDATA[
      R(T(K(x,T(y,z)),z * u),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(8192(a,1),1326(a,1,1,1))].">
      <j1 rule="para" parents="8192 1326"/>
    </justification>
  </clause>

  <clause id="8253">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(8192(a,1),1196(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8192 1196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8254">
    <literal><![CDATA[
      L(T(K(x,T(y,z * u)),u),u,z) = (z * (K(x,y) * u)) / (z * u)
    ]]></literal>
    <justification jstring="[para(8192(a,1),2609(a,1,1,1))].">
      <j1 rule="para" parents="8192 2609"/>
    </justification>
  </clause>

  <clause id="8255">
    <literal><![CDATA[
      T(x,T(y,z)) * (x \ z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6489,a,8193,a)].">
      <j1 rule="hyper" parents="6489 8193"/>
    </justification>
  </clause>

  <clause id="8256">
    <literal><![CDATA[
      x / (x * K(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(225,a,8193,a(flip),b,7914,a)].">
      <j1 rule="hyper" parents="225 8193 7914"/>
    </justification>
  </clause>

  <clause id="8257">
    <literal><![CDATA[
      R(x / K(y,T(z,u)),K(y,T(z,u)),u) = (x * u) / (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(225,a,8193,a(flip),b,650,a),flip(a)].">
      <j1 rule="hyper" parents="225 8193 650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8258">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(y,x)) = z
    ]]></literal>
    <justification jstring="[hyper(145,a,8193,a(flip),b,7914,a)].">
      <j1 rule="hyper" parents="145 8193 7914"/>
    </justification>
  </clause>

  <clause id="8259">
    <literal><![CDATA[
      (x * K(y,z)) / (y \ x) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(142,a,8193,a(flip),b,5778,a)].">
      <j1 rule="hyper" parents="142 8193 5778"/>
    </justification>
  </clause>

  <clause id="8260">
    <literal><![CDATA[
      (x * K(y,z)) \ (K(y,T(z,x)) * (x * u)) = L(u,x,K(y,T(z,x)))
    ]]></literal>
    <justification jstring="[para(8193(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8193 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8261">
    <literal><![CDATA[
      K(x,y \ z) * y = y * K(x,z / y)
    ]]></literal>
    <justification jstring="[para(117(a,1),8193(a,1,1,2))].">
      <j1 rule="para" parents="117 8193"/>
    </justification>
  </clause>

  <clause id="8262">
    <literal><![CDATA[
      K(x,T(y,z \ y)) * (y / z) = (y / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4461(a,1),8193(a,1,1,2))].">
      <j1 rule="para" parents="4461 8193"/>
    </justification>
  </clause>

  <clause id="8263">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = R(x,K(T(y,z),u),z * K(u,y)) * z
    ]]></literal>
    <justification jstring="[para(8193(a,1),6200(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="8193 6200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8264">
    <literal><![CDATA[
      K(x \ (y \ z),T(y,z)) = K((y \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(7420,a,8204,a)].">
      <j1 rule="hyper" parents="7420 8204"/>
    </justification>
  </clause>

  <clause id="8265">
    <literal><![CDATA[
      K(x / y,z) * (y \ x) = T(y \ x,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(144,a,8204,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 8204 5739"/>
    </justification>
  </clause>

  <clause id="8266">
    <literal><![CDATA[
      K(x / y,z / x) = K(y \ x,x \ z)
    ]]></literal>
    <justification jstring="[para(117(a,1),8204(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 8204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8267">
    <literal><![CDATA[
      L(x,K(y / z,u),z \ y) = x
    ]]></literal>
    <justification jstring="[para(8204(a,1),4869(a,1,2))].">
      <j1 rule="para" parents="8204 4869"/>
    </justification>
  </clause>

  <clause id="8268">
    <literal><![CDATA[
      (x \ y) * (y * K(y / x,z)) = T(x \ y,z) * y
    ]]></literal>
    <justification jstring="[para(8204(a,1),7950(a,1,2,2))].">
      <j1 rule="para" parents="8204 7950"/>
    </justification>
  </clause>

  <clause id="8269">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u \ (y \ u)) = x
    ]]></literal>
    <justification jstring="[para(6583(a,1),8267(a,1,2))].">
      <j1 rule="para" parents="6583 8267"/>
    </justification>
  </clause>

  <clause id="8271">
    <literal><![CDATA[
      T(x,T(y \ z,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(143,a,8207,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 8207 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8272">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(z * x) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8031,a(flip),b,8207,a)].">
      <j1 rule="hyper" parents="64 8031 8207"/>
    </justification>
  </clause>

  <clause id="8273">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8003,a(flip),b,8207,a)].">
      <j1 rule="hyper" parents="64 8003 8207"/>
    </justification>
  </clause>

  <clause id="8275">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7399,a(flip),b,8207,a)].">
      <j1 rule="hyper" parents="64 7399 8207"/>
    </justification>
  </clause>

  <clause id="8276">
    <literal><![CDATA[
      K(x,y / (y / z)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(82(a,1),8207(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 8207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8277">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6580,a,b,8212,a),flip(a)].">
      <j1 rule="hyper" parents="373 6580 8212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8279">
    <literal><![CDATA[
      L(x * K((y * z) / y,x),u,w) / L(x,u,w) = K(z,T(L(x,u,w),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6549,a,b,8214,a)].">
      <j1 rule="hyper" parents="64 6549 8214"/>
    </justification>
  </clause>

  <clause id="8280">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,6358,a,b,8214,a)].">
      <j1 rule="hyper" parents="64 6358 8214"/>
    </justification>
  </clause>

  <clause id="8281">
    <literal><![CDATA[
      K(((x * y) * z) / (x * (y * z)),u) = K(a(x,y,z),T(u,x * (y * z)))
    ]]></literal>
    <justification jstring="[para(88(a,1),8214(a,1,1,1))].">
      <j1 rule="para" parents="88 8214"/>
    </justification>
  </clause>

  <clause id="8282">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6756,a,b,8215,a)].">
      <j1 rule="hyper" parents="64 6756 8215"/>
    </justification>
  </clause>

  <clause id="8283">
    <literal><![CDATA[
      K(x / y,z) * (y \ x) = T(y \ x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(144,a,8215,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 8215 5739"/>
    </justification>
  </clause>

  <clause id="8284">
    <literal><![CDATA[
      K(x \ y,T(T(z,x),u)) = K(y / x,T(z,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),8215(a,1,2))].">
      <j1 rule="para" parents="23 8215"/>
    </justification>
  </clause>

  <clause id="8285">
    <literal><![CDATA[
      K((x * y) / x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8215(a,1),6038(a,1))].">
      <j1 rule="para" parents="8215 6038"/>
    </justification>
  </clause>

  <clause id="8286">
    <literal><![CDATA[
      x * T(x \ y,T(z,x)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(8215(a,1),6763(a,2,2))].">
      <j1 rule="para" parents="8215 6763"/>
    </justification>
  </clause>

  <clause id="8287">
    <literal><![CDATA[
      K(x \ y,T(z,x)) / (x \ y) = (1 / (x \ y)) * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(8215(a,1),6862(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8215 6862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8288">
    <literal><![CDATA[
      K(x,T((y * x) \ z,y)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,8031,a(flip),b,8216,a)].">
      <j1 rule="hyper" parents="64 8031 8216"/>
    </justification>
  </clause>

  <clause id="8289">
    <literal><![CDATA[
      (T(x \ y,x) \ z) * T(x \ y,x) = z * K(T(x \ y,x) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,8216,a(flip),b,95,a),flip(a)].">
      <j1 rule="hyper" parents="145 8216 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8290">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,T(a(y,z,u),y * (z * u)))
    ]]></literal>
    <justification jstring="[para(14(a,2),8216(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14 8216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8291">
    <literal><![CDATA[
      K(x,(y * (z * u)) / (y * z)) = K(x,T(L(u,z,y),y * z))
    ]]></literal>
    <justification jstring="[para(18(a,2),8216(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18 8216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8292">
    <literal><![CDATA[
      K(x,T((y * z) \ (y * u),z)) = K(x,L(u / z,z,y))
    ]]></literal>
    <justification jstring="[para(1207(a,1),8217(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1207 8217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8293">
    <literal><![CDATA[
      T(x,(y * z) / y) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(255(a,1),8223(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="255 8223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8294">
    <literal><![CDATA[
      T(x,y \ K(z,y \ 1)) = x * K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(5866(a,1),8223(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5866 8223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8295">
    <literal><![CDATA[
      K(x,T(y,z)) \ (z / x) = (z / x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8030(a,1),8224(a,1,1))].">
      <j1 rule="para" parents="8030 8224"/>
    </justification>
  </clause>

  <clause id="8296">
    <literal><![CDATA[
      K(T(x,x \ y),((x \ 1) * y) \ z) = K(x,z / ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[para(4909(a,1),8228(a,1,1))].">
      <j1 rule="para" parents="4909 8228"/>
    </justification>
  </clause>

  <clause id="8297">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5724,a,b,8229,a)].">
      <j1 rule="hyper" parents="64 5724 8229"/>
    </justification>
  </clause>

  <clause id="8298">
    <literal><![CDATA[
      K(x,(y * z) / y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8229(a,2),8019(a,1))].">
      <j1 rule="para" parents="8229 8019"/>
    </justification>
  </clause>

  <clause id="8300">
    <literal><![CDATA[
      (x * (y / z)) / T(y / z,x) = T(x,T(z \ y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,4649,a,b,8241,a)].">
      <j1 rule="hyper" parents="373 4649 8241"/>
    </justification>
  </clause>

  <clause id="8301">
    <literal><![CDATA[
      T(x,T(y * z,u) / y) = T(x,y \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(5440(a,1),8241(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5440 8241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8302">
    <literal><![CDATA[
      T(T(x,y / z),K(z,z \ y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8241(a,1),7842(a,1,1))].">
      <j1 rule="para" parents="8241 7842"/>
    </justification>
  </clause>

  <clause id="8305">
    <literal><![CDATA[
      T(x,T(T(y \ (z \ y),T(z,u)),y)) = T(x,(((z \ 1) \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[para(7279(a,1),8242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7279 8242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8306">
    <literal><![CDATA[
      K(x,y \ z) * (z * K(z / y,x)) = z
    ]]></literal>
    <justification jstring="[para(7902(a,1),8248(a,1,1))].">
      <j1 rule="para" parents="7902 8248"/>
    </justification>
  </clause>

  <clause id="8307">
    <literal><![CDATA[
      T(x / y,T(z \ x,y)) = T(x / y,x / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8013,a,b,8271,a)].">
      <j1 rule="hyper" parents="64 8013 8271"/>
    </justification>
  </clause>

  <clause id="8308">
    <literal><![CDATA[
      K(x,y / (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8276(a,2),7970(a,1))].">
      <j1 rule="para" parents="8276 7970"/>
    </justification>
  </clause>

  <clause id="8309">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6881(a,1),8173(a,1,1))].">
      <j1 rule="para" parents="6881 8173"/>
    </justification>
  </clause>

  <clause id="8310">
    <literal><![CDATA[
      T(K(x,y),y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(6051(a,1),8249(a,1,1))].">
      <j1 rule="para" parents="6051 8249"/>
    </justification>
  </clause>

  <clause id="8311">
    <literal><![CDATA[
      K(x \ y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(6761(a,1),8249(a,1))].">
      <j1 rule="para" parents="6761 8249"/>
    </justification>
  </clause>

  <clause id="8312">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7433(a,2),8249(a,1))].">
      <j1 rule="para" parents="7433 8249"/>
    </justification>
  </clause>

  <clause id="8313">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7867(a,2),8249(a,1))].">
      <j1 rule="para" parents="7867 8249"/>
    </justification>
  </clause>

  <clause id="8314">
    <literal><![CDATA[
      T(K(x \ y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7874(a,1),8249(a,1,1))].">
      <j1 rule="para" parents="7874 8249"/>
    </justification>
  </clause>

  <clause id="8315">
    <literal><![CDATA[
      T(K(x \ y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7917(a,1),8249(a,1,1))].">
      <j1 rule="para" parents="7917 8249"/>
    </justification>
  </clause>

  <clause id="8316">
    <literal><![CDATA[
      T(K(x,y / z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8207(a,1),8249(a,1,1))].">
      <j1 rule="para" parents="8207 8249"/>
    </justification>
  </clause>

  <clause id="8317">
    <literal><![CDATA[
      K(x / y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(8212(a,1),8249(a,1))].">
      <j1 rule="para" parents="8212 8249"/>
    </justification>
  </clause>

  <clause id="8318">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u \ (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(8269(a,1),51(a,2))].">
      <j1 rule="para" parents="8269 51"/>
    </justification>
  </clause>

  <clause id="8319">
    <literal><![CDATA[
      T(K(x,y),(z * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6729(a,2),8310(a,1))].">
      <j1 rule="para" parents="6729 8310"/>
    </justification>
  </clause>

  <clause id="8320">
    <literal><![CDATA[
      K(T(x,y),T(T(z,y),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(23(a,1),8312(a,1,2))].">
      <j1 rule="para" parents="23 8312"/>
    </justification>
  </clause>

  <clause id="8321">
    <literal><![CDATA[
      K(T(x,y),R(T(z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(27(a,2),8312(a,1,2))].">
      <j1 rule="para" parents="27 8312"/>
    </justification>
  </clause>

  <clause id="8322">
    <literal><![CDATA[
      K(x \ y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(117(a,1),8312(a,1,1))].">
      <j1 rule="para" parents="117 8312"/>
    </justification>
  </clause>

  <clause id="8323">
    <literal><![CDATA[
      K(T(x,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(117(a,1),8312(a,1,2))].">
      <j1 rule="para" parents="117 8312"/>
    </justification>
  </clause>

  <clause id="8324">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(237(a,1),8312(a,1,1))].">
      <j1 rule="para" parents="237 8312"/>
    </justification>
  </clause>

  <clause id="8325">
    <literal><![CDATA[
      K(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(117(a,1),8313(a,1,2,1))].">
      <j1 rule="para" parents="117 8313"/>
    </justification>
  </clause>

  <clause id="8326">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8108,a,b,8065,a),flip(a)].">
      <j1 rule="hyper" parents="373 8108 8065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8327">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(8065(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8065 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8328">
    <literal><![CDATA[
      T(T(x,y) * K(z,x),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4001(a,2),8069(a,1,1))].">
      <j1 rule="para" parents="4001 8069"/>
    </justification>
  </clause>

  <clause id="8329">
    <literal><![CDATA[
      T(x / y,x * (y \ x)) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(40,a,5132,a,b,8071,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 5132 8071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8330">
    <literal><![CDATA[
      x / T((y \ x) \ x,z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(79(a,1),8071(a,2,1,1))].">
      <j1 rule="para" parents="79 8071"/>
    </justification>
  </clause>

  <clause id="8331">
    <literal><![CDATA[
      T(x / (x / y),z) \ x = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),8071(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 8071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8332">
    <literal><![CDATA[
      T((x \ y) \ y,z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(79(a,1),8074(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 8074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8333">
    <literal><![CDATA[
      ((x \ T(y,x)) \ y) \ y = T(T(x,y) \ y,x)
    ]]></literal>
    <justification jstring="[para(4629(a,1),8074(a,1,1,1))].">
      <j1 rule="para" parents="4629 8074"/>
    </justification>
  </clause>

  <clause id="8334">
    <literal><![CDATA[
      K(x,T(T(y / z,u),y)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(8074(a,1),7422(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8074 7422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8335">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6708,a,b,8080,a)].">
      <j1 rule="hyper" parents="64 6708 8080"/>
    </justification>
  </clause>

  <clause id="8337">
    <literal><![CDATA[
      K((x * y) / x,T(z \ 1,u)) = K(y,T(T(z,u) \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,8214,a(flip),b,8081,a),flip(a)].">
      <j1 rule="hyper" parents="373 8214 8081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8338">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(143,a,8081,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 8081 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8339">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = T(K(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7867,a(flip),b,8081,a),flip(a)].">
      <j1 rule="hyper" parents="64 7867 8081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8340">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(117(a,1),8081(a,2,2,1))].">
      <j1 rule="para" parents="117 8081"/>
    </justification>
  </clause>

  <clause id="8341">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ z) = u
    ]]></literal>
    <justification jstring="[para(8081(a,2),7008(a,1))].">
      <j1 rule="para" parents="8081 7008"/>
    </justification>
  </clause>

  <clause id="8342">
    <literal><![CDATA[
      T(x,T((y / z) \ 1,y)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(82(a,1),8083(a,2,2,2))].">
      <j1 rule="para" parents="82 8083"/>
    </justification>
  </clause>

  <clause id="8344">
    <literal><![CDATA[
      K(x,T(y,z)) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8087(a,1),44(a,1))].">
      <j1 rule="para" parents="8087 44"/>
    </justification>
  </clause>

  <clause id="8345">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) \ K(y,x) = T(K(y,x),T(z,y \ u))
    ]]></literal>
    <justification jstring="[para(7976(a,1),8095(a,1,1,2))].">
      <j1 rule="para" parents="7976 8095"/>
    </justification>
  </clause>

  <clause id="8346">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = K(x,K(y,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7462(a,1),8102(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7462 8102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8347">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,u))) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(7869(a,1),8120(a,1,2,2))].">
      <j1 rule="para" parents="7869 8120"/>
    </justification>
  </clause>

  <clause id="8348">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,8136,a(flip),b,6223,a)].">
      <j1 rule="hyper" parents="145 8136 6223"/>
    </justification>
  </clause>

  <clause id="8349">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,x) = x * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(8136(a,1),6088(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8136 6088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8350">
    <literal><![CDATA[
      K(x,T(y,z)) * K(x,K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,8087,a(flip),b,8141,a)].">
      <j1 rule="hyper" parents="144 8087 8141"/>
    </justification>
  </clause>

  <clause id="8351">
    <literal><![CDATA[
      (x / y) * K(z,K(y,y \ x)) = (y \ x) * K(y,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,8156,a(flip),b,6442,a),flip(a)].">
      <j1 rule="hyper" parents="145 8156 6442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8352">
    <literal><![CDATA[
      T(K(x,y) \ z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(269,a,7806,a,b,8158,a)].">
      <j1 rule="hyper" parents="269 7806 8158"/>
    </justification>
  </clause>

  <clause id="8353">
    <literal><![CDATA[
      K(K(x,y),z) * T(u,K(x,y)) = T(K(x,y),z) * (u * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,8158,a(flip),b,5779,a)].">
      <j1 rule="hyper" parents="145 8158 5779"/>
    </justification>
  </clause>

  <clause id="8354">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,x) = K(y,x) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(8163(a,1),265(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8163 265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8355">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,z) = K(y,z) * (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(8163(a,1),7818(a,1,1))].">
      <j1 rule="para" parents="8163 7818"/>
    </justification>
  </clause>

  <clause id="8356">
    <literal><![CDATA[
      T(x * y,K(z,y)) = T(x,K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(8184,a,8167,a)].">
      <j1 rule="hyper" parents="8184 8167"/>
    </justification>
  </clause>

  <clause id="8357">
    <literal><![CDATA[
      K(x,y) \ z != u * K(y,x)
    ]]></literal>
    <literal><![CDATA[
      T(u,K(x,y)) = z
    ]]></literal>
    <justification jstring="[para(8169(a,1),48(a,1)),flip(a)].">
      <j1 rule="para" parents="8169 48"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8358">
    <literal><![CDATA[
      T(x * K(y,z),u) / x = x \ T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(8172(a,1),5439(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8172 5439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8359">
    <literal><![CDATA[
      T(x * y,K(y,z)) = x * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8167,a,b,8185,a)].">
      <j1 rule="hyper" parents="64 8167 8185"/>
    </justification>
  </clause>

  <clause id="8360">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7869(a,1),8188(a,1,1,2))].">
      <j1 rule="para" parents="7869 8188"/>
    </justification>
  </clause>

  <clause id="8361">
    <literal><![CDATA[
      K(x \ y,z) \ (y * K(y / x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = y
    ]]></literal>
    <justification jstring="[para(8196(a,1),335(a,1,2))].">
      <j1 rule="para" parents="8196 335"/>
    </justification>
  </clause>

  <clause id="8362">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = x \ T(x * K(x / y,z),x)
    ]]></literal>
    <justification jstring="[para(8196(a,2),6320(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8196 6320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8363">
    <literal><![CDATA[
      K(x \ (y \ z),y) * z = z * K(z / (y * x),y)
    ]]></literal>
    <justification jstring="[para(7380(a,1),8196(a,1,1))].">
      <j1 rule="para" parents="7380 8196"/>
    </justification>
  </clause>

  <clause id="8364">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) / T(z,y) = 1 / (K(z,x) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(225,a,8211,a(flip),b,5805,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 8211 5805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8365">
    <literal><![CDATA[
      (T(T(x,y),T(z,y)) * u) / (T(K(x,y),T(x,z)) * u) = R(T(x,z),T(K(x,y),T(x,z)),u)
    ]]></literal>
    <justification jstring="[para(8240(a,2),263(a,1,1,1))].">
      <j1 rule="para" parents="8240 263"/>
    </justification>
  </clause>

  <clause id="8366">
    <literal><![CDATA[
      K(x \ y,y) * T(y / x,z) = T(T(y / x,y),T(z,y))
    ]]></literal>
    <justification jstring="[para(6778(a,1),8240(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6778 8240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8367">
    <literal><![CDATA[
      T(x,T(y,z)) * T(z,x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(6490,a,8245,a)].">
      <j1 rule="hyper" parents="6490 8245"/>
    </justification>
  </clause>

  <clause id="8368">
    <literal><![CDATA[
      K(x,T(y,z)) \ (z * y) = z * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7914,a,b,8245,a)].">
      <j1 rule="hyper" parents="64 7914 8245"/>
    </justification>
  </clause>

  <clause id="8369">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,y) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(142,a,8245,a(flip),b,6022,a(flip))].">
      <j1 rule="hyper" parents="142 8245 6022"/>
    </justification>
  </clause>

  <clause id="8370">
    <literal><![CDATA[
      (x * T(y,z)) / (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8245(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8245 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8371">
    <literal><![CDATA[
      K(T(x,y),z) * (y * x) = y * T(x,z)
    ]]></literal>
    <justification jstring="[para(7869(a,2),8245(a,1,1))].">
      <j1 rule="para" parents="7869 8245"/>
    </justification>
  </clause>

  <clause id="8372">
    <literal><![CDATA[
      T(K(x,y),z) * ((x \ z) * x) = (x \ z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8006(a,1),8245(a,1,1))].">
      <j1 rule="para" parents="8006 8245"/>
    </justification>
  </clause>

  <clause id="8373">
    <literal><![CDATA[
      (x * K(y,z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8255(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8255 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8374">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u / x)) * y) = R(T(K(z,x \ u),x * y),x,y)
    ]]></literal>
    <justification jstring="[para(8261(a,1),796(a,1,2,1))].">
      <j1 rule="para" parents="8261 796"/>
    </justification>
  </clause>

  <clause id="8378">
    <literal><![CDATA[
      T(K(x \ y,z * (y \ x)),x) = K((x / y) \ 1,z * (x / y))
    ]]></literal>
    <justification jstring="[para(7239(a,1),8277(a,1,1))].">
      <j1 rule="para" parents="7239 8277"/>
    </justification>
  </clause>

  <clause id="8380">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(1203(a,2),8293(a,1,2))].">
      <j1 rule="para" parents="1203 8293"/>
    </justification>
  </clause>

  <clause id="8381">
    <literal><![CDATA[
      T(K(x,y \ ((z * u) * (1 / u))),((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(493,a,2135,a,b,8306,a)].">
      <j1 rule="hyper" parents="493 2135 8306"/>
    </justification>
  </clause>

  <clause id="8382">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(x,y) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7914,a,b,8326,a)].">
      <j1 rule="hyper" parents="64 7914 8326"/>
    </justification>
  </clause>

  <clause id="8383">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8326(a,1),6909(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8326 6909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8384">
    <literal><![CDATA[
      T(x \ y,z) * K(x,x \ y) = T(y / x,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(41,a,278,a,b,8328,a),flip(a)].">
      <j1 rule="hyper" parents="41 278 8328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8385">
    <literal><![CDATA[
      x / T(T(y,y \ x),z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(116(a,2),8330(a,1,2,1))].">
      <j1 rule="para" parents="116 8330"/>
    </justification>
  </clause>

  <clause id="8387">
    <literal><![CDATA[
      x / T(T(x,y),z) = T(T(x,y),z) \ x
    ]]></literal>
    <justification jstring="[para(3985(a,1),8330(a,1,2,1))].">
      <j1 rule="para" parents="3985 8330"/>
    </justification>
  </clause>

  <clause id="8388">
    <literal><![CDATA[
      x / (x / T(y,z)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(226,a,8331,a)].">
      <j1 rule="hyper" parents="226 8331"/>
    </justification>
  </clause>

  <clause id="8389">
    <literal><![CDATA[
      T(x / (x / (y \ 1)),y * x) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(40,a,4915,a(flip),b,8331,a),flip(a)].">
      <j1 rule="hyper" parents="40 4915 8331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8390">
    <literal><![CDATA[
      x / (x / T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x / (x / y),z) = u
    ]]></literal>
    <justification jstring="[para(8331(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8331 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8391">
    <literal><![CDATA[
      T(T(x,x \ y),z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,866,a,b,8332,a)].">
      <j1 rule="hyper" parents="64 866 8332"/>
    </justification>
  </clause>

  <clause id="8392">
    <literal><![CDATA[
      T(T(x,y),x \ z) = (T(x,y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,367,a,b,8332,a)].">
      <j1 rule="hyper" parents="64 367 8332"/>
    </justification>
  </clause>

  <clause id="8393">
    <literal><![CDATA[
      x * ((T(y,x) \ z) \ z) = ((y \ z) \ z) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,8332,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 8332 22"/>
    </justification>
  </clause>

  <clause id="8394">
    <literal><![CDATA[
      T(((x / y) \ z) \ z,y) = ((y \ x) \ z) \ z
    ]]></literal>
    <justification jstring="[para(117(a,1),8332(a,2,1,1))].">
      <j1 rule="para" parents="117 8332"/>
    </justification>
  </clause>

  <clause id="8397">
    <literal><![CDATA[
      K(x,1 / T(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(6513,a,8335,a)].">
      <j1 rule="hyper" parents="6513 8335"/>
    </justification>
  </clause>

  <clause id="8398">
    <literal><![CDATA[
      K(x,1 / T(y,z)) = T(K(x,1 / y),z)
    ]]></literal>
    <justification jstring="[para(3566(a,1),8335(a,1,2))].">
      <j1 rule="para" parents="3566 8335"/>
    </justification>
  </clause>

  <clause id="8399">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) \ ((x * y) / x)) = (x \ y) / T((x * y) / x,T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(8338(a,2),4585(a,2,2))].">
      <j1 rule="para" parents="8338 4585"/>
    </justification>
  </clause>

  <clause id="8400">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = K(x,T(z \ y,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,7006,a,b,8339,a)].">
      <j1 rule="hyper" parents="373 7006 8339"/>
    </justification>
  </clause>

  <clause id="8401">
    <literal><![CDATA[
      x * T(K(x,y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(8339(a,1),5767(a,1,2))].">
      <j1 rule="para" parents="8339 5767"/>
    </justification>
  </clause>

  <clause id="8402">
    <literal><![CDATA[
      K(T(x,(y / z) \ 1),y) = K(T(x,y \ z),y)
    ]]></literal>
    <justification jstring="[para(8342(a,1),7855(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8342 7855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8403">
    <literal><![CDATA[
      x \ (y * T(x,T(y,z))) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7820,a,b,8348,a)].">
      <j1 rule="hyper" parents="64 7820 8348"/>
    </justification>
  </clause>

  <clause id="8404">
    <literal><![CDATA[
      T(x,y) * T(K(y,x),z) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7878,a(flip),b,8348,a)].">
      <j1 rule="hyper" parents="64 7878 8348"/>
    </justification>
  </clause>

  <clause id="8405">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,z)) = T(x,K(y,y \ z))
    ]]></literal>
    <justification jstring="[para(7976(a,1),8348(a,1,2))].">
      <j1 rule="para" parents="7976 8348"/>
    </justification>
  </clause>

  <clause id="8406">
    <literal><![CDATA[
      T(x \ y,K(z,x)) = x \ T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,5432,a(flip),b,8356,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 5432 8356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8407">
    <literal><![CDATA[
      T((1 / x) * y,K(x,y)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(2898(a,1),8356(a,2,1))].">
      <j1 rule="para" parents="2898 8356"/>
    </justification>
  </clause>

  <clause id="8408">
    <literal><![CDATA[
      T(T(x,y) * z,K(y,z)) = T(x,T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(7840(a,1),8356(a,2,1))].">
      <j1 rule="para" parents="7840 8356"/>
    </justification>
  </clause>

  <clause id="8409">
    <literal><![CDATA[
      T(x * T(y,K(x,z)),y) = T(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[para(8359(a,1),7841(a,1,1))].">
      <j1 rule="para" parents="8359 7841"/>
    </justification>
  </clause>

  <clause id="8410">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z)) = x * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(6240,a,8360,a)].">
      <j1 rule="hyper" parents="6240 8360"/>
    </justification>
  </clause>

  <clause id="8412">
    <literal><![CDATA[
      K(x,y) \ (R(x,z,u) * y) = R(x,z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(7876(a,1),8368(a,1,1))].">
      <j1 rule="para" parents="7876 8368"/>
    </justification>
  </clause>

  <clause id="8413">
    <literal><![CDATA[
      (x * T(y,z \ y)) / T(x,y) = T(y,T(y * (z \ 1),x))
    ]]></literal>
    <justification jstring="[para(2781(a,1),8369(a,1,1,2))].">
      <j1 rule="para" parents="2781 8369"/>
    </justification>
  </clause>

  <clause id="8414">
    <literal><![CDATA[
      L(T(x,y),z,u) / T(x,w) = T(x,w) \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5624(a,1),8385(a,1,2,1))].">
      <j1 rule="para" parents="5624 8385"/>
    </justification>
  </clause>

  <clause id="8415">
    <literal><![CDATA[
      T(x / (x / (y / z)),z) = x / (x / (z \ y))
    ]]></literal>
    <justification jstring="[para(117(a,1),8388(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 8388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8416">
    <literal><![CDATA[
      x \ K(x * y,x \ 1) = y / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(41,a,5866,a,b,8389,a)].">
      <j1 rule="hyper" parents="41 5866 8389"/>
    </justification>
  </clause>

  <clause id="8418">
    <literal><![CDATA[
      T(T(x,y),x \ y) = (x \ T(y,x)) \ y
    ]]></literal>
    <justification jstring="[para(4632(a,1),8392(a,2,1))].">
      <j1 rule="para" parents="4632 8392"/>
    </justification>
  </clause>

  <clause id="8419">
    <literal><![CDATA[
      T(T(x,y),x \ 1) * K(z,T(x,y) \ 1) = T(T(x,y) \ 1,z) \ 1
    ]]></literal>
    <justification jstring="[para(8392(a,2),5792(a,1,1))].">
      <j1 rule="para" parents="8392 5792"/>
    </justification>
  </clause>

  <clause id="8420">
    <literal><![CDATA[
      T(K(x,1 / T(y,z)),z) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(8201,a,8398,a(flip))].">
      <j1 rule="hyper" parents="8201 8398"/>
    </justification>
  </clause>

  <clause id="8422">
    <literal><![CDATA[
      ((x \ y) \ y) * T(K(x \ y,x),z) = T(x,K(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(869,a,8404,a)].">
      <j1 rule="hyper" parents="869 8404"/>
    </justification>
  </clause>

  <clause id="8423">
    <literal><![CDATA[
      x * T(x \ y,K(z,x)) = T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,8406,a,b,xx)].">
      <j1 rule="hyper" parents="145 8406"/>
    </justification>
  </clause>

  <clause id="8424">
    <literal><![CDATA[
      T((x \ T(y,x)) \ y,K(z,x \ y)) = T(T(x,y),T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(8418(a,1),8162(a,1,1))].">
      <j1 rule="para" parents="8418 8162"/>
    </justification>
  </clause>

  <clause id="8425">
    <literal><![CDATA[
      K(x,1 / T(T(y,z),z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8398,a,b,8420,a)].">
      <j1 rule="hyper" parents="64 8398 8420"/>
    </justification>
  </clause>

  <clause id="8426">
    <literal><![CDATA[
      T(x,K(y,z)) / z = T(x / z,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(142,a,8423,a(flip),b,525,a)].">
      <j1 rule="hyper" parents="142 8423 525"/>
    </justification>
  </clause>

  <clause id="8427">
    <literal><![CDATA[
      K(x,1 / ((y * z) / y)) = K(x,1 / T(z,y))
    ]]></literal>
    <justification jstring="[para(255(a,1),8425(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="255 8425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8428">
    <literal><![CDATA[
      K(x,1 / T(y,z / y)) = K(x,1 / (z / (z / y)))
    ]]></literal>
    <justification jstring="[para(276(a,1),8425(a,1,2,2,1))].">
      <j1 rule="para" parents="276 8425"/>
    </justification>
  </clause>

  <clause id="8429">
    <literal><![CDATA[
      T(T(x,y) / z,K(y,z)) = T(x,T(y,z)) / z
    ]]></literal>
    <justification jstring="[para(7840(a,1),8426(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7840 8426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8430">
    <literal><![CDATA[
      T(K(x,y),K(x,z) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7715,a(flip),b,7784,a)].">
      <j1 rule="hyper" parents="64 7715 7784"/>
    </justification>
  </clause>

  <clause id="8432">
    <literal><![CDATA[
      T(K(x,y),K(z,x) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[para(6161(a,1),8430(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6161 8430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8433">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(6092(a,1),7836(a,1))].">
      <j1 rule="para" parents="6092 7836"/>
    </justification>
  </clause>

  <clause id="8434">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(8092(a,1),8433(a,1))].">
      <j1 rule="para" parents="8092 8433"/>
    </justification>
  </clause>

  <clause id="8435">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8109(a,1),8433(a,1))].">
      <j1 rule="para" parents="8109 8433"/>
    </justification>
  </clause>

  <clause id="8436">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8112(a,1),8433(a,1))].">
      <j1 rule="para" parents="8112 8433"/>
    </justification>
  </clause>

  <clause id="8437">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8123(a,1),8433(a,1))].">
      <j1 rule="para" parents="8123 8433"/>
    </justification>
  </clause>

  <clause id="8438">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8109(a,2),8434(a,1))].">
      <j1 rule="para" parents="8109 8434"/>
    </justification>
  </clause>

  <clause id="8439">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8126(a,1),8434(a,1))].">
      <j1 rule="para" parents="8126 8434"/>
    </justification>
  </clause>

  <clause id="8440">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,T(y,u))) = w
    ]]></literal>
    <justification jstring="[para(8138(a,2),8436(a,1))].">
      <j1 rule="para" parents="8138 8436"/>
    </justification>
  </clause>

  <clause id="8441">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T(x \ L(x,y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ L(x,y,z),K(w,u)) = v5
    ]]></literal>
    <justification jstring="[para(5931(a,2),8437(a,1))].">
      <j1 rule="para" parents="5931 8437"/>
    </justification>
  </clause>

  <clause id="8443">
    <literal><![CDATA[
      K(R(x / y,z,u) / w,y \ x) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w \ R(x / y,z,u),y \ x) = v5
    ]]></literal>
    <justification jstring="[para(6063(a,1),7897(a,1,2))].">
      <j1 rule="para" parents="6063 7897"/>
    </justification>
  </clause>

  <clause id="8445">
    <literal><![CDATA[
      T(x,y) != K(z,(y \ u) \ 1)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(6700(a,2),7966(a,2))].">
      <j1 rule="para" parents="6700 7966"/>
    </justification>
  </clause>

  <clause id="8446">
    <literal><![CDATA[
      K(x * y,T(z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6729(a,1),8021(a,1,2))].">
      <j1 rule="para" parents="6729 8021"/>
    </justification>
  </clause>

  <clause id="8447">
    <literal><![CDATA[
      K(x,T(y,z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7867(a,2),8022(a,1))].">
      <j1 rule="para" parents="7867 8022"/>
    </justification>
  </clause>

  <clause id="8449">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8234,a(flip),b,8236,a),flip(a)].">
      <j1 rule="hyper" parents="373 8234 8236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8450">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ (x * u)))
    ]]></literal>
    <justification jstring="[para(630(a,1),8449(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="630 8449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8451">
    <literal><![CDATA[
      K(L((x \ y) / z,z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ y,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(1208(a,2),8285(a,1,1))].">
      <j1 rule="para" parents="1208 8285"/>
    </justification>
  </clause>

  <clause id="8452">
    <literal><![CDATA[
      K(T(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(8233(a,2),8308(a,1))].">
      <j1 rule="para" parents="8233 8308"/>
    </justification>
  </clause>

  <clause id="8453">
    <literal><![CDATA[
      K(((x \ y) \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7871(a,2),8311(a,1))].">
      <j1 rule="para" parents="7871 8311"/>
    </justification>
  </clause>

  <clause id="8454">
    <literal><![CDATA[
      K(T(x \ y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7433(a,2),8315(a,1))].">
      <j1 rule="para" parents="7433 8315"/>
    </justification>
  </clause>

  <clause id="8455">
    <literal><![CDATA[
      K(x,R(x,y,z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ R(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(4107(a,1),8316(a,1))].">
      <j1 rule="para" parents="4107 8316"/>
    </justification>
  </clause>

  <clause id="8456">
    <literal><![CDATA[
      K(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(7867(a,2),8316(a,1))].">
      <j1 rule="para" parents="7867 8316"/>
    </justification>
  </clause>

  <clause id="8457">
    <literal><![CDATA[
      K(x / y,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(201(a,1),8317(a,1,2))].">
      <j1 rule="para" parents="201 8317"/>
    </justification>
  </clause>

  <clause id="8458">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y * x,z),u) = w
    ]]></literal>
    <justification jstring="[para(5434(a,1),8317(a,1,1))].">
      <j1 rule="para" parents="5434 8317"/>
    </justification>
  </clause>

  <clause id="8459">
    <literal><![CDATA[
      K(x / ((y * z) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(8212(a,1),8319(a,1))].">
      <j1 rule="para" parents="8212 8319"/>
    </justification>
  </clause>

  <clause id="8460">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / (x / y),y \ x) = u
    ]]></literal>
    <justification jstring="[para(319(a,1),8322(a,1,2))].">
      <j1 rule="para" parents="319 8322"/>
    </justification>
  </clause>

  <clause id="8461">
    <literal><![CDATA[
      K(x,T(y * (L(y,z,u) \ w),L(y,z,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * w) / L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(2329(a,1),8325(a,1,2,1))].">
      <j1 rule="para" parents="2329 8325"/>
    </justification>
  </clause>

  <clause id="8462">
    <literal><![CDATA[
      K(x,y \ T(z * y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * z,u) / y) = w
    ]]></literal>
    <justification jstring="[para(5440(a,1),8325(a,1,2))].">
      <j1 rule="para" parents="5440 8325"/>
    </justification>
  </clause>

  <clause id="8463">
    <literal><![CDATA[
      K(x,(y * z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(5144(a,1),8456(a,1,2))].">
      <j1 rule="para" parents="5144 8456"/>
    </justification>
  </clause>

  <clause id="8464">
    <literal><![CDATA[
      T(T(x,y) * (x \ z),x) = T(x,y) * (x \ T(z,x))
    ]]></literal>
    <justification jstring="[hyper(269,a,7794,a,b,2399,a)].">
      <j1 rule="hyper" parents="269 7794 2399"/>
    </justification>
  </clause>

  <clause id="8465">
    <literal><![CDATA[
      T(T(x,y) \ L(x,z,u),x) = T(x,y) \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,5550,a(flip),b,7795,a),flip(a)].">
      <j1 rule="hyper" parents="139 5550 7795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8466">
    <literal><![CDATA[
      T(T(x,y) \ T(x * z,u),x) = T(x,y) \ T(z * x,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,5430,a(flip),b,7795,a),flip(a)].">
      <j1 rule="hyper" parents="139 5430 7795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8467">
    <literal><![CDATA[
      x * K(T(y,z) \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,6763,a(flip),b,7795,a)].">
      <j1 rule="hyper" parents="64 6763 7795"/>
    </justification>
  </clause>

  <clause id="8468">
    <literal><![CDATA[
      K(T(x,y) \ z,x) = K(x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,354,a,b,8467,a),flip(a)].">
      <j1 rule="hyper" parents="35 354 8467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8469">
    <literal><![CDATA[
      x / T(y,T(y,z) \ x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(36,a,6311,a,b,8467,a(flip))].">
      <j1 rule="hyper" parents="36 6311 8467"/>
    </justification>
  </clause>

  <clause id="8471">
    <literal><![CDATA[
      K(x \ T(y,x),x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4651,a(flip),b,8468,a)].">
      <j1 rule="hyper" parents="64 4651 8468"/>
    </justification>
  </clause>

  <clause id="8472">
    <literal><![CDATA[
      T(x,T(x,y) \ z) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(37,a,301,a,b,8469,a),flip(a)].">
      <j1 rule="hyper" parents="37 301 8469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8473">
    <literal><![CDATA[
      x / T(y / z,(z \ y) \ x) = (y / z) \ x
    ]]></literal>
    <justification jstring="[para(117(a,1),8469(a,1,2,2,1))].">
      <j1 rule="para" parents="117 8469"/>
    </justification>
  </clause>

  <clause id="8474">
    <literal><![CDATA[
      x / T(y / (y / z),z \ x) = (y / (y / z)) \ x
    ]]></literal>
    <justification jstring="[para(276(a,1),8469(a,1,2,2,1))].">
      <j1 rule="para" parents="276 8469"/>
    </justification>
  </clause>

  <clause id="8475">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4662,a,b,8471,a)].">
      <j1 rule="hyper" parents="64 4662 8471"/>
    </justification>
  </clause>

  <clause id="8476">
    <literal><![CDATA[
      T(x,y) / (T(x,y) / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,8471,a(flip),b,5790,a),flip(a)].">
      <j1 rule="hyper" parents="145 8471 5790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8477">
    <literal><![CDATA[
      T(x,y / T(x,z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7473,a,b,8472,a)].">
      <j1 rule="hyper" parents="64 7473 8472"/>
    </justification>
  </clause>

  <clause id="8478">
    <literal><![CDATA[
      (x * y) / T((y \ x) * y,y) = T(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4898,a,b,8472,a)].">
      <j1 rule="hyper" parents="64 4898 8472"/>
    </justification>
  </clause>

  <clause id="8479">
    <literal><![CDATA[
      T(x,x \ (T(x,y) * z)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8472(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8480">
    <literal><![CDATA[
      T(x / y,(x / y) \ z) = T(x / y,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(117(a,1),8472(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="117 8472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8482">
    <literal><![CDATA[
      T(x,K(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6071(a,1),8479(a,1,2))].">
      <j1 rule="para" parents="6071 8479"/>
    </justification>
  </clause>

  <clause id="8483">
    <literal><![CDATA[
      T(x,K(x,y) * L(K(z,x),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,4036,a(flip),b,8482,a),flip(a)].">
      <j1 rule="hyper" parents="373 4036 8482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8484">
    <literal><![CDATA[
      T(T(x,y),K(x,z) * u) = T(T(x,u),y)
    ]]></literal>
    <justification jstring="[para(8482(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8482 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8485">
    <literal><![CDATA[
      K(K(x,y) * z,x) = T(x,z) \ x
    ]]></literal>
    <justification jstring="[para(8482(a,1),5731(a,2,1))].">
      <j1 rule="para" parents="8482 5731"/>
    </justification>
  </clause>

  <clause id="8486">
    <literal><![CDATA[
      T(x,K(y,x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6161(a,1),8482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6161 8482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8490">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,K(x,u) * y)) = T(x * K(z,x),K(x,u) * y)
    ]]></literal>
    <justification jstring="[para(8482(a,1),6237(a,1,1))].">
      <j1 rule="para" parents="8482 6237"/>
    </justification>
  </clause>

  <clause id="8491">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,(x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(6270(a,1),8482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 8482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8492">
    <literal><![CDATA[
      T(x \ y,(y / x) \ z) = T(x \ y,(x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(6292(a,1),8482(a,1,2))].">
      <j1 rule="para" parents="6292 8482"/>
    </justification>
  </clause>

  <clause id="8493">
    <literal><![CDATA[
      T(x,y \ T(z,x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6417(a,1),8482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6417 8482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8494">
    <literal><![CDATA[
      T(T(x,y),K(x,z) * u) = T(T(x,y),u)
    ]]></literal>
    <justification jstring="[para(8205(a,1),8482(a,1,2,1))].">
      <j1 rule="para" parents="8205 8482"/>
    </justification>
  </clause>

  <clause id="8495">
    <literal><![CDATA[
      T(x,y * K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(8193(a,1),8482(a,1,2))].">
      <j1 rule="para" parents="8193 8482"/>
    </justification>
  </clause>

  <clause id="8496">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,u)) = K((K(y,z) * u) / x,y)
    ]]></literal>
    <justification jstring="[para(8482(a,1),8204(a,1,2))].">
      <j1 rule="para" parents="8482 8204"/>
    </justification>
  </clause>

  <clause id="8497">
    <literal><![CDATA[
      T(x,y * K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(8258(a,1),8482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8258 8482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8499">
    <literal><![CDATA[
      T(x,K(y,x) * z) = x * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5753,a(flip),b,8486,a),flip(a)].">
      <j1 rule="hyper" parents="373 5753 8486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8500">
    <literal><![CDATA[
      T(((K(x,y) * z) \ y) \ T(y,z),y) = ((K(x,y) * z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(8486(a,1),1586(a,1,1,2))].">
      <j1 rule="para" parents="8486 1586"/>
    </justification>
  </clause>

  <clause id="8501">
    <literal><![CDATA[
      T(x,y * T(z,x)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(6367(a,1),8486(a,1,2))].">
      <j1 rule="para" parents="6367 8486"/>
    </justification>
  </clause>

  <clause id="8502">
    <literal><![CDATA[
      K(x,y * K(x,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,8495,a(flip),b,5753,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 8495 5753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8503">
    <literal><![CDATA[
      (x * K(y,z)) * L(T(y,x),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(y,u,w) * (x * K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(8495(a,1),464(a,1,2,1))].">
      <j1 rule="para" parents="8495 464"/>
    </justification>
  </clause>

  <clause id="8504">
    <literal><![CDATA[
      T(x * K(y,z),L(T(y,x),u,w)) = T(x * K(y,z),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(8495(a,1),4635(a,1,2,1))].">
      <j1 rule="para" parents="8495 4635"/>
    </justification>
  </clause>

  <clause id="8505">
    <literal><![CDATA[
      T(x \ y,z * ((x \ y) \ y)) = T(x \ y,z * x)
    ]]></literal>
    <justification jstring="[para(6326(a,1),8495(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6326 8495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8506">
    <literal><![CDATA[
      T(x,y * L(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6670(a,1),8495(a,1,2,2))].">
      <j1 rule="para" parents="6670 8495"/>
    </justification>
  </clause>

  <clause id="8508">
    <literal><![CDATA[
      T(x,y * (z * x)) = T(x,y * (x * z))
    ]]></literal>
    <justification jstring="[para(7591(a,1),8495(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7591 8495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8509">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(8495(a,1),7869(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8495 7869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8510">
    <literal><![CDATA[
      T(T(x,y),z * K(x,u)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(8205(a,1),8495(a,1,2,2))].">
      <j1 rule="para" parents="8205 8495"/>
    </justification>
  </clause>

  <clause id="8511">
    <literal><![CDATA[
      T(T(x,y),z * K(u,x)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(8497(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8497 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8512">
    <literal><![CDATA[
      T(x,(y / T(x,z)) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6311(a,2),8497(a,1,2))].">
      <j1 rule="para" parents="6311 8497"/>
    </justification>
  </clause>

  <clause id="8513">
    <literal><![CDATA[
      K(T(x,y),(y * K(z,x)) \ u) = K(x,u / (y * K(z,x)))
    ]]></literal>
    <justification jstring="[para(8497(a,1),8228(a,1,1))].">
      <j1 rule="para" parents="8497 8228"/>
    </justification>
  </clause>

  <clause id="8514">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5731,a,b,8485,a),flip(a)].">
      <j1 rule="hyper" parents="373 5731 8485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8515">
    <literal><![CDATA[
      K(K(x,y) * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(8485(a,2),5824(a,1))].">
      <j1 rule="para" parents="8485 5824"/>
    </justification>
  </clause>

  <clause id="8516">
    <literal><![CDATA[
      K(x * y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[para(5796(a,1),8514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5796 8514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8517">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(5755(a,1),8514(a,1,1))].">
      <j1 rule="para" parents="5755 8514"/>
    </justification>
  </clause>

  <clause id="8518">
    <literal><![CDATA[
      K(x,K(x,y) * z) = K(z,x) \ 1
    ]]></literal>
    <justification jstring="[para(8514(a,1),6092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8514 6092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8519">
    <literal><![CDATA[
      K(x * (y / x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(5781(a,1),8514(a,1,1))].">
      <j1 rule="para" parents="5781 8514"/>
    </justification>
  </clause>

  <clause id="8520">
    <literal><![CDATA[
      K(K(x,y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(6161(a,1),8514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6161 8514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8521">
    <literal><![CDATA[
      L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[para(8514(a,1),6918(a,1,1))].">
      <j1 rule="para" parents="8514 6918"/>
    </justification>
  </clause>

  <clause id="8522">
    <literal><![CDATA[
      K(x \ T(y,z),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6417(a,1),8514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6417 8514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8523">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(8514(a,1),8092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8514 8092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8524">
    <literal><![CDATA[
      K(K(x,y) * z,T(x,u)) = K(z,T(x,u))
    ]]></literal>
    <justification jstring="[para(8205(a,1),8514(a,1,1,1))].">
      <j1 rule="para" parents="8205 8514"/>
    </justification>
  </clause>

  <clause id="8525">
    <literal><![CDATA[
      K(x * K(y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8193(a,1),8514(a,1,1))].">
      <j1 rule="para" parents="8193 8514"/>
    </justification>
  </clause>

  <clause id="8526">
    <literal><![CDATA[
      K(x * K(y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(8258(a,1),8514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8258 8514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8527">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(8245(a,1),8514(a,1,1))].">
      <j1 rule="para" parents="8245 8514"/>
    </justification>
  </clause>

  <clause id="8528">
    <literal><![CDATA[
      K(x * (y \ 1),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,6991,a(flip),b,8516,a),flip(a)].">
      <j1 rule="hyper" parents="373 6991 8516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8529">
    <literal><![CDATA[
      K(x * (y \ 1),x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7573,a(flip),b,8516,a),flip(a)].">
      <j1 rule="hyper" parents="64 7573 8516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8530">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(8516(a,2),6353(a,1,2))].">
      <j1 rule="para" parents="8516 6353"/>
    </justification>
  </clause>

  <clause id="8531">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[para(8516(a,2),6506(a,1,1))].">
      <j1 rule="para" parents="8516 6506"/>
    </justification>
  </clause>

  <clause id="8532">
    <literal><![CDATA[
      T(x * (y * z),K(z * y,z)) = (y * z) * T(x,T(y * z,z))
    ]]></literal>
    <justification jstring="[para(8516(a,1),6998(a,1,2))].">
      <j1 rule="para" parents="8516 6998"/>
    </justification>
  </clause>

  <clause id="8533">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8516(a,2),6496(a,1,2))].">
      <j1 rule="para" parents="8516 6496"/>
    </justification>
  </clause>

  <clause id="8534">
    <literal><![CDATA[
      K(x * T(y,z),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(6367(a,1),8520(a,1,1))].">
      <j1 rule="para" parents="6367 8520"/>
    </justification>
  </clause>

  <clause id="8535">
    <literal><![CDATA[
      K(K(x,y) * z,T(y,u)) = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(7919(a,1),8520(a,1,1,1))].">
      <j1 rule="para" parents="7919 8520"/>
    </justification>
  </clause>

  <clause id="8537">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = R(x * K(u,x),y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(8525(a,1),7073(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8525 7073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8538">
    <literal><![CDATA[
      K(x * K(y,z),z) = 1 / K(z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6091,a,b,8526,a),flip(a)].">
      <j1 rule="hyper" parents="373 6091 8526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8539">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7310(a,1),8526(a,1,1,2))].">
      <j1 rule="para" parents="7310 8526"/>
    </justification>
  </clause>

  <clause id="8540">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7869(a,1),8526(a,1,1,2))].">
      <j1 rule="para" parents="7869 8526"/>
    </justification>
  </clause>

  <clause id="8541">
    <literal><![CDATA[
      T(x,y \ (z / x)) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(117(a,1),8493(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 8493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8542">
    <literal><![CDATA[
      K(x,K(y,x) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(5826,a,8499,a)].">
      <j1 rule="hyper" parents="5826 8499"/>
    </justification>
  </clause>

  <clause id="8543">
    <literal><![CDATA[
      T(x,K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(8499(a,2),5767(a,1))].">
      <j1 rule="para" parents="8499 5767"/>
    </justification>
  </clause>

  <clause id="8544">
    <literal><![CDATA[
      K(x,K(y,x) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),8542(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 8542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8545">
    <literal><![CDATA[
      K(x,K(x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6161(a,1),8542(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6161 8542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8546">
    <literal><![CDATA[
      K(x,T(x,y) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(5811(a,1),8542(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5811 8542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8547">
    <literal><![CDATA[
      K(x,T(y,x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6075(a,1),8542(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6075 8542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8548">
    <literal><![CDATA[
      K(x,T(x,y) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(6157(a,1),8542(a,1,2))].">
      <j1 rule="para" parents="6157 8542"/>
    </justification>
  </clause>

  <clause id="8549">
    <literal><![CDATA[
      K(x,y * K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6823(a,1),8542(a,1,2))].">
      <j1 rule="para" parents="6823 8542"/>
    </justification>
  </clause>

  <clause id="8550">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8248(a,1),8542(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8248 8542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8551">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = K(x,y) * K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(8544(a,1),8097(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8544 8097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8552">
    <literal><![CDATA[
      K(x,y \ T(y * z,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6418(a,1),8545(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6418 8545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8553">
    <literal><![CDATA[
      K(x,y * T(x,z)) = K(x,y * x)
    ]]></literal>
    <justification jstring="[para(8245(a,1),8545(a,1,2))].">
      <j1 rule="para" parents="8245 8545"/>
    </justification>
  </clause>

  <clause id="8554">
    <literal><![CDATA[
      R(K(x,y),y * K(z,x),u) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[para(8549(a,1),4524(a,1,1))].">
      <j1 rule="para" parents="8549 4524"/>
    </justification>
  </clause>

  <clause id="8555">
    <literal><![CDATA[
      K(x,y / T(z,x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(6848(a,1),8549(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6848 8549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8556">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(6887(a,1),8549(a,1,2))].">
      <j1 rule="para" parents="6887 8549"/>
    </justification>
  </clause>

  <clause id="8557">
    <literal><![CDATA[
      K(x,K(y,x * K(y,z))) = 1
    ]]></literal>
    <justification jstring="[para(8550(a,2),3996(a,1,2))].">
      <j1 rule="para" parents="8550 3996"/>
    </justification>
  </clause>

  <clause id="8558">
    <literal><![CDATA[
      K(x,y * L(K(x,z),u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6670(a,1),8550(a,1,2,2))].">
      <j1 rule="para" parents="6670 8550"/>
    </justification>
  </clause>

  <clause id="8559">
    <literal><![CDATA[
      K(x,y * (z * x)) = K(x,y * (x * z))
    ]]></literal>
    <justification jstring="[para(7591(a,1),8550(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7591 8550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8560">
    <literal><![CDATA[
      K(x,T(K(y,x) * z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(7665(a,1),8550(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7665 8550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8561">
    <literal><![CDATA[
      K(x,y * K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8502(a,2),5827(a,1))].">
      <j1 rule="para" parents="8502 5827"/>
    </justification>
  </clause>

  <clause id="8562">
    <literal><![CDATA[
      T(x,x * (y / T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4705,a,8512,a)].">
      <j1 rule="hyper" parents="4705 8512"/>
    </justification>
  </clause>

  <clause id="8563">
    <literal><![CDATA[
      K(x,K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(8518(a,2),6101(a,1))].">
      <j1 rule="para" parents="8518 6101"/>
    </justification>
  </clause>

  <clause id="8564">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),8522(a,1,1,2))].">
      <j1 rule="para" parents="22 8522"/>
    </justification>
  </clause>

  <clause id="8565">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8516,a(flip),b,8527,a),flip(a)].">
      <j1 rule="hyper" parents="373 8516 8527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8566">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(6752(a,1),8534(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6752 8534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8567">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (R(z,u,z) \ y),z)
    ]]></literal>
    <justification jstring="[para(7407(a,1),8534(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7407 8534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8568">
    <literal><![CDATA[
      K(x * K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(8538(a,2),6100(a,1))].">
      <j1 rule="para" parents="8538 6100"/>
    </justification>
  </clause>

  <clause id="8569">
    <literal><![CDATA[
      K(T(x,T(y,z)) * u,y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(6570(a,1),8540(a,1,1))].">
      <j1 rule="para" parents="6570 8540"/>
    </justification>
  </clause>

  <clause id="8570">
    <literal><![CDATA[
      K(x,T(x * K(y,z),y)) = K(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(7812(a,2),8546(a,1,2))].">
      <j1 rule="para" parents="7812 8546"/>
    </justification>
  </clause>

  <clause id="8571">
    <literal><![CDATA[
      K(x,R(y / x,z,u) \ w) = K(x,R(x \ y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(280(a,1),8547(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="280 8547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8572">
    <literal><![CDATA[
      K(x,y * T(x,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6142,a(flip),b,8553,a),flip(a)].">
      <j1 rule="hyper" parents="373 6142 8553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8573">
    <literal><![CDATA[
      K(x,y / T(z / T(u,z),x)) = K(x,y / (T(z,u) / u))
    ]]></literal>
    <justification jstring="[para(4657(a,1),8555(a,1,2,2))].">
      <j1 rule="para" parents="4657 8555"/>
    </justification>
  </clause>

  <clause id="8575">
    <literal><![CDATA[
      K(x * (y / T(x,z)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),8565(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 8565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8576">
    <literal><![CDATA[
      T(x,y * (z * K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(100(a,1),8506(a,1,2))].">
      <j1 rule="para" parents="100 8506"/>
    </justification>
  </clause>

  <clause id="8577">
    <literal><![CDATA[
      T(x,y * K(L(x,z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7369(a,1),8506(a,1,2,2))].">
      <j1 rule="para" parents="7369 8506"/>
    </justification>
  </clause>

  <clause id="8578">
    <literal><![CDATA[
      K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(5796(a,1),8515(a,1,1))].">
      <j1 rule="para" parents="5796 8515"/>
    </justification>
  </clause>

  <clause id="8579">
    <literal><![CDATA[
      K(T(x,y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(6157(a,1),8515(a,1,1))].">
      <j1 rule="para" parents="6157 8515"/>
    </justification>
  </clause>

  <clause id="8580">
    <literal><![CDATA[
      K(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8193(a,1),8515(a,1,1))].">
      <j1 rule="para" parents="8193 8515"/>
    </justification>
  </clause>

  <clause id="8581">
    <literal><![CDATA[
      K(x * (y * K(z,u)),u) = K(x * y,u)
    ]]></literal>
    <justification jstring="[para(100(a,1),8539(a,1,1))].">
      <j1 rule="para" parents="100 8539"/>
    </justification>
  </clause>

  <clause id="8582">
    <literal><![CDATA[
      K(x * (y * K(z,u)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(7318(a,1),8539(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7318 8539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8583">
    <literal><![CDATA[
      K(x * K(y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7538(a,1),8539(a,1,1,2))].">
      <j1 rule="para" parents="7538 8539"/>
    </justification>
  </clause>

  <clause id="8584">
    <literal><![CDATA[
      T(x,(x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y / x) * z) = u
    ]]></literal>
    <justification jstring="[para(6553(a,1),8543(a,1,2))].">
      <j1 rule="para" parents="6553 8543"/>
    </justification>
  </clause>

  <clause id="8585">
    <literal><![CDATA[
      K(x,y * (z * K(x,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(100(a,1),8558(a,1,2))].">
      <j1 rule="para" parents="100 8558"/>
    </justification>
  </clause>

  <clause id="8586">
    <literal><![CDATA[
      K(x,y / T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(6245(a,1),8561(a,1,2))].">
      <j1 rule="para" parents="6245 8561"/>
    </justification>
  </clause>

  <clause id="8587">
    <literal><![CDATA[
      K(x,y / (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z / x)) = u
    ]]></literal>
    <justification jstring="[para(6455(a,1),8561(a,1,2))].">
      <j1 rule="para" parents="6455 8561"/>
    </justification>
  </clause>

  <clause id="8588">
    <literal><![CDATA[
      K(x,y * (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * x)) = u
    ]]></literal>
    <justification jstring="[para(7591(a,1),8561(a,1,2))].">
      <j1 rule="para" parents="7591 8561"/>
    </justification>
  </clause>

  <clause id="8589">
    <literal><![CDATA[
      K(x,T(y,x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(6157(a,1),8563(a,1,2))].">
      <j1 rule="para" parents="6157 8563"/>
    </justification>
  </clause>

  <clause id="8590">
    <literal><![CDATA[
      K(x \ T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(2433(a,1),8568(a,1,1))].">
      <j1 rule="para" parents="2433 8568"/>
    </justification>
  </clause>

  <clause id="8591">
    <literal><![CDATA[
      K(K(x,y) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6576(a,1),8568(a,1,1))].">
      <j1 rule="para" parents="6576 8568"/>
    </justification>
  </clause>

  <clause id="8592">
    <literal><![CDATA[
      K(K(x,y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(7436(a,1),8568(a,1,1))].">
      <j1 rule="para" parents="7436 8568"/>
    </justification>
  </clause>

  <clause id="8593">
    <literal><![CDATA[
      T(x,L(x,y,z) * (z * y)) = T(x,z * (y * x))
    ]]></literal>
    <justification jstring="[para(609(a,1),8577(a,1,2))].">
      <j1 rule="para" parents="609 8577"/>
    </justification>
  </clause>

  <clause id="8595">
    <literal><![CDATA[
      K((L(x,y,z) \ u) * L(x,y,z),x) = K(u,x)
    ]]></literal>
    <justification jstring="[para(354(a,1),8583(a,1,1))].">
      <j1 rule="para" parents="354 8583"/>
    </justification>
  </clause>

  <clause id="8596">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(6270(a,1),8591(a,1,1))].">
      <j1 rule="para" parents="6270 8591"/>
    </justification>
  </clause>

  <clause id="8597">
    <literal><![CDATA[
      T(T(x,y),T(x,z) * u) = T(T(x,y),x * u)
    ]]></literal>
    <justification jstring="[para(5755(a,1),8494(a,1,2))].">
      <j1 rule="para" parents="5755 8494"/>
    </justification>
  </clause>

  <clause id="8598">
    <literal><![CDATA[
      T(T(x,y),T(x,z) \ u) = T(T(x,y),x \ u)
    ]]></literal>
    <justification jstring="[para(6075(a,1),8494(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6075 8494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8599">
    <literal><![CDATA[
      T(T(x,y),z \ T(u,x)) = T(T(x,y),z \ u)
    ]]></literal>
    <justification jstring="[para(6417(a,1),8494(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6417 8494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8600">
    <literal><![CDATA[
      T(x * K(y,T(x,z * (u * x))),y) = T(x,K(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(8508(a,2),8360(a,1,1,2,2))].">
      <j1 rule="para" parents="8508 8360"/>
    </justification>
  </clause>

  <clause id="8601">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7869,a(flip),b,8509,a),flip(a)].">
      <j1 rule="hyper" parents="373 7869 8509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8602">
    <literal><![CDATA[
      T(T(x / y,z),u * (x / y)) = T(T(x / y,z),u * (y \ x))
    ]]></literal>
    <justification jstring="[para(6872(a,1),8510(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6872 8510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8603">
    <literal><![CDATA[
      T(T(x / y,z),u * K(w,y \ x)) = T(T(x / y,u),z)
    ]]></literal>
    <justification jstring="[para(7902(a,1),8511(a,1,2,2))].">
      <j1 rule="para" parents="7902 8511"/>
    </justification>
  </clause>

  <clause id="8604">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,8092,a(flip),b,8523,a),flip(a)].">
      <j1 rule="hyper" parents="373 8092 8523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8605">
    <literal><![CDATA[
      K(x * y,T(y,z)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5796(a,1),8524(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5796 8524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8606">
    <literal><![CDATA[
      K(T(x,y) * z,T(x,u)) = K(x * z,T(x,u))
    ]]></literal>
    <justification jstring="[para(5755(a,1),8524(a,1,1))].">
      <j1 rule="para" parents="5755 8524"/>
    </justification>
  </clause>

  <clause id="8607">
    <literal><![CDATA[
      (K(x,y) * z) * K(z,T(y,u)) = T(K(x,y) * z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,8535,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 8535 5726"/>
    </justification>
  </clause>

  <clause id="8608">
    <literal><![CDATA[
      K(x / y,z * (y * (x / y))) = K(x / y,z * x)
    ]]></literal>
    <justification jstring="[para(12(a,1),8559(a,2,2,2))].">
      <j1 rule="para" parents="12 8559"/>
    </justification>
  </clause>

  <clause id="8609">
    <literal><![CDATA[
      K(x,T(y * K(z,x),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(6823(a,1),8560(a,1,2,1))].">
      <j1 rule="para" parents="6823 8560"/>
    </justification>
  </clause>

  <clause id="8610">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7489,a(flip),b,8564,a),flip(a)].">
      <j1 rule="hyper" parents="64 7489 8564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8611">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),T(y,T(x,w))) = R(x,T(y,T(x,w)),R(x,z,u))
    ]]></literal>
    <justification jstring="[para(8569(a,1),6236(a,1,1,2))].">
      <j1 rule="para" parents="8569 6236"/>
    </justification>
  </clause>

  <clause id="8612">
    <literal><![CDATA[
      T(x,y * (K(x,z) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(7879(a,1),8576(a,1,2,2))].">
      <j1 rule="para" parents="7879 8576"/>
    </justification>
  </clause>

  <clause id="8613">
    <literal><![CDATA[
      T(x,y * T(z,K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(8113(a,1),8576(a,1,2,2))].">
      <j1 rule="para" parents="8113 8576"/>
    </justification>
  </clause>

  <clause id="8615">
    <literal><![CDATA[
      K(x * (y / T(z,u)),u) = K(x * (y / z),u)
    ]]></literal>
    <justification jstring="[para(6848(a,1),8581(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6848 8581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8616">
    <literal><![CDATA[
      K(x * (K(y,z) * u),y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(7903(a,1),8581(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7903 8581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8617">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (y / T(z,u)),z)
    ]]></literal>
    <justification jstring="[para(7101(a,1),8582(a,1,1,2))].">
      <j1 rule="para" parents="7101 8582"/>
    </justification>
  </clause>

  <clause id="8618">
    <literal><![CDATA[
      K(x * (T(y,z) * u),y) = K(x * (y * u),y)
    ]]></literal>
    <justification jstring="[para(8047(a,1),8582(a,1,1,2))].">
      <j1 rule="para" parents="8047 8582"/>
    </justification>
  </clause>

  <clause id="8619">
    <literal><![CDATA[
      K(x,y * (z / T(u,x))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(6245(a,1),8585(a,1,2,2))].">
      <j1 rule="para" parents="6245 8585"/>
    </justification>
  </clause>

  <clause id="8620">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(6471(a,1),8601(a,1,2,2))].">
      <j1 rule="para" parents="6471 8601"/>
    </justification>
  </clause>

  <clause id="8621">
    <literal><![CDATA[
      K(x,T(y,T(z,K(u,x)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8093(a,1),8601(a,1,2,2))].">
      <j1 rule="para" parents="8093 8601"/>
    </justification>
  </clause>

  <clause id="8622">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(y * x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5796(a,1),8604(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5796 8604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8623">
    <literal><![CDATA[
      K(K(x,y) * z,K(y,u)) = K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(6161(a,1),8604(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6161 8604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8624">
    <literal><![CDATA[
      R(x,K(y,z) * u,K(u,K(y,w))) = x
    ]]></literal>
    <justification jstring="[para(8604(a,1),7206(a,1,3))].">
      <j1 rule="para" parents="8604 7206"/>
    </justification>
  </clause>

  <clause id="8625">
    <literal><![CDATA[
      K(x * K(y,z),K(y,u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(8193(a,1),8604(a,1,1))].">
      <j1 rule="para" parents="8193 8604"/>
    </justification>
  </clause>

  <clause id="8626">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(8604(a,2),8436(a,1))].">
      <j1 rule="para" parents="8604 8436"/>
    </justification>
  </clause>

  <clause id="8627">
    <literal><![CDATA[
      K(x,T(y * (z / x),u)) = K(x,T(y * (x \ z),u))
    ]]></literal>
    <justification jstring="[para(6872(a,1),8609(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6872 8609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8628">
    <literal><![CDATA[
      K(x,T(y / (z / x),u)) = K(x,T(y / (x \ z),u))
    ]]></literal>
    <justification jstring="[para(6887(a,1),8609(a,1,2,1))].">
      <j1 rule="para" parents="6887 8609"/>
    </justification>
  </clause>

  <clause id="8629">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7489,a(flip),b,8610,a),flip(a)].">
      <j1 rule="hyper" parents="64 7489 8610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8630">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(x \ (z * y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7381,a(flip),b,8610,a),flip(a)].">
      <j1 rule="hyper" parents="64 7381 8610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8631">
    <literal><![CDATA[
      K(L(x,y,z),u * (K(x,w) * v5)) = L(x,y,z) / L(x * K(u * v5,x),y,z)
    ]]></literal>
    <justification jstring="[para(8616(a,1),6548(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8616 6548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8632">
    <literal><![CDATA[
      K(x * (K(y,z) * u),R(y,w,v5)) = R(y,w,v5) \ R(y * K(x * u,y),w,v5)
    ]]></literal>
    <justification jstring="[para(8616(a,1),6550(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8616 6550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8633">
    <literal><![CDATA[
      T(K(x,y),T(z,K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7867,a(flip),b,8621,a)].">
      <j1 rule="hyper" parents="64 7867 8621"/>
    </justification>
  </clause>

  <clause id="8634">
    <literal><![CDATA[
      K(x,y * K(x,z)) * K(y * T(x,z),x) = x \ R(x,y * K(x,z),x)
    ]]></literal>
    <justification jstring="[para(6850(a,1),8530(a,1,2,1))].">
      <j1 rule="para" parents="6850 8530"/>
    </justification>
  </clause>

  <clause id="8635">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(22(a,1),8590(a,1,1,2))].">
      <j1 rule="para" parents="22 8590"/>
    </justification>
  </clause>

  <clause id="8636">
    <literal><![CDATA[
      K(x,y) \ ((y * z) / y) = (T(y,x) * z) / y
    ]]></literal>
    <justification jstring="[hyper(6206,a,7802,a)].">
      <j1 rule="hyper" parents="6206 7802"/>
    </justification>
  </clause>

  <clause id="8637">
    <literal><![CDATA[
      (T(x * y,y) / y) * T(y,z) = T(x * T(y,z),y)
    ]]></literal>
    <justification jstring="[para(6852(a,1),7821(a,2,1))].">
      <j1 rule="para" parents="6852 7821"/>
    </justification>
  </clause>

  <clause id="8638">
    <literal><![CDATA[
      T((x / y) * K(y,z),y) != u * K(y,z)
    ]]></literal>
    <literal><![CDATA[
      y \ x = u
    ]]></literal>
    <justification jstring="[para(7823(a,2),45(a,1))].">
      <j1 rule="para" parents="7823 45"/>
    </justification>
  </clause>

  <clause id="8639">
    <literal><![CDATA[
      T(T(x * K(y,z),u),T(z,y)) = T(T(K(y,z) * x,z),u)
    ]]></literal>
    <justification jstring="[para(7851(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7851 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8640">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,T(T(x,y) * z,y)) = (x * (T(T(x,y),y) * z)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(4957(a,1),7913(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4957 7913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8641">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(u,x) = T(x,u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2070(a,1),7948(a,1,2,2))].">
      <j1 rule="para" parents="2070 7948"/>
    </justification>
  </clause>

  <clause id="8642">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(u,x) = T(x,u) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5571(a,1),7948(a,1,2,2))].">
      <j1 rule="para" parents="5571 7948"/>
    </justification>
  </clause>

  <clause id="8643">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[para(7406(a,1),7948(a,1,2))].">
      <j1 rule="para" parents="7406 7948"/>
    </justification>
  </clause>

  <clause id="8644">
    <literal><![CDATA[
      K(x,y * (T(z,x) \ u)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(7948(a,1),8585(a,1,2,2))].">
      <j1 rule="para" parents="7948 8585"/>
    </justification>
  </clause>

  <clause id="8645">
    <literal><![CDATA[
      K(x,T(y,T(z,x) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(7948(a,1),8601(a,1,2,2))].">
      <j1 rule="para" parents="7948 8601"/>
    </justification>
  </clause>

  <clause id="8646">
    <literal><![CDATA[
      (T(x,y) \ z) * K(T(x,z),y) = x \ z
    ]]></literal>
    <justification jstring="[hyper(6897,a,8643,a)].">
      <j1 rule="hyper" parents="6897 8643"/>
    </justification>
  </clause>

  <clause id="8647">
    <literal><![CDATA[
      (x \ y) \ (T(x,z) \ y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(149,a,8643,a)].">
      <j1 rule="hyper" parents="149 8643"/>
    </justification>
  </clause>

  <clause id="8648">
    <literal><![CDATA[
      (x \ T(y,x)) * K(z,T(x,y)) = T(x,z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4619(a,1),8643(a,1,2,2))].">
      <j1 rule="para" parents="4619 8643"/>
    </justification>
  </clause>

  <clause id="8649">
    <literal><![CDATA[
      ((x \ y) \ x) * K(z,y / x) = T(x \ y,z) \ x
    ]]></literal>
    <justification jstring="[para(8216(a,1),8643(a,1,2))].">
      <j1 rule="para" parents="8216 8643"/>
    </justification>
  </clause>

  <clause id="8650">
    <literal><![CDATA[
      T(x / T(T(y,x),z),y) = y \ (K(z,y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(7952(a,1),6921(a,1,1))].">
      <j1 rule="para" parents="7952 6921"/>
    </justification>
  </clause>

  <clause id="8651">
    <literal><![CDATA[
      ((x \ y) * z) * K(x,T(x \ y,z)) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,5982,a(flip),b,7960,a),flip(a)].">
      <j1 rule="hyper" parents="373 5982 7960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8653">
    <literal><![CDATA[
      (x \ y) * T(x / y,T(x \ y,y)) = (1 / (1 / (x \ y))) * (x / y)
    ]]></literal>
    <justification jstring="[para(7980(a,1),4319(a,1,2))].">
      <j1 rule="para" parents="7980 4319"/>
    </justification>
  </clause>

  <clause id="8654">
    <literal><![CDATA[
      K(x \ y,z \ (x \ y)) * (y / x) = T(y / x,T((x * z) \ y,x))
    ]]></literal>
    <justification jstring="[para(7084(a,1),7980(a,1,1))].">
      <j1 rule="para" parents="7084 7980"/>
    </justification>
  </clause>

  <clause id="8655">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) \ ((T(x,y) \ 1) \ K(z,x)) = T(x,y) \ (T(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[para(8000(a,1),3575(a,2,2))].">
      <j1 rule="para" parents="8000 3575"/>
    </justification>
  </clause>

  <clause id="8656">
    <literal><![CDATA[
      K(x,y) * (x * z) != (x * z) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8011(a,1),44(a,1))].">
      <j1 rule="para" parents="8011 44"/>
    </justification>
  </clause>

  <clause id="8657">
    <literal><![CDATA[
      T(x,y) / T(x * K(z,T(x,u)),y) = K(x,T(T(z,u),y))
    ]]></literal>
    <justification jstring="[para(7869(a,1),8044(a,1,2,1,2))].">
      <j1 rule="para" parents="7869 8044"/>
    </justification>
  </clause>

  <clause id="8658">
    <literal><![CDATA[
      T(T(x,y) * T(x,T(z,y)),x \ 1) = x * (((x \ 1) \ T(T(x,y),z)) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(8067(a,2),1181(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8067 1181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8659">
    <literal><![CDATA[
      x / T(y,T(y \ x,z)) = T(y \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7159,a(flip),b,8072,a),flip(a)].">
      <j1 rule="hyper" parents="373 7159 8072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8660">
    <literal><![CDATA[
      T(x * K(y,x),z) \ (y * x) = y * K(z,x)
    ]]></literal>
    <justification jstring="[para(5721(a,1),8073(a,1,1,1))].">
      <j1 rule="para" parents="5721 8073"/>
    </justification>
  </clause>

  <clause id="8661">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (x * K(z,y * K(z,y))) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,5863,a(flip),b,8075,a),flip(a)].">
      <j1 rule="hyper" parents="373 5863 8075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8662">
    <literal><![CDATA[
      K(T(x * y,T(x,z)) \ ((x * T(y,K(x,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),x) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(8086(a,1),6336(a,1,1,1))].">
      <j1 rule="para" parents="8086 6336"/>
    </justification>
  </clause>

  <clause id="8663">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(u,T(y,K(x,z))) * w) = y * (T(T(y,K(x,z)),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(139,a,5810,a(flip),b,8114,a)].">
      <j1 rule="hyper" parents="139 5810 8114"/>
    </justification>
  </clause>

  <clause id="8664">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / K(x,y)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(6878(a,2),8124(a,1,2))].">
      <j1 rule="para" parents="6878 8124"/>
    </justification>
  </clause>

  <clause id="8665">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(T(z,y),K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(5923(a,1),8127(a,1,1,2))].">
      <j1 rule="para" parents="5923 8127"/>
    </justification>
  </clause>

  <clause id="8666">
    <literal><![CDATA[
      K(x,K(y,z)) * (y \ u) = T(y,K(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(8108(a,1),8147(a,1,1))].">
      <j1 rule="para" parents="8108 8147"/>
    </justification>
  </clause>

  <clause id="8667">
    <literal><![CDATA[
      K(x * T(y,z),T(u,K(y,z))) = K(K(y,z) * (x * y),u)
    ]]></literal>
    <justification jstring="[para(8165(a,1),7869(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8165 7869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8668">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8179(a,1),8173(a,1,1))].">
      <j1 rule="para" parents="8179 8173"/>
    </justification>
  </clause>

  <clause id="8669">
    <literal><![CDATA[
      K(T(x,y),T(z,L(z,u,w) * y)) = K(x,L(z,y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(2332(a,1),8226(a,1,2))].">
      <j1 rule="para" parents="2332 8226"/>
    </justification>
  </clause>

  <clause id="8670">
    <literal><![CDATA[
      K(R(T(x,y),z,u),L(y,w,v5)) = K(R(x,z,u),L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(201(a,1),8227(a,1,2))].">
      <j1 rule="para" parents="201 8227"/>
    </justification>
  </clause>

  <clause id="8671">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,y \ x))
    ]]></literal>
    <justification jstring="[para(4769(a,1),8227(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4769 8227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8672">
    <literal><![CDATA[
      K(T(x * K(y \ x,x),x),z) = K(x,T(z,T(y,x) \ x))
    ]]></literal>
    <justification jstring="[para(6820(a,1),8231(a,1,1))].">
      <j1 rule="para" parents="6820 8231"/>
    </justification>
  </clause>

  <clause id="8674">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8240(a,1),8235(a,1,1))].">
      <j1 rule="para" parents="8240 8235"/>
    </justification>
  </clause>

  <clause id="8675">
    <literal><![CDATA[
      T(x,T(T(y * K(z,y \ u),w),T(u / y,z))) = T(x,T(u / T(u / y,z),w))
    ]]></literal>
    <justification jstring="[para(8049(a,1),8243(a,1,2,1,1))].">
      <j1 rule="para" parents="8049 8243"/>
    </justification>
  </clause>

  <clause id="8676">
    <literal><![CDATA[
      K(x,T(y,z)) * (z / y) = z / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6245,a(flip),b,8246,a),flip(a)].">
      <j1 rule="hyper" parents="373 6245 8246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8677">
    <literal><![CDATA[
      K(x,y \ z) * (z / (z / y)) = z / T(z / y,x)
    ]]></literal>
    <justification jstring="[para(7423(a,1),8676(a,1,1))].">
      <j1 rule="para" parents="7423 8676"/>
    </justification>
  </clause>

  <clause id="8678">
    <literal><![CDATA[
      K(x,y) * (z / T(y,z)) = z / T(T(y,z),x)
    ]]></literal>
    <justification jstring="[para(8203(a,1),8676(a,1,1))].">
      <j1 rule="para" parents="8203 8676"/>
    </justification>
  </clause>

  <clause id="8679">
    <literal><![CDATA[
      x / T(y,T(z,x)) = K(z,y) * (x / y)
    ]]></literal>
    <justification jstring="[para(8205(a,1),8676(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8205 8676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8680">
    <literal><![CDATA[
      T(x,y) \ (x * (z / x)) = z / T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,6155,a,b,8679,a)].">
      <j1 rule="hyper" parents="373 6155 8679"/>
    </justification>
  </clause>

  <clause id="8681">
    <literal><![CDATA[
      K(x,y) * ((x \ y) / y) = (x \ y) / T(y,x)
    ]]></literal>
    <justification jstring="[para(4467(a,1),8679(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4467 8679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8682">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = y * T(y \ T(x,y),T(z,T(x,y)))
    ]]></literal>
    <justification jstring="[para(4630(a,1),8247(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4630 8247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8683">
    <literal><![CDATA[
      K(x \ (y \ z),y) * z = z * K((y \ z) / x,y)
    ]]></literal>
    <justification jstring="[para(8264(a,1),7879(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8264 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8684">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8273,a(flip),b,8275,a)].">
      <j1 rule="hyper" parents="64 8273 8275"/>
    </justification>
  </clause>

  <clause id="8685">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) * u != u * w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z / (x \ y),u)) = w
    ]]></literal>
    <justification jstring="[para(8275(a,2),7955(a,1,1))].">
      <j1 rule="para" parents="8275 7955"/>
    </justification>
  </clause>

  <clause id="8686">
    <literal><![CDATA[
      K(x,(x \ y) / (x \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(10(a,1),8684(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 8684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8687">
    <literal><![CDATA[
      K(x,(x \ y) / (z / x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8556,a,b,8686,a)].">
      <j1 rule="hyper" parents="64 8556 8686"/>
    </justification>
  </clause>

  <clause id="8688">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(11(a,1),8687(a,1,2,2))].">
      <j1 rule="para" parents="11 8687"/>
    </justification>
  </clause>

  <clause id="8690">
    <literal><![CDATA[
      T(x \ y,T(z,y)) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,8265,a(flip),b,8283,a)].">
      <j1 rule="hyper" parents="64 8265 8283"/>
    </justification>
  </clause>

  <clause id="8691">
    <literal><![CDATA[
      K(x,T(y \ x,T(z,y))) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(8690(a,1),7856(a,1,2))].">
      <j1 rule="para" parents="8690 7856"/>
    </justification>
  </clause>

  <clause id="8692">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = K(z \ y,z) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8302(a,1),8166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8302 8166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8695">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(T(x,z),u,w) / y) = v5
    ]]></literal>
    <justification jstring="[para(7423(a,1),8324(a,1))].">
      <j1 rule="para" parents="7423 8324"/>
    </justification>
  </clause>

  <clause id="8696">
    <literal><![CDATA[
      K(T(x,y),T(z \ y,u)) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(8312,a,8334,a),flip(a)].">
      <j1 rule="hyper" parents="8312 8334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8697">
    <literal><![CDATA[
      K(x,T(T(y / z,y),u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),8334(a,1,2))].">
      <j1 rule="para" parents="23 8334"/>
    </justification>
  </clause>

  <clause id="8698">
    <literal><![CDATA[
      K(x,T(y / z,u)) * y = y * K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(8334(a,1),7879(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8334 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8699">
    <literal><![CDATA[
      K(x,T(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8334(a,1),8313(a,1))].">
      <j1 rule="para" parents="8334 8313"/>
    </justification>
  </clause>

  <clause id="8701">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(8340(a,2),7007(a,1))].">
      <j1 rule="para" parents="8340 7007"/>
    </justification>
  </clause>

  <clause id="8702">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(8340(a,1),7879(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8340 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8703">
    <literal><![CDATA[
      (((x / y) \ z) \ z) * y = y * (((y \ x) \ z) \ z)
    ]]></literal>
    <justification jstring="[para(117(a,1),8393(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="117 8393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8706">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8348,a(flip),b,8405,a),flip(a)].">
      <j1 rule="hyper" parents="64 8348 8405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8707">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8153,a,b,8706,a),flip(a)].">
      <j1 rule="hyper" parents="373 8153 8706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8708">
    <literal><![CDATA[
      T(x * K(y,y \ z),K(y,z)) = K(y,y \ z) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,8164,a(flip),b,8706,a),flip(a)].">
      <j1 rule="hyper" parents="64 8164 8706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8709">
    <literal><![CDATA[
      T(K(x \ y,x) * z,K(x,y)) = z * K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8163,a(flip),b,8706,a),flip(a)].">
      <j1 rule="hyper" parents="64 8163 8706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8710">
    <literal><![CDATA[
      T(x * K(y \ z,y),K(y,z)) = K(y \ z,y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,6881,a(flip),b,8706,a),flip(a)].">
      <j1 rule="hyper" parents="64 6881 8706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8711">
    <literal><![CDATA[
      T(T(x,y / z),K(y,z)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8302,a(flip),b,8707,a),flip(a)].">
      <j1 rule="hyper" parents="64 8302 8707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8712">
    <literal><![CDATA[
      T(x * K(y,y \ z),K(z,y)) = K(y,y \ z) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,8164,a(flip),b,8707,a),flip(a)].">
      <j1 rule="hyper" parents="64 8164 8707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8713">
    <literal><![CDATA[
      T(x,K(y * z,y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),8707(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8714">
    <literal><![CDATA[
      T(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8707(a,2),8184(a,1))].">
      <j1 rule="para" parents="8707 8184"/>
    </justification>
  </clause>

  <clause id="8715">
    <literal><![CDATA[
      T(x,K(y * z,y)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8153,a,b,8713,a),flip(a)].">
      <j1 rule="hyper" parents="373 8153 8713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8716">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,T(z * y,z))
    ]]></literal>
    <justification jstring="[para(8715(a,1),7841(a,1,1))].">
      <j1 rule="para" parents="8715 7841"/>
    </justification>
  </clause>

  <clause id="8717">
    <literal><![CDATA[
      T(x,K(y / z,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8519(a,1),8715(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8519 8715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8718">
    <literal><![CDATA[
      T(x * (y / z),K(y,z)) = (y / z) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7000,a(flip),b,8717,a),flip(a)].">
      <j1 rule="hyper" parents="64 7000 8717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8719">
    <literal><![CDATA[
      T(1 / (x / y),K(x,y)) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2898,a(flip),b,8717,a),flip(a)].">
      <j1 rule="hyper" parents="64 2898 8717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8720">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(481,a,8711,a)].">
      <j1 rule="hyper" parents="481 8711"/>
    </justification>
  </clause>

  <clause id="8721">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8178,a(flip),b,8711,a),flip(a)].">
      <j1 rule="hyper" parents="64 8178 8711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8722">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(41,a,7825,a,b,8711,a)].">
      <j1 rule="hyper" parents="41 7825 8711"/>
    </justification>
  </clause>

  <clause id="8723">
    <literal><![CDATA[
      T(x / (y / z),z \ y) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(117(a,1),8711(a,1,1)),flip(a)].">
      <j1 rule="para" parents="117 8711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8724">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8711(a,1),7831(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8711 7831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8725">
    <literal><![CDATA[
      T(1 / (x / y),T(x,y)) = T(1 / (x / y),x)
    ]]></literal>
    <justification jstring="[para(8719(a,1),7841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8719 7841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8726">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(((z \ 1) \ 1) \ u) \ y) = T(x,y / (((z \ 1) \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(6527(a,1),8721(a,1,1,2))].">
      <j1 rule="para" parents="6527 8721"/>
    </justification>
  </clause>

  <clause id="8727">
    <literal><![CDATA[
      T(T(x,y / z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8722(a,1),7831(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8722 7831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8728">
    <literal><![CDATA[
      T(x,K(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8153(a,1),8714(a,1))].">
      <j1 rule="para" parents="8153 8714"/>
    </justification>
  </clause>

  <clause id="8730">
    <literal><![CDATA[
      T(T(x \ y,x) * z,K(x,y)) = (x \ y) * (z * K(x \ y,x))
    ]]></literal>
    <justification jstring="[hyper(8728,a,7188,a)].">
      <j1 rule="hyper" parents="8728 7188"/>
    </justification>
  </clause>

  <clause id="8731">
    <literal><![CDATA[
      T((((x \ y) \ 1) \ z) \ z,K(x,y)) = T((x \ y) \ 1,(x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(8728,a,4919,a)].">
      <j1 rule="hyper" parents="8728 4919"/>
    </justification>
  </clause>

  <clause id="8732">
    <literal><![CDATA[
      K(T(x * y,T(y,z)) \ ((x * T(y,K(x,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(8409(a,1),6336(a,1,1,1))].">
      <j1 rule="para" parents="8409 6336"/>
    </justification>
  </clause>

  <clause id="8733">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z)) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8410(a,2),44(a,1))].">
      <j1 rule="para" parents="8410 44"/>
    </justification>
  </clause>

  <clause id="8734">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8410(a,1),5901(a,1,1))].">
      <j1 rule="para" parents="8410 5901"/>
    </justification>
  </clause>

  <clause id="8737">
    <literal><![CDATA[
      R(x / y,z,u) / (R(x / y,z,u) / (y \ x)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(2085(a,1),8415(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2085 8415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8738">
    <literal><![CDATA[
      (x \ K(x * y,x \ 1)) \ y = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(143,a,8416,a,b,171,a)].">
      <j1 rule="hyper" parents="143 8416 171"/>
    </justification>
  </clause>

  <clause id="8739">
    <literal><![CDATA[
      (x \ y) / ((x \ y) / (x \ 1)) = x \ K(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),8416(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 8416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8740">
    <literal><![CDATA[
      K(x,1 / T(1 / y,z)) = K(x,y * K(1 / y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6961,a(flip),b,8427,a),flip(a)].">
      <j1 rule="hyper" parents="64 6961 8427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8741">
    <literal><![CDATA[
      (T(x,y) \ y) * x != z * K(x \ y,x)
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(8475(a,1),153(a,1,2)),flip(a),flip(b)].">
      <j1 rule="para" parents="8475 153"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8742">
    <literal><![CDATA[
      T(T(x * K(x \ y,x),y),z) = L(T(x,z),x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(8476(a,1),7536(a,1,1,1))].">
      <j1 rule="para" parents="8476 7536"/>
    </justification>
  </clause>

  <clause id="8744">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(8528(a,1),7352(a,1,1,1))].">
      <j1 rule="para" parents="8528 7352"/>
    </justification>
  </clause>

  <clause id="8745">
    <literal><![CDATA[
      R(T(T(x,y),x * z),z,T(x,y)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(8597(a,1),4626(a,1,1))].">
      <j1 rule="para" parents="8597 4626"/>
    </justification>
  </clause>

  <clause id="8746">
    <literal><![CDATA[
      T(x,T(T(y,z),y * u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(8597(a,1),7427(a,1,2))].">
      <j1 rule="para" parents="8597 7427"/>
    </justification>
  </clause>

  <clause id="8747">
    <literal><![CDATA[
      K(x * (y * y),T(x,z)) = K(y * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6511,a(flip),b,8606,a),flip(a)].">
      <j1 rule="hyper" parents="64 6511 8606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8748">
    <literal><![CDATA[
      K(x * (((y \ 1) \ z) / z),y) = K(x * (z \ ((y \ 1) \ z)),y)
    ]]></literal>
    <justification jstring="[para(4584(a,1),8615(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4584 8615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8749">
    <literal><![CDATA[
      K(x,T(y,z)) \ ((R(z,u,w) * T(y,z)) / T(y,z)) = (T(T(y,z),x) * R(T(z,y),u,w)) / T(y,z)
    ]]></literal>
    <justification jstring="[para(4641(a,1),8636(a,1,2,1))].">
      <j1 rule="para" parents="4641 8636"/>
    </justification>
  </clause>

  <clause id="8750">
    <literal><![CDATA[
      K(x,1) * ((y \ R(y,z,u)) / K(x,R(y,w,v5))) = K(R(y,w,v5),x) * (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(7276(a,1),8664(a,1,1,2))].">
      <j1 rule="para" parents="7276 8664"/>
    </justification>
  </clause>

  <clause id="8751">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(u,T(y,K(x,z))) * w) = y \ (((u * T(y,K(x,z))) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(139,a,6356,a(flip),b,8666,a)].">
      <j1 rule="hyper" parents="139 6356 8666"/>
    </justification>
  </clause>

  <clause id="8752">
    <literal><![CDATA[
      (K(x,y) * T(x,K(z,u))) \ x = K(z,K(u,x)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8092(a,1),8674(a,2,1))].">
      <j1 rule="para" parents="8092 8674"/>
    </justification>
  </clause>

  <clause id="8753">
    <literal><![CDATA[
      T(T(x,1),y) \ R(z,T(T(x,1),y) \ 1,T(T(x,1),y)) = T(z * (K(y,x) * (1 / T(x,1))),T(T(x,1),y))
    ]]></literal>
    <justification jstring="[para(8678(a,2),2978(a,2,1,2))].">
      <j1 rule="para" parents="8678 2978"/>
    </justification>
  </clause>

  <clause id="8754">
    <literal><![CDATA[
      x / T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = (x * (1 / T(T(z,1),y))) \ x
    ]]></literal>
    <justification jstring="[para(8678(a,2),6987(a,1,2,1,2))].">
      <j1 rule="para" parents="8678 6987"/>
    </justification>
  </clause>

  <clause id="8755">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,y \ z))
    ]]></literal>
    <justification jstring="[para(117(a,1),8691(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 8691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8756">
    <literal><![CDATA[
      K(x,T(T(y \ z,u),z)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(8019,a,8696,a)].">
      <j1 rule="hyper" parents="8019 8696"/>
    </justification>
  </clause>

  <clause id="8757">
    <literal><![CDATA[
      T(x,T(T(y / z,y),u)) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(143,a,8697,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 8697 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8758">
    <literal><![CDATA[
      K(x,R(T(y \ z,z * u),y,u)) = K(x,T((y * u) \ (z * u),y))
    ]]></literal>
    <justification jstring="[para(1497(a,1),8697(a,1,2))].">
      <j1 rule="para" parents="1497 8697"/>
    </justification>
  </clause>

  <clause id="8759">
    <literal><![CDATA[
      T(x,x \ y) * T(1 / (x / y),x) = (1 / (x / y)) * T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(8725(a,1),7426(a,1,2))].">
      <j1 rule="para" parents="8725 7426"/>
    </justification>
  </clause>

  <clause id="8760">
    <literal><![CDATA[
      R(K(x / y,z),x,u) = K((x * u) / (y * u),z)
    ]]></literal>
    <justification jstring="[para(82(a,1),7762(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 7762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8761">
    <literal><![CDATA[
      R(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(223(a,1),7762(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="223 7762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8763">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7885(a,1),7868(a,1,2))].">
      <j1 rule="para" parents="7885 7868"/>
    </justification>
  </clause>

  <clause id="8764">
    <literal><![CDATA[
      K(T(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) * u = w
    ]]></literal>
    <justification jstring="[para(6156(a,1),7924(a,1))].">
      <j1 rule="para" parents="6156 7924"/>
    </justification>
  </clause>

  <clause id="8765">
    <literal><![CDATA[
      x * K(T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(6878(a,1),7930(a,1))].">
      <j1 rule="para" parents="6878 7930"/>
    </justification>
  </clause>

  <clause id="8766">
    <literal><![CDATA[
      T(x,x * y) \ T(x,y) = L(x,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,5756,a,b,7932,a)].">
      <j1 rule="hyper" parents="139 5756 7932"/>
    </justification>
  </clause>

  <clause id="8767">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = x * (L(x,y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,7932,a(flip),b,6131,a)].">
      <j1 rule="hyper" parents="145 7932 6131"/>
    </justification>
  </clause>

  <clause id="8768">
    <literal><![CDATA[
      L(x,y,x) \ x = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6343,a(flip),b,8766,a),flip(a)].">
      <j1 rule="hyper" parents="64 6343 8766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8769">
    <literal><![CDATA[
      x / L(x,y,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5558,a,b,8768,a)].">
      <j1 rule="hyper" parents="64 5558 8768"/>
    </justification>
  </clause>

  <clause id="8770">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ x = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(8768(a,1),5559(a,1,1))].">
      <j1 rule="para" parents="8768 5559"/>
    </justification>
  </clause>

  <clause id="8772">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8087(a,1),8103(a,1))].">
      <j1 rule="para" parents="8087 8103"/>
    </justification>
  </clause>

  <clause id="8773">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(8138(a,2),8103(a,1,2))].">
      <j1 rule="para" parents="8138 8103"/>
    </justification>
  </clause>

  <clause id="8774">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8445,a,8200,a),flip(a)].">
      <j1 rule="hyper" parents="8445 8200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8775">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(7562,a,8521,a)].">
      <j1 rule="hyper" parents="7562 8521"/>
    </justification>
  </clause>

  <clause id="8776">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8514,a(flip),b,8775,a),flip(a)].">
      <j1 rule="hyper" parents="373 8514 8775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8778">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y)
    ]]></literal>
    <justification jstring="[para(346(a,1),8776(a,1,1))].">
      <j1 rule="para" parents="346 8776"/>
    </justification>
  </clause>

  <clause id="8779">
    <literal><![CDATA[
      K(x,y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8554(a,1),432(a,1)),flip(b)].">
      <j1 rule="para" parents="8554 432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8780">
    <literal><![CDATA[
      K(x,y \ T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2433(a,1),8779(a,1,2))].">
      <j1 rule="para" parents="2433 8779"/>
    </justification>
  </clause>

  <clause id="8781">
    <literal><![CDATA[
      K(x,y / (z / x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(6887(a,1),8779(a,1,2))].">
      <j1 rule="para" parents="6887 8779"/>
    </justification>
  </clause>

  <clause id="8782">
    <literal><![CDATA[
      K(x,T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(6570(a,1),8779(a,1,2))].">
      <j1 rule="para" parents="6570 8779"/>
    </justification>
  </clause>

  <clause id="8783">
    <literal><![CDATA[
      K(x,K(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7436(a,1),8779(a,1,2))].">
      <j1 rule="para" parents="7436 8779"/>
    </justification>
  </clause>

  <clause id="8785">
    <literal><![CDATA[
      K(x,y \ (x \ (z * x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(22(a,1),8780(a,1,2,2))].">
      <j1 rule="para" parents="22 8780"/>
    </justification>
  </clause>

  <clause id="8786">
    <literal><![CDATA[
      K(K(x,y) * (K(y,z) * u),K(y,w)) = K(y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(8626,a,8623,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8626 8623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8787">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(7488(a,2),8635(a,1))].">
      <j1 rule="para" parents="7488 8635"/>
    </justification>
  </clause>

  <clause id="8789">
    <literal><![CDATA[
      T(T(x,K(y,z)),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),8724(a,1))].">
      <j1 rule="para" parents="23 8724"/>
    </justification>
  </clause>

  <clause id="8790">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(8159(a,2),8724(a,1))].">
      <j1 rule="para" parents="8159 8724"/>
    </justification>
  </clause>

  <clause id="8791">
    <literal><![CDATA[
      K((x * y) / (z * y),T(u,x)) = R(K(z \ x,u),x,y)
    ]]></literal>
    <justification jstring="[para(7874(a,1),8760(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7874 8760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8792">
    <literal><![CDATA[
      K((x * y) / z,x) = K(x / (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4524,a(flip),b,8761,a),flip(a)].">
      <j1 rule="hyper" parents="64 4524 8761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8793">
    <literal><![CDATA[
      K((x * y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6778,a(flip),b,8792,a),flip(a)].">
      <j1 rule="hyper" parents="373 6778 8792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8794">
    <literal><![CDATA[
      T(K(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7433(a,1),8764(a,1,1))].">
      <j1 rule="para" parents="7433 8764"/>
    </justification>
  </clause>

  <clause id="8795">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(7433(a,1),8765(a,1,2))].">
      <j1 rule="para" parents="7433 8765"/>
    </justification>
  </clause>

  <clause id="8797">
    <literal><![CDATA[
      K((x * y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(8629(a,1),8787(a,1))].">
      <j1 rule="para" parents="8629 8787"/>
    </justification>
  </clause>

  <clause id="8798">
    <literal><![CDATA[
      T(x,y \ T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(x,z) / y) = u
    ]]></literal>
    <justification jstring="[para(3999(a,1),8789(a,1,1))].">
      <j1 rule="para" parents="3999 8789"/>
    </justification>
  </clause>

  <clause id="8799">
    <literal><![CDATA[
      K((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(7263(a,1),8797(a,1))].">
      <j1 rule="para" parents="7263 8797"/>
    </justification>
  </clause>

  <clause id="8800">
    <literal><![CDATA[
      K(x / ((y * z) * x),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z \ (y \ 1),y) = u
    ]]></literal>
    <justification jstring="[para(6582(a,2),8799(a,1))].">
      <j1 rule="para" parents="6582 8799"/>
    </justification>
  </clause>

  <clause id="8801">
    <literal><![CDATA[
      T((K(x,y) * K(y,z)) \ (K(x,y) * (u * K(y,z))),K(x,y)) = R(T(u,K(x,y) * K(y,z)),K(x,y),K(y,z))
    ]]></literal>
    <justification jstring="[para(7786(a,1),1756(a,1,1,2))].">
      <j1 rule="para" parents="7786 1756"/>
    </justification>
  </clause>

  <clause id="8802">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7786(a,1),8164(a,1,1))].">
      <j1 rule="para" parents="7786 8164"/>
    </justification>
  </clause>

  <clause id="8803">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6324,a(flip),b,7814,a),flip(a)].">
      <j1 rule="hyper" parents="373 6324 7814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8804">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(6471(a,1),8803(a,1,2,1))].">
      <j1 rule="para" parents="6471 8803"/>
    </justification>
  </clause>

  <clause id="8805">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6871(a,1),8803(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6871 8803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8806">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) \ u) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(7026(a,1),8803(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7026 8803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8807">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7456(a,1),8803(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7456 8803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8808">
    <literal><![CDATA[
      K(x,(K(x,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7879(a,1),8803(a,1,2,1))].">
      <j1 rule="para" parents="7879 8803"/>
    </justification>
  </clause>

  <clause id="8810">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = (w * K(y \ u,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(373,a,6882,a,b,8805,a),flip(a)].">
      <j1 rule="hyper" parents="373 6882 8805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8811">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[hyper(143,a,8807,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 8807 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8812">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7791,a(flip),b,8807,a)].">
      <j1 rule="hyper" parents="64 7791 8807"/>
    </justification>
  </clause>

  <clause id="8813">
    <literal><![CDATA[
      K(x,(y * z) \ ((K(x,u) * y) * z)) = K(x,a(K(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(14(a,2),8808(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 8808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8814">
    <literal><![CDATA[
      T(x,y \ (K(z,x) * u)) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7793,a(flip),b,8811,a),flip(a)].">
      <j1 rule="hyper" parents="64 7793 8811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8816">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(5796(a,1),8812(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5796 8812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8817">
    <literal><![CDATA[
      K(x,y \ ((x \ z) * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5947(a,1),8812(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5947 8812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8818">
    <literal><![CDATA[
      K(x,y \ (z * K(x,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(8193(a,1),8812(a,1,2,2))].">
      <j1 rule="para" parents="8193 8812"/>
    </justification>
  </clause>

  <clause id="8820">
    <literal><![CDATA[
      T(x,y \ T(x,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(5797(a,1),8814(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5797 8814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8821">
    <literal><![CDATA[
      T(x,y \ K(x,z)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(6076(a,1),8814(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6076 8814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8822">
    <literal><![CDATA[
      T(x,y \ ((z / x) \ u)) = T(x,y \ ((x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(6283(a,1),8814(a,1,2,2))].">
      <j1 rule="para" parents="6283 8814"/>
    </justification>
  </clause>

  <clause id="8823">
    <literal><![CDATA[
      T(x,T(x,y) / z) = T(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(8798,a,8820,a)].">
      <j1 rule="hyper" parents="8798 8820"/>
    </justification>
  </clause>

  <clause id="8824">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,7149,a,b,8816,a)].">
      <j1 rule="hyper" parents="373 7149 8816"/>
    </justification>
  </clause>

  <clause id="8825">
    <literal><![CDATA[
      K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(6471(a,1),8818(a,1,2,2))].">
      <j1 rule="para" parents="6471 8818"/>
    </justification>
  </clause>

  <clause id="8826">
    <literal><![CDATA[
      K(x,y \ (z * (u * x))) = K(x,y \ (z * (x * u)))
    ]]></literal>
    <justification jstring="[para(7591(a,1),8818(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7591 8818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8827">
    <literal><![CDATA[
      T(x,(x \ y) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(143,a,8824,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 8824 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8828">
    <literal><![CDATA[
      K(x,y \ (((x \ y) * z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),8824(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8829">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (x \ y)) \ u)
    ]]></literal>
    <justification jstring="[para(8824(a,1),7081(a,1,1))].">
      <j1 rule="para" parents="8824 7081"/>
    </justification>
  </clause>

  <clause id="8830">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,8491,a,b,8827,a)].">
      <j1 rule="hyper" parents="64 8491 8827"/>
    </justification>
  </clause>

  <clause id="8831">
    <literal><![CDATA[
      K(x,T(y,(y \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8827(a,2),7557(a,1,2))].">
      <j1 rule="para" parents="8827 7557"/>
    </justification>
  </clause>

  <clause id="8832">
    <literal><![CDATA[
      L(T(x,y \ (z * x)),u,w) \ L(x,u,w) = K((y / x) \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(8830(a,1),5801(a,1,1,1))].">
      <j1 rule="para" parents="8830 5801"/>
    </justification>
  </clause>

  <clause id="8833">
    <literal><![CDATA[
      K(x,T(y,(y * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(9(a,1),8831(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 8831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8834">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(8021,a,8833,a),flip(a)].">
      <j1 rule="hyper" parents="8021 8833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8835">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8605,a,b,8834,a),flip(a)].">
      <j1 rule="hyper" parents="373 8605 8834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8836">
    <literal><![CDATA[
      K(x * y,T(y,x \ z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8605,a,b,8835,a)].">
      <j1 rule="hyper" parents="64 8605 8835"/>
    </justification>
  </clause>

  <clause id="8837">
    <literal><![CDATA[
      K(x * y,T(y,x * z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),8836(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 8836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8838">
    <literal><![CDATA[
      T(x * K(y,z / x),x \ z) = T(x \ z,y) \ z
    ]]></literal>
    <justification jstring="[para(8261(a,1),7815(a,1,1))].">
      <j1 rule="para" parents="8261 7815"/>
    </justification>
  </clause>

  <clause id="8839">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = K(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(8794,a,7835,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8794 7835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8840">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,T(y,x)) * u = w
    ]]></literal>
    <justification jstring="[para(7835(a,2),8794(a,1))].">
      <j1 rule="para" parents="7835 8794"/>
    </justification>
  </clause>

  <clause id="8841">
    <literal><![CDATA[
      (x \ R(x,y,z)) * T(K(u,x),w) = R(x,y,z) * (x \ K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[hyper(1937,a,7898,a),flip(a)].">
      <j1 rule="hyper" parents="1937 7898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8842">
    <literal><![CDATA[
      x * K(y,L(T(z,x),u,w)) != v5 * v6
    ]]></literal>
    <literal><![CDATA[
      v5 \ (K(y,L(z,u,w)) * x) = v6
    ]]></literal>
    <justification jstring="[para(7954(a,2),720(a,1))].">
      <j1 rule="para" parents="7954 720"/>
    </justification>
  </clause>

  <clause id="8843">
    <literal><![CDATA[
      x * K(y,(1 / x) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(1639(a,1),7954(a,1,2,2))].">
      <j1 rule="para" parents="1639 7954"/>
    </justification>
  </clause>

  <clause id="8844">
    <literal><![CDATA[
      T(x * K(1 / y,x),y) / (y * T(x,y)) = R(T(1 / y,x),y,T(x,y))
    ]]></literal>
    <justification jstring="[para(7985(a,2),6269(a,1,1))].">
      <j1 rule="para" parents="7985 6269"/>
    </justification>
  </clause>

  <clause id="8845">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,u) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,7099,a(flip),b,7998,a),flip(a)].">
      <j1 rule="hyper" parents="373 7099 7998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8846">
    <literal><![CDATA[
      (x * K(y,y * z)) / T(y,z) = x / R(y,z,y)
    ]]></literal>
    <justification jstring="[para(6342(a,1),7998(a,2,2))].">
      <j1 rule="para" parents="6342 7998"/>
    </justification>
  </clause>

  <clause id="8847">
    <literal><![CDATA[
      ((x * T(y,z)) / y) * ((u * y) / u) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(6656,a,7999,a)].">
      <j1 rule="hyper" parents="6656 7999"/>
    </justification>
  </clause>

  <clause id="8848">
    <literal><![CDATA[
      K(x,R(T(y,x \ z),u,w)) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(27(a,2),8008(a,2,2))].">
      <j1 rule="para" parents="27 8008"/>
    </justification>
  </clause>

  <clause id="8849">
    <literal><![CDATA[
      1 * T((x \ 1) * y,K(z,T(u,x \ y))) = T(T((x \ 1) * y,x \ y),K(z,u))
    ]]></literal>
    <justification jstring="[para(5133(a,1),8068(a,1,1))].">
      <j1 rule="para" parents="5133 8068"/>
    </justification>
  </clause>

  <clause id="8850">
    <literal><![CDATA[
      x / (x * (y * K(z,y \ 1))) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(6485(a,1),8077(a,1,2))].">
      <j1 rule="para" parents="6485 8077"/>
    </justification>
  </clause>

  <clause id="8851">
    <literal><![CDATA[
      (x * K(y,z)) * T(K(z,y),u) = x * K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(6871(a,1),8100(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6871 8100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8852">
    <literal><![CDATA[
      T(T(x,L(K(y,z),u,w)),L(K(y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(4899,a,8202,a)].">
      <j1 rule="hyper" parents="4899 8202"/>
    </justification>
  </clause>

  <clause id="8853">
    <literal><![CDATA[
      T(L(K(x,y),z,u) \ w,L(K(x,y),z,u)) = w / L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(913,a,8852,a)].">
      <j1 rule="hyper" parents="913 8852"/>
    </justification>
  </clause>

  <clause id="8854">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * (z * K(y,v5)) = (z * K(y,v5)) * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8495(a,1),8209(a,1,1,1,2))].">
      <j1 rule="para" parents="8495 8209"/>
    </justification>
  </clause>

  <clause id="8855">
    <literal><![CDATA[
      T(x,K(y,z \ 1) / z) = x * K(T(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5234,a,b,8294,a)].">
      <j1 rule="hyper" parents="64 5234 8294"/>
    </justification>
  </clause>

  <clause id="8856">
    <literal><![CDATA[
      T(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8300(a,1),4675(a,1))].">
      <j1 rule="para" parents="8300 4675"/>
    </justification>
  </clause>

  <clause id="8857">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,8102,a(flip),b,8346,a),flip(a)].">
      <j1 rule="hyper" parents="373 8102 8346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8858">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),K(u,y) \ z)
    ]]></literal>
    <justification jstring="[para(7826(a,1),8857(a,1,2))].">
      <j1 rule="para" parents="7826 8857"/>
    </justification>
  </clause>

  <clause id="8859">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,x * u))) = T(K(x,y),T(z,u * x))
    ]]></literal>
    <justification jstring="[para(4683(a,1),8347(a,1,2,2,2))].">
      <j1 rule="para" parents="4683 8347"/>
    </justification>
  </clause>

  <clause id="8860">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,z) = z * (T(T(z,y),y) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,7247,a(flip),b,8355,a),flip(a)].">
      <j1 rule="hyper" parents="373 7247 8355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8862">
    <literal><![CDATA[
      K(x,y * z) \ ((x * y) * z) = R(x,y,z) * T(y * z,x)
    ]]></literal>
    <justification jstring="[para(111(a,1),8412(a,1,2))].">
      <j1 rule="para" parents="111 8412"/>
    </justification>
  </clause>

  <clause id="8863">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(64,a,8397,a(flip),b,8428,a)].">
      <j1 rule="hyper" parents="64 8397 8428"/>
    </justification>
  </clause>

  <clause id="8864">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),8464(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8865">
    <literal><![CDATA[
      T(1 / (1 / x),x \ y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(37,a,5132,a(flip),b,8474,a),flip(a)].">
      <j1 rule="hyper" parents="37 5132 8474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8866">
    <literal><![CDATA[
      ((1 / x) * y) \ L(y,x,x) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4929,a,b,8865,a)].">
      <j1 rule="hyper" parents="64 4929 8865"/>
    </justification>
  </clause>

  <clause id="8867">
    <literal><![CDATA[
      L((x \ y) \ y,x,x) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,827,a(flip),b,8865,a)].">
      <j1 rule="hyper" parents="64 827 8865"/>
    </justification>
  </clause>

  <clause id="8868">
    <literal><![CDATA[
      L((x \ y) \ y,x,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4683,a(flip),b,8867,a),flip(a)].">
      <j1 rule="hyper" parents="373 4683 8867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8869">
    <literal><![CDATA[
      L(T(x,x \ y),x,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1071,a,b,8868,a)].">
      <j1 rule="hyper" parents="64 1071 8868"/>
    </justification>
  </clause>

  <clause id="8870">
    <literal><![CDATA[
      1 / (K(x \ y,x) / x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5952,a(flip),b,8869,a)].">
      <j1 rule="hyper" parents="64 5952 8869"/>
    </justification>
  </clause>

  <clause id="8871">
    <literal><![CDATA[
      R(T(x,x * y),x,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(42,a,4754,a,b,8869,a)].">
      <j1 rule="hyper" parents="42 4754 8869"/>
    </justification>
  </clause>

  <clause id="8872">
    <literal><![CDATA[
      1 / T(x,x \ y) = T(x,x * y) \ 1
    ]]></literal>
    <justification jstring="[para(8869(a,1),3571(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8869 3571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8873">
    <literal><![CDATA[
      T(T(x,x \ 1),y * x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4697,a,b,8871,a)].">
      <j1 rule="hyper" parents="64 4697 8871"/>
    </justification>
  </clause>

  <clause id="8874">
    <literal><![CDATA[
      T(x,x \ (x \ y)) = R(T(x,y),x,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),8871(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 8871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8875">
    <literal><![CDATA[
      (x \ 1) * T(x,x \ y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(8871(a,1),6365(a,2,2)),flip(a)].">
      <j1 rule="para" parents="8871 6365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8876">
    <literal><![CDATA[
      R(T(x,y),x,x) \ y = (x \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[para(8874(a,1),4714(a,1,1))].">
      <j1 rule="para" parents="8874 4714"/>
    </justification>
  </clause>

  <clause id="8877">
    <literal><![CDATA[
      x / R(T(y,x),y,y) = (y \ (x / y)) * y
    ]]></literal>
    <justification jstring="[para(8874(a,1),7199(a,1,2))].">
      <j1 rule="para" parents="8874 7199"/>
    </justification>
  </clause>

  <clause id="8878">
    <literal><![CDATA[
      K(x \ y,x) / x = x \ K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(37,a,5877,a(flip),b,8870,a),flip(a)].">
      <j1 rule="hyper" parents="37 5877 8870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8879">
    <literal><![CDATA[
      (T(x,x * y) \ 1) * x = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(8870(a,1),223(a,1,1,1))].">
      <j1 rule="para" parents="8870 223"/>
    </justification>
  </clause>

  <clause id="8880">
    <literal><![CDATA[
      x * (1 / T(x,x \ y)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,8872,a,b,5783,a(flip))].">
      <j1 rule="hyper" parents="145 8872 5783"/>
    </justification>
  </clause>

  <clause id="8881">
    <literal><![CDATA[
      (T(x,x * y) \ 1) * (y / x) = (x * x) \ y
    ]]></literal>
    <justification jstring="[para(8872(a,1),7055(a,1,1))].">
      <j1 rule="para" parents="8872 7055"/>
    </justification>
  </clause>

  <clause id="8882">
    <literal><![CDATA[
      T((x \ 1) \ 1,y * x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,866,a(flip),b,8873,a)].">
      <j1 rule="hyper" parents="64 866 8873"/>
    </justification>
  </clause>

  <clause id="8883">
    <literal><![CDATA[
      T(x,x \ 1) * (y * x) = (y * x) * T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,8873,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 8873 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8884">
    <literal><![CDATA[
      K(x \ (x \ y),x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),8879(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 8879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8885">
    <literal><![CDATA[
      K(x \ (x \ y),x) = (x \ K(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,5939,a(flip),b,8884,a),flip(a)].">
      <j1 rule="hyper" parents="373 5939 8884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8886">
    <literal><![CDATA[
      ((1 / x) * y) \ L(y,x,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4683,a(flip),b,8866,a),flip(a)].">
      <j1 rule="hyper" parents="373 4683 8866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8887">
    <literal><![CDATA[
      ((1 / x) * y) * T(x,x * y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,4683,a(flip),b,8866,a)].">
      <j1 rule="hyper" parents="145 4683 8866"/>
    </justification>
  </clause>

  <clause id="8888">
    <literal><![CDATA[
      ((T(x,x * y) \ 1) * (y / x)) \ (y / x) = (y / x) / T((x * x) \ y,T(x,x * y))
    ]]></literal>
    <justification jstring="[para(8881(a,1),4594(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8881 4594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8889">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,8097,a(flip),b,8551,a),flip(a)].">
      <j1 rule="hyper" parents="373 8097 8551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8890">
    <literal><![CDATA[
      T(x,T(y / (z / x),u)) = T(x,T(y / (x \ z),u))
    ]]></literal>
    <justification jstring="[hyper(143,a,8628,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 8628 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8891">
    <literal><![CDATA[
      T((x \ y) * T(x,z),x) = (x \ T(y,x)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(3428(a,1),8637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3428 8637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8892">
    <literal><![CDATA[
      T(x,x \ 1) \ R(x,y,z) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3513,a(flip),b,8641,a),flip(a)].">
      <j1 rule="hyper" parents="64 3513 8641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8893">
    <literal><![CDATA[
      (x \ R(x,y,z)) * T(K(u,x),w) = T(x,T(u,w)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(7433(a,1),8641(a,1,2))].">
      <j1 rule="para" parents="7433 8641"/>
    </justification>
  </clause>

  <clause id="8894">
    <literal><![CDATA[
      T(x,x \ 1) \ L(x,y,z) = (x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5613,a(flip),b,8642,a),flip(a)].">
      <j1 rule="hyper" parents="64 5613 8642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8895">
    <literal><![CDATA[
      T(x / T(T(y,x),z),y) = T(y,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6137,a(flip),b,8650,a),flip(a)].">
      <j1 rule="hyper" parents="373 6137 8650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8896">
    <literal><![CDATA[
      T(x / T(T(y,z),x),y) = T(y,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(23(a,1),8895(a,1,1,2))].">
      <j1 rule="para" parents="23 8895"/>
    </justification>
  </clause>

  <clause id="8900">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(y / (x * z),x)
    ]]></literal>
    <justification jstring="[hyper(35,a,8363,a(flip),b,8683,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 8363 8683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8901">
    <literal><![CDATA[
      x * K(y,T(z \ x,u)) != w * x
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x / z,u)) = w
    ]]></literal>
    <justification jstring="[para(8698(a,1),45(a,1))].">
      <j1 rule="para" parents="8698 45"/>
    </justification>
  </clause>

  <clause id="8902">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,(z \ (z * y)) \ 1)
    ]]></literal>
    <justification jstring="[para(5934(a,1),8702(a,1,1,2))].">
      <j1 rule="para" parents="5934 8702"/>
    </justification>
  </clause>

  <clause id="8903">
    <literal><![CDATA[
      K(x,x \ y) * (z / (y / x)) = T(z / (x \ y),K(x,y))
    ]]></literal>
    <justification jstring="[para(6455(a,1),8708(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6455 8708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8904">
    <literal><![CDATA[
      ((x \ y) \ z) * K(x \ y,x) = T((y / x) \ z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6292(a,1),8709(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6292 8709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8905">
    <literal><![CDATA[
      K(x \ y,x) * (z * (y / x)) = T(z * (x \ y),K(x,y))
    ]]></literal>
    <justification jstring="[para(6886(a,1),8710(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6886 8710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8906">
    <literal><![CDATA[
      K(x \ y,x) * (z / (x \ y)) = T(z / (y / x),K(x,y))
    ]]></literal>
    <justification jstring="[para(6887(a,1),8710(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6887 8710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8907">
    <literal><![CDATA[
      T(T((x / y) \ z,K(x,y)),u) = T(T(z / (x / y),u),y \ x)
    ]]></literal>
    <justification jstring="[para(8723(a,1),23(a,1,1))].">
      <j1 rule="para" parents="8723 23"/>
    </justification>
  </clause>

  <clause id="8908">
    <literal><![CDATA[
      K(x,y * K(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8397,a(flip),b,8740,a),flip(a)].">
      <j1 rule="hyper" parents="64 8397 8740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8909">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(8592,a,8778,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8592 8778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8910">
    <literal><![CDATA[
      K((x * T(y,z)) \ u,z) = K((x * y) \ u,z)
    ]]></literal>
    <justification jstring="[para(6249(a,1),8909(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6249 8909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8911">
    <literal><![CDATA[
      K(T(x \ T(y,x),z) \ u,z) = K((T(x,y) \ y) \ u,z)
    ]]></literal>
    <justification jstring="[para(5820(a,1),8909(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5820 8909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8912">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ u,y)
    ]]></literal>
    <justification jstring="[para(7456(a,1),8909(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7456 8909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8913">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(7591(a,1),8909(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7591 8909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8914">
    <literal><![CDATA[
      K(x \ K(y,z),y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(6832,a,8912,a)].">
      <j1 rule="hyper" parents="6832 8912"/>
    </justification>
  </clause>

  <clause id="8915">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7792,a(flip),b,8912,a)].">
      <j1 rule="hyper" parents="64 7792 8912"/>
    </justification>
  </clause>

  <clause id="8916">
    <literal><![CDATA[
      K(x,y) * K(z \ 1,x) = z * T(z \ K(x,y),x)
    ]]></literal>
    <justification jstring="[para(8914(a,1),6763(a,2,2)),flip(a)].">
      <j1 rule="para" parents="8914 6763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8918">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(6161(a,1),8915(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6161 8915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8919">
    <literal><![CDATA[
      K(x \ (y / z),z \ y) = K(x \ (z \ y),z \ y)
    ]]></literal>
    <justification jstring="[para(5956(a,1),8915(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5956 8915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8920">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(8205(a,1),8915(a,1,1,2,1))].">
      <j1 rule="para" parents="8205 8915"/>
    </justification>
  </clause>

  <clause id="8921">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(8193(a,1),8915(a,1,1,2))].">
      <j1 rule="para" parents="8193 8915"/>
    </justification>
  </clause>

  <clause id="8922">
    <literal><![CDATA[
      K(x \ (y / (z * y)),z \ 1) = K(x \ ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(6382(a,1),8918(a,1,1,2))].">
      <j1 rule="para" parents="6382 8918"/>
    </justification>
  </clause>

  <clause id="8923">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u)
    ]]></literal>
    <justification jstring="[para(7591(a,1),8921(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7591 8921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8924">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * (x \ z)) \ u)) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(8804(a,1),6177(a,1,2,2))].">
      <j1 rule="para" parents="8804 6177"/>
    </justification>
  </clause>

  <clause id="8925">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(8810(a,2),6899(a,1))].">
      <j1 rule="para" parents="8810 6899"/>
    </justification>
  </clause>

  <clause id="8926">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ u) = w
    ]]></literal>
    <justification jstring="[para(6576(a,1),8925(a,1,2,1))].">
      <j1 rule="para" parents="6576 8925"/>
    </justification>
  </clause>

  <clause id="8927">
    <literal><![CDATA[
      K(x,(T(y,x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(6570(a,1),8925(a,1,2,1))].">
      <j1 rule="para" parents="6570 8925"/>
    </justification>
  </clause>

  <clause id="8928">
    <literal><![CDATA[
      K(T(x,y),(z * K(u,x)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z \ w) = v5
    ]]></literal>
    <justification jstring="[para(7919(a,1),8925(a,1,2,1,2))].">
      <j1 rule="para" parents="7919 8925"/>
    </justification>
  </clause>

  <clause id="8929">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(7791(a,1),8926(a,1))].">
      <j1 rule="para" parents="7791 8926"/>
    </justification>
  </clause>

  <clause id="8930">
    <literal><![CDATA[
      K(x,y \ (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * x)) = u
    ]]></literal>
    <justification jstring="[para(5796(a,1),8929(a,1,2,2))].">
      <j1 rule="para" parents="5796 8929"/>
    </justification>
  </clause>

  <clause id="8931">
    <literal><![CDATA[
      L(T(x,y \ ((x \ z) \ u)),w,v5) \ L(x,w,v5) = K(y \ ((z / x) \ u),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(8822(a,1),5801(a,1,1,1))].">
      <j1 rule="para" parents="8822 5801"/>
    </justification>
  </clause>

  <clause id="8932">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ (z * (x \ u))) = K(x,(z * (u / x)) \ (y \ (z * (u / x))))
    ]]></literal>
    <justification jstring="[hyper(8463,a,8825,a),flip(a)].">
      <j1 rule="hyper" parents="8463 8825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8933">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8088(a,1),8839(a,1,1))].">
      <j1 rule="para" parents="8088 8839"/>
    </justification>
  </clause>

  <clause id="8934">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x,z) = K(x,z) / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(332,a,8845,a),flip(a)].">
      <j1 rule="hyper" parents="332 8845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8935">
    <literal><![CDATA[
      ((x * K(y,z)) / z) * K(z,u) = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[para(6312(a,2),8845(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6312 8845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8936">
    <literal><![CDATA[
      K(x,R(T(y,x * z),u,w)) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),8848(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8937">
    <literal><![CDATA[
      (x \ R(x,y,x)) * T(K(y,x),z) = K(y * x,x) * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8531(a,1),8851(a,1,1))].">
      <j1 rule="para" parents="8531 8851"/>
    </justification>
  </clause>

  <clause id="8938">
    <literal><![CDATA[
      K(x,K(y,z \ 1) / z) = K(T(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(5826,a,8855,a)].">
      <j1 rule="hyper" parents="5826 8855"/>
    </justification>
  </clause>

  <clause id="8939">
    <literal><![CDATA[
      K(T(x,((y \ 1) / ((1 / (y \ 1)) \ z)) \ 1),y \ 1) = K(x,K(z,y \ 1) / y)
    ]]></literal>
    <justification jstring="[para(7430(a,1),8938(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7430 8938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8940">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,8889,a(flip),b,8858,a),flip(a)].">
      <j1 rule="hyper" parents="373 8889 8858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8942">
    <literal><![CDATA[
      T(K(x,y),z * K(y,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6878(a,1),8940(a,1,2))].">
      <j1 rule="para" parents="6878 8940"/>
    </justification>
  </clause>

  <clause id="8943">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ (z / x)) = (z / T(x,y)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(6245(a,1),8860(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6245 8860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8944">
    <literal><![CDATA[
      T(T(x,y) * R(x \ z,u,w),x) = T(x,y) * R(x \ T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(2820(a,1),8864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2820 8864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8945">
    <literal><![CDATA[
      K(((x \ 1) * (y * x)) \ z,x) = K(L(y,x,x \ 1) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5269,a(flip),b,8913,a),flip(a)].">
      <j1 rule="hyper" parents="373 5269 8913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8946">
    <literal><![CDATA[
      R((x \ y) * K(z \ (x \ y),x \ y),u,w) \ R(x \ y,u,w) = K(R(x \ y,u,w),z \ (y / x))
    ]]></literal>
    <justification jstring="[para(8919(a,1),7073(a,1,1,1,2))].">
      <j1 rule="para" parents="8919 7073"/>
    </justification>
  </clause>

  <clause id="8947">
    <literal><![CDATA[
      K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(L(u,z,y),y * z,x),y)
    ]]></literal>
    <justification jstring="[para(602(a,1),8923(a,2,1))].">
      <j1 rule="para" parents="602 8923"/>
    </justification>
  </clause>

  <clause id="8948">
    <literal><![CDATA[
      K(x,y) \ (K(x,K(y,z)) \ u) = K(x,T(y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(757,a,8933,a),flip(a)].">
      <j1 rule="hyper" parents="757 8933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8949">
    <literal><![CDATA[
      K(x,(x * y) \ ((x * z) * y)) = K(x,R(T(z,y),x,y))
    ]]></literal>
    <justification jstring="[hyper(5981,a,8936,a)].">
      <j1 rule="hyper" parents="5981 8936"/>
    </justification>
  </clause>

  <clause id="8950">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(7886(a,1),7819(a,1,2))].">
      <j1 rule="para" parents="7886 7819"/>
    </justification>
  </clause>

  <clause id="8951">
    <literal><![CDATA[
      T(x \ R(x,y,x),y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6496,a,8950,a),flip(a)].">
      <j1 rule="hyper" parents="6496 8950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8952">
    <literal><![CDATA[
      (x * (y \ R(y,x,y))) / x = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(313,a,8951,a)].">
      <j1 rule="hyper" parents="313 8951"/>
    </justification>
  </clause>

  <clause id="8953">
    <literal><![CDATA[
      (T(x * y,x) / x) / y = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(7023(a,1),8952(a,1,1))].">
      <j1 rule="para" parents="7023 8952"/>
    </justification>
  </clause>

  <clause id="8954">
    <literal><![CDATA[
      L(x,T(y,z),x) != u * K(y,T(x,z))
    ]]></literal>
    <literal><![CDATA[
      T(x,x * T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7911(a,1),45(a,1))].">
      <j1 rule="para" parents="7911 45"/>
    </justification>
  </clause>

  <clause id="8955">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * z != v5 * v6
    ]]></literal>
    <literal><![CDATA[
      (z * K(x,L(y,u,w))) / v6 = v5
    ]]></literal>
    <justification jstring="[para(25(a,2),8250(a,1,1,2))].">
      <j1 rule="para" parents="25 8250"/>
    </justification>
  </clause>

  <clause id="8956">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(7888(a,1),8401(a,1))].">
      <j1 rule="para" parents="7888 8401"/>
    </justification>
  </clause>

  <clause id="8957">
    <literal><![CDATA[
      (T(x,y) \ y) * ((x \ y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(8741,a,6326,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8741 6326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8958">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8763,a,8064,a)].">
      <j1 rule="hyper" parents="8763 8064"/>
    </justification>
  </clause>

  <clause id="8959">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8434,a,8958,a)].">
      <j1 rule="hyper" parents="8434 8958"/>
    </justification>
  </clause>

  <clause id="8960">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,8622,a,b,8958,a)].">
      <j1 rule="hyper" parents="64 8622 8958"/>
    </justification>
  </clause>

  <clause id="8961">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(10(a,1),8958(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 8958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8962">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),8959(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 8959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8963">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6142(a,2),8959(a,1,2))].">
      <j1 rule="para" parents="6142 8959"/>
    </justification>
  </clause>

  <clause id="8964">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(6368(a,1),8959(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6368 8959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8965">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8088,a,b,8960,a),flip(a)].">
      <j1 rule="hyper" parents="373 8088 8960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8967">
    <literal><![CDATA[
      K(x \ y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8434,a,8961,a)].">
      <j1 rule="hyper" parents="8434 8961"/>
    </justification>
  </clause>

  <clause id="8968">
    <literal><![CDATA[
      T(x,K(y,x \ z)) = K(z,K(x,y)) * x
    ]]></literal>
    <justification jstring="[para(8961(a,1),8115(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8961 8115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8969">
    <literal><![CDATA[
      K(x,K(x \ y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8439,a,8962,a)].">
      <j1 rule="hyper" parents="8439 8962"/>
    </justification>
  </clause>

  <clause id="8970">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8108,a,b,8963,a),flip(a)].">
      <j1 rule="hyper" parents="373 8108 8963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8971">
    <literal><![CDATA[
      K(x,K(a(y,z,u),(y * z) * u)) = K(x,K(a(y,z,u),y * (z * u)))
    ]]></literal>
    <justification jstring="[para(88(a,1),8963(a,1,2,2))].">
      <j1 rule="para" parents="88 8963"/>
    </justification>
  </clause>

  <clause id="8972">
    <literal><![CDATA[
      K(x,K(y,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8963(a,2),8437(a,1))].">
      <j1 rule="para" parents="8963 8437"/>
    </justification>
  </clause>

  <clause id="8973">
    <literal><![CDATA[
      K(x,K(y \ x,z)) = K(y,K(y \ x,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),8965(a,1,1))].">
      <j1 rule="para" parents="10 8965"/>
    </justification>
  </clause>

  <clause id="8974">
    <literal><![CDATA[
      K(x * y,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8965(a,1),8089(a,1,2))].">
      <j1 rule="para" parents="8965 8089"/>
    </justification>
  </clause>

  <clause id="8975">
    <literal><![CDATA[
      K(x \ y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8967(a,2),8436(a,1))].">
      <j1 rule="para" parents="8967 8436"/>
    </justification>
  </clause>

  <clause id="8976">
    <literal><![CDATA[
      K(x,K(x \ y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8110,a,b,8969,a),flip(a)].">
      <j1 rule="hyper" parents="373 8110 8969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8977">
    <literal><![CDATA[
      K(x,K(x \ y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8969(a,2),8439(a,1))].">
      <j1 rule="para" parents="8969 8439"/>
    </justification>
  </clause>

  <clause id="8978">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8436,a,8970,a)].">
      <j1 rule="hyper" parents="8436 8970"/>
    </justification>
  </clause>

  <clause id="8979">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8437,a,8976,a)].">
      <j1 rule="hyper" parents="8437 8976"/>
    </justification>
  </clause>

  <clause id="8980">
    <literal><![CDATA[
      T(x,K(y,z * x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,8978,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 8978 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8981">
    <literal><![CDATA[
      T(x,K(y,z * x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8153,a,b,8980,a),flip(a)].">
      <j1 rule="hyper" parents="373 8153 8980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8982">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),8980(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 8980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8983">
    <literal><![CDATA[
      T((x * y) \ y,K(z,x * y)) = (x * y) \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,8981,a(flip),b,8423,a),flip(a)].">
      <j1 rule="hyper" parents="139 8981 8423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8984">
    <literal><![CDATA[
      T(x,K(y,x \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8129,a(flip),b,8968,a),flip(a)].">
      <j1 rule="hyper" parents="373 8129 8968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8985">
    <literal><![CDATA[
      T(x,K(x \ y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8184,a,8984,a)].">
      <j1 rule="hyper" parents="8184 8984"/>
    </justification>
  </clause>

  <clause id="8986">
    <literal><![CDATA[
      T(x / y,K(z,y)) = T(x / y,K(z,x))
    ]]></literal>
    <justification jstring="[para(82(a,1),8984(a,1,2,2))].">
      <j1 rule="para" parents="82 8984"/>
    </justification>
  </clause>

  <clause id="8987">
    <literal><![CDATA[
      K(x,K(y \ x,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,8969,a(flip),b,8973,a),flip(a)].">
      <j1 rule="hyper" parents="373 8969 8973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8988">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8434,a,8987,a)].">
      <j1 rule="hyper" parents="8434 8987"/>
    </justification>
  </clause>

  <clause id="8989">
    <literal><![CDATA[
      K(x,K(y \ x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8088,a,b,8987,a),flip(a)].">
      <j1 rule="hyper" parents="373 8088 8987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8990">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,8088,a,b,8988,a),flip(a)].">
      <j1 rule="hyper" parents="373 8088 8988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8991">
    <literal><![CDATA[
      K(x,K(x / y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(82(a,1),8989(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 8989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8992">
    <literal><![CDATA[
      K(x \ y,z) * K(y,K(x,z)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(8989(a,1),6779(a,1,2))].">
      <j1 rule="para" parents="8989 6779"/>
    </justification>
  </clause>

  <clause id="8994">
    <literal><![CDATA[
      K(x,K(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8990(a,2),8434(a,1))].">
      <j1 rule="para" parents="8990 8434"/>
    </justification>
  </clause>

  <clause id="8995">
    <literal><![CDATA[
      K(x,K(x / y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8126,a,b,8991,a),flip(a)].">
      <j1 rule="hyper" parents="373 8126 8991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8997">
    <literal><![CDATA[
      K(x,K(y,x / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8437,a,8995,a)].">
      <j1 rule="hyper" parents="8437 8995"/>
    </justification>
  </clause>

  <clause id="8998">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,8997,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 8997 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8999">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),8997(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 8997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9000">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x / z,y) = K(z \ x,y)
    ]]></literal>
    <justification jstring="[para(8997(a,1),7936(a,1,1))].">
      <j1 rule="para" parents="8997 7936"/>
    </justification>
  </clause>

  <clause id="9001">
    <literal><![CDATA[
      T(x,K(y,z \ x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),8998(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 8998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9002">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),K(z,(y * x) / u)) = (T(y * x,K(z,u)) / x) / y
    ]]></literal>
    <justification jstring="[para(8998(a,1),6589(a,2,1,1))].">
      <j1 rule="para" parents="8998 6589"/>
    </justification>
  </clause>

  <clause id="9003">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ x) = T(z \ x,K(x,y))
    ]]></literal>
    <justification jstring="[para(8999(a,1),8122(a,1,1))].">
      <j1 rule="para" parents="8999 8122"/>
    </justification>
  </clause>

  <clause id="9004">
    <literal><![CDATA[
      T(x,K(y,z \ x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8153,a,b,9001,a),flip(a)].">
      <j1 rule="hyper" parents="373 8153 9001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9005">
    <literal><![CDATA[
      K(x,y) \ T(x / z,K(y,z)) = (x / z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,8986,a,b,6175,a)].">
      <j1 rule="hyper" parents="139 8986 6175"/>
    </justification>
  </clause>

  <clause id="9006">
    <literal><![CDATA[
      K(x,K(y \ z,T(y,u))) = K(y,K(z,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(8975,a,8138,a),flip(a)].">
      <j1 rule="hyper" parents="8975 8138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9007">
    <literal><![CDATA[
      K(x,K(y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8126(a,1),8994(a,1))].">
      <j1 rule="para" parents="8126 8994"/>
    </justification>
  </clause>

  <clause id="9008">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(9007,a,8964,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="9007 8964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9009">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8437,a,9008,a)].">
      <j1 rule="hyper" parents="8437 9008"/>
    </justification>
  </clause>

  <clause id="9010">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8126,a,b,9008,a),flip(a)].">
      <j1 rule="hyper" parents="373 8126 9008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9011">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8108,a,b,9008,a),flip(a)].">
      <j1 rule="hyper" parents="373 8108 9008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9012">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(143,a,9008,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 9008 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9013">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6700(a,1),9008(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6700 9008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9014">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(9008(a,2),8437(a,1))].">
      <j1 rule="para" parents="9008 8437"/>
    </justification>
  </clause>

  <clause id="9015">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8108,a,b,9009,a),flip(a)].">
      <j1 rule="hyper" parents="373 8108 9009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9016">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8110,a(flip),b,9009,a),flip(a)].">
      <j1 rule="hyper" parents="373 8110 9009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9017">
    <literal><![CDATA[
      K(x,y * ((z \ (y \ 1)) * z)) = K(x,K(y * z,z))
    ]]></literal>
    <justification jstring="[para(6677(a,2),9009(a,1,2))].">
      <j1 rule="para" parents="6677 9009"/>
    </justification>
  </clause>

  <clause id="9018">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,9010,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 9010 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9019">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8964,a(flip),b,9010,a)].">
      <j1 rule="hyper" parents="64 8964 9010"/>
    </justification>
  </clause>

  <clause id="9020">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(82(a,1),9010(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 9010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9021">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[para(6375(a,1),9010(a,1,2))].">
      <j1 rule="para" parents="6375 9010"/>
    </justification>
  </clause>

  <clause id="9022">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(6378(a,2),9010(a,1,2))].">
      <j1 rule="para" parents="6378 9010"/>
    </justification>
  </clause>

  <clause id="9023">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6700(a,1),9010(a,1,2))].">
      <j1 rule="para" parents="6700 9010"/>
    </justification>
  </clause>

  <clause id="9024">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8435,a,9011,a)].">
      <j1 rule="hyper" parents="8435 9011"/>
    </justification>
  </clause>

  <clause id="9025">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(82(a,1),9011(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 9011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9026">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(9012(a,2),8184(a,1))].">
      <j1 rule="para" parents="9012 8184"/>
    </justification>
  </clause>

  <clause id="9028">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,(T(u,x) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(6696(a,1),9016(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6696 9016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9029">
    <literal><![CDATA[
      K(x,y \ 1) * T(z,K(x,y)) = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,9018,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 9018 22"/>
    </justification>
  </clause>

  <clause id="9030">
    <literal><![CDATA[
      T(x,K(y,z \ y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,9019,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 9019 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9032">
    <literal><![CDATA[
      T(1 / x,K(y,z)) = K(x,K(y,z)) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,9024,a(flip),b,5989,a),flip(a)].">
      <j1 rule="hyper" parents="142 9024 5989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9033">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) = x \ K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,9024,a(flip),b,5743,a),flip(a)].">
      <j1 rule="hyper" parents="139 9024 5743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9034">
    <literal><![CDATA[
      (T(x * y,K(z,u)) / y) / x = K(z,K(u,(1 / y) / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,6589,a(flip),b,9025,a)].">
      <j1 rule="hyper" parents="64 6589 9025"/>
    </justification>
  </clause>

  <clause id="9035">
    <literal><![CDATA[
      K(1 / x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(9025(a,2),8437(a,1))].">
      <j1 rule="para" parents="9025 8437"/>
    </justification>
  </clause>

  <clause id="9036">
    <literal><![CDATA[
      K(x,K(y \ (z * u),u \ (z \ 1))) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(7669(a,1),9013(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7669 9013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9037">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(9013(a,1),8437(a,1))].">
      <j1 rule="para" parents="9013 8437"/>
    </justification>
  </clause>

  <clause id="9038">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(9022(a,2),8437(a,1))].">
      <j1 rule="para" parents="9022 8437"/>
    </justification>
  </clause>

  <clause id="9039">
    <literal><![CDATA[
      x * T(x \ y,K(z,u)) = y * K(z,K(u,y \ x))
    ]]></literal>
    <justification jstring="[para(9023(a,1),8132(a,2,2))].">
      <j1 rule="para" parents="9023 8132"/>
    </justification>
  </clause>

  <clause id="9040">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) = T(x,K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,8145,a,b,9033,a),flip(a)].">
      <j1 rule="hyper" parents="373 8145 9033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9041">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) = x \ K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8108(a,1),9033(a,2,2))].">
      <j1 rule="para" parents="8108 9033"/>
    </justification>
  </clause>

  <clause id="9042">
    <literal><![CDATA[
      T(1 / x,K(y,z)) \ 1 = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(40,a,8074,a,b,9040,a(flip))].">
      <j1 rule="hyper" parents="40 8074 9040"/>
    </justification>
  </clause>

  <clause id="9043">
    <literal><![CDATA[
      T(T(x,y) \ 1,K(z,y)) = T(x,T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(8162(a,1),9040(a,2,1))].">
      <j1 rule="para" parents="8162 9040"/>
    </justification>
  </clause>

  <clause id="9044">
    <literal><![CDATA[
      L(T(x \ 1,K(y,z)),x,y) = (y * x) \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(9041(a,2),5768(a,1,1))].">
      <j1 rule="para" parents="9041 5768"/>
    </justification>
  </clause>

  <clause id="9045">
    <literal><![CDATA[
      1 / T(x,K(y,z)) = T(1 / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(226,a,9042,a)].">
      <j1 rule="hyper" parents="226 9042"/>
    </justification>
  </clause>

  <clause id="9046">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = 1 / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(225,a,6881,a(flip),b,9042,a),flip(a)].">
      <j1 rule="hyper" parents="225 6881 9042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9047">
    <literal><![CDATA[
      K(x,K(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6041(a,2),9014(a,1,2))].">
      <j1 rule="para" parents="6041 9014"/>
    </justification>
  </clause>

  <clause id="9048">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(6375(a,1),9014(a,1,2))].">
      <j1 rule="para" parents="6375 9014"/>
    </justification>
  </clause>

  <clause id="9049">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(6378(a,2),9014(a,1,2))].">
      <j1 rule="para" parents="6378 9014"/>
    </justification>
  </clause>

  <clause id="9050">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(6700(a,1),9026(a,1,2))].">
      <j1 rule="para" parents="6700 9026"/>
    </justification>
  </clause>

  <clause id="9051">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,K(w,u) / z)) = v5
    ]]></literal>
    <justification jstring="[para(6915(a,1),9047(a,1,2))].">
      <j1 rule="para" parents="6915 9047"/>
    </justification>
  </clause>

  <clause id="9052">
    <literal><![CDATA[
      K(x / y,z) * K(x,K(y,z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,8992,a(flip),b,8141,a)].">
      <j1 rule="hyper" parents="144 8992 8141"/>
    </justification>
  </clause>

  <clause id="9053">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(8088(a,1),9000(a,1,1))].">
      <j1 rule="para" parents="8088 9000"/>
    </justification>
  </clause>

  <clause id="9054">
    <literal><![CDATA[
      T(x \ y,K(y,z)) = T(x,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[hyper(8104,a,9003,a),flip(a)].">
      <j1 rule="hyper" parents="8104 9003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9055">
    <literal><![CDATA[
      K(x,K(y \ z,T(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,T(z,u))) = w
    ]]></literal>
    <justification jstring="[para(9006(a,2),8440(a,1))].">
      <j1 rule="para" parents="9006 8440"/>
    </justification>
  </clause>

  <clause id="9056">
    <literal><![CDATA[
      K(x / y,z * (x \ y)) * K(x,K(y,z * (x \ y))) = K(y \ x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,7238,a,b,9052,a),flip(a)].">
      <j1 rule="hyper" parents="373 7238 9052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9057">
    <literal><![CDATA[
      K(x / y,z) * K(z,K(y,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(8088(a,1),9052(a,1,2))].">
      <j1 rule="para" parents="8088 9052"/>
    </justification>
  </clause>

  <clause id="9058">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ z,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[hyper(8148,a,9053,a)].">
      <j1 rule="hyper" parents="8148 9053"/>
    </justification>
  </clause>

  <clause id="9059">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,x) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6187,a,9057,a)].">
      <j1 rule="hyper" parents="6187 9057"/>
    </justification>
  </clause>

  <clause id="9060">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z \ y,x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[para(8110(a,2),9058(a,1,1))].">
      <j1 rule="para" parents="8110 9058"/>
    </justification>
  </clause>

  <clause id="9061">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ y,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(8126(a,1),9058(a,1,1))].">
      <j1 rule="para" parents="8126 9058"/>
    </justification>
  </clause>

  <clause id="9062">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(6897,a,9059,a)].">
      <j1 rule="hyper" parents="6897 9059"/>
    </justification>
  </clause>

  <clause id="9063">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(8148,a,9062,a)].">
      <j1 rule="hyper" parents="8148 9062"/>
    </justification>
  </clause>

  <clause id="9064">
    <literal><![CDATA[
      K(x,K(y,z \ (y * u))) * K(x,y \ ((y \ z) \ u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(7149(a,1),9062(a,1,1,2))].">
      <j1 rule="para" parents="7149 9062"/>
    </justification>
  </clause>

  <clause id="9065">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[para(8110(a,1),9062(a,1,1))].">
      <j1 rule="para" parents="8110 9062"/>
    </justification>
  </clause>

  <clause id="9066">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(8126(a,1),9062(a,1,1))].">
      <j1 rule="para" parents="8126 9062"/>
    </justification>
  </clause>

  <clause id="9067">
    <literal><![CDATA[
      K(x,y / z) * K(x,K(z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(7445,a,9063,a)].">
      <j1 rule="hyper" parents="7445 9063"/>
    </justification>
  </clause>

  <clause id="9068">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z / x) = K(y,x \ z)
    ]]></literal>
    <justification jstring="[para(8108(a,1),9063(a,1,1))].">
      <j1 rule="para" parents="8108 9063"/>
    </justification>
  </clause>

  <clause id="9069">
    <literal><![CDATA[
      K(x,((y * z) \ z) * K(y * z,1 / y)) = K(z,K(x,y * z)) * K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[para(6384(a,2),9065(a,2,2)),flip(a)].">
      <j1 rule="para" parents="6384 9065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9070">
    <literal><![CDATA[
      K(x,y \ z) * K(x,K(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(7445,a,9066,a)].">
      <j1 rule="hyper" parents="7445 9066"/>
    </justification>
  </clause>

  <clause id="9071">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) * K(x,((u * z) \ u) \ y) = K(x,y / ((u * z) \ u))
    ]]></literal>
    <justification jstring="[para(6705(a,1),9066(a,1,1,2))].">
      <j1 rule="para" parents="6705 9066"/>
    </justification>
  </clause>

  <clause id="9072">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,(u / (z * u)) \ y) = K(x,y / (u / (z * u)))
    ]]></literal>
    <justification jstring="[para(9022(a,1),9066(a,1,1))].">
      <j1 rule="para" parents="9022 9066"/>
    </justification>
  </clause>

  <clause id="9073">
    <literal><![CDATA[
      K(x,K(y,x / (1 / (1 / z)))) * K(y,(x / (1 / (1 / z))) / x) = K(y,1 / (1 / (x \ (x / z))))
    ]]></literal>
    <justification jstring="[para(3942(a,2),9068(a,2,2))].">
      <j1 rule="para" parents="3942 9068"/>
    </justification>
  </clause>

  <clause id="9074">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) * K(x,K(y,z \ (y * u))) = K(x,y / ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(7149(a,1),9070(a,1,2,2))].">
      <j1 rule="para" parents="7149 9070"/>
    </justification>
  </clause>

  <clause id="9075">
    <literal><![CDATA[
      K(x,y) \ T(x / z,K(z,y)) = (x / z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8153(a,1),9005(a,1,2))].">
      <j1 rule="para" parents="8153 9005"/>
    </justification>
  </clause>

  <clause id="9076">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y \ z,z))
    ]]></literal>
    <justification jstring="[para(7571(a,1),9017(a,2,2))].">
      <j1 rule="para" parents="7571 9017"/>
    </justification>
  </clause>

  <clause id="9077">
    <literal><![CDATA[
      T(x / y,K(y,z)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8357,a,9075,a),flip(a)].">
      <j1 rule="hyper" parents="8357 9075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9078">
    <literal><![CDATA[
      x / (y * K(K(y,z),y \ x)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8050,a,b,9077,a)].">
      <j1 rule="hyper" parents="64 8050 9077"/>
    </justification>
  </clause>

  <clause id="9079">
    <literal><![CDATA[
      x / (y * K(y,K(z,y \ x))) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8092(a,1),9078(a,1,2,2))].">
      <j1 rule="para" parents="8092 9078"/>
    </justification>
  </clause>

  <clause id="9080">
    <literal><![CDATA[
      x / (y * K(y,K(x,z))) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8979(a,1),9079(a,1,2,2))].">
      <j1 rule="para" parents="8979 9079"/>
    </justification>
  </clause>

  <clause id="9081">
    <literal><![CDATA[
      x / T(y,K(z,x)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8139(a,1),9080(a,1,2))].">
      <j1 rule="para" parents="8139 9080"/>
    </justification>
  </clause>

  <clause id="9082">
    <literal><![CDATA[
      x / T(y,K(z,x)) = T(x / y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,8153,a,b,9081,a),flip(a)].">
      <j1 rule="hyper" parents="373 8153 9081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9083">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * y))) = K(x,R(T(z,y),x,y))
    ]]></literal>
    <justification jstring="[hyper(7417,a,8949,a)].">
      <j1 rule="hyper" parents="7417 8949"/>
    </justification>
  </clause>

  <clause id="9084">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * x) * z) = K(y,R(T(x,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7296,a(flip),b,9083,a)].">
      <j1 rule="hyper" parents="64 7296 9083"/>
    </justification>
  </clause>

  <clause id="9085">
    <literal><![CDATA[
      (x / (y * x)) * ((1 / y) \ (z * (y \ 1))) = (K(y \ 1,y) * z) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(7770(a,1),4824(a,1,2))].">
      <j1 rule="para" parents="7770 4824"/>
    </justification>
  </clause>

  <clause id="9086">
    <literal><![CDATA[
      R(K(x,y),z,R(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(664,a,7776,a)].">
      <j1 rule="hyper" parents="664 7776"/>
    </justification>
  </clause>

  <clause id="9087">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * R(y,u,w) = K(y,x) * ((x * z) * R(y,u,w))
    ]]></literal>
    <justification jstring="[para(4534(a,1),7776(a,1,1))].">
      <j1 rule="para" parents="4534 7776"/>
    </justification>
  </clause>

  <clause id="9088">
    <literal><![CDATA[
      K(x,y) * ((y * x) * R(x,z,u)) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(5796(a,1),7776(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5796 7776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9089">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,7756,a(flip),b,9086,a)].">
      <j1 rule="hyper" parents="64 7756 9086"/>
    </justification>
  </clause>

  <clause id="9090">
    <literal><![CDATA[
      K(x,y) * R(x,z,R(x,u,w)) = R(T(x,y),z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(144,a,9089,a(flip),b,5815,a)].">
      <j1 rule="hyper" parents="144 9089 5815"/>
    </justification>
  </clause>

  <clause id="9092">
    <literal><![CDATA[
      T((x \ K(y,x)) \ L((x \ 1) * (z / (x \ 1)),u,w),K(x,y)) = (L(z,u,w) / (x \ 1)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5547(a,1),7810(a,2,1))].">
      <j1 rule="para" parents="5547 7810"/>
    </justification>
  </clause>

  <clause id="9093">
    <literal><![CDATA[
      T(x \ y,z) \ K(x \ y,x) = T(y / x,T(z,x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,6428,a,b,7990,a)].">
      <j1 rule="hyper" parents="64 6428 7990"/>
    </justification>
  </clause>

  <clause id="9094">
    <literal><![CDATA[
      K(R(x,y,z),T(u,x \ w)) = K(R(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,7756,a(flip),b,8009,a),flip(a)].">
      <j1 rule="hyper" parents="64 7756 8009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9095">
    <literal><![CDATA[
      K(R(x,y,z),T(u,w)) * K(T(u,x \ w),R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,9094,a,b,6871,a),flip(a)].">
      <j1 rule="hyper" parents="140 9094 6871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9096">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(R(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(6682(a,1),8099(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6682 8099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9097">
    <literal><![CDATA[
      K(R(K(x,y),z,u),w) = K(y,R(K(x,w),z,u))
    ]]></literal>
    <justification jstring="[para(6682(a,1),8125(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6682 8125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9098">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,R(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9096,a,b,9097,a)].">
      <j1 rule="hyper" parents="64 9096 9097"/>
    </justification>
  </clause>

  <clause id="9099">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,R(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(8108(a,1),9098(a,1,1))].">
      <j1 rule="para" parents="8108 9098"/>
    </justification>
  </clause>

  <clause id="9100">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,((x / y) \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(12(a,1),8133(a,1,2,1))].">
      <j1 rule="para" parents="12 8133"/>
    </justification>
  </clause>

  <clause id="9101">
    <literal><![CDATA[
      T(x / T(x / (x / y),z),y) = T(x / T(y,z),K(y,z))
    ]]></literal>
    <justification jstring="[para(8388(a,1),8187(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8388 8187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9102">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,8226,a(flip),b,8238,a),flip(a)].">
      <j1 rule="hyper" parents="373 8226 8238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9104">
    <literal><![CDATA[
      K(x,L(y,z * K(y,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,7539,a(flip),b,9102,a)].">
      <j1 rule="hyper" parents="64 7539 9102"/>
    </justification>
  </clause>

  <clause id="9105">
    <literal><![CDATA[
      L(K(x,y),y * z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(115(a,1),9102(a,1,2))].">
      <j1 rule="para" parents="115 9102"/>
    </justification>
  </clause>

  <clause id="9106">
    <literal><![CDATA[
      L(K(x,y / z),y,u) = K(x,L(y / z,z,u))
    ]]></literal>
    <justification jstring="[para(247(a,1),9102(a,1,2))].">
      <j1 rule="para" parents="247 9102"/>
    </justification>
  </clause>

  <clause id="9107">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(248(a,1),9102(a,1,2)),flip(a)].">
      <j1 rule="para" parents="248 9102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9108">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * ((y * z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,9105,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 9105 18"/>
    </justification>
  </clause>

  <clause id="9109">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(5776(a,1),9105(a,1,2))].">
      <j1 rule="para" parents="5776 9105"/>
    </justification>
  </clause>

  <clause id="9110">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),y) = u
    ]]></literal>
    <justification jstring="[para(9105(a,1),7562(a,1))].">
      <j1 rule="para" parents="9105 7562"/>
    </justification>
  </clause>

  <clause id="9111">
    <literal><![CDATA[
      L(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1607(a,1),9107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1607 9107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9112">
    <literal><![CDATA[
      K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y \ 1,u) \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(9111(a,1),7304(a,1))].">
      <j1 rule="para" parents="9111 7304"/>
    </justification>
  </clause>

  <clause id="9114">
    <literal><![CDATA[
      K(x,L(y,K(y,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(7879(a,1),9104(a,1,2,2))].">
      <j1 rule="para" parents="7879 9104"/>
    </justification>
  </clause>

  <clause id="9115">
    <literal><![CDATA[
      ((x * (y * K(z,y))) / x) / ((x * y) / x) = K(T(z,x),y)
    ]]></literal>
    <justification jstring="[para(5721(a,1),8297(a,1,1,1,2))].">
      <j1 rule="para" parents="5721 8297"/>
    </justification>
  </clause>

  <clause id="9116">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z),u)) = K(x,T(T(y,z) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(8285,a,8337,a)].">
      <j1 rule="hyper" parents="8285 8337"/>
    </justification>
  </clause>

  <clause id="9117">
    <literal><![CDATA[
      K(x,T(T((y / z) \ 1,z),u)) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(117(a,1),9116(a,2,2,1,1))].">
      <j1 rule="para" parents="117 9116"/>
    </justification>
  </clause>

  <clause id="9118">
    <literal><![CDATA[
      T(K(x,y),T(z,x \ u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8095,a(flip),b,8345,a),flip(a)].">
      <j1 rule="hyper" parents="64 8095 8345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9119">
    <literal><![CDATA[
      T(K(x,y),T(z,x * u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),9118(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9120">
    <literal><![CDATA[
      1 / (K(x,y) * T(x,z)) = K(y,x) / T(x,z)
    ]]></literal>
    <justification jstring="[para(8205(a,1),8364(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8205 8364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9121">
    <literal><![CDATA[
      K(x,y) / T(y,T(z,x)) = 1 / T(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(8041(a,1),9120(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8041 9120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9123">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,z \ y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(4707(a,1),8380(a,1,2,1))].">
      <j1 rule="para" parents="4707 8380"/>
    </justification>
  </clause>

  <clause id="9124">
    <literal><![CDATA[
      T(x,T(x * (y \ 1),z)) = T(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8369,a(flip),b,8413,a),flip(a)].">
      <j1 rule="hyper" parents="64 8369 8413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9125">
    <literal><![CDATA[
      ((x \ y) \ y) * T(K(x \ y,x),z) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8985,a(flip),b,8422,a),flip(a)].">
      <j1 rule="hyper" parents="373 8985 8422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9126">
    <literal><![CDATA[
      ((x \ y) \ y) * T(K(x \ y,x),z) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8153,a,b,9125,a),flip(a)].">
      <j1 rule="hyper" parents="373 8153 9125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9127">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K((K(z,u) * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8920,a(flip),b,8496,a)].">
      <j1 rule="hyper" parents="64 8920 8496"/>
    </justification>
  </clause>

  <clause id="9128">
    <literal><![CDATA[
      K((K(x,y) * z) / u,x) = K(z / u,x)
    ]]></literal>
    <justification jstring="[hyper(8311,a,9127,a),flip(a)].">
      <j1 rule="hyper" parents="8311 9127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9130">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = (w * K(z / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(9128(a,1),6882(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9128 6882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9131">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6882,a(flip),b,9130,a),flip(a)].">
      <j1 rule="hyper" parents="373 6882 9130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9132">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(x * y) / z)
    ]]></literal>
    <justification jstring="[para(5796(a,1),9131(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5796 9131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9133">
    <literal><![CDATA[
      K(x,(T(y,x) * z) / u) = K(x,(y * z) / u)
    ]]></literal>
    <justification jstring="[para(5811(a,1),9131(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5811 9131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9134">
    <literal><![CDATA[
      K(x,(y * T(x,z)) / u) = K(x,(y * x) / u)
    ]]></literal>
    <justification jstring="[para(8245(a,1),9131(a,1,2,1))].">
      <j1 rule="para" parents="8245 9131"/>
    </justification>
  </clause>

  <clause id="9135">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8684,a(flip),b,9132,a),flip(a)].">
      <j1 rule="hyper" parents="373 8684 9132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9136">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (z / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,8556,a,b,9135,a),flip(a)].">
      <j1 rule="hyper" parents="373 8556 9135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9137">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(143,a,9135,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 9135 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9138">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(9136(a,2),8781(a,1))].">
      <j1 rule="para" parents="9136 8781"/>
    </justification>
  </clause>

  <clause id="9139">
    <literal><![CDATA[
      K(x,(T(y / (z \ u),x) * K(z \ u,z)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[para(6887(a,1),9133(a,2,2,1))].">
      <j1 rule="para" parents="6887 9133"/>
    </justification>
  </clause>

  <clause id="9140">
    <literal><![CDATA[
      K(x,(y * T(x,z)) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(9134(a,2),9138(a,1))].">
      <j1 rule="para" parents="9134 9138"/>
    </justification>
  </clause>

  <clause id="9141">
    <literal><![CDATA[
      K(x * (R(y,z,y) \ u),y) = K(x * (u / T(y,z)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8617,a(flip),b,8567,a),flip(a)].">
      <j1 rule="hyper" parents="64 8617 8567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9142">
    <literal><![CDATA[
      K(x * (R(x,y,x) \ z),x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,8575,a(flip),b,9141,a),flip(a)].">
      <j1 rule="hyper" parents="373 8575 9141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9143">
    <literal><![CDATA[
      K(R(x,y,x) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),9142(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 9142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9144">
    <literal><![CDATA[
      K(x,y / (T(z,u) / u)) = K(x,y / (z / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(8586,a,8573,a),flip(a)].">
      <j1 rule="hyper" parents="8586 8573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9145">
    <literal><![CDATA[
      T(K(x,y) * z,T(y,u)) = K(x,y) * T(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(6940,a,8607,a),flip(a)].">
      <j1 rule="hyper" parents="6940 8607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9146">
    <literal><![CDATA[
      K(T(K(x,y) * z,T(y,u)) \ 1,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(z,T(y,u)) \ K(y,x),w) = v5
    ]]></literal>
    <justification jstring="[para(9145(a,2),6832(a,1,1,1))].">
      <j1 rule="para" parents="9145 6832"/>
    </justification>
  </clause>

  <clause id="9147">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(8162(a,1),8665(a,2,1))].">
      <j1 rule="para" parents="8162 8665"/>
    </justification>
  </clause>

  <clause id="9148">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,9094,a(flip),b,8671,a),flip(a)].">
      <j1 rule="hyper" parents="373 9094 8671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9149">
    <literal><![CDATA[
      K(R(x,y / x,z),T(u,y)) = K((y * z) / ((y / x) * z),u)
    ]]></literal>
    <justification jstring="[para(112(a,1),9148(a,1,1)),flip(a)].">
      <j1 rule="para" parents="112 9148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9150">
    <literal><![CDATA[
      K(T(x * K(y \ (z * x),x),x),u) = K(x,T(u,T(z \ y,x) \ x))
    ]]></literal>
    <justification jstring="[para(7568(a,1),8672(a,1,1,1,2))].">
      <j1 rule="para" parents="7568 8672"/>
    </justification>
  </clause>

  <clause id="9151">
    <literal><![CDATA[
      (K(x,K(y,z)) * T(x,K(u,w))) \ x = K(u,K(w,x)) * K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8112(a,1),8752(a,2,2))].">
      <j1 rule="para" parents="8112 8752"/>
    </justification>
  </clause>

  <clause id="9152">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),8902(a,2,2,2,1))].">
      <j1 rule="para" parents="9 8902"/>
    </justification>
  </clause>

  <clause id="9153">
    <literal><![CDATA[
      L(K(x,K(y \ 1,z) * (u \ w)),u \ w,u) = K(x,(K(z,y \ K(y,u)) * u) \ w)
    ]]></literal>
    <justification jstring="[para(9152(a,2),7121(a,2,2,1))].">
      <j1 rule="para" parents="9152 7121"/>
    </justification>
  </clause>

  <clause id="9154">
    <literal><![CDATA[
      K(x / y,y) * (z * (x / y)) = T(z * (y \ x),K(y,x))
    ]]></literal>
    <justification jstring="[para(6116(a,2),8905(a,1,1))].">
      <j1 rule="para" parents="6116 8905"/>
    </justification>
  </clause>

  <clause id="9155">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((x \ T(y,x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(8579,a,8911,a),flip(a)].">
      <j1 rule="hyper" parents="8579 8911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9156">
    <literal><![CDATA[
      ((x * K(y,z)) * K(z,u)) / z = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6863,a,b,8935,a)].">
      <j1 rule="hyper" parents="64 6863 8935"/>
    </justification>
  </clause>

  <clause id="9157">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ (z / x)) = z / T(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6319,a(flip),b,8943,a),flip(a)].">
      <j1 rule="hyper" parents="373 6319 8943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9158">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,u)) * x) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(2823(a,2),9088(a,1,2))].">
      <j1 rule="para" parents="2823 9088"/>
    </justification>
  </clause>

  <clause id="9159">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,R(x,u,w))) * x) = (y * R(T(x,y),z,R(x,u,w))) * x
    ]]></literal>
    <justification jstring="[para(9090(a,1),7765(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9090 7765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9160">
    <literal><![CDATA[
      (a(x,y,y) * (y * y)) \ K(x \ ((x * y) * y),x) = T(((x * y) * y) / x,T(y * y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(1045(a,1),9093(a,1,1))].">
      <j1 rule="para" parents="1045 9093"/>
    </justification>
  </clause>

  <clause id="9161">
    <literal><![CDATA[
      K(T(x,y \ z),R(y,u,w)) = K(T(x,z),R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(6096,a,9095,a),flip(a)].">
      <j1 rule="hyper" parents="6096 9095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9162">
    <literal><![CDATA[
      T(x / T(x / (x / y),z),y) = K(z,y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6865,a(flip),b,9101,a),flip(a)].">
      <j1 rule="hyper" parents="373 6865 9101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9163">
    <literal><![CDATA[
      T(x / T(y * K(y \ x,y),z),y) = K(z,y) * (x / y)
    ]]></literal>
    <justification jstring="[para(5793(a,1),9162(a,1,1,2,1))].">
      <j1 rule="para" parents="5793 9162"/>
    </justification>
  </clause>

  <clause id="9164">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,9114,a(flip),b,9109,a),flip(a)].">
      <j1 rule="hyper" parents="373 9114 9109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9166">
    <literal><![CDATA[
      K(T(x,y),z) * ((y * z) / y) = (y * (z * K(x,z))) / y
    ]]></literal>
    <justification jstring="[hyper(156,a,9115,a)].">
      <j1 rule="hyper" parents="156 9115"/>
    </justification>
  </clause>

  <clause id="9167">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) * z = z * K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(9117(a,1),7953(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9117 7953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9168">
    <literal><![CDATA[
      T(x * (y \ z),K(y,z)) = (y \ z) * T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6404,a(flip),b,9154,a),flip(a)].">
      <j1 rule="hyper" parents="64 6404 9154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9169">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,8846,a(flip),b,9156,a),flip(a)].">
      <j1 rule="hyper" parents="144 8846 9156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9170">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,6312,a,b,9156,a)].">
      <j1 rule="hyper" parents="38 6312 9156"/>
    </justification>
  </clause>

  <clause id="9171">
    <literal><![CDATA[
      ((x * K(y,z)) * K(u,y)) * K(z,y) = x * K(u,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,9170,a,b,6878,a)].">
      <j1 rule="hyper" parents="144 9170 6878"/>
    </justification>
  </clause>

  <clause id="9172">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u)
    ]]></literal>
    <justification jstring="[para(6871(a,1),9170(a,2,1))].">
      <j1 rule="para" parents="6871 9170"/>
    </justification>
  </clause>

  <clause id="9173">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x * K(z,u)) * K(y,z) = w
    ]]></literal>
    <justification jstring="[para(9171(a,1),6909(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9171 6909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9174">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ (x * K(y,u)) = v5
    ]]></literal>
    <justification jstring="[para(9172(a,2),720(a,1))].">
      <j1 rule="para" parents="9172 720"/>
    </justification>
  </clause>

  <clause id="9175">
    <literal><![CDATA[
      T(x / T(y * K(y \ x,y),y / x),y) = (x / y) * K(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,2906,a(flip),b,9163,a),flip(a)].">
      <j1 rule="hyper" parents="373 2906 9163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9176">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(225,a,9166,a(flip),b,6156,a)].">
      <j1 rule="hyper" parents="225 9166 6156"/>
    </justification>
  </clause>

  <clause id="9177">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(9166(a,1),6189(a,1,2))].">
      <j1 rule="para" parents="9166 6189"/>
    </justification>
  </clause>

  <clause id="9178">
    <literal><![CDATA[
      L(K(x,T((y \ z) \ u,w)),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(7867(a,2),7870(a,1,1))].">
      <j1 rule="para" parents="7867 7870"/>
    </justification>
  </clause>

  <clause id="9179">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),T(w,y * R(x,z,u))) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,7869,a(flip),b,7921,a),flip(a)].">
      <j1 rule="hyper" parents="373 7869 7921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9180">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z)
    ]]></literal>
    <justification jstring="[para(7879(a,1),8253(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7879 8253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9181">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,w) = K(x,T(z \ y,u) \ 1)
    ]]></literal>
    <justification jstring="[para(7867(a,2),8400(a,1,1))].">
      <j1 rule="para" parents="7867 8400"/>
    </justification>
  </clause>

  <clause id="9182">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(5905(a,1),8742(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5905 8742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9183">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25,a,b,9182,a),flip(a)].">
      <j1 rule="hyper" parents="373 25 9182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9184">
    <literal><![CDATA[
      L(R(T(x,y),z,u),x \ T(w,x),x) = R(L(T(x,y),x \ w,x),z,u)
    ]]></literal>
    <justification jstring="[para(9183(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9183 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9185">
    <literal><![CDATA[
      K(x,R(T(K(x,y),z * u),z,u)) = K(x,a(K(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(796(a,1),8813(a,1,2))].">
      <j1 rule="para" parents="796 8813"/>
    </justification>
  </clause>

  <clause id="9186">
    <literal><![CDATA[
      K(x,a(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,7896,a(flip),b,9185,a),flip(a)].">
      <j1 rule="hyper" parents="64 7896 9185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9188">
    <literal><![CDATA[
      T(x,a(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,9186,a)].">
      <j1 rule="hyper" parents="57 9186"/>
    </justification>
  </clause>

  <clause id="9189">
    <literal><![CDATA[
      T(a(K(x,y),z,u),x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(55,a,9188,a)].">
      <j1 rule="hyper" parents="55 9188"/>
    </justification>
  </clause>

  <clause id="9190">
    <literal><![CDATA[
      K(x,y) * a(K(x,z),u,w) = a(K(x,z),u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9188(a,1),7437(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9188 7437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9191">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) * x = x * K(a(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(9189(a,1),7437(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9189 7437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9192">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(8088(a,1),8840(a,1,1))].">
      <j1 rule="para" parents="8088 8840"/>
    </justification>
  </clause>

  <clause id="9193">
    <literal><![CDATA[
      x * K(y,(x \ 1) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(6526(a,1),8843(a,1,2))].">
      <j1 rule="para" parents="6526 8843"/>
    </justification>
  </clause>

  <clause id="9194">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / (y * K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(8928,a,8513,a)].">
      <j1 rule="hyper" parents="8928 8513"/>
    </justification>
  </clause>

  <clause id="9195">
    <literal><![CDATA[
      K(x,y / (z * K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8323,a,9194,a),flip(a)].">
      <j1 rule="hyper" parents="8323 9194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9196">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[para(94(a,1),9195(a,1,2,2))].">
      <j1 rule="para" parents="94 9195"/>
    </justification>
  </clause>

  <clause id="9197">
    <literal><![CDATA[
      K(x,y / (T(z,x) / u)) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[para(2458(a,1),9195(a,1,2,2))].">
      <j1 rule="para" parents="2458 9195"/>
    </justification>
  </clause>

  <clause id="9198">
    <literal><![CDATA[
      K(x,y / (z * K(x,u))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(6871(a,1),9195(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6871 9195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9199">
    <literal><![CDATA[
      K(x,y / (z * T(u,x))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(6852(a,1),9195(a,1,2,2))].">
      <j1 rule="para" parents="6852 9195"/>
    </justification>
  </clause>

  <clause id="9200">
    <literal><![CDATA[
      K(x,y / (T(z,x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(6570(a,1),9195(a,1,2,2))].">
      <j1 rule="para" parents="6570 9195"/>
    </justification>
  </clause>

  <clause id="9201">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,7680,a(flip),b,9196,a),flip(a)].">
      <j1 rule="hyper" parents="373 7680 9196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9203">
    <literal><![CDATA[
      K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[para(112(a,2),9196(a,2,2)),flip(a)].">
      <j1 rule="para" parents="112 9196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9204">
    <literal><![CDATA[
      K(x,y / ((z / x) * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[para(8651(a,1),9198(a,1,2,2))].">
      <j1 rule="para" parents="8651 9198"/>
    </justification>
  </clause>

  <clause id="9205">
    <literal><![CDATA[
      K(x,y / (T(z \ T(u,z),x) / w)) = K(x,y / ((T(z,u) \ u) / w))
    ]]></literal>
    <justification jstring="[para(4799(a,1),9197(a,1,2,2,1))].">
      <j1 rule="para" parents="4799 9197"/>
    </justification>
  </clause>

  <clause id="9206">
    <literal><![CDATA[
      K(x,(y / z) \ (x \ 1)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(12(a,1),9201(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 9201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9207">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,((y \ z) / z) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(4810(a,1),9201(a,1,2,2,1))].">
      <j1 rule="para" parents="4810 9201"/>
    </justification>
  </clause>

  <clause id="9208">
    <literal><![CDATA[
      K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,5929,a(flip),b,9203,a)].">
      <j1 rule="hyper" parents="64 5929 9203"/>
    </justification>
  </clause>

  <clause id="9209">
    <literal><![CDATA[
      K(x,L(y,z,T(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,7143,a,b,9108,a),flip(a)].">
      <j1 rule="hyper" parents="35 7143 9108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9210">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(25(a,1),9209(a,1,2))].">
      <j1 rule="para" parents="25 9209"/>
    </justification>
  </clause>

  <clause id="9211">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = K((y * z) / ((y / x) * z),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(8313,a,9149,a)].">
      <j1 rule="hyper" parents="8313 9149"/>
    </justification>
  </clause>

  <clause id="9212">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(6937,a,9178,a)].">
      <j1 rule="hyper" parents="6937 9178"/>
    </justification>
  </clause>

  <clause id="9213">
    <literal><![CDATA[
      K(x,T(y,z * R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9089,a(flip),b,9179,a)].">
      <j1 rule="hyper" parents="64 9089 9179"/>
    </justification>
  </clause>

  <clause id="9215">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),9213(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 9213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9216">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,w) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,8081,a,b,9181,a),flip(a)].">
      <j1 rule="hyper" parents="373 8081 9181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9217">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,x \ y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(8976(a,1),9192(a,1,1))].">
      <j1 rule="para" parents="8976 9192"/>
    </justification>
  </clause>

  <clause id="9218">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(8208,a,9193,a)].">
      <j1 rule="hyper" parents="8208 9193"/>
    </justification>
  </clause>

  <clause id="9219">
    <literal><![CDATA[
      R(K((x / y) \ x,z),x,u) = K(R(y,x / y,u),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,8791,a(flip),b,9211,a)].">
      <j1 rule="hyper" parents="373 8791 9211"/>
    </justification>
  </clause>

  <clause id="9220">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),9219(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 9219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9221">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(11(a,1),9220(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 9220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9223">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(4604,a,9216,a),flip(a)].">
      <j1 rule="hyper" parents="4604 9216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9224">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ y,u)) = w
    ]]></literal>
    <justification jstring="[para(9216(a,1),623(a,1)),flip(b)].">
      <j1 rule="para" parents="9216 623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9225">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,u)) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(143,a,9223,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 9223 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9226">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T((y \ z) \ 1,u)) = K(((y \ z) \ 1) * x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8605,a,b,9223,a)].">
      <j1 rule="hyper" parents="64 8605 9223"/>
    </justification>
  </clause>

  <clause id="9227">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(9223(a,2),8699(a,1))].">
      <j1 rule="para" parents="9223 8699"/>
    </justification>
  </clause>

  <clause id="9228">
    <literal><![CDATA[
      x * K(y,T((x \ z) \ 1,u)) != w * x
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x / z,u)) = w
    ]]></literal>
    <justification jstring="[para(9223(a,2),8901(a,1,2))].">
      <j1 rule="para" parents="9223 8901"/>
    </justification>
  </clause>

  <clause id="9229">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ 1) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(8956,a,9225,a)].">
      <j1 rule="hyper" parents="8956 9225"/>
    </justification>
  </clause>

  <clause id="9230">
    <literal><![CDATA[
      T(x,((y \ z) * u) \ u) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(6826,a,9229,a)].">
      <j1 rule="hyper" parents="6826 9229"/>
    </justification>
  </clause>

  <clause id="9231">
    <literal><![CDATA[
      T(x,y \ T(z,z \ y)) = T(x,T(y \ z,z))
    ]]></literal>
    <justification jstring="[para(6980(a,1),9230(a,1,2))].">
      <j1 rule="para" parents="6980 9230"/>
    </justification>
  </clause>

  <clause id="9232">
    <literal><![CDATA[
      T(x,y \ T(z,z \ y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8271,a(flip),b,9231,a),flip(a)].">
      <j1 rule="hyper" parents="373 8271 9231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9233">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(9(a,1),9227(a,1,2,1,1))].">
      <j1 rule="para" parents="9 9227"/>
    </justification>
  </clause>

  <clause id="9234">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(8082(a,1),9227(a,1))].">
      <j1 rule="para" parents="8082 9227"/>
    </justification>
  </clause>

  <clause id="9235">
    <literal><![CDATA[
      K(x,y / (y * z)) = K(x,(z * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(9233,a,8082,a)].">
      <j1 rule="hyper" parents="9233 8082"/>
    </justification>
  </clause>

  <clause id="9236">
    <literal><![CDATA[
      K(x,y / (y * z)) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(9233,a,8056,a)].">
      <j1 rule="hyper" parents="9233 8056"/>
    </justification>
  </clause>

  <clause id="9237">
    <literal><![CDATA[
      K(x,T(1 / y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(6055(a,2),9233(a,1))].">
      <j1 rule="para" parents="6055 9233"/>
    </justification>
  </clause>

  <clause id="9238">
    <literal><![CDATA[
      K(x,y / (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(9235(a,2),8463(a,1))].">
      <j1 rule="para" parents="9235 8463"/>
    </justification>
  </clause>

  <clause id="9239">
    <literal><![CDATA[
      T(x,y / (y * z)) = T(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(143,a,9236,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 9236 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9240">
    <literal><![CDATA[
      T(x,y \ K(y,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6259,a,b,9239,a)].">
      <j1 rule="hyper" parents="64 6259 9239"/>
    </justification>
  </clause>

  <clause id="9241">
    <literal><![CDATA[
      K((x * y) / x,x / (x * z)) = K(y,1 / z)
    ]]></literal>
    <justification jstring="[hyper(9237,a,7919,a)].">
      <j1 rule="hyper" parents="9237 7919"/>
    </justification>
  </clause>

  <clause id="9242">
    <literal><![CDATA[
      K((x * y) / x,1 / ((x * z) / x)) = K(y,1 / z)
    ]]></literal>
    <justification jstring="[hyper(6516,a,9241,a)].">
      <j1 rule="hyper" parents="6516 9241"/>
    </justification>
  </clause>

  <clause id="9243">
    <literal><![CDATA[
      (((x * y) / x) \ z) * K(y,1 / y) = (1 / (1 / ((x * y) / x))) \ z
    ]]></literal>
    <justification jstring="[para(9242(a,1),3681(a,1,2))].">
      <j1 rule="para" parents="9242 3681"/>
    </justification>
  </clause>

  <clause id="9244">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u \ z,y)) = w
    ]]></literal>
    <justification jstring="[para(8056(a,1),9224(a,1))].">
      <j1 rule="para" parents="8056 9224"/>
    </justification>
  </clause>

  <clause id="9245">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = z * T(z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,525,a(flip),b,7813,a),flip(a)].">
      <j1 rule="hyper" parents="373 525 7813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9246">
    <literal><![CDATA[
      T(x * K(x \ y,y \ x),x \ y) = (1 / (1 / (x \ y))) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,4340,a(flip),b,7822,a),flip(a)].">
      <j1 rule="hyper" parents="373 4340 7822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9247">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,z) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,6600,a(flip),b,7957,a),flip(a)].">
      <j1 rule="hyper" parents="64 6600 7957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9248">
    <literal><![CDATA[
      K(x,y \ 1) * K(y \ 1,y) = y \ (1 / T(1 / y,x))
    ]]></literal>
    <justification jstring="[para(6041(a,1),9247(a,1,1))].">
      <j1 rule="para" parents="6041 9247"/>
    </justification>
  </clause>

  <clause id="9249">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * u) = K(x,y) * (T(z,K(y,x)) * u)
    ]]></literal>
    <justification jstring="[para(8192(a,1),8171(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8192 8171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9250">
    <literal><![CDATA[
      (1 / (x \ y)) * K(y / x,z) = K(y / x,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(8215(a,1),8287(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8215 8287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9251">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(9250(a,1),400(a,1))].">
      <j1 rule="para" parents="9250 400"/>
    </justification>
  </clause>

  <clause id="9252">
    <literal><![CDATA[
      1 / (x \ K(y,1 / x)) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(9251,a,7268,a),flip(a)].">
      <j1 rule="hyper" parents="9251 7268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9253">
    <literal><![CDATA[
      1 / ((x * (y \ 1)) / x) = y * K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(6044(a,1),9252(a,1,2))].">
      <j1 rule="para" parents="6044 9252"/>
    </justification>
  </clause>

  <clause id="9254">
    <literal><![CDATA[
      1 / ((x * ((y / z) \ 1)) / x) = (y / z) * K(z / y,x)
    ]]></literal>
    <justification jstring="[para(6581(a,1),9253(a,2,2))].">
      <j1 rule="para" parents="6581 9253"/>
    </justification>
  </clause>

  <clause id="9255">
    <literal><![CDATA[
      K(T(x,y),((x \ 1) * y) \ z) = K(x,z / ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7392,a(flip),b,8296,a)].">
      <j1 rule="hyper" parents="64 7392 8296"/>
    </justification>
  </clause>

  <clause id="9256">
    <literal><![CDATA[
      K(T(x,T(y,x)),((T(x,y) \ 1) * y) \ z) = K(x,z / ((x \ 1) * T(y,x)))
    ]]></literal>
    <justification jstring="[para(6271(a,2),9255(a,1,2,1))].">
      <j1 rule="para" parents="6271 9255"/>
    </justification>
  </clause>

  <clause id="9257">
    <literal><![CDATA[
      K(x,K(y,z)) * T(u,K(y,z)) = T(K(y,z),x) * (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(8123(a,1),8353(a,1,1))].">
      <j1 rule="para" parents="8123 8353"/>
    </justification>
  </clause>

  <clause id="9258">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x) * (z * K(x,y))) = L(z * K(x,y),K(y,x),z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,4694,a(flip),b,8354,a),flip(a)].">
      <j1 rule="hyper" parents="36 4694 8354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9259">
    <literal><![CDATA[
      T(K(x,y) * z,u) * T(K(y,x),T(w,T(K(x,y) * z,u))) = K(K(y,x),w) * (K(y,x) * T(z * K(x,y),u))
    ]]></literal>
    <justification jstring="[para(8354(a,1),7993(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8354 7993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9260">
    <literal><![CDATA[
      K((x / y) \ 1,z * (x / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z * (y \ x)) = u
    ]]></literal>
    <justification jstring="[para(8378(a,1),8315(a,1))].">
      <j1 rule="para" parents="8378 8315"/>
    </justification>
  </clause>

  <clause id="9261">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,y)) = K(((x \ 1) \ z) / y,x)
    ]]></literal>
    <justification jstring="[hyper(8451,a,7382,a)].">
      <j1 rule="hyper" parents="8451 7382"/>
    </justification>
  </clause>

  <clause id="9262">
    <literal><![CDATA[
      T(x * (y * z),K(z * y,z)) != (y * z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y * z,z)) = u
    ]]></literal>
    <justification jstring="[para(8532(a,2),44(a,1))].">
      <j1 rule="para" parents="8532 44"/>
    </justification>
  </clause>

  <clause id="9263">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5253,a(flip),b,8566,a)].">
      <j1 rule="hyper" parents="64 5253 8566"/>
    </justification>
  </clause>

  <clause id="9264">
    <literal><![CDATA[
      T(T(x / y,x \ y),z * (y \ x)) = T(((x / y) \ 1) \ 1,z * (x / y))
    ]]></literal>
    <justification jstring="[para(3815(a,1),8602(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3815 8602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9265">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (x * K(z,y)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(5856(a,1),8661(a,1,2,2))].">
      <j1 rule="para" parents="5856 8661"/>
    </justification>
  </clause>

  <clause id="9267">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = (y / z) \ (x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,6613,a(flip),b,8692,a),flip(a)].">
      <j1 rule="hyper" parents="373 6613 8692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9268">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = K(x,y / z) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,9267,a(flip),b,5776,a)].">
      <j1 rule="hyper" parents="139 9267 5776"/>
    </justification>
  </clause>

  <clause id="9270">
    <literal><![CDATA[
      R(x / y,z,u) / (R(x / y,z,u) / (y \ x)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,117,a(flip),b,8737,a),flip(a)].">
      <j1 rule="hyper" parents="373 117 8737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9271">
    <literal><![CDATA[
      K(x * ((T(y,y \ 1) * z) \ (((y \ 1) \ 1) \ (T(y,y \ 1) * z))),y \ 1) = K(x * (z / (T(y,y \ 1) * z)),y \ 1)
    ]]></literal>
    <justification jstring="[para(501(a,1),8748(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="501 8748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9272">
    <literal><![CDATA[
      T(K(x,y) * T(z,K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * (K(y,u) \ z))
    ]]></literal>
    <justification jstring="[para(7806(a,1),8802(a,1,1,2))].">
      <j1 rule="para" parents="7806 8802"/>
    </justification>
  </clause>

  <clause id="9273">
    <literal><![CDATA[
      (x * K(y,z)) * ((u * y) / u) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(6847(a,1),8847(a,1,1))].">
      <j1 rule="para" parents="6847 8847"/>
    </justification>
  </clause>

  <clause id="9274">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(u,y)) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(5960,a,9273,a)].">
      <j1 rule="hyper" parents="5960 9273"/>
    </justification>
  </clause>

  <clause id="9275">
    <literal><![CDATA[
      T(K(x,y),T(z,u * x)) = T(K(x,y),T(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(8773,a,8859,a),flip(a)].">
      <j1 rule="hyper" parents="8773 8859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9276">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,x * z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7863,a(flip),b,9275,a),flip(a)].">
      <j1 rule="hyper" parents="64 7863 9275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9277">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8988,a(flip),b,9076,a),flip(a)].">
      <j1 rule="hyper" parents="373 8988 9076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9278">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(82(a,1),9277(a,1,2,2,1,2))].">
      <j1 rule="para" parents="82 9277"/>
    </justification>
  </clause>

  <clause id="9279">
    <literal><![CDATA[
      K(x,(y \ 1) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6526,a(flip),b,9278,a)].">
      <j1 rule="hyper" parents="64 6526 9278"/>
    </justification>
  </clause>

  <clause id="9280">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(9161(a,1),9123(a,2,2))].">
      <j1 rule="para" parents="9161 9123"/>
    </justification>
  </clause>

  <clause id="9281">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,R(y / (y / z),u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,8380,a,b,9280,a)].">
      <j1 rule="hyper" parents="373 8380 9280"/>
    </justification>
  </clause>

  <clause id="9282">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ u,x)) = z * T(z \ (K(x,y) * u),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),9245(a,1,2,2,1,2))].">
      <j1 rule="para" parents="9 9245"/>
    </justification>
  </clause>

  <clause id="9283">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,K(y,z)) = T(K(y,z),x) * (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7811,a,b,9257,a)].">
      <j1 rule="hyper" parents="64 7811 9257"/>
    </justification>
  </clause>

  <clause id="9284">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (((x * y) \ x) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5249,a(flip),b,9263,a),flip(a)].">
      <j1 rule="hyper" parents="373 5249 9263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9285">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,9247,a(flip),b,9268,a),flip(a)].">
      <j1 rule="hyper" parents="373 9247 9268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9286">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9119,a(flip),b,9276,a)].">
      <j1 rule="hyper" parents="64 9119 9276"/>
    </justification>
  </clause>

  <clause id="9287">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = u
    ]]></literal>
    <justification jstring="[para(9286(a,1),7964(a,1))].">
      <j1 rule="para" parents="9286 7964"/>
    </justification>
  </clause>

  <clause id="9288">
    <literal><![CDATA[
      ((1 / x) * y) * T(((1 / x) * y) \ (K(z,u) * y),z) = K(z,u) * (K(x,z) * y)
    ]]></literal>
    <justification jstring="[para(6694(a,1),9282(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6694 9282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9289">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,K(y,z)) = K(y,T(z,x)) * (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8794,a,9283,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8794 9283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9290">
    <literal><![CDATA[
      K(x,(y * T(z,x \ 1)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7081,a(flip),b,8060,a),flip(a)].">
      <j1 rule="hyper" parents="64 7081 8060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9291">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ z) = K(x,(y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(115(a,1),9290(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="115 9290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9292">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(7867(a,2),8252(a,1,1))].">
      <j1 rule="para" parents="7867 8252"/>
    </justification>
  </clause>

  <clause id="9293">
    <literal><![CDATA[
      R(x * K(y,T(z,u)),K(z,T(y,u)),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(7908(a,1),8257(a,1,1))].">
      <j1 rule="para" parents="7908 8257"/>
    </justification>
  </clause>

  <clause id="9294">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,7073,a(flip),b,8537,a),flip(a)].">
      <j1 rule="hyper" parents="373 7073 8537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9295">
    <literal><![CDATA[
      K(R(x,y,z),u * K(w,x)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(6871(a,1),9294(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6871 9294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9296">
    <literal><![CDATA[
      K(x * y,y) * K(x,K(y,z)) = T(y,T(x,z)) \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8893,a(flip),b,8937,a),flip(a)].">
      <j1 rule="hyper" parents="64 8893 8937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9297">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(9296(a,1),8974(a,1))].">
      <j1 rule="para" parents="9296 8974"/>
    </justification>
  </clause>

  <clause id="9298">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(9228,a,9167,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="9228 9167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9299">
    <literal><![CDATA[
      T(x,T((y / z) \ 1,u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(143,a,9298,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 9298 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9301">
    <literal><![CDATA[
      T(x,T((y / (z * K(y,u))) \ 1,w)) = T(x,T((z / y) * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(6863(a,1),9299(a,2,2,1))].">
      <j1 rule="para" parents="6863 9299"/>
    </justification>
  </clause>

  <clause id="9302">
    <literal><![CDATA[
      K(x / y,z * (y / x)) = K(x / y,z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(9260,a,6580,a),flip(a)].">
      <j1 rule="hyper" parents="9260 6580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9303">
    <literal><![CDATA[
      T(x,y) * K(x * y,(y * x) \ x) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(6981(a,1),6267(a,1,2,2))].">
      <j1 rule="para" parents="6981 6267"/>
    </justification>
  </clause>

  <clause id="9304">
    <literal><![CDATA[
      x \ (T((y * x) / y,z) * u) = K(y,x) * (K(x,T(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(8214(a,1),6395(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8214 6395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9305">
    <literal><![CDATA[
      ((x \ 1) \ x) * (T(y,T(x,x \ 1) * T(x,x \ 1)) * z) = y * ((T(x,x \ 1) * T(x,x \ 1)) * z)
    ]]></literal>
    <justification jstring="[hyper(38,a,1523,a(flip),b,6427,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 1523 6427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9306">
    <literal><![CDATA[
      (1 / (1 / ((x / y) / x))) * (1 / (1 / y)) = ((x / y) / x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,6146,a,b,6965,a)].">
      <j1 rule="hyper" parents="64 6146 6965"/>
    </justification>
  </clause>

  <clause id="9307">
    <literal><![CDATA[
      (x \ y) * ((K(x,x \ y) * z) / T(z,K(u,w))) = (y / x) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(8177(a,1),6969(a,1,2,2))].">
      <j1 rule="para" parents="8177 6969"/>
    </justification>
  </clause>

  <clause id="9308">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),7020(a,1,1,2,2,1))].">
      <j1 rule="para" parents="10 7020"/>
    </justification>
  </clause>

  <clause id="9309">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,6375,a(flip),b,9308,a),flip(a)].">
      <j1 rule="hyper" parents="373 6375 9308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9310">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z / (x * y)) = u
    ]]></literal>
    <justification jstring="[para(9308(a,2),6447(a,1))].">
      <j1 rule="para" parents="9308 6447"/>
    </justification>
  </clause>

  <clause id="9311">
    <literal><![CDATA[
      R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y
    ]]></literal>
    <justification jstring="[para(9309(a,1),678(a,1,1))].">
      <j1 rule="para" parents="9309 678"/>
    </justification>
  </clause>

  <clause id="9312">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,L(y,w,v5)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(606,a,7181,a)].">
      <j1 rule="hyper" parents="606 7181"/>
    </justification>
  </clause>

  <clause id="9313">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(593(a,1),9312(a,1,3))].">
      <j1 rule="para" parents="593 9312"/>
    </justification>
  </clause>

  <clause id="9314">
    <literal><![CDATA[
      K(x,L(T(y,z),u,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9164,a(flip),b,9313,a)].">
      <j1 rule="hyper" parents="64 9164 9313"/>
    </justification>
  </clause>

  <clause id="9315">
    <literal><![CDATA[
      K((x \ 1) * y,T(x \ 1,z)) = K(x \ y,T(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7572,a(flip),b,9313,a)].">
      <j1 rule="hyper" parents="64 7572 9313"/>
    </justification>
  </clause>

  <clause id="9316">
    <literal><![CDATA[
      K((x \ y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7529,a(flip),b,9313,a),flip(a)].">
      <j1 rule="hyper" parents="64 7529 9313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9317">
    <literal><![CDATA[
      K(x,L(y \ z,u,z / y)) = K(x,T(z / y,T(y,z)))
    ]]></literal>
    <justification jstring="[para(4470(a,1),9314(a,1,2,1))].">
      <j1 rule="para" parents="4470 9314"/>
    </justification>
  </clause>

  <clause id="9318">
    <literal><![CDATA[
      K(x,L(y \ z,u,z / y)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4470(a,1),9317(a,2,2))].">
      <j1 rule="para" parents="4470 9317"/>
    </justification>
  </clause>

  <clause id="9319">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T((x \ y) \ 1,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,9223,a(flip),b,9315,a),flip(a)].">
      <j1 rule="hyper" parents="373 9223 9315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9320">
    <literal><![CDATA[
      (x \ (x / y)) * ((((x \ (x / y)) \ 1) * ((x \ (x / y)) \ 1)) * z) = (1 / (T(1,y \ 1) / (T(x \ (x / y),1) \ 1))) * z
    ]]></literal>
    <justification jstring="[para(7205(a,2),1088(a,2,1,2))].">
      <j1 rule="para" parents="7205 1088"/>
    </justification>
  </clause>

  <clause id="9321">
    <literal><![CDATA[
      (x * K(y,z \ 1)) * z = (x * z) * K(y,z \ 1)
    ]]></literal>
    <justification jstring="[para(6362(a,1),7248(a,1,1))].">
      <j1 rule="para" parents="6362 7248"/>
    </justification>
  </clause>

  <clause id="9322">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,(y \ 1) \ 1) = (x * K(z,y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(6047(a,1),9321(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6047 9321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9323">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = (x * (z \ 1)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6047(a,1),9322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6047 9322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9324">
    <literal><![CDATA[
      R(x / T(y,z),y,y \ 1) = (x * (y \ 1)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6331,a,9323,a)].">
      <j1 rule="hyper" parents="6331 9323"/>
    </justification>
  </clause>

  <clause id="9325">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (z \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,6483,a(flip),b,9323,a),flip(a)].">
      <j1 rule="hyper" parents="373 6483 9323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9326">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,5938,a,b,9325,a),flip(a)].">
      <j1 rule="hyper" parents="373 5938 9325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9327">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,6817,a(flip),b,9326,a(flip))].">
      <j1 rule="hyper" parents="139 6817 9326"/>
    </justification>
  </clause>

  <clause id="9328">
    <literal><![CDATA[
      (x * K(y,z)) * (T(y,z) \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(6871(a,1),9326(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6871 9326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9329">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = ((y \ x) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,362,a(flip),b,9327,a),flip(a)].">
      <j1 rule="hyper" parents="373 362 9327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9330">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,z) = x / (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(142,a,12,a(flip),b,9328,a),flip(a)].">
      <j1 rule="hyper" parents="142 12 9328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9331">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,9329,a(flip),b,5434,a),flip(a)].">
      <j1 rule="hyper" parents="144 9329 5434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9332">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = x / (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,6621,a,b,9330,a)].">
      <j1 rule="hyper" parents="64 6621 9330"/>
    </justification>
  </clause>

  <clause id="9333">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) \ y = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,4593,a(flip),b,9331,a)].">
      <j1 rule="hyper" parents="64 4593 9331"/>
    </justification>
  </clause>

  <clause id="9334">
    <literal><![CDATA[
      ((((x / y) \ 1) * x) \ x) \ x = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(82(a,1),9333(a,2,1,1,1))].">
      <j1 rule="para" parents="82 9333"/>
    </justification>
  </clause>

  <clause id="9335">
    <literal><![CDATA[
      ((x / y) \ 1) * (y * (x / y)) = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,4598,a(flip),b,9334,a)].">
      <j1 rule="hyper" parents="64 4598 9334"/>
    </justification>
  </clause>

  <clause id="9336">
    <literal><![CDATA[
      T(x,T(((y / z) \ 1) * y,y)) = T(x,((z \ y) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(9334(a,1),7428(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9334 7428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9337">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,y * (z / y),(z / y) \ 1)) = K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(9335(a,1),7088(a,2,2,1))].">
      <j1 rule="para" parents="9335 7088"/>
    </justification>
  </clause>

  <clause id="9338">
    <literal><![CDATA[
      ((x * T(y,z)) * (y \ 1)) * K(z,y) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),9324(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 9324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9339">
    <literal><![CDATA[
      (x * T(y,z)) * (y \ K(z,y)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,6483,a(flip),b,9338,a)].">
      <j1 rule="hyper" parents="64 6483 9338"/>
    </justification>
  </clause>

  <clause id="9340">
    <literal><![CDATA[
      (x * y) * (x \ K(y,x)) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(718,a,9339,a)].">
      <j1 rule="hyper" parents="718 9339"/>
    </justification>
  </clause>

  <clause id="9341">
    <literal><![CDATA[
      (x * y) \ R(y,x,x \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,9340,a(flip),b,5938,a)].">
      <j1 rule="hyper" parents="139 9340 5938"/>
    </justification>
  </clause>

  <clause id="9342">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(5652(a,1),7252(a,1,1,2))].">
      <j1 rule="para" parents="5652 7252"/>
    </justification>
  </clause>

  <clause id="9343">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) = T((x \ y) * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,6721,a(flip),b,7302,a)].">
      <j1 rule="hyper" parents="145 6721 7302"/>
    </justification>
  </clause>

  <clause id="9344">
    <literal><![CDATA[
      K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u)
    ]]></literal>
    <justification jstring="[para(6840(a,1),7361(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6840 7361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9345">
    <literal><![CDATA[
      ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(145,a,9344,a,b,xx)].">
      <j1 rule="hyper" parents="145 9344"/>
    </justification>
  </clause>

  <clause id="9346">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) = (x * z) \ ((x * K(y,u)) * z)
    ]]></literal>
    <justification jstring="[para(9345(a,1),6882(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9345 6882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9347">
    <literal><![CDATA[
      K(x,y \ ((z * K(u,x)) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(9345(a,1),8818(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9345 8818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9348">
    <literal><![CDATA[
      K(x,y / ((z * K(u,x)) * w)) = K(x,y / (z * w))
    ]]></literal>
    <justification jstring="[para(9345(a,1),9198(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9345 9198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9349">
    <literal><![CDATA[
      K(x,y \ ((z * K(x,u)) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(6871(a,1),9347(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6871 9347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9350">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(94(a,1),9348(a,1,2,2,1))].">
      <j1 rule="para" parents="94 9348"/>
    </justification>
  </clause>

  <clause id="9351">
    <literal><![CDATA[
      K(x,y / (((x \ z) * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(354(a,1),9348(a,1,2,2,1))].">
      <j1 rule="para" parents="354 9348"/>
    </justification>
  </clause>

  <clause id="9352">
    <literal><![CDATA[
      K(x,y / ((K(x,z) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(7903(a,1),9348(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7903 9348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9353">
    <literal><![CDATA[
      K(x,y \ (((z / x) * u) * w)) = K(x,y \ (((x \ z) * u) * w))
    ]]></literal>
    <justification jstring="[para(8651(a,1),9349(a,1,2,2,1))].">
      <j1 rule="para" parents="8651 9349"/>
    </justification>
  </clause>

  <clause id="9354">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),7609(a,1,2))].">
      <j1 rule="para" parents="9 7609"/>
    </justification>
  </clause>

  <clause id="9355">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(x / ((y * z) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9284,a(flip),b,9354,a)].">
      <j1 rule="hyper" parents="64 9284 9354"/>
    </justification>
  </clause>

  <clause id="9356">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(9355(a,2),8459(a,1))].">
      <j1 rule="para" parents="9355 8459"/>
    </justification>
  </clause>

  <clause id="9357">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = T(K(x,y) * z,z) / z
    ]]></literal>
    <justification jstring="[para(5912(a,1),7613(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5912 7613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9358">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = z \ T(z * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5434,a(flip),b,9357,a),flip(a)].">
      <j1 rule="hyper" parents="373 5434 9357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9359">
    <literal><![CDATA[
      K(x,y / T(z \ y,y)) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(6447,a,9358,a)].">
      <j1 rule="hyper" parents="6447 9358"/>
    </justification>
  </clause>

  <clause id="9360">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(4884(a,1),9359(a,1,2))].">
      <j1 rule="para" parents="4884 9359"/>
    </justification>
  </clause>

  <clause id="9361">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = K(y,T(x / z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,7284,a,b,9360,a)].">
      <j1 rule="hyper" parents="373 7284 9360"/>
    </justification>
  </clause>

  <clause id="9362">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * T(x,x \ 1) = (x \ 1) \ (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(5593(a,1),7689(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5593 7689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9363">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(145,a,5240,a(flip),b,9362,a(flip))].">
      <j1 rule="hyper" parents="145 5240 9362"/>
    </justification>
  </clause>

  <clause id="9364">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = (x \ 1) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,7708,a,b,9363,a)].">
      <j1 rule="hyper" parents="373 7708 9363"/>
    </justification>
  </clause>

  <clause id="9365">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) = x \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1848,a,b,9363,a),flip(a)].">
      <j1 rule="hyper" parents="373 1848 9363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9366">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,405,a,b,9363,a),flip(a)].">
      <j1 rule="hyper" parents="35 405 9363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9367">
    <literal><![CDATA[
      (x \ 1) * a(y,y,x) = L(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[para(1243(a,1),9363(a,1,2))].">
      <j1 rule="para" parents="1243 9363"/>
    </justification>
  </clause>

  <clause id="9368">
    <literal><![CDATA[
      (x / (y \ 1)) * (L(y,z,u) \ 1) = (x / y) * (y * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(9363(a,1),1627(a,1,2))].">
      <j1 rule="para" parents="9363 1627"/>
    </justification>
  </clause>

  <clause id="9369">
    <literal><![CDATA[
      (L(x,y,y) \ 1) * L(z,a(y,y,x),x) = (x \ 1) * (a(y,y,x) * z)
    ]]></literal>
    <justification jstring="[para(9367(a,1),1630(a,1,1))].">
      <j1 rule="para" parents="9367 1630"/>
    </justification>
  </clause>

  <clause id="9370">
    <literal><![CDATA[
      (x \ 1) \ ((L(x,y,y) \ 1) * z) = x \ ((x * a(y,y,x)) * z)
    ]]></literal>
    <justification jstring="[para(9367(a,1),1600(a,1,2,1))].">
      <j1 rule="para" parents="9367 1600"/>
    </justification>
  </clause>

  <clause id="9371">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(39,a,1148,a,b,9365,a(flip))].">
      <j1 rule="hyper" parents="39 1148 9365"/>
    </justification>
  </clause>

  <clause id="9372">
    <literal><![CDATA[
      (1 / x) \ (L(x,y,z) \ x) = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,9371,a(flip),b,559,a)].">
      <j1 rule="hyper" parents="139 9371 559"/>
    </justification>
  </clause>

  <clause id="9373">
    <literal><![CDATA[
      (x \ 1) * L(L(x,y,z) \ x,u,w) = x \ L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(9371(a,1),1149(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9371 1149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9374">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(3452,a,9364,a)].">
      <j1 rule="hyper" parents="3452 9364"/>
    </justification>
  </clause>

  <clause id="9375">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(226,a,9374,a)].">
      <j1 rule="hyper" parents="226 9374"/>
    </justification>
  </clause>

  <clause id="9376">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L(x,y,z) \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(157,a,9374,a)].">
      <j1 rule="hyper" parents="157 9374"/>
    </justification>
  </clause>

  <clause id="9377">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (x * x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,5605,a,b,9374,a)].">
      <j1 rule="hyper" parents="64 5605 9374"/>
    </justification>
  </clause>

  <clause id="9378">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ 1 = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1309(a,1),9374(a,1,1))].">
      <j1 rule="para" parents="1309 9374"/>
    </justification>
  </clause>

  <clause id="9379">
    <literal><![CDATA[
      x / (((L(y,z,u) \ y) \ 1) * x) = ((y \ L(y,z,u)) \ x) / x
    ]]></literal>
    <justification jstring="[para(9374(a,1),2013(a,1,2,1,1))].">
      <j1 rule="para" parents="9374 2013"/>
    </justification>
  </clause>

  <clause id="9380">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ 1 = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(5574(a,1),9374(a,1,1))].">
      <j1 rule="para" parents="5574 9374"/>
    </justification>
  </clause>

  <clause id="9381">
    <literal><![CDATA[
      (L(x,y,z) \ x) / (x \ 1) = ((x \ L(x,y,z)) \ 1) * x
    ]]></literal>
    <justification jstring="[para(9374(a,1),5648(a,1,1))].">
      <j1 rule="para" parents="9374 5648"/>
    </justification>
  </clause>

  <clause id="9382">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = (L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,5658,a,b,9375,a),flip(a)].">
      <j1 rule="hyper" parents="373 5658 9375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9383">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * (L(x,y,z) \ x)) * u = (L(x,y,z) \ x) * ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(9375(a,1),538(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9375 538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9384">
    <literal><![CDATA[
      ((x \ 1) \ ((y * x) \ y)) * (L(x \ 1,x,y) \ (x \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(241(a,1),9376(a,1,1,2))].">
      <j1 rule="para" parents="241 9376"/>
    </justification>
  </clause>

  <clause id="9385">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ z) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(9377(a,1),2183(a,1,3))].">
      <j1 rule="para" parents="9377 2183"/>
    </justification>
  </clause>

  <clause id="9386">
    <literal><![CDATA[
      L(x,y,R(L(z,u,w) \ z,v5,v6)) = L(x,y,R(z * L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(9377(a,1),2282(a,1,3,1))].">
      <j1 rule="para" parents="9377 2282"/>
    </justification>
  </clause>

  <clause id="9387">
    <literal><![CDATA[
      a(L(x,y,z) \ x,u,w) = a(x * L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(9377(a,1),2666(a,1,1))].">
      <j1 rule="para" parents="9377 2666"/>
    </justification>
  </clause>

  <clause id="9388">
    <literal><![CDATA[
      L(x,y,z * L(z,u,u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(1243(a,1),9385(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1243 9385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9389">
    <literal><![CDATA[
      L(x,y,y) \ ((x \ L(x,y,y)) * z) = L(x \ z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,5695,a(flip),b,9388,a)].">
      <j1 rule="hyper" parents="64 5695 9388"/>
    </justification>
  </clause>

  <clause id="9390">
    <literal><![CDATA[
      L(x,y,L(z,u,u) * z) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(275(a,2),9388(a,1,3))].">
      <j1 rule="para" parents="275 9388"/>
    </justification>
  </clause>

  <clause id="9391">
    <literal><![CDATA[
      a(x * L(x,y,y),z,u) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(1243(a,1),9387(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1243 9387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9392">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ 1) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5684,a(flip),b,9366,a)].">
      <j1 rule="hyper" parents="64 5684 9366"/>
    </justification>
  </clause>

  <clause id="9393">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ 1 = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,9366,a(flip),b,9378,a),flip(a)].">
      <j1 rule="hyper" parents="373 9366 9378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9394">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,u,w) \ (L(x,y,z) \ 1) = L(x * L(x \ 1,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(4273(a,1),9380(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4273 9380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9395">
    <literal><![CDATA[
      (L(x,y,z) \ x) / (x \ 1) = (L(x,y,z) \ x) * x
    ]]></literal>
    <justification jstring="[para(9374(a,1),9381(a,2,1))].">
      <j1 rule="para" parents="9374 9381"/>
    </justification>
  </clause>

  <clause id="9396">
    <literal><![CDATA[
      1 / (x \ (x \ L(x,y,z))) = (L(x,y,z) \ x) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,5650,a(flip),b,9395,a)].">
      <j1 rule="hyper" parents="64 5650 9395"/>
    </justification>
  </clause>

  <clause id="9397">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * x) \ 1 = x \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(215,a,9396,a)].">
      <j1 rule="hyper" parents="215 9396"/>
    </justification>
  </clause>

  <clause id="9398">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * (L(x \ 1,x,y) \ (x \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(3793(a,1),9384(a,1,1))].">
      <j1 rule="para" parents="3793 9384"/>
    </justification>
  </clause>

  <clause id="9399">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * (x \ (L(1 / x,x,y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(9392(a,1),9398(a,1,2))].">
      <j1 rule="para" parents="9392 9398"/>
    </justification>
  </clause>

  <clause id="9400">
    <literal><![CDATA[
      K(a(x,y,z),T((((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u),x * (y * z))) = K(a(x,y,z),(((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u))
    ]]></literal>
    <justification jstring="[para(6254(a,1),8032(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6254 8032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9401">
    <literal><![CDATA[
      T(x * K(y,T(z,u)),K(u,K(y,z))) = K(y,K(z,u)) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(7867(a,2),8105(a,1,1,2))].">
      <j1 rule="para" parents="7867 8105"/>
    </justification>
  </clause>

  <clause id="9402">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) * (y / u) = T(y,K(x,z)) / u
    ]]></literal>
    <justification jstring="[para(8154(a,1),8128(a,1,1))].">
      <j1 rule="para" parents="8154 8128"/>
    </justification>
  </clause>

  <clause id="9403">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = ((T(y,K(x,z)) / u) * u) / y
    ]]></literal>
    <justification jstring="[para(9402(a,1),113(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9402 113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9404">
    <literal><![CDATA[
      x * (T(y,K(z,u)) / w) != y / w
    ]]></literal>
    <literal><![CDATA[
      K((T(y,u) / w) / (y / w),z) = x
    ]]></literal>
    <justification jstring="[para(9402(a,1),6186(a,1,2))].">
      <j1 rule="para" parents="9402 6186"/>
    </justification>
  </clause>

  <clause id="9405">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,(((y \ 1) \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8243,a(flip),b,8305,a)].">
      <j1 rule="hyper" parents="64 8243 8305"/>
    </justification>
  </clause>

  <clause id="9406">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,((y \ 1) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,4814,a(flip),b,9405,a),flip(a)].">
      <j1 rule="hyper" parents="373 4814 9405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9408">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,5119,a(flip),b,9406,a),flip(a)].">
      <j1 rule="hyper" parents="373 5119 9406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9409">
    <literal><![CDATA[
      T(T(x,y),x \ 1) * K(z,T(x \ 1,y)) = T(T(x,y) \ 1,z) \ 1
    ]]></literal>
    <justification jstring="[para(8081(a,2),8419(a,1,2))].">
      <j1 rule="para" parents="8081 8419"/>
    </justification>
  </clause>

  <clause id="9410">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x,u) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(8482(a,1),8490(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8482 8490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9411">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6237,a(flip),b,9410,a),flip(a)].">
      <j1 rule="hyper" parents="373 6237 9410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9413">
    <literal><![CDATA[
      T(x * K((K(x,y) * z) * R(x,u,w),x),z) = R(x,K(x,y) * z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,6236,a(flip),b,9411,a),flip(a)].">
      <j1 rule="hyper" parents="64 6236 9411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9414">
    <literal><![CDATA[
      (x \ y) * T(x / y,x \ y) = (1 / (1 / (x \ y))) * (x / y)
    ]]></literal>
    <justification jstring="[para(8005(a,1),8653(a,1,2))].">
      <j1 rule="para" parents="8005 8653"/>
    </justification>
  </clause>

  <clause id="9415">
    <literal><![CDATA[
      (1 / (1 / (x \ y))) * (x / y) = (x / y) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(328,a,9414,a),flip(a)].">
      <j1 rule="hyper" parents="328 9414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9417">
    <literal><![CDATA[
      T(x / y,T((y * z) \ x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x / y,T(z \ (y \ x),y)) = u
    ]]></literal>
    <justification jstring="[para(8654(a,1),7982(a,1))].">
      <j1 rule="para" parents="8654 7982"/>
    </justification>
  </clause>

  <clause id="9418">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(35,a,8247,a(flip),b,8682,a)].">
      <j1 rule="hyper" parents="35 8247 8682"/>
    </justification>
  </clause>

  <clause id="9419">
    <literal><![CDATA[
      K(x,x \ y) * ((1 / (x / y)) * x) = (1 / (x / y)) * T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6022,a,b,8759,a)].">
      <j1 rule="hyper" parents="64 6022 8759"/>
    </justification>
  </clause>

  <clause id="9420">
    <literal><![CDATA[
      R(x,y,z) * (x \ K(u,T(x,w))) = T(x,T(u,w)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8893,a(flip),b,8841,a),flip(a)].">
      <j1 rule="hyper" parents="64 8893 8841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9421">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (z \ y)) \ u,z) = w
    ]]></literal>
    <justification jstring="[para(8924(a,1),6303(a,1))].">
      <j1 rule="para" parents="8924 6303"/>
    </justification>
  </clause>

  <clause id="9422">
    <literal><![CDATA[
      T(T(x,x * y) * R(x \ (x * y),z,u),x) = T(x * R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4664,a(flip),b,8944,a),flip(a)].">
      <j1 rule="hyper" parents="373 4664 8944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9423">
    <literal><![CDATA[
      K(T(x * K(y \ (x \ (z * x)),x),x),u) = K(x,T(u,T(z \ (x * y),x) \ x))
    ]]></literal>
    <justification jstring="[para(7380(a,1),9150(a,1,1,1,2))].">
      <j1 rule="para" parents="7380 9150"/>
    </justification>
  </clause>

  <clause id="9424">
    <literal><![CDATA[
      (K(x,K(y,z)) * T(y,K(u,w))) \ y = K(u,K(w,y)) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8110(a,1),9151(a,1,1,1))].">
      <j1 rule="para" parents="8110 9151"/>
    </justification>
  </clause>

  <clause id="9425">
    <literal><![CDATA[
      L(R(T(x,y),z,u),x \ T(w,x),x) = L(R(T(x,y),z,u),x \ w,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,29,a(flip),b,9184,a),flip(a)].">
      <j1 rule="hyper" parents="373 29 9184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9426">
    <literal><![CDATA[
      K(x,y / ((T(z,u) \ u) / w)) = K(x,y / ((z \ T(u,z)) / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9197,a(flip),b,9205,a),flip(a)].">
      <j1 rule="hyper" parents="64 9197 9205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9427">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,9206,a(flip),b,9207,a),flip(a)].">
      <j1 rule="hyper" parents="373 9206 9207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9428">
    <literal><![CDATA[
      K(x,R(x \ y,x,z / y)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,9208,a,b,9427,a)].">
      <j1 rule="hyper" parents="64 9208 9427"/>
    </justification>
  </clause>

  <clause id="9429">
    <literal><![CDATA[
      K(x,R(x \ (y / z),x,y / (y / z))) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(82(a,1),9428(a,2,2,2,1))].">
      <j1 rule="para" parents="82 9428"/>
    </justification>
  </clause>

  <clause id="9430">
    <literal><![CDATA[
      (1 / (1 / ((x * y) / x))) \ K(x,y) = (y \ 1) * K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(5759(a,1),9243(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5759 9243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9431">
    <literal><![CDATA[
      (1 / (1 / ((x * y) / x))) \ K(x,y) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(373,a,5822,a(flip),b,9430,a),flip(a)].">
      <j1 rule="hyper" parents="373 5822 9430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9432">
    <literal><![CDATA[
      x \ L(L(x,y,z) \ x,L(x,y,z),z * y) = (x \ 1) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(2869(a,2),9373(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2869 9373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9433">
    <literal><![CDATA[
      (x \ 1) * a(y,z,x) = x \ a(y,z,x)
    ]]></literal>
    <justification jstring="[para(2869(a,2),9432(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2869 9432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9434">
    <literal><![CDATA[
      R(x,x,a(y,z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,1997,a,b,9433,a(flip))].">
      <j1 rule="hyper" parents="40 1997 9433"/>
    </justification>
  </clause>

  <clause id="9435">
    <literal><![CDATA[
      L(a(x,y,z),z,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,1148,a,b,9433,a(flip))].">
      <j1 rule="hyper" parents="39 1148 9433"/>
    </justification>
  </clause>

  <clause id="9436">
    <literal><![CDATA[
      (x \ a(y,z,x)) * ((x * a(y,z,x)) \ u) = (x \ 1) * (x \ u)
    ]]></literal>
    <justification jstring="[para(9433(a,1),1628(a,1,1))].">
      <j1 rule="para" parents="9433 1628"/>
    </justification>
  </clause>

  <clause id="9437">
    <literal><![CDATA[
      a(x \ a(y,z,x),u,w) = a(x * a(y,z,x),u,w)
    ]]></literal>
    <justification jstring="[para(9433(a,1),2662(a,1,1))].">
      <j1 rule="para" parents="9433 2662"/>
    </justification>
  </clause>

  <clause id="9438">
    <literal><![CDATA[
      a((x \ a(y,z,x)) * u,w,v5) = a((x * a(y,z,x)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(9433(a,1),2690(a,1,1,1))].">
      <j1 rule="para" parents="9433 2690"/>
    </justification>
  </clause>

  <clause id="9439">
    <literal><![CDATA[
      (x * x) * a(y,z,x) = x * (x * a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(144,a,9434,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 9434 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9440">
    <literal><![CDATA[
      (1 / x) \ a(y,z,x) = x * a(y,z,x)
    ]]></literal>
    <justification jstring="[para(9434(a,1),1913(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9434 1913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9441">
    <literal><![CDATA[
      R(x,x,x) * a(y,z,x) = (x \ 1) \ a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,9435,a(flip),b,1665,a),flip(a)].">
      <j1 rule="hyper" parents="139 9435 1665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9442">
    <literal><![CDATA[
      (x \ 1) * a(y,z,x \ 1) = x \ a(y,z,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,9435,a(flip),b,568,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 9435 568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9443">
    <literal><![CDATA[
      x \ (y \ ((y * x) * x)) = x * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1046,a,b,9440,a)].">
      <j1 rule="hyper" parents="64 1046 9440"/>
    </justification>
  </clause>

  <clause id="9444">
    <literal><![CDATA[
      T(a(x,y,z) / (1 / z),u) \ a(x,y,z) = a(x,y,z) / T(z * a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(9440(a,1),8071(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9440 8071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9445">
    <literal><![CDATA[
      L(x * a(y,x,x),x,y) = x
    ]]></literal>
    <justification jstring="[para(9443(a,1),596(a,1,1))].">
      <j1 rule="para" parents="9443 596"/>
    </justification>
  </clause>

  <clause id="9446">
    <literal><![CDATA[
      L(L(x * a(y,x,x),z,u),x,y) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(9445(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9445 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9447">
    <literal><![CDATA[
      x \ (y \ ((y * x) * L(x,z,u))) = L(x * a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(42,a,596,a,b,9446,a)].">
      <j1 rule="hyper" parents="42 596 9446"/>
    </justification>
  </clause>

  <clause id="9448">
    <literal><![CDATA[
      L((x * y) * (1 / x),z,u) = (x * L(y,z,u)) * (1 / x)
    ]]></literal>
    <justification jstring="[para(566(a,1),5552(a,1,1)),flip(a)].">
      <j1 rule="para" parents="566 5552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9449">
    <literal><![CDATA[
      ((x * y) \ ((x \ 1) \ y)) \ 1 = ((x \ 1) \ y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1137(a,1),5664(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1137 5664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9450">
    <literal><![CDATA[
      K(x,y) * (T(x,z) * T(y,x)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(4506(a,1),5872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4506 5872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9452">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * (y * x)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[para(6022(a,2),9450(a,1,2))].">
      <j1 rule="para" parents="6022 9450"/>
    </justification>
  </clause>

  <clause id="9453">
    <literal><![CDATA[
      K(x,y) * (y * T(x,z)) = T(x,T(z,y)) * y
    ]]></literal>
    <justification jstring="[para(8367(a,1),9450(a,1,2))].">
      <j1 rule="para" parents="8367 9450"/>
    </justification>
  </clause>

  <clause id="9454">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,7805,a,b,9453,a(flip))].">
      <j1 rule="hyper" parents="36 7805 9453"/>
    </justification>
  </clause>

  <clause id="9455">
    <literal><![CDATA[
      K(x,y) \ T(x,T(z,y)) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(149,a,9454,a)].">
      <j1 rule="hyper" parents="149 9454"/>
    </justification>
  </clause>

  <clause id="9456">
    <literal><![CDATA[
      K(x \ y,x) * T(y / x,z) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5774(a,1),9454(a,1,2,1))].">
      <j1 rule="para" parents="5774 9454"/>
    </justification>
  </clause>

  <clause id="9457">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(9455(a,1),290(a,1,2))].">
      <j1 rule="para" parents="9455 290"/>
    </justification>
  </clause>

  <clause id="9458">
    <literal><![CDATA[
      T(T(x * K(y * R(x,z,u),x),w),y) = R(T(y \ (y * x),w),y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(5909(a,1),1497(a,1,1,1))].">
      <j1 rule="para" parents="5909 1497"/>
    </justification>
  </clause>

  <clause id="9459">
    <literal><![CDATA[
      (x * (K(x,y) * (z * R(x,u,w)))) \ ((T(x,y) * z) * R(x,u,w)) = a(x,K(x,y) * z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(7776(a,1),6084(a,1,1,2))].">
      <j1 rule="para" parents="7776 6084"/>
    </justification>
  </clause>

  <clause id="9460">
    <literal><![CDATA[
      R(x,y,z) * (x * (R((u * x) / u,y,z) \ 1)) = x * K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(1203(a,2),6255(a,1,2,2,1))].">
      <j1 rule="para" parents="1203 6255"/>
    </justification>
  </clause>

  <clause id="9461">
    <literal><![CDATA[
      T((x \ y) * (y \ x),z) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(6498,a,9343,a),flip(a)].">
      <j1 rule="hyper" parents="6498 9343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9462">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,9461,a)].">
      <j1 rule="hyper" parents="55 9461"/>
    </justification>
  </clause>

  <clause id="9463">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) * z = z * ((x \ y) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(145,a,9461,a(flip),b,4471,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 9461 4471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9465">
    <literal><![CDATA[
      T(x,((y * z) \ y) * z) = x
    ]]></literal>
    <justification jstring="[para(9(a,1),9462(a,1,2,2))].">
      <j1 rule="para" parents="9 9462"/>
    </justification>
  </clause>

  <clause id="9466">
    <literal><![CDATA[
      T(x,y * (z \ (z / y))) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),9462(a,1,2,1))].">
      <j1 rule="para" parents="82 9462"/>
    </justification>
  </clause>

  <clause id="9467">
    <literal><![CDATA[
      T(x,(y \ (y / z)) * z) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),9462(a,1,2,2))].">
      <j1 rule="para" parents="82 9462"/>
    </justification>
  </clause>

  <clause id="9468">
    <literal><![CDATA[
      ((((x * y) \ x) * y) \ z) \ z = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(4722,a,9465,a)].">
      <j1 rule="hyper" parents="4722 9465"/>
    </justification>
  </clause>

  <clause id="9469">
    <literal><![CDATA[
      T(((x * y) \ x) * y,z) = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(55,a,9465,a)].">
      <j1 rule="hyper" parents="55 9465"/>
    </justification>
  </clause>

  <clause id="9470">
    <literal><![CDATA[
      (x \ (x / (1 / (1 / y)))) \ y = y / (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(9466(a,1),5138(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9466 5138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9471">
    <literal><![CDATA[
      K(x,(y \ (y / z)) * z) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,9467,a)].">
      <j1 rule="hyper" parents="56 9467"/>
    </justification>
  </clause>

  <clause id="9472">
    <literal><![CDATA[
      T((x \ (x / y)) * y,z) = (x \ (x / y)) * y
    ]]></literal>
    <justification jstring="[hyper(55,a,9467,a)].">
      <j1 rule="hyper" parents="55 9467"/>
    </justification>
  </clause>

  <clause id="9473">
    <literal><![CDATA[
      K(x,y * ((z * y) \ z)) = 1
    ]]></literal>
    <justification jstring="[para(211(a,1),9471(a,1,2,1))].">
      <j1 rule="para" parents="211 9471"/>
    </justification>
  </clause>

  <clause id="9474">
    <literal><![CDATA[
      K(x,y * L(y \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[para(448(a,1),9471(a,1,2,1))].">
      <j1 rule="para" parents="448 9471"/>
    </justification>
  </clause>

  <clause id="9475">
    <literal><![CDATA[
      K(x * ((y * x) \ y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,9473,a,b,6076,a),flip(a)].">
      <j1 rule="hyper" parents="140 9473 6076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9476">
    <literal><![CDATA[
      (((x * y) \ x) * y) / (z * z) = ((z * z) \ ((x * y) \ x)) * y
    ]]></literal>
    <justification jstring="[hyper(142,a,9469,a(flip),b,830,a)].">
      <j1 rule="hyper" parents="142 9469 830"/>
    </justification>
  </clause>

  <clause id="9477">
    <literal><![CDATA[
      (x / T((y \ (y / x)) * x,z)) * x = (1 / (1 / (y \ (y / x)))) \ x
    ]]></literal>
    <justification jstring="[para(9472(a,2),2014(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9472 2014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9478">
    <literal><![CDATA[
      (x / T((y \ (y / x)) * x,z)) * x = (y \ (y / (1 / (1 / x)))) \ x
    ]]></literal>
    <justification jstring="[para(3942(a,1),9477(a,2,1))].">
      <j1 rule="para" parents="3942 9477"/>
    </justification>
  </clause>

  <clause id="9479">
    <literal><![CDATA[
      (x / T((y \ (y / x)) * x,z)) * x = x / (y \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,9470,a(flip),b,9478,a),flip(a)].">
      <j1 rule="hyper" parents="373 9470 9478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9480">
    <literal><![CDATA[
      (((x \ (x / y)) * y) \ y) * y = y / (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(301(a,1),9479(a,1,1))].">
      <j1 rule="para" parents="301 9479"/>
    </justification>
  </clause>

  <clause id="9481">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) * y = y / (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(2620(a,1),9480(a,1,1))].">
      <j1 rule="para" parents="2620 9480"/>
    </justification>
  </clause>

  <clause id="9482">
    <literal><![CDATA[
      K(x,y \ z) * K((z \ y) \ x,x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(8529(a,1),6718(a,1,2))].">
      <j1 rule="para" parents="8529 6718"/>
    </justification>
  </clause>

  <clause id="9483">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(7568(a,1),9482(a,1,2))].">
      <j1 rule="para" parents="7568 9482"/>
    </justification>
  </clause>

  <clause id="9484">
    <literal><![CDATA[
      (x * (y * T(z,y))) \ ((x * y) * T(z,y)) = a(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[para(6856(a,1),6874(a,1,2))].">
      <j1 rule="para" parents="6856 6874"/>
    </justification>
  </clause>

  <clause id="9485">
    <literal><![CDATA[
      (x * (y * T(x,z))) \ ((x * y) * T(x,z)) = a(x,y * K(x,z),x)
    ]]></literal>
    <justification jstring="[para(7139(a,1),6874(a,1,2))].">
      <j1 rule="para" parents="7139 6874"/>
    </justification>
  </clause>

  <clause id="9486">
    <literal><![CDATA[
      a(x,y * K(z,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(9484(a,1),959(a,1))].">
      <j1 rule="para" parents="9484 959"/>
    </justification>
  </clause>

  <clause id="9487">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = a(x,y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(959,a,9485,a),flip(a)].">
      <j1 rule="hyper" parents="959 9485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9488">
    <literal><![CDATA[
      x * (L(x \ y,z,u) * K(x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(y / x,z,u) * T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(7135(a,1),6977(a,1))].">
      <j1 rule="para" parents="7135 6977"/>
    </justification>
  </clause>

  <clause id="9489">
    <literal><![CDATA[
      (x * K(y,z)) / (z \ 1) = x / (z \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,8016,a(flip),b,7116,a),flip(a)].">
      <j1 rule="hyper" parents="64 8016 7116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9491">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x / (y \ K(y,x))
    ]]></literal>
    <justification jstring="[para(5753(a,2),9489(a,1,1))].">
      <j1 rule="para" parents="5753 9489"/>
    </justification>
  </clause>

  <clause id="9492">
    <literal><![CDATA[
      (T(x,y) / (y \ 1)) \ x = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(143,a,9491,a,b,171,a)].">
      <j1 rule="hyper" parents="143 9491 171"/>
    </justification>
  </clause>

  <clause id="9493">
    <literal><![CDATA[
      x \ (x / (y \ K(y,x))) = (x / (y \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(139,a,9491,a(flip),b,4401,a(flip))].">
      <j1 rule="hyper" parents="139 9491 4401"/>
    </justification>
  </clause>

  <clause id="9495">
    <literal><![CDATA[
      (x / ((x \ y) \ 1)) / x = x \ (x / ((y / x) \ 1))
    ]]></literal>
    <justification jstring="[para(6256(a,1),9493(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6256 9493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9496">
    <literal><![CDATA[
      x * ((x / ((x \ y) \ 1)) / x) = x / ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,9495,a,b,xx)].">
      <j1 rule="hyper" parents="145 9495"/>
    </justification>
  </clause>

  <clause id="9498">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / (y \ T(x,y \ 1))
    ]]></literal>
    <justification jstring="[para(4394(a,1),7339(a,2,2))].">
      <j1 rule="para" parents="4394 7339"/>
    </justification>
  </clause>

  <clause id="9499">
    <literal><![CDATA[
      x / (y \ T(x,y \ 1)) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,4405,a(flip),b,9498,a),flip(a)].">
      <j1 rule="hyper" parents="64 4405 9498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9500">
    <literal><![CDATA[
      (T(x,(y \ 1) \ 1) / (y \ 1)) \ x = x / ((y \ 1) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(3871(a,1),9499(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3871 9499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9501">
    <literal><![CDATA[
      x / ((y \ 1) \ T(x,y)) = (T(x,y) / (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(3871(a,1),9500(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3871 9500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9502">
    <literal><![CDATA[
      ((T(x,y) / (y \ 1)) \ x) \ x = (y \ 1) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(215,a,9501,a)].">
      <j1 rule="hyper" parents="215 9501"/>
    </justification>
  </clause>

  <clause id="9504">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(9492(a,1),9502(a,1,1))].">
      <j1 rule="para" parents="9492 9502"/>
    </justification>
  </clause>

  <clause id="9505">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ ((x \ 1) \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,3420,a,b,9504,a),flip(a)].">
      <j1 rule="hyper" parents="373 3420 9504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9506">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4407,a(flip),b,9504,a),flip(a)].">
      <j1 rule="hyper" parents="373 4407 9504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9507">
    <literal><![CDATA[
      x \ ((y \ K(y,x)) \ x) = ((y \ 1) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(139,a,9504,a,b,4407,a(flip))].">
      <j1 rule="hyper" parents="139 9504 4407"/>
    </justification>
  </clause>

  <clause id="9512">
    <literal><![CDATA[
      L(K(x,T(y,z)),z,L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,L(y,u,w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(7593(a,2),7526(a,1))].">
      <j1 rule="para" parents="7593 7526"/>
    </justification>
  </clause>

  <clause id="9513">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(9512,a,9312,a)].">
      <j1 rule="hyper" parents="9512 9312"/>
    </justification>
  </clause>

  <clause id="9514">
    <literal><![CDATA[
      K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7875,a(flip),b,9513,a),flip(a)].">
      <j1 rule="hyper" parents="64 7875 9513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9515">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),9513(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9516">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(8593(a,1),9513(a,1,2))].">
      <j1 rule="para" parents="8593 9513"/>
    </justification>
  </clause>

  <clause id="9517">
    <literal><![CDATA[
      K(x,T(y \ z,u * z)) = K(x,T(y \ z,u * y))
    ]]></literal>
    <justification jstring="[para(10(a,1),9516(a,1,2,2,2))].">
      <j1 rule="para" parents="10 9516"/>
    </justification>
  </clause>

  <clause id="9518">
    <literal><![CDATA[
      K(x,T(y,z * (y * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(8508(a,1),9516(a,1,2))].">
      <j1 rule="para" parents="8508 9516"/>
    </justification>
  </clause>

  <clause id="9519">
    <literal><![CDATA[
      K(x * y,T(x,z * y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(8447,a,9518,a),flip(a)].">
      <j1 rule="hyper" parents="8447 9518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9520">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),9518(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9521">
    <literal><![CDATA[
      K(T(x,y) * z,T(x,u * z)) = K(x * z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8606,a,b,9519,a)].">
      <j1 rule="hyper" parents="64 8606 9519"/>
    </justification>
  </clause>

  <clause id="9522">
    <literal><![CDATA[
      K(T(x,y * (x \ z)),u) = w / (K(u,T(x,y * z)) * w)
    ]]></literal>
    <justification jstring="[para(9520(a,1),6160(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9520 6160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9523">
    <literal><![CDATA[
      T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(9514(a,1),5855(a,1,2))].">
      <j1 rule="para" parents="9514 5855"/>
    </justification>
  </clause>

  <clause id="9524">
    <literal><![CDATA[
      K(x,T(y \ x,z * y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(8447,a,9517,a),flip(a)].">
      <j1 rule="hyper" parents="8447 9517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9525">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),9524(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 9524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9526">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8755,a(flip),b,9525,a)].">
      <j1 rule="hyper" parents="64 8755 9525"/>
    </justification>
  </clause>

  <clause id="9527">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = y \ R(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,9523,a(flip),b,6088,a),flip(a)].">
      <j1 rule="hyper" parents="139 9523 6088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9528">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = x \ R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,9523,a(flip),b,5776,a),flip(a)].">
      <j1 rule="hyper" parents="139 9523 5776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9529">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,L(y,u,w))) = L(K(z * L(y,u,w),y),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(9523(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9523 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9530">
    <literal><![CDATA[
      K(T(x,y * (x \ z)),u) = K(T(x,y * z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6160,a(flip),b,9522,a),flip(a)].">
      <j1 rule="hyper" parents="373 6160 9522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9531">
    <literal><![CDATA[
      K(T(x,y * (x \ z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u,y * z)) = w
    ]]></literal>
    <justification jstring="[para(9530(a,2),8019(a,1))].">
      <j1 rule="para" parents="9530 8019"/>
    </justification>
  </clause>

  <clause id="9532">
    <literal><![CDATA[
      K(x,T(y,z * (x \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(9531,a,7869,a),flip(a)].">
      <j1 rule="hyper" parents="9531 7869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9533">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8620,a,b,9532,a)].">
      <j1 rule="hyper" parents="64 8620 9532"/>
    </justification>
  </clause>

  <clause id="9534">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (y * (x \ z))) = w
    ]]></literal>
    <justification jstring="[para(9532(a,1),8325(a,1))].">
      <j1 rule="para" parents="9532 8325"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(7321(a,1),7671(a,1))].">
      <j1 rule="para" parents="7321 7671"/>
    </justification>
  </clause>

  <clause id="9536">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * K(z,y)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(6156(a,1),9535(a,1,1,2))].">
      <j1 rule="para" parents="6156 9535"/>
    </justification>
  </clause>

  <clause id="9537">
    <literal><![CDATA[
      L(x * K(y,T(x,z)),u,w) / L(x,u,w) = K(y,T(L(x,u,w),z))
    ]]></literal>
    <justification jstring="[para(8214(a,1),8279(a,1,1,1,2))].">
      <j1 rule="para" parents="8214 8279"/>
    </justification>
  </clause>

  <clause id="9538">
    <literal><![CDATA[
      L(x * K(y,T(x,z)),u,w) / L(x,u,w) = K(y,L(T(x,z),u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),9537(a,2,2))].">
      <j1 rule="para" parents="25 9537"/>
    </justification>
  </clause>

  <clause id="9539">
    <literal><![CDATA[
      L(x * K(y,T(x,z)),u,w) / L(x,u,w) = K(y,L(T(x,x * z),u,w))
    ]]></literal>
    <justification jstring="[para(7421(a,1),9538(a,1,1,1,2))].">
      <j1 rule="para" parents="7421 9538"/>
    </justification>
  </clause>

  <clause id="9540">
    <literal><![CDATA[
      K(R(x \ R(x,y,z),x,y * z),u) = K(a(x,y,z),T(u,x * (y * z)))
    ]]></literal>
    <justification jstring="[para(2295(a,2),8281(a,1,1))].">
      <j1 rule="para" parents="2295 8281"/>
    </justification>
  </clause>

  <clause id="9541">
    <literal><![CDATA[
      K(x,a(y,z,u)) * K(x,K(a(y,z,u),y * (z * u))) = K(x,((y * z) * u) / (y * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,8087,a,b,8290,a)].">
      <j1 rule="hyper" parents="373 8087 8290"/>
    </justification>
  </clause>

  <clause id="9542">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * T(x,z),x)
    ]]></literal>
    <justification jstring="[para(8550(a,1),8634(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8550 8634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9544">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * x,x)
    ]]></literal>
    <justification jstring="[para(8527(a,1),9542(a,2,2))].">
      <j1 rule="para" parents="8527 9542"/>
    </justification>
  </clause>

  <clause id="9546">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9544(a,2),8533(a,1))].">
      <j1 rule="para" parents="9544 8533"/>
    </justification>
  </clause>

  <clause id="9547">
    <literal><![CDATA[
      K((x / y) \ z,L(y,u,w)) = K(x \ (z * y),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5974,a,8832,a),flip(a)].">
      <j1 rule="hyper" parents="5974 8832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9548">
    <literal><![CDATA[
      T(x,y * y) / (y * T(x,y)) = R(T(1 / y,x),y,T(x,y))
    ]]></literal>
    <justification jstring="[para(7581(a,1),8844(a,1,1))].">
      <j1 rule="para" parents="7581 8844"/>
    </justification>
  </clause>

  <clause id="9549">
    <literal><![CDATA[
      R(T(1 / x,y),x,T(y,x)) = T(y,x * x) / (y * x)
    ]]></literal>
    <justification jstring="[para(115(a,1),9548(a,1,2)),flip(a)].">
      <j1 rule="para" parents="115 9548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9550">
    <literal><![CDATA[
      T(x,x \ y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = u
    ]]></literal>
    <justification jstring="[para(9452(a,1),9217(a,1))].">
      <j1 rule="para" parents="9452 9217"/>
    </justification>
  </clause>

  <clause id="9551">
    <literal><![CDATA[
      T(x / y,T(z \ (y \ x),y)) = T(x / y,x / (y * z))
    ]]></literal>
    <justification jstring="[hyper(9417,a,8307,a)].">
      <j1 rule="hyper" parents="9417 8307"/>
    </justification>
  </clause>

  <clause id="9552">
    <literal><![CDATA[
      R(x,y,z) * (R((u * x) / u,y,z) \ x) = x * K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(3243(a,1),9460(a,1,2))].">
      <j1 rule="para" parents="3243 9460"/>
    </justification>
  </clause>

  <clause id="9553">
    <literal><![CDATA[
      R((x * y) / x,z,y) \ y = R(y,z,y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,7389,a(flip),b,9552,a),flip(a)].">
      <j1 rule="hyper" parents="139 7389 9552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9554">
    <literal><![CDATA[
      K(x,L(T(y,y * z),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9538,a(flip),b,9539,a),flip(a)].">
      <j1 rule="hyper" parents="64 9538 9539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9555">
    <literal><![CDATA[
      K(R(K(x,y) \ R(K(x,y),z,u),K(x,y),z * u),((z * u) \ K(y,x)) \ 1) = K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1)
    ]]></literal>
    <justification jstring="[para(6194(a,1),9540(a,2,2))].">
      <j1 rule="para" parents="6194 9540"/>
    </justification>
  </clause>

  <clause id="9556">
    <literal><![CDATA[
      K(x,K(y,R(z \ R(z,u,w),z,u * w) \ 1)) = K(x,K(a(z,u,w),T(y,z * (u * w))))
    ]]></literal>
    <justification jstring="[para(9540(a,1),9008(a,2,2))].">
      <j1 rule="para" parents="9540 9008"/>
    </justification>
  </clause>

  <clause id="9557">
    <literal><![CDATA[
      T(x,x \ y) \ R(T(x,x \ y),z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[hyper(139,a,5878,a(flip),b,5810,a),flip(a)].">
      <j1 rule="hyper" parents="139 5878 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9558">
    <literal><![CDATA[
      a((x \ y) * K((y / x) \ y,y / x),y / (y / x),z) = a(x \ y,x,z)
    ]]></literal>
    <justification jstring="[para(7937(a,1),6398(a,1,1,2))].">
      <j1 rule="para" parents="7937 6398"/>
    </justification>
  </clause>

  <clause id="9559">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) / (T((x \ 1) \ 1,y) * K(z,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6047(a,1),6421(a,1,2,2))].">
      <j1 rule="para" parents="6047 6421"/>
    </justification>
  </clause>

  <clause id="9560">
    <literal><![CDATA[
      (x \ K(y,x)) \ L((x \ 1) * z,u,w) = T(x,y) * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,5755,a(flip),b,6604,a),flip(a)].">
      <j1 rule="hyper" parents="373 5755 6604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9561">
    <literal><![CDATA[
      R(R(x,y,z),y * z,K(z,u)) = ((x * y) * T(z,u)) / (y * T(z,u))
    ]]></literal>
    <justification jstring="[para(6852(a,1),6926(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6852 6926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9562">
    <literal><![CDATA[
      R(R(x,y,z),y * z,K(z,u)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,20,a,b,9561,a),flip(a)].">
      <j1 rule="hyper" parents="373 20 9561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9563">
    <literal><![CDATA[
      R(R(x,y,z),y * z,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(9561(a,2),666(a,1))].">
      <j1 rule="para" parents="9561 666"/>
    </justification>
  </clause>

  <clause id="9564">
    <literal><![CDATA[
      R(x,K(y,z),T(u,K(y,w))) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,8624,a(flip),b,9562,a),flip(a)].">
      <j1 rule="hyper" parents="64 8624 9562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9566">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,8198,a,b,9564,a)].">
      <j1 rule="hyper" parents="64 8198 9564"/>
    </justification>
  </clause>

  <clause id="9567">
    <literal><![CDATA[
      R(x,K(y,z),T(K(z,y) * u,K(y,w))) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(9564(a,2),6195(a,1,1))].">
      <j1 rule="para" parents="9564 6195"/>
    </justification>
  </clause>

  <clause id="9569">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u * K(z,w)) = R(x,K(y,z),u * K(z,w))
    ]]></literal>
    <justification jstring="[para(8942(a,1),9566(a,1,2))].">
      <j1 rule="para" parents="8942 9566"/>
    </justification>
  </clause>

  <clause id="9570">
    <literal><![CDATA[
      R(x,K(y,T(z,u)),u * K(z,w)) = R(x,K(y,z),u * K(z,w))
    ]]></literal>
    <justification jstring="[para(7867(a,2),9569(a,1,2))].">
      <j1 rule="para" parents="7867 9569"/>
    </justification>
  </clause>

  <clause id="9571">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(6934(a,1),7028(a,2,2,2))].">
      <j1 rule="para" parents="6934 7028"/>
    </justification>
  </clause>

  <clause id="9572">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(115(a,1),7251(a,1,1,2,2))].">
      <j1 rule="para" parents="115 7251"/>
    </justification>
  </clause>

  <clause id="9573">
    <literal><![CDATA[
      ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(5639(a,2),9572(a,1,1))].">
      <j1 rule="para" parents="5639 9572"/>
    </justification>
  </clause>

  <clause id="9574">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(7564,a,9573,a),flip(a)].">
      <j1 rule="hyper" parents="7564 9573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9575">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(9573(a,1),7564(a,1))].">
      <j1 rule="para" parents="9573 7564"/>
    </justification>
  </clause>

  <clause id="9576">
    <literal><![CDATA[
      T(x,(y * (z * x)) \ u) = T(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(143,a,9574,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 9574 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9577">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),9574(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 9574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9578">
    <literal><![CDATA[
      (x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y)
    ]]></literal>
    <justification jstring="[para(9574(a,1),6882(a,1,1,2))].">
      <j1 rule="para" parents="9574 6882"/>
    </justification>
  </clause>

  <clause id="9579">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(8785,a,9577,a)].">
      <j1 rule="hyper" parents="8785 9577"/>
    </justification>
  </clause>

  <clause id="9580">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,8804,a(flip),b,9579,a)].">
      <j1 rule="hyper" parents="64 8804 9579"/>
    </justification>
  </clause>

  <clause id="9581">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(9579(a,1),6177(a,1,2,2))].">
      <j1 rule="para" parents="9579 6177"/>
    </justification>
  </clause>

  <clause id="9582">
    <literal><![CDATA[
      L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) = K(x,(u * (y * (z / x))) \ w)
    ]]></literal>
    <justification jstring="[para(9579(a,1),7081(a,1,1))].">
      <j1 rule="para" parents="9579 7081"/>
    </justification>
  </clause>

  <clause id="9583">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,8829,a,b,9580,a)].">
      <j1 rule="hyper" parents="64 8829 9580"/>
    </justification>
  </clause>

  <clause id="9584">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * y) \ (z \ u),z)
    ]]></literal>
    <justification jstring="[hyper(6899,a,9578,a),flip(a)].">
      <j1 rule="hyper" parents="6899 9578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9585">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ (z \ u),z) = w
    ]]></literal>
    <justification jstring="[para(9578(a,1),6899(a,1))].">
      <j1 rule="para" parents="9578 6899"/>
    </justification>
  </clause>

  <clause id="9586">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) = K((x * z) \ (y \ u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8913,a(flip),b,9584,a)].">
      <j1 rule="hyper" parents="64 8913 9584"/>
    </justification>
  </clause>

  <clause id="9587">
    <literal><![CDATA[
      L(x * K((y * z) \ (x \ u),x),w,v5) / L(x,w,v5) = K((y * (z * x)) \ u,L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(9584(a,1),6549(a,1,1,1,2))].">
      <j1 rule="para" parents="9584 6549"/>
    </justification>
  </clause>

  <clause id="9588">
    <literal><![CDATA[
      K((x * y) \ ((1 / y) \ z),1 / y) = K(x \ z,1 / y)
    ]]></literal>
    <justification jstring="[para(81(a,1),9586(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="81 9586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9589">
    <literal><![CDATA[
      K((x * (y \ z)) \ ((1 / (y \ z)) \ u),1 / (y \ z)) = K(x \ u,z \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6699,a(flip),b,9588,a),flip(a)].">
      <j1 rule="hyper" parents="373 6699 9588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9590">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ (y \ u),y) = w
    ]]></literal>
    <justification jstring="[para(8913(a,1),9585(a,1))].">
      <j1 rule="para" parents="8913 9585"/>
    </justification>
  </clause>

  <clause id="9591">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z)
    ]]></literal>
    <justification jstring="[hyper(6303,a,9581,a),flip(a)].">
      <j1 rule="hyper" parents="6303 9581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9592">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y)
    ]]></literal>
    <justification jstring="[hyper(9421,a,9591,a)].">
      <j1 rule="hyper" parents="9421 9591"/>
    </justification>
  </clause>

  <clause id="9593">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(x \ (z * y),y)
    ]]></literal>
    <justification jstring="[para(8(a,1),9592(a,2,1,1))].">
      <j1 rule="para" parents="8 9592"/>
    </justification>
  </clause>

  <clause id="9594">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7597,a,b,9593,a)].">
      <j1 rule="hyper" parents="64 7597 9593"/>
    </justification>
  </clause>

  <clause id="9595">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ ((z * y) * x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7567,a,b,9593,a)].">
      <j1 rule="hyper" parents="64 7567 9593"/>
    </justification>
  </clause>

  <clause id="9596">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),9593(a,2,1,2))].">
      <j1 rule="para" parents="7 9593"/>
    </justification>
  </clause>

  <clause id="9597">
    <literal><![CDATA[
      x * (y \ K(y \ x,x)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(9596(a,1),6691(a,1,2,2))].">
      <j1 rule="para" parents="9596 6691"/>
    </justification>
  </clause>

  <clause id="9598">
    <literal><![CDATA[
      ((x * (K(y \ x,x) * (y \ 1))) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(9597(a,1),2949(a,2,2,1))].">
      <j1 rule="para" parents="9597 2949"/>
    </justification>
  </clause>

  <clause id="9599">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((z \ y) \ x,x) = u
    ]]></literal>
    <justification jstring="[para(9594(a,2),7570(a,1))].">
      <j1 rule="para" parents="9594 7570"/>
    </justification>
  </clause>

  <clause id="9600">
    <literal><![CDATA[
      T(x \ (x / y),z) * T(x,y \ 1) = K(z,y \ 1) \ (x / y)
    ]]></literal>
    <justification jstring="[para(82(a,1),7282(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 7282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9602">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(5868(a,1),7300(a,1,1,2))].">
      <j1 rule="para" parents="5868 7300"/>
    </justification>
  </clause>

  <clause id="9603">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (T(y,z) * z)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(5825(a,1),9602(a,1,2,2))].">
      <j1 rule="para" parents="5825 9602"/>
    </justification>
  </clause>

  <clause id="9604">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (y \ 1),1 / y)
    ]]></literal>
    <justification jstring="[para(3731(a,1),7525(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3731 7525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9605">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5255,a,b,9604,a),flip(a)].">
      <j1 rule="hyper" parents="373 5255 9604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9606">
    <literal><![CDATA[
      K((x / y) / (1 / y),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5255,a,b,9605,a)].">
      <j1 rule="hyper" parents="64 5255 9605"/>
    </justification>
  </clause>

  <clause id="9607">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[para(9606(a,1),5751(a,2,2))].">
      <j1 rule="para" parents="9606 5751"/>
    </justification>
  </clause>

  <clause id="9608">
    <literal><![CDATA[
      R(x * R(K(y,x),z,u),w,x) = R(x,w,x) * R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(6682(a,1),7534(a,1,1,2))].">
      <j1 rule="para" parents="6682 7534"/>
    </justification>
  </clause>

  <clause id="9609">
    <literal><![CDATA[
      (x \ T(y,x)) \ (x \ (y * T(x,T(y,z)))) = T(T(x,T(y,z)),x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8599,a(flip),b,7535,a),flip(a)].">
      <j1 rule="hyper" parents="373 8599 7535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9610">
    <literal><![CDATA[
      (x \ T(y,x)) \ T(y,K(x,z)) = T(T(x,T(y,z)),x \ y)
    ]]></literal>
    <justification jstring="[para(8403(a,1),9609(a,1,2))].">
      <j1 rule="para" parents="8403 9609"/>
    </justification>
  </clause>

  <clause id="9611">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,y) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6706,a(flip),b,7559,a)].">
      <j1 rule="hyper" parents="64 6706 7559"/>
    </justification>
  </clause>

  <clause id="9613">
    <literal><![CDATA[
      (T(x * y,z) / y) * (x \ 1) = (1 / y) * (x \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(1506(a,1),7648(a,1,1))].">
      <j1 rule="para" parents="1506 7648"/>
    </justification>
  </clause>

  <clause id="9614">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ T((x \ y) * x,x)) = (x \ T(y,x)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(3428(a,1),9613(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3428 9613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9616">
    <literal><![CDATA[
      L(x \ 1,x,K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(7773,a,7335,a)].">
      <j1 rule="hyper" parents="7773 7335"/>
    </justification>
  </clause>

  <clause id="9617">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(8193(a,1),9616(a,1,3))].">
      <j1 rule="para" parents="8193 9616"/>
    </justification>
  </clause>

  <clause id="9618">
    <literal><![CDATA[
      L(x \ 1,T(x,y),z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(7354,a,9617,a)].">
      <j1 rule="hyper" parents="7354 9617"/>
    </justification>
  </clause>

  <clause id="9619">
    <literal><![CDATA[
      L(x \ 1,x,y) * L(L(x \ 1,T(x,z),y) \ 1,u,w) = L((x \ 1) * L((x \ 1) \ 1,u,w),T(x,z),y)
    ]]></literal>
    <justification jstring="[para(9618(a,1),4273(a,1,1))].">
      <j1 rule="para" parents="9618 4273"/>
    </justification>
  </clause>

  <clause id="9620">
    <literal><![CDATA[
      K(x \ y,x) * L(T(x,x \ y),z,u) = y \ ((L(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[para(1958(a,1),8010(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1958 8010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9621">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = K(T(x / (x / y),x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,7284,a,b,8362,a),flip(a)].">
      <j1 rule="hyper" parents="373 7284 8362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9622">
    <literal><![CDATA[
      K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,7378,a(flip),b,8947,a),flip(a)].">
      <j1 rule="hyper" parents="373 7378 8947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9623">
    <literal><![CDATA[
      K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z)
    ]]></literal>
    <justification jstring="[hyper(9590,a,9622,a)].">
      <j1 rule="hyper" parents="9590 9622"/>
    </justification>
  </clause>

  <clause id="9625">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = (T(z * y,K(x,u)) / y) / z
    ]]></literal>
    <justification jstring="[hyper(9035,a,9002,a)].">
      <j1 rule="hyper" parents="9035 9002"/>
    </justification>
  </clause>

  <clause id="9626">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = K(x,K(u,(1 / y) / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,9034,a(flip),b,9625,a),flip(a)].">
      <j1 rule="hyper" parents="373 9034 9625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9627">
    <literal><![CDATA[
      K(x,K((1 / (y \ z)) / u,R(u / y,y,y \ z))) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[para(677(a,2),9626(a,1,2,2))].">
      <j1 rule="para" parents="677 9626"/>
    </justification>
  </clause>

  <clause id="9628">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,((u * z) \ u) \ y) = K(x,y / ((u * z) \ u))
    ]]></literal>
    <justification jstring="[para(9010(a,1),9071(a,1,1))].">
      <j1 rule="para" parents="9010 9071"/>
    </justification>
  </clause>

  <clause id="9629">
    <literal><![CDATA[
      K(T(x,y),((T(x,y) \ 1) * y) \ z) = K(x,z / ((x \ 1) * T(y,x)))
    ]]></literal>
    <justification jstring="[para(4619(a,1),9256(a,1,1))].">
      <j1 rule="para" parents="4619 9256"/>
    </justification>
  </clause>

  <clause id="9630">
    <literal><![CDATA[
      K(T(x,y),((T(x,y) \ 1) * y) \ z) = K(x,z / ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,9199,a(flip),b,9629,a),flip(a)].">
      <j1 rule="hyper" parents="373 9199 9629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9631">
    <literal><![CDATA[
      T(T(x / y,x \ y),z * (y \ x)) = T(x / y,(x / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,8882,a(flip),b,9264,a),flip(a)].">
      <j1 rule="hyper" parents="373 8882 9264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9633">
    <literal><![CDATA[
      (x \ y) * ((K(x,x \ y) * z) / T(z,K(u,w))) = (y / x) * K(z,K(u,u \ w))
    ]]></literal>
    <justification jstring="[para(8706(a,1),9307(a,1,2,2))].">
      <j1 rule="para" parents="8706 9307"/>
    </justification>
  </clause>

  <clause id="9634">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(9224,a,9319,a)].">
      <j1 rule="hyper" parents="9224 9319"/>
    </justification>
  </clause>

  <clause id="9635">
    <literal><![CDATA[
      T(T(x,x * y) * R(y,z,u),x) = T(x * R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),9422(a,1,1,2,1))].">
      <j1 rule="para" parents="9 9422"/>
    </justification>
  </clause>

  <clause id="9636">
    <literal><![CDATA[
      a((x \ y) * K(x,y / x),y / (y / x),z) = a(x \ y,x,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),9558(a,1,1,2,1))].">
      <j1 rule="para" parents="82 9558"/>
    </justification>
  </clause>

  <clause id="9638">
    <literal><![CDATA[
      a(x / y,x / (x / y),z) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[para(5822(a,1),9636(a,1,1))].">
      <j1 rule="para" parents="5822 9636"/>
    </justification>
  </clause>

  <clause id="9639">
    <literal><![CDATA[
      a(((x * y) / x) / T(x,y),((x * y) / x) / (((x * y) / x) / T(x,y)),z) = a(x \ y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4469(a,1),9638(a,2,1))].">
      <j1 rule="para" parents="4469 9638"/>
    </justification>
  </clause>

  <clause id="9640">
    <literal><![CDATA[
      K((x * ((y * z) \ y)) \ ((1 / ((y * z) \ y)) \ u),1 / ((y * z) \ y)) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9589(a,2,2))].">
      <j1 rule="para" parents="9 9589"/>
    </justification>
  </clause>

  <clause id="9641">
    <literal><![CDATA[
      (x \ T(y,x)) * ((x \ y) \ 1) = (1 / x) * ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(5486(a,1),9614(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5486 9614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9642">
    <literal><![CDATA[
      K(x,y) = (y \ T(x,y)) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(137,a,6462,a(flip),b,9641,a)].">
      <j1 rule="hyper" parents="137 6462 9641"/>
    </justification>
  </clause>

  <clause id="9643">
    <literal><![CDATA[
      (x \ T(x * y,x)) * (y \ 1) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),9642(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 9642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9644">
    <literal><![CDATA[
      (x \ T(x * K(y,z),x)) * (K(z,y) * 1) = K(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(6156(a,1),9643(a,1,2))].">
      <j1 rule="para" parents="6156 9643"/>
    </justification>
  </clause>

  <clause id="9645">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * (K(z,x) * 1) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(9360(a,2),9644(a,1,1))].">
      <j1 rule="para" parents="9360 9644"/>
    </justification>
  </clause>

  <clause id="9646">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(738,a,9645,a)].">
      <j1 rule="hyper" parents="738 9645"/>
    </justification>
  </clause>

  <clause id="9647">
    <literal><![CDATA[
      T(K(x \ y,x) * L(x,z,u),x \ y) = y \ ((L(x,z,u) * (x \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7799,a,b,9620,a)].">
      <j1 rule="hyper" parents="64 7799 9620"/>
    </justification>
  </clause>

  <clause id="9648">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4883(a,1),9621(a,2,1))].">
      <j1 rule="para" parents="4883 9621"/>
    </justification>
  </clause>

  <clause id="9649">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,9648,a(flip),b,8362,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 9648 8362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9650">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ ((L(y,z,u) * (y \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7770,a(flip),b,9647,a)].">
      <j1 rule="hyper" parents="64 7770 9647"/>
    </justification>
  </clause>

  <clause id="9651">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * (y * (z * ((y \ 1) / z)))
    ]]></literal>
    <justification jstring="[hyper(334,a,5623,a),flip(a)].">
      <j1 rule="hyper" parents="334 5623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9652">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * K(z,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(7197(a,1),9651(a,2,2))].">
      <j1 rule="para" parents="7197 9651"/>
    </justification>
  </clause>

  <clause id="9653">
    <literal><![CDATA[
      K(x,(y * z) \ (x \ y)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(35,a,7196,a,b,9652,a(flip))].">
      <j1 rule="hyper" parents="35 7196 9652"/>
    </justification>
  </clause>

  <clause id="9654">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = (u * K(z,y \ (z \ 1))) \ u
    ]]></literal>
    <justification jstring="[para(9653(a,1),6882(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9653 6882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9655">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = K(y \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6882,a(flip),b,9654,a),flip(a)].">
      <j1 rule="hyper" parents="373 6882 9654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9656">
    <literal><![CDATA[
      K((x \ y) \ (z \ 1),z) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),9655(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 9655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9657">
    <literal><![CDATA[
      K((x * (y \ z)) \ 1,x) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7380,a,b,9656,a)].">
      <j1 rule="hyper" parents="64 7380 9656"/>
    </justification>
  </clause>

  <clause id="9658">
    <literal><![CDATA[
      K(L(x * (y \ z),x \ 1,u) \ 1,x) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(9112,a,9657,a)].">
      <j1 rule="hyper" parents="9112 9657"/>
    </justification>
  </clause>

  <clause id="9659">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) * (z * u) = (K(x,y \ 1) * z) * u
    ]]></literal>
    <justification jstring="[para(6363(a,1),6364(a,2,1))].">
      <j1 rule="para" parents="6363 6364"/>
    </justification>
  </clause>

  <clause id="9660">
    <literal><![CDATA[
      R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,111,a,b,9659,a)].">
      <j1 rule="hyper" parents="36 111 9659"/>
    </justification>
  </clause>

  <clause id="9661">
    <literal><![CDATA[
      K(x,R(y,x,z) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,4601,a(flip),b,9659,a),flip(a)].">
      <j1 rule="hyper" parents="36 4601 9659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9662">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w) \ 1) = K(x,R(y,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(31(a,1),9661(a,1,2,1))].">
      <j1 rule="para" parents="31 9661"/>
    </justification>
  </clause>

  <clause id="9663">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6047(a,1),9660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6047 9660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9664">
    <literal><![CDATA[
      K(x,R(y / z,u,w) \ 1) = R(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(6375(a,1),9660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6375 9660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9665">
    <literal><![CDATA[
      K(x,R(y \ z,u,w) \ 1) = R(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6700(a,1),9660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6700 9660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9666">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(9660(a,1),9099(a,2,2))].">
      <j1 rule="para" parents="9660 9099"/>
    </justification>
  </clause>

  <clause id="9667">
    <literal><![CDATA[
      R(K(x,y),z,u) \ w = R(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(9663(a,1),6686(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9663 6686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9668">
    <literal><![CDATA[
      K(R(K(x,y),z,u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(9663(a,1),8514(a,1,1,1))].">
      <j1 rule="para" parents="9663 8514"/>
    </justification>
  </clause>

  <clause id="9669">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(9663(a,1),8545(a,1,2,1))].">
      <j1 rule="para" parents="9663 8545"/>
    </justification>
  </clause>

  <clause id="9670">
    <literal><![CDATA[
      K((K(x,y) * z) * u,x) = K(z * u,x)
    ]]></literal>
    <justification jstring="[para(111(a,1),9668(a,1,1))].">
      <j1 rule="para" parents="111 9668"/>
    </justification>
  </clause>

  <clause id="9671">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(7756(a,1),9668(a,1,1,1))].">
      <j1 rule="para" parents="7756 9668"/>
    </justification>
  </clause>

  <clause id="9672">
    <literal><![CDATA[
      K(x,(K(x,y) * z) * u) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(111(a,1),9669(a,1,2))].">
      <j1 rule="para" parents="111 9669"/>
    </justification>
  </clause>

  <clause id="9673">
    <literal><![CDATA[
      K(x,K(R(x,y,z),u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(7756(a,1),9669(a,1,2,1))].">
      <j1 rule="para" parents="7756 9669"/>
    </justification>
  </clause>

  <clause id="9674">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) = K(u * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(5796(a,1),9671(a,1,1))].">
      <j1 rule="para" parents="5796 9671"/>
    </justification>
  </clause>

  <clause id="9675">
    <literal><![CDATA[
      K(T(x,R(y,z,u)) * w,y) = K(x * w,y)
    ]]></literal>
    <justification jstring="[para(5811(a,1),9671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5811 9671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9676">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,T(x,v5)) = K(w,T(x,v5))
    ]]></literal>
    <justification jstring="[para(8227(a,1),9671(a,1,1,1))].">
      <j1 rule="para" parents="8227 9671"/>
    </justification>
  </clause>

  <clause id="9677">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) = K(x,u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(5796(a,1),9673(a,1,2))].">
      <j1 rule="para" parents="5796 9673"/>
    </justification>
  </clause>

  <clause id="9678">
    <literal><![CDATA[
      K(x,T(R(x,y,z),u) \ w) = K(x,R(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(6075(a,1),9673(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6075 9673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9679">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,(R(x,z,u) \ y) \ w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),9673(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 9673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9680">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * w) = K(x,R(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(6028(a,1),9673(a,1,2))].">
      <j1 rule="para" parents="6028 9673"/>
    </justification>
  </clause>

  <clause id="9681">
    <literal><![CDATA[
      K(x,y * K(z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8258(a,1),9673(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8258 9673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9682">
    <literal><![CDATA[
      K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8098(a,1),9673(a,1,2))].">
      <j1 rule="para" parents="8098 9673"/>
    </justification>
  </clause>

  <clause id="9683">
    <literal><![CDATA[
      K(x,y / (z / R(x,u,w))) = K(x,y / (R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(6887(a,1),9681(a,1,2))].">
      <j1 rule="para" parents="6887 9681"/>
    </justification>
  </clause>

  <clause id="9684">
    <literal><![CDATA[
      K(x,(y * x) * z) = K(x,(x * y) * z)
    ]]></literal>
    <justification jstring="[para(5796(a,1),9672(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5796 9672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9685">
    <literal><![CDATA[
      K(x,(T(y,x) * z) * u) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(5811(a,1),9672(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5811 9672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9686">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) * u) = K(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[para(6417(a,1),9672(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6417 9672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9687">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(117(a,1),9682(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 9682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9688">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(460,a,9667,a)].">
      <j1 rule="hyper" parents="460 9667"/>
    </justification>
  </clause>

  <clause id="9689">
    <literal><![CDATA[
      R(K(x,y),z,u) \ (z * u) = (K(y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,111,a(flip),b,9667,a),flip(a)].">
      <j1 rule="hyper" parents="373 111 9667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9690">
    <literal><![CDATA[
      R(K(x,y),y / x,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,6307,a(flip),b,9667,a),flip(a)].">
      <j1 rule="hyper" parents="64 6307 9667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9691">
    <literal><![CDATA[
      R(K(T(T(x,y),y * z),u),y,z) = ((y * z) \ ((y * K(u,x)) * z)) \ 1
    ]]></literal>
    <justification jstring="[para(9292(a,1),9688(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9292 9688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9692">
    <literal><![CDATA[
      K(x * R(y,z,y),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9143,a(flip),b,9674,a),flip(a)].">
      <j1 rule="hyper" parents="64 9143 9674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9693">
    <literal><![CDATA[
      T(x * K(R(x,y,z) * u,x),u) = R(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(9674(a,2),6236(a,1,1,2))].">
      <j1 rule="para" parents="9674 6236"/>
    </justification>
  </clause>

  <clause id="9694">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = 1 / (x \ K(x * y,x))
    ]]></literal>
    <justification jstring="[para(9692(a,1),5877(a,2,2,2))].">
      <j1 rule="para" parents="9692 5877"/>
    </justification>
  </clause>

  <clause id="9695">
    <literal><![CDATA[
      K(x,(y \ (z / x)) * u) = K(x,(y \ (x \ z)) * u)
    ]]></literal>
    <justification jstring="[para(117(a,1),9686(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="117 9686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9696">
    <literal><![CDATA[
      K(x * T(R(y,z,u),w),T(T(y,v5),K(R(y,z,u),w))) = K(x * R(y,z,u),T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,8667,a,b,9676,a)].">
      <j1 rule="hyper" parents="64 8667 9676"/>
    </justification>
  </clause>

  <clause id="9697">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5877,a,b,9694,a),flip(a)].">
      <j1 rule="hyper" parents="373 5877 9694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9698">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5753,a(flip),b,9697,a),flip(a)].">
      <j1 rule="hyper" parents="373 5753 9697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9699">
    <literal><![CDATA[
      K(x,y * R(x,z,x)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5826,a,9698,a)].">
      <j1 rule="hyper" parents="5826 9698"/>
    </justification>
  </clause>

  <clause id="9700">
    <literal><![CDATA[
      K(x,R(x,y,x) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9677,a,b,9699,a)].">
      <j1 rule="hyper" parents="64 9677 9699"/>
    </justification>
  </clause>

  <clause id="9701">
    <literal><![CDATA[
      K(R(x,y,x),R(x,z,x) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(7432,a,9700,a)].">
      <j1 rule="hyper" parents="7432 9700"/>
    </justification>
  </clause>

  <clause id="9702">
    <literal><![CDATA[
      R(K(x,y / z),y,u) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(6514,a,9664,a),flip(a)].">
      <j1 rule="hyper" parents="6514 9664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9703">
    <literal><![CDATA[
      R(K(x,y / z),y,z \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(684(a,1),9664(a,1,2)),flip(a)].">
      <j1 rule="para" parents="684 9664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9704">
    <literal><![CDATA[
      R(K(x,y / z),y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * u) / (z * u)) = w
    ]]></literal>
    <justification jstring="[para(9664(a,1),6514(a,1))].">
      <j1 rule="para" parents="9664 6514"/>
    </justification>
  </clause>

  <clause id="9705">
    <literal><![CDATA[
      R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(12(a,1),9702(a,2,2,1))].">
      <j1 rule="para" parents="12 9702"/>
    </justification>
  </clause>

  <clause id="9706">
    <literal><![CDATA[
      R(K(x,y / (z / u)),y,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(12(a,1),9702(a,2,2,2))].">
      <j1 rule="para" parents="12 9702"/>
    </justification>
  </clause>

  <clause id="9707">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),9702(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 9702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9708">
    <literal><![CDATA[
      R(K(x,R(y,z,u) \ y),y,w) = K(x,(y * w) / (R(y,z,u) * w))
    ]]></literal>
    <justification jstring="[para(2156(a,1),9702(a,1,1,2))].">
      <j1 rule="para" parents="2156 9702"/>
    </justification>
  </clause>

  <clause id="9709">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (w / R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9086,a(flip),b,9706,a),flip(a)].">
      <j1 rule="hyper" parents="64 9086 9706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9710">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[para(6126(a,1),9706(a,1,1))].">
      <j1 rule="para" parents="6126 9706"/>
    </justification>
  </clause>

  <clause id="9711">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(108(a,2),9707(a,1,2))].">
      <j1 rule="para" parents="108 9707"/>
    </justification>
  </clause>

  <clause id="9712">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) \ x = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,7763,a(flip),b,9711,a)].">
      <j1 rule="hyper" parents="64 7763 9711"/>
    </justification>
  </clause>

  <clause id="9713">
    <literal><![CDATA[
      x / R(K(y,z),u,w) = x * R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(225,a,9711,a(flip),b,7763,a(flip))].">
      <j1 rule="hyper" parents="225 9711 7763"/>
    </justification>
  </clause>

  <clause id="9714">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * R(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,9711,a(flip),b,7763,a(flip))].">
      <j1 rule="hyper" parents="145 9711 7763"/>
    </justification>
  </clause>

  <clause id="9715">
    <literal><![CDATA[
      R(K(x,y),y * z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),9711(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9716">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,T(z,y),u))
    ]]></literal>
    <justification jstring="[para(22(a,2),9711(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="22 9711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9717">
    <literal><![CDATA[
      R(K(x,R(y,z,u)),(y * z) * u,w) = K(x,R(R(y,z,u),z * u,w))
    ]]></literal>
    <justification jstring="[para(210(a,1),9711(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="210 9711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9718">
    <literal><![CDATA[
      R(K(x,y),K(z,y) * u,w) = K(x,R(y,T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[para(6137(a,1),9711(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6137 9711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9719">
    <literal><![CDATA[
      K(x * y,R(x,y,z)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(4600,a,9715,a),flip(a)].">
      <j1 rule="hyper" parents="4600 9715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9720">
    <literal><![CDATA[
      K(R(x,y,z),y) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9221,a(flip),b,9715,a)].">
      <j1 rule="hyper" parents="64 9221 9715"/>
    </justification>
  </clause>

  <clause id="9721">
    <literal><![CDATA[
      K(x,R(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7761,a(flip),b,9715,a),flip(a)].">
      <j1 rule="hyper" parents="64 7761 9715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9722">
    <literal><![CDATA[
      K(R(x,y * z,u) \ 1,y) = K(x \ 1,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,6681,a(flip),b,9715,a)].">
      <j1 rule="hyper" parents="64 6681 9715"/>
    </justification>
  </clause>

  <clause id="9723">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = T(K(x,R(y,u,w)),z)
    ]]></literal>
    <justification jstring="[para(9715(a,1),27(a,2,1))].">
      <j1 rule="para" parents="9715 27"/>
    </justification>
  </clause>

  <clause id="9724">
    <literal><![CDATA[
      K(x,R(y,z,u)) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(9715(a,1),4540(a,1,1))].">
      <j1 rule="para" parents="9715 4540"/>
    </justification>
  </clause>

  <clause id="9725">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) = K(T(x,z),R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(8205(a,1),9715(a,1,1))].">
      <j1 rule="para" parents="8205 9715"/>
    </justification>
  </clause>

  <clause id="9726">
    <literal><![CDATA[
      R(K(x,y),T(y,T(z,u)) * u,w) = K(x,R(y,u * K(y,z),w))
    ]]></literal>
    <justification jstring="[para(8221(a,2),9715(a,1,2))].">
      <j1 rule="para" parents="8221 9715"/>
    </justification>
  </clause>

  <clause id="9727">
    <literal><![CDATA[
      K(L(x,x,y),z) = K(x,R(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,7372,a,b,9721,a)].">
      <j1 rule="hyper" parents="373 7372 9721"/>
    </justification>
  </clause>

  <clause id="9728">
    <literal><![CDATA[
      T(x,R(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,9721,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 9721 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9730">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(y / (z / x),u))
    ]]></literal>
    <justification jstring="[para(1033(a,1),9728(a,1,2))].">
      <j1 rule="para" parents="1033 9728"/>
    </justification>
  </clause>

  <clause id="9732">
    <literal><![CDATA[
      K(x,R(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(9727(a,1),7413(a,1))].">
      <j1 rule="para" parents="9727 7413"/>
    </justification>
  </clause>

  <clause id="9733">
    <literal><![CDATA[
      R(x * R(K(y,x),z,u),w,x) \ R(x,w,x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(9608(a,2),9712(a,1,1))].">
      <j1 rule="para" parents="9608 9712"/>
    </justification>
  </clause>

  <clause id="9734">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(4600,a,9710,a),flip(a)].">
      <j1 rule="hyper" parents="4600 9710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9735">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(y / (x * z)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,6375,a,b,9710,a),flip(a)].">
      <j1 rule="hyper" parents="373 6375 9710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9736">
    <literal><![CDATA[
      K(x,(x * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(9710(a,1),4600(a,1))].">
      <j1 rule="para" parents="9710 4600"/>
    </justification>
  </clause>

  <clause id="9738">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8273,a,b,9734,a)].">
      <j1 rule="hyper" parents="64 8273 9734"/>
    </justification>
  </clause>

  <clause id="9739">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8684,a(flip),b,9734,a)].">
      <j1 rule="hyper" parents="64 8684 9734"/>
    </justification>
  </clause>

  <clause id="9740">
    <literal><![CDATA[
      K(x,(L(y,z,u) / y) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(3190(a,1),9734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3190 9734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9741">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(8587,a,9739,a)].">
      <j1 rule="hyper" parents="8587 9739"/>
    </justification>
  </clause>

  <clause id="9742">
    <literal><![CDATA[
      T(x,y / (x \ z)) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(143,a,9739,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 9739 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9743">
    <literal><![CDATA[
      K(x,((x * y) / z) \ x) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),9739(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9744">
    <literal><![CDATA[
      K(x,(y / z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (x \ y)) = u
    ]]></literal>
    <justification jstring="[para(9741(a,1),8781(a,1))].">
      <j1 rule="para" parents="9741 8781"/>
    </justification>
  </clause>

  <clause id="9745">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9137,a,b,9742,a)].">
      <j1 rule="hyper" parents="64 9137 9742"/>
    </justification>
  </clause>

  <clause id="9746">
    <literal><![CDATA[
      K(x,(K(y,x * z) * (y \ (x * z))) \ x) = K(x,R(y,y \ (x * z),y) / z)
    ]]></literal>
    <justification jstring="[para(7721(a,1),9743(a,1,2,1))].">
      <j1 rule="para" parents="7721 9743"/>
    </justification>
  </clause>

  <clause id="9747">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) * u = u * K(x,T((y / z) \ x,u))
    ]]></literal>
    <justification jstring="[para(9738(a,2),7879(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9738 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9748">
    <literal><![CDATA[
      K(x,y / (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(8684(a,1),9736(a,1))].">
      <j1 rule="para" parents="8684 9736"/>
    </justification>
  </clause>

  <clause id="9749">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(9132(a,2),9736(a,1))].">
      <j1 rule="para" parents="9132 9736"/>
    </justification>
  </clause>

  <clause id="9750">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (y * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (x \ z)) = w
    ]]></literal>
    <justification jstring="[para(7079(a,2),9744(a,1))].">
      <j1 rule="para" parents="7079 9744"/>
    </justification>
  </clause>

  <clause id="9751">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(9749,a,8272,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="9749 8272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9752">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9212,a,b,9751,a)].">
      <j1 rule="hyper" parents="64 9212 9751"/>
    </justification>
  </clause>

  <clause id="9753">
    <literal><![CDATA[
      K(x,((y * z) / y) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),9752(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 9752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9754">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,(z / (z / y)) \ x)
    ]]></literal>
    <justification jstring="[para(4707(a,1),9753(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4707 9753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9755">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) \ w) = K(x,R(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(27(a,2),9678(a,1,2,1))].">
      <j1 rule="para" parents="27 9678"/>
    </justification>
  </clause>

  <clause id="9756">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,T(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7867,a,b,9723,a),flip(a)].">
      <j1 rule="hyper" parents="373 7867 9723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9757">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(y / (x \ z),u))
    ]]></literal>
    <justification jstring="[hyper(373,a,8890,a(flip),b,9730,a),flip(a)].">
      <j1 rule="hyper" parents="373 8890 9730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9758">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9526,a(flip),b,9754,a),flip(a)].">
      <j1 rule="hyper" parents="64 9526 9754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9759">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,((x * z) / y) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9743,a(flip),b,9758,a),flip(a)].">
      <j1 rule="hyper" parents="64 9743 9758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9760">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(x,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7989,a,b,9755,a)].">
      <j1 rule="hyper" parents="64 7989 9755"/>
    </justification>
  </clause>

  <clause id="9761">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(27(a,2),9756(a,2,2))].">
      <j1 rule="para" parents="27 9756"/>
    </justification>
  </clause>

  <clause id="9762">
    <literal><![CDATA[
      K(x,((x * y) / z) / y) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(8023,a,9759,a),flip(a)].">
      <j1 rule="hyper" parents="8023 9759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9764">
    <literal><![CDATA[
      K(x,R(x,y,z) \ ((x * R(T(x,u),y,z)) / w)) = K(x,T(w \ x,R(T(x,u),y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9762,a(flip),b,9760,a),flip(a)].">
      <j1 rule="hyper" parents="64 9762 9760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9765">
    <literal><![CDATA[
      R(K(x,T(y,z)),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(7867(a,2),9761(a,1,1))].">
      <j1 rule="para" parents="7867 9761"/>
    </justification>
  </clause>

  <clause id="9766">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ u,w)) = R(K(x,T(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),9765(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 9765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9767">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,671,a(flip),b,9766,a),flip(a)].">
      <j1 rule="hyper" parents="373 671 9766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9768">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,7867,a(flip),b,9767,a),flip(a)].">
      <j1 rule="hyper" parents="373 7867 9767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9769">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,(((y * z) * u) / ((x * z) * u)) \ 1)
    ]]></literal>
    <justification jstring="[para(688(a,1),9662(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="688 9662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9770">
    <literal><![CDATA[
      R(T(K(x,(y / z) \ x),u),x,z) = T(K(x,(y / (x * z)) \ 1),u)
    ]]></literal>
    <justification jstring="[para(9735(a,1),27(a,2,1))].">
      <j1 rule="para" parents="9735 27"/>
    </justification>
  </clause>

  <clause id="9771">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,9010,a(flip),b,9666,a),flip(a)].">
      <j1 rule="hyper" parents="373 9010 9666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9772">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(9010(a,1),9771(a,1,1))].">
      <j1 rule="para" parents="9010 9771"/>
    </justification>
  </clause>

  <clause id="9773">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,K(z,R(x,u,w)))
    ]]></literal>
    <justification jstring="[para(9011(a,1),9771(a,1,1))].">
      <j1 rule="para" parents="9011 9771"/>
    </justification>
  </clause>

  <clause id="9774">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9099,a(flip),b,9772,a)].">
      <j1 rule="hyper" parents="64 9099 9772"/>
    </justification>
  </clause>

  <clause id="9775">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9098,a(flip),b,9773,a)].">
      <j1 rule="hyper" parents="64 9098 9773"/>
    </justification>
  </clause>

  <clause id="9776">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(143,a,9774,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 9774 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9777">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(143,a,9775,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 9775 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9778">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w))) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9776,a(flip),b,9777,a)].">
      <j1 rule="hyper" parents="64 9776 9777"/>
    </justification>
  </clause>

  <clause id="9779">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9215,a(flip),b,9687,a),flip(a)].">
      <j1 rule="hyper" parents="64 9215 9687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9781">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),9779(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9782">
    <literal><![CDATA[
      K(x,T(y \ (R(x,z,u) * w),w)) = K(x,(R(x,z,u) * w) / y)
    ]]></literal>
    <justification jstring="[hyper(8699,a,9781,a),flip(a)].">
      <j1 rule="hyper" parents="8699 9781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9783">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,y) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,8087,a,b,9781,a),flip(a)].">
      <j1 rule="hyper" parents="373 8087 9781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9784">
    <literal><![CDATA[
      K(x \ 1,T(y,x \ z)) = K(x \ 1,T(y,z))
    ]]></literal>
    <justification jstring="[para(2998(a,1),9781(a,1,2,2))].">
      <j1 rule="para" parents="2998 9781"/>
    </justification>
  </clause>

  <clause id="9785">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8344,a,9783,a)].">
      <j1 rule="hyper" parents="8344 9783"/>
    </justification>
  </clause>

  <clause id="9786">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(9783(a,2),8089(a,1))].">
      <j1 rule="para" parents="9783 8089"/>
    </justification>
  </clause>

  <clause id="9787">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),9785(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 9785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9788">
    <literal><![CDATA[
      K(x,K(y,(x * z) * u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(111(a,1),9785(a,1,2,2))].">
      <j1 rule="para" parents="111 9785"/>
    </justification>
  </clause>

  <clause id="9789">
    <literal><![CDATA[
      K(x,K(y,z \ R(x,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(9037,a,9787,a)].">
      <j1 rule="hyper" parents="9037 9787"/>
    </justification>
  </clause>

  <clause id="9790">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) / w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(82(a,1),9789(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 9789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9791">
    <literal><![CDATA[
      K(x,K(y,z * R(x,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(9049,a,9790,a),flip(a)].">
      <j1 rule="hyper" parents="9049 9790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9792">
    <literal><![CDATA[
      K(x,K(y,(y * z) * u)) = K(y,K(x,z * u))
    ]]></literal>
    <justification jstring="[hyper(8436,a,9788,a)].">
      <j1 rule="hyper" parents="8436 9788"/>
    </justification>
  </clause>

  <clause id="9793">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(y,x) = K(y,T(x,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(9788(a,1),8137(a,1,1))].">
      <j1 rule="para" parents="9788 8137"/>
    </justification>
  </clause>

  <clause id="9794">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * u) / ((y \ z) * u)) = w
    ]]></literal>
    <justification jstring="[para(79(a,1),9704(a,1,1,2))].">
      <j1 rule="para" parents="79 9704"/>
    </justification>
  </clause>

  <clause id="9795">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (R(x,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,9683,a(flip),b,9709,a),flip(a)].">
      <j1 rule="hyper" parents="373 9683 9709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9796">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(8321,a,9725,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8321 9725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9797">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(9725(a,2),8321(a,1))].">
      <j1 rule="para" parents="9725 8321"/>
    </justification>
  </clause>

  <clause id="9798">
    <literal><![CDATA[
      K(x,R(y,T(y,z) \ u,w)) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),9796(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 9796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9799">
    <literal><![CDATA[
      R(K(x,y),K(z,y) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,9718,a,b,9798,a)].">
      <j1 rule="hyper" parents="64 9718 9798"/>
    </justification>
  </clause>

  <clause id="9800">
    <literal><![CDATA[
      R(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(672,a,9799,a),flip(a)].">
      <j1 rule="hyper" parents="672 9799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9802">
    <literal><![CDATA[
      R(K(x,y),y \ K(y,z),u) = R(K(x,y),y \ 1,u)
    ]]></literal>
    <justification jstring="[para(6180(a,1),9799(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6180 9799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9803">
    <literal><![CDATA[
      R(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6106,a,b,9800,a)].">
      <j1 rule="hyper" parents="64 6106 9800"/>
    </justification>
  </clause>

  <clause id="9804">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(x,y) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,9803,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 9803 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9805">
    <literal><![CDATA[
      R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5) = K(x,y) * R(R(K(x,y),K(y,w),v5) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(9803(a,1),5362(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9803 5362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9806">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = ((((x \ 1) * (K(y,x) * u)) / ((x \ 1) * u)) * (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(9802(a,2),2738(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9802 2738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9807">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(606,a,9804,a)].">
      <j1 rule="hyper" parents="606 9804"/>
    </justification>
  </clause>

  <clause id="9808">
    <literal><![CDATA[
      (K(x,y) * (K(y,z) * u)) / (K(x,y) * K(y,z)) = u * K(K(x,y) * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(142,a,9804,a(flip),b,5722,a)].">
      <j1 rule="hyper" parents="142 9804 5722"/>
    </justification>
  </clause>

  <clause id="9809">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(3320(a,2),9804(a,1,1))].">
      <j1 rule="para" parents="3320 9804"/>
    </justification>
  </clause>

  <clause id="9810">
    <literal><![CDATA[
      K(x,y) * (K(y,T(x,z)) * u) = K(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[para(8064(a,1),9804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8064 9804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9811">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(9807(a,1),334(a,1,2))].">
      <j1 rule="para" parents="9807 334"/>
    </justification>
  </clause>

  <clause id="9812">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) * u = K(x,y) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[para(9807(a,1),6285(a,1,2))].">
      <j1 rule="para" parents="9807 6285"/>
    </justification>
  </clause>

  <clause id="9813">
    <literal><![CDATA[
      K(x,y) * (K(x,K(y,z)) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(6187,a,9810,a)].">
      <j1 rule="hyper" parents="6187 9810"/>
    </justification>
  </clause>

  <clause id="9814">
    <literal><![CDATA[
      (K(x,y) * K(x,y)) * z = y * (T(T(y,x),x) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,7247,a(flip),b,9812,a),flip(a)].">
      <j1 rule="hyper" parents="373 7247 9812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9815">
    <literal><![CDATA[
      T(K(x,y) \ T(K(x,T(y,z)) * u,w),K(x,y)) = K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w)
    ]]></literal>
    <justification jstring="[para(9813(a,1),5440(a,1,1,2,1))].">
      <j1 rule="para" parents="9813 5440"/>
    </justification>
  </clause>

  <clause id="9816">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(5572(a,1),9740(a,1,2,1))].">
      <j1 rule="para" parents="5572 9740"/>
    </justification>
  </clause>

  <clause id="9817">
    <literal><![CDATA[
      K(x,T(y,(y * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(8383,a,9793,a),flip(a)].">
      <j1 rule="hyper" parents="8383 9793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9818">
    <literal><![CDATA[
      K(x,T(y,(y \ z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),9817(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 9817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9819">
    <literal><![CDATA[
      K(x \ y,T(x,y * z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(8023,a,9818,a),flip(a)].">
      <j1 rule="hyper" parents="8023 9818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9820">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(x \ (y / z),T(x,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),9819(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 9819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9821">
    <literal><![CDATA[
      L(T(K(x \ y,T(x,z)),z),z,y) = (y * (K(x \ y,x) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[para(9819(a,1),8254(a,1,1,1))].">
      <j1 rule="para" parents="9819 8254"/>
    </justification>
  </clause>

  <clause id="9822">
    <literal><![CDATA[
      K(x,L(y,z,u) \ (y * x)) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7083,a(flip),b,9816,a)].">
      <j1 rule="hyper" parents="64 7083 9816"/>
    </justification>
  </clause>

  <clause id="9823">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = K(x,y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(2329(a,1),9822(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2329 9822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9824">
    <literal><![CDATA[
      K(x,R(y,z * K(y,u),w)) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(9797,a,9726,a),flip(a)].">
      <j1 rule="hyper" parents="9797 9726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9826">
    <literal><![CDATA[
      K(x,R(y,T(z,y),u)) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(5748(a,1),9824(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5748 9824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9827">
    <literal><![CDATA[
      K(x,R(y,K(y,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(7879(a,1),9824(a,1,2,2))].">
      <j1 rule="para" parents="7879 9824"/>
    </justification>
  </clause>

  <clause id="9828">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9716,a,b,9826,a)].">
      <j1 rule="hyper" parents="64 9716 9826"/>
    </justification>
  </clause>

  <clause id="9829">
    <literal><![CDATA[
      R(K(x,y \ z),z,u) = K(x,R(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),9828(a,1,2))].">
      <j1 rule="para" parents="10 9828"/>
    </justification>
  </clause>

  <clause id="9830">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = (v5 * K(w,R(x,z,u))) \ v5
    ]]></literal>
    <justification jstring="[para(9827(a,1),6882(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9827 6882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9831">
    <literal><![CDATA[
      R(K(x,y \ R(y,z,u)),R(y,z,u),z * u) = K(x,((y * z) * u) / (y * (z * u)))
    ]]></literal>
    <justification jstring="[para(2295(a,1),9829(a,2,2))].">
      <j1 rule="para" parents="2295 9829"/>
    </justification>
  </clause>

  <clause id="9832">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,6882,a(flip),b,9830,a),flip(a)].">
      <j1 rule="hyper" parents="373 6882 9830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9833">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = K(R(x,x \ u,w),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7758,a(flip),b,9832,a)].">
      <j1 rule="hyper" parents="64 7758 9832"/>
    </justification>
  </clause>

  <clause id="9834">
    <literal><![CDATA[
      K(R(x,K(y,x) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(6161(a,1),9832(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6161 9832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9836">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,7757,a(flip),b,9833,a),flip(a)].">
      <j1 rule="hyper" parents="373 7757 9833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9837">
    <literal><![CDATA[
      R(K(x,y),z / x,u) = R(K(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(5720(a,1),9836(a,1,2))].">
      <j1 rule="para" parents="5720 9836"/>
    </justification>
  </clause>

  <clause id="9838">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(9837(a,1),9690(a,1,1))].">
      <j1 rule="para" parents="9837 9690"/>
    </justification>
  </clause>

  <clause id="9839">
    <literal><![CDATA[
      x * ((y / T(z,y)) * u) != (y / z) * u
    ]]></literal>
    <literal><![CDATA[
      R(K(z,y),z \ y,u) = x
    ]]></literal>
    <justification jstring="[para(9838(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="9838 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9840">
    <literal><![CDATA[
      K(x,T(y / (x \ z),u)) = K(x,T((z / y) \ x,u))
    ]]></literal>
    <justification jstring="[hyper(8685,a,9747,a)].">
      <j1 rule="hyper" parents="8685 9747"/>
    </justification>
  </clause>

  <clause id="9841">
    <literal><![CDATA[
      x * K(x,T((y / z) \ x,u)) = T(x,T(z / (x \ y),u))
    ]]></literal>
    <justification jstring="[hyper(145,a,9840,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 9840 5726"/>
    </justification>
  </clause>

  <clause id="9842">
    <literal><![CDATA[
      T(x,T(y / (x \ z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T((z / y) \ x,u)) = w
    ]]></literal>
    <justification jstring="[para(9841(a,1),5767(a,1))].">
      <j1 rule="para" parents="9841 5767"/>
    </justification>
  </clause>

  <clause id="9843">
    <literal><![CDATA[
      K(x,K(R(y,z,u) \ y,R(w,y,v5))) = K(x,K(w,(y * v5) / (R(y,z,u) * v5)))
    ]]></literal>
    <justification jstring="[para(9708(a,1),9775(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9708 9775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9844">
    <literal><![CDATA[
      R(T(K(x,(y / z) \ x),u),x,z) = K(x,T((y / (x * z)) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,7867,a,b,9770,a),flip(a)].">
      <j1 rule="hyper" parents="373 7867 9770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9845">
    <literal><![CDATA[
      R(K(x,T((y / z) \ x,u)),x,z) = K(x,T((y / (x * z)) \ 1,u))
    ]]></literal>
    <justification jstring="[para(7867(a,2),9844(a,1,1))].">
      <j1 rule="para" parents="7867 9844"/>
    </justification>
  </clause>

  <clause id="9846">
    <literal><![CDATA[
      K(x,T((y / (x * z)) \ 1,u)) = K(x,T((y / z) \ x,u))
    ]]></literal>
    <justification jstring="[hyper(4600,a,9845,a),flip(a)].">
      <j1 rule="hyper" parents="4600 9845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9848">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8084,a(flip),b,9846,a),flip(a)].">
      <j1 rule="hyper" parents="64 8084 9846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9849">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,8816,a,b,9848,a),flip(a)].">
      <j1 rule="hyper" parents="373 8816 9848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9850">
    <literal><![CDATA[
      K(x,T(y / (x \ z),z)) = K(x,z \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9840,a,b,9848,a)].">
      <j1 rule="hyper" parents="64 9840 9848"/>
    </justification>
  </clause>

  <clause id="9851">
    <literal><![CDATA[
      K(x,y \ (x * (z \ y))) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(79(a,1),9848(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 9848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9852">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),y) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[para(9849(a,1),8200(a,1,1))].">
      <j1 rule="para" parents="9849 8200"/>
    </justification>
  </clause>

  <clause id="9853">
    <literal><![CDATA[
      T(x,y \ (x * (z \ y))) = T(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(143,a,9851,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 9851 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9854">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,T(u \ z,y))) = K(x,z \ ((y \ (z * (u \ y))) \ z))
    ]]></literal>
    <justification jstring="[para(9851(a,1),7517(a,1,2,2))].">
      <j1 rule="para" parents="9851 7517"/>
    </justification>
  </clause>

  <clause id="9855">
    <literal><![CDATA[
      K(x,(y / z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = u
    ]]></literal>
    <justification jstring="[para(9852(a,1),9287(a,1))].">
      <j1 rule="para" parents="9852 9287"/>
    </justification>
  </clause>

  <clause id="9856">
    <literal><![CDATA[
      R(K(T(x,y),T(z,y * u)),y,u) = ((y * u) \ ((y * K(z,x)) * u)) \ 1
    ]]></literal>
    <justification jstring="[para(7869(a,1),9691(a,1,1))].">
      <j1 rule="para" parents="7869 9691"/>
    </justification>
  </clause>

  <clause id="9857">
    <literal><![CDATA[
      (x * (K(y \ x,y) * z)) / (x * z) = L(K(y \ x,y),z,x)
    ]]></literal>
    <justification jstring="[para(8200(a,1),9821(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8200 9821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9858">
    <literal><![CDATA[
      L(K(x \ y,x),z,y) * (y * z) = y * (K(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(156,a,9857,a)].">
      <j1 rule="hyper" parents="156 9857"/>
    </justification>
  </clause>

  <clause id="9860">
    <literal><![CDATA[
      L(K(x,y),z,y * x) * ((y * x) * z) = (y * x) * (K(y \ (y * x),y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9858(a,1,1,1,1))].">
      <j1 rule="para" parents="9 9858"/>
    </justification>
  </clause>

  <clause id="9861">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),z,u) = ((z * u) \ ((z * K(y,x)) * u)) \ 1
    ]]></literal>
    <justification jstring="[para(7915(a,1),9856(a,1,1))].">
      <j1 rule="para" parents="7915 9856"/>
    </justification>
  </clause>

  <clause id="9862">
    <literal><![CDATA[
      ((x * y) \ ((x * K(z,u)) * y)) \ 1 = (x * y) \ ((x * K(u,z)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9292,a(flip),b,9861,a),flip(a)].">
      <j1 rule="hyper" parents="64 9292 9861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9863">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) \ 1 = (x * z) \ ((x * K(u,y)) * z)
    ]]></literal>
    <justification jstring="[para(9346(a,2),9862(a,1,1))].">
      <j1 rule="para" parents="9346 9862"/>
    </justification>
  </clause>

  <clause id="9864">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u)) * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,((x / u) * y) \ (x * y)) = w
    ]]></literal>
    <justification jstring="[para(9863(a,1),6101(a,1))].">
      <j1 rule="para" parents="9863 6101"/>
    </justification>
  </clause>

  <clause id="9865">
    <literal><![CDATA[
      T((x / (y * K(z,y))) * y,z / (z / y)) = ((z * y) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(6676,a,7411,a),flip(a)].">
      <j1 rule="hyper" parents="6676 7411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9866">
    <literal><![CDATA[
      T(x * K(y,z),z / (z / y)) = ((z * y) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[para(6968(a,1),9865(a,1,1))].">
      <j1 rule="para" parents="6968 9865"/>
    </justification>
  </clause>

  <clause id="9867">
    <literal><![CDATA[
      K((x * y) \ z,L(y,u,w)) = K(x \ (y \ z),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,6549,a(flip),b,7515,a),flip(a)].">
      <j1 rule="hyper" parents="64 6549 7515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9868">
    <literal><![CDATA[
      K(L(x \ y,x,z),L(x,u,w)) = K(z \ (x \ (z * y)),L(x,u,w))
    ]]></literal>
    <justification jstring="[para(102(a,2),9867(a,1,1))].">
      <j1 rule="para" parents="102 9867"/>
    </justification>
  </clause>

  <clause id="9869">
    <literal><![CDATA[
      K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(7694,a,9342,a),flip(a)].">
      <j1 rule="hyper" parents="7694 9342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9870">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),9869(a,2,2,1))].">
      <j1 rule="para" parents="10 9869"/>
    </justification>
  </clause>

  <clause id="9871">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ x)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(79(a,1),9869(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 9869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9872">
    <literal><![CDATA[
      K(x,x \ (x * y)) = K(x,K(z \ x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7734,a(flip),b,9870,a),flip(a)].">
      <j1 rule="hyper" parents="64 7734 9870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9874">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9872(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 9872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9875">
    <literal><![CDATA[
      K(x * y,K(y,x) * z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9874(a,1,2,1,1))].">
      <j1 rule="para" parents="9 9874"/>
    </justification>
  </clause>

  <clause id="9877">
    <literal><![CDATA[
      K(x,(x / y) * z) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(6553(a,1),9874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6553 9874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9878">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y * x,z),y * x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(9875(a,1),5785(a,1,1,2))].">
      <j1 rule="para" parents="9875 5785"/>
    </justification>
  </clause>

  <clause id="9879">
    <literal><![CDATA[
      K(x * y,T(x,y) * z) = K(x * y,x * z)
    ]]></literal>
    <justification jstring="[para(5811(a,1),9875(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5811 9875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9880">
    <literal><![CDATA[
      K(x,((y / T(z,z \ x)) * z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(423(a,1),9871(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="423 9871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9881">
    <literal><![CDATA[
      K(x,(y * K(z \ x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6311(a,1),9880(a,1,2,1))].">
      <j1 rule="para" parents="6311 9880"/>
    </justification>
  </clause>

  <clause id="9882">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5795(a,1),9881(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5795 9881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9883">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,9878,a(flip),b,6853,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 9878 6853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9884">
    <literal><![CDATA[
      (x * T(K(y,z),u)) * T(K(z,y),u) = R(x,T(K(y,z),u),T(K(z,y),u))
    ]]></literal>
    <justification jstring="[para(7880(a,1),7963(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7880 7963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9885">
    <literal><![CDATA[
      R(x,T(K(y,z),u),T(K(z,y),u)) != w * T(K(z,y),u)
    ]]></literal>
    <literal><![CDATA[
      x * T(K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(9884(a,1),45(a,1))].">
      <j1 rule="para" parents="9884 45"/>
    </justification>
  </clause>

  <clause id="9886">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,T(y,T(x,w)),R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7477,a(flip),b,8611,a)].">
      <j1 rule="hyper" parents="64 7477 8611"/>
    </justification>
  </clause>

  <clause id="9888">
    <literal><![CDATA[
      R(x,T(y,T(x,z)),R(x,u,w)) = R(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,6236,a(flip),b,9886,a),flip(a)].">
      <j1 rule="hyper" parents="64 6236 9886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9889">
    <literal><![CDATA[
      R(T(x,y),T(z,x),R(T(x,y),u,w)) = R(T(x,y),z,R(T(x,y),u,w))
    ]]></literal>
    <justification jstring="[para(8213(a,1),9888(a,1,2))].">
      <j1 rule="para" parents="8213 9888"/>
    </justification>
  </clause>

  <clause id="9890">
    <literal><![CDATA[
      K(L(x,y,z),u * (K(x,w) * v5)) = K(L(x,y,z),u * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,6548,a(flip),b,8631,a),flip(a)].">
      <j1 rule="hyper" parents="373 6548 8631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9891">
    <literal><![CDATA[
      K(x * (K(y,z) * u),R(y,w,v5)) = K(x * u,R(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,6550,a(flip),b,8632,a),flip(a)].">
      <j1 rule="hyper" parents="373 6550 8632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9892">
    <literal><![CDATA[
      K(x * y,R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(5848(a,1),9891(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5848 9891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9893">
    <literal><![CDATA[
      K(T(x,T(y,z)) \ K(y,u),w) = T(K(x \ K(y,u),w),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(9146,a,6839,a)].">
      <j1 rule="hyper" parents="9146 6839"/>
    </justification>
  </clause>

  <clause id="9894">
    <literal><![CDATA[
      T(K((x / y) \ K(y,z),u),T(y,x)) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7631,a(flip),b,9893,a),flip(a)].">
      <j1 rule="hyper" parents="64 7631 9893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9895">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,x)) = K((x / y) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(8201,a,9894,a)].">
      <j1 rule="hyper" parents="8201 9894"/>
    </justification>
  </clause>

  <clause id="9896">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = T(y,K(x,z)) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,170,a(flip),b,9403,a),flip(a)].">
      <j1 rule="hyper" parents="373 170 9403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9897">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,5739,a,b,9896,a),flip(a)].">
      <j1 rule="hyper" parents="373 5739 9896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9899">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8108,a,b,9897,a),flip(a)].">
      <j1 rule="hyper" parents="373 8108 9897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9900">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,K(x,w) * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(9670(a,1),9413(a,1,1,2))].">
      <j1 rule="para" parents="9670 9413"/>
    </justification>
  </clause>

  <clause id="9901">
    <literal><![CDATA[
      R(x,K(x,y) * z,R(x,u,w)) = R(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,6236,a(flip),b,9900,a),flip(a)].">
      <j1 rule="hyper" parents="64 6236 9900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9903">
    <literal><![CDATA[
      T(T(x * K(y * R(x,z,u),x),w),y) = R(T(x,w),y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),9458(a,2,1,1))].">
      <j1 rule="para" parents="9 9458"/>
    </justification>
  </clause>

  <clause id="9904">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(8163(a,1),9567(a,1,1,3))].">
      <j1 rule="para" parents="8163 9567"/>
    </justification>
  </clause>

  <clause id="9905">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(6156(a,1),9904(a,2,2))].">
      <j1 rule="para" parents="6156 9904"/>
    </justification>
  </clause>

  <clause id="9906">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,9583,a(flip),b,9582,a),flip(a)].">
      <j1 rule="hyper" parents="64 9583 9582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9907">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ (K(x * z,y) * x)) = K(x,R(y,y \ (x * z),y) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7085,a(flip),b,9746,a)].">
      <j1 rule="hyper" parents="64 7085 9746"/>
    </justification>
  </clause>

  <clause id="9908">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,6375,a(flip),b,9769,a),flip(a)].">
      <j1 rule="hyper" parents="373 6375 9769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9909">
    <literal><![CDATA[
      R(K(x,x / y),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9664,a(flip),b,9908,a)].">
      <j1 rule="hyper" parents="64 9664 9908"/>
    </justification>
  </clause>

  <clause id="9910">
    <literal><![CDATA[
      R(K(x,y \ x),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(6126(a,1),9909(a,1,1))].">
      <j1 rule="para" parents="6126 9909"/>
    </justification>
  </clause>

  <clause id="9911">
    <literal><![CDATA[
      K(x,((x * y) * z) / ((u * y) * z)) = K(R(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7756,a(flip),b,9910,a),flip(a)].">
      <j1 rule="hyper" parents="64 7756 9910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9912">
    <literal><![CDATA[
      K(R(x,x \ y,z),u \ x) = K(x,(y * z) / ((u * (x \ y)) * z))
    ]]></literal>
    <justification jstring="[para(10(a,1),9911(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 9911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9913">
    <literal><![CDATA[
      K(x,((y * z) * R(x,y,z)) / ((u * (K(y * z,x) * y)) * z)) = K(R(x,K(y * z,x) * y,z),u \ x)
    ]]></literal>
    <justification jstring="[para(6394(a,1),9911(a,1,2,1))].">
      <j1 rule="para" parents="6394 9911"/>
    </justification>
  </clause>

  <clause id="9914">
    <literal><![CDATA[
      K(x,(y * z) / ((u * (x \ y)) * z)) = R(K(x,u \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7757,a(flip),b,9912,a),flip(a)].">
      <j1 rule="hyper" parents="64 7757 9912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9915">
    <literal><![CDATA[
      K(x,K(R(y,z,u),R(z,w,v5) \ z)) = K(x,K(y,(z * u) / (R(z,w,v5) * u)))
    ]]></literal>
    <justification jstring="[hyper(8437,a,9843,a)].">
      <j1 rule="hyper" parents="8437 9843"/>
    </justification>
  </clause>

  <clause id="9916">
    <literal><![CDATA[
      L(K(x,y),z,y * x) * ((y * x) * z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),9860(a,2,2,1,1))].">
      <j1 rule="para" parents="9 9860"/>
    </justification>
  </clause>

  <clause id="9917">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / ((x * y) * z) = L(K(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(154,a,9916,a)].">
      <j1 rule="hyper" parents="154 9916"/>
    </justification>
  </clause>

  <clause id="9918">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / (z * T(x * y,z)) = L(K(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(142,a,9916,a(flip),b,251,a)].">
      <j1 rule="hyper" parents="142 9916 251"/>
    </justification>
  </clause>

  <clause id="9919">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,x * y) = u
    ]]></literal>
    <justification jstring="[para(9916(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9916 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9921">
    <literal><![CDATA[
      ((K(x,y) * z) * T(y * x,z)) / (z * T(y * x,z)) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[para(9883(a,2),9918(a,1,1))].">
      <j1 rule="para" parents="9883 9918"/>
    </justification>
  </clause>

  <clause id="9922">
    <literal><![CDATA[
      K(x,K(y,(z * u) / (R(z,w,v5) * u))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(R(z,w,v5) \ z,R(y,z,u))) = v6
    ]]></literal>
    <justification jstring="[para(9915(a,1),8437(a,1))].">
      <j1 rule="para" parents="9915 8437"/>
    </justification>
  </clause>

  <clause id="9923">
    <literal><![CDATA[
      L(K(x,y),z,y * x) != u
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,T(y * x,z)) = u
    ]]></literal>
    <justification jstring="[para(9921(a,1),666(a,1))].">
      <j1 rule="para" parents="9921 666"/>
    </justification>
  </clause>

  <clause id="9924">
    <literal><![CDATA[
      (x \ (y \ ((1 / y) \ x))) \ 1 = (y \ ((1 / y) \ x)) \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),5689(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 5689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9927">
    <literal><![CDATA[
      L(T(x * K(y,x),y),z,u) / (x * K(y,x)) = (K(x,y) / x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(6452(a,1),5865(a,2,1))].">
      <j1 rule="para" parents="6452 5865"/>
    </justification>
  </clause>

  <clause id="9928">
    <literal><![CDATA[
      L(x,y,z) / (x * K(u,x)) = (K(x,u) / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5785(a,1),9927(a,1,1,1))].">
      <j1 rule="para" parents="5785 9927"/>
    </justification>
  </clause>

  <clause id="9929">
    <literal><![CDATA[
      ((K(x,y) / x) * L(x,z,u)) \ L(x,z,u) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(215,a,9928,a)].">
      <j1 rule="hyper" parents="215 9928"/>
    </justification>
  </clause>

  <clause id="9930">
    <literal><![CDATA[
      ((K(R(x,y,x),z) / R(x,y,x)) * x) \ L(R(x,y,x),y,x) = R(x,y,x) * K(z,R(x,y,x))
    ]]></literal>
    <justification jstring="[para(4733(a,1),9929(a,1,1,2))].">
      <j1 rule="para" parents="4733 9929"/>
    </justification>
  </clause>

  <clause id="9931">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,T(T(x,y) * z,y)) = (x * (x * z)) / ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(8214(a,1),5914(a,1,2))].">
      <j1 rule="para" parents="8214 5914"/>
    </justification>
  </clause>

  <clause id="9932">
    <literal><![CDATA[
      T(K(x,y),z) * R(T(K(y,x),z),u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(7880(a,1),6109(a,1,2,1))].">
      <j1 rule="para" parents="7880 6109"/>
    </justification>
  </clause>

  <clause id="9933">
    <literal><![CDATA[
      K(x,T(y,z)) * R(T(K(y,x),z),u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(8794,a,9932,a)].">
      <j1 rule="hyper" parents="8794 9932"/>
    </justification>
  </clause>

  <clause id="9934">
    <literal><![CDATA[
      K(x,T(y,z)) * R(K(y,T(x,z)),u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(7867(a,2),9933(a,1,2,1))].">
      <j1 rule="para" parents="7867 9933"/>
    </justification>
  </clause>

  <clause id="9935">
    <literal><![CDATA[
      T((T(x,y) \ z) / ((T(x,y) \ z) / y),x) = T(y,x) * K(y \ (x \ z),T(y,x))
    ]]></literal>
    <justification jstring="[hyper(8390,a,6151,a)].">
      <j1 rule="hyper" parents="8390 6151"/>
    </justification>
  </clause>

  <clause id="9936">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(u,z)) = y \ (y * x)
    ]]></literal>
    <justification jstring="[para(6161(a,1),6204(a,2,2))].">
      <j1 rule="para" parents="6161 6204"/>
    </justification>
  </clause>

  <clause id="9937">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(9936(a,2),335(a,1))].">
      <j1 rule="para" parents="9936 335"/>
    </justification>
  </clause>

  <clause id="9939">
    <literal><![CDATA[
      L(x,y,K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(7775(a,1),9937(a,1))].">
      <j1 rule="para" parents="7775 9937"/>
    </justification>
  </clause>

  <clause id="9940">
    <literal><![CDATA[
      (K(x,y) * R(K(x,y) \ 1,z,u)) * w = K(x,y) * (R(K(y,x),z,u) * w)
    ]]></literal>
    <justification jstring="[para(267(a,1),6300(a,1,2)),flip(a)].">
      <j1 rule="para" parents="267 6300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9941">
    <literal><![CDATA[
      (K(x,y) * R(K(y,x),z,u)) * w = K(x,y) * (R(K(y,x),z,u) * w)
    ]]></literal>
    <justification jstring="[para(6092(a,1),9940(a,1,1,2,1))].">
      <j1 rule="para" parents="6092 9940"/>
    </justification>
  </clause>

  <clause id="9942">
    <literal><![CDATA[
      K(1 / x,x) \ (R(1 / L(x,y,z),L(x,y,z),K(1 / x,x)) * ((u * (1 / (1 / L(x,y,z)))) / u)) = K(u,1 / (K(1 / x,x) \ R(1 / L(x,y,z),L(x,y,z),K(1 / x,x))))
    ]]></literal>
    <justification jstring="[para(7325(a,1),7040(a,1,2,2,1,2))].">
      <j1 rule="para" parents="7325 7040"/>
    </justification>
  </clause>

  <clause id="9943">
    <literal><![CDATA[
      T(K(x * R(1 / y,y,z),y \ 1) / y,x) = R(1 / y,x,z / (y * z))
    ]]></literal>
    <justification jstring="[para(6050(a,1),7071(a,1,1))].">
      <j1 rule="para" parents="6050 7071"/>
    </justification>
  </clause>

  <clause id="9944">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,3083,a(flip),b,7273,a),flip(a)].">
      <j1 rule="hyper" parents="373 3083 7273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9945">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,4801,a(flip),b,9944,a),flip(a)].">
      <j1 rule="hyper" parents="373 4801 9944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9946">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,y) \ y) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[para(8385(a,1),9945(a,1,2))].">
      <j1 rule="para" parents="8385 9945"/>
    </justification>
  </clause>

  <clause id="9947">
    <literal><![CDATA[
      T(((T(x,y) \ y) * ((x \ y) \ y)) / (T(x,y) \ y),x * (y / T(x,y))) = L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(9946(a,1),770(a,1,2))].">
      <j1 rule="para" parents="9946 770"/>
    </justification>
  </clause>

  <clause id="9948">
    <literal><![CDATA[
      K(x,y / (K(z * u,u \ 1) \ z)) = K(x,y / ((u \ 1) * (z / (1 / u))))
    ]]></literal>
    <justification jstring="[para(7524(a,1),7636(a,1,2,2,1))].">
      <j1 rule="para" parents="7524 7636"/>
    </justification>
  </clause>

  <clause id="9949">
    <literal><![CDATA[
      (x * (T(T(x,y),y) * z)) / T(x,y) = (x * (x * z)) / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9931,a(flip),b,8640,a),flip(a)].">
      <j1 rule="hyper" parents="64 9931 8640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9950">
    <literal><![CDATA[
      (x * (T(T(x,x * x),x * x) * y)) / T(x,x * x) = (x * (x * y)) / R(x,x,x)
    ]]></literal>
    <justification jstring="[para(20(a,2),9949(a,2,2))].">
      <j1 rule="para" parents="20 9949"/>
    </justification>
  </clause>

  <clause id="9951">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) * K(z,x) = (T(x,y) \ 1) \ K(z,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,9,a(flip),b,8655,a)].">
      <j1 rule="hyper" parents="145 9 8655"/>
    </justification>
  </clause>

  <clause id="9953">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) / ((T(x,y) \ 1) \ K(z,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9951(a,1),9559(a,1,2))].">
      <j1 rule="para" parents="9951 9559"/>
    </justification>
  </clause>

  <clause id="9954">
    <literal><![CDATA[
      T(T(x,y) * T(x,T(z,y)),x \ 1) = x * T(((x \ 1) \ T(x,y)) * (x \ 1),z)
    ]]></literal>
    <justification jstring="[para(5432(a,2),8658(a,2,2))].">
      <j1 rule="para" parents="5432 8658"/>
    </justification>
  </clause>

  <clause id="9955">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(z \ u) \ y) = T(x,y / (((z \ 1) \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5220,a(flip),b,8726,a)].">
      <j1 rule="hyper" parents="64 5220 8726"/>
    </justification>
  </clause>

  <clause id="9956">
    <literal><![CDATA[
      T(x,y / (((z \ 1) \ 1) \ u)) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(8790,a,9955,a),flip(a)].">
      <j1 rule="hyper" parents="8790 9955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9957">
    <literal><![CDATA[
      x \ (((y * T(x,K(z,u))) / y) * w) = x * (T(T(x,K(z,u)),y) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,8663,a(flip),b,8751,a),flip(a)].">
      <j1 rule="hyper" parents="64 8663 8751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9958">
    <literal><![CDATA[
      x \ (T((y * x) / y,K(z,u)) * w) = x * (T(T(x,K(z,u)),y) \ w)
    ]]></literal>
    <justification jstring="[para(541(a,1),9957(a,1,2,1))].">
      <j1 rule="para" parents="541 9957"/>
    </justification>
  </clause>

  <clause id="9959">
    <literal><![CDATA[
      K(x,y) * (K(y,T(K(z,u),x)) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,9304,a(flip),b,9958,a)].">
      <j1 rule="hyper" parents="64 9304 9958"/>
    </justification>
  </clause>

  <clause id="9960">
    <literal><![CDATA[
      K(x,y) * (K(y,K(z,T(u,x))) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[para(7867(a,2),9959(a,1,2,1,2))].">
      <j1 rule="para" parents="7867 9959"/>
    </justification>
  </clause>

  <clause id="9961">
    <literal><![CDATA[
      T(T((x \ 1) * y,x \ y),K(z,u)) = T((x \ 1) * y,K(z,T(u,x \ y)))
    ]]></literal>
    <justification jstring="[hyper(147,a,8849,a),flip(a)].">
      <j1 rule="hyper" parents="147 8849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9962">
    <literal><![CDATA[
      T((x \ 1) * y,K(z,T(u,x \ y))) = T((x \ 1) * y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5128(a,1),9961(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5128 9961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9963">
    <literal><![CDATA[
      (x \ 1) * (K(x \ 1,K(y,T(z,x \ L((x \ 1) \ 1,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7355,a,9962,a)].">
      <j1 rule="hyper" parents="7355 9962"/>
    </justification>
  </clause>

  <clause id="9964">
    <literal><![CDATA[
      K(T(x,((y \ 1) / ((1 / (y \ 1)) \ z)) \ 1),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,8938,a(flip),b,8939,a),flip(a)].">
      <j1 rule="hyper" parents="373 8938 8939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9965">
    <literal><![CDATA[
      K(T(x,((y \ 1) / (y \ z)) \ 1),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),9964(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="79 9964"/>
    </justification>
  </clause>

  <clause id="9966">
    <literal><![CDATA[
      K(T(x,(y \ 1) \ (y \ z)),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,8402,a(flip),b,9965,a)].">
      <j1 rule="hyper" parents="64 8402 9965"/>
    </justification>
  </clause>

  <clause id="9968">
    <literal><![CDATA[
      K(T(x,y \ z),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(8452,a,9966,a)].">
      <j1 rule="hyper" parents="8452 9966"/>
    </justification>
  </clause>

  <clause id="9969">
    <literal><![CDATA[
      (x / (y * x)) * ((1 / y) \ (z * (y \ 1))) = K(y \ 1,y) * (z * (x / (y * x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,2227,a(flip),b,9085,a),flip(a)].">
      <j1 rule="hyper" parents="373 2227 9085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9970">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,R(x,u,w))) * x) = (R(x,z,R(x,u,w)) * y) * x
    ]]></literal>
    <justification jstring="[para(267(a,1),9159(a,2,1))].">
      <j1 rule="para" parents="267 9159"/>
    </justification>
  </clause>

  <clause id="9971">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * w) * x = (x * w) * R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9158,a(flip),b,9970,a),flip(a)].">
      <j1 rule="hyper" parents="64 9158 9970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9972">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K(z * ((x \ y) \ 1),T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(9224,a,9226,a),flip(a)].">
      <j1 rule="hyper" parents="9224 9226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9973">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,u)) = K((y \ z) \ x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9634,a(flip),b,9972,a),flip(a)].">
      <j1 rule="hyper" parents="64 9634 9972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9974">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,z)) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(373,a,8216,a(flip),b,9973,a),flip(a)].">
      <j1 rule="hyper" parents="373 8216 9973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9975">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),y / z) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8325,a,9974,a)].">
      <j1 rule="hyper" parents="8325 9974"/>
    </justification>
  </clause>

  <clause id="9976">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ K(y,z),y)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2880,a(flip),b,9288,a)].">
      <j1 rule="hyper" parents="64 2880 9288"/>
    </justification>
  </clause>

  <clause id="9977">
    <literal><![CDATA[
      (K(x,y) * K((1 / z) \ 1,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(8916(a,2),9976(a,1,1))].">
      <j1 rule="para" parents="8916 9976"/>
    </justification>
  </clause>

  <clause id="9978">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(82(a,1),9977(a,1,1,2,1))].">
      <j1 rule="para" parents="82 9977"/>
    </justification>
  </clause>

  <clause id="9979">
    <literal><![CDATA[
      L(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(606,a,9978,a)].">
      <j1 rule="hyper" parents="606 9978"/>
    </justification>
  </clause>

  <clause id="9980">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9809,a(flip),b,9978,a),flip(a)].">
      <j1 rule="hyper" parents="64 9809 9978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9981">
    <literal><![CDATA[
      L(x,K(y,z),K(u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,6285,a,b,9978,a)].">
      <j1 rule="hyper" parents="35 6285 9978"/>
    </justification>
  </clause>

  <clause id="9982">
    <literal><![CDATA[
      x \ (K(y,z) * (K(u,y) * x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * K(u,y),x) = w
    ]]></literal>
    <justification jstring="[para(9978(a,1),336(a,1,2))].">
      <j1 rule="para" parents="9978 336"/>
    </justification>
  </clause>

  <clause id="9984">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(3320(a,1),9978(a,1,1))].">
      <j1 rule="para" parents="3320 9978"/>
    </justification>
  </clause>

  <clause id="9985">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ u = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7067,a(flip),b,9979,a)].">
      <j1 rule="hyper" parents="64 7067 9979"/>
    </justification>
  </clause>

  <clause id="9986">
    <literal><![CDATA[
      L(x,L(K(y,z),u,w),K(z,v5)) = x
    ]]></literal>
    <justification jstring="[para(7310(a,1),9979(a,1,2))].">
      <j1 rule="para" parents="7310 9979"/>
    </justification>
  </clause>

  <clause id="9987">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(7869(a,1),9979(a,1,2))].">
      <j1 rule="para" parents="7869 9979"/>
    </justification>
  </clause>

  <clause id="9988">
    <literal><![CDATA[
      (K(x,y) * K(z,T(x,u))) * w = K(x,y) * (K(z,T(x,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(1960,a,9987,a),flip(a)].">
      <j1 rule="hyper" parents="1960 9987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9989">
    <literal><![CDATA[
      (K(x,y) * L(K(z,x),u,w)) * v5 = K(x,y) * (L(K(z,x),u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(1960,a,9986,a),flip(a)].">
      <j1 rule="hyper" parents="1960 9986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9990">
    <literal><![CDATA[
      T(x,y) \ (x * (K(x,z) * u)) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6155,a,b,9980,a)].">
      <j1 rule="hyper" parents="373 6155 9980"/>
    </justification>
  </clause>

  <clause id="9991">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(x,y) \ u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,168,a(flip),b,9980,a),flip(a)].">
      <j1 rule="hyper" parents="373 168 9980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9992">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * (K(y,x) * u)) = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(6161(a,1),9980(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6161 9980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9994">
    <literal><![CDATA[
      K(L(x,y / x,z),u) * (K(u,w) * v5) = K(u,w) * (L(K(x,u),y,z) * v5)
    ]]></literal>
    <justification jstring="[para(7376(a,1),9980(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7376 9980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9995">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * (K(x,y) * u) = w
    ]]></literal>
    <justification jstring="[para(9984(a,1),9811(a,1))].">
      <j1 rule="para" parents="9984 9811"/>
    </justification>
  </clause>

  <clause id="9996">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ u = K(y,x) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,9980,a(flip),b,9985,a),flip(a)].">
      <j1 rule="hyper" parents="373 9980 9985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9997">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) \ u = K(y,x) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(3320(a,1),9985(a,1,1))].">
      <j1 rule="para" parents="3320 9985"/>
    </justification>
  </clause>

  <clause id="9998">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(u,w)),K(u,w)) = K(y,v5) * (K(x,y) * (K(y,v5) \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8157,a,b,9991,a)].">
      <j1 rule="hyper" parents="373 8157 9991"/>
    </justification>
  </clause>

  <clause id="9999">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),K(x,z) * u) = (K(x,z) * u) \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(493,a,9992,a(flip),b,9809,a)].">
      <j1 rule="hyper" parents="493 9992 9809"/>
    </justification>
  </clause>

  <clause id="10000">
    <literal><![CDATA[
      (K(x,y) * (K(x,z) * u)) / (K(x,y) * u) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,9992,a(flip),b,6156,a)].">
      <j1 rule="hyper" parents="225 9992 6156"/>
    </justification>
  </clause>

  <clause id="10001">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,u) * z) = K(u,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,9992,a(flip),b,9804,a)].">
      <j1 rule="hyper" parents="142 9992 9804"/>
    </justification>
  </clause>

  <clause id="10003">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) \ u = (K(y,x) * K(z,y)) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,9978,a,b,9997,a),flip(a)].">
      <j1 rule="hyper" parents="373 9978 9997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10004">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(144,a,8110,a,b,10000,a)].">
      <j1 rule="hyper" parents="144 8110 10000"/>
    </justification>
  </clause>

  <clause id="10005">
    <literal><![CDATA[
      x / (K(y \ x,z) * (y * (x / y))) = K(z,y \ x) * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(6179(a,1),10001(a,1,1))].">
      <j1 rule="para" parents="6179 10001"/>
    </justification>
  </clause>

  <clause id="10007">
    <literal><![CDATA[
      L((K(x,y) * K(z,x)) \ 1,K(x,y) * K(z,x),u) \ K(K(x,y) * K(z,x),u) = (((K(y,x) * K(x,z)) \ u) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(10003(a,2),7661(a,2,1,1))].">
      <j1 rule="para" parents="10003 7661"/>
    </justification>
  </clause>

  <clause id="10008">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(5776(a,1),9990(a,1,2))].">
      <j1 rule="para" parents="5776 9990"/>
    </justification>
  </clause>

  <clause id="10009">
    <literal><![CDATA[
      x \ (T(x,y) * (K(z,x) * u)) = T(x,z) \ (T(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6071,a,b,10008,a)].">
      <j1 rule="hyper" parents="373 6071 10008"/>
    </justification>
  </clause>

  <clause id="10010">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * (K(y,x) * u) = w
    ]]></literal>
    <justification jstring="[para(10009(a,1),6087(a,1))].">
      <j1 rule="para" parents="10009 6087"/>
    </justification>
  </clause>

  <clause id="10011">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * (K(x,z) * u) = w
    ]]></literal>
    <justification jstring="[para(9985(a,2),9995(a,1))].">
      <j1 rule="para" parents="9985 9995"/>
    </justification>
  </clause>

  <clause id="10012">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(8110(a,2),10004(a,2,2,1))].">
      <j1 rule="para" parents="8110 10004"/>
    </justification>
  </clause>

  <clause id="10013">
    <literal><![CDATA[
      K(x,y) * (K(z,K(u,x)) * (K(x,y) \ w)) = K(z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[hyper(397,a,10012,a),flip(a)].">
      <j1 rule="hyper" parents="397 10012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10014">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ w)) = K(u,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(8110(a,2),10013(a,1,2,1))].">
      <j1 rule="para" parents="8110 10013"/>
    </justification>
  </clause>

  <clause id="10015">
    <literal><![CDATA[
      x / (K(((y \ 1) * x) \ x,z) * (((y \ 1) * x) * R(y,y \ 1,x))) = K(z,((y \ 1) * x) \ x) * K(((y \ 1) * x) \ x,(y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(239(a,2),10005(a,1,2,2,2))].">
      <j1 rule="para" parents="239 10005"/>
    </justification>
  </clause>

  <clause id="10016">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,w) * v5) = K(y,w) * (L(K(x,y),z,u) * v5)
    ]]></literal>
    <justification jstring="[para(7376(a,1),9994(a,1,1))].">
      <j1 rule="para" parents="7376 9994"/>
    </justification>
  </clause>

  <clause id="10017">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,u)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,9272,a,b,9998,a),flip(a)].">
      <j1 rule="hyper" parents="41 9272 9998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10018">
    <literal><![CDATA[
      T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,7615,a(flip),b,10017,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 7615 10017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10020">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(x * K(y,u),K(y,z)) = K(y,u)
    ]]></literal>
    <justification jstring="[hyper(1036,a,10018,a)].">
      <j1 rule="hyper" parents="1036 10018"/>
    </justification>
  </clause>

  <clause id="10021">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) \ T(x,K(z,u)) = K(z,y)
    ]]></literal>
    <justification jstring="[para(6871(a,1),10020(a,1,2,1))].">
      <j1 rule="para" parents="6871 10020"/>
    </justification>
  </clause>

  <clause id="10022">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) = T(x,K(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,6882,a,b,10021,a),flip(a)].">
      <j1 rule="hyper" parents="40 6882 10021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10023">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,u)) = K(x,y) * T(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,7683,a(flip),b,10022,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 7683 10022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10024">
    <literal><![CDATA[
      T(x * K(L(y \ 1,z,u) \ 1,w),K(w,v5)) = T(x,K(w,v5)) * L(K(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(7310(a,1),10022(a,2,2))].">
      <j1 rule="para" parents="7310 10022"/>
    </justification>
  </clause>

  <clause id="10025">
    <literal><![CDATA[
      K(x,K(y,z)) * T(y,K(x,u)) = T(T(y,K(x,z)),K(x,u))
    ]]></literal>
    <justification jstring="[para(8115(a,1),10023(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8115 10023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10026">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,R(u,w,v5))) = K(x,y) * T(z,K(u,R(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(9778(a,1),10023(a,2,2))].">
      <j1 rule="para" parents="9778 10023"/>
    </justification>
  </clause>

  <clause id="10027">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) \ x = K(y,K(u,x)) * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(10025(a,1),9424(a,1,1))].">
      <j1 rule="para" parents="10025 9424"/>
    </justification>
  </clause>

  <clause id="10028">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) \ x = K(x,K(y,u)) * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8110(a,1),10027(a,2,1))].">
      <j1 rule="para" parents="8110 10027"/>
    </justification>
  </clause>

  <clause id="10029">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) \ x = K(x,K(y,u)) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8108(a,1),10028(a,2,2))].">
      <j1 rule="para" parents="8108 10028"/>
    </justification>
  </clause>

  <clause id="10030">
    <literal><![CDATA[
      K(x,T(y,T(z \ (x * u),x) \ x)) = K(T(x * K(u \ z,x),x),y)
    ]]></literal>
    <justification jstring="[para(8564(a,1),9423(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8564 9423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10031">
    <literal><![CDATA[
      K(x,T(y,T(z \ (x * u),x) \ x)) = K(x * K(u \ z,x),y)
    ]]></literal>
    <justification jstring="[para(3163(a,1),10030(a,2,1))].">
      <j1 rule="para" parents="3163 10030"/>
    </justification>
  </clause>

  <clause id="10032">
    <literal><![CDATA[
      K(x,T(y,T(z \ (x * u),x) \ x)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8234,a(flip),b,10031,a),flip(a)].">
      <j1 rule="hyper" parents="373 8234 10031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10033">
    <literal><![CDATA[
      K(x,T(y,(z \ (x * u)) \ x)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8645,a(flip),b,10032,a)].">
      <j1 rule="hyper" parents="64 8645 10032"/>
    </justification>
  </clause>

  <clause id="10034">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,L(y,u,w))) = K(z * L(y,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8001,a(flip),b,9529,a),flip(a)].">
      <j1 rule="hyper" parents="373 8001 9529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10036">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,1770,a(flip),b,9557,a)].">
      <j1 rule="hyper" parents="64 1770 9557"/>
    </justification>
  </clause>

  <clause id="10037">
    <literal><![CDATA[
      (T(x * (y \ 1),x) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(7052(a,1),9598(a,1,1,1))].">
      <j1 rule="para" parents="7052 9598"/>
    </justification>
  </clause>

  <clause id="10038">
    <literal><![CDATA[
      (x \ R(x,y \ 1,x)) / (T(x * (y \ 1),x) / x) = y
    ]]></literal>
    <justification jstring="[hyper(142,a,8953,a(flip),b,10037,a(flip))].">
      <j1 rule="hyper" parents="142 8953 10037"/>
    </justification>
  </clause>

  <clause id="10039">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * K(K(z,u),w)) = (y / x) * K(w,K(z,z \ u))
    ]]></literal>
    <justification jstring="[para(6243(a,1),9633(a,1,2))].">
      <j1 rule="para" parents="6243 9633"/>
    </justification>
  </clause>

  <clause id="10040">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * K(z,K(u,w))) = (y / x) * K(w,K(z,z \ u))
    ]]></literal>
    <justification jstring="[para(8092(a,1),10039(a,1,2,2))].">
      <j1 rule="para" parents="8092 10039"/>
    </justification>
  </clause>

  <clause id="10041">
    <literal><![CDATA[
      T((T(x,y) \ z) / ((T(x,y) \ z) / y),x) != T(y,x) * u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),T(y,x)) = u
    ]]></literal>
    <justification jstring="[para(9935(a,2),44(a,1))].">
      <j1 rule="para" parents="9935 44"/>
    </justification>
  </clause>

  <clause id="10042">
    <literal><![CDATA[
      T((T(x,y) \ z) / ((T(x,y) \ z) / y),x) \ T(y,x) = K(T(y,x),y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(9935(a,2),6110(a,1,1))].">
      <j1 rule="para" parents="9935 6110"/>
    </justification>
  </clause>

  <clause id="10043">
    <literal><![CDATA[
      T(T(x,y) * T(x,T(z,y)),x \ 1) = x * T(T(((x \ 1) \ x) * (x \ 1),y),z)
    ]]></literal>
    <justification jstring="[para(5432(a,2),9954(a,2,2,1))].">
      <j1 rule="para" parents="5432 9954"/>
    </justification>
  </clause>

  <clause id="10044">
    <literal><![CDATA[
      T(x * L(K(y,z),u,w),K(z,v5)) = T(x,K(z,v5)) * L(K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(7310(a,1),10024(a,1,1,2))].">
      <j1 rule="para" parents="7310 10024"/>
    </justification>
  </clause>

  <clause id="10045">
    <literal><![CDATA[
      T(L(K(x,y),z,u) \ w,K(y,v5)) = L(K(x,y),z,u) \ T(w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(36,a,5432,a(flip),b,10044,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 5432 10044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10046">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * w,K(x,v5)) = L(K(y,x),z,u) \ T(w,K(x,v5))
    ]]></literal>
    <justification jstring="[para(7326(a,1),10045(a,1,1))].">
      <j1 rule="para" parents="7326 10045"/>
    </justification>
  </clause>

  <clause id="10047">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * w,K(x,v5)) = L(K(x,y),z,u) * T(w,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,7326,a(flip),b,10046,a),flip(a)].">
      <j1 rule="hyper" parents="373 7326 10046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10048">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * T(w,L(K(x,y),z,u)),K(x,v5)) = T(w,K(x,v5)) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,265,a(flip),b,10047,a),flip(a)].">
      <j1 rule="hyper" parents="373 265 10047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10049">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,K(x,z) * u,R(x,w,v5)) = x \ (y \ ((R(x,u,R(x,w,v5)) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[para(9901(a,1),10036(a,2,2,2,1,1))].">
      <j1 rule="para" parents="9901 10036"/>
    </justification>
  </clause>

  <clause id="10050">
    <literal><![CDATA[
      K(T(x,y),x \ (y \ z)) != u \ T(x,y)
    ]]></literal>
    <literal><![CDATA[
      T((T(y,x) \ z) / ((T(y,x) \ z) / x),y) = u
    ]]></literal>
    <justification jstring="[para(10042(a,1),49(a,1))].">
      <j1 rule="para" parents="10042 49"/>
    </justification>
  </clause>

  <clause id="10051">
    <literal><![CDATA[
      T(T(x,y) * T(x,T(z,y)),x \ 1) = x * T(T((x \ 1) \ 1,y),z)
    ]]></literal>
    <justification jstring="[para(1131(a,1),10043(a,2,2,1,1))].">
      <j1 rule="para" parents="1131 10043"/>
    </justification>
  </clause>

  <clause id="10052">
    <literal><![CDATA[
      T(x * T(T(x,y),z),x \ 1) = x * T(T((x \ 1) \ 1,y),z)
    ]]></literal>
    <justification jstring="[para(8067(a,1),10051(a,1,1))].">
      <j1 rule="para" parents="8067 10051"/>
    </justification>
  </clause>

  <clause id="10053">
    <literal><![CDATA[
      ((x / y) * (y * T(z,u))) / x = T(((x / y) * (y * z)) / x,u)
    ]]></literal>
    <justification jstring="[para(7368(a,1),6821(a,1,1))].">
      <j1 rule="para" parents="7368 6821"/>
    </justification>
  </clause>

  <clause id="10054">
    <literal><![CDATA[
      ((x / y) * (y * T((y \ 1) \ 1,z))) / x = T(((x / y) * ((1 / y) \ y)) / x,z)
    ]]></literal>
    <justification jstring="[para(1134(a,1),10053(a,2,1,1,2))].">
      <j1 rule="para" parents="1134 10053"/>
    </justification>
  </clause>

  <clause id="10055">
    <literal><![CDATA[
      T(((x / (y \ 1)) * ((y \ 1) * y)) / x,y \ z) = ((x / (y \ 1)) * K(y,y * z)) / x
    ]]></literal>
    <justification jstring="[para(8875(a,1),10053(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8875 10053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10056">
    <literal><![CDATA[
      ((x / y) * ((1 / y) \ T(y,z))) / x = T(((x / y) * ((1 / y) \ y)) / x,z)
    ]]></literal>
    <justification jstring="[para(1490(a,1),10054(a,1,1,2))].">
      <j1 rule="para" parents="1490 10054"/>
    </justification>
  </clause>

  <clause id="10057">
    <literal><![CDATA[
      ((x / y) * ((1 / y) \ T(y,z))) / x = T((x / (y \ 1)) / x,z)
    ]]></literal>
    <justification jstring="[para(1590(a,1),10056(a,2,1,1))].">
      <j1 rule="para" parents="1590 10056"/>
    </justification>
  </clause>

  <clause id="10058">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K((R(x,y,z) \ 1) \ 1,u) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(5366(a,1),7270(a,1,2,1,1))].">
      <j1 rule="para" parents="5366 7270"/>
    </justification>
  </clause>

  <clause id="10059">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(R(x,y,z),u) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3779(a,1),10058(a,1,2))].">
      <j1 rule="para" parents="3779 10058"/>
    </justification>
  </clause>

  <clause id="10060">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = R(x,K(y,T(u,z)),z * K(u,y)) * z
    ]]></literal>
    <justification jstring="[para(7869(a,1),8263(a,2,1,2))].">
      <j1 rule="para" parents="7869 8263"/>
    </justification>
  </clause>

  <clause id="10061">
    <literal><![CDATA[
      K(x \ ((y / z) \ u),L(z,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x \ ((z \ y) \ u),L(z,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(8931(a,1),5974(a,1))].">
      <j1 rule="para" parents="8931 5974"/>
    </justification>
  </clause>

  <clause id="10062">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),x * K(y,z)) = T(K(y,z) * x,T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(6175(a,1),9258(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6175 9258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10063">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),x * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * x,x) = u
    ]]></literal>
    <justification jstring="[para(10062(a,2),7465(a,1))].">
      <j1 rule="para" parents="10062 7465"/>
    </justification>
  </clause>

  <clause id="10064">
    <literal><![CDATA[
      ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9705,a(flip),b,9311,a),flip(a)].">
      <j1 rule="hyper" parents="64 9705 9311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10065">
    <literal><![CDATA[
      ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(5515(a,1),10064(a,1,1))].">
      <j1 rule="para" parents="5515 10064"/>
    </justification>
  </clause>

  <clause id="10066">
    <literal><![CDATA[
      K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u))
    ]]></literal>
    <justification jstring="[hyper(9310,a,10065,a)].">
      <j1 rule="hyper" parents="9310 10065"/>
    </justification>
  </clause>

  <clause id="10067">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9196,a(flip),b,10066,a),flip(a)].">
      <j1 rule="hyper" parents="64 9196 10066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10068">
    <literal><![CDATA[
      K(x,R(y / (z * u),z * u,x)) = K(x,(y * x) / ((z * x) * u))
    ]]></literal>
    <justification jstring="[para(112(a,2),10066(a,1,2))].">
      <j1 rule="para" parents="112 10066"/>
    </justification>
  </clause>

  <clause id="10069">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9350,a(flip),b,10067,a)].">
      <j1 rule="hyper" parents="64 9350 10067"/>
    </justification>
  </clause>

  <clause id="10070">
    <literal><![CDATA[
      x * K(x,y / (x * (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[hyper(145,a,10069,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 10069 5726"/>
    </justification>
  </clause>

  <clause id="10071">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y / (x * (z * u)))) = K(y / ((x * z) * u),x)
    ]]></literal>
    <justification jstring="[para(10069(a,1),6177(a,1,2,2))].">
      <j1 rule="para" parents="10069 6177"/>
    </justification>
  </clause>

  <clause id="10072">
    <literal><![CDATA[
      K(x,(y * x) / ((z * x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z * u)) = w
    ]]></literal>
    <justification jstring="[para(10068(a,1),9732(a,1))].">
      <j1 rule="para" parents="10068 9732"/>
    </justification>
  </clause>

  <clause id="10073">
    <literal><![CDATA[
      K(x / ((y * z) * u),y) = K(x / (y * (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(6303,a,10071,a),flip(a)].">
      <j1 rule="hyper" parents="6303 10071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10074">
    <literal><![CDATA[
      K(x / (y * (z * x)),y) = K(z \ (y \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(8800,a,10073,a),flip(a)].">
      <j1 rule="hyper" parents="8800 10073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10075">
    <literal><![CDATA[
      K((x \ y) / (z * y),z) = K(x \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),10074(a,1,1,2,2))].">
      <j1 rule="para" parents="10 10074"/>
    </justification>
  </clause>

  <clause id="10076">
    <literal><![CDATA[
      K(x * R(T(y,z),u,w),T(T(y,v5),K(R(y,u,w),z))) = K(x * R(y,u,w),T(y,v5))
    ]]></literal>
    <justification jstring="[para(27(a,2),9696(a,1,1,2))].">
      <j1 rule="para" parents="27 9696"/>
    </justification>
  </clause>

  <clause id="10077">
    <literal><![CDATA[
      K(x,R(x,y,z) \ ((x * R(T(x,u),y,z)) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w \ x) = v5
    ]]></literal>
    <justification jstring="[para(9764(a,2),8324(a,1))].">
      <j1 rule="para" parents="9764 8324"/>
    </justification>
  </clause>

  <clause id="10078">
    <literal><![CDATA[
      L((x * x) * y,x,x) / T(x,x * x) = (x * (x * y)) / R(x,x,x)
    ]]></literal>
    <justification jstring="[para(4960(a,1),9950(a,1,1))].">
      <j1 rule="para" parents="4960 9950"/>
    </justification>
  </clause>

  <clause id="10079">
    <literal><![CDATA[
      L((x * x) * y,x,x) / L(x,x,x) = (x * (x * y)) / R(x,x,x)
    ]]></literal>
    <justification jstring="[para(118(a,1),10078(a,1,2))].">
      <j1 rule="para" parents="118 10078"/>
    </justification>
  </clause>

  <clause id="10080">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = R(x,K(y,u),z * K(u,y)) * z
    ]]></literal>
    <justification jstring="[para(9570(a,1),10060(a,2,1))].">
      <j1 rule="para" parents="9570 10060"/>
    </justification>
  </clause>

  <clause id="10081">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * (K(u,T(y,z)) * z) = (x * K(y,u)) * (K(u,y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,9905,a(flip),b,10080,a),flip(a)].">
      <j1 rule="hyper" parents="373 9905 10080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10082">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (K(z,T(y,u)) * u) = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(7869(a,1),10081(a,1,1,2))].">
      <j1 rule="para" parents="7869 10081"/>
    </justification>
  </clause>

  <clause id="10083">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (u * K(z,y)) = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(8193(a,1),10082(a,1,2))].">
      <j1 rule="para" parents="8193 10082"/>
    </justification>
  </clause>

  <clause id="10084">
    <literal><![CDATA[
      (K(x,T(y,z)) * a(K(x,u),w,v5)) * (z * K(y,x)) = (a(K(x,u),w,v5) * K(x,y)) * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(9190(a,2),10083(a,1,1))].">
      <j1 rule="para" parents="9190 10083"/>
    </justification>
  </clause>

  <clause id="10085">
    <literal><![CDATA[
      K(x * R(T(y,z),u,w),T(T(y,v5),K(z,R(y,u,w)))) = K(x * R(y,u,w),T(y,v5))
    ]]></literal>
    <justification jstring="[para(8153(a,1),10076(a,1,2))].">
      <j1 rule="para" parents="8153 10076"/>
    </justification>
  </clause>

  <clause id="10086">
    <literal><![CDATA[
      K(x * R(T(y,z),u,w),T(y,v5)) = K(x * R(y,u,w),T(y,v5))
    ]]></literal>
    <justification jstring="[para(4014(a,1),10085(a,1,2))].">
      <j1 rule="para" parents="4014 10085"/>
    </justification>
  </clause>

  <clause id="10088">
    <literal><![CDATA[
      T(T(x,y) * K(z * R(x,u,w),T(x,y)),z) = R(T(x,y),z,R(T(x,y),u,w))
    ]]></literal>
    <justification jstring="[para(10086(a,1),6236(a,1,1,2))].">
      <j1 rule="para" parents="10086 6236"/>
    </justification>
  </clause>

  <clause id="10089">
    <literal><![CDATA[
      T(T(x * K(y * R(x,z,u),x),w),y) = R(T(x,w),y,R(T(x,w),z,u))
    ]]></literal>
    <justification jstring="[para(6237(a,1),10088(a,1,1))].">
      <j1 rule="para" parents="6237 10088"/>
    </justification>
  </clause>

  <clause id="10090">
    <literal><![CDATA[
      R(T(x,y),z,R(T(x,y),u,w)) = R(T(x,y),z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9903,a(flip),b,10089,a),flip(a)].">
      <j1 rule="hyper" parents="64 9903 10089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10091">
    <literal><![CDATA[
      R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = ((x * y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(6249(a,1),6327(a,2,1))].">
      <j1 rule="para" parents="6249 6327"/>
    </justification>
  </clause>

  <clause id="10092">
    <literal><![CDATA[
      R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,20,a,b,10091,a),flip(a)].">
      <j1 rule="hyper" parents="373 20 10091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10094">
    <literal><![CDATA[
      R(x,y,T(x,z)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7178,a(flip),b,10092,a)].">
      <j1 rule="hyper" parents="64 7178 10092"/>
    </justification>
  </clause>

  <clause id="10095">
    <literal><![CDATA[
      R(R(x,y,(z \ u) \ u),y * T(z,z \ u),K(z \ u,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(116(a,1),10092(a,1,1,3))].">
      <j1 rule="para" parents="116 10092"/>
    </justification>
  </clause>

  <clause id="10097">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = T(R(x,z,x),y)
    ]]></literal>
    <justification jstring="[para(10094(a,1),27(a,2,1))].">
      <j1 rule="para" parents="10094 27"/>
    </justification>
  </clause>

  <clause id="10098">
    <literal><![CDATA[
      R(x / y,z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(117(a,1),10094(a,1,3)),flip(a)].">
      <j1 rule="para" parents="117 10094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10100">
    <literal><![CDATA[
      T(x,R(y,z,T(y,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(10094(a,2),7404(a,1,2))].">
      <j1 rule="para" parents="10094 7404"/>
    </justification>
  </clause>

  <clause id="10101">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,z)) = T(x,y / (y / z))
    ]]></literal>
    <justification jstring="[para(276(a,1),10100(a,1,2,3))].">
      <j1 rule="para" parents="276 10100"/>
    </justification>
  </clause>

  <clause id="10102">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,27,a,b,10097,a),flip(a)].">
      <j1 rule="hyper" parents="373 27 10097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10103">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4684,a(flip),b,10097,a),flip(a)].">
      <j1 rule="hyper" parents="373 4684 10097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10106">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,z)) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,4729,a(flip),b,10102,a),flip(a)].">
      <j1 rule="hyper" parents="373 4729 10102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10107">
    <literal><![CDATA[
      R(T(x,y),z,x) \ T(T(x,y) * z,T(x,y)) = T(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(10102(a,1),1941(a,1,1))].">
      <j1 rule="para" parents="10102 1941"/>
    </justification>
  </clause>

  <clause id="10108">
    <literal><![CDATA[
      R(T(x * K(y,x),y),z,x * K(y,x)) = R(x,z,T(x * K(y,x),u))
    ]]></literal>
    <justification jstring="[para(5785(a,1),10102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5785 10102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10109">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(7162(a,2),10098(a,1,1))].">
      <j1 rule="para" parents="7162 10098"/>
    </justification>
  </clause>

  <clause id="10110">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,T(x,K(y,z))) = T(K(z,y),T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(7818(a,1),10107(a,1,2,1))].">
      <j1 rule="para" parents="7818 10107"/>
    </justification>
  </clause>

  <clause id="10111">
    <literal><![CDATA[
      R(x,y,T(x * K(z,x),u)) = R(x,y,x * K(z,x))
    ]]></literal>
    <justification jstring="[para(5785(a,1),10108(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5785 10108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10112">
    <literal><![CDATA[
      R(x,y,x * K(z,x)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5785(a,1),10111(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5785 10111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10113">
    <literal><![CDATA[
      R(x \ y,z,y / x) = R(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(5774(a,1),10112(a,1,3))].">
      <j1 rule="para" parents="5774 10112"/>
    </justification>
  </clause>

  <clause id="10114">
    <literal><![CDATA[
      (((x * y) \ x) * z) / T((x * y) \ x,u) = z * (K(y \ 1,z) * K(u,y \ 1))
    ]]></literal>
    <justification jstring="[para(6705(a,1),6790(a,2,2,2))].">
      <j1 rule="para" parents="6705 6790"/>
    </justification>
  </clause>

  <clause id="10115">
    <literal><![CDATA[
      (((x * y) \ x) * z) / T((x * y) \ x,u) = ((y \ 1) * z) / T(y \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6393,a(flip),b,10114,a),flip(a)].">
      <j1 rule="hyper" parents="373 6393 10114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10117">
    <literal><![CDATA[
      ((x \ y) \ R(x \ y,z,x \ y)) * (y / x) = R((x \ y) * K(x,x \ y),z,x \ y)
    ]]></literal>
    <justification jstring="[para(2071(a,1),7532(a,1,1))].">
      <j1 rule="para" parents="2071 7532"/>
    </justification>
  </clause>

  <clause id="10118">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) \ ((x * y) / x)) = (x \ y) / T(y * K(x,y),x \ 1)
    ]]></literal>
    <justification jstring="[para(8190(a,1),8399(a,2,2))].">
      <j1 rule="para" parents="8190 8399"/>
    </justification>
  </clause>

  <clause id="10119">
    <literal><![CDATA[
      1 * ((x \ R(x,y,z)) / K(u,R(x,w,v5))) = K(R(x,w,v5),u) * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(375(a,1),8750(a,1,1))].">
      <j1 rule="para" parents="375 8750"/>
    </justification>
  </clause>

  <clause id="10121">
    <literal><![CDATA[
      1 * ((x \ R(x,y,z)) * K(R(x,u,w),v5)) = K(R(x,u,w),v5) * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(6878(a,1),10119(a,1,2))].">
      <j1 rule="para" parents="6878 10119"/>
    </justification>
  </clause>

  <clause id="10122">
    <literal><![CDATA[
      K(R(x,y,z),u) * (x \ R(x,y,z)) = 1 * (x \ R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(10059(a,1),10121(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10059 10121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10123">
    <literal><![CDATA[
      K(R(x,y,z),u) * (x \ R(x,y,z)) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,7,a(flip),b,10122,a),flip(a)].">
      <j1 rule="hyper" parents="373 7 10122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10124">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (y \ R(T(y,x),z,u)) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(6187,a,10123,a)].">
      <j1 rule="hyper" parents="6187 10123"/>
    </justification>
  </clause>

  <clause id="10125">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) * (K(z,y) \ R(T(K(z,y),x),u,w)) = K(z,y) \ R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(9775(a,1),10124(a,1,1))].">
      <j1 rule="para" parents="9775 10124"/>
    </justification>
  </clause>

  <clause id="10126">
    <literal><![CDATA[
      ((T(x,x * y) \ 1) * (y / x)) \ (y / x) = (y / x) / T((x * x) \ y,T(x,y))
    ]]></literal>
    <justification jstring="[para(7427(a,1),8888(a,2,2))].">
      <j1 rule="para" parents="7427 8888"/>
    </justification>
  </clause>

  <clause id="10127">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (u \ (y * (z / x)))) = K(x,(u * (y * z)) \ ((y * (x \ z)) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,9906,a(flip),b,8932,a),flip(a)].">
      <j1 rule="hyper" parents="64 9906 8932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10128">
    <literal><![CDATA[
      K(x,((y * z) \ z) * K(y * z,1 / y)) = K(z,K(x,y)) * K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[para(8978(a,1),9069(a,2,1))].">
      <j1 rule="para" parents="8978 9069"/>
    </justification>
  </clause>

  <clause id="10129">
    <literal><![CDATA[
      K(x,((y * z) \ z) * K(y * z,1 / y)) = K(z,K(x,y)) * K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(9235(a,2),10128(a,2,2))].">
      <j1 rule="para" parents="9235 10128"/>
    </justification>
  </clause>

  <clause id="10130">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(u,K(x,z)) * K(x,u / (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7022,a,b,10129,a)].">
      <j1 rule="hyper" parents="64 7022 10129"/>
    </justification>
  </clause>

  <clause id="10131">
    <literal><![CDATA[
      K(x,1 / (1 / (y \ (y / z)))) = K(u,K(x,z)) * K(x,u / (u * z))
    ]]></literal>
    <justification jstring="[hyper(6515,a,10130,a)].">
      <j1 rule="hyper" parents="6515 10130"/>
    </justification>
  </clause>

  <clause id="10133">
    <literal><![CDATA[
      K((x * ((y * z) \ y)) \ ((1 / ((y * z) \ y)) \ u),y \ (y * z)) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[hyper(7010,a,9640,a)].">
      <j1 rule="hyper" parents="7010 9640"/>
    </justification>
  </clause>

  <clause id="10134">
    <literal><![CDATA[
      K((x * ((y * z) \ y)) \ ((1 / ((y * z) \ y)) \ u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),10133(a,1,2))].">
      <j1 rule="para" parents="9 10133"/>
    </justification>
  </clause>

  <clause id="10135">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ ((1 / ((x * y) \ x)) \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(8799,a,10134,a)].">
      <j1 rule="hyper" parents="8799 10134"/>
    </justification>
  </clause>

  <clause id="10136">
    <literal><![CDATA[
      T(((x / (y \ 1)) * ((y \ 1) * y)) / x,y \ z) = (x / (T(y,y * z) \ 1)) / x
    ]]></literal>
    <justification jstring="[para(9330(a,1),10055(a,2,1))].">
      <j1 rule="para" parents="9330 10055"/>
    </justification>
  </clause>

  <clause id="10137">
    <literal><![CDATA[
      ((x \ y) \ R(x \ y,z,x \ y)) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(5774(a,1),10117(a,2,1))].">
      <j1 rule="para" parents="5774 10117"/>
    </justification>
  </clause>

  <clause id="10138">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * (u / x)))
    ]]></literal>
    <justification jstring="[hyper(8058,a,10127,a),flip(a)].">
      <j1 rule="hyper" parents="8058 10127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10139">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,9533,a(flip),b,10138,a),flip(a)].">
      <j1 rule="hyper" parents="373 9533 10138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10140">
    <literal><![CDATA[
      K(x,T((y / (z * u)) \ 1,z * u)) = K(x,y \ ((z * (x \ u)) * x))
    ]]></literal>
    <justification jstring="[para(12(a,1),10139(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 10139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10141">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(8701,a,10140,a),flip(a)].">
      <j1 rule="hyper" parents="8701 10140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10142">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * u)) = w
    ]]></literal>
    <justification jstring="[para(10140(a,1),8701(a,1))].">
      <j1 rule="para" parents="10140 8701"/>
    </justification>
  </clause>

  <clause id="10143">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(5978,a,10141,a),flip(a)].">
      <j1 rule="hyper" parents="5978 10141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10144">
    <literal><![CDATA[
      K(x,y \ ((x \ y) * z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8828,a(flip),b,10141,a),flip(a)].">
      <j1 rule="hyper" parents="64 8828 10141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10145">
    <literal><![CDATA[
      K(x,x \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(10141(a,1),5978(a,1))].">
      <j1 rule="para" parents="10141 5978"/>
    </justification>
  </clause>

  <clause id="10146">
    <literal><![CDATA[
      K(x * (y \ z),y) \ u = K(y,y \ (x * z)) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,10143,a,b,6162,a),flip(a)].">
      <j1 rule="hyper" parents="144 10143 6162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10147">
    <literal><![CDATA[
      T(x,x \ (y * z)) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(143,a,10143,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 10143 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10148">
    <literal><![CDATA[
      K(x,y * (x \ 1)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(8(a,1),10143(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8 10143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10149">
    <literal><![CDATA[
      K(x,x \ (y * (x * z))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),10143(a,2,2,2))].">
      <j1 rule="para" parents="9 10143"/>
    </justification>
  </clause>

  <clause id="10150">
    <literal><![CDATA[
      x * K(y,x * (y \ 1)) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,10148,a,b,5961,a)].">
      <j1 rule="hyper" parents="145 10148 5961"/>
    </justification>
  </clause>

  <clause id="10151">
    <literal><![CDATA[
      K(x,y * (1 / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6519,a,b,10148,a)].">
      <j1 rule="hyper" parents="64 6519 10148"/>
    </justification>
  </clause>

  <clause id="10152">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6521,a(flip),b,10148,a),flip(a)].">
      <j1 rule="hyper" parents="64 6521 10148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10153">
    <literal><![CDATA[
      K(x,x \ ((x \ y) \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),10144(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 10144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10154">
    <literal><![CDATA[
      (x * y) / T(z,x * (z \ y)) = z \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(225,a,10147,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 10147 116"/>
    </justification>
  </clause>

  <clause id="10156">
    <literal><![CDATA[
      K(x,x \ (y * (z * x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8826,a,b,10149,a)].">
      <j1 rule="hyper" parents="64 8826 10149"/>
    </justification>
  </clause>

  <clause id="10157">
    <literal><![CDATA[
      T(x,K(y,z * (y * u))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(10149(a,1),8706(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10149 8706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10158">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,x) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),10150(a,1,2,2))].">
      <j1 rule="para" parents="12 10150"/>
    </justification>
  </clause>

  <clause id="10159">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = y * K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[para(82(a,1),10150(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="82 10150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10160">
    <literal><![CDATA[
      (x \ 1) * (y / (x \ 1)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(6521(a,1),10150(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6521 10150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10161">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(9(a,1),10153(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 10153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10162">
    <literal><![CDATA[
      K(x,K(y,z * (u * y))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(10156(a,1),8962(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10156 8962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10163">
    <literal><![CDATA[
      K(x,y \ (x \ z)) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7417,a,10161,a)].">
      <j1 rule="hyper" parents="7417 10161"/>
    </justification>
  </clause>

  <clause id="10164">
    <literal><![CDATA[
      K(x,x \ (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(10161(a,1),7417(a,1))].">
      <j1 rule="para" parents="10161 7417"/>
    </justification>
  </clause>

  <clause id="10165">
    <literal><![CDATA[
      K(x,x \ (y \ (z * x))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(8785,a,10163,a),flip(a)].">
      <j1 rule="hyper" parents="8785 10163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10166">
    <literal><![CDATA[
      x \ K(y,y \ (x \ 1)) = y * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,10163,a(flip),b,7197,a)].">
      <j1 rule="hyper" parents="139 10163 7197"/>
    </justification>
  </clause>

  <clause id="10167">
    <literal><![CDATA[
      K(x,x \ (y \ (x * z))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),10163(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 10163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10168">
    <literal><![CDATA[
      K(x,y \ (x \ (y * z))) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),10163(a,2,2,2))].">
      <j1 rule="para" parents="9 10163"/>
    </justification>
  </clause>

  <clause id="10169">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10165(a,1),8962(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10165 8962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10170">
    <literal><![CDATA[
      K(x,K(y,z \ (y * u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10167(a,1),8962(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10167 8962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10171">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5924,a(flip),b,10168,a),flip(a)].">
      <j1 rule="hyper" parents="373 5924 10168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10172">
    <literal><![CDATA[
      T(x,y \ (x \ (y * z))) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(143,a,10168,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 10168 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10173">
    <literal><![CDATA[
      (x * y) * K(z,z \ y) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(10168(a,1),7201(a,1,2))].">
      <j1 rule="para" parents="10168 7201"/>
    </justification>
  </clause>

  <clause id="10174">
    <literal><![CDATA[
      K(x,L(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7267,a,10171,a)].">
      <j1 rule="hyper" parents="7267 10171"/>
    </justification>
  </clause>

  <clause id="10175">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9110,a,10174,a)].">
      <j1 rule="hyper" parents="9110 10174"/>
    </justification>
  </clause>

  <clause id="10178">
    <literal><![CDATA[
      T(x,L(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,10174,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 10174 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10179">
    <literal><![CDATA[
      L(K(x,y),y * x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9105,a,b,10174,a)].">
      <j1 rule="hyper" parents="64 9105 10174"/>
    </justification>
  </clause>

  <clause id="10180">
    <literal><![CDATA[
      T(x,L(y,x,z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,10174,a(flip),b,5726,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 10174 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10181">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(10174(a,1),7591(a,1,2))].">
      <j1 rule="para" parents="10174 7591"/>
    </justification>
  </clause>

  <clause id="10182">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(346(a,1),10175(a,1,1))].">
      <j1 rule="para" parents="346 10175"/>
    </justification>
  </clause>

  <clause id="10183">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(630(a,1),10175(a,1,1)),flip(a)].">
      <j1 rule="para" parents="630 10175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10184">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(L(x,y,v5),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(10175(a,1),9164(a,1,1))].">
      <j1 rule="para" parents="10175 9164"/>
    </justification>
  </clause>

  <clause id="10186">
    <literal><![CDATA[
      L(x,y,z) * T(y,x) = y * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,10178,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 10178 22"/>
    </justification>
  </clause>

  <clause id="10187">
    <literal><![CDATA[
      T(L(x,y,z),(z * (y * x)) \ ((z * y) * u)) = T(L(x,y,z),L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(645(a,1),10178(a,1,2))].">
      <j1 rule="para" parents="645 10178"/>
    </justification>
  </clause>

  <clause id="10188">
    <literal><![CDATA[
      L(x,y,z) = (z * T(y,x)) \ (z * (T(y,x) * x))
    ]]></literal>
    <justification jstring="[para(10178(a,1),9603(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10178 9603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10190">
    <literal><![CDATA[
      T(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(10180(a,2),5767(a,1))].">
      <j1 rule="para" parents="10180 5767"/>
    </justification>
  </clause>

  <clause id="10191">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(1083,a,10181,a)].">
      <j1 rule="hyper" parents="1083 10181"/>
    </justification>
  </clause>

  <clause id="10192">
    <literal><![CDATA[
      K(x,y) / (x * y) = 1 / (y * x)
    ]]></literal>
    <justification jstring="[hyper(519,a,10181,a)].">
      <j1 rule="hyper" parents="519 10181"/>
    </justification>
  </clause>

  <clause id="10193">
    <literal><![CDATA[
      (x / (y * z)) * (z * y) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(390,a,10181,a),flip(a)].">
      <j1 rule="hyper" parents="390 10181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10194">
    <literal><![CDATA[
      T(x * (y * z),K(y,z)) = K(y,z) * (x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(145,a,10181,a(flip),b,8169,a),flip(a)].">
      <j1 rule="hyper" parents="145 10181 8169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10195">
    <literal><![CDATA[
      (x * (y * z)) / T(y,z) = (x * (z * y)) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,10181,a(flip),b,6840,a)].">
      <j1 rule="hyper" parents="142 10181 6840"/>
    </justification>
  </clause>

  <clause id="10196">
    <literal><![CDATA[
      (x * y) * K(z \ y,z) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),10181(a,1,1,2))].">
      <j1 rule="para" parents="10 10181"/>
    </justification>
  </clause>

  <clause id="10197">
    <literal><![CDATA[
      x * K(y \ (z \ x),y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[para(75(a,1),10181(a,1,1))].">
      <j1 rule="para" parents="75 10181"/>
    </justification>
  </clause>

  <clause id="10198">
    <literal><![CDATA[
      K(x * (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (z * y),z) = u
    ]]></literal>
    <justification jstring="[para(10181(a,1),8568(a,1,1))].">
      <j1 rule="para" parents="10181 8568"/>
    </justification>
  </clause>

  <clause id="10200">
    <literal><![CDATA[
      R(x,y,T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(9563,a,10191,a)].">
      <j1 rule="hyper" parents="9563 10191"/>
    </justification>
  </clause>

  <clause id="10201">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(10191(a,1),52(a,2))].">
      <j1 rule="para" parents="10191 52"/>
    </justification>
  </clause>

  <clause id="10202">
    <literal><![CDATA[
      R(x,y,z) = ((x * y) * T(z,y)) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,264,a,b,10200,a),flip(a)].">
      <j1 rule="hyper" parents="64 264 10200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10203">
    <literal><![CDATA[
      T(x,y * y) / (x * y) = R(T(1 / y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9549,a(flip),b,10200,a)].">
      <j1 rule="hyper" parents="64 9549 10200"/>
    </justification>
  </clause>

  <clause id="10204">
    <literal><![CDATA[
      R(x,y / z,z) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7109,a(flip),b,10200,a)].">
      <j1 rule="hyper" parents="64 7109 10200"/>
    </justification>
  </clause>

  <clause id="10205">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = R(x / z,z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,680,a(flip),b,10200,a)].">
      <j1 rule="hyper" parents="64 680 10200"/>
    </justification>
  </clause>

  <clause id="10206">
    <literal><![CDATA[
      R(x,y,z) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,10200,a(flip),b,264,a)].">
      <j1 rule="hyper" parents="144 10200 264"/>
    </justification>
  </clause>

  <clause id="10207">
    <literal><![CDATA[
      R(x,y,z / y) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(117(a,1),10200(a,1,3)),flip(a)].">
      <j1 rule="para" parents="117 10200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10209">
    <literal><![CDATA[
      R(x,x,y) * T(y,x) = (1 / x) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(10200(a,1),1913(a,1,1))].">
      <j1 rule="para" parents="10200 1913"/>
    </justification>
  </clause>

  <clause id="10211">
    <literal><![CDATA[
      R(x,y,K(z,T(u,y))) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(7867(a,2),10200(a,1,3))].">
      <j1 rule="para" parents="7867 10200"/>
    </justification>
  </clause>

  <clause id="10212">
    <literal><![CDATA[
      K(x,x \ 1) / (x * (y \ (x \ y))) = 1 / ((y \ (x \ y)) * x)
    ]]></literal>
    <justification jstring="[para(7256(a,1),10192(a,1,1))].">
      <j1 rule="para" parents="7256 10192"/>
    </justification>
  </clause>

  <clause id="10213">
    <literal><![CDATA[
      R(x,y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(9562(a,1),10201(a,1))].">
      <j1 rule="para" parents="9562 10201"/>
    </justification>
  </clause>

  <clause id="10214">
    <literal><![CDATA[
      x \ ((y * (x / z)) * z) = R(T(y,x),z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1030,a,b,10204,a)].">
      <j1 rule="hyper" parents="64 1030 10204"/>
    </justification>
  </clause>

  <clause id="10215">
    <literal><![CDATA[
      ((x * (y / z)) * z) / y = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,113,a,b,10204,a)].">
      <j1 rule="hyper" parents="64 113 10204"/>
    </justification>
  </clause>

  <clause id="10216">
    <literal><![CDATA[
      R(K(x,(y / z) / u),z \ y,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9705,a(flip),b,10204,a),flip(a)].">
      <j1 rule="hyper" parents="64 9705 10204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10217">
    <literal><![CDATA[
      R(x / y,y \ x,y) = y / (((x / y) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1991,a(flip),b,10204,a),flip(a)].">
      <j1 rule="hyper" parents="64 1991 10204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10218">
    <literal><![CDATA[
      R(x / (y / z),z \ y,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,678,a(flip),b,10204,a),flip(a)].">
      <j1 rule="hyper" parents="64 678 10204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10219">
    <literal><![CDATA[
      R(x,y \ z,y) * z = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,10204,a(flip),b,113,a)].">
      <j1 rule="hyper" parents="144 10204 113"/>
    </justification>
  </clause>

  <clause id="10220">
    <literal><![CDATA[
      L(R(x,x,y),x,x) = R(x,x,y / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,3020,a,b,10207,a)].">
      <j1 rule="hyper" parents="373 3020 10207"/>
    </justification>
  </clause>

  <clause id="10221">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),y,u) = z
    ]]></literal>
    <justification jstring="[para(4524(a,1),10213(a,1))].">
      <j1 rule="para" parents="4524 10213"/>
    </justification>
  </clause>

  <clause id="10222">
    <literal><![CDATA[
      K(x \ (y \ z),y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(8797,a,10182,a)].">
      <j1 rule="hyper" parents="8797 10182"/>
    </justification>
  </clause>

  <clause id="10223">
    <literal><![CDATA[
      K(x \ (y \ (z * x)),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8787,a,10182,a),flip(a)].">
      <j1 rule="hyper" parents="8787 10182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10224">
    <literal><![CDATA[
      K(x \ (y \ z),x) * z = z * K(z / (y * x),x)
    ]]></literal>
    <justification jstring="[para(10182(a,1),8196(a,1,1))].">
      <j1 rule="para" parents="10182 8196"/>
    </justification>
  </clause>

  <clause id="10225">
    <literal><![CDATA[
      ((x * T(y,x)) * L(x,y,z)) \ (x * (y * L(x,y,z))) = K(L(x,y,z),x * T(y,x))
    ]]></literal>
    <justification jstring="[para(10186(a,1),2333(a,1,2,2))].">
      <j1 rule="para" parents="10186 2333"/>
    </justification>
  </clause>

  <clause id="10226">
    <literal><![CDATA[
      (x / ((y \ z) * y)) * z = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(397,a,10193,a)].">
      <j1 rule="hyper" parents="397 10193"/>
    </justification>
  </clause>

  <clause id="10227">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = (x * y) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(142,a,6852,a(flip),b,10193,a)].">
      <j1 rule="hyper" parents="142 6852 10193"/>
    </justification>
  </clause>

  <clause id="10228">
    <literal><![CDATA[
      (x / y) * ((z \ y) * z) = x * K(z \ y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),10193(a,1,1,2))].">
      <j1 rule="para" parents="10 10193"/>
    </justification>
  </clause>

  <clause id="10229">
    <literal><![CDATA[
      (x \ y) * K(x \ (z \ y),z) = (z \ (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,10222,a,b,95,a)].">
      <j1 rule="hyper" parents="145 10222 95"/>
    </justification>
  </clause>

  <clause id="10230">
    <literal><![CDATA[
      x * K(y \ (z \ u),z) = x * K(z \ (y \ u),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,10222,a,b,9,a)].">
      <j1 rule="hyper" parents="145 10222 9"/>
    </justification>
  </clause>

  <clause id="10231">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7489,a(flip),b,10222,a),flip(a)].">
      <j1 rule="hyper" parents="64 7489 10222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10232">
    <literal><![CDATA[
      K(x \ (((x \ y) * z) \ y),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z \ 1,x) = u
    ]]></literal>
    <justification jstring="[para(10222(a,1),6802(a,1))].">
      <j1 rule="para" parents="10222 6802"/>
    </justification>
  </clause>

  <clause id="10233">
    <literal><![CDATA[
      K(L(x * (y \ z),x \ 1,y) \ u,x) = K(x \ (((x \ 1) * ((y * (x \ 1)) \ z)) \ u),x)
    ]]></literal>
    <justification jstring="[para(1806(a,1),10231(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1806 10231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10234">
    <literal><![CDATA[
      K(L(x,y,z) \ ((x \ (1 / L(x,y,z))) \ u),L(x,y,z)) = K((1 / x) \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5401(a,1),10231(a,1,1,2,1))].">
      <j1 rule="para" parents="5401 10231"/>
    </justification>
  </clause>

  <clause id="10235">
    <literal><![CDATA[
      (x * (y * z)) / (L(y,z,x) * z) = R(x,z,L(y,z,x))
    ]]></literal>
    <justification jstring="[para(988(a,1),10202(a,2,1)),flip(a)].">
      <j1 rule="para" parents="988 10202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10236">
    <literal><![CDATA[
      R((x * T(y,z)) / y,y,z) = ((x * y) * z) / (z * y)
    ]]></literal>
    <justification jstring="[para(6858(a,1),10205(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6858 10205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10237">
    <literal><![CDATA[
      R(R(x,y,x) / x,x,z) = (z * R(x,y,x)) / (z * x)
    ]]></literal>
    <justification jstring="[para(7408(a,1),10205(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7408 10205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10238">
    <literal><![CDATA[
      R(x,y,z) * (x \ (z * y)) = x \ ((x * y) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,10206,a(flip),b,1902,a),flip(a)].">
      <j1 rule="hyper" parents="139 10206 1902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10239">
    <literal><![CDATA[
      R(x / (y / (y * K(z,u))),K(u,z),y * K(z,u)) = (x * (y * K(z,u))) / y
    ]]></literal>
    <justification jstring="[para(6882(a,1),10218(a,1,2))].">
      <j1 rule="para" parents="6882 10218"/>
    </justification>
  </clause>

  <clause id="10240">
    <literal><![CDATA[
      (x * y) * K(x * (z \ y),z) = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,10154,a(flip),b,6312,a),flip(a)].">
      <j1 rule="hyper" parents="144 10154 6312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10241">
    <literal><![CDATA[
      K(x,K(y / z,u * z)) = K(x,K(y / z,u * y))
    ]]></literal>
    <justification jstring="[para(8608(a,1),10162(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8608 10162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10242">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = K(x,K(y,z \ R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(1898(a,1),10169(a,1,2,2))].">
      <j1 rule="para" parents="1898 10169"/>
    </justification>
  </clause>

  <clause id="10243">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((y \ z) \ u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(10170(a,1),9064(a,1,1))].">
      <j1 rule="para" parents="10170 9064"/>
    </justification>
  </clause>

  <clause id="10244">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) * K(x,K(y,z \ u)) = K(x,y / ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(10170(a,1),9074(a,1,2))].">
      <j1 rule="para" parents="10170 9074"/>
    </justification>
  </clause>

  <clause id="10245">
    <literal><![CDATA[
      (x / y) * (z * (y / z)) = x * K(z,z \ y)
    ]]></literal>
    <justification jstring="[hyper(390,a,10173,a),flip(a)].">
      <j1 rule="hyper" parents="390 10173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10247">
    <literal><![CDATA[
      x * (((x * y) \ y) * (x * y)) = y / (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(6145,a,10196,a),flip(a)].">
      <j1 rule="hyper" parents="6145 10196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10248">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(234,a,10196,a),flip(a)].">
      <j1 rule="hyper" parents="234 10196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10249">
    <literal><![CDATA[
      T(x * ((y \ z) * y),K(y,z)) = K(y \ z,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(10196(a,1),8710(a,1,1))].">
      <j1 rule="para" parents="10196 8710"/>
    </justification>
  </clause>

  <clause id="10250">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,T(K(z \ y,z),u))
    ]]></literal>
    <justification jstring="[para(10248(a,1),6639(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10248 6639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10251">
    <literal><![CDATA[
      (x / (x / y)) / ((y \ x) * y) = y / x
    ]]></literal>
    <justification jstring="[hyper(142,a,6596,a(flip),b,10226,a),flip(a)].">
      <j1 rule="hyper" parents="142 6596 10226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10252">
    <literal><![CDATA[
      (x \ y) / ((x \ y) * x) = (y / x) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,5774,a(flip),b,10226,a),flip(a)].">
      <j1 rule="hyper" parents="142 5774 10226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10253">
    <literal><![CDATA[
      (x / y) \ (y / (y / x)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(215,a,10251,a)].">
      <j1 rule="hyper" parents="215 10251"/>
    </justification>
  </clause>

  <clause id="10254">
    <literal><![CDATA[
      K(((x \ y) * x) / (z * (y / (y / x))),z) = K((x / y) \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[para(10253(a,1),10075(a,1,1,1))].">
      <j1 rule="para" parents="10253 10075"/>
    </justification>
  </clause>

  <clause id="10255">
    <literal><![CDATA[
      K(x,x \ T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (x \ (y * z))) = u
    ]]></literal>
    <justification jstring="[para(22(a,2),10164(a,1,2,2))].">
      <j1 rule="para" parents="22 10164"/>
    </justification>
  </clause>

  <clause id="10256">
    <literal><![CDATA[
      L(x,T(y,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,18,a,b,10188,a)].">
      <j1 rule="hyper" parents="373 18 10188"/>
    </justification>
  </clause>

  <clause id="10257">
    <literal><![CDATA[
      (x * T(y,K(z,u))) \ (x * (K(z,u) * y)) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(8172(a,1),10188(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8172 10188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10259">
    <literal><![CDATA[
      L(x,y / x,z) = L(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(117(a,1),10256(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 10256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10260">
    <literal><![CDATA[
      L(x,K(y,T(z,x)),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(7867(a,2),10256(a,1,2))].">
      <j1 rule="para" parents="7867 10256"/>
    </justification>
  </clause>

  <clause id="10261">
    <literal><![CDATA[
      L(x,x \ (y \ z),y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,711,a(flip),b,10259,a),flip(a)].">
      <j1 rule="hyper" parents="64 711 10259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10262">
    <literal><![CDATA[
      L(x,x \ y,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,104,a(flip),b,10259,a),flip(a)].">
      <j1 rule="hyper" parents="64 104 10259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10263">
    <literal><![CDATA[
      x / L(y,y \ (z \ x),z) = z * ((z \ x) / y)
    ]]></literal>
    <justification jstring="[hyper(225,a,10259,a(flip),b,711,a(flip))].">
      <j1 rule="hyper" parents="225 10259 711"/>
    </justification>
  </clause>

  <clause id="10264">
    <literal><![CDATA[
      (x * y) / L(z,z \ y,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[hyper(225,a,10259,a(flip),b,104,a(flip))].">
      <j1 rule="hyper" parents="225 10259 104"/>
    </justification>
  </clause>

  <clause id="10265">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(10259(a,1),7376(a,1,1))].">
      <j1 rule="para" parents="10259 7376"/>
    </justification>
  </clause>

  <clause id="10266">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(10259(a,1),7594(a,1,1))].">
      <j1 rule="para" parents="10259 7594"/>
    </justification>
  </clause>

  <clause id="10267">
    <literal><![CDATA[
      L(K(x,y),x * z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),10265(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 10265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10268">
    <literal><![CDATA[
      K(L(x,y,z),x * y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(6487,a,10267,a),flip(a)].">
      <j1 rule="hyper" parents="6487 10267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10269">
    <literal><![CDATA[
      K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7080,a(flip),b,10267,a),flip(a)].">
      <j1 rule="hyper" parents="64 7080 10267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10270">
    <literal><![CDATA[
      L(K(x,y),T(x,z) * u,w) = K(L(T(x,z),u,w),T(y,z))
    ]]></literal>
    <justification jstring="[para(8205(a,1),10267(a,1,1))].">
      <j1 rule="para" parents="8205 10267"/>
    </justification>
  </clause>

  <clause id="10271">
    <literal><![CDATA[
      1 / L(x,x \ y,y) = (1 / y) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(225,a,10262,a,b,552,a)].">
      <j1 rule="hyper" parents="225 10262 552"/>
    </justification>
  </clause>

  <clause id="10272">
    <literal><![CDATA[
      K(x,T(L(y,y \ z,u),u * z)) = K(x,(u * z) / (u * (z / y)))
    ]]></literal>
    <justification jstring="[para(10262(a,2),8207(a,1,2,1))].">
      <j1 rule="para" parents="10262 8207"/>
    </justification>
  </clause>

  <clause id="10273">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) * (u * (z / y)) = (u * (z / y)) * K(x,(u * z) / (u * (z / y)))
    ]]></literal>
    <justification jstring="[para(10262(a,2),8261(a,1,1,2))].">
      <j1 rule="para" parents="10262 8261"/>
    </justification>
  </clause>

  <clause id="10274">
    <literal><![CDATA[
      T(x * (y / z),L(z,z \ y,x)) = L(z,z \ y,x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(10264(a,1),117(a,1,1))].">
      <j1 rule="para" parents="10264 117"/>
    </justification>
  </clause>

  <clause id="10275">
    <literal><![CDATA[
      1 / L(x,x \ y,y) = y * ((y \ 1) / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1217,a(flip),b,10271,a),flip(a)].">
      <j1 rule="hyper" parents="373 1217 10271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10276">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),K(y,x),z) = w
    ]]></literal>
    <justification jstring="[para(5783(a,2),10266(a,1,1,2))].">
      <j1 rule="para" parents="5783 10266"/>
    </justification>
  </clause>

  <clause id="10277">
    <literal><![CDATA[
      K(x \ (y * z),x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(8037,a,10146,a)].">
      <j1 rule="hyper" parents="8037 10146"/>
    </justification>
  </clause>

  <clause id="10278">
    <literal><![CDATA[
      K(x * (y \ z),y) * (x * z) = (y \ (x * z)) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,5947,a(flip),b,10146,a)].">
      <j1 rule="hyper" parents="145 5947 10146"/>
    </justification>
  </clause>

  <clause id="10279">
    <literal><![CDATA[
      K(x \ (y * (x * z)),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),10277(a,2,1,2))].">
      <j1 rule="para" parents="9 10277"/>
    </justification>
  </clause>

  <clause id="10280">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),10277(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 10277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10281">
    <literal><![CDATA[
      x / (T(y,x) \ 1) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9330,a(flip),b,10158,a)].">
      <j1 rule="hyper" parents="64 9330 10158"/>
    </justification>
  </clause>

  <clause id="10282">
    <literal><![CDATA[
      x / (y \ K(x,y)) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(5783(a,1),10281(a,1,2))].">
      <j1 rule="para" parents="5783 10281"/>
    </justification>
  </clause>

  <clause id="10283">
    <literal><![CDATA[
      x \ (y / (x \ K(y,x))) = (y / (x \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(139,a,10282,a,b,xx)].">
      <j1 rule="hyper" parents="139 10282"/>
    </justification>
  </clause>

  <clause id="10284">
    <literal><![CDATA[
      K(1 / x,y / (1 / x)) = K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[hyper(35,a,355,a,b,10159,a(flip))].">
      <j1 rule="hyper" parents="35 355 10159"/>
    </justification>
  </clause>

  <clause id="10285">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(3776(a,1),10159(a,2,2))].">
      <j1 rule="para" parents="3776 10159"/>
    </justification>
  </clause>

  <clause id="10286">
    <literal><![CDATA[
      K(x,y * K(1 / y,z * y)) = T(K(x,y),z / (1 / y))
    ]]></literal>
    <justification jstring="[para(10284(a,1),8908(a,1,2,2))].">
      <j1 rule="para" parents="10284 8908"/>
    </justification>
  </clause>

  <clause id="10287">
    <literal><![CDATA[
      x * (y * K(x \ 1,y * x)) = L(y / (x \ 1),x,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,10160,a(flip),b,1148,a)].">
      <j1 rule="hyper" parents="145 10160 1148"/>
    </justification>
  </clause>

  <clause id="10288">
    <literal><![CDATA[
      (x \ 1) * ((y / x) / (x \ 1)) = (y / x) * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),10160(a,2,2,2))].">
      <j1 rule="para" parents="12 10160"/>
    </justification>
  </clause>

  <clause id="10289">
    <literal><![CDATA[
      ((x / y) \ 1) * (z / ((x / y) \ 1)) = z * K(y / x,z * (x / y))
    ]]></literal>
    <justification jstring="[para(6580(a,1),10160(a,2,2))].">
      <j1 rule="para" parents="6580 10160"/>
    </justification>
  </clause>

  <clause id="10290">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) = K(x \ (y * z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(8596,a,10183,a)].">
      <j1 rule="hyper" parents="8596 10183"/>
    </justification>
  </clause>

  <clause id="10291">
    <literal><![CDATA[
      ((x * x) \ (y \ (x * x))) * y = K(x * (y \ x),y)
    ]]></literal>
    <justification jstring="[hyper(35,a,126,a,b,10240,a)].">
      <j1 rule="hyper" parents="35 126 10240"/>
    </justification>
  </clause>

  <clause id="10292">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(6266,a,10285,a)].">
      <j1 rule="hyper" parents="6266 10285"/>
    </justification>
  </clause>

  <clause id="10293">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (x \ y))
    ]]></literal>
    <justification jstring="[para(6756(a,1),10285(a,2,2))].">
      <j1 rule="para" parents="6756 10285"/>
    </justification>
  </clause>

  <clause id="10294">
    <literal><![CDATA[
      K(x \ (y * z),y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / (x / y),y \ x) = u
    ]]></literal>
    <justification jstring="[para(10290(a,1),8460(a,1))].">
      <j1 rule="para" parents="10290 8460"/>
    </justification>
  </clause>

  <clause id="10295">
    <literal><![CDATA[
      (T(x,y * y) \ 1) * x = K(y * (x \ y),x)
    ]]></literal>
    <justification jstring="[para(1457(a,1),10291(a,1,1))].">
      <j1 rule="para" parents="1457 10291"/>
    </justification>
  </clause>

  <clause id="10296">
    <literal><![CDATA[
      1 / T(x,y * (x \ y)) = T(x,y * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,5788,a(flip),b,10295,a)].">
      <j1 rule="hyper" parents="36 5788 10295"/>
    </justification>
  </clause>

  <clause id="10297">
    <literal><![CDATA[
      R(T(x,y * y),x,x) = T(x,y * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(37,a,3567,a,b,10296,a)].">
      <j1 rule="hyper" parents="37 3567 10296"/>
    </justification>
  </clause>

  <clause id="10298">
    <literal><![CDATA[
      K(L(x,y,z),L(y,u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9164,a(flip),b,10184,a),flip(a)].">
      <j1 rule="hyper" parents="64 9164 10184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10300">
    <literal><![CDATA[
      K(x \ (y \ (x * z)),L(y,u,w)) = K(y \ z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9868,a(flip),b,10298,a)].">
      <j1 rule="hyper" parents="64 9868 10298"/>
    </justification>
  </clause>

  <clause id="10301">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K((y * (x \ z)) / y,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(1392(a,1),10298(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1392 10298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10302">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),u \ z,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[para(9739(a,1),10216(a,1,1))].">
      <j1 rule="para" parents="9739 10216"/>
    </justification>
  </clause>

  <clause id="10303">
    <literal><![CDATA[
      x * (R(x,y,L(z,y,x)) \ (z * y)) = L(z,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(37,a,1906,a,b,10235,a)].">
      <j1 rule="hyper" parents="37 1906 10235"/>
    </justification>
  </clause>

  <clause id="10304">
    <literal><![CDATA[
      ((x * y) * z) / (z * y) = R(x * K(y,z),y,z)
    ]]></literal>
    <justification jstring="[para(6847(a,1),10236(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6847 10236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10305">
    <literal><![CDATA[
      R((x / y) * K(y,z),y,z) = (x * z) / (z * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),10304(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 10304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10306">
    <literal><![CDATA[
      R(x * K(T(y,x),z),T(y,x),z) = ((y * x) * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(115(a,1),10304(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="115 10304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10307">
    <literal><![CDATA[
      R((x \ R(x,y,z)) * K(x,u),x,u) = (R(x,y,z) * u) / (u * x)
    ]]></literal>
    <justification jstring="[para(2069(a,1),10304(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2069 10304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10308">
    <literal><![CDATA[
      R(x * K(K(y,T(z,x)),u),K(y,T(z,x)),u) = ((K(y,z) * x) * u) / (u * K(y,T(z,x)))
    ]]></literal>
    <justification jstring="[para(7879(a,1),10304(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7879 10304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10309">
    <literal><![CDATA[
      L(R(x \ K(x,y),x,y),x,x) = (1 * y) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,579,a,b,10305,a)].">
      <j1 rule="hyper" parents="64 579 10305"/>
    </justification>
  </clause>

  <clause id="10310">
    <literal><![CDATA[
      R(R((x / y) * K(y,z),u,w),y,z) = R((x * z) / (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(10305(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10305 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10311">
    <literal><![CDATA[
      R((x \ 1) * K(R(x,x,x),y),R(x,x,x),y) = (1 * y) / (y * R(x,x,x))
    ]]></literal>
    <justification jstring="[para(1420(a,1),10305(a,1,1,1))].">
      <j1 rule="para" parents="1420 10305"/>
    </justification>
  </clause>

  <clause id="10312">
    <literal><![CDATA[
      R(((x * x) \ (x \ 1)) * K(x,y),x,y) = ((x \ (1 / x)) * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(5223(a,1),10305(a,1,1,1))].">
      <j1 rule="para" parents="5223 10305"/>
    </justification>
  </clause>

  <clause id="10313">
    <literal><![CDATA[
      L(K(x,y),T(x,z) * u,w) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8225,a(flip),b,10270,a),flip(a)].">
      <j1 rule="hyper" parents="373 8225 10270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10315">
    <literal><![CDATA[
      K(L(x,T(x,y) \ z,u),w) = L(K(x,w),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),10313(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 10313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10316">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,615,a(flip),b,10315,a),flip(a)].">
      <j1 rule="hyper" parents="373 615 10315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10317">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = T(K(x,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8908,a(flip),b,10286,a),flip(a)].">
      <j1 rule="hyper" parents="64 8908 10286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10318">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(64,a,8863,a(flip),b,10317,a),flip(a)].">
      <j1 rule="hyper" parents="64 8863 10317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10319">
    <literal><![CDATA[
      K(x,1 / (y / (y / (1 / z)))) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(8020,a,10318,a),flip(a)].">
      <j1 rule="hyper" parents="8020 10318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10320">
    <literal><![CDATA[
      (x \ 1) \ ((y \ (y / x)) * y) = (y / x) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,6425,a,b,10288,a)].">
      <j1 rule="hyper" parents="139 6425 10288"/>
    </justification>
  </clause>

  <clause id="10321">
    <literal><![CDATA[
      (x / (y \ x)) / ((y \ x) \ 1) = ((y \ x) \ 1) \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(79(a,1),10320(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 10320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10323">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x * z)) = u
    ]]></literal>
    <justification jstring="[para(10(a,1),10142(a,1,2,2,1))].">
      <j1 rule="para" parents="10 10142"/>
    </justification>
  </clause>

  <clause id="10324">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * L(K(z,y),u,x) = x * T(u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(40,a,7315,a,b,10257,a)].">
      <j1 rule="hyper" parents="40 7315 10257"/>
    </justification>
  </clause>

  <clause id="10325">
    <literal><![CDATA[
      K(L(x,y * z,u),(u \ (u * (x * y))) \ (x * (y * z))) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[para(602(a,1),10269(a,2,2))].">
      <j1 rule="para" parents="602 10269"/>
    </justification>
  </clause>

  <clause id="10326">
    <literal><![CDATA[
      L(K(x,y),K(z,x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10276,a,10316,a)].">
      <j1 rule="hyper" parents="10276 10316"/>
    </justification>
  </clause>

  <clause id="10327">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,10326,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 10326 18"/>
    </justification>
  </clause>

  <clause id="10328">
    <literal><![CDATA[
      L(L(K(x,y),z,u),K(w,x),v5) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(10326(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10326 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10329">
    <literal><![CDATA[
      (x * K(y,z)) * R(K(z,u),w,v5) = x * (K(y,z) * R(K(z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(10326(a,1),514(a,1,2,1))].">
      <j1 rule="para" parents="10326 514"/>
    </justification>
  </clause>

  <clause id="10330">
    <literal><![CDATA[
      x / L(L(K(y,z),u,w),K(v5,y),v6) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(225,a,10328,a,b,7315,a)].">
      <j1 rule="hyper" parents="225 10328 7315"/>
    </justification>
  </clause>

  <clause id="10331">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(9173,a,10327,a)].">
      <j1 rule="hyper" parents="9173 10327"/>
    </justification>
  </clause>

  <clause id="10332">
    <literal><![CDATA[
      (x * (K(y,z) * K(z,u))) * K(u,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6897,a,10327,a)].">
      <j1 rule="hyper" parents="6897 10327"/>
    </justification>
  </clause>

  <clause id="10333">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(664,a,10327,a)].">
      <j1 rule="hyper" parents="664 10327"/>
    </justification>
  </clause>

  <clause id="10334">
    <literal><![CDATA[
      x * (K(y,z) * K(z,z * y)) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,9169,a(flip),b,10327,a),flip(a)].">
      <j1 rule="hyper" parents="64 9169 10327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10335">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(3320(a,2),10327(a,2,2))].">
      <j1 rule="para" parents="3320 10327"/>
    </justification>
  </clause>

  <clause id="10336">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(10333(a,1),52(a,2))].">
      <j1 rule="para" parents="10333 52"/>
    </justification>
  </clause>

  <clause id="10337">
    <literal><![CDATA[
      R(x,T(K(y,z),u),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(3068(a,1),10333(a,1,2))].">
      <j1 rule="para" parents="3068 10333"/>
    </justification>
  </clause>

  <clause id="10338">
    <literal><![CDATA[
      (x * R(R(x,K(y,z),K(z,u)) \ (x * K(y,z)),w,v5)) * K(z,u) = R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u))
    ]]></literal>
    <justification jstring="[para(10333(a,1),4213(a,1,1,1))].">
      <j1 rule="para" parents="10333 4213"/>
    </justification>
  </clause>

  <clause id="10339">
    <literal><![CDATA[
      R(x,L(K(y,z),u,w),K(z,v5)) = x
    ]]></literal>
    <justification jstring="[para(7310(a,1),10333(a,1,2))].">
      <j1 rule="para" parents="7310 10333"/>
    </justification>
  </clause>

  <clause id="10341">
    <literal><![CDATA[
      R(x,T(K(y,z),u),T(K(z,w),v5)) = x
    ]]></literal>
    <justification jstring="[para(7867(a,1),10337(a,1,3))].">
      <j1 rule="para" parents="7867 10337"/>
    </justification>
  </clause>

  <clause id="10342">
    <literal><![CDATA[
      R(x,K(y,z),R(K(z,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      x = v6
    ]]></literal>
    <justification jstring="[para(9663(a,1),10336(a,1,3))].">
      <j1 rule="para" parents="9663 10336"/>
    </justification>
  </clause>

  <clause id="10343">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) * K(z,v5) = x * (L(K(y,z),u,w) * K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(144,a,10339,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 10339 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10344">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,w)) = L(K(z,u),y,x) * K(u,w)
    ]]></literal>
    <justification jstring="[para(10339(a,1),691(a,1,1))].">
      <j1 rule="para" parents="10339 691"/>
    </justification>
  </clause>

  <clause id="10345">
    <literal><![CDATA[
      T(K(x,y),z) * T(K(y,u),K(x,y) * z) = z \ (K(y,u) * (K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(10341(a,1),1318(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10341 1318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10346">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      w * T(K(z,y),u) = x
    ]]></literal>
    <justification jstring="[para(10341(a,1),9885(a,1)),flip(a)].">
      <j1 rule="para" parents="10341 9885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10347">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(3320(a,2),10331(a,2,2))].">
      <j1 rule="para" parents="3320 10331"/>
    </justification>
  </clause>

  <clause id="10348">
    <literal><![CDATA[
      L(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,7318,a,b,10332,a)].">
      <j1 rule="hyper" parents="35 7318 10332"/>
    </justification>
  </clause>

  <clause id="10349">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * K(z,y) = x * K(u,y)
    ]]></literal>
    <justification jstring="[para(3320(a,2),10332(a,1,1,2))].">
      <j1 rule="para" parents="3320 10332"/>
    </justification>
  </clause>

  <clause id="10350">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,z) = x * (K(y,z) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,10348,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 10348 18"/>
    </justification>
  </clause>

  <clause id="10352">
    <literal><![CDATA[
      T(L(x,K(y,z),K(z,u)) * K(y,z),K(z,u)) = K(y,z) * T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(269,a,10335,a,b,793,a)].">
      <j1 rule="hyper" parents="269 10335 793"/>
    </justification>
  </clause>

  <clause id="10353">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(u,y)) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6245(a,1),10335(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6245 10335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10354">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * K(y,u)) = K(y,u) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(9174,a,10347,a)].">
      <j1 rule="hyper" parents="9174 10347"/>
    </justification>
  </clause>

  <clause id="10356">
    <literal><![CDATA[
      ((K(x,y) \ z) * ((K(x,y) \ 1) \ 1)) * K(u,x) = ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x))
    ]]></literal>
    <justification jstring="[para(3920(a,1),10347(a,1,1))].">
      <j1 rule="para" parents="3920 10347"/>
    </justification>
  </clause>

  <clause id="10357">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * (K(z,y) * K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,10332,a,b,10349,a(flip))].">
      <j1 rule="hyper" parents="36 10332 10349"/>
    </justification>
  </clause>

  <clause id="10358">
    <literal><![CDATA[
      (x * K(y,z)) * (K(u,y) * K(z,y)) = x * K(u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9171,a(flip),b,10350,a),flip(a)].">
      <j1 rule="hyper" parents="64 9171 10350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10359">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ z) = z * (K(y,x) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,8860,a(flip),b,10350,a)].">
      <j1 rule="hyper" parents="64 8860 10350"/>
    </justification>
  </clause>

  <clause id="10360">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * z) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,8355,a(flip),b,10350,a)].">
      <j1 rule="hyper" parents="64 8355 10350"/>
    </justification>
  </clause>

  <clause id="10361">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * K(x,u)) = K(x,u) * K(T(y,z),x)
    ]]></literal>
    <justification jstring="[para(7879(a,1),10354(a,1,1))].">
      <j1 rule="para" parents="7879 10354"/>
    </justification>
  </clause>

  <clause id="10362">
    <literal><![CDATA[
      L((K(x,y) * K(z,x)) \ 1,K(x,y) * K(z,x),u) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(471,a,10357,a)].">
      <j1 rule="hyper" parents="471 10357"/>
    </justification>
  </clause>

  <clause id="10363">
    <literal><![CDATA[
      x / (K(y,z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(z,y) * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(10357(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="10357 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10364">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,10359,a(flip),b,9814,a)].">
      <j1 rule="hyper" parents="269 10359 9814"/>
    </justification>
  </clause>

  <clause id="10365">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(10364(a,1),50(a,2))].">
      <j1 rule="para" parents="10364 50"/>
    </justification>
  </clause>

  <clause id="10366">
    <literal><![CDATA[
      (K(x,y) * K(x,y)) * (z * x) = z * (K(x,y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(10364(a,1),6877(a,1,2,1))].">
      <j1 rule="para" parents="10364 6877"/>
    </justification>
  </clause>

  <clause id="10367">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(x,z) * (K(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,10360,a(flip),b,6071,a)].">
      <j1 rule="hyper" parents="145 10360 6071"/>
    </justification>
  </clause>

  <clause id="10368">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(6504(a,1),10334(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6504 10334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10369">
    <literal><![CDATA[
      R(x,y,x) \ x = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(459,a,10368,a)].">
      <j1 rule="hyper" parents="459 10368"/>
    </justification>
  </clause>

  <clause id="10370">
    <literal><![CDATA[
      x \ (x \ L(x,y,x)) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,10369,a(flip),b,1909,a)].">
      <j1 rule="hyper" parents="139 10369 1909"/>
    </justification>
  </clause>

  <clause id="10371">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = T(x,z) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(10370(a,1),5634(a,2,2))].">
      <j1 rule="para" parents="10370 5634"/>
    </justification>
  </clause>

  <clause id="10372">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(y * z,y)) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,7100,a(flip),b,10353,a),flip(a)].">
      <j1 rule="hyper" parents="373 7100 10353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10373">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * K(x,u)) = K(x,u) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7904,a(flip),b,10361,a),flip(a)].">
      <j1 rule="hyper" parents="373 7904 10361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10374">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * (z * x)) = z * (K(x,y) * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9812,a(flip),b,10366,a)].">
      <j1 rule="hyper" parents="64 9812 10366"/>
    </justification>
  </clause>

  <clause id="10375">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(T(x,z),z) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,6121,a(flip),b,10367,a),flip(a)].">
      <j1 rule="hyper" parents="373 6121 10367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10376">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,u) * z) = K(x,T(u,z)) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7879(a,1),10373(a,1,2))].">
      <j1 rule="para" parents="7879 10373"/>
    </justification>
  </clause>

  <clause id="10377">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * (z * x)) = z * T(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(6114(a,1),10374(a,2,2))].">
      <j1 rule="para" parents="6114 10374"/>
    </justification>
  </clause>

  <clause id="10378">
    <literal><![CDATA[
      ((x * (K(y,z) * u)) / (x * T(u,K(y,z)))) \ T(x * (K(y,z) * u),L(K(z,y),u,x)) = T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x)
    ]]></literal>
    <justification jstring="[para(10324(a,1),7213(a,1,1,2))].">
      <j1 rule="para" parents="10324 7213"/>
    </justification>
  </clause>

  <clause id="10379">
    <literal><![CDATA[
      (x / (K(y,z) * L(K(z,u),w,v5))) * K(y,z) = x * L(K(u,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(1292,a,10330,a)].">
      <j1 rule="hyper" parents="1292 10330"/>
    </justification>
  </clause>

  <clause id="10380">
    <literal><![CDATA[
      (K(x,y) * (K(y,z) * u)) * (K(y,x) * K(z,y)) = u * K(K(x,y) * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(10363,a,9808,a)].">
      <j1 rule="hyper" parents="10363 9808"/>
    </justification>
  </clause>

  <clause id="10381">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(10242(a,2),9037(a,1))].">
      <j1 rule="para" parents="10242 9037"/>
    </justification>
  </clause>

  <clause id="10382">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,K(z \ y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(7867(a,2),10250(a,2,2))].">
      <j1 rule="para" parents="7867 10250"/>
    </justification>
  </clause>

  <clause id="10383">
    <literal><![CDATA[
      ((x \ y) \ 1) \ ((y \ x) * y) = x / ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),10321(a,1,1)),flip(a)].">
      <j1 rule="para" parents="79 10321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10384">
    <literal><![CDATA[
      x / ((x \ L(x,y,z)) \ 1) = ((x \ L(x,y,z)) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(5548(a,1),10383(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5548 10383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10385">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = R(x,y,x) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,3239,a(flip),b,10371,a),flip(a)].">
      <j1 rule="hyper" parents="373 3239 10371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10386">
    <literal><![CDATA[
      x \ (K(x,y) * L(x,z,x)) = R(x,z,x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(6135(a,1),10385(a,1,2))].">
      <j1 rule="para" parents="6135 10385"/>
    </justification>
  </clause>

  <clause id="10387">
    <literal><![CDATA[
      R(x,y,x) \ T(x,z) = x \ L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(7490(a,1),10386(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7490 10386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10388">
    <literal><![CDATA[
      R((x * y) / x,z,y) \ y = y \ L(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9553,a,b,10387,a)].">
      <j1 rule="hyper" parents="64 9553 10387"/>
    </justification>
  </clause>

  <clause id="10389">
    <literal><![CDATA[
      T(x / ((y \ L(T(y,z),u,y)) \ y),T(R((z * y) / z,u,y),y)) = ((R((z * y) / z,u,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(10388(a,1),7450(a,1,1,2,1))].">
      <j1 rule="para" parents="10388 7450"/>
    </justification>
  </clause>

  <clause id="10390">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,T(y,u))) = w
    ]]></literal>
    <justification jstring="[para(10382(a,2),9055(a,1))].">
      <j1 rule="para" parents="10382 9055"/>
    </justification>
  </clause>

  <clause id="10391">
    <literal><![CDATA[
      K(x,L(T(y,z * u),y \ u,z)) = K(x,(z * u) / (z * (u / y)))
    ]]></literal>
    <justification jstring="[para(25(a,2),10272(a,1,2))].">
      <j1 rule="para" parents="25 10272"/>
    </justification>
  </clause>

  <clause id="10392">
    <literal><![CDATA[
      ((x * y) * z) / (z * T(x,y)) = R(K(x,z) * y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(7437(a,1),10306(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7437 10306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10393">
    <literal><![CDATA[
      ((x / y) \ 1) * (z / ((x / y) \ 1)) = z * K(y / x,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(9302(a,1),10289(a,2,2))].">
      <j1 rule="para" parents="9302 10289"/>
    </justification>
  </clause>

  <clause id="10394">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K(y \ (y * (x \ z)),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,7501,a(flip),b,10301,a),flip(a)].">
      <j1 rule="hyper" parents="373 7501 10301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10395">
    <literal><![CDATA[
      (x * K(y,z)) * R(K(z,u),w,v5) = x * (R(K(z,u),w,v5) * K(y,z))
    ]]></literal>
    <justification jstring="[para(3326(a,2),10329(a,2,2))].">
      <j1 rule="para" parents="3326 10329"/>
    </justification>
  </clause>

  <clause id="10396">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * R(K(y,u),w,v5)) = x * R(K(y,u),w,v5)
    ]]></literal>
    <justification jstring="[para(6871(a,1),10329(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6871 10329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10397">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) * K(z,v5) = x * (K(z,v5) * L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(3322(a,1),10343(a,2,2))].">
      <j1 rule="para" parents="3322 10343"/>
    </justification>
  </clause>

  <clause id="10398">
    <literal><![CDATA[
      K(((x / y) \ z) / y,L(y,u,w)) = K(x \ z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,1571,a(flip),b,10394,a),flip(a)].">
      <j1 rule="hyper" parents="373 1571 10394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10399">
    <literal><![CDATA[
      K(x \ ((y / x) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(8457,a,10398,a)].">
      <j1 rule="hyper" parents="8457 10398"/>
    </justification>
  </clause>

  <clause id="10401">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(10061,a,10399,a)].">
      <j1 rule="hyper" parents="10061 10399"/>
    </justification>
  </clause>

  <clause id="10402">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * (z * K(y,x)) = z * (R(K(x,y),u,w) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,8854,a,b,10395,a)].">
      <j1 rule="hyper" parents="64 8854 10395"/>
    </justification>
  </clause>

  <clause id="10403">
    <literal><![CDATA[
      x / (K(y,z) * R(K(z,u),w,v5)) = (x * R(K(u,z),w,v5)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,9714,a(flip),b,10396,a)].">
      <j1 rule="hyper" parents="142 9714 10396"/>
    </justification>
  </clause>

  <clause id="10404">
    <literal><![CDATA[
      (x * (K(y,z) * L(K(u,y),w,v5))) * K(z,y) = x * L(K(u,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(6897,a,10397,a)].">
      <j1 rule="hyper" parents="6897 10397"/>
    </justification>
  </clause>

  <clause id="10405">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = L(K(z,u),y,x) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(6901,a,10344,a)].">
      <j1 rule="hyper" parents="6901 10344"/>
    </justification>
  </clause>

  <clause id="10406">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,z)) = K(u,z) * L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,3322,a(flip),b,10405,a),flip(a)].">
      <j1 rule="hyper" parents="373 3322 10405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10407">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z * K(x,y),u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6871(a,1),10406(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6871 10406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10408">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7346(a,1),10407(a,1,2))].">
      <j1 rule="para" parents="7346 10407"/>
    </justification>
  </clause>

  <clause id="10409">
    <literal><![CDATA[
      T(x,a(y,z,K(x,u))) = x
    ]]></literal>
    <justification jstring="[para(10407(a,1),8483(a,1,2))].">
      <j1 rule="para" parents="10407 8483"/>
    </justification>
  </clause>

  <clause id="10410">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(w,z) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,z) * a(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(10409(a,1),7889(a,1,2,2))].">
      <j1 rule="para" parents="10409 7889"/>
    </justification>
  </clause>

  <clause id="10411">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = L(K(x,y),u,z)
    ]]></literal>
    <justification jstring="[hyper(6187,a,10408,a)].">
      <j1 rule="hyper" parents="6187 10408"/>
    </justification>
  </clause>

  <clause id="10412">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(3324,a,10408,a)].">
      <j1 rule="hyper" parents="3324 10408"/>
    </justification>
  </clause>

  <clause id="10413">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,L(x,z,u) \ 1) = a(u,z,K(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(6666(a,1),10408(a,1,2))].">
      <j1 rule="para" parents="6666 10408"/>
    </justification>
  </clause>

  <clause id="10414">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z * y,K(x,y))
    ]]></literal>
    <justification jstring="[para(7369(a,1),10408(a,1,2))].">
      <j1 rule="para" parents="7369 10408"/>
    </justification>
  </clause>

  <clause id="10415">
    <literal><![CDATA[
      K(x,x * y) * K(z \ ((z * y) * x),x) = a(z,y,K(x,x * y))
    ]]></literal>
    <justification jstring="[para(9595(a,1),10408(a,1,2))].">
      <j1 rule="para" parents="9595 10408"/>
    </justification>
  </clause>

  <clause id="10416">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(x,y)) * w
    ]]></literal>
    <justification jstring="[para(10408(a,1),9989(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10408 9989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10417">
    <literal><![CDATA[
      (x / a(y,z,K(u,w))) * K(u,w) = x * L(K(u,w),z,y)
    ]]></literal>
    <justification jstring="[para(10408(a,1),10379(a,1,1,2))].">
      <j1 rule="para" parents="10408 10379"/>
    </justification>
  </clause>

  <clause id="10418">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * K(w,u) = x * L(K(w,u),z,y)
    ]]></literal>
    <justification jstring="[para(10408(a,1),10404(a,1,1,2))].">
      <j1 rule="para" parents="10408 10404"/>
    </justification>
  </clause>

  <clause id="10419">
    <literal><![CDATA[
      L(K(x,y),z,u) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7328,a,10412,a)].">
      <j1 rule="hyper" parents="7328 10412"/>
    </justification>
  </clause>

  <clause id="10420">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * y,K(y,x))
    ]]></literal>
    <justification jstring="[para(7538(a,1),10412(a,1,1))].">
      <j1 rule="para" parents="7538 10412"/>
    </justification>
  </clause>

  <clause id="10421">
    <literal><![CDATA[
      K(a(x,y,z),u) * a(x * y,z,K(L(z,y,x) \ z,u)) = K(L(z,y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(7531(a,1),10419(a,1,1))].">
      <j1 rule="para" parents="7531 10419"/>
    </justification>
  </clause>

  <clause id="10422">
    <literal><![CDATA[
      (x / (x / y)) * K(L(y,z,u),y \ x) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,10414,a(flip),b,6443,a),flip(a)].">
      <j1 rule="hyper" parents="145 10414 6443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10423">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(y,x)) * w
    ]]></literal>
    <justification jstring="[hyper(64,a,10016,a,b,10416,a)].">
      <j1 rule="hyper" parents="64 10016 10416"/>
    </justification>
  </clause>

  <clause id="10424">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(K(z,u),y,x) * w) = K(z,u) * w
    ]]></literal>
    <justification jstring="[para(7327(a,1),10416(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7327 10416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10425">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = x * a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,10417,a,b,10418,a)].">
      <j1 rule="hyper" parents="36 10417 10418"/>
    </justification>
  </clause>

  <clause id="10426">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ x = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(461,a,10425,a)].">
      <j1 rule="hyper" parents="461 10425"/>
    </justification>
  </clause>

  <clause id="10427">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 * a(y,z,K(w,u)) = x
    ]]></literal>
    <justification jstring="[para(10425(a,1),156(a,1))].">
      <j1 rule="para" parents="10425 156"/>
    </justification>
  </clause>

  <clause id="10428">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ x != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(w,u)) = v5
    ]]></literal>
    <justification jstring="[para(10425(a,1),305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="10425 305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10429">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * a(y,z,K(w,u)) = v5
    ]]></literal>
    <justification jstring="[para(10426(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="10426 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10430">
    <literal><![CDATA[
      (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) != v6
    ]]></literal>
    <literal><![CDATA[
      a(z,u,K(v5,w)) = v6
    ]]></literal>
    <justification jstring="[para(361(a,1),10428(a,1))].">
      <j1 rule="para" parents="361 10428"/>
    </justification>
  </clause>

  <clause id="10431">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(x,y)) \ w
    ]]></literal>
    <justification jstring="[hyper(139,a,6161,a(flip),b,10424,a),flip(a)].">
      <j1 rule="hyper" parents="139 6161 10424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10432">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(x,y,K(u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(64,a,10423,a(flip),b,10431,a),flip(a)].">
      <j1 rule="hyper" parents="64 10423 10431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10433">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(225,a,10423,a(flip),b,10431,a(flip))].">
      <j1 rule="hyper" parents="225 10423 10431"/>
    </justification>
  </clause>

  <clause id="10434">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,L(L(x \ 1,z,u),w,v5) \ 1) = a(v5,w,K(L(x \ 1,z,u) \ 1,y))
    ]]></literal>
    <justification jstring="[para(7310(a,1),10413(a,1,1))].">
      <j1 rule="para" parents="7310 10413"/>
    </justification>
  </clause>

  <clause id="10435">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ K(w,u) = K(w,u) * a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(10410,a,10432,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="10410 10432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10436">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ K(w,u) != K(w,u) * v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = v5
    ]]></literal>
    <justification jstring="[para(10435(a,2),44(a,1))].">
      <j1 rule="para" parents="10435 44"/>
    </justification>
  </clause>

  <clause id="10437">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) * a(y,z,K(x,x * z)) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(10415(a,1),6178(a,1,2))].">
      <j1 rule="para" parents="10415 6178"/>
    </justification>
  </clause>

  <clause id="10438">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[hyper(36,a,10419,a,b,10437,a)].">
      <j1 rule="hyper" parents="36 10419 10437"/>
    </justification>
  </clause>

  <clause id="10439">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(10(a,1),10438(a,2,2,2,1))].">
      <j1 rule="para" parents="10 10438"/>
    </justification>
  </clause>

  <clause id="10440">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[para(6142(a,2),10438(a,1,1))].">
      <j1 rule="para" parents="6142 10438"/>
    </justification>
  </clause>

  <clause id="10441">
    <literal><![CDATA[
      L(K(L(x,y,z),y * L(x,y,z)),y,z) = K(L(x,y,z),y * x)
    ]]></literal>
    <justification jstring="[para(344(a,1),10440(a,2,2))].">
      <j1 rule="para" parents="344 10440"/>
    </justification>
  </clause>

  <clause id="10442">
    <literal><![CDATA[
      L(K(L(x,y,z),y * L(x,y,z)),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,7481,a(flip),b,10441,a),flip(a)].">
      <j1 rule="hyper" parents="373 7481 10441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10444">
    <literal><![CDATA[
      R((x \ 1) * K(x,y),R(x,x,x),y) = (1 * y) / (y * R(x,x,x))
    ]]></literal>
    <justification jstring="[para(7388(a,1),10311(a,1,1,2))].">
      <j1 rule="para" parents="7388 10311"/>
    </justification>
  </clause>

  <clause id="10445">
    <literal><![CDATA[
      R(x \ K(x,y),R(x,x,x),y) = (1 * y) / (y * R(x,x,x))
    ]]></literal>
    <justification jstring="[para(4087(a,1),10444(a,1,1))].">
      <j1 rule="para" parents="4087 10444"/>
    </justification>
  </clause>

  <clause id="10447">
    <literal><![CDATA[
      x \ (K(y,z) * (K(u,y) * x)) = T(K(u,y),x) * T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(8432(a,1),10345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8432 10345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10449">
    <literal><![CDATA[
      T(K(x,y),z) * T(K(y,u),z) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(y,u) * K(x,y),z) = w
    ]]></literal>
    <justification jstring="[para(10447(a,1),9982(a,1))].">
      <j1 rule="para" parents="10447 9982"/>
    </justification>
  </clause>

  <clause id="10450">
    <literal><![CDATA[
      x / T(x / y,T(L(y,z,u),y)) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[hyper(7991,a,10422,a)].">
      <j1 rule="hyper" parents="7991 10422"/>
    </justification>
  </clause>

  <clause id="10451">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(201(a,1),10450(a,1,2,2))].">
      <j1 rule="para" parents="201 10450"/>
    </justification>
  </clause>

  <clause id="10452">
    <literal><![CDATA[
      L(T(x,(y * (z * x)) \ ((y * z) * u)),z,y) = T(L(x,z,y),L(x,z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25,a,b,10187,a)].">
      <j1 rule="hyper" parents="64 25 10187"/>
    </justification>
  </clause>

  <clause id="10453">
    <literal><![CDATA[
      R(x / K(y,T(z,u)),K(y,z),u * K(z,y)) = (x * (u * K(z,y))) / u
    ]]></literal>
    <justification jstring="[para(8256(a,1),10239(a,1,1,2))].">
      <j1 rule="para" parents="8256 10239"/>
    </justification>
  </clause>

  <clause id="10454">
    <literal><![CDATA[
      R(x * K(y,T(z,u)),K(z,y),u * K(y,z)) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[para(7908(a,1),10453(a,1,1))].">
      <j1 rule="para" parents="7908 10453"/>
    </justification>
  </clause>

  <clause id="10455">
    <literal><![CDATA[
      L(T(x,(y * z) \ (x \ ((y * z) * u))),z,y) = T(L(x,z,y),L(x,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(9576(a,1),10452(a,1,1))].">
      <j1 rule="para" parents="9576 10452"/>
    </justification>
  </clause>

  <clause id="10456">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ u) = L(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(10172(a,1),10455(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10172 10455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10457">
    <literal><![CDATA[
      L(T(x,x \ y),z,u) = (L(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(478,a,10456,a),flip(a)].">
      <j1 rule="hyper" parents="478 10456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10458">
    <literal><![CDATA[
      x / L(T(y,y \ x),z,u) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,10456,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 10456 116"/>
    </justification>
  </clause>

  <clause id="10459">
    <literal><![CDATA[
      T(x,L(x,y,z) \ u) = T(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(42,a,25,a,b,10456,a(flip))].">
      <j1 rule="hyper" parents="42 25 10456"/>
    </justification>
  </clause>

  <clause id="10460">
    <literal><![CDATA[
      T(x,x \ L(L(x,y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,5571,a(flip),b,10456,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="42 5571 10456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10461">
    <literal><![CDATA[
      (L(x,y,z) \ u) / (L(T(x,x \ w),y,z) \ u) = K(L(x,y,z),L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(10456(a,1),6136(a,1,2,1))].">
      <j1 rule="para" parents="10456 6136"/>
    </justification>
  </clause>

  <clause id="10463">
    <literal><![CDATA[
      L(L(x,y,z),u,w) / x = x \ L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(225,a,10460,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 10460 116"/>
    </justification>
  </clause>

  <clause id="10466">
    <literal><![CDATA[
      (L(x / y,z,u) \ x) \ x = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(848(a,1),10457(a,1,1)),flip(a)].">
      <j1 rule="para" parents="848 10457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10467">
    <literal><![CDATA[
      x / L(y \ x,z,u) = L(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(848(a,1),10458(a,1,2,1))].">
      <j1 rule="para" parents="848 10458"/>
    </justification>
  </clause>

  <clause id="10468">
    <literal><![CDATA[
      L(x / (x / y),z,u) \ x = x / L(y,z,u)
    ]]></literal>
    <justification jstring="[para(412(a,1),10458(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="412 10458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10469">
    <literal><![CDATA[
      x / L(L(x,y,z),u,w) = L(L(x,y,z),u,w) \ x
    ]]></literal>
    <justification jstring="[para(5557(a,1),10458(a,1,2,1))].">
      <j1 rule="para" parents="5557 10458"/>
    </justification>
  </clause>

  <clause id="10471">
    <literal><![CDATA[
      L((x \ y) / z,z,x) \ (x \ y) = (x \ y) / ((x * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(225,a,346,a(flip),b,10466,a),flip(a)].">
      <j1 rule="hyper" parents="225 346 10466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10472">
    <literal><![CDATA[
      x / (x / L(y \ x,z,u)) = L(x / y,z,u)
    ]]></literal>
    <justification jstring="[para(10466(a,1),216(a,1,2,2))].">
      <j1 rule="para" parents="10466 216"/>
    </justification>
  </clause>

  <clause id="10473">
    <literal><![CDATA[
      L(x / (x / y),z,u) = x / (x / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(226,a,10468,a),flip(a)].">
      <j1 rule="hyper" parents="226 10468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10474">
    <literal><![CDATA[
      x / L(T(x,y),z,u) = L(T(x,y),z,u) \ x
    ]]></literal>
    <justification jstring="[para(3982(a,1),10468(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3982 10468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10475">
    <literal><![CDATA[
      L(x / (x / (y \ z)),y,y) = x / (x / ((1 / y) * z))
    ]]></literal>
    <justification jstring="[para(569(a,1),10473(a,2,2,2))].">
      <j1 rule="para" parents="569 10473"/>
    </justification>
  </clause>

  <clause id="10479">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ u) = K(L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,6290,a(flip),b,10461,a),flip(a)].">
      <j1 rule="hyper" parents="64 6290 10461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10480">
    <literal><![CDATA[
      ((x * y) * L(y,x,z)) \ (y * (x * L(y,x,z))) = K(L(y,x,z),y * T(x,y))
    ]]></literal>
    <justification jstring="[para(115(a,1),10225(a,1,1,1))].">
      <j1 rule="para" parents="115 10225"/>
    </justification>
  </clause>

  <clause id="10481">
    <literal><![CDATA[
      K(L(x,y,z),x * T(y,x)) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(3199,a,10480,a),flip(a)].">
      <j1 rule="hyper" parents="3199 10480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10482">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(115(a,1),10481(a,1,2))].">
      <j1 rule="para" parents="115 10481"/>
    </justification>
  </clause>

  <clause id="10483">
    <literal><![CDATA[
      K(x,y * L(x,y,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(7482,a,10482,a),flip(a)].">
      <j1 rule="hyper" parents="7482 10482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10485">
    <literal><![CDATA[
      L(K(x,x * y),z * x,u) = K(L(x,z,u),y * L(x,y,w))
    ]]></literal>
    <justification jstring="[para(10483(a,1),7369(a,1,1))].">
      <j1 rule="para" parents="10483 7369"/>
    </justification>
  </clause>

  <clause id="10486">
    <literal><![CDATA[
      K(L(x,y,z),u * L(x,u,w)) = K(L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(7562,a,10485,a),flip(a)].">
      <j1 rule="hyper" parents="7562 10485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10487">
    <literal><![CDATA[
      L(K(L(x,y,z),x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(10486(a,1),10442(a,1,1))].">
      <j1 rule="para" parents="10486 10442"/>
    </justification>
  </clause>

  <clause id="10488">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(10268(a,1),10487(a,1,1))].">
      <j1 rule="para" parents="10268 10487"/>
    </justification>
  </clause>

  <clause id="10490">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10439,a(flip),b,10488,a)].">
      <j1 rule="hyper" parents="64 10439 10488"/>
    </justification>
  </clause>

  <clause id="10491">
    <literal><![CDATA[
      a(x,y,K(z * y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,10488,a(flip),b,10411,a),flip(a)].">
      <j1 rule="hyper" parents="138 10488 10411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10493">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(53,a,10491,a)].">
      <j1 rule="hyper" parents="53 10491"/>
    </justification>
  </clause>

  <clause id="10494">
    <literal><![CDATA[
      a(x,y,K(y * z,z)) = 1
    ]]></literal>
    <justification jstring="[para(8516(a,2),10491(a,1,3))].">
      <j1 rule="para" parents="8516 10491"/>
    </justification>
  </clause>

  <clause id="10495">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,10494,a)].">
      <j1 rule="hyper" parents="53 10494"/>
    </justification>
  </clause>

  <clause id="10496">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(z * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(9599,a,10493,a)].">
      <j1 rule="hyper" parents="9599 10493"/>
    </justification>
  </clause>

  <clause id="10497">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9594,a(flip),b,10493,a)].">
      <j1 rule="hyper" parents="64 9594 10493"/>
    </justification>
  </clause>

  <clause id="10498">
    <literal><![CDATA[
      a(x,y,K(z,y * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,10495,a(flip),b,10411,a),flip(a)].">
      <j1 rule="hyper" parents="138 10495 10411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10499">
    <literal><![CDATA[
      K(x,y \ (x * z)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(10323,a,10490,a)].">
      <j1 rule="hyper" parents="10323 10490"/>
    </justification>
  </clause>

  <clause id="10500">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(7093,a,10490,a)].">
      <j1 rule="hyper" parents="7093 10490"/>
    </justification>
  </clause>

  <clause id="10501">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,u) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,10488,a,b,10490,a)].">
      <j1 rule="hyper" parents="373 10488 10490"/>
    </justification>
  </clause>

  <clause id="10502">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = K(x,x * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(2329(a,1),10490(a,1,2))].">
      <j1 rule="para" parents="2329 10490"/>
    </justification>
  </clause>

  <clause id="10503">
    <literal><![CDATA[
      K(x * ((y * x) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8787,a,10497,a),flip(a)].">
      <j1 rule="hyper" parents="8787 10497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10505">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8610,a,b,10497,a)].">
      <j1 rule="hyper" parents="64 8610 10497"/>
    </justification>
  </clause>

  <clause id="10506">
    <literal><![CDATA[
      K(x \ (y * z),y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8630,a(flip),b,10497,a)].">
      <j1 rule="hyper" parents="64 8630 10497"/>
    </justification>
  </clause>

  <clause id="10507">
    <literal><![CDATA[
      T(x,y \ (x * z)) = T(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(143,a,10499,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 10499 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10508">
    <literal><![CDATA[
      K(x,x * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * x)) = u
    ]]></literal>
    <justification jstring="[para(10499(a,1),8930(a,1))].">
      <j1 rule="para" parents="10499 8930"/>
    </justification>
  </clause>

  <clause id="10509">
    <literal><![CDATA[
      K(x,(y / R(y,z,u)) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(2156(a,2),10500(a,1,2,1))].">
      <j1 rule="para" parents="2156 10500"/>
    </justification>
  </clause>

  <clause id="10510">
    <literal><![CDATA[
      K(x * (y \ 1),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(10505(a,1),6827(a,1))].">
      <j1 rule="para" parents="10505 6827"/>
    </justification>
  </clause>

  <clause id="10511">
    <literal><![CDATA[
      T(x,x * (y \ (z \ y))) = T(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9853,a(flip),b,10507,a),flip(a)].">
      <j1 rule="hyper" parents="64 9853 10507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10512">
    <literal><![CDATA[
      K(x \ (y \ x),z) * T(z,T(y \ z,x)) = L(z,x \ (y \ x),z)
    ]]></literal>
    <justification jstring="[para(10511(a,1),6080(a,1,2))].">
      <j1 rule="para" parents="10511 6080"/>
    </justification>
  </clause>

  <clause id="10513">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * x)) = w
    ]]></literal>
    <justification jstring="[para(10488(a,2),10508(a,1))].">
      <j1 rule="para" parents="10488 10508"/>
    </justification>
  </clause>

  <clause id="10514">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(10501(a,1),623(a,1)),flip(b)].">
      <j1 rule="para" parents="10501 623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10515">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = w
    ]]></literal>
    <justification jstring="[para(2329(a,1),10514(a,1,2))].">
      <j1 rule="para" parents="2329 10514"/>
    </justification>
  </clause>

  <clause id="10516">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ x)) = T(x,x * (L(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(143,a,10502,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 10502 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10517">
    <literal><![CDATA[
      K(x,T(y \ (R(y,z,u) * x),T(y,R(y,z,u)))) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(9855,a,10509,a)].">
      <j1 rule="hyper" parents="9855 10509"/>
    </justification>
  </clause>

  <clause id="10518">
    <literal><![CDATA[
      K(x,(y * (x \ 1)) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * x)) = u
    ]]></literal>
    <justification jstring="[para(7158(a,1),10513(a,1))].">
      <j1 rule="para" parents="7158 10513"/>
    </justification>
  </clause>

  <clause id="10519">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(10518,a,9291,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="10518 9291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10521">
    <literal><![CDATA[
      K(x,((x \ 1) * y) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,8817,a(flip),b,10519,a),flip(a)].">
      <j1 rule="hyper" parents="373 8817 10519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10522">
    <literal><![CDATA[
      K(T(x,y),y \ (z * T(x,y))) = K(x,z / ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9630,a(flip),b,10519,a),flip(a)].">
      <j1 rule="hyper" parents="64 9630 10519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10523">
    <literal><![CDATA[
      K(x,(y * (x \ 1)) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9291,a(flip),b,10521,a)].">
      <j1 rule="hyper" parents="64 9291 10521"/>
    </justification>
  </clause>

  <clause id="10524">
    <literal><![CDATA[
      K(x,L(y,x \ 1,x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7155,a(flip),b,10521,a)].">
      <j1 rule="hyper" parents="64 7155 10521"/>
    </justification>
  </clause>

  <clause id="10525">
    <literal><![CDATA[
      K(x,T((x \ 1) \ y,z) \ u) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[para(774(a,1),10524(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="774 10524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10526">
    <literal><![CDATA[
      K(x,(y / (x \ 1)) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(12(a,1),10523(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 10523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10527">
    <literal><![CDATA[
      K(x,(y * T(x,z)) / z) = K(x,y / ((x \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(8323,a,10522,a)].">
      <j1 rule="hyper" parents="8323 10522"/>
    </justification>
  </clause>

  <clause id="10528">
    <literal><![CDATA[
      K(x,y / ((x \ 1) * z)) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(9140,a,10527,a),flip(a)].">
      <j1 rule="hyper" parents="9140 10527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10529">
    <literal><![CDATA[
      K(x,(((x \ 1) * y) * z) / (x \ z)) = K(T(x,x \ 1),R(y,x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8230,a(flip),b,10528,a),flip(a)].">
      <j1 rule="hyper" parents="64 8230 10528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10530">
    <literal><![CDATA[
      K(x,(((x \ 1) * y) * z) / (x \ z)) = K(x,R(y,x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,3780,a(flip),b,10529,a),flip(a)].">
      <j1 rule="hyper" parents="373 3780 10529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10531">
    <literal><![CDATA[
      K(x,(y / (((x \ 1) * z) * y)) \ x) = K(x,R(z,x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(9748,a,10530,a)].">
      <j1 rule="hyper" parents="9748 10530"/>
    </justification>
  </clause>

  <clause id="10532">
    <literal><![CDATA[
      R(K(x,(x \ 1) \ y),y,z) = K(x,(z / (((x \ 1) * ((x \ 1) \ y)) * z)) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,9829,a,b,10531,a)].">
      <j1 rule="hyper" parents="373 9829 10531"/>
    </justification>
  </clause>

  <clause id="10533">
    <literal><![CDATA[
      K(x,T(R(y,z,u) * (y \ x),T(y,R(y,z,u)))) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(1898(a,1),10517(a,1,2,1))].">
      <j1 rule="para" parents="1898 10517"/>
    </justification>
  </clause>

  <clause id="10534">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,(z / (((x \ 1) * ((x \ 1) \ y)) * z)) \ x)
    ]]></literal>
    <justification jstring="[para(7157(a,1),10532(a,1,1))].">
      <j1 rule="para" parents="7157 10532"/>
    </justification>
  </clause>

  <clause id="10535">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,(z / (y * z)) \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),10534(a,2,2,1,2,1))].">
      <j1 rule="para" parents="10 10534"/>
    </justification>
  </clause>

  <clause id="10536">
    <literal><![CDATA[
      K(x,R(y \ 1,y,z) \ x) = R(K(x,x * y),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6546,a,b,10535,a)].">
      <j1 rule="hyper" parents="373 6546 10535"/>
    </justification>
  </clause>

  <clause id="10538">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = x * R(K(x,x * y),y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,10536,a(flip),b,5726,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 10536 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10539">
    <literal><![CDATA[
      K(x,T(R(y,z,u) * (y \ x),y)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(197(a,1),10533(a,1,2,2))].">
      <j1 rule="para" parents="197 10533"/>
    </justification>
  </clause>

  <clause id="10540">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,u) * K(x,y)) = T(z * K(x,y),K(y,u))
    ]]></literal>
    <justification jstring="[para(9979(a,1),10352(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9979 10352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10541">
    <literal><![CDATA[
      K(x,y) * T(z,K(x,y) * K(y,u)) = T(z * K(x,y),K(y,u))
    ]]></literal>
    <justification jstring="[para(3320(a,1),10540(a,1,2,2))].">
      <j1 rule="para" parents="3320 10540"/>
    </justification>
  </clause>

  <clause id="10542">
    <literal><![CDATA[
      T((K(x,y) \ z) * K(x,y),K(y,u)) \ z = K(K(x,y) * K(y,u),K(x,y) \ z)
    ]]></literal>
    <justification jstring="[para(10541(a,1),6324(a,1,1))].">
      <j1 rule="para" parents="10541 6324"/>
    </justification>
  </clause>

  <clause id="10543">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(x,y) \ u) = T(T(u,K(x,y)),K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(7806(a,1),10542(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7806 10542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10544">
    <literal><![CDATA[
      K(x,x * y) \ (L(K(x,x * y),z,u) * T(x,y)) = L(K(x * y,x),z,u) \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,7326,a,b,6351,a),flip(a)].">
      <j1 rule="hyper" parents="373 7326 6351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10545">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,z / (y * z)) = K(((x * (y * z)) / z) \ 1,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(6385,a,6685,a),flip(a)].">
      <j1 rule="hyper" parents="6385 6685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10547">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,z / (y * z)) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,6580,a(flip),b,10545,a),flip(a)].">
      <j1 rule="hyper" parents="373 6580 10545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10548">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(6385,a,10547,a)].">
      <j1 rule="hyper" parents="6385 10547"/>
    </justification>
  </clause>

  <clause id="10550">
    <literal><![CDATA[
      K(R(1 / x,x,y) / z,x \ 1) = K(y / (z * (x * y)),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,6580,a(flip),b,10548,a)].">
      <j1 rule="hyper" parents="64 6580 10548"/>
    </justification>
  </clause>

  <clause id="10551">
    <literal><![CDATA[
      K(x \ R(1 / y,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(8443,a,10550,a)].">
      <j1 rule="hyper" parents="8443 10550"/>
    </justification>
  </clause>

  <clause id="10552">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5265,a(flip),b,10551,a)].">
      <j1 rule="hyper" parents="64 5265 10551"/>
    </justification>
  </clause>

  <clause id="10553">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (x / (z * x)),z \ 1)
    ]]></literal>
    <justification jstring="[para(244(a,1),10551(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="244 10551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10554">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ ((z * x) \ x),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,8922,a(flip),b,10553,a),flip(a)].">
      <j1 rule="hyper" parents="373 8922 10553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10555">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x / ((z \ 1) * x)),z) = u
    ]]></literal>
    <justification jstring="[para(10553(a,2),7419(a,1))].">
      <j1 rule="para" parents="10553 7419"/>
    </justification>
  </clause>

  <clause id="10556">
    <literal><![CDATA[
      x / (y * K(1 / z,z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5086,a(flip),b,6914,a)].">
      <j1 rule="hyper" parents="64 5086 6914"/>
    </justification>
  </clause>

  <clause id="10558">
    <literal><![CDATA[
      K(x,1 / x) * (y / L(x,z,u)) = y / (1 / (1 / L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(7325(a,1),10556(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7325 10556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10559">
    <literal><![CDATA[
      K(x,L(L(x \ (y \ (z * x)),u,w),x,y)) = K(x,y \ T(y * L(y \ z,u,w),x))
    ]]></literal>
    <justification jstring="[para(22(a,2),7265(a,2,2,2))].">
      <j1 rule="para" parents="22 7265"/>
    </justification>
  </clause>

  <clause id="10560">
    <literal><![CDATA[
      K(x,L(L(x \ (y \ (z * x)),u,w),x,y)) = K(x,L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,8552,a(flip),b,10559,a),flip(a)].">
      <j1 rule="hyper" parents="373 8552 10559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10562">
    <literal><![CDATA[
      K(x,L((y / x) \ z,u,w)) = K(x,L(y \ (z * x),u,w))
    ]]></literal>
    <justification jstring="[para(1717(a,1),10560(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1717 10560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10563">
    <literal><![CDATA[
      K(x,L(y \ (((y / x) * z) * x),u,w)) = K(x,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),10562(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 10562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10564">
    <literal><![CDATA[
      L(K(x,y \ (((y / x) * z) * x)),((y / x) * z) * x,u) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7082,a,b,10563,a)].">
      <j1 rule="hyper" parents="64 7082 10563"/>
    </justification>
  </clause>

  <clause id="10565">
    <literal><![CDATA[
      L(K(x,y \ (((x \ y) * z) * x)),((y / x) * z) * x,u) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(9353(a,1),10564(a,1,1))].">
      <j1 rule="para" parents="9353 10564"/>
    </justification>
  </clause>

  <clause id="10566">
    <literal><![CDATA[
      L(K(x,y),((z / x) * y) * x,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(8828(a,1),10565(a,1,1))].">
      <j1 rule="para" parents="8828 10565"/>
    </justification>
  </clause>

  <clause id="10567">
    <literal><![CDATA[
      K(L(x,(y / x) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(7562,a,10566,a)].">
      <j1 rule="hyper" parents="7562 10566"/>
    </justification>
  </clause>

  <clause id="10569">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,9473,a(flip),b,10567,a),flip(a)].">
      <j1 rule="hyper" parents="64 9473 10567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10570">
    <literal><![CDATA[
      a(x,y,K(z,L(y,u,w))) = 1
    ]]></literal>
    <justification jstring="[para(10567(a,1),6476(a,1,3))].">
      <j1 rule="para" parents="10567 6476"/>
    </justification>
  </clause>

  <clause id="10571">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,7281,a(flip),b,10569,a)].">
      <j1 rule="hyper" parents="64 7281 10569"/>
    </justification>
  </clause>

  <clause id="10573">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,10571,a)].">
      <j1 rule="hyper" parents="57 10571"/>
    </justification>
  </clause>

  <clause id="10574">
    <literal><![CDATA[
      K((x / y) \ z,R((x / y) \ 1,x / y,y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6054,a(flip),b,7681,a),flip(a)].">
      <j1 rule="hyper" parents="373 6054 7681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10575">
    <literal><![CDATA[
      K((x / y) \ z,T(y / x,x / y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[para(857(a,1),10574(a,1,2))].">
      <j1 rule="para" parents="857 10574"/>
    </justification>
  </clause>

  <clause id="10576">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((x / y) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(7483,a,10575,a),flip(a)].">
      <j1 rule="hyper" parents="7483 10575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10577">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,7558,a(flip),b,10576,a),flip(a)].">
      <j1 rule="hyper" parents="373 7558 10576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10578">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K(u \ (L(x,y,z) * w),T(x,L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(8019,a,7699,a),flip(a)].">
      <j1 rule="hyper" parents="8019 7699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10579">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * K(z,y)) * (y * z)) = L(K(z,y),T(x,y * z),y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,7747,a)].">
      <j1 rule="hyper" parents="64 249 7747"/>
    </justification>
  </clause>

  <clause id="10580">
    <literal><![CDATA[
      K(x,((y / z) * (z * x)) \ (y * (z * x))) = L(K(x,z),T(y,z * x),z * x)
    ]]></literal>
    <justification jstring="[hyper(9864,a,10579,a)].">
      <j1 rule="hyper" parents="9864 10579"/>
    </justification>
  </clause>

  <clause id="10581">
    <literal><![CDATA[
      K(x,((y / z) * z) \ (x \ (y * (z * x)))) = L(K(x,z),T(y,z * x),z * x)
    ]]></literal>
    <justification jstring="[hyper(9575,a,10580,a)].">
      <j1 rule="hyper" parents="9575 10580"/>
    </justification>
  </clause>

  <clause id="10582">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,z \ (x \ (z * (y * x))))
    ]]></literal>
    <justification jstring="[para(12(a,1),10581(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 10581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10583">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7266,a(flip),b,10582,a),flip(a)].">
      <j1 rule="hyper" parents="373 7266 10582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10584">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,10583,a(flip),b,7747,a)].">
      <j1 rule="hyper" parents="145 10583 7747"/>
    </justification>
  </clause>

  <clause id="10585">
    <literal><![CDATA[
      K(x,L(y,x,((y * x) * z) / (y * x))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[para(255(a,1),10583(a,1,2)),flip(a)].">
      <j1 rule="para" parents="255 10583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10586">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10174,a(flip),b,10585,a),flip(a)].">
      <j1 rule="hyper" parents="64 10174 10585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10589">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,10586,a(flip),b,9917,a)].">
      <j1 rule="hyper" parents="144 10586 9917"/>
    </justification>
  </clause>

  <clause id="10591">
    <literal><![CDATA[
      T(x * K(y,z),z * y) = (z * y) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(7592,a,10584,a),flip(a)].">
      <j1 rule="hyper" parents="7592 10584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10592">
    <literal><![CDATA[
      (x * (y * z)) / (z * y) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(281,a,10591,a)].">
      <j1 rule="hyper" parents="281 10591"/>
    </justification>
  </clause>

  <clause id="10593">
    <literal><![CDATA[
      (x / ((y * z) / y)) * (y * z) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(7015,a,10592,a)].">
      <j1 rule="hyper" parents="7015 10592"/>
    </justification>
  </clause>

  <clause id="10594">
    <literal><![CDATA[
      (T(x,y) \ 1) * (x * y) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(6040,a,10592,a),flip(a)].">
      <j1 rule="hyper" parents="6040 10592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10595">
    <literal><![CDATA[
      (x / (y * z)) * K(y,z) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(466,a,10592,a),flip(a)].">
      <j1 rule="hyper" parents="466 10592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10597">
    <literal><![CDATA[
      ((1 / x) * (x * y)) / (y * x) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,6862,a(flip),b,10592,a),flip(a)].">
      <j1 rule="hyper" parents="373 6862 10592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10598">
    <literal><![CDATA[
      ((x / y) * (z * y)) / (y * z) = x / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6245,a(flip),b,10592,a),flip(a)].">
      <j1 rule="hyper" parents="373 6245 10592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10599">
    <literal><![CDATA[
      (x * T(y,z)) * (z * y) = (x * y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,6852,a(flip),b,10592,a)].">
      <j1 rule="hyper" parents="144 6852 10592"/>
    </justification>
  </clause>

  <clause id="10600">
    <literal><![CDATA[
      (x * (y * z)) / T(z * y,u) = (x * K(y,z)) * K(u,z * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,10592,a(flip),b,6242,a),flip(a)].">
      <j1 rule="hyper" parents="144 10592 6242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10601">
    <literal><![CDATA[
      (x * K(y \ z,y)) * z = x * ((y \ z) * y)
    ]]></literal>
    <justification jstring="[para(10592(a,1),385(a,1,1))].">
      <j1 rule="para" parents="10592 385"/>
    </justification>
  </clause>

  <clause id="10602">
    <literal><![CDATA[
      (x * K(y,z)) * (z * y) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * (y * z)) = w
    ]]></literal>
    <justification jstring="[para(10592(a,1),391(a,1,1))].">
      <j1 rule="para" parents="10592 391"/>
    </justification>
  </clause>

  <clause id="10603">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = (x / (z * y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(10193(a,1),10592(a,1,1))].">
      <j1 rule="para" parents="10193 10592"/>
    </justification>
  </clause>

  <clause id="10604">
    <literal><![CDATA[
      x * (K(y * z,x) * K(y,z)) = ((y * z) * x) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(5913,a,10595,a)].">
      <j1 rule="hyper" parents="5913 10595"/>
    </justification>
  </clause>

  <clause id="10605">
    <literal><![CDATA[
      T((x / (y * z)) / T(z,y),z) = z \ (x / (z * y))
    ]]></literal>
    <justification jstring="[hyper(493,a,10595,a(flip),b,6311,a)].">
      <j1 rule="hyper" parents="493 10595 6311"/>
    </justification>
  </clause>

  <clause id="10606">
    <literal><![CDATA[
      (x / (y * z)) * T(y,z) = (x / (z * y)) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,10595,a(flip),b,6847,a),flip(a)].">
      <j1 rule="hyper" parents="144 10595 6847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10607">
    <literal><![CDATA[
      (x / (y * z)) * (z * K(y,z)) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,10595,a(flip),b,5703,a),flip(a)].">
      <j1 rule="hyper" parents="144 10595 5703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10608">
    <literal><![CDATA[
      (x / y) * K(z,z \ y) = x / ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),10595(a,1,1,2))].">
      <j1 rule="para" parents="10 10595"/>
    </justification>
  </clause>

  <clause id="10609">
    <literal><![CDATA[
      (x / y) * K(y / z,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(12(a,1),10595(a,1,1,2))].">
      <j1 rule="para" parents="12 10595"/>
    </justification>
  </clause>

  <clause id="10610">
    <literal><![CDATA[
      K(x,y / (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x * z)) = u
    ]]></literal>
    <justification jstring="[para(10595(a,1),8561(a,1,2))].">
      <j1 rule="para" parents="10595 8561"/>
    </justification>
  </clause>

  <clause id="10611">
    <literal><![CDATA[
      K(x / (y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / (z * y),y) = u
    ]]></literal>
    <justification jstring="[para(10595(a,1),8568(a,1,1))].">
      <j1 rule="para" parents="10595 8568"/>
    </justification>
  </clause>

  <clause id="10612">
    <literal><![CDATA[
      K(x / (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / (z * y),z) = u
    ]]></literal>
    <justification jstring="[para(10595(a,1),8580(a,1,1))].">
      <j1 rule="para" parents="10595 8580"/>
    </justification>
  </clause>

  <clause id="10613">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,T(z,u) \ 1)) = K(x,((T(z,u) \ 1) * y) \ ((z \ 1) * (u * z)))
    ]]></literal>
    <justification jstring="[para(10594(a,1),7088(a,2,2,2))].">
      <j1 rule="para" parents="10594 7088"/>
    </justification>
  </clause>

  <clause id="10614">
    <literal><![CDATA[
      L(x,y,y) / (x * y) = K(y,x) / y
    ]]></literal>
    <justification jstring="[para(559(a,1),10597(a,1,1))].">
      <j1 rule="para" parents="559 10597"/>
    </justification>
  </clause>

  <clause id="10615">
    <literal><![CDATA[
      T(K(x,y) / x,y * x) = (y * x) \ L(y,x,x)
    ]]></literal>
    <justification jstring="[para(10614(a,1),117(a,1,1))].">
      <j1 rule="para" parents="10614 117"/>
    </justification>
  </clause>

  <clause id="10616">
    <literal><![CDATA[
      (x / T(y,z)) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(10598(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="10598 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10617">
    <literal><![CDATA[
      (x / (y \ z)) * ((y \ z) * y) = (x / (z / y)) * z
    ]]></literal>
    <justification jstring="[para(6887(a,1),10601(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6887 10601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10618">
    <literal><![CDATA[
      T(x,y) * T(z / (x * y),T(x,y)) = (z / (y * x)) * x
    ]]></literal>
    <justification jstring="[hyper(329,a,10606,a)].">
      <j1 rule="hyper" parents="329 10606"/>
    </justification>
  </clause>

  <clause id="10619">
    <literal><![CDATA[
      R(x \ 1,x,y) * K(z,z \ y) = (x \ y) / ((z \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3006,a,b,10608,a)].">
      <j1 rule="hyper" parents="64 3006 10608"/>
    </justification>
  </clause>

  <clause id="10620">
    <literal><![CDATA[
      (x / ((y \ z) * y)) * (y \ z) = (x / z) * (z / y)
    ]]></literal>
    <justification jstring="[para(10608(a,1),6064(a,1,1))].">
      <j1 rule="para" parents="10608 6064"/>
    </justification>
  </clause>

  <clause id="10621">
    <literal><![CDATA[
      1 / ((x * ((x / y) \ 1)) / x) = x / (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,9254,a,b,10609,a)].">
      <j1 rule="hyper" parents="64 9254 10609"/>
    </justification>
  </clause>

  <clause id="10622">
    <literal><![CDATA[
      (x / y) * K(z \ y,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(6116(a,1),10609(a,1,2))].">
      <j1 rule="para" parents="6116 10609"/>
    </justification>
  </clause>

  <clause id="10623">
    <literal><![CDATA[
      K(x / ((y * x) * z),z) = K(y \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(10611,a,10074,a)].">
      <j1 rule="hyper" parents="10611 10074"/>
    </justification>
  </clause>

  <clause id="10624">
    <literal><![CDATA[
      K((x / y) \ (z \ 1),z) = K(y / (x * z),z)
    ]]></literal>
    <justification jstring="[para(12(a,1),10623(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 10623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10625">
    <literal><![CDATA[
      K(((x \ y) * x) / (z * (y / (y / x))),z) = K(y / (x * z),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10254,a,b,10624,a)].">
      <j1 rule="hyper" parents="64 10254 10624"/>
    </justification>
  </clause>

  <clause id="10626">
    <literal><![CDATA[
      (x / (y * T(z,u))) * T((y * z) / y,u) = (x / (T(z,u) * y)) * T(z,u)
    ]]></literal>
    <justification jstring="[para(5853(a,2),10607(a,1,2))].">
      <j1 rule="para" parents="5853 10607"/>
    </justification>
  </clause>

  <clause id="10627">
    <literal><![CDATA[
      L(x,x \ y,x \ y) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(573,a,10617,a)].">
      <j1 rule="hyper" parents="573 10617"/>
    </justification>
  </clause>

  <clause id="10628">
    <literal><![CDATA[
      a(x \ y,x \ y,x) = ((1 / (y / x)) * y) \ x
    ]]></literal>
    <justification jstring="[para(10617(a,1),1242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10617 1242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10629">
    <literal><![CDATA[
      L(L(x,y,z),x \ u,x \ u) = L((1 / (u / x)) * u,y,z)
    ]]></literal>
    <justification jstring="[para(10627(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10627 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10630">
    <literal><![CDATA[
      a(x,L(x,x \ y,x \ y),z) = a((1 / (y / x)) * y,x,z)
    ]]></literal>
    <justification jstring="[para(10627(a,1),2784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10627 2784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10631">
    <literal><![CDATA[
      (x \ y) * ((x / y) * (y / x)) = R(x \ y,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,10620,a(flip),b,1986,a)].">
      <j1 rule="hyper" parents="145 10620 1986"/>
    </justification>
  </clause>

  <clause id="10632">
    <literal><![CDATA[
      (x * ((x / y) \ 1)) / x = (x / (x * (y / x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,10621,a),flip(a)].">
      <j1 rule="hyper" parents="215 10621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10633">
    <literal><![CDATA[
      x / (x * (((y / x) \ 1) \ 1)) = ((x * ((x / y) \ 1)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(10632(a,2),3741(a,2,1))].">
      <j1 rule="para" parents="10632 3741"/>
    </justification>
  </clause>

  <clause id="10634">
    <literal><![CDATA[
      (x / (y * K(x,x \ y))) \ 1 = (x * ((x / y) \ 1)) / x
    ]]></literal>
    <justification jstring="[para(5963(a,2),10632(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5963 10632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10635">
    <literal><![CDATA[
      T(x,y) * R(x \ 1,x,y) = (y / (y * x)) * x
    ]]></literal>
    <justification jstring="[para(4092(a,1),10618(a,1,2))].">
      <j1 rule="para" parents="4092 10618"/>
    </justification>
  </clause>

  <clause id="10636">
    <literal><![CDATA[
      ((x * K(y,z)) * z) \ (x * (y * z)) = L(y,z,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(10602,a,100,a(flip))].">
      <j1 rule="hyper" parents="10602 100"/>
    </justification>
  </clause>

  <clause id="10637">
    <literal><![CDATA[
      a(x,L(x,x \ y,x \ y),z) = a((y / x) * y,x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2642,a(flip),b,10630,a),flip(a)].">
      <j1 rule="hyper" parents="373 2642 10630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10638">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ (x * (z * y)) = L(z,y,x * K(z,y))
    ]]></literal>
    <justification jstring="[para(5700(a,1),10636(a,1,1))].">
      <j1 rule="para" parents="5700 10636"/>
    </justification>
  </clause>

  <clause id="10639">
    <literal><![CDATA[
      K(R(x \ (y / z),x,y / (y / z)),x) = K(y / (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6659,a,b,10625,a)].">
      <j1 rule="hyper" parents="64 6659 10625"/>
    </justification>
  </clause>

  <clause id="10640">
    <literal><![CDATA[
      (x * y) \ (R(T(z * K(x,z),u),x,y) \ ((x * z) * y)) = K(u,(x * y) \ ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(27(a,2),8079(a,1,2,1))].">
      <j1 rule="para" parents="27 8079"/>
    </justification>
  </clause>

  <clause id="10641">
    <literal><![CDATA[
      R(T(x,y),T(K(x,z),T(x,y)),u) = (T(T(x,z),T(y,z)) * u) / (K(x,z) * u)
    ]]></literal>
    <justification jstring="[para(4082(a,1),8365(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4082 8365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10642">
    <literal><![CDATA[
      (T(T(x,y),T(z,y)) * u) / (K(x,y) * u) = R(T(x,z),K(x,y),u)
    ]]></literal>
    <justification jstring="[para(4082(a,1),10641(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4082 10641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10644">
    <literal><![CDATA[
      (K(x,y) * z) * R((K(x,y) * z) \ (T(T(x,y),T(u,y)) * z),w,v5) = R(R(T(x,u),K(x,y),z),w,v5) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(10642(a,1),843(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10642 843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10646">
    <literal><![CDATA[
      K(x,R(K(y,R(z,u,w) \ z),z,u * w)) = K(x,K(a(z,u,w),T(y,z * (u * w))))
    ]]></literal>
    <justification jstring="[para(9665(a,1),9556(a,1,2))].">
      <j1 rule="para" parents="9665 9556"/>
    </justification>
  </clause>

  <clause id="10647">
    <literal><![CDATA[
      K(x,K(R(y,z,u) \ y,R(w,y,z * u))) = K(x,K(a(y,z,u),T(w,y * (z * u))))
    ]]></literal>
    <justification jstring="[hyper(64,a,9775,a(flip),b,10646,a)].">
      <j1 rule="hyper" parents="64 9775 10646"/>
    </justification>
  </clause>

  <clause id="10648">
    <literal><![CDATA[
      K((x * (y * z)) \ u,L(z,w,v5)) = K((x * y) \ (z \ u),L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,6549,a(flip),b,9587,a),flip(a)].">
      <j1 rule="hyper" parents="64 6549 9587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10649">
    <literal><![CDATA[
      L(K(L(x,y,z) \ u,L(x,w,v5)),u,z * y) = K((z * y) \ (x \ ((z * y) * u)),L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(7599,a,10648,a)].">
      <j1 rule="hyper" parents="7599 10648"/>
    </justification>
  </clause>

  <clause id="10650">
    <literal><![CDATA[
      T(x * L(K(y,z),u,w),K(y,v5)) = T(x,K(y,v5)) * L(K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(115(a,1),10048(a,1,1))].">
      <j1 rule="para" parents="115 10048"/>
    </justification>
  </clause>

  <clause id="10651">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,x) = T(K(z,y),T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(8015(a,1),10110(a,1,2))].">
      <j1 rule="para" parents="8015 10110"/>
    </justification>
  </clause>

  <clause id="10652">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,8633,a(flip),b,10651,a),flip(a)].">
      <j1 rule="hyper" parents="373 8633 10651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10654">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) * (K(z,y) \ R(K(z,T(y,x)),u,w)) = K(z,y) \ R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(7867(a,2),10125(a,1,2,2,1))].">
      <j1 rule="para" parents="7867 10125"/>
    </justification>
  </clause>

  <clause id="10655">
    <literal><![CDATA[
      K(L(x * (y \ z),x \ 1,y) \ 1,x) = K(((y * (x \ 1)) \ z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(10232,a,10233,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="10232 10233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10656">
    <literal><![CDATA[
      K(L(x * (y \ z),x \ 1,y) \ 1,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z \ (y * (x \ 1)),x) = u
    ]]></literal>
    <justification jstring="[para(10655(a,2),6827(a,1))].">
      <j1 rule="para" parents="10655 6827"/>
    </justification>
  </clause>

  <clause id="10657">
    <literal><![CDATA[
      K(x \ (y * (z \ 1)),z) = K(x \ (z \ y),z)
    ]]></literal>
    <justification jstring="[hyper(10656,a,9658,a)].">
      <j1 rule="hyper" parents="10656 9658"/>
    </justification>
  </clause>

  <clause id="10658">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7401,a(flip),b,10657,a),flip(a)].">
      <j1 rule="hyper" parents="64 7401 10657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10659">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,7513,a(flip),b,10658,a),flip(a)].">
      <j1 rule="hyper" parents="373 7513 10658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10660">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(8635,a,10659,a)].">
      <j1 rule="hyper" parents="8635 10659"/>
    </justification>
  </clause>

  <clause id="10661">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K((x * y) \ (z * y),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8945,a(flip),b,10660,a)].">
      <j1 rule="hyper" parents="64 8945 10660"/>
    </justification>
  </clause>

  <clause id="10662">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(8787,a,10661,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8787 10661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10663">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z \ u,x),y) = K(L(z,x,x \ 1) \ u,T(x,y))
    ]]></literal>
    <justification jstring="[para(10662(a,1),6391(a,1,2,1,2))].">
      <j1 rule="para" parents="10662 6391"/>
    </justification>
  </clause>

  <clause id="10664">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,T(y,u)) = K(x \ z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(6607,a,10663,a),flip(a)].">
      <j1 rule="hyper" parents="6607 10663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10665">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(1638(a,1),10664(a,1,1,1))].">
      <j1 rule="para" parents="1638 10664"/>
    </justification>
  </clause>

  <clause id="10666">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5259,a(flip),b,10665,a)].">
      <j1 rule="hyper" parents="64 5259 10665"/>
    </justification>
  </clause>

  <clause id="10667">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,9316,a(flip),b,10666,a),flip(a)].">
      <j1 rule="hyper" parents="373 9316 10666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10668">
    <literal><![CDATA[
      K(x \ (y * z),T(y,x)) = K(((y \ 1) \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9261,a(flip),b,10667,a),flip(a)].">
      <j1 rule="hyper" parents="64 9261 10667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10669">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((x * y) / z,x)
    ]]></literal>
    <justification jstring="[hyper(8322,a,10668,a),flip(a)].">
      <j1 rule="hyper" parents="8322 10668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10670">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,8793,a(flip),b,10669,a),flip(a)].">
      <j1 rule="hyper" parents="373 8793 10669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10671">
    <literal><![CDATA[
      K((x / ((y \ 1) * z)) \ y,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),10670(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 10670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10672">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),z) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),10671(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 10671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10673">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(6337,a,10672,a)].">
      <j1 rule="hyper" parents="6337 10672"/>
    </justification>
  </clause>

  <clause id="10674">
    <literal><![CDATA[
      K(x \ (y / ((z \ 1) * y)),z) = K(x \ z,z)
    ]]></literal>
    <justification jstring="[hyper(10555,a,10673,a)].">
      <j1 rule="hyper" parents="10555 10673"/>
    </justification>
  </clause>

  <clause id="10675">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[para(2984(a,2),10674(a,1,1,2))].">
      <j1 rule="para" parents="2984 10674"/>
    </justification>
  </clause>

  <clause id="10676">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (z \ 1),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,10552,a(flip),b,10675,a)].">
      <j1 rule="hyper" parents="64 10552 10675"/>
    </justification>
  </clause>

  <clause id="10678">
    <literal><![CDATA[
      K(x \ ((y * z) \ z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,10554,a(flip),b,10676,a)].">
      <j1 rule="hyper" parents="64 10554 10676"/>
    </justification>
  </clause>

  <clause id="10680">
    <literal><![CDATA[
      R(x * K(y,K(T(z,x),u)),K(y,T(z,x)),u) = ((K(y,z) * x) * u) / (u * K(y,T(z,x)))
    ]]></literal>
    <justification jstring="[para(8092(a,1),10308(a,1,1,2))].">
      <j1 rule="para" parents="8092 10308"/>
    </justification>
  </clause>

  <clause id="10681">
    <literal><![CDATA[
      K(L(x,y * z,u),(x * y) \ (x * (y * z))) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),10325(a,1,2,1))].">
      <j1 rule="para" parents="9 10325"/>
    </justification>
  </clause>

  <clause id="10683">
    <literal><![CDATA[
      K(L(x,y * z,u),L(z,y,x)) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[para(18(a,2),10681(a,1,2))].">
      <j1 rule="para" parents="18 10681"/>
    </justification>
  </clause>

  <clause id="10684">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[hyper(7585,a,10683,a)].">
      <j1 rule="hyper" parents="7585 10683"/>
    </justification>
  </clause>

  <clause id="10685">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(z,x * y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,7396,a(flip),b,10684,a),flip(a)].">
      <j1 rule="hyper" parents="373 7396 10684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10687">
    <literal><![CDATA[
      K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),10685(a,2,2,2))].">
      <j1 rule="para" parents="10 10685"/>
    </justification>
  </clause>

  <clause id="10688">
    <literal><![CDATA[
      K(x,L(y,x * (z / y),u)) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12(a,1),10685(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 10685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10689">
    <literal><![CDATA[
      K(L(x,T(y * (x \ z),y),u),R(y,x \ z,y)) = K(x,L(R(y,x \ z,y),z,u))
    ]]></literal>
    <justification jstring="[para(4741(a,1),10687(a,1,1,2))].">
      <j1 rule="para" parents="4741 10687"/>
    </justification>
  </clause>

  <clause id="10690">
    <literal><![CDATA[
      K(L(x,T(y * (x \ z),y),u),y) = K(x,L(R(y,x \ z,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(7403,a,10689,a)].">
      <j1 rule="hyper" parents="7403 10689"/>
    </justification>
  </clause>

  <clause id="10692">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K(u \ (L(x,y,z) * w),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,9515,a(flip),b,10578,a),flip(a)].">
      <j1 rule="hyper" parents="373 9515 10578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10694">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((L(x,y,z) * w) / u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,8215,a(flip),b,10692,a),flip(a)].">
      <j1 rule="hyper" parents="373 8215 10692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10695">
    <literal><![CDATA[
      R(T(x * K(y,x),z),y,u) \ ((y * x) * u) = (y * u) * K(z,(y * u) \ ((y * x) * u))
    ]]></literal>
    <justification jstring="[hyper(157,a,10640,a),flip(a)].">
      <j1 rule="hyper" parents="157 10640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10696">
    <literal><![CDATA[
      (x * y) * K(z,(x * y) \ ((x * u) * y)) != w
    ]]></literal>
    <literal><![CDATA[
      R(T(u * K(x,u),z),x,y) \ ((x * u) * y) = w
    ]]></literal>
    <justification jstring="[para(10640(a,1),290(a,1,2))].">
      <j1 rule="para" parents="10640 290"/>
    </justification>
  </clause>

  <clause id="10697">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) * (K(y,z) * R(K(z,T(y,x)),u,w)) = K(z,y) \ R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(6156(a,1),10654(a,1,2))].">
      <j1 rule="para" parents="6156 10654"/>
    </justification>
  </clause>

  <clause id="10698">
    <literal><![CDATA[
      x * (K(y,z) * R(K(z,T(y,u)),w,v5)) != K(z,y) \ R(K(z,y),w,v5)
    ]]></literal>
    <literal><![CDATA[
      K(u,K(y,R(z,w,v5))) = x
    ]]></literal>
    <justification jstring="[para(10697(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="10697 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10699">
    <literal><![CDATA[
      (((x * K(y,z)) * R(z,u,w)) / (x * K(y,z))) * x = (x * (K(y,z) * R(z,u,w))) / K(y,z)
    ]]></literal>
    <justification jstring="[para(5710(a,1),7183(a,2,1))].">
      <j1 rule="para" parents="5710 7183"/>
    </justification>
  </clause>

  <clause id="10700">
    <literal><![CDATA[
      ((K(R(x,y,x),z) / R(x,y,x)) * x) \ x = R(x,y,x) * K(z,R(x,y,x))
    ]]></literal>
    <justification jstring="[para(4733(a,1),9930(a,1,2))].">
      <j1 rule="para" parents="4733 9930"/>
    </justification>
  </clause>

  <clause id="10701">
    <literal><![CDATA[
      ((K(R(x,y,x),z) / R(x,y,x)) * x) \ x = R(x * K(z,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6388,a(flip),b,10700,a),flip(a)].">
      <j1 rule="hyper" parents="373 6388 10700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10702">
    <literal><![CDATA[
      ((K(x,y) / R(x,z,x)) * x) \ x = R(x * K(y,x),z,x)
    ]]></literal>
    <justification jstring="[para(7388(a,1),10701(a,1,1,1,1))].">
      <j1 rule="para" parents="7388 10701"/>
    </justification>
  </clause>

  <clause id="10703">
    <literal><![CDATA[
      (R(x,y,x) \ T(x,z)) \ x = R(x * K(z,x),y,x)
    ]]></literal>
    <justification jstring="[para(6673(a,1),10702(a,1,1))].">
      <j1 rule="para" parents="6673 10702"/>
    </justification>
  </clause>

  <clause id="10705">
    <literal><![CDATA[
      (x \ L(T(x,y),z,x)) \ x = R(x * K(y,x),z,x)
    ]]></literal>
    <justification jstring="[para(10387(a,1),10703(a,1,1))].">
      <j1 rule="para" parents="10387 10703"/>
    </justification>
  </clause>

  <clause id="10706">
    <literal><![CDATA[
      (((x * K(y,z)) * R(z,u,w)) / (x * K(y,z))) * x = (x * (K(y,z) * R(z,u,w))) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6878,a(flip),b,10699,a),flip(a)].">
      <j1 rule="hyper" parents="373 6878 10699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10707">
    <literal><![CDATA[
      ((x * (K(y,z) * R(z,u,w))) / (x * K(y,z))) * x = (x * (K(y,z) * R(z,u,w))) * K(z,y)
    ]]></literal>
    <justification jstring="[para(5710(a,1),10706(a,1,1,1))].">
      <j1 rule="para" parents="5710 10706"/>
    </justification>
  </clause>

  <clause id="10708">
    <literal><![CDATA[
      R((x * (K(y,z) * z)) / (x * K(y,z)),u,w) * x = (x * (K(y,z) * R(z,u,w))) * K(z,y)
    ]]></literal>
    <justification jstring="[para(3119(a,2),10707(a,1,1))].">
      <j1 rule="para" parents="3119 10707"/>
    </justification>
  </clause>

  <clause id="10709">
    <literal><![CDATA[
      R((x * (y * K(z,y))) / (x * K(z,y)),u,w) * x = (x * (K(z,y) * R(y,u,w))) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3994(a,1),10708(a,1,1,1,1,2))].">
      <j1 rule="para" parents="3994 10708"/>
    </justification>
  </clause>

  <clause id="10710">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = (x * (K(w,y) * R(y,z,u))) * K(y,w)
    ]]></literal>
    <justification jstring="[para(9265(a,1),10709(a,1,1,1))].">
      <j1 rule="para" parents="9265 10709"/>
    </justification>
  </clause>

  <clause id="10711">
    <literal><![CDATA[
      (x * (K(y,z) * R(z,u,w))) * K(z,y) = x * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(1277,a,10710,a),flip(a)].">
      <j1 rule="hyper" parents="1277 10710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10713">
    <literal><![CDATA[
      (x * (R(y,z,u) * K(w,y))) * K(y,w) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(4003(a,2),10711(a,1,1,2))].">
      <j1 rule="para" parents="4003 10711"/>
    </justification>
  </clause>

  <clause id="10714">
    <literal><![CDATA[
      L(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,7318,a,b,10713,a)].">
      <j1 rule="hyper" parents="35 7318 10713"/>
    </justification>
  </clause>

  <clause id="10715">
    <literal><![CDATA[
      a(x,R(y,z,u),K(y,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,10714,a,b,10419,a),flip(a)].">
      <j1 rule="hyper" parents="138 10714 10419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10716">
    <literal><![CDATA[
      K(x,(y \ z) \ R(x,u,w)) = K(x,z \ (y * R(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7080,a(flip),b,10714,a),flip(a)].">
      <j1 rule="hyper" parents="64 7080 10714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10717">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),x \ (K(y,z) * u),K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[para(10147(a,1),6203(a,1,1))].">
      <j1 rule="para" parents="10147 6203"/>
    </justification>
  </clause>

  <clause id="10718">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * ((u \ z) * T(T(u,u \ z),x))) = y * z
    ]]></literal>
    <justification jstring="[para(517(a,1),6420(a,1,2))].">
      <j1 rule="para" parents="517 6420"/>
    </justification>
  </clause>

  <clause id="10719">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (T(u,x) * (u \ z))) = y * z
    ]]></literal>
    <justification jstring="[para(265(a,1),10718(a,1,2,2))].">
      <j1 rule="para" parents="265 10718"/>
    </justification>
  </clause>

  <clause id="10720">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[para(5778(a,1),10719(a,1,2,2))].">
      <j1 rule="para" parents="5778 10719"/>
    </justification>
  </clause>

  <clause id="10721">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * (K(z,u) * y)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(225,a,10720,a(flip),b,6156,a),flip(a)].">
      <j1 rule="hyper" parents="225 10720 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10722">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (K(y,x) * w)) = R(y,z,u) * w
    ]]></literal>
    <justification jstring="[para(1901(a,1),10720(a,1,1,2))].">
      <j1 rule="para" parents="1901 10720"/>
    </justification>
  </clause>

  <clause id="10723">
    <literal><![CDATA[
      K(x,(y * (K(z,x) * u)) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(10720(a,1),8808(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10720 8808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10724">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,x) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(10720(a,1),8812(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10720 8812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10725">
    <literal><![CDATA[
      K(x,y / ((z * (K(u,x) * w)) * v5)) = K(x,y / ((z * w) * v5))
    ]]></literal>
    <justification jstring="[para(10720(a,1),9352(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10720 9352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10726">
    <literal><![CDATA[
      K(x,L(L(y,z,K(u,x)),K(u,x) * z,w)) = K(x,(w * (K(u,x) * z)) \ (w * (z * y)))
    ]]></literal>
    <justification jstring="[para(602(a,1),10724(a,1,2))].">
      <j1 rule="para" parents="602 10724"/>
    </justification>
  </clause>

  <clause id="10728">
    <literal><![CDATA[
      R(x,y,z) * (K(u,x) * w) = K(u,x) * (R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(6161(a,1),10722(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6161 10722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10729">
    <literal><![CDATA[
      K(x,y) * (R(T(y,z),u,w) * (K(T(y,z),T(x,z)) * v5)) = R(T(y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(8205(a,1),10722(a,1,1))].">
      <j1 rule="para" parents="8205 10722"/>
    </justification>
  </clause>

  <clause id="10732">
    <literal><![CDATA[
      R(K(x,y),R(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4864,a,10728,a)].">
      <j1 rule="hyper" parents="4864 10728"/>
    </justification>
  </clause>

  <clause id="10733">
    <literal><![CDATA[
      R(x,y,x) * (K(z,x) * (x \ u)) = K(z,x) * ((u / x) * R(x,y,x))
    ]]></literal>
    <justification jstring="[para(7495(a,1),10728(a,2,2))].">
      <j1 rule="para" parents="7495 10728"/>
    </justification>
  </clause>

  <clause id="10734">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = (v5 * K(y,x)) \ v5
    ]]></literal>
    <justification jstring="[para(10732(a,1),9712(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10732 9712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10735">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(10734(a,2),6899(a,1))].">
      <j1 rule="para" parents="10734 6899"/>
    </justification>
  </clause>

  <clause id="10736">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(x,y,z) / (w / u)) = v5
    ]]></literal>
    <justification jstring="[para(9706(a,1),10735(a,1))].">
      <j1 rule="para" parents="9706 10735"/>
    </justification>
  </clause>

  <clause id="10737">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = K((u * z) / (u * (x \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,9180,a,b,10721,a)].">
      <j1 rule="hyper" parents="373 9180 10721"/>
    </justification>
  </clause>

  <clause id="10738">
    <literal><![CDATA[
      L(K(x,T(T(y,z * u),u)),u,z) = K((z * u) / (z * (x \ u)),y)
    ]]></literal>
    <justification jstring="[para(23(a,1),10737(a,1,1,2))].">
      <j1 rule="para" parents="23 10737"/>
    </justification>
  </clause>

  <clause id="10739">
    <literal><![CDATA[
      L(K(T(T(x,y),z * y),u),y,z) * w = K((z * y) / (z * (u \ y)),x) \ w
    ]]></literal>
    <justification jstring="[para(10737(a,1),7326(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10737 7326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10740">
    <literal><![CDATA[
      K(x,y) * ((z / y) * R(y,u,y)) = R(y,u,y) * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(6157(a,1),10733(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6157 10733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10741">
    <literal><![CDATA[
      L(K(T(T(x,y),z * y),u),y,z) * w = K(x,(z * y) / (z * (u \ y))) * w
    ]]></literal>
    <justification jstring="[hyper(373,a,6156,a(flip),b,10739,a),flip(a)].">
      <j1 rule="hyper" parents="373 6156 10739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10742">
    <literal><![CDATA[
      L(K(x,T(T(y,z * u),u)),u,z) * w = K(x,(z * u) / (z * (y \ u))) * w
    ]]></literal>
    <justification jstring="[para(7901(a,1),10741(a,1,1,1))].">
      <j1 rule="para" parents="7901 10741"/>
    </justification>
  </clause>

  <clause id="10743">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) * w = K(z,(x * y) / (x * (u \ y))) * w
    ]]></literal>
    <justification jstring="[para(10738(a,1),10742(a,1,1))].">
      <j1 rule="para" parents="10738 10742"/>
    </justification>
  </clause>

  <clause id="10744">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = K(z,(x * y) / (x * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(141,a,10743,a,b,8,a(flip))].">
      <j1 rule="hyper" parents="141 10743 8"/>
    </justification>
  </clause>

  <clause id="10745">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * (K(x,u) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10721,a(flip),b,10744,a),flip(a)].">
      <j1 rule="hyper" parents="64 10721 10744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10746">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * z) = y * (K(x,u) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,10744,a(flip),b,10721,a(flip))].">
      <j1 rule="hyper" parents="144 10744 10721"/>
    </justification>
  </clause>

  <clause id="10747">
    <literal><![CDATA[
      K(x,((y * x) * z) / ((y * x) * (y \ z))) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,y * x) = u
    ]]></literal>
    <justification jstring="[para(10745(a,2),9919(a,1))].">
      <j1 rule="para" parents="10745 9919"/>
    </justification>
  </clause>

  <clause id="10748">
    <literal><![CDATA[
      K(x,T(y,z)) * (y * u) = y * (K(x,T(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(2417(a,1),10746(a,1,1,2))].">
      <j1 rule="para" parents="2417 10746"/>
    </justification>
  </clause>

  <clause id="10749">
    <literal><![CDATA[
      K(x,((y * x) * z) / (x * (y * (y \ z)))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(10747,a,10067,a),flip(a)].">
      <j1 rule="hyper" parents="10747 10067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10750">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,((y * x) * z) / (x * z))
    ]]></literal>
    <justification jstring="[para(10(a,1),10749(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 10749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10751">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[para(20(a,2),10750(a,2,2))].">
      <j1 rule="para" parents="20 10750"/>
    </justification>
  </clause>

  <clause id="10753">
    <literal><![CDATA[
      R(K(x,y),z,T(y * x,z)) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(9923,a,10751,a)].">
      <j1 rule="hyper" parents="9923 10751"/>
    </justification>
  </clause>

  <clause id="10754">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10586,a(flip),b,10751,a),flip(a)].">
      <j1 rule="hyper" parents="64 10586 10751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10755">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(5980,a,10754,a)].">
      <j1 rule="hyper" parents="5980 10754"/>
    </justification>
  </clause>

  <clause id="10758">
    <literal><![CDATA[
      T(x,R(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,10754,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 10754 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10759">
    <literal><![CDATA[
      K(R(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9720,a,b,10754,a)].">
      <j1 rule="hyper" parents="64 9720 10754"/>
    </justification>
  </clause>

  <clause id="10760">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9429,a(flip),b,10754,a)].">
      <j1 rule="hyper" parents="64 9429 10754"/>
    </justification>
  </clause>

  <clause id="10761">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(31(a,1),10754(a,1,2))].">
      <j1 rule="para" parents="31 10754"/>
    </justification>
  </clause>

  <clause id="10762">
    <literal><![CDATA[
      T(R(x,y,z),(u * (y * z)) / ((x * y) * z)) = T(R(x,y,z),u / R(x,y,z))
    ]]></literal>
    <justification jstring="[para(687(a,1),10758(a,1,2))].">
      <j1 rule="para" parents="687 10758"/>
    </justification>
  </clause>

  <clause id="10764">
    <literal><![CDATA[
      K(x / (y * z),z) = K(z \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10639,a(flip),b,10759,a)].">
      <j1 rule="hyper" parents="64 10639 10759"/>
    </justification>
  </clause>

  <clause id="10765">
    <literal><![CDATA[
      K(x,y) * ((x * y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,10759,a(flip),b,7356,a)].">
      <j1 rule="hyper" parents="144 10759 7356"/>
    </justification>
  </clause>

  <clause id="10766">
    <literal><![CDATA[
      K(x / (1 / y),1 / y) = K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[para(674(a,1),10759(a,1,1)),flip(a)].">
      <j1 rule="para" parents="674 10759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10767">
    <literal><![CDATA[
      K(x,y) / R(x,y,y \ 1) = 1 / ((y * x) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(10759(a,1),6451(a,1,1))].">
      <j1 rule="para" parents="10759 6451"/>
    </justification>
  </clause>

  <clause id="10768">
    <literal><![CDATA[
      K(x,R(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10755(a,2),5977(a,1))].">
      <j1 rule="para" parents="10755 5977"/>
    </justification>
  </clause>

  <clause id="10769">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(9084(a,2),10768(a,1))].">
      <j1 rule="para" parents="9084 10768"/>
    </justification>
  </clause>

  <clause id="10771">
    <literal><![CDATA[
      L(K(x,y),z,y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10751(a,2),10768(a,1))].">
      <j1 rule="para" parents="10751 10768"/>
    </justification>
  </clause>

  <clause id="10772">
    <literal><![CDATA[
      K(x,y / (x * z)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(10610,a,10760,a)].">
      <j1 rule="hyper" parents="10610 10760"/>
    </justification>
  </clause>

  <clause id="10774">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8688,a,b,10760,a)].">
      <j1 rule="hyper" parents="64 8688 10760"/>
    </justification>
  </clause>

  <clause id="10775">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,10066,a(flip),b,10760,a)].">
      <j1 rule="hyper" parents="64 10066 10760"/>
    </justification>
  </clause>

  <clause id="10776">
    <literal><![CDATA[
      K(x / (y * z),y) = K(y \ (x / z),y)
    ]]></literal>
    <justification jstring="[hyper(10612,a,10764,a)].">
      <j1 rule="hyper" parents="10612 10764"/>
    </justification>
  </clause>

  <clause id="10778">
    <literal><![CDATA[
      K(x \ (y \ z),x) * z = z * K(x \ (z / y),x)
    ]]></literal>
    <justification jstring="[para(10764(a,1),10224(a,2,2))].">
      <j1 rule="para" parents="10764 10224"/>
    </justification>
  </clause>

  <clause id="10779">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10583(a,1),10771(a,1))].">
      <j1 rule="para" parents="10583 10771"/>
    </justification>
  </clause>

  <clause id="10780">
    <literal><![CDATA[
      K(x,T((y * x) \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ (y \ z),u)) = w
    ]]></literal>
    <justification jstring="[para(708(a,1),10779(a,1,2))].">
      <j1 rule="para" parents="708 10779"/>
    </justification>
  </clause>

  <clause id="10781">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = u
    ]]></literal>
    <justification jstring="[para(9107(a,1),10779(a,1))].">
      <j1 rule="para" parents="9107 10779"/>
    </justification>
  </clause>

  <clause id="10782">
    <literal><![CDATA[
      x * K(x,x \ (y / (z * u))) = T(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(10772(a,1),10070(a,1,2))].">
      <j1 rule="para" parents="10772 10070"/>
    </justification>
  </clause>

  <clause id="10783">
    <literal><![CDATA[
      K(x,x \ ((x * y) / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(9(a,1),10774(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 10774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10784">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(x \ (y / z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8900,a,b,10776,a)].">
      <j1 rule="hyper" parents="64 8900 10776"/>
    </justification>
  </clause>

  <clause id="10785">
    <literal><![CDATA[
      K(x,x \ ((y \ 1) \ (x * z))) = K(x,z / T(y \ 1,y * (x * z)))
    ]]></literal>
    <justification jstring="[para(4915(a,1),10783(a,1,2,2))].">
      <j1 rule="para" parents="4915 10783"/>
    </justification>
  </clause>

  <clause id="10786">
    <literal><![CDATA[
      K(x \ (y / z),x) * z = z * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(10784(a,1),7457(a,1,1))].">
      <j1 rule="para" parents="10784 7457"/>
    </justification>
  </clause>

  <clause id="10787">
    <literal><![CDATA[
      R(K(x,R(y,x,z)),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9717,a,b,10761,a)].">
      <j1 rule="hyper" parents="64 9717 10761"/>
    </justification>
  </clause>

  <clause id="10788">
    <literal><![CDATA[
      K(x,R(y,x,z)) * ((y * x) * z) = (K(x,y) * z) * T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,10753,a(flip),b,264,a)].">
      <j1 rule="hyper" parents="144 10753 264"/>
    </justification>
  </clause>

  <clause id="10789">
    <literal><![CDATA[
      ((x * y) / x) \ ((y * x) * z) = y \ ((T(y,x) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,10765,a(flip),b,5809,a),flip(a)].">
      <j1 rule="hyper" parents="139 10765 5809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10790">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = y * K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[para(10766(a,1),6122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10766 6122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10791">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) * y,1 / y)
    ]]></literal>
    <justification jstring="[para(10766(a,1),9607(a,2,2))].">
      <j1 rule="para" parents="10766 9607"/>
    </justification>
  </clause>

  <clause id="10792">
    <literal><![CDATA[
      K((x * y) \ (z \ ((x * y) * u)),L(z,y,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(z,y,x) \ u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(10649(a,1),10781(a,1))].">
      <j1 rule="para" parents="10649 10781"/>
    </justification>
  </clause>

  <clause id="10793">
    <literal><![CDATA[
      K(x,x \ (y / ((x \ z) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9351,a(flip),b,10775,a),flip(a)].">
      <j1 rule="hyper" parents="64 9351 10775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10794">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(7955,a,10786,a)].">
      <j1 rule="hyper" parents="7955 10786"/>
    </justification>
  </clause>

  <clause id="10795">
    <literal><![CDATA[
      K(x \ (y / z),T(x,y)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9820,a(flip),b,10794,a)].">
      <j1 rule="hyper" parents="64 9820 10794"/>
    </justification>
  </clause>

  <clause id="10796">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = (u * K(z \ (x \ y),x)) \ u
    ]]></literal>
    <justification jstring="[para(10795(a,1),6882(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10795 6882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10797">
    <literal><![CDATA[
      x / T(1 / y,x * y) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[hyper(36,a,6311,a,b,10790,a)].">
      <j1 rule="hyper" parents="36 6311 10790"/>
    </justification>
  </clause>

  <clause id="10798">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[para(6699(a,1),10790(a,2,2))].">
      <j1 rule="para" parents="6699 10790"/>
    </justification>
  </clause>

  <clause id="10799">
    <literal><![CDATA[
      (x / y) / T(1 / y,x) = (1 / y) \ (x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),10797(a,1,2,2))].">
      <j1 rule="para" parents="12 10797"/>
    </justification>
  </clause>

  <clause id="10800">
    <literal><![CDATA[
      ((x / y) / (1 / y)) / T(1 / (1 / y),y \ x) = (1 / (1 / y)) \ ((x / y) / (1 / y))
    ]]></literal>
    <justification jstring="[para(7505(a,1),10799(a,1,2))].">
      <j1 rule="para" parents="7505 10799"/>
    </justification>
  </clause>

  <clause id="10801">
    <literal><![CDATA[
      K(x,(x * y) / (z * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10783,a(flip),b,10793,a),flip(a)].">
      <j1 rule="hyper" parents="64 10783 10793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10802">
    <literal><![CDATA[
      K(x,y / ((x \ z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z * u) / y) \ x) = w
    ]]></literal>
    <justification jstring="[para(10801(a,1),9736(a,1))].">
      <j1 rule="para" parents="10801 9736"/>
    </justification>
  </clause>

  <clause id="10803">
    <literal><![CDATA[
      1 / ((x * (L(x,y,z) \ 1)) * (x \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4946,a(flip),b,10767,a),flip(a)].">
      <j1 rule="hyper" parents="64 4946 10767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10805">
    <literal><![CDATA[
      1 / ((L(x,y,z) \ x) * (x \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1846(a,1),10803(a,1,2,1))].">
      <j1 rule="para" parents="1846 10803"/>
    </justification>
  </clause>

  <clause id="10806">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,10805,a),flip(a)].">
      <j1 rule="hyper" parents="215 10805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10807">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(x,y,z) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(149,a,10806,a)].">
      <j1 rule="hyper" parents="149 10806"/>
    </justification>
  </clause>

  <clause id="10808">
    <literal><![CDATA[
      T(x,y / ((x * z) * u)) = T(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(5767,a,10782,a),flip(a)].">
      <j1 rule="hyper" parents="5767 10782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10809">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,6882,a(flip),b,10796,a),flip(a)].">
      <j1 rule="hyper" parents="373 6882 10796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10810">
    <literal><![CDATA[
      K(x,T(x \ (y / z),y)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(8019,a,10809,a)].">
      <j1 rule="hyper" parents="8019 10809"/>
    </justification>
  </clause>

  <clause id="10811">
    <literal><![CDATA[
      K(x \ (y / z),x) \ y = y * K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(10809(a,1),7436(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10809 7436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10812">
    <literal><![CDATA[
      K(x,(y \ z) \ (x \ z)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),10810(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 10810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10813">
    <literal><![CDATA[
      K(x,T(x \ (y \ z),y)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[hyper(10780,a,8288,a)].">
      <j1 rule="hyper" parents="10780 8288"/>
    </justification>
  </clause>

  <clause id="10814">
    <literal><![CDATA[
      K(x,T(x \ (y \ z),y)) = K(x,x \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(373,a,10760,a(flip),b,10813,a),flip(a)].">
      <j1 rule="hyper" parents="373 10760 10813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10815">
    <literal><![CDATA[
      K(T(x,y),x \ (y \ z)) = K(x,x \ (z / y))
    ]]></literal>
    <justification jstring="[hyper(7970,a,10814,a)].">
      <j1 rule="hyper" parents="7970 10814"/>
    </justification>
  </clause>

  <clause id="10816">
    <literal><![CDATA[
      K(x,x \ ((y * z) / y)) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),10814(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 10814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10817">
    <literal><![CDATA[
      K(T(x,y),x \ (y \ z)) = (u * K(x \ (z / y),x)) \ u
    ]]></literal>
    <justification jstring="[hyper(373,a,6882,a,b,10815,a),flip(a)].">
      <j1 rule="hyper" parents="373 6882 10815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10818">
    <literal><![CDATA[
      T((T(x,y) \ z) / ((T(x,y) \ z) / y),x) = T(y,x) * K(y \ (z / x),y)
    ]]></literal>
    <justification jstring="[hyper(10050,a,10817,a)].">
      <j1 rule="hyper" parents="10050 10817"/>
    </justification>
  </clause>

  <clause id="10819">
    <literal><![CDATA[
      R(K(x,y),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[para(10754(a,1),10787(a,1,1))].">
      <j1 rule="para" parents="10754 10787"/>
    </justification>
  </clause>

  <clause id="10821">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * (K(x,y) * x)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,9724,a(flip),b,10788,a),flip(a)].">
      <j1 rule="hyper" parents="64 9724 10788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10822">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(5848(a,1),10821(a,2,1))].">
      <j1 rule="para" parents="5848 10821"/>
    </justification>
  </clause>

  <clause id="10823">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,9883,a(flip),b,10822,a)].">
      <j1 rule="hyper" parents="64 9883 10822"/>
    </justification>
  </clause>

  <clause id="10824">
    <literal><![CDATA[
      (x * y) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,10822,a(flip),b,9883,a(flip))].">
      <j1 rule="hyper" parents="139 10822 9883"/>
    </justification>
  </clause>

  <clause id="10825">
    <literal><![CDATA[
      L(x,K(y,z),z * y) = x
    ]]></literal>
    <justification jstring="[hyper(1078,a,10823,a)].">
      <j1 rule="hyper" parents="1078 10823"/>
    </justification>
  </clause>

  <clause id="10826">
    <literal><![CDATA[
      K(x,y) \ ((y * x) \ z) = (x * y) \ z
    ]]></literal>
    <justification jstring="[hyper(757,a,10823,a),flip(a)].">
      <j1 rule="hyper" parents="757 10823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10827">
    <literal><![CDATA[
      (x * y) \ T(y * x,z) = K(y,x) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,5753,a,b,10823,a)].">
      <j1 rule="hyper" parents="139 5753 10823"/>
    </justification>
  </clause>

  <clause id="10828">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,6852,a(flip),b,10823,a)].">
      <j1 rule="hyper" parents="139 6852 10823"/>
    </justification>
  </clause>

  <clause id="10829">
    <literal><![CDATA[
      (x * y) \ (((y \ 1) \ x) \ (y * x)) = K(y,x) * (((y \ 1) \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,2955,a(flip),b,10823,a)].">
      <j1 rule="hyper" parents="139 2955 10823"/>
    </justification>
  </clause>

  <clause id="10830">
    <literal><![CDATA[
      (x * y) \ ((y * z) * (z \ x)) = K(y,x) * a(y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,957,a(flip),b,10823,a)].">
      <j1 rule="hyper" parents="139 957 10823"/>
    </justification>
  </clause>

  <clause id="10831">
    <literal><![CDATA[
      ((x \ y) * x) \ (y * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,167,a(flip),b,10823,a)].">
      <j1 rule="hyper" parents="139 167 10823"/>
    </justification>
  </clause>

  <clause id="10832">
    <literal><![CDATA[
      ((x * y) * z) \ ((z * x) * y) = K(z,x * y) * a(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,88,a(flip),b,10823,a)].">
      <j1 rule="hyper" parents="139 88 10823"/>
    </justification>
  </clause>

  <clause id="10833">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,10823,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 10823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10834">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,10589,a,b,10823,a)].">
      <j1 rule="hyper" parents="64 10589 10823"/>
    </justification>
  </clause>

  <clause id="10835">
    <literal><![CDATA[
      K(x,y) \ ((x * y) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,10823,a(flip),b,10589,a)].">
      <j1 rule="hyper" parents="139 10823 10589"/>
    </justification>
  </clause>

  <clause id="10837">
    <literal><![CDATA[
      (x * (y * z)) \ (x * ((z * y) * u)) = L(K(z,y) * u,y * z,x)
    ]]></literal>
    <justification jstring="[para(10823(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10823 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10839">
    <literal><![CDATA[
      (x * y) * (y \ K(y,x)) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(4097(a,1),10823(a,1,2))].">
      <j1 rule="para" parents="4097 10823"/>
    </justification>
  </clause>

  <clause id="10840">
    <literal><![CDATA[
      (x * y) * (T(x,y) \ z) = (y * x) * (x \ z)
    ]]></literal>
    <justification jstring="[para(6075(a,1),10823(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6075 10823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10841">
    <literal><![CDATA[
      K(((x * y) * z) / (y * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y) * z,T(u,y * x)) = w
    ]]></literal>
    <justification jstring="[para(10823(a,1),8285(a,1,1,1))].">
      <j1 rule="para" parents="10823 8285"/>
    </justification>
  </clause>

  <clause id="10842">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,T(x,z)) * u) = (z * K(x,y)) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(8839(a,1),10823(a,1,2))].">
      <j1 rule="para" parents="8839 10823"/>
    </justification>
  </clause>

  <clause id="10843">
    <literal><![CDATA[
      K(x,x \ y) * (y \ z) = ((x \ y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(145,a,174,a(flip),b,10826,a)].">
      <j1 rule="hyper" parents="145 174 10826"/>
    </justification>
  </clause>

  <clause id="10844">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) = x * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,10826,a(flip),b,6221,a),flip(a)].">
      <j1 rule="hyper" parents="145 10826 6221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10845">
    <literal><![CDATA[
      K(x \ y,x) \ (y \ z) = ((x \ y) * x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),10826(a,1,2,1))].">
      <j1 rule="para" parents="10 10826"/>
    </justification>
  </clause>

  <clause id="10846">
    <literal><![CDATA[
      K(x,y) \ K(y * x,z) = (x * y) \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(5726(a,2),10826(a,1,2))].">
      <j1 rule="para" parents="5726 10826"/>
    </justification>
  </clause>

  <clause id="10847">
    <literal><![CDATA[
      ((x * y) \ z) * L(u,(y * x) \ z,K(y,x)) = K(y,x) * (((y * x) \ z) * u)
    ]]></literal>
    <justification jstring="[para(10826(a,1),6182(a,1,1))].">
      <j1 rule="para" parents="10826 6182"/>
    </justification>
  </clause>

  <clause id="10848">
    <literal><![CDATA[
      T((x * y) \ z,K(y,x)) = ((y * x) \ z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(10826(a,1),7806(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10826 7806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10849">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((y * x) \ z) = u
    ]]></literal>
    <justification jstring="[para(10833(a,1),6296(a,1,2))].">
      <j1 rule="para" parents="10833 6296"/>
    </justification>
  </clause>

  <clause id="10850">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(759,a,10834,a)].">
      <j1 rule="hyper" parents="759 10834"/>
    </justification>
  </clause>

  <clause id="10851">
    <literal><![CDATA[
      K(x,y) * (z * (y * x)) = (x * y) * T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(737,a,10834,a)].">
      <j1 rule="hyper" parents="737 10834"/>
    </justification>
  </clause>

  <clause id="10852">
    <literal><![CDATA[
      (x * y) \ K(x,y) = (y * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(721,a,10834,a)].">
      <j1 rule="hyper" parents="721 10834"/>
    </justification>
  </clause>

  <clause id="10853">
    <literal><![CDATA[
      (x * y) * ((y * x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(397,a,10834,a),flip(a)].">
      <j1 rule="hyper" parents="397 10834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10854">
    <literal><![CDATA[
      K(x,y * z) \ ((x * y) * z) = ((y * z) * x) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,88,a(flip),b,10834,a)].">
      <j1 rule="hyper" parents="139 88 10834"/>
    </justification>
  </clause>

  <clause id="10855">
    <literal><![CDATA[
      T(x,y) * ((y * x) * z) = x * ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,10834,a(flip),b,6155,a)].">
      <j1 rule="hyper" parents="145 10834 6155"/>
    </justification>
  </clause>

  <clause id="10856">
    <literal><![CDATA[
      K(x,y) * (x \ ((y * x) * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,10834,a(flip),b,6133,a),flip(a)].">
      <j1 rule="hyper" parents="139 10834 6133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10857">
    <literal><![CDATA[
      T(x,y) \ ((x * y) * z) = x \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,10834,a(flip),b,5810,a),flip(a)].">
      <j1 rule="hyper" parents="139 10834 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10858">
    <literal><![CDATA[
      K(x \ y,x) * (y * z) = ((x \ y) * x) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),10834(a,1,2,1))].">
      <j1 rule="para" parents="10 10834"/>
    </justification>
  </clause>

  <clause id="10859">
    <literal><![CDATA[
      K(x,y) * R(y,x,x \ 1) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(297(a,1),10834(a,1,2))].">
      <j1 rule="para" parents="297 10834"/>
    </justification>
  </clause>

  <clause id="10860">
    <literal><![CDATA[
      K(x,y) * ((y * (x / z)) * z) = (x * y) * a(y,x / z,z)
    ]]></literal>
    <justification jstring="[para(958(a,1),10834(a,1,2))].">
      <j1 rule="para" parents="958 10834"/>
    </justification>
  </clause>

  <clause id="10861">
    <literal><![CDATA[
      K(x,(x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * x) * z) = u
    ]]></literal>
    <justification jstring="[para(10834(a,1),8563(a,1,2))].">
      <j1 rule="para" parents="10834 8563"/>
    </justification>
  </clause>

  <clause id="10862">
    <literal><![CDATA[
      K(x \ ((y * z) * u),z) = K(x \ ((z * y) * u),z)
    ]]></literal>
    <justification jstring="[para(10834(a,1),8915(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10834 8915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10863">
    <literal><![CDATA[
      K(x,y \ ((x * z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((z * x) * u)) = w
    ]]></literal>
    <justification jstring="[para(10834(a,1),8929(a,1,2,2))].">
      <j1 rule="para" parents="10834 8929"/>
    </justification>
  </clause>

  <clause id="10865">
    <literal><![CDATA[
      ((x \ y) * x) \ 1 = y \ K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(402,a,10852,a),flip(a)].">
      <j1 rule="hyper" parents="402 10852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10866">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ K(x,K(y,z)) = (K(y \ 1,z) * x) \ 1
    ]]></literal>
    <justification jstring="[para(9009(a,1),10852(a,1,2))].">
      <j1 rule="para" parents="9009 10852"/>
    </justification>
  </clause>

  <clause id="10867">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(7350,a,10835,a)].">
      <j1 rule="hyper" parents="7350 10835"/>
    </justification>
  </clause>

  <clause id="10868">
    <literal><![CDATA[
      L(K(x,y),y * x,z) \ ((x * y) * u) = (y * x) * u
    ]]></literal>
    <justification jstring="[para(10179(a,2),10835(a,1,1))].">
      <j1 rule="para" parents="10179 10835"/>
    </justification>
  </clause>

  <clause id="10869">
    <literal><![CDATA[
      (K(x,y) * (x * y)) \ z = (x * y) \ (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(7120,a,10867,a),flip(a)].">
      <j1 rule="hyper" parents="7120 10867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10870">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(10867(a,1),51(a,2))].">
      <j1 rule="para" parents="10867 51"/>
    </justification>
  </clause>

  <clause id="10871">
    <literal><![CDATA[
      x \ (K(y,y \ x) * z) = ((y \ x) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(402,a,10850,a)].">
      <j1 rule="hyper" parents="402 10850"/>
    </justification>
  </clause>

  <clause id="10872">
    <literal><![CDATA[
      (x * R(y,x,z)) \ (K(x,R(y,x,z)) * ((y * x) * z)) = L(z,x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,656,a(flip),b,10850,a),flip(a)].">
      <j1 rule="hyper" parents="373 656 10850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10873">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,174,a(flip),b,10850,a)].">
      <j1 rule="hyper" parents="145 174 10850"/>
    </justification>
  </clause>

  <clause id="10874">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * z) = (y * x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(5755(a,1),10850(a,1,2))].">
      <j1 rule="para" parents="5755 10850"/>
    </justification>
  </clause>

  <clause id="10875">
    <literal><![CDATA[
      (x * y) * ((y * x) \ (K(x,y) * z)) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,10360,a(flip),b,10853,a),flip(a)].">
      <j1 rule="hyper" parents="373 10360 10853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10876">
    <literal><![CDATA[
      (x * (y * L(x,z,u))) \ ((y * L(x,z,u)) * T(x,y)) = x \ R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,9527,a(flip),b,10828,a),flip(a)].">
      <j1 rule="hyper" parents="373 9527 10828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10877">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,x / y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4765,a(flip),b,10828,a),flip(a)].">
      <j1 rule="hyper" parents="64 4765 10828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10878">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (u * L(T(x,w),y,z)) = K(u,L(x,y,z)) * K(L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(25(a,2),10828(a,1,2,2))].">
      <j1 rule="para" parents="25 10828"/>
    </justification>
  </clause>

  <clause id="10879">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(10828(a,2),3325(a,1))].">
      <j1 rule="para" parents="10828 3325"/>
    </justification>
  </clause>

  <clause id="10880">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6518,a,b,10877,a)].">
      <j1 rule="hyper" parents="64 6518 10877"/>
    </justification>
  </clause>

  <clause id="10881">
    <literal><![CDATA[
      a(x,y / x,x) \ K(y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(10877(a,1),6882(a,1,1))].">
      <j1 rule="para" parents="10877 6882"/>
    </justification>
  </clause>

  <clause id="10882">
    <literal><![CDATA[
      a(x,(x * y) / x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),10880(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 10880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10883">
    <literal><![CDATA[
      x \ R(x,T(y,x),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(256(a,1),10882(a,1,2)),flip(a)].">
      <j1 rule="para" parents="256 10882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10884">
    <literal><![CDATA[
      x \ R(x,y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(4788(a,1),10883(a,1,2))].">
      <j1 rule="para" parents="4788 10883"/>
    </justification>
  </clause>

  <clause id="10885">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9546,a,10884,a),flip(a)].">
      <j1 rule="hyper" parents="9546 10884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10886">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6509,a,10884,a)].">
      <j1 rule="hyper" parents="6509 10884"/>
    </justification>
  </clause>

  <clause id="10887">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(6495,a,10884,a)].">
      <j1 rule="hyper" parents="6495 10884"/>
    </justification>
  </clause>

  <clause id="10888">
    <literal><![CDATA[
      R(x,y,x) / x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2087,a,10884,a)].">
      <j1 rule="hyper" parents="2087 10884"/>
    </justification>
  </clause>

  <clause id="10889">
    <literal><![CDATA[
      x * a(x,y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(157,a,10884,a)].">
      <j1 rule="hyper" parents="157 10884"/>
    </justification>
  </clause>

  <clause id="10890">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9483,a,b,10884,a)].">
      <j1 rule="hyper" parents="64 9483 10884"/>
    </justification>
  </clause>

  <clause id="10891">
    <literal><![CDATA[
      L(x,y,x) \ x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8768,a,b,10884,a)].">
      <j1 rule="hyper" parents="64 8768 10884"/>
    </justification>
  </clause>

  <clause id="10892">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8531,a,b,10884,a)].">
      <j1 rule="hyper" parents="64 8531 10884"/>
    </justification>
  </clause>

  <clause id="10893">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6518,a(flip),b,10884,a)].">
      <j1 rule="hyper" parents="64 6518 10884"/>
    </justification>
  </clause>

  <clause id="10894">
    <literal><![CDATA[
      x / a(x,y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(225,a,10884,a(flip),b,8768,a)].">
      <j1 rule="hyper" parents="225 10884 8768"/>
    </justification>
  </clause>

  <clause id="10895">
    <literal><![CDATA[
      L(x,y,x) * a(x,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,10884,a(flip),b,8768,a)].">
      <j1 rule="hyper" parents="145 10884 8768"/>
    </justification>
  </clause>

  <clause id="10896">
    <literal><![CDATA[
      T(x,y) * a(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,10884,a(flip),b,7493,a)].">
      <j1 rule="hyper" parents="145 10884 7493"/>
    </justification>
  </clause>

  <clause id="10897">
    <literal><![CDATA[
      a(x,y,x) * L(x,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,10884,a(flip),b,8769,a)].">
      <j1 rule="hyper" parents="144 10884 8769"/>
    </justification>
  </clause>

  <clause id="10898">
    <literal><![CDATA[
      a(x,y,x) * x = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,10884,a(flip),b,2071,a)].">
      <j1 rule="hyper" parents="144 10884 2071"/>
    </justification>
  </clause>

  <clause id="10899">
    <literal><![CDATA[
      a(x,y,x) != x \ z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(10884(a,1),48(a,1))].">
      <j1 rule="para" parents="10884 48"/>
    </justification>
  </clause>

  <clause id="10900">
    <literal><![CDATA[
      L(x \ a(y,z,y),x,y) = (y * x) \ R(y,z,y)
    ]]></literal>
    <justification jstring="[para(10884(a,1),346(a,1,1,2))].">
      <j1 rule="para" parents="10884 346"/>
    </justification>
  </clause>

  <clause id="10902">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(10884(a,1),6884(a,1,1))].">
      <j1 rule="para" parents="10884 6884"/>
    </justification>
  </clause>

  <clause id="10903">
    <literal><![CDATA[
      T(x * y,x) / x = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(10884(a,1),7023(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10884 7023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10904">
    <literal><![CDATA[
      a(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(10884(a,1),6495(a,1))].">
      <j1 rule="para" parents="10884 6495"/>
    </justification>
  </clause>

  <clause id="10905">
    <literal><![CDATA[
      a(x,y,x) \ x = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(10884(a,1),8770(a,1,1))].">
      <j1 rule="para" parents="10884 8770"/>
    </justification>
  </clause>

  <clause id="10906">
    <literal><![CDATA[
      a(x \ y,z,x \ y) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(10884(a,1),10137(a,1,1))].">
      <j1 rule="para" parents="10884 10137"/>
    </justification>
  </clause>

  <clause id="10907">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = R(a(y,z,y),y,x)
    ]]></literal>
    <justification jstring="[para(10888(a,1),10237(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10888 10237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10908">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(10889(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="10889 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10909">
    <literal><![CDATA[
      x / a(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(10891(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="10891 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10910">
    <literal><![CDATA[
      L(x \ a(y,z,y),x,L(y,z,y)) = (L(y,z,y) * x) \ y
    ]]></literal>
    <justification jstring="[para(10891(a,1),346(a,1,1,2))].">
      <j1 rule="para" parents="10891 346"/>
    </justification>
  </clause>

  <clause id="10911">
    <literal><![CDATA[
      a(x,y,x) \ 1 = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[para(10891(a,1),5658(a,1,1))].">
      <j1 rule="para" parents="10891 5658"/>
    </justification>
  </clause>

  <clause id="10912">
    <literal><![CDATA[
      L(x,y,x) != x / z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(10894(a,1),46(a,1))].">
      <j1 rule="para" parents="10894 46"/>
    </justification>
  </clause>

  <clause id="10913">
    <literal><![CDATA[
      L(a((x \ 1) \ y,z,(x \ 1) \ y) \ ((x \ 1) \ y),x,x) = L(x * y,z,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(10905(a,2),1143(a,1,1))].">
      <j1 rule="para" parents="10905 1143"/>
    </justification>
  </clause>

  <clause id="10914">
    <literal><![CDATA[
      K(x,x * y) * a(x,y,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6187,a,10886,a)].">
      <j1 rule="hyper" parents="6187 10886"/>
    </justification>
  </clause>

  <clause id="10915">
    <literal><![CDATA[
      a(x,y,x) * (K(x,x * y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,10886,a(flip),b,10001,a)].">
      <j1 rule="hyper" parents="144 10886 10001"/>
    </justification>
  </clause>

  <clause id="10916">
    <literal><![CDATA[
      a(x,y,x) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(10886(a,1),6882(a,1,1))].">
      <j1 rule="para" parents="10886 6882"/>
    </justification>
  </clause>

  <clause id="10917">
    <literal><![CDATA[
      a(x,y,x) * K(x,x * y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(10886(a,1),6891(a,1,1))].">
      <j1 rule="para" parents="10886 6891"/>
    </justification>
  </clause>

  <clause id="10918">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(10886(a,1),9804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10886 9804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10919">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(6187,a,10887,a)].">
      <j1 rule="hyper" parents="6187 10887"/>
    </justification>
  </clause>

  <clause id="10920">
    <literal><![CDATA[
      a(x,y,x) \ K(x,y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(10887(a,1),6882(a,1,1))].">
      <j1 rule="para" parents="10887 6882"/>
    </justification>
  </clause>

  <clause id="10921">
    <literal><![CDATA[
      (x / y) * a(y,z,y) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(10887(a,1),10372(a,1,2))].">
      <j1 rule="para" parents="10887 10372"/>
    </justification>
  </clause>

  <clause id="10922">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(6897,a,10892,a)].">
      <j1 rule="hyper" parents="6897 10892"/>
    </justification>
  </clause>

  <clause id="10923">
    <literal><![CDATA[
      K(x * y,y) * (K(y,x) * z) = a(y,x,y) * z
    ]]></literal>
    <justification jstring="[para(10892(a,1),9804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10892 9804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10924">
    <literal><![CDATA[
      a(x,y \ 1,x) \ K(y \ x,x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,8529,a(flip),b,10902,a)].">
      <j1 rule="hyper" parents="139 8529 10902"/>
    </justification>
  </clause>

  <clause id="10925">
    <literal><![CDATA[
      a(1 / ((x * y) \ x),T(z,y),1 / ((x * y) \ x)) * K(T(z,y),1 / ((x * y) \ x)) = K(z * (1 / ((x * y) \ x)),1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(6752(a,1),10902(a,2,1))].">
      <j1 rule="para" parents="6752 10902"/>
    </justification>
  </clause>

  <clause id="10926">
    <literal><![CDATA[
      a(T(x,y * z),z,T(x,y * z)) * K(z,T(x,y)) = K(T(x,y * z) * z,T(x,y * z))
    ]]></literal>
    <justification jstring="[para(8031(a,1),10902(a,1,2))].">
      <j1 rule="para" parents="8031 10902"/>
    </justification>
  </clause>

  <clause id="10927">
    <literal><![CDATA[
      R(T(x * y,x) / x,z,u) = R(y,z,u) * a(x,R(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2822,a,b,10903,a)].">
      <j1 rule="hyper" parents="64 2822 10903"/>
    </justification>
  </clause>

  <clause id="10928">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(10(a,1),10903(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 10903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10929">
    <literal><![CDATA[
      T(x * a(y,x,y),y) = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(10903(a,1),117(a,1,1))].">
      <j1 rule="para" parents="10903 117"/>
    </justification>
  </clause>

  <clause id="10930">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * (T(u * L(z,y,x),u) / u)) = L(a(u,L(z,y,x),u),L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(10903(a,2),601(a,1,2,2))].">
      <j1 rule="para" parents="10903 601"/>
    </justification>
  </clause>

  <clause id="10931">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(L(a(u,z,u),z,y),y * z,x) = w
    ]]></literal>
    <justification jstring="[para(10903(a,2),1081(a,1,2,2,2))].">
      <j1 rule="para" parents="10903 1081"/>
    </justification>
  </clause>

  <clause id="10932">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(6353(a,2),10908(a,1))].">
      <j1 rule="para" parents="6353 10908"/>
    </justification>
  </clause>

  <clause id="10933">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),10914(a,1,1,2))].">
      <j1 rule="para" parents="10 10914"/>
    </justification>
  </clause>

  <clause id="10934">
    <literal><![CDATA[
      L(a(x,y,x),K(x,x * y),z) = (z * K(x,x * y)) \ (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(10914(a,1),18(a,2,2,2))].">
      <j1 rule="para" parents="10914 18"/>
    </justification>
  </clause>

  <clause id="10935">
    <literal><![CDATA[
      a(x,x \ y,x) * K(x,y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),10917(a,1,2,2))].">
      <j1 rule="para" parents="10 10917"/>
    </justification>
  </clause>

  <clause id="10936">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8516,a,b,10919,a),flip(a)].">
      <j1 rule="hyper" parents="373 8516 10919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10937">
    <literal><![CDATA[
      K(x,y) \ K(x * y,y) = a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,8516,a,b,10919,a)].">
      <j1 rule="hyper" parents="139 8516 10919"/>
    </justification>
  </clause>

  <clause id="10938">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10884,a(flip),b,10885,a),flip(a)].">
      <j1 rule="hyper" parents="373 10884 10885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10939">
    <literal><![CDATA[
      a(x,y * K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(10885(a,2),10908(a,1))].">
      <j1 rule="para" parents="10885 10908"/>
    </justification>
  </clause>

  <clause id="10940">
    <literal><![CDATA[
      a(x,y \ T(z,x),x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(7026(a,1),10938(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7026 10938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10941">
    <literal><![CDATA[
      a(x,x \ y,x) = T(x,y) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,4729,a(flip),b,10896,a),flip(a)].">
      <j1 rule="hyper" parents="139 4729 10896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10942">
    <literal><![CDATA[
      T(x,y) \ T(x,x \ y) = a(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,4685,a(flip),b,10896,a)].">
      <j1 rule="hyper" parents="139 4685 10896"/>
    </justification>
  </clause>

  <clause id="10943">
    <literal><![CDATA[
      (x / y) \ (x / L(y,z,y)) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(149,a,10921,a)].">
      <j1 rule="hyper" parents="149 10921"/>
    </justification>
  </clause>

  <clause id="10944">
    <literal><![CDATA[
      (x * y) / L(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),10921(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 10921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10945">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(3202,a,10944,a)].">
      <j1 rule="hyper" parents="3202 10944"/>
    </justification>
  </clause>

  <clause id="10946">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * y) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(215,a,10944,a)].">
      <j1 rule="hyper" parents="215 10944"/>
    </justification>
  </clause>

  <clause id="10947">
    <literal><![CDATA[
      x * (L(x,y,x) \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7553,a(flip),b,10945,a)].">
      <j1 rule="hyper" parents="64 7553 10945"/>
    </justification>
  </clause>

  <clause id="10948">
    <literal><![CDATA[
      (x * L(y,z,y)) * a(y,z,y) = x * y
    ]]></literal>
    <justification jstring="[para(11(a,1),10945(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 10945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10949">
    <literal><![CDATA[
      ((x * y) * a(T(y,x),z,T(y,x))) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(1296(a,1),10946(a,1,2))].">
      <j1 rule="para" parents="1296 10946"/>
    </justification>
  </clause>

  <clause id="10950">
    <literal><![CDATA[
      (T(x * y,x) / x) \ (y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(10903(a,2),10946(a,1,1))].">
      <j1 rule="para" parents="10903 10946"/>
    </justification>
  </clause>

  <clause id="10951">
    <literal><![CDATA[
      (x \ y) * a(x,z,x) = L(x,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(2346,a,10947,a),flip(a)].">
      <j1 rule="hyper" parents="2346 10947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10952">
    <literal><![CDATA[
      (L(x,y,x) * z) * a(x,y,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(739,a,10947,a),flip(a)].">
      <j1 rule="hyper" parents="739 10947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10953">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8767,a,b,10947,a)].">
      <j1 rule="hyper" parents="64 8767 10947"/>
    </justification>
  </clause>

  <clause id="10954">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = u * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7587,a,b,10947,a)].">
      <j1 rule="hyper" parents="64 7587 10947"/>
    </justification>
  </clause>

  <clause id="10955">
    <literal><![CDATA[
      L(x,y,x) * (z * a(x,y,x)) = x * z
    ]]></literal>
    <justification jstring="[hyper(145,a,10947,a(flip),b,2329,a)].">
      <j1 rule="hyper" parents="145 10947 2329"/>
    </justification>
  </clause>

  <clause id="10956">
    <literal><![CDATA[
      a(x,x \ y,x) * (K(x,y) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,10893,a(flip),b,10001,a)].">
      <j1 rule="hyper" parents="144 10893 10001"/>
    </justification>
  </clause>

  <clause id="10957">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ u,L(x,y,z)) = K(u,L(x,y,z)) * K(L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[para(10479(a,1),10893(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10479 10893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10958">
    <literal><![CDATA[
      a(x,y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9487(a,1),10939(a,1))].">
      <j1 rule="para" parents="9487 10939"/>
    </justification>
  </clause>

  <clause id="10959">
    <literal><![CDATA[
      (T(x * K(y \ x,z),x) / x) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(8196(a,1),10950(a,1,2))].">
      <j1 rule="para" parents="8196 10950"/>
    </justification>
  </clause>

  <clause id="10960">
    <literal><![CDATA[
      (x * K(y \ z,y)) * (T(x / z,(y \ z) * y) \ u) = (((y \ z) * y) * (x / z)) * ((x / z) \ u)
    ]]></literal>
    <justification jstring="[para(10228(a,1),10840(a,1,1))].">
      <j1 rule="para" parents="10228 10840"/>
    </justification>
  </clause>

  <clause id="10961">
    <literal><![CDATA[
      ((x \ y) * x) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ y) * z = u
    ]]></literal>
    <justification jstring="[para(10843(a,1),739(a,1))].">
      <j1 rule="para" parents="10843 739"/>
    </justification>
  </clause>

  <clause id="10962">
    <literal><![CDATA[
      T(x,y) * L(y \ z,y,x) = x * ((y * x) \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,632,a,b,10844,a)].">
      <j1 rule="hyper" parents="64 632 10844"/>
    </justification>
  </clause>

  <clause id="10963">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * ((y * x) \ z)) = w
    ]]></literal>
    <justification jstring="[para(10844(a,2),720(a,1))].">
      <j1 rule="para" parents="10844 720"/>
    </justification>
  </clause>

  <clause id="10964">
    <literal><![CDATA[
      L(x / (y * z),z \ (y * z),z) = (z * (y * ((z * y) \ x))) / (y * z)
    ]]></literal>
    <justification jstring="[para(10844(a,1),1757(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10844 1757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10965">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * (((x * (y * K(x,z))) * K(x,z)) \ u)
    ]]></literal>
    <justification jstring="[para(8179(a,1),10844(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8179 10844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10966">
    <literal><![CDATA[
      K(x \ y,x) * K((x \ y) * x,z) = y \ T((x \ y) * x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5726,a,b,10845,a)].">
      <j1 rule="hyper" parents="145 5726 10845"/>
    </justification>
  </clause>

  <clause id="10967">
    <literal><![CDATA[
      T(x,y \ 1) \ ((x * (1 / y)) * z) = x \ (((1 / y) * x) * z)
    ]]></literal>
    <justification jstring="[para(3870(a,1),10857(a,1,1))].">
      <j1 rule="para" parents="3870 10857"/>
    </justification>
  </clause>

  <clause id="10968">
    <literal><![CDATA[
      T(x,y) \ (y \ ((x * y) * z)) = x \ (y \ ((y * x) * z))
    ]]></literal>
    <justification jstring="[para(10857(a,1),5019(a,1,2))].">
      <j1 rule="para" parents="10857 5019"/>
    </justification>
  </clause>

  <clause id="10969">
    <literal><![CDATA[
      T(x \ ((x * y) * z),K(x,y)) = (x \ ((y * x) * z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(10857(a,1),7809(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10857 7809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10970">
    <literal><![CDATA[
      K(x \ y,x) * (z * y) = ((x \ y) * x) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(737,a,10858,a)].">
      <j1 rule="hyper" parents="737 10858"/>
    </justification>
  </clause>

  <clause id="10971">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * x) * z) = (y / x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,10858,a(flip),b,6370,a)].">
      <j1 rule="hyper" parents="139 10858 6370"/>
    </justification>
  </clause>

  <clause id="10972">
    <literal><![CDATA[
      K((x * T(y,x * y)) \ z,x * y) * (z * u) = (((x * y) \ z) * (x * y)) * u
    ]]></literal>
    <justification jstring="[para(8910(a,2),10858(a,1,1))].">
      <j1 rule="para" parents="8910 10858"/>
    </justification>
  </clause>

  <clause id="10973">
    <literal><![CDATA[
      x * (((y \ x) * y) \ z) != u * w
    ]]></literal>
    <literal><![CDATA[
      (K(y,y \ x) * z) / w = u
    ]]></literal>
    <justification jstring="[para(10871(a,1),392(a,1,2))].">
      <j1 rule="para" parents="10871 392"/>
    </justification>
  </clause>

  <clause id="10974">
    <literal><![CDATA[
      ((x \ y) * x) \ (x \ y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(5720(a,1),10871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5720 10871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10975">
    <literal><![CDATA[
      L(x \ 1,x,x \ y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(472,a,10974,a)].">
      <j1 rule="hyper" parents="472 10974"/>
    </justification>
  </clause>

  <clause id="10976">
    <literal><![CDATA[
      x * L(y \ 1,y,y \ z) = x * (z \ (z / y))
    ]]></literal>
    <justification jstring="[para(10974(a,1),439(a,2,2))].">
      <j1 rule="para" parents="10974 439"/>
    </justification>
  </clause>

  <clause id="10977">
    <literal><![CDATA[
      x \ (x / y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * L(y \ 1,y,y \ x) = u
    ]]></literal>
    <justification jstring="[para(10974(a,1),788(a,1))].">
      <j1 rule="para" parents="10974 788"/>
    </justification>
  </clause>

  <clause id="10979">
    <literal><![CDATA[
      L(T(x,y) \ z,x,y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5030,a(flip),b,10874,a)].">
      <j1 rule="hyper" parents="64 5030 10874"/>
    </justification>
  </clause>

  <clause id="10980">
    <literal><![CDATA[
      L(x,y,z) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[para(9(a,1),10979(a,1,1))].">
      <j1 rule="para" parents="9 10979"/>
    </justification>
  </clause>

  <clause id="10981">
    <literal><![CDATA[
      (x * y) \ (y * (z * T(x,y))) = L(T(z,T(x,y)),x,y)
    ]]></literal>
    <justification jstring="[para(22(a,2),10979(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22 10979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10982">
    <literal><![CDATA[
      L(L(T(x,y),z,u) \ w,L(x,z,u),y) = (L(x,z,u) * y) \ (y * w)
    ]]></literal>
    <justification jstring="[para(25(a,2),10979(a,1,1,1))].">
      <j1 rule="para" parents="25 10979"/>
    </justification>
  </clause>

  <clause id="10983">
    <literal><![CDATA[
      L(L(T(x,y) \ z,u,w),x,y) = L((x * y) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(10979(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10979 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10984">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) \ y = z
    ]]></literal>
    <justification jstring="[para(10979(a,2),341(a,1))].">
      <j1 rule="para" parents="10979 341"/>
    </justification>
  </clause>

  <clause id="10985">
    <literal><![CDATA[
      (x * y) \ (y * (x * z)) = L(K(y,x) * z,x,y)
    ]]></literal>
    <justification jstring="[para(6155(a,1),10979(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6155 10979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10986">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,261,a(flip),b,10980,a)].">
      <j1 rule="hyper" parents="373 261 10980"/>
    </justification>
  </clause>

  <clause id="10987">
    <literal><![CDATA[
      (x * (T(y,x) * z)) / L(z,y,x) = y * x
    ]]></literal>
    <justification jstring="[hyper(225,a,10980,a,b,xx)].">
      <j1 rule="hyper" parents="225 10980"/>
    </justification>
  </clause>

  <clause id="10988">
    <literal><![CDATA[
      (x \ y) * (T(x,x \ y) * z) = y * L(z,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,10980,a,b,174,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 10980 174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10989">
    <literal><![CDATA[
      (x * y) * L(z,x,y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,10980,a,b,xx)].">
      <j1 rule="hyper" parents="145 10980"/>
    </justification>
  </clause>

  <clause id="10990">
    <literal><![CDATA[
      x * (T(y,x) * T(z,y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(39,a,121,a,b,10980,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 121 10980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10991">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * (T(y,z) * u))) = L(L(u,y,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(10980(a,2),102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10980 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10992">
    <literal><![CDATA[
      (x * y) \ ((x * y) / (1 / x)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[para(5037(a,2),10980(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5037 10980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10993">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * (K(x,T(y,z)) * u)) = L(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7867(a,2),10980(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7867 10980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10994">
    <literal><![CDATA[
      L(L(x,y,z),u * w,K(w,u)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,10867,a,b,10986,a)].">
      <j1 rule="hyper" parents="373 10867 10986"/>
    </justification>
  </clause>

  <clause id="10995">
    <literal><![CDATA[
      L(x,y \ (z * y),y) = L(x,z,y)
    ]]></literal>
    <justification jstring="[para(22(a,1),10986(a,1,2))].">
      <j1 rule="para" parents="22 10986"/>
    </justification>
  </clause>

  <clause id="10996">
    <literal><![CDATA[
      L(x,y / z,z) = L(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(117(a,1),10986(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 10986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10997">
    <literal><![CDATA[
      L(x,(y \ z) \ z,y \ z) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(116(a,1),10986(a,1,2))].">
      <j1 rule="para" parents="116 10986"/>
    </justification>
  </clause>

  <clause id="10999">
    <literal><![CDATA[
      L((x / y) \ z,y \ x,y) = (y * (x / y)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,10996,a),flip(a)].">
      <j1 rule="hyper" parents="64 102 10996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11000">
    <literal><![CDATA[
      (x * ((y * y) \ z)) * L(u,x / (y * y),z) = z * (T(x / (y * y),z) * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,897,a(flip),b,10987,a)].">
      <j1 rule="hyper" parents="144 897 10987"/>
    </justification>
  </clause>

  <clause id="11001">
    <literal><![CDATA[
      (x \ 1) * (T(y,x \ 1) * (y \ z)) = (y * (x \ 1)) * ((x * y) \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1647,a(flip),b,10989,a),flip(a)].">
      <j1 rule="hyper" parents="64 1647 10989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11002">
    <literal><![CDATA[
      x * (T(y,x) * L(z,x,y)) = y * (x * L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,513,a(flip),b,10989,a),flip(a)].">
      <j1 rule="hyper" parents="64 513 10989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11003">
    <literal><![CDATA[
      x \ (y * (x * L(z,y,x))) = T(y,x) * L(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,513,a(flip),b,10989,a(flip))].">
      <j1 rule="hyper" parents="139 513 10989"/>
    </justification>
  </clause>

  <clause id="11004">
    <literal><![CDATA[
      L(((x \ y) \ y) \ z,x,x \ y) = y \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(743,a,10997,a),flip(a)].">
      <j1 rule="hyper" parents="743 10997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11005">
    <literal><![CDATA[
      a(x,y,x) * (K(x,x * y) * ((x * y) \ z)) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(373,a,10833,a(flip),b,10915,a),flip(a)].">
      <j1 rule="hyper" parents="373 10833 10915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11006">
    <literal><![CDATA[
      K(x,x * y) * (a(x,y,x) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(6187,a,10918,a)].">
      <j1 rule="hyper" parents="6187 10918"/>
    </justification>
  </clause>

  <clause id="11008">
    <literal><![CDATA[
      a(x,y,x) * (K(y,x) * z) = K(x * y,x) * z
    ]]></literal>
    <justification jstring="[para(6161(a,1),10918(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6161 10918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11009">
    <literal><![CDATA[
      K(x * y,y) * (x * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(4534(a,1),10923(a,1,2))].">
      <j1 rule="para" parents="4534 10923"/>
    </justification>
  </clause>

  <clause id="11010">
    <literal><![CDATA[
      K(x,x * y) * (z * a(x,y,x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(6187,a,10953,a)].">
      <j1 rule="hyper" parents="6187 10953"/>
    </justification>
  </clause>

  <clause id="11011">
    <literal><![CDATA[
      a(x,y,x) * z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10918,a(flip),b,10953,a)].">
      <j1 rule="hyper" parents="64 10918 10953"/>
    </justification>
  </clause>

  <clause id="11012">
    <literal><![CDATA[
      T(a(x,y,x),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(269,a,10918,a(flip),b,10953,a(flip))].">
      <j1 rule="hyper" parents="269 10918 10953"/>
    </justification>
  </clause>

  <clause id="11013">
    <literal><![CDATA[
      T(x,a(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(269,a,10953,a(flip),b,10918,a(flip))].">
      <j1 rule="hyper" parents="269 10953 10918"/>
    </justification>
  </clause>

  <clause id="11014">
    <literal><![CDATA[
      x / a(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(8638,a,11013,a),flip(a)].">
      <j1 rule="hyper" parents="8638 11013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11015">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ z = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4722,a,11013,a)].">
      <j1 rule="hyper" parents="4722 11013"/>
    </justification>
  </clause>

  <clause id="11016">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(2159,a,11013,a)].">
      <j1 rule="hyper" parents="2159 11013"/>
    </justification>
  </clause>

  <clause id="11017">
    <literal><![CDATA[
      K(x,a(y,z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(56,a,11013,a)].">
      <j1 rule="hyper" parents="56 11013"/>
    </justification>
  </clause>

  <clause id="11018">
    <literal><![CDATA[
      a(x,y,x) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(11013(a,1),271(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11013 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11019">
    <literal><![CDATA[
      a(x,y,x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(11013(a,1),328(a,1,2))].">
      <j1 rule="para" parents="11013 328"/>
    </justification>
  </clause>

  <clause id="11020">
    <literal><![CDATA[
      T(a(x,y,x),z) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10884,a,b,11012,a),flip(a)].">
      <j1 rule="hyper" parents="373 10884 11012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11021">
    <literal><![CDATA[
      x * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) * x = u
    ]]></literal>
    <justification jstring="[para(11012(a,1),328(a,1,2))].">
      <j1 rule="para" parents="11012 328"/>
    </justification>
  </clause>

  <clause id="11022">
    <literal><![CDATA[
      L(a(x,y,x),z,u) * w = w * L(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11012(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11012 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11023">
    <literal><![CDATA[
      R(a(x,y,x),z,u) * w = w * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11012(a,1),267(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11012 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11025">
    <literal><![CDATA[
      a(x,y,x) * (L(x,y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(373,a,10952,a(flip),b,11011,a),flip(a)].">
      <j1 rule="hyper" parents="373 10952 11011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11026">
    <literal><![CDATA[
      a(x,y,x) * (z / x) = z / L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10921,a(flip),b,11011,a),flip(a)].">
      <j1 rule="hyper" parents="373 10921 11011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11027">
    <literal><![CDATA[
      a(x,y,x) * T(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10896,a(flip),b,11011,a),flip(a)].">
      <j1 rule="hyper" parents="373 10896 11011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11028">
    <literal><![CDATA[
      a(x,x,x) * K(x,y) = T(x,y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6035,a(flip),b,11011,a),flip(a)].">
      <j1 rule="hyper" parents="373 6035 11011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11029">
    <literal><![CDATA[
      a(x,y,x) \ (x * z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,10952,a(flip),b,11011,a)].">
      <j1 rule="hyper" parents="139 10952 11011"/>
    </justification>
  </clause>

  <clause id="11030">
    <literal><![CDATA[
      a(x,y,x) \ (L(x,y,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,10951,a(flip),b,11011,a)].">
      <j1 rule="hyper" parents="139 10951 11011"/>
    </justification>
  </clause>

  <clause id="11031">
    <literal><![CDATA[
      a(x,y,x) \ (z * x) = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,10948,a(flip),b,11011,a)].">
      <j1 rule="hyper" parents="139 10948 11011"/>
    </justification>
  </clause>

  <clause id="11032">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (a(y,z,y) * (u * x)) = R(T(u,x * a(y,z,y)),x,a(y,z,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,11011,a,b,841,a)].">
      <j1 rule="hyper" parents="139 11011 841"/>
    </justification>
  </clause>

  <clause id="11033">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(11011(a,1),290(a,1))].">
      <j1 rule="para" parents="11011 290"/>
    </justification>
  </clause>

  <clause id="11034">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (a(y,z,y) * (u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(u,x),x,a(y,z,y)) = w
    ]]></literal>
    <justification jstring="[para(11011(a,1),1021(a,1,1))].">
      <j1 rule="para" parents="11011 1021"/>
    </justification>
  </clause>

  <clause id="11035">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ (x * (a(z,u,z) * (y * w))) = L(L(w,y,a(z,u,z)),a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[para(11011(a,1),602(a,1,1,2))].">
      <j1 rule="para" parents="11011 602"/>
    </justification>
  </clause>

  <clause id="11036">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ ((x * a(z,u,z)) * (L(y,a(z,u,z),x) * w)) = L(w,L(y,a(z,u,z),x),x * a(z,u,z))
    ]]></literal>
    <justification jstring="[para(11011(a,1),601(a,1,1,2))].">
      <j1 rule="para" parents="11011 601"/>
    </justification>
  </clause>

  <clause id="11037">
    <literal><![CDATA[
      x * (a(x,y,x) \ z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(11016(a,1),10955(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11016 10955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11038">
    <literal><![CDATA[
      T(a(x / y,z,x / y),u) = (x / y) \ R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(10098(a,1),11020(a,2,2))].">
      <j1 rule="para" parents="10098 11020"/>
    </justification>
  </clause>

  <clause id="11040">
    <literal><![CDATA[
      a(x * y,z,x * y) \ (y * x) = L(x * y,z,x * y) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,94,a(flip),b,11025,a)].">
      <j1 rule="hyper" parents="139 94 11025"/>
    </justification>
  </clause>

  <clause id="11041">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,11025,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 11025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11042">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(x / y,z,x / y) * (x / y)
    ]]></literal>
    <justification jstring="[para(7162(a,1),11027(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7162 11027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11044">
    <literal><![CDATA[
      a(x,y,x) \ y = x \ ((x * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(139,a,4725,a,b,11037,a),flip(a)].">
      <j1 rule="hyper" parents="139 4725 11037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11045">
    <literal><![CDATA[
      a(x,x \ y,x) \ y = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,964,a,b,11037,a),flip(a)].">
      <j1 rule="hyper" parents="35 964 11037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11046">
    <literal><![CDATA[
      a(x,x \ y,x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(11041(a,1),1370(a,1))].">
      <j1 rule="para" parents="11041 1370"/>
    </justification>
  </clause>

  <clause id="11048">
    <literal><![CDATA[
      L(K(x,K(y,z)) * (u * K(z,y)),K(y,z),x) = (K(y,z) * x) \ (x * T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(8158(a,1),10985(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8158 10985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11049">
    <literal><![CDATA[
      L(x,T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(10994(a,1),616(a,1))].">
      <j1 rule="para" parents="10994 616"/>
    </justification>
  </clause>

  <clause id="11050">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(10994(a,1),7416(a,1,2))].">
      <j1 rule="para" parents="10994 7416"/>
    </justification>
  </clause>

  <clause id="11051">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10994(a,1),7787(a,1,2))].">
      <j1 rule="para" parents="10994 7787"/>
    </justification>
  </clause>

  <clause id="11053">
    <literal><![CDATA[
      K(x,L(y,z / u,u)) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[para(117(a,1),11051(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 11051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11054">
    <literal><![CDATA[
      K(x,y) * (a(x,y,x) \ z) = K(x,x * y) * z
    ]]></literal>
    <justification jstring="[hyper(397,a,11006,a),flip(a)].">
      <j1 rule="hyper" parents="397 11006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11055">
    <literal><![CDATA[
      K(x,x * y) * (a(x,y,x) * (L(y,z,u) * x)) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,7244,a(flip),b,11006,a),flip(a)].">
      <j1 rule="hyper" parents="373 7244 11006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11056">
    <literal><![CDATA[
      (x * y) * a(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,10887,a(flip),b,10827,a)].">
      <j1 rule="hyper" parents="145 10887 10827"/>
    </justification>
  </clause>

  <clause id="11057">
    <literal><![CDATA[
      (x * y) \ T(y * x,y) != z
    ]]></literal>
    <literal><![CDATA[
      a(y,x,y) = z
    ]]></literal>
    <justification jstring="[para(10827(a,2),10932(a,1))].">
      <j1 rule="para" parents="10827 10932"/>
    </justification>
  </clause>

  <clause id="11058">
    <literal><![CDATA[
      a(x,y,x) * (y * x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(11021,a,11056,a)].">
      <j1 rule="hyper" parents="11021 11056"/>
    </justification>
  </clause>

  <clause id="11059">
    <literal><![CDATA[
      a(x,y,x) \ T(x * y,x) = y * x
    ]]></literal>
    <justification jstring="[hyper(36,a,11016,a,b,11056,a)].">
      <j1 rule="hyper" parents="36 11016 11056"/>
    </justification>
  </clause>

  <clause id="11060">
    <literal><![CDATA[
      R(T(x,T(x * y,x)),y * x,a(x,y,x)) = ((y * x) * a(x,y,x)) \ ((x * y) * x)
    ]]></literal>
    <justification jstring="[para(11056(a,1),1345(a,1,1,2))].">
      <j1 rule="para" parents="11056 1345"/>
    </justification>
  </clause>

  <clause id="11061">
    <literal><![CDATA[
      T(x * (y * z),K(y,z)) = (y * z) * T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10194,a,b,10851,a)].">
      <j1 rule="hyper" parents="64 10194 10851"/>
    </justification>
  </clause>

  <clause id="11062">
    <literal><![CDATA[
      (x * y) \ (K(y,x) * z) = (T(x,y) * y) \ z
    ]]></literal>
    <justification jstring="[para(5755(a,1),10869(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5755 10869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11063">
    <literal><![CDATA[
      K(x,y) * (z * a(y,u,y)) = y * (L(T(y,x),u,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,10954,a(flip),b,6131,a)].">
      <j1 rule="hyper" parents="145 10954 6131"/>
    </justification>
  </clause>

  <clause id="11064">
    <literal><![CDATA[
      x * L(y,z,z \ x) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,344,a(flip),b,10971,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 344 10971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11065">
    <literal><![CDATA[
      (T(x,y) \ z) \ (((T(x,y) \ z) * x) * T(x,y)) = (z / T(x,y)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(2515(a,1),10971(a,1,2))].">
      <j1 rule="para" parents="2515 10971"/>
    </justification>
  </clause>

  <clause id="11066">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,y \ x) * x
    ]]></literal>
    <justification jstring="[hyper(464,a,11064,a),flip(a)].">
      <j1 rule="hyper" parents="464 11064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11067">
    <literal><![CDATA[
      x \ ((x / y) * (y * z)) = L(z,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(149,a,11064,a)].">
      <j1 rule="hyper" parents="149 11064"/>
    </justification>
  </clause>

  <clause id="11068">
    <literal><![CDATA[
      L(x,x,x \ y) = y \ (y / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(139,a,809,a(flip),b,11064,a),flip(a)].">
      <j1 rule="hyper" parents="139 809 11064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11069">
    <literal><![CDATA[
      L(T(x,y),y,y \ z) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(139,a,251,a(flip),b,11064,a),flip(a)].">
      <j1 rule="hyper" parents="139 251 11064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11070">
    <literal><![CDATA[
      L(x \ y,x,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,11064,a),flip(a)].">
      <j1 rule="hyper" parents="139 168 11064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11071">
    <literal><![CDATA[
      L(x,y,z / y) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(35,a,592,a,b,11064,a)].">
      <j1 rule="hyper" parents="35 592 11064"/>
    </justification>
  </clause>

  <clause id="11072">
    <literal><![CDATA[
      L(x * K(y,x),z,z \ y) = ((y / z) * (z * x)) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,11064,a(flip),b,5862,a),flip(a)].">
      <j1 rule="hyper" parents="142 11064 5862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11073">
    <literal><![CDATA[
      L((x * y) / x,z,z \ x) = ((x / z) * (z * y)) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,11064,a(flip),b,837,a),flip(a)].">
      <j1 rule="hyper" parents="142 11064 837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11074">
    <literal><![CDATA[
      ((x / y) * (y * x)) / x = L(x,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(142,a,11064,a(flip),b,275,a)].">
      <j1 rule="hyper" parents="142 11064 275"/>
    </justification>
  </clause>

  <clause id="11075">
    <literal><![CDATA[
      L(x,y,y) * L(z,y,(y \ 1) * x) = (L(x,y,y) / y) * (y * z)
    ]]></literal>
    <justification jstring="[para(1148(a,1),11064(a,1,2,3))].">
      <j1 rule="para" parents="1148 11064"/>
    </justification>
  </clause>

  <clause id="11076">
    <literal><![CDATA[
      (x * (1 / y)) * L(z,x,x \ (x * (1 / y))) = (K(x,y \ 1) / y) * (x * z)
    ]]></literal>
    <justification jstring="[para(6361(a,2),11064(a,2,1))].">
      <j1 rule="para" parents="6361 11064"/>
    </justification>
  </clause>

  <clause id="11077">
    <literal><![CDATA[
      L(L(x,y,y \ z),K(u \ w,u),w / u) = L(x,y,z / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6125,a,b,11071,a)].">
      <j1 rule="hyper" parents="373 6125 11071"/>
    </justification>
  </clause>

  <clause id="11078">
    <literal><![CDATA[
      x \ ((((x / y) / z) * (z * y)) * y) = L(y,z,z \ (x / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,3208,a,b,11071,a)].">
      <j1 rule="hyper" parents="64 3208 11071"/>
    </justification>
  </clause>

  <clause id="11079">
    <literal><![CDATA[
      L(L(x \ ((y / x) \ z),u,w),x,x \ y) = L(y \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,1717,a(flip),b,11071,a),flip(a)].">
      <j1 rule="hyper" parents="64 1717 11071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11080">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ z) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),11071(a,1,3)),flip(a)].">
      <j1 rule="para" parents="79 11071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11081">
    <literal><![CDATA[
      (x * T(y,(x / z) * z)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,z \ x) * ((x / z) * z)
    ]]></literal>
    <justification jstring="[para(11071(a,1),1375(a,2,1))].">
      <j1 rule="para" parents="11071 1375"/>
    </justification>
  </clause>

  <clause id="11082">
    <literal><![CDATA[
      L(x,x,R(T(y,x),y,x)) = ((1 / y) \ x) \ (((1 / y) \ x) / (1 / x))
    ]]></literal>
    <justification jstring="[para(1917(a,2),11068(a,1,3))].">
      <j1 rule="para" parents="1917 11068"/>
    </justification>
  </clause>

  <clause id="11083">
    <literal><![CDATA[
      x * L(y,z,z \ x) != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(11067(a,1),290(a,1,2))].">
      <j1 rule="para" parents="11067 290"/>
    </justification>
  </clause>

  <clause id="11084">
    <literal><![CDATA[
      (x \ 1) * L(y,z,z \ x) = ((x \ 1) / z) * (z * y)
    ]]></literal>
    <justification jstring="[para(11067(a,1),1599(a,1,2))].">
      <j1 rule="para" parents="11067 1599"/>
    </justification>
  </clause>

  <clause id="11085">
    <literal><![CDATA[
      x \ ((x / y) * a(y,y,y)) = L(1 / y,y,y \ x)
    ]]></literal>
    <justification jstring="[para(1852(a,2),11067(a,1,2,2))].">
      <j1 rule="para" parents="1852 11067"/>
    </justification>
  </clause>

  <clause id="11086">
    <literal><![CDATA[
      (x * y) \ (((x * y) / x) * z) = L(x \ z,x,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),11070(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 11070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11087">
    <literal><![CDATA[
      L(x \ L(y \ z,y,y \ u),x,u) = (u * x) \ ((u / y) * z)
    ]]></literal>
    <justification jstring="[para(11070(a,2),346(a,1,1,2))].">
      <j1 rule="para" parents="11070 346"/>
    </justification>
  </clause>

  <clause id="11088">
    <literal><![CDATA[
      L((x * K(y,z)) \ u,x * K(y,z),K(z,y)) = x \ ((x / (x * K(y,z))) * u)
    ]]></literal>
    <justification jstring="[para(6882(a,1),11070(a,1,3))].">
      <j1 rule="para" parents="6882 11070"/>
    </justification>
  </clause>

  <clause id="11089">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,u \ z) * z = (z / u) * (u * K(x,y))
    ]]></literal>
    <justification jstring="[para(8200(a,1),11066(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8200 11066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11090">
    <literal><![CDATA[
      L(x \ T(y,(x * z) / x),x,z) = (x * z) \ (y * ((x * z) / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,11086,a),flip(a)].">
      <j1 rule="hyper" parents="64 249 11086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11091">
    <literal><![CDATA[
      x \ (y * ((1 / x) \ L(x \ L(x,z,u),y,x))) = T(y,x) * L(x \ L(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(5607(a,2),11003(a,1,2,2))].">
      <j1 rule="para" parents="5607 11003"/>
    </justification>
  </clause>

  <clause id="11092">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) / (x * y) = L(a(z,u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,100,a(flip),b,11022,a)].">
      <j1 rule="hyper" parents="142 100 11022"/>
    </justification>
  </clause>

  <clause id="11093">
    <literal><![CDATA[
      T(x,R(a(y,z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(272,a,11023,a)].">
      <j1 rule="hyper" parents="272 11023"/>
    </justification>
  </clause>

  <clause id="11094">
    <literal><![CDATA[
      T(x * (y * z),K(z * y,z)) = (y * z) * T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8715,a,b,11061,a)].">
      <j1 rule="hyper" parents="64 8715 11061"/>
    </justification>
  </clause>

  <clause id="11095">
    <literal><![CDATA[
      L(K(x,y),y * x,z) \ (x * (y * u)) = (y * x) * L(u,y,x)
    ]]></literal>
    <justification jstring="[para(100(a,1),10868(a,1,2))].">
      <j1 rule="para" parents="100 10868"/>
    </justification>
  </clause>

  <clause id="11096">
    <literal><![CDATA[
      x * (y * L(y \ z,x,y)) = y * (x * ((y * x) \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(145,a,10962,a(flip),b,11003,a),flip(a)].">
      <j1 rule="hyper" parents="145 10962 11003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11097">
    <literal><![CDATA[
      T(x,y) * T(R(z,x,y),x * y) = T(L(z,x,y) * x,y)
    ]]></literal>
    <justification jstring="[hyper(269,a,510,a(flip),b,10990,a),flip(a)].">
      <j1 rule="hyper" parents="269 510 10990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11098">
    <literal><![CDATA[
      L(x,y,((z \ 1) * (T(u,z) * T(w,u * z))) * v5) = L(x,y,(L(w,u,z) * (u * z)) * v5)
    ]]></literal>
    <justification jstring="[para(10990(a,1),2271(a,2,3,1))].">
      <j1 rule="para" parents="10990 2271"/>
    </justification>
  </clause>

  <clause id="11099">
    <literal><![CDATA[
      L((x \ R(y,x,x)) \ z,y * (1 / x),(y * (1 / x)) \ R(y,x,x)) = R(y,x,x) \ (((y * (1 / x)) \ R(y,x,x)) * z)
    ]]></literal>
    <justification jstring="[para(1409(a,1),11004(a,1,1,1,1))].">
      <j1 rule="para" parents="1409 11004"/>
    </justification>
  </clause>

  <clause id="11100">
    <literal><![CDATA[
      L(((x * a(y,z,x)) \ a(y,z,x)) \ u,1 / x,(1 / x) \ a(y,z,x)) = a(y,z,x) \ (((1 / x) \ a(y,z,x)) * u)
    ]]></literal>
    <justification jstring="[para(9440(a,1),11004(a,1,1,1,1))].">
      <j1 rule="para" parents="9440 11004"/>
    </justification>
  </clause>

  <clause id="11101">
    <literal><![CDATA[
      L(T((x \ 1) \ 1,y) * K(z,T((x \ 1) \ 1,y)),x,x \ z) = ((z / x) * ((1 / x) \ T(x,y))) / z
    ]]></literal>
    <justification jstring="[para(1490(a,1),11072(a,2,1,2))].">
      <j1 rule="para" parents="1490 11072"/>
    </justification>
  </clause>

  <clause id="11102">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(y \ x,z,y \ x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,10109,a,b,10906,a)].">
      <j1 rule="hyper" parents="373 10109 10906"/>
    </justification>
  </clause>

  <clause id="11103">
    <literal><![CDATA[
      T(x,T(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(9262,a,11094,a)].">
      <j1 rule="hyper" parents="9262 11094"/>
    </justification>
  </clause>

  <clause id="11104">
    <literal><![CDATA[
      T(x,((y \ z) \ 1) * z) = T(x,z * ((z / y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,9336,a(flip),b,11103,a)].">
      <j1 rule="hyper" parents="64 9336 11103"/>
    </justification>
  </clause>

  <clause id="11105">
    <literal><![CDATA[
      T(x / y,T(z * y,x)) = T(x / y,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8013,a(flip),b,11103,a)].">
      <j1 rule="hyper" parents="64 8013 11103"/>
    </justification>
  </clause>

  <clause id="11106">
    <literal><![CDATA[
      T(x * y,y) * T(z,y * x) = z * T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,11103,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 11103 22"/>
    </justification>
  </clause>

  <clause id="11107">
    <literal><![CDATA[
      T(x,y * (z / y)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),11103(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 11103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11108">
    <literal><![CDATA[
      K(x,y * z) * (z * x) = z * T(x,z * y)
    ]]></literal>
    <justification jstring="[para(11103(a,1),7993(a,2,2))].">
      <j1 rule="para" parents="11103 7993"/>
    </justification>
  </clause>

  <clause id="11109">
    <literal><![CDATA[
      (x * (y / x)) * T(z,T(y,x)) = z * (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(145,a,11107,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 11107 22"/>
    </justification>
  </clause>

  <clause id="11110">
    <literal><![CDATA[
      R(T(x / y,T(z,y)),y,z / y) = (y * (z / y)) \ (x * (z / y))
    ]]></literal>
    <justification jstring="[para(11107(a,1),1326(a,1,1))].">
      <j1 rule="para" parents="11107 1326"/>
    </justification>
  </clause>

  <clause id="11111">
    <literal><![CDATA[
      T(x,T(T(y * z,u),z)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(5443(a,1),11107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5443 11107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11112">
    <literal><![CDATA[
      K(T(x,y),y * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(36,a,8371,a,b,11108,a)].">
      <j1 rule="hyper" parents="36 8371 11108"/>
    </justification>
  </clause>

  <clause id="11113">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(36,a,8245,a,b,11108,a)].">
      <j1 rule="hyper" parents="36 8245 11108"/>
    </justification>
  </clause>

  <clause id="11114">
    <literal><![CDATA[
      K(x / y,y * z) = K(y \ x,z * y)
    ]]></literal>
    <justification jstring="[hyper(8454,a,11112,a)].">
      <j1 rule="hyper" parents="8454 11112"/>
    </justification>
  </clause>

  <clause id="11115">
    <literal><![CDATA[
      T(K(x,y * z),y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7433,a(flip),b,11112,a)].">
      <j1 rule="hyper" parents="64 7433 11112"/>
    </justification>
  </clause>

  <clause id="11116">
    <literal><![CDATA[
      K(x / y,z * x) = K(y \ x,x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7387,a(flip),b,11112,a),flip(a)].">
      <j1 rule="hyper" parents="64 7387 11112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11117">
    <literal><![CDATA[
      T(x * y,K(z,y * x)) = x * y
    ]]></literal>
    <justification jstring="[para(11112(a,1),3993(a,1,2))].">
      <j1 rule="para" parents="11112 3993"/>
    </justification>
  </clause>

  <clause id="11118">
    <literal><![CDATA[
      T(x,T(y * z,y)) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[para(11112(a,1),7905(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11112 7905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11119">
    <literal><![CDATA[
      K(x,y * z) * z = z * K(x,z * y)
    ]]></literal>
    <justification jstring="[para(11112(a,1),8194(a,1,1))].">
      <j1 rule="para" parents="11112 8194"/>
    </justification>
  </clause>

  <clause id="11121">
    <literal><![CDATA[
      K(x / y,x * z) = K(y \ x,z * x)
    ]]></literal>
    <justification jstring="[hyper(8311,a,11113,a)].">
      <j1 rule="hyper" parents="8311 11113"/>
    </justification>
  </clause>

  <clause id="11122">
    <literal><![CDATA[
      T(x,T(y * z,y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(143,a,11113,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 11113 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11123">
    <literal><![CDATA[
      K(x,(y \ z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),11113(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 11113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11124">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(115(a,1),11113(a,1,2,1))].">
      <j1 rule="para" parents="115 11113"/>
    </justification>
  </clause>

  <clause id="11125">
    <literal><![CDATA[
      (x * y) \ (x * K(z,y * x)) = T(x * y,z) \ x
    ]]></literal>
    <justification jstring="[para(11113(a,1),7951(a,1,2,2))].">
      <j1 rule="para" parents="11113 7951"/>
    </justification>
  </clause>

  <clause id="11126">
    <literal><![CDATA[
      K(x,y * z) * T(y,z) = T(y,z) * K(x,z * y)
    ]]></literal>
    <justification jstring="[para(11113(a,1),7958(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11113 7958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11127">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(41,a,8200,a,b,11115,a)].">
      <j1 rule="hyper" parents="41 8200 11115"/>
    </justification>
  </clause>

  <clause id="11128">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8716,a,b,11122,a)].">
      <j1 rule="hyper" parents="64 8716 11122"/>
    </justification>
  </clause>

  <clause id="11129">
    <literal><![CDATA[
      T(x,(y \ z) * y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),11122(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 11122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11130">
    <literal><![CDATA[
      K(x,T(T(y * z,u),y)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(5430(a,1),11123(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5430 11123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11131">
    <literal><![CDATA[
      K(x,T(y * K(z,u),z)) = K(x,(z \ y) * T(z,u))
    ]]></literal>
    <justification jstring="[para(7128(a,1),11123(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7128 11123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11132">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,(z \ y) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),11127(a,1,2,1))].">
      <j1 rule="para" parents="10 11127"/>
    </justification>
  </clause>

  <clause id="11133">
    <literal><![CDATA[
      K(x,y * (z / y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),11127(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 11127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11134">
    <literal><![CDATA[
      K(x,T((y * z) * u,z * u)) = K(x,(z * u) * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(111(a,1),11127(a,1,2,1))].">
      <j1 rule="para" parents="111 11127"/>
    </justification>
  </clause>

  <clause id="11135">
    <literal><![CDATA[
      T((x * y) * K(z,y * x),z) = T(x * y,K(z,y))
    ]]></literal>
    <justification jstring="[para(11127(a,1),8360(a,1,1,2))].">
      <j1 rule="para" parents="11127 8360"/>
    </justification>
  </clause>

  <clause id="11136">
    <literal><![CDATA[
      K(x / y,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z * y) = u
    ]]></literal>
    <justification jstring="[para(11127(a,1),8317(a,1))].">
      <j1 rule="para" parents="11127 8317"/>
    </justification>
  </clause>

  <clause id="11137">
    <literal><![CDATA[
      T(x,(y \ z) * y) = x / K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,7909,a,b,11129,a),flip(a)].">
      <j1 rule="hyper" parents="373 7909 11129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11138">
    <literal><![CDATA[
      T(x,T(T(y * z,u),y)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(5430(a,1),11129(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5430 11129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11139">
    <literal><![CDATA[
      K(x,T(T(y * z,u),z)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(5443(a,1),11133(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5443 11133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11140">
    <literal><![CDATA[
      (x * y) * K(x \ 1,y * x) = L(y,x,x) / (1 / x)
    ]]></literal>
    <justification jstring="[para(11114(a,1),5894(a,1,2))].">
      <j1 rule="para" parents="11114 5894"/>
    </justification>
  </clause>

  <clause id="11141">
    <literal><![CDATA[
      T(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(11118(a,2),5767(a,1))].">
      <j1 rule="para" parents="11118 5767"/>
    </justification>
  </clause>

  <clause id="11142">
    <literal><![CDATA[
      K(x,T(y,z) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11127,a(flip),b,11124,a),flip(a)].">
      <j1 rule="hyper" parents="64 11127 11124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11143">
    <literal><![CDATA[
      T(x,T(y,z) * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(143,a,11142,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 11142 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11144">
    <literal><![CDATA[
      T(x,T(y,z) * z) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,11142,a(flip),b,5726,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 11142 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11145">
    <literal><![CDATA[
      K(x,y * (z * K(y,z))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(5785(a,1),11142(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5785 11142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11146">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y \ (T(u,z) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(T(u,z) * z) / y) = w
    ]]></literal>
    <justification jstring="[para(11142(a,1),8789(a,1,1,2))].">
      <j1 rule="para" parents="11142 8789"/>
    </justification>
  </clause>

  <clause id="11147">
    <literal><![CDATA[
      K(T(x,y) * y,z) = z / T(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(225,a,11143,a(flip),b,5804,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 11143 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11148">
    <literal><![CDATA[
      (T(x,y) * y) * T(z,y * x) = z * (T(x,y) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,11143,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 11143 22"/>
    </justification>
  </clause>

  <clause id="11149">
    <literal><![CDATA[
      T(x,T(y \ z,u) * y) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(278(a,1),11143(a,1,2,1))].">
      <j1 rule="para" parents="278 11143"/>
    </justification>
  </clause>

  <clause id="11150">
    <literal><![CDATA[
      T(x,(T(y,z * u) * z) * u) = T(x,(z * u) * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(511(a,1),11143(a,1,2))].">
      <j1 rule="para" parents="511 11143"/>
    </justification>
  </clause>

  <clause id="11151">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8159,a(flip),b,11128,a)].">
      <j1 rule="hyper" parents="64 8159 11128"/>
    </justification>
  </clause>

  <clause id="11152">
    <literal><![CDATA[
      T(x,K(y,z)) * (z * y) = (z * y) * T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,11128,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 11128 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11153">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = T(z * K(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(6881(a,1),11128(a,1,1))].">
      <j1 rule="para" parents="6881 11128"/>
    </justification>
  </clause>

  <clause id="11154">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(8153(a,1),11128(a,1,1))].">
      <j1 rule="para" parents="8153 11128"/>
    </justification>
  </clause>

  <clause id="11155">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,11123,a(flip),b,11132,a),flip(a)].">
      <j1 rule="hyper" parents="373 11123 11132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11156">
    <literal><![CDATA[
      K((x \ y) \ z,T(y,x)) = K(z / (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(8322,a,11155,a),flip(a)].">
      <j1 rule="hyper" parents="8322 11155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11157">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7424,a,b,11155,a)].">
      <j1 rule="hyper" parents="64 7424 11155"/>
    </justification>
  </clause>

  <clause id="11158">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7497,a(flip),b,11155,a)].">
      <j1 rule="hyper" parents="64 7497 11155"/>
    </justification>
  </clause>

  <clause id="11159">
    <literal><![CDATA[
      (x \ y) * K(z,T(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (x \ y) = u
    ]]></literal>
    <justification jstring="[para(11155(a,1),7889(a,1,2))].">
      <j1 rule="para" parents="11155 7889"/>
    </justification>
  </clause>

  <clause id="11160">
    <literal><![CDATA[
      K(x,T(y,z)) * (y / z) = (y / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(11155(a,1),8262(a,1,1))].">
      <j1 rule="para" parents="11155 8262"/>
    </justification>
  </clause>

  <clause id="11161">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(8446,a,11157,a),flip(a)].">
      <j1 rule="hyper" parents="8446 11157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11162">
    <literal><![CDATA[
      K(x,T(T(y,z),z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8203,a(flip),b,11157,a),flip(a)].">
      <j1 rule="hyper" parents="373 8203 11157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11163">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,11157,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 11157 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11164">
    <literal><![CDATA[
      K(x,T(y,z \ x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8033,a(flip),b,11157,a)].">
      <j1 rule="hyper" parents="64 8033 11157"/>
    </justification>
  </clause>

  <clause id="11166">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1),u,w)) = K(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[para(25(a,2),11157(a,1,2))].">
      <j1 rule="para" parents="25 11157"/>
    </justification>
  </clause>

  <clause id="11167">
    <literal><![CDATA[
      K(x,T(y,1 / z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(82(a,1),11157(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 11157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11168">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u / z))
    ]]></literal>
    <justification jstring="[para(4818(a,1),11157(a,1,2))].">
      <j1 rule="para" parents="4818 11157"/>
    </justification>
  </clause>

  <clause id="11169">
    <literal><![CDATA[
      (x \ 1) * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(11157(a,1),7889(a,1,2))].">
      <j1 rule="para" parents="11157 7889"/>
    </justification>
  </clause>

  <clause id="11170">
    <literal><![CDATA[
      T(x,T(y * z,z \ 1)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11103,a(flip),b,11163,a),flip(a)].">
      <j1 rule="hyper" parents="373 11103 11163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11171">
    <literal><![CDATA[
      K(x,T(y,x / z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7862,a,b,11164,a)].">
      <j1 rule="hyper" parents="64 7862 11164"/>
    </justification>
  </clause>

  <clause id="11172">
    <literal><![CDATA[
      K(x,T(y * (z \ x),z)) = K(x,(z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11127,a(flip),b,11164,a),flip(a)].">
      <j1 rule="hyper" parents="64 11127 11164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11173">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = (z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,11164,a(flip),b,8192,a)].">
      <j1 rule="hyper" parents="144 11164 8192"/>
    </justification>
  </clause>

  <clause id="11174">
    <literal><![CDATA[
      (x / y) * K(x,T(z,y)) = K(x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(11164(a,1),8036(a,1,2))].">
      <j1 rule="para" parents="11164 8036"/>
    </justification>
  </clause>

  <clause id="11175">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(5823,a,11137,a)].">
      <j1 rule="hyper" parents="5823 11137"/>
    </justification>
  </clause>

  <clause id="11176">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,11164,a,b,11175,a),flip(a)].">
      <j1 rule="hyper" parents="373 11164 11175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11177">
    <literal><![CDATA[
      K(x * y,T(z,x)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),11175(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 11175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11178">
    <literal><![CDATA[
      K(x * y,(z * x) \ x) = K(y * x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(8341,a,11177,a)].">
      <j1 rule="hyper" parents="8341 11177"/>
    </justification>
  </clause>

  <clause id="11179">
    <literal><![CDATA[
      K(x * y,y \ z) = K(y * x,z / y)
    ]]></literal>
    <justification jstring="[hyper(8325,a,11177,a),flip(a)].">
      <j1 rule="hyper" parents="8325 11177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11180">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(8313,a,11177,a),flip(a)].">
      <j1 rule="hyper" parents="8313 11177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11181">
    <literal><![CDATA[
      K(T(x * y,x),z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(7970,a,11177,a)].">
      <j1 rule="hyper" parents="7970 11177"/>
    </justification>
  </clause>

  <clause id="11182">
    <literal><![CDATA[
      K((x \ y) * z,T(x,y)) = K(z * (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(7420,a,11177,a)].">
      <j1 rule="hyper" parents="7420 11177"/>
    </justification>
  </clause>

  <clause id="11183">
    <literal><![CDATA[
      K(x * R(y,z,u),T(y,x)) = K(x * R(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,9674,a(flip),b,11177,a),flip(a)].">
      <j1 rule="hyper" parents="373 9674 11177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11184">
    <literal><![CDATA[
      K((x \ 1) * y,T(z,x)) = K(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11157,a(flip),b,11177,a)].">
      <j1 rule="hyper" parents="64 11157 11177"/>
    </justification>
  </clause>

  <clause id="11185">
    <literal><![CDATA[
      K(x * y,z * x) = K(y * x,x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11113,a(flip),b,11177,a)].">
      <j1 rule="hyper" parents="64 11113 11177"/>
    </justification>
  </clause>

  <clause id="11186">
    <literal><![CDATA[
      K(x * y,z) * y = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,11177,a(flip),b,8192,a)].">
      <j1 rule="hyper" parents="144 11177 8192"/>
    </justification>
  </clause>

  <clause id="11187">
    <literal><![CDATA[
      K(x * y,x \ z) = K(y * x,z / x)
    ]]></literal>
    <justification jstring="[para(117(a,1),11177(a,1,2))].">
      <j1 rule="para" parents="117 11177"/>
    </justification>
  </clause>

  <clause id="11188">
    <literal><![CDATA[
      K(x * y,z) * x = x * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(11177(a,1),7879(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11177 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11189">
    <literal><![CDATA[
      K(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(11177(a,1),8313(a,1))].">
      <j1 rule="para" parents="11177 8313"/>
    </justification>
  </clause>

  <clause id="11190">
    <literal><![CDATA[
      K(x * y,(z * y) \ y) = K(y * x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(8341,a,11180,a)].">
      <j1 rule="hyper" parents="8341 11180"/>
    </justification>
  </clause>

  <clause id="11191">
    <literal><![CDATA[
      K(x * (y \ z),T(z,y)) = K((y \ z) * x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11155,a(flip),b,11180,a)].">
      <j1 rule="hyper" parents="64 11155 11180"/>
    </justification>
  </clause>

  <clause id="11192">
    <literal><![CDATA[
      (x * y) * K(y * x,z) = T(x * y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,11180,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 11180 5726"/>
    </justification>
  </clause>

  <clause id="11193">
    <literal><![CDATA[
      K(x * (y / x),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(12(a,1),11180(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 11180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11194">
    <literal><![CDATA[
      K(x * T(x \ y,z),T(u,x)) = K(x * T(y / x,z),u)
    ]]></literal>
    <justification jstring="[para(525(a,1),11180(a,1,1))].">
      <j1 rule="para" parents="525 11180"/>
    </justification>
  </clause>

  <clause id="11195">
    <literal><![CDATA[
      K(x * y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(11180(a,1),8313(a,1))].">
      <j1 rule="para" parents="11180 8313"/>
    </justification>
  </clause>

  <clause id="11196">
    <literal><![CDATA[
      K((x * y) * (z / (y * x)),u) = K(z * K(x,y),T(u,x * y))
    ]]></literal>
    <justification jstring="[para(10193(a,1),11180(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10193 11180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11197">
    <literal><![CDATA[
      K(x * K((x \ y) \ 1,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(6573(a,1),11193(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6573 11193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11198">
    <literal><![CDATA[
      K(x * K(y \ x,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(6770(a,1),11193(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6770 11193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11199">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(x \ (u * (y / u)),z) = K((u * (y / u)) / x,z)
    ]]></literal>
    <justification jstring="[para(11193(a,1),9061(a,1,1,2))].">
      <j1 rule="para" parents="11193 9061"/>
    </justification>
  </clause>

  <clause id="11200">
    <literal><![CDATA[
      T(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(11144(a,2),5767(a,1))].">
      <j1 rule="para" parents="11144 5767"/>
    </justification>
  </clause>

  <clause id="11201">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5787,a,b,11147,a),flip(a)].">
      <j1 rule="hyper" parents="373 5787 11147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11202">
    <literal><![CDATA[
      ((T(x,y) * y) \ z) * K(y * x,(T(x,y) * y) \ z) = z / (T(x,y) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,11201,a(flip),b,5879,a)].">
      <j1 rule="hyper" parents="145 11201 5879"/>
    </justification>
  </clause>

  <clause id="11203">
    <literal><![CDATA[
      K(x * y,z) * (T(y,x) * x) = T(T(y,x) * x,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,11201,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 11201 5739"/>
    </justification>
  </clause>

  <clause id="11204">
    <literal><![CDATA[
      T(x,y * z) \ T(x,K(z,y)) = K(z * y,T(x,K(z,y)))
    ]]></literal>
    <justification jstring="[para(11151(a,1),5800(a,1,1))].">
      <j1 rule="para" parents="11151 5800"/>
    </justification>
  </clause>

  <clause id="11205">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,7470,a(flip),b,11158,a),flip(a)].">
      <j1 rule="hyper" parents="373 7470 11158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11206">
    <literal><![CDATA[
      K(x,T(y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(11158(a,1),7420(a,1))].">
      <j1 rule="para" parents="11158 7420"/>
    </justification>
  </clause>

  <clause id="11207">
    <literal><![CDATA[
      K(x,T(y,z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(11158(a,1),8021(a,1))].">
      <j1 rule="para" parents="11158 8021"/>
    </justification>
  </clause>

  <clause id="11208">
    <literal><![CDATA[
      T(x * y,T(z,y)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(143,a,11161,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 11161 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11209">
    <literal><![CDATA[
      K(x * y,1 / y) = K(y * x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(6513,a,11179,a)].">
      <j1 rule="hyper" parents="6513 11179"/>
    </justification>
  </clause>

  <clause id="11210">
    <literal><![CDATA[
      K(T(x,y * z) * z,z * y) = K(z * x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8534,a(flip),b,11185,a),flip(a)].">
      <j1 rule="hyper" parents="64 8534 11185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11211">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ (x * K(z * x,y))) = K(x,R(y,y \ (x * z),y) / z)
    ]]></literal>
    <justification jstring="[para(11188(a,1),9907(a,1,2,2))].">
      <j1 rule="para" parents="11188 9907"/>
    </justification>
  </clause>

  <clause id="11212">
    <literal><![CDATA[
      K((x \ y) * x,1 / x) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),11209(a,2,1))].">
      <j1 rule="para" parents="10 11209"/>
    </justification>
  </clause>

  <clause id="11213">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(8716(a,2),11141(a,1))].">
      <j1 rule="para" parents="8716 11141"/>
    </justification>
  </clause>

  <clause id="11215">
    <literal><![CDATA[
      K(x * K(y,(x \ z) \ 1),T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(((y * (z \ x)) / y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(6360(a,2),11195(a,1,1))].">
      <j1 rule="para" parents="6360 11195"/>
    </justification>
  </clause>

  <clause id="11216">
    <literal><![CDATA[
      T(x,T(y \ z,u) * y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * T(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(278(a,1),11200(a,1,2,1))].">
      <j1 rule="para" parents="278 11200"/>
    </justification>
  </clause>

  <clause id="11217">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7424(a,2),11206(a,1))].">
      <j1 rule="para" parents="7424 11206"/>
    </justification>
  </clause>

  <clause id="11218">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(7497(a,1),11206(a,1))].">
      <j1 rule="para" parents="7497 11206"/>
    </justification>
  </clause>

  <clause id="11219">
    <literal><![CDATA[
      K(x,(y \ z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(11132(a,1),11206(a,1))].">
      <j1 rule="para" parents="11132 11206"/>
    </justification>
  </clause>

  <clause id="11220">
    <literal><![CDATA[
      K((x \ y) * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(11176(a,2),11207(a,1))].">
      <j1 rule="para" parents="11176 11207"/>
    </justification>
  </clause>

  <clause id="11221">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(4818(a,1),11217(a,1,2))].">
      <j1 rule="para" parents="4818 11217"/>
    </justification>
  </clause>

  <clause id="11222">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ (z \ u))) = w
    ]]></literal>
    <justification jstring="[para(7451(a,1),11217(a,1,2))].">
      <j1 rule="para" parents="7451 11217"/>
    </justification>
  </clause>

  <clause id="11223">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,T(u,z))) = w
    ]]></literal>
    <justification jstring="[para(7500(a,1),11217(a,1,2))].">
      <j1 rule="para" parents="7500 11217"/>
    </justification>
  </clause>

  <clause id="11224">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T((z \ 1) * y,z)) = u
    ]]></literal>
    <justification jstring="[para(11113(a,1),11217(a,1))].">
      <j1 rule="para" parents="11113 11217"/>
    </justification>
  </clause>

  <clause id="11225">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,T(u,y * x)) = w
    ]]></literal>
    <justification jstring="[para(10850(a,1),11220(a,1,1,1))].">
      <j1 rule="para" parents="10850 11220"/>
    </justification>
  </clause>

  <clause id="11226">
    <literal><![CDATA[
      T(x,T(T(y * z,z),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),11111(a,1,2))].">
      <j1 rule="para" parents="23 11111"/>
    </justification>
  </clause>

  <clause id="11227">
    <literal><![CDATA[
      K(x / y,T(z * y,u)) = K(y \ x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(8317,a,11130,a),flip(a)].">
      <j1 rule="hyper" parents="8317 11130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11228">
    <literal><![CDATA[
      K(x,T(y * z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(11130(a,1),8313(a,1))].">
      <j1 rule="para" parents="11130 8313"/>
    </justification>
  </clause>

  <clause id="11229">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,w),y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(z / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(836(a,1),11228(a,1,2,1))].">
      <j1 rule="para" parents="836 11228"/>
    </justification>
  </clause>

  <clause id="11230">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),L(u,z,y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,z,y) * (z * y)) = w
    ]]></literal>
    <justification jstring="[para(10989(a,1),11228(a,1,2,1))].">
      <j1 rule="para" parents="10989 11228"/>
    </justification>
  </clause>

  <clause id="11231">
    <literal><![CDATA[
      K(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(11124(a,1),11228(a,1))].">
      <j1 rule="para" parents="11124 11228"/>
    </justification>
  </clause>

  <clause id="11232">
    <literal><![CDATA[
      T(x,T(T(y * z,y),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),11138(a,1,2))].">
      <j1 rule="para" parents="23 11138"/>
    </justification>
  </clause>

  <clause id="11233">
    <literal><![CDATA[
      K(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(11139(a,1),8313(a,1))].">
      <j1 rule="para" parents="11139 8313"/>
    </justification>
  </clause>

  <clause id="11234">
    <literal><![CDATA[
      K(x,L(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * L(x,y,z)) = w
    ]]></literal>
    <justification jstring="[para(7877(a,1),11233(a,1))].">
      <j1 rule="para" parents="7877 11233"/>
    </justification>
  </clause>

  <clause id="11235">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,10539,a(flip),b,11172,a),flip(a)].">
      <j1 rule="hyper" parents="64 10539 11172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11236">
    <literal><![CDATA[
      T(x,y) * K(y * x,y \ 1) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(11178(a,1),9303(a,1,2))].">
      <j1 rule="para" parents="11178 9303"/>
    </justification>
  </clause>

  <clause id="11237">
    <literal><![CDATA[
      K(x * (y \ z),y) * ((y \ z) * x) = T((y \ z) * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(144,a,11182,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 11182 5739"/>
    </justification>
  </clause>

  <clause id="11238">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K(z * ((x \ y) \ 1),x / y)
    ]]></literal>
    <justification jstring="[hyper(7484,a,11184,a)].">
      <j1 rule="hyper" parents="7484 11184"/>
    </justification>
  </clause>

  <clause id="11239">
    <literal><![CDATA[
      K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) = K(y \ (1 * ((x * (1 \ z)) / x)),T(u,y))
    ]]></literal>
    <justification jstring="[para(3096(a,1),11184(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3096 11184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11240">
    <literal><![CDATA[
      K(T(x * y,(z * y) \ y) \ ((x * y) * u),w) = K(K(y * x,z \ 1) \ u,w)
    ]]></literal>
    <justification jstring="[para(11190(a,1),6282(a,2,1,1))].">
      <j1 rule="para" parents="11190 6282"/>
    </justification>
  </clause>

  <clause id="11241">
    <literal><![CDATA[
      (x \ y) * K((y \ x) * z,x) = T(x,z * (y \ x)) \ y
    ]]></literal>
    <justification jstring="[hyper(145,a,11191,a(flip),b,8647,a)].">
      <j1 rule="hyper" parents="145 11191 8647"/>
    </justification>
  </clause>

  <clause id="11242">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),y),w)) = T(x,T(y * T(z / y,u),w))
    ]]></literal>
    <justification jstring="[para(525(a,1),11226(a,1,2,1,1))].">
      <j1 rule="para" parents="525 11226"/>
    </justification>
  </clause>

  <clause id="11243">
    <literal><![CDATA[
      T(x,T(T(K(y,z) * (u / y),u / y),w)) = T(x,T(u / ((z * y) / z),w))
    ]]></literal>
    <justification jstring="[para(6888(a,2),11226(a,2,2,1))].">
      <j1 rule="para" parents="6888 11226"/>
    </justification>
  </clause>

  <clause id="11244">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,T(T(z \ y,T(u,z)) * z,w))
    ]]></literal>
    <justification jstring="[para(8286(a,1),11232(a,1,2,1,1))].">
      <j1 rule="para" parents="8286 11232"/>
    </justification>
  </clause>

  <clause id="11245">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(8153(a,1),11213(a,1,1))].">
      <j1 rule="para" parents="8153 11213"/>
    </justification>
  </clause>

  <clause id="11246">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(11164(a,2),11218(a,1))].">
      <j1 rule="para" parents="11164 11218"/>
    </justification>
  </clause>

  <clause id="11247">
    <literal><![CDATA[
      L(x \ K(y,x * z),x,z) = T(z * x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(764,a,11125,a)].">
      <j1 rule="hyper" parents="764 11125"/>
    </justification>
  </clause>

  <clause id="11248">
    <literal><![CDATA[
      (K(x * y,z) * T(x,y)) \ T(x,y) = K(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(8053,a,11126,a)].">
      <j1 rule="hyper" parents="8053 11126"/>
    </justification>
  </clause>

  <clause id="11249">
    <literal><![CDATA[
      (T((x * x) \ y,K(x * x,y)) * K(x * x,y)) * T(z,y / (x * x)) = z * (T((x * x) \ y,K(x * x,y)) * K(x * x,y))
    ]]></literal>
    <justification jstring="[para(7723(a,1),11148(a,1,2,2))].">
      <j1 rule="para" parents="7723 11148"/>
    </justification>
  </clause>

  <clause id="11250">
    <literal><![CDATA[
      (T(x \ ((y * x) * z),K(x,y)) * K(x,y)) * T(u,x \ ((x * y) * z)) = u * (T(x \ ((y * x) * z),K(x,y)) * K(x,y))
    ]]></literal>
    <justification jstring="[para(10856(a,1),11148(a,1,2,2))].">
      <j1 rule="para" parents="10856 11148"/>
    </justification>
  </clause>

  <clause id="11251">
    <literal><![CDATA[
      T(x,y * T(T(y * (z / y),u) / y,w)) = T(x,T(T(z,u) / y,w) * y)
    ]]></literal>
    <justification jstring="[para(5427(a,1),11149(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5427 11149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11252">
    <literal><![CDATA[
      T(x * (y * z),K(y,z)) = T(x,K(z,y)) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,11061,a,b,11152,a)].">
      <j1 rule="hyper" parents="373 11061 11152"/>
    </justification>
  </clause>

  <clause id="11253">
    <literal><![CDATA[
      K(T(K(x,y) * z,x * y),u) = K(z * K(x,y),T(u,y * x))
    ]]></literal>
    <justification jstring="[para(11153(a,2),7869(a,1,1))].">
      <j1 rule="para" parents="11153 7869"/>
    </justification>
  </clause>

  <clause id="11254">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),11166(a,2,2))].">
      <j1 rule="para" parents="25 11166"/>
    </justification>
  </clause>

  <clause id="11255">
    <literal><![CDATA[
      T(x,y) * K(y * R(x,z,u),x) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(11183(a,1),5852(a,1,2))].">
      <j1 rule="para" parents="11183 5852"/>
    </justification>
  </clause>

  <clause id="11256">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,K(w,x * R(y,z,u))) = T(K(x * R(y,z,u),T(y,x)),w)
    ]]></literal>
    <justification jstring="[para(11183(a,2),8120(a,2,1))].">
      <j1 rule="para" parents="11183 8120"/>
    </justification>
  </clause>

  <clause id="11257">
    <literal><![CDATA[
      K(x * y,z) * T(x,y) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,6882,a,b,11248,a),flip(a)].">
      <j1 rule="hyper" parents="40 6882 11248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11258">
    <literal><![CDATA[
      T(x * (y * z),K(z,y)) = T(x,K(z,y)) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(8184,a,11252,a)].">
      <j1 rule="hyper" parents="8184 11252"/>
    </justification>
  </clause>

  <clause id="11259">
    <literal><![CDATA[
      K(x,L(T(y / ((z * u) \ z),u),w,v5)) = K(x,L(((z * u) \ z) \ y,w,v5))
    ]]></literal>
    <justification jstring="[para(6746(a,1),11254(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6746 11254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11260">
    <literal><![CDATA[
      x * (y * K(x \ 1,y * x)) = L(y,x,x) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7153,a(flip),b,11140,a)].">
      <j1 rule="hyper" parents="64 7153 11140"/>
    </justification>
  </clause>

  <clause id="11261">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(11246,a,10033,a)].">
      <j1 rule="hyper" parents="11246 10033"/>
    </justification>
  </clause>

  <clause id="11262">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),11261(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 11261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11263">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,8087,a,b,11262,a)].">
      <j1 rule="hyper" parents="373 8087 11262"/>
    </justification>
  </clause>

  <clause id="11264">
    <literal><![CDATA[
      K(x,T(y,z \ (x * u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8450,a(flip),b,11262,a)].">
      <j1 rule="hyper" parents="64 8450 11262"/>
    </justification>
  </clause>

  <clause id="11265">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(11262(a,1),7420(a,1))].">
      <j1 rule="para" parents="11262 7420"/>
    </justification>
  </clause>

  <clause id="11266">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = y \ R(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,11255,a(flip),b,6088,a),flip(a)].">
      <j1 rule="hyper" parents="139 11255 6088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11267">
    <literal><![CDATA[
      T(x,y) * (K(y * R(x,z,u),x) * w) = R(x,y,R(x,z,u)) * w
    ]]></literal>
    <justification jstring="[para(11255(a,1),4443(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11255 4443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11268">
    <literal><![CDATA[
      L(x / (y \ 1),y,y) = L(x,y,y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10287,a(flip),b,11260,a)].">
      <j1 rule="hyper" parents="64 10287 11260"/>
    </justification>
  </clause>

  <clause id="11269">
    <literal><![CDATA[
      K(x,T(x \ y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(11158(a,1),11265(a,1))].">
      <j1 rule="para" parents="11158 11265"/>
    </justification>
  </clause>

  <clause id="11270">
    <literal><![CDATA[
      T(x,y) * R(T(z,x * y),x,y) = T(L(z,x,y) * x,y)
    ]]></literal>
    <justification jstring="[para(27(a,2),11097(a,1,2))].">
      <j1 rule="para" parents="27 11097"/>
    </justification>
  </clause>

  <clause id="11271">
    <literal><![CDATA[
      K((x \ 1) * T((x \ 1) \ y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[hyper(11217,a,11194,a)].">
      <j1 rule="hyper" parents="11217 11194"/>
    </justification>
  </clause>

  <clause id="11272">
    <literal><![CDATA[
      T(x,y * z) \ T(x,K(y,z)) = K(z * y,T(x,K(z,y)))
    ]]></literal>
    <justification jstring="[para(8153(a,1),11204(a,1,2))].">
      <j1 rule="para" parents="8153 11204"/>
    </justification>
  </clause>

  <clause id="11273">
    <literal><![CDATA[
      K(x,K(y,(x \ z) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(35,a,8087,a,b,11263,a)].">
      <j1 rule="hyper" parents="35 8087 11263"/>
    </justification>
  </clause>

  <clause id="11274">
    <literal><![CDATA[
      K(x,K(y,z \ (x \ u))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(9037,a,11273,a)].">
      <j1 rule="hyper" parents="9037 11273"/>
    </justification>
  </clause>

  <clause id="11275">
    <literal><![CDATA[
      K(x,K(y,z \ (x \ u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,9023,a,b,11274,a),flip(a)].">
      <j1 rule="hyper" parents="373 9023 11274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11276">
    <literal><![CDATA[
      K(x,K(y,z \ (x * u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(9(a,1),11275(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 11275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11277">
    <literal><![CDATA[
      K(x * y,T(z,K(x,y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y * x) \ K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(11272(a,1),6424(a,1))].">
      <j1 rule="para" parents="11272 6424"/>
    </justification>
  </clause>

  <clause id="11278">
    <literal><![CDATA[
      R(T(x,y * y),y,y) \ (y \ (x * y)) = K(y,x * y) * a(y,y,y \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,1344,a(flip),b,10830,a)].">
      <j1 rule="hyper" parents="64 1344 10830"/>
    </justification>
  </clause>

  <clause id="11279">
    <literal><![CDATA[
      (x * x) \ (K(x,y) * a(x,x,x \ y)) = T(y * x,x * x) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,10830,a(flip),b,1460,a)].">
      <j1 rule="hyper" parents="139 10830 1460"/>
    </justification>
  </clause>

  <clause id="11280">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = R(z,x,y) * T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8862,a(flip),b,10854,a),flip(a)].">
      <j1 rule="hyper" parents="64 8862 10854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11281">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,x) = ((y * z) * x) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6975,a,11280,a(flip))].">
      <j1 rule="hyper" parents="6975 11280"/>
    </justification>
  </clause>

  <clause id="11282">
    <literal><![CDATA[
      K(x,y \ z) * K(x * (y \ z),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(10497(a,1),10890(a,1,2))].">
      <j1 rule="para" parents="10497 10890"/>
    </justification>
  </clause>

  <clause id="11283">
    <literal><![CDATA[
      a(x,y,x) * (T(x * y,x) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(6157(a,1),11005(a,1,2))].">
      <j1 rule="para" parents="6157 11005"/>
    </justification>
  </clause>

  <clause id="11284">
    <literal><![CDATA[
      L(x,y,z / y) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(11077(a,1),4497(a,1))].">
      <j1 rule="para" parents="11077 4497"/>
    </justification>
  </clause>

  <clause id="11285">
    <literal><![CDATA[
      x * (y * L(y \ (x \ z),x,y)) = y * (x * ((y * x) \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),11096(a,2,2,2,2))].">
      <j1 rule="para" parents="10 11096"/>
    </justification>
  </clause>

  <clause id="11286">
    <literal><![CDATA[
      (x * (y * L(y \ z,x,y))) \ (x * z) = a(y,x,(y * x) \ (x * z))
    ]]></literal>
    <justification jstring="[para(11096(a,2),91(a,1,1))].">
      <j1 rule="para" parents="11096 91"/>
    </justification>
  </clause>

  <clause id="11287">
    <literal><![CDATA[
      T(x,(T(y,z * z) * z) * z) = T(T(x,z * z),R(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,1773,a,b,11150,a),flip(a)].">
      <j1 rule="hyper" parents="373 1773 11150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11288">
    <literal><![CDATA[
      (x * (y * R(x,z,u))) \ ((y * R(x,z,u)) * T(x,y)) = x \ R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10828,a,b,11266,a)].">
      <j1 rule="hyper" parents="64 10828 11266"/>
    </justification>
  </clause>

  <clause id="11289">
    <literal><![CDATA[
      a(x,(y \ z) \ 1,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,x) = u
    ]]></literal>
    <justification jstring="[para(11282(a,1),10932(a,1))].">
      <j1 rule="para" parents="11282 10932"/>
    </justification>
  </clause>

  <clause id="11290">
    <literal><![CDATA[
      T(x * L(x \ y,x,z),z) = x * ((z * x) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(269,a,2841,a(flip),b,11285,a(flip))].">
      <j1 rule="hyper" parents="269 2841 11285"/>
    </justification>
  </clause>

  <clause id="11291">
    <literal><![CDATA[
      x * ((y \ 1) * L((y \ 1) \ (x \ z),x,y)) = (y \ 1) * (x * (((y \ 1) * x) \ z))
    ]]></literal>
    <justification jstring="[para(1631(a,1),11285(a,1,2,2))].">
      <j1 rule="para" parents="1631 11285"/>
    </justification>
  </clause>

  <clause id="11292">
    <literal><![CDATA[
      x * ((y * x) \ ((x * z) * y)) = T(x * L(z,x,y),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),11290(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 11290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11293">
    <literal><![CDATA[
      (x * y) * ((T(y,x) * x) \ z) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(11062(a,1),10875(a,1,2))].">
      <j1 rule="para" parents="11062 10875"/>
    </justification>
  </clause>

  <clause id="11294">
    <literal><![CDATA[
      R(x,y,z) * a(u,R(x,y,z),u) = R(x * a(u,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(10903(a,1),10927(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10903 10927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11295">
    <literal><![CDATA[
      a(x,R(y,z,u),x) * R(y,z,u) = R(y * a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(11021,a,11294,a)].">
      <j1 rule="hyper" parents="11021 11294"/>
    </justification>
  </clause>

  <clause id="11296">
    <literal><![CDATA[
      K(x \ y,x) * K(y,T(z,x)) = y \ T((x \ y) * x,z)
    ]]></literal>
    <justification jstring="[para(11175(a,1),10966(a,1,2))].">
      <j1 rule="para" parents="11175 10966"/>
    </justification>
  </clause>

  <clause id="11297">
    <literal><![CDATA[
      L(K(x,K(y,z)),z * K(x,y),u) \ (K(x,y) * (z * w)) = (z * K(x,y)) * L(w,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8092(a,1),11095(a,1,1,1))].">
      <j1 rule="para" parents="8092 11095"/>
    </justification>
  </clause>

  <clause id="11298">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K((x \ y) \ z,x / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,9975,a(flip),b,11238,a),flip(a)].">
      <j1 rule="hyper" parents="373 9975 11238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11299">
    <literal><![CDATA[
      (((x \ y) * x) \ z) * K(y,((x \ y) * x) \ z) = (K(x,x \ y) * z) / y
    ]]></literal>
    <justification jstring="[hyper(10973,a,5722,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="10973 5722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11300">
    <literal><![CDATA[
      L(x,y,y) * L(z,y,y * x) = (L(x,y,y) / y) * (y * z)
    ]]></literal>
    <justification jstring="[para(2211(a,1),11075(a,1,2))].">
      <j1 rule="para" parents="2211 11075"/>
    </justification>
  </clause>

  <clause id="11301">
    <literal><![CDATA[
      (x * y) \ (z * ((x * y) / x)) = L(x \ T(z,T(y,x)),x,y)
    ]]></literal>
    <justification jstring="[para(8242(a,1),11090(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8242 11090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11302">
    <literal><![CDATA[
      R(T(x / y,T(z,y)),y,y \ z) = (y * (z / y)) \ (x * (z / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,10207,a(flip),b,11110,a)].">
      <j1 rule="hyper" parents="64 10207 11110"/>
    </justification>
  </clause>

  <clause id="11303">
    <literal><![CDATA[
      T(T(x,y),z) * (K(z * R(T(x,y),u,w),T(x,y)) * v5) = R(T(x,y),z,R(x,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(10090(a,1),11267(a,2,1))].">
      <j1 rule="para" parents="10090 11267"/>
    </justification>
  </clause>

  <clause id="11304">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10167,a(flip),b,10785,a),flip(a)].">
      <j1 rule="hyper" parents="64 10167 10785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11305">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(11212(a,1),10791(a,2,2))].">
      <j1 rule="para" parents="11212 10791"/>
    </justification>
  </clause>

  <clause id="11306">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = K(x,1 / y) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,4531,a(flip),b,11305,a),flip(a)].">
      <j1 rule="hyper" parents="373 4531 11305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11307">
    <literal><![CDATA[
      x / ((y / (x \ y)) / (1 / (x \ y))) = K(y,1 / (x \ y)) / (x \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),11306(a,1,1))].">
      <j1 rule="para" parents="79 11306"/>
    </justification>
  </clause>

  <clause id="11308">
    <literal><![CDATA[
      L(a(x,y,x),K(x,x * y),z) = K(x,y) * K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10354,a(flip),b,10934,a),flip(a)].">
      <j1 rule="hyper" parents="373 10354 10934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11310">
    <literal><![CDATA[
      L(a(x,y,x),K(x,x * y),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10887,a(flip),b,11308,a),flip(a)].">
      <j1 rule="hyper" parents="373 10887 11308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11311">
    <literal><![CDATA[
      x / a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      (x / (K(y,y * z) * a(y,z,y))) * K(y,y * z) = u
    ]]></literal>
    <justification jstring="[para(11310(a,1),1292(a,1,2))].">
      <j1 rule="para" parents="11310 1292"/>
    </justification>
  </clause>

  <clause id="11312">
    <literal><![CDATA[
      a(x / y,z,x / y) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(36,a,11042,a(flip),b,11102,a(flip))].">
      <j1 rule="hyper" parents="36 11042 11102"/>
    </justification>
  </clause>

  <clause id="11313">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) * y,w)) = T(x,T(y * T(z / y,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11232,a(flip),b,11242,a)].">
      <j1 rule="hyper" parents="64 11232 11242"/>
    </justification>
  </clause>

  <clause id="11314">
    <literal><![CDATA[
      T(x,T(y * T((y * z) / y,u),w)) = T(x,T(T(z,u) * y,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),11313(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 11313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11315">
    <literal><![CDATA[
      (x * (y * L(z,x,y))) \ (x * (y * z)) = a(y,x,(y * x) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(9(a,1),11286(a,1,1,2,2,1))].">
      <j1 rule="para" parents="9 11286"/>
    </justification>
  </clause>

  <clause id="11316">
    <literal><![CDATA[
      K(x,1 / (y \ x)) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(79(a,1),11307(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 11307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11317">
    <literal><![CDATA[
      K(x,y / x) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(6273(a,1),11316(a,1,1))].">
      <j1 rule="para" parents="6273 11316"/>
    </justification>
  </clause>

  <clause id="11318">
    <literal><![CDATA[
      ((x * ((K(y,x / y) / (x \ y)) \ 1)) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(11317(a,2),10633(a,2,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11317 10633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11319">
    <literal><![CDATA[
      (x * (y * ((x * y) \ z))) / (y * x) = L(z / (y * x),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10995,a(flip),b,10964,a),flip(a)].">
      <j1 rule="hyper" parents="64 10995 10964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11320">
    <literal><![CDATA[
      K(x \ (y \ z),T(x,y)) = K(x \ (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(10041,a,10818,a)].">
      <j1 rule="hyper" parents="10041 10818"/>
    </justification>
  </clause>

  <clause id="11321">
    <literal><![CDATA[
      K(x \ ((y * z) / y),x) = K(x \ z,T(x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),11320(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 11320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11322">
    <literal><![CDATA[
      K(x \ ((y * z) / y),(x \ ((y * z) / y)) \ ((y * z) / y)) = K(x \ z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5927,a,b,11321,a)].">
      <j1 rule="hyper" parents="64 5927 11321"/>
    </justification>
  </clause>

  <clause id="11323">
    <literal><![CDATA[
      (x * R(y,x,z)) \ (K(x,y) * ((y * x) * z)) = L(z,x,R(y,x,z))
    ]]></literal>
    <justification jstring="[para(10754(a,1),10872(a,1,2,1))].">
      <j1 rule="para" parents="10754 10872"/>
    </justification>
  </clause>

  <clause id="11325">
    <literal><![CDATA[
      (x * R(y,x,z)) \ ((x * y) * z) = L(z,x,R(y,x,z))
    ]]></literal>
    <justification jstring="[para(10834(a,1),11323(a,1,2))].">
      <j1 rule="para" parents="10834 11323"/>
    </justification>
  </clause>

  <clause id="11326">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y * x) \ (y * z)) = (y \ 1) * (K(x,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(5778(a,1),11001(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5778 11001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11327">
    <literal><![CDATA[
      ((x * y) * ((T(y,x) * x) \ z)) / (x * y) = z / (T(y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(5880,a,11202,a)].">
      <j1 rule="hyper" parents="5880 11202"/>
    </justification>
  </clause>

  <clause id="11328">
    <literal><![CDATA[
      (x * (K(y,z) * K(y,z))) / (y * z) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[para(11293(a,1),11327(a,1,1))].">
      <j1 rule="para" parents="11293 11327"/>
    </justification>
  </clause>

  <clause id="11329">
    <literal><![CDATA[
      T(x,T(y / ((z * u) / z),w)) = T(x,T((y / u) * K(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11226,a(flip),b,11243,a),flip(a)].">
      <j1 rule="hyper" parents="64 11226 11243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11330">
    <literal><![CDATA[
      T(x,y * T(T(y * (z / y),u) / y,w)) = T(x,y * T(y \ T(z,u),w))
    ]]></literal>
    <justification jstring="[para(525(a,1),11251(a,2,2))].">
      <j1 rule="para" parents="525 11251"/>
    </justification>
  </clause>

  <clause id="11331">
    <literal><![CDATA[
      (x * (y * L(z,x,y))) \ (x * (y * z)) = a(y,x,L(K(x,y) * z,y,x))
    ]]></literal>
    <justification jstring="[para(10985(a,1),11315(a,2,3))].">
      <j1 rule="para" parents="10985 11315"/>
    </justification>
  </clause>

  <clause id="11332">
    <literal><![CDATA[
      R(T(x,(y * (z * u)) / ((x * z) * u)),z,u) = T(R(x,z,u),y / R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,10762,a)].">
      <j1 rule="hyper" parents="64 27 10762"/>
    </justification>
  </clause>

  <clause id="11333">
    <literal><![CDATA[
      (x \ T(K(y \ x,z) * x,x)) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(8358(a,1),10959(a,1,1))].">
      <j1 rule="para" parents="8358 10959"/>
    </justification>
  </clause>

  <clause id="11334">
    <literal><![CDATA[
      (x * (1 / y)) * L(z,x,1 / y) = (K(x,y \ 1) / y) * (x * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),11076(a,1,2,3))].">
      <j1 rule="para" parents="9 11076"/>
    </justification>
  </clause>

  <clause id="11336">
    <literal><![CDATA[
      (K(x,y \ 1) / y) * (x * z) = (x * (1 / y)) * L(z,x,y)
    ]]></literal>
    <justification jstring="[para(1643(a,1),11334(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1643 11334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11337">
    <literal><![CDATA[
      L((x * K(y,z)) \ u,x * K(y,z),K(z,y)) = x \ (K(z,T(y,x)) * u)
    ]]></literal>
    <justification jstring="[para(8256(a,1),11088(a,2,2,1))].">
      <j1 rule="para" parents="8256 11088"/>
    </justification>
  </clause>

  <clause id="11338">
    <literal><![CDATA[
      (x / (K(y,y * z) * a(y,z,y))) * K(y,y * z) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(11311,a,11014,a)].">
      <j1 rule="hyper" parents="11311 11014"/>
    </justification>
  </clause>

  <clause id="11339">
    <literal><![CDATA[
      (x / K(y,z)) * K(y,y * z) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[para(10914(a,1),11338(a,1,1,2))].">
      <j1 rule="para" parents="10914 11338"/>
    </justification>
  </clause>

  <clause id="11340">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = a(z,y,z) \ x
    ]]></literal>
    <justification jstring="[para(6878(a,1),11339(a,1,1))].">
      <j1 rule="para" parents="6878 11339"/>
    </justification>
  </clause>

  <clause id="11341">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,9169,a(flip),b,11340,a)].">
      <j1 rule="hyper" parents="64 9169 11340"/>
    </justification>
  </clause>

  <clause id="11342">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11014,a,b,11341,a),flip(a)].">
      <j1 rule="hyper" parents="373 11014 11341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11343">
    <literal><![CDATA[
      (x * a(y,z,y)) / R(y,z,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(142,a,11,a(flip),b,11342,a),flip(a)].">
      <j1 rule="hyper" parents="142 11 11342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11344">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10368,a(flip),b,11342,a)].">
      <j1 rule="hyper" parents="64 10368 11342"/>
    </justification>
  </clause>

  <clause id="11345">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(156,a,11343,a)].">
      <j1 rule="hyper" parents="156 11343"/>
    </justification>
  </clause>

  <clause id="11346">
    <literal><![CDATA[
      (x * y) * a(y,z,y) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,11,a(flip),b,11343,a),flip(a)].">
      <j1 rule="hyper" parents="144 11 11343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11347">
    <literal><![CDATA[
      x / (y \ L(y,z,y)) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,11,a(flip),b,11344,a)].">
      <j1 rule="hyper" parents="142 11 11344"/>
    </justification>
  </clause>

  <clause id="11348">
    <literal><![CDATA[
      x * (a(y,z,y) \ 1) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[para(10911(a,2),11344(a,1,2))].">
      <j1 rule="para" parents="10911 11344"/>
    </justification>
  </clause>

  <clause id="11349">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7495,a,b,11345,a)].">
      <j1 rule="hyper" parents="64 7495 11345"/>
    </justification>
  </clause>

  <clause id="11350">
    <literal><![CDATA[
      (x / y) * R(y,z,y) != x * u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(11345(a,2),44(a,1))].">
      <j1 rule="para" parents="11345 44"/>
    </justification>
  </clause>

  <clause id="11351">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ T(z,y)) = x * a(y,y \ z,y)
    ]]></literal>
    <justification jstring="[para(4745(a,1),11345(a,1,2))].">
      <j1 rule="para" parents="4745 11345"/>
    </justification>
  </clause>

  <clause id="11352">
    <literal><![CDATA[
      K(x,y) * ((z / y) * R(y,u,y)) = y * (L(T(y,x),u,y) \ z)
    ]]></literal>
    <justification jstring="[para(11345(a,2),11063(a,1,2))].">
      <j1 rule="para" parents="11345 11063"/>
    </justification>
  </clause>

  <clause id="11353">
    <literal><![CDATA[
      a(x,y,x) * (z * x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(11021,a,11346,a)].">
      <j1 rule="hyper" parents="11021 11346"/>
    </justification>
  </clause>

  <clause id="11354">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,11346,a(flip),b,11011,a)].">
      <j1 rule="hyper" parents="142 11346 11011"/>
    </justification>
  </clause>

  <clause id="11355">
    <literal><![CDATA[
      (x * (y * R(z,u,z))) / (x * (y * z)) = L(a(z,u,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(11346(a,1),11092(a,1,1,2))].">
      <j1 rule="para" parents="11346 11092"/>
    </justification>
  </clause>

  <clause id="11356">
    <literal><![CDATA[
      (((x * y) / a(z,u,z)) * w) / ((y * (a(z,u,z) \ 1)) * w) = R(R(x,y,a(z,u,z) \ 1),y * (a(z,u,z) \ 1),w)
    ]]></literal>
    <justification jstring="[para(11348(a,1),660(a,1,1,1))].">
      <j1 rule="para" parents="11348 660"/>
    </justification>
  </clause>

  <clause id="11357">
    <literal><![CDATA[
      (x * y) * a(x,z,x) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(739,a,11349,a),flip(a)].">
      <j1 rule="hyper" parents="739 11349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11358">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,11011,a,b,11349,a),flip(a)].">
      <j1 rule="hyper" parents="373 11011 11349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11359">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,u,x) = K(y,T(x,z)) * a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9420,a(flip),b,11349,a)].">
      <j1 rule="hyper" parents="64 9420 11349"/>
    </justification>
  </clause>

  <clause id="11360">
    <literal><![CDATA[
      (R(x,y,x) \ z) * a(x,y,x) = x \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,1899,a(flip),b,11349,a),flip(a)].">
      <j1 rule="hyper" parents="64 1899 11349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11361">
    <literal><![CDATA[
      x * (y * a(x,z,x)) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,11349,a(flip),b,1898,a)].">
      <j1 rule="hyper" parents="145 11349 1898"/>
    </justification>
  </clause>

  <clause id="11362">
    <literal><![CDATA[
      (x * R(x \ y,z,x \ y)) / y = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(142,a,11353,a(flip),b,168,a(flip))].">
      <j1 rule="hyper" parents="142 11353 168"/>
    </justification>
  </clause>

  <clause id="11363">
    <literal><![CDATA[
      K(x,x * y) * (L(y,z,u) * R(x,y,x)) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(11353(a,1),11055(a,1,2))].">
      <j1 rule="para" parents="11353 11055"/>
    </justification>
  </clause>

  <clause id="11364">
    <literal><![CDATA[
      R(a(x,y,x),x,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10907,a(flip),b,11354,a)].">
      <j1 rule="hyper" parents="64 10907 11354"/>
    </justification>
  </clause>

  <clause id="11365">
    <literal><![CDATA[
      ((x * y) * R(L(z,y,x),u,L(z,y,x))) / (x * (y * z)) = a(L(z,y,x),u,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(100(a,1),11354(a,1,2))].">
      <j1 rule="para" parents="100 11354"/>
    </justification>
  </clause>

  <clause id="11367">
    <literal><![CDATA[
      ((a(R(x,y,z),u,R(x,y,z)) * R(x,y,z)) * (y * z)) / ((x * y) * z) = a(R(x,y,z),u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,661,a,b,11364,a)].">
      <j1 rule="hyper" parents="64 661 11364"/>
    </justification>
  </clause>

  <clause id="11368">
    <literal><![CDATA[
      a(x,y,x) * (x * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(11021,a,11357,a)].">
      <j1 rule="hyper" parents="11021 11357"/>
    </justification>
  </clause>

  <clause id="11369">
    <literal><![CDATA[
      a(x,y,x) * (R(x,y,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,1899,a(flip),b,11358,a),flip(a)].">
      <j1 rule="hyper" parents="64 1899 11358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11370">
    <literal><![CDATA[
      x * (a(x,y,x) * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,11358,a(flip),b,1898,a)].">
      <j1 rule="hyper" parents="145 11358 1898"/>
    </justification>
  </clause>

  <clause id="11371">
    <literal><![CDATA[
      a(x,y,x) \ (x \ z) = R(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,1899,a(flip),b,11358,a(flip))].">
      <j1 rule="hyper" parents="139 1899 11358"/>
    </justification>
  </clause>

  <clause id="11372">
    <literal><![CDATA[
      R((x * (x \ y)) * (x \ y),z,x) = (a(x,z,x) * y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(11358(a,1),2106(a,2,1))].">
      <j1 rule="para" parents="11358 2106"/>
    </justification>
  </clause>

  <clause id="11373">
    <literal><![CDATA[
      x * a(y,y \ x,y) = T(y * (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(269,a,10219,a(flip),b,11361,a),flip(a)].">
      <j1 rule="hyper" parents="269 10219 11361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11374">
    <literal><![CDATA[
      R(x,y,x) * (z / x) = x * (z / L(x,y,x))
    ]]></literal>
    <justification jstring="[para(10921(a,1),11361(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10921 11361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11375">
    <literal><![CDATA[
      R(x,y,x) * (a(x,y,x) \ z) = x * z
    ]]></literal>
    <justification jstring="[para(11016(a,1),11361(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11016 11361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11376">
    <literal><![CDATA[
      ((R(x,y,x) * z) * u) / ((x * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(a(x,y,x),x * z,u) = w
    ]]></literal>
    <justification jstring="[para(11368(a,1),666(a,1,1,1))].">
      <j1 rule="para" parents="11368 666"/>
    </justification>
  </clause>

  <clause id="11377">
    <literal><![CDATA[
      x * a(y,y \ x,y) = y * (T(x,y) / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5431,a(flip),b,11373,a),flip(a)].">
      <j1 rule="hyper" parents="373 5431 11373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11378">
    <literal><![CDATA[
      x \ (y * (T(x,y) / y)) = a(y,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,5431,a(flip),b,11373,a)].">
      <j1 rule="hyper" parents="139 5431 11373"/>
    </justification>
  </clause>

  <clause id="11379">
    <literal><![CDATA[
      a(x,x \ y,x) * y = x * (T(y,x) / x)
    ]]></literal>
    <justification jstring="[hyper(11021,a,11377,a)].">
      <j1 rule="hyper" parents="11021 11377"/>
    </justification>
  </clause>

  <clause id="11380">
    <literal><![CDATA[
      x \ (y * (T(x,y) / y)) != z
    ]]></literal>
    <literal><![CDATA[
      a(y,y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(11377(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11377 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11381">
    <literal><![CDATA[
      L(x,y,z) \ (u * (L(T(x,u),y,z) / u)) = a(u,u \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(25(a,2),11378(a,1,2,2,1))].">
      <j1 rule="para" parents="25 11378"/>
    </justification>
  </clause>

  <clause id="11382">
    <literal><![CDATA[
      R(1 / x,y,x) = 1 / L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,2169,a(flip),b,11374,a(flip))].">
      <j1 rule="hyper" parents="35 2169 11374"/>
    </justification>
  </clause>

  <clause id="11383">
    <literal><![CDATA[
      1 / L(L(x,y,z),x,L(x,y,z)) = (1 * x) / (x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,3204,a(flip),b,11382,a),flip(a)].">
      <j1 rule="hyper" parents="64 3204 11382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11384">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(9297,a,11359,a),flip(a)].">
      <j1 rule="hyper" parents="9297 11359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11385">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (K(x,T(y,z)) * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(11384(a,1),10946(a,1,1))].">
      <j1 rule="para" parents="11384 10946"/>
    </justification>
  </clause>

  <clause id="11386">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (y * K(x,T(y,z))) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(4011(a,1),11385(a,1,2))].">
      <j1 rule="para" parents="4011 11385"/>
    </justification>
  </clause>

  <clause id="11387">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7928,a,11386,a)].">
      <j1 rule="hyper" parents="7928 11386"/>
    </justification>
  </clause>

  <clause id="11388">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(5445(a,1),11387(a,1,1))].">
      <j1 rule="para" parents="5445 11387"/>
    </justification>
  </clause>

  <clause id="11389">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,T(y * x,z)) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4012,a(flip),b,11388,a)].">
      <j1 rule="hyper" parents="64 4012 11388"/>
    </justification>
  </clause>

  <clause id="11390">
    <literal><![CDATA[
      K(x \ 1,T(y,z)) * T(y,T(x \ y,z)) = L(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(9124(a,1),11389(a,1,2))].">
      <j1 rule="para" parents="9124 11389"/>
    </justification>
  </clause>

  <clause id="11391">
    <literal><![CDATA[
      K(x * y,z) * T(z,T(z * (y * x),y)) = L(z,y * x,z)
    ]]></literal>
    <justification jstring="[para(11177(a,1),11389(a,1,1))].">
      <j1 rule="para" parents="11177 11389"/>
    </justification>
  </clause>

  <clause id="11392">
    <literal><![CDATA[
      K(x \ (y \ x),z) * T(z,T(y \ z,x)) = L(z,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(7978(a,2),11390(a,1,1))].">
      <j1 rule="para" parents="7978 11390"/>
    </justification>
  </clause>

  <clause id="11393">
    <literal><![CDATA[
      K((x / y) \ 1,z) * T(z,T(z * ((y / x) * ((y / x) \ ((x / y) \ 1))),y / x)) = L(z,(y / x) * ((y / x) \ ((x / y) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(5199(a,1),11391(a,1,1,1))].">
      <j1 rule="para" parents="5199 11391"/>
    </justification>
  </clause>

  <clause id="11394">
    <literal><![CDATA[
      L(x,y \ (z \ y),x) = L(x,z \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10512,a(flip),b,11392,a)].">
      <j1 rule="hyper" parents="64 10512 11392"/>
    </justification>
  </clause>

  <clause id="11396">
    <literal><![CDATA[
      L(x,y \ (x \ y),x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1157,a(flip),b,11394,a),flip(a)].">
      <j1 rule="hyper" parents="373 1157 11394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11397">
    <literal><![CDATA[
      L(x,(y / z) \ 1,x) = L(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),11394(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 11394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11398">
    <literal><![CDATA[
      (x * ((y \ (x \ y)) * x)) / (1 / (1 / x)) = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(225,a,11396,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="225 11396 18"/>
    </justification>
  </clause>

  <clause id="11399">
    <literal><![CDATA[
      L(x,y * (y \ ((z / u) \ 1)),x) = L(x,z \ u,x)
    ]]></literal>
    <justification jstring="[para(10(a,2),11397(a,1,2))].">
      <j1 rule="para" parents="10 11397"/>
    </justification>
  </clause>

  <clause id="11400">
    <literal><![CDATA[
      R(x,y,x) * (T(x,z) \ u) = x * (L(T(x,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10740,a(flip),b,11352,a)].">
      <j1 rule="hyper" parents="64 10740 11352"/>
    </justification>
  </clause>

  <clause id="11401">
    <literal><![CDATA[
      K(x,y) * (x * (L(T(x,z),u,x) \ w)) = R(T(x,y),u,x) * (T(x,z) \ w)
    ]]></literal>
    <justification jstring="[para(11400(a,1),7393(a,1,2))].">
      <j1 rule="para" parents="11400 7393"/>
    </justification>
  </clause>

  <clause id="11402">
    <literal><![CDATA[
      1 / L(L(x,y,z),x,L(x,y,z)) = x / (x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,172,a(flip),b,11383,a),flip(a)].">
      <j1 rule="hyper" parents="373 172 11383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11403">
    <literal><![CDATA[
      L(x,y,z) \ L(u * (T(x,u) / u),y,z) = a(u,u \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5618(a,2),11381(a,1,2))].">
      <j1 rule="para" parents="5618 11381"/>
    </justification>
  </clause>

  <clause id="11404">
    <literal><![CDATA[
      R(T(x,y),z,x) * (T(x,u) \ w) = T(x,y) * (L(T(x,u),z,x) \ w)
    ]]></literal>
    <justification jstring="[hyper(5985,a,11401,a),flip(a)].">
      <j1 rule="hyper" parents="5985 11401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11405">
    <literal><![CDATA[
      R(T(x,(y * (z * u)) / ((x * z) * u)),z,u) = T(R(x,z,u),R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4636,a(flip),b,11332,a),flip(a)].">
      <j1 rule="hyper" parents="373 4636 11332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11406">
    <literal><![CDATA[
      (x \ T(x * K(x / y,z),x)) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(8196(a,1),11333(a,1,1,2,1))].">
      <j1 rule="para" parents="8196 11333"/>
    </justification>
  </clause>

  <clause id="11407">
    <literal><![CDATA[
      R(T(x,(y * (z * u)) / ((x * z) * u)),z,u) = R(T(x,R(x,z,u) \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,27,a,b,11405,a),flip(a)].">
      <j1 rule="hyper" parents="373 27 11405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11408">
    <literal><![CDATA[
      R(T(x,x \ ((y * (z * u)) / (z * u))),z,u) = R(T(x,R(x,z,u) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(10808(a,1),11407(a,1,1))].">
      <j1 rule="para" parents="10808 11407"/>
    </justification>
  </clause>

  <clause id="11409">
    <literal><![CDATA[
      R(T(x,R(x,y,z) \ u),y,z) = R(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),11408(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 11408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11410">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(762,a,11409,a),flip(a)].">
      <j1 rule="hyper" parents="762 11409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11411">
    <literal><![CDATA[
      T(x,R(x,y,z) \ u) = (x \ u) \ u
    ]]></literal>
    <justification jstring="[hyper(43,a,1769,a(flip),b,11409,a),flip(a)].">
      <j1 rule="hyper" parents="43 1769 11409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11412">
    <literal><![CDATA[
      T(x / y,y * (x \ z)) = ((x / y) \ z) \ z
    ]]></literal>
    <justification jstring="[para(684(a,1),11411(a,1,2))].">
      <j1 rule="para" parents="684 11411"/>
    </justification>
  </clause>

  <clause id="11414">
    <literal><![CDATA[
      x / R(T(y,y \ x),z,u) = R(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,11410,a,b,xx)].">
      <j1 rule="hyper" parents="225 11410"/>
    </justification>
  </clause>

  <clause id="11415">
    <literal><![CDATA[
      R((x \ y) \ y,z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,1769,a(flip),b,11410,a)].">
      <j1 rule="hyper" parents="64 1769 11410"/>
    </justification>
  </clause>

  <clause id="11416">
    <literal><![CDATA[
      x / R((y \ x) \ x,z,u) = R(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,1769,a(flip),b,11410,a(flip))].">
      <j1 rule="hyper" parents="225 1769 11410"/>
    </justification>
  </clause>

  <clause id="11417">
    <literal><![CDATA[
      (R(x,y,z) \ (x * u)) \ (x * u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),11410(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 11410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11418">
    <literal><![CDATA[
      (R(x / y,z,u) \ x) \ x = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(848(a,1),11410(a,1,1)),flip(a)].">
      <j1 rule="para" parents="848 11410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11419">
    <literal><![CDATA[
      R(T(x,x \ y),x,y) = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(1997(a,1),11410(a,2,1))].">
      <j1 rule="para" parents="1997 11410"/>
    </justification>
  </clause>

  <clause id="11420">
    <literal><![CDATA[
      R(T(x,x \ y),x,x \ y) = ((1 / x) * y) \ y
    ]]></literal>
    <justification jstring="[para(2016(a,1),11410(a,2,1))].">
      <j1 rule="para" parents="2016 11410"/>
    </justification>
  </clause>

  <clause id="11421">
    <literal><![CDATA[
      (R(K(x,y),z,u) \ w) \ w = R(T(K(x,y),w),z,u)
    ]]></literal>
    <justification jstring="[para(8889(a,1),11410(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8889 11410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11422">
    <literal><![CDATA[
      R((x \ y) \ y,x,y) = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,1769,a(flip),b,11419,a)].">
      <j1 rule="hyper" parents="64 1769 11419"/>
    </justification>
  </clause>

  <clause id="11423">
    <literal><![CDATA[
      (x \ y) * (((x \ 1) * y) \ y) = (x \ 1) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(11422(a,1),1935(a,1,2))].">
      <j1 rule="para" parents="11422 1935"/>
    </justification>
  </clause>

  <clause id="11424">
    <literal><![CDATA[
      T(((x / y) \ z) \ z,y) = T(y \ x,y * (x \ z))
    ]]></literal>
    <justification jstring="[para(11412(a,1),278(a,1,1))].">
      <j1 rule="para" parents="11412 278"/>
    </justification>
  </clause>

  <clause id="11425">
    <literal><![CDATA[
      x / R(y \ x,z,u) = R(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(848(a,1),11414(a,1,2,1))].">
      <j1 rule="para" parents="848 11414"/>
    </justification>
  </clause>

  <clause id="11426">
    <literal><![CDATA[
      R(x / (x / y),z,u) \ x = x / R(y,z,u)
    ]]></literal>
    <justification jstring="[para(412(a,1),11414(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="412 11414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11427">
    <literal><![CDATA[
      1 / R(R(x,x,x),y,z) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1417(a,1),11414(a,1,2,1))].">
      <j1 rule="para" parents="1417 11414"/>
    </justification>
  </clause>

  <clause id="11429">
    <literal><![CDATA[
      R(((x * K(y,x)) \ y) \ y,z,u) = (R(x,z,u) \ ((R(x,z,u) * y) / R(x,z,u))) \ y
    ]]></literal>
    <justification jstring="[para(6551(a,1),11415(a,2,1))].">
      <j1 rule="para" parents="6551 11415"/>
    </justification>
  </clause>

  <clause id="11430">
    <literal><![CDATA[
      x / R(T(x,y),z,u) = R(T(x,y),z,u) \ x
    ]]></literal>
    <justification jstring="[para(3985(a,1),11416(a,1,2,1))].">
      <j1 rule="para" parents="3985 11416"/>
    </justification>
  </clause>

  <clause id="11431">
    <literal><![CDATA[
      x / R(T(y \ x,z),u,w) = R(T(x / y,z),u,w) \ x
    ]]></literal>
    <justification jstring="[para(8074(a,1),11416(a,1,2,1))].">
      <j1 rule="para" parents="8074 11416"/>
    </justification>
  </clause>

  <clause id="11432">
    <literal><![CDATA[
      R(1 / x,x,x * y) \ 1 = 1 / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(225,a,3025,a(flip),b,11418,a),flip(a)].">
      <j1 rule="hyper" parents="225 3025 11418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11433">
    <literal><![CDATA[
      K(x * R(1 / y,z,u),w) = K(x * R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(11418(a,1),5256(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11418 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11434">
    <literal><![CDATA[
      K(x,R(x / y,z,u) \ w) = K(x,R(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(11418(a,1),9882(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11418 9882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11435">
    <literal><![CDATA[
      1 / R(x \ 1,y,z) = x * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2468,a(flip),b,11425,a),flip(a)].">
      <j1 rule="hyper" parents="373 2468 11425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11436">
    <literal><![CDATA[
      R(x / (x / y),z,u) = x / (x / R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(226,a,11426,a),flip(a)].">
      <j1 rule="hyper" parents="226 11426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11437">
    <literal><![CDATA[
      R(x / (x * x),y,z) \ 1 = 1 / R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(2029(a,1),11426(a,1,1,1))].">
      <j1 rule="para" parents="2029 11426"/>
    </justification>
  </clause>

  <clause id="11438">
    <literal><![CDATA[
      R(x,x,x \ y) \ 1 = 1 / R(x,x,y)
    ]]></literal>
    <justification jstring="[para(3021(a,1),11426(a,1,1))].">
      <j1 rule="para" parents="3021 11426"/>
    </justification>
  </clause>

  <clause id="11439">
    <literal><![CDATA[
      R(T(1 / (1 / x),y),z,u) \ 1 = 1 / R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3570(a,1),11426(a,1,1,1))].">
      <j1 rule="para" parents="3570 11426"/>
    </justification>
  </clause>

  <clause id="11441">
    <literal><![CDATA[
      1 / R(x,x,x * y) = R(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),11438(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="9 11438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11442">
    <literal><![CDATA[
      R(R(x,x,x),x,y) = R(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(37,a,11427,a,b,11441,a)].">
      <j1 rule="hyper" parents="37 11427 11441"/>
    </justification>
  </clause>

  <clause id="11443">
    <literal><![CDATA[
      R(T(x,x \ 1),x,y) = R(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(37,a,11414,a,b,11441,a)].">
      <j1 rule="hyper" parents="37 11414 11441"/>
    </justification>
  </clause>

  <clause id="11444">
    <literal><![CDATA[
      a(x,y,R(z \ 1,u,w) \ 1) = a(x,y,z * (R(z,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(11435(a,1),5342(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11435 5342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11445">
    <literal><![CDATA[
      R(x / (x / (y * y)),z,u) = x / (x / (y * y))
    ]]></literal>
    <justification jstring="[para(655(a,1),11436(a,2,2,2))].">
      <j1 rule="para" parents="655 11436"/>
    </justification>
  </clause>

  <clause id="11446">
    <literal><![CDATA[
      R(x * K(x \ y,x),z,u) = y / (y / R(x,z,u))
    ]]></literal>
    <justification jstring="[para(5793(a,1),11436(a,1,1))].">
      <j1 rule="para" parents="5793 11436"/>
    </justification>
  </clause>

  <clause id="11447">
    <literal><![CDATA[
      (x \ y) \ ((1 / x) \ (x \ y)) = ((1 / x) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,1917,a(flip),b,11420,a)].">
      <j1 rule="hyper" parents="64 1917 11420"/>
    </justification>
  </clause>

  <clause id="11448">
    <literal><![CDATA[
      (x * y) / ((x / (z * z)) * y) = x / (x / (z * z))
    ]]></literal>
    <justification jstring="[hyper(1084,a,11445,a)].">
      <j1 rule="hyper" parents="1084 11445"/>
    </justification>
  </clause>

  <clause id="11449">
    <literal><![CDATA[
      (x / (x / (y * y))) \ (z * u) = ((x / (x / (y * y))) \ z) * u
    ]]></literal>
    <justification jstring="[para(11445(a,1),649(a,1,1))].">
      <j1 rule="para" parents="11445 649"/>
    </justification>
  </clause>

  <clause id="11450">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = (x * u) \ (x * (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(1905(a,1),11417(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1905 11417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11451">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(T(K(y,x),z * u),z,u)
    ]]></literal>
    <justification jstring="[para(9689(a,1),11421(a,1,1))].">
      <j1 rule="para" parents="9689 11421"/>
    </justification>
  </clause>

  <clause id="11452">
    <literal><![CDATA[
      (x \ y) * (((x \ 1) * y) \ y) = x \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1166,a(flip),b,11423,a),flip(a)].">
      <j1 rule="hyper" parents="373 1166 11423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11453">
    <literal><![CDATA[
      T(x \ y,x * (y \ z)) = ((x \ y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,8394,a(flip),b,11424,a),flip(a)].">
      <j1 rule="hyper" parents="64 8394 11424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11454">
    <literal><![CDATA[
      (x * x) * (R(x,y,z) \ 1) = 1 / R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2153,a(flip),b,11437,a)].">
      <j1 rule="hyper" parents="64 2153 11437"/>
    </justification>
  </clause>

  <clause id="11455">
    <literal><![CDATA[
      T(R(x * K(x \ y,x),z,u),y) = L(R(x,z,u),R(x,z,u) \ y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(11446(a,2),4771(a,1,1))].">
      <j1 rule="para" parents="11446 4771"/>
    </justification>
  </clause>

  <clause id="11456">
    <literal><![CDATA[
      (x * y) / (x * ((z * z) \ y)) = x / (x / (z * z))
    ]]></literal>
    <justification jstring="[para(897(a,1),11448(a,1,2))].">
      <j1 rule="para" parents="897 11448"/>
    </justification>
  </clause>

  <clause id="11457">
    <literal><![CDATA[
      (x * ((y * y) * z)) / (x * z) = x / (x / (y * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),11456(a,1,2,2))].">
      <j1 rule="para" parents="9 11456"/>
    </justification>
  </clause>

  <clause id="11458">
    <literal><![CDATA[
      (x / (x / (y * y))) \ z = x * ((y * y) \ (x \ z))
    ]]></literal>
    <justification jstring="[para(11456(a,1),349(a,1,1))].">
      <j1 rule="para" parents="11456 349"/>
    </justification>
  </clause>

  <clause id="11459">
    <literal><![CDATA[
      (x / (x / (y * y))) * z = x * ((y * y) * (x \ z))
    ]]></literal>
    <justification jstring="[para(11457(a,1),385(a,1,1))].">
      <j1 rule="para" parents="11457 385"/>
    </justification>
  </clause>

  <clause id="11460">
    <literal><![CDATA[
      x * ((x * x) \ (x \ y)) = (x * L(x,x,x)) \ y
    ]]></literal>
    <justification jstring="[para(4806(a,1),11458(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4806 11458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11461">
    <literal><![CDATA[
      x * ((x * x) * (x \ y)) = (x * L(x,x,x)) * y
    ]]></literal>
    <justification jstring="[para(4806(a,1),11459(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4806 11459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11462">
    <literal><![CDATA[
      R(T(1 / x,y),x,y) \ 1 = 1 / (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(2985(a,1),11431(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2985 11431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11463">
    <literal><![CDATA[
      R(T(1 / x,y),x,y) = 1 / (1 / (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(226,a,11462,a),flip(a)].">
      <j1 rule="hyper" parents="226 11462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11464">
    <literal><![CDATA[
      T(R(T(1 / x,y),x,y),x) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(11463(a,2),3689(a,1,1))].">
      <j1 rule="para" parents="11463 3689"/>
    </justification>
  </clause>

  <clause id="11465">
    <literal><![CDATA[
      T(K(x * R(y \ 1,y,z),y \ 1) / y,x) = R(1 / y,x,z / (y * z))
    ]]></literal>
    <justification jstring="[para(11433(a,1),9943(a,1,1,1))].">
      <j1 rule="para" parents="11433 9943"/>
    </justification>
  </clause>

  <clause id="11466">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),1 / x,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(1002(a,1),11439(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1002 11439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11467">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(K(y,T(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(7867(a,2),11451(a,2,1))].">
      <j1 rule="para" parents="7867 11451"/>
    </justification>
  </clause>

  <clause id="11468">
    <literal><![CDATA[
      ((K(x,T(y,z)) * L(x,u,w)) * z) \ (L(x,u,w) * z) = R(K(y,L(x,z,L(x,u,w))),L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(8669(a,1),11467(a,2,1))].">
      <j1 rule="para" parents="8669 11467"/>
    </justification>
  </clause>

  <clause id="11469">
    <literal><![CDATA[
      ((x / (x / (y * y))) \ z) * u = x * ((y * y) \ (x \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11458,a(flip),b,11449,a),flip(a)].">
      <j1 rule="hyper" parents="64 11458 11449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11470">
    <literal><![CDATA[
      (x * ((y * y) \ (x \ z))) * u = x * ((y * y) \ (x \ (z * u)))
    ]]></literal>
    <justification jstring="[para(11458(a,1),11469(a,1,1))].">
      <j1 rule="para" parents="11458 11469"/>
    </justification>
  </clause>

  <clause id="11471">
    <literal><![CDATA[
      x \ ((x * ((y * y) \ (x \ z))) * u) = (y * y) \ (x \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(720,a,11470,a)].">
      <j1 rule="hyper" parents="720 11470"/>
    </justification>
  </clause>

  <clause id="11472">
    <literal><![CDATA[
      x \ (((x * L(x,x,x)) \ y) * z) = (x * x) \ (x \ (y * z))
    ]]></literal>
    <justification jstring="[para(11460(a,1),11471(a,1,2,1))].">
      <j1 rule="para" parents="11460 11471"/>
    </justification>
  </clause>

  <clause id="11473">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = L(T(R(x,y,z),u),u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,262,a(flip),b,11450,a),flip(a)].">
      <j1 rule="hyper" parents="373 262 11450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11474">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = R(T(x,x * u),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1338,a(flip),b,11473,a),flip(a)].">
      <j1 rule="hyper" parents="373 1338 11473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11475">
    <literal><![CDATA[
      R(T(x,x * y),z,u) \ R(x,z,u) = K(R(x,z,u) * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(11474(a,1),5802(a,1,1))].">
      <j1 rule="para" parents="11474 5802"/>
    </justification>
  </clause>

  <clause id="11476">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(2979(a,1),11466(a,1,2))].">
      <j1 rule="para" parents="2979 11466"/>
    </justification>
  </clause>

  <clause id="11477">
    <literal><![CDATA[
      1 / R(T(x,(x \ 1) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(3150(a,1),11476(a,1,2,1))].">
      <j1 rule="para" parents="3150 11476"/>
    </justification>
  </clause>

  <clause id="11478">
    <literal><![CDATA[
      (((1 / x) * (y * x)) \ (y * x)) \ 1 = 1 / R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(4907(a,1),11477(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4907 11477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11479">
    <literal><![CDATA[
      K(R(x,y,z) * u,R(x,y,z)) = K(x * u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(5975,a,11475,a),flip(a)].">
      <j1 rule="hyper" parents="5975 11475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11480">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8578,a,11479,a)].">
      <j1 rule="hyper" parents="8578 11479"/>
    </justification>
  </clause>

  <clause id="11481">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(x * y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,9892,a,b,11480,a),flip(a)].">
      <j1 rule="hyper" parents="373 9892 11480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11482">
    <literal><![CDATA[
      1 / R(T(x,y),x \ 1,y * x) = (L(y,x,x \ 1) \ (x * y)) \ 1
    ]]></literal>
    <justification jstring="[para(4988(a,1),11478(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4988 11478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11483">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = R(T(y,x),y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(215,a,11482,a)].">
      <j1 rule="hyper" parents="215 11482"/>
    </justification>
  </clause>

  <clause id="11484">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ (x * y) = R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3770,a(flip),b,11483,a)].">
      <j1 rule="hyper" parents="64 3770 11483"/>
    </justification>
  </clause>

  <clause id="11485">
    <literal><![CDATA[
      R(T(x * K(x \ y,x),y),z,u) = L(R(x,z,u),R(x,z,u) \ y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,11455,a)].">
      <j1 rule="hyper" parents="64 27 11455"/>
    </justification>
  </clause>

  <clause id="11486">
    <literal><![CDATA[
      L(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = R(L(x,x \ u,x),y,z)
    ]]></literal>
    <justification jstring="[para(5905(a,1),11485(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5905 11485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11487">
    <literal><![CDATA[
      L(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = L(R(x,y,z),x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,29,a(flip),b,11486,a),flip(a)].">
      <j1 rule="hyper" parents="373 29 11486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11488">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = (L(R(x,y,z),x \ u,x) * u) \ (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(11487(a,1),1968(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11487 1968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11489">
    <literal><![CDATA[
      K(x,y) * (R(T(y,z),u,w) * (K(y,x) * v5)) = R(T(y,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(8205(a,1),10729(a,1,2,2,1))].">
      <j1 rule="para" parents="8205 10729"/>
    </justification>
  </clause>

  <clause id="11491">
    <literal><![CDATA[
      (x * (y * L(x,z,u))) \ ((x * y) * L(x,z,u)) = x \ R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(3207(a,1),10876(a,1,2))].">
      <j1 rule="para" parents="3207 10876"/>
    </justification>
  </clause>

  <clause id="11492">
    <literal><![CDATA[
      x \ R(x,y,L(x,z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(959,a,11491,a),flip(a)].">
      <j1 rule="hyper" parents="959 11491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11494">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9528,a,b,11492,a)].">
      <j1 rule="hyper" parents="64 9528 11492"/>
    </justification>
  </clause>

  <clause id="11495">
    <literal><![CDATA[
      a(x,y * K(L(x,z,u),y),L(x,z,u)) = x \ R(x,y,T(L(x,z,u),y))
    ]]></literal>
    <justification jstring="[para(7111(a,1),11492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7111 11492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11496">
    <literal><![CDATA[
      a(x,y * K(L(x,z,u),y),L(x,z,u)) = x \ R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(10200(a,1),11495(a,2,2))].">
      <j1 rule="para" parents="10200 11495"/>
    </justification>
  </clause>

  <clause id="11497">
    <literal><![CDATA[
      a(x,y * K(L(x,z,u),y),L(x,z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,11492,a(flip),b,11496,a),flip(a)].">
      <j1 rule="hyper" parents="373 11492 11496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11498">
    <literal><![CDATA[
      a(x,y,T(L(x,z,u),y)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(9486,a,11497,a)].">
      <j1 rule="hyper" parents="9486 11497"/>
    </justification>
  </clause>

  <clause id="11499">
    <literal><![CDATA[
      a(x,y,L(T(x,y),z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(25(a,2),11498(a,1,3))].">
      <j1 rule="para" parents="25 11498"/>
    </justification>
  </clause>

  <clause id="11500">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (u * L(T(x,x \ u),y,z)) = a(x,x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,3518,a(flip),b,11499,a)].">
      <j1 rule="hyper" parents="64 3518 11499"/>
    </justification>
  </clause>

  <clause id="11501">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(L(y,z,u),y \ x) = a(y,y \ x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11500,a(flip),b,10878,a),flip(a)].">
      <j1 rule="hyper" parents="64 11500 10878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11502">
    <literal><![CDATA[
      K((L(x,y,x) * y) \ z,y * x) * (z * u) = (((y * x) \ z) * (y * x)) * u
    ]]></literal>
    <justification jstring="[para(4694(a,1),10972(a,1,1,1,1))].">
      <j1 rule="para" parents="4694 10972"/>
    </justification>
  </clause>

  <clause id="11503">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[para(1182(a,1),11271(a,1,1))].">
      <j1 rule="para" parents="1182 11271"/>
    </justification>
  </clause>

  <clause id="11504">
    <literal><![CDATA[
      K((x \ 1) * T(y / (x \ 1),z),u) = K(x \ T(y * x,z),u)
    ]]></literal>
    <justification jstring="[hyper(8458,a,11503,a),flip(a)].">
      <j1 rule="hyper" parents="8458 11503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11505">
    <literal><![CDATA[
      R(T(x,y * y),y,y) \ (y \ (x * y)) = K(y,y * x) * a(y,y,y \ (x * y))
    ]]></literal>
    <justification jstring="[para(6142(a,1),11278(a,2,1))].">
      <j1 rule="para" parents="6142 11278"/>
    </justification>
  </clause>

  <clause id="11506">
    <literal><![CDATA[
      (x * (y * R(x,z,u))) \ ((x * y) * R(x,z,u)) = x \ R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(2832(a,1),11288(a,1,2))].">
      <j1 rule="para" parents="2832 11288"/>
    </justification>
  </clause>

  <clause id="11507">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(959,a,11506,a),flip(a)].">
      <j1 rule="hyper" parents="959 11506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11508">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11506(a,1),959(a,1))].">
      <j1 rule="para" parents="11506 959"/>
    </justification>
  </clause>

  <clause id="11509">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11266,a,b,11507,a)].">
      <j1 rule="hyper" parents="64 11266 11507"/>
    </justification>
  </clause>

  <clause id="11510">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) \ x = a(x,y,R(x,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(11507(a,1),5382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11507 5382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11511">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),T(z,x),R(T(x,y),u,w)) = a(T(x,y),z,R(T(x,y),u,w))
    ]]></literal>
    <justification jstring="[para(9889(a,2),11507(a,1,2))].">
      <j1 rule="para" parents="9889 11507"/>
    </justification>
  </clause>

  <clause id="11512">
    <literal><![CDATA[
      R(T(x,y),T(y,x),R(T(x,y),z,u)) \ T(x,y) = a(x,y,R(T(x,y),z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(5048(a,1),11510(a,2,1))].">
      <j1 rule="para" parents="5048 11510"/>
    </justification>
  </clause>

  <clause id="11513">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) * K(x,y * R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11509(a,1),6891(a,1,1))].">
      <j1 rule="para" parents="11509 6891"/>
    </justification>
  </clause>

  <clause id="11514">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(x,K(y,w)) = a(y,x,R(y,z,u)) * T(K(x,y),w)
    ]]></literal>
    <justification jstring="[para(11509(a,1),8851(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11509 8851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11515">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,T(x,R(y,w,v5))) = a(y,T(x,R(y,w,v5)),R(y,z,u))
    ]]></literal>
    <justification jstring="[para(9675(a,1),11509(a,1,1))].">
      <j1 rule="para" parents="9675 11509"/>
    </justification>
  </clause>

  <clause id="11516">
    <literal><![CDATA[
      a(x,y / R(x,z,u),R(x,z,u)) * K(x,y) = K(x,y / R(x,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),11513(a,1,2,2))].">
      <j1 rule="para" parents="12 11513"/>
    </justification>
  </clause>

  <clause id="11517">
    <literal><![CDATA[
      K(x \ ((y * z) / y),T((x \ ((y * z) / y)) \ z,y)) = K(x \ z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,10816,a(flip),b,11322,a)].">
      <j1 rule="hyper" parents="64 10816 11322"/>
    </justification>
  </clause>

  <clause id="11518">
    <literal><![CDATA[
      a(T(x,y),T(z,x),R(T(x,y),u,w)) = a(T(x,y),z,R(T(x,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(11508,a,11511,a)].">
      <j1 rule="hyper" parents="11508 11511"/>
    </justification>
  </clause>

  <clause id="11519">
    <literal><![CDATA[
      a(T(x,y),T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5056,a(flip),b,11518,a),flip(a)].">
      <j1 rule="hyper" parents="64 5056 11518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11520">
    <literal><![CDATA[
      a(x,y,R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(5049,a,11519,a)].">
      <j1 rule="hyper" parents="5049 11519"/>
    </justification>
  </clause>

  <clause id="11521">
    <literal><![CDATA[
      R(T(x,y),y,R(T(x,y),z,u)) \ T(x,y) = a(x,y,R(T(x,y),z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(9889(a,1),11512(a,1,1))].">
      <j1 rule="para" parents="9889 11512"/>
    </justification>
  </clause>

  <clause id="11522">
    <literal><![CDATA[
      R(T(x,y),y,R(T(x,y),z,u)) \ T(x,y) = a(R(x,z,u),y,x) \ 1
    ]]></literal>
    <justification jstring="[para(11520(a,1),11521(a,2,1))].">
      <j1 rule="para" parents="11520 11521"/>
    </justification>
  </clause>

  <clause id="11523">
    <literal><![CDATA[
      a(T(x,y),y,R(T(x,y),z,u)) \ 1 = a(R(x,z,u),y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,11510,a(flip),b,11522,a)].">
      <j1 rule="hyper" parents="64 11510 11522"/>
    </justification>
  </clause>

  <clause id="11524">
    <literal><![CDATA[
      R(T(x,y * a(z,u,z)),y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),y,a(z,u,z)) = w
    ]]></literal>
    <justification jstring="[para(11032(a,1),11034(a,1))].">
      <j1 rule="para" parents="11032 11034"/>
    </justification>
  </clause>

  <clause id="11525">
    <literal><![CDATA[
      ((x * y) * a(y,x,y)) \ ((y * x) * y) = R(T(y,y * x),x * y,a(y,x,y))
    ]]></literal>
    <justification jstring="[para(4619(a,1),11060(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4619 11060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11526">
    <literal><![CDATA[
      (x \ 1) * (y * (((x \ 1) * y) \ z)) = y * (x \ L(x * (y \ z),y,x))
    ]]></literal>
    <justification jstring="[para(1389(a,1),11291(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1389 11291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11527">
    <literal><![CDATA[
      a(x,T(y,R(x,z,u)),R(x,w,v5)) = K(y * R(x,w,v5),x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7876(a,1),11515(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7876 11515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11528">
    <literal><![CDATA[
      a(x,T(y,R(x,z,u)),R(x,w,v5)) = a(x,y,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,11509,a(flip),b,11527,a),flip(a)].">
      <j1 rule="hyper" parents="373 11509 11527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11530">
    <literal><![CDATA[
      a(x,y / R(x,z,u),R(x,w,v5)) = a(x,R(x,z,u) \ y,R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(117(a,1),11528(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 11528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11531">
    <literal><![CDATA[
      a(x,T(y,x),R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(431(a,1),11528(a,1,2,2))].">
      <j1 rule="para" parents="431 11528"/>
    </justification>
  </clause>

  <clause id="11532">
    <literal><![CDATA[
      a(x,R(x,y,z) \ u,R(x,y,z)) * K(x,u) = K(x,u / R(x,y,z))
    ]]></literal>
    <justification jstring="[para(11530(a,1),11516(a,1,1))].">
      <j1 rule="para" parents="11530 11516"/>
    </justification>
  </clause>

  <clause id="11533">
    <literal><![CDATA[
      a(x,R(x,y,z) \ u,R(x,y,z)) * K(x,u) = K(x,R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,7933,a(flip),b,11532,a),flip(a)].">
      <j1 rule="hyper" parents="373 7933 11532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11534">
    <literal><![CDATA[
      K(x,(y * (K(z,x) * u)) \ (y * (u * w))) = K(x,L(w,K(z,x) * u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7790,a(flip),b,10726,a),flip(a)].">
      <j1 rule="hyper" parents="64 7790 10726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11536">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,(w * u) \ (w * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,10723,a(flip),b,11534,a),flip(a)].">
      <j1 rule="hyper" parents="64 10723 11534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11538">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(18(a,2),11536(a,2,2))].">
      <j1 rule="para" parents="18 11536"/>
    </justification>
  </clause>

  <clause id="11539">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(6161(a,1),11538(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6161 11538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11540">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(11539(a,1),6177(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11539 6177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11541">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6177,a(flip),b,11540,a),flip(a)].">
      <j1 rule="hyper" parents="373 6177 11540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11542">
    <literal><![CDATA[
      K(L(x,T(y,z),u),z) = K(L(x,y,u),z)
    ]]></literal>
    <justification jstring="[para(5797(a,1),11541(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5797 11541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11543">
    <literal><![CDATA[
      K(x,L(R(y,x \ z,y),z,u)) = K(L(x,y * (x \ z),u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10690,a(flip),b,11542,a)].">
      <j1 rule="hyper" parents="64 10690 11542"/>
    </justification>
  </clause>

  <clause id="11544">
    <literal><![CDATA[
      K(L(x,y,z) \ u,L(x,y,z)) = K(x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(10792,a,10300,a)].">
      <j1 rule="hyper" parents="10792 10300"/>
    </justification>
  </clause>

  <clause id="11545">
    <literal><![CDATA[
      K(x \ ((x \ (1 / L(x,y,z))) \ u),L(x,y,z)) = K((1 / x) \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10234,a(flip),b,11544,a),flip(a)].">
      <j1 rule="hyper" parents="64 10234 11544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11546">
    <literal><![CDATA[
      K((1 / L(x,y,z)) \ u,L(x,y,z)) = K((1 / x) \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10401,a(flip),b,11545,a)].">
      <j1 rule="hyper" parents="64 10401 11545"/>
    </justification>
  </clause>

  <clause id="11547">
    <literal><![CDATA[
      K(L(x,y,z) * u,L(x,y,z)) = K((1 / x) \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6990,a(flip),b,11546,a)].">
      <j1 rule="hyper" parents="64 6990 11546"/>
    </justification>
  </clause>

  <clause id="11548">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K((1 / y) \ x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8578,a,11547,a)].">
      <j1 rule="hyper" parents="8578 11547"/>
    </justification>
  </clause>

  <clause id="11549">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K(1 \ (x * y),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,9547,a(flip),b,11548,a),flip(a)].">
      <j1 rule="hyper" parents="373 9547 11548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11550">
    <literal><![CDATA[
      K(x * L(y,z,u),L(y,z,u)) = K(x * y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(66(a,1),11549(a,2,1))].">
      <j1 rule="para" parents="66 11549"/>
    </justification>
  </clause>

  <clause id="11551">
    <literal><![CDATA[
      T(L(x,y,z) * K(u * x,L(x,y,z)),u) = R(L(x,y,z),u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(11550(a,1),5902(a,1,1,2))].">
      <j1 rule="para" parents="11550 5902"/>
    </justification>
  </clause>

  <clause id="11552">
    <literal><![CDATA[
      K(x * y,L(y,z,u)) * K(L(y,z,u),L(y,z,u) \ (x * L(y,z,u))) = a(L(y,z,u),L(y,z,u) \ (x * L(y,z,u)),L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11550(a,1),10893(a,1,1))].">
      <j1 rule="para" parents="11550 10893"/>
    </justification>
  </clause>

  <clause id="11553">
    <literal><![CDATA[
      T(L(x * K(y * x,x),z,u),y) = R(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(6547(a,1),11551(a,1,1))].">
      <j1 rule="para" parents="6547 11551"/>
    </justification>
  </clause>

  <clause id="11554">
    <literal><![CDATA[
      T(L(x * K(x * y,x),z,u),y) = R(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(8516(a,1),11553(a,1,1,1,2))].">
      <j1 rule="para" parents="8516 11553"/>
    </justification>
  </clause>

  <clause id="11555">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,y,z)) = L(T(x * K(x * u,x),u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,25,a,b,11554,a),flip(a)].">
      <j1 rule="hyper" parents="64 25 11554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11556">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,y,z)) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(6235(a,1),11555(a,2,1))].">
      <j1 rule="para" parents="6235 11555"/>
    </justification>
  </clause>

  <clause id="11557">
    <literal><![CDATA[
      R(L(x,y,x),y,L(x,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,4733,a(flip),b,11556,a),flip(a)].">
      <j1 rule="hyper" parents="373 4733 11556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11558">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,x),y,z) = a(L(x,y,z),u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,11556,a(flip),b,10889,a)].">
      <j1 rule="hyper" parents="139 11556 10889"/>
    </justification>
  </clause>

  <clause id="11559">
    <literal><![CDATA[
      R(x,y,L(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(42,a,29,a(flip),b,11556,a(flip))].">
      <j1 rule="hyper" parents="42 29 11556"/>
    </justification>
  </clause>

  <clause id="11560">
    <literal><![CDATA[
      K(x,L(R(y,z,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11556(a,1),7403(a,1,2))].">
      <j1 rule="para" parents="11556 7403"/>
    </justification>
  </clause>

  <clause id="11561">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,5902,a,b,11559,a)].">
      <j1 rule="hyper" parents="373 5902 11559"/>
    </justification>
  </clause>

  <clause id="11563">
    <literal><![CDATA[
      L(R(x,L(x,y,z),x),u,w) / L(x,y,z) = L(x,u,w) * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(11559(a,1),1410(a,1,1,1))].">
      <j1 rule="para" parents="11559 1410"/>
    </justification>
  </clause>

  <clause id="11564">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = (w * T(y,x)) \ (w * R(y,x,y))
    ]]></literal>
    <justification jstring="[para(11559(a,1),10034(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11559 10034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11565">
    <literal><![CDATA[
      T(R(x,y,z) * K(u * x,R(x,y,z)),u) = R(R(x,y,z),u,L(R(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(11481(a,1),11561(a,1,1,2))].">
      <j1 rule="para" parents="11481 11561"/>
    </justification>
  </clause>

  <clause id="11566">
    <literal><![CDATA[
      K(L(x,y * (x \ z),u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11543(a,1),11560(a,1))].">
      <j1 rule="para" parents="11543 11560"/>
    </justification>
  </clause>

  <clause id="11567">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8002,a(flip),b,11564,a),flip(a)].">
      <j1 rule="hyper" parents="373 8002 11564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11569">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),x) = K(u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8595,a(flip),b,11567,a),flip(a)].">
      <j1 rule="hyper" parents="64 8595 11567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11570">
    <literal><![CDATA[
      K(x * (y * z),z) = K(z * (x * y),z)
    ]]></literal>
    <justification jstring="[para(100(a,1),11567(a,1,1))].">
      <j1 rule="para" parents="100 11567"/>
    </justification>
  </clause>

  <clause id="11573">
    <literal><![CDATA[
      T(x * K(y,x),x * (L(x,z,u) \ y)) = x
    ]]></literal>
    <justification jstring="[para(11569(a,1),5785(a,1,1,2))].">
      <j1 rule="para" parents="11569 5785"/>
    </justification>
  </clause>

  <clause id="11574">
    <literal><![CDATA[
      K(x * (y * z),y) = K(y * (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(10198,a,11570,a)].">
      <j1 rule="hyper" parents="10198 11570"/>
    </justification>
  </clause>

  <clause id="11575">
    <literal><![CDATA[
      T(x,x * (L(x,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(11573(a,1),5857(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11573 5857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11576">
    <literal><![CDATA[
      T(x,L(x,y,z) * u) = T(x,x * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),11575(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 11575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11577">
    <literal><![CDATA[
      T(x,y) \ ((x \ (x * (L(x,z,u) \ y))) \ (x * (L(x,z,u) \ y))) = a(x,x \ (x * (L(x,z,u) \ y)),x)
    ]]></literal>
    <justification jstring="[para(11575(a,1),10941(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11575 10941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11578">
    <literal><![CDATA[
      T(x,L(x,y,z) * u) = x * K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5753,a(flip),b,11576,a),flip(a)].">
      <j1 rule="hyper" parents="373 5753 11576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11579">
    <literal><![CDATA[
      T(x,y * (z * x)) = T(x,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8593,a(flip),b,11576,a)].">
      <j1 rule="hyper" parents="64 8593 11576"/>
    </justification>
  </clause>

  <clause id="11581">
    <literal><![CDATA[
      T(x,y * (y * x)) = T(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,766,a(flip),b,11579,a),flip(a)].">
      <j1 rule="hyper" parents="373 766 11579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11582">
    <literal><![CDATA[
      T(x,y * (x * y)) = T(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8508,a(flip),b,11581,a)].">
      <j1 rule="hyper" parents="64 8508 11581"/>
    </justification>
  </clause>

  <clause id="11583">
    <literal><![CDATA[
      K(x,L(x,y,z) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(5826,a,11578,a)].">
      <j1 rule="hyper" parents="5826 11578"/>
    </justification>
  </clause>

  <clause id="11584">
    <literal><![CDATA[
      K(x,y * L(x,z,u)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(11234,a,11583,a)].">
      <j1 rule="hyper" parents="11234 11583"/>
    </justification>
  </clause>

  <clause id="11586">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) * (y * x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(442(a,1),11584(a,1,2)),flip(a)].">
      <j1 rule="para" parents="442 11584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11588">
    <literal><![CDATA[
      T(R(x * K(y * x,x),z,u),y) = R(R(x,z,u),y,L(R(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(6388(a,1),11565(a,1,1))].">
      <j1 rule="para" parents="6388 11565"/>
    </justification>
  </clause>

  <clause id="11589">
    <literal><![CDATA[
      T(R(x * K(x * y,x),z,u),y) = R(R(x,z,u),y,L(R(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(8516(a,1),11588(a,1,1,1,2))].">
      <j1 rule="para" parents="8516 11588"/>
    </justification>
  </clause>

  <clause id="11590">
    <literal><![CDATA[
      R(T(x * K(x * y,x),y),z,u) = R(R(x,z,u),y,L(R(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27,a,b,11589,a)].">
      <j1 rule="hyper" parents="64 27 11589"/>
    </justification>
  </clause>

  <clause id="11591">
    <literal><![CDATA[
      R(R(x,y,z),u,L(R(x,y,z),w,v5)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(6235(a,1),11590(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6235 11590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11592">
    <literal><![CDATA[
      R(R(x,y,z),u,R(x,y,z)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11559,a(flip),b,11591,a)].">
      <j1 rule="hyper" parents="64 11559 11591"/>
    </justification>
  </clause>

  <clause id="11593">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(43,a,31,a,b,11592,a(flip))].">
      <j1 rule="hyper" parents="43 31 11592"/>
    </justification>
  </clause>

  <clause id="11595">
    <literal><![CDATA[
      K(x,R(y,z,R(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11593(a,2),7402(a,1,2))].">
      <j1 rule="para" parents="11593 7402"/>
    </justification>
  </clause>

  <clause id="11596">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,R(z,u,R(T(z,y),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(8321,a,11595,a),flip(a)].">
      <j1 rule="hyper" parents="8321 11595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11599">
    <literal><![CDATA[
      K(x,R(y,z,R(T(y,u),w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8312,a,11596,a),flip(a)].">
      <j1 rule="hyper" parents="8312 11596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11601">
    <literal><![CDATA[
      K(x,y) * (y \ R(T(y,x),z,R(T(y,u),w,v5))) = y \ R(y,z,R(T(y,u),w,v5))
    ]]></literal>
    <justification jstring="[para(11599(a,1),10124(a,1,1))].">
      <j1 rule="para" parents="11599 10124"/>
    </justification>
  </clause>

  <clause id="11602">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,R(T(x,u),w,v5)) = x \ R(x,z,R(T(x,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(6301,a,11601,a)].">
      <j1 rule="hyper" parents="6301 11601"/>
    </justification>
  </clause>

  <clause id="11603">
    <literal><![CDATA[
      K(x,y) * (y \ R(T(y,x),z,R(y,u,w))) = y \ R(y,z,R(T(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(10090(a,1),11601(a,1,2,2))].">
      <j1 rule="para" parents="10090 11601"/>
    </justification>
  </clause>

  <clause id="11604">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(T(x,z),y,R(T(x,z),u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11602(a,1),11508(a,1))].">
      <j1 rule="para" parents="11602 11508"/>
    </justification>
  </clause>

  <clause id="11605">
    <literal><![CDATA[
      (1 / (1 / x)) \ ((y / x) / (1 / x)) = ((y / x) / (1 / x)) / T(x,y * x)
    ]]></literal>
    <justification jstring="[para(8865(a,1),10800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8865 10800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11606">
    <literal><![CDATA[
      (1 / (1 / x)) \ ((y / x) / (1 / x)) = ((y / x) / (1 / x)) / T(x,x * y)
    ]]></literal>
    <justification jstring="[para(4683(a,1),11605(a,2,2))].">
      <j1 rule="para" parents="4683 11605"/>
    </justification>
  </clause>

  <clause id="11607">
    <literal><![CDATA[
      ((x / y) / (1 / y)) / T(y,y * x) = y \ ((x / y) / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,3721,a(flip),b,11606,a),flip(a)].">
      <j1 rule="hyper" parents="64 3721 11606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11608">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ u,L(x,y,z)) = a(x,x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,11501,a(flip),b,10957,a),flip(a)].">
      <j1 rule="hyper" parents="373 11501 10957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11609">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * x),L(x,y,z)) = K(u * x,L(x,y,z)) * K(L(x,y,z),T(u,x))
    ]]></literal>
    <justification jstring="[para(22(a,2),10957(a,2,2,2))].">
      <j1 rule="para" parents="22 10957"/>
    </justification>
  </clause>

  <clause id="11610">
    <literal><![CDATA[
      (x * (y * R(z,u,L(z,y,x)))) / (x * (y * z)) = a(L(z,y,x),u,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(514(a,1),11365(a,1,1))].">
      <j1 rule="para" parents="514 11365"/>
    </justification>
  </clause>

  <clause id="11611">
    <literal><![CDATA[
      (x * (y * R(z,u,z))) / (x * (y * z)) = a(L(z,y,x),u,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(11559(a,1),11610(a,1,1,2,2))].">
      <j1 rule="para" parents="11559 11610"/>
    </justification>
  </clause>

  <clause id="11612">
    <literal><![CDATA[
      L(a(x,y,x),z * x,u) = a(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11355,a(flip),b,11611,a)].">
      <j1 rule="hyper" parents="64 11355 11611"/>
    </justification>
  </clause>

  <clause id="11614">
    <literal><![CDATA[
      a(L(x,y / x,z),u,L(x,y / x,z)) = L(a(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),11612(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 11612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11615">
    <literal><![CDATA[
      R(((x * K(y,x)) \ y) \ y,z,u) = (R(x,z,u) \ y) \ T(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,7732,a(flip),b,11429,a),flip(a)].">
      <j1 rule="hyper" parents="373 7732 11429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11616">
    <literal><![CDATA[
      (R(x,y,z) \ u) \ T(u,R(x,y,z)) = R((x \ u) \ T(u,x),y,z)
    ]]></literal>
    <justification jstring="[para(7725(a,1),11615(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7725 11615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11617">
    <literal><![CDATA[
      (x / R(y,z,u)) * R((y \ w) \ T(w,y),z,u) = x * a(R(y,z,u),R(y,z,u) \ w,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(11616(a,1),11351(a,1,2))].">
      <j1 rule="para" parents="11616 11351"/>
    </justification>
  </clause>

  <clause id="11618">
    <literal><![CDATA[
      L(a(x \ y,z,(x \ 1) \ y) \ ((x \ 1) \ y),x,x) = L(x * y,z,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(2675(a,1),10913(a,1,1,1))].">
      <j1 rule="para" parents="2675 10913"/>
    </justification>
  </clause>

  <clause id="11619">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,K(w,x)) = T(K(x * R(y,z,u),T(y,x)),w)
    ]]></literal>
    <justification jstring="[para(9791(a,1),11256(a,1,2))].">
      <j1 rule="para" parents="9791 11256"/>
    </justification>
  </clause>

  <clause id="11620">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(x,K(y,w)) = T(K(x * R(y,z,u),T(y,x)),w)
    ]]></literal>
    <justification jstring="[para(8110(a,1),11619(a,1,2))].">
      <j1 rule="para" parents="8110 11619"/>
    </justification>
  </clause>

  <clause id="11622">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(x,K(y,w)) = T(K(x * R(y,z,u),y),w)
    ]]></literal>
    <justification jstring="[para(11183(a,1),11620(a,2,1))].">
      <j1 rule="para" parents="11183 11620"/>
    </justification>
  </clause>

  <clause id="11623">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) * T(K(y,x),w) = T(K(y * R(x,z,u),x),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11514,a(flip),b,11622,a)].">
      <j1 rule="hyper" parents="64 11514 11622"/>
    </justification>
  </clause>

  <clause id="11624">
    <literal><![CDATA[
      T(K(x * R(y,z,u),y),w) * T(K(y,x),w) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10346,a,11623,a)].">
      <j1 rule="hyper" parents="10346 11623"/>
    </justification>
  </clause>

  <clause id="11625">
    <literal><![CDATA[
      T(K(x,y) * K(y * R(x,z,u),x),w) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(10449,a,11624,a)].">
      <j1 rule="hyper" parents="10449 11624"/>
    </justification>
  </clause>

  <clause id="11626">
    <literal><![CDATA[
      T(T(x,y),z) * (K(z * R(x,u,w),T(x,y)) * v5) = R(T(x,y),z,R(x,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(10086(a,1),11303(a,1,2,1))].">
      <j1 rule="para" parents="10086 11303"/>
    </justification>
  </clause>

  <clause id="11627">
    <literal><![CDATA[
      T(T(x,y),z) * (T(T(x,y),z * R(x,u,w)) \ v5) = R(T(x,y),z,R(x,u,w)) * (T(x,y) \ v5)
    ]]></literal>
    <justification jstring="[para(6157(a,1),11626(a,1,2))].">
      <j1 rule="para" parents="6157 11626"/>
    </justification>
  </clause>

  <clause id="11629">
    <literal><![CDATA[
      K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) = K(y \ (1 * ((x * z) / x)),T(u,y))
    ]]></literal>
    <justification jstring="[para(66(a,1),11239(a,2,1,2,2,1,2))].">
      <j1 rule="para" parents="66 11239"/>
    </justification>
  </clause>

  <clause id="11630">
    <literal><![CDATA[
      K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) = K(y \ ((x * z) / x),T(u,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),11629(a,2,1,2))].">
      <j1 rule="para" parents="7 11629"/>
    </justification>
  </clause>

  <clause id="11631">
    <literal><![CDATA[
      K(((x * ((y \ 1) \ (y \ z))) / x) * (y \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(((x * z) / x) / y,u) = w
    ]]></literal>
    <justification jstring="[para(11630(a,2),8322(a,1))].">
      <j1 rule="para" parents="11630 8322"/>
    </justification>
  </clause>

  <clause id="11632">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(x,y) * (z * u)) = (z * K(x,y)) * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(594(a,1),11297(a,1,1))].">
      <j1 rule="para" parents="594 11297"/>
    </justification>
  </clause>

  <clause id="11633">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(y,x) \ (z * u)) = (z * K(x,y)) * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6156(a,2),11632(a,1,2))].">
      <j1 rule="para" parents="6156 11632"/>
    </justification>
  </clause>

  <clause id="11634">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = L(T(K(x * y,x),z) \ 1,K(x * y,x),y)
    ]]></literal>
    <justification jstring="[para(8110(a,1),6657(a,1,2,2))].">
      <j1 rule="para" parents="8110 6657"/>
    </justification>
  </clause>

  <clause id="11635">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,(1 / z) \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,10812,a(flip),b,7264,a),flip(a)].">
      <j1 rule="hyper" parents="373 10812 7264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11636">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,(z \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(5112(a,1),11635(a,2,2))].">
      <j1 rule="para" parents="5112 11635"/>
    </justification>
  </clause>

  <clause id="11637">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(11269,a,11636,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="11269 11636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11638">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,11157,a(flip),b,11637,a),flip(a)].">
      <j1 rule="hyper" parents="373 11157 11637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11639">
    <literal><![CDATA[
      K(x,T(x \ y,z)) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(10779,a,11638,a),flip(a)].">
      <j1 rule="hyper" parents="10779 11638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11641">
    <literal><![CDATA[
      T(x,T(x \ y,z)) = T(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,11639,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 11639 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11642">
    <literal><![CDATA[
      K(x,y \ (x \ (z * y))) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[hyper(10255,a,11639,a(flip))].">
      <j1 rule="hyper" parents="10255 11639"/>
    </justification>
  </clause>

  <clause id="11643">
    <literal><![CDATA[
      K(x,x \ T(x * y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),11639(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 11639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11644">
    <literal><![CDATA[
      K(x,x \ T(y,z)) \ 1 = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[para(11639(a,1),7899(a,1,1))].">
      <j1 rule="para" parents="11639 7899"/>
    </justification>
  </clause>

  <clause id="11645">
    <literal><![CDATA[
      T(T(x,x \ T(y,z)),T(u,x)) = T(T(x,u),T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(11641(a,1),4633(a,1,1))].">
      <j1 rule="para" parents="11641 4633"/>
    </justification>
  </clause>

  <clause id="11646">
    <literal><![CDATA[
      K(x,T(y,z) / x) = K(x,T(y / x,z))
    ]]></literal>
    <justification jstring="[para(5427(a,1),11643(a,1,2))].">
      <j1 rule="para" parents="5427 11643"/>
    </justification>
  </clause>

  <clause id="11647">
    <literal><![CDATA[
      K(x \ 1,T(R(y,x,1 / x),z) / (x \ 1)) = K(x \ 1,T(y * x,z))
    ]]></literal>
    <justification jstring="[para(3753(a,1),11646(a,2,2,1))].">
      <j1 rule="para" parents="3753 11646"/>
    </justification>
  </clause>

  <clause id="11648">
    <literal><![CDATA[
      K(x,T(x \ y,y \ (x * z))) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[para(73(a,1),11642(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="73 11642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11649">
    <literal><![CDATA[
      K(x \ T(y,z),x) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(6101,a,11644,a)].">
      <j1 rule="hyper" parents="6101 11644"/>
    </justification>
  </clause>

  <clause id="11650">
    <literal><![CDATA[
      T(T(x,y),T(x \ z,u)) = T(T(x,y),x \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(4728,a,11645,a),flip(a)].">
      <j1 rule="hyper" parents="4728 11645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11651">
    <literal><![CDATA[
      T((x \ T(y,x)) \ y,K(z,x \ y)) = T(T(x,y),x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8424,a,b,11650,a)].">
      <j1 rule="hyper" parents="64 8424 11650"/>
    </justification>
  </clause>

  <clause id="11652">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11264,a(flip),b,11648,a)].">
      <j1 rule="hyper" parents="64 11264 11648"/>
    </justification>
  </clause>

  <clause id="11653">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ z) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(11265,a,11652,a),flip(a)].">
      <j1 rule="hyper" parents="11265 11652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11654">
    <literal><![CDATA[
      K(x \ 1,T(y * x,z)) = K(x \ 1,T(y,z) * x)
    ]]></literal>
    <justification jstring="[para(3754(a,1),11647(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3754 11647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11655">
    <literal><![CDATA[
      K(1 / x,x * T(y,z)) = K(x \ 1,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,11114,a,b,11654,a)].">
      <j1 rule="hyper" parents="373 11114 11654"/>
    </justification>
  </clause>

  <clause id="11656">
    <literal><![CDATA[
      K(1 / x,T(y * x,z)) = K(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,3776,a,b,11655,a)].">
      <j1 rule="hyper" parents="373 3776 11655"/>
    </justification>
  </clause>

  <clause id="11657">
    <literal><![CDATA[
      T(1 / x,T(y * x,z)) = T(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,11656,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 11656 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11658">
    <literal><![CDATA[
      L(K(x,y),z,u) * L(L(K(y,x),z,u),w,v5) = a(v5,w,K(L(x \ 1,z,u) \ 1,y))
    ]]></literal>
    <justification jstring="[para(6672(a,1),10434(a,1,2))].">
      <j1 rule="para" parents="6672 10434"/>
    </justification>
  </clause>

  <clause id="11659">
    <literal><![CDATA[
      L(K(x,y),z,u) * L(L(K(y,x),z,u),w,v5) = a(v5,w,L(K(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(7310(a,1),11658(a,2,3))].">
      <j1 rule="para" parents="7310 11658"/>
    </justification>
  </clause>

  <clause id="11660">
    <literal><![CDATA[
      K(T(x,y),z) * (K(z * R(x,u,w),T(x,y)) * v5) = R(T(x,y),z,R(x,u,w)) * (T(x,y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(6493,a,11627,a)].">
      <j1 rule="hyper" parents="6493 11627"/>
    </justification>
  </clause>

  <clause id="11661">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = L(K(x,T(x * y,z)),K(x * y,x),y)
    ]]></literal>
    <justification jstring="[para(7440(a,1),11634(a,2,1))].">
      <j1 rule="para" parents="7440 11634"/>
    </justification>
  </clause>

  <clause id="11662">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,10326,a(flip),b,11661,a),flip(a)].">
      <j1 rule="hyper" parents="373 10326 11661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11664">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ (K(x,z) * K(y,K(u,y * K(x,z)))) = K(y,T(y * K(x,z),u))
    ]]></literal>
    <justification jstring="[para(9360(a,2),11662(a,1,1))].">
      <j1 rule="para" parents="9360 11662"/>
    </justification>
  </clause>

  <clause id="11665">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ (K(x,z) * 1) = K(y,T(y * K(x,z),x))
    ]]></literal>
    <justification jstring="[para(8557(a,1),11664(a,1,2,2))].">
      <j1 rule="para" parents="8557 11664"/>
    </justification>
  </clause>

  <clause id="11666">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ K(x,z) = K(y,T(y * K(x,z),x))
    ]]></literal>
    <justification jstring="[hyper(341,a,11665,a)].">
      <j1 rule="hyper" parents="341 11665"/>
    </justification>
  </clause>

  <clause id="11667">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) * K(z,y) = K(x,T(x * K(z,y),z))
    ]]></literal>
    <justification jstring="[hyper(6198,a,11666,a)].">
      <j1 rule="hyper" parents="6198 11666"/>
    </justification>
  </clause>

  <clause id="11668">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,T(y * K(z,x),z))
    ]]></literal>
    <justification jstring="[para(9361(a,1),11667(a,1,1))].">
      <j1 rule="para" parents="9361 11667"/>
    </justification>
  </clause>

  <clause id="11669">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,8570,a(flip),b,11668,a),flip(a)].">
      <j1 rule="hyper" parents="373 8570 11668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11670">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9646,a(flip),b,11669,a)].">
      <j1 rule="hyper" parents="64 9646 11669"/>
    </justification>
  </clause>

  <clause id="11671">
    <literal><![CDATA[
      T(T(x * K(x,x * K(y,z)),u),K(z,y)) = R(T(x,u),K(z,y),x)
    ]]></literal>
    <justification jstring="[para(11670(a,1),6662(a,1,1,1,2))].">
      <j1 rule="para" parents="11670 6662"/>
    </justification>
  </clause>

  <clause id="11672">
    <literal><![CDATA[
      T(T(T(x,x * K(y,z)),u),K(z,y)) = R(T(x,u),K(z,y),x)
    ]]></literal>
    <justification jstring="[para(5753(a,2),11671(a,1,1,1))].">
      <j1 rule="para" parents="5753 11671"/>
    </justification>
  </clause>

  <clause id="11673">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) = T(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7832,a,11672,a),flip(a)].">
      <j1 rule="hyper" parents="7832 11672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11674">
    <literal><![CDATA[
      T(x,x * K(y,z)) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(11673(a,1),10652(a,1,1))].">
      <j1 rule="para" parents="11673 10652"/>
    </justification>
  </clause>

  <clause id="11675">
    <literal><![CDATA[
      T(x,x * K((y * z) \ (u * w),w)) \ T(K(w,(y * (w \ z)) \ u) * x,x) = K(w,T((y * (w \ z)) \ u,x))
    ]]></literal>
    <justification jstring="[para(9592(a,1),11674(a,1,1,2,2))].">
      <j1 rule="para" parents="9592 11674"/>
    </justification>
  </clause>

  <clause id="11676">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(y * R(x,u,w),T(x,z)) * v5) = R(T(x,z),y,R(x,u,w)) * (T(x,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(8764,a,11660,a)].">
      <j1 rule="hyper" parents="8764 11660"/>
    </justification>
  </clause>

  <clause id="11677">
    <literal><![CDATA[
      x * ((((x \ L(x,y,z)) \ 1) \ L(x,y,z)) \ u) = ((x \ L(x,y,z)) \ (L(x,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[para(9374(a,1),5592(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9374 5592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11678">
    <literal><![CDATA[
      ((x * y) * R((x * y) \ x,z,u)) * T(y,w) = (x * y) * (T(y,w) * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(5761(a,1),6943(a,2,2,2,1))].">
      <j1 rule="para" parents="5761 6943"/>
    </justification>
  </clause>

  <clause id="11680">
    <literal><![CDATA[
      R(x,x \ 1,y \ R(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(7024,a,10038,a)].">
      <j1 rule="hyper" parents="7024 10038"/>
    </justification>
  </clause>

  <clause id="11681">
    <literal><![CDATA[
      R(x,x \ 1,a(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(10884(a,1),11680(a,1,3))].">
      <j1 rule="para" parents="10884 11680"/>
    </justification>
  </clause>

  <clause id="11682">
    <literal><![CDATA[
      (x \ 1) * a(y,x \ 1,y) = x \ a(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(11681(a,1),475(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11681 475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11683">
    <literal><![CDATA[
      T(x \ a(y,x \ 1,y),y) = y \ T(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(11682(a,1),10929(a,1,1))].">
      <j1 rule="para" parents="11682 10929"/>
    </justification>
  </clause>

  <clause id="11684">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = (y \ T(y * (x \ 1),y)) * R(T(x \ a(y,x \ 1,y),y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(11683(a,1),3216(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11683 3216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11685">
    <literal><![CDATA[
      K(x \ (x * (y / x)),z * ((x * (y / x)) \ x)) = K(y / x,(y \ (y / (y / x))) * z)
    ]]></literal>
    <justification jstring="[hyper(6038,a,7242,a),flip(a)].">
      <j1 rule="hyper" parents="6038 7242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11687">
    <literal><![CDATA[
      K(x \ (x * (y / x)),z * ((x * (y / x)) \ x)) = K(y / x,(y \ ((y / x) \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,9695,a(flip),b,11685,a),flip(a)].">
      <j1 rule="hyper" parents="373 9695 11685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11688">
    <literal><![CDATA[
      K(x \ (x * (y / x)),z * ((x * (y / x)) \ x)) = K(y / x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(82(a,1),11687(a,2,2,1,2))].">
      <j1 rule="para" parents="82 11687"/>
    </justification>
  </clause>

  <clause id="11689">
    <literal><![CDATA[
      K(x / y,z * ((y * (x / y)) \ y)) = K(x / y,(x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(6038,a,11688,a)].">
      <j1 rule="hyper" parents="6038 11688"/>
    </justification>
  </clause>

  <clause id="11691">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K((y * (x / y)) \ y,(x / y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),7243(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 7243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11692">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K((x / y) \ 1,(x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6766,a(flip),b,11691,a),flip(a)].">
      <j1 rule="hyper" parents="373 6766 11691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11695">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K(y / x,(x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6580,a(flip),b,11692,a),flip(a)].">
      <j1 rule="hyper" parents="373 6580 11692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11696">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),T(z / x,y)) = T(T(x * K(y,x \ z),u),T(x \ z,y))
    ]]></literal>
    <justification jstring="[para(6247(a,1),8076(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6247 8076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11697">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),T(z / x,y)) = T(T(K(y,x \ z) * x,x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,8639,a(flip),b,11696,a),flip(a)].">
      <j1 rule="hyper" parents="373 8639 11696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11698">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),T(z / x,y)) = T(T(x \ z,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(7815(a,1),11697(a,2,1))].">
      <j1 rule="para" parents="7815 11697"/>
    </justification>
  </clause>

  <clause id="11699">
    <literal><![CDATA[
      T(x,T(y / T(y / z,u),w)) = T(x,T(T(z \ y,u) \ y,w))
    ]]></literal>
    <justification jstring="[para(11698(a,1),8675(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11698 8675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11700">
    <literal><![CDATA[
      K(x,K(y,x / z)) * K(y,(x / (1 / (1 / z))) / x) = K(y,1 / (1 / (x \ (x / z))))
    ]]></literal>
    <justification jstring="[para(6538(a,1),9073(a,1,1,2))].">
      <j1 rule="para" parents="6538 9073"/>
    </justification>
  </clause>

  <clause id="11701">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,(x / (1 / (1 / z))) / x) = K(y,1 / (1 / (x \ (x / z))))
    ]]></literal>
    <justification jstring="[para(8997(a,1),11700(a,1,1))].">
      <j1 rule="para" parents="8997 11700"/>
    </justification>
  </clause>

  <clause id="11702">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) / y) = K(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(35,a,10131,a(flip),b,11701,a),flip(a)].">
      <j1 rule="hyper" parents="35 10131 11701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11703">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6059,a(flip),b,11702,a)].">
      <j1 rule="hyper" parents="64 6059 11702"/>
    </justification>
  </clause>

  <clause id="11705">
    <literal><![CDATA[
      T(T(x,y) * L(x \ (z / (x \ 1)),u,w),K(x,y)) = (L(z,u,w) / (x \ 1)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9560(a,1),9092(a,1,1))].">
      <j1 rule="para" parents="9560 9092"/>
    </justification>
  </clause>

  <clause id="11706">
    <literal><![CDATA[
      x * (L(x \ (y / (x \ 1)),z,u) * K(x,w)) = (L(y,z,u) / (x \ 1)) * K(x,w)
    ]]></literal>
    <justification jstring="[hyper(8668,a,11705,a)].">
      <j1 rule="hyper" parents="8668 11705"/>
    </justification>
  </clause>

  <clause id="11707">
    <literal><![CDATA[
      L((x / (y \ 1)) / y,z,u) * T(y,w) = (L(x,z,u) / (y \ 1)) * K(y,w)
    ]]></literal>
    <justification jstring="[hyper(9488,a,11706,a)].">
      <j1 rule="hyper" parents="9488 11706"/>
    </justification>
  </clause>

  <clause id="11708">
    <literal><![CDATA[
      L((x / (y \ 1)) / y,z,u) * T(y,w) = L(x,z,u) / (T(y,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,9330,a(flip),b,11707,a),flip(a)].">
      <j1 rule="hyper" parents="373 9330 11707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11709">
    <literal><![CDATA[
      (T(x,y) * (z * R(x,u,w))) \ ((T(x,y) * z) * R(x,u,w)) = a(x,K(x,y) * z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(5776(a,1),9459(a,1,1))].">
      <j1 rule="para" parents="5776 9459"/>
    </justification>
  </clause>

  <clause id="11710">
    <literal><![CDATA[
      a(x,K(x,y) * z,R(x,u,w)) = a(T(x,y),z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(959,a,11709,a),flip(a)].">
      <j1 rule="hyper" parents="959 11709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11711">
    <literal><![CDATA[
      a(x,K(x,y) * z,R(x,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11709(a,1),959(a,1))].">
      <j1 rule="para" parents="11709 959"/>
    </justification>
  </clause>

  <clause id="11712">
    <literal><![CDATA[
      a(T(x,y),T(x,y) \ z,R(x,u,w)) = a(x,x \ z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(6075(a,1),11710(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6075 11710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11713">
    <literal><![CDATA[
      a(x / y,((y * x) / y) / (((y * x) / y) / T(y,x)),z) = a(y \ x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(2518(a,1),9639(a,1,1))].">
      <j1 rule="para" parents="2518 9639"/>
    </justification>
  </clause>

  <clause id="11714">
    <literal><![CDATA[
      a(x / y,((y * x) / y) / (x / y),z) = a(y \ x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(2518(a,1),11713(a,1,2,2))].">
      <j1 rule="para" parents="2518 11713"/>
    </justification>
  </clause>

  <clause id="11715">
    <literal><![CDATA[
      R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5) = K(x,y) * R(K(x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(9803(a,1),9805(a,2,2,1,1))].">
      <j1 rule="para" parents="9803 9805"/>
    </justification>
  </clause>

  <clause id="11716">
    <literal><![CDATA[
      R(K(x,y) * R(K(x,y) \ 1,z,u),K(y,w),v5) = K(x,y) * R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(6092(a,1),11715(a,2,2,1))].">
      <j1 rule="para" parents="6092 11715"/>
    </justification>
  </clause>

  <clause id="11718">
    <literal><![CDATA[
      R(K(x,y) * R(K(y,x),z,u),K(y,w),v5) = K(x,y) * R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(6092(a,1),11716(a,1,1,2,1))].">
      <j1 rule="para" parents="6092 11716"/>
    </justification>
  </clause>

  <clause id="11719">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (K(x,y) * (z * u)) = K(y,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,6196,a(flip),b,11718,a)].">
      <j1 rule="hyper" parents="64 6196 11718"/>
    </justification>
  </clause>

  <clause id="11720">
    <literal><![CDATA[
      L(x,K(y,z),R(K(u,y) * R(K(y,u),w,v5),K(y,z),x)) = ((K(u,y) * R(K(y,u),w,v5)) * K(y,z)) \ (((K(u,y) * R(K(y,u),w,v5)) * K(y,z)) * x)
    ]]></literal>
    <justification jstring="[para(11718(a,1),656(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11718 656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11721">
    <literal><![CDATA[
      R(K(x,y) * R(K(y,x),z,u),K(y,w),v5) * v6 = K(x,y) * (R(K(y,x),z,u) * v6)
    ]]></literal>
    <justification jstring="[para(11718(a,2),9941(a,1,1))].">
      <j1 rule="para" parents="11718 9941"/>
    </justification>
  </clause>

  <clause id="11723">
    <literal><![CDATA[
      R(K(x,K(y,z)) * R(K(y,K(z,x)),u,w),K(K(y,z),v5),v6) * v7 = K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * v7)
    ]]></literal>
    <justification jstring="[para(8092(a,1),11721(a,1,1,1,2,1))].">
      <j1 rule="para" parents="8092 11721"/>
    </justification>
  </clause>

  <clause id="11724">
    <literal><![CDATA[
      K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = T(K(x,T(y,z)) * u,w) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8352,a(flip),b,9815,a),flip(a)].">
      <j1 rule="hyper" parents="64 8352 9815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11725">
    <literal><![CDATA[
      ((K(x,y) * z) * ((K(y,x) \ 1) \ 1)) * K(u,y) = ((1 / (1 / K(y,x))) \ z) * (K(y,x) * K(u,y))
    ]]></literal>
    <justification jstring="[para(6156(a,1),10356(a,1,1,1))].">
      <j1 rule="para" parents="6156 10356"/>
    </justification>
  </clause>

  <clause id="11726">
    <literal><![CDATA[
      (x * K(y \ z,y)) * (T(x / z,T(z,y)) \ u) = (((y \ z) * y) * (x / z)) * ((x / z) \ u)
    ]]></literal>
    <justification jstring="[para(11129(a,1),10960(a,1,2,1))].">
      <j1 rule="para" parents="11129 10960"/>
    </justification>
  </clause>

  <clause id="11727">
    <literal><![CDATA[
      (x * K(y \ z,y)) * (T(z \ x,K(z,y)) \ u) = (((y \ z) * y) * (x / z)) * ((x / z) \ u)
    ]]></literal>
    <justification jstring="[para(7159(a,1),11726(a,1,2,1))].">
      <j1 rule="para" parents="7159 11726"/>
    </justification>
  </clause>

  <clause id="11728">
    <literal><![CDATA[
      (x * K(y \ z,y)) * (T(z \ x,K(y,z)) \ u) = (((y \ z) * y) * (x / z)) * ((x / z) \ u)
    ]]></literal>
    <justification jstring="[para(8153(a,1),11727(a,1,2,1))].">
      <j1 rule="para" parents="8153 11727"/>
    </justification>
  </clause>

  <clause id="11729">
    <literal><![CDATA[
      (x * T(y,(x / z) * z)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,z \ x) * x
    ]]></literal>
    <justification jstring="[para(12(a,1),11081(a,2,2))].">
      <j1 rule="para" parents="12 11081"/>
    </justification>
  </clause>

  <clause id="11730">
    <literal><![CDATA[
      (x * T(y,x)) / a(x / z,z,T(y,(x / z) * z)) = L(y,z,z \ x) * x
    ]]></literal>
    <justification jstring="[para(12(a,1),11729(a,1,1,2,2))].">
      <j1 rule="para" parents="12 11729"/>
    </justification>
  </clause>

  <clause id="11731">
    <literal><![CDATA[
      (x * y) / a(y / z,z,T(x,(y / z) * z)) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,250,a(flip),b,11730,a)].">
      <j1 rule="hyper" parents="64 250 11730"/>
    </justification>
  </clause>

  <clause id="11732">
    <literal><![CDATA[
      (L(x,y,z) * (K(x,T(u,w)) * w)) \ (L(x,y,z) * w) = R(K(u,L(x,w,L(x,y,z))),L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(4867(a,1),11468(a,1,1))].">
      <j1 rule="para" parents="4867 11468"/>
    </justification>
  </clause>

  <clause id="11733">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * x),L(x,y,z)) = K(u * x,L(x,y,z)) * K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(7920(a,1),11609(a,2,2))].">
      <j1 rule="para" parents="7920 11609"/>
    </justification>
  </clause>

  <clause id="11734">
    <literal><![CDATA[
      x * a(R(y,z,u),R(y,z,u) \ (w * y),R(y,z,u)) = (x / R(y,z,u)) * R(R(y,w,y),z,u)
    ]]></literal>
    <justification jstring="[para(4793(a,1),11617(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4793 11617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11735">
    <literal><![CDATA[
      ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)) = ((K(y,x) * z) * K(x,y)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(3831(a,1),11725(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3831 11725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11736">
    <literal><![CDATA[
      ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)) = T(z,K(x,y)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(7808(a,1),11735(a,2,1))].">
      <j1 rule="para" parents="7808 11735"/>
    </justification>
  </clause>

  <clause id="11737">
    <literal><![CDATA[
      ((1 / (1 / K(x,y))) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,10022,a,b,11736,a),flip(a)].">
      <j1 rule="hyper" parents="373 10022 11736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11738">
    <literal><![CDATA[
      (K(x,y) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y))
    ]]></literal>
    <justification jstring="[para(3835(a,1),11737(a,1,1,1))].">
      <j1 rule="para" parents="3835 11737"/>
    </justification>
  </clause>

  <clause id="11739">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z * K(u,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(6156(a,1),11738(a,1,1))].">
      <j1 rule="para" parents="6156 11738"/>
    </justification>
  </clause>

  <clause id="11740">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z * K(u,y),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8153,a,b,11739,a),flip(a)].">
      <j1 rule="hyper" parents="373 8153 11739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11741">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y,x),K(x,u)) = z * K(K(u,x) * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10380,a(flip),b,11739,a),flip(a)].">
      <j1 rule="hyper" parents="64 10380 11739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11742">
    <literal><![CDATA[
      (K(x,y) * z) * (K(u,y) * K(y,x)) = T(z * K(u,y),K(x,y))
    ]]></literal>
    <justification jstring="[para(3320(a,1),11740(a,1,2))].">
      <j1 rule="para" parents="3320 11740"/>
    </justification>
  </clause>

  <clause id="11743">
    <literal><![CDATA[
      T(x * K(y,z),K(u,z)) / (K(u,z) * x) = (K(y,z) * K(z,u)) * K(K(u,z) * x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(142,a,11742,a(flip),b,5722,a)].">
      <j1 rule="hyper" parents="142 11742 5722"/>
    </justification>
  </clause>

  <clause id="11744">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(T(x,K(z,u)),K(z,y))
    ]]></literal>
    <justification jstring="[para(8160(a,1),11741(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8160 11741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11745">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(x,w))) \ (L(x,y,z) * u) = R(K(w,L(x,u,L(x,y,z))),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(8193(a,1),11732(a,1,1,2))].">
      <j1 rule="para" parents="8193 11732"/>
    </justification>
  </clause>

  <clause id="11746">
    <literal><![CDATA[
      R(K(x,L(y,z,L(y,u,w))),L(y,u,w),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7294,a,11745,a),flip(a)].">
      <j1 rule="hyper" parents="7294 11745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11747">
    <literal><![CDATA[
      R(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7698(a,1),11746(a,1,1))].">
      <j1 rule="para" parents="7698 11746"/>
    </justification>
  </clause>

  <clause id="11748">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K(L(x,y,z) / (w / u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8761,a(flip),b,11747,a)].">
      <j1 rule="hyper" parents="64 8761 11747"/>
    </justification>
  </clause>

  <clause id="11750">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K((w / u) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6822,a(flip),b,11748,a),flip(a)].">
      <j1 rule="hyper" parents="373 6822 11748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11751">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((u / w) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10694,a,b,11750,a)].">
      <j1 rule="hyper" parents="64 10694 11750"/>
    </justification>
  </clause>

  <clause id="11752">
    <literal><![CDATA[
      K((x / y) \ L(z,u,w),z) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y / (L(z,u,w) \ x),z) = v5
    ]]></literal>
    <justification jstring="[para(11751(a,1),8453(a,1))].">
      <j1 rule="para" parents="11751 8453"/>
    </justification>
  </clause>

  <clause id="11753">
    <literal><![CDATA[
      L(x,L(y,K(z,u),u),(z * u) / z) = (u * (K(z,u) * y)) \ ((u * K(z,u)) * (y * x))
    ]]></literal>
    <justification jstring="[para(4490(a,1),5910(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4490 5910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11754">
    <literal><![CDATA[
      L(x,L(y,K(z,u),u),(z * u) / z) = (u * (K(z,u) * y)) \ (u * (K(z,u) * (y * x)))
    ]]></literal>
    <justification jstring="[para(4442(a,1),11753(a,2,2))].">
      <j1 rule="para" parents="4442 11753"/>
    </justification>
  </clause>

  <clause id="11755">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,u) = L(x,L(y,K(z,u),u),(z * u) / z)
    ]]></literal>
    <justification jstring="[hyper(373,a,602,a(flip),b,11754,a)].">
      <j1 rule="hyper" parents="373 602 11754"/>
    </justification>
  </clause>

  <clause id="11756">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,u) = L(x,y,(z * u) / z)
    ]]></literal>
    <justification jstring="[para(4490(a,1),11755(a,2,2))].">
      <j1 rule="para" parents="4490 11755"/>
    </justification>
  </clause>

  <clause id="11757">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,u) = L(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,6433,a(flip),b,11756,a),flip(a)].">
      <j1 rule="hyper" parents="373 6433 11756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11758">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,z)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,4947,a(flip),b,11757,a)].">
      <j1 rule="hyper" parents="64 4947 11757"/>
    </justification>
  </clause>

  <clause id="11759">
    <literal><![CDATA[
      L(x,y,K(z,u * u)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,1438,a(flip),b,11757,a),flip(a)].">
      <j1 rule="hyper" parents="42 1438 11757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11760">
    <literal><![CDATA[
      L(x,y,K(z * z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(9937,a,11759,a)].">
      <j1 rule="hyper" parents="9937 11759"/>
    </justification>
  </clause>

  <clause id="11761">
    <literal><![CDATA[
      L(x,y,K(z * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(11760(a,1),51(a,2))].">
      <j1 rule="para" parents="11760 51"/>
    </justification>
  </clause>

  <clause id="11762">
    <literal><![CDATA[
      L(x,y,T(z,u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(11761,a,11758,a),flip(a)].">
      <j1 rule="hyper" parents="11761 11758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11763">
    <literal><![CDATA[
      L(x,y,T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10870,a,11758,a),flip(a)].">
      <j1 rule="hyper" parents="10870 11758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11764">
    <literal><![CDATA[
      L(x,y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7779,a(flip),b,11758,a),flip(a)].">
      <j1 rule="hyper" parents="64 7779 11758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11765">
    <literal><![CDATA[
      L(x,y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(11758(a,1),10870(a,1))].">
      <j1 rule="para" parents="11758 10870"/>
    </justification>
  </clause>

  <clause id="11766">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,T(y,x)) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,6983,a(flip),b,11763,a),flip(a)].">
      <j1 rule="hyper" parents="373 6983 11763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11767">
    <literal><![CDATA[
      L(T(x,y),z,T(u,z)) = T(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,25,a(flip),b,11763,a),flip(a)].">
      <j1 rule="hyper" parents="373 25 11763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11768">
    <literal><![CDATA[
      L(x,y,z \ K(y,z \ 1)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(5866(a,1),11763(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5866 11763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11770">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = T(L(x,z,x),y)
    ]]></literal>
    <justification jstring="[para(11764(a,1),25(a,2,1))].">
      <j1 rule="para" parents="11764 25"/>
    </justification>
  </clause>

  <clause id="11772">
    <literal><![CDATA[
      L(x,(y * y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,3271,a,b,11762,a)].">
      <j1 rule="hyper" parents="64 3271 11762"/>
    </justification>
  </clause>

  <clause id="11774">
    <literal><![CDATA[
      L(x,y,z * (u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2961,a(flip),b,11772,a)].">
      <j1 rule="hyper" parents="64 2961 11772"/>
    </justification>
  </clause>

  <clause id="11775">
    <literal><![CDATA[
      L(x,(y * y) \ z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11776">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(245(a,1),11772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="245 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11777">
    <literal><![CDATA[
      L(x,(1 / y) * z,u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(310(a,1),11772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="310 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11778">
    <literal><![CDATA[
      L(x,y * (y * z),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(100(a,1),11772(a,1,2))].">
      <j1 rule="para" parents="100 11772"/>
    </justification>
  </clause>

  <clause id="11779">
    <literal><![CDATA[
      L(x,((y * y) \ z) * u,w) = L(x,z * u,w)
    ]]></literal>
    <justification jstring="[para(126(a,1),11772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="126 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11780">
    <literal><![CDATA[
      L(x,(y * (y * z)) * u,w) = L(x,L(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[para(605(a,1),11772(a,1,2))].">
      <j1 rule="para" parents="605 11772"/>
    </justification>
  </clause>

  <clause id="11781">
    <literal><![CDATA[
      L(x,(((y * y) \ z) * u) * w,v5) = L(x,(z * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(805(a,1),11772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="805 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11782">
    <literal><![CDATA[
      L(x,(((y * y) / z) * u) * w,v5) = L(x,((1 / z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(1074(a,1),11772(a,1,2))].">
      <j1 rule="para" parents="1074 11772"/>
    </justification>
  </clause>

  <clause id="11783">
    <literal><![CDATA[
      L(x,((y * (y * z)) * u) * w,v5) = L(x,(L(z,y,y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(1314(a,1),11772(a,1,2))].">
      <j1 rule="para" parents="1314 11772"/>
    </justification>
  </clause>

  <clause id="11784">
    <literal><![CDATA[
      L(x,(R(1 / y,z,u) * w) * v5,v6) = L(x,(R(y,z,u) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(3384(a,1),11772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3384 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11785">
    <literal><![CDATA[
      a(L(x \ ((y * y) \ z),x,x),u,w) = a((y * y) * (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(11772(a,1),3493(a,1,1))].">
      <j1 rule="para" parents="11772 3493"/>
    </justification>
  </clause>

  <clause id="11786">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(5602(a,1),11772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5602 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11787">
    <literal><![CDATA[
      L(x,(y \ L(y,z,u)) * w,v5) = L(x,(y * L(y,z,u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(5621(a,1),11772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5621 11772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11788">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(6871(a,1),11772(a,1,2))].">
      <j1 rule="para" parents="6871 11772"/>
    </justification>
  </clause>

  <clause id="11789">
    <literal><![CDATA[
      L(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4605,a,11776,a),flip(a)].">
      <j1 rule="hyper" parents="4605 11776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11791">
    <literal><![CDATA[
      L(x,1 / y,z \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2274,a,11776,a)].">
      <j1 rule="hyper" parents="2274 11776"/>
    </justification>
  </clause>

  <clause id="11792">
    <literal><![CDATA[
      L(x,x,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(922,a,11776,a),flip(a)].">
      <j1 rule="hyper" parents="922 11776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11793">
    <literal><![CDATA[
      L(T(1 / x,y) \ z,x,y) = ((1 / x) * y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10979,a(flip),b,11776,a),flip(a)].">
      <j1 rule="hyper" parents="64 10979 11776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11794">
    <literal><![CDATA[
      L(x,y \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5321,a(flip),b,11776,a)].">
      <j1 rule="hyper" parents="64 5321 11776"/>
    </justification>
  </clause>

  <clause id="11795">
    <literal><![CDATA[
      x / L(y,y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(225,a,11776,a(flip),b,246,a(flip))].">
      <j1 rule="hyper" parents="225 11776 246"/>
    </justification>
  </clause>

  <clause id="11796">
    <literal><![CDATA[
      (x * (1 / y)) * L(z,y,x) = x * ((1 / y) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,11776,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 11776 18"/>
    </justification>
  </clause>

  <clause id="11797">
    <literal><![CDATA[
      (x * (1 / y)) * L(L(z,y,x),u,w) = x * ((1 / y) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(11776(a,1),513(a,1,2,1))].">
      <j1 rule="para" parents="11776 513"/>
    </justification>
  </clause>

  <clause id="11798">
    <literal><![CDATA[
      K(L(x,1 / y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11776(a,2),10175(a,1,1))].">
      <j1 rule="para" parents="11776 10175"/>
    </justification>
  </clause>

  <clause id="11799">
    <literal><![CDATA[
      L(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(6105,a,11789,a)].">
      <j1 rule="hyper" parents="6105 11789"/>
    </justification>
  </clause>

  <clause id="11800">
    <literal><![CDATA[
      L(x,y \ 1,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(3779(a,1),11789(a,1,3))].">
      <j1 rule="para" parents="3779 11789"/>
    </justification>
  </clause>

  <clause id="11801">
    <literal><![CDATA[
      (K(x,y \ 1) * y) * z = K(x,y \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[para(11789(a,1),6285(a,1,2))].">
      <j1 rule="para" parents="11789 6285"/>
    </justification>
  </clause>

  <clause id="11802">
    <literal><![CDATA[
      L(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(8282(a,1),11789(a,1,3))].">
      <j1 rule="para" parents="8282 11789"/>
    </justification>
  </clause>

  <clause id="11803">
    <literal><![CDATA[
      L(x,y,K(z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(11799(a,1),51(a,2))].">
      <j1 rule="para" parents="11799 51"/>
    </justification>
  </clause>

  <clause id="11804">
    <literal><![CDATA[
      L(x,y \ (y / z),K(u,z)) = x
    ]]></literal>
    <justification jstring="[para(6710(a,1),11799(a,1,3))].">
      <j1 rule="para" parents="6710 11799"/>
    </justification>
  </clause>

  <clause id="11805">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(8205(a,1),11800(a,1,3))].">
      <j1 rule="para" parents="8205 11800"/>
    </justification>
  </clause>

  <clause id="11806">
    <literal><![CDATA[
      L(x,y \ 1,z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(2275,a,11794,a)].">
      <j1 rule="hyper" parents="2275 11794"/>
    </justification>
  </clause>

  <clause id="11807">
    <literal><![CDATA[
      L(x,y \ 1,z \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2274,a,11794,a)].">
      <j1 rule="hyper" parents="2274 11794"/>
    </justification>
  </clause>

  <clause id="11808">
    <literal><![CDATA[
      L((x \ 1) \ 1,x,y) = (y * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[hyper(642,a,11794,a),flip(a)].">
      <j1 rule="hyper" parents="642 11794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11809">
    <literal><![CDATA[
      L((x * (y \ 1)) \ (x * z),y,y) = L(y * z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1390,a,b,11794,a)].">
      <j1 rule="hyper" parents="64 1390 11794"/>
    </justification>
  </clause>

  <clause id="11810">
    <literal><![CDATA[
      L(T((x \ 1) \ (y \ z),u),x,y) = T((y * (x \ 1)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,708,a(flip),b,11794,a),flip(a)].">
      <j1 rule="hyper" parents="64 708 11794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11811">
    <literal><![CDATA[
      L(T(x,x \ 1),x,y) = (y * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,447,a(flip),b,11794,a),flip(a)].">
      <j1 rule="hyper" parents="64 447 11794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11812">
    <literal><![CDATA[
      L((x \ 1) \ (y \ z),x,y) = (y * (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,346,a(flip),b,11794,a),flip(a)].">
      <j1 rule="hyper" parents="64 346 11794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11813">
    <literal><![CDATA[
      L((x \ 1) \ y,x,z) = (z * (x \ 1)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,11794,a),flip(a)].">
      <j1 rule="hyper" parents="64 102 11794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11814">
    <literal><![CDATA[
      ((x \ 1) * y) * L(z,x,y) = y * (T(x \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,11794,a(flip),b,10980,a(flip))].">
      <j1 rule="hyper" parents="145 11794 10980"/>
    </justification>
  </clause>

  <clause id="11815">
    <literal><![CDATA[
      (x * (y \ 1)) * L(z,y,x) = x * ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,11794,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 11794 18"/>
    </justification>
  </clause>

  <clause id="11816">
    <literal><![CDATA[
      (x \ 1) / L(y,y,x) = (x \ 1) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(225,a,11792,a,b,1228,a)].">
      <j1 rule="hyper" parents="225 11792 1228"/>
    </justification>
  </clause>

  <clause id="11817">
    <literal><![CDATA[
      L(x \ L(y,y,z),x,z * (1 / y)) = ((z * (1 / y)) * x) \ z
    ]]></literal>
    <justification jstring="[para(11792(a,2),346(a,1,1,2))].">
      <j1 rule="para" parents="11792 346"/>
    </justification>
  </clause>

  <clause id="11818">
    <literal><![CDATA[
      L(x,x,y) \ x = x * (((y * (1 / x)) \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(11792(a,1),1846(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11792 1846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11819">
    <literal><![CDATA[
      T(x * (1 / y),y) = L(y,y,x) \ x
    ]]></literal>
    <justification jstring="[para(11792(a,2),6809(a,2,1))].">
      <j1 rule="para" parents="11792 6809"/>
    </justification>
  </clause>

  <clause id="11820">
    <literal><![CDATA[
      ((x * y) / x) / L(z,z,(x * y) / x) = y * (K(x,y) * (1 / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,5911,a(flip),b,11795,a),flip(a)].">
      <j1 rule="hyper" parents="373 5911 11795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11821">
    <literal><![CDATA[
      L(x / (x / y),y,x) = x / (x * (1 / y))
    ]]></literal>
    <justification jstring="[hyper(225,a,11795,a(flip),b,10468,a),flip(a)].">
      <j1 rule="hyper" parents="225 11795 10468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11822">
    <literal><![CDATA[
      T((x * (1 / y)) * L(L(y,y,x),z,u),L(y,y,x)) = L(y,y,x) \ (x * L(L(y,y,x),z,u))
    ]]></literal>
    <justification jstring="[para(11795(a,1),3192(a,1,1,1))].">
      <j1 rule="para" parents="11795 3192"/>
    </justification>
  </clause>

  <clause id="11823">
    <literal><![CDATA[
      R(x,L(y,y,z) \ z,L(y,y,z)) * z = (x * (z * (1 / y))) * L(y,y,z)
    ]]></literal>
    <justification jstring="[para(11795(a,1),10219(a,2,1,2))].">
      <j1 rule="para" parents="11795 10219"/>
    </justification>
  </clause>

  <clause id="11824">
    <literal><![CDATA[
      K((x * (1 / y)) \ z,y) = K((1 / y) \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(346(a,1),11798(a,1,1))].">
      <j1 rule="para" parents="346 11798"/>
    </justification>
  </clause>

  <clause id="11825">
    <literal><![CDATA[
      L(x,(y * z) \ z,K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(11(a,1),11802(a,1,3,1))].">
      <j1 rule="para" parents="11 11802"/>
    </justification>
  </clause>

  <clause id="11826">
    <literal><![CDATA[
      (K(x,y) \ (z \ (z / x))) * u = K(y,x) * ((z \ (z / x)) * u)
    ]]></literal>
    <justification jstring="[para(11804(a,1),6182(a,1,2))].">
      <j1 rule="para" parents="11804 6182"/>
    </justification>
  </clause>

  <clause id="11827">
    <literal><![CDATA[
      K(x,y) * (((x * y) \ y) * z) = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[para(11825(a,1),10847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11825 10847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11829">
    <literal><![CDATA[
      L(x,y,z * (u * u)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,1631,a,b,11774,a),flip(a)].">
      <j1 rule="hyper" parents="373 1631 11774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11830">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(x,y,y),x) = ((x * y) * y) \ ((x * (y * y)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,961,a(flip),b,11774,a),flip(a)].">
      <j1 rule="hyper" parents="64 961 11774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11831">
    <literal><![CDATA[
      L(x,y,z / (u * u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),11774(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12 11774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11832">
    <literal><![CDATA[
      L(x,y,R(z * (u * u),w,v5)) = L(x,y,R(z,w,v5))
    ]]></literal>
    <justification jstring="[para(2102(a,2),11774(a,1,3))].">
      <j1 rule="para" parents="2102 11774"/>
    </justification>
  </clause>

  <clause id="11833">
    <literal><![CDATA[
      L(x,(y \ (z * z)) \ 1,u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5326,a,b,11775,a)].">
      <j1 rule="hyper" parents="64 5326 11775"/>
    </justification>
  </clause>

  <clause id="11834">
    <literal><![CDATA[
      (x * (y / (z * z))) \ (x * y) = L(z * z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10262,a(flip),b,11775,a)].">
      <j1 rule="hyper" parents="64 10262 11775"/>
    </justification>
  </clause>

  <clause id="11835">
    <literal><![CDATA[
      (x * ((y * y) \ z)) \ (x * z) = L(T(y * y,z),z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,851,a(flip),b,11775,a)].">
      <j1 rule="hyper" parents="64 851 11775"/>
    </justification>
  </clause>

  <clause id="11836">
    <literal><![CDATA[
      (x * y) / L(z * z,y,x) = x * (y / (z * z))
    ]]></literal>
    <justification jstring="[hyper(225,a,11775,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 11775 10262"/>
    </justification>
  </clause>

  <clause id="11837">
    <literal><![CDATA[
      L(x,L(y \ z,y,y),u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(102(a,2),11775(a,1,2))].">
      <j1 rule="para" parents="102 11775"/>
    </justification>
  </clause>

  <clause id="11838">
    <literal><![CDATA[
      L(x,R((y * y) \ z,u,w),v5) = L(x,R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(2051(a,2),11775(a,1,2))].">
      <j1 rule="para" parents="2051 11775"/>
    </justification>
  </clause>

  <clause id="11839">
    <literal><![CDATA[
      L(x,K(y,z),y * z) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,10825,a(flip),b,11788,a),flip(a)].">
      <j1 rule="hyper" parents="373 10825 11788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11840">
    <literal><![CDATA[
      L(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,5707,a(flip),b,11788,a),flip(a)].">
      <j1 rule="hyper" parents="373 5707 11788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11841">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,K(y,x),z) = z * (K(x,T(y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,11788,a,b,10993,a)].">
      <j1 rule="hyper" parents="145 11788 10993"/>
    </justification>
  </clause>

  <clause id="11842">
    <literal><![CDATA[
      L(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(11840(a,1),25(a,2,1))].">
      <j1 rule="para" parents="11840 25"/>
    </justification>
  </clause>

  <clause id="11843">
    <literal><![CDATA[
      (x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(11840(a,1),513(a,1,2,1))].">
      <j1 rule="para" parents="11840 513"/>
    </justification>
  </clause>

  <clause id="11844">
    <literal><![CDATA[
      L(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(5726(a,1),11840(a,1,2))].">
      <j1 rule="para" parents="5726 11840"/>
    </justification>
  </clause>

  <clause id="11845">
    <literal><![CDATA[
      (x * (K(y,z) * y)) * K(y,u) = x * (K(y,z) * T(y,u))
    ]]></literal>
    <justification jstring="[para(11840(a,1),7368(a,1,2,1))].">
      <j1 rule="para" parents="11840 7368"/>
    </justification>
  </clause>

  <clause id="11846">
    <literal><![CDATA[
      ((x * y) * K(x,y)) \ z = K(x,y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(710,a,11839,a),flip(a)].">
      <j1 rule="hyper" parents="710 11839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11847">
    <literal><![CDATA[
      L(x,K(y,y \ z),z) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),11839(a,1,3))].">
      <j1 rule="para" parents="10 11839"/>
    </justification>
  </clause>

  <clause id="11848">
    <literal><![CDATA[
      (x * (y / x)) \ (y * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,7684,a(flip),b,11847,a)].">
      <j1 rule="hyper" parents="64 7684 11847"/>
    </justification>
  </clause>

  <clause id="11849">
    <literal><![CDATA[
      x * (K(y,y \ x) * z) = (y * (x / y)) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,11847,a(flip),b,6265,a),flip(a)].">
      <j1 rule="hyper" parents="145 11847 6265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11850">
    <literal><![CDATA[
      L(L(T(x,y),z,u),K(x,w),v5) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11842(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11842 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11851">
    <literal><![CDATA[
      (x * K(y,z)) * L(T(y,u),w,v5) = x * (K(y,z) * L(T(y,u),w,v5))
    ]]></literal>
    <justification jstring="[para(11842(a,1),513(a,1,2,1))].">
      <j1 rule="para" parents="11842 513"/>
    </justification>
  </clause>

  <clause id="11852">
    <literal><![CDATA[
      L((1 / x) \ T(y,x \ 1),x,x) = ((x * x) \ 1) \ (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,1016,a(flip),b,11791,a),flip(a)].">
      <j1 rule="hyper" parents="64 1016 11791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11853">
    <literal><![CDATA[
      L(x,y \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(11806(a,2),2275(a,1))].">
      <j1 rule="para" parents="11806 2275"/>
    </justification>
  </clause>

  <clause id="11854">
    <literal><![CDATA[
      L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(11807(a,1),2275(a,1))].">
      <j1 rule="para" parents="11807 2275"/>
    </justification>
  </clause>

  <clause id="11855">
    <literal><![CDATA[
      L(x,y \ 1,z \ L(z,u,u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(5665(a,1),11807(a,1,3))].">
      <j1 rule="para" parents="5665 11807"/>
    </justification>
  </clause>

  <clause id="11856">
    <literal><![CDATA[
      L(x,x,y) \ y = x \ R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1406,a(flip),b,11819,a),flip(a)].">
      <j1 rule="hyper" parents="64 1406 11819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11857">
    <literal><![CDATA[
      x * (L(x,x,y) \ y) = R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,11819,a(flip),b,1406,a(flip))].">
      <j1 rule="hyper" parents="145 11819 1406"/>
    </justification>
  </clause>

  <clause id="11858">
    <literal><![CDATA[
      L(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(6092(a,1),11853(a,1,2))].">
      <j1 rule="para" parents="6092 11853"/>
    </justification>
  </clause>

  <clause id="11860">
    <literal><![CDATA[
      T(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(11767(a,1),11765(a,1))].">
      <j1 rule="para" parents="11767 11765"/>
    </justification>
  </clause>

  <clause id="11861">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25,a,b,11770,a),flip(a)].">
      <j1 rule="hyper" parents="373 25 11770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11863">
    <literal><![CDATA[
      L(T(x,y),y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,x * y) = u
    ]]></literal>
    <justification jstring="[para(11770(a,2),789(a,1))].">
      <j1 rule="para" parents="11770 789"/>
    </justification>
  </clause>

  <clause id="11864">
    <literal><![CDATA[
      L(x,(y \ 1) * z,u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),11777(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 11777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11865">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),w) = L(x,y * R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(2067(a,1),11777(a,1,2))].">
      <j1 rule="para" parents="2067 11777"/>
    </justification>
  </clause>

  <clause id="11866">
    <literal><![CDATA[
      L(x,y,z * (u * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(11829(a,2),2275(a,1))].">
      <j1 rule="para" parents="11829 2275"/>
    </justification>
  </clause>

  <clause id="11867">
    <literal><![CDATA[
      L(x,y \ (z * z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(11853,a,11833,a)].">
      <j1 rule="hyper" parents="11853 11833"/>
    </justification>
  </clause>

  <clause id="11869">
    <literal><![CDATA[
      x * ((x \ (y * y)) * z) = (y * y) * L(z,x,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,11867,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 11867 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11870">
    <literal><![CDATA[
      L(x,(y * y) / z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(82(a,1),11867(a,1,2)),flip(a)].">
      <j1 rule="para" parents="82 11867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11871">
    <literal><![CDATA[
      L(x,y \ (y * z),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(70(a,1),11867(a,1,2)),flip(a)].">
      <j1 rule="para" parents="70 11867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11872">
    <literal><![CDATA[
      L(x,L(y \ z,y,z),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(102(a,2),11867(a,1,2))].">
      <j1 rule="para" parents="102 11867"/>
    </justification>
  </clause>

  <clause id="11873">
    <literal><![CDATA[
      L(x,y \ (z \ (1 / z)),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(1090(a,1),11867(a,1,2,2))].">
      <j1 rule="para" parents="1090 11867"/>
    </justification>
  </clause>

  <clause id="11874">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(9377(a,1),11867(a,1,2))].">
      <j1 rule="para" parents="9377 11867"/>
    </justification>
  </clause>

  <clause id="11876">
    <literal><![CDATA[
      L(T((x \ y) * T(x,y),x),z,(x \ y) * T(x,y)) = L((x \ y) * x,z,T((x \ y) * T(x,y),u))
    ]]></literal>
    <justification jstring="[para(4701(a,1),11861(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4701 11861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11877">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = u * a(T(x,y),z,T(x,y))
    ]]></literal>
    <justification jstring="[para(11861(a,1),10947(a,1,2,1))].">
      <j1 rule="para" parents="11861 10947"/>
    </justification>
  </clause>

  <clause id="11878">
    <literal><![CDATA[
      L(x,a(y,y,z) * z,u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(5669(a,1),11864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5669 11864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11879">
    <literal><![CDATA[
      L(x,y \ a(z,u,y),w) = L(x,y * a(z,u,y),w)
    ]]></literal>
    <justification jstring="[para(9433(a,1),11864(a,1,2))].">
      <j1 rule="para" parents="9433 11864"/>
    </justification>
  </clause>

  <clause id="11880">
    <literal><![CDATA[
      L(T((x / y) \ 1,y * (x / y)) \ 1,(x / y) \ 1,T(y * (x / y),(x / y) \ 1)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(9335(a,1),11766(a,2,1))].">
      <j1 rule="para" parents="9335 11766"/>
    </justification>
  </clause>

  <clause id="11881">
    <literal><![CDATA[
      L(T(x,x \ 1),x,y * x) = R(y,x,x \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(297(a,1),11811(a,2,1))].">
      <j1 rule="para" parents="297 11811"/>
    </justification>
  </clause>

  <clause id="11882">
    <literal><![CDATA[
      L(L(x,x,y),(y \ 1) / L(x,x,y),y) = (y * ((y \ 1) * (1 / x))) \ 1
    ]]></literal>
    <justification jstring="[para(11816(a,1),711(a,2,1,2))].">
      <j1 rule="para" parents="11816 711"/>
    </justification>
  </clause>

  <clause id="11883">
    <literal><![CDATA[
      L(x * K(y,x),x,x * y) = (x * y) / ((x * y) * (1 / x))
    ]]></literal>
    <justification jstring="[para(6906(a,1),11821(a,1,1))].">
      <j1 rule="para" parents="6906 11821"/>
    </justification>
  </clause>

  <clause id="11884">
    <literal><![CDATA[
      L(x,y \ z,L(y \ z,y,y)) = L(x,y * z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2482,a(flip),b,11837,a)].">
      <j1 rule="hyper" parents="64 2482 11837"/>
    </justification>
  </clause>

  <clause id="11885">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),z,x) = w
    ]]></literal>
    <justification jstring="[para(11770(a,2),11860(a,1))].">
      <j1 rule="para" parents="11770 11860"/>
    </justification>
  </clause>

  <clause id="11886">
    <literal><![CDATA[
      L(x,(y * y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(2961(a,2),11866(a,1))].">
      <j1 rule="para" parents="2961 11866"/>
    </justification>
  </clause>

  <clause id="11887">
    <literal><![CDATA[
      L(a(x,y,y \ x),x * y,y) = (y * L(y \ x,y,x)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,5643,a(flip),b,11872,a),flip(a)].">
      <j1 rule="hyper" parents="64 5643 11872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11888">
    <literal><![CDATA[
      L(x,y * (y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,L(z,y,y),u) = w
    ]]></literal>
    <justification jstring="[para(100(a,1),11886(a,1,2))].">
      <j1 rule="para" parents="100 11886"/>
    </justification>
  </clause>

  <clause id="11889">
    <literal><![CDATA[
      L(x,((1 / y) * z) * u,w) = L(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[para(535(a,1),11779(a,1,2,1))].">
      <j1 rule="para" parents="535 11779"/>
    </justification>
  </clause>

  <clause id="11891">
    <literal><![CDATA[
      (x * (y / x)) * ((y / x) \ z) = y * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,6292,a(flip),b,11848,a)].">
      <j1 rule="hyper" parents="145 6292 11848"/>
    </justification>
  </clause>

  <clause id="11892">
    <literal><![CDATA[
      K(x \ y,x) * (y \ z) = (x * (y / x)) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),11848(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 11848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11893">
    <literal><![CDATA[
      x \ ((y * (x / y)) * z) = K(y,y \ x) * z
    ]]></literal>
    <justification jstring="[hyper(149,a,11849,a)].">
      <j1 rule="hyper" parents="149 11849"/>
    </justification>
  </clause>

  <clause id="11894">
    <literal><![CDATA[
      T(x,x \ y) * ((x * (y / x)) \ z) = x * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,11892,a(flip),b,6155,a)].">
      <j1 rule="hyper" parents="145 11892 6155"/>
    </justification>
  </clause>

  <clause id="11895">
    <literal><![CDATA[
      (x / y) * ((y * (x / y)) \ z) = (y \ x) * (x \ z)
    ]]></literal>
    <justification jstring="[para(11892(a,1),6592(a,1,2))].">
      <j1 rule="para" parents="11892 6592"/>
    </justification>
  </clause>

  <clause id="11896">
    <literal><![CDATA[
      T((x * (y / x)) \ z,K(x,y)) = (y \ z) * K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(11892(a,1),8709(a,1,1))].">
      <j1 rule="para" parents="11892 8709"/>
    </justification>
  </clause>

  <clause id="11898">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,y,z) * u) = L((x \ 1) \ u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,1810,a(flip),b,11813,a)].">
      <j1 rule="hyper" parents="373 1810 11813"/>
    </justification>
  </clause>

  <clause id="11899">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (R(x,y,z) * u) = L((x \ 1) \ u,x,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1794(a,1),11813(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1794 11813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11900">
    <literal><![CDATA[
      (1 / L(x,y,z)) * (x * u) = x * ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7749,a(flip),b,11815,a)].">
      <j1 rule="hyper" parents="64 7749 11815"/>
    </justification>
  </clause>

  <clause id="11901">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(u,x,R(x,y,z)) = R(x,y,z) * ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1794(a,1),11815(a,1,1))].">
      <j1 rule="para" parents="1794 11815"/>
    </justification>
  </clause>

  <clause id="11902">
    <literal><![CDATA[
      (x * (R(x,y,z) \ 1)) * L(u,x,R(x,y,z)) = x * ((R(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(2554(a,1),11815(a,1,2))].">
      <j1 rule="para" parents="2554 11815"/>
    </justification>
  </clause>

  <clause id="11903">
    <literal><![CDATA[
      (x * y) / ((y / (z * z)) * ((x * (y / (z * z))) \ (x * y))) = R(x,y / (z * z),L(z * z,y,x))
    ]]></literal>
    <justification jstring="[para(11834(a,1),109(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11834 109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11904">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(3348(a,1),11801(a,1,1))].">
      <j1 rule="para" parents="3348 11801"/>
    </justification>
  </clause>

  <clause id="11905">
    <literal><![CDATA[
      K((x * (1 / y)) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6990,a(flip),b,11824,a),flip(a)].">
      <j1 rule="hyper" parents="373 6990 11824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11906">
    <literal><![CDATA[
      L(x,R(1 / y,z,u),w) = L(x,R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(309(a,1),11838(a,1,2,1))].">
      <j1 rule="para" parents="309 11838"/>
    </justification>
  </clause>

  <clause id="11907">
    <literal><![CDATA[
      L(x,R((1 / y) * z,u,w),v5) = L(x,R(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(535(a,1),11838(a,1,2,1))].">
      <j1 rule="para" parents="535 11838"/>
    </justification>
  </clause>

  <clause id="11908">
    <literal><![CDATA[
      L(x,R(y \ 1,z,u),w) = L(x,R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(79(a,1),11906(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 11906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11909">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(u,R(x,y,z),x) = x * (R(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(11908(a,1),2011(a,1,2))].">
      <j1 rule="para" parents="11908 2011"/>
    </justification>
  </clause>

  <clause id="11910">
    <literal><![CDATA[
      K(x,y) \ ((x * y) \ z) = (T(x,y) * y) \ z
    ]]></literal>
    <justification jstring="[para(6329(a,1),11846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6329 11846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11911">
    <literal><![CDATA[
      (x * y) * (K(x,y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[hyper(787,a,11910,a),flip(a)].">
      <j1 rule="hyper" parents="787 11910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11912">
    <literal><![CDATA[
      (x * y) * (K(x,z) * T(x,y)) = (T(x,y) * y) * T(x,z)
    ]]></literal>
    <justification jstring="[para(6405(a,1),11911(a,1,2))].">
      <j1 rule="para" parents="6405 11911"/>
    </justification>
  </clause>

  <clause id="11913">
    <literal><![CDATA[
      (T(x,y) * (y * z)) \ ((T(x,y) * y) * z) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(11911(a,1),6598(a,1,2))].">
      <j1 rule="para" parents="11911 6598"/>
    </justification>
  </clause>

  <clause id="11914">
    <literal><![CDATA[
      L(x,y * R(y,z,u),y) = L(x,y,y * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,2858,a(flip),b,11865,a),flip(a)].">
      <j1 rule="hyper" parents="64 2858 11865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11915">
    <literal><![CDATA[
      L(x,y * R(y,z,z \ 1),u) = L(x,a(y,z,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(982(a,1),11865(a,1,2)),flip(a)].">
      <j1 rule="para" parents="982 11865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11916">
    <literal><![CDATA[
      L(x,y * L(y,z,z),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(1243(a,1),11874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1243 11874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11917">
    <literal><![CDATA[
      L(x,L(y,z,z) * y,u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(275(a,2),11916(a,1,2))].">
      <j1 rule="para" parents="275 11916"/>
    </justification>
  </clause>

  <clause id="11918">
    <literal><![CDATA[
      L(x,((y \ 1) * z) * u,w) = L(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),11889(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11919">
    <literal><![CDATA[
      R(T(x,y),z / x,(z / x) \ y) = y \ (z * ((x \ z) \ y))
    ]]></literal>
    <justification jstring="[hyper(139,a,11891,a(flip),b,994,a),flip(a)].">
      <j1 rule="hyper" parents="139 11891 994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11920">
    <literal><![CDATA[
      K(x,y \ 1) * (y * z) = y * (K(x,y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(4496,a,11904,a),flip(a)].">
      <j1 rule="hyper" parents="4496 11904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11921">
    <literal><![CDATA[
      L(x,((y \ 1) * (y * L(y,z,u))) * w,v5) = L(x,L(y,z,u) * ((y * y) * w),v5)
    ]]></literal>
    <justification jstring="[para(1750(a,1),11918(a,2,2))].">
      <j1 rule="para" parents="1750 11918"/>
    </justification>
  </clause>

  <clause id="11922">
    <literal><![CDATA[
      x \ (K(y,x \ 1) * z) = K(y,x \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(759,a,11920,a)].">
      <j1 rule="hyper" parents="759 11920"/>
    </justification>
  </clause>

  <clause id="11924">
    <literal><![CDATA[
      1 \ (x * (K(y,x \ 1) * z)) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,66,a,b,11920,a)].">
      <j1 rule="hyper" parents="373 66 11920"/>
    </justification>
  </clause>

  <clause id="11925">
    <literal><![CDATA[
      (x \ 1) * (x \ ((x * y) * L(z,x,y))) = y * (T(x \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1596,a,b,11814,a)].">
      <j1 rule="hyper" parents="64 1596 11814"/>
    </justification>
  </clause>

  <clause id="11926">
    <literal><![CDATA[
      L(x,y,z) * (T(x \ 1,L(x,y,z)) * u) = (x \ 1) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2483,a(flip),b,11814,a),flip(a)].">
      <j1 rule="hyper" parents="64 2483 11814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11928">
    <literal><![CDATA[
      L(x,y \ z,y * z) = L(x,y * z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2187,a(flip),b,11884,a)].">
      <j1 rule="hyper" parents="64 2187 11884"/>
    </justification>
  </clause>

  <clause id="11929">
    <literal><![CDATA[
      L(x,(((1 / y) * z) * u) * w,v5) = L(x,((y * z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(535(a,1),11781(a,1,2,1,1))].">
      <j1 rule="para" parents="535 11781"/>
    </justification>
  </clause>

  <clause id="11930">
    <literal><![CDATA[
      K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = (y * (K(z,x) * L(z,u,w))) \ (y * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(11843(a,1),9344(a,2,1))].">
      <j1 rule="para" parents="11843 9344"/>
    </justification>
  </clause>

  <clause id="11931">
    <literal><![CDATA[
      (x * T(y,z)) * K(y,u) = x * (K(y,z) * T(y,u))
    ]]></literal>
    <justification jstring="[para(5756(a,2),11845(a,1,1,2))].">
      <j1 rule="para" parents="5756 11845"/>
    </justification>
  </clause>

  <clause id="11932">
    <literal><![CDATA[
      T(x,(T(y,z * (K(u,w) * T(u,v5))) * (z * T(u,w))) * K(u,v5)) = T(x,((z * T(u,w)) * K(u,v5)) * R(y,z * T(u,w),K(u,v5)))
    ]]></literal>
    <justification jstring="[para(11931(a,1),11150(a,1,2,1,1,2))].">
      <j1 rule="para" parents="11931 11150"/>
    </justification>
  </clause>

  <clause id="11933">
    <literal><![CDATA[
      L(R(x,x,x),x,y * x) = R(y,x,x \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(1417(a,1),11881(a,1,1))].">
      <j1 rule="para" parents="1417 11881"/>
    </justification>
  </clause>

  <clause id="11934">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(u,x,L(x,y,z)) = x * ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5597,a,b,11900,a)].">
      <j1 rule="hyper" parents="64 5597 11900"/>
    </justification>
  </clause>

  <clause id="11935">
    <literal><![CDATA[
      L(x,R((y \ 1) * z,u,w),v5) = L(x,R(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),11907(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 11907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11936">
    <literal><![CDATA[
      L(T(x \ 1,y) \ z,x \ 1,x) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(6169,a,11924,a)].">
      <j1 rule="hyper" parents="6169 11924"/>
    </justification>
  </clause>

  <clause id="11938">
    <literal><![CDATA[
      L(x \ (1 * ((y \ 1) \ x)),y,y) = x \ ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(11919(a,1),2302(a,1,1))].">
      <j1 rule="para" parents="11919 2302"/>
    </justification>
  </clause>

  <clause id="11939">
    <literal><![CDATA[
      L(x \ ((y \ 1) \ x),y,y) = x \ ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(7(a,1),11938(a,1,1,2))].">
      <j1 rule="para" parents="7 11938"/>
    </justification>
  </clause>

  <clause id="11941">
    <literal><![CDATA[
      L(x \ (((1 / y) \ 1) \ x),1 / y,1 / y) = x \ (L(y,y,y) \ x)
    ]]></literal>
    <justification jstring="[para(818(a,2),11939(a,2,2,1))].">
      <j1 rule="para" parents="818 11939"/>
    </justification>
  </clause>

  <clause id="11942">
    <literal><![CDATA[
      L(x,(((y * y) / z) * u) * w,v5) = L(x,(z * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,11889,a(flip),b,11782,a),flip(a)].">
      <j1 rule="hyper" parents="373 11889 11782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11943">
    <literal><![CDATA[
      L(x,((y \ (z * z)) * u) * w,v5) = L(x,(y * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),11942(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 11942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11944">
    <literal><![CDATA[
      a(T(x,y),z,T(x,y)) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,10954,a(flip),b,11877,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 10954 11877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11946">
    <literal><![CDATA[
      ((x * y) * a(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(11944(a,1),10949(a,1,1,2))].">
      <j1 rule="para" parents="11944 10949"/>
    </justification>
  </clause>

  <clause id="11947">
    <literal><![CDATA[
      K(T(x,y * z) * z,T(x,y * z)) = a(x,z,x) * K(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(11944(a,1),10926(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11944 10926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11948">
    <literal><![CDATA[
      L(x,(((y \ 1) * z) * u) * w,v5) = L(x,((y * z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),11929(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 11929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11949">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(11346(a,1),11946(a,1,1))].">
      <j1 rule="para" parents="11346 11946"/>
    </justification>
  </clause>

  <clause id="11951">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(y,x),z,y) = u
    ]]></literal>
    <justification jstring="[para(11949(a,2),11885(a,1))].">
      <j1 rule="para" parents="11949 11885"/>
    </justification>
  </clause>

  <clause id="11952">
    <literal><![CDATA[
      L(x,(L(y \ z,K(y,y \ u),K(y,y \ u)) * w) * v5,v6) = L(x,((K(y,y \ u) * ((u / (u / y)) \ z)) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(6413(a,2),11783(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6413 11783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11953">
    <literal><![CDATA[
      a((x * x) * (y * z),u,w) = a(y * ((x * x) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(2694,a,11785,a),flip(a)].">
      <j1 rule="hyper" parents="2694 11785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11955">
    <literal><![CDATA[
      a(x * ((y * y) \ z),u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2639,a(flip),b,11953,a),flip(a)].">
      <j1 rule="hyper" parents="64 2639 11953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11957">
    <literal><![CDATA[
      a(x * ((y * y) * z),u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),11955(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 11955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11958">
    <literal><![CDATA[
      a(x * (y * y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(191(a,1),11955(a,1,1)),flip(a)].">
      <j1 rule="para" parents="191 11955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11959">
    <literal><![CDATA[
      a(x * (((y * y) \ z) * u),w,v5) = a(x * (z * u),w,v5)
    ]]></literal>
    <justification jstring="[para(484(a,1),11955(a,1,1,2))].">
      <j1 rule="para" parents="484 11955"/>
    </justification>
  </clause>

  <clause id="11960">
    <literal><![CDATA[
      a(x,(y * y) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(3381,a,11958,a)].">
      <j1 rule="hyper" parents="3381 11958"/>
    </justification>
  </clause>

  <clause id="11961">
    <literal><![CDATA[
      a(L(x,x,x),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2640,a(flip),b,11958,a)].">
      <j1 rule="hyper" parents="64 2640 11958"/>
    </justification>
  </clause>

  <clause id="11962">
    <literal><![CDATA[
      a((x * y) * y,z,u) = a(R(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[para(111(a,1),11958(a,1,1))].">
      <j1 rule="para" parents="111 11958"/>
    </justification>
  </clause>

  <clause id="11963">
    <literal><![CDATA[
      a(x * (y \ (1 / y)),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(1090(a,1),11958(a,1,1,2))].">
      <j1 rule="para" parents="1090 11958"/>
    </justification>
  </clause>

  <clause id="11965">
    <literal><![CDATA[
      a(x,(y * y) \ z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),11960(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 11960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11966">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(245(a,1),11960(a,1,2)),flip(a)].">
      <j1 rule="para" parents="245 11960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11967">
    <literal><![CDATA[
      a(x,(1 / y) * z,u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(310(a,1),11960(a,1,2)),flip(a)].">
      <j1 rule="para" parents="310 11960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11968">
    <literal><![CDATA[
      a(x,y * (y * z),u) = a(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(100(a,1),11960(a,1,2))].">
      <j1 rule="para" parents="100 11960"/>
    </justification>
  </clause>

  <clause id="11969">
    <literal><![CDATA[
      a(x,((y * y) \ z) * u,w) = a(x,z * u,w)
    ]]></literal>
    <justification jstring="[para(126(a,1),11960(a,1,2)),flip(a)].">
      <j1 rule="para" parents="126 11960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11970">
    <literal><![CDATA[
      a(x,((y * z) * y) * z,u) = a(x,a(y * z,y,z),u)
    ]]></literal>
    <justification jstring="[para(88(a,1),11960(a,1,2))].">
      <j1 rule="para" parents="88 11960"/>
    </justification>
  </clause>

  <clause id="11971">
    <literal><![CDATA[
      a(x,(y / (1 / z)) \ u,w) = a(x,(y / z) \ u,w)
    ]]></literal>
    <justification jstring="[para(891(a,1),11960(a,1,2)),flip(a)].">
      <j1 rule="para" parents="891 11960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11972">
    <literal><![CDATA[
      a(x,(y * (y * z)) * u,w) = a(x,L(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[para(605(a,1),11960(a,1,2))].">
      <j1 rule="para" parents="605 11960"/>
    </justification>
  </clause>

  <clause id="11973">
    <literal><![CDATA[
      a(x,(((y * y) \ z) * u) * w,v5) = a(x,(z * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(805(a,1),11960(a,1,2)),flip(a)].">
      <j1 rule="para" parents="805 11960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11974">
    <literal><![CDATA[
      a(x,T(y,z * z) * u,w) = a(x,y * ((z * z) * u),w)
    ]]></literal>
    <justification jstring="[para(1434(a,1),11960(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1434 11960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11975">
    <literal><![CDATA[
      a(x,((y * (y * z)) * u) * w,v5) = a(x,(L(z,y,y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(1314(a,1),11960(a,1,2))].">
      <j1 rule="para" parents="1314 11960"/>
    </justification>
  </clause>

  <clause id="11976">
    <literal><![CDATA[
      a(x,R((y * y) * z,u,w),v5) = a(x,R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(1981(a,2),11960(a,1,2))].">
      <j1 rule="para" parents="1981 11960"/>
    </justification>
  </clause>

  <clause id="11977">
    <literal><![CDATA[
      a(x,R(y / (1 / z),u,w) \ v5,v6) = a(x,R(y / z,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(2475(a,1),11960(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2475 11960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11978">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),w) = a(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(5602(a,1),11960(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5602 11960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11979">
    <literal><![CDATA[
      a(x,K(y,z) * T(y,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(6850(a,1),11960(a,1,2))].">
      <j1 rule="para" parents="6850 11960"/>
    </justification>
  </clause>

  <clause id="11980">
    <literal><![CDATA[
      a(x,y \ 1,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5355,a(flip),b,11966,a)].">
      <j1 rule="hyper" parents="64 5355 11966"/>
    </justification>
  </clause>

  <clause id="11982">
    <literal><![CDATA[
      a(x,L(y \ z,y,y),u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(102(a,2),11965(a,1,2))].">
      <j1 rule="para" parents="102 11965"/>
    </justification>
  </clause>

  <clause id="11983">
    <literal><![CDATA[
      a(x,((y * z) * z) \ u,w) = a(x,R(y,z,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(875(a,1),11965(a,1,2))].">
      <j1 rule="para" parents="875 11965"/>
    </justification>
  </clause>

  <clause id="11984">
    <literal><![CDATA[
      a(x,(y \ 1) * z,u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),11967(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 11967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11985">
    <literal><![CDATA[
      a(x,y \ R(y,z,u),w) = a(x,y * R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(2067(a,1),11967(a,1,2))].">
      <j1 rule="para" parents="2067 11967"/>
    </justification>
  </clause>

  <clause id="11986">
    <literal><![CDATA[
      a(x * (((y * y) / z) * u),w,v5) = a(x * ((1 / z) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(556(a,1),11957(a,1,1,2))].">
      <j1 rule="para" parents="556 11957"/>
    </justification>
  </clause>

  <clause id="11987">
    <literal><![CDATA[
      a(x * ((T(y,z * z) / u) * w),v5,v6) = a(x * (((y * (z * z)) / u) * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(1459(a,1),11957(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1459 11957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11988">
    <literal><![CDATA[
      a(x * (((y * y) * L((y * y) \ 1,z,u)) * w),v5,v6) = a(x * (w * L(w \ ((y * y) \ w),z,u)),v5,v6)
    ]]></literal>
    <justification jstring="[para(2732(a,1),11957(a,1,1,2))].">
      <j1 rule="para" parents="2732 11957"/>
    </justification>
  </clause>

  <clause id="11989">
    <literal><![CDATA[
      a(x * (y \ L(y,z,u)),w,v5) = a(x * (y * L(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(5602(a,1),11957(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5602 11957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11990">
    <literal><![CDATA[
      a(x,(((y * z) * y) * z) * u,w) = a(x,a(y * z,y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(14(a,2),11969(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14 11969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11991">
    <literal><![CDATA[
      a(x,((1 / y) * z) * u,w) = a(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[para(535(a,1),11969(a,1,2,1))].">
      <j1 rule="para" parents="535 11969"/>
    </justification>
  </clause>

  <clause id="11992">
    <literal><![CDATA[
      a(x,L(y \ z,y,y) * u,w) = a(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[para(102(a,2),11969(a,1,2,1))].">
      <j1 rule="para" parents="102 11969"/>
    </justification>
  </clause>

  <clause id="11993">
    <literal><![CDATA[
      a(x,((1 / y) / z) * u,w) = a(x,(y / z) * u,w)
    ]]></literal>
    <justification jstring="[para(887(a,1),11969(a,1,2,1))].">
      <j1 rule="para" parents="887 11969"/>
    </justification>
  </clause>

  <clause id="11994">
    <literal><![CDATA[
      a(x,((y / (1 / z)) \ u) * w,v5) = a(x,((y / z) \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(876(a,1),11969(a,1,2,1))].">
      <j1 rule="para" parents="876 11969"/>
    </justification>
  </clause>

  <clause id="11995">
    <literal><![CDATA[
      a(x,R(1 / y,z,u),w) = a(x,R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(245(a,1),11976(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="245 11976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11996">
    <literal><![CDATA[
      a(x,R(y \ 1,z,u),w) = a(x,R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(79(a,1),11995(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 11995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11997">
    <literal><![CDATA[
      a(x,y * R(y,z,z \ 1),u) = a(x,a(y,z,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(982(a,1),11985(a,1,2)),flip(a)].">
      <j1 rule="para" parents="982 11985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11998">
    <literal><![CDATA[
      a(x,((y \ 1) * z) * u,w) = a(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),11991(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 11991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11999">
    <literal><![CDATA[
      a(x,(y \ R(y,z,u)) * w,v5) = a(x,(y * R(y,z,u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(2067(a,1),11991(a,1,2,1))].">
      <j1 rule="para" parents="2067 11991"/>
    </justification>
  </clause>

  <clause id="12000">
    <literal><![CDATA[
      a(x,((y \ 1) * (y * L(y,z,u))) * w,v5) = a(x,L(y,z,u) * ((y * y) * w),v5)
    ]]></literal>
    <justification jstring="[para(1750(a,1),11998(a,2,2))].">
      <j1 rule="para" parents="1750 11998"/>
    </justification>
  </clause>

  <clause id="12001">
    <literal><![CDATA[
      a(x,R(y * (y * z),u,w) * v5,v6) = a(x,L(R(z,u,w),y,y) * v5,v6)
    ]]></literal>
    <justification jstring="[para(2137(a,2),11972(a,1,2,1))].">
      <j1 rule="para" parents="2137 11972"/>
    </justification>
  </clause>

  <clause id="12002">
    <literal><![CDATA[
      a(x,(((1 / y) * z) * u) * w,v5) = a(x,((y * z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(535(a,1),11973(a,1,2,1,1))].">
      <j1 rule="para" parents="535 11973"/>
    </justification>
  </clause>

  <clause id="12003">
    <literal><![CDATA[
      a(x,(y * R(y,z,z \ 1)) * u,w) = a(x,a(y,z,z \ 1) * u,w)
    ]]></literal>
    <justification jstring="[para(982(a,1),11999(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="982 11999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12004">
    <literal><![CDATA[
      ((x * x) \ 1) \ (y * (x \ 1)) = L(x,x,x) * T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,1256,a(flip),b,11852,a),flip(a)].">
      <j1 rule="hyper" parents="64 1256 11852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12005">
    <literal><![CDATA[
      L(x,x,x) * T(y,x \ 1) = (x * x) * (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,554,a(flip),b,12004,a),flip(a)].">
      <j1 rule="hyper" parents="64 554 12004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12006">
    <literal><![CDATA[
      a(x,y,K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(T(x,y),y,z) = u
    ]]></literal>
    <justification jstring="[para(11913(a,1),959(a,1))].">
      <j1 rule="para" parents="11913 959"/>
    </justification>
  </clause>

  <clause id="12007">
    <literal><![CDATA[
      (x \ 1) * (x \ (y * (T(x,y) * z))) = y * (T(x \ 1,y) * z)
    ]]></literal>
    <justification jstring="[para(10989(a,1),11925(a,1,2,2))].">
      <j1 rule="para" parents="10989 11925"/>
    </justification>
  </clause>

  <clause id="12008">
    <literal><![CDATA[
      (x \ 1) \ (y * (T(x \ 1,y) * z)) = x \ (y * (T(x,y) * z))
    ]]></literal>
    <justification jstring="[hyper(149,a,12007,a)].">
      <j1 rule="hyper" parents="149 12007"/>
    </justification>
  </clause>

  <clause id="12009">
    <literal><![CDATA[
      a(x,y,x) * K(y,T(x,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9521,a(flip),b,11947,a),flip(a)].">
      <j1 rule="hyper" parents="64 9521 11947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12011">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7929,a,12009,a)].">
      <j1 rule="hyper" parents="7929 12009"/>
    </justification>
  </clause>

  <clause id="12013">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,T(y / x,u)) * K((x / y) \ 1,T(z,u)) = a((x / y) \ 1,z,(x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(9298(a,1),12011(a,1,1))].">
      <j1 rule="para" parents="9298 12011"/>
    </justification>
  </clause>

  <clause id="12014">
    <literal><![CDATA[
      x * (K(y,z) * L(T(y,x),u,w)) = L(y,u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8503,a,11851,a),flip(a)].">
      <j1 rule="hyper" parents="8503 11851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12015">
    <literal><![CDATA[
      L(L(T(x,y),z,u),K(x,w),y) \ (L(x,z,u) * (y * K(x,w))) = T(y * K(x,w),L(L(T(x,y),z,u),K(x,w),y))
    ]]></literal>
    <justification jstring="[hyper(612,a,12014,a),flip(a)].">
      <j1 rule="hyper" parents="612 12014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12016">
    <literal><![CDATA[
      L((x \ 1) \ T(y,L(x,z,u)),x,L(x,z,u)) = (x \ L(x,z,u)) \ (y * L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,11898,a),flip(a)].">
      <j1 rule="hyper" parents="64 249 11898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12017">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(u,x,R(x,y,z)) = x * (R(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[para(2554(a,1),11909(a,1,2))].">
      <j1 rule="para" parents="2554 11909"/>
    </justification>
  </clause>

  <clause id="12018">
    <literal><![CDATA[
      L(x \ (y \ x),1 / y,1 / y) = x \ (L(y,y,y) \ x)
    ]]></literal>
    <justification jstring="[para(82(a,1),11941(a,1,1,2,1))].">
      <j1 rule="para" parents="82 11941"/>
    </justification>
  </clause>

  <clause id="12019">
    <literal><![CDATA[
      L(x \ (y \ x),y,y) = x \ (L(y,y,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1158,a(flip),b,12018,a)].">
      <j1 rule="hyper" parents="64 1158 12018"/>
    </justification>
  </clause>

  <clause id="12021">
    <literal><![CDATA[
      R(x,y,z) * ((x \ 1) * u) = x * (R(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11901,a(flip),b,12017,a)].">
      <j1 rule="hyper" parents="64 11901 12017"/>
    </justification>
  </clause>

  <clause id="12022">
    <literal><![CDATA[
      x * (x * (R(x \ 1,y,z) * u)) = R(x,y,z) * L(u,x,x)
    ]]></literal>
    <justification jstring="[para(12021(a,1),1912(a,1,2))].">
      <j1 rule="para" parents="12021 1912"/>
    </justification>
  </clause>

  <clause id="12023">
    <literal><![CDATA[
      (R(x,y,z) \ 1) \ L((R(x,y,z) \ 1) * u,x,x) = x * (x * (R(x \ 1,y,z) * (R(x,y,z) \ u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,5546,a,b,12022,a)].">
      <j1 rule="hyper" parents="373 5546 12022"/>
    </justification>
  </clause>

  <clause id="12024">
    <literal><![CDATA[
      L(L(x,x,y),(y \ 1) * (1 / x),y) = (y * ((y \ 1) * (1 / x))) \ 1
    ]]></literal>
    <justification jstring="[para(11816(a,1),11882(a,1,2))].">
      <j1 rule="para" parents="11816 11882"/>
    </justification>
  </clause>

  <clause id="12025">
    <literal><![CDATA[
      L(L(x,x,y),(y \ 1) * (x \ 1),y) = (y * ((y \ 1) * (1 / x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,5322,a(flip),b,12024,a)].">
      <j1 rule="hyper" parents="64 5322 12024"/>
    </justification>
  </clause>

  <clause id="12026">
    <literal><![CDATA[
      (R(x,y,z) \ x) * L(u,x,R(x,y,z)) = x * ((R(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1909(a,1),11902(a,1,1))].">
      <j1 rule="para" parents="1909 11902"/>
    </justification>
  </clause>

  <clause id="12027">
    <literal><![CDATA[
      L(x,L((y \ 1) * (y * y),z,u) * w,v5) = L(x,L(y,z,u) * ((y * y) * w),v5)
    ]]></literal>
    <justification jstring="[para(5645(a,2),11921(a,1,2,1))].">
      <j1 rule="para" parents="5645 11921"/>
    </justification>
  </clause>

  <clause id="12028">
    <literal><![CDATA[
      a(x,L((y \ 1) * (y * y),z,u) * w,v5) = a(x,L(y,z,u) * ((y * y) * w),v5)
    ]]></literal>
    <justification jstring="[para(5645(a,2),12000(a,1,2,1))].">
      <j1 rule="para" parents="5645 12000"/>
    </justification>
  </clause>

  <clause id="12029">
    <literal><![CDATA[
      T(x * ((1 / y) * L(y,z,u)),L(y,y,x)) = L(y,y,x) \ (x * L(L(y,y,x),z,u))
    ]]></literal>
    <justification jstring="[para(11797(a,1),11822(a,1,1))].">
      <j1 rule="para" parents="11797 11822"/>
    </justification>
  </clause>

  <clause id="12030">
    <literal><![CDATA[
      L(x,x,y) \ (y * L(L(x,x,y),z,u)) = T(y * (x \ L(x,z,u)),L(x,x,y))
    ]]></literal>
    <justification jstring="[para(5590(a,1),12029(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5590 12029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12031">
    <literal><![CDATA[
      L(x,x,y) \ (y * L(L(x,x,y),z,u)) = T(y * (x \ L(x,z,u)),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,7544,a(flip),b,12030,a),flip(a)].">
      <j1 rule="hyper" parents="373 7544 12030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12033">
    <literal><![CDATA[
      L((x \ y) * x,z,T((x \ y) * T(x,y),u)) = L((x \ y) * x,z,(x \ y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(4701(a,1),11876(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4701 11876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12034">
    <literal><![CDATA[
      K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = L(K(x,T(z,L(z,u,w))),L(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(7460,a,11930,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="7460 11930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12035">
    <literal><![CDATA[
      K(x,((y / z) * L(z,u,w)) \ (y * L(z,u,w))) = L(K(x,z),L(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(198(a,1),12034(a,2,1,2))].">
      <j1 rule="para" parents="198 12034"/>
    </justification>
  </clause>

  <clause id="12036">
    <literal><![CDATA[
      L(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3187(a,1),12035(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3187 12035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12037">
    <literal><![CDATA[
      K((x \ 1) * L(y,z,u),y) = K(x \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7572,a(flip),b,12036,a)].">
      <j1 rule="hyper" parents="64 7572 12036"/>
    </justification>
  </clause>

  <clause id="12038">
    <literal><![CDATA[
      K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7529,a(flip),b,12036,a),flip(a)].">
      <j1 rule="hyper" parents="64 7529 12036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12039">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11567,a(flip),b,12037,a),flip(a)].">
      <j1 rule="hyper" parents="64 11567 12037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12041">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8529,a(flip),b,12039,a),flip(a)].">
      <j1 rule="hyper" parents="373 8529 12039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12042">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(11752,a,12041,a)].">
      <j1 rule="hyper" parents="11752 12041"/>
    </justification>
  </clause>

  <clause id="12043">
    <literal><![CDATA[
      (L(x,y,z) * K((u \ x) \ x,x)) * u = (x \ (L(x,y,z) * u)) * x
    ]]></literal>
    <justification jstring="[para(12041(a,1),7645(a,1,1,2))].">
      <j1 rule="para" parents="12041 7645"/>
    </justification>
  </clause>

  <clause id="12044">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12041,a(flip),b,12038,a),flip(a)].">
      <j1 rule="hyper" parents="64 12041 12038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12046">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,10496,a(flip),b,12044,a),flip(a)].">
      <j1 rule="hyper" parents="373 10496 12044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12047">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6783,a(flip),b,12044,a),flip(a)].">
      <j1 rule="hyper" parents="373 6783 12044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12048">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = w
    ]]></literal>
    <justification jstring="[para(12044(a,2),6784(a,1))].">
      <j1 rule="para" parents="12044 6784"/>
    </justification>
  </clause>

  <clause id="12049">
    <literal><![CDATA[
      K(x / L(y,z,u),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),12047(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 12047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12050">
    <literal><![CDATA[
      T(x * L(y,z,u),K(x,y)) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(12047(a,1),6252(a,1,2))].">
      <j1 rule="para" parents="12047 6252"/>
    </justification>
  </clause>

  <clause id="12051">
    <literal><![CDATA[
      K(x \ (y * (z * x)),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * z,x) = u
    ]]></literal>
    <justification jstring="[para(100(a,1),12048(a,1,1,2))].">
      <j1 rule="para" parents="100 12048"/>
    </justification>
  </clause>

  <clause id="12052">
    <literal><![CDATA[
      T(x * ((y * z) \ (y * u)),K(x,z \ u)) = x * L(z \ u,z,y)
    ]]></literal>
    <justification jstring="[para(102(a,1),12050(a,1,1,2))].">
      <j1 rule="para" parents="102 12050"/>
    </justification>
  </clause>

  <clause id="12053">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u)
    ]]></literal>
    <justification jstring="[para(100(a,1),12046(a,1,1,2))].">
      <j1 rule="para" parents="100 12046"/>
    </justification>
  </clause>

  <clause id="12054">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(8797,a,12053,a)].">
      <j1 rule="hyper" parents="8797 12053"/>
    </justification>
  </clause>

  <clause id="12055">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(x \ (z * u),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,10503,a(flip),b,12054,a),flip(a)].">
      <j1 rule="hyper" parents="373 10503 12054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12056">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9623,a(flip),b,12055,a)].">
      <j1 rule="hyper" parents="64 9623 12055"/>
    </justification>
  </clause>

  <clause id="12057">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(18(a,2),12056(a,2,1))].">
      <j1 rule="para" parents="18 12056"/>
    </justification>
  </clause>

  <clause id="12058">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(11566,a,12057,a),flip(a)].">
      <j1 rule="hyper" parents="11566 12057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12059">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10266,a,12058,a)].">
      <j1 rule="hyper" parents="10266 12058"/>
    </justification>
  </clause>

  <clause id="12060">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(12058(a,1),10266(a,1))].">
      <j1 rule="para" parents="12058 10266"/>
    </justification>
  </clause>

  <clause id="12061">
    <literal><![CDATA[
      K(x,L(y,T(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11844(a,1),12058(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11844 12058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12062">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,T(x,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(346(a,1),12061(a,1,2))].">
      <j1 rule="para" parents="346 12061"/>
    </justification>
  </clause>

  <clause id="12063">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = K(x,L(T(z,u),u,y))
    ]]></literal>
    <justification jstring="[hyper(7612,a,12059,a)].">
      <j1 rule="hyper" parents="7612 12059"/>
    </justification>
  </clause>

  <clause id="12064">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(7610,a,12059,a),flip(a)].">
      <j1 rule="hyper" parents="7610 12059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12065">
    <literal><![CDATA[
      K(L(x,y,z),u) \ 1 = L(K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6092,a,b,12059,a)].">
      <j1 rule="hyper" parents="373 6092 12059"/>
    </justification>
  </clause>

  <clause id="12066">
    <literal><![CDATA[
      L(K(x,y \ z),y,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7088,a(flip),b,12059,a),flip(a)].">
      <j1 rule="hyper" parents="373 7088 12059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12067">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * K(L(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(225,a,12059,a,b,6882,a)].">
      <j1 rule="hyper" parents="225 12059 6882"/>
    </justification>
  </clause>

  <clause id="12068">
    <literal><![CDATA[
      K(L(x,y,z),u) \ w = L(K(u,x),y,z) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,12059,a,b,6162,a),flip(a)].">
      <j1 rule="hyper" parents="144 12059 6162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12069">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10411,a,b,12059,a)].">
      <j1 rule="hyper" parents="64 10411 12059"/>
    </justification>
  </clause>

  <clause id="12070">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9107,a,b,12059,a)].">
      <j1 rule="hyper" parents="64 9107 12059"/>
    </justification>
  </clause>

  <clause id="12071">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7537,a,b,12059,a)].">
      <j1 rule="hyper" parents="64 7537 12059"/>
    </justification>
  </clause>

  <clause id="12072">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,L(y / z,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9106,a(flip),b,12059,a)].">
      <j1 rule="hyper" parents="64 9106 12059"/>
    </justification>
  </clause>

  <clause id="12073">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,u,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,7080,a(flip),b,12059,a),flip(a)].">
      <j1 rule="hyper" parents="64 7080 12059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12074">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u)) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,6666,a(flip),b,12059,a),flip(a)].">
      <j1 rule="hyper" parents="64 6666 12059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12075">
    <literal><![CDATA[
      x * K(y,L(z,u,u \ x)) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,12059,a(flip),b,11067,a)].">
      <j1 rule="hyper" parents="145 12059 11067"/>
    </justification>
  </clause>

  <clause id="12076">
    <literal><![CDATA[
      x * K(y,L(z,u \ x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,12059,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="145 12059 101"/>
    </justification>
  </clause>

  <clause id="12077">
    <literal><![CDATA[
      (x * y) * K(z,L(u,x,y)) = y * (T(x,y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,12059,a(flip),b,10980,a(flip))].">
      <j1 rule="hyper" parents="145 12059 10980"/>
    </justification>
  </clause>

  <clause id="12078">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,12059,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 12059 18"/>
    </justification>
  </clause>

  <clause id="12080">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),y,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(346(a,1),12059(a,2,2))].">
      <j1 rule="para" parents="346 12059"/>
    </justification>
  </clause>

  <clause id="12081">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),y \ z,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(630(a,1),12059(a,2,2))].">
      <j1 rule="para" parents="630 12059"/>
    </justification>
  </clause>

  <clause id="12082">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * y,K(z,L(u,y,x))) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(12059(a,1),597(a,1,2,2))].">
      <j1 rule="para" parents="12059 597"/>
    </justification>
  </clause>

  <clause id="12083">
    <literal><![CDATA[
      (L(K(x,y),z,u) \ K(x,w)) \ T(x,w) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12059(a,2),6664(a,1,1,1))].">
      <j1 rule="para" parents="12059 6664"/>
    </justification>
  </clause>

  <clause id="12084">
    <literal><![CDATA[
      K(x,L(T(x,y) * z,u,w)) = L(K(x,x * z),u,w)
    ]]></literal>
    <justification jstring="[para(8546(a,1),12059(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8546 12059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12085">
    <literal><![CDATA[
      T(L(K(x,y),z,u) \ w,K(x,L(y,z,u))) = w / L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(12059(a,1),8853(a,1,2))].">
      <j1 rule="para" parents="12059 8853"/>
    </justification>
  </clause>

  <clause id="12086">
    <literal><![CDATA[
      K(x,L(y \ (z \ u),z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(12059(a,1),9535(a,1))].">
      <j1 rule="para" parents="12059 9535"/>
    </justification>
  </clause>

  <clause id="12087">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(12059(a,1),10408(a,1,2))].">
      <j1 rule="para" parents="12059 10408"/>
    </justification>
  </clause>

  <clause id="12088">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(12059(a,1),10412(a,1,1))].">
      <j1 rule="para" parents="12059 10412"/>
    </justification>
  </clause>

  <clause id="12089">
    <literal><![CDATA[
      L(K(x,((y \ z) \ z) \ u),y,y \ z) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(11004(a,1),12059(a,2,2))].">
      <j1 rule="para" parents="11004 12059"/>
    </justification>
  </clause>

  <clause id="12090">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(40,a,7319,a,b,12065,a)].">
      <j1 rule="hyper" parents="40 7319 12065"/>
    </justification>
  </clause>

  <clause id="12091">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12065(a,1),6101(a,1))].">
      <j1 rule="para" parents="12065 6101"/>
    </justification>
  </clause>

  <clause id="12092">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,8110,a,b,12090,a),flip(a)].">
      <j1 rule="hyper" parents="373 8110 12090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12093">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12059,a(flip),b,12090,a),flip(a)].">
      <j1 rule="hyper" parents="64 12059 12090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12094">
    <literal><![CDATA[
      L(K((x \ 1) \ y,z),x \ 1,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(629(a,1),12090(a,2,1))].">
      <j1 rule="para" parents="629 12090"/>
    </justification>
  </clause>

  <clause id="12095">
    <literal><![CDATA[
      L(K(x,y),z,u) \ R(y,w,y) = R(T(y,L(x,z,u)),w,y)
    ]]></literal>
    <justification jstring="[para(12090(a,2),7492(a,1,1))].">
      <j1 rule="para" parents="12090 7492"/>
    </justification>
  </clause>

  <clause id="12096">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(w,K(y,L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(12090(a,2),7830(a,1,1))].">
      <j1 rule="para" parents="12090 7830"/>
    </justification>
  </clause>

  <clause id="12097">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(12090(a,2),8126(a,1,2))].">
      <j1 rule="para" parents="12090 8126"/>
    </justification>
  </clause>

  <clause id="12098">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,L(x,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(12090(a,2),8439(a,1))].">
      <j1 rule="para" parents="12090 8439"/>
    </justification>
  </clause>

  <clause id="12099">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(12090(a,1),10408(a,1,2))].">
      <j1 rule="para" parents="12090 10408"/>
    </justification>
  </clause>

  <clause id="12100">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (K(y,L(x,z,u)) * w) = w
    ]]></literal>
    <justification jstring="[hyper(144,a,12093,a(flip),b,6160,a)].">
      <j1 rule="hyper" parents="144 12093 6160"/>
    </justification>
  </clause>

  <clause id="12101">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,x \ y,x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(630(a,1),12093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="630 12093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12102">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,L(y,z,u))) = (L(y,z,u) * x) / T(L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(12093(a,1),6393(a,1,2,1))].">
      <j1 rule="para" parents="12093 6393"/>
    </justification>
  </clause>

  <clause id="12103">
    <literal><![CDATA[
      ((x * y) * K(z,L(u,y,x))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(12093(a,1),6870(a,1,1,2))].">
      <j1 rule="para" parents="12093 6870"/>
    </justification>
  </clause>

  <clause id="12104">
    <literal><![CDATA[
      K(x * K(y,L(x,z,u)),w) = K(x,T(w,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(12093(a,1),8234(a,1,1,2))].">
      <j1 rule="para" parents="12093 8234"/>
    </justification>
  </clause>

  <clause id="12105">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,L(y,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(12093(a,1),8437(a,1,2))].">
      <j1 rule="para" parents="12093 8437"/>
    </justification>
  </clause>

  <clause id="12106">
    <literal><![CDATA[
      K(x,K(x / y,L(z,u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(12093(a,1),8995(a,2,2))].">
      <j1 rule="para" parents="12093 8995"/>
    </justification>
  </clause>

  <clause id="12107">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(x,L(w,y,z)))) / L(T(x,w),y,z) = (L(x,y,z) * u) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(12093(a,1),7168(a,1,1,2,2))].">
      <j1 rule="para" parents="12093 7168"/>
    </justification>
  </clause>

  <clause id="12108">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,T((y / z) \ 1,y),u)) = K(x,L(((y / z) \ 1) \ z,z,u))
    ]]></literal>
    <justification jstring="[para(4918(a,2),12070(a,1,2,2))].">
      <j1 rule="para" parents="4918 12070"/>
    </justification>
  </clause>

  <clause id="12109">
    <literal><![CDATA[
      (x * (y / z)) * K(u,(x * y) / (x * (y / z))) = K(u,L(z,y,x)) * (x * (y / z))
    ]]></literal>
    <justification jstring="[para(12070(a,1),10273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12070 10273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12111">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = v5
    ]]></literal>
    <justification jstring="[para(12059(a,1),12060(a,1,2))].">
      <j1 rule="para" parents="12059 12060"/>
    </justification>
  </clause>

  <clause id="12112">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(12093(a,2),12060(a,1))].">
      <j1 rule="para" parents="12093 12060"/>
    </justification>
  </clause>

  <clause id="12113">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = w
    ]]></literal>
    <justification jstring="[para(7082(a,1),12091(a,1))].">
      <j1 rule="para" parents="7082 12091"/>
    </justification>
  </clause>

  <clause id="12114">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(7320(a,2),12091(a,1))].">
      <j1 rule="para" parents="7320 12091"/>
    </justification>
  </clause>

  <clause id="12115">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y * x,z)) = w
    ]]></literal>
    <justification jstring="[para(7369(a,1),12091(a,1))].">
      <j1 rule="para" parents="7369 12091"/>
    </justification>
  </clause>

  <clause id="12116">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(10411(a,2),12091(a,1))].">
      <j1 rule="para" parents="10411 12091"/>
    </justification>
  </clause>

  <clause id="12117">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(12090(a,1),12091(a,1))].">
      <j1 rule="para" parents="12090 12091"/>
    </justification>
  </clause>

  <clause id="12118">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(z,K(x,y)),u,w) = v5
    ]]></literal>
    <justification jstring="[para(8110(a,2),12112(a,1))].">
      <j1 rule="para" parents="8110 12112"/>
    </justification>
  </clause>

  <clause id="12119">
    <literal><![CDATA[
      L(K(x,y),z,u) \ R(T(x,L(y,z,u)),w,x) = R(x,w,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,7492,a(flip),b,12068,a(flip))].">
      <j1 rule="hyper" parents="139 7492 12068"/>
    </justification>
  </clause>

  <clause id="12120">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,L(u,y,x)) = K(z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,12069,a(flip),b,10435,a)].">
      <j1 rule="hyper" parents="145 12069 10435"/>
    </justification>
  </clause>

  <clause id="12121">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(12069(a,1),6188(a,1,2)),flip(b)].">
      <j1 rule="para" parents="12069 6188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12122">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) / u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(12072(a,2),11050(a,1))].">
      <j1 rule="para" parents="12072 11050"/>
    </justification>
  </clause>

  <clause id="12123">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(12087(a,1),6088(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12087 6088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12124">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10420,a(flip),b,12088,a)].">
      <j1 rule="hyper" parents="64 10420 12088"/>
    </justification>
  </clause>

  <clause id="12125">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,z))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8110(a,2),12124(a,1,3))].">
      <j1 rule="para" parents="8110 12124"/>
    </justification>
  </clause>

  <clause id="12126">
    <literal><![CDATA[
      K(x,K(y / z,L(u,y,w))) = K(x,K(u,L(y / z,z,w)))
    ]]></literal>
    <justification jstring="[para(9106(a,1),12097(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9106 12097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12127">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10414,a(flip),b,12099,a)].">
      <j1 rule="hyper" parents="64 10414 12099"/>
    </justification>
  </clause>

  <clause id="12128">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      (u * x) / T(u,L(x,z,y)) = w
    ]]></literal>
    <justification jstring="[para(12099(a,1),6503(a,1,2))].">
      <j1 rule="para" parents="12099 6503"/>
    </justification>
  </clause>

  <clause id="12129">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,y \ z,K(x,y))
    ]]></literal>
    <justification jstring="[para(12058(a,1),12099(a,1,2))].">
      <j1 rule="para" parents="12058 12099"/>
    </justification>
  </clause>

  <clause id="12130">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,L(y,u,w))) = a(w,u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(12096(a,1),12099(a,1,2))].">
      <j1 rule="para" parents="12096 12099"/>
    </justification>
  </clause>

  <clause id="12131">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(12127(a,1),10451(a,2,2))].">
      <j1 rule="para" parents="12127 10451"/>
    </justification>
  </clause>

  <clause id="12133">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(12120(a,1),6909(a,1,1)),flip(b)].">
      <j1 rule="para" parents="12120 6909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12134">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[para(115(a,1),12064(a,2,2,1))].">
      <j1 rule="para" parents="115 12064"/>
    </justification>
  </clause>

  <clause id="12135">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u \ 1),T(z * u,u \ 1),(u * z) \ z)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[para(6985(a,1),12064(a,2,2,2))].">
      <j1 rule="para" parents="6985 12064"/>
    </justification>
  </clause>

  <clause id="12136">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z \ u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(12066(a,1),12091(a,1))].">
      <j1 rule="para" parents="12066 12091"/>
    </justification>
  </clause>

  <clause id="12137">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,R(1 / y,y,z))) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[para(452(a,1),12073(a,1,2,1,1))].">
      <j1 rule="para" parents="452 12073"/>
    </justification>
  </clause>

  <clause id="12138">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,L(w,L(x,y,z) \ 1,x)) = x * ((L(x,y,z) \ 1) * K(u,w))
    ]]></literal>
    <justification jstring="[para(1846(a,1),12078(a,1,1))].">
      <j1 rule="para" parents="1846 12078"/>
    </justification>
  </clause>

  <clause id="12139">
    <literal><![CDATA[
      x * (y * K(x * y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,L(z,y,x)) = u
    ]]></literal>
    <justification jstring="[para(12078(a,1),5767(a,1))].">
      <j1 rule="para" parents="12078 5767"/>
    </justification>
  </clause>

  <clause id="12140">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(T(z,w),y / z,x)) = x * (y / T(z,T(u,w)))
    ]]></literal>
    <justification jstring="[para(7910(a,1),12078(a,2,2))].">
      <j1 rule="para" parents="7910 12078"/>
    </justification>
  </clause>

  <clause id="12141">
    <literal><![CDATA[
      K(x,(T(y * z,x) * K(u,L(w,z,y))) / v5) = K(x,(y * (z * K(u,w))) / v5)
    ]]></literal>
    <justification jstring="[para(12078(a,1),9133(a,2,2,1))].">
      <j1 rule="para" parents="12078 9133"/>
    </justification>
  </clause>

  <clause id="12142">
    <literal><![CDATA[
      K(x,y / (z * (u * K(x,w)))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(12078(a,1),9198(a,1,2,2))].">
      <j1 rule="para" parents="12078 9198"/>
    </justification>
  </clause>

  <clause id="12143">
    <literal><![CDATA[
      K(x,y / (T(z * u,x) * K(w,L(v5,u,z)))) = K(x,y / (z * (u * K(w,v5))))
    ]]></literal>
    <justification jstring="[para(12078(a,1),9200(a,2,2,2))].">
      <j1 rule="para" parents="12078 9200"/>
    </justification>
  </clause>

  <clause id="12144">
    <literal><![CDATA[
      K(x,(T(y * z,x) * K(u,L(w,z,y))) * v5) = K(x,(y * (z * K(u,w))) * v5)
    ]]></literal>
    <justification jstring="[para(12078(a,1),9685(a,2,2,1))].">
      <j1 rule="para" parents="12078 9685"/>
    </justification>
  </clause>

  <clause id="12145">
    <literal><![CDATA[
      (x * y) * K(z,K(u,L(w,y,x))) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(12059(a,1),12078(a,1,2,2))].">
      <j1 rule="para" parents="12059 12078"/>
    </justification>
  </clause>

  <clause id="12146">
    <literal><![CDATA[
      L(K((x \ 1) \ (y \ z),y),x \ 1,x) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,10277,a,b,12094,a),flip(a)].">
      <j1 rule="hyper" parents="373 10277 12094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12147">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12115,a,12093,a)].">
      <j1 rule="hyper" parents="12115 12093"/>
    </justification>
  </clause>

  <clause id="12148">
    <literal><![CDATA[
      K(x,L(y,z / x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),12147(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 12147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12149">
    <literal><![CDATA[
      (x * (y / z)) * K(z,L(u,y,x)) = x * ((y / z) * K(z,u))
    ]]></literal>
    <justification jstring="[para(12148(a,1),12078(a,1,2))].">
      <j1 rule="para" parents="12148 12078"/>
    </justification>
  </clause>

  <clause id="12150">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,x \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,8548,a(flip),b,12062,a),flip(a)].">
      <j1 rule="hyper" parents="373 8548 12062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12152">
    <literal><![CDATA[
      K(x,L(T(x,y) * z,u,w)) = K(x,L(x * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,12059,a(flip),b,12084,a),flip(a)].">
      <j1 rule="hyper" parents="373 12059 12084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12153">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(x / w,(z * y) \ u))
    ]]></literal>
    <justification jstring="[para(346(a,1),12106(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="346 12106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12154">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,12087,a(flip),b,12129,a),flip(a)].">
      <j1 rule="hyper" parents="64 12087 12129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12155">
    <literal><![CDATA[
      K(x,y / (z * ((u / x) * w))) = K(x,y / (z * ((x \ u) * w)))
    ]]></literal>
    <justification jstring="[para(8651(a,1),12142(a,1,2,2,2))].">
      <j1 rule="para" parents="8651 12142"/>
    </justification>
  </clause>

  <clause id="12156">
    <literal><![CDATA[
      K(x,((y \ 1) * T(z \ u,y)) \ ((T(y,z \ u) \ 1) * u)) = K(x,L(T(z,u),u,T(y,z \ u) \ 1))
    ]]></literal>
    <justification jstring="[para(6271(a,1),12063(a,1,2,1))].">
      <j1 rule="para" parents="6271 12063"/>
    </justification>
  </clause>

  <clause id="12157">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = x * K(z,x \ ((x / y) * (u * y)))
    ]]></literal>
    <justification jstring="[para(11069(a,1),12075(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11069 12075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12158">
    <literal><![CDATA[
      x \ (y * K(z,y \ (x * u))) = (x \ y) * K(z,(x \ y) \ u)
    ]]></literal>
    <justification jstring="[para(12081(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="12081 598"/>
    </justification>
  </clause>

  <clause id="12159">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,L(y,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(8108(a,1),12098(a,1,1))].">
      <j1 rule="para" parents="8108 12098"/>
    </justification>
  </clause>

  <clause id="12160">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,L(w,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(8126(a,1),12105(a,1))].">
      <j1 rule="para" parents="8126 12105"/>
    </justification>
  </clause>

  <clause id="12161">
    <literal><![CDATA[
      K(x,K(y,L(z,1 / u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,L(y,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(11776(a,2),12105(a,1,2,2))].">
      <j1 rule="para" parents="11776 12105"/>
    </justification>
  </clause>

  <clause id="12162">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(3320(a,2),12121(a,1))].">
      <j1 rule="para" parents="3320 12121"/>
    </justification>
  </clause>

  <clause id="12163">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(12129(a,1),12121(a,1))].">
      <j1 rule="para" parents="12129 12121"/>
    </justification>
  </clause>

  <clause id="12164">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(10414(a,1),12133(a,1))].">
      <j1 rule="para" parents="10414 12133"/>
    </justification>
  </clause>

  <clause id="12165">
    <literal><![CDATA[
      K(x,L(T(y \ 1,((y * z) \ z) \ z) \ u,u,((y * z) \ z) \ z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(4595(a,1),12134(a,2,2,1))].">
      <j1 rule="para" parents="4595 12134"/>
    </justification>
  </clause>

  <clause id="12166">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(10420(a,1),12162(a,1))].">
      <j1 rule="para" parents="10420 12162"/>
    </justification>
  </clause>

  <clause id="12167">
    <literal><![CDATA[
      K(x,x * y) \ (L(K(x,x * y),z,u) * T(x,y)) = R(T(x,L(x * y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10544,a,b,12095,a)].">
      <j1 rule="hyper" parents="64 10544 12095"/>
    </justification>
  </clause>

  <clause id="12168">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(y / u,(z * y) \ K(z,1 / z)))
    ]]></literal>
    <justification jstring="[para(641(a,1),12126(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="641 12126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12169">
    <literal><![CDATA[
      L(x,y,z) \ ((u / x) \ (L(x,y,z) * (x \ u))) = x \ (x * a(z,y,K(x \ u,x)))
    ]]></literal>
    <justification jstring="[para(12131(a,1),9285(a,2,2))].">
      <j1 rule="para" parents="12131 9285"/>
    </justification>
  </clause>

  <clause id="12170">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = w
    ]]></literal>
    <justification jstring="[para(12064(a,2),12136(a,1))].">
      <j1 rule="para" parents="12064 12136"/>
    </justification>
  </clause>

  <clause id="12171">
    <literal><![CDATA[
      x * (y * K(z,K(x * y,u))) = T(x * y,K(z,L(u,y,x)))
    ]]></literal>
    <justification jstring="[hyper(8116,a,12145,a),flip(a)].">
      <j1 rule="hyper" parents="8116 12145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12172">
    <literal><![CDATA[
      L(K((x \ y) \ z,y),x \ 1,x) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[para(7644(a,1),12146(a,1,1))].">
      <j1 rule="para" parents="7644 12146"/>
    </justification>
  </clause>

  <clause id="12173">
    <literal><![CDATA[
      K(x,K(y,L(z,1 / u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(12161,a,xx),flip(a)].">
      <j1 rule="hyper" parents="12161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12174">
    <literal><![CDATA[
      x * (y * K(z,K(u,x * y))) = T(x * y,K(z,L(u,y,x)))
    ]]></literal>
    <justification jstring="[para(8126(a,1),12171(a,1,2,2))].">
      <j1 rule="para" parents="8126 12171"/>
    </justification>
  </clause>

  <clause id="12175">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(12078(a,1),12103(a,1,1))].">
      <j1 rule="para" parents="12078 12103"/>
    </justification>
  </clause>

  <clause id="12176">
    <literal><![CDATA[
      L(x,y * K(x,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(6876,a,12175,a)].">
      <j1 rule="hyper" parents="6876 12175"/>
    </justification>
  </clause>

  <clause id="12177">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * K(x,y))) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[para(115(a,1),12175(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="115 12175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12178">
    <literal><![CDATA[
      L(x,y \ T(z,x),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(7026(a,1),12176(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7026 12176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12179">
    <literal><![CDATA[
      L(x,K(x,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(7879(a,1),12176(a,1,2))].">
      <j1 rule="para" parents="7879 12176"/>
    </justification>
  </clause>

  <clause id="12180">
    <literal><![CDATA[
      L(x,T(y,x) \ z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(7948(a,1),12176(a,1,2))].">
      <j1 rule="para" parents="7948 12176"/>
    </justification>
  </clause>

  <clause id="12181">
    <literal><![CDATA[
      L(T(x,y),K(x,z) * u,w) = L(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8205(a,1),12179(a,1,2,1))].">
      <j1 rule="para" parents="8205 12179"/>
    </justification>
  </clause>

  <clause id="12182">
    <literal><![CDATA[
      K(x,y \ z) \ T(x,(y \ z) * x) = L(x,y \ T(z,x),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6349,a,b,12178,a)].">
      <j1 rule="hyper" parents="373 6349 12178"/>
    </justification>
  </clause>

  <clause id="12183">
    <literal><![CDATA[
      T(x,y) * L(y,z \ x,z) = z * ((z \ T(x,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,12178,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="145 12178 101"/>
    </justification>
  </clause>

  <clause id="12185">
    <literal><![CDATA[
      L(x,(y \ T(x,y \ x)) \ z,u) = L(x,(y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[para(4466(a,1),12180(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4466 12180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12186">
    <literal><![CDATA[
      L(T(x,y),z / x,u) = L(T(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(5720(a,1),12181(a,1,2))].">
      <j1 rule="para" parents="5720 12181"/>
    </justification>
  </clause>

  <clause id="12187">
    <literal><![CDATA[
      L(T(x,y),T(x,z) \ u,w) = L(T(x,y),x \ u,w)
    ]]></literal>
    <justification jstring="[para(6075(a,1),12181(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6075 12181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12189">
    <literal><![CDATA[
      L(x,y,z * K(x,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,10638,a(flip),b,12177,a)].">
      <j1 rule="hyper" parents="373 10638 12177"/>
    </justification>
  </clause>

  <clause id="12190">
    <literal><![CDATA[
      L(x,y,T((y * x) \ z,K(x,y))) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(10848(a,2),12189(a,1,3))].">
      <j1 rule="para" parents="10848 12189"/>
    </justification>
  </clause>

  <clause id="12191">
    <literal><![CDATA[
      K(x,L(T(y,z),y \ u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(12187(a,1),12070(a,1,2))].">
      <j1 rule="para" parents="12187 12070"/>
    </justification>
  </clause>

  <clause id="12192">
    <literal><![CDATA[
      K(x,(y * z) / (y * (z / u))) = K(x,L(T(u,y * z),z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,10391,a(flip),b,12191,a)].">
      <j1 rule="hyper" parents="64 10391 12191"/>
    </justification>
  </clause>

  <clause id="12193">
    <literal><![CDATA[
      K(x,L(T(y,z),u / y,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(12186(a,2),12191(a,1,2))].">
      <j1 rule="para" parents="12186 12191"/>
    </justification>
  </clause>

  <clause id="12194">
    <literal><![CDATA[
      K(x,L(T(y,z),u * y,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(11(a,1),12193(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 12193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12195">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z,K(w,L(u,y,x))) * K(z,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(12130(a,1),7445(a,1))].">
      <j1 rule="para" parents="12130 7445"/>
    </justification>
  </clause>

  <clause id="12196">
    <literal><![CDATA[
      K(x,y / (x * ((x \ z) * u))) = K(x,x \ (y / ((z / x) * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,10772,a(flip),b,12155,a),flip(a)].">
      <j1 rule="hyper" parents="64 10772 12155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12197">
    <literal><![CDATA[
      K(x / (y \ z),u) \ (y \ z) = y \ (z * K(u,z \ (y * x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,7992,a,b,12158,a)].">
      <j1 rule="hyper" parents="373 7992 12158"/>
    </justification>
  </clause>

  <clause id="12198">
    <literal><![CDATA[
      x * K(y \ x,x \ (y * z)) = y * (((y \ x) \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,5752,a,b,12158,a),flip(a)].">
      <j1 rule="hyper" parents="145 5752 12158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12199">
    <literal><![CDATA[
      T(x \ y,y \ (x * z)) = ((x \ y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(35,a,6763,a,b,12198,a(flip))].">
      <j1 rule="hyper" parents="35 6763 12198"/>
    </justification>
  </clause>

  <clause id="12200">
    <literal><![CDATA[
      T(x \ y,y \ z) = ((x \ y) \ (x \ z)) \ (x \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),12199(a,1,2,2))].">
      <j1 rule="para" parents="10 12199"/>
    </justification>
  </clause>

  <clause id="12201">
    <literal><![CDATA[
      K(x,x \ (y / ((z / x) * u))) = K(x,x \ (y / ((x \ z) * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,10772,a(flip),b,12196,a),flip(a)].">
      <j1 rule="hyper" parents="64 10772 12196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12202">
    <literal><![CDATA[
      K(x / (y \ z),u) \ (y \ z) = y \ (K((y * x) / z,u) \ z)
    ]]></literal>
    <justification jstring="[para(7992(a,2),12197(a,2,2))].">
      <j1 rule="para" parents="7992 12197"/>
    </justification>
  </clause>

  <clause id="12203">
    <literal><![CDATA[
      T(x / (y \ z),u) \ x = y \ (K((y * x) / z,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(6665,a,12202,a)].">
      <j1 rule="hyper" parents="6665 12202"/>
    </justification>
  </clause>

  <clause id="12204">
    <literal><![CDATA[
      T(1 / (x \ y),z) \ 1 = x \ (K(x / y,z) \ y)
    ]]></literal>
    <justification jstring="[para(8(a,1),12203(a,2,2,1,1,1))].">
      <j1 rule="para" parents="8 12203"/>
    </justification>
  </clause>

  <clause id="12205">
    <literal><![CDATA[
      T(1 / (x \ (x / y)),z) \ 1 = x \ (K(y,T(z,x)) \ (x / y))
    ]]></literal>
    <justification jstring="[para(8222(a,1),12204(a,2,2,1))].">
      <j1 rule="para" parents="8222 12204"/>
    </justification>
  </clause>

  <clause id="12206">
    <literal><![CDATA[
      T(1 / (x \ (x / y)),z) \ 1 = x \ ((x / y) * K(z,y))
    ]]></literal>
    <justification jstring="[para(8295(a,1),12205(a,2,2))].">
      <j1 rule="para" parents="8295 12205"/>
    </justification>
  </clause>

  <clause id="12207">
    <literal><![CDATA[
      T(1 / (x \ (x / y)),z) \ 1 = x \ (x / T(y,z))
    ]]></literal>
    <justification jstring="[para(6245(a,1),12206(a,2,2))].">
      <j1 rule="para" parents="6245 12206"/>
    </justification>
  </clause>

  <clause id="12208">
    <literal><![CDATA[
      K(x,y) \ (z \ (z / x)) = z \ (z / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6773,a(flip),b,12207,a)].">
      <j1 rule="hyper" parents="64 6773 12207"/>
    </justification>
  </clause>

  <clause id="12210">
    <literal><![CDATA[
      K(x,y) * ((z \ (z / y)) * u) = (z \ (z / T(y,x))) * u
    ]]></literal>
    <justification jstring="[para(12208(a,1),11826(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12208 11826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12211">
    <literal><![CDATA[
      K(x,y) \ ((z \ (z / x)) * u) = (z \ (z / T(x,y))) * u
    ]]></literal>
    <justification jstring="[hyper(6206,a,12210,a)].">
      <j1 rule="hyper" parents="6206 12210"/>
    </justification>
  </clause>

  <clause id="12212">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * w,K(y,L(x,z,u))) = w / L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(7326(a,1),12085(a,1,1))].">
      <j1 rule="para" parents="7326 12085"/>
    </justification>
  </clause>

  <clause id="12213">
    <literal><![CDATA[
      T(L(K(x,y),z,u) * w,K(y,L(x,z,u))) = w * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,7317,a(flip),b,12212,a),flip(a)].">
      <j1 rule="hyper" parents="373 7317 12212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12214">
    <literal><![CDATA[
      T(x * L(K(y,z),u,w),K(z,L(y,u,w))) = L(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[hyper(8182,a,12213,a)].">
      <j1 rule="hyper" parents="8182 12213"/>
    </justification>
  </clause>

  <clause id="12215">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = (L(x,y,z) * K(u,x)) * u
    ]]></literal>
    <justification jstring="[para(6783(a,1),12043(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6783 12043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12216">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6850,a(flip),b,12215,a),flip(a)].">
      <j1 rule="hyper" parents="373 6850 12215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12217">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(2325(a,1),12216(a,1,1))].">
      <j1 rule="para" parents="2325 12216"/>
    </justification>
  </clause>

  <clause id="12218">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x,u,w))) * x = L(x,y,z) * L(x,u,w)
    ]]></literal>
    <justification jstring="[para(201(a,1),12217(a,2,2))].">
      <j1 rule="para" parents="201 12217"/>
    </justification>
  </clause>

  <clause id="12219">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ (L(y,z,u) * T(x,y))
    ]]></literal>
    <justification jstring="[para(12217(a,1),9650(a,2,2))].">
      <j1 rule="para" parents="12217 9650"/>
    </justification>
  </clause>

  <clause id="12220">
    <literal><![CDATA[
      (L(x,y,z) * L(x,u,w)) / x = L(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(154,a,12218,a)].">
      <j1 rule="hyper" parents="154 12218"/>
    </justification>
  </clause>

  <clause id="12221">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = T(L(y,z,u) * K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6853,a,b,12219,a),flip(a)].">
      <j1 rule="hyper" parents="373 6853 12219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12222">
    <literal><![CDATA[
      x * K(y,x \ ((x / z) * (u * z))) = (x / z) * (K(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(7893,a,12157,a),flip(a)].">
      <j1 rule="hyper" parents="7893 12157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12223">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(T(z,w),y,x)) = x * (y / T(z,T(u,w)))
    ]]></literal>
    <justification jstring="[para(12193(a,1),12140(a,1,2))].">
      <j1 rule="para" parents="12193 12140"/>
    </justification>
  </clause>

  <clause id="12224">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,R(y \ 1,y,z))) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[para(3852(a,1),12137(a,1,2))].">
      <j1 rule="para" parents="3852 12137"/>
    </justification>
  </clause>

  <clause id="12225">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,L(y,z,u))) = (L(y,z,u) * x) / L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),12102(a,2,2))].">
      <j1 rule="para" parents="25 12102"/>
    </justification>
  </clause>

  <clause id="12226">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(T(z,x * y),y,x)) = K(u,L(z,y,x)) * (x * (y / z))
    ]]></literal>
    <justification jstring="[para(12192(a,1),12109(a,1,2))].">
      <j1 rule="para" parents="12192 12109"/>
    </justification>
  </clause>

  <clause id="12227">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * (z / y)) = u * (z / T(y,T(x,u * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12223,a(flip),b,12226,a),flip(a)].">
      <j1 rule="hyper" parents="64 12223 12226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12228">
    <literal><![CDATA[
      K(x,x * y) \ (L(K(x * y,x),z,u) \ T(x,y)) = R(T(x,L(x * y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[para(7326(a,2),12167(a,1,2))].">
      <j1 rule="para" parents="7326 12167"/>
    </justification>
  </clause>

  <clause id="12229">
    <literal><![CDATA[
      L(x,y,z) \ T(L(x,y,z) * K(u,x),u) = x \ (x * a(z,y,K(x \ u,x)))
    ]]></literal>
    <justification jstring="[para(12221(a,1),12169(a,1,2))].">
      <j1 rule="para" parents="12221 12169"/>
    </justification>
  </clause>

  <clause id="12230">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(L(x,z,y),u) * K(u,x)
    ]]></literal>
    <justification jstring="[hyper(7824,a,12229,a),flip(a)].">
      <j1 rule="hyper" parents="7824 12229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12231">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(x,L(u,z,y)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(12093(a,1),12230(a,2,1))].">
      <j1 rule="para" parents="12093 12230"/>
    </justification>
  </clause>

  <clause id="12232">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,12088,a(flip),b,12231,a),flip(a)].">
      <j1 rule="hyper" parents="373 12088 12231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12233">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(396,a,12232,a)].">
      <j1 rule="hyper" parents="396 12232"/>
    </justification>
  </clause>

  <clause id="12235">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),12233(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="9 12233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12236">
    <literal><![CDATA[
      a(x,y,K(z * u,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(6115(a,1),12233(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6115 12233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12237">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(6585(a,1),12233(a,1,3))].">
      <j1 rule="para" parents="6585 12233"/>
    </justification>
  </clause>

  <clause id="12238">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(u,u * z))
    ]]></literal>
    <justification jstring="[para(6766(a,1),12233(a,1,3))].">
      <j1 rule="para" parents="6766 12233"/>
    </justification>
  </clause>

  <clause id="12239">
    <literal><![CDATA[
      a(x,y,K(z \ (u * w),w)) = a(x,y,K(z \ u,w))
    ]]></literal>
    <justification jstring="[para(10223(a,1),12233(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10223 12233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12240">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) \ K(w,z) = K(w,z) * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(12235(a,2),10435(a,1,1))].">
      <j1 rule="para" parents="12235 10435"/>
    </justification>
  </clause>

  <clause id="12241">
    <literal><![CDATA[
      a(x,y,K(x * z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,7141,a(flip),b,12236,a),flip(a)].">
      <j1 rule="hyper" parents="373 7141 12236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12242">
    <literal><![CDATA[
      L(K(x * y,y),z,x) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,12241,a)].">
      <j1 rule="hyper" parents="53 12241"/>
    </justification>
  </clause>

  <clause id="12243">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,x * y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(12242(a,1),7894(a,2,1))].">
      <j1 rule="para" parents="12242 7894"/>
    </justification>
  </clause>

  <clause id="12244">
    <literal><![CDATA[
      a(x,y,K(z,z * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(10436,a,12240,a)].">
      <j1 rule="hyper" parents="10436 12240"/>
    </justification>
  </clause>

  <clause id="12245">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12238,a,b,12244,a)].">
      <j1 rule="hyper" parents="64 12238 12244"/>
    </justification>
  </clause>

  <clause id="12246">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),12244(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 12244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12247">
    <literal><![CDATA[
      a(x,y,K(z,u * z)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(6142(a,2),12244(a,1,3))].">
      <j1 rule="para" parents="6142 12244"/>
    </justification>
  </clause>

  <clause id="12248">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u * z)) = a(x,y,K(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(11586(a,1),12244(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11586 12244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12249">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12245,a(flip),b,12248,a),flip(a)].">
      <j1 rule="hyper" parents="64 12245 12248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12250">
    <literal><![CDATA[
      a(x,y,K(z \ u,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12237,a(flip),b,12249,a)].">
      <j1 rule="hyper" parents="64 12237 12249"/>
    </justification>
  </clause>

  <clause id="12251">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) = a(x,y,K(w,u \ z))
    ]]></literal>
    <justification jstring="[para(6756(a,1),12249(a,1,3))].">
      <j1 rule="para" parents="6756 12249"/>
    </justification>
  </clause>

  <clause id="12252">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(6783(a,1),12250(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6783 12250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12253">
    <literal><![CDATA[
      a(x,y,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(12252(a,1),6936(a,1))].">
      <j1 rule="para" parents="12252 6936"/>
    </justification>
  </clause>

  <clause id="12254">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(8837(a,1),12243(a,1,2,2))].">
      <j1 rule="para" parents="8837 12243"/>
    </justification>
  </clause>

  <clause id="12255">
    <literal><![CDATA[
      K(x * y,y) * (x * z) = x * (K(x * y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(7893,a,12254,a),flip(a)].">
      <j1 rule="hyper" parents="7893 12254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12256">
    <literal><![CDATA[
      x * (K(x * y,y) * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11009,a(flip),b,12255,a),flip(a)].">
      <j1 rule="hyper" parents="64 11009 12255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12257">
    <literal><![CDATA[
      a(x,y,x) * (y * z) = y * (a(x,y,x) * z)
    ]]></literal>
    <justification jstring="[para(10923(a,1),12256(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10923 12256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12258">
    <literal><![CDATA[
      x * (a(y,x,y) * (x \ z)) = a(y,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(397,a,12257,a),flip(a)].">
      <j1 rule="hyper" parents="397 12257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12259">
    <literal><![CDATA[
      K(R(x \ y,z,u),w \ (y / x)) = K(R(x \ y,z,u),w \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7074,a,8946,a),flip(a)].">
      <j1 rule="hyper" parents="7074 8946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12260">
    <literal><![CDATA[
      K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(x \ (x * y),z,u),w * K(x,y))
    ]]></literal>
    <justification jstring="[para(5898(a,1),12259(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5898 12259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12265">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * L(T(u * z,u) / u,y,x)) = L(a(u,L(z,y,x),u),L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(3449(a,2),10930(a,1,2,2))].">
      <j1 rule="para" parents="3449 10930"/>
    </justification>
  </clause>

  <clause id="12266">
    <literal><![CDATA[
      (R(R(x,y,z),u,R(x,y,z)) * (y * z)) / ((x * y) * z) = a(R(x,y,z),u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(10898(a,1),11367(a,1,1,1))].">
      <j1 rule="para" parents="10898 11367"/>
    </justification>
  </clause>

  <clause id="12267">
    <literal><![CDATA[
      ((R(x,y,R(x,z,u)) * z) * u) / ((x * z) * u) = a(R(x,z,u),y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(506(a,1),12266(a,1,1))].">
      <j1 rule="para" parents="506 12266"/>
    </justification>
  </clause>

  <clause id="12268">
    <literal><![CDATA[
      ((R(x,y,x) * z) * u) / ((x * z) * u) = a(R(x,z,u),y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(11593(a,1),12267(a,1,1,1,1))].">
      <j1 rule="para" parents="11593 12267"/>
    </justification>
  </clause>

  <clause id="12269">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * z) * u = (R(x,y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(38,a,12267,a,b,12268,a)].">
      <j1 rule="hyper" parents="38 12267 12268"/>
    </justification>
  </clause>

  <clause id="12270">
    <literal><![CDATA[
      a(R(x,y,z),u,R(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      R(a(x,u,x),x * y,z) = w
    ]]></literal>
    <justification jstring="[para(12268(a,1),11376(a,1))].">
      <j1 rule="para" parents="12268 11376"/>
    </justification>
  </clause>

  <clause id="12272">
    <literal><![CDATA[
      (R(T(x,y),z,T(x,y)) * u) * w = (R(T(x,y),z,R(x,u,w)) * u) * w
    ]]></literal>
    <justification jstring="[para(10090(a,1),12269(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10090 12269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12273">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,T(R(x,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(373,a,1968,a(flip),b,11488,a),flip(a)].">
      <j1 rule="hyper" parents="373 1968 11488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12274">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,R(T(x,u),y,z))
    ]]></literal>
    <justification jstring="[para(27(a,2),12273(a,2,3))].">
      <j1 rule="para" parents="27 12273"/>
    </justification>
  </clause>

  <clause id="12275">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) * K((x / y) \ 1,T(z,y \ x)) = a((x / y) \ 1,z,(x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(6057(a,1),12013(a,1,1))].">
      <j1 rule="para" parents="6057 12013"/>
    </justification>
  </clause>

  <clause id="12276">
    <literal><![CDATA[
      (R(x,y,z) \ 1) \ L((R(x,y,z) \ 1) * u,x,x) = x * (x * ((x \ 1) * (x \ u)))
    ]]></literal>
    <justification jstring="[para(2767(a,1),12023(a,2,2,2))].">
      <j1 rule="para" parents="2767 12023"/>
    </justification>
  </clause>

  <clause id="12277">
    <literal><![CDATA[
      (R(x,y,z) \ 1) \ L((R(x,y,z) \ 1) * u,x,x) = x * ((1 / x) * u)
    ]]></literal>
    <justification jstring="[para(1127(a,1),12276(a,2,2))].">
      <j1 rule="para" parents="1127 12276"/>
    </justification>
  </clause>

  <clause id="12279">
    <literal><![CDATA[
      R(x,y,z) * L(R(x,y,z) \ u,x,x) = x * ((1 / x) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5546,a(flip),b,12277,a)].">
      <j1 rule="hyper" parents="64 5546 12277"/>
    </justification>
  </clause>

  <clause id="12280">
    <literal><![CDATA[
      x * ((1 / x) * (y * R(x,z,u))) = L(y,x,x) * R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(1306,a,12279,a),flip(a)].">
      <j1 rule="hyper" parents="1306 12279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12281">
    <literal><![CDATA[
      L(x * R((y \ 1) \ 1,z,u),y,y) = L(x,y,y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5272,a,b,12280,a)].">
      <j1 rule="hyper" parents="64 5272 12280"/>
    </justification>
  </clause>

  <clause id="12282">
    <literal><![CDATA[
      L(x * R(T(y,y \ 1),z,u),y,y) = L(x,y,y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(116(a,2),12281(a,1,1,2,1))].">
      <j1 rule="para" parents="116 12281"/>
    </justification>
  </clause>

  <clause id="12283">
    <literal><![CDATA[
      L(a(x,L(y,z,u),x),L(y,z,u),u * z) = (u * (z * y)) \ (u * (z * (T(x * y,x) / x)))
    ]]></literal>
    <justification jstring="[para(100(a,1),12265(a,1,2)),flip(a)].">
      <j1 rule="para" parents="100 12265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12284">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K((y / x) \ 1,T(z,x \ y)) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(10577(a,1),12275(a,1,1))].">
      <j1 rule="para" parents="10577 12275"/>
    </justification>
  </clause>

  <clause id="12285">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,T(z,x \ y)) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(6580(a,1),12284(a,1,2))].">
      <j1 rule="para" parents="6580 12284"/>
    </justification>
  </clause>

  <clause id="12286">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(11205(a,1),12285(a,1,2))].">
      <j1 rule="para" parents="11205 12285"/>
    </justification>
  </clause>

  <clause id="12287">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L((x \ 1) \ u,x,L(x,y,z)) = ((1 / (L(x,y,z) * (x \ 1))) / (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(11794(a,1),5681(a,1,2))].">
      <j1 rule="para" parents="11794 5681"/>
    </justification>
  </clause>

  <clause id="12288">
    <literal><![CDATA[
      ((1 / (L(x,y,z) * (x \ 1))) / (x \ 1)) * u = x * ((L(x,y,z) \ 1) * ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11934,a(flip),b,12287,a),flip(a)].">
      <j1 rule="hyper" parents="64 11934 12287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12289">
    <literal><![CDATA[
      ((1 / (x \ L(x,y,z))) / (x \ 1)) * u = x * ((L(x,y,z) \ 1) * ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(1807(a,1),12288(a,1,1,1,2))].">
      <j1 rule="para" parents="1807 12288"/>
    </justification>
  </clause>

  <clause id="12290">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * ((x \ 1) \ u)) = ((L(x,y,z) \ x) / (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(5659(a,1),12289(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5659 12289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12291">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((z \ 1) * ((y * z) / y))) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(5759(a,1),6456(a,1,2,2,1))].">
      <j1 rule="para" parents="5759 6456"/>
    </justification>
  </clause>

  <clause id="12293">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((T(z,y) \ 1) * z)) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(6970(a,1),12291(a,1,2,2))].">
      <j1 rule="para" parents="6970 12291"/>
    </justification>
  </clause>

  <clause id="12294">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 \ (1 / y),(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(187,a,12293,a)].">
      <j1 rule="hyper" parents="187 12293"/>
    </justification>
  </clause>

  <clause id="12295">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 / y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(66(a,1),12294(a,2,1))].">
      <j1 rule="para" parents="66 12294"/>
    </justification>
  </clause>

  <clause id="12296">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ (y \ 1) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,4040,a(flip),b,12295,a)].">
      <j1 rule="hyper" parents="139 4040 12295"/>
    </justification>
  </clause>

  <clause id="12297">
    <literal><![CDATA[
      (K(x,y) * K(x,T(y,z))) \ (T(K(x,y),z) * T(x,x \ y)) = L(R(x,x \ y,x),K(x,y),T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(7867(a,2),6507(a,1,1,2))].">
      <j1 rule="para" parents="7867 6507"/>
    </justification>
  </clause>

  <clause id="12298">
    <literal><![CDATA[
      T(x \ 1,y * x) * L(T(x \ 1,x * y) \ 1,z,u) = T(x \ L(x,z,u),y * x)
    ]]></literal>
    <justification jstring="[para(1804(a,1),7233(a,2,1))].">
      <j1 rule="para" parents="1804 7233"/>
    </justification>
  </clause>

  <clause id="12299">
    <literal><![CDATA[
      R((x * R(K(y,z),u,u \ 1)) * K(z,y),K(y,z),R(K(z,y),u,u \ 1)) = x / a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(9713(a,1),7246(a,1,1,1))].">
      <j1 rule="para" parents="9713 7246"/>
    </justification>
  </clause>

  <clause id="12300">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = K(z,(1 / y) \ 1) * T(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(6705(a,1),8052(a,2,1))].">
      <j1 rule="para" parents="6705 8052"/>
    </justification>
  </clause>

  <clause id="12301">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = K(z,y) * T(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(82(a,1),12300(a,2,1,2))].">
      <j1 rule="para" parents="82 12300"/>
    </justification>
  </clause>

  <clause id="12303">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = T(K(z,y) * (x * (1 / y)),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,7811,a,b,12301,a),flip(a)].">
      <j1 rule="hyper" parents="373 7811 12301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12304">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = T(y,z) \ R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,7817,a(flip),b,12303,a),flip(a)].">
      <j1 rule="hyper" parents="373 7817 12303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12305">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(12304(a,1),8078(a,1,2))].">
      <j1 rule="para" parents="12304 8078"/>
    </justification>
  </clause>

  <clause id="12306">
    <literal><![CDATA[
      ((x \ 1) \ x) * (T(y,x * T(T(x,x \ 1),x \ 1)) * z) = y * ((T(x,x \ 1) * T(x,x \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(6250(a,1),9305(a,1,2,1,2))].">
      <j1 rule="para" parents="6250 9305"/>
    </justification>
  </clause>

  <clause id="12307">
    <literal><![CDATA[
      K(R(x,K(y * z,x) * y,z),u \ x) = K(x,((y * z) * R(x,y,z)) / ((u * y) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10725,a(flip),b,9913,a),flip(a)].">
      <j1 rule="hyper" parents="64 10725 9913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12309">
    <literal><![CDATA[
      T(x,y) \ ((x \ (x * (L(x,z,u) \ y))) \ (x * (L(x,z,u) \ y))) = a(x,L(x,z,u) \ y,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),11577(a,2,2))].">
      <j1 rule="para" parents="9 11577"/>
    </justification>
  </clause>

  <clause id="12311">
    <literal><![CDATA[
      T(x,y) \ T(x,L(x,z,u) \ y) = a(x,L(x,z,u) \ y,x)
    ]]></literal>
    <justification jstring="[para(366(a,2),12309(a,1,2))].">
      <j1 rule="para" parents="366 12309"/>
    </justification>
  </clause>

  <clause id="12312">
    <literal><![CDATA[
      a(x,L(x,y,z) \ u,x) = T(x,u) \ T(x,x \ u)
    ]]></literal>
    <justification jstring="[para(10459(a,1),12311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10459 12311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12313">
    <literal><![CDATA[
      a(x,L(x,y,z) \ u,x) = a(x,x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10942,a(flip),b,12312,a),flip(a)].">
      <j1 rule="hyper" parents="373 10942 12312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12315">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) / (K(u,z) * x) = (K(y,z) * K(z,u)) * K(K(u,z) * x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[para(8153(a,1),11743(a,1,1))].">
      <j1 rule="para" parents="8153 11743"/>
    </justification>
  </clause>

  <clause id="12316">
    <literal><![CDATA[
      (K(x,y) \ K(y,T(x,z))) \ (T(K(y,x),z) * T(y,y \ x)) = L(R(y,y \ x,y),K(y,x),T(K(y,x),z))
    ]]></literal>
    <justification jstring="[para(6156(a,2),12297(a,1,1))].">
      <j1 rule="para" parents="6156 12297"/>
    </justification>
  </clause>

  <clause id="12317">
    <literal><![CDATA[
      (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = (x * K(z * L(y,u,w),y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6962,a(flip),b,7349,a),flip(a)].">
      <j1 rule="hyper" parents="373 6962 7349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12318">
    <literal><![CDATA[
      (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = x * (K(y,z) * K(z * L(y,u,w),y))
    ]]></literal>
    <justification jstring="[hyper(373,a,10335,a(flip),b,12317,a),flip(a)].">
      <j1 rule="hyper" parents="373 10335 12317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12319">
    <literal><![CDATA[
      (x / (y * K(z,y))) * R(y * K(z,y),z,L(y,u,w)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(11494(a,1),12318(a,2,2))].">
      <j1 rule="para" parents="11494 12318"/>
    </justification>
  </clause>

  <clause id="12320">
    <literal><![CDATA[
      ((x / y) * K(y,z)) * R(y * K(z,y),z,L(y,u,w)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(6974,a,12319,a)].">
      <j1 rule="hyper" parents="6974 12319"/>
    </justification>
  </clause>

  <clause id="12321">
    <literal><![CDATA[
      ((x / y) * K(y,z)) * (y * K(z * L(y,u,w),y)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(7072(a,1),12320(a,1,2))].">
      <j1 rule="para" parents="7072 12320"/>
    </justification>
  </clause>

  <clause id="12322">
    <literal><![CDATA[
      (x / y) * (T(y,z) * K(z * L(y,u,w),y)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9274,a(flip),b,12321,a)].">
      <j1 rule="hyper" parents="64 9274 12321"/>
    </justification>
  </clause>

  <clause id="12323">
    <literal><![CDATA[
      (x / y) * R(y,z,L(y,u,w)) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(9523(a,1),12322(a,1,2))].">
      <j1 rule="para" parents="9523 12322"/>
    </justification>
  </clause>

  <clause id="12324">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(11559(a,1),12323(a,1,2))].">
      <j1 rule="para" parents="11559 12323"/>
    </justification>
  </clause>

  <clause id="12325">
    <literal><![CDATA[
      (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(R(y,z,u),w,L(R(y,z,u),v5,v6))
    ]]></literal>
    <justification jstring="[para(11591(a,1),12323(a,1,2))].">
      <j1 rule="para" parents="11591 12323"/>
    </justification>
  </clause>

  <clause id="12326">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(11350,a,12324,a),flip(a)].">
      <j1 rule="hyper" parents="11350 12324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12328">
    <literal><![CDATA[
      T(x,y) \ R(z,T(T(x,1),y) \ 1,T(T(x,1),y)) = T(z * (K(y,x) * (1 / T(x,1))),T(T(x,1),y))
    ]]></literal>
    <justification jstring="[para(372(a,1),8753(a,1,1,1))].">
      <j1 rule="para" parents="372 8753"/>
    </justification>
  </clause>

  <clause id="12329">
    <literal><![CDATA[
      T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = T(z,y) \ R(x,T(z,y) \ 1,T(T(z,1),y))
    ]]></literal>
    <justification jstring="[para(372(a,1),12328(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="372 12328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12330">
    <literal><![CDATA[
      T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = T(z,y) \ R(x,T(z,y) \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[para(372(a,1),12329(a,2,2,3,1))].">
      <j1 rule="para" parents="372 12329"/>
    </justification>
  </clause>

  <clause id="12331">
    <literal><![CDATA[
      R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) = T(L(T(x,K(z,u)),K(z,u),K(y,z)),K(y,z))
    ]]></literal>
    <justification jstring="[para(262(a,1),8801(a,1,1)),flip(a)].">
      <j1 rule="para" parents="262 8801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12332">
    <literal><![CDATA[
      R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) = T(T(x,K(z,u)),K(y,z))
    ]]></literal>
    <justification jstring="[para(9807(a,1),12331(a,2,1))].">
      <j1 rule="para" parents="9807 12331"/>
    </justification>
  </clause>

  <clause id="12333">
    <literal><![CDATA[
      R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) = T(T(x,K(z,u)),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8153,a,b,12332,a),flip(a)].">
      <j1 rule="hyper" parents="373 8153 12332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12335">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(10336,a,12333,a),flip(a)].">
      <j1 rule="hyper" parents="10336 12333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12337">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(3320(a,2),12335(a,2,2))].">
      <j1 rule="para" parents="3320 12335"/>
    </justification>
  </clause>

  <clause id="12338">
    <literal><![CDATA[
      T(x,K(y,z) * K(z,u)) \ x = K(x,K(z,y)) * K(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(12335(a,1),10029(a,1,1))].">
      <j1 rule="para" parents="12335 10029"/>
    </justification>
  </clause>

  <clause id="12339">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8170,a,12337,a)].">
      <j1 rule="hyper" parents="8170 12337"/>
    </justification>
  </clause>

  <clause id="12340">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(481,a,12337,a)].">
      <j1 rule="hyper" parents="481 12337"/>
    </justification>
  </clause>

  <clause id="12341">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11744,a,b,12337,a)].">
      <j1 rule="hyper" parents="64 11744 12337"/>
    </justification>
  </clause>

  <clause id="12342">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(u,R(y,w,v5))) = T(x,K(y,z) * K(R(u,w,v5),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9778,a,b,12337,a)].">
      <j1 rule="hyper" parents="64 9778 12337"/>
    </justification>
  </clause>

  <clause id="12343">
    <literal><![CDATA[
      T(x,K(y,z) * K(R(u,w / u,v5),y)) = T(T(x,R(K(u,y),w,v5)),K(y,z))
    ]]></literal>
    <justification jstring="[para(9220(a,1),12339(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9220 12339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12344">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(x,y) \ u) = T(u,K(y,z) * K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(12339(a,1),10543(a,2,1))].">
      <j1 rule="para" parents="12339 10543"/>
    </justification>
  </clause>

  <clause id="12345">
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,12337,a(flip),b,12340,a)].">
      <j1 rule="hyper" parents="64 12337 12340"/>
    </justification>
  </clause>

  <clause id="12346">
    <literal><![CDATA[
      T(x * K(K(y,z) * K(u,y),x),K(y,u) * K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(6240,a,12345,a)].">
      <j1 rule="hyper" parents="6240 12345"/>
    </justification>
  </clause>

  <clause id="12347">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(5851,a,12345,a)].">
      <j1 rule="hyper" parents="5851 12345"/>
    </justification>
  </clause>

  <clause id="12348">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / T(((K(y,z) * K(u,y)) \ x) * (K(y,z) * K(u,y)),K(y,u) * K(z,y)) = T(K(y,z) * K(u,y),(K(y,z) * K(u,y)) \ x)
    ]]></literal>
    <justification jstring="[para(12345(a,1),8478(a,1,2))].">
      <j1 rule="para" parents="12345 8478"/>
    </justification>
  </clause>

  <clause id="12349">
    <literal><![CDATA[
      x * K(K(y,z) * K(u,y),x) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(3320(a,2),12341(a,1,2,1))].">
      <j1 rule="para" parents="3320 12341"/>
    </justification>
  </clause>

  <clause id="12350">
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u) * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(12346(a,1),5901(a,1,1))].">
      <j1 rule="para" parents="12346 5901"/>
    </justification>
  </clause>

  <clause id="12351">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),u) = K(u,K(y,x) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,12341,a,b,12347,a)].">
      <j1 rule="hyper" parents="35 12341 12347"/>
    </justification>
  </clause>

  <clause id="12352">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,z) * K(y,x))
    ]]></literal>
    <justification jstring="[para(3320(a,2),12351(a,1,1))].">
      <j1 rule="para" parents="3320 12351"/>
    </justification>
  </clause>

  <clause id="12353">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(y,x) * K(x,z))
    ]]></literal>
    <justification jstring="[para(3320(a,1),12352(a,2,2))].">
      <j1 rule="para" parents="3320 12352"/>
    </justification>
  </clause>

  <clause id="12354">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,5753,a(flip),b,12349,a),flip(a)].">
      <j1 rule="hyper" parents="35 5753 12349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12355">
    <literal><![CDATA[
      T(T(x,K(y,z) * K(u,y)),K(y,u) * K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(12349(a,1),12346(a,1,1))].">
      <j1 rule="para" parents="12349 12346"/>
    </justification>
  </clause>

  <clause id="12356">
    <literal><![CDATA[
      K(x,K(y,z) * K(u,y)) = K(x,K(z,y) * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12353,a(flip),b,12354,a),flip(a)].">
      <j1 rule="hyper" parents="64 12353 12354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12357">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * K(u,K(x,y) * K(z,x)) = T(K(x,y) * K(z,x),u)
    ]]></literal>
    <justification jstring="[hyper(145,a,12354,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 12354 5726"/>
    </justification>
  </clause>

  <clause id="12358">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u) * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(12337(a,2),12350(a,1))].">
      <j1 rule="para" parents="12337 12350"/>
    </justification>
  </clause>

  <clause id="12360">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,u) * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(8153(a,1),12358(a,1,1))].">
      <j1 rule="para" parents="8153 12358"/>
    </justification>
  </clause>

  <clause id="12361">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(z,y) * K(y,u),x)
    ]]></literal>
    <justification jstring="[hyper(5824,a,12338,a),flip(a)].">
      <j1 rule="hyper" parents="5824 12338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12362">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,12351,a(flip),b,12361,a),flip(a)].">
      <j1 rule="hyper" parents="373 12351 12361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12363">
    <literal><![CDATA[
      K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(v5,K(y,x)) * K(v5,R(K(y,w),z,u))
    ]]></literal>
    <justification jstring="[para(9707(a,1),12361(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9707 12361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12364">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(y,z) * K(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,12354,a,b,12362,a),flip(a)].">
      <j1 rule="hyper" parents="373 12354 12362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12365">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ K(u,K(z,w)))) = K(u,K(z,x) * K(w,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10014,a,b,12362,a)].">
      <j1 rule="hyper" parents="64 10014 12362"/>
    </justification>
  </clause>

  <clause id="12366">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K((K(x,y) * K(z,x)) \ u,K(x,y)) * K((K(x,y) * K(z,x)) \ u,K(x,z))) = (((K(x,y) * K(z,x)) \ u) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(12362(a,2),5937(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12362 5937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12367">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x * K(y,u),K(y,w)) = K(x * K(y,u),K(y,z) * K(w,y))
    ]]></literal>
    <justification jstring="[para(8625(a,1),12362(a,1,1))].">
      <j1 rule="para" parents="8625 12362"/>
    </justification>
  </clause>

  <clause id="12368">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(z,y)) = T(x,K(z,y) * K(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(12360,a,12342,a)].">
      <j1 rule="hyper" parents="12360 12342"/>
    </justification>
  </clause>

  <clause id="12369">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(x,y) \ u) = K(K(y,z) * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5731,a,b,12344,a),flip(a)].">
      <j1 rule="hyper" parents="373 5731 12344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12370">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(y,x) * u) = K(K(y,z) * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(6156(a,1),12369(a,1,2))].">
      <j1 rule="para" parents="6156 12369"/>
    </justification>
  </clause>

  <clause id="12371">
    <literal><![CDATA[
      T(x,K(y,z) * K(R(z,u,w),y)) = T(x,K(y,z) * K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(3320(a,1),12368(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3320 12368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12372">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(z,y)) = T(x,K(y,z) * K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(12350,a,12371,a)].">
      <j1 rule="hyper" parents="12350 12371"/>
    </justification>
  </clause>

  <clause id="12373">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(z,R(y,u,w))) = T(x,K(y,R(z,u,w)) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,5753,a(flip),b,12372,a)].">
      <j1 rule="hyper" parents="373 5753 12372"/>
    </justification>
  </clause>

  <clause id="12374">
    <literal><![CDATA[
      T(x,K(y,z) * K(R(u,w / u,v5),y)) = T(T(x,K(y,R(u,w,v5))),K(y,z))
    ]]></literal>
    <justification jstring="[para(9777(a,1),12343(a,2,1))].">
      <j1 rule="para" parents="9777 12343"/>
    </justification>
  </clause>

  <clause id="12375">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),u) * u = u * (K(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(144,a,12357,a(flip),b,5721,a)].">
      <j1 rule="hyper" parents="144 12357 5721"/>
    </justification>
  </clause>

  <clause id="12376">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / x != w
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * K(u,y),x) = w
    ]]></literal>
    <justification jstring="[para(12375(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="12375 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12377">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) / (K(u,z) * x) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(z,u) * K(y,z),K(u,z) * x) = w
    ]]></literal>
    <justification jstring="[para(11739(a,1),12376(a,1,1))].">
      <j1 rule="para" parents="11739 12376"/>
    </justification>
  </clause>

  <clause id="12378">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w)) * K(z,y)) = K(x,K(y,z) * K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(35,a,5753,a(flip),b,12373,a)].">
      <j1 rule="hyper" parents="35 5753 12373"/>
    </justification>
  </clause>

  <clause id="12379">
    <literal><![CDATA[
      T(x,K(y,z) * K(R(u,w / u,v5),y)) = T(x,K(y,z) * K(R(u,w,v5),y))
    ]]></literal>
    <justification jstring="[hyper(373,a,12340,a(flip),b,12374,a),flip(a)].">
      <j1 rule="hyper" parents="373 12340 12374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12380">
    <literal><![CDATA[
      T(x,K(y,z) * R(K(u,y),w,v5)) = T(x,K(y,z) * K(R(u,w,v5),y))
    ]]></literal>
    <justification jstring="[para(9220(a,1),12379(a,1,2,2))].">
      <j1 rule="para" parents="9220 12379"/>
    </justification>
  </clause>

  <clause id="12381">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(v5,y)) = T(x,K(y,v5) * R(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,12345,a,b,12380,a)].">
      <j1 rule="hyper" parents="373 12345 12380"/>
    </justification>
  </clause>

  <clause id="12382">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ K(z,K(u,w)))) = K(u,K(z,x) * K(w,z))
    ]]></literal>
    <justification jstring="[para(8108(a,1),12365(a,1,2,2,2))].">
      <j1 rule="para" parents="8108 12365"/>
    </justification>
  </clause>

  <clause id="12383">
    <literal><![CDATA[
      K(x * K(y,z),K(y,u) * K(w,y)) = K(x,K(y,u)) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(8625(a,1),12367(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8625 12367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12384">
    <literal><![CDATA[
      K(x * K(y,z),K(y,u) * K(w,y)) = K(x,K(y,u) * K(w,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,12362,a(flip),b,12383,a),flip(a)].">
      <j1 rule="hyper" parents="373 12362 12383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12385">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(12383(a,1),8568(a,1))].">
      <j1 rule="para" parents="12383 8568"/>
    </justification>
  </clause>

  <clause id="12387">
    <literal><![CDATA[
      K(K(x,y) * z,K(y,u) * K(w,y)) = K(z,K(y,u) * K(w,y))
    ]]></literal>
    <justification jstring="[para(7456(a,1),12384(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7456 12384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12388">
    <literal><![CDATA[
      K(K(x,y) * z,K(u,y) * K(y,w)) = K(z,K(y,u) * K(w,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,12356,a(flip),b,12387,a)].">
      <j1 rule="hyper" parents="64 12356 12387"/>
    </justification>
  </clause>

  <clause id="12389">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) / (K(u,z) * x) = (K(y,z) * K(z,u)) * K(x,K(z,y) * K(u,z))
    ]]></literal>
    <justification jstring="[para(12388(a,1),12315(a,2,2))].">
      <j1 rule="para" parents="12388 12315"/>
    </justification>
  </clause>

  <clause id="12390">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,K(y,x) * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(12361(a,1),12385(a,1))].">
      <j1 rule="para" parents="12361 12385"/>
    </justification>
  </clause>

  <clause id="12391">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,K(x,y) * K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(12364(a,1),12385(a,1))].">
      <j1 rule="para" parents="12364 12385"/>
    </justification>
  </clause>

  <clause id="12392">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),K(y,x) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,K(y,z) * K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(12370(a,2),12391(a,1))].">
      <j1 rule="para" parents="12370 12391"/>
    </justification>
  </clause>

  <clause id="12393">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(z,K(x,y) * K(u,x))
    ]]></literal>
    <justification jstring="[hyper(4542,a,12382,a)].">
      <j1 rule="hyper" parents="4542 12382"/>
    </justification>
  </clause>

  <clause id="12394">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(z,u)) = K(z,K(y,x) * K(u,y))
    ]]></literal>
    <justification jstring="[para(8108(a,1),12393(a,1,1))].">
      <j1 rule="para" parents="8108 12393"/>
    </justification>
  </clause>

  <clause id="12395">
    <literal><![CDATA[
      K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(v5,K(y,x)) * K(v5,K(y,R(w,z,u)))
    ]]></literal>
    <justification jstring="[para(9774(a,1),12363(a,2,2))].">
      <j1 rule="para" parents="9774 12363"/>
    </justification>
  </clause>

  <clause id="12396">
    <literal><![CDATA[
      K(K(x,y) * K(y,(z * u) / ((w \ z) * u)),v5) = K(K(x,y) * K(y,R(w,z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,12361,a(flip),b,12395,a),flip(a)].">
      <j1 rule="hyper" parents="373 12361 12395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12397">
    <literal><![CDATA[
      K(K(x,y) * R(K(y,z),u,w),v5) = K(K(x,y) * K(y,R(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(9707(a,1),12396(a,1,1,2))].">
      <j1 rule="para" parents="9707 12396"/>
    </justification>
  </clause>

  <clause id="12398">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) / (K(u,z) * x) = K(y,z) * (K(z,u) * K(x,K(z,y) * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,9804,a(flip),b,12389,a),flip(a)].">
      <j1 rule="hyper" parents="373 9804 12389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12400">
    <literal><![CDATA[
      L((x \ 1) * L((x \ 1) \ 1,y,z),T(x,u),w) = L(x \ 1,x,w) * L(L(x \ 1,x,w) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(9618(a,1),9619(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9618 9619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12401">
    <literal><![CDATA[
      L((x \ 1) * L((x \ 1) \ 1,y,z),T(x,u),w) = L((x \ 1) * L((x \ 1) \ 1,y,z),x,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,4273,a(flip),b,12400,a),flip(a)].">
      <j1 rule="hyper" parents="373 4273 12400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12403">
    <literal><![CDATA[
      L((x \ 1) * L((x \ 1) \ 1,y,z),T(x,u),w) = L(x \ L(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[para(1804(a,1),12401(a,2,1))].">
      <j1 rule="para" parents="1804 12401"/>
    </justification>
  </clause>

  <clause id="12404">
    <literal><![CDATA[
      L(x \ L(x,y,z),T(x,u),w) = L(x \ L(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[para(1804(a,1),12403(a,1,1))].">
      <j1 rule="para" parents="1804 12403"/>
    </justification>
  </clause>

  <clause id="12405">
    <literal><![CDATA[
      a(x,T(y,z),K(u,y \ L(y,w,v5))) * K(u,L(y \ L(y,w,v5),y,x)) = K(u,y \ L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(12404(a,1),12120(a,1,2,2))].">
      <j1 rule="para" parents="12404 12120"/>
    </justification>
  </clause>

  <clause id="12406">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (K(y,x) * (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(7625(a,1),9806(a,2,1,1))].">
      <j1 rule="para" parents="7625 9806"/>
    </justification>
  </clause>

  <clause id="12407">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (T(x,y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(6157(a,1),12406(a,2,1))].">
      <j1 rule="para" parents="6157 12406"/>
    </justification>
  </clause>

  <clause id="12409">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ 1,z) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(188(a,1),12407(a,1,2,1,2,2))].">
      <j1 rule="para" parents="188 12407"/>
    </justification>
  </clause>

  <clause id="12410">
    <literal><![CDATA[
      (x \ 1) * (K(y,x) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(4526(a,1),12409(a,1,2,1))].">
      <j1 rule="para" parents="4526 12409"/>
    </justification>
  </clause>

  <clause id="12411">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((x \ 1) * z) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(759,a,12410,a)].">
      <j1 rule="hyper" parents="759 12410"/>
    </justification>
  </clause>

  <clause id="12412">
    <literal><![CDATA[
      L(K(x,y) * z,y,y) = y * ((T(y,x) \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,12410,a(flip),b,1148,a),flip(a)].">
      <j1 rule="hyper" parents="145 12410 1148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12414">
    <literal><![CDATA[
      (T(x,y) \ 1) * (x \ z) = (x \ 1) * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[para(6157(a,1),12410(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6157 12410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12415">
    <literal><![CDATA[
      T(x / R(y * K(z,y),u,y),T(R((z * y) / z,u,y),y)) = ((R((z * y) / z,u,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(10705(a,1),10389(a,1,1,2))].">
      <j1 rule="para" parents="10705 10389"/>
    </justification>
  </clause>

  <clause id="12416">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),T(R((u * y) / u,z,y),y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(7561(a,1),12415(a,1,1))].">
      <j1 rule="para" parents="7561 12415"/>
    </justification>
  </clause>

  <clause id="12417">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),R(T((u * y) / u,y),z,y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(27(a,2),12416(a,1,2))].">
      <j1 rule="para" parents="27 12416"/>
    </justification>
  </clause>

  <clause id="12418">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),R((u * y) / u,z,y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[para(314(a,1),12417(a,1,2,1))].">
      <j1 rule="para" parents="314 12417"/>
    </justification>
  </clause>

  <clause id="12419">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),R(u / (u / y),z,y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,9281,a(flip),b,12418,a)].">
      <j1 rule="hyper" parents="64 9281 12418"/>
    </justification>
  </clause>

  <clause id="12420">
    <literal><![CDATA[
      T((x / R(y,z,y)) * K(y,u),u / (u / y)) = ((R((u * y) / u,z,y) \ y) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,10101,a(flip),b,12419,a)].">
      <j1 rule="hyper" parents="64 10101 12419"/>
    </justification>
  </clause>

  <clause id="12422">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = ((x * y) / x) \ ((u / R(y,z,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9866,a(flip),b,12420,a),flip(a)].">
      <j1 rule="hyper" parents="64 9866 12420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12423">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = ((x * y) / x) \ (y * (R(y,z,y) \ u))
    ]]></literal>
    <justification jstring="[para(7494(a,1),12422(a,2,2))].">
      <j1 rule="para" parents="7494 12422"/>
    </justification>
  </clause>

  <clause id="12424">
    <literal><![CDATA[
      ((R((x * y) / x,z,y) \ y) \ y) \ u = T(y,x) * (y \ (R(y,z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,4954,a(flip),b,12423,a),flip(a)].">
      <j1 rule="hyper" parents="373 4954 12423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12425">
    <literal><![CDATA[
      ((x \ L(T(x,y),z,x)) \ x) \ u = T(x,y) * (x \ (R(x,z,x) \ u))
    ]]></literal>
    <justification jstring="[para(10388(a,1),12424(a,1,1,1))].">
      <j1 rule="para" parents="10388 12424"/>
    </justification>
  </clause>

  <clause id="12426">
    <literal><![CDATA[
      T(x,y) * (x \ (R(x,z,x) \ u)) = R(x * K(y,x),z,x) \ u
    ]]></literal>
    <justification jstring="[para(10705(a,1),12425(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10705 12425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12427">
    <literal><![CDATA[
      R(x * K(y,x),z,x) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (R(x,z,x) \ u) = w
    ]]></literal>
    <justification jstring="[para(12426(a,1),6030(a,1))].">
      <j1 rule="para" parents="12426 6030"/>
    </justification>
  </clause>

  <clause id="12428">
    <literal><![CDATA[
      K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(y,z,u),w * K(x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),12260(a,2,1,1))].">
      <j1 rule="para" parents="9 12260"/>
    </justification>
  </clause>

  <clause id="12429">
    <literal><![CDATA[
      K(R(x \ (x * y),z,u),R(y / w,w,K(x,y)) \ (x \ (x * y))) = K(R(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,9295,a(flip),b,12428,a),flip(a)].">
      <j1 rule="hyper" parents="373 9295 12428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12431">
    <literal><![CDATA[
      K(R(x,y,z),R(x / u,u,K(w,x)) \ (w \ (w * x))) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),12429(a,1,1,1))].">
      <j1 rule="para" parents="9 12429"/>
    </justification>
  </clause>

  <clause id="12432">
    <literal><![CDATA[
      K(R(x,y,z),R(x / u,u,K(w,x)) \ x) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),12431(a,1,2,2))].">
      <j1 rule="para" parents="9 12431"/>
    </justification>
  </clause>

  <clause id="12433">
    <literal><![CDATA[
      K(R(x,y,z),R(x / u,u,L(K(w,x),v5,v6)) \ x) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(7310(a,1),12432(a,1,2,1,3))].">
      <j1 rule="para" parents="7310 12432"/>
    </justification>
  </clause>

  <clause id="12434">
    <literal><![CDATA[
      T(K(x,y) * z,u) * T(K(y,x),T(w,T(K(x,y) * z,u))) = K(y,K(x,w)) * (K(y,x) * T(z * K(x,y),u))
    ]]></literal>
    <justification jstring="[para(8092(a,1),9259(a,2,1))].">
      <j1 rule="para" parents="8092 9259"/>
    </justification>
  </clause>

  <clause id="12436">
    <literal><![CDATA[
      T(x,x * K((y * z) \ (u * w),w)) \ T(K(w,(y * z) \ (u * w)) * x,x) = K(w,T((y * (w \ z)) \ u,x))
    ]]></literal>
    <justification jstring="[para(9580(a,1),11675(a,1,2,1,1))].">
      <j1 rule="para" parents="9580 11675"/>
    </justification>
  </clause>

  <clause id="12437">
    <literal><![CDATA[
      T(K(x,y) * z,u) * T(K(y,x),T(w,T(K(x,y) * z,u))) = K(y,T(x,w)) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,8933,a(flip),b,12434,a),flip(a)].">
      <j1 rule="hyper" parents="373 8933 12434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12438">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x,T(w,T(K(x,y) * z,u)))) = K(y,T(x,w)) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(8795,a,12437,a)].">
      <j1 rule="hyper" parents="8795 12437"/>
    </justification>
  </clause>

  <clause id="12440">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,w)) = K(x,T((y * z) \ (u * x),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11674,a(flip),b,12436,a),flip(a)].">
      <j1 rule="hyper" parents="64 11674 12436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12441">
    <literal><![CDATA[
      K(x,T((y * z) \ (u * x),y * z)) = K(x,u / (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(9534,a,12440,a),flip(a)].">
      <j1 rule="hyper" parents="9534 12440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12442">
    <literal><![CDATA[
      K(x,(y * x) / (z * u)) = K(x,y / (z * (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(8325,a,12441,a)].">
      <j1 rule="hyper" parents="8325 12441"/>
    </justification>
  </clause>

  <clause id="12443">
    <literal><![CDATA[
      K(x,y / (z * (x \ u))) = K(x,((z * u) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(9749,a,12442,a),flip(a)].">
      <j1 rule="hyper" parents="9749 12442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12444">
    <literal><![CDATA[
      R(K(x,((y * z) / (u / w)) \ x),w \ u,w) = K(x,u / ((y * (x \ z)) * w))
    ]]></literal>
    <justification jstring="[para(12443(a,1),10216(a,1,1))].">
      <j1 rule="para" parents="12443 10216"/>
    </justification>
  </clause>

  <clause id="12445">
    <literal><![CDATA[
      K(x,y / ((x \ (z * u)) * w)) = K(x,y / ((z * (x \ u)) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,10302,a(flip),b,12444,a)].">
      <j1 rule="hyper" parents="64 10302 12444"/>
    </justification>
  </clause>

  <clause id="12446">
    <literal><![CDATA[
      K(x,y / ((z * (x \ u)) * w)) = K(x,(((z * u) * w) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(10802,a,12445,a),flip(a)].">
      <j1 rule="hyper" parents="10802 12445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12447">
    <literal><![CDATA[
      K(x,(((y * z) * u) / (z * u)) \ x) = R(K(x,y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9914,a(flip),b,12446,a),flip(a)].">
      <j1 rule="hyper" parents="64 9914 12446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12448">
    <literal><![CDATA[
      R(K(x,y \ x),z,u) = K(x,R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(20(a,2),12447(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20 12447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12449">
    <literal><![CDATA[
      K(x,R(y \ x,z,u) \ x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6128(a,1),12448(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6128 12448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12450">
    <literal><![CDATA[
      R(K(x,R(y \ x,z,u) \ x),w,v5) = K(x,R(R(x / y,z,u),w,v5) \ x)
    ]]></literal>
    <justification jstring="[para(11434(a,1),12448(a,1,1))].">
      <j1 rule="para" parents="11434 12448"/>
    </justification>
  </clause>

  <clause id="12451">
    <literal><![CDATA[
      K(x,R(R(x / y,z,u),w,v5) \ x) = R(R(K(x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(12449(a,1),12450(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12449 12450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12452">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),x * u) = T(x \ L(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[hyper(7234,a,12298,a)].">
      <j1 rule="hyper" parents="7234 12298"/>
    </justification>
  </clause>

  <clause id="12453">
    <literal><![CDATA[
      T(x \ L(x,y,z),u * x) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(1804(a,1),12452(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1804 12452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12454">
    <literal><![CDATA[
      L(x \ (y * z),x,K(y * z,y)) = (K(y,T(y,y * z) * z) \ x) \ T(T(T(y,y * z) * z,y),y)
    ]]></literal>
    <justification jstring="[para(8517(a,1),7351(a,1,3))].">
      <j1 rule="para" parents="8517 7351"/>
    </justification>
  </clause>

  <clause id="12456">
    <literal><![CDATA[
      R(K(x,K(y,z)) * K(y,K(z,R(x,u,w))),K(K(y,z),v5),v6) * v7 = K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * v7)
    ]]></literal>
    <justification jstring="[para(9772(a,1),11723(a,1,1,1,2))].">
      <j1 rule="para" parents="9772 11723"/>
    </justification>
  </clause>

  <clause id="12457">
    <literal><![CDATA[
      T(x * K(y,z),L(L(T(y,x),u,w),K(y,z),x)) = L(T(y,x),u,w) \ (L(y,u,w) * (x * K(y,z)))
    ]]></literal>
    <justification jstring="[para(11850(a,1),12015(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11850 12015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12458">
    <literal><![CDATA[
      T(x * K(y,z),L(L(T(y,x),u,w),K(y,z),x)) = K(x,L(y,u,w)) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,6295,a(flip),b,12457,a),flip(a)].">
      <j1 rule="hyper" parents="373 6295 12457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12460">
    <literal><![CDATA[
      T(x * K(y,z),L(L(T(y,x),u,w),K(y,z),x)) = T(x,L(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5755,a(flip),b,12458,a),flip(a)].">
      <j1 rule="hyper" parents="373 5755 12458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12461">
    <literal><![CDATA[
      T(x * K(y,z),L(T(y,x),u,w)) = T(x,L(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(11850(a,1),12460(a,1,2))].">
      <j1 rule="para" parents="11850 12460"/>
    </justification>
  </clause>

  <clause id="12462">
    <literal><![CDATA[
      T(x * K(y,z),L(y,u,w)) = T(x,L(y,u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8504,a(flip),b,12461,a)].">
      <j1 rule="hyper" parents="64 8504 12461"/>
    </justification>
  </clause>

  <clause id="12464">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,12123,a(flip),b,12462,a),flip(a)].">
      <j1 rule="hyper" parents="373 12123 12462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12465">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(12464(a,1),5857(a,1,1))].">
      <j1 rule="para" parents="12464 5857"/>
    </justification>
  </clause>

  <clause id="12466">
    <literal><![CDATA[
      R(K(x,K(y,z) * K(R(z,u,w),y)),K(K(y,x),v5),v6) * v7 = K(z,K(y,x)) * (R(K(K(y,x),z),u,w) * v7)
    ]]></literal>
    <justification jstring="[para(12394(a,1),12456(a,1,1,1))].">
      <j1 rule="para" parents="12394 12456"/>
    </justification>
  </clause>

  <clause id="12467">
    <literal><![CDATA[
      (T(x \ (x / y),(x \ (x / y)) \ 1) * T(x,y \ 1)) \ z = (x / y) \ (K(x \ (x / y),(x / y) \ x) \ z)
    ]]></literal>
    <justification jstring="[para(4338(a,1),7272(a,2,2,1))].">
      <j1 rule="para" parents="4338 7272"/>
    </justification>
  </clause>

  <clause id="12468">
    <literal><![CDATA[
      (T(x \ (x / y),(x \ (x / y)) \ 1) * T(x,y \ 1)) \ z = (x / y) \ (K(x \ (x / y),y) \ z)
    ]]></literal>
    <justification jstring="[para(82(a,1),12467(a,2,2,1,2))].">
      <j1 rule="para" parents="82 12467"/>
    </justification>
  </clause>

  <clause id="12469">
    <literal><![CDATA[
      (T(x \ (x / y),(x \ (x / y)) \ 1) * T(x,y \ 1)) \ z = (x / y) \ (((y \ 1) * y) \ z)
    ]]></literal>
    <justification jstring="[para(4357(a,1),12468(a,2,2,1))].">
      <j1 rule="para" parents="4357 12468"/>
    </justification>
  </clause>

  <clause id="12470">
    <literal><![CDATA[
      (x / y) \ (((y \ 1) * y) \ z) = ((((x \ (x / y)) \ 1) \ 1) * T(x,y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(116(a,1),12469(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="116 12469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12472">
    <literal><![CDATA[
      (x / y) \ (((y \ 1) * y) \ z) = ((x \ (x / ((y \ 1) \ 1))) * T(x,y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(3935(a,1),12470(a,2,1,1))].">
      <j1 rule="para" parents="3935 12470"/>
    </justification>
  </clause>

  <clause id="12473">
    <literal><![CDATA[
      (x / y) \ (((y \ 1) * y) \ z) = (x / ((y \ 1) \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(6426(a,1),12472(a,2,1))].">
      <j1 rule="para" parents="6426 12472"/>
    </justification>
  </clause>

  <clause id="12474">
    <literal><![CDATA[
      R(x,(((y / z) \ 1) \ 1) \ (((z \ 1) * z) \ u),w) = R(x,(y / ((z \ 1) \ 1)) \ u,w)
    ]]></literal>
    <justification jstring="[para(12473(a,1),3030(a,2,2))].">
      <j1 rule="para" parents="12473 3030"/>
    </justification>
  </clause>

  <clause id="12475">
    <literal><![CDATA[
      R(x,(((y / z) \ 1) \ ((z \ 1) * z)) \ u,w) = R(x,(y / ((z \ 1) \ 1)) \ u,w)
    ]]></literal>
    <justification jstring="[para(5294(a,1),12474(a,1,2))].">
      <j1 rule="para" parents="5294 12474"/>
    </justification>
  </clause>

  <clause id="12476">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ z) * L(T(K(x,u),K(x,y) \ z),w,v5)) = z * L(T(K(x,u),z),w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),7716(a,2,2,1,2))].">
      <j1 rule="para" parents="10 7716"/>
    </justification>
  </clause>

  <clause id="12477">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) \ z) * L(T(K(x,u),K(x,y) \ z),w,v5)) = L(K(x,u),w,v5) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,266,a(flip),b,12476,a),flip(a)].">
      <j1 rule="hyper" parents="373 266 12476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12478">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(x,y) \ v5)) = L(K(x,z),u,w) * v5
    ]]></literal>
    <justification jstring="[hyper(64,a,520,a(flip),b,12477,a)].">
      <j1 rule="hyper" parents="64 520 12477"/>
    </justification>
  </clause>

  <clause id="12479">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * v5)) = L(K(x,z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(6156(a,1),12478(a,1,2,2))].">
      <j1 rule="para" parents="6156 12478"/>
    </justification>
  </clause>

  <clause id="12480">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * L(L(K(x,z),u,w) \ 1,v5,v6))) = L(K(x,z) * L(K(x,z) \ 1,v5,v6),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,4273,a(flip),b,12479,a),flip(a)].">
      <j1 rule="hyper" parents="373 4273 12479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12488">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * ((x * ((y * K(x,z)) * K(x,z))) \ u)
    ]]></literal>
    <justification jstring="[para(7135(a,1),10965(a,2,2,1))].">
      <j1 rule="para" parents="7135 10965"/>
    </justification>
  </clause>

  <clause id="12489">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * ((x * (y * (K(x,z) * K(x,z)))) \ u)
    ]]></literal>
    <justification jstring="[para(10350(a,1),12488(a,2,2,1,2))].">
      <j1 rule="para" parents="10350 12488"/>
    </justification>
  </clause>

  <clause id="12490">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * ((T(T(x,z),z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(10375(a,1),12489(a,2,2,1))].">
      <j1 rule="para" parents="10375 12489"/>
    </justification>
  </clause>

  <clause id="12491">
    <literal><![CDATA[
      R((x \ y) * x,((x \ y) * x) \ x,x \ ((x \ y) * x)) = ((y \ T(x,x \ y)) * T(x \ y,x)) \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(22(a,2),6986(a,2,1,2))].">
      <j1 rule="para" parents="22 6986"/>
    </justification>
  </clause>

  <clause id="12492">
    <literal><![CDATA[
      T(T(x,y) / (T(y,x) \ x),y * (x / T(y,x))) = L((y \ x) \ x,T(y,x) \ x,(y \ x) \ x)
    ]]></literal>
    <justification jstring="[para(8957(a,1),9947(a,1,1,1))].">
      <j1 rule="para" parents="8957 9947"/>
    </justification>
  </clause>

  <clause id="12493">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,x * (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4631(a,1),12492(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4631 12492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12494">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8562,a(flip),b,12493,a),flip(a)].">
      <j1 rule="hyper" parents="373 8562 12493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12496">
    <literal><![CDATA[
      (((K(x,y) * K(y,z)) \ u) \ u) \ 1 = (K(x,y) * K(y,z)) \ K(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[para(10362(a,1),10007(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10362 10007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12497">
    <literal><![CDATA[
      (((K(x,y) * K(y,z)) \ u) \ u) \ 1 = (K(y,x) * K(z,y)) * K(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,10003,a(flip),b,12496,a),flip(a)].">
      <j1 rule="hyper" parents="373 10003 12496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12499">
    <literal><![CDATA[
      (((K(x,y) * K(y,z)) \ u) \ u) \ 1 = T(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5753,a,b,12497,a),flip(a)].">
      <j1 rule="hyper" parents="373 5753 12497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12500">
    <literal><![CDATA[
      ((K(x,y) * (K(z,x) * u)) \ u) \ 1 = T(K(x,y) * K(z,x),u)
    ]]></literal>
    <justification jstring="[para(9997(a,1),12499(a,1,1,1))].">
      <j1 rule="para" parents="9997 12499"/>
    </justification>
  </clause>

  <clause id="12501">
    <literal><![CDATA[
      ((K(x,y) * (K(y,z) * u)) \ u) \ 1 = T(K(y,z) * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(9980(a,1),12500(a,1,1,1))].">
      <j1 rule="para" parents="9980 12500"/>
    </justification>
  </clause>

  <clause id="12502">
    <literal><![CDATA[
      (K(x,y) * z) * R((K(x,y) * z) \ (T(T(x,y),T(u,y)) * z),w,v5) = (R(T(x,u),w,v5) * K(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,506,a(flip),b,10644,a),flip(a)].">
      <j1 rule="hyper" parents="373 506 10644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12503">
    <literal><![CDATA[
      (K(x,y) * R(K(x,y) \ T(T(x,y),T(z,y)),u,w)) * v5 = (R(T(x,z),u,w) * K(x,y)) * v5
    ]]></literal>
    <justification jstring="[hyper(64,a,2789,a(flip),b,12502,a)].">
      <j1 rule="hyper" parents="64 2789 12502"/>
    </justification>
  </clause>

  <clause id="12504">
    <literal><![CDATA[
      (K(x,y) * R(T(T(x,y),T(z,y)) * K(y,x),u,w)) * v5 = (R(T(x,z),u,w) * K(x,y)) * v5
    ]]></literal>
    <justification jstring="[para(6173(a,1),12503(a,1,1,2,1))].">
      <j1 rule="para" parents="6173 12503"/>
    </justification>
  </clause>

  <clause id="12505">
    <literal><![CDATA[
      (K(x,y) * R(x * K(T(x,y),T(z,y)),u,w)) * v5 = (R(T(x,z),u,w) * K(x,y)) * v5
    ]]></literal>
    <justification jstring="[para(6602(a,1),12504(a,1,1,2,1))].">
      <j1 rule="para" parents="6602 12504"/>
    </justification>
  </clause>

  <clause id="12506">
    <literal><![CDATA[
      (R(T(x,y),z,u) * K(x,w)) * v5 = (K(x,w) * R(T(x,y),z,u)) * v5
    ]]></literal>
    <justification jstring="[para(8223(a,1),12505(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8223 12505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12507">
    <literal><![CDATA[
      (K(x,y) * R(T(x,z),u,w)) * v5 = R(T(x,z),u,w) * (K(x,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,4844,a(flip),b,12506,a),flip(a)].">
      <j1 rule="hyper" parents="64 4844 12506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12509">
    <literal><![CDATA[
      (K(x,y) \ (R(T(x,z),u,w) * (K(x,y) * v5))) / (K(x,y) \ (R(T(x,z),u,w) * v5)) = R(K(x,y),R(T(x,z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(12507(a,1),1939(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12507 1939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12510">
    <literal><![CDATA[
      (K(x,y) * (R(T(y,z),u,w) * (K(y,x) * v5))) / (K(y,x) \ (R(T(y,z),u,w) * v5)) = R(K(y,x),R(T(y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[para(6156(a,1),12509(a,1,1))].">
      <j1 rule="para" parents="6156 12509"/>
    </justification>
  </clause>

  <clause id="12511">
    <literal><![CDATA[
      (R(T(x,y),z,u) * w) / (K(x,v5) \ (R(T(x,y),z,u) * w)) = R(K(x,v5),R(T(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(11489(a,1),12510(a,1,1))].">
      <j1 rule="para" parents="11489 12510"/>
    </justification>
  </clause>

  <clause id="12512">
    <literal><![CDATA[
      R(K(x,y),R(T(x,z),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(330,a,12511,a)].">
      <j1 rule="hyper" parents="330 12511"/>
    </justification>
  </clause>

  <clause id="12515">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * (w \ 1)) = K(x,R(T(x,y),z,u) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,9703,a(flip),b,12512,a)].">
      <j1 rule="hyper" parents="64 9703 12512"/>
    </justification>
  </clause>

  <clause id="12516">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * (w \ 1)) = K(x,w \ R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,7971,a(flip),b,12515,a),flip(a)].">
      <j1 rule="hyper" parents="373 7971 12515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12517">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,R(x,u,w) * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,9680,a(flip),b,12516,a),flip(a)].">
      <j1 rule="hyper" parents="64 9680 12516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12519">
    <literal><![CDATA[
      K(x,R(x,y,z) * (u \ 1)) = K(x,u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(114(a,1),12517(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="114 12517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12520">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,y \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,12517,a,b,12519,a)].">
      <j1 rule="hyper" parents="64 12517 12519"/>
    </justification>
  </clause>

  <clause id="12521">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(8695,a,12520,a)].">
      <j1 rule="hyper" parents="8695 12520"/>
    </justification>
  </clause>

  <clause id="12523">
    <literal><![CDATA[
      R(x,y,y) \ (((x * (1 / y)) \ R(x,y,y)) * z) = L((y \ R(x,y,y)) \ z,x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(1409(a,1),11099(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1409 11099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12524">
    <literal><![CDATA[
      R(x,y,y) \ (((x * (1 / y)) \ R(x,y,y)) * z) = L((y \ R(x,y,y)) \ z,x * (y \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5322,a(flip),b,12523,a),flip(a)].">
      <j1 rule="hyper" parents="373 5322 12523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12525">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * L(L(K(x,z),u,w) \ 1,v5,v6))) = L(K(x,z) * L(K(z,x),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(6092(a,1),12480(a,2,1,2,1))].">
      <j1 rule="para" parents="6092 12480"/>
    </justification>
  </clause>

  <clause id="12526">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * L(L(K(x,z),u,w) \ 1,v5,v6))) = L(a(v6,v5,K(x,z)),u,w)
    ]]></literal>
    <justification jstring="[para(10408(a,1),12525(a,2,1))].">
      <j1 rule="para" parents="10408 12525"/>
    </justification>
  </clause>

  <clause id="12527">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * L(L(K(z,x),u,w),v5,v6))) = L(a(v6,v5,K(x,z)),u,w)
    ]]></literal>
    <justification jstring="[para(7319(a,1),12526(a,1,2,2,2,1))].">
      <j1 rule="para" parents="7319 12526"/>
    </justification>
  </clause>

  <clause id="12528">
    <literal><![CDATA[
      L(K(x,y),z,u) * L(L(K(y,x),z,u),w,v5) = L(a(v5,w,K(x,y)),z,u)
    ]]></literal>
    <justification jstring="[hyper(6346,a,12527,a)].">
      <j1 rule="hyper" parents="6346 12527"/>
    </justification>
  </clause>

  <clause id="12529">
    <literal><![CDATA[
      a(x,y,L(K(z,u),w,v5)) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,11659,a(flip),b,12528,a)].">
      <j1 rule="hyper" parents="64 11659 12528"/>
    </justification>
  </clause>

  <clause id="12530">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),z,w) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(6918(a,1),12529(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6918 12529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12531">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(12059(a,1),12529(a,1,3))].">
      <j1 rule="para" parents="12059 12529"/>
    </justification>
  </clause>

  <clause id="12532">
    <literal><![CDATA[
      a(x,y,a(z,u,K(y,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,12530,a)].">
      <j1 rule="hyper" parents="54 12530"/>
    </justification>
  </clause>

  <clause id="12533">
    <literal><![CDATA[
      a(x,T(y,z),a(u,w,K(y,v5))) = 1
    ]]></literal>
    <justification jstring="[para(8205(a,1),12532(a,1,3,3))].">
      <j1 rule="para" parents="8205 12532"/>
    </justification>
  </clause>

  <clause id="12534">
    <literal><![CDATA[
      (x * y) * a(z,u,K(w,L(v5,y,x))) = x * (y * a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(145,a,12531,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="145 12531 18"/>
    </justification>
  </clause>

  <clause id="12535">
    <literal><![CDATA[
      K(x * ((T(y,y \ 1) * z) \ (((y \ 1) \ 1) \ (T(y,y \ 1) * z))),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(3032(a,1),9271(a,2,1,2))].">
      <j1 rule="para" parents="3032 9271"/>
    </justification>
  </clause>

  <clause id="12536">
    <literal><![CDATA[
      K(x * ((T(y,y \ 1) * z) \ z),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(501(a,1),12535(a,1,1,2,2))].">
      <j1 rule="para" parents="501 12535"/>
    </justification>
  </clause>

  <clause id="12537">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(3154(a,1),12536(a,1,1,2))].">
      <j1 rule="para" parents="3154 12536"/>
    </justification>
  </clause>

  <clause id="12538">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5264,a(flip),b,12537,a),flip(a)].">
      <j1 rule="hyper" parents="64 5264 12537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12539">
    <literal><![CDATA[
      (x \ (x / y)) * (((x \ (x / y)) \ 1) * ((x \ (x / y)) \ z)) = (1 / (T(1,y \ 1) / (T(x \ (x / y),1) \ 1))) * z
    ]]></literal>
    <justification jstring="[para(584(a,1),9320(a,1,2))].">
      <j1 rule="para" parents="584 9320"/>
    </justification>
  </clause>

  <clause id="12540">
    <literal><![CDATA[
      L((x \ (x / y)) \ z,x \ (x / y),x \ (x / y)) = (1 / (T(1,y \ 1) / (T(x \ (x / y),1) \ 1))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,1139,a(flip),b,12539,a)].">
      <j1 rule="hyper" parents="64 1139 12539"/>
    </justification>
  </clause>

  <clause id="12541">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u)) = (x * R(x \ (x * K(y,z)),w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(10333(a,1),10338(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10333 10338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12542">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) * (R(K(y,z),w,v5) * K(z,u)) = (x * R(K(y,z),w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),12541(a,2,1,2,1))].">
      <j1 rule="para" parents="9 12541"/>
    </justification>
  </clause>

  <clause id="12544">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * K(z,v5) = x * (R(K(y,z),u,w) * K(z,v5))
    ]]></literal>
    <justification jstring="[para(10333(a,1),12542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10333 12542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12545">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * K(z,v5) = x * (K(z,v5) * R(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(3323(a,1),12544(a,2,2))].">
      <j1 rule="para" parents="3323 12544"/>
    </justification>
  </clause>

  <clause id="12546">
    <literal><![CDATA[
      x / (K(y,z) * R(K(z,u),w,v5)) = x * (K(z,y) * R(K(u,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,10403,a,b,12545,a)].">
      <j1 rule="hyper" parents="64 10403 12545"/>
    </justification>
  </clause>

  <clause id="12547">
    <literal><![CDATA[
      R(x * (K(y,z) * R(K(z,y),u,u \ 1)),K(z,y),R(K(y,z),u,u \ 1)) = x / a(K(y,z),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(12545(a,1),12299(a,1,1))].">
      <j1 rule="para" parents="12545 12299"/>
    </justification>
  </clause>

  <clause id="12548">
    <literal><![CDATA[
      (x * (K(y,z) * R(K(z,u),w,v5))) * (K(z,y) * R(K(u,z),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(288,a,12546,a),flip(a)].">
      <j1 rule="hyper" parents="288 12546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12549">
    <literal><![CDATA[
      R(x * a(K(y,z),u,u \ 1),K(y,z),R(K(z,y),u,u \ 1)) = x / a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(6172(a,1),12547(a,1,1,2))].">
      <j1 rule="para" parents="6172 12547"/>
    </justification>
  </clause>

  <clause id="12550">
    <literal><![CDATA[
      x / a(K(y,z),u,u \ 1) = x * a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(10342,a,12549,a),flip(a)].">
      <j1 rule="hyper" parents="10342 12549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12551">
    <literal><![CDATA[
      a(K(x,y),z,z \ 1) \ 1 = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(753,a,12550,a)].">
      <j1 rule="hyper" parents="753 12550"/>
    </justification>
  </clause>

  <clause id="12553">
    <literal><![CDATA[
      T(x,a(K(y,z),u,u \ 1)) = x
    ]]></literal>
    <justification jstring="[para(12551(a,1),10573(a,1,2))].">
      <j1 rule="para" parents="12551 10573"/>
    </justification>
  </clause>

  <clause id="12554">
    <literal><![CDATA[
      T(x,a(K(y,z),u \ 1,u)) = x
    ]]></literal>
    <justification jstring="[para(5340(a,1),12553(a,1,2))].">
      <j1 rule="para" parents="5340 12553"/>
    </justification>
  </clause>

  <clause id="12555">
    <literal><![CDATA[
      T(a(K(x,y),z \ 1,z),u) = a(K(x,y),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(55,a,12554,a)].">
      <j1 rule="hyper" parents="55 12554"/>
    </justification>
  </clause>

  <clause id="12556">
    <literal><![CDATA[
      T(a(K(x,y),z \ 1,z),u) = K(x,y) \ R(K(x,y),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,3844,a,b,12555,a),flip(a)].">
      <j1 rule="hyper" parents="373 3844 12555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12557">
    <literal><![CDATA[
      T(K(x,y) * R(K(y,x),z \ 1,z),u) = K(y,x) \ R(K(y,x),z \ 1,z)
    ]]></literal>
    <justification jstring="[para(6184(a,2),12556(a,1,1))].">
      <j1 rule="para" parents="6184 12556"/>
    </justification>
  </clause>

  <clause id="12558">
    <literal><![CDATA[
      K(x,T(y,z)) * R(K(y,T(x,z)),u \ 1,u) = K(y,x) \ R(K(y,x),u \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9934,a,b,12557,a)].">
      <j1 rule="hyper" parents="64 9934 12557"/>
    </justification>
  </clause>

  <clause id="12559">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * R(K(y,T(z,x)),u \ 1,u)) = K(y,z) \ R(K(y,z),u \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,8839,a,b,12558,a)].">
      <j1 rule="hyper" parents="64 8839 12558"/>
    </justification>
  </clause>

  <clause id="12560">
    <literal><![CDATA[
      K(x,K(y,R(z,u \ 1,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(10698,a,12559,a)].">
      <j1 rule="hyper" parents="10698 12559"/>
    </justification>
  </clause>

  <clause id="12561">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(2981(a,1),12560(a,1,2,2))].">
      <j1 rule="para" parents="2981 12560"/>
    </justification>
  </clause>

  <clause id="12562">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8126,a,b,12561,a),flip(a)].">
      <j1 rule="hyper" parents="373 8126 12561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12563">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(675(a,1),12562(a,1,2,2))].">
      <j1 rule="para" parents="675 12562"/>
    </justification>
  </clause>

  <clause id="12564">
    <literal><![CDATA[
      T(x,K(y,z * (u \ 1))) = T(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(143,a,12563,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 12563 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12565">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(6519(a,2),12563(a,1,2))].">
      <j1 rule="para" parents="6519 12563"/>
    </justification>
  </clause>

  <clause id="12566">
    <literal><![CDATA[
      K(x,K(y,z / (u \ 1))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(6521(a,1),12563(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6521 12563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12567">
    <literal><![CDATA[
      T(x,K(y,z * (x \ 1))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8982,a(flip),b,12564,a),flip(a)].">
      <j1 rule="hyper" parents="373 8982 12564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12568">
    <literal><![CDATA[
      T(T(x,K(y,z / u)),(z * (u \ 1)) * y) = T(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(12564(a,1),11128(a,1,1))].">
      <j1 rule="para" parents="12564 11128"/>
    </justification>
  </clause>

  <clause id="12569">
    <literal><![CDATA[
      T(x \ 1,K(y,z * x)) = T(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[para(6521(a,1),12567(a,1,2))].">
      <j1 rule="para" parents="6521 12567"/>
    </justification>
  </clause>

  <clause id="12570">
    <literal><![CDATA[
      K(x,K(y,K(z,y) / u)) = K(x,K(y,1 / u))
    ]]></literal>
    <justification jstring="[para(8542(a,1),12565(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8542 12565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12571">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(9048,a,12566,a)].">
      <j1 rule="hyper" parents="9048 12566"/>
    </justification>
  </clause>

  <clause id="12572">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8437,a,12566,a)].">
      <j1 rule="hyper" parents="8437 12566"/>
    </justification>
  </clause>

  <clause id="12573">
    <literal><![CDATA[
      K(x,K(T(y,z),z * u)) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(7902(a,1),12566(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7902 12566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12574">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) * L((x \ 1) \ K(K(y,z * x),x \ 1),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x))
    ]]></literal>
    <justification jstring="[para(12569(a,1),5944(a,1,1))].">
      <j1 rule="para" parents="12569 5944"/>
    </justification>
  </clause>

  <clause id="12575">
    <literal><![CDATA[
      (K(x,y) / z) * K(u,K(y,1 / z)) = T(K(x,y) / z,K(u,y))
    ]]></literal>
    <justification jstring="[para(12570(a,1),8121(a,1,2))].">
      <j1 rule="para" parents="12570 8121"/>
    </justification>
  </clause>

  <clause id="12576">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),12571(a,2,2,2))].">
      <j1 rule="para" parents="12 12571"/>
    </justification>
  </clause>

  <clause id="12577">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(6525(a,2),12571(a,1,2))].">
      <j1 rule="para" parents="6525 12571"/>
    </justification>
  </clause>

  <clause id="12578">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(8436,a,12576,a)].">
      <j1 rule="hyper" parents="8436 12576"/>
    </justification>
  </clause>

  <clause id="12579">
    <literal><![CDATA[
      a(x,y * ((1 / z) / u),K(w,K(v5,u * z))) = a(x,y,K((1 / z) / u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(12577(a,1),12125(a,1,3))].">
      <j1 rule="para" parents="12577 12125"/>
    </justification>
  </clause>

  <clause id="12580">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9028,a(flip),b,12578,a)].">
      <j1 rule="hyper" parents="64 9028 12578"/>
    </justification>
  </clause>

  <clause id="12582">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / u) = T(z,K(x,y)) / u
    ]]></literal>
    <justification jstring="[para(12580(a,1),9402(a,1,1))].">
      <j1 rule="para" parents="12580 9402"/>
    </justification>
  </clause>

  <clause id="12583">
    <literal><![CDATA[
      R(K(x,K(y,z)),z / u,u) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(12580(a,1),9899(a,1,1))].">
      <j1 rule="para" parents="12580 9899"/>
    </justification>
  </clause>

  <clause id="12584">
    <literal><![CDATA[
      R(K(x,K(y,z)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8126(a,1),12583(a,1,1))].">
      <j1 rule="para" parents="8126 12583"/>
    </justification>
  </clause>

  <clause id="12586">
    <literal><![CDATA[
      K(x,K(y,R(z,x / u,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9773,a(flip),b,12584,a)].">
      <j1 rule="hyper" parents="64 9773 12584"/>
    </justification>
  </clause>

  <clause id="12587">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(79(a,1),12586(a,1,2,2,2))].">
      <j1 rule="para" parents="79 12586"/>
    </justification>
  </clause>

  <clause id="12588">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,K(x,y)) / u) = z / u
    ]]></literal>
    <justification jstring="[hyper(8148,a,12582,a)].">
      <j1 rule="hyper" parents="8148 12582"/>
    </justification>
  </clause>

  <clause id="12589">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(y,K(z,x)) * u
    ]]></literal>
    <justification jstring="[hyper(740,a,12582,a),flip(a)].">
      <j1 rule="hyper" parents="740 12582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12591">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,K(z,y)) / u) = x / u
    ]]></literal>
    <justification jstring="[para(8088(a,1),12588(a,1,1))].">
      <j1 rule="para" parents="8088 12588"/>
    </justification>
  </clause>

  <clause id="12592">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8110(a,1),12589(a,2,1))].">
      <j1 rule="para" parents="8110 12589"/>
    </justification>
  </clause>

  <clause id="12593">
    <literal><![CDATA[
      K((T(x,y) / z) / (x / z),u) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(9404,a,12591,a)].">
      <j1 rule="hyper" parents="9404 12591"/>
    </justification>
  </clause>

  <clause id="12594">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ T(x,K(y,z)) = u \ x
    ]]></literal>
    <justification jstring="[hyper(215,a,12592,a)].">
      <j1 rule="hyper" parents="215 12592"/>
    </justification>
  </clause>

  <clause id="12595">
    <literal><![CDATA[
      K((T(x \ L(x,y,z),x * u) / w) / ((x \ L(x,y,z)) / w),v5) = K(x \ L(x,y,z),K(u * x,v5))
    ]]></literal>
    <justification jstring="[para(12453(a,1),12593(a,1,1,1,1))].">
      <j1 rule="para" parents="12453 12593"/>
    </justification>
  </clause>

  <clause id="12596">
    <literal><![CDATA[
      L(x \ y,x,K(y,K(z,u))) = x \ y
    ]]></literal>
    <justification jstring="[hyper(5850,a,12594,a)].">
      <j1 rule="hyper" parents="5850 12594"/>
    </justification>
  </clause>

  <clause id="12597">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,u \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,12596,a)].">
      <j1 rule="hyper" parents="54 12596"/>
    </justification>
  </clause>

  <clause id="12598">
    <literal><![CDATA[
      a(K(x * y,K(z,u)),x,y) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),12597(a,1,3))].">
      <j1 rule="para" parents="9 12597"/>
    </justification>
  </clause>

  <clause id="12599">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = 1
    ]]></literal>
    <justification jstring="[para(7830(a,2),12597(a,1,1))].">
      <j1 rule="para" parents="7830 12597"/>
    </justification>
  </clause>

  <clause id="12600">
    <literal><![CDATA[
      a(K(x,K(y,z * u)),z,u) = 1
    ]]></literal>
    <justification jstring="[para(8088(a,1),12598(a,1,1))].">
      <j1 rule="para" parents="8088 12598"/>
    </justification>
  </clause>

  <clause id="12601">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = K(w,K(v5,v6)) * K(w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,8140,a,b,12599,a),flip(a)].">
      <j1 rule="hyper" parents="373 8140 12599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12602">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(11112(a,1),12573(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11112 12573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12603">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(9037,a,12602,a)].">
      <j1 rule="hyper" parents="9037 12602"/>
    </justification>
  </clause>

  <clause id="12604">
    <literal><![CDATA[
      K(x,K(y,((z / u) \ 1) \ u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),12602(a,2,2,2))].">
      <j1 rule="para" parents="12 12602"/>
    </justification>
  </clause>

  <clause id="12605">
    <literal><![CDATA[
      x * (y * K(z,K(u,x * y))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[para(12602(a,1),8134(a,1,2,2))].">
      <j1 rule="para" parents="12602 8134"/>
    </justification>
  </clause>

  <clause id="12606">
    <literal><![CDATA[
      K(x,K(y \ (z * u),z * u)) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9036,a(flip),b,12603,a),flip(a)].">
      <j1 rule="hyper" parents="64 9036 12603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12607">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,x))
    ]]></literal>
    <justification jstring="[para(12604(a,1),9100(a,2,2))].">
      <j1 rule="para" parents="12604 9100"/>
    </justification>
  </clause>

  <clause id="12609">
    <literal><![CDATA[
      T(x * y,K(z,L(u,y,x))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12174,a(flip),b,12605,a)].">
      <j1 rule="hyper" parents="64 12174 12605"/>
    </justification>
  </clause>

  <clause id="12610">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * y,K(z,u)) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(12609(a,1),12082(a,1,2))].">
      <j1 rule="para" parents="12609 12082"/>
    </justification>
  </clause>

  <clause id="12611">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = K(w,K(v5,R(v6,v7,v7 \ w))) * K(v6,K(w,v5))
    ]]></literal>
    <justification jstring="[para(12587(a,1),12601(a,2,2))].">
      <j1 rule="para" parents="12587 12601"/>
    </justification>
  </clause>

  <clause id="12612">
    <literal><![CDATA[
      T(x * y,K(z,u)) \ (x * (y * K(z,u))) = T(L(K(z,u),y,x),T(x * y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(12610(a,1),117(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12610 117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12613">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),T(x * y,K(z,u)) \ (x * (y * K(z,u)))) = T(x * y,K(z,u)) / ((x * (y * K(z,u))) / L(K(z,u),y,x))
    ]]></literal>
    <justification jstring="[para(12610(a,1),5966(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12610 5966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12614">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = T(K(x,y),1 / z) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,8106,a(flip),b,12575,a),flip(a)].">
      <j1 rule="hyper" parents="64 8106 12575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12615">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = K(x,T(y,1 / z)) / z
    ]]></literal>
    <justification jstring="[para(7867(a,2),12614(a,2,1))].">
      <j1 rule="para" parents="7867 12614"/>
    </justification>
  </clause>

  <clause id="12616">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = K(x,T(y,z)) / z
    ]]></literal>
    <justification jstring="[para(11167(a,1),12615(a,2,1))].">
      <j1 rule="para" parents="11167 12615"/>
    </justification>
  </clause>

  <clause id="12617">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) * K(u,z) = K(x,T(y,z)) / T(z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,12616,a,b,6242,a)].">
      <j1 rule="hyper" parents="144 12616 6242"/>
    </justification>
  </clause>

  <clause id="12618">
    <literal><![CDATA[
      K(x,K(y * z,(y \ u) \ z)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8994,a,12606,a),flip(a)].">
      <j1 rule="hyper" parents="8994 12606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12619">
    <literal><![CDATA[
      K(x,K(y * z,z \ (y \ u))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(9037,a,12618,a)].">
      <j1 rule="hyper" parents="9037 12618"/>
    </justification>
  </clause>

  <clause id="12620">
    <literal><![CDATA[
      K(x,K((y * z) * u,u \ ((y * z) \ (y * (z * u))))) = K(x,K(y * (z * u),a(y,z,u) * (y * (z * u))))
    ]]></literal>
    <justification jstring="[para(6144(a,2),12619(a,2,2))].">
      <j1 rule="para" parents="6144 12619"/>
    </justification>
  </clause>

  <clause id="12621">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = K(w,K(v5,R(v6,v7,v7 \ w))) * K(w,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(8110(a,2),12611(a,2,2))].">
      <j1 rule="para" parents="8110 12611"/>
    </justification>
  </clause>

  <clause id="12622">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,u \ x) = K(w,K(v5,R(v6,v7,v7 \ w))) * K(w,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(7830(a,1),12621(a,1,1))].">
      <j1 rule="para" parents="7830 12621"/>
    </justification>
  </clause>

  <clause id="12623">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x)) * K(z,y)) = a(K(w,K(v5,v6)),v7,v7 \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,12362,a(flip),b,12622,a)].">
      <j1 rule="hyper" parents="373 12362 12622"/>
    </justification>
  </clause>

  <clause id="12624">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x)) * K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,12600,a(flip),b,12623,a),flip(a)].">
      <j1 rule="hyper" parents="373 12600 12623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12625">
    <literal><![CDATA[
      K(x,K(y,z) * K(z,R(y,u,u \ x))) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,12378,a(flip),b,12624,a)].">
      <j1 rule="hyper" parents="64 12378 12624"/>
    </justification>
  </clause>

  <clause id="12626">
    <literal><![CDATA[
      K(x * y,K(z,u) * K(u,R(z,x,y))) = 1
    ]]></literal>
    <justification jstring="[para(9(a,1),12625(a,1,2,2,2,3))].">
      <j1 rule="para" parents="9 12625"/>
    </justification>
  </clause>

  <clause id="12627">
    <literal><![CDATA[
      T(x * y,K(z,u)) \ (x * (y * K(z,u))) = L(T(K(z,u),x * y),y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,4634,a(flip),b,12612,a),flip(a)].">
      <j1 rule="hyper" parents="373 4634 12612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12628">
    <literal><![CDATA[
      T(x * y,K(z,u)) \ (x * (y * K(z,u))) = L(K(z,T(u,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(7867(a,2),12627(a,2,1))].">
      <j1 rule="para" parents="7867 12627"/>
    </justification>
  </clause>

  <clause id="12629">
    <literal><![CDATA[
      K(K(((x \ L(x,y,z)) / u) / (u \ 1),x * w),v5) = K(x \ L(x,y,z),K(w * x,v5))
    ]]></literal>
    <justification jstring="[para(6163(a,2),12595(a,1,1))].">
      <j1 rule="para" parents="6163 12595"/>
    </justification>
  </clause>

  <clause id="12630">
    <literal><![CDATA[
      K(x,K(((y \ L(y,z,u)) / w) / (w \ 1),y * v5)) = K(y \ L(y,z,u),K(v5 * y,x))
    ]]></literal>
    <justification jstring="[hyper(8438,a,12629,a)].">
      <j1 rule="hyper" parents="8438 12629"/>
    </justification>
  </clause>

  <clause id="12631">
    <literal><![CDATA[
      K(x,K(y * z,((y \ L(y,u,w)) / v5) * v5)) = K(y \ L(y,u,w),K(z * y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,12572,a(flip),b,12630,a)].">
      <j1 rule="hyper" parents="64 12572 12630"/>
    </justification>
  </clause>

  <clause id="12632">
    <literal><![CDATA[
      K(x \ L(x,y,z),K(u * x,w)) = K(w,K(x * u,x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(12(a,1),12631(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 12631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12633">
    <literal><![CDATA[
      K(x,K(y * z,y \ L(y,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * y,y \ L(y,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(12632(a,1),8434(a,1))].">
      <j1 rule="para" parents="12632 8434"/>
    </justification>
  </clause>

  <clause id="12634">
    <literal><![CDATA[
      K(x,K(y * (z * u),a(y,z,u) * (y * (z * u)))) = K(x,K((y * z) * u,u \ L(u,z,y)))
    ]]></literal>
    <justification jstring="[para(18(a,2),12620(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="18 12620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12635">
    <literal><![CDATA[
      T((x \ ((y * x) * z)) * K(x,y),K(x,y)) * T(u,x \ ((x * y) * z)) = u * (T(x \ ((y * x) * z),K(x,y)) * K(x,y))
    ]]></literal>
    <justification jstring="[para(10018(a,2),11250(a,1,1))].">
      <j1 rule="para" parents="10018 11250"/>
    </justification>
  </clause>

  <clause id="12636">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) * L((x \ 1) \ K(y,K(z * x,x \ 1)),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x))
    ]]></literal>
    <justification jstring="[para(8092(a,1),12574(a,1,2,1,2))].">
      <j1 rule="para" parents="8092 12574"/>
    </justification>
  </clause>

  <clause id="12637">
    <literal><![CDATA[
      T(T(x \ ((x * y) * z),K(x,y)),K(x,y)) * T(u,x \ ((x * y) * z)) = u * (T(x \ ((y * x) * z),K(x,y)) * K(x,y))
    ]]></literal>
    <justification jstring="[para(10969(a,2),12635(a,1,1,1))].">
      <j1 rule="para" parents="10969 12635"/>
    </justification>
  </clause>

  <clause id="12638">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) * L((x \ 1) \ K(y,K(x,z * x)),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x))
    ]]></literal>
    <justification jstring="[para(9008(a,1),12636(a,1,2,1,2))].">
      <j1 rule="para" parents="9008 12636"/>
    </justification>
  </clause>

  <clause id="12639">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) * L((x \ 1) \ K(x,K(y,z)),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x))
    ]]></literal>
    <justification jstring="[para(8970(a,1),12638(a,1,2,1,2))].">
      <j1 rule="para" parents="8970 12638"/>
    </justification>
  </clause>

  <clause id="12640">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) * L(T(T(x,K(y,z)),x \ 1),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x))
    ]]></literal>
    <justification jstring="[para(5730(a,2),12639(a,1,2,1))].">
      <j1 rule="para" parents="5730 12639"/>
    </justification>
  </clause>

  <clause id="12641">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) * (L(T(x,K(y,z)),u,w) * (x \ 1)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x))
    ]]></literal>
    <justification jstring="[hyper(6492,a,12640,a)].">
      <j1 rule="hyper" parents="6492 12640"/>
    </justification>
  </clause>

  <clause id="12642">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w * x)) = K(x,K(u,w)) * (L(T(x,K(u,w)),y,z) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(9024(a,1),12641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9024 12641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12643">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w * x)) = K(x,K(u,w)) * (x \ L(T(x,K(u,w)),y,z))
    ]]></literal>
    <justification jstring="[para(2464(a,1),12642(a,2,2))].">
      <j1 rule="para" parents="2464 12642"/>
    </justification>
  </clause>

  <clause id="12644">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w * x)) = T(x,K(u,w)) \ L(T(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,8147,a(flip),b,12643,a),flip(a)].">
      <j1 rule="hyper" parents="373 8147 12643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12645">
    <literal><![CDATA[
      (x \ ((x * y) * z)) * T(u,x \ ((x * y) * z)) = u * (T(x \ ((y * x) * z),K(x,y)) * K(x,y))
    ]]></literal>
    <justification jstring="[para(8157(a,1),12637(a,1,1))].">
      <j1 rule="para" parents="8157 12637"/>
    </justification>
  </clause>

  <clause id="12647">
    <literal><![CDATA[
      K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u) = K((x \ u) \ u,w \ (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),7670(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 7670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12648">
    <literal><![CDATA[
      K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u) = K(x,T(w \ (R(x,y,z) * u),u))
    ]]></literal>
    <justification jstring="[hyper(373,a,7871,a(flip),b,12647,a),flip(a)].">
      <j1 rule="hyper" parents="373 7871 12647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12650">
    <literal><![CDATA[
      K(T(x,R(x,y,z) * (x \ u)),(R(x,y,z) \ w) \ u) = K(x,(R(x,y,z) * u) / w)
    ]]></literal>
    <justification jstring="[hyper(373,a,9782,a(flip),b,12648,a),flip(a)].">
      <j1 rule="hyper" parents="373 9782 12648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12651">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,R(x,y,z) * w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(9531,a,12650,a)].">
      <j1 rule="hyper" parents="9531 12650"/>
    </justification>
  </clause>

  <clause id="12652">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(9786,a,12651,a)].">
      <j1 rule="hyper" parents="9786 12651"/>
    </justification>
  </clause>

  <clause id="12653">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,u / (R(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(8699,a,12652,a),flip(a)].">
      <j1 rule="hyper" parents="8699 12652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12655">
    <literal><![CDATA[
      K(x,R(x,y,z) / (u / w)) = K(x,w / (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(10736,a,12653,a)].">
      <j1 rule="hyper" parents="10736 12653"/>
    </justification>
  </clause>

  <clause id="12656">
    <literal><![CDATA[
      K(x,(y * z) / (R(x,y,z) \ u)) = K(x,((x * y) * z) / u)
    ]]></literal>
    <justification jstring="[para(111(a,1),12653(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="111 12653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12657">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(8455,a,12655,a),flip(a)].">
      <j1 rule="hyper" parents="8455 12655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12658">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9795,a,b,12657,a)].">
      <j1 rule="hyper" parents="64 9795 12657"/>
    </justification>
  </clause>

  <clause id="12659">
    <literal><![CDATA[
      K(R(x,K(y * z,x) * y,z),u \ x) = K(x,(((u * y) * z) / (y * z)) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12307,a,b,12658,a)].">
      <j1 rule="hyper" parents="64 12307 12658"/>
    </justification>
  </clause>

  <clause id="12660">
    <literal><![CDATA[
      K(R(x,K(y * z,x) * y,z),u \ x) = K(x,R(u,y,z) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(20(a,2),12659(a,2,2,1))].">
      <j1 rule="para" parents="20 12659"/>
    </justification>
  </clause>

  <clause id="12661">
    <literal><![CDATA[
      K(x,R(y,z,u) \ R(x,z,u)) = K(R(x,z,u),y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9834,a(flip),b,12660,a),flip(a)].">
      <j1 rule="hyper" parents="64 9834 12660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12663">
    <literal><![CDATA[
      K(R(K(x,y) * R(K(y,x),z,u),K(y,x),z * u),((z * u) \ K(x,y)) \ 1) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(6156(a,1),9555(a,1,1,1))].">
      <j1 rule="para" parents="6156 9555"/>
    </justification>
  </clause>

  <clause id="12664">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,T(y * (x / y),(x / y) \ 1)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(7232(a,1),11880(a,1,1,1))].">
      <j1 rule="para" parents="7232 11880"/>
    </justification>
  </clause>

  <clause id="12665">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,y * (T(x,(x / y) \ 1) / y)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(5431(a,1),12664(a,1,3))].">
      <j1 rule="para" parents="5431 12664"/>
    </justification>
  </clause>

  <clause id="12666">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,y * (T(x,x \ y) / y)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(4579(a,1),12665(a,1,3,2,1))].">
      <j1 rule="para" parents="4579 12665"/>
    </justification>
  </clause>

  <clause id="12667">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,(x \ y) \ T(y,y \ x)) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[para(7338(a,2),12666(a,1,3))].">
      <j1 rule="para" parents="7338 12666"/>
    </justification>
  </clause>

  <clause id="12668">
    <literal><![CDATA[
      K(x,L(T(y \ 1,T(y * z,z)) \ u,u,((y * z) \ z) \ z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(7428(a,1),12165(a,1,2,1,1))].">
      <j1 rule="para" parents="7428 12165"/>
    </justification>
  </clause>

  <clause id="12669">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z * y) \ u,u,((y * z) \ z) \ z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(11103(a,1),12668(a,1,2,1,1))].">
      <j1 rule="para" parents="11103 12668"/>
    </justification>
  </clause>

  <clause id="12670">
    <literal><![CDATA[
      K(K(x,y) * R(K(y,x),z,u),((z * u) \ K(x,y)) \ 1) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(11718(a,1),12663(a,1,1))].">
      <j1 rule="para" parents="11718 12663"/>
    </justification>
  </clause>

  <clause id="12671">
    <literal><![CDATA[
      K(K(x,y) * R(K(y,x),z,u),K(y,x) * (z * u)) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,6714,a(flip),b,12670,a)].">
      <j1 rule="hyper" parents="64 6714 12670"/>
    </justification>
  </clause>

  <clause id="12673">
    <literal><![CDATA[
      K(K(x,y) * K(y,R(x,z,u)),K(y,x) * (z * u)) = K(a(K(y,x),z,u),((z * u) \ K(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,12397,a(flip),b,12671,a)].">
      <j1 rule="hyper" parents="64 12397 12671"/>
    </justification>
  </clause>

  <clause id="12674">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = K(z * u,K(x,R(y,z,u)) * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(12392,a,12673,a),flip(a)].">
      <j1 rule="hyper" parents="12392 12673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12675">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = K(z * u,K(x,y) * K(y,R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,12378,a(flip),b,12674,a),flip(a)].">
      <j1 rule="hyper" parents="373 12378 12674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12676">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,12626,a(flip),b,12675,a),flip(a)].">
      <j1 rule="hyper" parents="373 12626 12675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12678">
    <literal><![CDATA[
      K(a(K(x,y),z,u),K(x,y) * (z * u)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,6714,a(flip),b,12676,a)].">
      <j1 rule="hyper" parents="64 6714 12676"/>
    </justification>
  </clause>

  <clause id="12679">
    <literal><![CDATA[
      1 * (((K(x,y) * z) * u) / (K(x,y) * (z * u))) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(12678(a,1),5958(a,1,1))].">
      <j1 rule="para" parents="12678 5958"/>
    </justification>
  </clause>

  <clause id="12680">
    <literal><![CDATA[
      1 * (K(x,y) * R(K(y,x),z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11719(a,1),12679(a,1,2))].">
      <j1 rule="para" parents="11719 12679"/>
    </justification>
  </clause>

  <clause id="12681">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(147,a,12680,a)].">
      <j1 rule="hyper" parents="147 12680"/>
    </justification>
  </clause>

  <clause id="12682">
    <literal><![CDATA[
      1 * (K(x,K(y,z)) * R(K(x,K(y,z)),u,w)) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(8123(a,1),12680(a,1,2,1))].">
      <j1 rule="para" parents="8123 12680"/>
    </justification>
  </clause>

  <clause id="12683">
    <literal><![CDATA[
      K(x,y) * a(K(x,y),z,u) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(6187,a,12681,a)].">
      <j1 rule="hyper" parents="6187 12681"/>
    </justification>
  </clause>

  <clause id="12684">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(3327,a,12681,a)].">
      <j1 rule="hyper" parents="3327 12681"/>
    </justification>
  </clause>

  <clause id="12685">
    <literal><![CDATA[
      T(x,y) * a(K(x,y),z,u) = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,12681,a(flip),b,6155,a)].">
      <j1 rule="hyper" parents="145 12681 6155"/>
    </justification>
  </clause>

  <clause id="12687">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(9660(a,1),12681(a,1,2))].">
      <j1 rule="para" parents="9660 12681"/>
    </justification>
  </clause>

  <clause id="12688">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z * x,u)
    ]]></literal>
    <justification jstring="[para(9828(a,1),12681(a,1,2))].">
      <j1 rule="para" parents="9828 12681"/>
    </justification>
  </clause>

  <clause id="12689">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(z,y)) = T(x,a(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(12681(a,1),12381(a,2,2))].">
      <j1 rule="para" parents="12681 12381"/>
    </justification>
  </clause>

  <clause id="12690">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * (K(y,z) * R(K(z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[para(12681(a,1),12548(a,1,1,2))].">
      <j1 rule="para" parents="12681 12548"/>
    </justification>
  </clause>

  <clause id="12691">
    <literal><![CDATA[
      (a(K(x,T(y,z)),u,w) * K(x,y)) * (K(y,x) * z) = R(K(x,T(y,z)),u,w) * (z * K(y,x))
    ]]></literal>
    <justification jstring="[para(12683(a,1),10084(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12683 10084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12692">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * (z * K(y,x)) = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(12684(a,1),10402(a,2,2))].">
      <j1 rule="para" parents="12684 10402"/>
    </justification>
  </clause>

  <clause id="12693">
    <literal><![CDATA[
      T(x,y) * a(K(x,y),z,u) != x * w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(12685(a,2),44(a,1))].">
      <j1 rule="para" parents="12685 44"/>
    </justification>
  </clause>

  <clause id="12694">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * a(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(12681(a,1),12690(a,1,2))].">
      <j1 rule="para" parents="12681 12690"/>
    </justification>
  </clause>

  <clause id="12696">
    <literal><![CDATA[
      (T(x,x \ y) * a(K(z,u),w,v5)) \ ((x \ y) \ y) = a(K(u,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(139,a,116,a(flip),b,12694,a)].">
      <j1 rule="hyper" parents="139 116 12694"/>
    </justification>
  </clause>

  <clause id="12698">
    <literal><![CDATA[
      x * a(K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 * a(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(12694(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="12694 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12699">
    <literal><![CDATA[
      1 * (K(x,K(y,z)) * K(y,K(z,R(x,u,w)))) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(9773(a,1),12682(a,1,2,2))].">
      <j1 rule="para" parents="9773 12682"/>
    </justification>
  </clause>

  <clause id="12700">
    <literal><![CDATA[
      1 * K(x,K(y,z) * K(R(z,u,w),y)) = a(K(z,K(y,x)),u,w)
    ]]></literal>
    <justification jstring="[para(12394(a,1),12699(a,1,2))].">
      <j1 rule="para" parents="12394 12699"/>
    </justification>
  </clause>

  <clause id="12701">
    <literal><![CDATA[
      (a(K(x,T(y,z)),u,w) * K(x,y)) * (K(y,x) * z) = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,12692,a(flip),b,12691,a),flip(a)].">
      <j1 rule="hyper" parents="373 12692 12691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12702">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ T(1 / y,1 / (1 / ((x * y) / x))) = (1 / y) * (1 / (1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(9431(a,1),6457(a,2,1))].">
      <j1 rule="para" parents="9431 6457"/>
    </justification>
  </clause>

  <clause id="12703">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ T(1 / y,(x * y) / x) = (1 / y) * (1 / (1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(3869(a,1),12702(a,1,2))].">
      <j1 rule="para" parents="3869 12702"/>
    </justification>
  </clause>

  <clause id="12704">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (1 / ((y * x) / y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(4040(a,1),12703(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4040 12703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12705">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,12296,a(flip),b,12704,a),flip(a)].">
      <j1 rule="hyper" parents="373 12296 12704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12707">
    <literal><![CDATA[
      (K(x * x,y) * ((x * x) \ y)) * T(z,y / (x * x)) = z * (T((x * x) \ y,K(x * x,y)) * K(x * x,y))
    ]]></literal>
    <justification jstring="[para(8172(a,1),11249(a,1,1))].">
      <j1 rule="para" parents="8172 11249"/>
    </justification>
  </clause>

  <clause id="12708">
    <literal><![CDATA[
      x * (T((y * y) \ z,K(y * y,z)) * K(y * y,z)) = (z / (y * y)) * T(x,z / (y * y))
    ]]></literal>
    <justification jstring="[para(7723(a,1),12707(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7723 12707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12709">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * R(R(x * T(x \ 1,u),y,z) \ 1,w,v5) = R((x * T(x \ 1,u)) * R(K(u,x \ 1),w,v5),y,z)
    ]]></literal>
    <justification jstring="[para(5990(a,1),6440(a,1,1))].">
      <j1 rule="para" parents="5990 6440"/>
    </justification>
  </clause>

  <clause id="12710">
    <literal><![CDATA[
      R((x * T(x \ 1,y)) * R(K(y,x \ 1),z,u),w,v5) = K(R(x,w,v5) \ 1,y) * R(K(R(x,w,v5) \ 1,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(5990(a,1),12709(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5990 12709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12711">
    <literal><![CDATA[
      R((x * T(x \ 1,y)) * R(K(y,x \ 1),z,u),w,v5) = K(R(x,w,v5) \ 1,y) * R(K(y,R(x,w,v5) \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(6092(a,1),12710(a,2,2,1))].">
      <j1 rule="para" parents="6092 12710"/>
    </justification>
  </clause>

  <clause id="12712">
    <literal><![CDATA[
      R((x * T(x \ 1,y)) * R(K(y,x \ 1),z,u),w,v5) = K(R(x,w,v5) \ 1,y) * K(y,R(R(x,w,v5),z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(9660(a,1),12711(a,2,2))].">
      <j1 rule="para" parents="9660 12711"/>
    </justification>
  </clause>

  <clause id="12713">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * K(u,R(R(x,y,z),w,v5) \ 1) = R(K(x \ 1,u) * R(K(u,x \ 1),w,v5),y,z)
    ]]></literal>
    <justification jstring="[para(5743(a,1),12712(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5743 12712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12714">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * K(u,R(R(x,y,z),w,v5) \ 1) = R(K(x \ 1,u) * K(u,R(x,w,v5) \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(9660(a,1),12713(a,2,1,2))].">
      <j1 rule="para" parents="9660 12713"/>
    </justification>
  </clause>

  <clause id="12715">
    <literal><![CDATA[
      R(K(x \ 1,y) * K(y,R(x,z,u) \ 1),w,v5) = a(K(y,R(x,w,v5) \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12687,a(flip),b,12714,a),flip(a)].">
      <j1 rule="hyper" parents="64 12687 12714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12716">
    <literal><![CDATA[
      K(x / y,z) * T(z,T(z * ((x / y) * ((x / y) \ ((y / x) \ 1))),x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(6580(a,1),11393(a,1,1))].">
      <j1 rule="para" parents="6580 11393"/>
    </justification>
  </clause>

  <clause id="12717">
    <literal><![CDATA[
      K(x / y,z) * T(z,T(z * ((y / x) \ 1),x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),12716(a,1,2,2,1,2))].">
      <j1 rule="para" parents="10 12716"/>
    </justification>
  </clause>

  <clause id="12719">
    <literal><![CDATA[
      K(x / y,z) * T(z,T((y / x) \ z,x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(9124(a,1),12717(a,1,2))].">
      <j1 rule="para" parents="9124 12717"/>
    </justification>
  </clause>

  <clause id="12720">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * L(x,y,z)),L(x,y,z)) = K(u * x,L(x,y,z)) * K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5924(a,1),11552(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5924 11552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12721">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),T(x * y,K(z,u)) \ (x * (y * K(z,u)))) = T(x * y,K(z,u)) / (x * y)
    ]]></literal>
    <justification jstring="[para(213(a,1),12613(a,2,2))].">
      <j1 rule="para" parents="213 12613"/>
    </justification>
  </clause>

  <clause id="12722">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),T(x * y,K(z,u)) \ (x * (y * K(z,u)))) = K(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,5739,a,b,12721,a),flip(a)].">
      <j1 rule="hyper" parents="373 5739 12721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12724">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),T(x * y,K(z,u)) \ (x * (y * K(z,u)))) = K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8110,a,b,12722,a),flip(a)].">
      <j1 rule="hyper" parents="373 8110 12722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12725">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),L(K(z,T(u,x * y)),y,x)) = K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[para(12628(a,1),12724(a,1,2))].">
      <j1 rule="para" parents="12628 12724"/>
    </justification>
  </clause>

  <clause id="12726">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),K(z,L(T(u,x * y),y,x))) = K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[para(12059(a,1),12725(a,1,2))].">
      <j1 rule="para" parents="12059 12725"/>
    </justification>
  </clause>

  <clause id="12727">
    <literal><![CDATA[
      K(x,K(T(y * z,K(x,u)),L(T(u,y * z),z,y))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8436,a,12726,a)].">
      <j1 rule="hyper" parents="8436 12726"/>
    </justification>
  </clause>

  <clause id="12728">
    <literal><![CDATA[
      K(x,K(y * z,L(T(u,y * z),z,y))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(7485,a,12727,a)].">
      <j1 rule="hyper" parents="7485 12727"/>
    </justification>
  </clause>

  <clause id="12729">
    <literal><![CDATA[
      K(x,K(y * z,L(u,z,y))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[para(5925(a,1),12728(a,1,2))].">
      <j1 rule="para" parents="5925 12728"/>
    </justification>
  </clause>

  <clause id="12730">
    <literal><![CDATA[
      x / (T(K(y,z),x) * (((y \ 1) * x) * R(y,y \ 1,x))) = K(z,((y \ 1) * x) \ x) * K(((y \ 1) * x) \ x,(y \ 1) * x)
    ]]></literal>
    <justification jstring="[para(7014(a,1),10015(a,1,2,1))].">
      <j1 rule="para" parents="7014 10015"/>
    </justification>
  </clause>

  <clause id="12731">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ z) * K(((y \ 1) * z) \ z,(y \ 1) * z) = z / (T(K(y,x),z) * ((y \ z) * y))
    ]]></literal>
    <justification jstring="[para(4420(a,1),12730(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4420 12730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12732">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ z) * K(((y \ 1) * z) \ z,(y \ 1) * z) = z / ((y \ z) * T(y,x))
    ]]></literal>
    <justification jstring="[para(8372(a,1),12731(a,2,2))].">
      <j1 rule="para" parents="8372 12731"/>
    </justification>
  </clause>

  <clause id="12733">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ (y * z)) * K(((y \ 1) * (y * z)) \ (y * z),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),12732(a,2,2,1))].">
      <j1 rule="para" parents="9 12732"/>
    </justification>
  </clause>

  <clause id="12734">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,z * y)) * K(((y \ 1) * (y * z)) \ (y * z),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(11484(a,1),12733(a,1,1,2))].">
      <j1 rule="para" parents="11484 12733"/>
    </justification>
  </clause>

  <clause id="12735">
    <literal><![CDATA[
      T(K(x,y),z) * K(((y \ 1) * (y * z)) \ (y * z),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(9768(a,1),12734(a,1,1))].">
      <j1 rule="para" parents="9768 12734"/>
    </justification>
  </clause>

  <clause id="12737">
    <literal><![CDATA[
      T(K(x,y),z) * K(R(T(y,z),y \ 1,z * y),(y \ 1) * (y * z)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(11484(a,1),12735(a,1,2,1))].">
      <j1 rule="para" parents="11484 12735"/>
    </justification>
  </clause>

  <clause id="12738">
    <literal><![CDATA[
      T(K(x,y),z) * K(R(T(y,z),y \ 1,z * y),L(z,y,y \ 1)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(6545(a,1),12737(a,1,2))].">
      <j1 rule="para" parents="6545 12737"/>
    </justification>
  </clause>

  <clause id="12739">
    <literal><![CDATA[
      T(K(x,y),z) * K(R(y,y \ 1,z * y),L(z,y,y \ 1)) = (y * z) / (z * T(y,x))
    ]]></literal>
    <justification jstring="[para(8670(a,1),12738(a,1,2))].">
      <j1 rule="para" parents="8670 12738"/>
    </justification>
  </clause>

  <clause id="12740">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x),y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7766(a,1),12739(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7766 12739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12741">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x) * K(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,7797,a,b,12740,a),flip(a)].">
      <j1 rule="hyper" parents="373 7797 12740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12743">
    <literal><![CDATA[
      R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = K(u,u * x) * T(u * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(9701(a,1),7638(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9701 7638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12744">
    <literal><![CDATA[
      R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = T(K(u,u * x) * (u * R(x,y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,7769,a,b,12743,a),flip(a)].">
      <j1 rule="hyper" parents="373 7769 12743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12746">
    <literal><![CDATA[
      R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = T(T(u,u * x) * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5755(a,1),12744(a,2,1))].">
      <j1 rule="para" parents="5755 12744"/>
    </justification>
  </clause>

  <clause id="12747">
    <literal><![CDATA[
      R(x,y,z) * T(R(u,R(x,y,z),u),R(u,R(x,y,z),u) * x) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,9635,a(flip),b,12746,a),flip(a)].">
      <j1 rule="hyper" parents="373 9635 12746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12748">
    <literal><![CDATA[
      R(x,y,z) * R(T(u,x * R(u,R(x,y,z),u)),R(x,y,z),u) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[para(4691(a,2),12747(a,1,2))].">
      <j1 rule="para" parents="4691 12747"/>
    </justification>
  </clause>

  <clause id="12749">
    <literal><![CDATA[
      R(x,y,z) * R(T(u,u * x),R(x,y,z),u) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[para(9697(a,1),12748(a,1,2,1))].">
      <j1 rule="para" parents="9697 12748"/>
    </justification>
  </clause>

  <clause id="12750">
    <literal><![CDATA[
      R(x,y,z) * R(T(u,x * u),R(x,y,z),u) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[para(4683(a,2),12749(a,1,2,1))].">
      <j1 rule="para" parents="4683 12749"/>
    </justification>
  </clause>

  <clause id="12752">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K((K(x,y) * K(z,x)) \ u,K(x,y)) * K((K(x,y) * K(z,x)) \ u,K(x,z))) = ((K(y,x) * (K(x,z) * u)) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(9996(a,1),12366(a,2,1,1))].">
      <j1 rule="para" parents="9996 12366"/>
    </justification>
  </clause>

  <clause id="12753">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K((K(x,y) * K(z,x)) \ u,K(x,y)) * K((K(x,y) * K(z,x)) \ u,K(x,z))) = T(K(x,z) * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,12501,a(flip),b,12752,a),flip(a)].">
      <j1 rule="hyper" parents="373 12501 12752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12754">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K(K(y,x) * (K(x,z) * u),K(x,y)) * K((K(x,y) * K(z,x)) \ u,K(x,z))) = T(K(x,z) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(9996(a,1),12753(a,1,2,1,1))].">
      <j1 rule="para" parents="9996 12753"/>
    </justification>
  </clause>

  <clause id="12755">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K(x,K(u,y)) * K((K(x,y) * K(z,x)) \ u,K(x,z))) = T(K(x,z) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(8786(a,1),12754(a,1,2,1))].">
      <j1 rule="para" parents="8786 12754"/>
    </justification>
  </clause>

  <clause id="12756">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K(x,K(y,u)) * K((K(x,y) * K(z,x)) \ u,K(x,z))) = T(K(x,z) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(8126(a,1),12755(a,1,2,1))].">
      <j1 rule="para" parents="8126 12755"/>
    </justification>
  </clause>

  <clause id="12758">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K(x,K(y,u)) * K(K(y,x) * (K(x,z) * u),K(x,z))) = T(K(x,z) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(9996(a,1),12756(a,1,2,2,1))].">
      <j1 rule="para" parents="9996 12756"/>
    </justification>
  </clause>

  <clause id="12759">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ (K(x,K(y,u)) * K(x,K(u,z))) = T(K(x,z) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(8786(a,1),12758(a,1,2,2))].">
      <j1 rule="para" parents="8786 12758"/>
    </justification>
  </clause>

  <clause id="12761">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ K(u,K(x,y) * K(z,x)) = T(K(x,z) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(12393(a,1),12759(a,1,2))].">
      <j1 rule="para" parents="12393 12759"/>
    </justification>
  </clause>

  <clause id="12762">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * K(u,K(y,x) * K(z,y))) = T(K(y,z) * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(10011,a,12761,a)].">
      <j1 rule="hyper" parents="10011 12761"/>
    </justification>
  </clause>

  <clause id="12763">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) / (K(u,z) * x) = T(K(z,u) * K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12398,a,b,12762,a)].">
      <j1 rule="hyper" parents="64 12398 12762"/>
    </justification>
  </clause>

  <clause id="12764">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),K(y,x) * u) = T(K(x,y) * K(z,x),u)
    ]]></literal>
    <justification jstring="[hyper(12377,a,12763,a)].">
      <j1 rule="hyper" parents="12377 12763"/>
    </justification>
  </clause>

  <clause id="12765">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = (y \ T(y * (x \ 1),y)) * R((y \ T(y * (x \ 1),y)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(11683(a,1),11684(a,2,2,1,1))].">
      <j1 rule="para" parents="11683 11684"/>
    </justification>
  </clause>

  <clause id="12766">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ (T(y * (x \ 1),y) * R(T(y * (x \ 1),y) \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,2743,a(flip),b,12765,a),flip(a)].">
      <j1 rule="hyper" parents="373 2743 12765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12767">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T((y * (x \ 1)) * R((y * (x \ 1)) \ y,z,u),y)
    ]]></literal>
    <justification jstring="[para(3107(a,1),12766(a,2,2))].">
      <j1 rule="para" parents="3107 12766"/>
    </justification>
  </clause>

  <clause id="12768">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T(y * ((x \ 1) * R((x \ 1) \ 1,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1300(a,1),12767(a,2,2,1))].">
      <j1 rule="para" parents="1300 12767"/>
    </justification>
  </clause>

  <clause id="12769">
    <literal><![CDATA[
      T((x \ a(y,x \ 1,y)) * R((x \ a(y,x \ 1,y)) \ 1,z,u),y) = y \ T(y * (x \ R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1793(a,1),12768(a,2,2,1,2))].">
      <j1 rule="para" parents="1793 12768"/>
    </justification>
  </clause>

  <clause id="12770">
    <literal><![CDATA[
      T(x \ (a(y,x \ 1,y) * R(a(y,x \ 1,y) \ x,z,u)),y) = y \ T(y * (x \ R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[para(2743(a,1),12769(a,1,1))].">
      <j1 rule="para" parents="2743 12769"/>
    </justification>
  </clause>

  <clause id="12771">
    <literal><![CDATA[
      K(a(x,y,z),T((((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u),x * (y * z))) = K(a(x,y,z),K((x * y) * z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,9279,a(flip),b,9400,a),flip(a)].">
      <j1 rule="hyper" parents="373 9279 9400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12772">
    <literal><![CDATA[
      K(a(x,y,z),T((((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u),x * (y * z))) = K(u,K(a(x,y,z),(x * y) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8110,a(flip),b,12771,a),flip(a)].">
      <j1 rule="hyper" parents="373 8110 12771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12773">
    <literal><![CDATA[
      ((x * (K(y,z) * u)) / (x * T(u,K(y,z)))) \ T(x * (K(y,z) * u),K(z,L(y,u,x))) = T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x)
    ]]></literal>
    <justification jstring="[para(12059(a,1),10378(a,1,2,2))].">
      <j1 rule="para" parents="12059 10378"/>
    </justification>
  </clause>

  <clause id="12774">
    <literal><![CDATA[
      L(x,K(y,z),R(K(u,y) * R(K(y,u),w,v5),K(y,z),x)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,9,a(flip),b,11720,a),flip(a)].">
      <j1 rule="hyper" parents="373 9 11720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12776">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y) * R(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(11718(a,1),12774(a,1,3))].">
      <j1 rule="para" parents="11718 12774"/>
    </justification>
  </clause>

  <clause id="12778">
    <literal><![CDATA[
      L(x,K(y,z),a(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(12681(a,1),12776(a,1,3))].">
      <j1 rule="para" parents="12681 12776"/>
    </justification>
  </clause>

  <clause id="12779">
    <literal><![CDATA[
      (a(K(x,y),z,u) * K(x,w)) * v5 = a(K(x,y),z,u) * (K(x,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(1960,a,12778,a),flip(a)].">
      <j1 rule="hyper" parents="1960 12778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12780">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) * (K(x,y) * (K(y,x) * z)) = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,12701,a(flip),b,12779,a),flip(a)].">
      <j1 rule="hyper" parents="64 12701 12779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12781">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) * z = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(6161(a,1),12780(a,1,2))].">
      <j1 rule="para" parents="6161 12780"/>
    </justification>
  </clause>

  <clause id="12782">
    <literal><![CDATA[
      x * a(K(y,T(z,x)),u,w) = a(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(8203(a,1),12781(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8203 12781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12783">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) = T(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(270,a,12782,a),flip(a)].">
      <j1 rule="hyper" parents="270 12782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12784">
    <literal><![CDATA[
      (x * T(y,K(z,u))) * K(u,K(L(z,y,x),x * (K(z,u) * y))) = T(x * (K(z,u) * y),L(K(u,z),y,x)) * L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12607,a(flip),b,12773,a)].">
      <j1 rule="hyper" parents="64 12607 12773"/>
    </justification>
  </clause>

  <clause id="12785">
    <literal><![CDATA[
      T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(z,K(L(y,u,x),x * u))
    ]]></literal>
    <justification jstring="[para(9890(a,1),12784(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9890 12784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12786">
    <literal><![CDATA[
      T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(z,K(x * u,L(y,u,x)))
    ]]></literal>
    <justification jstring="[para(8126(a,1),12785(a,2,2))].">
      <j1 rule="para" parents="8126 12785"/>
    </justification>
  </clause>

  <clause id="12788">
    <literal><![CDATA[
      T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(z,K(y,x * u))
    ]]></literal>
    <justification jstring="[para(12729(a,1),12786(a,2,2))].">
      <j1 rule="para" parents="12729 12786"/>
    </justification>
  </clause>

  <clause id="12789">
    <literal><![CDATA[
      T(x * (K(y,z) * u),L(K(z,y),u,x)) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(y,K(z,x * u))
    ]]></literal>
    <justification jstring="[para(8108(a,1),12788(a,2,2))].">
      <j1 rule="para" parents="8108 12788"/>
    </justification>
  </clause>

  <clause id="12790">
    <literal><![CDATA[
      T(x * (K(y,z) * u),K(z,L(y,u,x))) * L(K(z,y),u,x) = (x * T(u,K(y,z))) * K(y,K(z,x * u))
    ]]></literal>
    <justification jstring="[para(12059(a,1),12789(a,1,1,2))].">
      <j1 rule="para" parents="12059 12789"/>
    </justification>
  </clause>

  <clause id="12791">
    <literal><![CDATA[
      T((x * (K(y,z) * u)) * L(K(z,y),u,x),K(z,L(y,u,x))) = (x * T(u,K(y,z))) * K(y,K(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10650,a,b,12790,a)].">
      <j1 rule="hyper" parents="64 10650 12790"/>
    </justification>
  </clause>

  <clause id="12792">
    <literal><![CDATA[
      (x * T(y,K(z,u))) * K(z,K(u,x * y)) = T(x * T(y,K(z,u)),K(u,L(z,y,x)))
    ]]></literal>
    <justification jstring="[para(10324(a,1),12791(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10324 12791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12793">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(u,L(z,y,x))) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ ((x * T(y,K(z,u))) * K(z,K(u,x * y))) = v5
    ]]></literal>
    <justification jstring="[para(12792(a,1),720(a,1))].">
      <j1 rule="para" parents="12792 720"/>
    </justification>
  </clause>

  <clause id="12794">
    <literal><![CDATA[
      T((((x * y) \ x) * (z * K(y \ 1,u))) / T((x * y) \ x,u),(((x * y) \ x) * z) / L(y \ 1,y,x)) = (((x * y) \ x) * z) / L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(6766(a,1),7167(a,1,1,1,2,2))].">
      <j1 rule="para" parents="6766 7167"/>
    </justification>
  </clause>

  <clause id="12796">
    <literal><![CDATA[
      T(((x \ 1) * (y * K(x \ 1,z))) / T(x \ 1,z),(((u * x) \ u) * y) / L(x \ 1,x,u)) = (((u * x) \ u) * y) / L(x \ 1,x,u)
    ]]></literal>
    <justification jstring="[para(10115(a,1),12794(a,1,1))].">
      <j1 rule="para" parents="10115 12794"/>
    </justification>
  </clause>

  <clause id="12797">
    <literal><![CDATA[
      T(((x \ 1) * y) / (x \ 1),(((z * x) \ z) * y) / L(x \ 1,x,z)) = (((z * x) \ z) * y) / L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[para(7140(a,1),12796(a,1,1))].">
      <j1 rule="para" parents="7140 12796"/>
    </justification>
  </clause>

  <clause id="12799">
    <literal><![CDATA[
      (((x * y) \ x) * z) / L(y \ 1,y,x) = ((y \ 1) * z) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(203,a,12797,a)].">
      <j1 rule="hyper" parents="203 12797"/>
    </justification>
  </clause>

  <clause id="12800">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / T((K(z,y) * (K(y,u) * x)) * (K(y,z) * K(u,y)),K(y,u) * K(z,y)) = T(K(y,z) * K(u,y),(K(y,z) * K(u,y)) \ x)
    ]]></literal>
    <justification jstring="[para(9996(a,1),12348(a,1,2,1,1))].">
      <j1 rule="para" parents="9996 12348"/>
    </justification>
  </clause>

  <clause id="12801">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / T(T((K(y,u) * x) * K(u,y),K(y,z)),K(y,u) * K(z,y)) = T(K(y,z) * K(u,y),(K(y,z) * K(u,y)) \ x)
    ]]></literal>
    <justification jstring="[para(11739(a,1),12800(a,1,2,1))].">
      <j1 rule="para" parents="11739 12800"/>
    </justification>
  </clause>

  <clause id="12802">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / T(T(T(x,K(y,u)),K(y,z)),K(y,u) * K(z,y)) = T(K(y,z) * K(u,y),(K(y,z) * K(u,y)) \ x)
    ]]></literal>
    <justification jstring="[para(8160(a,1),12801(a,1,2,1,1))].">
      <j1 rule="para" parents="8160 12801"/>
    </justification>
  </clause>

  <clause id="12803">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) / T(T(x,K(y,z) * K(u,y)),K(y,u) * K(z,y)) = T(K(y,z) * K(u,y),(K(y,z) * K(u,y)) \ x)
    ]]></literal>
    <justification jstring="[para(12340(a,1),12802(a,1,2,1))].">
      <j1 rule="para" parents="12340 12802"/>
    </justification>
  </clause>

  <clause id="12804">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),(K(x,y) * K(z,x)) \ u) = (u * (K(x,y) * K(z,x))) / u
    ]]></literal>
    <justification jstring="[para(12355(a,1),12803(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12355 12803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12805">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),(K(x,y) * K(z,x)) \ u) = T(K(x,y) * K(z,x),u)
    ]]></literal>
    <justification jstring="[hyper(12376,a,12804,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="12376 12804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12806">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),K(y,x) * (K(x,z) * u)) = T(K(x,y) * K(z,x),u)
    ]]></literal>
    <justification jstring="[para(9996(a,1),12805(a,1,2))].">
      <j1 rule="para" parents="9996 12805"/>
    </justification>
  </clause>

  <clause id="12807">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),K(x,z) * u) = T(K(x,y) * K(z,x),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12764,a(flip),b,12806,a)].">
      <j1 rule="hyper" parents="64 12764 12806"/>
    </justification>
  </clause>

  <clause id="12808">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,u) * z) = T(K(x,u) * K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9999,a(flip),b,12807,a)].">
      <j1 rule="hyper" parents="64 9999 12807"/>
    </justification>
  </clause>

  <clause id="12809">
    <literal><![CDATA[
      K(x,T(y,z)) * K(u,T(x,z)) = T(K(x,y) * K(u,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10376,a(flip),b,12808,a)].">
      <j1 rule="hyper" parents="64 10376 12808"/>
    </justification>
  </clause>

  <clause id="12810">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(u,T(x,z)) * w) = T(K(x,y) * K(u,x),z) * w
    ]]></literal>
    <justification jstring="[para(12809(a,1),9988(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12809 9988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12811">
    <literal><![CDATA[
      T(K(x,y) * K(y * R(x,z,u),x),w) * v5 = R(T(x,w),y,R(x,z,u)) * (T(x,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,11676,a(flip),b,12810,a),flip(a)].">
      <j1 rule="hyper" parents="64 11676 12810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12812">
    <literal><![CDATA[
      R(T(x,y),z,R(x,u,w)) * (T(x,y) \ v5) = a(x,z,R(x,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(11625(a,1),12811(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11625 12811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12813">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(141,a,12812,a(flip),b,1794,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="141 12812 1794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12815">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,1770,a(flip),b,12813,a)].">
      <j1 rule="hyper" parents="64 1770 12813"/>
    </justification>
  </clause>

  <clause id="12816">
    <literal><![CDATA[
      x \ R(T(x,y),z,R(x,u,w)) = K(x,y) * a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,12813,a(flip),b,6066,a),flip(a)].">
      <j1 rule="hyper" parents="145 12813 6066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12817">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * a(y,z,R(y,u,w))) = y \ R(y,z,R(T(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(12816(a,1),11603(a,1,2))].">
      <j1 rule="para" parents="12816 11603"/>
    </justification>
  </clause>

  <clause id="12818">
    <literal><![CDATA[
      a(x,K(x,y) * z,R(x,u,w)) = x \ (v5 \ ((R(x,z,R(x,u,w)) * (x \ v5)) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,10049,a(flip),b,12815,a),flip(a)].">
      <j1 rule="hyper" parents="64 10049 12815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12819">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,z),u,w)) = a(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(6188,a,12817,a)].">
      <j1 rule="hyper" parents="6188 12817"/>
    </justification>
  </clause>

  <clause id="12820">
    <literal><![CDATA[
      a(T(x,y),z,R(T(x,y),u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(11604,a,12819,a)].">
      <j1 rule="hyper" parents="11604 12819"/>
    </justification>
  </clause>

  <clause id="12822">
    <literal><![CDATA[
      a(R(x,y,z),u,x) \ 1 = a(x,u,R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(12820(a,1),11523(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12820 11523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12823">
    <literal><![CDATA[
      a(R(x,y,z),u,x) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(325,a,12822,a),flip(a)].">
      <j1 rule="hyper" parents="325 12822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12825">
    <literal><![CDATA[
      (x * L(R(T(y,x),z,u),y \ T(x,y),y)) \ (x * R(T(y,x),z,u)) = a(R(T(y,x),z,u),T(y,x) \ x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,5052,a,b,12823,a)].">
      <j1 rule="hyper" parents="373 5052 12823"/>
    </justification>
  </clause>

  <clause id="12827">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = x \ (v5 \ ((R(x,z,R(x,u,w)) * (x \ v5)) * x))
    ]]></literal>
    <justification jstring="[hyper(11711,a,12818,a)].">
      <j1 rule="hyper" parents="11711 12818"/>
    </justification>
  </clause>

  <clause id="12830">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = x \ (v5 \ ((x * (x \ v5)) * R(x,z,R(x,u,w))))
    ]]></literal>
    <justification jstring="[para(9971(a,1),12827(a,2,2,2))].">
      <j1 rule="para" parents="9971 12827"/>
    </justification>
  </clause>

  <clause id="12831">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = x \ (v5 \ (v5 * R(x,z,R(x,u,w))))
    ]]></literal>
    <justification jstring="[para(10(a,1),12830(a,2,2,2,1))].">
      <j1 rule="para" parents="10 12830"/>
    </justification>
  </clause>

  <clause id="12832">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = x \ R(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),12831(a,2,2))].">
      <j1 rule="para" parents="9 12831"/>
    </justification>
  </clause>

  <clause id="12834">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,11507,a(flip),b,12832,a),flip(a)].">
      <j1 rule="hyper" parents="373 11507 12832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12835">
    <literal><![CDATA[
      a(x,T(x,y) \ z,R(x,u,w)) = a(x,x \ z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11712,a(flip),b,12834,a),flip(a)].">
      <j1 rule="hyper" parents="64 11712 12834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12836">
    <literal><![CDATA[
      a(x,T(y,x),R(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12834(a,1),5049(a,1))].">
      <j1 rule="para" parents="12834 5049"/>
    </justification>
  </clause>

  <clause id="12838">
    <literal><![CDATA[
      (x * L(R(T(y,x),z,u),y \ x,y)) \ (x * R(T(y,x),z,u)) = a(R(T(y,x),z,u),T(y,x) \ x,T(y,x))
    ]]></literal>
    <justification jstring="[para(9425(a,1),12825(a,1,1,2))].">
      <j1 rule="para" parents="9425 12825"/>
    </justification>
  </clause>

  <clause id="12839">
    <literal><![CDATA[
      (L(R(x,y,z),x \ u,x) * u) \ (u * R(T(x,u),y,z)) = a(R(T(x,u),y,z),T(x,u) \ u,T(x,u))
    ]]></literal>
    <justification jstring="[para(835(a,1),12838(a,1,1))].">
      <j1 rule="para" parents="835 12838"/>
    </justification>
  </clause>

  <clause id="12840">
    <literal><![CDATA[
      a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = (L(R(x,z,u),x \ y,x) * y) \ (R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(267(a,1),12839(a,1,2)),flip(a)].">
      <j1 rule="para" parents="267 12839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12841">
    <literal><![CDATA[
      a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = a(x,x \ y,T(R(x,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(373,a,1968,a(flip),b,12840,a),flip(a)].">
      <j1 rule="hyper" parents="373 1968 12840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12842">
    <literal><![CDATA[
      a(R(T(x,y),z,u),T(x,y) \ y,T(x,y)) = a(x,x \ y,R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(27(a,2),12841(a,2,3))].">
      <j1 rule="para" parents="27 12841"/>
    </justification>
  </clause>

  <clause id="12843">
    <literal><![CDATA[
      a(T(x,y),T(x,y) \ y,R(T(x,y),z,u)) = a(x,x \ y,R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12823,a(flip),b,12842,a)].">
      <j1 rule="hyper" parents="64 12823 12842"/>
    </justification>
  </clause>

  <clause id="12844">
    <literal><![CDATA[
      a(x,T(x,y) \ y,R(x,z,u)) = a(x,x \ y,R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12820,a(flip),b,12843,a)].">
      <j1 rule="hyper" parents="64 12820 12843"/>
    </justification>
  </clause>

  <clause id="12846">
    <literal><![CDATA[
      a(x,x \ y,R(T(x,y),z,u)) = a(x,x \ y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12835,a(flip),b,12844,a),flip(a)].">
      <j1 rule="hyper" parents="64 12835 12844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12848">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,T(R(x,y,z),u)) = a(x,x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12274,a,b,12846,a)].">
      <j1 rule="hyper" parents="64 12274 12846"/>
    </justification>
  </clause>

  <clause id="12849">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z) \ u,R(x,y,z)) = a(x,x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(10958,a,12848,a)].">
      <j1 rule="hyper" parents="10958 12848"/>
    </justification>
  </clause>

  <clause id="12850">
    <literal><![CDATA[
      (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,y \ (w * y),R(y,z,u))
    ]]></literal>
    <justification jstring="[para(12849(a,1),11734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12849 11734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12851">
    <literal><![CDATA[
      (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,T(w,y),R(y,z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),12850(a,2,2,2))].">
      <j1 rule="para" parents="22 12850"/>
    </justification>
  </clause>

  <clause id="12852">
    <literal><![CDATA[
      (x / R(y,z,u)) * R(R(y,w,y),z,u) = x * a(y,w,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(11531(a,1),12851(a,2,2))].">
      <j1 rule="para" parents="11531 12851"/>
    </justification>
  </clause>

  <clause id="12853">
    <literal><![CDATA[
      x * a(R(y,z,u),w,L(R(y,z,u),v5,v6)) = x * a(y,w,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12325,a(flip),b,12852,a)].">
      <j1 rule="hyper" parents="64 12325 12852"/>
    </justification>
  </clause>

  <clause id="12854">
    <literal><![CDATA[
      x * a(R(y,z,u),w,R(y,z,u)) = x * a(y,w,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(593(a,1),12853(a,1,2,3))].">
      <j1 rule="para" parents="593 12853"/>
    </justification>
  </clause>

  <clause id="12855">
    <literal><![CDATA[
      a(R(x,y,z),u,R(x,y,z)) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(11018,a,12854,a)].">
      <j1 rule="hyper" parents="11018 12854"/>
    </justification>
  </clause>

  <clause id="12856">
    <literal><![CDATA[
      R(a(x,y,x),x * z,u) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(12270,a,12855,a)].">
      <j1 rule="hyper" parents="12270 12855"/>
    </justification>
  </clause>

  <clause id="12857">
    <literal><![CDATA[
      a(x,R(x,y,z) \ u,R(x,y,z)) = a(x,x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12849,a(flip),b,12855,a),flip(a)].">
      <j1 rule="hyper" parents="64 12849 12855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12858">
    <literal><![CDATA[
      a(x,y,R(x,x \ z,u)) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12856(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 12856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12859">
    <literal><![CDATA[
      R(T(x,y),z,R(x,x \ u,w)) = T(x,y) * R(a(x,z,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,12858,a(flip),b,12813,a),flip(a)].">
      <j1 rule="hyper" parents="145 12858 12813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12860">
    <literal><![CDATA[
      R(x,y,R(x,x \ z,u)) = x * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,12858,a(flip),b,11507,a),flip(a)].">
      <j1 rule="hyper" parents="145 12858 11507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12861">
    <literal><![CDATA[
      T(x,y) * R(a(T(x,y),z,T(x,y)),u,w) = R(T(x,y),z,R(x,T(x,y) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,10090,a(flip),b,12860,a),flip(a)].">
      <j1 rule="hyper" parents="64 10090 12860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12862">
    <literal><![CDATA[
      a(x,x \ y,R(x,z,u)) * K(x,y) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(12857(a,1),11533(a,1,1))].">
      <j1 rule="para" parents="12857 11533"/>
    </justification>
  </clause>

  <clause id="12863">
    <literal><![CDATA[
      R(T(x,y),z,R(x,T(x,y) \ u,w)) = T(x,y) * R(a(x,z,x),u,w)
    ]]></literal>
    <justification jstring="[para(11944(a,1),12861(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11944 12861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12864">
    <literal><![CDATA[
      R(T(x,y),z,R(x,T(x,y) \ u,w)) = R(T(x,y),z,R(x,x \ u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,12859,a,b,12863,a),flip(a)].">
      <j1 rule="hyper" parents="373 12859 12863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12866">
    <literal><![CDATA[
      (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (R(T(x,y),z,R(x,x \ u,w)) * (T(x,y) \ u)) * w
    ]]></literal>
    <justification jstring="[para(12864(a,1),12272(a,2,1,1))].">
      <j1 rule="para" parents="12864 12272"/>
    </justification>
  </clause>

  <clause id="12867">
    <literal><![CDATA[
      (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (a(x,z,R(x,x \ u,w)) * u) * w
    ]]></literal>
    <justification jstring="[para(12812(a,1),12866(a,2,1))].">
      <j1 rule="para" parents="12812 12866"/>
    </justification>
  </clause>

  <clause id="12869">
    <literal><![CDATA[
      (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (R(a(x,z,x),u,w) * u) * w
    ]]></literal>
    <justification jstring="[para(12858(a,1),12867(a,2,1,1))].">
      <j1 rule="para" parents="12858 12867"/>
    </justification>
  </clause>

  <clause id="12870">
    <literal><![CDATA[
      (R(T(x,y),z,x) * (T(x,y) \ u)) * w = (R(a(x,z,x),u,w) * u) * w
    ]]></literal>
    <justification jstring="[para(10102(a,1),12869(a,1,1,1))].">
      <j1 rule="para" parents="10102 12869"/>
    </justification>
  </clause>

  <clause id="12872">
    <literal><![CDATA[
      (T(x,y) * (L(T(x,y),z,x) \ u)) * w = (R(a(x,z,x),u,w) * u) * w
    ]]></literal>
    <justification jstring="[para(11404(a,1),12870(a,1,1))].">
      <j1 rule="para" parents="11404 12870"/>
    </justification>
  </clause>

  <clause id="12873">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * z) * u = (z * a(x,y,x)) * u
    ]]></literal>
    <justification jstring="[para(10954(a,1),12872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10954 12872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12874">
    <literal><![CDATA[
      ((a(x,y,x) * z) * u) \ ((z * a(x,y,x)) * u) = a(R(a(x,y,x),z,u),z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,12873,a(flip),b,962,a)].">
      <j1 rule="hyper" parents="139 12873 962"/>
    </justification>
  </clause>

  <clause id="12875">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = K(z,T(a(x,y,x),u))
    ]]></literal>
    <justification jstring="[hyper(10769,a,12874,a),flip(a)].">
      <j1 rule="hyper" parents="10769 12874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12876">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = K(z,a(x,y,x))
    ]]></literal>
    <justification jstring="[para(11012(a,1),12875(a,2,2))].">
      <j1 rule="para" parents="11012 12875"/>
    </justification>
  </clause>

  <clause id="12877">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,11017,a(flip),b,12876,a),flip(a)].">
      <j1 rule="hyper" parents="373 11017 12876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12880">
    <literal><![CDATA[
      L(x,y,R(a(z,u,z),y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,12877,a)].">
      <j1 rule="hyper" parents="53 12877"/>
    </justification>
  </clause>

  <clause id="12881">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * (T(z,R(a(x,y,x),z,u)) * u)) / u = z * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(225,a,12880,a(flip),b,10980,a(flip))].">
      <j1 rule="hyper" parents="225 12880 10980"/>
    </justification>
  </clause>

  <clause id="12882">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * (z * u)) / u = z * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11093(a,1),12881(a,1,1,2,1))].">
      <j1 rule="para" parents="11093 12881"/>
    </justification>
  </clause>

  <clause id="12883">
    <literal><![CDATA[
      x * R(a(y,z,y),x,u) = a(y,z,y) * x
    ]]></literal>
    <justification jstring="[hyper(667,a,12882,a),flip(a)].">
      <j1 rule="hyper" parents="667 12882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12885">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,11011,a(flip),b,12883,a),flip(a)].">
      <j1 rule="hyper" parents="35 11011 12883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12887">
    <literal><![CDATA[
      ((a(x,y,x) * R(z,u,w)) * (u * w)) / ((z * u) * w) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,661,a,b,12885,a)].">
      <j1 rule="hyper" parents="64 661 12885"/>
    </justification>
  </clause>

  <clause id="12888">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12856,a(flip),b,12885,a)].">
      <j1 rule="hyper" parents="64 12856 12885"/>
    </justification>
  </clause>

  <clause id="12889">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(144,a,12885,a(flip),b,108,a(flip))].">
      <j1 rule="hyper" parents="144 12885 108"/>
    </justification>
  </clause>

  <clause id="12890">
    <literal><![CDATA[
      (a(x,y,x) * z) * u = a(x,y,x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,12885,a(flip),b,20,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 12885 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12891">
    <literal><![CDATA[
      a(x,y,x) * (1 / z) = a(x,y,x) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,12885,a(flip),b,2980,a),flip(a)].">
      <j1 rule="hyper" parents="142 12885 2980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12892">
    <literal><![CDATA[
      (a(x,y,x) * (z * u)) / u = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(12885(a,1),350(a,1,1,1))].">
      <j1 rule="para" parents="12885 350"/>
    </justification>
  </clause>

  <clause id="12894">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[para(12885(a,1),12880(a,1,3))].">
      <j1 rule="para" parents="12885 12880"/>
    </justification>
  </clause>

  <clause id="12895">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = z \ (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(743,a,12894,a),flip(a)].">
      <j1 rule="hyper" parents="743 12894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12896">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(710,a,12894,a),flip(a)].">
      <j1 rule="hyper" parents="710 12894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12897">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = a(x,y,x) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(225,a,12894,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 12894 10262"/>
    </justification>
  </clause>

  <clause id="12898">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(12894(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="12894 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12899">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12894(a,1),51(a,2))].">
      <j1 rule="para" parents="12894 51"/>
    </justification>
  </clause>

  <clause id="12900">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ (x * (a(z,u,z) * (y * w))) = L(w,a(z,u,z) * y,x)
    ]]></literal>
    <justification jstring="[para(12894(a,1),11035(a,2,1))].">
      <j1 rule="para" parents="12894 11035"/>
    </justification>
  </clause>

  <clause id="12903">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,12326,a,b,12888,a),flip(a)].">
      <j1 rule="hyper" parents="373 12326 12888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12904">
    <literal><![CDATA[
      a(R(x,y,z),u,R(x,y,z)) = a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12855,a,b,12888,a)].">
      <j1 rule="hyper" parents="64 12855 12888"/>
    </justification>
  </clause>

  <clause id="12905">
    <literal><![CDATA[
      (1 / x) * a(y,z,y) = a(y,z,y) / x
    ]]></literal>
    <justification jstring="[hyper(11019,a,12891,a)].">
      <j1 rule="hyper" parents="11019 12891"/>
    </justification>
  </clause>

  <clause id="12906">
    <literal><![CDATA[
      a(x,y,x) \ (a(x,y,x) / z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(149,a,12891,a)].">
      <j1 rule="hyper" parents="149 12891"/>
    </justification>
  </clause>

  <clause id="12907">
    <literal><![CDATA[
      a(x,T(y,x),L(x,z,u)) = a(x,y,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(12836,a,12903,a),flip(a)].">
      <j1 rule="hyper" parents="12836 12903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12909">
    <literal><![CDATA[
      a(x,y,x) * ((x * z) * u) = (R(x,y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,12904,a(flip),b,12268,a)].">
      <j1 rule="hyper" parents="144 12904 12268"/>
    </justification>
  </clause>

  <clause id="12910">
    <literal><![CDATA[
      L(R(x,y,z),u,R(x,y,z)) \ w = (R(x,y,z) \ w) * a(x,u,x)
    ]]></literal>
    <justification jstring="[para(12904(a,1),10951(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12904 10951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12911">
    <literal><![CDATA[
      (x \ 1) * (x \ a(y,z,y)) = x \ (a(y,z,y) / x)
    ]]></literal>
    <justification jstring="[hyper(139,a,12905,a(flip),b,1127,a),flip(a)].">
      <j1 rule="hyper" parents="139 12905 1127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12912">
    <literal><![CDATA[
      a(x,y,x) * ((x \ z) * u) = (L(x,y,x) \ z) * u
    ]]></literal>
    <justification jstring="[para(11030(a,1),12889(a,1,2,1))].">
      <j1 rule="para" parents="11030 12889"/>
    </justification>
  </clause>

  <clause id="12913">
    <literal><![CDATA[
      a(x,y,x) * ((1 / z) * u) = (a(x,y,x) / z) * u
    ]]></literal>
    <justification jstring="[para(12906(a,1),12889(a,1,2,1))].">
      <j1 rule="para" parents="12906 12889"/>
    </justification>
  </clause>

  <clause id="12914">
    <literal><![CDATA[
      R((x * (x \ y)) * (x \ y),z,x) = a(x,z,x) * (y * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,11372,a,b,12890,a)].">
      <j1 rule="hyper" parents="64 11372 12890"/>
    </justification>
  </clause>

  <clause id="12915">
    <literal><![CDATA[
      (a(x,y,x) * (z * (u * w))) \ (((a(x,y,x) * z) * u) * w) = a(a(x,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(12890(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12890 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12916">
    <literal><![CDATA[
      (a(x,y,x) * (z * u)) \ ((a(x,y,x) * z) * (u * w)) = L(w,u,a(x,y,x) * z)
    ]]></literal>
    <justification jstring="[para(12890(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12890 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12917">
    <literal><![CDATA[
      ((a(x,y,x) * (z * u)) * w) / (u * w) = R(a(x,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(12890(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12890 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12918">
    <literal><![CDATA[
      x \ (a(y,z,y) * (u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(a(y,z,y) * u,x) = w
    ]]></literal>
    <justification jstring="[para(12890(a,1),336(a,1,2))].">
      <j1 rule="para" parents="12890 336"/>
    </justification>
  </clause>

  <clause id="12919">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ ((x * (a(y,z,y) * u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(12890(a,1),959(a,1,1,2))].">
      <j1 rule="para" parents="12890 959"/>
    </justification>
  </clause>

  <clause id="12920">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = a(y,z,y) * (x * u)
    ]]></literal>
    <justification jstring="[para(11011(a,1),12890(a,1,1))].">
      <j1 rule="para" parents="11011 12890"/>
    </justification>
  </clause>

  <clause id="12921">
    <literal><![CDATA[
      (x * y) \ (a(y,z,y) * u) = (x * L(y,z,y)) \ u
    ]]></literal>
    <justification jstring="[para(11031(a,1),12895(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11031 12895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12922">
    <literal><![CDATA[
      (x * a(y,z,y)) \ u = x \ (a(y,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(11011(a,1),12896(a,1,1))].">
      <j1 rule="para" parents="11011 12896"/>
    </justification>
  </clause>

  <clause id="12923">
    <literal><![CDATA[
      (1 / x) \ (a(y,z,y) \ u) = (a(y,z,y) / x) \ u
    ]]></literal>
    <justification jstring="[para(12891(a,1),12896(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12891 12896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12924">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = (z / u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,11011,a(flip),b,12897,a),flip(a)].">
      <j1 rule="hyper" parents="373 11011 12897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12926">
    <literal><![CDATA[
      a(x,x \ (y * x),L(x,z,u)) = a(x,y,R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(22(a,1),12907(a,1,2))].">
      <j1 rule="para" parents="22 12907"/>
    </justification>
  </clause>

  <clause id="12927">
    <literal><![CDATA[
      (x * a(y,x,y)) * z = x * (a(y,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,12257,a(flip),b,12920,a),flip(a)].">
      <j1 rule="hyper" parents="373 12257 12920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12928">
    <literal><![CDATA[
      (a(x,y,x) * ((z * u) * w)) / (u * w) = R(z,u,w) * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(20(a,2),12924(a,2,1))].">
      <j1 rule="para" parents="20 12924"/>
    </justification>
  </clause>

  <clause id="12929">
    <literal><![CDATA[
      (x / y) * a(x,z,x) = R(x,z,x) / y
    ]]></literal>
    <justification jstring="[para(10898(a,1),12924(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10898 12924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12931">
    <literal><![CDATA[
      (x * L(y,z,y)) \ (u / y) = (x * y) \ (u / L(y,z,y))
    ]]></literal>
    <justification jstring="[para(11026(a,1),12921(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11026 12921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12932">
    <literal><![CDATA[
      (x * x) * (a(y,z,y) \ u) = x * ((a(y,z,y) / x) \ u)
    ]]></literal>
    <justification jstring="[hyper(145,a,12923,a(flip),b,539,a),flip(a)].">
      <j1 rule="hyper" parents="145 12923 539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12933">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * x),L(x,y,z)) = a(x,u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,11608,a,b,12926,a)].">
      <j1 rule="hyper" parents="64 11608 12926"/>
    </justification>
  </clause>

  <clause id="12934">
    <literal><![CDATA[
      (R(x * a(y,x,y),z,u) * (z * u)) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(11295(a,1),12887(a,1,1,1))].">
      <j1 rule="para" parents="11295 12887"/>
    </justification>
  </clause>

  <clause id="12935">
    <literal><![CDATA[
      (a(x,y,x) * ((z * u) * w)) / (u * w) = R(a(x,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(12890(a,1),12917(a,1,1))].">
      <j1 rule="para" parents="12890 12917"/>
    </justification>
  </clause>

  <clause id="12936">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) = R(z,u,w) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12928,a(flip),b,12935,a),flip(a)].">
      <j1 rule="hyper" parents="64 12928 12935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12937">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) = a(x,y,x) * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11011,a,b,12936,a),flip(a)].">
      <j1 rule="hyper" parents="373 11011 12936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12938">
    <literal><![CDATA[
      T(x \ R(a(y,x \ 1,y) * (a(y,x \ 1,y) \ x),z,u),y) = y \ T(y * (x \ R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[para(12937(a,2),12770(a,1,1,2))].">
      <j1 rule="para" parents="12937 12770"/>
    </justification>
  </clause>

  <clause id="12939">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = K(y * x,L(x,w,v5)) * K(L(x,w,v5),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11733,a(flip),b,12933,a),flip(a)].">
      <j1 rule="hyper" parents="64 11733 12933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12940">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z) \ (u * L(x,y,z)),L(x,y,z)) = a(x,u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,12720,a,b,12939,a)].">
      <j1 rule="hyper" parents="373 12720 12939"/>
    </justification>
  </clause>

  <clause id="12942">
    <literal><![CDATA[
      (((x * a(y,x,y)) * z) * u) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(111(a,1),12934(a,1,1))].">
      <j1 rule="para" parents="111 12934"/>
    </justification>
  </clause>

  <clause id="12943">
    <literal><![CDATA[
      ((x * (a(y,x,y) * z)) * u) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12927(a,1),12942(a,1,1,1))].">
      <j1 rule="para" parents="12927 12942"/>
    </justification>
  </clause>

  <clause id="12944">
    <literal><![CDATA[
      ((x * (a(y,x,y) * (x \ z))) * u) / (z * u) = a(y,R(x,x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(10(a,1),12943(a,1,2,1))].">
      <j1 rule="para" parents="10 12943"/>
    </justification>
  </clause>

  <clause id="12945">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = ((a(x,y,x) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(12258(a,1),12944(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12258 12944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12946">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,20,a,b,12945,a),flip(a)].">
      <j1 rule="hyper" parents="373 20 12945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12947">
    <literal><![CDATA[
      R(a(x,y,x),y * z,u) = a(x,R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),12946(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 12946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12948">
    <literal><![CDATA[
      a(x,R(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12885,a(flip),b,12947,a),flip(a)].">
      <j1 rule="hyper" parents="64 12885 12947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12949">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,R(y,w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,12885,a,b,12948,a)].">
      <j1 rule="hyper" parents="373 12885 12948"/>
    </justification>
  </clause>

  <clause id="12950">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(12948(a,1),10905(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12948 10905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12951">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = a(x,z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(12948(a,1),11027(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12948 11027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12952">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10905,a(flip),b,12950,a),flip(a)].">
      <j1 rule="hyper" parents="373 10905 12950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12953">
    <literal><![CDATA[
      L(x,(y / z) / u,x) = L(x,y / (u * z),x)
    ]]></literal>
    <justification jstring="[para(351(a,1),12952(a,1,2)),flip(a)].">
      <j1 rule="para" parents="351 12952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12955">
    <literal><![CDATA[
      a(x,R(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(12949(a,1),432(a,1)),flip(b)].">
      <j1 rule="para" parents="12949 432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12956">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,11027,a(flip),b,12951,a),flip(a)].">
      <j1 rule="hyper" parents="373 11027 12951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12957">
    <literal><![CDATA[
      R(x,y,z) * R(T(u,x * u),x,u) = T(u * R(x,y,z),u * x)
    ]]></literal>
    <justification jstring="[para(12956(a,1),12750(a,1,2))].">
      <j1 rule="para" parents="12956 12750"/>
    </justification>
  </clause>

  <clause id="12958">
    <literal><![CDATA[
      T(x * R(y,z,u),x * y) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1057(a,1),12957(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1057 12957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12960">
    <literal><![CDATA[
      (x * R(y,z,u)) / (R(y,z,u) * T(x,y)) = K(x * y,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(225,a,12958,a(flip),b,5804,a(flip))].">
      <j1 rule="hyper" parents="225 12958 5804"/>
    </justification>
  </clause>

  <clause id="12961">
    <literal><![CDATA[
      T(K(x,y) * K(y,R(x,z,u)),R(x,z,u)) = K(y * x,y * R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12741,a(flip),b,12960,a)].">
      <j1 rule="hyper" parents="64 12741 12960"/>
    </justification>
  </clause>

  <clause id="12962">
    <literal><![CDATA[
      T(a(K(x,y),z * y,u),R(y,z,u)) = K(x * y,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(12688(a,1),12961(a,1,1))].">
      <j1 rule="para" parents="12688 12961"/>
    </justification>
  </clause>

  <clause id="12963">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,T(y,R(y,z,u))),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12783,a,b,12962,a),flip(a)].">
      <j1 rule="hyper" parents="64 12783 12962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12964">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(197(a,1),12963(a,2,1,2))].">
      <j1 rule="para" parents="197 12963"/>
    </justification>
  </clause>

  <clause id="12965">
    <literal><![CDATA[
      R(K(x * y,x * R(y,z,u)),x * R(y,z,u),w) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(10221,a,12964,a)].">
      <j1 rule="hyper" parents="10221 12964"/>
    </justification>
  </clause>

  <clause id="12966">
    <literal><![CDATA[
      K(x,(x / y) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),12964(a,1,1))].">
      <j1 rule="para" parents="12 12964"/>
    </justification>
  </clause>

  <clause id="12967">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9877,a(flip),b,12966,a)].">
      <j1 rule="hyper" parents="64 9877 12966"/>
    </justification>
  </clause>

  <clause id="12968">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11235,a(flip),b,12967,a)].">
      <j1 rule="hyper" parents="64 11235 12967"/>
    </justification>
  </clause>

  <clause id="12969">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(y \ x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(6116(a,1),12968(a,2,1))].">
      <j1 rule="para" parents="6116 12968"/>
    </justification>
  </clause>

  <clause id="12970">
    <literal><![CDATA[
      R(a(K(x,y),z * y,u),x * R(y,z,u),w) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(12964(a,1),12965(a,1,1))].">
      <j1 rule="para" parents="12964 12965"/>
    </justification>
  </clause>

  <clause id="12972">
    <literal><![CDATA[
      a(L(x,y,z),T(u,L(x,y,z)),L(x,y,z)) = a(x,u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(22(a,2),12940(a,1,2))].">
      <j1 rule="para" parents="22 12940"/>
    </justification>
  </clause>

  <clause id="12973">
    <literal><![CDATA[
      (a(x,y,x) * (z * u)) \ (a(x,y,x) * (z * (u * w))) = L(w,u,a(x,y,x) * z)
    ]]></literal>
    <justification jstring="[para(12890(a,1),12916(a,1,2))].">
      <j1 rule="para" parents="12890 12916"/>
    </justification>
  </clause>

  <clause id="12974">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(u,w,u)) = L(x,y,a(u,w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(1081,a,12973,a)].">
      <j1 rule="hyper" parents="1081 12973"/>
    </justification>
  </clause>

  <clause id="12975">
    <literal><![CDATA[
      L(x,y,a(z,u,z) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(12899,a,12974,a),flip(a)].">
      <j1 rule="hyper" parents="12899 12974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12977">
    <literal><![CDATA[
      L(x,y,a(z,u,z) \ w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),12975(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 12975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12978">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(10897(a,1),12975(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10897 12975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12979">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(10898(a,1),12975(a,1,3))].">
      <j1 rule="para" parents="10898 12975"/>
    </justification>
  </clause>

  <clause id="12980">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(10902(a,1),12975(a,1,3))].">
      <j1 rule="para" parents="10902 12975"/>
    </justification>
  </clause>

  <clause id="12981">
    <literal><![CDATA[
      L(x,y,K(z,z * u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(10917(a,1),12975(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10917 12975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12982">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(10935(a,1),12975(a,1,3))].">
      <j1 rule="para" parents="10935 12975"/>
    </justification>
  </clause>

  <clause id="12983">
    <literal><![CDATA[
      L(x,y,z * a(u,w,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(11011(a,1),12975(a,1,3))].">
      <j1 rule="para" parents="11011 12975"/>
    </justification>
  </clause>

  <clause id="12984">
    <literal><![CDATA[
      L(x,y,L(z,u,z) * w) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(11025(a,1),12975(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11025 12975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12985">
    <literal><![CDATA[
      L(x,y,T(z * u,z)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(11058(a,1),12975(a,1,3))].">
      <j1 rule="para" parents="11058 12975"/>
    </justification>
  </clause>

  <clause id="12986">
    <literal><![CDATA[
      L(x,y,z * R(u,w,u)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(11353(a,1),12975(a,1,3))].">
      <j1 rule="para" parents="11353 12975"/>
    </justification>
  </clause>

  <clause id="12987">
    <literal><![CDATA[
      L(x,y,R(z,u,z) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(11369(a,1),12975(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11369 12975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12988">
    <literal><![CDATA[
      L(x,y,z * (T(u,z) / z)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(11379(a,1),12975(a,1,3))].">
      <j1 rule="para" parents="11379 12975"/>
    </justification>
  </clause>

  <clause id="12989">
    <literal><![CDATA[
      L(x,y,R(a(z,u,z) * w,v5,v6)) = L(x,y,R(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(12937(a,2),12975(a,1,3))].">
      <j1 rule="para" parents="12937 12975"/>
    </justification>
  </clause>

  <clause id="12990">
    <literal><![CDATA[
      x \ L(y,x,L(x,z,x)) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,12978,a,b,1139,a)].">
      <j1 rule="hyper" parents="139 12978 1139"/>
    </justification>
  </clause>

  <clause id="12991">
    <literal><![CDATA[
      L(x \ a(y,z,y),x,y) = (L(y,z,y) * x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,10910,a(flip),b,12978,a),flip(a)].">
      <j1 rule="hyper" parents="64 10910 12978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12992">
    <literal><![CDATA[
      L(x,y,T(z / u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(4731(a,1),12978(a,1,3))].">
      <j1 rule="para" parents="4731 12978"/>
    </justification>
  </clause>

  <clause id="12993">
    <literal><![CDATA[
      ((x * (y * x)) / x) * L(z,y,x) = L(x,y,x) * (y * z)
    ]]></literal>
    <justification jstring="[para(12978(a,1),4757(a,1,2))].">
      <j1 rule="para" parents="12978 4757"/>
    </justification>
  </clause>

  <clause id="12994">
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(12494(a,1),12978(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12494 12978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12996">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(4803(a,1),12979(a,1,3))].">
      <j1 rule="para" parents="4803 12979"/>
    </justification>
  </clause>

  <clause id="12997">
    <literal><![CDATA[
      L(x,y,L(R(z,u,z),w,v5)) = L(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(11556(a,1),12979(a,1,3))].">
      <j1 rule="para" parents="11556 12979"/>
    </justification>
  </clause>

  <clause id="12998">
    <literal><![CDATA[
      L(x,y,K(z \ u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(10881(a,1),12977(a,1,3))].">
      <j1 rule="para" parents="10881 12977"/>
    </justification>
  </clause>

  <clause id="12999">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(y,T(y,y * z) * z) \ x) \ T(T(T(y,y * z) * z,y),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12454,a(flip),b,12980,a),flip(a)].">
      <j1 rule="hyper" parents="64 12454 12980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13000">
    <literal><![CDATA[
      L(x,y,K(z,u * z)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(6142(a,2),12981(a,1,3))].">
      <j1 rule="para" parents="6142 12981"/>
    </justification>
  </clause>

  <clause id="13001">
    <literal><![CDATA[
      L(x,y,K(z \ 1,((u * z) \ u) * w)) = L(x,y,K((u * z) \ u,w))
    ]]></literal>
    <justification jstring="[para(6766(a,1),12981(a,1,3))].">
      <j1 rule="para" parents="6766 12981"/>
    </justification>
  </clause>

  <clause id="13002">
    <literal><![CDATA[
      L(x,y,K(z * u,(z * u) * (u \ 1))) = L(x,y,K(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(7520(a,1),12981(a,2,3))].">
      <j1 rule="para" parents="7520 12981"/>
    </justification>
  </clause>

  <clause id="13003">
    <literal><![CDATA[
      L(x \ y,z,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(9939,a,12982,a)].">
      <j1 rule="hyper" parents="9939 12982"/>
    </justification>
  </clause>

  <clause id="13004">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),w,a(v5,v6,v5)) = L(x,y,K(z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,12894,a,b,12982,a)].">
      <j1 rule="hyper" parents="373 12894 12982"/>
    </justification>
  </clause>

  <clause id="13005">
    <literal><![CDATA[
      (K(x,y) * z) / (x \ y) = K(x,y) * (z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(225,a,13003,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 13003 10262"/>
    </justification>
  </clause>

  <clause id="13006">
    <literal><![CDATA[
      L(x,y,(z \ u) * z) = L(x,y,T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),12985(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 12985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13007">
    <literal><![CDATA[
      L(x,y,T((z \ u) * z,z \ u)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),12985(a,2,3))].">
      <j1 rule="para" parents="10 12985"/>
    </justification>
  </clause>

  <clause id="13008">
    <literal><![CDATA[
      L(x,y,T((T(z,z \ u) / u) * u,T(z,z \ u) / u)) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(7338(a,2),12985(a,2,3))].">
      <j1 rule="para" parents="7338 12985"/>
    </justification>
  </clause>

  <clause id="13009">
    <literal><![CDATA[
      L(x,y,(z * u) / z) = L(x,y,z * (u / z))
    ]]></literal>
    <justification jstring="[para(255(a,1),12988(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="255 12988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13010">
    <literal><![CDATA[
      L(x,y,y / z) = L(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(11765,a,12992,a)].">
      <j1 rule="hyper" parents="11765 12992"/>
    </justification>
  </clause>

  <clause id="13011">
    <literal><![CDATA[
      L(x,y,(z * u) \ u) = L(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[para(5144(a,1),12992(a,1,3))].">
      <j1 rule="para" parents="5144 12992"/>
    </justification>
  </clause>

  <clause id="13012">
    <literal><![CDATA[
      L(x,y * z,(y * z) / y) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),13010(a,2,3))].">
      <j1 rule="para" parents="9 13010"/>
    </justification>
  </clause>

  <clause id="13013">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,T(z * u,z))
    ]]></literal>
    <justification jstring="[para(6745(a,2),12994(a,1,3))].">
      <j1 rule="para" parents="6745 12994"/>
    </justification>
  </clause>

  <clause id="13014">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),w)) = L(x,y,T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(8391(a,2),12994(a,1,3))].">
      <j1 rule="para" parents="8391 12994"/>
    </justification>
  </clause>

  <clause id="13015">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z * y) \ u,u,T(y * z,z))) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(12994(a,1),12669(a,1,2))].">
      <j1 rule="para" parents="12994 12669"/>
    </justification>
  </clause>

  <clause id="13016">
    <literal><![CDATA[
      L(x,y,T(z,z \ ((u \ w) \ z))) = L(x,y,T(z,w \ (u * z)))
    ]]></literal>
    <justification jstring="[para(7086(a,1),12996(a,2,3))].">
      <j1 rule="para" parents="7086 12996"/>
    </justification>
  </clause>

  <clause id="13017">
    <literal><![CDATA[
      L(x,y \ z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(4604,a,12998,a),flip(a)].">
      <j1 rule="hyper" parents="4604 12998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13018">
    <literal><![CDATA[
      L(x,y / z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,6123,a(flip),b,12998,a),flip(a)].">
      <j1 rule="hyper" parents="64 6123 12998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13019">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,y,K(u,u \ z))
    ]]></literal>
    <justification jstring="[para(6118(a,1),12998(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6118 12998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13020">
    <literal><![CDATA[
      (K(x,y) * (y \ x)) \ z = (y \ x) \ (K(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(710,a,13017,a),flip(a)].">
      <j1 rule="hyper" parents="710 13017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13021">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) * z = K(x,y) * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(13017(a,1),6285(a,1,2))].">
      <j1 rule="para" parents="13017 6285"/>
    </justification>
  </clause>

  <clause id="13022">
    <literal><![CDATA[
      K(x,y) * ((x / y) * z) = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(13018(a,1),6306(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13018 6306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13023">
    <literal><![CDATA[
      L(T((x \ y) * x,z),u,T((x \ y) * x,w)) = L(T((x \ y) * x,z),u,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,11861,a,b,13006,a)].">
      <j1 rule="hyper" parents="64 11861 13006"/>
    </justification>
  </clause>

  <clause id="13024">
    <literal><![CDATA[
      L(x,y,(z \ T(u * K(z,u),w)) * z) = L(x,y,T(u,w))
    ]]></literal>
    <justification jstring="[para(5857(a,1),13006(a,2,3))].">
      <j1 rule="para" parents="5857 13006"/>
    </justification>
  </clause>

  <clause id="13025">
    <literal><![CDATA[
      L(x,y,(((z \ u) \ w) \ w) * ((z \ u) \ w)) = L(x,y,T(w,u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(7086(a,1),13006(a,2,3))].">
      <j1 rule="para" parents="7086 13006"/>
    </justification>
  </clause>

  <clause id="13026">
    <literal><![CDATA[
      L(x,y,T(z * K(u,w),u)) = L(x,y,(u \ z) * T(u,w))
    ]]></literal>
    <justification jstring="[para(7128(a,1),13006(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7128 13006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13027">
    <literal><![CDATA[
      L(x,y,L(z * u,z,z)) = L(x,y,z * L(u,z,z))
    ]]></literal>
    <justification jstring="[para(1257(a,1),12984(a,1,3))].">
      <j1 rule="para" parents="1257 12984"/>
    </justification>
  </clause>

  <clause id="13028">
    <literal><![CDATA[
      L(x,y,z * T(u,u \ w)) = L(x,y,z * T(u,w))
    ]]></literal>
    <justification jstring="[para(4803(a,1),12986(a,1,3,2))].">
      <j1 rule="para" parents="4803 12986"/>
    </justification>
  </clause>

  <clause id="13029">
    <literal><![CDATA[
      L(x,y,(z \ T(u,z \ u)) \ w) = L(x,y,(u / z) \ w)
    ]]></literal>
    <justification jstring="[para(4791(a,1),12987(a,1,3,1))].">
      <j1 rule="para" parents="4791 12987"/>
    </justification>
  </clause>

  <clause id="13030">
    <literal><![CDATA[
      L(x,y * z,z * K(y,z)) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(5721(a,1),13012(a,1,3))].">
      <j1 rule="para" parents="5721 13012"/>
    </justification>
  </clause>

  <clause id="13031">
    <literal><![CDATA[
      K(x,y) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(6187,a,13022,a)].">
      <j1 rule="hyper" parents="6187 13022"/>
    </justification>
  </clause>

  <clause id="13032">
    <literal><![CDATA[
      K(x,y) * ((x / y) * z) = (T(x,y) / y) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,4655,a,b,13022,a),flip(a)].">
      <j1 rule="hyper" parents="373 4655 13022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13033">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9839,a,13031,a)].">
      <j1 rule="hyper" parents="9839 13031"/>
    </justification>
  </clause>

  <clause id="13034">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),13033(a,1,2))].">
      <j1 rule="para" parents="9 13033"/>
    </justification>
  </clause>

  <clause id="13036">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[para(13034(a,1),10538(a,2,2))].">
      <j1 rule="para" parents="13034 10538"/>
    </justification>
  </clause>

  <clause id="13037">
    <literal><![CDATA[
      (x / y) \ (K(x,y) \ z) = (T(x,y) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(757,a,13032,a),flip(a)].">
      <j1 rule="hyper" parents="757 13032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13038">
    <literal><![CDATA[
      (x / y) \ (K(y,x) * z) = (T(x,y) / y) \ z
    ]]></literal>
    <justification jstring="[para(6156(a,1),13037(a,1,2))].">
      <j1 rule="para" parents="6156 13037"/>
    </justification>
  </clause>

  <clause id="13039">
    <literal><![CDATA[
      (((x \ y) * T(x,y)) / x) \ (K(x,(x \ y) * T(x,y)) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(4701(a,1),13038(a,2,1,1))].">
      <j1 rule="para" parents="4701 13038"/>
    </justification>
  </clause>

  <clause id="13041">
    <literal><![CDATA[
      (L(x,y,x) * z) \ x = (x * z) \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10900,a(flip),b,12991,a),flip(a)].">
      <j1 rule="hyper" parents="64 10900 12991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13042">
    <literal><![CDATA[
      L(x,y,L(L(z,u,z),w,v5)) = L(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(11557(a,1),12997(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="11557 12997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13043">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5753,a,b,13036,a),flip(a)].">
      <j1 rule="hyper" parents="373 5753 13036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13045">
    <literal><![CDATA[
      T(x,(y / (z * y)) \ x) = T(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5129,a(flip),b,13043,a)].">
      <j1 rule="hyper" parents="64 5129 13043"/>
    </justification>
  </clause>

  <clause id="13046">
    <literal><![CDATA[
      T(x,(y / z) \ x) = T(x,x * (z / y))
    ]]></literal>
    <justification jstring="[para(12(a,1),13045(a,1,2,1,2))].">
      <j1 rule="para" parents="12 13045"/>
    </justification>
  </clause>

  <clause id="13047">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9745,a,b,13046,a)].">
      <j1 rule="hyper" parents="64 9745 13046"/>
    </justification>
  </clause>

  <clause id="13048">
    <literal><![CDATA[
      x * K(x,x * (y / z)) = T(x,(y * x) / z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5753,a(flip),b,13047,a)].">
      <j1 rule="hyper" parents="373 5753 13047"/>
    </justification>
  </clause>

  <clause id="13049">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(35,a,5753,a(flip),b,13048,a)].">
      <j1 rule="hyper" parents="35 5753 13048"/>
    </justification>
  </clause>

  <clause id="13050">
    <literal><![CDATA[
      K(x,x * (y / ((z * x) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(10072,a,13049,a),flip(a)].">
      <j1 rule="hyper" parents="10072 13049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13051">
    <literal><![CDATA[
      K(x,(y / z) \ x) = K(x,x * (z / y))
    ]]></literal>
    <justification jstring="[hyper(9749,a,13049,a)].">
      <j1 rule="hyper" parents="9749 13049"/>
    </justification>
  </clause>

  <clause id="13052">
    <literal><![CDATA[
      (x * K(y,y * (z / u))) / (y \ x) = T(y,T((z * y) / u,x))
    ]]></literal>
    <justification jstring="[para(13049(a,1),8259(a,1,1,2))].">
      <j1 rule="para" parents="13049 8259"/>
    </justification>
  </clause>

  <clause id="13053">
    <literal><![CDATA[
      K(x,(y / z) \ x) \ T(x,z / y) = R(x,z / y,x)
    ]]></literal>
    <justification jstring="[para(13051(a,2),6305(a,1,1))].">
      <j1 rule="para" parents="13051 6305"/>
    </justification>
  </clause>

  <clause id="13054">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,12985,a(flip),b,13013,a),flip(a)].">
      <j1 rule="hyper" parents="373 12985 13013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13055">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),w)) = L(x,y,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(23(a,1),13014(a,2,3))].">
      <j1 rule="para" parents="23 13014"/>
    </justification>
  </clause>

  <clause id="13056">
    <literal><![CDATA[
      (x \ y) \ (K(y,x) \ z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(6157(a,1),13020(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6157 13020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13057">
    <literal><![CDATA[
      (x \ y) \ (K(x,y) * z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(6156(a,1),13056(a,1,2))].">
      <j1 rule="para" parents="6156 13056"/>
    </justification>
  </clause>

  <clause id="13058">
    <literal><![CDATA[
      L(x,y,(z / u) * T(u,w)) = L(x,y,z * K(u,u \ w))
    ]]></literal>
    <justification jstring="[para(6840(a,1),13028(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6840 13028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13059">
    <literal><![CDATA[
      ((x * (y * x)) / x) \ (L(x,y,x) * z) = L(y \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,12993,a)].">
      <j1 rule="hyper" parents="139 168 12993"/>
    </justification>
  </clause>

  <clause id="13061">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13004(a,1),616(a,1))].">
      <j1 rule="para" parents="13004 616"/>
    </justification>
  </clause>

  <clause id="13062">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13019(a,2),13061(a,1))].">
      <j1 rule="para" parents="13019 13061"/>
    </justification>
  </clause>

  <clause id="13063">
    <literal><![CDATA[
      L(x,y,T((z \ (u * K(z,u))) * z,w)) = L(x,y,T(u,w))
    ]]></literal>
    <justification jstring="[para(5432(a,2),13024(a,1,3))].">
      <j1 rule="para" parents="5432 13024"/>
    </justification>
  </clause>

  <clause id="13064">
    <literal><![CDATA[
      L((x \ y) * x,z,T((x \ y) * T(x,y),u)) = L((x \ y) * x,z,T(y * K(x,y),x))
    ]]></literal>
    <justification jstring="[hyper(373,a,12033,a,b,13026,a)].">
      <j1 rule="hyper" parents="373 12033 13026"/>
    </justification>
  </clause>

  <clause id="13065">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ w)) = L(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(6840(a,1),13058(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6840 13058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13066">
    <literal><![CDATA[
      L(x,y,T((z \ u) * z,w)) = L(x,y,T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(5749(a,1),13063(a,1,3,1,1,2))].">
      <j1 rule="para" parents="5749 13063"/>
    </justification>
  </clause>

  <clause id="13067">
    <literal><![CDATA[
      L(x,y,T((z \ u) * T(z,u),w)) = L(x,y,T(u,w))
    ]]></literal>
    <justification jstring="[para(5916(a,1),13063(a,1,3,1))].">
      <j1 rule="para" parents="5916 13063"/>
    </justification>
  </clause>

  <clause id="13068">
    <literal><![CDATA[
      L(x,y,T(T(z,u),u \ z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13007,a(flip),b,13066,a),flip(a)].">
      <j1 rule="hyper" parents="64 13007 13066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13069">
    <literal><![CDATA[
      L(x,y,T(T(z,u \ z),u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(23(a,1),13068(a,1,3))].">
      <j1 rule="para" parents="23 13068"/>
    </justification>
  </clause>

  <clause id="13070">
    <literal><![CDATA[
      L(x,y,T(z,(u \ w) \ 1)) = L(x,y,T(z,w \ (u * z)))
    ]]></literal>
    <justification jstring="[para(4575(a,1),13016(a,1,3))].">
      <j1 rule="para" parents="4575 13016"/>
    </justification>
  </clause>

  <clause id="13071">
    <literal><![CDATA[
      L(x,y,T(z,u \ (w * z))) = L(x,y,T(z,u \ w))
    ]]></literal>
    <justification jstring="[para(6704(a,1),13070(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6704 13070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13072">
    <literal><![CDATA[
      T(x,T((y * x) / z,u)) = T(x,T(x * (y / z),u))
    ]]></literal>
    <justification jstring="[hyper(8373,a,13052,a),flip(a)].">
      <j1 rule="hyper" parents="8373 13052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13073">
    <literal><![CDATA[
      T(x,T(y / (x \ z),u)) = T(x,T(x * (y / z),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9757,a(flip),b,13072,a)].">
      <j1 rule="hyper" parents="64 9757 13072"/>
    </justification>
  </clause>

  <clause id="13074">
    <literal><![CDATA[
      T(x,T((y / z) \ x,u)) = T(x,T(x * (z / y),u))
    ]]></literal>
    <justification jstring="[hyper(9842,a,13073,a)].">
      <j1 rule="hyper" parents="9842 13073"/>
    </justification>
  </clause>

  <clause id="13075">
    <literal><![CDATA[
      K(x / y,z) * T(z,T(z * (x / y),x / y)) = L(z,(x / y) * ((x / y) \ ((y / x) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(13074(a,1),12719(a,1,2))].">
      <j1 rule="para" parents="13074 12719"/>
    </justification>
  </clause>

  <clause id="13076">
    <literal><![CDATA[
      L(x,y,K(z \ 1,((u * z) \ u) * w)) = L(x,y,K(z \ 1,w))
    ]]></literal>
    <justification jstring="[para(6766(a,1),13001(a,2,3))].">
      <j1 rule="para" parents="6766 13001"/>
    </justification>
  </clause>

  <clause id="13078">
    <literal><![CDATA[
      L(x,y,K(z * u,R(z,u,u \ 1))) = L(x,y,K(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(297(a,1),13002(a,1,3,2))].">
      <j1 rule="para" parents="297 13002"/>
    </justification>
  </clause>

  <clause id="13079">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u * z,u))
    ]]></literal>
    <justification jstring="[para(9719(a,1),13078(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9719 13078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13081">
    <literal><![CDATA[
      L(x,y,T(z,u \ (w * z))) = L(x,y,(w \ u) * (z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(4507(a,1),13025(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4507 13025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13082">
    <literal><![CDATA[
      L(x,y,(z \ u) * (w / (z \ u))) = L(x,y,T(w,u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13071,a(flip),b,13081,a),flip(a)].">
      <j1 rule="hyper" parents="64 13071 13081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13083">
    <literal><![CDATA[
      L(T((x \ y) * x,z),u,T(T(y,x),w)) = L(T((x \ y) * x,z),u,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,13066,a(flip),b,13023,a)].">
      <j1 rule="hyper" parents="64 13066 13023"/>
    </justification>
  </clause>

  <clause id="13084">
    <literal><![CDATA[
      (a(x,y,x) * (z * (u * w))) \ ((a(x,y,x) * (z * u)) * w) = a(a(x,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(12890(a,1),12915(a,1,2,1))].">
      <j1 rule="para" parents="12890 12915"/>
    </justification>
  </clause>

  <clause id="13085">
    <literal><![CDATA[
      ((x \ y) * K(x,y)) \ (K(x,(x \ y) * T(x,y)) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(6847(a,1),13039(a,1,1))].">
      <j1 rule="para" parents="6847 13039"/>
    </justification>
  </clause>

  <clause id="13086">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ (K(x,(x \ y) * T(x,y)) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(7130(a,2),13085(a,1,1))].">
      <j1 rule="para" parents="7130 13085"/>
    </justification>
  </clause>

  <clause id="13087">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ (K(x,x * (x \ y)) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(8572(a,1),13086(a,1,2,1))].">
      <j1 rule="para" parents="8572 13086"/>
    </justification>
  </clause>

  <clause id="13088">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ (K(x,y) * z) = (((x \ y) * x) / x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),13087(a,1,2,1,2))].">
      <j1 rule="para" parents="10 13087"/>
    </justification>
  </clause>

  <clause id="13090">
    <literal><![CDATA[
      L((x \ y) * x,z,T((x \ y) * T(x,y),u)) = L((x \ y) * x,z,y)
    ]]></literal>
    <justification jstring="[para(5785(a,1),13064(a,2,3))].">
      <j1 rule="para" parents="5785 13064"/>
    </justification>
  </clause>

  <clause id="13091">
    <literal><![CDATA[
      L((x \ y) * x,z,T(y,u)) = L((x \ y) * x,z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13067,a(flip),b,13090,a)].">
      <j1 rule="hyper" parents="64 13067 13090"/>
    </justification>
  </clause>

  <clause id="13093">
    <literal><![CDATA[
      L(T((x \ y) * x,z),u,T(y,w)) = T(L((x \ y) * x,u,y),z)
    ]]></literal>
    <justification jstring="[para(13091(a,1),25(a,2,1))].">
      <j1 rule="para" parents="13091 25"/>
    </justification>
  </clause>

  <clause id="13094">
    <literal><![CDATA[
      L(T((x \ y) * x,z),u,T(y,w)) = L(T((x \ y) * x,z),u,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,25,a,b,13093,a),flip(a)].">
      <j1 rule="hyper" parents="373 25 13093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13095">
    <literal><![CDATA[
      L(T((x \ y) * x,z),u,T(T(y,x),w)) = L(T((x \ y) * x,z),u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13083,a,b,13094,a)].">
      <j1 rule="hyper" parents="64 13083 13094"/>
    </justification>
  </clause>

  <clause id="13097">
    <literal><![CDATA[
      (a(x,y,x) * (z * (u * w))) \ (a(x,y,x) * ((z * u) * w)) = a(a(x,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(12890(a,1),13084(a,1,2))].">
      <j1 rule="para" parents="12890 13084"/>
    </justification>
  </clause>

  <clause id="13098">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),a(u,w,u)) = a(a(u,w,u) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1082,a,13097,a)].">
      <j1 rule="hyper" parents="1082 13097"/>
    </justification>
  </clause>

  <clause id="13099">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(12899,a,13098,a),flip(a)].">
      <j1 rule="hyper" parents="12899 13098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13101">
    <literal><![CDATA[
      a(a(x,y,x) \ z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),13099(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13103">
    <literal><![CDATA[
      a(R(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(10898(a,1),13099(a,1,1))].">
      <j1 rule="para" parents="10898 13099"/>
    </justification>
  </clause>

  <clause id="13104">
    <literal><![CDATA[
      a(K(x * y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(10902(a,1),13099(a,1,1))].">
      <j1 rule="para" parents="10902 13099"/>
    </justification>
  </clause>

  <clause id="13105">
    <literal><![CDATA[
      a(K(x,x \ y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(10935(a,1),13099(a,1,1))].">
      <j1 rule="para" parents="10935 13099"/>
    </justification>
  </clause>

  <clause id="13106">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(11011(a,1),13099(a,1,1))].">
      <j1 rule="para" parents="11011 13099"/>
    </justification>
  </clause>

  <clause id="13107">
    <literal><![CDATA[
      a(T(x * y,x),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(11058(a,1),13099(a,1,1))].">
      <j1 rule="para" parents="11058 13099"/>
    </justification>
  </clause>

  <clause id="13108">
    <literal><![CDATA[
      a(R(x,y,x) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(11368(a,1),13099(a,1,1))].">
      <j1 rule="para" parents="11368 13099"/>
    </justification>
  </clause>

  <clause id="13109">
    <literal><![CDATA[
      a((L(x,y,x) \ z) * u,w,v5) = a((x \ z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(12912(a,1),13099(a,1,1))].">
      <j1 rule="para" parents="12912 13099"/>
    </justification>
  </clause>

  <clause id="13110">
    <literal><![CDATA[
      a(R(a(x,y,x) * z,u,w),v5,v6) = a(R(z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(12937(a,2),13099(a,1,1))].">
      <j1 rule="para" parents="12937 13099"/>
    </justification>
  </clause>

  <clause id="13111">
    <literal><![CDATA[
      a((x \ y) \ y,z,u) = a(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(10106(a,1),13103(a,1,1))].">
      <j1 rule="para" parents="10106 13103"/>
    </justification>
  </clause>

  <clause id="13112">
    <literal><![CDATA[
      a(L(R(x,y,x),z,u),w,v5) = a(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(11556(a,1),13103(a,1,1))].">
      <j1 rule="para" parents="11556 13103"/>
    </justification>
  </clause>

  <clause id="13113">
    <literal><![CDATA[
      a(K(x \ y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(10881(a,1),13101(a,1,1))].">
      <j1 rule="para" parents="10881 13101"/>
    </justification>
  </clause>

  <clause id="13114">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(x \ y,y),z,u)
    ]]></literal>
    <justification jstring="[para(10924(a,1),13101(a,1,1))].">
      <j1 rule="para" parents="10924 13101"/>
    </justification>
  </clause>

  <clause id="13115">
    <literal><![CDATA[
      a(T(x,y) / y,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(10928(a,1),13106(a,1,1))].">
      <j1 rule="para" parents="10928 13106"/>
    </justification>
  </clause>

  <clause id="13116">
    <literal><![CDATA[
      a(T(x * (y / x),x),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(11373(a,1),13106(a,1,1))].">
      <j1 rule="para" parents="11373 13106"/>
    </justification>
  </clause>

  <clause id="13117">
    <literal><![CDATA[
      a(T(x * ((x / y) / x),T(x,y \ 1)),z,u) = a(x * ((y \ x) / x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5476,a(flip),b,13111,a),flip(a)].">
      <j1 rule="hyper" parents="64 5476 13111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13118">
    <literal><![CDATA[
      a(T(x / y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(82(a,1),13111(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 13111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13119">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12969,a,b,13113,a)].">
      <j1 rule="hyper" parents="64 12969 13113"/>
    </justification>
  </clause>

  <clause id="13120">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(6118(a,1),13113(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6118 13113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13121">
    <literal><![CDATA[
      a(x * (y / x),x,z) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(5051,a,13116,a)].">
      <j1 rule="hyper" parents="5051 13116"/>
    </justification>
  </clause>

  <clause id="13122">
    <literal><![CDATA[
      a((x * y) \ y,z,u) = a(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[para(5144(a,1),13118(a,1,1))].">
      <j1 rule="para" parents="5144 13118"/>
    </justification>
  </clause>

  <clause id="13123">
    <literal><![CDATA[
      a(T(x,x \ y) * z,u,w) = a(T(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(4803(a,1),13108(a,1,1,1))].">
      <j1 rule="para" parents="4803 13108"/>
    </justification>
  </clause>

  <clause id="13124">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,13105,a(flip),b,13120,a),flip(a)].">
      <j1 rule="hyper" parents="373 13105 13120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13125">
    <literal><![CDATA[
      a(K(x \ y,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(6128(a,1),13124(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6128 13124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13126">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13114,a,b,13125,a)].">
      <j1 rule="hyper" parents="64 13114 13125"/>
    </justification>
  </clause>

  <clause id="13127">
    <literal><![CDATA[
      a(K(x,y \ 1),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3779(a,1),13126(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3779 13126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13128">
    <literal><![CDATA[
      a(R(K(x,y),(y * x) * z,u),w,v5) = a(K(R(y,x * z,u) \ 1,x),w,v5)
    ]]></literal>
    <justification jstring="[para(10819(a,2),13126(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10819 13126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13129">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12687,a,b,13127,a)].">
      <j1 rule="hyper" parents="64 12687 13127"/>
    </justification>
  </clause>

  <clause id="13130">
    <literal><![CDATA[
      a(L(L(x,y,x),z,u),w,v5) = a(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(11557(a,1),13112(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11557 13112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13131">
    <literal><![CDATA[
      a(L(L(x,y,z),u,x),w,v5) = a(L(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(30(a,1),13130(a,1,1))].">
      <j1 rule="para" parents="30 13130"/>
    </justification>
  </clause>

  <clause id="13132">
    <literal><![CDATA[
      (x * K(y \ R(y,z,u),x)) \ L(x,y \ R(y,z,u),x) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,6517,a,b,13119,a)].">
      <j1 rule="hyper" parents="64 6517 13119"/>
    </justification>
  </clause>

  <clause id="13133">
    <literal><![CDATA[
      a(R(a(x,y,x) * z,u,w) * (v5 \ (1 / v5)),v6,v7) = a(R(z,u,w),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,11963,a,b,13110,a)].">
      <j1 rule="hyper" parents="64 11963 13110"/>
    </justification>
  </clause>

  <clause id="13134">
    <literal><![CDATA[
      a(R((a(x,y,x) * z) * (u \ (1 / u)),w,v5),v6,v7) = a(R(z,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(2180(a,2),13133(a,1,1))].">
      <j1 rule="para" parents="2180 13133"/>
    </justification>
  </clause>

  <clause id="13135">
    <literal><![CDATA[
      a(R(a(x,y,x) * (z * (u \ (1 / u))),w,v5),v6,v7) = a(R(z,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(12890(a,1),13134(a,1,1,1))].">
      <j1 rule="para" parents="12890 13134"/>
    </justification>
  </clause>

  <clause id="13136">
    <literal><![CDATA[
      a(R(K(x,y),(y * x) * z,u),w,v5) = a(K(y \ 1,R(x,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(9722(a,1),13128(a,2,1))].">
      <j1 rule="para" parents="9722 13128"/>
    </justification>
  </clause>

  <clause id="13137">
    <literal><![CDATA[
      a(R(K(x,y),(y * x) * z,u),w,v5) = a(K(R(x,z,u),y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,13126,a(flip),b,13136,a),flip(a)].">
      <j1 rule="hyper" parents="373 13126 13136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13138">
    <literal><![CDATA[
      a(K(x,R(y,x * z,u)),w,v5) = a(K(R(x,z,u),y),w,v5)
    ]]></literal>
    <justification jstring="[para(10819(a,1),13137(a,1,1))].">
      <j1 rule="para" parents="10819 13137"/>
    </justification>
  </clause>

  <clause id="13139">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),T(z,z \ u) / u)) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(12(a,1),13008(a,1,3,1))].">
      <j1 rule="para" parents="12 13008"/>
    </justification>
  </clause>

  <clause id="13141">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),u \ T(z,z \ u))) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(4461(a,1),13139(a,1,3))].">
      <j1 rule="para" parents="4461 13139"/>
    </justification>
  </clause>

  <clause id="13142">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),z / u)) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(9232(a,1),13141(a,1,3))].">
      <j1 rule="para" parents="9232 13141"/>
    </justification>
  </clause>

  <clause id="13143">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ u),u \ z)) = L(x,y,(z \ u) \ T(u,u \ z))
    ]]></literal>
    <justification jstring="[para(7452(a,1),13142(a,1,3))].">
      <j1 rule="para" parents="7452 13142"/>
    </justification>
  </clause>

  <clause id="13144">
    <literal><![CDATA[
      L(x,y,(z \ u) \ T(u,u \ z)) = L(x,y,T(T(z,u \ z),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13014,a(flip),b,13143,a),flip(a)].">
      <j1 rule="hyper" parents="64 13014 13143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13145">
    <literal><![CDATA[
      L(x,y,(z \ u) \ T(u,u \ z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,13069,a(flip),b,13144,a),flip(a)].">
      <j1 rule="hyper" parents="373 13069 13144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13147">
    <literal><![CDATA[
      L(T((x / y) \ 1,x) \ 1,(x / y) \ 1,x) = (((y \ x) \ 1) * x) \ (y * (x / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,12667,a(flip),b,13145,a),flip(a)].">
      <j1 rule="hyper" parents="64 12667 13145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13148">
    <literal><![CDATA[
      (((x \ y) \ 1) * y) \ (x * (y / x)) = (((y / x) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(10984,a,13147,a),flip(a)].">
      <j1 rule="hyper" parents="10984 13147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13150">
    <literal><![CDATA[
      (K(x,T(x,x * y) * y) \ z) \ T(T(T(x,x * y) * y,x),x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7122,a(flip),b,12999,a),flip(a)].">
      <j1 rule="hyper" parents="64 7122 12999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13151">
    <literal><![CDATA[
      (K(x,x * y) \ z) \ T(T(T(x,x * y) * y,x),x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(8546(a,1),13150(a,1,1,1))].">
      <j1 rule="para" parents="8546 13150"/>
    </justification>
  </clause>

  <clause id="13152">
    <literal><![CDATA[
      (K(x,x * y) \ z) \ T(x * y,x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(4478(a,1),13151(a,1,2,1))].">
      <j1 rule="para" parents="4478 13151"/>
    </justification>
  </clause>

  <clause id="13154">
    <literal><![CDATA[
      L(x,(y / z) * ((y / z) \ ((z / y) \ 1)),x) = K(y / z,x) * T(x,x * (y / z))
    ]]></literal>
    <justification jstring="[para(7860(a,1),13075(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7860 13075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13155">
    <literal><![CDATA[
      L(x,(y / z) * ((y / z) \ ((z / y) \ 1)),x) = L(x,y / z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6080,a(flip),b,13154,a),flip(a)].">
      <j1 rule="hyper" parents="373 6080 13154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13156">
    <literal><![CDATA[
      L(x,y / z,x) = L(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11399,a(flip),b,13155,a),flip(a)].">
      <j1 rule="hyper" parents="64 11399 13155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13158">
    <literal><![CDATA[
      L(x,(y / z) / u,x) = L(x,(u * z) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12953,a,b,13156,a)].">
      <j1 rule="hyper" parents="64 12953 13156"/>
    </justification>
  </clause>

  <clause id="13159">
    <literal><![CDATA[
      L(x,(y \ z) \ z,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),13156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 13156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13160">
    <literal><![CDATA[
      L(x,R(y \ R(y,z,u),y,z * u),x) = L(x,(y * (z * u)) \ ((y * z) * u),x)
    ]]></literal>
    <justification jstring="[para(2295(a,2),13156(a,1,2))].">
      <j1 rule="para" parents="2295 13156"/>
    </justification>
  </clause>

  <clause id="13161">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(366(a,2),13159(a,1,2))].">
      <j1 rule="para" parents="366 13159"/>
    </justification>
  </clause>

  <clause id="13162">
    <literal><![CDATA[
      L(x,T(y,z),x) = T(x,T(x * y,u)) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,11388,a,b,13161,a),flip(a)].">
      <j1 rule="hyper" parents="373 11388 13161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13163">
    <literal><![CDATA[
      L(x,T(y,z),x) = x / a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10894,a,b,13161,a),flip(a)].">
      <j1 rule="hyper" parents="373 10894 13161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13164">
    <literal><![CDATA[
      a(x,T(y,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(10912,a,13163,a)].">
      <j1 rule="hyper" parents="10912 13163"/>
    </justification>
  </clause>

  <clause id="13165">
    <literal><![CDATA[
      L(x,T(y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(13163(a,2),10909(a,1))].">
      <j1 rule="para" parents="13163 10909"/>
    </justification>
  </clause>

  <clause id="13166">
    <literal><![CDATA[
      a(x,T(y,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10884,a,b,13164,a),flip(a)].">
      <j1 rule="hyper" parents="373 10884 13164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13168">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,12972,a(flip),b,13164,a),flip(a)].">
      <j1 rule="hyper" parents="64 12972 13164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13169">
    <literal><![CDATA[
      a(x,y / z,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(117(a,1),13164(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 13164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13170">
    <literal><![CDATA[
      a(x,R(y / z,u,w),x) = a(x,R(z \ y,u,w),x)
    ]]></literal>
    <justification jstring="[para(280(a,1),13164(a,1,2)),flip(a)].">
      <j1 rule="para" parents="280 13164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13171">
    <literal><![CDATA[
      a(x,R(y / z,z,u),x) = a(x,(z * u) \ (y * u),x)
    ]]></literal>
    <justification jstring="[para(681(a,1),13164(a,1,2)),flip(a)].">
      <j1 rule="para" parents="681 13164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13172">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(5785(a,1),13164(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5785 13164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13173">
    <literal><![CDATA[
      a(1 / ((x * y) \ x),z,1 / ((x * y) \ x)) * K(T(z,y),1 / ((x * y) \ x)) = K(z * (1 / ((x * y) \ x)),1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(13164(a,1),10925(a,1,1))].">
      <j1 rule="para" parents="13164 10925"/>
    </justification>
  </clause>

  <clause id="13174">
    <literal><![CDATA[
      R(x,T(y,z),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(10899,a,13166,a)].">
      <j1 rule="hyper" parents="10899 13166"/>
    </justification>
  </clause>

  <clause id="13175">
    <literal><![CDATA[
      a(x,T(y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(13166(a,2),10908(a,1))].">
      <j1 rule="para" parents="13166 10908"/>
    </justification>
  </clause>

  <clause id="13179">
    <literal><![CDATA[
      T(x,y) * R(z,x,z) = T(z * T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,13174,a(flip),b,4736,a)].">
      <j1 rule="hyper" parents="145 13174 4736"/>
    </justification>
  </clause>

  <clause id="13180">
    <literal><![CDATA[
      R(x,y / z,x) = R(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(117(a,1),13174(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 13174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13184">
    <literal><![CDATA[
      K(x,(y / z) \ x) \ T(x,z / y) = R(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13053,a,b,13180,a)].">
      <j1 rule="hyper" parents="64 13053 13180"/>
    </justification>
  </clause>

  <clause id="13185">
    <literal><![CDATA[
      a(x,y \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z / y,x) = u
    ]]></literal>
    <justification jstring="[para(117(a,1),13175(a,1,2))].">
      <j1 rule="para" parents="117 13175"/>
    </justification>
  </clause>

  <clause id="13186">
    <literal><![CDATA[
      T(x * T(y \ (y / z),K(z,u)),x) = (y \ (y / z)) * R(x,y \ (y / z),x)
    ]]></literal>
    <justification jstring="[para(6772(a,1),13179(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6772 13179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13187">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,12888,a(flip),b,13168,a),flip(a)].">
      <j1 rule="hyper" parents="373 12888 13168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13189">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,x),y,z) = a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11558,a,b,13187,a)].">
      <j1 rule="hyper" parents="64 11558 13187"/>
    </justification>
  </clause>

  <clause id="13190">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11614,a(flip),b,13187,a)].">
      <j1 rule="hyper" parents="64 11614 13187"/>
    </justification>
  </clause>

  <clause id="13191">
    <literal><![CDATA[
      L(x,y,z) * a(x,u,x) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,13187,a(flip),b,11558,a)].">
      <j1 rule="hyper" parents="145 13187 11558"/>
    </justification>
  </clause>

  <clause id="13192">
    <literal><![CDATA[
      a(x,L(x,y,z) \ u,x) \ u = (L(x,y,z) \ u) * T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(13187(a,1),11045(a,1,1))].">
      <j1 rule="para" parents="13187 11045"/>
    </justification>
  </clause>

  <clause id="13194">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y * K(w,y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13172,a,b,13190,a),flip(a)].">
      <j1 rule="hyper" parents="373 13172 13190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13196">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,13190,a(flip),b,5027,a)].">
      <j1 rule="hyper" parents="145 13190 5027"/>
    </justification>
  </clause>

  <clause id="13197">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (u * a(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(144,a,13190,a(flip),b,11092,a)].">
      <j1 rule="hyper" parents="144 13190 11092"/>
    </justification>
  </clause>

  <clause id="13199">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = (x \ y) * a(z,u,z)
    ]]></literal>
    <justification jstring="[para(13190(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="13190 598"/>
    </justification>
  </clause>

  <clause id="13201">
    <literal><![CDATA[
      a(x,y * K(z,y),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(13194(a,1),623(a,1)),flip(b)].">
      <j1 rule="para" parents="13194 623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13202">
    <literal><![CDATA[
      L(a(x,L(y,z,u),x),w,v5) = a(x,L(y * K(v6,y),z,u),x)
    ]]></literal>
    <justification jstring="[para(6547(a,1),13194(a,2,2))].">
      <j1 rule="para" parents="6547 13194"/>
    </justification>
  </clause>

  <clause id="13203">
    <literal><![CDATA[
      L(a(x,y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(13194(a,2),10939(a,1))].">
      <j1 rule="para" parents="13194 10939"/>
    </justification>
  </clause>

  <clause id="13204">
    <literal><![CDATA[
      a(x,y / z,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,x) = u
    ]]></literal>
    <justification jstring="[para(5774(a,1),13201(a,1,2))].">
      <j1 rule="para" parents="5774 13201"/>
    </justification>
  </clause>

  <clause id="13206">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(664,a,13196,a)].">
      <j1 rule="hyper" parents="664 13196"/>
    </justification>
  </clause>

  <clause id="13207">
    <literal><![CDATA[
      ((x * y) * (z * a(u,w,u))) / ((y * z) * a(u,w,u)) = R(R(x,y,z),y * z,a(u,w,u))
    ]]></literal>
    <justification jstring="[para(13196(a,1),660(a,1,1))].">
      <j1 rule="para" parents="13196 660"/>
    </justification>
  </clause>

  <clause id="13208">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (a(z,u,z) * y)
    ]]></literal>
    <justification jstring="[para(11011(a,2),13196(a,2,2))].">
      <j1 rule="para" parents="11011 13196"/>
    </justification>
  </clause>

  <clause id="13209">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ w = (x * y) \ (a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(13196(a,1),12922(a,1,1))].">
      <j1 rule="para" parents="13196 12922"/>
    </justification>
  </clause>

  <clause id="13210">
    <literal><![CDATA[
      L(x,y,z * (u * a(w,v5,w))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(13196(a,1),12983(a,1,3))].">
      <j1 rule="para" parents="13196 12983"/>
    </justification>
  </clause>

  <clause id="13211">
    <literal><![CDATA[
      L(T(x,y),y,a(z,u,z)) = T(x,y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(11524,a,13206,a)].">
      <j1 rule="hyper" parents="11524 13206"/>
    </justification>
  </clause>

  <clause id="13213">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = (x \ u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(759,a,13197,a)].">
      <j1 rule="hyper" parents="759 13197"/>
    </justification>
  </clause>

  <clause id="13214">
    <literal><![CDATA[
      (x \ (a(y,z,y) \ u)) * a(y,z,y) = x \ u
    ]]></literal>
    <justification jstring="[hyper(757,a,13197,a),flip(a)].">
      <j1 rule="hyper" parents="757 13197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13215">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,z)) = a(z,u,z) * y
    ]]></literal>
    <justification jstring="[hyper(397,a,13197,a),flip(a)].">
      <j1 rule="hyper" parents="397 13197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13217">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = x * (u * a(y,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,12920,a,b,13197,a)].">
      <j1 rule="hyper" parents="64 12920 13197"/>
    </justification>
  </clause>

  <clause id="13218">
    <literal><![CDATA[
      (x * y) \ (x * (a(z,u,z) * (y * w))) = L(w * a(z,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(13197(a,2),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13197 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13219">
    <literal><![CDATA[
      a(x,y,x) * (z * (x \ u)) = z * (L(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(10951(a,1),13197(a,2,2))].">
      <j1 rule="para" parents="10951 13197"/>
    </justification>
  </clause>

  <clause id="13220">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(11011(a,2),13197(a,2,2))].">
      <j1 rule="para" parents="11011 13197"/>
    </justification>
  </clause>

  <clause id="13221">
    <literal><![CDATA[
      a(x,y,x) * (z * (a(x,y,x) \ u)) = z * u
    ]]></literal>
    <justification jstring="[para(11016(a,1),13197(a,2,2))].">
      <j1 rule="para" parents="11016 13197"/>
    </justification>
  </clause>

  <clause id="13222">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = a(z,u,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11011,a,b,13199,a),flip(a)].">
      <j1 rule="hyper" parents="373 11011 13199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13223">
    <literal><![CDATA[
      (x \ (x / y)) * a(y,y,y) = L(1 / y,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11085,a(flip),b,13199,a),flip(a)].">
      <j1 rule="hyper" parents="64 11085 13199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13224">
    <literal><![CDATA[
      (x \ y) * a(y,z,y) = x \ R(y,z,y)
    ]]></literal>
    <justification jstring="[para(10889(a,1),13199(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10889 13199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13225">
    <literal><![CDATA[
      (x \ L(y,z,y)) * a(y,z,y) = x \ y
    ]]></literal>
    <justification jstring="[para(10895(a,1),13199(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10895 13199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13226">
    <literal><![CDATA[
      (x \ K(y,z)) * a(y,y \ z,y) = x \ K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(10933(a,1),13199(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10933 13199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13227">
    <literal><![CDATA[
      (x \ (1 / y)) * a(z,u,z) = x \ (a(z,u,z) / y)
    ]]></literal>
    <justification jstring="[para(12905(a,1),13199(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12905 13199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13228">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,u))) = (x \ (y * z)) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(13196(a,1),13199(a,1,2))].">
      <j1 rule="para" parents="13196 13199"/>
    </justification>
  </clause>

  <clause id="13229">
    <literal><![CDATA[
      a(x,y,x) * (z \ x) = z \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(11021,a,13224,a)].">
      <j1 rule="hyper" parents="11021 13224"/>
    </justification>
  </clause>

  <clause id="13231">
    <literal><![CDATA[
      a(x \ R(y,z,y),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[para(13224(a,1),13106(a,1,1))].">
      <j1 rule="para" parents="13224 13106"/>
    </justification>
  </clause>

  <clause id="13232">
    <literal><![CDATA[
      a(x,y,x) * (z \ L(x,y,x)) = z \ x
    ]]></literal>
    <justification jstring="[hyper(11021,a,13225,a)].">
      <j1 rule="hyper" parents="11021 13225"/>
    </justification>
  </clause>

  <clause id="13233">
    <literal><![CDATA[
      a(x,y,x) \ (z \ x) = z \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,11016,a,b,13225,a)].">
      <j1 rule="hyper" parents="36 11016 13225"/>
    </justification>
  </clause>

  <clause id="13234">
    <literal><![CDATA[
      a(x \ L(y,z,y),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[para(13225(a,1),13106(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13225 13106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13235">
    <literal><![CDATA[
      (x * y) \ L(y,x,y) = T(y * x,y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,11283,a(flip),b,13232,a)].">
      <j1 rule="hyper" parents="64 11283 13232"/>
    </justification>
  </clause>

  <clause id="13236">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,z \ ((x * (z * y)) / x),z) = T(z * (z \ ((x * (z * y)) / x)),z) \ z
    ]]></literal>
    <justification jstring="[para(5499(a,1),13235(a,1,1))].">
      <j1 rule="para" parents="5499 13235"/>
    </justification>
  </clause>

  <clause id="13237">
    <literal><![CDATA[
      a(x,y,x) * (z \ 1) = z \ a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(458,a,13208,a),flip(a)].">
      <j1 rule="hyper" parents="458 13208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13238">
    <literal><![CDATA[
      a(x * (a(y,z,y) * u),w,v5) = a(x * u,w,v5)
    ]]></literal>
    <justification jstring="[para(13208(a,1),13106(a,1,1))].">
      <j1 rule="para" parents="13208 13106"/>
    </justification>
  </clause>

  <clause id="13239">
    <literal><![CDATA[
      a(x,y,x) * ((z \ 1) * u) = (z \ a(x,y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,13237,a(flip),b,12892,a),flip(a)].">
      <j1 rule="hyper" parents="144 13237 12892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13240">
    <literal><![CDATA[
      (x \ 1) \ (a(y,z,y) \ u) = (x \ a(y,z,y)) \ u
    ]]></literal>
    <justification jstring="[para(13237(a,1),12896(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13237 12896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13241">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = a(y,z,y) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11011,a,b,13213,a),flip(a)].">
      <j1 rule="hyper" parents="373 11011 13213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13243">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = (z \ u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12895,a,b,13213,a)].">
      <j1 rule="hyper" parents="64 12895 13213"/>
    </justification>
  </clause>

  <clause id="13244">
    <literal><![CDATA[
      (x \ ((y * z) * u)) * a(y,w,y) = x \ ((R(y,w,y) * z) * u)
    ]]></literal>
    <justification jstring="[para(12909(a,1),13213(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12909 13213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13245">
    <literal><![CDATA[
      a(x,y,x) \ (z \ u) = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(36,a,11016,a,b,13214,a)].">
      <j1 rule="hyper" parents="36 11016 13214"/>
    </justification>
  </clause>

  <clause id="13246">
    <literal><![CDATA[
      ((a(x,y,x) * z) \ u) * a(x,y,x) = z \ u
    ]]></literal>
    <justification jstring="[para(12896(a,2),13214(a,1,1))].">
      <j1 rule="para" parents="12896 13214"/>
    </justification>
  </clause>

  <clause id="13247">
    <literal><![CDATA[
      (x \ (y * x)) * a(z,u,z) = T(y * a(z,u,z),x)
    ]]></literal>
    <justification jstring="[hyper(269,a,12920,a,b,13215,a),flip(a)].">
      <j1 rule="hyper" parents="269 12920 13215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13248">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = x * (a(y,z,y) * u)
    ]]></literal>
    <justification jstring="[para(11011(a,2),13217(a,2,2))].">
      <j1 rule="para" parents="11011 13217"/>
    </justification>
  </clause>

  <clause id="13249">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,13220,a)].">
      <j1 rule="hyper" parents="139 168 13220"/>
    </justification>
  </clause>

  <clause id="13251">
    <literal><![CDATA[
      L(x,y,R(z * (a(u,w,u) * v5),v6,v7)) = L(x,y,R(z * v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(13220(a,1),12989(a,1,3,1))].">
      <j1 rule="para" parents="13220 12989"/>
    </justification>
  </clause>

  <clause id="13252">
    <literal><![CDATA[
      a(x,y,x) * (z * (u \ 1)) = z * (u \ a(x,y,x))
    ]]></literal>
    <justification jstring="[para(13237(a,1),13220(a,2,2))].">
      <j1 rule="para" parents="13237 13220"/>
    </justification>
  </clause>

  <clause id="13253">
    <literal><![CDATA[
      (a(x,y,x) \ z) * u = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12889,a(flip),b,13221,a),flip(a)].">
      <j1 rule="hyper" parents="64 12889 13221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13254">
    <literal><![CDATA[
      x \ ((a(y,z,y) \ x) * u) = a(y,z,y) \ u
    ]]></literal>
    <justification jstring="[hyper(139,a,13221,a(flip),b,12889,a(flip))].">
      <j1 rule="hyper" parents="139 13221 12889"/>
    </justification>
  </clause>

  <clause id="13255">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      z * (a(x,y,x) \ u) = w
    ]]></literal>
    <justification jstring="[para(13221(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13221 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13256">
    <literal><![CDATA[
      L(x,y,z * (a(u,w,u) \ v5)) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(13221(a,1),12975(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13221 12975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13257">
    <literal><![CDATA[
      a(x,y,x) * (z \ L(x,u,w)) = z \ L(R(x,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(13191(a,1),13222(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13191 13222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13258">
    <literal><![CDATA[
      x \ (y * (a(z,u,z) * w)) = a(z,u,z) * (x \ (y * w))
    ]]></literal>
    <justification jstring="[para(13208(a,1),13222(a,1,2))].">
      <j1 rule="para" parents="13208 13222"/>
    </justification>
  </clause>

  <clause id="13259">
    <literal><![CDATA[
      a(x,y,x) * (z \ (u * z)) = T(a(x,y,x) * u,z)
    ]]></literal>
    <justification jstring="[hyper(12918,a,13241,a),flip(a)].">
      <j1 rule="hyper" parents="12918 13241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13260">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = a(x,y,x) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12895,a,b,13241,a)].">
      <j1 rule="hyper" parents="64 12895 13241"/>
    </justification>
  </clause>

  <clause id="13261">
    <literal><![CDATA[
      a(x,y,x) * ((z * x) \ u) = (z * L(x,y,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,12921,a(flip),b,13241,a),flip(a)].">
      <j1 rule="hyper" parents="64 12921 13241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13262">
    <literal><![CDATA[
      x / (y * a(z,u,z)) = a(z,u,z) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(225,a,221,a(flip),b,13243,a)].">
      <j1 rule="hyper" parents="225 221 13243"/>
    </justification>
  </clause>

  <clause id="13263">
    <literal><![CDATA[
      ((x * y) \ z) * a(x,u,x) = (L(x,u,x) * y) \ z
    ]]></literal>
    <justification jstring="[para(11029(a,1),13243(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11029 13243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13264">
    <literal><![CDATA[
      (x * a(y,z,y)) \ u = a(y,z,y) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,12922,a,b,13245,a)].">
      <j1 rule="hyper" parents="373 12922 13245"/>
    </justification>
  </clause>

  <clause id="13265">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = a(x,y,x) \ (z \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,12896,a,b,13245,a)].">
      <j1 rule="hyper" parents="373 12896 13245"/>
    </justification>
  </clause>

  <clause id="13266">
    <literal><![CDATA[
      a(x,y,x) * ((z * a(x,y,x)) \ u) = z \ u
    ]]></literal>
    <justification jstring="[hyper(145,a,12922,a,b,13245,a)].">
      <j1 rule="hyper" parents="145 12922 13245"/>
    </justification>
  </clause>

  <clause id="13267">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) * z) \ u) = z \ u
    ]]></literal>
    <justification jstring="[hyper(145,a,12896,a,b,13245,a)].">
      <j1 rule="hyper" parents="145 12896 13245"/>
    </justification>
  </clause>

  <clause id="13268">
    <literal><![CDATA[
      (x \ (a(y,z,y) \ u)) * a(y,z,y) != w
    ]]></literal>
    <literal><![CDATA[
      x \ u = w
    ]]></literal>
    <justification jstring="[para(13245(a,1),11033(a,1,1))].">
      <j1 rule="para" parents="13245 11033"/>
    </justification>
  </clause>

  <clause id="13269">
    <literal><![CDATA[
      L(x,a(y,z,y),u) = x
    ]]></literal>
    <justification jstring="[hyper(606,a,13248,a)].">
      <j1 rule="hyper" parents="606 13248"/>
    </justification>
  </clause>

  <clause id="13270">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ (((x * a(y,z,y)) * u) * w) = a(x * a(y,z,y),u,w)
    ]]></literal>
    <justification jstring="[para(13248(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13248 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13271">
    <literal><![CDATA[
      x / (a(y,z,y) \ u) = (x / u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(225,a,13269,a(flip),b,634,a(flip))].">
      <j1 rule="hyper" parents="225 13269 634"/>
    </justification>
  </clause>

  <clause id="13272">
    <literal><![CDATA[
      (x / a(y,z,y)) * u = x * (a(y,z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(145,a,13269,a(flip),b,11070,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 13269 11070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13273">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ ((x * a(z,u,z)) * (y * w)) = L(w,L(y,a(z,u,z),x),x * a(z,u,z))
    ]]></literal>
    <justification jstring="[para(13269(a,1),11036(a,1,2,2,1))].">
      <j1 rule="para" parents="13269 11036"/>
    </justification>
  </clause>

  <clause id="13274">
    <literal><![CDATA[
      (x * y) * (a(x,z,x) \ u) = (L(x,z,x) * y) * u
    ]]></literal>
    <justification jstring="[para(11029(a,1),13253(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11029 13253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13275">
    <literal><![CDATA[
      (x \ y) \ ((x \ L(y,z,y)) * u) = a(y,z,y) \ u
    ]]></literal>
    <justification jstring="[para(13233(a,1),13254(a,1,2,1))].">
      <j1 rule="para" parents="13233 13254"/>
    </justification>
  </clause>

  <clause id="13276">
    <literal><![CDATA[
      a(x,y,x) \ (z / x) = z / R(x,y,x)
    ]]></literal>
    <justification jstring="[para(10889(a,1),13262(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10889 13262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13277">
    <literal><![CDATA[
      L(x,y,z / (u * a(w,v5,w))) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(13262(a,2),12977(a,1,3))].">
      <j1 rule="para" parents="13262 12977"/>
    </justification>
  </clause>

  <clause id="13278">
    <literal><![CDATA[
      L(x,y,z / R(u,w,u)) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(13276(a,1),12977(a,1,3))].">
      <j1 rule="para" parents="13276 12977"/>
    </justification>
  </clause>

  <clause id="13279">
    <literal><![CDATA[
      a(x / R(y,z,y),u,w) = a(x / y,u,w)
    ]]></literal>
    <justification jstring="[para(13276(a,1),13101(a,1,1))].">
      <j1 rule="para" parents="13276 13101"/>
    </justification>
  </clause>

  <clause id="13280">
    <literal><![CDATA[
      L(x,y,K(z,u) * (z \ u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(7721(a,1),13278(a,1,3))].">
      <j1 rule="para" parents="7721 13278"/>
    </justification>
  </clause>

  <clause id="13281">
    <literal><![CDATA[
      a(K(x,y) * (x \ y),z,u) = a(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(7721(a,1),13279(a,1,1))].">
      <j1 rule="para" parents="7721 13279"/>
    </justification>
  </clause>

  <clause id="13282">
    <literal><![CDATA[
      a(x,y,x) \ ((x \ z) \ u) = (L(x,y,x) \ z) \ u
    ]]></literal>
    <justification jstring="[para(10951(a,1),13264(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10951 13264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13283">
    <literal><![CDATA[
      a(x,y,x) \ (L(x,z,u) \ w) = L(R(x,y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(13191(a,1),13264(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13191 13264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13284">
    <literal><![CDATA[
      a(x,y,x) \ ((z \ 1) \ u) = (z \ a(x,y,x)) \ u
    ]]></literal>
    <justification jstring="[para(13237(a,1),13265(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13237 13265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13285">
    <literal><![CDATA[
      a(x,y,x) * ((z * R(x,y,x)) \ u) = (z * x) \ u
    ]]></literal>
    <justification jstring="[para(11346(a,1),13266(a,1,2,1))].">
      <j1 rule="para" parents="11346 13266"/>
    </justification>
  </clause>

  <clause id="13286">
    <literal><![CDATA[
      a(x,y,x) * ((z \ a(x,y,x)) \ u) = (z \ 1) \ u
    ]]></literal>
    <justification jstring="[para(13237(a,1),13267(a,1,2,1))].">
      <j1 rule="para" parents="13237 13267"/>
    </justification>
  </clause>

  <clause id="13287">
    <literal><![CDATA[
      ((x * y) * (a(z,u,z) \ w)) / ((y * (a(z,u,z) \ 1)) * w) = R(R(x,y,a(z,u,z) \ 1),y * (a(z,u,z) \ 1),w)
    ]]></literal>
    <justification jstring="[para(13272(a,1),11356(a,1,1))].">
      <j1 rule="para" parents="13272 11356"/>
    </justification>
  </clause>

  <clause id="13288">
    <literal><![CDATA[
      ((K(x,y) * (x \ y)) * z) \ ((K(x,y) * (x \ y)) * (z * u)) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18,a(flip),b,13280,a)].">
      <j1 rule="hyper" parents="64 18 13280"/>
    </justification>
  </clause>

  <clause id="13289">
    <literal><![CDATA[
      L(x,y,((z * u) / z) \ z) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(6077(a,2),13280(a,1,3))].">
      <j1 rule="para" parents="6077 13280"/>
    </justification>
  </clause>

  <clause id="13290">
    <literal><![CDATA[
      L(x,y,z / T(u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(256(a,1),13289(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="256 13289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13291">
    <literal><![CDATA[
      L(x,y,z * a(u,w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(13210(a,1),11866(a,1))].">
      <j1 rule="para" parents="13210 11866"/>
    </justification>
  </clause>

  <clause id="13292">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(10919(a,1),13291(a,1,3))].">
      <j1 rule="para" parents="10919 13291"/>
    </justification>
  </clause>

  <clause id="13293">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(12899,a,13211,a),flip(a)].">
      <j1 rule="hyper" parents="12899 13211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13294">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(13211(a,1),12898(a,1)),flip(b)].">
      <j1 rule="para" parents="13211 12898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13296">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,13293,a(flip),b,5753,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 13293 5753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13297">
    <literal><![CDATA[
      T(x,(y * z) * y) = T(x,y * (z * y))
    ]]></literal>
    <justification jstring="[para(88(a,1),13293(a,1,2))].">
      <j1 rule="para" parents="88 13293"/>
    </justification>
  </clause>

  <clause id="13298">
    <literal><![CDATA[
      T(x,y * L(z,u,z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(10948(a,1),13293(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10948 13293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13299">
    <literal><![CDATA[
      T(x,T(y,z) / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(10928(a,1),13293(a,1,2))].">
      <j1 rule="para" parents="10928 13293"/>
    </justification>
  </clause>

  <clause id="13300">
    <literal><![CDATA[
      T(x,a(y,z,y) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(11011(a,2),13293(a,1,2))].">
      <j1 rule="para" parents="11011 13293"/>
    </justification>
  </clause>

  <clause id="13301">
    <literal><![CDATA[
      T(x,a(y,z,y) \ u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(11016(a,1),13293(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11016 13293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13302">
    <literal><![CDATA[
      T(x,y * (z * a(u,w,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(13196(a,1),13293(a,1,2))].">
      <j1 rule="para" parents="13196 13293"/>
    </justification>
  </clause>

  <clause id="13303">
    <literal><![CDATA[
      T(x,y \ R(z,u,z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(13224(a,1),13293(a,1,2))].">
      <j1 rule="para" parents="13224 13293"/>
    </justification>
  </clause>

  <clause id="13304">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = u / T(u,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,13300,a(flip),b,5804,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 13300 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13305">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(11008(a,1),13300(a,1,2))].">
      <j1 rule="para" parents="11008 13300"/>
    </justification>
  </clause>

  <clause id="13306">
    <literal><![CDATA[
      T(x,K(y,y \ z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(10956(a,1),13300(a,1,2))].">
      <j1 rule="para" parents="10956 13300"/>
    </justification>
  </clause>

  <clause id="13307">
    <literal><![CDATA[
      T(x,T(y * z,y) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(11283(a,1),13300(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11283 13300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13309">
    <literal><![CDATA[
      T(x,y / R(z,u,z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(13276(a,1),13301(a,1,2))].">
      <j1 rule="para" parents="13276 13301"/>
    </justification>
  </clause>

  <clause id="13310">
    <literal><![CDATA[
      T(x,y / T(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4630(a,1),13299(a,1,2))].">
      <j1 rule="para" parents="4630 13299"/>
    </justification>
  </clause>

  <clause id="13311">
    <literal><![CDATA[
      T(x,y / T(T(z,y),u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(23(a,1),13310(a,1,2,2))].">
      <j1 rule="para" parents="23 13310"/>
    </justification>
  </clause>

  <clause id="13312">
    <literal><![CDATA[
      T(x,((y * y) * z) / T(u,(y * y) * z)) = T(x,((y * y) \ u) \ z)
    ]]></literal>
    <justification jstring="[para(804(a,2),13310(a,2,2))].">
      <j1 rule="para" parents="804 13310"/>
    </justification>
  </clause>

  <clause id="13313">
    <literal><![CDATA[
      T(x,T(y,z \ u) * (u / T(z,u))) = T(x,(u / T(z,u)) * y)
    ]]></literal>
    <justification jstring="[para(13310(a,1),11143(a,1,2,1))].">
      <j1 rule="para" parents="13310 11143"/>
    </justification>
  </clause>

  <clause id="13314">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5726,a,b,13296,a),flip(a)].">
      <j1 rule="hyper" parents="373 5726 13296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13315">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(13296(a,2),5827(a,1))].">
      <j1 rule="para" parents="13296 5827"/>
    </justification>
  </clause>

  <clause id="13316">
    <literal><![CDATA[
      K(x,y * L(z,u,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(10948(a,1),13314(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10948 13314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13317">
    <literal><![CDATA[
      K(x,T(y,z) / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(10928(a,1),13314(a,1,2))].">
      <j1 rule="para" parents="10928 13314"/>
    </justification>
  </clause>

  <clause id="13318">
    <literal><![CDATA[
      K(x,a(y,z,y) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(11011(a,2),13314(a,1,2))].">
      <j1 rule="para" parents="11011 13314"/>
    </justification>
  </clause>

  <clause id="13319">
    <literal><![CDATA[
      K(x,R(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(11357(a,1),13314(a,1,2))].">
      <j1 rule="para" parents="11357 13314"/>
    </justification>
  </clause>

  <clause id="13320">
    <literal><![CDATA[
      K(x,R(y,z,y) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(11360(a,1),13314(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11360 13314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13321">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) / w) = K(x,u / w)
    ]]></literal>
    <justification jstring="[para(12924(a,2),13314(a,1,2))].">
      <j1 rule="para" parents="12924 13314"/>
    </justification>
  </clause>

  <clause id="13322">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(13196(a,1),13314(a,1,2))].">
      <j1 rule="para" parents="13196 13314"/>
    </justification>
  </clause>

  <clause id="13323">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) * w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(13213(a,2),13314(a,1,2))].">
      <j1 rule="para" parents="13213 13314"/>
    </justification>
  </clause>

  <clause id="13324">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) \ w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(13214(a,1),13314(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13214 13314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13325">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) \ w) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(13246(a,1),13314(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13246 13314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13326">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(10956(a,1),13318(a,1,2))].">
      <j1 rule="para" parents="10956 13318"/>
    </justification>
  </clause>

  <clause id="13327">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(11283(a,1),13318(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11283 13318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13328">
    <literal><![CDATA[
      K(x,(a(y,z,y) \ u) * w) = K(x,u * w)
    ]]></literal>
    <justification jstring="[para(12889(a,1),13318(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12889 13318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13329">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) \ w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(13221(a,1),13318(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13221 13318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13330">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) / z) = K(x,z \ L(y,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,2),13317(a,1,2,1))].">
      <j1 rule="para" parents="25 13317"/>
    </justification>
  </clause>

  <clause id="13331">
    <literal><![CDATA[
      K(x,(y \ z) / y) = K(x,y \ (z / y))
    ]]></literal>
    <justification jstring="[para(117(a,1),13317(a,1,2,1))].">
      <j1 rule="para" parents="117 13317"/>
    </justification>
  </clause>

  <clause id="13333">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),y * (T(u,z) / z)) = T(x,(T(u,z) / z) * y)
    ]]></literal>
    <justification jstring="[para(13317(a,1),11154(a,1,1,2))].">
      <j1 rule="para" parents="13317 11154"/>
    </justification>
  </clause>

  <clause id="13334">
    <literal><![CDATA[
      T(x,y * T(z / u,z)) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(4731(a,1),13298(a,1,2,2))].">
      <j1 rule="para" parents="4731 13298"/>
    </justification>
  </clause>

  <clause id="13335">
    <literal><![CDATA[
      T(x,y * T(z,z * u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4732(a,1),13298(a,1,2,2))].">
      <j1 rule="para" parents="4732 13298"/>
    </justification>
  </clause>

  <clause id="13336">
    <literal><![CDATA[
      T(x,y \ T(z,z \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4803(a,1),13303(a,1,2,2))].">
      <j1 rule="para" parents="4803 13303"/>
    </justification>
  </clause>

  <clause id="13337">
    <literal><![CDATA[
      T(x,y \ T(z,z * u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(10103(a,1),13303(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10103 13303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13338">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(10106(a,1),13303(a,1,2,2))].">
      <j1 rule="para" parents="10106 13303"/>
    </justification>
  </clause>

  <clause id="13339">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = w
    ]]></literal>
    <justification jstring="[para(13304(a,2),5874(a,1))].">
      <j1 rule="para" parents="13304 5874"/>
    </justification>
  </clause>

  <clause id="13340">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) = u / T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(11008(a,1),13304(a,1,1))].">
      <j1 rule="para" parents="11008 13304"/>
    </justification>
  </clause>

  <clause id="13342">
    <literal><![CDATA[
      T(x,y / T(z,z \ u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(4803(a,1),13309(a,1,2,2))].">
      <j1 rule="para" parents="4803 13309"/>
    </justification>
  </clause>

  <clause id="13343">
    <literal><![CDATA[
      T(x,y / ((z \ u) \ u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(10106(a,1),13309(a,1,2,2))].">
      <j1 rule="para" parents="10106 13309"/>
    </justification>
  </clause>

  <clause id="13344">
    <literal><![CDATA[
      K(x,y * T(z / u,z)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(4731(a,1),13316(a,1,2,2))].">
      <j1 rule="para" parents="4731 13316"/>
    </justification>
  </clause>

  <clause id="13345">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4732(a,1),13316(a,1,2,2))].">
      <j1 rule="para" parents="4732 13316"/>
    </justification>
  </clause>

  <clause id="13346">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(12494(a,1),13316(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12494 13316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13348">
    <literal><![CDATA[
      K(x,T(y,y * z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(10103(a,1),13319(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10103 13319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13349">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(10106(a,1),13319(a,1,2,1))].">
      <j1 rule="para" parents="10106 13319"/>
    </justification>
  </clause>

  <clause id="13350">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4803(a,1),13320(a,1,2,1))].">
      <j1 rule="para" parents="4803 13320"/>
    </justification>
  </clause>

  <clause id="13351">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(10106(a,1),13320(a,1,2,1))].">
      <j1 rule="para" parents="10106 13320"/>
    </justification>
  </clause>

  <clause id="13352">
    <literal><![CDATA[
      T(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(10928(a,1),13294(a,1,2))].">
      <j1 rule="para" parents="10928 13294"/>
    </justification>
  </clause>

  <clause id="13353">
    <literal><![CDATA[
      K(x,y * K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2096(a,1),13315(a,1,2,2))].">
      <j1 rule="para" parents="2096 13315"/>
    </justification>
  </clause>

  <clause id="13354">
    <literal><![CDATA[
      K(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(10928(a,1),13315(a,1,2))].">
      <j1 rule="para" parents="10928 13315"/>
    </justification>
  </clause>

  <clause id="13355">
    <literal><![CDATA[
      K(x,R(y,z,y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / u) = w
    ]]></literal>
    <justification jstring="[para(12929(a,1),13315(a,1,2))].">
      <j1 rule="para" parents="12929 13315"/>
    </justification>
  </clause>

  <clause id="13356">
    <literal><![CDATA[
      T(T(x,K(y,z \ (u / z))),y / ((z \ u) / z)) = T(x,((z \ u) / z) \ y)
    ]]></literal>
    <justification jstring="[para(13331(a,1),8720(a,1,1,2))].">
      <j1 rule="para" parents="13331 8720"/>
    </justification>
  </clause>

  <clause id="13357">
    <literal><![CDATA[
      K(x * a(y,z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(11011(a,1),13339(a,1,1))].">
      <j1 rule="para" parents="11011 13339"/>
    </justification>
  </clause>

  <clause id="13358">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(11008(a,1),13339(a,1,1))].">
      <j1 rule="para" parents="11008 13339"/>
    </justification>
  </clause>

  <clause id="13359">
    <literal><![CDATA[
      K(K(x,x \ y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(10956(a,1),13339(a,1,1))].">
      <j1 rule="para" parents="10956 13339"/>
    </justification>
  </clause>

  <clause id="13360">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(13357,a,xx),flip(a)].">
      <j1 rule="hyper" parents="13357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13361">
    <literal><![CDATA[
      K(T(x,y) / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(10928(a,1),13357(a,1,1))].">
      <j1 rule="para" parents="10928 13357"/>
    </justification>
  </clause>

  <clause id="13363">
    <literal><![CDATA[
      K(L(x,y,x) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(10952(a,1),13360(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10952 13360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13366">
    <literal><![CDATA[
      K(x \ L(y,z,y),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(13225(a,1),13360(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13225 13360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13367">
    <literal><![CDATA[
      K(x \ (a(y,z,y) * u),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(13213(a,2),13360(a,1,1))].">
      <j1 rule="para" parents="13213 13360"/>
    </justification>
  </clause>

  <clause id="13368">
    <literal><![CDATA[
      K((a(x,y,x) \ z) \ u,w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(13243(a,2),13360(a,1,1))].">
      <j1 rule="para" parents="13243 13360"/>
    </justification>
  </clause>

  <clause id="13369">
    <literal><![CDATA[
      K(T(x,x * y) * z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4732(a,1),13363(a,1,1,1))].">
      <j1 rule="para" parents="4732 13363"/>
    </justification>
  </clause>

  <clause id="13370">
    <literal><![CDATA[
      K(x \ T(y / z,y),u) = K(x \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(4731(a,1),13366(a,1,1,2))].">
      <j1 rule="para" parents="4731 13366"/>
    </justification>
  </clause>

  <clause id="13371">
    <literal><![CDATA[
      K(x \ T(y,y * z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4732(a,1),13366(a,1,1,2))].">
      <j1 rule="para" parents="4732 13366"/>
    </justification>
  </clause>

  <clause id="13372">
    <literal><![CDATA[
      T(x,y * (T(z,u) / u)) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(10928(a,1),13302(a,1,2,2))].">
      <j1 rule="para" parents="10928 13302"/>
    </justification>
  </clause>

  <clause id="13373">
    <literal><![CDATA[
      K(x,T(y * z,y) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(11058(a,1),13321(a,1,2,1))].">
      <j1 rule="para" parents="11058 13321"/>
    </justification>
  </clause>

  <clause id="13374">
    <literal><![CDATA[
      K(x,y * ((z * u) * z)) = K(x,y * (z * (u * z)))
    ]]></literal>
    <justification jstring="[para(88(a,1),13322(a,1,2,2))].">
      <j1 rule="para" parents="88 13322"/>
    </justification>
  </clause>

  <clause id="13375">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(10914(a,1),13322(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10914 13322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13376">
    <literal><![CDATA[
      K(x,y * (z * L(u,w,u))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(10948(a,1),13322(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10948 13322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13377">
    <literal><![CDATA[
      K(x,y * (T(z,u) / u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(10928(a,1),13322(a,1,2,2))].">
      <j1 rule="para" parents="10928 13322"/>
    </justification>
  </clause>

  <clause id="13378">
    <literal><![CDATA[
      K(x,y * K(z,z \ u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(10933(a,1),13322(a,1,2,2))].">
      <j1 rule="para" parents="10933 13322"/>
    </justification>
  </clause>

  <clause id="13379">
    <literal><![CDATA[
      K(x,y * (R(z,u,z) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(11357(a,1),13322(a,1,2,2))].">
      <j1 rule="para" parents="11357 13322"/>
    </justification>
  </clause>

  <clause id="13380">
    <literal><![CDATA[
      K(x,y * (z * (u * a(w,v5,w)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(13196(a,1),13322(a,1,2,2))].">
      <j1 rule="para" parents="13196 13322"/>
    </justification>
  </clause>

  <clause id="13381">
    <literal><![CDATA[
      K(x,y * (z \ L(u,w,u))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(13225(a,1),13322(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13225 13322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13382">
    <literal><![CDATA[
      K(x,y \ (L(z,u,z) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(11025(a,1),13323(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11025 13323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13383">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(11058(a,1),13323(a,1,2,2))].">
      <j1 rule="para" parents="11058 13323"/>
    </justification>
  </clause>

  <clause id="13384">
    <literal><![CDATA[
      K(x,y \ (z * R(u,w,u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(11353(a,1),13323(a,1,2,2))].">
      <j1 rule="para" parents="11353 13323"/>
    </justification>
  </clause>

  <clause id="13385">
    <literal><![CDATA[
      K(x,y \ K(z \ u,z)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(10881(a,1),13324(a,1,2,2))].">
      <j1 rule="para" parents="10881 13324"/>
    </justification>
  </clause>

  <clause id="13386">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(10924(a,1),13324(a,1,2,2))].">
      <j1 rule="para" parents="10924 13324"/>
    </justification>
  </clause>

  <clause id="13387">
    <literal><![CDATA[
      K(x,K(y * z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10902(a,1),13325(a,1,2,1))].">
      <j1 rule="para" parents="10902 13325"/>
    </justification>
  </clause>

  <clause id="13388">
    <literal><![CDATA[
      K(x,K(y * z,z) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(10922(a,1),13325(a,1,2,1))].">
      <j1 rule="para" parents="10922 13325"/>
    </justification>
  </clause>

  <clause id="13389">
    <literal><![CDATA[
      K(x,(T(y * z,y) \ u) \ w) = K(x,((z * y) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(11283(a,1),13325(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11283 13325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13390">
    <literal><![CDATA[
      K(x,(y * (z * a(u,w,u))) \ v5) = K(x,(y * z) \ v5)
    ]]></literal>
    <justification jstring="[para(13197(a,1),13325(a,1,2,1))].">
      <j1 rule="para" parents="13197 13325"/>
    </justification>
  </clause>

  <clause id="13391">
    <literal><![CDATA[
      K(x,(y \ R(z,u,z)) \ w) = K(x,(y \ z) \ w)
    ]]></literal>
    <justification jstring="[para(13229(a,1),13325(a,1,2,1))].">
      <j1 rule="para" parents="13229 13325"/>
    </justification>
  </clause>

  <clause id="13392">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(10881(a,1),13328(a,1,2,1))].">
      <j1 rule="para" parents="10881 13328"/>
    </justification>
  </clause>

  <clause id="13393">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) * w) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(11029(a,1),13328(a,1,2,1))].">
      <j1 rule="para" parents="11029 13328"/>
    </justification>
  </clause>

  <clause id="13394">
    <literal><![CDATA[
      K(x,T(y * z,y) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(11059(a,1),13328(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11059 13328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13395">
    <literal><![CDATA[
      K(x,y * K(z \ u,z)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(10881(a,1),13329(a,1,2,2))].">
      <j1 rule="para" parents="10881 13329"/>
    </justification>
  </clause>

  <clause id="13396">
    <literal><![CDATA[
      T(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(4630(a,1),13352(a,1,2))].">
      <j1 rule="para" parents="4630 13352"/>
    </justification>
  </clause>

  <clause id="13397">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(3620(a,1),13353(a,1,2))].">
      <j1 rule="para" parents="3620 13353"/>
    </justification>
  </clause>

  <clause id="13398">
    <literal><![CDATA[
      K(x,(1 / (1 / y)) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(3633(a,1),13353(a,1,2))].">
      <j1 rule="para" parents="3633 13353"/>
    </justification>
  </clause>

  <clause id="13399">
    <literal><![CDATA[
      K(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(4630(a,1),13354(a,1,2))].">
      <j1 rule="para" parents="4630 13354"/>
    </justification>
  </clause>

  <clause id="13400">
    <literal><![CDATA[
      K(x / T(y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(13361,a,9418,a),flip(a)].">
      <j1 rule="hyper" parents="13361 9418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13401">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(13400(a,1),9649(a,2,2))].">
      <j1 rule="para" parents="13400 9649"/>
    </justification>
  </clause>

  <clause id="13402">
    <literal><![CDATA[
      K(x \ K(y,y \ z),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[para(10935(a,1),13367(a,1,1,2))].">
      <j1 rule="para" parents="10935 13367"/>
    </justification>
  </clause>

  <clause id="13403">
    <literal><![CDATA[
      K(x \ T(y * z,y),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(11058(a,1),13367(a,1,1,2))].">
      <j1 rule="para" parents="11058 13367"/>
    </justification>
  </clause>

  <clause id="13404">
    <literal><![CDATA[
      K(x \ (T(y * z,y) \ u),w) = K(x \ ((z * y) \ u),w)
    ]]></literal>
    <justification jstring="[para(11283(a,1),13367(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11283 13367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13405">
    <literal><![CDATA[
      K(K(x * y,x) \ z,u) = K(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(10916(a,1),13368(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10916 13368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13406">
    <literal><![CDATA[
      K((L(x,y,x) * z) \ u,w) = K((x * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(11029(a,1),13368(a,1,1,1))].">
      <j1 rule="para" parents="11029 13368"/>
    </justification>
  </clause>

  <clause id="13407">
    <literal><![CDATA[
      K(T(x * y,x) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(11059(a,1),13368(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11059 13368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13408">
    <literal><![CDATA[
      T(x,(y / T(z,y)) / T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ (y / T(z,y))) = w
    ]]></literal>
    <justification jstring="[para(13310(a,1),13396(a,1,2,2))].">
      <j1 rule="para" parents="13310 13396"/>
    </justification>
  </clause>

  <clause id="13409">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13305(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13410">
    <literal><![CDATA[
      T(x,K(y,z) * ((z / y) \ u)) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(6270(a,1),13306(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 13306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13411">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ u,w)) = K(x,w) * T(x * K(w,x),(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(145,a,13307,a(flip),b,9455,a),flip(a)].">
      <j1 rule="hyper" parents="145 13307 9455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13412">
    <literal><![CDATA[
      T(x,((y \ z) * y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13307(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13413">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y)) * w) = K(x,K(y,z \ u) * w)
    ]]></literal>
    <justification jstring="[para(10165(a,1),13326(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10165 13326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13414">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13327(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13415">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) * K(y,(T(u * z,u) \ w) \ x) = K(y,x / (T(u * z,u) \ w))
    ]]></literal>
    <justification jstring="[para(13327(a,1),9065(a,1,1,2))].">
      <j1 rule="para" parents="13327 9065"/>
    </justification>
  </clause>

  <clause id="13416">
    <literal><![CDATA[
      T(x,y * (x / z)) = T(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,8501,a(flip),b,13334,a)].">
      <j1 rule="hyper" parents="64 8501 13334"/>
    </justification>
  </clause>

  <clause id="13417">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = x \ T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,13335,a(flip),b,5753,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 13335 5753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13418">
    <literal><![CDATA[
      T(x,y \ T(z,z \ x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,8493,a(flip),b,13336,a),flip(a)].">
      <j1 rule="hyper" parents="373 8493 13336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13419">
    <literal><![CDATA[
      T(x,y \ T(z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9232,a(flip),b,13336,a),flip(a)].">
      <j1 rule="hyper" parents="64 9232 13336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13420">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),z \ w)) = T(x,y \ T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(8598(a,1),13336(a,1,2,2))].">
      <j1 rule="para" parents="8598 13336"/>
    </justification>
  </clause>

  <clause id="13421">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),u)) = K(x,u) * T(x * K(u,x),z / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,13419,a(flip),b,9455,a),flip(a)].">
      <j1 rule="hyper" parents="145 13419 9455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13422">
    <literal><![CDATA[
      T(x,y \ ((z * z) * T(u,(z * z) \ y))) = T(x,u / ((z * z) \ y))
    ]]></literal>
    <justification jstring="[para(804(a,1),13419(a,1,2))].">
      <j1 rule="para" parents="804 13419"/>
    </justification>
  </clause>

  <clause id="13423">
    <literal><![CDATA[
      T(x,(y * y) * (z \ T(u,z / (y * y)))) = T(x,u / (z / (y * y)))
    ]]></literal>
    <justification jstring="[para(890(a,1),13419(a,1,2))].">
      <j1 rule="para" parents="890 13419"/>
    </justification>
  </clause>

  <clause id="13424">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(4632(a,2),13419(a,1,2))].">
      <j1 rule="para" parents="4632 13419"/>
    </justification>
  </clause>

  <clause id="13425">
    <literal><![CDATA[
      T(x,y / z) \ (T(z \ T(y,z),x) \ u) = x \ ((z \ T(y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(13419(a,1),5019(a,1,1))].">
      <j1 rule="para" parents="13419 5019"/>
    </justification>
  </clause>

  <clause id="13426">
    <literal><![CDATA[
      K(x,T(y,z / u) * (u \ T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ T(z,u)) * y) = w
    ]]></literal>
    <justification jstring="[para(13419(a,1),11231(a,1,2,1))].">
      <j1 rule="para" parents="13419 11231"/>
    </justification>
  </clause>

  <clause id="13427">
    <literal><![CDATA[
      T(x,y \ (x / z)) = T(x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[para(848(a,1),13418(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="848 13418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13428">
    <literal><![CDATA[
      T(x,T(y \ T(z,z * u),w)) = K(x,w) * T(x * K(w,x),y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,13337,a(flip),b,9455,a),flip(a)].">
      <j1 rule="hyper" parents="145 13337 9455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13429">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ T(y,z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,863,a(flip),b,13338,a),flip(a)].">
      <j1 rule="hyper" parents="64 863 13338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13430">
    <literal><![CDATA[
      T(x,y / T(z * K(u,z \ w),w)) = T(x,y / (T(z \ w,u) \ w))
    ]]></literal>
    <justification jstring="[para(6247(a,1),13343(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6247 13343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13431">
    <literal><![CDATA[
      T(x,y / T((z \ u) \ u,w)) = T(x,y / T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(8332(a,2),13343(a,1,2,2))].">
      <j1 rule="para" parents="8332 13343"/>
    </justification>
  </clause>

  <clause id="13432">
    <literal><![CDATA[
      T(x,y / (((z * K(u,w / z)) \ (z \ w)) \ (z \ w))) = T(x,y / (T(z \ w,u) \ w))
    ]]></literal>
    <justification jstring="[para(8838(a,1),13343(a,2,2,2))].">
      <j1 rule="para" parents="8838 13343"/>
    </justification>
  </clause>

  <clause id="13433">
    <literal><![CDATA[
      K(x,y * T(z,u * z)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4683(a,2),13345(a,1,2,2))].">
      <j1 rule="para" parents="4683 13345"/>
    </justification>
  </clause>

  <clause id="13434">
    <literal><![CDATA[
      K(x,y * T(z,u * (w * z))) = K(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[para(11579(a,2),13345(a,1,2,2))].">
      <j1 rule="para" parents="11579 13345"/>
    </justification>
  </clause>

  <clause id="13435">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = w / (K(y * T(z,u),x) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,6160,a,b,13346,a),flip(a)].">
      <j1 rule="hyper" parents="373 6160 13346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13436">
    <literal><![CDATA[
      K(x,y * T((z \ u) \ u,w)) = K(x,y * T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(8332(a,2),13346(a,1,2,2))].">
      <j1 rule="para" parents="8332 13346"/>
    </justification>
  </clause>

  <clause id="13437">
    <literal><![CDATA[
      K(x,y * T(T(z,z \ u),w)) = K(x,y * T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(8391(a,2),13346(a,1,2,2))].">
      <j1 rule="para" parents="8391 13346"/>
    </justification>
  </clause>

  <clause id="13438">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,w,v5)) = K(L(x,w,v5),T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(12117,a,13348,a)].">
      <j1 rule="hyper" parents="12117 13348"/>
    </justification>
  </clause>

  <clause id="13439">
    <literal><![CDATA[
      K(x,R(T(y / z,((y * u) / (z * u)) * w),z,u) * v5) = K(x,T((y * u) / (z * u),w) * v5)
    ]]></literal>
    <justification jstring="[para(679(a,1),13348(a,1,2,1))].">
      <j1 rule="para" parents="679 13348"/>
    </justification>
  </clause>

  <clause id="13440">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),y * K(z,z \ u)) * w) = K(x,T(y / ((z \ u) * z),u) * w)
    ]]></literal>
    <justification jstring="[para(10226(a,1),13348(a,1,2,1,2))].">
      <j1 rule="para" parents="10226 13348"/>
    </justification>
  </clause>

  <clause id="13441">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) = x \ T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5726,a(flip),b,13349,a),flip(a)].">
      <j1 rule="hyper" parents="373 5726 13349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13442">
    <literal><![CDATA[
      T(x,((y \ z) \ z) * u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(143,a,13349,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 13349 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13443">
    <literal><![CDATA[
      K(x,T(y / z,y) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(82(a,1),13349(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="82 13349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13444">
    <literal><![CDATA[
      K(x,T(y / z,y) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(848(a,1),13350(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="848 13350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13445">
    <literal><![CDATA[
      K(x,T(y,y \ x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(13350(a,2),8589(a,1))].">
      <j1 rule="para" parents="13350 8589"/>
    </justification>
  </clause>

  <clause id="13446">
    <literal><![CDATA[
      K(x,L(((y \ z) \ z) \ u,w,v5)) = K(L(x,w,v5),T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(12117,a,13351,a)].">
      <j1 rule="hyper" parents="12117 13351"/>
    </justification>
  </clause>

  <clause id="13447">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,((y \ z) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,13350,a,b,13351,a)].">
      <j1 rule="hyper" parents="373 13350 13351"/>
    </justification>
  </clause>

  <clause id="13448">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = (w * K(T(y,z) \ u,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(373,a,6882,a,b,13351,a),flip(a)].">
      <j1 rule="hyper" parents="373 6882 13351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13449">
    <literal><![CDATA[
      K(x,T(((y / z) \ 1) * y,y) \ u) = K(x,(((z \ y) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(9334(a,1),13351(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9334 13351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13450">
    <literal><![CDATA[
      L(K(x,T(y,z) \ u),y,y \ z) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(13351(a,1),12089(a,1,1))].">
      <j1 rule="para" parents="13351 12089"/>
    </justification>
  </clause>

  <clause id="13451">
    <literal><![CDATA[
      K(x,((y \ z) \ z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) / u) = w
    ]]></literal>
    <justification jstring="[para(10106(a,1),13355(a,1,2,1))].">
      <j1 rule="para" parents="10106 13355"/>
    </justification>
  </clause>

  <clause id="13452">
    <literal><![CDATA[
      K(x \ (y / z),y) = K(x \ (z \ y),y)
    ]]></literal>
    <justification jstring="[hyper(8590,a,13370,a)].">
      <j1 rule="hyper" parents="8590 13370"/>
    </justification>
  </clause>

  <clause id="13453">
    <literal><![CDATA[
      K(x \ R(y / z,z,u),y * u) = K(x \ ((z * u) \ (y * u)),y * u)
    ]]></literal>
    <justification jstring="[para(112(a,2),13452(a,1,1,2))].">
      <j1 rule="para" parents="112 13452"/>
    </justification>
  </clause>

  <clause id="13454">
    <literal><![CDATA[
      K(R(x / y,y,x \ T(z,z * u)) \ T(z,u),w) = K(y * (x \ T(z,z * u)),w)
    ]]></literal>
    <justification jstring="[para(684(a,1),13371(a,1,1)),flip(a)].">
      <j1 rule="para" parents="684 13371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13455">
    <literal><![CDATA[
      T(x,y * (T(z,u) / u)) = x * K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,5753,a(flip),b,13372,a),flip(a)].">
      <j1 rule="hyper" parents="373 5753 13372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13456">
    <literal><![CDATA[
      T(x,y * (z / T(u,z))) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(4630(a,1),13372(a,1,2,2))].">
      <j1 rule="para" parents="4630 13372"/>
    </justification>
  </clause>

  <clause id="13457">
    <literal><![CDATA[
      K(x,((y \ z) * y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13373(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13458">
    <literal><![CDATA[
      K(x,T(L(y,z,y) * u,y) / w) = K(x,(u * L(y,z,y)) / w)
    ]]></literal>
    <justification jstring="[para(7546(a,1),13373(a,1,2,1))].">
      <j1 rule="para" parents="7546 13373"/>
    </justification>
  </clause>

  <clause id="13459">
    <literal><![CDATA[
      K(x,y * (z / T(u,z))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(4630(a,1),13377(a,1,2,2))].">
      <j1 rule="para" parents="4630 13377"/>
    </justification>
  </clause>

  <clause id="13460">
    <literal><![CDATA[
      K(x,y * K(z * (u \ w),(z * (u \ w)) \ z)) = K(x,y * K((u * (1 / z)) \ w,z))
    ]]></literal>
    <justification jstring="[para(11905(a,2),13378(a,2,2,2))].">
      <j1 rule="para" parents="11905 13378"/>
    </justification>
  </clause>

  <clause id="13461">
    <literal><![CDATA[
      T(x,y \ T(z * u,z)) = T(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(143,a,13383,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 13383 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13462">
    <literal><![CDATA[
      K(x,y \ ((z \ u) * z)) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),13383(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13463">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13387(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13464">
    <literal><![CDATA[
      K(x,K(y,z \ y) \ u) = K(x,K(z,z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13388(a,1,2,1,1))].">
      <j1 rule="para" parents="10 13388"/>
    </justification>
  </clause>

  <clause id="13465">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = x \ T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5726,a(flip),b,13392,a),flip(a)].">
      <j1 rule="hyper" parents="373 5726 13392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13466">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ y) \ u)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(6292(a,1),13392(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6292 13392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13467">
    <literal><![CDATA[
      T(x,T(y * z,y) * u) = T(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[hyper(143,a,13394,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 13394 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13468">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13394(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13469">
    <literal><![CDATA[
      (x \ (x * K(y \ x,z))) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(13401(a,1),11406(a,1,1,2))].">
      <j1 rule="para" parents="13401 11406"/>
    </justification>
  </clause>

  <clause id="13470">
    <literal><![CDATA[
      K(x \ K(y,z \ 1),u) = K(x \ K(y,z \ y),u)
    ]]></literal>
    <justification jstring="[para(5962(a,1),13402(a,1,1,2))].">
      <j1 rule="para" parents="5962 13402"/>
    </justification>
  </clause>

  <clause id="13471">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11649,a(flip),b,13403,a)].">
      <j1 rule="hyper" parents="64 11649 13403"/>
    </justification>
  </clause>

  <clause id="13472">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13403(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13473">
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),x) \ u,w) = K(K(y,x) \ u,w)
    ]]></literal>
    <justification jstring="[para(7435(a,1),13405(a,2,1,1))].">
      <j1 rule="para" parents="7435 13405"/>
    </justification>
  </clause>

  <clause id="13474">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13407(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13475">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) * a(w,v5,K((z * y) \ u,x)) = K(x,L(T(y * z,y) \ u,v5,w))
    ]]></literal>
    <justification jstring="[para(13407(a,1),12069(a,1,2,3))].">
      <j1 rule="para" parents="13407 12069"/>
    </justification>
  </clause>

  <clause id="13476">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) = u / T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(225,a,13409,a(flip),b,5804,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 13409 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13477">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,6729,a(flip),b,13412,a),flip(a)].">
      <j1 rule="hyper" parents="64 6729 13412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13478">
    <literal><![CDATA[
      K(x,T(y,z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(13414(a,1),9234(a,1))].">
      <j1 rule="para" parents="13414 9234"/>
    </justification>
  </clause>

  <clause id="13479">
    <literal><![CDATA[
      (((x \ y) * x) \ z) * K(y,T(y,x) \ z) = (K(x,x \ y) * z) / y
    ]]></literal>
    <justification jstring="[para(13414(a,1),11299(a,1,2))].">
      <j1 rule="para" parents="13414 11299"/>
    </justification>
  </clause>

  <clause id="13480">
    <literal><![CDATA[
      K(x,y \ T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(4632(a,1),13478(a,1,2))].">
      <j1 rule="para" parents="4632 13478"/>
    </justification>
  </clause>

  <clause id="13481">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(z,z \ u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(z,z \ u) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(13306(a,1),13478(a,1,2,1))].">
      <j1 rule="para" parents="13306 13478"/>
    </justification>
  </clause>

  <clause id="13482">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(u \ z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(u \ z,u) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(13409(a,1),13478(a,1,2,1))].">
      <j1 rule="para" parents="13409 13478"/>
    </justification>
  </clause>

  <clause id="13483">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(13480,a,xx),flip(a)].">
      <j1 rule="hyper" parents="13480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13484">
    <literal><![CDATA[
      K(x,((y \ z) \ 1) \ T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / ((y \ z) \ 1)) = w
    ]]></literal>
    <justification jstring="[para(6704(a,1),13480(a,1,2,2))].">
      <j1 rule="para" parents="6704 13480"/>
    </justification>
  </clause>

  <clause id="13485">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ T(u,z / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y \ z,z)) = w
    ]]></literal>
    <justification jstring="[para(8271(a,1),13480(a,1,2,2))].">
      <j1 rule="para" parents="8271 13480"/>
    </justification>
  </clause>

  <clause id="13486">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ T(u,z / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (T(y,z) \ z)) = w
    ]]></literal>
    <justification jstring="[para(13424(a,1),13480(a,1,2,2))].">
      <j1 rule="para" parents="13424 13480"/>
    </justification>
  </clause>

  <clause id="13487">
    <literal><![CDATA[
      K(x,(y * (y * z)) \ T(z,y * y)) = K(x,z / (y * (y * z)))
    ]]></literal>
    <justification jstring="[para(11581(a,1),13483(a,1,2,2))].">
      <j1 rule="para" parents="11581 13483"/>
    </justification>
  </clause>

  <clause id="13488">
    <literal><![CDATA[
      K(x,L(y \ T(z,y),u,w)) = L(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(13483(a,1),12059(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13483 12059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13489">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = (w * K(u,(y \ x) \ z)) \ w
    ]]></literal>
    <justification jstring="[para(13444(a,1),6882(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13444 6882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13490">
    <literal><![CDATA[
      K(x,y * (z / L(T(u,z),w,v5))) = K(x,y * (L(u,w,v5) \ z))
    ]]></literal>
    <justification jstring="[para(25(a,2),13459(a,1,2,2,2))].">
      <j1 rule="para" parents="25 13459"/>
    </justification>
  </clause>

  <clause id="13491">
    <literal><![CDATA[
      T(x,y \ T(z * u,u)) = T(x,y \ (T(z,u) * u))
    ]]></literal>
    <justification jstring="[para(115(a,1),13461(a,1,2,2,1))].">
      <j1 rule="para" parents="115 13461"/>
    </justification>
  </clause>

  <clause id="13492">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y / z) \ u)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(6609(a,1),13463(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6609 13463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13493">
    <literal><![CDATA[
      T(x,((y \ z) * y) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13467(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13494">
    <literal><![CDATA[
      T(x,((K(y * z,y) * u) * T(y,z)) * w) = T(x,T(R(y,z,y) * u,T(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(6355(a,1),13467(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6355 13467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13495">
    <literal><![CDATA[
      L(x,y,z / T(u * (w / u),u)) = L(x,y,z / w)
    ]]></literal>
    <justification jstring="[para(11373(a,1),13277(a,1,3,2))].">
      <j1 rule="para" parents="11373 13277"/>
    </justification>
  </clause>

  <clause id="13496">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13079(a,2),13292(a,1))].">
      <j1 rule="para" parents="13079 13292"/>
    </justification>
  </clause>

  <clause id="13497">
    <literal><![CDATA[
      K(x,y * (z * L(T(u,w),v5,u))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(11861(a,1),13376(a,1,2,2,2))].">
      <j1 rule="para" parents="11861 13376"/>
    </justification>
  </clause>

  <clause id="13498">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) * w)) = K(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(10106(a,1),13379(a,1,2,2,1))].">
      <j1 rule="para" parents="10106 13379"/>
    </justification>
  </clause>

  <clause id="13499">
    <literal><![CDATA[
      K(x,y * (z \ T(u / w,u))) = K(x,y * (z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(4731(a,1),13381(a,1,2,2,2))].">
      <j1 rule="para" parents="4731 13381"/>
    </justification>
  </clause>

  <clause id="13500">
    <literal><![CDATA[
      K(x,y * (z \ T(u,u * w))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(4732(a,1),13381(a,1,2,2,2))].">
      <j1 rule="para" parents="4732 13381"/>
    </justification>
  </clause>

  <clause id="13501">
    <literal><![CDATA[
      K(x,y \ (T(z / u,z) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(4731(a,1),13382(a,1,2,2,1))].">
      <j1 rule="para" parents="4731 13382"/>
    </justification>
  </clause>

  <clause id="13502">
    <literal><![CDATA[
      K(x,y \ (((z \ u) \ u) * w)) = K(x,y \ (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(12494(a,1),13382(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12494 13382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13503">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) \ w))) = K(x,y \ (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(10106(a,1),13384(a,1,2,2,2))].">
      <j1 rule="para" parents="10106 13384"/>
    </justification>
  </clause>

  <clause id="13504">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(1 / y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(3569(a,1),13397(a,1,2,1))].">
      <j1 rule="para" parents="3569 13397"/>
    </justification>
  </clause>

  <clause id="13505">
    <literal><![CDATA[
      K((x * y) \ z,y * x) * (z * u) = (((y * x) \ z) * (y * x)) * u
    ]]></literal>
    <justification jstring="[para(13406(a,1),11502(a,1,1))].">
      <j1 rule="para" parents="13406 11502"/>
    </justification>
  </clause>

  <clause id="13507">
    <literal><![CDATA[
      R((x * (x \ y)) * (x \ y),z,x) = y * (L(x,z,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12914,a,b,13219,a)].">
      <j1 rule="hyper" parents="64 12914 13219"/>
    </justification>
  </clause>

  <clause id="13508">
    <literal><![CDATA[
      a(x,y,x) * (z * (u \ (1 / w))) = z * (u \ (a(x,y,x) / w))
    ]]></literal>
    <justification jstring="[para(13227(a,1),13197(a,2,2))].">
      <j1 rule="para" parents="13227 13197"/>
    </justification>
  </clause>

  <clause id="13509">
    <literal><![CDATA[
      L(x,y,R(z * (a(u,w,u) * ((v5 \ 1) * (v5 \ a(u,w,u)))),v6,v7)) = L(x,y,R(z,v6,v7))
    ]]></literal>
    <justification jstring="[para(13239(a,2),11832(a,1,3,1,2))].">
      <j1 rule="para" parents="13239 11832"/>
    </justification>
  </clause>

  <clause id="13510">
    <literal><![CDATA[
      L((x \ a(y,z,y)) \ u,x,x) = x * (a(y,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(13240(a,1),1137(a,1,1))].">
      <j1 rule="para" parents="13240 1137"/>
    </justification>
  </clause>

  <clause id="13511">
    <literal><![CDATA[
      T(a(x,y,x) * z,u) = a(x,y,x) * T(z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),13259(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22 13259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13512">
    <literal><![CDATA[
      T(x * a(y,z,y),u) = a(y,z,y) * T(x,u)
    ]]></literal>
    <justification jstring="[para(11011(a,1),13511(a,1,1))].">
      <j1 rule="para" parents="11011 13511"/>
    </justification>
  </clause>

  <clause id="13513">
    <literal><![CDATA[
      a(x,y,x) \ T(z * a(x,y,x),u) = T(z,u)
    ]]></literal>
    <justification jstring="[hyper(1036,a,13512,a)].">
      <j1 rule="hyper" parents="1036 13512"/>
    </justification>
  </clause>

  <clause id="13514">
    <literal><![CDATA[
      T(a(x,y,x) \ z,u) = a(x,y,x) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(11016(a,1),13513(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11016 13513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13515">
    <literal><![CDATA[
      (((x * x) \ y) * z) * a(x,u,x) = (L(x,u,x) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(484(a,1),13263(a,1,1))].">
      <j1 rule="para" parents="484 13263"/>
    </justification>
  </clause>

  <clause id="13516">
    <literal><![CDATA[
      ((x * y) \ z) * (u * a(x,w,x)) = ((L(x,w,x) * y) \ z) * u
    ]]></literal>
    <justification jstring="[para(13263(a,1),13217(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13263 13217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13517">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * u) \ w) = v5
    ]]></literal>
    <justification jstring="[para(13263(a,1),13315(a,1,2))].">
      <j1 rule="para" parents="13263 13315"/>
    </justification>
  </clause>

  <clause id="13518">
    <literal><![CDATA[
      L(x,y,(L(z,u,z) * w) * v5) = L(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[para(13274(a,1),13256(a,1,3))].">
      <j1 rule="para" parents="13274 13256"/>
    </justification>
  </clause>

  <clause id="13519">
    <literal><![CDATA[
      (a(x,y,x) \ z) * L(((u \ x) \ ((u \ L(x,y,x)) * z)) \ ((u \ L(x,y,x)) * z),w,v5) = L(u \ x,w,v5) * ((u \ x) \ ((u \ L(x,y,x)) * z))
    ]]></literal>
    <justification jstring="[para(13275(a,1),839(a,1,1))].">
      <j1 rule="para" parents="13275 839"/>
    </justification>
  </clause>

  <clause id="13520">
    <literal><![CDATA[
      L(x,y,(L(z,u,z) \ w) \ v5) = L(x,y,(z \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(13282(a,1),12977(a,1,3))].">
      <j1 rule="para" parents="13282 12977"/>
    </justification>
  </clause>

  <clause id="13521">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) / (z \ 1)) = K(x,(z \ 1) \ L(y / (z * y),u,w))
    ]]></literal>
    <justification jstring="[para(4823(a,1),13330(a,1,2,1,1))].">
      <j1 rule="para" parents="4823 13330"/>
    </justification>
  </clause>

  <clause id="13522">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5787,a,b,13340,a),flip(a)].">
      <j1 rule="hyper" parents="373 5787 13340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13523">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13522(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 13522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13524">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) = K(K(y,x) * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(11892(a,1),13523(a,1,1))].">
      <j1 rule="para" parents="11892 13523"/>
    </justification>
  </clause>

  <clause id="13525">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13417(a,2),5827(a,1))].">
      <j1 rule="para" parents="13417 5827"/>
    </justification>
  </clause>

  <clause id="13526">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(13441(a,2),5827(a,1))].">
      <j1 rule="para" parents="13441 5827"/>
    </justification>
  </clause>

  <clause id="13527">
    <literal><![CDATA[
      T(x,y * (T(z,u) / u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (u \ z)) = w
    ]]></literal>
    <justification jstring="[para(13455(a,2),5767(a,1))].">
      <j1 rule="para" parents="13455 5767"/>
    </justification>
  </clause>

  <clause id="13528">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(13465(a,2),5827(a,1))].">
      <j1 rule="para" parents="13465 5827"/>
    </justification>
  </clause>

  <clause id="13529">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(13476(a,2),5874(a,1))].">
      <j1 rule="para" parents="13476 5874"/>
    </justification>
  </clause>

  <clause id="13530">
    <literal><![CDATA[
      K(x,L(y \ T(z,y),u,w)) = K(x,L(z / y,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,12059,a(flip),b,13488,a),flip(a)].">
      <j1 rule="hyper" parents="373 12059 13488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13531">
    <literal><![CDATA[
      L(x,y,(z * (u / z)) \ z) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13290,a(flip),b,13495,a)].">
      <j1 rule="hyper" parents="64 13290 13495"/>
    </justification>
  </clause>

  <clause id="13532">
    <literal><![CDATA[
      L(x,y,z / (u * z)) = L(x,y,(z * u) \ z)
    ]]></literal>
    <justification jstring="[para(11(a,1),13531(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="11 13531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13533">
    <literal><![CDATA[
      L(x,y,z \ (z / (z / u))) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(6018(a,1),13531(a,1,3))].">
      <j1 rule="para" parents="6018 13531"/>
    </justification>
  </clause>

  <clause id="13534">
    <literal><![CDATA[
      L(x,y,((z * (1 / u)) * (z / (z * (1 / u)))) \ (z * (1 / u))) = L(x,y,K(z,u \ 1) / u)
    ]]></literal>
    <justification jstring="[para(6361(a,2),13531(a,2,3))].">
      <j1 rule="para" parents="6361 13531"/>
    </justification>
  </clause>

  <clause id="13535">
    <literal><![CDATA[
      L(x,y,(z \ u) / u) = L(x,y,u \ (u / z))
    ]]></literal>
    <justification jstring="[para(79(a,1),13533(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="79 13533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13536">
    <literal><![CDATA[
      L(x,y,y \ (y / z)) = L(x,y,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(11284,a,13535,a),flip(a)].">
      <j1 rule="hyper" parents="11284 13535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13537">
    <literal><![CDATA[
      K(x,L((y / (z * y)) \ T(u,z \ 1),w,v5)) = K(x,L(u / (y / (z * y)),w,v5))
    ]]></literal>
    <justification jstring="[para(4817(a,1),13530(a,1,2,1,2))].">
      <j1 rule="para" parents="4817 13530"/>
    </justification>
  </clause>

  <clause id="13538">
    <literal><![CDATA[
      K(x,L(((y * z) \ y) \ T(u,z \ 1),w,v5)) = K(x,L(u / ((y * z) \ y),w,v5))
    ]]></literal>
    <justification jstring="[para(6729(a,1),13530(a,1,2,1,2))].">
      <j1 rule="para" parents="6729 13530"/>
    </justification>
  </clause>

  <clause id="13539">
    <literal><![CDATA[
      T(x,T(x * y,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8954,a,13162,a),flip(a)].">
      <j1 rule="hyper" parents="8954 13162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13540">
    <literal><![CDATA[
      T(x,T(x * (x \ y),z)) = T(x,y * K(x \ y,z))
    ]]></literal>
    <justification jstring="[para(6763(a,1),13539(a,2,2))].">
      <j1 rule="para" parents="6763 13539"/>
    </justification>
  </clause>

  <clause id="13542">
    <literal><![CDATA[
      T(x,y * K(x \ y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),13540(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13543">
    <literal><![CDATA[
      T(x \ y,y * K(x,T(z,y))) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(7871(a,1),13542(a,1,2,2))].">
      <j1 rule="para" parents="7871 13542"/>
    </justification>
  </clause>

  <clause id="13544">
    <literal><![CDATA[
      T(x \ y,K(x,z) * y) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(7879(a,1),13543(a,1,2))].">
      <j1 rule="para" parents="7879 13543"/>
    </justification>
  </clause>

  <clause id="13545">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / T(T(y \ u,T(u,z)),w)) = T(x,T(y \ u,w) \ (K(y,z) * u))
    ]]></literal>
    <justification jstring="[para(13544(a,1),13311(a,1,2,2,1))].">
      <j1 rule="para" parents="13544 13311"/>
    </justification>
  </clause>

  <clause id="13546">
    <literal><![CDATA[
      a(x,R(y \ z,y,u),x) = a(x,(y * u) \ (z * u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13170,a(flip),b,13171,a)].">
      <j1 rule="hyper" parents="64 13170 13171"/>
    </justification>
  </clause>

  <clause id="13547">
    <literal><![CDATA[
      L(x,y,z \ K(u,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(13226(a,1),13291(a,1,3))].">
      <j1 rule="para" parents="13226 13291"/>
    </justification>
  </clause>

  <clause id="13548">
    <literal><![CDATA[
      K(x,y \ K(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13226(a,1),13315(a,1,2))].">
      <j1 rule="para" parents="13226 13315"/>
    </justification>
  </clause>

  <clause id="13549">
    <literal><![CDATA[
      K(x \ K(y,y \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(13226(a,1),13357(a,1,1))].">
      <j1 rule="para" parents="13226 13357"/>
    </justification>
  </clause>

  <clause id="13550">
    <literal><![CDATA[
      K(x,y * (z * (L(u,w,u) \ v5))) = K(x,y * (z * (u \ v5)))
    ]]></literal>
    <justification jstring="[para(10951(a,1),13380(a,1,2,2,2))].">
      <j1 rule="para" parents="10951 13380"/>
    </justification>
  </clause>

  <clause id="13551">
    <literal><![CDATA[
      K(x,y * (z * K(u,u \ w))) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(10933(a,1),13380(a,1,2,2,2))].">
      <j1 rule="para" parents="10933 13380"/>
    </justification>
  </clause>

  <clause id="13552">
    <literal><![CDATA[
      K(x,y * (K(z,z * u) * w)) = K(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[para(11010(a,1),13380(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11010 13380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13553">
    <literal><![CDATA[
      K(x,y * (z * (u \ K(w,w \ v5)))) = K(x,y * (z * (u \ K(w,v5))))
    ]]></literal>
    <justification jstring="[para(13226(a,1),13380(a,1,2,2,2))].">
      <j1 rule="para" parents="13226 13380"/>
    </justification>
  </clause>

  <clause id="13554">
    <literal><![CDATA[
      K(x,(y * K(z * u,u)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(10936(a,1),13390(a,1,2,1,2))].">
      <j1 rule="para" parents="10936 13390"/>
    </justification>
  </clause>

  <clause id="13555">
    <literal><![CDATA[
      K(x,((y \ z) \ z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(13451,a,xx),flip(a)].">
      <j1 rule="hyper" parents="13451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13556">
    <literal><![CDATA[
      T(x,((y \ z) \ z) / u) = T(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(143,a,13555,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 13555 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13557">
    <literal><![CDATA[
      K(x,T(y / z,y) / u) = K(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[para(82(a,1),13555(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="82 13555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13558">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,T(y * (1 / z),y) / u)
    ]]></literal>
    <justification jstring="[para(6809(a,2),13555(a,1,2,1))].">
      <j1 rule="para" parents="6809 13555"/>
    </justification>
  </clause>

  <clause id="13559">
    <literal><![CDATA[
      K(x,T(y,T(z,u) / w) * (((z \ u) \ u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(((z \ u) \ u) / w) * y) = v5
    ]]></literal>
    <justification jstring="[para(13556(a,1),11231(a,1,2,1))].">
      <j1 rule="para" parents="13556 11231"/>
    </justification>
  </clause>

  <clause id="13560">
    <literal><![CDATA[
      L(x,y,L(z * u,z,z) * w) = L(x,y,(z * L(u,z,z)) * w)
    ]]></literal>
    <justification jstring="[para(1257(a,1),13518(a,1,3,1))].">
      <j1 rule="para" parents="1257 13518"/>
    </justification>
  </clause>

  <clause id="13561">
    <literal><![CDATA[
      L(x,y,((z / (u * z)) * z) \ w) = L(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(2024(a,1),13520(a,1,3,1))].">
      <j1 rule="para" parents="2024 13520"/>
    </justification>
  </clause>

  <clause id="13562">
    <literal><![CDATA[
      K(x,T(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(116(a,2),13526(a,1,2,1))].">
      <j1 rule="para" parents="116 13526"/>
    </justification>
  </clause>

  <clause id="13563">
    <literal><![CDATA[
      a(x,(y * z) \ (u * z),x) = a(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(12955,a,13546,a),flip(a)].">
      <j1 rule="hyper" parents="12955 13546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13564">
    <literal><![CDATA[
      a(x,(y * z) \ (u * z),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ u,x) = w
    ]]></literal>
    <justification jstring="[para(13546(a,1),12955(a,1))].">
      <j1 rule="para" parents="13546 12955"/>
    </justification>
  </clause>

  <clause id="13566">
    <literal><![CDATA[
      a(x,y \ z,x) = a(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11965,a(flip),b,13563,a),flip(a)].">
      <j1 rule="hyper" parents="64 11965 13563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13567">
    <literal><![CDATA[
      a(x,(y * z) \ z,x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),13563(a,1,2,2))].">
      <j1 rule="para" parents="7 13563"/>
    </justification>
  </clause>

  <clause id="13568">
    <literal><![CDATA[
      a(x,y / (z * y),x) = a(x,z \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(13185,a,13567,a)].">
      <j1 rule="hyper" parents="13185 13567"/>
    </justification>
  </clause>

  <clause id="13569">
    <literal><![CDATA[
      a(x,((y * (z * (u * K(w,w \ 1)))) \ ((y * z) * u)) \ 1,x) = a(x,K(w,w \ 1) / a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(5350(a,1),13568(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5350 13568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13570">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u) * w) = v5
    ]]></literal>
    <justification jstring="[para(10147(a,1),13562(a,1,2,1))].">
      <j1 rule="para" parents="10147 13562"/>
    </justification>
  </clause>

  <clause id="13571">
    <literal><![CDATA[
      a(x,y \ (z * T(y,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,K(u,y) \ z,x) = w
    ]]></literal>
    <justification jstring="[para(5797(a,1),13564(a,1,2,1))].">
      <j1 rule="para" parents="5797 13564"/>
    </justification>
  </clause>

  <clause id="13572">
    <literal><![CDATA[
      (x * (y * (z * a(u,w,u)))) \ v5 = (x * (y * z)) \ (a(u,w,u) \ v5)
    ]]></literal>
    <justification jstring="[para(13196(a,1),13209(a,1,1,2))].">
      <j1 rule="para" parents="13196 13209"/>
    </justification>
  </clause>

  <clause id="13573">
    <literal><![CDATA[
      ((x * (y * (z * a(u,w,u)))) \ ((x * y) * z)) * a(u,w,u) = a(x,y,z * a(u,w,u))
    ]]></literal>
    <justification jstring="[hyper(959,a,13228,a),flip(a)].">
      <j1 rule="hyper" parents="959 13228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13574">
    <literal><![CDATA[
      L(R(x,y,x),z,u) \ x = L(x,z,u) \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13233,a(flip),b,13283,a),flip(a)].">
      <j1 rule="hyper" parents="64 13233 13283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13575">
    <literal><![CDATA[
      R(x,y,x) * (L(R(x,y,x),z,u) \ w) = x * (L(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(13283(a,1),11375(a,1,2))].">
      <j1 rule="para" parents="13283 11375"/>
    </justification>
  </clause>

  <clause id="13576">
    <literal><![CDATA[
      K(x,y * T(z,u * (z * w))) = K(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[para(8508(a,1),13434(a,1,2,2))].">
      <j1 rule="para" parents="8508 13434"/>
    </justification>
  </clause>

  <clause id="13577">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13435(a,2),6189(a,1))].">
      <j1 rule="para" parents="13435 6189"/>
    </justification>
  </clause>

  <clause id="13578">
    <literal><![CDATA[
      K(x,y * T(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(116(a,2),13577(a,1,2,2))].">
      <j1 rule="para" parents="116 13577"/>
    </justification>
  </clause>

  <clause id="13579">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(13448(a,2),6899(a,1))].">
      <j1 rule="para" parents="13448 6899"/>
    </justification>
  </clause>

  <clause id="13580">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(116(a,2),13579(a,1,2,1))].">
      <j1 rule="para" parents="116 13579"/>
    </justification>
  </clause>

  <clause id="13581">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6882,a(flip),b,13489,a),flip(a)].">
      <j1 rule="hyper" parents="373 6882 13489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13582">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(13489(a,2),6899(a,1))].">
      <j1 rule="para" parents="13489 6899"/>
    </justification>
  </clause>

  <clause id="13583">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),13581(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 13581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13584">
    <literal><![CDATA[
      K(T(x,y) \ y,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(8453,a,13583,a),flip(a)].">
      <j1 rule="hyper" parents="8453 13583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13585">
    <literal><![CDATA[
      K(T(x,x \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(116(a,2),13583(a,1,1,1))].">
      <j1 rule="para" parents="116 13583"/>
    </justification>
  </clause>

  <clause id="13586">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(13583(a,2),8579(a,1))].">
      <j1 rule="para" parents="13583 8579"/>
    </justification>
  </clause>

  <clause id="13587">
    <literal><![CDATA[
      K(x \ T(y,x),z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4651,a(flip),b,13584,a)].">
      <j1 rule="hyper" parents="64 4651 13584"/>
    </justification>
  </clause>

  <clause id="13588">
    <literal><![CDATA[
      K(T(x * y,y) \ ((x * y) * z),u) = K(K(y * x,x \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11240,a(flip),b,13585,a),flip(a)].">
      <j1 rule="hyper" parents="64 11240 13585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13589">
    <literal><![CDATA[
      K((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ 1) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(372(a,1),13582(a,1,1,1))].">
      <j1 rule="para" parents="372 13582"/>
    </justification>
  </clause>

  <clause id="13590">
    <literal><![CDATA[
      R(x * (y \ x),z,y) = x * (L(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),13507(a,1,1,1))].">
      <j1 rule="para" parents="10 13507"/>
    </justification>
  </clause>

  <clause id="13591">
    <literal><![CDATA[
      x * R(x \ (y \ x),z,y) = L(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(35,a,2125,a,b,13590,a(flip))].">
      <j1 rule="hyper" parents="35 2125 13590"/>
    </justification>
  </clause>

  <clause id="13593">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,x)) = y * a(x,z,x)
    ]]></literal>
    <justification jstring="[para(13591(a,2),10947(a,1,2))].">
      <j1 rule="para" parents="13591 10947"/>
    </justification>
  </clause>

  <clause id="13594">
    <literal><![CDATA[
      (x * y) \ (y * a(x,z,x)) = R((x * y) \ y,z,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,13593,a(flip),b,1709,a)].">
      <j1 rule="hyper" parents="139 13593 1709"/>
    </justification>
  </clause>

  <clause id="13595">
    <literal><![CDATA[
      ((x * y) \ y) * a(x,z,x) = R((x * y) \ y,z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13199,a(flip),b,13594,a)].">
      <j1 rule="hyper" parents="64 13199 13594"/>
    </justification>
  </clause>

  <clause id="13596">
    <literal><![CDATA[
      R((x * y) \ y,z,x) = (L(x,z,x) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,13263,a(flip),b,13595,a),flip(a)].">
      <j1 rule="hyper" parents="64 13263 13595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13597">
    <literal><![CDATA[
      K(x,y * (K(z,z \ u) * w)) = K(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),13552(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 13552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13598">
    <literal><![CDATA[
      K(x,y * ((z / (z / u)) \ w)) = K(x,y * (K(u,z) * (u \ w)))
    ]]></literal>
    <justification jstring="[para(6413(a,2),13597(a,1,2,2))].">
      <j1 rule="para" parents="6413 13597"/>
    </justification>
  </clause>

  <clause id="13599">
    <literal><![CDATA[
      a(x,L(y * K(z,y),u,w),x) = (w * (u * y)) \ (w * (u * (T(x * y,x) / x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12283,a(flip),b,13202,a),flip(a)].">
      <j1 rule="hyper" parents="64 12283 13202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13600">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,y,y \ z)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(12091,a,13450,a)].">
      <j1 rule="hyper" parents="12091 13450"/>
    </justification>
  </clause>

  <clause id="13601">
    <literal><![CDATA[
      K(x,y * (z * T(T(u / w,u),v5))) = K(x,y * (z * T(w \ u,v5)))
    ]]></literal>
    <justification jstring="[para(4761(a,1),13497(a,1,2,2,2))].">
      <j1 rule="para" parents="4761 13497"/>
    </justification>
  </clause>

  <clause id="13602">
    <literal><![CDATA[
      K(x,y * (z * (u / T(w,u)))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(4885(a,1),13550(a,1,2,2,2))].">
      <j1 rule="para" parents="4885 13550"/>
    </justification>
  </clause>

  <clause id="13603">
    <literal><![CDATA[
      T(x,y * (z * (u / T(w,u)))) = T(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(143,a,13602,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 13602 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13604">
    <literal><![CDATA[
      T(x,T(y,z \ u) * (z \ u)) = T(x,(u / T(z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13456,a(flip),b,13313,a)].">
      <j1 rule="hyper" parents="64 13456 13313"/>
    </justification>
  </clause>

  <clause id="13605">
    <literal><![CDATA[
      T(x,(y / T(z,y)) * u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(11200,a,13604,a),flip(a)].">
      <j1 rule="hyper" parents="11200 13604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13606">
    <literal><![CDATA[
      T(x,(T(y,z) / z) * u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(4630(a,2),13605(a,1,2,1))].">
      <j1 rule="para" parents="4630 13605"/>
    </justification>
  </clause>

  <clause id="13607">
    <literal><![CDATA[
      T(x,(T(y,1 / (1 / (z / y))) / (1 / (1 / (z / y)))) * u) = T(x,((y / z) * y) * u)
    ]]></literal>
    <justification jstring="[para(2015(a,1),13606(a,2,2,1))].">
      <j1 rule="para" parents="2015 13606"/>
    </justification>
  </clause>

  <clause id="13608">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,9454,a(flip),b,13421,a),flip(a)].">
      <j1 rule="hyper" parents="373 9454 13421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13609">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(13438(a,2),12117(a,1))].">
      <j1 rule="para" parents="13438 12117"/>
    </justification>
  </clause>

  <clause id="13610">
    <literal><![CDATA[
      K(x,L(((y \ z) \ z) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(13446(a,2),12117(a,1))].">
      <j1 rule="para" parents="13446 12117"/>
    </justification>
  </clause>

  <clause id="13611">
    <literal><![CDATA[
      a(R(x * (y \ (a(z,u,z) / y)),w,v5),v6,v7) = a(R(x,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(13508(a,1),13135(a,1,1,1))].">
      <j1 rule="para" parents="13508 13135"/>
    </justification>
  </clause>

  <clause id="13612">
    <literal><![CDATA[
      ((x * x) \ y) * (z * a(x,u,x)) = (L(x,u,x) * x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13196,a(flip),b,13515,a)].">
      <j1 rule="hyper" parents="64 13196 13515"/>
    </justification>
  </clause>

  <clause id="13613">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,((1 / z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(373,a,13373,a(flip),b,13558,a),flip(a)].">
      <j1 rule="hyper" parents="373 13373 13558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13614">
    <literal><![CDATA[
      (L(x,y,x) * x) \ (z * u) = ((L(x,y,x) * x) \ z) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,13516,a(flip),b,13612,a),flip(a)].">
      <j1 rule="hyper" parents="64 13516 13612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13615">
    <literal><![CDATA[
      (L(x,y,x) * x) \ (z * (x * u)) = ((x * x) \ z) * (R(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(11357(a,1),13612(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11357 13612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13616">
    <literal><![CDATA[
      (L(x,y,x) * x) \ (z * u) = ((x * L(x,y,x)) \ z) * u
    ]]></literal>
    <justification jstring="[para(275(a,1),13614(a,2,1,1))].">
      <j1 rule="para" parents="275 13614"/>
    </justification>
  </clause>

  <clause id="13617">
    <literal><![CDATA[
      (x * L(x,y,x)) \ (z * u) = ((x * L(x,y,x)) \ z) * u
    ]]></literal>
    <justification jstring="[para(275(a,1),13616(a,1,1))].">
      <j1 rule="para" parents="275 13616"/>
    </justification>
  </clause>

  <clause id="13618">
    <literal><![CDATA[
      ((x * L(x,y,x)) \ z) \ u = z \ ((x * L(x,y,x)) * u)
    ]]></literal>
    <justification jstring="[hyper(731,a,13617,a)].">
      <j1 rule="hyper" parents="731 13617"/>
    </justification>
  </clause>

  <clause id="13619">
    <literal><![CDATA[
      ((x * L(x,y,x)) \ z) / u = (x * L(x,y,x)) \ (z / u)
    ]]></literal>
    <justification jstring="[hyper(225,a,343,a(flip),b,13618,a)].">
      <j1 rule="hyper" parents="225 343 13618"/>
    </justification>
  </clause>

  <clause id="13620">
    <literal><![CDATA[
      (((x * L(x,y,x)) \ z) * u) / w = (x * L(x,y,x)) \ ((z * u) / w)
    ]]></literal>
    <justification jstring="[para(13617(a,1),13619(a,1,1))].">
      <j1 rule="para" parents="13617 13619"/>
    </justification>
  </clause>

  <clause id="13621">
    <literal><![CDATA[
      a(x,y,x) * ((z * u) \ (z * (u * w))) = L(w * a(x,y,x),u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13258,a(flip),b,13218,a)].">
      <j1 rule="hyper" parents="64 13258 13218"/>
    </justification>
  </clause>

  <clause id="13622">
    <literal><![CDATA[
      L(x * a(y,z,y),u,w) = a(y,z,y) * L(x,u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),13621(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 13621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13623">
    <literal><![CDATA[
      L(x * a(y,z,y),u,w) = L(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11011,a(flip),b,13622,a),flip(a)].">
      <j1 rule="hyper" parents="373 11011 13622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13624">
    <literal><![CDATA[
      L(x,y,L(z * a(u,w,u),v5,v6)) = L(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(13622(a,2),12975(a,1,3))].">
      <j1 rule="para" parents="13622 12975"/>
    </justification>
  </clause>

  <clause id="13625">
    <literal><![CDATA[
      a(L(x * a(y,z,y),u,w),v5,v6) = a(L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(13622(a,2),13099(a,1,1))].">
      <j1 rule="para" parents="13622 13099"/>
    </justification>
  </clause>

  <clause id="13626">
    <literal><![CDATA[
      a(x,y,x) \ L(a(x,y,x) * z,u,w) = L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,5545,a,b,13623,a(flip))].">
      <j1 rule="hyper" parents="36 5545 13623"/>
    </justification>
  </clause>

  <clause id="13627">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) = a(x,y,x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,5544,a(flip),b,13623,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 5544 13623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13628">
    <literal><![CDATA[
      a(x,y,x) \ L(x,z,u) = L(L(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(10897(a,1),13626(a,1,2,1))].">
      <j1 rule="para" parents="10897 13626"/>
    </justification>
  </clause>

  <clause id="13629">
    <literal><![CDATA[
      L(x,y,z) \ L(a(u,w,u) * x,y,z) = a(u,w,u)
    ]]></literal>
    <justification jstring="[para(13626(a,1),11015(a,1,1))].">
      <j1 rule="para" parents="13626 11015"/>
    </justification>
  </clause>

  <clause id="13630">
    <literal><![CDATA[
      a(x,y,x) * (L(x,z,u) \ w) = L(L(x,y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(13628(a,1),13260(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13628 13260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13631">
    <literal><![CDATA[
      (x / L(y,z,u)) * a(y,w,y) = x / L(L(y,w,y),z,u)
    ]]></literal>
    <justification jstring="[para(13628(a,1),13271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13628 13271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13632">
    <literal><![CDATA[
      L(K(x,y),z,u) \ L(K(x,x \ y),z,u) = a(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10935(a,1),13629(a,1,2,1))].">
      <j1 rule="para" parents="10935 13629"/>
    </justification>
  </clause>

  <clause id="13633">
    <literal><![CDATA[
      L(x,y,z) \ L(u * (T(x,u) / u),y,z) = a(u,u \ x,u)
    ]]></literal>
    <justification jstring="[para(11379(a,1),13629(a,1,2,1))].">
      <j1 rule="para" parents="11379 13629"/>
    </justification>
  </clause>

  <clause id="13634">
    <literal><![CDATA[
      L(x,y,L(z * (u * a(w,v5,w)),v6,v7)) = L(x,y,L(z * u,v6,v7))
    ]]></literal>
    <justification jstring="[para(13196(a,1),13624(a,1,3,1))].">
      <j1 rule="para" parents="13196 13624"/>
    </justification>
  </clause>

  <clause id="13635">
    <literal><![CDATA[
      a(L(x * (y * a(z,u,z)),w,v5),v6,v7) = a(L(x * y,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(13196(a,1),13625(a,1,1,1))].">
      <j1 rule="para" parents="13196 13625"/>
    </justification>
  </clause>

  <clause id="13636">
    <literal><![CDATA[
      L(L(x,y,x),z,u) \ L(x,w,v5) = L(x,z,u) \ L(R(x,y,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,13257,a(flip),b,13630,a),flip(a)].">
      <j1 rule="hyper" parents="64 13257 13630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13637">
    <literal><![CDATA[
      R(x,y,x) * (L(x,z,u) \ w) = x * (L(L(x,y,x),z,u) \ w)
    ]]></literal>
    <justification jstring="[para(13630(a,1),11370(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13630 11370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13638">
    <literal><![CDATA[
      L(K(x,y / ((x \ z) * u)),w,v5) \ L(K(x,x \ (y / ((z / x) * u))),w,v5) = a(x,x \ (y / ((z / x) * u)),x)
    ]]></literal>
    <justification jstring="[para(9204(a,1),13632(a,1,1,1))].">
      <j1 rule="para" parents="9204 13632"/>
    </justification>
  </clause>

  <clause id="13639">
    <literal><![CDATA[
      a(x,x \ L(y,z,u),x) = a(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11403,a(flip),b,13633,a)].">
      <j1 rule="hyper" parents="64 11403 13633"/>
    </justification>
  </clause>

  <clause id="13641">
    <literal><![CDATA[
      a(x,x \ ((y * z) \ u),x) = a(x,x \ (z \ (y \ u)),x)
    ]]></literal>
    <justification jstring="[para(346(a,1),13639(a,1,2,2))].">
      <j1 rule="para" parents="346 13639"/>
    </justification>
  </clause>

  <clause id="13642">
    <literal><![CDATA[
      a(x,x \ ((y \ z) \ u),x) = a(x,x \ (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[para(630(a,1),13639(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="630 13639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13643">
    <literal><![CDATA[
      L(x,y,L((z / (u * (w \ 1))) * ((w \ (1 / w)) * a(v5,v6,v5)),v7,v8)) = L(x,y,L(z / (w * T(u,w \ 1)),v7,v8))
    ]]></literal>
    <justification jstring="[para(1625(a,1),13634(a,2,3,1))].">
      <j1 rule="para" parents="1625 13634"/>
    </justification>
  </clause>

  <clause id="13644">
    <literal><![CDATA[
      a(L((x / (y * (z \ 1))) * ((z \ (1 / z)) * a(u,w,u)),v5,v6),v7,v8) = a(L(x / (z * T(y,z \ 1)),v5,v6),v7,v8)
    ]]></literal>
    <justification jstring="[para(1625(a,1),13635(a,2,1,1))].">
      <j1 rule="para" parents="1625 13635"/>
    </justification>
  </clause>

  <clause id="13645">
    <literal><![CDATA[
      a(x,x \ y,x) \ y = (L(x,z,u) \ y) * T(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12313(a,1),13192(a,1,1))].">
      <j1 rule="para" parents="12313 13192"/>
    </justification>
  </clause>

  <clause id="13646">
    <literal><![CDATA[
      (L(x,y,z) \ u) * T(L(x,y,z),u) = (x \ u) * T(x,u)
    ]]></literal>
    <justification jstring="[hyper(11046,a,13645,a),flip(a)].">
      <j1 rule="hyper" parents="11046 13645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13648">
    <literal><![CDATA[
      (L(x,y,z) \ u) * L(T(x,u),y,z) = (x \ u) * T(x,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),13646(a,1,2))].">
      <j1 rule="para" parents="25 13646"/>
    </justification>
  </clause>

  <clause id="13649">
    <literal><![CDATA[
      T(x,y / z) \ (T(z \ T(y,z),x) \ u) = x \ ((T(z,y) \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4632(a,2),13425(a,2,2,1))].">
      <j1 rule="para" parents="4632 13425"/>
    </justification>
  </clause>

  <clause id="13650">
    <literal><![CDATA[
      (((x \ y) * x) \ z) * K(y,y \ z) = (K(x,x \ y) * z) / y
    ]]></literal>
    <justification jstring="[para(8548(a,1),13479(a,1,2))].">
      <j1 rule="para" parents="8548 13479"/>
    </justification>
  </clause>

  <clause id="13653">
    <literal><![CDATA[
      K(K(x * y,y \ 1) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y * x,x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(13588(a,1),6336(a,1))].">
      <j1 rule="para" parents="13588 6336"/>
    </justification>
  </clause>

  <clause id="13654">
    <literal><![CDATA[
      (x * L(x,y,x)) \ (z * (x * u)) = ((x * x) \ z) * (R(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(275(a,1),13615(a,1,1))].">
      <j1 rule="para" parents="275 13615"/>
    </justification>
  </clause>

  <clause id="13655">
    <literal><![CDATA[
      x \ ((T(y,z) \ z) \ u) = x \ ((y \ T(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13425,a(flip),b,13649,a),flip(a)].">
      <j1 rule="hyper" parents="64 13425 13649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13656">
    <literal><![CDATA[
      K(x \ y,z) \ (y * K(y / x,z)) = L(y,K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(9(a,1),13469(a,1,1))].">
      <j1 rule="para" parents="9 13469"/>
    </justification>
  </clause>

  <clause id="13657">
    <literal><![CDATA[
      L(x,K(y \ x,z),x) = x
    ]]></literal>
    <justification jstring="[hyper(8361,a,13656,a)].">
      <j1 rule="hyper" parents="8361 13656"/>
    </justification>
  </clause>

  <clause id="13659">
    <literal><![CDATA[
      L(x,K(y,z),x) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),13657(a,1,2,1))].">
      <j1 rule="para" parents="82 13657"/>
    </justification>
  </clause>

  <clause id="13660">
    <literal><![CDATA[
      T(x,x * K(y,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(11863,a,13659,a)].">
      <j1 rule="hyper" parents="11863 13659"/>
    </justification>
  </clause>

  <clause id="13661">
    <literal><![CDATA[
      T(K(x,y) * z,z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10063,a,13659,a)].">
      <j1 rule="hyper" parents="10063 13659"/>
    </justification>
  </clause>

  <clause id="13662">
    <literal><![CDATA[
      T(x * K(y,z),L(x,K(y,z),x)) = x \ (x * (K(y,z) * x))
    ]]></literal>
    <justification jstring="[para(13659(a,1),589(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13659 589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13664">
    <literal><![CDATA[
      K(x * K(y,z),x) = T(x,K(y,z)) \ x
    ]]></literal>
    <justification jstring="[para(13660(a,1),5731(a,2,1))].">
      <j1 rule="para" parents="13660 5731"/>
    </justification>
  </clause>

  <clause id="13665">
    <literal><![CDATA[
      K(K(x,y) * z,z) * (((K(x,y) * z) * u) * z) = ((z * K(x,y)) * u) * z
    ]]></literal>
    <justification jstring="[para(13661(a,1),7804(a,2,1,1))].">
      <j1 rule="para" parents="13661 7804"/>
    </justification>
  </clause>

  <clause id="13666">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5731,a,b,13664,a),flip(a)].">
      <j1 rule="hyper" parents="373 5731 13664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13667">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8123,a(flip),b,13666,a),flip(a)].">
      <j1 rule="hyper" parents="373 8123 13666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13668">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,8092,a(flip),b,13666,a),flip(a)].">
      <j1 rule="hyper" parents="373 8092 13666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13669">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * K(y,z),L(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(13667(a,1),12091(a,1,1))].">
      <j1 rule="para" parents="13667 12091"/>
    </justification>
  </clause>

  <clause id="13670">
    <literal><![CDATA[
      K(K(x,y) * z,z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8578,a,13668,a)].">
      <j1 rule="hyper" parents="8578 13668"/>
    </justification>
  </clause>

  <clause id="13671">
    <literal><![CDATA[
      T(x * K(y,z),L(x,K(y,z),x)) = x \ (x * (K(z,y) \ x))
    ]]></literal>
    <justification jstring="[para(6156(a,2),13662(a,2,2,2))].">
      <j1 rule="para" parents="6156 13662"/>
    </justification>
  </clause>

  <clause id="13672">
    <literal><![CDATA[
      T(x * K(y,z),L(x,K(y,z),x)) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,9,a(flip),b,13671,a),flip(a)].">
      <j1 rule="hyper" parents="373 9 13671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13673">
    <literal><![CDATA[
      T(x * K(y,z),x) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(7552,a,13672,a)].">
      <j1 rule="hyper" parents="7552 13672"/>
    </justification>
  </clause>

  <clause id="13676">
    <literal><![CDATA[
      T(x,K(y,z) \ u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(13673(a,1),11122(a,1,2))].">
      <j1 rule="para" parents="13673 11122"/>
    </justification>
  </clause>

  <clause id="13677">
    <literal><![CDATA[
      T(x,y * (T(y,z) \ u)) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5780(a,2),13676(a,1,2))].">
      <j1 rule="para" parents="5780 13676"/>
    </justification>
  </clause>

  <clause id="13678">
    <literal><![CDATA[
      T(x,K(y,z) * (y * u)) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(6131(a,1),13676(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6131 13676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13679">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T((z * y) \ u,w)) = v5
    ]]></literal>
    <justification jstring="[para(13411(a,2),9457(a,1))].">
      <j1 rule="para" parents="13411 9457"/>
    </justification>
  </clause>

  <clause id="13680">
    <literal><![CDATA[
      T(x,T(y \ T(z,z * u),w)) = T(x,T(y \ T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(373,a,9454,a(flip),b,13428,a),flip(a)].">
      <j1 rule="hyper" parents="373 9454 13428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13681">
    <literal><![CDATA[
      K(x,K(y,z)) * (((K(x,y) * z) * u) * z) = ((z * K(x,y)) * u) * z
    ]]></literal>
    <justification jstring="[para(13670(a,1),13665(a,1,1))].">
      <j1 rule="para" parents="13670 13665"/>
    </justification>
  </clause>

  <clause id="13682">
    <literal><![CDATA[
      (K(x,y) * ((x \ y) * z)) \ ((K(x,y) * (x \ y)) * (z * u)) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[para(13021(a,1),13288(a,1,1))].">
      <j1 rule="para" parents="13021 13288"/>
    </justification>
  </clause>

  <clause id="13683">
    <literal><![CDATA[
      (K(x,y) * ((x \ y) * z)) \ (K(x,y) * ((x \ y) * (z * u))) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[para(13021(a,1),13682(a,1,2))].">
      <j1 rule="para" parents="13021 13682"/>
    </justification>
  </clause>

  <clause id="13684">
    <literal><![CDATA[
      L(L(x,y,z \ u),(z \ u) * y,K(z,u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(1081,a,13683,a)].">
      <j1 rule="hyper" parents="1081 13683"/>
    </justification>
  </clause>

  <clause id="13685">
    <literal><![CDATA[
      L(x,R(y \ R(y,z,u),y,z * u),x) = L(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(14(a,2),13160(a,2,2))].">
      <j1 rule="para" parents="14 13160"/>
    </justification>
  </clause>

  <clause id="13686">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = L(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12952,a(flip),b,13685,a)].">
      <j1 rule="hyper" parents="64 12952 13685"/>
    </justification>
  </clause>

  <clause id="13688">
    <literal><![CDATA[
      (x * K(y \ R(y,z,u),x)) \ L(x,a(y,z,u),x) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(13686(a,1),13132(a,1,2))].">
      <j1 rule="para" parents="13686 13132"/>
    </justification>
  </clause>

  <clause id="13689">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) * (x \ L(x,a(y,z,u),x)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(7069,a,13688,a)].">
      <j1 rule="hyper" parents="7069 13688"/>
    </justification>
  </clause>

  <clause id="13691">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,(x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(5906(a,1),13599(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5906 13599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13692">
    <literal><![CDATA[
      L(L(a(x,y,x),y,z),z * y,u) = a(x,(u * (z * y)) / (u * z),x)
    ]]></literal>
    <justification jstring="[hyper(10931,a,13691,a)].">
      <j1 rule="hyper" parents="10931 13691"/>
    </justification>
  </clause>

  <clause id="13693">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * (z * y)) / (u * z),x)
    ]]></literal>
    <justification jstring="[para(13190(a,1),13692(a,1,1))].">
      <j1 rule="para" parents="13190 13692"/>
    </justification>
  </clause>

  <clause id="13694">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * z) \ (u * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13169,a(flip),b,13693,a),flip(a)].">
      <j1 rule="hyper" parents="373 13169 13693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13696">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(18(a,2),13694(a,2,2))].">
      <j1 rule="para" parents="18 13694"/>
    </justification>
  </clause>

  <clause id="13697">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(13203,a,13696,a),flip(a)].">
      <j1 rule="hyper" parents="13203 13696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13698">
    <literal><![CDATA[
      a(x,L(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(13696(a,1),13203(a,1))].">
      <j1 rule="para" parents="13696 13203"/>
    </justification>
  </clause>

  <clause id="13700">
    <literal><![CDATA[
      a(x,y \ z,x) = a(x,y * z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11982,a(flip),b,13697,a),flip(a)].">
      <j1 rule="hyper" parents="64 11982 13697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13701">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = x * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,13697,a(flip),b,10884,a),flip(a)].">
      <j1 rule="hyper" parents="145 13697 10884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13702">
    <literal><![CDATA[
      a(x,(y * z) \ u,x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(346(a,1),13697(a,1,2))].">
      <j1 rule="para" parents="346 13697"/>
    </justification>
  </clause>

  <clause id="13703">
    <literal><![CDATA[
      a(x,(y \ z) \ u,x) = a(x,z \ (y * u),x)
    ]]></literal>
    <justification jstring="[para(630(a,1),13697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="630 13697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13704">
    <literal><![CDATA[
      a(x,(y * z) \ (z * u),x) = a(x,T(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[para(638(a,1),13697(a,1,2))].">
      <j1 rule="para" parents="638 13697"/>
    </justification>
  </clause>

  <clause id="13705">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(13697(a,1),10905(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13697 10905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13706">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (a(x,y,x) \ w) = K(x,x * L(y,z,u)) * w
    ]]></literal>
    <justification jstring="[para(13697(a,1),11054(a,1,2,1))].">
      <j1 rule="para" parents="13697 11054"/>
    </justification>
  </clause>

  <clause id="13707">
    <literal><![CDATA[
      a(x,y * z,x) = a(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13566,a(flip),b,13700,a)].">
      <j1 rule="hyper" parents="64 13566 13700"/>
    </justification>
  </clause>

  <clause id="13708">
    <literal><![CDATA[
      a(x,K(y,z) \ (y * u),x) = a(x,T(y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(5755(a,1),13700(a,2,2))].">
      <j1 rule="para" parents="5755 13700"/>
    </justification>
  </clause>

  <clause id="13709">
    <literal><![CDATA[
      K(x,y * z) * K(x * (y * z),x) = a(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(10904,a,13707,a)].">
      <j1 rule="hyper" parents="10904 13707"/>
    </justification>
  </clause>

  <clause id="13710">
    <literal><![CDATA[
      a(x,y * (z / y),x) = a(x,z,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),13707(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 13707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13711">
    <literal><![CDATA[
      a(x,y \ T(z,y \ 1),x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(4399(a,2),13710(a,1,2))].">
      <j1 rule="para" parents="4399 13710"/>
    </justification>
  </clause>

  <clause id="13712">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10889,a(flip),b,13701,a),flip(a)].">
      <j1 rule="hyper" parents="373 10889 13701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13713">
    <literal><![CDATA[
      L(x,y,z) * R(u,x,u) = T(u * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(145,a,13712,a(flip),b,4736,a)].">
      <j1 rule="hyper" parents="145 13712 4736"/>
    </justification>
  </clause>

  <clause id="13714">
    <literal><![CDATA[
      R(x,(1 / y) * z,x) = R(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(569(a,1),13712(a,1,2))].">
      <j1 rule="para" parents="569 13712"/>
    </justification>
  </clause>

  <clause id="13715">
    <literal><![CDATA[
      R(x,(y * z) \ u,x) = R(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(346(a,1),13712(a,1,2))].">
      <j1 rule="para" parents="346 13712"/>
    </justification>
  </clause>

  <clause id="13716">
    <literal><![CDATA[
      R(x,(y \ z) \ u,x) = R(x,z \ (y * u),x)
    ]]></literal>
    <justification jstring="[para(630(a,1),13712(a,1,2)),flip(a)].">
      <j1 rule="para" parents="630 13712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13717">
    <literal><![CDATA[
      L(R(x,x,x),y,z) / L(x,u,w) = L(x,y,z) * (1 / L(x,u,w))
    ]]></literal>
    <justification jstring="[para(13712(a,1),11563(a,1,1,1))].">
      <j1 rule="para" parents="13712 11563"/>
    </justification>
  </clause>

  <clause id="13718">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10905,a(flip),b,13705,a),flip(a)].">
      <j1 rule="hyper" parents="373 10905 13705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13719">
    <literal><![CDATA[
      L(T(x,y),L(z,u,w),x) = L(T(x,y),z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(11885,a,13718,a)].">
      <j1 rule="hyper" parents="11885 13718"/>
    </justification>
  </clause>

  <clause id="13720">
    <literal><![CDATA[
      L(x,y \ z,x) = L(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11872,a(flip),b,13718,a),flip(a)].">
      <j1 rule="hyper" parents="64 11872 13718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13721">
    <literal><![CDATA[
      L(x,y \ z,x) = L(x,y * z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11837,a(flip),b,13718,a),flip(a)].">
      <j1 rule="hyper" parents="64 11837 13718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13722">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,x) = L(x,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(2869(a,2),13718(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2869 13718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13723">
    <literal><![CDATA[
      L(x,y * (z \ y),x) = L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13159,a(flip),b,13720,a),flip(a)].">
      <j1 rule="hyper" parents="64 13159 13720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13724">
    <literal><![CDATA[
      L(x \ y,y * x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,818,a(flip),b,13720,a),flip(a)].">
      <j1 rule="hyper" parents="64 818 13720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13725">
    <literal><![CDATA[
      x * L(L(y,x * y,y),z,u) = y * ((y \ x) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13720(a,1),963(a,1,2,1))].">
      <j1 rule="para" parents="13720 963"/>
    </justification>
  </clause>

  <clause id="13726">
    <literal><![CDATA[
      L(x,y * x,x) \ y = y / T(x,y)
    ]]></literal>
    <justification jstring="[para(13720(a,1),4885(a,1,1))].">
      <j1 rule="para" parents="13720 4885"/>
    </justification>
  </clause>

  <clause id="13727">
    <literal><![CDATA[
      L(x,(y / z) / u,x) = L(x,(u * z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13158,a,b,13721,a)].">
      <j1 rule="hyper" parents="64 13158 13721"/>
    </justification>
  </clause>

  <clause id="13728">
    <literal><![CDATA[
      L(x \ (y \ x),x * (y \ x),x \ (y \ x)) = x \ ((1 / (1 / y)) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3734,a(flip),b,13721,a),flip(a)].">
      <j1 rule="hyper" parents="64 3734 13721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13729">
    <literal><![CDATA[
      L(x,x * y,x) \ y = y / T(x,y)
    ]]></literal>
    <justification jstring="[para(13721(a,1),4885(a,1,1))].">
      <j1 rule="para" parents="13721 4885"/>
    </justification>
  </clause>

  <clause id="13730">
    <literal><![CDATA[
      L(x,y * (z \ y),x) = a(x,z,x) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,10905,a,b,13723,a),flip(a)].">
      <j1 rule="hyper" parents="373 10905 13723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13731">
    <literal><![CDATA[
      L((1 / x) \ y,z * ((1 / x) \ y),x \ y) \ z = z / T((1 / x) \ y,z)
    ]]></literal>
    <justification jstring="[para(2230(a,1),13726(a,1,1))].">
      <j1 rule="para" parents="2230 13726"/>
    </justification>
  </clause>

  <clause id="13732">
    <literal><![CDATA[
      a(x,(y * z) \ u,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ (y \ u),x) = w
    ]]></literal>
    <justification jstring="[para(346(a,1),13698(a,1,2))].">
      <j1 rule="para" parents="346 13698"/>
    </justification>
  </clause>

  <clause id="13733">
    <literal><![CDATA[
      R(x,y \ z,x) = R(x,y * z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2969,a(flip),b,13714,a),flip(a)].">
      <j1 rule="hyper" parents="64 2969 13714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13734">
    <literal><![CDATA[
      R(x,x * y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4745,a(flip),b,13733,a),flip(a)].">
      <j1 rule="hyper" parents="64 4745 13733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13735">
    <literal><![CDATA[
      T(x,y) / R(y,y * x,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,13733,a(flip),b,4745,a(flip))].">
      <j1 rule="hyper" parents="225 13733 4745"/>
    </justification>
  </clause>

  <clause id="13736">
    <literal><![CDATA[
      R(x,y \ (y \ z),x) = R(x,z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),13733(a,2,2))].">
      <j1 rule="para" parents="10 13733"/>
    </justification>
  </clause>

  <clause id="13737">
    <literal><![CDATA[
      R(T(x,y),z \ u,x) = T(R(x,z * u,x),y)
    ]]></literal>
    <justification jstring="[para(13733(a,1),27(a,2,1))].">
      <j1 rule="para" parents="13733 27"/>
    </justification>
  </clause>

  <clause id="13738">
    <literal><![CDATA[
      (1 / (x \ y)) * R(z,x * y,z) = T(z * (1 / (x \ y)),z)
    ]]></literal>
    <justification jstring="[para(13733(a,1),4742(a,1,2))].">
      <j1 rule="para" parents="13733 4742"/>
    </justification>
  </clause>

  <clause id="13739">
    <literal><![CDATA[
      T(K(x,y) * (x \ y),x) = R(x,x * y,x) \ y
    ]]></literal>
    <justification jstring="[para(13733(a,1),7724(a,2,1))].">
      <j1 rule="para" parents="13733 7724"/>
    </justification>
  </clause>

  <clause id="13740">
    <literal><![CDATA[
      T(x * T(y \ (y / z),K(z,u)),x) = (y \ (y / z)) * R(x,y * (y / z),x)
    ]]></literal>
    <justification jstring="[para(13733(a,1),13186(a,2,2))].">
      <j1 rule="para" parents="13733 13186"/>
    </justification>
  </clause>

  <clause id="13741">
    <literal><![CDATA[
      R(x,y \ (y \ (z * u)),x) = R(x,z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13733,a,b,13736,a),flip(a)].">
      <j1 rule="hyper" parents="373 13733 13736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13742">
    <literal><![CDATA[
      a(x,y * (z \ y),x) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,10905,a,b,13730,a(flip))].">
      <j1 rule="hyper" parents="40 10905 13730"/>
    </justification>
  </clause>

  <clause id="13743">
    <literal><![CDATA[
      a(x,y * (z \ y),x) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10884,a,b,13742,a),flip(a)].">
      <j1 rule="hyper" parents="373 10884 13742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13744">
    <literal><![CDATA[
      R(x,y * (z \ y),x) = R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(10899,a,13743,a)].">
      <j1 rule="hyper" parents="10899 13743"/>
    </justification>
  </clause>

  <clause id="13745">
    <literal><![CDATA[
      a(x,y \ (z \ (u * y)),x) = a(x,z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(13564,a,13702,a),flip(a)].">
      <j1 rule="hyper" parents="13564 13702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13746">
    <literal><![CDATA[
      a(x,T(y \ z,u) \ T(w,T(z \ y,u)),x) = a(x,T(y \ z,u) \ w,x)
    ]]></literal>
    <justification jstring="[para(9229(a,1),13711(a,1,2,2))].">
      <j1 rule="para" parents="9229 13711"/>
    </justification>
  </clause>

  <clause id="13747">
    <literal><![CDATA[
      L(x,y \ (z / u),x) = L(x,(y * u) * z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13156,a(flip),b,13727,a)].">
      <j1 rule="hyper" parents="64 13156 13727"/>
    </justification>
  </clause>

  <clause id="13748">
    <literal><![CDATA[
      R(T(x,y),z \ u,x) = R(T(x,y),z * u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,27,a,b,13737,a),flip(a)].">
      <j1 rule="hyper" parents="373 27 13737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13749">
    <literal><![CDATA[
      R(x,(K(y,z) \ y) \ u,x) = R(x,T(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[para(6401(a,1),13741(a,1,2))].">
      <j1 rule="para" parents="6401 13741"/>
    </justification>
  </clause>

  <clause id="13750">
    <literal><![CDATA[
      a(x,y \ (z \ u),x) = a(x,z \ (u / y),x)
    ]]></literal>
    <justification jstring="[para(12(a,1),13745(a,1,2,2,2))].">
      <j1 rule="para" parents="12 13745"/>
    </justification>
  </clause>

  <clause id="13751">
    <literal><![CDATA[
      L(x,(y * z) * u,x) = L(x,y * (u / z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13721,a(flip),b,13747,a),flip(a)].">
      <j1 rule="hyper" parents="64 13721 13747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13752">
    <literal><![CDATA[
      R(T(x,y),x * y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4685,a(flip),b,13748,a),flip(a)].">
      <j1 rule="hyper" parents="64 4685 13748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13753">
    <literal><![CDATA[
      R(x,x * y,x) * y = y * T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,13752,a(flip),b,122,a),flip(a)].">
      <j1 rule="hyper" parents="145 13752 122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13754">
    <literal><![CDATA[
      K(x \ (y / z),u) \ K((x \ (y / z)) * u,u) = a(u,z \ (x \ y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,10937,a,b,13750,a)].">
      <j1 rule="hyper" parents="373 10937 13750"/>
    </justification>
  </clause>

  <clause id="13755">
    <literal><![CDATA[
      K(x,x * y) * T(x * L(y,z,u),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(13713(a,1),11363(a,1,2))].">
      <j1 rule="para" parents="13713 11363"/>
    </justification>
  </clause>

  <clause id="13756">
    <literal><![CDATA[
      L(T(x,y),L(z,u,w),x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,11861,a(flip),b,13719,a),flip(a)].">
      <j1 rule="hyper" parents="373 11861 13719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13758">
    <literal><![CDATA[
      L(T(x,y),z \ u,x) = L(T(x,y),z * u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11837,a(flip),b,13756,a),flip(a)].">
      <j1 rule="hyper" parents="64 11837 13756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13759">
    <literal><![CDATA[
      a(x,y \ (z \ (y * u)),x) = a(x,T(z,y) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13702,a(flip),b,13704,a)].">
      <j1 rule="hyper" parents="64 13702 13704"/>
    </justification>
  </clause>

  <clause id="13760">
    <literal><![CDATA[
      a(x,K(y \ (y / z),u) \ ((y \ (y / z)) * w),x) = a(x,T(T(y \ (y / z),u),z \ 1) * w,x)
    ]]></literal>
    <justification jstring="[para(6753(a,2),13708(a,2,2,1))].">
      <j1 rule="para" parents="6753 13708"/>
    </justification>
  </clause>

  <clause id="13761">
    <literal><![CDATA[
      R(x,((y * z) / y) \ u,x) = R(x,T(z,y) \ u,x)
    ]]></literal>
    <justification jstring="[para(5955(a,1),13749(a,1,2,1))].">
      <j1 rule="para" parents="5955 13749"/>
    </justification>
  </clause>

  <clause id="13762">
    <literal><![CDATA[
      a(x,T(y,z) \ (z \ u),x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(10(a,1),13759(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 13759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13763">
    <literal><![CDATA[
      K(x,y * z) * K(x * (y * z),x) = x \ R(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10884,a,b,13709,a),flip(a)].">
      <j1 rule="hyper" parents="373 10884 13709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13764">
    <literal><![CDATA[
      R(x,y * z,x) = R(x,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(6508,a,13763,a(flip))].">
      <j1 rule="hyper" parents="6508 13763"/>
    </justification>
  </clause>

  <clause id="13765">
    <literal><![CDATA[
      R(x,y * x,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13734,a(flip),b,13764,a),flip(a)].">
      <j1 rule="hyper" parents="373 13734 13764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13766">
    <literal><![CDATA[
      T(x,y) / R(y,x * y,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,13764,a,b,13734,a(flip))].">
      <j1 rule="hyper" parents="225 13764 13734"/>
    </justification>
  </clause>

  <clause id="13767">
    <literal><![CDATA[
      (x \ 1) / R(y \ (x \ y),(x \ 1) * (y \ (x \ y)),y \ (x \ y)) = (y \ (x \ y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(1927(a,1),13766(a,1,1))].">
      <j1 rule="para" parents="1927 13766"/>
    </justification>
  </clause>

  <clause id="13768">
    <literal><![CDATA[
      ((x / y) / x) / R(y,(1 / (1 / ((x / y) / x))) * y,y) = y \ (1 / (1 / ((x / y) / x)))
    ]]></literal>
    <justification jstring="[para(3823(a,1),13766(a,1,1))].">
      <j1 rule="para" parents="3823 13766"/>
    </justification>
  </clause>

  <clause id="13769">
    <literal><![CDATA[
      T(x,y * y) / R(y * (y * x),x * (y * (y * x)),y * (y * x)) = (y * (y * x)) \ x
    ]]></literal>
    <justification jstring="[para(11581(a,1),13766(a,1,1))].">
      <j1 rule="para" parents="11581 13766"/>
    </justification>
  </clause>

  <clause id="13770">
    <literal><![CDATA[
      T(x,y * y) / R(y * (x * y),x * (y * (x * y)),y * (x * y)) = (y * (x * y)) \ x
    ]]></literal>
    <justification jstring="[para(11582(a,1),13766(a,1,1))].">
      <j1 rule="para" parents="11582 13766"/>
    </justification>
  </clause>

  <clause id="13771">
    <literal><![CDATA[
      T(K(x,x * y) * (x * L(y,z,u)),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7769,a,b,13755,a)].">
      <j1 rule="hyper" parents="64 7769 13755"/>
    </justification>
  </clause>

  <clause id="13772">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5755(a,1),13771(a,1,1))].">
      <j1 rule="para" parents="5755 13771"/>
    </justification>
  </clause>

  <clause id="13773">
    <literal><![CDATA[
      T(x * L(y,z,u),x * y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4940,a(flip),b,13772,a)].">
      <j1 rule="hyper" parents="64 4940 13772"/>
    </justification>
  </clause>

  <clause id="13774">
    <literal><![CDATA[
      (x * L(y,z,u)) \ (L(y,z,u) * T(x,y)) = K(x * L(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,13773,a(flip),b,5753,a(flip))].">
      <j1 rule="hyper" parents="139 13773 5753"/>
    </justification>
  </clause>

  <clause id="13775">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (a(x,y,x) \ w) != v5 * w
    ]]></literal>
    <literal><![CDATA[
      K(x,x * L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(13706(a,2),45(a,1))].">
      <j1 rule="para" parents="13706 45"/>
    </justification>
  </clause>

  <clause id="13777">
    <literal><![CDATA[
      L(x \ (y \ x),y,x \ (y \ x)) = x \ ((1 / (1 / y)) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13723,a(flip),b,13728,a)].">
      <j1 rule="hyper" parents="64 13723 13728"/>
    </justification>
  </clause>

  <clause id="13779">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = K(x,y) * K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(10879,a,13774,a),flip(a)].">
      <j1 rule="hyper" parents="10879 13774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13780">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,12099,a(flip),b,13779,a),flip(a)].">
      <j1 rule="hyper" parents="373 12099 13779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13781">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = a(u,z,K(x / L(y,z,u),y))
    ]]></literal>
    <justification jstring="[para(12(a,1),13780(a,1,1))].">
      <j1 rule="para" parents="12 13780"/>
    </justification>
  </clause>

  <clause id="13782">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x / L(y,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9823,a(flip),b,13781,a)].">
      <j1 rule="hyper" parents="64 9823 13781"/>
    </justification>
  </clause>

  <clause id="13783">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(12049(a,1),13782(a,2,3))].">
      <j1 rule="para" parents="12049 13782"/>
    </justification>
  </clause>

  <clause id="13784">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,12233,a(flip),b,13783,a),flip(a)].">
      <j1 rule="hyper" parents="373 12233 13783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13786">
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(10515,a,13784,a)].">
      <j1 rule="hyper" parents="10515 13784"/>
    </justification>
  </clause>

  <clause id="13787">
    <literal><![CDATA[
      (x * K(L(y,z,u) \ y,x)) \ L(x,L(y,z,u) \ y,x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6517,a,b,13786,a)].">
      <j1 rule="hyper" parents="64 6517 13786"/>
    </justification>
  </clause>

  <clause id="13788">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ y),x) = a(u,z,K(x / (L(y,z,u) \ y),y))
    ]]></literal>
    <justification jstring="[para(12(a,1),13786(a,1,2))].">
      <j1 rule="para" parents="12 13786"/>
    </justification>
  </clause>

  <clause id="13789">
    <literal><![CDATA[
      K((L(x,y,z) \ x) \ u,u) = a(z,y,K(u / (L(x,y,z) \ x),x))
    ]]></literal>
    <justification jstring="[hyper(6835,a,13788,a)].">
      <j1 rule="hyper" parents="6835 13788"/>
    </justification>
  </clause>

  <clause id="13790">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K(x / (L(y,z,u) \ y),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,10496,a(flip),b,13789,a)].">
      <j1 rule="hyper" parents="64 10496 13789"/>
    </justification>
  </clause>

  <clause id="13791">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K((y / x) \ y,y))
    ]]></literal>
    <justification jstring="[para(12042(a,1),13790(a,2,3))].">
      <j1 rule="para" parents="12042 13790"/>
    </justification>
  </clause>

  <clause id="13792">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(82(a,1),13791(a,2,3,1))].">
      <j1 rule="para" parents="82 13791"/>
    </justification>
  </clause>

  <clause id="13795">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(13792(a,1),6160(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13792 6160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13796">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,10433,a(flip),b,13795,a),flip(a)].">
      <j1 rule="hyper" parents="373 10433 13795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13797">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,13796,a(flip),b,5726,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 13796 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13798">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(u,w,v5))) = a(x,y,a(v5,w,K(u,z)))
    ]]></literal>
    <justification jstring="[para(13796(a,1),12244(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13796 12244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13799">
    <literal><![CDATA[
      a(x,y,K(L(z,u,w) \ z,v5)) = a(x,y,a(w,u,K(z,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12251,a,b,13798,a)].">
      <j1 rule="hyper" parents="64 12251 13798"/>
    </justification>
  </clause>

  <clause id="13800">
    <literal><![CDATA[
      a(x,T(y,z),a(u,w,K(y,v5))) * K(v5,L(y \ L(y,w,u),y,x)) = K(v5,y \ L(y,w,u))
    ]]></literal>
    <justification jstring="[para(13798(a,1),12405(a,1,1))].">
      <j1 rule="para" parents="13798 12405"/>
    </justification>
  </clause>

  <clause id="13801">
    <literal><![CDATA[
      K(a(x,y,z),u) * a(x * y,z,a(x,y,K(z,u))) = K(L(z,y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(13799(a,1),10421(a,1,2))].">
      <j1 rule="para" parents="13799 10421"/>
    </justification>
  </clause>

  <clause id="13802">
    <literal><![CDATA[
      (x * K(L(y,z,u) \ y,x)) \ L(x,a(u,z,y),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(13722(a,1),13787(a,1,2))].">
      <j1 rule="para" parents="13722 13787"/>
    </justification>
  </clause>

  <clause id="13803">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) * (x \ L(x,a(u,z,y),x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7069,a,13802,a)].">
      <j1 rule="hyper" parents="7069 13802"/>
    </justification>
  </clause>

  <clause id="13804">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u) * 1
    ]]></literal>
    <justification jstring="[para(12532(a,1),13801(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12532 13801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13805">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a(flip),b,13804,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 13804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13807">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = T((x \ 1) \ 1,w) / ((T(x,w) \ 1) \ K(a(u,z,y),x))
    ]]></literal>
    <justification jstring="[para(13805(a,1),9953(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13805 9953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13808">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = K(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,9953,a(flip),b,13807,a),flip(a)].">
      <j1 rule="hyper" parents="373 9953 13807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13809">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(143,a,13808,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 13808 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13810">
    <literal><![CDATA[
      T(x,a(y,z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,5616,a(flip),b,13809,a),flip(a)].">
      <j1 rule="hyper" parents="64 5616 13809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13811">
    <literal><![CDATA[
      (x * a(y,z,x)) \ (a(y,z,x) * u) = L(x \ u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(13810(a,1),10979(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13810 10979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13812">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ ((x * (a(y,z,y) * u)) * w) = a(x * a(y,z,y),u,w)
    ]]></literal>
    <justification jstring="[para(13248(a,1),13270(a,1,2,1))].">
      <j1 rule="para" parents="13248 13270"/>
    </justification>
  </clause>

  <clause id="13813">
    <literal><![CDATA[
      K(x,y * K((z * (1 / u)) \ w,u)) = K(x,y * K(u * (z \ w),(z \ w) \ 1))
    ]]></literal>
    <justification jstring="[para(6705(a,1),13460(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6705 13460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13814">
    <literal><![CDATA[
      K(x,y * K((z * (1 / u)) \ w,u)) = K(x,y * K(u * (z \ w),w \ z))
    ]]></literal>
    <justification jstring="[para(6700(a,1),13813(a,2,2,2))].">
      <j1 rule="para" parents="6700 13813"/>
    </justification>
  </clause>

  <clause id="13816">
    <literal><![CDATA[
      K(x,y * K(z * (u \ w),w \ u)) = K(x,y * K(z * (u \ w),z))
    ]]></literal>
    <justification jstring="[para(11905(a,1),13814(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11905 13814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13817">
    <literal><![CDATA[
      L(x,y,R(z * (a(u,w,u) * (v5 \ (a(u,w,u) / v5))),v6,v7)) = L(x,y,R(z,v6,v7))
    ]]></literal>
    <justification jstring="[para(12911(a,1),13509(a,1,3,1,2,2))].">
      <j1 rule="para" parents="12911 13509"/>
    </justification>
  </clause>

  <clause id="13818">
    <literal><![CDATA[
      L(x,y,R(z * (u \ (a(w,v5,w) / u)),v6,v7)) = L(x,y,R(z,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,13251,a(flip),b,13817,a)].">
      <j1 rule="hyper" parents="64 13251 13817"/>
    </justification>
  </clause>

  <clause id="13820">
    <literal><![CDATA[
      ((x * (y * z)) \ (a(u,w,u) \ ((x * y) * z))) * a(u,w,u) = a(x,y,z * a(u,w,u))
    ]]></literal>
    <justification jstring="[para(13572(a,1),13573(a,1,1))].">
      <j1 rule="para" parents="13572 13573"/>
    </justification>
  </clause>

  <clause id="13821">
    <literal><![CDATA[
      T(x,(T(y,z / y) / (1 / (1 / (z / y)))) * u) = T(x,((y / z) * y) * u)
    ]]></literal>
    <justification jstring="[para(3869(a,1),13607(a,1,2,1,1))].">
      <j1 rule="para" parents="3869 13607"/>
    </justification>
  </clause>

  <clause id="13822">
    <literal><![CDATA[
      T(x,(T(y,y \ z) / (1 / (1 / (z / y)))) * u) = T(x,((y / z) * y) * u)
    ]]></literal>
    <justification jstring="[para(4636(a,1),13821(a,1,2,1,1))].">
      <j1 rule="para" parents="4636 13821"/>
    </justification>
  </clause>

  <clause id="13823">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(12919,a,13812,a),flip(a)].">
      <j1 rule="hyper" parents="12919 13812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13824">
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13106,a(flip),b,13823,a),flip(a)].">
      <j1 rule="hyper" parents="64 13106 13823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13826">
    <literal><![CDATA[
      a(x,a(y,z,y) \ u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),13824(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 13824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13827">
    <literal><![CDATA[
      a(x,L(y,y,y),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(5563(a,1),13824(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5563 13824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13828">
    <literal><![CDATA[
      a(x,L(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(10897(a,1),13824(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10897 13824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13829">
    <literal><![CDATA[
      a(x,R(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(10898(a,1),13824(a,1,2))].">
      <j1 rule="para" parents="10898 13824"/>
    </justification>
  </clause>

  <clause id="13830">
    <literal><![CDATA[
      a(x,L(y,z,y) * u,w) = a(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(11025(a,1),13824(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11025 13824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13831">
    <literal><![CDATA[
      a(x,T(y * z,y),u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(11058(a,1),13824(a,1,2))].">
      <j1 rule="para" parents="11058 13824"/>
    </justification>
  </clause>

  <clause id="13832">
    <literal><![CDATA[
      a(x,y * (T(z,y) / y),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(11379(a,1),13824(a,1,2))].">
      <j1 rule="para" parents="11379 13824"/>
    </justification>
  </clause>

  <clause id="13833">
    <literal><![CDATA[
      a(x,y \ R(z,u,z),w) = a(x,y \ z,w)
    ]]></literal>
    <justification jstring="[para(13229(a,1),13824(a,1,2))].">
      <j1 rule="para" parents="13229 13824"/>
    </justification>
  </clause>

  <clause id="13834">
    <literal><![CDATA[
      a(x,y * (a(z,u,z) * w),v5) = a(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(13220(a,1),13824(a,1,2))].">
      <j1 rule="para" parents="13220 13824"/>
    </justification>
  </clause>

  <clause id="13835">
    <literal><![CDATA[
      a(x,y \ (z * a(u,w,u)),v5) = a(x,y \ z,v5)
    ]]></literal>
    <justification jstring="[para(13222(a,2),13824(a,1,2))].">
      <j1 rule="para" parents="13222 13824"/>
    </justification>
  </clause>

  <clause id="13836">
    <literal><![CDATA[
      a(x,(y * a(z,u,z)) \ w,v5) = a(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(13266(a,1),13824(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13266 13824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13837">
    <literal><![CDATA[
      a(x,(y * L(z,u,z)) \ w,v5) = a(x,(y * z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(13261(a,1),13824(a,1,2))].">
      <j1 rule="para" parents="13261 13824"/>
    </justification>
  </clause>

  <clause id="13838">
    <literal><![CDATA[
      a(x,y \ (y * z),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(617(a,1),13828(a,1,2))].">
      <j1 rule="para" parents="617 13828"/>
    </justification>
  </clause>

  <clause id="13839">
    <literal><![CDATA[
      a(x,y / (T(y,z) / z),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(4886(a,1),13828(a,1,2))].">
      <j1 rule="para" parents="4886 13828"/>
    </justification>
  </clause>

  <clause id="13840">
    <literal><![CDATA[
      a(x,L(y \ 1,y,z),u) = a(x,(z * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(442(a,1),13838(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="442 13838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13841">
    <literal><![CDATA[
      a(x,((y \ 1) * y) \ z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(2095(a,1),13826(a,1,2,1))].">
      <j1 rule="para" parents="2095 13826"/>
    </justification>
  </clause>

  <clause id="13842">
    <literal><![CDATA[
      a(x,(y \ z) * y,u) = a(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),13831(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 13831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13843">
    <literal><![CDATA[
      a(x,y * (((y \ T(z,y)) * T(y,u)) / y),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(8891(a,1),13832(a,1,2,2,1))].">
      <j1 rule="para" parents="8891 13832"/>
    </justification>
  </clause>

  <clause id="13844">
    <literal><![CDATA[
      a(x,y \ ((z * (1 / z)) \ u),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(5292(a,1),13841(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5292 13841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13845">
    <literal><![CDATA[
      (x * y) / a(T(x,x \ z) / z,T(z,x),y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(13842(a,1),4777(a,1,2))].">
      <j1 rule="para" parents="13842 4777"/>
    </justification>
  </clause>

  <clause id="13846">
    <literal><![CDATA[
      a(x,L(y * z,y,y),u) = a(x,y * L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(1257(a,1),13830(a,1,2))].">
      <j1 rule="para" parents="1257 13830"/>
    </justification>
  </clause>

  <clause id="13847">
    <literal><![CDATA[
      a(x,y * (z * (u \ a(w,v5,w))),v6) = a(x,y * (z * (u \ 1)),v6)
    ]]></literal>
    <justification jstring="[para(13252(a,1),13834(a,1,2,2))].">
      <j1 rule="para" parents="13252 13834"/>
    </justification>
  </clause>

  <clause id="13848">
    <literal><![CDATA[
      a(x,y \ (T(z * u,z) / z),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(10903(a,2),13835(a,1,2,2))].">
      <j1 rule="para" parents="10903 13835"/>
    </justification>
  </clause>

  <clause id="13849">
    <literal><![CDATA[
      a(x,y \ T(z * u,z),w) = a(x,y \ (u * z),w)
    ]]></literal>
    <justification jstring="[para(11056(a,1),13835(a,1,2,2))].">
      <j1 rule="para" parents="11056 13835"/>
    </justification>
  </clause>

  <clause id="13850">
    <literal><![CDATA[
      a(x,y \ (z * (T(u,z) / z)),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(11377(a,1),13835(a,1,2,2))].">
      <j1 rule="para" parents="11377 13835"/>
    </justification>
  </clause>

  <clause id="13851">
    <literal><![CDATA[
      a(x,((y * z) * y) \ u,w) = a(x,(y * (z * y)) \ u,w)
    ]]></literal>
    <justification jstring="[para(88(a,1),13836(a,1,2,1))].">
      <j1 rule="para" parents="88 13836"/>
    </justification>
  </clause>

  <clause id="13852">
    <literal><![CDATA[
      a(x,y \ (z * ((1 / z) * u)),w) = a(x,y \ L(u,1 / z,z),w)
    ]]></literal>
    <justification jstring="[para(18(a,2),13844(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18 13844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13853">
    <literal><![CDATA[
      a(x,y \ (z \ T(y * u,y)),x) = a(x,z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13750,a,b,13848,a)].">
      <j1 rule="hyper" parents="64 13750 13848"/>
    </justification>
  </clause>

  <clause id="13854">
    <literal><![CDATA[
      a(x,T(y,z) \ T(y * u,y),x) = a(x,K(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[para(6021(a,1),13853(a,1,2))].">
      <j1 rule="para" parents="6021 13853"/>
    </justification>
  </clause>

  <clause id="13855">
    <literal><![CDATA[
      a(x,y \ (z * ((1 / z) * u)),w) = a(x,y \ L(u,z \ 1,z),w)
    ]]></literal>
    <justification jstring="[para(1653(a,1),13852(a,2,2,2))].">
      <j1 rule="para" parents="1653 13852"/>
    </justification>
  </clause>

  <clause id="13856">
    <literal><![CDATA[
      a(x,y * ((y \ T(z,y)) * K(y,u)),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(6847(a,1),13843(a,1,2,2))].">
      <j1 rule="para" parents="6847 13843"/>
    </justification>
  </clause>

  <clause id="13857">
    <literal><![CDATA[
      a(x,y * (y \ (T(z,y) * K(y,u))),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(7129(a,2),13856(a,1,2,2))].">
      <j1 rule="para" parents="7129 13856"/>
    </justification>
  </clause>

  <clause id="13858">
    <literal><![CDATA[
      a(x,y * (y \ (y \ (z * T(y,u)))),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(7820(a,2),13857(a,1,2,2,2))].">
      <j1 rule="para" parents="7820 13857"/>
    </justification>
  </clause>

  <clause id="13859">
    <literal><![CDATA[
      a(x,y \ (z * T(y,u)),w) = a(x,(y \ z) * T(y,u),w)
    ]]></literal>
    <justification jstring="[para(10(a,1),13858(a,1,2))].">
      <j1 rule="para" parents="10 13858"/>
    </justification>
  </clause>

  <clause id="13861">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u)) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(13268,a,13820,a),flip(a)].">
      <j1 rule="hyper" parents="13268 13820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13863">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,14,a,b,13861,a),flip(a)].">
      <j1 rule="hyper" parents="373 14 13861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13864">
    <literal><![CDATA[
      a(x,y,R(z,u,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(10889(a,1),13863(a,1,3))].">
      <j1 rule="para" parents="10889 13863"/>
    </justification>
  </clause>

  <clause id="13865">
    <literal><![CDATA[
      a(x,y,L(z,u,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(10895(a,1),13863(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10895 13863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13866">
    <literal><![CDATA[
      a(x,y,L(z,u,z) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(10952(a,1),13863(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10952 13863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13867">
    <literal><![CDATA[
      a(x,y,a(z,u,z) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(11011(a,2),13863(a,1,3))].">
      <j1 rule="para" parents="11011 13863"/>
    </justification>
  </clause>

  <clause id="13868">
    <literal><![CDATA[
      a(x,y,a(z,u,z) \ w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(11016(a,1),13863(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11016 13863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13869">
    <literal><![CDATA[
      a(x,y,T(z * u,z)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(11056(a,1),13863(a,1,3))].">
      <j1 rule="para" parents="11056 13863"/>
    </justification>
  </clause>

  <clause id="13870">
    <literal><![CDATA[
      a(x,y,z * R(u,w,u)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(11346(a,1),13863(a,1,3))].">
      <j1 rule="para" parents="11346 13863"/>
    </justification>
  </clause>

  <clause id="13871">
    <literal><![CDATA[
      a(x,y,R(z,u,z) \ w) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(11360(a,1),13863(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11360 13863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13872">
    <literal><![CDATA[
      a(x,y,z * (u * a(w,v5,w))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(13196(a,1),13863(a,1,3))].">
      <j1 rule="para" parents="13196 13863"/>
    </justification>
  </clause>

  <clause id="13873">
    <literal><![CDATA[
      a(x,y,z \ ((R(u,w,u) * v5) * v6)) = a(x,y,z \ ((u * v5) * v6))
    ]]></literal>
    <justification jstring="[para(13244(a,1),13863(a,1,3))].">
      <j1 rule="para" parents="13244 13863"/>
    </justification>
  </clause>

  <clause id="13874">
    <literal><![CDATA[
      a(x,y,L(z * a(u,w,u),v5,v6)) = a(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(13623(a,2),13863(a,1,3))].">
      <j1 rule="para" parents="13623 13863"/>
    </justification>
  </clause>

  <clause id="13875">
    <literal><![CDATA[
      a(x,y,z \ (z * u)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(617(a,1),13865(a,1,3))].">
      <j1 rule="para" parents="617 13865"/>
    </justification>
  </clause>

  <clause id="13876">
    <literal><![CDATA[
      a(x,y,L(z,u * u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(614(a,1),13865(a,1,3))].">
      <j1 rule="para" parents="614 13865"/>
    </justification>
  </clause>

  <clause id="13877">
    <literal><![CDATA[
      a(x,y,z \ L(u,z,z)) = a(x,y,(z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1139(a,1),13875(a,1,3,2))].">
      <j1 rule="para" parents="1139 13875"/>
    </justification>
  </clause>

  <clause id="13878">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,u) \ v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(13221(a,1),13867(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13221 13867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13879">
    <literal><![CDATA[
      a(x,y,(z * R(u,w,u)) \ v5) = a(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(13285(a,1),13867(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13285 13867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13880">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (z * u)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(3693(a,1),13868(a,1,3))].">
      <j1 rule="para" parents="3693 13868"/>
    </justification>
  </clause>

  <clause id="13881">
    <literal><![CDATA[
      a(x,y,(L(z,u,z) \ w) \ v5) = a(x,y,(z \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(13282(a,1),13868(a,1,3))].">
      <j1 rule="para" parents="13282 13868"/>
    </justification>
  </clause>

  <clause id="13882">
    <literal><![CDATA[
      a(x,y,z * L(L(u,w,u),v5,v6)) = a(x,y,z * L(u,v5,v6))
    ]]></literal>
    <justification jstring="[para(13628(a,1),13878(a,1,3,2))].">
      <j1 rule="para" parents="13628 13878"/>
    </justification>
  </clause>

  <clause id="13883">
    <literal><![CDATA[
      a(x,y,L(z * R(u,w,u),v5,v6)) = a(x,y,L(z * u,v5,v6))
    ]]></literal>
    <justification jstring="[para(11346(a,1),13874(a,1,3,1))].">
      <j1 rule="para" parents="11346 13874"/>
    </justification>
  </clause>

  <clause id="13884">
    <literal><![CDATA[
      ((x * y) * (z * a(u,w,u))) / (y * (z * a(u,w,u))) = R(R(x,y,z),y * z,a(u,w,u))
    ]]></literal>
    <justification jstring="[para(13196(a,1),13207(a,1,2))].">
      <j1 rule="para" parents="13196 13207"/>
    </justification>
  </clause>

  <clause id="13885">
    <literal><![CDATA[
      ((x / y) / x) / R(y,y * ((x / y) / x),y) = y \ (1 / (1 / ((x / y) / x)))
    ]]></literal>
    <justification jstring="[para(3825(a,1),13768(a,1,2,2))].">
      <j1 rule="para" parents="3825 13768"/>
    </justification>
  </clause>

  <clause id="13886">
    <literal><![CDATA[
      1 * K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12533(a,1),13800(a,1,1))].">
      <j1 rule="para" parents="12533 13800"/>
    </justification>
  </clause>

  <clause id="13887">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,w)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(147,a,13886,a)].">
      <j1 rule="hyper" parents="147 13886"/>
    </justification>
  </clause>

  <clause id="13889">
    <literal><![CDATA[
      K(x,a(y,z,u) \ 1) = K(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7337,a(flip),b,13887,a)].">
      <j1 rule="hyper" parents="64 7337 13887"/>
    </justification>
  </clause>

  <clause id="13891">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = T(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(143,a,13889,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 13889 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13892">
    <literal><![CDATA[
      K(x,K(y,z \ L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,a(w,u,z))) = v5
    ]]></literal>
    <justification jstring="[para(13889(a,1),9014(a,1,2))].">
      <j1 rule="para" parents="13889 9014"/>
    </justification>
  </clause>

  <clause id="13893">
    <literal><![CDATA[
      L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),x) = T(x,x * (u \ L(u,z,y)))
    ]]></literal>
    <justification jstring="[para(13891(a,2),765(a,1,1))].">
      <j1 rule="para" parents="13891 765"/>
    </justification>
  </clause>

  <clause id="13894">
    <literal><![CDATA[
      L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),x) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,13797,a(flip),b,13893,a),flip(a)].">
      <j1 rule="hyper" parents="373 13797 13893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13895">
    <literal><![CDATA[
      R(R(x,y,z),y * z,a(u,w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = v5
    ]]></literal>
    <justification jstring="[para(13884(a,1),666(a,1))].">
      <j1 rule="para" parents="13884 666"/>
    </justification>
  </clause>

  <clause id="13896">
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13895,a,13206,a)].">
      <j1 rule="hyper" parents="13895 13206"/>
    </justification>
  </clause>

  <clause id="13897">
    <literal><![CDATA[
      R(x,y,a(z,u,z) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(5094,a,13896,a)].">
      <j1 rule="hyper" parents="5094 13896"/>
    </justification>
  </clause>

  <clause id="13898">
    <literal><![CDATA[
      R(x,y,z * L(u,w,u)) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(10948(a,1),13896(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10948 13896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13899">
    <literal><![CDATA[
      R(x,y,L(z,u,z) \ w) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(10951(a,1),13896(a,1,3))].">
      <j1 rule="para" parents="10951 13896"/>
    </justification>
  </clause>

  <clause id="13900">
    <literal><![CDATA[
      R(x,y,a(z,u,z) \ w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[para(11016(a,1),13896(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11016 13896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13901">
    <literal><![CDATA[
      R(x,y,R(z,u,z) * w) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(11357(a,1),13896(a,1,3))].">
      <j1 rule="para" parents="11357 13896"/>
    </justification>
  </clause>

  <clause id="13902">
    <literal><![CDATA[
      R(x,y,R(z,u,z) \ w) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(11360(a,1),13896(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11360 13896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13903">
    <literal><![CDATA[
      R(x,y,z \ L(u,w,u)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(13225(a,1),13896(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13225 13896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13904">
    <literal><![CDATA[
      R(x,y,L(z \ 1,u,z) \ w) = R(x,y,(z \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(1631(a,1),13899(a,1,3,1))].">
      <j1 rule="para" parents="1631 13899"/>
    </justification>
  </clause>

  <clause id="13905">
    <literal><![CDATA[
      R(x,y,(1 / z) \ u) = R(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(2445(a,1),13902(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2445 13902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13906">
    <literal><![CDATA[
      R(x,y,z \ T(u,u * w)) = R(x,y,z \ T(u,w))
    ]]></literal>
    <justification jstring="[para(4732(a,1),13903(a,1,3,2))].">
      <j1 rule="para" parents="4732 13903"/>
    </justification>
  </clause>

  <clause id="13907">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) \ w)) = R(x,y,z \ T(u,w))
    ]]></literal>
    <justification jstring="[para(12494(a,1),13903(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="12494 13903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13908">
    <literal><![CDATA[
      K(R(x / y,y,x \ T(z,u)) \ T(z,u),w) = K(y * (x \ T(z,z * u)),w)
    ]]></literal>
    <justification jstring="[para(13906(a,1),13454(a,1,1,1))].">
      <j1 rule="para" parents="13906 13454"/>
    </justification>
  </clause>

  <clause id="13909">
    <literal><![CDATA[
      K(x * (y \ T(z,z * u)),w) = K(x * (y \ T(z,u)),w)
    ]]></literal>
    <justification jstring="[para(684(a,1),13908(a,1,1)),flip(a)].">
      <j1 rule="para" parents="684 13908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13910">
    <literal><![CDATA[
      K(x,(y * z) \ u) * a(w,v5,K((y * z) \ u,x)) = K(x,L(T(z * y,z) \ u,v5,w))
    ]]></literal>
    <justification jstring="[para(13327(a,1),13475(a,1,1))].">
      <j1 rule="para" parents="13327 13475"/>
    </justification>
  </clause>

  <clause id="13911">
    <literal><![CDATA[
      K(x,L(T(y * z,y) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L((z * y) \ u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(13910(a,1),12116(a,1))].">
      <j1 rule="para" parents="13910 12116"/>
    </justification>
  </clause>

  <clause id="13912">
    <literal><![CDATA[
      L(x,y,((z \ u) * z) \ (u * (1 / z))) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(7633(a,1),13534(a,1,3,1))].">
      <j1 rule="para" parents="7633 13534"/>
    </justification>
  </clause>

  <clause id="13913">
    <literal><![CDATA[
      L(x,y,K(z,z \ u) * (1 / z)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(10831(a,1),13912(a,1,3))].">
      <j1 rule="para" parents="10831 13912"/>
    </justification>
  </clause>

  <clause id="13914">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,K(u,u \ z) / u)
    ]]></literal>
    <justification jstring="[para(4602(a,1),13913(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4602 13913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13915">
    <literal><![CDATA[
      x \ T(x * (y \ R(y,z,u)),x) = T(y \ R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(10(a,1),12938(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 12938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13916">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(1942,a,13915,a)].">
      <j1 rule="hyper" parents="1942 13915"/>
    </justification>
  </clause>

  <clause id="13917">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(4734,a,13916,a)].">
      <j1 rule="hyper" parents="4734 13916"/>
    </justification>
  </clause>

  <clause id="13918">
    <literal><![CDATA[
      R(x,y * R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13733,a(flip),b,13916,a)].">
      <j1 rule="hyper" parents="64 13733 13916"/>
    </justification>
  </clause>

  <clause id="13919">
    <literal><![CDATA[
      L(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13686,a(flip),b,13917,a)].">
      <j1 rule="hyper" parents="64 13686 13917"/>
    </justification>
  </clause>

  <clause id="13920">
    <literal><![CDATA[
      R(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(4933,a,13919,a)].">
      <j1 rule="hyper" parents="4933 13919"/>
    </justification>
  </clause>

  <clause id="13921">
    <literal><![CDATA[
      L(x \ 1,a(y,z,u),x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(2275,a,13919,a)].">
      <j1 rule="hyper" parents="2275 13919"/>
    </justification>
  </clause>

  <clause id="13922">
    <literal><![CDATA[
      L(1 / x,a(y,z,u),x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(2273,a,13919,a)].">
      <j1 rule="hyper" parents="2273 13919"/>
    </justification>
  </clause>

  <clause id="13923">
    <literal><![CDATA[
      1 / a(x,y,z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(1655,a,13919,a)].">
      <j1 rule="hyper" parents="1655 13919"/>
    </justification>
  </clause>

  <clause id="13925">
    <literal><![CDATA[
      a(x,a(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,13919,a,b,10897,a),flip(a)].">
      <j1 rule="hyper" parents="140 13919 10897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13926">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13722,a,b,13919,a)].">
      <j1 rule="hyper" parents="64 13722 13919"/>
    </justification>
  </clause>

  <clause id="13927">
    <literal><![CDATA[
      L((1 / x) \ y,a(z,u,w),x \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,2230,a(flip),b,13919,a)].">
      <j1 rule="hyper" parents="64 2230 13919"/>
    </justification>
  </clause>

  <clause id="13928">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (a(x,y,z) \ 1) = a(x,y,z) \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(13919(a,1),1640(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13919 1640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13929">
    <literal><![CDATA[
      (x * a(y,z,u)) * R(x,w,v5) = x * (a(y,z,u) * R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(13919(a,1),514(a,1,2,1))].">
      <j1 rule="para" parents="13919 514"/>
    </justification>
  </clause>

  <clause id="13930">
    <literal><![CDATA[
      T(x * a(y,z,u),x) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(13919(a,1),4724(a,1,1,1))].">
      <j1 rule="para" parents="13919 4724"/>
    </justification>
  </clause>

  <clause id="13931">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ 1 = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1418,a(flip),b,13920,a)].">
      <j1 rule="hyper" parents="64 1418 13920"/>
    </justification>
  </clause>

  <clause id="13932">
    <literal><![CDATA[
      x * a(y,a(z,u,w),y) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,13925,a,b,68,a)].">
      <j1 rule="hyper" parents="145 13925 68"/>
    </justification>
  </clause>

  <clause id="13933">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ w = w
    ]]></literal>
    <justification jstring="[para(13925(a,2),66(a,1,1))].">
      <j1 rule="para" parents="13925 66"/>
    </justification>
  </clause>

  <clause id="13934">
    <literal><![CDATA[
      R(x,(y / z) * (y * (z \ 1)),x) = x
    ]]></literal>
    <justification jstring="[para(675(a,1),13918(a,1,2,2))].">
      <j1 rule="para" parents="675 13918"/>
    </justification>
  </clause>

  <clause id="13935">
    <literal><![CDATA[
      R(x,(y * z) * (z \ y),x) = x
    ]]></literal>
    <justification jstring="[para(995(a,1),13918(a,1,2))].">
      <j1 rule="para" parents="995 13918"/>
    </justification>
  </clause>

  <clause id="13936">
    <literal><![CDATA[
      T(x,x * (L(y,z,u) \ y)) = T(x,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(11863,a,13926,a)].">
      <j1 rule="hyper" parents="11863 13926"/>
    </justification>
  </clause>

  <clause id="13938">
    <literal><![CDATA[
      x * (y \ L(y,a(z,u,w),y)) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,13932,a(flip),b,11347,a)].">
      <j1 rule="hyper" parents="144 13932 11347"/>
    </justification>
  </clause>

  <clause id="13939">
    <literal><![CDATA[
      a(x,a(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      1 = w
    ]]></literal>
    <justification jstring="[para(13932(a,1),151(a,1)),flip(a)].">
      <j1 rule="para" parents="13932 151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13940">
    <literal><![CDATA[
      T(x * y,y \ x) / (y \ x) = (y \ x) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(225,a,13935,a(flip),b,13765,a(flip))].">
      <j1 rule="hyper" parents="225 13935 13765"/>
    </justification>
  </clause>

  <clause id="13941">
    <literal><![CDATA[
      ((x \ y) \ (y * x)) * (x \ y) = T(y * x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,13935,a(flip),b,13765,a(flip))].">
      <j1 rule="hyper" parents="145 13935 13765"/>
    </justification>
  </clause>

  <clause id="13942">
    <literal><![CDATA[
      L(L(x \ 1,y,z),a(u,w,v5),x) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(13921(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13921 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13943">
    <literal><![CDATA[
      L((x * y) \ (y * 1),a(z,u,w),T(x,y)) = L(T(x,y) \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(13921(a,1),10983(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13921 10983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13944">
    <literal><![CDATA[
      x * (T(a(y,z,u) \ 1,x) * (1 / x)) = ((a(y,z,u) \ 1) * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(13922(a,1),11814(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13922 11814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13945">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(13923(a,1),305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="13923 305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13946">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (a(x,y,z) \ u) = (a(x,y,z) * a(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(13923(a,1),536(a,1,1))].">
      <j1 rule="para" parents="13923 536"/>
    </justification>
  </clause>

  <clause id="13947">
    <literal><![CDATA[
      a(x,y,z) * ((a(x,y,z) \ 1) \ u) = (a(x,y,z) * a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(13923(a,1),538(a,1,2,1))].">
      <j1 rule="para" parents="13923 538"/>
    </justification>
  </clause>

  <clause id="13948">
    <literal><![CDATA[
      L(x \ a(y,z,u),x,a(y,z,u)) = ((a(y,z,u) \ 1) * x) \ 1
    ]]></literal>
    <justification jstring="[para(13923(a,1),917(a,2,1,1))].">
      <j1 rule="para" parents="13923 917"/>
    </justification>
  </clause>

  <clause id="13949">
    <literal><![CDATA[
      (x \ 1) * (x \ (a(y,z,u) \ 1)) = (x \ (1 / x)) / a(y,z,u)
    ]]></literal>
    <justification jstring="[para(13923(a,1),1539(a,1,2,2))].">
      <j1 rule="para" parents="13923 1539"/>
    </justification>
  </clause>

  <clause id="13950">
    <literal><![CDATA[
      R(a(x,y,z),a(x,y,z),u) * u = (a(x,y,z) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(13923(a,1),1913(a,2,1))].">
      <j1 rule="para" parents="13923 1913"/>
    </justification>
  </clause>

  <clause id="13951">
    <literal><![CDATA[
      a(x,y,z) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(14(a,1),13931(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14 13931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13952">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),a(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u = w
    ]]></literal>
    <justification jstring="[para(13931(a,1),1174(a,1,1,1))].">
      <j1 rule="para" parents="13931 1174"/>
    </justification>
  </clause>

  <clause id="13953">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,13803,a(flip),b,13938,a),flip(a)].">
      <j1 rule="hyper" parents="64 13803 13938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13954">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13689,a(flip),b,13938,a)].">
      <j1 rule="hyper" parents="64 13689 13938"/>
    </justification>
  </clause>

  <clause id="13955">
    <literal><![CDATA[
      L(x,a(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(13938(a,1),153(a,1)),flip(a)].">
      <j1 rule="para" parents="13938 153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13956">
    <literal><![CDATA[
      x \ T((x / a(y,z,u)) * a(y,z,u),x / a(y,z,u)) = K(a(y,z,u),a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,13930,a,b,5963,a)].">
      <j1 rule="hyper" parents="139 13930 5963"/>
    </justification>
  </clause>

  <clause id="13958">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13808,a(flip),b,13953,a),flip(a)].">
      <j1 rule="hyper" parents="64 13808 13953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13959">
    <literal><![CDATA[
      x \ T(x,a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,5726,a(flip),b,13958,a)].">
      <j1 rule="hyper" parents="373 5726 13958"/>
    </justification>
  </clause>

  <clause id="13960">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * T(y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,13958,a,b,6908,a)].">
      <j1 rule="hyper" parents="145 13958 6908"/>
    </justification>
  </clause>

  <clause id="13961">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,13958,a,b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 13958 5726"/>
    </justification>
  </clause>

  <clause id="13962">
    <literal><![CDATA[
      a(x,y,K(z,u)) * z = T(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(144,a,13958,a,b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 13958 5739"/>
    </justification>
  </clause>

  <clause id="13963">
    <literal><![CDATA[
      K(x,a(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,7141,a(flip),b,13958,a),flip(a)].">
      <j1 rule="hyper" parents="64 7141 13958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13964">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13958(a,2),5767(a,1,2))].">
      <j1 rule="para" parents="13958 5767"/>
    </justification>
  </clause>

  <clause id="13965">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = K(u,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[para(13958(a,1),10432(a,2,1))].">
      <j1 rule="para" parents="13958 10432"/>
    </justification>
  </clause>

  <clause id="13966">
    <literal><![CDATA[
      K(x,a(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(13958(a,1),12253(a,1))].">
      <j1 rule="para" parents="13958 12253"/>
    </justification>
  </clause>

  <clause id="13967">
    <literal><![CDATA[
      T(x,a(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,13963,a)].">
      <j1 rule="hyper" parents="57 13963"/>
    </justification>
  </clause>

  <clause id="13968">
    <literal><![CDATA[
      T(a(x,y,z),x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(55,a,13967,a)].">
      <j1 rule="hyper" parents="55 13967"/>
    </justification>
  </clause>

  <clause id="13969">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,a(x,y,u)) = w
    ]]></literal>
    <justification jstring="[para(13959(a,1),5827(a,1))].">
      <j1 rule="para" parents="13959 5827"/>
    </justification>
  </clause>

  <clause id="13970">
    <literal><![CDATA[
      T(x,a(y,x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,6935,a(flip),b,13961,a),flip(a)].">
      <j1 rule="hyper" parents="64 6935 13961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13971">
    <literal><![CDATA[
      T(x,a(y,z,L(u,w,x))) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(7394(a,1),13961(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="7394 13961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13972">
    <literal><![CDATA[
      (x * a(y,x,z)) / x = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,13970,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="225 13970 22"/>
    </justification>
  </clause>

  <clause id="13973">
    <literal><![CDATA[
      a(x,y,z) * y = y * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,13970,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 13970 22"/>
    </justification>
  </clause>

  <clause id="13974">
    <literal><![CDATA[
      T(a(x,y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(13972(a,1),340(a,1,1)),flip(b)].">
      <j1 rule="para" parents="13972 340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13975">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(14(a,1),13945(a,1,1,1))].">
      <j1 rule="para" parents="14 13945"/>
    </justification>
  </clause>

  <clause id="13977">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(8037,a,13965,a),flip(a)].">
      <j1 rule="hyper" parents="8037 13965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13978">
    <literal><![CDATA[
      a(x,y,K(z,a(x,y,z) \ u)) * u = a(x,y,z) * (u / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(6302,a,13965,a)].">
      <j1 rule="hyper" parents="6302 13965"/>
    </justification>
  </clause>

  <clause id="13979">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = T(K(a(x,y,z),u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,7867,a(flip),b,13977,a),flip(a)].">
      <j1 rule="hyper" parents="373 7867 13977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13980">
    <literal><![CDATA[
      a(x,y,z) * a(x,y,K(z,u)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(145,a,13977,a,b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 13977 5726"/>
    </justification>
  </clause>

  <clause id="13981">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(13977(a,2),5785(a,1,1,2))].">
      <j1 rule="para" parents="13977 5785"/>
    </justification>
  </clause>

  <clause id="13982">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(u,a(x,y,z)) \ w = v5
    ]]></literal>
    <justification jstring="[para(13977(a,2),6301(a,1,1))].">
      <j1 rule="para" parents="13977 6301"/>
    </justification>
  </clause>

  <clause id="13983">
    <literal><![CDATA[
      T(x,a(y,z,z)) = x
    ]]></literal>
    <justification jstring="[para(6935(a,1),13981(a,1,1))].">
      <j1 rule="para" parents="6935 13981"/>
    </justification>
  </clause>

  <clause id="13984">
    <literal><![CDATA[
      T(a(x,y,y),z) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(55,a,13983,a)].">
      <j1 rule="hyper" parents="55 13983"/>
    </justification>
  </clause>

  <clause id="13985">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(11980(a,1),13983(a,1,2))].">
      <j1 rule="para" parents="11980 13983"/>
    </justification>
  </clause>

  <clause id="13987">
    <literal><![CDATA[
      T(a(x,y,y \ 1),z) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(55,a,13985,a)].">
      <j1 rule="hyper" parents="55 13985"/>
    </justification>
  </clause>

  <clause id="13988">
    <literal><![CDATA[
      T(x,y \ (z * ((y \ z) \ 1))) = x
    ]]></literal>
    <justification jstring="[para(980(a,1),13985(a,1,2))].">
      <j1 rule="para" parents="980 13985"/>
    </justification>
  </clause>

  <clause id="13989">
    <literal><![CDATA[
      T(x \ (y * ((x \ y) \ 1)),z) = x \ (y * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(55,a,13988,a)].">
      <j1 rule="hyper" parents="55 13988"/>
    </justification>
  </clause>

  <clause id="13990">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = T(a(x,y,K(z,u)),w)
    ]]></literal>
    <justification jstring="[para(13977(a,2),13979(a,2,1))].">
      <j1 rule="para" parents="13977 13979"/>
    </justification>
  </clause>

  <clause id="13991">
    <literal><![CDATA[
      a(x,y,K(z,T(u,y))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(13974,a,13990,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13974 13990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13992">
    <literal><![CDATA[
      (x \ 1) * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x \ 1,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12249(a,1),13964(a,1,2))].">
      <j1 rule="para" parents="12249 13964"/>
    </justification>
  </clause>

  <clause id="13993">
    <literal><![CDATA[
      T(x,a(y,z,L(u,w,x))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(13971(a,2),13964(a,1))].">
      <j1 rule="para" parents="13971 13964"/>
    </justification>
  </clause>

  <clause id="13994">
    <literal><![CDATA[
      T(a(x,y,z),K(u,y)) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[para(8096(a,1),13980(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8096 13980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13995">
    <literal><![CDATA[
      T(a(x,y \ z,u),K(y,z)) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(141,a,13994,a(flip),b,8706,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="141 13994 8706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13996">
    <literal><![CDATA[
      a(x,y \ z,u) * K(y,z) = K(y,z) * a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,13995,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 13995 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13997">
    <literal><![CDATA[
      T(x,y * (L(y,z,u) \ x)) = T(x,L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10516,a,b,13936,a)].">
      <j1 rule="hyper" parents="64 10516 13936"/>
    </justification>
  </clause>

  <clause id="13998">
    <literal><![CDATA[
      T(x * y,y \ x) / ((y \ x) \ (x * y)) = (y \ x) * K((y \ x) \ (x * y),y \ x)
    ]]></literal>
    <justification jstring="[para(13940(a,1),8476(a,1,2))].">
      <j1 rule="para" parents="13940 8476"/>
    </justification>
  </clause>

  <clause id="13999">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 = T(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13968,a,b,13951,a),flip(a)].">
      <j1 rule="hyper" parents="64 13968 13951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14000">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ a(x,y,z) = a(x,y,z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(13920(a,1),13950(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13920 13950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14001">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,R(x,z,u)) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12862,a(flip),b,13996,a),flip(a)].">
      <j1 rule="hyper" parents="64 12862 13996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14002">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * (a(x,y,z) \ u) = (a(x,y,z) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(14000(a,1),1131(a,1,1))].">
      <j1 rule="para" parents="14000 1131"/>
    </justification>
  </clause>

  <clause id="14003">
    <literal><![CDATA[
      (a(x,y,z) \ (a(x,y,z) \ 1)) * u = (a(x,y,z) * a(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(14000(a,1),1546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14000 1546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14004">
    <literal><![CDATA[
      x * (a(y,z,u) \ (a(y,z,u) \ 1)) = x / (a(y,z,u) * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14000(a,1),1618(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14000 1618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14005">
    <literal><![CDATA[
      (x \ L(x,y,y)) \ (a(y,y,x) * z) = (a(y,y,x) * a(y,y,x)) * z
    ]]></literal>
    <justification jstring="[para(14000(a,1),5672(a,2,1))].">
      <j1 rule="para" parents="14000 5672"/>
    </justification>
  </clause>

  <clause id="14006">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,u) * a(x,x \ u,x)
    ]]></literal>
    <justification jstring="[para(12888(a,1),14001(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12888 14001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14007">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,10933,a(flip),b,14006,a),flip(a)].">
      <j1 rule="hyper" parents="373 10933 14006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14009">
    <literal><![CDATA[
      K(x,K(y,R(y,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(14006(a,2),13314(a,1,2))].">
      <j1 rule="para" parents="14006 13314"/>
    </justification>
  </clause>

  <clause id="14010">
    <literal><![CDATA[
      K(x,x \ ((x * R(T(x,y),z,u)) / w)) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(10077,a,14007,a),flip(a)].">
      <j1 rule="hyper" parents="10077 14007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14011">
    <literal><![CDATA[
      K(x,x \ ((x * y) * z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(210(a,1),14007(a,1,2)),flip(a)].">
      <j1 rule="para" parents="210 14007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14012">
    <literal><![CDATA[
      K(x / y,(x * (y \ 1)) \ z) = K(x / y,(x / y) \ z)
    ]]></literal>
    <justification jstring="[para(675(a,1),14007(a,1,2,1))].">
      <j1 rule="para" parents="675 14007"/>
    </justification>
  </clause>

  <clause id="14013">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(649(a,1),14007(a,1,2)),flip(a)].">
      <j1 rule="para" parents="649 14007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14014">
    <literal><![CDATA[
      K(x,y * ((x * y) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(420(a,1),14007(a,1,2))].">
      <j1 rule="para" parents="420 14007"/>
    </justification>
  </clause>

  <clause id="14015">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) * K(x,K(y,R(x / y,u,w) \ z)) = K(y \ x,R(x / y,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(14007(a,1),9052(a,1,1))].">
      <j1 rule="para" parents="14007 9052"/>
    </justification>
  </clause>

  <clause id="14016">
    <literal><![CDATA[
      K(x,x \ ((y * x) * z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(10863,a,14011,a)].">
      <j1 rule="hyper" parents="10863 14011"/>
    </justification>
  </clause>

  <clause id="14017">
    <literal><![CDATA[
      T((x * y) * z,K(x,y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(14011(a,1),6263(a,1,2))].">
      <j1 rule="para" parents="14011 6263"/>
    </justification>
  </clause>

  <clause id="14018">
    <literal><![CDATA[
      K(x,(x \ y) * z) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(10145,a,14013,a),flip(a)].">
      <j1 rule="hyper" parents="10145 14013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14019">
    <literal><![CDATA[
      K(x,y * ((y * x) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14016(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 14016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14020">
    <literal><![CDATA[
      K(x \ K(y,(z * y) * u),w) = K(x \ K(y,z * u),w)
    ]]></literal>
    <justification jstring="[para(14016(a,1),13402(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14016 13402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14021">
    <literal><![CDATA[
      x * K(y,(y \ z) * u) = x * K(y,z * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(145,a,14018,a,b,9,a)].">
      <j1 rule="hyper" parents="145 14018 9"/>
    </justification>
  </clause>

  <clause id="14022">
    <literal><![CDATA[
      T(x,(x \ y) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(143,a,14018,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 14018 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14023">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ z) = K(x \ y,x * (y \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),14019(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 14019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14024">
    <literal><![CDATA[
      T(x,(y / x) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(8584,a,14022,a)].">
      <j1 rule="hyper" parents="8584 14022"/>
    </justification>
  </clause>

  <clause id="14025">
    <literal><![CDATA[
      K(x,K(y,R(x \ y,z,u) \ w)) = K(x,K(x \ y,w))
    ]]></literal>
    <justification jstring="[hyper(8977,a,14009,a)].">
      <j1 rule="hyper" parents="8977 14009"/>
    </justification>
  </clause>

  <clause id="14026">
    <literal><![CDATA[
      x * K(y \ z,y * (z \ x)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(145,a,14023,a(flip),b,5961,a)].">
      <j1 rule="hyper" parents="145 14023 5961"/>
    </justification>
  </clause>

  <clause id="14027">
    <literal><![CDATA[
      (x \ y) \ K(x \ y,x * (y \ 1)) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,14023,a(flip),b,1724,a(flip))].">
      <j1 rule="hyper" parents="139 14023 1724"/>
    </justification>
  </clause>

  <clause id="14028">
    <literal><![CDATA[
      (x \ (y \ 1)) \ K(x \ (y \ 1),x * y) = 1 / (x \ (y \ 1))
    ]]></literal>
    <justification jstring="[para(6521(a,1),14027(a,1,2))].">
      <j1 rule="para" parents="6521 14027"/>
    </justification>
  </clause>

  <clause id="14029">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10783,a(flip),b,14010,a)].">
      <j1 rule="hyper" parents="64 10783 14010"/>
    </justification>
  </clause>

  <clause id="14030">
    <literal><![CDATA[
      K(x,y \ R(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12521,a(flip),b,14029,a)].">
      <j1 rule="hyper" parents="64 12521 14029"/>
    </justification>
  </clause>

  <clause id="14032">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12657,a,b,14030,a)].">
      <j1 rule="hyper" parents="64 12657 14030"/>
    </justification>
  </clause>

  <clause id="14033">
    <literal><![CDATA[
      K(R(x,y,z),u \ x) = K(x,R(u,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12661,a(flip),b,14030,a)].">
      <j1 rule="hyper" parents="64 12661 14030"/>
    </justification>
  </clause>

  <clause id="14034">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10716,a(flip),b,14030,a)].">
      <j1 rule="hyper" parents="64 10716 14030"/>
    </justification>
  </clause>

  <clause id="14036">
    <literal><![CDATA[
      K(x,R(R(x / y,y,L(K(z,x),u,w)),v5,v6) \ x) = K(R(x,v5,v6),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12433,a(flip),b,14033,a),flip(a)].">
      <j1 rule="hyper" parents="64 12433 14033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14038">
    <literal><![CDATA[
      K(x,((x * y) * z) / u) = K(x,(u / (y * z)) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12656,a(flip),b,14032,a)].">
      <j1 rule="hyper" parents="64 12656 14032"/>
    </justification>
  </clause>

  <clause id="14040">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,10500,a(flip),b,14034,a),flip(a)].">
      <j1 rule="hyper" parents="373 10500 14034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14042">
    <literal><![CDATA[
      K(x,K(y,R(x \ y,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,8976,a(flip),b,14025,a),flip(a)].">
      <j1 rule="hyper" parents="373 8976 14025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14043">
    <literal><![CDATA[
      K(x,K(y,R(y \ x,z,u) \ w)) = K(y,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(8436,a,14042,a)].">
      <j1 rule="hyper" parents="8436 14042"/>
    </justification>
  </clause>

  <clause id="14044">
    <literal><![CDATA[
      K(x,K(y,R(y \ x,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,8108,a,b,14043,a),flip(a)].">
      <j1 rule="hyper" parents="373 8108 14043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14045">
    <literal><![CDATA[
      (x \ y) * ((y * z) / (x \ y)) = (y * z) * K(x \ y,x * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),14026(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 14026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14046">
    <literal><![CDATA[
      T(a(x,y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(13999(a,1),13975(a,1))].">
      <j1 rule="para" parents="13999 13975"/>
    </justification>
  </clause>

  <clause id="14047">
    <literal><![CDATA[
      T(a(1 / x,y,z),x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      a(x \ 1,y,z) = u
    ]]></literal>
    <justification jstring="[para(2654(a,2),14046(a,1,1))].">
      <j1 rule="para" parents="2654 14046"/>
    </justification>
  </clause>

  <clause id="14048">
    <literal><![CDATA[
      L((x * y) \ (y * 1),a(z,u,w),T(x,y)) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,6983,a(flip),b,13943,a),flip(a)].">
      <j1 rule="hyper" parents="373 6983 13943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14049">
    <literal><![CDATA[
      L((x * y) \ y,a(z,u,w),T(x,y)) = (x * y) \ y
    ]]></literal>
    <justification jstring="[para(8(a,1),14048(a,1,1,2))].">
      <j1 rule="para" parents="8 14048"/>
    </justification>
  </clause>

  <clause id="14050">
    <literal><![CDATA[
      (x \ L(x,y,y)) * (a(y,y,x) \ 1) = a(y,y,x) \ (a(y,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(5665(a,1),13928(a,1,1))].">
      <j1 rule="para" parents="5665 13928"/>
    </justification>
  </clause>

  <clause id="14051">
    <literal><![CDATA[
      a(x,x,y) * ((y \ L(y,x,x)) \ z) = (a(x,x,y) * a(x,x,y)) * z
    ]]></literal>
    <justification jstring="[para(5665(a,1),13947(a,1,2,1))].">
      <j1 rule="para" parents="5665 13947"/>
    </justification>
  </clause>

  <clause id="14052">
    <literal><![CDATA[
      a(x,y,z) * ((a(x,y,z) * a(x,y,z)) \ u) = (a(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(733,a,14002,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="733 14002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14053">
    <literal><![CDATA[
      (a(x,x,y) * a(x,x,y)) * L(y,x,x) = (a(x,x,y) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(5567(a,1),14002(a,1,2))].">
      <j1 rule="para" parents="5567 14002"/>
    </justification>
  </clause>

  <clause id="14054">
    <literal><![CDATA[
      (1 / (1 / a(x,x,y))) * y = (a(x,x,y) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,5677,a(flip),b,14053,a)].">
      <j1 rule="hyper" parents="64 5677 14053"/>
    </justification>
  </clause>

  <clause id="14055">
    <literal><![CDATA[
      R(R(K(x,y),y,L(K(z,x),u,w)),v5,v6) = K(R(x,v5,v6),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12451,a(flip),b,14036,a)].">
      <j1 rule="hyper" parents="64 12451 14036"/>
    </justification>
  </clause>

  <clause id="14056">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(4524(a,1),14055(a,1,1))].">
      <j1 rule="para" parents="4524 14055"/>
    </justification>
  </clause>

  <clause id="14058">
    <literal><![CDATA[
      R(x * K(R(y,z,u),x),w,x) \ R(x,w,x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(14056(a,1),9733(a,1,1,1,2))].">
      <j1 rule="para" parents="14056 9733"/>
    </justification>
  </clause>

  <clause id="14059">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (R(x,w,x) \ R(x,w,x)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(12427,a,14058,a)].">
      <j1 rule="hyper" parents="12427 14058"/>
    </justification>
  </clause>

  <clause id="14060">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(229,a,14059,a),flip(a)].">
      <j1 rule="hyper" parents="229 14059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14061">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14059(a,1),228(a,1)),flip(b)].">
      <j1 rule="para" parents="14059 228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14063">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,R(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,14056,a(flip),b,14060,a)].">
      <j1 rule="hyper" parents="64 14056 14060"/>
    </justification>
  </clause>

  <clause id="14064">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,14060,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 14060 20"/>
    </justification>
  </clause>

  <clause id="14065">
    <literal><![CDATA[
      K(x,(y * z) * (z \ 1)) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(297(a,2),14060(a,2,2)),flip(a)].">
      <j1 rule="para" parents="297 14060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14068">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(14060(a,1),12681(a,1,2))].">
      <j1 rule="para" parents="14060 12681"/>
    </justification>
  </clause>

  <clause id="14070">
    <literal><![CDATA[
      a(K(x,R(y,z,u) \ 1),w,v5) = a(K(y,R(x,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(14063(a,1),13127(a,2,1))].">
      <j1 rule="para" parents="14063 13127"/>
    </justification>
  </clause>

  <clause id="14071">
    <literal><![CDATA[
      a(K(x,R(y,x * z,u)),w,v5) = a(K(x,R(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(14063(a,1),13138(a,2,1))].">
      <j1 rule="para" parents="14063 13138"/>
    </justification>
  </clause>

  <clause id="14072">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12688,a(flip),b,14068,a)].">
      <j1 rule="hyper" parents="64 12688 14068"/>
    </justification>
  </clause>

  <clause id="14073">
    <literal><![CDATA[
      K(x,K(y,z) * K(R(z,u,w),y)) = K(a(K(y,z),u,w),x)
    ]]></literal>
    <justification jstring="[para(14068(a,1),12351(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14068 12351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14074">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,K(x,y) * K(R(y,z,u),x)) = v5
    ]]></literal>
    <justification jstring="[para(14068(a,1),12390(a,1,1))].">
      <j1 rule="para" parents="14068 12390"/>
    </justification>
  </clause>

  <clause id="14076">
    <literal><![CDATA[
      (K(x,y) * z) * u != w * (z * u)
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14064(a,1),45(a,1))].">
      <j1 rule="para" parents="14064 45"/>
    </justification>
  </clause>

  <clause id="14077">
    <literal><![CDATA[
      ((x * y) * z) / ((K(u,x) * y) * z) = T(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(14064(a,1),6222(a,1,2))].">
      <j1 rule="para" parents="14064 6222"/>
    </justification>
  </clause>

  <clause id="14078">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = R(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(11224,a,14065,a)].">
      <j1 rule="hyper" parents="11224 14065"/>
    </justification>
  </clause>

  <clause id="14079">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[para(5756(a,2),14077(a,1,2,1))].">
      <j1 rule="para" parents="5756 14077"/>
    </justification>
  </clause>

  <clause id="14080">
    <literal><![CDATA[
      R(T(x,y),T(y,x),z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(4677,a,14079,a)].">
      <j1 rule="hyper" parents="4677 14079"/>
    </justification>
  </clause>

  <clause id="14081">
    <literal><![CDATA[
      R(x,T(y,x),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(163,a,14080,a(flip))].">
      <j1 rule="hyper" parents="163 14080"/>
    </justification>
  </clause>

  <clause id="14083">
    <literal><![CDATA[
      R(x,y,z) = ((y * x) * z) / (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,263,a,b,14081,a),flip(a)].">
      <j1 rule="hyper" parents="64 263 14081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14086">
    <literal><![CDATA[
      R(x,y,z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[para(14081(a,1),648(a,1,1))].">
      <j1 rule="para" parents="14081 648"/>
    </justification>
  </clause>

  <clause id="14087">
    <literal><![CDATA[
      ((x * y) * z) * a(R(y,x,z),T(x,y),z) = (R(y,T(x,y),z) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(14081(a,1),1950(a,1,2,1))].">
      <j1 rule="para" parents="14081 1950"/>
    </justification>
  </clause>

  <clause id="14088">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * (K(x,y) * z)) = R(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(10823(a,1),14083(a,2,1)),flip(a)].">
      <j1 rule="para" parents="10823 14083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14089">
    <literal><![CDATA[
      R(x,(y * y) * z,u) \ (((y * y) * (z * x)) * u) = T((y * y) * z,x) * u
    ]]></literal>
    <justification jstring="[para(33(a,1),14086(a,1,2,1))].">
      <j1 rule="para" parents="33 14086"/>
    </justification>
  </clause>

  <clause id="14090">
    <literal><![CDATA[
      K(x,(((y * x) * z) / R(x,y,z)) \ u) = K(x,(T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(14086(a,1),9679(a,2,2,1))].">
      <j1 rule="para" parents="14086 9679"/>
    </justification>
  </clause>

  <clause id="14091">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,9218,a(flip),b,14078,a),flip(a)].">
      <j1 rule="hyper" parents="64 9218 14078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14092">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(14061,a,14091,a)].">
      <j1 rule="hyper" parents="14061 14091"/>
    </justification>
  </clause>

  <clause id="14093">
    <literal><![CDATA[
      R(K(x \ 1,y) * K(y,R(x,z,u) \ 1),w,v5) = a(K(x,R(y,w,v5)),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12715,a,b,14070,a)].">
      <j1 rule="hyper" parents="64 12715 14070"/>
    </justification>
  </clause>

  <clause id="14094">
    <literal><![CDATA[
      R(K(a(K(x,y),z,u),w),K(K(x,w),v5),v6) * v7 = K(y,K(x,w)) * (R(K(K(x,w),y),z,u) * v7)
    ]]></literal>
    <justification jstring="[para(14073(a,1),12466(a,1,1,1))].">
      <j1 rule="para" parents="14073 12466"/>
    </justification>
  </clause>

  <clause id="14095">
    <literal><![CDATA[
      R(x,y,K(x,y) * z) = ((x * y) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(5829(a,1),14088(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5829 14088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14096">
    <literal><![CDATA[
      R(x,y,K(x,y) * z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,20,a,b,14095,a),flip(a)].">
      <j1 rule="hyper" parents="373 20 14095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14098">
    <literal><![CDATA[
      R(x,y,K(x,y) \ z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14096(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 14096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14099">
    <literal><![CDATA[
      K(x,(((y * x) * z) / R(x,y,z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(14090(a,2),8927(a,1))].">
      <j1 rule="para" parents="14090 8927"/>
    </justification>
  </clause>

  <clause id="14100">
    <literal><![CDATA[
      (x \ L(x,y,y)) * (x \ L(x,y,y)) = a(y,y,x) \ (a(y,y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5667,a(flip),b,14050,a)].">
      <j1 rule="hyper" parents="64 5667 14050"/>
    </justification>
  </clause>

  <clause id="14101">
    <literal><![CDATA[
      a(x,x,y) * ((y \ L(y,x,x)) \ z) = ((a(x,x,y) \ 1) \ a(x,x,y)) * z
    ]]></literal>
    <justification jstring="[para(14000(a,2),14051(a,2,1))].">
      <j1 rule="para" parents="14000 14051"/>
    </justification>
  </clause>

  <clause id="14102">
    <literal><![CDATA[
      (a(x,x,y) * a(x,x,y)) \ y = a(x,x,y) \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,5669,a(flip),b,14052,a),flip(a)].">
      <j1 rule="hyper" parents="139 5669 14052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14103">
    <literal><![CDATA[
      (x * y) \ (y * (a(z,u,w) * ((a(z,u,w) * a(z,u,w)) \ T(x,y)))) = L(T(a(z,u,w) \ 1,T(x,y)),x,y)
    ]]></literal>
    <justification jstring="[para(14052(a,2),10981(a,1,2,2))].">
      <j1 rule="para" parents="14052 10981"/>
    </justification>
  </clause>

  <clause id="14104">
    <literal><![CDATA[
      (a(x,x,y) \ L(y,x,x)) * (y \ z) = (a(x,x,y) * a(x,x,y)) \ z
    ]]></literal>
    <justification jstring="[para(14102(a,1),802(a,1,1))].">
      <j1 rule="para" parents="14102 802"/>
    </justification>
  </clause>

  <clause id="14105">
    <literal><![CDATA[
      a(x,a(y,y,z) \ L(z,y,y),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(14102(a,1),11965(a,1,2))].">
      <j1 rule="para" parents="14102 11965"/>
    </justification>
  </clause>

  <clause id="14106">
    <literal><![CDATA[
      x * ((a(y,y,x) \ L(x,y,y)) \ z) = (a(y,y,x) * a(y,y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(733,a,14104,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="733 14104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14107">
    <literal><![CDATA[
      a(K(x,R(y,z,u)),w,v5) = R(a(K(x,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(13129(a,1),14093(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13129 14093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14108">
    <literal><![CDATA[
      a(K(x,R(y,x * R(y,z,u),w)),z * y,u) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,12970,a(flip),b,14107,a),flip(a)].">
      <j1 rule="hyper" parents="373 12970 14107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14109">
    <literal><![CDATA[
      a(K(x,R(y,R(y,z,u),w)),z * y,u) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14071,a(flip),b,14108,a)].">
      <j1 rule="hyper" parents="64 14071 14108"/>
    </justification>
  </clause>

  <clause id="14110">
    <literal><![CDATA[
      (a(x,x,y) \ (a(x,x,y) \ 1)) \ z = a(x,x,y) * ((y \ L(y,x,x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1549,a,b,14101,a)].">
      <j1 rule="hyper" parents="373 1549 14101"/>
    </justification>
  </clause>

  <clause id="14111">
    <literal><![CDATA[
      ((x \ L(x,y,y)) * (x \ L(x,y,y))) \ z = a(y,y,x) * ((x \ L(x,y,y)) \ z)
    ]]></literal>
    <justification jstring="[para(14100(a,2),14110(a,1,1))].">
      <j1 rule="para" parents="14100 14110"/>
    </justification>
  </clause>

  <clause id="14112">
    <literal><![CDATA[
      R(x,y,z) \ (((u * u) * (y * x)) * z) = T((u * u) * y,x) * z
    ]]></literal>
    <justification jstring="[para(2965(a,1),14089(a,1,1))].">
      <j1 rule="para" parents="2965 14089"/>
    </justification>
  </clause>

  <clause id="14113">
    <literal><![CDATA[
      R(x,y,z) \ ((u * u) * ((y * x) * z)) = T((u * u) * y,x) * z
    ]]></literal>
    <justification jstring="[para(33(a,1),14112(a,1,2))].">
      <j1 rule="para" parents="33 14112"/>
    </justification>
  </clause>

  <clause id="14115">
    <literal><![CDATA[
      (x \ y) * K((x \ y) \ (y * x),x \ y) = (x \ y) * K(y * x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5844,a(flip),b,13998,a),flip(a)].">
      <j1 rule="hyper" parents="64 5844 13998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14116">
    <literal><![CDATA[
      K(a(x,y,z),a(x,y,z) \ u) = u \ T(u,u / a(x,y,z))
    ]]></literal>
    <justification jstring="[para(12(a,1),13956(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 13956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14117">
    <literal><![CDATA[
      K(a(x,y,z),a(x,y,z) \ u) = u \ T(u,a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(4461(a,1),14116(a,2,2))].">
      <j1 rule="para" parents="4461 14116"/>
    </justification>
  </clause>

  <clause id="14118">
    <literal><![CDATA[
      K(a(x,y,z),a(x,y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,a(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(14117(a,2),5827(a,1))].">
      <j1 rule="para" parents="14117 5827"/>
    </justification>
  </clause>

  <clause id="14119">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(y,z,K(u,a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(14118,a,13977,a(flip))].">
      <j1 rule="hyper" parents="14118 13977"/>
    </justification>
  </clause>

  <clause id="14120">
    <literal><![CDATA[
      K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * v5) = K(a(K(y,x),u,w),z) * v5
    ]]></literal>
    <justification jstring="[para(431(a,1),14094(a,1,1)),flip(a)].">
      <j1 rule="para" parents="431 14094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14121">
    <literal><![CDATA[
      K(x,K(y,z)) * (R(K(K(y,z),x),u,w) * y) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,9191,a(flip),b,14120,a),flip(a)].">
      <j1 rule="hyper" parents="373 9191 14120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14122">
    <literal><![CDATA[
      K(x,K(y,z)) * (R(K(y,K(z,x)),u,w) * y) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(8092(a,1),14121(a,1,2,1,1))].">
      <j1 rule="para" parents="8092 14121"/>
    </justification>
  </clause>

  <clause id="14123">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(y,K(z,R(x,u,w))) * y) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(9772(a,1),14122(a,1,2,1))].">
      <j1 rule="para" parents="9772 14122"/>
    </justification>
  </clause>

  <clause id="14124">
    <literal><![CDATA[
      K(x,K(y,z)) * T(y,K(z,R(x,u,w))) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[para(5756(a,2),14123(a,1,2))].">
      <j1 rule="para" parents="5756 14123"/>
    </justification>
  </clause>

  <clause id="14125">
    <literal><![CDATA[
      T(K(x,K(y,z)) * y,K(x,R(z,u,w))) = y * K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10026,a,b,14124,a)].">
      <j1 rule="hyper" parents="64 10026 14124"/>
    </justification>
  </clause>

  <clause id="14126">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,R(z,u,w))) = x * K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(8115(a,1),14125(a,1,1))].">
      <j1 rule="para" parents="8115 14125"/>
    </justification>
  </clause>

  <clause id="14127">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w)) * K(z,y)) = x * K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(12358,a,14126,a)].">
      <j1 rule="hyper" parents="12358 14126"/>
    </justification>
  </clause>

  <clause id="14128">
    <literal><![CDATA[
      x * K(a(K(x,y),z,u),w) = T(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12689,a(flip),b,14127,a),flip(a)].">
      <j1 rule="hyper" parents="64 12689 14127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14129">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) = K(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,5753,a(flip),b,14128,a),flip(a)].">
      <j1 rule="hyper" parents="35 5753 14128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14130">
    <literal><![CDATA[
      K(x,K(y,z) * K(R(z,u,w),y)) = K(y,a(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(14074,a,14129,a)].">
      <j1 rule="hyper" parents="14074 14129"/>
    </justification>
  </clause>

  <clause id="14131">
    <literal><![CDATA[
      1 * K(x,a(K(y,z),u,w)) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(14130(a,1),12700(a,1,2))].">
      <j1 rule="para" parents="14130 12700"/>
    </justification>
  </clause>

  <clause id="14132">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(y,a(K(z,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(147,a,14131,a),flip(a)].">
      <j1 rule="hyper" parents="147 14131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14133">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,14129,a,b,14132,a),flip(a)].">
      <j1 rule="hyper" parents="373 14129 14132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14134">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(x,a(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(8108(a,1),14132(a,1,1))].">
      <j1 rule="para" parents="8108 14132"/>
    </justification>
  </clause>

  <clause id="14135">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(8108(a,1),14133(a,1,1))].">
      <j1 rule="para" parents="8108 14133"/>
    </justification>
  </clause>

  <clause id="14136">
    <literal><![CDATA[
      K(a(K(x,y),z * y,u),w) = a(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(14072(a,2),14133(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14072 14133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14137">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = K(x,K(z,y \ R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(13954(a,1),14134(a,2,2))].">
      <j1 rule="para" parents="13954 14134"/>
    </justification>
  </clause>

  <clause id="14138">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = a(K(y,K(x,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14135,a,b,14136,a)].">
      <j1 rule="hyper" parents="64 14135 14136"/>
    </justification>
  </clause>

  <clause id="14139">
    <literal><![CDATA[
      K(x,K(y,z \ R(z,u,w))) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14138,a(flip),b,14137,a),flip(a)].">
      <j1 rule="hyper" parents="64 14138 14137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14140">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,10242,a,b,14139,a)].">
      <j1 rule="hyper" parents="64 10242 14139"/>
    </justification>
  </clause>

  <clause id="14141">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(8110(a,2),14140(a,2,1))].">
      <j1 rule="para" parents="8110 14140"/>
    </justification>
  </clause>

  <clause id="14142">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) \ z)) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(10381,a,14141,a)].">
      <j1 rule="hyper" parents="10381 14141"/>
    </justification>
  </clause>

  <clause id="14143">
    <literal><![CDATA[
      K(x,K(y,(z * u) / (R(z,w,v5) * u))) = a(K(x,K(R(y,z,u),z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,9915,a(flip),b,14142,a)].">
      <j1 rule="hyper" parents="64 9915 14142"/>
    </justification>
  </clause>

  <clause id="14144">
    <literal><![CDATA[
      K(x,K(y,(z * u) / (R(z,w,v5) * u))) = a(K(x,K(z,R(y,z,u))),w,v5)
    ]]></literal>
    <justification jstring="[para(8126(a,1),14143(a,2,1))].">
      <j1 rule="para" parents="8126 14143"/>
    </justification>
  </clause>

  <clause id="14145">
    <literal><![CDATA[
      K(x,K(y,(z * u) / (R(z,w,v5) * u))) = a(K(x,K(z,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(10754(a,1),14144(a,2,1,2))].">
      <j1 rule="para" parents="10754 14144"/>
    </justification>
  </clause>

  <clause id="14146">
    <literal><![CDATA[
      K(x,K(R(y,z,u) \ y,R(w,y,v5))) = a(K(x,K(y,w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(9922,a,14145,a)].">
      <j1 rule="hyper" parents="9922 14145"/>
    </justification>
  </clause>

  <clause id="14149">
    <literal><![CDATA[
      K(x,K(a(y,z,u),T(w,y * (z * u)))) = a(K(x,K(y,w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10647,a(flip),b,14146,a)].">
      <j1 rule="hyper" parents="64 10647 14146"/>
    </justification>
  </clause>

  <clause id="14151">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ (x * (a(z,u,z) * (y * w))) = L(w,L(y,a(z,u,z),x),x * a(z,u,z))
    ]]></literal>
    <justification jstring="[para(13248(a,1),13273(a,1,2))].">
      <j1 rule="para" parents="13248 13273"/>
    </justification>
  </clause>

  <clause id="14152">
    <literal><![CDATA[
      a(x,K(y \ 1,z) \ ((u \ (u / y)) * w),x) = a(x,T(T(u \ (u / y),z),y \ 1) * w,x)
    ]]></literal>
    <justification jstring="[para(6767(a,1),13760(a,1,2,1))].">
      <j1 rule="para" parents="6767 13760"/>
    </justification>
  </clause>

  <clause id="14154">
    <literal><![CDATA[
      L(x,L(y,a(z,u,z),w),w * a(z,u,z)) = L(x,a(z,u,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,12900,a(flip),b,14151,a),flip(a)].">
      <j1 rule="hyper" parents="64 12900 14151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14155">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w * a(y,z,y))
    ]]></literal>
    <justification jstring="[para(13269(a,1),14154(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13269 14154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14156">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,12983,a(flip),b,14155,a),flip(a)].">
      <j1 rule="hyper" parents="373 12983 14155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14158">
    <literal><![CDATA[
      L(x,L(y,y,y),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11878,a(flip),b,14156,a)].">
      <j1 rule="hyper" parents="64 11878 14156"/>
    </justification>
  </clause>

  <clause id="14159">
    <literal><![CDATA[
      L(x,a(y,z,y) \ u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),14156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14160">
    <literal><![CDATA[
      L(x,L(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(10897(a,1),14156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10897 14156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14161">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(10898(a,1),14156(a,1,2))].">
      <j1 rule="para" parents="10898 14156"/>
    </justification>
  </clause>

  <clause id="14162">
    <literal><![CDATA[
      L(x,K(y * z,y),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(10902(a,1),14156(a,1,2))].">
      <j1 rule="para" parents="10902 14156"/>
    </justification>
  </clause>

  <clause id="14163">
    <literal><![CDATA[
      L(x,K(y,y * z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(10917(a,1),14156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10917 14156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14164">
    <literal><![CDATA[
      L(x,y / L(z,u,z),w) = L(x,y / z,w)
    ]]></literal>
    <justification jstring="[para(11026(a,1),14156(a,1,2))].">
      <j1 rule="para" parents="11026 14156"/>
    </justification>
  </clause>

  <clause id="14165">
    <literal><![CDATA[
      L(x,T(y * z,y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(11058(a,1),14156(a,1,2))].">
      <j1 rule="para" parents="11058 14156"/>
    </justification>
  </clause>

  <clause id="14166">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,w) = L(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(10956(a,1),14156(a,1,2))].">
      <j1 rule="para" parents="10956 14156"/>
    </justification>
  </clause>

  <clause id="14167">
    <literal><![CDATA[
      L(x,R(y,z,y) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(11369(a,1),14156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11369 14156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14168">
    <literal><![CDATA[
      L(L(x,x,x) \ K(y,z),x,y) = (y * L(x,x,x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5768,a(flip),b,14158,a),flip(a)].">
      <j1 rule="hyper" parents="64 5768 14158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14169">
    <literal><![CDATA[
      L(R(x,y,z),L(u,w,u),v5) = R(L(x,u,v5),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29,a,b,14160,a),flip(a)].">
      <j1 rule="hyper" parents="373 29 14160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14171">
    <literal><![CDATA[
      (x * L(y,z,y)) * L(u,y,x) = x * (L(y,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,14160,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 14160 18"/>
    </justification>
  </clause>

  <clause id="14172">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(12494(a,1),14160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12494 14160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14173">
    <literal><![CDATA[
      L(R(x,y,x) \ 1,x,y) = T(x * y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,4750,a(flip),b,14161,a),flip(a)].">
      <j1 rule="hyper" parents="64 4750 14161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14174">
    <literal><![CDATA[
      L(T(R(x,y,x) \ (z \ u),w),x,z) = T((z * R(x,y,x)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,708,a(flip),b,14161,a),flip(a)].">
      <j1 rule="hyper" parents="64 708 14161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14175">
    <literal><![CDATA[
      L(x,T(y,y \ z),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4803(a,1),14161(a,1,2))].">
      <j1 rule="para" parents="4803 14161"/>
    </justification>
  </clause>

  <clause id="14176">
    <literal><![CDATA[
      L(x,L(R(y,z,y),u,w),v5) = L(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(11556(a,1),14161(a,1,2))].">
      <j1 rule="para" parents="11556 14161"/>
    </justification>
  </clause>

  <clause id="14177">
    <literal><![CDATA[
      L(x,K(y \ z,y),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(10881(a,1),14159(a,1,2))].">
      <j1 rule="para" parents="10881 14159"/>
    </justification>
  </clause>

  <clause id="14178">
    <literal><![CDATA[
      L(x,y / (z * a(u,w,u)),v5) = L(x,y / z,v5)
    ]]></literal>
    <justification jstring="[para(13262(a,2),14159(a,1,2))].">
      <j1 rule="para" parents="13262 14159"/>
    </justification>
  </clause>

  <clause id="14179">
    <literal><![CDATA[
      L(x,y / R(z,u,z),w) = L(x,y / z,w)
    ]]></literal>
    <justification jstring="[para(13276(a,1),14159(a,1,2))].">
      <j1 rule="para" parents="13276 14159"/>
    </justification>
  </clause>

  <clause id="14180">
    <literal><![CDATA[
      L(x,K(y * z,(y * z) * (z \ 1)),u) = L(x,K(z * y,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(7520(a,1),14163(a,2,2))].">
      <j1 rule="para" parents="7520 14163"/>
    </justification>
  </clause>

  <clause id="14181">
    <literal><![CDATA[
      L(x,y * z,z) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(11049,a,14165,a),flip(a)].">
      <j1 rule="hyper" parents="11049 14165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14182">
    <literal><![CDATA[
      L(x,(y \ z) * y,u) = L(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),14165(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 14165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14183">
    <literal><![CDATA[
      L(x,T(y * (z / y),y),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),14165(a,2,2))].">
      <j1 rule="para" parents="12 14165"/>
    </justification>
  </clause>

  <clause id="14184">
    <literal><![CDATA[
      L((x * y) \ z,y * x,y) = (y * (x * y)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,14181,a),flip(a)].">
      <j1 rule="hyper" parents="64 102 14181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14185">
    <literal><![CDATA[
      L(x,y * z,z) \ u = L(x,z * y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(62,a,14181,a)].">
      <j1 rule="hyper" parents="62 14181"/>
    </justification>
  </clause>

  <clause id="14186">
    <literal><![CDATA[
      L(x,y,y) * L(z,x * y,y) = y * (((y \ 1) * x) * z)
    ]]></literal>
    <justification jstring="[para(14181(a,2),1820(a,1,2))].">
      <j1 rule="para" parents="14181 1820"/>
    </justification>
  </clause>

  <clause id="14187">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),u) = L(x,T(y * z,y),u)
    ]]></literal>
    <justification jstring="[para(6745(a,2),14172(a,1,2))].">
      <j1 rule="para" parents="6745 14172"/>
    </justification>
  </clause>

  <clause id="14188">
    <literal><![CDATA[
      K(x,L((((y * z) \ y) \ y) \ u,T(y * z,y),z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(14172(a,1),7095(a,1,2))].">
      <j1 rule="para" parents="14172 7095"/>
    </justification>
  </clause>

  <clause id="14189">
    <literal><![CDATA[
      L(x,T(y,z),T((y / z) \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(14175(a,1),5044(a,1))].">
      <j1 rule="para" parents="14175 5044"/>
    </justification>
  </clause>

  <clause id="14190">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,T(T(y,z),z \ y),u)
    ]]></literal>
    <justification jstring="[para(13477(a,1),14175(a,1,2))].">
      <j1 rule="para" parents="13477 14175"/>
    </justification>
  </clause>

  <clause id="14191">
    <literal><![CDATA[
      L(x,K(y,z),z \ y) = x
    ]]></literal>
    <justification jstring="[hyper(4872,a,14177,a),flip(a)].">
      <j1 rule="hyper" parents="4872 14177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14192">
    <literal><![CDATA[
      L(x,K(y,z),y \ z) = x
    ]]></literal>
    <justification jstring="[hyper(11858,a,14191,a)].">
      <j1 rule="hyper" parents="11858 14191"/>
    </justification>
  </clause>

  <clause id="14193">
    <literal><![CDATA[
      ((x \ y) * K(x,y)) \ z = K(x,y) \ ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(710,a,14192,a),flip(a)].">
      <j1 rule="hyper" parents="710 14192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14194">
    <literal><![CDATA[
      L(x,T(y,z \ y),u) = L(x,z * (y / z),u)
    ]]></literal>
    <justification jstring="[para(4507(a,1),14182(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4507 14182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14195">
    <literal><![CDATA[
      L(x,y * (z / T(y,z)),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4658(a,1),14183(a,1,2))].">
      <j1 rule="para" parents="4658 14183"/>
    </justification>
  </clause>

  <clause id="14196">
    <literal><![CDATA[
      L(x,T((y / T(z,y)) * z,y / T(z,y)),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14165,a,b,14195,a)].">
      <j1 rule="hyper" parents="64 14165 14195"/>
    </justification>
  </clause>

  <clause id="14197">
    <literal><![CDATA[
      L(x,(y * z) / y,u) = L(x,y * (z / y),u)
    ]]></literal>
    <justification jstring="[para(692(a,1),14164(a,1,2)),flip(a)].">
      <j1 rule="para" parents="692 14164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14198">
    <literal><![CDATA[
      L(x,(y \ T(z,y \ z)) \ u,w) = L(x,(z / y) \ u,w)
    ]]></literal>
    <justification jstring="[para(4791(a,1),14167(a,1,2,1))].">
      <j1 rule="para" parents="4791 14167"/>
    </justification>
  </clause>

  <clause id="14199">
    <literal><![CDATA[
      L(x,y / T(z,z \ u),w) = L(x,y / T(z,u),w)
    ]]></literal>
    <justification jstring="[para(4803(a,1),14179(a,1,2,2))].">
      <j1 rule="para" parents="4803 14179"/>
    </justification>
  </clause>

  <clause id="14201">
    <literal><![CDATA[
      L(x,R(y,z,y) \ 1,L(R(y,z,y) \ 1,y,z)) = L(x,T(y * z,y) \ z,R(y,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(14173(a,1),2482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14173 2482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14202">
    <literal><![CDATA[
      a(R(x,y,x) \ 1,L(R(x,y,x) \ 1,x,y),z) = a(T(x * y,x) \ y,R(x,y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(14173(a,1),2784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14173 2784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14203">
    <literal><![CDATA[
      L(x,y / T(z * (u / z),z),w) = L(x,y / u,w)
    ]]></literal>
    <justification jstring="[para(11373(a,1),14178(a,1,2,2))].">
      <j1 rule="para" parents="11373 14178"/>
    </justification>
  </clause>

  <clause id="14204">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,14165,a(flip),b,14187,a),flip(a)].">
      <j1 rule="hyper" parents="373 14165 14187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14205">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u \ 1),u * z,(u * z) \ z)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[para(14204(a,1),12135(a,1,2))].">
      <j1 rule="para" parents="14204 12135"/>
    </justification>
  </clause>

  <clause id="14206">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ z = K(x,y) \ ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(7130(a,2),14193(a,1,1))].">
      <j1 rule="para" parents="7130 14193"/>
    </justification>
  </clause>

  <clause id="14207">
    <literal><![CDATA[
      L(x,y / T(z,y),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(301(a,1),14199(a,1,2)),flip(a)].">
      <j1 rule="para" parents="301 14199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14208">
    <literal><![CDATA[
      L(x,(y * (z / y)) \ y,u) = L(x,y / z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14207,a(flip),b,14203,a)].">
      <j1 rule="hyper" parents="64 14207 14203"/>
    </justification>
  </clause>

  <clause id="14209">
    <literal><![CDATA[
      L(x,y / (z * y),u) = L(x,(y * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),14208(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 14208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14210">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * ((x \ y) \ z) = u
    ]]></literal>
    <justification jstring="[para(14206(a,2),6198(a,1))].">
      <j1 rule="para" parents="14206 6198"/>
    </justification>
  </clause>

  <clause id="14211">
    <literal><![CDATA[
      (x * L(y,z,y)) * u != x * (L(y,z,y) * w)
    ]]></literal>
    <literal><![CDATA[
      L(w,y,x) = u
    ]]></literal>
    <justification jstring="[para(14171(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="14171 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14212">
    <literal><![CDATA[
      L(x,(x \ y) * x,(x \ y) * x) * L(z,(y / (y / x)) * y,(x \ y) * x) = ((x \ y) * x) * (((((x \ y) * x) \ 1) * x) * z)
    ]]></literal>
    <justification jstring="[para(4804(a,2),14186(a,1,2,2))].">
      <j1 rule="para" parents="4804 14186"/>
    </justification>
  </clause>

  <clause id="14213">
    <literal><![CDATA[
      L(x,T(T(y,z),y / T(z,y)),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(4627(a,1),14196(a,1,2,1))].">
      <j1 rule="para" parents="4627 14196"/>
    </justification>
  </clause>

  <clause id="14214">
    <literal><![CDATA[
      L(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,u),x) = z
    ]]></literal>
    <justification jstring="[para(14213(a,1),13165(a,1))].">
      <j1 rule="para" parents="14213 13165"/>
    </justification>
  </clause>

  <clause id="14215">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(13310(a,1),14213(a,1,2))].">
      <j1 rule="para" parents="13310 14213"/>
    </justification>
  </clause>

  <clause id="14216">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,w),x) = u
    ]]></literal>
    <justification jstring="[para(11388(a,2),14214(a,1))].">
      <j1 rule="para" parents="11388 14214"/>
    </justification>
  </clause>

  <clause id="14217">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14190,a,b,14215,a)].">
      <j1 rule="hyper" parents="64 14190 14215"/>
    </justification>
  </clause>

  <clause id="14218">
    <literal><![CDATA[
      L(x,T(y,z),z \ 1) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(11049,a,14217,a)].">
      <j1 rule="hyper" parents="11049 14217"/>
    </justification>
  </clause>

  <clause id="14220">
    <literal><![CDATA[
      L(x,T(y,z),(z \ y) \ 1) = L(x,y,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,14215,a(flip),b,14218,a),flip(a)].">
      <j1 rule="hyper" parents="64 14215 14218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14221">
    <literal><![CDATA[
      L(x,y * (z / y),(y \ z) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,14194,a(flip),b,14218,a)].">
      <j1 rule="hyper" parents="64 14194 14218"/>
    </justification>
  </clause>

  <clause id="14222">
    <literal><![CDATA[
      L(x,(x / y) \ z,u) = L(x,(y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12185,a(flip),b,14198,a),flip(a)].">
      <j1 rule="hyper" parents="64 12185 14198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14223">
    <literal><![CDATA[
      K(x,y) * ((y \ x) \ (K(y,x) * z)) = (((y \ x) * y) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(14210,a,13088,a)].">
      <j1 rule="hyper" parents="14210 13088"/>
    </justification>
  </clause>

  <clause id="14224">
    <literal><![CDATA[
      (((x \ y) * x) / x) \ z = K(y,x) * ((T(x,y) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(13057(a,1),14223(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13057 14223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14225">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) \ x) \ z) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[para(11(a,1),14224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 14224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14227">
    <literal><![CDATA[
      L(x,K(y * z,R(y,z,z \ 1)),u) = L(x,K(z * y,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(297(a,1),14180(a,1,2,2))].">
      <j1 rule="para" parents="297 14180"/>
    </justification>
  </clause>

  <clause id="14228">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(z * y,z),u)
    ]]></literal>
    <justification jstring="[para(9719(a,1),14227(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9719 14227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14229">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,14162,a(flip),b,14228,a),flip(a)].">
      <j1 rule="hyper" parents="373 14162 14228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14231">
    <literal><![CDATA[
      L(x,R(y,z,y) \ 1,L(R(y,z,y) \ 1,y,z)) = L(x,T(y * z,y) \ z,R(y,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,1631,a(flip),b,14201,a),flip(a)].">
      <j1 rule="hyper" parents="373 1631 14201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14232">
    <literal><![CDATA[
      L(x,R(y,z,y) \ 1,L(R(y,z,y) \ 1,y,z)) = L(x,T(y * z,y) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,12979,a(flip),b,14231,a),flip(a)].">
      <j1 rule="hyper" parents="373 12979 14231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14234">
    <literal><![CDATA[
      a(R(x,y,x) \ 1,L(R(x,y,x) \ 1,x,y),z) = a(T(x * y,x) \ y,R(x,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,11980,a(flip),b,14202,a),flip(a)].">
      <j1 rule="hyper" parents="373 11980 14202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14235">
    <literal><![CDATA[
      a(R(x,y,x) \ 1,L(R(x,y,x) \ 1,x,y),z) = a(T(x * y,x) \ y,x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,13829,a(flip),b,14234,a),flip(a)].">
      <j1 rule="hyper" parents="373 13829 14234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14237">
    <literal><![CDATA[
      K(x,L((((y * z) \ y) \ y) \ u,z * y,z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(14165(a,1),14188(a,1,2))].">
      <j1 rule="para" parents="14165 14188"/>
    </justification>
  </clause>

  <clause id="14238">
    <literal><![CDATA[
      a(x,((y * z) * u) \ (y * (z * (u * K(w,w \ 1)))),x) = a(x,K(w,w \ 1) / a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(11289,a,13569,a)].">
      <j1 rule="hyper" parents="11289 13569"/>
    </justification>
  </clause>

  <clause id="14239">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ (z * (u * (y * K(w,w \ 1))))),x) = a(x,K(w,w \ 1) / a(z,u,y),x)
    ]]></literal>
    <justification jstring="[hyper(13732,a,14238,a)].">
      <j1 rule="hyper" parents="13732 14238"/>
    </justification>
  </clause>

  <clause id="14240">
    <literal><![CDATA[
      a(x,y \ L(y * K(z,z \ 1),u,w),x) = a(x,K(z,z \ 1) / a(w,u,y),x)
    ]]></literal>
    <justification jstring="[para(18(a,2),14239(a,1,2,2))].">
      <j1 rule="para" parents="18 14239"/>
    </justification>
  </clause>

  <clause id="14241">
    <literal><![CDATA[
      a(x,(y \ L(y,z,u)) * K(w,w \ 1),x) = a(x,K(w,w \ 1) / a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(5315(a,1),14240(a,1,2))].">
      <j1 rule="para" parents="5315 14240"/>
    </justification>
  </clause>

  <clause id="14242">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) = a(x,K(w,w \ 1) / a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5356,a(flip),b,14241,a)].">
      <j1 rule="hyper" parents="64 5356 14241"/>
    </justification>
  </clause>

  <clause id="14243">
    <literal><![CDATA[
      a(x,a(y,z,u) \ K(w,w \ 1),x) = a(x,u \ L(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13169,a(flip),b,14242,a)].">
      <j1 rule="hyper" parents="373 13169 14242"/>
    </justification>
  </clause>

  <clause id="14245">
    <literal><![CDATA[
      a(x,a(y,z,u) \ 1,x) = a(x,u \ L(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(381(a,1),14243(a,1,2,2))].">
      <j1 rule="para" parents="381 14243"/>
    </justification>
  </clause>

  <clause id="14246">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) * a(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = R(T(u,u * (a(x,y,z) \ 1)),(a(x,y,z) \ 1) * u,a(u,a(x,y,z) \ 1,u))
    ]]></literal>
    <justification jstring="[para(14245(a,1),11525(a,1,1,2))].">
      <j1 rule="para" parents="14245 11525"/>
    </justification>
  </clause>

  <clause id="14247">
    <literal><![CDATA[
      L(K(x,y / ((x \ z) * u)),w,v5) \ L(K(x,x \ (y / ((x \ z) * u))),w,v5) = a(x,x \ (y / ((z / x) * u)),x)
    ]]></literal>
    <justification jstring="[para(12201(a,1),13638(a,1,2,1))].">
      <j1 rule="para" parents="12201 13638"/>
    </justification>
  </clause>

  <clause id="14248">
    <literal><![CDATA[
      L(x,y,L((z / (u * (w \ 1))) * (w \ (a(v5,v6,v5) / w)),v7,v8)) = L(x,y,L(z / (w * T(u,w \ 1)),v7,v8))
    ]]></literal>
    <justification jstring="[para(13227(a,1),13643(a,1,3,1,2))].">
      <j1 rule="para" parents="13227 13643"/>
    </justification>
  </clause>

  <clause id="14249">
    <literal><![CDATA[
      a(L((x / (y * (z \ 1))) * (z \ (a(u,w,u) / z)),v5,v6),v7,v8) = a(L(x / (z * T(y,z \ 1)),v5,v6),v7,v8)
    ]]></literal>
    <justification jstring="[para(13227(a,1),13644(a,1,1,1,2))].">
      <j1 rule="para" parents="13227 13644"/>
    </justification>
  </clause>

  <clause id="14250">
    <literal><![CDATA[
      a(x,x \ (y / ((z / x) * u)),x) = a(x,x \ (y / ((x \ z) * u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13632,a(flip),b,14247,a),flip(a)].">
      <j1 rule="hyper" parents="64 13632 14247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14251">
    <literal><![CDATA[
      R(R(x,y,a(z,u,z) \ 1),y * (a(z,u,z) \ 1),w) = ((x * y) * (a(z,u,z) \ w)) / ((y / a(z,u,z)) * w)
    ]]></literal>
    <justification jstring="[para(11348(a,1),13287(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11348 13287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14252">
    <literal><![CDATA[
      R(R(x,y,a(z,u,z) \ 1),y * (a(z,u,z) \ 1),w) = ((x * y) * (a(z,u,z) \ w)) / (y * (a(z,u,z) \ w))
    ]]></literal>
    <justification jstring="[para(13272(a,1),14251(a,2,2))].">
      <j1 rule="para" parents="13272 14251"/>
    </justification>
  </clause>

  <clause id="14253">
    <literal><![CDATA[
      R(R(x,y,a(z,u,z) \ 1),y * (a(z,u,z) \ 1),w) = R(x,y,a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,20,a,b,14252,a),flip(a)].">
      <j1 rule="hyper" parents="373 20 14252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14254">
    <literal><![CDATA[
      R(x,y * (a(z,u,z) \ 1),w) = R(x,y,a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(13897(a,1),14253(a,1,1))].">
      <j1 rule="para" parents="13897 14253"/>
    </justification>
  </clause>

  <clause id="14255">
    <literal><![CDATA[
      R(x,y / a(z,u,z),w) = R(x,y,a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(11348(a,1),14254(a,1,2))].">
      <j1 rule="para" parents="11348 14254"/>
    </justification>
  </clause>

  <clause id="14256">
    <literal><![CDATA[
      R(x,y * a(z,u,z),a(z,u,z) \ w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[para(11(a,1),14255(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 14255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14257">
    <literal><![CDATA[
      R(x,y * a(z,u,z),w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13900,a(flip),b,14256,a)].">
      <j1 rule="hyper" parents="64 13900 14256"/>
    </justification>
  </clause>

  <clause id="14259">
    <literal><![CDATA[
      R(x,R(y,z,y),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(10889(a,1),14257(a,1,2))].">
      <j1 rule="para" parents="10889 14257"/>
    </justification>
  </clause>

  <clause id="14260">
    <literal><![CDATA[
      R(x,y * L(z,u,z),w) = R(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(10948(a,1),14257(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10948 14257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14261">
    <literal><![CDATA[
      R(x,a(y,z,y) \ u,w) = R(x,u,w)
    ]]></literal>
    <justification jstring="[para(11016(a,1),14257(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11016 14257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14262">
    <literal><![CDATA[
      (1 * x) / (x * R(y,y,y)) = R(y \ K(y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10445,a(flip),b,14259,a)].">
      <j1 rule="hyper" parents="64 10445 14259"/>
    </justification>
  </clause>

  <clause id="14263">
    <literal><![CDATA[
      R(x,((y \ 1) * y) \ z,u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(2095(a,1),14261(a,1,2,1))].">
      <j1 rule="para" parents="2095 14261"/>
    </justification>
  </clause>

  <clause id="14264">
    <literal><![CDATA[
      R(x,((y \ 1) * y) \ (((z \ 1) \ 1) \ u),w) = R(x,z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,3030,a(flip),b,14263,a),flip(a)].">
      <j1 rule="hyper" parents="373 3030 14263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14266">
    <literal><![CDATA[
      R(x \ K(x,y),x,y) = T(y / (y * x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3827,a(flip),b,14262,a),flip(a)].">
      <j1 rule="hyper" parents="64 3827 14262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14267">
    <literal><![CDATA[
      R((x * x) \ (y \ K(y,z)),y,z) = (x * x) \ T(z / (z * y),y)
    ]]></literal>
    <justification jstring="[para(14266(a,1),2051(a,2,2))].">
      <j1 rule="para" parents="14266 2051"/>
    </justification>
  </clause>

  <clause id="14268">
    <literal><![CDATA[
      L(T(x / (x * y),y),y,y) = (1 * x) / (x * y)
    ]]></literal>
    <justification jstring="[para(14266(a,1),10309(a,1,1))].">
      <j1 rule="para" parents="14266 10309"/>
    </justification>
  </clause>

  <clause id="14269">
    <literal><![CDATA[
      L(T(x / (x * y),y),y,y) = x / (x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,172,a(flip),b,14268,a),flip(a)].">
      <j1 rule="hyper" parents="373 172 14268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14270">
    <literal><![CDATA[
      (x \ 1) * T(y / (y * x),x) = x \ (y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(139,a,14269,a(flip),b,1139,a),flip(a)].">
      <j1 rule="hyper" parents="139 14269 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14271">
    <literal><![CDATA[
      (x * (x * T(y / (y * x),x))) \ z = (y / (y * x)) \ ((x * x) \ z)
    ]]></literal>
    <justification jstring="[para(14269(a,1),881(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14269 881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14272">
    <literal><![CDATA[
      (x \ 1) * (x \ (y / (y * x))) = (x \ (y / (y * x))) / x
    ]]></literal>
    <justification jstring="[para(14270(a,1),1685(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14270 1685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14273">
    <literal><![CDATA[
      R(x,((y \ 1) \ ((z \ 1) * z)) \ u,w) = R(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(5299(a,1),14264(a,1,2))].">
      <j1 rule="para" parents="5299 14264"/>
    </justification>
  </clause>

  <clause id="14274">
    <literal><![CDATA[
      R(x,(y / ((z \ 1) \ 1)) \ u,w) = R(x,(y / z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,12475,a(flip),b,14273,a)].">
      <j1 rule="hyper" parents="64 12475 14273"/>
    </justification>
  </clause>

  <clause id="14276">
    <literal><![CDATA[
      a(((x * y) \ x) \ 1,z,((x * y) \ x) \ 1) * K(T(z,y),1 / ((x * y) \ x)) = K(z * (1 / ((x * y) \ x)),1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(11312(a,1),13173(a,1,1))].">
      <j1 rule="para" parents="11312 13173"/>
    </justification>
  </clause>

  <clause id="14278">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = (a(y,w,y) \ v5) * L((a(y,w,y) \ v5) \ ((x \ L(y,w,y)) * v5),z,u)
    ]]></literal>
    <justification jstring="[para(13275(a,1),13519(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13275 13519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14279">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = (a(y,w,y) \ v5) * L((v5 \ ((x \ L(y,w,y)) * v5)) * a(y,w,y),z,u)
    ]]></literal>
    <justification jstring="[para(13243(a,1),14278(a,2,2,1))].">
      <j1 rule="para" parents="13243 14278"/>
    </justification>
  </clause>

  <clause id="14281">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = (a(y,w,y) \ v5) * L(T((x \ L(y,w,y)) * a(y,w,y),v5),z,u)
    ]]></literal>
    <justification jstring="[para(13247(a,1),14279(a,2,2,1))].">
      <j1 rule="para" parents="13247 14279"/>
    </justification>
  </clause>

  <clause id="14282">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = (a(y,w,y) \ v5) * L(T(x \ y,v5),z,u)
    ]]></literal>
    <justification jstring="[para(13225(a,1),14281(a,2,2,1,1))].">
      <j1 rule="para" parents="13225 14281"/>
    </justification>
  </clause>

  <clause id="14283">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = v5 * (a(y,w,y) \ L(T(x \ y,v5),z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13253,a(flip),b,14282,a),flip(a)].">
      <j1 rule="hyper" parents="373 13253 14282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14285">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = v5 * L(a(y,w,y) \ T(x \ y,v5),z,u)
    ]]></literal>
    <justification jstring="[para(13627(a,2),14283(a,2,2))].">
      <j1 rule="para" parents="13627 14283"/>
    </justification>
  </clause>

  <clause id="14286">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = v5 * L(T(a(y,w,y) \ (x \ y),v5),z,u)
    ]]></literal>
    <justification jstring="[para(13514(a,2),14285(a,2,2,1))].">
      <j1 rule="para" parents="13514 14285"/>
    </justification>
  </clause>

  <clause id="14287">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = v5 * L(T(x \ L(y,w,y),v5),z,u)
    ]]></literal>
    <justification jstring="[para(13233(a,1),14286(a,2,2,1,1))].">
      <j1 rule="para" parents="13233 14286"/>
    </justification>
  </clause>

  <clause id="14288">
    <literal><![CDATA[
      L(x \ y,z,u) * ((x \ y) \ ((x \ L(y,w,y)) * v5)) = L(x \ L(y,w,y),z,u) * v5
    ]]></literal>
    <justification jstring="[hyper(373,a,266,a(flip),b,14287,a),flip(a)].">
      <j1 rule="hyper" parents="373 266 14287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14289">
    <literal><![CDATA[
      L(x \ y,z,u) * (a(y,w,y) \ v5) = L(x \ L(y,w,y),z,u) * v5
    ]]></literal>
    <justification jstring="[para(13275(a,1),14288(a,1,2))].">
      <j1 rule="para" parents="13275 14288"/>
    </justification>
  </clause>

  <clause id="14291">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) * a(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = R(T(u,a(x,y,z) \ u),(a(x,y,z) \ 1) * u,a(u,a(x,y,z) \ 1,u))
    ]]></literal>
    <justification jstring="[para(2781(a,1),14246(a,2,1))].">
      <j1 rule="para" parents="2781 14246"/>
    </justification>
  </clause>

  <clause id="14292">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) * a(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = T(u,a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,13206,a(flip),b,14291,a),flip(a)].">
      <j1 rule="hyper" parents="373 13206 14291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14294">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * R(u,z \ L(z,y,x),u)) \ ((u * (a(x,y,z) \ 1)) * u) = T(u,a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(11346(a,1),14292(a,1,1))].">
      <j1 rule="para" parents="11346 14292"/>
    </justification>
  </clause>

  <clause id="14295">
    <literal><![CDATA[
      L(T(x,a(y,z,u) \ 1),u \ L(u,z,y),x) = T(x,a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(11951,a,14294,a)].">
      <j1 rule="hyper" parents="11951 14294"/>
    </justification>
  </clause>

  <clause id="14296">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,13894,a(flip),b,14295,a),flip(a)].">
      <j1 rule="hyper" parents="64 13894 14295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14297">
    <literal><![CDATA[
      T(K(x,y \ ((z * u) * (u \ 1))),((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[para(6642(a,1),8381(a,1,1))].">
      <j1 rule="para" parents="6642 8381"/>
    </justification>
  </clause>

  <clause id="14298">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[para(297(a,1),14297(a,1,1,2,2))].">
      <j1 rule="para" parents="297 14297"/>
    </justification>
  </clause>

  <clause id="14299">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = K(1 / y,y) \ ((1 / L(y,z,u)) * ((x * (1 / (1 / L(y,z,u)))) / x))
    ]]></literal>
    <justification jstring="[para(5088(a,1),9942(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5088 9942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14300">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = K(1 / y,y) \ ((1 / L(y,z,u)) * (1 / (1 / ((x * L(y,z,u)) / x))))
    ]]></literal>
    <justification jstring="[para(3701(a,1),14299(a,2,2,2))].">
      <j1 rule="para" parents="3701 14299"/>
    </justification>
  </clause>

  <clause id="14302">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = K(1 / y,y) \ ((T(L(y,z,u),x) \ 1) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12705(a,1),14300(a,2,2))].">
      <j1 rule="para" parents="12705 14300"/>
    </justification>
  </clause>

  <clause id="14303">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = K(y,1 / y) * ((T(L(y,z,u),x) \ 1) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,6156,a(flip),b,14302,a),flip(a)].">
      <j1 rule="hyper" parents="373 6156 14302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14304">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ R(1 / L(y,z,u),L(y,z,u),K(1 / y,y)))) = (T(L(y,z,u),x) \ 1) * L((y \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,7056,a(flip),b,14303,a),flip(a)].">
      <j1 rule="hyper" parents="373 7056 14303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14305">
    <literal><![CDATA[
      K(x,1 / (K(1 / y,y) \ (1 / L(y,z,u)))) = (T(L(y,z,u),x) \ 1) * L((y \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(5088(a,1),14304(a,1,2,2,2))].">
      <j1 rule="para" parents="5088 14304"/>
    </justification>
  </clause>

  <clause id="14307">
    <literal><![CDATA[
      K(x,1 / (K(y,1 / y) * (1 / L(y,z,u)))) = (T(L(y,z,u),x) \ 1) * L((y \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(6156(a,1),14305(a,1,2,2))].">
      <j1 rule="para" parents="6156 14305"/>
    </justification>
  </clause>

  <clause id="14308">
    <literal><![CDATA[
      (T(L(x,y,z),u) \ 1) * L((x \ 1) \ 1,y,z) = K(u,1 / (1 / (1 / (1 / L(x,y,z)))))
    ]]></literal>
    <justification jstring="[para(10558(a,1),14307(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10558 14307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14309">
    <literal><![CDATA[
      (T(L(x,y,z),u) \ 1) * L((x \ 1) \ 1,y,z) = K(u,T(L(x,y,z),1))
    ]]></literal>
    <justification jstring="[hyper(373,a,10319,a(flip),b,14308,a),flip(a)].">
      <j1 rule="hyper" parents="373 10319 14308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14310">
    <literal><![CDATA[
      (T(L(x,y,z),u) \ 1) * L((x \ 1) \ 1,y,z) = K(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(372(a,1),14309(a,2,2))].">
      <j1 rule="para" parents="372 14309"/>
    </justification>
  </clause>

  <clause id="14311">
    <literal><![CDATA[
      (x \ 1) * (K(x \ 1,K(y,T(z,L(x,u,w) * (1 / x)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(5627(a,1),9963(a,1,2,1,2,2,2))].">
      <j1 rule="para" parents="5627 9963"/>
    </justification>
  </clause>

  <clause id="14312">
    <literal><![CDATA[
      (x \ 1) * (K(x \ 1,K(y,T(z,x \ L(x,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(5122(a,1),14311(a,1,2,1,2,2))].">
      <j1 rule="para" parents="5122 14311"/>
    </justification>
  </clause>

  <clause id="14313">
    <literal><![CDATA[
      (x \ 1) * (K(y,K(x \ 1,T(z,x \ L(x,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(8108(a,1),14312(a,1,2,1))].">
      <j1 rule="para" parents="8108 14312"/>
    </justification>
  </clause>

  <clause id="14314">
    <literal><![CDATA[
      (x \ 1) * (K(y,K(x \ 1,T(z,L(x,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(9784(a,1),14313(a,1,2,1,2))].">
      <j1 rule="para" parents="9784 14313"/>
    </justification>
  </clause>

  <clause id="14315">
    <literal><![CDATA[
      (x \ 1) * (K(y,K(x \ 1,z)) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(8040(a,1),14314(a,1,2,1,2))].">
      <j1 rule="para" parents="8040 14314"/>
    </justification>
  </clause>

  <clause id="14317">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(9015(a,1),14315(a,1,2,1))].">
      <j1 rule="para" parents="9015 14315"/>
    </justification>
  </clause>

  <clause id="14318">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(K(y,T(z,L(x,u,w) * (1 / x))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(5627(a,1),14317(a,1,2,2,1,2,1,2,2))].">
      <j1 rule="para" parents="5627 14317"/>
    </justification>
  </clause>

  <clause id="14319">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(K(y,T(z,x \ L(x,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(5122(a,1),14318(a,1,2,2,1,2,1,2))].">
      <j1 rule="para" parents="5122 14318"/>
    </justification>
  </clause>

  <clause id="14320">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(y,K(T(z,x \ L(x,u,w)),x \ 1)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(8092(a,1),14319(a,1,2,2,1,2))].">
      <j1 rule="para" parents="8092 14319"/>
    </justification>
  </clause>

  <clause id="14321">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(y,K(T(z,L(x,u,w)),x \ 1)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(9968(a,1),14320(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="9968 14320"/>
    </justification>
  </clause>

  <clause id="14322">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(y,K(z,x \ 1)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(8057(a,1),14321(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="8057 14321"/>
    </justification>
  </clause>

  <clause id="14324">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(x,K(y,z)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(9011(a,1),14322(a,1,2,2,1,2))].">
      <j1 rule="para" parents="9011 14322"/>
    </justification>
  </clause>

  <clause id="14325">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L(T(T(x,K(y,z)),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(5730(a,2),14324(a,1,2,2,1))].">
      <j1 rule="para" parents="5730 14324"/>
    </justification>
  </clause>

  <clause id="14326">
    <literal><![CDATA[
      (x \ 1) * T(K(x,K(y,z)) * L(T(x,K(y,z)),u,w),x \ 1) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(7677(a,2),14325(a,1,2))].">
      <j1 rule="para" parents="7677 14325"/>
    </justification>
  </clause>

  <clause id="14327">
    <literal><![CDATA[
      K(x,K(y,z)) * (L(T(x,K(y,z)),u,w) * (x \ 1)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7336,a(flip),b,14326,a)].">
      <j1 rule="hyper" parents="64 7336 14326"/>
    </justification>
  </clause>

  <clause id="14328">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w)) = K(x,K(u,w)) * (x \ L(T(x,K(u,w)),y,z))
    ]]></literal>
    <justification jstring="[para(2464(a,1),14327(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2464 14327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14329">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w)) = T(x,K(u,w)) \ L(T(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,8147,a(flip),b,14328,a),flip(a)].">
      <j1 rule="hyper" parents="373 8147 14328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14330">
    <literal><![CDATA[
      T(x,K(y,z)) \ L(T(x,K(y,z)),u,w) = T(x \ L(x,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(1804(a,1),14329(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1804 14329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14331">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w * x)) = T(x \ L(x,y,z),K(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,12644,a,b,14330,a)].">
      <j1 rule="hyper" parents="64 12644 14330"/>
    </justification>
  </clause>

  <clause id="14332">
    <literal><![CDATA[
      T(x \ L(x,y,z),K(u,w * x)) = T(x \ L(x,y,z),K(u,w))
    ]]></literal>
    <justification jstring="[para(1804(a,1),14331(a,1,1))].">
      <j1 rule="para" parents="1804 14331"/>
    </justification>
  </clause>

  <clause id="14333">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T(x \ L(x,y,z),K(u,w)) = K(x \ L(x,y,z),K(w * x,u))
    ]]></literal>
    <justification jstring="[para(14332(a,1),8152(a,1,2))].">
      <j1 rule="para" parents="14332 8152"/>
    </justification>
  </clause>

  <clause id="14334">
    <literal><![CDATA[
      K(x \ L(x,y,z),K(u * x,w)) = K(x \ L(x,y,z),K(u,w))
    ]]></literal>
    <justification jstring="[hyper(8441,a,14333,a),flip(a)].">
      <j1 rule="hyper" parents="8441 14333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14335">
    <literal><![CDATA[
      K(x \ L(x,y,z),K(u * x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,K(w,x \ L(x,y,z))) = v5
    ]]></literal>
    <justification jstring="[para(14334(a,2),8439(a,1))].">
      <j1 rule="para" parents="14334 8439"/>
    </justification>
  </clause>

  <clause id="14336">
    <literal><![CDATA[
      K(x,K(y * z,y \ L(y,u,w))) = K(z,K(x,y \ L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(14335,a,12632,a),flip(a)].">
      <j1 rule="hyper" parents="14335 12632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14337">
    <literal><![CDATA[
      K(x,K(y * z,y \ L(y,u,w))) = K(x,K(z,y \ L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,8108,a,b,14336,a),flip(a)].">
      <j1 rule="hyper" parents="373 8108 14336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14338">
    <literal><![CDATA[
      K(x,K(y * z,z \ L(z,u,w))) = K(x,K(y,z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(12633,a,14337,a)].">
      <j1 rule="hyper" parents="12633 14337"/>
    </justification>
  </clause>

  <clause id="14339">
    <literal><![CDATA[
      K(x,K(y * (z * u),a(y,z,u) * (y * (z * u)))) = K(x,K(y * z,u \ L(u,z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12634,a,b,14338,a)].">
      <j1 rule="hyper" parents="64 12634 14338"/>
    </justification>
  </clause>

  <clause id="14340">
    <literal><![CDATA[
      K(x,K(y * (z * u),a(y,z,u) * (y * (z * u)))) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(13892,a,14339,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13892 14339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14341">
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(8972,a,14340,a)].">
      <j1 rule="hyper" parents="8972 14340"/>
    </justification>
  </clause>

  <clause id="14342">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = w
    ]]></literal>
    <justification jstring="[para(14340(a,1),8972(a,1))].">
      <j1 rule="para" parents="14340 8972"/>
    </justification>
  </clause>

  <clause id="14343">
    <literal><![CDATA[
      K(x,K(a(y,z,u),(y * z) * u)) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,8971,a,b,14341,a)].">
      <j1 rule="hyper" parents="64 8971 14341"/>
    </justification>
  </clause>

  <clause id="14344">
    <literal><![CDATA[
      K(a(x,y,z),T((((x * y) * z) \ 1) * ((u \ ((x * y) * z)) * u),x * (y * z))) = K(u,K(x * y,a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12772,a,b,14343,a)].">
      <j1 rule="hyper" parents="64 12772 14343"/>
    </justification>
  </clause>

  <clause id="14345">
    <literal><![CDATA[
      K(x,K(a(y,z,u),T((y * z) * u,y * (z * u)))) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(10390,a,14344,a)].">
      <j1 rule="hyper" parents="10390 14344"/>
    </justification>
  </clause>

  <clause id="14346">
    <literal><![CDATA[
      a(K(x,K(y,(y * z) * u)),z,u) = K(x,K(y * z,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14149,a(flip),b,14345,a)].">
      <j1 rule="hyper" parents="64 14149 14345"/>
    </justification>
  </clause>

  <clause id="14347">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = a(K(y,K(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(9792(a,1),14346(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9792 14346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14348">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,12600,a(flip),b,14347,a),flip(a)].">
      <j1 rule="hyper" parents="373 12600 14347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14349">
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = 1
    ]]></literal>
    <justification jstring="[hyper(14342,a,14348,a)].">
      <j1 rule="hyper" parents="14342 14348"/>
    </justification>
  </clause>

  <clause id="14352">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u)) * 1
    ]]></literal>
    <justification jstring="[para(14349(a,1),9541(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14349 9541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14353">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a(flip),b,14352,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 14352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14354">
    <literal><![CDATA[
      R(K(x,y \ R(y,z,u)),R(y,z,u),z * u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(141,a,14352,a(flip),b,9831,a),flip(a)].">
      <j1 rule="hyper" parents="141 14352 9831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14356">
    <literal><![CDATA[
      R(a(K(x,y),z * y,u),R(y,z,u),z * u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(13954(a,2),14354(a,1,1))].">
      <j1 rule="para" parents="13954 14354"/>
    </justification>
  </clause>

  <clause id="14357">
    <literal><![CDATA[
      a(K(x,R(y,R(y,z,u),z * u)),z * y,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14107,a,b,14356,a)].">
      <j1 rule="hyper" parents="64 14107 14356"/>
    </justification>
  </clause>

  <clause id="14358">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14109,a(flip),b,14357,a)].">
      <j1 rule="hyper" parents="64 14109 14357"/>
    </justification>
  </clause>

  <clause id="14360">
    <literal><![CDATA[
      a(K(x,y),z,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14072,a(flip),b,14358,a)].">
      <j1 rule="hyper" parents="64 14072 14358"/>
    </justification>
  </clause>

  <clause id="14361">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13954,a(flip),b,14358,a)].">
      <j1 rule="hyper" parents="64 13954 14358"/>
    </justification>
  </clause>

  <clause id="14362">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13958,a,b,14360,a),flip(a)].">
      <j1 rule="hyper" parents="373 13958 14360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14363">
    <literal><![CDATA[
      a(K(x,y),z,z) = 1
    ]]></literal>
    <justification jstring="[hyper(13966,a,14360,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13966 14360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14364">
    <literal><![CDATA[
      (K(x,y) * z) * z = K(x,y) * (z * z)
    ]]></literal>
    <justification jstring="[hyper(1432,a,14363,a)].">
      <j1 rule="hyper" parents="1432 14363"/>
    </justification>
  </clause>

  <clause id="14365">
    <literal><![CDATA[
      L(x,x,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,14363,a)].">
      <j1 rule="hyper" parents="53 14363"/>
    </justification>
  </clause>

  <clause id="14366">
    <literal><![CDATA[
      K(x,y) * (1 / z) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(225,a,14365,a(flip),b,11792,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 14365 11792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14367">
    <literal><![CDATA[
      a(K(x * y,z),x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,10494,a(flip),b,14362,a),flip(a)].">
      <j1 rule="hyper" parents="373 10494 14362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14368">
    <literal><![CDATA[
      (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) = a(K(z,w),u,v5)
    ]]></literal>
    <justification jstring="[para(14362(a,1),12696(a,1,1,2))].">
      <j1 rule="para" parents="14362 12696"/>
    </justification>
  </clause>

  <clause id="14369">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14362(a,2),13969(a,1))].">
      <j1 rule="para" parents="14362 13969"/>
    </justification>
  </clause>

  <clause id="14370">
    <literal><![CDATA[
      a(K(x,y * z),y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,13127,a(flip),b,14367,a)].">
      <j1 rule="hyper" parents="64 13127 14367"/>
    </justification>
  </clause>

  <clause id="14372">
    <literal><![CDATA[
      L(x,y,K(z,y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,14370,a)].">
      <j1 rule="hyper" parents="53 14370"/>
    </justification>
  </clause>

  <clause id="14376">
    <literal><![CDATA[
      L(x \ y,x,K(z,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),14372(a,1,3,2))].">
      <j1 rule="para" parents="10 14372"/>
    </justification>
  </clause>

  <clause id="14377">
    <literal><![CDATA[
      L(x,y / x,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(12(a,1),14372(a,1,3,2))].">
      <j1 rule="para" parents="12 14372"/>
    </justification>
  </clause>

  <clause id="14378">
    <literal><![CDATA[
      L(x,(y \ z) / x,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(13062,a,14377,a)].">
      <j1 rule="hyper" parents="13062 14377"/>
    </justification>
  </clause>

  <clause id="14379">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,10259,a(flip),b,14377,a)].">
      <j1 rule="hyper" parents="64 10259 14377"/>
    </justification>
  </clause>

  <clause id="14380">
    <literal><![CDATA[
      L(x,x \ T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(7919(a,1),14379(a,1,3))].">
      <j1 rule="para" parents="7919 14379"/>
    </justification>
  </clause>

  <clause id="14381">
    <literal><![CDATA[
      L(x \ (y \ z),x,K(y,z)) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(13062,a,14376,a)].">
      <j1 rule="hyper" parents="13062 14376"/>
    </justification>
  </clause>

  <clause id="14382">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,14376,a(flip),b,4005,a(flip))].">
      <j1 rule="hyper" parents="145 14376 4005"/>
    </justification>
  </clause>

  <clause id="14383">
    <literal><![CDATA[
      K(x,y) * (K(y,x) / z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(6187,a,14366,a)].">
      <j1 rule="hyper" parents="6187 14366"/>
    </justification>
  </clause>

  <clause id="14384">
    <literal><![CDATA[
      K(x,y) / (z \ 1) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(740,a,14366,a),flip(a)].">
      <j1 rule="hyper" parents="740 14366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14386">
    <literal><![CDATA[
      x * (K(y,z) * (1 / u)) = x * (K(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(145,a,14366,a,b,9,a)].">
      <j1 rule="hyper" parents="145 14366 9"/>
    </justification>
  </clause>

  <clause id="14388">
    <literal><![CDATA[
      a(x,x,x) \ (1 / y) = K(x,x * x) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,6185,a(flip),b,14366,a)].">
      <j1 rule="hyper" parents="64 6185 14366"/>
    </justification>
  </clause>

  <clause id="14389">
    <literal><![CDATA[
      (x * y) * (K(y,x) / z) = (y * x) * (1 / z)
    ]]></literal>
    <justification jstring="[hyper(145,a,14366,a(flip),b,10824,a)].">
      <j1 rule="hyper" parents="145 14366 10824"/>
    </justification>
  </clause>

  <clause id="14390">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) / z) = (y / x) * (1 / z)
    ]]></literal>
    <justification jstring="[hyper(145,a,14366,a(flip),b,6442,a)].">
      <j1 rule="hyper" parents="145 14366 6442"/>
    </justification>
  </clause>

  <clause id="14391">
    <literal><![CDATA[
      T(x,y) * (1 / z) = x * (K(x,y) / z)
    ]]></literal>
    <justification jstring="[hyper(145,a,14366,a(flip),b,6071,a),flip(a)].">
      <j1 rule="hyper" parents="145 14366 6071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14392">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) / z) = x \ (1 / z)
    ]]></literal>
    <justification jstring="[hyper(139,a,14366,a(flip),b,5778,a)].">
      <j1 rule="hyper" parents="139 14366 5778"/>
    </justification>
  </clause>

  <clause id="14393">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(38,a,3868,a,b,14366,a(flip))].">
      <j1 rule="hyper" parents="38 3868 14366"/>
    </justification>
  </clause>

  <clause id="14394">
    <literal><![CDATA[
      K(x,y) / T(z,z \ 1) = K(x,y) * (z \ 1)
    ]]></literal>
    <justification jstring="[para(301(a,1),14366(a,1,2)),flip(a)].">
      <j1 rule="para" parents="301 14366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14395">
    <literal><![CDATA[
      x * (K(x,x * x) / y) = L(x,x,x) * (1 / y)
    ]]></literal>
    <justification jstring="[para(14366(a,1),6086(a,1,2))].">
      <j1 rule="para" parents="14366 6086"/>
    </justification>
  </clause>

  <clause id="14396">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(14366(a,1),7785(a,1,1))].">
      <j1 rule="para" parents="14366 7785"/>
    </justification>
  </clause>

  <clause id="14397">
    <literal><![CDATA[
      (K(x,y) / z) * K(y,x) = T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(14366(a,1),8160(a,1,1))].">
      <j1 rule="para" parents="14366 8160"/>
    </justification>
  </clause>

  <clause id="14399">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (K(z,z \ u) / w)))
    ]]></literal>
    <justification jstring="[para(14366(a,1),7249(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14366 7249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14400">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14061,a,14393,a)].">
      <j1 rule="hyper" parents="14061 14393"/>
    </justification>
  </clause>

  <clause id="14401">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14091,a(flip),b,14393,a)].">
      <j1 rule="hyper" parents="64 14091 14393"/>
    </justification>
  </clause>

  <clause id="14403">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,y) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,14393,a(flip),b,297,a)].">
      <j1 rule="hyper" parents="139 14393 297"/>
    </justification>
  </clause>

  <clause id="14404">
    <literal><![CDATA[
      (K(x,y) \ z) \ 1 = z \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,14393,a(flip),b,701,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 14393 701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14405">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,R(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,14393,a,b,14400,a)].">
      <j1 rule="hyper" parents="373 14393 14400"/>
    </justification>
  </clause>

  <clause id="14406">
    <literal><![CDATA[
      K(x,y * (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(675(a,1),14400(a,1,2))].">
      <j1 rule="para" parents="675 14400"/>
    </justification>
  </clause>

  <clause id="14410">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,14393,a,b,14401,a)].">
      <j1 rule="hyper" parents="373 14393 14401"/>
    </justification>
  </clause>

  <clause id="14411">
    <literal><![CDATA[
      K(x,L(y,z,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1631(a,1),14401(a,1,2))].">
      <j1 rule="para" parents="1631 14401"/>
    </justification>
  </clause>

  <clause id="14412">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1636(a,1),14401(a,1,2))].">
      <j1 rule="para" parents="1636 14401"/>
    </justification>
  </clause>

  <clause id="14413">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(1637(a,1),14401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1637 14401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14414">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(1638(a,1),14401(a,1,2))].">
      <j1 rule="para" parents="1638 14401"/>
    </justification>
  </clause>

  <clause id="14415">
    <literal><![CDATA[
      T(x,L(y,z,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,14411,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 14411 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14416">
    <literal><![CDATA[
      a(x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,14411,a,b,12120,a),flip(a)].">
      <j1 rule="hyper" parents="140 14411 12120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14417">
    <literal><![CDATA[
      K(x,(y \ z) \ y) = K(x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,12073,a(flip),b,14411,a),flip(a)].">
      <j1 rule="hyper" parents="64 12073 14411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14418">
    <literal><![CDATA[
      T(x,L(y,z,z)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,14411,a(flip),b,5726,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 14411 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14419">
    <literal><![CDATA[
      K(x,(y * y) \ z) = K(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[para(346(a,1),14411(a,1,2))].">
      <j1 rule="para" parents="346 14411"/>
    </justification>
  </clause>

  <clause id="14420">
    <literal><![CDATA[
      K(x,T((y \ 1) \ z,u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(1141(a,1),14411(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1141 14411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14421">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[para(1143(a,1),14411(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1143 14411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14422">
    <literal><![CDATA[
      a(x * y,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(12166,a,14416,a)].">
      <j1 rule="hyper" parents="12166 14416"/>
    </justification>
  </clause>

  <clause id="14423">
    <literal><![CDATA[
      a(1 / x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,2641,a,b,14416,a)].">
      <j1 rule="hyper" parents="64 2641 14416"/>
    </justification>
  </clause>

  <clause id="14424">
    <literal><![CDATA[
      K(a(x,x,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,13977,a(flip),b,14416,a)].">
      <j1 rule="hyper" parents="64 13977 14416"/>
    </justification>
  </clause>

  <clause id="14425">
    <literal><![CDATA[
      T(a(x,x,y),z) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(57,a,14424,a)].">
      <j1 rule="hyper" parents="57 14424"/>
    </justification>
  </clause>

  <clause id="14426">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(569(a,1),14415(a,1,2))].">
      <j1 rule="para" parents="569 14415"/>
    </justification>
  </clause>

  <clause id="14427">
    <literal><![CDATA[
      T(x,(y * y) \ z) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[para(346(a,1),14415(a,1,2))].">
      <j1 rule="para" parents="346 14415"/>
    </justification>
  </clause>

  <clause id="14428">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(576(a,1),14415(a,1,2)),flip(a)].">
      <j1 rule="para" parents="576 14415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14429">
    <literal><![CDATA[
      T(x,((y \ 1) \ y) * z) = T(x,y * (y * z))
    ]]></literal>
    <justification jstring="[para(1144(a,1),14415(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1144 14415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14430">
    <literal><![CDATA[
      x \ (L(y,x * z,x) * L(z,x,x)) = ((x \ 1) * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(14415(a,1),1871(a,2,2))].">
      <j1 rule="para" parents="14415 1871"/>
    </justification>
  </clause>

  <clause id="14433">
    <literal><![CDATA[
      T(x,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,14425,a)].">
      <j1 rule="hyper" parents="55 14425"/>
    </justification>
  </clause>

  <clause id="14434">
    <literal><![CDATA[
      T(x,a(y \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[para(2653(a,2),14433(a,1,2))].">
      <j1 rule="para" parents="2653 14433"/>
    </justification>
  </clause>

  <clause id="14435">
    <literal><![CDATA[
      x / a(y \ 1,y,z) = a(y \ 1,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(8638,a,14434,a),flip(a)].">
      <j1 rule="hyper" parents="8638 14434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14436">
    <literal><![CDATA[
      K(x,(y * z) \ 1) = K(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(12086,a,14412,a)].">
      <j1 rule="hyper" parents="12086 14412"/>
    </justification>
  </clause>

  <clause id="14437">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12060,a,14412,a)].">
      <j1 rule="hyper" parents="12060 14412"/>
    </justification>
  </clause>

  <clause id="14438">
    <literal><![CDATA[
      T(x,L(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(14418(a,2),5767(a,1))].">
      <j1 rule="para" parents="14418 5767"/>
    </justification>
  </clause>

  <clause id="14440">
    <literal><![CDATA[
      K((x \ y) \ z,y) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12172,a(flip),b,14437,a),flip(a)].">
      <j1 rule="hyper" parents="64 12172 14437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14441">
    <literal><![CDATA[
      K((x \ 1) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12094,a(flip),b,14437,a),flip(a)].">
      <j1 rule="hyper" parents="64 12094 14437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14442">
    <literal><![CDATA[
      K(x,y) / (z * K(x,y)) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(142,a,14437,a(flip),b,1156,a)].">
      <j1 rule="hyper" parents="142 14437 1156"/>
    </justification>
  </clause>

  <clause id="14443">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,14437,a(flip),b,1156,a)].">
      <j1 rule="hyper" parents="139 14437 1156"/>
    </justification>
  </clause>

  <clause id="14444">
    <literal><![CDATA[
      (x \ 1) * K(y,z) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,14437,a(flip),b,293,a),flip(a)].">
      <j1 rule="hyper" parents="139 14437 293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14445">
    <literal><![CDATA[
      1 / (x \ K(y,z)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(740,a,14383,a),flip(a)].">
      <j1 rule="hyper" parents="740 14383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14446">
    <literal><![CDATA[
      K(x,y) * (1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(14383(a,1),6188(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14383 6188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14447">
    <literal><![CDATA[
      (T(x,y) \ z) * ((x \ z) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(6660,a,14384,a)].">
      <j1 rule="hyper" parents="6660 14384"/>
    </justification>
  </clause>

  <clause id="14448">
    <literal><![CDATA[
      (((x \ y) * x) \ z) * ((y \ z) \ 1) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(144,a,10843,a(flip),b,14384,a)].">
      <j1 rule="hyper" parents="144 10843 14384"/>
    </justification>
  </clause>

  <clause id="14449">
    <literal><![CDATA[
      (T(x,y) * z) \ K(x,y) = (x * z) \ 1
    ]]></literal>
    <justification jstring="[para(5755(a,1),14403(a,1,1))].">
      <j1 rule="para" parents="5755 14403"/>
    </justification>
  </clause>

  <clause id="14450">
    <literal><![CDATA[
      (K(x,y) * z) \ 1 = z \ K(y,x)
    ]]></literal>
    <justification jstring="[para(6161(a,1),14403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6161 14403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14451">
    <literal><![CDATA[
      K(K(x,y) * z,(K(x,y) * z) \ K(x,y)) = (z \ 1) \ (K(x,y) / (K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(14403(a,1),5879(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14403 5879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14452">
    <literal><![CDATA[
      (T(x,y) \ z) \ 1 = (x \ z) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(6075(a,1),14403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6075 14403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14453">
    <literal><![CDATA[
      T(x,K(y,z)) \ K(z,y) = (x * K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(6175(a,1),14403(a,1,1))].">
      <j1 rule="para" parents="6175 14403"/>
    </justification>
  </clause>

  <clause id="14454">
    <literal><![CDATA[
      ((x / y) \ z) \ K(y \ x,y) = ((y \ x) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(6292(a,1),14403(a,1,1))].">
      <j1 rule="para" parents="6292 14403"/>
    </justification>
  </clause>

  <clause id="14455">
    <literal><![CDATA[
      ((x \ y) * z) \ K(x \ y,x) = ((y / x) * z) \ 1
    ]]></literal>
    <justification jstring="[para(6553(a,1),14403(a,1,1))].">
      <j1 rule="para" parents="6553 14403"/>
    </justification>
  </clause>

  <clause id="14456">
    <literal><![CDATA[
      ((x / (x / y)) \ z) \ 1 = (y \ z) \ K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(6599(a,1),14403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6599 14403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14457">
    <literal><![CDATA[
      T(T(x,y),z) \ K(x,y) = T(x,T(z,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8041(a,1),14403(a,1,1))].">
      <j1 rule="para" parents="8041 14403"/>
    </justification>
  </clause>

  <clause id="14458">
    <literal><![CDATA[
      ((x * y) \ z) \ K(y,x) = ((y * x) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(10833(a,1),14403(a,1,1))].">
      <j1 rule="para" parents="10833 14403"/>
    </justification>
  </clause>

  <clause id="14460">
    <literal><![CDATA[
      (a(x,x,x) \ y) \ 1 = y \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1853(a,1),14404(a,1,1,1))].">
      <j1 rule="para" parents="1853 14404"/>
    </justification>
  </clause>

  <clause id="14461">
    <literal><![CDATA[
      T(x,y * (z \ 1)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(143,a,14406,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 14406 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14462">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6519,a,b,14406,a)].">
      <j1 rule="hyper" parents="64 6519 14406"/>
    </justification>
  </clause>

  <clause id="14463">
    <literal><![CDATA[
      K(x,y / (z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6521,a(flip),b,14406,a),flip(a)].">
      <j1 rule="hyper" parents="64 6521 14406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14464">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(82(a,1),14406(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 14406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14465">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u / ((y \ z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(13484,a,14413,a),flip(a)].">
      <j1 rule="hyper" parents="13484 14413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14466">
    <literal><![CDATA[
      K(x,(y \ 1) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(13397,a,14413,a),flip(a)].">
      <j1 rule="hyper" parents="13397 14413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14467">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11113,a,b,14413,a)].">
      <j1 rule="hyper" parents="373 11113 14413"/>
    </justification>
  </clause>

  <clause id="14468">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) / (z \ 1)) = K(x,z * L(y / (z * y),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13521,a,b,14413,a)].">
      <j1 rule="hyper" parents="64 13521 14413"/>
    </justification>
  </clause>

  <clause id="14469">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6528,a,b,14413,a)].">
      <j1 rule="hyper" parents="64 6528 14413"/>
    </justification>
  </clause>

  <clause id="14470">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = x * K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,14413,a(flip),b,5726,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 14413 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14471">
    <literal><![CDATA[
      (x \ (y \ 1)) \ K(x \ (y \ 1),y * x) = 1 / (x \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(139,a,14413,a(flip),b,4338,a)].">
      <j1 rule="hyper" parents="139 14413 4338"/>
    </justification>
  </clause>

  <clause id="14473">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(14413(a,1),12059(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14413 12059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14474">
    <literal><![CDATA[
      K(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14413(a,1),13397(a,1))].">
      <j1 rule="para" parents="14413 13397"/>
    </justification>
  </clause>

  <clause id="14475">
    <literal><![CDATA[
      K(x,y \ ((1 / y) \ z)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14414(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14476">
    <literal><![CDATA[
      T(x * (1 / y),K(z,y \ x)) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(14414(a,1),11117(a,1,2))].">
      <j1 rule="para" parents="14414 11117"/>
    </justification>
  </clause>

  <clause id="14477">
    <literal><![CDATA[
      K(x,(1 / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(14414(a,1),13398(a,1))].">
      <j1 rule="para" parents="14414 13398"/>
    </justification>
  </clause>

  <clause id="14478">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5118,a(flip),b,14426,a),flip(a)].">
      <j1 rule="hyper" parents="64 5118 14426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14479">
    <literal><![CDATA[
      T(x,(y \ 1) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5110,a(flip),b,14426,a)].">
      <j1 rule="hyper" parents="64 5110 14426"/>
    </justification>
  </clause>

  <clause id="14480">
    <literal><![CDATA[
      ((1 / x) * y) * T(z,x \ y) = z * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,14426,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 14426 22"/>
    </justification>
  </clause>

  <clause id="14481">
    <literal><![CDATA[
      T(x,y \ ((1 / y) \ z)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14426(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14482">
    <literal><![CDATA[
      L(x,y,1 / z) * ((1 / z) * y) = (1 / z) * (y * T(x,z \ y))
    ]]></literal>
    <justification jstring="[para(14426(a,1),793(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14426 793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14483">
    <literal><![CDATA[
      T(x,y \ T(z,y \ 1)) = T(x,z * (1 / y))
    ]]></literal>
    <justification jstring="[para(3873(a,1),14426(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3873 14426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14484">
    <literal><![CDATA[
      T(1 / x,y) * R(T(z,x \ y),1 / x,y) = T(L(z,1 / x,y) * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(14426(a,1),11270(a,1,2,1))].">
      <j1 rule="para" parents="14426 11270"/>
    </justification>
  </clause>

  <clause id="14485">
    <literal><![CDATA[
      T(x / ((y \ 1) \ z),y * z) = ((y \ 1) \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,14428,a),flip(a)].">
      <j1 rule="hyper" parents="467 14428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14486">
    <literal><![CDATA[
      ((x \ 1) \ y) * T(z,x * y) = z * ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,14428,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 14428 22"/>
    </justification>
  </clause>

  <clause id="14487">
    <literal><![CDATA[
      T(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(569(a,1),14438(a,1,2))].">
      <j1 rule="para" parents="569 14438"/>
    </justification>
  </clause>

  <clause id="14488">
    <literal><![CDATA[
      T(x,(y * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(346(a,1),14438(a,1,2))].">
      <j1 rule="para" parents="346 14438"/>
    </justification>
  </clause>

  <clause id="14490">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5254,a,b,14441,a)].">
      <j1 rule="hyper" parents="64 5254 14441"/>
    </justification>
  </clause>

  <clause id="14491">
    <literal><![CDATA[
      K((x \ 1) \ (y \ 1),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,10678,a(flip),b,14441,a)].">
      <j1 rule="hyper" parents="64 10678 14441"/>
    </justification>
  </clause>

  <clause id="14492">
    <literal><![CDATA[
      K((x \ 1) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5252,a(flip),b,14441,a),flip(a)].">
      <j1 rule="hyper" parents="64 5252 14441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14493">
    <literal><![CDATA[
      K((1 / x) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),14441(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 14441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14494">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K(x * y,z)
    ]]></literal>
    <justification jstring="[para(14441(a,1),6811(a,2,2))].">
      <j1 rule="para" parents="14441 6811"/>
    </justification>
  </clause>

  <clause id="14495">
    <literal><![CDATA[
      x * (y * K(x * y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(14441(a,1),6816(a,1,2,2))].">
      <j1 rule="para" parents="14441 6816"/>
    </justification>
  </clause>

  <clause id="14496">
    <literal><![CDATA[
      T(x * K(y * x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(14441(a,1),6989(a,1,1,2))].">
      <j1 rule="para" parents="14441 6989"/>
    </justification>
  </clause>

  <clause id="14497">
    <literal><![CDATA[
      (x * K(y * (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(14441(a,1),7200(a,1,1,2))].">
      <j1 rule="para" parents="14441 7200"/>
    </justification>
  </clause>

  <clause id="14500">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u,z \ 1))
    ]]></literal>
    <justification jstring="[para(14441(a,1),12998(a,1,3))].">
      <j1 rule="para" parents="14441 12998"/>
    </justification>
  </clause>

  <clause id="14501">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(14441(a,1),14177(a,1,2))].">
      <j1 rule="para" parents="14441 14177"/>
    </justification>
  </clause>

  <clause id="14502">
    <literal><![CDATA[
      K(x,y) / ((L(z,u,w) \ z) * K(x,y)) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,9382,a(flip),b,14442,a),flip(a)].">
      <j1 rule="hyper" parents="373 9382 14442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14503">
    <literal><![CDATA[
      (1 / x) \ K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(14442(a,1),305(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14442 305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14504">
    <literal><![CDATA[
      K(x \ 1,x) / ((x \ 1) * y) = 1 / ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(3623(a,1),14442(a,1,2))].">
      <j1 rule="para" parents="3623 14442"/>
    </justification>
  </clause>

  <clause id="14505">
    <literal><![CDATA[
      K(x,y) / (z / T(y,x)) = 1 / (z / y)
    ]]></literal>
    <justification jstring="[para(6245(a,1),14442(a,1,2))].">
      <j1 rule="para" parents="6245 14442"/>
    </justification>
  </clause>

  <clause id="14506">
    <literal><![CDATA[
      K(x,x \ y) / (z * (y / x)) = 1 / (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(6471(a,1),14442(a,1,2))].">
      <j1 rule="para" parents="6471 14442"/>
    </justification>
  </clause>

  <clause id="14507">
    <literal><![CDATA[
      1 / (x * K(y,z)) = K(z,y) / x
    ]]></literal>
    <justification jstring="[para(6871(a,1),14442(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6871 14442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14508">
    <literal><![CDATA[
      K(x \ y,x) / (z / (y / x)) = 1 / (z / (x \ y))
    ]]></literal>
    <justification jstring="[para(6887(a,1),14442(a,1,2))].">
      <j1 rule="para" parents="6887 14442"/>
    </justification>
  </clause>

  <clause id="14509">
    <literal><![CDATA[
      L(x,y,((1 / z) * K(u,w)) \ v5) = L(x,y,(z \ K(u,w)) \ v5)
    ]]></literal>
    <justification jstring="[para(14442(a,1),13561(a,1,3,1,1))].">
      <j1 rule="para" parents="14442 13561"/>
    </justification>
  </clause>

  <clause id="14511">
    <literal><![CDATA[
      (x \ K(y,z)) / K(y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(142,a,207,a(flip),b,14443,a(flip))].">
      <j1 rule="hyper" parents="142 207 14443"/>
    </justification>
  </clause>

  <clause id="14513">
    <literal><![CDATA[
      R(x / y,y,x \ 1) \ K(z,u) = (y * (x \ 1)) * K(z,u)
    ]]></literal>
    <justification jstring="[para(676(a,2),14443(a,1,1))].">
      <j1 rule="para" parents="676 14443"/>
    </justification>
  </clause>

  <clause id="14516">
    <literal><![CDATA[
      (x \ K(y,x)) * K(z,u) = T(x,y) \ K(z,u)
    ]]></literal>
    <justification jstring="[para(5877(a,2),14443(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5877 14443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14517">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ K(u,w) = (L(x,y,z) \ x) * K(u,w)
    ]]></literal>
    <justification jstring="[para(9375(a,1),14443(a,1,1))].">
      <j1 rule="para" parents="9375 14443"/>
    </justification>
  </clause>

  <clause id="14518">
    <literal><![CDATA[
      (1 / x) \ K(y,z * u) = x * K(y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(14413(a,1),14443(a,1,2))].">
      <j1 rule="para" parents="14413 14443"/>
    </justification>
  </clause>

  <clause id="14519">
    <literal><![CDATA[
      x \ K(y,T(z,x)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(11169,a,14444,a),flip(a)].">
      <j1 rule="hyper" parents="11169 14444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14520">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(6897,a,14444,a)].">
      <j1 rule="hyper" parents="6897 14444"/>
    </justification>
  </clause>

  <clause id="14521">
    <literal><![CDATA[
      K(x,y) * T(z \ 1,K(x,y)) = z \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(329,a,14444,a)].">
      <j1 rule="hyper" parents="329 14444"/>
    </justification>
  </clause>

  <clause id="14522">
    <literal><![CDATA[
      x * ((y \ 1) * K(z,u)) = x * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,14444,a,b,9,a)].">
      <j1 rule="hyper" parents="145 14444 9"/>
    </justification>
  </clause>

  <clause id="14523">
    <literal><![CDATA[
      x \ K(y \ (x \ 1),z) = y * T(y \ (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6763,a,b,14444,a),flip(a)].">
      <j1 rule="hyper" parents="64 6763 14444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14524">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ K(u,w) = (R(x,y,z) \ x) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,5384,a(flip),b,14444,a),flip(a)].">
      <j1 rule="hyper" parents="64 5384 14444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14526">
    <literal><![CDATA[
      (x \ K(y,z)) * (z * y) = (x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,14444,a(flip),b,10592,a)].">
      <j1 rule="hyper" parents="144 14444 10592"/>
    </justification>
  </clause>

  <clause id="14527">
    <literal><![CDATA[
      (x \ K(y,z)) * y = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,14444,a(flip),b,6847,a)].">
      <j1 rule="hyper" parents="144 14444 6847"/>
    </justification>
  </clause>

  <clause id="14528">
    <literal><![CDATA[
      (x \ 1) * (y * K(z,y)) = (x \ K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,14444,a(flip),b,5703,a),flip(a)].">
      <j1 rule="hyper" parents="144 14444 5703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14530">
    <literal><![CDATA[
      (x * K(y,z)) / a(x / (u \ 1),u \ 1,K(y,z)) = (x / (u \ 1)) * (u \ K(y,z))
    ]]></literal>
    <justification jstring="[para(14444(a,1),955(a,2,2))].">
      <j1 rule="para" parents="14444 955"/>
    </justification>
  </clause>

  <clause id="14531">
    <literal><![CDATA[
      T(x,y * ((1 / z) * K(u,w))) = T(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(14444(a,1),5301(a,2,2,2))].">
      <j1 rule="para" parents="14444 5301"/>
    </justification>
  </clause>

  <clause id="14533">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) = K(z,y)
    ]]></literal>
    <justification jstring="[para(14444(a,1),6882(a,1,1))].">
      <j1 rule="para" parents="14444 6882"/>
    </justification>
  </clause>

  <clause id="14535">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(14444(a,1),6881(a,1,1))].">
      <j1 rule="para" parents="14444 6881"/>
    </justification>
  </clause>

  <clause id="14537">
    <literal><![CDATA[
      T(x \ K(y,z),K(y,z)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(14444(a,1),8164(a,1,1))].">
      <j1 rule="para" parents="14444 8164"/>
    </justification>
  </clause>

  <clause id="14538">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(14444(a,1),7838(a,1,1))].">
      <j1 rule="para" parents="14444 7838"/>
    </justification>
  </clause>

  <clause id="14539">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,L(w,L(x,y,z) \ 1,x)) = x * (L(x,y,z) \ K(u,w))
    ]]></literal>
    <justification jstring="[para(14444(a,1),12138(a,2,2))].">
      <j1 rule="para" parents="14444 12138"/>
    </justification>
  </clause>

  <clause id="14541">
    <literal><![CDATA[
      T(K(x,y) * z,z \ K(y,x)) = (z \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(14445(a,1),117(a,1,1))].">
      <j1 rule="para" parents="14445 117"/>
    </justification>
  </clause>

  <clause id="14542">
    <literal><![CDATA[
      (a(x,x,x) * y) \ 1 = y \ K(x,x * x)
    ]]></literal>
    <justification jstring="[para(98(a,1),14450(a,1,1,1))].">
      <j1 rule="para" parents="98 14450"/>
    </justification>
  </clause>

  <clause id="14543">
    <literal><![CDATA[
      L(x,y,z / (1 / (K(u,w) * v5))) = L(x,y,z / (v5 \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(14450(a,1),3853(a,2,3,2))].">
      <j1 rule="para" parents="14450 3853"/>
    </justification>
  </clause>

  <clause id="14544">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(14450(a,1),14406(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14450 14406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14545">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5113,a,b,14461,a)].">
      <j1 rule="hyper" parents="64 5113 14461"/>
    </justification>
  </clause>

  <clause id="14546">
    <literal><![CDATA[
      T(x,(1 / y) / z) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,14426,a(flip),b,14461,a),flip(a)].">
      <j1 rule="hyper" parents="64 14426 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14547">
    <literal><![CDATA[
      T(x,y / (z \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5115,a(flip),b,14461,a),flip(a)].">
      <j1 rule="hyper" parents="64 5115 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14548">
    <literal><![CDATA[
      T(x,y * ((z * z) * (u \ 1))) = T(x,(y * (z * z)) / u)
    ]]></literal>
    <justification jstring="[para(34(a,1),14461(a,1,2))].">
      <j1 rule="para" parents="34 14461"/>
    </justification>
  </clause>

  <clause id="14549">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(82(a,1),14461(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14550">
    <literal><![CDATA[
      T(x,y / ((z * z) \ u)) = T(x,y * (u \ (z * z)))
    ]]></literal>
    <justification jstring="[para(550(a,1),14461(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="550 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14551">
    <literal><![CDATA[
      T(x,y * ((z * z) * (u \ 1))) = T(x,y / (u / (z * z)))
    ]]></literal>
    <justification jstring="[para(890(a,1),14461(a,1,2,2))].">
      <j1 rule="para" parents="890 14461"/>
    </justification>
  </clause>

  <clause id="14552">
    <literal><![CDATA[
      L(x,y \ 1,z) * (z * (y \ 1)) = z * ((y \ 1) * T(x,z / y))
    ]]></literal>
    <justification jstring="[para(14461(a,1),793(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14461 793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14553">
    <literal><![CDATA[
      T(x,y / (K(z,u) * w)) = T(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(14450(a,1),14461(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14450 14461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14554">
    <literal><![CDATA[
      K(x / (x / y),z / u) = K(y,T(z * (1 / u),x))
    ]]></literal>
    <justification jstring="[hyper(8237,a,14462,a),flip(a)].">
      <j1 rule="hyper" parents="8237 14462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14555">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * K(u,y / z)) = K(x,T(y * (1 / z),u))
    ]]></literal>
    <justification jstring="[para(14462(a,1),8220(a,1,2,2))].">
      <j1 rule="para" parents="14462 8220"/>
    </justification>
  </clause>

  <clause id="14556">
    <literal><![CDATA[
      K(x,y * z) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[para(14463(a,1),6418(a,1,1))].">
      <j1 rule="para" parents="14463 6418"/>
    </justification>
  </clause>

  <clause id="14558">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(14463(a,1),12059(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14463 12059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14560">
    <literal><![CDATA[
      K(x,y \ L(x,z,u)) = K(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,11584,a(flip),b,14466,a),flip(a)].">
      <j1 rule="hyper" parents="64 11584 14466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14563">
    <literal><![CDATA[
      K(x,y * ((1 / y) * z)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),14469(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 14469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14564">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(1 / y,z) * u)
    ]]></literal>
    <justification jstring="[para(6071(a,1),14469(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6071 14469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14565">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,x * y) = (x * x) * (y / x)
    ]]></literal>
    <justification jstring="[para(14469(a,1),7211(a,1,2))].">
      <j1 rule="para" parents="14469 7211"/>
    </justification>
  </clause>

  <clause id="14566">
    <literal><![CDATA[
      K(x,L((1 / y) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(14469(a,1),12059(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14469 12059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14567">
    <literal><![CDATA[
      1 / T((1 / x) / y,x * y) = ((1 / x) / y) \ 1
    ]]></literal>
    <justification jstring="[hyper(225,a,14478,a(flip),b,3815,a(flip))].">
      <j1 rule="hyper" parents="225 14478 3815"/>
    </justification>
  </clause>

  <clause id="14568">
    <literal><![CDATA[
      ((1 / x) \ y) * T(z,x * y) = z * ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,14478,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 14478 22"/>
    </justification>
  </clause>

  <clause id="14569">
    <literal><![CDATA[
      T(x / ((y \ 1) * z),y \ z) = ((y \ 1) * z) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,14479,a),flip(a)].">
      <j1 rule="hyper" parents="467 14479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14571">
    <literal><![CDATA[
      T(x,(y \ 1) / z) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,14461,a(flip),b,14479,a)].">
      <j1 rule="hyper" parents="64 14461 14479"/>
    </justification>
  </clause>

  <clause id="14572">
    <literal><![CDATA[
      ((x \ 1) * y) * T(z,x \ y) = z * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,14479,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 14479 22"/>
    </justification>
  </clause>

  <clause id="14573">
    <literal><![CDATA[
      (1 / x) * (1 * (T(y,x \ (x \ 1)) \ z)) = x * (y \ (((x \ 1) * (x \ 1)) * z))
    ]]></literal>
    <justification jstring="[para(14479(a,1),3516(a,1,2,2,1))].">
      <j1 rule="para" parents="14479 3516"/>
    </justification>
  </clause>

  <clause id="14574">
    <literal><![CDATA[
      K((x \ 1) * y,z) = T(z,x \ y) \ z
    ]]></literal>
    <justification jstring="[para(14479(a,1),5731(a,2,1))].">
      <j1 rule="para" parents="14479 5731"/>
    </justification>
  </clause>

  <clause id="14576">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ u,y \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / ((y \ 1) * z)) = w
    ]]></literal>
    <justification jstring="[para(14479(a,1),8325(a,1,2))].">
      <j1 rule="para" parents="14479 8325"/>
    </justification>
  </clause>

  <clause id="14578">
    <literal><![CDATA[
      ((1 / x) \ y) / L(T(x,y),z,u) = L(x,z,u) \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(14481(a,1),10458(a,1,2,1))].">
      <j1 rule="para" parents="14481 10458"/>
    </justification>
  </clause>

  <clause id="14579">
    <literal><![CDATA[
      K(x * ((1 / x) * y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6038,a,14490,a),flip(a)].">
      <j1 rule="hyper" parents="6038 14490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14580">
    <literal><![CDATA[
      K((1 / x) \ y,z / x) = K(y * x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,11179,a,b,14490,a),flip(a)].">
      <j1 rule="hyper" parents="373 11179 14490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14581">
    <literal><![CDATA[
      K(R(x,x \ (1 / y),y) \ z,u) = K(((x \ (1 / y)) * y) * z,u)
    ]]></literal>
    <justification jstring="[para(715(a,2),14490(a,1,1,1))].">
      <j1 rule="para" parents="715 14490"/>
    </justification>
  </clause>

  <clause id="14582">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(11189,a,14492,a),flip(a)].">
      <j1 rule="hyper" parents="11189 14492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14586">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,11193,a(flip),b,14492,a),flip(a)].">
      <j1 rule="hyper" parents="64 11193 14492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14587">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14492(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 14492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14590">
    <literal><![CDATA[
      K((x * x) \ y,z) = K(x \ (x \ y),z)
    ]]></literal>
    <justification jstring="[para(536(a,1),14493(a,1,1))].">
      <j1 rule="para" parents="536 14493"/>
    </justification>
  </clause>

  <clause id="14591">
    <literal><![CDATA[
      T(R(T(x,x * y),x,y),K((1 / x) * y,z)) = ((1 / x) * y) \ T(y,K(x \ y,z))
    ]]></literal>
    <justification jstring="[para(14493(a,1),7164(a,2,2,2))].">
      <j1 rule="para" parents="14493 7164"/>
    </justification>
  </clause>

  <clause id="14592">
    <literal><![CDATA[
      (K(x,y) / z) \ 1 = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(215,a,14507,a)].">
      <j1 rule="hyper" parents="215 14507"/>
    </justification>
  </clause>

  <clause id="14593">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = (z * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(14507(a,1),117(a,1,1))].">
      <j1 rule="para" parents="14507 117"/>
    </justification>
  </clause>

  <clause id="14596">
    <literal><![CDATA[
      K(K(x,y) / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((z * K(y,x)) \ 1,u) = w
    ]]></literal>
    <justification jstring="[para(14507(a,1),3777(a,1,1))].">
      <j1 rule="para" parents="14507 3777"/>
    </justification>
  </clause>

  <clause id="14597">
    <literal><![CDATA[
      K(x,y) / (1 / x) = 1 / (K(y,x) / x)
    ]]></literal>
    <justification jstring="[para(5704(a,1),14507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5704 14507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14598">
    <literal><![CDATA[
      K(x,y) / (1 / y) = 1 / (K(y,x) / y)
    ]]></literal>
    <justification jstring="[para(6862(a,1),14507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6862 14507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14599">
    <literal><![CDATA[
      K(x,y * (z / ((u * K(w,v5)) \ 1))) = K(x,y * (z / (K(v5,w) / u)))
    ]]></literal>
    <justification jstring="[para(14507(a,1),6536(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14507 6536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14600">
    <literal><![CDATA[
      K(x,(y / (1 / (K(z,u) / w))) * v5) = K(x,(y / (w * K(u,z))) * v5)
    ]]></literal>
    <justification jstring="[para(14507(a,1),7288(a,1,2,1,2,2))].">
      <j1 rule="para" parents="14507 7288"/>
    </justification>
  </clause>

  <clause id="14601">
    <literal><![CDATA[
      1 / T(x * K(y,z),y) = K(z,y) / T(x,y)
    ]]></literal>
    <justification jstring="[para(7812(a,2),14507(a,1,2))].">
      <j1 rule="para" parents="7812 14507"/>
    </justification>
  </clause>

  <clause id="14602">
    <literal><![CDATA[
      K(x,y / (K(z,u) / w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(14507(a,1),14464(a,1,2,2))].">
      <j1 rule="para" parents="14507 14464"/>
    </justification>
  </clause>

  <clause id="14603">
    <literal><![CDATA[
      (x \ 1) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ K(y,z) = u
    ]]></literal>
    <justification jstring="[para(14511(a,1),285(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14511 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14605">
    <literal><![CDATA[
      (x \ K(y,z * (y \ u))) \ (x \ 1) = K((y \ z) * u,y)
    ]]></literal>
    <justification jstring="[para(14018(a,1),14533(a,1,1,2))].">
      <j1 rule="para" parents="14018 14533"/>
    </justification>
  </clause>

  <clause id="14606">
    <literal><![CDATA[
      T(x * K(y,x),y \ 1) = T(x,(1 / y) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7589,a,b,14545,a)].">
      <j1 rule="hyper" parents="64 7589 14545"/>
    </justification>
  </clause>

  <clause id="14608">
    <literal><![CDATA[
      T(x,y / (z \ K(u,w))) = T(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(14445(a,1),14545(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14445 14545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14609">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) * z) = T(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),14547(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 14547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14610">
    <literal><![CDATA[
      K(x / (y \ 1),z) = T(z,x * y) \ z
    ]]></literal>
    <justification jstring="[para(14547(a,1),5731(a,2,1))].">
      <j1 rule="para" parents="14547 5731"/>
    </justification>
  </clause>

  <clause id="14611">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[para(14547(a,1),11168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14547 11168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14612">
    <literal><![CDATA[
      T(x,T(y,z * u) * (z / (1 / u))) = T(x,(z / (1 / u)) * y)
    ]]></literal>
    <justification jstring="[para(14549(a,1),11143(a,1,2,1))].">
      <j1 rule="para" parents="14549 11143"/>
    </justification>
  </clause>

  <clause id="14613">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) = K(x,u * ((1 / u) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,14412,a,b,14563,a)].">
      <j1 rule="hyper" parents="373 14412 14563"/>
    </justification>
  </clause>

  <clause id="14614">
    <literal><![CDATA[
      ((1 / (x / y)) * x) * K(z * ((1 / z) * x),x \ y) = x * (1 / (x / y))
    ]]></literal>
    <justification jstring="[para(14579(a,2),6919(a,1,2))].">
      <j1 rule="para" parents="14579 6919"/>
    </justification>
  </clause>

  <clause id="14615">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5251,a,b,14587,a),flip(a)].">
      <j1 rule="hyper" parents="373 5251 14587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14616">
    <literal><![CDATA[
      x \ K(x,x \ K(y,z)) = (K(y,z) / x) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6258,a(flip),b,14592,a)].">
      <j1 rule="hyper" parents="64 6258 14592"/>
    </justification>
  </clause>

  <clause id="14618">
    <literal><![CDATA[
      ((x * ((x \ y) * K(x / y,y))) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(14592(a,1),11318(a,1,1,1,2))].">
      <j1 rule="para" parents="14592 11318"/>
    </justification>
  </clause>

  <clause id="14619">
    <literal><![CDATA[
      T(x * (y * (x \ 1)),y) = x * (y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,5461,a(flip),b,14609,a),flip(a)].">
      <j1 rule="hyper" parents="64 5461 14609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14620">
    <literal><![CDATA[
      K(x,R(y,z,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14076,a,14364,a)].">
      <j1 rule="hyper" parents="14076 14364"/>
    </justification>
  </clause>

  <clause id="14621">
    <literal><![CDATA[
      K(x,T(y / (1 / z),u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(1414(a,1),14620(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1414 14620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14622">
    <literal><![CDATA[
      (x * K(y,x)) / z = K(y,x) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(407,a,14382,a)].">
      <j1 rule="hyper" parents="407 14382"/>
    </justification>
  </clause>

  <clause id="14623">
    <literal><![CDATA[
      (1 / x) * ((K(y,z) / x) \ y) = y * K(z,y)
    ]]></literal>
    <justification jstring="[para(14383(a,1),14382(a,1,1))].">
      <j1 rule="para" parents="14383 14382"/>
    </justification>
  </clause>

  <clause id="14624">
    <literal><![CDATA[
      T(x,(y \ z) \ y) = T(x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(143,a,14417,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 14417 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14625">
    <literal><![CDATA[
      K(x * ((y * y) \ 1),x) = T(x,y \ (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(14427(a,1),6352(a,2,1))].">
      <j1 rule="para" parents="14427 6352"/>
    </justification>
  </clause>

  <clause id="14626">
    <literal><![CDATA[
      T(x,y \ ((z * z) * T(u,z \ (z \ y)))) = T(x,u / ((z * z) \ y))
    ]]></literal>
    <justification jstring="[para(14427(a,1),13422(a,1,2,2,2))].">
      <j1 rule="para" parents="14427 13422"/>
    </justification>
  </clause>

  <clause id="14627">
    <literal><![CDATA[
      K(x,1 / (y * z)) = K(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(6513,a,14436,a)].">
      <j1 rule="hyper" parents="6513 14436"/>
    </justification>
  </clause>

  <clause id="14628">
    <literal><![CDATA[
      T(x,(y * z) \ 1) = T(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(143,a,14436,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 14436 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14629">
    <literal><![CDATA[
      (x * y) \ K(x * y,y \ (x \ 1)) = 1 / (x * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,14436,a(flip),b,1724,a(flip))].">
      <j1 rule="hyper" parents="139 14436 1724"/>
    </justification>
  </clause>

  <clause id="14630">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) * u) \ 1) = K(x,u \ (y \ K(y \ z,y)))
    ]]></literal>
    <justification jstring="[para(5937(a,1),14436(a,2,2,2))].">
      <j1 rule="para" parents="5937 14436"/>
    </justification>
  </clause>

  <clause id="14631">
    <literal><![CDATA[
      K(x \ ((y \ x) * z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(13586,a,14440,a),flip(a)].">
      <j1 rule="hyper" parents="13586 14440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14633">
    <literal><![CDATA[
      K(x \ ((x / y) * z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),14440(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 14440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14635">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(((y \ z) \ 1) / x,K(u,y))
    ]]></literal>
    <justification jstring="[para(14447(a,1),11116(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14447 11116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14636">
    <literal><![CDATA[
      ((1 / T(x,y)) \ T(T(x,y),z)) \ K(x,y) = (x * T((T(x,y) \ 1) \ 1,z)) \ 1
    ]]></literal>
    <justification jstring="[para(1490(a,1),14449(a,1,1))].">
      <j1 rule="para" parents="1490 14449"/>
    </justification>
  </clause>

  <clause id="14637">
    <literal><![CDATA[
      (x \ K(T(x,y) \ 1,z)) \ K(x,y) = T(T(x,y) \ 1,z) \ 1
    ]]></literal>
    <justification jstring="[para(5762(a,1),14452(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5762 14452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14638">
    <literal><![CDATA[
      T(x,(y \ z) \ K(y,u)) = T(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[para(14452(a,1),6704(a,1,2))].">
      <j1 rule="para" parents="14452 6704"/>
    </justification>
  </clause>

  <clause id="14639">
    <literal><![CDATA[
      K((x \ y) \ K(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(14452(a,1),6827(a,1,1))].">
      <j1 rule="para" parents="14452 6827"/>
    </justification>
  </clause>

  <clause id="14640">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ K(z,w))) = K(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(14452(a,1),14406(a,1,2,2))].">
      <j1 rule="para" parents="14452 14406"/>
    </justification>
  </clause>

  <clause id="14641">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(14467(a,1),11233(a,1))].">
      <j1 rule="para" parents="14467 11233"/>
    </justification>
  </clause>

  <clause id="14642">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(14470(a,2),5767(a,1))].">
      <j1 rule="para" parents="14470 5767"/>
    </justification>
  </clause>

  <clause id="14643">
    <literal><![CDATA[
      x * (K(y * x,z) * y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,11188,a,b,14494,a)].">
      <j1 rule="hyper" parents="145 11188 14494"/>
    </justification>
  </clause>

  <clause id="14644">
    <literal><![CDATA[
      x * (T(y,x * (y \ z)) \ z) = T(x * (y \ z),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,8643,a(flip),b,14494,a)].">
      <j1 rule="hyper" parents="145 8643 14494"/>
    </justification>
  </clause>

  <clause id="14645">
    <literal><![CDATA[
      T(x * y,z) / y = x * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5434,a,b,14494,a)].">
      <j1 rule="hyper" parents="64 5434 14494"/>
    </justification>
  </clause>

  <clause id="14646">
    <literal><![CDATA[
      (x * K(y * x,z)) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,14494,a(flip),b,5434,a)].">
      <j1 rule="hyper" parents="144 14494 5434"/>
    </justification>
  </clause>

  <clause id="14647">
    <literal><![CDATA[
      L(x * K(y * x,z),y,y) = (1 / y) * T(y * x,z)
    ]]></literal>
    <justification jstring="[para(14494(a,1),569(a,1,1))].">
      <j1 rule="para" parents="14494 569"/>
    </justification>
  </clause>

  <clause id="14648">
    <literal><![CDATA[
      L(x * K(y * x,z),y,z) = (z * y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(14494(a,1),521(a,1,1))].">
      <j1 rule="para" parents="14494 521"/>
    </justification>
  </clause>

  <clause id="14650">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(14494(a,2),6882(a,1,1))].">
      <j1 rule="para" parents="14494 6882"/>
    </justification>
  </clause>

  <clause id="14651">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x * y) = u
    ]]></literal>
    <justification jstring="[para(14494(a,2),6899(a,1,1))].">
      <j1 rule="para" parents="14494 6899"/>
    </justification>
  </clause>

  <clause id="14653">
    <literal><![CDATA[
      x \ T(x * y,T(z,y)) = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(11180(a,1),14494(a,2,2))].">
      <j1 rule="para" parents="11180 14494"/>
    </justification>
  </clause>

  <clause id="14654">
    <literal><![CDATA[
      T(x * y,L(z,y,x)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(12139,a,14495,a)].">
      <j1 rule="hyper" parents="12139 14495"/>
    </justification>
  </clause>

  <clause id="14655">
    <literal><![CDATA[
      ((x * K(y * x,z)) * y) \ T(x * K(y * x,z),y) = T(y * x,z) \ (x * K(y * x,z))
    ]]></literal>
    <justification jstring="[para(14495(a,1),6981(a,2,1))].">
      <j1 rule="para" parents="14495 6981"/>
    </justification>
  </clause>

  <clause id="14656">
    <literal><![CDATA[
      x * (y * K(y * x,x)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(8516(a,2),14495(a,1,2,2))].">
      <j1 rule="para" parents="8516 14495"/>
    </justification>
  </clause>

  <clause id="14657">
    <literal><![CDATA[
      x * (y * K(y * x,z)) = T(x * y,T(z,y))
    ]]></literal>
    <justification jstring="[para(11180(a,1),14495(a,1,2,2))].">
      <j1 rule="para" parents="11180 14495"/>
    </justification>
  </clause>

  <clause id="14658">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,589,a,b,14654,a)].">
      <j1 rule="hyper" parents="64 589 14654"/>
    </justification>
  </clause>

  <clause id="14659">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * x)) / T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(225,a,14654,a(flip),b,589,a),flip(a)].">
      <j1 rule="hyper" parents="225 14654 589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14660">
    <literal><![CDATA[
      L(x,y,z) * T(z * y,x) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,14654,a(flip),b,589,a)].">
      <j1 rule="hyper" parents="145 14654 589"/>
    </justification>
  </clause>

  <clause id="14661">
    <literal><![CDATA[
      T(x * y,(x * y) \ z) = T(x * y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(346(a,1),14654(a,1,2))].">
      <j1 rule="para" parents="346 14654"/>
    </justification>
  </clause>

  <clause id="14662">
    <literal><![CDATA[
      x / T((x / (y * z)) * y,z) = ((x / (y * z)) * y) \ x
    ]]></literal>
    <justification jstring="[para(14654(a,1),1293(a,1,2))].">
      <j1 rule="para" parents="14654 1293"/>
    </justification>
  </clause>

  <clause id="14663">
    <literal><![CDATA[
      (x \ y) \ K(z,T(x,y)) = K(z,x) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(7406(a,1),14519(a,1,2))].">
      <j1 rule="para" parents="7406 14519"/>
    </justification>
  </clause>

  <clause id="14664">
    <literal><![CDATA[
      K(x,y) * (T(x,z) \ 1) = T(x,z) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(7467(a,1),14519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7467 14519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14665">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = z \ K(x,y)
    ]]></literal>
    <justification jstring="[para(8203(a,1),14519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8203 14519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14666">
    <literal><![CDATA[
      K(x,y * z) * (z \ 1) = z \ K(x,z * y)
    ]]></literal>
    <justification jstring="[para(11127(a,1),14519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11127 14519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14667">
    <literal><![CDATA[
      T((x \ 1) \ K(y,x),y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(269,a,14527,a,b,3880,a(flip))].">
      <j1 rule="hyper" parents="269 14527 3880"/>
    </justification>
  </clause>

  <clause id="14668">
    <literal><![CDATA[
      ((x / (x / y)) \ 1) * y = (y \ 1) * T(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6429,a,b,14527,a)].">
      <j1 rule="hyper" parents="64 6429 14527"/>
    </justification>
  </clause>

  <clause id="14669">
    <literal><![CDATA[
      ((x * y) \ 1) * T(x,y) = ((y * x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(10852(a,1),14527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10852 14527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14670">
    <literal><![CDATA[
      K((x \ K(y,z)) * y,u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(14527(a,2),14492(a,1,1))].">
      <j1 rule="para" parents="14527 14492"/>
    </justification>
  </clause>

  <clause id="14671">
    <literal><![CDATA[
      T(K(x,(y * K(z \ u,z)) * w),w \ T(w * (y * K(z \ u,z)),x)) = (w \ T(w * (y * K(z \ u,z)),x)) \ ((y / (u / z)) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(493,a,6966,a,b,14556,a)].">
      <j1 rule="hyper" parents="493 6966 14556"/>
    </justification>
  </clause>

  <clause id="14672">
    <literal><![CDATA[
      T(K(x,(y * K(z,z \ u)) * w),w \ T(w * (y * K(z,z \ u)),x)) = (w \ T(w * (y * K(z,z \ u)),x)) \ ((y / z) * ((z \ u) \ u))
    ]]></literal>
    <justification jstring="[hyper(493,a,6849,a,b,14556,a)].">
      <j1 rule="hyper" parents="493 6849 14556"/>
    </justification>
  </clause>

  <clause id="14673">
    <literal><![CDATA[
      T(K(x,K(y \ (z * (u \ 1)),w) * v5),v5 \ T(v5 * K(y \ (z * (u \ 1)),w),x)) = (v5 \ T(v5 * K(y \ (z * (u \ 1)),w),x)) \ K(y \ (z * (1 / u)),w)
    ]]></literal>
    <justification jstring="[hyper(493,a,5267,a,b,14556,a)].">
      <j1 rule="hyper" parents="493 5267 14556"/>
    </justification>
  </clause>

  <clause id="14674">
    <literal><![CDATA[
      K((x \ 1) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(14574(a,2),5824(a,1))].">
      <j1 rule="para" parents="14574 5824"/>
    </justification>
  </clause>

  <clause id="14675">
    <literal><![CDATA[
      K(x * (y \ 1),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(8311,a,14582,a),flip(a)].">
      <j1 rule="hyper" parents="8311 14582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14676">
    <literal><![CDATA[
      K(x * (y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / y,z) = u
    ]]></literal>
    <justification jstring="[para(14582(a,1),8311(a,1))].">
      <j1 rule="para" parents="14582 8311"/>
    </justification>
  </clause>

  <clause id="14677">
    <literal><![CDATA[
      K(x \ 1,y) * a(y,x \ 1,y) = K(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10919,a,b,14675,a)].">
      <j1 rule="hyper" parents="64 10919 14675"/>
    </justification>
  </clause>

  <clause id="14678">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5249,a,b,14675,a)].">
      <j1 rule="hyper" parents="64 5249 14675"/>
    </justification>
  </clause>

  <clause id="14679">
    <literal><![CDATA[
      K((1 / x) / y,z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14493,a(flip),b,14675,a),flip(a)].">
      <j1 rule="hyper" parents="64 14493 14675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14680">
    <literal><![CDATA[
      K((x \ 1) / y,z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14492,a(flip),b,14675,a),flip(a)].">
      <j1 rule="hyper" parents="64 14492 14675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14681">
    <literal><![CDATA[
      K(x / (y \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5256,a(flip),b,14675,a),flip(a)].">
      <j1 rule="hyper" parents="64 5256 14675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14682">
    <literal><![CDATA[
      (x * (y \ 1)) * K(x / y,z) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,14675,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 14675 5726"/>
    </justification>
  </clause>

  <clause id="14683">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(82(a,1),14675(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="82 14675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14684">
    <literal><![CDATA[
      K(x * R(y / z,z,y \ 1),u) = K(x / (z * (y \ 1)),u)
    ]]></literal>
    <justification jstring="[para(676(a,2),14678(a,1,1,2))].">
      <j1 rule="para" parents="676 14678"/>
    </justification>
  </clause>

  <clause id="14685">
    <literal><![CDATA[
      x * ((1 / y) * K(x / y,z)) = T(x * (1 / y),z)
    ]]></literal>
    <justification jstring="[para(14678(a,1),14495(a,1,2,2))].">
      <j1 rule="para" parents="14678 14495"/>
    </justification>
  </clause>

  <clause id="14686">
    <literal><![CDATA[
      K((x * (y \ 1)) * y,z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),14681(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 14681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14687">
    <literal><![CDATA[
      K(x / (1 / y),z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,14441,a,b,14683,a),flip(a)].">
      <j1 rule="hyper" parents="373 14441 14683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14688">
    <literal><![CDATA[
      K(x * (y / (1 / z)),y / (1 / z)) * K(y * z,x) = a(y / (1 / z),x,y / (1 / z))
    ]]></literal>
    <justification jstring="[para(14683(a,1),10892(a,1,2))].">
      <j1 rule="para" parents="14683 10892"/>
    </justification>
  </clause>

  <clause id="14689">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y * (x * (y \ 1)),z) = K(x,z) * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(14686(a,1),11188(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14686 11188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14690">
    <literal><![CDATA[
      K(x \ (x \ y),x * x) = K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6608,a(flip),b,14590,a),flip(a)].">
      <j1 rule="hyper" parents="64 6608 14590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14691">
    <literal><![CDATA[
      (((1 / x) \ K(x,y)) \ (1 / x)) * K(z,1 / (K(y,x) / x)) = T((1 / x) \ K(x,y),z) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(14597(a,1),8649(a,1,2,2))].">
      <j1 rule="para" parents="14597 8649"/>
    </justification>
  </clause>

  <clause id="14692">
    <literal><![CDATA[
      1 / (K(x,x \ 1) / x) = (x \ 1) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,816,a(flip),b,14598,a),flip(a)].">
      <j1 rule="hyper" parents="64 816 14598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14693">
    <literal><![CDATA[
      T(1 / (K(x,y) / x),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(14598(a,1),6446(a,1,1))].">
      <j1 rule="para" parents="14598 6446"/>
    </justification>
  </clause>

  <clause id="14694">
    <literal><![CDATA[
      K(x / (y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(14610(a,2),5824(a,1))].">
      <j1 rule="para" parents="14610 5824"/>
    </justification>
  </clause>

  <clause id="14695">
    <literal><![CDATA[
      ((x * y) / x) / z = K(x,y) * (y / z)
    ]]></literal>
    <justification jstring="[para(5721(a,2),14622(a,1,1))].">
      <j1 rule="para" parents="5721 14622"/>
    </justification>
  </clause>

  <clause id="14696">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) / z) = (y / x) / z
    ]]></literal>
    <justification jstring="[para(5774(a,1),14622(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5774 14622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14697">
    <literal><![CDATA[
      T(K(x,y) * (y / T(z,K(x,y))),z) = z \ (y * T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(14622(a,1),6921(a,1,1))].">
      <j1 rule="para" parents="14622 6921"/>
    </justification>
  </clause>

  <clause id="14698">
    <literal><![CDATA[
      x / T(x * (y * z),z \ (y \ 1)) = (x * (y * z)) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,14628,a(flip),b,6745,a(flip))].">
      <j1 rule="hyper" parents="225 14628 6745"/>
    </justification>
  </clause>

  <clause id="14699">
    <literal><![CDATA[
      ((x * y) \ z) / T(z,y \ (x \ 1)) = z \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(14628(a,1),4576(a,1,2))].">
      <j1 rule="para" parents="14628 4576"/>
    </justification>
  </clause>

  <clause id="14700">
    <literal><![CDATA[
      K(x \ (y * z),z) = K((x \ z) * y,z)
    ]]></literal>
    <justification jstring="[hyper(12051,a,14631,a),flip(a)].">
      <j1 rule="hyper" parents="12051 14631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14701">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),14631(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14702">
    <literal><![CDATA[
      K(x \ ((y / x) \ z),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),14633(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14703">
    <literal><![CDATA[
      T(x * y,z) / y = K(x * y,z) * x
    ]]></literal>
    <justification jstring="[hyper(35,a,5443,a,b,14643,a)].">
      <j1 rule="hyper" parents="35 5443 14643"/>
    </justification>
  </clause>

  <clause id="14704">
    <literal><![CDATA[
      (x \ y) * (K(y,z) * x) = T((x \ y) * x,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),14643(a,1,2,1,1))].">
      <j1 rule="para" parents="10 14643"/>
    </justification>
  </clause>

  <clause id="14706">
    <literal><![CDATA[
      K(x * K(y * x,z),T(u,y)) = K(y \ T(x * y,z),u)
    ]]></literal>
    <justification jstring="[para(14645(a,1),7917(a,1,1))].">
      <j1 rule="para" parents="14645 7917"/>
    </justification>
  </clause>

  <clause id="14707">
    <literal><![CDATA[
      (x * K(y,z)) * (y / x) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(12(a,1),14646(a,1,1,2,1))].">
      <j1 rule="para" parents="12 14646"/>
    </justification>
  </clause>

  <clause id="14708">
    <literal><![CDATA[
      (x \ (1 / x)) * K((x \ (1 / x)) * y,y) = y \ ((x \ 1) * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(139,a,1269,a(flip),b,14656,a),flip(a)].">
      <j1 rule="hyper" parents="139 1269 14656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14709">
    <literal><![CDATA[
      K(x,T(y,L(z,z,z))) * (1 / z) = L(z,z,z) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(822(a,1),14665(a,1,2))].">
      <j1 rule="para" parents="822 14665"/>
    </justification>
  </clause>

  <clause id="14710">
    <literal><![CDATA[
      R(x * K(y,x),x,x) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(41,a,6386,a,b,14667,a)].">
      <j1 rule="hyper" parents="41 6386 14667"/>
    </justification>
  </clause>

  <clause id="14711">
    <literal><![CDATA[
      K(x \ y,x * x) = K(x * y,x * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),14690(a,1,1,2))].">
      <j1 rule="para" parents="9 14690"/>
    </justification>
  </clause>

  <clause id="14712">
    <literal><![CDATA[
      (1 / (K(x,y) / x)) * y = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(145,a,14693,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 14693 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14713">
    <literal><![CDATA[
      (R(K(x,y) * (y / z),u,w) * z) * x = (z * x) * R((z * x) \ (x * y),u,w)
    ]]></literal>
    <justification jstring="[para(14695(a,1),2729(a,1,1,1,1))].">
      <j1 rule="para" parents="14695 2729"/>
    </justification>
  </clause>

  <clause id="14714">
    <literal><![CDATA[
      K((x \ y) * z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10497,a(flip),b,14700,a),flip(a)].">
      <j1 rule="hyper" parents="64 10497 14700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14715">
    <literal><![CDATA[
      K((1 / x) \ ((x * y) \ z),L(y,x,x \ 1)) = K(L(y,x,x \ 1) \ z,L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1641(a,1),14701(a,1,1,2,1))].">
      <j1 rule="para" parents="1641 14701"/>
    </justification>
  </clause>

  <clause id="14716">
    <literal><![CDATA[
      K((x * y) \ z,x * y) = K(y \ (x \ z),x * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),14702(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 14702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14717">
    <literal><![CDATA[
      K((x \ 1) \ ((y * x) \ z),R(y,x,x \ 1)) = K(R(y,x,x \ 1) \ z,R(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(494(a,1),14702(a,1,1,2,1))].">
      <j1 rule="para" parents="494 14702"/>
    </justification>
  </clause>

  <clause id="14718">
    <literal><![CDATA[
      (T(x,(x \ y) * z) \ y) * z = T((x \ y) * z,x)
    ]]></literal>
    <justification jstring="[hyper(6660,a,14703,a)].">
      <j1 rule="hyper" parents="6660 14703"/>
    </justification>
  </clause>

  <clause id="14719">
    <literal><![CDATA[
      (x \ y) * K(x * y,x * x) = T(x \ y,x * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,14711,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 14711 5726"/>
    </justification>
  </clause>

  <clause id="14720">
    <literal><![CDATA[
      (x \ y) * ((y * x) / (x \ y)) = (y * x) * K(x * y,x * x)
    ]]></literal>
    <justification jstring="[para(14711(a,1),14045(a,2,2))].">
      <j1 rule="para" parents="14711 14045"/>
    </justification>
  </clause>

  <clause id="14721">
    <literal><![CDATA[
      K((x / y) * z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(7742,a,14714,a)].">
      <j1 rule="hyper" parents="7742 14714"/>
    </justification>
  </clause>

  <clause id="14722">
    <literal><![CDATA[
      (x \ y) * K(x * (y \ z),x) = T(x,z * (y \ x)) \ y
    ]]></literal>
    <justification jstring="[para(14714(a,1),11241(a,1,2))].">
      <j1 rule="para" parents="14714 11241"/>
    </justification>
  </clause>

  <clause id="14723">
    <literal><![CDATA[
      K((x * y) * (T(x,y) \ z),x * y) = K(y * z,x * y)
    ]]></literal>
    <justification jstring="[para(214(a,1),14721(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="214 14721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14724">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ ((x * y) / x)) = z \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6412,a(flip),b,14381,a)].">
      <j1 rule="hyper" parents="64 6412 14381"/>
    </justification>
  </clause>

  <clause id="14725">
    <literal><![CDATA[
      L(x \ (T(y,z) \ z),x,K(T(y,z),z)) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(4632(a,1),14381(a,2,2))].">
      <j1 rule="para" parents="4632 14381"/>
    </justification>
  </clause>

  <clause id="14726">
    <literal><![CDATA[
      K(x,y) * (K(z,u) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / T(u,z) = w
    ]]></literal>
    <justification jstring="[para(5799(a,2),14446(a,1,2))].">
      <j1 rule="para" parents="5799 14446"/>
    </justification>
  </clause>

  <clause id="14727">
    <literal><![CDATA[
      (x \ y) \ K(y,y \ 1) = (x \ L(y,y,y)) \ 1
    ]]></literal>
    <justification jstring="[para(13233(a,1),14460(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13233 14460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14728">
    <literal><![CDATA[
      (L(x,y,z) \ u) \ K(x,x \ 1) = (L(R(x,x,x),y,z) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(13283(a,1),14460(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13283 14460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14729">
    <literal><![CDATA[
      K(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(6526(a,2),14474(a,1))].">
      <j1 rule="para" parents="6526 14474"/>
    </justification>
  </clause>

  <clause id="14730">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(u,z) / y) \ w) = v5
    ]]></literal>
    <justification jstring="[para(14592(a,1),14474(a,1,2,1))].">
      <j1 rule="para" parents="14592 14474"/>
    </justification>
  </clause>

  <clause id="14731">
    <literal><![CDATA[
      K(x,L((y * z) \ y,u,w) * z) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z * L((y * z) \ y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(3082(a,1),14477(a,1,2))].">
      <j1 rule="para" parents="3082 14477"/>
    </justification>
  </clause>

  <clause id="14732">
    <literal><![CDATA[
      T(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(5110(a,1),14487(a,1))].">
      <j1 rule="para" parents="5110 14487"/>
    </justification>
  </clause>

  <clause id="14733">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(6091(a,1),14487(a,1,2,1))].">
      <j1 rule="para" parents="6091 14487"/>
    </justification>
  </clause>

  <clause id="14734">
    <literal><![CDATA[
      (K(x,y) * z) \ K(u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      (z \ K(y,x)) * K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(14445(a,1),14503(a,1,1))].">
      <j1 rule="para" parents="14445 14503"/>
    </justification>
  </clause>

  <clause id="14735">
    <literal><![CDATA[
      (x * y) \ K(x,x * x) = (R(x,x,x) * y) \ 1
    ]]></literal>
    <justification jstring="[para(3686(a,1),14542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3686 14542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14736">
    <literal><![CDATA[
      (x * a(y,y,y)) \ 1 = x \ K(y,y * y)
    ]]></literal>
    <justification jstring="[para(11011(a,1),14542(a,1,1))].">
      <j1 rule="para" parents="11011 14542"/>
    </justification>
  </clause>

  <clause id="14737">
    <literal><![CDATA[
      K(x,y \ L(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6368,a(flip),b,14560,a),flip(a)].">
      <j1 rule="hyper" parents="373 6368 14560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14738">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(11304(a,2),14641(a,1))].">
      <j1 rule="para" parents="11304 14641"/>
    </justification>
  </clause>

  <clause id="14739">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((T(z,u) \ u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(13655(a,2),14641(a,1,2))].">
      <j1 rule="para" parents="13655 14641"/>
    </justification>
  </clause>

  <clause id="14740">
    <literal><![CDATA[
      L(x,y / x,z) \ (z * y) = T(z * (y / x),x)
    ]]></literal>
    <justification jstring="[para(12(a,1),14658(a,1,2,2))].">
      <j1 rule="para" parents="12 14658"/>
    </justification>
  </clause>

  <clause id="14741">
    <literal><![CDATA[
      (x * (y * z)) / T(x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(14658(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14658 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14742">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,y,z) \ (z * L(y,x,x)) = T(z * y,a(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(5668(a,1),14658(a,1,2,2))].">
      <j1 rule="para" parents="5668 14658"/>
    </justification>
  </clause>

  <clause id="14743">
    <literal><![CDATA[
      L(x,y * K(x,y),z) \ (z * (x * y)) = T(z * (y * K(x,y)),x)
    ]]></literal>
    <justification jstring="[para(5722(a,1),14658(a,1,2,2))].">
      <j1 rule="para" parents="5722 14658"/>
    </justification>
  </clause>

  <clause id="14744">
    <literal><![CDATA[
      (x * (y * z)) * K(z,x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,14659,a,b,6312,a),flip(a)].">
      <j1 rule="hyper" parents="144 14659 6312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14745">
    <literal><![CDATA[
      (x * y) / T(x * z,z \ y) = L(z \ y,z,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),14659(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 14659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14747">
    <literal><![CDATA[
      (x * ((a(y,y,x) \ 1) * z)) / T(L(x,y,y),z) = L(z,a(y,y,x) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5668(a,1),14659(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5668 14659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14748">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) * (y * z)) / T(L(y,x,x),z) = L(z,y,a(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(5669(a,1),14659(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5669 14659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14750">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * K(z,T(u,y)),y) = L(y,K(z,T(u,y)),x)
    ]]></literal>
    <justification jstring="[para(8193(a,1),14659(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8193 14659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14751">
    <literal><![CDATA[
      L(x,y,z) * (x \ (z * y)) = (z * (y * x)) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,14660,a(flip),b,12217,a),flip(a)].">
      <j1 rule="hyper" parents="142 14660 12217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14753">
    <literal><![CDATA[
      L(K(x,y),z / y,u) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(6245(a,1),14660(a,2,2))].">
      <j1 rule="para" parents="6245 14660"/>
    </justification>
  </clause>

  <clause id="14754">
    <literal><![CDATA[
      K((1 / x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(5253(a,2),14674(a,1))].">
      <j1 rule="para" parents="5253 14674"/>
    </justification>
  </clause>

  <clause id="14755">
    <literal><![CDATA[
      K((x \ K(y,z)) * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(14527(a,2),14674(a,1,1))].">
      <j1 rule="para" parents="14527 14674"/>
    </justification>
  </clause>

  <clause id="14756">
    <literal><![CDATA[
      K(x / (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(5255(a,2),14694(a,1))].">
      <j1 rule="para" parents="5255 14694"/>
    </justification>
  </clause>

  <clause id="14757">
    <literal><![CDATA[
      R(T(x * K(y,x),z),x,x) = T((x \ 1) \ K(y,x),z)
    ]]></literal>
    <justification jstring="[para(14710(a,1),27(a,2,1))].">
      <j1 rule="para" parents="14710 27"/>
    </justification>
  </clause>

  <clause id="14758">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ K(z,y)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(14445(a,1),14729(a,1,2,1))].">
      <j1 rule="para" parents="14445 14729"/>
    </justification>
  </clause>

  <clause id="14759">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14428(a,2),14732(a,1))].">
      <j1 rule="para" parents="14428 14732"/>
    </justification>
  </clause>

  <clause id="14760">
    <literal><![CDATA[
      (x \ (x / y)) \ K(y,y * y) = L(1 / y,y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(13223(a,1),14736(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13223 14736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14761">
    <literal><![CDATA[
      K((x * x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (x \ y),z) = u
    ]]></literal>
    <justification jstring="[para(536(a,1),14754(a,1,1))].">
      <j1 rule="para" parents="536 14754"/>
    </justification>
  </clause>

  <clause id="14762">
    <literal><![CDATA[
      K(x / (K(y,z) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * (u \ K(z,y)),w) = v5
    ]]></literal>
    <justification jstring="[para(14445(a,1),14756(a,1,1,2))].">
      <j1 rule="para" parents="14445 14756"/>
    </justification>
  </clause>

  <clause id="14763">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(14687(a,1),14756(a,1))].">
      <j1 rule="para" parents="14687 14756"/>
    </justification>
  </clause>

  <clause id="14764">
    <literal><![CDATA[
      K((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(5254(a,2),14763(a,1))].">
      <j1 rule="para" parents="5254 14763"/>
    </justification>
  </clause>

  <clause id="14765">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((z \ K(y,x)) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(14445(a,1),14764(a,1,1,1))].">
      <j1 rule="para" parents="14445 14764"/>
    </justification>
  </clause>

  <clause id="14766">
    <literal><![CDATA[
      (x / (x / (y \ 1))) * T(y,y \ 1) = K((y \ 1) \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,5723,a,b,14394,a)].">
      <j1 rule="hyper" parents="144 5723 14394"/>
    </justification>
  </clause>

  <clause id="14767">
    <literal><![CDATA[
      T(K(x,y) * (z \ 1),z) = T(z,z \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(14394(a,1),3878(a,1,1))].">
      <j1 rule="para" parents="14394 3878"/>
    </justification>
  </clause>

  <clause id="14768">
    <literal><![CDATA[
      K(x,T(y,z)) / z = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12616,a(flip),b,14396,a)].">
      <j1 rule="hyper" parents="64 12616 14396"/>
    </justification>
  </clause>

  <clause id="14769">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(y,T(z,x)) / T(x,u)
    ]]></literal>
    <justification jstring="[para(14396(a,1),12617(a,1,1))].">
      <j1 rule="para" parents="14396 12617"/>
    </justification>
  </clause>

  <clause id="14770">
    <literal><![CDATA[
      K(x,y * ((1 / z) * K(u,w))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(14396(a,1),13344(a,1,2,2))].">
      <j1 rule="para" parents="14396 13344"/>
    </justification>
  </clause>

  <clause id="14771">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = (1 / x) * K(z,y)
    ]]></literal>
    <justification jstring="[para(14507(a,2),14396(a,1,1))].">
      <j1 rule="para" parents="14507 14396"/>
    </justification>
  </clause>

  <clause id="14772">
    <literal><![CDATA[
      (1 / x) * K(y,z / x) = K(y,x \ z) / x
    ]]></literal>
    <justification jstring="[para(117(a,1),14768(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="117 14768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14773">
    <literal><![CDATA[
      (x * K(y,z)) / a(x / (1 / u),1 / u,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(14768(a,2),955(a,2,2))].">
      <j1 rule="para" parents="14768 955"/>
    </justification>
  </clause>

  <clause id="14774">
    <literal><![CDATA[
      (1 / x) * K(y / x,z) = K(x \ y,z) / x
    ]]></literal>
    <justification jstring="[para(7917(a,1),14768(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7917 14768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14775">
    <literal><![CDATA[
      (K(x,y) / z) * K(y,x) = 1 / T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,9045,a,b,14397,a),flip(a)].">
      <j1 rule="hyper" parents="373 9045 14397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14776">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(14405(a,1),672(a,1))].">
      <j1 rule="para" parents="14405 672"/>
    </justification>
  </clause>

  <clause id="14779">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(675(a,1),14776(a,1,2))].">
      <j1 rule="para" parents="675 14776"/>
    </justification>
  </clause>

  <clause id="14780">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(779(a,1),14776(a,1,2))].">
      <j1 rule="para" parents="779 14776"/>
    </justification>
  </clause>

  <clause id="14781">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(14092(a,1),14776(a,1))].">
      <j1 rule="para" parents="14092 14776"/>
    </justification>
  </clause>

  <clause id="14782">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(1636(a,1),14781(a,1,2))].">
      <j1 rule="para" parents="1636 14781"/>
    </justification>
  </clause>

  <clause id="14783">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ 1,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(11936(a,1),14782(a,1,2))].">
      <j1 rule="para" parents="11936 14782"/>
    </justification>
  </clause>

  <clause id="14784">
    <literal><![CDATA[
      K(L(x,y \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(12093(a,2),14782(a,1))].">
      <j1 rule="para" parents="12093 14782"/>
    </justification>
  </clause>

  <clause id="14785">
    <literal><![CDATA[
      K(K(x,y \ 1) * (y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y \ 1,x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(11936(a,1),14784(a,1,1))].">
      <j1 rule="para" parents="11936 14784"/>
    </justification>
  </clause>

  <clause id="14786">
    <literal><![CDATA[
      K(x,y * (K(z,y) * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * K(z,y)) / u) = w
    ]]></literal>
    <justification jstring="[para(4442(a,1),14779(a,1,2))].">
      <j1 rule="para" parents="4442 14779"/>
    </justification>
  </clause>

  <clause id="14787">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(5783(a,1),14779(a,1,2,2))].">
      <j1 rule="para" parents="5783 14779"/>
    </justification>
  </clause>

  <clause id="14788">
    <literal><![CDATA[
      K(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(6519(a,2),14779(a,1))].">
      <j1 rule="para" parents="6519 14779"/>
    </justification>
  </clause>

  <clause id="14789">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ K(z,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (T(z,w) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(14452(a,1),14779(a,1,2,2))].">
      <j1 rule="para" parents="14452 14779"/>
    </justification>
  </clause>

  <clause id="14790">
    <literal><![CDATA[
      K(x,y * (K(z,u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (w * K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(14507(a,1),14788(a,1,2,2))].">
      <j1 rule="para" parents="14507 14788"/>
    </justification>
  </clause>

  <clause id="14793">
    <literal><![CDATA[
      L(T((x \ 1) \ 1,y) * K(z,T(x * 1,y)),x,x \ z) = ((z / x) * ((1 / x) \ T(x,y))) / z
    ]]></literal>
    <justification jstring="[para(14420(a,1),11101(a,1,1,2))].">
      <j1 rule="para" parents="14420 11101"/>
    </justification>
  </clause>

  <clause id="14794">
    <literal><![CDATA[
      T(x,(y / z) * ((y / z) * (z * u))) = T(x,(((y / z) \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[para(1548(a,1),14429(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1548 14429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14795">
    <literal><![CDATA[
      T((x * y) * (1 / x),K(z,y)) = (x * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(9(a,1),14476(a,1,2,2))].">
      <j1 rule="para" parents="9 14476"/>
    </justification>
  </clause>

  <clause id="14796">
    <literal><![CDATA[
      T(x,y \ T(z,y \ 1)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,14545,a(flip),b,14483,a),flip(a)].">
      <j1 rule="hyper" parents="373 14545 14483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14797">
    <literal><![CDATA[
      T(T(x,y * x) * K(L(x,y,x) * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(4694(a,1),14496(a,1,1,2,1))].">
      <j1 rule="para" parents="4694 14496"/>
    </justification>
  </clause>

  <clause id="14798">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = y \ T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(11180(a,1),14496(a,1,1,2))].">
      <j1 rule="para" parents="11180 14496"/>
    </justification>
  </clause>

  <clause id="14799">
    <literal><![CDATA[
      T(x,y) \ K(x \ 1,T(z,y)) = T(x \ K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8066,a(flip),b,14516,a),flip(a)].">
      <j1 rule="hyper" parents="64 8066 14516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14800">
    <literal><![CDATA[
      (x \ K(x \ y,y)) * y = T((x \ 1) * y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6814,a(flip),b,14528,a),flip(a)].">
      <j1 rule="hyper" parents="64 6814 14528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14801">
    <literal><![CDATA[
      T(T(x \ K(y,z),u),K(y,z)) = T(K(y,z) * (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(14535(a,1),8159(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14535 8159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14802">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(14586(a,2),11217(a,1))].">
      <j1 rule="para" parents="14586 11217"/>
    </justification>
  </clause>

  <clause id="14803">
    <literal><![CDATA[
      K(x,y) / T(T(x,z),y) = 1 / T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(8328(a,1),14601(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8328 14601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14804">
    <literal><![CDATA[
      T(x * K(y,x),y \ 1) = T(x,y \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,14546,a(flip),b,14606,a),flip(a)].">
      <j1 rule="hyper" parents="373 14546 14606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14805">
    <literal><![CDATA[
      (x * (y * (x \ 1))) / R(y,y * (x * (y * (x \ 1))),y) = y \ (x * (y * (x \ 1)))
    ]]></literal>
    <justification jstring="[para(14619(a,1),13735(a,1,1))].">
      <j1 rule="para" parents="14619 13735"/>
    </justification>
  </clause>

  <clause id="14806">
    <literal><![CDATA[
      K(x,T(y / (K(z,u) * w),v5)) = K(x,T(y * (w \ K(u,z)),v5))
    ]]></literal>
    <justification jstring="[para(14445(a,1),14621(a,1,2,1,2))].">
      <j1 rule="para" parents="14445 14621"/>
    </justification>
  </clause>

  <clause id="14807">
    <literal><![CDATA[
      K(x,L(T(1 / y,(K(z,u) / y) \ z) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(14623(a,1),12134(a,2,2,1))].">
      <j1 rule="para" parents="14623 12134"/>
    </justification>
  </clause>

  <clause id="14808">
    <literal><![CDATA[
      K(x,y) * (x \ K(z,x)) = T(x,z) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5938,a(flip),b,14664,a)].">
      <j1 rule="hyper" parents="64 5938 14664"/>
    </justification>
  </clause>

  <clause id="14809">
    <literal><![CDATA[
      (((x \ y) * (y \ x)) \ 1) * (((x \ y) \ 1) \ 1) = (((y \ x) * (x \ y)) \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[para(3799(a,1),14669(a,1,2))].">
      <j1 rule="para" parents="3799 14669"/>
    </justification>
  </clause>

  <clause id="14810">
    <literal><![CDATA[
      1 / (x / (x * x)) = (x \ 1) * (x * x)
    ]]></literal>
    <justification jstring="[para(1729(a,1),14692(a,1,2))].">
      <j1 rule="para" parents="1729 14692"/>
    </justification>
  </clause>

  <clause id="14811">
    <literal><![CDATA[
      R(((x \ 1) * (x * x)) * K(x / (x * x),y),x / (x * x),y) = (1 * y) / (y * (x / (x * x)))
    ]]></literal>
    <justification jstring="[para(14810(a,1),10305(a,1,1,1))].">
      <j1 rule="para" parents="14810 10305"/>
    </justification>
  </clause>

  <clause id="14813">
    <literal><![CDATA[
      (x / y) \ ((x / y) / z) = (y \ x) \ ((y \ x) / z)
    ]]></literal>
    <justification jstring="[hyper(139,a,14696,a(flip),b,6062,a)].">
      <j1 rule="hyper" parents="139 14696 6062"/>
    </justification>
  </clause>

  <clause id="14814">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(149,a,14704,a)].">
      <j1 rule="hyper" parents="149 14704"/>
    </justification>
  </clause>

  <clause id="14815">
    <literal><![CDATA[
      K(x,y * ((((K(z,u) / z) \ 1) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(14712(a,1),6636(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14712 6636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14816">
    <literal><![CDATA[
      T(x,y) \ (1 / T(x,T(z,y))) = x \ (1 / T(T(x,z),y))
    ]]></literal>
    <justification jstring="[para(14803(a,1),14392(a,1,2))].">
      <j1 rule="para" parents="14803 14392"/>
    </justification>
  </clause>

  <clause id="14817">
    <literal><![CDATA[
      T(x \ y,x \ (x \ 1)) = T(y / x,x \ 1)
    ]]></literal>
    <justification jstring="[para(5774(a,1),14804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5774 14804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14818">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) \ ((x * y) / x)) = (x \ y) / T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(14804(a,1),10118(a,2,2))].">
      <j1 rule="para" parents="14804 10118"/>
    </justification>
  </clause>

  <clause id="14819">
    <literal><![CDATA[
      T(x,y) / (z \ x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,5435,a(flip),b,14814,a)].">
      <j1 rule="hyper" parents="64 5435 14814"/>
    </justification>
  </clause>

  <clause id="14820">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,14814,a(flip),b,5435,a(flip))].">
      <j1 rule="hyper" parents="144 14814 5435"/>
    </justification>
  </clause>

  <clause id="14821">
    <literal><![CDATA[
      a(T((x \ y) * x,z),u,T((x \ y) * x,z)) \ (K(y,z) * x) = (x \ y) \ L(T((x \ y) * x,z),u,T((x \ y) * x,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,14814,a(flip),b,13232,a)].">
      <j1 rule="hyper" parents="139 14814 13232"/>
    </justification>
  </clause>

  <clause id="14822">
    <literal><![CDATA[
      (T(x,y) \ z) * ((x \ z) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(6660,a,14819,a)].">
      <j1 rule="hyper" parents="6660 14819"/>
    </justification>
  </clause>

  <clause id="14824">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) = z \ x
    ]]></literal>
    <justification jstring="[hyper(215,a,14819,a)].">
      <j1 rule="hyper" parents="215 14819"/>
    </justification>
  </clause>

  <clause id="14825">
    <literal><![CDATA[
      K(x,y) * (x / z) = T(x,y) / z
    ]]></literal>
    <justification jstring="[para(82(a,1),14819(a,1,2)),flip(a)].">
      <j1 rule="para" parents="82 14819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14826">
    <literal><![CDATA[
      K(x * y,z) * (y * K(x,y)) = T(x * y,z) / x
    ]]></literal>
    <justification jstring="[para(5859(a,1),14819(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5859 14819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14827">
    <literal><![CDATA[
      K(x,y) * (z * K(z \ x,z)) = T(x,y) / (x / z)
    ]]></literal>
    <justification jstring="[para(6148(a,1),14819(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6148 14819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14828">
    <literal><![CDATA[
      K(x,y) * (L(x,z,u) \ x) = L(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,14820,a(flip),b,4867,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 14820 4867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14829">
    <literal><![CDATA[
      a(T(T(x,y),K(x,y) * z),u,w) = a((z \ x) * (K(x,y) * z),u,w)
    ]]></literal>
    <justification jstring="[para(14820(a,1),13107(a,1,1,1))].">
      <j1 rule="para" parents="14820 13107"/>
    </justification>
  </clause>

  <clause id="14830">
    <literal><![CDATA[
      a(x,y,T(T(z,u),K(z,u) * w)) = a(x,y,(w \ z) * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[para(14820(a,1),13869(a,1,3,1))].">
      <j1 rule="para" parents="14820 13869"/>
    </justification>
  </clause>

  <clause id="14831">
    <literal><![CDATA[
      (T(x,y) * z) \ T(x,y) = (x * z) \ x
    ]]></literal>
    <justification jstring="[para(5755(a,1),14824(a,1,1))].">
      <j1 rule="para" parents="5755 14824"/>
    </justification>
  </clause>

  <clause id="14832">
    <literal><![CDATA[
      (K(x,y) \ z) \ T(y,x) = z \ y
    ]]></literal>
    <justification jstring="[para(6156(a,2),14824(a,1,1))].">
      <j1 rule="para" parents="6156 14824"/>
    </justification>
  </clause>

  <clause id="14833">
    <literal><![CDATA[
      (K(x,y) * z) \ y = z \ T(y,x)
    ]]></literal>
    <justification jstring="[para(6161(a,1),14824(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6161 14824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14834">
    <literal><![CDATA[
      (T(x,y) * z) \ y = (x * z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5811(a,1),14824(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5811 14824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14835">
    <literal><![CDATA[
      ((x / y) * z) \ T(y,y \ x) = ((y \ x) * z) \ y
    ]]></literal>
    <justification jstring="[para(5982(a,1),14824(a,1,1))].">
      <j1 rule="para" parents="5982 14824"/>
    </justification>
  </clause>

  <clause id="14836">
    <literal><![CDATA[
      (((x \ y) \ y) * z) \ T(x,x \ y) = (x * z) \ x
    ]]></literal>
    <justification jstring="[para(6025(a,1),14824(a,1,1))].">
      <j1 rule="para" parents="6025 14824"/>
    </justification>
  </clause>

  <clause id="14837">
    <literal><![CDATA[
      ((x / T(y,x)) * z) \ T(x,y) = ((x / y) * z) \ x
    ]]></literal>
    <justification jstring="[para(13022(a,1),14824(a,1,1))].">
      <j1 rule="para" parents="13022 14824"/>
    </justification>
  </clause>

  <clause id="14838">
    <literal><![CDATA[
      R(x,y,z \ T(K(u,w) * v5,T(u,w))) = R(x,y,z \ ((v5 \ u) \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(14824(a,1),13907(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="14824 13907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14839">
    <literal><![CDATA[
      (K(x,y) / z) \ T(x,y) = (1 / z) \ x
    ]]></literal>
    <justification jstring="[para(14366(a,1),14824(a,1,1))].">
      <j1 rule="para" parents="14366 14824"/>
    </justification>
  </clause>

  <clause id="14840">
    <literal><![CDATA[
      (K(x,y) / z) \ y = (1 / z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(14383(a,1),14824(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14383 14824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14841">
    <literal><![CDATA[
      K(x,y) \ (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(6206,a,14825,a)].">
      <j1 rule="hyper" parents="6206 14825"/>
    </justification>
  </clause>

  <clause id="14842">
    <literal><![CDATA[
      K(x,y) * (T(y,x) / z) = y / z
    ]]></literal>
    <justification jstring="[hyper(6187,a,14825,a)].">
      <j1 rule="hyper" parents="6187 14825"/>
    </justification>
  </clause>

  <clause id="14844">
    <literal><![CDATA[
      T(x,y) * (x / z) = x * (T(x,y) / z)
    ]]></literal>
    <justification jstring="[hyper(145,a,14825,a(flip),b,6071,a),flip(a)].">
      <j1 rule="hyper" parents="145 14825 6071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14845">
    <literal><![CDATA[
      (x / y) \ (T(x,z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,14825,a(flip),b,11174,a)].">
      <j1 rule="hyper" parents="139 14825 11174"/>
    </justification>
  </clause>

  <clause id="14846">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / z) = x \ (x / z)
    ]]></literal>
    <justification jstring="[hyper(139,a,14825,a(flip),b,5778,a)].">
      <j1 rule="hyper" parents="139 14825 5778"/>
    </justification>
  </clause>

  <clause id="14847">
    <literal><![CDATA[
      ((x \ y) \ y) / z = K(x,x \ y) * (x / z)
    ]]></literal>
    <justification jstring="[para(116(a,1),14825(a,2,1)),flip(a)].">
      <j1 rule="para" parents="116 14825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14848">
    <literal><![CDATA[
      T(T(x,y) / z,K(x,y)) = (x / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(14825(a,1),7785(a,1,1))].">
      <j1 rule="para" parents="14825 7785"/>
    </justification>
  </clause>

  <clause id="14849">
    <literal><![CDATA[
      (T(x,y) / z) \ K(K(x,y),x / z) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(14825(a,1),10852(a,1,1))].">
      <j1 rule="para" parents="14825 10852"/>
    </justification>
  </clause>

  <clause id="14850">
    <literal><![CDATA[
      T(x,K(y,z) \ (z / u)) = T(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(14825(a,1),13676(a,2,2))].">
      <j1 rule="para" parents="14825 13676"/>
    </justification>
  </clause>

  <clause id="14851">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,y) = (x / z) \ 1
    ]]></literal>
    <justification jstring="[para(14825(a,1),14403(a,1,1))].">
      <j1 rule="para" parents="14825 14403"/>
    </justification>
  </clause>

  <clause id="14852">
    <literal><![CDATA[
      (T(x,y) / z) \ 1 = (x / z) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(14825(a,1),14450(a,1,1))].">
      <j1 rule="para" parents="14825 14450"/>
    </justification>
  </clause>

  <clause id="14853">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(225,a,14832,a(flip),b,13152,a(flip))].">
      <j1 rule="hyper" parents="225 14832 13152"/>
    </justification>
  </clause>

  <clause id="14854">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (T(K(x,y),z) * z) \ y
    ]]></literal>
    <justification jstring="[para(4453(a,1),14832(a,1,1))].">
      <j1 rule="para" parents="4453 14832"/>
    </justification>
  </clause>

  <clause id="14855">
    <literal><![CDATA[
      T(x \ T(y,z),(K(z,y) * x) \ y) = (K(z,y) * x) \ y
    ]]></literal>
    <justification jstring="[hyper(504,a,xx,b,14833,a)].">
      <j1 rule="hyper" parents="504 14833"/>
    </justification>
  </clause>

  <clause id="14856">
    <literal><![CDATA[
      x / (y \ T(x,z)) = K(z,x) * y
    ]]></literal>
    <justification jstring="[hyper(226,a,14833,a)].">
      <j1 rule="hyper" parents="226 14833"/>
    </justification>
  </clause>

  <clause id="14858">
    <literal><![CDATA[
      (x \ (y \ x)) \ T(y \ 1,x) = ((y \ x) / x) \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(6241(a,1),14833(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6241 14833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14859">
    <literal><![CDATA[
      ((x \ y) \ z) \ T(x,y / x) = ((y / x) \ z) \ x
    ]]></literal>
    <justification jstring="[para(6283(a,1),14833(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6283 14833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14860">
    <literal><![CDATA[
      T((x \ T(y,z)) \ T(y,x),y) = ((K(z,y) * x) \ y) \ y
    ]]></literal>
    <justification jstring="[para(14833(a,1),8500(a,1,1,1))].">
      <j1 rule="para" parents="14833 8500"/>
    </justification>
  </clause>

  <clause id="14861">
    <literal><![CDATA[
      (x * K(y * x,z)) \ z = x \ T(z,x * y)
    ]]></literal>
    <justification jstring="[para(11188(a,1),14833(a,1,1))].">
      <j1 rule="para" parents="11188 14833"/>
    </justification>
  </clause>

  <clause id="14862">
    <literal><![CDATA[
      (((x * y) \ y) * z) \ T(y,x) = (((y * x) \ y) * z) \ y
    ]]></literal>
    <justification jstring="[para(11827(a,1),14833(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11827 14833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14863">
    <literal><![CDATA[
      K(x,T(y,z)) \ ((z * (y / z)) / u) = T(z * (y / z),x) / u
    ]]></literal>
    <justification jstring="[para(11133(a,1),14841(a,1,1))].">
      <j1 rule="para" parents="11133 14841"/>
    </justification>
  </clause>

  <clause id="14864">
    <literal><![CDATA[
      K(x \ y,x) * (((x \ y) \ y) / z) = x / z
    ]]></literal>
    <justification jstring="[para(116(a,1),14842(a,1,2,1))].">
      <j1 rule="para" parents="116 14842"/>
    </justification>
  </clause>

  <clause id="14865">
    <literal><![CDATA[
      K(x,y) * (x / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(14842(a,1),6188(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14842 6188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14866">
    <literal><![CDATA[
      K(x,(T(y,x) / z) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(14842(a,1),9672(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14842 9672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14868">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) \ K(y,T(z,x)) = (x \ u) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,7867,a,b,14822,a)].">
      <j1 rule="hyper" parents="139 7867 14822"/>
    </justification>
  </clause>

  <clause id="14870">
    <literal><![CDATA[
      L(x \ 1,x,T(y,z)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(472,a,14831,a)].">
      <j1 rule="hyper" parents="472 14831"/>
    </justification>
  </clause>

  <clause id="14871">
    <literal><![CDATA[
      L(x \ 1,x,y) = (T(y,z) * x) \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,241,a,b,14831,a)].">
      <j1 rule="hyper" parents="373 241 14831"/>
    </justification>
  </clause>

  <clause id="14872">
    <literal><![CDATA[
      (x * T(x,y)) \ x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(338,a,14831,a),flip(a)].">
      <j1 rule="hyper" parents="338 14831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14873">
    <literal><![CDATA[
      K(x,(((y * z) \ y) \ T(y,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,u) * z,T(y,u)) * w) = v5
    ]]></literal>
    <justification jstring="[para(14831(a,1),13526(a,1,2,1,1))].">
      <j1 rule="para" parents="14831 13526"/>
    </justification>
  </clause>

  <clause id="14874">
    <literal><![CDATA[
      (x * T(1 / x,y)) \ x = 1 / T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,885,a(flip),b,14872,a)].">
      <j1 rule="hyper" parents="64 885 14872"/>
    </justification>
  </clause>

  <clause id="14875">
    <literal><![CDATA[
      L(x \ 1,x,T(y,z)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,241,a,b,14870,a),flip(a)].">
      <j1 rule="hyper" parents="373 241 14870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14876">
    <literal><![CDATA[
      L(x \ 1,x,y \ z) = ((z / y) * x) \ (z / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12992,a(flip),b,14870,a)].">
      <j1 rule="hyper" parents="64 12992 14870"/>
    </justification>
  </clause>

  <clause id="14877">
    <literal><![CDATA[
      (x * ((x * y) / x)) \ y = (x * y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4450(a,1),14834(a,1,1))].">
      <j1 rule="para" parents="4450 14834"/>
    </justification>
  </clause>

  <clause id="14878">
    <literal><![CDATA[
      ((x \ (y \ x)) \ 1) \ T(y,y \ 1) = (1 / (x \ (y \ x))) \ y
    ]]></literal>
    <justification jstring="[para(7298(a,1),14839(a,1,1))].">
      <j1 rule="para" parents="7298 14839"/>
    </justification>
  </clause>

  <clause id="14879">
    <literal><![CDATA[
      (1 / (x \ y)) \ T(x,x \ y) = (1 / (y / x)) \ x
    ]]></literal>
    <justification jstring="[para(6450(a,1),14840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6450 14840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14880">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x / z,(x / z) \ (T(x,y) / z)) = (K(x,T(y,z)) * (x / z)) \ 1
    ]]></literal>
    <justification jstring="[para(14845(a,1),10865(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14845 10865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14882">
    <literal><![CDATA[
      T(x,y) \ R(1 / y,y,x) = x \ (x / (x * y))
    ]]></literal>
    <justification jstring="[para(4718(a,1),14846(a,1,2))].">
      <j1 rule="para" parents="4718 14846"/>
    </justification>
  </clause>

  <clause id="14883">
    <literal><![CDATA[
      T(x,(y / z) \ K(u,y)) = T(x,z / T(y,u))
    ]]></literal>
    <justification jstring="[para(14852(a,1),4818(a,1,2))].">
      <j1 rule="para" parents="14852 4818"/>
    </justification>
  </clause>

  <clause id="14884">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,6156,a(flip),b,14853,a),flip(a)].">
      <j1 rule="hyper" parents="373 6156 14853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14885">
    <literal><![CDATA[
      (K(x,y) * z) \ (x * y) = z \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(215,a,14884,a)].">
      <j1 rule="hyper" parents="215 14884"/>
    </justification>
  </clause>

  <clause id="14886">
    <literal><![CDATA[
      ((x \ y) * x) / (z \ y) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(10(a,1),14884(a,1,2,2))].">
      <j1 rule="para" parents="10 14884"/>
    </justification>
  </clause>

  <clause id="14887">
    <literal><![CDATA[
      K(x,y) * ((y * x) / z) = (x * y) / z
    ]]></literal>
    <justification jstring="[para(82(a,1),14884(a,1,2)),flip(a)].">
      <j1 rule="para" parents="82 14884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14888">
    <literal><![CDATA[
      K(x \ y,x) * (y / z) = ((x \ y) * x) / z
    ]]></literal>
    <justification jstring="[para(343(a,1),14884(a,1,2)),flip(a)].">
      <j1 rule="para" parents="343 14884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14889">
    <literal><![CDATA[
      K(x,y) * ((y / z) * (z * x)) = (x * y) / a(y / z,z,x)
    ]]></literal>
    <justification jstring="[para(93(a,1),14884(a,1,2)),flip(a)].">
      <j1 rule="para" parents="93 14884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14890">
    <literal><![CDATA[
      ((x * y) * z) / T(z * x,y) = K(x * y,z) * L(y,x,z)
    ]]></literal>
    <justification jstring="[para(14658(a,1),14884(a,1,2))].">
      <j1 rule="para" parents="14658 14884"/>
    </justification>
  </clause>

  <clause id="14891">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * (y * x)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(40,a,4988,a(flip),b,14885,a),flip(a)].">
      <j1 rule="hyper" parents="40 4988 14885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14892">
    <literal><![CDATA[
      (T(x,y) \ z) \ (y * x) = (x \ z) \ (x * y)
    ]]></literal>
    <justification jstring="[para(6075(a,1),14885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6075 14885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14893">
    <literal><![CDATA[
      (((x * y) / x) * z) \ (x * y) = (y * z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(5729(a,1),14885(a,1,1))].">
      <j1 rule="para" parents="5729 14885"/>
    </justification>
  </clause>

  <clause id="14894">
    <literal><![CDATA[
      ((x * y) * (x \ 1)) \ (x * y) = R(y,x,x \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(10859(a,1),14885(a,1,1))].">
      <j1 rule="para" parents="10859 14885"/>
    </justification>
  </clause>

  <clause id="14895">
    <literal><![CDATA[
      (T(x,y) / z) \ (x * y) = (x / z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(14825(a,1),14885(a,1,1))].">
      <j1 rule="para" parents="14825 14885"/>
    </justification>
  </clause>

  <clause id="14896">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / z) = x \ ((y * x) / z)
    ]]></literal>
    <justification jstring="[hyper(139,a,14887,a(flip),b,5810,a),flip(a)].">
      <j1 rule="hyper" parents="139 14887 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14897">
    <literal><![CDATA[
      ((x * y) / z) \ K(x,y) = ((y * x) / z) \ 1
    ]]></literal>
    <justification jstring="[para(14887(a,1),14403(a,1,1))].">
      <j1 rule="para" parents="14887 14403"/>
    </justification>
  </clause>

  <clause id="14898">
    <literal><![CDATA[
      ((x * y) / z) \ T(x,y) = ((y * x) / z) \ x
    ]]></literal>
    <justification jstring="[para(14887(a,1),14824(a,1,1))].">
      <j1 rule="para" parents="14887 14824"/>
    </justification>
  </clause>

  <clause id="14899">
    <literal><![CDATA[
      K(x * y,z) * T(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,z) / T(y,x) = u
    ]]></literal>
    <justification jstring="[para(4649(a,1),14865(a,1,2))].">
      <j1 rule="para" parents="4649 14865"/>
    </justification>
  </clause>

  <clause id="14900">
    <literal><![CDATA[
      (x * T(T(x,y),z)) \ T(T(x,y),z) = L(x \ 1,x,T(x,y))
    ]]></literal>
    <justification jstring="[para(306(a,1),14871(a,2,1)),flip(a)].">
      <j1 rule="para" parents="306 14871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14901">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ y) / z) = (y / x) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(145,a,14847,a,b,6442,a)].">
      <j1 rule="hyper" parents="145 14847 6442"/>
    </justification>
  </clause>

  <clause id="14902">
    <literal><![CDATA[
      T(x,K(y,T(y,z) \ z) \ ((T(y,z) \ z) / u)) = T(x,(((y \ T(z,y)) \ z) \ z) / u)
    ]]></literal>
    <justification jstring="[para(8333(a,2),14850(a,2,2,1))].">
      <j1 rule="para" parents="8333 14850"/>
    </justification>
  </clause>

  <clause id="14903">
    <literal><![CDATA[
      ((x \ y) \ y) \ (((x \ y) \ y) / z) = x \ (x / z)
    ]]></literal>
    <justification jstring="[para(14864(a,1),6291(a,2,2))].">
      <j1 rule="para" parents="14864 6291"/>
    </justification>
  </clause>

  <clause id="14904">
    <literal><![CDATA[
      K(x,(T(T(y,x),z) / u) * w) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[para(23(a,1),14866(a,1,2,1,1))].">
      <j1 rule="para" parents="23 14866"/>
    </justification>
  </clause>

  <clause id="14905">
    <literal><![CDATA[
      T(x,(y \ z) / T(z,u)) = T(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),14883(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 14883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14906">
    <literal><![CDATA[
      (x \ T(y,x)) \ (y * x) = (x \ y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(4632(a,1),14892(a,1,1))].">
      <j1 rule="para" parents="4632 14892"/>
    </justification>
  </clause>

  <clause id="14907">
    <literal><![CDATA[
      T(x,y * y) \ (x * L(y,y,x)) = x \ (((y * y) * x) / y)
    ]]></literal>
    <justification jstring="[para(2849(a,1),14896(a,1,2))].">
      <j1 rule="para" parents="2849 14896"/>
    </justification>
  </clause>

  <clause id="14908">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ T(K(y,z),x)) \ w) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(14897(a,1),8806(a,2,2,1))].">
      <j1 rule="para" parents="14897 8806"/>
    </justification>
  </clause>

  <clause id="14909">
    <literal><![CDATA[
      ((x * T(y,x)) / z) \ T(x,T(y,x)) = ((y * ((y * x) / y)) / z) \ x
    ]]></literal>
    <justification jstring="[para(4450(a,1),14898(a,2,1,1))].">
      <j1 rule="para" parents="4450 14898"/>
    </justification>
  </clause>

  <clause id="14910">
    <literal><![CDATA[
      x * (K(x \ 1,x) / y) = L(x,x,x) * (1 / y)
    ]]></literal>
    <justification jstring="[para(6345(a,2),14395(a,1,2,1))].">
      <j1 rule="para" parents="6345 14395"/>
    </justification>
  </clause>

  <clause id="14911">
    <literal><![CDATA[
      T(x,((y * y) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ (y \ (z * u))) = w
    ]]></literal>
    <justification jstring="[para(484(a,1),14488(a,1,2))].">
      <j1 rule="para" parents="484 14488"/>
    </justification>
  </clause>

  <clause id="14912">
    <literal><![CDATA[
      K(x,y * ((1 / y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(14613(a,1),7395(a,1))].">
      <j1 rule="para" parents="14613 7395"/>
    </justification>
  </clause>

  <clause id="14913">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z * (K(1 / y,z) * u)) = w
    ]]></literal>
    <justification jstring="[para(6090(a,1),14912(a,1,2,2))].">
      <j1 rule="para" parents="6090 14912"/>
    </justification>
  </clause>

  <clause id="14914">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = z \ (K(x,y) * (x \ y))
    ]]></literal>
    <justification jstring="[para(14378(a,1),14740(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14378 14740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14915">
    <literal><![CDATA[
      (x * y) / T(x * z,z \ y) = (x * z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,102,a(flip),b,14745,a),flip(a)].">
      <j1 rule="hyper" parents="373 102 14745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14916">
    <literal><![CDATA[
      L((x * y) \ x,x * y,z) = (z * x) / T(z * (x * y),y \ 1)
    ]]></literal>
    <justification jstring="[para(6729(a,1),14745(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6729 14745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14917">
    <literal><![CDATA[
      T(x,((((y \ 1) \ 1) \ z) / z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) = w
    ]]></literal>
    <justification jstring="[para(2039(a,2),14759(a,1,2,1))].">
      <j1 rule="para" parents="2039 14759"/>
    </justification>
  </clause>

  <clause id="14918">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / (y * z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(3004(a,2),14759(a,1,2,1))].">
      <j1 rule="para" parents="3004 14759"/>
    </justification>
  </clause>

  <clause id="14919">
    <literal><![CDATA[
      T(x,(y \ (y / ((z \ 1) \ 1))) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(3935(a,1),14759(a,1,2,1))].">
      <j1 rule="para" parents="3935 14759"/>
    </justification>
  </clause>

  <clause id="14920">
    <literal><![CDATA[
      ((x / y) / x) / (1 / y) = ((x / y) / x) * y
    ]]></literal>
    <justification jstring="[hyper(225,a,2577,a(flip),b,14876,a(flip))].">
      <j1 rule="hyper" parents="225 2577 14876"/>
    </justification>
  </clause>

  <clause id="14921">
    <literal><![CDATA[
      ((x / (y \ 1)) / x) * (y \ 1) = ((x / (y \ 1)) / x) / y
    ]]></literal>
    <justification jstring="[para(79(a,1),14920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="79 14920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14922">
    <literal><![CDATA[
      (K(x,y) / x) * (y * x) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,7691,a(flip),b,14891,a)].">
      <j1 rule="hyper" parents="64 7691 14891"/>
    </justification>
  </clause>

  <clause id="14923">
    <literal><![CDATA[
      x * (((1 / x) \ 1) * (K(1 / x,(1 / x) \ 1) / y)) = L(x * ((x \ 1) \ (1 / y)),x,x)
    ]]></literal>
    <justification jstring="[para(14390(a,2),7605(a,2,2)),flip(a)].">
      <j1 rule="para" parents="14390 7605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14924">
    <literal><![CDATA[
      K(x,L((y / z) * z,T((y / z) \ 1,y),u)) = K(x,L(((y / z) \ 1) \ z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12108,a(flip),b,14421,a),flip(a)].">
      <j1 rule="hyper" parents="64 12108 14421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14925">
    <literal><![CDATA[
      K(x,L(T(1 / (1 / y),z) * u,w,v5)) = K(x,L((1 / T(y,z)) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(3566(a,1),14421(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3566 14421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14926">
    <literal><![CDATA[
      ((((x * y) \ x) \ T(((x * y) \ x) * z,y)) \ u) * ((z \ u) \ 1) = K(((x * y) \ x) \ 1,(((x * y) \ x) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(6748(a,2),14448(a,1,1,1))].">
      <j1 rule="para" parents="6748 14448"/>
    </justification>
  </clause>

  <clause id="14927">
    <literal><![CDATA[
      ((x / (x * y)) \ z) \ K(y \ 1,x * y) = (((x * y) \ x) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(6766(a,1),14454(a,1,2))].">
      <j1 rule="para" parents="6766 14454"/>
    </justification>
  </clause>

  <clause id="14928">
    <literal><![CDATA[
      (((x * y) \ x) * z) \ K(y \ 1,x * y) = ((x / (x * y)) * z) \ 1
    ]]></literal>
    <justification jstring="[para(6766(a,1),14455(a,1,2))].">
      <j1 rule="para" parents="6766 14455"/>
    </justification>
  </clause>

  <clause id="14929">
    <literal><![CDATA[
      (x \ y) \ K(x \ 1,x) = (L(x,x,x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(818(a,2),14456(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="818 14456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14930">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(14473(a,2),12091(a,1))].">
      <j1 rule="para" parents="14473 12091"/>
    </justification>
  </clause>

  <clause id="14931">
    <literal><![CDATA[
      (x / y) * ((1 / (z / y)) * z) = ((1 / (z / y)) * z) * (y \ x)
    ]]></literal>
    <justification jstring="[para(848(a,1),14480(a,1,2)),flip(a)].">
      <j1 rule="para" parents="848 14480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14932">
    <literal><![CDATA[
      T((x \ 1) \ y,x * x) = (x \ y) * ((x \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1480,a,b,14486,a),flip(a)].">
      <j1 rule="hyper" parents="35 1480 14486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14933">
    <literal><![CDATA[
      T(x,y * y) \ ((y \ (y \ 1)) * z) = (x * ((y \ 1) \ y)) \ z
    ]]></literal>
    <justification jstring="[para(14486(a,1),1556(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14486 1556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14934">
    <literal><![CDATA[
      (x \ (y * z)) * K(x * (y \ (x \ (y * z))),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(36,a,5653,a(flip),b,14497,a),flip(a)].">
      <j1 rule="hyper" parents="36 5653 14497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14935">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(13496,a,14500,a),flip(a)].">
      <j1 rule="hyper" parents="13496 14500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14936">
    <literal><![CDATA[
      L(x,y,K(z \ 1,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(6047(a,1),14935(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6047 14935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14937">
    <literal><![CDATA[
      L(x,y,K(((z * u) \ z) * w,u)) = L(x,y,K(u \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13076,a(flip),b,14936,a),flip(a)].">
      <j1 rule="hyper" parents="64 13076 14936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14938">
    <literal><![CDATA[
      L(x,K(y,z \ 1),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14229,a(flip),b,14501,a),flip(a)].">
      <j1 rule="hyper" parents="64 14229 14501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14939">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(6047(a,1),14938(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6047 14938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14940">
    <literal><![CDATA[
      L(x,K(y,z),u \ (z \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(8318,a,14939,a),flip(a)].">
      <j1 rule="hyper" parents="8318 14939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14941">
    <literal><![CDATA[
      K(x,x * x) / ((x \ 1) * y) = 1 / ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(6345(a,1),14504(a,1,1))].">
      <j1 rule="para" parents="6345 14504"/>
    </justification>
  </clause>

  <clause id="14942">
    <literal><![CDATA[
      x * K(y,(z \ 1) \ (z \ u)) = (1 / x) \ K(y,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),14518(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 14518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14943">
    <literal><![CDATA[
      T(x,(y / z) * (u * u)) = T(x,y * (z \ (u * u)))
    ]]></literal>
    <justification jstring="[para(900(a,1),14550(a,1,2))].">
      <j1 rule="para" parents="900 14550"/>
    </justification>
  </clause>

  <clause id="14944">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(8237,a,14554,a),flip(a)].">
      <j1 rule="hyper" parents="8237 14554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14945">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(14554(a,1),8237(a,1))].">
      <j1 rule="para" parents="14554 8237"/>
    </justification>
  </clause>

  <clause id="14946">
    <literal><![CDATA[
      T(x,T(y * (1 / z),u)) = T(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(143,a,14944,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 14944 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14947">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),14944(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 14944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14948">
    <literal><![CDATA[
      K(x,T(y / (z * K(u,w)),v5)) = K(x,T(y * (K(w,u) / z),v5))
    ]]></literal>
    <justification jstring="[para(14507(a,1),14944(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="14507 14944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14949">
    <literal><![CDATA[
      T(x,T(y * (z \ 1),u)) = T(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5424,a(flip),b,14946,a)].">
      <j1 rule="hyper" parents="64 5424 14946"/>
    </justification>
  </clause>

  <clause id="14950">
    <literal><![CDATA[
      T(x,T(y / (z \ 1),u)) = T(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),14946(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 14946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14951">
    <literal><![CDATA[
      T(x * (y * (z \ 1)),K(y * (z \ 1),u)) = (y * (z \ 1)) * T(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[para(14949(a,1),6998(a,2,2))].">
      <j1 rule="para" parents="14949 6998"/>
    </justification>
  </clause>

  <clause id="14952">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(14558(a,2),12091(a,1))].">
      <j1 rule="para" parents="14558 12091"/>
    </justification>
  </clause>

  <clause id="14953">
    <literal><![CDATA[
      K(x,L((1 / y) \ z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(14566(a,2),12091(a,1))].">
      <j1 rule="para" parents="14566 12091"/>
    </justification>
  </clause>

  <clause id="14954">
    <literal><![CDATA[
      1 / T((1 / x) / (y / x),T(y,x)) = ((1 / x) / (y / x)) \ 1
    ]]></literal>
    <justification jstring="[para(11107(a,1),14567(a,1,2))].">
      <j1 rule="para" parents="11107 14567"/>
    </justification>
  </clause>

  <clause id="14955">
    <literal><![CDATA[
      T(x * ((x \ 1) \ y),x * x) = y * ((1 / x) \ x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1526,a(flip),b,14568,a),flip(a)].">
      <j1 rule="hyper" parents="35 1526 14568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14956">
    <literal><![CDATA[
      ((1 / x) \ y) * ((x * y) \ z) = (z / (x * y)) * ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(117(a,1),14568(a,1,2))].">
      <j1 rule="para" parents="117 14568"/>
    </justification>
  </clause>

  <clause id="14957">
    <literal><![CDATA[
      K(x,y * z) * ((1 / y) \ z) = ((1 / y) \ z) * K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3991(a,1),14568(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3991 14568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14958">
    <literal><![CDATA[
      (x / ((y \ 1) * z)) * (y \ z) = (y \ z) * (((y \ 1) * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,14569,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 14569 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14959">
    <literal><![CDATA[
      T(x / ((y \ 1) * z),z / y) = T(((y \ 1) * z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(14569(a,1),8722(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14569 8722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14960">
    <literal><![CDATA[
      (((x / y) \ 1) * x) * T(z,y) = z * (((x / y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(82(a,1),14572(a,1,2,2))].">
      <j1 rule="para" parents="82 14572"/>
    </justification>
  </clause>

  <clause id="14961">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(14615(a,2),8515(a,1))].">
      <j1 rule="para" parents="14615 8515"/>
    </justification>
  </clause>

  <clause id="14962">
    <literal><![CDATA[
      K(x \ T((x \ 1) \ y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y * K((x \ 1) \ y,z),u) = w
    ]]></literal>
    <justification jstring="[para(6812(a,1),14961(a,1,1,2))].">
      <j1 rule="para" parents="6812 14961"/>
    </justification>
  </clause>

  <clause id="14963">
    <literal><![CDATA[
      x \ K(x,x \ K(y,z)) = T(1 / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,14397,a(flip),b,14616,a),flip(a)].">
      <j1 rule="hyper" parents="373 14397 14616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14964">
    <literal><![CDATA[
      x * (K(x,K(y,z)) / x) = K(x,x \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,9032,a(flip),b,14963,a)].">
      <j1 rule="hyper" parents="145 9032 14963"/>
    </justification>
  </clause>

  <clause id="14965">
    <literal><![CDATA[
      T(x,K(y,z)) * (1 / x) = K(x,x \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,14391,a,b,14964,a)].">
      <j1 rule="hyper" parents="64 14391 14964"/>
    </justification>
  </clause>

  <clause id="14966">
    <literal><![CDATA[
      K(x * ((y * y) \ 1),x) = K(y \ (y \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5731,a,b,14625,a),flip(a)].">
      <j1 rule="hyper" parents="373 5731 14625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14967">
    <literal><![CDATA[
      K((x * x) \ y,y) = K(x \ (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(10510,a,14966,a)].">
      <j1 rule="hyper" parents="10510 14966"/>
    </justification>
  </clause>

  <clause id="14968">
    <literal><![CDATA[
      K(x \ (x \ 1),y) = K(x \ (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(14761,a,14967,a),flip(a)].">
      <j1 rule="hyper" parents="14761 14967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14969">
    <literal><![CDATA[
      T(x * y,y \ (x \ z)) = ((x * y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(478,a,14661,a),flip(a)].">
      <j1 rule="hyper" parents="478 14661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14970">
    <literal><![CDATA[
      T(x * y,y \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x * y) \ z) \ z = u
    ]]></literal>
    <justification jstring="[para(14661(a,1),478(a,1))].">
      <j1 rule="para" parents="14661 478"/>
    </justification>
  </clause>

  <clause id="14971">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),(x \ y) * (L(x \ y,z,u) \ (x * L(x \ y,z,u)))) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,13997,a,b,14969,a)].">
      <j1 rule="hyper" parents="64 13997 14969"/>
    </justification>
  </clause>

  <clause id="14972">
    <literal><![CDATA[
      T((x \ 1) * y,y \ x) = (((x \ 1) * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,5197,a(flip),b,14969,a)].">
      <j1 rule="hyper" parents="64 5197 14969"/>
    </justification>
  </clause>

  <clause id="14973">
    <literal><![CDATA[
      x \ (((x * y) \ z) \ z) = y * K(x * y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(139,a,14969,a(flip),b,14495,a)].">
      <j1 rule="hyper" parents="139 14969 14495"/>
    </justification>
  </clause>

  <clause id="14974">
    <literal><![CDATA[
      T((x / y) * z,z \ y) = (((x / y) * z) \ x) \ x
    ]]></literal>
    <justification jstring="[para(82(a,1),14969(a,1,2,2))].">
      <j1 rule="para" parents="82 14969"/>
    </justification>
  </clause>

  <clause id="14975">
    <literal><![CDATA[
      (x \ (y * (x * z))) \ K(u,T(x,y * z)) = K(u,x) * ((x \ (y * (x * z))) \ 1)
    ]]></literal>
    <justification jstring="[para(9518(a,1),14663(a,1,2))].">
      <j1 rule="para" parents="9518 14663"/>
    </justification>
  </clause>

  <clause id="14976">
    <literal><![CDATA[
      ((x / (x / y)) \ 1) * y = K(y,y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,8875,a(flip),b,14668,a),flip(a)].">
      <j1 rule="hyper" parents="373 8875 14668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14977">
    <literal><![CDATA[
      ((x / (x / y)) \ 1) * y = K(y,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6142,a,b,14976,a),flip(a)].">
      <j1 rule="hyper" parents="373 6142 14976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14978">
    <literal><![CDATA[
      K(x,y * x) / x = x \ K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(142,a,14977,a(flip),b,6429,a(flip))].">
      <j1 rule="hyper" parents="142 14977 6429"/>
    </justification>
  </clause>

  <clause id="14979">
    <literal><![CDATA[
      (x \ K(x,x \ y)) \ (y * x) = (1 / x) \ T(y * x,x)
    ]]></literal>
    <justification jstring="[para(14978(a,1),14840(a,1,1))].">
      <j1 rule="para" parents="14978 14840"/>
    </justification>
  </clause>

  <clause id="14980">
    <literal><![CDATA[
      x * (K(y \ x,z) / y) = T(x * (1 / y),z)
    ]]></literal>
    <justification jstring="[para(14774(a,1),14685(a,1,2))].">
      <j1 rule="para" parents="14774 14685"/>
    </justification>
  </clause>

  <clause id="14981">
    <literal><![CDATA[
      x * (K(y \ x,y) / y) = L(y,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,11819,a(flip),b,14980,a),flip(a)].">
      <j1 rule="hyper" parents="373 11819 14980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14982">
    <literal><![CDATA[
      x * (1 / T(y,y \ x)) = L(y,y,x) \ x
    ]]></literal>
    <justification jstring="[para(5799(a,1),14981(a,1,2))].">
      <j1 rule="para" parents="5799 14981"/>
    </justification>
  </clause>

  <clause id="14983">
    <literal><![CDATA[
      x * (y \ K(y * x,y)) = L(y,y,x) \ x
    ]]></literal>
    <justification jstring="[para(8878(a,1),14981(a,1,2))].">
      <j1 rule="para" parents="8878 14981"/>
    </justification>
  </clause>

  <clause id="14985">
    <literal><![CDATA[
      x \ T(x * (1 / y),y) = 1 / T(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,11819,a,b,14982,a)].">
      <j1 rule="hyper" parents="139 11819 14982"/>
    </justification>
  </clause>

  <clause id="14986">
    <literal><![CDATA[
      x * (T(y,y * x) \ 1) = L(y,y,x) \ x
    ]]></literal>
    <justification jstring="[para(8872(a,1),14982(a,1,2))].">
      <j1 rule="para" parents="8872 14982"/>
    </justification>
  </clause>

  <clause id="14987">
    <literal><![CDATA[
      x \ (L(y,y,x) \ x) = T(y,y * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,14983,a(flip),b,5938,a)].">
      <j1 rule="hyper" parents="139 14983 5938"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      x * (y \ K(x * y,y)) = L(y,y,x) \ x
    ]]></literal>
    <justification jstring="[para(8516(a,2),14983(a,1,2,2))].">
      <j1 rule="para" parents="8516 14983"/>
    </justification>
  </clause>

  <clause id="14989">
    <literal><![CDATA[
      x * (T(1 / y,y \ x) \ 1) = L(1 / y,1 / y,x) \ x
    ]]></literal>
    <justification jstring="[para(14426(a,1),14986(a,1,2,1))].">
      <j1 rule="para" parents="14426 14986"/>
    </justification>
  </clause>

  <clause id="14990">
    <literal><![CDATA[
      (1 / T(x,x \ y)) * y = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,14985,a(flip),b,5434,a)].">
      <j1 rule="hyper" parents="144 14985 5434"/>
    </justification>
  </clause>

  <clause id="14991">
    <literal><![CDATA[
      (T(x,x * y) \ 1) * y = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[para(8872(a,1),14990(a,1,1))].">
      <j1 rule="para" parents="8872 14990"/>
    </justification>
  </clause>

  <clause id="14992">
    <literal><![CDATA[
      (T(x,y * (x \ z)) \ y) * z = T((x \ y) * z,x)
    ]]></literal>
    <justification jstring="[para(14022(a,1),14718(a,1,1,1))].">
      <j1 rule="para" parents="14022 14718"/>
    </justification>
  </clause>

  <clause id="14993">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,K(y,x) * z,x * y) = w
    ]]></literal>
    <justification jstring="[para(10823(a,1),14741(a,1,2,1))].">
      <j1 rule="para" parents="10823 14741"/>
    </justification>
  </clause>

  <clause id="14994">
    <literal><![CDATA[
      1 / (K(x,y) * z) = (1 / z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9046,a(flip),b,14771,a)].">
      <j1 rule="hyper" parents="64 9046 14771"/>
    </justification>
  </clause>

  <clause id="14995">
    <literal><![CDATA[
      K(x,y) * ((1 / z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / (K(w,u) * z) = v5
    ]]></literal>
    <justification jstring="[para(14994(a,1),14446(a,1,2))].">
      <j1 rule="para" parents="14994 14446"/>
    </justification>
  </clause>

  <clause id="14996">
    <literal><![CDATA[
      T((x * y) * (1 / x),K(y,z)) = (x * y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(8728,a,14795,a)].">
      <j1 rule="hyper" parents="8728 14795"/>
    </justification>
  </clause>

  <clause id="14997">
    <literal><![CDATA[
      K(x,y) * T(y \ 1,T(z,x)) = T(y \ K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6226,a(flip),b,14799,a)].">
      <j1 rule="hyper" parents="64 6226 14799"/>
    </justification>
  </clause>

  <clause id="14998">
    <literal><![CDATA[
      ((x / y) \ 1) * ((y \ x) \ ((y \ x) / z)) = ((x / y) \ 1) / z
    ]]></literal>
    <justification jstring="[hyper(145,a,14813,a(flip),b,1215,a)].">
      <j1 rule="hyper" parents="145 14813 1215"/>
    </justification>
  </clause>

  <clause id="14999">
    <literal><![CDATA[
      R(T(x / (x * y),(x * y) * y),x * y,y) = ((((x * y) \ z) \ z) * y) \ T(x * y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1326,a,b,14836,a)].">
      <j1 rule="hyper" parents="373 1326 14836"/>
    </justification>
  </clause>

  <clause id="15000">
    <literal><![CDATA[
      (((x \ y) \ y) * z) \ ((x \ y) \ y) = (x * z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,361,a(flip),b,14836,a)].">
      <j1 rule="hyper" parents="64 361 14836"/>
    </justification>
  </clause>

  <clause id="15001">
    <literal><![CDATA[
      L(x \ y,x,z / T(y,z)) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(4654,a,14837,a)].">
      <j1 rule="hyper" parents="4654 14837"/>
    </justification>
  </clause>

  <clause id="15002">
    <literal><![CDATA[
      L(x \ y,x,y \ z) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,13290,a(flip),b,15001,a)].">
      <j1 rule="hyper" parents="64 13290 15001"/>
    </justification>
  </clause>

  <clause id="15003">
    <literal><![CDATA[
      x / L(y \ z,y,z \ x) = (x / z) * y
    ]]></literal>
    <justification jstring="[hyper(225,a,13290,a(flip),b,15001,a(flip))].">
      <j1 rule="hyper" parents="225 13290 15001"/>
    </justification>
  </clause>

  <clause id="15004">
    <literal><![CDATA[
      ((x \ y) * z) \ ((x \ y) * x) = ((y / x) * z) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,15002,a)].">
      <j1 rule="hyper" parents="64 102 15002"/>
    </justification>
  </clause>

  <clause id="15005">
    <literal><![CDATA[
      (x \ y) / (K(z,x) \ y) = ((x \ y) / y) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(225,a,14940,a(flip),b,15002,a(flip))].">
      <j1 rule="hyper" parents="225 14940 15002"/>
    </justification>
  </clause>

  <clause id="15006">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = ((z / (y * x)) * y) \ z
    ]]></literal>
    <justification jstring="[para(9(a,1),15002(a,1,1))].">
      <j1 rule="para" parents="9 15002"/>
    </justification>
  </clause>

  <clause id="15007">
    <literal><![CDATA[
      x / L(y,z,(z * y) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(9(a,1),15003(a,1,2,1))].">
      <j1 rule="para" parents="9 15003"/>
    </justification>
  </clause>

  <clause id="15008">
    <literal><![CDATA[
      L(x,y,(y * x) \ ((y \ z) * x)) = (y \ R(z,y,x)) \ ((y \ z) * x)
    ]]></literal>
    <justification jstring="[para(2145(a,1),15006(a,2,1))].">
      <j1 rule="para" parents="2145 15006"/>
    </justification>
  </clause>

  <clause id="15009">
    <literal><![CDATA[
      ((x \ y) \ z) \ ((x \ y) \ y) = ((y / x) \ z) \ x
    ]]></literal>
    <justification jstring="[para(4666(a,1),14859(a,1,2))].">
      <j1 rule="para" parents="4666 14859"/>
    </justification>
  </clause>

  <clause id="15010">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) \ (z * K(x,y)) = (K(x,y) * u) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(8192(a,1),14893(a,1,1,1))].">
      <j1 rule="para" parents="8192 14893"/>
    </justification>
  </clause>

  <clause id="15011">
    <literal><![CDATA[
      (x \ y) * ((y / x) * (x / y)) = R(x \ y,x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,14901,a(flip),b,3008,a)].">
      <j1 rule="hyper" parents="145 14901 3008"/>
    </justification>
  </clause>

  <clause id="15012">
    <literal><![CDATA[
      (((x \ y) \ 1) \ y) * (x \ (x / z)) = (((x \ y) \ 1) \ y) / z
    ]]></literal>
    <justification jstring="[hyper(145,a,14903,a(flip),b,1613,a)].">
      <j1 rule="hyper" parents="145 14903 1613"/>
    </justification>
  </clause>

  <clause id="15013">
    <literal><![CDATA[
      (x \ y) * ((x \ 1) \ x) = T(y / (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7578,a(flip),b,14932,a),flip(a)].">
      <j1 rule="hyper" parents="64 7578 14932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15014">
    <literal><![CDATA[
      (x \ (x \ 1)) * ((x \ y) \ z) = T(y / (x \ 1),x) \ z
    ]]></literal>
    <justification jstring="[para(15013(a,1),1554(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15013 1554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15015">
    <literal><![CDATA[
      a(x,x,x) \ (1 / ((x \ 1) * y)) = 1 / ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14388,a,b,14941,a)].">
      <j1 rule="hyper" parents="64 14388 14941"/>
    </justification>
  </clause>

  <clause id="15016">
    <literal><![CDATA[
      (1 / (x \ T(y,z))) \ K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(7027,a,14942,a),flip(a)].">
      <j1 rule="hyper" parents="7027 14942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15017">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(14503,a,15016,a)].">
      <j1 rule="hyper" parents="14503 15016"/>
    </justification>
  </clause>

  <clause id="15020">
    <literal><![CDATA[
      (x \ T(y,z)) \ (x \ y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,15016,a(flip),b,14443,a(flip))].">
      <j1 rule="hyper" parents="139 15016 14443"/>
    </justification>
  </clause>

  <clause id="15021">
    <literal><![CDATA[
      (x \ y) * K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(6897,a,15017,a)].">
      <j1 rule="hyper" parents="6897 15017"/>
    </justification>
  </clause>

  <clause id="15022">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(782,a,15017,a),flip(a)].">
      <j1 rule="hyper" parents="782 15017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15023">
    <literal><![CDATA[
      T(x \ T(y,z),K(z,y)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(269,a,15017,a,b,6161,a)].">
      <j1 rule="hyper" parents="269 15017 6161"/>
    </justification>
  </clause>

  <clause id="15024">
    <literal><![CDATA[
      x / (y * K(z,x)) = T(x,z) / y
    ]]></literal>
    <justification jstring="[hyper(225,a,221,a(flip),b,15017,a(flip))].">
      <j1 rule="hyper" parents="225 221 15017"/>
    </justification>
  </clause>

  <clause id="15025">
    <literal><![CDATA[
      (x \ T(y,y \ z)) * (y \ z) = (x \ y) * (z / y)
    ]]></literal>
    <justification jstring="[hyper(144,a,15017,a(flip),b,6971,a),flip(a)].">
      <j1 rule="hyper" parents="144 15017 6971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15026">
    <literal><![CDATA[
      (x \ T(y,z)) * T(z,y) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,15017,a(flip),b,6847,a),flip(a)].">
      <j1 rule="hyper" parents="144 15017 6847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15027">
    <literal><![CDATA[
      (x \ T(y,z)) / T(y,z) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,15017,a(flip),b,6311,a),flip(a)].">
      <j1 rule="hyper" parents="142 15017 6311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15028">
    <literal><![CDATA[
      (x \ (y \ z)) * K(y,z / y) = x \ (z / y)
    ]]></literal>
    <justification jstring="[para(117(a,1),15017(a,1,1,2))].">
      <j1 rule="para" parents="117 15017"/>
    </justification>
  </clause>

  <clause id="15029">
    <literal><![CDATA[
      ((x \ T(y,z)) * T(K(z,y),u)) * K(z,y) = (x \ y) * T(K(z,y),u)
    ]]></literal>
    <justification jstring="[para(15017(a,1),2515(a,2,1))].">
      <j1 rule="para" parents="15017 2515"/>
    </justification>
  </clause>

  <clause id="15030">
    <literal><![CDATA[
      (x \ y) \ (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(15017(a,1),6882(a,1,1))].">
      <j1 rule="para" parents="15017 6882"/>
    </justification>
  </clause>

  <clause id="15031">
    <literal><![CDATA[
      (x \ y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(15017(a,1),6909(a,1,1)),flip(b)].">
      <j1 rule="para" parents="15017 6909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15032">
    <literal><![CDATA[
      K(x * (y \ T(z,u)),z) = K(x * (y \ z),z)
    ]]></literal>
    <justification jstring="[para(15017(a,1),8581(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15017 8581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15033">
    <literal><![CDATA[
      ((1 / x) \ y) * K(z,y) = (K(y,z) / x) \ y
    ]]></literal>
    <justification jstring="[para(14839(a,1),15017(a,1,1))].">
      <j1 rule="para" parents="14839 15017"/>
    </justification>
  </clause>

  <clause id="15034">
    <literal><![CDATA[
      (x / y) \ T(x,z) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(782,a,15021,a),flip(a)].">
      <j1 rule="hyper" parents="782 15021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15035">
    <literal><![CDATA[
      x \ ((y \ z) \ z) = (x \ y) * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,361,a(flip),b,15021,a)].">
      <j1 rule="hyper" parents="373 361 15021"/>
    </justification>
  </clause>

  <clause id="15036">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11173,a,b,15021,a)].">
      <j1 rule="hyper" parents="64 11173 15021"/>
    </justification>
  </clause>

  <clause id="15038">
    <literal><![CDATA[
      T(x,y) / (z * K(x,y)) = x / z
    ]]></literal>
    <justification jstring="[hyper(225,a,221,a(flip),b,15021,a(flip))].">
      <j1 rule="hyper" parents="225 221 15021"/>
    </justification>
  </clause>

  <clause id="15039">
    <literal><![CDATA[
      (x / y) * (y * K(x,z)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,221,a(flip),b,15021,a(flip))].">
      <j1 rule="hyper" parents="145 221 15021"/>
    </justification>
  </clause>

  <clause id="15040">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ y) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(142,a,15021,a(flip),b,11173,a)].">
      <j1 rule="hyper" parents="142 15021 11173"/>
    </justification>
  </clause>

  <clause id="15041">
    <literal><![CDATA[
      (x \ T(y,z)) / T(K(y,z),u) = (x \ y) * K(u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(142,a,15021,a(flip),b,5875,a)].">
      <j1 rule="hyper" parents="142 15021 5875"/>
    </justification>
  </clause>

  <clause id="15042">
    <literal><![CDATA[
      T(x,y) * K(x * y,z) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),15021(a,1,1))].">
      <j1 rule="para" parents="22 15021"/>
    </justification>
  </clause>

  <clause id="15043">
    <literal><![CDATA[
      (x \ L(y,z,u)) * K(L(y,z,u),w) = x \ L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),15021(a,2,2))].">
      <j1 rule="para" parents="25 15021"/>
    </justification>
  </clause>

  <clause id="15045">
    <literal><![CDATA[
      (x \ (y / z)) * K(y / z,z) = x \ (z \ y)
    ]]></literal>
    <justification jstring="[para(117(a,1),15021(a,2,2))].">
      <j1 rule="para" parents="117 15021"/>
    </justification>
  </clause>

  <clause id="15046">
    <literal><![CDATA[
      T(x,x \ 1) * (y \ x) = x * (y \ T(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(15021(a,1),3661(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15021 3661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15047">
    <literal><![CDATA[
      (x \ (y * (z / y))) * K(y * (z / y),u) = x \ (y * (T(z,u) / y))
    ]]></literal>
    <justification jstring="[para(5431(a,1),15021(a,2,2))].">
      <j1 rule="para" parents="5431 15021"/>
    </justification>
  </clause>

  <clause id="15048">
    <literal><![CDATA[
      (x * K(y,z)) \ T(x,u) = K(z,y) * K(x,u)
    ]]></literal>
    <justification jstring="[para(6882(a,1),15021(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6882 15021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15049">
    <literal><![CDATA[
      ((x \ y) / y) * K(y,z) = (x \ T(y,z)) / y
    ]]></literal>
    <justification jstring="[para(15021(a,1),6863(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15021 6863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15050">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(K(x,y),z \ x) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(15021(a,1),10852(a,2,1))].">
      <j1 rule="para" parents="15021 10852"/>
    </justification>
  </clause>

  <clause id="15051">
    <literal><![CDATA[
      (x * T(x,y)) \ T(x,z) = (1 / T(x,y)) * K(x,z)
    ]]></literal>
    <justification jstring="[para(14872(a,1),15021(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14872 15021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15053">
    <literal><![CDATA[
      T(x,y) / (z \ y) = x / (z \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(225,a,15021,a(flip),b,15022,a),flip(a)].">
      <j1 rule="hyper" parents="225 15021 15022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15055">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x / (K(y,x) / y)
    ]]></literal>
    <justification jstring="[hyper(225,a,6862,a(flip),b,15022,a),flip(a)].">
      <j1 rule="hyper" parents="225 6862 15022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15056">
    <literal><![CDATA[
      T(x,y) / (z / T(y,x)) = x / (z / y)
    ]]></literal>
    <justification jstring="[hyper(225,a,6848,a(flip),b,15022,a),flip(a)].">
      <j1 rule="hyper" parents="225 6848 15022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15057">
    <literal><![CDATA[
      T(x,y) / (z / T(x,y)) = x / (z / T(T(x,y),y))
    ]]></literal>
    <justification jstring="[hyper(225,a,6319,a(flip),b,15022,a),flip(a)].">
      <j1 rule="hyper" parents="225 6319 15022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15058">
    <literal><![CDATA[
      T(x,y) / (z * T(x,y)) = x / (z * x)
    ]]></literal>
    <justification jstring="[hyper(225,a,6249,a(flip),b,15022,a),flip(a)].">
      <j1 rule="hyper" parents="225 6249 15022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15059">
    <literal><![CDATA[
      (x * y) / (z * K(u,y * x)) = K(x,y) * (T(y * x,u) / z)
    ]]></literal>
    <justification jstring="[hyper(225,a,15022,a(flip),b,14885,a)].">
      <j1 rule="hyper" parents="225 15022 14885"/>
    </justification>
  </clause>

  <clause id="15060">
    <literal><![CDATA[
      (x \ y) * K(y \ x,y) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[para(6734(a,1),15022(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6734 15022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15061">
    <literal><![CDATA[
      (x \ y) * K(x / y,y) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[para(6806(a,1),15022(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6806 15022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15063">
    <literal><![CDATA[
      (x * y) / (z * K(u,y * x)) = T(x * y,T(u,x)) / z
    ]]></literal>
    <justification jstring="[para(11112(a,1),15024(a,1,2,2))].">
      <j1 rule="para" parents="11112 15024"/>
    </justification>
  </clause>

  <clause id="15066">
    <literal><![CDATA[
      (x / (y / z)) * (y / T(z,x)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,6245,a(flip),b,15034,a)].">
      <j1 rule="hyper" parents="145 6245 15034"/>
    </justification>
  </clause>

  <clause id="15067">
    <literal><![CDATA[
      x / (y * K(x,z)) = K(z,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(225,a,15034,a(flip),b,14833,a)].">
      <j1 rule="hyper" parents="225 15034 14833"/>
    </justification>
  </clause>

  <clause id="15068">
    <literal><![CDATA[
      L(x \ (y * K(z,u)),x,z / y) = ((z / y) * x) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(15034(a,1),346(a,1,1,2))].">
      <j1 rule="para" parents="15034 346"/>
    </justification>
  </clause>

  <clause id="15069">
    <literal><![CDATA[
      (x / y) * (y * K(x,z)) = (K(x,z) * u) * (u \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,14820,a,b,15039,a),flip(a)].">
      <j1 rule="hyper" parents="373 14820 15039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15070">
    <literal><![CDATA[
      ((x * y) \ y) * T(x,y) = ((y * x) \ y) * x
    ]]></literal>
    <justification jstring="[para(6981(a,1),15026(a,1,1))].">
      <j1 rule="para" parents="6981 15026"/>
    </justification>
  </clause>

  <clause id="15071">
    <literal><![CDATA[
      R((x \ y) * x,((x \ y) * x) \ x,x \ ((x \ y) * x)) = ((y \ x) * (x \ y)) \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(15026(a,1),12491(a,2,1))].">
      <j1 rule="para" parents="15026 12491"/>
    </justification>
  </clause>

  <clause id="15072">
    <literal><![CDATA[
      (R(T(x,y),z,u) \ x) / x = 1 / R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2836,a(flip),b,15027,a),flip(a)].">
      <j1 rule="hyper" parents="64 2836 15027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15073">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(225,a,15036,a(flip),b,7914,a)].">
      <j1 rule="hyper" parents="225 15036 7914"/>
    </justification>
  </clause>

  <clause id="15074">
    <literal><![CDATA[
      x \ T(y,T(z,x)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(8203(a,1),15036(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8203 15036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15075">
    <literal><![CDATA[
      K(x / y,z) * (y \ (y \ x)) = y \ T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(8215(a,1),15036(a,1,1))].">
      <j1 rule="para" parents="8215 15036"/>
    </justification>
  </clause>

  <clause id="15076">
    <literal><![CDATA[
      (x \ T(y * x,z)) / (x \ (y * x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,11180,a(flip),b,15040,a),flip(a)].">
      <j1 rule="hyper" parents="373 11180 15040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15077">
    <literal><![CDATA[
      T(x,y) / ((y * x) \ y) = x / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(6981(a,1),15053(a,2,2))].">
      <j1 rule="para" parents="6981 15053"/>
    </justification>
  </clause>

  <clause id="15078">
    <literal><![CDATA[
      T(K(x,y) / x,(K(x,y) / x) \ y) = T(K(x,y) / x,T(y,x) / (1 / x))
    ]]></literal>
    <justification jstring="[para(15055(a,2),4636(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15055 4636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15079">
    <literal><![CDATA[
      (x * K(x \ y,y \ x)) / (K(x \ y,x * K(x \ y,y \ x)) / (x \ y)) = ((1 / (1 / (x \ y))) \ y) / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(9246(a,1),15055(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9246 15055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15080">
    <literal><![CDATA[
      K(x,y) * (y / (z / x)) = y / (z / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,15056,a(flip),b,14841,a)].">
      <j1 rule="hyper" parents="145 15056 14841"/>
    </justification>
  </clause>

  <clause id="15081">
    <literal><![CDATA[
      R(1 / x,x,T(y,z)) = y / (x * y)
    ]]></literal>
    <justification jstring="[hyper(476,a,15058,a)].">
      <j1 rule="hyper" parents="476 15058"/>
    </justification>
  </clause>

  <clause id="15082">
    <literal><![CDATA[
      R(1 / x,x,y) = T(y,z) / (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,244,a,b,15058,a)].">
      <j1 rule="hyper" parents="373 244 15058"/>
    </justification>
  </clause>

  <clause id="15083">
    <literal><![CDATA[
      K(x,y) * (y / (z * y)) = y / (z * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,15058,a(flip),b,14841,a)].">
      <j1 rule="hyper" parents="145 15058 14841"/>
    </justification>
  </clause>

  <clause id="15085">
    <literal><![CDATA[
      R(1 / x,x,y \ z) = (z / y) / (x * (z / y))
    ]]></literal>
    <justification jstring="[para(117(a,1),15081(a,1,3))].">
      <j1 rule="para" parents="117 15081"/>
    </justification>
  </clause>

  <clause id="15086">
    <literal><![CDATA[
      T((x * K(y,z)) / (u / K(z,y)),u / T(K(z,y),x * K(y,z))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(493,a,6881,a(flip),b,15066,a)].">
      <j1 rule="hyper" parents="493 6881 15066"/>
    </justification>
  </clause>

  <clause id="15087">
    <literal><![CDATA[
      (x \ y) / (z * K(x \ y,x)) = (y / x) / z
    ]]></literal>
    <justification jstring="[hyper(373,a,14696,a(flip),b,15067,a),flip(a)].">
      <j1 rule="hyper" parents="373 14696 15067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15088">
    <literal><![CDATA[
      K(x,(K(y,z) * (z / u)) \ 1) = K(x,(u / z) * K(z,y))
    ]]></literal>
    <justification jstring="[para(15067(a,1),6955(a,1,2,1))].">
      <j1 rule="para" parents="15067 6955"/>
    </justification>
  </clause>

  <clause id="15089">
    <literal><![CDATA[
      T(x,T((K(y,z) * (z / u)) \ 1,w)) = T(x,T((u / z) * K(z,y),w))
    ]]></literal>
    <justification jstring="[para(15067(a,1),9301(a,1,2,1,1))].">
      <j1 rule="para" parents="15067 9301"/>
    </justification>
  </clause>

  <clause id="15090">
    <literal><![CDATA[
      T(x,T(K(y,z) * (u \ y),w) * u) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u * T(T(y,T(z,u)) / u,w)) = v5
    ]]></literal>
    <justification jstring="[para(15074(a,1),11216(a,1,2,1,1))].">
      <j1 rule="para" parents="15074 11216"/>
    </justification>
  </clause>

  <clause id="15091">
    <literal><![CDATA[
      R(1 / x,x,y) \ T(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(143,a,15082,a,b,171,a)].">
      <j1 rule="hyper" parents="143 15082 171"/>
    </justification>
  </clause>

  <clause id="15092">
    <literal><![CDATA[
      (x \ (y \ z)) * K(y,y \ z) = x \ (z / y)
    ]]></literal>
    <justification jstring="[para(5926(a,1),15028(a,1,2))].">
      <j1 rule="para" parents="5926 15028"/>
    </justification>
  </clause>

  <clause id="15093">
    <literal><![CDATA[
      (x \ ((y \ z) \ z)) * (y \ z) = (x \ y) * (z / y)
    ]]></literal>
    <justification jstring="[para(15035(a,2),6064(a,1,1))].">
      <j1 rule="para" parents="15035 6064"/>
    </justification>
  </clause>

  <clause id="15094">
    <literal><![CDATA[
      (x \ ((y \ z) \ z)) * y = (x \ y) * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[para(15035(a,2),6869(a,1,1))].">
      <j1 rule="para" parents="15035 6869"/>
    </justification>
  </clause>

  <clause id="15095">
    <literal><![CDATA[
      T(x,y) * (z * K(x * y,z)) = (y \ T(x * y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,15042,a(flip),b,5703,a),flip(a)].">
      <j1 rule="hyper" parents="144 15042 5703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15096">
    <literal><![CDATA[
      x \ (y \ T(x * y,z)) = K(x,y) * K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,15042,a(flip),b,5776,a)].">
      <j1 rule="hyper" parents="139 15042 5776"/>
    </justification>
  </clause>

  <clause id="15097">
    <literal><![CDATA[
      (x \ (y / z)) * K(z \ y,z) = x \ (z \ y)
    ]]></literal>
    <justification jstring="[para(6116(a,1),15045(a,1,2))].">
      <j1 rule="para" parents="6116 15045"/>
    </justification>
  </clause>

  <clause id="15098">
    <literal><![CDATA[
      R(x \ 1,x,y) * K(y,z) = (x \ T(y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,3006,a,b,15049,a)].">
      <j1 rule="hyper" parents="64 3006 15049"/>
    </justification>
  </clause>

  <clause id="15099">
    <literal><![CDATA[
      ((x * (y / x)) \ x) * y = (y \ x) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(15060(a,1),10601(a,1,1))].">
      <j1 rule="para" parents="15060 10601"/>
    </justification>
  </clause>

  <clause id="15100">
    <literal><![CDATA[
      (x \ y) / (z / T(x,x \ y)) = (y / x) / (z / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,14696,a(flip),b,15080,a),flip(a)].">
      <j1 rule="hyper" parents="64 14696 15080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15101">
    <literal><![CDATA[
      (x / (T(y,x) \ z)) * ((T(y,x) \ z) * T(y,x)) = (K(y,x) * (x / (z / y))) * z
    ]]></literal>
    <justification jstring="[para(15080(a,2),10617(a,2,1))].">
      <j1 rule="para" parents="15080 10617"/>
    </justification>
  </clause>

  <clause id="15102">
    <literal><![CDATA[
      K(x,y) * (y / ((T(z,z * T(y,x)) \ 1) * y)) = y / T((1 / z) * T(y,x),z)
    ]]></literal>
    <justification jstring="[para(14991(a,1),15083(a,2,2))].">
      <j1 rule="para" parents="14991 15083"/>
    </justification>
  </clause>

  <clause id="15103">
    <literal><![CDATA[
      ((1 / x) \ y) / (z * K(y * x,x \ 1)) = (y / (1 / x)) / z
    ]]></literal>
    <justification jstring="[para(14580(a,1),15087(a,1,2,2))].">
      <j1 rule="para" parents="14580 15087"/>
    </justification>
  </clause>

  <clause id="15104">
    <literal><![CDATA[
      ((x \ y) / z) \ (y / x) = z * K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(782,a,15092,a),flip(a)].">
      <j1 rule="hyper" parents="782 15092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15105">
    <literal><![CDATA[
      K(x \ y,x) / (z \ (x \ y)) = 1 / (z \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(225,a,15092,a(flip),b,14592,a),flip(a)].">
      <j1 rule="hyper" parents="225 15092 14592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15106">
    <literal><![CDATA[
      (x \ (y \ z)) * ((y \ z) \ z) = (x \ (z / y)) * y
    ]]></literal>
    <justification jstring="[para(15092(a,1),6869(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15092 6869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15107">
    <literal><![CDATA[
      K(x,x \ y) * (z \ (x \ y)) = T(z \ (y / x),K(y,x))
    ]]></literal>
    <justification jstring="[para(15092(a,1),8712(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15092 8712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15108">
    <literal><![CDATA[
      K(x,y / (T(z \ (u \ w),x) * K(u,u \ w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[para(15092(a,1),9200(a,2,2,2))].">
      <j1 rule="para" parents="15092 9200"/>
    </justification>
  </clause>

  <clause id="15109">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) * K(u,w))) = K(x,y * (z \ (w / u)))
    ]]></literal>
    <justification jstring="[para(15092(a,1),13551(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15092 13551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15111">
    <literal><![CDATA[
      (1 / x) / (y \ ((1 / (1 / x)) \ z)) = (x \ 1) / (y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(225,a,5212,a(flip),b,15104,a)].">
      <j1 rule="hyper" parents="225 5212 15104"/>
    </justification>
  </clause>

  <clause id="15113">
    <literal><![CDATA[
      R(1 / x,x,y \ z) \ (z / y) = x * (z / y)
    ]]></literal>
    <justification jstring="[hyper(143,a,15085,a,b,171,a)].">
      <j1 rule="hyper" parents="143 15085 171"/>
    </justification>
  </clause>

  <clause id="15114">
    <literal><![CDATA[
      (x \ 1) \ (y / (y * x)) = x * (y / (y * x))
    ]]></literal>
    <justification jstring="[para(3808(a,1),15113(a,1,1))].">
      <j1 rule="para" parents="3808 15113"/>
    </justification>
  </clause>

  <clause id="15116">
    <literal><![CDATA[
      ((x \ 1) * y) * ((1 / x) \ x) = T(x * y,x * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),14955(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 14955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15117">
    <literal><![CDATA[
      L(x \ y,x,y \ z) \ z = T((z / y) * x,x \ y)
    ]]></literal>
    <justification jstring="[para(15002(a,2),14974(a,2,1)),flip(a)].">
      <j1 rule="para" parents="15002 14974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15118">
    <literal><![CDATA[
      T(x,y * (T(z \ 1,T(u,w)) \ K(z,w))) = T(x,y / T(z \ K(w,z),u))
    ]]></literal>
    <justification jstring="[para(14997(a,1),14553(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14997 14553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15119">
    <literal><![CDATA[
      (x * (y \ (x \ y))) \ x = 1 / (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,2572,a(flip),b,15000,a),flip(a)].">
      <j1 rule="hyper" parents="64 2572 15000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15120">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) \ x = K(u,L(z,y,y \ x))
    ]]></literal>
    <justification jstring="[hyper(12114,a,15004,a),flip(a)].">
      <j1 rule="hyper" parents="12114 15004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15121">
    <literal><![CDATA[
      L(x,x \ y,y \ z) = ((z / y) * (y / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,10262,a,b,15004,a)].">
      <j1 rule="hyper" parents="64 10262 15004"/>
    </justification>
  </clause>

  <clause id="15122">
    <literal><![CDATA[
      x / L(y,y \ z,z \ x) = (x / z) * (z / y)
    ]]></literal>
    <justification jstring="[hyper(225,a,10262,a,b,15004,a(flip))].">
      <j1 rule="hyper" parents="225 10262 15004"/>
    </justification>
  </clause>

  <clause id="15123">
    <literal><![CDATA[
      (((x * x) \ y) * z) \ T(y,x * x) = ((y / (x * x)) * z) \ y
    ]]></literal>
    <justification jstring="[para(798(a,1),15004(a,1,2))].">
      <j1 rule="para" parents="798 15004"/>
    </justification>
  </clause>

  <clause id="15124">
    <literal><![CDATA[
      (((x \ 1) \ y) / z) \ (((x \ 1) \ x) * (x \ 1)) = ((x / (x \ 1)) * ((x \ y) / z)) \ x
    ]]></literal>
    <justification jstring="[para(1478(a,1),15004(a,1,1))].">
      <j1 rule="para" parents="1478 15004"/>
    </justification>
  </clause>

  <clause id="15125">
    <literal><![CDATA[
      a(L(x,x \ y,y \ (z * z)),u,w) = a(((z * z) / y) * (y / x),u,w)
    ]]></literal>
    <justification jstring="[para(15121(a,2),2666(a,1,1))].">
      <j1 rule="para" parents="15121 2666"/>
    </justification>
  </clause>

  <clause id="15126">
    <literal><![CDATA[
      x / L(y,y \ z,z \ x) = (z \ x) * (((z \ x) \ x) / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,14901,a,b,15122,a),flip(a)].">
      <j1 rule="hyper" parents="373 14901 15122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15127">
    <literal><![CDATA[
      (x \ y) / (K(x,z) * y) = ((x \ y) / y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(6156(a,1),15005(a,1,2))].">
      <j1 rule="para" parents="6156 15005"/>
    </justification>
  </clause>

  <clause id="15128">
    <literal><![CDATA[
      (x \ y) \ ((1 / (x \ y)) \ y) = ((y / x) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,1166,a(flip),b,15009,a)].">
      <j1 rule="hyper" parents="64 1166 15009"/>
    </justification>
  </clause>

  <clause id="15129">
    <literal><![CDATA[
      (((x \ y) * x) \ x) * (x \ y) = (y \ x) * (y / x)
    ]]></literal>
    <justification jstring="[para(6980(a,2),15025(a,1,1))].">
      <j1 rule="para" parents="6980 15025"/>
    </justification>
  </clause>

  <clause id="15130">
    <literal><![CDATA[
      (x * T(x,y)) \ T(x,z) = K(x,z) / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8934,a(flip),b,15051,a),flip(a)].">
      <j1 rule="hyper" parents="373 8934 15051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15131">
    <literal><![CDATA[
      T(K(x,y) * z,z \ x) = T(z,z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(269,a,15069,a(flip),b,5038,a)].">
      <j1 rule="hyper" parents="269 15069 5038"/>
    </justification>
  </clause>

  <clause id="15132">
    <literal><![CDATA[
      R(T(x,x \ 1),y,z) \ x = (R(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,11414,a(flip),b,15072,a),flip(a)].">
      <j1 rule="hyper" parents="144 11414 15072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15133">
    <literal><![CDATA[
      (x \ T(y * x,z)) / T(y,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),15076(a,1,2))].">
      <j1 rule="para" parents="22 15076"/>
    </justification>
  </clause>

  <clause id="15134">
    <literal><![CDATA[
      R(K(x * y,z),T(y,x),T(y,x) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) = u
    ]]></literal>
    <justification jstring="[para(15133(a,1),719(a,1,1))].">
      <j1 rule="para" parents="15133 719"/>
    </justification>
  </clause>

  <clause id="15135">
    <literal><![CDATA[
      (x \ y) / (T(x,x * y) \ 1) = (y / x) / (1 / x)
    ]]></literal>
    <justification jstring="[para(8872(a,1),15100(a,1,2))].">
      <j1 rule="para" parents="8872 15100"/>
    </justification>
  </clause>

  <clause id="15136">
    <literal><![CDATA[
      (x \ 1) * (x \ (((x \ 1) * y) \ z)) = T(x * y,x * x) \ z
    ]]></literal>
    <justification jstring="[para(15116(a,1),1672(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15116 1672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15137">
    <literal><![CDATA[
      R((x \ y) * x,((x \ y) * x) \ x,x \ y) \ y = (y \ x) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,974,a,b,15129,a)].">
      <j1 rule="hyper" parents="64 974 15129"/>
    </justification>
  </clause>

  <clause id="15138">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(K(y,z) * x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(9550,a,15131,a(flip))].">
      <j1 rule="hyper" parents="9550 15131"/>
    </justification>
  </clause>

  <clause id="15139">
    <literal><![CDATA[
      (x \ y) / (T(x,y * x) \ 1) = (y / x) / (1 / x)
    ]]></literal>
    <justification jstring="[para(4683(a,2),15135(a,1,2,1))].">
      <j1 rule="para" parents="4683 15135"/>
    </justification>
  </clause>

  <clause id="15140">
    <literal><![CDATA[
      K((x \ y) \ K(x,z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,1 / z),u) = w
    ]]></literal>
    <justification jstring="[para(6041(a,1),14639(a,1,1,2))].">
      <j1 rule="para" parents="6041 14639"/>
    </justification>
  </clause>

  <clause id="15141">
    <literal><![CDATA[
      L(x * K(y * x,y),y,y) = ((1 / y) * x) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,1052,a(flip),b,14647,a),flip(a)].">
      <j1 rule="hyper" parents="373 1052 14647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15142">
    <literal><![CDATA[
      L(x * K(x * y,y),y,y) = ((1 / y) * x) * y
    ]]></literal>
    <justification jstring="[para(8516(a,2),15141(a,1,1,2))].">
      <j1 rule="para" parents="8516 15141"/>
    </justification>
  </clause>

  <clause id="15143">
    <literal><![CDATA[
      L(x * K(x * y,y),y,y) \ (x * (1 / y)) = L(y \ K(x,1 / y),y,(1 / y) * x)
    ]]></literal>
    <justification jstring="[para(15142(a,2),639(a,2,1)),flip(a)].">
      <j1 rule="para" parents="15142 639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15144">
    <literal><![CDATA[
      T(x,y \ 1) \ ((x * (1 / y)) * y) = x \ L(x * K(x * y,y),y,y)
    ]]></literal>
    <justification jstring="[para(15142(a,2),10967(a,2,2))].">
      <j1 rule="para" parents="15142 10967"/>
    </justification>
  </clause>

  <clause id="15145">
    <literal><![CDATA[
      (x * T(y,z)) \ ((T(y,z) * z) * x) = L(z * K(z * y,x),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(11201(a,1),14648(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11201 14648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15146">
    <literal><![CDATA[
      a(x,x,x) / ((1 / x) * y) = 1 / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(39,a,12906,a,b,15015,a)].">
      <j1 rule="hyper" parents="39 12906 15015"/>
    </justification>
  </clause>

  <clause id="15147">
    <literal><![CDATA[
      T((x / y) * (z \ 1),(z \ 1) \ y) = L((z \ 1) \ y,z,y \ x) \ x
    ]]></literal>
    <justification jstring="[para(11794(a,1),15117(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11794 15117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15148">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      (x / u) * (u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15120(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15120 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15149">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,14463,a(flip),b,14465,a),flip(a)].">
      <j1 rule="hyper" parents="373 14463 14465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15150">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * (z \ y)) = K(x,(z \ y) * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(201(a,1),15149(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="201 15149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15151">
    <literal><![CDATA[
      T(x,(y * (z * z)) / u) = T(x,y / (u / (z * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14548,a(flip),b,14551,a)].">
      <j1 rule="hyper" parents="64 14548 14551"/>
    </justification>
  </clause>

  <clause id="15152">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(y \ 1,z) * u)
    ]]></literal>
    <justification jstring="[para(3776(a,1),14564(a,2,2,1))].">
      <j1 rule="para" parents="3776 14564"/>
    </justification>
  </clause>

  <clause id="15153">
    <literal><![CDATA[
      K((x \ y) * z,x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(6603,a,14605,a),flip(a)].">
      <j1 rule="hyper" parents="6603 14605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15154">
    <literal><![CDATA[
      K(x \ (y * z),x) = K((x \ y) * z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10277,a,b,15153,a)].">
      <j1 rule="hyper" parents="373 10277 15153"/>
    </justification>
  </clause>

  <clause id="15155">
    <literal><![CDATA[
      K(x * (y \ (y \ z)),y) * ((y \ x) * z) = (y \ ((y \ x) * z)) * y
    ]]></literal>
    <justification jstring="[para(15153(a,1),10278(a,1,1))].">
      <j1 rule="para" parents="15153 10278"/>
    </justification>
  </clause>

  <clause id="15156">
    <literal><![CDATA[
      K(x \ ((x * y) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),15154(a,2,1,1))].">
      <j1 rule="para" parents="9 15154"/>
    </justification>
  </clause>

  <clause id="15157">
    <literal><![CDATA[
      K(x,y \ K((z \ u) * w,z)) = K(x,y \ K(u * w,z))
    ]]></literal>
    <justification jstring="[para(15154(a,1),13385(a,1,2,2))].">
      <j1 rule="para" parents="15154 13385"/>
    </justification>
  </clause>

  <clause id="15158">
    <literal><![CDATA[
      (x \ y) * K(((x \ y) \ y) * x,x \ y) = (x \ y) * K(y * x,x \ y)
    ]]></literal>
    <justification jstring="[para(15154(a,1),14115(a,1,2))].">
      <j1 rule="para" parents="15154 14115"/>
    </justification>
  </clause>

  <clause id="15159">
    <literal><![CDATA[
      K(x \ ((y * x) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10862,a,b,15156,a)].">
      <j1 rule="hyper" parents="64 10862 15156"/>
    </justification>
  </clause>

  <clause id="15160">
    <literal><![CDATA[
      K(x * y,z) / (z \ ((z * x) * y)) = 1 / (((z * x) * y) / z)
    ]]></literal>
    <justification jstring="[para(15156(a,1),6450(a,1,1))].">
      <j1 rule="para" parents="15156 6450"/>
    </justification>
  </clause>

  <clause id="15161">
    <literal><![CDATA[
      T(((x * y) * y) / x,T(y * y,x)) \ 1 = (a(x,y,y) * (y * y)) \ K(y * y,x)
    ]]></literal>
    <justification jstring="[para(15156(a,1),9160(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15156 9160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15162">
    <literal><![CDATA[
      K((x \ y) \ (y * z),x \ y) = K(x * z,x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),15159(a,1,1,2,1))].">
      <j1 rule="para" parents="10 15159"/>
    </justification>
  </clause>

  <clause id="15163">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(x * (y \ z),x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),15162(a,1,1,2))].">
      <j1 rule="para" parents="10 15162"/>
    </justification>
  </clause>

  <clause id="15164">
    <literal><![CDATA[
      K(x \ (y * z),y \ x) = K(y * (x \ z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10183,a(flip),b,15163,a)].">
      <j1 rule="hyper" parents="64 10183 15163"/>
    </justification>
  </clause>

  <clause id="15165">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),z \ u)) = a(x,y,K(w,z \ u))
    ]]></literal>
    <justification jstring="[para(15163(a,1),12233(a,1,3))].">
      <j1 rule="para" parents="15163 12233"/>
    </justification>
  </clause>

  <clause id="15166">
    <literal><![CDATA[
      K(x / (y / z),z \ y) = K(z * (y \ x),z \ y)
    ]]></literal>
    <justification jstring="[hyper(10294,a,15164,a)].">
      <j1 rule="hyper" parents="10294 15164"/>
    </justification>
  </clause>

  <clause id="15167">
    <literal><![CDATA[
      L(x,x,x) \ K(y,z) = K(y,T(z,x)) * (1 / x)
    ]]></literal>
    <justification jstring="[para(7544(a,1),14709(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7544 14709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15168">
    <literal><![CDATA[
      L(x,x,x) \ K(y,z) = K(y,T(z,x)) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,14366,a(flip),b,15167,a),flip(a)].">
      <j1 rule="hyper" parents="373 14366 15167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15172">
    <literal><![CDATA[
      L(K(x,T(y,z)) / z,z,x) = (x * L(z,z,z)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(15168(a,1),14168(a,1,1))].">
      <j1 rule="para" parents="15168 14168"/>
    </justification>
  </clause>

  <clause id="15173">
    <literal><![CDATA[
      T(x / T(y,y * (x \ z)),y) = T(y,z * (x \ y)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,7184,a,b,14722,a)].">
      <j1 rule="hyper" parents="64 7184 14722"/>
    </justification>
  </clause>

  <clause id="15174">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),T(x * y,K(y,z)) \ y) = (K(z,y) * (x * T(y,z))) \ y
    ]]></literal>
    <justification jstring="[para(6920(a,1),14855(a,1,2,1))].">
      <j1 rule="para" parents="6920 14855"/>
    </justification>
  </clause>

  <clause id="15175">
    <literal><![CDATA[
      T((x \ T(y,z)) \ T(y,x),y) = (x \ T(y,z)) \ y
    ]]></literal>
    <justification jstring="[para(14833(a,1),14860(a,2,1))].">
      <j1 rule="para" parents="14833 14860"/>
    </justification>
  </clause>

  <clause id="15176">
    <literal><![CDATA[
      R(x,y,z \ T(T(u,K(w,v5)) \ v6,K(w,T(v5,u)))) = R(x,y,z \ (((u \ v6) \ K(w,v5)) \ K(w,T(v5,u))))
    ]]></literal>
    <justification jstring="[para(14868(a,1),13907(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="14868 13907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15177">
    <literal><![CDATA[
      K(x,(T(T(y * z,x),z \ 1) / u) * w) = K(x,((((y * z) \ y) \ y) / u) * w)
    ]]></literal>
    <justification jstring="[para(6745(a,1),14904(a,2,2,1,1))].">
      <j1 rule="para" parents="6745 14904"/>
    </justification>
  </clause>

  <clause id="15178">
    <literal><![CDATA[
      L(x,y,K(((z * u) \ z) * w,u)) = L(x,y,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,14936,a(flip),b,14937,a),flip(a)].">
      <j1 rule="hyper" parents="373 14936 14937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15179">
    <literal><![CDATA[
      (x \ T(y,z)) / K(y,T(z,u)) = (x \ y) * K(u,K(y,z))
    ]]></literal>
    <justification jstring="[para(7867(a,2),15041(a,1,2))].">
      <j1 rule="para" parents="7867 15041"/>
    </justification>
  </clause>

  <clause id="15181">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15088(a,1),7011(a,1))].">
      <j1 rule="para" parents="15088 7011"/>
    </justification>
  </clause>

  <clause id="15182">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,T(y,u)) = (x \ y) * K(u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7930,a,15179,a)].">
      <j1 rule="hyper" parents="7930 15179"/>
    </justification>
  </clause>

  <clause id="15183">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,T(y,u)) = (x \ y) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8110(a,2),15182(a,2,2))].">
      <j1 rule="para" parents="8110 15182"/>
    </justification>
  </clause>

  <clause id="15184">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,T(y,u)) = x \ T(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15021,a(flip),b,15183,a),flip(a)].">
      <j1 rule="hyper" parents="373 15021 15183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15185">
    <literal><![CDATA[
      L(x \ (T(y,z) \ z),x,K(y,z)) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(6111(a,1),14725(a,1,3))].">
      <j1 rule="para" parents="6111 14725"/>
    </justification>
  </clause>

  <clause id="15186">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ y) = z \ (x \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,6279,a(flip),b,15185,a)].">
      <j1 rule="hyper" parents="64 6279 15185"/>
    </justification>
  </clause>

  <clause id="15187">
    <literal><![CDATA[
      ((x * y) / x) \ (x \ y) = y \ (x \ T(y,x))
    ]]></literal>
    <justification jstring="[para(5718(a,2),15186(a,1,1))].">
      <j1 rule="para" parents="5718 15186"/>
    </justification>
  </clause>

  <clause id="15188">
    <literal><![CDATA[
      L((x \ 1) \ 1,x,x * y) = R(y,x,x \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11808,a,b,14894,a)].">
      <j1 rule="hyper" parents="64 11808 14894"/>
    </justification>
  </clause>

  <clause id="15189">
    <literal><![CDATA[
      (x * T(T(x,y),z)) \ T(T(x,y),z) = L(x \ 1,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,14875,a(flip),b,14900,a),flip(a)].">
      <j1 rule="hyper" parents="373 14875 14900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15191">
    <literal><![CDATA[
      (x * T(T(x,y),z)) \ T(T(x,y),z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(373,a,434,a(flip),b,15189,a),flip(a)].">
      <j1 rule="hyper" parents="373 434 15189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15192">
    <literal><![CDATA[
      T(x * T(T(x,y),z),x \ 1) = (1 / x) \ T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(15191(a,1),4590(a,2,1))].">
      <j1 rule="para" parents="15191 4590"/>
    </justification>
  </clause>

  <clause id="15193">
    <literal><![CDATA[
      x * T(T((x \ 1) \ 1,y),z) = (1 / x) \ T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10052,a(flip),b,15192,a)].">
      <j1 rule="hyper" parents="64 10052 15192"/>
    </justification>
  </clause>

  <clause id="15194">
    <literal><![CDATA[
      K(x * x,y) * L(x,x,y) = y \ (((x * x) * y) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6155,a(flip),b,14907,a)].">
      <j1 rule="hyper" parents="64 6155 14907"/>
    </justification>
  </clause>

  <clause id="15195">
    <literal><![CDATA[
      K(x,L(y / T((z \ u) \ 1,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * (z \ T(u,u \ z)),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(7656(a,1),14952(a,1,2,1,2))].">
      <j1 rule="para" parents="7656 14952"/>
    </justification>
  </clause>

  <clause id="15197">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(x * (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(14763,a,14491,a),flip(a)].">
      <j1 rule="hyper" parents="14763 14491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15198">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,8528,a(flip),b,15197,a),flip(a)].">
      <j1 rule="hyper" parents="373 8528 15197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15199">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,12538,a,b,15198,a)].">
      <j1 rule="hyper" parents="64 12538 15198"/>
    </justification>
  </clause>

  <clause id="15201">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,z / (x * z))
    ]]></literal>
    <justification jstring="[para(15199(a,1),11465(a,1,1,1))].">
      <j1 rule="para" parents="15199 11465"/>
    </justification>
  </clause>

  <clause id="15202">
    <literal><![CDATA[
      R(1 / x,y,z / (x * z)) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,8744,a(flip),b,15201,a),flip(a)].">
      <j1 rule="hyper" parents="64 8744 15201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15204">
    <literal><![CDATA[
      R(1 / (x / y),z,(x / y) \ 1) = R(1 / (x / y),z,y / x)
    ]]></literal>
    <justification jstring="[para(12(a,1),15202(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="12 15202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15205">
    <literal><![CDATA[
      L(x,y,z / ((1 / u) * K(w,v5))) = L(x,y,z / (u \ K(w,v5)))
    ]]></literal>
    <justification jstring="[para(14994(a,1),14543(a,1,3,2))].">
      <j1 rule="para" parents="14994 14543"/>
    </justification>
  </clause>

  <clause id="15206">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * K(u,y / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(14555(a,2),14945(a,1))].">
      <j1 rule="para" parents="14555 14945"/>
    </justification>
  </clause>

  <clause id="15207">
    <literal><![CDATA[
      T(x,T(y,z * u) * (u / (1 / z))) = T(x,(u / (1 / z)) * T(y,K(u,z)))
    ]]></literal>
    <justification jstring="[para(11154(a,1),14612(a,1,2,1))].">
      <j1 rule="para" parents="11154 14612"/>
    </justification>
  </clause>

  <clause id="15208">
    <literal><![CDATA[
      K(x,y \ (((z \ u) \ u) \ 1)) = K(x,y \ (z \ K(z \ u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14436,a(flip),b,14630,a)].">
      <j1 rule="hyper" parents="64 14436 14630"/>
    </justification>
  </clause>

  <clause id="15209">
    <literal><![CDATA[
      (x \ K(x \ 1,T(y,z))) \ K(x,z) = T(T(x,z) \ 1,y) \ 1
    ]]></literal>
    <justification jstring="[para(7872(a,1),14637(a,1,1,2))].">
      <j1 rule="para" parents="7872 14637"/>
    </justification>
  </clause>

  <clause id="15210">
    <literal><![CDATA[
      T(K(x,y) * T(y / z,K(x,y)),z) = z \ (y * T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(9082(a,1),14697(a,1,1,2))].">
      <j1 rule="para" parents="9082 14697"/>
    </justification>
  </clause>

  <clause id="15211">
    <literal><![CDATA[
      T(x * y,T(y * y,y)) = (y \ x) * ((x * y) / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,11192,a(flip),b,14720,a)].">
      <j1 rule="hyper" parents="373 11192 14720"/>
    </justification>
  </clause>

  <clause id="15212">
    <literal><![CDATA[
      (x \ y) * ((y * x) / (x \ y)) = T(y * x,x * x)
    ]]></literal>
    <justification jstring="[hyper(11141,a,15211,a),flip(a)].">
      <j1 rule="hyper" parents="11141 15211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15213">
    <literal><![CDATA[
      (x / (x / (y \ 1))) * T(y,y \ 1) = K(y * x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,14441,a(flip),b,14766,a),flip(a)].">
      <j1 rule="hyper" parents="373 14441 14766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15214">
    <literal><![CDATA[
      K(x * y,x \ 1) * K(x \ 1,x) = (y / (y / (x \ 1))) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,15213,a(flip),b,6322,a)].">
      <j1 rule="hyper" parents="144 15213 6322"/>
    </justification>
  </clause>

  <clause id="15215">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,x / z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8092(a,1),14849(a,1,2))].">
      <j1 rule="para" parents="8092 14849"/>
    </justification>
  </clause>

  <clause id="15216">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (z * K(x,y)) \ y
    ]]></literal>
    <justification jstring="[para(8181(a,1),14854(a,2,1))].">
      <j1 rule="para" parents="8181 14854"/>
    </justification>
  </clause>

  <clause id="15217">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(z,z \ y) = T(z * (y / z),x) / y
    ]]></literal>
    <justification jstring="[para(6016(a,1),14863(a,1,2))].">
      <j1 rule="para" parents="6016 14863"/>
    </justification>
  </clause>

  <clause id="15218">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(z,z \ y) = (z * (T(y,x) / z)) / y
    ]]></literal>
    <justification jstring="[para(5431(a,1),15217(a,2,1))].">
      <j1 rule="para" parents="5431 15217"/>
    </justification>
  </clause>

  <clause id="15219">
    <literal><![CDATA[
      T(x,y * y) \ ((y \ (y \ 1)) * z) = (y \ (y \ 1)) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1554,a(flip),b,14933,a),flip(a)].">
      <j1 rule="hyper" parents="373 1554 14933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15220">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,y \ (w * R(x,z,u)))
    ]]></literal>
    <justification jstring="[para(14934(a,1),9681(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14934 9681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15221">
    <literal><![CDATA[
      (x \ (y * z)) * K(y \ (y * z),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(10280(a,1),14934(a,1,2))].">
      <j1 rule="para" parents="10280 14934"/>
    </justification>
  </clause>

  <clause id="15222">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),15221(a,1,2,1))].">
      <j1 rule="para" parents="9 15221"/>
    </justification>
  </clause>

  <clause id="15224">
    <literal><![CDATA[
      ((x * y) / z) \ (y * x) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(782,a,15222,a),flip(a)].">
      <j1 rule="hyper" parents="782 15222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15225">
    <literal><![CDATA[
      T((x \ (y * z)) / (y * z),z * y) = (z * y) \ (x \ (z * y))
    ]]></literal>
    <justification jstring="[hyper(493,a,15222,a(flip),b,10193,a)].">
      <j1 rule="hyper" parents="493 15222 10193"/>
    </justification>
  </clause>

  <clause id="15226">
    <literal><![CDATA[
      (x * y) / (z * K(x,y)) = (y * x) / z
    ]]></literal>
    <justification jstring="[hyper(225,a,221,a(flip),b,15222,a(flip))].">
      <j1 rule="hyper" parents="225 221 15222"/>
    </justification>
  </clause>

  <clause id="15227">
    <literal><![CDATA[
      T(x,y) / (z \ (x * y)) = x / (z \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(225,a,15222,a(flip),b,15034,a)].">
      <j1 rule="hyper" parents="225 15222 15034"/>
    </justification>
  </clause>

  <clause id="15228">
    <literal><![CDATA[
      (x \ (y * z)) * T(z,y) = (x \ (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,15222,a(flip),b,6847,a),flip(a)].">
      <j1 rule="hyper" parents="144 15222 6847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15229">
    <literal><![CDATA[
      (x \ (y * z)) / T(y,z) = (x \ (z * y)) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,15222,a(flip),b,6840,a)].">
      <j1 rule="hyper" parents="142 15222 6840"/>
    </justification>
  </clause>

  <clause id="15230">
    <literal><![CDATA[
      (x \ y) * K(z \ y,z) = x \ ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),15222(a,1,1,2))].">
      <j1 rule="para" parents="10 15222"/>
    </justification>
  </clause>

  <clause id="15232">
    <literal><![CDATA[
      (x * (y * z)) \ (z * (x * y)) = a(x,y,z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(14(a,2),15222(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14 15222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15233">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = (y * z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(210(a,1),15222(a,1,1)),flip(a)].">
      <j1 rule="para" parents="210 15222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15235">
    <literal><![CDATA[
      (x * y) / (z * T(x,y)) = (y * x) / (z * x)
    ]]></literal>
    <justification jstring="[hyper(6941,a,15224,a)].">
      <j1 rule="hyper" parents="6941 15224"/>
    </justification>
  </clause>

  <clause id="15236">
    <literal><![CDATA[
      x / (y * K(z,z \ x)) = ((z \ x) * z) / y
    ]]></literal>
    <justification jstring="[hyper(40,a,343,a,b,15224,a)].">
      <j1 rule="hyper" parents="40 343 15224"/>
    </justification>
  </clause>

  <clause id="15237">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = K(x,y) * ((x * y) / z)
    ]]></literal>
    <justification jstring="[hyper(225,a,15224,a(flip),b,14885,a)].">
      <j1 rule="hyper" parents="225 15224 14885"/>
    </justification>
  </clause>

  <clause id="15238">
    <literal><![CDATA[
      (x * y) / (z * K(y,T(x,y))) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[hyper(225,a,15224,a(flip),b,249,a(flip))].">
      <j1 rule="hyper" parents="225 15224 249"/>
    </justification>
  </clause>

  <clause id="15239">
    <literal><![CDATA[
      x / (y * K(x / z,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(15224(a,1),386(a,1,2))].">
      <j1 rule="para" parents="15224 386"/>
    </justification>
  </clause>

  <clause id="15240">
    <literal><![CDATA[
      (x * y) / ((x * y) * y) = (y * x) / ((y * x) * y)
    ]]></literal>
    <justification jstring="[para(1296(a,1),15235(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1296 15235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15241">
    <literal><![CDATA[
      x / (y * K(z \ x,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(6116(a,1),15239(a,1,2,2))].">
      <j1 rule="para" parents="6116 15239"/>
    </justification>
  </clause>

  <clause id="15242">
    <literal><![CDATA[
      (x * (y / x)) / (z * (y / x)) = y / (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(6872(a,1),15239(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6872 15239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15243">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[para(5923(a,1),15238(a,1,2,2))].">
      <j1 rule="para" parents="5923 15238"/>
    </justification>
  </clause>

  <clause id="15244">
    <literal><![CDATA[
      K(x,y) * ((x * y) / z) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,15237,a(flip),b,15243,a)].">
      <j1 rule="hyper" parents="64 15237 15243"/>
    </justification>
  </clause>

  <clause id="15245">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = y * T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6852,a(flip),b,15233,a),flip(a)].">
      <j1 rule="hyper" parents="373 6852 15233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15246">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,14040,a(flip),b,15220,a),flip(a)].">
      <j1 rule="hyper" parents="373 14040 15220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15247">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,u \ (w * R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7635,a,b,15220,a)].">
      <j1 rule="hyper" parents="64 7635 15220"/>
    </justification>
  </clause>

  <clause id="15249">
    <literal><![CDATA[
      K(x,x * (R(x,y,z) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15246(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 15246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15250">
    <literal><![CDATA[
      K(x,y \ ((x * z) * u)) = K(x,x * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[para(111(a,1),15246(a,1,2,2))].">
      <j1 rule="para" parents="111 15246"/>
    </justification>
  </clause>

  <clause id="15252">
    <literal><![CDATA[
      K(x,(x * y) * z) = K(x,x * (y * z))
    ]]></literal>
    <justification jstring="[para(210(a,1),15249(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="210 15249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15253">
    <literal><![CDATA[
      K(x,(y * x) * z) = K(x,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(10861,a,15252,a)].">
      <j1 rule="hyper" parents="10861 15252"/>
    </justification>
  </clause>

  <clause id="15254">
    <literal><![CDATA[
      K(x \ y,(x \ y) * (x * z)) = K(x \ y,y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),15253(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 15253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15255">
    <literal><![CDATA[
      K(x,y \ ((z * u) * x)) = K(x,y \ ((x * z) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,10490,a,b,15250,a)].">
      <j1 rule="hyper" parents="373 10490 15250"/>
    </justification>
  </clause>

  <clause id="15256">
    <literal><![CDATA[
      K(x \ y,y * x) = K(x \ y,x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6675,a(flip),b,15254,a),flip(a)].">
      <j1 rule="hyper" parents="64 6675 15254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15257">
    <literal><![CDATA[
      K(x \ y,y * x) = K(x * y,x * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,14711,a(flip),b,15256,a),flip(a)].">
      <j1 rule="hyper" parents="373 14711 15256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15258">
    <literal><![CDATA[
      T(x * y,T(y * y,y)) = x * (y * K(y \ x,x * y))
    ]]></literal>
    <justification jstring="[para(15257(a,2),14657(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15257 14657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15259">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,y \ (w * R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9679,a,b,15247,a)].">
      <j1 rule="hyper" parents="64 9679 15247"/>
    </justification>
  </clause>

  <clause id="15260">
    <literal><![CDATA[
      x * (y * K(y \ x,x * y)) = T(x * y,y * y)
    ]]></literal>
    <justification jstring="[hyper(11141,a,15258,a),flip(a)].">
      <j1 rule="hyper" parents="11141 15258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15261">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,14040,a(flip),b,15259,a),flip(a)].">
      <j1 rule="hyper" parents="373 14040 15259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15263">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(15261(a,1),14099(a,1))].">
      <j1 rule="para" parents="15261 14099"/>
    </justification>
  </clause>

  <clause id="15265">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z \ x)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8092(a,1),15050(a,1,2))].">
      <j1 rule="para" parents="8092 15050"/>
    </justification>
  </clause>

  <clause id="15266">
    <literal><![CDATA[
      K(x,y) * (T(y * x,z) / u) = T(x * y,T(z,x)) / u
    ]]></literal>
    <justification jstring="[hyper(64,a,15063,a(flip),b,15059,a),flip(a)].">
      <j1 rule="hyper" parents="64 15063 15059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15268">
    <literal><![CDATA[
      (x * y) \ ((z * z) * T(x,z * z)) = ((x / (z * z)) * y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,942,a(flip),b,15123,a)].">
      <j1 rule="hyper" parents="64 942 15123"/>
    </justification>
  </clause>

  <clause id="15269">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,5756,a(flip),b,15138,a)].">
      <j1 rule="hyper" parents="36 5756 15138"/>
    </justification>
  </clause>

  <clause id="15270">
    <literal><![CDATA[
      ((x * y) * z) / T(x,y * z) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(37,a,14505,a,b,15160,a)].">
      <j1 rule="hyper" parents="37 14505 15160"/>
    </justification>
  </clause>

  <clause id="15271">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (1 / (x / y)) \ R(1 / (x / y),z,y / x)
    ]]></literal>
    <justification jstring="[para(15204(a,1),11038(a,2,2))].">
      <j1 rule="para" parents="15204 11038"/>
    </justification>
  </clause>

  <clause id="15272">
    <literal><![CDATA[
      T(x \ 1,T(y,z)) \ K(x,z) = T(T(x,z) \ 1,y) \ 1
    ]]></literal>
    <justification jstring="[para(5762(a,1),15209(a,1,1))].">
      <j1 rule="para" parents="5762 15209"/>
    </justification>
  </clause>

  <clause id="15273">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = y \ (x * T(K(z,x),y))
    ]]></literal>
    <justification jstring="[para(115(a,1),15210(a,1,1))].">
      <j1 rule="para" parents="115 15210"/>
    </justification>
  </clause>

  <clause id="15274">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = y \ (x * K(z,T(x,y)))
    ]]></literal>
    <justification jstring="[para(7867(a,2),15273(a,2,2,2))].">
      <j1 rule="para" parents="7867 15273"/>
    </justification>
  </clause>

  <clause id="15275">
    <literal><![CDATA[
      x \ (1 / T(1 / x,x * y)) = (y / (y / (x \ 1))) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,9248,a(flip),b,15214,a)].">
      <j1 rule="hyper" parents="64 9248 15214"/>
    </justification>
  </clause>

  <clause id="15276">
    <literal><![CDATA[
      x \ (1 / T(x \ 1,x \ y)) = (y / (y / (x \ 1))) * x
    ]]></literal>
    <justification jstring="[para(5131(a,1),15275(a,1,2,2))].">
      <j1 rule="para" parents="5131 15275"/>
    </justification>
  </clause>

  <clause id="15277">
    <literal><![CDATA[
      x \ (T(1 / x,x \ y) \ 1) = (y / (y / (x \ 1))) * x
    ]]></literal>
    <justification jstring="[para(3565(a,1),15276(a,1,2))].">
      <j1 rule="para" parents="3565 15276"/>
    </justification>
  </clause>

  <clause id="15278">
    <literal><![CDATA[
      (x / (x / (y \ 1))) * y = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,8051,a(flip),b,15277,a),flip(a)].">
      <j1 rule="hyper" parents="64 8051 15277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15279">
    <literal><![CDATA[
      K(x \ (x \ y),x \ 1) = (x \ K(y,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(8739(a,1),15278(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8739 15278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15280">
    <literal><![CDATA[
      x \ K(x \ (x \ y),x \ 1) = T(x \ K(y,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(493,a,15279,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="493 15279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15281">
    <literal><![CDATA[
      T(x \ K(x * y,x \ 1),x) = x \ K(x \ y,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),15280(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 15280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15282">
    <literal><![CDATA[
      T(x \ K(y * x,x \ 1),x) = x \ K(x \ y,x \ 1)
    ]]></literal>
    <justification jstring="[para(7520(a,2),15281(a,1,1,2))].">
      <j1 rule="para" parents="7520 15281"/>
    </justification>
  </clause>

  <clause id="15283">
    <literal><![CDATA[
      K(x \ y,x \ 1) / x = x \ K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(281,a,15282,a)].">
      <j1 rule="hyper" parents="281 15282"/>
    </justification>
  </clause>

  <clause id="15284">
    <literal><![CDATA[
      T(K(x * (y \ (y / z)),(y \ (y / z)) \ 1) / (y \ (y / z)),z \ 1) = K((y \ (y / z)) \ x,(y \ (y / z)) \ 1) / (y \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,6754,a,b,15283,a)].">
      <j1 rule="hyper" parents="373 6754 15283"/>
    </justification>
  </clause>

  <clause id="15285">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8997(a,1),15215(a,1,2))].">
      <j1 rule="para" parents="8997 15215"/>
    </justification>
  </clause>

  <clause id="15286">
    <literal><![CDATA[
      (x \ (x \ 1)) * (y \ ((x \ 1) \ z)) = T(y,x * x) \ (x \ z)
    ]]></literal>
    <justification jstring="[para(1551(a,1),15219(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1551 15219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15287">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8999(a,1),15265(a,1,2))].">
      <j1 rule="para" parents="8999 15265"/>
    </justification>
  </clause>

  <clause id="15288">
    <literal><![CDATA[
      ((x \ y) \ K(z,y)) * K(y,K(z,x)) = (x \ T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(14734,a,15287,a)].">
      <j1 rule="hyper" parents="14734 15287"/>
    </justification>
  </clause>

  <clause id="15289">
    <literal><![CDATA[
      ((x / (y * y)) * z) \ x = (x * z) \ (x * (y * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,15268,a),flip(a)].">
      <j1 rule="hyper" parents="64 249 15268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15290">
    <literal><![CDATA[
      (x * ((y * y) \ z)) \ x = (x * z) \ (x * (y * y))
    ]]></literal>
    <justification jstring="[para(897(a,1),15289(a,1,1))].">
      <j1 rule="para" parents="897 15289"/>
    </justification>
  </clause>

  <clause id="15291">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * y)) = (x * ((1 / y) * z)) \ x
    ]]></literal>
    <justification jstring="[para(535(a,1),15290(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="535 15290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15292">
    <literal><![CDATA[
      (1 / x) * (y * T(z,x \ y)) = L(z,y,x) * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(1643(a,1),14482(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1643 14482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15293">
    <literal><![CDATA[
      L(x,y,z) \ (z * (x * y)) = T(z * (y * K(x,y)),x)
    ]]></literal>
    <justification jstring="[para(12176(a,1),14743(a,1,1))].">
      <j1 rule="para" parents="12176 14743"/>
    </justification>
  </clause>

  <clause id="15294">
    <literal><![CDATA[
      L(x,(T((y * z) * (z * K(y,z)),y) * u) * w,v5) = L(x,(L(y,z,y * z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(15293(a,1),11943(a,1,2,1,1))].">
      <j1 rule="para" parents="15293 11943"/>
    </justification>
  </clause>

  <clause id="15296">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * z) = T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(14995,a,8158,a)].">
      <j1 rule="hyper" parents="14995 8158"/>
    </justification>
  </clause>

  <clause id="15297">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(10430,a,14368,a),flip(a)].">
      <j1 rule="hyper" parents="10430 14368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15298">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14368(a,1),10430(a,1))].">
      <j1 rule="para" parents="14368 10430"/>
    </justification>
  </clause>

  <clause id="15299">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(14369,a,15297,a),flip(a)].">
      <j1 rule="hyper" parents="14369 15297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15300">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,14362,a(flip),b,15297,a),flip(a)].">
      <j1 rule="hyper" parents="64 14362 15297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15301">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / a(x,z,K(u,y)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(225,a,15297,a(flip),b,14,a(flip))].">
      <j1 rule="hyper" parents="225 15297 14"/>
    </justification>
  </clause>

  <clause id="15302">
    <literal><![CDATA[
      (K(x,y) * (z * u)) * a(x,z,K(u,y)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(145,a,15297,a(flip),b,14,a(flip))].">
      <j1 rule="hyper" parents="145 15297 14"/>
    </justification>
  </clause>

  <clause id="15303">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,14361,a,b,15299,a)].">
      <j1 rule="hyper" parents="373 14361 15299"/>
    </justification>
  </clause>

  <clause id="15304">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13808,a,b,15299,a)].">
      <j1 rule="hyper" parents="373 13808 15299"/>
    </justification>
  </clause>

  <clause id="15305">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,15299,a,b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 15299 5726"/>
    </justification>
  </clause>

  <clause id="15306">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(144,a,15299,a,b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 15299 5739"/>
    </justification>
  </clause>

  <clause id="15307">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) / x = T(1 / x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(142,a,15299,a,b,5989,a)].">
      <j1 rule="hyper" parents="142 15299 5989"/>
    </justification>
  </clause>

  <clause id="15308">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(15299(a,2),5767(a,1,2))].">
      <j1 rule="para" parents="15299 5767"/>
    </justification>
  </clause>

  <clause id="15309">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,w)) != x * v5
    ]]></literal>
    <literal><![CDATA[
      T(y,a(w,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(15299(a,2),6924(a,1,2))].">
      <j1 rule="para" parents="15299 6924"/>
    </justification>
  </clause>

  <clause id="15310">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * T(y,a(w,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(15299(a,2),6940(a,1,2))].">
      <j1 rule="para" parents="15299 6940"/>
    </justification>
  </clause>

  <clause id="15311">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,v5) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(15299(a,2),12059(a,1,1))].">
      <j1 rule="para" parents="15299 12059"/>
    </justification>
  </clause>

  <clause id="15312">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(z,K(x,a(w,y,u)))
    ]]></literal>
    <justification jstring="[para(15299(a,1),13958(a,2,2))].">
      <j1 rule="para" parents="15299 13958"/>
    </justification>
  </clause>

  <clause id="15313">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(u,y,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(15299(a,2),13965(a,2,1))].">
      <j1 rule="para" parents="15299 13965"/>
    </justification>
  </clause>

  <clause id="15314">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(13969,a,15300,a),flip(a)].">
      <j1 rule="hyper" parents="13969 15300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15315">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,15297,a,b,15300,a)].">
      <j1 rule="hyper" parents="373 15297 15300"/>
    </justification>
  </clause>

  <clause id="15316">
    <literal><![CDATA[
      a(x,y,K(z,T(u,y))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,13991,a,b,15300,a)].">
      <j1 rule="hyper" parents="373 13991 15300"/>
    </justification>
  </clause>

  <clause id="15317">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13796,a,b,15300,a)].">
      <j1 rule="hyper" parents="373 13796 15300"/>
    </justification>
  </clause>

  <clause id="15318">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,12246,a,b,15300,a)].">
      <j1 rule="hyper" parents="373 12246 15300"/>
    </justification>
  </clause>

  <clause id="15319">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,12249,a(flip),b,15300,a),flip(a)].">
      <j1 rule="hyper" parents="373 12249 15300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15320">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,12154,a(flip),b,15300,a),flip(a)].">
      <j1 rule="hyper" parents="373 12154 15300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15321">
    <literal><![CDATA[
      a(x,y,K(y * x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,10498,a(flip),b,15300,a),flip(a)].">
      <j1 rule="hyper" parents="373 10498 15300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15322">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (a(u,y,K(z,x)) * w) = w
    ]]></literal>
    <justification jstring="[hyper(144,a,15300,a,b,10433,a)].">
      <j1 rule="hyper" parents="144 15300 10433"/>
    </justification>
  </clause>

  <clause id="15323">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12252,a,b,15300,a)].">
      <j1 rule="hyper" parents="64 12252 15300"/>
    </justification>
  </clause>

  <clause id="15324">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(u,z,K(y \ x,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,12251,a,b,15300,a),flip(a)].">
      <j1 rule="hyper" parents="64 12251 15300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15325">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12246,a,b,15300,a)].">
      <j1 rule="hyper" parents="64 12246 15300"/>
    </justification>
  </clause>

  <clause id="15326">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12233,a,b,15300,a)].">
      <j1 rule="hyper" parents="64 12233 15300"/>
    </justification>
  </clause>

  <clause id="15327">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12127,a,b,15300,a)].">
      <j1 rule="hyper" parents="64 12127 15300"/>
    </justification>
  </clause>

  <clause id="15328">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,12088,a,b,15300,a)].">
      <j1 rule="hyper" parents="64 12088 15300"/>
    </justification>
  </clause>

  <clause id="15329">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,12087,a,b,15300,a)].">
      <j1 rule="hyper" parents="64 12087 15300"/>
    </justification>
  </clause>

  <clause id="15330">
    <literal><![CDATA[
      a(L(x,y,z),x,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,10570,a(flip),b,15300,a),flip(a)].">
      <j1 rule="hyper" parents="64 10570 15300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15331">
    <literal><![CDATA[
      a(x,y,K(z,x * y)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,10491,a(flip),b,15300,a),flip(a)].">
      <j1 rule="hyper" parents="64 10491 15300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15332">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,15300,a(flip),b,13959,a)].">
      <j1 rule="hyper" parents="145 15300 13959"/>
    </justification>
  </clause>

  <clause id="15333">
    <literal><![CDATA[
      a(x,y,K(z * (u / T(w,x)),v5)) = a(v5,y,K(x,z * (u / w)))
    ]]></literal>
    <justification jstring="[para(8619(a,1),15300(a,2,3))].">
      <j1 rule="para" parents="8619 15300"/>
    </justification>
  </clause>

  <clause id="15334">
    <literal><![CDATA[
      a(x,y,K(z * (T(u,x) \ w),v5)) = a(v5,y,K(x,z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(8644(a,1),15300(a,2,3))].">
      <j1 rule="para" parents="8644 15300"/>
    </justification>
  </clause>

  <clause id="15335">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * a(w,z,K(u,y)) = v5
    ]]></literal>
    <justification jstring="[para(15300(a,2),10429(a,1,2))].">
      <j1 rule="para" parents="15300 10429"/>
    </justification>
  </clause>

  <clause id="15336">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(15300(a,1),12069(a,1,2))].">
      <j1 rule="para" parents="15300 12069"/>
    </justification>
  </clause>

  <clause id="15337">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(15300(a,2),12069(a,1,2))].">
      <j1 rule="para" parents="15300 12069"/>
    </justification>
  </clause>

  <clause id="15338">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,L(z,y,u)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(15300(a,2),12120(a,1,1))].">
      <j1 rule="para" parents="15300 12120"/>
    </justification>
  </clause>

  <clause id="15339">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15300(a,1),12116(a,1,2))].">
      <j1 rule="para" parents="15300 12116"/>
    </justification>
  </clause>

  <clause id="15340">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15300(a,2),12116(a,1,2))].">
      <j1 rule="para" parents="15300 12116"/>
    </justification>
  </clause>

  <clause id="15341">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(15300(a,1),13962(a,1,1))].">
      <j1 rule="para" parents="15300 13962"/>
    </justification>
  </clause>

  <clause id="15342">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(15300(a,1),13964(a,1,2))].">
      <j1 rule="para" parents="15300 13964"/>
    </justification>
  </clause>

  <clause id="15343">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(15300(a,1),14296(a,2,2))].">
      <j1 rule="para" parents="15300 14296"/>
    </justification>
  </clause>

  <clause id="15344">
    <literal><![CDATA[
      a(L(x,y,y),z,K(u,w)) = a(u,z,K(w,x))
    ]]></literal>
    <justification jstring="[para(14411(a,1),15300(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14411 15300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15345">
    <literal><![CDATA[
      L(K(x * y,z),x,y) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,15321,a)].">
      <j1 rule="hyper" parents="53 15321"/>
    </justification>
  </clause>

  <clause id="15346">
    <literal><![CDATA[
      a(x,y,K(x * y,z)) = 1
    ]]></literal>
    <justification jstring="[para(11177(a,1),15321(a,1,3))].">
      <j1 rule="para" parents="11177 15321"/>
    </justification>
  </clause>

  <clause id="15347">
    <literal><![CDATA[
      a(x,y,K(z,x * (y * z))) = 1
    ]]></literal>
    <justification jstring="[hyper(12166,a,15331,a)].">
      <j1 rule="hyper" parents="12166 15331"/>
    </justification>
  </clause>

  <clause id="15348">
    <literal><![CDATA[
      L(K(x * y,z),y,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,15346,a)].">
      <j1 rule="hyper" parents="53 15346"/>
    </justification>
  </clause>

  <clause id="15349">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(15330(a,1),12069(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15330 12069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15350">
    <literal><![CDATA[
      K(a(x,y,z),x * (y * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,13977,a(flip),b,15347,a)].">
      <j1 rule="hyper" parents="64 13977 15347"/>
    </justification>
  </clause>

  <clause id="15351">
    <literal><![CDATA[
      a(x,y,z) = 1 * (((x * y) * z) / (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(15350(a,1),5958(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15350 5958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15352">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,y)) = x \ T(y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,15314,a,b,15030,a)].">
      <j1 rule="hyper" parents="145 15314 15030"/>
    </justification>
  </clause>

  <clause id="15353">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * w) = T(u,a(z,y,x)) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,15314,a,b,5733,a)].">
      <j1 rule="hyper" parents="144 15314 5733"/>
    </justification>
  </clause>

  <clause id="15354">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u != w
    ]]></literal>
    <literal><![CDATA[
      T(u,a(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(15314(a,2),5816(a,1,1))].">
      <j1 rule="para" parents="15314 5816"/>
    </justification>
  </clause>

  <clause id="15355">
    <literal><![CDATA[
      a(K(x,y),z,u) = K(a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13977,a(flip),b,15315,a),flip(a)].">
      <j1 rule="hyper" parents="373 13977 15315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15356">
    <literal><![CDATA[
      x * a(K(y,z),u,w) = x * a(w,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,15315,a,b,9,a)].">
      <j1 rule="hyper" parents="145 15315 9"/>
    </justification>
  </clause>

  <clause id="15357">
    <literal><![CDATA[
      K(x * y,L(z,y,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(12091,a,15348,a)].">
      <j1 rule="hyper" parents="12091 15348"/>
    </justification>
  </clause>

  <clause id="15358">
    <literal><![CDATA[
      K(x * y,(x * y) \ z) = K(x * y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,12080,a(flip),b,15348,a)].">
      <j1 rule="hyper" parents="64 12080 15348"/>
    </justification>
  </clause>

  <clause id="15359">
    <literal><![CDATA[
      K(x * y,z \ R(z,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,14422,a(flip),b,15303,a),flip(a)].">
      <j1 rule="hyper" parents="373 14422 15303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15360">
    <literal><![CDATA[
      T(x \ R(x,y,z),y * z) * 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,15359,a(flip),b,5731,a(flip))].">
      <j1 rule="hyper" parents="145 15359 5731"/>
    </justification>
  </clause>

  <clause id="15361">
    <literal><![CDATA[
      T(x,a(y * z,u,y)) = x * a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(12244(a,1),15305(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12244 15305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15362">
    <literal><![CDATA[
      x * a(x,y,a(z,u,K(w,v5))) = T(x,a(v5,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(13977(a,2),15305(a,1,2,3))].">
      <j1 rule="para" parents="13977 15305"/>
    </justification>
  </clause>

  <clause id="15363">
    <literal><![CDATA[
      x * a(x,y,a(z,u,K(w,v5))) = T(x,a(a(v5,u,w),y,z))
    ]]></literal>
    <justification jstring="[para(15299(a,2),15305(a,1,2,3))].">
      <j1 rule="para" parents="15299 15305"/>
    </justification>
  </clause>

  <clause id="15364">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ x = T(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10432,a,b,15306,a)].">
      <j1 rule="hyper" parents="64 10432 15306"/>
    </justification>
  </clause>

  <clause id="15365">
    <literal><![CDATA[
      a(x,y,K(z \ (u * x),w)) = a(w,y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[para(10165(a,1),15318(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10165 15318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15366">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,15300,a(flip),b,15319,a),flip(a)].">
      <j1 rule="hyper" parents="373 15300 15319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15367">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,2653,a(flip),b,15319,a)].">
      <j1 rule="hyper" parents="64 2653 15319"/>
    </justification>
  </clause>

  <clause id="15368">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[para(15319(a,1),12069(a,1,2))].">
      <j1 rule="para" parents="15319 12069"/>
    </justification>
  </clause>

  <clause id="15369">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(15319(a,1),12116(a,1,2))].">
      <j1 rule="para" parents="15319 12116"/>
    </justification>
  </clause>

  <clause id="15370">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15300,a,b,15367,a)].">
      <j1 rule="hyper" parents="373 15300 15367"/>
    </justification>
  </clause>

  <clause id="15371">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,15297,a,b,15367,a)].">
      <j1 rule="hyper" parents="373 15297 15367"/>
    </justification>
  </clause>

  <clause id="15372">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15314,a(flip),b,15367,a),flip(a)].">
      <j1 rule="hyper" parents="373 15314 15367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15374">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,15299,a(flip),b,15367,a),flip(a)].">
      <j1 rule="hyper" parents="373 15299 15367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15375">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(15367(a,1),12069(a,1,2))].">
      <j1 rule="para" parents="15367 12069"/>
    </justification>
  </clause>

  <clause id="15376">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(15367(a,1),15305(a,1,2))].">
      <j1 rule="para" parents="15367 15305"/>
    </justification>
  </clause>

  <clause id="15377">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(x,K(z,a(u,y,w)))
    ]]></literal>
    <justification jstring="[para(15372(a,1),15372(a,2,2))].">
      <j1 rule="para" parents="15372 15372"/>
    </justification>
  </clause>

  <clause id="15378">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15300,a,b,15320,a),flip(a)].">
      <j1 rule="hyper" parents="373 15300 15320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15379">
    <literal><![CDATA[
      a(x \ y,z,K(u,x)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,15300,a(flip),b,15325,a)].">
      <j1 rule="hyper" parents="64 15300 15325"/>
    </justification>
  </clause>

  <clause id="15380">
    <literal><![CDATA[
      a(x,y,K(z,x \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15300,a(flip),b,15326,a)].">
      <j1 rule="hyper" parents="64 15300 15326"/>
    </justification>
  </clause>

  <clause id="15381">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(15327(a,1),12164(a,1))].">
      <j1 rule="para" parents="15327 12164"/>
    </justification>
  </clause>

  <clause id="15382">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(15327(a,1),15305(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15327 15305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15383">
    <literal><![CDATA[
      (x * y) / T(x,L(y,z,u)) = T(y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(12128,a,15332,a)].">
      <j1 rule="hyper" parents="12128 15332"/>
    </justification>
  </clause>

  <clause id="15384">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,K(z \ 1,x)) = T(L(x,y,z),a(z \ 1,w,u))
    ]]></literal>
    <justification jstring="[para(7397(a,1),15332(a,1,2,3))].">
      <j1 rule="para" parents="7397 15332"/>
    </justification>
  </clause>

  <clause id="15385">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),y) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(15332(a,1),12465(a,1,1))].">
      <j1 rule="para" parents="15332 12465"/>
    </justification>
  </clause>

  <clause id="15386">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[para(15332(a,1),13981(a,1,1))].">
      <j1 rule="para" parents="15332 13981"/>
    </justification>
  </clause>

  <clause id="15387">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(w,a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[para(15386(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="15386 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15389">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(15349(a,2),152(a,1))].">
      <j1 rule="para" parents="15349 152"/>
    </justification>
  </clause>

  <clause id="15390">
    <literal><![CDATA[
      a(K(x,y) / z,u,K(w,v5)) = a(z * K(y,x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[para(14592(a,1),15366(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14592 15366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15391">
    <literal><![CDATA[
      a(x,y * z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13838,a(flip),b,15378,a),flip(a)].">
      <j1 rule="hyper" parents="64 13838 15378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15392">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),15379(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 15379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15393">
    <literal><![CDATA[
      a(L(x,y,z) \ u,w,K(z,x)) = a(u,w,K(z,L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(7394(a,1),15379(a,1,3))].">
      <j1 rule="para" parents="7394 15379"/>
    </justification>
  </clause>

  <clause id="15394">
    <literal><![CDATA[
      a(x,y,K(z,x * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),15380(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 15380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15395">
    <literal><![CDATA[
      T(T(x,y),a(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(481,a,15385,a)].">
      <j1 rule="hyper" parents="481 15385"/>
    </justification>
  </clause>

  <clause id="15396">
    <literal><![CDATA[
      T(x,a(y,z,u)) * y = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,15385,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 15385 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15397">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),L(u,z,y)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(15386(a,1),15385(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15386 15385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15398">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(y,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8110(a,2),15391(a,1,3))].">
      <j1 rule="para" parents="8110 15391"/>
    </justification>
  </clause>

  <clause id="15399">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,x)) = T(x * y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(15392(a,1),15305(a,1,2))].">
      <j1 rule="para" parents="15392 15305"/>
    </justification>
  </clause>

  <clause id="15400">
    <literal><![CDATA[
      T(x,a(x * y,z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(15394(a,1),15305(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15394 15305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15401">
    <literal><![CDATA[
      T(x,L(y,z,u)) != T(w,a(y,z,u))
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(15395(a,1),50(a,1))].">
      <j1 rule="para" parents="15395 50"/>
    </justification>
  </clause>

  <clause id="15402">
    <literal><![CDATA[
      T(x,a(a(y,x,z),u,w)) = T(x,L(a(y,x,z),u,w))
    ]]></literal>
    <justification jstring="[para(13970(a,1),15395(a,1,1))].">
      <j1 rule="para" parents="13970 15395"/>
    </justification>
  </clause>

  <clause id="15403">
    <literal><![CDATA[
      T(x,L(y,z,u)) != T(w,y)
    ]]></literal>
    <literal><![CDATA[
      T(w,a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[para(15397(a,1),50(a,1)),flip(a)].">
      <j1 rule="para" parents="15397 50"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15404">
    <literal><![CDATA[
      K(L(x,y,z) * T(u,a(z,y,x)),w) = K(T(u,x) * L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(15397(a,1),11201(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="15397 11201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15405">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(15315(a,1),15298(a,1))].">
      <j1 rule="para" parents="15315 15298"/>
    </justification>
  </clause>

  <clause id="15406">
    <literal><![CDATA[
      a(L(x,y,y),z,K(u,L(w,v5,v6))) = a(u,z,K(w,L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[para(12093(a,1),15344(a,2,3))].">
      <j1 rule="para" parents="12093 15344"/>
    </justification>
  </clause>

  <clause id="15407">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(15297(a,2),15381(a,1))].">
      <j1 rule="para" parents="15297 15381"/>
    </justification>
  </clause>

  <clause id="15409">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15370(a,1),15381(a,1))].">
      <j1 rule="para" parents="15370 15381"/>
    </justification>
  </clause>

  <clause id="15410">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(15320(a,2),15381(a,1))].">
      <j1 rule="para" parents="15320 15381"/>
    </justification>
  </clause>

  <clause id="15411">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15326(a,2),15381(a,1))].">
      <j1 rule="para" parents="15326 15381"/>
    </justification>
  </clause>

  <clause id="15412">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(15378(a,2),15381(a,1))].">
      <j1 rule="para" parents="15378 15381"/>
    </justification>
  </clause>

  <clause id="15413">
    <literal><![CDATA[
      a(x,y,K(z,x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(15380(a,2),15381(a,1))].">
      <j1 rule="para" parents="15380 15381"/>
    </justification>
  </clause>

  <clause id="15414">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(2482(a,2),15389(a,1,2))].">
      <j1 rule="para" parents="2482 15389"/>
    </justification>
  </clause>

  <clause id="15415">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,K(w,z))) = v5
    ]]></literal>
    <justification jstring="[para(8112(a,1),15405(a,1,3))].">
      <j1 rule="para" parents="8112 15405"/>
    </justification>
  </clause>

  <clause id="15416">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(12087(a,2),15405(a,1))].">
      <j1 rule="para" parents="12087 15405"/>
    </justification>
  </clause>

  <clause id="15417">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(13792(a,2),15405(a,1))].">
      <j1 rule="para" parents="13792 15405"/>
    </justification>
  </clause>

  <clause id="15418">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15414,a,xx),flip(a)].">
      <j1 rule="hyper" parents="15414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15419">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w) \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11794(a,2),15418(a,1,2))].">
      <j1 rule="para" parents="11794 15418"/>
    </justification>
  </clause>

  <clause id="15420">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,x) = K(z,L(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,12120,a(flip),b,15313,a)].">
      <j1 rule="hyper" parents="145 12120 15313"/>
    </justification>
  </clause>

  <clause id="15421">
    <literal><![CDATA[
      (a(x,y,K(z,u)) \ T(w,a(u,y,K(z,x)) * v5)) / (a(u,y,K(z,x)) * w) = K(w,v5 * a(u,y,K(z,x)))
    ]]></literal>
    <justification jstring="[hyper(142,a,15313,a,b,11108,a)].">
      <j1 rule="hyper" parents="142 15313 11108"/>
    </justification>
  </clause>

  <clause id="15422">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) * a(y,z,K(x,u)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,15317,a(flip),b,10920,a)].">
      <j1 rule="hyper" parents="145 15317 10920"/>
    </justification>
  </clause>

  <clause id="15423">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) * w = v5
    ]]></literal>
    <justification jstring="[para(15322(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15322 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15424">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(6897,a,15328,a)].">
      <j1 rule="hyper" parents="6897 15328"/>
    </justification>
  </clause>

  <clause id="15425">
    <literal><![CDATA[
      T(x,y) * a(x,z,K(u,y)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,15328,a(flip),b,6422,a)].">
      <j1 rule="hyper" parents="145 15328 6422"/>
    </justification>
  </clause>

  <clause id="15426">
    <literal><![CDATA[
      K(x,y) * (K(y,L(x,z,u)) * w) = a(y,z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[para(15328(a,1),9809(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15328 9809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15427">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = u / a(L(x,y,z) \ u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(15329(a,1),15241(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15329 15241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15428">
    <literal><![CDATA[
      K(x,L(y,z,u)) * a(x,z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10427,a,15336,a)].">
      <j1 rule="hyper" parents="10427 15336"/>
    </justification>
  </clause>

  <clause id="15430">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(10715(a,1),15336(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10715 15336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15431">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y \ (u / w),y)) = K(x,L(y,z,u / (y * w)))
    ]]></literal>
    <justification jstring="[para(10776(a,1),15336(a,1,2,3))].">
      <j1 rule="para" parents="10776 15336"/>
    </justification>
  </clause>

  <clause id="15432">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,z,y \ u))
    ]]></literal>
    <justification jstring="[para(12233(a,1),15336(a,1,2))].">
      <j1 rule="para" parents="12233 15336"/>
    </justification>
  </clause>

  <clause id="15433">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[para(12250(a,1),15336(a,1,2))].">
      <j1 rule="para" parents="12250 15336"/>
    </justification>
  </clause>

  <clause id="15434">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,(u \ 1) * w))
    ]]></literal>
    <justification jstring="[para(14492(a,1),15336(a,1,2,3))].">
      <j1 rule="para" parents="14492 15336"/>
    </justification>
  </clause>

  <clause id="15435">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u * w,y)) = K(x,L(y,z,u / (w \ 1)))
    ]]></literal>
    <justification jstring="[para(14681(a,1),15336(a,1,2,3))].">
      <j1 rule="para" parents="14681 15336"/>
    </justification>
  </clause>

  <clause id="15436">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,y) * a(x,z,K(u * (w \ y),y))
    ]]></literal>
    <justification jstring="[para(15032(a,1),15336(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="15032 15336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15437">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,y) * a(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[para(15378(a,1),15336(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15378 15336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15438">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u / (w * v5))) = K(x,L(y,z,u / (T(w,x) * v5)))
    ]]></literal>
    <justification jstring="[para(9200(a,1),15337(a,1,2,3))].">
      <j1 rule="para" parents="9200 15337"/>
    </justification>
  </clause>

  <clause id="15439">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,w \ 1) \ 1)) = K(x,y) * a(y,z,1)
    ]]></literal>
    <justification jstring="[para(10571(a,1),15337(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="10571 15337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15440">
    <literal><![CDATA[
      K(x,L(y,z,(u * T(x,w)) \ v5)) = K(x,y) * a(y,z,K(x,x \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(12150(a,1),15337(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="12150 15337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15441">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u * (w * K(v5,v6)))) = K(x,L(y,z,u / (K(v6,v5) / w)))
    ]]></literal>
    <justification jstring="[para(14602(a,1),15337(a,1,2,3))].">
      <j1 rule="para" parents="14602 15337"/>
    </justification>
  </clause>

  <clause id="15442">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(5826,a,15343,a)].">
      <j1 rule="hyper" parents="5826 15343"/>
    </justification>
  </clause>

  <clause id="15443">
    <literal><![CDATA[
      a(x,y,K(z,a(x,y,z) \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,14119,a(flip),b,15442,a)].">
      <j1 rule="hyper" parents="64 14119 15442"/>
    </justification>
  </clause>

  <clause id="15444">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,10419,a(flip),b,15356,a)].">
      <j1 rule="hyper" parents="139 10419 15356"/>
    </justification>
  </clause>

  <clause id="15445">
    <literal><![CDATA[
      x * a(K(y,z),u,w) != v5 * a(w,u,K(z,y))
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(15356(a,1),45(a,2))].">
      <j1 rule="para" parents="15356 45"/>
    </justification>
  </clause>

  <clause id="15446">
    <literal><![CDATA[
      T(x,a(y * z,u,y)) = T(x,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,15305,a(flip),b,15361,a),flip(a)].">
      <j1 rule="hyper" parents="373 15305 15361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15447">
    <literal><![CDATA[
      T(x,a(y \ z,u,y)) = T(x,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),15446(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 15446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15448">
    <literal><![CDATA[
      K(x,y) * a(x,z,a(y,u,K(w,v5))) = K(x,L(y,z,a(w,u,v5)))
    ]]></literal>
    <justification jstring="[para(15372(a,2),15375(a,1,2,3))].">
      <j1 rule="para" parents="15372 15375"/>
    </justification>
  </clause>

  <clause id="15449">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13961,a(flip),b,15382,a),flip(a)].">
      <j1 rule="hyper" parents="373 13961 15382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15450">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15382(a,2),13964(a,1))].">
      <j1 rule="para" parents="15382 13964"/>
    </justification>
  </clause>

  <clause id="15451">
    <literal><![CDATA[
      T(x,a(x * y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15305,a(flip),b,15400,a),flip(a)].">
      <j1 rule="hyper" parents="373 15305 15400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15452">
    <literal><![CDATA[
      T(x,a(x \ y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),15451(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 15451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15453">
    <literal><![CDATA[
      K(x,L(y,z,u * L(u \ 1,u,w))) = a(y,z,1) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9474(a,1),15420(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="9474 15420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15454">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,12059,a,b,15424,a),flip(a)].">
      <j1 rule="hyper" parents="373 12059 15424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15455">
    <literal><![CDATA[
      T(x,y) * a(K(x,y),z,u) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(15297(a,2),15425(a,1,2))].">
      <j1 rule="para" parents="15297 15425"/>
    </justification>
  </clause>

  <clause id="15456">
    <literal><![CDATA[
      a(K(x,y),z,u) \ T(y,x) = T(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(15444(a,1),12083(a,1,1))].">
      <j1 rule="para" parents="15444 12083"/>
    </justification>
  </clause>

  <clause id="15457">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(x,K(u,w)) = K(u,K(w,L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,12092,a(flip),b,15454,a),flip(a)].">
      <j1 rule="hyper" parents="373 12092 15454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15458">
    <literal><![CDATA[
      L(K(x,y),z,u) != w * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(15454(a,1),45(a,1))].">
      <j1 rule="para" parents="15454 45"/>
    </justification>
  </clause>

  <clause id="15459">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(x,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,K(w,L(x,y,z))) = v5
    ]]></literal>
    <justification jstring="[para(15454(a,2),12098(a,1))].">
      <j1 rule="para" parents="15454 12098"/>
    </justification>
  </clause>

  <clause id="15460">
    <literal><![CDATA[
      T(x,y) * a(K(x,y),z,u) = x * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,5753,a(flip),b,15455,a),flip(a)].">
      <j1 rule="hyper" parents="373 5753 15455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15462">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7,a(flip),b,15351,a),flip(a)].">
      <j1 rule="hyper" parents="373 7 15351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15463">
    <literal><![CDATA[
      a(x,y,z) * (x * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,15351,a,b,7,a(flip))].">
      <j1 rule="hyper" parents="144 15351 7"/>
    </justification>
  </clause>

  <clause id="15465">
    <literal><![CDATA[
      a(x,y,z) = (z * (x * y)) / ((x * (y * z)) * K(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,15226,a,b,15462,a),flip(a)].">
      <j1 rule="hyper" parents="373 15226 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15466">
    <literal><![CDATA[
      (x * (y * z)) / (y * (z * T(x,y * z))) = a(y,z,T(x,y * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,250,a(flip),b,15462,a)].">
      <j1 rule="hyper" parents="373 250 15462"/>
    </justification>
  </clause>

  <clause id="15467">
    <literal><![CDATA[
      a(x,y,z) \ ((x * y) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(143,a,15462,a,b,171,a)].">
      <j1 rule="hyper" parents="143 15462 171"/>
    </justification>
  </clause>

  <clause id="15468">
    <literal><![CDATA[
      (x * y) / (z * ((z \ x) * y)) = a(z,z \ x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),15462(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15469">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / (x * z) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),15462(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15470">
    <literal><![CDATA[
      (x * y) / ((x / z) * (z * y)) = a(x / z,z,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),15462(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15471">
    <literal><![CDATA[
      (((x / (y * z)) * y) * z) / x = a(x / (y * z),y,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),15462(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15472">
    <literal><![CDATA[
      ((x * y) * z) / (y * (T(x,y) * z)) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(115(a,1),15462(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="115 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15473">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (x * (z * y)) = a(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[para(115(a,1),15462(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="115 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15474">
    <literal><![CDATA[
      ((x * R(x,y,z)) * u) / (R(x,y,z) * (x * u)) = a(R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(274(a,1),15462(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="274 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15475">
    <literal><![CDATA[
      ((x * L(y,z,u)) * y) / (x * (y * L(y,z,u))) = a(x,L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(275(a,1),15462(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="275 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15476">
    <literal><![CDATA[
      (L(x,y,z) * u) / ((x \ L(x,y,z)) * (x * u)) = a(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(5550(a,1),15462(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5550 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15477">
    <literal><![CDATA[
      (L(x,y,y) * z) / ((a(y,y,x) \ 1) * (x * z)) = a(a(y,y,x) \ 1,x,z)
    ]]></literal>
    <justification jstring="[para(5669(a,1),15462(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5669 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15478">
    <literal><![CDATA[
      K((x * (y * z)) / ((x * y) * z),u) = K(a(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(15462(a,2),6580(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="15462 6580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15480">
    <literal><![CDATA[
      ((x * y) * z) / ((y * z) * x) = a(x,y,z) * K(x,y * z)
    ]]></literal>
    <justification jstring="[para(15462(a,2),10595(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15462 10595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15481">
    <literal><![CDATA[
      a(x,x \ y,z) \ (y * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,167,a(flip),b,15463,a)].">
      <j1 rule="hyper" parents="139 167 15463"/>
    </justification>
  </clause>

  <clause id="15482">
    <literal><![CDATA[
      ((x * y) * z) / L(y * z,x,a(x,y,z)) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(142,a,15463,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="142 15463 100"/>
    </justification>
  </clause>

  <clause id="15484">
    <literal><![CDATA[
      R(x,a(y,z,u) * ((y * z) * u),x) = R(x,y * (z * u),x)
    ]]></literal>
    <justification jstring="[para(15467(a,1),13733(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15467 13733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15485">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * z) != w
    ]]></literal>
    <literal><![CDATA[
      T(u * z,a(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(12247(a,1),15354(a,1,1))].">
      <j1 rule="para" parents="12247 15354"/>
    </justification>
  </clause>

  <clause id="15487">
    <literal><![CDATA[
      a(x,y,K(z \ (u \ w),u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z \ w,u)) = v5
    ]]></literal>
    <justification jstring="[para(10222(a,2),15411(a,1,3))].">
      <j1 rule="para" parents="10222 15411"/>
    </justification>
  </clause>

  <clause id="15488">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15412,a,15300,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="15412 15300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15489">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(y,x) \ a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(139,a,15488,a(flip),b,12087,a),flip(a)].">
      <j1 rule="hyper" parents="139 15488 12087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15490">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(15488(a,1),15305(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15488 15305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15491">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(15488(a,1),15332(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15488 15332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15492">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15305,a(flip),b,15490,a),flip(a)].">
      <j1 rule="hyper" parents="373 15305 15490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15493">
    <literal><![CDATA[
      T(T(x,y),a(z,x \ u,w)) = T(T(x,a(z,u,w)),y)
    ]]></literal>
    <justification jstring="[para(15492(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15492 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15494">
    <literal><![CDATA[
      T(x * K(y,z),a(u,K(z,y),w)) = T(x * K(y,z),a(u,x,w))
    ]]></literal>
    <justification jstring="[para(6882(a,1),15492(a,1,2,2))].">
      <j1 rule="para" parents="6882 15492"/>
    </justification>
  </clause>

  <clause id="15495">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,15332,a(flip),b,15491,a),flip(a)].">
      <j1 rule="hyper" parents="373 15332 15491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15496">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(15491(a,2),15342(a,1))].">
      <j1 rule="para" parents="15491 15342"/>
    </justification>
  </clause>

  <clause id="15497">
    <literal><![CDATA[
      T(x,a(y,z * u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),15495(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 15495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15498">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = a(z,y,u) * (x / a(z,y,u))
    ]]></literal>
    <justification jstring="[para(15443(a,1),13978(a,1,1))].">
      <j1 rule="para" parents="15443 13978"/>
    </justification>
  </clause>

  <clause id="15499">
    <literal><![CDATA[
      a(x,x \ y,y \ z) \ z = x * ((x \ y) * (y \ z))
    ]]></literal>
    <justification jstring="[para(15468(a,1),349(a,1,1))].">
      <j1 rule="para" parents="15468 349"/>
    </justification>
  </clause>

  <clause id="15500">
    <literal><![CDATA[
      (L(x,y,y) * z) / (x * ((a(y,y,x) \ 1) * z)) = a(x,x \ L(x,y,y),z)
    ]]></literal>
    <justification jstring="[para(5665(a,2),15468(a,1,2,2,1))].">
      <j1 rule="para" parents="5665 15468"/>
    </justification>
  </clause>

  <clause id="15501">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,x,x) \ 1) = ((x * x) * (x \ y)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1847,a,b,15469,a)].">
      <j1 rule="hyper" parents="373 1847 15469"/>
    </justification>
  </clause>

  <clause id="15502">
    <literal><![CDATA[
      ((x * x) * (x \ y)) / (x * y) = L(x \ y,x,x) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1243,a,b,15469,a),flip(a)].">
      <j1 rule="hyper" parents="373 1243 15469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15503">
    <literal><![CDATA[
      a(x,x \ (x \ y),x) \ ((x \ y) * x) = y * K(x \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10197,a,b,15481,a),flip(a)].">
      <j1 rule="hyper" parents="373 10197 15481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15504">
    <literal><![CDATA[
      T(1 / x,a(y,z,u)) = a(x,z,K(y,u)) / x
    ]]></literal>
    <justification jstring="[para(15366(a,1),15307(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15366 15307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15505">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,12531,a,b,15311,a)].">
      <j1 rule="hyper" parents="64 12531 15311"/>
    </justification>
  </clause>

  <clause id="15506">
    <literal><![CDATA[
      K(x * (y \ 1),(y \ 1) \ (x \ z)) = K(x / y,(x * (y \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(14676,a,15358,a),flip(a)].">
      <j1 rule="hyper" parents="14676 15358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15507">
    <literal><![CDATA[
      T(x \ R(x,y,z),y * z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(152,a,15360,a)].">
      <j1 rule="hyper" parents="152 15360"/>
    </justification>
  </clause>

  <clause id="15508">
    <literal><![CDATA[
      K(x,L(y,z,u)) * a(x,w,K(y,u)) = K(x,L(L(y,z,u),w,u \ 1))
    ]]></literal>
    <justification jstring="[para(7373(a,1),15368(a,1,2,3))].">
      <j1 rule="para" parents="7373 15368"/>
    </justification>
  </clause>

  <clause id="15509">
    <literal><![CDATA[
      K(x,y) * a(x,z,a(y,u,K(w,v5))) = K(x,L(y,z,a(v5,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(15299(a,2),15368(a,1,2,3))].">
      <j1 rule="para" parents="15299 15368"/>
    </justification>
  </clause>

  <clause id="15510">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(u,K(w,y)))
    ]]></literal>
    <justification jstring="[para(8110(a,2),15398(a,2,3))].">
      <j1 rule="para" parents="8110 15398"/>
    </justification>
  </clause>

  <clause id="15511">
    <literal><![CDATA[
      K(x,L(y,z,y \ u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15336,a(flip),b,15432,a),flip(a)].">
      <j1 rule="hyper" parents="64 15336 15432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15512">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15368,a(flip),b,15433,a)].">
      <j1 rule="hyper" parents="64 15368 15433"/>
    </justification>
  </clause>

  <clause id="15513">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,(w \ u) \ y))
    ]]></literal>
    <justification jstring="[para(12251(a,2),15433(a,1,2))].">
      <j1 rule="para" parents="12251 15433"/>
    </justification>
  </clause>

  <clause id="15514">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,15336,a(flip),b,15437,a),flip(a)].">
      <j1 rule="hyper" parents="373 15336 15437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15515">
    <literal><![CDATA[
      K(x,L(y \ (z \ u),u,z)) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(12086,a,15514,a),flip(a)].">
      <j1 rule="hyper" parents="12086 15514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15516">
    <literal><![CDATA[
      K(x,L(y,z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,10174,a(flip),b,15514,a),flip(a)].">
      <j1 rule="hyper" parents="373 10174 15514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15517">
    <literal><![CDATA[
      T(x,L(y,z \ u,z)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,15514,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 15514 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15518">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),15514(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 15514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15519">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u \ 1),z)) = K(x,L(y,R(z,u,u \ 1),z))
    ]]></literal>
    <justification jstring="[para(982(a,1),15514(a,1,2,2))].">
      <j1 rule="para" parents="982 15514"/>
    </justification>
  </clause>

  <clause id="15520">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,z,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(630(a,1),15514(a,1,2)),flip(a)].">
      <j1 rule="para" parents="630 15514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15521">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),L(u,z,z \ 1))) = K(x,L(y,u,L(u,z,z \ 1)))
    ]]></literal>
    <justification jstring="[para(2673(a,1),15514(a,1,2,2))].">
      <j1 rule="para" parents="2673 15514"/>
    </justification>
  </clause>

  <clause id="15522">
    <literal><![CDATA[
      K(x,L(y,z * u,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10995(a,1),15514(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10995 15514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15523">
    <literal><![CDATA[
      K(x,L(y,z,u \ z)) = K(x,L(y,u,u \ z))
    ]]></literal>
    <justification jstring="[para(10997(a,1),15514(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10997 15514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15524">
    <literal><![CDATA[
      x * K(y,L(z,x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[para(15514(a,1),12076(a,1,2))].">
      <j1 rule="para" parents="15514 12076"/>
    </justification>
  </clause>

  <clause id="15525">
    <literal><![CDATA[
      K(x,(y * z) \ x) = K(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(12086,a,15516,a)].">
      <j1 rule="hyper" parents="12086 15516"/>
    </justification>
  </clause>

  <clause id="15526">
    <literal><![CDATA[
      T(x,L(y,z \ x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,15516,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 15516 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15527">
    <literal><![CDATA[
      K(x,(y \ x) \ z) = K(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(630(a,1),15516(a,1,2)),flip(a)].">
      <j1 rule="para" parents="630 15516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15528">
    <literal><![CDATA[
      K(x,L(y,z,z \ x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(10997(a,1),15516(a,1,2))].">
      <j1 rule="para" parents="10997 15516"/>
    </justification>
  </clause>

  <clause id="15529">
    <literal><![CDATA[
      T(x,(y \ x) \ z) = T(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(630(a,1),15526(a,1,2)),flip(a)].">
      <j1 rule="para" parents="630 15526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15530">
    <literal><![CDATA[
      K(x,T(y,z) * L(z,u \ y,u)) = K(x,L(z,u \ y,u) * y)
    ]]></literal>
    <justification jstring="[para(15526(a,1),11142(a,1,2,1))].">
      <j1 rule="para" parents="15526 11142"/>
    </justification>
  </clause>

  <clause id="15531">
    <literal><![CDATA[
      L(K(x,y),z,z \ x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12060,a,15528,a)].">
      <j1 rule="hyper" parents="12060 15528"/>
    </justification>
  </clause>

  <clause id="15532">
    <literal><![CDATA[
      T(x,L(y,z * u,z)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),15517(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 15517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15533">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) = x \ T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,5726,a(flip),b,15518,a),flip(a)].">
      <j1 rule="hyper" parents="373 5726 15518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15534">
    <literal><![CDATA[
      K(x,L(y,z * u,z \ 1)) = K(x,L(y,u,z \ 1))
    ]]></literal>
    <justification jstring="[para(11864(a,1),15518(a,1,2))].">
      <j1 rule="para" parents="11864 15518"/>
    </justification>
  </clause>

  <clause id="15535">
    <literal><![CDATA[
      K(x * y,L(z,x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(15522(a,1),10779(a,1))].">
      <j1 rule="para" parents="15522 10779"/>
    </justification>
  </clause>

  <clause id="15536">
    <literal><![CDATA[
      T(x,(y * z) \ x) = T(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(143,a,15525,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 15525 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15537">
    <literal><![CDATA[
      K(x,T(y,y \ x) \ z) = K(x,x \ ((y \ x) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13447,a,b,15527,a)].">
      <j1 rule="hyper" parents="64 13447 15527"/>
    </justification>
  </clause>

  <clause id="15538">
    <literal><![CDATA[
      T(T(x,x \ (y * z)),u) \ T(x,u) = K((y \ x) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(15529(a,1),5800(a,1,1,1))].">
      <j1 rule="para" parents="15529 5800"/>
    </justification>
  </clause>

  <clause id="15539">
    <literal><![CDATA[
      T(x * y,L(z,y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(15532(a,1),10190(a,1))].">
      <j1 rule="para" parents="15532 10190"/>
    </justification>
  </clause>

  <clause id="15540">
    <literal><![CDATA[
      T(x,L(y,z \ T(u * z,w),T(u,z))) = T(x,L(y,K(u * z,w),T(u,z)))
    ]]></literal>
    <justification jstring="[para(15042(a,1),15532(a,1,2,2))].">
      <j1 rule="para" parents="15042 15532"/>
    </justification>
  </clause>

  <clause id="15541">
    <literal><![CDATA[
      K(x,L(y \ z,u,y \ u)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[para(11070(a,1),15523(a,2,2))].">
      <j1 rule="para" parents="11070 15523"/>
    </justification>
  </clause>

  <clause id="15542">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * z))) = K(x,L(T(u,z),y,z \ y))
    ]]></literal>
    <justification jstring="[para(11069(a,1),15523(a,2,2)),flip(a)].">
      <j1 rule="para" parents="11069 15523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15543">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,((z \ u) / w) \ (u / z))) = K(x,L(y,u / z,w * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(15104(a,1),15523(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="15104 15523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15544">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(15533(a,2),5827(a,1))].">
      <j1 rule="para" parents="15533 5827"/>
    </justification>
  </clause>

  <clause id="15545">
    <literal><![CDATA[
      T(x * (y / z),L(z,z \ y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * (y / z),z) = u
    ]]></literal>
    <justification jstring="[para(10259(a,1),15539(a,1,2))].">
      <j1 rule="para" parents="10259 15539"/>
    </justification>
  </clause>

  <clause id="15546">
    <literal><![CDATA[
      K(x,(y * z) \ L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (y \ L(y,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(15515(a,1),15414(a,1))].">
      <j1 rule="para" parents="15515 15414"/>
    </justification>
  </clause>

  <clause id="15547">
    <literal><![CDATA[
      K(x,(y \ R(y,z,u)) \ w) = K(x,R(y,z,u) \ (y * w))
    ]]></literal>
    <justification jstring="[hyper(141,a,15430,a(flip),b,15520,a(flip))].">
      <j1 rule="hyper" parents="141 15430 15520"/>
    </justification>
  </clause>

  <clause id="15548">
    <literal><![CDATA[
      x \ (K(y,L(z,u,x)) * u) = (x \ u) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(8842,a,15524,a)].">
      <j1 rule="hyper" parents="8842 15524"/>
    </justification>
  </clause>

  <clause id="15549">
    <literal><![CDATA[
      x \ (y * K(z,L(u,y,x))) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(720,a,15524,a)].">
      <j1 rule="hyper" parents="720 15524"/>
    </justification>
  </clause>

  <clause id="15550">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(10(a,1),15544(a,1,2,2))].">
      <j1 rule="para" parents="10 15544"/>
    </justification>
  </clause>

  <clause id="15551">
    <literal><![CDATA[
      K(x,L(y,z * u,z \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z \ 1)) = w
    ]]></literal>
    <justification jstring="[para(11864(a,1),15544(a,1,2))].">
      <j1 rule="para" parents="11864 15544"/>
    </justification>
  </clause>

  <clause id="15552">
    <literal><![CDATA[
      x \ (y * K(z,y)) = (x \ y) * K(z,y)
    ]]></literal>
    <justification jstring="[para(7540(a,1),15549(a,1,2,2))].">
      <j1 rule="para" parents="7540 15549"/>
    </justification>
  </clause>

  <clause id="15554">
    <literal><![CDATA[
      x \ ((y * z) / y) = (x \ z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5889,a,b,15552,a)].">
      <j1 rule="hyper" parents="64 5889 15552"/>
    </justification>
  </clause>

  <clause id="15555">
    <literal><![CDATA[
      (x \ K(y,z)) * K(u,K(y,z)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(8156(a,1),15552(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8156 15552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15556">
    <literal><![CDATA[
      ((x * y) / x) / (z * K(x,y)) = y / z
    ]]></literal>
    <justification jstring="[hyper(225,a,221,a(flip),b,15554,a)].">
      <j1 rule="hyper" parents="225 221 15554"/>
    </justification>
  </clause>

  <clause id="15557">
    <literal><![CDATA[
      K(x,y) * (z \ ((y * x) / y)) = T(z \ x,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,15554,a,b,8169,a)].">
      <j1 rule="hyper" parents="145 15554 8169"/>
    </justification>
  </clause>

  <clause id="15559">
    <literal><![CDATA[
      (x * (y * z)) / x = y * (z * K(x,y * z))
    ]]></literal>
    <justification jstring="[hyper(144,a,11,a(flip),b,15556,a),flip(a)].">
      <j1 rule="hyper" parents="144 11 15556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15560">
    <literal><![CDATA[
      ((x * y) / x) / (y / x) = y / (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(6864(a,1),15556(a,1,2))].">
      <j1 rule="para" parents="6864 15556"/>
    </justification>
  </clause>

  <clause id="15561">
    <literal><![CDATA[
      T(x * (y * K(z,x * y)),z) = x * y
    ]]></literal>
    <justification jstring="[para(15559(a,1),255(a,1,1))].">
      <j1 rule="para" parents="15559 255"/>
    </justification>
  </clause>

  <clause id="15562">
    <literal><![CDATA[
      (x * y) \ ((x * R(x,y,y \ x)) / (x * y)) = (x * (y * K(y \ x,x * y))) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(15559(a,1),4955(a,2,1))].">
      <j1 rule="para" parents="15559 4955"/>
    </justification>
  </clause>

  <clause id="15563">
    <literal><![CDATA[
      K(x,y * (z * K(u,y * z))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(15559(a,1),8217(a,1,2))].">
      <j1 rule="para" parents="15559 8217"/>
    </justification>
  </clause>

  <clause id="15564">
    <literal><![CDATA[
      T(x * (K(y,z) * K(z,x)),z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(8549(a,1),15561(a,1,1,2,2))].">
      <j1 rule="para" parents="8549 15561"/>
    </justification>
  </clause>

  <clause id="15565">
    <literal><![CDATA[
      a(x / y,x / (T(x,y) / y),z) = a(y \ x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(15560(a,1),11714(a,1,2))].">
      <j1 rule="para" parents="15560 11714"/>
    </justification>
  </clause>

  <clause id="15566">
    <literal><![CDATA[
      T(x * a(y,x,y),y) = x * K(x * y,y)
    ]]></literal>
    <justification jstring="[para(10892(a,1),15564(a,1,1,2))].">
      <j1 rule="para" parents="10892 15564"/>
    </justification>
  </clause>

  <clause id="15567">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12693,a,15460,a)].">
      <j1 rule="hyper" parents="12693 15460"/>
    </justification>
  </clause>

  <clause id="15568">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(14061,a,15567,a)].">
      <j1 rule="hyper" parents="14061 15567"/>
    </justification>
  </clause>

  <clause id="15569">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(9794,a,15567,a)].">
      <j1 rule="hyper" parents="9794 15567"/>
    </justification>
  </clause>

  <clause id="15570">
    <literal><![CDATA[
      K(x,L(y / z,y,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(9704,a,15567,a),flip(a)].">
      <j1 rule="hyper" parents="9704 15567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15571">
    <literal><![CDATA[
      R(K(x,y),z,u) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,12059,a,b,15567,a),flip(a)].">
      <j1 rule="hyper" parents="373 12059 15567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15572">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,14056,a(flip),b,15567,a)].">
      <j1 rule="hyper" parents="64 14056 15567"/>
    </justification>
  </clause>

  <clause id="15573">
    <literal><![CDATA[
      K(x,L(y / (z / u),y,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9706,a(flip),b,15567,a),flip(a)].">
      <j1 rule="hyper" parents="64 9706 15567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15574">
    <literal><![CDATA[
      K(x / (y / z),L(u,x,z)) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,8761,a(flip),b,15567,a),flip(a)].">
      <j1 rule="hyper" parents="64 8761 15567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15575">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6681,a(flip),b,15567,a)].">
      <j1 rule="hyper" parents="64 6681 15567"/>
    </justification>
  </clause>

  <clause id="15576">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) * u = (K(x,y) * (u / z)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,15567,a(flip),b,10215,a)].">
      <j1 rule="hyper" parents="144 15567 10215"/>
    </justification>
  </clause>

  <clause id="15577">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * z) = (K(x,y) * z) * T(u,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,15567,a(flip),b,10202,a(flip))].">
      <j1 rule="hyper" parents="144 15567 10202"/>
    </justification>
  </clause>

  <clause id="15578">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,15567,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 15567 20"/>
    </justification>
  </clause>

  <clause id="15579">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * z) * u = w
    ]]></literal>
    <justification jstring="[para(15567(a,1),327(a,1,1))].">
      <j1 rule="para" parents="15567 327"/>
    </justification>
  </clause>

  <clause id="15580">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) = w
    ]]></literal>
    <justification jstring="[para(15567(a,1),977(a,1,1))].">
      <j1 rule="para" parents="15567 977"/>
    </justification>
  </clause>

  <clause id="15581">
    <literal><![CDATA[
      K(x,L(y / z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * u) / (z * u)) = w
    ]]></literal>
    <justification jstring="[para(15567(a,1),9704(a,1))].">
      <j1 rule="para" parents="15567 9704"/>
    </justification>
  </clause>

  <clause id="15582">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,12059,a,b,15568,a)].">
      <j1 rule="hyper" parents="373 12059 15568"/>
    </justification>
  </clause>

  <clause id="15583">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(143,a,15568,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 15568 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15584">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7360,a,b,15568,a)].">
      <j1 rule="hyper" parents="64 7360 15568"/>
    </justification>
  </clause>

  <clause id="15585">
    <literal><![CDATA[
      K(x,L(T(y \ z,z * u),y,u)) = K(x,T((y * u) \ (z * u),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,8758,a(flip),b,15568,a),flip(a)].">
      <j1 rule="hyper" parents="64 8758 15568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15586">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(112(a,1),15568(a,1,2)),flip(a)].">
      <j1 rule="para" parents="112 15568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15587">
    <literal><![CDATA[
      K(x,L((y / z) / u,u,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(351(a,1),15568(a,1,2)),flip(a)].">
      <j1 rule="para" parents="351 15568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15588">
    <literal><![CDATA[
      K(x,L(y \ (z / u),y,u)) = K(x,T(z / (y * u),y))
    ]]></literal>
    <justification jstring="[para(856(a,1),15568(a,1,2)),flip(a)].">
      <j1 rule="para" parents="856 15568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15589">
    <literal><![CDATA[
      K(x,K((1 / (y \ z)) / u,L(u / y,y,y \ z))) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[para(15568(a,1),9627(a,1,2))].">
      <j1 rule="para" parents="15568 9627"/>
    </justification>
  </clause>

  <clause id="15590">
    <literal><![CDATA[
      K(x,L(y / (z / u),u \ z,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(10218(a,1),15568(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10218 15568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15591">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,L(u,w,v5))) = K(x,L(y,z,R(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(15568(a,1),15337(a,1,2,3))].">
      <j1 rule="para" parents="15568 15337"/>
    </justification>
  </clause>

  <clause id="15592">
    <literal><![CDATA[
      L(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,8761,a(flip),b,15571,a),flip(a)].">
      <j1 rule="hyper" parents="64 8761 15571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15593">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6681,a(flip),b,15571,a),flip(a)].">
      <j1 rule="hyper" parents="64 6681 15571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15594">
    <literal><![CDATA[
      L(K(x,y),z,u) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,15571,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 15571 20"/>
    </justification>
  </clause>

  <clause id="15595">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(15571(a,1),8210(a,2,2))].">
      <j1 rule="para" parents="15571 8210"/>
    </justification>
  </clause>

  <clause id="15596">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15571(a,2),12091(a,1))].">
      <j1 rule="para" parents="15571 12091"/>
    </justification>
  </clause>

  <clause id="15597">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (u * (K(x,y) * z)) = z * T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(15571(a,1),15245(a,1,1))].">
      <j1 rule="para" parents="15571 15245"/>
    </justification>
  </clause>

  <clause id="15598">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,12093,a,b,15572,a),flip(a)].">
      <j1 rule="hyper" parents="373 12093 15572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15599">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,R(y,z,u))) = (R(y,z,u) * x) / R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(15572(a,1),6618(a,1,2,1))].">
      <j1 rule="para" parents="15572 6618"/>
    </justification>
  </clause>

  <clause id="15600">
    <literal><![CDATA[
      (R(x,y,z) * (u * K(x,L(w,y,z)))) / R(T(x,w),y,z) = (R(x,y,z) * u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(15572(a,1),7169(a,1,1,2,2))].">
      <j1 rule="para" parents="15572 7169"/>
    </justification>
  </clause>

  <clause id="15601">
    <literal><![CDATA[
      a(L(x,y,y),z,K(u,L(w,v5,v6))) = a(R(u,v5,v6),z,K(w,x))
    ]]></literal>
    <justification jstring="[para(15572(a,1),15344(a,1,3))].">
      <j1 rule="para" parents="15572 15344"/>
    </justification>
  </clause>

  <clause id="15602">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * z) * R(x,y,z)) = L(K(y * z,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,659,a,b,15582,a)].">
      <j1 rule="hyper" parents="373 659 15582"/>
    </justification>
  </clause>

  <clause id="15603">
    <literal><![CDATA[
      L(K(x,y / (z / u)),u \ z,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(10218(a,1),15582(a,2,2))].">
      <j1 rule="para" parents="10218 15582"/>
    </justification>
  </clause>

  <clause id="15604">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15582(a,1),12091(a,1))].">
      <j1 rule="para" parents="15582 12091"/>
    </justification>
  </clause>

  <clause id="15605">
    <literal><![CDATA[
      K(L(x,y,z),u) \ u = T(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,5804,a(flip),b,15583,a)].">
      <j1 rule="hyper" parents="373 5804 15583"/>
    </justification>
  </clause>

  <clause id="15606">
    <literal><![CDATA[
      T(x,(T(y,z * z) * z) * z) = T(T(x,z * z),L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11287,a,b,15583,a)].">
      <j1 rule="hyper" parents="64 11287 15583"/>
    </justification>
  </clause>

  <clause id="15607">
    <literal><![CDATA[
      T(x,L(y,z,u)) * R(T(y,x),z,u) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,15583,a(flip),b,4670,a)].">
      <j1 rule="hyper" parents="144 15583 4670"/>
    </justification>
  </clause>

  <clause id="15608">
    <literal><![CDATA[
      T(x,L(y / z,z,u)) = T(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(112(a,1),15583(a,1,2)),flip(a)].">
      <j1 rule="para" parents="112 15583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15609">
    <literal><![CDATA[
      T(x,L((y / z) / u,u,z)) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(351(a,1),15583(a,1,2)),flip(a)].">
      <j1 rule="para" parents="351 15583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15610">
    <literal><![CDATA[
      K(x,T(y \ R(z,u,w),L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(z,u,w) / y) = v5
    ]]></literal>
    <justification jstring="[para(15583(a,1),8699(a,1,2))].">
      <j1 rule="para" parents="15583 8699"/>
    </justification>
  </clause>

  <clause id="15611">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w)) \ ((R(w,v5,v6) * T(u,w)) / T(u,w)) = (T(T(u,w),R(x,y,z)) * R(T(w,u),v5,v6)) / T(u,w)
    ]]></literal>
    <justification jstring="[para(15583(a,2),8749(a,2,1,1))].">
      <j1 rule="para" parents="15583 8749"/>
    </justification>
  </clause>

  <clause id="15612">
    <literal><![CDATA[
      T(x,T(R(y,z,u) * w,L(y,z,u)) * v5) = T(x,(w * R(y,z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(15583(a,1),13467(a,1,2,1))].">
      <j1 rule="para" parents="15583 13467"/>
    </justification>
  </clause>

  <clause id="15613">
    <literal><![CDATA[
      K(L(x,y,z),u) * ((x * y) * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,15598,a(flip),b,7356,a)].">
      <j1 rule="hyper" parents="144 15598 7356"/>
    </justification>
  </clause>

  <clause id="15614">
    <literal><![CDATA[
      K(L(x / y,y,z),u) = K((x * z) / (y * z),u)
    ]]></literal>
    <justification jstring="[para(112(a,1),15598(a,1,1)),flip(a)].">
      <j1 rule="para" parents="112 15598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15615">
    <literal><![CDATA[
      T(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15605(a,1),5871(a,1))].">
      <j1 rule="para" parents="15605 5871"/>
    </justification>
  </clause>

  <clause id="15616">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(9707(a,2),15596(a,1))].">
      <j1 rule="para" parents="9707 15596"/>
    </justification>
  </clause>

  <clause id="15617">
    <literal><![CDATA[
      K(x,(y * z) / (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / u,u,z)) = w
    ]]></literal>
    <justification jstring="[para(112(a,1),15604(a,1,2))].">
      <j1 rule="para" parents="112 15604"/>
    </justification>
  </clause>

  <clause id="15618">
    <literal><![CDATA[
      K(x \ 1,L(T(y,z),u,(x * u) \ z)) = K(z \ (u * ((x * u) \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8055,a(flip),b,15575,a),flip(a)].">
      <j1 rule="hyper" parents="64 8055 15575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15619">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((z \ (x * (y \ z))) \ 1,u)
    ]]></literal>
    <justification jstring="[para(1379(a,1),15575(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1379 15575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15620">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(L(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(7304,a,15593,a),flip(a)].">
      <j1 rule="hyper" parents="7304 15593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15621">
    <literal><![CDATA[
      (x \ K(L(y,z,u) \ 1,w)) \ (x \ 1) = K(w,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(15620(a,1),14533(a,1,1,2))].">
      <j1 rule="para" parents="15620 14533"/>
    </justification>
  </clause>

  <clause id="15622">
    <literal><![CDATA[
      K(x,L(y * z,y,u)) = K(x,(y * u) / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(14952,a,15570,a)].">
      <j1 rule="hyper" parents="14952 15570"/>
    </justification>
  </clause>

  <clause id="15623">
    <literal><![CDATA[
      K(x,(y * (y \ z)) / (u * (y \ z))) = K(x,L(y / u,z,y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15523,a,b,15570,a),flip(a)].">
      <j1 rule="hyper" parents="64 15523 15570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15624">
    <literal><![CDATA[
      a(x,y,K(z,y / (u / z))) \ K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(139,a,15573,a(flip),b,15424,a)].">
      <j1 rule="hyper" parents="139 15573 15424"/>
    </justification>
  </clause>

  <clause id="15625">
    <literal><![CDATA[
      (K(x,y) * z) * (u * u) = K(x,y) * (z * (u * u))
    ]]></literal>
    <justification jstring="[para(594(a,1),15578(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="594 15578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15626">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,K(w,L(v5,z,u))) \ 1) = K(x,((K(w,v5) * z) * u) \ (K(w,L(v5,z,u)) * y))
    ]]></literal>
    <justification jstring="[para(15578(a,1),6711(a,2,2,1))].">
      <j1 rule="para" parents="15578 6711"/>
    </justification>
  </clause>

  <clause id="15627">
    <literal><![CDATA[
      T((K(x,y) * z) * u,K(x,L(y,z,u))) = (z * u) * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(15578(a,1),7785(a,1,1))].">
      <j1 rule="para" parents="15578 7785"/>
    </justification>
  </clause>

  <clause id="15628">
    <literal><![CDATA[
      K(x,L(y,z,z \ (u \ z))) * (z * (z \ (z / u))) = (K(x,y) * z) * (z \ (z / u))
    ]]></literal>
    <justification jstring="[para(13536(a,1),15578(a,1,1,2))].">
      <j1 rule="para" parents="13536 15578"/>
    </justification>
  </clause>

  <clause id="15629">
    <literal><![CDATA[
      K(x * y,L(z / x,x,y)) = K(x * y,(x * y) \ (z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,5926,a(flip),b,15586,a),flip(a)].">
      <j1 rule="hyper" parents="373 5926 15586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15630">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) * (z * u) = (z * u) * K(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(15586(a,2),7956(a,1,1))].">
      <j1 rule="para" parents="15586 7956"/>
    </justification>
  </clause>

  <clause id="15631">
    <literal><![CDATA[
      K(x,L((y / T(z,u \ 1)) / (w / (u * w)),w / (u * w),T(z,u \ 1))) = K(x,y / (z * (w / (u * w))))
    ]]></literal>
    <justification jstring="[para(4824(a,1),15587(a,2,2,2))].">
      <j1 rule="para" parents="4824 15587"/>
    </justification>
  </clause>

  <clause id="15632">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,y / z,z))) = K(x,K(w,y / (u * z)))
    ]]></literal>
    <justification jstring="[para(15587(a,1),12126(a,2,2))].">
      <j1 rule="para" parents="15587 12126"/>
    </justification>
  </clause>

  <clause id="15633">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,x \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      y \ (x * (K((x \ y) / (z / x),u) * (x \ y))) = w
    ]]></literal>
    <justification jstring="[para(15592(a,1),7895(a,1))].">
      <j1 rule="para" parents="15592 7895"/>
    </justification>
  </clause>

  <clause id="15634">
    <literal><![CDATA[
      L(K(x,y),z,u) * (z * u) = (K(y,x) \ z) * u
    ]]></literal>
    <justification jstring="[para(6156(a,2),15594(a,2,1))].">
      <j1 rule="para" parents="6156 15594"/>
    </justification>
  </clause>

  <clause id="15635">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),z / ((u \ 1) \ 1),u)) = T(x,(y * u) / ((u * (1 / u)) \ z))
    ]]></literal>
    <justification jstring="[para(5287(a,1),15608(a,2,2,2))].">
      <j1 rule="para" parents="5287 15608"/>
    </justification>
  </clause>

  <clause id="15636">
    <literal><![CDATA[
      T(x,L((y / K(z,L(u,w,v5))) / (v5 * w),v5 * w,K(z,L(u,w,v5)))) = T(x,y / (v5 * (w * K(z,u))))
    ]]></literal>
    <justification jstring="[para(12078(a,1),15609(a,2,2,2))].">
      <j1 rule="para" parents="12078 15609"/>
    </justification>
  </clause>

  <clause id="15637">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(((x \ z) * x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(8451,a,15614,a)].">
      <j1 rule="hyper" parents="8451 15614"/>
    </justification>
  </clause>

  <clause id="15638">
    <literal><![CDATA[
      L(K(x,y),z,z \ u) * u = (K(y,x) \ z) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(397,a,15634,a)].">
      <j1 rule="hyper" parents="397 15634"/>
    </justification>
  </clause>

  <clause id="15639">
    <literal><![CDATA[
      L(K(x,y),z,(K(y,x) \ z) \ u) \ u = z * ((K(y,x) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,15634,a)].">
      <j1 rule="hyper" parents="139 10 15634"/>
    </justification>
  </clause>

  <clause id="15640">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (z * u) = (K(x,y) \ z) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,7326,a,b,15634,a)].">
      <j1 rule="hyper" parents="64 7326 15634"/>
    </justification>
  </clause>

  <clause id="15641">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,L((y * z) \ u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(12113,a,15534,a)].">
      <j1 rule="hyper" parents="12113 15534"/>
    </justification>
  </clause>

  <clause id="15642">
    <literal><![CDATA[
      K(x,L((((y * z) \ y) \ y) \ u,y,z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14237,a(flip),b,15534,a),flip(a)].">
      <j1 rule="hyper" parents="64 14237 15534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15643">
    <literal><![CDATA[
      K(x,L(y,z \ u,z \ 1)) = K(x,L(y,u,z \ 1))
    ]]></literal>
    <justification jstring="[para(10(a,1),15534(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 15534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15644">
    <literal><![CDATA[
      K(x,x \ ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(15537(a,1),13445(a,1))].">
      <j1 rule="para" parents="15537 13445"/>
    </justification>
  </clause>

  <clause id="15645">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(15644,a,10156,a)].">
      <j1 rule="hyper" parents="15644 10156"/>
    </justification>
  </clause>

  <clause id="15646">
    <literal><![CDATA[
      K(x,(y \ x) * z) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(10514,a,15645,a),flip(a)].">
      <j1 rule="hyper" parents="10514 15645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15648">
    <literal><![CDATA[
      K(x,K(y,(z \ y) * u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(15645(a,1),10169(a,1,2))].">
      <j1 rule="para" parents="15645 10169"/>
    </justification>
  </clause>

  <clause id="15649">
    <literal><![CDATA[
      T(x,(y \ x) * z) = T(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(143,a,15646,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 15646 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15651">
    <literal><![CDATA[
      T(x,(y \ x) * (z \ x)) = T(x,x * (y \ (x / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13416,a(flip),b,15649,a)].">
      <j1 rule="hyper" parents="64 13416 15649"/>
    </justification>
  </clause>

  <clause id="15652">
    <literal><![CDATA[
      T(x,x * (y \ (x \ y))) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,9462,a(flip),b,15649,a),flip(a)].">
      <j1 rule="hyper" parents="64 9462 15649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15653">
    <literal><![CDATA[
      T((x \ (y \ x)) * y,y) = (x \ (y \ x)) * y
    ]]></literal>
    <justification jstring="[para(15652(a,1),4695(a,1,1,2))].">
      <j1 rule="para" parents="15652 4695"/>
    </justification>
  </clause>

  <clause id="15654">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[para(15648(a,1),9062(a,1,1))].">
      <j1 rule="para" parents="15648 9062"/>
    </justification>
  </clause>

  <clause id="15655">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(15648(a,1),9070(a,1,2))].">
      <j1 rule="para" parents="15648 9070"/>
    </justification>
  </clause>

  <clause id="15656">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,K(y,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(8088(a,1),15555(a,1,2))].">
      <j1 rule="para" parents="8088 15555"/>
    </justification>
  </clause>

  <clause id="15657">
    <literal><![CDATA[
      (x \ K(y,z)) * K(y,K(z,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(8110(a,2),15555(a,1,2))].">
      <j1 rule="para" parents="8110 15555"/>
    </justification>
  </clause>

  <clause id="15658">
    <literal><![CDATA[
      T(((1 / x) * y) \ y,K(y,1 / x)) = K(y,1 / x) * L(x,x,x \ ((1 / x) * y))
    ]]></literal>
    <justification jstring="[para(11068(a,2),15557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11068 15557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15659">
    <literal><![CDATA[
      K(x,y * (((z * y) \ u) * K(z,z \ u))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(14014(a,1),15563(a,1,2,2,2))].">
      <j1 rule="para" parents="14014 15563"/>
    </justification>
  </clause>

  <clause id="15660">
    <literal><![CDATA[
      K(x,y) * (z * (K(K(x,y) * z,u) * K(K(x,y) * z,u))) = T(K(x,y) * z,u) * K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(6281,a,15625,a),flip(a)].">
      <j1 rule="hyper" parents="6281 15625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15661">
    <literal><![CDATA[
      T(x,x * (y \ (x / z))) = T(x,x * (y \ (z \ x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15649,a(flip),b,15651,a),flip(a)].">
      <j1 rule="hyper" parents="64 15649 15651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15662">
    <literal><![CDATA[
      (x \ y) \ K(z,T(y,x)) = (x \ T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,15288,a(flip),b,15656,a),flip(a)].">
      <j1 rule="hyper" parents="64 15288 15656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15663">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * a(u,z,K(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(10425(a,1),15335(a,1))].">
      <j1 rule="para" parents="10425 15335"/>
    </justification>
  </clause>

  <clause id="15664">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ y)) = w
    ]]></literal>
    <justification jstring="[para(12250(a,1),15339(a,1,2))].">
      <j1 rule="para" parents="12250 15339"/>
    </justification>
  </clause>

  <clause id="15665">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(15437(a,2),15339(a,1))].">
      <j1 rule="para" parents="15437 15339"/>
    </justification>
  </clause>

  <clause id="15666">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(w,y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(15415,a,15370,a)].">
      <j1 rule="hyper" parents="15415 15370"/>
    </justification>
  </clause>

  <clause id="15667">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,K(w,x))) = v5
    ]]></literal>
    <justification jstring="[para(15370(a,1),15415(a,1))].">
      <j1 rule="para" parents="15370 15415"/>
    </justification>
  </clause>

  <clause id="15668">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(z,K(x,w)))
    ]]></literal>
    <justification jstring="[para(8126(a,1),15666(a,1,3))].">
      <j1 rule="para" parents="8126 15666"/>
    </justification>
  </clause>

  <clause id="15669">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * K(x,K(z,y)) = a(z,u,K(x,K(w,y)))
    ]]></literal>
    <justification jstring="[hyper(12195,a,15668,a)].">
      <j1 rule="hyper" parents="12195 15668"/>
    </justification>
  </clause>

  <clause id="15670">
    <literal><![CDATA[
      K(x * L(T(y,x),z,u),y * x) = a(T(y,x),z,K(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(15417,a,14723,a),flip(a)].">
      <j1 rule="hyper" parents="15417 14723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15671">
    <literal><![CDATA[
      K(x,L(y,z,u)) * z = (K(x,y) * (z / u)) * u
    ]]></literal>
    <justification jstring="[para(15514(a,1),15576(a,1,1))].">
      <j1 rule="para" parents="15514 15576"/>
    </justification>
  </clause>

  <clause id="15672">
    <literal><![CDATA[
      (x * K(y,L(z,x,u))) / u = K(y,T(z,x)) * (x / u)
    ]]></literal>
    <justification jstring="[hyper(8955,a,15671,a)].">
      <j1 rule="hyper" parents="8955 15671"/>
    </justification>
  </clause>

  <clause id="15673">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * z) / u = K(x,y) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(724,a,15671,a)].">
      <j1 rule="hyper" parents="724 15671"/>
    </justification>
  </clause>

  <clause id="15674">
    <literal><![CDATA[
      (K(x,y) * (z / u)) * u != w * v5
    ]]></literal>
    <literal><![CDATA[
      (K(x,L(y,z,u)) * z) / v5 = w
    ]]></literal>
    <justification jstring="[para(15671(a,1),724(a,1))].">
      <j1 rule="para" parents="15671 724"/>
    </justification>
  </clause>

  <clause id="15675">
    <literal><![CDATA[
      T(L(x,y,K(z,L(u,y * x,x))),x \ (K(z,L(u,y * x,x)) * y)) = (x \ (K(z,L(u,y * x,x)) * y)) \ (K(z,u) * ((y * x) / x))
    ]]></literal>
    <justification jstring="[hyper(493,a,15673,a(flip),b,14751,a)].">
      <j1 rule="hyper" parents="493 15673 14751"/>
    </justification>
  </clause>

  <clause id="15676">
    <literal><![CDATA[
      (K(x * y,z) * y) / x = K(x * y,z) * (y / x)
    ]]></literal>
    <justification jstring="[para(15357(a,1),15673(a,1,1,1))].">
      <j1 rule="para" parents="15357 15673"/>
    </justification>
  </clause>

  <clause id="15677">
    <literal><![CDATA[
      (x * K(x * y,z)) / y = K(y * x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(11186(a,1),15676(a,1,1))].">
      <j1 rule="para" parents="11186 15676"/>
    </justification>
  </clause>

  <clause id="15678">
    <literal><![CDATA[
      K(x,L(y,z,(T(y,x) * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(15584(a,1),385(a,1,1))].">
      <j1 rule="para" parents="15584 385"/>
    </justification>
  </clause>

  <clause id="15679">
    <literal><![CDATA[
      K(x,T(y / (z * u),z)) = K(x,(u * z) \ (u * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(7611,a,15588,a),flip(a)].">
      <j1 rule="hyper" parents="7611 15588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15680">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,(z * y) \ K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(641(a,1),15588(a,1,2)),flip(a)].">
      <j1 rule="para" parents="641 15588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15681">
    <literal><![CDATA[
      K(x,L(y / (z / u),z,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(15665,a,15590,a)].">
      <j1 rule="hyper" parents="15665 15590"/>
    </justification>
  </clause>

  <clause id="15682">
    <literal><![CDATA[
      T(x,L(y / (z / u),z,u)) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(143,a,15681,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 15681 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15683">
    <literal><![CDATA[
      T(x,L(y / K(z * u,w),z \ T(u * z,w),T(u,z))) = T(x,(y * T(u,z)) / (z \ T(u * z,w)))
    ]]></literal>
    <justification jstring="[para(15133(a,1),15682(a,1,2,1,2))].">
      <j1 rule="para" parents="15133 15682"/>
    </justification>
  </clause>

  <clause id="15684">
    <literal><![CDATA[
      L(K(x,((y / z) / u) \ x),z \ y,z) = K(x,((x * u) * z) / y)
    ]]></literal>
    <justification jstring="[para(9734(a,1),15603(a,1,1))].">
      <j1 rule="para" parents="9734 15603"/>
    </justification>
  </clause>

  <clause id="15685">
    <literal><![CDATA[
      T(T(x,y),L(y,z,u)) * R(T(y,x),z,u) = T(x,y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(4619(a,1),15607(a,1,2,1))].">
      <j1 rule="para" parents="4619 15607"/>
    </justification>
  </clause>

  <clause id="15686">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,T(y,z),1 / z)) = K(x,(y * (1 / T(z,y))) / ((u \ 1) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(6330(a,1),15622(a,2,2,1))].">
      <j1 rule="para" parents="6330 15622"/>
    </justification>
  </clause>

  <clause id="15687">
    <literal><![CDATA[
      a(x,y,K(y * z,u)) * K(x,(y * u) / ((z \ 1) * u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(15622(a,1),15338(a,1,2))].">
      <j1 rule="para" parents="15622 15338"/>
    </justification>
  </clause>

  <clause id="15688">
    <literal><![CDATA[
      x * L(K(y,T(z,x)),u,u \ x) = (K(z,y) \ u) * (u \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7891,a,b,15638,a)].">
      <j1 rule="hyper" parents="64 7891 15638"/>
    </justification>
  </clause>

  <clause id="15690">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * a(w,z,K(y,u)) = v5
    ]]></literal>
    <justification jstring="[para(15300(a,1),15663(a,1,2))].">
      <j1 rule="para" parents="15300 15663"/>
    </justification>
  </clause>

  <clause id="15692">
    <literal><![CDATA[
      T(x,a(y,z,a(u,w,v5))) != x * v6
    ]]></literal>
    <literal><![CDATA[
      a(x,z,a(u,w,K(v5,y))) = v6
    ]]></literal>
    <justification jstring="[para(15362(a,1),44(a,1))].">
      <j1 rule="para" parents="15362 44"/>
    </justification>
  </clause>

  <clause id="15693">
    <literal><![CDATA[
      T(x,a(a(y,z,u),w,v5)) = T(x,a(y,w,a(v5,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15362,a(flip),b,15363,a),flip(a)].">
      <j1 rule="hyper" parents="64 15362 15363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15694">
    <literal><![CDATA[
      T(x,a(y,z,a(u,x,w))) = T(x,L(a(y,x,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15402,a(flip),b,15693,a),flip(a)].">
      <j1 rule="hyper" parents="64 15402 15693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15695">
    <literal><![CDATA[
      a(L(x,y,z) \ u,w,K(z,x)) = a(u,w,K(z,x))
    ]]></literal>
    <justification jstring="[para(7394(a,1),15393(a,2,3))].">
      <j1 rule="para" parents="7394 15393"/>
    </justification>
  </clause>

  <clause id="15697">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (K(u,L(x,y,z)) * w) = K(u,x) * w
    ]]></literal>
    <justification jstring="[para(12100(a,1),15426(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12100 15426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15698">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ (y * u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(982(a,1),15547(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="982 15547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15699">
    <literal><![CDATA[
      a(x \ y,T(x,y),z) = a(y / x,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13839,a(flip),b,15565,a),flip(a)].">
      <j1 rule="hyper" parents="64 13839 15565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15701">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = (((w \ v5) \ v5) * K(u,((x \ z) * x) / (y * x))) \ T(w,w \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,6883,a,b,15637,a),flip(a)].">
      <j1 rule="hyper" parents="373 6883 15637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15702">
    <literal><![CDATA[
      K(T(x,y),(z * y) \ u) = 1 / K(((z \ u) * z) / (y * z),x)
    ]]></literal>
    <justification jstring="[hyper(225,a,15637,a(flip),b,6092,a),flip(a)].">
      <j1 rule="hyper" parents="225 15637 6092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15703">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(x,z,K(y,u)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(10429,a,15301,a)].">
      <j1 rule="hyper" parents="10429 15301"/>
    </justification>
  </clause>

  <clause id="15704">
    <literal><![CDATA[
      T(x * y,a(x,z,u)) = x * T(y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(15310,a,15399,a),flip(a)].">
      <j1 rule="hyper" parents="15310 15399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15705">
    <literal><![CDATA[
      T(x,a(y,z,u)) / y = T(x / y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,5431,a(flip),b,15704,a(flip))].">
      <j1 rule="hyper" parents="35 5431 15704"/>
    </justification>
  </clause>

  <clause id="15706">
    <literal><![CDATA[
      K(x,L(y,z,u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(15433(a,1),15369(a,1))].">
      <j1 rule="para" parents="15433 15369"/>
    </justification>
  </clause>

  <clause id="15707">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,w \ 1) \ 1)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(427(a,1),15439(a,2,2))].">
      <j1 rule="para" parents="427 15439"/>
    </justification>
  </clause>

  <clause id="15708">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,w \ 1) \ 1)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(15707(a,2),152(a,1))].">
      <j1 rule="para" parents="15707 152"/>
    </justification>
  </clause>

  <clause id="15710">
    <literal><![CDATA[
      K(x,L(y,z,u * L(u \ 1,u,w))) = 1 * K(x,y)
    ]]></literal>
    <justification jstring="[para(427(a,1),15453(a,2,1))].">
      <j1 rule="para" parents="427 15453"/>
    </justification>
  </clause>

  <clause id="15711">
    <literal><![CDATA[
      K(x,L(y,z,u * L(u \ 1,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(15710(a,2),146(a,1)),flip(b)].">
      <j1 rule="para" parents="15710 146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15713">
    <literal><![CDATA[
      a(x,y,z) = (z * (x * y)) / (L(z,y,x) * (x * y))
    ]]></literal>
    <justification jstring="[para(14744(a,1),15465(a,2,2))].">
      <j1 rule="para" parents="14744 15465"/>
    </justification>
  </clause>

  <clause id="15714">
    <literal><![CDATA[
      a(x,y,z) * (L(z,y,x) * (x * y)) = z * (x * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,15713,a,b,xx)].">
      <j1 rule="hyper" parents="144 15713"/>
    </justification>
  </clause>

  <clause id="15715">
    <literal><![CDATA[
      a(x,y,z) \ (z * (x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(143,a,15713,a,b,171,a)].">
      <j1 rule="hyper" parents="143 15713 171"/>
    </justification>
  </clause>

  <clause id="15716">
    <literal><![CDATA[
      (x * (y * z)) / (L(x,z,y) * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,x) = u
    ]]></literal>
    <justification jstring="[para(15714(a,1),287(a,1,1)),flip(b)].">
      <j1 rule="para" parents="15714 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15717">
    <literal><![CDATA[
      ((x * (1 / y)) * R(y,z,u)) / L(y \ R(y,z,u),x,a(x,1 / y,R(y,z,u))) = a(x,1 / y,R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(2067(a,1),15482(a,1,2,1))].">
      <j1 rule="para" parents="2067 15482"/>
    </justification>
  </clause>

  <clause id="15718">
    <literal><![CDATA[
      T(x * y,a(y,z,u)) = T(x,a(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(15485,a,15353,a)].">
      <j1 rule="hyper" parents="15485 15353"/>
    </justification>
  </clause>

  <clause id="15719">
    <literal><![CDATA[
      T(x * y,a(y,z,u)) = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15396,a(flip),b,15718,a),flip(a)].">
      <j1 rule="hyper" parents="373 15396 15718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15720">
    <literal><![CDATA[
      (x * x) * ((x \ y) / (x * y)) = L(x \ y,x,x) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,807,a(flip),b,15502,a)].">
      <j1 rule="hyper" parents="64 807 15502"/>
    </justification>
  </clause>

  <clause id="15721">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u \ x)) = (x / u) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(15542(a,1),12222(a,1,2))].">
      <j1 rule="para" parents="15542 12222"/>
    </justification>
  </clause>

  <clause id="15722">
    <literal><![CDATA[
      T(K(x,T(y,z * u)) * z,u) = T(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(269,a,15595,a,b,10989,a(flip))].">
      <j1 rule="hyper" parents="269 15595 10989"/>
    </justification>
  </clause>

  <clause id="15723">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x * y)) = T(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(8203(a,1),15722(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8203 15722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15724">
    <literal><![CDATA[
      K((T(x,y) * K(z,u)) \ 1,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((K(z,T(u,x * y)) * x) \ 1,T(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(15722(a,1),8018(a,1,1,1))].">
      <j1 rule="para" parents="15722 8018"/>
    </justification>
  </clause>

  <clause id="15725">
    <literal><![CDATA[
      K(x,y * T(K(x,z) * u,w)) = K(x,y * T(u,w))
    ]]></literal>
    <justification jstring="[para(15723(a,1),8585(a,1,2,2))].">
      <j1 rule="para" parents="15723 8585"/>
    </justification>
  </clause>

  <clause id="15726">
    <literal><![CDATA[
      a(R(x,y,z),u,K(w,v5)) = a(x,u,K(w,L(v5,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15406,a(flip),b,15601,a),flip(a)].">
      <j1 rule="hyper" parents="64 15406 15601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15727">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,x))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13103,a(flip),b,15726,a),flip(a)].">
      <j1 rule="hyper" parents="64 13103 15726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15728">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(u,w,x) = T(L(u,w,x),a(z,y,x))
    ]]></literal>
    <justification jstring="[para(15727(a,1),15341(a,1,1))].">
      <j1 rule="para" parents="15727 15341"/>
    </justification>
  </clause>

  <clause id="15729">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(u,w,x) = L(T(u,a(z,y,x)),w,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25,a,b,15728,a),flip(a)].">
      <j1 rule="hyper" parents="373 25 15728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15730">
    <literal><![CDATA[
      T(x,(T(y,z * z) * z) * z) = T(T(x,L(y,z,z)),z * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,23,a,b,15606,a),flip(a)].">
      <j1 rule="hyper" parents="373 23 15606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15731">
    <literal><![CDATA[
      T(x,(T(y,z * z) * z) * z) = T(x,(z * z) * L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,1773,a(flip),b,15606,a),flip(a)].">
      <j1 rule="hyper" parents="373 1773 15606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15732">
    <literal><![CDATA[
      K(x * (y \ z),L(y / x,x,y \ z)) = K(x * (y \ z),(x * (y \ z)) \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),15629(a,2,2,2))].">
      <j1 rule="para" parents="10 15629"/>
    </justification>
  </clause>

  <clause id="15733">
    <literal><![CDATA[
      K(x,y) * a(x,z,a(y,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,(L(w,u,v5) \ w) \ y)) = v6
    ]]></literal>
    <justification jstring="[para(15304(a,1),15664(a,1,2,3))].">
      <j1 rule="para" parents="15304 15664"/>
    </justification>
  </clause>

  <clause id="15734">
    <literal><![CDATA[
      K(x,L(K(y,T(z,x)),u,u \ x)) \ ((K(z,y) \ u) * (u \ x)) = L(K(y,T(z,x)),u,u \ x) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,15688,a(flip),b,5796,a)].">
      <j1 rule="hyper" parents="139 15688 5796"/>
    </justification>
  </clause>

  <clause id="15735">
    <literal><![CDATA[
      (x * x) * ((x \ y) / (x * y)) = ((1 / x) * y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(569(a,1),15720(a,2,1))].">
      <j1 rule="para" parents="569 15720"/>
    </justification>
  </clause>

  <clause id="15736">
    <literal><![CDATA[
      x * K(y,L(T(z,K(z,y) / u),x,(K(z,y) / u) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(14383(a,1),15721(a,2,2))].">
      <j1 rule="para" parents="14383 15721"/>
    </justification>
  </clause>

  <clause id="15737">
    <literal><![CDATA[
      T(x,(T(y,z * z) * z) * z) = T(T(x,y),z * z)
    ]]></literal>
    <justification jstring="[para(14415(a,1),15730(a,2,1))].">
      <j1 rule="para" parents="14415 15730"/>
    </justification>
  </clause>

  <clause id="15739">
    <literal><![CDATA[
      T(x,(T(y,z * z) * z) * z) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[para(100(a,1),15731(a,2,2))].">
      <j1 rule="para" parents="100 15731"/>
    </justification>
  </clause>

  <clause id="15740">
    <literal><![CDATA[
      T(T(x,y),z * z) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15737,a(flip),b,15739,a)].">
      <j1 rule="hyper" parents="64 15737 15739"/>
    </justification>
  </clause>

  <clause id="15741">
    <literal><![CDATA[
      T(T(x,y * y),z) = T(x,y * (y * z))
    ]]></literal>
    <justification jstring="[hyper(481,a,15740,a)].">
      <j1 rule="hyper" parents="481 15740"/>
    </justification>
  </clause>

  <clause id="15742">
    <literal><![CDATA[
      T(x,(y * y) * z) = T(x,y * (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1775,a(flip),b,15740,a)].">
      <j1 rule="hyper" parents="64 1775 15740"/>
    </justification>
  </clause>

  <clause id="15743">
    <literal><![CDATA[
      (x * x) * T(y,x * (x * z)) = T(y,z) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,15740,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 15740 22"/>
    </justification>
  </clause>

  <clause id="15744">
    <literal><![CDATA[
      T(x / y,z * (z * y)) = T(y \ x,z * z)
    ]]></literal>
    <justification jstring="[para(117(a,1),15740(a,1,1)),flip(a)].">
      <j1 rule="para" parents="117 15740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15745">
    <literal><![CDATA[
      T(x,K(y,z) * (K(y,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u) = w
    ]]></literal>
    <justification jstring="[para(15740(a,1),10365(a,1))].">
      <j1 rule="para" parents="15740 10365"/>
    </justification>
  </clause>

  <clause id="15746">
    <literal><![CDATA[
      L(T(x,y * (y * z)),u * u,w) = T(T(x,y * y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,593,a,b,15741,a)].">
      <j1 rule="hyper" parents="373 593 15741"/>
    </justification>
  </clause>

  <clause id="15747">
    <literal><![CDATA[
      T(T(x,y * (y * z)),u) = T(T(x,z),y * (y * u))
    ]]></literal>
    <justification jstring="[para(15740(a,1),15741(a,1,1))].">
      <j1 rule="para" parents="15740 15741"/>
    </justification>
  </clause>

  <clause id="15748">
    <literal><![CDATA[
      x \ T(x,y * (y * z)) = K(x,(y * y) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,15742,a(flip),b,5753,a(flip))].">
      <j1 rule="hyper" parents="139 15742 5753"/>
    </justification>
  </clause>

  <clause id="15749">
    <literal><![CDATA[
      T(x,((y * y) * z) / T(u,y * (y * z))) = T(x,((y * y) \ u) \ z)
    ]]></literal>
    <justification jstring="[para(15742(a,1),13312(a,1,2,2))].">
      <j1 rule="para" parents="15742 13312"/>
    </justification>
  </clause>

  <clause id="15750">
    <literal><![CDATA[
      T((x \ y) \ z,x * x) = T(z / (x \ y),x * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),15744(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 15744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15751">
    <literal><![CDATA[
      T(x / ((y \ z) / z),R(y,y,z)) = T(((y \ z) / z) \ x,y * y)
    ]]></literal>
    <justification jstring="[para(3012(a,1),15744(a,1,2))].">
      <j1 rule="para" parents="3012 15744"/>
    </justification>
  </clause>

  <clause id="15752">
    <literal><![CDATA[
      K(x,(y * y) * z) = K(x,y * (y * z))
    ]]></literal>
    <justification jstring="[hyper(5827,a,15748,a),flip(a)].">
      <j1 rule="hyper" parents="5827 15748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15753">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(6161(a,1),15745(a,1,2,2))].">
      <j1 rule="para" parents="6161 15745"/>
    </justification>
  </clause>

  <clause id="15754">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(6075(a,1),15745(a,1,2,2))].">
      <j1 rule="para" parents="6075 15745"/>
    </justification>
  </clause>

  <clause id="15755">
    <literal><![CDATA[
      T(x,y * T(T(z,u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(10377(a,1),15745(a,1,2))].">
      <j1 rule="para" parents="10377 15745"/>
    </justification>
  </clause>

  <clause id="15756">
    <literal><![CDATA[
      T(x,K(y,z) * ((z * y) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(10833(a,1),15745(a,1,2,2))].">
      <j1 rule="para" parents="10833 15745"/>
    </justification>
  </clause>

  <clause id="15757">
    <literal><![CDATA[
      T(x,K(y,z) * (z * u)) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15753,a,13678,a)].">
      <j1 rule="hyper" parents="15753 13678"/>
    </justification>
  </clause>

  <clause id="15758">
    <literal><![CDATA[
      T(x,K(y,y \ z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15753,a,13409,a)].">
      <j1 rule="hyper" parents="15753 13409"/>
    </justification>
  </clause>

  <clause id="15759">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15753,a,xx)].">
      <j1 rule="hyper" parents="15753"/>
    </justification>
  </clause>

  <clause id="15760">
    <literal><![CDATA[
      T(x,K(T(y,z),z / u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u \ z,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(7902(a,2),15753(a,1,2,1))].">
      <j1 rule="para" parents="7902 15753"/>
    </justification>
  </clause>

  <clause id="15761">
    <literal><![CDATA[
      x \ T(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,15759,a,b,5753,a(flip))].">
      <j1 rule="hyper" parents="139 15759 5753"/>
    </justification>
  </clause>

  <clause id="15762">
    <literal><![CDATA[
      T(x,K(y,z) * (T(z,y) \ u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(6075(a,1),15759(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6075 15759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15763">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(6157(a,1),15759(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6157 15759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15764">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(u,z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(u,z) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(15759(a,1),13478(a,1,2,1))].">
      <j1 rule="para" parents="15759 13478"/>
    </justification>
  </clause>

  <clause id="15765">
    <literal><![CDATA[
      T(x,T(y \ z,y) * u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(5982(a,1),15757(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5982 15757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15766">
    <literal><![CDATA[
      T(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15758(a,2),15753(a,1))].">
      <j1 rule="para" parents="15758 15753"/>
    </justification>
  </clause>

  <clause id="15767">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5827,a,15761,a)].">
      <j1 rule="hyper" parents="5827 15761"/>
    </justification>
  </clause>

  <clause id="15768">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15761(a,1),5827(a,1))].">
      <j1 rule="para" parents="15761 5827"/>
    </justification>
  </clause>

  <clause id="15769">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(13528,a,15767,a),flip(a)].">
      <j1 rule="hyper" parents="13528 15767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15770">
    <literal><![CDATA[
      K(x,K(y,z) * (z * u)) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5755(a,1),15767(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5755 15767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15771">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(6156(a,2),15767(a,1,2))].">
      <j1 rule="para" parents="6156 15767"/>
    </justification>
  </clause>

  <clause id="15772">
    <literal><![CDATA[
      K(x,K(y,z) * (T(y,z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(5811(a,1),15767(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5811 15767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15773">
    <literal><![CDATA[
      K(x,K(y,z) * (T(z,y) \ u)) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(6075(a,1),15767(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6075 15767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15774">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(6157(a,1),15767(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6157 15767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15775">
    <literal><![CDATA[
      K(x,K(y,z \ u) * (u / z)) = K(x,T(u / z,T(y,z)))
    ]]></literal>
    <justification jstring="[para(7980(a,1),15767(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7980 15767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15776">
    <literal><![CDATA[
      K(x,K(y,z) * ((y * z) * u)) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(10834(a,1),15767(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10834 15767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15777">
    <literal><![CDATA[
      K(x,K(y,z) \ (y * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5755(a,1),15771(a,2,2))].">
      <j1 rule="para" parents="5755 15771"/>
    </justification>
  </clause>

  <clause id="15778">
    <literal><![CDATA[
      K(x,K(y,z) \ (z \ u)) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(6157(a,1),15771(a,2,2))].">
      <j1 rule="para" parents="6157 15771"/>
    </justification>
  </clause>

  <clause id="15779">
    <literal><![CDATA[
      T(x,T(T(y,z),z) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6299(a,1),15762(a,1,2))].">
      <j1 rule="para" parents="6299 15762"/>
    </justification>
  </clause>

  <clause id="15780">
    <literal><![CDATA[
      T(x,T(y \ z,y) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(117(a,1),15779(a,1,2,1,1))].">
      <j1 rule="para" parents="117 15779"/>
    </justification>
  </clause>

  <clause id="15781">
    <literal><![CDATA[
      T(x,((y * z) / y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(255(a,1),15779(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="255 15779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15782">
    <literal><![CDATA[
      T(x,((y \ z) \ K(u,z \ y)) \ w) = T(x,T((y \ z) \ 1,u) \ w)
    ]]></literal>
    <justification jstring="[para(6715(a,1),15779(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6715 15779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15783">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * (((y \ u) / u) \ w)) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[para(6583(a,1),15763(a,1,2,1))].">
      <j1 rule="para" parents="6583 15763"/>
    </justification>
  </clause>

  <clause id="15784">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) \ z) * u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(4679(a,1),15765(a,1,2,1))].">
      <j1 rule="para" parents="4679 15765"/>
    </justification>
  </clause>

  <clause id="15785">
    <literal><![CDATA[
      K(x,y * (K(z,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4534(a,1),15770(a,1,2))].">
      <j1 rule="para" parents="4534 15770"/>
    </justification>
  </clause>

  <clause id="15786">
    <literal><![CDATA[
      K(x,T(y \ z,y) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(5982(a,1),15770(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5982 15770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15787">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(6078(a,1),15772(a,1,2))].">
      <j1 rule="para" parents="6078 15772"/>
    </justification>
  </clause>

  <clause id="15788">
    <literal><![CDATA[
      K(x,T(T(y \ z,u),y) * w) = K(x,T(z / y,u) * w)
    ]]></literal>
    <justification jstring="[para(278(a,1),15787(a,1,2,1,1))].">
      <j1 rule="para" parents="278 15787"/>
    </justification>
  </clause>

  <clause id="15789">
    <literal><![CDATA[
      K(x,T(T(R(y,z,u),w),w) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(111(a,1),15787(a,2,2))].">
      <j1 rule="para" parents="111 15787"/>
    </justification>
  </clause>

  <clause id="15790">
    <literal><![CDATA[
      K(x,T(L(y \ z,u,w),y) * v5) = K(x,L(z / y,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(279(a,1),15787(a,1,2,1,1))].">
      <j1 rule="para" parents="279 15787"/>
    </justification>
  </clause>

  <clause id="15791">
    <literal><![CDATA[
      K(x,T(T(y,z),z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6299(a,1),15773(a,1,2))].">
      <j1 rule="para" parents="6299 15773"/>
    </justification>
  </clause>

  <clause id="15792">
    <literal><![CDATA[
      K(x,T(y \ z,y) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(117(a,1),15791(a,1,2,1,1))].">
      <j1 rule="para" parents="117 15791"/>
    </justification>
  </clause>

  <clause id="15793">
    <literal><![CDATA[
      K(x,((y * z) / y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(255(a,1),15791(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="255 15791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15794">
    <literal><![CDATA[
      K(x,T(T(y \ z,u),y) \ w) = K(x,T(z / y,u) \ w)
    ]]></literal>
    <justification jstring="[para(278(a,1),15791(a,1,2,1,1))].">
      <j1 rule="para" parents="278 15791"/>
    </justification>
  </clause>

  <clause id="15795">
    <literal><![CDATA[
      K(x,(L(y,z,y) * z) \ u) = K(x,T(z * y,y) \ u)
    ]]></literal>
    <justification jstring="[para(4724(a,1),15791(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4724 15791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15796">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,(z / (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4769(a,1),15791(a,1,2,1,1))].">
      <j1 rule="para" parents="4769 15791"/>
    </justification>
  </clause>

  <clause id="15797">
    <literal><![CDATA[
      K(x,K(y / z,u) * ((y * (z \ 1)) \ w)) = K(x,T(y * (z \ 1),u) \ w)
    ]]></literal>
    <justification jstring="[para(14675(a,1),15774(a,1,2,1))].">
      <j1 rule="para" parents="14675 15774"/>
    </justification>
  </clause>

  <clause id="15798">
    <literal><![CDATA[
      T(x,T((y / (z \ 1)) / y,y) \ u) = T(x,((y / (z \ K(z,y))) / y) \ u)
    ]]></literal>
    <justification jstring="[para(9493(a,1),15780(a,1,2,1,1))].">
      <j1 rule="para" parents="9493 15780"/>
    </justification>
  </clause>

  <clause id="15799">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,((y / u) / K(y \ z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(14864(a,1),15781(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14864 15781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15800">
    <literal><![CDATA[
      K(x,(y * K(z,y)) / u) = K(x,T(y,z) * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(14786,a,15785,a)].">
      <j1 rule="hyper" parents="14786 15785"/>
    </justification>
  </clause>

  <clause id="15801">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (K(u,y / z) * w)) = K(x,T(y * (1 / z),u) * w)
    ]]></literal>
    <justification jstring="[para(14462(a,1),15785(a,1,2,2,1))].">
      <j1 rule="para" parents="14462 15785"/>
    </justification>
  </clause>

  <clause id="15802">
    <literal><![CDATA[
      K(x,T((y * z) \ u,y * z) * (z * K(y,z))) = K(x,(u / (z * y)) * z)
    ]]></literal>
    <justification jstring="[para(10607(a,1),15786(a,2,2))].">
      <j1 rule="para" parents="10607 15786"/>
    </justification>
  </clause>

  <clause id="15803">
    <literal><![CDATA[
      K(x,((K(y,y \ z) * u) / z) * w) = K(x,T(((y \ z) * y) \ u,z) * w)
    ]]></literal>
    <justification jstring="[para(10871(a,1),15786(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10871 15786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15804">
    <literal><![CDATA[
      K(x,T(((y \ z) * y) \ u,T(z,y)) * w) = K(x,(u / ((y \ z) * y)) * w)
    ]]></literal>
    <justification jstring="[para(11129(a,1),15786(a,1,2,1))].">
      <j1 rule="para" parents="11129 15786"/>
    </justification>
  </clause>

  <clause id="15805">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(z,y) * u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(5015(a,1),15793(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5015 15793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15806">
    <literal><![CDATA[
      T(x,y * T(T(z,u),u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(15755,a,xx),flip(a)].">
      <j1 rule="hyper" parents="15755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15807">
    <literal><![CDATA[
      T(x,y * T(z \ u,z)) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(117(a,1),15806(a,1,2,2,1))].">
      <j1 rule="para" parents="117 15806"/>
    </justification>
  </clause>

  <clause id="15808">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(255(a,1),15806(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="255 15806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15809">
    <literal><![CDATA[
      T(x,y * (z * K(u,z))) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(5785(a,1),15806(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5785 15806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15810">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z * T(T(u,w),w))) = K(x,(z * T(T(u,w),w)) * y)
    ]]></literal>
    <justification jstring="[para(15806(a,1),11142(a,1,2,1))].">
      <j1 rule="para" parents="15806 11142"/>
    </justification>
  </clause>

  <clause id="15811">
    <literal><![CDATA[
      x * ((T(y,y \ 1) * T(y,y \ 1)) * z) = ((y \ 1) \ y) * (T(x,y * y) * z)
    ]]></literal>
    <justification jstring="[para(15806(a,1),12306(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15806 12306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15812">
    <literal><![CDATA[
      T(x,(y / z) * (y / z)) = T(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[para(6251(a,1),15807(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6251 15807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15813">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = x * K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,5753,a(flip),b,15808,a),flip(a)].">
      <j1 rule="hyper" parents="373 5753 15808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15814">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = u / T(u,x * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(225,a,15808,a(flip),b,5804,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 15808 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15815">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15769(a,2),15768(a,1))].">
      <j1 rule="para" parents="15769 15768"/>
    </justification>
  </clause>

  <clause id="15816">
    <literal><![CDATA[
      T(x,y \ 1) * (y * y) = (y * y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),15743(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 15743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15817">
    <literal><![CDATA[
      T(x,y \ (y \ z)) * (y * y) = (y * y) * T(x,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),15743(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 15743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15818">
    <literal><![CDATA[
      T(T(x,y),z * (z * u)) = T(T(x,u),z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(481,a,15747,a)].">
      <j1 rule="hyper" parents="481 15747"/>
    </justification>
  </clause>

  <clause id="15819">
    <literal><![CDATA[
      T(T(x,y),z * (z * x)) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(468,a,15747,a),flip(a)].">
      <j1 rule="hyper" parents="468 15747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15820">
    <literal><![CDATA[
      T(T(x,y),z * (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (z * y)) = u
    ]]></literal>
    <justification jstring="[para(15747(a,1),468(a,1))].">
      <j1 rule="para" parents="15747 468"/>
    </justification>
  </clause>

  <clause id="15821">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(10765(a,1),15776(a,1,2))].">
      <j1 rule="para" parents="10765 15776"/>
    </justification>
  </clause>

  <clause id="15822">
    <literal><![CDATA[
      T(x,(T(y,z) * z) * u) = T(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[hyper(143,a,15821,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 15821 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15823">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,(y * (z / y)) * u)
    ]]></literal>
    <justification jstring="[para(117(a,1),15821(a,1,2,1,1))].">
      <j1 rule="para" parents="117 15821"/>
    </justification>
  </clause>

  <clause id="15824">
    <literal><![CDATA[
      K(x,(T(y \ z,K(y,u)) * T(y,u)) * w) = K(x,(T(y,u) * (z / y)) * w)
    ]]></literal>
    <justification jstring="[para(7159(a,1),15821(a,1,2,1,1))].">
      <j1 rule="para" parents="7159 15821"/>
    </justification>
  </clause>

  <clause id="15825">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * (u / y))) * w) = K(x,((T(y,z) \ u) * y) * w)
    ]]></literal>
    <justification jstring="[para(7816(a,1),15821(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7816 15821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15826">
    <literal><![CDATA[
      T(x,(y * (T(y,z \ y) / z)) * u) = T(x,((y / z) * y) * u)
    ]]></literal>
    <justification jstring="[para(4465(a,1),15822(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4465 15822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15827">
    <literal><![CDATA[
      T(x,T(y \ z,z) * u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13442,a(flip),b,15784,a)].">
      <j1 rule="hyper" parents="64 13442 15784"/>
    </justification>
  </clause>

  <clause id="15828">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(13580,a,15796,a),flip(a)].">
      <j1 rule="hyper" parents="13580 15796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15829">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15796(a,1),13580(a,1))].">
      <j1 rule="para" parents="15796 13580"/>
    </justification>
  </clause>

  <clause id="15830">
    <literal><![CDATA[
      T(x,(y / (y / z)) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(143,a,15828,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 15828 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15831">
    <literal><![CDATA[
      K(x,(y / (y / T(z,u))) \ w) = K(x,T(T(z,y),u) \ w)
    ]]></literal>
    <justification jstring="[para(23(a,1),15828(a,2,2,1))].">
      <j1 rule="para" parents="23 15828"/>
    </justification>
  </clause>

  <clause id="15832">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(79(a,1),15828(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 15828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15833">
    <literal><![CDATA[
      K((x / (x / y)) \ z,u) = u / T(u,T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(225,a,15830,a(flip),b,5804,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 15830 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15834">
    <literal><![CDATA[
      T(x,(y / ((y / z) * (u * u))) \ w) = T(x,T((u * u) \ z,y) \ w)
    ]]></literal>
    <justification jstring="[para(900(a,1),15830(a,1,2,1,2))].">
      <j1 rule="para" parents="900 15830"/>
    </justification>
  </clause>

  <clause id="15835">
    <literal><![CDATA[
      T(x,(y * y) * ((z / (z / u)) \ w)) = T(T(x,T(u,z) \ w),y * y)
    ]]></literal>
    <justification jstring="[para(15830(a,1),1775(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15830 1775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15836">
    <literal><![CDATA[
      K(x,T(y,T(z,u) \ w) * ((u / (u / z)) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((u / (u / z)) \ w) * y) = v5
    ]]></literal>
    <justification jstring="[para(15830(a,1),11231(a,1,2,1))].">
      <j1 rule="para" parents="15830 11231"/>
    </justification>
  </clause>

  <clause id="15837">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / T(z \ y,y))
    ]]></literal>
    <justification jstring="[hyper(13485,a,15832,a),flip(a)].">
      <j1 rule="hyper" parents="13485 15832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15838">
    <literal><![CDATA[
      K(x,(y * K(z,y)) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(373,a,14406,a(flip),b,15800,a),flip(a)].">
      <j1 rule="hyper" parents="373 14406 15800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15839">
    <literal><![CDATA[
      K(x,((y * z) / y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(5721(a,2),15838(a,1,2,1))].">
      <j1 rule="para" parents="5721 15838"/>
    </justification>
  </clause>

  <clause id="15840">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(5749(a,1),15838(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5749 15838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15841">
    <literal><![CDATA[
      K(x,T(y \ z,y) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(5774(a,1),15838(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5774 15838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15842">
    <literal><![CDATA[
      K(x,((y * z) / T(y,u)) / w) = K(x,T(z * K(u,y),y) / w)
    ]]></literal>
    <justification jstring="[para(7172(a,1),15840(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7172 15840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15843">
    <literal><![CDATA[
      K(x,T(T(y,T(z,u)),u) / w) = K(x,(T(y,z) * K(u,y)) / w)
    ]]></literal>
    <justification jstring="[para(8328(a,1),15840(a,1,2,1,1))].">
      <j1 rule="para" parents="8328 15840"/>
    </justification>
  </clause>

  <clause id="15844">
    <literal><![CDATA[
      K(x,(((y * z) / y) * K(y,u)) / w) = K(x,T(z * K(y,u),y) / w)
    ]]></literal>
    <justification jstring="[para(7142(a,1),15839(a,1,2,1))].">
      <j1 rule="para" parents="7142 15839"/>
    </justification>
  </clause>

  <clause id="15845">
    <literal><![CDATA[
      K(x,T(y * K(z,u),z / y) / w) = K(x,(T(z,u) / (z / y)) / w)
    ]]></literal>
    <justification jstring="[para(15039(a,1),15839(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="15039 15839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15846">
    <literal><![CDATA[
      T(x,T(y \ z,y) / u) = T(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[hyper(143,a,15841,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 15841 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15847">
    <literal><![CDATA[
      K(x,T((T(y,z) \ z) \ u,y \ z) / w) = K(x,((K(y,z) * u) / (y \ z)) / w)
    ]]></literal>
    <justification jstring="[para(13057(a,1),15841(a,1,2,1,1))].">
      <j1 rule="para" parents="13057 15841"/>
    </justification>
  </clause>

  <clause id="15848">
    <literal><![CDATA[
      K(x,T((T(y,z) \ z) \ u,z / y) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[para(13424(a,1),15841(a,1,2,1))].">
      <j1 rule="para" parents="13424 15841"/>
    </justification>
  </clause>

  <clause id="15849">
    <literal><![CDATA[
      T(x * K(y \ z,x),z \ y) = T(x,(y / z) * (y / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7582,a,b,15812,a)].">
      <j1 rule="hyper" parents="373 7582 15812"/>
    </justification>
  </clause>

  <clause id="15850">
    <literal><![CDATA[
      T(T(x,y),(z \ u) * (z \ u)) = T(x,(u / z) * ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15740,a(flip),b,15812,a),flip(a)].">
      <j1 rule="hyper" parents="64 15740 15812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15851">
    <literal><![CDATA[
      K(x,y * ((z * u) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(5826,a,15813,a)].">
      <j1 rule="hyper" parents="5826 15813"/>
    </justification>
  </clause>

  <clause id="15852">
    <literal><![CDATA[
      K(x,y * T(z \ u,z)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),15851(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 15851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15853">
    <literal><![CDATA[
      K(x,y * T(T(z,u),u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(256(a,1),15851(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="256 15851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15854">
    <literal><![CDATA[
      K(x,y * (z * K(u,z))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(5721(a,1),15851(a,1,2,2))].">
      <j1 rule="para" parents="5721 15851"/>
    </justification>
  </clause>

  <clause id="15855">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * ((z / w) / K(z \ u,z)))
    ]]></literal>
    <justification jstring="[para(14864(a,1),15851(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14864 15851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15856">
    <literal><![CDATA[
      K(x,(y * z) * T(T(L(u,z,y),w),w)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(100(a,1),15853(a,2,2))].">
      <j1 rule="para" parents="100 15853"/>
    </justification>
  </clause>

  <clause id="15857">
    <literal><![CDATA[
      K(x,y * (z / (z / u))) = K(x,y * ((u \ z) \ z))
    ]]></literal>
    <justification jstring="[para(4719(a,1),15852(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4719 15852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15858">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ (u \ z))) = K(x,y * ((u \ z) / z))
    ]]></literal>
    <justification jstring="[para(4720(a,1),15852(a,1,2,2))].">
      <j1 rule="para" parents="4720 15852"/>
    </justification>
  </clause>

  <clause id="15859">
    <literal><![CDATA[
      K(x,(y / z) * (y / z)) = K(x,(z \ y) * (z \ y))
    ]]></literal>
    <justification jstring="[para(6251(a,1),15852(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6251 15852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15860">
    <literal><![CDATA[
      K(x,T((L(y,z,u) \ w) * y,a(y,z,u))) = K(x,y * (w / L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(15719(a,2),15852(a,1,2))].">
      <j1 rule="para" parents="15719 15852"/>
    </justification>
  </clause>

  <clause id="15861">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * (((1 / z) * u) * K(z,(1 / z) * u)))
    ]]></literal>
    <justification jstring="[para(4596(a,1),15854(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4596 15854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15862">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5787,a,b,15814,a),flip(a)].">
      <j1 rule="hyper" parents="373 5787 15814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15863">
    <literal><![CDATA[
      K(x * T(T(y,z),z),u) = K(x * y,u)
    ]]></literal>
    <justification jstring="[para(256(a,1),15862(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="256 15862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15864">
    <literal><![CDATA[
      K(x * T(y,y \ z),u) = K(x * (z / (z / y)),u)
    ]]></literal>
    <justification jstring="[para(4707(a,1),15862(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4707 15862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15865">
    <literal><![CDATA[
      K(x * (y * K(z,y)),u) = K(x * T(y,z),u)
    ]]></literal>
    <justification jstring="[para(5721(a,1),15862(a,1,1,2))].">
      <j1 rule="para" parents="5721 15862"/>
    </justification>
  </clause>

  <clause id="15866">
    <literal><![CDATA[
      T((x * x) \ y,x \ (x \ z)) = T(y / (x * x),z)
    ]]></literal>
    <justification jstring="[hyper(36,a,525,a,b,15817,a),flip(a)].">
      <j1 rule="hyper" parents="36 525 15817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15867">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) * (y * y) = (y * y) * x
    ]]></literal>
    <justification jstring="[para(372(a,1),15817(a,2,2))].">
      <j1 rule="para" parents="372 15817"/>
    </justification>
  </clause>

  <clause id="15868">
    <literal><![CDATA[
      T((1 / x) * y,x \ (x \ 1)) = (x * y) / (x * x)
    ]]></literal>
    <justification jstring="[hyper(142,a,310,a(flip),b,15867,a),flip(a)].">
      <j1 rule="hyper" parents="142 310 15867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15869">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(36,a,15817,a,b,15867,a),flip(a)].">
      <j1 rule="hyper" parents="36 15817 15867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15870">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) = x * K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,5722,a,b,15867,a),flip(a)].">
      <j1 rule="hyper" parents="36 5722 15867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15871">
    <literal><![CDATA[
      K(x,y \ (y \ 1)) = K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(5826,a,15870,a)].">
      <j1 rule="hyper" parents="5826 15870"/>
    </justification>
  </clause>

  <clause id="15872">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) \ z = K(x,y * y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(15870(a,2),6414(a,1,1))].">
      <j1 rule="para" parents="15870 6414"/>
    </justification>
  </clause>

  <clause id="15873">
    <literal><![CDATA[
      T(T(x,y \ (y \ 1)),z) = T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(481,a,15869,a)].">
      <j1 rule="hyper" parents="481 15869"/>
    </justification>
  </clause>

  <clause id="15874">
    <literal><![CDATA[
      T((x * y) / x,z \ (z \ x)) = T(y,z \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(255(a,1),15869(a,1,1)),flip(a)].">
      <j1 rule="para" parents="255 15869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15875">
    <literal><![CDATA[
      T(T(x,y \ (y \ z)),u) = T(T(x,z),y \ (y \ u))
    ]]></literal>
    <justification jstring="[para(15869(a,1),15873(a,1,1))].">
      <j1 rule="para" parents="15869 15873"/>
    </justification>
  </clause>

  <clause id="15876">
    <literal><![CDATA[
      T(T(x,y \ z),y * (y * u)) = T(T(x,u),y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),15818(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 15818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15877">
    <literal><![CDATA[
      K(x,(y * (z / y)) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13468,a(flip),b,15823,a),flip(a)].">
      <j1 rule="hyper" parents="64 13468 15823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15878">
    <literal><![CDATA[
      K(x,T(y * z,z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),15877(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 15877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15879">
    <literal><![CDATA[
      K(x,T(y * (z / y),u) * w) = K(x,T(T(z,u),y) * w)
    ]]></literal>
    <justification jstring="[para(5431(a,2),15877(a,1,2,1))].">
      <j1 rule="para" parents="5431 15877"/>
    </justification>
  </clause>

  <clause id="15880">
    <literal><![CDATA[
      K((x / (x / y)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5787,a,b,15833,a),flip(a)].">
      <j1 rule="hyper" parents="373 5787 15833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15881">
    <literal><![CDATA[
      K(x,T((y / (y / z)) \ u,w)) = T(x,w) / T(x * K(T(z,y) \ u,x),w)
    ]]></literal>
    <justification jstring="[para(15880(a,1),8044(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="15880 8044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15882">
    <literal><![CDATA[
      K(x,y * (z / (z / u))) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,13346,a(flip),b,15857,a),flip(a)].">
      <j1 rule="hyper" parents="373 13346 15857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15883">
    <literal><![CDATA[
      K(x,y * T(z \ u,u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(79(a,1),15882(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="79 15882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15884">
    <literal><![CDATA[
      K(x,L(y * T(z \ u,u),w,v5)) = K(L(x,w,v5),y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(12117,a,15883,a)].">
      <j1 rule="hyper" parents="12117 15883"/>
    </justification>
  </clause>

  <clause id="15885">
    <literal><![CDATA[
      T(1 / x,x \ (x \ y)) = T(x / (x * x),y)
    ]]></literal>
    <justification jstring="[para(309(a,1),15866(a,1,1))].">
      <j1 rule="para" parents="309 15866"/>
    </justification>
  </clause>

  <clause id="15886">
    <literal><![CDATA[
      L(1 / x,1 / x,x \ y) \ (x \ y) = (x \ y) * (T(x / (x * x),y) \ 1)
    ]]></literal>
    <justification jstring="[para(15885(a,1),14989(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15885 14989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15887">
    <literal><![CDATA[
      L(T(x \ y,x \ (x \ 1)),x,x) = (x * y) / (x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,578,a,b,15868,a)].">
      <j1 rule="hyper" parents="64 578 15868"/>
    </justification>
  </clause>

  <clause id="15888">
    <literal><![CDATA[
      K(x \ (x \ 1),y) = K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(39,a,14808,a(flip),b,15872,a),flip(a)].">
      <j1 rule="hyper" parents="39 14808 15872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15889">
    <literal><![CDATA[
      K(x \ (x \ y),y) = K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,14968,a(flip),b,15888,a)].">
      <j1 rule="hyper" parents="64 14968 15888"/>
    </justification>
  </clause>

  <clause id="15890">
    <literal><![CDATA[
      K(x,(x / y) * (x / y)) = K((x / y) \ y,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),15889(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="82 15889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15891">
    <literal><![CDATA[
      (((x \ (x \ y)) \ y) \ z) * K((x \ (x \ y)) \ y,x \ (x \ y)) = T((y / (x \ (x \ y))) \ z,K(y,x * x))
    ]]></literal>
    <justification jstring="[para(15889(a,1),8904(a,2,2))].">
      <j1 rule="para" parents="15889 8904"/>
    </justification>
  </clause>

  <clause id="15892">
    <literal><![CDATA[
      R((x \ (x \ y)) \ y,x \ (x \ y),(x \ (x \ y)) \ y) = T((x \ (x \ y)) \ y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,1032,a(flip),b,15874,a)].">
      <j1 rule="hyper" parents="64 1032 15874"/>
    </justification>
  </clause>

  <clause id="15893">
    <literal><![CDATA[
      T(T(x,y * z),y \ (y \ u)) = T(T(x,y \ z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),15875(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 15875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15894">
    <literal><![CDATA[
      T(T(x,y * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (y * z)) = u
    ]]></literal>
    <justification jstring="[para(15746(a,1),623(a,1)),flip(b)].">
      <j1 rule="para" parents="15746 623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15895">
    <literal><![CDATA[
      T(T(x,y),z * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * (z * y)) = u
    ]]></literal>
    <justification jstring="[para(23(a,1),15894(a,1))].">
      <j1 rule="para" parents="23 15894"/>
    </justification>
  </clause>

  <clause id="15896">
    <literal><![CDATA[
      T(x,(y * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (y * z)) = u
    ]]></literal>
    <justification jstring="[para(1773(a,1),15894(a,1))].">
      <j1 rule="para" parents="1773 15894"/>
    </justification>
  </clause>

  <clause id="15897">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(13517,a,15795,a),flip(a)].">
      <j1 rule="hyper" parents="13517 15795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15898">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15795(a,1),13517(a,1))].">
      <j1 rule="para" parents="15795 13517"/>
    </justification>
  </clause>

  <clause id="15899">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),15897(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 15897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15900">
    <literal><![CDATA[
      K(x,T((y * z) * (K(z,y) / z),K(z,y) / z) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(14922(a,1),15897(a,2,2,1))].">
      <j1 rule="para" parents="14922 15897"/>
    </justification>
  </clause>

  <clause id="15901">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,w,v5)) = K(L(x,w,v5),T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(12117,a,15899,a)].">
      <j1 rule="hyper" parents="12117 15899"/>
    </justification>
  </clause>

  <clause id="15902">
    <literal><![CDATA[
      K(x,T(y,z) \ (z * x)) = K(x,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(9750,a,15899,a),flip(a)].">
      <j1 rule="hyper" parents="9750 15899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15903">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,(y * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,13414,a,b,15899,a)].">
      <j1 rule="hyper" parents="373 13414 15899"/>
    </justification>
  </clause>

  <clause id="15904">
    <literal><![CDATA[
      K(x,(y * ((y * z) / y)) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,13327,a(flip),b,15899,a),flip(a)].">
      <j1 rule="hyper" parents="373 13327 15899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15905">
    <literal><![CDATA[
      T(x,(y * (z / y)) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(143,a,15899,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 15899 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15906">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(y \ T(z,y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(4399(a,2),15899(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4399 15899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15907">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u) \ w)),((u * (z / u)) \ w) * y) = T(x,y * ((u * (z / u)) \ w))
    ]]></literal>
    <justification jstring="[para(15899(a,1),11128(a,1,1,2))].">
      <j1 rule="para" parents="15899 11128"/>
    </justification>
  </clause>

  <clause id="15908">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(z,y) * x)) = K(x,T(z,y) / (x \ y))
    ]]></literal>
    <justification jstring="[para(4619(a,1),15902(a,1,2,1))].">
      <j1 rule="para" parents="4619 15902"/>
    </justification>
  </clause>

  <clause id="15909">
    <literal><![CDATA[
      T(x,T(y,z) \ T(u,z * (y / z))) = T(x,u / (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13419,a(flip),b,15905,a),flip(a)].">
      <j1 rule="hyper" parents="64 13419 15905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15910">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) \ 1 = K(((y \ z) * y) \ u,x)
    ]]></literal>
    <justification jstring="[para(15903(a,1),6092(a,1,1))].">
      <j1 rule="para" parents="15903 6092"/>
    </justification>
  </clause>

  <clause id="15911">
    <literal><![CDATA[
      K(x,(T(y,z) * z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(256(a,1),15904(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="256 15904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15912">
    <literal><![CDATA[
      K(x,((y \ z) * (K(y,u) \ y)) \ w) = K(x,(y * (z / T(y,u))) \ w)
    ]]></literal>
    <justification jstring="[para(7198(a,1),15911(a,1,2,1))].">
      <j1 rule="para" parents="7198 15911"/>
    </justification>
  </clause>

  <clause id="15913">
    <literal><![CDATA[
      L(T(x / y,y \ 1),y,y) = (y * x) / (y * y)
    ]]></literal>
    <justification jstring="[para(14817(a,1),15887(a,1,1))].">
      <j1 rule="para" parents="14817 15887"/>
    </justification>
  </clause>

  <clause id="15914">
    <literal><![CDATA[
      x * ((y / x) * (x \ 1)) = (x * y) / (x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1140,a(flip),b,15913,a)].">
      <j1 rule="hyper" parents="64 1140 15913"/>
    </justification>
  </clause>

  <clause id="15915">
    <literal><![CDATA[
      (x * (y * x)) / (x * x) = x * (y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(11(a,1),15914(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 15914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15916">
    <literal><![CDATA[
      (x * x) * ((x * (y * x)) \ z) = (x * (y * (x \ 1))) \ z
    ]]></literal>
    <justification jstring="[para(15915(a,1),890(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15915 890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15917">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * ((z / y) \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(13449(a,1),15898(a,1))].">
      <j1 rule="para" parents="13449 15898"/>
    </justification>
  </clause>

  <clause id="15918">
    <literal><![CDATA[
      K(x,T(y / (y / z),u) \ w) = K(x,T(T(z,y),u) \ w)
    ]]></literal>
    <justification jstring="[para(8388(a,1),15831(a,1,2,1))].">
      <j1 rule="para" parents="8388 15831"/>
    </justification>
  </clause>

  <clause id="15919">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(13480,a,15837,a),flip(a)].">
      <j1 rule="hyper" parents="13480 15837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15920">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(15837(a,1),13480(a,1))].">
      <j1 rule="para" parents="15837 13480"/>
    </justification>
  </clause>

  <clause id="15921">
    <literal><![CDATA[
      K(x,y / (z / (z / u))) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(82(a,1),15919(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="82 15919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15922">
    <literal><![CDATA[
      T(x,y / (z / (z / u))) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,15921,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 15921 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15923">
    <literal><![CDATA[
      T(x,T(y,z / T(u,w)) * (z / (w / (w / u)))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / (w / (w / u))) * y) = v5
    ]]></literal>
    <justification jstring="[para(15922(a,1),11200(a,1,2,1))].">
      <j1 rule="para" parents="15922 11200"/>
    </justification>
  </clause>

  <clause id="15924">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15832,a(flip),b,15906,a),flip(a)].">
      <j1 rule="hyper" parents="64 15832 15906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15925">
    <literal><![CDATA[
      K(x,T(y,z) / (x \ z)) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,15805,a(flip),b,15908,a),flip(a)].">
      <j1 rule="hyper" parents="64 15805 15908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15926">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K((x * (y / x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(6101,a,15910,a),flip(a)].">
      <j1 rule="hyper" parents="6101 15910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15927">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13474,a(flip),b,15926,a),flip(a)].">
      <j1 rule="hyper" parents="64 13474 15926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15928">
    <literal><![CDATA[
      K(K(x,y) * (x \ z),u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13524,a(flip),b,15927,a)].">
      <j1 rule="hyper" parents="64 13524 15927"/>
    </justification>
  </clause>

  <clause id="15929">
    <literal><![CDATA[
      K(T(x * y,y) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(11(a,1),15927(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 15927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15930">
    <literal><![CDATA[
      K(T(x \ y,x) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(6292(a,1),15928(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6292 15928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15931">
    <literal><![CDATA[
      (T(x \ y,x) \ z) * T(x \ y,x) = z * K((y / x) \ z,y / x)
    ]]></literal>
    <justification jstring="[para(15930(a,1),8289(a,2,2))].">
      <j1 rule="para" parents="15930 8289"/>
    </justification>
  </clause>

  <clause id="15932">
    <literal><![CDATA[
      (x * x) * (((x * (y * x)) \ z) * u) = ((x * (y * (x \ 1))) \ z) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,15916,a(flip),b,127,a),flip(a)].">
      <j1 rule="hyper" parents="144 15916 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15933">
    <literal><![CDATA[
      K(x,R(T(T(y,z),z),u,w) * (u * w)) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(1068(a,2),15789(a,1,2,1))].">
      <j1 rule="para" parents="1068 15789"/>
    </justification>
  </clause>

  <clause id="15934">
    <literal><![CDATA[
      K(x,(y * z) * T(L(T(u,w),z,y),w)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(25(a,2),15856(a,1,2,2,1))].">
      <j1 rule="para" parents="25 15856"/>
    </justification>
  </clause>

  <clause id="15935">
    <literal><![CDATA[
      K(x,(T(T(y,z),z) * u) * w) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(111(a,1),15933(a,1,2))].">
      <j1 rule="para" parents="111 15933"/>
    </justification>
  </clause>

  <clause id="15936">
    <literal><![CDATA[
      K(x,(((y * z) / y) * u) * w) = K(x,(T(z,y) * u) * w)
    ]]></literal>
    <justification jstring="[para(255(a,1),15935(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="255 15935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15937">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * u)) * w) = K(x,(T(y,z) * u) * w)
    ]]></literal>
    <justification jstring="[para(5911(a,1),15936(a,1,2,1))].">
      <j1 rule="para" parents="5911 15936"/>
    </justification>
  </clause>

  <clause id="15938">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(988(a,1),15934(a,1,2))].">
      <j1 rule="para" parents="988 15934"/>
    </justification>
  </clause>

  <clause id="15939">
    <literal><![CDATA[
      K(x,y * (z * T(T(u,w),w))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(517(a,1),15934(a,1,2))].">
      <j1 rule="para" parents="517 15934"/>
    </justification>
  </clause>

  <clause id="15940">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) = x \ T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,5726,a(flip),b,15938,a),flip(a)].">
      <j1 rule="hyper" parents="373 5726 15938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15941">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(143,a,15938,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 15938 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15942">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * ((w * u) / w))) = K(x,y * (((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(8242(a,1),15938(a,1,2,2,1))].">
      <j1 rule="para" parents="8242 15938"/>
    </justification>
  </clause>

  <clause id="15943">
    <literal><![CDATA[
      T(x,y \ (T(z,u) * u)) = T(x,(y \ 1) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(14732,a,15941,a)].">
      <j1 rule="hyper" parents="14732 15941"/>
    </justification>
  </clause>

  <clause id="15944">
    <literal><![CDATA[
      T(x,y * (T(z \ u,w) * z)) = T(x,y * (z * T(u / z,w)))
    ]]></literal>
    <justification jstring="[para(278(a,1),15941(a,1,2,2,1))].">
      <j1 rule="para" parents="278 15941"/>
    </justification>
  </clause>

  <clause id="15945">
    <literal><![CDATA[
      K(x,y * (z * T(u \ w,w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13601,a(flip),b,15939,a)].">
      <j1 rule="hyper" parents="64 13601 15939"/>
    </justification>
  </clause>

  <clause id="15946">
    <literal><![CDATA[
      K(x,y * (z * T(u \ w,u))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[para(117(a,1),15939(a,1,2,2,2,1))].">
      <j1 rule="para" parents="117 15939"/>
    </justification>
  </clause>

  <clause id="15947">
    <literal><![CDATA[
      K(x,y * (z * ((u * w) / u))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[para(255(a,1),15939(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="255 15939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15948">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(15940(a,2),5827(a,1))].">
      <j1 rule="para" parents="15940 5827"/>
    </justification>
  </clause>

  <clause id="15949">
    <literal><![CDATA[
      T(x,y \ (T(z,u) * u)) = T(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,14479,a(flip),b,15943,a),flip(a)].">
      <j1 rule="hyper" parents="373 14479 15943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15950">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y \ (z * u)) = T(x,(T(u,z) * z) / y)
    ]]></literal>
    <justification jstring="[hyper(11146,a,15949,a),flip(a)].">
      <j1 rule="hyper" parents="11146 15949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15951">
    <literal><![CDATA[
      T(x,y \ T(z * u,u)) = T(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13491,a,b,15949,a)].">
      <j1 rule="hyper" parents="64 13491 15949"/>
    </justification>
  </clause>

  <clause id="15952">
    <literal><![CDATA[
      T(x,y \ T(z * K(u,w),w)) = T(x,y \ (w * (z / T(w,u))))
    ]]></literal>
    <justification jstring="[para(6311(a,1),15951(a,1,2,2,1))].">
      <j1 rule="para" parents="6311 15951"/>
    </justification>
  </clause>

  <clause id="15953">
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) * w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(15339,a,15434,a),flip(a)].">
      <j1 rule="hyper" parents="15339 15434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15954">
    <literal><![CDATA[
      K(x,L(y,z,u / (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u * w)) = v5
    ]]></literal>
    <justification jstring="[para(15435(a,1),15339(a,1))].">
      <j1 rule="para" parents="15435 15339"/>
    </justification>
  </clause>

  <clause id="15955">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = a(w,u \ z,K(u,K(x,y))) * K(w,K(x,y))
    ]]></literal>
    <justification jstring="[para(101(a,2),15457(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="101 15457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15956">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ y)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(15339,a,15513,a),flip(a)].">
      <j1 rule="hyper" parents="15339 15513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15957">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(15513(a,1),15339(a,1))].">
      <j1 rule="para" parents="15513 15339"/>
    </justification>
  </clause>

  <clause id="15958">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ 1)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(15706,a,15956,a)].">
      <j1 rule="hyper" parents="15706 15956"/>
    </justification>
  </clause>

  <clause id="15959">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ u)) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[para(9(a,1),15958(a,1,2,3,1)),flip(a)].">
      <j1 rule="para" parents="9 15958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15960">
    <literal><![CDATA[
      K(x,L(y,z * u,(z * u) \ z)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,15523,a(flip),b,15959,a)].">
      <j1 rule="hyper" parents="64 15523 15959"/>
    </justification>
  </clause>

  <clause id="15961">
    <literal><![CDATA[
      K(x,L(y,z,L(u \ 1,u,w))) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[para(241(a,2),15959(a,1,2,3))].">
      <j1 rule="para" parents="241 15959"/>
    </justification>
  </clause>

  <clause id="15962">
    <literal><![CDATA[
      K(x,L(y,z * u,u \ 1)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,15959,a(flip),b,15960,a)].">
      <j1 rule="hyper" parents="64 15959 15960"/>
    </justification>
  </clause>

  <clause id="15963">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,((y * z) * (z \ 1)) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(15581,a,15962,a),flip(a)].">
      <j1 rule="hyper" parents="15581 15962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15965">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ 1)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(15512(a,2),15957(a,1))].">
      <j1 rule="para" parents="15512 15957"/>
    </justification>
  </clause>

  <clause id="15966">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u \ 1),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(141,a,15430,a(flip),b,15519,a),flip(a)].">
      <j1 rule="hyper" parents="141 15430 15519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15967">
    <literal><![CDATA[
      K(x,L(y \ a(z,u,u \ 1),y,z)) = K(x,y \ a(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(12170,a,15966,a)].">
      <j1 rule="hyper" parents="12170 15966"/>
    </justification>
  </clause>

  <clause id="15968">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * u) = K(x,z * ((z \ T(u,y)) * y))
    ]]></literal>
    <justification jstring="[para(12183(a,1),15530(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12183 15530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15969">
    <literal><![CDATA[
      K((x \ y) \ z,T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x * z),T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(15538(a,1),5973(a,1))].">
      <j1 rule="para" parents="15538 5973"/>
    </justification>
  </clause>

  <clause id="15970">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(z / (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(15969,a,11156,a)].">
      <j1 rule="hyper" parents="15969 11156"/>
    </justification>
  </clause>

  <clause id="15971">
    <literal><![CDATA[
      K(x / (y \ z),z) = K(z \ (x * y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13471,a(flip),b,15970,a),flip(a)].">
      <j1 rule="hyper" parents="64 13471 15970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15972">
    <literal><![CDATA[
      K(x \ (y * (x / z)),x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),15971(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="82 15971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15973">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ (z * (x * y)),R(x,y,y \ 1)) = K(z / (y \ 1),R(x,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(482(a,1),15971(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="482 15971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15974">
    <literal><![CDATA[
      a(x,y,K(z / u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,y,K(x,w \ (z * (w / u)))) = v5
    ]]></literal>
    <justification jstring="[para(15972(a,1),15405(a,1,3))].">
      <j1 rule="para" parents="15972 15405"/>
    </justification>
  </clause>

  <clause id="15975">
    <literal><![CDATA[
      L(x,x \ y,z) \ (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(z * (y / x),x) = u
    ]]></literal>
    <justification jstring="[para(10274(a,1),15545(a,1))].">
      <j1 rule="para" parents="10274 15545"/>
    </justification>
  </clause>

  <clause id="15976">
    <literal><![CDATA[
      L(x,x \ (y \ z),K(y,z)) \ ((y \ z) * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * ((y \ z) / x),x) = u
    ]]></literal>
    <justification jstring="[para(7130(a,1),15975(a,1,2))].">
      <j1 rule="para" parents="7130 15975"/>
    </justification>
  </clause>

  <clause id="15977">
    <literal><![CDATA[
      K(x,L(y,z,R(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5))) = v6
    ]]></literal>
    <justification jstring="[para(15591(a,1),15340(a,1))].">
      <j1 rule="para" parents="15591 15340"/>
    </justification>
  </clause>

  <clause id="15978">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,L(y \ 1,y,z))) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(15977,a,12224,a)].">
      <j1 rule="hyper" parents="15977 12224"/>
    </justification>
  </clause>

  <clause id="15979">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,15345,a(flip),b,15602,a)].">
      <j1 rule="hyper" parents="145 15345 15602"/>
    </justification>
  </clause>

  <clause id="15980">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11281,a(flip),b,15979,a)].">
      <j1 rule="hyper" parents="64 11281 15979"/>
    </justification>
  </clause>

  <clause id="15981">
    <literal><![CDATA[
      a(x,y,z) = ((y * z) * x) \ ((y * z) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,15979,a(flip),b,11281,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 15979 11281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15982">
    <literal><![CDATA[
      R(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(15309,a,15980,a),flip(a)].">
      <j1 rule="hyper" parents="15309 15980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15983">
    <literal><![CDATA[
      (1 / (x * y)) * R(x * y,x,y) = a(x * y,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,310,a,b,15980,a)].">
      <j1 rule="hyper" parents="35 310 15980"/>
    </justification>
  </clause>

  <clause id="15984">
    <literal><![CDATA[
      x * a(x,y,y) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,33,a(flip),b,15980,a(flip))].">
      <j1 rule="hyper" parents="35 33 15980"/>
    </justification>
  </clause>

  <clause id="15985">
    <literal><![CDATA[
      (x * ((y * z) * u)) \ (x * ((y * z) * R(u,y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      L(a(u,y,z),(y * z) * u,x) = w
    ]]></literal>
    <justification jstring="[para(15980(a,1),608(a,1,2,2))].">
      <j1 rule="para" parents="15980 608"/>
    </justification>
  </clause>

  <clause id="15986">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(u,z,K(x,T(y,z))) = (z * K(x,T(y,z))) * R(u,z,K(x,T(y,z)))
    ]]></literal>
    <justification jstring="[para(7879(a,1),15980(a,1,1,1))].">
      <j1 rule="para" parents="7879 15980"/>
    </justification>
  </clause>

  <clause id="15987">
    <literal><![CDATA[
      x \ R(x,y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(149,a,15984,a)].">
      <j1 rule="hyper" parents="149 15984"/>
    </justification>
  </clause>

  <clause id="15988">
    <literal><![CDATA[
      a(x,(y \ 1) * z,(y \ 1) * z) = x \ R(x,y * z,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,3018,a(flip),b,15984,a),flip(a)].">
      <j1 rule="hyper" parents="139 3018 15984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15989">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,u,u),y,z) = a(L(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,29,a(flip),b,15984,a)].">
      <j1 rule="hyper" parents="139 29 15984"/>
    </justification>
  </clause>

  <clause id="15990">
    <literal><![CDATA[
      R(x,y,y) / x = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,2076,a,b,15984,a)].">
      <j1 rule="hyper" parents="35 2076 15984"/>
    </justification>
  </clause>

  <clause id="15991">
    <literal><![CDATA[
      T(x,y) \ R(x,z,z) = K(y,x) * a(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,15984,a(flip),b,5829,a)].">
      <j1 rule="hyper" parents="139 15984 5829"/>
    </justification>
  </clause>

  <clause id="15992">
    <literal><![CDATA[
      (x * (a(x,y,y) * z)) \ (R(x,y,y) * z) = a(x,a(x,y,y),z)
    ]]></literal>
    <justification jstring="[para(15984(a,1),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="15984 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15993">
    <literal><![CDATA[
      R(x,y,y) \ (x * (a(x,y,y) * z)) = L(z,a(x,y,y),x)
    ]]></literal>
    <justification jstring="[para(15984(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="15984 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15994">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(x,y,y),x) = R(x,y,y) \ (x * z)
    ]]></literal>
    <justification jstring="[para(15984(a,1),102(a,2,1))].">
      <j1 rule="para" parents="15984 102"/>
    </justification>
  </clause>

  <clause id="15995">
    <literal><![CDATA[
      x * R(x \ a(x,y,y),z,u) = x \ R(R(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[para(15984(a,1),2124(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15984 2124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15996">
    <literal><![CDATA[
      (R(x,y,y) * z) / (x * (a(x,y,y) * z)) = a(x,a(x,y,y),z)
    ]]></literal>
    <justification jstring="[para(15984(a,1),15462(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="15984 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15997">
    <literal><![CDATA[
      x \ (y * R(y \ x,z,z)) = a(x \ y,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2744,a(flip),b,15987,a)].">
      <j1 rule="hyper" parents="64 2744 15987"/>
    </justification>
  </clause>

  <clause id="15998">
    <literal><![CDATA[
      a(x,y,y) * x = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,15987,a(flip),b,2071,a)].">
      <j1 rule="hyper" parents="144 15987 2071"/>
    </justification>
  </clause>

  <clause id="15999">
    <literal><![CDATA[
      a(x,y,y) / R(x,y,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(142,a,15987,a(flip),b,2067,a)].">
      <j1 rule="hyper" parents="142 15987 2067"/>
    </justification>
  </clause>

  <clause id="16000">
    <literal><![CDATA[
      R(1 / x,y,y) = a(x,y,y) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,15987,a(flip),b,2007,a),flip(a)].">
      <j1 rule="hyper" parents="142 15987 2007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16001">
    <literal><![CDATA[
      (1 / x) \ a(x,y,y) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,15987,a(flip),b,2067,a)].">
      <j1 rule="hyper" parents="139 15987 2067"/>
    </justification>
  </clause>

  <clause id="16002">
    <literal><![CDATA[
      R(x \ 1,y,y) = x \ a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,15987,a(flip),b,1987,a),flip(a)].">
      <j1 rule="hyper" parents="139 15987 1987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16003">
    <literal><![CDATA[
      a(x,y,y) \ R(x,y,y) = x
    ]]></literal>
    <justification jstring="[para(15987(a,1),2072(a,1,1))].">
      <j1 rule="para" parents="15987 2072"/>
    </justification>
  </clause>

  <clause id="16004">
    <literal><![CDATA[
      L(x,y,z * R(z,u,u)) = L(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(15987(a,1),2212(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15987 2212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16005">
    <literal><![CDATA[
      L(x,y,y * R(y,z,z)) = L(x,a(y,z,z),y)
    ]]></literal>
    <justification jstring="[para(15987(a,1),2858(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15987 2858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16006">
    <literal><![CDATA[
      R(x,y * R(y,z,z),u) = R(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(15987(a,1),3019(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15987 3019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16007">
    <literal><![CDATA[
      R(x,y,y) \ x = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[para(15987(a,1),5382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15987 5382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16008">
    <literal><![CDATA[
      a(x,y * R(y,z,z),u) = a(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(15987(a,1),11985(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15987 11985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16009">
    <literal><![CDATA[
      a(x,(y * R(y,z,z)) * u,w) = a(x,a(y,z,z) * u,w)
    ]]></literal>
    <justification jstring="[para(15987(a,1),11999(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15987 11999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16010">
    <literal><![CDATA[
      T(x \ R(x,y,y),z) = a(x,y,y)
    ]]></literal>
    <justification jstring="[para(15987(a,2),13984(a,1,1))].">
      <j1 rule="para" parents="15987 13984"/>
    </justification>
  </clause>

  <clause id="16011">
    <literal><![CDATA[
      (R(x,y,y) \ x) * K(z,u) = a(x,y,y) \ K(z,u)
    ]]></literal>
    <justification jstring="[para(15987(a,1),14524(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15987 14524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16012">
    <literal><![CDATA[
      R(x,y,y) * L(z,x,a(x,y,y)) = a(x,y,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,15998,a(flip),b,213,a)].">
      <j1 rule="hyper" parents="144 15998 213"/>
    </justification>
  </clause>

  <clause id="16014">
    <literal><![CDATA[
      (x * a(y,z,z)) \ (x * R(y,z,z)) = L(y,a(y,z,z),x)
    ]]></literal>
    <justification jstring="[para(15998(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="15998 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16015">
    <literal><![CDATA[
      x * L(y \ z,y,a(y,u,u)) = x * (R(y,u,u) \ (a(y,u,u) * z))
    ]]></literal>
    <justification jstring="[para(15998(a,1),632(a,2,2,1))].">
      <j1 rule="para" parents="15998 632"/>
    </justification>
  </clause>

  <clause id="16016">
    <literal><![CDATA[
      (R(x,y,y) * z) / (a(x,y,y) * (x * z)) = a(a(x,y,y),x,z)
    ]]></literal>
    <justification jstring="[para(15998(a,1),15462(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="15998 15462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16017">
    <literal><![CDATA[
      (a(x,y,y) * a(x,y,y)) \ R(x,y,y) = (a(x,y,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(16003(a,1),13946(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16003 13946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16018">
    <literal><![CDATA[
      a(x / (1 / y),y,y) / (x * y) = 1 / (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(1407(a,1),15999(a,1,2))].">
      <j1 rule="para" parents="1407 15999"/>
    </justification>
  </clause>

  <clause id="16019">
    <literal><![CDATA[
      a(R(x \ a(x,y,y),z,u),w,v5) = a(R(R(x,y,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(16001(a,1),2698(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="16001 2698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16020">
    <literal><![CDATA[
      R(x,x \ a(x,y,y),z) = (a(x,y,y) * z) / (R(x \ 1,y,y) * z)
    ]]></literal>
    <justification jstring="[para(16002(a,2),108(a,2,2,1))].">
      <j1 rule="para" parents="16002 108"/>
    </justification>
  </clause>

  <clause id="16021">
    <literal><![CDATA[
      x \ (a(x,y,y) \ 1) = R(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,16007,a(flip),b,1909,a)].">
      <j1 rule="hyper" parents="139 16007 1909"/>
    </justification>
  </clause>

  <clause id="16022">
    <literal><![CDATA[
      (a(x,y,y) \ 1) \ x = R(x,y,y)
    ]]></literal>
    <justification jstring="[para(16007(a,1),2157(a,1,1))].">
      <j1 rule="para" parents="16007 2157"/>
    </justification>
  </clause>

  <clause id="16023">
    <literal><![CDATA[
      R((x * y) / (y * y),z,u) \ R((x / y) * K(y,y),z,u) = a(R((x / y) * K(y,y),z,u),y,y) \ 1
    ]]></literal>
    <justification jstring="[para(10310(a,1),16007(a,1,1))].">
      <j1 rule="para" parents="10310 16007"/>
    </justification>
  </clause>

  <clause id="16024">
    <literal><![CDATA[
      L(x,R(y,z,z) \ y,u) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(16007(a,2),11794(a,1,2))].">
      <j1 rule="para" parents="16007 11794"/>
    </justification>
  </clause>

  <clause id="16025">
    <literal><![CDATA[
      L(x,y,a(z,u,u) \ z) = L(x,y,R(z,u,u))
    ]]></literal>
    <justification jstring="[para(16022(a,1),2234(a,1,3)),flip(a)].">
      <j1 rule="para" parents="16022 2234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16026">
    <literal><![CDATA[
      R(x,(a(y,z,z) \ y) * u,w) = R(x,R(y,z,z) * u,w)
    ]]></literal>
    <justification jstring="[para(16022(a,1),3029(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16022 3029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16027">
    <literal><![CDATA[
      x \ (y * R(y \ x,z,z)) = a((x \ y) \ 1,z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2653,a,b,15997,a),flip(a)].">
      <j1 rule="hyper" parents="373 2653 15997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16028">
    <literal><![CDATA[
      x * R(x \ (y * y),z,z) = (y * y) * a(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,2637,a(flip),b,15997,a),flip(a)].">
      <j1 rule="hyper" parents="145 2637 15997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16029">
    <literal><![CDATA[
      (x * y) \ (((z * x) * y) * R(((z * x) * y) \ (x * y),u,u)) = a(R(T(z,x * y),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(796(a,1),15997(a,2,1))].">
      <j1 rule="para" parents="796 15997"/>
    </justification>
  </clause>

  <clause id="16030">
    <literal><![CDATA[
      x \ (y * (z * R(z \ (y \ x),u,u))) = a(x \ (y * z),u,u)
    ]]></literal>
    <justification jstring="[para(1709(a,1),15997(a,1,2))].">
      <j1 rule="para" parents="1709 15997"/>
    </justification>
  </clause>

  <clause id="16031">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,102,a,b,15981,a),flip(a)].">
      <j1 rule="hyper" parents="373 102 15981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16032">
    <literal><![CDATA[
      L((1 / x) * R(x,y,z),x,y * z) = L(a(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(15981(a,2),1313(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15981 1313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16033">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),x,y * z) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(15981(a,2),637(a,2,1))].">
      <j1 rule="para" parents="15981 637"/>
    </justification>
  </clause>

  <clause id="16034">
    <literal><![CDATA[
      (K(x,y) * ((y * z) * x)) \ ((y * (K(x,y) * z)) * R(x,y,K(x,y) * z)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7765(a,1),15981(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7765 15981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16035">
    <literal><![CDATA[
      (R(x,y,y) * z) \ ((x * a(x,y,y)) * R(z,x,a(x,y,y))) = a(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(15984(a,1),15981(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="15984 15981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16036">
    <literal><![CDATA[
      L(x \ R(x,y,y \ z),x,z) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),16031(a,2,3)),flip(a)].">
      <j1 rule="para" parents="10 16031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16037">
    <literal><![CDATA[
      L(x \ (y * R(y \ x,z,u)),x \ y,z * u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(2744(a,1),16031(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2744 16031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16038">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),L(x,u,w),y * z) = a(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(4246(a,1),16031(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4246 16031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16039">
    <literal><![CDATA[
      a(x,y \ R(y,z,u),x) = a(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(16031(a,2),13697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16031 13697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16041">
    <literal><![CDATA[
      a(x,y \ R(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      1 = w
    ]]></literal>
    <justification jstring="[para(16039(a,2),13939(a,1))].">
      <j1 rule="para" parents="16039 13939"/>
    </justification>
  </clause>

  <clause id="16043">
    <literal><![CDATA[
      L(L(x,y,z) \ R(L(x,y,z),u,u \ x),x,L(x,y,z)) = a(L(x,y,z),u,u \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2482,a(flip),b,16036,a)].">
      <j1 rule="hyper" parents="64 2482 16036"/>
    </justification>
  </clause>

  <clause id="16044">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,z \ x)) = a(y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,16036,a)].">
      <j1 rule="hyper" parents="64 102 16036"/>
    </justification>
  </clause>

  <clause id="16045">
    <literal><![CDATA[
      (x * y) * a(y,z,z \ x) = x * R(y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,16036,a(flip),b,102,a(flip))].">
      <j1 rule="hyper" parents="145 16036 102"/>
    </justification>
  </clause>

  <clause id="16046">
    <literal><![CDATA[
      (x * y) * a(x * y,x,y) = R(x * y,x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,15983,a(flip),b,2067,a(flip))].">
      <j1 rule="hyper" parents="145 15983 2067"/>
    </justification>
  </clause>

  <clause id="16047">
    <literal><![CDATA[
      a(x * y,x,y) * (x * y) = R(x * y,x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,15983,a(flip),b,1868,a(flip))].">
      <j1 rule="hyper" parents="144 15983 1868"/>
    </justification>
  </clause>

  <clause id="16048">
    <literal><![CDATA[
      a(x,y,y) \ K(x,z) = R(x,y,y) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(15031,a,16011,a),flip(a)].">
      <j1 rule="hyper" parents="15031 16011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16049">
    <literal><![CDATA[
      a(x,y,y) \ K(z \ x,z) = R(x,y,y) \ ((z \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,15230,a(flip),b,16011,a),flip(a)].">
      <j1 rule="hyper" parents="64 15230 16011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16050">
    <literal><![CDATA[
      x * ((y * y) * a(x,z,z)) = R(x * (y * y),z,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,16028,a(flip),b,2124,a)].">
      <j1 rule="hyper" parents="145 16028 2124"/>
    </justification>
  </clause>

  <clause id="16051">
    <literal><![CDATA[
      (x * y) * a(y,z,(z \ 1) \ x) = x * R(y,z \ 1,(z \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,11980,a(flip),b,16044,a)].">
      <j1 rule="hyper" parents="145 11980 16044"/>
    </justification>
  </clause>

  <clause id="16052">
    <literal><![CDATA[
      K(R(x * (y * y),z,z),((y * y) * a(x,z,z)) \ 1) * ((x * ((y * y) * a(x,z,z))) \ x) = x / (x * ((y * y) * a(x,z,z)))
    ]]></literal>
    <justification jstring="[para(16050(a,1),6739(a,1,1,1))].">
      <j1 rule="para" parents="16050 6739"/>
    </justification>
  </clause>

  <clause id="16053">
    <literal><![CDATA[
      a(L(x,y,z),L(x,u,w),L(x,u,w)) = L(x,y,z) \ L(R(x,L(x,u,w),x),y,z)
    ]]></literal>
    <justification jstring="[para(11559(a,1),15989(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11559 15989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16054">
    <literal><![CDATA[
      ((x * y) * y) \ ((x * (y * y)) * z) = R(x,y,y) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11830,a(flip),b,15994,a)].">
      <j1 rule="hyper" parents="64 11830 15994"/>
    </justification>
  </clause>

  <clause id="16055">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,y * z) = L(a(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(2067(a,1),16032(a,1,1))].">
      <j1 rule="para" parents="2067 16032"/>
    </justification>
  </clause>

  <clause id="16056">
    <literal><![CDATA[
      L(a(x,y,z),x,x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16031,a,b,16055,a),flip(a)].">
      <j1 rule="hyper" parents="64 16031 16055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16057">
    <literal><![CDATA[
      x \ R(x,y,(y \ 1) \ x) = a(x,y,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(42,a,2191,a,b,16055,a),flip(a)].">
      <j1 rule="hyper" parents="42 2191 16055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16058">
    <literal><![CDATA[
      (x * x) * a(x,y,z) = x * (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,16056,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 16056 18"/>
    </justification>
  </clause>

  <clause id="16059">
    <literal><![CDATA[
      (x \ 1) * a(x,y,z) = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,16056,a(flip),b,1139,a),flip(a)].">
      <j1 rule="hyper" parents="139 16056 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16060">
    <literal><![CDATA[
      (1 / x) \ a(x,y,z) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,16056,a(flip),b,559,a)].">
      <j1 rule="hyper" parents="139 16056 559"/>
    </justification>
  </clause>

  <clause id="16061">
    <literal><![CDATA[
      (x \ 1) * a(x \ 1,y,z) = x \ a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,16056,a(flip),b,568,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 16056 568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16062">
    <literal><![CDATA[
      L(L(x,a(y,z,u),y),y * a(y,z,u),y) = a(y,z,u) \ L(a(y,z,u) * x,y,y)
    ]]></literal>
    <justification jstring="[para(16056(a,1),2290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16056 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16063">
    <literal><![CDATA[
      x * (x * (R(x,y,z) \ a(x,u,w))) = R(1 / x,y,z) \ a(x,u,w)
    ]]></literal>
    <justification jstring="[para(16056(a,1),2636(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16056 2636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16064">
    <literal><![CDATA[
      L(a(x,y,z) / (x \ 1),x,x) = a(x,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(16056(a,1),11268(a,2,1))].">
      <j1 rule="para" parents="16056 11268"/>
    </justification>
  </clause>

  <clause id="16065">
    <literal><![CDATA[
      (x \ 1) \ (x \ a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,16059,a)].">
      <j1 rule="hyper" parents="149 16059"/>
    </justification>
  </clause>

  <clause id="16066">
    <literal><![CDATA[
      L(x,y \ a(y,z,u),w) = L(x,y * a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(16059(a,1),11864(a,1,2))].">
      <j1 rule="para" parents="16059 11864"/>
    </justification>
  </clause>

  <clause id="16067">
    <literal><![CDATA[
      a(x,y,(y \ 1) \ x) * x = R(x,y,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(144,a,16057,a(flip),b,2071,a)].">
      <j1 rule="hyper" parents="144 16057 2071"/>
    </justification>
  </clause>

  <clause id="16068">
    <literal><![CDATA[
      x \ a(x \ 1,y,z) != u * a(x \ 1,y,z)
    ]]></literal>
    <literal><![CDATA[
      x \ 1 = u
    ]]></literal>
    <justification jstring="[para(16061(a,1),45(a,1))].">
      <j1 rule="para" parents="16061 45"/>
    </justification>
  </clause>

  <clause id="16069">
    <literal><![CDATA[
      L(x \ ((x / y) * R(y,z,u)),y,z * u) = L(a(y,z,u),y,y \ x)
    ]]></literal>
    <justification jstring="[para(11070(a,1),16033(a,1,1))].">
      <j1 rule="para" parents="11070 16033"/>
    </justification>
  </clause>

  <clause id="16070">
    <literal><![CDATA[
      R(x,y,y) \ (x * y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3203,a,b,16054,a),flip(a)].">
      <j1 rule="hyper" parents="64 3203 16054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16071">
    <literal><![CDATA[
      (x * y) / L(y,y,x) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(225,a,3203,a,b,16054,a(flip))].">
      <j1 rule="hyper" parents="225 3203 16054"/>
    </justification>
  </clause>

  <clause id="16072">
    <literal><![CDATA[
      R(x,y,y) * L(y,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(145,a,3203,a,b,16054,a(flip))].">
      <j1 rule="hyper" parents="145 3203 16054"/>
    </justification>
  </clause>

  <clause id="16073">
    <literal><![CDATA[
      ((x * y) * y) \ (x * ((y * y) * z)) = R(x,y,y) \ (x * z)
    ]]></literal>
    <justification jstring="[para(34(a,1),16054(a,1,2))].">
      <j1 rule="para" parents="34 16054"/>
    </justification>
  </clause>

  <clause id="16074">
    <literal><![CDATA[
      x * (R(x,y,y) \ y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1907,a(flip),b,16070,a)].">
      <j1 rule="hyper" parents="64 1907 16070"/>
    </justification>
  </clause>

  <clause id="16075">
    <literal><![CDATA[
      R(x,y,y) \ y = x \ L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,16070,a(flip),b,1907,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 16070 1907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16076">
    <literal><![CDATA[
      L(x,x,R(y,x,x)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,2850,a,b,16071,a)].">
      <j1 rule="hyper" parents="37 2850 16071"/>
    </justification>
  </clause>

  <clause id="16077">
    <literal><![CDATA[
      L(x,x,a(y,x,x) \ y) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16025,a,b,16076,a)].">
      <j1 rule="hyper" parents="64 16025 16076"/>
    </justification>
  </clause>

  <clause id="16078">
    <literal><![CDATA[
      R(x,y,y) \ (x * ((y * y) \ z)) = ((x * y) * y) \ (x * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),16073(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 16073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16079">
    <literal><![CDATA[
      x * (R(x,y,y) \ ((y * y) \ z)) = ((x * y) * y) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1907,a(flip),b,16078,a)].">
      <j1 rule="hyper" parents="64 1907 16078"/>
    </justification>
  </clause>

  <clause id="16080">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6603,a,15621,a),flip(a)].">
      <j1 rule="hyper" parents="6603 15621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16081">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T((u * z) / y,y / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1035(a,1),16080(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1035 16080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16082">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * K(x,K(y,z)) = a(z,u,K(x,K(w,y)))
    ]]></literal>
    <justification jstring="[para(8126(a,1),15669(a,1,2))].">
      <j1 rule="para" parents="8126 15669"/>
    </justification>
  </clause>

  <clause id="16083">
    <literal><![CDATA[
      a(T(x,y),z,K(u,x * y)) = K(L(x,z,u) * y,x * y)
    ]]></literal>
    <justification jstring="[para(266(a,1),15670(a,1,1)),flip(a)].">
      <j1 rule="para" parents="266 15670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16084">
    <literal><![CDATA[
      K(T(x,y),(z * y) \ u) = K(x,((z \ u) * z) / (y * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,6091,a(flip),b,15702,a),flip(a)].">
      <j1 rule="hyper" parents="373 6091 15702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16085">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,((y \ u) * y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(8019,a,16084,a)].">
      <j1 rule="hyper" parents="8019 16084"/>
    </justification>
  </clause>

  <clause id="16086">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,T(u,y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,13457,a(flip),b,16085,a),flip(a)].">
      <j1 rule="hyper" parents="373 13457 16085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16087">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ u) / (T(u * z,z \ 1) * ((z * u) \ u))) = K(x,T(T(u,z) \ y,T(u * z,z \ 1)))
    ]]></literal>
    <justification jstring="[para(6985(a,1),16086(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6985 16086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16088">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u) / (z \ K(u,u \ (z \ 1)))) = K(x,T((((z \ 1) / u) * u) \ y,u))
    ]]></literal>
    <justification jstring="[para(10166(a,2),16086(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10166 16086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16089">
    <literal><![CDATA[
      K(x,T(T(y,z),T(u,z)) / w) = K(x,(T(y,u) * K(z,y)) / w)
    ]]></literal>
    <justification jstring="[para(23(a,1),15843(a,1,2,1))].">
      <j1 rule="para" parents="23 15843"/>
    </justification>
  </clause>

  <clause id="16090">
    <literal><![CDATA[
      T(x,(y / z) * ((y / z) * u)) = T(x,(z \ y) * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(15895,a,15850,a),flip(a)].">
      <j1 rule="hyper" parents="15895 15850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16091">
    <literal><![CDATA[
      K(x,L(y * T(z \ u,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * (u / z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(15884(a,2),12117(a,1))].">
      <j1 rule="para" parents="15884 12117"/>
    </justification>
  </clause>

  <clause id="16092">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(z,y) \ u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(15901(a,2),12117(a,1))].">
      <j1 rule="para" parents="15901 12117"/>
    </justification>
  </clause>

  <clause id="16093">
    <literal><![CDATA[
      T(x,T(y,z) \ T(u,T(y,z))) = T(x,u / (z * (y / z)))
    ]]></literal>
    <justification jstring="[para(11107(a,1),15909(a,1,2,2))].">
      <j1 rule="para" parents="11107 15909"/>
    </justification>
  </clause>

  <clause id="16094">
    <literal><![CDATA[
      T(x,y / (z * (u / z))) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13419,a(flip),b,16093,a),flip(a)].">
      <j1 rule="hyper" parents="64 13419 16093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16095">
    <literal><![CDATA[
      T(x,(T(y,z) * z) / u) = T(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(8789,a,15950,a),flip(a)].">
      <j1 rule="hyper" parents="8789 15950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16096">
    <literal><![CDATA[
      T(x,(T(y,z) * z) / y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(11(a,1),16095(a,2,2))].">
      <j1 rule="para" parents="11 16095"/>
    </justification>
  </clause>

  <clause id="16097">
    <literal><![CDATA[
      R((a(x,y,y) * a(x,y,y)) \ x,y,y) = (a(x,y,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,2051,a,b,16017,a)].">
      <j1 rule="hyper" parents="64 2051 16017"/>
    </justification>
  </clause>

  <clause id="16098">
    <literal><![CDATA[
      K(K(x,L(y,z,u)) * K(y,x),w) = a(y,z,K(w,K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12364,a(flip),b,16082,a)].">
      <j1 rule="hyper" parents="64 12364 16082"/>
    </justification>
  </clause>

  <clause id="16099">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(10420(a,1),16098(a,1,1))].">
      <j1 rule="para" parents="10420 16098"/>
    </justification>
  </clause>

  <clause id="16100">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(u,x)))
    ]]></literal>
    <justification jstring="[para(8126(a,1),16099(a,2,3))].">
      <j1 rule="para" parents="8126 16099"/>
    </justification>
  </clause>

  <clause id="16105">
    <literal><![CDATA[
      (x * (y * z)) / (L(x,z,y) * (y * z)) = a(y,z,T(x,y * z))
    ]]></literal>
    <justification jstring="[para(793(a,1),15466(a,1,2))].">
      <j1 rule="para" parents="793 15466"/>
    </justification>
  </clause>

  <clause id="16106">
    <literal><![CDATA[
      a(x,y,T(z,x * y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(15716,a,16105,a),flip(a)].">
      <j1 rule="hyper" parents="15716 16105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16107">
    <literal><![CDATA[
      a(x,y,T(z,x * y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(16105(a,1),15716(a,1))].">
      <j1 rule="para" parents="16105 15716"/>
    </justification>
  </clause>

  <clause id="16109">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) * a(z,y,x) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,16106,a(flip),b,2603,a)].">
      <j1 rule="hyper" parents="145 16106 2603"/>
    </justification>
  </clause>

  <clause id="16110">
    <literal><![CDATA[
      (x * y) / a(y / z,z,x) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[para(16106(a,1),11731(a,1,2))].">
      <j1 rule="para" parents="16106 11731"/>
    </justification>
  </clause>

  <clause id="16111">
    <literal><![CDATA[
      K(x,y) * ((y / z) * (z * x)) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,14889,a,b,16110,a)].">
      <j1 rule="hyper" parents="64 14889 16110"/>
    </justification>
  </clause>

  <clause id="16112">
    <literal><![CDATA[
      ((x / y) * (y * z)) \ K(x,z) = (L(z,y,y \ x) * x) \ 1
    ]]></literal>
    <justification jstring="[para(16111(a,1),14450(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16111 14450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16113">
    <literal><![CDATA[
      ((x * x) * (x \ y)) / (x * y) = (x \ y) * (((1 / x) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(569(a,1),15501(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="569 15501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16114">
    <literal><![CDATA[
      a(x,x * (x \ y),x) \ ((x \ y) * x) = y * K(x \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(13700(a,1),15503(a,1,1))].">
      <j1 rule="para" parents="13700 15503"/>
    </justification>
  </clause>

  <clause id="16115">
    <literal><![CDATA[
      L(K(x,y),z,u) * (u * (K(y,x) * z)) = z * T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(7329,a,15597,a)].">
      <j1 rule="hyper" parents="7329 15597"/>
    </justification>
  </clause>

  <clause id="16116">
    <literal><![CDATA[
      K(x,L(y / z,u,y \ u)) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[para(10(a,1),15623(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 15623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16118">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) / u,z \ y,T(y,z \ 1) \ (z \ y))) = K(x,(z \ y) / (u * T(y \ (z \ y),y)))
    ]]></literal>
    <justification jstring="[para(4720(a,2),16116(a,2,2,2,2))].">
      <j1 rule="para" parents="4720 16116"/>
    </justification>
  </clause>

  <clause id="16119">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y / z,z))) = K(x,K(w,y / ((1 / u) * z)))
    ]]></literal>
    <justification jstring="[para(14683(a,1),15632(a,1,2))].">
      <j1 rule="para" parents="14683 15632"/>
    </justification>
  </clause>

  <clause id="16120">
    <literal><![CDATA[
      K(x,(y * z) \ R(y,u,u \ 1)) = K(x,z \ a(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(985(a,1),15967(a,1,2))].">
      <j1 rule="para" parents="985 15967"/>
    </justification>
  </clause>

  <clause id="16121">
    <literal><![CDATA[
      L(L(T(x,y) \ R(y \ (x * y),z,u),(x * y) \ y,z * u),x,y) = a((x * y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10983,a,b,16037,a)].">
      <j1 rule="hyper" parents="64 10983 16037"/>
    </justification>
  </clause>

  <clause id="16122">
    <literal><![CDATA[
      a(x,y,x) \ ((x \ y) * x) = y * K(x \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(10(a,1),16114(a,1,1,2))].">
      <j1 rule="para" parents="10 16114"/>
    </justification>
  </clause>

  <clause id="16123">
    <literal><![CDATA[
      x * K(y \ (y \ x),y) = (y \ x) * L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11031,a(flip),b,16122,a),flip(a)].">
      <j1 rule="hyper" parents="64 11031 16122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16124">
    <literal><![CDATA[
      T((x * (K(y,z) * u)) * L(K(z,y),u,x),K(y,L(z,u,x))) = u * T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12214,a,b,16115,a)].">
      <j1 rule="hyper" parents="64 12214 16115"/>
    </justification>
  </clause>

  <clause id="16125">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(35,a,8011,a,b,14689,a),flip(a)].">
      <j1 rule="hyper" parents="35 8011 14689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16126">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(16125(a,2),11217(a,1))].">
      <j1 rule="para" parents="16125 11217"/>
    </justification>
  </clause>

  <clause id="16127">
    <literal><![CDATA[
      (x \ (1 / x)) * K((x \ (1 / x)) * (x * y),x * y) = (x * y) \ ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),14708(a,2,2,2))].">
      <j1 rule="para" parents="9 14708"/>
    </justification>
  </clause>

  <clause id="16128">
    <literal><![CDATA[
      (x \ (1 / x)) * K((x \ (1 / x)) * ((x \ 1) \ y),(x \ 1) \ y) = ((x \ 1) \ y) \ ((1 / (1 / x)) \ y)
    ]]></literal>
    <justification jstring="[para(7033(a,1),14708(a,2,2))].">
      <j1 rule="para" parents="7033 14708"/>
    </justification>
  </clause>

  <clause id="16129">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * (y * u))) = T(x,(((z / y) \ 1) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16090,a(flip),b,14794,a)].">
      <j1 rule="hyper" parents="64 16090 14794"/>
    </justification>
  </clause>

  <clause id="16130">
    <literal><![CDATA[
      a((x \ y) * (K(y,z) * x),u,w) = a(T(T(y,x),z),u,w)
    ]]></literal>
    <justification jstring="[para(8484(a,1),14829(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8484 14829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16132">
    <literal><![CDATA[
      a(T((x \ y) * x,z),u,w) = a(T(T(y,x),z),u,w)
    ]]></literal>
    <justification jstring="[para(14704(a,1),16130(a,1,1))].">
      <j1 rule="para" parents="14704 16130"/>
    </justification>
  </clause>

  <clause id="16133">
    <literal><![CDATA[
      a(x,y,(z \ u) * (K(u,w) * z)) = a(x,y,T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(8484(a,1),14830(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8484 14830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16135">
    <literal><![CDATA[
      a(x,y,T((z \ u) * z,w)) = a(x,y,T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(14704(a,1),16133(a,1,3))].">
      <j1 rule="para" parents="14704 16133"/>
    </justification>
  </clause>

  <clause id="16136">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(115(a,1),14909(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="115 14909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16137">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4619(a,1),16136(a,2,2))].">
      <j1 rule="para" parents="4619 16136"/>
    </justification>
  </clause>

  <clause id="16138">
    <literal><![CDATA[
      (((x / (x * y)) * y) \ 1) \ K(y \ 1,x * y) = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[para(14928(a,1),9468(a,1,1))].">
      <j1 rule="para" parents="14928 9468"/>
    </justification>
  </clause>

  <clause id="16139">
    <literal><![CDATA[
      ((x \ T(y,z)) * K(z,T(y,u))) * K(z,y) = (x \ y) * T(K(z,y),u)
    ]]></literal>
    <justification jstring="[para(7867(a,2),15029(a,1,1,2))].">
      <j1 rule="para" parents="7867 15029"/>
    </justification>
  </clause>

  <clause id="16140">
    <literal><![CDATA[
      K(x,x \ y) * K(x * (y / x),z) = y \ (x * (T(y,z) / x))
    ]]></literal>
    <justification jstring="[para(5961(a,1),15047(a,1,1))].">
      <j1 rule="para" parents="5961 15047"/>
    </justification>
  </clause>

  <clause id="16141">
    <literal><![CDATA[
      K(x,x \ y) * K(y,T(z,x)) = y \ (x * (T(y,z) / x))
    ]]></literal>
    <justification jstring="[para(11193(a,1),16140(a,1,2))].">
      <j1 rule="para" parents="11193 16140"/>
    </justification>
  </clause>

  <clause id="16142">
    <literal><![CDATA[
      K(x \ y,x) \ K(y,T(z,x)) = y \ (x * (T(y,z) / x))
    ]]></literal>
    <justification jstring="[hyper(6206,a,16141,a)].">
      <j1 rule="hyper" parents="6206 16141"/>
    </justification>
  </clause>

  <clause id="16143">
    <literal><![CDATA[
      T(x,T((y / z) \ K(y,u),w)) = T(x,T((z / y) * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(14450(a,1),15089(a,1,2,1))].">
      <j1 rule="para" parents="14450 15089"/>
    </justification>
  </clause>

  <clause id="16144">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) * (1 \ T(1 / (y / z),y))) = K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(7655(a,1),15150(a,1,2,1,1))].">
      <j1 rule="para" parents="7655 15150"/>
    </justification>
  </clause>

  <clause id="16145">
    <literal><![CDATA[
      K(x,L(((y * (z * y)) / y) \ y,u,w) * (a(y,z,y) \ z)) = K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w))
    ]]></literal>
    <justification jstring="[para(11044(a,2),15150(a,1,2,2))].">
      <j1 rule="para" parents="11044 15150"/>
    </justification>
  </clause>

  <clause id="16146">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,K(z \ 1,x)) = L(T(x,a(z \ 1,w,u)),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,25,a,b,15384,a),flip(a)].">
      <j1 rule="hyper" parents="373 25 15384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16147">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u / w,y)) = K(x,L(y,z,u / (y * w)))
    ]]></literal>
    <justification jstring="[para(12233(a,1),15431(a,1,2))].">
      <j1 rule="para" parents="12233 15431"/>
    </justification>
  </clause>

  <clause id="16148">
    <literal><![CDATA[
      ((x * R(x,y,z)) * u) / (x * (R(x,y,z) * u)) = a(R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(1897(a,1),15474(a,1,2))].">
      <j1 rule="para" parents="1897 15474"/>
    </justification>
  </clause>

  <clause id="16149">
    <literal><![CDATA[
      ((x * y) * L(y,z,u)) / (x * (y * L(y,z,u))) = a(x,L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(3184(a,1),15475(a,1,1))].">
      <j1 rule="para" parents="3184 15475"/>
    </justification>
  </clause>

  <clause id="16150">
    <literal><![CDATA[
      K(x * (y \ 1),y * (x \ z)) = K(x / y,(x * (y \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(14641,a,15506,a)].">
      <j1 rule="hyper" parents="14641 15506"/>
    </justification>
  </clause>

  <clause id="16151">
    <literal><![CDATA[
      K(x / y,(x * (y \ 1)) \ z) = K(x / y,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(14676,a,16150,a),flip(a)].">
      <j1 rule="hyper" parents="14676 16150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16152">
    <literal><![CDATA[
      K(x / y,(x * (y \ 1)) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,(x \ z) * y) = u
    ]]></literal>
    <justification jstring="[para(16151(a,2),11136(a,1))].">
      <j1 rule="para" parents="16151 11136"/>
    </justification>
  </clause>

  <clause id="16153">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) = K(y \ x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(16152,a,14012,a),flip(a)].">
      <j1 rule="hyper" parents="16152 14012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16154">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,(x \ z) * y) = u
    ]]></literal>
    <justification jstring="[para(14012(a,1),16152(a,1))].">
      <j1 rule="para" parents="14012 16152"/>
    </justification>
  </clause>

  <clause id="16155">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,R(y / x,u,w) \ z)) = K(x \ y,R(y / x,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(16153(a,1),14015(a,1,1))].">
      <j1 rule="para" parents="16153 14015"/>
    </justification>
  </clause>

  <clause id="16156">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15428,a(flip),b,15508,a),flip(a)].">
      <j1 rule="hyper" parents="64 15428 15508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16157">
    <literal><![CDATA[
      K(x,L(L(y,z,u \ 1),z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(30(a,1),16156(a,1,2))].">
      <j1 rule="para" parents="30 16156"/>
    </justification>
  </clause>

  <clause id="16158">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(346(a,1),16156(a,1,2,1))].">
      <j1 rule="para" parents="346 16156"/>
    </justification>
  </clause>

  <clause id="16159">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1631(a,1),16156(a,1,2))].">
      <j1 rule="para" parents="1631 16156"/>
    </justification>
  </clause>

  <clause id="16160">
    <literal><![CDATA[
      T(x,L(L(y,z,u),z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,16159,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 16159 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16161">
    <literal><![CDATA[
      T(x,L((y * z) \ u,z,y)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(346(a,1),16160(a,1,2,1))].">
      <j1 rule="para" parents="346 16160"/>
    </justification>
  </clause>

  <clause id="16162">
    <literal><![CDATA[
      T(x,L((y * z) \ (z * u),y,z)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(10979(a,1),16160(a,1,2,1))].">
      <j1 rule="para" parents="10979 16160"/>
    </justification>
  </clause>

  <clause id="16163">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ 1))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(16157(a,1),12078(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16157 12078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16164">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(16157(a,1),15549(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16157 15549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16165">
    <literal><![CDATA[
      (K(x,L(y,z,u \ 1)) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(16157(a,1),15578(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16157 15578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16166">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z / u) = (K(x,y) * z) / u
    ]]></literal>
    <justification jstring="[para(16157(a,1),15673(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="16157 15673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16167">
    <literal><![CDATA[
      K(x,L(T(y,z * u),u,z \ 1)) = K(x,u \ (z \ (y * (z * u))))
    ]]></literal>
    <justification jstring="[para(22(a,2),16158(a,1,2,1))].">
      <j1 rule="para" parents="22 16158"/>
    </justification>
  </clause>

  <clause id="16168">
    <literal><![CDATA[
      K(x,L(a(y,y \ z,u),(y \ z) * u,y \ 1)) = K(x,((y \ z) * u) \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[para(90(a,1),16158(a,1,2,1))].">
      <j1 rule="para" parents="90 16158"/>
    </justification>
  </clause>

  <clause id="16169">
    <literal><![CDATA[
      x * K(y,L(T(z,u * x),x,u \ 1)) = u \ (K(y,z) * (u * x))
    ]]></literal>
    <justification jstring="[hyper(139,a,7879,a(flip),b,16163,a),flip(a)].">
      <j1 rule="hyper" parents="139 7879 16163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16171">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ u))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(15512(a,1),16163(a,1,2,2))].">
      <j1 rule="para" parents="15512 16163"/>
    </justification>
  </clause>

  <clause id="16172">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(35,a,12158,a(flip),b,16164,a),flip(a)].">
      <j1 rule="hyper" parents="35 12158 16164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16173">
    <literal><![CDATA[
      (K(x,L(y,z * u,(z \ K(u,z)) \ 1)) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(9340(a,1),16165(a,2,2))].">
      <j1 rule="para" parents="9340 16165"/>
    </justification>
  </clause>

  <clause id="16174">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,(K(x,y) / x) \ u))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14922(a,1),16171(a,2,1))].">
      <j1 rule="para" parents="14922 16171"/>
    </justification>
  </clause>

  <clause id="16175">
    <literal><![CDATA[
      x * K(y,x \ (z \ (u * (z * x)))) = z \ (K(y,u) * (z * x))
    ]]></literal>
    <justification jstring="[para(16167(a,1),16169(a,1,2))].">
      <j1 rule="para" parents="16167 16169"/>
    </justification>
  </clause>

  <clause id="16176">
    <literal><![CDATA[
      x \ (K(y,R(z,x,u)) * (x * u)) = u * K(y,u \ (x \ ((z * x) * u)))
    ]]></literal>
    <justification jstring="[para(111(a,1),16175(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="111 16175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16177">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,v5) \ 1)) = K(x,L(y,z,a(v5,w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15448,a(flip),b,15509,a),flip(a)].">
      <j1 rule="hyper" parents="64 15448 15509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16178">
    <literal><![CDATA[
      K(x,L(y,z,a(u \ 1,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15708,a,16177,a),flip(a)].">
      <j1 rule="hyper" parents="15708 16177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16179">
    <literal><![CDATA[
      K(x,(a(y \ 1,y,z) \ u) \ w) = K(x,u \ (a(y \ 1,y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15520,a(flip),b,16178,a),flip(a)].">
      <j1 rule="hyper" parents="64 15520 16178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16180">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,16158,a(flip),b,15641,a),flip(a)].">
      <j1 rule="hyper" parents="373 16158 15641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16181">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * w) = K(x,(T(y,z) * (u / y)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15937,a(flip),b,15825,a),flip(a)].">
      <j1 rule="hyper" parents="64 15937 15825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16182">
    <literal><![CDATA[
      T(x,(y * y) * ((z / (z / u)) \ w)) = T(x,y * (y * (T(u,z) \ w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,15740,a(flip),b,15835,a),flip(a)].">
      <j1 rule="hyper" parents="373 15740 15835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16183">
    <literal><![CDATA[
      (T(x \ y,x) \ z) * T(x \ y,x) = ((y / x) \ z) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,354,a(flip),b,15931,a),flip(a)].">
      <j1 rule="hyper" parents="373 354 15931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16184">
    <literal><![CDATA[
      (T((x * (y / z)) \ (y / z),x * (y / z)) \ u) * T((x * (y / z)) \ (y / z),x * (y / z)) = (R(1 / x,x,z \ y) \ u) * ((y / z) / (x * (y / z)))
    ]]></literal>
    <justification jstring="[para(15085(a,2),16183(a,2,1,1))].">
      <j1 rule="para" parents="15085 16183"/>
    </justification>
  </clause>

  <clause id="16185">
    <literal><![CDATA[
      x \ R(x,y * z,(y \ 1) * z) = a(x,y * z,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11984,a(flip),b,15988,a),flip(a)].">
      <j1 rule="hyper" parents="64 11984 15988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16186">
    <literal><![CDATA[
      (x * y) * a(y,z,(z \ 1) \ x) = x * R(y,z,(z \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(2975(a,1),16051(a,2,2))].">
      <j1 rule="para" parents="2975 16051"/>
    </justification>
  </clause>

  <clause id="16187">
    <literal><![CDATA[
      T(x,(((y / z) \ 1) \ y) * (z \ u)) = T(x,(z \ y) * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),16129(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 16129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16188">
    <literal><![CDATA[
      (x \ T(y,K(z,u))) * K(z,y) = (x \ y) * T(K(z,y),u)
    ]]></literal>
    <justification jstring="[para(15184(a,1),16139(a,1,1))].">
      <j1 rule="para" parents="15184 16139"/>
    </justification>
  </clause>

  <clause id="16189">
    <literal><![CDATA[
      L(T(x,a(y \ 1,z,u)),w,y) = L(x,w,y) * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(12249(a,1),16146(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12249 16146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16190">
    <literal><![CDATA[
      L(x,y,z) != L(u,y,z) * a(w,v5,K(u,z))
    ]]></literal>
    <literal><![CDATA[
      T(u,a(z \ 1,v5,w)) = x
    ]]></literal>
    <justification jstring="[para(16189(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="16189 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16191">
    <literal><![CDATA[
      a(R(x,y,z),x,u) = a(x,R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15462,a,b,16148,a),flip(a)].">
      <j1 rule="hyper" parents="64 15462 16148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16192">
    <literal><![CDATA[
      a(x,L(y,z,u),y) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15462,a,b,16149,a),flip(a)].">
      <j1 rule="hyper" parents="64 15462 16149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16193">
    <literal><![CDATA[
      a(x,y \ (z \ u),L(y \ (z \ u),y,z)) = a(x,(z * y) \ u,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(346(a,1),16192(a,1,2)),flip(a)].">
      <j1 rule="para" parents="346 16192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16194">
    <literal><![CDATA[
      a(x,y,L(y,y \ z,y \ z)) = a(x,(1 / (z / y)) * z,y)
    ]]></literal>
    <justification jstring="[para(10627(a,1),16192(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10627 16192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16195">
    <literal><![CDATA[
      a(x,R(y,z,y) \ 1,L(R(y,z,y) \ 1,y,z)) = a(x,T(y * z,y) \ z,R(y,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(14173(a,1),16192(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14173 16192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16196">
    <literal><![CDATA[
      a(x,y,L(y,y \ z,y \ z)) = a(x,(z / y) * z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11967,a(flip),b,16194,a),flip(a)].">
      <j1 rule="hyper" parents="373 11967 16194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16197">
    <literal><![CDATA[
      T(x,y * (y * ((z / (z / u)) \ w))) = T(x,y * (y * (T(u,z) \ w)))
    ]]></literal>
    <justification jstring="[hyper(15896,a,16182,a)].">
      <j1 rule="hyper" parents="15896 16182"/>
    </justification>
  </clause>

  <clause id="16198">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * K(z,T(u,y)),y) = L(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10260,a(flip),b,14750,a),flip(a)].">
      <j1 rule="hyper" parents="373 10260 14750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16199">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(12059(a,1),14753(a,1,1))].">
      <j1 rule="para" parents="12059 14753"/>
    </justification>
  </clause>

  <clause id="16200">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),T(x,z)) = K(y * K((x \ 1) \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(14962,a,11649,a),flip(a)].">
      <j1 rule="hyper" parents="14962 11649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16201">
    <literal><![CDATA[
      K(x * K((y \ 1) \ x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(14961,a,16200,a),flip(a)].">
      <j1 rule="hyper" parents="14961 16200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16203">
    <literal><![CDATA[
      K(x * K(y * x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(14441(a,1),16201(a,1,1,2))].">
      <j1 rule="para" parents="14441 16201"/>
    </justification>
  </clause>

  <clause id="16204">
    <literal><![CDATA[
      T(x,x * (y * K(x * y,z))) * K(y,T(x,z)) = L(x,y * K(x * y,z),x)
    ]]></literal>
    <justification jstring="[hyper(145,a,16203,a(flip),b,6341,a(flip))].">
      <j1 rule="hyper" parents="145 16203 6341"/>
    </justification>
  </clause>

  <clause id="16205">
    <literal><![CDATA[
      a(L(x,x \ y,y),z,u) = a(((w * w) / y) * (y / x),z,u)
    ]]></literal>
    <justification jstring="[para(2183(a,1),15125(a,1,1))].">
      <j1 rule="para" parents="2183 15125"/>
    </justification>
  </clause>

  <clause id="16207">
    <literal><![CDATA[
      x \ L(x * K(x * y,y),y,y) = T(x,y \ 1) \ R(x,y,y)
    ]]></literal>
    <justification jstring="[para(1405(a,1),15144(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1405 15144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16208">
    <literal><![CDATA[
      x \ L(x * K(x * y,y),y,y) = K(y \ 1,x) * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,15991,a(flip),b,16207,a),flip(a)].">
      <j1 rule="hyper" parents="373 15991 16207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16209">
    <literal><![CDATA[
      K(x \ 1,y) * a(y,x,x) = y \ (((1 / x) * y) * x)
    ]]></literal>
    <justification jstring="[para(15142(a,1),16208(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15142 16208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16210">
    <literal><![CDATA[
      L((x \ 1) \ y,x,y \ z) \ z = T((z / y) * (x \ 1),x * y)
    ]]></literal>
    <justification jstring="[hyper(14642,a,15147,a),flip(a)].">
      <j1 rule="hyper" parents="14642 15147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16211">
    <literal><![CDATA[
      T((x / (y \ 1)) * (L(y,z,u) \ 1),L(y,z,u) * (y \ 1)) = L(y \ L(y,z,u),L(y,z,u),(y \ 1) \ x) \ x
    ]]></literal>
    <justification jstring="[para(4233(a,1),16210(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4233 16210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16212">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(x,K(z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z,K(w,L(x,y,u))) = v5
    ]]></literal>
    <justification jstring="[para(8108(a,1),15459(a,1,1,3))].">
      <j1 rule="para" parents="8108 15459"/>
    </justification>
  </clause>

  <clause id="16213">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((x * (y \ z)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6756,a(flip),b,15619,a),flip(a)].">
      <j1 rule="hyper" parents="373 6756 15619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16214">
    <literal><![CDATA[
      K((x / y) \ 1,T(L(z,y,y \ u),u)) = K((x * (y \ u)) \ u,z)
    ]]></literal>
    <justification jstring="[hyper(8018,a,16213,a)].">
      <j1 rule="hyper" parents="8018 16213"/>
    </justification>
  </clause>

  <clause id="16215">
    <literal><![CDATA[
      K((x / y) \ 1,L(T(z,u),y,y \ u)) = K((x * (y \ u)) \ u,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),16214(a,1,2))].">
      <j1 rule="para" parents="25 16214"/>
    </justification>
  </clause>

  <clause id="16216">
    <literal><![CDATA[
      a(x,y,K(z,(u / y) \ z)) \ K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(9741(a,1),15624(a,1,1,3))].">
      <j1 rule="para" parents="9741 15624"/>
    </justification>
  </clause>

  <clause id="16217">
    <literal><![CDATA[
      (x * y) * K(z,(x * y) \ (u * y)) = (K(z,u / x) * x) * y
    ]]></literal>
    <justification jstring="[hyper(15579,a,15630,a),flip(a)].">
      <j1 rule="hyper" parents="15579 15630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16218">
    <literal><![CDATA[
      (x * y) * K(z,(x * y) \ (u * y)) = (x * K(z,x \ u)) * y
    ]]></literal>
    <justification jstring="[para(7956(a,1),16217(a,2,1))].">
      <j1 rule="para" parents="7956 16217"/>
    </justification>
  </clause>

  <clause id="16219">
    <literal><![CDATA[
      R(T(x * K(y,x),z),y,u) \ ((y * x) * u) = (y * K(z,y \ (y * x))) * u
    ]]></literal>
    <justification jstring="[hyper(10696,a,16218,a)].">
      <j1 rule="hyper" parents="10696 16218"/>
    </justification>
  </clause>

  <clause id="16220">
    <literal><![CDATA[
      x * K(y,x \ (z \ ((u * z) * x))) = z \ ((K(y,u) * z) * x)
    ]]></literal>
    <justification jstring="[para(14064(a,1),16176(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14064 16176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16221">
    <literal><![CDATA[
      T(x,K(y,x \ (z \ ((u * z) * x)))) \ (z \ ((K(y,u) * z) * x)) = T(K(y,x \ (z \ ((u * z) * x))),x)
    ]]></literal>
    <justification jstring="[hyper(139,a,16220,a(flip),b,4650,a)].">
      <j1 rule="hyper" parents="139 16220 4650"/>
    </justification>
  </clause>

  <clause id="16222">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(12071(a,1),16199(a,1,1))].">
      <j1 rule="para" parents="12071 16199"/>
    </justification>
  </clause>

  <clause id="16223">
    <literal><![CDATA[
      a(x,y,K(z,u / y)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(15323(a,1),16216(a,1,1))].">
      <j1 rule="para" parents="15323 16216"/>
    </justification>
  </clause>

  <clause id="16224">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) * z) = K(x,z * L(y / (z * y),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14463,a(flip),b,14468,a)].">
      <j1 rule="hyper" parents="64 14463 14468"/>
    </justification>
  </clause>

  <clause id="16225">
    <literal><![CDATA[
      ((1 / (x / y)) * x) * K(z * ((1 / z) * x),(y \ x) \ 1) = x * (1 / (x / y))
    ]]></literal>
    <justification jstring="[para(6700(a,2),14614(a,1,2))].">
      <j1 rule="para" parents="6700 14614"/>
    </justification>
  </clause>

  <clause id="16226">
    <literal><![CDATA[
      (x * ((a(y,y,x) \ 1) * z)) / L(T(x,z),y,y) = L(z,a(y,y,x) \ 1,x)
    ]]></literal>
    <justification jstring="[para(25(a,2),14747(a,1,2))].">
      <j1 rule="para" parents="25 14747"/>
    </justification>
  </clause>

  <clause id="16227">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) * (y * z)) / L(T(y,z),x,x) = L(z,y,a(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(25(a,2),14748(a,1,2))].">
      <j1 rule="para" parents="25 14748"/>
    </justification>
  </clause>

  <clause id="16228">
    <literal><![CDATA[
      (x \ y) / T(y,x \ (x \ 1)) = ((x * y) / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(4469(a,1),14818(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4469 14818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16229">
    <literal><![CDATA[
      (x \ y) / T(y,x \ (x \ 1)) = y \ (x \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,15187,a(flip),b,16228,a),flip(a)].">
      <j1 rule="hyper" parents="373 15187 16228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16230">
    <literal><![CDATA[
      R(x,y,z \ T(u * K(w,v5),w)) = R(x,y,z \ ((u \ w) \ T(w,v5)))
    ]]></literal>
    <justification jstring="[para(7852(a,1),14838(a,1,3,2))].">
      <j1 rule="para" parents="7852 14838"/>
    </justification>
  </clause>

  <clause id="16231">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ K(y,T(z,x))) \ w) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(7867(a,2),14908(a,1,2,1,2))].">
      <j1 rule="para" parents="7867 14908"/>
    </justification>
  </clause>

  <clause id="16232">
    <literal><![CDATA[
      K(x,L(T(1 / (1 / y),z) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(14925(a,2),14953(a,1))].">
      <j1 rule="para" parents="14925 14953"/>
    </justification>
  </clause>

  <clause id="16233">
    <literal><![CDATA[
      T(K(x,y) / x,(K(x,y) / x) \ y) = T(K(x,y) / x,T(y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,14549,a(flip),b,15078,a),flip(a)].">
      <j1 rule="hyper" parents="373 14549 15078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16234">
    <literal><![CDATA[
      T(K(x,y) / x,(K(x,y) / x) \ y) = T(K(x,y) / x,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11143,a(flip),b,16233,a),flip(a)].">
      <j1 rule="hyper" parents="373 11143 16233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16235">
    <literal><![CDATA[
      (x \ y) * K(x * ((x \ y) \ y),x \ y) = (x \ y) * K(y * x,x \ y)
    ]]></literal>
    <justification jstring="[para(371(a,1),15158(a,1,2,1))].">
      <j1 rule="para" parents="371 15158"/>
    </justification>
  </clause>

  <clause id="16236">
    <literal><![CDATA[
      K(x,L(y,z,(u * T(x,w)) \ v5)) = K(x,y) * a(u \ v5,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(15325(a,1),15440(a,2,2))].">
      <j1 rule="para" parents="15325 15440"/>
    </justification>
  </clause>

  <clause id="16237">
    <literal><![CDATA[
      K(x,L(y,z,(u * T(x,w)) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(16236(a,2),12116(a,1))].">
      <j1 rule="para" parents="16236 12116"/>
    </justification>
  </clause>

  <clause id="16238">
    <literal><![CDATA[
      K(x,L(y,z,(u * x) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(114(a,1),16237(a,1,2,3,1,2))].">
      <j1 rule="para" parents="114 16237"/>
    </justification>
  </clause>

  <clause id="16239">
    <literal><![CDATA[
      K(x,L(y,z,(u * x) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(16238,a,xx),flip(a)].">
      <j1 rule="hyper" parents="16238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16240">
    <literal><![CDATA[
      K(x \ 1,L(y,z,x \ u)) = K(x \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(185(a,1),16239(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="185 16239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16241">
    <literal><![CDATA[
      (L(x,y,y) * z) / ((a(y,y,x) \ 1) * (x * z)) = a(a(y,y,x),x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2653,a(flip),b,15477,a),flip(a)].">
      <j1 rule="hyper" parents="373 2653 15477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16242">
    <literal><![CDATA[
      (L(x,y,y) * z) / (x * ((a(y,y,x) \ 1) * z)) = a(x,x * L(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,11978,a(flip),b,15500,a),flip(a)].">
      <j1 rule="hyper" parents="373 11978 15500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16243">
    <literal><![CDATA[
      T(x,((y / (z \ K(z,y))) / y) \ u) = T(x,(y \ (y / (z \ 1))) \ u)
    ]]></literal>
    <justification jstring="[para(117(a,1),15798(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="117 15798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16244">
    <literal><![CDATA[
      K(x,T((y * z) \ u,y * z) * T(z,y)) = K(x,(u / (z * y)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,15854,a(flip),b,15802,a)].">
      <j1 rule="hyper" parents="64 15854 15802"/>
    </justification>
  </clause>

  <clause id="16245">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z * u)) = K(x,(z * T(T(u,w),w)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15939,a(flip),b,15810,a)].">
      <j1 rule="hyper" parents="64 15939 15810"/>
    </justification>
  </clause>

  <clause id="16246">
    <literal><![CDATA[
      K(x,(y * T(T(z,u),u)) * w) = K(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[hyper(11231,a,16245,a),flip(a)].">
      <j1 rule="hyper" parents="11231 16245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16248">
    <literal><![CDATA[
      T(x,(y * T(T(z,u),u)) * w) = T(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[hyper(143,a,16246,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 16246 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16250">
    <literal><![CDATA[
      T(x,(y * T(z \ u,z)) * w) = T(x,(y * (u / z)) * w)
    ]]></literal>
    <justification jstring="[para(117(a,1),16248(a,1,2,1,2,1))].">
      <j1 rule="para" parents="117 16248"/>
    </justification>
  </clause>

  <clause id="16251">
    <literal><![CDATA[
      T(x,(y * (z * K(u,z))) * w) = T(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(5785(a,1),16248(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5785 16248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16252">
    <literal><![CDATA[
      T(x,(y * R(z \ u,z,z \ u)) * w) = T(x,(y * (T(u,z \ u) / z)) * w)
    ]]></literal>
    <justification jstring="[para(4510(a,1),16250(a,1,2,1,2))].">
      <j1 rule="para" parents="4510 16250"/>
    </justification>
  </clause>

  <clause id="16253">
    <literal><![CDATA[
      K(x,T((y / (y / z)) \ u,w)) = K(x,T(T(z,y) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,8044,a(flip),b,15881,a),flip(a)].">
      <j1 rule="hyper" parents="373 8044 15881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16254">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * T(u,w))) = K(x,y * (((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15947,a(flip),b,15942,a)].">
      <j1 rule="hyper" parents="64 15947 15942"/>
    </justification>
  </clause>

  <clause id="16255">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) * w)) = K(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(15948,a,16254,a),flip(a)].">
      <j1 rule="hyper" parents="15948 16254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16256">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(u,z) * w)) = v5
    ]]></literal>
    <justification jstring="[para(16254(a,1),15948(a,1))].">
      <j1 rule="para" parents="16254 15948"/>
    </justification>
  </clause>

  <clause id="16257">
    <literal><![CDATA[
      T(x,y * (((z * u) / z) * w)) = T(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(143,a,16255,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 16255 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16258">
    <literal><![CDATA[
      K(x,y * (T(z \ u,z) * w)) = K(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),16255(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 16255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16259">
    <literal><![CDATA[
      K(x,y * (T(T(z,u),u) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(256(a,1),16255(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="256 16255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16260">
    <literal><![CDATA[
      K(x,y * (z * (T(T(z,u),u) \ w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),16259(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 16259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16261">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(7247(a,2),16260(a,1,2,2))].">
      <j1 rule="para" parents="7247 16260"/>
    </justification>
  </clause>

  <clause id="16262">
    <literal><![CDATA[
      K(x,y * (z / T(T(u,w),w))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(9157(a,1),16260(a,1,2,2))].">
      <j1 rule="para" parents="9157 16260"/>
    </justification>
  </clause>

  <clause id="16263">
    <literal><![CDATA[
      K(x,y * (z * (K(u,w) * K(u,w)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(10359(a,1),16260(a,1,2,2))].">
      <j1 rule="para" parents="10359 16260"/>
    </justification>
  </clause>

  <clause id="16264">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (K(z,u) * w))) = T(x,y * w)
    ]]></literal>
    <justification jstring="[hyper(143,a,16261,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 16261 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16265">
    <literal><![CDATA[
      K(x,y * K(z,u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(6093(a,1),16261(a,1,2,2))].">
      <j1 rule="para" parents="6093 16261"/>
    </justification>
  </clause>

  <clause id="16266">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (K(u,z) * w))
    ]]></literal>
    <justification jstring="[para(6161(a,1),16261(a,1,2,2,2))].">
      <j1 rule="para" parents="6161 16261"/>
    </justification>
  </clause>

  <clause id="16267">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (z \ w))) = K(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(6075(a,1),16261(a,1,2,2,2))].">
      <j1 rule="para" parents="6075 16261"/>
    </justification>
  </clause>

  <clause id="16269">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,13375,a,b,16265,a)].">
      <j1 rule="hyper" parents="373 13375 16265"/>
    </justification>
  </clause>

  <clause id="16270">
    <literal><![CDATA[
      T(x,y * K(z,u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,16265,a,b,6406,a)].">
      <j1 rule="hyper" parents="143 16265 6406"/>
    </justification>
  </clause>

  <clause id="16271">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6245(a,1),16265(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6245 16265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16272">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(15021(a,1),16265(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15021 16265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16273">
    <literal><![CDATA[
      x / T(x,y * K(z,u)) = K(y * K(u,z),x)
    ]]></literal>
    <justification jstring="[hyper(225,a,16270,a,b,5804,a(flip))].">
      <j1 rule="hyper" parents="225 16270 5804"/>
    </justification>
  </clause>

  <clause id="16274">
    <literal><![CDATA[
      T(x,(y / z) * K(z,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6245(a,1),16270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6245 16270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16275">
    <literal><![CDATA[
      T(x,(y \ z) * K(u,z)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(15021(a,1),16270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15021 16270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16276">
    <literal><![CDATA[
      T(x,y * K(z,z * u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,16269,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 16269 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16277">
    <literal><![CDATA[
      K(x,y \ T(z,z * u)) = K(x,(y \ z) * K(u,z))
    ]]></literal>
    <justification jstring="[para(15021(a,1),16269(a,1,2))].">
      <j1 rule="para" parents="15021 16269"/>
    </justification>
  </clause>

  <clause id="16278">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(6888(a,2),16271(a,1,2))].">
      <j1 rule="para" parents="6888 16271"/>
    </justification>
  </clause>

  <clause id="16279">
    <literal><![CDATA[
      K(x,y / T(z \ u,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(6887(a,1),16271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6887 16271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16281">
    <literal><![CDATA[
      K(x,y / T(z,z \ u)) = K(x,y / (u / (u / z)))
    ]]></literal>
    <justification jstring="[para(6958(a,2),16271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6958 16271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16282">
    <literal><![CDATA[
      K(x,y / T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(16271(a,1),15181(a,1))].">
      <j1 rule="para" parents="16271 15181"/>
    </justification>
  </clause>

  <clause id="16283">
    <literal><![CDATA[
      K(x,y \ T(z \ u,z)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(15092(a,1),16272(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15092 16272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16284">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(15552(a,2),16272(a,1,2))].">
      <j1 rule="para" parents="15552 16272"/>
    </justification>
  </clause>

  <clause id="16286">
    <literal><![CDATA[
      K(x * K(y,z),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(5874,a,16273,a)].">
      <j1 rule="hyper" parents="5874 16273"/>
    </justification>
  </clause>

  <clause id="16287">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(16273(a,1),5874(a,1))].">
      <j1 rule="para" parents="16273 5874"/>
    </justification>
  </clause>

  <clause id="16288">
    <literal><![CDATA[
      K((1 / x) * K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(14754,a,16286,a),flip(a)].">
      <j1 rule="hyper" parents="14754 16286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16289">
    <literal><![CDATA[
      K((x / y) * K(y,z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[para(6245(a,1),16286(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6245 16286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16290">
    <literal><![CDATA[
      K((x * K(y,z)) * K(y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(6871(a,1),16286(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6871 16286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16291">
    <literal><![CDATA[
      K((x \ y) * K(z,y),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(15021(a,1),16286(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15021 16286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16292">
    <literal><![CDATA[
      K(x * (K(y,z) * K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(10350(a,1),16290(a,1,1))].">
      <j1 rule="para" parents="10350 16290"/>
    </justification>
  </clause>

  <clause id="16293">
    <literal><![CDATA[
      K(x,y) * (x * (K(z,u) * K(z,u))) = T(x * (K(z,u) * K(z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(144,a,16292,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 16292 5739"/>
    </justification>
  </clause>

  <clause id="16294">
    <literal><![CDATA[
      T(x,T(y / (y / z),u) * K(y / z,w)) = T(x,(y * K(z,u)) / T(y / z,w))
    ]]></literal>
    <justification jstring="[para(6774(a,1),16274(a,1,2,1))].">
      <j1 rule="para" parents="6774 16274"/>
    </justification>
  </clause>

  <clause id="16295">
    <literal><![CDATA[
      T(x,y / ((z * u) / z)) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(6888(a,2),16274(a,1,2))].">
      <j1 rule="para" parents="6888 16274"/>
    </justification>
  </clause>

  <clause id="16297">
    <literal><![CDATA[
      T(x,y / T(z \ u,z)) = T(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(6887(a,1),16274(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6887 16274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16298">
    <literal><![CDATA[
      K(x,T(y,z / T(u,w)) \ ((z / u) * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((z / u) * K(u,w)) / y) = v5
    ]]></literal>
    <justification jstring="[para(16274(a,1),13478(a,1,2,1))].">
      <j1 rule="para" parents="16274 13478"/>
    </justification>
  </clause>

  <clause id="16299">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,T(y,z))) = K(x,u / ((z * y) / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,13483,a,b,16278,a)].">
      <j1 rule="hyper" parents="373 13483 16278"/>
    </justification>
  </clause>

  <clause id="16301">
    <literal><![CDATA[
      K(x,y \ T(z * K(u,z \ w),T(w / z,u))) = K(x,y \ (w / T(w / z,u)))
    ]]></literal>
    <justification jstring="[para(8049(a,1),16283(a,1,2,2,1))].">
      <j1 rule="para" parents="8049 16283"/>
    </justification>
  </clause>

  <clause id="16302">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(7092,a,16284,a)].">
      <j1 rule="hyper" parents="7092 16284"/>
    </justification>
  </clause>

  <clause id="16303">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5749(a,1),16284(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5749 16284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16305">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),u)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(143,a,16303,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 16303 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16306">
    <literal><![CDATA[
      K(x,y \ T(z * (u / T(z,u)),z)) = K(x,y \ (z * (u / z)))
    ]]></literal>
    <justification jstring="[para(4658(a,1),16303(a,1,2,2,1))].">
      <j1 rule="para" parents="4658 16303"/>
    </justification>
  </clause>

  <clause id="16307">
    <literal><![CDATA[
      K(x \ K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(14754,a,16288,a)].">
      <j1 rule="hyper" parents="14754 16288"/>
    </justification>
  </clause>

  <clause id="16308">
    <literal><![CDATA[
      K(x \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(16288(a,1),14754(a,1))].">
      <j1 rule="para" parents="16288 14754"/>
    </justification>
  </clause>

  <clause id="16309">
    <literal><![CDATA[
      K(x \ K(y \ z,y),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13549,a,16307,a),flip(a)].">
      <j1 rule="hyper" parents="13549 16307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16310">
    <literal><![CDATA[
      (x \ K(y \ K(z,u),w)) \ (x \ 1) = K(w,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(16307(a,1),14533(a,1,1,2))].">
      <j1 rule="para" parents="16307 14533"/>
    </justification>
  </clause>

  <clause id="16311">
    <literal><![CDATA[
      K((x \ y) \ K(z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(16307(a,1),14639(a,1))].">
      <j1 rule="para" parents="16307 14639"/>
    </justification>
  </clause>

  <clause id="16312">
    <literal><![CDATA[
      K(x / ((y * z) / y),u) = K(x / T(z,y),u)
    ]]></literal>
    <justification jstring="[para(6888(a,2),16289(a,1,1))].">
      <j1 rule="para" parents="6888 16289"/>
    </justification>
  </clause>

  <clause id="16313">
    <literal><![CDATA[
      K(x \ ((y * z) / y),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(15554(a,2),16291(a,1,1))].">
      <j1 rule="para" parents="15554 16291"/>
    </justification>
  </clause>

  <clause id="16314">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),z)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(531(a,1),16295(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="531 16295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16315">
    <literal><![CDATA[
      T(x,y / T(z * K(u,z),w)) = T(x,y / T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(5900(a,2),16295(a,1,2,2))].">
      <j1 rule="para" parents="5900 16295"/>
    </justification>
  </clause>

  <clause id="16316">
    <literal><![CDATA[
      T(x,y / ((z * u) / T(z,w))) = T(x,y / T(u * K(w,z),z))
    ]]></literal>
    <justification jstring="[para(7170(a,1),16295(a,1,2,2))].">
      <j1 rule="para" parents="7170 16295"/>
    </justification>
  </clause>

  <clause id="16317">
    <literal><![CDATA[
      T(x,y / (((z * u) / z) * K(z,w))) = T(x,y / T(u * K(z,w),z))
    ]]></literal>
    <justification jstring="[para(7142(a,1),16295(a,1,2,2))].">
      <j1 rule="para" parents="7142 16295"/>
    </justification>
  </clause>

  <clause id="16318">
    <literal><![CDATA[
      T(x \ y,z / (y / x)) = T(x \ y,(x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8477,a(flip),b,16297,a),flip(a)].">
      <j1 rule="hyper" parents="64 8477 16297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16319">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u \ 1,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[para(3776(a,1),16302(a,1,2,2))].">
      <j1 rule="para" parents="3776 16302"/>
    </justification>
  </clause>

  <clause id="16321">
    <literal><![CDATA[
      K(x \ K(y \ z,z),u) = K(x \ K(y,y \ z),u)
    ]]></literal>
    <justification jstring="[para(6118(a,1),16309(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6118 16309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16322">
    <literal><![CDATA[
      K(x \ K(y * (z \ u),z),w) = K(x \ K(z,y * u),w)
    ]]></literal>
    <justification jstring="[para(10277(a,1),16309(a,1,1,2))].">
      <j1 rule="para" parents="10277 16309"/>
    </justification>
  </clause>

  <clause id="16323">
    <literal><![CDATA[
      K(x \ K((y * K(z,z \ u)) \ w,y * K(z,u)),v5) = K(x \ K(y * K(z,z \ u),w),v5)
    ]]></literal>
    <justification jstring="[para(13378(a,1),16309(a,1,1,2))].">
      <j1 rule="para" parents="13378 16309"/>
    </justification>
  </clause>

  <clause id="16324">
    <literal><![CDATA[
      T(T(x,y / ((z * u) / z)),K(y / T(u,z),w)) = T(x,T(y / ((z * u) / z),w))
    ]]></literal>
    <justification jstring="[para(16312(a,1),7840(a,1,2))].">
      <j1 rule="para" parents="16312 7840"/>
    </justification>
  </clause>

  <clause id="16325">
    <literal><![CDATA[
      K(x,y * (T(z,u) \ u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13459,a(flip),b,16262,a)].">
      <j1 rule="hyper" parents="64 13459 16262"/>
    </justification>
  </clause>

  <clause id="16326">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / (w / (w / u))))
    ]]></literal>
    <justification jstring="[para(4769(a,1),16262(a,1,2,2,2,1))].">
      <j1 rule="para" parents="4769 16262"/>
    </justification>
  </clause>

  <clause id="16327">
    <literal><![CDATA[
      T(x,y * (T(z,u) \ u)) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(143,a,16325,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 16325 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16328">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(4632(a,1),16325(a,1,2,2))].">
      <j1 rule="para" parents="4632 16325"/>
    </justification>
  </clause>

  <clause id="16329">
    <literal><![CDATA[
      K(x,T(y,z / u) * (z / u)) = K(x,(u \ T(z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(13426,a,16328,a),flip(a)].">
      <j1 rule="hyper" parents="13426 16328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16330">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ T(u,(y * x) * z))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,13050,a(flip),b,16328,a),flip(a)].">
      <j1 rule="hyper" parents="373 13050 16328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16331">
    <literal><![CDATA[
      K(x * (y / x),z * (u / w)) = K(y,T(z * (w \ T(u,w)),x))
    ]]></literal>
    <justification jstring="[hyper(64,a,11193,a(flip),b,16328,a),flip(a)].">
      <j1 rule="hyper" parents="64 11193 16328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16332">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ T(z / u,T(z,u \ 1)))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[para(6231(a,1),16328(a,2,2,2))].">
      <j1 rule="para" parents="6231 16328"/>
    </justification>
  </clause>

  <clause id="16333">
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) = K(x,y * (z * K(w,u)))
    ]]></literal>
    <justification jstring="[para(10358(a,1),16263(a,1,2,2))].">
      <j1 rule="para" parents="10358 16263"/>
    </justification>
  </clause>

  <clause id="16334">
    <literal><![CDATA[
      T(x,y * (K(z,u) * (u * w))) = T(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[para(5811(a,1),16264(a,1,2,2,2))].">
      <j1 rule="para" parents="5811 16264"/>
    </justification>
  </clause>

  <clause id="16335">
    <literal><![CDATA[
      K(x,y * (K(z * u,z) * w)) = K(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,13552,a(flip),b,16266,a),flip(a)].">
      <j1 rule="hyper" parents="373 13552 16266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16336">
    <literal><![CDATA[
      K(x,y \ T(z,z * u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,16272,a(flip),b,16277,a),flip(a)].">
      <j1 rule="hyper" parents="373 16272 16277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16337">
    <literal><![CDATA[
      K(x,y \ T(z,z \ u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),16336(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 16336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16338">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(116(a,1),16337(a,1,2,2))].">
      <j1 rule="para" parents="116 16337"/>
    </justification>
  </clause>

  <clause id="16339">
    <literal><![CDATA[
      K(x,y / (z / (z / (z / u)))) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[para(848(a,1),16281(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="848 16281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16340">
    <literal><![CDATA[
      K(x \ K(y \ z,z),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,13402,a(flip),b,16321,a),flip(a)].">
      <j1 rule="hyper" parents="373 13402 16321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16341">
    <literal><![CDATA[
      K(x \ K(y,z \ y),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(16308,a,16340,a)].">
      <j1 rule="hyper" parents="16308 16340"/>
    </justification>
  </clause>

  <clause id="16342">
    <literal><![CDATA[
      K(x \ K(y,z \ 1),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13470,a,b,16341,a)].">
      <j1 rule="hyper" parents="64 13470 16341"/>
    </justification>
  </clause>

  <clause id="16343">
    <literal><![CDATA[
      K((x \ y) \ K(z,x),u) = K(y \ T(x,1 / z),u)
    ]]></literal>
    <justification jstring="[hyper(15140,a,16342,a),flip(a)].">
      <j1 rule="hyper" parents="15140 16342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16344">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w,u))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(15021(a,1),16333(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15021 16333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16345">
    <literal><![CDATA[
      K(x,y / T(z / u,z)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15921,a(flip),b,16339,a)].">
      <j1 rule="hyper" parents="64 15921 16339"/>
    </justification>
  </clause>

  <clause id="16346">
    <literal><![CDATA[
      K(x,y / ((z \ u) \ u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),16345(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 16345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16347">
    <literal><![CDATA[
      K(x,y / T(1 / L(z,u,u \ 1),a(u \ 1,u,z))) = K(x,y / (z \ a(u \ 1,u,z)))
    ]]></literal>
    <justification jstring="[para(5594(a,1),16346(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5594 16346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16348">
    <literal><![CDATA[
      K(x \ T(y,1 / z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(16311,a,16343,a),flip(a)].">
      <j1 rule="hyper" parents="16311 16343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16349">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(79(a,1),16348(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 16348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16350">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) * a(w,v5,K(y \ T(z,u),x)) = K(x,L(y \ T(z,u \ 1),v5,w))
    ]]></literal>
    <justification jstring="[para(16349(a,1),12069(a,1,2,3))].">
      <j1 rule="para" parents="16349 12069"/>
    </justification>
  </clause>

  <clause id="16351">
    <literal><![CDATA[
      T(x,y * (z * (K(u,z) * w))) = T(x,y * (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(5911(a,1),16257(a,1,2,2))].">
      <j1 rule="para" parents="5911 16257"/>
    </justification>
  </clause>

  <clause id="16352">
    <literal><![CDATA[
      K(x,y * ((z / (z / u)) \ w)) = K(x,y * (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13598,a,b,16267,a)].">
      <j1 rule="hyper" parents="64 13598 16267"/>
    </justification>
  </clause>

  <clause id="16353">
    <literal><![CDATA[
      K(x,y * (T(z \ u,z) \ w)) = K(x,y * ((u / z) \ w))
    ]]></literal>
    <justification jstring="[para(6292(a,1),16267(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6292 16267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16354">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16299(a,1),13480(a,1))].">
      <j1 rule="para" parents="16299 13480"/>
    </justification>
  </clause>

  <clause id="16355">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(6888(a,1),16354(a,1,2))].">
      <j1 rule="para" parents="6888 16354"/>
    </justification>
  </clause>

  <clause id="16356">
    <literal><![CDATA[
      K(x,y \ K(z,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(6603,a,16310,a)].">
      <j1 rule="hyper" parents="6603 16310"/>
    </justification>
  </clause>

  <clause id="16357">
    <literal><![CDATA[
      K(x,y \ K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16310(a,1),6603(a,1))].">
      <j1 rule="para" parents="16310 6603"/>
    </justification>
  </clause>

  <clause id="16358">
    <literal><![CDATA[
      K(x,y) * K(z,z \ K(y,x)) = z * (K(x,y) / z)
    ]]></literal>
    <justification jstring="[hyper(145,a,16356,a,b,5961,a)].">
      <j1 rule="hyper" parents="145 16356 5961"/>
    </justification>
  </clause>

  <clause id="16359">
    <literal><![CDATA[
      T(x,y / T(((z \ u) \ u) \ u,w)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(4721(a,1),16314(a,1,2,2))].">
      <j1 rule="para" parents="4721 16314"/>
    </justification>
  </clause>

  <clause id="16360">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(11231,a,16329,a),flip(a)].">
      <j1 rule="hyper" parents="11231 16329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16361">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) * u) = w
    ]]></literal>
    <justification jstring="[para(16329(a,1),11231(a,1))].">
      <j1 rule="para" parents="16329 11231"/>
    </justification>
  </clause>

  <clause id="16362">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(4632(a,2),16360(a,1,2,1))].">
      <j1 rule="para" parents="4632 16360"/>
    </justification>
  </clause>

  <clause id="16363">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) * u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(143,a,16362,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 16362 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16364">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) * u) = w
    ]]></literal>
    <justification jstring="[para(4632(a,2),16361(a,1,2,1))].">
      <j1 rule="para" parents="4632 16361"/>
    </justification>
  </clause>

  <clause id="16365">
    <literal><![CDATA[
      K(x,(T(y,T(z,u)) \ (u * (z / u))) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((u * (z / u)) / y) * w) = v5
    ]]></literal>
    <justification jstring="[para(11107(a,1),16364(a,1,2,1,1))].">
      <j1 rule="para" parents="11107 16364"/>
    </justification>
  </clause>

  <clause id="16366">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) / u))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(15554(a,2),16344(a,1,2,2))].">
      <j1 rule="para" parents="15554 16344"/>
    </justification>
  </clause>

  <clause id="16367">
    <literal><![CDATA[
      K(x,y * (z \ T(T(u,w),w))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(256(a,1),16366(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="256 16366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16368">
    <literal><![CDATA[
      K(x,y \ ((z / T(u,z)) * u)) = K(x,y \ (u * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13383,a(flip),b,16306,a)].">
      <j1 rule="hyper" parents="64 13383 16306"/>
    </justification>
  </clause>

  <clause id="16369">
    <literal><![CDATA[
      K(x,y \ (z * (u / z))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(4627(a,1),16368(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4627 16368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16370">
    <literal><![CDATA[
      K(x,T(y / (z * u),z)) = K(x,(u * z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15679,a,b,16369,a)].">
      <j1 rule="hyper" parents="64 15679 16369"/>
    </justification>
  </clause>

  <clause id="16371">
    <literal><![CDATA[
      K(x,y \ T(z * u,u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),16369(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 16369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16372">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(4399(a,2),16369(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4399 16369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16373">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (T(z,u) * u))
    ]]></literal>
    <justification jstring="[para(4450(a,2),16369(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4450 16369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16374">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),z \ u)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),16370(a,2,2,1))].">
      <j1 rule="para" parents="10 16370"/>
    </justification>
  </clause>

  <clause id="16375">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13383,a(flip),b,16373,a),flip(a)].">
      <j1 rule="hyper" parents="64 13383 16373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16376">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * T(w * u,u))) = K(x,y \ (T(w * u,u) * z))
    ]]></literal>
    <justification jstring="[para(11103(a,1),16375(a,1,2,2,1))].">
      <j1 rule="para" parents="11103 16375"/>
    </justification>
  </clause>

  <clause id="16377">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((u \ 1) \ w))) = K(x,y \ (((u \ 1) \ w) * z))
    ]]></literal>
    <justification jstring="[para(14428(a,1),16375(a,1,2,2,1))].">
      <j1 rule="para" parents="14428 16375"/>
    </justification>
  </clause>

  <clause id="16378">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((1 / u) \ w))) = K(x,y \ (((1 / u) \ w) * z))
    ]]></literal>
    <justification jstring="[para(14478(a,1),16375(a,1,2,2,1))].">
      <j1 rule="para" parents="14478 16375"/>
    </justification>
  </clause>

  <clause id="16379">
    <literal><![CDATA[
      K(x,T(y * (z \ T(u,z)),w)) = K(x,T(y * (u / z),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11193,a(flip),b,16331,a),flip(a)].">
      <j1 rule="hyper" parents="64 11193 16331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16380">
    <literal><![CDATA[
      K(x,T(y * (T(z,u) \ u),w)) = K(x,T(y * (u / z),w))
    ]]></literal>
    <justification jstring="[para(4632(a,2),16379(a,1,2,1,2))].">
      <j1 rule="para" parents="4632 16379"/>
    </justification>
  </clause>

  <clause id="16381">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),u)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13431,a(flip),b,16359,a)].">
      <j1 rule="hyper" parents="64 13431 16359"/>
    </justification>
  </clause>

  <clause id="16382">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,u),w)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(23(a,1),16381(a,1,2,2))].">
      <j1 rule="para" parents="23 16381"/>
    </justification>
  </clause>

  <clause id="16383">
    <literal><![CDATA[
      T(x * (K(y,z) * K(y,z)),u) = T(x,u) * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5985,a,16293,a),flip(a)].">
      <j1 rule="hyper" parents="5985 16293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16384">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,(y * x) * z)) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(15263,a,16330,a)].">
      <j1 rule="hyper" parents="15263 16330"/>
    </justification>
  </clause>

  <clause id="16385">
    <literal><![CDATA[
      (x * ((a(y,y,x) \ 1) * z)) / L(T(x,z),y,y) = L(z,a(y,y,x),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,11794,a(flip),b,16226,a),flip(a)].">
      <j1 rule="hyper" parents="373 11794 16226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16386">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) * (y * z)) / L(T(y,z),x,x) = L(z,y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,1631,a(flip),b,16227,a),flip(a)].">
      <j1 rule="hyper" parents="373 1631 16227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16387">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((u \ 1) \ w))) = K(x,y \ (((1 / u) \ w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6643,a(flip),b,16378,a)].">
      <j1 rule="hyper" parents="64 6643 16378"/>
    </justification>
  </clause>

  <clause id="16388">
    <literal><![CDATA[
      K(x,y \ (((1 / z) \ u) * w)) = K(x,y \ (((z \ 1) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16377,a(flip),b,16387,a),flip(a)].">
      <j1 rule="hyper" parents="64 16377 16387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16389">
    <literal><![CDATA[
      T(T(x,x * y) * K(L(x,y,x) * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(4683(a,1),14797(a,1,1,1))].">
      <j1 rule="para" parents="4683 14797"/>
    </justification>
  </clause>

  <clause id="16390">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),L(u,z,z \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(15521(a,2),15389(a,1))].">
      <j1 rule="para" parents="15521 15389"/>
    </justification>
  </clause>

  <clause id="16391">
    <literal><![CDATA[
      K(x,y \ (L(y,z,z \ 1) * u)) = K(x,a(z \ 1,z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(16390,a,7094,a),flip(a)].">
      <j1 rule="hyper" parents="16390 7094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16392">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,a(z \ 1,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(2325(a,1),16391(a,1,2))].">
      <j1 rule="para" parents="2325 16391"/>
    </justification>
  </clause>

  <clause id="16393">
    <literal><![CDATA[
      K(x * (y \ z),(x * (y \ z)) \ z) = K(x * (y \ z),y / x)
    ]]></literal>
    <justification jstring="[hyper(15535,a,15732,a),flip(a)].">
      <j1 rule="hyper" parents="15535 15732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16394">
    <literal><![CDATA[
      L(1 / x,1 / x,x \ y) \ (x \ y) = (x \ y) * (1 / T(1 / x,y))
    ]]></literal>
    <justification jstring="[para(3572(a,1),15886(a,2,2))].">
      <j1 rule="para" parents="3572 15886"/>
    </justification>
  </clause>

  <clause id="16395">
    <literal><![CDATA[
      L(1 / x,x,x \ y) \ (x \ y) = (x \ y) * (1 / T(1 / x,y))
    ]]></literal>
    <justification jstring="[para(11776(a,1),16394(a,1,1))].">
      <j1 rule="para" parents="11776 16394"/>
    </justification>
  </clause>

  <clause id="16396">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,R(y,z,z \ 1) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(297(a,1),15963(a,2,2,1))].">
      <j1 rule="para" parents="297 15963"/>
    </justification>
  </clause>

  <clause id="16397">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15961,a(flip),b,15978,a)].">
      <j1 rule="hyper" parents="64 15961 15978"/>
    </justification>
  </clause>

  <clause id="16399">
    <literal><![CDATA[
      K(x,y \ (R(1 / z,z,y) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16180,a(flip),b,16397,a),flip(a)].">
      <j1 rule="hyper" parents="64 16180 16397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16400">
    <literal><![CDATA[
      K(x,y \ ((z / y) \ u)) = K(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[para(454(a,1),16399(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="454 16399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16401">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z \ ((z / u) * w)) = K(y,T(z \ ((u / z) \ w),x))
    ]]></literal>
    <justification jstring="[hyper(14802,a,16400,a),flip(a)].">
      <j1 rule="hyper" parents="14802 16400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16402">
    <literal><![CDATA[
      K(x,T(y \ ((z / y) \ u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),w)) = v5
    ]]></literal>
    <justification jstring="[para(16401(a,1),14802(a,1))].">
      <j1 rule="para" parents="16401 14802"/>
    </justification>
  </clause>

  <clause id="16403">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T(((u * z) / y) \ 1,y / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8081,a,b,16081,a),flip(a)].">
      <j1 rule="hyper" parents="373 8081 16081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16404">
    <literal><![CDATA[
      a(x,(y * z) \ u,z \ (y \ u)) = a(x,z \ (y \ u),(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(346(a,1),16193(a,1,3)),flip(a)].">
      <j1 rule="para" parents="346 16193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16405">
    <literal><![CDATA[
      a(x,(y \ z) \ (y \ u),(y * (y \ z)) \ u) = a(x,z \ u,(y \ z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),16404(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 16404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16406">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) = L(x,y * K(x * y,z),x)
    ]]></literal>
    <justification jstring="[para(14495(a,1),16204(a,1,1,2))].">
      <j1 rule="para" parents="14495 16204"/>
    </justification>
  </clause>

  <clause id="16407">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y * K(x * y,u),x)
    ]]></literal>
    <justification jstring="[hyper(14216,a,16406,a)].">
      <j1 rule="hyper" parents="14216 16406"/>
    </justification>
  </clause>

  <clause id="16409">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,x \ T(x * y,u),x)
    ]]></literal>
    <justification jstring="[para(14494(a,2),16407(a,2,2))].">
      <j1 rule="para" parents="14494 16407"/>
    </justification>
  </clause>

  <clause id="16410">
    <literal><![CDATA[
      L(x,x \ T(x * y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(13165,a,16409,a),flip(a)].">
      <j1 rule="hyper" parents="13165 16409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16411">
    <literal><![CDATA[
      L(x,x \ T(y,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),16410(a,1,2,2,1))].">
      <j1 rule="para" parents="10 16410"/>
    </justification>
  </clause>

  <clause id="16413">
    <literal><![CDATA[
      L(x,x \ (y / z),x) = L(x,x \ (z \ y),x)
    ]]></literal>
    <justification jstring="[para(117(a,1),16411(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 16411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16414">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,z \ (x \ (x * (z * y))),z) = T(z * (z \ ((x * (z * y)) / x)),z) \ z
    ]]></literal>
    <justification jstring="[para(16413(a,1),13236(a,1,2))].">
      <j1 rule="para" parents="16413 13236"/>
    </justification>
  </clause>

  <clause id="16415">
    <literal><![CDATA[
      R(T(x * K(y,x),z),y,u) \ ((y * x) * u) = (y * K(z,x)) * u
    ]]></literal>
    <justification jstring="[para(9(a,1),16219(a,2,1,2,2))].">
      <j1 rule="para" parents="9 16219"/>
    </justification>
  </clause>

  <clause id="16416">
    <literal><![CDATA[
      K(x,(y * z) \ ((y * u) * z)) = (y * z) \ ((y * K(x,u)) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,16415,a(flip),b,10695,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 16415 10695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16417">
    <literal><![CDATA[
      K(x,(y * z) \ ((y * (u / y)) * z)) = R(T(K(x,y \ u),y * z),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,8374,a(flip),b,16416,a),flip(a)].">
      <j1 rule="hyper" parents="373 8374 16416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16418">
    <literal><![CDATA[
      T(T(x,x * y) * K(x * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(13363(a,1),16389(a,1,1,2))].">
      <j1 rule="para" parents="13363 16389"/>
    </justification>
  </clause>

  <clause id="16419">
    <literal><![CDATA[
      T(T(x * K(x * y,z),x * y),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(7812(a,2),16418(a,1,1))].">
      <j1 rule="para" parents="7812 16418"/>
    </justification>
  </clause>

  <clause id="16421">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(481,a,16419,a)].">
      <j1 rule="hyper" parents="481 16419"/>
    </justification>
  </clause>

  <clause id="16422">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,x * y) * y,z)
    ]]></literal>
    <justification jstring="[para(4683(a,1),16421(a,2,2,1,1))].">
      <j1 rule="para" parents="4683 16421"/>
    </justification>
  </clause>

  <clause id="16423">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T(y / (u * z),y / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,9298,a(flip),b,16403,a),flip(a)].">
      <j1 rule="hyper" parents="373 9298 16403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16424">
    <literal><![CDATA[
      K(x,T(y / (z * u),y / u)) = K(x,(u * z) \ (u * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(7009,a,16423,a),flip(a)].">
      <j1 rule="hyper" parents="7009 16423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16425">
    <literal><![CDATA[
      K(x,T(y / (z * (z \ u)),y / (z \ u))) = K(x,T(u,z) \ ((z \ u) * (y / (z \ u))))
    ]]></literal>
    <justification jstring="[hyper(373,a,13414,a(flip),b,16424,a),flip(a)].">
      <j1 rule="hyper" parents="373 13414 16424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16426">
    <literal><![CDATA[
      K(x,T(y / ((z / (z * u)) * (z * u)),y / (z * u))) = K(x,(z * K(z * u,u \ 1)) \ ((z * u) * (y / (z * u))))
    ]]></literal>
    <justification jstring="[para(6738(a,1),16424(a,2,2,1))].">
      <j1 rule="para" parents="6738 16424"/>
    </justification>
  </clause>

  <clause id="16427">
    <literal><![CDATA[
      K(K(x,y) * z,(K(x,y) * z) \ K(x,y)) = (z \ 1) \ T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(15296(a,1),14451(a,2,2))].">
      <j1 rule="para" parents="15296 14451"/>
    </justification>
  </clause>

  <clause id="16428">
    <literal><![CDATA[
      K(K(x,y) * z,(K(x,y) * z) \ K(x,y)) = z * T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,4903,a(flip),b,16427,a),flip(a)].">
      <j1 rule="hyper" parents="373 4903 16427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16429">
    <literal><![CDATA[
      K(K(x,y) * z,z \ 1) = z * T(1 / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6825,a,16428,a)].">
      <j1 rule="hyper" parents="6825 16428"/>
    </justification>
  </clause>

  <clause id="16431">
    <literal><![CDATA[
      (x \ 1) * R(T(y,x \ L(x,z,u)),1 / x,L(x,z,u)) = T(L(y,1 / x,L(x,z,u)) * (1 / x),L(x,z,u))
    ]]></literal>
    <justification jstring="[para(5600(a,1),14484(a,1,1))].">
      <j1 rule="para" parents="5600 14484"/>
    </justification>
  </clause>

  <clause id="16432">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,w) = x * (L(x,y,z) \ K(u,w))
    ]]></literal>
    <justification jstring="[para(15419(a,1),14539(a,1,2))].">
      <j1 rule="para" parents="15419 14539"/>
    </justification>
  </clause>

  <clause id="16433">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ K(u,w) = x * (L(x,y,z) \ K(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14517,a,b,16432,a)].">
      <j1 rule="hyper" parents="64 14517 16432"/>
    </justification>
  </clause>

  <clause id="16434">
    <literal><![CDATA[
      K(x,y) / (z * (L(z,u,w) \ K(x,y))) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(16432(a,1),14502(a,1,2))].">
      <j1 rule="para" parents="16432 14502"/>
    </justification>
  </clause>

  <clause id="16436">
    <literal><![CDATA[
      (1 / x) * (T(y,x \ (x \ 1)) \ z) = x * (y \ (((x \ 1) * (x \ 1)) * z))
    ]]></literal>
    <justification jstring="[para(7(a,1),14573(a,1,2))].">
      <j1 rule="para" parents="7 14573"/>
    </justification>
  </clause>

  <clause id="16437">
    <literal><![CDATA[
      (1 / x) * (T(y,x \ (x \ 1)) \ z) = x * (y \ ((x \ 1) * (x \ z)))
    ]]></literal>
    <justification jstring="[para(584(a,1),16436(a,2,2,2))].">
      <j1 rule="para" parents="584 16436"/>
    </justification>
  </clause>

  <clause id="16438">
    <literal><![CDATA[
      K(x,y * (((z * K(u,z)) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(6453(a,1),14815(a,1,2,2,1,1))].">
      <j1 rule="para" parents="6453 14815"/>
    </justification>
  </clause>

  <clause id="16439">
    <literal><![CDATA[
      K(x,y * ((z * (1 / (1 / u))) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(5722(a,1),16438(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5722 16438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16440">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,T((y / z) \ 1,y),u))
    ]]></literal>
    <justification jstring="[para(12(a,1),14924(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 14924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16441">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(y / z) \ 1,u))
    ]]></literal>
    <justification jstring="[para(10256(a,1),16440(a,2,2))].">
      <j1 rule="para" parents="10256 16440"/>
    </justification>
  </clause>

  <clause id="16442">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(14222(a,1),16441(a,2,2))].">
      <j1 rule="para" parents="14222 16441"/>
    </justification>
  </clause>

  <clause id="16443">
    <literal><![CDATA[
      K(x,L((y / z) * z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(14930,a,16442,a)].">
      <j1 rule="hyper" parents="14930 16442"/>
    </justification>
  </clause>

  <clause id="16444">
    <literal><![CDATA[
      K(x,L(y,(z \ y) \ 1,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),16443(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 16443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16445">
    <literal><![CDATA[
      T(x * (y * (z \ 1)),K(y * (z \ 1),z)) = (y * (z \ 1)) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(117(a,1),14951(a,2,2,2))].">
      <j1 rule="para" parents="117 14951"/>
    </justification>
  </clause>

  <clause id="16446">
    <literal><![CDATA[
      T(x * (y * (z \ 1)),K(y / z,z)) = (y * (z \ 1)) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(14675(a,1),16445(a,1,2))].">
      <j1 rule="para" parents="14675 16445"/>
    </justification>
  </clause>

  <clause id="16447">
    <literal><![CDATA[
      T(x * (y * (z \ 1)),K(y,z)) = (y * (z \ 1)) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8717,a(flip),b,16446,a)].">
      <j1 rule="hyper" parents="64 8717 16446"/>
    </justification>
  </clause>

  <clause id="16448">
    <literal><![CDATA[
      (T(x,y \ 1) * (y \ 1)) * T(K((y \ 1) * x,z),y \ T(x,y \ 1)) = T(T(T(x,y \ 1) * (y \ 1),z),K(T(x,y \ 1),y))
    ]]></literal>
    <justification jstring="[para(11203(a,1),16447(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11203 16447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16449">
    <literal><![CDATA[
      L(x,T(x,y) \ z,(T(x,y) \ z) \ y) * y = (K(x,y) * (y / (z / x))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,11066,a(flip),b,15101,a)].">
      <j1 rule="hyper" parents="64 11066 15101"/>
    </justification>
  </clause>

  <clause id="16450">
    <literal><![CDATA[
      K(x,y) * (y / ((T(z,T(z * y,x)) \ 1) * y)) = y / T((1 / z) * T(y,x),z)
    ]]></literal>
    <justification jstring="[para(13539(a,2),15102(a,1,2,2,1,1))].">
      <j1 rule="para" parents="13539 15102"/>
    </justification>
  </clause>

  <clause id="16451">
    <literal><![CDATA[
      K(x,(T(y * z,z \ 1) / u) * w) = K(x,((((y * z) \ y) \ y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14904,a(flip),b,15177,a)].">
      <j1 rule="hyper" parents="64 14904 15177"/>
    </justification>
  </clause>

  <clause id="16452">
    <literal><![CDATA[
      x * (K(y,L(x,z,u)) * K(w,L(y,z,u))) = (R(y,z,u) * x) / R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(15568(a,1),15599(a,1,2,2))].">
      <j1 rule="para" parents="15568 15599"/>
    </justification>
  </clause>

  <clause id="16453">
    <literal><![CDATA[
      x * ((y * T(T(y,y \ 1),y \ 1)) * z) = ((y \ 1) \ y) * (T(x,y * y) * z)
    ]]></literal>
    <justification jstring="[para(6250(a,1),15811(a,1,2,1))].">
      <j1 rule="para" parents="6250 15811"/>
    </justification>
  </clause>

  <clause id="16455">
    <literal><![CDATA[
      (R(x,y,y) * z) \ (R(x,y,y) * R(z,x,a(x,y,y))) = a(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(15984(a,1),16035(a,1,2,1))].">
      <j1 rule="para" parents="15984 16035"/>
    </justification>
  </clause>

  <clause id="16456">
    <literal><![CDATA[
      a(L(x,y,z),L(x,u,w),L(x,u,w)) = L(x,y,z) \ L(R(x,x,x),y,z)
    ]]></literal>
    <justification jstring="[para(13712(a,1),16053(a,2,2,1))].">
      <j1 rule="para" parents="13712 16053"/>
    </justification>
  </clause>

  <clause id="16457">
    <literal><![CDATA[
      a(L(x,y,z),L(x,u,w),L(x,u,w)) = a(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13189,a(flip),b,16456,a),flip(a)].">
      <j1 rule="hyper" parents="373 13189 16456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16460">
    <literal><![CDATA[
      ((1 / (x / y)) * x) * K(((1 / (x / z)) * x) * (z \ x),(y \ x) \ 1) = x * (1 / (x / y))
    ]]></literal>
    <justification jstring="[para(14931(a,1),16225(a,1,2,1))].">
      <j1 rule="para" parents="14931 16225"/>
    </justification>
  </clause>

  <clause id="16461">
    <literal><![CDATA[
      T(T(x,y / T(z,u)),K(y / T(z,u),w)) = T(x,T(y / ((u * z) / u),w))
    ]]></literal>
    <justification jstring="[para(16295(a,1),16324(a,1,1))].">
      <j1 rule="para" parents="16295 16324"/>
    </justification>
  </clause>

  <clause id="16462">
    <literal><![CDATA[
      T(x,T(y / ((z * u) / z),w)) = T(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(7857,a,16461,a),flip(a)].">
      <j1 rule="hyper" parents="7857 16461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16463">
    <literal><![CDATA[
      T(x,T((y / z) * K(z,u),w)) = T(x,T(y / T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11329,a(flip),b,16462,a)].">
      <j1 rule="hyper" parents="64 11329 16462"/>
    </justification>
  </clause>

  <clause id="16464">
    <literal><![CDATA[
      T(x,T((y / z) \ K(y,u),w)) = T(x,T(z / T(y,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16143,a,b,16463,a)].">
      <j1 rule="hyper" parents="64 16143 16463"/>
    </justification>
  </clause>

  <clause id="16465">
    <literal><![CDATA[
      (R(x,y,z) * u) / R(T(x,w),y,z) = (L(x,y,z) * u) / L(T(x,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12225,a(flip),b,16452,a),flip(a)].">
      <j1 rule="hyper" parents="64 12225 16452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16466">
    <literal><![CDATA[
      ((x \ 1) \ x) * (T(y,x * x) * z) = y * ((x * (T(x \ 1,x) \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(4797(a,1),16453(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4797 16453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16467">
    <literal><![CDATA[
      ((x \ 1) \ x) * (T(y,x * x) * z) = y * (((x \ 1) \ x) * z)
    ]]></literal>
    <justification jstring="[para(1476(a,1),16466(a,2,2,1))].">
      <j1 rule="para" parents="1476 16466"/>
    </justification>
  </clause>

  <clause id="16468">
    <literal><![CDATA[
      (x \ 1) * (y * (((x \ 1) \ x) * z)) = x * (T(y,x * x) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,16467,a(flip),b,1115,a)].">
      <j1 rule="hyper" parents="145 16467 1115"/>
    </justification>
  </clause>

  <clause id="16469">
    <literal><![CDATA[
      T(R(T(x,x * y),x,y),K((1 / x) * y,z)) = ((1 / x) * y) \ T(y,K(z,x \ y))
    ]]></literal>
    <justification jstring="[para(8153(a,1),14591(a,2,2))].">
      <j1 rule="para" parents="8153 14591"/>
    </justification>
  </clause>

  <clause id="16470">
    <literal><![CDATA[
      T(((x * y) * y) / x,T(y * y,x)) \ 1 = (y * y) \ (a(x,y,y) \ K(y * y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,486,a(flip),b,15161,a),flip(a)].">
      <j1 rule="hyper" parents="373 486 15161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16471">
    <literal><![CDATA[
      T(((1 / x) * y) \ y,K(y,1 / x)) = K(y,x \ 1) * L(x,x,x \ ((1 / x) * y))
    ]]></literal>
    <justification jstring="[para(6041(a,1),15658(a,2,1))].">
      <j1 rule="para" parents="6041 15658"/>
    </justification>
  </clause>

  <clause id="16472">
    <literal><![CDATA[
      K(x,L(y,z,(L(u,w,v5) \ u) \ y)) = K(x,L(y,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(15733,a,15448,a)].">
      <j1 rule="hyper" parents="15733 15448"/>
    </justification>
  </clause>

  <clause id="16473">
    <literal><![CDATA[
      K(x,L(y,z,u \ L(u,w,v5))) = K(x,L(y,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(15957,a,16472,a)].">
      <j1 rule="hyper" parents="15957 16472"/>
    </justification>
  </clause>

  <clause id="16474">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) = K(x,L(y,z,z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15523,a(flip),b,16473,a),flip(a)].">
      <j1 rule="hyper" parents="64 15523 16473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16475">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) = K(x,L(y,z,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,16473,a(flip),b,16474,a),flip(a)].">
      <j1 rule="hyper" parents="373 16473 16474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16476">
    <literal><![CDATA[
      K(x,T((y * z) * (1 / y),K(y,z) / y) \ u) = K(x,L(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(14389(a,1),15900(a,1,2,1,1))].">
      <j1 rule="para" parents="14389 15900"/>
    </justification>
  </clause>

  <clause id="16477">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = a(w,z,K(u,K(x,y))) * K(w,K(x,y))
    ]]></literal>
    <justification jstring="[para(15378(a,1),15955(a,2,1))].">
      <j1 rule="para" parents="15378 15955"/>
    </justification>
  </clause>

  <clause id="16478">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = K(x,K(y,L(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,15457,a(flip),b,16477,a),flip(a)].">
      <j1 rule="hyper" parents="373 15457 16477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16479">
    <literal><![CDATA[
      K(x,K(y,L(z,u \ w,u))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[para(101(a,1),16478(a,1,2,2))].">
      <j1 rule="para" parents="101 16478"/>
    </justification>
  </clause>

  <clause id="16480">
    <literal><![CDATA[
      K(x,K(y,L(z,u / w,w))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(10996(a,2),16479(a,1,2,2))].">
      <j1 rule="para" parents="10996 16479"/>
    </justification>
  </clause>

  <clause id="16481">
    <literal><![CDATA[
      L(L(x \ R(x,y,y \ x),z,u),x,L(x,z,u)) = a(L(x,z,u),y,y \ x)
    ]]></literal>
    <justification jstring="[para(4246(a,1),16043(a,1,1))].">
      <j1 rule="para" parents="4246 16043"/>
    </justification>
  </clause>

  <clause id="16482">
    <literal><![CDATA[
      L(L(a(x,y,y \ x),z,u),x,L(x,z,u)) = a(L(x,z,u),y,y \ x)
    ]]></literal>
    <justification jstring="[para(2090(a,1),16481(a,1,1,1))].">
      <j1 rule="para" parents="2090 16481"/>
    </justification>
  </clause>

  <clause id="16483">
    <literal><![CDATA[
      T(R(T(x,x * y),x,y),K((1 / x) * y,z)) = ((1 / x) * y) \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(9004(a,1),16469(a,2,2))].">
      <j1 rule="para" parents="9004 16469"/>
    </justification>
  </clause>

  <clause id="16484">
    <literal><![CDATA[
      T(((1 / x) * y) \ y,K((1 / x) * y,z)) = ((1 / x) * y) \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(1342(a,1),16483(a,1,1))].">
      <j1 rule="para" parents="1342 16483"/>
    </justification>
  </clause>

  <clause id="16485">
    <literal><![CDATA[
      T(((1 / x) * y) \ y,K(y,1 / x)) = K(y,x \ 1) * L(x,x,(x \ 1) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1128(a,1),16471(a,2,2,3))].">
      <j1 rule="para" parents="1128 16471"/>
    </justification>
  </clause>

  <clause id="16486">
    <literal><![CDATA[
      T(((1 / x) * y) \ y,K(y,1 / x)) = K(y,x \ 1) * L(x,x,x * (x \ y))
    ]]></literal>
    <justification jstring="[para(2211(a,1),16485(a,2,2))].">
      <j1 rule="para" parents="2211 16485"/>
    </justification>
  </clause>

  <clause id="16487">
    <literal><![CDATA[
      T(((1 / x) * y) \ y,K(y,1 / x)) = K(y,x \ 1) * L(x,x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),16486(a,2,2,3))].">
      <j1 rule="para" parents="10 16486"/>
    </justification>
  </clause>

  <clause id="16488">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(u,K(((y \ z) \ 1) / x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8108,a,b,14635,a),flip(a)].">
      <j1 rule="hyper" parents="373 8108 14635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16489">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x / z,(x / z) \ (T(x,y) / z)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(14825(a,1),14880(a,2,1))].">
      <j1 rule="para" parents="14825 14880"/>
    </justification>
  </clause>

  <clause id="16490">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x / z,K(x,T(y,z))) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(14845(a,1),16489(a,1,2,2))].">
      <j1 rule="para" parents="14845 16489"/>
    </justification>
  </clause>

  <clause id="16491">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(x / z,T(y,z))) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(8108(a,1),16490(a,1,2))].">
      <j1 rule="para" parents="8108 16490"/>
    </justification>
  </clause>

  <clause id="16492">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(z \ x,y)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(7917(a,1),16491(a,1,2,2))].">
      <j1 rule="para" parents="7917 16491"/>
    </justification>
  </clause>

  <clause id="16493">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(z,y)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(8989(a,1),16492(a,1,2))].">
      <j1 rule="para" parents="8989 16492"/>
    </justification>
  </clause>

  <clause id="16494">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(8126(a,1),16493(a,1,2))].">
      <j1 rule="para" parents="8126 16493"/>
    </justification>
  </clause>

  <clause id="16495">
    <literal><![CDATA[
      T(x,K(y,y \ z) \ ((T(y,z) \ z) / u)) = T(x,(((y \ T(z,y)) \ z) \ z) / u)
    ]]></literal>
    <justification jstring="[para(8548(a,1),14902(a,1,2,1))].">
      <j1 rule="para" parents="8548 14902"/>
    </justification>
  </clause>

  <clause id="16497">
    <literal><![CDATA[
      (((x \ 1) \ y) / z) \ ((x \ 1) \ 1) = ((x / (x \ 1)) * ((x \ y) / z)) \ x
    ]]></literal>
    <justification jstring="[para(1131(a,1),15124(a,1,2))].">
      <j1 rule="para" parents="1131 15124"/>
    </justification>
  </clause>

  <clause id="16498">
    <literal><![CDATA[
      (((x \ 1) \ y) / z) \ ((x \ 1) \ 1) = (x * ((x \ 1) \ ((x \ y) / z))) \ x
    ]]></literal>
    <justification jstring="[para(1177(a,1),16497(a,2,1))].">
      <j1 rule="para" parents="1177 16497"/>
    </justification>
  </clause>

  <clause id="16499">
    <literal><![CDATA[
      (((x \ 1) \ y) / z) \ ((x \ 1) \ 1) = (x * (x \ (((1 / x) \ y) / z))) \ x
    ]]></literal>
    <justification jstring="[para(7299(a,1),16498(a,2,1,2))].">
      <j1 rule="para" parents="7299 16498"/>
    </justification>
  </clause>

  <clause id="16500">
    <literal><![CDATA[
      (((x \ 1) \ y) / z) \ ((x \ 1) \ 1) = (((1 / x) \ y) / z) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,174,a(flip),b,16499,a),flip(a)].">
      <j1 rule="hyper" parents="373 174 16499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16502">
    <literal><![CDATA[
      K(x * y,L(z,u,u \ 1)) = (x \ T(y * x,z)) * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(15134,a,14410,a),flip(a)].">
      <j1 rule="hyper" parents="15134 14410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16503">
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(15134,a,14393,a)].">
      <j1 rule="hyper" parents="15134 14393"/>
    </justification>
  </clause>

  <clause id="16504">
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(16502(a,1),7416(a,1))].">
      <j1 rule="para" parents="16502 7416"/>
    </justification>
  </clause>

  <clause id="16505">
    <literal><![CDATA[
      L(x * K(x * y,y),y,y) \ (x * (1 / y)) = L(y \ K(x,y \ 1),y,(1 / y) * x)
    ]]></literal>
    <justification jstring="[para(6041(a,1),15143(a,2,1,2))].">
      <j1 rule="para" parents="6041 15143"/>
    </justification>
  </clause>

  <clause id="16506">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x / y) * R((x / y) \ 1,z,y / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1781,a(flip),b,15271,a),flip(a)].">
      <j1 rule="hyper" parents="373 1781 15271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16507">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,y / x)) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,2863,a(flip),b,16506,a),flip(a)].">
      <j1 rule="hyper" parents="373 2863 16506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16508">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(10113(a,1),16507(a,2,1,2))].">
      <j1 rule="para" parents="10113 16507"/>
    </justification>
  </clause>

  <clause id="16509">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11362,a(flip),b,16508,a),flip(a)].">
      <j1 rule="hyper" parents="373 11362 16508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16510">
    <literal><![CDATA[
      T(a(1 / (x / y),z,(x / y) \ 1),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(5342(a,1),16509(a,1,1))].">
      <j1 rule="para" parents="5342 16509"/>
    </justification>
  </clause>

  <clause id="16511">
    <literal><![CDATA[
      a((x / y) \ 1,z,(x / y) \ 1) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(14047,a,16510,a)].">
      <j1 rule="hyper" parents="14047 16510"/>
    </justification>
  </clause>

  <clause id="16512">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12286,a,b,16511,a)].">
      <j1 rule="hyper" parents="64 12286 16511"/>
    </justification>
  </clause>

  <clause id="16513">
    <literal><![CDATA[
      K(x,L(T(y * z,y) \ u,y,z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(13610,a,15642,a)].">
      <j1 rule="hyper" parents="13610 15642"/>
    </justification>
  </clause>

  <clause id="16514">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y \ 1)) = K(x,R(z,y,y \ 1) \ ((y \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(13911,a,16513,a)].">
      <j1 rule="hyper" parents="13911 16513"/>
    </justification>
  </clause>

  <clause id="16515">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ ((z \ 1) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16158,a(flip),b,16514,a),flip(a)].">
      <j1 rule="hyper" parents="64 16158 16514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16516">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * u)) = K(x,(y / z) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(675(a,1),16515(a,1,2,1))].">
      <j1 rule="para" parents="675 16515"/>
    </justification>
  </clause>

  <clause id="16517">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * (z * u))) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),16516(a,2,2,2))].">
      <j1 rule="para" parents="9 16516"/>
    </justification>
  </clause>

  <clause id="16518">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ L(u,z,z \ 1)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7035,a(flip),b,16517,a)].">
      <j1 rule="hyper" parents="64 7035 16517"/>
    </justification>
  </clause>

  <clause id="16519">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,((y / u) * K(y,y \ z)) \ w)
    ]]></literal>
    <justification jstring="[para(6878(a,1),15799(a,2,2,1))].">
      <j1 rule="para" parents="6878 15799"/>
    </justification>
  </clause>

  <clause id="16520">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * ((z / w) * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(6878(a,1),15855(a,2,2,2))].">
      <j1 rule="para" parents="6878 15855"/>
    </justification>
  </clause>

  <clause id="16521">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * (((1 / z) * u) * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(14414(a,1),15861(a,2,2,2,2))].">
      <j1 rule="para" parents="14414 15861"/>
    </justification>
  </clause>

  <clause id="16522">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * ((1 / z) * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(10173(a,1),16521(a,2,2,2))].">
      <j1 rule="para" parents="10173 16521"/>
    </justification>
  </clause>

  <clause id="16523">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * ((((1 / u) * z) \ z) \ z))
    ]]></literal>
    <justification jstring="[para(1635(a,1),16522(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1635 16522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16524">
    <literal><![CDATA[
      K(x,y * T((1 / z) * u,u)) = K(x,y * L(u / z,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,13346,a(flip),b,16523,a)].">
      <j1 rule="hyper" parents="373 13346 16523"/>
    </justification>
  </clause>

  <clause id="16525">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,L(u,y,x))) = y * T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(10324(a,1),16124(a,1,1))].">
      <j1 rule="para" parents="10324 16124"/>
    </justification>
  </clause>

  <clause id="16526">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(u,L(z,y,x))) = y * T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(8153(a,1),16525(a,1,1,2))].">
      <j1 rule="para" parents="8153 16525"/>
    </justification>
  </clause>

  <clause id="16527">
    <literal><![CDATA[
      x \ ((y * T(x,K(z,u))) * K(z,K(u,y * x))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[hyper(12793,a,16526,a)].">
      <j1 rule="hyper" parents="12793 16526"/>
    </justification>
  </clause>

  <clause id="16528">
    <literal><![CDATA[
      x \ ((y * T(x,K(z,u))) * (K(u,T(z,y * x)) * K(z,u))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(8326(a,2),16527(a,1,2,2))].">
      <j1 rule="para" parents="8326 16527"/>
    </justification>
  </clause>

  <clause id="16529">
    <literal><![CDATA[
      x \ (((y * T(x,K(z,u))) * K(z,u)) * K(u,T(z,y * x))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(10335(a,2),16528(a,1,2))].">
      <j1 rule="para" parents="10335 16528"/>
    </justification>
  </clause>

  <clause id="16530">
    <literal><![CDATA[
      x \ (((y * T(x,K(z,u))) * K(z,u)) * K(u,T(z,y * T(x,K(z,w))))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(8613(a,2),16529(a,1,2,2,2))].">
      <j1 rule="para" parents="8613 16529"/>
    </justification>
  </clause>

  <clause id="16531">
    <literal><![CDATA[
      a(x,y \ z,K(u,L(y,(y \ z) * u,y \ 1))) = K(x,((y \ z) * u) \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15505,a,b,16168,a)].">
      <j1 rule="hyper" parents="64 15505 16168"/>
    </justification>
  </clause>

  <clause id="16532">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(z,u) \ ((u \ z) * (y / (u \ z))))
    ]]></literal>
    <justification jstring="[para(10(a,1),16425(a,1,2,1,2))].">
      <j1 rule="para" parents="10 16425"/>
    </justification>
  </clause>

  <clause id="16533">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(u,K((y \ z) \ (x \ 1),y))
    ]]></literal>
    <justification jstring="[para(14680(a,1),16488(a,2,2))].">
      <j1 rule="para" parents="14680 16488"/>
    </justification>
  </clause>

  <clause id="16534">
    <literal><![CDATA[
      L(x * K(x * y,y),y,y) \ (x * (1 / y)) = L(y \ K(x,y \ 1),y,y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2186,a(flip),b,16505,a),flip(a)].">
      <j1 rule="hyper" parents="373 2186 16505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16535">
    <literal><![CDATA[
      a(x,y \ z,K(u,L(y,(y \ z) * u,1))) = K(x,((y \ z) * u) \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[para(15511(a,1),16531(a,1,3))].">
      <j1 rule="para" parents="15511 16531"/>
    </justification>
  </clause>

  <clause id="16536">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,y \ z,K(u,y))
    ]]></literal>
    <justification jstring="[para(621(a,1),16535(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="621 16535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16537">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,12154,a(flip),b,16536,a),flip(a)].">
      <j1 rule="hyper" parents="373 12154 16536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16538">
    <literal><![CDATA[
      K(x,(y / (y / ((z \ u) * y))) \ (z \ (u * ((((z \ u) * y) \ y) * ((z \ u) * y))))) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[para(10247(a,1),16537(a,1,2,1))].">
      <j1 rule="para" parents="10247 16537"/>
    </justification>
  </clause>

  <clause id="16539">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(u,K(z \ (y * (x \ 1)),y))
    ]]></literal>
    <justification jstring="[para(7381(a,1),16533(a,2,2))].">
      <j1 rule="para" parents="7381 16533"/>
    </justification>
  </clause>

  <clause id="16540">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(y,K(u,z \ (y * (x \ 1))))
    ]]></literal>
    <justification jstring="[hyper(373,a,8110,a(flip),b,16539,a),flip(a)].">
      <j1 rule="hyper" parents="373 8110 16539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16541">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(y,K(u,z \ (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,11276,a(flip),b,16540,a),flip(a)].">
      <j1 rule="hyper" parents="373 11276 16540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16542">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,L(x,y,y \ 1)) = K((1 / y) \ ((y * x) \ z),x)
    ]]></literal>
    <justification jstring="[hyper(14781,a,14715,a),flip(a)].">
      <j1 rule="hyper" parents="14781 14715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16544">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,L(x,y,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * ((y * x) \ z),x) = u
    ]]></literal>
    <justification jstring="[para(16542(a,2),14764(a,1))].">
      <j1 rule="para" parents="16542 14764"/>
    </justification>
  </clause>

  <clause id="16545">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ z,R(x,y,y \ 1)) = K((y \ 1) \ ((x * y) \ z),x)
    ]]></literal>
    <justification jstring="[hyper(14776,a,14717,a),flip(a)].">
      <j1 rule="hyper" parents="14776 14717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16547">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ z,R(x,y,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * ((x * y) \ z),x) = u
    ]]></literal>
    <justification jstring="[para(16545(a,2),14763(a,1))].">
      <j1 rule="para" parents="16545 14763"/>
    </justification>
  </clause>

  <clause id="16548">
    <literal><![CDATA[
      (x * K(y,z)) / a(x / (1 / u),u \ 1,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(5355(a,1),14773(a,1,2))].">
      <j1 rule="para" parents="5355 14773"/>
    </justification>
  </clause>

  <clause id="16549">
    <literal><![CDATA[
      x * (((1 / x) \ 1) * (K(1 / x,(1 / x) \ 1) / y)) = L(((1 / x) \ x) / y,x,x)
    ]]></literal>
    <justification jstring="[para(1448(a,1),14923(a,2,1))].">
      <j1 rule="para" parents="1448 14923"/>
    </justification>
  </clause>

  <clause id="16550">
    <literal><![CDATA[
      x * (x * (K(1 / x,(1 / x) \ 1) / y)) = L(((1 / x) \ x) / y,x,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),16549(a,1,2,1))].">
      <j1 rule="para" parents="82 16549"/>
    </justification>
  </clause>

  <clause id="16552">
    <literal><![CDATA[
      x * (x * (K(x \ 1,x) / y)) = L(((1 / x) \ x) / y,x,x)
    ]]></literal>
    <justification jstring="[para(1731(a,1),16550(a,1,2,2,1))].">
      <j1 rule="para" parents="1731 16550"/>
    </justification>
  </clause>

  <clause id="16553">
    <literal><![CDATA[
      L(((1 / x) \ x) / y,x,x) = x * (L(x,x,x) * (1 / y))
    ]]></literal>
    <justification jstring="[para(14910(a,1),16552(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14910 16552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16554">
    <literal><![CDATA[
      (x * y) \ ((x * R(x,y,y \ x)) / (x * y)) = T(x * y,y * y) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(15260(a,1),15562(a,2,1))].">
      <j1 rule="para" parents="15260 15562"/>
    </justification>
  </clause>

  <clause id="16555">
    <literal><![CDATA[
      (x * y) \ (((x * y) * (y \ x)) / (x * y)) = T(x * y,y * y) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(995(a,1),16554(a,1,2,1))].">
      <j1 rule="para" parents="995 16554"/>
    </justification>
  </clause>

  <clause id="16556">
    <literal><![CDATA[
      (x * y) \ ((y \ x) * K(x * y,y \ x)) = T(x * y,y * y) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5889,a(flip),b,16555,a)].">
      <j1 rule="hyper" parents="64 5889 16555"/>
    </justification>
  </clause>

  <clause id="16557">
    <literal><![CDATA[
      (L(x,y,z) * (u * K(x,L(w,y,z)))) / L(T(x,w),y,z) = (R(x,y,z) * u) / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16465,a(flip),b,15600,a)].">
      <j1 rule="hyper" parents="64 16465 15600"/>
    </justification>
  </clause>

  <clause id="16558">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,T(y,z),z \ 1)) = K(x,(y * (1 / T(z,y))) / ((u \ 1) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(1648(a,1),15686(a,1,2))].">
      <j1 rule="para" parents="1648 15686"/>
    </justification>
  </clause>

  <clause id="16559">
    <literal><![CDATA[
      K(x,T(y,T(z,u) \ w) * (T(z,u) \ w)) = K(x,((u / (u / z)) \ w) * y)
    ]]></literal>
    <justification jstring="[hyper(15836,a,16352,a),flip(a)].">
      <j1 rule="hyper" parents="15836 16352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16560">
    <literal><![CDATA[
      K(x,((y / (y / z)) \ u) * w) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(11231,a,16559,a),flip(a)].">
      <j1 rule="hyper" parents="11231 16559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16561">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ (z * (x * y)),R(x,y,y \ 1)) = K(z / (y \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,14400,a(flip),b,15973,a),flip(a)].">
      <j1 rule="hyper" parents="373 14400 15973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16563">
    <literal><![CDATA[
      K(R(x,y,y \ 1) \ (z * (x * y)),R(x,y,y \ 1)) = K(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,14681,a(flip),b,16561,a),flip(a)].">
      <j1 rule="hyper" parents="373 14681 16561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16564">
    <literal><![CDATA[
      K(x * ((y * x) \ (z * (y * x))),y) = K(z * x,y)
    ]]></literal>
    <justification jstring="[hyper(16547,a,16563,a)].">
      <j1 rule="hyper" parents="16547 16563"/>
    </justification>
  </clause>

  <clause id="16565">
    <literal><![CDATA[
      K(x * T(y,z * x),z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),16564(a,1,1,2))].">
      <j1 rule="para" parents="22 16564"/>
    </justification>
  </clause>

  <clause id="16566">
    <literal><![CDATA[
      K(T(x,y * z) * z,y) = K(z * x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15863,a(flip),b,16565,a),flip(a)].">
      <j1 rule="hyper" parents="64 15863 16565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16567">
    <literal><![CDATA[
      K(T((x \ y) \ z,u * K(x \ y,x)) * K(x \ y,x),u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(6292(a,1),16566(a,2,1))].">
      <j1 rule="para" parents="6292 16566"/>
    </justification>
  </clause>

  <clause id="16568">
    <literal><![CDATA[
      K(x,y / (z \ a(u \ 1,u,z))) = K(x,y / (1 / L(z,u,u \ 1)))
    ]]></literal>
    <justification jstring="[para(14434(a,1),16347(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14434 16347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16570">
    <literal><![CDATA[
      (R(x,y,z) * u) / R(x,y,z) = (L(x,y,z) * u) / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12107,a(flip),b,16557,a),flip(a)].">
      <j1 rule="hyper" parents="64 12107 16557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16571">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / ((u \ 1) * (1 / z))) = K(x,L(T(y,z) * u,y,z \ 1))
    ]]></literal>
    <justification jstring="[para(14218(a,1),16558(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14218 16558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16572">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / ((u \ 1) * (z \ 1))) = K(x,L(T(y,z) * u,y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,7105,a(flip),b,16571,a)].">
      <j1 rule="hyper" parents="64 7105 16571"/>
    </justification>
  </clause>

  <clause id="16573">
    <literal><![CDATA[
      ((x * ((y * (x / y)) \ y)) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(15061(a,1),14618(a,1,1,1,2))].">
      <j1 rule="para" parents="15061 14618"/>
    </justification>
  </clause>

  <clause id="16574">
    <literal><![CDATA[
      x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(6402(a,1),16573(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6402 16573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16575">
    <literal><![CDATA[
      x / (x * ((1 / ((x / ((x \ y) \ 1)) / x)) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(3949(a,2),16574(a,1,2,2,1))].">
      <j1 rule="para" parents="3949 16574"/>
    </justification>
  </clause>

  <clause id="16576">
    <literal><![CDATA[
      x / (x * ((x / ((x \ y) \ 1)) / x)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),16575(a,1,2,2))].">
      <j1 rule="para" parents="82 16575"/>
    </justification>
  </clause>

  <clause id="16578">
    <literal><![CDATA[
      x / (x / ((y / x) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(9496(a,1),16576(a,1,2))].">
      <j1 rule="para" parents="9496 16576"/>
    </justification>
  </clause>

  <clause id="16579">
    <literal><![CDATA[
      1 / (x / (x / ((y / x) \ 1))) = (x / (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(225,a,16578,a,b,xx)].">
      <j1 rule="hyper" parents="225 16578"/>
    </justification>
  </clause>

  <clause id="16580">
    <literal><![CDATA[
      T(x * y,z) \ T(x * K(y * x,z),y) = T(y * x,z) \ (x * K(y * x,z))
    ]]></literal>
    <justification jstring="[para(14646(a,1),14655(a,1,1))].">
      <j1 rule="para" parents="14646 14655"/>
    </justification>
  </clause>

  <clause id="16581">
    <literal><![CDATA[
      T(x * y,z) \ (y \ T(x * y,z)) = T(y * x,z) \ (x * K(y * x,z))
    ]]></literal>
    <justification jstring="[para(14496(a,1),16580(a,1,2))].">
      <j1 rule="para" parents="14496 16580"/>
    </justification>
  </clause>

  <clause id="16582">
    <literal><![CDATA[
      T((x * y) \ y,K(x * y,z)) = T(y * x,z) \ (x \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7132,a(flip),b,16581,a)].">
      <j1 rule="hyper" parents="373 7132 16581"/>
    </justification>
  </clause>

  <clause id="16583">
    <literal><![CDATA[
      T(x * y,z) \ (y \ T(x * y,z)) = T(y * x,z) \ (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(14494(a,2),16581(a,2,2))].">
      <j1 rule="para" parents="14494 16581"/>
    </justification>
  </clause>

  <clause id="16584">
    <literal><![CDATA[
      T((x * y) \ y,K(z,x * y)) = T(y * x,z) \ (x \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(8184,a,16582,a)].">
      <j1 rule="hyper" parents="8184 16582"/>
    </justification>
  </clause>

  <clause id="16585">
    <literal><![CDATA[
      T(x * y,z) \ (y \ T(x * y,z)) = (y * x) \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8983,a(flip),b,16584,a),flip(a)].">
      <j1 rule="hyper" parents="64 8983 16584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16586">
    <literal><![CDATA[
      T(x * y,z) \ (x \ T(x * y,z)) = (x * y) \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16585,a(flip),b,16583,a),flip(a)].">
      <j1 rule="hyper" parents="64 16585 16583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16587">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,((z \ u) / w) \ (u / z))) = K(x,L(y,u / z,w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(13065(a,1),15543(a,2,2))].">
      <j1 rule="para" parents="13065 15543"/>
    </justification>
  </clause>

  <clause id="16588">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,w * K(z,z \ u))) = K(x,L(y,u / z,w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(15104(a,1),16587(a,1,2,3))].">
      <j1 rule="para" parents="15104 16587"/>
    </justification>
  </clause>

  <clause id="16589">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(((x \ z) * x) / (y * x),u) = w
    ]]></literal>
    <justification jstring="[para(15701(a,2),6945(a,1))].">
      <j1 rule="para" parents="15701 6945"/>
    </justification>
  </clause>

  <clause id="16590">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = (((w \ v5) \ v5) * K(u,T(z,x) / (y * x))) \ T(w,w \ v5)
    ]]></literal>
    <justification jstring="[para(13457(a,1),15701(a,2,1,2))].">
      <j1 rule="para" parents="13457 15701"/>
    </justification>
  </clause>

  <clause id="16591">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(T(z,x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6883,a(flip),b,16590,a),flip(a)].">
      <j1 rule="hyper" parents="373 6883 16590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16592">
    <literal><![CDATA[
      K((x * ((y \ 1) / z)) \ u,T(w,z * y)) = K(T(u,x) / (((y \ 1) / z) * x),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14611,a(flip),b,16591,a)].">
      <j1 rule="hyper" parents="64 14611 16591"/>
    </justification>
  </clause>

  <clause id="16593">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,T(u,y * x)) = K(T(z,y) / (((x \ 1) / y) * y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15927,a(flip),b,16592,a)].">
      <j1 rule="hyper" parents="64 15927 16592"/>
    </justification>
  </clause>

  <clause id="16594">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * a(x,z,K(y,u)) = (z * K(x,T(y,z))) * R(u,z,K(x,T(y,z)))
    ]]></literal>
    <justification jstring="[para(15316(a,1),15986(a,1,2))].">
      <j1 rule="para" parents="15316 15986"/>
    </justification>
  </clause>

  <clause id="16595">
    <literal><![CDATA[
      (x * K(y,T(z,x))) * R(u,x,K(y,T(z,x))) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15703,a(flip),b,16594,a),flip(a)].">
      <j1 rule="hyper" parents="64 15703 16594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16596">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,T(y,z))) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(7879(a,1),16595(a,1,1))].">
      <j1 rule="para" parents="7879 16595"/>
    </justification>
  </clause>

  <clause id="16597">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,y)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(10211(a,1),16596(a,1,2))].">
      <j1 rule="para" parents="10211 16596"/>
    </justification>
  </clause>

  <clause id="16598">
    <literal><![CDATA[
      R(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(606,a,16597,a),flip(a)].">
      <j1 rule="hyper" parents="606 16597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16599">
    <literal><![CDATA[
      L((x * K(y,z)) / u,u,K(z,y)) = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6912,a,16598,a),flip(a)].">
      <j1 rule="hyper" parents="6912 16598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16600">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = (y * K(z,u)) / ((x \ y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(1264,a,16598,a),flip(a)].">
      <j1 rule="hyper" parents="1264 16598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16601">
    <literal><![CDATA[
      L(x / y,y,K(z,u)) = (x * K(z,u)) / (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(1084,a,16598,a),flip(a)].">
      <j1 rule="hyper" parents="1084 16598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16602">
    <literal><![CDATA[
      ((x * (y * z)) * K(z,u)) / (y * T(z,u)) = L(x,y * z,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,6922,a,b,16598,a)].">
      <j1 rule="hyper" parents="64 6922 16598"/>
    </justification>
  </clause>

  <clause id="16603">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15982,a(flip),b,16598,a),flip(a)].">
      <j1 rule="hyper" parents="64 15982 16598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16604">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (y * K(z,u)) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,16598,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 16598 20"/>
    </justification>
  </clause>

  <clause id="16605">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) \ (y * K(z,u)) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(16598(a,1),649(a,1,1))].">
      <j1 rule="para" parents="16598 649"/>
    </justification>
  </clause>

  <clause id="16606">
    <literal><![CDATA[
      L(R(x,y,z),y * z,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(16598(a,1),9563(a,1))].">
      <j1 rule="para" parents="16598 9563"/>
    </justification>
  </clause>

  <clause id="16607">
    <literal><![CDATA[
      R(x,y,a(z,u,K(w,v5))) = L(x,y,K(a(z,u,w),v5))
    ]]></literal>
    <justification jstring="[para(13977(a,2),16598(a,1,3))].">
      <j1 rule="para" parents="13977 16598"/>
    </justification>
  </clause>

  <clause id="16608">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,15495,a,b,16603,a)].">
      <j1 rule="hyper" parents="373 15495 16603"/>
    </justification>
  </clause>

  <clause id="16609">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15332,a,b,16603,a)].">
      <j1 rule="hyper" parents="373 15332 16603"/>
    </justification>
  </clause>

  <clause id="16610">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15306,a,b,16603,a)].">
      <j1 rule="hyper" parents="373 15306 16603"/>
    </justification>
  </clause>

  <clause id="16611">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15305,a,b,16603,a)].">
      <j1 rule="hyper" parents="373 15305 16603"/>
    </justification>
  </clause>

  <clause id="16612">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13809,a,b,16603,a)].">
      <j1 rule="hyper" parents="373 13809 16603"/>
    </justification>
  </clause>

  <clause id="16613">
    <literal><![CDATA[
      L(x * y,z,K(u,y)) = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15719,a(flip),b,16603,a),flip(a)].">
      <j1 rule="hyper" parents="373 15719 16603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16614">
    <literal><![CDATA[
      L(1 / x,y,K(z,u)) = a(x,y,K(u,z)) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,15504,a(flip),b,16603,a),flip(a)].">
      <j1 rule="hyper" parents="373 15504 16603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16615">
    <literal><![CDATA[
      L(x,y \ z,K(y,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,15495,a(flip),b,16603,a),flip(a)].">
      <j1 rule="hyper" parents="373 15495 16603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16616">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = T(T(x,a(w,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,15493,a(flip),b,16603,a),flip(a)].">
      <j1 rule="hyper" parents="373 15493 16603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16617">
    <literal><![CDATA[
      L(T(x,y),z,K(u,y)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15395,a(flip),b,16603,a),flip(a)].">
      <j1 rule="hyper" parents="373 15395 16603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16618">
    <literal><![CDATA[
      L(a(x,y,y \ 1),z,K(u,w)) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,13987,a(flip),b,16603,a),flip(a)].">
      <j1 rule="hyper" parents="373 13987 16603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16619">
    <literal><![CDATA[
      L(x / a(y,z,u),z,K(u,y)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,117,a(flip),b,16603,a),flip(a)].">
      <j1 rule="hyper" parents="373 117 16603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16620">
    <literal><![CDATA[
      (x / y) * L(y,z,K(u,w)) = x * K(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,16603,a,b,6844,a)].">
      <j1 rule="hyper" parents="145 16603 6844"/>
    </justification>
  </clause>

  <clause id="16621">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(139,a,16603,a,b,15376,a)].">
      <j1 rule="hyper" parents="139 16603 15376"/>
    </justification>
  </clause>

  <clause id="16622">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,16603,a,b,13961,a)].">
      <j1 rule="hyper" parents="139 16603 13961"/>
    </justification>
  </clause>

  <clause id="16623">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),a(z,y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,15386,a(flip),b,16603,a),flip(a)].">
      <j1 rule="hyper" parents="42 15386 16603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16624">
    <literal><![CDATA[
      L(x,y,K(L(z,u,x),w)) = T(x,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(13993,a,16603,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13993 16603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16625">
    <literal><![CDATA[
      L(x / a(y,z,u),z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(16603(a,2),467(a,1))].">
      <j1 rule="para" parents="16603 467"/>
    </justification>
  </clause>

  <clause id="16626">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(16603(a,1),6105(a,1))].">
      <j1 rule="para" parents="16603 6105"/>
    </justification>
  </clause>

  <clause id="16627">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * L(y,u,K(w,z))
    ]]></literal>
    <justification jstring="[para(16603(a,2),13960(a,2,2))].">
      <j1 rule="para" parents="16603 13960"/>
    </justification>
  </clause>

  <clause id="16628">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),u) = T(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(16603(a,2),15385(a,1,1))].">
      <j1 rule="para" parents="16603 15385"/>
    </justification>
  </clause>

  <clause id="16629">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,y)) = x \ L(y,u,K(z,w))
    ]]></literal>
    <justification jstring="[para(16603(a,2),15352(a,2,2))].">
      <j1 rule="para" parents="16603 15352"/>
    </justification>
  </clause>

  <clause id="16630">
    <literal><![CDATA[
      L(x,y,K(z,u)) / u = T(x / u,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(16603(a,2),15705(a,1,1))].">
      <j1 rule="para" parents="16603 15705"/>
    </justification>
  </clause>

  <clause id="16631">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),z,K(y,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,15395,a,b,16623,a),flip(a)].">
      <j1 rule="hyper" parents="41 15395 16623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16632">
    <literal><![CDATA[
      L(x,y,K(z,u)) * a(z,y,u) = a(z,y,u) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,16623,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 16623 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16633">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(16608(a,1),15496(a,1))].">
      <j1 rule="para" parents="16608 15496"/>
    </justification>
  </clause>

  <clause id="16634">
    <literal><![CDATA[
      a(x,y,z) \ L(u,y,K(x,z)) = u / a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,16610,a(flip),b,15498,a(flip))].">
      <j1 rule="hyper" parents="139 16610 15498"/>
    </justification>
  </clause>

  <clause id="16635">
    <literal><![CDATA[
      L(x * L(x \ y,z,u),z,K(x \ y,u)) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(14970,a,16612,a),flip(a)].">
      <j1 rule="hyper" parents="14970 16612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16636">
    <literal><![CDATA[
      L(T(x,y),z,K(y,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(6105,a,16617,a)].">
      <j1 rule="hyper" parents="6105 16617"/>
    </justification>
  </clause>

  <clause id="16637">
    <literal><![CDATA[
      a(x,y,K(z,u)) != u \ w
    ]]></literal>
    <literal><![CDATA[
      L(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(16621(a,1),48(a,1))].">
      <j1 rule="para" parents="16621 48"/>
    </justification>
  </clause>

  <clause id="16638">
    <literal><![CDATA[
      L(T(T(x,L(y,z,u)),y),z,K(y,u)) \ w = K(L(y,z,u),x) * (T(x,L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(16636(a,2),6299(a,2,1)),flip(a)].">
      <j1 rule="para" parents="16636 6299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16639">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,x))) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(10567(a,1),16624(a,1,3))].">
      <j1 rule="para" parents="10567 16624"/>
    </justification>
  </clause>

  <clause id="16640">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(16626,a,16623,a)].">
      <j1 rule="hyper" parents="16626 16623"/>
    </justification>
  </clause>

  <clause id="16641">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(15376(a,2),16626(a,1))].">
      <j1 rule="para" parents="15376 16626"/>
    </justification>
  </clause>

  <clause id="16642">
    <literal><![CDATA[
      L((K(x,y) * z) \ u,z,K(y,x)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(7120,a,16640,a),flip(a)].">
      <j1 rule="hyper" parents="7120 16640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16643">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,x))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,16603,a,b,16639,a),flip(a)].">
      <j1 rule="hyper" parents="373 16603 16639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16644">
    <literal><![CDATA[
      L(x / y,z,K(u,y)) = L(x,z,K(u,y)) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,16603,a,b,16630,a)].">
      <j1 rule="hyper" parents="373 16603 16630"/>
    </justification>
  </clause>

  <clause id="16645">
    <literal><![CDATA[
      L(x * y,z,K(u,x)) = x * L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(38,a,1194,a(flip),b,16644,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 1194 16644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16646">
    <literal><![CDATA[
      K(x,y) \ L((z * K(x,L(y,z,a(u,w,v5)))) / a(u,w,v5),w,K(v5,u)) = T(a(u,w,v5) \ z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(493,a,16619,a,b,15549,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="493 16619 15549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16647">
    <literal><![CDATA[
      x / a(y,z,x) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[para(7772(a,1),16634(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7772 16634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16648">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(15332(a,1),16641(a,1))].">
      <j1 rule="para" parents="15332 16641"/>
    </justification>
  </clause>

  <clause id="16649">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(15449(a,2),16648(a,1))].">
      <j1 rule="para" parents="15449 16648"/>
    </justification>
  </clause>

  <clause id="16650">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15982(a,2),16648(a,1))].">
      <j1 rule="para" parents="15982 16648"/>
    </justification>
  </clause>

  <clause id="16651">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(16608(a,1),16648(a,1))].">
      <j1 rule="para" parents="16608 16648"/>
    </justification>
  </clause>

  <clause id="16652">
    <literal><![CDATA[
      L(x,y \ z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(16615(a,2),16648(a,1))].">
      <j1 rule="para" parents="16615 16648"/>
    </justification>
  </clause>

  <clause id="16653">
    <literal><![CDATA[
      R(x,y,a(z,u,K(w,v5))) = L(x,y,a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(13977(a,2),16607(a,2,3))].">
      <j1 rule="para" parents="13977 16607"/>
    </justification>
  </clause>

  <clause id="16654">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = T(L(x,z,K(u,w)),y)
    ]]></literal>
    <justification jstring="[para(16603(a,2),16616(a,2,1))].">
      <j1 rule="para" parents="16603 16616"/>
    </justification>
  </clause>

  <clause id="16655">
    <literal><![CDATA[
      (x / y) * L(y,z,K(u,w)) = x * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(15299(a,2),16620(a,2,2))].">
      <j1 rule="para" parents="15299 16620"/>
    </justification>
  </clause>

  <clause id="16656">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(162,a,16654,a(flip))].">
      <j1 rule="hyper" parents="162 16654"/>
    </justification>
  </clause>

  <clause id="16657">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),z,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(16654(a,2),11860(a,1))].">
      <j1 rule="para" parents="16654 11860"/>
    </justification>
  </clause>

  <clause id="16658">
    <literal><![CDATA[
      L(x,x \ y,a(z,u,K(w,v5))) = L(x,y,K(a(z,u,w),v5))
    ]]></literal>
    <justification jstring="[para(13977(a,2),16656(a,1,3))].">
      <j1 rule="para" parents="13977 16656"/>
    </justification>
  </clause>

  <clause id="16659">
    <literal><![CDATA[
      a(x,(y * K(z,u)) * L(w / y,y,K(z,u)),x) = a(x,w * K(z,u),x)
    ]]></literal>
    <justification jstring="[para(16601(a,2),13710(a,1,2,2))].">
      <j1 rule="para" parents="16601 13710"/>
    </justification>
  </clause>

  <clause id="16660">
    <literal><![CDATA[
      L(x,y,K(z,T(u,y))) * (K(z,u) * y) = (x * y) * K(z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(7893,a,16604,a)].">
      <j1 rule="hyper" parents="7893 16604"/>
    </justification>
  </clause>

  <clause id="16661">
    <literal><![CDATA[
      L(x,1 / T(y,z),K(y,u)) * (K(y,u) / T(y,z)) = (x * (1 / T(y,z))) * K(y,u)
    ]]></literal>
    <justification jstring="[para(8934(a,1),16604(a,1,2))].">
      <j1 rule="para" parents="8934 16604"/>
    </justification>
  </clause>

  <clause id="16662">
    <literal><![CDATA[
      (x * y) * K(z,y * x) = x * (y * K(z,y * x))
    ]]></literal>
    <justification jstring="[para(14372(a,1),16604(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14372 16604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16663">
    <literal><![CDATA[
      T(x * (y * K(z,y * x)),z) = T(x * y,K(z,y))
    ]]></literal>
    <justification jstring="[para(16662(a,1),11135(a,1,1))].">
      <j1 rule="para" parents="16662 11135"/>
    </justification>
  </clause>

  <clause id="16664">
    <literal><![CDATA[
      T(x * (y * K(z,y * x)),z) = T(x * y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8153,a,b,16663,a),flip(a)].">
      <j1 rule="hyper" parents="373 8153 16663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16665">
    <literal><![CDATA[
      x \ (K(y,z) * R(K(z,y) * x,u,u \ 1)) = L(a(K(z,y) * x,u,u \ 1),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(982(a,1),16642(a,1,1)),flip(a)].">
      <j1 rule="para" parents="982 16642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16666">
    <literal><![CDATA[
      L(x,x \ y,a(z,u,K(w,v5))) = L(x,y,a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(13977(a,2),16658(a,2,3))].">
      <j1 rule="para" parents="13977 16658"/>
    </justification>
  </clause>

  <clause id="16667">
    <literal><![CDATA[
      (x * K(y,z)) / ((u \ x) * K(y,z)) = L(u,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16656,a(flip),b,16600,a),flip(a)].">
      <j1 rule="hyper" parents="64 16656 16600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16668">
    <literal><![CDATA[
      (x * K(y,z)) / (L(x,u,u \ 1) * K(y,z)) = L(a(u \ 1,u,x),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5588(a,1),16667(a,1,2,1))].">
      <j1 rule="para" parents="5588 16667"/>
    </justification>
  </clause>

  <clause id="16669">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = (z \ (x \ y)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15976,a,16605,a)].">
      <j1 rule="hyper" parents="15976 16605"/>
    </justification>
  </clause>

  <clause id="16670">
    <literal><![CDATA[
      L(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(5963(a,1),16605(a,1,2))].">
      <j1 rule="para" parents="5963 16605"/>
    </justification>
  </clause>

  <clause id="16671">
    <literal><![CDATA[
      x \ (T(y,z) * K(u,y)) = (x \ T(y,z)) * K(u,y)
    ]]></literal>
    <justification jstring="[para(14380(a,1),16605(a,1,1))].">
      <j1 rule="para" parents="14380 16605"/>
    </justification>
  </clause>

  <clause id="16672">
    <literal><![CDATA[
      (x \ T(y,K(z,u))) * K(z,y) = x \ (y * K(z,T(y,u)))
    ]]></literal>
    <justification jstring="[para(8349(a,1),16671(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8349 16671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16673">
    <literal><![CDATA[
      x \ (K(y,z) * (y \ z)) = (x \ (y \ z)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14914,a(flip),b,16669,a)].">
      <j1 rule="hyper" parents="64 14914 16669"/>
    </justification>
  </clause>

  <clause id="16674">
    <literal><![CDATA[
      x \ (y \ ((y * z) / y)) = (x \ (y \ z)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6410,a,b,16673,a)].">
      <j1 rule="hyper" parents="64 6410 16673"/>
    </justification>
  </clause>

  <clause id="16675">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ ((x * y) / x)) = (z \ (x \ T(y,x))) * K(x,y)
    ]]></literal>
    <justification jstring="[para(15186(a,1),16674(a,2,1))].">
      <j1 rule="para" parents="15186 16674"/>
    </justification>
  </clause>

  <clause id="16676">
    <literal><![CDATA[
      x \ (y * K(z,T(y,u))) = (x \ y) * T(K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16188,a(flip),b,16672,a),flip(a)].">
      <j1 rule="hyper" parents="64 16188 16672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16677">
    <literal><![CDATA[
      x \ (y * K(z,T(y,u))) = (x \ y) * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,7878,a,b,16676,a),flip(a)].">
      <j1 rule="hyper" parents="373 7878 16676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16678">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = (y \ x) * K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15274,a,b,16677,a)].">
      <j1 rule="hyper" parents="64 15274 16677"/>
    </justification>
  </clause>

  <clause id="16679">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = K(z,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(11159,a,16678,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="11159 16678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16680">
    <literal><![CDATA[
      T(x * K(y,z),x \ z) = K(y,z) * ((x \ z) \ z)
    ]]></literal>
    <justification jstring="[para(79(a,1),16679(a,1,1,1))].">
      <j1 rule="para" parents="79 16679"/>
    </justification>
  </clause>

  <clause id="16681">
    <literal><![CDATA[
      ((x * (T(y * z,x) / x)) * K(z,u)) / (y * T(z,u)) = L(a(x,x \ (y * z),x),y * z,K(z,u))
    ]]></literal>
    <justification jstring="[para(11379(a,1),16602(a,1,1,1))].">
      <j1 rule="para" parents="11379 16602"/>
    </justification>
  </clause>

  <clause id="16682">
    <literal><![CDATA[
      (L(K(x,T(y,z)) \ z,K(x,T(y,z)),K(x,T(y,z))) \ L(K(x,T(y,z)) \ (z * u),K(x,T(y,z)),K(x,T(y,z)))) * (K(x,y) * z) = (u * z) * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(2710(a,2),16660(a,1,1))].">
      <j1 rule="para" parents="2710 16660"/>
    </justification>
  </clause>

  <clause id="16683">
    <literal><![CDATA[
      (x \ (y \ T(z,y))) * K(y,z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14724,a(flip),b,16675,a),flip(a)].">
      <j1 rule="hyper" parents="64 14724 16675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16684">
    <literal><![CDATA[
      (x \ (y \ z)) * K(z,y) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6897,a,16683,a)].">
      <j1 rule="hyper" parents="6897 16683"/>
    </justification>
  </clause>

  <clause id="16685">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) * K(u,w))) = K(x,y * (z \ (u \ T(w,u))))
    ]]></literal>
    <justification jstring="[para(16684(a,1),16333(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16684 16333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16686">
    <literal><![CDATA[
      K(x,y * (z \ (u \ T(w,u)))) = K(x,y * (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15109,a(flip),b,16685,a),flip(a)].">
      <j1 rule="hyper" parents="64 15109 16685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16687">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(12982(a,1),16670(a,1,1))].">
      <j1 rule="para" parents="12982 16670"/>
    </justification>
  </clause>

  <clause id="16688">
    <literal><![CDATA[
      (x \ y) * K(z,z \ y) = x \ (z * (y / z))
    ]]></literal>
    <justification jstring="[para(14379(a,1),16687(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14379 16687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16689">
    <literal><![CDATA[
      ((x \ y) * x) \ (y * (z / y)) = (K(x,x \ y) * z) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,13650,a(flip),b,16688,a),flip(a)].">
      <j1 rule="hyper" parents="64 13650 16688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16690">
    <literal><![CDATA[
      R(x,y,z) \ (u * ((x \ R(x,y,z)) / u)) = (x \ 1) * K(u,u \ (x \ R(x,y,z)))
    ]]></literal>
    <justification jstring="[para(1796(a,1),16688(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1796 16688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16691">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w / u)))) = K(x,y * ((z \ w) * K(u,w)))
    ]]></literal>
    <justification jstring="[para(16688(a,1),13551(a,1,2,2))].">
      <j1 rule="para" parents="16688 13551"/>
    </justification>
  </clause>

  <clause id="16692">
    <literal><![CDATA[
      K(x,y * ((z * y) \ (z * (u / z)))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(16688(a,1),15659(a,1,2,2))].">
      <j1 rule="para" parents="16688 15659"/>
    </justification>
  </clause>

  <clause id="16693">
    <literal><![CDATA[
      (K(x,x \ y) * z) / y = K(x,x \ y) * (z / y)
    ]]></literal>
    <justification jstring="[hyper(10961,a,16689,a),flip(a)].">
      <j1 rule="hyper" parents="10961 16689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16694">
    <literal><![CDATA[
      K(x,T(((y \ z) * y) \ u,z) * w) = K(x,(K(y,y \ z) * (u / z)) * w)
    ]]></literal>
    <justification jstring="[para(16693(a,1),15803(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16693 15803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16695">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w / u)))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,16344,a(flip),b,16691,a),flip(a)].">
      <j1 rule="hyper" parents="373 16344 16691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16696">
    <literal><![CDATA[
      K(x,y * (z \ T(u * w,w))) = K(x,y * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[para(11(a,1),16695(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 16695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16697">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,y * ((z * y) \ T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16695,a(flip),b,16692,a),flip(a)].">
      <j1 rule="hyper" parents="64 16695 16692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16698">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,K(y,u)) * (K(y,u) / T(y,z)) = (x * (1 / T(y,z))) * K(y,u)
    ]]></literal>
    <justification jstring="[para(5321(a,1),16661(a,1,1))].">
      <j1 rule="para" parents="5321 16661"/>
    </justification>
  </clause>

  <clause id="16699">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * K(y,u) = x * (K(y,u) / T(y,z))
    ]]></literal>
    <justification jstring="[para(11805(a,1),16698(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11805 16698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16700">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (K(y,z) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7754,a,b,16699,a)].">
      <j1 rule="hyper" parents="64 7754 16699"/>
    </justification>
  </clause>

  <clause id="16701">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(5757(a,1),16700(a,2,2))].">
      <j1 rule="para" parents="5757 16700"/>
    </justification>
  </clause>

  <clause id="16702">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2994,a,16701,a),flip(a)].">
      <j1 rule="hyper" parents="2994 16701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16704">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(7755,a,16702,a)].">
      <j1 rule="hyper" parents="7755 16702"/>
    </justification>
  </clause>

  <clause id="16705">
    <literal><![CDATA[
      T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = T(z,y) \ R(x,z \ 1,z)
    ]]></literal>
    <justification jstring="[para(16704(a,1),12330(a,2,2))].">
      <j1 rule="para" parents="16704 12330"/>
    </justification>
  </clause>

  <clause id="16706">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = (x * (1 / T(T(y,1),z))) \ x
    ]]></literal>
    <justification jstring="[para(16705(a,1),8754(a,1,2))].">
      <j1 rule="para" parents="16705 8754"/>
    </justification>
  </clause>

  <clause id="16708">
    <literal><![CDATA[
      (x * (1 / T(T(y,1),z))) \ x = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12305,a(flip),b,16706,a),flip(a)].">
      <j1 rule="hyper" parents="64 12305 16706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16709">
    <literal><![CDATA[
      T((x * (1 / y)) \ x,z) = (x * (1 / T(y,z))) \ x
    ]]></literal>
    <justification jstring="[para(372(a,1),16708(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="372 16708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16710">
    <literal><![CDATA[
      K(x,y \ (T((z * (1 / u)) \ z,w) \ z)) = K(x,y \ T(z * (1 / T(u,w)),z))
    ]]></literal>
    <justification jstring="[para(16709(a,2),16338(a,1,2,2,1))].">
      <j1 rule="para" parents="16709 16338"/>
    </justification>
  </clause>

  <clause id="16711">
    <literal><![CDATA[
      L(T(T(x,L(y,z,u)),y),z,K(y,u)) \ w = K(y,L(x,z,u)) * (T(x,L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(12093(a,1),16638(a,2,1))].">
      <j1 rule="para" parents="12093 16638"/>
    </justification>
  </clause>

  <clause id="16712">
    <literal><![CDATA[
      L(T(T(x,y),L(y,z,u)),z,K(y,u)) \ w = K(y,L(x,z,u)) * (T(x,L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(23(a,1),16711(a,1,1,1))].">
      <j1 rule="para" parents="23 16711"/>
    </justification>
  </clause>

  <clause id="16713">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (T(y,L(x,z,u)) \ w) = T(T(y,x),x) \ w
    ]]></literal>
    <justification jstring="[para(16631(a,1),16712(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16631 16712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16715">
    <literal><![CDATA[
      x \ (K(y,z) * R(K(z,y) * x,u,u \ 1)) = a(K(z,y) * x,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,16618,a(flip),b,16665,a),flip(a)].">
      <j1 rule="hyper" parents="373 16618 16665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16717">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u) / (z \ K(u,u \ (z \ 1)))) = K(x,T((z \ 1) \ y,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),16088(a,2,2,1,1))].">
      <j1 rule="para" parents="12 16088"/>
    </justification>
  </clause>

  <clause id="16718">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u) / (z \ K(u,u \ (z \ 1)))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,14420,a(flip),b,16717,a),flip(a)].">
      <j1 rule="hyper" parents="373 14420 16717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16720">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / (z \ K(u,u \ (z \ 1)))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(14571(a,1),16718(a,1,2,1))].">
      <j1 rule="para" parents="14571 16718"/>
    </justification>
  </clause>

  <clause id="16721">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / (u * ((z \ 1) / u))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(10166(a,1),16720(a,1,2,2))].">
      <j1 rule="para" parents="10166 16720"/>
    </justification>
  </clause>

  <clause id="16722">
    <literal><![CDATA[
      L(L(T(x,y) \ R(T(x,y),z,u),(x * y) \ y,z * u),x,y) = a((x * y) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),16121(a,1,1,1,2,1))].">
      <j1 rule="para" parents="22 16121"/>
    </justification>
  </clause>

  <clause id="16723">
    <literal><![CDATA[
      a(x,R(y,z,y) \ 1,L(R(y,z,y) \ 1,y,z)) = a(x,T(y * z,y) \ z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,13871,a(flip),b,16195,a),flip(a)].">
      <j1 rule="hyper" parents="373 13871 16195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16725">
    <literal><![CDATA[
      x \ (((y * T(x,K(z,u))) * K(z,u)) * ((K(z,u) * (y * T(x,K(z,w)))) \ (y * T(x,K(z,w))))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(7459(a,2),16530(a,1,2,2))].">
      <j1 rule="para" parents="7459 16530"/>
    </justification>
  </clause>

  <clause id="16726">
    <literal><![CDATA[
      L(T((x \ 1) \ 1,y) * K(z,T(x,y)),x,x \ z) = ((z / x) * ((1 / x) \ T(x,y))) / z
    ]]></literal>
    <justification jstring="[para(8(a,1),14793(a,1,1,2,2,1))].">
      <j1 rule="para" parents="8 14793"/>
    </justification>
  </clause>

  <clause id="16727">
    <literal><![CDATA[
      R(((x \ 1) * (x * x)) * K(x \ 1,y),x / (x * x),y) = (1 * y) / (y * (x / (x * x)))
    ]]></literal>
    <justification jstring="[para(6582(a,1),14811(a,1,1,2))].">
      <j1 rule="para" parents="6582 14811"/>
    </justification>
  </clause>

  <clause id="16728">
    <literal><![CDATA[
      R((x \ 1) * ((x * x) * K(x \ 1,y)),x / (x * x),y) = (1 * y) / (y * (x / (x * x)))
    ]]></literal>
    <justification jstring="[para(34(a,1),16727(a,1,1))].">
      <j1 rule="para" parents="34 16727"/>
    </justification>
  </clause>

  <clause id="16730">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = u / a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(15695(a,1),15427(a,2,2))].">
      <j1 rule="para" parents="15695 15427"/>
    </justification>
  </clause>

  <clause id="16732">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),z / u,u)) = T(x,(y * u) / ((u * (1 / u)) \ z))
    ]]></literal>
    <justification jstring="[para(5323(a,1),15635(a,1,2))].">
      <j1 rule="para" parents="5323 15635"/>
    </justification>
  </clause>

  <clause id="16733">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),u \ z,u)) = T(x,(y * u) / ((u * (1 / u)) \ z))
    ]]></literal>
    <justification jstring="[para(10996(a,1),16732(a,1,2))].">
      <j1 rule="para" parents="10996 16732"/>
    </justification>
  </clause>

  <clause id="16734">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),u \ z,u)) = T(x,(y * T(u,u \ 1)) / z)
    ]]></literal>
    <justification jstring="[para(5290(a,1),16733(a,2,2))].">
      <j1 rule="para" parents="5290 16733"/>
    </justification>
  </clause>

  <clause id="16735">
    <literal><![CDATA[
      T(x,L(y / (z / ((u \ 1) \ 1)),u \ z,u)) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5298,a(flip),b,16734,a),flip(a)].">
      <j1 rule="hyper" parents="373 5298 16734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16736">
    <literal><![CDATA[
      R((x \ (x \ y)) \ y,y,(x \ (x \ y)) \ y) = T((x \ (x \ y)) \ y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,13736,a(flip),b,15892,a)].">
      <j1 rule="hyper" parents="64 13736 15892"/>
    </justification>
  </clause>

  <clause id="16738">
    <literal><![CDATA[
      (x * y) \ (((z * x) * R((z * x) \ x,u,u)) * y) = a(R(T(z,x * y),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(2789(a,1),16029(a,1,2))].">
      <j1 rule="para" parents="2789 16029"/>
    </justification>
  </clause>

  <clause id="16739">
    <literal><![CDATA[
      (x * y) \ (((z \ R(z,u,u)) * x) * y) = a(R(T(z,x * y),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(2480(a,1),16738(a,1,2,1))].">
      <j1 rule="para" parents="2480 16738"/>
    </justification>
  </clause>

  <clause id="16740">
    <literal><![CDATA[
      (x * y) \ ((a(z,u,u) * x) * y) = a(R(T(z,x * y),x,y),u,u)
    ]]></literal>
    <justification jstring="[para(15987(a,1),16739(a,1,2,1,1))].">
      <j1 rule="para" parents="15987 16739"/>
    </justification>
  </clause>

  <clause id="16741">
    <literal><![CDATA[
      a(R(T(x,y * z),y,z),u,u) = R(T(a(x,u,u),y * z),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,796,a(flip),b,16740,a),flip(a)].">
      <j1 rule="hyper" parents="64 796 16740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16742">
    <literal><![CDATA[
      a(R(T(x,y * z),y,z),u,u) = R(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[para(13984(a,1),16741(a,2,1))].">
      <j1 rule="para" parents="13984 16741"/>
    </justification>
  </clause>

  <clause id="16744">
    <literal><![CDATA[
      (T(x,y) \ (1 / x)) * K(z,1 / (K(y,x) / x)) = T((1 / x) \ K(x,y),z) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(5760(a,2),14691(a,1,1,1))].">
      <j1 rule="para" parents="5760 14691"/>
    </justification>
  </clause>

  <clause id="16745">
    <literal><![CDATA[
      (x \ (1 / T(x,y))) * K(z,1 / (K(y,x) / x)) = T((1 / x) \ K(x,y),z) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(3978(a,1),16744(a,1,1))].">
      <j1 rule="para" parents="3978 16744"/>
    </justification>
  </clause>

  <clause id="16746">
    <literal><![CDATA[
      L(K(x,K(y,T(z,x))),u,u \ x) \ ((K(z,y) \ u) * (u \ x)) = L(K(y,T(z,x)),u,u \ x) * x
    ]]></literal>
    <justification jstring="[para(12059(a,2),15734(a,1,1))].">
      <j1 rule="para" parents="12059 15734"/>
    </justification>
  </clause>

  <clause id="16747">
    <literal><![CDATA[
      (K(x,y) * ((y * z) * x)) \ ((y * (K(x,y) * z)) * R(x,y,z)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(14096(a,1),16034(a,1,2,2))].">
      <j1 rule="para" parents="14096 16034"/>
    </justification>
  </clause>

  <clause id="16748">
    <literal><![CDATA[
      (K(x,y) * ((y * z) * x)) \ (K(x,y) * ((y * z) * R(x,y,z))) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(9087(a,1),16747(a,1,2))].">
      <j1 rule="para" parents="9087 16747"/>
    </justification>
  </clause>

  <clause id="16749">
    <literal><![CDATA[
      L(a(x,y,z),(y * z) * x,K(x,y)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(15985,a,16748,a)].">
      <j1 rule="hyper" parents="15985 16748"/>
    </justification>
  </clause>

  <clause id="16750">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,R(x \ y,u,w) \ z)) = K(x \ y,R(y / x,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(8571(a,1),16155(a,1,2,2))].">
      <j1 rule="para" parents="8571 16155"/>
    </justification>
  </clause>

  <clause id="16751">
    <literal><![CDATA[
      (K(x,L(y,z * u,T(T(z,z \ 1),u))) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(5945(a,2),16173(a,1,1,1,2,3))].">
      <j1 rule="para" parents="5945 16173"/>
    </justification>
  </clause>

  <clause id="16752">
    <literal><![CDATA[
      ((x * (T(y * z,x) / x)) * K(z,u)) / (y * T(z,u)) = a(x,x \ (y * z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13190,a(flip),b,16681,a),flip(a)].">
      <j1 rule="hyper" parents="373 13190 16681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16754">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,u \ x) \ ((K(y,z) \ u) * (u \ x)) = L(K(z,T(y,x)),u,u \ x) * x
    ]]></literal>
    <justification jstring="[para(8151(a,1),16746(a,1,1,1))].">
      <j1 rule="para" parents="8151 16746"/>
    </justification>
  </clause>

  <clause id="16755">
    <literal><![CDATA[
      K(x,K(y,z)) \ ((K(y,z) \ u) * (u \ x)) = L(K(z,T(y,x)),u,u \ x) * x
    ]]></literal>
    <justification jstring="[para(15531(a,1),16754(a,1,1))].">
      <j1 rule="para" parents="15531 16754"/>
    </justification>
  </clause>

  <clause id="16757">
    <literal><![CDATA[
      K(x \ y,R(y / x,z,u) \ w) = K(x \ y,(y \ w) * x) * K(y,K(x,w))
    ]]></literal>
    <justification jstring="[para(14044(a,1),16750(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14044 16750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16758">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,z)) = K(x \ y,x * (y \ z))
    ]]></literal>
    <justification jstring="[para(684(a,1),16757(a,1,2)),flip(a)].">
      <j1 rule="para" parents="684 16757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16760">
    <literal><![CDATA[
      (K(x,L(y,z * u,T(T(z,1),u))) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(13055(a,1),16751(a,1,1,1,2))].">
      <j1 rule="para" parents="13055 16751"/>
    </justification>
  </clause>

  <clause id="16761">
    <literal><![CDATA[
      (K(x,L(y,z * u,T(z,u))) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(372(a,1),16760(a,1,1,1,2,3,1))].">
      <j1 rule="para" parents="372 16760"/>
    </justification>
  </clause>

  <clause id="16762">
    <literal><![CDATA[
      R(T(x / (x * y),(x * y) * y),x * y,y) = ((((x * y) \ z) \ z) * y) \ T(x * y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(14661(a,1),14999(a,2,2))].">
      <j1 rule="para" parents="14661 14999"/>
    </justification>
  </clause>

  <clause id="16763">
    <literal><![CDATA[
      T(x,L((y * K(L(z,u,w),v5)) / (w * u),w * u,K(v5,L(z,u,w)))) = T(x,y / (w * (u * K(v5,z))))
    ]]></literal>
    <justification jstring="[para(6878(a,1),15636(a,1,2,1,1))].">
      <j1 rule="para" parents="6878 15636"/>
    </justification>
  </clause>

  <clause id="16764">
    <literal><![CDATA[
      T(x,L(y * K(z,u * w),u \ T(w * u,z),T(w,u))) = T(x,(y * T(w,u)) / (u \ T(w * u,z)))
    ]]></literal>
    <justification jstring="[para(6878(a,1),15683(a,1,2,1))].">
      <j1 rule="para" parents="6878 15683"/>
    </justification>
  </clause>

  <clause id="16765">
    <literal><![CDATA[
      T(x * (x \ ((y * (x * z)) / y)),x) \ x = ((y * (z * x)) / y) \ L(x,z,x)
    ]]></literal>
    <justification jstring="[para(69(a,1),16414(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="69 16414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16766">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,y,z) = T((x * (z * y)) / x,z) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),16765(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 16765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16768">
    <literal><![CDATA[
      K(x,y) \ L(K(x,T(y,z)) * (z / a(u,w,v5)),w,K(v5,u)) = T(a(u,w,v5) \ z,K(x,y))
    ]]></literal>
    <justification jstring="[para(15672(a,1),16646(a,1,2,1))].">
      <j1 rule="para" parents="15672 16646"/>
    </justification>
  </clause>

  <clause id="16769">
    <literal><![CDATA[
      K(x,y) * L(K(y,T(x,z)) * (z / a(u,w,v5)),w,K(v5,u)) = T(a(u,w,v5) \ z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(6198,a,16768,a)].">
      <j1 rule="hyper" parents="6198 16768"/>
    </justification>
  </clause>

  <clause id="16770">
    <literal><![CDATA[
      T(x,L((y * K(z,L(u,w,v5))) / (v5 * w),v5 * w,K(u,L(z,w,v5)))) = T(x,y / (v5 * (w * K(u,z))))
    ]]></literal>
    <justification jstring="[para(12093(a,1),16763(a,1,2,1,1,2))].">
      <j1 rule="para" parents="12093 16763"/>
    </justification>
  </clause>

  <clause id="16771">
    <literal><![CDATA[
      K(x,y) * (z * (K(K(x,y) * z,u) * K(K(x,y) * z,u))) = T(T(K(x,y) * z,u),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6113,a(flip),b,15660,a),flip(a)].">
      <j1 rule="hyper" parents="373 6113 15660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16772">
    <literal><![CDATA[
      R(R(x / y,y,y),z,u) \ R((x / y) * K(y,y),z,u) = a(R((x / y) * K(y,y),z,u),y,y) \ 1
    ]]></literal>
    <justification jstring="[para(112(a,2),16023(a,1,1,1))].">
      <j1 rule="para" parents="112 16023"/>
    </justification>
  </clause>

  <clause id="16773">
    <literal><![CDATA[
      R(R(x / y,y,y),z,u) \ R(x / y,z,u) = a(R((x / y) * K(y,y),z,u),y,y) \ 1
    ]]></literal>
    <justification jstring="[para(204(a,1),16772(a,1,2,1))].">
      <j1 rule="para" parents="204 16772"/>
    </justification>
  </clause>

  <clause id="16775">
    <literal><![CDATA[
      (x \ (1 / x)) * K((x \ 1) * (x \ ((x \ 1) \ y)),(x \ 1) \ y) = ((x \ 1) \ y) \ ((1 / (1 / x)) \ y)
    ]]></literal>
    <justification jstring="[para(1098(a,1),16128(a,1,2,1))].">
      <j1 rule="para" parents="1098 16128"/>
    </justification>
  </clause>

  <clause id="16776">
    <literal><![CDATA[
      (x \ (1 / x)) * K((1 / (1 / x)) \ y,(x \ 1) \ y) = ((x \ 1) \ y) \ ((1 / (1 / x)) \ y)
    ]]></literal>
    <justification jstring="[para(7033(a,1),16775(a,1,2,1))].">
      <j1 rule="para" parents="7033 16775"/>
    </justification>
  </clause>

  <clause id="16777">
    <literal><![CDATA[
      (x \ (1 / x)) * K((1 / (1 / x)) \ y,x * y) = ((x \ 1) \ y) \ ((1 / (1 / x)) \ y)
    ]]></literal>
    <justification jstring="[para(14413(a,1),16776(a,1,2))].">
      <j1 rule="para" parents="14413 16776"/>
    </justification>
  </clause>

  <clause id="16778">
    <literal><![CDATA[
      ((x \ 1) \ y) \ ((1 / (1 / x)) \ y) = (x \ (1 / x)) * K(x \ y,x * y)
    ]]></literal>
    <justification jstring="[para(5260(a,1),16777(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5260 16777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16779">
    <literal><![CDATA[
      K(x,L((y / T(z,u \ 1)) / (w / (u * w)),(w * u) \ w,T(z,u \ 1))) = K(x,y / (z * (w / (u * w))))
    ]]></literal>
    <justification jstring="[para(14209(a,1),15631(a,1,2))].">
      <j1 rule="para" parents="14209 15631"/>
    </justification>
  </clause>

  <clause id="16780">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ u) / (T(u * z,z \ 1) * ((z * u) \ u))) = K(x,T(T(u,z) \ y,z * u))
    ]]></literal>
    <justification jstring="[para(11170(a,1),16087(a,2,2))].">
      <j1 rule="para" parents="11170 16087"/>
    </justification>
  </clause>

  <clause id="16781">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / (T(z * u,u \ 1) * ((u * z) \ z))) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(7453(a,1),16780(a,1,2,1))].">
      <j1 rule="para" parents="7453 16780"/>
    </justification>
  </clause>

  <clause id="16782">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / (K(z * u,u \ 1) * T(z,u))) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(6984(a,1),16781(a,1,2,2))].">
      <j1 rule="para" parents="6984 16781"/>
    </justification>
  </clause>

  <clause id="16783">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / T(K(z * u,u \ 1) * z,u)) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(7600(a,2),16782(a,1,2,2))].">
      <j1 rule="para" parents="7600 16782"/>
    </justification>
  </clause>

  <clause id="16784">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / T(z * K(u * z,u \ 1),u)) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(11188(a,1),16783(a,1,2,2,1))].">
      <j1 rule="para" parents="11188 16783"/>
    </justification>
  </clause>

  <clause id="16785">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / (u \ T(z * u,u \ 1))) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(14496(a,1),16784(a,1,2,2))].">
      <j1 rule="para" parents="14496 16784"/>
    </justification>
  </clause>

  <clause id="16786">
    <literal><![CDATA[
      T((x / (y \ 1)) * (L(y,z,u) \ 1),L(y,z,u) * (y \ 1)) = L(y \ L(y,z,u),L(y,z,u),y \ x) \ x
    ]]></literal>
    <justification jstring="[para(2234(a,1),16211(a,2,1))].">
      <j1 rule="para" parents="2234 16211"/>
    </justification>
  </clause>

  <clause id="16787">
    <literal><![CDATA[
      ((((x * y) \ x) \ T(((x * y) \ x) * z,y)) \ u) * ((z \ u) \ 1) = K(((x * y) \ x) \ 1,z * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,10152,a(flip),b,14926,a),flip(a)].">
      <j1 rule="hyper" parents="373 10152 14926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16788">
    <literal><![CDATA[
      ((((x * y) \ x) \ T(((x * y) \ x) * z,y)) \ u) * ((z \ u) \ 1) = K(y,z * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,6759,a(flip),b,16787,a),flip(a)].">
      <j1 rule="hyper" parents="373 6759 16787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16790">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),(x \ y) * T(x,L(x \ y,z,u))) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[para(22(a,2),14971(a,1,2,2))].">
      <j1 rule="para" parents="22 14971"/>
    </justification>
  </clause>

  <clause id="16791">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),L(x * (x \ y),z,K(u,x \ y))) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[para(16613(a,2),16790(a,1,2))].">
      <j1 rule="para" parents="16613 16790"/>
    </justification>
  </clause>

  <clause id="16792">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),L(y,z,K(u,x \ y))) = ((x * L(x \ y,z,u)) \ y) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),16791(a,1,2,1))].">
      <j1 rule="para" parents="10 16791"/>
    </justification>
  </clause>

  <clause id="16793">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),u / T(K(z,y),x * K(y,z))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6878(a,1),15086(a,1,1,2))].">
      <j1 rule="para" parents="6878 15086"/>
    </justification>
  </clause>

  <clause id="16794">
    <literal><![CDATA[
      K(L(x,y,z),T(T(u,w),v5)) \ ((R(w,v6,v7) * T(u,w)) / T(u,w)) = (T(T(u,w),R(T(x,v5),y,z)) * R(T(w,u),v6,v7)) / T(u,w)
    ]]></literal>
    <justification jstring="[para(7916(a,1),15611(a,1,1))].">
      <j1 rule="para" parents="7916 15611"/>
    </justification>
  </clause>

  <clause id="16795">
    <literal><![CDATA[
      K(x,T(y / z,y / (z * u))) = K(x,(z * K(z * u,u \ 1)) \ ((z * u) * (y / (z * u))))
    ]]></literal>
    <justification jstring="[para(12(a,1),16426(a,1,2,1,2))].">
      <j1 rule="para" parents="12 16426"/>
    </justification>
  </clause>

  <clause id="16796">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(6982(a,2),16725(a,1,2))].">
      <j1 rule="para" parents="6982 16725"/>
    </justification>
  </clause>

  <clause id="16797">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,15759,a,b,16796,a),flip(a)].">
      <j1 rule="hyper" parents="373 15759 16796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16798">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z \ u,z) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13409,a,b,16796,a),flip(a)].">
      <j1 rule="hyper" parents="373 13409 16796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16799">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,u)) = y * T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(157,a,16796,a),flip(a)].">
      <j1 rule="hyper" parents="157 16796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16800">
    <literal><![CDATA[
      T(x * T(1 / x,K(y,z)),K(y,z)) = K(x,K(z,y) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(39,a,5760,a(flip),b,16796,a),flip(a)].">
      <j1 rule="hyper" parents="39 5760 16796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16801">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),K(u,z) * y) = y \ T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),16796(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 16796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16802">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(u * T((K(x,y) * z) / K(x,y),K(y,x)),K(y,x)) = T(u,T(K(x,y),z) * z)
    ]]></literal>
    <justification jstring="[para(4450(a,2),16796(a,2,2))].">
      <j1 rule="para" parents="4450 16796"/>
    </justification>
  </clause>

  <clause id="16803">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,z)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(8153(a,1),16796(a,1,2,1,2))].">
      <j1 rule="para" parents="8153 16796"/>
    </justification>
  </clause>

  <clause id="16804">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u \ 1)) = T(y,K(u \ 1,z) * x)
    ]]></literal>
    <justification jstring="[para(9018(a,1),16796(a,1,2,1,2))].">
      <j1 rule="para" parents="9018 16796"/>
    </justification>
  </clause>

  <clause id="16805">
    <literal><![CDATA[
      K(x \ T(T(y * T(z,K(u,w)),K(u,w)) / z,T(y * T(z,K(u,w)),K(u,w))),v5) = K(x \ T(y,K(w,u) * z),v5)
    ]]></literal>
    <justification jstring="[para(16796(a,1),13370(a,2,1,2))].">
      <j1 rule="para" parents="16796 13370"/>
    </justification>
  </clause>

  <clause id="16806">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,K(u,z) * x) = w
    ]]></literal>
    <justification jstring="[para(16797(a,2),15753(a,1))].">
      <j1 rule="para" parents="16797 15753"/>
    </justification>
  </clause>

  <clause id="16807">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),K(z,u) \ y) = y \ T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(14733,a,16801,a)].">
      <j1 rule="hyper" parents="14733 16801"/>
    </justification>
  </clause>

  <clause id="16808">
    <literal><![CDATA[
      K(x,y * (z \ T((u \ (K(w,v5) * z)) * T(z,K(w,v5)),K(v5,w)))) = K(x,y * ((K(w,v5) * z) / u))
    ]]></literal>
    <justification jstring="[para(16803(a,2),15883(a,1,2,2))].">
      <j1 rule="para" parents="16803 15883"/>
    </justification>
  </clause>

  <clause id="16809">
    <literal><![CDATA[
      T(R(x * K(K(y,z),u),K(w,v5),w),K(y,z) \ u) = u \ T(x * u,K(y,z))
    ]]></literal>
    <justification jstring="[para(6310(a,2),16807(a,1,1))].">
      <j1 rule="para" parents="6310 16807"/>
    </justification>
  </clause>

  <clause id="16810">
    <literal><![CDATA[
      T(x * T(1 / x,K(y,z)),K(y,z)) = K(x,x \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,10151,a(flip),b,16800,a),flip(a)].">
      <j1 rule="hyper" parents="373 10151 16800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16811">
    <literal><![CDATA[
      T(K(K(x,y) * z,z \ 1),K(x,y)) = K(z,z \ K(y,x))
    ]]></literal>
    <justification jstring="[para(16429(a,2),16810(a,1,1))].">
      <j1 rule="para" parents="16429 16810"/>
    </justification>
  </clause>

  <clause id="16812">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(16798(a,1),16806(a,1))].">
      <j1 rule="para" parents="16798 16806"/>
    </justification>
  </clause>

  <clause id="16813">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u \ 1,z) * x)
    ]]></literal>
    <justification jstring="[para(9018(a,1),16804(a,1,2))].">
      <j1 rule="para" parents="9018 16804"/>
    </justification>
  </clause>

  <clause id="16814">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(16813(a,1),16806(a,1))].">
      <j1 rule="para" parents="16813 16806"/>
    </justification>
  </clause>

  <clause id="16815">
    <literal><![CDATA[
      T(x,K(y,z) * (((y \ u) / u) \ w)) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(16814,a,15783,a)].">
      <j1 rule="hyper" parents="16814 15783"/>
    </justification>
  </clause>

  <clause id="16816">
    <literal><![CDATA[
      T(x,K(y,z \ 1) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(16814,a,15759,a),flip(a)].">
      <j1 rule="hyper" parents="16814 15759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16817">
    <literal><![CDATA[
      T(x,K(1 / y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(3776(a,2),16814(a,1,2,1))].">
      <j1 rule="para" parents="3776 16814"/>
    </justification>
  </clause>

  <clause id="16818">
    <literal><![CDATA[
      T(x,K(y,z \ 1) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,15759,a,b,16816,a),flip(a)].">
      <j1 rule="hyper" parents="373 15759 16816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16819">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = x \ T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(16816(a,1),15761(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16816 15761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16820">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = u / T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(225,a,16818,a(flip),b,5804,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 16818 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16821">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5726,a,b,16819,a),flip(a)].">
      <j1 rule="hyper" parents="373 5726 16819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16822">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,15761,a(flip),b,16819,a),flip(a)].">
      <j1 rule="hyper" parents="373 15761 16819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16823">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(16819(a,2),5827(a,1))].">
      <j1 rule="para" parents="16819 5827"/>
    </justification>
  </clause>

  <clause id="16824">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15768,a,16821,a)].">
      <j1 rule="hyper" parents="15768 16821"/>
    </justification>
  </clause>

  <clause id="16825">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15152,a,b,16821,a)].">
      <j1 rule="hyper" parents="64 15152 16821"/>
    </justification>
  </clause>

  <clause id="16826">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(K(z,y \ K(y,u)) * u) \ w)
    ]]></literal>
    <justification jstring="[para(16821(a,1),9153(a,1,1))].">
      <j1 rule="para" parents="16821 9153"/>
    </justification>
  </clause>

  <clause id="16827">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(15768,a,16822,a)].">
      <j1 rule="hyper" parents="15768 16822"/>
    </justification>
  </clause>

  <clause id="16828">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(u,z \ y) * w)
    ]]></literal>
    <justification jstring="[para(6756(a,1),16822(a,1,2,1))].">
      <j1 rule="para" parents="6756 16822"/>
    </justification>
  </clause>

  <clause id="16829">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(9029(a,1),16824(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9029 16824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16830">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(K(y \ K(y,u),z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(16824(a,1),7695(a,1,1))].">
      <j1 rule="para" parents="16824 7695"/>
    </justification>
  </clause>

  <clause id="16831">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,K(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(14783,a,16827,a)].">
      <j1 rule="hyper" parents="14783 16827"/>
    </justification>
  </clause>

  <clause id="16832">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5787,a,b,16820,a),flip(a)].">
      <j1 rule="hyper" parents="373 5787 16820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16833">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(K(y,x) * (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(14785,a,16832,a)].">
      <j1 rule="hyper" parents="14785 16832"/>
    </justification>
  </clause>

  <clause id="16834">
    <literal><![CDATA[
      K(x,y * (K(1 / z,y) * u)) = K(x,K(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(14913,a,16825,a)].">
      <j1 rule="hyper" parents="14913 16825"/>
    </justification>
  </clause>

  <clause id="16835">
    <literal><![CDATA[
      K(x,K(y,z \ y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(16828(a,1),13528(a,1))].">
      <j1 rule="para" parents="16828 13528"/>
    </justification>
  </clause>

  <clause id="16836">
    <literal><![CDATA[
      K(x,K(y \ (z \ 1),u) * w) = K(x,K(u,z * y) * w)
    ]]></literal>
    <justification jstring="[para(14413(a,1),16828(a,2,2,1))].">
      <j1 rule="para" parents="14413 16828"/>
    </justification>
  </clause>

  <clause id="16837">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,15770,a(flip),b,16831,a),flip(a)].">
      <j1 rule="hyper" parents="373 15770 16831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16838">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(13504,a,16837,a)].">
      <j1 rule="hyper" parents="13504 16837"/>
    </justification>
  </clause>

  <clause id="16839">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z) \ u,w,v5)) = K(L(x,w,v5),T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(12117,a,16837,a)].">
      <j1 rule="hyper" parents="12117 16837"/>
    </justification>
  </clause>

  <clause id="16840">
    <literal><![CDATA[
      T(x,T(y \ 1,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(143,a,16837,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 16837 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16841">
    <literal><![CDATA[
      K(x,T(1 / y,z) * u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(82(a,1),16837(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="82 16837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16842">
    <literal><![CDATA[
      K(x,T(y \ 1,z) * u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(79(a,1),16838(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 16838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16843">
    <literal><![CDATA[
      T(x,T(y \ 1,z) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(143,a,16842,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 16842 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16844">
    <literal><![CDATA[
      K(T(x \ 1,y) * z,u) = u / T(u,T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(225,a,16843,a(flip),b,5804,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 16843 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16845">
    <literal><![CDATA[
      (x * T(y,T(z,u) \ w)) / (x * y) = K(y,T(T(z \ 1,u) * w,x))
    ]]></literal>
    <justification jstring="[para(16843(a,1),8280(a,1,1,2))].">
      <j1 rule="para" parents="16843 8280"/>
    </justification>
  </clause>

  <clause id="16846">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) \ v5) = T(x,T(u \ K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(14450(a,1),16843(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14450 16843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16847">
    <literal><![CDATA[
      T(x,T((y \ z) \ K(y,u),w) * v5) = T(x,T(T(y,u) \ z,w) \ v5)
    ]]></literal>
    <justification jstring="[para(14452(a,1),16843(a,1,2,1,1))].">
      <j1 rule="para" parents="14452 16843"/>
    </justification>
  </clause>

  <clause id="16848">
    <literal><![CDATA[
      T(T(x,T(y,z) \ u),w * (w * x)) = T(x,w * (w * (T(y \ 1,z) * u)))
    ]]></literal>
    <justification jstring="[para(16843(a,1),15819(a,1,1))].">
      <j1 rule="para" parents="16843 15819"/>
    </justification>
  </clause>

  <clause id="16849">
    <literal><![CDATA[
      K(T(x \ 1,y) * z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5787,a,b,16844,a),flip(a)].">
      <j1 rule="hyper" parents="373 5787 16844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16850">
    <literal><![CDATA[
      K(T(1 / x,y) \ z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(82(a,1),16849(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 16849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16851">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5257,a(flip),b,16850,a)].">
      <j1 rule="hyper" parents="64 5257 16850"/>
    </justification>
  </clause>

  <clause id="16852">
    <literal><![CDATA[
      K(K(x,y) * (y * z),u) = K(T(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16833,a(flip),b,16851,a)].">
      <j1 rule="hyper" parents="64 16833 16851"/>
    </justification>
  </clause>

  <clause id="16853">
    <literal><![CDATA[
      K(T(x,y) / (((z \ 1) / y) * y),u) = K(T(z,y) * x,T(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16593,a(flip),b,16851,a)].">
      <j1 rule="hyper" parents="64 16593 16851"/>
    </justification>
  </clause>

  <clause id="16854">
    <literal><![CDATA[
      K(T(x \ y,x) * z,u) = K((y / x) * z,u)
    ]]></literal>
    <justification jstring="[para(5982(a,1),16852(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5982 16852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16855">
    <literal><![CDATA[
      K(T(x,y) * z,y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * z,y * x) = u
    ]]></literal>
    <justification jstring="[para(16852(a,1),7741(a,1))].">
      <j1 rule="para" parents="16852 7741"/>
    </justification>
  </clause>

  <clause id="16856">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,K(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(16835,a,15774,a),flip(a)].">
      <j1 rule="hyper" parents="16835 15774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16857">
    <literal><![CDATA[
      K(x,K(y \ z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15767(a,1),16835(a,1))].">
      <j1 rule="para" parents="15767 16835"/>
    </justification>
  </clause>

  <clause id="16858">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(6157(a,1),16856(a,2,2))].">
      <j1 rule="para" parents="6157 16856"/>
    </justification>
  </clause>

  <clause id="16859">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,K(u,z \ y) * (y / z))
    ]]></literal>
    <justification jstring="[hyper(16857,a,15775,a),flip(a)].">
      <j1 rule="hyper" parents="16857 15775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16860">
    <literal><![CDATA[
      K(x,y * K(z,u \ 1)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(8166(a,1),16829(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8166 16829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16861">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16265,a,b,16860,a)].">
      <j1 rule="hyper" parents="64 16265 16860"/>
    </justification>
  </clause>

  <clause id="16862">
    <literal><![CDATA[
      T(x,y * K(z \ 1,u)) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(143,a,16861,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 16861 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16863">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = 1 / K(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(225,a,16861,a(flip),b,6092,a),flip(a)].">
      <j1 rule="hyper" parents="225 16861 6092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16864">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6091,a(flip),b,16863,a),flip(a)].">
      <j1 rule="hyper" parents="373 6091 16863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16865">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(16287,a,16864,a)].">
      <j1 rule="hyper" parents="16287 16864"/>
    </justification>
  </clause>

  <clause id="16866">
    <literal><![CDATA[
      K(x * K(x \ y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11197,a(flip),b,16864,a),flip(a)].">
      <j1 rule="hyper" parents="64 11197 16864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16867">
    <literal><![CDATA[
      K(x * K(x \ y,z),T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(((z * (y \ x)) / z) * y,u) = w
    ]]></literal>
    <justification jstring="[para(16865(a,1),11215(a,1))].">
      <j1 rule="para" parents="16865 11215"/>
    </justification>
  </clause>

  <clause id="16868">
    <literal><![CDATA[
      K(x,y * (K(1 / z,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,15770,a(flip),b,16834,a),flip(a)].">
      <j1 rule="hyper" parents="373 15770 16834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16869">
    <literal><![CDATA[
      K(x,y * (K(z \ 1,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(3776(a,1),16868(a,1,2,2,1))].">
      <j1 rule="para" parents="3776 16868"/>
    </justification>
  </clause>

  <clause id="16870">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15785,a(flip),b,16869,a)].">
      <j1 rule="hyper" parents="64 15785 16869"/>
    </justification>
  </clause>

  <clause id="16871">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[para(14628(a,1),16870(a,1,2,1))].">
      <j1 rule="para" parents="14628 16870"/>
    </justification>
  </clause>

  <clause id="16872">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z) \ u,w,v5)) = K(x,L(T(y,z) * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,12093,a(flip),b,16839,a),flip(a)].">
      <j1 rule="hyper" parents="373 12093 16839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16873">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(16839(a,2),12117(a,1))].">
      <j1 rule="para" parents="16839 12117"/>
    </justification>
  </clause>

  <clause id="16874">
    <literal><![CDATA[
      K(x,L(T(1 / y,z) * u,w,v5)) = K(x,L(T(y,z) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(82(a,1),16872(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 16872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16875">
    <literal><![CDATA[
      K(x,L(T(1 / y,z) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(16874(a,1),16232(a,1))].">
      <j1 rule="para" parents="16874 16232"/>
    </justification>
  </clause>

  <clause id="16876">
    <literal><![CDATA[
      K(x,T(T(y \ 1,z) * u,w)) = K(x,T(T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(8370,a,16845,a),flip(a)].">
      <j1 rule="hyper" parents="8370 16845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16877">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,y * x)) = K(T(z,y) / (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),16853(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 16853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16878">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,y * x)) = K(T(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,14681,a(flip),b,16877,a),flip(a)].">
      <j1 rule="hyper" parents="373 14681 16877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16880">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,15775,a(flip),b,16859,a),flip(a)].">
      <j1 rule="hyper" parents="373 15775 16859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16881">
    <literal><![CDATA[
      K(x,T(y / z,y / (z * u))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(9551(a,1),16880(a,1,2))].">
      <j1 rule="para" parents="9551 16880"/>
    </justification>
  </clause>

  <clause id="16882">
    <literal><![CDATA[
      K(x,(y * K(y * z,z \ 1)) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16795,a(flip),b,16881,a)].">
      <j1 rule="hyper" parents="64 16795 16881"/>
    </justification>
  </clause>

  <clause id="16883">
    <literal><![CDATA[
      K(x,T(y / z,T(T(z \ (u \ z),T(u,w)),z))) = K(x,T(y / z,y / (((u \ 1) \ 1) \ z)))
    ]]></literal>
    <justification jstring="[para(7279(a,1),16881(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7279 16881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16884">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(16867,a,16866,a)].">
      <j1 rule="hyper" parents="16867 16866"/>
    </justification>
  </clause>

  <clause id="16885">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K((z \ 1) * T((z \ y) / (z \ 1),x),u)
    ]]></literal>
    <justification jstring="[hyper(11631,a,16884,a)].">
      <j1 rule="hyper" parents="11631 16884"/>
    </justification>
  </clause>

  <clause id="16886">
    <literal><![CDATA[
      K(x \ T((x \ y) * x,z),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11504,a(flip),b,16885,a)].">
      <j1 rule="hyper" parents="373 11504 16885"/>
    </justification>
  </clause>

  <clause id="16887">
    <literal><![CDATA[
      K(T(x \ T(y,z),x),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[para(5452(a,1),16886(a,1,1))].">
      <j1 rule="para" parents="5452 16886"/>
    </justification>
  </clause>

  <clause id="16888">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(8454,a,16887,a),flip(a)].">
      <j1 rule="hyper" parents="8454 16887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16889">
    <literal><![CDATA[
      K(T(T(x,y),y) / z,u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[para(256(a,1),16888(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="256 16888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16890">
    <literal><![CDATA[
      K((x * y) \ T(z,x),T(u,y)) = K(z / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16591,a,b,16889,a)].">
      <j1 rule="hyper" parents="64 16591 16889"/>
    </justification>
  </clause>

  <clause id="16891">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(y * K(y * (T(x,y) * z),x),T(u,z))
    ]]></literal>
    <justification jstring="[para(14653(a,1),16890(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14653 16890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16892">
    <literal><![CDATA[
      T(x,y * (y * (T(z \ 1,u) * w))) = T(x,y * (y * (T(z,u) \ w)))
    ]]></literal>
    <justification jstring="[hyper(15820,a,16848,a),flip(a)].">
      <j1 rule="hyper" parents="15820 16848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16893">
    <literal><![CDATA[
      T(R(x * K(y,K(z,u)),K(w,v5),w),K(y,z) \ u) = u \ T(x * u,K(y,z))
    ]]></literal>
    <justification jstring="[para(8092(a,1),16809(a,1,1,1,2))].">
      <j1 rule="para" parents="8092 16809"/>
    </justification>
  </clause>

  <clause id="16894">
    <literal><![CDATA[
      K(x,(K(y,z \ K(z,u)) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(9536,a,16826,a),flip(a)].">
      <j1 rule="hyper" parents="9536 16826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16895">
    <literal><![CDATA[
      K(x,(y * K(z,u \ 1)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(9152(a,1),16894(a,1,2,1))].">
      <j1 rule="para" parents="9152 16894"/>
    </justification>
  </clause>

  <clause id="16896">
    <literal><![CDATA[
      K(x,(K(y \ K(y,z),u) * z) \ w) = K(x,(z * K(u,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(9536,a,16830,a),flip(a)].">
      <j1 rule="hyper" parents="9536 16830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16897">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ w) = K(x,(y * K(u,z)) \ w)
    ]]></literal>
    <justification jstring="[para(7286(a,1),16896(a,1,2,1))].">
      <j1 rule="para" parents="7286 16896"/>
    </justification>
  </clause>

  <clause id="16898">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ K(u,K(y * K(u,z),z))) = K(x,(L(K(u,z),y,K(u,z)) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(8118(a,1),16897(a,2,2))].">
      <j1 rule="para" parents="8118 16897"/>
    </justification>
  </clause>

  <clause id="16899">
    <literal><![CDATA[
      K(x,(y * K(y * z,z)) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16895,a(flip),b,16882,a)].">
      <j1 rule="hyper" parents="64 16895 16882"/>
    </justification>
  </clause>

  <clause id="16900">
    <literal><![CDATA[
      K(x,(y * K(y,z)) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13554,a(flip),b,16899,a)].">
      <j1 rule="hyper" parents="64 13554 16899"/>
    </justification>
  </clause>

  <clause id="16901">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[para(5753(a,2),16900(a,1,2,1))].">
      <j1 rule="para" parents="5753 16900"/>
    </justification>
  </clause>

  <clause id="16902">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * T(z,y)) * (u / (y * T(z,y))))) = K(x,T(u / y,T(T(z,y),y)))
    ]]></literal>
    <justification jstring="[para(4619(a,1),16901(a,1,2,1))].">
      <j1 rule="para" parents="4619 16901"/>
    </justification>
  </clause>

  <clause id="16903">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(y * K(y * (x * z),x),T(u,z))
    ]]></literal>
    <justification jstring="[para(8618(a,1),16891(a,2,1,2))].">
      <j1 rule="para" parents="8618 16891"/>
    </justification>
  </clause>

  <clause id="16905">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (y * T(z,y))))) = K(x,T(u / y,T(T(z,y),y)))
    ]]></literal>
    <justification jstring="[para(115(a,1),16902(a,1,2,2,1))].">
      <j1 rule="para" parents="115 16902"/>
    </justification>
  </clause>

  <clause id="16906">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,T(T(z,y),y)))
    ]]></literal>
    <justification jstring="[para(115(a,1),16905(a,1,2,2,2,2))].">
      <j1 rule="para" parents="115 16905"/>
    </justification>
  </clause>

  <clause id="16907">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[para(8213(a,1),16906(a,2,2))].">
      <j1 rule="para" parents="8213 16906"/>
    </justification>
  </clause>

  <clause id="16908">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,z * y)) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16369,a(flip),b,16907,a)].">
      <j1 rule="hyper" parents="64 16369 16907"/>
    </justification>
  </clause>

  <clause id="16910">
    <literal><![CDATA[
      K(x,T(y * z,(y * z) \ z) \ T(u,z * K(y \ 1,z * y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(7241(a,1),16908(a,1,2,2,2))].">
      <j1 rule="para" parents="7241 16908"/>
    </justification>
  </clause>

  <clause id="16911">
    <literal><![CDATA[
      K(x,T(y / z,T(T(z \ (u \ z),T(u,w)),z))) = K(x,T(y / z,y / (u \ z)))
    ]]></literal>
    <justification jstring="[para(9956(a,1),16883(a,2,2))].">
      <j1 rule="para" parents="9956 16883"/>
    </justification>
  </clause>

  <clause id="16912">
    <literal><![CDATA[
      K(x,T(y / z,T((u \ z) / z,T(u,w)))) = K(x,T(y / z,y / (u \ z)))
    ]]></literal>
    <justification jstring="[para(8243(a,1),16911(a,1,2))].">
      <j1 rule="para" parents="8243 16911"/>
    </justification>
  </clause>

  <clause id="16913">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u \ 1))
    ]]></literal>
    <justification jstring="[para(9408(a,1),16912(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9408 16912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16914">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,11157,a(flip),b,16913,a),flip(a)].">
      <j1 rule="hyper" parents="373 11157 16913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16916">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z \ y) * (u / (z \ y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16532,a(flip),b,16914,a)].">
      <j1 rule="hyper" parents="64 16532 16914"/>
    </justification>
  </clause>

  <clause id="16917">
    <literal><![CDATA[
      K(x,T(y,T(y,z) / z) \ (T(z,y) * (u / ((T(y,z) / z) \ y)))) = K(x,T(u / y,T(y,z) / z))
    ]]></literal>
    <justification jstring="[para(4628(a,1),16916(a,1,2,2,1))].">
      <j1 rule="para" parents="4628 16916"/>
    </justification>
  </clause>

  <clause id="16918">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ K(u,K(y,z))) = K(x,(L(K(u,z),y,K(u,z)) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(8526(a,1),16898(a,1,2,2,2))].">
      <j1 rule="para" parents="8526 16898"/>
    </justification>
  </clause>

  <clause id="16919">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ K(y,K(z,u))) = K(x,(L(K(u,z),y,K(u,z)) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(8110(a,2),16918(a,1,2,2))].">
      <j1 rule="para" parents="8110 16918"/>
    </justification>
  </clause>

  <clause id="16921">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,K(y,z)) * u) \ 1) = K(x,(K(z \ 1,y) * u) \ 1)
    ]]></literal>
    <justification jstring="[para(10866(a,1),16919(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10866 16919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16922">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,K(y,z)) * u) \ 1) = K(x,u \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,6713,a(flip),b,16921,a),flip(a)].">
      <j1 rule="hyper" parents="373 6713 16921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16923">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(13517,a,16922,a)].">
      <j1 rule="hyper" parents="13517 16922"/>
    </justification>
  </clause>

  <clause id="16924">
    <literal><![CDATA[
      K(x,y \ K(z,u \ 1)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(7011,a,16923,a),flip(a)].">
      <j1 rule="hyper" parents="7011 16923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16927">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(16357,a,16924,a)].">
      <j1 rule="hyper" parents="16357 16924"/>
    </justification>
  </clause>

  <clause id="16928">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(6047(a,1),16924(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6047 16924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16929">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16319,a(flip),b,16927,a),flip(a)].">
      <j1 rule="hyper" parents="64 16319 16927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16930">
    <literal><![CDATA[
      K(x,y \ K(z \ u,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13386,a(flip),b,16928,a)].">
      <j1 rule="hyper" parents="64 13386 16928"/>
    </justification>
  </clause>

  <clause id="16931">
    <literal><![CDATA[
      K(x,y \ K(z,u \ z)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(16357,a,16930,a)].">
      <j1 rule="hyper" parents="16357 16930"/>
    </justification>
  </clause>

  <clause id="16932">
    <literal><![CDATA[
      K(x,y \ T(z,1 / u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16302,a(flip),b,16929,a),flip(a)].">
      <j1 rule="hyper" parents="64 16302 16929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16933">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),16932(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="79 16932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16934">
    <literal><![CDATA[
      K(x,y \ T(z * (u \ 1),u)) = K(x,y \ ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16371,a(flip),b,16933,a),flip(a)].">
      <j1 rule="hyper" parents="64 16371 16933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16935">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w \ u))) = K(x,y \ T(z,T(w,u)))
    ]]></literal>
    <justification jstring="[para(7451(a,1),16933(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7451 16933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16936">
    <literal><![CDATA[
      K(x,y \ T(z,u)) * a(w,v5,K(y \ T(z,u),x)) = K(x,L(y \ T(z,u \ 1),v5,w))
    ]]></literal>
    <justification jstring="[para(16933(a,1),16350(a,1,1))].">
      <j1 rule="para" parents="16933 16350"/>
    </justification>
  </clause>

  <clause id="16937">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ R(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(1042(a,1),16934(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1042 16934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16938">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((z \ 1) * y) \ R(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(12136,a,16937,a)].">
      <j1 rule="hyper" parents="12136 16937"/>
    </justification>
  </clause>

  <clause id="16939">
    <literal><![CDATA[
      K(x,y \ R(z,u,u \ 1)) = K(x,y \ L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,7035,a(flip),b,16937,a),flip(a)].">
      <j1 rule="hyper" parents="64 7035 16937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16940">
    <literal><![CDATA[
      K(x,(y * z) \ L(y,u,u \ 1)) = K(x,z \ a(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,16120,a(flip),b,16939,a),flip(a)].">
      <j1 rule="hyper" parents="64 16120 16939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16941">
    <literal><![CDATA[
      K(x,y \ L(z / u,u,u \ 1)) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(675(a,1),16939(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="675 16939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16942">
    <literal><![CDATA[
      K(x,y \ (z \ L(z,u,u \ 1))) = K(x,y \ a(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(15546,a,16940,a)].">
      <j1 rule="hyper" parents="15546 16940"/>
    </justification>
  </clause>

  <clause id="16943">
    <literal><![CDATA[
      K(x,(y \ 1) \ a(z,u,u \ 1)) = K(x,y * (z \ L(z,u,u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(14641,a,16942,a),flip(a)].">
      <j1 rule="hyper" parents="14641 16942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16944">
    <literal><![CDATA[
      K(x,y * (z \ L(z,u,u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * a(z,u,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(16943(a,1),14641(a,1))].">
      <j1 rule="para" parents="16943 14641"/>
    </justification>
  </clause>

  <clause id="16945">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ R(u,y,y \ 1)) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16172,a(flip),b,16938,a),flip(a)].">
      <j1 rule="hyper" parents="64 16172 16938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16946">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ L(u,y,y \ 1)) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16939,a(flip),b,16945,a)].">
      <j1 rule="hyper" parents="64 16939 16945"/>
    </justification>
  </clause>

  <clause id="16947">
    <literal><![CDATA[
      K(x,L(y \ T(z,u \ 1),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ T(z,u),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(16936(a,1),12116(a,1))].">
      <j1 rule="para" parents="16936 12116"/>
    </justification>
  </clause>

  <clause id="16948">
    <literal><![CDATA[
      K(x,L(((y * z) \ y) \ T(u,z),w,v5)) = K(x,L(u / ((y * z) \ y),w,v5))
    ]]></literal>
    <justification jstring="[hyper(16947,a,13538,a)].">
      <j1 rule="hyper" parents="16947 13538"/>
    </justification>
  </clause>

  <clause id="16949">
    <literal><![CDATA[
      K(x,L((y / (z * y)) \ T(u,z),w,v5)) = K(x,L(u / (y / (z * y)),w,v5))
    ]]></literal>
    <justification jstring="[hyper(16947,a,13537,a)].">
      <j1 rule="hyper" parents="16947 13537"/>
    </justification>
  </clause>

  <clause id="16950">
    <literal><![CDATA[
      K(x,y * (z \ T((u \ (z * K(w,v5))) * z,K(v5,w)))) = K(x,y * ((K(w,v5) * z) / u))
    ]]></literal>
    <justification jstring="[para(15228(a,1),16808(a,1,2,2,2,1))].">
      <j1 rule="para" parents="15228 16808"/>
    </justification>
  </clause>

  <clause id="16951">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ (T(z,y) * (u / ((T(y,z) / z) \ y)))) = K(x,T(u / y,T(y,z) / z))
    ]]></literal>
    <justification jstring="[para(8823(a,1),16917(a,1,2,1))].">
      <j1 rule="para" parents="8823 16917"/>
    </justification>
  </clause>

  <clause id="16952">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ (T(z,y) * (u / T(z,y)))) = K(x,T(u / y,T(y,z) / z))
    ]]></literal>
    <justification jstring="[para(4628(a,1),16951(a,1,2,2,2,2))].">
      <j1 rule="para" parents="4628 16951"/>
    </justification>
  </clause>

  <clause id="16954">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(z,y) * (u / T(z,y)))) = K(x,T(u / y,T(y,z) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16858,a(flip),b,16952,a)].">
      <j1 rule="hyper" parents="64 16858 16952"/>
    </justification>
  </clause>

  <clause id="16955">
    <literal><![CDATA[
      K(x,T(y,z) \ (T(z,y) * (u / T(z,y)))) = K(x,T(u / y,z \ y))
    ]]></literal>
    <justification jstring="[para(13299(a,1),16954(a,2,2))].">
      <j1 rule="para" parents="13299 16954"/>
    </justification>
  </clause>

  <clause id="16956">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,T(z,y))) = K(x,T(u / y,z \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16369,a(flip),b,16955,a)].">
      <j1 rule="hyper" parents="64 16369 16955"/>
    </justification>
  </clause>

  <clause id="16957">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,z * K(y \ 1,z * y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13447,a(flip),b,16910,a)].">
      <j1 rule="hyper" parents="64 13447 16910"/>
    </justification>
  </clause>

  <clause id="16958">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,z * K(y,z * y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(16862(a,1),16957(a,1,2,2))].">
      <j1 rule="para" parents="16862 16957"/>
    </justification>
  </clause>

  <clause id="16959">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,z * K(y,y * z))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(6142(a,1),16958(a,1,2,2,2,2))].">
      <j1 rule="para" parents="6142 16958"/>
    </justification>
  </clause>

  <clause id="16960">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,z * K(z,y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(16276(a,1),16959(a,1,2,2))].">
      <j1 rule="para" parents="16276 16959"/>
    </justification>
  </clause>

  <clause id="16961">
    <literal><![CDATA[
      K(x,(((y * z) \ z) \ z) \ T(u,T(z,y))) = K(x,T(u / (y * z),(y * z) \ z))
    ]]></literal>
    <justification jstring="[para(5753(a,2),16960(a,1,2,2,2))].">
      <j1 rule="para" parents="5753 16960"/>
    </justification>
  </clause>

  <clause id="16962">
    <literal><![CDATA[
      K(x,T(y / (z * u),(z * u) \ u)) = K(x,T(z * u,u) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(13579,a,16961,a),flip(a)].">
      <j1 rule="hyper" parents="13579 16961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16963">
    <literal><![CDATA[
      K(x,T(y / (z * u),(z * u) \ u)) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,15897,a(flip),b,16962,a),flip(a)].">
      <j1 rule="hyper" parents="373 15897 16962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16964">
    <literal><![CDATA[
      K(x,T(y / (z * u),u \ (z \ u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(7453(a,1),16963(a,1,2))].">
      <j1 rule="para" parents="7453 16963"/>
    </justification>
  </clause>

  <clause id="16965">
    <literal><![CDATA[
      K(x,T(y / (z * u),T(z,u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(11223,a,16964,a)].">
      <j1 rule="hyper" parents="11223 16964"/>
    </justification>
  </clause>

  <clause id="16966">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,T((z * u) \ z,z * u)))
    ]]></literal>
    <justification jstring="[para(6004(a,1),16965(a,2,2,1))].">
      <j1 rule="para" parents="6004 16965"/>
    </justification>
  </clause>

  <clause id="16967">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * T((K(y,z) * x) / K(y,z),K(z,y)),K(z,y)) = T(u,T(K(y,z),x) * x)
    ]]></literal>
    <justification jstring="[para(8177(a,1),16802(a,1,1))].">
      <j1 rule="para" parents="8177 16802"/>
    </justification>
  </clause>

  <clause id="16968">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * T(T(x,K(y,z)),K(z,y)),K(z,y)) = T(u,T(K(y,z),x) * x)
    ]]></literal>
    <justification jstring="[para(8177(a,1),16967(a,1,2,1,2,1))].">
      <j1 rule="para" parents="8177 16967"/>
    </justification>
  </clause>

  <clause id="16969">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * x,K(z,y)) = T(u,T(K(y,z),x) * x)
    ]]></literal>
    <justification jstring="[para(7825(a,1),16968(a,1,2,1,2))].">
      <j1 rule="para" parents="7825 16968"/>
    </justification>
  </clause>

  <clause id="16970">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * x,K(y,z)) = T(u,T(K(y,z),x) * x)
    ]]></literal>
    <justification jstring="[para(8153(a,1),16969(a,1,2))].">
      <j1 rule="para" parents="8153 16969"/>
    </justification>
  </clause>

  <clause id="16971">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * x,K(y,z)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,11143,a(flip),b,16970,a),flip(a)].">
      <j1 rule="hyper" parents="373 11143 16970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16972">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(u * x,K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(u,x * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16970(a,2),11200(a,1))].">
      <j1 rule="para" parents="16970 11200"/>
    </justification>
  </clause>

  <clause id="16973">
    <literal><![CDATA[
      a(T((x \ y) * x,z),u,T(T(y,x),z)) \ (K(y,z) * x) = (x \ y) \ L(T((x \ y) * x,z),u,T((x \ y) * x,z))
    ]]></literal>
    <justification jstring="[para(16135(a,1),14821(a,1,1))].">
      <j1 rule="para" parents="16135 14821"/>
    </justification>
  </clause>

  <clause id="16974">
    <literal><![CDATA[
      a(T(T(x,y),z),u,T(T(x,y),z)) \ (K(x,z) * y) = (y \ x) \ L(T((y \ x) * y,z),u,T((y \ x) * y,z))
    ]]></literal>
    <justification jstring="[para(16132(a,1),16973(a,1,1))].">
      <j1 rule="para" parents="16132 16973"/>
    </justification>
  </clause>

  <clause id="16975">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,z),u,T((x \ y) * x,z)) = a(T(y,x),u,T(y,x)) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(11944(a,1),16974(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11944 16974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16976">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,z),u,T((x \ y) * x,z)) = a(y,u,y) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(11944(a,1),16975(a,2,1))].">
      <j1 rule="para" parents="11944 16975"/>
    </justification>
  </clause>

  <clause id="16978">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,z),u,T((x \ y) * x,z)) = K(y,z) * (a(y,u,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13249,a(flip),b,16976,a),flip(a)].">
      <j1 rule="hyper" parents="373 13249 16976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16980">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,z),u,T(T(y,x),z)) = K(y,z) * (a(y,u,y) \ x)
    ]]></literal>
    <justification jstring="[para(13066(a,1),16978(a,1,2))].">
      <j1 rule="para" parents="13066 16978"/>
    </justification>
  </clause>

  <clause id="16981">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,z),u,y) = K(y,z) * (a(y,u,y) \ x)
    ]]></literal>
    <justification jstring="[para(13095(a,1),16980(a,1,2))].">
      <j1 rule="para" parents="13095 16980"/>
    </justification>
  </clause>

  <clause id="16983">
    <literal><![CDATA[
      (x * K(x \ y,y \ x)) / (K(x \ y,x) / (x \ y)) = ((1 / (1 / (x \ y))) \ y) / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(7225(a,1),15079(a,1,2,1))].">
      <j1 rule="para" parents="7225 15079"/>
    </justification>
  </clause>

  <clause id="16984">
    <literal><![CDATA[
      ((1 / (1 / (x \ y))) \ y) / (1 / (x \ y)) = (x * K(x \ y,y \ x)) / (1 / (y / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,6466,a(flip),b,16983,a),flip(a)].">
      <j1 rule="hyper" parents="64 6466 16983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16987">
    <literal><![CDATA[
      (T(x,y \ 1) * (y \ 1)) * T(K(y \ x,z),y \ T(x,y \ 1)) = T(T(T(x,y \ 1) * (y \ 1),z),K(T(x,y \ 1),y))
    ]]></literal>
    <justification jstring="[para(14492(a,1),16448(a,1,2,1))].">
      <j1 rule="para" parents="14492 16448"/>
    </justification>
  </clause>

  <clause id="16988">
    <literal><![CDATA[
      T(T(T(x,y \ 1) * (y \ 1),z),K(T(x,y \ 1),y)) = (T(x,y \ 1) * (y \ 1)) * T(K(y \ x,z),x / y)
    ]]></literal>
    <justification jstring="[para(14796(a,1),16987(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14796 16987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16989">
    <literal><![CDATA[
      T(T(T(x,y \ 1) * (y \ 1),z),K(T(x,y \ 1),y)) = (T(x,y \ 1) * (y \ 1)) * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4096(a,1),16988(a,2,2))].">
      <j1 rule="para" parents="4096 16988"/>
    </justification>
  </clause>

  <clause id="16990">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w)) \ ((R(w,v5,v6) * T(u,w)) / T(u,w)) = (T(T(u,w),R(T(x,u),y,z)) * R(T(w,u),v5,v6)) / T(u,w)
    ]]></literal>
    <justification jstring="[para(200(a,1),16794(a,1,1,2))].">
      <j1 rule="para" parents="200 16794"/>
    </justification>
  </clause>

  <clause id="16991">
    <literal><![CDATA[
      (T(T(x,y),R(T(y,x),z,u)) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ ((R(y,w,v5) * T(x,y)) / T(x,y))
    ]]></literal>
    <justification jstring="[para(7920(a,1),16990(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7920 16990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16992">
    <literal><![CDATA[
      (T(T(x,y),R(T(y,x),z,u)) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ R(y,w,v5)
    ]]></literal>
    <justification jstring="[para(11(a,1),16991(a,2,2))].">
      <j1 rule="para" parents="11 16991"/>
    </justification>
  </clause>

  <clause id="16994">
    <literal><![CDATA[
      (T(T(x,y),L(T(y,x),z,u)) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ R(y,w,v5)
    ]]></literal>
    <justification jstring="[para(15583(a,1),16992(a,1,1,1))].">
      <j1 rule="para" parents="15583 16992"/>
    </justification>
  </clause>

  <clause id="16995">
    <literal><![CDATA[
      (T(T(x,L(y,z,u)),y) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ R(y,w,v5)
    ]]></literal>
    <justification jstring="[para(4713(a,1),16994(a,1,1,1))].">
      <j1 rule="para" parents="4713 16994"/>
    </justification>
  </clause>

  <clause id="16996">
    <literal><![CDATA[
      (T(T(x,y),L(y,z,u)) * R(T(y,x),w,v5)) / T(x,y) = K(L(y,z,u),x) \ R(y,w,v5)
    ]]></literal>
    <justification jstring="[para(23(a,1),16995(a,1,1,1))].">
      <j1 rule="para" parents="23 16995"/>
    </justification>
  </clause>

  <clause id="16997">
    <literal><![CDATA[
      K(L(x,y,z),u) \ R(x,y,z) = (T(u,x) * R(x,y,z)) / T(u,x)
    ]]></literal>
    <justification jstring="[para(15685(a,1),16996(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15685 16996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16998">
    <literal><![CDATA[
      K(L(x,y,z),u) \ R(x,y,z) = R(K(x,u) \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6552,a(flip),b,16997,a),flip(a)].">
      <j1 rule="hyper" parents="373 6552 16997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16999">
    <literal><![CDATA[
      R(K(x,y) \ x,y,z) = K(x,y) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10175(a,1),16998(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10175 16998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17000">
    <literal><![CDATA[
      K(x,y) \ R(x,y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5968,a(flip),b,16999,a),flip(a)].">
      <j1 rule="hyper" parents="64 5968 16999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17001">
    <literal><![CDATA[
      K(x,L(((y * (z * y)) / y) \ L(y,z,y),u,w) * z) = K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w))
    ]]></literal>
    <justification jstring="[para(14289(a,1),16145(a,1,2))].">
      <j1 rule="para" parents="14289 16145"/>
    </justification>
  </clause>

  <clause id="17002">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w)) = K(x,L(T((y * (y * z)) / y,y) \ y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(16766(a,1),17001(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="16766 17001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17003">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w)) = K(x,L((y * z) \ y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(255(a,1),17002(a,2,2,1,1,1))].">
      <j1 rule="para" parents="255 17002"/>
    </justification>
  </clause>

  <clause id="17005">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z * L((y * z) \ y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(17003(a,2),14731(a,1))].">
      <j1 rule="para" parents="17003 14731"/>
    </justification>
  </clause>

  <clause id="17006">
    <literal><![CDATA[
      T(K(x * (y \ (y / z)),(y \ (y / z)) \ 1) / (y \ (y / z)),z \ 1) = K((y \ (y / z)) \ x,z) / (y \ (y / z))
    ]]></literal>
    <justification jstring="[para(6710(a,1),15284(a,2,1))].">
      <j1 rule="para" parents="6710 15284"/>
    </justification>
  </clause>

  <clause id="17008">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),x \ (K(y,L(z,u * x,x)) * u))
    ]]></literal>
    <justification jstring="[para(16643(a,1),15675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16643 15675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17009">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),x \ (K(y,L(z,u,x)) * u))
    ]]></literal>
    <justification jstring="[para(15522(a,1),17008(a,2,2,2,1))].">
      <j1 rule="para" parents="15522 17008"/>
    </justification>
  </clause>

  <clause id="17011">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),(x \ u) * K(y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(15548(a,1),17009(a,2,2))].">
      <j1 rule="para" parents="15548 17009"/>
    </justification>
  </clause>

  <clause id="17012">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) * T(1 / (y / z),y)) = K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(66(a,1),16144(a,1,2,2))].">
      <j1 rule="para" parents="66 16144"/>
    </justification>
  </clause>

  <clause id="17013">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,z / (z * u)))
    ]]></literal>
    <justification jstring="[para(8241(a,1),16966(a,2,2,2))].">
      <j1 rule="para" parents="8241 16966"/>
    </justification>
  </clause>

  <clause id="17014">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,z \ (u \ z)))
    ]]></literal>
    <justification jstring="[para(9239(a,1),17013(a,2,2,2))].">
      <j1 rule="para" parents="9239 17013"/>
    </justification>
  </clause>

  <clause id="17015">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(u \ 1,z * u)) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,16935,a(flip),b,17014,a),flip(a)].">
      <j1 rule="hyper" parents="373 16935 17014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17016">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(z * u,u)) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,16897,a(flip),b,17015,a),flip(a)].">
      <j1 rule="hyper" parents="373 16897 17015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17017">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,(z * K(z,u)) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,13554,a(flip),b,17016,a),flip(a)].">
      <j1 rule="hyper" parents="373 13554 17016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17018">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,T(z,u) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(5753(a,2),17017(a,2,2,1))].">
      <j1 rule="para" parents="5753 17017"/>
    </justification>
  </clause>

  <clause id="17019">
    <literal><![CDATA[
      K(x,T(y / ((z * u) * ((z * u) \ z)),T(z * u,(z * u) \ z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,16956,a(flip),b,17018,a),flip(a)].">
      <j1 rule="hyper" parents="373 16956 17018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17020">
    <literal><![CDATA[
      K(x,T(y / z,T(z * u,(z * u) \ z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[para(10(a,1),17019(a,1,2,1,2))].">
      <j1 rule="para" parents="10 17019"/>
    </justification>
  </clause>

  <clause id="17021">
    <literal><![CDATA[
      K(x,T(y / z,T(z * u,z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[para(7410(a,1),17020(a,1,2))].">
      <j1 rule="para" parents="7410 17020"/>
    </justification>
  </clause>

  <clause id="17022">
    <literal><![CDATA[
      K(x,T(y / z,u \ z)) = K(x,T(y / z,u * z))
    ]]></literal>
    <justification jstring="[para(11122(a,1),17021(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11122 17021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17023">
    <literal><![CDATA[
      K(x,T((y * z) / z,u * z)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(11(a,1),17022(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 17022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17024">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(11(a,1),17023(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 17023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17025">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(11218,a,17024,a)].">
      <j1 rule="hyper" parents="11218 17024"/>
    </justification>
  </clause>

  <clause id="17026">
    <literal><![CDATA[
      K(x,T((y \ z) / u,y * z)) = K(x,u \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(8456,a,17024,a),flip(a)].">
      <j1 rule="hyper" parents="8456 17024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17027">
    <literal><![CDATA[
      K(x \ y,T(z,x * y)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(5977,a,17024,a),flip(a)].">
      <j1 rule="hyper" parents="5977 17024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17028">
    <literal><![CDATA[
      x \ T(x,T(y,z * u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,5726,a(flip),b,17024,a)].">
      <j1 rule="hyper" parents="373 5726 17024"/>
    </justification>
  </clause>

  <clause id="17029">
    <literal><![CDATA[
      T(x,T(y,z \ u)) = T(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(143,a,17024,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 17024 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17030">
    <literal><![CDATA[
      K(x,T(y,z \ (z \ u))) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),17024(a,2,2,2))].">
      <j1 rule="para" parents="10 17024"/>
    </justification>
  </clause>

  <clause id="17031">
    <literal><![CDATA[
      K(x,T(y,z * z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(379(a,1),17024(a,1,2)),flip(a)].">
      <j1 rule="para" parents="379 17024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17032">
    <literal><![CDATA[
      K(x,T(y,z \ (z \ 1))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(377(a,1),17024(a,2,2))].">
      <j1 rule="para" parents="377 17024"/>
    </justification>
  </clause>

  <clause id="17033">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z * u)) = K(y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[para(17024(a,1),8064(a,1,2))].">
      <j1 rule="para" parents="17024 8064"/>
    </justification>
  </clause>

  <clause id="17035">
    <literal><![CDATA[
      K(x,(y * y) * z) = K(x,z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(11233,a,17031,a),flip(a)].">
      <j1 rule="hyper" parents="11233 17031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17036">
    <literal><![CDATA[
      K(x / (y * y),z) = K((y * y) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(8322,a,17031,a)].">
      <j1 rule="hyper" parents="8322 17031"/>
    </justification>
  </clause>

  <clause id="17037">
    <literal><![CDATA[
      T(x,T(y,z * z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,17031,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 17031 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17038">
    <literal><![CDATA[
      K(x,K(y,z * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,17031,a,b,8350,a),flip(a)].">
      <j1 rule="hyper" parents="138 17031 8350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17039">
    <literal><![CDATA[
      x * ((y * y) * K(x,z)) = T(x,z) * (y * y)
    ]]></literal>
    <justification jstring="[para(17031(a,1),7950(a,1,2,2))].">
      <j1 rule="para" parents="17031 7950"/>
    </justification>
  </clause>

  <clause id="17040">
    <literal><![CDATA[
      K(x,y) * ((y \ (z * (y * z))) \ 1) = (y \ (z * (y * z))) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(17031(a,1),14975(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17031 14975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17041">
    <literal><![CDATA[
      T(x,K(y,z * z)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,17038,a)].">
      <j1 rule="hyper" parents="57 17038"/>
    </justification>
  </clause>

  <clause id="17042">
    <literal><![CDATA[
      T(x,K(y * y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(8728,a,17041,a)].">
      <j1 rule="hyper" parents="8728 17041"/>
    </justification>
  </clause>

  <clause id="17043">
    <literal><![CDATA[
      T(x,y / (z * z)) = T(x,(z * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(8727,a,17041,a),flip(a)].">
      <j1 rule="hyper" parents="8727 17041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17044">
    <literal><![CDATA[
      x * (y * K(x,z * z)) = T(x,z * z) * y
    ]]></literal>
    <justification jstring="[hyper(8668,a,17041,a)].">
      <j1 rule="hyper" parents="8668 17041"/>
    </justification>
  </clause>

  <clause id="17045">
    <literal><![CDATA[
      K(x * x,y) * z = z * K(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(8309,a,17041,a),flip(a)].">
      <j1 rule="hyper" parents="8309 17041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17046">
    <literal><![CDATA[
      T(x,T(y * y,z)) = T(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(8189,a,17041,a)].">
      <j1 rule="hyper" parents="8189 17041"/>
    </justification>
  </clause>

  <clause id="17047">
    <literal><![CDATA[
      K(x,y * y) * z = z * K(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(7837,a,17041,a),flip(a)].">
      <j1 rule="hyper" parents="7837 17041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17048">
    <literal><![CDATA[
      T(x,(y * y) * z) = T(x,z * (y * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,11151,a(flip),b,17041,a)].">
      <j1 rule="hyper" parents="64 11151 17041"/>
    </justification>
  </clause>

  <clause id="17049">
    <literal><![CDATA[
      T(K(x,x \ (y * y)),z) = K(x,x \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(269,a,8708,a(flip),b,17041,a(flip))].">
      <j1 rule="hyper" parents="269 8708 17041"/>
    </justification>
  </clause>

  <clause id="17050">
    <literal><![CDATA[
      K(x,T(y * y,z)) = K(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(38,a,12616,a(flip),b,17041,a(flip))].">
      <j1 rule="hyper" parents="38 12616 17041"/>
    </justification>
  </clause>

  <clause id="17051">
    <literal><![CDATA[
      K(x * x,T(y,z)) = K(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(8733,a,17042,a)].">
      <j1 rule="hyper" parents="8733 17042"/>
    </justification>
  </clause>

  <clause id="17052">
    <literal><![CDATA[
      T((x * x) / y,K(y,z)) = (x * x) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,9077,a,b,17042,a)].">
      <j1 rule="hyper" parents="64 9077 17042"/>
    </justification>
  </clause>

  <clause id="17053">
    <literal><![CDATA[
      T(x * x,K(y,z)) = x * x
    ]]></literal>
    <justification jstring="[hyper(35,a,8359,a(flip),b,17042,a(flip))].">
      <j1 rule="hyper" parents="35 8359 17042"/>
    </justification>
  </clause>

  <clause id="17054">
    <literal><![CDATA[
      T((x * x) \ y,T(z,y)) = T((x * x) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,8690,a,b,17037,a)].">
      <j1 rule="hyper" parents="64 8690 17037"/>
    </justification>
  </clause>

  <clause id="17055">
    <literal><![CDATA[
      T(x,T((y * y) * z,u)) = T(x,T(z * (y * y),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11138,a(flip),b,17037,a),flip(a)].">
      <j1 rule="hyper" parents="64 11138 17037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17056">
    <literal><![CDATA[
      T(x,y * ((y \ 1) \ (z / (y * u)))) = T(x,z / ((y \ 1) * u))
    ]]></literal>
    <justification jstring="[para(4210(a,1),17037(a,1,2))].">
      <j1 rule="para" parents="4210 17037"/>
    </justification>
  </clause>

  <clause id="17057">
    <literal><![CDATA[
      K(x,y) / (z * z) = (z * z) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(225,a,17053,a(flip),b,850,a)].">
      <j1 rule="hyper" parents="225 17053 850"/>
    </justification>
  </clause>

  <clause id="17060">
    <literal><![CDATA[
      (x * x) \ (a(y,x,x) \ K(x * x,y)) = T(((y * x) * x) / y,x * x) \ 1
    ]]></literal>
    <justification jstring="[para(17046(a,1),16470(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17046 16470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17061">
    <literal><![CDATA[
      K(x * (y * y),T(x,z)) = K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,8747,a,b,17051,a)].">
      <j1 rule="hyper" parents="64 8747 17051"/>
    </justification>
  </clause>

  <clause id="17062">
    <literal><![CDATA[
      (x \ T(y,z * z)) \ 1 = (x \ y) \ K(z * z,y)
    ]]></literal>
    <justification jstring="[para(17051(a,1),15662(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17051 15662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17063">
    <literal><![CDATA[
      T(K(x * x,y) * z,u) = T(z,u) * K(x * x,y)
    ]]></literal>
    <justification jstring="[para(17051(a,1),15722(a,1,1,1))].">
      <j1 rule="para" parents="17051 15722"/>
    </justification>
  </clause>

  <clause id="17064">
    <literal><![CDATA[
      T(T(x,y),z \ (z \ 1)) = T(x,y) * K(z * z,x)
    ]]></literal>
    <justification jstring="[para(17051(a,1),15870(a,2,2))].">
      <j1 rule="para" parents="17051 15870"/>
    </justification>
  </clause>

  <clause id="17065">
    <literal><![CDATA[
      K((x \ y) * z,T(u,y * x)) = K(z * (x \ y),u)
    ]]></literal>
    <justification jstring="[hyper(11195,a,17025,a),flip(a)].">
      <j1 rule="hyper" parents="11195 17025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17066">
    <literal><![CDATA[
      K(x,T(y,z * u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17024,a(flip),b,17025,a)].">
      <j1 rule="hyper" parents="64 17024 17025"/>
    </justification>
  </clause>

  <clause id="17067">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),u * z)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16374,a(flip),b,17025,a),flip(a)].">
      <j1 rule="hyper" parents="64 16374 17025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17068">
    <literal><![CDATA[
      K(x,T(y * (z \ u),u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(17025(a,1),11228(a,1))].">
      <j1 rule="para" parents="17025 11228"/>
    </justification>
  </clause>

  <clause id="17069">
    <literal><![CDATA[
      K(x,T((y \ z) * u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (y \ z)) = w
    ]]></literal>
    <justification jstring="[para(17025(a,1),11233(a,1))].">
      <j1 rule="para" parents="17025 11233"/>
    </justification>
  </clause>

  <clause id="17070">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(17025(a,1),11218(a,1))].">
      <j1 rule="para" parents="17025 11218"/>
    </justification>
  </clause>

  <clause id="17071">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / ((y \ 1) * z)) = w
    ]]></literal>
    <justification jstring="[para(17025(a,1),14576(a,1))].">
      <j1 rule="para" parents="17025 14576"/>
    </justification>
  </clause>

  <clause id="17072">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ T(w * y,K(z,u))) = K(x,T(w,K(z,u) \ y))
    ]]></literal>
    <justification jstring="[para(16971(a,2),17025(a,2,2)),flip(a)].">
      <j1 rule="para" parents="16971 17025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17073">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17025,a(flip),b,17030,a)].">
      <j1 rule="hyper" parents="64 17025 17030"/>
    </justification>
  </clause>

  <clause id="17074">
    <literal><![CDATA[
      K(x,y * (z * z)) = K(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15752,a(flip),b,17035,a),flip(a)].">
      <j1 rule="hyper" parents="64 15752 17035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17075">
    <literal><![CDATA[
      K(x / (y * y),z) = K(y \ (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,14590,a(flip),b,17036,a),flip(a)].">
      <j1 rule="hyper" parents="373 14590 17036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17076">
    <literal><![CDATA[
      T(x,y / (z * z)) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,14427,a(flip),b,17043,a),flip(a)].">
      <j1 rule="hyper" parents="373 14427 17043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17077">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) \ z = (x \ z) * K(x,y * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15872,a,b,17047,a)].">
      <j1 rule="hyper" parents="64 15872 17047"/>
    </justification>
  </clause>

  <clause id="17078">
    <literal><![CDATA[
      T(x,y * (z * z)) = T(x,z * (z * y))
    ]]></literal>
    <justification jstring="[hyper(15896,a,17048,a),flip(a)].">
      <j1 rule="hyper" parents="15896 17048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17079">
    <literal><![CDATA[
      T(T(x,y),z * z) = T(x,y * (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1775,a,b,17048,a)].">
      <j1 rule="hyper" parents="64 1775 17048"/>
    </justification>
  </clause>

  <clause id="17080">
    <literal><![CDATA[
      T(x,((y * y) * z) / u) = T(x,(z / u) * (y * y))
    ]]></literal>
    <justification jstring="[para(807(a,2),17048(a,1,2))].">
      <j1 rule="para" parents="807 17048"/>
    </justification>
  </clause>

  <clause id="17081">
    <literal><![CDATA[
      T(x,((y * z) \ u) * (z * z)) = T(x,R(y / z,z,z) \ u)
    ]]></literal>
    <justification jstring="[para(948(a,1),17048(a,1,2)),flip(a)].">
      <j1 rule="para" parents="948 17048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17082">
    <literal><![CDATA[
      ((x * x) \ K(y,z)) * u = K(y,z) * ((x * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(144,a,17057,a(flip),b,896,a)].">
      <j1 rule="hyper" parents="144 17057 896"/>
    </justification>
  </clause>

  <clause id="17084">
    <literal><![CDATA[
      K(x * (y * z),T(u,z * y)) = K((y * z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(11189,a,17066,a),flip(a)].">
      <j1 rule="hyper" parents="11189 17066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17085">
    <literal><![CDATA[
      K(x,T(y \ (z * u),u * z)) = K(x,(z * u) / y)
    ]]></literal>
    <justification jstring="[hyper(8699,a,17066,a),flip(a)].">
      <j1 rule="hyper" parents="8699 17066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17086">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z * y)) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(8325,a,17066,a),flip(a)].">
      <j1 rule="hyper" parents="8325 17066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17087">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,9516,a,b,17066,a)].">
      <j1 rule="hyper" parents="373 9516 17066"/>
    </justification>
  </clause>

  <clause id="17088">
    <literal><![CDATA[
      x * K(y,T(z,u * w)) = x * K(y,T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(145,a,17066,a,b,9,a)].">
      <j1 rule="hyper" parents="145 17066 9"/>
    </justification>
  </clause>

  <clause id="17089">
    <literal><![CDATA[
      T(x,T(y,z * u)) = T(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(143,a,17066,a,b,6406,a)].">
      <j1 rule="hyper" parents="143 17066 6406"/>
    </justification>
  </clause>

  <clause id="17090">
    <literal><![CDATA[
      K(x,T(y,z * (u / z))) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),17066(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 17066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17093">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(11129(a,1),17073(a,1,2))].">
      <j1 rule="para" parents="11129 17073"/>
    </justification>
  </clause>

  <clause id="17094">
    <literal><![CDATA[
      K(x * ((y \ z) * y),T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(((y \ z) * y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(17073(a,1),11189(a,1))].">
      <j1 rule="para" parents="17073 11189"/>
    </justification>
  </clause>

  <clause id="17095">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(11233,a,17093,a),flip(a)].">
      <j1 rule="hyper" parents="11233 17093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17096">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z))) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(11222,a,17093,a)].">
      <j1 rule="hyper" parents="11222 17093"/>
    </justification>
  </clause>

  <clause id="17097">
    <literal><![CDATA[
      K(x * T(y,z),T(u,y)) = K(T(y,z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(11189,a,17093,a),flip(a)].">
      <j1 rule="hyper" parents="11189 17093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17098">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8772,a,17093,a)].">
      <j1 rule="hyper" parents="8772 17093"/>
    </justification>
  </clause>

  <clause id="17099">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8456,a,17093,a),flip(a)].">
      <j1 rule="hyper" parents="8456 17093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17100">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x)) = K(z / T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(8322,a,17093,a),flip(a)].">
      <j1 rule="hyper" parents="8322 17093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17101">
    <literal><![CDATA[
      K(x \ T(y,z),T(u,y)) = K(T(y,z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(8311,a,17093,a),flip(a)].">
      <j1 rule="hyper" parents="8311 17093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17103">
    <literal><![CDATA[
      K(x * y,T(z,T(x,u))) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,11177,a(flip),b,17093,a),flip(a)].">
      <j1 rule="hyper" parents="373 11177 17093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17105">
    <literal><![CDATA[
      K(x \ y,T(z,T(y,u))) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,8204,a(flip),b,17093,a),flip(a)].">
      <j1 rule="hyper" parents="373 8204 17093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17106">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,17093,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 17093 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17108">
    <literal><![CDATA[
      K(x,T(y,z)) * T(z,u) = T(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,17093,a(flip),b,8192,a)].">
      <j1 rule="hyper" parents="144 17093 8192"/>
    </justification>
  </clause>

  <clause id="17109">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(117(a,1),17093(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 17093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17110">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x)) = K(z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(17093(a,1),7879(a,1,2))].">
      <j1 rule="para" parents="17093 7879"/>
    </justification>
  </clause>

  <clause id="17111">
    <literal><![CDATA[
      K(x * T(y,z),T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(17093(a,1),11189(a,1))].">
      <j1 rule="para" parents="17093 11189"/>
    </justification>
  </clause>

  <clause id="17112">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * T(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(17093(a,1),11195(a,1))].">
      <j1 rule="para" parents="17093 11195"/>
    </justification>
  </clause>

  <clause id="17113">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,T(z,u))) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(17093(a,1),12011(a,1,1))].">
      <j1 rule="para" parents="17093 12011"/>
    </justification>
  </clause>

  <clause id="17114">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x,w)) = K(y,T(x,w)) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(17093(a,1),12438(a,1,2))].">
      <j1 rule="para" parents="17093 12438"/>
    </justification>
  </clause>

  <clause id="17118">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,7867,a(flip),b,17098,a),flip(a)].">
      <j1 rule="hyper" parents="373 7867 17098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17119">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) = K(x \ T(y,z),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9895,a(flip),b,17098,a)].">
      <j1 rule="hyper" parents="64 9895 17098"/>
    </justification>
  </clause>

  <clause id="17120">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y)) = T(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8856,a,17106,a),flip(a)].">
      <j1 rule="hyper" parents="8856 17106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17121">
    <literal><![CDATA[
      T(x,T(T(y,z) / u,y)) = T(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7554,a,17106,a),flip(a)].">
      <j1 rule="hyper" parents="7554 17106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17122">
    <literal><![CDATA[
      K(T(x,y),z) \ T(z,T(u,x)) = T(T(z,u),T(x,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,17106,a(flip),b,8045,a)].">
      <j1 rule="hyper" parents="139 17106 8045"/>
    </justification>
  </clause>

  <clause id="17123">
    <literal><![CDATA[
      T(x,T(y,z / u)) = T(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(117(a,1),17106(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 17106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17124">
    <literal><![CDATA[
      T(x,T(T(y,z),u)) = T(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(4633(a,1),17106(a,1,2))].">
      <j1 rule="para" parents="4633 17106"/>
    </justification>
  </clause>

  <clause id="17125">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = y * T(y \ T(x,y),T(z,x))
    ]]></literal>
    <justification jstring="[para(17106(a,1),8682(a,2,2))].">
      <j1 rule="para" parents="17106 8682"/>
    </justification>
  </clause>

  <clause id="17127">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8191,a,17118,a)].">
      <j1 rule="hyper" parents="8191 17118"/>
    </justification>
  </clause>

  <clause id="17130">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17118(a,2),7964(a,1))].">
      <j1 rule="para" parents="17118 7964"/>
    </justification>
  </clause>

  <clause id="17132">
    <literal><![CDATA[
      K(x,K(y,z) / u) = K(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8316,a,17127,a),flip(a)].">
      <j1 rule="hyper" parents="8316 17127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17133">
    <literal><![CDATA[
      K(K(x,y) / z,u) = K(z \ K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(8314,a,17127,a)].">
      <j1 rule="hyper" parents="8314 17127"/>
    </justification>
  </clause>

  <clause id="17134">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8249,a,17127,a),flip(a)].">
      <j1 rule="hyper" parents="8249 17127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17137">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7433,a,b,17127,a)].">
      <j1 rule="hyper" parents="64 7433 17127"/>
    </justification>
  </clause>

  <clause id="17138">
    <literal><![CDATA[
      K(K(x,y) * z,z \ 1) = K(z,z \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,16811,a(flip),b,17127,a),flip(a)].">
      <j1 rule="hyper" parents="64 16811 17127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17139">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11115,a(flip),b,17127,a),flip(a)].">
      <j1 rule="hyper" parents="64 11115 17127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17140">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,17127,a(flip),b,6158,a),flip(a)].">
      <j1 rule="hyper" parents="145 17127 6158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17141">
    <literal><![CDATA[
      K(x,y) * K(z,u) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,17127,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 17127 22"/>
    </justification>
  </clause>

  <clause id="17142">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * K(z,u)) = K(u,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,17127,a(flip),b,8158,a)].">
      <j1 rule="hyper" parents="142 17127 8158"/>
    </justification>
  </clause>

  <clause id="17143">
    <literal><![CDATA[
      K(x,K(K(y,z),u)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,17127,a(flip),b,8129,a),flip(a)].">
      <j1 rule="hyper" parents="140 17127 8129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17144">
    <literal><![CDATA[
      T(x \ K(y,z),K(u,x)) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,17127,a(flip),b,8423,a),flip(a)].">
      <j1 rule="hyper" parents="139 17127 8423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17146">
    <literal><![CDATA[
      x * (K(y,z) * K(u,w)) = x * (K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(17127(a,1),251(a,1,2,2))].">
      <j1 rule="para" parents="17127 251"/>
    </justification>
  </clause>

  <clause id="17149">
    <literal><![CDATA[
      x * (K(y,z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (K(u,w) * K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(17127(a,1),737(a,1,2,2))].">
      <j1 rule="para" parents="17127 737"/>
    </justification>
  </clause>

  <clause id="17153">
    <literal><![CDATA[
      K(x,y) * T(x,K(z,u)) = T(T(x,K(z,u)),y)
    ]]></literal>
    <justification jstring="[para(17127(a,1),7438(a,1,1))].">
      <j1 rule="para" parents="17127 7438"/>
    </justification>
  </clause>

  <clause id="17154">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(17127(a,1),7831(a,1,1)),flip(b)].">
      <j1 rule="para" parents="17127 7831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17155">
    <literal><![CDATA[
      T(x * K(y,z),K(x,u)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(17127(a,1),8062(a,2,2))].">
      <j1 rule="para" parents="17127 8062"/>
    </justification>
  </clause>

  <clause id="17156">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(17127(a,1),8249(a,1))].">
      <j1 rule="para" parents="17127 8249"/>
    </justification>
  </clause>

  <clause id="17157">
    <literal><![CDATA[
      T(x,K(K(y,z),u)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,17143,a)].">
      <j1 rule="hyper" parents="57 17143"/>
    </justification>
  </clause>

  <clause id="17158">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ 1) = u \ K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(14538,a,17157,a)].">
      <j1 rule="hyper" parents="14538 17157"/>
    </justification>
  </clause>

  <clause id="17159">
    <literal><![CDATA[
      T(x,K(y,z) / u) = T(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8727,a,17157,a),flip(a)].">
      <j1 rule="hyper" parents="8727 17157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17161">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8309,a,17157,a),flip(a)].">
      <j1 rule="hyper" parents="8309 17157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17162">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(8189,a,17157,a)].">
      <j1 rule="hyper" parents="8189 17157"/>
    </justification>
  </clause>

  <clause id="17163">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(8184,a,17157,a)].">
      <j1 rule="hyper" parents="8184 17157"/>
    </justification>
  </clause>

  <clause id="17164">
    <literal><![CDATA[
      T(x,T(K(y,z),u)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7857,a,17157,a)].">
      <j1 rule="hyper" parents="7857 17157"/>
    </justification>
  </clause>

  <clause id="17165">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11151,a(flip),b,17157,a),flip(a)].">
      <j1 rule="hyper" parents="64 11151 17157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17166">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(17157(a,1),7832(a,1,1))].">
      <j1 rule="para" parents="17157 7832"/>
    </justification>
  </clause>

  <clause id="17167">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(17157(a,1),7848(a,1))].">
      <j1 rule="para" parents="17157 7848"/>
    </justification>
  </clause>

  <clause id="17170">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17157(a,1),8309(a,1))].">
      <j1 rule="para" parents="17157 8309"/>
    </justification>
  </clause>

  <clause id="17171">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17157(a,1),11245(a,1,1))].">
      <j1 rule="para" parents="17157 11245"/>
    </justification>
  </clause>

  <clause id="17172">
    <literal><![CDATA[
      K(x \ K(y,z),x) * (u * K(y,z)) = u * ((x \ K(y,z)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10249,a(flip),b,17163,a)].">
      <j1 rule="hyper" parents="64 10249 17163"/>
    </justification>
  </clause>

  <clause id="17173">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9401,a(flip),b,17163,a)].">
      <j1 rule="hyper" parents="64 9401 17163"/>
    </justification>
  </clause>

  <clause id="17174">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(38,a,12616,a(flip),b,17163,a(flip))].">
      <j1 rule="hyper" parents="38 12616 17163"/>
    </justification>
  </clause>

  <clause id="17175">
    <literal><![CDATA[
      T(x,y / K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(17163(a,1),8727(a,1))].">
      <j1 rule="para" parents="17163 8727"/>
    </justification>
  </clause>

  <clause id="17176">
    <literal><![CDATA[
      K(((x \ y) * x) / (K(z,u) * x),w) = K((x * K(z,u)) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(16589,a,17134,a)].">
      <j1 rule="hyper" parents="16589 17134"/>
    </justification>
  </clause>

  <clause id="17177">
    <literal><![CDATA[
      K(x,y * z) \ K(x,K(y,z)) = K(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(11277,a,17134,a)].">
      <j1 rule="hyper" parents="11277 17134"/>
    </justification>
  </clause>

  <clause id="17178">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(11195,a,17134,a),flip(a)].">
      <j1 rule="hyper" parents="11195 17134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17179">
    <literal><![CDATA[
      K(x \ y,T(z * y,K(u,w))) = K(y / x,y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,11121,a,b,17134,a),flip(a)].">
      <j1 rule="hyper" parents="373 11121 17134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17180">
    <literal><![CDATA[
      K(x,T(y \ z,K(u,w))) = K(x,T(z / y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7423,a,b,17134,a),flip(a)].">
      <j1 rule="hyper" parents="373 7423 17134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17182">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,T(u * K(y,z),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11139,a(flip),b,17134,a)].">
      <j1 rule="hyper" parents="64 11139 17134"/>
    </justification>
  </clause>

  <clause id="17183">
    <literal><![CDATA[
      K(x,T(K(y,z) / u,w)) = K(x,T(u \ K(y,z),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,8756,a(flip),b,17134,a)].">
      <j1 rule="hyper" parents="64 8756 17134"/>
    </justification>
  </clause>

  <clause id="17184">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) = K(z * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,8667,a(flip),b,17134,a)].">
      <j1 rule="hyper" parents="64 8667 17134"/>
    </justification>
  </clause>

  <clause id="17185">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * x) = K(z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,17134,a(flip),b,8280,a)].">
      <j1 rule="hyper" parents="144 17134 8280"/>
    </justification>
  </clause>

  <clause id="17186">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(6321(a,1),17134(a,1,2))].">
      <j1 rule="para" parents="6321 17134"/>
    </justification>
  </clause>

  <clause id="17187">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[para(7188(a,1),17134(a,1,2))].">
      <j1 rule="para" parents="7188 17134"/>
    </justification>
  </clause>

  <clause id="17189">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(17134(a,1),8312(a,1))].">
      <j1 rule="para" parents="17134 8312"/>
    </justification>
  </clause>

  <clause id="17190">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(8352(a,1),17134(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8352 17134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17191">
    <literal><![CDATA[
      x \ T(T(x,K(y,z)),u) = K(x,K(y,z)) * K(x,u)
    ]]></literal>
    <justification jstring="[para(17134(a,1),8043(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17134 8043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17192">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u * z)) = K(x,u * ((y \ z) * y))
    ]]></literal>
    <justification jstring="[para(10249(a,1),17134(a,1,2))].">
      <j1 rule="para" parents="10249 17134"/>
    </justification>
  </clause>

  <clause id="17193">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(17134(a,1),11189(a,1))].">
      <j1 rule="para" parents="17134 11189"/>
    </justification>
  </clause>

  <clause id="17194">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(17134(a,1),11228(a,1))].">
      <j1 rule="para" parents="17134 11228"/>
    </justification>
  </clause>

  <clause id="17195">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17134(a,1),11233(a,1))].">
      <j1 rule="para" parents="17134 11233"/>
    </justification>
  </clause>

  <clause id="17197">
    <literal><![CDATA[
      K(x * (y * K(x,z)),u) = K(T(x,z) * y,u)
    ]]></literal>
    <justification jstring="[para(7188(a,1),17137(a,1,1))].">
      <j1 rule="para" parents="7188 17137"/>
    </justification>
  </clause>

  <clause id="17199">
    <literal><![CDATA[
      K(K(x,y) \ z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(8352(a,1),17137(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8352 17137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17200">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(17137(a,1),8320(a,1))].">
      <j1 rule="para" parents="17137 8320"/>
    </justification>
  </clause>

  <clause id="17203">
    <literal><![CDATA[
      T(x * K(y,z),T(u,x)) = T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11208,a(flip),b,17162,a)].">
      <j1 rule="hyper" parents="64 11208 17162"/>
    </justification>
  </clause>

  <clause id="17204">
    <literal><![CDATA[
      T(K(x,y) / z,u * z) = T(K(x,y) / z,z * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11105,a(flip),b,17162,a),flip(a)].">
      <j1 rule="hyper" parents="64 11105 17162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17205">
    <literal><![CDATA[
      T(x \ K(y,z),T(u,x)) = T(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,8690,a(flip),b,17162,a)].">
      <j1 rule="hyper" parents="64 8690 17162"/>
    </justification>
  </clause>

  <clause id="17206">
    <literal><![CDATA[
      T(x,T(T(y,K(z,u)),w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(23(a,1),17162(a,1,2))].">
      <j1 rule="para" parents="23 17162"/>
    </justification>
  </clause>

  <clause id="17207">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),y) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,K(z,u)) \ x = w
    ]]></literal>
    <justification jstring="[para(17162(a,1),467(a,1))].">
      <j1 rule="para" parents="17162 467"/>
    </justification>
  </clause>

  <clause id="17208">
    <literal><![CDATA[
      T(x,R(K(y,z) \ u,K(y,z),w)) = T(x,(u * w) / (K(y,z) * w))
    ]]></literal>
    <justification jstring="[para(855(a,1),17162(a,1,2))].">
      <j1 rule="para" parents="855 17162"/>
    </justification>
  </clause>

  <clause id="17209">
    <literal><![CDATA[
      T(x,K(y,z) * (u * K(z,y))) = T(x,u)
    ]]></literal>
    <justification jstring="[para(6175(a,2),17162(a,1,2))].">
      <j1 rule="para" parents="6175 17162"/>
    </justification>
  </clause>

  <clause id="17210">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) = T(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(6321(a,1),17162(a,1,2))].">
      <j1 rule="para" parents="6321 17162"/>
    </justification>
  </clause>

  <clause id="17211">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) = T(x,u / T(z,y))
    ]]></literal>
    <justification jstring="[para(6865(a,1),17162(a,1,2))].">
      <j1 rule="para" parents="6865 17162"/>
    </justification>
  </clause>

  <clause id="17212">
    <literal><![CDATA[
      T(x,K(y,z) \ u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(8352(a,1),17162(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8352 17162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17214">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(x,K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x \ u = w
    ]]></literal>
    <justification jstring="[para(7809(a,2),17166(a,1))].">
      <j1 rule="para" parents="7809 17166"/>
    </justification>
  </clause>

  <clause id="17215">
    <literal><![CDATA[
      T(x,K(T(y,z),u)) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(6785(a,1),17164(a,1,2))].">
      <j1 rule="para" parents="6785 17164"/>
    </justification>
  </clause>

  <clause id="17216">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7867(a,2),17164(a,1,2))].">
      <j1 rule="para" parents="7867 17164"/>
    </justification>
  </clause>

  <clause id="17217">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(7884(a,1),17164(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7884 17164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17218">
    <literal><![CDATA[
      T(x,K(y,z * u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(11115(a,1),17164(a,1,2))].">
      <j1 rule="para" parents="11115 17164"/>
    </justification>
  </clause>

  <clause id="17220">
    <literal><![CDATA[
      K(T(x,y),K(z,u)) = K(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(8312,a,17174,a),flip(a)].">
      <j1 rule="hyper" parents="8312 17174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17221">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8126,a,b,17174,a),flip(a)].">
      <j1 rule="hyper" parents="373 8126 17174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17222">
    <literal><![CDATA[
      (x * y) * K(x,K(z,u)) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,17174,a(flip),b,8048,a)].">
      <j1 rule="hyper" parents="145 17174 8048"/>
    </justification>
  </clause>

  <clause id="17223">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(6785(a,1),17174(a,1,2))].">
      <j1 rule="para" parents="6785 17174"/>
    </justification>
  </clause>

  <clause id="17224">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7867(a,2),17174(a,1,2))].">
      <j1 rule="para" parents="7867 17174"/>
    </justification>
  </clause>

  <clause id="17225">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(7884(a,1),17174(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7884 17174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17226">
    <literal><![CDATA[
      K(x,K(y,z * u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(11115(a,1),17174(a,1,2))].">
      <j1 rule="para" parents="11115 17174"/>
    </justification>
  </clause>

  <clause id="17227">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,w) = T(u,w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(17174(a,1),15722(a,1,1,1))].">
      <j1 rule="para" parents="17174 15722"/>
    </justification>
  </clause>

  <clause id="17228">
    <literal><![CDATA[
      T(T(x,T(y,z)),K(y,u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(7857,a,17215,a),flip(a)].">
      <j1 rule="hyper" parents="7857 17215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17229">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u)) = T(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(17215(a,1),7841(a,1,1))].">
      <j1 rule="para" parents="17215 7841"/>
    </justification>
  </clause>

  <clause id="17230">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u) \ z) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z / T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(17215(a,1),8789(a,1,1))].">
      <j1 rule="para" parents="17215 8789"/>
    </justification>
  </clause>

  <clause id="17232">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) \ y) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(17216(a,1),8721(a,1,1))].">
      <j1 rule="para" parents="17216 8721"/>
    </justification>
  </clause>

  <clause id="17233">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) * y) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(17216(a,1),11128(a,1,1))].">
      <j1 rule="para" parents="17216 11128"/>
    </justification>
  </clause>

  <clause id="17234">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8439,a,17220,a)].">
      <j1 rule="hyper" parents="8439 17220"/>
    </justification>
  </clause>

  <clause id="17235">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(8436,a,17220,a)].">
      <j1 rule="hyper" parents="8436 17220"/>
    </justification>
  </clause>

  <clause id="17236">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z / y))
    ]]></literal>
    <justification jstring="[para(6761(a,1),17221(a,1,2))].">
      <j1 rule="para" parents="6761 17221"/>
    </justification>
  </clause>

  <clause id="17237">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(7867(a,2),17221(a,1,2))].">
      <j1 rule="para" parents="7867 17221"/>
    </justification>
  </clause>

  <clause id="17238">
    <literal><![CDATA[
      K(x,K(y / z,u)) = K(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(7884(a,1),17221(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7884 17221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17241">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ T(y,u),z) = K(T(y,u) / x,z)
    ]]></literal>
    <justification jstring="[para(17223(a,1),9061(a,1,1))].">
      <j1 rule="para" parents="17223 9061"/>
    </justification>
  </clause>

  <clause id="17242">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(x,T(y,z))) = R(z * K(x,K(y,u)),K(x,T(y,z)),u)
    ]]></literal>
    <justification jstring="[para(17223(a,1),10680(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="17223 10680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17244">
    <literal><![CDATA[
      (x \ K(y,T(z,u))) * K(y,K(z,w)) = x \ K(y,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(17223(a,1),15657(a,1,2))].">
      <j1 rule="para" parents="17223 15657"/>
    </justification>
  </clause>

  <clause id="17245">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8436,a,17224,a)].">
      <j1 rule="hyper" parents="8436 17224"/>
    </justification>
  </clause>

  <clause id="17247">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(17224(a,2),8436(a,1))].">
      <j1 rule="para" parents="17224 8436"/>
    </justification>
  </clause>

  <clause id="17249">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * u) \ (w * z)))
    ]]></literal>
    <justification jstring="[para(8292(a,1),17224(a,1,2))].">
      <j1 rule="para" parents="8292 17224"/>
    </justification>
  </clause>

  <clause id="17250">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ (u * (y / u)),z) = K((u * (y / u)) / x,z)
    ]]></literal>
    <justification jstring="[para(17224(a,1),11199(a,1,1))].">
      <j1 rule="para" parents="17224 11199"/>
    </justification>
  </clause>

  <clause id="17253">
    <literal><![CDATA[
      K(x * y,K(z,u)) = K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[para(11113(a,1),17234(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11113 17234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17254">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(17235(a,2),8436(a,1))].">
      <j1 rule="para" parents="17235 8436"/>
    </justification>
  </clause>

  <clause id="17255">
    <literal><![CDATA[
      K(x,K(y,(z \ u) * z)) = K(x,K(u,y))
    ]]></literal>
    <justification jstring="[para(11123(a,2),17237(a,1,2))].">
      <j1 rule="para" parents="11123 17237"/>
    </justification>
  </clause>

  <clause id="17257">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(17245(a,1),7962(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17245 7962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17258">
    <literal><![CDATA[
      K(x,y) * (K(z,K(y,u)) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[para(17245(a,1),9960(a,1,2,1))].">
      <j1 rule="para" parents="17245 9960"/>
    </justification>
  </clause>

  <clause id="17260">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6321(a,1),17156(a,1,2))].">
      <j1 rule="para" parents="6321 17156"/>
    </justification>
  </clause>

  <clause id="17261">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) * z) = w
    ]]></literal>
    <justification jstring="[para(7188(a,1),17156(a,1,2))].">
      <j1 rule="para" parents="7188 17156"/>
    </justification>
  </clause>

  <clause id="17262">
    <literal><![CDATA[
      K(x,y / K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(7826(a,1),17156(a,1,2))].">
      <j1 rule="para" parents="7826 17156"/>
    </justification>
  </clause>

  <clause id="17263">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ y) = w
    ]]></literal>
    <justification jstring="[para(8352(a,1),17156(a,1,2))].">
      <j1 rule="para" parents="8352 17156"/>
    </justification>
  </clause>

  <clause id="17264">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8722(a,1),17156(a,1,2))].">
      <j1 rule="para" parents="8722 17156"/>
    </justification>
  </clause>

  <clause id="17265">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * T(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(8667(a,1),17156(a,1))].">
      <j1 rule="para" parents="8667 17156"/>
    </justification>
  </clause>

  <clause id="17266">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(11151(a,1),17156(a,1,2))].">
      <j1 rule="para" parents="11151 17156"/>
    </justification>
  </clause>

  <clause id="17267">
    <literal><![CDATA[
      K(x,y * L(z \ u,z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w * z) \ (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(12052(a,1),17156(a,1,2))].">
      <j1 rule="para" parents="12052 17156"/>
    </justification>
  </clause>

  <clause id="17268">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15023(a,1),17156(a,1,2))].">
      <j1 rule="para" parents="15023 17156"/>
    </justification>
  </clause>

  <clause id="17269">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6321(a,1),17167(a,1,2))].">
      <j1 rule="para" parents="6321 17167"/>
    </justification>
  </clause>

  <clause id="17270">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(7840(a,1),17167(a,1,2))].">
      <j1 rule="para" parents="7840 17167"/>
    </justification>
  </clause>

  <clause id="17271">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(u * K(y,z),w)) = v5
    ]]></literal>
    <justification jstring="[para(11111(a,1),17167(a,1))].">
      <j1 rule="para" parents="11111 17167"/>
    </justification>
  </clause>

  <clause id="17272">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15023(a,1),17167(a,1,2))].">
      <j1 rule="para" parents="15023 17167"/>
    </justification>
  </clause>

  <clause id="17273">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(8352(a,1),17189(a,1,1))].">
      <j1 rule="para" parents="8352 17189"/>
    </justification>
  </clause>

  <clause id="17274">
    <literal><![CDATA[
      K((x / y) * K(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z) / y,u) = w
    ]]></literal>
    <justification jstring="[para(14848(a,1),17189(a,1,1))].">
      <j1 rule="para" parents="14848 17189"/>
    </justification>
  </clause>

  <clause id="17275">
    <literal><![CDATA[
      K(x * x,x * (x * y)) = K(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7727,a(flip),b,17074,a),flip(a)].">
      <j1 rule="hyper" parents="64 7727 17074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17276">
    <literal><![CDATA[
      T(x,K(y / (z * z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z \ (z \ y)) * w) = v5
    ]]></literal>
    <justification jstring="[para(17075(a,2),15753(a,1,2,1))].">
      <j1 rule="para" parents="17075 15753"/>
    </justification>
  </clause>

  <clause id="17277">
    <literal><![CDATA[
      x * K(x / (y * y),y) = (y \ x) * L(y,x,y)
    ]]></literal>
    <justification jstring="[para(17075(a,2),16123(a,1,2))].">
      <j1 rule="para" parents="17075 16123"/>
    </justification>
  </clause>

  <clause id="17278">
    <literal><![CDATA[
      x * (T((y * y) \ z,K(y * y,z)) * K(y * y,z)) = (z / (y * y)) * T(x,y \ (y \ z))
    ]]></literal>
    <justification jstring="[para(17076(a,1),12708(a,2,2))].">
      <j1 rule="para" parents="17076 12708"/>
    </justification>
  </clause>

  <clause id="17279">
    <literal><![CDATA[
      T(x,(y * y) * (z \ T(u,y \ (y \ z)))) = T(x,u / (z / (y * y)))
    ]]></literal>
    <justification jstring="[para(17076(a,1),13423(a,1,2,2,2))].">
      <j1 rule="para" parents="17076 13423"/>
    </justification>
  </clause>

  <clause id="17280">
    <literal><![CDATA[
      T(x / y,y * (z * z)) = T(y \ x,z * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,15744,a(flip),b,17078,a),flip(a)].">
      <j1 rule="hyper" parents="373 15744 17078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17281">
    <literal><![CDATA[
      T(1 / x,y * (x * x)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5135,a(flip),b,17078,a),flip(a)].">
      <j1 rule="hyper" parents="373 5135 17078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17282">
    <literal><![CDATA[
      T(x,y * (y * (z / (y * u)))) = T(x,z / ((1 / y) * u))
    ]]></literal>
    <justification jstring="[para(901(a,1),17078(a,1,2)),flip(a)].">
      <j1 rule="para" parents="901 17078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17283">
    <literal><![CDATA[
      T(x * ((y * y) * z),x * (y * y)) = T(x * z,x) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4890,a(flip),b,17079,a),flip(a)].">
      <j1 rule="hyper" parents="64 4890 17079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17284">
    <literal><![CDATA[
      K(x,T(y,z * (u \ z))) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17024,a(flip),b,17096,a)].">
      <j1 rule="hyper" parents="64 17024 17096"/>
    </justification>
  </clause>

  <clause id="17285">
    <literal><![CDATA[
      K(x * y,T(x,z) * u) = K(y * x,u * T(x,z))
    ]]></literal>
    <justification jstring="[hyper(11228,a,17103,a)].">
      <j1 rule="hyper" parents="11228 17103"/>
    </justification>
  </clause>

  <clause id="17287">
    <literal><![CDATA[
      T(x,y) * K(z \ x,u) = K(x / z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,17105,a(flip),b,8192,a),flip(a)].">
      <j1 rule="hyper" parents="144 17105 8192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17289">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17024,a(flip),b,17109,a),flip(a)].">
      <j1 rule="hyper" parents="373 17024 17109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17290">
    <literal><![CDATA[
      x \ (y * (K((y \ x) / (z / y),u) * (y \ x))) = K(((y \ x) * y) / z,T(u,x / y))
    ]]></literal>
    <justification jstring="[hyper(15633,a,17109,a(flip))].">
      <j1 rule="hyper" parents="15633 17109"/>
    </justification>
  </clause>

  <clause id="17293">
    <literal><![CDATA[
      T(x,T(y,z / u)) = T(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17029,a(flip),b,17123,a),flip(a)].">
      <j1 rule="hyper" parents="373 17029 17123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17294">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,K(z,1 / z) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,15680,a,b,17132,a)].">
      <j1 rule="hyper" parents="373 15680 17132"/>
    </justification>
  </clause>

  <clause id="17295">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(y / u,K(z,1 / z) / (z * y)))
    ]]></literal>
    <justification jstring="[para(17132(a,2),12168(a,2,2))].">
      <j1 rule="para" parents="17132 12168"/>
    </justification>
  </clause>

  <clause id="17296">
    <literal><![CDATA[
      K((x * K(y,z)) \ 1,u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(14596,a,17133,a)].">
      <j1 rule="hyper" parents="14596 17133"/>
    </justification>
  </clause>

  <clause id="17297">
    <literal><![CDATA[
      K((x / y) \ K(z,u),L(w,K(z,u),y)) = K((K(z,u) * y) / x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15574,a(flip),b,17133,a),flip(a)].">
      <j1 rule="hyper" parents="64 15574 17133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17298">
    <literal><![CDATA[
      K(x,y * K(z,u \ z)) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16835,a,17139,a),flip(a)].">
      <j1 rule="hyper" parents="16835 17139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17299">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(16823,a,17139,a),flip(a)].">
      <j1 rule="hyper" parents="16823 17139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17300">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(15768,a,17139,a)].">
      <j1 rule="hyper" parents="15768 17139"/>
    </justification>
  </clause>

  <clause id="17301">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) = K(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,16271,a(flip),b,17139,a),flip(a)].">
      <j1 rule="hyper" parents="373 16271 17139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17302">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15771,a,b,17139,a)].">
      <j1 rule="hyper" parents="64 15771 17139"/>
    </justification>
  </clause>

  <clause id="17303">
    <literal><![CDATA[
      K(x,(y * z) * K(u,y)) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,15770,a(flip),b,17139,a),flip(a)].">
      <j1 rule="hyper" parents="64 15770 17139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17304">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * u)) = K(x,w * (u * K(y,z)))
    ]]></literal>
    <justification jstring="[para(12078(a,1),17139(a,2,2))].">
      <j1 rule="para" parents="12078 17139"/>
    </justification>
  </clause>

  <clause id="17306">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17139(a,2),16355(a,1))].">
      <j1 rule="para" parents="17139 16355"/>
    </justification>
  </clause>

  <clause id="17307">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(17139(a,1),16823(a,1))].">
      <j1 rule="para" parents="17139 16823"/>
    </justification>
  </clause>

  <clause id="17308">
    <literal><![CDATA[
      K(x,y * K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(17139(a,1),16835(a,1))].">
      <j1 rule="para" parents="17139 16835"/>
    </justification>
  </clause>

  <clause id="17309">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(u,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6156,a,b,17140,a)].">
      <j1 rule="hyper" parents="373 6156 17140"/>
    </justification>
  </clause>

  <clause id="17310">
    <literal><![CDATA[
      x \ (T(x,y) * K(z,u)) = K(u,z) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6071,a,b,17140,a)].">
      <j1 rule="hyper" parents="373 6071 17140"/>
    </justification>
  </clause>

  <clause id="17312">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,T(z,w)) \ K(y,x) = v5
    ]]></literal>
    <justification jstring="[para(17140(a,2),7925(a,1))].">
      <j1 rule="para" parents="17140 7925"/>
    </justification>
  </clause>

  <clause id="17314">
    <literal><![CDATA[
      R(K(x,y) \ (z / K(u,w)),K(x,y),K(u,w)) = T(z / (K(u,w) * K(x,y)),K(x,y))
    ]]></literal>
    <justification jstring="[para(17141(a,1),856(a,2,1,2))].">
      <j1 rule="para" parents="17141 856"/>
    </justification>
  </clause>

  <clause id="17315">
    <literal><![CDATA[
      ((x \ y) \ (y / x)) * K(z,u) = K(z,u) * K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5879(a,2),17141(a,1,1))].">
      <j1 rule="para" parents="5879 17141"/>
    </justification>
  </clause>

  <clause id="17316">
    <literal><![CDATA[
      x / y != K(z,u) * K(w,v5)
    ]]></literal>
    <literal><![CDATA[
      (K(v5,w) \ K(z,u)) * y = x
    ]]></literal>
    <justification jstring="[para(17141(a,1),6208(a,2))].">
      <j1 rule="para" parents="17141 6208"/>
    </justification>
  </clause>

  <clause id="17317">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) / x = (K(z,u) / x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(17141(a,1),6863(a,1,1))].">
      <j1 rule="para" parents="17141 6863"/>
    </justification>
  </clause>

  <clause id="17318">
    <literal><![CDATA[
      x * (K(y,z) * K(y * z,x)) = ((y * z) * x) / (z * y)
    ]]></literal>
    <justification jstring="[para(17141(a,1),10604(a,1,2))].">
      <j1 rule="para" parents="17141 10604"/>
    </justification>
  </clause>

  <clause id="17319">
    <literal><![CDATA[
      K(x * ((y \ z) \ z),u) = K(x * T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(38,a,13435,a(flip),b,17142,a)].">
      <j1 rule="hyper" parents="38 13435 17142"/>
    </justification>
  </clause>

  <clause id="17320">
    <literal><![CDATA[
      T(x * (y \ K(z,u)),K(x,y)) = x * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[para(17144(a,1),8062(a,2,2))].">
      <j1 rule="para" parents="17144 8062"/>
    </justification>
  </clause>

  <clause id="17321">
    <literal><![CDATA[
      T(x \ K(y,z),u / x) = T(x \ K(y,z),x \ u)
    ]]></literal>
    <justification jstring="[para(17144(a,1),8720(a,1,1))].">
      <j1 rule="para" parents="17144 8720"/>
    </justification>
  </clause>

  <clause id="17322">
    <literal><![CDATA[
      (x \ K(y,z)) \ T(u * (x \ K(y,z)),K(x,w)) = T(u,K(w,x) * (x \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(17144(a,1),16803(a,1,2,1,2))].">
      <j1 rule="para" parents="17144 16803"/>
    </justification>
  </clause>

  <clause id="17324">
    <literal><![CDATA[
      T((x * K(y,z)) * u,K(x,u)) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(17155(a,1),8356(a,2,1))].">
      <j1 rule="para" parents="17155 8356"/>
    </justification>
  </clause>

  <clause id="17325">
    <literal><![CDATA[
      T(x * K(y,z),x / u) = T(x * K(y,z),u \ x)
    ]]></literal>
    <justification jstring="[para(17155(a,1),8720(a,1,1))].">
      <j1 rule="para" parents="17155 8720"/>
    </justification>
  </clause>

  <clause id="17326">
    <literal><![CDATA[
      K(x,T((y * z) * (1 / y),y \ K(y,z)) \ u) = K(x,L(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(17159(a,1),16476(a,1,2,1))].">
      <j1 rule="para" parents="17159 16476"/>
    </justification>
  </clause>

  <clause id="17327">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ K(z,y)),x,(K(z,y) / u) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(17159(a,1),15736(a,1,2,2,1))].">
      <j1 rule="para" parents="17159 15736"/>
    </justification>
  </clause>

  <clause id="17328">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,K(y,u)) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(9192,a,17161,a),flip(a)].">
      <j1 rule="hyper" parents="9192 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17329">
    <literal><![CDATA[
      (x \ y) * K(x,K(z,u)) = T(x,K(z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(8150,a,17161,a),flip(a)].">
      <j1 rule="hyper" parents="8150 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17330">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8149,a,17161,a)].">
      <j1 rule="hyper" parents="8149 17161"/>
    </justification>
  </clause>

  <clause id="17331">
    <literal><![CDATA[
      (x \ y) * K(z,K(u,x)) = T(x,K(z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(8104,a,17161,a),flip(a)].">
      <j1 rule="hyper" parents="8104 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17332">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * z = u * T(u \ z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,9039,a,b,17161,a),flip(a)].">
      <j1 rule="hyper" parents="373 9039 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17333">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ K(y,z)) = u \ K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,15555,a(flip),b,17161,a),flip(a)].">
      <j1 rule="hyper" parents="373 15555 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17334">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) * (w * u) = w * (u * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,12145,a(flip),b,17161,a),flip(a)].">
      <j1 rule="hyper" parents="373 12145 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17335">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / x) = u / T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8142,a(flip),b,17161,a),flip(a)].">
      <j1 rule="hyper" parents="373 8142 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17336">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / T(x,K(y,z))) = u / x
    ]]></literal>
    <justification jstring="[hyper(373,a,6848,a(flip),b,17161,a),flip(a)].">
      <j1 rule="hyper" parents="373 6848 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17337">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(144,a,17161,a,b,8141,a)].">
      <j1 rule="hyper" parents="144 17161 8141"/>
    </justification>
  </clause>

  <clause id="17339">
    <literal><![CDATA[
      (x \ y) * K(z,K(x,u)) = T(x,K(z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,8666,a(flip),b,17161,a),flip(a)].">
      <j1 rule="hyper" parents="64 8666 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17341">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(8110(a,1),17161(a,1,1))].">
      <j1 rule="para" parents="8110 17161"/>
    </justification>
  </clause>

  <clause id="17342">
    <literal><![CDATA[
      x * (y * K(z,K(u,x))) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(17161(a,1),8130(a,1,2))].">
      <j1 rule="para" parents="17161 8130"/>
    </justification>
  </clause>

  <clause id="17344">
    <literal><![CDATA[
      K(x,y) * (z * K(x,K(y,u))) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[para(17161(a,1),9813(a,1,2))].">
      <j1 rule="para" parents="17161 9813"/>
    </justification>
  </clause>

  <clause id="17346">
    <literal><![CDATA[
      T(x,y * K(z \ u,z)) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16812,a,17165,a),flip(a)].">
      <j1 rule="hyper" parents="16812 17165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17347">
    <literal><![CDATA[
      T(x,y * K(z,z \ u)) = T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(15766,a,17165,a),flip(a)].">
      <j1 rule="hyper" parents="15766 17165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17348">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(15753,a,17165,a)].">
      <j1 rule="hyper" parents="15753 17165"/>
    </justification>
  </clause>

  <clause id="17349">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ z)) = T(x,u \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,16275,a(flip),b,17165,a),flip(a)].">
      <j1 rule="hyper" parents="373 16275 17165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17350">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,u)) = y * T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,17165,a(flip),b,16797,a),flip(a)].">
      <j1 rule="hyper" parents="145 17165 16797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17351">
    <literal><![CDATA[
      T(x,K(y,z) * (u * z)) = T(x,u * ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(6464(a,1),17165(a,2,2))].">
      <j1 rule="para" parents="6464 17165"/>
    </justification>
  </clause>

  <clause id="17353">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(17165(a,1),15753(a,1))].">
      <j1 rule="para" parents="17165 15753"/>
    </justification>
  </clause>

  <clause id="17354">
    <literal><![CDATA[
      K(x * K(y \ z,y),u) = K(K(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(13529,a,17178,a),flip(a)].">
      <j1 rule="hyper" parents="13529 17178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17355">
    <literal><![CDATA[
      K(x * K(y,y \ z),u) = K(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(13359,a,17178,a),flip(a)].">
      <j1 rule="hyper" parents="13359 17178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17356">
    <literal><![CDATA[
      K(x * K(y * z,y),u) = K(K(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(13358,a,17178,a),flip(a)].">
      <j1 rule="hyper" parents="13358 17178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17357">
    <literal><![CDATA[
      K(x * K(y,z),y * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(7741,a,17178,a),flip(a)].">
      <j1 rule="hyper" parents="7741 17178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17358">
    <literal><![CDATA[
      K(x * K(y \ z,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(7738,a,17178,a),flip(a)].">
      <j1 rule="hyper" parents="7738 17178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17359">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,16286,a,b,17178,a),flip(a)].">
      <j1 rule="hyper" parents="373 16286 17178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17360">
    <literal><![CDATA[
      K(K(x,y) * z,u / z) = K(K(x,y) * z,z \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11179,a,b,17178,a),flip(a)].">
      <j1 rule="hyper" parents="373 11179 17178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17361">
    <literal><![CDATA[
      K(K(x,y) * (z \ y),u) = K(z \ T(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,16291,a(flip),b,17178,a),flip(a)].">
      <j1 rule="hyper" parents="373 16291 17178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17362">
    <literal><![CDATA[
      K(K(x,y) * z,u) * w = K(z * K(x,y),u) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,17178,a,b,11,a)].">
      <j1 rule="hyper" parents="144 17178 11"/>
    </justification>
  </clause>

  <clause id="17363">
    <literal><![CDATA[
      K(x * K(y,z),x \ y) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15269,a(flip),b,17178,a),flip(a)].">
      <j1 rule="hyper" parents="64 15269 17178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17364">
    <literal><![CDATA[
      K((x \ y) * K(z,x),u) = K(T(x,z) \ y,u)
    ]]></literal>
    <justification jstring="[para(6157(a,1),17178(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6157 17178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17365">
    <literal><![CDATA[
      K(x * K(y,z),T(u,(K(y,z) * x) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,T(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(17178(a,1),8021(a,1))].">
      <j1 rule="para" parents="17178 8021"/>
    </justification>
  </clause>

  <clause id="17366">
    <literal><![CDATA[
      K(x * K(y * z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(17178(a,1),13358(a,1))].">
      <j1 rule="para" parents="17178 13358"/>
    </justification>
  </clause>

  <clause id="17367">
    <literal><![CDATA[
      K(x * K(y \ z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(17178(a,1),13529(a,1))].">
      <j1 rule="para" parents="17178 13529"/>
    </justification>
  </clause>

  <clause id="17368">
    <literal><![CDATA[
      K(x * K(K(y,z) * u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * K(w,u * K(y,z)),v5) = v6
    ]]></literal>
    <justification jstring="[para(17178(a,2),16287(a,1,1,2))].">
      <j1 rule="para" parents="17178 16287"/>
    </justification>
  </clause>

  <clause id="17369">
    <literal><![CDATA[
      K(x / ((y \ z) \ z),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(6316(a,2),17358(a,1,1))].">
      <j1 rule="para" parents="6316 17358"/>
    </justification>
  </clause>

  <clause id="17370">
    <literal><![CDATA[
      K(x * (y / z),y) = K(x * (z \ y),y)
    ]]></literal>
    <justification jstring="[para(6886(a,1),17358(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6886 17358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17371">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ (u * z)) = K(x,u * (y * (z / y)))
    ]]></literal>
    <justification jstring="[para(10173(a,1),17190(a,2,2))].">
      <j1 rule="para" parents="10173 17190"/>
    </justification>
  </clause>

  <clause id="17372">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ (u / z)) = K(x,u / (y * (z / y)))
    ]]></literal>
    <justification jstring="[para(10622(a,1),17190(a,2,2))].">
      <j1 rule="para" parents="10622 17190"/>
    </justification>
  </clause>

  <clause id="17373">
    <literal><![CDATA[
      K(K(x,y) \ z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,16286,a,b,17199,a),flip(a)].">
      <j1 rule="hyper" parents="373 16286 17199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17374">
    <literal><![CDATA[
      K(K(x,y) \ (z / y),u) = K(z / T(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,16289,a(flip),b,17199,a),flip(a)].">
      <j1 rule="hyper" parents="373 16289 17199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17375">
    <literal><![CDATA[
      K(x * K(y,z),u) * (K(z,y) \ x) = T(K(z,y) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,17199,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 17199 5739"/>
    </justification>
  </clause>

  <clause id="17376">
    <literal><![CDATA[
      T(x,T(T(y,T(z,u)) * u,w)) = T(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(8408(a,1),17206(a,1,2,1))].">
      <j1 rule="para" parents="8408 17206"/>
    </justification>
  </clause>

  <clause id="17377">
    <literal><![CDATA[
      T(x,K(y,z) \ u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,16270,a,b,17212,a),flip(a)].">
      <j1 rule="hyper" parents="373 16270 17212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17378">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(u / z) \ y) = T(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(17217(a,1),8721(a,1,1))].">
      <j1 rule="para" parents="17217 8721"/>
    </justification>
  </clause>

  <clause id="17379">
    <literal><![CDATA[
      T(x,K(y,z * (y * u))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,10157,a,b,17218,a)].">
      <j1 rule="hyper" parents="373 10157 17218"/>
    </justification>
  </clause>

  <clause id="17380">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(z,w * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(y,K(w * u,z) * x) = v5
    ]]></literal>
    <justification jstring="[para(17218(a,1),16806(a,1,2,1,2))].">
      <j1 rule="para" parents="17218 16806"/>
    </justification>
  </clause>

  <clause id="17381">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(9048,a,17225,a)].">
      <j1 rule="hyper" parents="9048 17225"/>
    </justification>
  </clause>

  <clause id="17382">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(x / w,u / (z * y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,12153,a,b,17225,a)].">
      <j1 rule="hyper" parents="373 12153 17225"/>
    </justification>
  </clause>

  <clause id="17385">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,u * z)) = w
    ]]></literal>
    <justification jstring="[para(17226(a,1),8436(a,1))].">
      <j1 rule="para" parents="17226 8436"/>
    </justification>
  </clause>

  <clause id="17386">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(17236(a,1),8437(a,1))].">
      <j1 rule="para" parents="17236 8437"/>
    </justification>
  </clause>

  <clause id="17387">
    <literal><![CDATA[
      K(x,K(y \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(17236(a,2),8437(a,1))].">
      <j1 rule="para" parents="17236 8437"/>
    </justification>
  </clause>

  <clause id="17388">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(17238(a,1),8437(a,1))].">
      <j1 rule="para" parents="17238 8437"/>
    </justification>
  </clause>

  <clause id="17389">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(17253(a,1),8439(a,1))].">
      <j1 rule="para" parents="17253 8439"/>
    </justification>
  </clause>

  <clause id="17390">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[para(17253(a,1),14494(a,2,2))].">
      <j1 rule="para" parents="17253 14494"/>
    </justification>
  </clause>

  <clause id="17391">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,10241,a(flip),b,17255,a)].">
      <j1 rule="hyper" parents="64 10241 17255"/>
    </justification>
  </clause>

  <clause id="17392">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ y) = u \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,15021,a(flip),b,17257,a),flip(a)].">
      <j1 rule="hyper" parents="373 15021 17257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17393">
    <literal><![CDATA[
      K(x \ 1,y * (x * x)) = T(x \ 1,y) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,17281,a(flip),b,6001,a),flip(a)].">
      <j1 rule="hyper" parents="144 17281 6001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17394">
    <literal><![CDATA[
      K(x * (y * (z \ y)),T(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * (z \ y)) * x,u) = w
    ]]></literal>
    <justification jstring="[para(17284(a,1),11189(a,1))].">
      <j1 rule="para" parents="17284 11189"/>
    </justification>
  </clause>

  <clause id="17395">
    <literal><![CDATA[
      K(x,T(y,z * u)) / (u / z) = (1 / (u / z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(17289(a,1),14768(a,1,1))].">
      <j1 rule="para" parents="17289 14768"/>
    </justification>
  </clause>

  <clause id="17396">
    <literal><![CDATA[
      T(x,T(y,z * (u * z))) = T(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),17293(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 17293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17397">
    <literal><![CDATA[
      T(x,T(y,(z \ u) * u)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),17293(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 17293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17399">
    <literal><![CDATA[
      K(x,K(y,z) * (u * z)) = K(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[para(6852(a,1),17300(a,2,2))].">
      <j1 rule="para" parents="6852 17300"/>
    </justification>
  </clause>

  <clause id="17400">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(17300(a,2),13353(a,1))].">
      <j1 rule="para" parents="17300 13353"/>
    </justification>
  </clause>

  <clause id="17401">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17302(a,2),16355(a,1))].">
      <j1 rule="para" parents="17302 16355"/>
    </justification>
  </clause>

  <clause id="17402">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(w,v5) = K(v5,w) \ K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(12059(a,2),17309(a,1,1))].">
      <j1 rule="para" parents="12059 17309"/>
    </justification>
  </clause>

  <clause id="17403">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,7820,a,b,17330,a),flip(a)].">
      <j1 rule="hyper" parents="373 7820 17330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17404">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u \ x) = u \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,15021,a(flip),b,17330,a),flip(a)].">
      <j1 rule="hyper" parents="373 15021 17330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17405">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * x) = u * T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,6852,a(flip),b,17330,a),flip(a)].">
      <j1 rule="hyper" parents="373 6852 17330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17406">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(17330(a,1),396(a,1))].">
      <j1 rule="para" parents="17330 396"/>
    </justification>
  </clause>

  <clause id="17408">
    <literal><![CDATA[
      T(R(K(x,K(y,z)) \ u,K(w,v5),w),K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(17330(a,2),16893(a,1,1,1))].">
      <j1 rule="para" parents="17330 16893"/>
    </justification>
  </clause>

  <clause id="17410">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(y,K(z,x)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(6278,a,17341,a),flip(a)].">
      <j1 rule="hyper" parents="6278 17341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17411">
    <literal><![CDATA[
      T(x,y * K(z \ u,z)) = T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(15766,a,17348,a),flip(a)].">
      <j1 rule="hyper" parents="15766 17348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17413">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ 1)) = T(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,14479,a(flip),b,17348,a),flip(a)].">
      <j1 rule="hyper" parents="373 14479 17348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17414">
    <literal><![CDATA[
      x \ T(y,K(z,u) * w) = x \ T(y,w * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,17348,a,b,10,a)].">
      <j1 rule="hyper" parents="139 17348 10"/>
    </justification>
  </clause>

  <clause id="17415">
    <literal><![CDATA[
      T(x / (y * K(z,u)),K(u,z) * y) != w
    ]]></literal>
    <literal><![CDATA[
      (y * K(z,u)) \ x = w
    ]]></literal>
    <justification jstring="[para(17348(a,2),467(a,1))].">
      <j1 rule="para" parents="17348 467"/>
    </justification>
  </clause>

  <clause id="17416">
    <literal><![CDATA[
      T(x,K(y \ K(z,u),w) * K(u,z)) = T(x,y * T(y \ K(z,u),w))
    ]]></literal>
    <justification jstring="[para(6763(a,2),17348(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6763 17348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17417">
    <literal><![CDATA[
      T(x,K(y,z) * (u * z)) = T(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[para(6852(a,1),17348(a,2,2))].">
      <j1 rule="para" parents="6852 17348"/>
    </justification>
  </clause>

  <clause id="17418">
    <literal><![CDATA[
      T(x,K(y,y \ z) * (u * (z / y))) = T(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[para(6886(a,1),17348(a,2,2))].">
      <j1 rule="para" parents="6886 17348"/>
    </justification>
  </clause>

  <clause id="17419">
    <literal><![CDATA[
      T(x,(y / z) * K(u,y)) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(14825(a,1),17348(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14825 17348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17421">
    <literal><![CDATA[
      K((x * y) * K(y,z),y * z) = K(y * x,z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11185,a,b,17357,a),flip(a)].">
      <j1 rule="hyper" parents="373 11185 17357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17423">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,17178,a,b,17359,a)].">
      <j1 rule="hyper" parents="373 17178 17359"/>
    </justification>
  </clause>

  <clause id="17424">
    <literal><![CDATA[
      K(x * K(y,z),x \ z) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15269,a(flip),b,17359,a),flip(a)].">
      <j1 rule="hyper" parents="64 15269 17359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17425">
    <literal><![CDATA[
      T(x * K(y,z),K(K(z,y) * x,u) * w) = T(x * K(y,z),w)
    ]]></literal>
    <justification jstring="[para(17359(a,2),8482(a,1,2,1))].">
      <j1 rule="para" parents="17359 8482"/>
    </justification>
  </clause>

  <clause id="17426">
    <literal><![CDATA[
      K((x / y) * K(z,x),u) = K(T(x,z) / y,u)
    ]]></literal>
    <justification jstring="[para(14825(a,1),17359(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14825 17359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17427">
    <literal><![CDATA[
      K(x \ (y * (z \ x)),x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,15971,a(flip),b,17369,a)].">
      <j1 rule="hyper" parents="64 15971 17369"/>
    </justification>
  </clause>

  <clause id="17428">
    <literal><![CDATA[
      K(x,K(y * (z \ u),(y * (z \ u)) \ u) * w) = K(x,K(y * (u / z),u) * w)
    ]]></literal>
    <justification jstring="[para(17370(a,2),13326(a,2,2,1))].">
      <j1 rule="para" parents="17370 13326"/>
    </justification>
  </clause>

  <clause id="17429">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),17381(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 17381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17430">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ (z * (y * x)),L(x,y,y \ 1)) = K(z / (1 / y),L(x,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(1641(a,1),17427(a,1,1,2,2))].">
      <j1 rule="para" parents="1641 17427"/>
    </justification>
  </clause>

  <clause id="17431">
    <literal><![CDATA[
      K(x,K(y / z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y * (z \ u),u) * w) = v5
    ]]></literal>
    <justification jstring="[para(17427(a,1),13528(a,1,2,1))].">
      <j1 rule="para" parents="17427 13528"/>
    </justification>
  </clause>

  <clause id="17432">
    <literal><![CDATA[
      (x \ y) * K(z,K(u,x)) = y * T(y \ (x \ y),K(z,u))
    ]]></literal>
    <justification jstring="[para(17429(a,1),8132(a,2,2)),flip(a)].">
      <j1 rule="para" parents="17429 8132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17433">
    <literal><![CDATA[
      K(x,K(y * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * y,u)) = w
    ]]></literal>
    <justification jstring="[para(11181(a,1),17254(a,1,2))].">
      <j1 rule="para" parents="11181 17254"/>
    </justification>
  </clause>

  <clause id="17434">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,T(x,v5))) = w
    ]]></literal>
    <justification jstring="[para(17234(a,1),17254(a,1))].">
      <j1 rule="para" parents="17234 17254"/>
    </justification>
  </clause>

  <clause id="17436">
    <literal><![CDATA[
      K(x,(1 / y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) / z) = u
    ]]></literal>
    <justification jstring="[para(2353(a,1),17400(a,1,2))].">
      <j1 rule="para" parents="2353 17400"/>
    </justification>
  </clause>

  <clause id="17437">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(3895(a,1),17400(a,1,2))].">
      <j1 rule="para" parents="3895 17400"/>
    </justification>
  </clause>

  <clause id="17438">
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) = w
    ]]></literal>
    <justification jstring="[para(5186(a,1),17400(a,1,2))].">
      <j1 rule="para" parents="5186 17400"/>
    </justification>
  </clause>

  <clause id="17439">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(17028(a,1),5827(a,1))].">
      <j1 rule="para" parents="17028 5827"/>
    </justification>
  </clause>

  <clause id="17440">
    <literal><![CDATA[
      R(T(x \ 1,y) * (x * x),x / (x * x),y) = (1 * y) / (y * (x / (x * x)))
    ]]></literal>
    <justification jstring="[para(17039(a,1),16728(a,1,1))].">
      <j1 rule="para" parents="17039 16728"/>
    </justification>
  </clause>

  <clause id="17441">
    <literal><![CDATA[
      x * (y * K(x \ 1,x)) = T(x,x * x) * y
    ]]></literal>
    <justification jstring="[para(6345(a,2),17044(a,1,2,2))].">
      <j1 rule="para" parents="6345 17044"/>
    </justification>
  </clause>

  <clause id="17442">
    <literal><![CDATA[
      K(x,T(x \ (y * y),z)) = K(x,x \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(17130,a,17049,a)].">
      <j1 rule="hyper" parents="17130 17049"/>
    </justification>
  </clause>

  <clause id="17443">
    <literal><![CDATA[
      ((T(x,x * y) \ 1) * (y / x)) \ (y / x) = (y / x) / T((x * x) \ y,x)
    ]]></literal>
    <justification jstring="[para(17054(a,1),10126(a,2,2))].">
      <j1 rule="para" parents="17054 10126"/>
    </justification>
  </clause>

  <clause id="17444">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,u * (x * z)))
    ]]></literal>
    <justification jstring="[para(17087(a,1),8600(a,1,1,2))].">
      <j1 rule="para" parents="17087 8600"/>
    </justification>
  </clause>

  <clause id="17445">
    <literal><![CDATA[
      K(T(x \ 1,y) * z,T(u,x)) = K(z * T(x \ 1,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11162,a(flip),b,17097,a),flip(a)].">
      <j1 rule="hyper" parents="64 11162 17097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17446">
    <literal><![CDATA[
      K(T(x * x,y) / z,u) = K(z \ T(x * x,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17031,a(flip),b,17101,a),flip(a)].">
      <j1 rule="hyper" parents="64 17031 17101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17447">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * T(z,w) = T(z,w) * K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),17108(a,1,1,2))].">
      <j1 rule="para" parents="23 17108"/>
    </justification>
  </clause>

  <clause id="17448">
    <literal><![CDATA[
      T(x,y) * K(z / x,u) = K(x \ z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7917(a,1),17108(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7917 17108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17449">
    <literal><![CDATA[
      T(x,y) * K(z,x * u) = K(z,u * x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(11113(a,1),17108(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11113 17108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17451">
    <literal><![CDATA[
      T(x,y) * K(z,L(T(u,x),w,v5)) = K(z,L(u,w,v5)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(25(a,2),17110(a,1,2,2))].">
      <j1 rule="para" parents="25 17110"/>
    </justification>
  </clause>

  <clause id="17452">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x)) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ (K(u,z) \ T(x,y)) = v5
    ]]></literal>
    <justification jstring="[para(17110(a,2),6209(a,1))].">
      <j1 rule="para" parents="17110 6209"/>
    </justification>
  </clause>

  <clause id="17453">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(y,w)) = T(x,T(y,w) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(8466(a,1),17120(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8466 17120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17454">
    <literal><![CDATA[
      T((L(K(x,x \ K(y,z)),u,w) \ K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(504,a,5548,a,b,17138,a)].">
      <j1 rule="hyper" parents="504 5548 17138"/>
    </justification>
  </clause>

  <clause id="17456">
    <literal><![CDATA[
      T(T(x * x,K(y,z)),u) = K(x * x,u) * (x * x)
    ]]></literal>
    <justification jstring="[para(17053(a,1),17153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17053 17153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17457">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(40,a,6882,a,b,17177,a)].">
      <j1 rule="hyper" parents="40 6882 17177"/>
    </justification>
  </clause>

  <clause id="17458">
    <literal><![CDATA[
      K(x,(T(y,z) \ (y * u)) * w) \ K(x,K(K(y,z) \ u,w)) = K(w * (T(y,z) \ (y * u)),x)
    ]]></literal>
    <justification jstring="[para(6282(a,1),17177(a,1,2,2))].">
      <j1 rule="para" parents="6282 17177"/>
    </justification>
  </clause>

  <clause id="17459">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) \ K(x,K(L(y,z,K(u,w)),z * K(u,w))) = K((z * K(u,w)) * L(y,z,K(u,w)),x)
    ]]></literal>
    <justification jstring="[para(16604(a,1),17177(a,1,1,2))].">
      <j1 rule="para" parents="16604 17177"/>
    </justification>
  </clause>

  <clause id="17461">
    <literal><![CDATA[
      K(x,K(y / (z / u),u \ z) * (w * (y / (z / u)))) = K(x,w * T((z / u) \ y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(8723(a,1),17186(a,2,2,2))].">
      <j1 rule="para" parents="8723 17186"/>
    </justification>
  </clause>

  <clause id="17462">
    <literal><![CDATA[
      K(x,y * (z * K(u,y))) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16333,a,b,17187,a)].">
      <j1 rule="hyper" parents="64 16333 17187"/>
    </justification>
  </clause>

  <clause id="17463">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * (u * K(T(y,z) \ z,w))) = K(x,T(y \ T(z,y),w) * u)
    ]]></literal>
    <justification jstring="[para(4799(a,1),17187(a,2,2,1))].">
      <j1 rule="para" parents="4799 17187"/>
    </justification>
  </clause>

  <clause id="17464">
    <literal><![CDATA[
      K(T(x * y,x) * (z * K(T(x * y,x),u)),w) = K(T(T(x * y,u),T(x,y)) * z,w)
    ]]></literal>
    <justification jstring="[para(4481(a,2),17197(a,2,1,1))].">
      <j1 rule="para" parents="4481 17197"/>
    </justification>
  </clause>

  <clause id="17466">
    <literal><![CDATA[
      T(x * K(y,z),T(u / x,w)) = T(x * K(y,z),T(x \ u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,8243,a(flip),b,17203,a)].">
      <j1 rule="hyper" parents="64 8243 17203"/>
    </justification>
  </clause>

  <clause id="17468">
    <literal><![CDATA[
      (x * y) \ (y * ((y \ K(z,u)) * T(x,y))) = L(T(y \ K(z,u),x),x,y)
    ]]></literal>
    <justification jstring="[para(17205(a,1),10981(a,2,1))].">
      <j1 rule="para" parents="17205 10981"/>
    </justification>
  </clause>

  <clause id="17469">
    <literal><![CDATA[
      T(x,K(y,(z * z) \ u) * ((w / u) * (z * z))) = T(x,w / T((z * z) \ u,y))
    ]]></literal>
    <justification jstring="[para(900(a,1),17211(a,1,2,2))].">
      <j1 rule="para" parents="900 17211"/>
    </justification>
  </clause>

  <clause id="17470">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z * K(w,y)))) = T(x,u / T(z * K(w,y),y))
    ]]></literal>
    <justification jstring="[para(8549(a,1),17211(a,1,2,1))].">
      <j1 rule="para" parents="8549 17211"/>
    </justification>
  </clause>

  <clause id="17471">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(T(y,x),u)) = T(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,4712,a,b,17228,a)].">
      <j1 rule="hyper" parents="64 4712 17228"/>
    </justification>
  </clause>

  <clause id="17472">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17124,a,b,17229,a),flip(a)].">
      <j1 rule="hyper" parents="373 17124 17229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17473">
    <literal><![CDATA[
      K((K(x,T(y,z * u)) * z) \ 1,T(w,u)) = K(T(z,u) \ K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(15724,a,17296,a)].">
      <j1 rule="hyper" parents="15724 17296"/>
    </justification>
  </clause>

  <clause id="17474">
    <literal><![CDATA[
      K(x,T(K(y,z) \ (K(y,z) / u),w) * K(z,y \ z)) = K(x,(K(y,z) / u) * K(u \ 1,w))
    ]]></literal>
    <justification jstring="[para(5994(a,2),17298(a,2,2))].">
      <j1 rule="para" parents="5994 17298"/>
    </justification>
  </clause>

  <clause id="17475">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * u)) = K(x,w * (u * K(y \ 1,z)))
    ]]></literal>
    <justification jstring="[para(12078(a,1),17299(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12078 17299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17476">
    <literal><![CDATA[
      T(T(x,K(y,z / T(u,w))),(K(u,w) * (z / u)) \ y) = T(x,y / (K(u,w) * (z / u)))
    ]]></literal>
    <justification jstring="[para(17301(a,1),8721(a,1,1,2))].">
      <j1 rule="para" parents="17301 8721"/>
    </justification>
  </clause>

  <clause id="17477">
    <literal><![CDATA[
      K(x,y) \ K(y,T(x,z)) = y \ T(T(y,x),T(x,z))
    ]]></literal>
    <justification jstring="[para(7441(a,1),17310(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7441 17310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17478">
    <literal><![CDATA[
      K(x * T(y,y \ z),u) = K(x * T(y,z),u)
    ]]></literal>
    <justification jstring="[para(116(a,2),17319(a,1,1,2))].">
      <j1 rule="para" parents="116 17319"/>
    </justification>
  </clause>

  <clause id="17479">
    <literal><![CDATA[
      (x \ y) * K(x * T(x,y),x \ y) = (x \ y) * K(y * x,x \ y)
    ]]></literal>
    <justification jstring="[para(17319(a,1),16235(a,1,2))].">
      <j1 rule="para" parents="17319 16235"/>
    </justification>
  </clause>

  <clause id="17480">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) / T(x,K(y,z)) = (x \ u) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,17329,a(flip),b,6840,a)].">
      <j1 rule="hyper" parents="142 17329 6840"/>
    </justification>
  </clause>

  <clause id="17481">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / T(x,K(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      u / x = w
    ]]></literal>
    <justification jstring="[para(17335(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="17335 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17482">
    <literal><![CDATA[
      T(x,K(y,z)) * (u / T(x,K(y,z))) = x * (u / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,17336,a(flip),b,6071,a),flip(a)].">
      <j1 rule="hyper" parents="145 17336 6071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17483">
    <literal><![CDATA[
      K(T((x \ y) \ z,K(y,x) * u) * K(x \ y,x),u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(17346(a,1),16567(a,1,1,1))].">
      <j1 rule="para" parents="17346 16567"/>
    </justification>
  </clause>

  <clause id="17484">
    <literal><![CDATA[
      T(x / y,K(y,x) * z) = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,8603,a,b,17347,a)].">
      <j1 rule="hyper" parents="41 8603 17347"/>
    </justification>
  </clause>

  <clause id="17485">
    <literal><![CDATA[
      K(x / y,K(y,x) * z) = (x / y) \ T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,17484,a(flip),b,5753,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 17484 5753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17486">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) = K(z * ((y \ x) * y),u)
    ]]></literal>
    <justification jstring="[para(10196(a,1),17354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10196 17354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17487">
    <literal><![CDATA[
      K(x * K(y * (z * u),z),w) = K(K(y * u,z) * x,w)
    ]]></literal>
    <justification jstring="[para(11574(a,2),17356(a,1,1,2))].">
      <j1 rule="para" parents="11574 17356"/>
    </justification>
  </clause>

  <clause id="17488">
    <literal><![CDATA[
      ((x \ (y * (x * z))) \ u) * K(x \ (y * (x * z)),x) = T(((y * (x * z)) / x) \ u,K(x,z * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,8904,a,b,17379,a)].">
      <j1 rule="hyper" parents="64 8904 17379"/>
    </justification>
  </clause>

  <clause id="17489">
    <literal><![CDATA[
      K(x,y) * (z \ T(y,K(x,u))) = K(x,T(y,u)) * (z \ y)
    ]]></literal>
    <justification jstring="[para(17392(a,1),9813(a,1,2))].">
      <j1 rule="para" parents="17392 9813"/>
    </justification>
  </clause>

  <clause id="17490">
    <literal><![CDATA[
      K(x,K(y,L(y \ z,u,w)) * (v5 * L(z / y,u,w))) = K(x,v5 * T(L(z / y,u,w),y))
    ]]></literal>
    <justification jstring="[para(5928(a,1),17399(a,1,2,1))].">
      <j1 rule="para" parents="5928 17399"/>
    </justification>
  </clause>

  <clause id="17491">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u * x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(139,a,17405,a(flip),b,5780,a),flip(a)].">
      <j1 rule="hyper" parents="139 17405 5780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17492">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * z) = u * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8110(a,2),17405(a,1,1))].">
      <j1 rule="para" parents="8110 17405"/>
    </justification>
  </clause>

  <clause id="17493">
    <literal><![CDATA[
      R(T((x / (y \ z)) / u,K(y,z) * u),u,K(y \ z,y)) = (u * K(y \ z,y)) \ (x / (z / y))
    ]]></literal>
    <justification jstring="[para(17411(a,1),6995(a,1,1))].">
      <j1 rule="para" parents="17411 6995"/>
    </justification>
  </clause>

  <clause id="17494">
    <literal><![CDATA[
      T(x,K(y,z * (u / z)) * (w * K(z,z \ u))) = T(x,(w / u) * T(z * (u / z),y))
    ]]></literal>
    <justification jstring="[para(10245(a,1),17417(a,1,2,2))].">
      <j1 rule="para" parents="10245 17417"/>
    </justification>
  </clause>

  <clause id="17495">
    <literal><![CDATA[
      T(x,((y * z) / T(y,u)) * K(w,y * (z * K(u,y)))) = T(x,T(y * (z * K(u,y)),w) / y)
    ]]></literal>
    <justification jstring="[para(7170(a,1),17419(a,1,2,1))].">
      <j1 rule="para" parents="7170 17419"/>
    </justification>
  </clause>

  <clause id="17497">
    <literal><![CDATA[
      T(x,(y / (z * K(u,w))) * K(z,T(z \ w,u))) = T(x,y / T(z * K(u,w),z \ w))
    ]]></literal>
    <justification jstring="[para(17424(a,1),16274(a,1,2,2))].">
      <j1 rule="para" parents="17424 16274"/>
    </justification>
  </clause>

  <clause id="17498">
    <literal><![CDATA[
      K(x,y * (z \ T(T(u,w),w))) = K(x,K(y,z \ u)) * K(x,(z \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,16367,a,b,17457,a)].">
      <j1 rule="hyper" parents="373 16367 17457"/>
    </justification>
  </clause>

  <clause id="17499">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z * x) = K(y,x * z)
    ]]></literal>
    <justification jstring="[para(8108(a,1),17457(a,1,1))].">
      <j1 rule="para" parents="8108 17457"/>
    </justification>
  </clause>

  <clause id="17500">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,(z \ T(T(u,w),w)) * y) = K(x,y * (z \ T(T(u,w),w)))
    ]]></literal>
    <justification jstring="[para(16303(a,1),17457(a,1,1,2))].">
      <j1 rule="para" parents="16303 17457"/>
    </justification>
  </clause>

  <clause id="17501">
    <literal><![CDATA[
      K(x,T(y,z) * (u * z)) = K(x,y * (u * T(z,y)))
    ]]></literal>
    <justification jstring="[para(6852(a,1),17462(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6852 17462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17502">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * (u * K(w,y / z))) = K(x,T(y * (z \ 1),w) * u)
    ]]></literal>
    <justification jstring="[para(14406(a,1),17462(a,1,2,2,2))].">
      <j1 rule="para" parents="14406 17462"/>
    </justification>
  </clause>

  <clause id="17503">
    <literal><![CDATA[
      T((1 / x) * y,T(T(x,y),z)) = T((1 / x) * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(8407(a,1),17472(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8407 17472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17504">
    <literal><![CDATA[
      K(x * (y / (y / z)),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15864,a(flip),b,17478,a)].">
      <j1 rule="hyper" parents="64 15864 17478"/>
    </justification>
  </clause>

  <clause id="17505">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * z) = u * T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,8143,a(flip),b,17492,a)].">
      <j1 rule="hyper" parents="64 8143 17492"/>
    </justification>
  </clause>

  <clause id="17506">
    <literal><![CDATA[
      K(x,T(y,z)) \ (u * z) = K(x,y) \ (u * T(z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(17492(a,1),8948(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17492 8948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17507">
    <literal><![CDATA[
      K(x * T(y \ z,z),u) = K(x * (z / y),u)
    ]]></literal>
    <justification jstring="[para(79(a,1),17504(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 17504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17508">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * T(z,K(x,y)) = ((z * K(x,y)) * u) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,13681,a(flip),b,17505,a),flip(a)].">
      <j1 rule="hyper" parents="64 13681 17505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17509">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(8110(a,1),17170(a,1,1))].">
      <j1 rule="para" parents="8110 17170"/>
    </justification>
  </clause>

  <clause id="17510">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15759(a,1),17171(a,1))].">
      <j1 rule="para" parents="15759 17171"/>
    </justification>
  </clause>

  <clause id="17511">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(17348(a,1),17171(a,1))].">
      <j1 rule="para" parents="17348 17171"/>
    </justification>
  </clause>

  <clause id="17512">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(16286(a,1),17193(a,1))].">
      <j1 rule="para" parents="16286 17193"/>
    </justification>
  </clause>

  <clause id="17513">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(16864(a,2),17193(a,1))].">
      <j1 rule="para" parents="16864 17193"/>
    </justification>
  </clause>

  <clause id="17514">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * K(y,z \ (y * u))) = v5
    ]]></literal>
    <justification jstring="[para(8816(a,2),17195(a,1,2,1))].">
      <j1 rule="para" parents="8816 17195"/>
    </justification>
  </clause>

  <clause id="17515">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(17300(a,1),17195(a,1))].">
      <j1 rule="para" parents="17300 17195"/>
    </justification>
  </clause>

  <clause id="17516">
    <literal><![CDATA[
      K(x,y * K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(17298(a,2),17195(a,1))].">
      <j1 rule="para" parents="17298 17195"/>
    </justification>
  </clause>

  <clause id="17517">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u / z),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u / T(z,y),w)) = v5
    ]]></literal>
    <justification jstring="[para(6865(a,1),17200(a,1,2,1))].">
      <j1 rule="para" parents="6865 17200"/>
    </justification>
  </clause>

  <clause id="17518">
    <literal><![CDATA[
      K(x,(y / z) \ T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y) \ z) = w
    ]]></literal>
    <justification jstring="[para(15034(a,2),17263(a,1,2))].">
      <j1 rule="para" parents="15034 17263"/>
    </justification>
  </clause>

  <clause id="17519">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(16265(a,1),17263(a,1))].">
      <j1 rule="para" parents="16265 17263"/>
    </justification>
  </clause>

  <clause id="17520">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(17300(a,2),17263(a,1))].">
      <j1 rule="para" parents="17300 17263"/>
    </justification>
  </clause>

  <clause id="17521">
    <literal><![CDATA[
      K(x,K(y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(17302(a,2),17263(a,1))].">
      <j1 rule="para" parents="17302 17263"/>
    </justification>
  </clause>

  <clause id="17522">
    <literal><![CDATA[
      K(x,T(y,(z / u) * (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,L(w,u,u \ z) * z)) = v5
    ]]></literal>
    <justification jstring="[para(11064(a,1),17266(a,1,2,2))].">
      <j1 rule="para" parents="11064 17266"/>
    </justification>
  </clause>

  <clause id="17523">
    <literal><![CDATA[
      K(x,T(y,z / (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(14549(a,2),17266(a,1,2))].">
      <j1 rule="para" parents="14549 17266"/>
    </justification>
  </clause>

  <clause id="17524">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(17024(a,2),17266(a,1))].">
      <j1 rule="para" parents="17024 17266"/>
    </justification>
  </clause>

  <clause id="17525">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(17289(a,2),17266(a,1))].">
      <j1 rule="para" parents="17289 17266"/>
    </justification>
  </clause>

  <clause id="17526">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(16286(a,1),17273(a,1))].">
      <j1 rule="para" parents="16286 17273"/>
    </justification>
  </clause>

  <clause id="17527">
    <literal><![CDATA[
      K(K(x,y) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(17373(a,2),17273(a,1))].">
      <j1 rule="para" parents="17373 17273"/>
    </justification>
  </clause>

  <clause id="17528">
    <literal><![CDATA[
      K(x \ (x \ y),x) * y = (x \ y) * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10224,a,b,17277,a)].">
      <j1 rule="hyper" parents="64 10224 17277"/>
    </justification>
  </clause>

  <clause id="17529">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,(u * w) \ (z * w))) = v5
    ]]></literal>
    <justification jstring="[para(15586(a,2),17386(a,1,2))].">
      <j1 rule="para" parents="15586 17386"/>
    </justification>
  </clause>

  <clause id="17530">
    <literal><![CDATA[
      K(x,K(y,(1 / z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(14414(a,2),17388(a,1,2))].">
      <j1 rule="para" parents="14414 17388"/>
    </justification>
  </clause>

  <clause id="17531">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,(u * w) * R(z,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(111(a,1),17389(a,1,2,2))].">
      <j1 rule="para" parents="111 17389"/>
    </justification>
  </clause>

  <clause id="17532">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(12603(a,2),17389(a,1))].">
      <j1 rule="para" parents="12603 17389"/>
    </justification>
  </clause>

  <clause id="17535">
    <literal><![CDATA[
      K(x,y / (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(14406(a,1),17437(a,1))].">
      <j1 rule="para" parents="14406 17437"/>
    </justification>
  </clause>

  <clause id="17536">
    <literal><![CDATA[
      K(x,y / (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(6530(a,2),17535(a,1))].">
      <j1 rule="para" parents="6530 17535"/>
    </justification>
  </clause>

  <clause id="17537">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (y \ z)) = w
    ]]></literal>
    <justification jstring="[para(14465(a,2),17535(a,1))].">
      <j1 rule="para" parents="14465 17535"/>
    </justification>
  </clause>

  <clause id="17538">
    <literal><![CDATA[
      K(x,y / (z \ a(u \ 1,u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(16568(a,2),17536(a,1))].">
      <j1 rule="para" parents="16568 17536"/>
    </justification>
  </clause>

  <clause id="17539">
    <literal><![CDATA[
      K(x,T(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * u) * K(y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(8839(a,1),17509(a,1))].">
      <j1 rule="para" parents="8839 17509"/>
    </justification>
  </clause>

  <clause id="17540">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13375(a,2),17515(a,1))].">
      <j1 rule="para" parents="13375 17515"/>
    </justification>
  </clause>

  <clause id="17541">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(17521,a,13463,a)].">
      <j1 rule="hyper" parents="17521 13463"/>
    </justification>
  </clause>

  <clause id="17542">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(L(z,u,w),y) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(12059(a,2),17521(a,1,2,1))].">
      <j1 rule="para" parents="12059 17521"/>
    </justification>
  </clause>

  <clause id="17543">
    <literal><![CDATA[
      T(x,K(y,y \ z) \ u) = T(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(143,a,17541,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 17541 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17544">
    <literal><![CDATA[
      K(x,K(y,z \ y) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13464,a,b,17541,a)].">
      <j1 rule="hyper" parents="64 13464 17541"/>
    </justification>
  </clause>

  <clause id="17545">
    <literal><![CDATA[
      K(x,K(y \ z,z) \ u) = K(x,K(z,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(5962(a,1),17541(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5962 17541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17546">
    <literal><![CDATA[
      T(x,(((y \ T(z,y)) \ z) \ z) / u) = T(x,K(z,y) \ ((T(y,z) \ z) / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16495,a(flip),b,17543,a)].">
      <j1 rule="hyper" parents="64 16495 17543"/>
    </justification>
  </clause>

  <clause id="17547">
    <literal><![CDATA[
      K(x,K(y \ z,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(17521,a,17544,a)].">
      <j1 rule="hyper" parents="17521 17544"/>
    </justification>
  </clause>

  <clause id="17548">
    <literal><![CDATA[
      K(x,T(y * (z / u),z * u)) = K(x,(z / u) * y)
    ]]></literal>
    <justification jstring="[hyper(17525,a,11127,a)].">
      <j1 rule="hyper" parents="17525 11127"/>
    </justification>
  </clause>

  <clause id="17549">
    <literal><![CDATA[
      K(K(x,x * y) \ z,u) = K(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(17527,a,13405,a)].">
      <j1 rule="hyper" parents="17527 13405"/>
    </justification>
  </clause>

  <clause id="17550">
    <literal><![CDATA[
      K(K(x * y,y \ 1) \ z,u) = K(K(y \ 1,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(11586(a,1),17549(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11586 17549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17551">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8064,a(flip),b,17033,a),flip(a)].">
      <j1 rule="hyper" parents="64 8064 17033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17552">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(9037,a,17551,a)].">
      <j1 rule="hyper" parents="9037 17551"/>
    </justification>
  </clause>

  <clause id="17553">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(143,a,17551,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 17551 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17554">
    <literal><![CDATA[
      K(x,K(y / z,u)) = K(x,K(u,z * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17238,a,b,17551,a)].">
      <j1 rule="hyper" parents="64 17238 17551"/>
    </justification>
  </clause>

  <clause id="17555">
    <literal><![CDATA[
      (x \ y) * K(z,K(u,x * y)) = T(x \ y,K(z,u))
    ]]></literal>
    <justification jstring="[para(17551(a,1),8121(a,1,2))].">
      <j1 rule="para" parents="17551 8121"/>
    </justification>
  </clause>

  <clause id="17556">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(17551(a,1),9037(a,1))].">
      <j1 rule="para" parents="17551 9037"/>
    </justification>
  </clause>

  <clause id="17557">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(143,a,17552,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 17552 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17558">
    <literal><![CDATA[
      K(x,K(y,z * u)) * ((u \ z) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(u \ z,K(x,y)) \ w = v5
    ]]></literal>
    <justification jstring="[para(17552(a,1),8104(a,1,1))].">
      <j1 rule="para" parents="17552 8104"/>
    </justification>
  </clause>

  <clause id="17559">
    <literal><![CDATA[
      T(x,K(y \ z,u)) = T(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8184,a,17553,a)].">
      <j1 rule="hyper" parents="8184 17553"/>
    </justification>
  </clause>

  <clause id="17560">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17217,a,b,17553,a)].">
      <j1 rule="hyper" parents="64 17217 17553"/>
    </justification>
  </clause>

  <clause id="17561">
    <literal><![CDATA[
      T(x,K(y,z * (z * u))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),17553(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 17553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17562">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(17553(a,1),11245(a,1,1))].">
      <j1 rule="para" parents="17553 11245"/>
    </justification>
  </clause>

  <clause id="17563">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (T(u,z) / z)) = T(x,(T(u,z) / z) * y)
    ]]></literal>
    <justification jstring="[para(17553(a,1),13333(a,1,1))].">
      <j1 rule="para" parents="17553 13333"/>
    </justification>
  </clause>

  <clause id="17564">
    <literal><![CDATA[
      T(T(x,K(y,z * (u / z))),y / ((z \ u) / z)) = T(x,((z \ u) / z) \ y)
    ]]></literal>
    <justification jstring="[para(17553(a,1),13356(a,1,1))].">
      <j1 rule="para" parents="17553 13356"/>
    </justification>
  </clause>

  <clause id="17565">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(z,u \ w)) = T(y,K(u \ w,z) * x)
    ]]></literal>
    <justification jstring="[para(17553(a,1),16796(a,1,2,1,2))].">
      <j1 rule="para" parents="17553 16796"/>
    </justification>
  </clause>

  <clause id="17566">
    <literal><![CDATA[
      T(x,K(y,z * u)) \ T(w * x,K(y,z \ u)) = T(w,x * K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(17553(a,1),16971(a,1,1))].">
      <j1 rule="para" parents="17553 16971"/>
    </justification>
  </clause>

  <clause id="17567">
    <literal><![CDATA[
      (x / y) * K(z,K(u,y * x)) = T(x / y,K(z,u))
    ]]></literal>
    <justification jstring="[para(17554(a,1),8113(a,1,2))].">
      <j1 rule="para" parents="17554 8113"/>
    </justification>
  </clause>

  <clause id="17568">
    <literal><![CDATA[
      T(x / y,K(z,u)) * ((y \ x) \ 1) = K(z,K(u,y * x)) * K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(17554(a,1),8119(a,2,1))].">
      <j1 rule="para" parents="17554 8119"/>
    </justification>
  </clause>

  <clause id="17569">
    <literal><![CDATA[
      T(x,K(y,z * (u * z))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),17560(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 17560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17570">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),(u * (z \ 1)) * y) = T(x,y * (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(17560(a,1),12568(a,1,1))].">
      <j1 rule="para" parents="17560 12568"/>
    </justification>
  </clause>

  <clause id="17571">
    <literal><![CDATA[
      T(x,K(y,z * (u * u))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(17074(a,2),17561(a,1,2))].">
      <j1 rule="para" parents="17074 17561"/>
    </justification>
  </clause>

  <clause id="17572">
    <literal><![CDATA[
      T((x * y) * y,K(z,x)) = (x * y) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,11117,a(flip),b,17569,a),flip(a)].">
      <j1 rule="hyper" parents="64 11117 17569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17573">
    <literal><![CDATA[
      T(x,K(y,z * (u * u))) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8153,a,b,17571,a),flip(a)].">
      <j1 rule="hyper" parents="373 8153 17571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17574">
    <literal><![CDATA[
      T((x * y) * y,K(x,z)) = (x * y) * y
    ]]></literal>
    <justification jstring="[hyper(8728,a,17572,a)].">
      <j1 rule="hyper" parents="8728 17572"/>
    </justification>
  </clause>

  <clause id="17575">
    <literal><![CDATA[
      T(T(x,y * (z * z)),K(y,u)) = T(x,T(y * (z * z),u))
    ]]></literal>
    <justification jstring="[hyper(8189,a,17573,a),flip(a)].">
      <j1 rule="hyper" parents="8189 17573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17576">
    <literal><![CDATA[
      T(x,y) * K(z * z,x) = T(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15869,a(flip),b,17064,a),flip(a)].">
      <j1 rule="hyper" parents="64 15869 17064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17577">
    <literal><![CDATA[
      x \ T(x,y \ (y \ z)) = K(x,z) * K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,17576,a(flip),b,5776,a)].">
      <j1 rule="hyper" parents="139 17576 5776"/>
    </justification>
  </clause>

  <clause id="17578">
    <literal><![CDATA[
      T(x,y \ (y \ x)) = x * K(y * y,x)
    ]]></literal>
    <justification jstring="[para(114(a,1),17576(a,1,1)),flip(a)].">
      <j1 rule="para" parents="114 17576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17579">
    <literal><![CDATA[
      K(x,y \ (y \ x)) = K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(5826,a,17578,a)].">
      <j1 rule="hyper" parents="5826 17578"/>
    </justification>
  </clause>

  <clause id="17580">
    <literal><![CDATA[
      K(x * x,y) * (T(x \ (x \ y),y) / z) = (x \ (x \ y)) / z
    ]]></literal>
    <justification jstring="[para(17579(a,1),14842(a,1,1))].">
      <j1 rule="para" parents="17579 14842"/>
    </justification>
  </clause>

  <clause id="17581">
    <literal><![CDATA[
      K(x \ (x \ 1),T(y,z)) = K(y,x * x)
    ]]></literal>
    <justification jstring="[hyper(35,a,8648,a,b,17077,a(flip))].">
      <j1 rule="hyper" parents="35 8648 17077"/>
    </justification>
  </clause>

  <clause id="17582">
    <literal><![CDATA[
      K(x \ (x \ 1),T(y,z)) = K(x \ (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,15888,a,b,17581,a),flip(a)].">
      <j1 rule="hyper" parents="373 15888 17581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17583">
    <literal><![CDATA[
      K(x \ (x \ 1),T(y,z)) = K((x * x) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,14590,a,b,17582,a),flip(a)].">
      <j1 rule="hyper" parents="373 14590 17582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17584">
    <literal><![CDATA[
      K((x * x) \ 1,T(y,z)) = K((x * x) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14590,a,b,17583,a)].">
      <j1 rule="hyper" parents="64 14590 17583"/>
    </justification>
  </clause>

  <clause id="17585">
    <literal><![CDATA[
      K(x \ ((y * y) \ x),z) = K((y * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7978,a,b,17584,a)].">
      <j1 rule="hyper" parents="64 7978 17584"/>
    </justification>
  </clause>

  <clause id="17586">
    <literal><![CDATA[
      K(x \ ((y * y) \ x),z) = K(y \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,14590,a(flip),b,17585,a),flip(a)].">
      <j1 rule="hyper" parents="373 14590 17585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17587">
    <literal><![CDATA[
      K(x \ ((y * y) \ x),z) = K(z,y * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,15888,a(flip),b,17586,a),flip(a)].">
      <j1 rule="hyper" parents="373 15888 17586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17588">
    <literal><![CDATA[
      T(x,(y / T(z,u * (u * y))) * (u * u)) = T(x,((u * u) \ z) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15749,a(flip),b,17080,a),flip(a)].">
      <j1 rule="hyper" parents="64 15749 17080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17589">
    <literal><![CDATA[
      (K(x,y) * ((z * z) \ u)) \ (u * ((z * z) \ K(x,y))) = K(u,(z * z) \ K(x,y))
    ]]></literal>
    <justification jstring="[para(17082(a,1),16(a,2,1)),flip(a)].">
      <j1 rule="para" parents="17082 16"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17590">
    <literal><![CDATA[
      K((x * y) * T(z,y),T(u,y * z)) = K((z * y) * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10206(a,1),17084(a,1,1))].">
      <j1 rule="para" parents="10206 17084"/>
    </justification>
  </clause>

  <clause id="17591">
    <literal><![CDATA[
      K(x,T(L(y \ z,y,y \ u),z * (u / y))) = K(x,((u / y) * z) / u)
    ]]></literal>
    <justification jstring="[para(11070(a,2),17085(a,1,2,1))].">
      <j1 rule="para" parents="11070 17085"/>
    </justification>
  </clause>

  <clause id="17592">
    <literal><![CDATA[
      K(x,T(L(y \ z,y,z \ u),y * (u / z))) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[para(15002(a,2),17086(a,1,2,1))].">
      <j1 rule="para" parents="15002 17086"/>
    </justification>
  </clause>

  <clause id="17593">
    <literal><![CDATA[
      T(x,y) \ T(K(z,u) * x,y) = K(z,T(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(139,a,15723,a(flip),b,17088,a)].">
      <j1 rule="hyper" parents="139 15723 17088"/>
    </justification>
  </clause>

  <clause id="17594">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,w)) = K((x / y) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,17098,a,b,17119,a)].">
      <j1 rule="hyper" parents="373 17098 17119"/>
    </justification>
  </clause>

  <clause id="17595">
    <literal><![CDATA[
      K(x,T(y,z)) \ T(y,T(u,x)) = T(T(y,u),T(x,z))
    ]]></literal>
    <justification jstring="[para(7869(a,1),17122(a,1,1))].">
      <j1 rule="para" parents="7869 17122"/>
    </justification>
  </clause>

  <clause id="17596">
    <literal><![CDATA[
      (K(x,L(y,z,K(u,w) * K(v5,v6))) * z) / (K(v5,v6) * K(u,w)) = K(x,y) * (z / (K(u,w) * K(v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(15674,a,17146,a)].">
      <j1 rule="hyper" parents="15674 17146"/>
    </justification>
  </clause>

  <clause id="17598">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) != u * w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17173(a,2),44(a,1))].">
      <j1 rule="para" parents="17173 44"/>
    </justification>
  </clause>

  <clause id="17599">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(z,y)) = u * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(8088(a,1),17173(a,1,1))].">
      <j1 rule="para" parents="8088 17173"/>
    </justification>
  </clause>

  <clause id="17600">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u / z),w)) = K(x,T(u / T(z,y),w))
    ]]></literal>
    <justification jstring="[para(6245(a,1),17182(a,2,2,1))].">
      <j1 rule="para" parents="6245 17182"/>
    </justification>
  </clause>

  <clause id="17601">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * (u / z),w)) = K(x,T(u / ((y \ z) * y),w))
    ]]></literal>
    <justification jstring="[para(10608(a,1),17182(a,2,2,1))].">
      <j1 rule="para" parents="10608 17182"/>
    </justification>
  </clause>

  <clause id="17603">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = T(x,w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(17161(a,1),17227(a,1,1))].">
      <j1 rule="para" parents="17161 17227"/>
    </justification>
  </clause>

  <clause id="17604">
    <literal><![CDATA[
      T(T(x,K(y,z \ y)),T(z \ y,u) \ y) = T(x,T(y / z,u) \ y)
    ]]></literal>
    <justification jstring="[para(8071(a,1),17232(a,2,2))].">
      <j1 rule="para" parents="8071 17232"/>
    </justification>
  </clause>

  <clause id="17605">
    <literal><![CDATA[
      T(T(x,K(y,y \ z)),y * T(z / y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(11216,a,17233,a)].">
      <j1 rule="hyper" parents="11216 17233"/>
    </justification>
  </clause>

  <clause id="17606">
    <literal><![CDATA[
      K(x * y,z * T(y,x)) = K(y * x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9879,a(flip),b,17285,a),flip(a)].">
      <j1 rule="hyper" parents="64 9879 17285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17607">
    <literal><![CDATA[
      T(K(x,((y * K(z,u)) * w) * v5),v5 \ T(v5 * ((y * K(z,u)) * w),x)) = (v5 \ T(v5 * ((y * K(z,u)) * w),x)) \ T((y * K(z,u)) * w,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(493,a,17324,a,b,14556,a)].">
      <j1 rule="hyper" parents="493 17324 14556"/>
    </justification>
  </clause>

  <clause id="17608">
    <literal><![CDATA[
      T(x * K(y,z),x * (u \ 1)) = T(x * K(y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,14461,a,b,17325,a)].">
      <j1 rule="hyper" parents="64 14461 17325"/>
    </justification>
  </clause>

  <clause id="17609">
    <literal><![CDATA[
      T(x / T(y * K(y \ x,y),x \ y),y) = (x / y) * K(y / x,y)
    ]]></literal>
    <justification jstring="[para(17325(a,1),9175(a,1,1,2))].">
      <j1 rule="para" parents="17325 9175"/>
    </justification>
  </clause>

  <clause id="17610">
    <literal><![CDATA[
      T(x,K(y,T(y \ z,u)) * (w * T(y \ z,u))) = T(x,w * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(531(a,1),17351(a,2,2,2))].">
      <j1 rule="para" parents="531 17351"/>
    </justification>
  </clause>

  <clause id="17611">
    <literal><![CDATA[
      (K(x * K(y,z),u) * w) \ (K(K(y,z) * x,u) * T(w,v5)) = K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(139,a,17362,a,b,6852,a)].">
      <j1 rule="hyper" parents="139 17362 6852"/>
    </justification>
  </clause>

  <clause id="17612">
    <literal><![CDATA[
      K(x / K(y,z),K(y,z)) \ T(u,x / K(y,z)) = (x / K(y,z)) \ (u * (K(y,z) \ x))
    ]]></literal>
    <justification jstring="[para(117(a,1),17403(a,2,2,2))].">
      <j1 rule="para" parents="117 17403"/>
    </justification>
  </clause>

  <clause id="17613">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,z) = z \ (u * T(z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(8110(a,2),17403(a,1,1))].">
      <j1 rule="para" parents="8110 17403"/>
    </justification>
  </clause>

  <clause id="17614">
    <literal><![CDATA[
      K(x,(y \ T(T(z,K(u,w) * v5),x)) * v6) = K(x,(y \ T(z,v5 * K(w,u))) * v6)
    ]]></literal>
    <justification jstring="[para(17414(a,1),9686(a,2,2,1))].">
      <j1 rule="para" parents="17414 9686"/>
    </justification>
  </clause>

  <clause id="17615">
    <literal><![CDATA[
      K(x * T(y,z),y * z) = K(y * x,z * y)
    ]]></literal>
    <justification jstring="[para(6852(a,1),17421(a,1,1))].">
      <j1 rule="para" parents="6852 17421"/>
    </justification>
  </clause>

  <clause id="17616">
    <literal><![CDATA[
      K(x \ T(y * y,y),z) = K(((1 / y) \ y) / x,z)
    ]]></literal>
    <justification jstring="[para(562(a,1),17446(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="562 17446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17617">
    <literal><![CDATA[
      T(x,L(y / K(z \ u,w),K(z \ u,w),T(z,v5))) = T(x,(y * T(z,v5)) / (T(z,v5) * K(u / z,w)))
    ]]></literal>
    <justification jstring="[para(17448(a,2),15608(a,2,2,2))].">
      <j1 rule="para" parents="17448 15608"/>
    </justification>
  </clause>

  <clause id="17618">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(T(z,x),u)) = T(x,T(T(z,u),y))
    ]]></literal>
    <justification jstring="[para(8153(a,1),17471(a,1,1))].">
      <j1 rule="para" parents="8153 17471"/>
    </justification>
  </clause>

  <clause id="17619">
    <literal><![CDATA[
      (x \ T(T(x,y),T(y,z))) \ (T(K(x,y),z) * T(x,x \ y)) = L(R(x,x \ y,x),K(x,y),T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(17477(a,1),12316(a,1,1))].">
      <j1 rule="para" parents="17477 12316"/>
    </justification>
  </clause>

  <clause id="17620">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),w) / y = y \ T(T(y,K(z,u)) * x,w)
    ]]></literal>
    <justification jstring="[hyper(5467,a,17482,a),flip(a)].">
      <j1 rule="hyper" parents="5467 17482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17621">
    <literal><![CDATA[
      T(x,K(y,z)) * ((x * T(x \ u,w)) / T(x,K(y,z))) = x * T(u / x,w)
    ]]></literal>
    <justification jstring="[para(531(a,1),17482(a,2,2))].">
      <j1 rule="para" parents="531 17482"/>
    </justification>
  </clause>

  <clause id="17622">
    <literal><![CDATA[
      K(x / y,K(y,x) * z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5726,a,b,17485,a),flip(a)].">
      <j1 rule="hyper" parents="373 5726 17485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17623">
    <literal><![CDATA[
      K(x / y,(y / T(x,y)) * z) = K(x / y,(y / x) * z)
    ]]></literal>
    <justification jstring="[para(13022(a,1),17622(a,1,2))].">
      <j1 rule="para" parents="13022 17622"/>
    </justification>
  </clause>

  <clause id="17624">
    <literal><![CDATA[
      K(x * ((y \ z) * y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17184,a(flip),b,17486,a),flip(a)].">
      <j1 rule="hyper" parents="64 17184 17486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17625">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * T(K(x,y) \ z,K(x,y))) = (z * K(y,x)) \ (u * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(8352(a,1),17491(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8352 17491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17627">
    <literal><![CDATA[
      K(x,T(y,z) * (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,y) * x)) = u
    ]]></literal>
    <justification jstring="[para(17501(a,2),8588(a,1))].">
      <j1 rule="para" parents="17501 8588"/>
    </justification>
  </clause>

  <clause id="17628">
    <literal><![CDATA[
      K(x,K(y,z \ 1) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17547,a(flip),b,17545,a),flip(a)].">
      <j1 rule="hyper" parents="64 17547 17545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17629">
    <literal><![CDATA[
      K(x,K(y \ 1,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(17521,a,17628,a)].">
      <j1 rule="hyper" parents="17521 17628"/>
    </justification>
  </clause>

  <clause id="17630">
    <literal><![CDATA[
      K(x,T(y,z \ 1) \ u) = K(x,K(y,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(6066(a,1),17628(a,1,2))].">
      <j1 rule="para" parents="6066 17628"/>
    </justification>
  </clause>

  <clause id="17631">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1)) \ w) = K(x,K(y,u * z) \ w)
    ]]></literal>
    <justification jstring="[para(14436(a,1),17628(a,1,2,1))].">
      <j1 rule="para" parents="14436 17628"/>
    </justification>
  </clause>

  <clause id="17632">
    <literal><![CDATA[
      K(x,K(y \ 1,z * y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,13388,a(flip),b,17629,a),flip(a)].">
      <j1 rule="hyper" parents="373 13388 17629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17633">
    <literal><![CDATA[
      K(x,T(y * (T(T(z,u),w) \ z),z * T(T(z,u),w))) = K(x,(z / T(T(z,u),w)) * y)
    ]]></literal>
    <justification jstring="[para(8387(a,1),17548(a,1,2,1,2))].">
      <j1 rule="para" parents="8387 17548"/>
    </justification>
  </clause>

  <clause id="17634">
    <literal><![CDATA[
      T(x / (y \ (y / x)),K(z,u)) = (x / (y \ (y / x))) * K(z,1)
    ]]></literal>
    <justification jstring="[para(9471(a,1),17567(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9471 17567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17635">
    <literal><![CDATA[
      K(x,y) * K(z * z,x) = K(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(5827,a,17577,a),flip(a)].">
      <j1 rule="hyper" parents="5827 17577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17636">
    <literal><![CDATA[
      (x / T(y,z * z)) * K(y,u) = (x / y) * K(y,z \ (z \ u))
    ]]></literal>
    <justification jstring="[para(17635(a,1),10353(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17635 10353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17637">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),u) \ T(K(w,v5) * L(x,y,K(z,u)),u) = K(w,T(v5,L(u * x,y,K(z,u))))
    ]]></literal>
    <justification jstring="[para(16645(a,2),17593(a,2,2,2))].">
      <j1 rule="para" parents="16645 17593"/>
    </justification>
  </clause>

  <clause id="17638">
    <literal><![CDATA[
      K(x,T(y,z)) \ T(y,u \ x) = T(T(y,x / u),T(x,z))
    ]]></literal>
    <justification jstring="[para(7429(a,1),17595(a,1,2))].">
      <j1 rule="para" parents="7429 17595"/>
    </justification>
  </clause>

  <clause id="17639">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * T(u,K(x,y))) = L(u * K(y,T(x,z)),K(x,y),z)
    ]]></literal>
    <justification jstring="[para(17599(a,1),11048(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17599 11048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17641">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,w) = K(x,K(y,z)) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,5432,a(flip),b,17603,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 5432 17603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17642">
    <literal><![CDATA[
      (x * (T(y,z) * K(u,K(w,v5)))) \ (x * (y * K(u,K(w,v5)))) = K(z,y * K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(17603(a,1),6323(a,1,1,2))].">
      <j1 rule="para" parents="17603 6323"/>
    </justification>
  </clause>

  <clause id="17643">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) / K(y,z) = T(x,w) / T(K(y,z),u)
    ]]></literal>
    <justification jstring="[para(17603(a,2),8131(a,1,1))].">
      <j1 rule="para" parents="17603 8131"/>
    </justification>
  </clause>

  <clause id="17644">
    <literal><![CDATA[
      T((x \ y) * y,K(x,z)) = (x \ y) * y
    ]]></literal>
    <justification jstring="[hyper(41,a,17397,a,b,17618,a),flip(a)].">
      <j1 rule="hyper" parents="41 17397 17618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17645">
    <literal><![CDATA[
      T((x \ y) * y,T(x,z)) = T((x \ y) * y,x)
    ]]></literal>
    <justification jstring="[para(17644(a,1),7841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17644 7841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17646">
    <literal><![CDATA[
      K(x,T(y,z \ 1) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(6066(a,1),17630(a,2,2))].">
      <j1 rule="para" parents="6066 17630"/>
    </justification>
  </clause>

  <clause id="17647">
    <literal><![CDATA[
      K(x,T(T((y \ 1) \ z,u),y) \ w) = K(x,T(z / (y \ 1),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15794,a(flip),b,17646,a),flip(a)].">
      <j1 rule="hyper" parents="64 15794 17646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17648">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(x * u,w) = T(T(x,K(y,z)) * u,w)
    ]]></literal>
    <justification jstring="[para(8146(a,1),17641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8146 17641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17649">
    <literal><![CDATA[
      (T(x,K(y,z)) * (K(x,K(y,z)) \ T(u,w))) / T(x,K(y,z)) = T((x * u) / T(x,K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(17641(a,1),6276(a,1,1,2))].">
      <j1 rule="para" parents="17641 6276"/>
    </justification>
  </clause>

  <clause id="17650">
    <literal><![CDATA[
      K(T(x,y) * z,T(T(u,x),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z * T(x,y),T(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(23(a,1),17112(a,1,2))].">
      <j1 rule="para" parents="23 17112"/>
    </justification>
  </clause>

  <clause id="17651">
    <literal><![CDATA[
      K(T(T(x * y,x),z) * u,T(w,y * x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u * T(T(x * y,x),z),w) = v5
    ]]></literal>
    <justification jstring="[para(11122(a,1),17112(a,1,2))].">
      <j1 rule="para" parents="11122 17112"/>
    </justification>
  </clause>

  <clause id="17652">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) * K((x \ y) \ 1,T(z,T(x,u))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(8774(a,1),17113(a,1,1))].">
      <j1 rule="para" parents="8774 17113"/>
    </justification>
  </clause>

  <clause id="17653">
    <literal><![CDATA[
      K(x,K(y / z,u) * (w * ((z / y) \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * T((z / y) \ 1,u)) = v5
    ]]></literal>
    <justification jstring="[para(6580(a,1),17260(a,1,2,1))].">
      <j1 rule="para" parents="6580 17260"/>
    </justification>
  </clause>

  <clause id="17654">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * (u * (K(w,z) * y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(K(w,z) * y,z \ 1)) = v5
    ]]></literal>
    <justification jstring="[para(7507(a,1),17260(a,1,2,1))].">
      <j1 rule="para" parents="7507 17260"/>
    </justification>
  </clause>

  <clause id="17655">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (K(w,z) * y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(K(w,z) * y,z)) = v5
    ]]></literal>
    <justification jstring="[para(8520(a,1),17260(a,1,2,1))].">
      <j1 rule="para" parents="8520 17260"/>
    </justification>
  </clause>

  <clause id="17656">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15771(a,2),17260(a,1))].">
      <j1 rule="para" parents="15771 17260"/>
    </justification>
  </clause>

  <clause id="17657">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(17300(a,1),17268(a,1))].">
      <j1 rule="para" parents="17300 17268"/>
    </justification>
  </clause>

  <clause id="17658">
    <literal><![CDATA[
      T(x,K(y / z,u) * T(z * (y / z),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * K(y,w)) * T(y / z,u)) = v5
    ]]></literal>
    <justification jstring="[para(14707(a,1),17269(a,1,2,2))].">
      <j1 rule="para" parents="14707 17269"/>
    </justification>
  </clause>

  <clause id="17659">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15759(a,1),17272(a,1))].">
      <j1 rule="para" parents="15759 17272"/>
    </justification>
  </clause>

  <clause id="17660">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * (v5 / w)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 / T(w,a(y,z,u))) = v6
    ]]></literal>
    <justification jstring="[para(15374(a,2),17306(a,1,2,1))].">
      <j1 rule="para" parents="15374 17306"/>
    </justification>
  </clause>

  <clause id="17661">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / u)) = w
    ]]></literal>
    <justification jstring="[para(17226(a,1),17530(a,1))].">
      <j1 rule="para" parents="17226 17530"/>
    </justification>
  </clause>

  <clause id="17662">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),((y \ z) \ 1) * (T(y,u) \ z)) = K(y,K(u,z * x))
    ]]></literal>
    <justification jstring="[hyper(17532,a,16541,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17532 16541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17663">
    <literal><![CDATA[
      K(x,y * K(z,(u * z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u * w,z)) = v5
    ]]></literal>
    <justification jstring="[para(15253(a,2),17540(a,1,2,2))].">
      <j1 rule="para" parents="15253 17540"/>
    </justification>
  </clause>

  <clause id="17664">
    <literal><![CDATA[
      K(x,y * K(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16265(a,1),17540(a,1))].">
      <j1 rule="para" parents="16265 17540"/>
    </justification>
  </clause>

  <clause id="17665">
    <literal><![CDATA[
      K(x,(y \ z) * K(u \ (w * (v5 \ 1)),z)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = v6
    ]]></literal>
    <justification jstring="[para(5267(a,1),17657(a,1,2,2))].">
      <j1 rule="para" parents="5267 17657"/>
    </justification>
  </clause>

  <clause id="17666">
    <literal><![CDATA[
      K(x,y * K(z * (u \ w),w \ u)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u \ w,z)) = v5
    ]]></literal>
    <justification jstring="[para(13816(a,2),17664(a,1))].">
      <j1 rule="para" parents="13816 17664"/>
    </justification>
  </clause>

  <clause id="17667">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) = K(x,u * ((z \ y) * z))
    ]]></literal>
    <justification jstring="[hyper(13528,a,17192,a)].">
      <j1 rule="hyper" parents="13528 17192"/>
    </justification>
  </clause>

  <clause id="17668">
    <literal><![CDATA[
      K(x,y * ((z \ u) * z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(17260,a,17667,a),flip(a)].">
      <j1 rule="hyper" parents="17260 17667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17669">
    <literal><![CDATA[
      K(x,y * ((z \ u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(17667(a,1),17260(a,1))].">
      <j1 rule="para" parents="17667 17260"/>
    </justification>
  </clause>

  <clause id="17671">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * ((z \ K(z,u)) \ u))
    ]]></literal>
    <justification jstring="[para(9505(a,2),17668(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9505 17668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17673">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * K(y,y \ z))) = T(x,z / ((1 / (y \ z)) * y))
    ]]></literal>
    <justification jstring="[para(5946(a,1),17282(a,1,2,2,2))].">
      <j1 rule="para" parents="5946 17282"/>
    </justification>
  </clause>

  <clause id="17674">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,6644,a(flip),b,17294,a),flip(a)].">
      <j1 rule="hyper" parents="373 6644 17294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17675">
    <literal><![CDATA[
      K(x,y / (y * (y * z))) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(9237,a,17674,a)].">
      <j1 rule="hyper" parents="9237 17674"/>
    </justification>
  </clause>

  <clause id="17677">
    <literal><![CDATA[
      K(x / y,z) * K(y,y \ x) = (y \ x) \ T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(15031,a,17315,a),flip(a)].">
      <j1 rule="hyper" parents="15031 17315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17678">
    <literal><![CDATA[
      T(x * T(y,x * K(z,u)),K(z,u)) = y * T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(8182,a,17350,a)].">
      <j1 rule="hyper" parents="8182 17350"/>
    </justification>
  </clause>

  <clause id="17680">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * y)) = K(x,u * (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13463,a(flip),b,17371,a)].">
      <j1 rule="hyper" parents="64 13463 17371"/>
    </justification>
  </clause>

  <clause id="17681">
    <literal><![CDATA[
      K(x,y * (z * (u / z))) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(17656,a,17680,a),flip(a)].">
      <j1 rule="hyper" parents="17656 17680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17682">
    <literal><![CDATA[
      T(x,y * (z * (u / z))) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,17681,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 17681 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17683">
    <literal><![CDATA[
      K(x,y * T(z * u,u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),17681(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 17681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17684">
    <literal><![CDATA[
      T(x,y * T(z * (u / z),w)) = T(x,y * T(T(u,w),z))
    ]]></literal>
    <justification jstring="[para(5431(a,2),17682(a,1,2,2))].">
      <j1 rule="para" parents="5431 17682"/>
    </justification>
  </clause>

  <clause id="17685">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (1 / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16524,a(flip),b,17683,a)].">
      <j1 rule="hyper" parents="64 16524 17683"/>
    </justification>
  </clause>

  <clause id="17686">
    <literal><![CDATA[
      K(x,y * T(T(z / u,T(w,u)) * v5,K(u \ z,w) * v5)) = K(x,y * ((K(u \ z,w) * v5) * (z / u)))
    ]]></literal>
    <justification jstring="[para(7983(a,1),17683(a,1,2,2,1))].">
      <j1 rule="para" parents="7983 17683"/>
    </justification>
  </clause>

  <clause id="17687">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) = K(x,u / (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17541,a(flip),b,17372,a)].">
      <j1 rule="hyper" parents="64 17541 17372"/>
    </justification>
  </clause>

  <clause id="17688">
    <literal><![CDATA[
      K(x,y / (z * (u / z))) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(17401,a,17687,a),flip(a)].">
      <j1 rule="hyper" parents="17401 17687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17689">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * (u / (1 / z)))) = K(x,y / T(u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,7106,a,b,17688,a)].">
      <j1 rule="hyper" parents="64 7106 17688"/>
    </justification>
  </clause>

  <clause id="17690">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / T(z \ 1,u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16721,a(flip),b,17688,a),flip(a)].">
      <j1 rule="hyper" parents="64 16721 17688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17691">
    <literal><![CDATA[
      K(x,y / T(z * u,u)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(11(a,1),17688(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 17688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17692">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(4399(a,2),17688(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4399 17688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17693">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,T(T(z \ y,u) * z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11244,a,b,17376,a)].">
      <j1 rule="hyper" parents="64 11244 17376"/>
    </justification>
  </clause>

  <clause id="17694">
    <literal><![CDATA[
      K(x,y) \ K(L(x,z,u),y) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15444,a(flip),b,17402,a),flip(a)].">
      <j1 rule="hyper" parents="64 15444 17402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17695">
    <literal><![CDATA[
      K(x,y) * K(a(z,u,y),x) = K(L(x,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(145,a,15355,a(flip),b,17694,a)].">
      <j1 rule="hyper" parents="145 15355 17694"/>
    </justification>
  </clause>

  <clause id="17696">
    <literal><![CDATA[
      T(x,y) / T(x,a(z,u,y)) = K(L(x,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(6502,a,17695,a)].">
      <j1 rule="hyper" parents="6502 17695"/>
    </justification>
  </clause>

  <clause id="17697">
    <literal><![CDATA[
      T(x,y) / (a(x,z,K(u,y)) \ x) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(15364(a,2),17696(a,1,2))].">
      <j1 rule="para" parents="15364 17696"/>
    </justification>
  </clause>

  <clause id="17698">
    <literal><![CDATA[
      T(x,y) / (a(K(x,y),z,u) \ x) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(15297(a,2),17697(a,1,2,1))].">
      <j1 rule="para" parents="15297 17697"/>
    </justification>
  </clause>

  <clause id="17699">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(y,x) = a(K(y,x),z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(37,a,6160,a,b,17698,a)].">
      <j1 rule="hyper" parents="37 6160 17698"/>
    </justification>
  </clause>

  <clause id="17700">
    <literal><![CDATA[
      T(K(x,L(y,z,u)) * y,x) = a(K(y,x),z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,7769,a,b,17699,a)].">
      <j1 rule="hyper" parents="64 7769 17699"/>
    </justification>
  </clause>

  <clause id="17701">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = a(K(x,y),z,u) \ x
    ]]></literal>
    <justification jstring="[para(4015(a,1),17700(a,1,1))].">
      <j1 rule="para" parents="4015 17700"/>
    </justification>
  </clause>

  <clause id="17702">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = a(x,z,K(u,y)) \ x
    ]]></literal>
    <justification jstring="[para(15297(a,1),17701(a,2,1))].">
      <j1 rule="para" parents="15297 17701"/>
    </justification>
  </clause>

  <clause id="17703">
    <literal><![CDATA[
      T(x * K(y,L(x,z,u)),y) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,15364,a(flip),b,17702,a),flip(a)].">
      <j1 rule="hyper" parents="373 15364 17702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17704">
    <literal><![CDATA[
      x * T(x \ (y \ x),K(z,u)) = T(y,K(z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,17331,a(flip),b,17432,a),flip(a)].">
      <j1 rule="hyper" parents="64 17331 17432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17705">
    <literal><![CDATA[
      T(x \ (y \ x),K(z,u)) = x \ (T(y,K(z,u)) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,17331,a(flip),b,17432,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 17331 17432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17706">
    <literal><![CDATA[
      T(x,K(y,z * (x * u))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8734,a,17444,a),flip(a)].">
      <j1 rule="hyper" parents="8734 17444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17707">
    <literal><![CDATA[
      K(T(x,y) \ z,T(u,x)) = K(z * T(x \ 1,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16849,a(flip),b,17445,a)].">
      <j1 rule="hyper" parents="64 16849 17445"/>
    </justification>
  </clause>

  <clause id="17708">
    <literal><![CDATA[
      K(x * T(y \ 1,z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17100,a(flip),b,17707,a),flip(a)].">
      <j1 rule="hyper" parents="64 17100 17707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17709">
    <literal><![CDATA[
      K(x * T(y \ 1,z),u) = u / T(u,x / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,5787,a(flip),b,17708,a),flip(a)].">
      <j1 rule="hyper" parents="373 5787 17708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17710">
    <literal><![CDATA[
      K(x * T(1 / y,z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5263,a,b,17708,a)].">
      <j1 rule="hyper" parents="64 5263 17708"/>
    </justification>
  </clause>

  <clause id="17711">
    <literal><![CDATA[
      K((1 / x) / T(y,z),u) = K(x \ T(1 / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(14754,a,17710,a),flip(a)].">
      <j1 rule="hyper" parents="14754 17710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17712">
    <literal><![CDATA[
      T(x,y * T(z \ 1,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(5870,a,17709,a)].">
      <j1 rule="hyper" parents="5870 17709"/>
    </justification>
  </clause>

  <clause id="17713">
    <literal><![CDATA[
      T(x,y * T(1 / z,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5124,a,b,17712,a)].">
      <j1 rule="hyper" parents="64 5124 17712"/>
    </justification>
  </clause>

  <clause id="17714">
    <literal><![CDATA[
      T(x,y / T((z * z) \ u,w)) = T(x,y * T(u \ (z * z),w))
    ]]></literal>
    <justification jstring="[para(550(a,1),17712(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="550 17712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17715">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,v5)) = T(x,y * T(w \ K(u,z),v5))
    ]]></literal>
    <justification jstring="[para(14450(a,1),17712(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14450 17712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17716">
    <literal><![CDATA[
      T(x,y * T((z * K(u * z,w)) \ 1,u)) = T(x,y / (u \ T(z * u,w)))
    ]]></literal>
    <justification jstring="[para(14496(a,1),17712(a,2,2,2))].">
      <j1 rule="para" parents="14496 17712"/>
    </justification>
  </clause>

  <clause id="17717">
    <literal><![CDATA[
      T(x,y / T(z \ 1,u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),17713(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 17713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17718">
    <literal><![CDATA[
      T(x,y / T(z \ K(u,z),w)) = T(x,y * T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(5877(a,2),17713(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5877 17713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17719">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),v5)) = T(x,y * T(K(w,u) / z,v5))
    ]]></literal>
    <justification jstring="[para(14507(a,1),17713(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14507 17713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17720">
    <literal><![CDATA[
      K(x \ T(1 / y,z),u) = K(x \ (T(y,z) \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14679,a(flip),b,17711,a),flip(a)].">
      <j1 rule="hyper" parents="64 14679 17711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17721">
    <literal><![CDATA[
      K(x,T(T(y,z),u * w)) * T(z,v5) = T(z,v5) * K(x,T(y,w * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17088,a,b,17447,a),flip(a)].">
      <j1 rule="hyper" parents="373 17088 17447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17722">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(K(y * z,x) * y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16903,a,b,17487,a)].">
      <j1 rule="hyper" parents="64 16903 17487"/>
    </justification>
  </clause>

  <clause id="17723">
    <literal><![CDATA[
      K(x,T(y,z \ u)) \ (w * (u / z)) = K(x,y) \ (w * T(u / z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(17109(a,1),17506(a,1,1))].">
      <j1 rule="para" parents="17109 17506"/>
    </justification>
  </clause>

  <clause id="17724">
    <literal><![CDATA[
      K(K(x \ 1,y) \ z,u) = K(K(x * y,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(13653,a,17550,a),flip(a)].">
      <j1 rule="hyper" parents="13653 17550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17726">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,z) / x,u) = w
    ]]></literal>
    <justification jstring="[para(17594(a,1),8314(a,1))].">
      <j1 rule="para" parents="17594 8314"/>
    </justification>
  </clause>

  <clause id="17727">
    <literal><![CDATA[
      K((x / y) \ K(z,y),u) = K(T(y,z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(17726,a,16307,a),flip(a)].">
      <j1 rule="hyper" parents="17726 16307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17728">
    <literal><![CDATA[
      K((x / y) \ K(z \ K(u,w),y),v5) = K(T(y,z \ K(w,u \ w)) / x,v5)
    ]]></literal>
    <justification jstring="[para(16341(a,1),17727(a,1,1,2))].">
      <j1 rule="para" parents="16341 17727"/>
    </justification>
  </clause>

  <clause id="17729">
    <literal><![CDATA[
      K(x,K(y,z)) \ (x * (T(u,w) / x)) = T(T(x,K(y,z)) * (u / x),w)
    ]]></literal>
    <justification jstring="[para(5431(a,1),17648(a,1,2))].">
      <j1 rule="para" parents="5431 17648"/>
    </justification>
  </clause>

  <clause id="17730">
    <literal><![CDATA[
      T(x / y,z) * ((y \ x) \ 1) = (y \ x) \ T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6409,a,b,17677,a)].">
      <j1 rule="hyper" parents="64 6409 17677"/>
    </justification>
  </clause>

  <clause id="17731">
    <literal><![CDATA[
      T(x * T(y,K(z,u) \ x),K(z,u)) = y * T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(17377(a,2),17678(a,1,1,2))].">
      <j1 rule="para" parents="17377 17678"/>
    </justification>
  </clause>

  <clause id="17732">
    <literal><![CDATA[
      T(x,y * T(z * (u / z),w)) = T(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(23(a,1),17684(a,2,2,2))].">
      <j1 rule="para" parents="23 17684"/>
    </justification>
  </clause>

  <clause id="17733">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z \ 1))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(15920,a,17692,a),flip(a)].">
      <j1 rule="hyper" parents="15920 17692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17734">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / ((z * u) / u)) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16785,a(flip),b,17733,a),flip(a)].">
      <j1 rule="hyper" parents="64 16785 17733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17735">
    <literal><![CDATA[
      T(x,R(y / y,y,y) \ ((z \ ((y * y) * u)) / w)) = T(x,((T(z,y * y) \ u) / w) * (y * y))
    ]]></literal>
    <justification jstring="[para(1529(a,1),17081(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1529 17081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17736">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * z) / (w * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,17225,a,b,17249,a),flip(a)].">
      <j1 rule="hyper" parents="373 17225 17249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17737">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) * K(y,K(x,z)) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(17539,a,15036,a)].">
      <j1 rule="hyper" parents="17539 15036"/>
    </justification>
  </clause>

  <clause id="17738">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(z,y) = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(36,a,17410,a,b,17737,a)].">
      <j1 rule="hyper" parents="36 17410 17737"/>
    </justification>
  </clause>

  <clause id="17739">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = K(y,x) * (z \ y)
    ]]></literal>
    <justification jstring="[para(8177(a,2),17738(a,1,1))].">
      <j1 rule="para" parents="8177 17738"/>
    </justification>
  </clause>

  <clause id="17740">
    <literal><![CDATA[
      (x * K(y,z)) \ z = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,15216,a(flip),b,17739,a)].">
      <j1 rule="hyper" parents="64 15216 17739"/>
    </justification>
  </clause>

  <clause id="17741">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ z = K(z,T(y,u)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(7869(a,1),17740(a,1,1,2))].">
      <j1 rule="para" parents="7869 17740"/>
    </justification>
  </clause>

  <clause id="17742">
    <literal><![CDATA[
      K(x,y) * ((z \ T(x,y)) \ x) = (z \ x) \ x
    ]]></literal>
    <justification jstring="[para(15017(a,1),17740(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15017 17740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17743">
    <literal><![CDATA[
      K(x,y) * ((z \ y) \ y) = (z \ T(y,x)) \ y
    ]]></literal>
    <justification jstring="[hyper(6187,a,17742,a)].">
      <j1 rule="hyper" parents="6187 17742"/>
    </justification>
  </clause>

  <clause id="17744">
    <literal><![CDATA[
      T(x * K(y,z),x \ z) = (x \ T(z,y)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,16680,a,b,17743,a)].">
      <j1 rule="hyper" parents="64 16680 17743"/>
    </justification>
  </clause>

  <clause id="17745">
    <literal><![CDATA[
      (x \ T(K(y,z),u)) \ K(y,z) = (x \ K(y,z)) \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17333,a(flip),b,17743,a),flip(a)].">
      <j1 rule="hyper" parents="64 17333 17743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17746">
    <literal><![CDATA[
      (x * K(y,T(z \ u,z))) \ (z \ u) = K(u / z,y) * (x \ (z \ u))
    ]]></literal>
    <justification jstring="[para(8215(a,1),17741(a,2,1))].">
      <j1 rule="para" parents="8215 17741"/>
    </justification>
  </clause>

  <clause id="17747">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = w
    ]]></literal>
    <justification jstring="[para(8110(a,1),17598(a,1,1))].">
      <j1 rule="para" parents="8110 17598"/>
    </justification>
  </clause>

  <clause id="17748">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,6535,a(flip),b,17685,a),flip(a)].">
      <j1 rule="hyper" parents="373 6535 17685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17749">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) = w
    ]]></literal>
    <justification jstring="[para(17685(a,2),17438(a,1))].">
      <j1 rule="para" parents="17685 17438"/>
    </justification>
  </clause>

  <clause id="17750">
    <literal><![CDATA[
      K(x,K(y,(z * (u * w)) / (z * w))) = K(x,K(y,L(u,w,z)))
    ]]></literal>
    <justification jstring="[para(11(a,1),17736(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="11 17736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17751">
    <literal><![CDATA[
      T(x * T(x \ y,T(z,y)),x) = T(y,x) * K(y / T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2915,a,b,17125,a)].">
      <j1 rule="hyper" parents="373 2915 17125"/>
    </justification>
  </clause>

  <clause id="17754">
    <literal><![CDATA[
      (T(x,K(y,L(z,u,w)) * v5) * K(y,L(T(z,x),u,w))) / (K(y,L(z,u,w)) * x) = K(x,v5 * K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(142,a,17451,a,b,11108,a)].">
      <j1 rule="hyper" parents="142 17451 11108"/>
    </justification>
  </clause>

  <clause id="17755">
    <literal><![CDATA[
      K(x,y \ T(z * K(u,z \ w),T(z \ w,u))) = K(x,y \ (w / T(w / z,u)))
    ]]></literal>
    <justification jstring="[para(17466(a,1),16301(a,1,2,2))].">
      <j1 rule="para" parents="17466 16301"/>
    </justification>
  </clause>

  <clause id="17756">
    <literal><![CDATA[
      K(x \ T(y \ T(T(y,K(z,u)) * w,K(z,u)),T(w * T(y,K(z,u)),K(z,u))),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[para(17620(a,1),16805(a,1,1,2,1))].">
      <j1 rule="para" parents="17620 16805"/>
    </justification>
  </clause>

  <clause id="17757">
    <literal><![CDATA[
      T(x / (y \ (y / x)),K(z,u)) = (x / (y \ (y / x))) * 1
    ]]></literal>
    <justification jstring="[para(375(a,1),17634(a,2,2))].">
      <j1 rule="para" parents="375 17634"/>
    </justification>
  </clause>

  <clause id="17758">
    <literal><![CDATA[
      T(x / (y \ (y / x)),K(z,u)) = x / (y \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a(flip),b,17757,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 17757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17760">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,w) / K(x,y) = T(K(x,y) * u,w) / T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(17328(a,1),17643(a,1,1,1))].">
      <j1 rule="para" parents="17328 17643"/>
    </justification>
  </clause>

  <clause id="17761">
    <literal><![CDATA[
      ((x \ K(y,z)) \ K(y,T(z,u))) * K(y,K(z,w)) = (x \ T(K(y,z),u)) \ K(y,T(z,w))
    ]]></literal>
    <justification jstring="[para(17745(a,1),15657(a,1,1))].">
      <j1 rule="para" parents="17745 15657"/>
    </justification>
  </clause>

  <clause id="17762">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = T(x * K(x / y,z),y)
    ]]></literal>
    <justification jstring="[para(8247(a,1),17751(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8247 17751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17763">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = T(x,y) * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(13400(a,1),17762(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13400 17762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17764">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = K(x / y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,17287,a(flip),b,17763,a),flip(a)].">
      <j1 rule="hyper" parents="373 17287 17763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17765">
    <literal><![CDATA[
      K(((x \ y) * x) * z,u) = K(z * T(y,x),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(17094,a,17624,a)].">
      <j1 rule="hyper" parents="17094 17624"/>
    </justification>
  </clause>

  <clause id="17766">
    <literal><![CDATA[
      K(((x \ y) * x) * z,u) = K(T(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,17097,a(flip),b,17765,a),flip(a)].">
      <j1 rule="hyper" parents="373 17097 17765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17767">
    <literal><![CDATA[
      K(T(x * y,x) * z,u) = K((y * x) * z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),17766(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 17766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17768">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) * a(w,v5,K(T(z,y) * u,x)) = K(x,L(((y \ z) * y) * u,v5,w))
    ]]></literal>
    <justification jstring="[para(17766(a,1),12069(a,1,2,3))].">
      <j1 rule="para" parents="17766 12069"/>
    </justification>
  </clause>

  <clause id="17769">
    <literal><![CDATA[
      T(x,R(K(y,z) * u,K(z,y),w)) = T(x,(u * w) / (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(6156(a,1),17208(a,1,2,1))].">
      <j1 rule="para" parents="6156 17208"/>
    </justification>
  </clause>

  <clause id="17770">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,u / (z * y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,8991,a(flip),b,17382,a),flip(a)].">
      <j1 rule="hyper" parents="373 8991 17382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17771">
    <literal><![CDATA[
      K(x,K((y \ z) / u,L(w,u,y))) = K(x,K(w,z / (y * u)))
    ]]></literal>
    <justification jstring="[hyper(17387,a,17770,a)].">
      <j1 rule="hyper" parents="17387 17770"/>
    </justification>
  </clause>

  <clause id="17772">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,L(w,u,z))) = K(x,K(w,(y * z) / (z * u)))
    ]]></literal>
    <justification jstring="[para(22(a,2),17771(a,1,2,1,1))].">
      <j1 rule="para" parents="22 17771"/>
    </justification>
  </clause>

  <clause id="17773">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,y)) = y \ (K(u,z) \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(17452,a,6197,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17452 6197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17774">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(z,u) = z \ (K(x,y) \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(17312,a,17773,a)].">
      <j1 rule="hyper" parents="17312 17773"/>
    </justification>
  </clause>

  <clause id="17775">
    <literal><![CDATA[
      x \ (K(y,z) \ T(x,x \ z)) = z \ (x * (T(z,y) / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,16142,a(flip),b,17773,a),flip(a)].">
      <j1 rule="hyper" parents="64 16142 17773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17776">
    <literal><![CDATA[
      x \ (K(y,z) \ T(x,x \ z)) = (x * (T(z,y) / x)) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,15218,a(flip),b,17774,a),flip(a)].">
      <j1 rule="hyper" parents="64 15218 17774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17777">
    <literal><![CDATA[
      (x * (T(y,z) / x)) / y = y \ (x * (T(y,z) / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,17775,a(flip),b,17776,a),flip(a)].">
      <j1 rule="hyper" parents="64 17775 17776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17778">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,w))) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17304,a(flip),b,17475,a),flip(a)].">
      <j1 rule="hyper" parents="64 17304 17475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17779">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9571,a,b,17778,a)].">
      <j1 rule="hyper" parents="64 9571 17778"/>
    </justification>
  </clause>

  <clause id="17780">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(5753(a,2),17779(a,2,2,2))].">
      <j1 rule="para" parents="5753 17779"/>
    </justification>
  </clause>

  <clause id="17781">
    <literal><![CDATA[
      K(x,y / ((z * (u \ 1)) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(14779,a,17780,a)].">
      <j1 rule="hyper" parents="14779 17780"/>
    </justification>
  </clause>

  <clause id="17782">
    <literal><![CDATA[
      K(x,y / T(z \ 1,u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(16354,a,17781,a)].">
      <j1 rule="hyper" parents="16354 17781"/>
    </justification>
  </clause>

  <clause id="17783">
    <literal><![CDATA[
      K(x,y * T(z,z * (x * y))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(14738,a,17782,a),flip(a)].">
      <j1 rule="hyper" parents="14738 17782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17784">
    <literal><![CDATA[
      K(x,L(y / T(z \ 1,u),w,v5)) = K(L(x,w,v5),y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(12117,a,17782,a)].">
      <j1 rule="hyper" parents="12117 17782"/>
    </justification>
  </clause>

  <clause id="17785">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * T(z,u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17690,a(flip),b,17782,a),flip(a)].">
      <j1 rule="hyper" parents="64 17690 17782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17786">
    <literal><![CDATA[
      K(x,y * T(1 / z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(82(a,1),17782(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="82 17782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17787">
    <literal><![CDATA[
      K(x,y * T(z,x * y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(13525,a,17783,a)].">
      <j1 rule="hyper" parents="13525 17783"/>
    </justification>
  </clause>

  <clause id="17788">
    <literal><![CDATA[
      T(x,y * T(z,x * y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(143,a,17787,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 17787 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17789">
    <literal><![CDATA[
      T(x,y * K(z,u)) \ T(y * T(T(x,y * K(z,u)),K(z,u)),K(u,z)) = T(y,x * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16803,a,b,17788,a)].">
      <j1 rule="hyper" parents="64 16803 17788"/>
    </justification>
  </clause>

  <clause id="17790">
    <literal><![CDATA[
      K(x,(1 / y) / T(z,u)) = K(x,y \ T(1 / z,u))
    ]]></literal>
    <justification jstring="[hyper(14729,a,17786,a),flip(a)].">
      <j1 rule="hyper" parents="14729 17786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17791">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / T(y / z,y)) = K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17012,a(flip),b,17786,a),flip(a)].">
      <j1 rule="hyper" parents="64 17012 17786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17792">
    <literal><![CDATA[
      K(x,y * T(z \ 1,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,6544,a(flip),b,17786,a)].">
      <j1 rule="hyper" parents="64 6544 17786"/>
    </justification>
  </clause>

  <clause id="17793">
    <literal><![CDATA[
      K(x,T(y,z * u) * T(u,z)) = K(x,T(u * y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16871,a(flip),b,17785,a)].">
      <j1 rule="hyper" parents="64 16871 17785"/>
    </justification>
  </clause>

  <clause id="17794">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16244,a(flip),b,17793,a),flip(a)].">
      <j1 rule="hyper" parents="64 16244 17793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17795">
    <literal><![CDATA[
      K(x,((((y \ (z * u)) \ 1) \ y) \ y) * T(u,z)) = K(x,T(u * ((y \ (z * u)) \ 1),z))
    ]]></literal>
    <justification jstring="[para(7235(a,1),17793(a,1,2,1))].">
      <j1 rule="para" parents="7235 17793"/>
    </justification>
  </clause>

  <clause id="17796">
    <literal><![CDATA[
      K(x,y * ((z * y) \ T(u,z))) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16697,a(flip),b,17794,a)].">
      <j1 rule="hyper" parents="64 16697 17794"/>
    </justification>
  </clause>

  <clause id="17797">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[para(14834(a,2),17796(a,1,2,2))].">
      <j1 rule="para" parents="14834 17796"/>
    </justification>
  </clause>

  <clause id="17798">
    <literal><![CDATA[
      K(x,L(y / T(z \ 1,u),w,v5)) = K(x,L(y * T(z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,12093,a(flip),b,17784,a),flip(a)].">
      <j1 rule="hyper" parents="373 12093 17784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17799">
    <literal><![CDATA[
      K(x,L(y * (z \ T(u,u \ z)),w,v5)) = K(x,L(y * T(z \ u,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(15195,a,17798,a)].">
      <j1 rule="hyper" parents="15195 17798"/>
    </justification>
  </clause>

  <clause id="17800">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(T(x,z) * y,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(17650,a,16878,a)].">
      <j1 rule="hyper" parents="17650 16878"/>
    </justification>
  </clause>

  <clause id="17801">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(y * T(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11180,a(flip),b,17800,a),flip(a)].">
      <j1 rule="hyper" parents="373 11180 17800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17802">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * T(z * y,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17590,a(flip),b,17801,a)].">
      <j1 rule="hyper" parents="64 17590 17801"/>
    </justification>
  </clause>

  <clause id="17803">
    <literal><![CDATA[
      T(x,L(K(y,z) * u,K(z,y),w)) = T(x,(u * w) / (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(15615,a,17769,a)].">
      <j1 rule="hyper" parents="15615 17769"/>
    </justification>
  </clause>

  <clause id="17804">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ T(w * y,K(z,u))) = K(x,T(w,K(u,z) * y))
    ]]></literal>
    <justification jstring="[para(6156(a,1),17072(a,2,2,2))].">
      <j1 rule="para" parents="6156 17072"/>
    </justification>
  </clause>

  <clause id="17805">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) != K(z,K(y,u)) * w
    ]]></literal>
    <literal><![CDATA[
      K(z \ (x * (y / x)),u) = w
    ]]></literal>
    <justification jstring="[para(17250(a,1),44(a,1))].">
      <j1 rule="para" parents="17250 44"/>
    </justification>
  </clause>

  <clause id="17807">
    <literal><![CDATA[
      T(x,y * (y * (z \ T(u,y \ (y \ z))))) = T(x,u / (z / (y * y)))
    ]]></literal>
    <justification jstring="[hyper(15896,a,17279,a)].">
      <j1 rule="hyper" parents="15896 17279"/>
    </justification>
  </clause>

  <clause id="17808">
    <literal><![CDATA[
      K(x \ K(T(y,x * z),u),T(w,z)) = K(T(x,z) \ K(y,u),w)
    ]]></literal>
    <justification jstring="[hyper(6832,a,17473,a)].">
      <j1 rule="hyper" parents="6832 17473"/>
    </justification>
  </clause>

  <clause id="17809">
    <literal><![CDATA[
      K(x \ K(y,T(z,x * u)),T(w,u)) = K(T(x,u) \ K(y,z),w)
    ]]></literal>
    <justification jstring="[para(7869(a,1),17808(a,1,1,2))].">
      <j1 rule="para" parents="7869 17808"/>
    </justification>
  </clause>

  <clause id="17810">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (z \ u)) = T(x,(T(u,z) / z) * y)
    ]]></literal>
    <justification jstring="[hyper(13527,a,17563,a)].">
      <j1 rule="hyper" parents="13527 17563"/>
    </justification>
  </clause>

  <clause id="17811">
    <literal><![CDATA[
      T(x,(T(y,z) / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * u) = w
    ]]></literal>
    <justification jstring="[para(17810(a,1),17562(a,1))].">
      <j1 rule="para" parents="17810 17562"/>
    </justification>
  </clause>

  <clause id="17812">
    <literal><![CDATA[
      T(x,(T(y,y \ z) / (z / y)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,((z / y) \ y) * u) = w
    ]]></literal>
    <justification jstring="[para(4636(a,1),17811(a,1,2,1,1))].">
      <j1 rule="para" parents="4636 17811"/>
    </justification>
  </clause>

  <clause id="17813">
    <literal><![CDATA[
      T(T(x,K(y,z * u)),y * (u * (z \ 1))) = T(x,(u * (z \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(8157(a,1),17570(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8157 17570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17814">
    <literal><![CDATA[
      T(x,(y / T(z,u * (u * y))) * (u * u)) = T(x,z \ ((u * u) * y))
    ]]></literal>
    <justification jstring="[para(804(a,1),17588(a,2,2))].">
      <j1 rule="para" parents="804 17588"/>
    </justification>
  </clause>

  <clause id="17815">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z \ y,u) \ y) = T(x,T(y / z,u) \ y)
    ]]></literal>
    <justification jstring="[para(9030(a,1),17604(a,1,1))].">
      <j1 rule="para" parents="9030 17604"/>
    </justification>
  </clause>

  <clause id="17816">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y \ z,u) \ z) = T(x,T(z / y,u) \ z)
    ]]></literal>
    <justification jstring="[para(8153(a,1),17815(a,1,1))].">
      <j1 rule="para" parents="8153 17815"/>
    </justification>
  </clause>

  <clause id="17817">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * T(y / z,u)) = T(x,z * T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(8707(a,1),17605(a,1,1))].">
      <j1 rule="para" parents="8707 17605"/>
    </justification>
  </clause>

  <clause id="17818">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(373,a,11313,a(flip),b,17693,a),flip(a)].">
      <j1 rule="hyper" parents="373 11313 17693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17819">
    <literal><![CDATA[
      T(x,y) * K(z,T(T(u,x),w * v5)) = K(z,T(u,v5 * w)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8219(a,1),17721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8219 17721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17820">
    <literal><![CDATA[
      (x * K(y,z / u)) \ (u \ z) = K(z / u,y) * (x \ (u \ z))
    ]]></literal>
    <justification jstring="[para(8216(a,1),17746(a,1,1,2))].">
      <j1 rule="para" parents="8216 17746"/>
    </justification>
  </clause>

  <clause id="17821">
    <literal><![CDATA[
      T(x,y / ((K(z / u,w) * (u \ (u \ z))) \ (u \ z))) = T(x,y / (T(u \ z,w) \ z))
    ]]></literal>
    <justification jstring="[para(17820(a,1),13432(a,1,2,2,1))].">
      <j1 rule="para" parents="17820 13432"/>
    </justification>
  </clause>

  <clause id="17822">
    <literal><![CDATA[
      T(T(x,K(y,(z * z) * T(u,z))),y * ((z * z) * (T(u,z \ 1) \ 1))) = T(x,((z * z) * (T(u,z \ 1) \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(15816(a,1),17813(a,1,1,2,2))].">
      <j1 rule="para" parents="15816 17813"/>
    </justification>
  </clause>

  <clause id="17823">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(u,z) = T(K(x,T(y,u)) * u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,15723,a(flip),b,17819,a),flip(a)].">
      <j1 rule="hyper" parents="64 15723 17819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17824">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(u,z) = T(u * K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8193(a,1),17823(a,2,1))].">
      <j1 rule="para" parents="8193 17823"/>
    </justification>
  </clause>

  <clause id="17825">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7875(a,1),17824(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7875 17824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17826">
    <literal><![CDATA[
      T(x * K(y,z * z),u) = K(y,z * z) * T(x,u)
    ]]></literal>
    <justification jstring="[para(17050(a,1),17824(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17050 17824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17827">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(z,u) = T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(17066(a,1),17824(a,1,1))].">
      <j1 rule="para" parents="17066 17824"/>
    </justification>
  </clause>

  <clause id="17828">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,11257,a(flip),b,17825,a),flip(a)].">
      <j1 rule="hyper" parents="373 11257 17825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17829">
    <literal><![CDATA[
      T(x * y,z) / T(y,x) = T(x * K(x * y,z),y)
    ]]></literal>
    <justification jstring="[hyper(14899,a,17825,a(flip))].">
      <j1 rule="hyper" parents="14899 17825"/>
    </justification>
  </clause>

  <clause id="17830">
    <literal><![CDATA[
      T(x * K(x \ y,z),y) = K(x \ y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(17027(a,1),17827(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17027 17827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17831">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,11236,a(flip),b,17828,a),flip(a)].">
      <j1 rule="hyper" parents="373 11236 17828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17832">
    <literal><![CDATA[
      T(x,y / (z * ((u * K(u * z,w)) / z))) = T(x,y / (T(u,z) * K(z * u,w)))
    ]]></literal>
    <justification jstring="[para(17828(a,1),16094(a,2,2,2))].">
      <j1 rule="para" parents="17828 16094"/>
    </justification>
  </clause>

  <clause id="17833">
    <literal><![CDATA[
      (x * y) / (K(z * K(z * u,w),T(x,u)) * y) = T(x,T(z * u,w) / T(u,z))
    ]]></literal>
    <justification jstring="[para(17829(a,2),7923(a,2,2))].">
      <j1 rule="para" parents="17829 7923"/>
    </justification>
  </clause>

  <clause id="17834">
    <literal><![CDATA[
      T(x,T(T(y * K(y * z,u),z),y * z)) = T(x,T(z,y) \ T(y * z,u))
    ]]></literal>
    <justification jstring="[para(17829(a,1),17121(a,1,2,1))].">
      <j1 rule="para" parents="17829 17121"/>
    </justification>
  </clause>

  <clause id="17835">
    <literal><![CDATA[
      T(x * K(x \ y,z),y) = T(x,y) * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,17448,a,b,17830,a),flip(a)].">
      <j1 rule="hyper" parents="373 17448 17830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17836">
    <literal><![CDATA[
      x \ T(y * x,x \ 1) = (y * x) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7560,a(flip),b,17831,a)].">
      <j1 rule="hyper" parents="64 7560 17831"/>
    </justification>
  </clause>

  <clause id="17837">
    <literal><![CDATA[
      K(x,L((y * z) / u,y * z,y / (z * y))) = K(x,(z \ T(y * z,z \ 1)) / (u * (y / (z * y))))
    ]]></literal>
    <justification jstring="[para(17836(a,2),15570(a,2,2,1))].">
      <j1 rule="para" parents="17836 15570"/>
    </justification>
  </clause>

  <clause id="17838">
    <literal><![CDATA[
      K(x,y * K(z,u \ (z * w))) = K(x,K(z,u \ w) * y)
    ]]></literal>
    <justification jstring="[hyper(17514,a,13413,a)].">
      <j1 rule="hyper" parents="17514 13413"/>
    </justification>
  </clause>

  <clause id="17839">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u)) * w) = K(x,w * K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),17838(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 17838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17840">
    <literal><![CDATA[
      K(x,L(T(y \ z,z * (u / y)),y,y \ u)) = K(x,((u / y) * z) / u)
    ]]></literal>
    <justification jstring="[para(25(a,2),17591(a,1,2))].">
      <j1 rule="para" parents="25 17591"/>
    </justification>
  </clause>

  <clause id="17841">
    <literal><![CDATA[
      K(x,L(T(y \ z,y * (u / z)),y,z \ u)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[para(25(a,2),17592(a,1,2))].">
      <j1 rule="para" parents="25 17592"/>
    </justification>
  </clause>

  <clause id="17844">
    <literal><![CDATA[
      (x / y) / T((y * y) \ x,y) = ((y * y) \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[para(8881(a,1),17443(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8881 17443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17845">
    <literal><![CDATA[
      (x / y) / T((y * y) \ x,y) = x \ ((y * y) * (x / y))
    ]]></literal>
    <justification jstring="[hyper(373,a,804,a(flip),b,17844,a),flip(a)].">
      <j1 rule="hyper" parents="373 804 17844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17846">
    <literal><![CDATA[
      K(K(x,y) * T((y \ x) \ z,K(x,y) * u),u) = K((x / y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(17367,a,17483,a)].">
      <j1 rule="hyper" parents="17367 17483"/>
    </justification>
  </clause>

  <clause id="17847">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u))),y / ((u \ z) / u)) = T(x,((u \ z) / u) \ y)
    ]]></literal>
    <justification jstring="[para(11133(a,1),17564(a,1,1,2))].">
      <j1 rule="para" parents="11133 17564"/>
    </justification>
  </clause>

  <clause id="17848">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / ((u \ z) / u)) = T(x,((u \ z) / u) \ y)
    ]]></literal>
    <justification jstring="[para(17216(a,1),17847(a,1,1))].">
      <j1 rule="para" parents="17216 17847"/>
    </justification>
  </clause>

  <clause id="17850">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(z,u * w)) = T(y,K(u \ w,z) * x)
    ]]></literal>
    <justification jstring="[para(17553(a,1),17565(a,1,2))].">
      <j1 rule="para" parents="17553 17565"/>
    </justification>
  </clause>

  <clause id="17851">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(z,w * u)) = T(y,K(u \ w,z) * x)
    ]]></literal>
    <justification jstring="[para(17557(a,1),17565(a,1,2))].">
      <j1 rule="para" parents="17557 17565"/>
    </justification>
  </clause>

  <clause id="17852">
    <literal><![CDATA[
      T(x,K(y,z * u)) \ T(w * x,K(y,z * u)) = T(w,x * K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(17553(a,1),17566(a,1,2))].">
      <j1 rule="para" parents="17553 17566"/>
    </justification>
  </clause>

  <clause id="17853">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(z,z \ u) = (z \ u) \ T(u / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17730,a(flip),b,17568,a),flip(a)].">
      <j1 rule="hyper" parents="64 17730 17568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17854">
    <literal><![CDATA[
      T(x,K(y,T(y \ z,u)) * ((y \ z) * T(T(y \ z,u),u))) = T(x,T(y \ z,u) * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(6250(a,1),17610(a,1,2,2))].">
      <j1 rule="para" parents="6250 17610"/>
    </justification>
  </clause>

  <clause id="17855">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),(y \ z) \ (T(y,u) \ z)) = K(y,K(u,z * x))
    ]]></literal>
    <justification jstring="[hyper(14474,a,17662,a)].">
      <j1 rule="hyper" parents="14474 17662"/>
    </justification>
  </clause>

  <clause id="17856">
    <literal><![CDATA[
      K(x \ ((y \ z) \ 1),K(u,T(y,z))) = K(y,K(u,z * x))
    ]]></literal>
    <justification jstring="[para(8647(a,1),17855(a,1,2))].">
      <j1 rule="para" parents="8647 17855"/>
    </justification>
  </clause>

  <clause id="17857">
    <literal><![CDATA[
      K(x,K(y,T(z \ ((y \ u) \ 1),w))) = K(y,K(x,u * z))
    ]]></literal>
    <justification jstring="[hyper(17434,a,17856,a)].">
      <j1 rule="hyper" parents="17434 17856"/>
    </justification>
  </clause>

  <clause id="17858">
    <literal><![CDATA[
      K(x,K(y,z \ ((x \ u) \ 1))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(17247,a,17857,a)].">
      <j1 rule="hyper" parents="17247 17857"/>
    </justification>
  </clause>

  <clause id="17860">
    <literal><![CDATA[
      K(x,K(y,z * (x \ u))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(17532,a,17858,a)].">
      <j1 rule="hyper" parents="17532 17858"/>
    </justification>
  </clause>

  <clause id="17861">
    <literal><![CDATA[
      T(x,y / ((1 / (z \ y)) * z)) = T(x,(z \ y) * (y / z))
    ]]></literal>
    <justification jstring="[para(5774(a,1),17673(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5774 17673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17862">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(y * K(z * y,x),T(u,z))
    ]]></literal>
    <justification jstring="[para(11188(a,1),17722(a,2,1))].">
      <j1 rule="para" parents="11188 17722"/>
    </justification>
  </clause>

  <clause id="17863">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z * y)) = K(x,T(u,y \ (z \ y)) / y)
    ]]></literal>
    <justification jstring="[para(11(a,1),17734(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 17734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17864">
    <literal><![CDATA[
      T(K(x,y) * z,u) / T(K(x,y),w) = T(K(x,T(y,w)) * z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(6898,a,17760,a),flip(a)].">
      <j1 rule="hyper" parents="6898 17760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17865">
    <literal><![CDATA[
      K(x,L(y * (z \ T(u,u \ z)),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * (u / z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(17799(a,2),16091(a,1))].">
      <j1 rule="para" parents="17799 16091"/>
    </justification>
  </clause>

  <clause id="17866">
    <literal><![CDATA[
      T(x,y \ T(T(z,z * y) * y,u)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(16422(a,1),17834(a,1,2))].">
      <j1 rule="para" parents="16422 17834"/>
    </justification>
  </clause>

  <clause id="17867">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) = T(x,K(y * z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(16806,a,17850,a),flip(a)].">
      <j1 rule="hyper" parents="16806 17850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17868">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y * z,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(17850(a,1),16806(a,1))].">
      <j1 rule="para" parents="17850 16806"/>
    </justification>
  </clause>

  <clause id="17869">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(17867(a,1),16812(a,1))].">
      <j1 rule="para" parents="17867 16812"/>
    </justification>
  </clause>

  <clause id="17870">
    <literal><![CDATA[
      T(x,y * K(z,u \ w)) = T(x,y * K(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(16972,a,17852,a),flip(a)].">
      <j1 rule="hyper" parents="16972 17852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17871">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(z \ T(y * z,x),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,14706,a(flip),b,17862,a),flip(a)].">
      <j1 rule="hyper" parents="373 14706 17862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17872">
    <literal><![CDATA[
      K(K(T(x,y),z) * y,T(u,z * T(x,y))) = K(z \ T(y * z,x),u)
    ]]></literal>
    <justification jstring="[hyper(10841,a,17871,a)].">
      <j1 rule="hyper" parents="10841 17871"/>
    </justification>
  </clause>

  <clause id="17873">
    <literal><![CDATA[
      K(x * K(y,z),T(u,z * T(y,x))) = K(z \ T(x * z,y),u)
    ]]></literal>
    <justification jstring="[para(8194(a,1),17872(a,1,1))].">
      <j1 rule="para" parents="8194 17872"/>
    </justification>
  </clause>

  <clause id="17874">
    <literal><![CDATA[
      T(K(x,y) * z,u) / K(x,T(y,w)) = T(K(x,T(y,w)) * z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7867(a,2),17864(a,1,2))].">
      <j1 rule="para" parents="7867 17864"/>
    </justification>
  </clause>

  <clause id="17875">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,w) * K(y,x) = T(K(x,y) * u,w) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7930,a,17874,a),flip(a)].">
      <j1 rule="hyper" parents="7930 17874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17876">
    <literal><![CDATA[
      K(x,y) \ T((K(x,K(y,z)) * u) * K(x,y),w) = T(K(x,y) * u,w) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11724,a,b,17875,a)].">
      <j1 rule="hyper" parents="64 11724 17875"/>
    </justification>
  </clause>

  <clause id="17878">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(431(a,1),17408(a,1,1))].">
      <j1 rule="para" parents="431 17408"/>
    </justification>
  </clause>

  <clause id="17879">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17641,a(flip),b,17878,a)].">
      <j1 rule="hyper" parents="64 17641 17878"/>
    </justification>
  </clause>

  <clause id="17880">
    <literal><![CDATA[
      (x \ K(y,z)) \ T(u * (x \ K(y,z)),K(x,w)) = T(u,T(x,w) \ K(y,z))
    ]]></literal>
    <justification jstring="[para(6157(a,1),17322(a,2,2))].">
      <j1 rule="para" parents="6157 17322"/>
    </justification>
  </clause>

  <clause id="17881">
    <literal><![CDATA[
      K(x,K(y * (z \ u),z / y) * w) = K(x,K(y * (u / z),u) * w)
    ]]></literal>
    <justification jstring="[para(16393(a,1),17428(a,1,2,1))].">
      <j1 rule="para" parents="16393 17428"/>
    </justification>
  </clause>

  <clause id="17882">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * (u * K(z / y,w))) = K(x,T(y \ T(z,y),w) * u)
    ]]></literal>
    <justification jstring="[para(13584(a,1),17463(a,1,2,2,2))].">
      <j1 rule="para" parents="13584 17463"/>
    </justification>
  </clause>

  <clause id="17883">
    <literal><![CDATA[
      T(x,K(y,z \ (z \ u)) * ((w / u) * (z * z))) = T(x,w / T((z * z) \ u,y))
    ]]></literal>
    <justification jstring="[para(14419(a,1),17469(a,1,2,1))].">
      <j1 rule="para" parents="14419 17469"/>
    </justification>
  </clause>

  <clause id="17884">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ T(z,v5 * K(w,u))) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,9686,a(flip),b,17614,a)].">
      <j1 rule="hyper" parents="64 9686 17614"/>
    </justification>
  </clause>

  <clause id="17885">
    <literal><![CDATA[
      K(x,y \ T(K(z,u \ w) * u,u \ w)) = K(x,y \ (w / T(w / u,z)))
    ]]></literal>
    <justification jstring="[para(7851(a,1),17755(a,1,2,2))].">
      <j1 rule="para" parents="7851 17755"/>
    </justification>
  </clause>

  <clause id="17886">
    <literal><![CDATA[
      K(x,y \ (z / T(z / u,w))) = K(x,y \ (T(u \ z,w) \ z))
    ]]></literal>
    <justification jstring="[para(7815(a,1),17885(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7815 17885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17887">
    <literal><![CDATA[
      T(x,y / (z * (K(z * u,w) * (u / z)))) = T(x,y / (T(u,z) * K(z * u,w)))
    ]]></literal>
    <justification jstring="[para(15677(a,1),17832(a,1,2,2,2))].">
      <j1 rule="para" parents="15677 17832"/>
    </justification>
  </clause>

  <clause id="17889">
    <literal><![CDATA[
      R(K(x,y) \ (z * K(u,w)),K(x,y),K(w,u)) = T(z / (K(w,u) * K(x,y)),K(x,y))
    ]]></literal>
    <justification jstring="[para(6878(a,1),17314(a,1,1,2))].">
      <j1 rule="para" parents="6878 17314"/>
    </justification>
  </clause>

  <clause id="17890">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) = T(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(17380,a,17851,a),flip(a)].">
      <j1 rule="hyper" parents="17380 17851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17891">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z * y,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(17851(a,1),17380(a,1))].">
      <j1 rule="para" parents="17851 17380"/>
    </justification>
  </clause>

  <clause id="17892">
    <literal><![CDATA[
      T(x,K(y \ z,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,13305,a(flip),b,17890,a),flip(a)].">
      <j1 rule="hyper" parents="373 13305 17890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17893">
    <literal><![CDATA[
      (x \ T(y * x,K(z * u,w) * v5)) * (T(y,x) \ 1) = K(x * y,K(u \ z,w) * v5)
    ]]></literal>
    <justification jstring="[para(17890(a,1),16503(a,1,1,2))].">
      <j1 rule="para" parents="17890 16503"/>
    </justification>
  </clause>

  <clause id="17894">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(z \ u,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(z \ u,u) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(17892(a,1),13478(a,1,2,1))].">
      <j1 rule="para" parents="17892 13478"/>
    </justification>
  </clause>

  <clause id="17895">
    <literal><![CDATA[
      R(K(x,y) * (z * K(u,w)),K(y,x),K(w,u)) = T(z / (K(w,u) * K(y,x)),K(y,x))
    ]]></literal>
    <justification jstring="[para(6156(a,1),17889(a,1,1))].">
      <j1 rule="para" parents="6156 17889"/>
    </justification>
  </clause>

  <clause id="17896">
    <literal><![CDATA[
      x \ (y * ((y \ x) * K((z / y) \ (y \ x),u))) = K(((y \ x) * y) / z,T(u,x / y))
    ]]></literal>
    <justification jstring="[para(6780(a,1),17290(a,1,2,2))].">
      <j1 rule="para" parents="6780 17290"/>
    </justification>
  </clause>

  <clause id="17897">
    <literal><![CDATA[
      K(T(x * y,x) * (z * K(y * x,u)),w) = K(T(T(x * y,u),T(x,y)) * z,w)
    ]]></literal>
    <justification jstring="[para(11181(a,1),17464(a,1,1,2,2))].">
      <j1 rule="para" parents="11181 17464"/>
    </justification>
  </clause>

  <clause id="17898">
    <literal><![CDATA[
      K(T(T(x * y,z),T(x,y)) * u,w) = K((y * x) * (u * K(y * x,z)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17767,a(flip),b,17897,a),flip(a)].">
      <j1 rule="hyper" parents="64 17767 17897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17899">
    <literal><![CDATA[
      K(T(T(x * y,z),T(x,y)) * u,w) = K(T(y * x,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,17197,a(flip),b,17898,a),flip(a)].">
      <j1 rule="hyper" parents="373 17197 17898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17900">
    <literal><![CDATA[
      K(T(T(x * y,x),z) * u,w) = K(T(y * x,z) * u,w)
    ]]></literal>
    <justification jstring="[para(4481(a,1),17899(a,1,1,1))].">
      <j1 rule="para" parents="4481 17899"/>
    </justification>
  </clause>

  <clause id="17901">
    <literal><![CDATA[
      K(T(x * y,z) * u,T(w,x * y)) = K(u * T(T(y * x,y),z),w)
    ]]></literal>
    <justification jstring="[hyper(17651,a,17900,a),flip(a)].">
      <j1 rule="hyper" parents="17651 17900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17902">
    <literal><![CDATA[
      K(x * T(T(y * z,y),u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * T(z * y,u),w) = v5
    ]]></literal>
    <justification jstring="[para(17901(a,1),17112(a,1))].">
      <j1 rule="para" parents="17901 17112"/>
    </justification>
  </clause>

  <clause id="17903">
    <literal><![CDATA[
      K(x * T(y * z,z),u) = K(x * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(17902,a,15863,a)].">
      <j1 rule="hyper" parents="17902 15863"/>
    </justification>
  </clause>

  <clause id="17904">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17802,a,b,17903,a)].">
      <j1 rule="hyper" parents="64 17802 17903"/>
    </justification>
  </clause>

  <clause id="17905">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),T(u,w)) \ K(x * (y * z),K(u,w)) = K(u,(x * y) * R(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(139,a,17904,a(flip),b,8065,a)].">
      <j1 rule="hyper" parents="139 17904 8065"/>
    </justification>
  </clause>

  <clause id="17906">
    <literal><![CDATA[
      K((((x * y) \ z) * y) * (z / (y * ((x * y) \ z))),u) = K(((x * y) \ z) * (y * x),u)
    ]]></literal>
    <justification jstring="[para(109(a,1),17904(a,1,1,2))].">
      <j1 rule="para" parents="109 17904"/>
    </justification>
  </clause>

  <clause id="17907">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u) \ w)),(K(z,u) * (w / z)) \ y) = T(x,y / (K(z,u) * (w / z)))
    ]]></literal>
    <justification jstring="[para(17217(a,1),17476(a,1,1))].">
      <j1 rule="para" parents="17217 17476"/>
    </justification>
  </clause>

  <clause id="17908">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * (w * K(u,u \ z))) = T(x,(w / z) * T(u * (z / u),y))
    ]]></literal>
    <justification jstring="[para(11133(a,1),17494(a,1,2,1))].">
      <j1 rule="para" parents="11133 17494"/>
    </justification>
  </clause>

  <clause id="17909">
    <literal><![CDATA[
      K(x,(y \ T(T(z,u),u)) * w) = K(x,(y \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(35,a,17498,a(flip),b,17500,a),flip(a)].">
      <j1 rule="hyper" parents="35 17498 17500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17910">
    <literal><![CDATA[
      K(x,(T(y,z) / z) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(16361,a,17909,a)].">
      <j1 rule="hyper" parents="16361 17909"/>
    </justification>
  </clause>

  <clause id="17911">
    <literal><![CDATA[
      K(x,(y \ ((z * u) / z)) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[para(255(a,1),17909(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="255 17909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17913">
    <literal><![CDATA[
      K(x,(y / T(z,y)) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(4630(a,1),17910(a,1,2,1))].">
      <j1 rule="para" parents="4630 17910"/>
    </justification>
  </clause>

  <clause id="17914">
    <literal><![CDATA[
      K(x / y,(y / x) * z) = K(x / y,(x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,17623,a(flip),b,17913,a)].">
      <j1 rule="hyper" parents="64 17623 17913"/>
    </justification>
  </clause>

  <clause id="17915">
    <literal><![CDATA[
      K(x,((y / (K(z,u) * w)) / T(v5,y * (w \ K(u,z)))) * v6) = K(x,(v5 \ (y / (K(z,u) * w))) * v6)
    ]]></literal>
    <justification jstring="[para(14553(a,1),17913(a,1,2,1,2))].">
      <j1 rule="para" parents="14553 17913"/>
    </justification>
  </clause>

  <clause id="17916">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K(y / x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11695,a,b,17914,a)].">
      <j1 rule="hyper" parents="64 11695 17914"/>
    </justification>
  </clause>

  <clause id="17917">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = (z * K(y,x)) \ (u * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(8352(a,1),17625(a,1,2,2))].">
      <j1 rule="para" parents="8352 17625"/>
    </justification>
  </clause>

  <clause id="17918">
    <literal><![CDATA[
      K(x,T(L(y,K(z,K(u,w)),v5),K(z,K(u,w)))) = K(x,y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7712,a(flip),b,17642,a)].">
      <j1 rule="hyper" parents="64 7712 17642"/>
    </justification>
  </clause>

  <clause id="17919">
    <literal><![CDATA[
      K(x,L(y,K(z,K(u,w)),v5)) = K(x,y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(17156,a,17918,a)].">
      <j1 rule="hyper" parents="17156 17918"/>
    </justification>
  </clause>

  <clause id="17920">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15711,a,17919,a),flip(a)].">
      <j1 rule="hyper" parents="15711 17919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17922">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17919(a,1),7395(a,1))].">
      <j1 rule="para" parents="17919 7395"/>
    </justification>
  </clause>

  <clause id="17923">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(17519,a,17920,a)].">
      <j1 rule="hyper" parents="17519 17920"/>
    </justification>
  </clause>

  <clause id="17924">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(17307,a,17920,a)].">
      <j1 rule="hyper" parents="17307 17920"/>
    </justification>
  </clause>

  <clause id="17925">
    <literal><![CDATA[
      K(x,K(K(y,z),u) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(17263,a,17920,a)].">
      <j1 rule="hyper" parents="17263 17920"/>
    </justification>
  </clause>

  <clause id="17926">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(16355,a,17920,a)].">
      <j1 rule="hyper" parents="16355 17920"/>
    </justification>
  </clause>

  <clause id="17927">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,17920,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 17920 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17928">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2433(a,1),17920(a,1,2))].">
      <j1 rule="para" parents="2433 17920"/>
    </justification>
  </clause>

  <clause id="17929">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) = K(x,y / w)
    ]]></literal>
    <justification jstring="[para(2458(a,1),17920(a,1,2))].">
      <j1 rule="para" parents="2458 17920"/>
    </justification>
  </clause>

  <clause id="17930">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(6852(a,1),17920(a,1,2))].">
      <j1 rule="para" parents="6852 17920"/>
    </justification>
  </clause>

  <clause id="17931">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(6570(a,1),17920(a,1,2))].">
      <j1 rule="para" parents="6570 17920"/>
    </justification>
  </clause>

  <clause id="17932">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10181(a,1),17920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10181 17920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17933">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(12145(a,1),17920(a,1,2))].">
      <j1 rule="para" parents="12145 17920"/>
    </justification>
  </clause>

  <clause id="17934">
    <literal><![CDATA[
      K(x,T(K(y,K(z,u)) * w,v5)) = K(x,T(w,v5))
    ]]></literal>
    <justification jstring="[para(17227(a,2),17920(a,1,2))].">
      <j1 rule="para" parents="17227 17920"/>
    </justification>
  </clause>

  <clause id="17935">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[para(17328(a,1),17920(a,1,2))].">
      <j1 rule="para" parents="17328 17920"/>
    </justification>
  </clause>

  <clause id="17936">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,(u * K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(10835(a,1),17923(a,1,2))].">
      <j1 rule="para" parents="10835 17923"/>
    </justification>
  </clause>

  <clause id="17937">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(143,a,17924,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 17924 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17938">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * w) = K(x,T(y,z) * w)
    ]]></literal>
    <justification jstring="[para(9147(a,1),17924(a,1,2))].">
      <j1 rule="para" parents="9147 17924"/>
    </justification>
  </clause>

  <clause id="17939">
    <literal><![CDATA[
      K(x,(T(y,K(z,u)) * w) * v5) = K(x,(y * w) * v5)
    ]]></literal>
    <justification jstring="[para(15613(a,1),17924(a,1,2))].">
      <j1 rule="para" parents="15613 17924"/>
    </justification>
  </clause>

  <clause id="17940">
    <literal><![CDATA[
      K(x,y * K(z,T(u,w))) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(17173(a,1),17924(a,1,2))].">
      <j1 rule="para" parents="17173 17924"/>
    </justification>
  </clause>

  <clause id="17941">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16274,a(flip),b,17927,a)].">
      <j1 rule="hyper" parents="64 16274 17927"/>
    </justification>
  </clause>

  <clause id="17942">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = w / T(w,x)
    ]]></literal>
    <justification jstring="[hyper(225,a,17927,a(flip),b,5804,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 17927 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17943">
    <literal><![CDATA[
      T(x,y \ T(z,K(u,w))) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2433(a,1),17927(a,1,2))].">
      <j1 rule="para" parents="2433 17927"/>
    </justification>
  </clause>

  <clause id="17944">
    <literal><![CDATA[
      T(x,y * T(z,K(u,w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(6852(a,1),17927(a,1,2))].">
      <j1 rule="para" parents="6852 17927"/>
    </justification>
  </clause>

  <clause id="17945">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) * w) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(6570(a,1),17927(a,1,2))].">
      <j1 rule="para" parents="6570 17927"/>
    </justification>
  </clause>

  <clause id="17946">
    <literal><![CDATA[
      T(x,y * (z * T(u,K(w,v5)))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(7368(a,1),17927(a,1,2))].">
      <j1 rule="para" parents="7368 17927"/>
    </justification>
  </clause>

  <clause id="17947">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[para(8646(a,1),17927(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8646 17927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17948">
    <literal><![CDATA[
      T(x,y * (K(z,u) * w)) = T(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10181(a,1),17927(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10181 17927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17949">
    <literal><![CDATA[
      T(x,y * (z * K(u,K(w,v5)))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(12145(a,1),17927(a,1,2))].">
      <j1 rule="para" parents="12145 17927"/>
    </justification>
  </clause>

  <clause id="17950">
    <literal><![CDATA[
      T(x,T(K(y,K(z,u)) * w,v5)) = T(x,T(w,v5))
    ]]></literal>
    <justification jstring="[para(17227(a,2),17927(a,1,2))].">
      <j1 rule="para" parents="17227 17927"/>
    </justification>
  </clause>

  <clause id="17951">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[para(17328(a,1),17927(a,1,2))].">
      <j1 rule="para" parents="17328 17927"/>
    </justification>
  </clause>

  <clause id="17952">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(15756,a,17937,a),flip(a)].">
      <j1 rule="hyper" parents="15756 17937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17953">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) * w) = T(x,T(y,z) * w)
    ]]></literal>
    <justification jstring="[para(9147(a,1),17937(a,1,2))].">
      <j1 rule="para" parents="9147 17937"/>
    </justification>
  </clause>

  <clause id="17954">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(17173(a,1),17937(a,1,2))].">
      <j1 rule="para" parents="17173 17937"/>
    </justification>
  </clause>

  <clause id="17955">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / T(y,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,13483,a,b,17926,a)].">
      <j1 rule="hyper" parents="373 13483 17926"/>
    </justification>
  </clause>

  <clause id="17956">
    <literal><![CDATA[
      K(x,y / T(z,u / w)) = K(x,y / T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(7845(a,1),17926(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7845 17926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17957">
    <literal><![CDATA[
      K(x,y \ T(z,u / w)) = K(x,y \ T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(7845(a,1),17928(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7845 17928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17958">
    <literal><![CDATA[
      K(x,y \ ((z * u) * K(w,L(v5,z,u)))) = K(x,y \ ((K(w,v5) * z) * u))
    ]]></literal>
    <justification jstring="[para(15627(a,1),17928(a,1,2,2))].">
      <j1 rule="para" parents="15627 17928"/>
    </justification>
  </clause>

  <clause id="17959">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) / w) = K(x,T(y,z) / w)
    ]]></literal>
    <justification jstring="[para(7840(a,1),17929(a,1,2,1))].">
      <j1 rule="para" parents="7840 17929"/>
    </justification>
  </clause>

  <clause id="17960">
    <literal><![CDATA[
      K(x,T(y,z / u) / w) = K(x,T(y,u \ z) / w)
    ]]></literal>
    <justification jstring="[para(7845(a,1),17929(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7845 17929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17961">
    <literal><![CDATA[
      K(x,((y * z) * K(u,L(w,y,z))) / v5) = K(x,((K(u,w) * y) * z) / v5)
    ]]></literal>
    <justification jstring="[para(15627(a,1),17929(a,1,2,1))].">
      <j1 rule="para" parents="15627 17929"/>
    </justification>
  </clause>

  <clause id="17962">
    <literal><![CDATA[
      K(x,y * (K(z,u) / w)) = K(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15883,a(flip),b,17930,a)].">
      <j1 rule="hyper" parents="64 15883 17930"/>
    </justification>
  </clause>

  <clause id="17963">
    <literal><![CDATA[
      K(x,y * L(T(z,K(u,w)),v5,v6)) = K(x,y * L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(25(a,2),17930(a,1,2,2))].">
      <j1 rule="para" parents="25 17930"/>
    </justification>
  </clause>

  <clause id="17964">
    <literal><![CDATA[
      K(x,y * T(z,T(u,w))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(7840(a,1),17930(a,1,2,2))].">
      <j1 rule="para" parents="7840 17930"/>
    </justification>
  </clause>

  <clause id="17965">
    <literal><![CDATA[
      K(x,y * T(z / T(u,w),u)) = K(x,y * (T(u,w) \ z))
    ]]></literal>
    <justification jstring="[para(7854(a,1),17930(a,1,2,2))].">
      <j1 rule="para" parents="7854 17930"/>
    </justification>
  </clause>

  <clause id="17966">
    <literal><![CDATA[
      K(x,y * T(z,u * w)) = K(x,y * T(z,w * u))
    ]]></literal>
    <justification jstring="[para(11151(a,1),17930(a,1,2,2))].">
      <j1 rule="para" parents="11151 17930"/>
    </justification>
  </clause>

  <clause id="17967">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ z))) = K(x,y * (w \ T(z,u)))
    ]]></literal>
    <justification jstring="[para(15023(a,1),17930(a,1,2,2))].">
      <j1 rule="para" parents="15023 17930"/>
    </justification>
  </clause>

  <clause id="17968">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)),w) * v5) = K(x,T(y,w) * v5)
    ]]></literal>
    <justification jstring="[para(23(a,1),17931(a,1,2,1))].">
      <j1 rule="para" parents="23 17931"/>
    </justification>
  </clause>

  <clause id="17969">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z) * w) = K(x,(T(z,u) \ y) * w)
    ]]></literal>
    <justification jstring="[para(7854(a,1),17931(a,1,2,1))].">
      <j1 rule="para" parents="7854 17931"/>
    </justification>
  </clause>

  <clause id="17970">
    <literal><![CDATA[
      K(x,T(y,z * u) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[para(11151(a,1),17931(a,1,2,1))].">
      <j1 rule="para" parents="11151 17931"/>
    </justification>
  </clause>

  <clause id="17971">
    <literal><![CDATA[
      K(x,((y * z) * K(u,L(w,y,z))) * v5) = K(x,((K(u,w) * y) * z) * v5)
    ]]></literal>
    <justification jstring="[para(15627(a,1),17931(a,1,2,1))].">
      <j1 rule="para" parents="15627 17931"/>
    </justification>
  </clause>

  <clause id="17972">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(7840(a,1),17941(a,1,2,2))].">
      <j1 rule="para" parents="7840 17941"/>
    </justification>
  </clause>

  <clause id="17973">
    <literal><![CDATA[
      T(x,y / T(T(z,T(u,w)),v5)) = T(x,y / T(T(z,u),v5))
    ]]></literal>
    <justification jstring="[para(7844(a,1),17941(a,1,2,2))].">
      <j1 rule="para" parents="7844 17941"/>
    </justification>
  </clause>

  <clause id="17974">
    <literal><![CDATA[
      T(x,y / T(z,u / w)) = T(x,y / T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(7845(a,1),17941(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7845 17941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17975">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,v5)) = T(x,y / T(w * K(z,u),v5))
    ]]></literal>
    <justification jstring="[para(7807(a,1),17941(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7807 17941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17976">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,5787,a,b,17942,a),flip(a)].">
      <j1 rule="hyper" parents="373 5787 17942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17977">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(17942(a,2),5874(a,1))].">
      <j1 rule="para" parents="17942 5874"/>
    </justification>
  </clause>

  <clause id="17978">
    <literal><![CDATA[
      K(K(x,K(y,z)) \ u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(17526,a,17976,a)].">
      <j1 rule="hyper" parents="17526 17976"/>
    </justification>
  </clause>

  <clause id="17979">
    <literal><![CDATA[
      K(x \ T(y,K(z,u)),w) = K(x \ y,w)
    ]]></literal>
    <justification jstring="[para(2433(a,1),17976(a,1,1))].">
      <j1 rule="para" parents="2433 17976"/>
    </justification>
  </clause>

  <clause id="17980">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(u,K(w,v5))) = x * T(y * K(u,K(w,v5)),z)
    ]]></literal>
    <justification jstring="[para(17976(a,1),6850(a,1,1,2))].">
      <j1 rule="para" parents="17976 6850"/>
    </justification>
  </clause>

  <clause id="17981">
    <literal><![CDATA[
      K(T(x,K(y,z)) * u,w) = K(x * u,w)
    ]]></literal>
    <justification jstring="[para(6570(a,1),17976(a,1,1))].">
      <j1 rule="para" parents="6570 17976"/>
    </justification>
  </clause>

  <clause id="17982">
    <literal><![CDATA[
      K(T(x,K(y,z)) \ u,w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(8646(a,1),17976(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8646 17976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17983">
    <literal><![CDATA[
      K(x * (K(y,z) * u),w) = K(x * (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(10181(a,1),17976(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10181 17976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17984">
    <literal><![CDATA[
      K(x / (K(y,z) * u),w) = K(x / (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(10595(a,1),17976(a,1,1))].">
      <j1 rule="para" parents="10595 17976"/>
    </justification>
  </clause>

  <clause id="17985">
    <literal><![CDATA[
      K(x * (y * K(z,K(u,w))),v5) = K(x * y,v5)
    ]]></literal>
    <justification jstring="[para(12145(a,1),17976(a,1,1))].">
      <j1 rule="para" parents="12145 17976"/>
    </justification>
  </clause>

  <clause id="17986">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(17978(a,1),6038(a,1))].">
      <j1 rule="para" parents="17978 6038"/>
    </justification>
  </clause>

  <clause id="17987">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w))) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(7840(a,1),17943(a,1,2,2))].">
      <j1 rule="para" parents="7840 17943"/>
    </justification>
  </clause>

  <clause id="17988">
    <literal><![CDATA[
      T(x,T(y,z * u) * (u / (1 / z))) = T(x,(u / (1 / z)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15207,a,b,17944,a)].">
      <j1 rule="hyper" parents="64 15207 17944"/>
    </justification>
  </clause>

  <clause id="17989">
    <literal><![CDATA[
      T(x,y * T(T(z,K(u,w)),v5)) = T(x,y * T(z,v5))
    ]]></literal>
    <justification jstring="[para(23(a,1),17944(a,1,2,2))].">
      <j1 rule="para" parents="23 17944"/>
    </justification>
  </clause>

  <clause id="17990">
    <literal><![CDATA[
      T(x,y * T(z,T(u,w))) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(7840(a,1),17944(a,1,2,2))].">
      <j1 rule="para" parents="7840 17944"/>
    </justification>
  </clause>

  <clause id="17991">
    <literal><![CDATA[
      T(x,y * (K(z,u) \ w)) = T(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(8352(a,1),17944(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8352 17944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17993">
    <literal><![CDATA[
      T(x,(K(y,z) * (u / z)) * w) = T(x,(u / T(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(6865(a,1),17945(a,1,2,1))].">
      <j1 rule="para" parents="6865 17945"/>
    </justification>
  </clause>

  <clause id="17994">
    <literal><![CDATA[
      T(x,((y * z) * K(u,L(w,y,z))) * v5) = T(x,((K(u,w) * y) * z) * v5)
    ]]></literal>
    <justification jstring="[para(15627(a,1),17945(a,1,2,1))].">
      <j1 rule="para" parents="15627 17945"/>
    </justification>
  </clause>

  <clause id="17995">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = (K(z,y) * (x * T(y,z))) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,15174,a(flip),b,17947,a),flip(a)].">
      <j1 rule="hyper" parents="64 15174 17947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17996">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) \ w) = T(x,T(y,z) \ w)
    ]]></literal>
    <justification jstring="[para(7840(a,1),17947(a,1,2,1))].">
      <j1 rule="para" parents="7840 17947"/>
    </justification>
  </clause>

  <clause id="17997">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) \ v5) = T(x,T(u * K(y,z),w) \ v5)
    ]]></literal>
    <justification jstring="[para(7807(a,1),17947(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7807 17947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17998">
    <literal><![CDATA[
      K(x \ T(y,T(z,u)),w) = K(x \ T(y,z),w)
    ]]></literal>
    <justification jstring="[para(7840(a,1),17979(a,1,1,2))].">
      <j1 rule="para" parents="7840 17979"/>
    </justification>
  </clause>

  <clause id="17999">
    <literal><![CDATA[
      K(x \ (K(y,z) \ u),w) = K(x \ (u * K(z,y)),w)
    ]]></literal>
    <justification jstring="[para(8352(a,1),17979(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8352 17979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18000">
    <literal><![CDATA[
      K((x \ K(y \ z,u)) * (y \ T(z,K(w,v5))),v6) = K(x \ T(y \ T(z,K(w,v5)),u),v6)
    ]]></literal>
    <justification jstring="[para(17979(a,1),14670(a,1,1,1,2))].">
      <j1 rule="para" parents="17979 14670"/>
    </justification>
  </clause>

  <clause id="18001">
    <literal><![CDATA[
      K(T(x,y * z) * u,w) = K(T(x,z * y) * u,w)
    ]]></literal>
    <justification jstring="[para(11151(a,1),17981(a,1,1,1))].">
      <j1 rule="para" parents="11151 17981"/>
    </justification>
  </clause>

  <clause id="18002">
    <literal><![CDATA[
      K(T(x,T(y,z)) \ u,w) = K(T(x,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(7840(a,1),17982(a,1,1,1))].">
      <j1 rule="para" parents="7840 17982"/>
    </justification>
  </clause>

  <clause id="18003">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = v5
    ]]></literal>
    <justification jstring="[para(2433(a,1),17922(a,1,2))].">
      <j1 rule="para" parents="2433 17922"/>
    </justification>
  </clause>

  <clause id="18004">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / w) = v5
    ]]></literal>
    <justification jstring="[para(2458(a,1),17922(a,1,2))].">
      <j1 rule="para" parents="2458 17922"/>
    </justification>
  </clause>

  <clause id="18005">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(6576(a,1),17922(a,1,2))].">
      <j1 rule="para" parents="6576 17922"/>
    </justification>
  </clause>

  <clause id="18006">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(6852(a,1),17922(a,1,2))].">
      <j1 rule="para" parents="6852 17922"/>
    </justification>
  </clause>

  <clause id="18007">
    <literal><![CDATA[
      K(x,y * (z * T(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * u)) = v6
    ]]></literal>
    <justification jstring="[para(7368(a,1),17922(a,1,2))].">
      <j1 rule="para" parents="7368 17922"/>
    </justification>
  </clause>

  <clause id="18008">
    <literal><![CDATA[
      K(x,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,K(w,v5)) \ z) = u
    ]]></literal>
    <justification jstring="[para(8646(a,1),17922(a,1,2))].">
      <j1 rule="para" parents="8646 17922"/>
    </justification>
  </clause>

  <clause id="18009">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = v5
    ]]></literal>
    <justification jstring="[para(8142(a,1),17922(a,1,2))].">
      <j1 rule="para" parents="8142 17922"/>
    </justification>
  </clause>

  <clause id="18010">
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (K(u,w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(10181(a,1),17922(a,1,2))].">
      <j1 rule="para" parents="10181 17922"/>
    </justification>
  </clause>

  <clause id="18011">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(12145(a,1),17922(a,1,2))].">
      <j1 rule="para" parents="12145 17922"/>
    </justification>
  </clause>

  <clause id="18012">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (K(u,w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(14934(a,1),17922(a,1,2))].">
      <j1 rule="para" parents="14934 17922"/>
    </justification>
  </clause>

  <clause id="18013">
    <literal><![CDATA[
      K(x,y \ K(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(15555(a,1),17922(a,1,2))].">
      <j1 rule="para" parents="15555 17922"/>
    </justification>
  </clause>

  <clause id="18014">
    <literal><![CDATA[
      K(x,K(K(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(17300(a,2),17922(a,1))].">
      <j1 rule="para" parents="17300 17922"/>
    </justification>
  </clause>

  <clause id="18015">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(17329(a,1),17922(a,1,2))].">
      <j1 rule="para" parents="17329 17922"/>
    </justification>
  </clause>

  <clause id="18016">
    <literal><![CDATA[
      K(x \ T(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,w) = v5
    ]]></literal>
    <justification jstring="[para(2433(a,1),17977(a,1,1))].">
      <j1 rule="para" parents="2433 17977"/>
    </justification>
  </clause>

  <clause id="18017">
    <literal><![CDATA[
      K(T(x,K(y,z)) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / u,w) = v5
    ]]></literal>
    <justification jstring="[para(2458(a,1),17977(a,1,1))].">
      <j1 rule="para" parents="2458 17977"/>
    </justification>
  </clause>

  <clause id="18018">
    <literal><![CDATA[
      K(x \ K(y,T(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(15555(a,1),17977(a,1,1))].">
      <j1 rule="para" parents="15555 17977"/>
    </justification>
  </clause>

  <clause id="18019">
    <literal><![CDATA[
      K(T(x,K(y,z)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(17329(a,1),17977(a,1,1))].">
      <j1 rule="para" parents="17329 17977"/>
    </justification>
  </clause>

  <clause id="18020">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((z * K(x,y)) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(10833(a,1),17986(a,1,1))].">
      <j1 rule="para" parents="10833 17986"/>
    </justification>
  </clause>

  <clause id="18021">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * w) = v5
    ]]></literal>
    <justification jstring="[para(9147(a,1),18005(a,1,2))].">
      <j1 rule="para" parents="9147 18005"/>
    </justification>
  </clause>

  <clause id="18022">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(z,u) * y) / w) = v5
    ]]></literal>
    <justification jstring="[para(14887(a,1),18005(a,1,2))].">
      <j1 rule="para" parents="14887 18005"/>
    </justification>
  </clause>

  <clause id="18023">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(z,u) * y) \ w) = v5
    ]]></literal>
    <justification jstring="[para(10833(a,1),18014(a,1,2))].">
      <j1 rule="para" parents="10833 18014"/>
    </justification>
  </clause>

  <clause id="18024">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5)))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(2433(a,1),17933(a,1,2,2))].">
      <j1 rule="para" parents="2433 17933"/>
    </justification>
  </clause>

  <clause id="18025">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w)) / v5)) = K(x,y * (z / v5))
    ]]></literal>
    <justification jstring="[para(2458(a,1),17933(a,1,2,2))].">
      <j1 rule="para" parents="2458 17933"/>
    </justification>
  </clause>

  <clause id="18026">
    <literal><![CDATA[
      K(x,y * (K(z,K(u,w)) * v5)) = K(x,y * v5)
    ]]></literal>
    <justification jstring="[para(6576(a,1),17933(a,1,2,2))].">
      <j1 rule="para" parents="6576 17933"/>
    </justification>
  </clause>

  <clause id="18027">
    <literal><![CDATA[
      K(x,y * K(z,u / w)) = K(x,y * K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(9067(a,1),17933(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9067 17933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18028">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,K(v5,v6))))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(12145(a,1),17933(a,1,2,2))].">
      <j1 rule="para" parents="12145 17933"/>
    </justification>
  </clause>

  <clause id="18029">
    <literal><![CDATA[
      K(x,T(y / T(z,K(u,w)),v5)) = K(x,T(y / z,v5))
    ]]></literal>
    <justification jstring="[para(17335(a,1),17934(a,1,2,1))].">
      <j1 rule="para" parents="17335 17934"/>
    </justification>
  </clause>

  <clause id="18030">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,K(z,y) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,15767,a,b,17935,a),flip(a)].">
      <j1 rule="hyper" parents="373 15767 17935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18031">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,w * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17139,a(flip),b,17935,a),flip(a)].">
      <j1 rule="hyper" parents="373 17139 17935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18032">
    <literal><![CDATA[
      K(x,K(y,z / u) * w) = K(x,K(y,u \ z) * w)
    ]]></literal>
    <justification jstring="[para(117(a,1),17935(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="117 17935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18033">
    <literal><![CDATA[
      K(x,K(y / z,u) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[para(7874(a,1),17935(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7874 17935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18034">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(17935(a,2),15768(a,1))].">
      <j1 rule="para" parents="17935 15768"/>
    </justification>
  </clause>

  <clause id="18035">
    <literal><![CDATA[
      K(x,T(y,z) * T(z,u)) = K(x,T(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(11231,a,17938,a),flip(a)].">
      <j1 rule="hyper" parents="11231 17938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18036">
    <literal><![CDATA[
      K(x,T(((y \ z) * y) \ u,z) * w) = K(x,(u / ((y \ z) * y)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15804,a(flip),b,17938,a),flip(a)].">
      <j1 rule="hyper" parents="64 15804 17938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18038">
    <literal><![CDATA[
      K(x,y * K(z,T(u,w))) = K(x,K(u,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,17190,a,b,17940,a),flip(a)].">
      <j1 rule="hyper" parents="373 17190 17940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18039">
    <literal><![CDATA[
      T(x,y * (T(z,K(u,w)) * v5)) = T(x,y * (z * v5))
    ]]></literal>
    <justification jstring="[para(6570(a,1),17949(a,1,2,2))].">
      <j1 rule="para" parents="6570 17949"/>
    </justification>
  </clause>

  <clause id="18040">
    <literal><![CDATA[
      T(x,y * K(z / u,w)) = T(x,y * K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(6779(a,1),17949(a,1,2,2))].">
      <j1 rule="para" parents="6779 17949"/>
    </justification>
  </clause>

  <clause id="18041">
    <literal><![CDATA[
      T(x,y * (T(z,K(u,w)) \ v5)) = T(x,y * (z \ v5))
    ]]></literal>
    <justification jstring="[para(8646(a,1),17949(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8646 17949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18042">
    <literal><![CDATA[
      T(x,T(T(y,K(z,u)) * w,v5)) = T(x,T(y * w,v5))
    ]]></literal>
    <justification jstring="[para(5755(a,1),17950(a,1,2,1))].">
      <j1 rule="para" parents="5755 17950"/>
    </justification>
  </clause>

  <clause id="18044">
    <literal><![CDATA[
      T(x,K(T(y,z),u) * w) = T(x,K(u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(15753,a,17951,a)].">
      <j1 rule="hyper" parents="15753 17951"/>
    </justification>
  </clause>

  <clause id="18045">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(z,y) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,15759,a,b,17951,a),flip(a)].">
      <j1 rule="hyper" parents="373 15759 17951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18046">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(17951(a,2),15753(a,1))].">
      <j1 rule="para" parents="17951 15753"/>
    </justification>
  </clause>

  <clause id="18047">
    <literal><![CDATA[
      T(x,((K(y * z,y) * u) * T(y,z)) * w) = T(x,T(R(y,z,y) * u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13494,a,b,17953,a)].">
      <j1 rule="hyper" parents="64 13494 17953"/>
    </justification>
  </clause>

  <clause id="18048">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,17348,a,b,17954,a),flip(a)].">
      <j1 rule="hyper" parents="373 17348 17954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18049">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,T(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(15723(a,1),17954(a,1,2))].">
      <j1 rule="para" parents="15723 17954"/>
    </justification>
  </clause>

  <clause id="18050">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * y) = v5
    ]]></literal>
    <justification jstring="[para(17954(a,2),17353(a,1))].">
      <j1 rule="para" parents="17954 17353"/>
    </justification>
  </clause>

  <clause id="18051">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) / w) = T(x,T(y,z) / w)
    ]]></literal>
    <justification jstring="[hyper(143,a,17959,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 17959 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18052">
    <literal><![CDATA[
      K(x,(T(y,z) * K(u,y)) / w) = K(x,T(T(y,u),z) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16089,a(flip),b,17959,a)].">
      <j1 rule="hyper" parents="64 16089 17959"/>
    </justification>
  </clause>

  <clause id="18053">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y) / w) = K(x,(u \ T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13557,a(flip),b,17959,a),flip(a)].">
      <j1 rule="hyper" parents="64 13557 17959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18054">
    <literal><![CDATA[
      K(x,y * T(T(z,T(u,w)),v5)) = K(x,y * T(T(z,v5),u))
    ]]></literal>
    <justification jstring="[para(23(a,1),17964(a,1,2,2))].">
      <j1 rule="para" parents="23 17964"/>
    </justification>
  </clause>

  <clause id="18055">
    <literal><![CDATA[
      K(x,y * T(T(T(z,u),T(z,u) \ w),v5)) = K(x,y * T(T((T(z,u) \ w) \ w,v5),z))
    ]]></literal>
    <justification jstring="[para(534(a,1),17964(a,1,2,2))].">
      <j1 rule="para" parents="534 17964"/>
    </justification>
  </clause>

  <clause id="18056">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13342,a,b,17972,a),flip(a)].">
      <j1 rule="hyper" parents="373 13342 17972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18057">
    <literal><![CDATA[
      T(x,T(y,z) / T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(17972(a,1),13396(a,1))].">
      <j1 rule="para" parents="17972 13396"/>
    </justification>
  </clause>

  <clause id="18058">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),w) = K(x * K(y,z),w)
    ]]></literal>
    <justification jstring="[para(7503(a,1),17985(a,1,1,2))].">
      <j1 rule="para" parents="7503 17985"/>
    </justification>
  </clause>

  <clause id="18059">
    <literal><![CDATA[
      K(x * K(T(y,z),u),w) = K(x * K(y,u),w)
    ]]></literal>
    <justification jstring="[para(7866(a,1),17985(a,1,1,2))].">
      <j1 rule="para" parents="7866 17985"/>
    </justification>
  </clause>

  <clause id="18060">
    <literal><![CDATA[
      T(x,T(y,z) \ T(u,y)) = T(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13419,a(flip),b,17987,a),flip(a)].">
      <j1 rule="hyper" parents="64 13419 17987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18061">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z \ T(y * z,u))
    ]]></literal>
    <justification jstring="[para(14798(a,2),17987(a,1,2))].">
      <j1 rule="para" parents="14798 17987"/>
    </justification>
  </clause>

  <clause id="18062">
    <literal><![CDATA[
      T(x,y * T(T(z,u) \ w,z)) = T(x,y * (w / T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15807,a(flip),b,17990,a),flip(a)].">
      <j1 rule="hyper" parents="64 15807 17990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18063">
    <literal><![CDATA[
      R(T(x / y,y * T(z,u)),y,T(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      (y * T(z,T(u,w))) \ (x * T(z,T(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(17990(a,1),1329(a,1,1))].">
      <j1 rule="para" parents="17990 1329"/>
    </justification>
  </clause>

  <clause id="18064">
    <literal><![CDATA[
      T(x,y * T(z / T(T(u,w),z),u)) = T(x,y * (T(T(u,w),z) \ z))
    ]]></literal>
    <justification jstring="[para(4479(a,1),17990(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4479 17990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18065">
    <literal><![CDATA[
      K(T(x * K(x * y,z),y),u) = K(y \ T(x * y,z),u)
    ]]></literal>
    <justification jstring="[para(14798(a,2),17998(a,1,1))].">
      <j1 rule="para" parents="14798 17998"/>
    </justification>
  </clause>

  <clause id="18066">
    <literal><![CDATA[
      K(T(x * y,x) \ ((x * T(y,K(x,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),x) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(18002(a,1),8662(a,1))].">
      <j1 rule="para" parents="18002 8662"/>
    </justification>
  </clause>

  <clause id="18067">
    <literal><![CDATA[
      K(T(x * y,y) \ ((x * T(y,K(x,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(18002(a,1),8732(a,1))].">
      <j1 rule="para" parents="18002 8732"/>
    </justification>
  </clause>

  <clause id="18068">
    <literal><![CDATA[
      K(x,y * (z * K(u,T(w,v5)))) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(17173(a,1),18026(a,1,2,2))].">
      <j1 rule="para" parents="17173 18026"/>
    </justification>
  </clause>

  <clause id="18069">
    <literal><![CDATA[
      K(x,T(y * K(z,u),w)) = K(x,K(u,z) * T(y,w))
    ]]></literal>
    <justification jstring="[para(17824(a,1),18030(a,1,2))].">
      <j1 rule="para" parents="17824 18030"/>
    </justification>
  </clause>

  <clause id="18070">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * K(w,y)) = K(x,T(T(y,z),w) \ u)
    ]]></literal>
    <justification jstring="[para(6157(a,1),18031(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6157 18031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18071">
    <literal><![CDATA[
      K(x,T(y * K(z,u),w)) = K(x,T(y,w) * K(z,u))
    ]]></literal>
    <justification jstring="[para(17824(a,1),18031(a,1,2))].">
      <j1 rule="para" parents="17824 18031"/>
    </justification>
  </clause>

  <clause id="18072">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * w) = K(x,T(w,y) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17938,a,b,18035,a)].">
      <j1 rule="hyper" parents="373 17938 18035"/>
    </justification>
  </clause>

  <clause id="18073">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ w) = K(x,K(z,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(17519,a,18038,a)].">
      <j1 rule="hyper" parents="17519 18038"/>
    </justification>
  </clause>

  <clause id="18074">
    <literal><![CDATA[
      K(x,K(y,z * u) \ w) = K(x,w * K(u * z,y))
    ]]></literal>
    <justification jstring="[para(11177(a,1),18038(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11177 18038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18075">
    <literal><![CDATA[
      T(x,K(y * z,u) * w) = T(x,K(u,z * y) * w)
    ]]></literal>
    <justification jstring="[para(11112(a,1),18044(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11112 18044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18076">
    <literal><![CDATA[
      T(x,K(y / z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z \ y,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(18044(a,1),15760(a,1))].">
      <j1 rule="para" parents="18044 15760"/>
    </justification>
  </clause>

  <clause id="18078">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ T(y,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(T(y,w),z)) = v5
    ]]></literal>
    <justification jstring="[para(18045(a,1),17659(a,1))].">
      <j1 rule="para" parents="18045 17659"/>
    </justification>
  </clause>

  <clause id="18079">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),K(z,y) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17011,a,b,18048,a)].">
      <j1 rule="hyper" parents="64 17011 18048"/>
    </justification>
  </clause>

  <clause id="18080">
    <literal><![CDATA[
      T(x,K(y \ z,y) * (u / (y * K(w,z)))) = T(x,u / T(y * K(w,z),y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17497,a(flip),b,18048,a),flip(a)].">
      <j1 rule="hyper" parents="64 17497 18048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18081">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y) / w) = T(x,(u / T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15846,a(flip),b,18051,a),flip(a)].">
      <j1 rule="hyper" parents="64 15846 18051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18082">
    <literal><![CDATA[
      K(x * K(y,T(y \ z,u)),w) = K(K(y,z) * x,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,17355,a(flip),b,18058,a),flip(a)].">
      <j1 rule="hyper" parents="373 17355 18058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18083">
    <literal><![CDATA[
      K(K(x,T(y,z)) * u,w) = K(u * K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(17512,a,18059,a)].">
      <j1 rule="hyper" parents="17512 18059"/>
    </justification>
  </clause>

  <clause id="18084">
    <literal><![CDATA[
      K((T(x,y) / z) * K(x,u),w) = K(T(T(x,y),u) / z,w)
    ]]></literal>
    <justification jstring="[hyper(17274,a,18059,a),flip(a)].">
      <j1 rule="hyper" parents="17274 18059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18085">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ w) = K(x,K(y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(17521,a,18073,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17521 18073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18086">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(18073(a,2),17521(a,1))].">
      <j1 rule="para" parents="18073 17521"/>
    </justification>
  </clause>

  <clause id="18087">
    <literal><![CDATA[
      K(((K(x,T(y,z)) * u) * w) / a(x,u,K(w,T(y,z))),v5) = K((u * w) * K(y,x),v5)
    ]]></literal>
    <justification jstring="[para(15301(a,2),18083(a,1,1))].">
      <j1 rule="para" parents="15301 18083"/>
    </justification>
  </clause>

  <clause id="18088">
    <literal><![CDATA[
      K(x,K(y,z / u) \ w) = K(x,K(y,u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(117(a,1),18085(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="117 18085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18089">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) \ w) = v5
    ]]></literal>
    <justification jstring="[para(18085(a,2),17521(a,1))].">
      <j1 rule="para" parents="18085 17521"/>
    </justification>
  </clause>

  <clause id="18090">
    <literal><![CDATA[
      K(x,y \ T(z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(8722(a,1),18003(a,1,2,2))].">
      <j1 rule="para" parents="8722 18003"/>
    </justification>
  </clause>

  <clause id="18091">
    <literal><![CDATA[
      K(x,y \ T(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(11151(a,1),18003(a,1,2,2))].">
      <j1 rule="para" parents="11151 18003"/>
    </justification>
  </clause>

  <clause id="18092">
    <literal><![CDATA[
      K(x,T(y,z / u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z) / w) = v5
    ]]></literal>
    <justification jstring="[para(8722(a,1),18004(a,1,2,1))].">
      <j1 rule="para" parents="8722 18004"/>
    </justification>
  </clause>

  <clause id="18093">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w * K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(6881(a,1),18006(a,1,2,2))].">
      <j1 rule="para" parents="6881 18006"/>
    </justification>
  </clause>

  <clause id="18094">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w / T(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(6865(a,1),18006(a,1,2,2))].">
      <j1 rule="para" parents="6865 18006"/>
    </justification>
  </clause>

  <clause id="18095">
    <literal><![CDATA[
      K(x,y * T(z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(8722(a,1),18006(a,1,2,2))].">
      <j1 rule="para" parents="8722 18006"/>
    </justification>
  </clause>

  <clause id="18096">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,w) / u)) = v5
    ]]></literal>
    <justification jstring="[para(14848(a,1),18006(a,1,2,2))].">
      <j1 rule="para" parents="14848 18006"/>
    </justification>
  </clause>

  <clause id="18097">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w \ T(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(15023(a,1),18006(a,1,2,2))].">
      <j1 rule="para" parents="15023 18006"/>
    </justification>
  </clause>

  <clause id="18098">
    <literal><![CDATA[
      K(x,y * (K(z,u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w \ K(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(15883(a,1),18006(a,1))].">
      <j1 rule="para" parents="15883 18006"/>
    </justification>
  </clause>

  <clause id="18099">
    <literal><![CDATA[
      K(x,y / L(T(z,K(u,w)),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y / L(z,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(25(a,2),18009(a,1,2,2))].">
      <j1 rule="para" parents="25 18009"/>
    </justification>
  </clause>

  <clause id="18100">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (K(u,w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(7785(a,1),18009(a,1,2,2))].">
      <j1 rule="para" parents="7785 18009"/>
    </justification>
  </clause>

  <clause id="18101">
    <literal><![CDATA[
      K(x,y / (K(z,u) * (w \ z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (w \ T(z,u))) = v5
    ]]></literal>
    <justification jstring="[para(15023(a,1),18009(a,1,2,2))].">
      <j1 rule="para" parents="15023 18009"/>
    </justification>
  </clause>

  <clause id="18102">
    <literal><![CDATA[
      K(x,y \ T(z * y,K(u,w))) = K(x,T(z,K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(18015,a,17804,a)].">
      <j1 rule="hyper" parents="18015 17804"/>
    </justification>
  </clause>

  <clause id="18103">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14453(a,1),18015(a,1,2))].">
      <j1 rule="para" parents="14453 18015"/>
    </justification>
  </clause>

  <clause id="18104">
    <literal><![CDATA[
      K(x \ T(y,T(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(7840(a,1),18016(a,1,1,2))].">
      <j1 rule="para" parents="7840 18016"/>
    </justification>
  </clause>

  <clause id="18105">
    <literal><![CDATA[
      K(T(x,T(y,z)) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y) / u,w) = v5
    ]]></literal>
    <justification jstring="[para(7840(a,1),18017(a,1,1,1))].">
      <j1 rule="para" parents="7840 18017"/>
    </justification>
  </clause>

  <clause id="18106">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((K(y,z) * x) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(7785(a,1),18019(a,1,1,1))].">
      <j1 rule="para" parents="7785 18019"/>
    </justification>
  </clause>

  <clause id="18107">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,16333,a,b,17932,a),flip(a)].">
      <j1 rule="hyper" parents="373 16333 17932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18108">
    <literal><![CDATA[
      K(x,y * (z * K(u,u \ w))) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,13551,a,b,17932,a)].">
      <j1 rule="hyper" parents="373 13551 17932"/>
    </justification>
  </clause>

  <clause id="18109">
    <literal><![CDATA[
      K(x,y * (K(z,z \ u) * w)) = K(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,13551,a(flip),b,17932,a),flip(a)].">
      <j1 rule="hyper" parents="373 13551 17932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18110">
    <literal><![CDATA[
      K(x,(T(y,z) * (u / y)) * w) = K(x,((y \ u) * T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15824,a(flip),b,17939,a)].">
      <j1 rule="hyper" parents="64 15824 17939"/>
    </justification>
  </clause>

  <clause id="18111">
    <literal><![CDATA[
      K(x,((y / K(z,u)) * w) * v5) = K(x,((K(u,z) * y) * w) * v5)
    ]]></literal>
    <justification jstring="[para(6181(a,1),17939(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6181 17939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18112">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,v5 \ w)))
    ]]></literal>
    <justification jstring="[para(7845(a,1),17946(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7845 17946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18113">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) = K(x,u \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(13399,a,17956,a),flip(a)].">
      <j1 rule="hyper" parents="13399 17956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18114">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u \ w)) = K(x,y / T(z,w / u))
    ]]></literal>
    <justification jstring="[hyper(373,a,16271,a,b,17956,a)].">
      <j1 rule="hyper" parents="373 16271 17956"/>
    </justification>
  </clause>

  <clause id="18115">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (y / z)) = w
    ]]></literal>
    <justification jstring="[para(17956(a,1),13399(a,1))].">
      <j1 rule="para" parents="17956 13399"/>
    </justification>
  </clause>

  <clause id="18117">
    <literal><![CDATA[
      K(x,T((T(y,z) \ z) \ u,y \ z) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15848,a(flip),b,17960,a),flip(a)].">
      <j1 rule="hyper" parents="64 15848 17960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18118">
    <literal><![CDATA[
      K(x,T(y * K(z,u),y \ z) / w) = K(x,(T(z,u) / (z / y)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15845,a(flip),b,17960,a),flip(a)].">
      <j1 rule="hyper" parents="64 15845 17960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18119">
    <literal><![CDATA[
      K(x,T(y,z \ u) / (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u / z) \ y) = w
    ]]></literal>
    <justification jstring="[para(17960(a,1),13354(a,1))].">
      <j1 rule="para" parents="17960 13354"/>
    </justification>
  </clause>

  <clause id="18120">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(14790,a,17962,a)].">
      <j1 rule="hyper" parents="14790 17962"/>
    </justification>
  </clause>

  <clause id="18121">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z * K(w,u))) = v5
    ]]></literal>
    <justification jstring="[para(17962(a,1),14790(a,1))].">
      <j1 rule="para" parents="17962 14790"/>
    </justification>
  </clause>

  <clause id="18122">
    <literal><![CDATA[
      K(x,y * T(z,y * x)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,17787,a(flip),b,17966,a),flip(a)].">
      <j1 rule="hyper" parents="373 17787 17966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18123">
    <literal><![CDATA[
      K(x,y * T(z,(z * u) * w)) = K(x,y * T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13576,a(flip),b,17966,a),flip(a)].">
      <j1 rule="hyper" parents="373 13576 17966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18124">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * z)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[hyper(11231,a,17970,a),flip(a)].">
      <j1 rule="hyper" parents="11231 17970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18125">
    <literal><![CDATA[
      T(x,(y \ z) / T(z,u / w)) = T(x,y \ K(w \ u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,14905,a(flip),b,17974,a),flip(a)].">
      <j1 rule="hyper" parents="373 14905 17974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18126">
    <literal><![CDATA[
      K(x / (y * K(z,u)),w) = K(x * (y \ K(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(14762,a,17984,a),flip(a)].">
      <j1 rule="hyper" parents="14762 17984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18127">
    <literal><![CDATA[
      K(x \ (K(y,z) \ u),x) \ (u * K(z,y)) = x * ((u * K(z,y)) / x)
    ]]></literal>
    <justification jstring="[para(17999(a,2),6174(a,1,1))].">
      <j1 rule="para" parents="17999 6174"/>
    </justification>
  </clause>

  <clause id="18128">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ (z * K(w,v5))) * z))) = K(x,y * ((K(w,v5) * z) / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16950,a(flip),b,18024,a),flip(a)].">
      <j1 rule="hyper" parents="64 16950 18024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18129">
    <literal><![CDATA[
      K(x,y * (z \ (u * T(z,K(w,v5))))) = K(x,y * T(u,K(v5,w) * z))
    ]]></literal>
    <justification jstring="[para(16796(a,1),18024(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16796 18024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18130">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) = K(x,y * (T(z,w \ u) / v5))
    ]]></literal>
    <justification jstring="[para(7845(a,1),18025(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7845 18025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18131">
    <literal><![CDATA[
      K(x,T(y / T(z,z \ u),w)) = K(x,T(y / ((z \ u) \ u),w))
    ]]></literal>
    <justification jstring="[para(4075(a,1),18029(a,1,2,1,2))].">
      <j1 rule="para" parents="4075 18029"/>
    </justification>
  </clause>

  <clause id="18132">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(y * (u / z),u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17881,a(flip),b,18032,a),flip(a)].">
      <j1 rule="hyper" parents="64 17881 18032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18133">
    <literal><![CDATA[
      K(x,K(y * (z \ u),u) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(17431,a,18033,a)].">
      <j1 rule="hyper" parents="17431 18033"/>
    </justification>
  </clause>

  <clause id="18134">
    <literal><![CDATA[
      K(x,K(y \ z,u) * (w * ((y / z) \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * T((y / z) \ 1,u)) = v5
    ]]></literal>
    <justification jstring="[para(18033(a,1),17653(a,1))].">
      <j1 rule="para" parents="18033 17653"/>
    </justification>
  </clause>

  <clause id="18135">
    <literal><![CDATA[
      T(x,y * (T(z,T(u,w)) * v5)) = T(x,y * (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(7840(a,1),18039(a,1,2,2,1))].">
      <j1 rule="para" parents="7840 18039"/>
    </justification>
  </clause>

  <clause id="18136">
    <literal><![CDATA[
      T(x,T(y / (y / z),u) * K(z \ y,w)) = T(x,(y * K(z,u)) / T(y / z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16294,a(flip),b,18040,a),flip(a)].">
      <j1 rule="hyper" parents="64 16294 18040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18137">
    <literal><![CDATA[
      T(x,y * (T(z,u * w) \ v5)) = T(x,y * (T(z,w * u) \ v5))
    ]]></literal>
    <justification jstring="[para(11151(a,1),18041(a,1,2,2,1))].">
      <j1 rule="para" parents="11151 18041"/>
    </justification>
  </clause>

  <clause id="18139">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,17165,a,b,18049,a),flip(a)].">
      <j1 rule="hyper" parents="373 17165 18049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18140">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,T(u,w) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,16270,a,b,18049,a),flip(a)].">
      <j1 rule="hyper" parents="373 16270 18049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18141">
    <literal><![CDATA[
      T(x,((y \ z) * y) * K(u,w)) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,13493,a,b,18049,a)].">
      <j1 rule="hyper" parents="373 13493 18049"/>
    </justification>
  </clause>

  <clause id="18142">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,K(z,y) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17182,a,b,18069,a)].">
      <j1 rule="hyper" parents="64 17182 18069"/>
    </justification>
  </clause>

  <clause id="18143">
    <literal><![CDATA[
      K(x,T(y * K(z,z \ u),w)) = K(x,T(y,w) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13378,a(flip),b,18071,a),flip(a)].">
      <j1 rule="hyper" parents="373 13378 18071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18145">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w)) * v5) = K(x,T(v5,y) * T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17966,a,b,18072,a),flip(a)].">
      <j1 rule="hyper" parents="373 17966 18072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18146">
    <literal><![CDATA[
      K(x,K(y,z \ u) \ ((u / z) \ w)) = K(x,T(u / z,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15778,a(flip),b,18088,a),flip(a)].">
      <j1 rule="hyper" parents="64 15778 18088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18147">
    <literal><![CDATA[
      K(x,y * (K(z \ u,z) * w)) = K(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,13551,a(flip),b,18107,a),flip(a)].">
      <j1 rule="hyper" parents="373 13551 18107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18148">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / z))) = K(x,y * (w / T(z,u)))
    ]]></literal>
    <justification jstring="[para(6245(a,1),18107(a,2,2,2))].">
      <j1 rule="para" parents="6245 18107"/>
    </justification>
  </clause>

  <clause id="18149">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * T(u,z)))
    ]]></literal>
    <justification jstring="[para(6852(a,1),18107(a,2,2,2))].">
      <j1 rule="para" parents="6852 18107"/>
    </justification>
  </clause>

  <clause id="18150">
    <literal><![CDATA[
      K(x,y * (z * K(u,z * y))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(14643(a,1),18107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14643 18107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18151">
    <literal><![CDATA[
      K(x,y * (K(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(18107(a,2),17261(a,1))].">
      <j1 rule="para" parents="18107 17261"/>
    </justification>
  </clause>

  <clause id="18152">
    <literal><![CDATA[
      T(x,y / (z * K(u,w))) = T(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(143,a,18120,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 18120 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18153">
    <literal><![CDATA[
      K(x,y * (T(z \ (u \ w),x) \ K(u \ w,u))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15108,a(flip),b,18120,a),flip(a)].">
      <j1 rule="hyper" parents="64 15108 18120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18154">
    <literal><![CDATA[
      K(x,y * (T(z * u,x) \ K(L(w,u,z),v5))) = K(x,y / (z * (u * K(v5,w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,12143,a(flip),b,18120,a),flip(a)].">
      <j1 rule="hyper" parents="64 12143 18120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18155">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(u,w))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(6245(a,1),18120(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6245 18120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18156">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(w,u))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(6852(a,1),18120(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6852 18120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18157">
    <literal><![CDATA[
      K(x,y * (z \ K(y,u))) = K(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(15024(a,1),18120(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15024 18120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18158">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) \ K(u,w))) = K(x,y / (z \ (u \ T(w,u))))
    ]]></literal>
    <justification jstring="[para(16684(a,1),18120(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16684 18120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18159">
    <literal><![CDATA[
      T(x,y * (z \ K(y,u))) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[hyper(143,a,18157,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 18157 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18160">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) * (w \ K(y * u,v5))) = K(x,T(L(y,z,y) * u,v5) / w)
    ]]></literal>
    <justification jstring="[para(13363(a,1),18157(a,1,2,2,2))].">
      <j1 rule="para" parents="13363 18157"/>
    </justification>
  </clause>

  <clause id="18161">
    <literal><![CDATA[
      T(x,(y * (z * K(u,z))) * (w \ K(y * T(z,u),v5))) = T(x,T(y * (z * K(u,z)),v5) / w)
    ]]></literal>
    <justification jstring="[para(15865(a,1),18159(a,1,2,2,2))].">
      <j1 rule="para" parents="15865 18159"/>
    </justification>
  </clause>

  <clause id="18162">
    <literal><![CDATA[
      K(x,T(y,(z / y) * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(10219(a,2),18124(a,2,2))].">
      <j1 rule="para" parents="10219 18124"/>
    </justification>
  </clause>

  <clause id="18164">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,T(K(z,y) * u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,18049,a,b,18140,a)].">
      <j1 rule="hyper" parents="373 18049 18140"/>
    </justification>
  </clause>

  <clause id="18165">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,15767,a,b,18142,a),flip(a)].">
      <j1 rule="hyper" parents="373 15767 18142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18166">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,T(u,w) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,17139,a(flip),b,18142,a),flip(a)].">
      <j1 rule="hyper" parents="373 17139 18142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18167">
    <literal><![CDATA[
      T(x,y * (z * K(u,z * y))) = T(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(143,a,18150,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 18150 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18168">
    <literal><![CDATA[
      K(x,y * (z \ ((((z \ u) * y) \ u) * ((z \ u) * y)))) = K(x,T(y * (z \ u),((z \ u) * y) \ u))
    ]]></literal>
    <justification jstring="[para(15230(a,1),18150(a,1,2,2))].">
      <j1 rule="para" parents="15230 18150"/>
    </justification>
  </clause>

  <clause id="18169">
    <literal><![CDATA[
      T(x,y * (((z * u) / z) \ K(w,z))) = T(x,y / T(u * K(z,w),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16317,a(flip),b,18152,a),flip(a)].">
      <j1 rule="hyper" parents="64 16317 18152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18170">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,T(K(z,y) * u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,18142,a,b,18165,a)].">
      <j1 rule="hyper" parents="373 18142 18165"/>
    </justification>
  </clause>

  <clause id="18171">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,T(u * K(z,y),w))
    ]]></literal>
    <justification jstring="[hyper(373,a,18069,a,b,18165,a),flip(a)].">
      <j1 rule="hyper" parents="373 18069 18165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18172">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * K(y,z)),w)) = K(x,T(T(u,K(z,y)),w))
    ]]></literal>
    <justification jstring="[para(8158(a,1),18170(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8158 18170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18173">
    <literal><![CDATA[
      K(x,T(K(y,z) * (z / u),w)) = K(x,T(T(z,y) / u,w))
    ]]></literal>
    <justification jstring="[para(14825(a,1),18170(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14825 18170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18174">
    <literal><![CDATA[
      K(x,T((y / z) * K(z,u),w)) = K(x,T(y / T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(17517,a,18171,a),flip(a)].">
      <j1 rule="hyper" parents="17517 18171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18175">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ u)) = v6
    ]]></literal>
    <justification jstring="[para(2433(a,1),18011(a,1,2,2))].">
      <j1 rule="para" parents="2433 18011"/>
    </justification>
  </clause>

  <clause id="18176">
    <literal><![CDATA[
      K(x,y * (K(z,K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(6576(a,1),18011(a,1,2,2))].">
      <j1 rule="para" parents="6576 18011"/>
    </justification>
  </clause>

  <clause id="18177">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / u)) = v6
    ]]></literal>
    <justification jstring="[para(8142(a,1),18011(a,1,2,2))].">
      <j1 rule="para" parents="8142 18011"/>
    </justification>
  </clause>

  <clause id="18178">
    <literal><![CDATA[
      K(x,y * (z \ K(u,T(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(15555(a,1),18011(a,1,2,2))].">
      <j1 rule="para" parents="15555 18011"/>
    </justification>
  </clause>

  <clause id="18179">
    <literal><![CDATA[
      K(x,y * T(z * K(u,K(w,v5)),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,v6)) = v7
    ]]></literal>
    <justification jstring="[para(17603(a,2),18011(a,1,2,2))].">
      <j1 rule="para" parents="17603 18011"/>
    </justification>
  </clause>

  <clause id="18180">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,u \ z)) = K(x,z \ ((y \ (z * (u \ y))) \ z))
    ]]></literal>
    <justification jstring="[hyper(18013,a,9854,a)].">
      <j1 rule="hyper" parents="18013 9854"/>
    </justification>
  </clause>

  <clause id="18181">
    <literal><![CDATA[
      K(x,y \ K(z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(8207(a,1),18013(a,1,2,2))].">
      <j1 rule="para" parents="8207 18013"/>
    </justification>
  </clause>

  <clause id="18182">
    <literal><![CDATA[
      K(x,y \ K(z * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u * z,w)) = v5
    ]]></literal>
    <justification jstring="[para(11177(a,1),18013(a,1,2,2))].">
      <j1 rule="para" parents="11177 18013"/>
    </justification>
  </clause>

  <clause id="18183">
    <literal><![CDATA[
      K(T(x,y) \ K(z,u),w) = K(x \ K(z,u),T(w,y))
    ]]></literal>
    <justification jstring="[hyper(18018,a,17809,a),flip(a)].">
      <j1 rule="hyper" parents="18018 17809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18184">
    <literal><![CDATA[
      K(x \ K(y,z * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,u * z),w) = v5
    ]]></literal>
    <justification jstring="[para(11113(a,1),18018(a,1,1,2))].">
      <j1 rule="para" parents="11113 18018"/>
    </justification>
  </clause>

  <clause id="18187">
    <literal><![CDATA[
      K((x / y) \ K(z,u),T(w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ K(z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(18183(a,1),13582(a,1))].">
      <j1 rule="para" parents="18183 13582"/>
    </justification>
  </clause>

  <clause id="18188">
    <literal><![CDATA[
      K(x,T((y / (y / z)) \ K(u,w),v5)) = T(x,v5) / T(x * K(z \ K(u,w),T(x,y)),v5)
    ]]></literal>
    <justification jstring="[para(18183(a,1),15881(a,2,2,1,2))].">
      <j1 rule="para" parents="18183 15881"/>
    </justification>
  </clause>

  <clause id="18189">
    <literal><![CDATA[
      K(x,T(y,z \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z) * w) = v5
    ]]></literal>
    <justification jstring="[para(117(a,1),18021(a,1,2,1,2))].">
      <j1 rule="para" parents="117 18021"/>
    </justification>
  </clause>

  <clause id="18190">
    <literal><![CDATA[
      K(x,K(y * z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z * y) * w) = v5
    ]]></literal>
    <justification jstring="[para(11177(a,1),18034(a,1,2,1))].">
      <j1 rule="para" parents="11177 18034"/>
    </justification>
  </clause>

  <clause id="18191">
    <literal><![CDATA[
      T(x,K(T(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(7869(a,2),18046(a,1,2,1))].">
      <j1 rule="para" parents="7869 18046"/>
    </justification>
  </clause>

  <clause id="18192">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,z)),w) / T(v5,y * T(z,u))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 \ T(y * (z * K(u,z)),w)) = v6
    ]]></literal>
    <justification jstring="[para(15809(a,1),18057(a,1,2,2))].">
      <j1 rule="para" parents="15809 18057"/>
    </justification>
  </clause>

  <clause id="18193">
    <literal><![CDATA[
      K(x,((y * z) / y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u / z) \ K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6960(a,1),18103(a,1))].">
      <j1 rule="para" parents="6960 18103"/>
    </justification>
  </clause>

  <clause id="18194">
    <literal><![CDATA[
      K(x,K(y,z) * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(4534(a,2),18151(a,1,2))].">
      <j1 rule="para" parents="4534 18151"/>
    </justification>
  </clause>

  <clause id="18195">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,u) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(9147(a,1),18176(a,1,2,2))].">
      <j1 rule="para" parents="9147 18176"/>
    </justification>
  </clause>

  <clause id="18196">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(16831(a,2),18194(a,1))].">
      <j1 rule="para" parents="16831 18194"/>
    </justification>
  </clause>

  <clause id="18197">
    <literal><![CDATA[
      K(x,(L(T(y,K(z,u)),w,v5) \ v6) * ((v6 \ L(T(y,K(z,u)),w,v5)) * v6)) = K(x,((v6 * (L(T(y,K(z,u)),w,v5) / v6)) \ v6) * L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(15099(a,1),17963(a,1,2))].">
      <j1 rule="para" parents="15099 17963"/>
    </justification>
  </clause>

  <clause id="18198">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / T(T(y \ u,u),w)) = T(x,T(y \ u,w) \ (K(y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13545,a(flip),b,17973,a),flip(a)].">
      <j1 rule="hyper" parents="64 13545 17973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18199">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * v6) * ((v6 * (z * K(u,K(w,v5)))) / v6))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[para(4853(a,2),18028(a,1,2,2))].">
      <j1 rule="para" parents="4853 18028"/>
    </justification>
  </clause>

  <clause id="18200">
    <literal><![CDATA[
      K(x,y * (z * K(u / w,v5))) = K(x,y * (z * K(w \ u,v5)))
    ]]></literal>
    <justification jstring="[para(6779(a,1),18028(a,1,2,2,2))].">
      <j1 rule="para" parents="6779 18028"/>
    </justification>
  </clause>

  <clause id="18201">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * (v6 * K(z * K(u,K(w,v5)),v7))) * z)) = K(x,y * (((z * K(u,K(w,v5))) * v6) * T(z * K(u,K(w,v5)),v7)))
    ]]></literal>
    <justification jstring="[para(7139(a,1),18028(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7139 18028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18202">
    <literal><![CDATA[
      K(x,y * (z * T(u,T(w,v5)))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(8027(a,1),18028(a,1,2,2,2))].">
      <j1 rule="para" parents="8027 18028"/>
    </justification>
  </clause>

  <clause id="18203">
    <literal><![CDATA[
      K(x,y * (z * (u * (w * K(v5,K(v6,v7)))))) = K(x,y * (z * (u * w)))
    ]]></literal>
    <justification jstring="[para(12145(a,1),18028(a,1,2,2,2))].">
      <j1 rule="para" parents="12145 18028"/>
    </justification>
  </clause>

  <clause id="18204">
    <literal><![CDATA[
      K(x,y * (z * T(u * K(w,K(v5,v6)),v7))) = K(x,y * (z * T(u,v7)))
    ]]></literal>
    <justification jstring="[para(17603(a,2),18028(a,1,2,2,2))].">
      <j1 rule="para" parents="17603 18028"/>
    </justification>
  </clause>

  <clause id="18206">
    <literal><![CDATA[
      K(x,T(y * ((y / z) / y),y) / u) = K(x,(z \ T(y,z \ 1)) / u)
    ]]></literal>
    <justification jstring="[para(4396(a,1),18053(a,1,2,1,1))].">
      <j1 rule="para" parents="4396 18053"/>
    </justification>
  </clause>

  <clause id="18207">
    <literal><![CDATA[
      K(x,y * T(T(T(z,T(u,w)),v5 * z),v6)) = K(x,y * T(T(T(z,z * v5),v6),u))
    ]]></literal>
    <justification jstring="[para(4693(a,1),18054(a,1,2,2,1))].">
      <j1 rule="para" parents="4693 18054"/>
    </justification>
  </clause>

  <clause id="18208">
    <literal><![CDATA[
      T(x,y * T(T(T(z,u),w) \ v5,T(z,w))) = T(x,y * (v5 / T(T(z,w),u)))
    ]]></literal>
    <justification jstring="[para(23(a,1),18062(a,1,2,2,1,1))].">
      <j1 rule="para" parents="23 18062"/>
    </justification>
  </clause>

  <clause id="18209">
    <literal><![CDATA[
      K(x \ T(y * x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y * K(y * x,z),T(u,x)) = w
    ]]></literal>
    <justification jstring="[para(18065(a,1),8019(a,1))].">
      <j1 rule="para" parents="18065 8019"/>
    </justification>
  </clause>

  <clause id="18210">
    <literal><![CDATA[
      K(x,T(y,z) * (u * K(w,y))) = K(x,T(T(y,z),w) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17462,a(flip),b,18068,a),flip(a)].">
      <j1 rule="hyper" parents="64 17462 18068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18211">
    <literal><![CDATA[
      K(x,y * (z * K(u * w,v5))) = K(x,y * (z * K(w * u,v5)))
    ]]></literal>
    <justification jstring="[para(11177(a,1),18068(a,1,2,2,2))].">
      <j1 rule="para" parents="11177 18068"/>
    </justification>
  </clause>

  <clause id="18212">
    <literal><![CDATA[
      K(K(x,y) * (T(y * x,z) / u),w) = K(T(T(y * x,z),y) / u,w)
    ]]></literal>
    <justification jstring="[hyper(17366,a,18084,a)].">
      <j1 rule="hyper" parents="17366 18084"/>
    </justification>
  </clause>

  <clause id="18214">
    <literal><![CDATA[
      K(x,T(y * z,K(u,w)) / y) = K(x,T(z,K(w,u) * y))
    ]]></literal>
    <justification jstring="[hyper(8462,a,18102,a)].">
      <j1 rule="hyper" parents="8462 18102"/>
    </justification>
  </clause>

  <clause id="18215">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * (K(z,u) * (z / w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16520,a,b,18108,a)].">
      <j1 rule="hyper" parents="64 16520 18108"/>
    </justification>
  </clause>

  <clause id="18216">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ (y * K(z,z \ u)) = K(w,x * (K(z,u) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,14650,a,b,18108,a)].">
      <j1 rule="hyper" parents="64 14650 18108"/>
    </justification>
  </clause>

  <clause id="18217">
    <literal><![CDATA[
      K(x,y * (z / (u / (u / w)))) = K(x,y * (K(w,u) * (z / w)))
    ]]></literal>
    <justification jstring="[para(6958(a,2),18108(a,1,2,2))].">
      <j1 rule="para" parents="6958 18108"/>
    </justification>
  </clause>

  <clause id="18218">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(10173(a,1),18108(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10173 18108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18219">
    <literal><![CDATA[
      K(x,y / T(z,z / u)) = K(x,(y / z) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(17516,a,18114,a),flip(a)].">
      <j1 rule="hyper" parents="17516 18114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18220">
    <literal><![CDATA[
      K(x,y / T(z,z / u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6245(a,1),18219(a,2,2))].">
      <j1 rule="para" parents="6245 18219"/>
    </justification>
  </clause>

  <clause id="18221">
    <literal><![CDATA[
      K(x,y / T(z * u,u)) = K(x,y / T(z * u,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),18220(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 18220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18222">
    <literal><![CDATA[
      K(x,y / T(z * u,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17691,a(flip),b,18221,a),flip(a)].">
      <j1 rule="hyper" parents="64 17691 18221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18223">
    <literal><![CDATA[
      T(x,y / T(z * u,z)) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(143,a,18222,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 18222 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18224">
    <literal><![CDATA[
      K(x,y / ((z \ u) * z)) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),18222(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 18222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18225">
    <literal><![CDATA[
      T(x,y / (z \ T(((K(u,w) * z) * v5) * T(z,K(u,w)),K(w,u)))) = T(x,y / (v5 * (K(u,w) * z)))
    ]]></literal>
    <justification jstring="[para(16803(a,2),18223(a,1,2,2))].">
      <j1 rule="para" parents="16803 18223"/>
    </justification>
  </clause>

  <clause id="18226">
    <literal><![CDATA[
      T(x,y / T((z * K(u,w)) * v5,K(u,w) * z)) = T(x,y / (v5 * (z * K(u,w))))
    ]]></literal>
    <justification jstring="[para(17165(a,2),18223(a,1,2,2))].">
      <j1 rule="para" parents="17165 18223"/>
    </justification>
  </clause>

  <clause id="18227">
    <literal><![CDATA[
      K(x,(y / ((z \ u) * z)) * (K(w,y / T(u,z)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(18224(a,1),18151(a,1,2,2,1))].">
      <j1 rule="para" parents="18224 18151"/>
    </justification>
  </clause>

  <clause id="18228">
    <literal><![CDATA[
      T(x,y \ K(z / u,w)) = T(x,y \ K(u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14905,a(flip),b,18125,a)].">
      <j1 rule="hyper" parents="64 14905 18125"/>
    </justification>
  </clause>

  <clause id="18229">
    <literal><![CDATA[
      T(x,y * (z * (K(T(u,w),z) * v5))) = T(x,y * (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16351,a,b,18135,a)].">
      <j1 rule="hyper" parents="64 16351 18135"/>
    </justification>
  </clause>

  <clause id="18230">
    <literal><![CDATA[
      T(x,y * (T(z,u) * T(u,w))) = T(x,y * (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15941,a(flip),b,18135,a),flip(a)].">
      <j1 rule="hyper" parents="64 15941 18135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18231">
    <literal><![CDATA[
      K(x,T(y * K(z,z \ u),w)) = K(x,T(K(u,z) * y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,18166,a,b,18143,a),flip(a)].">
      <j1 rule="hyper" parents="373 18166 18143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18232">
    <literal><![CDATA[
      K(x,y * ((z * (u / z)) \ w)) = K(x,y * ((u \ w) * K(z,u)))
    ]]></literal>
    <justification jstring="[para(11892(a,1),18147(a,1,2,2))].">
      <j1 rule="para" parents="11892 18147"/>
    </justification>
  </clause>

  <clause id="18233">
    <literal><![CDATA[
      K(x,T(y / ((z * u) / z),w)) = K(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[para(6888(a,2),18174(a,1,2,1))].">
      <j1 rule="para" parents="6888 18174"/>
    </justification>
  </clause>

  <clause id="18234">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,(w * y) / w)
    ]]></literal>
    <justification jstring="[hyper(18004,a,18214,a),flip(a)].">
      <j1 rule="hyper" parents="18004 18214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18236">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,8217,a(flip),b,18234,a),flip(a)].">
      <j1 rule="hyper" parents="373 8217 18234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18237">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(18234(a,2),8298(a,1))].">
      <j1 rule="para" parents="18234 8298"/>
    </justification>
  </clause>

  <clause id="18238">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(17266,a,18236,a)].">
      <j1 rule="hyper" parents="17266 18236"/>
    </justification>
  </clause>

  <clause id="18239">
    <literal><![CDATA[
      K(x,T(y,K(z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(17070,a,18236,a)].">
      <j1 rule="hyper" parents="17070 18236"/>
    </justification>
  </clause>

  <clause id="18241">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(143,a,18236,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 18236 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18243">
    <literal><![CDATA[
      K(x,T(y,T(z,u) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(5755(a,1),18236(a,1,2,2))].">
      <j1 rule="para" parents="5755 18236"/>
    </justification>
  </clause>

  <clause id="18244">
    <literal><![CDATA[
      K(x,T(y,T(z,u) \ w)) = K(x,T(y,z \ w))
    ]]></literal>
    <justification jstring="[para(6075(a,1),18236(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6075 18236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18245">
    <literal><![CDATA[
      K(x,T(y,(z / u) * w)) = K(x,T(y,(u \ z) * w))
    ]]></literal>
    <justification jstring="[para(5982(a,1),18236(a,1,2,2))].">
      <j1 rule="para" parents="5982 18236"/>
    </justification>
  </clause>

  <clause id="18246">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(6417(a,1),18236(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6417 18236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18247">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(x,y) * K(y,T(x,w))
    ]]></literal>
    <justification jstring="[para(18236(a,1),8111(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18236 8111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18249">
    <literal><![CDATA[
      K(x,T(y,z * (u / w))) = K(x,T(y,z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(17418(a,1),18236(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17418 18236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18250">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8772,a,18238,a)].">
      <j1 rule="hyper" parents="8772 18238"/>
    </justification>
  </clause>

  <clause id="18252">
    <literal><![CDATA[
      K(x,T(y,K(z,u) / w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17289,a,b,18238,a)].">
      <j1 rule="hyper" parents="64 17289 18238"/>
    </justification>
  </clause>

  <clause id="18253">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = (z * K(u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,18238,a(flip),b,8192,a)].">
      <j1 rule="hyper" parents="144 18238 8192"/>
    </justification>
  </clause>

  <clause id="18254">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u / (x * K(y,z)),w) = v5
    ]]></literal>
    <justification jstring="[para(18238(a,1),8322(a,1))].">
      <j1 rule="para" parents="18238 8322"/>
    </justification>
  </clause>

  <clause id="18256">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[para(9345(a,1),18238(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9345 18238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18257">
    <literal><![CDATA[
      K(x * (y * K(z,u)),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K((y * K(z,u)) * x,w) = v5
    ]]></literal>
    <justification jstring="[para(18238(a,1),11189(a,1))].">
      <j1 rule="para" parents="18238 11189"/>
    </justification>
  </clause>

  <clause id="18258">
    <literal><![CDATA[
      T(x,T(y,K(z,u) \ w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(143,a,18239,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 18239 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18260">
    <literal><![CDATA[
      T(x,T(y,T(z,u) * w)) = T(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(5755(a,1),18241(a,1,2,2))].">
      <j1 rule="para" parents="5755 18241"/>
    </justification>
  </clause>

  <clause id="18261">
    <literal><![CDATA[
      T(x,T(y,(z * u) * w)) = T(x,T(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(10834(a,1),18241(a,1,2,2))].">
      <j1 rule="para" parents="10834 18241"/>
    </justification>
  </clause>

  <clause id="18262">
    <literal><![CDATA[
      T(x,T(y,(T(z,u) * w) * v5)) = T(x,T(y,(z * w) * v5))
    ]]></literal>
    <justification jstring="[para(15613(a,1),18241(a,1,2,2))].">
      <j1 rule="para" parents="15613 18241"/>
    </justification>
  </clause>

  <clause id="18265">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),u / K(z,T(y,x))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(18250(a,1),16793(a,1,2,2))].">
      <j1 rule="para" parents="18250 16793"/>
    </justification>
  </clause>

  <clause id="18266">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(u,w) / z) = (K(u,w) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,18252,a(flip),b,8192,a)].">
      <j1 rule="hyper" parents="144 18252 8192"/>
    </justification>
  </clause>

  <clause id="18267">
    <literal><![CDATA[
      T(x,T((K(y,z) \ u) \ w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w / (K(y,z) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(18258(a,1),8856(a,1))].">
      <j1 rule="para" parents="18258 8856"/>
    </justification>
  </clause>

  <clause id="18268">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(17266,a,18243,a)].">
      <j1 rule="hyper" parents="17266 18243"/>
    </justification>
  </clause>

  <clause id="18270">
    <literal><![CDATA[
      T(x,T(y,T(z,u) \ w)) = T(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17029,a,b,18260,a)].">
      <j1 rule="hyper" parents="64 17029 18260"/>
    </justification>
  </clause>

  <clause id="18271">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = v5
    ]]></literal>
    <justification jstring="[para(18268(a,2),17266(a,1))].">
      <j1 rule="para" parents="18268 17266"/>
    </justification>
  </clause>

  <clause id="18272">
    <literal><![CDATA[
      T(T(x,y) \ z,K(u,x * z)) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(41,a,17471,a,b,18270,a)].">
      <j1 rule="hyper" parents="41 17471 18270"/>
    </justification>
  </clause>

  <clause id="18273">
    <literal><![CDATA[
      K(x,T(y,T(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * w)) = v5
    ]]></literal>
    <justification jstring="[para(5755(a,1),18237(a,1,2,2))].">
      <j1 rule="para" parents="5755 18237"/>
    </justification>
  </clause>

  <clause id="18274">
    <literal><![CDATA[
      K(x,T(y,K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(6156(a,2),18237(a,1,2,2))].">
      <j1 rule="para" parents="6156 18237"/>
    </justification>
  </clause>

  <clause id="18275">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(5919(a,1),18237(a,1,2,2))].">
      <j1 rule="para" parents="5919 18237"/>
    </justification>
  </clause>

  <clause id="18276">
    <literal><![CDATA[
      K(x,T(y,z * T(z \ u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = v5
    ]]></literal>
    <justification jstring="[para(5754(a,1),18237(a,1,2,2))].">
      <j1 rule="para" parents="5754 18237"/>
    </justification>
  </clause>

  <clause id="18277">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(6823(a,1),18237(a,1,2,2))].">
      <j1 rule="para" parents="6823 18237"/>
    </justification>
  </clause>

  <clause id="18278">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z \ u)) = v5
    ]]></literal>
    <justification jstring="[para(6578(a,1),18237(a,1,2,2))].">
      <j1 rule="para" parents="6578 18237"/>
    </justification>
  </clause>

  <clause id="18279">
    <literal><![CDATA[
      T(K(x,y),K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(7867(a,1),18237(a,1))].">
      <j1 rule="para" parents="7867 18237"/>
    </justification>
  </clause>

  <clause id="18280">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,(u * z) * w)) = v5
    ]]></literal>
    <justification jstring="[para(10834(a,1),18237(a,1,2,2))].">
      <j1 rule="para" parents="10834 18237"/>
    </justification>
  </clause>

  <clause id="18281">
    <literal><![CDATA[
      K(x,T(y,z / (u \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z / (w / u))) = v5
    ]]></literal>
    <justification jstring="[para(6455(a,1),18277(a,1,2,2))].">
      <j1 rule="para" parents="6455 18277"/>
    </justification>
  </clause>

  <clause id="18282">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z / (w \ u))) = v5
    ]]></literal>
    <justification jstring="[para(6887(a,1),18277(a,1,2,2))].">
      <j1 rule="para" parents="6887 18277"/>
    </justification>
  </clause>

  <clause id="18283">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(7867(a,1),18277(a,1))].">
      <j1 rule="para" parents="7867 18277"/>
    </justification>
  </clause>

  <clause id="18284">
    <literal><![CDATA[
      K(x,T(y,z \ (u / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z \ (w \ u))) = v5
    ]]></literal>
    <justification jstring="[para(15028(a,1),18277(a,1,2,2))].">
      <j1 rule="para" parents="15028 18277"/>
    </justification>
  </clause>

  <clause id="18285">
    <literal><![CDATA[
      K(x,T(y,L(z,u,u \ w) * w)) = K(x,T(y,(u \ w) * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(17522,a,18245,a)].">
      <j1 rule="hyper" parents="17522 18245"/>
    </justification>
  </clause>

  <clause id="18286">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,8111,a(flip),b,18247,a),flip(a)].">
      <j1 rule="hyper" parents="373 8111 18247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18287">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(w,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,7461,a(flip),b,18247,a),flip(a)].">
      <j1 rule="hyper" parents="373 7461 18247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18289">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(17389,a,18286,a)].">
      <j1 rule="hyper" parents="17389 18286"/>
    </justification>
  </clause>

  <clause id="18290">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(143,a,18286,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 18286 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18291">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17551,a,b,18286,a)].">
      <j1 rule="hyper" parents="64 17551 18286"/>
    </justification>
  </clause>

  <clause id="18292">
    <literal><![CDATA[
      K(x,K(y,((z * u) / z) * w)) = K(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[para(5729(a,1),18286(a,1,2,2))].">
      <j1 rule="para" parents="5729 18286"/>
    </justification>
  </clause>

  <clause id="18293">
    <literal><![CDATA[
      K(x,K(y,z / T(u,w))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(8676(a,1),18286(a,1,2,2))].">
      <j1 rule="para" parents="8676 18286"/>
    </justification>
  </clause>

  <clause id="18294">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ (K(u,w) * z),y) = K((K(u,w) * z) / x,y)
    ]]></literal>
    <justification jstring="[para(18286(a,1),9058(a,1,1))].">
      <j1 rule="para" parents="18286 9058"/>
    </justification>
  </clause>

  <clause id="18295">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(10834(a,1),18286(a,1,2,2))].">
      <j1 rule="para" parents="10834 18286"/>
    </justification>
  </clause>

  <clause id="18296">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[para(14887(a,1),18286(a,1,2,2))].">
      <j1 rule="para" parents="14887 18286"/>
    </justification>
  </clause>

  <clause id="18297">
    <literal><![CDATA[
      K(x,K(y,(K(z,u) * w) / v5)) = K(x,K(y,w / v5))
    ]]></literal>
    <justification jstring="[para(16166(a,1),18286(a,1,2,2))].">
      <j1 rule="para" parents="16166 18286"/>
    </justification>
  </clause>

  <clause id="18298">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,(K(u,w) * z) * x) = K(y,x * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[para(18286(a,1),17499(a,1,1))].">
      <j1 rule="para" parents="18286 17499"/>
    </justification>
  </clause>

  <clause id="18299">
    <literal><![CDATA[
      K(x,K(y,z \ K(u,w))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(17556,a,18287,a)].">
      <j1 rule="hyper" parents="17556 18287"/>
    </justification>
  </clause>

  <clause id="18301">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) = K(w,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17551,a,b,18287,a)].">
      <j1 rule="hyper" parents="64 17551 18287"/>
    </justification>
  </clause>

  <clause id="18303">
    <literal><![CDATA[
      K(x,K(y,z)) * K((K(u,w) * x) \ z,y) = K(z / (K(u,w) * x),y)
    ]]></literal>
    <justification jstring="[para(18287(a,1),9060(a,1,1))].">
      <j1 rule="para" parents="18287 9060"/>
    </justification>
  </clause>

  <clause id="18304">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(9051,a,18289,a)].">
      <j1 rule="hyper" parents="9051 18289"/>
    </justification>
  </clause>

  <clause id="18305">
    <literal><![CDATA[
      K(x,K(y,z / ((u * w) / u))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(6400(a,1),18289(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6400 18289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18306">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(6455(a,1),18289(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6455 18289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18307">
    <literal><![CDATA[
      K(x,K(y,z * (u / w))) = K(x,K(y,z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(6471(a,1),18289(a,1,2,2))].">
      <j1 rule="para" parents="6471 18289"/>
    </justification>
  </clause>

  <clause id="18308">
    <literal><![CDATA[
      K(x,K(y,z / (u / (u / w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(6957(a,2),18289(a,1,2,2))].">
      <j1 rule="para" parents="6957 18289"/>
    </justification>
  </clause>

  <clause id="18309">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(u,w)) = T(z * K(u,w),K(x,y))
    ]]></literal>
    <justification jstring="[para(18289(a,1),8122(a,1,1))].">
      <j1 rule="para" parents="18289 8122"/>
    </justification>
  </clause>

  <clause id="18310">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) * v5)) = K(x,K(y,z * v5))
    ]]></literal>
    <justification jstring="[para(9345(a,1),18289(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9345 18289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18311">
    <literal><![CDATA[
      K(x,K(y,z \ (u / w))) = K(x,K(y,z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(15028(a,1),18289(a,1,2,2))].">
      <j1 rule="para" parents="15028 18289"/>
    </justification>
  </clause>

  <clause id="18312">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8153,a,b,18290,a),flip(a)].">
      <j1 rule="hyper" parents="373 8153 18290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18313">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17557,a,b,18290,a)].">
      <j1 rule="hyper" parents="64 17557 18290"/>
    </justification>
  </clause>

  <clause id="18314">
    <literal><![CDATA[
      T(x,K(y,T(z,u) * w)) = T(x,K(y,z * w))
    ]]></literal>
    <justification jstring="[para(5755(a,1),18290(a,1,2,2))].">
      <j1 rule="para" parents="5755 18290"/>
    </justification>
  </clause>

  <clause id="18315">
    <literal><![CDATA[
      T(x,K(y,T(z,u) \ w)) = T(x,K(y,z \ w))
    ]]></literal>
    <justification jstring="[para(6075(a,1),18290(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6075 18290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18316">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ w)) = T(x,K(y,(u \ z) \ w))
    ]]></literal>
    <justification jstring="[para(6270(a,1),18290(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6270 18290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18317">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(18290(a,2),8184(a,1))].">
      <j1 rule="para" parents="18290 8184"/>
    </justification>
  </clause>

  <clause id="18318">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,K(w,v5) * u)) = T(y,K(K(w,v5) * u,z) * x)
    ]]></literal>
    <justification jstring="[para(18290(a,1),16796(a,1,2,1,2))].">
      <j1 rule="para" parents="18290 16796"/>
    </justification>
  </clause>

  <clause id="18319">
    <literal><![CDATA[
      T(x,K(y,z * (u * K(w,v5)))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(17304(a,1),18290(a,1,2))].">
      <j1 rule="para" parents="17304 18290"/>
    </justification>
  </clause>

  <clause id="18321">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * T(K(x,y) \ z,K(w,v5))) = K(w,K(v5,z)) \ T(u,K(x,y) \ z)
    ]]></literal>
    <justification jstring="[para(18291(a,1),17613(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18291 17613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18322">
    <literal><![CDATA[
      K(x,K(K(y,z) \ u,w)) = K(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9013,a,b,18299,a)].">
      <j1 rule="hyper" parents="64 9013 18299"/>
    </justification>
  </clause>

  <clause id="18324">
    <literal><![CDATA[
      x * T(x \ K(y,z),K(u,w)) = K(x,K(u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(18301(a,1),17332(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18301 17332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18325">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8126,a,b,18304,a),flip(a)].">
      <j1 rule="hyper" parents="373 8126 18304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18326">
    <literal><![CDATA[
      T(x,K(y \ T(z,u),w)) = T(x,K(w,y \ z))
    ]]></literal>
    <justification jstring="[para(6417(a,1),18312(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6417 18312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18327">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) = T(x,K(y,K(v5,v6) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,18290,a,b,18313,a),flip(a)].">
      <j1 rule="hyper" parents="373 18290 18313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18328">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) / w,v5,v6))) = K(x,K(w,L(y,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(12160,a,18325,a)].">
      <j1 rule="hyper" parents="12160 18325"/>
    </justification>
  </clause>

  <clause id="18329">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(9038,a,18325,a),flip(a)].">
      <j1 rule="hyper" parents="9038 18325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18330">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(z * y,y / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17295,a,b,18325,a)].">
      <j1 rule="hyper" parents="64 17295 18325"/>
    </justification>
  </clause>

  <clause id="18331">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(K(w,v5) / y,z)) = u
    ]]></literal>
    <justification jstring="[para(18325(a,1),8437(a,1))].">
      <j1 rule="para" parents="18325 8437"/>
    </justification>
  </clause>

  <clause id="18332">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(18325(a,1),9038(a,1))].">
      <j1 rule="para" parents="18325 9038"/>
    </justification>
  </clause>

  <clause id="18333">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(17433,a,18329,a)].">
      <j1 rule="hyper" parents="17433 18329"/>
    </justification>
  </clause>

  <clause id="18334">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,w)) = K(x,K(y / u,w))
    ]]></literal>
    <justification jstring="[para(2458(a,1),18329(a,1,2,1))].">
      <j1 rule="para" parents="2458 18329"/>
    </justification>
  </clause>

  <clause id="18336">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) * w,v5,v6))) = K(x,K(w,L(y,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(12105,a,18333,a)].">
      <j1 rule="hyper" parents="12105 18333"/>
    </justification>
  </clause>

  <clause id="18337">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) * K(x,K(u,w)) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,18333,a(flip),b,8382,a)].">
      <j1 rule="hyper" parents="145 18333 8382"/>
    </justification>
  </clause>

  <clause id="18338">
    <literal><![CDATA[
      T(x,K(y,z * T(u,w))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17218,a,b,18314,a)].">
      <j1 rule="hyper" parents="64 17218 18314"/>
    </justification>
  </clause>

  <clause id="18339">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(T(z,w) \ u) * y) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (T(z,w) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(18315(a,1),11213(a,1,1))].">
      <j1 rule="para" parents="18315 11213"/>
    </justification>
  </clause>

  <clause id="18340">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),((w * (z / w)) \ u) * y) = T(x,y * ((w * (z / w)) \ u))
    ]]></literal>
    <justification jstring="[para(18315(a,1),15907(a,1,1))].">
      <j1 rule="para" parents="18315 15907"/>
    </justification>
  </clause>

  <clause id="18341">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(u / T(z,w)) \ y) = T(x,y / (u / T(z,w)))
    ]]></literal>
    <justification jstring="[para(18315(a,1),17378(a,1,1))].">
      <j1 rule="para" parents="18315 17378"/>
    </justification>
  </clause>

  <clause id="18342">
    <literal><![CDATA[
      (x \ T(y,z)) \ T(u,K(x \ T(y,z),w)) = T((x \ T(y,z)) \ u,K(w,x \ y))
    ]]></literal>
    <justification jstring="[hyper(8063,a,18326,a)].">
      <j1 rule="hyper" parents="8063 18326"/>
    </justification>
  </clause>

  <clause id="18343">
    <literal><![CDATA[
      K(x,K(y / z,L(u,z,w))) = K(x,K(u,(y * w) / (w * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17772,a(flip),b,18334,a),flip(a)].">
      <j1 rule="hyper" parents="64 17772 18334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18344">
    <literal><![CDATA[
      T(x,K(y,(z * u) * T(z,w))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17561,a(flip),b,18338,a),flip(a)].">
      <j1 rule="hyper" parents="373 17561 18338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18345">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u * K(v5,v6),w))
    ]]></literal>
    <justification jstring="[hyper(18331,a,18329,a(flip))].">
      <j1 rule="hyper" parents="18331 18329"/>
    </justification>
  </clause>

  <clause id="18346">
    <literal><![CDATA[
      K(L(x,y,z),T(u,w * (v5 \ v6))) = K(x,L(T(u,w * (v6 / v5)),y,z))
    ]]></literal>
    <justification jstring="[hyper(12117,a,18249,a),flip(a)].">
      <j1 rule="hyper" parents="12117 18249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18347">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,w / (u * z)))
    ]]></literal>
    <justification jstring="[hyper(9048,a,18296,a),flip(a)].">
      <j1 rule="hyper" parents="9048 18296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18348">
    <literal><![CDATA[
      K(x,K(y,((z * u) * w) / (w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,17750,a(flip),b,18296,a),flip(a)].">
      <j1 rule="hyper" parents="373 17750 18296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18349">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * (w * z)) / T(w * u,a(w,z,z \ u)))) = K(x,K(y,a(w,z,z \ u)))
    ]]></literal>
    <justification jstring="[para(1376(a,1),18296(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1376 18296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18350">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w / (u * z))) = v5
    ]]></literal>
    <justification jstring="[para(18296(a,1),9048(a,1))].">
      <j1 rule="para" parents="18296 9048"/>
    </justification>
  </clause>

  <clause id="18351">
    <literal><![CDATA[
      K(x,K(y,z / (K(u,w) * v5))) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(9048,a,18297,a)].">
      <j1 rule="hyper" parents="9048 18297"/>
    </justification>
  </clause>

  <clause id="18352">
    <literal><![CDATA[
      K(x,K(y,(z * T(u,w)) / v5)) = K(x,K(y,(z * u) / v5))
    ]]></literal>
    <justification jstring="[para(6367(a,1),18297(a,1,2,2,1))].">
      <j1 rule="para" parents="6367 18297"/>
    </justification>
  </clause>

  <clause id="18353">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(18306(a,2),8087(a,1,2))].">
      <j1 rule="para" parents="18306 8087"/>
    </justification>
  </clause>

  <clause id="18354">
    <literal><![CDATA[
      L(K(x,K(y,z / (u / w))),v5,v6) = K(y,K(z / (w \ u),L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[para(18306(a,2),12092(a,1,1))].">
      <j1 rule="para" parents="18306 12092"/>
    </justification>
  </clause>

  <clause id="18356">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / w) * v5)) = K(x,K(y,(z / w) * v5))
    ]]></literal>
    <justification jstring="[para(2458(a,1),18310(a,1,2,2,1))].">
      <j1 rule="para" parents="2458 18310"/>
    </justification>
  </clause>

  <clause id="18357">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * v5)) = K(x,K(y,((u \ z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(8651(a,1),18310(a,1,2,2,1))].">
      <j1 rule="para" parents="8651 18310"/>
    </justification>
  </clause>

  <clause id="18358">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,v5 * z)) = v6
    ]]></literal>
    <justification jstring="[para(18310(a,2),17389(a,1))].">
      <j1 rule="para" parents="18310 17389"/>
    </justification>
  </clause>

  <clause id="18359">
    <literal><![CDATA[
      T(x,K(y,z * (u \ T(w,v5)))) = T(x,K(y,z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(2433(a,1),18319(a,1,2,2,2))].">
      <j1 rule="para" parents="2433 18319"/>
    </justification>
  </clause>

  <clause id="18360">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(w,x \ K(y,z))) = (x \ K(y,z)) \ T(u,K(w,K(v5,v6) * x))
    ]]></literal>
    <justification jstring="[hyper(139,a,18327,a(flip),b,8423,a),flip(a)].">
      <j1 rule="hyper" parents="139 18327 8423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18361">
    <literal><![CDATA[
      T(T(x,y \ K(z,u)),K(w,K(v5,v6) * y)) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ K(z,u),w)) = v7
    ]]></literal>
    <justification jstring="[para(18327(a,1),8189(a,1))].">
      <j1 rule="para" parents="18327 8189"/>
    </justification>
  </clause>

  <clause id="18362">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,K(u,w) * v5)),K(z,v5 \ K(v6,v7))) = T(y,K(v5 \ K(v6,v7),z) * x)
    ]]></literal>
    <justification jstring="[para(18327(a,1),16796(a,1,2,1,2))].">
      <j1 rule="para" parents="18327 16796"/>
    </justification>
  </clause>

  <clause id="18363">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(w,L(K(v5,v6) / y,y,v7)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12126,a(flip),b,18345,a),flip(a)].">
      <j1 rule="hyper" parents="64 12126 18345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18364">
    <literal><![CDATA[
      K(x,K(y,z / (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(18347(a,1),9048(a,1))].">
      <j1 rule="para" parents="18347 9048"/>
    </justification>
  </clause>

  <clause id="18365">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,(u * z) / w)) = v5
    ]]></literal>
    <justification jstring="[para(18347(a,2),9048(a,1))].">
      <j1 rule="para" parents="18347 9048"/>
    </justification>
  </clause>

  <clause id="18366">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) / v5)) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[para(8248(a,1),18351(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8248 18351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18367">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,(v5 * v6) / z))
    ]]></literal>
    <justification jstring="[para(7760(a,1),18351(a,1,2,2,2))].">
      <j1 rule="para" parents="7760 18351"/>
    </justification>
  </clause>

  <clause id="18368">
    <literal><![CDATA[
      K(x,K(y,z / u)) * (w * K(x,y)) = w * K(x,T(y,(u * K(v5,v6)) / z))
    ]]></literal>
    <justification jstring="[para(18366(a,1),17173(a,1,1))].">
      <j1 rule="para" parents="18366 17173"/>
    </justification>
  </clause>

  <clause id="18369">
    <literal><![CDATA[
      K(x * K(y,z),T(u,z * y)) = K(z \ T(x * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(18271,a,17873,a)].">
      <j1 rule="hyper" parents="18271 17873"/>
    </justification>
  </clause>

  <clause id="18370">
    <literal><![CDATA[
      T(x * K(y,z),K(u,w)) = T(x,K(w,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(269,a,18253,a(flip),b,9249,a(flip))].">
      <j1 rule="hyper" parents="269 18253 9249"/>
    </justification>
  </clause>

  <clause id="18371">
    <literal><![CDATA[
      K(x,y) * ((1 / y) * K(z,u)) = ((1 / y) * K(z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6052(a,1),18253(a,1,1))].">
      <j1 rule="para" parents="6052 18253"/>
    </justification>
  </clause>

  <clause id="18372">
    <literal><![CDATA[
      T(x * K(y,z),K(u,w)) = T(x,K(u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(8184,a,18370,a)].">
      <j1 rule="hyper" parents="8184 18370"/>
    </justification>
  </clause>

  <clause id="18374">
    <literal><![CDATA[
      T(x,K(y,z)) * K(u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x * K(u,w),K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(18370(a,1),8184(a,1))].">
      <j1 rule="para" parents="18370 8184"/>
    </justification>
  </clause>

  <clause id="18375">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,w)) = K(x,y) * T(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(36,a,7683,a(flip),b,18372,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 7683 18372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18376">
    <literal><![CDATA[
      T(K(x,y) \ z,K(u,w)) = K(x,y) \ T(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(36,a,5432,a(flip),b,18372,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 5432 18372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18381">
    <literal><![CDATA[
      T(x \ K(y,z),K(u,w)) = T(x,K(u,w)) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,17705,a(flip),b,18376,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 17705 18376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18382">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) = (x * K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,14453,a(flip),b,18381,a),flip(a)].">
      <j1 rule="hyper" parents="373 14453 18381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18383">
    <literal><![CDATA[
      T(x,K(y,z)) \ K(y,z) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,14537,a(flip),b,18381,a),flip(a)].">
      <j1 rule="hyper" parents="64 14537 18381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18384">
    <literal><![CDATA[
      (x * K(y,z)) \ 1 = K(z,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(14538,a,18382,a),flip(a)].">
      <j1 rule="hyper" parents="14538 18382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18385">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = K(y,x) * ((x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,15285,a,b,18384,a)].">
      <j1 rule="hyper" parents="64 15285 18384"/>
    </justification>
  </clause>

  <clause id="18386">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = K(x,y) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,14593,a,b,18384,a)].">
      <j1 rule="hyper" parents="64 14593 18384"/>
    </justification>
  </clause>

  <clause id="18387">
    <literal><![CDATA[
      K(x,y) * ((z \ 1) \ 1) = (z \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(14444(a,1),18384(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14444 18384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18388">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * (v5 \ 1)))) = K(x,y * (z / (K(u,w) / v5)))
    ]]></literal>
    <justification jstring="[para(18384(a,1),14599(a,1,2,2,2))].">
      <j1 rule="para" parents="18384 14599"/>
    </justification>
  </clause>

  <clause id="18389">
    <literal><![CDATA[
      T(x,y * T(K(z,u * w) * (w \ 1),u)) = T(x,y / (u \ T(w * u,z)))
    ]]></literal>
    <justification jstring="[para(18384(a,1),17716(a,1,2,2,1))].">
      <j1 rule="para" parents="18384 17716"/>
    </justification>
  </clause>

  <clause id="18390">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) / T(T(K(z,y),(x \ 1) \ 1),u) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(18387(a,1),7947(a,1,1))].">
      <j1 rule="para" parents="18387 7947"/>
    </justification>
  </clause>

  <clause id="18391">
    <literal><![CDATA[
      T(x,T(y,(z * T(u,w)) * v5)) = T(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18261,a,b,18262,a)].">
      <j1 rule="hyper" parents="64 18261 18262"/>
    </justification>
  </clause>

  <clause id="18392">
    <literal><![CDATA[
      K(x,T(y,z)) / T(z,u) = (K(u,z) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14726,a,18266,a)].">
      <j1 rule="hyper" parents="14726 18266"/>
    </justification>
  </clause>

  <clause id="18393">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = (K(u,x) / x) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14769,a,b,18392,a)].">
      <j1 rule="hyper" parents="64 14769 18392"/>
    </justification>
  </clause>

  <clause id="18394">
    <literal><![CDATA[
      x * T(T(x,y) \ 1,K(z,u)) = K(x,K(z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5783(a,2),18324(a,1,2,1))].">
      <j1 rule="para" parents="5783 18324"/>
    </justification>
  </clause>

  <clause id="18395">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) / w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,L(w,v5,v6))) = v7
    ]]></literal>
    <justification jstring="[para(18328(a,2),12105(a,1))].">
      <j1 rule="para" parents="18328 12105"/>
    </justification>
  </clause>

  <clause id="18396">
    <literal><![CDATA[
      K(x,K(y,z / (T(u,w) * v5))) = K(x,K(y,(v5 * u) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18347,a(flip),b,18352,a)].">
      <j1 rule="hyper" parents="64 18347 18352"/>
    </justification>
  </clause>

  <clause id="18397">
    <literal><![CDATA[
      K(x,K(y,((z / (z / u)) / w) * v5)) = K(x,K(y,(u / w) * v5))
    ]]></literal>
    <justification jstring="[para(276(a,1),18356(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="276 18356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18398">
    <literal><![CDATA[
      K(T(K(x,y) * z,x * y),u) = K(y \ T(z * y,x),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11253,a,b,18369,a)].">
      <j1 rule="hyper" parents="64 11253 18369"/>
    </justification>
  </clause>

  <clause id="18399">
    <literal><![CDATA[
      (T(x,T(y,z)) / z) \ 1 = K(y,x) * ((x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,16494,a(flip),b,18385,a)].">
      <j1 rule="hyper" parents="64 16494 18385"/>
    </justification>
  </clause>

  <clause id="18400">
    <literal><![CDATA[
      T(x,T(T(y * T(z,u),w),(z * y) * v5)) = T(x,T(T(y * T(z,u),w),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,8746,a(flip),b,18391,a),flip(a)].">
      <j1 rule="hyper" parents="64 8746 18391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18401">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,v5 / ((w \ u) * z)))
    ]]></literal>
    <justification jstring="[para(117(a,1),18396(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="117 18396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18402">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,x * y)) = K(y \ T(z * y,x),u)
    ]]></literal>
    <justification jstring="[hyper(8019,a,18398,a)].">
      <j1 rule="hyper" parents="8019 18398"/>
    </justification>
  </clause>

  <clause id="18403">
    <literal><![CDATA[
      K(x,y * (z * (K(u,w) / v5))) = K(x,y * (z * (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(18007,a,15945,a),flip(a)].">
      <j1 rule="hyper" parents="18007 15945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18404">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * T(u,v5 / w))) = v6
    ]]></literal>
    <justification jstring="[para(7845(a,1),18007(a,1,2,2,2))].">
      <j1 rule="para" parents="7845 18007"/>
    </justification>
  </clause>

  <clause id="18405">
    <literal><![CDATA[
      K(x,y * (K(z,z \ u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(18109(a,2),18010(a,1))].">
      <j1 rule="para" parents="18109 18010"/>
    </justification>
  </clause>

  <clause id="18406">
    <literal><![CDATA[
      K(x,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(w,v5) * (y / K(w,v5))) \ z) = u
    ]]></literal>
    <justification jstring="[para(12(a,1),18023(a,1,2,1))].">
      <j1 rule="para" parents="12 18023"/>
    </justification>
  </clause>

  <clause id="18408">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,z * (y * x))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(18091,a,16384,a)].">
      <j1 rule="hyper" parents="18091 16384"/>
    </justification>
  </clause>

  <clause id="18409">
    <literal><![CDATA[
      K(x,y * (K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (w * K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(6156(a,2),18093(a,1,2,2))].">
      <j1 rule="para" parents="6156 18093"/>
    </justification>
  </clause>

  <clause id="18410">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / T(v5,T(z,u) \ y)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 \ (y / T(z,T(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(17996(a,1),18115(a,1,2,2))].">
      <j1 rule="para" parents="17996 18115"/>
    </justification>
  </clause>

  <clause id="18411">
    <literal><![CDATA[
      K(x,y * (z \ (K(u,w) * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ (v5 * K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(6881(a,1),18175(a,1,2,2,2))].">
      <j1 rule="para" parents="6881 18175"/>
    </justification>
  </clause>

  <clause id="18412">
    <literal><![CDATA[
      K(x,y * (z \ T(u,T(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ T(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(7840(a,1),18175(a,1,2,2,2))].">
      <j1 rule="para" parents="7840 18175"/>
    </justification>
  </clause>

  <clause id="18413">
    <literal><![CDATA[
      K(x,y * (z \ (K(u,w) * (v5 \ 1)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ (v5 \ K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(14535(a,1),18175(a,1,2,2,2))].">
      <j1 rule="para" parents="14535 18175"/>
    </justification>
  </clause>

  <clause id="18414">
    <literal><![CDATA[
      K(x,y * (z / T(u,T(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / T(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(7840(a,1),18177(a,1,2,2,2))].">
      <j1 rule="para" parents="7840 18177"/>
    </justification>
  </clause>

  <clause id="18415">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * (v5 \ 1)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / (v5 \ K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(14535(a,1),18177(a,1,2,2,2))].">
      <j1 rule="para" parents="14535 18177"/>
    </justification>
  </clause>

  <clause id="18416">
    <literal><![CDATA[
      K(x,y \ K(z * (u \ w),u)) = K(x,y \ K(w * z,u))
    ]]></literal>
    <justification jstring="[hyper(18182,a,15157,a)].">
      <j1 rule="hyper" parents="18182 15157"/>
    </justification>
  </clause>

  <clause id="18417">
    <literal><![CDATA[
      K(x,y \ K(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(w * u,z)) = v5
    ]]></literal>
    <justification jstring="[para(16356(a,1),18182(a,1))].">
      <j1 rule="para" parents="16356 18182"/>
    </justification>
  </clause>

  <clause id="18418">
    <literal><![CDATA[
      K(x \ K(y,z * (u * y)),w) = K(x \ K(y,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(18184,a,14020,a)].">
      <j1 rule="hyper" parents="18184 14020"/>
    </justification>
  </clause>

  <clause id="18419">
    <literal><![CDATA[
      K(x \ K(y,z * u),w) = K(x \ K(y,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(18184,a,xx)].">
      <j1 rule="hyper" parents="18184"/>
    </justification>
  </clause>

  <clause id="18420">
    <literal><![CDATA[
      K((x * y) \ T(x,z * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y \ K(x,u * z),w) = v5
    ]]></literal>
    <justification jstring="[para(7628(a,2),18184(a,1))].">
      <j1 rule="para" parents="7628 18184"/>
    </justification>
  </clause>

  <clause id="18421">
    <literal><![CDATA[
      K(x,(y / z) \ K(u,z)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[hyper(18193,a,15839,a)].">
      <j1 rule="hyper" parents="18193 15839"/>
    </justification>
  </clause>

  <clause id="18422">
    <literal><![CDATA[
      K(x,(y / z) \ K(z,u)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[hyper(16357,a,18421,a)].">
      <j1 rule="hyper" parents="16357 18421"/>
    </justification>
  </clause>

  <clause id="18423">
    <literal><![CDATA[
      K(x,(y / z) \ K(z,u \ w)) = K(x,T(z,w / u) / y)
    ]]></literal>
    <justification jstring="[hyper(18181,a,18422,a)].">
      <j1 rule="hyper" parents="18181 18422"/>
    </justification>
  </clause>

  <clause id="18424">
    <literal><![CDATA[
      K(x,(y / (z * K(u,w))) \ K(z,u)) = K(x,T(z * K(u,w),u) / y)
    ]]></literal>
    <justification jstring="[para(8525(a,1),18422(a,1,2,2))].">
      <j1 rule="para" parents="8525 18422"/>
    </justification>
  </clause>

  <clause id="18425">
    <literal><![CDATA[
      K(x,(y / (z * K(u,w))) \ K(z,T(z \ u,w))) = K(x,T(z * K(u,w),z \ u) / y)
    ]]></literal>
    <justification jstring="[para(17363(a,1),18422(a,1,2,2))].">
      <j1 rule="para" parents="17363 18422"/>
    </justification>
  </clause>

  <clause id="18426">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,(u / y) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16931,a(flip),b,18423,a),flip(a)].">
      <j1 rule="hyper" parents="64 16931 18423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18427">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(373,a,18422,a(flip),b,18426,a),flip(a)].">
      <j1 rule="hyper" parents="373 18422 18426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18428">
    <literal><![CDATA[
      K(x,T(y,z \ y) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(18092,a,18427,a)].">
      <j1 rule="hyper" parents="18092 18427"/>
    </justification>
  </clause>

  <clause id="18429">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,T(y,z) / (u * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16086,a,b,18427,a)].">
      <j1 rule="hyper" parents="64 16086 18427"/>
    </justification>
  </clause>

  <clause id="18430">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ y)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(15536(a,1),18428(a,1,2,1))].">
      <j1 rule="para" parents="15536 18428"/>
    </justification>
  </clause>

  <clause id="18431">
    <literal><![CDATA[
      K(x,T(y,z \ (y / u)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(13427(a,2),18430(a,1,2,1))].">
      <j1 rule="para" parents="13427 18430"/>
    </justification>
  </clause>

  <clause id="18432">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,((y / z) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(18119,a,18431,a),flip(a)].">
      <j1 rule="hyper" parents="18119 18431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18433">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w) * v5)) = K(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(18280,a,18243,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18280 18243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18435">
    <literal><![CDATA[
      K(x,K(y / (z \ u),L(w,u,z))) = K(x,K(w,(y * z) / (z * (z \ u))))
    ]]></literal>
    <justification jstring="[hyper(64,a,16479,a(flip),b,18343,a)].">
      <j1 rule="hyper" parents="64 16479 18343"/>
    </justification>
  </clause>

  <clause id="18436">
    <literal><![CDATA[
      K(x,K(T(R(y,K(z,u),w),K(z,u)),L(v5,K(z,u) * w,v6))) = K(x,K(v5,(((K(z,u) * y) * w) * v6) / (v6 * (K(z,u) * w))))
    ]]></literal>
    <justification jstring="[para(8176(a,1),18343(a,1,2,1))].">
      <j1 rule="para" parents="8176 18343"/>
    </justification>
  </clause>

  <clause id="18437">
    <literal><![CDATA[
      K(x,K(y,(z / T(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,v5 * (z / u))) = v6
    ]]></literal>
    <justification jstring="[para(6245(a,1),18358(a,1,2,2,1))].">
      <j1 rule="para" parents="6245 18358"/>
    </justification>
  </clause>

  <clause id="18438">
    <literal><![CDATA[
      K(x,K(y,z * T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = v5
    ]]></literal>
    <justification jstring="[para(6850(a,1),18358(a,1,2,2))].">
      <j1 rule="para" parents="6850 18358"/>
    </justification>
  </clause>

  <clause id="18439">
    <literal><![CDATA[
      K(x,K(y,z * (u * K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * u)) = v6
    ]]></literal>
    <justification jstring="[para(17226(a,1),18358(a,1))].">
      <j1 rule="para" parents="17226 18358"/>
    </justification>
  </clause>

  <clause id="18440">
    <literal><![CDATA[
      K(x,K(y,z * (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(94(a,1),18439(a,1,2,2,2))].">
      <j1 rule="para" parents="94 18439"/>
    </justification>
  </clause>

  <clause id="18441">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),v5)) = T(x,y * T(z \ K(w,u),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,17715,a(flip),b,17975,a),flip(a)].">
      <j1 rule="hyper" parents="64 17715 17975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18443">
    <literal><![CDATA[
      T(x,T(y * K(z,u),w) \ v5) = T(x,T(y \ K(u,z),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,16846,a(flip),b,17997,a),flip(a)].">
      <j1 rule="hyper" parents="64 16846 17997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18445">
    <literal><![CDATA[
      K(x,K(y,z * u) \ ((u / (z \ 1)) \ w)) = K(x,T(u / (z \ 1),y) \ w)
    ]]></literal>
    <justification jstring="[para(14413(a,1),18146(a,1,2,1))].">
      <j1 rule="para" parents="14413 18146"/>
    </justification>
  </clause>

  <clause id="18446">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * K(y,z)),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(18172(a,2),17200(a,1))].">
      <j1 rule="para" parents="18172 17200"/>
    </justification>
  </clause>

  <clause id="18447">
    <literal><![CDATA[
      K(x,(y / z) * (u * K(z \ y,w))) = K(x,T(y / z,w) * u)
    ]]></literal>
    <justification jstring="[hyper(17261,a,18200,a),flip(a)].">
      <j1 rule="hyper" parents="17261 18200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18448">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * (u * K(y \ z,w))) = K(x,T(y \ T(z,y),w) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17882,a(flip),b,18200,a),flip(a)].">
      <j1 rule="hyper" parents="64 17882 18200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18449">
    <literal><![CDATA[
      K(x,y * (z / (u / (u / w)))) = K(x,y * (z / T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18148,a(flip),b,18217,a),flip(a)].">
      <j1 rule="hyper" parents="373 18148 18217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18450">
    <literal><![CDATA[
      T(x,y * (z / (u / (u / w)))) = T(x,y * (z / T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(143,a,18449,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 18449 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18451">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16326,a,b,18449,a)].">
      <j1 rule="hyper" parents="64 16326 18449"/>
    </justification>
  </clause>

  <clause id="18452">
    <literal><![CDATA[
      T(x,T(y,z / T(u,w)) * (z / T(u,w))) = T(x,(z / (w / (w / u))) * y)
    ]]></literal>
    <justification jstring="[hyper(15923,a,18450,a),flip(a)].">
      <j1 rule="hyper" parents="15923 18450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18453">
    <literal><![CDATA[
      K(x,y * (z / ((u \ w) \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(116(a,1),18451(a,1,2,2,2))].">
      <j1 rule="para" parents="116 18451"/>
    </justification>
  </clause>

  <clause id="18454">
    <literal><![CDATA[
      K(x,y * (z * (u * (w / u)))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18149,a(flip),b,18218,a),flip(a)].">
      <j1 rule="hyper" parents="64 18149 18218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18455">
    <literal><![CDATA[
      T(x,y * (z * (u * K(w,z)))) = T(x,y * (T(z,w) * u))
    ]]></literal>
    <justification jstring="[para(8194(a,1),18229(a,1,2,2,2))].">
      <j1 rule="para" parents="8194 18229"/>
    </justification>
  </clause>

  <clause id="18456">
    <literal><![CDATA[
      T(x,y * ((1 / z) * (u * K(w,z \ 1)))) = T(x,y * (T(1 / z,w) * u))
    ]]></literal>
    <justification jstring="[para(6041(a,1),18455(a,1,2,2,2,2))].">
      <j1 rule="para" parents="6041 18455"/>
    </justification>
  </clause>

  <clause id="18457">
    <literal><![CDATA[
      K(x,y * T(z / T(u,w),u)) = K(x,y * ((w * (u / w)) \ z))
    ]]></literal>
    <justification jstring="[para(7184(a,2),18232(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7184 18232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18458">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,T(K(y,z) * u,w)) * K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,13326,a,b,18337,a)].">
      <j1 rule="hyper" parents="373 13326 18337"/>
    </justification>
  </clause>

  <clause id="18460">
    <literal><![CDATA[
      K(x,K(y,((z \ (z * ((1 / z) * u))) * w) * v5)) = K(x,K(y,(L(u / z,z,1 / z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(1209(a,1),18357(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="1209 18357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18461">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,z / (v5 * v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,9021,a,b,18367,a),flip(a)].">
      <j1 rule="hyper" parents="373 9021 18367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18462">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(u,x) / (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(14995,a,18371,a),flip(a)].">
      <j1 rule="hyper" parents="14995 18371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18463">
    <literal><![CDATA[
      K(x,y) / (K(z,u) * y) = (K(x,y) / y) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,18393,a(flip),b,18462,a),flip(a)].">
      <j1 rule="hyper" parents="64 18393 18462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18464">
    <literal><![CDATA[
      K(x,L(K(y,z),K(u,w) / w,v5)) * K(K(y,z),x) = a(v5,K(u,w) / (K(z,y) * w),K(K(y,z),x))
    ]]></literal>
    <justification jstring="[para(18463(a,2),10420(a,2,2))].">
      <j1 rule="para" parents="18463 10420"/>
    </justification>
  </clause>

  <clause id="18465">
    <literal><![CDATA[
      K(x,K(y,z * ((u / (u / w)) / v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(17389,a,18397,a)].">
      <j1 rule="hyper" parents="17389 18397"/>
    </justification>
  </clause>

  <clause id="18466">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (w \ K(z,z \ u))))
    ]]></literal>
    <justification jstring="[hyper(64,a,14399,a,b,18403,a)].">
      <j1 rule="hyper" parents="64 14399 18403"/>
    </justification>
  </clause>

  <clause id="18467">
    <literal><![CDATA[
      T(x,y * T(K(z,u) / w,v5)) = T(x,y * T(w \ K(z,u),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,17719,a(flip),b,18441,a)].">
      <j1 rule="hyper" parents="64 17719 18441"/>
    </justification>
  </clause>

  <clause id="18468">
    <literal><![CDATA[
      K(x,y * ((z * (u / z)) \ w)) = K(x,y * (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17965,a(flip),b,18457,a),flip(a)].">
      <j1 rule="hyper" parents="64 17965 18457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18469">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) = K(x,K(y,z / (v6 * u)))
    ]]></literal>
    <justification jstring="[hyper(18364,a,18461,a)].">
      <j1 rule="hyper" parents="18364 18461"/>
    </justification>
  </clause>

  <clause id="18470">
    <literal><![CDATA[
      K(x,K(y,((z \ u) / w) * v5)) = K(x,K(y,v5 * ((u / z) / w)))
    ]]></literal>
    <justification jstring="[para(79(a,1),18465(a,1,2,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 18465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18471">
    <literal><![CDATA[
      K(x,K(y,(z / u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,((v6 / (v6 / z)) / u) * w)) = v5
    ]]></literal>
    <justification jstring="[para(18465(a,1),17389(a,1))].">
      <j1 rule="para" parents="18465 17389"/>
    </justification>
  </clause>

  <clause id="18472">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / (u * v6))) = v7
    ]]></literal>
    <justification jstring="[para(18469(a,2),18364(a,1))].">
      <j1 rule="para" parents="18469 18364"/>
    </justification>
  </clause>

  <clause id="18473">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ T(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(18107(a,1),18097(a,1))].">
      <j1 rule="para" parents="18107 18097"/>
    </justification>
  </clause>

  <clause id="18474">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w))) = K(x,y * (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(18195,a,15938,a)].">
      <j1 rule="hyper" parents="18195 15938"/>
    </justification>
  </clause>

  <clause id="18475">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * (w / u))) = K(x,y * (T(u \ w,u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15946,a(flip),b,18474,a)].">
      <j1 rule="hyper" parents="64 15946 18474"/>
    </justification>
  </clause>

  <clause id="18476">
    <literal><![CDATA[
      K(x,y * (T(z,T(u \ w,u)) * v5)) = K(x,y * (T(v5,z) * T(z,w / u)))
    ]]></literal>
    <justification jstring="[para(8241(a,1),18474(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8241 18474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18477">
    <literal><![CDATA[
      K(x,K((1 / y) / z,L(z / u,u,y))) = K(x,K(y * z,z / u))
    ]]></literal>
    <justification jstring="[hyper(17387,a,18330,a)].">
      <j1 rule="hyper" parents="17387 18330"/>
    </justification>
  </clause>

  <clause id="18479">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ T(z / u,z))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(18412,a,16332,a)].">
      <j1 rule="hyper" parents="18412 16332"/>
    </justification>
  </clause>

  <clause id="18480">
    <literal><![CDATA[
      K(x,y * (z / T(u,T(w,v5)))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(18414,a,xx),flip(a)].">
      <j1 rule="hyper" parents="18414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18481">
    <literal><![CDATA[
      K(x * (y / T(z,T(u,w))),v5) = K(v5,x * (y / T(z,u))) \ 1
    ]]></literal>
    <justification jstring="[para(18480(a,1),6092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18480 6092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18482">
    <literal><![CDATA[
      K(x * (y / T(z,T(u,w))),v5) = K(x * (y / T(z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,6092,a(flip),b,18481,a),flip(a)].">
      <j1 rule="hyper" parents="373 6092 18481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18483">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w / u)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ T(w,u))) = v5
    ]]></literal>
    <justification jstring="[para(16691(a,2),18473(a,1))].">
      <j1 rule="para" parents="16691 18473"/>
    </justification>
  </clause>

  <clause id="18484">
    <literal><![CDATA[
      K(x,K((y \ z) * u,u / y)) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15589,a(flip),b,18477,a),flip(a)].">
      <j1 rule="hyper" parents="64 15589 18477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18485">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,(1 / (z \ u)) / y))
    ]]></literal>
    <justification jstring="[hyper(8437,a,18484,a)].">
      <j1 rule="hyper" parents="8437 18484"/>
    </justification>
  </clause>

  <clause id="18486">
    <literal><![CDATA[
      K(x,K(y,(1 / (z \ y)) / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17391,a(flip),b,18485,a),flip(a)].">
      <j1 rule="hyper" parents="64 17391 18485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18487">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u / (y / z)))
    ]]></literal>
    <justification jstring="[para(82(a,1),18486(a,1,2,2,1,2))].">
      <j1 rule="para" parents="82 18486"/>
    </justification>
  </clause>

  <clause id="18488">
    <literal><![CDATA[
      K(x,K(y,z / (y / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12577,a(flip),b,18487,a),flip(a)].">
      <j1 rule="hyper" parents="64 12577 18487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18489">
    <literal><![CDATA[
      K(x,K(y,z * (y / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18308,a(flip),b,18488,a),flip(a)].">
      <j1 rule="hyper" parents="64 18308 18488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18490">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(y,K(x,z / u))
    ]]></literal>
    <justification jstring="[hyper(8436,a,18489,a)].">
      <j1 rule="hyper" parents="8436 18489"/>
    </justification>
  </clause>

  <clause id="18491">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(373,a,8108,a,b,18490,a),flip(a)].">
      <j1 rule="hyper" parents="373 8108 18490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18492">
    <literal><![CDATA[
      K(x,y * (z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u \ T(z,u))) = w
    ]]></literal>
    <justification jstring="[para(9(a,1),18483(a,1,2,2))].">
      <j1 rule="para" parents="9 18483"/>
    </justification>
  </clause>

  <clause id="18494">
    <literal><![CDATA[
      T(x,y * T(z / T(T(u,w),z),u)) = T(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,16327,a(flip),b,18064,a),flip(a)].">
      <j1 rule="hyper" parents="373 16327 18064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18495">
    <literal><![CDATA[
      T(x,y * (T(z,u) \ T(w,z))) = T(x,y * (w / T(z,u)))
    ]]></literal>
    <justification jstring="[para(8896(a,1),18494(a,1,2,2))].">
      <j1 rule="para" parents="8896 18494"/>
    </justification>
  </clause>

  <clause id="18496">
    <literal><![CDATA[
      K(x,y * T(z * K(u,K(w,v5)),u)) = K(x,y * T(z,K(v5,w) * u))
    ]]></literal>
    <justification jstring="[para(6853(a,2),18129(a,1,2,2))].">
      <j1 rule="para" parents="6853 18129"/>
    </justification>
  </clause>

  <clause id="18497">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(y * (z \ u),u) * w)
    ]]></literal>
    <justification jstring="[para(17370(a,1),18132(a,2,2,1))].">
      <j1 rule="para" parents="17370 18132"/>
    </justification>
  </clause>

  <clause id="18498">
    <literal><![CDATA[
      K(x,y * (z * (u * (K(w,K(v5,v6)) * v7)))) = K(x,y * (z * (u * v7)))
    ]]></literal>
    <justification jstring="[para(6576(a,1),18203(a,1,2,2,2,2))].">
      <j1 rule="para" parents="6576 18203"/>
    </justification>
  </clause>

  <clause id="18499">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(((z / y) / z) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13373,a(flip),b,18206,a),flip(a)].">
      <j1 rule="hyper" parents="64 13373 18206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18500">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(12(a,1),18499(a,2,2,1))].">
      <j1 rule="para" parents="12 18499"/>
    </justification>
  </clause>

  <clause id="18502">
    <literal><![CDATA[
      K(T(T(x * y,z),x) / u,w) = K(T(y * x,T(z,y)) / u,w)
    ]]></literal>
    <justification jstring="[para(15266(a,1),18212(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15266 18212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18503">
    <literal><![CDATA[
      K(T(T(x * y,z),x) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(T(y * x,z) / u,w) = v5
    ]]></literal>
    <justification jstring="[para(18502(a,2),18105(a,1))].">
      <j1 rule="para" parents="18502 18105"/>
    </justification>
  </clause>

  <clause id="18504">
    <literal><![CDATA[
      K(T(x * y,y) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(18503,a,16889,a)].">
      <j1 rule="hyper" parents="18503 16889"/>
    </justification>
  </clause>

  <clause id="18505">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),18504(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 18504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18506">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = (w * K((z * y) / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(18504(a,1),6882(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18504 6882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18507">
    <literal><![CDATA[
      K(T((x * y) * (K(y,x) / y),K(y,x) / y) / z,u) = K(L(x,y,y \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(14922(a,1),18504(a,2,1,1))].">
      <j1 rule="para" parents="14922 18504"/>
    </justification>
  </clause>

  <clause id="18508">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(z,K(y,u)) * K(z \ T(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,17241,a,b,18505,a),flip(a)].">
      <j1 rule="hyper" parents="373 17241 18505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18509">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6882,a(flip),b,18506,a),flip(a)].">
      <j1 rule="hyper" parents="373 6882 18506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18510">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) / u) = w
    ]]></literal>
    <justification jstring="[para(18506(a,2),6899(a,1))].">
      <j1 rule="para" parents="18506 6899"/>
    </justification>
  </clause>

  <clause id="18511">
    <literal><![CDATA[
      K(x,(y * (z / y)) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(12(a,1),18509(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 18509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18512">
    <literal><![CDATA[
      K(x,(y * ((y * z) / y)) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(373,a,13373,a(flip),b,18511,a),flip(a)].">
      <j1 rule="hyper" parents="373 13373 18511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18513">
    <literal><![CDATA[
      K(x,T(y,z) / (u * (y / z))) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[para(15242(a,1),18511(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15242 18511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18514">
    <literal><![CDATA[
      K(x,(T(y,z) * z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(256(a,1),18512(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="256 18512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18515">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(15617,a,18514,a)].">
      <j1 rule="hyper" parents="15617 18514"/>
    </justification>
  </clause>

  <clause id="18516">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,y,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(12122,a,18515,a)].">
      <j1 rule="hyper" parents="12122 18515"/>
    </justification>
  </clause>

  <clause id="18517">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18429,a,b,18513,a)].">
      <j1 rule="hyper" parents="64 18429 18513"/>
    </justification>
  </clause>

  <clause id="18518">
    <literal><![CDATA[
      K(x \ (y * (z / y)),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(17805,a,18508,a)].">
      <j1 rule="hyper" parents="17805 18508"/>
    </justification>
  </clause>

  <clause id="18519">
    <literal><![CDATA[
      K(x \ T(y * z,z),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(11(a,1),18518(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 18518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18520">
    <literal><![CDATA[
      K(x,y \ T(z * u,u)) * a(w,v5,K(y \ (u * z),x)) = K(x,L(y \ T(z * u,u),v5,w))
    ]]></literal>
    <justification jstring="[para(18519(a,1),12069(a,1,2,3))].">
      <j1 rule="para" parents="18519 12069"/>
    </justification>
  </clause>

  <clause id="18521">
    <literal><![CDATA[
      K(x,L(T(y,z * (u / w)),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z * (w \ u)),v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(18346(a,1),12117(a,1))].">
      <j1 rule="para" parents="18346 12117"/>
    </justification>
  </clause>

  <clause id="18522">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * u,w)) = K(x,T(K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(36,a,18337,a,b,18458,a(flip))].">
      <j1 rule="hyper" parents="36 18337 18458"/>
    </justification>
  </clause>

  <clause id="18523">
    <literal><![CDATA[
      T(x,T(K(y,y \ z) * u,w)) = T(x,T(K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(143,a,18522,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 18522 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18524">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w)) = K(x,T(K(z,u) * (y / u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17601,a(flip),b,18522,a)].">
      <j1 rule="hyper" parents="64 17601 18522"/>
    </justification>
  </clause>

  <clause id="18525">
    <literal><![CDATA[
      T(x,T(K(y \ z,y) * u,w)) = T(x,T(K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18164,a,b,18523,a)].">
      <j1 rule="hyper" parents="64 18164 18523"/>
    </justification>
  </clause>

  <clause id="18526">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w)) = K(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(373,a,17600,a(flip),b,18524,a),flip(a)].">
      <j1 rule="hyper" parents="373 17600 18524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18527">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z * u)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17067,a(flip),b,18526,a),flip(a)].">
      <j1 rule="hyper" parents="64 17067 18526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18528">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ (u \ z))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13499,a(flip),b,18479,a)].">
      <j1 rule="hyper" parents="64 13499 18479"/>
    </justification>
  </clause>

  <clause id="18529">
    <literal><![CDATA[
      K(x,y * ((z \ u) / u)) = K(x,y * (u \ (u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15858,a(flip),b,18528,a)].">
      <j1 rule="hyper" parents="64 15858 18528"/>
    </justification>
  </clause>

  <clause id="18530">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w) * v5)) = K(x,y * T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(18179,a,18496,a),flip(a)].">
      <j1 rule="hyper" parents="18179 18496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18531">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(18496(a,1),18179(a,1))].">
      <j1 rule="para" parents="18496 18179"/>
    </justification>
  </clause>

  <clause id="18533">
    <literal><![CDATA[
      K(x,y * T(z,u * K(w,v5))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17966,a,b,18530,a)].">
      <j1 rule="hyper" parents="64 17966 18530"/>
    </justification>
  </clause>

  <clause id="18534">
    <literal><![CDATA[
      K(x,y * T(z,T(K(u,w) * v5,v6))) = K(x,y * T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,17964,a,b,18530,a)].">
      <j1 rule="hyper" parents="64 17964 18530"/>
    </justification>
  </clause>

  <clause id="18535">
    <literal><![CDATA[
      K(x,y * T((K(z,u) * w) \ v5,w)) = K(x,y * (v5 / (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15852,a(flip),b,18530,a),flip(a)].">
      <j1 rule="hyper" parents="64 15852 18530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18536">
    <literal><![CDATA[
      K(x,y * T(z,u * (w * v5))) = K(x,y * T(z,u * (v5 * w)))
    ]]></literal>
    <justification jstring="[para(7591(a,1),18533(a,1,2,2,2))].">
      <j1 rule="para" parents="7591 18533"/>
    </justification>
  </clause>

  <clause id="18537">
    <literal><![CDATA[
      K(x,y * T(z,u * T(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u * w)) = v6
    ]]></literal>
    <justification jstring="[para(6367(a,1),18531(a,1,2,2,2))].">
      <j1 rule="para" parents="6367 18531"/>
    </justification>
  </clause>

  <clause id="18538">
    <literal><![CDATA[
      K(x,y * T(z,u * K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = v6
    ]]></literal>
    <justification jstring="[para(6823(a,1),18531(a,1,2,2,2))].">
      <j1 rule="para" parents="6823 18531"/>
    </justification>
  </clause>

  <clause id="18539">
    <literal><![CDATA[
      K(x,y * T(z,u \ (w / v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u \ (v5 \ w))) = v6
    ]]></literal>
    <justification jstring="[para(15028(a,1),18538(a,1,2,2,2))].">
      <j1 rule="para" parents="15028 18538"/>
    </justification>
  </clause>

  <clause id="18540">
    <literal><![CDATA[
      K(T(x,y),z * T(u,z * x)) = K(T(x,y),u * z)
    ]]></literal>
    <justification jstring="[hyper(18537,a,18122,a)].">
      <j1 rule="hyper" parents="18537 18122"/>
    </justification>
  </clause>

  <clause id="18541">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,18133,a(flip),b,18497,a),flip(a)].">
      <j1 rule="hyper" parents="373 18133 18497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18542">
    <literal><![CDATA[
      K(x,y \ (z * (T(u,z) * K(w,v5)))) = K(x,y \ ((K(w,v5) * u) * z))
    ]]></literal>
    <justification jstring="[para(12077(a,1),17958(a,1,2,2))].">
      <j1 rule="para" parents="12077 17958"/>
    </justification>
  </clause>

  <clause id="18543">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * K(u,w))) / v5) = K(x,((K(u,w) * z) * y) / v5)
    ]]></literal>
    <justification jstring="[para(12077(a,1),17961(a,1,2,1))].">
      <j1 rule="para" parents="12077 17961"/>
    </justification>
  </clause>

  <clause id="18544">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * K(u,w))) * v5) = K(x,((K(u,w) * z) * y) * v5)
    ]]></literal>
    <justification jstring="[para(12077(a,1),17971(a,1,2,1))].">
      <j1 rule="para" parents="12077 17971"/>
    </justification>
  </clause>

  <clause id="18545">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u)) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(14024(a,1),18162(a,1,2,1))].">
      <j1 rule="para" parents="14024 18162"/>
    </justification>
  </clause>

  <clause id="18546">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[hyper(13570,a,18545,a)].">
      <j1 rule="hyper" parents="13570 18545"/>
    </justification>
  </clause>

  <clause id="18547">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[para(10219(a,1),18546(a,2,2))].">
      <j1 rule="para" parents="10219 18546"/>
    </justification>
  </clause>

  <clause id="18549">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T(x * y,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[para(6920(a,1),17995(a,2,1))].">
      <j1 rule="para" parents="6920 17995"/>
    </justification>
  </clause>

  <clause id="18550">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,9054,a,b,18549,a),flip(a)].">
      <j1 rule="hyper" parents="373 9054 18549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18552">
    <literal><![CDATA[
      K(x,((K(y,z) * u) / (y \ z)) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15847,a(flip),b,18117,a)].">
      <j1 rule="hyper" parents="64 15847 18117"/>
    </justification>
  </clause>

  <clause id="18553">
    <literal><![CDATA[
      K(x,(K(y,z) * (u / (y \ z))) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[para(13005(a,1),18552(a,1,2,1))].">
      <j1 rule="para" parents="13005 18552"/>
    </justification>
  </clause>

  <clause id="18555">
    <literal><![CDATA[
      K(x,y * T(z \ (u * K(w,v5)),u)) = K(x,y * ((K(w,v5) * u) / z))
    ]]></literal>
    <justification jstring="[para(22(a,2),18128(a,1,2,2))].">
      <j1 rule="para" parents="22 18128"/>
    </justification>
  </clause>

  <clause id="18556">
    <literal><![CDATA[
      T(x,y * T(T(T(z,u),w) \ v5,z)) = T(x,y * (v5 / T(T(z,w),u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17990,a(flip),b,18208,a)].">
      <j1 rule="hyper" parents="64 17990 18208"/>
    </justification>
  </clause>

  <clause id="18558">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(w,L(y,y,v7)))
    ]]></literal>
    <justification jstring="[hyper(18395,a,18363,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18395 18363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18559">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,8155,a(flip),b,18558,a),flip(a)].">
      <j1 rule="hyper" parents="373 8155 18558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18560">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w),v5))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(18332,a,18559,a)].">
      <j1 rule="hyper" parents="18332 18559"/>
    </justification>
  </clause>

  <clause id="18562">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) / v5)) = K(x,T(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(17598,a,18368,a),flip(a)].">
      <j1 rule="hyper" parents="17598 18368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18563">
    <literal><![CDATA[
      K(x,T(y,(z / T(u,w)) / v5)) = K(x,T(y,v5 / (z / u)))
    ]]></literal>
    <justification jstring="[para(6245(a,1),18562(a,1,2,2,1))].">
      <j1 rule="para" parents="6245 18562"/>
    </justification>
  </clause>

  <clause id="18564">
    <literal><![CDATA[
      K(x,T(y,z / (u / T(w,v5)))) = K(x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(11221,a,18563,a)].">
      <j1 rule="hyper" parents="11221 18563"/>
    </justification>
  </clause>

  <clause id="18565">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),w / (v5 / T(v6,v7)))) = K(x,T(y,w / (v5 / v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,9210,a(flip),b,18564,a),flip(a)].">
      <j1 rule="hyper" parents="373 9210 18564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18566">
    <literal><![CDATA[
      K(x,T(y,z / (u / (w / v5)))) = K(x,T(y,z / (u / (v5 \ w))))
    ]]></literal>
    <justification jstring="[para(117(a,1),18564(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="117 18564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18567">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = K(1 / x,T(y,z / (u / w))) / x
    ]]></literal>
    <justification jstring="[para(18564(a,1),5933(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18564 5933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18568">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,z * w),w)) = T(x,y / (w \ T(z * w,u)))
    ]]></literal>
    <justification jstring="[para(14666(a,1),18389(a,1,2,2,1))].">
      <j1 rule="para" parents="14666 18389"/>
    </justification>
  </clause>

  <clause id="18569">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),w),T(z,y) * v5)) = T(x,T(T(y * T(y \ z,u),w),v5))
    ]]></literal>
    <justification jstring="[para(13493(a,1),18400(a,1,2))].">
      <j1 rule="para" parents="13493 18400"/>
    </justification>
  </clause>

  <clause id="18570">
    <literal><![CDATA[
      K(x,(y / z) * (u * K(z \ y,w))) = K(x,T(z \ T(y,z),w) * u)
    ]]></literal>
    <justification jstring="[hyper(16364,a,18448,a)].">
      <j1 rule="hyper" parents="16364 18448"/>
    </justification>
  </clause>

  <clause id="18571">
    <literal><![CDATA[
      K(x,T(y \ T(z,y),u) * w) = K(x,T(z / y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,18447,a(flip),b,18570,a),flip(a)].">
      <j1 rule="hyper" parents="64 18447 18570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18572">
    <literal><![CDATA[
      K(x,T(L(y \ z,y,z \ u) \ T(u,L(y \ z,y,z \ u)),w) * v5) = K(x,T((u / z) * y,w) * v5)
    ]]></literal>
    <justification jstring="[para(15003(a,1),18571(a,2,2,1,1))].">
      <j1 rule="para" parents="15003 18571"/>
    </justification>
  </clause>

  <clause id="18573">
    <literal><![CDATA[
      T(x,(y / (z / (z / u))) * w) = T(x,(y / T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(11200,a,18452,a),flip(a)].">
      <j1 rule="hyper" parents="11200 18452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18574">
    <literal><![CDATA[
      T(x,(T(y,y \ z) / T(z / y,1)) * u) = T(x,((y / z) * y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13822,a(flip),b,18573,a),flip(a)].">
      <j1 rule="hyper" parents="64 13822 18573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18575">
    <literal><![CDATA[
      T(x,(T(y,y \ z) / (z / y)) * u) = T(x,((y / z) * y) * u)
    ]]></literal>
    <justification jstring="[para(372(a,1),18574(a,1,2,1,2))].">
      <j1 rule="para" parents="372 18574"/>
    </justification>
  </clause>

  <clause id="18576">
    <literal><![CDATA[
      T(x,((y / z) * y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,((z / y) \ y) * u) = w
    ]]></literal>
    <justification jstring="[para(18575(a,1),17812(a,1))].">
      <j1 rule="para" parents="18575 17812"/>
    </justification>
  </clause>

  <clause id="18577">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * (u * K(w,z \ 1)))) = T(x,y * (T(1 / z,w) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5301,a(flip),b,18456,a)].">
      <j1 rule="hyper" parents="64 5301 18456"/>
    </justification>
  </clause>

  <clause id="18578">
    <literal><![CDATA[
      T(x,y * (T(1 / z,u) * w)) = T(x,y * (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18455,a(flip),b,18577,a),flip(a)].">
      <j1 rule="hyper" parents="64 18455 18577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18580">
    <literal><![CDATA[
      K(x,y * (T(z * u,x) \ K(w,L(v5,u,z)))) = K(x,y / (z * (u * K(v5,w))))
    ]]></literal>
    <justification jstring="[para(12093(a,1),18154(a,1,2,2,2))].">
      <j1 rule="para" parents="12093 18154"/>
    </justification>
  </clause>

  <clause id="18581">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u) \ w)),(T(z,v5) \ w) * y) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (T(z,v5) \ w)) = v6
    ]]></literal>
    <justification jstring="[para(18315(a,2),18339(a,1,1))].">
      <j1 rule="para" parents="18315 18339"/>
    </justification>
  </clause>

  <clause id="18582">
    <literal><![CDATA[
      T(T(x,y \ K(z,u)),K(y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ K(z,u),w)) = v5
    ]]></literal>
    <justification jstring="[para(18312(a,1),18361(a,1))].">
      <j1 rule="para" parents="18312 18361"/>
    </justification>
  </clause>

  <clause id="18583">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) / v5))) = K(x,y * (z / (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(18415,a,18388,a),flip(a)].">
      <j1 rule="hyper" parents="18415 18388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18584">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ L(T(K(y,z) / u,(K(y,z) / u) \ 1),w,v5)) = K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z))))
    ]]></literal>
    <justification jstring="[para(5630(a,2),18583(a,1,2))].">
      <j1 rule="para" parents="5630 18583"/>
    </justification>
  </clause>

  <clause id="18585">
    <literal><![CDATA[
      K(x,L(T(y \ z,y * (z \ u)),y,z \ u)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(18521,a,17841,a)].">
      <j1 rule="hyper" parents="18521 17841"/>
    </justification>
  </clause>

  <clause id="18586">
    <literal><![CDATA[
      K(x,L(T(y \ z,z * (y \ u)),y,y \ u)) = K(x,((u / y) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(18521,a,17840,a)].">
      <j1 rule="hyper" parents="18521 17840"/>
    </justification>
  </clause>

  <clause id="18587">
    <literal><![CDATA[
      K(x,T((y * (y \ z)) \ (u * (y \ z)),y)) = K(x,((z / y) * u) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,15585,a(flip),b,18586,a)].">
      <j1 rule="hyper" parents="64 15585 18586"/>
    </justification>
  </clause>

  <clause id="18588">
    <literal><![CDATA[
      K(x,T(y \ (z * (u \ y)),u)) = K(x,((y / u) * z) / y)
    ]]></literal>
    <justification jstring="[para(10(a,1),18587(a,1,2,1,1))].">
      <j1 rule="para" parents="10 18587"/>
    </justification>
  </clause>

  <clause id="18590">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),z \ w)) = T(x,K(w,z) * (y / (z * K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(16812,a,18080,a),flip(a)].">
      <j1 rule="hyper" parents="16812 18080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18592">
    <literal><![CDATA[
      T(x,T(K(y,z \ u) * (u / (u / z)),w)) = T(x,(u * K(z,w)) / T(u / z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,18140,a,b,18136,a)].">
      <j1 rule="hyper" parents="64 18140 18136"/>
    </justification>
  </clause>

  <clause id="18593">
    <literal><![CDATA[
      K(x,T(L(y,z,y) * u,w) / v5) = K(x,(y * u) * (v5 \ K(y * u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13393,a(flip),b,18160,a),flip(a)].">
      <j1 rule="hyper" parents="64 13393 18160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18595">
    <literal><![CDATA[
      K(x,T(L(y,z,y) * u,w) / v5) = K(x,T(y * u,w) / v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,18157,a(flip),b,18593,a),flip(a)].">
      <j1 rule="hyper" parents="373 18157 18593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18596">
    <literal><![CDATA[
      K(x,(y * L(z,u,z)) / w) = K(x,T(z * y,z) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13458,a(flip),b,18595,a)].">
      <j1 rule="hyper" parents="64 13458 18595"/>
    </justification>
  </clause>

  <clause id="18598">
    <literal><![CDATA[
      K(x,(y * L(z,u,z)) / w) = K(x,(y * z) / w)
    ]]></literal>
    <justification jstring="[hyper(373,a,13373,a(flip),b,18596,a),flip(a)].">
      <j1 rule="hyper" parents="373 13373 18596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18599">
    <literal><![CDATA[
      K(x,(y * T(z,z * u)) / w) = K(x,(y * T(z,u)) / w)
    ]]></literal>
    <justification jstring="[para(4732(a,1),18598(a,1,2,1,2))].">
      <j1 rule="para" parents="4732 18598"/>
    </justification>
  </clause>

  <clause id="18600">
    <literal><![CDATA[
      K(x,(y * T(z,z \ u)) / w) = K(x,(y * T(z,u)) / w)
    ]]></literal>
    <justification jstring="[para(10(a,1),18599(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 18599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18601">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,u)) = K(x,z \ ((y \ (z * (u \ y))) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16931,a(flip),b,18180,a)].">
      <j1 rule="hyper" parents="64 16931 18180"/>
    </justification>
  </clause>

  <clause id="18602">
    <literal><![CDATA[
      K(x,(y \ (z * (u \ y))) \ K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T((z * (u \ y)) \ y,z)) = w
    ]]></literal>
    <justification jstring="[para(18601(a,2),9244(a,1))].">
      <j1 rule="para" parents="18601 9244"/>
    </justification>
  </clause>

  <clause id="18604">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / T(u / y,w)) = T(x,T(y \ u,w) \ (K(y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16382,a(flip),b,18198,a)].">
      <j1 rule="hyper" parents="64 16382 18198"/>
    </justification>
  </clause>

  <clause id="18605">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * (T(z,u) / w))
    ]]></literal>
    <justification jstring="[para(14825(a,1),18215(a,2,2,2))].">
      <j1 rule="para" parents="14825 18215"/>
    </justification>
  </clause>

  <clause id="18606">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) / w)) = K(x,y * (T(z,u) / w))
    ]]></literal>
    <justification jstring="[hyper(18006,a,18605,a)].">
      <j1 rule="hyper" parents="18006 18605"/>
    </justification>
  </clause>

  <clause id="18607">
    <literal><![CDATA[
      K(x,T(y,T(z,u) / w) * (T(z,u) / w)) = K(x,(((z \ u) \ u) / w) * y)
    ]]></literal>
    <justification jstring="[hyper(13559,a,18606,a),flip(a)].">
      <j1 rule="hyper" parents="13559 18606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18609">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) / u) * w) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(11231,a,18607,a),flip(a)].">
      <j1 rule="hyper" parents="11231 18607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18610">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = v5 \ T(x * T(v5,K(w,u)),K(w,u))
    ]]></literal>
    <justification jstring="[para(18290(a,1),18318(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18290 18318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18611">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,16796,a(flip),b,18610,a),flip(a)].">
      <j1 rule="hyper" parents="373 16796 18610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18612">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(18610(a,2),16806(a,1))].">
      <j1 rule="para" parents="18610 16806"/>
    </justification>
  </clause>

  <clause id="18614">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w) * v5)) = T(x,K(v5,z) * y)
    ]]></literal>
    <justification jstring="[hyper(17510,a,18611,a)].">
      <j1 rule="hyper" parents="17510 18611"/>
    </justification>
  </clause>

  <clause id="18615">
    <literal><![CDATA[
      T(x,y * K(K(z,u) * w,v5)) = T(x,K(w,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(17171,a,18611,a)].">
      <j1 rule="hyper" parents="17171 18611"/>
    </justification>
  </clause>

  <clause id="18616">
    <literal><![CDATA[
      T(x,K(y,z) * ((K(u,w) * y) \ v5)) = T(x,T(K(u,w) * y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(15754,a,18611,a),flip(a)].">
      <j1 rule="hyper" parents="15754 18611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18618">
    <literal><![CDATA[
      T(x * K(y,z),K(x,u) * w) = T(x * K(y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17425,a(flip),b,18611,a),flip(a)].">
      <j1 rule="hyper" parents="64 17425 18611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18619">
    <literal><![CDATA[
      T(x,K(T(y,z) \ u,w) * v5) = T(x,K(y \ u,w) * v5)
    ]]></literal>
    <justification jstring="[para(6075(a,1),18611(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6075 18611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18620">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (K(w,v5) * y))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,u * T(K(w,v5) * y,z)) = v6
    ]]></literal>
    <justification jstring="[para(18611(a,1),17269(a,1))].">
      <j1 rule="para" parents="18611 17269"/>
    </justification>
  </clause>

  <clause id="18621">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = (K(v6 * K(v7,v8),v9) * x) \ (K(K(v7,v8) * v6,v9) * T(x,K(u,w) * v5))
    ]]></literal>
    <justification jstring="[para(18611(a,1),17611(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18611 17611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18622">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w) * v5)) = T(x,y * K(v5,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17165,a(flip),b,18614,a),flip(a)].">
      <j1 rule="hyper" parents="373 17165 18614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18623">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w) * v5)) = T(x,K(u * v5,z) * y)
    ]]></literal>
    <justification jstring="[para(5755(a,1),18614(a,1,2,2,2))].">
      <j1 rule="para" parents="5755 18614"/>
    </justification>
  </clause>

  <clause id="18624">
    <literal><![CDATA[
      x * T(x \ R(x,y,K(K(z,u) * w,v5)),K(w,v5) * y) = R(x,y,K(K(z,u) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(145,a,18615,a(flip),b,15507,a(flip))].">
      <j1 rule="hyper" parents="145 18615 15507"/>
    </justification>
  </clause>

  <clause id="18626">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,K(u \ v5,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(17659,a,18619,a)].">
      <j1 rule="hyper" parents="17659 18619"/>
    </justification>
  </clause>

  <clause id="18627">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,K(v5 * u,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17890,a(flip),b,18626,a),flip(a)].">
      <j1 rule="hyper" parents="373 17890 18626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18628">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,y \ T(z,v5 * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17349,a(flip),b,18627,a),flip(a)].">
      <j1 rule="hyper" parents="373 17349 18627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18629">
    <literal><![CDATA[
      T(x,y \ T(z,u \ w)) = T(x,y \ T(z,w * u))
    ]]></literal>
    <justification jstring="[para(114(a,1),18628(a,1,2,2,2,1))].">
      <j1 rule="para" parents="114 18628"/>
    </justification>
  </clause>

  <clause id="18630">
    <literal><![CDATA[
      (x \ T(y * x,z \ T(u,w * v5))) * (T(y,x) \ 1) = K(x * y,z \ T(u,v5 \ w))
    ]]></literal>
    <justification jstring="[para(18629(a,1),16503(a,1,1,2))].">
      <j1 rule="para" parents="18629 16503"/>
    </justification>
  </clause>

  <clause id="18631">
    <literal><![CDATA[
      T(x,K(y,z) * ((K(u,w) * y) \ v5)) = T(x,T(y \ K(w,u),z) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,16846,a(flip),b,18616,a),flip(a)].">
      <j1 rule="hyper" parents="373 16846 18616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18633">
    <literal><![CDATA[
      (x \ T(y,x)) \ T(y,K(x \ T(y,x),z)) = T(T(x,y),x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,11651,a(flip),b,18342,a),flip(a)].">
      <j1 rule="hyper" parents="373 11651 18342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18634">
    <literal><![CDATA[
      (x \ T(y,x)) \ T(y,K(z,x \ y)) = T(T(x,y),x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(18326(a,1),18633(a,1,2))].">
      <j1 rule="para" parents="18326 18633"/>
    </justification>
  </clause>

  <clause id="18635">
    <literal><![CDATA[
      (x \ T(y,x)) \ T(y,K(x,z)) = T(T(x,y),x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(9004(a,1),18634(a,1,2))].">
      <j1 rule="para" parents="9004 18634"/>
    </justification>
  </clause>

  <clause id="18637">
    <literal><![CDATA[
      T(T(x,T(y,z)),x \ y) = T(T(x,y),x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9610,a(flip),b,18635,a)].">
      <j1 rule="hyper" parents="64 9610 18635"/>
    </justification>
  </clause>

  <clause id="18638">
    <literal><![CDATA[
      T(T(x,x \ y),T(y,z)) = T(T(x,y),x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(481,a,18637,a)].">
      <j1 rule="hyper" parents="481 18637"/>
    </justification>
  </clause>

  <clause id="18639">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / T(y / z,w)) = T(x,T(y / T(y / z,w),u))
    ]]></literal>
    <justification jstring="[para(8677(a,1),18592(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8677 18592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18640">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / T(y / z,w)) = T(x,T(T(z \ y,w) \ y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,11699,a(flip),b,18639,a),flip(a)].">
      <j1 rule="hyper" parents="373 11699 18639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18641">
    <literal><![CDATA[
      K(T((x * y) * (1 / x),K(x,y) / x) / z,u) = K(L(y,x,x \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(14389(a,1),18507(a,1,1,1,1))].">
      <j1 rule="para" parents="14389 18507"/>
    </justification>
  </clause>

  <clause id="18642">
    <literal><![CDATA[
      K(T((x * y) * (1 / x),x \ K(x,y)) / z,u) = K(L(y,x,x \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(17159(a,1),18641(a,1,1,1))].">
      <j1 rule="para" parents="17159 18641"/>
    </justification>
  </clause>

  <clause id="18643">
    <literal><![CDATA[
      (x \ T(K(y,z),u)) \ K(y,T(z,w)) = (x \ K(y,z)) \ K(y,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17244,a(flip),b,17761,a),flip(a)].">
      <j1 rule="hyper" parents="64 17244 17761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18644">
    <literal><![CDATA[
      (x \ K(y,T(z,u))) \ K(y,T(z,w)) = (x \ K(y,z)) \ K(y,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(7867(a,2),18643(a,1,1,2))].">
      <j1 rule="para" parents="7867 18643"/>
    </justification>
  </clause>

  <clause id="18645">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) \ 1,y) * T(u,z)) = K(x,T(u * ((y \ (z * u)) \ 1),z))
    ]]></literal>
    <justification jstring="[hyper(13526,a,17795,a)].">
      <j1 rule="hyper" parents="13526 17795"/>
    </justification>
  </clause>

  <clause id="18646">
    <literal><![CDATA[
      K(x,T(y * ((z \ (u * y)) \ 1),u)) = K(x,T(z \ (u * y),z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16842,a(flip),b,18645,a),flip(a)].">
      <j1 rule="hyper" parents="64 16842 18645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18647">
    <literal><![CDATA[
      K(x,T(y * ((z \ (u * y)) \ 1),u)) = K(x,((u * y) / z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15792,a(flip),b,18646,a),flip(a)].">
      <j1 rule="hyper" parents="373 15792 18646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18648">
    <literal><![CDATA[
      K(x,((y * z) / u) \ T(z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z / (u \ (y * z)),y)) = w
    ]]></literal>
    <justification jstring="[para(18647(a,1),14780(a,1))].">
      <j1 rule="para" parents="18647 14780"/>
    </justification>
  </clause>

  <clause id="18649">
    <literal><![CDATA[
      T(x,y / ((z \ T(z \ u,w)) \ (z \ u))) = T(x,y / (T(z \ u,w) \ u))
    ]]></literal>
    <justification jstring="[para(15075(a,1),17821(a,1,2,2,1))].">
      <j1 rule="para" parents="15075 17821"/>
    </justification>
  </clause>

  <clause id="18650">
    <literal><![CDATA[
      K(x,y) \ T(K(x,K(y,z)) * (u * K(x,y)),w) = T(K(x,y) * u,w) * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7783(a,1),17876(a,1,2,1))].">
      <j1 rule="para" parents="7783 17876"/>
    </justification>
  </clause>

  <clause id="18651">
    <literal><![CDATA[
      K(x * y,K(z \ u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * y,K(u * z,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(17893(a,1),16504(a,1))].">
      <j1 rule="para" parents="17893 16504"/>
    </justification>
  </clause>

  <clause id="18652">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = y \ (y * K((x * (z / x)) \ y,u))
    ]]></literal>
    <justification jstring="[para(7596(a,1),17896(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7596 17896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18653">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = K((x * (z / x)) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,9,a(flip),b,18652,a),flip(a)].">
      <j1 rule="hyper" parents="373 9 18652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18654">
    <literal><![CDATA[
      K((x * ((y * ((x \ z) * x)) / x)) \ z,u) = K(1 / y,T(u,z / x))
    ]]></literal>
    <justification jstring="[hyper(6803,a,18653,a),flip(a)].">
      <j1 rule="hyper" parents="6803 18653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18656">
    <literal><![CDATA[
      K((x * ((y * ((x \ z) * x)) / x)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(1 / y,T(u,z / x)) = w
    ]]></literal>
    <justification jstring="[para(18653(a,1),6803(a,1))].">
      <j1 rule="para" parents="18653 6803"/>
    </justification>
  </clause>

  <clause id="18657">
    <literal><![CDATA[
      K(x * K((y * z) \ x,z),T(u,((y * z) \ x) * z)) = K(((y * z) \ x) * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11196,a(flip),b,17906,a)].">
      <j1 rule="hyper" parents="64 11196 17906"/>
    </justification>
  </clause>

  <clause id="18658">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(K(z,w) * (u / z)) \ y) = T(x,y / (K(z,w) * (u / z)))
    ]]></literal>
    <justification jstring="[para(18315(a,1),17907(a,1,1))].">
      <j1 rule="para" parents="18315 17907"/>
    </justification>
  </clause>

  <clause id="18660">
    <literal><![CDATA[
      K(x,y * T(T((T(z,u) \ w) \ w,v5),z)) = K(x,y * T(T(T(z,u),z \ w),v5))
    ]]></literal>
    <justification jstring="[para(8598(a,1),18055(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8598 18055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18662">
    <literal><![CDATA[
      K(x,T((y / (y / z)) \ K(u,w),v5)) = K(x,T(T(z \ K(u,w),y),v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,8657,a(flip),b,18188,a),flip(a)].">
      <j1 rule="hyper" parents="373 8657 18188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18663">
    <literal><![CDATA[
      K(x,T(T(y \ K(z,u),w),v5)) = K(x,T(T(y,w) \ K(z,u),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16253,a(flip),b,18662,a),flip(a)].">
      <j1 rule="hyper" parents="64 16253 18662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18664">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ ((y / z) * ((z \ u) \ u)) = K(w,x * (K(z,u) * y))
    ]]></literal>
    <justification jstring="[para(6849(a,2),18216(a,1,2))].">
      <j1 rule="para" parents="6849 18216"/>
    </justification>
  </clause>

  <clause id="18665">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,K(x,y) \ z) = (K(x,y) \ z) \ (u * (z * K(y,x)))
    ]]></literal>
    <justification jstring="[para(8352(a,1),18321(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8352 18321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18666">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17879,a(flip),b,18665,a),flip(a)].">
      <j1 rule="hyper" parents="64 17879 18665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18667">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17917,a(flip),b,18666,a)].">
      <j1 rule="hyper" parents="64 17917 18666"/>
    </justification>
  </clause>

  <clause id="18668">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8153(a,1),18667(a,2,2))].">
      <j1 rule="para" parents="8153 18667"/>
    </justification>
  </clause>

  <clause id="18669">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(w,K(v5,v6) * x)) = (x \ K(y,z)) \ T(u,K(w,K(v7,v8) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,18327,a(flip),b,18360,a)].">
      <j1 rule="hyper" parents="64 18327 18360"/>
    </justification>
  </clause>

  <clause id="18670">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) / T(T(K(z,y),x),u) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3871(a,1),18390(a,1,2,1))].">
      <j1 rule="para" parents="3871 18390"/>
    </justification>
  </clause>

  <clause id="18671">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) / T(K(z,T(y,x)),u) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(7867(a,2),18670(a,1,2,1))].">
      <j1 rule="para" parents="7867 18670"/>
    </justification>
  </clause>

  <clause id="18672">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) / K(z,T(T(y,x),u)) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(7867(a,2),18671(a,1,2))].">
      <j1 rule="para" parents="7867 18671"/>
    </justification>
  </clause>

  <clause id="18673">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) * K(T(T(y,x),u),z) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6898,a,18672,a)].">
      <j1 rule="hyper" parents="6898 18672"/>
    </justification>
  </clause>

  <clause id="18674">
    <literal><![CDATA[
      ((x \ K(y,z)) \ 1) * K(y,T(T(z,u),x)) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(7901(a,1),18673(a,1,2))].">
      <j1 rule="para" parents="7901 18673"/>
    </justification>
  </clause>

  <clause id="18675">
    <literal><![CDATA[
      (x \ K(y,z)) \ K(y,T(T(z,u),x)) = K(u,K(z,y)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(14603,a,18674,a)].">
      <j1 rule="hyper" parents="14603 18674"/>
    </justification>
  </clause>

  <clause id="18676">
    <literal><![CDATA[
      (x \ K(y,z)) \ K(y,T(T(z,u),x)) = K(y,K(z,u)) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(8088(a,1),18675(a,2,1))].">
      <j1 rule="para" parents="8088 18675"/>
    </justification>
  </clause>

  <clause id="18677">
    <literal><![CDATA[
      (x \ K(y,z)) \ K(y,T(T(z,u),x)) = (x \ 1) \ K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17158,a(flip),b,18676,a),flip(a)].">
      <j1 rule="hyper" parents="373 17158 18676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18678">
    <literal><![CDATA[
      K(x,(y / (z * K(u,w))) \ K(z,z \ u)) = K(x,T(z * K(u,w),z \ u) / y)
    ]]></literal>
    <justification jstring="[hyper(18013,a,18425,a)].">
      <j1 rule="hyper" parents="18013 18425"/>
    </justification>
  </clause>

  <clause id="18679">
    <literal><![CDATA[
      K(x,T(y * K(z,u),y \ z) / w) = K(x,(w / (y * K(z,u))) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(13548,a,18678,a),flip(a)].">
      <j1 rule="hyper" parents="13548 18678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18680">
    <literal><![CDATA[
      K(x,T(y * K(z,u),y \ z) / w) = K(x,T(y * K(z,u),z) / w)
    ]]></literal>
    <justification jstring="[hyper(373,a,18424,a(flip),b,18679,a),flip(a)].">
      <j1 rule="hyper" parents="373 18424 18679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18681">
    <literal><![CDATA[
      K(x,(T(y,z) / (y / u)) / w) = K(x,T(u * K(y,z),y) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,18118,a(flip),b,18680,a)].">
      <j1 rule="hyper" parents="64 18118 18680"/>
    </justification>
  </clause>

  <clause id="18682">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (w \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(373,a,13553,a(flip),b,18466,a),flip(a)].">
      <j1 rule="hyper" parents="373 13553 18466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18683">
    <literal><![CDATA[
      K(x,y * (T(z / u,u) * (w \ 1))) = K(x,y * ((z / u) * (w \ K(u,z))))
    ]]></literal>
    <justification jstring="[hyper(16256,a,18682,a)].">
      <j1 rule="hyper" parents="16256 18682"/>
    </justification>
  </clause>

  <clause id="18684">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) = K(x,y * ((u \ z) * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(117(a,1),18683(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="117 18683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18685">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),w),z * v5)) = T(x,T(T(y * T(y \ z,u),w),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18260,a(flip),b,18569,a)].">
      <j1 rule="hyper" parents="64 18260 18569"/>
    </justification>
  </clause>

  <clause id="18687">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),y),w)) = T(x,T(y * T(z / y,u),z * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11242,a(flip),b,18685,a),flip(a)].">
      <j1 rule="hyper" parents="64 11242 18685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18688">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),z * w)) = T(x,T(y * T(z / y,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11242,a(flip),b,18687,a),flip(a)].">
      <j1 rule="hyper" parents="64 11242 18687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18689">
    <literal><![CDATA[
      x * T(x \ L(x,y,K(K(z,u) * w,v5)),K(w,v5) * y) = R(x,y,K(K(z,u) * w,v5))
    ]]></literal>
    <justification jstring="[para(16598(a,1),18624(a,1,2,1,2))].">
      <j1 rule="para" parents="16598 18624"/>
    </justification>
  </clause>

  <clause id="18690">
    <literal><![CDATA[
      K(x * y,z \ T(u,w \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z \ T(u,v5 * w)) = v6
    ]]></literal>
    <justification jstring="[para(18630(a,1),16504(a,1))].">
      <j1 rule="para" parents="18630 16504"/>
    </justification>
  </clause>

  <clause id="18691">
    <literal><![CDATA[
      K(x,y) \ T(z * K(x,T(y,u)),w) = T(K(x,y) * z,w) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(17173(a,1),18650(a,1,2,1))].">
      <j1 rule="para" parents="17173 18650"/>
    </justification>
  </clause>

  <clause id="18692">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x,w)) = K(y,x) * T(z * K(x,T(y,w)),u)
    ]]></literal>
    <justification jstring="[hyper(6198,a,18691,a),flip(a)].">
      <j1 rule="hyper" parents="6198 18691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18693">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),w) = K(x,y) * T(u * K(y,T(x,z)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17114,a(flip),b,18692,a)].">
      <j1 rule="hyper" parents="64 17114 18692"/>
    </justification>
  </clause>

  <clause id="18694">
    <literal><![CDATA[
      K(x * K(y \ (z \ x),y),T(u,((z * y) \ x) * y)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[para(10182(a,1),18657(a,1,1,2))].">
      <j1 rule="para" parents="10182 18657"/>
    </justification>
  </clause>

  <clause id="18696">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(w,K(v5,v6) * x)) = (x \ K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[para(18312(a,1),18669(a,2,2))].">
      <j1 rule="para" parents="18312 18669"/>
    </justification>
  </clause>

  <clause id="18697">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(x,w)) = (x \ K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(18317,a,18696,a)].">
      <j1 rule="hyper" parents="18317 18696"/>
    </justification>
  </clause>

  <clause id="18698">
    <literal><![CDATA[
      T((x \ K(y,z)) \ (u * (x \ K(y,z))),K(x,w)) = T(u,T(x,w) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17880,a(flip),b,18697,a),flip(a)].">
      <j1 rule="hyper" parents="373 17880 18697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18699">
    <literal><![CDATA[
      T(T(x,y \ K(z,u)),K(y,w)) = T(x,T(y,w) \ K(z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),18698(a,1,1))].">
      <j1 rule="para" parents="22 18698"/>
    </justification>
  </clause>

  <clause id="18700">
    <literal><![CDATA[
      T(x,T(y,z) \ K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ K(u,w),z)) = v5
    ]]></literal>
    <justification jstring="[para(18699(a,1),18582(a,1))].">
      <j1 rule="para" parents="18699 18582"/>
    </justification>
  </clause>

  <clause id="18701">
    <literal><![CDATA[
      x * T(a(y,z,K(x,K(u,w) * v5)),K(v5,y) * z) = R(x,z,K(K(u,w) * v5,y))
    ]]></literal>
    <justification jstring="[para(16622(a,1),18689(a,1,2,1))].">
      <j1 rule="para" parents="16622 18689"/>
    </justification>
  </clause>

  <clause id="18702">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,(K(z,y) / u) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(8821(a,1),17327(a,1,2,2,1))].">
      <j1 rule="para" parents="8821 17327"/>
    </justification>
  </clause>

  <clause id="18704">
    <literal><![CDATA[
      K(x * ((x * y) \ (z * (x * y))),y) = K(z / (1 / x),L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(16544,a,17430,a)].">
      <j1 rule="hyper" parents="16544 17430"/>
    </justification>
  </clause>

  <clause id="18705">
    <literal><![CDATA[
      K(x / (1 / y),L(z,y,y \ 1)) = K(y * T(x,y * z),z)
    ]]></literal>
    <justification jstring="[para(22(a,2),18704(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="22 18704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18706">
    <literal><![CDATA[
      K(x * T(y,x * z),z) = K(y / (1 / x),z)
    ]]></literal>
    <justification jstring="[hyper(14781,a,18705,a),flip(a)].">
      <j1 rule="hyper" parents="14781 18705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18708">
    <literal><![CDATA[
      K(x * T(y,x * z),z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,14683,a(flip),b,18706,a),flip(a)].">
      <j1 rule="hyper" parents="373 14683 18706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18709">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(y,x),u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17846,a(flip),b,18708,a),flip(a)].">
      <j1 rule="hyper" parents="64 17846 18708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18710">
    <literal><![CDATA[
      K(x,K(y,L(y \ z,u,w)) * (v5 * L(z / y,u,w))) = K(x,v5 * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(279(a,1),17490(a,2,2,2))].">
      <j1 rule="para" parents="279 17490"/>
    </justification>
  </clause>

  <clause id="18711">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (K(w,z) * y))) = K(x,u * T(K(w,z) * y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(17654,a,16827,a),flip(a)].">
      <j1 rule="hyper" parents="17654 16827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18712">
    <literal><![CDATA[
      K(x,y * T(K(z,u) * w,u \ 1)) = K(x,y * T(K(z,u) * w,u))
    ]]></literal>
    <justification jstring="[hyper(17655,a,18711,a),flip(a)].">
      <j1 rule="hyper" parents="17655 18711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18713">
    <literal><![CDATA[
      K(x,y * T(K(x,z) * u,z)) = K(x,y * T(u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,15725,a(flip),b,18712,a),flip(a)].">
      <j1 rule="hyper" parents="64 15725 18712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18714">
    <literal><![CDATA[
      K(x,y * T(z,u \ 1)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15725,a(flip),b,18713,a),flip(a)].">
      <j1 rule="hyper" parents="64 15725 18713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18716">
    <literal><![CDATA[
      T(x,y * T(z,u \ 1)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(143,a,18714,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 18714 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18717">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15852,a(flip),b,18714,a),flip(a)].">
      <j1 rule="hyper" parents="64 15852 18714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18718">
    <literal><![CDATA[
      T(x,(y * ((z \ 1) * K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(6856(a,2),18716(a,1,2))].">
      <j1 rule="para" parents="6856 18716"/>
    </justification>
  </clause>

  <clause id="18719">
    <literal><![CDATA[
      K(x,y * ((z \ K(z,u)) \ u)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17671,a(flip),b,18717,a)].">
      <j1 rule="hyper" parents="64 17671 18717"/>
    </justification>
  </clause>

  <clause id="18720">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(4029(a,1),18718(a,1,2,1,2))].">
      <j1 rule="para" parents="4029 18718"/>
    </justification>
  </clause>

  <clause id="18721">
    <literal><![CDATA[
      T(x,K(y / z,u) * T(T(y,z),w)) = T(x,(z * K(y,w)) * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(17658,a,17732,a),flip(a)].">
      <j1 rule="hyper" parents="17658 17732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18722">
    <literal><![CDATA[
      T(x,T(K(y / z,u) * T(y,z),w)) = T(x,(z * K(y,w)) * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18139,a,b,18721,a)].">
      <j1 rule="hyper" parents="64 18139 18721"/>
    </justification>
  </clause>

  <clause id="18723">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,(z * K(y,w)) * T(y / z,u))
    ]]></literal>
    <justification jstring="[para(17764(a,2),18722(a,1,2,1))].">
      <j1 rule="para" parents="17764 18722"/>
    </justification>
  </clause>

  <clause id="18724">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * T(z / y,w)) = T(x,T(y * T(z / y,w),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17818,a(flip),b,18723,a),flip(a)].">
      <j1 rule="hyper" parents="64 17818 18723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18725">
    <literal><![CDATA[
      x * (T((y * y) \ z,K(y * y,z)) * K(y * y,z)) = z * ((y * y) \ T(x,y \ (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,897,a(flip),b,17278,a),flip(a)].">
      <j1 rule="hyper" parents="373 897 17278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18726">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * (w * (u / (z / y)))) = K(x,w * T((z / y) \ u,K(z,y)))
    ]]></literal>
    <justification jstring="[para(15166(a,1),17461(a,1,2,1))].">
      <j1 rule="para" parents="15166 17461"/>
    </justification>
  </clause>

  <clause id="18727">
    <literal><![CDATA[
      K(x,T(K(y,z) * (K(z,y) / u),w) * K(y,z \ y)) = K(x,(K(z,y) / u) * K(u \ 1,w))
    ]]></literal>
    <justification jstring="[para(6156(a,1),17474(a,1,2,1,1))].">
      <j1 rule="para" parents="6156 17474"/>
    </justification>
  </clause>

  <clause id="18728">
    <literal><![CDATA[
      T(x,((y * z) / T(y,u)) * K(w,T(y,u) * z)) = T(x,T(y * (z * K(u,y)),w) / y)
    ]]></literal>
    <justification jstring="[para(17462(a,1),17495(a,1,2,2))].">
      <j1 rule="para" parents="17462 17495"/>
    </justification>
  </clause>

  <clause id="18729">
    <literal><![CDATA[
      T(x,K(y * z,u) * ((y * z) / T(y,w))) = T(x,T(y * (z * K(w,y)),u) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,18623,a(flip),b,18728,a)].">
      <j1 rule="hyper" parents="64 18623 18728"/>
    </justification>
  </clause>

  <clause id="18731">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,y)),w) / y) = T(x,T(y * z,w) / T(y,u))
    ]]></literal>
    <justification jstring="[para(14825(a,1),18729(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14825 18729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18732">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,y)),w) / y) = T(x,T(y,u) \ T(z * y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,17453,a(flip),b,18731,a),flip(a)].">
      <j1 rule="hyper" parents="373 17453 18731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18733">
    <literal><![CDATA[
      T(x,y \ T((z * K(u,y)) * y,w)) = T(x,T(y,u) \ T(z * y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,8301,a(flip),b,18732,a)].">
      <j1 rule="hyper" parents="64 8301 18732"/>
    </justification>
  </clause>

  <clause id="18734">
    <literal><![CDATA[
      T(x,y \ T(z * (y * K(u,y)),w)) = T(x,T(y,u) \ T(z * y,w))
    ]]></literal>
    <justification jstring="[para(5700(a,1),18733(a,1,2,2,1))].">
      <j1 rule="para" parents="5700 18733"/>
    </justification>
  </clause>

  <clause id="18735">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,K(u,w)) = T((x * y) / T(x,K(u,w)),z)
    ]]></literal>
    <justification jstring="[para(6067(a,1),17649(a,1,1))].">
      <j1 rule="para" parents="6067 17649"/>
    </justification>
  </clause>

  <clause id="18736">
    <literal><![CDATA[
      (x * T(x \ y,z)) / T(x,K(u,w)) = T(y / T(x,K(u,w)),z)
    ]]></literal>
    <justification jstring="[para(10(a,1),18735(a,2,1,1))].">
      <j1 rule="para" parents="10 18735"/>
    </justification>
  </clause>

  <clause id="18738">
    <literal><![CDATA[
      T(x,K(y,z)) * T(u / T(x,K(y,z)),w) = x * T(u / x,w)
    ]]></literal>
    <justification jstring="[para(18736(a,1),17621(a,1,2))].">
      <j1 rule="para" parents="18736 17621"/>
    </justification>
  </clause>

  <clause id="18739">
    <literal><![CDATA[
      T((x / T(y,K(z,u))) * T(T(y,K(z,u)),K(w,v5) \ (x / T(y,K(z,u)))),K(w,v5)) = y * T(x / y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,17731,a,b,18738,a)].">
      <j1 rule="hyper" parents="64 17731 18738"/>
    </justification>
  </clause>

  <clause id="18740">
    <literal><![CDATA[
      K(x,T(y,z) * u) * a(w,v5,K(T(y,z) * u,x)) = K(x,L(((z \ y) * z) * u,v5,w))
    ]]></literal>
    <justification jstring="[para(13468(a,1),17768(a,1,1))].">
      <j1 rule="para" parents="13468 17768"/>
    </justification>
  </clause>

  <clause id="18741">
    <literal><![CDATA[
      K(x,L(((y \ z) * y) * u,w,v5)) = K(x,L(T(z,y) * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(12116,a,18740,a),flip(a)].">
      <j1 rule="hyper" parents="12116 18740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18742">
    <literal><![CDATA[
      T(x,y * K(z,u)) \ T(y * T(T(x,K(z,u)),y * K(z,u)),K(u,z)) = T(y,x * K(z,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),17789(a,1,2,1,2))].">
      <j1 rule="para" parents="23 17789"/>
    </justification>
  </clause>

  <clause id="18743">
    <literal><![CDATA[
      K(x * (y * z),T(u,w)) \ K(x * (y * z),K(u,w)) = K(u,(x * y) * R(z,y,x))
    ]]></literal>
    <justification jstring="[para(17904(a,1),17905(a,1,1))].">
      <j1 rule="para" parents="17904 17905"/>
    </justification>
  </clause>

  <clause id="18744">
    <literal><![CDATA[
      K(x,(y * z) * R(u,z,y)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(8327,a,18743,a),flip(a)].">
      <j1 rule="hyper" parents="8327 18743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18745">
    <literal><![CDATA[
      K(x,(y * (y \ z)) * R(T(u,z),y \ z,y)) = K(x,L(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(964(a,1),18744(a,2,2))].">
      <j1 rule="para" parents="964 18744"/>
    </justification>
  </clause>

  <clause id="18746">
    <literal><![CDATA[
      K(x,((y / z) * z) * R(T(u,y),z,y / z)) = K(x,L(u,z,z \ y) * y)
    ]]></literal>
    <justification jstring="[para(11066(a,1),18744(a,2,2))].">
      <j1 rule="para" parents="11066 18744"/>
    </justification>
  </clause>

  <clause id="18747">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u \ y,u)) = K(x,L(z,u \ y,u) * y)
    ]]></literal>
    <justification jstring="[para(10(a,1),18745(a,1,2,1))].">
      <j1 rule="para" parents="10 18745"/>
    </justification>
  </clause>

  <clause id="18749">
    <literal><![CDATA[
      K(x,R(y,z \ u,z) * u) = K(x,L(y,z \ u,z) * u)
    ]]></literal>
    <justification jstring="[para(267(a,1),18747(a,1,2))].">
      <j1 rule="para" parents="267 18747"/>
    </justification>
  </clause>

  <clause id="18750">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * u) = K(x,(y * (u / z)) * z)
    ]]></literal>
    <justification jstring="[para(10219(a,1),18749(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10219 18749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18751">
    <literal><![CDATA[
      K(x,y * ((y \ T(z,u)) * u)) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15968,a(flip),b,18750,a)].">
      <j1 rule="hyper" parents="64 15968 18750"/>
    </justification>
  </clause>

  <clause id="18752">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u,y / u)) = K(x,L(z,u,u \ y) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),18746(a,1,2,1))].">
      <j1 rule="para" parents="12 18746"/>
    </justification>
  </clause>

  <clause id="18754">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u,u \ y)) = K(x,L(z,u,u \ y) * y)
    ]]></literal>
    <justification jstring="[para(10207(a,1),18752(a,1,2,2))].">
      <j1 rule="para" parents="10207 18752"/>
    </justification>
  </clause>

  <clause id="18755">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(y * z) * (z \ u))
    ]]></literal>
    <justification jstring="[para(994(a,1),18754(a,1,2)),flip(a)].">
      <j1 rule="para" parents="994 18754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18756">
    <literal><![CDATA[
      T(x,(y * T(z,u)) * (w \ K(y * T(z,u),v5))) = T(x,T(y * (z * K(u,z)),v5) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16251,a(flip),b,18161,a)].">
      <j1 rule="hyper" parents="64 16251 18161"/>
    </justification>
  </clause>

  <clause id="18757">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,z)),w) / v5) = T(x,T(y * T(z,u),w) / v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,18159,a(flip),b,18756,a),flip(a)].">
      <j1 rule="hyper" parents="64 18159 18756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18758">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * (w * z)) / T(w * u,a(w,z,z \ u)))) = a(y,z,K(x,K(z \ u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,15312,a,b,18349,a),flip(a)].">
      <j1 rule="hyper" parents="373 15312 18349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18759">
    <literal><![CDATA[
      T(x,K(y \ K(z,u),w) * v5) = v5 \ T(x * T(v5,K(w,K(v6,v7) * y)),K(w,K(v8,v9) * y))
    ]]></literal>
    <justification jstring="[para(18327(a,1),18362(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18327 18362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18760">
    <literal><![CDATA[
      K(x,y \ (z * u)) * a(w,v5,K(y \ (z * u),x)) = K(x,L(y \ T(u * z,z),v5,w))
    ]]></literal>
    <justification jstring="[para(16371(a,1),18520(a,1,1))].">
      <j1 rule="para" parents="16371 18520"/>
    </justification>
  </clause>

  <clause id="18761">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ (u * z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(18760(a,1),12116(a,1))].">
      <j1 rule="para" parents="18760 12116"/>
    </justification>
  </clause>

  <clause id="18762">
    <literal><![CDATA[
      x * ((y * y) \ T(z,y \ (y \ x))) = z * (K(y * y,x) * ((y * y) \ x))
    ]]></literal>
    <justification jstring="[para(8172(a,1),18725(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8172 18725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18763">
    <literal><![CDATA[
      x * ((y * y) \ T(z,y \ (y \ x))) = z * (x / (y * y))
    ]]></literal>
    <justification jstring="[para(7723(a,1),18762(a,2,2))].">
      <j1 rule="para" parents="7723 18762"/>
    </justification>
  </clause>

  <clause id="18764">
    <literal><![CDATA[
      (x * x) \ T(y,x \ (x \ 1)) = y / (x * x)
    ]]></literal>
    <justification jstring="[hyper(137,a,18763,a,b,587,a(flip))].">
      <j1 rule="hyper" parents="137 18763 587"/>
    </justification>
  </clause>

  <clause id="18765">
    <literal><![CDATA[
      (x * x) * (y / (x * x)) = T(y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(157,a,18764,a)].">
      <j1 rule="hyper" parents="157 18764"/>
    </justification>
  </clause>

  <clause id="18766">
    <literal><![CDATA[
      T(x * (y * x),x \ (x \ 1)) = (x * x) * (x * (y * (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(145,a,15915,a(flip),b,18764,a),flip(a)].">
      <j1 rule="hyper" parents="145 15915 18764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18767">
    <literal><![CDATA[
      (x * x) \ T(y,x \ (x \ z)) = T(y,z) / (x * x)
    ]]></literal>
    <justification jstring="[para(15869(a,1),18764(a,1,2))].">
      <j1 rule="para" parents="15869 18764"/>
    </justification>
  </clause>

  <clause id="18768">
    <literal><![CDATA[
      (x / (y * y)) \ ((y * y) \ z) = T(x,y \ (y \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(18765(a,1),487(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18765 487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18769">
    <literal><![CDATA[
      T(x * (y * y),y \ (y \ z)) = T((y * y) * x,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,5434,a(flip),b,18767,a),flip(a)].">
      <j1 rule="hyper" parents="39 5434 18767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18770">
    <literal><![CDATA[
      x * (T(y,x) / (z * z)) = y * (x / (z * z))
    ]]></literal>
    <justification jstring="[para(18767(a,1),18763(a,1,2))].">
      <j1 rule="para" parents="18767 18763"/>
    </justification>
  </clause>

  <clause id="18771">
    <literal><![CDATA[
      T(x / (1 / y),y \ (y \ z)) = T((y * y) * (x / y),z)
    ]]></literal>
    <justification jstring="[para(809(a,1),18769(a,1,1))].">
      <j1 rule="para" parents="809 18769"/>
    </justification>
  </clause>

  <clause id="18772">
    <literal><![CDATA[
      (x * x) * (y \ ((x * x) \ z)) = T(y,x \ (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,890,a(flip),b,18768,a)].">
      <j1 rule="hyper" parents="64 890 18768"/>
    </justification>
  </clause>

  <clause id="18773">
    <literal><![CDATA[
      T(x,y \ (y \ 1)) \ y = (y * y) * (x \ (1 / y))
    ]]></literal>
    <justification jstring="[para(309(a,1),18772(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="309 18772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18774">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) * (y \ L((x \ 1) \ z,x,x \ 1)) = T(y,(x \ 1) \ ((x \ 1) \ 1)) \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(11813(a,2),18772(a,1,2,2))].">
      <j1 rule="para" parents="11813 18772"/>
    </justification>
  </clause>

  <clause id="18775">
    <literal><![CDATA[
      x * ((x \ 1) \ (y \ (x \ 1))) = T(y,x \ (x \ 1)) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,5222,a,b,18773,a)].">
      <j1 rule="hyper" parents="373 5222 18773"/>
    </justification>
  </clause>

  <clause id="18776">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(y,z,u) \ 1)) \ a(y,z,u) = (a(y,z,u) * a(y,z,u)) * (x \ (a(y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[para(13923(a,1),18773(a,2,2,2))].">
      <j1 rule="para" parents="13923 18773"/>
    </justification>
  </clause>

  <clause id="18777">
    <literal><![CDATA[
      (x \ (y \ 1)) \ ((y \ 1) * (y \ z)) = (T(x,y \ (y \ 1)) \ y) \ z
    ]]></literal>
    <justification jstring="[para(18775(a,1),1621(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18775 1621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18778">
    <literal><![CDATA[
      T(x * (y * x),x \ (x \ 1)) = x * (x * T(y,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,1179,a(flip),b,18766,a),flip(a)].">
      <j1 rule="hyper" parents="373 1179 18766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18779">
    <literal><![CDATA[
      K(x,K(y \ z,u) * (w * (u / (y / z)))) = K(x,w * T((y / z) \ u,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18541,a(flip),b,18726,a)].">
      <j1 rule="hyper" parents="64 18541 18726"/>
    </justification>
  </clause>

  <clause id="18780">
    <literal><![CDATA[
      K(x,K(y,z) * T(K(z,y) * (K(y,z) / u),w)) = K(x,(K(y,z) / u) * K(u \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(17308,a,18727,a)].">
      <j1 rule="hyper" parents="17308 18727"/>
    </justification>
  </clause>

  <clause id="18781">
    <literal><![CDATA[
      K(x,T((K(y,z) * (K(z,y) / u)) * K(y,z),w)) = K(x,(K(z,y) / u) * K(u \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18069,a,b,18780,a)].">
      <j1 rule="hyper" parents="64 18069 18780"/>
    </justification>
  </clause>

  <clause id="18782">
    <literal><![CDATA[
      K(x,T(K(y,z) * ((K(z,y) / u) * K(y,z)),w)) = K(x,(K(z,y) / u) * K(u \ 1,w))
    ]]></literal>
    <justification jstring="[para(7783(a,1),18781(a,1,2,1))].">
      <j1 rule="para" parents="7783 18781"/>
    </justification>
  </clause>

  <clause id="18783">
    <literal><![CDATA[
      K(x,(K(y,z) / u) * K(u \ 1,w)) = K(x,T(K(y,z) / u,w))
    ]]></literal>
    <justification jstring="[hyper(18446,a,18782,a),flip(a)].">
      <j1 rule="hyper" parents="18446 18782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18784">
    <literal><![CDATA[
      K(x,(K(y,z) / u) * K(u \ 1,w)) = K(x,T(u \ K(y,z),w))
    ]]></literal>
    <justification jstring="[hyper(373,a,17183,a(flip),b,18783,a),flip(a)].">
      <j1 rule="hyper" parents="373 17183 18783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18785">
    <literal><![CDATA[
      K(x,K(y,z) * (K(u,w) / y)) = K(x,T(y \ K(u,w),z))
    ]]></literal>
    <justification jstring="[hyper(17307,a,18784,a)].">
      <j1 rule="hyper" parents="17307 18784"/>
    </justification>
  </clause>

  <clause id="18786">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ K(u,w))) = K(x,T(y \ K(u,w),z))
    ]]></literal>
    <justification jstring="[hyper(18098,a,18785,a)].">
      <j1 rule="hyper" parents="18098 18785"/>
    </justification>
  </clause>

  <clause id="18787">
    <literal><![CDATA[
      K(x,T(y \ K(z,u),w)) = K(x,T(y,w) \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15774,a(flip),b,18786,a),flip(a)].">
      <j1 rule="hyper" parents="64 15774 18786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18788">
    <literal><![CDATA[
      T(x,y * K(z,u)) \ T(y * T(T(x,K(z,u)),y * K(z,u)),K(z,u)) = T(y,x * K(z,u))
    ]]></literal>
    <justification jstring="[para(8153(a,1),18742(a,1,2))].">
      <j1 rule="para" parents="8153 18742"/>
    </justification>
  </clause>

  <clause id="18789">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * (w * z)) / T(w * u,a(w,z,z \ u)))) = a(y,z,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[para(17236(a,1),18758(a,2,3))].">
      <j1 rule="para" parents="17236 18758"/>
    </justification>
  </clause>

  <clause id="18790">
    <literal><![CDATA[
      T(x,K(y \ K(z,u),w) * v5) = T(x,K(K(v6,v7) * y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,16796,a(flip),b,18759,a),flip(a)].">
      <j1 rule="hyper" parents="373 16796 18759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18792">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * K(v5,v6)) = T(x,u * T(u \ K(v6,v5),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17416,a(flip),b,18790,a),flip(a)].">
      <j1 rule="hyper" parents="64 17416 18790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18794">
    <literal><![CDATA[
      T(x,y * T(y \ K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,w) * K(u,z)) = v5
    ]]></literal>
    <justification jstring="[para(18792(a,1),18612(a,1))].">
      <j1 rule="para" parents="18792 18612"/>
    </justification>
  </clause>

  <clause id="18795">
    <literal><![CDATA[
      T(x,y * K(z,u)) \ (T(x,K(z,u)) * T(y,K(z,u))) = T(y,x * K(z,u))
    ]]></literal>
    <justification jstring="[para(17678(a,1),18788(a,1,2))].">
      <j1 rule="para" parents="17678 18788"/>
    </justification>
  </clause>

  <clause id="18796">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(u * K(y,z),x) * T(u,K(y,z))) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(10010,a,18795,a)].">
      <j1 rule="hyper" parents="10010 18795"/>
    </justification>
  </clause>

  <clause id="18797">
    <literal><![CDATA[
      K(x,K(y,z)) * T(K(u * K(y,z),x) * u,K(y,z)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(18375(a,2),18796(a,1,2))].">
      <j1 rule="para" parents="18375 18796"/>
    </justification>
  </clause>

  <clause id="18798">
    <literal><![CDATA[
      K(x,K(y,z)) * T(u * K(K(y,z) * u,x),K(y,z)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(11188(a,1),18797(a,1,2,1))].">
      <j1 rule="para" parents="11188 18797"/>
    </justification>
  </clause>

  <clause id="18799">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(y,z) \ T(u * K(y,z),x)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(14496(a,1),18798(a,1,2))].">
      <j1 rule="para" parents="14496 18798"/>
    </justification>
  </clause>

  <clause id="18800">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * T(u * K(y,z),x)) = T(u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(6156(a,1),18799(a,1,2))].">
      <j1 rule="para" parents="6156 18799"/>
    </justification>
  </clause>

  <clause id="18801">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),z) = T(u,z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(8840,a,18800,a)].">
      <j1 rule="hyper" parents="8840 18800"/>
    </justification>
  </clause>

  <clause id="18802">
    <literal><![CDATA[
      K(x,y) * T(z * K(y,T(x,u)),u) = T(z,u * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,18693,a(flip),b,18801,a)].">
      <j1 rule="hyper" parents="64 18693 18801"/>
    </justification>
  </clause>

  <clause id="18803">
    <literal><![CDATA[
      T(x * K(y,T(z,u)),u) = K(y,z) * T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6187,a,18802,a),flip(a)].">
      <j1 rule="hyper" parents="6187 18802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18804">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * K(z,T(u,y)),y) = R(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[hyper(225,a,18803,a,b,15245,a)].">
      <j1 rule="hyper" parents="225 18803 15245"/>
    </justification>
  </clause>

  <clause id="18806">
    <literal><![CDATA[
      R(x,K(y,z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16198,a(flip),b,18804,a),flip(a)].">
      <j1 rule="hyper" parents="64 16198 18804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18807">
    <literal><![CDATA[
      L((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(6913,a,18806,a),flip(a)].">
      <j1 rule="hyper" parents="6913 18806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18808">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(x,T(y,z))) = L(z * K(x,K(y,u)),K(x,T(y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17242,a,b,18806,a)].">
      <j1 rule="hyper" parents="64 17242 18806"/>
    </justification>
  </clause>

  <clause id="18809">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u * K(y,z)) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[hyper(64,a,10454,a(flip),b,18806,a),flip(a)].">
      <j1 rule="hyper" parents="64 10454 18806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18810">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,T(y,u)),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9293,a(flip),b,18806,a),flip(a)].">
      <j1 rule="hyper" parents="64 9293 18806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18812">
    <literal><![CDATA[
      L(x,K(y,z),u) * (K(y,z) * u) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,18806,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 18806 20"/>
    </justification>
  </clause>

  <clause id="18813">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(18806(a,1),9905(a,1,1))].">
      <j1 rule="para" parents="18806 9905"/>
    </justification>
  </clause>

  <clause id="18814">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),u) = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),18807(a,1,1,1))].">
      <j1 rule="para" parents="11 18807"/>
    </justification>
  </clause>

  <clause id="18815">
    <literal><![CDATA[
      K(x,y) * L(K(y,x) * z,K(x,y),u) = ((z * u) / (K(x,y) * u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(18814(a,1),6956(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18814 6956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18816">
    <literal><![CDATA[
      K(L((x \ y) * K(z,u),K(u,z),x),w) = K((x * K(u,z)) \ y,w)
    ]]></literal>
    <justification jstring="[para(18814(a,2),17176(a,1,1))].">
      <j1 rule="para" parents="18814 17176"/>
    </justification>
  </clause>

  <clause id="18817">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * (w * z)) / (w * u))) = a(y,z,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18293,a(flip),b,18789,a)].">
      <j1 rule="hyper" parents="64 18293 18789"/>
    </justification>
  </clause>

  <clause id="18819">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ T(K(w,v5) * L(x,z,K(u,y)),y) = K(w,T(v5,L(y * x,z,K(u,y))))
    ]]></literal>
    <justification jstring="[para(16628(a,1),17637(a,1,1))].">
      <j1 rule="para" parents="16628 17637"/>
    </justification>
  </clause>

  <clause id="18820">
    <literal><![CDATA[
      T(x,R(y / y,y,y) \ ((z \ ((y * y) * u)) / w)) = T(x,(T(z,y * y) \ u) * (w \ (y * y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,14943,a(flip),b,17735,a),flip(a)].">
      <j1 rule="hyper" parents="373 14943 17735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18821">
    <literal><![CDATA[
      K((x * y) \ ((y * T(x,K(y,z))) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(y * T(x,K(y,z)),y) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(13407(a,1),18066(a,1))].">
      <j1 rule="para" parents="13407 18066"/>
    </justification>
  </clause>

  <clause id="18823">
    <literal><![CDATA[
      K((x * y) \ ((y * T(x,K(y,z))) * u),w) = K(K(y * T(x,K(y,z)),x) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(18067,a,15929,a),flip(a)].">
      <j1 rule="hyper" parents="18067 15929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18825">
    <literal><![CDATA[
      K((x * y) \ ((y * T(x,K(y,z))) * u),w) = K(K(y * x,x) \ u,w)
    ]]></literal>
    <justification jstring="[para(8527(a,1),18823(a,2,1,1))].">
      <j1 rule="para" parents="8527 18823"/>
    </justification>
  </clause>

  <clause id="18826">
    <literal><![CDATA[
      K(K(x * T(y,K(x,z)),x) \ u,w) = K(K(x * y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(18821,a,18825,a)].">
      <j1 rule="hyper" parents="18821 18825"/>
    </justification>
  </clause>

  <clause id="18828">
    <literal><![CDATA[
      K(K(x * y,y) \ z,u) = K(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13473,a(flip),b,18826,a),flip(a)].">
      <j1 rule="hyper" parents="64 13473 18826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18829">
    <literal><![CDATA[
      K(K(x \ 1,y) \ z,u) = K(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17724,a,b,18828,a)].">
      <j1 rule="hyper" parents="64 17724 18828"/>
    </justification>
  </clause>

  <clause id="18830">
    <literal><![CDATA[
      K(K(x,y) \ (z / u),w) \ K((K(y \ 1,x) \ (z / u)) * w,w) = a(w,u \ (K(y \ 1,x) \ z),w)
    ]]></literal>
    <justification jstring="[para(18829(a,1),13754(a,1,1))].">
      <j1 rule="para" parents="18829 13754"/>
    </justification>
  </clause>

  <clause id="18831">
    <literal><![CDATA[
      K(x,K(y,(L(z / u,u,1 / u) * w) * v5)) = K(x,K(y,(((1 / u) * z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(9(a,1),18460(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9 18460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18832">
    <literal><![CDATA[
      K(x,K(y,(z * u) * R(L(w / v5,v5,1 / v5),z,u))) = K(x,K(y,(((1 / v5) * w) * z) * u))
    ]]></literal>
    <justification jstring="[hyper(17531,a,18831,a)].">
      <j1 rule="hyper" parents="17531 18831"/>
    </justification>
  </clause>

  <clause id="18834">
    <literal><![CDATA[
      K(x,K(y,(z * u) * L(R(w / v5,z,u),v5,1 / v5))) = K(x,K(y,(((1 / v5) * w) * z) * u))
    ]]></literal>
    <justification jstring="[para(29(a,1),18832(a,1,2,2,2))].">
      <j1 rule="para" parents="29 18832"/>
    </justification>
  </clause>

  <clause id="18835">
    <literal><![CDATA[
      T(((x * (y * z)) / y) \ u,K(y,z * x)) = ((y \ (x * (y * z))) \ u) * K(x * z,y)
    ]]></literal>
    <justification jstring="[para(10279(a,1),17488(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10279 17488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18836">
    <literal><![CDATA[
      ((x \ (y * (x * y))) \ z) * K(y * y,x) = ((y * (x * y)) / x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,17041,a(flip),b,18835,a),flip(a)].">
      <j1 rule="hyper" parents="64 17041 18835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18837">
    <literal><![CDATA[
      T(x,(y \ z) * (K(y,T(y \ z,u)) * T(T(y \ z,u),u))) = T(x,T(y \ z,u) * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(10748(a,1),17854(a,1,2))].">
      <j1 rule="para" parents="10748 17854"/>
    </justification>
  </clause>

  <clause id="18838">
    <literal><![CDATA[
      T(x,y / (z \ T(((z * K(u,w)) * v5) * z,K(w,u)))) = T(x,y / (v5 * (K(u,w) * z)))
    ]]></literal>
    <justification jstring="[para(17508(a,1),18225(a,1,2,2,2,1))].">
      <j1 rule="para" parents="17508 18225"/>
    </justification>
  </clause>

  <clause id="18839">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w) / w,v5))) * K(K(z,y),x) = a(v5,K(u,w) / (K(y,z) * w),K(K(z,y),x))
    ]]></literal>
    <justification jstring="[para(12097(a,1),18464(a,1,1))].">
      <j1 rule="para" parents="12097 18464"/>
    </justification>
  </clause>

  <clause id="18840">
    <literal><![CDATA[
      T(x,L(y * K(z,u \ w),K(u \ w,z),T(u,v5))) = T(x,(y * T(u,v5)) / (T(u,v5) * K(w / u,z)))
    ]]></literal>
    <justification jstring="[para(6878(a,1),17617(a,1,2,1))].">
      <j1 rule="para" parents="6878 17617"/>
    </justification>
  </clause>

  <clause id="18841">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K((x \ y) \ 1,T(z,T(x,u))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(11298(a,1),17652(a,1,1))].">
      <j1 rule="para" parents="11298 17652"/>
    </justification>
  </clause>

  <clause id="18842">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(y \ x,T(z,T(x,u))) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(6756(a,1),18841(a,1,2))].">
      <j1 rule="para" parents="6756 18841"/>
    </justification>
  </clause>

  <clause id="18843">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(17105(a,1),18842(a,1,2))].">
      <j1 rule="para" parents="17105 18842"/>
    </justification>
  </clause>

  <clause id="18844">
    <literal><![CDATA[
      a((x \ y) \ 1,z,(x \ y) \ 1) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,16512,a(flip),b,18843,a),flip(a)].">
      <j1 rule="hyper" parents="64 16512 18843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18845">
    <literal><![CDATA[
      a(x \ (x * y),z,x \ (x * y)) * K(T(z,y),1 / ((x * y) \ x)) = K(z * (1 / ((x * y) \ x)),1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(18844(a,1),14276(a,1,1))].">
      <j1 rule="para" parents="18844 14276"/>
    </justification>
  </clause>

  <clause id="18846">
    <literal><![CDATA[
      K(x,L((y * z) / u,y * z,(y * z) \ y)) = K(x,(z \ T(y * z,z \ 1)) / (u * (y / (z * y))))
    ]]></literal>
    <justification jstring="[para(13532(a,1),17837(a,1,2))].">
      <j1 rule="para" parents="13532 17837"/>
    </justification>
  </clause>

  <clause id="18847">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K((K(y \ 1,z) \ (x / y)) * u,u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(17374(a,1),18830(a,1,1))].">
      <j1 rule="para" parents="17374 18830"/>
    </justification>
  </clause>

  <clause id="18848">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K(u * (K(y \ 1,z) \ (x / y)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(8516(a,1),18847(a,1,2))].">
      <j1 rule="para" parents="8516 18847"/>
    </justification>
  </clause>

  <clause id="18849">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K(K(y \ 1,z) \ (u * (x / y)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(10506(a,2),18848(a,1,2))].">
      <j1 rule="para" parents="10506 18848"/>
    </justification>
  </clause>

  <clause id="18850">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K(K(z,y) \ (u * (x / y)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(18829(a,1),18849(a,1,2))].">
      <j1 rule="para" parents="18829 18849"/>
    </justification>
  </clause>

  <clause id="18851">
    <literal><![CDATA[
      K(x,(y \ T(z * y,y \ 1)) / (u * (z / (y * z)))) = K(x,L((z * y) / u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,15960,a(flip),b,18846,a),flip(a)].">
      <j1 rule="hyper" parents="64 15960 18846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18852">
    <literal><![CDATA[
      K(x,((y * z) / z) / (u * (y / (z * y)))) = K(x,L((y * z) / u,y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,18500,a(flip),b,18851,a)].">
      <j1 rule="hyper" parents="64 18500 18851"/>
    </justification>
  </clause>

  <clause id="18853">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,y / (u * (y / (z * y))))
    ]]></literal>
    <justification jstring="[para(11(a,1),18852(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 18852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18854">
    <literal><![CDATA[
      (x \ T(T(x,y),T(y,z))) \ (K(x,T(y,z)) * T(x,x \ y)) = L(R(x,x \ y,x),K(x,y),T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(7867(a,2),17619(a,1,2,1))].">
      <j1 rule="para" parents="7867 17619"/>
    </justification>
  </clause>

  <clause id="18855">
    <literal><![CDATA[
      K(x,y * T(T(z / u,T(w,u)) * v5,v5)) = K(x,y * ((K(u \ z,w) * v5) * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(18531,a,17686,a)].">
      <j1 rule="hyper" parents="18531 17686"/>
    </justification>
  </clause>

  <clause id="18857">
    <literal><![CDATA[
      K(x,y * ((K(z \ u,w) * v5) * (u / z))) = K(x,y * (v5 * T(u / z,T(w,z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,17683,a(flip),b,18855,a),flip(a)].">
      <j1 rule="hyper" parents="64 17683 18855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18858">
    <literal><![CDATA[
      K(x,y * ((K(z \ u,w) * v5) * (u / z))) = K(x,y * (v5 * T(u / z,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18202,a(flip),b,18857,a),flip(a)].">
      <j1 rule="hyper" parents="373 18202 18857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18860">
    <literal><![CDATA[
      K(x,y * (K(z \ u,w) * (v5 * (u / z)))) = K(x,y * (v5 * T(u / z,w)))
    ]]></literal>
    <justification jstring="[para(8017(a,1),18858(a,1,2,2))].">
      <j1 rule="para" parents="8017 18858"/>
    </justification>
  </clause>

  <clause id="18862">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = L(T(x,K(z,y) * (x \ u)),u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,25,a,b,18079,a),flip(a)].">
      <j1 rule="hyper" parents="373 25 18079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18863">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),u * K(y,T(z,x))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(7908(a,1),18265(a,1,2))].">
      <j1 rule="para" parents="7908 18265"/>
    </justification>
  </clause>

  <clause id="18865">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,17611,a(flip),b,18621,a),flip(a)].">
      <j1 rule="hyper" parents="373 17611 18621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18866">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(18190,a,18865,a)].">
      <j1 rule="hyper" parents="18190 18865"/>
    </justification>
  </clause>

  <clause id="18867">
    <literal><![CDATA[
      K(x,y * K(K(z,u) * w,v5)) = K(x,K(w,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(17195,a,18865,a)].">
      <j1 rule="hyper" parents="17195 18865"/>
    </justification>
  </clause>

  <clause id="18868">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(w,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,15767,a,b,18865,a),flip(a)].">
      <j1 rule="hyper" parents="373 15767 18865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18869">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,u) * v5) = v6
    ]]></literal>
    <justification jstring="[para(18865(a,2),15768(a,1))].">
      <j1 rule="para" parents="18865 15768"/>
    </justification>
  </clause>

  <clause id="18871">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y * K(v5,v6)) * u) = w
    ]]></literal>
    <justification jstring="[para(18865(a,1),18190(a,1))].">
      <j1 rule="para" parents="18865 18190"/>
    </justification>
  </clause>

  <clause id="18872">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w)) * v5) = K(x,K(z,y) * (y * v5))
    ]]></literal>
    <justification jstring="[para(5755(a,1),18866(a,1,2))].">
      <j1 rule="para" parents="5755 18866"/>
    </justification>
  </clause>

  <clause id="18873">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(18868(a,2),15768(a,1))].">
      <j1 rule="para" parents="18868 15768"/>
    </justification>
  </clause>

  <clause id="18874">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w)) * v5) = K(x,T(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,15770,a(flip),b,18872,a),flip(a)].">
      <j1 rule="hyper" parents="373 15770 18872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18875">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) * v5) = T(x,T(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(143,a,18874,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 18874 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18876">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),u) * w) = K(x,T(y / ((z \ u) * z),y) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13440,a(flip),b,18874,a)].">
      <j1 rule="hyper" parents="64 13440 18874"/>
    </justification>
  </clause>

  <clause id="18877">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * w) * v5) = T(x,T(y,w) * v5)
    ]]></literal>
    <justification jstring="[para(6576(a,1),18875(a,1,2,1,2))].">
      <j1 rule="para" parents="6576 18875"/>
    </justification>
  </clause>

  <clause id="18878">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * w) * v5) = T(x,T(y,w * K(v6,v7)) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,18875,a,b,18877,a),flip(a)].">
      <j1 rule="hyper" parents="373 18875 18877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18879">
    <literal><![CDATA[
      K(x,K(y / z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z \ y,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(5720(a,1),18873(a,1,2,1,1))].">
      <j1 rule="para" parents="5720 18873"/>
    </justification>
  </clause>

  <clause id="18880">
    <literal><![CDATA[
      K(x,K(y,z / u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u \ z,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(6156(a,2),18879(a,1,2))].">
      <j1 rule="para" parents="6156 18879"/>
    </justification>
  </clause>

  <clause id="18881">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) * (z / (1 / K(v5,v6)))) = T(x,(z / (1 / K(v5,v6))) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17988,a(flip),b,18878,a),flip(a)].">
      <j1 rule="hyper" parents="64 17988 18878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18883">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),u) * w) = K(x,(((z \ u) * z) \ y) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,13443,a(flip),b,18876,a),flip(a)].">
      <j1 rule="hyper" parents="373 13443 18876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18884">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) * (z / K(v5,v6))) = T(x,(z / (1 / K(v6,v5))) * y)
    ]]></literal>
    <justification jstring="[para(6091(a,1),18881(a,1,2,2,2))].">
      <j1 rule="para" parents="6091 18881"/>
    </justification>
  </clause>

  <clause id="18885">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) * (z * K(v5,v6))) = T(x,(z / (1 / K(v5,v6))) * y)
    ]]></literal>
    <justification jstring="[para(6878(a,1),18884(a,1,2,2))].">
      <j1 rule="para" parents="6878 18884"/>
    </justification>
  </clause>

  <clause id="18886">
    <literal><![CDATA[
      (x \ T(T(x,y),T(y,z))) \ (K(y,T(x,z)) \ T(x,x \ y)) = L(R(x,x \ y,x),K(x,y),T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(7914(a,2),18854(a,1,2))].">
      <j1 rule="para" parents="7914 18854"/>
    </justification>
  </clause>

  <clause id="18887">
    <literal><![CDATA[
      (x \ (K(y,L(z,u,x)) * u)) \ (K(y,z) * ((u * x) / x)) = L(T(x,K(z,y) * (x \ u)),u,K(y,z))
    ]]></literal>
    <justification jstring="[para(15522(a,1),18862(a,1,1,2,1))].">
      <j1 rule="para" parents="15522 18862"/>
    </justification>
  </clause>

  <clause id="18888">
    <literal><![CDATA[
      ((x \ y) * K(z,T(u,y))) \ (K(z,u) * ((y * x) / x)) = L(T(x,K(u,z) * (x \ y)),y,K(z,u))
    ]]></literal>
    <justification jstring="[para(15548(a,1),18887(a,1,1))].">
      <j1 rule="para" parents="15548 18887"/>
    </justification>
  </clause>

  <clause id="18889">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),u,K(z,y)) = ((x \ u) * K(z,T(y,u))) \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),18888(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 18888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18890">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),K(z,y) * u) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(18050,a,18863,a)].">
      <j1 rule="hyper" parents="18050 18863"/>
    </justification>
  </clause>

  <clause id="18891">
    <literal><![CDATA[
      (x / T(K(y,z),u * K(z,y))) \ (K(z,y) * u) = (x * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(17415,a,18890,a),flip(a)].">
      <j1 rule="hyper" parents="17415 18890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18893">
    <literal><![CDATA[
      (x / K(y,T(z,u))) \ (K(z,y) * u) = (x * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(18250(a,1),18891(a,1,1,2))].">
      <j1 rule="para" parents="18250 18891"/>
    </justification>
  </clause>

  <clause id="18894">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ (K(y,z) * u) = (x * K(y,z)) \ (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(7908(a,1),18893(a,1,1))].">
      <j1 rule="para" parents="7908 18893"/>
    </justification>
  </clause>

  <clause id="18896">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),u,K(z,y)) = ((x \ u) * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,18889,a,b,18894,a)].">
      <j1 rule="hyper" parents="64 18889 18894"/>
    </justification>
  </clause>

  <clause id="18897">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = (x \ T(T(x,y),T(y,z))) \ T(T(x,y / x),T(y,z))
    ]]></literal>
    <justification jstring="[para(17638(a,1),18886(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17638 18886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18898">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = (x \ T(T(x,y),T(y,z))) \ T(T(x,x \ y),T(y,z))
    ]]></literal>
    <justification jstring="[para(4636(a,1),18897(a,2,2,1))].">
      <j1 rule="para" parents="4636 18897"/>
    </justification>
  </clause>

  <clause id="18899">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = (x \ T(T(x,y),T(y,z))) \ T(T(x,y),x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(18638(a,1),18898(a,2,2))].">
      <j1 rule="para" parents="18638 18898"/>
    </justification>
  </clause>

  <clause id="18900">
    <literal><![CDATA[
      (x \ (1 / x)) * (y \ L((x \ 1) \ z,x,x \ 1)) = T(y,(x \ 1) \ ((x \ 1) \ 1)) \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(1090(a,1),18774(a,1,1))].">
      <j1 rule="para" parents="1090 18774"/>
    </justification>
  </clause>

  <clause id="18901">
    <literal><![CDATA[
      T(x,(y \ 1) \ ((y \ 1) \ 1)) \ ((y \ 1) * z) = (y \ (1 / y)) * (x \ (y * z))
    ]]></literal>
    <justification jstring="[para(1637(a,1),18900(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1637 18900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18902">
    <literal><![CDATA[
      T(x,(y \ 1) \ ((y \ 1) \ 1)) \ ((y \ 1) * z) = (y \ 1) * (y \ (x \ (y * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,1098,a(flip),b,18901,a),flip(a)].">
      <j1 rule="hyper" parents="373 1098 18901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18903">
    <literal><![CDATA[
      T(x,(y \ 1) \ y) \ ((y \ 1) * z) = (y \ 1) * (y \ (x \ (y * z)))
    ]]></literal>
    <justification jstring="[para(5197(a,1),18902(a,1,1))].">
      <j1 rule="para" parents="5197 18902"/>
    </justification>
  </clause>

  <clause id="18904">
    <literal><![CDATA[
      T(x,y * y) \ ((y \ 1) * z) = (y \ 1) * (y \ (x \ (y * z)))
    ]]></literal>
    <justification jstring="[para(14428(a,1),18903(a,1,1))].">
      <j1 rule="para" parents="14428 18903"/>
    </justification>
  </clause>

  <clause id="18905">
    <literal><![CDATA[
      (x * x) \ (y \ ((1 / (1 / x)) * z)) = (x \ 1) * (x \ (y \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,2050,a,b,18904,a)].">
      <j1 rule="hyper" parents="64 2050 18904"/>
    </justification>
  </clause>

  <clause id="18906">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(L(u,w,K(z,y)),w * K(z,y))) = K((w * K(z,y)) * L(u,w,K(z,y)),x)
    ]]></literal>
    <justification jstring="[para(17190(a,2),17459(a,1,1))].">
      <j1 rule="para" parents="17190 17459"/>
    </justification>
  </clause>

  <clause id="18907">
    <literal><![CDATA[
      T((x / T(y,K(z,u))) * T(T(y,K(z,u)),K(w,v5) \ (T(y,K(z,u)) \ x)),K(w,v5)) = y * T(x / y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(8541(a,1),18739(a,1,1,2))].">
      <j1 rule="para" parents="8541 18739"/>
    </justification>
  </clause>

  <clause id="18908">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(L(u,w,K(z,y)),K(y,z) \ w)) = K((w * K(z,y)) * L(u,w,K(z,y)),x)
    ]]></literal>
    <justification jstring="[para(17190(a,2),18906(a,1,2,2))].">
      <j1 rule="para" parents="17190 18906"/>
    </justification>
  </clause>

  <clause id="18909">
    <literal><![CDATA[
      K(x \ T(y \ T(T(y,K(z,u)) * w,K(z,u)),w * T(y,K(z,u))),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(18104,a,17756,a)].">
      <j1 rule="hyper" parents="18104 17756"/>
    </justification>
  </clause>

  <clause id="18911">
    <literal><![CDATA[
      K(x \ T(y \ T(T(y,K(z,u)) * w,K(z,u)),w * y),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[para(17944(a,1),18909(a,1,1,2))].">
      <j1 rule="para" parents="17944 18909"/>
    </justification>
  </clause>

  <clause id="18913">
    <literal><![CDATA[
      T(T(x,K(y,z * (z * T(u,z)))),y * ((z * z) * (T(u,z \ 1) \ 1))) = T(x,((z * z) * (T(u,z \ 1) \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(15752(a,1),17822(a,1,1,2))].">
      <j1 rule="para" parents="15752 17822"/>
    </justification>
  </clause>

  <clause id="18914">
    <literal><![CDATA[
      T(T(x,K(y,z * (u * z))),y * ((z * z) * (T(u,z \ 1) \ 1))) = T(x,((z * z) * (T(u,z \ 1) \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(115(a,1),18913(a,1,1,2,2,2))].">
      <j1 rule="para" parents="115 18913"/>
    </justification>
  </clause>

  <clause id="18915">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * ((u * u) * (T(z,u \ 1) \ 1))) = T(x,((u * u) * (T(z,u \ 1) \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(17569(a,1),18914(a,1,1))].">
      <j1 rule="para" parents="17569 18914"/>
    </justification>
  </clause>

  <clause id="18917">
    <literal><![CDATA[
      a(x,y,z \ (z * x)) * K(T(y,x),1 / ((z * x) \ z)) = K(y * (1 / ((z * x) \ z)),1 / ((z * x) \ z))
    ]]></literal>
    <justification jstring="[para(9(a,1),18845(a,1,1,1))].">
      <j1 rule="para" parents="9 18845"/>
    </justification>
  </clause>

  <clause id="18918">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(T(x,z),1 / ((y * z) \ y))
    ]]></literal>
    <justification jstring="[para(9(a,1),18917(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="9 18917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18919">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(T(x,z),y \ (y * z))
    ]]></literal>
    <justification jstring="[para(6699(a,1),18918(a,2,2))].">
      <j1 rule="para" parents="6699 18918"/>
    </justification>
  </clause>

  <clause id="18921">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(T(x,z),z)
    ]]></literal>
    <justification jstring="[para(9(a,1),18919(a,2,2,2))].">
      <j1 rule="para" parents="9 18919"/>
    </justification>
  </clause>

  <clause id="18922">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(x,z)
    ]]></literal>
    <justification jstring="[para(6111(a,1),18921(a,2,2))].">
      <j1 rule="para" parents="6111 18921"/>
    </justification>
  </clause>

  <clause id="18923">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,10902,a(flip),b,18922,a),flip(a)].">
      <j1 rule="hyper" parents="373 10902 18922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18924">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),y \ (y * z)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(7010,a,18923,a)].">
      <j1 rule="hyper" parents="7010 18923"/>
    </justification>
  </clause>

  <clause id="18925">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),18924(a,1,2))].">
      <j1 rule="para" parents="9 18924"/>
    </justification>
  </clause>

  <clause id="18926">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5249,a(flip),b,18925,a)].">
      <j1 rule="hyper" parents="64 5249 18925"/>
    </justification>
  </clause>

  <clause id="18927">
    <literal><![CDATA[
      K(((x * y) \ x) \ z,y) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(9356,a,18926,a)].">
      <j1 rule="hyper" parents="9356 18926"/>
    </justification>
  </clause>

  <clause id="18928">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ z),y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),18927(a,2,1))].">
      <j1 rule="para" parents="10 18927"/>
    </justification>
  </clause>

  <clause id="18929">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10135,a(flip),b,18928,a),flip(a)].">
      <j1 rule="hyper" parents="64 10135 18928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18930">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(13589,a,18929,a)].">
      <j1 rule="hyper" parents="13589 18929"/>
    </justification>
  </clause>

  <clause id="18932">
    <literal><![CDATA[
      K(x * ((y * z) \ y),z) = K(z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9611,a(flip),b,18930,a)].">
      <j1 rule="hyper" parents="64 9611 18930"/>
    </justification>
  </clause>

  <clause id="18934">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (y \ x),x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),18932(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 18932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18935">
    <literal><![CDATA[
      x * K(x * (y \ z),z \ y) = ((z \ y) \ x) * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,18934,a(flip),b,95,a)].">
      <j1 rule="hyper" parents="145 18934 95"/>
    </justification>
  </clause>

  <clause id="18936">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10798,a,b,18935,a)].">
      <j1 rule="hyper" parents="64 10798 18935"/>
    </justification>
  </clause>

  <clause id="18937">
    <literal><![CDATA[
      x / T(y \ z,x * (z \ y)) = (y \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(36,a,6311,a,b,18935,a(flip))].">
      <j1 rule="hyper" parents="36 6311 18935"/>
    </justification>
  </clause>

  <clause id="18938">
    <literal><![CDATA[
      x * K(x * (y \ z),(y \ z) \ 1) = ((z \ y) \ x) * (z \ y)
    ]]></literal>
    <justification jstring="[para(6700(a,2),18935(a,1,2))].">
      <j1 rule="para" parents="6700 18935"/>
    </justification>
  </clause>

  <clause id="18939">
    <literal><![CDATA[
      T(x \ y,z * (y \ x)) = ((x \ y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(215,a,18937,a),flip(a)].">
      <j1 rule="hyper" parents="215 18937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18940">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ z),x / (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(18937(a,1),8586(a,1,2))].">
      <j1 rule="para" parents="18937 8586"/>
    </justification>
  </clause>

  <clause id="18941">
    <literal><![CDATA[
      T(x \ y,y \ (x * z)) = T(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,12199,a,b,18939,a)].">
      <j1 rule="hyper" parents="373 12199 18939"/>
    </justification>
  </clause>

  <clause id="18942">
    <literal><![CDATA[
      x * K(y \ x,z * (x \ y)) = y * (((y \ x) \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,18939,a(flip),b,6812,a),flip(a)].">
      <j1 rule="hyper" parents="145 18939 6812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18943">
    <literal><![CDATA[
      (((x \ y) \ 1) \ z) * ((x \ y) \ 1) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3717,a(flip),b,18936,a)].">
      <j1 rule="hyper" parents="64 3717 18936"/>
    </justification>
  </clause>

  <clause id="18944">
    <literal><![CDATA[
      K(((1 / (x \ y)) * ((z * (((y \ x) \ u) * (y \ x))) / (1 / (x \ y)))) \ u,w) = K(1 / z,T(w,u / (1 / (x \ y))))
    ]]></literal>
    <justification jstring="[para(18936(a,1),18654(a,1,1,1,2,1,2))].">
      <j1 rule="para" parents="18936 18654"/>
    </justification>
  </clause>

  <clause id="18945">
    <literal><![CDATA[
      ((x \ y) \ ((1 / (x / y)) * x)) * (x \ y) = x * (1 / (x / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16460,a(flip),b,18938,a),flip(a)].">
      <j1 rule="hyper" parents="64 16460 18938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18946">
    <literal><![CDATA[
      ((x * y) \ x) \ T(((x * y) \ x) * z,y) = ((x \ (x * y)) \ z) * (x \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,6748,a,b,18943,a)].">
      <j1 rule="hyper" parents="64 6748 18943"/>
    </justification>
  </clause>

  <clause id="18947">
    <literal><![CDATA[
      ((x \ y) * z) * (z / ((x \ y) * z)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4416,a(flip),b,18943,a)].">
      <j1 rule="hyper" parents="64 4416 18943"/>
    </justification>
  </clause>

  <clause id="18948">
    <literal><![CDATA[
      ((x * y) \ x) \ T(((x * y) \ x) * z,y) = (y \ z) * (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),18946(a,2,1,1))].">
      <j1 rule="para" parents="9 18946"/>
    </justification>
  </clause>

  <clause id="18949">
    <literal><![CDATA[
      ((x * y) \ x) \ T(((x * y) \ x) * z,y) = (y \ z) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,169,a(flip),b,18948,a),flip(a)].">
      <j1 rule="hyper" parents="373 169 18948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18951">
    <literal><![CDATA[
      K(x,y * ((z * x) \ z)) = (((x \ y) * x) \ u) * ((y \ u) \ 1)
    ]]></literal>
    <justification jstring="[para(18949(a,1),16788(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="18949 16788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18952">
    <literal><![CDATA[
      K(x,y * ((z * x) \ z)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,14448,a(flip),b,18951,a),flip(a)].">
      <j1 rule="hyper" parents="373 14448 18951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18954">
    <literal><![CDATA[
      K(x / y,(x / y) \ z) = K(x / y,(x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11689,a(flip),b,18952,a),flip(a)].">
      <j1 rule="hyper" parents="64 11689 18952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18955">
    <literal><![CDATA[
      K(x / y,(x \ y) * z) = K(y \ x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(16154,a,18954,a),flip(a)].">
      <j1 rule="hyper" parents="16154 18954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18957">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (y \ (y * (x / y)))) = K(x \ y,(y \ z) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,17916,a,b,18955,a)].">
      <j1 rule="hyper" parents="64 17916 18955"/>
    </justification>
  </clause>

  <clause id="18958">
    <literal><![CDATA[
      K(x \ (x / (x / y)),z * (x / y)) = K(x \ y,(y \ z) * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),18957(a,1,2,2))].">
      <j1 rule="para" parents="9 18957"/>
    </justification>
  </clause>

  <clause id="18959">
    <literal><![CDATA[
      K((x / y) \ 1,z * (x / y)) = K(x \ y,(y \ z) * x)
    ]]></literal>
    <justification jstring="[hyper(6828,a,18958,a)].">
      <j1 rule="hyper" parents="6828 18958"/>
    </justification>
  </clause>

  <clause id="18961">
    <literal><![CDATA[
      K(x / y,z * (x \ y)) = K(y \ x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(9260,a,18959,a)].">
      <j1 rule="hyper" parents="9260 18959"/>
    </justification>
  </clause>

  <clause id="18963">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,z * (y \ x))) = K(x \ y,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(18961(a,1),9056(a,1,1))].">
      <j1 rule="para" parents="18961 9056"/>
    </justification>
  </clause>

  <clause id="18964">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,x * z)) = K(x \ y,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(17860(a,1),18963(a,1,2))].">
      <j1 rule="para" parents="17860 18963"/>
    </justification>
  </clause>

  <clause id="18965">
    <literal><![CDATA[
      K(x \ y,(y \ z) * x) * K(y,K(x,z)) = K(x \ y,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(8959(a,1),18964(a,1,2))].">
      <j1 rule="para" parents="8959 18964"/>
    </justification>
  </clause>

  <clause id="18966">
    <literal><![CDATA[
      K(x \ y,(y \ x) * z) = K(x \ y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16758,a(flip),b,18965,a),flip(a)].">
      <j1 rule="hyper" parents="64 16758 18965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18967">
    <literal><![CDATA[
      x * K(y \ z,(z \ y) * x) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(18966(a,2),14026(a,1,2))].">
      <j1 rule="para" parents="18966 14026"/>
    </justification>
  </clause>

  <clause id="18968">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,7018,a,b,18967,a)].">
      <j1 rule="hyper" parents="64 7018 18967"/>
    </justification>
  </clause>

  <clause id="18969">
    <literal><![CDATA[
      x * K(y \ z,x * (z \ y)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(7238(a,1),18967(a,1,2))].">
      <j1 rule="para" parents="7238 18967"/>
    </justification>
  </clause>

  <clause id="18970">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,10293,a,b,18969,a)].">
      <j1 rule="hyper" parents="64 10293 18969"/>
    </justification>
  </clause>

  <clause id="18971">
    <literal><![CDATA[
      K(((x \ y) * ((z * (((x \ y) \ u) * (x \ y))) / (x \ y))) \ u,w) = K(1 / z,T(w,u / (1 / (y \ x))))
    ]]></literal>
    <justification jstring="[para(18970(a,1),18944(a,1,1,1))].">
      <j1 rule="para" parents="18970 18944"/>
    </justification>
  </clause>

  <clause id="18972">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(18656,a,18971,a),flip(a)].">
      <j1 rule="hyper" parents="18656 18971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18973">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(18281,a,18972,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18281 18972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18974">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u / w)))) = K(1 / x,T(y,z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18566,a,b,18973,a)].">
      <j1 rule="hyper" parents="64 18566 18973"/>
    </justification>
  </clause>

  <clause id="18975">
    <literal><![CDATA[
      K(1 / x,T(y,z / (u / w))) = K(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(17523,a,18974,a),flip(a)].">
      <j1 rule="hyper" parents="17523 18974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18976">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = K(1 / x,T(y,(w / u) * z)) / x
    ]]></literal>
    <justification jstring="[para(18975(a,1),18567(a,2,1))].">
      <j1 rule="para" parents="18975 18567"/>
    </justification>
  </clause>

  <clause id="18977">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = T(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,5933,a(flip),b,18976,a),flip(a)].">
      <j1 rule="hyper" parents="373 5933 18976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18978">
    <literal><![CDATA[
      T(T(1 / (1 / L(x,y,z)),T(u,(w / v5) * v6)),1 / x) = T(L(x,y,z),T(u,v6 / (v5 / T(w,v7))))
    ]]></literal>
    <justification jstring="[para(18977(a,1),4327(a,1,1))].">
      <j1 rule="para" parents="18977 4327"/>
    </justification>
  </clause>

  <clause id="18979">
    <literal><![CDATA[
      T(L(x,y,z),T(u,w / (v5 / T(v6,v7)))) = T(L(x,y,z),T(u,(v6 / v5) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,4327,a(flip),b,18978,a),flip(a)].">
      <j1 rule="hyper" parents="64 4327 18978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18980">
    <literal><![CDATA[
      K(T(x,y / (z / T(u,w))),L(v5,v6,v7)) = (T(L(v5,v6,v7),T(x,(u / z) * y)) \ 1) * L((v5 \ 1) \ 1,v6,v7)
    ]]></literal>
    <justification jstring="[para(18979(a,1),14310(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="18979 14310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18981">
    <literal><![CDATA[
      K(T(x,y / (z / T(u,w))),L(v5,v6,v7)) = K(T(x,(u / z) * y),L(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(373,a,14310,a(flip),b,18980,a),flip(a)].">
      <j1 rule="hyper" parents="373 14310 18980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18982">
    <literal><![CDATA[
      K(T(x,y / (z / T(u,w))),L(v5,v6,v7)) = K(x,T(L(v5,v6,v7),(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,7869,a(flip),b,18981,a),flip(a)].">
      <j1 rule="hyper" parents="373 7869 18981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18983">
    <literal><![CDATA[
      K(x,T(L(y,z,u),w / (v5 / T(v6,v7)))) = K(x,T(L(y,z,u),(v6 / v5) * w))
    ]]></literal>
    <justification jstring="[hyper(8019,a,18982,a)].">
      <j1 rule="hyper" parents="8019 18982"/>
    </justification>
  </clause>

  <clause id="18984">
    <literal><![CDATA[
      K(x,T(L(y,z,u),w / (v5 / v6))) = K(x,T(L(y,z,u),(v6 / v5) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18564,a(flip),b,18983,a)].">
      <j1 rule="hyper" parents="64 18564 18983"/>
    </justification>
  </clause>

  <clause id="18985">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),(T(w,v5) / v6) * v7)) = K(x,T(y,v7 / (v6 / w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18565,a(flip),b,18984,a),flip(a)].">
      <j1 rule="hyper" parents="64 18565 18984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18986">
    <literal><![CDATA[
      K(x,T(y,(T(z,u) / w) * v5)) = K(x,T(y,v5 / (w / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9210,a(flip),b,18985,a)].">
      <j1 rule="hyper" parents="64 9210 18985"/>
    </justification>
  </clause>

  <clause id="18987">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[para(114(a,1),18986(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="114 18986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18988">
    <literal><![CDATA[
      K(x,T(y,z / (u \ w))) = K(x,T(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(18282,a,18987,a)].">
      <j1 rule="hyper" parents="18282 18987"/>
    </justification>
  </clause>

  <clause id="18990">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,(z / u) * w)) = K(x,T(y,w / (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,8087,a,b,18988,a)].">
      <j1 rule="hyper" parents="373 8087 18988"/>
    </justification>
  </clause>

  <clause id="18991">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(35,a,18353,a,b,18990,a)].">
      <j1 rule="hyper" parents="35 18353 18990"/>
    </justification>
  </clause>

  <clause id="18992">
    <literal><![CDATA[
      K(x,K(y,(z / u) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(9048,a,18991,a)].">
      <j1 rule="hyper" parents="9048 18991"/>
    </justification>
  </clause>

  <clause id="18993">
    <literal><![CDATA[
      K(x,K(y,((z / u) / z) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18308,a(flip),b,18991,a),flip(a)].">
      <j1 rule="hyper" parents="64 18308 18991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18994">
    <literal><![CDATA[
      K(x,K(y,(z / (z * u)) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18305,a(flip),b,18991,a),flip(a)].">
      <j1 rule="hyper" parents="64 18305 18991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18995">
    <literal><![CDATA[
      L(K(x,K(y,(z / u) * w)),v5,v6) = K(y,K(w / (z \ u),L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[para(18991(a,1),18354(a,1,1))].">
      <j1 rule="para" parents="18991 18354"/>
    </justification>
  </clause>

  <clause id="18996">
    <literal><![CDATA[
      K(x,K(y,z * (u / (u * w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[hyper(17389,a,18994,a)].">
      <j1 rule="hyper" parents="17389 18994"/>
    </justification>
  </clause>

  <clause id="18997">
    <literal><![CDATA[
      K(x,K(y,z / (u \ w))) = K(x,K(y,z * (u / w)))
    ]]></literal>
    <justification jstring="[para(10(a,1),18996(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 18996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18998">
    <literal><![CDATA[
      K(x,K(y / (z \ u),L(w,v5,v6))) = K(x,K((z / u) * y,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(12098,a,18995,a),flip(a)].">
      <j1 rule="hyper" parents="12098 18995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18999">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u * y) / (y * (y \ z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,18435,a(flip),b,18998,a),flip(a)].">
      <j1 rule="hyper" parents="64 18435 18998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19000">
    <literal><![CDATA[
      K(x,K(((y / z) / y) * u,L(w,v5,v6))) = K(x,K(u / z,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(82(a,1),18998(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="82 18998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19001">
    <literal><![CDATA[
      K(x,K(y * ((z / u) / z),L(w,v5,v6))) = K(x,K(y / u,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(17433,a,19000,a)].">
      <j1 rule="hyper" parents="17433 19000"/>
    </justification>
  </clause>

  <clause id="19002">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u * y) / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),18999(a,2,2,2,2))].">
      <j1 rule="para" parents="10 18999"/>
    </justification>
  </clause>

  <clause id="19003">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,18296,a,b,19002,a),flip(a)].">
      <j1 rule="hyper" parents="373 18296 19002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19004">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,(y * u) / z)) = v5
    ]]></literal>
    <justification jstring="[para(19002(a,2),18365(a,1))].">
      <j1 rule="para" parents="19002 18365"/>
    </justification>
  </clause>

  <clause id="19005">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,z,y))) = K(x,K(w,(y * ((v5 / u) / v5)) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19001,a(flip),b,19003,a)].">
      <j1 rule="hyper" parents="64 19001 19003"/>
    </justification>
  </clause>

  <clause id="19006">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,(u * y) / z)) = v5
    ]]></literal>
    <justification jstring="[para(19003(a,2),18365(a,1))].">
      <j1 rule="para" parents="19003 18365"/>
    </justification>
  </clause>

  <clause id="19007">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,z,y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,(y * (1 / u)) / z)) = v5
    ]]></literal>
    <justification jstring="[para(14678(a,1),19004(a,1,2))].">
      <j1 rule="para" parents="14678 19004"/>
    </justification>
  </clause>

  <clause id="19008">
    <literal><![CDATA[
      K(x,K((y / z) / (1 / u),L(w,z,y))) = K(x,K(w,(T(y,u) / (1 / u)) / z))
    ]]></literal>
    <justification jstring="[para(4404(a,2),19005(a,2,2,2,1))].">
      <j1 rule="para" parents="4404 19005"/>
    </justification>
  </clause>

  <clause id="19009">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(z * (1 / w)) / v5))
    ]]></literal>
    <justification jstring="[hyper(19007,a,19005,a),flip(a)].">
      <j1 rule="hyper" parents="19007 19005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19010">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(T(y,u) / (1 / u)) / z))
    ]]></literal>
    <justification jstring="[para(14683(a,1),19008(a,1,2))].">
      <j1 rule="para" parents="14683 19008"/>
    </justification>
  </clause>

  <clause id="19011">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / (1 / u)) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = v5
    ]]></literal>
    <justification jstring="[para(19010(a,1),19004(a,1))].">
      <j1 rule="para" parents="19010 19004"/>
    </justification>
  </clause>

  <clause id="19012">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / T(u,z)) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(19011,a,18992,a),flip(a)].">
      <j1 rule="hyper" parents="19011 18992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19013">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) / w))) = K(x,K(y,(w * u) / z))
    ]]></literal>
    <justification jstring="[hyper(18437,a,19012,a)].">
      <j1 rule="hyper" parents="18437 19012"/>
    </justification>
  </clause>

  <clause id="19014">
    <literal><![CDATA[
      K(x,K(y,((z \ 1) / u) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18470,a,b,19013,a)].">
      <j1 rule="hyper" parents="64 18470 19013"/>
    </justification>
  </clause>

  <clause id="19015">
    <literal><![CDATA[
      K(x,K(y,(z * (1 / u)) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18465,a(flip),b,19013,a),flip(a)].">
      <j1 rule="hyper" parents="64 18465 19013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19016">
    <literal><![CDATA[
      K(x,K(y,((z / (z / (u \ 1))) / w) * v5)) = K(x,K(y,(w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(18471,a,19014,a)].">
      <j1 rule="hyper" parents="18471 19014"/>
    </justification>
  </clause>

  <clause id="19017">
    <literal><![CDATA[
      K(x,K(y,z / ((1 / u) * w))) = K(x,K(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(18350,a,19015,a)].">
      <j1 rule="hyper" parents="18350 19015"/>
    </justification>
  </clause>

  <clause id="19018">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(w / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,19009,a,b,19015,a)].">
      <j1 rule="hyper" parents="64 19009 19015"/>
    </justification>
  </clause>

  <clause id="19019">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y / z,z))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16119,a,b,19017,a)].">
      <j1 rule="hyper" parents="64 16119 19017"/>
    </justification>
  </clause>

  <clause id="19020">
    <literal><![CDATA[
      K(x,K(y,((1 / z) * u) / (((1 / z) * u) * w))) = K(x,K(y,(z / u) * (((1 / z) * u) / w)))
    ]]></literal>
    <justification jstring="[para(11703(a,1),19017(a,1,2))].">
      <j1 rule="para" parents="11703 19017"/>
    </justification>
  </clause>

  <clause id="19021">
    <literal><![CDATA[
      K(x,K(y,((z / (z / ((u / z) \ 1))) / w) * v5)) = K(x,K(y,v5 / (((z / (z / u)) / z) * w)))
    ]]></literal>
    <justification jstring="[para(16579(a,1),19017(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="16579 19017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19022">
    <literal><![CDATA[
      K(x,K(y,z / (((u / w) / u) * v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(18350,a,19018,a)].">
      <j1 rule="hyper" parents="18350 19018"/>
    </justification>
  </clause>

  <clause id="19023">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y,z))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16480,a(flip),b,19019,a)].">
      <j1 rule="hyper" parents="64 16480 19019"/>
    </justification>
  </clause>

  <clause id="19024">
    <literal><![CDATA[
      K(x,K(y,(z / u) * (((1 / z) * u) / (((1 / z) * u) * w)))) = K(x,K(y,1 / (w * ((1 / z) * u))))
    ]]></literal>
    <justification jstring="[para(17675(a,1),19020(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17675 19020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19025">
    <literal><![CDATA[
      K(x,K(y,((z / (z / ((u / z) \ 1))) / w) * v5)) = K(x,K(y,((z / u) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,19022,a(flip),b,19021,a),flip(a)].">
      <j1 rule="hyper" parents="373 19022 19021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19027">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,((w / u) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,19016,a(flip),b,19025,a)].">
      <j1 rule="hyper" parents="64 19016 19025"/>
    </justification>
  </clause>

  <clause id="19028">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) / v5)) = K(x,K(y,((u / z) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(18365,a,19027,a)].">
      <j1 rule="hyper" parents="18365 19027"/>
    </justification>
  </clause>

  <clause id="19030">
    <literal><![CDATA[
      K(x,K(y,z / ((u \ w) * v5))) = K(x,K(y,((u / w) / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18401,a(flip),b,19027,a)].">
      <j1 rule="hyper" parents="64 18401 19027"/>
    </justification>
  </clause>

  <clause id="19031">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * w) / v5)) = K(x,K(y,((z / u) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(9048,a,19030,a)].">
      <j1 rule="hyper" parents="9048 19030"/>
    </justification>
  </clause>

  <clause id="19032">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(y,z,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18817,a(flip),b,19031,a),flip(a)].">
      <j1 rule="hyper" parents="64 18817 19031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19033">
    <literal><![CDATA[
      K(x,K(y,(z * u) * ((w / u) / (z * w)))) = a(x,w,K(y,K(z,u / w)))
    ]]></literal>
    <justification jstring="[hyper(17385,a,19032,a)].">
      <j1 rule="hyper" parents="17385 19032"/>
    </justification>
  </clause>

  <clause id="19034">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(y,(u / z) * z,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,15510,a,b,19032,a),flip(a)].">
      <j1 rule="hyper" parents="373 15510 19032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19035">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,((y / w) / (u * y)) * (u * w))) = v5
    ]]></literal>
    <justification jstring="[para(19032(a,1),8436(a,1))].">
      <j1 rule="para" parents="19032 8436"/>
    </justification>
  </clause>

  <clause id="19036">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(x,u,K(y,K(z / u,w / u)))
    ]]></literal>
    <justification jstring="[para(12(a,1),19033(a,1,2,2,2,2))].">
      <j1 rule="para" parents="12 19033"/>
    </justification>
  </clause>

  <clause id="19037">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(y,u,K(x,K(w,u / z)))
    ]]></literal>
    <justification jstring="[para(12(a,1),19034(a,2,2))].">
      <j1 rule="para" parents="12 19034"/>
    </justification>
  </clause>

  <clause id="19038">
    <literal><![CDATA[
      K(x,K(y,(z / u) * (((1 / z) * u) / (((1 / z) * u) * w)))) = K(x,K(y,w * ((1 / z) * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,9020,a(flip),b,19024,a),flip(a)].">
      <j1 rule="hyper" parents="373 9020 19024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19039">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(u / w) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18996,a(flip),b,19038,a),flip(a)].">
      <j1 rule="hyper" parents="64 18996 19038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19041">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,18992,a(flip),b,19039,a),flip(a)].">
      <j1 rule="hyper" parents="373 18992 19039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19042">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(295(a,1),19041(a,1,2,2,2))].">
      <j1 rule="para" parents="295 19041"/>
    </justification>
  </clause>

  <clause id="19043">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,18292,a(flip),b,19042,a),flip(a)].">
      <j1 rule="hyper" parents="373 18292 19042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19045">
    <literal><![CDATA[
      K(x,K(y,R(z / u,w,v5) * (w * v5))) = K(x,K(y,(((1 / u) * z) * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18834,a(flip),b,19043,a),flip(a)].">
      <j1 rule="hyper" parents="64 18834 19043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19047">
    <literal><![CDATA[
      K(x,K(y,(((1 / z) * u) * w) * v5)) = K(x,K(y,((u / z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(111(a,1),19045(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="111 19045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19048">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) * v5)) = K(x,K(y,((w / u) * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18295,a,b,19047,a)].">
      <j1 rule="hyper" parents="64 18295 19047"/>
    </justification>
  </clause>

  <clause id="19049">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * T(v5,v6))) = K(x,K(y,v5 * (w * ((1 / u) * z))))
    ]]></literal>
    <justification jstring="[hyper(18438,a,19048,a),flip(a)].">
      <j1 rule="hyper" parents="18438 19048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19050">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) * (1 / v5)))
    ]]></literal>
    <justification jstring="[hyper(17661,a,19048,a)].">
      <j1 rule="hyper" parents="17661 19048"/>
    </justification>
  </clause>

  <clause id="19051">
    <literal><![CDATA[
      K(x,K(y,z * (u * ((1 / w) * v5)))) = K(x,K(y,z * ((v5 / w) * u)))
    ]]></literal>
    <justification jstring="[hyper(18438,a,19049,a),flip(a)].">
      <j1 rule="hyper" parents="18438 19049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19052">
    <literal><![CDATA[
      K(x,K(y,z * (((1 / u) * w) * v5))) = K(x,K(y,z * ((w / u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(18440,a,19051,a)].">
      <j1 rule="hyper" parents="18440 19051"/>
    </justification>
  </clause>

  <clause id="19053">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) / v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,12565,a(flip),b,19050,a),flip(a)].">
      <j1 rule="hyper" parents="373 12565 19050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19054">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((u / w) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,19028,a(flip),b,19053,a),flip(a)].">
      <j1 rule="hyper" parents="373 19028 19053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19055">
    <literal><![CDATA[
      K(x,K(y,z / (u * ((1 / w) * v5)))) = K(x,K(y,((w / v5) / u) * z))
    ]]></literal>
    <justification jstring="[hyper(9048,a,19054,a)].">
      <j1 rule="hyper" parents="9048 19054"/>
    </justification>
  </clause>

  <clause id="19056">
    <literal><![CDATA[
      K(x,K(y,((z / u) / w) * ((w * (1 / z)) * u))) = K(x,K(y,a(w,1 / z,u)))
    ]]></literal>
    <justification jstring="[para(14353(a,1),19055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14353 19055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19057">
    <literal><![CDATA[
      K(x,K(y,((z / u) / w) * ((w * (1 / z)) * u))) = a(x,1 / z,K(y,K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,15377,a,b,19056,a),flip(a)].">
      <j1 rule="hyper" parents="373 15377 19056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19058">
    <literal><![CDATA[
      K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w)) = K(x,L(y / ((y \ z) * y),u,w) / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16345,a(flip),b,17791,a),flip(a)].">
      <j1 rule="hyper" parents="64 16345 17791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19059">
    <literal><![CDATA[
      K(x,T(1 / (y / z),y) * L(T(1 / (y / z),y) \ 1,u,w)) = K(x,L(y / ((y \ z) * y),u,w) / (z \ y))
    ]]></literal>
    <justification jstring="[para(66(a,1),19058(a,1,2,1))].">
      <j1 rule="para" parents="66 19058"/>
    </justification>
  </clause>

  <clause id="19060">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * (K(z,u) * v5)))) = K(x,K(R(w,K(z,u),v5),L(y,K(z,u) * v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(17254,a,18436,a),flip(a)].">
      <j1 rule="hyper" parents="17254 18436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19062">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * (K(z,u) * v5)))) = K(x,K(w,L(L(y,K(z,u) * v5,v6),K(z,u),v5)))
    ]]></literal>
    <justification jstring="[para(15572(a,1),19060(a,2,2))].">
      <j1 rule="para" parents="15572 19060"/>
    </justification>
  </clause>

  <clause id="19063">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * (K(z,u) * v5)))) = K(x,K(w,L(y,K(z,u) * v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18560,a(flip),b,19062,a),flip(a)].">
      <j1 rule="hyper" parents="373 18560 19062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19064">
    <literal><![CDATA[
      K(x,K(y,(((K(z,u) * w) * v5) * v6) / (v6 * v5))) = K(x,K(w,L(y,K(z,u) * v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(18472,a,19063,a)].">
      <j1 rule="hyper" parents="18472 19063"/>
    </justification>
  </clause>

  <clause id="19066">
    <literal><![CDATA[
      K(x,K(y,L(K(z,u) * w,v5,v6))) = K(x,K(w,L(y,K(z,u) * v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18348,a(flip),b,19064,a)].">
      <j1 rule="hyper" parents="64 18348 19064"/>
    </justification>
  </clause>

  <clause id="19067">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w) * v5,v6))) = K(x,K(y,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18336,a(flip),b,19066,a),flip(a)].">
      <j1 rule="hyper" parents="64 18336 19066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19069">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(z,K(x,y)),K(v6,v7) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(19067(a,1),12118(a,1))].">
      <j1 rule="para" parents="19067 12118"/>
    </justification>
  </clause>

  <clause id="19070">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w) / v5,v6))) = K(x,K(y,L(z,1 / v5,v6)))
    ]]></literal>
    <justification jstring="[para(14366(a,1),19067(a,1,2,2,2))].">
      <j1 rule="para" parents="14366 19067"/>
    </justification>
  </clause>

  <clause id="19071">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w) / v5,v6))) = K(x,K(z,L(y,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,12173,a(flip),b,19070,a),flip(a)].">
      <j1 rule="hyper" parents="373 12173 19070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19072">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = K(v5,K(w,L(u,z,x))) * K(K(w,u),v5)
    ]]></literal>
    <justification jstring="[para(19071(a,1),18839(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19071 18839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19073">
    <literal><![CDATA[
      L(K(x,K(y,z)),K(u,w) * v5,v6) = a(x,v5,K(v6,K(y,z))) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(19069,a,15457,a(flip))].">
      <j1 rule="hyper" parents="19069 15457"/>
    </justification>
  </clause>

  <clause id="19074">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,K(v5,v6))) = a(x,u,K(w,K(v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(15458,a,19073,a)].">
      <j1 rule="hyper" parents="15458 19073"/>
    </justification>
  </clause>

  <clause id="19075">
    <literal><![CDATA[
      a(x,y / z,K(u,K(w,v5))) = a(x,z \ y,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(5720(a,1),19074(a,1,2))].">
      <j1 rule="para" parents="5720 19074"/>
    </justification>
  </clause>

  <clause id="19076">
    <literal><![CDATA[
      a(x,y * (z / y),K(u,K(w,v5))) = a(x,z,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(5781(a,1),19074(a,1,2))].">
      <j1 rule="para" parents="5781 19074"/>
    </justification>
  </clause>

  <clause id="19077">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w * y))) = a(x,w,K((1 / y) / w,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12579,a(flip),b,19076,a),flip(a)].">
      <j1 rule="hyper" parents="64 12579 19076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19078">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w * y))) = a(x,w,K(z,K(u,(1 / y) / w)))
    ]]></literal>
    <justification jstring="[para(8110(a,2),19077(a,2,3))].">
      <j1 rule="para" parents="8110 19077"/>
    </justification>
  </clause>

  <clause id="19079">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w * y))) = a(x,w,K(z,K(u,w * y)))
    ]]></literal>
    <justification jstring="[para(12577(a,1),19078(a,2,3))].">
      <j1 rule="para" parents="12577 19078"/>
    </justification>
  </clause>

  <clause id="19080">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(u,K(w,z))) = a(x,y,K(u,K(w,y * (y \ z))))
    ]]></literal>
    <justification jstring="[para(10(a,1),19079(a,1,3,2,2))].">
      <j1 rule="para" parents="10 19079"/>
    </justification>
  </clause>

  <clause id="19081">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(u,K(w,y * (y \ z))))
    ]]></literal>
    <justification jstring="[para(8110(a,1),19080(a,1,3))].">
      <j1 rule="para" parents="8110 19080"/>
    </justification>
  </clause>

  <clause id="19082">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(u,K(w,z)))
    ]]></literal>
    <justification jstring="[para(10(a,1),19081(a,2,3,2,2))].">
      <j1 rule="para" parents="10 19081"/>
    </justification>
  </clause>

  <clause id="19083">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8110(a,1),19082(a,2,3))].">
      <j1 rule="para" parents="8110 19082"/>
    </justification>
  </clause>

  <clause id="19084">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,z / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(82(a,1),19083(a,1,2,2))].">
      <j1 rule="para" parents="82 19083"/>
    </justification>
  </clause>

  <clause id="19085">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[para(8110(a,2),19084(a,1,3))].">
      <j1 rule="para" parents="8110 19084"/>
    </justification>
  </clause>

  <clause id="19086">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8110(a,2),19085(a,2,3))].">
      <j1 rule="para" parents="8110 19085"/>
    </justification>
  </clause>

  <clause id="19087">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(15667,a,19086,a)].">
      <j1 rule="hyper" parents="15667 19086"/>
    </justification>
  </clause>

  <clause id="19088">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(8126(a,1),19087(a,2,3))].">
      <j1 rule="para" parents="8126 19087"/>
    </justification>
  </clause>

  <clause id="19089">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = K(v5,K(w,L(u,z,x))) * K(v5,K(w,u))
    ]]></literal>
    <justification jstring="[para(8123(a,1),19072(a,2,2))].">
      <j1 rule="para" parents="8123 19072"/>
    </justification>
  </clause>

  <clause id="19091">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = K(K(w,L(u,z,x)) * K(u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,12364,a(flip),b,19089,a),flip(a)].">
      <j1 rule="hyper" parents="373 12364 19089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19092">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = K(a(x,z * u,K(u,w)),v5)
    ]]></literal>
    <justification jstring="[para(10420(a,1),19091(a,2,1))].">
      <j1 rule="para" parents="10420 19091"/>
    </justification>
  </clause>

  <clause id="19093">
    <literal><![CDATA[
      a(x,K(y,z) / (K(u,w) * z),K(K(w,u),v5)) = a(u,z,K(v5,K(w,x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,16100,a(flip),b,19092,a),flip(a)].">
      <j1 rule="hyper" parents="373 16100 19092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19094">
    <literal><![CDATA[
      a(x,(K(y,z) / z) * K(u,w),K(K(u,w),v5)) = a(w,z,K(v5,K(u,x)))
    ]]></literal>
    <justification jstring="[para(18463(a,1),19093(a,1,2))].">
      <j1 rule="para" parents="18463 19093"/>
    </justification>
  </clause>

  <clause id="19095">
    <literal><![CDATA[
      a(x,(K(y,z) / z) * K(u,w),K(v5,K(u,w))) = a(w,z,K(v5,K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(15409,a,19094,a)].">
      <j1 rule="hyper" parents="15409 19094"/>
    </justification>
  </clause>

  <clause id="19096">
    <literal><![CDATA[
      a(x,K(y,z) / z,K(u,K(w,v5))) = a(v5,z,K(u,K(w,x)))
    ]]></literal>
    <justification jstring="[hyper(12164,a,19095,a)].">
      <j1 rule="hyper" parents="12164 19095"/>
    </justification>
  </clause>

  <clause id="19097">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(188(a,1),19096(a,1,2,1))].">
      <j1 rule="para" parents="188 19096"/>
    </justification>
  </clause>

  <clause id="19098">
    <literal><![CDATA[
      K(x,K(y,((z / u) / w) * ((w * (1 / z)) * u))) = a(u,z,K(y,K(w,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19057,a,b,19097,a)].">
      <j1 rule="hyper" parents="64 19057 19097"/>
    </justification>
  </clause>

  <clause id="19099">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(x,z,K(u,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19088,a(flip),b,19097,a)].">
      <j1 rule="hyper" parents="64 19088 19097"/>
    </justification>
  </clause>

  <clause id="19100">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(y,z,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,15668,a,b,19099,a),flip(a)].">
      <j1 rule="hyper" parents="373 15668 19099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19101">
    <literal><![CDATA[
      K(x,K(y,((z / u) / w) * ((w * (1 / z)) * u))) = a(u,z,K(x,K(y,w)))
    ]]></literal>
    <justification jstring="[para(8110(a,1),19098(a,2,3))].">
      <j1 rule="para" parents="8110 19098"/>
    </justification>
  </clause>

  <clause id="19102">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (1 / (K(w,1 / z) / w))) * (((1 / z) * (1 / (1 / w))) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[para(14712(a,1),19101(a,1,2,2,2,1))].">
      <j1 rule="para" parents="14712 19101"/>
    </justification>
  </clause>

  <clause id="19103">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ L(T(K(y,z) / u,u * K(z,y)),w,v5)) = K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z))))
    ]]></literal>
    <justification jstring="[para(14592(a,1),18584(a,1,2,2,1,2))].">
      <j1 rule="para" parents="14592 18584"/>
    </justification>
  </clause>

  <clause id="19104">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ L(K(y,z) * (u \ 1),w,v5)) = K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z))))
    ]]></literal>
    <justification jstring="[para(18386(a,1),19103(a,1,2,2,1))].">
      <j1 rule="para" parents="18386 19103"/>
    </justification>
  </clause>

  <clause id="19105">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (1 / (K(w,1 / z) / w))) * (((1 / z) * w) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[para(16439(a,1),19102(a,1,2))].">
      <j1 rule="para" parents="16439 19102"/>
    </justification>
  </clause>

  <clause id="19106">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * K(1 / z,w))) * (((1 / z) * w) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[para(14600(a,1),19105(a,1,2))].">
      <j1 rule="para" parents="14600 19105"/>
    </justification>
  </clause>

  <clause id="19107">
    <literal><![CDATA[
      K(x,K(y,(((z / u) / w) * K(w,1 / z)) * (((1 / z) * w) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[para(6959(a,1),19106(a,1,2,2,1))].">
      <j1 rule="para" parents="6959 19106"/>
    </justification>
  </clause>

  <clause id="19108">
    <literal><![CDATA[
      K(x,K(y,(((z / u) / w) * K(w,1 / z)) * ((w / z) * u))) = a(u,z,K(x,K(y,1 / (K(w,1 / z) / w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,19052,a(flip),b,19107,a)].">
      <j1 rule="hyper" parents="64 19052 19107"/>
    </justification>
  </clause>

  <clause id="19109">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,1 / (K(z,1 / u) / z))))
    ]]></literal>
    <justification jstring="[hyper(18358,a,19108,a)].">
      <j1 rule="hyper" parents="18358 19108"/>
    </justification>
  </clause>

  <clause id="19110">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,z * K(1 / u,z))))
    ]]></literal>
    <justification jstring="[para(6915(a,1),19109(a,2,3,2))].">
      <j1 rule="para" parents="6915 19109"/>
    </justification>
  </clause>

  <clause id="19111">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(18289(a,1),19110(a,2,3))].">
      <j1 rule="para" parents="18289 19110"/>
    </justification>
  </clause>

  <clause id="19112">
    <literal><![CDATA[
      a(x,y,K(z,K(u / y,w / y))) = a(w,y,K(x,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19036,a(flip),b,19111,a)].">
      <j1 rule="hyper" parents="64 19036 19111"/>
    </justification>
  </clause>

  <clause id="19114">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(y,w / (y \ z)))) = a(w,y \ z,K(x,K(u,z)))
    ]]></literal>
    <justification jstring="[para(79(a,1),19112(a,1,3,2,1))].">
      <j1 rule="para" parents="79 19112"/>
    </justification>
  </clause>

  <clause id="19115">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(y,w * (y / z)))) = a(w,y \ z,K(x,K(u,z)))
    ]]></literal>
    <justification jstring="[para(18997(a,1),19114(a,1,3))].">
      <j1 rule="para" parents="18997 19114"/>
    </justification>
  </clause>

  <clause id="19116">
    <literal><![CDATA[
      a(x,y \ z,K(y,K(u,w * (y / z)))) = a(w,y \ z,K(x,K(u,z)))
    ]]></literal>
    <justification jstring="[para(8108(a,1),19115(a,1,3))].">
      <j1 rule="para" parents="8108 19115"/>
    </justification>
  </clause>

  <clause id="19117">
    <literal><![CDATA[
      a(x,y \ z,K(y,K(u,w / z))) = a(w,y \ z,K(x,K(u,z)))
    ]]></literal>
    <justification jstring="[para(18491(a,1),19116(a,1,3))].">
      <j1 rule="para" parents="18491 19116"/>
    </justification>
  </clause>

  <clause id="19118">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(w,z))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[hyper(15410,a,19117,a),flip(a)].">
      <j1 rule="hyper" parents="15410 19117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19119">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(z,w))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[para(8126(a,1),19118(a,1,3))].">
      <j1 rule="para" parents="8126 19118"/>
    </justification>
  </clause>

  <clause id="19120">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(u,y,K(z,K(w,x / y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19075,a,b,19119,a)].">
      <j1 rule="hyper" parents="64 19075 19119"/>
    </justification>
  </clause>

  <clause id="19121">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19100,a(flip),b,19120,a),flip(a)].">
      <j1 rule="hyper" parents="64 19100 19120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19122">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(8108(a,1),19121(a,2,3))].">
      <j1 rule="para" parents="8108 19121"/>
    </justification>
  </clause>

  <clause id="19123">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(19035,a,19122,a)].">
      <j1 rule="hyper" parents="19035 19122"/>
    </justification>
  </clause>

  <clause id="19124">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[para(8110(a,2),19123(a,2,3))].">
      <j1 rule="para" parents="8110 19123"/>
    </justification>
  </clause>

  <clause id="19125">
    <literal><![CDATA[
      a(x,y,K(z,K(u,y / w))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19037,a(flip),b,19124,a)].">
      <j1 rule="hyper" parents="64 19037 19124"/>
    </justification>
  </clause>

  <clause id="19126">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[para(9021(a,1),19125(a,1,3))].">
      <j1 rule="para" parents="9021 19125"/>
    </justification>
  </clause>

  <clause id="19127">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(y,u)))
    ]]></literal>
    <justification jstring="[para(8126(a,1),19126(a,2,3))].">
      <j1 rule="para" parents="8126 19126"/>
    </justification>
  </clause>

  <clause id="19128">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,z,K(x,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19122,a(flip),b,19127,a),flip(a)].">
      <j1 rule="hyper" parents="64 19122 19127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19129">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(z,K(x,w)) = L(K(z,K(x,w)),u,y)
    ]]></literal>
    <justification jstring="[para(19128(a,1),15454(a,1,1))].">
      <j1 rule="para" parents="19128 15454"/>
    </justification>
  </clause>

  <clause id="19130">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(x,K(z,w)) = L(K(z,K(x,w)),u,y)
    ]]></literal>
    <justification jstring="[para(8108(a,1),19129(a,1,2))].">
      <j1 rule="para" parents="8108 19129"/>
    </justification>
  </clause>

  <clause id="19131">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,w,u)))
    ]]></literal>
    <justification jstring="[hyper(16212,a,19130,a),flip(a)].">
      <j1 rule="hyper" parents="16212 19130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19132">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[hyper(12159,a,19131,a)].">
      <j1 rule="hyper" parents="12159 19131"/>
    </justification>
  </clause>

  <clause id="19133">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,19023,a(flip),b,19132,a),flip(a)].">
      <j1 rule="hyper" parents="373 19023 19132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19134">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,v5 \ ((v5 / (w * u)) * (w * (u * z)))))
    ]]></literal>
    <justification jstring="[para(972(a,1),19132(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="972 19132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19135">
    <literal><![CDATA[
      K(x,K(y,L(L(1 / z,z,u),w,u * z))) = K(x,K(y,1 / L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(7357(a,1),19132(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7357 19132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19136">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(z / w) * u))
    ]]></literal>
    <justification jstring="[hyper(19006,a,19133,a)].">
      <j1 rule="hyper" parents="19006 19133"/>
    </justification>
  </clause>

  <clause id="19137">
    <literal><![CDATA[
      K(x,K(y,L(L(1 / z,z,u),w,u * z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(19135(a,2),9047(a,1))].">
      <j1 rule="para" parents="19135 9047"/>
    </justification>
  </clause>

  <clause id="19138">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,((v5 / (w * u)) * (w * (u * z))) / v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,17225,a,b,19134,a),flip(a)].">
      <j1 rule="hyper" parents="373 17225 19134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19139">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,((v5 / (w * u)) / v5) * (w * (u * z))))
    ]]></literal>
    <justification jstring="[hyper(373,a,19136,a(flip),b,19138,a),flip(a)].">
      <j1 rule="hyper" parents="373 19136 19138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19140">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,(w * (u * z)) / (w * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18993,a(flip),b,19139,a),flip(a)].">
      <j1 rule="hyper" parents="373 18993 19139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19143">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,T(L(z,u,w),w * u)))
    ]]></literal>
    <justification jstring="[para(8291(a,1),19140(a,2,2))].">
      <j1 rule="para" parents="8291 19140"/>
    </justification>
  </clause>

  <clause id="19144">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5 / (w * u),w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,17224,a(flip),b,19143,a),flip(a)].">
      <j1 rule="hyper" parents="373 17224 19143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19147">
    <literal><![CDATA[
      K(x,K(y,L(L(z,u,w),v5,w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16480,a(flip),b,19144,a)].">
      <j1 rule="hyper" parents="64 16480 19144"/>
    </justification>
  </clause>

  <clause id="19148">
    <literal><![CDATA[
      K(x,K(y,L(1 / z,z,u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(19137,a,19147,a),flip(a)].">
      <j1 rule="hyper" parents="19137 19147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19150">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,1 / z))
    ]]></literal>
    <justification jstring="[para(7542(a,1),19148(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7542 19148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19152">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,9020,a(flip),b,19150,a),flip(a)].">
      <j1 rule="hyper" parents="373 9020 19150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19154">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ (w * u))) = K(x,K(y,w / z))
    ]]></literal>
    <justification jstring="[hyper(17529,a,19152,a)].">
      <j1 rule="hyper" parents="17529 19152"/>
    </justification>
  </clause>

  <clause id="19156">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12111,a,19152,a)].">
      <j1 rule="hyper" parents="12111 19152"/>
    </justification>
  </clause>

  <clause id="19162">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,19152,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 19152 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19163">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,L(z,u,w) / y) = K(x,y \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(19152(a,1),9063(a,1,1))].">
      <j1 rule="para" parents="19152 9063"/>
    </justification>
  </clause>

  <clause id="19164">
    <literal><![CDATA[
      (x * y) * K(z,K(u,w)) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(19152(a,1),12145(a,1,2))].">
      <j1 rule="para" parents="19152 12145"/>
    </justification>
  </clause>

  <clause id="19166">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(19152(a,1),17334(a,1,1))].">
      <j1 rule="para" parents="19152 17334"/>
    </justification>
  </clause>

  <clause id="19167">
    <literal><![CDATA[
      K(x * K(y,z),L(x,u,w)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(13669,a,19156,a)].">
      <j1 rule="hyper" parents="13669 19156"/>
    </justification>
  </clause>

  <clause id="19170">
    <literal><![CDATA[
      x * ((x \ y) * K(z,K(u,w))) = y * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,19156,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 19156 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19172">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = K(x,K(y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[para(19156(a,1),15594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19156 15594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19173">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = (K(x,K(y,z)) \ u) * w
    ]]></literal>
    <justification jstring="[para(19156(a,1),15640(a,1,1))].">
      <j1 rule="para" parents="19156 15640"/>
    </justification>
  </clause>

  <clause id="19176">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,L(x,u,w))) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8163,a(flip),b,19162,a),flip(a)].">
      <j1 rule="hyper" parents="373 8163 19162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19178">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(w,K(x,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      w * K(x,L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(19162(a,1),328(a,1,2))].">
      <j1 rule="para" parents="19162 328"/>
    </justification>
  </clause>

  <clause id="19179">
    <literal><![CDATA[
      T(x,K(y,(z \ u) \ w)) = T(x,K(y,u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(630(a,1),19162(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="630 19162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19180">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7537(a,1),19162(a,1,2))].">
      <j1 rule="para" parents="7537 19162"/>
    </justification>
  </clause>

  <clause id="19181">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(15403,a,19180,a)].">
      <j1 rule="hyper" parents="15403 19180"/>
    </justification>
  </clause>

  <clause id="19182">
    <literal><![CDATA[
      T(x / L(K(y,z),u,w),K(y,z)) = L(K(y,z),u,w) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,19180,a),flip(a)].">
      <j1 rule="hyper" parents="467 19180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19183">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w)) = T(x,K(y,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,19162,a,b,19180,a),flip(a)].">
      <j1 rule="hyper" parents="373 19162 19180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19184">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,16628,a(flip),b,19180,a),flip(a)].">
      <j1 rule="hyper" parents="41 16628 19180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19187">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(2149,a,19181,a),flip(a)].">
      <j1 rule="hyper" parents="2149 19181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19188">
    <literal><![CDATA[
      T(x,L(y,z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15395,a(flip),b,19181,a)].">
      <j1 rule="hyper" parents="64 15395 19181"/>
    </justification>
  </clause>

  <clause id="19189">
    <literal><![CDATA[
      T(a(x,y,K(z,u)),w) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(55,a,19181,a)].">
      <j1 rule="hyper" parents="55 19181"/>
    </justification>
  </clause>

  <clause id="19190">
    <literal><![CDATA[
      a(K(x,y),z,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,19181,a(flip),b,15728,a),flip(a)].">
      <j1 rule="hyper" parents="140 19181 15728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19191">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      w * a(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(19181(a,1),328(a,1,2))].">
      <j1 rule="para" parents="19181 328"/>
    </justification>
  </clause>

  <clause id="19192">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w) \ z)) = x
    ]]></literal>
    <justification jstring="[para(13953(a,2),19181(a,1,2))].">
      <j1 rule="para" parents="13953 19181"/>
    </justification>
  </clause>

  <clause id="19193">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w))) = x
    ]]></literal>
    <justification jstring="[para(13958(a,1),19181(a,1,2))].">
      <j1 rule="para" parents="13958 19181"/>
    </justification>
  </clause>

  <clause id="19194">
    <literal><![CDATA[
      T(x,K(a(y,z,u),w)) = x
    ]]></literal>
    <justification jstring="[para(13977(a,1),19181(a,1,2))].">
      <j1 rule="para" parents="13977 19181"/>
    </justification>
  </clause>

  <clause id="19195">
    <literal><![CDATA[
      R(x,y,T(z,K(u,w))) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(16606,a,19184,a)].">
      <j1 rule="hyper" parents="16606 19184"/>
    </justification>
  </clause>

  <clause id="19196">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(743,a,19184,a),flip(a)].">
      <j1 rule="hyper" parents="743 19184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19198">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[hyper(225,a,19184,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 19184 10262"/>
    </justification>
  </clause>

  <clause id="19199">
    <literal><![CDATA[
      (a(K(x,y),z,u) \ w) * a(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[hyper(144,a,16619,a(flip),b,19184,a(flip))].">
      <j1 rule="hyper" parents="144 16619 19184"/>
    </justification>
  </clause>

  <clause id="19200">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(19184(a,1),51(a,2))].">
      <j1 rule="para" parents="19184 51"/>
    </justification>
  </clause>

  <clause id="19201">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ (x * (K(y,K(z,u)) * (w * v5))) = L(v5,K(y,K(z,u)) * w,x)
    ]]></literal>
    <justification jstring="[para(19184(a,1),602(a,2,1))].">
      <j1 rule="para" parents="19184 602"/>
    </justification>
  </clause>

  <clause id="19202">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ ((K(x,K(y,z)) * u) * (w * v5)) = L(v5,L(w,u,K(x,K(y,z))),K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(19184(a,1),601(a,1,2,2,1))].">
      <j1 rule="para" parents="19184 601"/>
    </justification>
  </clause>

  <clause id="19203">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ ((x * (K(y,K(z,u)) * w)) * v5) = a(x,K(y,K(z,u)) * w,L(v5,w,K(y,K(z,u))))
    ]]></literal>
    <justification jstring="[para(19184(a,1),599(a,1,2,2))].">
      <j1 rule="para" parents="19184 599"/>
    </justification>
  </clause>

  <clause id="19208">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,w) = K(x,y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(1432,a,19190,a)].">
      <j1 rule="hyper" parents="1432 19190"/>
    </justification>
  </clause>

  <clause id="19210">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,19190,a)].">
      <j1 rule="hyper" parents="53 19190"/>
    </justification>
  </clause>

  <clause id="19211">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8733,a,19193,a)].">
      <j1 rule="hyper" parents="8733 19193"/>
    </justification>
  </clause>

  <clause id="19212">
    <literal><![CDATA[
      T(x,y / a(z,u,w)) = T(x,a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(8727,a,19193,a),flip(a)].">
      <j1 rule="hyper" parents="8727 19193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19214">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7857,a,19193,a)].">
      <j1 rule="hyper" parents="7857 19193"/>
    </justification>
  </clause>

  <clause id="19215">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11151,a(flip),b,19193,a)].">
      <j1 rule="hyper" parents="64 11151 19193"/>
    </justification>
  </clause>

  <clause id="19217">
    <literal><![CDATA[
      K(x,K(a(y,z,u),w)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,19193,a(flip),b,18309,a),flip(a)].">
      <j1 rule="hyper" parents="140 19193 18309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19218">
    <literal><![CDATA[
      T(x,K(a(y,z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(19193(a,1),7832(a,1,1))].">
      <j1 rule="para" parents="19193 7832"/>
    </justification>
  </clause>

  <clause id="19219">
    <literal><![CDATA[
      x \ T(y * x,K(a(z,u,w),v5)) = T(y,K(v5,a(z,u,w)) * x)
    ]]></literal>
    <justification jstring="[para(19193(a,1),16803(a,1,2,1,2))].">
      <j1 rule="para" parents="19193 16803"/>
    </justification>
  </clause>

  <clause id="19228">
    <literal><![CDATA[
      T(x / L(y,z,K(u,w)),y) = L(y,z,K(u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,19188,a),flip(a)].">
      <j1 rule="hyper" parents="467 19188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19229">
    <literal><![CDATA[
      ((x * L(x \ y,z,u)) \ y) \ y = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16792,a(flip),b,19188,a)].">
      <j1 rule="hyper" parents="64 16792 19188"/>
    </justification>
  </clause>

  <clause id="19230">
    <literal><![CDATA[
      T(x,(y * K(z,L(u,w,v5))) / (v5 * w)) = T(x,y / (v5 * (w * K(u,z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,16770,a(flip),b,19188,a),flip(a)].">
      <j1 rule="hyper" parents="64 16770 19188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19232">
    <literal><![CDATA[
      T(x,T((K(y,z) * u) \ w,v5)) = T(x,T(u \ (K(y,z) \ w),v5))
    ]]></literal>
    <justification jstring="[para(708(a,1),19188(a,1,2))].">
      <j1 rule="para" parents="708 19188"/>
    </justification>
  </clause>

  <clause id="19233">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,u \ (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(6190(a,1),19188(a,1,2))].">
      <j1 rule="para" parents="6190 19188"/>
    </justification>
  </clause>

  <clause id="19234">
    <literal><![CDATA[
      T(x,L(y,z,T(u,w))) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11758(a,1),19188(a,1,2))].">
      <j1 rule="para" parents="11758 19188"/>
    </justification>
  </clause>

  <clause id="19235">
    <literal><![CDATA[
      K(x,T(y,z) / L(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z,u,K(w,v5)) \ y) = v6
    ]]></literal>
    <justification jstring="[para(19188(a,1),13354(a,1,2,1))].">
      <j1 rule="para" parents="19188 13354"/>
    </justification>
  </clause>

  <clause id="19236">
    <literal><![CDATA[
      T(x,K(y,z \ L(z,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(9050,a,19192,a)].">
      <j1 rule="hyper" parents="9050 19192"/>
    </justification>
  </clause>

  <clause id="19237">
    <literal><![CDATA[
      T(K(x,y),a(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(16633,a,19210,a)].">
      <j1 rule="hyper" parents="16633 19210"/>
    </justification>
  </clause>

  <clause id="19238">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12091,a,19210,a)].">
      <j1 rule="hyper" parents="12091 19210"/>
    </justification>
  </clause>

  <clause id="19239">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(7562,a,19210,a)].">
      <j1 rule="hyper" parents="7562 19210"/>
    </justification>
  </clause>

  <clause id="19240">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ w) = K(x,u \ (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,12081,a(flip),b,19210,a),flip(a)].">
      <j1 rule="hyper" parents="64 12081 19210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19241">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K(z \ (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,7566,a(flip),b,19210,a),flip(a)].">
      <j1 rule="hyper" parents="64 7566 19210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19242">
    <literal><![CDATA[
      K(x,y) \ (z * K(u,w)) = (K(x,y) \ z) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,19210,a(flip),b,7065,a),flip(a)].">
      <j1 rule="hyper" parents="145 19210 7065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19244">
    <literal><![CDATA[
      L(K(x,y),z,L(K(u,w),v5,v6)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6670(a,1),19210(a,1,3))].">
      <j1 rule="para" parents="6670 19210"/>
    </justification>
  </clause>

  <clause id="19247">
    <literal><![CDATA[
      K(x,a(y,z,u) * w) = K(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11233,a,19211,a),flip(a)].">
      <j1 rule="hyper" parents="11233 19211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19248">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ w) * y) = K(x,y * (w / L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15860,a(flip),b,19211,a),flip(a)].">
      <j1 rule="hyper" parents="64 15860 19211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19249">
    <literal><![CDATA[
      (x \ a(y,z,u)) * K(w,x) = T(x,w) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,19211,a(flip),b,8647,a)].">
      <j1 rule="hyper" parents="145 19211 8647"/>
    </justification>
  </clause>

  <clause id="19250">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ x) = a(z,u,w) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,19211,a(flip),b,15040,a)].">
      <j1 rule="hyper" parents="144 19211 15040"/>
    </justification>
  </clause>

  <clause id="19251">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(19211(a,1),8313(a,1))].">
      <j1 rule="para" parents="19211 8313"/>
    </justification>
  </clause>

  <clause id="19253">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ 1) = a(z,u,w) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(19211(a,1),14519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19211 14519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19254">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(15395(a,1),19211(a,1,2))].">
      <j1 rule="para" parents="15395 19211"/>
    </justification>
  </clause>

  <clause id="19255">
    <literal><![CDATA[
      K(x,T(y,z \ L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8733,a,19236,a)].">
      <j1 rule="hyper" parents="8733 19236"/>
    </justification>
  </clause>

  <clause id="19256">
    <literal><![CDATA[
      T(K(x,y) * z,a(z,u,w)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(19237(a,1),15718(a,2,1))].">
      <j1 rule="para" parents="19237 15718"/>
    </justification>
  </clause>

  <clause id="19259">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11758(a,1),19238(a,1,2))].">
      <j1 rule="para" parents="11758 19238"/>
    </justification>
  </clause>

  <clause id="19260">
    <literal><![CDATA[
      K(x,L(y,z,u / w)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[para(13684(a,1),19238(a,1,2))].">
      <j1 rule="para" parents="13684 19238"/>
    </justification>
  </clause>

  <clause id="19261">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y / (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(16599(a,1),19238(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16599 19238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19262">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(u,K(y,z) \ w)) = K((w * K(z,y)) * L(u,w,K(z,y)),x)
    ]]></literal>
    <justification jstring="[para(19239(a,1),18908(a,1,2,2))].">
      <j1 rule="para" parents="19239 18908"/>
    </justification>
  </clause>

  <clause id="19265">
    <literal><![CDATA[
      R(x,y,T(z,T(u,w))) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7840(a,1),19195(a,1,3))].">
      <j1 rule="para" parents="7840 19195"/>
    </justification>
  </clause>

  <clause id="19266">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (K(x,K(y,z)) * (u * (w * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      L(v5,w,u) = v6
    ]]></literal>
    <justification jstring="[para(602(a,2),19200(a,1))].">
      <j1 rule="para" parents="602 19200"/>
    </justification>
  </clause>

  <clause id="19267">
    <literal><![CDATA[
      L(x,y,K(z,u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w \ K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(13684(a,1),19200(a,1))].">
      <j1 rule="para" parents="13684 19200"/>
    </justification>
  </clause>

  <clause id="19268">
    <literal><![CDATA[
      K(x,T(y \ R(z,u,w),z)) = K(x,R(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(15610,a,19254,a),flip(a)].">
      <j1 rule="hyper" parents="15610 19254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19269">
    <literal><![CDATA[
      K(x,T(y * (L(y,z,u) \ w),y)) = K(x,(y * w) / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8461,a,19254,a),flip(a)].">
      <j1 rule="hyper" parents="8461 19254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19271">
    <literal><![CDATA[
      K(x * K(y,L(x,z,u)),w) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,12104,a,b,19254,a)].">
      <j1 rule="hyper" parents="64 12104 19254"/>
    </justification>
  </clause>

  <clause id="19272">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ (w * z))) = K(x,T(y,u \ T(w,z)))
    ]]></literal>
    <justification jstring="[para(521(a,1),19254(a,1,2,2))].">
      <j1 rule="para" parents="521 19254"/>
    </justification>
  </clause>

  <clause id="19274">
    <literal><![CDATA[
      L(x,y,z) * K(u,T(w,x)) = K(u,w) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(19254(a,1),7879(a,1,2))].">
      <j1 rule="para" parents="19254 7879"/>
    </justification>
  </clause>

  <clause id="19275">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,z,y) * (z * y)) = w
    ]]></literal>
    <justification jstring="[para(19254(a,1),11230(a,1))].">
      <j1 rule="para" parents="19254 11230"/>
    </justification>
  </clause>

  <clause id="19277">
    <literal><![CDATA[
      K(x,T(y,R(z,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(15583(a,2),19254(a,1,2))].">
      <j1 rule="para" parents="15583 19254"/>
    </justification>
  </clause>

  <clause id="19278">
    <literal><![CDATA[
      K(x,T(y,(z / u) / w)) = K(x,T(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(15609(a,1),19254(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15609 19254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19279">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(11233,a,19255,a),flip(a)].">
      <j1 rule="hyper" parents="11233 19255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19280">
    <literal><![CDATA[
      K(x,y) * (z \ L(z,u,w)) = (z \ L(z,u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,19255,a(flip),b,8192,a)].">
      <j1 rule="hyper" parents="144 19255 8192"/>
    </justification>
  </clause>

  <clause id="19281">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13990,a,b,19189,a)].">
      <j1 rule="hyper" parents="64 13990 19189"/>
    </justification>
  </clause>

  <clause id="19282">
    <literal><![CDATA[
      T(x,L(y * K(z,u * w),u \ T(w * u,z),w)) = T(x,(y * T(w,u)) / (u \ T(w * u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16764,a(flip),b,19234,a),flip(a)].">
      <j1 rule="hyper" parents="64 16764 19234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19283">
    <literal><![CDATA[
      T(x,L(y,z \ T(u * z,w),u)) = T(x,L(y,K(u * z,w),T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15540,a(flip),b,19234,a),flip(a)].">
      <j1 rule="hyper" parents="64 15540 19234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19284">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ v6) = K(x,v5 \ (L(K(y,z),u,w) * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,12081,a(flip),b,19244,a),flip(a)].">
      <j1 rule="hyper" parents="64 12081 19244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19285">
    <literal><![CDATA[
      K(x,y) \ (z * L(K(u,w),v5,v6)) = (K(x,y) \ z) * L(K(u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(19244(a,1),15640(a,1,1))].">
      <j1 rule="para" parents="19244 15640"/>
    </justification>
  </clause>

  <clause id="19286">
    <literal><![CDATA[
      K(x,y / a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,a(z,u,w) \ y) = v5
    ]]></literal>
    <justification jstring="[para(8216(a,1),19251(a,1))].">
      <j1 rule="para" parents="8216 19251"/>
    </justification>
  </clause>

  <clause id="19287">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(15395(a,1),19251(a,1,2))].">
      <j1 rule="para" parents="15395 19251"/>
    </justification>
  </clause>

  <clause id="19288">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(16603(a,2),19251(a,1,2))].">
      <j1 rule="para" parents="16603 19251"/>
    </justification>
  </clause>

  <clause id="19289">
    <literal><![CDATA[
      K(x,L((y / T(z,u \ 1)) / (w / (u * w)),(w * u) \ w,z)) = K(x,y / (z * (w / (u * w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,16779,a(flip),b,19259,a),flip(a)].">
      <j1 rule="hyper" parents="64 16779 19259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19290">
    <literal><![CDATA[
      K(x,L((y / T(z,u)) / w,w,z)) = K(x,y / (w * T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15587,a(flip),b,19259,a),flip(a)].">
      <j1 rule="hyper" parents="64 15587 19259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19291">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z * y) \ u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13015,a(flip),b,19259,a),flip(a)].">
      <j1 rule="hyper" parents="64 13015 19259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19292">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) * (u \ 1))) = K(x,L(y,z,R(w,u,u \ 1)))
    ]]></literal>
    <justification jstring="[para(1042(a,1),19259(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="1042 19259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19293">
    <literal><![CDATA[
      (K(x,L(y,z * u,z)) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(19259(a,1),16761(a,1,1,1))].">
      <j1 rule="para" parents="19259 16761"/>
    </justification>
  </clause>

  <clause id="19294">
    <literal><![CDATA[
      R(T(x / y,y * T(z,u)),y,T(z,u)) = (y * T(z,T(u,w))) \ (x * T(z,T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(18063,a,19265,a),flip(a)].">
      <j1 rule="hyper" parents="18063 19265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19297">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,15300,a,b,19281,a),flip(a)].">
      <j1 rule="hyper" parents="373 15300 19281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19298">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,15300,a(flip),b,19281,a),flip(a)].">
      <j1 rule="hyper" parents="373 15300 19281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19299">
    <literal><![CDATA[
      a(x,y,K(z,u / w)) = a(x,y,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(117(a,1),19281(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="117 19281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19300">
    <literal><![CDATA[
      a(x,y,K(z / u,w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7874(a,1),19281(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7874 19281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19301">
    <literal><![CDATA[
      a(x,y,K(z,u * w)) = a(x,y,K(z,w * u))
    ]]></literal>
    <justification jstring="[para(11113(a,1),19281(a,1,3))].">
      <j1 rule="para" parents="11113 19281"/>
    </justification>
  </clause>

  <clause id="19302">
    <literal><![CDATA[
      a(x,y,K(z * u,w)) = a(x,y,K(u * z,w))
    ]]></literal>
    <justification jstring="[para(11177(a,1),19281(a,1,3))].">
      <j1 rule="para" parents="11177 19281"/>
    </justification>
  </clause>

  <clause id="19304">
    <literal><![CDATA[
      K(((K(x,T(y,z)) * u) * w) / a(x,u,K(w,y)),v5) = K((u * w) * K(y,x),v5)
    ]]></literal>
    <justification jstring="[para(19281(a,1),18087(a,1,1,2))].">
      <j1 rule="para" parents="19281 18087"/>
    </justification>
  </clause>

  <clause id="19305">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7537(a,1),19288(a,1))].">
      <j1 rule="para" parents="7537 19288"/>
    </justification>
  </clause>

  <clause id="19306">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(10688(a,1),19288(a,1))].">
      <j1 rule="para" parents="10688 19288"/>
    </justification>
  </clause>

  <clause id="19307">
    <literal><![CDATA[
      K(x,L(y,z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(13684(a,1),19288(a,1,2))].">
      <j1 rule="para" parents="13684 19288"/>
    </justification>
  </clause>

  <clause id="19308">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,19297,a(flip),b,13959,a),flip(a)].">
      <j1 rule="hyper" parents="145 19297 13959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19309">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(w,z,K(y * x,u))
    ]]></literal>
    <justification jstring="[para(11177(a,1),19297(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11177 19297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19311">
    <literal><![CDATA[
      a(T(x,y),z,K(u,w)) = a(x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(15405,a,19298,a)].">
      <j1 rule="hyper" parents="15405 19298"/>
    </justification>
  </clause>

  <clause id="19312">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(u,z,K(w,y * x))
    ]]></literal>
    <justification jstring="[para(11113(a,1),19298(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11113 19298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19313">
    <literal><![CDATA[
      L(K(x,y),z,L(K(u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v7
    ]]></literal>
    <justification jstring="[para(6670(a,1),19305(a,1,3))].">
      <j1 rule="para" parents="6670 19305"/>
    </justification>
  </clause>

  <clause id="19314">
    <literal><![CDATA[
      K(x,L(y \ z,u,K(w,v5)) \ 1) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = v6
    ]]></literal>
    <justification jstring="[para(6719(a,2),19305(a,1))].">
      <j1 rule="para" parents="6719 19305"/>
    </justification>
  </clause>

  <clause id="19315">
    <literal><![CDATA[
      K((x * K(y,z)) / (u * K(y,z)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / u,w) = v5
    ]]></literal>
    <justification jstring="[para(15614(a,1),19306(a,1))].">
      <j1 rule="para" parents="15614 19306"/>
    </justification>
  </clause>

  <clause id="19316">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16083,a(flip),b,19311,a)].">
      <j1 rule="hyper" parents="64 16083 19311"/>
    </justification>
  </clause>

  <clause id="19317">
    <literal><![CDATA[
      a(x / y,z,K(u,w)) = a(y \ x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13118,a(flip),b,19311,a),flip(a)].">
      <j1 rule="hyper" parents="64 13118 19311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19318">
    <literal><![CDATA[
      (x \ T(L(y,z,u),y * K(w,v5))) * K(y,K(w,v5)) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,19167,a(flip),b,15020,a)].">
      <j1 rule="hyper" parents="145 19167 15020"/>
    </justification>
  </clause>

  <clause id="19319">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(16649,a,19256,a)].">
      <j1 rule="hyper" parents="16649 19256"/>
    </justification>
  </clause>

  <clause id="19321">
    <literal><![CDATA[
      K(L(x,y,z) * K(u,x),w) = K(L(x,y,z),T(w,u))
    ]]></literal>
    <justification jstring="[para(16156(a,1),19271(a,1,1,2))].">
      <j1 rule="para" parents="16156 19271"/>
    </justification>
  </clause>

  <clause id="19322">
    <literal><![CDATA[
      (K(x,y) * z) / a(u,w,z) = a(u,w,z) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(19319(a,1),16634(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19319 16634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19325">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(19183(a,1),7552(a,1))].">
      <j1 rule="para" parents="19183 7552"/>
    </justification>
  </clause>

  <clause id="19330">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x)) = T(x,a(z,u,w)) \ y
    ]]></literal>
    <justification jstring="[hyper(13982,a,19187,a),flip(a)].">
      <j1 rule="hyper" parents="13982 19187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19331">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * z) = w * T(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13960,a(flip),b,19187,a),flip(a)].">
      <j1 rule="hyper" parents="373 13960 19187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19333">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = a(w,z,K(u,y)) * x
    ]]></literal>
    <justification jstring="[hyper(142,a,15322,a(flip),b,19187,a(flip))].">
      <j1 rule="hyper" parents="142 15322 19187"/>
    </justification>
  </clause>

  <clause id="19334">
    <literal><![CDATA[
      K(x,a(y,z,u)) * w = w * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(15299(a,1),19187(a,1,1))].">
      <j1 rule="para" parents="15299 19187"/>
    </justification>
  </clause>

  <clause id="19335">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      w * a(z,y,K(u,x)) = v5
    ]]></literal>
    <justification jstring="[para(19187(a,2),15663(a,1))].">
      <j1 rule="para" parents="19187 15663"/>
    </justification>
  </clause>

  <clause id="19336">
    <literal><![CDATA[
      a(K(x,y),z,u) \ (w * a(u,z,K(y,x))) = w
    ]]></literal>
    <justification jstring="[hyper(15445,a,19199,a)].">
      <j1 rule="hyper" parents="15445 19199"/>
    </justification>
  </clause>

  <clause id="19337">
    <literal><![CDATA[
      a(K(x,y),z,u) \ w = w * a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(12698,a,19199,a),flip(a)].">
      <j1 rule="hyper" parents="12698 19199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19338">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) / x = K(x,w / a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(142,a,19212,a(flip),b,5756,a(flip))].">
      <j1 rule="hyper" parents="142 19212 5756"/>
    </justification>
  </clause>

  <clause id="19339">
    <literal><![CDATA[
      T(x,(K(a(y,z,u),w) * v5) * a(y,z,u)) = T(x,T(a(y,z,u),w) * v5)
    ]]></literal>
    <justification jstring="[para(5776(a,1),19215(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5776 19215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19340">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),z * (a(w,v5,v6) * u))) = K(x,z \ T(y,a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[para(19215(a,1),18527(a,1,2,1,2))].">
      <j1 rule="para" parents="19215 18527"/>
    </justification>
  </clause>

  <clause id="19342">
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) \ w)) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(15954,a,19260,a),flip(a)].">
      <j1 rule="hyper" parents="15954 19260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19343">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ (z \ w))) = v5
    ]]></literal>
    <justification jstring="[para(346(a,1),19287(a,1,2,2))].">
      <j1 rule="para" parents="346 19287"/>
    </justification>
  </clause>

  <clause id="19344">
    <literal><![CDATA[
      a(x,y,K(y * z,u \ w)) * K(x,(y * (w / u)) / ((z \ 1) * (w / u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(19299(a,1),15687(a,1,1))].">
      <j1 rule="para" parents="19299 15687"/>
    </justification>
  </clause>

  <clause id="19345">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(19299(a,1),16223(a,1,1))].">
      <j1 rule="para" parents="19299 16223"/>
    </justification>
  </clause>

  <clause id="19346">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,(u * w) \ v5)) = K(x,L(y,z,v5 / (T(u,x) * w)))
    ]]></literal>
    <justification jstring="[para(19299(a,1),15438(a,1,2))].">
      <j1 rule="para" parents="19299 15438"/>
    </justification>
  </clause>

  <clause id="19347">
    <literal><![CDATA[
      a(x,y,K(z,x \ (u * (x / w)))) = a(z,y,K(w \ u,x))
    ]]></literal>
    <justification jstring="[hyper(15974,a,19300,a)].">
      <j1 rule="hyper" parents="15974 19300"/>
    </justification>
  </clause>

  <clause id="19348">
    <literal><![CDATA[
      K(x,y / z) * a(x,u,K(z \ y,w)) = K(x,L(y / z,u,w \ 1))
    ]]></literal>
    <justification jstring="[para(19300(a,1),15368(a,1,2))].">
      <j1 rule="para" parents="19300 15368"/>
    </justification>
  </clause>

  <clause id="19349">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,w / (y * u)))
    ]]></literal>
    <justification jstring="[para(19300(a,1),16147(a,1,2))].">
      <j1 rule="para" parents="19300 16147"/>
    </justification>
  </clause>

  <clause id="19350">
    <literal><![CDATA[
      a(x,y,K((z / (u / w)) * K(w,z),v5)) = a(x,y,K(z / (u / T(w,z)),v5))
    ]]></literal>
    <justification jstring="[para(15080(a,1),19302(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="15080 19302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19351">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15305,a(flip),b,19308,a),flip(a)].">
      <j1 rule="hyper" parents="373 15305 19308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19352">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(19308(a,2),15308(a,1))].">
      <j1 rule="para" parents="19308 15308"/>
    </justification>
  </clause>

  <clause id="19353">
    <literal><![CDATA[
      T(x,a(y,T(z,u),u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(7107(a,1),19351(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7107 19351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19354">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,u * z,u))
    ]]></literal>
    <justification jstring="[para(13831(a,1),19353(a,1,2))].">
      <j1 rule="para" parents="13831 19353"/>
    </justification>
  </clause>

  <clause id="19355">
    <literal><![CDATA[
      a(x * (y \ T(z,y)),u,K(w,v5)) = a(w,u,K(v5,(z / y) * x))
    ]]></literal>
    <justification jstring="[para(16360(a,1),19312(a,2,3))].">
      <j1 rule="para" parents="16360 19312"/>
    </justification>
  </clause>

  <clause id="19356">
    <literal><![CDATA[
      a(x * (T(y,z) / z),u,K(w,v5)) = a(w,u,K(v5,(z \ y) * x))
    ]]></literal>
    <justification jstring="[para(17910(a,1),19312(a,2,3))].">
      <j1 rule="para" parents="17910 19312"/>
    </justification>
  </clause>

  <clause id="19357">
    <literal><![CDATA[
      a(K(x,y),z,u \ w) = a(w / u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,15315,a,b,19317,a)].">
      <j1 rule="hyper" parents="373 15315 19317"/>
    </justification>
  </clause>

  <clause id="19358">
    <literal><![CDATA[
      (x * K(y,z)) / a((u \ 1) \ x,u \ 1,K(y,z)) = (x / (u \ 1)) * (u \ K(y,z))
    ]]></literal>
    <justification jstring="[para(19317(a,1),14530(a,1,2))].">
      <j1 rule="para" parents="19317 14530"/>
    </justification>
  </clause>

  <clause id="19359">
    <literal><![CDATA[
      (x * K(y,z)) / a((1 / u) \ x,u \ 1,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(19317(a,1),16548(a,1,2))].">
      <j1 rule="para" parents="19317 16548"/>
    </justification>
  </clause>

  <clause id="19360">
    <literal><![CDATA[
      T(x,K(y,(z \ u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u \ (z * w))) = v5
    ]]></literal>
    <justification jstring="[para(16172(a,1),19325(a,1,2))].">
      <j1 rule="para" parents="16172 19325"/>
    </justification>
  </clause>

  <clause id="19361">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = a(x,y,K(z,u)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,16730,a,b,19333,a)].">
      <j1 rule="hyper" parents="64 16730 19333"/>
    </justification>
  </clause>

  <clause id="19362">
    <literal><![CDATA[
      (x / y) * a(x,z,K(u,w)) = T(x,a(w,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(14865,a,19334,a),flip(a)].">
      <j1 rule="hyper" parents="14865 19334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19363">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15497,a(flip),b,19354,a),flip(a)].">
      <j1 rule="hyper" parents="373 15497 19354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19364">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(16648,a,19363,a)].">
      <j1 rule="hyper" parents="16648 19363"/>
    </justification>
  </clause>

  <clause id="19365">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,16603,a,b,19364,a),flip(a)].">
      <j1 rule="hyper" parents="373 16603 19364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19366">
    <literal><![CDATA[
      L(a(x,y,z),y * z,K(x,y)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16749,a(flip),b,19365,a),flip(a)].">
      <j1 rule="hyper" parents="64 16749 19365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19367">
    <literal><![CDATA[
      (x * T(y,T(z,x))) \ (K(y,z) * u) = L((x * y) \ u,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8059,a(flip),b,19365,a)].">
      <j1 rule="hyper" parents="64 8059 19365"/>
    </justification>
  </clause>

  <clause id="19368">
    <literal><![CDATA[
      a(x / y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,z,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(19357(a,1),15407(a,1))].">
      <j1 rule="para" parents="19357 15407"/>
    </justification>
  </clause>

  <clause id="19369">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ (w * u))) = K(x,K(y,z \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,17225,a(flip),b,19154,a),flip(a)].">
      <j1 rule="hyper" parents="373 17225 19154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19370">
    <literal><![CDATA[
      L(K(K(x,y),z) * ((u * w) \ v5),K(z,K(x,y)),u * w) = (u * (w * K(z,K(x,y)))) \ v5
    ]]></literal>
    <justification jstring="[para(19164(a,1),6191(a,2,1))].">
      <j1 rule="para" parents="19164 6191"/>
    </justification>
  </clause>

  <clause id="19372">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * (w \ x)) = u * (w \ T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(15021(a,1),19166(a,2,2))].">
      <j1 rule="para" parents="15021 19166"/>
    </justification>
  </clause>

  <clause id="19373">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(17161(a,2),19166(a,2,2))].">
      <j1 rule="para" parents="17161 19166"/>
    </justification>
  </clause>

  <clause id="19375">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * (x \ w)) = u * (T(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(17329(a,1),19166(a,2,2))].">
      <j1 rule="para" parents="17329 19166"/>
    </justification>
  </clause>

  <clause id="19377">
    <literal><![CDATA[
      x \ (y * (z * K(u,K(w,v5)))) = (x \ (y * z)) * K(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(139,a,19164,a(flip),b,19170,a)].">
      <j1 rule="hyper" parents="139 19164 19170"/>
    </justification>
  </clause>

  <clause id="19378">
    <literal><![CDATA[
      (x \ (y * z)) * K(y,K(u,w)) = x \ (T(y,K(u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,17222,a(flip),b,19170,a),flip(a)].">
      <j1 rule="hyper" parents="139 17222 19170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19379">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,K(u,w)) = x \ (y * T(z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(139,a,6852,a(flip),b,19170,a),flip(a)].">
      <j1 rule="hyper" parents="139 6852 19170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19380">
    <literal><![CDATA[
      x * (K(y,K(z,u)) * (x \ w)) = w * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(17161(a,2),19170(a,1,2))].">
      <j1 rule="para" parents="17161 19170"/>
    </justification>
  </clause>

  <clause id="19381">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,19166,a(flip),b,19172,a),flip(a)].">
      <j1 rule="hyper" parents="373 19166 19172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19382">
    <literal><![CDATA[
      T(T(x,(y \ z) \ u),K(w,z \ (y * u))) = T(x,T((y \ z) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(8189,a,19179,a),flip(a)].">
      <j1 rule="hyper" parents="8189 19179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19383">
    <literal><![CDATA[
      T(x,K(y,z \ (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,w \ (u \ z))) = v5
    ]]></literal>
    <justification jstring="[para(19179(a,1),9050(a,1))].">
      <j1 rule="para" parents="19179 9050"/>
    </justification>
  </clause>

  <clause id="19384">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ (K(x,K(y,z)) \ w) = u \ w
    ]]></literal>
    <justification jstring="[para(10(a,1),19196(a,2,2))].">
      <j1 rule="para" parents="10 19196"/>
    </justification>
  </clause>

  <clause id="19385">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(8143(a,2),19196(a,2,2))].">
      <j1 rule="para" parents="8143 19196"/>
    </justification>
  </clause>

  <clause id="19386">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[para(8143(a,2),19198(a,1,1))].">
      <j1 rule="para" parents="8143 19198"/>
    </justification>
  </clause>

  <clause id="19387">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) / v5 = K(z,K(u,w)) * ((x * y) / v5)
    ]]></literal>
    <justification jstring="[para(19166(a,1),19198(a,1,1))].">
      <j1 rule="para" parents="19166 19198"/>
    </justification>
  </clause>

  <clause id="19388">
    <literal><![CDATA[
      ((K(x,y) * (z * K(u,w))) * v5) / (K(u,w) * v5) = R(K(x,y) * z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(19208(a,1),20(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="19208 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19391">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ (K(u,z) \ (y * x)) = T(K(u,z) \ y,x)
    ]]></literal>
    <justification jstring="[para(7064(a,1),19228(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7064 19228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19392">
    <literal><![CDATA[
      K(x,(K(y,z) \ u) \ w) = K(x,u \ (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[para(6156(a,2),19240(a,2,2,2))].">
      <j1 rule="para" parents="6156 19240"/>
    </justification>
  </clause>

  <clause id="19393">
    <literal><![CDATA[
      K(x,(y * z) \ (K(u,y) * w)) = K(x,(T(y,u) * z) \ w)
    ]]></literal>
    <justification jstring="[para(6131(a,1),19240(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6131 19240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19394">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(x \ (K(z,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(18020,a,19241,a)].">
      <j1 rule="hyper" parents="18020 19241"/>
    </justification>
  </clause>

  <clause id="19396">
    <literal><![CDATA[
      (x \ y) * (a(z,u,w) \ T(x,x \ y)) = (y / x) * (a(z,u,w) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,19250,a(flip),b,6442,a)].">
      <j1 rule="hyper" parents="145 19250 6442"/>
    </justification>
  </clause>

  <clause id="19398">
    <literal><![CDATA[
      (a(x,y,z) * K(u,w)) \ 1 = a(x,y,z) \ K(w,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18384,a,b,19253,a)].">
      <j1 rule="hyper" parents="64 18384 19253"/>
    </justification>
  </clause>

  <clause id="19399">
    <literal><![CDATA[
      K(x,y) * (z \ L(z,u,u)) = a(u,u,z) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5667,a(flip),b,19253,a)].">
      <j1 rule="hyper" parents="64 5667 19253"/>
    </justification>
  </clause>

  <clause id="19400">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18120,a(flip),b,19261,a),flip(a)].">
      <j1 rule="hyper" parents="373 18120 19261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19401">
    <literal><![CDATA[
      K(x,T(y,z / (u * w))) = K(x,T(y,u \ (z / w)))
    ]]></literal>
    <justification jstring="[hyper(17264,a,19278,a),flip(a)].">
      <j1 rule="hyper" parents="17264 19278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19403">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15394,a(flip),b,19316,a),flip(a)].">
      <j1 rule="hyper" parents="373 15394 19316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19404">
    <literal><![CDATA[
      K(L(x,y,z) * K(u,x),w) = K(x,L(T(w,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,12093,a(flip),b,19321,a),flip(a)].">
      <j1 rule="hyper" parents="373 12093 19321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19405">
    <literal><![CDATA[
      T(x \ 1,a(y,z,u)) = T(x,a(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(13992,a,19330,a)].">
      <j1 rule="hyper" parents="13992 19330"/>
    </justification>
  </clause>

  <clause id="19406">
    <literal><![CDATA[
      K(x,y) / T(z \ 1,a(u,w,v5)) = K(x,y) * T(z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(225,a,19405,a,b,14403,a)].">
      <j1 rule="hyper" parents="225 19405 14403"/>
    </justification>
  </clause>

  <clause id="19407">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15541,a(flip),b,19342,a),flip(a)].">
      <j1 rule="hyper" parents="64 15541 19342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19408">
    <literal><![CDATA[
      (x / y) * a(x,z,K(u,w)) = L(x,z,K(u,w)) / y
    ]]></literal>
    <justification jstring="[para(16603(a,2),19362(a,2,1))].">
      <j1 rule="para" parents="16603 19362"/>
    </justification>
  </clause>

  <clause id="19409">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[para(12(a,1),19369(a,1,2,2,2))].">
      <j1 rule="para" parents="12 19369"/>
    </justification>
  </clause>

  <clause id="19410">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(8149,a,19373,a)].">
      <j1 rule="hyper" parents="8149 19373"/>
    </justification>
  </clause>

  <clause id="19412">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = u * (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,19373,a)].">
      <j1 rule="hyper" parents="139 168 19373"/>
    </justification>
  </clause>

  <clause id="19413">
    <literal><![CDATA[
      K(x,y * (z * (K(u,K(w,v5)) * v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * v6)) = v7
    ]]></literal>
    <justification jstring="[para(19373(a,1),18176(a,1,2,2))].">
      <j1 rule="para" parents="19373 18176"/>
    </justification>
  </clause>

  <clause id="19415">
    <literal><![CDATA[
      x \ T(y * K(z,K(u,w)),v5) = K(z,K(u,w)) * (x \ T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(139,a,17603,a,b,19380,a)].">
      <j1 rule="hyper" parents="139 17603 19380"/>
    </justification>
  </clause>

  <clause id="19416">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) = K(y,K(z,u)) * (x \ T(w,v5))
    ]]></literal>
    <justification jstring="[hyper(139,a,17227,a,b,19380,a)].">
      <j1 rule="hyper" parents="139 17227 19380"/>
    </justification>
  </clause>

  <clause id="19417">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ (w \ 1)) = u \ (w \ K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(139,a,14444,a(flip),b,19380,a),flip(a)].">
      <j1 rule="hyper" parents="139 14444 19380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19418">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) \ ((K(z,K(u,w)) * x) * (y * v5)) = L(v5,y,K(z,K(u,w)) * x)
    ]]></literal>
    <justification jstring="[para(19381(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="19381 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19419">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) / w != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / w) = v5
    ]]></literal>
    <justification jstring="[para(19386(a,2),8149(a,1))].">
      <j1 rule="para" parents="19386 8149"/>
    </justification>
  </clause>

  <clause id="19420">
    <literal><![CDATA[
      K(x,(K(y,z) * ((K(u,w) \ v5) / K(y,z))) \ v6) = K(x,v5 \ (K(w,u) \ v6))
    ]]></literal>
    <justification jstring="[hyper(18406,a,19392,a)].">
      <j1 rule="hyper" parents="18406 19392"/>
    </justification>
  </clause>

  <clause id="19421">
    <literal><![CDATA[
      K(x,(y / z) \ (K(((z \ 1) / (y / z)) \ 1,u) \ w)) = K(x,(T(y,u) / z) \ w)
    ]]></literal>
    <justification jstring="[para(7280(a,1),19392(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7280 19392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19422">
    <literal><![CDATA[
      K(x,y \ (K(y / x,z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(19392(a,1),7563(a,1))].">
      <j1 rule="para" parents="19392 7563"/>
    </justification>
  </clause>

  <clause id="19423">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ v6) = K(x,v5 \ (K(L(z,u,w),y) \ v6))
    ]]></literal>
    <justification jstring="[para(12059(a,2),19392(a,1,2,1,1))].">
      <j1 rule="para" parents="12059 19392"/>
    </justification>
  </clause>

  <clause id="19424">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(18022,a,19400,a)].">
      <j1 rule="hyper" parents="18022 19400"/>
    </justification>
  </clause>

  <clause id="19425">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / w) = T(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(143,a,19400,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 19400 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19426">
    <literal><![CDATA[
      K(x,T(y,z) * (u \ K(w,y))) = K(x,T(T(y,w),z) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18052,a(flip),b,19400,a),flip(a)].">
      <j1 rule="hyper" parents="64 18052 19400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19427">
    <literal><![CDATA[
      K(x,T(y * z,x) * (u \ K(w,L(v5,z,y)))) = K(x,(y * (z * K(w,v5))) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12141,a(flip),b,19400,a),flip(a)].">
      <j1 rule="hyper" parents="64 12141 19400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19428">
    <literal><![CDATA[
      K(x,T(y / (z \ u),x) * (w \ K(z \ u,z))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,9139,a(flip),b,19400,a),flip(a)].">
      <j1 rule="hyper" parents="64 9139 19400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19429">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(w,z))) = K(x,(y / T(z,w)) / u)
    ]]></literal>
    <justification jstring="[para(6245(a,1),19400(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6245 19400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19430">
    <literal><![CDATA[
      K(x,T(y * K(z,u),u) / w) = K(x,T(y,u) * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[para(7797(a,2),19400(a,1,2,1))].">
      <j1 rule="para" parents="7797 19400"/>
    </justification>
  </clause>

  <clause id="19431">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(w,T(z,v5)))) = K(x,(y / T(z,T(w,v5))) / u)
    ]]></literal>
    <justification jstring="[para(7910(a,1),19400(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7910 19400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19432">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (w * K(u,z))) = v5
    ]]></literal>
    <justification jstring="[para(19400(a,2),18121(a,1))].">
      <j1 rule="para" parents="19400 18121"/>
    </justification>
  </clause>

  <clause id="19433">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(17264,a,19401,a)].">
      <j1 rule="hyper" parents="17264 19401"/>
    </justification>
  </clause>

  <clause id="19434">
    <literal><![CDATA[
      K(K(x,y) * L(y,z,u),w) = K(y,L(T(w,x),z,u))
    ]]></literal>
    <justification jstring="[hyper(17193,a,19404,a)].">
      <j1 rule="hyper" parents="17193 19404"/>
    </justification>
  </clause>

  <clause id="19435">
    <literal><![CDATA[
      K(L(x,y,z) * K(u \ 1,x),w / (v5 / (u * v5))) = K(x,L((v5 / (u * v5)) \ w,y,z))
    ]]></literal>
    <justification jstring="[para(4819(a,1),19404(a,2,2,1))].">
      <j1 rule="para" parents="4819 19404"/>
    </justification>
  </clause>

  <clause id="19436">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18311,a(flip),b,19409,a),flip(a)].">
      <j1 rule="hyper" parents="373 18311 19409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19437">
    <literal><![CDATA[
      K(x,K(y,z \ (u / w))) = K(x,K(y,(z * w) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17551,a(flip),b,19409,a),flip(a)].">
      <j1 rule="hyper" parents="64 17551 19409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19438">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * (w / x)) = u * (w / T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(17335(a,1),19410(a,2,2))].">
      <j1 rule="para" parents="17335 19410"/>
    </justification>
  </clause>

  <clause id="19439">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * (w \ x)) = u * (w \ T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(17404(a,1),19412(a,2,2))].">
      <j1 rule="para" parents="17404 19412"/>
    </justification>
  </clause>

  <clause id="19440">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / w) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(143,a,19424,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 19424 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19441">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * (w \ K(z,u))) = K(x,(y / (T(z,u) \ u)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,18553,a(flip),b,19424,a),flip(a)].">
      <j1 rule="hyper" parents="64 18553 19424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19442">
    <literal><![CDATA[
      T(x,y * (T(y / z,u) \ K(z,w))) = T(x,T(T(z \ y,u) \ y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18640,a(flip),b,19425,a),flip(a)].">
      <j1 rule="hyper" parents="64 18640 19425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19443">
    <literal><![CDATA[
      K(x * K(y,z),T(u,K(y,z) \ (w / x))) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(17365,a,19433,a),flip(a)].">
      <j1 rule="hyper" parents="17365 19433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19444">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) * K(y,((z * u) \ w) \ x) = K(y,x / ((z * u) \ w))
    ]]></literal>
    <justification jstring="[para(19436(a,1),9065(a,1,1))].">
      <j1 rule="para" parents="19436 9065"/>
    </justification>
  </clause>

  <clause id="19445">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) * K(y,(T(u * z,u) \ w) \ x) = K(y,x / (T(u * z,u) \ w))
    ]]></literal>
    <justification jstring="[para(19436(a,1),13415(a,1,1))].">
      <j1 rule="para" parents="19436 13415"/>
    </justification>
  </clause>

  <clause id="19446">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17551,a(flip),b,19437,a),flip(a)].">
      <j1 rule="hyper" parents="64 17551 19437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19447">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ (K(y,w) * z)) = T(x,z * (T(z / y,u) \ K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18604,a(flip),b,19440,a)].">
      <j1 rule="hyper" parents="64 18604 19440"/>
    </justification>
  </clause>

  <clause id="19448">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) / w) / T(v5,u * (w \ K(y,z)))) * v6) = K(x,(v5 \ ((K(y,z) * u) / w)) * v6)
    ]]></literal>
    <justification jstring="[para(19440(a,1),17913(a,1,2,1,2))].">
      <j1 rule="para" parents="19440 17913"/>
    </justification>
  </clause>

  <clause id="19449">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,z * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18307,a(flip),b,19446,a),flip(a)].">
      <j1 rule="hyper" parents="373 18307 19446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19450">
    <literal><![CDATA[
      L(x,y,z \ K(z,z \ u)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[hyper(19267,a,13914,a(flip))].">
      <j1 rule="hyper" parents="19267 13914"/>
    </justification>
  </clause>

  <clause id="19451">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ u)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,(w * u) \ u)) = v5
    ]]></literal>
    <justification jstring="[para(13532(a,1),19307(a,1,2))].">
      <j1 rule="para" parents="13532 19307"/>
    </justification>
  </clause>

  <clause id="19452">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,K(x,z)) = L(T(x,a(u,w,z)),y,z)
    ]]></literal>
    <justification jstring="[hyper(19335,a,15729,a)].">
      <j1 rule="hyper" parents="19335 15729"/>
    </justification>
  </clause>

  <clause id="19453">
    <literal><![CDATA[
      (x * y) * a(z,u,K(x,w)) = T(x,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(19335,a,15353,a)].">
      <j1 rule="hyper" parents="19335 15353"/>
    </justification>
  </clause>

  <clause id="19454">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x \ K(z,y),u,K(v5,w)) = v6
    ]]></literal>
    <justification jstring="[para(15390(a,1),19368(a,1))].">
      <j1 rule="para" parents="15390 19368"/>
    </justification>
  </clause>

  <clause id="19455">
    <literal><![CDATA[
      T(x * K(L(y,z,u),w),K(w,y)) = L(K(w,y),z,u) \ x
    ]]></literal>
    <justification jstring="[para(12067(a,1),19182(a,1,1))].">
      <j1 rule="para" parents="12067 19182"/>
    </justification>
  </clause>

  <clause id="19457">
    <literal><![CDATA[
      K(x,y * ((K(z,L(y,u,w)) * v5) / L(y,u,w))) = K(x,(T(L(y,u,w),z) \ v5) * y)
    ]]></literal>
    <justification jstring="[para(6137(a,1),19248(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6137 19248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19458">
    <literal><![CDATA[
      K(x,y * ((K(z,z \ L(y,u,w)) * v5) / L(y,u,w))) = K(x,(((z \ L(y,u,w)) * z) \ v5) * y)
    ]]></literal>
    <justification jstring="[para(10871(a,1),19248(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10871 19248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19459">
    <literal><![CDATA[
      K(x,(K(y,L(z,u,w) \ 1) * (L(z,u,w) \ v5)) * z) = K(x,z * ((K(y,L(z,u,w) \ 1) * v5) / L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(11922(a,1),19248(a,1,2,1))].">
      <j1 rule="para" parents="11922 19248"/>
    </justification>
  </clause>

  <clause id="19460">
    <literal><![CDATA[
      K(x,T(y,z \ ((u * z) / w))) = K(x,T(y,w \ T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19433,a(flip),b,19272,a)].">
      <j1 rule="hyper" parents="64 19433 19272"/>
    </justification>
  </clause>

  <clause id="19461">
    <literal><![CDATA[
      K(x,(y \ L(y,z,z \ 1)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * a(y,z,z \ 1)) = w
    ]]></literal>
    <justification jstring="[para(19279(a,2),16944(a,1))].">
      <j1 rule="para" parents="19279 16944"/>
    </justification>
  </clause>

  <clause id="19462">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) \ (K(y,L(z,u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(15626(a,1),19314(a,1))].">
      <j1 rule="para" parents="15626 19314"/>
    </justification>
  </clause>

  <clause id="19463">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),u)) = a(x,y,K(w \ z,u))
    ]]></literal>
    <justification jstring="[hyper(15413,a,19347,a)].">
      <j1 rule="hyper" parents="15413 19347"/>
    </justification>
  </clause>

  <clause id="19464">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(17370(a,1),19463(a,1,3))].">
      <j1 rule="para" parents="17370 19463"/>
    </justification>
  </clause>

  <clause id="19465">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,y) * a(x,z,K(w \ u,y))
    ]]></literal>
    <justification jstring="[para(19464(a,1),15436(a,2,2))].">
      <j1 rule="para" parents="19464 15436"/>
    </justification>
  </clause>

  <clause id="19466">
    <literal><![CDATA[
      K(x,y) * (z * (u \ T(x,K(y,w)))) = K(x,T(y,w)) * (z * (u \ x))
    ]]></literal>
    <justification jstring="[para(19372(a,1),9813(a,1,2))].">
      <j1 rule="para" parents="19372 9813"/>
    </justification>
  </clause>

  <clause id="19467">
    <literal><![CDATA[
      K(x * (y \ T(z,K(u,w))),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ z),v5) = v6
    ]]></literal>
    <justification jstring="[para(19372(a,1),17986(a,1,1))].">
      <j1 rule="para" parents="19372 17986"/>
    </justification>
  </clause>

  <clause id="19468">
    <literal><![CDATA[
      K(x,T(y * (T(z,K(u,w)) \ v5),v6)) = K(x,T(y * (z \ v5),v6))
    ]]></literal>
    <justification jstring="[para(19375(a,1),17934(a,1,2,1))].">
      <j1 rule="para" parents="19375 17934"/>
    </justification>
  </clause>

  <clause id="19469">
    <literal><![CDATA[
      K(x,y \ (T(z,K(u,w)) * v5)) = K(x,y \ (z * v5))
    ]]></literal>
    <justification jstring="[para(19378(a,1),17920(a,1,2))].">
      <j1 rule="para" parents="19378 17920"/>
    </justification>
  </clause>

  <clause id="19470">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,K(w,v5)) * v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ (u * v6))) = v7
    ]]></literal>
    <justification jstring="[para(19378(a,1),18011(a,1,2,2))].">
      <j1 rule="para" parents="19378 18011"/>
    </justification>
  </clause>

  <clause id="19471">
    <literal><![CDATA[
      K(x,y \ (L(T(z,K(u,w)),v5,v6) * v7)) = K(x,y \ (L(z,v5,v6) * v7))
    ]]></literal>
    <justification jstring="[para(25(a,2),19469(a,1,2,2,1))].">
      <j1 rule="para" parents="25 19469"/>
    </justification>
  </clause>

  <clause id="19472">
    <literal><![CDATA[
      K(x,y \ (T(z,T(u,w)) * v5)) = K(x,y \ (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(7840(a,1),19469(a,1,2,2,1))].">
      <j1 rule="para" parents="7840 19469"/>
    </justification>
  </clause>

  <clause id="19473">
    <literal><![CDATA[
      T((x \ (y * z)) / ((K(u,w) * z) / K(u,w)),z) = z \ (x \ (y * T(z,K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(6967,a,19379,a)].">
      <j1 rule="hyper" parents="6967 19379"/>
    </justification>
  </clause>

  <clause id="19474">
    <literal><![CDATA[
      K(x,y \ (z * T(u,K(w,v5)))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(19379(a,1),17920(a,1,2))].">
      <j1 rule="para" parents="19379 17920"/>
    </justification>
  </clause>

  <clause id="19475">
    <literal><![CDATA[
      K(x,y \ (z * T(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * u)) = v6
    ]]></literal>
    <justification jstring="[para(19379(a,1),17922(a,1,2))].">
      <j1 rule="para" parents="19379 17922"/>
    </justification>
  </clause>

  <clause id="19476">
    <literal><![CDATA[
      K(x,y \ (z * L(T(u,K(w,v5)),v6,v7))) = K(x,y \ (z * L(u,v6,v7)))
    ]]></literal>
    <justification jstring="[para(25(a,2),19474(a,1,2,2,2))].">
      <j1 rule="para" parents="25 19474"/>
    </justification>
  </clause>

  <clause id="19477">
    <literal><![CDATA[
      T(T(x,K(y,z)) * (u / x),w) = x * (T(u,w) / T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17729,a(flip),b,19438,a)].">
      <j1 rule="hyper" parents="64 17729 19438"/>
    </justification>
  </clause>

  <clause id="19478">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,u \ z) * z = (K(y,x) \ u) * (u \ T(z,K(y,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16755,a(flip),b,19439,a)].">
      <j1 rule="hyper" parents="64 16755 19439"/>
    </justification>
  </clause>

  <clause id="19479">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,u \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(13547,a,19450,a),flip(a)].">
      <j1 rule="hyper" parents="13547 19450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19480">
    <literal><![CDATA[
      L(x,y,z \ K(u,z \ 1)) = L(x,y,z \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(19267,a,19479,a)].">
      <j1 rule="hyper" parents="19267 19479"/>
    </justification>
  </clause>

  <clause id="19481">
    <literal><![CDATA[
      L(x,y,z \ K(z,y)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,11768,a(flip),b,19480,a),flip(a)].">
      <j1 rule="hyper" parents="64 11768 19480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19482">
    <literal><![CDATA[
      L(x,T(y,z),(z \ T(y,z \ y)) \ 1) = L(x,T(y,z),(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(15662(a,1),19481(a,1,3))].">
      <j1 rule="para" parents="15662 19481"/>
    </justification>
  </clause>

  <clause id="19483">
    <literal><![CDATA[
      T(x,a(y \ 1,z,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(16190,a,19452,a(flip))].">
      <j1 rule="hyper" parents="16190 19452"/>
    </justification>
  </clause>

  <clause id="19484">
    <literal><![CDATA[
      K(x,y) \ (L(K(y,x),z,u) \ w) = (w * K(L(x,z,u),y)) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,19455,a(flip),b,6175,a)].">
      <j1 rule="hyper" parents="139 19455 6175"/>
    </justification>
  </clause>

  <clause id="19485">
    <literal><![CDATA[
      K(x,T(y,z \ ((u * z) / w))) = K(x,T(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,18246,a(flip),b,19460,a),flip(a)].">
      <j1 rule="hyper" parents="373 18246 19460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19486">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ (w * z)))) = K(x,T(y,u \ w))
    ]]></literal>
    <justification jstring="[hyper(18284,a,19485,a)].">
      <j1 rule="hyper" parents="18284 19485"/>
    </justification>
  </clause>

  <clause id="19489">
    <literal><![CDATA[
      K(x,(y * T(z,u)) \ (T(y,z) * w)) = K(x,(T(z,u) * y) \ (y * w))
    ]]></literal>
    <justification jstring="[para(10874(a,1),19472(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10874 19472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19490">
    <literal><![CDATA[
      K((x * K(y,z)) * (u \ K(z,y)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / u,w) = v5
    ]]></literal>
    <justification jstring="[para(18126(a,1),19315(a,1))].">
      <j1 rule="para" parents="18126 19315"/>
    </justification>
  </clause>

  <clause id="19491">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(19343,a,17024,a)].">
      <j1 rule="hyper" parents="19343 17024"/>
    </justification>
  </clause>

  <clause id="19492">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z \ (u * w))) = v5
    ]]></literal>
    <justification jstring="[para(18316(a,2),19360(a,1))].">
      <j1 rule="para" parents="18316 19360"/>
    </justification>
  </clause>

  <clause id="19493">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ (K(u,z) \ (y * x)) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ T(K(u,z) \ y,x) = v5
    ]]></literal>
    <justification jstring="[para(19391(a,2),1036(a,1))].">
      <j1 rule="para" parents="19391 1036"/>
    </justification>
  </clause>

  <clause id="19494">
    <literal><![CDATA[
      K(x \ T(y \ T(z,K(u,w)),v5),v6) = K((x \ K(y \ z,v5)) * (y \ z),v6)
    ]]></literal>
    <justification jstring="[hyper(19467,a,18000,a),flip(a)].">
      <j1 rule="hyper" parents="19467 18000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19495">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * (v5 \ u)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * (v5 \ T(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(15023(a,1),19475(a,1,2,2,2))].">
      <j1 rule="para" parents="15023 19475"/>
    </justification>
  </clause>

  <clause id="19496">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = v5 \ (x * v5)
    ]]></literal>
    <justification jstring="[para(19194(a,1),19219(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19194 19219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19497">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(19496(a,2),336(a,1))].">
      <j1 rule="para" parents="19496 336"/>
    </justification>
  </clause>

  <clause id="19499">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(13958(a,2),19497(a,1,2,1))].">
      <j1 rule="para" parents="13958 19497"/>
    </justification>
  </clause>

  <clause id="19500">
    <literal><![CDATA[
      T(x,y * a(z,u,K(w,v5))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(19499,a,19215,a),flip(a)].">
      <j1 rule="hyper" parents="19499 19215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19501">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(19499,a,xx),flip(a)].">
      <j1 rule="hyper" parents="19499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19502">
    <literal><![CDATA[
      T(x,(y * z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z * K(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(15463(a,1),19499(a,1,2))].">
      <j1 rule="para" parents="15463 19499"/>
    </justification>
  </clause>

  <clause id="19503">
    <literal><![CDATA[
      T(x,(K(y,z) * u) * w) = T(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[para(15302(a,1),19500(a,1,2))].">
      <j1 rule="para" parents="15302 19500"/>
    </justification>
  </clause>

  <clause id="19504">
    <literal><![CDATA[
      T(x,y * L(z,u,K(w,v5))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(16627(a,1),19500(a,1,2))].">
      <j1 rule="para" parents="16627 19500"/>
    </justification>
  </clause>

  <clause id="19505">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = v5 / T(v5,w)
    ]]></literal>
    <justification jstring="[hyper(225,a,19501,a(flip),b,5804,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 19501 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19506">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(15697(a,1),19501(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15697 19501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19507">
    <literal><![CDATA[
      (a(x,y,K(z,u)) \ T(w,v5)) / (a(u,y,K(z,x)) * w) = K(w,v5 * a(u,y,K(z,x)))
    ]]></literal>
    <justification jstring="[para(19501(a,1),15421(a,1,1,2))].">
      <j1 rule="para" parents="19501 15421"/>
    </justification>
  </clause>

  <clause id="19508">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,5787,a,b,19505,a),flip(a)].">
      <j1 rule="hyper" parents="373 5787 19505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19509">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(w,v5) = v6
    ]]></literal>
    <justification jstring="[para(19505(a,2),5874(a,1))].">
      <j1 rule="para" parents="19505 5874"/>
    </justification>
  </clause>

  <clause id="19510">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) * K(w,v5) = T(a(x,y,K(z,u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(145,a,19508,a(flip),b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 19508 5726"/>
    </justification>
  </clause>

  <clause id="19511">
    <literal><![CDATA[
      K(x * T(y,a(z,u,w)),v5) = K(x * y,v5)
    ]]></literal>
    <justification jstring="[para(19331(a,1),19508(a,1,1))].">
      <j1 rule="para" parents="19331 19508"/>
    </justification>
  </clause>

  <clause id="19512">
    <literal><![CDATA[
      K(T(x,y) * L(y,z,u),w) = K(L(y,z,u) * x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15404,a(flip),b,19511,a)].">
      <j1 rule="hyper" parents="64 15404 19511"/>
    </justification>
  </clause>

  <clause id="19513">
    <literal><![CDATA[
      K((x * y) * K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * (y * K(z,u)),w) = v5
    ]]></literal>
    <justification jstring="[para(15463(a,1),19509(a,1,1))].">
      <j1 rule="para" parents="15463 19509"/>
    </justification>
  </clause>

  <clause id="19514">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,15759,a,b,19506,a),flip(a)].">
      <j1 rule="hyper" parents="373 15759 19506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19515">
    <literal><![CDATA[
      T(x,T(y,L(z,u,w)) * v5) = T(x,K(y,z) * (y * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,13678,a(flip),b,19506,a)].">
      <j1 rule="hyper" parents="64 13678 19506"/>
    </justification>
  </clause>

  <clause id="19516">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * w) \ (K(z,L(u,v5,v6)) * w)) = T(x,(K(z,L(u,v5,v6)) * w) / y)
    ]]></literal>
    <justification jstring="[para(19506(a,1),13424(a,1,2,1))].">
      <j1 rule="para" parents="19506 13424"/>
    </justification>
  </clause>

  <clause id="19517">
    <literal><![CDATA[
      T(x,K(R(y,z,u),w) * v5) = T(x,K(y,w) * v5)
    ]]></literal>
    <justification jstring="[para(15572(a,2),19506(a,1,2,1))].">
      <j1 rule="para" parents="15572 19506"/>
    </justification>
  </clause>

  <clause id="19518">
    <literal><![CDATA[
      T(x,(K(y,z) * u) * w) = T(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[para(15578(a,1),19514(a,1,2))].">
      <j1 rule="para" parents="15578 19514"/>
    </justification>
  </clause>

  <clause id="19519">
    <literal><![CDATA[
      (T(x,K(y,z) * u) * K(z,L(T(y,x),w,v5))) / (K(z,L(y,w,v5)) * x) = K(x,u * K(z,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(19514(a,1),17754(a,1,1,1))].">
      <j1 rule="para" parents="19514 17754"/>
    </justification>
  </clause>

  <clause id="19520">
    <literal><![CDATA[
      T(x,K((y / z) / u,w) * v5) = T(x,K(y / (u * z),w) * v5)
    ]]></literal>
    <justification jstring="[para(351(a,1),19517(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="351 19517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19521">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / z) * w)) = T(x,(u / T(z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17993,a(flip),b,19503,a),flip(a)].">
      <j1 rule="hyper" parents="64 17993 19503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19522">
    <literal><![CDATA[
      T(x,K(y \ z,y) * ((z \ u) * w)) = T(x,((y * (z / y)) \ u) * w)
    ]]></literal>
    <justification jstring="[para(11892(a,1),19503(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11892 19503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19523">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = K(u * L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(16855,a,19512,a),flip(a)].">
      <j1 rule="hyper" parents="16855 19512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19525">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / y) * w)) = T(x,(u / T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17993,a(flip),b,19518,a),flip(a)].">
      <j1 rule="hyper" parents="64 17993 19518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19526">
    <literal><![CDATA[
      T(x,K(y,z) * ((y \ u) * w)) = T(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(6157(a,1),19518(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6157 19518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19527">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * K(y,z)) * w)) = T(x,T(u,K(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(8158(a,1),19518(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8158 19518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19528">
    <literal><![CDATA[
      T(x,(K(a(y,z,u),w) * v5) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 * v6) = v7
    ]]></literal>
    <justification jstring="[para(19518(a,2),19497(a,1))].">
      <j1 rule="para" parents="19518 19497"/>
    </justification>
  </clause>

  <clause id="19529">
    <literal><![CDATA[
      T(x,T(y,L(z,u,w)) * v5) = T(x,T(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,13678,a(flip),b,19515,a),flip(a)].">
      <j1 rule="hyper" parents="373 13678 19515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19530">
    <literal><![CDATA[
      T(x,T(R(y,z,u) * w,y) * v5) = T(x,(w * R(y,z,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,15612,a(flip),b,19529,a),flip(a)].">
      <j1 rule="hyper" parents="64 15612 19529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19531">
    <literal><![CDATA[
      K(x * L(y,z,u),y * x) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,19403,a(flip),b,19523,a),flip(a)].">
      <j1 rule="hyper" parents="64 19403 19523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19532">
    <literal><![CDATA[
      K(x * (1 / (1 / (y \ z))),(1 / (z \ y)) * x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[para(4305(a,1),19531(a,1,1,2))].">
      <j1 rule="para" parents="4305 19531"/>
    </justification>
  </clause>

  <clause id="19533">
    <literal><![CDATA[
      T(x,y * (z * K(u,K(w,v5) * v6))) = T(x,(y * z) * K(v6,u))
    ]]></literal>
    <justification jstring="[hyper(19502,a,18622,a)].">
      <j1 rule="hyper" parents="19502 18622"/>
    </justification>
  </clause>

  <clause id="19534">
    <literal><![CDATA[
      T(x,(y \ z) * (y * K(u,w))) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(19502,a,18141,a)].">
      <j1 rule="hyper" parents="19502 18141"/>
    </justification>
  </clause>

  <clause id="19535">
    <literal><![CDATA[
      T(x,y * (z * K(u,T(w,v5)))) = T(x,K(w,u) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(19502,a,18048,a)].">
      <j1 rule="hyper" parents="19502 18048"/>
    </justification>
  </clause>

  <clause id="19536">
    <literal><![CDATA[
      T(x,(y * z) * K(u,w * v5)) = T(x,y * (z * K(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(19502,a,17870,a),flip(a)].">
      <j1 rule="hyper" parents="19502 17870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19537">
    <literal><![CDATA[
      T(x,y * (z * K(u,u \ w))) = T(x,K(u,w) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(19502,a,17347,a)].">
      <j1 rule="hyper" parents="19502 17347"/>
    </justification>
  </clause>

  <clause id="19538">
    <literal><![CDATA[
      T(x,(y * z) * K(u,w)) = T(x,y * (z * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(19502,a,16270,a),flip(a)].">
      <j1 rule="hyper" parents="19502 16270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19539">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) = T(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(19502,a,17348,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19502 17348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19540">
    <literal><![CDATA[
      T(x,K(y,z) \ (u * w)) = T(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(19502,a,17212,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19502 17212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19541">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) = T(x,u * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(19502,a,17165,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19502 17165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19542">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) = T(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,17948,a,b,19539,a),flip(a)].">
      <j1 rule="hyper" parents="373 17948 19539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19543">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * z))) = T(x,u * (w * T(z,y)))
    ]]></literal>
    <justification jstring="[para(6852(a,1),19539(a,2,2,2))].">
      <j1 rule="para" parents="6852 19539"/>
    </justification>
  </clause>

  <clause id="19544">
    <literal><![CDATA[
      T(x,K(y,z) \ (u * w)) = T(x,u * (K(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,17991,a,b,19540,a),flip(a)].">
      <j1 rule="hyper" parents="373 17991 19540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19545">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) = T(x,u * (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,17948,a,b,19541,a),flip(a)].">
      <j1 rule="hyper" parents="373 17948 19541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19546">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * y))) = T(x,u * (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(6852(a,1),19541(a,2,2,2))].">
      <j1 rule="para" parents="6852 19541"/>
    </justification>
  </clause>

  <clause id="19547">
    <literal><![CDATA[
      T(x,y * (z * K(u,T(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,K(w,u) * (y * z)) = v6
    ]]></literal>
    <justification jstring="[para(19541(a,1),18046(a,1))].">
      <j1 rule="para" parents="19541 18046"/>
    </justification>
  </clause>

  <clause id="19548">
    <literal><![CDATA[
      T(x,y * (K(z \ u,z) * w)) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(15766,a,19542,a),flip(a)].">
      <j1 rule="hyper" parents="15766 19542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19549">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (y * w))) = T(x,u * (T(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,16334,a(flip),b,19542,a),flip(a)].">
      <j1 rule="hyper" parents="373 16334 19542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19550">
    <literal><![CDATA[
      T(x,y * (K(z \ 1,u) * w)) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16816,a(flip),b,19542,a),flip(a)].">
      <j1 rule="hyper" parents="64 16816 19542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19551">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (K(y,z) * w))) = T(x,u * w)
    ]]></literal>
    <justification jstring="[para(6161(a,1),19542(a,2,2,2))].">
      <j1 rule="para" parents="6161 19542"/>
    </justification>
  </clause>

  <clause id="19552">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (y \ w))) = T(x,u * (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[para(6157(a,1),19542(a,2,2,2))].">
      <j1 rule="para" parents="6157 19542"/>
    </justification>
  </clause>

  <clause id="19553">
    <literal><![CDATA[
      x \ T(x,K(y,z) \ (u * w)) = K(x,u * (K(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(139,a,19544,a,b,5753,a(flip))].">
      <j1 rule="hyper" parents="139 19544 5753"/>
    </justification>
  </clause>

  <clause id="19554">
    <literal><![CDATA[
      T(x,K(y,z) \ (u * (K(z,y) \ w))) = T(x,u * w)
    ]]></literal>
    <justification jstring="[para(6164(a,1),19544(a,2,2,2))].">
      <j1 rule="para" parents="6164 19544"/>
    </justification>
  </clause>

  <clause id="19555">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) \ (v5 * v6)) = T(x,v5 * (L(K(y,z),u,w) \ v6))
    ]]></literal>
    <justification jstring="[para(12059(a,2),19544(a,2,2,2,1))].">
      <j1 rule="para" parents="12059 19544"/>
    </justification>
  </clause>

  <clause id="19556">
    <literal><![CDATA[
      T(x,y * (K(z,z \ u) * w)) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(15766,a,19545,a),flip(a)].">
      <j1 rule="hyper" parents="15766 19545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19557">
    <literal><![CDATA[
      T(x,(y \ z) * (K(y,u) * w)) = T(x,(T(y,u) \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19526,a(flip),b,19545,a),flip(a)].">
      <j1 rule="hyper" parents="64 19526 19545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19558">
    <literal><![CDATA[
      T(x,y * (K(z,L(u,w,v5)) * v6)) = T(x,K(z,u) * (y * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,19506,a(flip),b,19545,a),flip(a)].">
      <j1 rule="hyper" parents="64 19506 19545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19559">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (z \ w))) = T(x,u * (T(z,y) \ w))
    ]]></literal>
    <justification jstring="[para(6157(a,1),19545(a,2,2,2))].">
      <j1 rule="para" parents="6157 19545"/>
    </justification>
  </clause>

  <clause id="19560">
    <literal><![CDATA[
      T(x,K(y,z) * (K(u,T(z,y)) * w)) = T(x,(w / z) * T(y * (z / y),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17908,a(flip),b,19537,a),flip(a)].">
      <j1 rule="hyper" parents="64 17908 19537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19561">
    <literal><![CDATA[
      T(x,K(T(y,z),T(u,z)) * (w * (v5 * T(u,z)))) = T(x,w * (v5 * (K(u,y) * T(u,z))))
    ]]></literal>
    <justification jstring="[para(8211(a,1),19543(a,2,2,2,2))].">
      <j1 rule="para" parents="8211 19543"/>
    </justification>
  </clause>

  <clause id="19562">
    <literal><![CDATA[
      T(x,y * (z * T(u,a(w,v5,v6)))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(19497,a,19546,a),flip(a)].">
      <j1 rule="hyper" parents="19497 19546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19563">
    <literal><![CDATA[
      T(x,y * T(K(z,u) * w,v5)) = T(x,y * (K(z,u) * T(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(18620,a,19546,a)].">
      <j1 rule="hyper" parents="18620 19546"/>
    </justification>
  </clause>

  <clause id="19564">
    <literal><![CDATA[
      T(x,K(T(y,z),u) * (w * (v5 * T(y,z)))) = T(x,w * (v5 * T(T(y,u),z)))
    ]]></literal>
    <justification jstring="[para(23(a,1),19546(a,2,2,2,2))].">
      <j1 rule="para" parents="23 19546"/>
    </justification>
  </clause>

  <clause id="19565">
    <literal><![CDATA[
      T(x,K(1 / (1 / (1 / y)),z) * (u * (y * ((y * y) \ w)))) = T(x,u * (T(1 / (1 / (1 / y)),z) * w))
    ]]></literal>
    <justification jstring="[para(2030(a,1),19549(a,1,2,2,2))].">
      <j1 rule="para" parents="2030 19549"/>
    </justification>
  </clause>

  <clause id="19566">
    <literal><![CDATA[
      T(x,y * (K(z \ 1,u) * (z \ w))) = T(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19550,a,b,19552,a)].">
      <j1 rule="hyper" parents="64 19550 19552"/>
    </justification>
  </clause>

  <clause id="19567">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) = K(x,u * (K(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(5827,a,19553,a)].">
      <j1 rule="hyper" parents="5827 19553"/>
    </justification>
  </clause>

  <clause id="19568">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (w * K(z,y))) = v5
    ]]></literal>
    <justification jstring="[para(19567(a,2),18409(a,1))].">
      <j1 rule="para" parents="19567 18409"/>
    </justification>
  </clause>

  <clause id="19569">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (z \ w))) = T(x,u * (((y \ z) * y) \ w))
    ]]></literal>
    <justification jstring="[para(10843(a,1),19556(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10843 19556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19570">
    <literal><![CDATA[
      T(x,(T(y,L(z \ u,w,u / z)) \ v5) * v6) = T(x,(y \ v5) * (K(y,z \ u) * v6))
    ]]></literal>
    <justification jstring="[para(9318(a,1),19557(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9318 19557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19571">
    <literal><![CDATA[
      K(K(x,y) * (z * u),w) = K(z * (u * K(y,x)),w)
    ]]></literal>
    <justification jstring="[hyper(19513,a,17359,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19513 17359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19572">
    <literal><![CDATA[
      K(K(x,y) * (z * u),w) = K(z * (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,17983,a,b,19571,a),flip(a)].">
      <j1 rule="hyper" parents="373 17983 19571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19573">
    <literal><![CDATA[
      K(K(x,y) * (z * u),w) = K(z * (K(x,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17423,a,b,19572,a)].">
      <j1 rule="hyper" parents="64 17423 19572"/>
    </justification>
  </clause>

  <clause id="19574">
    <literal><![CDATA[
      K(K(x \ y,x) * (z * ((x \ y) / u)),w) = K(z * ((y / x) / u),w)
    ]]></literal>
    <justification jstring="[para(14696(a,1),19572(a,2,1,2))].">
      <j1 rule="para" parents="14696 19572"/>
    </justification>
  </clause>

  <clause id="19575">
    <literal><![CDATA[
      K(x * (K(y,z) * u),w) = K(x * (K(z,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19572,a(flip),b,19573,a)].">
      <j1 rule="hyper" parents="64 19572 19573"/>
    </justification>
  </clause>

  <clause id="19576">
    <literal><![CDATA[
      K(x * (K(y,z) * (K(y,z) * u)),w) = K(x * u,w)
    ]]></literal>
    <justification jstring="[para(6161(a,1),19575(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6161 19575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19577">
    <literal><![CDATA[
      K(x * (y * T(T(z,u),u)),w) = K(x * (y * z),w)
    ]]></literal>
    <justification jstring="[para(10377(a,1),19576(a,1,1,2))].">
      <j1 rule="para" parents="10377 19576"/>
    </justification>
  </clause>

  <clause id="19578">
    <literal><![CDATA[
      K(x * (y * (z * K(u,z))),w) = K(x * (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[para(5785(a,1),19577(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5785 19577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19579">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(19568,a,17190,a),flip(a)].">
      <j1 rule="hyper" parents="19568 17190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19580">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(19568,a,15771,a),flip(a)].">
      <j1 rule="hyper" parents="19568 15771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19581">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(17190(a,1),19568(a,1))].">
      <j1 rule="para" parents="17190 19568"/>
    </justification>
  </clause>

  <clause id="19582">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(17194,a,19579,a)].">
      <j1 rule="hyper" parents="17194 19579"/>
    </justification>
  </clause>

  <clause id="19583">
    <literal><![CDATA[
      K(x,y * ((1 / z) * K(u,y / z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(15206,a,19579,a),flip(a)].">
      <j1 rule="hyper" parents="15206 19579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19584">
    <literal><![CDATA[
      K(x,(y * z) * K(u * (w \ v5),v5 \ w)) = K(x,y * (z * K((v5 \ w) \ u,v5 \ w)))
    ]]></literal>
    <justification jstring="[para(18934(a,1),19579(a,1,2,2))].">
      <j1 rule="para" parents="18934 19579"/>
    </justification>
  </clause>

  <clause id="19585">
    <literal><![CDATA[
      K(x,K(y,z * u) * (w * v5)) = K(x,w * (v5 * K(y,u * z)))
    ]]></literal>
    <justification jstring="[hyper(18190,a,19580,a)].">
      <j1 rule="hyper" parents="18190 19580"/>
    </justification>
  </clause>

  <clause id="19586">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,18107,a,b,19580,a),flip(a)].">
      <j1 rule="hyper" parents="373 18107 19580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19587">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,17932,a,b,19580,a),flip(a)].">
      <j1 rule="hyper" parents="373 17932 19580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19588">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,14770,a(flip),b,19580,a),flip(a)].">
      <j1 rule="hyper" parents="373 14770 19580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19589">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (w \ 1))) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[para(14444(a,1),19580(a,2,2,2))].">
      <j1 rule="para" parents="14444 19580"/>
    </justification>
  </clause>

  <clause id="19590">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (z / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (T(z,y) / w)) = v5
    ]]></literal>
    <justification jstring="[para(19580(a,2),18096(a,1))].">
      <j1 rule="para" parents="19580 18096"/>
    </justification>
  </clause>

  <clause id="19591">
    <literal><![CDATA[
      K(x,y / (K(z,u) / w)) = K(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,14602,a,b,19582,a)].">
      <j1 rule="hyper" parents="373 14602 19582"/>
    </justification>
  </clause>

  <clause id="19592">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,14770,a(flip),b,19582,a),flip(a)].">
      <j1 rule="hyper" parents="373 14770 19582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19593">
    <literal><![CDATA[
      K(x,y * (K(y \ 1,z) * u)) = K(x,T(y \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(14783,a,19587,a),flip(a)].">
      <j1 rule="hyper" parents="14783 19587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19594">
    <literal><![CDATA[
      K(x,y * (K(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * u) = w
    ]]></literal>
    <justification jstring="[para(19587(a,1),8563(a,1))].">
      <j1 rule="para" parents="19587 8563"/>
    </justification>
  </clause>

  <clause id="19595">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (v5 * v6)) = K(x,v5 * (K(z,L(y,u,w)) * v6))
    ]]></literal>
    <justification jstring="[para(12093(a,1),19587(a,1,2,1))].">
      <j1 rule="para" parents="12093 19587"/>
    </justification>
  </clause>

  <clause id="19596">
    <literal><![CDATA[
      K(x,y * (T(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(5755(a,1),19594(a,1,2,2))].">
      <j1 rule="para" parents="5755 19594"/>
    </justification>
  </clause>

  <clause id="19597">
    <literal><![CDATA[
      K(x,y * (T(z,x) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(16267(a,1),19594(a,1))].">
      <j1 rule="para" parents="16267 19594"/>
    </justification>
  </clause>

  <clause id="19598">
    <literal><![CDATA[
      (x \ (1 / T(x,y))) * K(z,K(x,y) * (1 * x)) = T((1 / x) \ K(x,y),z) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(19591(a,1),16745(a,1,2))].">
      <j1 rule="para" parents="19591 16745"/>
    </justification>
  </clause>

  <clause id="19599">
    <literal><![CDATA[
      K(x,y * (K(z,u \ y) / u)) = K(x,T(y / u,z))
    ]]></literal>
    <justification jstring="[para(14772(a,1),19583(a,1,2,2))].">
      <j1 rule="para" parents="14772 19583"/>
    </justification>
  </clause>

  <clause id="19600">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z \ y))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(18098,a,19599,a)].">
      <j1 rule="hyper" parents="18098 19599"/>
    </justification>
  </clause>

  <clause id="19601">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(u,T(u \ z,y)))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[para(11653(a,1),19600(a,1,2,2,2))].">
      <j1 rule="para" parents="11653 19600"/>
    </justification>
  </clause>

  <clause id="19602">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(w,z \ u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,w)) = v5
    ]]></literal>
    <justification jstring="[para(19589(a,1),18134(a,1))].">
      <j1 rule="para" parents="19589 18134"/>
    </justification>
  </clause>

  <clause id="19603">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19588,a(flip),b,19592,a)].">
      <j1 rule="hyper" parents="64 19588 19592"/>
    </justification>
  </clause>

  <clause id="19604">
    <literal><![CDATA[
      K(x,y * (z \ K(z,u))) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(14787,a,19603,a),flip(a)].">
      <j1 rule="hyper" parents="14787 19603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19605">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(u,w))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18156,a(flip),b,19603,a),flip(a)].">
      <j1 rule="hyper" parents="373 18156 19603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19606">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K((z \ 1) * u,u))) = K(x,y / ((z \ K(z \ u,u)) * u))
    ]]></literal>
    <justification jstring="[para(14800(a,2),19604(a,2,2,2))].">
      <j1 rule="para" parents="14800 19604"/>
    </justification>
  </clause>

  <clause id="19607">
    <literal><![CDATA[
      K(x,y * (K(y \ 1,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(19593(a,2),18196(a,1))].">
      <j1 rule="para" parents="19593 18196"/>
    </justification>
  </clause>

  <clause id="19609">
    <literal><![CDATA[
      L(x * L(x \ y,z,u),z,K(x \ y,u)) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16635,a,b,19229,a)].">
      <j1 rule="hyper" parents="64 16635 19229"/>
    </justification>
  </clause>

  <clause id="19610">
    <literal><![CDATA[
      T(x,T((K(y,z) \ u) \ w,v5)) = T(x,T(u \ (K(z,y) \ w),v5))
    ]]></literal>
    <justification jstring="[para(6156(a,2),19232(a,1,2,1,1))].">
      <j1 rule="para" parents="6156 19232"/>
    </justification>
  </clause>

  <clause id="19611">
    <literal><![CDATA[
      K(x,(y * z) / L(y,u,w)) = K(x,(L(y,u,w) \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(11233,a,19269,a),flip(a)].">
      <j1 rule="hyper" parents="11233 19269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19612">
    <literal><![CDATA[
      K(x,(y * z) / L(y,u,w)) = K(x,y * (z / L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,19248,a(flip),b,19611,a),flip(a)].">
      <j1 rule="hyper" parents="373 19248 19611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19613">
    <literal><![CDATA[
      K(x,L(y,z,u / (y * w))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(15339,a,19349,a),flip(a)].">
      <j1 rule="hyper" parents="15339 19349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19614">
    <literal><![CDATA[
      K(x,L(y,z,(y * u) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(19307,a,19613,a)].">
      <j1 rule="hyper" parents="19307 19613"/>
    </justification>
  </clause>

  <clause id="19615">
    <literal><![CDATA[
      x \ (y * (K(z,K(u,w)) * v5)) = (x \ (y * v5)) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(17161(a,2),19377(a,1,2,2))].">
      <j1 rule="para" parents="17161 19377"/>
    </justification>
  </clause>

  <clause id="19616">
    <literal><![CDATA[
      K(x,y) / L(z \ 1,u,K(w,v5)) = K(x,y) * T(z,a(v5,u,w))
    ]]></literal>
    <justification jstring="[para(16603(a,2),19406(a,1,2))].">
      <j1 rule="para" parents="16603 19406"/>
    </justification>
  </clause>

  <clause id="19617">
    <literal><![CDATA[
      K(x,T(y * (K(z,u) / w),v5)) = K(x,T(y * (w \ K(z,u)),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16380,a(flip),b,19468,a)].">
      <j1 rule="hyper" parents="64 16380 19468"/>
    </justification>
  </clause>

  <clause id="19618">
    <literal><![CDATA[
      T(a(x,y,K(z,u)) * w,v5) = a(x,y,K(z,u)) * T(w,v5)
    ]]></literal>
    <justification jstring="[hyper(6940,a,19510,a),flip(a)].">
      <j1 rule="hyper" parents="6940 19510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19619">
    <literal><![CDATA[
      T(a(x,y,K(z,u)) * w,v5) = T(w,v5) * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,19187,a(flip),b,19618,a),flip(a)].">
      <j1 rule="hyper" parents="373 19187 19618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19620">
    <literal><![CDATA[
      T(x,K(y / (z * u),w) * v5) = T(x,K(z \ (y / u),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(18076,a,19520,a),flip(a)].">
      <j1 rule="hyper" parents="18076 19520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19621">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * K(y,z)) * w)) = T(x,u * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,17945,a(flip),b,19527,a),flip(a)].">
      <j1 rule="hyper" parents="373 17945 19527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19623">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) = T(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19551,a(flip),b,19621,a)].">
      <j1 rule="hyper" parents="64 19551 19621"/>
    </justification>
  </clause>

  <clause id="19624">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) = T(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[para(6871(a,1),19621(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6871 19621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19625">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) = T(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,17948,a(flip),b,19623,a),flip(a)].">
      <j1 rule="hyper" parents="373 17948 19623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19626">
    <literal><![CDATA[
      T(x,(y * z) * (K(u,L(w,y,z)) * v5)) = T(x,((K(u,w) * y) * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,17994,a(flip),b,19623,a),flip(a)].">
      <j1 rule="hyper" parents="64 17994 19623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19627">
    <literal><![CDATA[
      T(x,K(y,z) * (u * T(z / u,w))) = T(x,T(u * T(z / u,w),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,18724,a(flip),b,19624,a),flip(a)].">
      <j1 rule="hyper" parents="64 18724 19624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19628">
    <literal><![CDATA[
      T(x,(y * K(z,T(u,w))) * v5) = T(x,K(u,z) * (y * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,19535,a(flip),b,19625,a),flip(a)].">
      <j1 rule="hyper" parents="373 19535 19625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19629">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) * v5) = T(x,K(z,y) * (T(u,w) * v5))
    ]]></literal>
    <justification jstring="[para(15723(a,1),19628(a,1,2,1))].">
      <j1 rule="para" parents="15723 19628"/>
    </justification>
  </clause>

  <clause id="19631">
    <literal><![CDATA[
      T(x,((K(y * z,y) * u) * T(y,z)) * w) = T(x,(u * R(y,z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,18047,a,b,19530,a)].">
      <j1 rule="hyper" parents="64 18047 19530"/>
    </justification>
  </clause>

  <clause id="19632">
    <literal><![CDATA[
      T(x,y * (z * K(u,K(w,v5) * v6))) = T(x,y * (z * K(v6,u)))
    ]]></literal>
    <justification jstring="[hyper(19502,a,19533,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19502 19533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19633">
    <literal><![CDATA[
      T(x,y * (z * K(u,w \ v5))) = T(x,y * (z * K(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(19502,a,19536,a),flip(a)].">
      <j1 rule="hyper" parents="19502 19536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19634">
    <literal><![CDATA[
      T(x,(T(y,z * T(K(u,w) * u,v5)) * (z * T(u,w))) * K(u,v5)) = T(x,((z * T(u,w)) * K(u,v5)) * R(y,z * T(u,w),K(u,v5)))
    ]]></literal>
    <justification jstring="[para(19563(a,2),11932(a,1,2,1,1))].">
      <j1 rule="para" parents="19563 11932"/>
    </justification>
  </clause>

  <clause id="19635">
    <literal><![CDATA[
      T(x,y * (z * T(z \ (u \ z),w))) = T(x,y * (T(u,w) \ z))
    ]]></literal>
    <justification jstring="[para(5998(a,1),19566(a,1,2,2))].">
      <j1 rule="para" parents="5998 19566"/>
    </justification>
  </clause>

  <clause id="19636">
    <literal><![CDATA[
      T(x,y * (((z \ u) * z) \ w)) = T(x,y * (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19559,a(flip),b,19569,a),flip(a)].">
      <j1 rule="hyper" parents="64 19559 19569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19637">
    <literal><![CDATA[
      K(x,y * (z * K((u * w) \ y,u * w))) = K(x,(((w * u) \ y) * (w * u)) * z)
    ]]></literal>
    <justification jstring="[para(13505(a,1),19585(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13505 19585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19638">
    <literal><![CDATA[
      T(x,T(y \ (K(z,u) \ w),y)) = T(x,w / (K(u,z) \ y))
    ]]></literal>
    <justification jstring="[hyper(18267,a,19610,a),flip(a)].">
      <j1 rule="hyper" parents="18267 19610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19639">
    <literal><![CDATA[
      T(x,y / (K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(K(u,z) \ y) / w) = v5
    ]]></literal>
    <justification jstring="[para(19638(a,1),8856(a,1))].">
      <j1 rule="para" parents="19638 8856"/>
    </justification>
  </clause>

  <clause id="19640">
    <literal><![CDATA[
      K(x,y) / L(z \ 1,u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(16603(a,2),19616(a,2,2))].">
      <j1 rule="para" parents="16603 19616"/>
    </justification>
  </clause>

  <clause id="19641">
    <literal><![CDATA[
      K(x,T(y / (z * K(u,w)),v5)) = K(x,T(y * (z \ K(w,u)),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,14948,a,b,19617,a)].">
      <j1 rule="hyper" parents="64 14948 19617"/>
    </justification>
  </clause>

  <clause id="19642">
    <literal><![CDATA[
      T(x,K(y \ (z / y),u) * w) = T(x,K(u,y \ (y \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(17276,a,19620,a),flip(a)].">
      <j1 rule="hyper" parents="17276 19620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19643">
    <literal><![CDATA[
      T(x,K(y,z) * (T(u \ z,w) * u)) = T(x,u * T(T(z,T(y,u)) / u,w))
    ]]></literal>
    <justification jstring="[hyper(15090,a,19629,a),flip(a)].">
      <j1 rule="hyper" parents="15090 19629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19644">
    <literal><![CDATA[
      T(x,T(y,z * K(u,w)) * (z * K(v5,v6 * v7))) = T(x,(z / (1 / K(v5,v6 \ v7))) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,18885,a(flip),b,19633,a),flip(a)].">
      <j1 rule="hyper" parents="64 18885 19633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19645">
    <literal><![CDATA[
      T(x,T(y \ (z \ y),u)) = T(x,y \ (T(z,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(41,a,15876,a,b,19635,a),flip(a)].">
      <j1 rule="hyper" parents="41 15876 19635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19646">
    <literal><![CDATA[
      K(x,T(y * (z \ K(y,u)),w)) = K(x,T(T(y,u) / z,w))
    ]]></literal>
    <justification jstring="[para(15024(a,1),19641(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15024 19641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19647">
    <literal><![CDATA[
      K(x,T(((y \ z) \ z) / u,w)) = K(x,T(y * (u \ K(y,y \ z)),w))
    ]]></literal>
    <justification jstring="[para(116(a,1),19646(a,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="116 19646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19648">
    <literal><![CDATA[
      T(x,K(y * (z / y),u) * w) = T(x,K(u,y \ (y \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(17868,a,19642,a)].">
      <j1 rule="hyper" parents="17868 19642"/>
    </justification>
  </clause>

  <clause id="19649">
    <literal><![CDATA[
      T(x,K(y,z \ (z \ u)) * w) = T(x,K(u,T(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(11193(a,1),19648(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11193 19648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19650">
    <literal><![CDATA[
      T(x,K(y,z \ (z \ u)) * w) = T(x,K(y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,18045,a(flip),b,19649,a),flip(a)].">
      <j1 rule="hyper" parents="373 18045 19649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19652">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / z) * (w * w))) = T(x,u / T((w * w) \ z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17883,a(flip),b,19650,a),flip(a)].">
      <j1 rule="hyper" parents="64 17883 19650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19653">
    <literal><![CDATA[
      T(x,K(y,z \ u) * w) = T(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),19650(a,1,2,1,2,2))].">
      <j1 rule="para" parents="9 19650"/>
    </justification>
  </clause>

  <clause id="19654">
    <literal><![CDATA[
      T(x,K(y,z * u) * (w * (y * v5))) = T(x,w * (T(y,z \ u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,19549,a(flip),b,19653,a),flip(a)].">
      <j1 rule="hyper" parents="64 19549 19653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19655">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(z,y,x)) = x * (y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(19178,a,16222,a)].">
      <j1 rule="hyper" parents="19178 16222"/>
    </justification>
  </clause>

  <clause id="19656">
    <literal><![CDATA[
      K(x,y * ((z * (u / w)) * K(L(w,u,z),v5))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(19655(a,1),16333(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19655 16333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19657">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * (u / z))) = K(x,w * (u / T(z,K(v5,v6) * y)))
    ]]></literal>
    <justification jstring="[para(19655(a,1),18867(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19655 18867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19658">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) * (u \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,L(w,u,u \ 1))) = v5
    ]]></literal>
    <justification jstring="[para(19292(a,2),15977(a,1))].">
      <j1 rule="para" parents="19292 15977"/>
    </justification>
  </clause>

  <clause id="19659">
    <literal><![CDATA[
      a(x \ y,x,K(z,u)) * K(z,(x * u) / y) = K(z,x / (y / u))
    ]]></literal>
    <justification jstring="[hyper(15423,a,19345,a)].">
      <j1 rule="hyper" parents="15423 19345"/>
    </justification>
  </clause>

  <clause id="19660">
    <literal><![CDATA[
      K(x,L(y * z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(14930,a,19407,a)].">
      <j1 rule="hyper" parents="14930 19407"/>
    </justification>
  </clause>

  <clause id="19661">
    <literal><![CDATA[
      K(x,L(((y \ L(y,z,u)) \ 1) \ w,y,y * (y \ L(y,z,u)))) = K(x,y \ ((((y \ L(y,z,u)) \ 1) \ y) * w))
    ]]></literal>
    <justification jstring="[para(10384(a,1),19407(a,2,2,2,1))].">
      <j1 rule="para" parents="10384 19407"/>
    </justification>
  </clause>

  <clause id="19662">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ ((z / (T(y,z) \ 1)) * u))
    ]]></literal>
    <justification jstring="[para(115(a,1),19660(a,1,2,3))].">
      <j1 rule="para" parents="115 19660"/>
    </justification>
  </clause>

  <clause id="19663">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * K(u,v5 / w))) = v6
    ]]></literal>
    <justification jstring="[para(9063(a,1),19413(a,1,2,2,2))].">
      <j1 rule="para" parents="9063 19413"/>
    </justification>
  </clause>

  <clause id="19664">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ w)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(19451,a,15959,a)].">
      <j1 rule="hyper" parents="19451 15959"/>
    </justification>
  </clause>

  <clause id="19665">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u \ 1),u * z,u \ 1)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14205,a(flip),b,19664,a),flip(a)].">
      <j1 rule="hyper" parents="64 14205 19664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19666">
    <literal><![CDATA[
      K(x,L(y,z,u \ (w \ u))) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[para(10(a,1),19664(a,1,2,3,1))].">
      <j1 rule="para" parents="10 19664"/>
    </justification>
  </clause>

  <clause id="19667">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((u / (z * u)) * y) \ u)
    ]]></literal>
    <justification jstring="[para(15002(a,1),19664(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15002 19664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19668">
    <literal><![CDATA[
      ((x * y) \ y) * ((((x * y) \ y) \ z) * K(u,w)) = z * K(u,L(w,z,x \ 1))
    ]]></literal>
    <justification jstring="[para(19664(a,1),15524(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19664 15524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19669">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = ((x \ y) / y) * (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(19666(a,1),12075(a,1,2))].">
      <j1 rule="para" parents="19666 12075"/>
    </justification>
  </clause>

  <clause id="19670">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z * (z \ (z / u))) = (K(x,y) * z) * (z \ (z / u))
    ]]></literal>
    <justification jstring="[para(19666(a,1),15628(a,1,1))].">
      <j1 rule="para" parents="19666 15628"/>
    </justification>
  </clause>

  <clause id="19671">
    <literal><![CDATA[
      T(x,(y * K(z,T(u,w))) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * (y * v5)) = v6
    ]]></literal>
    <justification jstring="[para(19625(a,2),19547(a,1))].">
      <j1 rule="para" parents="19625 19547"/>
    </justification>
  </clause>

  <clause id="19672">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / (u / w))) = K(x,y * T((u / w) \ z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(19590,a,18779,a)].">
      <j1 rule="hyper" parents="19590 18779"/>
    </justification>
  </clause>

  <clause id="19673">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) * K(x,(y * u) / z) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[para(15324(a,1),19659(a,1,1))].">
      <j1 rule="para" parents="15324 19659"/>
    </justification>
  </clause>

  <clause id="19674">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,(y * T(z,w)) / u) = K(x,y / (u / T(z,w)))
    ]]></literal>
    <justification jstring="[para(19297(a,1),19659(a,1,1))].">
      <j1 rule="para" parents="19297 19659"/>
    </justification>
  </clause>

  <clause id="19675">
    <literal><![CDATA[
      K(x,((y / (z * y)) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16172,a(flip),b,19667,a),flip(a)].">
      <j1 rule="hyper" parents="64 16172 19667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19676">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,((z / y) * u) \ z)
    ]]></literal>
    <justification jstring="[para(12(a,1),19675(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 19675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19677">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),((z / u) \ w) \ u) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,T(((u / z) * w) \ u,x)) = v5
    ]]></literal>
    <justification jstring="[para(19676(a,2),16126(a,1))].">
      <j1 rule="para" parents="19676 16126"/>
    </justification>
  </clause>

  <clause id="19678">
    <literal><![CDATA[
      ((x \ y) / y) * (y * K(z,u)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16164,a(flip),b,19669,a),flip(a)].">
      <j1 rule="hyper" parents="64 16164 19669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19679">
    <literal><![CDATA[
      (((T(x,K(y,z)) / u) \ x) / x) * (x * K(y,z)) = (x / u) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,14895,a(flip),b,19678,a),flip(a)].">
      <j1 rule="hyper" parents="373 14895 19678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19680">
    <literal><![CDATA[
      (x / y) \ (x * K(z,u)) = (y / x) * (x * K(z,u))
    ]]></literal>
    <justification jstring="[para(82(a,1),19678(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 19678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19681">
    <literal><![CDATA[
      K(x,(T((y \ z) / z,x) * (z * K(u,w))) * v5) = K(x,(y \ (z * K(u,w))) * v5)
    ]]></literal>
    <justification jstring="[para(19678(a,1),9685(a,2,2,1))].">
      <j1 rule="para" parents="19678 9685"/>
    </justification>
  </clause>

  <clause id="19682">
    <literal><![CDATA[
      K(x,y * T(z \ (u * K(w,v5)),u * K(w,v5))) = K(x,y * ((u * K(w,v5)) * ((z \ u) / u)))
    ]]></literal>
    <justification jstring="[para(19678(a,1),17683(a,1,2,2,1))].">
      <j1 rule="para" parents="19678 17683"/>
    </justification>
  </clause>

  <clause id="19683">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(x,y,K(u \ y,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(19191,a,19673,a)].">
      <j1 rule="hyper" parents="19191 19673"/>
    </justification>
  </clause>

  <clause id="19684">
    <literal><![CDATA[
      a(x,K(y,z) * u,K((T(y,z) \ z) \ u,w)) * K(x,((K(y,z) * u) * w) / (y \ z)) = K(x,(K(y,z) * u) / ((y \ z) / w))
    ]]></literal>
    <justification jstring="[para(13057(a,1),19673(a,1,1,3,1))].">
      <j1 rule="para" parents="13057 19673"/>
    </justification>
  </clause>

  <clause id="19685">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(z,y,K(x,u \ y)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(15690,a,19683,a)].">
      <j1 rule="hyper" parents="15690 19683"/>
    </justification>
  </clause>

  <clause id="19688">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ (L(K(y,z),u,w) \ v6)) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[para(10(a,1),19284(a,2,2,2))].">
      <j1 rule="para" parents="10 19284"/>
    </justification>
  </clause>

  <clause id="19689">
    <literal><![CDATA[
      (x \ L(T(y,y * K(z,u)),w,v5)) * K(y,K(z,u)) = x \ L(y,w,v5)
    ]]></literal>
    <justification jstring="[para(25(a,2),19318(a,1,1,2))].">
      <j1 rule="para" parents="25 19318"/>
    </justification>
  </clause>

  <clause id="19690">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(x,w,K(u \ y,z)) = K(x,L((y * z) / u,w,z \ 1))
    ]]></literal>
    <justification jstring="[para(12239(a,1),19348(a,1,2))].">
      <j1 rule="para" parents="12239 19348"/>
    </justification>
  </clause>

  <clause id="19691">
    <literal><![CDATA[
      T(T(x,y \ (z * z)),K(u,y \ (z * z))) = T(x,T((z \ y) \ z,u))
    ]]></literal>
    <justification jstring="[para(14624(a,1),19382(a,1,1))].">
      <j1 rule="para" parents="14624 19382"/>
    </justification>
  </clause>

  <clause id="19692">
    <literal><![CDATA[
      (x \ y) * (a(z,u,w) \ ((x \ y) \ y)) = (y / x) * (a(z,u,w) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,862,a(flip),b,19396,a)].">
      <j1 rule="hyper" parents="64 862 19396"/>
    </justification>
  </clause>

  <clause id="19693">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / v5) = K(x,(y / z) * (v5 \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(18178,a,19431,a),flip(a)].">
      <j1 rule="hyper" parents="18178 19431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19694">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / v5) = K(x,(y / T(z,u)) / v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,19429,a(flip),b,19693,a),flip(a)].">
      <j1 rule="hyper" parents="373 19429 19693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19695">
    <literal><![CDATA[
      K(x,y \ (z / T(u,T(w,v5)))) = K(x,(z / T(u,w)) / T(y,T(u,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(18410,a,19694,a)].">
      <j1 rule="hyper" parents="18410 19694"/>
    </justification>
  </clause>

  <clause id="19696">
    <literal><![CDATA[
      K(x * K(y,z),T(u,w / x)) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(18274,a,19443,a)].">
      <j1 rule="hyper" parents="18274 19443"/>
    </justification>
  </clause>

  <clause id="19697">
    <literal><![CDATA[
      K(x * K(y,z),T(u,x \ w)) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(17264,a,19696,a)].">
      <j1 rule="hyper" parents="17264 19696"/>
    </justification>
  </clause>

  <clause id="19699">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15336,a(flip),b,19465,a),flip(a)].">
      <j1 rule="hyper" parents="373 15336 19465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19700">
    <literal><![CDATA[
      K(x,L(y \ (L(T(z,K(u,w)),v5,v6) * v7),y,K(v7,L(T(z,K(u,w)),v5,v6)))) = K(x,(K(L(T(z,K(u,w)),v5,v6),v7) \ y) \ (v7 * L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(7122(a,2),19476(a,1,2))].">
      <j1 rule="para" parents="7122 19476"/>
    </justification>
  </clause>

  <clause id="19701">
    <literal><![CDATA[
      L(x,T(y,z),(y / z) \ 1) = L(x,T(y,z),(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,13029,a(flip),b,19482,a)].">
      <j1 rule="hyper" parents="64 13029 19482"/>
    </justification>
  </clause>

  <clause id="19702">
    <literal><![CDATA[
      T(x,K(y,z) * ((y \ u) * w)) = T(x,((z * (y / z)) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(16812,a,19522,a)].">
      <j1 rule="hyper" parents="16812 19522"/>
    </justification>
  </clause>

  <clause id="19703">
    <literal><![CDATA[
      T(x,((y * (z / y)) \ u) * w) = T(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19526,a(flip),b,19702,a),flip(a)].">
      <j1 rule="hyper" parents="64 19526 19702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19704">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(T(z,w) \ u) * y) = T(x,y * ((w * (z / w)) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18340,a(flip),b,19703,a),flip(a)].">
      <j1 rule="hyper" parents="64 18340 19703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19705">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ (v5 * v6)) = T(x,v5 * (L(K(y,z),u,w) \ v6))
    ]]></literal>
    <justification jstring="[para(12059(a,2),19555(a,1,2,1))].">
      <j1 rule="para" parents="12059 19555"/>
    </justification>
  </clause>

  <clause id="19706">
    <literal><![CDATA[
      K(x * ((1 / y) / z),u) = K(x * ((y \ 1) / z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5250,a(flip),b,19574,a),flip(a)].">
      <j1 rule="hyper" parents="64 5250 19574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19708">
    <literal><![CDATA[
      T(x,y / T((z * z) \ u,w)) = T(x,(y / T(u,w)) * (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19521,a(flip),b,19652,a),flip(a)].">
      <j1 rule="hyper" parents="64 19521 19652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19709">
    <literal><![CDATA[
      T(x,y / T((z * z) \ u,w)) = T(x,y * (T(u,w) \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,14943,a(flip),b,19708,a),flip(a)].">
      <j1 rule="hyper" parents="373 14943 19708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19710">
    <literal><![CDATA[
      T(x,y * T(z \ (u * u),w)) = T(x,y * (T(z,w) \ (u * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17714,a(flip),b,19709,a)].">
      <j1 rule="hyper" parents="64 17714 19709"/>
    </justification>
  </clause>

  <clause id="19711">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) * v5)) = T(x,y * (T(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,19549,a(flip),b,19654,a),flip(a)].">
      <j1 rule="hyper" parents="64 19549 19654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19712">
    <literal><![CDATA[
      T(x,y * (T(z,u * u) * w)) = T(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(379(a,1),19711(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="379 19711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19713">
    <literal><![CDATA[
      T(x,y * (((z * z) \ u) * w)) = T(x,y * (u * ((z * z) \ w)))
    ]]></literal>
    <justification jstring="[para(952(a,1),19712(a,1,2,2))].">
      <j1 rule="para" parents="952 19712"/>
    </justification>
  </clause>

  <clause id="19714">
    <literal><![CDATA[
      T(x,y * (((z * u) / z) * ((u * u) \ w))) = T(x,y * ((1 / T(u,z)) * w))
    ]]></literal>
    <justification jstring="[para(6973(a,1),19713(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6973 19713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19715">
    <literal><![CDATA[
      (x \ L(T(y,K(z,u)),w,v5)) * K(y,K(z,u)) = x \ L(y,w,v5)
    ]]></literal>
    <justification jstring="[para(13660(a,1),19689(a,1,1,2,1))].">
      <j1 rule="para" parents="13660 19689"/>
    </justification>
  </clause>

  <clause id="19716">
    <literal><![CDATA[
      T(x,K(y,z)) \ L(x,u,w) = x \ L(T(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(17214,a,19715,a),flip(a)].">
      <j1 rule="hyper" parents="17214 19715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19717">
    <literal><![CDATA[
      T(x,T((y \ z) \ y,u)) = T(x,T(z \ (y * y),u))
    ]]></literal>
    <justification jstring="[hyper(8189,a,19691,a),flip(a)].">
      <j1 rule="hyper" parents="8189 19691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19718">
    <literal><![CDATA[
      T(x,T(T(y * z,u) \ (y * y),w)) = T(x,T((z * K(y * z,u)) \ y,w))
    ]]></literal>
    <justification jstring="[para(14494(a,1),19717(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14494 19717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19719">
    <literal><![CDATA[
      ((x \ (x * y)) * (a(z,u,w) \ ((x \ (x * y)) \ (x * y)))) \ (x * y) = (y * (a(z,u,w) \ x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(19692(a,2),14893(a,1,1))].">
      <j1 rule="para" parents="19692 14893"/>
    </justification>
  </clause>

  <clause id="19721">
    <literal><![CDATA[
      T(x,y * ((z * u) \ K(w,L(v5,u,z)))) = T(x,y / (z * (u * K(v5,w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,19425,a(flip),b,19230,a)].">
      <j1 rule="hyper" parents="64 19425 19230"/>
    </justification>
  </clause>

  <clause id="19722">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w) * v5) = T(x,v5 * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(19528,a,19339,a),flip(a)].">
      <j1 rule="hyper" parents="19528 19339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19723">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u * a(w,v5,v6)) \ z) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,z / T(y,T(a(w,v5,v6),v8) * u)) = v7
    ]]></literal>
    <justification jstring="[para(19722(a,1),17230(a,1,2,1))].">
      <j1 rule="para" parents="19722 17230"/>
    </justification>
  </clause>

  <clause id="19724">
    <literal><![CDATA[
      (K(x,y) \ z) * (z \ T(u,K(x,y))) = (u / z) * (z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,11089,a(flip),b,19478,a),flip(a)].">
      <j1 rule="hyper" parents="64 11089 19478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19725">
    <literal><![CDATA[
      a(x,(y \ T(z,K(u,w))) \ ((K(u,w) \ y) \ v5),x) = a(x,((z / y) * (y * K(w,u))) \ v5,x)
    ]]></literal>
    <justification jstring="[para(19724(a,1),13702(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19724 13702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19726">
    <literal><![CDATA[
      T(x * L(x \ y,z,z \ 1),y) = x * L(x \ y,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(11803,a,19609,a),flip(a)].">
      <j1 rule="hyper" parents="11803 19609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19727">
    <literal><![CDATA[
      T(x * L(x \ y,z,z \ 1),y) != u
    ]]></literal>
    <literal><![CDATA[
      x * L(x \ y,z,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(19609(a,1),11803(a,1))].">
      <j1 rule="para" parents="19609 11803"/>
    </justification>
  </clause>

  <clause id="19728">
    <literal><![CDATA[
      T(x,((K(y,z) * u) * w) * v5) = T(x,K(y,z) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,19558,a(flip),b,19626,a),flip(a)].">
      <j1 rule="hyper" parents="64 19558 19626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19730">
    <literal><![CDATA[
      T(x,K(y * z,y) * ((u * T(y,z)) * w)) = T(x,(u * R(y,z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19728,a(flip),b,19631,a)].">
      <j1 rule="hyper" parents="64 19728 19631"/>
    </justification>
  </clause>

  <clause id="19731">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * T(z,y)) * w)) = T(x,(u * R(z,y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(17869,a,19730,a)].">
      <j1 rule="hyper" parents="17869 19730"/>
    </justification>
  </clause>

  <clause id="19732">
    <literal><![CDATA[
      K(x,L(y,z,u / (T(w,x) * v5))) = K(x,L(y,z,(w * v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(15340,a,19346,a),flip(a)].">
      <j1 rule="hyper" parents="15340 19346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19733">
    <literal><![CDATA[
      K(x,L(y,z,(T(u,x) * w) \ v5)) = K(x,L(y,z,(u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(19307,a,19732,a)].">
      <j1 rule="hyper" parents="19307 19732"/>
    </justification>
  </clause>

  <clause id="19734">
    <literal><![CDATA[
      K(x,L(y,z,(y * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(19733(a,1),15678(a,1,1))].">
      <j1 rule="para" parents="19733 15678"/>
    </justification>
  </clause>

  <clause id="19735">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(19614(a,1),19734(a,1,1))].">
      <j1 rule="para" parents="19614 19734"/>
    </justification>
  </clause>

  <clause id="19736">
    <literal><![CDATA[
      (x * y) * ((T(x,z) * y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(z,x) * y) * (y \ u) = w
    ]]></literal>
    <justification jstring="[para(19735(a,1),15580(a,1))].">
      <j1 rule="para" parents="19735 15580"/>
    </justification>
  </clause>

  <clause id="19737">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (K(z,T(x,z)) * y) * (y \ u)
    ]]></literal>
    <justification jstring="[hyper(19736,a,12490,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19736 12490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19738">
    <literal><![CDATA[
      a(x,y,K((z / (u / w)) * K(w,z),v5)) = a(x,y,K((u / T(w,z)) \ z,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,19300,a(flip),b,19350,a),flip(a)].">
      <j1 rule="hyper" parents="373 19300 19350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19739">
    <literal><![CDATA[
      K(x,(K(y,z) * ((K(u,T(w,v5)) \ v6) / K(y,z))) \ v7) = K(x,v6 \ (K(w,T(u,v5)) \ v7))
    ]]></literal>
    <justification jstring="[para(7869(a,1),19420(a,1,2,1,2,1,1))].">
      <j1 rule="para" parents="7869 19420"/>
    </justification>
  </clause>

  <clause id="19740">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ (K(y,w) * z)) = T(x,T(T(y \ z,u) \ z,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,19442,a(flip),b,19447,a),flip(a)].">
      <j1 rule="hyper" parents="373 19442 19447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19741">
    <literal><![CDATA[
      K(x \ T(y \ T(z,K(u,w)),v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y \ z,v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(19494(a,2),14755(a,1))].">
      <j1 rule="para" parents="19494 14755"/>
    </justification>
  </clause>

  <clause id="19742">
    <literal><![CDATA[
      K(x \ T(y \ (T(y,K(z,u)) * w),w * y),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(19741,a,18911,a)].">
      <j1 rule="hyper" parents="19741 18911"/>
    </justification>
  </clause>

  <clause id="19743">
    <literal><![CDATA[
      T(x,(y / z) * T(u * (z / u),w)) = T(x,z * (T(T(z,u),w) \ y))
    ]]></literal>
    <justification jstring="[para(6216(a,1),19560(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6216 19560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19744">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * T(z,v5)))) = T(x,u * (w * T(T(z,y),v5)))
    ]]></literal>
    <justification jstring="[hyper(18191,a,19564,a)].">
      <j1 rule="hyper" parents="18191 19564"/>
    </justification>
  </clause>

  <clause id="19746">
    <literal><![CDATA[
      T(x,K(y,z) * (u * T(z / u,w))) = T(x,u * T(T(z,T(y,u)) / u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15944,a(flip),b,19643,a)].">
      <j1 rule="hyper" parents="64 15944 19643"/>
    </justification>
  </clause>

  <clause id="19747">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / (u / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / w) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(19672(a,2),18006(a,1))].">
      <j1 rule="para" parents="19672 18006"/>
    </justification>
  </clause>

  <clause id="19748">
    <literal><![CDATA[
      ((x * K(K(y,z),u)) / u) * (u * K(y,z)) = (u / x) \ (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(15022(a,1),19679(a,1,1,1))].">
      <j1 rule="para" parents="15022 19679"/>
    </justification>
  </clause>

  <clause id="19749">
    <literal><![CDATA[
      (x / T(y,K(z,u))) * (y * K(z,u)) = (y / x) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(6312(a,1),19748(a,1,1))].">
      <j1 rule="para" parents="6312 19748"/>
    </justification>
  </clause>

  <clause id="19750">
    <literal><![CDATA[
      (x / y) \ (K(z,u) * x) = (y / x) * (K(z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(10616,a,19749,a),flip(a)].">
      <j1 rule="hyper" parents="10616 19749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19751">
    <literal><![CDATA[
      ((x \ y) / y) * (K(z,u) * y) = x \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,207,a(flip),b,19750,a),flip(a)].">
      <j1 rule="hyper" parents="64 207 19750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19752">
    <literal><![CDATA[
      (x \ y) / (K(x,z) * y) = (T(x,z) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,6020,a(flip),b,19751,a)].">
      <j1 rule="hyper" parents="142 6020 19751"/>
    </justification>
  </clause>

  <clause id="19753">
    <literal><![CDATA[
      ((x \ y) / y) * K(z,x) = (T(x,z) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,15127,a(flip),b,19752,a)].">
      <j1 rule="hyper" parents="64 15127 19752"/>
    </justification>
  </clause>

  <clause id="19754">
    <literal><![CDATA[
      L(K(x,y) * (((x \ z) / z) \ u),K(y,x),(x \ z) / z) = ((T(x,y) \ z) / z) \ u
    ]]></literal>
    <justification jstring="[para(19753(a,1),6191(a,2,1))].">
      <j1 rule="para" parents="19753 6191"/>
    </justification>
  </clause>

  <clause id="19755">
    <literal><![CDATA[
      K(x,y \ (z / T(u,T(w,v5)))) = K(x,y \ (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18113,a(flip),b,19695,a),flip(a)].">
      <j1 rule="hyper" parents="373 18113 19695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19756">
    <literal><![CDATA[
      T(x,y * ((z * (u / z)) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (T(u,z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(19704(a,1),18339(a,1))].">
      <j1 rule="para" parents="19704 18339"/>
    </justification>
  </clause>

  <clause id="19757">
    <literal><![CDATA[
      T(x,y * (((z * u) / z) * ((u * u) \ w))) = T(x,y * ((T(u,z) \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,5301,a(flip),b,19714,a),flip(a)].">
      <j1 rule="hyper" parents="373 5301 19714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19758">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(z \ T(y,z * y),u))
    ]]></literal>
    <justification jstring="[para(14861(a,1),19718(a,2,2,1))].">
      <j1 rule="para" parents="14861 19718"/>
    </justification>
  </clause>

  <clause id="19759">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(z \ T(y,y * z),u))
    ]]></literal>
    <justification jstring="[para(4683(a,1),19758(a,2,2,1,2))].">
      <j1 rule="para" parents="4683 19758"/>
    </justification>
  </clause>

  <clause id="19760">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(z \ T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13680,a(flip),b,19759,a),flip(a)].">
      <j1 rule="hyper" parents="373 13680 19759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19761">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13608,a(flip),b,19760,a),flip(a)].">
      <j1 rule="hyper" parents="373 13608 19760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19762">
    <literal><![CDATA[
      T(x,T((y * z) \ (z * z),u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(13679,a,19761,a)].">
      <j1 rule="hyper" parents="13679 19761"/>
    </justification>
  </clause>

  <clause id="19763">
    <literal><![CDATA[
      T(K(x,T(y,T(z / u,w)) * v5),v5 \ T(v5 * T(y,T(z / u,w)),x)) = (v5 \ T(v5 * T(y,T(z / u,w)),x)) \ T(y,T((u * z) \ (z * z),w))
    ]]></literal>
    <justification jstring="[hyper(493,a,19762,a,b,14556,a)].">
      <j1 rule="hyper" parents="493 19762 14556"/>
    </justification>
  </clause>

  <clause id="19764">
    <literal><![CDATA[
      a(x,y,K((z / T(u,w)) \ w,v5)) = a(x,y,K(T(w,u) / (z / u),v5))
    ]]></literal>
    <justification jstring="[para(17426(a,1),19738(a,1,3)),flip(a)].">
      <j1 rule="para" parents="17426 19738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19765">
    <literal><![CDATA[
      a(x,y,K((z / T(u,w)) \ w,v5)) = a(x,y,K((z / u) \ T(w,u),v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,19300,a(flip),b,19764,a),flip(a)].">
      <j1 rule="hyper" parents="373 19300 19764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19766">
    <literal><![CDATA[
      T(x,y * T(T(z,T(u,y)) / y,w)) = T(x,T(y * T(z / y,w),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19627,a(flip),b,19746,a),flip(a)].">
      <j1 rule="hyper" parents="64 19627 19746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19767">
    <literal><![CDATA[
      T(x,y * (T(z,u) * ((z * z) \ w))) = T(x,y * ((T(z,u) \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16257,a(flip),b,19757,a)].">
      <j1 rule="hyper" parents="64 16257 19757"/>
    </justification>
  </clause>

  <clause id="19769">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * ((K(u,T(x,w)) * y) * z),v5) = K((y * z) * K(x,u),v5)
    ]]></literal>
    <justification jstring="[para(19333(a,1),19304(a,1,1))].">
      <j1 rule="para" parents="19333 19304"/>
    </justification>
  </clause>

  <clause id="19770">
    <literal><![CDATA[
      ((K(x,y) * (z * K(u,w))) * v5) / (K(u,w) * v5) = L(K(x,y) * z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,18806,a(flip),b,19388,a),flip(a)].">
      <j1 rule="hyper" parents="373 18806 19388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19771">
    <literal><![CDATA[
      K(x,y * ((z * (u / w)) * K(w,L(v5,u,z)))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(12093(a,1),19656(a,1,2,2,2))].">
      <j1 rule="para" parents="12093 19656"/>
    </justification>
  </clause>

  <clause id="19772">
    <literal><![CDATA[
      K(x,y * (z / T(u,T(w,y * z)))) = K(x,y * (z / T(u,K(v5,v6) * w)))
    ]]></literal>
    <justification jstring="[para(12227(a,1),19657(a,1,2))].">
      <j1 rule="para" parents="12227 19657"/>
    </justification>
  </clause>

  <clause id="19773">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5) * v6))) = K(x,y * (z / T(u,v6)))
    ]]></literal>
    <justification jstring="[hyper(18414,a,19772,a),flip(a)].">
      <j1 rule="hyper" parents="18414 19772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19775">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) / T(v5,w))) = K(x,y * (v5 \ (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13459,a(flip),b,19773,a),flip(a)].">
      <j1 rule="hyper" parents="64 13459 19773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19776">
    <literal><![CDATA[
      (x / (y * x)) * ((y * x) * K(z,u)) = x * K(z,L(u,x,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(7076,a,19668,a)].">
      <j1 rule="hyper" parents="7076 19668"/>
    </justification>
  </clause>

  <clause id="19777">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z / u) = (K(x,y) * z) * (z \ (z / u))
    ]]></literal>
    <justification jstring="[hyper(397,a,19670,a)].">
      <j1 rule="hyper" parents="397 19670"/>
    </justification>
  </clause>

  <clause id="19780">
    <literal><![CDATA[
      (K(x,y) * z) \ ((K(x,y) * z) / u) = z \ (z / u)
    ]]></literal>
    <justification jstring="[hyper(139,a,16166,a(flip),b,19777,a(flip))].">
      <j1 rule="hyper" parents="139 16166 19777"/>
    </justification>
  </clause>

  <clause id="19781">
    <literal><![CDATA[
      x * L(y \ 1,y,y \ (K(z,u) * x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(10977,a,19780,a)].">
      <j1 rule="hyper" parents="10977 19780"/>
    </justification>
  </clause>

  <clause id="19782">
    <literal><![CDATA[
      x * L(y \ 1,y,y \ (x * K(z,u))) = x / y
    ]]></literal>
    <justification jstring="[para(6823(a,1),19781(a,1,2,3,2))].">
      <j1 rule="para" parents="6823 19781"/>
    </justification>
  </clause>

  <clause id="19783">
    <literal><![CDATA[
      x * L((y \ (x * K(z,u))) \ 1,y \ (x * K(z,u)),y) = x / (y \ (x * K(z,u)))
    ]]></literal>
    <justification jstring="[para(11080(a,1),19782(a,1,2))].">
      <j1 rule="para" parents="11080 19782"/>
    </justification>
  </clause>

  <clause id="19784">
    <literal><![CDATA[
      K((K(x,T(y,z)) * u) * w,v5) = K((u * w) * K(y,x),v5)
    ]]></literal>
    <justification jstring="[hyper(19509,a,19769,a)].">
      <j1 rule="hyper" parents="19509 19769"/>
    </justification>
  </clause>

  <clause id="19786">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K((z * u) * K(y,x),w)
    ]]></literal>
    <justification jstring="[para(114(a,1),19784(a,1,1,1,1,2))].">
      <j1 rule="para" parents="114 19784"/>
    </justification>
  </clause>

  <clause id="19787">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z * (u * K(y,x)),w) = v5
    ]]></literal>
    <justification jstring="[para(19786(a,2),19513(a,1))].">
      <j1 rule="para" parents="19786 19513"/>
    </justification>
  </clause>

  <clause id="19788">
    <literal><![CDATA[
      K(x * (y * K(z,u)),T(w,y)) = K(y * (K(u,z) * x),w)
    ]]></literal>
    <justification jstring="[hyper(19787,a,11180,a)].">
      <j1 rule="hyper" parents="19787 11180"/>
    </justification>
  </clause>

  <clause id="19789">
    <literal><![CDATA[
      K((x * K(y,z)) * u,w) = K(x * (K(z,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(18257,a,19788,a)].">
      <j1 rule="hyper" parents="18257 19788"/>
    </justification>
  </clause>

  <clause id="19790">
    <literal><![CDATA[
      K(x * (K(y,z) * (u \ K(y,z))),w) = K(x / u,w)
    ]]></literal>
    <justification jstring="[hyper(19490,a,19789,a),flip(a)].">
      <j1 rule="hyper" parents="19490 19789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19791">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K((K(u,w) * (y \ K(u,w))) * x,z)
    ]]></literal>
    <justification jstring="[hyper(17394,a,19790,a),flip(a)].">
      <j1 rule="hyper" parents="17394 19790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19792">
    <literal><![CDATA[
      K(x * (y \ K(y,z)),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[para(6075(a,1),19790(a,1,1,2))].">
      <j1 rule="para" parents="6075 19790"/>
    </justification>
  </clause>

  <clause id="19793">
    <literal><![CDATA[
      K((K(x,y) * (z \ K(x,y))) * u,w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(8317,a,19791,a),flip(a)].">
      <j1 rule="hyper" parents="8317 19791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19794">
    <literal><![CDATA[
      K((x \ K(y,z)) * (u * K(z,y)),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[hyper(19787,a,19793,a)].">
      <j1 rule="hyper" parents="19787 19793"/>
    </justification>
  </clause>

  <clause id="19795">
    <literal><![CDATA[
      K(x,y * (z * ((u / w) * K(w,v5)))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(12149(a,1),19771(a,1,2,2))].">
      <j1 rule="para" parents="12149 19771"/>
    </justification>
  </clause>

  <clause id="19796">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (u * z)) * (u \ K(z,u)) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(15518(a,1),19293(a,1,1,1))].">
      <j1 rule="para" parents="15518 19293"/>
    </justification>
  </clause>

  <clause id="19798">
    <literal><![CDATA[
      ((K(x,y) * z) * T(u,z)) * (u \ K(z,u)) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(15577(a,1),19796(a,1,1))].">
      <j1 rule="para" parents="15577 19796"/>
    </justification>
  </clause>

  <clause id="19799">
    <literal><![CDATA[
      R(K(x,y) * z,u,u \ 1) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,9339,a(flip),b,19798,a)].">
      <j1 rule="hyper" parents="64 9339 19798"/>
    </justification>
  </clause>

  <clause id="19801">
    <literal><![CDATA[
      R(K(x,y) * (z / u),u,u \ 1) = K(x,y) * (z * (u \ 1))
    ]]></literal>
    <justification jstring="[para(675(a,1),19799(a,2,2))].">
      <j1 rule="para" parents="675 19799"/>
    </justification>
  </clause>

  <clause id="19802">
    <literal><![CDATA[
      x \ R(K(y,z) * (K(z,y) * x),u,u \ 1) = a(K(z,y) * x,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(19799(a,2),16715(a,1,2))].">
      <j1 rule="para" parents="19799 16715"/>
    </justification>
  </clause>

  <clause id="19803">
    <literal><![CDATA[
      (K(x,y) * (z * (u \ 1))) / (u \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * (z / u)) * u = w
    ]]></literal>
    <justification jstring="[para(19801(a,1),703(a,1,1))].">
      <j1 rule="para" parents="19801 703"/>
    </justification>
  </clause>

  <clause id="19804">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = z \ R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(6161(a,1),19802(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6161 19802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19805">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = a(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,982,a(flip),b,19804,a),flip(a)].">
      <j1 rule="hyper" parents="373 982 19804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19806">
    <literal><![CDATA[
      a(x / y,z,z \ 1) = a(y \ x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,13281,a(flip),b,19805,a)].">
      <j1 rule="hyper" parents="64 13281 19805"/>
    </justification>
  </clause>

  <clause id="19807">
    <literal><![CDATA[
      a(T(x,y),z,z \ 1) = a(x,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(1886(a,2),19805(a,1,1))].">
      <j1 rule="para" parents="1886 19805"/>
    </justification>
  </clause>

  <clause id="19808">
    <literal><![CDATA[
      a(x \ T(y,z),u,u \ 1) = a(x \ y,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(6417(a,1),19805(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6417 19805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19809">
    <literal><![CDATA[
      T(x,y) * a(x,z,z \ 1) = R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,19807,a(flip),b,982,a)].">
      <j1 rule="hyper" parents="145 19807 982"/>
    </justification>
  </clause>

  <clause id="19810">
    <literal><![CDATA[
      a(x \ (y / (x \ 1)),x,x \ 1) = ((y / (x \ 1)) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,981,a(flip),b,19806,a),flip(a)].">
      <j1 rule="hyper" parents="64 981 19806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19811">
    <literal><![CDATA[
      a(x \ (y / z),u,u \ 1) = a(x \ (z \ y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(117(a,1),19808(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="117 19808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19812">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(19809(a,1),5039(a,2,2))].">
      <j1 rule="para" parents="19809 5039"/>
    </justification>
  </clause>

  <clause id="19813">
    <literal><![CDATA[
      a(x \ ((x \ 1) \ y),x,x \ 1) = ((y / (x \ 1)) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,19811,a(flip),b,19810,a)].">
      <j1 rule="hyper" parents="64 19811 19810"/>
    </justification>
  </clause>

  <clause id="19814">
    <literal><![CDATA[
      (R(x,y,y \ 1) * z) / R(x,y,y \ 1) = (x * z) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,267,a(flip),b,19812,a)].">
      <j1 rule="hyper" parents="142 267 19812"/>
    </justification>
  </clause>

  <clause id="19815">
    <literal><![CDATA[
      (L(x,y,y \ 1) * z) / L(x,y,y \ 1) = (x * z) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,16570,a(flip),b,19814,a)].">
      <j1 rule="hyper" parents="64 16570 19814"/>
    </justification>
  </clause>

  <clause id="19816">
    <literal><![CDATA[
      (L(x \ T(y,z),u,u \ 1) * K(z,y)) / L(x \ T(y,z),u,u \ 1) = (x \ y) / (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(15017(a,1),19815(a,2,1))].">
      <j1 rule="para" parents="15017 19815"/>
    </justification>
  </clause>

  <clause id="19817">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) / K(x,L(x,y,z) \ u) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,15341,a(flip),b,19361,a),flip(a)].">
      <j1 rule="hyper" parents="373 15341 19361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19818">
    <literal><![CDATA[
      (L(x,y,z) * (u / L(x,y,z))) * K(L(x,y,z) \ u,x) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(6898,a,19817,a)].">
      <j1 rule="hyper" parents="6898 19817"/>
    </justification>
  </clause>

  <clause id="19819">
    <literal><![CDATA[
      L(x,y,z) * T(u / L(x,y,z),T(x,u)) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(7944,a,19818,a)].">
      <j1 rule="hyper" parents="7944 19818"/>
    </justification>
  </clause>

  <clause id="19820">
    <literal><![CDATA[
      L(x,y,z) * T(u / L(x,y,z),x) = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(8061(a,1),19819(a,1,2))].">
      <j1 rule="para" parents="8061 19819"/>
    </justification>
  </clause>

  <clause id="19821">
    <literal><![CDATA[
      T(x * L(y,z,u),a(u,z,y)) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,1),19820(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 19820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19822">
    <literal><![CDATA[
      K(x,L(y,z,u) * T(w,y)) = K(x,w * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(19821(a,1),19211(a,1,2))].">
      <j1 rule="para" parents="19821 19211"/>
    </justification>
  </clause>

  <clause id="19823">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * T(y,z)) = K(x,y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(13578,a,19822,a)].">
      <j1 rule="hyper" parents="13578 19822"/>
    </justification>
  </clause>

  <clause id="19825">
    <literal><![CDATA[
      K(x,L((y / (z \ 1)) / z,u,w) * T(z,y / (z \ K(y,z)))) = K(x,z * L(z \ (y / (z \ K(y,z))),u,w))
    ]]></literal>
    <justification jstring="[para(10283(a,1),19823(a,1,2,1,1))].">
      <j1 rule="para" parents="10283 19823"/>
    </justification>
  </clause>

  <clause id="19826">
    <literal><![CDATA[
      T((x \ (y * z)) / T(z,K(u,w)),z) = z \ (x \ (y * T(z,K(u,w))))
    ]]></literal>
    <justification jstring="[para(8177(a,1),19473(a,1,1,2))].">
      <j1 rule="para" parents="8177 19473"/>
    </justification>
  </clause>

  <clause id="19827">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ (w * x)) = x \ (u \ (w * T(x,K(y,z))))
    ]]></literal>
    <justification jstring="[hyper(17207,a,19826,a)].">
      <j1 rule="hyper" parents="17207 19826"/>
    </justification>
  </clause>

  <clause id="19828">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(u,u \ z))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(18178,a,19601,a)].">
      <j1 rule="hyper" parents="18178 19601"/>
    </justification>
  </clause>

  <clause id="19829">
    <literal><![CDATA[
      K(x,y * (z * K((u * w) \ y,u * w))) = K(x,T(y,w * u) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,13468,a(flip),b,19637,a),flip(a)].">
      <j1 rule="hyper" parents="373 13468 19637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19830">
    <literal><![CDATA[
      K(x,y * (z * K(u \ (w \ y),w * u))) = K(x,T(y,u * w) * z)
    ]]></literal>
    <justification jstring="[para(14716(a,1),19829(a,1,2,2,2))].">
      <j1 rule="para" parents="14716 19829"/>
    </justification>
  </clause>

  <clause id="19831">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19683,a(flip),b,19690,a),flip(a)].">
      <j1 rule="hyper" parents="64 19683 19690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19832">
    <literal><![CDATA[
      K(x,L((y * z) * (u \ T(w,w \ u)),y,z \ 1)) = K(x,y / (T((u \ w) \ 1,w) / z))
    ]]></literal>
    <justification jstring="[hyper(15195,a,19831,a)].">
      <j1 rule="hyper" parents="15195 19831"/>
    </justification>
  </clause>

  <clause id="19833">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z \ 1)) = K(x,y / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(14952,a,19831,a)].">
      <j1 rule="hyper" parents="14952 19831"/>
    </justification>
  </clause>

  <clause id="19834">
    <literal><![CDATA[
      K(x,y / (z * (y / (u * y)))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18853,a(flip),b,19831,a)].">
      <j1 rule="hyper" parents="64 18853 19831"/>
    </justification>
  </clause>

  <clause id="19835">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[para(10(a,1),19834(a,1,2,2,2,2))].">
      <j1 rule="para" parents="10 19834"/>
    </justification>
  </clause>

  <clause id="19836">
    <literal><![CDATA[
      K(x \ T(K(y,K(z,u)) * w,w * y),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[para(6071(a,1),19742(a,1,1,2,1))].">
      <j1 rule="para" parents="6071 19742"/>
    </justification>
  </clause>

  <clause id="19837">
    <literal><![CDATA[
      K(K(x,K(y,z)) * (u \ T(w,w * x)),v5) = K(u \ T(w,K(z,y) * x),v5)
    ]]></literal>
    <justification jstring="[para(19416(a,1),19836(a,1,1))].">
      <j1 rule="para" parents="19416 19836"/>
    </justification>
  </clause>

  <clause id="19838">
    <literal><![CDATA[
      K(K(x,K(y,z)) * (u \ T(w,x)),v5) = K(u \ T(w,K(z,y) * x),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,13909,a(flip),b,19837,a)].">
      <j1 rule="hyper" parents="64 13909 19837"/>
    </justification>
  </clause>

  <clause id="19839">
    <literal><![CDATA[
      K(x \ T(y,K(z,u) * w),v5) = K(x \ T(y,w),v5)
    ]]></literal>
    <justification jstring="[hyper(17986,a,19838,a),flip(a)].">
      <j1 rule="hyper" parents="17986 19838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19840">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = K(y \ K(x,z * K(w,v5)),u)
    ]]></literal>
    <justification jstring="[hyper(18420,a,19839,a),flip(a)].">
      <j1 rule="hyper" parents="18420 19839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19841">
    <literal><![CDATA[
      K(x \ K(y,z * K(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,z),v5) = v6
    ]]></literal>
    <justification jstring="[para(19840(a,1),7629(a,1))].">
      <j1 rule="para" parents="19840 7629"/>
    </justification>
  </clause>

  <clause id="19842">
    <literal><![CDATA[
      K(x \ K(y,K(z,u) * w),v5) = K(x \ K(y,w),v5)
    ]]></literal>
    <justification jstring="[hyper(19841,a,18419,a),flip(a)].">
      <j1 rule="hyper" parents="19841 18419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19844">
    <literal><![CDATA[
      K(x,y \ K(z,K(u,w) * v5)) = (v6 * K(y \ K(z,v5),x)) \ v6
    ]]></literal>
    <justification jstring="[para(19842(a,1),6882(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="19842 6882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19845">
    <literal><![CDATA[
      K(x,y \ K(z,K(u,w) * v5)) = K(x,y \ K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,6882,a(flip),b,19844,a),flip(a)].">
      <j1 rule="hyper" parents="373 6882 19844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19846">
    <literal><![CDATA[
      K(x,y \ K(z * K(u,w),v5)) = K(x,y \ K(v5,z))
    ]]></literal>
    <justification jstring="[hyper(18417,a,19845,a)].">
      <j1 rule="hyper" parents="18417 19845"/>
    </justification>
  </clause>

  <clause id="19847">
    <literal><![CDATA[
      (x * T(y,T(z,u))) \ (w * T(y,T(z,u))) = (x * T(y,z)) \ (w * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(1329,a,19294,a),flip(a)].">
      <j1 rule="hyper" parents="1329 19294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19848">
    <literal><![CDATA[
      (x * T(y,T(z,u))) \ (z * T(y,T(z,u))) = (x * T(y,z)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,249,a(flip),b,19847,a),flip(a)].">
      <j1 rule="hyper" parents="373 249 19847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19849">
    <literal><![CDATA[
      K(x,y * ((K(z,L(y,u,w)) * v5) / L(y,u,w))) = K(x,(L(T(y,z),u,w) \ v5) * y)
    ]]></literal>
    <justification jstring="[para(25(a,2),19457(a,2,2,1,1))].">
      <j1 rule="para" parents="25 19457"/>
    </justification>
  </clause>

  <clause id="19850">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * T(w,v5)) / (a(x,y,K(z,u)) * w) = K(w,v5 * a(x,y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(15313(a,1),19507(a,1,1))].">
      <j1 rule="para" parents="15313 19507"/>
    </justification>
  </clause>

  <clause id="19852">
    <literal><![CDATA[
      K(x * (1 / (1 / (y \ z))),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(14729,a,19532,a)].">
      <j1 rule="hyper" parents="14729 19532"/>
    </justification>
  </clause>

  <clause id="19853">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,5258,a(flip),b,19852,a)].">
      <j1 rule="hyper" parents="64 5258 19852"/>
    </justification>
  </clause>

  <clause id="19854">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,14423,a(flip),b,19853,a),flip(a)].">
      <j1 rule="hyper" parents="373 14423 19853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19855">
    <literal><![CDATA[
      K(x * (y \ z),x / (z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(18940,a,19854,a)].">
      <j1 rule="hyper" parents="18940 19854"/>
    </justification>
  </clause>

  <clause id="19857">
    <literal><![CDATA[
      L(K(x,y) * (((x \ z) / z) \ u),K(y,x),z \ (z / x)) = ((T(x,y) \ z) / z) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,13535,a(flip),b,19754,a)].">
      <j1 rule="hyper" parents="64 13535 19754"/>
    </justification>
  </clause>

  <clause id="19858">
    <literal><![CDATA[
      x / (y \ (x * K(z,u))) = x * ((x * K(z,u)) \ y)
    ]]></literal>
    <justification jstring="[para(436(a,1),19783(a,1,2)),flip(a)].">
      <j1 rule="para" parents="436 19783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19859">
    <literal><![CDATA[
      x / ((y / x) * (x * K(z,u))) = x * ((x * K(z,u)) \ (x / y))
    ]]></literal>
    <justification jstring="[para(19680(a,1),19858(a,1,2))].">
      <j1 rule="para" parents="19680 19858"/>
    </justification>
  </clause>

  <clause id="19860">
    <literal><![CDATA[
      K(x,T(y,a(z,u,K(w,v5)))) = K(x,y * a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(8370,a,19850,a)].">
      <j1 rule="hyper" parents="8370 19850"/>
    </justification>
  </clause>

  <clause id="19861">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(19251,a,19860,a),flip(a)].">
      <j1 rule="hyper" parents="19251 19860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19862">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(19860(a,1),19251(a,1))].">
      <j1 rule="para" parents="19860 19251"/>
    </justification>
  </clause>

  <clause id="19864">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,19247,a,b,19861,a)].">
      <j1 rule="hyper" parents="64 19247 19861"/>
    </justification>
  </clause>

  <clause id="19865">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(v5,v6)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(12534(a,1),19861(a,1,2))].">
      <j1 rule="para" parents="12534 19861"/>
    </justification>
  </clause>

  <clause id="19866">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[para(15302(a,1),19861(a,1,2))].">
      <j1 rule="para" parents="15302 19861"/>
    </justification>
  </clause>

  <clause id="19867">
    <literal><![CDATA[
      K(x,y * L(z,u,K(w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(16627(a,1),19861(a,1,2))].">
      <j1 rule="para" parents="16627 19861"/>
    </justification>
  </clause>

  <clause id="19868">
    <literal><![CDATA[
      K(x,y \ L(z,u,K(w,v5))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(16629(a,1),19861(a,1,2))].">
      <j1 rule="para" parents="16629 19861"/>
    </justification>
  </clause>

  <clause id="19869">
    <literal><![CDATA[
      K(x,y / T(z,a(u,w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(17660,a,19864,a)].">
      <j1 rule="hyper" parents="17660 19864"/>
    </justification>
  </clause>

  <clause id="19870">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) \ v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),19864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 19864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19871">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(15697(a,1),19864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15697 19864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19872">
    <literal><![CDATA[
      K(x,a(K(y,z),u,w) \ v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[para(14362(a,2),19870(a,1,2,1))].">
      <j1 rule="para" parents="14362 19870"/>
    </justification>
  </clause>

  <clause id="19873">
    <literal><![CDATA[
      K(x,y) \ T(x,(a(K(z,u),w,v5) \ y) * x) = L(x,a(K(z,u),w,v5) \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(19872(a,1),12182(a,1,1))].">
      <j1 rule="para" parents="19872 12182"/>
    </justification>
  </clause>

  <clause id="19874">
    <literal><![CDATA[
      K(x,y * T((K(z,u) * w) \ v5,v6)) = K(x,y * T(w \ (K(z,u) \ v5),v6))
    ]]></literal>
    <justification jstring="[para(708(a,1),19867(a,1,2,2))].">
      <j1 rule="para" parents="708 19867"/>
    </justification>
  </clause>

  <clause id="19875">
    <literal><![CDATA[
      K(x,y * L((K(z,u) * w) \ v5,v6,v7)) = K(x,y * L(w \ (K(z,u) \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(709(a,1),19867(a,1,2,2))].">
      <j1 rule="para" parents="709 19867"/>
    </justification>
  </clause>

  <clause id="19876">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) \ ((w * v5) * K(z,u)))) = K(x,y * (v5 * K(w * v5,K(z,u))))
    ]]></literal>
    <justification jstring="[para(14648(a,1),19867(a,1,2,2))].">
      <j1 rule="para" parents="14648 19867"/>
    </justification>
  </clause>

  <clause id="19877">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) \ v5)) = K(x,y \ (w \ (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(6190(a,1),19868(a,1,2,2))].">
      <j1 rule="para" parents="6190 19868"/>
    </justification>
  </clause>

  <clause id="19878">
    <literal><![CDATA[
      K(x,y \ T(z,L(u,w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(16617(a,1),19868(a,1,2,2))].">
      <j1 rule="para" parents="16617 19868"/>
    </justification>
  </clause>

  <clause id="19879">
    <literal><![CDATA[
      K(x,y / (a(z,u,w) / v5)) = K(x,y / (v5 \ a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(15920,a,19869,a)].">
      <j1 rule="hyper" parents="15920 19869"/>
    </justification>
  </clause>

  <clause id="19881">
    <literal><![CDATA[
      K(x,y / L(z,u,K(w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(16603(a,2),19869(a,1,2,2))].">
      <j1 rule="para" parents="16603 19869"/>
    </justification>
  </clause>

  <clause id="19882">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w)) \ v5) = K(x,T(v5,y) / y)
    ]]></literal>
    <justification jstring="[hyper(19235,a,19881,a)].">
      <j1 rule="hyper" parents="19235 19881"/>
    </justification>
  </clause>

  <clause id="19883">
    <literal><![CDATA[
      K(x,y / ((z * ((K(u,w) * z) \ v5)) / z)) = K(x,y / ((K(u,w) \ v5) / z))
    ]]></literal>
    <justification jstring="[para(1208(a,1),19881(a,1,2,2))].">
      <j1 rule="para" parents="1208 19881"/>
    </justification>
  </clause>

  <clause id="19884">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) \ v5)) = K(x,y / (w \ (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(6190(a,1),19881(a,1,2,2))].">
      <j1 rule="para" parents="6190 19881"/>
    </justification>
  </clause>

  <clause id="19885">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(15302(a,1),19862(a,1,2))].">
      <j1 rule="para" parents="15302 19862"/>
    </justification>
  </clause>

  <clause id="19886">
    <literal><![CDATA[
      K(x,y * (T(z,y) * a(u,w,K(v5,v6)))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(115(a,1),19865(a,2,2))].">
      <j1 rule="para" parents="115 19865"/>
    </justification>
  </clause>

  <clause id="19887">
    <literal><![CDATA[
      K(x,y * ((z * u) * K(w,v5))) = K(x,y * (z * (u * K(w,v5))))
    ]]></literal>
    <justification jstring="[para(88(a,1),19865(a,1,2,2))].">
      <j1 rule="para" parents="88 19865"/>
    </justification>
  </clause>

  <clause id="19888">
    <literal><![CDATA[
      K(x,y * (R(z,z \ (u / a(w,v5,K(v6,v7))),a(w,v5,K(v6,v7))) \ u)) = K(x,y * (z \ (u / a(w,v5,K(v6,v7)))))
    ]]></literal>
    <justification jstring="[para(975(a,2),19865(a,1,2,2))].">
      <j1 rule="para" parents="975 19865"/>
    </justification>
  </clause>

  <clause id="19889">
    <literal><![CDATA[
      K(x,y * (T(z,a(u,w,v5)) \ v6)) = K(x,y * (z \ v6))
    ]]></literal>
    <justification jstring="[para(19330(a,1),19865(a,1,2,2))].">
      <j1 rule="para" parents="19330 19865"/>
    </justification>
  </clause>

  <clause id="19891">
    <literal><![CDATA[
      K(x,y * (K(z,L(u,w,v5)) * v6)) = K(x,K(u,z) * (y * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,19595,a(flip),b,19871,a)].">
      <j1 rule="hyper" parents="64 19595 19871"/>
    </justification>
  </clause>

  <clause id="19892">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u * L(z / y,w,v5))) = K(x,u * L(y \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18710,a(flip),b,19871,a),flip(a)].">
      <j1 rule="hyper" parents="64 18710 19871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19893">
    <literal><![CDATA[
      K(x,K((y \ z) \ u,w) * v5) = K(x,K(z \ (y * u),w) * v5)
    ]]></literal>
    <justification jstring="[para(12101(a,1),19871(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12101 19871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19894">
    <literal><![CDATA[
      K(x,y \ T(z,L(u / w,v5,v6))) = K(x,y \ T(z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17957,a(flip),b,19878,a),flip(a)].">
      <j1 rule="hyper" parents="373 17957 19878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19895">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w)) \ v5) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,13317,a(flip),b,19882,a),flip(a)].">
      <j1 rule="hyper" parents="373 13317 19882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19896">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w)) \ v5) = K(x,T(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(16617(a,1),19895(a,1,2,1))].">
      <j1 rule="para" parents="16617 19895"/>
    </justification>
  </clause>

  <clause id="19897">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,(y \ z) * K(u,w))
    ]]></literal>
    <justification jstring="[para(16605(a,1),19895(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16605 19895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19898">
    <literal><![CDATA[
      K(x,T(y,z) \ L(z,u,w)) = K(x,L(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(13478,a,19896,a),flip(a)].">
      <j1 rule="hyper" parents="13478 19896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19899">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,15767,a,b,19866,a),flip(a)].">
      <j1 rule="hyper" parents="373 15767 19866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19900">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) * w)) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[para(6157(a,1),19866(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6157 19866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19901">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ u) * w)) = K(x,(((z * y) / z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(6077(a,2),19866(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6077 19866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19902">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[para(14825(a,1),19866(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14825 19866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19903">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(19866(a,2),15768(a,1))].">
      <j1 rule="para" parents="19866 15768"/>
    </justification>
  </clause>

  <clause id="19904">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,(y \ w) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(18012,a,19897,a)].">
      <j1 rule="hyper" parents="18012 19897"/>
    </justification>
  </clause>

  <clause id="19905">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17139,a,b,19897,a),flip(a)].">
      <j1 rule="hyper" parents="373 17139 19897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19906">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * K(w,L(v5,u,z))) = K(x,y \ (z * (u * K(w,v5))))
    ]]></literal>
    <justification jstring="[para(12078(a,1),19897(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12078 19897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19908">
    <literal><![CDATA[
      K(x,L(y / z,u,w) / (1 / (z / y))) = K(x,(1 / (z / y)) \ L(y / z,u,w))
    ]]></literal>
    <justification jstring="[para(752(a,1),19898(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="752 19898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19909">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ w) = K(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(14758,a,19899,a)].">
      <j1 rule="hyper" parents="14758 19899"/>
    </justification>
  </clause>

  <clause id="19910">
    <literal><![CDATA[
      K(x,T(((y \ z) * y) \ u,z) * w) = K(x,K(y \ z,y) * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16694,a,b,19899,a)].">
      <j1 rule="hyper" parents="64 16694 19899"/>
    </justification>
  </clause>

  <clause id="19911">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) = K(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17936,a(flip),b,19899,a)].">
      <j1 rule="hyper" parents="64 17936 19899"/>
    </justification>
  </clause>

  <clause id="19912">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ u) * w)) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(6157(a,1),19899(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6157 19899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19913">
    <literal><![CDATA[
      K(x,K(y,z) * ((z / u) * w)) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[para(14825(a,1),19899(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14825 19899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19914">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[para(15244(a,1),19899(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15244 19899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19915">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(u,w) * (z * x)) = K(y,x * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(19899(a,1),18298(a,1,2))].">
      <j1 rule="para" parents="19899 18298"/>
    </justification>
  </clause>

  <clause id="19916">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,17300,a,b,19904,a),flip(a)].">
      <j1 rule="hyper" parents="373 17300 19904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19917">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,17139,a,b,19904,a),flip(a)].">
      <j1 rule="hyper" parents="373 17139 19904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19918">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) * w) \ v5) * K(y,L(z,u,w))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(19904(a,1),19462(a,1))].">
      <j1 rule="para" parents="19904 19462"/>
    </justification>
  </clause>

  <clause id="19919">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,w / T(y,z)) \ (w / y))) = K(x,((w / y) * K(y,z)) / u)
    ]]></literal>
    <justification jstring="[hyper(16298,a,19905,a),flip(a)].">
      <j1 rule="hyper" parents="16298 19905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19920">
    <literal><![CDATA[
      T(x,y \ (z * K(u,w))) = T(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(143,a,19905,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 19905 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19921">
    <literal><![CDATA[
      K(x,R(y,y \ (x * z),y) / z) = K(x,K(z * x,y) * ((y \ (x * z)) \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,11211,a(flip),b,19905,a)].">
      <j1 rule="hyper" parents="64 11211 19905"/>
    </justification>
  </clause>

  <clause id="19922">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * y))) = K(x,u \ (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(6852(a,1),19905(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6852 19905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19923">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w / (y \ z)))) = K(x,u \ (w / (z / y)))
    ]]></literal>
    <justification jstring="[para(6887(a,1),19905(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6887 19905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19924">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (w * z))) = K(x,u \ (w * (y * (z / y))))
    ]]></literal>
    <justification jstring="[para(10173(a,1),19905(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10173 19905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19925">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w * z))) = K(x,u \ (w * ((y \ z) * y)))
    ]]></literal>
    <justification jstring="[para(10196(a,1),19905(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10196 19905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19926">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(143,a,19909,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 19909 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19927">
    <literal><![CDATA[
      K(x,K(y,T(z,x)) * (((y * z) / u) * w)) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16231,a(flip),b,19909,a),flip(a)].">
      <j1 rule="hyper" parents="64 16231 19909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19928">
    <literal><![CDATA[
      K(x \ K(y,K(z,u) * (w * y)),v5) = K(x \ K(w \ K(z,u),y),v5)
    ]]></literal>
    <justification jstring="[para(19909(a,1),16341(a,1,1,2))].">
      <j1 rule="para" parents="19909 16341"/>
    </justification>
  </clause>

  <clause id="19929">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(14730,a,19911,a)].">
      <j1 rule="hyper" parents="14730 19911"/>
    </justification>
  </clause>

  <clause id="19930">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) * (T(u * z,x) * v5)) = K(x,(u * (z * K(w,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,12144,a(flip),b,19911,a),flip(a)].">
      <j1 rule="hyper" parents="64 12144 19911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19931">
    <literal><![CDATA[
      K(x,(y * K(z,K(u,w))) * v5) = K(x,y * v5)
    ]]></literal>
    <justification jstring="[hyper(18014,a,19911,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18014 19911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19932">
    <literal><![CDATA[
      K(x,K(y,z) * ((u / y) * w)) = K(x,(u / T(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(6245(a,1),19911(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6245 19911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19933">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ z) * w)) = K(x,(u \ T(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(15021(a,1),19911(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15021 19911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19934">
    <literal><![CDATA[
      K(x,K(y \ z,y) * ((u \ z) * w)) = K(x,(u \ (y * (z / y))) * w)
    ]]></literal>
    <justification jstring="[para(16688(a,1),19911(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16688 19911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19935">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * (v5 * v6))) = a(x,y,K(z,v6 * (v5 * K(w,u))))
    ]]></literal>
    <justification jstring="[para(19911(a,1),19301(a,1,3))].">
      <j1 rule="para" parents="19911 19301"/>
    </justification>
  </clause>

  <clause id="19936">
    <literal><![CDATA[
      K(x,(y * T(z,K(u,w))) * v5) = K(x,(y * z) * v5)
    ]]></literal>
    <justification jstring="[para(6852(a,1),19931(a,1,2,1))].">
      <j1 rule="para" parents="6852 19931"/>
    </justification>
  </clause>

  <clause id="19937">
    <literal><![CDATA[
      K(x,(T(y,K(z,u)) \ w) * v5) = K(x,(y \ w) * v5)
    ]]></literal>
    <justification jstring="[para(8646(a,1),19931(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8646 19931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19938">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(143,a,19916,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 19916 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19939">
    <literal><![CDATA[
      K(x,K(y,z) * ((y * u) \ w)) = K(x,(T(y,z) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19393,a(flip),b,19916,a),flip(a)].">
      <j1 rule="hyper" parents="64 19393 19916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19940">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * w))) = K(x,u \ (T(z,y) * w))
    ]]></literal>
    <justification jstring="[para(5755(a,1),19916(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5755 19916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19941">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (y \ w))) = K(x,u \ (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[para(6157(a,1),19916(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6157 19916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19942">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (z * w))) = K(x,u \ (((y \ z) * y) * w))
    ]]></literal>
    <justification jstring="[para(10858(a,1),19916(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10858 19916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19943">
    <literal><![CDATA[
      K(x,K(y \ z,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y \ z,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(17894,a,19917,a),flip(a)].">
      <j1 rule="hyper" parents="17894 19917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19944">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(z,y) * w) \ w)) = K(x,(K(y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(15764,a,19917,a),flip(a)].">
      <j1 rule="hyper" parents="15764 19917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19945">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (T(u,K(z,y) * w) \ w)) = K(x,(K(y \ z,y) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(13482,a,19917,a),flip(a)].">
      <j1 rule="hyper" parents="13482 19917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19946">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y,y \ z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(13481,a,19917,a),flip(a)].">
      <j1 rule="hyper" parents="13481 19917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19947">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * w))) = K(x,K(u,z) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[para(4534(a,1),19917(a,1,2,2))].">
      <j1 rule="para" parents="4534 19917"/>
    </justification>
  </clause>

  <clause id="19948">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (y * w))) = K(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[para(5755(a,1),19917(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5755 19917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19949">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (w \ (u / z))) = K(x,w \ (u / T(z,y)))
    ]]></literal>
    <justification jstring="[para(8676(a,1),19917(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8676 19917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19950">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((z * y) * w))) = K(x,u \ ((y * z) * w))
    ]]></literal>
    <justification jstring="[para(10834(a,1),19917(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10834 19917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19951">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,K(u,w) * (y \ z))) = K(x,v5 / T(y \ (z * K(u,w)),K(v6,v7)))
    ]]></literal>
    <justification jstring="[para(19920(a,1),17955(a,1,2,2))].">
      <j1 rule="para" parents="19920 17955"/>
    </justification>
  </clause>

  <clause id="19952">
    <literal><![CDATA[
      T(x,K(y,z \ u) * ((u \ z) * w)) = T(x,T((u \ z) \ 1,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15782,a(flip),b,19926,a),flip(a)].">
      <j1 rule="hyper" parents="64 15782 19926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19953">
    <literal><![CDATA[
      T(x,(K(y,z) / u) \ w) = T(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(143,a,19929,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 19929 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19954">
    <literal><![CDATA[
      K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z)))) = K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19104,a(flip),b,19929,a)].">
      <j1 rule="hyper" parents="64 19104 19929"/>
    </justification>
  </clause>

  <clause id="19955">
    <literal><![CDATA[
      K(x,(y * ((1 / z) * K(u,w))) * v5) = K(x,(y * (K(u,w) / z)) * v5)
    ]]></literal>
    <justification jstring="[para(14396(a,1),19936(a,1,2,1,2))].">
      <j1 rule="para" parents="14396 19936"/>
    </justification>
  </clause>

  <clause id="19956">
    <literal><![CDATA[
      K(x,(L(T(y,K(z,u)),w,v5) \ v6) * v7) = K(x,(L(y,w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[para(25(a,2),19937(a,1,2,1,1))].">
      <j1 rule="para" parents="25 19937"/>
    </justification>
  </clause>

  <clause id="19957">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ (y \ w))) = T(x,u \ (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[para(6157(a,1),19938(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6157 19938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19958">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,u) * (y \ w)) = v5
    ]]></literal>
    <justification jstring="[para(19938(a,2),15753(a,1))].">
      <j1 rule="para" parents="19938 15753"/>
    </justification>
  </clause>

  <clause id="19959">
    <literal><![CDATA[
      K(x,L(T(1 / y,K(z,u) * (y * z)) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(19953(a,1),14807(a,1,2,1,1))].">
      <j1 rule="para" parents="19953 14807"/>
    </justification>
  </clause>

  <clause id="19960">
    <literal><![CDATA[
      K(x,y * T(a(z,u,K(w,v5)) * v6,y)) = K(x,v6 * y)
    ]]></literal>
    <justification jstring="[para(19619(a,2),19886(a,1,2,2))].">
      <j1 rule="para" parents="19619 19886"/>
    </justification>
  </clause>

  <clause id="19961">
    <literal><![CDATA[
      K(x,y * (L(z,u,K(w,v5)) \ v6)) = K(x,y * (z \ v6))
    ]]></literal>
    <justification jstring="[para(16603(a,2),19889(a,1,2,2,1))].">
      <j1 rule="para" parents="16603 19889"/>
    </justification>
  </clause>

  <clause id="19962">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) * v6) = K(x,v5 * v6)
    ]]></literal>
    <justification jstring="[para(115(a,1),19960(a,1,2))].">
      <j1 rule="para" parents="115 19960"/>
    </justification>
  </clause>

  <clause id="19963">
    <literal><![CDATA[
      K(x,(y * a(z,u,K(w,v5))) * v6) = K(x,y * v6)
    ]]></literal>
    <justification jstring="[para(19187(a,1),19962(a,1,2,1))].">
      <j1 rule="para" parents="19187 19962"/>
    </justification>
  </clause>

  <clause id="19964">
    <literal><![CDATA[
      K(x,(y \ L(z,u,K(w,v5))) * v6) = K(x,(y \ z) * v6)
    ]]></literal>
    <justification jstring="[para(16629(a,1),19963(a,1,2,1))].">
      <j1 rule="para" parents="16629 19963"/>
    </justification>
  </clause>

  <clause id="19965">
    <literal><![CDATA[
      K(x,(L(y,z,K(u,w)) / v5) * v6) = K(x,(y / v5) * v6)
    ]]></literal>
    <justification jstring="[para(19408(a,1),19963(a,1,2,1))].">
      <j1 rule="para" parents="19408 19963"/>
    </justification>
  </clause>

  <clause id="19966">
    <literal><![CDATA[
      K(x,y * (L(z,u,a(w,v5,K(v6,v7))) \ v8)) = K(x,y * (z \ v8))
    ]]></literal>
    <justification jstring="[para(13780(a,1),19961(a,1,2,2,1,3))].">
      <j1 rule="para" parents="13780 19961"/>
    </justification>
  </clause>

  <clause id="19967">
    <literal><![CDATA[
      K(x,(y \ ((K(z,u) * (w * v5)) / (K(z,u) * w))) * v6) = K(x,(y \ (v5 * K(K(z,u) * w,v5))) * v6)
    ]]></literal>
    <justification jstring="[para(5906(a,1),19964(a,1,2,1,2))].">
      <j1 rule="para" parents="5906 19964"/>
    </justification>
  </clause>

  <clause id="19968">
    <literal><![CDATA[
      K(x,(T((K(y,z) * u) \ w,v5) / v6) * v7) = K(x,(T(u \ (K(y,z) \ w),v5) / v6) * v7)
    ]]></literal>
    <justification jstring="[para(708(a,1),19965(a,1,2,1,1))].">
      <j1 rule="para" parents="708 19965"/>
    </justification>
  </clause>

  <clause id="19969">
    <literal><![CDATA[
      K(x,(y \ z) * (u * K(w,y))) = K(x,(T(y,w) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,19582,a(flip),b,19900,a)].">
      <j1 rule="hyper" parents="64 19582 19900"/>
    </justification>
  </clause>

  <clause id="19970">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y \ u) * w)) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(6156(a,2),19900(a,1,2))].">
      <j1 rule="para" parents="6156 19900"/>
    </justification>
  </clause>

  <clause id="19971">
    <literal><![CDATA[
      K(x,(K(y,z) * (z / u)) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19899,a,b,19902,a)].">
      <j1 rule="hyper" parents="64 19899 19902"/>
    </justification>
  </clause>

  <clause id="19972">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,K(v5,v6) * z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(18869,a,19913,a)].">
      <j1 rule="hyper" parents="18869 19913"/>
    </justification>
  </clause>

  <clause id="19973">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(T(u,y) / z) * (z * y))
    ]]></literal>
    <justification jstring="[para(16111(a,1),19913(a,1,2))].">
      <j1 rule="para" parents="16111 19913"/>
    </justification>
  </clause>

  <clause id="19974">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * z))) = K(x,u \ (w * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15768,a,19922,a)].">
      <j1 rule="hyper" parents="15768 19922"/>
    </justification>
  </clause>

  <clause id="19975">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(15768,a,19933,a)].">
      <j1 rule="hyper" parents="15768 19933"/>
    </justification>
  </clause>

  <clause id="19976">
    <literal><![CDATA[
      K(x,((y \ z) \ T(z,u)) * w) = K(x,K(u,z) * (T(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13498,a(flip),b,19933,a),flip(a)].">
      <j1 rule="hyper" parents="64 13498 19933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19977">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (z * w))) = K(x,u \ (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(17520,a,19940,a)].">
      <j1 rule="hyper" parents="17520 19940"/>
    </justification>
  </clause>

  <clause id="19978">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (y * w))) = K(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[para(6156(a,2),19940(a,1,2))].">
      <j1 rule="para" parents="6156 19940"/>
    </justification>
  </clause>

  <clause id="19979">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (x * T(z,y))) = w
    ]]></literal>
    <justification jstring="[para(19940(a,2),10323(a,1))].">
      <j1 rule="para" parents="19940 10323"/>
    </justification>
  </clause>

  <clause id="19980">
    <literal><![CDATA[
      T(x,T(y,z) \ (y \ u)) = T(x,y \ (T(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(15754,a,19957,a)].">
      <j1 rule="hyper" parents="15754 19957"/>
    </justification>
  </clause>

  <clause id="19981">
    <literal><![CDATA[
      T(x,y \ (T(z,K(u,w)) \ v5)) = T(x,y \ (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,17937,a(flip),b,19957,a),flip(a)].">
      <j1 rule="hyper" parents="64 17937 19957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19982">
    <literal><![CDATA[
      T(x,T(y,z) \ (T(y,z) \ u)) = T(x,y \ (y \ u))
    ]]></literal>
    <justification jstring="[para(6075(a,1),19957(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6075 19957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19983">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,y \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[para(6157(a,1),19957(a,1,2))].">
      <j1 rule="para" parents="6157 19957"/>
    </justification>
  </clause>

  <clause id="19984">
    <literal><![CDATA[
      K(x,T(y,z \ (T(u,w) \ v5))) = K(x,T(y,z \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(19957(a,1),18236(a,1,2))].">
      <j1 rule="para" parents="19957 18236"/>
    </justification>
  </clause>

  <clause id="19985">
    <literal><![CDATA[
      T((x / T(y,K(z,u))) * T(T(y,K(z,u)),K(w,v5) \ (y \ x)),K(w,v5)) = y * T(x / y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(19981(a,1),18907(a,1,1,2))].">
      <j1 rule="para" parents="19981 18907"/>
    </justification>
  </clause>

  <clause id="19986">
    <literal><![CDATA[
      T(T(x,T(y,z) * u),y \ (y \ w)) = T(T(x,T(y,z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15893,a(flip),b,19982,a),flip(a)].">
      <j1 rule="hyper" parents="64 15893 19982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19987">
    <literal><![CDATA[
      T(x * K(y,x),K(y,T(z,u) \ (u \ w))) = x * K(y,T(x,z \ (T(u,z) \ w)))
    ]]></literal>
    <justification jstring="[para(19983(a,1),8410(a,2,2,2))].">
      <j1 rule="para" parents="19983 8410"/>
    </justification>
  </clause>

  <clause id="19988">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (w \ (y * z))) = K(x,(y \ u) * (w \ (z * y)))
    ]]></literal>
    <justification jstring="[para(15222(a,1),19969(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15222 19969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19989">
    <literal><![CDATA[
      K(x,(T(y,z) \ (y * u)) * w) = K(x,K(y,z) \ (u * w))
    ]]></literal>
    <justification jstring="[para(9(a,1),19970(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 19970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19990">
    <literal><![CDATA[
      K(x,(T(y \ z,y) / u) * w) = K(x,((z / y) / u) * w)
    ]]></literal>
    <justification jstring="[para(14696(a,1),19971(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14696 19971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19991">
    <literal><![CDATA[
      K(x,((y * z) / u) \ (T(y,w) * z)) = K(x,K(w,y) \ u)
    ]]></literal>
    <justification jstring="[para(82(a,1),19977(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 19977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19992">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(K(y,z) \ u,w)) = K(w * (T(y,z) \ (y * u)),x)
    ]]></literal>
    <justification jstring="[para(19989(a,1),17458(a,1,1))].">
      <j1 rule="para" parents="19989 17458"/>
    </justification>
  </clause>

  <clause id="19993">
    <literal><![CDATA[
      K(x,(T((K(y,z) * u) \ w,K(z,y) * u) / v5) * v6) = K(x,((w / (K(y,z) * u)) / v5) * v6)
    ]]></literal>
    <justification jstring="[para(15759(a,1),19990(a,1,2,1,1))].">
      <j1 rule="para" parents="15759 19990"/>
    </justification>
  </clause>

  <clause id="19994">
    <literal><![CDATA[
      K(x,y * (z * K(u,L(w,v5,v6)))) = K(x,K(w,u) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(18093,a,19891,a)].">
      <j1 rule="hyper" parents="18093 19891"/>
    </justification>
  </clause>

  <clause id="19996">
    <literal><![CDATA[
      K(x,y \ T(z,u / (w * v5))) = K(x,y \ T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(15609(a,1),19894(a,1,2,2))].">
      <j1 rule="para" parents="15609 19894"/>
    </justification>
  </clause>

  <clause id="19997">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * (y * w)) = v5
    ]]></literal>
    <justification jstring="[para(17936(a,1),19903(a,1))].">
      <j1 rule="para" parents="17936 19903"/>
    </justification>
  </clause>

  <clause id="19998">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y \ u,w) \ u)) = T(x,T(T(y \ u,w) \ u,z))
    ]]></literal>
    <justification jstring="[hyper(19958,a,19740,a)].">
      <j1 rule="hyper" parents="19958 19740"/>
    </justification>
  </clause>

  <clause id="19999">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(19958,a,19233,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19958 19233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20000">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * (u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(19233(a,2),19958(a,1))].">
      <j1 rule="para" parents="19233 19958"/>
    </justification>
  </clause>

  <clause id="20001">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),K(w,z) * ((u / z) \ y)) = T(x,y / (K(z,w) * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18658,a(flip),b,19999,a),flip(a)].">
      <j1 rule="hyper" parents="64 18658 19999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20002">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17952,a(flip),b,19999,a)].">
      <j1 rule="hyper" parents="64 17952 19999"/>
    </justification>
  </clause>

  <clause id="20003">
    <literal><![CDATA[
      T(x,K(y,z) * ((z / u) \ w)) = T(x,(T(z,y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(14825(a,1),19999(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14825 19999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20004">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,T(v5,v6))) = T(x,y / T(K(z,u) * w,K(u,z) * (w \ v5)))
    ]]></literal>
    <justification jstring="[para(19999(a,1),18056(a,2,2,2))].">
      <j1 rule="para" parents="19999 18056"/>
    </justification>
  </clause>

  <clause id="20005">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,15759,a,b,20002,a),flip(a)].">
      <j1 rule="hyper" parents="373 15759 20002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20006">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,K(y \ z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16519,a,b,20002,a)].">
      <j1 rule="hyper" parents="64 16519 20002"/>
    </justification>
  </clause>

  <clause id="20007">
    <literal><![CDATA[
      T(x,K(y \ z,y) * ((u \ (y \ z)) \ w)) = T(x,(u \ (z / y)) \ w)
    ]]></literal>
    <justification jstring="[para(15092(a,1),20002(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15092 20002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20008">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / z) \ w)) = T(x,(u / T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(6245(a,1),20005(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6245 20005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20009">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * y) \ w)) = T(x,(u * T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6852(a,1),20005(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6852 20005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20010">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / (y * z)) \ w)) = T(x,(u / (z * y)) \ w)
    ]]></literal>
    <justification jstring="[para(10595(a,1),20005(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10595 20005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20011">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(15021(a,1),20005(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15021 20005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20012">
    <literal><![CDATA[
      T(x,(T(y,z) / z) \ u) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13410,a(flip),b,20003,a),flip(a)].">
      <j1 rule="hyper" parents="64 13410 20003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20013">
    <literal><![CDATA[
      T(x,((y \ z) / y) \ u) = T(x,(y \ (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(117(a,1),20012(a,1,2,1,1))].">
      <j1 rule="para" parents="117 20012"/>
    </justification>
  </clause>

  <clause id="20014">
    <literal><![CDATA[
      T(x,(y * T(z,u)) \ T(z,w)) = T(x,(y * z) \ T(T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(18078,a,20009,a),flip(a)].">
      <j1 rule="hyper" parents="18078 20009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20015">
    <literal><![CDATA[
      T(x,(K(y,z) * T(u,w)) \ v5) = T(x,T(u \ K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,18631,a(flip),b,20009,a),flip(a)].">
      <j1 rule="hyper" parents="64 18631 20009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20016">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u * z)) = K(x,(z * u) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,18755,a(flip),b,19973,a),flip(a)].">
      <j1 rule="hyper" parents="64 18755 19973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20017">
    <literal><![CDATA[
      K(x,(T(y,((z \ 1) \ u) / u) / u) * ((z \ K(z,u)) \ u)) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(9506(a,2),20016(a,1,2,2))].">
      <j1 rule="para" parents="9506 20016"/>
    </justification>
  </clause>

  <clause id="20018">
    <literal><![CDATA[
      K(x,y * (z \ K(u,L(w,v5,v6)))) = K(x,K(w,u) * (y * (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14770,a(flip),b,19994,a)].">
      <j1 rule="hyper" parents="64 14770 19994"/>
    </justification>
  </clause>

  <clause id="20019">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ (K(z,w) * v5))) = K(x,y \ ((T(z,w) \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(6157(a,1),19877(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6157 19877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20020">
    <literal><![CDATA[
      K(x,y * (z * (u * K(y,w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w) * (z * u)) = v5
    ]]></literal>
    <justification jstring="[para(19887(a,1),17261(a,1))].">
      <j1 rule="para" parents="19887 17261"/>
    </justification>
  </clause>

  <clause id="20021">
    <literal><![CDATA[
      K(x,K(y \ (z * (u \ 1)),w) * v5) = K(x,K(w,u * (z \ y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,16836,a(flip),b,19893,a),flip(a)].">
      <j1 rule="hyper" parents="64 16836 19893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20022">
    <literal><![CDATA[
      K(x,(((y * z) / y) \ u) * w) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19912,a(flip),b,19901,a),flip(a)].">
      <j1 rule="hyper" parents="64 19912 19901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20023">
    <literal><![CDATA[
      K(x,((L(y,z,y) * z) \ u) * w) = K(x,(T(z * y,y) \ u) * w)
    ]]></literal>
    <justification jstring="[para(4725(a,1),20022(a,1,2,1,1))].">
      <j1 rule="para" parents="4725 20022"/>
    </justification>
  </clause>

  <clause id="20024">
    <literal><![CDATA[
      K(x,(T(y,y \ z) \ u) * w) = K(x,((z / (z / y)) \ u) * w)
    ]]></literal>
    <justification jstring="[para(4707(a,1),20022(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4707 20022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20025">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w / y))) = K(x,u \ (w / T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(18034,a,19949,a)].">
      <j1 rule="hyper" parents="18034 19949"/>
    </justification>
  </clause>

  <clause id="20027">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * (v5 \ ((y * z) * v6))) = K(x,v5 \ ((z * y) * v6))
    ]]></literal>
    <justification jstring="[hyper(18871,a,19950,a)].">
      <j1 rule="hyper" parents="18871 19950"/>
    </justification>
  </clause>

  <clause id="20028">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,T(y,z)) * w) = K(x,K(z,y) * (T(y * u,y) * w))
    ]]></literal>
    <justification jstring="[hyper(14873,a,19976,a)].">
      <j1 rule="hyper" parents="14873 19976"/>
    </justification>
  </clause>

  <clause id="20029">
    <literal><![CDATA[
      T(T(x,T(y \ z,u) * T(z / y,u)),(y \ z) \ ((y \ z) \ w)) = T(T(x,K(y,T(y \ z,u))),w)
    ]]></literal>
    <justification jstring="[para(5884(a,1),19986(a,2,1,2))].">
      <j1 rule="para" parents="5884 19986"/>
    </justification>
  </clause>

  <clause id="20030">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) \ v5)) = K(x,y \ T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(18090,a,19996,a)].">
      <j1 rule="hyper" parents="18090 19996"/>
    </justification>
  </clause>

  <clause id="20031">
    <literal><![CDATA[
      T(x,K(y * y,z) * ((y * y) * ((u / z) \ w))) = T(x,(u / (z * (y * y))) \ w)
    ]]></literal>
    <justification jstring="[para(905(a,1),20010(a,1,2,2))].">
      <j1 rule="para" parents="905 20010"/>
    </justification>
  </clause>

  <clause id="20032">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,y \ u),(x * y) \ T(T(y,u),z)) = (x * T(y,z)) \ ((y \ u) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13429,a(flip),b,20014,a),flip(a)].">
      <j1 rule="hyper" parents="64 13429 20014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20033">
    <literal><![CDATA[
      T(x,T(y \ K(z,u),w) * v5) = T(x,K(z,u) * (T(y,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(20000,a,20015,a),flip(a)].">
      <j1 rule="hyper" parents="20000 20015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20034">
    <literal><![CDATA[
      K(x,(T(y,y \ z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,16560,a(flip),b,20024,a),flip(a)].">
      <j1 rule="hyper" parents="373 16560 20024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20035">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(116(a,1),20034(a,1,2,1,1))].">
      <j1 rule="para" parents="116 20034"/>
    </justification>
  </clause>

  <clause id="20036">
    <literal><![CDATA[
      T(x,T(y * K(z,u),w) \ v5) = T(x,K(u,z) * (T(y,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18443,a,b,20033,a)].">
      <j1 rule="hyper" parents="64 18443 20033"/>
    </justification>
  </clause>

  <clause id="20037">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y \ u,w) \ v5)) = T(x,T(T(y,z) \ u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,16847,a(flip),b,20033,a),flip(a)].">
      <j1 rule="hyper" parents="64 16847 20033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20038">
    <literal><![CDATA[
      K(x,y * (z \ K(u,L(w,v5,v6)))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,19588,a(flip),b,20018,a),flip(a)].">
      <j1 rule="hyper" parents="373 19588 20018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20039">
    <literal><![CDATA[
      K(x,T(y * z,x) * (u \ K(w,v5))) = K(x,(y * (z * K(w,v5))) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,19427,a(flip),b,20038,a),flip(a)].">
      <j1 rule="hyper" parents="64 19427 20038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20040">
    <literal><![CDATA[
      K(x,y * (T(z * u,x) \ K(w,v5))) = K(x,y / (z * (u * K(v5,w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,18580,a(flip),b,20038,a),flip(a)].">
      <j1 rule="hyper" parents="64 18580 20038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20041">
    <literal><![CDATA[
      K(x,T(y,z) * (u * (w / y))) = K(x,y * (u * (w / T(y,z))))
    ]]></literal>
    <justification jstring="[hyper(20020,a,19795,a)].">
      <j1 rule="hyper" parents="20020 19795"/>
    </justification>
  </clause>

  <clause id="20042">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,18547,a(flip),b,20041,a),flip(a)].">
      <j1 rule="hyper" parents="64 18547 20041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20043">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) * K(x,K(u,w)) = K(x,w * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(17509,a,19915,a)].">
      <j1 rule="hyper" parents="17509 19915"/>
    </justification>
  </clause>

  <clause id="20044">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u / (z \ y)))
    ]]></literal>
    <justification jstring="[para(6599(a,1),19923(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6599 19923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20045">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,K(u,w) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(15815,a,19924,a),flip(a)].">
      <j1 rule="hyper" parents="15815 19924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20046">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,19974,a(flip),b,20045,a),flip(a)].">
      <j1 rule="hyper" parents="373 19974 20045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20047">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,w))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(11(a,1),20046(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 20046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20048">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * (u * w))) = K(x,y \ (T(w * u,u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16376,a(flip),b,20047,a),flip(a)].">
      <j1 rule="hyper" parents="64 16376 20047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20049">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,K(w,u) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(13528,a,19925,a),flip(a)].">
      <j1 rule="hyper" parents="13528 19925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20050">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,19922,a(flip),b,20049,a),flip(a)].">
      <j1 rule="hyper" parents="373 19922 20049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20051">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,u))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(9(a,1),20050(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 20050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20052">
    <literal><![CDATA[
      K(x \ K(y \ K(z,u),w),v5) = K(x \ K(w,y * K(z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,18418,a(flip),b,19928,a),flip(a)].">
      <j1 rule="hyper" parents="64 18418 19928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20053">
    <literal><![CDATA[
      K(x \ K(y \ K(z,u),w),v5) = K(x \ K(w,y),v5)
    ]]></literal>
    <justification jstring="[hyper(19841,a,20052,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19841 20052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20054">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) = K(T(y,z \ K(w,v5 \ w)) / x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17728,a(flip),b,20053,a),flip(a)].">
      <j1 rule="hyper" parents="64 17728 20053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20056">
    <literal><![CDATA[
      K(x,y \ K(z \ K(u,w),v5)) = (v6 * K(y \ K(v5,z),x)) \ v6
    ]]></literal>
    <justification jstring="[para(20053(a,1),6882(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="20053 6882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20057">
    <literal><![CDATA[
      K(T(x,y \ K(z,u \ z)) / w,v5) = K(T(x,y) / w,v5)
    ]]></literal>
    <justification jstring="[hyper(17726,a,20054,a),flip(a)].">
      <j1 rule="hyper" parents="17726 20054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20059">
    <literal><![CDATA[
      K(T(x,y \ K(z,u)) / w,v5) = K(T(x,y) / w,v5)
    ]]></literal>
    <justification jstring="[para(82(a,1),20057(a,1,1,1,2,2,2))].">
      <j1 rule="para" parents="82 20057"/>
    </justification>
  </clause>

  <clause id="20060">
    <literal><![CDATA[
      K(T((x * y) * (1 / x),x) / z,u) = K(L(y,x,x \ 1) / z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18642,a(flip),b,20059,a),flip(a)].">
      <j1 rule="hyper" parents="64 18642 20059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20061">
    <literal><![CDATA[
      K(T(x,y \ T(z,u)) / w,v5) = K(T(x,z \ y) / w,v5)
    ]]></literal>
    <justification jstring="[para(14638(a,1),20059(a,1,1,1))].">
      <j1 rule="para" parents="14638 20059"/>
    </justification>
  </clause>

  <clause id="20062">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) / v5) = (v6 * K(T(y,u \ z) / v5,x)) \ v6
    ]]></literal>
    <justification jstring="[para(20061(a,1),6882(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="20061 6882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20063">
    <literal><![CDATA[
      K(x,y \ K(z \ K(u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(v5,z)) = v6
    ]]></literal>
    <justification jstring="[para(20056(a,2),6899(a,1))].">
      <j1 rule="para" parents="20056 6899"/>
    </justification>
  </clause>

  <clause id="20065">
    <literal><![CDATA[
      K(((x * y) * (1 / y)) / z,u) = K(L(x,y,y \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(2135(a,1),20060(a,1,1,1))].">
      <j1 rule="para" parents="2135 20060"/>
    </justification>
  </clause>

  <clause id="20066">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),((z * u) * (1 / u)) * K(L(z,u,u \ 1) / y,x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[para(20065(a,1),14298(a,1,2,2))].">
      <j1 rule="para" parents="20065 14298"/>
    </justification>
  </clause>

  <clause id="20067">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ (z * (y / z))) * w)
    ]]></literal>
    <justification jstring="[hyper(13528,a,19934,a)].">
      <j1 rule="hyper" parents="13528 19934"/>
    </justification>
  </clause>

  <clause id="20068">
    <literal><![CDATA[
      K(x,(y \ (z * (u / z))) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19975,a(flip),b,20067,a),flip(a)].">
      <j1 rule="hyper" parents="64 19975 20067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20069">
    <literal><![CDATA[
      K(x,(T(y,T(z,u)) \ T(z,u)) * w) = K(x,((u * (z / u)) / y) * w)
    ]]></literal>
    <justification jstring="[hyper(16365,a,20068,a),flip(a)].">
      <j1 rule="hyper" parents="16365 20068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20070">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,K(z,u) * (y \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(15815,a,19942,a),flip(a)].">
      <j1 rule="hyper" parents="15815 19942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20071">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,19940,a(flip),b,20070,a),flip(a)].">
      <j1 rule="hyper" parents="373 19940 20070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20072">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (T(z / (u \ 1),z) * w))
    ]]></literal>
    <justification jstring="[para(9332(a,1),20071(a,1,2,2,1))].">
      <j1 rule="para" parents="9332 20071"/>
    </justification>
  </clause>

  <clause id="20073">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(z,y) * w) \ w)) = K(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,19424,a(flip),b,19944,a),flip(a)].">
      <j1 rule="hyper" parents="373 19424 19944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20074">
    <literal><![CDATA[
      T(x,(y \ z) * (u * K(w,z \ y))) = T(x,T((y \ z) \ 1,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,19541,a(flip),b,19952,a)].">
      <j1 rule="hyper" parents="64 19541 19952"/>
    </justification>
  </clause>

  <clause id="20075">
    <literal><![CDATA[
      K(x,(T(y,K(z,u) * w) / v5) * v6) = K(x,(T(y,w) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,19902,a(flip),b,19972,a),flip(a)].">
      <j1 rule="hyper" parents="64 19902 19972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20076">
    <literal><![CDATA[
      T(x,(y \ T(z \ u,z)) \ w) = T(x,(y \ (u / z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,20011,a(flip),b,20007,a)].">
      <j1 rule="hyper" parents="64 20011 20007"/>
    </justification>
  </clause>

  <clause id="20077">
    <literal><![CDATA[
      T(x,K(y \ (z * (u \ 1)),w) * v5) = T(x,K(w,u * (z \ y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(143,a,20021,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 20021 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20078">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,T(T(y,w) \ z,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,19998,a(flip),b,20037,a)].">
      <j1 rule="hyper" parents="64 19998 20037"/>
    </justification>
  </clause>

  <clause id="20080">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) / v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) * (v5 \ K(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(20039(a,1),8782(a,1))].">
      <j1 rule="para" parents="20039 8782"/>
    </justification>
  </clause>

  <clause id="20081">
    <literal><![CDATA[
      K(x,y / (z * (u * K(w,v5)))) = K(x,y * ((z * u) \ K(v5,w)))
    ]]></literal>
    <justification jstring="[hyper(19597,a,20040,a),flip(a)].">
      <j1 rule="hyper" parents="19597 20040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20083">
    <literal><![CDATA[
      K(x,y / ((z * u) * K(w,v5))) = K(x,y / (z * (u * K(w,v5))))
    ]]></literal>
    <justification jstring="[hyper(373,a,18120,a,b,20081,a)].">
      <j1 rule="hyper" parents="373 18120 20081"/>
    </justification>
  </clause>

  <clause id="20084">
    <literal><![CDATA[
      K(x,y / (z * (u * K(w,u)))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,19605,a(flip),b,20081,a),flip(a)].">
      <j1 rule="hyper" parents="373 19605 20081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20085">
    <literal><![CDATA[
      K(x,y / (z * T(T(u,w),w))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(5749(a,1),20084(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5749 20084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20086">
    <literal><![CDATA[
      K(x,y / (z * T(u \ w,u))) = K(x,y / (z * (w / u)))
    ]]></literal>
    <justification jstring="[para(5774(a,1),20084(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5774 20084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20087">
    <literal><![CDATA[
      K(x,y / (z * (T(u,z) * K(w,v5)))) = K(x,y / ((u * z) * K(w,v5)))
    ]]></literal>
    <justification jstring="[para(115(a,1),20083(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="115 20083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20088">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16375,a(flip),b,20048,a),flip(a)].">
      <j1 rule="hyper" parents="64 16375 20048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20089">
    <literal><![CDATA[
      K(x,y \ ((z * (u / z)) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[para(12(a,1),20088(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 20088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20090">
    <literal><![CDATA[
      R(T(K(x,y \ z),y * u),y,u) = K(x,(y * u) \ (T(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16417,a(flip),b,20089,a)].">
      <j1 rule="hyper" parents="64 16417 20089"/>
    </justification>
  </clause>

  <clause id="20091">
    <literal><![CDATA[
      R(K(x,T(y \ z,y * u)),y,u) = K(x,(y * u) \ (T(z,y) * u))
    ]]></literal>
    <justification jstring="[para(7867(a,2),20090(a,1,1))].">
      <j1 rule="para" parents="7867 20090"/>
    </justification>
  </clause>

  <clause id="20092">
    <literal><![CDATA[
      K(x,L(T(y \ z,y * u),y,u)) = K(x,(y * u) \ (T(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(15596,a,20091,a)].">
      <j1 rule="hyper" parents="15596 20091"/>
    </justification>
  </clause>

  <clause id="20093">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (T(z,y) * (z \ u))) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,18585,a(flip),b,20092,a),flip(a)].">
      <j1 rule="hyper" parents="64 18585 20092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20094">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) / v5) = K(x,T(y,u \ z) / v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,6882,a(flip),b,20062,a),flip(a)].">
      <j1 rule="hyper" parents="373 6882 20062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20095">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / w) = K(x,T(y,u) / w)
    ]]></literal>
    <justification jstring="[para(7409(a,1),20094(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7409 20094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20096">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z * y)) = K(x,T(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17863,a,b,20095,a)].">
      <j1 rule="hyper" parents="64 17863 20095"/>
    </justification>
  </clause>

  <clause id="20098">
    <literal><![CDATA[
      K(x,T(y \ ((z / y) \ u),(y \ z) * y)) = K(x,T((y \ z) \ u,y \ z) / y)
    ]]></literal>
    <justification jstring="[para(5045(a,1),20096(a,1,2,1))].">
      <j1 rule="para" parents="5045 20096"/>
    </justification>
  </clause>

  <clause id="20099">
    <literal><![CDATA[
      K(x,((y * (z / y)) / u) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(16364,a,20069,a),flip(a)].">
      <j1 rule="hyper" parents="16364 20069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20100">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((T(y,z) * z) / u) * w)
    ]]></literal>
    <justification jstring="[para(4450(a,2),20099(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4450 20099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20101">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,w * (u \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15768,a,20073,a)].">
      <j1 rule="hyper" parents="15768 20073"/>
    </justification>
  </clause>

  <clause id="20102">
    <literal><![CDATA[
      T(x,T(K(y,z \ u) * z,u)) = T(x,T((u \ z) \ 1,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,19534,a(flip),b,20074,a)].">
      <j1 rule="hyper" parents="64 19534 20074"/>
    </justification>
  </clause>

  <clause id="20103">
    <literal><![CDATA[
      T(x,T(y * K(z,y \ u),u)) = T(x,T((u \ y) \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(17271,a,20102,a)].">
      <j1 rule="hyper" parents="17271 20102"/>
    </justification>
  </clause>

  <clause id="20104">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,u) \ y) = T(x,T(z \ y,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(7556,a,20103,a),flip(a)].">
      <j1 rule="hyper" parents="7556 20103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20105">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) = T(x,T(z \ y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16840,a(flip),b,20104,a),flip(a)].">
      <j1 rule="hyper" parents="64 16840 20104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20106">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,11149,a(flip),b,20105,a),flip(a)].">
      <j1 rule="hyper" parents="373 11149 20105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20107">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,z * T(T(y,w) / z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,20078,a,b,20106,a)].">
      <j1 rule="hyper" parents="64 20078 20106"/>
    </justification>
  </clause>

  <clause id="20108">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * T(y / z,u)) = T(x,T(z / y,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,17816,a(flip),b,20106,a),flip(a)].">
      <j1 rule="hyper" parents="64 17816 20106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20109">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,T(w,z))) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(373,a,19766,a(flip),b,20107,a),flip(a)].">
      <j1 rule="hyper" parents="373 19766 20107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20110">
    <literal><![CDATA[
      T(x,T(y / z,u) \ y) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17817,a(flip),b,20108,a),flip(a)].">
      <j1 rule="hyper" parents="64 17817 20108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20111">
    <literal><![CDATA[
      T(x,y * K(z,u \ (w * (v5 \ 1)))) = T(x,K(z,v5 * (w \ u)) * y)
    ]]></literal>
    <justification jstring="[hyper(17510,a,20077,a)].">
      <j1 rule="hyper" parents="17510 20077"/>
    </justification>
  </clause>

  <clause id="20112">
    <literal><![CDATA[
      K(x,y / (z * (T(u,z) * K(w,v5)))) = K(x,y / (u * (z * K(w,v5))))
    ]]></literal>
    <justification jstring="[hyper(373,a,20083,a(flip),b,20087,a),flip(a)].">
      <j1 rule="hyper" parents="373 20083 20087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20113">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (K(z,y) * u)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[para(5778(a,1),20093(a,1,2,2))].">
      <j1 rule="para" parents="5778 20093"/>
    </justification>
  </clause>

  <clause id="20114">
    <literal><![CDATA[
      K(x,(T(y,z) * (z \ u)) \ u) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,19393,a(flip),b,20113,a)].">
      <j1 rule="hyper" parents="64 19393 20113"/>
    </justification>
  </clause>

  <clause id="20115">
    <literal><![CDATA[
      T(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = T(x,w * (u \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(143,a,20101,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 20101 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20116">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(17270,a,20109,a)].">
      <j1 rule="hyper" parents="17270 20109"/>
    </justification>
  </clause>

  <clause id="20118">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),w)) = T(x,y * T(T(z,w) / y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,20107,a(flip),b,20116,a),flip(a)].">
      <j1 rule="hyper" parents="64 20107 20116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20120">
    <literal><![CDATA[
      T(x,y * T(T(z,T(u,w)) / y,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y * T(z / y,v5),u)) = v6
    ]]></literal>
    <justification jstring="[para(20118(a,1),17270(a,1))].">
      <j1 rule="para" parents="20118 17270"/>
    </justification>
  </clause>

  <clause id="20121">
    <literal><![CDATA[
      K(x,y \ ((T(z,y) * K(u,w)) \ y)) = K(x,y / (z * (y * K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(9238,a,20112,a)].">
      <j1 rule="hyper" parents="9238 20112"/>
    </justification>
  </clause>

  <clause id="20122">
    <literal><![CDATA[
      K(x,(y * T(z,y)) * (u \ K(w,v5))) = K(x,((K(w,v5) * z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(20080,a,18543,a)].">
      <j1 rule="hyper" parents="20080 18543"/>
    </justification>
  </clause>

  <clause id="20123">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) / v5) = K(x,(u * w) * (v5 \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(115(a,1),20122(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="115 20122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20124">
    <literal><![CDATA[
      K(x,y * T((K(z,u) * w) \ v5,v6)) = K(x,y * T(w \ (K(u,z) * v5),v6))
    ]]></literal>
    <justification jstring="[para(6156(a,1),19874(a,2,2,2,1,2))].">
      <j1 rule="para" parents="6156 19874"/>
    </justification>
  </clause>

  <clause id="20125">
    <literal><![CDATA[
      K(x,y / T((K(z,u) * w) \ v5,w)) = K(x,y / ((K(z,u) \ v5) / w))
    ]]></literal>
    <justification jstring="[hyper(16354,a,19883,a)].">
      <j1 rule="hyper" parents="16354 19883"/>
    </justification>
  </clause>

  <clause id="20126">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(z / y,w,v5))) = K(x,u * L(y \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(15815,a,19892,a)].">
      <j1 rule="hyper" parents="15815 19892"/>
    </justification>
  </clause>

  <clause id="20128">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * L(y / z,w,v5)) = K(x,(y \ u) * L(z \ y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,19900,a(flip),b,20126,a)].">
      <j1 rule="hyper" parents="64 19900 20126"/>
    </justification>
  </clause>

  <clause id="20129">
    <literal><![CDATA[
      K(x,K((y * z) / y,y) * (u * L(K(z,y) * (y / z),w,v5))) = K(x,u * L(((y * z) / y) \ y,w,v5))
    ]]></literal>
    <justification jstring="[para(7165(a,1),20126(a,1,2,2,2,1))].">
      <j1 rule="para" parents="7165 20126"/>
    </justification>
  </clause>

  <clause id="20130">
    <literal><![CDATA[
      K(x,T(((y \ z) * y) \ u,z) * w) = K(x,K(z,y) * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,13392,a(flip),b,19910,a),flip(a)].">
      <j1 rule="hyper" parents="373 13392 19910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20131">
    <literal><![CDATA[
      K(x,T(((y \ z) * y) \ u,z) * w) = K(x,(u / T(z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,19932,a(flip),b,20130,a),flip(a)].">
      <j1 rule="hyper" parents="373 19932 20130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20132">
    <literal><![CDATA[
      K(x,(y / ((z \ u) * z)) * w) = K(x,(y / T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,18036,a(flip),b,20131,a)].">
      <j1 rule="hyper" parents="64 18036 20131"/>
    </justification>
  </clause>

  <clause id="20133">
    <literal><![CDATA[
      K(x,(y / T(z,u)) * (K(w,y / T(z,u)) * v5)) = K(x,T(y / ((u \ z) * u),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(18227,a,20132,a),flip(a)].">
      <j1 rule="hyper" parents="18227 20132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20134">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,(((y * z) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(18034,a,19927,a)].">
      <j1 rule="hyper" parents="18034 19927"/>
    </justification>
  </clause>

  <clause id="20136">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ 1) \ w) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19914,a(flip),b,20134,a),flip(a)].">
      <j1 rule="hyper" parents="64 19914 20134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20137">
    <literal><![CDATA[
      K(x,((T(y,z) * z) / u) * w) = K(x,((z * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(14641,a,20136,a),flip(a)].">
      <j1 rule="hyper" parents="14641 20136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20138">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((z * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,20100,a,b,20137,a)].">
      <j1 rule="hyper" parents="64 20100 20137"/>
    </justification>
  </clause>

  <clause id="20139">
    <literal><![CDATA[
      K(x,K(y,z) * (T(z * u,z) * w)) = K(x,(u * T(z,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13394,a(flip),b,20028,a),flip(a)].">
      <j1 rule="hyper" parents="64 13394 20028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20140">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) * w) = K(x,K(u,y) * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),20139(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 20139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20141">
    <literal><![CDATA[
      K(x,(T(y,z) * (u / y)) * w) = K(x,K(z,y) * (T(u,y) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18110,a,b,20140,a)].">
      <j1 rule="hyper" parents="64 18110 20140"/>
    </justification>
  </clause>

  <clause id="20142">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * w) = K(x,K(z,y) * (T(u,y) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16181,a,b,20141,a)].">
      <j1 rule="hyper" parents="64 16181 20141"/>
    </justification>
  </clause>

  <clause id="20143">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,13501,a(flip),b,20072,a),flip(a)].">
      <j1 rule="hyper" parents="373 13501 20072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20144">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19662,a,b,20143,a)].">
      <j1 rule="hyper" parents="64 19662 20143"/>
    </justification>
  </clause>

  <clause id="20145">
    <literal><![CDATA[
      K(x,y * T(z \ (K(u,w) * v5),z)) = K(x,y * (v5 / (K(w,u) * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18535,a(flip),b,20124,a),flip(a)].">
      <j1 rule="hyper" parents="64 18535 20124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20146">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) / v5)) = K(x,y * (w / (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15852,a(flip),b,20145,a)].">
      <j1 rule="hyper" parents="64 15852 20145"/>
    </justification>
  </clause>

  <clause id="20147">
    <literal><![CDATA[
      K(x,y * T(z \ (u * K(w,v5)),u)) = K(x,y * (u / (K(v5,w) * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18555,a,b,20146,a)].">
      <j1 rule="hyper" parents="64 18555 20146"/>
    </justification>
  </clause>

  <clause id="20148">
    <literal><![CDATA[
      K(x,(y / z) * L(z / y,u,w)) = K(x,(z \ y) * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(16364,a,20128,a)].">
      <j1 rule="hyper" parents="16364 20128"/>
    </justification>
  </clause>

  <clause id="20149">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (T(w * u,x) * v5)) = K(x,(w * (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[para(12093(a,1),19930(a,1,2,1))].">
      <j1 rule="para" parents="12093 19930"/>
    </justification>
  </clause>

  <clause id="20150">
    <literal><![CDATA[
      T(x,y * T(T(z,u) / y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y * T(z / y,w),u)) = v5
    ]]></literal>
    <justification jstring="[para(114(a,1),20120(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="114 20120"/>
    </justification>
  </clause>

  <clause id="20151">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((w * u) * v5)) = K(x,(w * (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(19596,a,20149,a)].">
      <j1 rule="hyper" parents="19596 20149"/>
    </justification>
  </clause>

  <clause id="20152">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) * v5) = K(x,K(w,u) * ((y * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,19871,a(flip),b,20151,a),flip(a)].">
      <j1 rule="hyper" parents="64 19871 20151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20154">
    <literal><![CDATA[
      K(x,K(y,z) * ((T((u \ w) / w,x) * w) * v5)) = K(x,(u \ (w * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,19681,a(flip),b,20152,a),flip(a)].">
      <j1 rule="hyper" parents="64 19681 20152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20155">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * T(w,u)) * v5)) = K(x,((K(z,y) * w) * u) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,18544,a(flip),b,20152,a),flip(a)].">
      <j1 rule="hyper" parents="64 18544 20152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20156">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) = K(x,K(z,y) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(115(a,1),20155(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="115 20155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20157">
    <literal><![CDATA[
      K(x,((y / K(z,u)) * w) * v5) = K(x,K(z,u) * ((y * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18111,a,b,20156,a)].">
      <j1 rule="hyper" parents="64 18111 20156"/>
    </justification>
  </clause>

  <clause id="20158">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) * v5) = K(x,K(u,z) * ((y * w) * v5))
    ]]></literal>
    <justification jstring="[para(6878(a,1),20157(a,1,2,1,1))].">
      <j1 rule="para" parents="6878 20157"/>
    </justification>
  </clause>

  <clause id="20159">
    <literal><![CDATA[
      K(x,y * L((K(z,u) * w) \ v5,v6,v7)) = K(x,y * L(w \ (K(u,z) * v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(6156(a,1),19875(a,2,2,2,1,2))].">
      <j1 rule="para" parents="6156 19875"/>
    </justification>
  </clause>

  <clause id="20160">
    <literal><![CDATA[
      K(x,L(y / z,u,w) / (1 / (z / y))) = K(x,(z / y) * L(y / z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,14469,a(flip),b,19908,a),flip(a)].">
      <j1 rule="hyper" parents="373 14469 19908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20161">
    <literal><![CDATA[
      K(x,L(y / z,u,w) * (z / y)) = K(x,(z / y) * L(y / z,u,w))
    ]]></literal>
    <justification jstring="[hyper(17536,a,20160,a)].">
      <j1 rule="hyper" parents="17536 20160"/>
    </justification>
  </clause>

  <clause id="20162">
    <literal><![CDATA[
      K(x,L(y / z,u,w) * (z / y)) = K(x,(y \ z) * L(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,20148,a(flip),b,20161,a),flip(a)].">
      <j1 rule="hyper" parents="373 20148 20161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20163">
    <literal><![CDATA[
      K(x,T(y,z / T(u,w)) \ (z / T(u,w))) = K(x,((z / u) * K(u,w)) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,20025,a(flip),b,19919,a)].">
      <j1 rule="hyper" parents="64 20025 19919"/>
    </justification>
  </clause>

  <clause id="20164">
    <literal><![CDATA[
      K(x,((y / z) * K(z,u)) / w) = K(x,(y / T(z,u)) / w)
    ]]></literal>
    <justification jstring="[hyper(13478,a,20163,a),flip(a)].">
      <j1 rule="hyper" parents="13478 20163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20165">
    <literal><![CDATA[
      K(x,((y * z) / T(y,u)) / w) = K(x,T(z * K(y,u),y) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15844,a(flip),b,20164,a),flip(a)].">
      <j1 rule="hyper" parents="64 15844 20164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20166">
    <literal><![CDATA[
      K(x,T(y * K(z,u),u) / w) = K(x,T(y * K(u,z),u) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15842,a(flip),b,20165,a)].">
      <j1 rule="hyper" parents="64 15842 20165"/>
    </justification>
  </clause>

  <clause id="20167">
    <literal><![CDATA[
      K(x,T(y * K(z,u),z) / w) = K(x,T(y,z) * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19430,a(flip),b,20166,a),flip(a)].">
      <j1 rule="hyper" parents="64 19430 20166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20168">
    <literal><![CDATA[
      K(x,(T(y,z) / (y / u)) / w) = K(x,T(u,y) * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18681,a,b,20167,a)].">
      <j1 rule="hyper" parents="64 18681 20167"/>
    </justification>
  </clause>

  <clause id="20169">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y \ z,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(16857,a,19943,a)].">
      <j1 rule="hyper" parents="16857 19943"/>
    </justification>
  </clause>

  <clause id="20170">
    <literal><![CDATA[
      K(x,(K(y \ z,z) * u) / w) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20101,a(flip),b,20169,a),flip(a)].">
      <j1 rule="hyper" parents="64 20101 20169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20171">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19424,a(flip),b,20170,a)].">
      <j1 rule="hyper" parents="64 19424 20170"/>
    </justification>
  </clause>

  <clause id="20172">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(z \ y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(13528,a,19945,a)].">
      <j1 rule="hyper" parents="13528 19945"/>
    </justification>
  </clause>

  <clause id="20173">
    <literal><![CDATA[
      K(x,(K(y \ z,y) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20101,a(flip),b,20172,a),flip(a)].">
      <j1 rule="hyper" parents="64 20101 20172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20174">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,u))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19424,a(flip),b,20173,a)].">
      <j1 rule="hyper" parents="64 19424 20173"/>
    </justification>
  </clause>

  <clause id="20175">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,T(y * (1 / z),z) / u)
    ]]></literal>
    <justification jstring="[para(7523(a,1),20173(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7523 20173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20176">
    <literal><![CDATA[
      K(x,T(y / (z \ u),x) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19428,a(flip),b,20174,a),flip(a)].">
      <j1 rule="hyper" parents="64 19428 20174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20177">
    <literal><![CDATA[
      K(x,y * (T(z \ (u \ w),x) \ K(u,w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18153,a(flip),b,20174,a),flip(a)].">
      <j1 rule="hyper" parents="64 18153 20174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20178">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,((1 / z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(373,a,13613,a(flip),b,20175,a),flip(a)].">
      <j1 rule="hyper" parents="373 13613 20175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20179">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6645,a(flip),b,20178,a),flip(a)].">
      <j1 rule="hyper" parents="373 6645 20178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20180">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(8782,a,20176,a)].">
      <j1 rule="hyper" parents="8782 20176"/>
    </justification>
  </clause>

  <clause id="20181">
    <literal><![CDATA[
      K(x,(y / (T(z,u) \ u)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19441,a(flip),b,20180,a)].">
      <j1 rule="hyper" parents="64 19441 20180"/>
    </justification>
  </clause>

  <clause id="20182">
    <literal><![CDATA[
      K(x,(y / (y / z)) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(79(a,1),20181(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 20181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20183">
    <literal><![CDATA[
      K(x,T(y * T(z,u),T(z,u)) / w) = K(x,(T(z,u) / (z / (y * z))) / w)
    ]]></literal>
    <justification jstring="[para(15058(a,1),20182(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="15058 20182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20184">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) \ K(u,w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(19597,a,20177,a)].">
      <j1 rule="hyper" parents="19597 20177"/>
    </justification>
  </clause>

  <clause id="20185">
    <literal><![CDATA[
      K(x,y / (z \ (u \ T(w,u)))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18158,a(flip),b,20184,a)].">
      <j1 rule="hyper" parents="64 18158 20184"/>
    </justification>
  </clause>

  <clause id="20186">
    <literal><![CDATA[
      K(x,T(y * T(z,u),T(z,u)) / w) = K(x,T(y * z,z) * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,20168,a(flip),b,20183,a),flip(a)].">
      <j1 rule="hyper" parents="373 20168 20183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20187">
    <literal><![CDATA[
      K(x,T(y * T(z,u),T(z,u)) / w) = K(x,(z * y) * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,15878,a(flip),b,20186,a),flip(a)].">
      <j1 rule="hyper" parents="373 15878 20186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20188">
    <literal><![CDATA[
      K(x,(y * z) * (u \ K(w,y))) = K(x,(T(y,w) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(18510,a,20187,a),flip(a)].">
      <j1 rule="hyper" parents="18510 20187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20189">
    <literal><![CDATA[
      K(x,(T(y,z) * (1 / z)) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,20179,a(flip),b,20188,a),flip(a)].">
      <j1 rule="hyper" parents="64 20179 20188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20190">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[para(6330(a,1),20189(a,1,2,1))].">
      <j1 rule="para" parents="6330 20189"/>
    </justification>
  </clause>

  <clause id="20191">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,((z \ 1) * y) / ((u \ 1) * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16572,a(flip),b,20190,a)].">
      <j1 rule="hyper" parents="64 16572 20190"/>
    </justification>
  </clause>

  <clause id="20192">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y,y \ z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(15815,a,19946,a)].">
      <j1 rule="hyper" parents="15815 19946"/>
    </justification>
  </clause>

  <clause id="20193">
    <literal><![CDATA[
      K(x,(K(y,y \ z) * u) / w) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20101,a(flip),b,20192,a),flip(a)].">
      <j1 rule="hyper" parents="64 20101 20192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20194">
    <literal><![CDATA[
      K(x,y * (z \ K(u,u \ w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19424,a(flip),b,20193,a)].">
      <j1 rule="hyper" parents="64 19424 20193"/>
    </justification>
  </clause>

  <clause id="20195">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y * ((z / u) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(19602,a,20194,a)].">
      <j1 rule="hyper" parents="19602 20194"/>
    </justification>
  </clause>

  <clause id="20196">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(z,u))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19828,a(flip),b,20194,a),flip(a)].">
      <j1 rule="hyper" parents="64 19828 20194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20197">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y / (z / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18155,a(flip),b,20195,a),flip(a)].">
      <j1 rule="hyper" parents="373 18155 20195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20198">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / T(z / u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17792,a(flip),b,20197,a),flip(a)].">
      <j1 rule="hyper" parents="64 17792 20197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20199">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,16345,a(flip),b,20198,a),flip(a)].">
      <j1 rule="hyper" parents="373 16345 20198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20200">
    <literal><![CDATA[
      T(x,y / (z / T(u,z))) = T(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(143,a,20199,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 20199 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20201">
    <literal><![CDATA[
      K(x,y / (T(z,u) / u)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9144,a,b,20199,a)].">
      <j1 rule="hyper" parents="64 9144 20199"/>
    </justification>
  </clause>

  <clause id="20202">
    <literal><![CDATA[
      T(x,y / ((z \ u) / z)) = T(x,y / (z \ (u / z)))
    ]]></literal>
    <justification jstring="[para(4652(a,1),20200(a,1,2,2))].">
      <j1 rule="para" parents="4652 20200"/>
    </justification>
  </clause>

  <clause id="20203">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / (u \ (z / u))) = T(x,((u \ z) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17848,a(flip),b,20202,a),flip(a)].">
      <j1 rule="hyper" parents="64 17848 20202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20204">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / (u \ (z / u))) = T(x,(u \ (z / u)) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,20013,a(flip),b,20203,a),flip(a)].">
      <j1 rule="hyper" parents="373 20013 20203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20205">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (T(z,u) \ (u * y))) = w
    ]]></literal>
    <justification jstring="[para(20196(a,1),14789(a,1))].">
      <j1 rule="para" parents="20196 14789"/>
    </justification>
  </clause>

  <clause id="20206">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(u / T(z,w)) \ y) = T(x,y / (K(z,w) * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20008,a(flip),b,20001,a)].">
      <j1 rule="hyper" parents="64 20008 20001"/>
    </justification>
  </clause>

  <clause id="20207">
    <literal><![CDATA[
      T(x,y / (K(z,u) * (w / z))) = T(x,y / (w / T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18341,a(flip),b,20206,a),flip(a)].">
      <j1 rule="hyper" parents="64 18341 20206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20208">
    <literal><![CDATA[
      T(x,y * ((z / u) \ K(w,u))) = T(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14553,a(flip),b,20207,a)].">
      <j1 rule="hyper" parents="64 14553 20207"/>
    </justification>
  </clause>

  <clause id="20209">
    <literal><![CDATA[
      T(x,y / ((z * u) / T(z,w))) = T(x,y / T(u * K(z,w),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18169,a(flip),b,20208,a),flip(a)].">
      <j1 rule="hyper" parents="64 18169 20208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20210">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),w)) = T(x,y / T(z * K(w,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16316,a(flip),b,20209,a)].">
      <j1 rule="hyper" parents="64 16316 20209"/>
    </justification>
  </clause>

  <clause id="20211">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),w)) = T(x,y * T(K(u,w) / z,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,17719,a(flip),b,20210,a),flip(a)].">
      <j1 rule="hyper" parents="373 17719 20210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20212">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z * K(w,y)))) = T(x,u * T(K(w,y) / z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17470,a,b,20211,a)].">
      <j1 rule="hyper" parents="64 17470 20211"/>
    </justification>
  </clause>

  <clause id="20213">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z * K(w,y)))) = T(x,u * T(z \ K(w,y),y))
    ]]></literal>
    <justification jstring="[hyper(373,a,18467,a(flip),b,20212,a),flip(a)].">
      <j1 rule="hyper" parents="373 18467 20212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20214">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),z \ w)) = T(x,y * T(z \ K(u,w),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18590,a,b,20213,a)].">
      <j1 rule="hyper" parents="64 18590 20213"/>
    </justification>
  </clause>

  <clause id="20215">
    <literal><![CDATA[
      T(x,y / ((z \ T(u,w)) \ u)) = T(x,y * T(z \ K(w,u),u))
    ]]></literal>
    <justification jstring="[para(17744(a,1),20214(a,1,2,2))].">
      <j1 rule="para" parents="17744 20214"/>
    </justification>
  </clause>

  <clause id="20216">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,z \ w),z \ w)) = T(x,y / (T(z \ w,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18649,a(flip),b,20215,a),flip(a)].">
      <j1 rule="hyper" parents="64 18649 20215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20217">
    <literal><![CDATA[
      T(x,T(y * y,z) * ((u / z) \ w)) = T(x,(u / (z * (y * y))) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13678,a(flip),b,20031,a)].">
      <j1 rule="hyper" parents="64 13678 20031"/>
    </justification>
  </clause>

  <clause id="20218">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) = K(x,T(y \ ((z / y) \ u),z))
    ]]></literal>
    <justification jstring="[hyper(18275,a,20098,a),flip(a)].">
      <j1 rule="hyper" parents="18275 20098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20220">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = w
    ]]></literal>
    <justification jstring="[para(20218(a,2),16402(a,1))].">
      <j1 rule="para" parents="20218 16402"/>
    </justification>
  </clause>

  <clause id="20221">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * T(u \ (w \ u),x)) * v5)) = K(x,(w \ (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[para(525(a,1),20154(a,1,2,2,1))].">
      <j1 rule="para" parents="525 20154"/>
    </justification>
  </clause>

  <clause id="20222">
    <literal><![CDATA[
      K(x,y) * (((x \ z) / z) \ u) = ((T(x,y) \ z) / z) \ u
    ]]></literal>
    <justification jstring="[hyper(6744,a,19857,a)].">
      <j1 rule="hyper" parents="6744 19857"/>
    </justification>
  </clause>

  <clause id="20224">
    <literal><![CDATA[
      T(x,((T(y,z) \ u) / u) \ w) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[para(20222(a,1),16815(a,1,2))].">
      <j1 rule="para" parents="20222 16815"/>
    </justification>
  </clause>

  <clause id="20225">
    <literal><![CDATA[
      K(x,y) \ T(x,x * (a(K(z,u),w,v5) \ y)) = L(x,a(K(z,u),w,v5) \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4683(a,1),19873(a,1,2))].">
      <j1 rule="para" parents="4683 19873"/>
    </justification>
  </clause>

  <clause id="20226">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * (T(v5,K(y,z) * v6) \ v6)) = T(x,(K(y,L(z,u,w)) * v6) / v5)
    ]]></literal>
    <justification jstring="[hyper(19958,a,19516,a)].">
      <j1 rule="hyper" parents="19958 19516"/>
    </justification>
  </clause>

  <clause id="20227">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (w * T(z,v5)))) = T(x,u * (w * (K(z,y) * T(z,v5))))
    ]]></literal>
    <justification jstring="[para(8205(a,1),19561(a,1,2,1))].">
      <j1 rule="para" parents="8205 19561"/>
    </justification>
  </clause>

  <clause id="20228">
    <literal><![CDATA[
      T(x,y * (z * (K(u,w) * T(u,v5)))) = T(x,y * (z * T(T(u,w),v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19744,a(flip),b,20227,a),flip(a)].">
      <j1 rule="hyper" parents="64 19744 20227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20230">
    <literal><![CDATA[
      K(x,y * (z * K((u \ w) \ v5,u \ w))) = K(x,(y * z) * K(w \ u,v5))
    ]]></literal>
    <justification jstring="[hyper(17666,a,19584,a),flip(a)].">
      <j1 rule="hyper" parents="17666 19584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20231">
    <literal><![CDATA[
      K(x,y * (z * K((u \ w) \ y,u \ w))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,17303,a(flip),b,20230,a),flip(a)].">
      <j1 rule="hyper" parents="373 17303 20230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20232">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),u \ w))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[para(15163(a,1),20231(a,1,2,2,2))].">
      <j1 rule="para" parents="15163 20231"/>
    </justification>
  </clause>

  <clause id="20233">
    <literal><![CDATA[
      (x \ (1 / T(x,y))) * K(z,K(x,y) * x) = T((1 / x) \ K(x,y),z) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),19598(a,1,2,2,2))].">
      <j1 rule="para" parents="7 19598"/>
    </justification>
  </clause>

  <clause id="20234">
    <literal><![CDATA[
      T((1 / x) \ K(x,y),z) \ (1 / x) = (x \ (1 / T(x,y))) * K(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(5756(a,2),20233(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5756 20233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20235">
    <literal><![CDATA[
      T((1 / T(x,y)) / T(x,T(z,y)),x) = T((1 / x) \ K(x,y),z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,7931,a,b,20234,a)].">
      <j1 rule="hyper" parents="373 7931 20234"/>
    </justification>
  </clause>

  <clause id="20236">
    <literal><![CDATA[
      T((1 / T(x,y)) / T(x,T(z,y)),x) = T(T(x,y),z) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(5760(a,2),20235(a,2,1,1))].">
      <j1 rule="para" parents="5760 20235"/>
    </justification>
  </clause>

  <clause id="20237">
    <literal><![CDATA[
      x \ (K(y,x) / T(x,T(z,y))) = T(T(x,y),z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5954,a(flip),b,20236,a)].">
      <j1 rule="hyper" parents="64 5954 20236"/>
    </justification>
  </clause>

  <clause id="20238">
    <literal><![CDATA[
      T(T(x,y),z) \ (1 / x) = x \ (1 / T(T(x,y),z))
    ]]></literal>
    <justification jstring="[para(9121(a,1),20237(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9121 20237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20239">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(z \ u,u))) = K(x,y / ((z \ K(z \ u,u)) * u))
    ]]></literal>
    <justification jstring="[para(7573(a,1),19606(a,1,2,2,2))].">
      <j1 rule="para" parents="7573 19606"/>
    </justification>
  </clause>

  <clause id="20240">
    <literal><![CDATA[
      K(x,y / ((z \ K(z \ u,u)) * u)) = K(x,y * (((z \ 1) * u) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20171,a(flip),b,20239,a),flip(a)].">
      <j1 rule="hyper" parents="64 20171 20239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20241">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / T((z \ 1) * u,u))
    ]]></literal>
    <justification jstring="[para(14800(a,1),20240(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14800 20240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20242">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,17691,a(flip),b,20241,a),flip(a)].">
      <j1 rule="hyper" parents="373 17691 20241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20243">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19605,a(flip),b,20242,a)].">
      <j1 rule="hyper" parents="64 19605 20242"/>
    </justification>
  </clause>

  <clause id="20244">
    <literal><![CDATA[
      K(x,y / (T(z,u) * (u \ 1))) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,20085,a(flip),b,20243,a),flip(a)].">
      <j1 rule="hyper" parents="64 20085 20243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20245">
    <literal><![CDATA[
      T(x,(y / (1 / K(z,u \ w))) * v5) = T(x,(y * K(z,u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(11200,a,19644,a),flip(a)].">
      <j1 rule="hyper" parents="11200 19644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20246">
    <literal><![CDATA[
      T(x,(y / (1 / K(z,u \ w))) * v5) = T(x,y * (K(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,19623,a(flip),b,20245,a),flip(a)].">
      <j1 rule="hyper" parents="373 19623 20245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20247">
    <literal><![CDATA[
      T(x,(y / K(z \ u,w)) * v5) = T(x,y * (K(w,z * u) * v5))
    ]]></literal>
    <justification jstring="[para(6091(a,1),20246(a,1,2,1,2))].">
      <j1 rule="para" parents="6091 20246"/>
    </justification>
  </clause>

  <clause id="20248">
    <literal><![CDATA[
      T(x,(y * K(z,u \ w)) * v5) = T(x,y * (K(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[para(6878(a,1),20247(a,1,2,1))].">
      <j1 rule="para" parents="6878 20247"/>
    </justification>
  </clause>

  <clause id="20249">
    <literal><![CDATA[
      T(x,y * (K(z,u \ w) * v5)) = T(x,y * (K(z,u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,19623,a(flip),b,20248,a)].">
      <j1 rule="hyper" parents="64 19623 20248"/>
    </justification>
  </clause>

  <clause id="20250">
    <literal><![CDATA[
      T(x,(T(y,L(z \ u,w,u / z)) \ v5) * v6) = T(x,(y \ v5) * (K(y,z * u) * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,19570,a,b,20249,a)].">
      <j1 rule="hyper" parents="64 19570 20249"/>
    </justification>
  </clause>

  <clause id="20251">
    <literal><![CDATA[
      T(x,(T(y,L(z \ u,w,u / z)) \ v5) * v6) = T(x,(T(y,z * u) \ v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,19557,a(flip),b,20250,a),flip(a)].">
      <j1 rule="hyper" parents="373 19557 20250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20252">
    <literal><![CDATA[
      T(x,(T(y,z \ u) \ w) * v5) = T(x,(T(y,z * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(593(a,1),20251(a,1,2,1,1,2))].">
      <j1 rule="para" parents="593 20251"/>
    </justification>
  </clause>

  <clause id="20253">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u) \ w)),(T(z,v5 * v6) \ w) * y) = T(x,y * (T(z,v5 \ v6) \ w))
    ]]></literal>
    <justification jstring="[hyper(18581,a,20252,a),flip(a)].">
      <j1 rule="hyper" parents="18581 20252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20254">
    <literal><![CDATA[
      T(x,(T(y,z * z) \ u) * w) = T(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[para(379(a,1),20252(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="379 20252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20255">
    <literal><![CDATA[
      T(x,R(y / y,y,y) \ ((z \ ((y * y) * u)) / w)) = T(x,(z \ u) * (w \ (y * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18820,a,b,20254,a)].">
      <j1 rule="hyper" parents="64 18820 20254"/>
    </justification>
  </clause>

  <clause id="20257">
    <literal><![CDATA[
      T(x,R(1,y,y) \ ((z \ ((y * y) * u)) / w)) = T(x,(z \ u) * (w \ (y * y)))
    ]]></literal>
    <justification jstring="[para(76(a,1),20255(a,1,2,1,1))].">
      <j1 rule="para" parents="76 20255"/>
    </justification>
  </clause>

  <clause id="20259">
    <literal><![CDATA[
      T(x,1 \ ((y \ ((z * z) * u)) / w)) = T(x,(y \ u) * (w \ (z * z)))
    ]]></literal>
    <justification jstring="[para(428(a,1),20257(a,1,2,1))].">
      <j1 rule="para" parents="428 20257"/>
    </justification>
  </clause>

  <clause id="20260">
    <literal><![CDATA[
      T(x,(y \ ((z * z) * u)) / w) = T(x,(y \ u) * (w \ (z * z)))
    ]]></literal>
    <justification jstring="[para(66(a,1),20259(a,1,2))].">
      <j1 rule="para" parents="66 20259"/>
    </justification>
  </clause>

  <clause id="20262">
    <literal><![CDATA[
      K(x,(K(y,T(z,u)) * ((K(w,T(v5,v6)) \ v7) * K(z,T(y,u)))) \ v8) = K(x,v7 \ (K(v5,T(w,v6)) \ v8))
    ]]></literal>
    <justification jstring="[para(7908(a,1),19739(a,1,2,1,2))].">
      <j1 rule="para" parents="7908 19739"/>
    </justification>
  </clause>

  <clause id="20263">
    <literal><![CDATA[
      K(x,(T((K(y,z) * u) \ w,v5) / v6) * v7) = K(x,(T(u \ (K(z,y) * w),v5) / v6) * v7)
    ]]></literal>
    <justification jstring="[para(6156(a,1),19968(a,2,2,1,1,1,2))].">
      <j1 rule="para" parents="6156 19968"/>
    </justification>
  </clause>

  <clause id="20264">
    <literal><![CDATA[
      K(x * (T(y,z) \ (y * u)),w) = K(w,K(y,z) \ (u * x)) \ K(u,K(w,x))
    ]]></literal>
    <justification jstring="[para(18322(a,1),19992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18322 19992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20265">
    <literal><![CDATA[
      K(x * (T(y,z) \ (y * u)),w) = K(w,K(y,z) \ (u * x)) \ K(w,K(u,x))
    ]]></literal>
    <justification jstring="[para(8108(a,1),20264(a,2,2))].">
      <j1 rule="para" parents="8108 20264"/>
    </justification>
  </clause>

  <clause id="20267">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,K(z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,13409,a(flip),b,20006,a),flip(a)].">
      <j1 rule="hyper" parents="373 13409 20006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20268">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,K(z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17947,a(flip),b,20267,a)].">
      <j1 rule="hyper" parents="64 17947 20267"/>
    </justification>
  </clause>

  <clause id="20269">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,(T(y,z) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,20003,a(flip),b,20268,a),flip(a)].">
      <j1 rule="hyper" parents="373 20003 20268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20271">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w) * v5) = K(x,T(y / T(u,z),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(18151,a,20133,a),flip(a)].">
      <j1 rule="hyper" parents="18151 20133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20272">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z) * w) = K(x,(((u \ z) * u) \ y) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,18883,a(flip),b,20271,a),flip(a)].">
      <j1 rule="hyper" parents="64 18883 20271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20273">
    <literal><![CDATA[
      K(x,(((y \ z) * y) \ u) * w) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17969,a(flip),b,20272,a),flip(a)].">
      <j1 rule="hyper" parents="64 17969 20272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20274">
    <literal><![CDATA[
      T(x,(K(y,L(z,u,w)) * v5) / v6) = T(x,K(y,z) * (T(v6,K(y,z) * v5) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,19506,a(flip),b,20226,a),flip(a)].">
      <j1 rule="hyper" parents="64 19506 20226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20276">
    <literal><![CDATA[
      T(x,(K(y,L(z,u,w)) * v5) / v6) = T(x,v5 * (v6 \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,20115,a(flip),b,20274,a),flip(a)].">
      <j1 rule="hyper" parents="373 20115 20274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20277">
    <literal><![CDATA[
      T(x,y * (z \ K(u,L(w,v5,v6)))) = T(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19440,a(flip),b,20276,a)].">
      <j1 rule="hyper" parents="64 19440 20276"/>
    </justification>
  </clause>

  <clause id="20278">
    <literal><![CDATA[
      T(x,y / (z * (u * K(w,v5)))) = T(x,y * ((z * u) \ K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19721,a(flip),b,20277,a)].">
      <j1 rule="hyper" parents="64 19721 20277"/>
    </justification>
  </clause>

  <clause id="20280">
    <literal><![CDATA[
      T(x,y * (T(z,u \ w) \ v5)) = T(x,y * (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(18581,a,20253,a),flip(a)].">
      <j1 rule="hyper" parents="18581 20253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20281">
    <literal><![CDATA[
      T(x,(y \ 1) * (T(z,u * w) \ v5)) = T(x,y \ (T(z,u \ w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(14732,a,20280,a),flip(a)].">
      <j1 rule="hyper" parents="14732 20280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20282">
    <literal><![CDATA[
      T(x,y * (T(z,u * u) \ w)) = T(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[para(379(a,1),20280(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="379 20280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20283">
    <literal><![CDATA[
      T(x,T(y \ z,u) * (u \ w)) = T(x,(y \ z) * (T(u,y * z) \ w))
    ]]></literal>
    <justification jstring="[para(6284(a,2),20280(a,1,2))].">
      <j1 rule="para" parents="6284 20280"/>
    </justification>
  </clause>

  <clause id="20284">
    <literal><![CDATA[
      T(x,y \ ((z * z) * u)) = T(x,(z * z) * (y \ u))
    ]]></literal>
    <justification jstring="[para(1460(a,1),20282(a,1,2))].">
      <j1 rule="para" parents="1460 20282"/>
    </justification>
  </clause>

  <clause id="20285">
    <literal><![CDATA[
      T(x,y \ ((z * z) * u)) = T(x,z * (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,15742,a(flip),b,20284,a),flip(a)].">
      <j1 rule="hyper" parents="373 15742 20284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20286">
    <literal><![CDATA[
      T(x,(y / T(z,u * (u * y))) * (u * u)) = T(x,u * (u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17814,a,b,20285,a)].">
      <j1 rule="hyper" parents="64 17814 20285"/>
    </justification>
  </clause>

  <clause id="20287">
    <literal><![CDATA[
      T(x,y * (y * (z \ T(u,y \ (y \ z))))) = T(x,u / ((y * y) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,14626,a(flip),b,20285,a),flip(a)].">
      <j1 rule="hyper" parents="64 14626 20285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20288">
    <literal><![CDATA[
      T(x,(y \ ((z * z) * u)) / T(w,z * (z * (y \ u)))) = T(x,w \ (y \ ((z * z) * u)))
    ]]></literal>
    <justification jstring="[para(20285(a,1),13310(a,1,2,2))].">
      <j1 rule="para" parents="20285 13310"/>
    </justification>
  </clause>

  <clause id="20289">
    <literal><![CDATA[
      T(x,y \ (T(z,u \ w) \ v5)) = T(x,y \ (T(z,u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(14732,a,20281,a),flip(a)].">
      <j1 rule="hyper" parents="14732 20281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20290">
    <literal><![CDATA[
      T(x,T(y \ z,u) * (u \ w)) = T(x,(y \ z) * (T(u,z * y) \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,18137,a,b,20283,a),flip(a)].">
      <j1 rule="hyper" parents="373 18137 20283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20291">
    <literal><![CDATA[
      T(x,y * (T(z,u * (u * y)) \ (u * u))) = T(x,u * (u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14943,a(flip),b,20286,a)].">
      <j1 rule="hyper" parents="64 14943 20286"/>
    </justification>
  </clause>

  <clause id="20292">
    <literal><![CDATA[
      T(x,y * (y * (z \ T(u,y \ (y \ z))))) = T(x,(u / z) * (y * y))
    ]]></literal>
    <justification jstring="[para(900(a,1),20287(a,2,2))].">
      <j1 rule="para" parents="900 20287"/>
    </justification>
  </clause>

  <clause id="20293">
    <literal><![CDATA[
      T(x,y / (z / (u * u))) = T(x,(y / z) * (u * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17807,a(flip),b,20292,a)].">
      <j1 rule="hyper" parents="64 17807 20292"/>
    </justification>
  </clause>

  <clause id="20294">
    <literal><![CDATA[
      T(x,y / (z / (u * u))) = T(x,y * (z \ (u * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,14943,a(flip),b,20293,a),flip(a)].">
      <j1 rule="hyper" parents="373 14943 20293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20295">
    <literal><![CDATA[
      T(x,(y * (z * z)) / u) = T(x,y * (u \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15151,a,b,20294,a)].">
      <j1 rule="hyper" parents="64 15151 20294"/>
    </justification>
  </clause>

  <clause id="20296">
    <literal><![CDATA[
      T(x,y * ((z * z) * (u \ 1))) = T(x,y * (u \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14551,a,b,20294,a)].">
      <j1 rule="hyper" parents="64 14551 20294"/>
    </justification>
  </clause>

  <clause id="20297">
    <literal><![CDATA[
      T(x,y * L((z / u) \ u,u \ z,u)) = T(x,(y * (u * u)) / (u * (z / u)))
    ]]></literal>
    <justification jstring="[para(10999(a,2),20295(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10999 20295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20298">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * (T(z,u \ 1) \ (u * u))) = T(x,((u * u) * (T(z,u \ 1) \ 1)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,18915,a(flip),b,20296,a),flip(a)].">
      <j1 rule="hyper" parents="64 18915 20296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20299">
    <literal><![CDATA[
      T(x,y * L((z / u) \ u,u \ z,u)) = T(x,(y * (u * u)) / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,16094,a(flip),b,20297,a),flip(a)].">
      <j1 rule="hyper" parents="373 16094 20297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20300">
    <literal><![CDATA[
      T(x,y * L((z / u) \ u,u \ z,u)) = T(x,y * (T(z,u) \ (u * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,20295,a(flip),b,20299,a),flip(a)].">
      <j1 rule="hyper" parents="373 20295 20299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20301">
    <literal><![CDATA[
      T(x,y * L((z / u) \ u,u \ z,u)) = T(x,y * T(z \ (u * u),u))
    ]]></literal>
    <justification jstring="[hyper(373,a,19710,a,b,20300,a),flip(a)].">
      <j1 rule="hyper" parents="373 19710 20300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20302">
    <literal><![CDATA[
      T(x,y * ((z * (u / z)) \ (z * z))) = T(x,y * T(u \ (z * z),z))
    ]]></literal>
    <justification jstring="[para(10999(a,1),20301(a,1,2,2))].">
      <j1 rule="para" parents="10999 20301"/>
    </justification>
  </clause>

  <clause id="20303">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,w * (w * (y \ z))) \ (w * w))) = T(x,u \ (y \ ((w * w) * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20260,a(flip),b,20288,a)].">
      <j1 rule="hyper" parents="64 20260 20288"/>
    </justification>
  </clause>

  <clause id="20304">
    <literal><![CDATA[
      T(x,y \ (z \ ((u * u) * w))) = T(x,u * (u * (y \ (z \ w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,20291,a(flip),b,20303,a),flip(a)].">
      <j1 rule="hyper" parents="64 20291 20303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20305">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * w)) \ (u * (K(x,K(y,z)) * (w * v5))) = L(v5,K(x,K(y,z)) * w,u)
    ]]></literal>
    <justification jstring="[para(19410(a,2),19201(a,1,1))].">
      <j1 rule="para" parents="19410 19201"/>
    </justification>
  </clause>

  <clause id="20306">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,(y * (u / y)) / (((u \ z) \ 1) * (u / y))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(15165(a,1),19344(a,1,1))].">
      <j1 rule="para" parents="15165 19344"/>
    </justification>
  </clause>

  <clause id="20307">
    <literal><![CDATA[
      L(K(x,K(y,z)) * ((u * w) \ v5),K(x,K(y,z)),u * w) = (u * (w * K(x,K(y,z)))) \ v5
    ]]></literal>
    <justification jstring="[para(8123(a,1),19370(a,1,1,1))].">
      <j1 rule="para" parents="8123 19370"/>
    </justification>
  </clause>

  <clause id="20308">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) \ (x * ((y * v5) * K(z,K(u,w)))) = L(v5,y,K(z,K(u,w)) * x)
    ]]></literal>
    <justification jstring="[para(19381(a,1),19418(a,1,2))].">
      <j1 rule="para" parents="19381 19418"/>
    </justification>
  </clause>

  <clause id="20309">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u \ 1),z,u \ 1)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(15551,a,19665,a)].">
      <j1 rule="hyper" parents="15551 19665"/>
    </justification>
  </clause>

  <clause id="20311">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u),z,u \ 1)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(16947,a,20309,a)].">
      <j1 rule="hyper" parents="16947 20309"/>
    </justification>
  </clause>

  <clause id="20312">
    <literal><![CDATA[
      K(x,(((y * z) \ z) * u) \ T(z,y)) = K(x,L(u \ (y * z),z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(18761,a,20311,a),flip(a)].">
      <j1 rule="hyper" parents="18761 20311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20313">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) = K(x,(((u * z) \ u) * y) \ u)
    ]]></literal>
    <justification jstring="[para(14862(a,1),20312(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14862 20312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20314">
    <literal><![CDATA[
      K(x,L((y * z) * (u / w),y,z \ 1)) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[hyper(17865,a,19832,a)].">
      <j1 rule="hyper" parents="17865 19832"/>
    </justification>
  </clause>

  <clause id="20315">
    <literal><![CDATA[
      K(x,y / (T((z \ u) \ 1,u) / w)) = K(x,y / (((u / z) \ 1) / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19833,a(flip),b,20314,a),flip(a)].">
      <j1 rule="hyper" parents="64 19833 20314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20316">
    <literal><![CDATA[
      T(K(x,(y * z) / ((u / w) \ 1)) * a(z,y,K(x,((u / w) \ 1) \ y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[hyper(504,a,19685,a,b,20315,a)].">
      <j1 rule="hyper" parents="504 19685 20315"/>
    </justification>
  </clause>

  <clause id="20317">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * w)) \ (K(x,K(y,z)) \ (u * (w * v5))) = L(v5,K(x,K(y,z)) * w,u)
    ]]></literal>
    <justification jstring="[para(19410(a,2),20305(a,1,2))].">
      <j1 rule="para" parents="19410 20305"/>
    </justification>
  </clause>

  <clause id="20318">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) \ (x * (y * (v5 * K(z,K(u,w))))) = L(v5,y,K(z,K(u,w)) * x)
    ]]></literal>
    <justification jstring="[para(19164(a,1),20308(a,1,2,2))].">
      <j1 rule="para" parents="19164 20308"/>
    </justification>
  </clause>

  <clause id="20319">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(K(u,w),v5)) = L(x,K(v5,K(u,w)) * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,7119,a(flip),b,20317,a)].">
      <j1 rule="hyper" parents="64 7119 20317"/>
    </justification>
  </clause>

  <clause id="20320">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,K(w,v5))) = L(x,K(v5,K(u,w)) * y,z)
    ]]></literal>
    <justification jstring="[para(8092(a,1),20319(a,1,3))].">
      <j1 rule="para" parents="8092 20319"/>
    </justification>
  </clause>

  <clause id="20321">
    <literal><![CDATA[
      L(x,K(y,K(z,u)) * w,v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(19200,a,20320,a),flip(a)].">
      <j1 rule="hyper" parents="19200 20320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20322">
    <literal><![CDATA[
      L(x,K(y,K(z,u)),w) = x
    ]]></literal>
    <justification jstring="[hyper(616,a,20321,a),flip(a)].">
      <j1 rule="hyper" parents="616 20321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20325">
    <literal><![CDATA[
      L(x,y * K(z,K(u,w)),v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(6823(a,1),20321(a,1,2))].">
      <j1 rule="para" parents="6823 20321"/>
    </justification>
  </clause>

  <clause id="20326">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(y,z),w)
    ]]></literal>
    <justification jstring="[para(7504(a,1),20321(a,1,2))].">
      <j1 rule="para" parents="7504 20321"/>
    </justification>
  </clause>

  <clause id="20327">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (K(y,K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(1960,a,20322,a),flip(a)].">
      <j1 rule="hyper" parents="1960 20322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20328">
    <literal><![CDATA[
      (x * K(y,K(z,u))) \ w = K(y,K(z,u)) \ (x \ w)
    ]]></literal>
    <justification jstring="[hyper(710,a,20322,a),flip(a)].">
      <j1 rule="hyper" parents="710 20322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20329">
    <literal><![CDATA[
      R(x,K(y,K(z,u)),w) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,18806,a,b,20322,a)].">
      <j1 rule="hyper" parents="64 18806 20322"/>
    </justification>
  </clause>

  <clause id="20330">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) \ v5 = K(z,K(u,w)) * ((x * y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,20307,a(flip),b,20322,a)].">
      <j1 rule="hyper" parents="64 20307 20322"/>
    </justification>
  </clause>

  <clause id="20331">
    <literal><![CDATA[
      (x / (K(y,K(z,u)) * w)) * K(y,K(z,u)) = x / w
    ]]></literal>
    <justification jstring="[hyper(225,a,20322,a(flip),b,15006,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 20322 15006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20332">
    <literal><![CDATA[
      ((x * y) * (K(z,K(u,w)) * v5)) / ((y * K(z,K(u,w))) * v5) = R(x,R(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(20329(a,1),661(a,1,1,1,2))].">
      <j1 rule="para" parents="20329 661"/>
    </justification>
  </clause>

  <clause id="20333">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),v5) = L(x,y \ (w * K(z,u)),v5)
    ]]></literal>
    <justification jstring="[para(14934(a,1),20325(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14934 20325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20335">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11788,a,b,20326,a),flip(a)].">
      <j1 rule="hyper" parents="373 11788 20326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20336">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,18810,a(flip),b,20326,a),flip(a)].">
      <j1 rule="hyper" parents="64 18810 20326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20337">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(20335(a,2),11858(a,1))].">
      <j1 rule="para" parents="20335 11858"/>
    </justification>
  </clause>

  <clause id="20338">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(x,T(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      L(z * K(x,K(y,u)),K(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(18808(a,2),20337(a,1))].">
      <j1 rule="para" parents="18808 20337"/>
    </justification>
  </clause>

  <clause id="20339">
    <literal><![CDATA[
      (x * (y * (K(z,K(u,w)) * v5))) \ ((x * (y * K(z,K(u,w)))) * v5) = a(x,y * K(z,K(u,w)),v5)
    ]]></literal>
    <justification jstring="[para(20327(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="20327 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20340">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ (((x * K(y,K(z,u))) * w) * v5) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(20327(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="20327 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20341">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * ((v6 * (z * K(u,K(w,v5)))) / v6))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[para(20327(a,1),18199(a,1,2,2,1))].">
      <j1 rule="para" parents="20327 18199"/>
    </justification>
  </clause>

  <clause id="20342">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) * v5 = (x * y) * (K(z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(19164(a,1),20327(a,1,1))].">
      <j1 rule="para" parents="19164 20327"/>
    </justification>
  </clause>

  <clause id="20343">
    <literal><![CDATA[
      (x * K(y,K(z,u))) \ w = (x \ w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17330,a(flip),b,20328,a),flip(a)].">
      <j1 rule="hyper" parents="373 17330 20328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20344">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(y,x) \ u) = K(y,T(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(8136(a,1),20328(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8136 20328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20345">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = K(x,K(y,z)) \ (u \ w)
    ]]></literal>
    <justification jstring="[para(17330(a,2),20328(a,1,1))].">
      <j1 rule="para" parents="17330 20328"/>
    </justification>
  </clause>

  <clause id="20346">
    <literal><![CDATA[
      x / (K(y,K(z,u)) * w) = K(y,K(z,u)) \ (x / w)
    ]]></literal>
    <justification jstring="[hyper(139,a,20331,a(flip),b,17161,a),flip(a)].">
      <j1 rule="hyper" parents="139 20331 17161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20347">
    <literal><![CDATA[
      x / (y * K(z,K(u,w))) = (x / y) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(225,a,221,a(flip),b,20343,a)].">
      <j1 rule="hyper" parents="225 221 20343"/>
    </justification>
  </clause>

  <clause id="20348">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w = (u \ w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(17161(a,2),20343(a,1,1))].">
      <j1 rule="para" parents="17161 20343"/>
    </justification>
  </clause>

  <clause id="20349">
    <literal><![CDATA[
      (x * K(y,z)) * L(u,x,K(y,z)) = K(z,T(y,x)) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11633,a(flip),b,20344,a)].">
      <j1 rule="hyper" parents="64 11633 20344"/>
    </justification>
  </clause>

  <clause id="20350">
    <literal><![CDATA[
      K(K(x,T(y,z)) \ u,w) = K(K(x,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(20344(a,1),17978(a,1,1))].">
      <j1 rule="para" parents="20344 17978"/>
    </justification>
  </clause>

  <clause id="20351">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u \ w) = u \ (K(x,K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19385,a(flip),b,20345,a),flip(a)].">
      <j1 rule="hyper" parents="64 19385 20345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20352">
    <literal><![CDATA[
      K(x,(K(y,K(z,u)) \ w) \ v5) = K(x,w \ v5)
    ]]></literal>
    <justification jstring="[para(20345(a,2),17923(a,1,2))].">
      <j1 rule="para" parents="20345 17923"/>
    </justification>
  </clause>

  <clause id="20353">
    <literal><![CDATA[
      K(x,(y * T(z,K(u,w))) \ v5) = K(x,(y * z) \ v5)
    ]]></literal>
    <justification jstring="[para(17405(a,1),20352(a,1,2,1))].">
      <j1 rule="para" parents="17405 20352"/>
    </justification>
  </clause>

  <clause id="20354">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)) * w,v5) \ v6) = K(x,T(y * w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(17648(a,1),20352(a,1,2,1))].">
      <j1 rule="para" parents="17648 20352"/>
    </justification>
  </clause>

  <clause id="20355">
    <literal><![CDATA[
      K(x,y \ (K(z,K(u,w)) \ v5)) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(19384(a,1),20352(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19384 20352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20356">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,K(w,v5)))) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(17404(a,1),20355(a,1,2,2))].">
      <j1 rule="para" parents="17404 20355"/>
    </justification>
  </clause>

  <clause id="20357">
    <literal><![CDATA[
      K(x,y \ ((z / K(u,w)) \ (v5 * (K(u,w) \ z)))) = K(x,y \ T(v5,z / K(u,w)))
    ]]></literal>
    <justification jstring="[para(17612(a,1),20355(a,1,2,2))].">
      <j1 rule="para" parents="17612 20355"/>
    </justification>
  </clause>

  <clause id="20358">
    <literal><![CDATA[
      K(x,y \ (K(z,T(u,w)) \ v5)) = K(x,y \ (K(z,u) \ v5))
    ]]></literal>
    <justification jstring="[para(20344(a,1),20355(a,1,2,2))].">
      <j1 rule="para" parents="20344 20355"/>
    </justification>
  </clause>

  <clause id="20359">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / (K(x,K(y,z)) \ w)) = u / w
    ]]></literal>
    <justification jstring="[para(10(a,1),20346(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 20346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20360">
    <literal><![CDATA[
      x / T(y * K(z,K(u,w)),v5) = (x / T(y,v5)) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(17603(a,2),20347(a,1,2))].">
      <j1 rule="para" parents="17603 20347"/>
    </justification>
  </clause>

  <clause id="20361">
    <literal><![CDATA[
      K(x,(y * (K(z,u) \ w)) \ v5) = K(x,(y * (w * K(u,z))) \ v5)
    ]]></literal>
    <justification jstring="[para(8352(a,1),20353(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="8352 20353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20362">
    <literal><![CDATA[
      K(x,y \ (K(z / u,w) \ v5)) = K(x,y \ (K(u \ z,w) \ v5))
    ]]></literal>
    <justification jstring="[para(7874(a,1),20358(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7874 20358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20364">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * T(u,K(x,y))) = (u * z) / (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17639,a,b,20336,a)].">
      <j1 rule="hyper" parents="64 17639 20336"/>
    </justification>
  </clause>

  <clause id="20365">
    <literal><![CDATA[
      a(x,K(y,T(z,u)) \ (u * (w / u)),x) = a(x,w * K(z,y),x)
    ]]></literal>
    <justification jstring="[para(20349(a,1),16659(a,1,2))].">
      <j1 rule="para" parents="20349 16659"/>
    </justification>
  </clause>

  <clause id="20367">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ v5 = K(y,K(z,u)) * ((x * w) \ v5)
    ]]></literal>
    <justification jstring="[para(17161(a,2),20330(a,1,1,2))].">
      <j1 rule="para" parents="17161 20330"/>
    </justification>
  </clause>

  <clause id="20368">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) * v5 = (x * w) * (K(y,K(z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(17161(a,2),20342(a,1,1,2))].">
      <j1 rule="para" parents="17161 20342"/>
    </justification>
  </clause>

  <clause id="20369">
    <literal><![CDATA[
      K(x,T((T(y,z) \ 1) \ z,u) \ w) = K(x,T(T(y,K(v5,v6)) * (((y \ 1) \ z) / y),u) \ w)
    ]]></literal>
    <justification jstring="[para(7189(a,2),20354(a,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7189 20354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20370">
    <literal><![CDATA[
      K(x,y / T(z * K(u,K(w,v5)),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,v6)) = v7
    ]]></literal>
    <justification jstring="[para(20360(a,2),17922(a,1,2))].">
      <j1 rule="para" parents="20360 17922"/>
    </justification>
  </clause>

  <clause id="20371">
    <literal><![CDATA[
      K(x,y \ (K(x \ y,z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(20362(a,1),19422(a,1))].">
      <j1 rule="para" parents="20362 19422"/>
    </justification>
  </clause>

  <clause id="20372">
    <literal><![CDATA[
      K(x,y \ ((z * K(u,w)) \ (v5 * (K(w,u) \ z)))) = K(x,y \ T(v5,z / K(w,u)))
    ]]></literal>
    <justification jstring="[para(6878(a,1),20357(a,1,2,2,1))].">
      <j1 rule="para" parents="6878 20357"/>
    </justification>
  </clause>

  <clause id="20373">
    <literal><![CDATA[
      K(x,y \ (z \ T(u * z,K(w,v5)))) = K(x,y \ T(u,z / K(v5,w)))
    ]]></literal>
    <justification jstring="[para(18668(a,1),20372(a,1,2,2))].">
      <j1 rule="para" parents="18668 20372"/>
    </justification>
  </clause>

  <clause id="20374">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ (u \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20356,a(flip),b,20373,a),flip(a)].">
      <j1 rule="hyper" parents="64 20356 20373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20376">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(22(a,2),20374(a,2,2,2))].">
      <j1 rule="para" parents="22 20374"/>
    </justification>
  </clause>

  <clause id="20377">
    <literal><![CDATA[
      K(x,y \ T(z,u * K(w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),20376(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 20376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20378">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w / v5))) = K(x,y \ T(z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(6904(a,1),20376(a,1,2,2,2))].">
      <j1 rule="para" parents="6904 20376"/>
    </justification>
  </clause>

  <clause id="20379">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w) * v5)) = K(x,y \ T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(18091,a,20377,a)].">
      <j1 rule="hyper" parents="18091 20377"/>
    </justification>
  </clause>

  <clause id="20380">
    <literal><![CDATA[
      T(x,y \ T(z,u * K(w,v5))) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(143,a,20377,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 20377 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20381">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ T(y,z)) = K(x,((z * K(u,w)) * y) \ y)
    ]]></literal>
    <justification jstring="[para(6981(a,1),20377(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6981 20377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20382">
    <literal><![CDATA[
      K(x,y \ T(z,T(u,w) * v5)) = K(x,y \ T(z,u * v5))
    ]]></literal>
    <justification jstring="[para(6570(a,1),20377(a,1,2,2,2))].">
      <j1 rule="para" parents="6570 20377"/>
    </justification>
  </clause>

  <clause id="20383">
    <literal><![CDATA[
      K(x,R(y / z,z,y \ T(u,K(w,v5) * v6)) \ T(u,v6)) = K(x,z * (y \ T(u,K(w,v5) * v6)))
    ]]></literal>
    <justification jstring="[para(684(a,1),20379(a,1,2)),flip(a)].">
      <j1 rule="para" parents="684 20379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20384">
    <literal><![CDATA[
      T(x,T(y * K(z,u),w) \ T(v5,y)) = T(x,v5 / T(y * K(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18060,a(flip),b,20380,a),flip(a)].">
      <j1 rule="hyper" parents="64 18060 20380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20385">
    <literal><![CDATA[
      K(x,y \ T(z,u * T(w,v5))) = K(x,y \ T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(18091,a,20382,a)].">
      <j1 rule="hyper" parents="18091 20382"/>
    </justification>
  </clause>

  <clause id="20386">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) \ w) = K(x,(y * K(z,u)) \ K(w,y))
    ]]></literal>
    <justification jstring="[hyper(7115,a,20381,a),flip(a)].">
      <j1 rule="hyper" parents="7115 20381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20387">
    <literal><![CDATA[
      T(x,K(y,z) * (T(u,w) \ T(v5,u))) = T(x,v5 / T(u * K(z,y),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,20036,a(flip),b,20384,a)].">
      <j1 rule="hyper" parents="64 20036 20384"/>
    </justification>
  </clause>

  <clause id="20388">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),v5)) = T(x,K(w,u) * (y / T(z,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18495,a(flip),b,20387,a),flip(a)].">
      <j1 rule="hyper" parents="64 18495 20387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20389">
    <literal><![CDATA[
      T(x,K(y,z) * (u / T(w,v5))) = T(x,u * T(w \ K(y,z),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18441,a(flip),b,20388,a),flip(a)].">
      <j1 rule="hyper" parents="64 18441 20388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20390">
    <literal><![CDATA[
      T(x,K(y \ z,u) * (w / T(y,z))) = T(x,w / (T(y \ z,u) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13430,a(flip),b,20388,a),flip(a)].">
      <j1 rule="hyper" parents="64 13430 20388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20391">
    <literal><![CDATA[
      T(x,K(y * z,u) * (w / T(z,y))) = T(x,w / (T(z \ y,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(17891,a,20390,a)].">
      <j1 rule="hyper" parents="17891 20390"/>
    </justification>
  </clause>

  <clause id="20392">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (u * (w * (v5 * K(x,K(y,z))))) = L(v5,w,K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(19166(a,2),20318(a,1,1))].">
      <j1 rule="para" parents="19166 20318"/>
    </justification>
  </clause>

  <clause id="20393">
    <literal><![CDATA[
      ((x * y) \ (x * (y * (z * K(u,K(w,v5)))))) * K(u,K(w,v5)) = L(z,y,K(u,K(w,v5)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,20348,a(flip),b,20392,a)].">
      <j1 rule="hyper" parents="64 20348 20392"/>
    </justification>
  </clause>

  <clause id="20394">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) * K(y,((z * u) \ w) \ x) = K(y,x / (T(u * z,u) \ w))
    ]]></literal>
    <justification jstring="[para(13389(a,1),19445(a,1,2))].">
      <j1 rule="para" parents="13389 19445"/>
    </justification>
  </clause>

  <clause id="20395">
    <literal><![CDATA[
      K(x,y / (T(z * u,z) \ w)) = K(x,y / ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19444,a(flip),b,20394,a),flip(a)].">
      <j1 rule="hyper" parents="64 19444 20394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20396">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * ((v5 \ z) / z))) = K(x,y * T(v5 \ (z * K(u,w)),z))
    ]]></literal>
    <justification jstring="[hyper(18538,a,19682,a),flip(a)].">
      <j1 rule="hyper" parents="18538 19682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20398">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * ((v5 \ z) / z))) = K(x,y * (z / (K(w,u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,20147,a(flip),b,20396,a),flip(a)].">
      <j1 rule="hyper" parents="373 20147 20396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20399">
    <literal><![CDATA[
      a(x,(y \ T(z,K(u,w))) \ ((K(u,w) \ y) \ v5),x) = a(x,(y * K(w,u)) \ ((z / y) \ v5),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13702,a(flip),b,19725,a),flip(a)].">
      <j1 rule="hyper" parents="373 13702 19725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20400">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (K(z,x) * y) * (y \ u)
    ]]></literal>
    <justification jstring="[para(5923(a,1),19737(a,2,1,1))].">
      <j1 rule="para" parents="5923 19737"/>
    </justification>
  </clause>

  <clause id="20401">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((T(x,z) * (y * K(x,z))) \ u) = (K(z,x) * y) * (y \ u)
    ]]></literal>
    <justification jstring="[para(5755(a,1),20400(a,1,2,1))].">
      <j1 rule="para" parents="5755 20400"/>
    </justification>
  </clause>

  <clause id="20402">
    <literal><![CDATA[
      (K(x,y) * (z * K(y,x))) * ((z * K(y,x)) \ u) = (K(x,y) * z) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(19736,a,20401,a)].">
      <j1 rule="hyper" parents="19736 20401"/>
    </justification>
  </clause>

  <clause id="20403">
    <literal><![CDATA[
      T(x,K(y,z)) * ((x * K(y,z)) \ u) = (K(z,y) * x) * (x \ u)
    ]]></literal>
    <justification jstring="[para(6175(a,1),20402(a,1,1))].">
      <j1 rule="para" parents="6175 20402"/>
    </justification>
  </clause>

  <clause id="20404">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * ((K(y,x) * z) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(10963,a,20403,a)].">
      <j1 rule="hyper" parents="10963 20403"/>
    </justification>
  </clause>

  <clause id="20405">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      z * ((K(y,x) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(20403(a,1),10849(a,1))].">
      <j1 rule="para" parents="20403 10849"/>
    </justification>
  </clause>

  <clause id="20406">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * u) = z \ ((K(y,x) * z) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),20404(a,1,2,2))].">
      <j1 rule="para" parents="9 20404"/>
    </justification>
  </clause>

  <clause id="20407">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(z,y))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,20364,a(flip),b,20406,a),flip(a)].">
      <j1 rule="hyper" parents="64 20364 20406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20408">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * (K(z,T(y,x)) * u)) = L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10993,a(flip),b,20406,a),flip(a)].">
      <j1 rule="hyper" parents="64 10993 20406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20409">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * (K(z,y) * u)) = L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(10842(a,1),20408(a,1,2))].">
      <j1 rule="para" parents="10842 20408"/>
    </justification>
  </clause>

  <clause id="20410">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6900,a,20409,a)].">
      <j1 rule="hyper" parents="6900 20409"/>
    </justification>
  </clause>

  <clause id="20411">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * u) = x * L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(157,a,20409,a),flip(a)].">
      <j1 rule="hyper" parents="157 20409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20412">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[hyper(64,a,18809,a(flip),b,20410,a),flip(a)].">
      <j1 rule="hyper" parents="64 18809 20410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20413">
    <literal><![CDATA[
      L(x,K(y,z),u \ T(z,y)) = L(x,K(y,z),u \ z)
    ]]></literal>
    <justification jstring="[para(15021(a,1),20410(a,1,3))].">
      <j1 rule="para" parents="15021 20410"/>
    </justification>
  </clause>

  <clause id="20414">
    <literal><![CDATA[
      L(x,K(y,z),u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(20410(a,1),18813(a,1,1))].">
      <j1 rule="para" parents="20410 18813"/>
    </justification>
  </clause>

  <clause id="20415">
    <literal><![CDATA[
      x * L(K(y,z) * u,K(z,y),x) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6161(a,1),20411(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6161 20411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20416">
    <literal><![CDATA[
      L(K(x,y) * z,K(y,x),u) * u = T(z,K(y,x)) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(7808(a,1),20414(a,2,1))].">
      <j1 rule="para" parents="7808 20414"/>
    </justification>
  </clause>

  <clause id="20417">
    <literal><![CDATA[
      (x * K(y,z)) * (x \ u) = x * ((x * K(z,y)) \ u)
    ]]></literal>
    <justification jstring="[para(6191(a,1),20415(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6191 20415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20418">
    <literal><![CDATA[
      K(x,y * (z \ T((u * K(w,v5)) * v6,L(K(w,v5) * v6,K(v5,w),u)))) = K(x,y * (z \ (L(K(w,v5) * v6,K(v5,w),u) * u)))
    ]]></literal>
    <justification jstring="[para(20415(a,1),16696(a,1,2,2,2,1))].">
      <j1 rule="para" parents="20415 16696"/>
    </justification>
  </clause>

  <clause id="20419">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * L(u \ 1,u,u \ (x * K(z,y)))) = x \ ((x * K(z,y)) / u)
    ]]></literal>
    <justification jstring="[hyper(139,a,10976,a,b,20417,a)].">
      <j1 rule="hyper" parents="139 10976 20417"/>
    </justification>
  </clause>

  <clause id="20420">
    <literal><![CDATA[
      (x * (y * K(z,u))) / y = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,20336,a(flip),b,20412,a),flip(a)].">
      <j1 rule="hyper" parents="64 20336 20412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20421">
    <literal><![CDATA[
      (x / (y * K(z,u))) * y = (x / y) * (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(144,a,170,a(flip),b,20420,a)].">
      <j1 rule="hyper" parents="144 170 20420"/>
    </justification>
  </clause>

  <clause id="20422">
    <literal><![CDATA[
      (K(x,L(y,z * (u * K(w,v5)),u)) * (z * (u * K(w,v5)))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(20420(a,1),15673(a,2,2))].">
      <j1 rule="para" parents="20420 15673"/>
    </justification>
  </clause>

  <clause id="20423">
    <literal><![CDATA[
      (x / ((y \ 1) * K(z,u))) * (y \ 1) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,14522,a(flip),b,20421,a),flip(a)].">
      <j1 rule="hyper" parents="373 14522 20421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20424">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = (x / (K(u,z) * y)) * y
    ]]></literal>
    <justification jstring="[para(7437(a,1),20421(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7437 20421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20425">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * u = (x / u) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(7893,a,20424,a),flip(a)].">
      <j1 rule="hyper" parents="7893 20424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20426">
    <literal><![CDATA[
      (x / (K(y,z) * (1 / u))) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[hyper(373,a,14386,a(flip),b,20425,a),flip(a)].">
      <j1 rule="hyper" parents="373 14386 20425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20427">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(y,z))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(8153(a,1),20407(a,1,2,2))].">
      <j1 rule="para" parents="8153 20407"/>
    </justification>
  </clause>

  <clause id="20428">
    <literal><![CDATA[
      x \ ((K(y,z) * (x * K(u,K(y,z)))) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(7175(a,2),20427(a,1,2))].">
      <j1 rule="para" parents="7175 20427"/>
    </justification>
  </clause>

  <clause id="20429">
    <literal><![CDATA[
      (x / (K(y,z) / u)) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(14366(a,1),20426(a,1,1,2))].">
      <j1 rule="para" parents="14366 20426"/>
    </justification>
  </clause>

  <clause id="20430">
    <literal><![CDATA[
      x \ ((K(y,z) * (x * K(y,K(z,u)))) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(8110(a,2),20428(a,1,2,1,2,2))].">
      <j1 rule="para" parents="8110 20428"/>
    </justification>
  </clause>

  <clause id="20431">
    <literal><![CDATA[
      x \ ((K(y,T(z,u)) * x) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(17344(a,1),20430(a,1,2,1))].">
      <j1 rule="para" parents="17344 20430"/>
    </justification>
  </clause>

  <clause id="20432">
    <literal><![CDATA[
      (x * y) / (y * K(z,T(u,x))) = y \ ((K(u,z) * y) * x)
    ]]></literal>
    <justification jstring="[para(8205(a,1),20431(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="8205 20431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20433">
    <literal><![CDATA[
      (x * K(y,z)) \ (x / u) = x \ ((x * K(z,y)) / u)
    ]]></literal>
    <justification jstring="[para(19782(a,1),20419(a,1,2))].">
      <j1 rule="para" parents="19782 20419"/>
    </justification>
  </clause>

  <clause id="20435">
    <literal><![CDATA[
      x / ((y / x) * (x * K(z,u))) = x * (x \ ((x * K(u,z)) / y))
    ]]></literal>
    <justification jstring="[para(20433(a,1),19859(a,2,2))].">
      <j1 rule="para" parents="20433 19859"/>
    </justification>
  </clause>

  <clause id="20436">
    <literal><![CDATA[
      x / ((y / x) * (x * K(z,u))) = (x * K(u,z)) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,10,a(flip),b,20435,a),flip(a)].">
      <j1 rule="hyper" parents="373 10 20435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20438">
    <literal><![CDATA[
      K(x,(T(y \ (K(z,u) * w),K(z,u) * y) / v5) * v6) = K(x,((w / (K(u,z) * y)) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,20263,a(flip),b,19993,a)].">
      <j1 rule="hyper" parents="64 20263 19993"/>
    </justification>
  </clause>

  <clause id="20439">
    <literal><![CDATA[
      T((x * T(y,y \ z)) \ T(y,y \ u),(x * y) \ T(T(y,u),z)) = (x * T(y,y \ z)) \ ((y \ u) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13420,a(flip),b,20032,a)].">
      <j1 rule="hyper" parents="64 13420 20032"/>
    </justification>
  </clause>

  <clause id="20440">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u \ 1)) = T(x,((u * u) * (T(z,u \ 1) \ 1)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,19710,a,b,20298,a)].">
      <j1 rule="hyper" parents="64 19710 20298"/>
    </justification>
  </clause>

  <clause id="20441">
    <literal><![CDATA[
      K(x,T((T(y,z) \ 1) \ z,u) \ w) = K(x,(y * (T((y \ 1) \ z,u) / T(y,K(v5,v6)))) \ w)
    ]]></literal>
    <justification jstring="[para(19477(a,1),20369(a,2,2,1))].">
      <j1 rule="para" parents="19477 20369"/>
    </justification>
  </clause>

  <clause id="20442">
    <literal><![CDATA[
      a(x,(y \ T(z,K(u,w))) \ ((K(u,w) \ y) \ v5),x) = a(x,K(w,u) \ (y \ ((z / y) \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13702,a(flip),b,20399,a),flip(a)].">
      <j1 rule="hyper" parents="373 13702 20399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20443">
    <literal><![CDATA[
      K(x,(T(y \ (K(z,u) * w),y) / v5) * v6) = K(x,((w / (K(u,z) * y)) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,20075,a(flip),b,20438,a)].">
      <j1 rule="hyper" parents="64 20075 20438"/>
    </justification>
  </clause>

  <clause id="20445">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) / w) / v5) * v6) = K(x,((u / (K(z,y) * w)) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,19990,a(flip),b,20443,a)].">
      <j1 rule="hyper" parents="64 19990 20443"/>
    </justification>
  </clause>

  <clause id="20446">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,((u * u) * (T(z,u \ 1) \ 1)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,18716,a(flip),b,20440,a)].">
      <j1 rule="hyper" parents="64 18716 20440"/>
    </justification>
  </clause>

  <clause id="20447">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,(u * u) * ((T(z,u \ 1) \ 1) * y))
    ]]></literal>
    <justification jstring="[para(33(a,1),20446(a,2,2))].">
      <j1 rule="para" parents="33 20446"/>
    </justification>
  </clause>

  <clause id="20448">
    <literal><![CDATA[
      a(x,(y \ T(z,K(u,w))) \ ((K(w,u) \ y) \ v5),x) = a(x,K(u,w) \ (y \ ((z / y) \ v5)),x)
    ]]></literal>
    <justification jstring="[para(8153(a,1),20442(a,1,2,1,2))].">
      <j1 rule="para" parents="8153 20442"/>
    </justification>
  </clause>

  <clause id="20449">
    <literal><![CDATA[
      a(x,T(y,K(z,u)) \ (w * ((K(u,z) \ w) \ v5)),x) = a(x,K(z,u) \ (w \ ((y / w) \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13703,a(flip),b,20448,a)].">
      <j1 rule="hyper" parents="64 13703 20448"/>
    </justification>
  </clause>

  <clause id="20450">
    <literal><![CDATA[
      K((x * K(y,z)) * L(u,x,K(y,z)),w) = K(w,K(z,y) \ (u * x)) \ K(w,K(u,x))
    ]]></literal>
    <justification jstring="[para(18291(a,1),19262(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18291 19262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20453">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(u,w)) = K(K(y,T(z,w)) \ (w * u),x)
    ]]></literal>
    <justification jstring="[para(20349(a,1),20450(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20349 20450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20454">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) \ K(x,K(u,w)) = K(K(y,z) \ (w * u),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,20350,a(flip),b,20453,a),flip(a)].">
      <j1 rule="hyper" parents="373 20350 20453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20456">
    <literal><![CDATA[
      K(x * (T(y,z) \ (y * u)),w) = K(K(y,z) \ (x * u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,20265,a,b,20454,a)].">
      <j1 rule="hyper" parents="64 20265 20454"/>
    </justification>
  </clause>

  <clause id="20457">
    <literal><![CDATA[
      K(K(x,y) \ (z * (u / x)),w) = K(z * (u / T(x,T(y,u))),w)
    ]]></literal>
    <justification jstring="[para(8680(a,1),20456(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8680 20456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20458">
    <literal><![CDATA[
      K(K(x,y) \ (z * (u / x)),w) = K(z * (u / T(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,18482,a(flip),b,20457,a),flip(a)].">
      <j1 rule="hyper" parents="373 18482 20457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20459">
    <literal><![CDATA[
      K(K(x,y) \ (z * (u / y)),w) = K(z * (u / T(y,x)),w)
    ]]></literal>
    <justification jstring="[hyper(17527,a,20458,a)].">
      <j1 rule="hyper" parents="17527 20458"/>
    </justification>
  </clause>

  <clause id="20461">
    <literal><![CDATA[
      K(x / T(y,z),u) \ K(u * (x / T(y,z)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[para(20459(a,1),18850(a,1,2))].">
      <j1 rule="para" parents="20459 18850"/>
    </justification>
  </clause>

  <clause id="20462">
    <literal><![CDATA[
      ((x / T(y,z)) * u) \ T(u * (x / T(y,z)),u) = a(u,y \ (K(y \ 1,z) \ x),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10846,a(flip),b,20461,a)].">
      <j1 rule="hyper" parents="64 10846 20461"/>
    </justification>
  </clause>

  <clause id="20463">
    <literal><![CDATA[
      a(x,y \ (K(y \ 1,z) \ u),x) = a(x,u / T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(11057,a,20462,a),flip(a)].">
      <j1 rule="hyper" parents="11057 20462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20464">
    <literal><![CDATA[
      a(x,y \ (K(y \ 1,z) \ u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,T(y,z) \ u,x) = w
    ]]></literal>
    <justification jstring="[para(20463(a,2),13204(a,1))].">
      <j1 rule="para" parents="20463 13204"/>
    </justification>
  </clause>

  <clause id="20467">
    <literal><![CDATA[
      K(x,y * ((K(z,z \ L(y,u,w)) * v5) / L(y,u,w))) = K(x,(T(L(y,u,w),z) \ v5) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,20273,a(flip),b,19458,a),flip(a)].">
      <j1 rule="hyper" parents="373 20273 19458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20468">
    <literal><![CDATA[
      K(x,y * ((K(z,z \ L(y,u,w)) * v5) / L(y,u,w))) = K(x,(L(T(y,z),u,w) \ v5) * y)
    ]]></literal>
    <justification jstring="[para(25(a,2),20467(a,2,2,1,1))].">
      <j1 rule="para" parents="25 20467"/>
    </justification>
  </clause>

  <clause id="20469">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,u / (((u \ z) \ 1) * (y \ u))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(15242(a,1),20306(a,1,2,2))].">
      <j1 rule="para" parents="15242 20306"/>
    </justification>
  </clause>

  <clause id="20470">
    <literal><![CDATA[
      (x * (y * (K(z,K(u,w)) * v5))) \ ((x * y) * (K(z,K(u,w)) * v5)) = a(x,y * K(z,K(u,w)),v5)
    ]]></literal>
    <justification jstring="[para(20342(a,1),20339(a,1,2))].">
      <j1 rule="para" parents="20342 20339"/>
    </justification>
  </clause>

  <clause id="20471">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ ((x * (K(y,K(z,u)) * w)) * v5) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(20327(a,1),20340(a,1,2,1))].">
      <j1 rule="para" parents="20327 20340"/>
    </justification>
  </clause>

  <clause id="20472">
    <literal><![CDATA[
      a(x,y * K(z,K(u,w)),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,K(u,w)) * v5) = v6
    ]]></literal>
    <justification jstring="[para(20470(a,1),959(a,1))].">
      <j1 rule="para" parents="20470 959"/>
    </justification>
  </clause>

  <clause id="20473">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * (w * v5))) \ ((x * w) * (K(y,K(z,u)) * v5)) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(20368(a,1),20471(a,1,2))].">
      <j1 rule="para" parents="20368 20471"/>
    </justification>
  </clause>

  <clause id="20474">
    <literal><![CDATA[
      ((x * (K(y,K(z,u)) * (w * v5))) \ ((x * w) * v5)) * K(y,K(z,u)) = a(x * K(y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,19615,a(flip),b,20473,a)].">
      <j1 rule="hyper" parents="64 19615 20473"/>
    </justification>
  </clause>

  <clause id="20475">
    <literal><![CDATA[
      (K(x,K(y,z)) * ((u * (w * v5)) \ ((u * w) * v5))) * K(x,K(y,z)) = a(u * K(x,K(y,z)),w,v5)
    ]]></literal>
    <justification jstring="[para(20367(a,1),20474(a,1,1))].">
      <j1 rule="para" parents="20367 20474"/>
    </justification>
  </clause>

  <clause id="20476">
    <literal><![CDATA[
      (K(x,K(y,z)) * a(u,w,v5)) * K(x,K(y,z)) = a(u * K(x,K(y,z)),w,v5)
    ]]></literal>
    <justification jstring="[para(14(a,2),20475(a,1,1,2))].">
      <j1 rule="para" parents="14 20475"/>
    </justification>
  </clause>

  <clause id="20477">
    <literal><![CDATA[
      a(x * K(y,K(z,u)),w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(17406,a,20476,a),flip(a)].">
      <j1 rule="hyper" parents="17406 20476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20479">
    <literal><![CDATA[
      a(T(x,T(y,z)),u,w) = a(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8027(a,1),20477(a,1,1))].">
      <j1 rule="para" parents="8027 20477"/>
    </justification>
  </clause>

  <clause id="20481">
    <literal><![CDATA[
      a(T(x * ((x / y) / x),x),z,u) = a(x * ((y \ x) / x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13117,a(flip),b,20479,a),flip(a)].">
      <j1 rule="hyper" parents="64 13117 20479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20483">
    <literal><![CDATA[
      a(x * ((y \ x) / x),z,u) = a(x / y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13116,a(flip),b,20481,a),flip(a)].">
      <j1 rule="hyper" parents="64 13116 20481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20485">
    <literal><![CDATA[
      a(T(x,y) * ((z \ x) / x),u,w) = a(T(x,y) / z,u,w)
    ]]></literal>
    <justification jstring="[para(15027(a,1),20483(a,1,1,2))].">
      <j1 rule="para" parents="15027 20483"/>
    </justification>
  </clause>

  <clause id="20486">
    <literal><![CDATA[
      a(T(x,y) * ((z \ x) / x),u,w) = a(T(x,x \ y) / z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13123,a(flip),b,20485,a)].">
      <j1 rule="hyper" parents="64 13123 20485"/>
    </justification>
  </clause>

  <clause id="20487">
    <literal><![CDATA[
      a(T(x,x \ y) / z,u,w) = a(T(x,y) / z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,20485,a(flip),b,20486,a),flip(a)].">
      <j1 rule="hyper" parents="64 20485 20486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20488">
    <literal><![CDATA[
      (x * y) / a(T(x,z) / z,T(z,x),y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(20487(a,1),13845(a,1,2))].">
      <j1 rule="para" parents="20487 13845"/>
    </justification>
  </clause>

  <clause id="20489">
    <literal><![CDATA[
      (x * y) / a(z \ x,T(z,x),y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(13115(a,1),20488(a,1,2))].">
      <j1 rule="para" parents="13115 20488"/>
    </justification>
  </clause>

  <clause id="20490">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(15699(a,1),20489(a,1,2))].">
      <j1 rule="para" parents="15699 20489"/>
    </justification>
  </clause>

  <clause id="20491">
    <literal><![CDATA[
      (x / ((x \ y) * x)) * (((x \ y) * x) * z) = (x / y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1290,a,20490,a),flip(a)].">
      <j1 rule="hyper" parents="1290 20490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20492">
    <literal><![CDATA[
      ((x / ((x \ y) * x)) * (((x \ y) * x) * z)) * u = ((x / y) * (y * z)) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,20491,a,b,11,a)].">
      <j1 rule="hyper" parents="144 20491 11"/>
    </justification>
  </clause>

  <clause id="20493">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * w = (x * K(z,L(u,x,(x \ y) \ 1))) * w
    ]]></literal>
    <justification jstring="[para(19776(a,1),20492(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19776 20492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20494">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * w = (x * K(z,L(u,x,y \ x))) * w
    ]]></literal>
    <justification jstring="[para(15958(a,1),20493(a,2,1,2))].">
      <j1 rule="para" parents="15958 20493"/>
    </justification>
  </clause>

  <clause id="20495">
    <literal><![CDATA[
      K(x,((y / (K(z,u) * w)) / T(v5,y * (w \ K(u,z)))) * v6) = K(x,(v5 \ ((K(u,z) * y) / w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,20445,a(flip),b,19448,a)].">
      <j1 rule="hyper" parents="64 20445 19448"/>
    </justification>
  </clause>

  <clause id="20496">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,y \ z)) = K(x,v5 / T(y \ (z * K(u,w)),K(v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20379,a(flip),b,19951,a)].">
      <j1 rule="hyper" parents="64 20379 19951"/>
    </justification>
  </clause>

  <clause id="20498">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,y \ z)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 / (y \ (z * K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(20496(a,2),18009(a,1))].">
      <j1 rule="para" parents="20496 18009"/>
    </justification>
  </clause>

  <clause id="20499">
    <literal><![CDATA[
      T(x * K(T(y,K(z,u)),K(w,v5) \ (y \ x)),K(w,v5)) = y * T(x / y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(6840(a,1),19985(a,1,1))].">
      <j1 rule="para" parents="6840 19985"/>
    </justification>
  </clause>

  <clause id="20501">
    <literal><![CDATA[
      T(x * K(y,K(z,u) \ (y \ x)),K(z,u)) = y * T(x / y,K(z,u))
    ]]></literal>
    <justification jstring="[para(2004(a,1),20499(a,1,1,2,1))].">
      <j1 rule="para" parents="2004 20499"/>
    </justification>
  </clause>

  <clause id="20502">
    <literal><![CDATA[
      T(K(x \ (y / K(z,u)),x) \ y,K(z,u)) = x * T(y / x,K(z,u))
    ]]></literal>
    <justification jstring="[para(10811(a,2),20501(a,1,1))].">
      <j1 rule="para" parents="10811 20501"/>
    </justification>
  </clause>

  <clause id="20503">
    <literal><![CDATA[
      T(K(x \ (y * K(z,u)),x) \ y,K(u,z)) = x * T(y / x,K(u,z))
    ]]></literal>
    <justification jstring="[para(6878(a,1),20502(a,1,1,1,1,2))].">
      <j1 rule="para" parents="6878 20502"/>
    </justification>
  </clause>

  <clause id="20504">
    <literal><![CDATA[
      T(K(x \ (K(y,z) \ u),x) \ u,K(y,z)) = x * T(u / x,K(y,z))
    ]]></literal>
    <justification jstring="[para(17999(a,2),20503(a,1,1,1))].">
      <j1 rule="para" parents="17999 20503"/>
    </justification>
  </clause>

  <clause id="20505">
    <literal><![CDATA[
      K(x \ (K(y,z) \ u),x) \ T(u,K(y,z)) = x * T(u / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18376,a(flip),b,20504,a)].">
      <j1 rule="hyper" parents="64 18376 20504"/>
    </justification>
  </clause>

  <clause id="20506">
    <literal><![CDATA[
      K(x,(K(y,T(z,u)) * (K(w,T(v5,v6)) \ (v7 * K(z,T(y,u))))) \ v8) = K(x,v7 \ (K(v5,T(w,v6)) \ v8))
    ]]></literal>
    <justification jstring="[para(19242(a,2),20262(a,1,2,1,2))].">
      <j1 rule="para" parents="19242 20262"/>
    </justification>
  </clause>

  <clause id="20507">
    <literal><![CDATA[
      K(x,(y \ ((K(z,u) * w) / v5)) * v6) = K(x,(y \ (w / (K(u,z) * v5))) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,17915,a(flip),b,20495,a),flip(a)].">
      <j1 rule="hyper" parents="64 17915 20495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20508">
    <literal><![CDATA[
      K(x,(y * K(z,T(u,w))) \ v5) = K(x,y \ (K(z,T(u,w)) \ v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),20506(a,1,2,1))].">
      <j1 rule="para" parents="10 20506"/>
    </justification>
  </clause>

  <clause id="20509">
    <literal><![CDATA[
      K(x,L(T(y,z * y) * u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(16873,a,19291,a)].">
      <j1 rule="hyper" parents="16873 19291"/>
    </justification>
  </clause>

  <clause id="20511">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(4683(a,1),20509(a,1,2,1,1))].">
      <j1 rule="para" parents="4683 20509"/>
    </justification>
  </clause>

  <clause id="20512">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(13609,a,20511,a)].">
      <j1 rule="hyper" parents="13609 20511"/>
    </justification>
  </clause>

  <clause id="20513">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * T(w,K(y,x) * v5)) / (K(x,L(y,z,u)) * w) = K(w,v5 * K(x,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(17451(a,1),19519(a,1,1))].">
      <j1 rule="para" parents="17451 19519"/>
    </justification>
  </clause>

  <clause id="20515">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,K(z,L(y,w,v5)))) = K(x,u * K(z,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(8370,a,20513,a)].">
      <j1 rule="hyper" parents="8370 20513"/>
    </justification>
  </clause>

  <clause id="20516">
    <literal><![CDATA[
      K(x,y * K(z,L(u,w,v5))) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(19176(a,1),20515(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19176 20515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20517">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,(y \ (z * u)) * K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19906,a(flip),b,20516,a)].">
      <j1 rule="hyper" parents="64 19906 20516"/>
    </justification>
  </clause>

  <clause id="20519">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) * w) \ v5) * K(z,y)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(20516(a,1),19918(a,1))].">
      <j1 rule="para" parents="20516 19918"/>
    </justification>
  </clause>

  <clause id="20521">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,K(w,v5) * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,17300,a,b,20517,a),flip(a)].">
      <j1 rule="hyper" parents="373 17300 20517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20522">
    <literal><![CDATA[
      K(x,(y \ (z * T(u,z))) * K(w,v5)) = K(x,y \ ((K(v5,w) * u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18542,a(flip),b,20517,a),flip(a)].">
      <j1 rule="hyper" parents="64 18542 20517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20523">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (w \ (v5 * u))) = K(x,w \ (v5 * (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[para(7879(a,1),20521(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7879 20521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20524">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) * v5)) = K(x,(y \ (w * v5)) * K(u,z))
    ]]></literal>
    <justification jstring="[para(115(a,1),20522(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="115 20522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20525">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) * v5)) = K(x,K(z,u) * (y \ (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,17300,a,b,20524,a),flip(a)].">
      <j1 rule="hyper" parents="373 17300 20524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20526">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) * w) \ (u * (w * v5))) * K(z,y)) = K(x,L(v5,w,K(y,z) * u))
    ]]></literal>
    <justification jstring="[para(18(a,2),20524(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 20524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20527">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y * w) * v5))) = K(x,u \ ((T(y,z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(5755(a,1),20525(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5755 20525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20528">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * v5))) = K(x,K(w,u) * (y \ (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(18034,a,20523,a),flip(a)].">
      <j1 rule="hyper" parents="18034 20523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20530">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,u) * (y \ (z * v5))) = v6
    ]]></literal>
    <justification jstring="[para(20523(a,1),18034(a,1))].">
      <j1 rule="para" parents="20523 18034"/>
    </justification>
  </clause>

  <clause id="20531">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * (v5 \ z)))) = K(x,u \ (w * (v5 \ T(z,y))))
    ]]></literal>
    <justification jstring="[hyper(19495,a,20528,a),flip(a)].">
      <j1 rule="hyper" parents="19495 20528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20533">
    <literal><![CDATA[
      K(x,y \ ((T(z,u * K(w,v5)) * u) * v6)) = K(x,y \ ((u * z) * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,20027,a(flip),b,20527,a),flip(a)].">
      <j1 rule="hyper" parents="64 20027 20527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20534">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * (w \ y))) = K(x,y \ (u * (w \ T(y,z))))
    ]]></literal>
    <justification jstring="[para(6157(a,1),20531(a,1,2))].">
      <j1 rule="para" parents="6157 20531"/>
    </justification>
  </clause>

  <clause id="20535">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) * u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(204(a,1),20533(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="204 20533"/>
    </justification>
  </clause>

  <clause id="20537">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(v5 * z) \ (v5 * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(20519,a,20526,a),flip(a)].">
      <j1 rule="hyper" parents="20519 20526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20538">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,L(y,z,v5))
    ]]></literal>
    <justification jstring="[para(18(a,2),20537(a,2,2))].">
      <j1 rule="para" parents="18 20537"/>
    </justification>
  </clause>

  <clause id="20539">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,K(z,u) * w)) = K(x,L(y,v5,w))
    ]]></literal>
    <justification jstring="[hyper(15550,a,20538,a)].">
      <j1 rule="hyper" parents="15550 20538"/>
    </justification>
  </clause>

  <clause id="20540">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(z * v5) / ((y \ z) * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,15569,a,b,20538,a),flip(a)].">
      <j1 rule="hyper" parents="373 15569 20538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20541">
    <literal><![CDATA[
      K(x,L(y,z,u * K(w,v5))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6823(a,1),20538(a,1,2,3))].">
      <j1 rule="para" parents="6823 20538"/>
    </justification>
  </clause>

  <clause id="20542">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * (K(w,v5) * u)) = (K(x,y) * z) * (K(w,v5) * u)
    ]]></literal>
    <justification jstring="[para(20538(a,1),15578(a,1,1))].">
      <j1 rule="para" parents="20538 15578"/>
    </justification>
  </clause>

  <clause id="20543">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,w)) = K(x,L(y,u / z,w * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16588,a(flip),b,20541,a),flip(a)].">
      <j1 rule="hyper" parents="64 16588 20541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20544">
    <literal><![CDATA[
      K(x,L(y,z,u * (w / v5))) = K(x,L(y,z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(6471(a,1),20541(a,1,2,3))].">
      <j1 rule="para" parents="6471 20541"/>
    </justification>
  </clause>

  <clause id="20545">
    <literal><![CDATA[
      K(x,L(y,z,u \ L(T(w,v5),v6,v7))) = K(x,L(y,z,u \ L(w,v6,v7)))
    ]]></literal>
    <justification jstring="[para(15043(a,1),20541(a,1,2,3))].">
      <j1 rule="para" parents="15043 20541"/>
    </justification>
  </clause>

  <clause id="20546">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = K(v5,x) * K(x,L(v5,y,z))
    ]]></literal>
    <justification jstring="[para(20541(a,1),15329(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20541 15329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20547">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * (u * K(w,v5))) = (K(x,y) * z) * (u * K(w,v5))
    ]]></literal>
    <justification jstring="[para(20541(a,1),15578(a,1,1))].">
      <j1 rule="para" parents="20541 15578"/>
    </justification>
  </clause>

  <clause id="20548">
    <literal><![CDATA[
      (K(x,L(y,z,K(u,w))) * z) / (K(v5,v6) * K(u,w)) = K(x,y) * (z / (K(u,w) * K(v5,v6)))
    ]]></literal>
    <justification jstring="[para(20541(a,1),17596(a,1,1,1))].">
      <j1 rule="para" parents="20541 17596"/>
    </justification>
  </clause>

  <clause id="20549">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = a(x,y,K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,15329,a(flip),b,20546,a),flip(a)].">
      <j1 rule="hyper" parents="373 15329 20546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20550">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20546(a,2),15416(a,1))].">
      <j1 rule="para" parents="20546 15416"/>
    </justification>
  </clause>

  <clause id="20551">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(15381,a,20549,a)].">
      <j1 rule="hyper" parents="15381 20549"/>
    </justification>
  </clause>

  <clause id="20552">
    <literal><![CDATA[
      a(x,y,K(z \ (u / w),v5)) = a(x,y,K(z \ (w \ u),v5))
    ]]></literal>
    <justification jstring="[para(15028(a,1),20549(a,1,3,1))].">
      <j1 rule="para" parents="15028 20549"/>
    </justification>
  </clause>

  <clause id="20553">
    <literal><![CDATA[
      a(x,y,K((z / u) \ w,v5)) = a(x,y,K((u \ z) \ w,v5))
    ]]></literal>
    <justification jstring="[para(18709(a,1),20549(a,1,3))].">
      <j1 rule="para" parents="18709 20549"/>
    </justification>
  </clause>

  <clause id="20554">
    <literal><![CDATA[
      a(x \ K(y,z),u,K(w,v5)) = a(w,u,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(19454,a,20551,a)].">
      <j1 rule="hyper" parents="19454 20551"/>
    </justification>
  </clause>

  <clause id="20555">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * v5)) = a(z,y,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,19312,a(flip),b,20551,a)].">
      <j1 rule="hyper" parents="64 19312 20551"/>
    </justification>
  </clause>

  <clause id="20556">
    <literal><![CDATA[
      L(1 / (x * K(y,z)),u,K(w,v5)) = a(w,u,K(x,v5)) / (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(20551(a,1),16614(a,2,1))].">
      <j1 rule="para" parents="20551 16614"/>
    </justification>
  </clause>

  <clause id="20557">
    <literal><![CDATA[
      a(x,y,K(z,u * (w * K(v5,v6)))) = a(z,y,K(w * u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,19935,a(flip),b,20555,a)].">
      <j1 rule="hyper" parents="64 19935 20555"/>
    </justification>
  </clause>

  <clause id="20558">
    <literal><![CDATA[
      a(x,y,K(z \ T(u,w),v5)) = a(v5,y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[para(6417(a,1),20555(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6417 20555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20559">
    <literal><![CDATA[
      T(x,a(K(y,z) * u,w,v5)) = x * a(v5,w,K(u,x))
    ]]></literal>
    <justification jstring="[para(20555(a,1),15305(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20555 15305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20560">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = x * T(a(x,y,K(w,v5)),K(w,v5) * y)
    ]]></literal>
    <justification jstring="[para(20555(a,1),18701(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20555 18701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20561">
    <literal><![CDATA[
      a(x,y,K((z / T(u,w)) \ w,v5)) = a(v5,y,K(x,(z / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19765,a,b,20558,a)].">
      <j1 rule="hyper" parents="64 19765 20558"/>
    </justification>
  </clause>

  <clause id="20562">
    <literal><![CDATA[
      T(x * y,a(K(z,u) * y,w,v5)) = (x * y) * a(v5,w,K(y,x))
    ]]></literal>
    <justification jstring="[para(12247(a,1),20559(a,2,2))].">
      <j1 rule="para" parents="12247 20559"/>
    </justification>
  </clause>

  <clause id="20563">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z * (w \ u),v5)) = v6
    ]]></literal>
    <justification jstring="[para(6471(a,1),20550(a,1,3,1))].">
      <j1 rule="para" parents="6471 20550"/>
    </justification>
  </clause>

  <clause id="20565">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5,u,K(z,w)) = v6
    ]]></literal>
    <justification jstring="[para(19309(a,2),20550(a,1))].">
      <j1 rule="para" parents="19309 20550"/>
    </justification>
  </clause>

  <clause id="20566">
    <literal><![CDATA[
      x * a(y,z,K(u \ (w \ v5),x)) = T(x,a(u \ (v5 / w),z,y))
    ]]></literal>
    <justification jstring="[para(20552(a,1),15332(a,1,2))].">
      <j1 rule="para" parents="20552 15332"/>
    </justification>
  </clause>

  <clause id="20568">
    <literal><![CDATA[
      K(x,L(y,z,u / (K(w,v5) / v6))) = K(x,y) * a(x,z,K(v6 * u,y))
    ]]></literal>
    <justification jstring="[para(20557(a,1),15441(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20557 15441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20569">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20540(a,2),15616(a,1))].">
      <j1 rule="para" parents="20540 15616"/>
    </justification>
  </clause>

  <clause id="20570">
    <literal><![CDATA[
      K(x,L(y,z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(5796(a,1),20569(a,1,2,3))].">
      <j1 rule="para" parents="5796 20569"/>
    </justification>
  </clause>

  <clause id="20571">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(6157(a,1),20569(a,1,2,3))].">
      <j1 rule="para" parents="6157 20569"/>
    </justification>
  </clause>

  <clause id="20572">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,(w * u) \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(10833(a,1),20569(a,1,2,3))].">
      <j1 rule="para" parents="10833 20569"/>
    </justification>
  </clause>

  <clause id="20573">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ 1))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(20570,a,15953,a)].">
      <j1 rule="hyper" parents="20570 15953"/>
    </justification>
  </clause>

  <clause id="20574">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,w \ 1))) = K(x,L(y,z,w \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(19658,a,20573,a)].">
      <j1 rule="hyper" parents="19658 20573"/>
    </justification>
  </clause>

  <clause id="20575">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) / u,z \ y,y \ (z \ y))) = K(x,(z \ y) / (u * T(y \ (z \ y),y)))
    ]]></literal>
    <justification jstring="[hyper(20571,a,16118,a)].">
      <j1 rule="hyper" parents="20571 16118"/>
    </justification>
  </clause>

  <clause id="20576">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((T(z,u) \ 1) * y) \ ((z \ 1) * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(20571,a,10613,a)].">
      <j1 rule="hyper" parents="20571 10613"/>
    </justification>
  </clause>

  <clause id="20577">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,w \ 1))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),20574(a,2,2,3))].">
      <j1 rule="para" parents="9 20574"/>
    </justification>
  </clause>

  <clause id="20578">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(16390,a,20577,a),flip(a)].">
      <j1 rule="hyper" parents="16390 20577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20579">
    <literal><![CDATA[
      K(x,(y * z) / a(u \ 1,u,z)) = K(x,y / (a(u \ 1,u,z) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15681,a(flip),b,20578,a)].">
      <j1 rule="hyper" parents="64 15681 20578"/>
    </justification>
  </clause>

  <clause id="20580">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,w)) = K(x,L(y,v5,w))
    ]]></literal>
    <justification jstring="[hyper(20569,a,20539,a)].">
      <j1 rule="hyper" parents="20569 20539"/>
    </justification>
  </clause>

  <clause id="20583">
    <literal><![CDATA[
      K(x,L(y,z \ (u \ w),z)) = K(x,L(y,w / u,z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11053,a(flip),b,20543,a)].">
      <j1 rule="hyper" parents="64 11053 20543"/>
    </justification>
  </clause>

  <clause id="20585">
    <literal><![CDATA[
      a(x,y,K((T(z,u) \ w) \ u,v5)) = a(v5,y,K(x,(w / z) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,20553,a(flip),b,20561,a)].">
      <j1 rule="hyper" parents="64 20553 20561"/>
    </justification>
  </clause>

  <clause id="20586">
    <literal><![CDATA[
      T(x * y,a(K(z,u) * y,w,v5)) = x * T(y,a(v5,w,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,13960,a(flip),b,20562,a),flip(a)].">
      <j1 rule="hyper" parents="373 13960 20562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20587">
    <literal><![CDATA[
      T(x,a(x \ ((y * x) / z),u,w)) = x * a(w,u,K(z \ y,x))
    ]]></literal>
    <justification jstring="[para(10223(a,1),20566(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="10223 20566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20588">
    <literal><![CDATA[
      T(x,a(y \ (z / u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y \ (u \ z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20566(a,1),15342(a,1))].">
      <j1 rule="para" parents="20566 15342"/>
    </justification>
  </clause>

  <clause id="20589">
    <literal><![CDATA[
      K(x,L(y,z / u,w * K(u,z))) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(15665,a,20583,a),flip(a)].">
      <j1 rule="hyper" parents="15665 20583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20590">
    <literal><![CDATA[
      K(x,L(y,z / u,w)) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,20541,a(flip),b,20589,a)].">
      <j1 rule="hyper" parents="64 20541 20589"/>
    </justification>
  </clause>

  <clause id="20592">
    <literal><![CDATA[
      K(x,L(y,(z * u) / z,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),20590(a,2,2,2))].">
      <j1 rule="para" parents="9 20590"/>
    </justification>
  </clause>

  <clause id="20593">
    <literal><![CDATA[
      K(x,L(y,z \ 1,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11776(a,1),20590(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11776 20590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20594">
    <literal><![CDATA[
      K(x,L(y,T(z,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(256(a,1),20592(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="256 20592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20598">
    <literal><![CDATA[
      K(x,L(y,L(T(z,u),w,v5),v6)) = K(x,L(y,L(z,w,v5),v6))
    ]]></literal>
    <justification jstring="[para(25(a,2),20594(a,1,2,2))].">
      <j1 rule="para" parents="25 20594"/>
    </justification>
  </clause>

  <clause id="20600">
    <literal><![CDATA[
      K(x,L(y,z * u,w)) = K(x,L(y,u * z,w))
    ]]></literal>
    <justification jstring="[para(14165(a,1),20594(a,1,2))].">
      <j1 rule="para" parents="14165 20594"/>
    </justification>
  </clause>

  <clause id="20601">
    <literal><![CDATA[
      K(x,L(y,L(z,u,K(w,v5)),v6)) = K(x,L(y,z,v6))
    ]]></literal>
    <justification jstring="[para(16603(a,2),20594(a,1,2,2))].">
      <j1 rule="para" parents="16603 20594"/>
    </justification>
  </clause>

  <clause id="20602">
    <literal><![CDATA[
      K(x,L(y,z * u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(20600(a,1),15551(a,1))].">
      <j1 rule="para" parents="20600 15551"/>
    </justification>
  </clause>

  <clause id="20603">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,v6)) = K(x,L(y,w \ (K(u,z) * v5),v6))
    ]]></literal>
    <justification jstring="[para(6190(a,1),20601(a,1,2,2))].">
      <j1 rule="para" parents="6190 20601"/>
    </justification>
  </clause>

  <clause id="20604">
    <literal><![CDATA[
      T(x,a(x \ ((y * x) / z),u,w)) = T(x,a(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,15332,a(flip),b,20587,a),flip(a)].">
      <j1 rule="hyper" parents="373 15332 20587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20605">
    <literal><![CDATA[
      a(x,y,K(z * (T(u,x) \ w),v5)) = a(v5,y,K(x,z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(20563,a,15333,a)].">
      <j1 rule="hyper" parents="20563 15333"/>
    </justification>
  </clause>

  <clause id="20606">
    <literal><![CDATA[
      a(x,y,K(z,u * (w / v5))) = a(x,y,K(z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15334,a(flip),b,20605,a),flip(a)].">
      <j1 rule="hyper" parents="64 15334 20605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20607">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5 * (v6 \ v7))) = a(v5 * (v7 / v6),u,K(z,w))
    ]]></literal>
    <justification jstring="[hyper(20565,a,20606,a),flip(a)].">
      <j1 rule="hyper" parents="20565 20606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20608">
    <literal><![CDATA[
      T(x,a(x \ (y \ (z * x)),u,w)) = T(x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(20588,a,20604,a)].">
      <j1 rule="hyper" parents="20588 20604"/>
    </justification>
  </clause>

  <clause id="20609">
    <literal><![CDATA[
      T(x,a(y \ (z * x),u,w)) = T(x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15452,a(flip),b,20608,a)].">
      <j1 rule="hyper" parents="64 15452 20608"/>
    </justification>
  </clause>

  <clause id="20610">
    <literal><![CDATA[
      T(x,a(y \ 1,z,u)) = T(x,a(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),20609(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 20609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20611">
    <literal><![CDATA[
      T(x,a(y \ x,z,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,19483,a(flip),b,20610,a),flip(a)].">
      <j1 rule="hyper" parents="64 19483 20610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20612">
    <literal><![CDATA[
      T(x * y,a(K(z,x) * y,u,w)) = T(x * y,a(w,u,T(x,z)))
    ]]></literal>
    <justification jstring="[para(6155(a,1),20611(a,1,2,1))].">
      <j1 rule="para" parents="6155 20611"/>
    </justification>
  </clause>

  <clause id="20613">
    <literal><![CDATA[
      T(x * y,a(K(z,x) * y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x * y,a(w,u,x)) = v5
    ]]></literal>
    <justification jstring="[para(20612(a,2),19352(a,1))].">
      <j1 rule="para" parents="20612 19352"/>
    </justification>
  </clause>

  <clause id="20614">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * T(y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(20613,a,20586,a)].">
      <j1 rule="hyper" parents="20613 20586"/>
    </justification>
  </clause>

  <clause id="20615">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * L(y,u,K(x,z))
    ]]></literal>
    <justification jstring="[para(16603(a,2),20614(a,2,2))].">
      <j1 rule="para" parents="16603 20614"/>
    </justification>
  </clause>

  <clause id="20616">
    <literal><![CDATA[
      T(x * K(y,z),a(u,w,x)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(19237(a,1),20614(a,2,2))].">
      <j1 rule="para" parents="19237 20614"/>
    </justification>
  </clause>

  <clause id="20617">
    <literal><![CDATA[
      T(T(x,y) * K(z,u),a(w,v5,x)) = T(x,y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(19352,a,20616,a)].">
      <j1 rule="hyper" parents="19352 20616"/>
    </justification>
  </clause>

  <clause id="20618">
    <literal><![CDATA[
      L(x * K(y,z),u,K(x,w)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(16649,a,20616,a)].">
      <j1 rule="hyper" parents="16649 20616"/>
    </justification>
  </clause>

  <clause id="20619">
    <literal><![CDATA[
      1 / T((x * K(y,z)) * K(a(u,w,x),v5),a(u,w,x)) = K(v5,a(u,w,x)) / (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(20616(a,1),14601(a,2,2))].">
      <j1 rule="para" parents="20616 14601"/>
    </justification>
  </clause>

  <clause id="20620">
    <literal><![CDATA[
      K(x,y) * (z * T(x * K(u,w),K(x,y) * z)) = (x * K(u,w)) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(20618(a,1),793(a,2,1))].">
      <j1 rule="para" parents="20618 793"/>
    </justification>
  </clause>

  <clause id="20621">
    <literal><![CDATA[
      L(x * y,z,K(x,u)) = x * L(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(16648,a,20615,a)].">
      <j1 rule="hyper" parents="16648 20615"/>
    </justification>
  </clause>

  <clause id="20622">
    <literal><![CDATA[
      K(x,L(y / z,L(T(u,w),v5,v6),y \ L(u,v5,v6))) = K(x,L(T(u,w),v5,v6) / (z * (y \ L(T(u,w),v5,v6))))
    ]]></literal>
    <justification jstring="[hyper(64,a,16116,a(flip),b,20545,a),flip(a)].">
      <j1 rule="hyper" parents="64 16116 20545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20623">
    <literal><![CDATA[
      a(x,y,K(z,u)) / (z * K(w,v5)) = L(K(v5,w) / z,y,K(x,u))
    ]]></literal>
    <justification jstring="[para(14507(a,1),20556(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14507 20556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20624">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = x * a(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(19189(a,1),20560(a,2,2))].">
      <j1 rule="para" parents="19189 20560"/>
    </justification>
  </clause>

  <clause id="20626">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,16611,a(flip),b,20624,a),flip(a)].">
      <j1 rule="hyper" parents="373 16611 20624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20628">
    <literal><![CDATA[
      L(x,y,K(K(z,u) * w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(16650,a,20626,a)].">
      <j1 rule="hyper" parents="16650 20626"/>
    </justification>
  </clause>

  <clause id="20629">
    <literal><![CDATA[
      L(x,(K(y,z) * u) \ w,K(K(y,z) * u,v5)) = L(x,w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(16651,a,20628,a)].">
      <j1 rule="hyper" parents="16651 20628"/>
    </justification>
  </clause>

  <clause id="20630">
    <literal><![CDATA[
      L(x,y,K(K(z,u) * w,v5)) = L(x,y,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,6104,a,b,20628,a),flip(a)].">
      <j1 rule="hyper" parents="373 6104 20628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20631">
    <literal><![CDATA[
      L(x,y,K(K(z,u) * w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20630(a,2),6105(a,1))].">
      <j1 rule="para" parents="20630 6105"/>
    </justification>
  </clause>

  <clause id="20632">
    <literal><![CDATA[
      L(x,(K(y,z) * u) \ w,K(u,v5)) = L(x,w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(20631,a,20629,a)].">
      <j1 rule="hyper" parents="20631 20629"/>
    </justification>
  </clause>

  <clause id="20634">
    <literal><![CDATA[
      K(x,L(y,z,u / (K(w,v5) / v6))) = K(x,L(y,z,v6 * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15336,a(flip),b,20568,a),flip(a)].">
      <j1 rule="hyper" parents="373 15336 20568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20636">
    <literal><![CDATA[
      K(x,y / (a(z \ 1,z,u) / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(z \ 1,z,u) \ (y * u)) = w
    ]]></literal>
    <justification jstring="[para(20579(a,1),19286(a,1))].">
      <j1 rule="para" parents="20579 19286"/>
    </justification>
  </clause>

  <clause id="20637">
    <literal><![CDATA[
      K(x,L(y,z \ (K(u,w) * v5),z)) = K(x,L(y,v5,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,20580,a(flip),b,20603,a),flip(a)].">
      <j1 rule="hyper" parents="64 20580 20603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20638">
    <literal><![CDATA[
      K(x,L(y,K(z,u) * w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(15665,a,20637,a)].">
      <j1 rule="hyper" parents="15665 20637"/>
    </justification>
  </clause>

  <clause id="20639">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = K(w,v5) * K(v5,L(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,20637,a(flip),b,15489,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 20637 15489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20640">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7416,a,20638,a),flip(a)].">
      <j1 rule="hyper" parents="7416 20638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20645">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(20638(a,1),7416(a,1))].">
      <j1 rule="para" parents="20638 7416"/>
    </justification>
  </clause>

  <clause id="20646">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) * v5,v6)) = K(x,L(y,w * v5,v6))
    ]]></literal>
    <justification jstring="[para(7760(a,1),20638(a,1,2,2))].">
      <j1 rule="para" parents="7760 20638"/>
    </justification>
  </clause>

  <clause id="20647">
    <literal><![CDATA[
      L(K(x,y),K(z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12060,a,20640,a)].">
      <j1 rule="hyper" parents="12060 20640"/>
    </justification>
  </clause>

  <clause id="20650">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,20640,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 20640 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20653">
    <literal><![CDATA[
      K(L(x,K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,12093,a,b,20640,a)].">
      <j1 rule="hyper" parents="64 12093 20640"/>
    </justification>
  </clause>

  <clause id="20654">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(z,u) \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16158,a(flip),b,20640,a),flip(a)].">
      <j1 rule="hyper" parents="64 16158 20640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20655">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15587,a(flip),b,20640,a),flip(a)].">
      <j1 rule="hyper" parents="64 15587 20640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20656">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,z \ (y * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12073,a(flip),b,20640,a),flip(a)].">
      <j1 rule="hyper" parents="64 12073 20640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20657">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[para(6191(a,1),20640(a,1,2))].">
      <j1 rule="para" parents="6191 20640"/>
    </justification>
  </clause>

  <clause id="20659">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(y,z) * K(u,w))
    ]]></literal>
    <justification jstring="[para(20640(a,1),12078(a,1,2))].">
      <j1 rule="para" parents="20640 12078"/>
    </justification>
  </clause>

  <clause id="20660">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) * w = K(x,y) * (K(z,u) * w)
    ]]></literal>
    <justification jstring="[para(20640(a,1),15578(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20640 15578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20661">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(y / w) * K(u,z))
    ]]></literal>
    <justification jstring="[para(18807(a,1),20640(a,1,2))].">
      <j1 rule="para" parents="18807 20640"/>
    </justification>
  </clause>

  <clause id="20666">
    <literal><![CDATA[
      x \ (K(y,z) * (x * K(u,w))) = K(u,w) * T(K(y,z),x * K(u,w))
    ]]></literal>
    <justification jstring="[para(20647(a,1),831(a,1,2,1))].">
      <j1 rule="para" parents="20647 831"/>
    </justification>
  </clause>

  <clause id="20669">
    <literal><![CDATA[
      L(K(x,y),L(K(z,u),w,v5),v6) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6670(a,1),20647(a,1,2))].">
      <j1 rule="para" parents="6670 20647"/>
    </justification>
  </clause>

  <clause id="20670">
    <literal><![CDATA[
      T(x,a(y,K(z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(15403,a,20650,a)].">
      <j1 rule="hyper" parents="15403 20650"/>
    </justification>
  </clause>

  <clause id="20673">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / (T(z,u) * K(w / z,v5))) = T(x,y * K(v5,z \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18840,a(flip),b,20650,a)].">
      <j1 rule="hyper" parents="64 18840 20650"/>
    </justification>
  </clause>

  <clause id="20674">
    <literal><![CDATA[
      T(x,(y / z) / K(u,w)) = T(x,y / (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15609,a(flip),b,20650,a),flip(a)].">
      <j1 rule="hyper" parents="64 15609 20650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20675">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(41,a,16628,a(flip),b,20650,a),flip(a)].">
      <j1 rule="hyper" parents="41 16628 20650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20676">
    <literal><![CDATA[
      R(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,15982,a,b,20670,a)].">
      <j1 rule="hyper" parents="64 15982 20670"/>
    </justification>
  </clause>

  <clause id="20677">
    <literal><![CDATA[
      T(x,a(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(20670(a,1),50(a,2))].">
      <j1 rule="para" parents="20670 50"/>
    </justification>
  </clause>

  <clause id="20678">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(20670(a,1),15401(a,2))].">
      <j1 rule="para" parents="20670 15401"/>
    </justification>
  </clause>

  <clause id="20679">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ w = K(z,u) \ (K(x,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(710,a,20675,a),flip(a)].">
      <j1 rule="hyper" parents="710 20675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20680">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ w = K(u,z) * (K(y,x) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,7067,a(flip),b,20675,a)].">
      <j1 rule="hyper" parents="64 7067 20675"/>
    </justification>
  </clause>

  <clause id="20682">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(20675(a,1),51(a,2))].">
      <j1 rule="para" parents="20675 51"/>
    </justification>
  </clause>

  <clause id="20688">
    <literal><![CDATA[
      T(x / (K(y,z) * K(u,w)),K(u,w)) = K(w,u) * (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17895,a(flip),b,20676,a)].">
      <j1 rule="hyper" parents="64 17895 20676"/>
    </justification>
  </clause>

  <clause id="20695">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K((x \ u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,18816,a(flip),b,20653,a)].">
      <j1 rule="hyper" parents="64 18816 20653"/>
    </justification>
  </clause>

  <clause id="20699">
    <literal><![CDATA[
      K(x,y) * ((x * K(z,u)) * w) = (T(x,y) * K(z,u)) * w
    ]]></literal>
    <justification jstring="[para(20653(a,1),15613(a,1,1))].">
      <j1 rule="para" parents="20653 15613"/>
    </justification>
  </clause>

  <clause id="20700">
    <literal><![CDATA[
      T(x * K(y,z),a(u,x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = v5
    ]]></literal>
    <justification jstring="[para(15494(a,1),20677(a,1))].">
      <j1 rule="para" parents="15494 20677"/>
    </justification>
  </clause>

  <clause id="20701">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * (y \ w)) = v5
    ]]></literal>
    <justification jstring="[para(6191(a,1),20645(a,1,2))].">
      <j1 rule="para" parents="6191 20645"/>
    </justification>
  </clause>

  <clause id="20703">
    <literal><![CDATA[
      K((K(x,y) * z) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((u / z) \ K(x,y),w) = v5
    ]]></literal>
    <justification jstring="[para(17297(a,1),20645(a,1))].">
      <j1 rule="para" parents="17297 20645"/>
    </justification>
  </clause>

  <clause id="20704">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,L(K(z,u),w,v5) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,12080,a(flip),b,20669,a)].">
      <j1 rule="hyper" parents="64 12080 20669"/>
    </justification>
  </clause>

  <clause id="20707">
    <literal><![CDATA[
      T(x,(y * z) / (K(u,w) * z)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(w,u) * y) = v5
    ]]></literal>
    <justification jstring="[para(17803(a,1),20678(a,1))].">
      <j1 rule="para" parents="17803 20678"/>
    </justification>
  </clause>

  <clause id="20708">
    <literal><![CDATA[
      T(x,L(y,z \ T(u * z,w),u)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(19283(a,2),20678(a,1))].">
      <j1 rule="para" parents="19283 20678"/>
    </justification>
  </clause>

  <clause id="20709">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) \ (w \ v5)) = K(x,w \ (K(y,T(z,u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,20508,a(flip),b,20654,a),flip(a)].">
      <j1 rule="hyper" parents="64 20508 20654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20710">
    <literal><![CDATA[
      K(x,K(y,z) \ ((u / z) \ w)) = K(x,(u / T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(6245(a,1),20654(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6245 20654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20711">
    <literal><![CDATA[
      K(x,K(y,z) \ ((u * y) \ w)) = K(x,(u * T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6852(a,1),20654(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6852 20654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20712">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(w,u) \ z))
    ]]></literal>
    <justification jstring="[para(6156(a,2),20655(a,2,2,2))].">
      <j1 rule="para" parents="6156 20655"/>
    </justification>
  </clause>

  <clause id="20713">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,K(u,w) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,19905,a(flip),b,20656,a),flip(a)].">
      <j1 rule="hyper" parents="373 19905 20656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20714">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(18023,a,20657,a)].">
      <j1 rule="hyper" parents="18023 20657"/>
    </justification>
  </clause>

  <clause id="20715">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,y \ (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,19905,a,b,20657,a),flip(a)].">
      <j1 rule="hyper" parents="373 19905 20657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20716">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17146,a,b,20659,a),flip(a)].">
      <j1 rule="hyper" parents="373 17146 20659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20717">
    <literal><![CDATA[
      (L(K(x,y) * K(z,u),w,K(v5,v6)) * a(v5,w,v6)) / K(z,u) = a(v5,w,v6) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,16632,a,b,20659,a)].">
      <j1 rule="hyper" parents="142 16632 20659"/>
    </justification>
  </clause>

  <clause id="20718">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(w,v5) = x * (K(z,L(u,x,y \ x)) * K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,20494,a,b,20659,a)].">
      <j1 rule="hyper" parents="64 20494 20659"/>
    </justification>
  </clause>

  <clause id="20719">
    <literal><![CDATA[
      (x * (y * z)) / T(z * y,u) = x * (K(y,z) * K(u,z * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,10600,a,b,20659,a)].">
      <j1 rule="hyper" parents="64 10600 20659"/>
    </justification>
  </clause>

  <clause id="20720">
    <literal><![CDATA[
      x * (K(y \ z,u) * K(y \ z,y)) = (x * T(y \ z,u)) / (z / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6996,a(flip),b,20659,a),flip(a)].">
      <j1 rule="hyper" parents="64 6996 20659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20721">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) / (u * w) = (x * K(y,z)) / (w * u)
    ]]></literal>
    <justification jstring="[hyper(142,a,20659,a(flip),b,10193,a)].">
      <j1 rule="hyper" parents="142 20659 10193"/>
    </justification>
  </clause>

  <clause id="20723">
    <literal><![CDATA[
      T(x * (K(y,z) * K(u,w)),K(w,u)) = K(u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(20659(a,1),6881(a,1,1))].">
      <j1 rule="para" parents="20659 6881"/>
    </justification>
  </clause>

  <clause id="20724">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(w,u) \ K(y,z))
    ]]></literal>
    <justification jstring="[para(17140(a,2),20659(a,2,2))].">
      <j1 rule="para" parents="17140 20659"/>
    </justification>
  </clause>

  <clause id="20727">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(z,y) * u) = (T(T(y,z),x) \ y) * u
    ]]></literal>
    <justification jstring="[para(6225(a,1),20660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6225 20660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20728">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) * w = K(z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(17141(a,1),20660(a,1,1))].">
      <j1 rule="para" parents="17141 20660"/>
    </justification>
  </clause>

  <clause id="20729">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,K(u,z) * (y / w))
    ]]></literal>
    <justification jstring="[hyper(373,a,17139,a,b,20661,a),flip(a)].">
      <j1 rule="hyper" parents="373 17139 20661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20730">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * (y / w)) = v5
    ]]></literal>
    <justification jstring="[para(20661(a,2),17194(a,1))].">
      <j1 rule="para" parents="20661 17194"/>
    </justification>
  </clause>

  <clause id="20731">
    <literal><![CDATA[
      T(x,(y / z) / K(u,w)) = T(x,y / (K(w,u) \ z))
    ]]></literal>
    <justification jstring="[para(6156(a,2),20674(a,2,2,2))].">
      <j1 rule="para" parents="6156 20674"/>
    </justification>
  </clause>

  <clause id="20732">
    <literal><![CDATA[
      (K(x,y) \ K(z,u)) \ w = K(z,u) \ (K(y,x) \ w)
    ]]></literal>
    <justification jstring="[para(6156(a,2),20679(a,1,1))].">
      <j1 rule="para" parents="6156 20679"/>
    </justification>
  </clause>

  <clause id="20733">
    <literal><![CDATA[
      (K(x,y) \ (K(z,u) \ w)) / w = K(y,x) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(744,a,20680,a)].">
      <j1 rule="hyper" parents="744 20680"/>
    </justification>
  </clause>

  <clause id="20735">
    <literal><![CDATA[
      K(x \ K(y,z),x) * (K(y,z) * u) = (x * (K(z,y) / x)) \ u
    ]]></literal>
    <justification jstring="[para(16358(a,1),20680(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16358 20680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20737">
    <literal><![CDATA[
      K((x \ y) * K(z,u),T(w,x)) = K(y / (x * K(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(18254,a,20695,a),flip(a)].">
      <j1 rule="hyper" parents="18254 20695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20738">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K((z \ u) * K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(18106,a,20695,a)].">
      <j1 rule="hyper" parents="18106 20695"/>
    </justification>
  </clause>

  <clause id="20741">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K((x \ u) * K(y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19394,a(flip),b,20695,a)].">
      <j1 rule="hyper" parents="64 19394 20695"/>
    </justification>
  </clause>

  <clause id="20742">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(u,y),w) = K((x \ T(y,u)) \ z,w)
    ]]></literal>
    <justification jstring="[para(15021(a,1),20695(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="15021 20695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20743">
    <literal><![CDATA[
      a(x \ (y * K(z,u)),w,K(v5,v6)) = a(v5,w,K((y \ x) * K(u,z),v6))
    ]]></literal>
    <justification jstring="[para(20695(a,1),15324(a,2,3))].">
      <j1 rule="para" parents="20695 15324"/>
    </justification>
  </clause>

  <clause id="20744">
    <literal><![CDATA[
      K(x \ K((y \ z) * K(u \ w,u),y * K(u,w)),v5) = K(x \ K(y * K(u,u \ w),z),v5)
    ]]></literal>
    <justification jstring="[para(20695(a,1),16323(a,1,1,2))].">
      <j1 rule="para" parents="20695 16323"/>
    </justification>
  </clause>

  <clause id="20745">
    <literal><![CDATA[
      x * K(a(y,x,z),L(x,u,w)) = T(x,a(w,u,a(y,x,z)))
    ]]></literal>
    <justification jstring="[hyper(20700,a,17703,a)].">
      <j1 rule="hyper" parents="20700 17703"/>
    </justification>
  </clause>

  <clause id="20746">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / (u \ T(z * u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * K(w,u * z)) = v5
    ]]></literal>
    <justification jstring="[para(19282(a,1),20708(a,1))].">
      <j1 rule="para" parents="19282 20708"/>
    </justification>
  </clause>

  <clause id="20747">
    <literal><![CDATA[
      K(x,y / (K(z,u) \ w)) = K(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(17262,a,20712,a),flip(a)].">
      <j1 rule="hyper" parents="17262 20712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20748">
    <literal><![CDATA[
      K(x,K(y,z) * ((y * (z \ u)) \ u)) = K(x,T((y * (z \ u)) \ u,y))
    ]]></literal>
    <justification jstring="[hyper(18602,a,20713,a),flip(a)].">
      <j1 rule="hyper" parents="18602 20713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20749">
    <literal><![CDATA[
      K(x,(y \ z) \ K(z,u)) = K(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,15774,a(flip),b,20713,a),flip(a)].">
      <j1 rule="hyper" parents="373 15774 20713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20750">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,z)) = K(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(6157(a,1),20713(a,2,2))].">
      <j1 rule="para" parents="6157 20713"/>
    </justification>
  </clause>

  <clause id="20751">
    <literal><![CDATA[
      T(x,(y \ z) \ K(z,u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(143,a,20749,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 20749 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20752">
    <literal><![CDATA[
      K(x,T(y,z \ K(u,w)) \ v5) = K(x,(v5 \ y) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(20063,a,20750,a),flip(a)].">
      <j1 rule="hyper" parents="20063 20750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20753">
    <literal><![CDATA[
      T(x,(y \ (z / u)) \ K(u \ z,w)) = T(x,T(z / u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,18228,a(flip),b,20751,a)].">
      <j1 rule="hyper" parents="64 18228 20751"/>
    </justification>
  </clause>

  <clause id="20754">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,K(y,z) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,15767,a,b,20714,a),flip(a)].">
      <j1 rule="hyper" parents="373 15767 20714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20755">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * x))) = K(x,K(u,z) * ((z \ y) \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,7634,a(flip),b,20714,a)].">
      <j1 rule="hyper" parents="64 7634 20714"/>
    </justification>
  </clause>

  <clause id="20756">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) \ w) = K(x,y \ (K(w,y) * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20386,a,b,20715,a)].">
      <j1 rule="hyper" parents="64 20386 20715"/>
    </justification>
  </clause>

  <clause id="20759">
    <literal><![CDATA[
      (x / y) * K(z,K(u,u \ w)) = ((y \ x) * K(u,K(w,z))) * K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10040,a(flip),b,20716,a)].">
      <j1 rule="hyper" parents="373 10040 20716"/>
    </justification>
  </clause>

  <clause id="20763">
    <literal><![CDATA[
      K(x,y) \ (L(K(y,x),z,u) \ w) = w * (K(x,y) \ K(L(x,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,19484,a,b,20724,a)].">
      <j1 rule="hyper" parents="64 19484 20724"/>
    </justification>
  </clause>

  <clause id="20768">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (w \ z))) = K(x,u / (w \ T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(18101,a,20729,a),flip(a)].">
      <j1 rule="hyper" parents="18101 20729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20769">
    <literal><![CDATA[
      K(x,K(y,z) * (u / w)) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14544,a(flip),b,20729,a),flip(a)].">
      <j1 rule="hyper" parents="64 14544 20729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20770">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (w \ z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (w \ T(z,y))) = v5
    ]]></literal>
    <justification jstring="[para(20729(a,1),18101(a,1))].">
      <j1 rule="para" parents="20729 18101"/>
    </justification>
  </clause>

  <clause id="20771">
    <literal><![CDATA[
      T(x,y / (K(z,u) \ w)) = T(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(17175,a,20731,a),flip(a)].">
      <j1 rule="hyper" parents="17175 20731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20772">
    <literal><![CDATA[
      (x \ T(T(x,y),T(y,z))) \ u = K(x,T(y,z)) \ (K(x,y) \ u)
    ]]></literal>
    <justification jstring="[para(17477(a,1),20732(a,1,1))].">
      <j1 rule="para" parents="17477 20732"/>
    </justification>
  </clause>

  <clause id="20773">
    <literal><![CDATA[
      (L(K(x,y),z,u) \ K(w,v5)) \ v6 = K(L(y,z,u),x) \ (K(w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(17402(a,2),20732(a,1,1))].">
      <j1 rule="para" parents="17402 20732"/>
    </justification>
  </clause>

  <clause id="20774">
    <literal><![CDATA[
      K(x,y) \ (K(z,u) \ w) = (K(z,u) \ K(y,x)) * w
    ]]></literal>
    <justification jstring="[hyper(17316,a,20733,a),flip(a)].">
      <j1 rule="hyper" parents="17316 20733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20775">
    <literal><![CDATA[
      K(x,y) \ (K(z,u) \ w) = (K(x,y) \ K(u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(6208,a,20733,a),flip(a)].">
      <j1 rule="hyper" parents="6208 20733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20776">
    <literal><![CDATA[
      K((x \ K(y,z)) * u,w) = K((x \ u) * K(y,z),w)
    ]]></literal>
    <justification jstring="[hyper(14765,a,20738,a)].">
      <j1 rule="hyper" parents="14765 20738"/>
    </justification>
  </clause>

  <clause id="20777">
    <literal><![CDATA[
      K(x,K(y,z)) * K((x \ z) * K(u,w),y) = K(z / (K(w,u) * x),y)
    ]]></literal>
    <justification jstring="[para(20738(a,1),18303(a,1,2))].">
      <j1 rule="para" parents="20738 18303"/>
    </justification>
  </clause>

  <clause id="20778">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K((x \ u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,16286,a,b,20741,a),flip(a)].">
      <j1 rule="hyper" parents="373 16286 20741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20779">
    <literal><![CDATA[
      K((x \ (y \ z)) * K(u,y),w) = K(x \ (T(y,u) \ z),w)
    ]]></literal>
    <justification jstring="[para(6157(a,1),20741(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6157 20741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20780">
    <literal><![CDATA[
      K(x,K(y \ 1,z * y) \ (u / z)) = K(x,u / ((y \ 1) * (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(64,a,9948,a(flip),b,20747,a),flip(a)].">
      <j1 rule="hyper" parents="64 9948 20747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20781">
    <literal><![CDATA[
      K(x,K(y,z) * ((T(y,z) \ u) \ w)) = K(x,(y \ u) \ w)
    ]]></literal>
    <justification jstring="[para(6075(a,1),20754(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6075 20754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20782">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ w)) = K(x,(T(z,y) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(6157(a,1),20754(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6157 20754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20783">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ T(w,u))) = K(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(18492,a,20769,a)].">
      <j1 rule="hyper" parents="18492 20769"/>
    </justification>
  </clause>

  <clause id="20784">
    <literal><![CDATA[
      T(x,K(y,z) * (u / w)) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(143,a,20769,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 20769 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20785">
    <literal><![CDATA[
      T(x,(K(y,z) \ u) / w) = T(x,K(y,z) \ (u / w))
    ]]></literal>
    <justification jstring="[hyper(19639,a,20771,a)].">
      <j1 rule="hyper" parents="19639 20771"/>
    </justification>
  </clause>

  <clause id="20786">
    <literal><![CDATA[
      K(x,y) \ (K(z,u) \ w) = K(z,u) \ (K(x,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,20774,a,b,20775,a)].">
      <j1 rule="hyper" parents="373 20774 20775"/>
    </justification>
  </clause>

  <clause id="20787">
    <literal><![CDATA[
      K((x \ y) * K(z,u),T(w,y)) = K(y * (x \ K(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(11189,a,20776,a),flip(a)].">
      <j1 rule="hyper" parents="11189 20776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20788">
    <literal><![CDATA[
      K((x \ K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * (x \ u),w) = v5
    ]]></literal>
    <justification jstring="[para(20776(a,2),17512(a,1))].">
      <j1 rule="para" parents="20776 17512"/>
    </justification>
  </clause>

  <clause id="20789">
    <literal><![CDATA[
      K(x,K(y,z)) * K((x \ z) * K(u,w),y) = K((K(w,u) * z) / x,y)
    ]]></literal>
    <justification jstring="[para(20778(a,1),18294(a,1,2))].">
      <j1 rule="para" parents="20778 18294"/>
    </justification>
  </clause>

  <clause id="20790">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,w),v5)) = T(x,y * (T(z,v5) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20389,a(flip),b,20784,a)].">
      <j1 rule="hyper" parents="64 20389 20784"/>
    </justification>
  </clause>

  <clause id="20791">
    <literal><![CDATA[
      T(x,K(y,z) \ ((T(z,y) \ u) / w)) = T(x,(z \ u) / w)
    ]]></literal>
    <justification jstring="[para(6165(a,1),20785(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6165 20785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20792">
    <literal><![CDATA[
      K(x,y) \ (K(z,u) \ T(w,K(x,y))) = K(z,u) \ (w * K(y,x))
    ]]></literal>
    <justification jstring="[para(8169(a,1),20786(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8169 20786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20793">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,15329,a(flip),b,20639,a),flip(a)].">
      <j1 rule="hyper" parents="373 15329 20639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20794">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,12087,a(flip),b,20639,a),flip(a)].">
      <j1 rule="hyper" parents="373 12087 20639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20795">
    <literal><![CDATA[
      a(x,T(y,z),K(u,w)) = a(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11979,a(flip),b,20794,a),flip(a)].">
      <j1 rule="hyper" parents="64 11979 20794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20799">
    <literal><![CDATA[
      a(x,T(y,z),K(u,w)) = w \ L(w,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,16621,a,b,20795,a),flip(a)].">
      <j1 rule="hyper" parents="373 16621 20795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20800">
    <literal><![CDATA[
      L(x,T(y,z),K(u,w)) = L(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(16637,a,20799,a)].">
      <j1 rule="hyper" parents="16637 20799"/>
    </justification>
  </clause>

  <clause id="20801">
    <literal><![CDATA[
      L(x,L(y,z,K(u,w)),K(v5,v6)) = L(x,y,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(16603(a,2),20800(a,1,2))].">
      <j1 rule="para" parents="16603 20800"/>
    </justification>
  </clause>

  <clause id="20802">
    <literal><![CDATA[
      L(x,(K(y,z) * u) \ w,K(v5,v6)) = L(x,u \ (K(z,y) * w),K(v5,v6))
    ]]></literal>
    <justification jstring="[para(6190(a,1),20801(a,1,2))].">
      <j1 rule="para" parents="6190 20801"/>
    </justification>
  </clause>

  <clause id="20803">
    <literal><![CDATA[
      K(x,L(y,z * (K(u,w) * v5),v6)) = K(x,L(y,v5 * z,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,20600,a,b,20646,a)].">
      <j1 rule="hyper" parents="64 20600 20646"/>
    </justification>
  </clause>

  <clause id="20804">
    <literal><![CDATA[
      K(x,(y / T(z,y)) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13492,a(flip),b,20710,a),flip(a)].">
      <j1 rule="hyper" parents="64 13492 20710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20805">
    <literal><![CDATA[
      K(x,(y / T(z,z \ u)) \ w) = K(x,K(u,z) \ ((y / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13463,a(flip),b,20710,a),flip(a)].">
      <j1 rule="hyper" parents="64 13463 20710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20806">
    <literal><![CDATA[
      K(x,(T(y,z) / z) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4630(a,2),20804(a,1,2,1))].">
      <j1 rule="para" parents="4630 20804"/>
    </justification>
  </clause>

  <clause id="20807">
    <literal><![CDATA[
      K(x,((L(y,z,y) * z) \ y) \ u) = K(x,(y / (z * y)) \ u)
    ]]></literal>
    <justification jstring="[para(4724(a,1),20804(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4724 20804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20808">
    <literal><![CDATA[
      K(x,K(y,z) \ ((u * z) \ w)) = K(x,(u * T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(17521,a,20711,a)].">
      <j1 rule="hyper" parents="17521 20711"/>
    </justification>
  </clause>

  <clause id="20809">
    <literal><![CDATA[
      T(T(x,y),z) \ (x * u) = (T(T(x,y),z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,6224,a(flip),b,20727,a)].">
      <j1 rule="hyper" parents="64 6224 20727"/>
    </justification>
  </clause>

  <clause id="20810">
    <literal><![CDATA[
      (T(T(x,y),z) \ x) * u = x * (T(T(x,y),z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5410,a(flip),b,20809,a),flip(a)].">
      <j1 rule="hyper" parents="64 5410 20809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20811">
    <literal><![CDATA[
      K((x \ y) * K(z,u),T(w,x)) = K(y * (x \ K(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,18126,a(flip),b,20737,a),flip(a)].">
      <j1 rule="hyper" parents="373 18126 20737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20812">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(y,u),w) = K((x \ T(y,u)) \ z,w)
    ]]></literal>
    <justification jstring="[hyper(16287,a,20742,a)].">
      <j1 rule="hyper" parents="16287 20742"/>
    </justification>
  </clause>

  <clause id="20813">
    <literal><![CDATA[
      x * a(y,x,K(z,L(x,u,w))) = T(x,a(w,u,a(y,x,z)))
    ]]></literal>
    <justification jstring="[para(13977(a,2),20745(a,1,2))].">
      <j1 rule="para" parents="13977 20745"/>
    </justification>
  </clause>

  <clause id="20814">
    <literal><![CDATA[
      K(x,T(y,z \ K(u,w)) \ v5) = K(x,T(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,20749,a(flip),b,20752,a),flip(a)].">
      <j1 rule="hyper" parents="373 20749 20752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20815">
    <literal><![CDATA[
      K(x,T((y * z) * (1 / y),y) \ u) = K(x,L(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17326,a(flip),b,20814,a),flip(a)].">
      <j1 rule="hyper" parents="64 17326 20814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20816">
    <literal><![CDATA[
      K(x,y / (z \ T(u,K(w,v5)))) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(18014,a,20768,a),flip(a)].">
      <j1 rule="hyper" parents="18014 20768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20817">
    <literal><![CDATA[
      T(x,y / (z \ T(u,K(w,v5)))) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(143,a,20816,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 20816 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20818">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y / (z \ (v5 * K(u,w))))
    ]]></literal>
    <justification jstring="[para(6881(a,1),20816(a,1,2,2,2))].">
      <j1 rule="para" parents="6881 20816"/>
    </justification>
  </clause>

  <clause id="20819">
    <literal><![CDATA[
      K(x,y / (z \ (u * T(z,K(w,v5))))) = K(x,y / T(u,K(v5,w) * z))
    ]]></literal>
    <justification jstring="[para(16796(a,1),20816(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16796 20816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20820">
    <literal><![CDATA[
      T(x,y / (z \ (((z * K(u,w)) * v5) * z))) = T(x,y / (v5 * (K(u,w) * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18838,a(flip),b,20817,a),flip(a)].">
      <j1 rule="hyper" parents="64 18838 20817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20821">
    <literal><![CDATA[
      K(K(x,y) * (z \ (x \ u)),w) = K(z \ (T(x,y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(17512,a,20779,a)].">
      <j1 rule="hyper" parents="17512 20779"/>
    </justification>
  </clause>

  <clause id="20822">
    <literal><![CDATA[
      a(x,y,K((T(z,u) \ w) \ v5,v6)) = a(v6,y,K(x,(z \ w) \ v5))
    ]]></literal>
    <justification jstring="[para(20781(a,1),20555(a,1,3)),flip(a)].">
      <j1 rule="para" parents="20781 20555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20823">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13466,a(flip),b,20782,a),flip(a)].">
      <j1 rule="hyper" parents="64 13466 20782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20824">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / (T(z,y) \ y))
    ]]></literal>
    <justification jstring="[hyper(13486,a,20823,a),flip(a)].">
      <j1 rule="hyper" parents="13486 20823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20825">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(143,a,20823,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 20823 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20826">
    <literal><![CDATA[
      T(x,(T(y,z / u) \ T(u \ z,u)) \ w) = T(x,(T(u \ z,u) / y) \ w)
    ]]></literal>
    <justification jstring="[para(8241(a,1),20825(a,1,2,1,1))].">
      <j1 rule="para" parents="8241 20825"/>
    </justification>
  </clause>

  <clause id="20827">
    <literal><![CDATA[
      K(x,(y / (T(z,u) \ u)) / T(w,(u / z) \ y)) = K(x,w \ (y / (T(z,u) \ u)))
    ]]></literal>
    <justification jstring="[para(20825(a,1),18113(a,1,2,2))].">
      <j1 rule="para" parents="20825 18113"/>
    </justification>
  </clause>

  <clause id="20828">
    <literal><![CDATA[
      T(x,(((y \ T(z,y)) \ z) \ z) / u) = T(x,(y \ z) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17546,a,b,20791,a)].">
      <j1 rule="hyper" parents="64 17546 20791"/>
    </justification>
  </clause>

  <clause id="20829">
    <literal><![CDATA[
      K(x,L(y,z * (u * K(w,v5)),v6)) = K(x,L(y,u * z,v6))
    ]]></literal>
    <justification jstring="[para(6823(a,1),20803(a,1,2,2,2))].">
      <j1 rule="para" parents="6823 20803"/>
    </justification>
  </clause>

  <clause id="20830">
    <literal><![CDATA[
      K(x * (y \ K(z,u)),T(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) * K(z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(20811(a,1),8313(a,1))].">
      <j1 rule="para" parents="20811 8313"/>
    </justification>
  </clause>

  <clause id="20831">
    <literal><![CDATA[
      K((x \ T(y,x)) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18709,a(flip),b,20812,a),flip(a)].">
      <j1 rule="hyper" parents="64 18709 20812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20832">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9155,a,b,20831,a)].">
      <j1 rule="hyper" parents="64 9155 20831"/>
    </justification>
  </clause>

  <clause id="20833">
    <literal><![CDATA[
      T(x,a(y,z,a(u,x,w))) = x * 1
    ]]></literal>
    <justification jstring="[para(10570(a,1),20813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10570 20813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20834">
    <literal><![CDATA[
      a(x,y,a(z,x,K(u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(15692,a,20833,a)].">
      <j1 rule="hyper" parents="15692 20833"/>
    </justification>
  </clause>

  <clause id="20835">
    <literal><![CDATA[
      T(x,L(a(y,x,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(141,a,20833,a(flip),b,15694,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="141 20833 15694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20837">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,y) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(53,a,20834,a)].">
      <j1 rule="hyper" parents="53 20834"/>
    </justification>
  </clause>

  <clause id="20838">
    <literal><![CDATA[
      T(a(x,y,z),a(y,u,w)) = (y * a(x,y,z)) / y
    ]]></literal>
    <justification jstring="[para(20835(a,1),15383(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20835 15383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20839">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,y))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12531,a,b,20837,a)].">
      <j1 rule="hyper" parents="64 12531 20837"/>
    </justification>
  </clause>

  <clause id="20840">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,z))) = K(x,y) * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(20839(a,1),15337(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20839 15337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20841">
    <literal><![CDATA[
      T(a(x,y,z),a(y,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,13972,a(flip),b,20838,a),flip(a)].">
      <j1 rule="hyper" parents="373 13972 20838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20842">
    <literal><![CDATA[
      T(a(x,y,z),a(u,w,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(15387,a,20841,a)].">
      <j1 rule="hyper" parents="15387 20841"/>
    </justification>
  </clause>

  <clause id="20843">
    <literal><![CDATA[
      T(a(x,y,z),a(u,x,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(55,a,20841,a)].">
      <j1 rule="hyper" parents="55 20841"/>
    </justification>
  </clause>

  <clause id="20844">
    <literal><![CDATA[
      T(a(x,y,z),a(u,z,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(55,a,20842,a)].">
      <j1 rule="hyper" parents="55 20842"/>
    </justification>
  </clause>

  <clause id="20845">
    <literal><![CDATA[
      L(a(x,y,z),x,K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(16648,a,20843,a)].">
      <j1 rule="hyper" parents="16648 20843"/>
    </justification>
  </clause>

  <clause id="20846">
    <literal><![CDATA[
      L(a(x,y,z),z,K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(16648,a,20844,a)].">
      <j1 rule="hyper" parents="16648 20844"/>
    </justification>
  </clause>

  <clause id="20847">
    <literal><![CDATA[
      R(K(x,y),z,L(a(z,u,w),z,K(x,y))) = (K(x,y) * (z * a(z,u,w))) / (z * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(20845(a,1),604(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="20845 604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20849">
    <literal><![CDATA[
      R(K(x,y),z,L(a(u,w,z),z,K(x,y))) = (K(x,y) * (z * a(u,w,z))) / (z * a(u,w,z))
    ]]></literal>
    <justification jstring="[para(20846(a,1),604(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="20846 604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20850">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,z))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15337,a(flip),b,20840,a),flip(a)].">
      <j1 rule="hyper" parents="373 15337 20840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20851">
    <literal><![CDATA[
      K(x,L(y,z,(z * u) \ w)) = K(x,L(y,z,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(346(a,1),20850(a,1,2,3))].">
      <j1 rule="para" parents="346 20850"/>
    </justification>
  </clause>

  <clause id="20852">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(13480,a,20824,a),flip(a)].">
      <j1 rule="hyper" parents="13480 20824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20853">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(20824(a,1),13480(a,1))].">
      <j1 rule="para" parents="20824 13480"/>
    </justification>
  </clause>

  <clause id="20854">
    <literal><![CDATA[
      K(T(x,y),T(z,y) / (y / x)) = K(T(x,y),y \ (z * T(x,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15925,a(flip),b,20852,a),flip(a)].">
      <j1 rule="hyper" parents="64 15925 20852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20855">
    <literal><![CDATA[
      K(x,y / (T(z,u / w) \ (w \ T(u,w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((w \ T(u,w)) / z)) = v5
    ]]></literal>
    <justification jstring="[para(13419(a,1),20853(a,1,2,2,1))].">
      <j1 rule="para" parents="13419 20853"/>
    </justification>
  </clause>

  <clause id="20857">
    <literal><![CDATA[
      T(x,T(T(y,z) \ z,y) / u) = T(x,(y \ z) / u)
    ]]></literal>
    <justification jstring="[para(8333(a,1),20828(a,1,2,1))].">
      <j1 rule="para" parents="8333 20828"/>
    </justification>
  </clause>

  <clause id="20858">
    <literal><![CDATA[
      T(x,(y / T(z,y)) / u) = T(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18081,a(flip),b,20857,a)].">
      <j1 rule="hyper" parents="64 18081 20857"/>
    </justification>
  </clause>

  <clause id="20859">
    <literal><![CDATA[
      T(x,(y \ z) / T(u,y \ z)) = T(x,u \ (z / T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(13408,a,20858,a),flip(a)].">
      <j1 rule="hyper" parents="13408 20858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20860">
    <literal><![CDATA[
      K(x,L(y,z,(u * z) \ w)) = K(x,L(y,z,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(20572,a,20851,a)].">
      <j1 rule="hyper" parents="20572 20851"/>
    </justification>
  </clause>

  <clause id="20861">
    <literal><![CDATA[
      T(x,y \ (z / T(u,z))) = T(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(13396,a,20859,a),flip(a)].">
      <j1 rule="hyper" parents="13396 20859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20862">
    <literal><![CDATA[
      K(x,y \ (z / T(u,z))) = (T(x,y \ (u \ z)) * R(x \ 1,x,w)) / ((w / (x * w)) * x)
    ]]></literal>
    <justification jstring="[para(20861(a,1),5987(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="20861 5987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20863">
    <literal><![CDATA[
      K(x \ 1,L(y,z,(x * z) \ u)) = K(x \ 1,L(y,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,16240,a(flip),b,20860,a),flip(a)].">
      <j1 rule="hyper" parents="373 16240 20860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20865">
    <literal><![CDATA[
      T(x,(y * z) * (z \ K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(14553(a,1),20707(a,1))].">
      <j1 rule="para" parents="14553 20707"/>
    </justification>
  </clause>

  <clause id="20866">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(20788,a,19794,a)].">
      <j1 rule="hyper" parents="20788 19794"/>
    </justification>
  </clause>

  <clause id="20867">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w * K(v5,z \ u)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(z \ u,w) = v6
    ]]></literal>
    <justification jstring="[para(20866(a,2),8779(a,1))].">
      <j1 rule="para" parents="20866 8779"/>
    </justification>
  </clause>

  <clause id="20868">
    <literal><![CDATA[
      K(x,((y * z) \ R(y,z,y)) \ u) = K(x,(y / (z * y)) \ u)
    ]]></literal>
    <justification jstring="[para(13041(a,1),20807(a,1,2,1))].">
      <j1 rule="para" parents="13041 20807"/>
    </justification>
  </clause>

  <clause id="20869">
    <literal><![CDATA[
      K(x,(y / (z * y)) \ u) = K(x,((y * z) \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13391,a(flip),b,20868,a),flip(a)].">
      <j1 rule="hyper" parents="64 13391 20868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20871">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,((u * z) \ u) \ y) = K(x,y / (u / (z * u)))
    ]]></literal>
    <justification jstring="[para(20869(a,1),9072(a,1,2))].">
      <j1 rule="para" parents="20869 9072"/>
    </justification>
  </clause>

  <clause id="20874">
    <literal><![CDATA[
      K(x,y \ (K(z,T(u,w)) \ v5)) = K(x,K(z,u) \ (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(18086,a,20709,a),flip(a)].">
      <j1 rule="hyper" parents="18086 20709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20875">
    <literal><![CDATA[
      K(x,y \ (K(z,T(u,w)) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ (y \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(20709(a,1),18089(a,1))].">
      <j1 rule="para" parents="20709 18089"/>
    </justification>
  </clause>

  <clause id="20877">
    <literal><![CDATA[
      K(x,(y * z) \ (K(z,T(u,w)) \ v5)) = K(x,(y * T(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,20711,a(flip),b,20874,a),flip(a)].">
      <j1 rule="hyper" parents="373 20711 20874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20878">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ w)) = K(x,u \ (K(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,20358,a(flip),b,20874,a),flip(a)].">
      <j1 rule="hyper" parents="64 20358 20874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20879">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ w)) = K(x,u \ (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(17521,a,20878,a)].">
      <j1 rule="hyper" parents="17521 20878"/>
    </justification>
  </clause>

  <clause id="20881">
    <literal><![CDATA[
      K(x,y \ (K(z \ 1,u) \ w)) = K(x,K(u,z) \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17629,a(flip),b,20878,a),flip(a)].">
      <j1 rule="hyper" parents="64 17629 20878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20882">
    <literal><![CDATA[
      K(x,y \ (K(z,u) \ (y * w))) = K(x,K(u,z) \ w)
    ]]></literal>
    <justification jstring="[para(9(a,1),20879(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 20879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20883">
    <literal><![CDATA[
      K(x,T(x \ y,z) \ (x \ (y * u))) = K(x,K(z,x \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(20371,a,20882,a)].">
      <j1 rule="hyper" parents="20371 20882"/>
    </justification>
  </clause>

  <clause id="20884">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z)) \ ((u / z) \ w)) = K(x,(T(u,y) / z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19421,a(flip),b,20881,a),flip(a)].">
      <j1 rule="hyper" parents="64 19421 20881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20885">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11328,a(flip),b,20721,a),flip(a)].">
      <j1 rule="hyper" parents="64 11328 20721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20886">
    <literal><![CDATA[
      (x / (y * z)) * K(z,y) = x / (T(y,z) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10603,a(flip),b,20885,a)].">
      <j1 rule="hyper" parents="64 10603 20885"/>
    </justification>
  </clause>

  <clause id="20887">
    <literal><![CDATA[
      K(K(x,y),z) \ ((u * (T(z,K(x,y)) * K(y,x))) / T(z,K(x,y))) = T((u * T(z,K(x,y))) / (z * K(x,y)),K(K(x,y),z))
    ]]></literal>
    <justification jstring="[hyper(493,a,20420,a,b,20886,a),flip(a)].">
      <j1 rule="hyper" parents="493 20420 20886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20888">
    <literal><![CDATA[
      x / (K(y,z) * K(u,w)) = x * (K(z,y) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,20688,a,b,20723,a)].">
      <j1 rule="hyper" parents="41 20688 20723"/>
    </justification>
  </clause>

  <clause id="20891">
    <literal><![CDATA[
      x * (K(y,z) * K(u \ K(y,z),u)) = x / (u * (K(z,y) / u))
    ]]></literal>
    <justification jstring="[para(16358(a,1),20888(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16358 20888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20892">
    <literal><![CDATA[
      (x * (K(y,z) / x)) \ u = ((x \ K(z,y)) * x) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,10858,a(flip),b,20735,a),flip(a)].">
      <j1 rule="hyper" parents="64 10858 20735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20893">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) = K(x,K(y,z) * (u \ (z * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19947,a(flip),b,20755,a),flip(a)].">
      <j1 rule="hyper" parents="64 19947 20755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20894">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) \ w) = K(x,T(y,w) \ K(u,z))
    ]]></literal>
    <justification jstring="[para(6137(a,1),20756(a,2,2))].">
      <j1 rule="para" parents="6137 20756"/>
    </justification>
  </clause>

  <clause id="20895">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) \ w) = K(x,T(y \ K(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(373,a,18787,a,b,20894,a),flip(a)].">
      <j1 rule="hyper" parents="373 18787 20894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20896">
    <literal><![CDATA[
      K(x,y \ ((z * K(u,w)) \ y)) = K(x,T(z \ K(w,u),y))
    ]]></literal>
    <justification jstring="[hyper(8463,a,20895,a)].">
      <j1 rule="hyper" parents="8463 20895"/>
    </justification>
  </clause>

  <clause id="20897">
    <literal><![CDATA[
      K(x,y / (z * (y * K(u,w)))) = K(x,T(T(z,y) \ K(w,u),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,20121,a(flip),b,20896,a)].">
      <j1 rule="hyper" parents="64 20121 20896"/>
    </justification>
  </clause>

  <clause id="20898">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = K(x,T(y,z)) \ (K(x,y) \ T(T(x,y),x \ T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18899,a,b,20772,a)].">
      <j1 rule="hyper" parents="64 18899 20772"/>
    </justification>
  </clause>

  <clause id="20899">
    <literal><![CDATA[
      K(x \ (K(y,z) \ u),x) \ (u * K(z,y)) = K(y,z) \ (x * T(u / x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(20505(a,1),20792(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20505 20792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20900">
    <literal><![CDATA[
      K(x,(y / T(z,z \ u)) \ w) = K(x,(y / T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,20710,a(flip),b,20805,a),flip(a)].">
      <j1 rule="hyper" parents="373 20710 20805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20901">
    <literal><![CDATA[
      K(x,(y / ((z \ u) \ u)) \ w) = K(x,(y / T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(116(a,1),20900(a,1,2,1,2))].">
      <j1 rule="para" parents="116 20900"/>
    </justification>
  </clause>

  <clause id="20902">
    <literal><![CDATA[
      a(x,y,K(z,(u / w) \ v5)) = a(x,y,K(z,(w \ u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,20585,a(flip),b,20822,a)].">
      <j1 rule="hyper" parents="64 20585 20822"/>
    </justification>
  </clause>

  <clause id="20903">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,(v5 \ v6) \ v7)) = a((v6 / v5) \ v7,u,K(z,w))
    ]]></literal>
    <justification jstring="[hyper(20565,a,20902,a),flip(a)].">
      <j1 rule="hyper" parents="20565 20902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20905">
    <literal><![CDATA[
      K(T(x,y),y \ (z * T(x,y))) = K(x,T(T(z,y) / (y / x),y))
    ]]></literal>
    <justification jstring="[hyper(8019,a,20854,a),flip(a)].">
      <j1 rule="hyper" parents="8019 20854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20906">
    <literal><![CDATA[
      K(x \ 1,L(T(y,z),u,u \ z)) = K(z \ (u * ((x * u) \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15618,a(flip),b,20863,a),flip(a)].">
      <j1 rule="hyper" parents="64 15618 20863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20907">
    <literal><![CDATA[
      K(x,T(y,z) \ (K(z,T(u,w)) \ v5)) = K(x,((z \ y) * T(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,13414,a(flip),b,20877,a)].">
      <j1 rule="hyper" parents="64 13414 20877"/>
    </justification>
  </clause>

  <clause id="20908">
    <literal><![CDATA[
      x / (y * (K(z,u) / y)) = x * ((y \ K(u,z)) * y)
    ]]></literal>
    <justification jstring="[para(354(a,1),20891(a,1,2)),flip(a)].">
      <j1 rule="para" parents="354 20891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20909">
    <literal><![CDATA[
      R(x * ((y \ K(z,u)) * y),y * (K(u,z) / y),x \ w) \ w = (y * (K(u,z) / y)) * (x \ w)
    ]]></literal>
    <justification jstring="[para(20908(a,1),684(a,1,1,1))].">
      <j1 rule="para" parents="20908 684"/>
    </justification>
  </clause>

  <clause id="20910">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (x * T(z,y))) = w
    ]]></literal>
    <justification jstring="[para(20893(a,2),19979(a,1))].">
      <j1 rule="para" parents="20893 19979"/>
    </justification>
  </clause>

  <clause id="20911">
    <literal><![CDATA[
      K(x,y / (z * (y * K(u,w)))) = K(x,T(T(z \ K(w,u),y),y))
    ]]></literal>
    <justification jstring="[hyper(373,a,18663,a,b,20897,a),flip(a)].">
      <j1 rule="hyper" parents="373 18663 20897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20912">
    <literal><![CDATA[
      K(T(x,y),y \ (z * T(x,y))) = K(x,T(T(z,y) / (x \ y),y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8628,a(flip),b,20905,a),flip(a)].">
      <j1 rule="hyper" parents="373 8628 20905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20913">
    <literal><![CDATA[
      K(x,y / (z * (y * K(u,w)))) = K(x,z \ K(w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,8203,a(flip),b,20911,a),flip(a)].">
      <j1 rule="hyper" parents="373 8203 20911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20915">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,(w / y) \ K(z,u))
    ]]></literal>
    <justification jstring="[para(20436(a,1),20913(a,1,2))].">
      <j1 rule="para" parents="20436 20913"/>
    </justification>
  </clause>

  <clause id="20916">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,(z / y) \ K(w,u))
    ]]></literal>
    <justification jstring="[hyper(19432,a,20915,a)].">
      <j1 rule="hyper" parents="19432 20915"/>
    </justification>
  </clause>

  <clause id="20917">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(w / y) \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(18100,a,20916,a)].">
      <j1 rule="hyper" parents="18100 20916"/>
    </justification>
  </clause>

  <clause id="20918">
    <literal><![CDATA[
      K(x,(y / z) \ K(u,w)) = K(x,K(u,w) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(20730,a,20917,a),flip(a)].">
      <j1 rule="hyper" parents="20730 20917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20919">
    <literal><![CDATA[
      K(x,(y / z) \ K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,w) * (z / y)) = v5
    ]]></literal>
    <justification jstring="[para(20917(a,1),20730(a,1))].">
      <j1 rule="para" parents="20917 20730"/>
    </justification>
  </clause>

  <clause id="20920">
    <literal><![CDATA[
      K(x,(y / z) \ K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z / T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(20918(a,2),17306(a,1))].">
      <j1 rule="para" parents="20918 17306"/>
    </justification>
  </clause>

  <clause id="20921">
    <literal><![CDATA[
      K(x,(y / z) \ K(y,u / (w * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,z / T(y,L((u / v5) / w,w,v5))) = v6
    ]]></literal>
    <justification jstring="[para(15587(a,1),20920(a,1,2,2))].">
      <j1 rule="para" parents="15587 20920"/>
    </justification>
  </clause>

  <clause id="20922">
    <literal><![CDATA[
      K(T(x,y),y \ (z * T(x,y))) = K(x,y \ (x * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,9850,a(flip),b,20912,a),flip(a)].">
      <j1 rule="hyper" parents="373 9850 20912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20923">
    <literal><![CDATA[
      K(x,(y * T(x,z)) / z) = K(x,z \ (x * T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(8323,a,20922,a)].">
      <j1 rule="hyper" parents="8323 20922"/>
    </justification>
  </clause>

  <clause id="20924">
    <literal><![CDATA[
      K(x,y \ (x * T(z,y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (x \ y)) = u
    ]]></literal>
    <justification jstring="[para(20923(a,1),9140(a,1))].">
      <j1 rule="para" parents="20923 9140"/>
    </justification>
  </clause>

  <clause id="20925">
    <literal><![CDATA[
      K(x,(y / T(z,u)) \ (x * T(w,y / ((z \ u) \ u)))) = K(x,w / (x \ (y / ((z \ u) \ u))))
    ]]></literal>
    <justification jstring="[hyper(20924,a,20901,a),flip(a)].">
      <j1 rule="hyper" parents="20924 20901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20927">
    <literal><![CDATA[
      K(x,((y * z) * (1 / z)) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(2135(a,1),20815(a,1,2,1))].">
      <j1 rule="para" parents="2135 20815"/>
    </justification>
  </clause>

  <clause id="20928">
    <literal><![CDATA[
      K(x,((y * z) * (z \ 1)) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,6646,a(flip),b,20927,a)].">
      <j1 rule="hyper" parents="64 6646 20927"/>
    </justification>
  </clause>

  <clause id="20929">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(297(a,1),20928(a,1,2,1))].">
      <j1 rule="para" parents="297 20928"/>
    </justification>
  </clause>

  <clause id="20930">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15698,a(flip),b,20929,a),flip(a)].">
      <j1 rule="hyper" parents="64 15698 20929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20931">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(2329(a,1),20930(a,1,2))].">
      <j1 rule="para" parents="2329 20930"/>
    </justification>
  </clause>

  <clause id="20932">
    <literal><![CDATA[
      K(x \ (y * (((z / y) * y) \ x)),u) = K((z * (y \ x)) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16215,a(flip),b,20906,a),flip(a)].">
      <j1 rule="hyper" parents="64 16215 20906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20933">
    <literal><![CDATA[
      K((x * (y \ z)) \ z,u) = K(z \ (y * (x \ z)),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),20932(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 20932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20935">
    <literal><![CDATA[
      x / (K(y \ (z * (u \ y)),w) * x) = K(w,(u * (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[para(20933(a,1),6160(a,1,2,1))].">
      <j1 rule="para" parents="20933 6160"/>
    </justification>
  </clause>

  <clause id="20936">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z \ (u * (w \ z)),y))) / x) = K(y,T((w * (u \ z)) \ z,x))
    ]]></literal>
    <justification jstring="[para(20933(a,1),9176(a,1,2,1,2,2))].">
      <j1 rule="para" parents="20933 9176"/>
    </justification>
  </clause>

  <clause id="20937">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (z * (y \ u))) = w
    ]]></literal>
    <justification jstring="[para(20935(a,1),6189(a,1))].">
      <j1 rule="para" parents="20935 6189"/>
    </justification>
  </clause>

  <clause id="20938">
    <literal><![CDATA[
      K(x,(x * y) \ (x * T(z,y * x))) = K(x,R(z,z \ (x * y),z) / y)
    ]]></literal>
    <justification jstring="[hyper(20910,a,19921,a(flip))].">
      <j1 rule="hyper" parents="20910 19921"/>
    </justification>
  </clause>

  <clause id="20939">
    <literal><![CDATA[
      a(x * (y / z),u,K(w,v5)) = a(x * (z \ y),u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(20565,a,20607,a),flip(a)].">
      <j1 rule="hyper" parents="20565 20607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20940">
    <literal><![CDATA[
      a(x * (y \ T(z,y)),u,K(w,v5)) = a(w,u,K(v5,(y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,19356,a(flip),b,20939,a),flip(a)].">
      <j1 rule="hyper" parents="64 19356 20939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20941">
    <literal><![CDATA[
      a(x,y,K(z,(u / w) * v5)) = a(x,y,K(z,(w \ u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,19355,a(flip),b,20940,a)].">
      <j1 rule="hyper" parents="64 19355 20940"/>
    </justification>
  </clause>

  <clause id="20942">
    <literal><![CDATA[
      x \ (K(y,z) \ (x * K(u,w))) = K(u,w) * T(K(z,y),x * K(u,w))
    ]]></literal>
    <justification jstring="[para(6156(a,2),20666(a,1,2))].">
      <j1 rule="para" parents="6156 20666"/>
    </justification>
  </clause>

  <clause id="20943">
    <literal><![CDATA[
      (x * T(y \ z,u)) / (z / y) = x * ((z / y) \ T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(7498(a,1),20720(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7498 20720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20944">
    <literal><![CDATA[
      x * ((y / z) \ T(z \ y,x)) = ((z \ y) * x) / (y / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,250,a(flip),b,20943,a),flip(a)].">
      <j1 rule="hyper" parents="64 250 20943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20945">
    <literal><![CDATA[
      a(x \ (y * K(z,u)),w,K(v5,v6)) = a(v5,w,K(y \ x,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,20549,a(flip),b,20743,a),flip(a)].">
      <j1 rule="hyper" parents="373 20549 20743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20947">
    <literal><![CDATA[
      K(x,T((y * (z \ u)) \ u,y)) = K(x,(T(y,z) * (z \ u)) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,19939,a(flip),b,20748,a),flip(a)].">
      <j1 rule="hyper" parents="64 19939 20748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20948">
    <literal><![CDATA[
      K(x,T((y * (z \ u)) \ u,y)) = K(x,u / ((u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,20114,a(flip),b,20947,a),flip(a)].">
      <j1 rule="hyper" parents="373 20114 20947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20949">
    <literal><![CDATA[
      K(x,y) \ (L(K(y,x),z,u) \ w) = w * a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(17694(a,1),20763(a,2,2))].">
      <j1 rule="para" parents="17694 20763"/>
    </justification>
  </clause>

  <clause id="20950">
    <literal><![CDATA[
      K(x,y) \ (L(K(y,x),z,u) \ w) = a(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(373,a,19337,a,b,20949,a),flip(a)].">
      <j1 rule="hyper" parents="373 19337 20949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20951">
    <literal><![CDATA[
      a(K(x * y,x),z,u) \ T(x,y) = R(T(x,L(x * y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12228,a(flip),b,20950,a),flip(a)].">
      <j1 rule="hyper" parents="64 12228 20950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20952">
    <literal><![CDATA[
      R(T(x,L(x * y,z,u)),y,x) = a(K(y,x),z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(13104(a,1),20951(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13104 20951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20953">
    <literal><![CDATA[
      R(T(x,L(x * y,z,u)),y,x) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15456,a(flip),b,20952,a),flip(a)].">
      <j1 rule="hyper" parents="373 15456 20952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20954">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = T(x,L(x * y,z,u))
    ]]></literal>
    <justification jstring="[para(20953(a,1),4754(a,1,1))].">
      <j1 rule="para" parents="20953 4754"/>
    </justification>
  </clause>

  <clause id="20955">
    <literal><![CDATA[
      L(K(x,x * y),z,u) \ T(x,L(y,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(20953(a,1),12119(a,1,2))].">
      <j1 rule="para" parents="20953 12119"/>
    </justification>
  </clause>

  <clause id="20956">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,L(z,u,w)),z,(x \ y) * x) = K(y,L(((x \ y) * x) * z,u,w)) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,20954,a,b,14704,a)].">
      <j1 rule="hyper" parents="139 20954 14704"/>
    </justification>
  </clause>

  <clause id="20957">
    <literal><![CDATA[
      L(K(x,x * (y / (z / ((u \ 1) \ 1)))),u \ z,u) \ T(x,(y * u) / z) = R(x,y / (z / ((u \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(16735(a,1),20955(a,1,2))].">
      <j1 rule="para" parents="16735 20955"/>
    </justification>
  </clause>

  <clause id="20958">
    <literal><![CDATA[
      (L(K(x,y),z,u) \ K(w,v5)) \ v6 = L(K(y,x),z,u) \ (K(w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(12090(a,2),20773(a,2,1))].">
      <j1 rule="para" parents="12090 20773"/>
    </justification>
  </clause>

  <clause id="20959">
    <literal><![CDATA[
      K(x,K(y,z)) * K((x \ z) * K(u,w),y) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z * (x \ K(u,w)),y) = v5
    ]]></literal>
    <justification jstring="[para(20777(a,2),14762(a,1))].">
      <j1 rule="para" parents="20777 14762"/>
    </justification>
  </clause>

  <clause id="20960">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(y,v5)) = L(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,20632,a(flip),b,20802,a),flip(a)].">
      <j1 rule="hyper" parents="64 20632 20802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20961">
    <literal><![CDATA[
      L(x,K(y,z) * u,K(w,v5)) = L(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(16652,a,20960,a)].">
      <j1 rule="hyper" parents="16652 20960"/>
    </justification>
  </clause>

  <clause id="20962">
    <literal><![CDATA[
      L(x,y * K(z,u),K(w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(6823(a,1),20961(a,1,2))].">
      <j1 rule="para" parents="6823 20961"/>
    </justification>
  </clause>

  <clause id="20963">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) * z) * u) = z * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(20961(a,1),6201(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20961 6201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20964">
    <literal><![CDATA[
      L(x,K(y,z) * u,a(w,v5,K(v6,v7))) = L(x,u,K(a(w,v5,v6),v7))
    ]]></literal>
    <justification jstring="[para(13977(a,2),20961(a,1,3))].">
      <j1 rule="para" parents="13977 20961"/>
    </justification>
  </clause>

  <clause id="20965">
    <literal><![CDATA[
      T(x,a(y,z * K(u,w),v5)) = L(x,z,K(v5,y))
    ]]></literal>
    <justification jstring="[hyper(16633,a,20962,a)].">
      <j1 rule="hyper" parents="16633 20962"/>
    </justification>
  </clause>

  <clause id="20966">
    <literal><![CDATA[
      L((x * K(y,z)) \ u,x,K(z,y)) = x \ (K(z,T(y,x)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11337,a(flip),b,20962,a),flip(a)].">
      <j1 rule="hyper" parents="64 11337 20962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20967">
    <literal><![CDATA[
      L(x,y \ (z * K(u,w)),K(v5,v6)) = L(x,y \ z,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(16164(a,1),20962(a,1,2))].">
      <j1 rule="para" parents="16164 20962"/>
    </justification>
  </clause>

  <clause id="20968">
    <literal><![CDATA[
      T(x,a(y,z * K(u,w),v5)) = T(x,a(y,z,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,16603,a(flip),b,20965,a),flip(a)].">
      <j1 rule="hyper" parents="373 16603 20965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20969">
    <literal><![CDATA[
      T(x,a(y,z * u,w)) = T(x,a(y,u * z,w))
    ]]></literal>
    <justification jstring="[para(94(a,1),20968(a,1,2,2))].">
      <j1 rule="para" parents="94 20968"/>
    </justification>
  </clause>

  <clause id="20971">
    <literal><![CDATA[
      T(x,a(y,y * z,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(16649,a,20969,a),flip(a)].">
      <j1 rule="hyper" parents="16649 20969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20972">
    <literal><![CDATA[
      T(x,a(y,y * z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(15450,a,20969,a),flip(a)].">
      <j1 rule="hyper" parents="15450 20969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20973">
    <literal><![CDATA[
      L(x,y * z,K(u,y)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(16648,a,20971,a)].">
      <j1 rule="hyper" parents="16648 20971"/>
    </justification>
  </clause>

  <clause id="20974">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = T(x,a(z \ y,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15447,a(flip),b,20972,a)].">
      <j1 rule="hyper" parents="64 15447 20972"/>
    </justification>
  </clause>

  <clause id="20975">
    <literal><![CDATA[
      L(a(x,y,z),z,K(x,y)) = a(x,y,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,19366,a(flip),b,20973,a),flip(a)].">
      <j1 rule="hyper" parents="64 19366 20973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20976">
    <literal><![CDATA[
      L(a(x,y,z),z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a(T(x,y),y,z) = u
    ]]></literal>
    <justification jstring="[para(20975(a,2),12006(a,1))].">
      <j1 rule="para" parents="20975 12006"/>
    </justification>
  </clause>

  <clause id="20977">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,15447,a(flip),b,20974,a),flip(a)].">
      <j1 rule="hyper" parents="373 15447 20974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20978">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,16603,a,b,20977,a),flip(a)].">
      <j1 rule="hyper" parents="373 16603 20977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20979">
    <literal><![CDATA[
      L(x,(y \ z) * u,K(y,z)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(16648,a,20978,a)].">
      <j1 rule="hyper" parents="16648 20978"/>
    </justification>
  </clause>

  <clause id="20980">
    <literal><![CDATA[
      L(L(x,y,z \ u),y,K(z,u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13684,a(flip),b,20979,a),flip(a)].">
      <j1 rule="hyper" parents="64 13684 20979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20981">
    <literal><![CDATA[
      L(x,K(y,z),u / w) = L(x,K(y,z),w \ u)
    ]]></literal>
    <justification jstring="[hyper(20682,a,20980,a),flip(a)].">
      <j1 rule="hyper" parents="20682 20980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20982">
    <literal><![CDATA[
      L(L(x,y,z),y,K(L(u \ 1,u,w),((w * u) \ w) * z)) = L(x,y,(((w * u) \ w) * z) / L(u \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(502(a,1),20980(a,1,1,3))].">
      <j1 rule="para" parents="502 20980"/>
    </justification>
  </clause>

  <clause id="20983">
    <literal><![CDATA[
      L(x,K(y,z),(u \ w) \ w) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(79(a,1),20981(a,1,3)),flip(a)].">
      <j1 rule="para" parents="79 20981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20984">
    <literal><![CDATA[
      a(T(x,y),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(20976,a,20846,a)].">
      <j1 rule="hyper" parents="20976 20846"/>
    </justification>
  </clause>

  <clause id="20985">
    <literal><![CDATA[
      a(x * (y / x),x,z) = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13116,a(flip),b,20984,a),flip(a)].">
      <j1 rule="hyper" parents="64 13116 20984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20986">
    <literal><![CDATA[
      a(x,T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13121,a(flip),b,20985,a)].">
      <j1 rule="hyper" parents="64 13121 20985"/>
    </justification>
  </clause>

  <clause id="20987">
    <literal><![CDATA[
      a(x,y,z) = ((y * x) * z) / (x * (T(y,x) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15472,a,b,20986,a),flip(a)].">
      <j1 rule="hyper" parents="64 15472 20986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20988">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * z) = x * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(143,a,20987,a,b,171,a)].">
      <j1 rule="hyper" parents="143 20987 171"/>
    </justification>
  </clause>

  <clause id="20989">
    <literal><![CDATA[
      a(x,y,T(z,x * T(y,x))) \ ((y * x) * T(z,x * T(y,x))) = L(z,T(y,x),x) * (x * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,793,a(flip),b,20988,a),flip(a)].">
      <j1 rule="hyper" parents="373 793 20988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20990">
    <literal><![CDATA[
      T((x / y) * L(y,x,K(z,u)),y) = y \ (K(z,u) * ((K(u,z) * x) * y))
    ]]></literal>
    <justification jstring="[hyper(493,a,20963,a,b,3194,a)].">
      <j1 rule="hyper" parents="493 20963 3194"/>
    </justification>
  </clause>

  <clause id="20991">
    <literal><![CDATA[
      (x * y) * (z * L(u,z,K(y,x))) = (y * x) * ((K(x,y) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,20963,a(flip),b,10824,a)].">
      <j1 rule="hyper" parents="145 20963 10824"/>
    </justification>
  </clause>

  <clause id="20993">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(v5,v6)) = L(x,y \ w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,20333,a,b,20967,a)].">
      <j1 rule="hyper" parents="64 20333 20967"/>
    </justification>
  </clause>

  <clause id="20994">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),x \ u,K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,10717,a(flip),b,20993,a),flip(a)].">
      <j1 rule="hyper" parents="64 10717 20993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20996">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)) * v5,a(v6,v7,K(v8,v9))) = L(x,v5,K(a(v6,v7,v8),v9))
    ]]></literal>
    <justification jstring="[para(13780(a,1),20964(a,1,2,1))].">
      <j1 rule="para" parents="13780 20964"/>
    </justification>
  </clause>

  <clause id="20997">
    <literal><![CDATA[
      K(x,y / T(z * K(u,K(w,v5)),u)) = K(x,y / T(z,K(v5,w) * u))
    ]]></literal>
    <justification jstring="[para(6853(a,2),20819(a,1,2,2))].">
      <j1 rule="para" parents="6853 20819"/>
    </justification>
  </clause>

  <clause id="20998">
    <literal><![CDATA[
      K(x,y / (z / (u * z))) = K(x,y / ((z * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9628,a(flip),b,20871,a),flip(a)].">
      <j1 rule="hyper" parents="64 9628 20871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20999">
    <literal><![CDATA[
      K(L(x,y,z) * K(u \ 1,x),w / ((v5 * u) \ v5)) = K(x,L((v5 / (u * v5)) \ w,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19435,a(flip),b,20998,a),flip(a)].">
      <j1 rule="hyper" parents="64 19435 20998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21000">
    <literal><![CDATA[
      a((x / y) \ z,u,K(w,v5)) = a((y \ x) \ z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(20565,a,20903,a),flip(a)].">
      <j1 rule="hyper" parents="20565 20903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21001">
    <literal><![CDATA[
      (x * K(y,z)) / a((u \ 1) \ x,u \ 1,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(21000(a,1),19359(a,1,2))].">
      <j1 rule="para" parents="21000 19359"/>
    </justification>
  </clause>

  <clause id="21002">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y) \ (T(z,y) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(20907(a,1),20875(a,1))].">
      <j1 rule="para" parents="20907 20875"/>
    </justification>
  </clause>

  <clause id="21003">
    <literal><![CDATA[
      x \ (K(y,z) \ (x * K(u,w))) = K(u,w) * T(K(z,y),K(w,u) \ x)
    ]]></literal>
    <justification jstring="[para(17212(a,2),20942(a,2,2))].">
      <j1 rule="para" parents="17212 20942"/>
    </justification>
  </clause>

  <clause id="21004">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (K(y,x) \ w) = a(K(x,y),z,u) \ w
    ]]></literal>
    <justification jstring="[para(15444(a,1),20958(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15444 20958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21005">
    <literal><![CDATA[
      a(K(x,y),z,u) \ (K(x,y) \ w) = L(K(x,y),z,u) \ w
    ]]></literal>
    <justification jstring="[para(6164(a,1),21004(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6164 21004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21006">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(21005(a,1),19872(a,1,2))].">
      <j1 rule="para" parents="21005 19872"/>
    </justification>
  </clause>

  <clause id="21007">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) \ v5) = K(x,K(w,y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(17542,a,21006,a)].">
      <j1 rule="hyper" parents="17542 21006"/>
    </justification>
  </clause>

  <clause id="21008">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = x \ T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,5726,a(flip),b,21006,a),flip(a)].">
      <j1 rule="hyper" parents="373 5726 21006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21009">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(143,a,21006,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 21006 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21010">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,20704,a,b,21006,a)].">
      <j1 rule="hyper" parents="64 20704 21006"/>
    </justification>
  </clause>

  <clause id="21011">
    <literal><![CDATA[
      K(x,y \ (K(z,L(u,w,v5)) \ v6)) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,20879,a(flip),b,21007,a)].">
      <j1 rule="hyper" parents="64 20879 21007"/>
    </justification>
  </clause>

  <clause id="21012">
    <literal><![CDATA[
      K(x,y \ (K(L(z,u,w),v5) \ v6)) = K(x,K(v5,z) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,20878,a(flip),b,21007,a)].">
      <j1 rule="hyper" parents="64 20878 21007"/>
    </justification>
  </clause>

  <clause id="21013">
    <literal><![CDATA[
      T(x,y * (L(K(z,u),w,v5) \ v6)) = T(x,K(z,u) \ (y * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,19705,a(flip),b,21009,a)].">
      <j1 rule="hyper" parents="64 19705 21009"/>
    </justification>
  </clause>

  <clause id="21014">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(21008(a,2),5827(a,1))].">
      <j1 rule="para" parents="21008 5827"/>
    </justification>
  </clause>

  <clause id="21015">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ (y \ v6)) = v7
    ]]></literal>
    <justification jstring="[para(20704(a,2),21014(a,1))].">
      <j1 rule="para" parents="20704 21014"/>
    </justification>
  </clause>

  <clause id="21017">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(u,w) \ ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[para(100(a,1),21010(a,1,2,1))].">
      <j1 rule="para" parents="100 21010"/>
    </justification>
  </clause>

  <clause id="21018">
    <literal><![CDATA[
      K(x,(K(y,z) \ (u * L(K(w,v5),v6,v7))) \ v8) = K(x,K(w,v5) \ ((K(y,z) \ u) \ v8))
    ]]></literal>
    <justification jstring="[para(19285(a,2),21010(a,1,2,1))].">
      <j1 rule="para" parents="19285 21010"/>
    </justification>
  </clause>

  <clause id="21019">
    <literal><![CDATA[
      K(x,y \ (L(K(z,u),w,v5) \ v6)) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[para(7537(a,1),21011(a,1,2,2,1))].">
      <j1 rule="para" parents="7537 21011"/>
    </justification>
  </clause>

  <clause id="21020">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ v6) = K(x,K(y,z) \ (v5 \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,19423,a,b,21012,a)].">
      <j1 rule="hyper" parents="64 19423 21012"/>
    </justification>
  </clause>

  <clause id="21022">
    <literal><![CDATA[
      T(x,K(y,z) \ (u * (K(z,y) \ w))) = T(x,u * (a(K(y,z),v5,v6) \ w))
    ]]></literal>
    <justification jstring="[para(21004(a,1),21013(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="21004 21013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21023">
    <literal><![CDATA[
      K(x,K(y,z) \ ((L(K(y,z),u,w) \ v5) \ v6)) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,19688,a(flip),b,21019,a),flip(a)].">
      <j1 rule="hyper" parents="64 19688 21019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21026">
    <literal><![CDATA[
      K(x,K(y,z) \ ((K(L(y,u,w),z) \ v5) \ v6)) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[para(7369(a,1),21023(a,1,2,2,1,1))].">
      <j1 rule="para" parents="7369 21023"/>
    </justification>
  </clause>

  <clause id="21027">
    <literal><![CDATA[
      K(x,(y * (K(z,u) \ w)) \ v5) = K(x,K(u,z) \ ((y * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,20361,a,b,21017,a)].">
      <j1 rule="hyper" parents="64 20361 21017"/>
    </justification>
  </clause>

  <clause id="21028">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[para(6156(a,1),21017(a,2,2))].">
      <j1 rule="para" parents="6156 21017"/>
    </justification>
  </clause>

  <clause id="21029">
    <literal><![CDATA[
      K(x,K(y,z) \ (((z \ u) * z) \ w)) = K(x,(z * (u / T(z,y))) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15912,a(flip),b,21027,a),flip(a)].">
      <j1 rule="hyper" parents="64 15912 21027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21030">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w) * v5)) = K(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(20370,a,20997,a),flip(a)].">
      <j1 rule="hyper" parents="20370 20997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21032">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w) * v5)) = T(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(143,a,21030,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 21030 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21033">
    <literal><![CDATA[
      K(x,y / T((K(z,u) * w) \ v5,w)) = K(x,y / (v5 / (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16279,a(flip),b,21030,a),flip(a)].">
      <j1 rule="hyper" parents="64 16279 21030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21034">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,T(v5,v6))) = T(x,y / T(K(z,u) * w,w \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,20004,a,b,21032,a)].">
      <j1 rule="hyper" parents="64 20004 21032"/>
    </justification>
  </clause>

  <clause id="21035">
    <literal><![CDATA[
      T(x,y / T((z * K(u,w)) * v5,z)) = T(x,y / (v5 * (z * K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,18226,a(flip),b,21032,a),flip(a)].">
      <j1 rule="hyper" parents="64 18226 21032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21036">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) * w,v5)) = T(x,(y \ v5) / T(v5,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14905,a(flip),b,21032,a)].">
      <j1 rule="hyper" parents="64 14905 21032"/>
    </justification>
  </clause>

  <clause id="21037">
    <literal><![CDATA[
      T(x,y / T(z,u * T(w,v5))) = T(x,y / T(z,u * w))
    ]]></literal>
    <justification jstring="[para(6367(a,1),21032(a,1,2,2,2))].">
      <j1 rule="para" parents="6367 21032"/>
    </justification>
  </clause>

  <clause id="21038">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) * w,v5)) = T(x,y \ K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,14905,a(flip),b,21036,a),flip(a)].">
      <j1 rule="hyper" parents="373 14905 21036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21039">
    <literal><![CDATA[
      T(x,y \ K(T(z,u) \ w,v5)) = T(x,y \ K(z \ w,v5))
    ]]></literal>
    <justification jstring="[para(6075(a,1),21038(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6075 21038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21040">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,z)),w) / T(v5,y * z)) = T(x,v5 \ T(y * (z * K(u,z)),w))
    ]]></literal>
    <justification jstring="[hyper(18192,a,21037,a),flip(a)].">
      <j1 rule="hyper" parents="18192 21037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21041">
    <literal><![CDATA[
      T(x,T(y * T(z,u),w) / T(v5,y * z)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 \ T(y * T(z,u),w)) = v6
    ]]></literal>
    <justification jstring="[para(21037(a,1),18057(a,1))].">
      <j1 rule="para" parents="21037 18057"/>
    </justification>
  </clause>

  <clause id="21042">
    <literal><![CDATA[
      T(x,(y \ (z / T(u,w))) \ K(u \ z,v5)) = T(x,T(z / T(u,w),v5) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,20753,a(flip),b,21039,a),flip(a)].">
      <j1 rule="hyper" parents="64 20753 21039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21043">
    <literal><![CDATA[
      x \ (K(y,z) \ (x * K(u,w))) = K(u,w) * K(z,T(y,K(w,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,7878,a,b,21003,a),flip(a)].">
      <j1 rule="hyper" parents="373 7878 21003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21044">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) \ w) = K(x,(y * (z / T(y,u))) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,20808,a(flip),b,21029,a)].">
      <j1 rule="hyper" parents="64 20808 21029"/>
    </justification>
  </clause>

  <clause id="21045">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K((K(y,z) * u) \ w,u)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[hyper(16282,a,21033,a)].">
      <j1 rule="hyper" parents="16282 21033"/>
    </justification>
  </clause>

  <clause id="21046">
    <literal><![CDATA[
      K(x,y / ((K(z,u) \ w) / v5)) = K(x,y / (w / (K(z,u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20125,a(flip),b,21033,a)].">
      <j1 rule="hyper" parents="64 20125 21033"/>
    </justification>
  </clause>

  <clause id="21047">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y / (w / (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(6156(a,1),21046(a,1,2,2,1))].">
      <j1 rule="para" parents="6156 21046"/>
    </justification>
  </clause>

  <clause id="21049">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,K(x,y) \ w)) = w \ (K(u,z) \ (w * K(y,x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,6156,a,b,21043,a)].">
      <j1 rule="hyper" parents="373 6156 21043"/>
    </justification>
  </clause>

  <clause id="21050">
    <literal><![CDATA[
      x \ (K(y,z) \ (x * K(u,w))) = K(w,u) \ K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(18239(a,1),21049(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18239 21049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21051">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,x * y)) = (x * y) \ (K(u,z) \ (y * x))
    ]]></literal>
    <justification jstring="[para(94(a,1),21050(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="94 21050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21053">
    <literal><![CDATA[
      K(x,y) \ K(z,T(u,y \ x)) = (x * y) \ (K(u,z) \ (y * x))
    ]]></literal>
    <justification jstring="[para(17025(a,2),21051(a,1,2))].">
      <j1 rule="para" parents="17025 21051"/>
    </justification>
  </clause>

  <clause id="21054">
    <literal><![CDATA[
      K(x,y) \ (y * K(z,T(u,y \ x))) = y * ((x * y) \ (K(u,z) \ (y * x)))
    ]]></literal>
    <justification jstring="[para(21053(a,1),4539(a,2,2))].">
      <j1 rule="para" parents="21053 4539"/>
    </justification>
  </clause>

  <clause id="21055">
    <literal><![CDATA[
      K(x,y \ (x \ (x * T(z,y * x)))) = K(x,R(z,z \ (x * y),z) / y)
    ]]></literal>
    <justification jstring="[hyper(7417,a,20938,a)].">
      <j1 rule="hyper" parents="7417 20938"/>
    </justification>
  </clause>

  <clause id="21056">
    <literal><![CDATA[
      T(x * a(y,x,K(z,u)),y) = y \ (K(z,u) * ((K(u,z) * x) * y))
    ]]></literal>
    <justification jstring="[para(16655(a,1),20990(a,1,1))].">
      <j1 rule="para" parents="16655 20990"/>
    </justification>
  </clause>

  <clause id="21057">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * u)) / u = z * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(281,a,21056,a)].">
      <j1 rule="hyper" parents="281 21056"/>
    </justification>
  </clause>

  <clause id="21058">
    <literal><![CDATA[
      T(x * a(y,x,K(z,u)),u) = u \ (K(y,z) * ((K(z,y) * x) * u))
    ]]></literal>
    <justification jstring="[para(15300(a,2),21056(a,1,1,2))].">
      <j1 rule="para" parents="15300 21056"/>
    </justification>
  </clause>

  <clause id="21059">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * (u \ 1))) / (u \ 1) = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(15366(a,1),21057(a,2,2))].">
      <j1 rule="para" parents="15366 21057"/>
    </justification>
  </clause>

  <clause id="21060">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)) * v5,a(v6,v7,K(v8,v9))) = L(x,v5,a(v6,v7,K(v8,v9)))
    ]]></literal>
    <justification jstring="[para(13977(a,2),20996(a,2,3))].">
      <j1 rule="para" parents="13977 20996"/>
    </justification>
  </clause>

  <clause id="21061">
    <literal><![CDATA[
      K(x,(y * (z / T(y,u))) \ w) = K(x,K(u,y) \ (T(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(21002,a,21044,a),flip(a)].">
      <j1 rule="hyper" parents="21002 21044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21062">
    <literal><![CDATA[
      K(x,T((T(y,z) \ 1) \ z,u) \ w) = K(x,K(K(v5,v6),y) \ (T(T((y \ 1) \ z,u),y) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,20441,a,b,21061,a)].">
      <j1 rule="hyper" parents="64 20441 21061"/>
    </justification>
  </clause>

  <clause id="21063">
    <literal><![CDATA[
      T(x,y * (a(K(z,u),w,v5) \ v6)) = T(x,y * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,19554,a(flip),b,21022,a),flip(a)].">
      <j1 rule="hyper" parents="64 19554 21022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21065">
    <literal><![CDATA[
      L(x,a(K(y,z),u,w) \ T(v5,x),x) = K(x,v5) \ T(x,x * v5)
    ]]></literal>
    <justification jstring="[para(21063(a,1),20225(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21063 20225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21066">
    <literal><![CDATA[
      L(x,a(K(y,z),u,w) \ T(v5,x),x) = L(x,v5,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6304,a(flip),b,21065,a),flip(a)].">
      <j1 rule="hyper" parents="373 6304 21065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21068">
    <literal><![CDATA[
      L(x,a(K(y,z),u,w) \ v5,x) = L(x,v5,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12178,a(flip),b,21066,a)].">
      <j1 rule="hyper" parents="64 12178 21066"/>
    </justification>
  </clause>

  <clause id="21070">
    <literal><![CDATA[
      a(x,a(K(y,z),u,w) \ v5,x) = (v6 / x) \ (v6 / L(x,v5,x))
    ]]></literal>
    <justification jstring="[para(21068(a,1),10943(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="21068 10943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21071">
    <literal><![CDATA[
      a(x,a(K(y,z),u,w) \ v5,x) = a(x,v5,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10943,a(flip),b,21070,a),flip(a)].">
      <j1 rule="hyper" parents="373 10943 21070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21072">
    <literal><![CDATA[
      a(x,(y * a(K(z,u),w,v5)) \ v6,x) = a(x,y \ v6,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13702,a,b,21071,a)].">
      <j1 rule="hyper" parents="64 13702 21071"/>
    </justification>
  </clause>

  <clause id="21073">
    <literal><![CDATA[
      a(x,L(K(y,z),u,w) \ v5,x) = a(x,K(y,z) \ v5,x)
    ]]></literal>
    <justification jstring="[para(21005(a,1),21071(a,1,2))].">
      <j1 rule="para" parents="21005 21071"/>
    </justification>
  </clause>

  <clause id="21074">
    <literal><![CDATA[
      a(x,(a(K(y,z),u,w) \ v5) \ v6,x) = a(x,v5 \ v6,x)
    ]]></literal>
    <justification jstring="[para(19199(a,1),21072(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19199 21072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21075">
    <literal><![CDATA[
      a(x,K(y,(z \ u) \ w) \ v5,x) = a(x,K(y,u \ (z * w)) \ v5,x)
    ]]></literal>
    <justification jstring="[para(7080(a,1),21073(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7080 21073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21076">
    <literal><![CDATA[
      a(x,y \ (a(K(z,u),w,v5) * v6),x) = a(x,y \ v6,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13703,a(flip),b,21074,a)].">
      <j1 rule="hyper" parents="64 13703 21074"/>
    </justification>
  </clause>

  <clause id="21077">
    <literal><![CDATA[
      a(x,y \ (a(K(z,u),w,v5) \ v6),x) = a(x,y \ v6,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),21076(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 21076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21078">
    <literal><![CDATA[
      a(x,y \ (z * a(u,w,K(v5,v6))),x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(19336(a,1),21077(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19336 21077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21079">
    <literal><![CDATA[
      a(x,y \ (L(K(z,u),w,v5) \ v6),x) = a(x,y \ (K(z,u) \ v6),x)
    ]]></literal>
    <justification jstring="[para(21005(a,1),21077(a,1,2,2))].">
      <j1 rule="para" parents="21005 21077"/>
    </justification>
  </clause>

  <clause id="21080">
    <literal><![CDATA[
      a(x,y \ ((z * u) * K(w,v5)),x) = a(x,y \ (z * (u * K(w,v5))),x)
    ]]></literal>
    <justification jstring="[para(88(a,1),21078(a,1,2,2))].">
      <j1 rule="para" parents="88 21078"/>
    </justification>
  </clause>

  <clause id="21081">
    <literal><![CDATA[
      a(x,y \ (z * ((K(u,w) \ z) \ v5)),x) = a(x,y \ (K(w,u) \ v5),x)
    ]]></literal>
    <justification jstring="[para(15639(a,1),21079(a,1,2,2))].">
      <j1 rule="para" parents="15639 21079"/>
    </justification>
  </clause>

  <clause id="21082">
    <literal><![CDATA[
      a(x,T(y \ (y / (z \ u)),w) * T(y,(z \ u) \ 1),x) = a(x,K(w,u \ (z * 1)) \ (y / (z \ u)),x)
    ]]></literal>
    <justification jstring="[para(9600(a,2),21075(a,1,2))].">
      <j1 rule="para" parents="9600 21075"/>
    </justification>
  </clause>

  <clause id="21083">
    <literal><![CDATA[
      K(x,R(y,y \ (x * z),y) / z) = K(x,z \ T(y,z * x))
    ]]></literal>
    <justification jstring="[para(9(a,1),21055(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 21055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21084">
    <literal><![CDATA[
      K(x,y \ T(z,y * x)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(13355,a,21083,a),flip(a)].">
      <j1 rule="hyper" parents="13355 21083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21086">
    <literal><![CDATA[
      K(x,(1 / y) \ T(T(z,y),(1 / y) * x)) = K(x,z / (K(y,z) / y))
    ]]></literal>
    <justification jstring="[para(15055(a,1),21084(a,2,2))].">
      <j1 rule="para" parents="15055 21084"/>
    </justification>
  </clause>

  <clause id="21087">
    <literal><![CDATA[
      K(x,(1 / y) \ T(T(z,y),y \ x)) = K(x,z / (K(y,z) / y))
    ]]></literal>
    <justification jstring="[para(14426(a,1),21086(a,1,2,2))].">
      <j1 rule="para" parents="14426 21086"/>
    </justification>
  </clause>

  <clause id="21088">
    <literal><![CDATA[
      K(x,y / (K(z,y) / z)) = K(x,z * T(T(y,z),z \ x))
    ]]></literal>
    <justification jstring="[hyper(14477,a,21087,a),flip(a)].">
      <j1 rule="hyper" parents="14477 21087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21089">
    <literal><![CDATA[
      K(x,y / (K(z,y) / z)) = K(x,T(y,z \ x) * z)
    ]]></literal>
    <justification jstring="[para(265(a,1),21088(a,2,2))].">
      <j1 rule="para" parents="265 21088"/>
    </justification>
  </clause>

  <clause id="21090">
    <literal><![CDATA[
      K(x,T(y,z \ x) * z) = K(x,y * (z * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14602,a(flip),b,21089,a),flip(a)].">
      <j1 rule="hyper" parents="64 14602 21089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21091">
    <literal><![CDATA[
      K(x,T(y,z \ x) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11145,a(flip),b,21090,a),flip(a)].">
      <j1 rule="hyper" parents="373 11145 21090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21092">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ x) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,9684,a,b,21091,a),flip(a)].">
      <j1 rule="hyper" parents="373 9684 21091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21093">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[para(6729(a,1),21092(a,1,2,1))].">
      <j1 rule="para" parents="6729 21092"/>
    </justification>
  </clause>

  <clause id="21094">
    <literal><![CDATA[
      K(x,T(y,z) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16870,a(flip),b,21093,a)].">
      <j1 rule="hyper" parents="64 16870 21093"/>
    </justification>
  </clause>

  <clause id="21096">
    <literal><![CDATA[
      K(x,y * (T(z,y) * x)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(17627,a,21094,a)].">
      <j1 rule="hyper" parents="17627 21094"/>
    </justification>
  </clause>

  <clause id="21097">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * u)) * K(u,(z * u) * y)) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[para(21096(a,1),8220(a,1,2,2))].">
      <j1 rule="para" parents="21096 8220"/>
    </justification>
  </clause>

  <clause id="21098">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) / u)) * u = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(19803,a,21059,a)].">
      <j1 rule="hyper" parents="19803 21059"/>
    </justification>
  </clause>

  <clause id="21099">
    <literal><![CDATA[
      (K(x,y) * (K(K(y,x),z) * u)) * (u \ (z * K(y,x))) = z * a(u \ (z * K(y,x)),z,K(y,x))
    ]]></literal>
    <justification jstring="[para(14884(a,1),21098(a,1,1,2))].">
      <j1 rule="para" parents="14884 21098"/>
    </justification>
  </clause>

  <clause id="21101">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / T(z * K(z \ u,w),u)) = T(x,y * K(w,z \ u))
    ]]></literal>
    <justification jstring="[para(17835(a,2),20673(a,1,2,2))].">
      <j1 rule="para" parents="17835 20673"/>
    </justification>
  </clause>

  <clause id="21102">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(x,x \ u) = (u / x) * K(z,K(x,x \ y))
    ]]></literal>
    <justification jstring="[para(17329(a,1),20759(a,2,1)),flip(a)].">
      <j1 rule="para" parents="17329 20759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21103">
    <literal><![CDATA[
      T(x \ y,K(y,z)) * K(x,x \ y) = (y / x) * K(z,K(x,x \ y))
    ]]></literal>
    <justification jstring="[para(9054(a,2),21102(a,1,1))].">
      <j1 rule="para" parents="9054 21102"/>
    </justification>
  </clause>

  <clause id="21104">
    <literal><![CDATA[
      T((x \ y) * K(x,x \ y),K(y,z)) = (y / x) * K(z,K(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(18374,a,21103,a)].">
      <j1 rule="hyper" parents="18374 21103"/>
    </justification>
  </clause>

  <clause id="21105">
    <literal><![CDATA[
      (x / y) * K(z,K(y,y \ x)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(5774(a,1),21104(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5774 21104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21106">
    <literal><![CDATA[
      (x \ y) * K(x,T(x \ y,z)) = T(y / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8351,a(flip),b,21105,a)].">
      <j1 rule="hyper" parents="64 8351 21105"/>
    </justification>
  </clause>

  <clause id="21107">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) = K(x,u / ((z \ 1) * (y / (1 / z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,17632,a(flip),b,20780,a)].">
      <j1 rule="hyper" parents="64 17632 20780"/>
    </justification>
  </clause>

  <clause id="21108">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * (u / (1 / z)))) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(17401,a,21107,a),flip(a)].">
      <j1 rule="hyper" parents="17401 21107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21109">
    <literal><![CDATA[
      K(x,y / T(z,u \ 1)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17689,a(flip),b,21108,a)].">
      <j1 rule="hyper" parents="64 17689 21108"/>
    </justification>
  </clause>

  <clause id="21110">
    <literal><![CDATA[
      K(x,(1 / y) / T(z,y)) = K(x,z \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(18115,a,21109,a),flip(a)].">
      <j1 rule="hyper" parents="18115 21109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21111">
    <literal><![CDATA[
      K(x,(1 / y) / (z / y)) = K(x,(y \ z) \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16279,a(flip),b,21110,a)].">
      <j1 rule="hyper" parents="64 16279 21110"/>
    </justification>
  </clause>

  <clause id="21112">
    <literal><![CDATA[
      K(x,(y \ 1) / (z / y)) = K(x,(y \ z) \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(17436,a,21111,a)].">
      <j1 rule="hyper" parents="17436 21111"/>
    </justification>
  </clause>

  <clause id="21113">
    <literal><![CDATA[
      K(x,(y \ 1) / (z / y)) = K(x,(y \ z) \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,6542,a(flip),b,21112,a),flip(a)].">
      <j1 rule="hyper" parents="373 6542 21112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21115">
    <literal><![CDATA[
      T(x,y / T((z * K(u,w)) * v5,z)) = T(x,y / (v5 * (K(u,w) * z)))
    ]]></literal>
    <justification jstring="[para(22(a,2),20820(a,1,2,2))].">
      <j1 rule="para" parents="22 20820"/>
    </justification>
  </clause>

  <clause id="21116">
    <literal><![CDATA[
      T(x,y / (z * (K(u,w) * v5))) = T(x,y / (z * (v5 * K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,21035,a(flip),b,21115,a),flip(a)].">
      <j1 rule="hyper" parents="64 21035 21115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21117">
    <literal><![CDATA[
      T(x,y / (z * (K(u,w) * v5))) = T(x,y * ((z * v5) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,20278,a(flip),b,21116,a),flip(a)].">
      <j1 rule="hyper" parents="373 20278 21116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21118">
    <literal><![CDATA[
      T(x,y * ((z * (u / z)) \ K(z * u,w))) = T(x,y / (T(u,z) * K(z * u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17887,a(flip),b,21117,a),flip(a)].">
      <j1 rule="hyper" parents="64 17887 21117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21119">
    <literal><![CDATA[
      T(x,(T(y,z / u) \ (z / u)) \ w) = T(x,(T(u \ z,u) / y) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,20076,a(flip),b,20826,a)].">
      <j1 rule="hyper" parents="64 20076 20826"/>
    </justification>
  </clause>

  <clause id="21120">
    <literal><![CDATA[
      T(x,(T(y \ z,y) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,20825,a(flip),b,21119,a),flip(a)].">
      <j1 rule="hyper" parents="64 20825 21119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21121">
    <literal><![CDATA[
      T(x,((((y \ z) \ z) \ z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(4679(a,1),21120(a,1,2,1,1))].">
      <j1 rule="para" parents="4679 21120"/>
    </justification>
  </clause>

  <clause id="21122">
    <literal><![CDATA[
      T(x,(T(y \ z,z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,20269,a(flip),b,21121,a)].">
      <j1 rule="hyper" parents="64 20269 21121"/>
    </justification>
  </clause>

  <clause id="21123">
    <literal><![CDATA[
      T(x,((y / z) / y) \ u) = T(x,(y \ (z \ y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,20012,a(flip),b,21122,a),flip(a)].">
      <j1 rule="hyper" parents="64 20012 21122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21124">
    <literal><![CDATA[
      T(x,(y \ ((z \ K(z,y)) \ y)) \ u) = T(x,(y \ (y / (z \ 1))) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16243,a(flip),b,21123,a),flip(a)].">
      <j1 rule="hyper" parents="64 16243 21123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21125">
    <literal><![CDATA[
      T(x,(((y \ 1) \ z) / z) \ u) = T(x,(z \ (z / (y \ 1))) \ u)
    ]]></literal>
    <justification jstring="[para(9507(a,1),21124(a,1,2,1))].">
      <j1 rule="para" parents="9507 21124"/>
    </justification>
  </clause>

  <clause id="21126">
    <literal><![CDATA[
      T(x,(y \ (y / ((z \ 1) \ 1))) \ u) = T(x,((z \ y) / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(14917,a,21125,a),flip(a)].">
      <j1 rule="hyper" parents="14917 21125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21127">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) = T(x,(z \ (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(14919,a,21126,a),flip(a)].">
      <j1 rule="hyper" parents="14919 21126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21128">
    <literal><![CDATA[
      T(x,T((y \ z) / z,u) \ w) = T(x,(z \ (z / T(y,u))) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,20224,a(flip),b,21127,a)].">
      <j1 rule="hyper" parents="64 20224 21127"/>
    </justification>
  </clause>

  <clause id="21129">
    <literal><![CDATA[
      K(x,K(y,(z \ u) \ (z \ 1)) \ ((u / z) \ w)) = K(x,(T(u,y) / z) \ w)
    ]]></literal>
    <justification jstring="[para(21113(a,1),20884(a,1,2,1))].">
      <j1 rule="para" parents="21113 20884"/>
    </justification>
  </clause>

  <clause id="21131">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,T(v5,v6))) = T(x,y * T(w \ K(u,z),w \ v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,17715,a(flip),b,21034,a),flip(a)].">
      <j1 rule="hyper" parents="373 17715 21034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21132">
    <literal><![CDATA[
      T(x,T((y \ z) / z,u) \ K(y \ z,w)) = T(x,T(z / T(y,u),w) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,21128,a,b,21042,a)].">
      <j1 rule="hyper" parents="64 21128 21042"/>
    </justification>
  </clause>

  <clause id="21133">
    <literal><![CDATA[
      T(x,(y * T(z,u)) * T(z \ K(w,z \ u),u)) = T(x,y * K(w,z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18441,a(flip),b,21101,a)].">
      <j1 rule="hyper" parents="64 18441 21101"/>
    </justification>
  </clause>

  <clause id="21134">
    <literal><![CDATA[
      K(x,K(y,z * (z \ u)) \ ((u / z) \ w)) = K(x,(T(u,y) / z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17631,a(flip),b,21129,a)].">
      <j1 rule="hyper" parents="64 17631 21129"/>
    </justification>
  </clause>

  <clause id="21135">
    <literal><![CDATA[
      K(x,K(y,z) \ ((z / u) \ w)) = K(x,(T(z,y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),21134(a,1,2,1,2))].">
      <j1 rule="para" parents="10 21134"/>
    </justification>
  </clause>

  <clause id="21136">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y / u) \ w)) = K(x,(T(y,z) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(17521,a,21135,a)].">
      <j1 rule="hyper" parents="17521 21135"/>
    </justification>
  </clause>

  <clause id="21137">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,w),z \ v5)) = T(x,y / T(K(w,u) * z,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,17972,a(flip),b,21131,a),flip(a)].">
      <j1 rule="hyper" parents="64 17972 21131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21138">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,w),z \ v5)) = T(x,y * T(z \ K(u,w),v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,17715,a(flip),b,21137,a),flip(a)].">
      <j1 rule="hyper" parents="373 17715 21137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21139">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,z \ w),w)) = T(x,y / (T(z \ w,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,20216,a(flip),b,21138,a),flip(a)].">
      <j1 rule="hyper" parents="64 20216 21138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21140">
    <literal><![CDATA[
      T(x,T(((y \ z) / z) \ K(y \ z,u),w)) = T(x,T(z / T(y,w),u) \ z)
    ]]></literal>
    <justification jstring="[hyper(18700,a,21132,a)].">
      <j1 rule="hyper" parents="18700 21132"/>
    </justification>
  </clause>

  <clause id="21141">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / (T(z \ u,w) \ u)) = T(x,y * K(w,z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,21139,a(flip),b,21133,a)].">
      <j1 rule="hyper" parents="64 21139 21133"/>
    </justification>
  </clause>

  <clause id="21142">
    <literal><![CDATA[
      T(x,T(y / T(z \ y,u),w)) = T(x,T(y / T(z,w),u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16464,a(flip),b,21140,a)].">
      <j1 rule="hyper" parents="64 16464 21140"/>
    </justification>
  </clause>

  <clause id="21143">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(y / T(z,w),u) \ y)
    ]]></literal>
    <justification jstring="[para(8071(a,1),21142(a,1,2,1))].">
      <j1 rule="para" parents="8071 21142"/>
    </justification>
  </clause>

  <clause id="21144">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,y * T(y \ T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(373,a,20110,a(flip),b,21143,a),flip(a)].">
      <j1 rule="hyper" parents="373 20110 21143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21145">
    <literal><![CDATA[
      T(x,y * T(T(y * (z / y),u) / y,w)) = T(x,T(T(y / z,w) \ y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,11330,a,b,21144,a)].">
      <j1 rule="hyper" parents="373 11330 21144"/>
    </justification>
  </clause>

  <clause id="21146">
    <literal><![CDATA[
      T(x,T(y * T((y * (z / y)) / y,u),w)) = T(x,T(T(y / z,u) \ y,w))
    ]]></literal>
    <justification jstring="[hyper(20150,a,21145,a)].">
      <j1 rule="hyper" parents="20150 21145"/>
    </justification>
  </clause>

  <clause id="21147">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(T(z / y,u) * y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,11314,a(flip),b,21146,a),flip(a)].">
      <j1 rule="hyper" parents="64 11314 21146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21148">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(y * T(y \ z,u),w))
    ]]></literal>
    <justification jstring="[para(525(a,1),21147(a,2,2,1))].">
      <j1 rule="para" parents="525 21147"/>
    </justification>
  </clause>

  <clause id="21149">
    <literal><![CDATA[
      T(x,T(y * T(y \ z,u),w)) = T(x,y * T(y \ T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,21144,a(flip),b,21148,a),flip(a)].">
      <j1 rule="hyper" parents="64 21144 21148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21150">
    <literal><![CDATA[
      K(x,y / (z \ a(u \ 1,u,z))) = K(x,a(u \ 1,u,z) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(20636,a,19879,a),flip(a)].">
      <j1 rule="hyper" parents="20636 19879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21151">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) \ (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * L(z,y,y \ 1)) = w
    ]]></literal>
    <justification jstring="[para(21150(a,1),17538(a,1))].">
      <j1 rule="para" parents="21150 17538"/>
    </justification>
  </clause>

  <clause id="21152">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,x,K(y \ x,u))
    ]]></literal>
    <justification jstring="[para(15328(a,1),20718(a,2,2))].">
      <j1 rule="para" parents="15328 20718"/>
    </justification>
  </clause>

  <clause id="21153">
    <literal><![CDATA[
      K((K(x,y) * z) / u,w) = K(z * (u \ K(y,x)),w)
    ]]></literal>
    <justification jstring="[hyper(20959,a,20789,a),flip(a)].">
      <j1 rule="hyper" parents="20959 20789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21154">
    <literal><![CDATA[
      K((x / y) \ K(z,u),w) = K(y * (x \ K(u,z)),w)
    ]]></literal>
    <justification jstring="[hyper(20703,a,21153,a)].">
      <j1 rule="hyper" parents="20703 21153"/>
    </justification>
  </clause>

  <clause id="21155">
    <literal><![CDATA[
      K(x * (y \ K(z,u)),T(w,y)) = K((x \ y) \ K(u,z),w)
    ]]></literal>
    <justification jstring="[hyper(18187,a,21154,a),flip(a)].">
      <j1 rule="hyper" parents="18187 21154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21156">
    <literal><![CDATA[
      K((x \ y) \ K(z,u),w) = K((y \ x) * K(u,z),w)
    ]]></literal>
    <justification jstring="[hyper(20830,a,21155,a),flip(a)].">
      <j1 rule="hyper" parents="20830 21155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21157">
    <literal><![CDATA[
      K(x,y) * (z * T(x * K(u,w),z)) = (x * K(u,w)) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(18618(a,1),20620(a,1,2,2))].">
      <j1 rule="para" parents="18618 20620"/>
    </justification>
  </clause>

  <clause id="21158">
    <literal><![CDATA[
      K(x,y) * ((x * K(z,u)) * w) = (x * K(z,u)) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[hyper(737,a,21157,a)].">
      <j1 rule="hyper" parents="737 21157"/>
    </justification>
  </clause>

  <clause id="21160">
    <literal><![CDATA[
      (x * K(y,z)) * (K(x,u) * w) = (T(x,u) * K(y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(64,a,20699,a(flip),b,21158,a),flip(a)].">
      <j1 rule="hyper" parents="64 20699 21158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21161">
    <literal><![CDATA[
      T((T(x,y) * K(z,u)) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1),w) = (x * K(z,u)) * (K(x,y) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,19726,a,b,21160,a)].">
      <j1 rule="hyper" parents="373 19726 21160"/>
    </justification>
  </clause>

  <clause id="21162">
    <literal><![CDATA[
      K(x,y) * ((T(x,y) * K(z,u)) \ w) = (x * K(z,u)) \ w
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,21160,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 21160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21163">
    <literal><![CDATA[
      K(x,(y / (z / u)) / T(w,(z / u) \ y)) = K(x,w \ (y / (T(u,z) \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20181,a(flip),b,20827,a)].">
      <j1 rule="hyper" parents="64 20181 20827"/>
    </justification>
  </clause>

  <clause id="21164">
    <literal><![CDATA[
      K(x,y \ (z / (T(u,w) \ w))) = K(x,y \ (z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(18115,a,21163,a),flip(a)].">
      <j1 rule="hyper" parents="18115 21163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21165">
    <literal><![CDATA[
      K(x,y \ (z / (T(u,w) \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z / (w / u))) = v5
    ]]></literal>
    <justification jstring="[para(21163(a,1),18115(a,1))].">
      <j1 rule="para" parents="21163 18115"/>
    </justification>
  </clause>

  <clause id="21166">
    <literal><![CDATA[
      K(x,y \ (z / (z / u))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),21164(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 21164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21167">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(79(a,1),21166(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="79 21166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21168">
    <literal><![CDATA[
      K(x,y \ T(z * (u * K(w,u \ 1)),z)) = K(x,y \ (z / T(z / (z * u),w)))
    ]]></literal>
    <justification jstring="[para(8850(a,1),21166(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8850 21166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21169">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,z \ 1))) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16372,a(flip),b,21167,a)].">
      <j1 rule="hyper" parents="64 16372 21167"/>
    </justification>
  </clause>

  <clause id="21170">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,(y / z) \ 1)))
    ]]></literal>
    <justification jstring="[para(6617(a,1),21169(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6617 21169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21171">
    <literal><![CDATA[
      K(x,y) \ (z * T(u / z,K(x,y))) = z * ((u * K(y,x)) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,18127,a(flip),b,20899,a),flip(a)].">
      <j1 rule="hyper" parents="64 18127 20899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21172">
    <literal><![CDATA[
      K(x,T(y,z \ u)) \ (z * (u / z)) = z * ((u * K(y,x)) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,17723,a,b,21171,a)].">
      <j1 rule="hyper" parents="64 17723 21171"/>
    </justification>
  </clause>

  <clause id="21173">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * u)) * K(z * y,u)) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[hyper(17663,a,21097,a)].">
      <j1 rule="hyper" parents="17663 21097"/>
    </justification>
  </clause>

  <clause id="21174">
    <literal><![CDATA[
      K(x,y * ((T(z,y) * u) * K(z * y,u))) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[hyper(19581,a,21173,a)].">
      <j1 rule="hyper" parents="19581 21173"/>
    </justification>
  </clause>

  <clause id="21175">
    <literal><![CDATA[
      K(x,y * (T(z,y) * (u * K(z * y,u)))) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19887,a(flip),b,21174,a)].">
      <j1 rule="hyper" parents="64 19887 21174"/>
    </justification>
  </clause>

  <clause id="21176">
    <literal><![CDATA[
      K(x,y * ((y \ T(z * y,u)) * u)) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[para(15095(a,1),21175(a,1,2,2))].">
      <j1 rule="para" parents="15095 21175"/>
    </justification>
  </clause>

  <clause id="21177">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = K(x,(u * ((z * y) / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,18751,a(flip),b,21176,a),flip(a)].">
      <j1 rule="hyper" parents="64 18751 21176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21178">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),21177(a,2,2,1,2))].">
      <j1 rule="para" parents="11 21177"/>
    </justification>
  </clause>

  <clause id="21179">
    <literal><![CDATA[
      K(x,L(y,z,u) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(19275,a,21178,a)].">
      <j1 rule="hyper" parents="19275 21178"/>
    </justification>
  </clause>

  <clause id="21180">
    <literal><![CDATA[
      T(x,L(y,z,u) * (z * u)) = T(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(143,a,21179,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 21179 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21181">
    <literal><![CDATA[
      K(x,((y * z) \ (z * u)) * (y * z)) = K(x,((T(y,z) \ u) * y) * z)
    ]]></literal>
    <justification jstring="[para(10979(a,1),21179(a,1,2,1))].">
      <j1 rule="para" parents="10979 21179"/>
    </justification>
  </clause>

  <clause id="21183">
    <literal><![CDATA[
      T(x,L(y,z \ K(u,z \ 1),u) * (u * (z \ 1))) = T(x,(y * (z \ K(u,z \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(5887(a,1),21180(a,1,2,2))].">
      <j1 rule="para" parents="5887 21180"/>
    </justification>
  </clause>

  <clause id="21184">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * z) = K(x,T(z * u,y * z))
    ]]></literal>
    <justification jstring="[hyper(11219,a,21181,a),flip(a)].">
      <j1 rule="hyper" parents="11219 21181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21185">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,z) * y)) = K(x,T(y * u,z * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,20142,a(flip),b,21184,a)].">
      <j1 rule="hyper" parents="64 20142 21184"/>
    </justification>
  </clause>

  <clause id="21186">
    <literal><![CDATA[
      K(x,T(y * z,u * y)) = K(x,T(z,u) * T(y,u))
    ]]></literal>
    <justification jstring="[hyper(17260,a,21185,a),flip(a)].">
      <j1 rule="hyper" parents="17260 21185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21187">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,(u / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,15786,a(flip),b,21186,a),flip(a)].">
      <j1 rule="hyper" parents="373 15786 21186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21188">
    <literal><![CDATA[
      T(x,y / (T(z,u) * K(u * z,w))) = T(x,y * (T(z,u) \ K(u * z,w)))
    ]]></literal>
    <justification jstring="[hyper(19756,a,21118,a),flip(a)].">
      <j1 rule="hyper" parents="19756 21118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21189">
    <literal><![CDATA[
      T(x,y / (T(z,u) * K(u * z,w))) = T(x,y * T(z \ K(u * z,w),u))
    ]]></literal>
    <justification jstring="[hyper(373,a,20790,a,b,21188,a),flip(a)].">
      <j1 rule="hyper" parents="373 20790 21188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21190">
    <literal><![CDATA[
      T(x,y / T(z * K(z * u,w),u)) = T(x,y * T(z \ K(u * z,w),u))
    ]]></literal>
    <justification jstring="[para(17828(a,2),21189(a,1,2,2))].">
      <j1 rule="para" parents="17828 21189"/>
    </justification>
  </clause>

  <clause id="21191">
    <literal><![CDATA[
      T(x,y * T(z \ K(u * z,w),u)) = T(x,y * T(z \ K(w,z * u),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18441,a(flip),b,21190,a),flip(a)].">
      <j1 rule="hyper" parents="64 18441 21190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21192">
    <literal><![CDATA[
      T(x,y * T(z \ K(u * z,w),u)) = T(x,y / (u \ T(z * u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18568,a(flip),b,21191,a),flip(a)].">
      <j1 rule="hyper" parents="373 18568 21191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21193">
    <literal><![CDATA[
      T(x,K(y * z,u) * (w / T(z,y))) = T(x,w / (y \ T(z * y,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20389,a,b,21192,a)].">
      <j1 rule="hyper" parents="64 20389 21192"/>
    </justification>
  </clause>

  <clause id="21194">
    <literal><![CDATA[
      T(x,y / (T(z \ u,w) \ u)) = T(x,y / (u \ T(z * u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20391,a(flip),b,21193,a)].">
      <j1 rule="hyper" parents="64 20391 21193"/>
    </justification>
  </clause>

  <clause id="21195">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / (u \ T(z * u,w))) = T(x,y * K(w,z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,21141,a(flip),b,21194,a),flip(a)].">
      <j1 rule="hyper" parents="64 21141 21194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21196">
    <literal><![CDATA[
      T(x,y * K(z,u \ w)) = T(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(20746,a,21195,a),flip(a)].">
      <j1 rule="hyper" parents="20746 21195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21197">
    <literal><![CDATA[
      (x \ T(y * x,z * K(u,w * v5))) * (T(y,x) \ 1) = K(x * y,z * K(u,v5 \ w))
    ]]></literal>
    <justification jstring="[para(21196(a,1),16503(a,1,1,2))].">
      <j1 rule="para" parents="21196 16503"/>
    </justification>
  </clause>

  <clause id="21198">
    <literal><![CDATA[
      K(x,y \ T(z * (u * K(w,u \ 1)),z)) = K(x,y \ (T((z * u) \ z,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17886,a(flip),b,21168,a),flip(a)].">
      <j1 rule="hyper" parents="373 17886 21168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21199">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,z / y)))
    ]]></literal>
    <justification jstring="[para(4818(a,1),21170(a,2,2,2,2))].">
      <j1 rule="para" parents="4818 21170"/>
    </justification>
  </clause>

  <clause id="21200">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ ((u * K(w,u \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13383,a(flip),b,21198,a),flip(a)].">
      <j1 rule="hyper" parents="64 13383 21198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21201">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (u * (K(w,u \ 1) * z)))
    ]]></literal>
    <justification jstring="[para(4495(a,1),21200(a,2,2,2))].">
      <j1 rule="para" parents="4495 21200"/>
    </justification>
  </clause>

  <clause id="21202">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,K(u \ 1,w) * (y \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,20528,a(flip),b,21201,a),flip(a)].">
      <j1 rule="hyper" parents="373 20528 21201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21203">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,K(u,w) * (y \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,16821,a(flip),b,21202,a),flip(a)].">
      <j1 rule="hyper" parents="373 16821 21202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21204">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,19948,a(flip),b,21203,a),flip(a)].">
      <j1 rule="hyper" parents="373 19948 21203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21205">
    <literal><![CDATA[
      K(x,y \ T(z * (1 / T(u,w)),z)) = K(x,y \ (T(1 / u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16710,a(flip),b,21204,a)].">
      <j1 rule="hyper" parents="64 16710 21204"/>
    </justification>
  </clause>

  <clause id="21206">
    <literal><![CDATA[
      K(x,y \ T(z * (1 / T(u,w)),z)) = K(x,y \ (T(u \ 1,w) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7034,a(flip),b,21205,a),flip(a)].">
      <j1 rule="hyper" parents="373 7034 21205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21207">
    <literal><![CDATA[
      K(x,y \ ((1 / T(z,u)) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13383,a(flip),b,21206,a)].">
      <j1 rule="hyper" parents="64 13383 21206"/>
    </justification>
  </clause>

  <clause id="21208">
    <literal><![CDATA[
      K(x,y \ (T(z \ 1,u) * w)) = K(x,y \ ((T(z,u) \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,6641,a(flip),b,21207,a),flip(a)].">
      <j1 rule="hyper" parents="64 6641 21207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21209">
    <literal><![CDATA[
      K(x,((y \ 1) * T(z \ u,y)) \ (T(y \ 1,z \ u) * u)) = K(x,L(T(z,u),u,T(y,z \ u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,12156,a(flip),b,21208,a),flip(a)].">
      <j1 rule="hyper" parents="373 12156 21208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21210">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * u) \ ((y \ 1) * (z * y))) = K(x,L(u \ (y * z),y * z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(12113,a,20576,a),flip(a)].">
      <j1 rule="hyper" parents="12113 20576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21211">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * u) \ ((y \ 1) * (z * y))) = K(x,(y \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16172,a(flip),b,20576,a),flip(a)].">
      <j1 rule="hyper" parents="64 16172 20576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21212">
    <literal><![CDATA[
      K(x,y / (T(z,u / w) \ (u / w))) = K(x,y / ((w \ T(u,w)) / z))
    ]]></literal>
    <justification jstring="[hyper(20855,a,20185,a),flip(a)].">
      <j1 rule="hyper" parents="20855 20185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21213">
    <literal><![CDATA[
      K(x,y / ((z \ T(u,z)) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(20853,a,21212,a),flip(a)].">
      <j1 rule="hyper" parents="20853 21212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21214">
    <literal><![CDATA[
      K(x,y / ((T(z,u) \ u) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9426,a,b,21213,a)].">
      <j1 rule="hyper" parents="64 9426 21213"/>
    </justification>
  </clause>

  <clause id="21215">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),u,K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[hyper(16657,a,20994,a)].">
      <j1 rule="hyper" parents="16657 20994"/>
    </justification>
  </clause>

  <clause id="21217">
    <literal><![CDATA[
      (K(x,y) * (z \ (K(y,x) * u))) \ u = ((z \ u) * K(x,y)) \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,18896,a(flip),b,21215,a),flip(a)].">
      <j1 rule="hyper" parents="64 18896 21215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21218">
    <literal><![CDATA[
      L(((x \ y) * K(z,u)) \ (y * K(z,u)),x \ (K(u,z) * y),K(u,z)) = (x \ (K(u,z) * y)) \ (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(21217(a,1),16642(a,1,1))].">
      <j1 rule="para" parents="21217 16642"/>
    </justification>
  </clause>

  <clause id="21219">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ (K(v6,v7) \ v8)) = K(x,K(z,u) \ ((K(v7,v6) \ y) \ v8))
    ]]></literal>
    <justification jstring="[hyper(64,a,19392,a(flip),b,21018,a)].">
      <j1 rule="hyper" parents="64 19392 21018"/>
    </justification>
  </clause>

  <clause id="21220">
    <literal><![CDATA[
      K(x,K(y,z) \ ((K(u,w) \ v5) \ v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ (v5 \ (K(w,u) \ v6))) = v7
    ]]></literal>
    <justification jstring="[para(21219(a,1),21015(a,1))].">
      <j1 rule="para" parents="21219 21015"/>
    </justification>
  </clause>

  <clause id="21221">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (K(z,L(y,w,v5)) \ v6))) = K(x,u \ v6)
    ]]></literal>
    <justification jstring="[hyper(21220,a,21026,a)].">
      <j1 rule="hyper" parents="21220 21026"/>
    </justification>
  </clause>

  <clause id="21222">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (L(K(z,y),w,v5) \ v6))) = K(x,u \ v6)
    ]]></literal>
    <justification jstring="[para(7537(a,1),21221(a,1,2,2,2,1))].">
      <j1 rule="para" parents="7537 21221"/>
    </justification>
  </clause>

  <clause id="21223">
    <literal><![CDATA[
      K(x,y \ (K(z,u) \ (L(K(u,z),w,v5) \ v6))) = K(x,y \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,20878,a(flip),b,21222,a)].">
      <j1 rule="hyper" parents="64 20878 21222"/>
    </justification>
  </clause>

  <clause id="21224">
    <literal><![CDATA[
      K(x,y \ (a(K(z,u),w,v5) \ v6)) = K(x,y \ v6)
    ]]></literal>
    <justification jstring="[para(20950(a,1),21223(a,1,2,2))].">
      <j1 rule="para" parents="20950 21223"/>
    </justification>
  </clause>

  <clause id="21225">
    <literal><![CDATA[
      K(x,y \ (z * a(u,w,K(v5,v6)))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(19336(a,1),21224(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19336 21224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21226">
    <literal><![CDATA[
      K(x,y \ K(z,L(u,w,v5))) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[para(12069(a,1),21225(a,1,2,2))].">
      <j1 rule="para" parents="12069 21225"/>
    </justification>
  </clause>

  <clause id="21227">
    <literal><![CDATA[
      K(x,y \ K(z,(u / w) / v5)) = K(x,y \ K(z,u / (v5 * w)))
    ]]></literal>
    <justification jstring="[para(15587(a,1),21226(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15587 21226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21228">
    <literal><![CDATA[
      K(x,y \ K(z,u / (w * v5))) = K(x,y \ K(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[hyper(18181,a,21227,a),flip(a)].">
      <j1 rule="hyper" parents="18181 21227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21229">
    <literal><![CDATA[
      K(x,(y / z) \ K(y,u \ (w / v5))) = K(x,z / T(y,L((w / v5) / u,u,v5)))
    ]]></literal>
    <justification jstring="[hyper(20921,a,21228,a),flip(a)].">
      <j1 rule="hyper" parents="20921 21228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21230">
    <literal><![CDATA[
      K(x,y / T(z,L((u / w) / v5,v5,w))) = K(x,y / T(z,v5 \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(20920,a,21229,a),flip(a)].">
      <j1 rule="hyper" parents="20920 21229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21231">
    <literal><![CDATA[
      K(x,y * T(z,L((u / w) / v5,v5,w))) = K(x,y / T(z \ 1,v5 \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17782,a(flip),b,21230,a)].">
      <j1 rule="hyper" parents="64 17782 21230"/>
    </justification>
  </clause>

  <clause id="21232">
    <literal><![CDATA[
      K(x,y * T(z,L((u / w) / v5,v5,w))) = K(x,y * T(z,v5 \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,17782,a(flip),b,21231,a),flip(a)].">
      <j1 rule="hyper" parents="373 17782 21231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21233">
    <literal><![CDATA[
      K(x,y * T(z,u / (w * v5))) = K(x,y * T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(15609(a,1),21232(a,1,2,2))].">
      <j1 rule="para" parents="15609 21232"/>
    </justification>
  </clause>

  <clause id="21234">
    <literal><![CDATA[
      K(x,y * T(z,(u * w) \ v5)) = K(x,y * T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(18095,a,21233,a)].">
      <j1 rule="hyper" parents="18095 21233"/>
    </justification>
  </clause>

  <clause id="21235">
    <literal><![CDATA[
      K(x,y * T(z,(u * w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u \ (w \ v5))) = v6
    ]]></literal>
    <justification jstring="[para(21234(a,2),18539(a,1))].">
      <j1 rule="para" parents="21234 18539"/>
    </justification>
  </clause>

  <clause id="21236">
    <literal><![CDATA[
      K(K(x,y) * L(y,z,u),w / ((v5 * x) \ v5)) = K(y,L((v5 / (x * v5)) \ w,z,u))
    ]]></literal>
    <justification jstring="[hyper(17513,a,20999,a)].">
      <j1 rule="hyper" parents="17513 20999"/>
    </justification>
  </clause>

  <clause id="21237">
    <literal><![CDATA[
      K(x,L(T(y / ((z * u) \ z),u),w,v5)) = K(x,L((z / (u * z)) \ y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,19434,a(flip),b,21236,a)].">
      <j1 rule="hyper" parents="64 19434 21236"/>
    </justification>
  </clause>

  <clause id="21238">
    <literal><![CDATA[
      K(x,L((y / (z * y)) \ u,w,v5)) = K(x,L(((y * z) \ y) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,11259,a(flip),b,21237,a),flip(a)].">
      <j1 rule="hyper" parents="64 11259 21237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21239">
    <literal><![CDATA[
      K(x,L(((y * z) \ y) \ T(u,z),w,v5)) = K(x,L(u / (y / (z * y)),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16949,a(flip),b,21238,a),flip(a)].">
      <j1 rule="hyper" parents="64 16949 21238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21240">
    <literal><![CDATA[
      K(x,L(y / (z / (u * z)),w,v5)) = K(x,L(y / ((z * u) \ z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,16948,a(flip),b,21239,a),flip(a)].">
      <j1 rule="hyper" parents="64 16948 21239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21241">
    <literal><![CDATA[
      K(x,L((y / T(z,u \ 1)) / ((w * u) \ w),(w * u) \ w,z)) = K(x,y / (z * (w / (u * w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,19289,a(flip),b,21240,a),flip(a)].">
      <j1 rule="hyper" parents="64 19289 21240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21242">
    <literal><![CDATA[
      T(x,T(y * T(z,u),w) / T(v5,y * z)) = T(x,v5 \ T(y * (z * K(u,z)),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18757,a(flip),b,21040,a)].">
      <j1 rule="hyper" parents="64 18757 21040"/>
    </justification>
  </clause>

  <clause id="21243">
    <literal><![CDATA[
      T(x,y \ T(z * (u * K(w,u)),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z * T(u,w),v5)) = v6
    ]]></literal>
    <justification jstring="[para(21242(a,1),21041(a,1))].">
      <j1 rule="para" parents="21242 21041"/>
    </justification>
  </clause>

  <clause id="21244">
    <literal><![CDATA[
      T(x,T(y,z) \ T(u * y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(u * T(y,z),w)) = v5
    ]]></literal>
    <justification jstring="[para(18734(a,1),21243(a,1))].">
      <j1 rule="para" parents="18734 21243"/>
    </justification>
  </clause>

  <clause id="21245">
    <literal><![CDATA[
      K(x * y,z * K(u,w \ v5)) = K(x * y,z * K(u,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(16504,a,21197,a),flip(a)].">
      <j1 rule="hyper" parents="16504 21197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21246">
    <literal><![CDATA[
      K(x * y,z * K(u,w \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z * K(u,v5 * w)) = v6
    ]]></literal>
    <justification jstring="[para(21197(a,1),16504(a,1))].">
      <j1 rule="para" parents="21197 16504"/>
    </justification>
  </clause>

  <clause id="21247">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w * K(v5,u * z)) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(20867,a,21245,a),flip(a)].">
      <j1 rule="hyper" parents="20867 21245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21248">
    <literal><![CDATA[
      K(x \ y,z * K(u,y * x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,20866,a(flip),b,21247,a)].">
      <j1 rule="hyper" parents="64 20866 21247"/>
    </justification>
  </clause>

  <clause id="21249">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ z) = w / (K(u \ z,x) * w)
    ]]></literal>
    <justification jstring="[para(21248(a,1),6160(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="21248 6160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21250">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,17142,a(flip),b,21249,a),flip(a)].">
      <j1 rule="hyper" parents="373 17142 21249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21251">
    <literal><![CDATA[
      K(x * K(y,T(z,u \ w) * v5),v5 \ T(z,w * u)) = K(x,v5 \ T(z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(18690,a,21250,a)].">
      <j1 rule="hyper" parents="18690 21250"/>
    </justification>
  </clause>

  <clause id="21252">
    <literal><![CDATA[
      K(x * K(y,T(z,u * w) * v5),v5 \ T(z,w * u)) = K(x,v5 \ T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(18091,a,21250,a)].">
      <j1 rule="hyper" parents="18091 21250"/>
    </justification>
  </clause>

  <clause id="21253">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ (w \ v5),u)),K(w \ (u \ v5),u) \ z) = K(x,K(w \ (u \ v5),u) \ z)
    ]]></literal>
    <justification jstring="[para(10230(a,1),21250(a,1,1,2,2))].">
      <j1 rule="para" parents="10230 21250"/>
    </justification>
  </clause>

  <clause id="21254">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w \ v5)),K(u,v5 / w) \ z) = K(x,K(u,v5 / w) \ z)
    ]]></literal>
    <justification jstring="[para(18027(a,1),21250(a,1,1,2))].">
      <j1 rule="para" parents="18027 21250"/>
    </justification>
  </clause>

  <clause id="21256">
    <literal><![CDATA[
      (K(x,y) * z) / (K(u,w) * K(v5,v6)) = K(x,y) * (z / (K(v5,v6) * K(u,w)))
    ]]></literal>
    <justification jstring="[para(19238(a,1),20548(a,1,1,1))].">
      <j1 rule="para" parents="19238 20548"/>
    </justification>
  </clause>

  <clause id="21258">
    <literal><![CDATA[
      (K(x,y) * z) * (K(u,w) * K(v5,v6)) = K(x,y) * (z / (K(v6,v5) * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20888,a(flip),b,21256,a)].">
      <j1 rule="hyper" parents="64 20888 21256"/>
    </justification>
  </clause>

  <clause id="21260">
    <literal><![CDATA[
      (K(x,y) * z) * (K(u,w) * K(v5,v6)) = K(x,y) * (z * (K(v5,v6) * K(u,w)))
    ]]></literal>
    <justification jstring="[para(20888(a,1),21258(a,2,2))].">
      <j1 rule="para" parents="20888 21258"/>
    </justification>
  </clause>

  <clause id="21261">
    <literal><![CDATA[
      L(K(x,y) * K(z,u),w,K(v5,v6)) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14211,a,21260,a)].">
      <j1 rule="hyper" parents="14211 21260"/>
    </justification>
  </clause>

  <clause id="21263">
    <literal><![CDATA[
      ((K(x,y) * K(z,u)) * a(w,v5,v6)) / K(x,y) = a(w,v5,v6) * K(z,u)
    ]]></literal>
    <justification jstring="[para(21261(a,1),20717(a,1,1,1))].">
      <j1 rule="para" parents="21261 20717"/>
    </justification>
  </clause>

  <clause id="21264">
    <literal><![CDATA[
      (K(x,y) * (K(z,u) * a(w,v5,v6))) / K(x,y) = a(w,v5,v6) * K(z,u)
    ]]></literal>
    <justification jstring="[para(20660(a,1),21263(a,1,1))].">
      <j1 rule="para" parents="20660 21263"/>
    </justification>
  </clause>

  <clause id="21266">
    <literal><![CDATA[
      T(K(x,y) * a(z,u,w),K(v5,v6)) = a(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8183,a,21264,a)].">
      <j1 rule="hyper" parents="8183 21264"/>
    </justification>
  </clause>

  <clause id="21267">
    <literal><![CDATA[
      1 / T((x * K(y,z)) * a(u,w,K(x,v5)),a(u,w,x)) = K(v5,a(u,w,x)) / (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(13977(a,2),20619(a,1,2,1,2))].">
      <j1 rule="para" parents="13977 20619"/>
    </justification>
  </clause>

  <clause id="21268">
    <literal><![CDATA[
      R(K(x,y),z,L(a(z,u,w),z,K(x,y))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11,a(flip),b,20847,a),flip(a)].">
      <j1 rule="hyper" parents="373 11 20847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21270">
    <literal><![CDATA[
      R(K(x,y),z,a(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(20845(a,1),21268(a,1,3))].">
      <j1 rule="para" parents="20845 21268"/>
    </justification>
  </clause>

  <clause id="21271">
    <literal><![CDATA[
      K(x,L(y,z,a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15596,a,21270,a)].">
      <j1 rule="hyper" parents="15596 21270"/>
    </justification>
  </clause>

  <clause id="21273">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16475,a,b,21271,a)].">
      <j1 rule="hyper" parents="64 16475 21271"/>
    </justification>
  </clause>

  <clause id="21274">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) = K(x,L(y,v5,a(v5,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(373,a,21271,a,b,21273,a),flip(a)].">
      <j1 rule="hyper" parents="373 21271 21273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21276">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(21274(a,2),7416(a,1))].">
      <j1 rule="para" parents="21274 7416"/>
    </justification>
  </clause>

  <clause id="21277">
    <literal><![CDATA[
      R(K(x,y),z,L(a(u,w,z),z,K(x,y))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11,a(flip),b,20849,a),flip(a)].">
      <j1 rule="hyper" parents="373 11 20849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21279">
    <literal><![CDATA[
      R(K(x,y),z,a(u,w,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(20846(a,1),21277(a,1,3))].">
      <j1 rule="para" parents="20846 21277"/>
    </justification>
  </clause>

  <clause id="21280">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15596,a,21279,a)].">
      <j1 rule="hyper" parents="15596 21279"/>
    </justification>
  </clause>

  <clause id="21282">
    <literal><![CDATA[
      (K(x,y) * z) / a(u,w,z) = K(x,y) * (z / a(u,w,z))
    ]]></literal>
    <justification jstring="[para(21280(a,1),15673(a,1,1,1))].">
      <j1 rule="para" parents="21280 15673"/>
    </justification>
  </clause>

  <clause id="21283">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * z) = K(u,w) * (z / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19322,a(flip),b,21282,a)].">
      <j1 rule="hyper" parents="64 19322 21282"/>
    </justification>
  </clause>

  <clause id="21284">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * z) = K(u,w) * (a(x,y,z) \ z)
    ]]></literal>
    <justification jstring="[para(16647(a,1),21283(a,2,2))].">
      <j1 rule="para" parents="16647 21283"/>
    </justification>
  </clause>

  <clause id="21285">
    <literal><![CDATA[
      K(x,y \ (z / T(u,z))) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,5987,a(flip),b,20862,a),flip(a)].">
      <j1 rule="hyper" parents="373 5987 20862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21286">
    <literal><![CDATA[
      K(x,y \ (T(z,u) / u)) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[para(4630(a,2),21285(a,1,2,2))].">
      <j1 rule="para" parents="4630 21285"/>
    </justification>
  </clause>

  <clause id="21287">
    <literal><![CDATA[
      K(x,y \ (T(z,u / w) / (T(w,u) \ u))) = K(x,y \ ((T(w,u) \ u) \ z))
    ]]></literal>
    <justification jstring="[para(13424(a,1),21286(a,1,2,2,1))].">
      <j1 rule="para" parents="13424 21286"/>
    </justification>
  </clause>

  <clause id="21288">
    <literal><![CDATA[
      K(x,y \ (T(z,u / w) / (u / w))) = K(x,y \ ((T(w,u) \ u) \ z))
    ]]></literal>
    <justification jstring="[hyper(21165,a,21287,a)].">
      <j1 rule="hyper" parents="21165 21287"/>
    </justification>
  </clause>

  <clause id="21289">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) \ u) \ w)) = K(x,y \ ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,21286,a(flip),b,21288,a),flip(a)].">
      <j1 rule="hyper" parents="64 21286 21288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21290">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((z / u) \ w)) = K(x,y * ((u \ T(z,u)) \ w))
    ]]></literal>
    <justification jstring="[hyper(14739,a,21289,a),flip(a)].">
      <j1 rule="hyper" parents="14739 21289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21291">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(21290(a,1),14641(a,1))].">
      <j1 rule="para" parents="21290 14641"/>
    </justification>
  </clause>

  <clause id="21292">
    <literal><![CDATA[
      K(x,y * ((T(z,u) \ u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(4632(a,2),21291(a,1,2,2,1))].">
      <j1 rule="para" parents="4632 21291"/>
    </justification>
  </clause>

  <clause id="21293">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,T(u,y)) / y) = (x / (y \ 1)) * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19358,a(flip),b,21001,a),flip(a)].">
      <j1 rule="hyper" parents="64 19358 21001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21294">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * u) \ ((y \ 1) * (z * y))) = K(x,L(u \ (y * z),z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,15534,a(flip),b,21210,a),flip(a)].">
      <j1 rule="hyper" parents="373 15534 21210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21295">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,21211,a(flip),b,21294,a),flip(a)].">
      <j1 rule="hyper" parents="64 21211 21294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21296">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,20313,a(flip),b,21295,a)].">
      <j1 rule="hyper" parents="64 20313 21295"/>
    </justification>
  </clause>

  <clause id="21297">
    <literal><![CDATA[
      K(x,y \ (z * (((y * u) \ y) \ y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(20937,a,21296,a)].">
      <j1 rule="hyper" parents="20937 21296"/>
    </justification>
  </clause>

  <clause id="21298">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * T(u,z \ 1)) \ y) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,15924,a(flip),b,21296,a),flip(a)].">
      <j1 rule="hyper" parents="373 15924 21296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21299">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) = K(x,((z \ y) * u) \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),21296(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 21296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21300">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * (u * K(w,L(v5,u,z)))) \ y) = K(x,((z \ u) * K(w,v5)) \ y)
    ]]></literal>
    <justification jstring="[para(15549(a,1),21296(a,2,2,1))].">
      <j1 rule="para" parents="15549 21296"/>
    </justification>
  </clause>

  <clause id="21301">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * u) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ u,K(v5,v6)) \ y) = w
    ]]></literal>
    <justification jstring="[para(21296(a,2),18008(a,1))].">
      <j1 rule="para" parents="21296 18008"/>
    </justification>
  </clause>

  <clause id="21302">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(21299(a,1),10244(a,1,1))].">
      <j1 rule="para" parents="21299 10244"/>
    </justification>
  </clause>

  <clause id="21303">
    <literal><![CDATA[
      K(x,y \ (z * T(y * u,y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13503,a(flip),b,21297,a)].">
      <j1 rule="hyper" parents="64 13503 21297"/>
    </justification>
  </clause>

  <clause id="21304">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ u) = K(x,u \ (z * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20051,a(flip),b,21303,a),flip(a)].">
      <j1 rule="hyper" parents="64 20051 21303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21305">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * y))) = K(x,(u \ z) \ y)
    ]]></literal>
    <justification jstring="[para(82(a,1),21304(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="82 21304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21306">
    <literal><![CDATA[
      K(x,y \ (R(1 / z,z,y) * (u * y))) = K(x,(u \ (z * y)) \ y)
    ]]></literal>
    <justification jstring="[para(452(a,1),21304(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="452 21304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21308">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,z \ ((z / u) * y))
    ]]></literal>
    <justification jstring="[para(12(a,1),21305(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="12 21305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21309">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z \ ((z / u) * w)) = K(y,T(((z / w) * u) \ z,x))
    ]]></literal>
    <justification jstring="[hyper(19677,a,21308,a),flip(a)].">
      <j1 rule="hyper" parents="19677 21308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21310">
    <literal><![CDATA[
      K(x,(y * ((z * u) \ z)) \ z) = K(x,(y / u) \ z)
    ]]></literal>
    <justification jstring="[para(6747(a,1),21298(a,1,2,1))].">
      <j1 rule="para" parents="6747 21298"/>
    </justification>
  </clause>

  <clause id="21311">
    <literal><![CDATA[
      K(x,y \ ((y * z) * (u \ y))) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(20937,a,21310,a)].">
      <j1 rule="hyper" parents="20937 21310"/>
    </justification>
  </clause>

  <clause id="21312">
    <literal><![CDATA[
      K(x,((y / z) / u) \ y) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(82(a,1),21311(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="82 21311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21313">
    <literal><![CDATA[
      K(x,y \ ((z * y) * (u \ y))) = K(x,(u / T(z,y)) \ y)
    ]]></literal>
    <justification jstring="[para(115(a,1),21311(a,1,2,2,1))].">
      <j1 rule="para" parents="115 21311"/>
    </justification>
  </clause>

  <clause id="21314">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) * ((y * z) \ T(z,y))))
    ]]></literal>
    <justification jstring="[para(14877(a,1),21311(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14877 21311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21315">
    <literal><![CDATA[
      T(x,((y / z) / u) \ y) = T(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(143,a,21312,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 21312 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21316">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18432,a,b,21312,a)].">
      <j1 rule="hyper" parents="64 18432 21312"/>
    </justification>
  </clause>

  <clause id="21317">
    <literal><![CDATA[
      K(x,(y / T(a(z \ 1,z,u),L(u,z,z \ 1))) \ L(u,z,z \ 1)) = K(x,L(u,z,z \ 1) \ (u * (y \ L(u,z,z \ 1))))
    ]]></literal>
    <justification jstring="[para(5564(a,1),21313(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5564 21313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21318">
    <literal><![CDATA[
      K(x,(y \ (z * u)) \ u) = K(x,u \ (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16399,a(flip),b,21306,a),flip(a)].">
      <j1 rule="hyper" parents="64 16399 21306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21319">
    <literal><![CDATA[
      T(K(x,y \ (z \ (u * y))),y) = K(x,y / (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(21318(a,1),8199(a,1,1))].">
      <j1 rule="para" parents="21318 8199"/>
    </justification>
  </clause>

  <clause id="21320">
    <literal><![CDATA[
      T(x,K(y,x \ (z \ ((u * z) * x)))) \ (z \ ((K(y,u) * z) * x)) = K(y,x / ((u * z) \ (z * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16221,a,b,21319,a)].">
      <j1 rule="hyper" parents="64 16221 21319"/>
    </justification>
  </clause>

  <clause id="21321">
    <literal><![CDATA[
      K(x,T(y \ (z * K(u,w)),K(v5,v6)) \ v7) = K(x,K(w,u) * ((((v7 * y) \ v7) * z) \ v7))
    ]]></literal>
    <justification jstring="[hyper(21301,a,21028,a)].">
      <j1 rule="hyper" parents="21301 21028"/>
    </justification>
  </clause>

  <clause id="21322">
    <literal><![CDATA[
      K(x,y / ((y \ z) \ u)) = K(x,y / ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15655,a(flip),b,21302,a),flip(a)].">
      <j1 rule="hyper" parents="64 15655 21302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21323">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,w)) = K(x,T(y \ ((y / u) * z),w))
    ]]></literal>
    <justification jstring="[hyper(16126,a,21309,a),flip(a)].">
      <j1 rule="hyper" parents="16126 21309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21324">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,y / (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18517,a(flip),b,21323,a),flip(a)].">
      <j1 rule="hyper" parents="64 18517 21323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21325">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) * ((((v5 * u) \ v5) * z) \ v5)) = K(x,((u \ z) * K(w,y)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,21028,a(flip),b,21300,a)].">
      <j1 rule="hyper" parents="64 21028 21300"/>
    </justification>
  </clause>

  <clause id="21326">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((((v5 * w) \ v5) * u) \ v5)) = K(x,((w \ u) * K(z,y)) \ v5)
    ]]></literal>
    <justification jstring="[para(12093(a,1),21325(a,1,2,1))].">
      <j1 rule="para" parents="12093 21325"/>
    </justification>
  </clause>

  <clause id="21327">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) = K(x,((w \ v5) * K(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,19871,a(flip),b,21326,a)].">
      <j1 rule="hyper" parents="64 19871 21326"/>
    </justification>
  </clause>

  <clause id="21329">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * ((w \ v5) \ u)) = v6
    ]]></literal>
    <justification jstring="[para(21327(a,2),20701(a,1))].">
      <j1 rule="para" parents="21327 20701"/>
    </justification>
  </clause>

  <clause id="21330">
    <literal><![CDATA[
      K(x,T(y \ (z * K(u,w)),K(v5,v6)) \ v7) = K(x,K(w,u) * ((y \ z) \ v7))
    ]]></literal>
    <justification jstring="[hyper(21329,a,21321,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21329 21321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21331">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y \ z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(18015,a,21330,a)].">
      <j1 rule="hyper" parents="18015 21330"/>
    </justification>
  </clause>

  <clause id="21332">
    <literal><![CDATA[
      1 / T(T(x,a(y,z,u)) * K(w,v5),a(y,z,x)) = K(u,a(y,z,x)) / (x * K(w,v5))
    ]]></literal>
    <justification jstring="[para(19453(a,1),21267(a,1,2,1))].">
      <j1 rule="para" parents="19453 21267"/>
    </justification>
  </clause>

  <clause id="21333">
    <literal><![CDATA[
      K(x,a(y,z,u)) / (u * K(w,v5)) = 1 / (T(u,a(y,z,x)) * K(w,v5))
    ]]></literal>
    <justification jstring="[para(20617(a,1),21332(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20617 21332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21334">
    <literal><![CDATA[
      K(x,a(y,z,u)) / (u * K(w,v5)) = K(v5,w) / T(u,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,14507,a(flip),b,21333,a),flip(a)].">
      <j1 rule="hyper" parents="373 14507 21333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21336">
    <literal><![CDATA[
      a(x,y,K(z,u)) / (z * K(w,v5)) = K(v5,w) / T(z,a(u,y,x))
    ]]></literal>
    <justification jstring="[para(15299(a,2),21334(a,1,1))].">
      <j1 rule="para" parents="15299 21334"/>
    </justification>
  </clause>

  <clause id="21337">
    <literal><![CDATA[
      a(x,y,K(z,u)) / (z * K(w,v5)) = K(v5,w) / L(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[para(16603(a,2),21336(a,2,2))].">
      <j1 rule="para" parents="16603 21336"/>
    </justification>
  </clause>

  <clause id="21338">
    <literal><![CDATA[
      L(K(x,y) / z,u,K(w,v5)) = K(x,y) / L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,20623,a(flip),b,21337,a)].">
      <j1 rule="hyper" parents="64 20623 21337"/>
    </justification>
  </clause>

  <clause id="21339">
    <literal><![CDATA[
      L(K(x,y) / (z \ 1),u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,19640,a(flip),b,21338,a),flip(a)].">
      <j1 rule="hyper" parents="373 19640 21338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21340">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(14384(a,1),21339(a,1,1))].">
      <j1 rule="para" parents="14384 21339"/>
    </justification>
  </clause>

  <clause id="21341">
    <literal><![CDATA[
      L(K(x,y) * (K(y,T(x,z)) * (z / a(u,w,v5))),w,K(v5,u)) = T(a(u,w,v5) \ z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,16769,a(flip),b,21340,a),flip(a)].">
      <j1 rule="hyper" parents="373 16769 21340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21342">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ T(L(K(w,v5) * x,z,K(u,y)),y) = K(w,T(v5,L(y * x,z,K(u,y))))
    ]]></literal>
    <justification jstring="[para(21340(a,2),18819(a,1,2,1))].">
      <j1 rule="para" parents="21340 18819"/>
    </justification>
  </clause>

  <clause id="21343">
    <literal><![CDATA[
      L(K(x,K(y,z)) * (z / a(u,w,v5)),w,K(v5,u)) = T(a(u,w,v5) \ z,K(x,y))
    ]]></literal>
    <justification jstring="[para(9810(a,1),21341(a,1,1))].">
      <j1 rule="para" parents="9810 21341"/>
    </justification>
  </clause>

  <clause id="21344">
    <literal><![CDATA[
      L(T(x,K(y,z)) / a(u,w,v5),w,K(v5,u)) = T(a(u,w,v5) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12582(a,1),21343(a,1,1))].">
      <j1 rule="para" parents="12582 21343"/>
    </justification>
  </clause>

  <clause id="21345">
    <literal><![CDATA[
      T(a(x,y,z) \ u,K(w,v5)) = a(x,y,z) \ T(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(16625,a,21344,a),flip(a)].">
      <j1 rule="hyper" parents="16625 21344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21346">
    <literal><![CDATA[
      T(a(x,y,z) \ (a(x,y,z) * u),K(w,v5)) = u * K(w,K(v5,u * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,17390,a(flip),b,21345,a),flip(a)].">
      <j1 rule="hyper" parents="373 17390 21345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21347">
    <literal><![CDATA[
      x * K(y,K(z,x * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),21346(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 21346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21348">
    <literal><![CDATA[
      T(a(x,y,z) * u,K(w,v5)) = a(x,y,z) * T(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(145,a,21347,a(flip),b,17390,a),flip(a)].">
      <j1 rule="hyper" parents="145 21347 17390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21349">
    <literal><![CDATA[
      x \ T(a(y,z,u) * (a(y,z,u) \ x),K(w,v5)) = K(w,K(v5,a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(139,a,21348,a,b,8132,a(flip))].">
      <j1 rule="hyper" parents="139 21348 8132"/>
    </justification>
  </clause>

  <clause id="21350">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) \ v5)) = v5 \ T(v5,K(x,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),21349(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 21349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21351">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) \ v5)) = K(v5,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,5726,a,b,21350,a),flip(a)].">
      <j1 rule="hyper" parents="373 5726 21350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21352">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,z)) = u * K(y,T(z,a(w,v5,v6) \ x))
    ]]></literal>
    <justification jstring="[para(21351(a,1),17173(a,1,1))].">
      <j1 rule="para" parents="21351 17173"/>
    </justification>
  </clause>

  <clause id="21353">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) \ v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(17747,a,21352,a),flip(a)].">
      <j1 rule="hyper" parents="17747 21352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21354">
    <literal><![CDATA[
      K(x,T(y,z * a(u,w,v5))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(17524,a,21353,a)].">
      <j1 rule="hyper" parents="17524 21353"/>
    </justification>
  </clause>

  <clause id="21355">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(17439,a,21353,a)].">
      <j1 rule="hyper" parents="17439 21353"/>
    </justification>
  </clause>

  <clause id="21356">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) = K(x,T(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(15467(a,1),21353(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15467 21353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21357">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,z * a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(21354(a,1),8360(a,1,1,2))].">
      <j1 rule="para" parents="21354 8360"/>
    </justification>
  </clause>

  <clause id="21358">
    <literal><![CDATA[
      K(x,T(y,z * (u * w))) = K(x,T(y,w * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(17266,a,21356,a),flip(a)].">
      <j1 rule="hyper" parents="17266 21356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21359">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,u * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19491,a,b,21356,a)].">
      <j1 rule="hyper" parents="64 19491 21356"/>
    </justification>
  </clause>

  <clause id="21360">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w) * v5)) = K(x,T(y,u * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18433,a,b,21356,a)].">
      <j1 rule="hyper" parents="64 18433 21356"/>
    </justification>
  </clause>

  <clause id="21362">
    <literal><![CDATA[
      T(x,T(y,z * (u * w))) = T(x,T(y,w * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(143,a,21358,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 21358 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21363">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w)) = K(x,T(y,z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(17524,a,21359,a)].">
      <j1 rule="hyper" parents="17524 21359"/>
    </justification>
  </clause>

  <clause id="21364">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w)) = K(x,T(y,u * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,21358,a(flip),b,21363,a),flip(a)].">
      <j1 rule="hyper" parents="373 21358 21363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21365">
    <literal><![CDATA[
      K(x,T(((y \ z) \ u) / w,z * (y * u))) = K(x,w \ ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17026,a(flip),b,21364,a),flip(a)].">
      <j1 rule="hyper" parents="64 17026 21364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21366">
    <literal><![CDATA[
      T(x,K(y,z * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8734,a,21357,a),flip(a)].">
      <j1 rule="hyper" parents="8734 21357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21367">
    <literal><![CDATA[
      T(x,K(y,(z * u) * w)) = T(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(88(a,1),21366(a,1,2,2))].">
      <j1 rule="para" parents="88 21366"/>
    </justification>
  </clause>

  <clause id="21368">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u * a(w,v5,v6))) = T(y,K(u * a(w,v5,v6),z) * x)
    ]]></literal>
    <justification jstring="[para(21366(a,1),16796(a,1,2,1,2))].">
      <j1 rule="para" parents="21366 16796"/>
    </justification>
  </clause>

  <clause id="21369">
    <literal><![CDATA[
      K(x,T(y,T(z * a(u,w,v5),v6) * v7)) = K(x,T(y,z * v7))
    ]]></literal>
    <justification jstring="[hyper(373,a,21355,a(flip),b,21360,a),flip(a)].">
      <j1 rule="hyper" parents="373 21355 21360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21370">
    <literal><![CDATA[
      K(x,T(y,(z * a(u,w,v5)) * v6)) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(18273,a,21369,a)].">
      <j1 rule="hyper" parents="18273 21369"/>
    </justification>
  </clause>

  <clause id="21371">
    <literal><![CDATA[
      K(x,T(y,z * (a(u,w,v5) * v6))) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,21356,a(flip),b,21370,a)].">
      <j1 rule="hyper" parents="64 21356 21370"/>
    </justification>
  </clause>

  <clause id="21372">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),z * u)) = K(x,z \ T(y,a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19340,a(flip),b,21371,a),flip(a)].">
      <j1 rule="hyper" parents="64 19340 21371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21374">
    <literal><![CDATA[
      T(x,K(y * a(z,u,w),v5) * v6) = v6 \ T(x * T(v6,K(v5,y)),K(v5,y))
    ]]></literal>
    <justification jstring="[para(21366(a,1),21368(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21366 21368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21375">
    <literal><![CDATA[
      T(x,K(y * a(z,u,w),v5) * v6) = T(x,K(y,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,16796,a(flip),b,21374,a),flip(a)].">
      <j1 rule="hyper" parents="373 16796 21374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21377">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,K(z,y) * (y \ v6))
    ]]></literal>
    <justification jstring="[para(6157(a,1),21375(a,1,2))].">
      <j1 rule="para" parents="6157 21375"/>
    </justification>
  </clause>

  <clause id="21378">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,T(y,z) \ v6)
    ]]></literal>
    <justification jstring="[para(6157(a,1),21377(a,2,2))].">
      <j1 rule="para" parents="6157 21377"/>
    </justification>
  </clause>

  <clause id="21379">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u) \ z) = T(x,z / T(y,T(a(w,v5,v6),v7) * u))
    ]]></literal>
    <justification jstring="[hyper(19723,a,21378,a),flip(a)].">
      <j1 rule="hyper" parents="19723 21378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21380">
    <literal><![CDATA[
      T(x,y / T(z,T(a(u,w,v5),v6) * v7)) = T(x,y / T(z,v7))
    ]]></literal>
    <justification jstring="[hyper(17230,a,21379,a),flip(a)].">
      <j1 rule="hyper" parents="17230 21379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21381">
    <literal><![CDATA[
      T(x,y / T(z,u * a(w,v5,v6))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(11143(a,1),21380(a,1,2,2))].">
      <j1 rule="para" parents="11143 21380"/>
    </justification>
  </clause>

  <clause id="21382">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),v7)) = (x * v7) \ (T(x,y / T(z,u)) * v7)
    ]]></literal>
    <justification jstring="[para(21381(a,1),8048(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="21381 8048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21383">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / T(z,u),v7)) = v8
    ]]></literal>
    <justification jstring="[para(21382(a,2),8070(a,1))].">
      <j1 rule="para" parents="21382 8070"/>
    </justification>
  </clause>

  <clause id="21384">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z * u)) = K(x,z \ T(y,a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[hyper(21383,a,21372,a)].">
      <j1 rule="hyper" parents="21383 21372"/>
    </justification>
  </clause>

  <clause id="21385">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * v6)) = K(x,y \ T(z,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,18527,a(flip),b,21384,a),flip(a)].">
      <j1 rule="hyper" parents="64 18527 21384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21386">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ T(K(w,v5) * x,L(y,z,u)) = K(w,T(v5,L(y * x,z,K(u,y))))
    ]]></literal>
    <justification jstring="[para(16628(a,1),21342(a,1,2))].">
      <j1 rule="para" parents="16628 21342"/>
    </justification>
  </clause>

  <clause id="21387">
    <literal><![CDATA[
      K(x,T(y,L(z * u,w,K(v5,z)))) = K(x,T(y,L(z,w,v5) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17593,a(flip),b,21386,a),flip(a)].">
      <j1 rule="hyper" parents="64 17593 21386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21388">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[hyper(19287,a,21387,a),flip(a)].">
      <j1 rule="hyper" parents="19287 21387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21389">
    <literal><![CDATA[
      K(x,T(y,z * L(u,w,v5))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(17266,a,21388,a)].">
      <j1 rule="hyper" parents="17266 21388"/>
    </justification>
  </clause>

  <clause id="21391">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * (z * w))) = K(x,T(y,w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18285,a(flip),b,21388,a)].">
      <j1 rule="hyper" parents="64 18285 21388"/>
    </justification>
  </clause>

  <clause id="21392">
    <literal><![CDATA[
      K(x,T(y,z * L(u,w,v5))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17066,a,b,21389,a),flip(a)].">
      <j1 rule="hyper" parents="373 17066 21389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21393">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,z * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(21392(a,1),8360(a,1,1,2))].">
      <j1 rule="para" parents="21392 8360"/>
    </justification>
  </clause>

  <clause id="21394">
    <literal><![CDATA[
      K(x,T(y,(z * u) * (z \ w))) = K(x,T(y,u * w))
    ]]></literal>
    <justification jstring="[hyper(17266,a,21391,a)].">
      <j1 rule="hyper" parents="17266 21391"/>
    </justification>
  </clause>

  <clause id="21396">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w)) = K(x,T(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(10(a,1),21394(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 21394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21397">
    <literal><![CDATA[
      K(x,T(y,z * (u \ w))) = K(x,T(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,21364,a(flip),b,21396,a),flip(a)].">
      <j1 rule="hyper" parents="64 21364 21396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21398">
    <literal><![CDATA[
      K(x * K(y \ (z \ x),y),T(u,x * ((z * y) \ y))) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18694,a(flip),b,21396,a),flip(a)].">
      <j1 rule="hyper" parents="64 18694 21396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21399">
    <literal><![CDATA[
      K(x,T(y,z * (u / w))) = K(x,T(y,z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18249,a,b,21397,a)].">
      <j1 rule="hyper" parents="64 18249 21397"/>
    </justification>
  </clause>

  <clause id="21400">
    <literal><![CDATA[
      K(x,T(T(y * (z / u),w) / v5,y * (u * z))) = K(x,v5 \ T(y * (z / u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17099,a(flip),b,21399,a),flip(a)].">
      <j1 rule="hyper" parents="64 17099 21399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21401">
    <literal><![CDATA[
      T(x,K(y,z * L(u,w,v5))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(8734,a,21393,a),flip(a)].">
      <j1 rule="hyper" parents="8734 21393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21402">
    <literal><![CDATA[
      T(x,K(y,z * ((u * w) \ v5))) = T(x,K(y,z * (w \ (u \ v5))))
    ]]></literal>
    <justification jstring="[para(346(a,1),21401(a,1,2,2,2))].">
      <j1 rule="para" parents="346 21401"/>
    </justification>
  </clause>

  <clause id="21403">
    <literal><![CDATA[
      T(x,K(y,z * ((u * z) \ w))) = T(x,K(y,u \ w))
    ]]></literal>
    <justification jstring="[para(10(a,1),21402(a,2,2,2))].">
      <j1 rule="para" parents="10 21402"/>
    </justification>
  </clause>

  <clause id="21404">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ w)) = T(x,K(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(12(a,1),21403(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 21403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21405">
    <literal><![CDATA[
      T(x,K(y,z \ (u * w))) = T(x,K(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(19492,a,21404,a)].">
      <j1 rule="hyper" parents="19492 21404"/>
    </justification>
  </clause>

  <clause id="21406">
    <literal><![CDATA[
      T(x,K(y,z \ (u \ w))) = T(x,K(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(19383,a,21405,a)].">
      <j1 rule="hyper" parents="19383 21405"/>
    </justification>
  </clause>

  <clause id="21407">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z * (u \ T(w,z)))) = x * K(y,T(x,w \ (T(z,w) \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19987,a(flip),b,21406,a),flip(a)].">
      <j1 rule="hyper" parents="64 19987 21406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21408">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z * (u \ w))) = x * K(y,T(x,w \ (T(z,w) \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18359,a(flip),b,21407,a)].">
      <j1 rule="hyper" parents="64 18359 21407"/>
    </justification>
  </clause>

  <clause id="21410">
    <literal><![CDATA[
      x * K(y,T(x,z \ (T(u,z) \ w))) = x * K(y,T(x,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,8410,a(flip),b,21408,a),flip(a)].">
      <j1 rule="hyper" parents="64 8410 21408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21411">
    <literal><![CDATA[
      x * K(y,T(x,z \ (u \ w))) = x * K(y,T(x,u * (w \ z)))
    ]]></literal>
    <justification jstring="[para(19984(a,1),21410(a,1,2))].">
      <j1 rule="para" parents="19984 21410"/>
    </justification>
  </clause>

  <clause id="21412">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(322,a,21411,a),flip(a)].">
      <j1 rule="hyper" parents="322 21411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21415">
    <literal><![CDATA[
      K(x,T(y,z * ((u * w) \ w))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19486,a(flip),b,21412,a),flip(a)].">
      <j1 rule="hyper" parents="64 19486 21412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21416">
    <literal><![CDATA[
      K(x * K(y \ (z \ x),y),T(u,x \ z)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,21415,a(flip),b,21398,a)].">
      <j1 rule="hyper" parents="64 21415 21398"/>
    </justification>
  </clause>

  <clause id="21418">
    <literal><![CDATA[
      K(K(x \ (y \ z),x) * z,T(u,y)) = K(((y * x) \ z) * (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,19697,a(flip),b,21416,a)].">
      <j1 rule="hyper" parents="64 19697 21416"/>
    </justification>
  </clause>

  <clause id="21419">
    <literal><![CDATA[
      K(x * K(y \ (x / z),y),T(u,z)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[para(10778(a,1),21418(a,1,1))].">
      <j1 rule="para" parents="10778 21418"/>
    </justification>
  </clause>

  <clause id="21420">
    <literal><![CDATA[
      K(K(x / y,z) * x,T(u,y)) = K(((y * z) \ x) * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(17367,a,21419,a)].">
      <j1 rule="hyper" parents="17367 21419"/>
    </justification>
  </clause>

  <clause id="21421">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) = K(z * K(x \ z,y),T(u,x))
    ]]></literal>
    <justification jstring="[para(6780(a,1),21420(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6780 21420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21422">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) = K(x * T(z / x,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11198,a(flip),b,21421,a),flip(a)].">
      <j1 rule="hyper" parents="373 11198 21421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21423">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,x * y)) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(11225,a,21422,a)].">
      <j1 rule="hyper" parents="11225 21422"/>
    </justification>
  </clause>

  <clause id="21424">
    <literal><![CDATA[
      K(x \ T(y * x,z),u) = K(x * T(y / x,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18402,a(flip),b,21423,a)].">
      <j1 rule="hyper" parents="64 18402 21423"/>
    </justification>
  </clause>

  <clause id="21425">
    <literal><![CDATA[
      K(x * K(x * y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(18209,a,21424,a)].">
      <j1 rule="hyper" parents="18209 21424"/>
    </justification>
  </clause>

  <clause id="21426">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(z,y)) = (x * w) / (K(z * T(y / z,u),x) * w)
    ]]></literal>
    <justification jstring="[para(21425(a,1),17833(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="21425 17833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21427">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(z,y)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,6159,a(flip),b,21426,a),flip(a)].">
      <j1 rule="hyper" parents="373 6159 21426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21428">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[para(17829(a,1),21427(a,1,2))].">
      <j1 rule="para" parents="17829 21427"/>
    </justification>
  </clause>

  <clause id="21429">
    <literal><![CDATA[
      T(x,y \ T(z * y,u)) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18061,a(flip),b,21428,a)].">
      <j1 rule="hyper" parents="64 18061 21428"/>
    </justification>
  </clause>

  <clause id="21430">
    <literal><![CDATA[
      T(x,y * T(T(z,z * y) / y,u)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17866,a(flip),b,21429,a),flip(a)].">
      <j1 rule="hyper" parents="64 17866 21429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21431">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),z * y)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(20150,a,21430,a)].">
      <j1 rule="hyper" parents="20150 21430"/>
    </justification>
  </clause>

  <clause id="21432">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),y)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18688,a(flip),b,21431,a)].">
      <j1 rule="hyper" parents="64 18688 21431"/>
    </justification>
  </clause>

  <clause id="21433">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,T(z / y,u) * y)
    ]]></literal>
    <justification jstring="[hyper(11141,a,21432,a),flip(a)].">
      <j1 rule="hyper" parents="11141 21432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21434">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(525(a,1),21433(a,2,2))].">
      <j1 rule="para" parents="525 21433"/>
    </justification>
  </clause>

  <clause id="21435">
    <literal><![CDATA[
      T(x,y \ T(z * T(y,z),u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(21244,a,21434,a)].">
      <j1 rule="hyper" parents="21244 21434"/>
    </justification>
  </clause>

  <clause id="21436">
    <literal><![CDATA[
      T(x,y \ T(y * z,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(115(a,1),21435(a,1,2,2,1))].">
      <j1 rule="para" parents="115 21435"/>
    </justification>
  </clause>

  <clause id="21437">
    <literal><![CDATA[
      K(x \ K(K(y,z) * (u \ w),u * K(z,y)),v5) = K(x \ K(u * K(z,z \ y),w),v5)
    ]]></literal>
    <justification jstring="[para(17354(a,1),20744(a,1,1,2))].">
      <j1 rule="para" parents="17354 20744"/>
    </justification>
  </clause>

  <clause id="21438">
    <literal><![CDATA[
      K(x \ K(K(y,z) * (u \ w),u),v5) = K(x \ K(u * K(z,z \ y),w),v5)
    ]]></literal>
    <justification jstring="[hyper(19841,a,21437,a)].">
      <j1 rule="hyper" parents="19841 21437"/>
    </justification>
  </clause>

  <clause id="21439">
    <literal><![CDATA[
      K(x \ K(y * K(z,z \ u),w),v5) = K(x \ K(y,K(u,z) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,16322,a(flip),b,21438,a),flip(a)].">
      <j1 rule="hyper" parents="64 16322 21438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21440">
    <literal><![CDATA[
      K(x \ K(y * K(z,z \ u),w),v5) = K(x \ K(y,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,19842,a(flip),b,21439,a),flip(a)].">
      <j1 rule="hyper" parents="373 19842 21439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21443">
    <literal><![CDATA[
      K(x \ K(K(y,z) * u,w),v5) = K(x \ K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(17355(a,1),21440(a,1,1,2))].">
      <j1 rule="para" parents="17355 21440"/>
    </justification>
  </clause>

  <clause id="21444">
    <literal><![CDATA[
      K((x \ 1) \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * K(K(v5,v6) * y,z),u) = w
    ]]></literal>
    <justification jstring="[para(21443(a,1),14763(a,1))].">
      <j1 rule="para" parents="21443 14763"/>
    </justification>
  </clause>

  <clause id="21445">
    <literal><![CDATA[
      K(x * K(K(y,z) * u,w),v5) = K((1 \ x) * K(w,u),v5)
    ]]></literal>
    <justification jstring="[hyper(21444,a,21156,a)].">
      <j1 rule="hyper" parents="21444 21156"/>
    </justification>
  </clause>

  <clause id="21446">
    <literal><![CDATA[
      K(x * K(K(y,z) * u,w),v5) = K(x * K(w,u),v5)
    ]]></literal>
    <justification jstring="[para(66(a,1),21445(a,2,1,1))].">
      <j1 rule="para" parents="66 21445"/>
    </justification>
  </clause>

  <clause id="21447">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w)),v5) = K(x * K(y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(17368,a,21446,a)].">
      <j1 rule="hyper" parents="17368 21446"/>
    </justification>
  </clause>

  <clause id="21448">
    <literal><![CDATA[
      K(x * K(y,T(z,u) * w),v5) = K(x * K(y,z * w),v5)
    ]]></literal>
    <justification jstring="[para(6570(a,1),21447(a,1,1,2,2))].">
      <j1 rule="para" parents="6570 21447"/>
    </justification>
  </clause>

  <clause id="21449">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ T(z,w * v5)) = K(x,u \ T(z,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,21252,a(flip),b,21448,a),flip(a)].">
      <j1 rule="hyper" parents="64 21252 21448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21450">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ T(z,w * v5)) = K(x,u \ T(z,v5 \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,21251,a(flip),b,21448,a),flip(a)].">
      <j1 rule="hyper" parents="64 21251 21448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21453">
    <literal><![CDATA[
      K(x,y \ T(z,u \ w)) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,21449,a(flip),b,21450,a),flip(a)].">
      <j1 rule="hyper" parents="64 21449 21450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21454">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,y * z)) = K(x,v5 / (y \ (z * K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(20498,a,21453,a),flip(a)].">
      <j1 rule="hyper" parents="20498 21453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21455">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w / v5))) = K(x,y \ T(z,(u * v5) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,20030,a(flip),b,21453,a)].">
      <j1 rule="hyper" parents="64 20030 21453"/>
    </justification>
  </clause>

  <clause id="21456">
    <literal><![CDATA[
      K(x,y \ T(z,u * u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(379(a,1),21453(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="379 21453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21457">
    <literal><![CDATA[
      K(x,y / (z * (z * y))) = K(x,(z * (z * y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13487,a(flip),b,21456,a)].">
      <j1 rule="hyper" parents="64 13487 21456"/>
    </justification>
  </clause>

  <clause id="21459">
    <literal><![CDATA[
      T(x,y / (z * (z * y))) = T(x,(z * (z * y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(143,a,21457,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 21457 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21460">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,21453,a(flip),b,21455,a),flip(a)].">
      <j1 rule="hyper" parents="64 21453 21455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21461">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,20378,a(flip),b,21460,a),flip(a)].">
      <j1 rule="hyper" parents="373 20378 21460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21462">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ w) \ T(v5,u * w))) = K(x,v5 / (u \ (w * K(z,y))))
    ]]></literal>
    <justification jstring="[hyper(64,a,21331,a(flip),b,21454,a)].">
      <j1 rule="hyper" parents="64 21331 21454"/>
    </justification>
  </clause>

  <clause id="21463">
    <literal><![CDATA[
      K(x,(y / T(z,u)) \ (x * T(w,y / T(z,u)))) = K(x,w / (x \ (y / ((z \ u) \ u))))
    ]]></literal>
    <justification jstring="[para(13343(a,1),20925(a,1,2,2,2))].">
      <j1 rule="para" parents="13343 20925"/>
    </justification>
  </clause>

  <clause id="21464">
    <literal><![CDATA[
      K(x,y / (x \ (z / ((u \ w) \ w)))) = K(x,y / (x \ (z / T(u,w))))
    ]]></literal>
    <justification jstring="[hyper(20924,a,21463,a),flip(a)].">
      <j1 rule="hyper" parents="20924 21463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21465">
    <literal><![CDATA[
      K(x,((y / ((z \ u) \ u)) / w) \ x) = K(x,w / (x \ (y / T(z,u))))
    ]]></literal>
    <justification jstring="[hyper(9748,a,21464,a)].">
      <j1 rule="hyper" parents="9748 21464"/>
    </justification>
  </clause>

  <clause id="21466">
    <literal><![CDATA[
      K(x,((y / ((z \ u) \ u)) / w) \ x) = K(x,((y / T(z,u)) / w) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,9739,a(flip),b,21465,a),flip(a)].">
      <j1 rule="hyper" parents="373 9739 21465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21467">
    <literal><![CDATA[
      K(x,T((y * (z \ u)) \ u,w)) = K(x,T(u \ (z * (y \ u)),w))
    ]]></literal>
    <justification jstring="[hyper(9177,a,20936,a),flip(a)].">
      <j1 rule="hyper" parents="9177 20936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21468">
    <literal><![CDATA[
      K(x,T(y \ (z * (u \ y)),u)) = K(x,y / ((y / z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,20948,a(flip),b,21467,a),flip(a)].">
      <j1 rule="hyper" parents="64 20948 21467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21469">
    <literal><![CDATA[
      K(x,((y / z) * u) / y) = K(x,y / ((y / u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18588,a(flip),b,21468,a)].">
      <j1 rule="hyper" parents="64 18588 21468"/>
    </justification>
  </clause>

  <clause id="21470">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K(u \ (K(z,y) * w),u)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[para(19241(a,1),21045(a,1,2,2))].">
      <j1 rule="para" parents="19241 21045"/>
    </justification>
  </clause>

  <clause id="21471">
    <literal><![CDATA[
      K(x,T(T((y \ 1) \ z,u),y) \ w) = K(x,T((T(y,z) \ 1) \ z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,17925,a(flip),b,21062,a)].">
      <j1 rule="hyper" parents="373 17925 21062"/>
    </justification>
  </clause>

  <clause id="21472">
    <literal><![CDATA[
      K(x,T((T(x,y) \ 1) \ y,z) \ u) = K(x,T((x \ 1) \ y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(8589,a,21471,a),flip(a)].">
      <j1 rule="hyper" parents="8589 21471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21474">
    <literal><![CDATA[
      K(x,T((T(y,z) \ 1) \ z,u) \ w) = K(x,T(z / (y \ 1),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17647,a(flip),b,21471,a),flip(a)].">
      <j1 rule="hyper" parents="64 17647 21471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21475">
    <literal><![CDATA[
      K(x,T((T(x,y) \ 1) \ y,z) \ u) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,10525,a(flip),b,21472,a),flip(a)].">
      <j1 rule="hyper" parents="373 10525 21472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21476">
    <literal><![CDATA[
      K(x,T(y / (x \ 1),z) \ u) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,21475,a(flip),b,21474,a),flip(a)].">
      <j1 rule="hyper" parents="64 21475 21474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21477">
    <literal><![CDATA[
      K(x,K(y,x * z) \ ((z / (x \ 1)) \ u)) = K(x,T(x * z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18445,a,b,21476,a)].">
      <j1 rule="hyper" parents="64 18445 21476"/>
    </justification>
  </clause>

  <clause id="21478">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K(K(z,y) * (u \ w),u)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[para(10277(a,1),21470(a,1,2,2))].">
      <j1 rule="para" parents="10277 21470"/>
    </justification>
  </clause>

  <clause id="21479">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K(w * K(z,y),u)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18416,a(flip),b,21478,a)].">
      <j1 rule="hyper" parents="64 18416 21478"/>
    </justification>
  </clause>

  <clause id="21480">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) \ w) / v5) \ K(u,w)) = K(x,v5 / (w / (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19846,a(flip),b,21479,a)].">
      <j1 rule="hyper" parents="64 19846 21479"/>
    </justification>
  </clause>

  <clause id="21481">
    <literal><![CDATA[
      K(x,K(y,z) * (u / ((K(w,v5) * y) \ z))) = K(x,u / (z / (K(w,v5) * y)))
    ]]></literal>
    <justification jstring="[hyper(20919,a,21480,a)].">
      <j1 rule="hyper" parents="20919 21480"/>
    </justification>
  </clause>

  <clause id="21483">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) \ T(v5,w))) = K(x,y / (v5 / (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(20770,a,21481,a)].">
      <j1 rule="hyper" parents="20770 21481"/>
    </justification>
  </clause>

  <clause id="21484">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * T(v5,z)))) = K(x,y / (v5 / (K(w,u) * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19884,a(flip),b,21483,a)].">
      <j1 rule="hyper" parents="64 19884 21483"/>
    </justification>
  </clause>

  <clause id="21485">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) / u,z \ y,z \ 1)) = K(x,(z \ y) / (u * T(y \ (z \ y),y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19666,a(flip),b,20575,a)].">
      <j1 rule="hyper" parents="64 19666 20575"/>
    </justification>
  </clause>

  <clause id="21487">
    <literal><![CDATA[
      K(x,(y \ z) / (u * T(z \ (y \ z),z))) = K(x,L(T(z,y \ 1) / u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,15643,a(flip),b,21485,a),flip(a)].">
      <j1 rule="hyper" parents="64 15643 21485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21488">
    <literal><![CDATA[
      K(x,(y \ z) / (u * T(z \ (y \ z),z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18516,a(flip),b,21487,a),flip(a)].">
      <j1 rule="hyper" parents="373 18516 21487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21489">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20086,a(flip),b,21488,a)].">
      <j1 rule="hyper" parents="64 20086 21488"/>
    </justification>
  </clause>

  <clause id="21490">
    <literal><![CDATA[
      K(x,((y \ 1) * z) / (u * (y \ 1))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,19835,a(flip),b,21489,a),flip(a)].">
      <j1 rule="hyper" parents="64 19835 21489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21491">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,20191,a,b,21490,a)].">
      <j1 rule="hyper" parents="64 20191 21490"/>
    </justification>
  </clause>

  <clause id="21492">
    <literal><![CDATA[
      (K(x,y) * (K(x,K(y,z)) * u)) * (u \ (z * K(y,x))) = z * a(u \ (z * K(y,x)),z,K(y,x))
    ]]></literal>
    <justification jstring="[para(8109(a,1),21099(a,1,1,2,1))].">
      <j1 rule="para" parents="8109 21099"/>
    </justification>
  </clause>

  <clause id="21493">
    <literal><![CDATA[
      K(x,y / (((z * u) \ z) * T(w,u \ 1))) = K(x,y / (w * (z / (u * z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,19290,a(flip),b,21241,a)].">
      <j1 rule="hyper" parents="64 19290 21241"/>
    </justification>
  </clause>

  <clause id="21494">
    <literal><![CDATA[
      K(x,y / (z * (u / (w * u)))) = K(x,y / (z * ((u * w) \ u)))
    ]]></literal>
    <justification jstring="[para(6747(a,1),21493(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6747 21493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21495">
    <literal><![CDATA[
      K(x,y / (z * ((y * u) \ y))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19834,a(flip),b,21494,a),flip(a)].">
      <j1 rule="hyper" parents="64 19834 21494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21496">
    <literal><![CDATA[
      K(x,((y / ((y * z) \ y)) * u) / y) = K(x,y / ((y / u) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,21469,a,b,21495,a)].">
      <j1 rule="hyper" parents="64 21469 21495"/>
    </justification>
  </clause>

  <clause id="21497">
    <literal><![CDATA[
      K(x,((y * z) * u) / y) = K(x,y / ((y / u) / z))
    ]]></literal>
    <justification jstring="[para(79(a,1),21496(a,1,2,1,1))].">
      <j1 rule="para" parents="79 21496"/>
    </justification>
  </clause>

  <clause id="21499">
    <literal><![CDATA[
      K(x,T(y,z) / ((T(y,z) / u) / (K(z,y) * w))) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[para(5829(a,1),21497(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5829 21497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21500">
    <literal><![CDATA[
      K(x,((y * z) * (u * K(y,w))) / y) = K(x,y / ((K(w,y) * (y / u)) / z))
    ]]></literal>
    <justification jstring="[para(15067(a,1),21497(a,2,2,2,1))].">
      <j1 rule="para" parents="15067 21497"/>
    </justification>
  </clause>

  <clause id="21501">
    <literal><![CDATA[
      K(x,y / ((K(z,y) * (y / u)) / w)) = K(x,((y * w) * u) * (y \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(20080,a,21500,a),flip(a)].">
      <j1 rule="hyper" parents="20080 21500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21502">
    <literal><![CDATA[
      K(x,y / ((K(z,y) * (y / u)) / w)) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,19604,a(flip),b,21501,a),flip(a)].">
      <j1 rule="hyper" parents="373 19604 21501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21503">
    <literal><![CDATA[
      (x * (T(T(x,K(y,z)),y) \ u)) * (u \ (z * K(x,y))) = z * a(u \ (z * K(x,y)),z,K(x,y))
    ]]></literal>
    <justification jstring="[para(17258(a,1),21492(a,1,1))].">
      <j1 rule="para" parents="17258 21492"/>
    </justification>
  </clause>

  <clause id="21504">
    <literal><![CDATA[
      (x * (T(x,T(y,z)) \ u)) * (u \ (z * K(x,y))) = z * a(u \ (z * K(x,y)),z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7841(a,1),21503(a,1,1,2,1))].">
      <j1 rule="para" parents="7841 21503"/>
    </justification>
  </clause>

  <clause id="21505">
    <literal><![CDATA[
      (K(T(x,y),z) * u) * (u \ (y * K(z,x))) = y * a(u \ (y * K(z,x)),y,K(z,x))
    ]]></literal>
    <justification jstring="[para(5810(a,1),21504(a,1,1))].">
      <j1 rule="para" parents="5810 21504"/>
    </justification>
  </clause>

  <clause id="21506">
    <literal><![CDATA[
      x * a(y \ (x * K(z,u)),x,K(z,u)) = y * ((K(z,T(u,x)) * y) \ (x * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(20405,a,21505,a),flip(a)].">
      <j1 rule="hyper" parents="20405 21505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21507">
    <literal><![CDATA[
      x * a(y \ (x * K(z,u)),x,K(z,u)) = y * ((K(z,u) * y) \ (K(z,u) * x))
    ]]></literal>
    <justification jstring="[para(15010(a,1),21506(a,2,2))].">
      <j1 rule="para" parents="15010 21506"/>
    </justification>
  </clause>

  <clause id="21508">
    <literal><![CDATA[
      x * a(y,x,K(x \ z,u)) = z * ((K(y,u) * z) \ (K(y,u) * x))
    ]]></literal>
    <justification jstring="[para(20945(a,1),21507(a,1,2))].">
      <j1 rule="para" parents="20945 21507"/>
    </justification>
  </clause>

  <clause id="21509">
    <literal><![CDATA[
      (x * y) * ((x * T(y,T(z,x))) \ (K(y,z) * u)) = u * a(y,u,K(u \ (x * y),z))
    ]]></literal>
    <justification jstring="[para(7993(a,1),21508(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7993 21508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21511">
    <literal><![CDATA[
      (x * y) * ((x * T(y,T(z,x))) \ (K(y,z) * u)) = u * a(z,u,K(y,u \ x))
    ]]></literal>
    <justification jstring="[para(15365(a,1),21509(a,2,2))].">
      <j1 rule="para" parents="15365 21509"/>
    </justification>
  </clause>

  <clause id="21512">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(19367(a,1),21511(a,1,2))].">
      <j1 rule="para" parents="19367 21511"/>
    </justification>
  </clause>

  <clause id="21513">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = u * (z * L(z \ (u \ x),u,K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(1718,a,21512,a),flip(a)].">
      <j1 rule="hyper" parents="1718 21512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21514">
    <literal><![CDATA[
      x * L(y * (y \ (x \ z)),x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(20621(a,2),21513(a,2,2)),flip(a)].">
      <j1 rule="para" parents="20621 21513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21515">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,y,K(z,y \ x))
    ]]></literal>
    <justification jstring="[para(10(a,1),21514(a,1,2,1))].">
      <j1 rule="para" parents="10 21514"/>
    </justification>
  </clause>

  <clause id="21517">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,y,K(x \ y,z))
    ]]></literal>
    <justification jstring="[para(12251(a,2),21515(a,2,2))].">
      <j1 rule="para" parents="12251 21515"/>
    </justification>
  </clause>

  <clause id="21518">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = K(x,T(y,z)) \ T(x,T(x \ T(y,z),y))
    ]]></literal>
    <justification jstring="[para(8042(a,1),20898(a,2,2))].">
      <j1 rule="para" parents="8042 20898"/>
    </justification>
  </clause>

  <clause id="21519">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = K(x,T(y,z)) \ T(x,x \ T(T(y,z),y))
    ]]></literal>
    <justification jstring="[para(11641(a,1),21518(a,2,2))].">
      <j1 rule="para" parents="11641 21518"/>
    </justification>
  </clause>

  <clause id="21520">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = K(x,T(y,z)) \ T(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(200(a,1),21519(a,2,2,2,2))].">
      <j1 rule="para" parents="200 21519"/>
    </justification>
  </clause>

  <clause id="21521">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),T(K(x,y),z)) = R(x,x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6350,a(flip),b,21520,a),flip(a)].">
      <j1 rule="hyper" parents="373 6350 21520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21522">
    <literal><![CDATA[
      L(R(x,x \ y,x),K(x,y),K(x,T(y,z))) = R(x,x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[para(7867(a,2),21521(a,1,3))].">
      <j1 rule="para" parents="7867 21521"/>
    </justification>
  </clause>

  <clause id="21523">
    <literal><![CDATA[
      R(x,x \ T(y,z),x) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(20682,a,21522,a),flip(a)].">
      <j1 rule="hyper" parents="20682 21522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21525">
    <literal><![CDATA[
      a(x,x \ T(y,z),x) = x \ R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,21523,a(flip),b,10889,a),flip(a)].">
      <j1 rule="hyper" parents="139 21523 10889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21526">
    <literal><![CDATA[
      a(x,x \ T(y,z),x) = a(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10884,a(flip),b,21525,a),flip(a)].">
      <j1 rule="hyper" parents="373 10884 21525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21527">
    <literal><![CDATA[
      a(x,x \ (y * z),x) = a(x,x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13849,a(flip),b,21526,a)].">
      <j1 rule="hyper" parents="64 13849 21526"/>
    </justification>
  </clause>

  <clause id="21528">
    <literal><![CDATA[
      a(x,x \ (y / z),x) = a(x,x \ (z \ y),x)
    ]]></literal>
    <justification jstring="[para(117(a,1),21526(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 21526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21529">
    <literal><![CDATA[
      a(x,x \ (y / ((z / x) * u)),x) = a(x,x \ (((x \ z) * u) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,14250,a,b,21528,a)].">
      <j1 rule="hyper" parents="64 14250 21528"/>
    </justification>
  </clause>

  <clause id="21530">
    <literal><![CDATA[
      a(x,x \ (y / ((z / x) * u)),x) = a(x,x \ (u \ ((x \ z) \ y)),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13641,a(flip),b,21529,a),flip(a)].">
      <j1 rule="hyper" parents="373 13641 21529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21531">
    <literal><![CDATA[
      a(x,x \ (((y / x) * z) \ u),x) = a(x,x \ (z \ ((x \ y) \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,21528,a(flip),b,21530,a)].">
      <j1 rule="hyper" parents="64 21528 21530"/>
    </justification>
  </clause>

  <clause id="21532">
    <literal><![CDATA[
      a(x,x \ (y \ ((z / x) \ u)),x) = a(x,x \ (y \ ((x \ z) \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13641,a(flip),b,21531,a)].">
      <j1 rule="hyper" parents="64 13641 21531"/>
    </justification>
  </clause>

  <clause id="21533">
    <literal><![CDATA[
      a(x,y,T(z,x * T(y,x))) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (x * T(y,x))
    ]]></literal>
    <justification jstring="[para(10986(a,1),20989(a,2,1))].">
      <j1 rule="para" parents="10986 20989"/>
    </justification>
  </clause>

  <clause id="21534">
    <literal><![CDATA[
      a(x,y,T(z,x * T(y,x))) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,251,a(flip),b,21533,a),flip(a)].">
      <j1 rule="hyper" parents="373 251 21533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21535">
    <literal><![CDATA[
      a(x,y,T(z,y * x)) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(115(a,1),21534(a,1,1,3,2))].">
      <j1 rule="para" parents="115 21534"/>
    </justification>
  </clause>

  <clause id="21536">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ w,v5)),K(u \ (v5 \ w),v5) \ z) = K(x,K(u \ (v5 \ w),v5) \ z)
    ]]></literal>
    <justification jstring="[para(13395(a,1),21253(a,1,1,2))].">
      <j1 rule="para" parents="13395 21253"/>
    </justification>
  </clause>

  <clause id="21537">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ w,v5)),K(v5,u \ (v5 \ w)) * z) = K(x,K(u \ (v5 \ w),v5) \ z)
    ]]></literal>
    <justification jstring="[para(6156(a,1),21536(a,1,2))].">
      <j1 rule="para" parents="6156 21536"/>
    </justification>
  </clause>

  <clause id="21538">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ w,v5)),z * K(v5,u \ w)) = K(x,K(u \ (v5 \ w),v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,17839,a(flip),b,21537,a)].">
      <j1 rule="hyper" parents="64 17839 21537"/>
    </justification>
  </clause>

  <clause id="21539">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ w,v5)),z * K(v5,w * u)) = K(x,K(u \ (v5 \ w),v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(21246,a,21538,a)].">
      <j1 rule="hyper" parents="21246 21538"/>
    </justification>
  </clause>

  <clause id="21540">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),z) \ w) = K(x,w * K(z,u * y))
    ]]></literal>
    <justification jstring="[hyper(8580,a,21539,a),flip(a)].">
      <j1 rule="hyper" parents="8580 21539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21541">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u)) * w) = K(x,w * K(y,u * z))
    ]]></literal>
    <justification jstring="[para(6156(a,1),21540(a,1,2))].">
      <j1 rule="para" parents="6156 21540"/>
    </justification>
  </clause>

  <clause id="21542">
    <literal><![CDATA[
      K(x,y * K(z,u \ w)) = K(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17839,a(flip),b,21541,a)].">
      <j1 rule="hyper" parents="64 17839 21541"/>
    </justification>
  </clause>

  <clause id="21543">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w * v5)),K(u,w / v5) \ z) = K(x,K(u,w / v5) \ z)
    ]]></literal>
    <justification jstring="[para(21542(a,1),21254(a,1,1,2))].">
      <j1 rule="para" parents="21542 21254"/>
    </justification>
  </clause>

  <clause id="21544">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w * v5)),K(v5 \ w,u) * z) = K(x,K(u,w / v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(18880,a,21543,a)].">
      <j1 rule="hyper" parents="18880 21543"/>
    </justification>
  </clause>

  <clause id="21545">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w * v5)),K(w * v5,u) * z) = K(x,K(u,w / v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(18651,a,21544,a)].">
      <j1 rule="hyper" parents="18651 21544"/>
    </justification>
  </clause>

  <clause id="21546">
    <literal><![CDATA[
      K(x,K(y,z / u) \ w) = K(x,K(z * u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(8580,a,21545,a),flip(a)].">
      <j1 rule="hyper" parents="8580 21545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21547">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(18880,a,21546,a)].">
      <j1 rule="hyper" parents="18880 21546"/>
    </justification>
  </clause>

  <clause id="21548">
    <literal><![CDATA[
      K(x,K(y * z,u) * w) = K(x,K(u,y \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16828,a(flip),b,21547,a),flip(a)].">
      <j1 rule="hyper" parents="64 16828 21547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21549">
    <literal><![CDATA[
      K(x,K(y * z,u) * (w * v5)) * K(x,K(w,v5)) = K(x,v5 * (K(u,z \ y) * w))
    ]]></literal>
    <justification jstring="[para(21547(a,1),20043(a,1,1))].">
      <j1 rule="para" parents="21547 20043"/>
    </justification>
  </clause>

  <clause id="21550">
    <literal><![CDATA[
      K(x,K(y,z \ u) * w) = K(x,w * K(z * u,y))
    ]]></literal>
    <justification jstring="[hyper(17195,a,21548,a),flip(a)].">
      <j1 rule="hyper" parents="17195 21548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21551">
    <literal><![CDATA[
      K(x,K(y,z \ u) * w) = K(x,K(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(15768,a,21548,a),flip(a)].">
      <j1 rule="hyper" parents="15768 21548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21552">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(y * z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,15767,a,b,21548,a)].">
      <j1 rule="hyper" parents="373 15767 21548"/>
    </justification>
  </clause>

  <clause id="21553">
    <literal><![CDATA[
      K(x,(y * z) * K(u * w,v5)) = K(x,y * (z * K(u \ w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19580,a(flip),b,21550,a),flip(a)].">
      <j1 rule="hyper" parents="64 19580 21550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21554">
    <literal><![CDATA[
      K(x,((y \ z) \ u) * K(y * z,w)) = K(x,T(y \ z,w) \ u)
    ]]></literal>
    <justification jstring="[para(6157(a,1),21550(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6157 21550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21555">
    <literal><![CDATA[
      K(x,K(y,z / u) * w) = K(x,K(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,18032,a,b,21551,a)].">
      <j1 rule="hyper" parents="64 18032 21551"/>
    </justification>
  </clause>

  <clause id="21556">
    <literal><![CDATA[
      K(x,K(y,z * u) * (w * v5)) = K(x,w * (v5 * K(y,z \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19582,a(flip),b,21551,a),flip(a)].">
      <j1 rule="hyper" parents="64 19582 21551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21557">
    <literal><![CDATA[
      K(x,K(y,z * u) * (w * v5)) = K(x,w * (K(y,u / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,19586,a(flip),b,21555,a),flip(a)].">
      <j1 rule="hyper" parents="64 19586 21555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21558">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,v5))) = K(x,y * (z * K(u * w,v5)))
    ]]></literal>
    <justification jstring="[hyper(19581,a,21553,a),flip(a)].">
      <j1 rule="hyper" parents="19581 21553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21559">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) = K(x,y * (z * K(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19585,a(flip),b,21556,a),flip(a)].">
      <j1 rule="hyper" parents="64 19585 21556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21560">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) = K(x,y * (z * K(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19582,a(flip),b,21556,a),flip(a)].">
      <j1 rule="hyper" parents="64 19582 21556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21561">
    <literal><![CDATA[
      K(x,y * (K(z,u / w) * v5)) = K(x,y * (K(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,19586,a(flip),b,21557,a),flip(a)].">
      <j1 rule="hyper" parents="64 19586 21557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21562">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w * v5,u))) = K(x,y * (z \ T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(18473,a,21558,a),flip(a)].">
      <j1 rule="hyper" parents="18473 21558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21563">
    <literal><![CDATA[
      K(x,y * (K(z \ u,w) * v5)) = K(x,y * (v5 * K(z * u,w)))
    ]]></literal>
    <justification jstring="[hyper(18010,a,21558,a)].">
      <j1 rule="hyper" parents="18010 21558"/>
    </justification>
  </clause>

  <clause id="21564">
    <literal><![CDATA[
      K(x,(y \ z) * (u * K(y * z,w))) = K(x,T(y \ z,w) * u)
    ]]></literal>
    <justification jstring="[hyper(17261,a,21558,a),flip(a)].">
      <j1 rule="hyper" parents="17261 21558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21565">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),w * u))) = K(x,T(y,u * w) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,19830,a(flip),b,21558,a),flip(a)].">
      <j1 rule="hyper" parents="64 19830 21558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21566">
    <literal><![CDATA[
      K(x,y * (z * K(u,w / v5))) = K(x,y * (z * K(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(19663,a,21559,a)].">
      <j1 rule="hyper" parents="19663 21559"/>
    </justification>
  </clause>

  <clause id="21567">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),w * u))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,20232,a(flip),b,21559,a),flip(a)].">
      <j1 rule="hyper" parents="64 20232 21559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21568">
    <literal><![CDATA[
      K(x,y * (z * K(u,w / v5))) = K(x,y * (z * K(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(19663,a,21560,a)].">
      <j1 rule="hyper" parents="19663 21560"/>
    </justification>
  </clause>

  <clause id="21569">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (K(u,z * y) * w)) = K(x,T(y * (1 / z),u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15801,a(flip),b,21561,a),flip(a)].">
      <j1 rule="hyper" parents="64 15801 21561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21570">
    <literal><![CDATA[
      K(x,y * (K(z \ u,w) * v5)) = K(x,y * (K(z * u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,17932,a,b,21563,a),flip(a)].">
      <j1 rule="hyper" parents="373 17932 21563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21571">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w * v5))) = K(x,y * (T(z,w / v5) / u))
    ]]></literal>
    <justification jstring="[hyper(18096,a,21566,a),flip(a)].">
      <j1 rule="hyper" parents="18096 21566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21572">
    <literal><![CDATA[
      K(x,T(y / z,u) * (w * K(v5,z * y))) = K(x,T(T(y / z,u),v5) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,18210,a(flip),b,21568,a),flip(a)].">
      <j1 rule="hyper" parents="64 18210 21568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21573">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * (u * K(w,z * y))) = K(x,T(y * (z \ 1),w) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17502,a(flip),b,21568,a),flip(a)].">
      <j1 rule="hyper" parents="64 17502 21568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21574">
    <literal><![CDATA[
      K(x,y * (z \ T(u,w \ v5))) = K(x,y * (z \ T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(18473,a,21562,a),flip(a)].">
      <j1 rule="hyper" parents="18473 21562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21575">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ w) \ T(v5,u * w))) = K(x,v5 * ((u \ w) \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20783,a(flip),b,21574,a),flip(a)].">
      <j1 rule="hyper" parents="64 20783 21574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21576">
    <literal><![CDATA[
      K(x,T(y,z \ u) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,21565,a(flip),b,21567,a),flip(a)].">
      <j1 rule="hyper" parents="64 21565 21567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21577">
    <literal><![CDATA[
      K(x,T(y,z / u) * w) = K(x,T(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(18189,a,21576,a)].">
      <j1 rule="hyper" parents="18189 21576"/>
    </justification>
  </clause>

  <clause id="21578">
    <literal><![CDATA[
      K(x,T(y,(z * u) * z) * w) = K(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),21576(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 21576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21579">
    <literal><![CDATA[
      K(x,T(y,z * (u * z)) * w) = K(x,T(y,u) * w)
    ]]></literal>
    <justification jstring="[para(13297(a,1),21578(a,1,2,1))].">
      <j1 rule="para" parents="13297 21578"/>
    </justification>
  </clause>

  <clause id="21580">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) = K(x,y * (T(z,u * w) / v5))
    ]]></literal>
    <justification jstring="[hyper(18096,a,21571,a),flip(a)].">
      <j1 rule="hyper" parents="18096 21571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21581">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / v5)) = K(x,y * (T(z,w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18130,a(flip),b,21580,a)].">
      <j1 rule="hyper" parents="64 18130 21580"/>
    </justification>
  </clause>

  <clause id="21582">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) / (w / u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w / u) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(21581(a,1),19747(a,1))].">
      <j1 rule="para" parents="21581 19747"/>
    </justification>
  </clause>

  <clause id="21583">
    <literal><![CDATA[
      K(x,T(1 / y,z) * (u * K(w,y))) = K(x,T(T(1 / y,z),w) * u)
    ]]></literal>
    <justification jstring="[para(8(a,1),21572(a,1,2,2,2,2))].">
      <j1 rule="para" parents="8 21572"/>
    </justification>
  </clause>

  <clause id="21584">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * K(w,y))) = K(x,T(T(1 / y,z),w) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16841,a(flip),b,21583,a)].">
      <j1 rule="hyper" parents="64 16841 21583"/>
    </justification>
  </clause>

  <clause id="21585">
    <literal><![CDATA[
      K(x,T(T(1 / y,z),u) * w) = K(x,(T(y,z) \ w) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,19897,a(flip),b,21584,a),flip(a)].">
      <j1 rule="hyper" parents="64 19897 21584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21586">
    <literal><![CDATA[
      K(x,T(T(1 / y,z),u) * w) = K(x,T(T(y,z),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,18070,a(flip),b,21585,a),flip(a)].">
      <j1 rule="hyper" parents="373 18070 21585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21587">
    <literal><![CDATA[
      K(x,y / (z \ (u * K(w,v5)))) = K(x,y * ((z \ u) \ K(v5,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,21462,a(flip),b,21575,a)].">
      <j1 rule="hyper" parents="64 21462 21575"/>
    </justification>
  </clause>

  <clause id="21588">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y * ((z \ v5) \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20818,a,b,21587,a)].">
      <j1 rule="hyper" parents="64 20818 21587"/>
    </justification>
  </clause>

  <clause id="21590">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ K(w,v5))) = K(x,y / (u / (K(w,v5) * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,21484,a(flip),b,21588,a),flip(a)].">
      <j1 rule="hyper" parents="64 21484 21588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21591">
    <literal><![CDATA[
      K(x,y / (z / (K(u,w) * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((z / v5) \ K(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(21590(a,1),21291(a,1))].">
      <j1 rule="para" parents="21590 21291"/>
    </justification>
  </clause>

  <clause id="21592">
    <literal><![CDATA[
      K(x,T(y,z) * (((T(y,z) / u) / w) \ K(z,y))) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(21591,a,21499,a)].">
      <j1 rule="hyper" parents="21591 21499"/>
    </justification>
  </clause>

  <clause id="21593">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y * ((w / v5) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(21591,a,21047,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21591 21047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21594">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w / v5) \ K(u,z))) = v6
    ]]></literal>
    <justification jstring="[para(21047(a,2),21591(a,1))].">
      <j1 rule="para" parents="21047 21591"/>
    </justification>
  </clause>

  <clause id="21595">
    <literal><![CDATA[
      K(x,y * (((z \ u) / w) \ K(z,v5))) = K(x,y / ((T(z,v5) \ u) / w))
    ]]></literal>
    <justification jstring="[para(6157(a,1),21593(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6157 21593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21596">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * v5)) = K(x,y * (K(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,20043,a(flip),b,21549,a),flip(a)].">
      <j1 rule="hyper" parents="64 20043 21549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21597">
    <literal><![CDATA[
      K(x,y * (K(z \ u,w * v5) * (v6 * (u / z)))) = K(x,y * (v6 * T(u / z,v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18860,a(flip),b,21596,a),flip(a)].">
      <j1 rule="hyper" parents="64 18860 21596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21598">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / ((T(y,z) / u) / w)) = K(x,((y * w) * u) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19426,a(flip),b,21592,a)].">
      <j1 rule="hyper" parents="64 19426 21592"/>
    </justification>
  </clause>

  <clause id="21599">
    <literal><![CDATA[
      K(x,((y * z) * u) / T(y,w)) = K(x,y / ((T(y,w) / u) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15840,a(flip),b,21598,a),flip(a)].">
      <j1 rule="hyper" parents="64 15840 21598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21601">
    <literal><![CDATA[
      K(x,y / ((K(z,y) * (y / u)) / w)) = K(x,y / ((T(y,z) / u) / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,21502,a,b,21599,a)].">
      <j1 rule="hyper" parents="64 21502 21599"/>
    </justification>
  </clause>

  <clause id="21602">
    <literal><![CDATA[
      K(x,y * (((y / z) / u) \ K(y,w))) = K(x,y / ((T(y,w) / z) / u))
    ]]></literal>
    <justification jstring="[hyper(21594,a,21601,a)].">
      <j1 rule="hyper" parents="21594 21601"/>
    </justification>
  </clause>

  <clause id="21603">
    <literal><![CDATA[
      K(x,T(y,z) / ((y / u) / w)) = K(x,y / ((T(y,z) / u) / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18157,a(flip),b,21602,a)].">
      <j1 rule="hyper" parents="64 18157 21602"/>
    </justification>
  </clause>

  <clause id="21604">
    <literal><![CDATA[
      K(x,y / ((T(y,z * u) / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,21316,a(flip),b,21603,a),flip(a)].">
      <j1 rule="hyper" parents="64 21316 21603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21605">
    <literal><![CDATA[
      K(x,y * (z * T(u / w,v5 \ v6))) = K(x,y * (z * T(u / w,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18860,a(flip),b,21597,a),flip(a)].">
      <j1 rule="hyper" parents="64 18860 21597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21606">
    <literal><![CDATA[
      T(x,K(y,z \ ((u * z) * x))) \ (z \ ((K(y,u) * z) * x)) = K(y,x / ((u * z) \ (z * x)))
    ]]></literal>
    <justification jstring="[para(8984(a,1),21320(a,1,1))].">
      <j1 rule="para" parents="8984 21320"/>
    </justification>
  </clause>

  <clause id="21607">
    <literal><![CDATA[
      T(x,K(y,((z * u) * x) * u)) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(17557(a,1),21606(a,1,1))].">
      <j1 rule="para" parents="17557 21606"/>
    </justification>
  </clause>

  <clause id="21608">
    <literal><![CDATA[
      T(x,K(y,(z * u) * (x * u))) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(21367(a,1),21607(a,1,1))].">
      <j1 rule="para" parents="21367 21607"/>
    </justification>
  </clause>

  <clause id="21609">
    <literal><![CDATA[
      T(x,K(y,z * (u * z))) \ (z \ ((K(y,u) * z) * x)) = K(y,x / ((u * z) \ (z * x)))
    ]]></literal>
    <justification jstring="[para(17706(a,1),21608(a,1,1))].">
      <j1 rule="para" parents="17706 21608"/>
    </justification>
  </clause>

  <clause id="21610">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(17569(a,1),21609(a,1,1))].">
      <j1 rule="para" parents="17569 21609"/>
    </justification>
  </clause>

  <clause id="21611">
    <literal><![CDATA[
      x \ (y \ ((K(z,u) * y) * T(x,K(z,u)))) = K(z,x / ((u * y) \ (y * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19827,a(flip),b,21610,a)].">
      <j1 rule="hyper" parents="64 19827 21610"/>
    </justification>
  </clause>

  <clause id="21613">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = y \ ((y * u) / (u * K(z,x)))
    ]]></literal>
    <justification jstring="[para(20427(a,1),21611(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20427 21611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21614">
    <literal><![CDATA[
      (K(x,L(y,z * u,z)) * (u * (z * K(w,v5)))) / z = K(x,y) * ((u * z) / (z * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(20829(a,1),20422(a,1,1,1))].">
      <j1 rule="para" parents="20829 20422"/>
    </justification>
  </clause>

  <clause id="21615">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (z * (u * K(w,v5)))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(15518(a,1),21614(a,1,1,1))].">
      <j1 rule="para" parents="15518 21614"/>
    </justification>
  </clause>

  <clause id="21617">
    <literal><![CDATA[
      ((K(x,y) * z) * (u * K(w,v5))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(20547(a,1),21615(a,1,1))].">
      <j1 rule="para" parents="20547 21615"/>
    </justification>
  </clause>

  <clause id="21618">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(w,v5)) = K(x,y) * ((z * u) / (u * K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20420,a(flip),b,21617,a)].">
      <j1 rule="hyper" parents="64 20420 21617"/>
    </justification>
  </clause>

  <clause id="21619">
    <literal><![CDATA[
      K(x,y) * ((z * u) / (u * K(x,T(y,z)))) = L(z * K(x,K(y,u)),K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(20338,a,21618,a),flip(a)].">
      <j1 rule="hyper" parents="20338 21618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21620">
    <literal><![CDATA[
      K(x,y) * (z \ ((K(y,x) * z) * u)) = L(u * K(x,K(y,z)),K(x,y),z)
    ]]></literal>
    <justification jstring="[para(20432(a,1),21619(a,1,2))].">
      <j1 rule="para" parents="20432 21619"/>
    </justification>
  </clause>

  <clause id="21621">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,L(z,u,w)),z,T(y,x)) = K(y,L(((x \ y) * x) * z,u,w)) * x
    ]]></literal>
    <justification jstring="[para(13006(a,1),20956(a,1,2))].">
      <j1 rule="para" parents="13006 20956"/>
    </justification>
  </clause>

  <clause id="21622">
    <literal><![CDATA[
      (x \ y) \ L(T((x \ y) * x,L(z,u,w)),z,y) = K(y,L(((x \ y) * x) * z,u,w)) * x
    ]]></literal>
    <justification jstring="[para(13094(a,1),21621(a,1,2))].">
      <j1 rule="para" parents="13094 21621"/>
    </justification>
  </clause>

  <clause id="21623">
    <literal><![CDATA[
      K(x,L(((y \ x) * y) * z,u,w)) * y = K(x,L(z,u,w)) * (a(x,z,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16981,a(flip),b,21622,a),flip(a)].">
      <j1 rule="hyper" parents="64 16981 21622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21625">
    <literal><![CDATA[
      K(x,L(T(x,y) * z,u,w)) * y = K(x,L(z,u,w)) * (a(x,z,x) \ y)
    ]]></literal>
    <justification jstring="[para(18741(a,1),21623(a,1,1))].">
      <j1 rule="para" parents="18741 21623"/>
    </justification>
  </clause>

  <clause id="21626">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (a(x,y,x) \ w) = K(x,L(x * y,z,u)) * w
    ]]></literal>
    <justification jstring="[para(12152(a,1),21625(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12152 21625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21627">
    <literal><![CDATA[
      K(x,L(x * y,z,u)) = K(x,x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(13775,a,21626,a),flip(a)].">
      <j1 rule="hyper" parents="13775 21626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21629">
    <literal><![CDATA[
      K(x,L(T(y,z),z,T(u,y \ z) \ 1)) = K(x,(T(y \ z,u) * (u \ 1)) \ ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19489,a(flip),b,21209,a),flip(a)].">
      <j1 rule="hyper" parents="64 19489 21209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21630">
    <literal><![CDATA[
      K(x,L(T(y,z),z,T(u,y \ z) \ 1)) = K(x,(T(y \ z,u) / u) \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,16516,a(flip),b,21629,a),flip(a)].">
      <j1 rule="hyper" parents="373 16516 21629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21631">
    <literal><![CDATA[
      K(x,L(T(y,z),z,T(u,y \ z) \ 1)) = K(x,(u \ (y \ z)) \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,20806,a(flip),b,21630,a),flip(a)].">
      <j1 rule="hyper" parents="373 20806 21630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21632">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ (y \ u)) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(20571,a,21631,a),flip(a)].">
      <j1 rule="hyper" parents="20571 21631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21633">
    <literal><![CDATA[
      T(K(x,L(T(y,z * y),z,u \ 1)),K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))) = K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(504,a,12194,a(flip),b,21632,a)].">
      <j1 rule="hyper" parents="504 12194 21632"/>
    </justification>
  </clause>

  <clause id="21634">
    <literal><![CDATA[
      T(x,K(1 / y,z) * (u * (y * ((y * y) \ w)))) = T(x,u * (T(1 / (1 / (1 / y)),z) * w))
    ]]></literal>
    <justification jstring="[para(3778(a,1),19565(a,1,2,1))].">
      <j1 rule="para" parents="3778 19565"/>
    </justification>
  </clause>

  <clause id="21635">
    <literal><![CDATA[
      T(x,K(y,z) * (u * (y * ((y * y) \ w)))) = T(x,u * (T(1 / (1 / (1 / y)),z) * w))
    ]]></literal>
    <justification jstring="[hyper(16817,a,21634,a)].">
      <j1 rule="hyper" parents="16817 21634"/>
    </justification>
  </clause>

  <clause id="21636">
    <literal><![CDATA[
      T(x,y * (T(1 / (1 / (1 / z)),u) * w)) = T(x,y * (T(z,u) * ((z * z) \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19549,a(flip),b,21635,a),flip(a)].">
      <j1 rule="hyper" parents="64 19549 21635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21637">
    <literal><![CDATA[
      T(x,y * (T((1 / (1 / z)) \ 1,u) * w)) = T(x,y * (T(z,u) * ((z * z) \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18578,a(flip),b,21636,a)].">
      <j1 rule="hyper" parents="64 18578 21636"/>
    </justification>
  </clause>

  <clause id="21638">
    <literal><![CDATA[
      T(x,y * (T(z,u) * ((z * z) \ w))) = T(x,y * (T(1 / z,u) * w))
    ]]></literal>
    <justification jstring="[para(82(a,1),21637(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="82 21637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21639">
    <literal><![CDATA[
      T(x,y * (T(z,u) * ((z * z) \ w))) = T(x,y * (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,18578,a(flip),b,21638,a),flip(a)].">
      <j1 rule="hyper" parents="373 18578 21638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21641">
    <literal><![CDATA[
      T(x,y * (T(z \ 1,u) * w)) = T(x,y * ((T(z,u) \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19767,a(flip),b,21639,a),flip(a)].">
      <j1 rule="hyper" parents="64 19767 21639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21642">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,(u * u) * (T(z \ 1,u \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,20447,a,b,21641,a)].">
      <j1 rule="hyper" parents="373 20447 21641"/>
    </justification>
  </clause>

  <clause id="21643">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,(u * u) * (T(z \ 1,u * 1) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,19711,a(flip),b,21642,a),flip(a)].">
      <j1 rule="hyper" parents="373 19711 21642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21644">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,(u * u) * (T(z \ 1,u) * y))
    ]]></literal>
    <justification jstring="[para(8(a,1),21643(a,2,2,2,1,2))].">
      <j1 rule="para" parents="8 21643"/>
    </justification>
  </clause>

  <clause id="21645">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,u * (u * (T(z \ 1,u) * y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,15742,a(flip),b,21644,a),flip(a)].">
      <j1 rule="hyper" parents="373 15742 21644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21646">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,u * (u * (T(z,u) \ y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,16892,a(flip),b,21645,a),flip(a)].">
      <j1 rule="hyper" parents="373 16892 21645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21647">
    <literal><![CDATA[
      (x * (a(y,z,u) \ ((w \ (w * x)) \ (w * x)))) \ (w * x) = (x * (a(y,z,u) \ w)) \ (x * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),19719(a,1,1,1))].">
      <j1 rule="para" parents="9 19719"/>
    </justification>
  </clause>

  <clause id="21648">
    <literal><![CDATA[
      (x * (a(y,z,u) \ T(w,x))) \ (w * x) = (x * (a(y,z,u) \ w)) \ (x * w)
    ]]></literal>
    <justification jstring="[para(366(a,2),21647(a,1,1,2,2))].">
      <j1 rule="para" parents="366 21647"/>
    </justification>
  </clause>

  <clause id="21649">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5))) = K(x,L(K(y,z) / u,w,v5) * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[para(14445(a,1),19954(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14445 19954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21650">
    <literal><![CDATA[
      K(x,(T(y,(z \ 1) \ 1) / u) * ((z \ K(z,u)) \ u)) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(4814(a,1),20017(a,1,2,1,1))].">
      <j1 rule="para" parents="4814 20017"/>
    </justification>
  </clause>

  <clause id="21651">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * ((z \ K(z,u)) \ u)) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(3871(a,1),21650(a,1,2,1,1))].">
      <j1 rule="para" parents="3871 21650"/>
    </justification>
  </clause>

  <clause id="21653">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u / (z \ 1))) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,18719,a(flip),b,21651,a)].">
      <j1 rule="hyper" parents="64 18719 21651"/>
    </justification>
  </clause>

  <clause id="21654">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u / (z \ 1))) = K(x,((z \ 1) \ u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(12(a,1),21653(a,2,2,1))].">
      <j1 rule="para" parents="12 21653"/>
    </justification>
  </clause>

  <clause id="21655">
    <literal><![CDATA[
      K(x,((((y * z) \ y) \ y) / u) * (u / ((z \ 1) \ 1))) = K(x,(((z \ 1) \ 1) \ u) * (u \ (y * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16451,a(flip),b,21654,a)].">
      <j1 rule="hyper" parents="64 16451 21654"/>
    </justification>
  </clause>

  <clause id="21657">
    <literal><![CDATA[
      K(x,((((y * z) \ y) \ y) / u) * (u / T(z,1))) = K(x,(((z \ 1) \ 1) \ u) * (u \ (y * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18453,a(flip),b,21655,a)].">
      <j1 rule="hyper" parents="64 18453 21655"/>
    </justification>
  </clause>

  <clause id="21658">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,((((u * y) \ u) \ u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[para(372(a,1),21657(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="372 21657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21659">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,(T(u * y,u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(373,a,18609,a(flip),b,21658,a),flip(a)].">
      <j1 rule="hyper" parents="373 18609 21658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21660">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(373,a,20138,a(flip),b,21659,a),flip(a)].">
      <j1 rule="hyper" parents="373 20138 21659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21661">
    <literal><![CDATA[
      K(x,(T(y,1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,20035,a(flip),b,21660,a)].">
      <j1 rule="hyper" parents="64 20035 21660"/>
    </justification>
  </clause>

  <clause id="21662">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,(y \ u) * (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(372(a,1),21661(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="372 21661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21663">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (z / y),w,v5))) = K(x,u * L(((z * y) / z) \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(6117(a,1),20129(a,1,2,1))].">
      <j1 rule="para" parents="6117 20129"/>
    </justification>
  </clause>

  <clause id="21664">
    <literal><![CDATA[
      T((x * T(y,y \ z)) \ T(y,y \ z),(x * y) \ y) = (x * T(y,y \ z)) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16305,a(flip),b,20439,a)].">
      <j1 rule="hyper" parents="64 16305 20439"/>
    </justification>
  </clause>

  <clause id="21665">
    <literal><![CDATA[
      T((x * y) \ y,K(y,y \ z)) = (x * T(y,y \ z)) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,18550,a(flip),b,21664,a)].">
      <j1 rule="hyper" parents="64 18550 21664"/>
    </justification>
  </clause>

  <clause id="21666">
    <literal><![CDATA[
      (x * T(y,y \ z)) \ ((y \ z) \ z) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8714,a,21665,a),flip(a)].">
      <j1 rule="hyper" parents="8714 21665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21667">
    <literal><![CDATA[
      a(x,T(y \ (y / (z \ u)),w) * T(y,u \ z),x) = a(x,K(w,u \ (z * 1)) \ (y / (z \ u)),x)
    ]]></literal>
    <justification jstring="[para(6704(a,1),21082(a,1,2,2))].">
      <j1 rule="para" parents="6704 21082"/>
    </justification>
  </clause>

  <clause id="21668">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) / (v5 * (y \ L(T(y,z),u,w)))) = K(x,L(y / v5,L(T(y,z),u,w),a(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16473,a(flip),b,20622,a),flip(a)].">
      <j1 rule="hyper" parents="64 16473 20622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21669">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) / (v5 * (y \ L(T(y,z),u,w)))) = K(x,L(y / v5,L(y,u,w),a(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,20598,a(flip),b,21668,a),flip(a)].">
      <j1 rule="hyper" parents="373 20598 21668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21671">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) / (v5 * (y \ L(T(y,z),u,w)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y / v5) = v6
    ]]></literal>
    <justification jstring="[para(21669(a,2),21276(a,1))].">
      <j1 rule="para" parents="21669 21276"/>
    </justification>
  </clause>

  <clause id="21672">
    <literal><![CDATA[
      L(L(x,y,z),y,K(u \ 1,((w * u) \ w) * z)) = L(x,y,(((w * u) \ w) * z) / L(u \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(6771(a,1),20982(a,1,3))].">
      <j1 rule="para" parents="6771 20982"/>
    </justification>
  </clause>

  <clause id="21673">
    <literal><![CDATA[
      L(L(x,y,z),y,K(((u * w) \ u) * z,w)) = L(x,y,(((u * w) \ u) * z) / L(w \ 1,w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14936,a(flip),b,21672,a)].">
      <j1 rule="hyper" parents="64 14936 21672"/>
    </justification>
  </clause>

  <clause id="21675">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,(((w * u) \ w) * z) / L(u \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,15178,a(flip),b,21673,a)].">
      <j1 rule="hyper" parents="64 15178 21673"/>
    </justification>
  </clause>

  <clause id="21677">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,((u \ 1) * z) / (u \ 1))
    ]]></literal>
    <justification jstring="[para(12799(a,1),21675(a,2,3))].">
      <j1 rule="para" parents="12799 21675"/>
    </justification>
  </clause>

  <clause id="21678">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,(u \ 1) * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,13009,a(flip),b,21677,a),flip(a)].">
      <j1 rule="hyper" parents="373 13009 21677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21679">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,T(z,1 \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13082,a(flip),b,21678,a),flip(a)].">
      <j1 rule="hyper" parents="373 13082 21678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21680">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(66(a,1),21679(a,2,3,2))].">
      <j1 rule="para" parents="66 21679"/>
    </justification>
  </clause>

  <clause id="21681">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(19200,a,21680,a),flip(a)].">
      <j1 rule="hyper" parents="19200 21680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21682">
    <literal><![CDATA[
      L(x,T(y,z),T(u,y)) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7994,a,21680,a),flip(a)].">
      <j1 rule="hyper" parents="7994 21680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21683">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,z) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(1435,a,21680,a)].">
      <j1 rule="hyper" parents="1435 21680"/>
    </justification>
  </clause>

  <clause id="21684">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12190,a(flip),b,21681,a),flip(a)].">
      <j1 rule="hyper" parents="64 12190 21681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21685">
    <literal><![CDATA[
      L(x,T(y,z),(y / z) \ 1) = L(x,y,(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(14189,a,21682,a),flip(a)].">
      <j1 rule="hyper" parents="14189 21682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21686">
    <literal><![CDATA[
      L(L(x,y,K(z * u,u \ 1)),y,z * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,13054,a(flip),b,21683,a),flip(a)].">
      <j1 rule="hyper" parents="373 13054 21683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21687">
    <literal><![CDATA[
      L(x,x,T(y,z)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[para(14365(a,1),21683(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14365 21683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21689">
    <literal><![CDATA[
      x / L(y,z,(y * z) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(225,a,21684,a(flip),b,15006,a(flip))].">
      <j1 rule="hyper" parents="225 21684 15006"/>
    </justification>
  </clause>

  <clause id="21690">
    <literal><![CDATA[
      1 / L(x,y,x * y) = (1 / (y * x)) * y
    ]]></literal>
    <justification jstring="[para(1631(a,1),21689(a,1,2))].">
      <j1 rule="para" parents="1631 21689"/>
    </justification>
  </clause>

  <clause id="21691">
    <literal><![CDATA[
      x / L(K(y,z),(z / u) \ 1,((T(z,T(y,u)) / u) \ 1) \ x) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(18399(a,2),21689(a,1,2,3,1))].">
      <j1 rule="para" parents="18399 21689"/>
    </justification>
  </clause>

  <clause id="21692">
    <literal><![CDATA[
      L(x,y,x * y) = ((1 / (y * x)) * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,21690,a),flip(a)].">
      <j1 rule="hyper" parents="215 21690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21693">
    <literal><![CDATA[
      1 / L(x,x * y,L(y,x,x)) = (1 / ((x * y) * x)) * (x * y)
    ]]></literal>
    <justification jstring="[para(2185(a,1),21690(a,1,2))].">
      <j1 rule="para" parents="2185 21690"/>
    </justification>
  </clause>

  <clause id="21694">
    <literal><![CDATA[
      L(x,(L(y,z,y * z) * u) * w,v5) = L(x,(((1 / (z * y)) * z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(21690(a,1),11889(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="21690 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21695">
    <literal><![CDATA[
      L(x \ 1,y,x * y) = ((1 / (y * (x \ 1))) * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,2211,a(flip),b,21692,a)].">
      <j1 rule="hyper" parents="64 2211 21692"/>
    </justification>
  </clause>

  <clause id="21696">
    <literal><![CDATA[
      L(x,T(y,z),(z \ y) \ 1) = L(x,y,(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,19701,a(flip),b,21685,a)].">
      <j1 rule="hyper" parents="64 19701 21685"/>
    </justification>
  </clause>

  <clause id="21697">
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = L(x,y,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,14220,a(flip),b,21696,a),flip(a)].">
      <j1 rule="hyper" parents="64 14220 21696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21698">
    <literal><![CDATA[
      L(x,(y * z) / y,(T(y,z) \ ((y * z) / y)) \ 1) = L(x,(y * z) / y,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(2518(a,1),21697(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2518 21697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21699">
    <literal><![CDATA[
      L(1 / x,y,x * y) \ 1 = (1 / (y * (x \ 1))) * y
    ]]></literal>
    <justification jstring="[hyper(40,a,10466,a,b,21695,a(flip))].">
      <j1 rule="hyper" parents="40 10466 21695"/>
    </justification>
  </clause>

  <clause id="21700">
    <literal><![CDATA[
      L(L(x,y,K(z,u * z)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(14935(a,1),21686(a,1,1))].">
      <j1 rule="para" parents="14935 21686"/>
    </justification>
  </clause>

  <clause id="21701">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(13000(a,1),21700(a,1,1))].">
      <j1 rule="para" parents="13000 21700"/>
    </justification>
  </clause>

  <clause id="21702">
    <literal><![CDATA[
      ((x * y) * (z * L(u,z,K(y,x)))) / T((x * y) * z,L(u,z,K(y,x))) = L(u,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,14659,a(flip),b,21701,a)].">
      <j1 rule="hyper" parents="64 14659 21701"/>
    </justification>
  </clause>

  <clause id="21703">
    <literal><![CDATA[
      L(x,(L(y,z,y * z) * u) * w,v5) = L(x,(((z * y) * z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,11929,a(flip),b,21694,a),flip(a)].">
      <j1 rule="hyper" parents="373 11929 21694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21704">
    <literal><![CDATA[
      L(x,(y * z) / y,(T(y,z) \ ((y * z) / y)) \ 1) = L(x,y * (z / y),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,14197,a(flip),b,21698,a),flip(a)].">
      <j1 rule="hyper" parents="373 14197 21698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21705">
    <literal><![CDATA[
      L(x,(y * z) / y,(y \ z) \ 1) = L(x,y * (z / y),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(4469(a,1),21704(a,1,3,1))].">
      <j1 rule="para" parents="4469 21704"/>
    </justification>
  </clause>

  <clause id="21706">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,y * (z / y),(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,14197,a(flip),b,21705,a),flip(a)].">
      <j1 rule="hyper" parents="64 14197 21705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21707">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,14221,a(flip),b,21706,a),flip(a)].">
      <j1 rule="hyper" parents="373 14221 21706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21708">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,z,(y \ z) \ 1)) = K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(21707(a,1),9337(a,1,2))].">
      <j1 rule="para" parents="21707 9337"/>
    </justification>
  </clause>

  <clause id="21709">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,L(u,z,K(x,y))) = L(u,z,x * y)
    ]]></literal>
    <justification jstring="[para(20991(a,1),21702(a,1,1))].">
      <j1 rule="para" parents="20991 21702"/>
    </justification>
  </clause>

  <clause id="21710">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,u) = L(u,z,x * y)
    ]]></literal>
    <justification jstring="[para(19188(a,1),21709(a,1,2))].">
      <j1 rule="para" parents="19188 21709"/>
    </justification>
  </clause>

  <clause id="21711">
    <literal><![CDATA[
      L(x,K(y,z) * u,z * y) = L(x,u,z * y)
    ]]></literal>
    <justification jstring="[hyper(14993,a,21710,a)].">
      <j1 rule="hyper" parents="14993 21710"/>
    </justification>
  </clause>

  <clause id="21713">
    <literal><![CDATA[
      L(x,K(y,z / y) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(12(a,1),21711(a,1,3))].">
      <j1 rule="para" parents="12 21711"/>
    </justification>
  </clause>

  <clause id="21714">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(5926(a,1),21713(a,1,2,1))].">
      <j1 rule="para" parents="5926 21713"/>
    </justification>
  </clause>

  <clause id="21715">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14166,a(flip),b,21714,a)].">
      <j1 rule="hyper" parents="64 14166 21714"/>
    </justification>
  </clause>

  <clause id="21716">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,z)
    ]]></literal>
    <justification jstring="[para(12(a,1),21715(a,2,3))].">
      <j1 rule="para" parents="12 21715"/>
    </justification>
  </clause>

  <clause id="21717">
    <literal><![CDATA[
      L(x,T(y,z),y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(5797(a,1),21716(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5797 21716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21719">
    <literal><![CDATA[
      L(x,K(y,z) * u,y) = L(x,u,y)
    ]]></literal>
    <justification jstring="[para(6161(a,1),21716(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6161 21716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21721">
    <literal><![CDATA[
      L(x,y \ K(z,u),z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(14665(a,1),21719(a,1,2))].">
      <j1 rule="para" parents="14665 21719"/>
    </justification>
  </clause>

  <clause id="21722">
    <literal><![CDATA[
      T(x,L(y,z \ 1,u) * (u * (z \ 1))) = T(x,(y * (z \ K(u,z \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(21721(a,1),21183(a,1,2,1))].">
      <j1 rule="para" parents="21721 21183"/>
    </justification>
  </clause>

  <clause id="21723">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,u / z)))
    ]]></literal>
    <justification jstring="[para(14552(a,1),21722(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14552 21722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21725">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,z \ u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18112,a(flip),b,21723,a),flip(a)].">
      <j1 rule="hyper" parents="373 18112 21723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21726">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * T(u,z \ y))) = T(x,(u * (z \ 1)) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18720,a(flip),b,21725,a),flip(a)].">
      <j1 rule="hyper" parents="64 18720 21725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21727">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,z,z \ y)) = K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(15965,a,21708,a)].">
      <j1 rule="hyper" parents="15965 21708"/>
    </justification>
  </clause>

  <clause id="21728">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,L(T(z,y) \ u,z,z \ y))
    ]]></literal>
    <justification jstring="[hyper(16092,a,21727,a),flip(a)].">
      <j1 rule="hyper" parents="16092 21727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21729">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13600,a(flip),b,21728,a),flip(a)].">
      <j1 rule="hyper" parents="373 13600 21728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21730">
    <literal><![CDATA[
      K(x,(y * ((y / z) \ 1)) \ (((y / z) \ 1) * u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(15917,a,21729,a)].">
      <j1 rule="hyper" parents="15917 21729"/>
    </justification>
  </clause>

  <clause id="21731">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ ((y / z) \ u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16516,a(flip),b,21730,a)].">
      <j1 rule="hyper" parents="64 16516 21730"/>
    </justification>
  </clause>

  <clause id="21732">
    <literal><![CDATA[
      K(x,y \ ((y \ z) \ u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(6617(a,1),21731(a,1,2))].">
      <j1 rule="para" parents="6617 21731"/>
    </justification>
  </clause>

  <clause id="21733">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((y \ z) * T(u,z / y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,21199,a,b,21732,a)].">
      <j1 rule="hyper" parents="64 21199 21732"/>
    </justification>
  </clause>

  <clause id="21734">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * (K(y,u) * w))) = K(x,y \ ((T(y,u) \ z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,20019,a(flip),b,21732,a),flip(a)].">
      <j1 rule="hyper" parents="64 20019 21732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21735">
    <literal><![CDATA[
      K(x,y \ (((K(z,y) * u) \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(6137(a,1),21732(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6137 21732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21736">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(21732(a,1),10243(a,1,2))].">
      <j1 rule="para" parents="21732 10243"/>
    </justification>
  </clause>

  <clause id="21737">
    <literal><![CDATA[
      K(x,K(y,z) * (z \ ((u \ z) * w))) = K(x,z \ ((T(z,y) \ u) \ w))
    ]]></literal>
    <justification jstring="[hyper(20530,a,21734,a)].">
      <j1 rule="hyper" parents="20530 21734"/>
    </justification>
  </clause>

  <clause id="21738">
    <literal><![CDATA[
      K(x,y \ ((T(y,z) \ u) \ w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[para(14833(a,1),21735(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14833 21735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21739">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(6157(a,1),21737(a,1,2))].">
      <j1 rule="para" parents="6157 21737"/>
    </justification>
  </clause>

  <clause id="21740">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,21738,a(flip),b,21739,a),flip(a)].">
      <j1 rule="hyper" parents="373 21738 21739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21741">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ T(u * (y \ z),K(y,z)))
    ]]></literal>
    <justification jstring="[para(9168(a,2),21733(a,2,2,2))].">
      <j1 rule="para" parents="9168 21733"/>
    </justification>
  </clause>

  <clause id="21742">
    <literal><![CDATA[
      K(x,((y \ z) \ u) / y) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15654,a(flip),b,21736,a),flip(a)].">
      <j1 rule="hyper" parents="64 15654 21736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21743">
    <literal><![CDATA[
      K(x,((y \ z) \ (((z \ y) * u) * (u / ((z \ y) * u)))) / y) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[para(4592(a,1),21742(a,2,2,1))].">
      <j1 rule="para" parents="4592 21742"/>
    </justification>
  </clause>

  <clause id="21744">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,17928,a(flip),b,21741,a),flip(a)].">
      <j1 rule="hyper" parents="373 17928 21741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21746">
    <literal><![CDATA[
      K(x,y \ (z / (y \ u))) = K(x,y \ (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20044,a(flip),b,21744,a)].">
      <j1 rule="hyper" parents="64 20044 21744"/>
    </justification>
  </clause>

  <clause id="21747">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * T(y,y \ z)) \ ((y \ z) \ z)))) = K(x,((y \ z) \ z) \ (u / T(w,T(y,z))))
    ]]></literal>
    <justification jstring="[para(7586(a,1),21746(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7586 21746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21748">
    <literal><![CDATA[
      K(x,((((y \ z) * u) \ u) \ u) / z) = K(x,((z \ y) \ (((z \ y) \ u) * (z \ y))) / z)
    ]]></literal>
    <justification jstring="[para(18947(a,1),21743(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="18947 21743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21749">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[para(22(a,2),21748(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="22 21748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21750">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[hyper(20220,a,21749,a)].">
      <j1 rule="hyper" parents="20220 21749"/>
    </justification>
  </clause>

  <clause id="21751">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,T((z \ y) * u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,13555,a(flip),b,21750,a),flip(a)].">
      <j1 rule="hyper" parents="373 13555 21750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21752">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * (z \ y)) / y) = w
    ]]></literal>
    <justification jstring="[para(21751(a,2),18510(a,1))].">
      <j1 rule="para" parents="21751 18510"/>
    </justification>
  </clause>

  <clause id="21753">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / u) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(21752,a,21324,a)].">
      <j1 rule="hyper" parents="21752 21324"/>
    </justification>
  </clause>

  <clause id="21754">
    <literal><![CDATA[
      K(x,(y * T(z,z \ u)) / u) = K(x,u / ((z \ u) * (y \ u)))
    ]]></literal>
    <justification jstring="[para(116(a,2),21753(a,1,2,1,2))].">
      <j1 rule="para" parents="116 21753"/>
    </justification>
  </clause>

  <clause id="21755">
    <literal><![CDATA[
      K(x,(y * (z \ L(T(y,K(u,w)),v5,v6))) / L(T(y,K(u,w)),v5,v6)) = K(x,L(T(y,K(u,w)),v5,v6) / (z * (T(y,K(u,w)) \ L(y,v5,v6))))
    ]]></literal>
    <justification jstring="[para(19716(a,2),21753(a,2,2,2,2))].">
      <j1 rule="para" parents="19716 21753"/>
    </justification>
  </clause>

  <clause id="21756">
    <literal><![CDATA[
      K(x,y / ((z \ y) * (u \ y))) = K(x,(u * T(z,y)) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,18600,a(flip),b,21754,a),flip(a)].">
      <j1 rule="hyper" parents="64 18600 21754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21757">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = K(x,(L(y \ K(z,u),w,v5) \ (y \ K(z,u))) \ 1)
    ]]></literal>
    <justification jstring="[para(16434(a,1),21756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16434 21756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21758">
    <literal><![CDATA[
      L(((x \ y) * K(z,u)) \ (y * K(z,u)),x \ y,K(u,z)) = (x \ (K(u,z) * y)) \ (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,20993,a(flip),b,21218,a)].">
      <j1 rule="hyper" parents="64 20993 21218"/>
    </justification>
  </clause>

  <clause id="21760">
    <literal><![CDATA[
      (x \ y) \ (K(z,T(u,x \ y)) * (y * K(u,z))) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,20966,a(flip),b,21758,a)].">
      <j1 rule="hyper" parents="64 20966 21758"/>
    </justification>
  </clause>

  <clause id="21761">
    <literal><![CDATA[
      (x \ y) \ (K(z,T(u,y * x)) * (y * K(u,z))) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(17025(a,1),21760(a,1,2,1))].">
      <j1 rule="para" parents="17025 21760"/>
    </justification>
  </clause>

  <clause id="21762">
    <literal><![CDATA[
      (x \ y) \ T(K(y * x,K(z,u)) * y,K(z,u)) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(9289(a,2),21761(a,1,2))].">
      <j1 rule="para" parents="9289 21761"/>
    </justification>
  </clause>

  <clause id="21763">
    <literal><![CDATA[
      (x \ y) \ T(K(z,K(u,y * x)) * y,K(z,u)) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(8110(a,2),21762(a,1,2,1,1))].">
      <j1 rule="para" parents="8110 21762"/>
    </justification>
  </clause>

  <clause id="21764">
    <literal><![CDATA[
      K(x,K(y,z * u)) * ((u \ z) \ T(z,K(x,y))) = (u \ (K(x,y) * z)) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,19416,a(flip),b,21763,a)].">
      <j1 rule="hyper" parents="64 19416 21763"/>
    </justification>
  </clause>

  <clause id="21765">
    <literal><![CDATA[
      T(x \ y,K(z,u)) \ T(y,K(z,u)) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(17558,a,21764,a)].">
      <j1 rule="hyper" parents="17558 21764"/>
    </justification>
  </clause>

  <clause id="21766">
    <literal><![CDATA[
      R(x,y,z \ (T(u \ w,K(v5,v6)) \ T(w,K(v5,v6)))) = R(x,y,z \ T(u,K(v5,v6) * w))
    ]]></literal>
    <justification jstring="[para(21765(a,2),13907(a,1,3,2))].">
      <j1 rule="para" parents="21765 13907"/>
    </justification>
  </clause>

  <clause id="21767">
    <literal><![CDATA[
      R(x,y,z \ (T(u \ w,K(v5,v6)) \ T(w,K(v5,v6)))) = R(x,y,z \ T(u,K(v6,v5) * w))
    ]]></literal>
    <justification jstring="[para(15759(a,1),21766(a,2,3,2))].">
      <j1 rule="para" parents="15759 21766"/>
    </justification>
  </clause>

  <clause id="21768">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (K(x,K(y,z)) * (u * (w * v5))) = L(v5,L(w,u,K(x,K(y,z))),K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(19172(a,1),19202(a,1,2))].">
      <j1 rule="para" parents="19172 19202"/>
    </justification>
  </clause>

  <clause id="21769">
    <literal><![CDATA[
      K(x,(K(y,L(z \ 1,u,w)) * (L(z,u,w) \ v5)) * z) = K(x,z * ((K(y,L(z,u,w) \ 1) * v5) / L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(12074(a,2),19459(a,1,2,1,1))].">
      <j1 rule="para" parents="12074 19459"/>
    </justification>
  </clause>

  <clause id="21770">
    <literal><![CDATA[
      K(x,L(((y \ L(y,z,u)) \ 1) \ w,y,L(y,z,u))) = K(x,y \ ((((y \ L(y,z,u)) \ 1) \ y) * w))
    ]]></literal>
    <justification jstring="[para(10(a,1),19661(a,1,2,3))].">
      <j1 rule="para" parents="10 19661"/>
    </justification>
  </clause>

  <clause id="21771">
    <literal><![CDATA[
      K(x,y \ ((((y \ L(y,z,u)) \ 1) \ y) * w)) = K(x,((y \ L(y,z,u)) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(15389,a,21770,a),flip(a)].">
      <j1 rule="hyper" parents="15389 21770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21773">
    <literal><![CDATA[
      K(x,y \ ((((y \ L(y,z,u)) \ 1) \ y) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,14413,a(flip),b,21771,a),flip(a)].">
      <j1 rule="hyper" parents="373 14413 21771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21774">
    <literal><![CDATA[
      K(x,y \ (((L(y,z,u) \ y) \ y) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(9374(a,1),21773(a,1,2,2,1,1))].">
      <j1 rule="para" parents="9374 21773"/>
    </justification>
  </clause>

  <clause id="21775">
    <literal><![CDATA[
      K(x,y \ (L(y,z,u) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(5559(a,1),21774(a,1,2,2,1))].">
      <j1 rule="para" parents="5559 21774"/>
    </justification>
  </clause>

  <clause id="21776">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[para(2325(a,1),21775(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2325 21775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21777">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,u * a(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(19461,a,21776,a),flip(a)].">
      <j1 rule="hyper" parents="19461 21776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21778">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * w) = T(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(143,a,21776,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 21776 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21779">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) \ u) = K(x,u * a(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,16392,a(flip),b,21777,a)].">
      <j1 rule="hyper" parents="64 16392 21777"/>
    </justification>
  </clause>

  <clause id="21780">
    <literal><![CDATA[
      K(x,(y * z) * a(z,u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(21779(a,1),21151(a,1))].">
      <j1 rule="para" parents="21779 21151"/>
    </justification>
  </clause>

  <clause id="21781">
    <literal><![CDATA[
      K(x,L((y / (z \ 1)) / z,u,w) * T(z,y * (K(z,y) * z))) = K(x,z * L(z \ (y / (z \ K(y,z))),u,w))
    ]]></literal>
    <justification jstring="[para(14608(a,1),19825(a,1,2,2))].">
      <j1 rule="para" parents="14608 19825"/>
    </justification>
  </clause>

  <clause id="21782">
    <literal><![CDATA[
      K(x,y * (R(z,z \ (a(u,w,K(v5,v6)) * v7),a(v6,w,K(v5,u))) \ v7)) = K(x,y * (z \ (v7 / a(v6,w,K(v5,u)))))
    ]]></literal>
    <justification jstring="[para(19333(a,1),19888(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="19333 19888"/>
    </justification>
  </clause>

  <clause id="21783">
    <literal><![CDATA[
      (K(x,K(y,z)) \ ((u * w) * v5)) / ((w * K(x,K(y,z))) * v5) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[para(19410(a,2),20332(a,1,1))].">
      <j1 rule="para" parents="19410 20332"/>
    </justification>
  </clause>

  <clause id="21784">
    <literal><![CDATA[
      L(K(x,((y / ((z \ 1) \ 1)) / u) \ x),z \ y,z) \ T(x,(u * z) / y) = R(x,u / (y / ((z \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(13051(a,2),20957(a,1,1,1))].">
      <j1 rule="para" parents="13051 20957"/>
    </justification>
  </clause>

  <clause id="21785">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * T(y,y \ z)) \ ((y \ z) \ z)))) = K(x,((y \ z) \ z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,19755,a(flip),b,21747,a),flip(a)].">
      <j1 rule="hyper" parents="373 19755 21747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21787">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * T(y,y \ z)) \ ((y \ z) \ z)))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,13351,a(flip),b,21785,a),flip(a)].">
      <j1 rule="hyper" parents="373 13351 21785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21788">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * T((w * y) \ y,K(y,z)))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[para(21666(a,1),21787(a,1,2,2,2))].">
      <j1 rule="para" parents="21666 21787"/>
    </justification>
  </clause>

  <clause id="21789">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(19475,a,21788,a)].">
      <j1 rule="hyper" parents="19475 21788"/>
    </justification>
  </clause>

  <clause id="21790">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(13579,a,21789,a)].">
      <j1 rule="hyper" parents="13579 21789"/>
    </justification>
  </clause>

  <clause id="21792">
    <literal><![CDATA[
      K(x,y \ (z * ((u * y) \ T(y,w)))) = K(x,T(y,w) \ (z / T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20534,a(flip),b,21790,a)].">
      <j1 rule="hyper" parents="64 20534 21790"/>
    </justification>
  </clause>

  <clause id="21793">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * u) / T(z,y))) = K(x,((z * ((z * y) / z)) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,21314,a,b,21792,a),flip(a)].">
      <j1 rule="hyper" parents="64 21314 21792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21794">
    <literal><![CDATA[
      K(x,T(y \ ((y * z) / u),K(y,u))) = K(x,((u * ((u * y) / u)) / z) \ y)
    ]]></literal>
    <justification jstring="[para(7160(a,2),21793(a,1,2))].">
      <j1 rule="para" parents="7160 21793"/>
    </justification>
  </clause>

  <clause id="21795">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[hyper(17156,a,21794,a),flip(a)].">
      <j1 rule="hyper" parents="17156 21794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21797">
    <literal><![CDATA[
      K(x,((y * z) / u) \ T(z,y)) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[para(16137(a,1),21795(a,1,2))].">
      <j1 rule="para" parents="16137 21795"/>
    </justification>
  </clause>

  <clause id="21798">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(18648,a,21797,a)].">
      <j1 rule="hyper" parents="18648 21797"/>
    </justification>
  </clause>

  <clause id="21799">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ (u * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(20205,a,21798,a)].">
      <j1 rule="hyper" parents="20205 21798"/>
    </justification>
  </clause>

  <clause id="21800">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = K(x,y \ ((y * (u * z)) / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,20395,a(flip),b,21799,a)].">
      <j1 rule="hyper" parents="64 20395 21799"/>
    </justification>
  </clause>

  <clause id="21801">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[para(5016(a,1),21799(a,1,2,2))].">
      <j1 rule="para" parents="5016 21799"/>
    </justification>
  </clause>

  <clause id="21802">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = K(x,(y \ K(z,u)) \ L(y \ K(z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,6700,a(flip),b,21757,a),flip(a)].">
      <j1 rule="hyper" parents="373 6700 21757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21803">
    <literal><![CDATA[
      L(x,L(y,z,K(u,K(w,v5))),K(u,K(w,v5)) * z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(19266,a,21768,a),flip(a)].">
      <j1 rule="hyper" parents="19266 21768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21804">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w)) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(19184(a,1),21803(a,1,2))].">
      <j1 rule="para" parents="19184 21803"/>
    </justification>
  </clause>

  <clause id="21805">
    <literal><![CDATA[
      ((x * y) \ (x * (y * (z * K(u,K(w,v5)))))) * K(u,K(w,v5)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,20393,a,b,21804,a)].">
      <j1 rule="hyper" parents="64 20393 21804"/>
    </justification>
  </clause>

  <clause id="21806">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w)) \ v5) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(6075(a,1),21804(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6075 21804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21807">
    <literal><![CDATA[
      L(x,y,z * T(u,K(w,v5))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(6367(a,1),21804(a,1,3))].">
      <j1 rule="para" parents="6367 21804"/>
    </justification>
  </clause>

  <clause id="21808">
    <literal><![CDATA[
      L(x,y,K(z,T(u,w))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(7504(a,1),21804(a,1,3))].">
      <j1 rule="para" parents="7504 21804"/>
    </justification>
  </clause>

  <clause id="21809">
    <literal><![CDATA[
      L(x,y,z / T(u,K(w,v5))) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(17335(a,1),21804(a,1,3))].">
      <j1 rule="para" parents="17335 21804"/>
    </justification>
  </clause>

  <clause id="21810">
    <literal><![CDATA[
      L(x,y,((1 / z) * K(u,w)) \ v5) = L(x,y,(K(u,w) / z) \ v5)
    ]]></literal>
    <justification jstring="[para(14396(a,1),21806(a,1,3,1))].">
      <j1 rule="para" parents="14396 21806"/>
    </justification>
  </clause>

  <clause id="21811">
    <literal><![CDATA[
      L(x,y,z * (T(u,T(w,v5)) / v5)) = L(x,y,z * (T(u,w) / v5))
    ]]></literal>
    <justification jstring="[para(8429(a,1),21807(a,1,3,2))].">
      <j1 rule="para" parents="8429 21807"/>
    </justification>
  </clause>

  <clause id="21812">
    <literal><![CDATA[
      L(x,y,z / ((1 / u) * K(w,v5))) = L(x,y,z / (K(w,v5) / u))
    ]]></literal>
    <justification jstring="[para(14396(a,1),21809(a,1,3,2))].">
      <j1 rule="para" parents="14396 21809"/>
    </justification>
  </clause>

  <clause id="21813">
    <literal><![CDATA[
      L(x,y,(K(z,u) / w) \ v5) = L(x,y,(w \ K(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,14509,a(flip),b,21810,a),flip(a)].">
      <j1 rule="hyper" parents="64 14509 21810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21814">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,(x \ K(x,y)) \ u))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(21813(a,1),16174(a,1,2,2,2))].">
      <j1 rule="para" parents="21813 16174"/>
    </justification>
  </clause>

  <clause id="21815">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,(u \ K(z,y)) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(21813(a,1),18702(a,1,2,2))].">
      <j1 rule="para" parents="21813 18702"/>
    </justification>
  </clause>

  <clause id="21816">
    <literal><![CDATA[
      L(x,y,z / (K(u,w) / v5)) = L(x,y,z / (v5 \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15205,a(flip),b,21812,a),flip(a)].">
      <j1 rule="hyper" parents="64 15205 21812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21817">
    <literal><![CDATA[
      K(x,L(y,z,u / (w \ K(v5,v6)))) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[para(21816(a,1),20634(a,1,2))].">
      <j1 rule="para" parents="21816 20634"/>
    </justification>
  </clause>

  <clause id="21818">
    <literal><![CDATA[
      K(x,L(y,z,(u \ K(w,v5)) \ v6)) = K(x,L(y,z,u * v6))
    ]]></literal>
    <justification jstring="[hyper(19307,a,21817,a)].">
      <j1 rule="hyper" parents="19307 21817"/>
    </justification>
  </clause>

  <clause id="21820">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) * K(y,K(z,u)) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[para(18(a,2),21805(a,1,1))].">
      <j1 rule="para" parents="18 21805"/>
    </justification>
  </clause>

  <clause id="21821">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) = L(x,w,v5) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(144,a,21820,a(flip),b,8141,a),flip(a)].">
      <j1 rule="hyper" parents="144 21820 8141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21822">
    <literal><![CDATA[
      L(K(x,K(y,z)) * u,w,v5) = L(u,w,v5) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(17337(a,1),21820(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="17337 21820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21823">
    <literal><![CDATA[
      K(x,L(y * K(z,K(u,w)),v5,v6)) = K(x,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[para(21820(a,1),17920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="21820 17920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21824">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) \ w,v5,v6)) = K(x,L(y \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(8646(a,1),21823(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8646 21823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21825">
    <literal><![CDATA[
      K(x,y * L(z * K(u,K(w,v5)),v6,v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(z,v6,v7)) = v8
    ]]></literal>
    <justification jstring="[para(21821(a,2),18011(a,1,2,2))].">
      <j1 rule="para" parents="21821 18011"/>
    </justification>
  </clause>

  <clause id="21826">
    <literal><![CDATA[
      K(x,y * L(K(z,K(u,w)) * v5,v6,v7)) = K(x,y * L(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(21822(a,2),17933(a,1,2,2))].">
      <j1 rule="para" parents="21822 17933"/>
    </justification>
  </clause>

  <clause id="21827">
    <literal><![CDATA[
      K(x,L(T(y,T(z,u)) \ w,v5,v6)) = K(x,L(T(y,z) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(7840(a,1),21824(a,1,2,1,1))].">
      <j1 rule="para" parents="7840 21824"/>
    </justification>
  </clause>

  <clause id="21828">
    <literal><![CDATA[
      K(x,y * L((z / K(u,w)) \ v5,v6,v7)) = K(x,y * L((K(u,w) \ z) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(6283(a,1),21826(a,1,2,2,1))].">
      <j1 rule="para" parents="6283 21826"/>
    </justification>
  </clause>

  <clause id="21829">
    <literal><![CDATA[
      K(x,y * L((K(z,u) \ w) \ v5,v6,v7)) = K(x,y * L((w * K(u,z)) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(6878(a,1),21828(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6878 21828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21830">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(21818(a,1),21815(a,1,2))].">
      <j1 rule="para" parents="21818 21815"/>
    </justification>
  </clause>

  <clause id="21831">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(11254(a,1),21830(a,1,2))].">
      <j1 rule="para" parents="11254 21830"/>
    </justification>
  </clause>

  <clause id="21833">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (1 / u)) * (K(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(373,a,20429,a(flip),b,21831,a),flip(a)].">
      <j1 rule="hyper" parents="373 20429 21831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21834">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,K(x,y) \ x))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(15956(a,1),21814(a,1,2,2))].">
      <j1 rule="para" parents="15956 21814"/>
    </justification>
  </clause>

  <clause id="21835">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,x * K(y,x)))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(5965(a,1),21834(a,1,2,2,2,3))].">
      <j1 rule="para" parents="5965 21834"/>
    </justification>
  </clause>

  <clause id="21836">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,x))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(13030(a,1),21835(a,1,2,2,2))].">
      <j1 rule="para" parents="13030 21835"/>
    </justification>
  </clause>

  <clause id="21837">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y,x))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(15522(a,1),21836(a,1,2,2))].">
      <j1 rule="para" parents="15522 21836"/>
    </justification>
  </clause>

  <clause id="21839">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * K(z,u))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(12077(a,1),21837(a,1,2))].">
      <j1 rule="para" parents="12077 21837"/>
    </justification>
  </clause>

  <clause id="21840">
    <literal><![CDATA[
      L(x * K(y,z),u,u \ 1) = L(x,u,u \ 1) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(7693,a,21839,a)].">
      <j1 rule="hyper" parents="7693 21839"/>
    </justification>
  </clause>

  <clause id="21841">
    <literal><![CDATA[
      (x * K(y,z)) / L(x * K(y,z),u,u \ 1) = L(a(u \ 1,u,x),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(21840(a,2),16668(a,1,2))].">
      <j1 rule="para" parents="21840 16668"/>
    </justification>
  </clause>

  <clause id="21842">
    <literal><![CDATA[
      L((x \ T(y,z)) * K(z,y),u,u \ 1) / L(x \ T(y,z),u,u \ 1) = (x \ y) / (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(21840(a,2),19816(a,1,1))].">
      <j1 rule="para" parents="21840 19816"/>
    </justification>
  </clause>

  <clause id="21843">
    <literal><![CDATA[
      L(x * K(y,z),u,u \ 1) \ (x * K(y,z)) = L(a(u \ 1,u,x),x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5560,a,21841,a)].">
      <j1 rule="hyper" parents="5560 21841"/>
    </justification>
  </clause>

  <clause id="21844">
    <literal><![CDATA[
      L(a(x \ 1,x,y),y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x \ 1,x,y * K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(21843(a,1),2676(a,1))].">
      <j1 rule="para" parents="21843 2676"/>
    </justification>
  </clause>

  <clause id="21845">
    <literal><![CDATA[
      a(x \ 1,x,y * K(z,u)) = a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(21844,a,20846,a)].">
      <j1 rule="hyper" parents="21844 20846"/>
    </justification>
  </clause>

  <clause id="21846">
    <literal><![CDATA[
      a(x \ 1,x,K(y,z) * u) = a(x \ 1,x,u)
    ]]></literal>
    <justification jstring="[para(6576(a,1),21845(a,1,3))].">
      <j1 rule="para" parents="6576 21845"/>
    </justification>
  </clause>

  <clause id="21847">
    <literal><![CDATA[
      a(x \ 1,x,y) \ (K(z,u) * y) = L(K(z,u) * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(21846(a,1),5588(a,1,1))].">
      <j1 rule="para" parents="21846 5588"/>
    </justification>
  </clause>

  <clause id="21848">
    <literal><![CDATA[
      K(x,y) * (a(z \ 1,z,u) \ u) = L(K(x,y) * u,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,21284,a(flip),b,21847,a)].">
      <j1 rule="hyper" parents="64 21284 21847"/>
    </justification>
  </clause>

  <clause id="21849">
    <literal><![CDATA[
      L(K(x,y) * z,u,u \ 1) = K(x,y) * L(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5588(a,1),21848(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5588 21848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21850">
    <literal><![CDATA[
      L(x \ y,z,z \ 1) / L(x \ T(y,u),z,z \ 1) = (x \ y) / (x \ T(y,u))
    ]]></literal>
    <justification jstring="[para(15017(a,1),21842(a,1,1,1))].">
      <j1 rule="para" parents="15017 21842"/>
    </justification>
  </clause>

  <clause id="21851">
    <literal><![CDATA[
      L(x \ y,z,z \ 1) / L(x \ T(y,u),z,z \ 1) = K(u,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,15073,a(flip),b,21850,a),flip(a)].">
      <j1 rule="hyper" parents="373 15073 21850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21853">
    <literal><![CDATA[
      K(x,K(y,L(z \ 1,u,w)) * ((L(z,u,w) \ v5) * z)) = K(x,z * ((K(y,L(z,u,w) \ 1) * v5) / L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(19885,a,21769,a)].">
      <j1 rule="hyper" parents="19885 21769"/>
    </justification>
  </clause>

  <clause id="21854">
    <literal><![CDATA[
      K(x,L((y / (z \ 1)) / z,u,w) * T(z,y * z)) = K(x,z * L(z \ (y / (z \ K(y,z))),u,w))
    ]]></literal>
    <justification jstring="[para(8612(a,1),21781(a,1,2,2))].">
      <j1 rule="para" parents="8612 21781"/>
    </justification>
  </clause>

  <clause id="21856">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,L(z,u,w) / (T(y,z * y) \ 1))
    ]]></literal>
    <justification jstring="[para(11708(a,1),21854(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11708 21854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21857">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,L(z,u,w) * T(y,z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,14463,a(flip),b,21856,a),flip(a)].">
      <j1 rule="hyper" parents="373 14463 21856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21858">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,L(z,u,w) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,13433,a(flip),b,21857,a),flip(a)].">
      <j1 rule="hyper" parents="373 13433 21857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21859">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,19822,a(flip),b,21858,a),flip(a)].">
      <j1 rule="hyper" parents="373 19822 21858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21860">
    <literal><![CDATA[
      K(x,y * L((z / (y \ 1)) / y,u,w)) = K(x,y * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(10283(a,1),21859(a,1,2,2,1))].">
      <j1 rule="para" parents="10283 21859"/>
    </justification>
  </clause>

  <clause id="21861">
    <literal><![CDATA[
      K(x,y * (L(z,z \ (a(u,w,K(v5,v6)) * v7),a(v6,w,K(v5,u))) \ v7)) = K(x,y * (z \ (v7 / a(v6,w,K(v5,u)))))
    ]]></literal>
    <justification jstring="[para(16653(a,1),21782(a,1,2,2,1))].">
      <j1 rule="para" parents="16653 21782"/>
    </justification>
  </clause>

  <clause id="21862">
    <literal><![CDATA[
      (K(x,K(y,z)) \ ((u * w) * v5)) / ((K(x,K(y,z)) \ w) * v5) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[para(17330(a,2),21783(a,1,2,1))].">
      <j1 rule="para" parents="17330 21783"/>
    </justification>
  </clause>

  <clause id="21863">
    <literal><![CDATA[
      L(K(x,((y / T(z,1)) / u) \ x),z \ y,z) \ T(x,(u * z) / y) = R(x,u / (y / ((z \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(21466(a,1),21784(a,1,1,1))].">
      <j1 rule="para" parents="21466 21784"/>
    </justification>
  </clause>

  <clause id="21864">
    <literal><![CDATA[
      L(K(x,((y / z) / u) \ x),z \ y,z) \ T(x,(u * z) / y) = R(x,u / (y / ((z \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(372(a,1),21863(a,1,1,1,2,1,1,2))].">
      <j1 rule="para" parents="372 21863"/>
    </justification>
  </clause>

  <clause id="21865">
    <literal><![CDATA[
      K(x,((x * y) * z) / u) \ T(x,(y * z) / u) = R(x,y / (u / ((z \ 1) \ 1)),x)
    ]]></literal>
    <justification jstring="[para(15684(a,1),21864(a,1,1))].">
      <j1 rule="para" parents="15684 21864"/>
    </justification>
  </clause>

  <clause id="21866">
    <literal><![CDATA[
      K(x,((x * y) * z) / u) \ T(x,(y * z) / u) = R(x,(u / ((z \ 1) \ 1)) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13180,a(flip),b,21865,a),flip(a)].">
      <j1 rule="hyper" parents="373 13180 21865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21867">
    <literal><![CDATA[
      K(x,((x * y) * z) / u) \ T(x,(y * z) / u) = R(x,(u / z) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,14274,a(flip),b,21866,a),flip(a)].">
      <j1 rule="hyper" parents="373 14274 21866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21868">
    <literal><![CDATA[
      K(x,(y / (z * u)) \ x) \ T(x,(z * u) / y) = R(x,(y / u) \ z,x)
    ]]></literal>
    <justification jstring="[para(14038(a,1),21867(a,1,1))].">
      <j1 rule="para" parents="14038 21867"/>
    </justification>
  </clause>

  <clause id="21869">
    <literal><![CDATA[
      R(x,(y / z) \ u,x) = R(x,y \ (u * z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13184,a(flip),b,21868,a),flip(a)].">
      <j1 rule="hyper" parents="64 13184 21868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21870">
    <literal><![CDATA[
      R(x,(y * z) \ (u * y),x) = R(x,T(z,y) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13761,a(flip),b,21869,a),flip(a)].">
      <j1 rule="hyper" parents="64 13761 21869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21871">
    <literal><![CDATA[
      R(x,y \ (z \ (u * z)),x) = R(x,T(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13715,a(flip),b,21870,a)].">
      <j1 rule="hyper" parents="64 13715 21870"/>
    </justification>
  </clause>

  <clause id="21872">
    <literal><![CDATA[
      R(x,T(y,z) \ u,x) = R(x,y \ T(u,z),x)
    ]]></literal>
    <justification jstring="[para(22(a,2),21871(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="22 21871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21873">
    <literal><![CDATA[
      x \ R(x,y \ T(z,u),x) = a(x,T(y,u) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,21872,a(flip),b,10889,a)].">
      <j1 rule="hyper" parents="139 21872 10889"/>
    </justification>
  </clause>

  <clause id="21874">
    <literal><![CDATA[
      a(x,T(y,z) \ u,x) = a(x,y \ T(u,z),x)
    ]]></literal>
    <justification jstring="[hyper(10908,a,21873,a),flip(a)].">
      <j1 rule="hyper" parents="10908 21873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21876">
    <literal><![CDATA[
      a(x,y \ (z \ (y * u)),x) = a(x,z \ T(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13759,a,b,21874,a)].">
      <j1 rule="hyper" parents="64 13759 21874"/>
    </justification>
  </clause>

  <clause id="21877">
    <literal><![CDATA[
      K(x,y * ((K(z,L(y,u,w) \ 1) * v5) / L(y,u,w))) = K(x,K(z,y \ 1) * ((L(y,u,w) \ v5) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,19871,a(flip),b,21853,a),flip(a)].">
      <j1 rule="hyper" parents="64 19871 21853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21879">
    <literal><![CDATA[
      K(x,y * ((K(z,L(y,u,w) \ 1) * v5) / L(y,u,w))) = K(x,K(z,y) * ((L(y,u,w) \ v5) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,16827,a(flip),b,21877,a),flip(a)].">
      <j1 rule="hyper" parents="373 16827 21877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21880">
    <literal><![CDATA[
      K(x,y * ((K(z,L(y,u,w) \ 1) * v5) / L(y,u,w))) = K(x,(L(y,u,w) \ v5) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17399,a(flip),b,21879,a),flip(a)].">
      <j1 rule="hyper" parents="373 17399 21879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21881">
    <literal><![CDATA[
      K(x,y * ((K(z,L(y \ 1,u,w)) * v5) / L(y,u,w))) = K(x,(L(y,u,w) \ v5) * T(y,z))
    ]]></literal>
    <justification jstring="[para(12074(a,2),21880(a,1,2,2,1,1))].">
      <j1 rule="para" parents="12074 21880"/>
    </justification>
  </clause>

  <clause id="21882">
    <literal><![CDATA[
      K(x,y * (L(z,a(u,w,K(v5,v6)) * v7,a(v6,w,K(v5,u))) \ v7)) = K(x,y * (z \ (v7 / a(v6,w,K(v5,u)))))
    ]]></literal>
    <justification jstring="[para(16666(a,1),21861(a,1,2,2,1))].">
      <j1 rule="para" parents="16666 21861"/>
    </justification>
  </clause>

  <clause id="21883">
    <literal><![CDATA[
      K(x,y * (L(z,u,a(w,v5,K(v6,v7))) \ u)) = K(x,y * (z \ (u / a(w,v5,K(v6,v7)))))
    ]]></literal>
    <justification jstring="[para(21060(a,1),21882(a,1,2,2,1))].">
      <j1 rule="para" parents="21060 21882"/>
    </justification>
  </clause>

  <clause id="21884">
    <literal><![CDATA[
      K(x,y * (L(z,u,a(w,v5,K(v6,v7))) \ u)) = K(x,y * (z \ (a(v7,v5,K(v6,w)) * u)))
    ]]></literal>
    <justification jstring="[para(19333(a,1),21883(a,2,2,2,2))].">
      <j1 rule="para" parents="19333 21883"/>
    </justification>
  </clause>

  <clause id="21886">
    <literal><![CDATA[
      K(x,y * (z \ (a(u,w,K(v5,v6)) * v7))) = K(x,y * (z \ v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,19966,a(flip),b,21884,a),flip(a)].">
      <j1 rule="hyper" parents="64 19966 21884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21888">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) * K(v5,v6)))) = K(x,y * (z \ (u * (w * K(v5,v6)))))
    ]]></literal>
    <justification jstring="[para(15463(a,1),21886(a,1,2,2,2))].">
      <j1 rule="para" parents="15463 21886"/>
    </justification>
  </clause>

  <clause id="21889">
    <literal><![CDATA[
      (K(x,K(y,z)) \ ((u * w) * v5)) / (K(x,K(y,z)) \ (w * v5)) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[para(19173(a,2),21862(a,1,2))].">
      <j1 rule="para" parents="19173 21862"/>
    </justification>
  </clause>

  <clause id="21890">
    <literal><![CDATA[
      K(x,K(y,z)) \ (((u * w) * v5) / (K(x,K(y,z)) \ (w * v5))) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(19419,a,21889,a)].">
      <j1 rule="hyper" parents="19419 21889"/>
    </justification>
  </clause>

  <clause id="21891">
    <literal><![CDATA[
      R(x,R(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5) = ((x * y) * v5) / (y * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,20359,a(flip),b,21890,a),flip(a)].">
      <j1 rule="hyper" parents="64 20359 21890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21893">
    <literal><![CDATA[
      R(x,R(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,20,a,b,21891,a),flip(a)].">
      <j1 rule="hyper" parents="373 20 21891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21894">
    <literal><![CDATA[
      R(x,y,K(z,K(u,w)) * v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[para(20329(a,1),21893(a,1,2))].">
      <j1 rule="para" parents="20329 21893"/>
    </justification>
  </clause>

  <clause id="21895">
    <literal><![CDATA[
      R(x,y,z \ T(u,K(w,v5))) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(6578(a,1),21894(a,1,3))].">
      <j1 rule="para" parents="6578 21894"/>
    </justification>
  </clause>

  <clause id="21897">
    <literal><![CDATA[
      R(x,y,z \ K(u,T(w,v5))) = R(x,y,z \ K(u,w))
    ]]></literal>
    <justification jstring="[para(17333(a,1),21894(a,1,3))].">
      <j1 rule="para" parents="17333 21894"/>
    </justification>
  </clause>

  <clause id="21898">
    <literal><![CDATA[
      R(x,y,z \ (u \ K(w,K(v5,v6)))) = R(x,y,z \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(19417(a,1),21894(a,1,3))].">
      <j1 rule="para" parents="19417 21894"/>
    </justification>
  </clause>

  <clause id="21899">
    <literal><![CDATA[
      R(x,y,z \ ((u \ T(K(w,v5),v6)) \ T(K(w,v5),u))) = R(x,y,z \ ((u \ T(K(w,v5),v6)) \ K(w,v5)))
    ]]></literal>
    <justification jstring="[para(15175(a,1),21895(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="15175 21895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21900">
    <literal><![CDATA[
      R(x,y,(z * u) \ (K(w,v5) \ (u * z))) = R(x,y,K(z,u) \ K(v5,w))
    ]]></literal>
    <justification jstring="[para(21051(a,1),21897(a,1,3))].">
      <j1 rule="para" parents="21051 21897"/>
    </justification>
  </clause>

  <clause id="21901">
    <literal><![CDATA[
      R(x,y,K(x,y) \ K(z,u)) \ (K(u,z) \ (y * x)) = y * ((x * y) \ (K(u,z) \ (y * x)))
    ]]></literal>
    <justification jstring="[para(21900(a,1),420(a,1,1))].">
      <j1 rule="para" parents="21900 420"/>
    </justification>
  </clause>

  <clause id="21902">
    <literal><![CDATA[
      R(x,y,K(z,u)) \ (K(u,z) \ (y * x)) = y * ((x * y) \ (K(u,z) \ (y * x)))
    ]]></literal>
    <justification jstring="[para(14098(a,1),21901(a,1,1))].">
      <j1 rule="para" parents="14098 21901"/>
    </justification>
  </clause>

  <clause id="21903">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ (K(u,z) \ (y * x)) = y * ((x * y) \ (K(u,z) \ (y * x)))
    ]]></literal>
    <justification jstring="[para(16598(a,1),21902(a,1,1))].">
      <j1 rule="para" parents="16598 21902"/>
    </justification>
  </clause>

  <clause id="21904">
    <literal><![CDATA[
      (x * y) \ (K(z,u) \ (y * x)) = y \ T(K(z,u) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(19493,a,21903,a),flip(a)].">
      <j1 rule="hyper" parents="19493 21903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21905">
    <literal><![CDATA[
      x * ((y * x) \ (K(z,u) \ (x * y))) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(z,u) \ x,y) = w
    ]]></literal>
    <justification jstring="[para(21904(a,2),290(a,1,2))].">
      <j1 rule="para" parents="21904 290"/>
    </justification>
  </clause>

  <clause id="21906">
    <literal><![CDATA[
      K(x,y) \ (y * K(z,T(u,y \ x))) = T(K(u,z) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(21905,a,21054,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="21905 21054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21907">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x \ y)) = T(K(u,z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(6213,a,21906,a)].">
      <j1 rule="hyper" parents="6213 21906"/>
    </justification>
  </clause>

  <clause id="21908">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,y \ x)) = T(K(u,z) \ x,y)
    ]]></literal>
    <justification jstring="[para(11158(a,1),21907(a,1,2))].">
      <j1 rule="para" parents="11158 21907"/>
    </justification>
  </clause>

  <clause id="21909">
    <literal><![CDATA[
      T(K(x,T(y,z \ u)) \ u,z) = T(u,z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8205(a,1),21908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8205 21908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21910">
    <literal><![CDATA[
      T(K(x,T(y,(((z / u) \ 1) * z) \ z)) \ (u * (z / u)),((u \ z) \ 1) * z) = T(u * (z / u),((u \ z) \ 1) * z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(13148(a,1),21909(a,1,1,1,2,2))].">
      <j1 rule="para" parents="13148 21909"/>
    </justification>
  </clause>

  <clause id="21911">
    <literal><![CDATA[
      R(x,y,z \ ((u \ T(K(w,v5),v6)) \ T(K(w,v5),u))) = R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6))))
    ]]></literal>
    <justification jstring="[para(17745(a,1),21899(a,2,3,2))].">
      <j1 rule="para" parents="17745 21899"/>
    </justification>
  </clause>

  <clause id="21912">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,T(v5,v6))) \ T(K(w,v5),u))) = R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6))))
    ]]></literal>
    <justification jstring="[para(7867(a,2),21911(a,1,3,2,1,2))].">
      <j1 rule="para" parents="7867 21911"/>
    </justification>
  </clause>

  <clause id="21913">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,T(v5,v6))) \ K(w,T(v5,u)))) = R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6))))
    ]]></literal>
    <justification jstring="[para(7867(a,2),21912(a,1,3,2,2))].">
      <j1 rule="para" parents="7867 21912"/>
    </justification>
  </clause>

  <clause id="21914">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(T(v5,v6),u)))) = R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6))))
    ]]></literal>
    <justification jstring="[para(18644(a,1),21913(a,1,3,2))].">
      <j1 rule="para" parents="18644 21913"/>
    </justification>
  </clause>

  <clause id="21915">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6)))) = R(x,y,z \ ((u \ 1) \ K(w,K(v5,v6))))
    ]]></literal>
    <justification jstring="[para(18677(a,1),21914(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="18677 21914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21916">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6)))) = R(x,y,z \ ((u \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,21898,a(flip),b,21915,a),flip(a)].">
      <j1 rule="hyper" parents="373 21898 21915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21918">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6)))) = R(x,y,z \ T(u,1))
    ]]></literal>
    <justification jstring="[hyper(373,a,13907,a(flip),b,21916,a),flip(a)].">
      <j1 rule="hyper" parents="373 13907 21916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21919">
    <literal><![CDATA[
      R(x,y,z \ ((u \ K(w,v5)) \ K(w,T(v5,v6)))) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(372(a,1),21918(a,2,3,2))].">
      <j1 rule="para" parents="372 21918"/>
    </justification>
  </clause>

  <clause id="21920">
    <literal><![CDATA[
      R(x,y,z \ T(T(u,K(w,v5)) \ v6,K(w,T(v5,u)))) = R(x,y,z \ (u \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,15176,a,b,21919,a)].">
      <j1 rule="hyper" parents="64 15176 21919"/>
    </justification>
  </clause>

  <clause id="21922">
    <literal><![CDATA[
      R(x,y,z \ (T(u,K(w,v5)) \ v6)) = R(x,y,z \ (u \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,21895,a(flip),b,21920,a)].">
      <j1 rule="hyper" parents="64 21895 21920"/>
    </justification>
  </clause>

  <clause id="21924">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) \ T(w,K(v5,v6)))) = R(x,y,z \ T(u,K(v6,v5) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,21767,a(flip),b,21922,a),flip(a)].">
      <j1 rule="hyper" parents="64 21767 21922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21926">
    <literal><![CDATA[
      R(x,y,z \ T(u * K(w,K(v5,v6)),w)) = R(x,y,z \ T(u,K(v6,v5) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16230,a,b,21924,a)].">
      <j1 rule="hyper" parents="64 16230 21924"/>
    </justification>
  </clause>

  <clause id="21927">
    <literal><![CDATA[
      R(x,y,K(z,K(u,w)) * (v5 \ T(v6,z))) = R(x,y,v5 \ T(v6,K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(19415(a,1),21926(a,1,3))].">
      <j1 rule="para" parents="19415 21926"/>
    </justification>
  </clause>

  <clause id="21928">
    <literal><![CDATA[
      R(x,y,z \ T(u,K(w,v5) * v6)) = R(x,y,z \ T(u,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,21894,a(flip),b,21927,a),flip(a)].">
      <j1 rule="hyper" parents="64 21894 21927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21930">
    <literal><![CDATA[
      K(x,R(y / z,z,y \ T(u,w)) \ T(u,w)) = K(x,z * (y \ T(u,K(v5,v6) * w)))
    ]]></literal>
    <justification jstring="[para(21928(a,1),20383(a,1,2,1))].">
      <j1 rule="para" parents="21928 20383"/>
    </justification>
  </clause>

  <clause id="21931">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5) * v6))) = K(x,y * (z \ T(u,v6)))
    ]]></literal>
    <justification jstring="[para(684(a,1),21930(a,1,2)),flip(a)].">
      <j1 rule="para" parents="684 21930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21933">
    <literal><![CDATA[
      x / K(y,L(z,(z / u) \ 1,((T(z,T(y,u)) / u) \ 1) \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(12059(a,1),21691(a,1,2))].">
      <j1 rule="para" parents="12059 21691"/>
    </justification>
  </clause>

  <clause id="21934">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,((T(z,T(y,u)) / u) \ 1) \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(14222(a,1),21933(a,1,2,2))].">
      <j1 rule="para" parents="14222 21933"/>
    </justification>
  </clause>

  <clause id="21935">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,x * (T(z,T(y,u)) / u))) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(19342(a,1),21934(a,1,2))].">
      <j1 rule="para" parents="19342 21934"/>
    </justification>
  </clause>

  <clause id="21936">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,x * (T(z,y) / u))) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(21811(a,1),21935(a,1,2,2))].">
      <j1 rule="para" parents="21811 21935"/>
    </justification>
  </clause>

  <clause id="21937">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,x * (u \ T(z,y)))) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(20544(a,1),21936(a,1,2))].">
      <j1 rule="para" parents="20544 21936"/>
    </justification>
  </clause>

  <clause id="21938">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,u \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(19699(a,1),21937(a,1,2))].">
      <j1 rule="para" parents="19699 21937"/>
    </justification>
  </clause>

  <clause id="21939">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(16444(a,1),21938(a,1,2))].">
      <j1 rule="para" parents="16444 21938"/>
    </justification>
  </clause>

  <clause id="21941">
    <literal><![CDATA[
      (x / (((y / z) \ 1) * K(u,y))) * ((y / z) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(21939(a,1),15148(a,1))].">
      <j1 rule="para" parents="21939 15148"/>
    </justification>
  </clause>

  <clause id="21942">
    <literal><![CDATA[
      (x / ((y / z) \ 1)) * ((y / z) \ K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(20423(a,1),21941(a,1))].">
      <j1 rule="para" parents="20423 21941"/>
    </justification>
  </clause>

  <clause id="21943">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * (w * v5))) \ ((u * (K(x,K(y,z)) * w)) * v5) = a(u,K(x,K(y,z)) * w,L(v5,w,K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(19410(a,2),19203(a,1,1))].">
      <j1 rule="para" parents="19410 19203"/>
    </justification>
  </clause>

  <clause id="21944">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * (K(u,K(w,v5)) * ((v6 * z) / v6)))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[para(19387(a,1),20341(a,1,2,2,2))].">
      <j1 rule="para" parents="19387 20341"/>
    </justification>
  </clause>

  <clause id="21945">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * (w * v5))) \ ((K(x,K(y,z)) \ (u * w)) * v5) = a(u,K(x,K(y,z)) * w,L(v5,w,K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(19410(a,2),21943(a,1,2,1))].">
      <j1 rule="para" parents="19410 21943"/>
    </justification>
  </clause>

  <clause id="21946">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * ((v6 * z) / v6))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[hyper(19413,a,21944,a)].">
      <j1 rule="hyper" parents="19413 21944"/>
    </justification>
  </clause>

  <clause id="21947">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v6))) = K(x,y * ((v6 * (z * K(u,K(w,v5)))) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15947,a(flip),b,21946,a)].">
      <j1 rule="hyper" parents="64 15947 21946"/>
    </justification>
  </clause>

  <clause id="21948">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * (w * v5))) \ (K(x,K(y,z)) \ ((u * w) * v5)) = a(u,K(x,K(y,z)) * w,L(v5,w,K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(19173(a,2),21945(a,1,2))].">
      <j1 rule="para" parents="19173 21945"/>
    </justification>
  </clause>

  <clause id="21949">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) * w,L(v5,w,K(y,K(z,u)))) = (x * (w * v5)) \ ((x * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,19384,a(flip),b,21948,a),flip(a)].">
      <j1 rule="hyper" parents="64 19384 21948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21951">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) * w,L(v5,w,K(y,K(z,u)))) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,14,a,b,21949,a),flip(a)].">
      <j1 rule="hyper" parents="373 14 21949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21952">
    <literal><![CDATA[
      a(x,K(K(y,z),u) \ w,L(v5,w,K(u,K(y,z)))) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(6156(a,2),21951(a,1,2))].">
      <j1 rule="para" parents="6156 21951"/>
    </justification>
  </clause>

  <clause id="21953">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) \ w,L(v5,w,K(u,K(y,z)))) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(8092(a,1),21952(a,1,2,1))].">
      <j1 rule="para" parents="8092 21952"/>
    </justification>
  </clause>

  <clause id="21954">
    <literal><![CDATA[
      a(x,K(y,K(z,u)) \ w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(19184(a,1),21953(a,1,3))].">
      <j1 rule="para" parents="19184 21953"/>
    </justification>
  </clause>

  <clause id="21955">
    <literal><![CDATA[
      a(x,T(y,K(z,u)) \ w,v5) = a(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(6066(a,1),21954(a,1,2))].">
      <j1 rule="para" parents="6066 21954"/>
    </justification>
  </clause>

  <clause id="21956">
    <literal><![CDATA[
      a(x,y * K(z,K(u,w)),v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(17330(a,1),21954(a,1,2))].">
      <j1 rule="para" parents="17330 21954"/>
    </justification>
  </clause>

  <clause id="21957">
    <literal><![CDATA[
      a(x,y \ T(z,K(u,w)),v5) = a(x,y \ z,v5)
    ]]></literal>
    <justification jstring="[para(17404(a,1),21954(a,1,2))].">
      <j1 rule="para" parents="17404 21954"/>
    </justification>
  </clause>

  <clause id="21958">
    <literal><![CDATA[
      a(x,K(y,T(z,u)) \ w,v5) = a(x,K(y,z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(20344(a,1),21954(a,1,2))].">
      <j1 rule="para" parents="20344 21954"/>
    </justification>
  </clause>

  <clause id="21959">
    <literal><![CDATA[
      a(x,y \ (K(z,K(u,w)) \ v5),v6) = a(x,y \ v5,v6)
    ]]></literal>
    <justification jstring="[para(20351(a,1),21954(a,1,2))].">
      <j1 rule="para" parents="20351 21954"/>
    </justification>
  </clause>

  <clause id="21960">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w)) * v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(20472,a,21956,a)].">
      <j1 rule="hyper" parents="20472 21956"/>
    </justification>
  </clause>

  <clause id="21961">
    <literal><![CDATA[
      a(x,y \ (z * T(u,K(w,v5))),v6) = a(x,y \ (z * u),v6)
    ]]></literal>
    <justification jstring="[para(19379(a,1),21956(a,1,2))].">
      <j1 rule="para" parents="19379 21956"/>
    </justification>
  </clause>

  <clause id="21962">
    <literal><![CDATA[
      a(x,y,T(z,T(u,w))) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(8028(a,1),21960(a,1,3))].">
      <j1 rule="para" parents="8028 21960"/>
    </justification>
  </clause>

  <clause id="21963">
    <literal><![CDATA[
      a(x,y,T(z,T(x * y,u))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,16106,a(flip),b,21962,a),flip(a)].">
      <j1 rule="hyper" parents="373 16106 21962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21964">
    <literal><![CDATA[
      a(x,y,T(z,y * x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(11103(a,1),21963(a,1,3))].">
      <j1 rule="para" parents="11103 21963"/>
    </justification>
  </clause>

  <clause id="21965">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(21964(a,1),21535(a,1,1))].">
      <j1 rule="para" parents="21964 21535"/>
    </justification>
  </clause>

  <clause id="21966">
    <literal><![CDATA[
      a(x,K(y,z) \ (u \ ((w / u) \ v5)),x) = a(x,w \ (u * ((K(z,y) \ u) \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,20449,a(flip),b,21955,a)].">
      <j1 rule="hyper" parents="64 20449 21955"/>
    </justification>
  </clause>

  <clause id="21967">
    <literal><![CDATA[
      a(x,K(y,z) \ (u \ w),x) = a(x,u \ (K(y,z) \ w),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13762,a(flip),b,21955,a)].">
      <j1 rule="hyper" parents="64 13762 21955"/>
    </justification>
  </clause>

  <clause id="21968">
    <literal><![CDATA[
      a(x,y \ T(z,T(u,w)),v5) = a(x,y \ T(z,u),v5)
    ]]></literal>
    <justification jstring="[para(7840(a,1),21957(a,1,2,2))].">
      <j1 rule="para" parents="7840 21957"/>
    </justification>
  </clause>

  <clause id="21969">
    <literal><![CDATA[
      a(x,K(y,z) \ u,w) = a(x,u * K(z,y),w)
    ]]></literal>
    <justification jstring="[para(8169(a,1),21957(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8169 21957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21970">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ w),v5) = a(x,y \ (w * K(u,z)),v5)
    ]]></literal>
    <justification jstring="[para(8352(a,1),21957(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8352 21957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21971">
    <literal><![CDATA[
      a(x,K(y,T(z,u)) \ (u * (w / u)),x) = a(x,K(y,z) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,20365,a,b,21969,a)].">
      <j1 rule="hyper" parents="373 20365 21969"/>
    </justification>
  </clause>

  <clause id="21972">
    <literal><![CDATA[
      a(x,y \ (T(z,K(u,w)) \ v5),v6) = a(x,y \ (z \ v5),v6)
    ]]></literal>
    <justification jstring="[para(6066(a,1),21959(a,1,2,2))].">
      <j1 rule="para" parents="6066 21959"/>
    </justification>
  </clause>

  <clause id="21973">
    <literal><![CDATA[
      a(x,T(y \ z,u) \ T(w,z \ y),x) = a(x,T(y \ z,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13746,a(flip),b,21968,a),flip(a)].">
      <j1 rule="hyper" parents="64 13746 21968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21974">
    <literal><![CDATA[
      a(x,y \ (z * (K(u,w) \ v5)),v6) = a(x,y \ (z * (v5 * K(w,u))),v6)
    ]]></literal>
    <justification jstring="[para(8352(a,1),21961(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8352 21961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21975">
    <literal><![CDATA[
      a(x,y \ (T(z,z \ u) \ w),v5) = a(x,y \ (((z \ u) \ u) \ w),v5)
    ]]></literal>
    <justification jstring="[para(4075(a,1),21972(a,1,2,2,1))].">
      <j1 rule="para" parents="4075 21972"/>
    </justification>
  </clause>

  <clause id="21976">
    <literal><![CDATA[
      a(x,K(y,z) \ (u * (w / u)),x) = a(x,K(y,z) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,21958,a(flip),b,21971,a)].">
      <j1 rule="hyper" parents="64 21958 21971"/>
    </justification>
  </clause>

  <clause id="21978">
    <literal><![CDATA[
      a(x,K(y,z) \ T(u,w),x) = a(x,K(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13850,a(flip),b,21976,a),flip(a)].">
      <j1 rule="hyper" parents="64 13850 21976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21979">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ T(y * T(w,v5),y)),x) = a(x,K(z,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13853,a,b,21978,a)].">
      <j1 rule="hyper" parents="64 13853 21978"/>
    </justification>
  </clause>

  <clause id="21980">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * T(z,y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(115(a,1),21965(a,1,2,2,2))].">
      <j1 rule="para" parents="115 21965"/>
    </justification>
  </clause>

  <clause id="21981">
    <literal><![CDATA[
      a(x,y,z) \ (z * (y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,21980,a)].">
      <j1 rule="hyper" parents="64 249 21980"/>
    </justification>
  </clause>

  <clause id="21982">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * (v5 * (w * u)))) = K(x,y \ T(z,L(v5,w,u) * (w * u)))
    ]]></literal>
    <justification jstring="[para(21981(a,1),21453(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="21981 21453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21984">
    <literal><![CDATA[
      a(x,y \ ((z * u) * K(w,v5)),x) = a(x,y \ (z * (K(v5,w) \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,21080,a,b,21974,a)].">
      <j1 rule="hyper" parents="373 21080 21974"/>
    </justification>
  </clause>

  <clause id="21985">
    <literal><![CDATA[
      a(x,y \ ((z * (1 / z)) \ (z \ u)),w) = a(x,y \ (((z \ 1) \ 1) \ u),w)
    ]]></literal>
    <justification jstring="[para(5179(a,2),21975(a,1,2,2))].">
      <j1 rule="para" parents="5179 21975"/>
    </justification>
  </clause>

  <clause id="21986">
    <literal><![CDATA[
      a(x,T(y,z) \ T(y * T(u,w),y),x) = a(x,K(y \ 1,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(20464,a,21979,a)].">
      <j1 rule="hyper" parents="20464 21979"/>
    </justification>
  </clause>

  <clause id="21987">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ (w * v5)),x) = a(x,y \ (w * (K(z,u) \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,21970,a,b,21984,a)].">
      <j1 rule="hyper" parents="64 21970 21984"/>
    </justification>
  </clause>

  <clause id="21988">
    <literal><![CDATA[
      a(x,K(y \ 1,z) \ u,x) = a(x,K(y,z) \ T(u,w),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13854,a(flip),b,21986,a),flip(a)].">
      <j1 rule="hyper" parents="64 13854 21986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21989">
    <literal><![CDATA[
      a(x,K(y \ 1,z) \ u,x) = a(x,K(y,z) \ u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,21978,a(flip),b,21988,a),flip(a)].">
      <j1 rule="hyper" parents="373 21978 21988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21990">
    <literal><![CDATA[
      a(x,T(T(y \ (y / z),u),z \ 1) * w,x) = a(x,K(z,u) \ ((y \ (y / z)) * w),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,14152,a(flip),b,21989,a)].">
      <j1 rule="hyper" parents="64 14152 21989"/>
    </justification>
  </clause>

  <clause id="21991">
    <literal><![CDATA[
      a(x,y \ (((z \ 1) \ 1) \ u),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13844,a(flip),b,21985,a),flip(a)].">
      <j1 rule="hyper" parents="64 13844 21985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21994">
    <literal><![CDATA[
      a(x,K(y,z) \ (u \ ((w / u) \ v5)),x) = a(x,w \ (K(y,z) \ v5),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,21081,a(flip),b,21966,a),flip(a)].">
      <j1 rule="hyper" parents="373 21081 21966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="21996">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ ((w / y) \ v5)),x) = a(x,w \ (K(z,u) \ v5),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,21967,a(flip),b,21994,a)].">
      <j1 rule="hyper" parents="64 21967 21994"/>
    </justification>
  </clause>

  <clause id="21997">
    <literal><![CDATA[
      a(x,x \ (K(y,z) \ ((x \ u) \ w)),x) = a(x,u \ (K(y,z) \ w),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,21532,a(flip),b,21996,a)].">
      <j1 rule="hyper" parents="64 21532 21996"/>
    </justification>
  </clause>

  <clause id="21998">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * (v5 * (w * u)))) = K(x,y \ T(z,(v5 * w) * u))
    ]]></literal>
    <justification jstring="[para(21180(a,1),21982(a,2,2,2))].">
      <j1 rule="para" parents="21180 21982"/>
    </justification>
  </clause>

  <clause id="21999">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * (v5 * (w * u)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,21461,a(flip),b,21998,a),flip(a)].">
      <j1 rule="hyper" parents="373 21461 21998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22000">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w \ v5))) = K(x,y \ T(z,u * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,21385,a(flip),b,21999,a),flip(a)].">
      <j1 rule="hyper" parents="64 21385 21999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22002">
    <literal><![CDATA[
      a(x,T(T(y \ (y / z),u),z \ 1) * w,x) = a(x,(y \ (y / T(z,u))) * w,x)
    ]]></literal>
    <justification jstring="[para(12211(a,1),21990(a,2,2))].">
      <j1 rule="para" parents="12211 21990"/>
    </justification>
  </clause>

  <clause id="22003">
    <literal><![CDATA[
      a(x,T(y \ (y / z),u) * w,x) = a(x,(y \ (y / T(z,u))) * w,x)
    ]]></literal>
    <justification jstring="[para(6753(a,1),22002(a,1,2,1))].">
      <j1 rule="para" parents="6753 22002"/>
    </justification>
  </clause>

  <clause id="22004">
    <literal><![CDATA[
      a(x,(y \ (y / T(z \ u,w))) * T(y,u \ z),x) = a(x,K(w,u \ (z * 1)) \ (y / (z \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,21667,a(flip),b,22003,a),flip(a)].">
      <j1 rule="hyper" parents="64 21667 22003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22005">
    <literal><![CDATA[
      a(x,y \ ((y / T(z \ u,w)) * T(y,u \ z)),x) = a(x,K(w,u \ (z * 1)) \ (y / (z \ u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13859,a,b,22004,a)].">
      <j1 rule="hyper" parents="64 13859 22004"/>
    </justification>
  </clause>

  <clause id="22006">
    <literal><![CDATA[
      a(x,K(y \ z,u) \ (u / T(z \ y,w)),x) = a(x,K(w,y \ (z * 1)) \ (u / (z \ y)),x)
    ]]></literal>
    <justification jstring="[hyper(13571,a,22005,a)].">
      <j1 rule="hyper" parents="13571 22005"/>
    </justification>
  </clause>

  <clause id="22007">
    <literal><![CDATA[
      a(x,K(y,z \ (u * 1)) \ (w / (u \ z)),x) = a(x,T(w,z \ u) / T(u \ z,y),x)
    ]]></literal>
    <justification jstring="[para(14841(a,1),22006(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14841 22006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22008">
    <literal><![CDATA[
      a(x,K(y,z \ (u * 1)) \ (w / (u \ z)),x) = a(x,T(u \ z,y) \ T(w,z \ u),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13169,a(flip),b,22007,a),flip(a)].">
      <j1 rule="hyper" parents="373 13169 22007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22009">
    <literal><![CDATA[
      a(x,K(y,z \ (u * 1)) \ (w / (u \ z)),x) = a(x,T(u \ z,y) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,21973,a(flip),b,22008,a),flip(a)].">
      <j1 rule="hyper" parents="373 21973 22008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22010">
    <literal><![CDATA[
      a(x,K(y,z \ u) \ (w / (u \ z)),x) = a(x,T(u \ z,y) \ w,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),22009(a,1,2,1,2,2))].">
      <j1 rule="para" parents="8 22009"/>
    </justification>
  </clause>

  <clause id="22011">
    <literal><![CDATA[
      a(x,(y \ z) \ (K(u,z \ y) \ w),x) = a(x,T(y \ z,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13750,a,b,22010,a)].">
      <j1 rule="hyper" parents="64 13750 22010"/>
    </justification>
  </clause>

  <clause id="22012">
    <literal><![CDATA[
      a(x,y \ (z * (K(u,y \ z) \ w)),x) = a(x,T(z \ y,u) \ w,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13703,a(flip),b,22011,a)].">
      <j1 rule="hyper" parents="64 13703 22011"/>
    </justification>
  </clause>

  <clause id="22013">
    <literal><![CDATA[
      a(x,y \ (z * (K(u,y \ z) \ w)),x) = a(x,(z \ y) \ T(w,u),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,21874,a(flip),b,22012,a),flip(a)].">
      <j1 rule="hyper" parents="373 21874 22012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22014">
    <literal><![CDATA[
      a(x,y \ (z * (K(u,y \ z) \ w)),x) = a(x,y \ (z * T(w,u)),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13703,a(flip),b,22013,a),flip(a)].">
      <j1 rule="hyper" parents="373 13703 22013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22015">
    <literal><![CDATA[
      a(x,y \ (K(z,y \ u) \ (u * w)),x) = a(x,y \ (u * T(w,z)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,21987,a,b,22014,a)].">
      <j1 rule="hyper" parents="64 21987 22014"/>
    </justification>
  </clause>

  <clause id="22016">
    <literal><![CDATA[
      L(K(x,K(y,x \ z) \ (z * u)),w,v5) \ L(K(x,x \ (K(y,x \ z) \ (z * u))),w,v5) = a(x,x \ (z * T(u,y)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13632,a,b,22015,a)].">
      <j1 rule="hyper" parents="64 13632 22015"/>
    </justification>
  </clause>

  <clause id="22017">
    <literal><![CDATA[
      K(x,L(T(1 / y,y * T(z,u)) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(17210(a,1),19959(a,1,2,1,1))].">
      <j1 rule="para" parents="17210 19959"/>
    </justification>
  </clause>

  <clause id="22018">
    <literal><![CDATA[
      K(x,L(T(1 / y,T(z * y,u)) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(11657(a,2),22017(a,1,2,1,1))].">
      <j1 rule="para" parents="11657 22017"/>
    </justification>
  </clause>

  <clause id="22019">
    <literal><![CDATA[
      K(x,L(T(1 / y,T(z * y,u)) \ w,w,(y \ K(z,u)) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(21813(a,1),22018(a,1,2))].">
      <j1 rule="para" parents="21813 22018"/>
    </justification>
  </clause>

  <clause id="22020">
    <literal><![CDATA[
      K(x,L(T(1 / y,T(z * y,u)) \ w,w,y * z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,21818,a(flip),b,22019,a)].">
      <j1 rule="hyper" parents="64 21818 22019"/>
    </justification>
  </clause>

  <clause id="22022">
    <literal><![CDATA[
      K(x,L(T(1 / y,z * y) \ u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,21827,a(flip),b,22020,a)].">
      <j1 rule="hyper" parents="64 21827 22020"/>
    </justification>
  </clause>

  <clause id="22023">
    <literal><![CDATA[
      K(x,L(T(y,z * y) * u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(16875,a,22022,a)].">
      <j1 rule="hyper" parents="16875 22022"/>
    </justification>
  </clause>

  <clause id="22025">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[para(4683(a,1),22023(a,1,2,1,1))].">
      <j1 rule="para" parents="4683 22023"/>
    </justification>
  </clause>

  <clause id="22026">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(13609,a,22025,a)].">
      <j1 rule="hyper" parents="13609 22025"/>
    </justification>
  </clause>

  <clause id="22027">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,K(z,w) * (z \ (((K(z,w) / y) \ z) * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,20657,a(flip),b,22026,a),flip(a)].">
      <j1 rule="hyper" parents="373 20657 22026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22028">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,T(z,w) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15774,a(flip),b,22027,a),flip(a)].">
      <j1 rule="hyper" parents="373 15774 22027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22029">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((K(z,w) / y) \ T(z,w)) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,21740,a(flip),b,22028,a),flip(a)].">
      <j1 rule="hyper" parents="373 21740 22028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22030">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((1 / y) \ z) * u))
    ]]></literal>
    <justification jstring="[para(14839(a,1),22029(a,2,2,2,1))].">
      <j1 rule="para" parents="14839 22029"/>
    </justification>
  </clause>

  <clause id="22031">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,16388,a(flip),b,22030,a),flip(a)].">
      <j1 rule="hyper" parents="373 16388 22030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22032">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,20512,a(flip),b,22031,a)].">
      <j1 rule="hyper" parents="64 20512 22031"/>
    </justification>
  </clause>

  <clause id="22033">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ (T(y * z,z) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,13502,a(flip),b,22032,a)].">
      <j1 rule="hyper" parents="64 13502 22032"/>
    </justification>
  </clause>

  <clause id="22034">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,20088,a(flip),b,22033,a)].">
      <j1 rule="hyper" parents="64 20088 22033"/>
    </justification>
  </clause>

  <clause id="22035">
    <literal><![CDATA[
      K(x,y * (z \ T((u * K(w,v5)) * v6,K(w,v5) * v6))) = K(x,y * (z \ (L(K(w,v5) * v6,K(v5,w),u) * u)))
    ]]></literal>
    <justification jstring="[para(20650(a,1),20418(a,1,2,2,2))].">
      <j1 rule="para" parents="20650 20418"/>
    </justification>
  </clause>

  <clause id="22036">
    <literal><![CDATA[
      K(x,y * (z \ T((u * K(w,v5)) * v6,v6))) = K(x,y * (z \ (L(K(w,v5) * v6,K(v5,w),u) * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,21931,a(flip),b,22035,a)].">
      <j1 rule="hyper" parents="64 21931 22035"/>
    </justification>
  </clause>

  <clause id="22039">
    <literal><![CDATA[
      K(x,y * (z \ (L(K(u,w) * v5,K(w,u),v6) * v6))) = K(x,y * (z \ (v5 * (v6 * K(u,w)))))
    ]]></literal>
    <justification jstring="[hyper(64,a,16696,a(flip),b,22036,a),flip(a)].">
      <j1 rule="hyper" parents="64 16696 22036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22040">
    <literal><![CDATA[
      K(K(x,y),z) \ ((u * (T(z,K(x,y)) * K(y,x))) / T(z,K(x,y))) = T((u * z) / (K(x,y) * z),K(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(10227(a,1),20887(a,2,1))].">
      <j1 rule="para" parents="10227 20887"/>
    </justification>
  </clause>

  <clause id="22041">
    <literal><![CDATA[
      K(K(x,y),z) \ ((u * (T(z,K(x,y)) * K(y,x))) / T(z,K(x,y))) = (u * z) / (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,17157,a(flip),b,22040,a),flip(a)].">
      <j1 rule="hyper" parents="373 17157 22040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22043">
    <literal><![CDATA[
      K(x,K(y,z)) \ ((u * (T(x,K(y,z)) * K(z,y))) / T(x,K(y,z))) = (u * x) / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(8123(a,1),22041(a,1,1))].">
      <j1 rule="para" parents="8123 22041"/>
    </justification>
  </clause>

  <clause id="22044">
    <literal><![CDATA[
      K(x,K(y,z)) \ ((u * (K(z,y) * x)) / T(x,K(y,z))) = (u * x) / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(7818(a,1),22043(a,1,2,1,2))].">
      <j1 rule="para" parents="7818 22043"/>
    </justification>
  </clause>

  <clause id="22045">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / u = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(17481,a,22044,a)].">
      <j1 rule="hyper" parents="17481 22044"/>
    </justification>
  </clause>

  <clause id="22046">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x * (T(y,u) / z)) / (y / z)
    ]]></literal>
    <justification jstring="[para(14825(a,1),22045(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14825 22045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22047">
    <literal><![CDATA[
      (K(x,L(y,z * (K(u,w) * v5),v5)) * (z * (K(u,w) * v5))) / v5 = K(x,y) * ((z * v5) / (K(w,u) * v5))
    ]]></literal>
    <justification jstring="[para(22045(a,1),15673(a,2,2))].">
      <j1 rule="para" parents="22045 15673"/>
    </justification>
  </clause>

  <clause id="22048">
    <literal><![CDATA[
      (K(x,L(y,z * u,z)) * (u * (K(w,v5) * z))) / z = K(x,y) * ((u * z) / (K(v5,w) * z))
    ]]></literal>
    <justification jstring="[para(20803(a,1),22047(a,1,1,1))].">
      <j1 rule="para" parents="20803 22047"/>
    </justification>
  </clause>

  <clause id="22049">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (z * (K(w,v5) * u))) / u = K(x,y) * ((z * u) / (K(v5,w) * u))
    ]]></literal>
    <justification jstring="[para(15518(a,1),22048(a,1,1,1))].">
      <j1 rule="para" parents="15518 22048"/>
    </justification>
  </clause>

  <clause id="22051">
    <literal><![CDATA[
      ((K(x,y) * z) * (K(u,w) * v5)) / v5 = K(x,y) * ((z * v5) / (K(w,u) * v5))
    ]]></literal>
    <justification jstring="[para(20542(a,1),22049(a,1,1))].">
      <j1 rule="para" parents="20542 22049"/>
    </justification>
  </clause>

  <clause id="22052">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (K(w,v5) * u) = K(x,y) * ((z * u) / (K(w,v5) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22045,a(flip),b,22051,a)].">
      <j1 rule="hyper" parents="64 22045 22051"/>
    </justification>
  </clause>

  <clause id="22053">
    <literal><![CDATA[
      K(x,y) * (((z * K(u,w)) * v5) / (K(u,w) * v5)) = L(K(x,y) * z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,19770,a(flip),b,22052,a),flip(a)].">
      <j1 rule="hyper" parents="64 19770 22052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22054">
    <literal><![CDATA[
      L(K(x,y) * z,K(u,w),v5) = K(x,y) * R(z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(20(a,2),22053(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20 22053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22055">
    <literal><![CDATA[
      L(K(x,y) * z,K(u,w),v5) = K(x,y) * L(z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(18806(a,1),22054(a,2,2))].">
      <j1 rule="para" parents="18806 22054"/>
    </justification>
  </clause>

  <clause id="22056">
    <literal><![CDATA[
      L(K(x,y) * (K(y,x) * z),K(x,y),u) = ((z * u) / (K(x,y) * u)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,18815,a(flip),b,22055,a),flip(a)].">
      <j1 rule="hyper" parents="373 18815 22055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22057">
    <literal><![CDATA[
      ((x * y) / (K(z,u) * y)) * K(z,u) = L(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(6161(a,1),22056(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6161 22056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22058">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(14842(a,1),22057(a,1,1,2))].">
      <j1 rule="para" parents="14842 22057"/>
    </justification>
  </clause>

  <clause id="22059">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,20981,a(flip),b,22058,a),flip(a)].">
      <j1 rule="hyper" parents="373 20981 22058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22060">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),u \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,20413,a(flip),b,22059,a),flip(a)].">
      <j1 rule="hyper" parents="373 20413 22059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22061">
    <literal><![CDATA[
      a(x,K(y,z) * u,K((z / y) \ u,w)) * K(x,((K(y,z) * u) * w) / (y \ z)) = K(x,(K(y,z) * u) / ((y \ z) / w))
    ]]></literal>
    <justification jstring="[para(20832(a,1),19684(a,1,1,3))].">
      <j1 rule="para" parents="20832 19684"/>
    </justification>
  </clause>

  <clause id="22062">
    <literal><![CDATA[
      a(x,K(y,z) * u,K((y \ z) \ u,w)) * K(x,((K(y,z) * u) * w) / (y \ z)) = K(x,(K(y,z) * u) / ((y \ z) / w))
    ]]></literal>
    <justification jstring="[para(20553(a,1),22061(a,1,1))].">
      <j1 rule="para" parents="20553 22061"/>
    </justification>
  </clause>

  <clause id="22063">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,((K(u,w) * y) * x) / (u \ w)) = K(z,(K(u,w) * y) / ((u \ w) / x))
    ]]></literal>
    <justification jstring="[para(20793(a,1),22062(a,1,1))].">
      <j1 rule="para" parents="20793 22062"/>
    </justification>
  </clause>

  <clause id="22064">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) * ((u \ w) \ K(u,w))) = K(z,(K(u,w) * y) / ((u \ w) / x))
    ]]></literal>
    <justification jstring="[para(20123(a,1),22063(a,1,2))].">
      <j1 rule="para" parents="20123 22063"/>
    </justification>
  </clause>

  <clause id="22066">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (T(u,w) \ w)) = K(z,(K(u,w) * y) / ((u \ w) / x))
    ]]></literal>
    <justification jstring="[para(14640(a,1),22064(a,1,2))].">
      <j1 rule="para" parents="14640 22064"/>
    </justification>
  </clause>

  <clause id="22067">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (w / u)) = K(z,(K(u,w) * y) / ((u \ w) / x))
    ]]></literal>
    <justification jstring="[para(20852(a,1),22066(a,1,2))].">
      <j1 rule="para" parents="20852 22066"/>
    </justification>
  </clause>

  <clause id="22068">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (w / u)) = K(z,y * (((u \ w) / x) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,19424,a(flip),b,22067,a),flip(a)].">
      <j1 rule="hyper" parents="373 19424 22067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22069">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (w / u)) = K(z,y / ((T(u,w) \ w) / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,21595,a(flip),b,22068,a),flip(a)].">
      <j1 rule="hyper" parents="373 21595 22068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22070">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (w / u)) = K(z,y / ((w / u) / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,21214,a(flip),b,22069,a),flip(a)].">
      <j1 rule="hyper" parents="373 21214 22069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22071">
    <literal><![CDATA[
      T(K(x,L(T(y,y * z),z,u \ 1)),K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))) = K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(4683(a,1),21633(a,1,1,2,1))].">
      <j1 rule="para" parents="4683 21633"/>
    </justification>
  </clause>

  <clause id="22072">
    <literal><![CDATA[
      T(K(x,L(T(y,z),z,u \ 1)),K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))) = K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(9554(a,1),22071(a,1,1))].">
      <j1 rule="para" parents="9554 22071"/>
    </justification>
  </clause>

  <clause id="22073">
    <literal><![CDATA[
      K(x,(y \ (z \ (u * z))) \ (y \ (u * z))) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(17154,a,22072,a),flip(a)].">
      <j1 rule="hyper" parents="17154 22072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22075">
    <literal><![CDATA[
      K(x,(y \ T(z,u)) \ (y \ (z * u))) = K(x,L(T(u,z),z,y \ 1))
    ]]></literal>
    <justification jstring="[para(22(a,2),22073(a,1,2,1,2))].">
      <j1 rule="para" parents="22 22073"/>
    </justification>
  </clause>

  <clause id="22076">
    <literal><![CDATA[
      T(K(x,T(y,T(1 \ (z / u),z))) \ (u * (z / u)),((u \ z) \ 1) * z) = T(u * (z / u),((u \ z) \ 1) * z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(9230(a,1),21910(a,1,1,1,2))].">
      <j1 rule="para" parents="9230 21910"/>
    </justification>
  </clause>

  <clause id="22077">
    <literal><![CDATA[
      T(K(x,T(y,T(z / u,z))) \ (u * (z / u)),((u \ z) \ 1) * z) = T(u * (z / u),((u \ z) \ 1) * z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(66(a,1),22076(a,1,1,1,2,2,1))].">
      <j1 rule="para" parents="66 22076"/>
    </justification>
  </clause>

  <clause id="22078">
    <literal><![CDATA[
      T(K(x,T(y,z \ u)) \ (z * (u / z)),((z \ u) \ 1) * u) = T(z * (u / z),((z \ u) \ 1) * u) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7429(a,1),22077(a,1,1,1,2))].">
      <j1 rule="para" parents="7429 22077"/>
    </justification>
  </clause>

  <clause id="22079">
    <literal><![CDATA[
      T(x * ((y * K(z,u)) / x),((x \ y) \ 1) * y) = T(x * (y / x),((x \ y) \ 1) * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(21172(a,1),22078(a,1,1))].">
      <j1 rule="para" parents="21172 22078"/>
    </justification>
  </clause>

  <clause id="22080">
    <literal><![CDATA[
      T(x * ((y * K(z,u)) / x),y * ((y / x) \ 1)) = T(x * (y / x),((x \ y) \ 1) * y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11104,a(flip),b,22079,a)].">
      <j1 rule="hyper" parents="64 11104 22079"/>
    </justification>
  </clause>

  <clause id="22081">
    <literal><![CDATA[
      T(x * (y / x),((x \ y) \ 1) * y) * K(z,u) = x * (T(y * K(z,u),y * ((y / x) \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5431,a(flip),b,22080,a),flip(a)].">
      <j1 rule="hyper" parents="64 5431 22080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22082">
    <literal><![CDATA[
      T(x * (y / x),((x \ y) \ 1) * y) * K(z,u) = x * (T(y * K(z,u),(y / x) \ y) / x)
    ]]></literal>
    <justification jstring="[para(17608(a,1),22081(a,2,2,1))].">
      <j1 rule="para" parents="17608 22081"/>
    </justification>
  </clause>

  <clause id="22083">
    <literal><![CDATA[
      T(x * (y / x),((x \ y) \ 1) * y) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(82(a,1),22082(a,2,2,1,2))].">
      <j1 rule="para" parents="82 22082"/>
    </justification>
  </clause>

  <clause id="22084">
    <literal><![CDATA[
      T(x * (y / x),y * ((y / x) \ 1)) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(11104(a,1),22083(a,1,1))].">
      <j1 rule="para" parents="11104 22083"/>
    </justification>
  </clause>

  <clause id="22085">
    <literal><![CDATA[
      (x * (T(y,y * ((y / x) \ 1)) / x)) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(5431(a,1),22084(a,1,1))].">
      <j1 rule="para" parents="5431 22084"/>
    </justification>
  </clause>

  <clause id="22086">
    <literal><![CDATA[
      (x * (T(y,(y / x) \ y) / x)) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(2781(a,1),22085(a,1,1,2,1))].">
      <j1 rule="para" parents="2781 22085"/>
    </justification>
  </clause>

  <clause id="22087">
    <literal><![CDATA[
      (x * (T(y,x) / x)) * K(z,u) = x * (T(y * K(z,u),x) / x)
    ]]></literal>
    <justification jstring="[para(82(a,1),22086(a,1,1,2,1,2))].">
      <j1 rule="para" parents="82 22086"/>
    </justification>
  </clause>

  <clause id="22088">
    <literal><![CDATA[
      (x * (T((y * z) * K(z,u),x) / x)) / (y * T(z,u)) = a(x,x \ (y * z),x)
    ]]></literal>
    <justification jstring="[para(22087(a,1),16752(a,1,1))].">
      <j1 rule="para" parents="22087 16752"/>
    </justification>
  </clause>

  <clause id="22089">
    <literal><![CDATA[
      (x * (T(y * T(z,u),x) / x)) / (y * T(z,u)) = a(x,x \ (y * z),x)
    ]]></literal>
    <justification jstring="[para(6852(a,1),22088(a,1,1,2,1,1))].">
      <j1 rule="para" parents="6852 22088"/>
    </justification>
  </clause>

  <clause id="22090">
    <literal><![CDATA[
      (x * T(y,z)) \ (u * (T(x * T(y,z),u) / u)) = a(u,u \ (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17777,a(flip),b,22089,a)].">
      <j1 rule="hyper" parents="64 17777 22089"/>
    </justification>
  </clause>

  <clause id="22091">
    <literal><![CDATA[
      a(x,x \ (y * T(z,u)),x) = a(x,x \ (y * z),x)
    ]]></literal>
    <justification jstring="[hyper(11380,a,22090,a)].">
      <j1 rule="hyper" parents="11380 22090"/>
    </justification>
  </clause>

  <clause id="22092">
    <literal><![CDATA[
      a(x,x \ (y * T(z,u)),x) = a(x,x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,21527,a,b,22091,a),flip(a)].">
      <j1 rule="hyper" parents="373 21527 22091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22093">
    <literal><![CDATA[
      a(x,x \ (1 \ (y * z)),x) = a(x,x \ (z * T(y,u)),x)
    ]]></literal>
    <justification jstring="[para(66(a,2),22092(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="66 22092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22094">
    <literal><![CDATA[
      a(x,x \ ((y \ 1) \ z),x) = a(x,x \ (z * T(y,u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13642,a,b,22093,a)].">
      <j1 rule="hyper" parents="64 13642 22093"/>
    </justification>
  </clause>

  <clause id="22095">
    <literal><![CDATA[
      a(x,x \ ((y \ 1) \ z),x) = a(x,x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,22091,a(flip),b,22094,a),flip(a)].">
      <j1 rule="hyper" parents="373 22091 22094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22096">
    <literal><![CDATA[
      a(x,x \ (y * (z \ 1)),x) = a(x,x \ (z \ y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,21991,a(flip),b,22095,a),flip(a)].">
      <j1 rule="hyper" parents="64 21991 22095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22097">
    <literal><![CDATA[
      a(x,x \ ((y \ 1) * z),x) = a(x,x \ (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,21527,a,b,22096,a)].">
      <j1 rule="hyper" parents="64 21527 22096"/>
    </justification>
  </clause>

  <clause id="22098">
    <literal><![CDATA[
      a(x,x \ (((T(y,z) \ 1) \ 1) * ((y \ 1) * u)),x) = a(x,x \ (K(z,y) \ u),x)
    ]]></literal>
    <justification jstring="[para(12411(a,1),22097(a,2,2,2))].">
      <j1 rule="para" parents="12411 22097"/>
    </justification>
  </clause>

  <clause id="22099">
    <literal><![CDATA[
      a(x,x \ (T(y,z) * ((1 / y) * u)),x) = a(x,x \ (K(z,y) \ u),x)
    ]]></literal>
    <justification jstring="[para(7710(a,1),22098(a,1,2,2))].">
      <j1 rule="para" parents="7710 22098"/>
    </justification>
  </clause>

  <clause id="22100">
    <literal><![CDATA[
      T(x,((y * T(z,u)) * K(z,w)) * R(v5,y * T(z,u),K(z,w))) = T(x,(T(v5,y * T(T(z,u),w)) * (y * T(z,u))) * K(z,w))
    ]]></literal>
    <justification jstring="[para(5756(a,2),19634(a,1,2,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5756 19634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22101">
    <literal><![CDATA[
      T(x,((y * T(z,u)) * K(z,w)) * R(v5,y * T(z,u),K(z,w))) = T(x,T(v5,y * T(T(z,u),w)) * ((y * T(z,u)) * K(z,w)))
    ]]></literal>
    <justification jstring="[hyper(19502,a,22100,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19502 22100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22102">
    <literal><![CDATA[
      T(x,((y * T(z,u)) * K(z,w)) * R(v5,y * T(z,u),K(z,w))) = T(x,T(v5,y * T(T(z,u),w)) * (y * (K(z,u) * T(z,w))))
    ]]></literal>
    <justification jstring="[para(11931(a,1),22101(a,2,2,2))].">
      <j1 rule="para" parents="11931 22101"/>
    </justification>
  </clause>

  <clause id="22103">
    <literal><![CDATA[
      T(x,((y * T(z,u)) * K(z,w)) * R(v5,y * T(z,u),K(z,w))) = T(x,T(v5,y * T(T(z,u),w)) * (y * T(T(z,u),w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,20228,a(flip),b,22102,a),flip(a)].">
      <j1 rule="hyper" parents="373 20228 22102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22104">
    <literal><![CDATA[
      T(x,((y * T(z,u)) * K(z,w)) * R(v5,y * T(z,u),K(z,w))) = T(x,(y * T(T(z,u),w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,11143,a(flip),b,22103,a),flip(a)].">
      <j1 rule="hyper" parents="373 11143 22103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22105">
    <literal><![CDATA[
      T(x,(y * (K(z,u) * T(z,w))) * R(v5,y * T(z,u),K(z,w))) = T(x,(y * T(T(z,u),w)) * v5)
    ]]></literal>
    <justification jstring="[para(11931(a,1),22104(a,1,2,1))].">
      <j1 rule="para" parents="11931 22104"/>
    </justification>
  </clause>

  <clause id="22106">
    <literal><![CDATA[
      T(x,(y * (K(z,u) * T(z,w))) * L(v5,y * T(z,u),K(z,w))) = T(x,(y * T(T(z,u),w)) * v5)
    ]]></literal>
    <justification jstring="[para(16598(a,1),22105(a,1,2,2))].">
      <j1 rule="para" parents="16598 22105"/>
    </justification>
  </clause>

  <clause id="22107">
    <literal><![CDATA[
      T(x,(y * (K(z,u) * T(z,w))) * v5) = T(x,(y * T(T(z,u),w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,19504,a(flip),b,22106,a)].">
      <j1 rule="hyper" parents="64 19504 22106"/>
    </justification>
  </clause>

  <clause id="22109">
    <literal><![CDATA[
      K(x,(L(T(y,K(z,u)),w,v5) \ v6) * T((v6 \ L(y,w,v5)) * v6,K(z,u))) = K(x,((v6 * (L(T(y,K(z,u)),w,v5) / v6)) \ v6) * L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(5454(a,2),18197(a,1,2,2))].">
      <j1 rule="para" parents="5454 18197"/>
    </justification>
  </clause>

  <clause id="22110">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)),w,v5) / (v6 * (T(y,K(z,u)) \ L(y,w,v5)))) = K(x,(y * (v6 \ L(T(y,K(z,u)),w,v5))) / L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(18099,a,21755,a),flip(a)].">
      <j1 rule="hyper" parents="18099 21755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22111">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)),w,v5) / (v6 * (T(y,K(z,u)) \ L(y,w,v5)))) = K(x,y * ((v6 \ L(T(y,K(z,u)),w,v5)) / L(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,19612,a(flip),b,22110,a),flip(a)].">
      <j1 rule="hyper" parents="373 19612 22110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22112">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)),w,v5) / (v6 * (y \ L(T(y,K(z,u)),w,v5)))) = K(x,y * ((v6 \ L(T(y,K(z,u)),w,v5)) / L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(19716(a,1),22111(a,1,2,2,2))].">
      <j1 rule="para" parents="19716 22111"/>
    </justification>
  </clause>

  <clause id="22113">
    <literal><![CDATA[
      K(x,y * ((z \ L(T(y,K(u,w)),v5,v6)) / L(y,v5,v6))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(21671,a,22112,a),flip(a)].">
      <j1 rule="hyper" parents="21671 22112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22114">
    <literal><![CDATA[
      K(x,y * ((z \ L(y,u,w)) / L(y,u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2004(a,1),22113(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="2004 22113"/>
    </justification>
  </clause>

  <clause id="22115">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ (L(y,z,u) / w))) = K(x,y / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,18529,a(flip),b,22114,a)].">
      <j1 rule="hyper" parents="64 18529 22114"/>
    </justification>
  </clause>

  <clause id="22116">
    <literal><![CDATA[
      K(x,((y * (L(T(z,K(u,w)),v5,v6) / y)) \ y) * L(z,v5,v6)) = K(x,(L(T(z,K(u,w)),v5,v6) \ y) * ((y \ L(z,v5,v6)) * y))
    ]]></literal>
    <justification jstring="[hyper(18006,a,22109,a),flip(a)].">
      <j1 rule="hyper" parents="18006 22109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22118">
    <literal><![CDATA[
      K(x,((y * (L(T(z,K(u,w)),v5,v6) / y)) \ y) * L(z,v5,v6)) = K(x,(L(T(z,K(u,w)),v5,v6) \ y) * T(L(z,v5,v6),y))
    ]]></literal>
    <justification jstring="[hyper(373,a,17668,a(flip),b,22116,a),flip(a)].">
      <j1 rule="hyper" parents="373 17668 22116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22119">
    <literal><![CDATA[
      K(x,((y * (L(T(z,K(u,w)),v5,v6) / y)) \ y) * L(z,v5,v6)) = K(x,(L(T(z,K(u,w)),v5,v6) \ y) * L(T(z,y),v5,v6))
    ]]></literal>
    <justification jstring="[para(25(a,2),22118(a,2,2,2))].">
      <j1 rule="para" parents="25 22118"/>
    </justification>
  </clause>

  <clause id="22120">
    <literal><![CDATA[
      K(x,((y * (L(T(z,K(u,w)),v5,v6) / y)) \ y) * L(z,v5,v6)) = K(x,(L(z,v5,v6) \ y) * L(T(z,y),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,19956,a(flip),b,22119,a),flip(a)].">
      <j1 rule="hyper" parents="373 19956 22119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22122">
    <literal><![CDATA[
      K(x,((y * (L(T(z,K(u,w)),v5,v6) / y)) \ y) * L(z,v5,v6)) = K(x,(z \ y) * T(z,y))
    ]]></literal>
    <justification jstring="[para(13648(a,1),22120(a,2,2))].">
      <j1 rule="para" parents="13648 22120"/>
    </justification>
  </clause>

  <clause id="22123">
    <literal><![CDATA[
      K(x,((y * (L(T(z,K(u,w)),v5,v6) / y)) \ y) * L(z,v5,v6)) = K(x,T(y * K(z,y),z))
    ]]></literal>
    <justification jstring="[hyper(373,a,11131,a,b,22122,a),flip(a)].">
      <j1 rule="hyper" parents="373 11131 22122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22125">
    <literal><![CDATA[
      K(x,((y * (L(T(z,K(u,w)),v5,v6) / y)) \ y) * L(z,v5,v6)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5785(a,1),22123(a,2,2))].">
      <j1 rule="para" parents="5785 22123"/>
    </justification>
  </clause>

  <clause id="22126">
    <literal><![CDATA[
      K(x,(L(y * (T(z,K(u,w)) / y),v5,v6) \ y) * L(z,v5,v6)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5618(a,2),22125(a,1,2,1,1))].">
      <j1 rule="para" parents="5618 22125"/>
    </justification>
  </clause>

  <clause id="22127">
    <literal><![CDATA[
      K(x,(L(y * (z / y),u,w) \ y) * L(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2004(a,1),22126(a,1,2,1,1,1,2,1))].">
      <j1 rule="para" parents="2004 22126"/>
    </justification>
  </clause>

  <clause id="22128">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ w) * L((w \ y) * w,z,u)) = K(x,w)
    ]]></literal>
    <justification jstring="[para(78(a,1),22127(a,1,2,1,1,1))].">
      <j1 rule="para" parents="78 22127"/>
    </justification>
  </clause>

  <clause id="22129">
    <literal><![CDATA[
      K(x,(y / (y / ((z \ u) * y))) \ (z \ (u * ((u \ z) * (y / (u \ z)))))) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[para(18968(a,1),16538(a,1,2,2,2,2))].">
      <j1 rule="para" parents="18968 16538"/>
    </justification>
  </clause>

  <clause id="22130">
    <literal><![CDATA[
      K(x,(y / (y / ((z \ u) * y))) \ L(y / (u \ z),u \ z,u)) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[para(101(a,1),22129(a,1,2,2))].">
      <j1 rule="para" parents="101 22129"/>
    </justification>
  </clause>

  <clause id="22131">
    <literal><![CDATA[
      K(x,T((y \ z) * u,u) \ L(u / (z \ y),z \ y,z)) = a(x,z,K((((y \ z) * u) \ u) * ((y \ z) * u),y))
    ]]></literal>
    <justification jstring="[hyper(15829,a,22130,a)].">
      <j1 rule="hyper" parents="15829 22130"/>
    </justification>
  </clause>

  <clause id="22132">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[hyper(15898,a,22131,a)].">
      <j1 rule="hyper" parents="15898 22131"/>
    </justification>
  </clause>

  <clause id="22133">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K((u \ z) * (y / (u \ z)),z))
    ]]></literal>
    <justification jstring="[para(18968(a,1),22132(a,2,3,1))].">
      <j1 rule="para" parents="18968 22132"/>
    </justification>
  </clause>

  <clause id="22134">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K(y,T(z,u \ z)))
    ]]></literal>
    <justification jstring="[para(11193(a,1),22133(a,2,3))].">
      <j1 rule="para" parents="11193 22133"/>
    </justification>
  </clause>

  <clause id="22135">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,19281,a(flip),b,22134,a),flip(a)].">
      <j1 rule="hyper" parents="373 19281 22134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22137">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y / (u \ z))) * K(x,L(y / (u \ z),u \ z,u) / (y * (z \ u))) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19163,a,b,22135,a)].">
      <j1 rule="hyper" parents="64 19163 22135"/>
    </justification>
  </clause>

  <clause id="22138">
    <literal><![CDATA[
      K(x,1) * K(x,L(y / (z \ u),z \ u,z) / (y * (u \ z))) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(19855(a,1),22137(a,1,1,2))].">
      <j1 rule="para" parents="19855 22137"/>
    </justification>
  </clause>

  <clause id="22139">
    <literal><![CDATA[
      K(x,L(y / (z \ u),z \ u,z) / (y * (u \ z))) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(380,a,22138,a)].">
      <j1 rule="hyper" parents="380 22138"/>
    </justification>
  </clause>

  <clause id="22141">
    <literal><![CDATA[
      K(x,L(y \ (L(T(z,K(u,w)),v5,v6) * v7),y,L(K(v7,T(z,K(u,w))),v5,v6))) = K(x,(K(L(T(z,K(u,w)),v5,v6),v7) \ y) \ (v7 * L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(12059(a,2),19700(a,1,2,3))].">
      <j1 rule="para" parents="12059 19700"/>
    </justification>
  </clause>

  <clause id="22142">
    <literal><![CDATA[
      K(x,L(y \ (L(T(z,K(u,w)),v5,v6) * v7),y,L(K(v7,z),v5,v6))) = K(x,(K(L(T(z,K(u,w)),v5,v6),v7) \ y) \ (v7 * L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(17134(a,1),22141(a,1,2,3,1))].">
      <j1 rule="para" parents="17134 22141"/>
    </justification>
  </clause>

  <clause id="22143">
    <literal><![CDATA[
      L(K(x,y \ (L(T(z,K(u,w)),v5,v6) * v7)),y,L(K(v7,z),v5,v6)) = K(x,(K(L(T(z,K(u,w)),v5,v6),v7) \ y) \ (v7 * L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(12060,a,22142,a)].">
      <j1 rule="hyper" parents="12060 22142"/>
    </justification>
  </clause>

  <clause id="22145">
    <literal><![CDATA[
      L(K(x,y \ (L(z,u,w) * v5)),y,L(K(v5,z),u,w)) = K(x,(K(L(T(z,K(v6,v7)),u,w),v5) \ y) \ (v5 * L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(19471(a,1),22143(a,1,1))].">
      <j1 rule="para" parents="19471 22143"/>
    </justification>
  </clause>

  <clause id="22146">
    <literal><![CDATA[
      K(x,(K(L(T(y,K(z,u)),w,v5),v6) \ v7) \ (v6 * L(y,w,v5))) = K(x,v7 \ (L(y,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(19313,a,22145,a),flip(a)].">
      <j1 rule="hyper" parents="19313 22145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22149">
    <literal><![CDATA[
      K(x,(L(K(T(y,K(z,u)),w),v5,v6) \ v7) \ (w * L(y,v5,v6))) = K(x,v7 \ (L(y,v5,v6) * w))
    ]]></literal>
    <justification jstring="[para(12090(a,2),22146(a,1,2,1,1))].">
      <j1 rule="para" parents="12090 22146"/>
    </justification>
  </clause>

  <clause id="22150">
    <literal><![CDATA[
      K(x,(L(K(y,z),u,w) \ v5) \ (z * L(y,u,w))) = K(x,v5 \ (L(y,u,w) * z))
    ]]></literal>
    <justification jstring="[para(2004(a,1),22149(a,1,2,1,1,1,1))].">
      <j1 rule="para" parents="2004 22149"/>
    </justification>
  </clause>

  <clause id="22151">
    <literal><![CDATA[
      K(x,K(y,z) \ (u \ (z * L(y,w,v5)))) = K(x,u \ (L(y,w,v5) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,21020,a(flip),b,22150,a)].">
      <j1 rule="hyper" parents="64 21020 22150"/>
    </justification>
  </clause>

  <clause id="22152">
    <literal><![CDATA[
      K(x,y \ (L(x,z,u) * w)) = K(x,y \ (w * L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(8783,a,22151,a),flip(a)].">
      <j1 rule="hyper" parents="8783 22151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22154">
    <literal><![CDATA[
      K(x,y \ (L(x,z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (w * L(x,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(22151(a,1),8783(a,1))].">
      <j1 rule="para" parents="22151 8783"/>
    </justification>
  </clause>

  <clause id="22155">
    <literal><![CDATA[
      L(K(x,(y \ z) \ L(x,u,w)),y \ z,y) = K(x,z \ (L(x,u,w) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,12081,a,b,22152,a)].">
      <j1 rule="hyper" parents="373 12081 22152"/>
    </justification>
  </clause>

  <clause id="22156">
    <literal><![CDATA[
      L(K(x,(y \ z) \ x),y \ z,y) = K(x,z \ (L(x,u,w) * y))
    ]]></literal>
    <justification jstring="[para(14737(a,1),22155(a,1,1))].">
      <j1 rule="para" parents="14737 22155"/>
    </justification>
  </clause>

  <clause id="22157">
    <literal><![CDATA[
      K(x,y \ (L(x,z,u) * w)) = K(x,y \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,12081,a(flip),b,22156,a),flip(a)].">
      <j1 rule="hyper" parents="64 12081 22156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22159">
    <literal><![CDATA[
      K(x,y \ (z * L(x,u,w))) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(22154,a,22157,a)].">
      <j1 rule="hyper" parents="22154 22157"/>
    </justification>
  </clause>

  <clause id="22161">
    <literal><![CDATA[
      K(x,y \ ((z * u) * x)) = K(x,y \ (z * (u * x)))
    ]]></literal>
    <justification jstring="[para(100(a,1),22159(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="100 22159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22162">
    <literal><![CDATA[
      K(x,y \ (z * ((z \ u) * x))) = K(x,y \ (u * x))
    ]]></literal>
    <justification jstring="[para(515(a,1),22159(a,1,2,2))].">
      <j1 rule="para" parents="515 22159"/>
    </justification>
  </clause>

  <clause id="22164">
    <literal><![CDATA[
      K(x,y \ ((z \ u) * (z * x))) = K(x,y \ (T(u,z) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,20071,a(flip),b,22161,a),flip(a)].">
      <j1 rule="hyper" parents="64 20071 22161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22165">
    <literal><![CDATA[
      K(x,y \ ((x * z) * u)) = K(x,y \ (z * (u * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15255,a(flip),b,22161,a)].">
      <j1 rule="hyper" parents="64 15255 22161"/>
    </justification>
  </clause>

  <clause id="22166">
    <literal><![CDATA[
      K(x,L(y \ (((z \ u) * x) * z),y,K(z,(z \ u) * x))) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[para(7122(a,2),22162(a,1,2))].">
      <j1 rule="para" parents="7122 22162"/>
    </justification>
  </clause>

  <clause id="22167">
    <literal><![CDATA[
      K(x,y \ ((z * x) * u)) = K(x,y \ (z * (u * x)))
    ]]></literal>
    <justification jstring="[hyper(10863,a,22165,a)].">
      <j1 rule="hyper" parents="10863 22165"/>
    </justification>
  </clause>

  <clause id="22168">
    <literal><![CDATA[
      K(x,L(y \ (((z \ u) * x) * z),y,K(z,z \ (u * x)))) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[para(14013(a,2),22166(a,1,2,3))].">
      <j1 rule="para" parents="14013 22166"/>
    </justification>
  </clause>

  <clause id="22169">
    <literal><![CDATA[
      K(x,L(y \ (((z \ u) * x) * z),y,K(z,u * x))) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[para(12982(a,1),22168(a,1,2))].">
      <j1 rule="para" parents="12982 22168"/>
    </justification>
  </clause>

  <clause id="22170">
    <literal><![CDATA[
      L(K(x,y \ (((z \ u) * x) * z)),y,K(z,u * x)) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(12060,a,22169,a)].">
      <j1 rule="hyper" parents="12060 22169"/>
    </justification>
  </clause>

  <clause id="22171">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * (z * x))),y,K(z,u * x)) = K(x,(K((z \ u) * x,z) \ y) \ (u * x))
    ]]></literal>
    <justification jstring="[para(22167(a,1),22170(a,1,1))].">
      <j1 rule="para" parents="22167 22170"/>
    </justification>
  </clause>

  <clause id="22172">
    <literal><![CDATA[
      L(K(x,y \ (T(z,u) * x)),y,K(u,z * x)) = K(x,(K((u \ z) * x,u) \ y) \ (z * x))
    ]]></literal>
    <justification jstring="[para(22164(a,1),22171(a,1,1))].">
      <j1 rule="para" parents="22164 22171"/>
    </justification>
  </clause>

  <clause id="22173">
    <literal><![CDATA[
      K(x,(K((y \ z) * x,y) \ u) \ (z * x)) = K(x,u \ (T(z,y) * x))
    ]]></literal>
    <justification jstring="[hyper(19305,a,22172,a),flip(a)].">
      <j1 rule="hyper" parents="19305 22172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22175">
    <literal><![CDATA[
      K(x,(K(y \ (z * x),y) \ u) \ (z * x)) = K(x,u \ (T(z,y) * x))
    ]]></literal>
    <justification jstring="[para(15154(a,2),22173(a,1,2,1,1))].">
      <j1 rule="para" parents="15154 22173"/>
    </justification>
  </clause>

  <clause id="22176">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ (u * x)) \ (u * x))) = K(x,y \ (T(u,z) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,19392,a(flip),b,22175,a)].">
      <j1 rule="hyper" parents="64 19392 22175"/>
    </justification>
  </clause>

  <clause id="22177">
    <literal><![CDATA[
      K(x,y \ ((z \ (u * x)) * z)) = K(x,y \ (T(u,z) * x))
    ]]></literal>
    <justification jstring="[para(5784(a,1),22176(a,1,2,2))].">
      <j1 rule="para" parents="5784 22176"/>
    </justification>
  </clause>

  <clause id="22178">
    <literal><![CDATA[
      K(x,y \ T(z * x,u)) = K(x,y \ (T(z,u) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,13462,a(flip),b,22177,a)].">
      <j1 rule="hyper" parents="64 13462 22177"/>
    </justification>
  </clause>

  <clause id="22179">
    <literal><![CDATA[
      K(x,((y * x) / z) \ (T(y,u) * x)) = K(x,K(u,y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(17518,a,22178,a),flip(a)].">
      <j1 rule="hyper" parents="17518 22178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22180">
    <literal><![CDATA[
      K(x,K(y,z * x) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,19991,a(flip),b,22179,a),flip(a)].">
      <j1 rule="hyper" parents="64 19991 22179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22182">
    <literal><![CDATA[
      K(x,y * K(x * z,u)) = K(x,K(u,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,18074,a(flip),b,22180,a)].">
      <j1 rule="hyper" parents="64 18074 22180"/>
    </justification>
  </clause>

  <clause id="22183">
    <literal><![CDATA[
      K(x,K(y,x * z) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(17263,a,22182,a)].">
      <j1 rule="hyper" parents="17263 22182"/>
    </justification>
  </clause>

  <clause id="22184">
    <literal><![CDATA[
      K(x,K(y,x * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(22183(a,2),17521(a,1))].">
      <j1 rule="para" parents="22183 17521"/>
    </justification>
  </clause>

  <clause id="22185">
    <literal><![CDATA[
      K(x,K(y,z) \ ((y / (x \ 1)) \ u)) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(22184,a,21477,a)].">
      <j1 rule="hyper" parents="22184 21477"/>
    </justification>
  </clause>

  <clause id="22186">
    <literal><![CDATA[
      K(x,(T(y,z) / (x \ 1)) \ u) = K(x,T(x * y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,21136,a(flip),b,22185,a)].">
      <j1 rule="hyper" parents="64 21136 22185"/>
    </justification>
  </clause>

  <clause id="22187">
    <literal><![CDATA[
      K(x,T(x * y,z) \ u) = K(x,T(y,z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10526,a(flip),b,22186,a),flip(a)].">
      <j1 rule="hyper" parents="64 10526 22186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22188">
    <literal><![CDATA[
      K(x,T(x \ y,z) \ (x \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),22187(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 22187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22189">
    <literal><![CDATA[
      K(x,T(y,z) \ (y * u)) = K(x,K(z,x \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,20883,a(flip),b,22188,a),flip(a)].">
      <j1 rule="hyper" parents="64 20883 22188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22190">
    <literal><![CDATA[
      K(x,K(y,x \ z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(6065(a,1),22189(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6065 22189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22191">
    <literal><![CDATA[
      K(x,y \ (K(z,x \ u) \ w)) = K(x,K(u,z) \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,20878,a(flip),b,22190,a)].">
      <j1 rule="hyper" parents="64 20878 22190"/>
    </justification>
  </clause>

  <clause id="22192">
    <literal><![CDATA[
      L(K(x,K(y,z) \ (y * u)),w,v5) \ L(K(x,x \ (K(z,x \ y) \ (y * u))),w,v5) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[para(22190(a,1),22016(a,1,1,1))].">
      <j1 rule="para" parents="22190 22016"/>
    </justification>
  </clause>

  <clause id="22193">
    <literal><![CDATA[
      L(K(x,T(y,z) * u),w,v5) \ L(K(x,x \ (K(z,x \ y) \ (y * u))),w,v5) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[para(15777(a,1),22192(a,1,1,1))].">
      <j1 rule="para" parents="15777 22192"/>
    </justification>
  </clause>

  <clause id="22194">
    <literal><![CDATA[
      L(K(x,T(y,z) * u),w,v5) \ L(K(x,K(y,z) \ (x \ (y * u))),w,v5) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[para(22191(a,1),22193(a,1,2,1))].">
      <j1 rule="para" parents="22191 22193"/>
    </justification>
  </clause>

  <clause id="22195">
    <literal><![CDATA[
      L(K(x,T(y,z) * u),w,v5) \ L(K(x,x \ (T(y,z) * u)),w,v5) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[para(19978(a,1),22194(a,1,2,1))].">
      <j1 rule="para" parents="19978 22194"/>
    </justification>
  </clause>

  <clause id="22196">
    <literal><![CDATA[
      a(x,x \ (T(y,z) * u),x) = a(x,x \ (y * T(u,z)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13632,a(flip),b,22195,a)].">
      <j1 rule="hyper" parents="64 13632 22195"/>
    </justification>
  </clause>

  <clause id="22197">
    <literal><![CDATA[
      a(x,x \ (y * T((1 / y) * z,u)),x) = a(x,x \ (K(u,y) \ z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,22099,a(flip),b,22196,a),flip(a)].">
      <j1 rule="hyper" parents="64 22099 22196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22198">
    <literal><![CDATA[
      a(x,x \ (K(y,z) \ u),x) = a(x,x \ (z * ((1 / z) * u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,22091,a(flip),b,22197,a),flip(a)].">
      <j1 rule="hyper" parents="64 22091 22197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22200">
    <literal><![CDATA[
      a(x,x \ L(y,z \ 1,z),x) = a(x,x \ (K(u,z) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13855,a(flip),b,22198,a)].">
      <j1 rule="hyper" parents="373 13855 22198"/>
    </justification>
  </clause>

  <clause id="22201">
    <literal><![CDATA[
      a(x,x \ (K(y,z) \ u),x) = a(x,x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13639,a(flip),b,22200,a),flip(a)].">
      <j1 rule="hyper" parents="64 13639 22200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22203">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ w),x) = a(x,x \ ((x \ y) \ w),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,21997,a(flip),b,22201,a)].">
      <j1 rule="hyper" parents="64 21997 22201"/>
    </justification>
  </clause>

  <clause id="22205">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ w),x) = a(x,x \ (y \ (x * w)),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13642,a(flip),b,22203,a),flip(a)].">
      <j1 rule="hyper" parents="373 13642 22203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22206">
    <literal><![CDATA[
      a(x,y \ T(z,x),x) = a(x,y \ (K(u,w) \ z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,21876,a(flip),b,22205,a)].">
      <j1 rule="hyper" parents="373 21876 22205"/>
    </justification>
  </clause>

  <clause id="22207">
    <literal><![CDATA[
      a(x,y \ (K(z,u) \ w),x) = a(x,y \ w,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10940,a(flip),b,22206,a),flip(a)].">
      <j1 rule="hyper" parents="64 10940 22206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22211">
    <literal><![CDATA[
      a(x,y \ (z / u),x) = a(x,y \ (u \ z),x)
    ]]></literal>
    <justification jstring="[para(5876(a,1),22207(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5876 22207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22212">
    <literal><![CDATA[
      a(x,y \ (T(z,u) \ w),x) = a(x,y \ (z \ w),x)
    ]]></literal>
    <justification jstring="[para(6066(a,1),22207(a,1,2,2))].">
      <j1 rule="para" parents="6066 22207"/>
    </justification>
  </clause>

  <clause id="22214">
    <literal><![CDATA[
      a(x,y \ (((z * u) * w) / (z * w)),x) = a(x,y \ R(u,z,w),x)
    ]]></literal>
    <justification jstring="[para(17000(a,1),22207(a,1,2,2))].">
      <j1 rule="para" parents="17000 22207"/>
    </justification>
  </clause>

  <clause id="22215">
    <literal><![CDATA[
      a(x,y \ (z \ u),x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13750,a,b,22211,a)].">
      <j1 rule="hyper" parents="64 13750 22211"/>
    </justification>
  </clause>

  <clause id="22216">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ w),x) = a(x,u \ (z \ (y \ w)),x)
    ]]></literal>
    <justification jstring="[hyper(13732,a,22215,a),flip(a)].">
      <j1 rule="hyper" parents="13732 22215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22218">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ w),x) = a(x,z \ (u \ (y \ w)),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,22215,a,b,22216,a),flip(a)].">
      <j1 rule="hyper" parents="373 22215 22216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22219">
    <literal><![CDATA[
      a(x,y \ (z \ (u \ (z * (y * w)))),x) = a(x,u \ L(w,y,z),x)
    ]]></literal>
    <justification jstring="[para(18(a,2),22216(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18 22216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22220">
    <literal><![CDATA[
      a(x,y \ ((z * T(u,w)) \ v5),x) = a(x,z \ (u \ (y \ v5)),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,22212,a(flip),b,22218,a),flip(a)].">
      <j1 rule="hyper" parents="373 22212 22218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22221">
    <literal><![CDATA[
      a(x,y \ ((z * u) \ ((z * w) * u)),x) = a(x,y \ R(w,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,22211,a(flip),b,22214,a)].">
      <j1 rule="hyper" parents="64 22211 22214"/>
    </justification>
  </clause>

  <clause id="22222">
    <literal><![CDATA[
      a(x,y \ R(z,u,T(w,T(u * z,v5))),x) = a(x,y \ ((u * T(w,u * z)) \ (w * (u * z))),x)
    ]]></literal>
    <justification jstring="[para(19848(a,1),22221(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19848 22221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22223">
    <literal><![CDATA[
      a(x,y \ R(z,u,T(w,T(u * z,v5))),x) = a(x,u \ (w \ (y \ (w * (u * z)))),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,22220,a(flip),b,22222,a),flip(a)].">
      <j1 rule="hyper" parents="373 22220 22222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22225">
    <literal><![CDATA[
      a(x,y \ R(z,u,T(w,T(u * z,v5))),x) = a(x,y \ L(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,22219,a(flip),b,22223,a),flip(a)].">
      <j1 rule="hyper" parents="373 22219 22223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22226">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(16041,a,22225,a),flip(a)].">
      <j1 rule="hyper" parents="16041 22225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22227">
    <literal><![CDATA[
      K(x,y \ L(y,z,u)) = 1 * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(22226(a,1),15422(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22226 15422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22228">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = a(y \ K(z,u),w,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(137,a,22227,a(flip),b,21802,a),flip(a)].">
      <j1 rule="hyper" parents="137 22227 21802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22230">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,20554,a(flip),b,22228,a),flip(a)].">
      <j1 rule="hyper" parents="373 20554 22228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22232">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) * K(u,z)) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[para(6878(a,1),22230(a,1,2))].">
      <j1 rule="para" parents="6878 22230"/>
    </justification>
  </clause>

  <clause id="22233">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (T(y,K(z,u)) * K(u,z))) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(19581,a,22232,a)].">
      <j1 rule="hyper" parents="19581 22232"/>
    </justification>
  </clause>

  <clause id="22234">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (K(u,z) * y)) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[para(7818(a,1),22233(a,1,2,2))].">
      <j1 rule="para" parents="7818 22233"/>
    </justification>
  </clause>

  <clause id="22235">
    <literal><![CDATA[
      T(K(x,K(y,y \ z) * (u * w)),w \ T(w * (u * K(y \ z,y)),x)) = (w \ T(w * (u * K(y \ z,y)),x)) \ ((u / (z / y)) * (y \ z))
    ]]></literal>
    <justification jstring="[para(19911(a,1),14671(a,1,1))].">
      <j1 rule="para" parents="19911 14671"/>
    </justification>
  </clause>

  <clause id="22236">
    <literal><![CDATA[
      T(K(x,K(y \ z,y) * (u * w)),w \ T(w * (u * K(y,y \ z)),x)) = (w \ T(w * (u * K(y,y \ z)),x)) \ ((u / y) * ((y \ z) \ z))
    ]]></literal>
    <justification jstring="[para(19911(a,1),14672(a,1,1))].">
      <j1 rule="para" parents="19911 14672"/>
    </justification>
  </clause>

  <clause id="22237">
    <literal><![CDATA[
      T((K(x,L(x \ K(y,z),u,w)) \ K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(12059(a,1),17454(a,1,1,1,1))].">
      <j1 rule="para" parents="12059 17454"/>
    </justification>
  </clause>

  <clause id="22238">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * (v6 * K(z * K(u,K(w,v5)),v7))) * z)) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z * K(u,K(w,v5)),v7)))
    ]]></literal>
    <justification jstring="[para(20327(a,1),18201(a,2,2,2,1))].">
      <j1 rule="para" parents="20327 18201"/>
    </justification>
  </clause>

  <clause id="22239">
    <literal><![CDATA[
      T((T(x,y) * K(z,u)) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1),w) = (x * K(z,u)) * L(K(x,y) * ((T(x,y) * K(z,u)) \ w),v5,v5 \ 1)
    ]]></literal>
    <justification jstring="[para(21849(a,2),21161(a,2,2))].">
      <j1 rule="para" parents="21849 21161"/>
    </justification>
  </clause>

  <clause id="22240">
    <literal><![CDATA[
      T(K(x,K(y,z) * (u * w)),w \ T(w * (u * K(y \ z,y)),x)) = (w \ T(w * (u * K(y \ z,y)),x)) \ ((u / (z / y)) * (y \ z))
    ]]></literal>
    <justification jstring="[para(13326(a,1),22235(a,1,1))].">
      <j1 rule="para" parents="13326 22235"/>
    </justification>
  </clause>

  <clause id="22241">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),w \ T(w * (u * K(y \ z,y)),x))) = (w \ T(w * (u * K(y \ z,y)),x)) \ ((u / (z / y)) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7964,a,22240,a)].">
      <j1 rule="hyper" parents="7964 22240"/>
    </justification>
  </clause>

  <clause id="22242">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),w \ (w * (u * K(y \ z,y))))) = (w \ T(w * (u * K(y \ z,y)),x)) \ ((u / (z / y)) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(18278,a,22241,a)].">
      <j1 rule="hyper" parents="18278 22241"/>
    </justification>
  </clause>

  <clause id="22244">
    <literal><![CDATA[
      (x \ T(x * (y * K(z \ u,z)),w)) \ ((y / (u / z)) * (z \ u)) = K(w,T(K(z,u) * (y * x),y * K(z \ u,z)))
    ]]></literal>
    <justification jstring="[para(9(a,1),22242(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 22242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22245">
    <literal><![CDATA[
      (x \ T(x * (y * K(z \ u,z)),w)) \ ((y / (u / z)) * (z \ u)) = K(w,T(K(z,u) * (y * x),y))
    ]]></literal>
    <justification jstring="[hyper(373,a,18238,a(flip),b,22244,a),flip(a)].">
      <j1 rule="hyper" parents="373 18238 22244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22248">
    <literal><![CDATA[
      T(K(x,K(y,z) * (u * w)),w \ T(w * (u * K(z,z \ y)),x)) = (w \ T(w * (u * K(z,z \ y)),x)) \ ((u / z) * ((z \ y) \ y))
    ]]></literal>
    <justification jstring="[para(13392(a,1),22236(a,1,1))].">
      <j1 rule="para" parents="13392 22236"/>
    </justification>
  </clause>

  <clause id="22249">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),w \ T(w * (u * K(z,z \ y)),x))) = (w \ T(w * (u * K(z,z \ y)),x)) \ ((u / z) * ((z \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(7964,a,22248,a)].">
      <j1 rule="hyper" parents="7964 22248"/>
    </justification>
  </clause>

  <clause id="22250">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),w \ (w * (u * K(z,z \ y))))) = (w \ T(w * (u * K(z,z \ y)),x)) \ ((u / z) * ((z \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(18278,a,22249,a)].">
      <j1 rule="hyper" parents="18278 22249"/>
    </justification>
  </clause>

  <clause id="22252">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ ((y / z) * ((z \ u) \ u)) = K(w,T(K(u,z) * (y * x),y * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(9(a,1),22250(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 22250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22253">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ ((y / z) * ((z \ u) \ u)) = K(w,T(K(u,z) * (y * x),y))
    ]]></literal>
    <justification jstring="[hyper(373,a,18238,a(flip),b,22252,a),flip(a)].">
      <j1 rule="hyper" parents="373 18238 22252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22256">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),u)) = K(x,w * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18664,a(flip),b,22253,a),flip(a)].">
      <j1 rule="hyper" parents="64 18664 22253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22257">
    <literal><![CDATA[
      (x \ T(x * (y * K(z \ u,z)),w)) \ ((y / (u / z)) * (z \ u)) = K(w,x * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,22245,a,b,22256,a)].">
      <j1 rule="hyper" parents="64 22245 22256"/>
    </justification>
  </clause>

  <clause id="22258">
    <literal><![CDATA[
      (x \ T(x * (y * K(z \ u,z)),w)) \ (y * K(z \ u,z)) = K(w,x * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[para(6966(a,1),22257(a,1,2))].">
      <j1 rule="para" parents="6966 22257"/>
    </justification>
  </clause>

  <clause id="22259">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,u))) = K(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[hyper(14651,a,22258,a)].">
      <j1 rule="hyper" parents="14651 22258"/>
    </justification>
  </clause>

  <clause id="22260">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ w) * u))) = K(x,y * (K(w,u) * (z \ w)))
    ]]></literal>
    <justification jstring="[para(15230(a,1),22259(a,1,2,2))].">
      <j1 rule="para" parents="15230 22259"/>
    </justification>
  </clause>

  <clause id="22261">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ w) * u))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,17967,a(flip),b,22260,a),flip(a)].">
      <j1 rule="hyper" parents="373 17967 22260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22262">
    <literal><![CDATA[
      K(x,T(y * (z \ u),((z \ u) * y) \ u)) = K(x,y * (z \ T(u,(z \ u) * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18168,a(flip),b,22261,a)].">
      <j1 rule="hyper" parents="64 18168 22261"/>
    </justification>
  </clause>

  <clause id="22263">
    <literal><![CDATA[
      K(x,T(y * (z \ u),((z \ u) * y) \ u)) = K(x,y * (z \ T(u,u * (z \ y))))
    ]]></literal>
    <justification jstring="[para(15649(a,1),22262(a,2,2,2,2))].">
      <j1 rule="para" parents="15649 22262"/>
    </justification>
  </clause>

  <clause id="22264">
    <literal><![CDATA[
      K(x,T(y * (z \ u),((z \ u) * y) \ u)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,13500,a(flip),b,22263,a),flip(a)].">
      <j1 rule="hyper" parents="373 13500 22263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22265">
    <literal><![CDATA[
      K(x,T(y * (z \ u),y \ ((z \ u) \ u))) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(19343,a,22264,a)].">
      <j1 rule="hyper" parents="19343 22264"/>
    </justification>
  </clause>

  <clause id="22266">
    <literal><![CDATA[
      K(x,T(y * (z \ u),y \ T(z,u))) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[para(13338(a,1),22265(a,1,2))].">
      <j1 rule="para" parents="13338 22265"/>
    </justification>
  </clause>

  <clause id="22267">
    <literal><![CDATA[
      K(x,T(y * (z \ u),y \ z)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(18278,a,22266,a)].">
      <j1 rule="hyper" parents="18278 22266"/>
    </justification>
  </clause>

  <clause id="22269">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z \ y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = w
    ]]></literal>
    <justification jstring="[para(22267(a,1),17524(a,1))].">
      <j1 rule="para" parents="22267 17524"/>
    </justification>
  </clause>

  <clause id="22270">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,y * (z \ T(u,z * y)))
    ]]></literal>
    <justification jstring="[hyper(22269,a,21574,a)].">
      <j1 rule="hyper" parents="22269 21574"/>
    </justification>
  </clause>

  <clause id="22271">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z * y))) = K(x,(u / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,21187,a(flip),b,22270,a),flip(a)].">
      <j1 rule="hyper" parents="64 21187 22270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22272">
    <literal><![CDATA[
      T((K(L(x \ K(y,z),u,w),x) * K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(6156(a,1),22237(a,1,1,1))].">
      <j1 rule="para" parents="6156 22237"/>
    </justification>
  </clause>

  <clause id="22273">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * (v6 * K(z * K(u,K(w,v5)),v7))) * z)) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18204,a(flip),b,22238,a),flip(a)].">
      <j1 rule="hyper" parents="373 18204 22238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22275">
    <literal><![CDATA[
      K(x,y * (((z * K(u,K(w,v5))) * (v6 * K(z,v7))) * z)) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7)))
    ]]></literal>
    <justification jstring="[para(17976(a,1),22273(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="17976 22273"/>
    </justification>
  </clause>

  <clause id="22277">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * (v6 * K(z,v7)))) * z)) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7)))
    ]]></literal>
    <justification jstring="[para(20327(a,1),22275(a,1,2,2,1))].">
      <j1 rule="para" parents="20327 22275"/>
    </justification>
  </clause>

  <clause id="22278">
    <literal><![CDATA[
      K(x,y * (z * ((K(u,K(w,v5)) * (v6 * K(z,v7))) * z))) = K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13374,a(flip),b,22277,a)].">
      <j1 rule="hyper" parents="64 13374 22277"/>
    </justification>
  </clause>

  <clause id="22279">
    <literal><![CDATA[
      K(x,y * (z * ((u * K(z,w)) * (z * K(v5,K(v6,v7)))))) = K(x,y * ((z * (K(v5,K(v6,v7)) * u)) * T(z,w)))
    ]]></literal>
    <justification jstring="[para(19381(a,1),22278(a,1,2,2,2))].">
      <j1 rule="para" parents="19381 22278"/>
    </justification>
  </clause>

  <clause id="22280">
    <literal><![CDATA[
      K(x,y * ((z * (K(u,K(w,v5)) * v6)) * T(z,v7))) = K(x,y * (z * (v6 * T(z * K(u,K(w,v5)),v7))))
    ]]></literal>
    <justification jstring="[para(17980(a,1),22279(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="17980 22279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22281">
    <literal><![CDATA[
      K(x,y * (z * (u * T(z * K(w,K(v5,v6)),u)))) = K(x,y * ((u * (z * K(w,K(v5,v6)))) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,21947,a(flip),b,22280,a),flip(a)].">
      <j1 rule="hyper" parents="64 21947 22280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22282">
    <literal><![CDATA[
      K(x,y * ((z * (u * K(w,K(v5,v6)))) * u)) = K(x,y * (u * ((u * K(w,K(v5,v6))) * z)))
    ]]></literal>
    <justification jstring="[para(115(a,1),22281(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="115 22281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22283">
    <literal><![CDATA[
      K(x,y * ((z * (u * K(w,K(v5,v6)))) * u)) = K(x,y * (u * (u * (K(w,K(v5,v6)) * z))))
    ]]></literal>
    <justification jstring="[para(20327(a,1),22282(a,2,2,2,2))].">
      <j1 rule="para" parents="20327 22282"/>
    </justification>
  </clause>

  <clause id="22284">
    <literal><![CDATA[
      K(x,y * ((z * (u * K(w,K(v5,v6)))) * u)) = K(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18498,a(flip),b,22283,a),flip(a)].">
      <j1 rule="hyper" parents="373 18498 22283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22286">
    <literal><![CDATA[
      K(x,y * ((z * u) * u)) = K(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[para(204(a,1),22284(a,1,2,2,1,2))].">
      <j1 rule="para" parents="204 22284"/>
    </justification>
  </clause>

  <clause id="22287">
    <literal><![CDATA[
      K(x,y * (((z * T(u,w)) * K(v5,u)) * K(v5,u))) = K(x,y * (K(v5,u) * ((K(v5,u) * z) * T(u,w))))
    ]]></literal>
    <justification jstring="[para(7780(a,2),22286(a,2,2,2,2))].">
      <j1 rule="para" parents="7780 22286"/>
    </justification>
  </clause>

  <clause id="22288">
    <literal><![CDATA[
      K(x,y * ((z * (T(u,w) * K(v5,u))) * K(v5,u))) = K(x,y * (K(v5,u) * ((K(v5,u) * z) * T(u,w))))
    ]]></literal>
    <justification jstring="[para(7999(a,1),22287(a,1,2,2,1))].">
      <j1 rule="para" parents="7999 22287"/>
    </justification>
  </clause>

  <clause id="22289">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * ((T(u,v5) * K(z,u)) * K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(64,a,19887,a(flip),b,22288,a),flip(a)].">
      <j1 rule="hyper" parents="64 19887 22288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22290">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * (T(u,v5) * (K(z,u) * K(z,u)))))
    ]]></literal>
    <justification jstring="[para(4443(a,1),22289(a,2,2,2,2))].">
      <j1 rule="para" parents="4443 22289"/>
    </justification>
  </clause>

  <clause id="22291">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * T(u * (K(z,u) * K(z,u)),v5)))
    ]]></literal>
    <justification jstring="[para(16383(a,2),22290(a,2,2,2,2))].">
      <j1 rule="para" parents="16383 22290"/>
    </justification>
  </clause>

  <clause id="22292">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * T((T(z,u) * u) / z,v5)))
    ]]></literal>
    <justification jstring="[para(6994(a,1),22291(a,2,2,2,2,1))].">
      <j1 rule="para" parents="6994 22291"/>
    </justification>
  </clause>

  <clause id="22293">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * (w * T(u,v5))))) = K(x,y * (w * T((T(z,u) * u) / z,v5)))
    ]]></literal>
    <justification jstring="[para(7780(a,1),22292(a,1,2,2,2))].">
      <j1 rule="para" parents="7780 22292"/>
    </justification>
  </clause>

  <clause id="22294">
    <literal><![CDATA[
      K(x,y * (z * T((T(u,w) * w) / u,v5))) = K(x,y * (z * T(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16261,a(flip),b,22293,a),flip(a)].">
      <j1 rule="hyper" parents="64 16261 22293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22296">
    <literal><![CDATA[
      K(x,y * (z * T(T(u * K(w,u),v5),w))) = K(x,y * (z * T((T(v6,u) * u) / v6,v5)))
    ]]></literal>
    <justification jstring="[para(5857(a,2),22294(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5857 22294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22297">
    <literal><![CDATA[
      K(x,y * (z * T(T(u * K(w,u),v5 \ v6),w))) = K(x,y * (z * T((T(v7,u) * u) / v7,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,21605,a(flip),b,22296,a),flip(a)].">
      <j1 rule="hyper" parents="373 21605 22296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22298">
    <literal><![CDATA[
      K(x,y * (z * T(T(u * K(w,u),v5 \ v6),w))) = K(x,y * (z * T(u,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,22294,a(flip),b,22297,a),flip(a)].">
      <j1 rule="hyper" parents="373 22294 22297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22299">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) = K(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(5785(a,1),22298(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5785 22298"/>
    </justification>
  </clause>

  <clause id="22300">
    <literal><![CDATA[
      K(x,y * (z * T(u,w / v5))) = K(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(18404,a,22299,a)].">
      <j1 rule="hyper" parents="18404 22299"/>
    </justification>
  </clause>

  <clause id="22301">
    <literal><![CDATA[
      T(x,y * (z * T(u,w \ v5))) = T(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(143,a,22299,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 22299 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22302">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(143,a,22300,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 22300 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22303">
    <literal><![CDATA[
      K(x,y * (T(z,T(u \ w,u)) * v5)) = K(x,y * (T(v5,z) * T(z,w * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18476,a,b,22300,a)].">
      <j1 rule="hyper" parents="64 18476 22300"/>
    </justification>
  </clause>

  <clause id="22304">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * T(u,y * z))) = T(x,(u * (z \ 1)) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,21726,a(flip),b,22301,a),flip(a)].">
      <j1 rule="hyper" parents="64 21726 22301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22305">
    <literal><![CDATA[
      K(T(x,y / z),(u * w) \ T(v5,w * (u * T(x,y * z)))) = K(T(x,y / z),v5 / (u * w))
    ]]></literal>
    <justification jstring="[para(22302(a,1),18408(a,1,2,2))].">
      <j1 rule="para" parents="22302 18408"/>
    </justification>
  </clause>

  <clause id="22306">
    <literal><![CDATA[
      K(x,y * (T(z,T(u \ w,u)) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,18474,a(flip),b,22303,a),flip(a)].">
      <j1 rule="hyper" parents="373 18474 22303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22307">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(18195,a,22306,a)].">
      <j1 rule="hyper" parents="18195 22306"/>
    </justification>
  </clause>

  <clause id="22308">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) = K(x,y * (T(w \ u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18475,a(flip),b,22307,a),flip(a)].">
      <j1 rule="hyper" parents="64 18475 22307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22309">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) = K(x,y * ((u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,16258,a(flip),b,22308,a),flip(a)].">
      <j1 rule="hyper" parents="373 16258 22308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22310">
    <literal><![CDATA[
      K(T(x,y / z),((z \ 1) * y) \ T(u,(x * (z \ 1)) * T(y,z))) = K(T(x,y / z),u / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[para(22304(a,1),22305(a,1,2,2))].">
      <j1 rule="para" parents="22304 22305"/>
    </justification>
  </clause>

  <clause id="22311">
    <literal><![CDATA[
      K(T(x,y / z),((z \ 1) * y) \ T(u,y * (x * (z \ 1)))) = K(T(x,y / z),u / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,20385,a(flip),b,22310,a)].">
      <j1 rule="hyper" parents="64 20385 22310"/>
    </justification>
  </clause>

  <clause id="22313">
    <literal><![CDATA[
      T((T(x,y) * K(z,u)) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1),w) = (x * K(z,u)) * L((x * K(z,u)) \ w,v5,v5 \ 1)
    ]]></literal>
    <justification jstring="[para(21162(a,1),22239(a,2,2,1))].">
      <j1 rule="para" parents="21162 22239"/>
    </justification>
  </clause>

  <clause id="22314">
    <literal><![CDATA[
      T((T(x,y) * K(z,u)) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1),w) = x * (K(z,u) * L(K(z,u) \ (x \ w),v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,1705,a(flip),b,22313,a),flip(a)].">
      <j1 rule="hyper" parents="373 1705 22313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22316">
    <literal><![CDATA[
      T((T(x,y) * K(z,u)) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1),w) = x * (K(z,u) * L(K(u,z) * (x \ w),v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[para(6156(a,1),22314(a,2,2,2,1))].">
      <j1 rule="para" parents="6156 22314"/>
    </justification>
  </clause>

  <clause id="22317">
    <literal><![CDATA[
      T((T(x,y) * K(z,u)) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1),w) = x * L(K(z,u) * (K(u,z) * (x \ w)),v5,v5 \ 1)
    ]]></literal>
    <justification jstring="[para(21849(a,2),22316(a,2,2))].">
      <j1 rule="para" parents="21849 22316"/>
    </justification>
  </clause>

  <clause id="22318">
    <literal><![CDATA[
      T((T(x,y) * K(z,u)) * L((T(x,y) * K(z,u)) \ w,v5,v5 \ 1),w) = x * L(x \ w,v5,v5 \ 1)
    ]]></literal>
    <justification jstring="[para(6161(a,1),22317(a,2,2,1))].">
      <j1 rule="para" parents="6161 22317"/>
    </justification>
  </clause>

  <clause id="22319">
    <literal><![CDATA[
      T(T(x,y) * (K(z,u) * L(K(z,u) \ (T(x,y) \ w),v5,v5 \ 1)),w) = x * L(x \ w,v5,v5 \ 1)
    ]]></literal>
    <justification jstring="[para(1705(a,1),22318(a,1,1))].">
      <j1 rule="para" parents="1705 22318"/>
    </justification>
  </clause>

  <clause id="22321">
    <literal><![CDATA[
      T(T(x,y) * (K(z,u) * L(K(u,z) * (T(x,y) \ w),v5,v5 \ 1)),w) = x * L(x \ w,v5,v5 \ 1)
    ]]></literal>
    <justification jstring="[para(6156(a,1),22319(a,1,1,2,2,1))].">
      <j1 rule="para" parents="6156 22319"/>
    </justification>
  </clause>

  <clause id="22322">
    <literal><![CDATA[
      T(T(x,y) * L(K(z,u) * (K(u,z) * (T(x,y) \ w)),v5,v5 \ 1),w) = x * L(x \ w,v5,v5 \ 1)
    ]]></literal>
    <justification jstring="[para(21849(a,2),22321(a,1,1,2))].">
      <j1 rule="para" parents="21849 22321"/>
    </justification>
  </clause>

  <clause id="22323">
    <literal><![CDATA[
      T(T(x,y) * L(T(x,y) \ z,u,u \ 1),z) = x * L(x \ z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(2357(a,1),22322(a,1,1,2,1))].">
      <j1 rule="para" parents="2357 22322"/>
    </justification>
  </clause>

  <clause id="22324">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ z,u,u \ 1) = x * L(x \ z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(19727,a,22323,a)].">
      <j1 rule="hyper" parents="19727 22323"/>
    </justification>
  </clause>

  <clause id="22325">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,z \ 1),u) = L(x \ T(y,u),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(3288,a,22324,a)].">
      <j1 rule="hyper" parents="3288 22324"/>
    </justification>
  </clause>

  <clause id="22326">
    <literal><![CDATA[
      (x \ (x * L(x \ y,z,z \ 1))) / L(x \ T(y,u),z,z \ 1) = K(u,T(x * L(x \ y,z,z \ 1),x))
    ]]></literal>
    <justification jstring="[para(22325(a,1),15073(a,1,2))].">
      <j1 rule="para" parents="22325 15073"/>
    </justification>
  </clause>

  <clause id="22327">
    <literal><![CDATA[
      K(x,y * L(((z \ T(u,w)) / (y \ 1)) / y,v5,v5 \ 1)) = K(x,y * (z \ T(z * L(z \ u,v5,v5 \ 1),w)))
    ]]></literal>
    <justification jstring="[para(22325(a,2),21860(a,2,2,2))].">
      <j1 rule="para" parents="22325 21860"/>
    </justification>
  </clause>

  <clause id="22328">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,u \ 1),y)) = L(y \ z,u,u \ 1) / L(y \ T(z,x),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),22326(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 22326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22329">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,u \ 1),y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,21851,a(flip),b,22328,a),flip(a)].">
      <j1 rule="hyper" parents="373 21851 22328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22331">
    <literal><![CDATA[
      K(x,y * L(z / y,u,u \ 1)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(11229,a,22329,a)].">
      <j1 rule="hyper" parents="11229 22329"/>
    </justification>
  </clause>

  <clause id="22333">
    <literal><![CDATA[
      K(x,T((y \ T(z,u)) / (w \ 1),w)) = K(x,w * (y \ T(y * L(y \ z,v5,v5 \ 1),u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22331,a(flip),b,22327,a)].">
      <j1 rule="hyper" parents="64 22331 22327"/>
    </justification>
  </clause>

  <clause id="22335">
    <literal><![CDATA[
      K(x,T((y \ T(z,u)) * w,w)) = K(x,w * (y \ T(y * L(y \ z,v5,v5 \ 1),u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14947,a(flip),b,22333,a)].">
      <j1 rule="hyper" parents="64 14947 22333"/>
    </justification>
  </clause>

  <clause id="22336">
    <literal><![CDATA[
      K(x,y * (z \ T(z * L(z \ u,w,w \ 1),v5))) = K(x,y * (z \ T(u,v5)))
    ]]></literal>
    <justification jstring="[hyper(11228,a,22335,a),flip(a)].">
      <j1 rule="hyper" parents="11228 22335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22337">
    <literal><![CDATA[
      K(x,y * L(z \ T(u,w),v5,v5 \ 1)) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(22325(a,1),22336(a,1,2,2))].">
      <j1 rule="para" parents="22325 22336"/>
    </justification>
  </clause>

  <clause id="22338">
    <literal><![CDATA[
      T((K(x \ K(y,z),L(x,u,w)) * K(x,x \ K(y,z))) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(12093(a,1),22272(a,1,1,1,1))].">
      <j1 rule="para" parents="12093 22272"/>
    </justification>
  </clause>

  <clause id="22339">
    <literal><![CDATA[
      T(a(x \ K(y,z),u,K(w,x)) * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(15328(a,1),22338(a,1,1,1))].">
      <j1 rule="para" parents="15328 22338"/>
    </justification>
  </clause>

  <clause id="22340">
    <literal><![CDATA[
      T(a(K(x,y),z,K(u,w)) * L(K(w,w \ K(x,y)),z,u),K(K(y,x) * w,w \ 1)) = K(K(y,x) * w,w \ 1)
    ]]></literal>
    <justification jstring="[para(15379(a,1),22339(a,1,1,1))].">
      <j1 rule="para" parents="15379 22339"/>
    </justification>
  </clause>

  <clause id="22341">
    <literal><![CDATA[
      T(1 * L(K(x,x \ K(y,z)),u,w),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(19190(a,1),22340(a,1,1,1))].">
      <j1 rule="para" parents="19190 22340"/>
    </justification>
  </clause>

  <clause id="22342">
    <literal><![CDATA[
      T(1 * K(x,L(x \ K(y,z),u,w)),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(7538(a,1),22341(a,1,1,2))].">
      <j1 rule="para" parents="7538 22341"/>
    </justification>
  </clause>

  <clause id="22344">
    <literal><![CDATA[
      T(K(x,L(x \ K(y,z),u,w)),K(K(z,y) * x,x \ 1)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),22342(a,1,1))].">
      <j1 rule="para" parents="7 22342"/>
    </justification>
  </clause>

  <clause id="22345">
    <literal><![CDATA[
      K(x,L(x \ K(y,z),u,w)) = K(K(z,y) * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(17154,a,22344,a)].">
      <j1 rule="hyper" parents="17154 22344"/>
    </justification>
  </clause>

  <clause id="22346">
    <literal><![CDATA[
      K(x,L(x \ K(y,z),u,w)) = K(x,x \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17138,a(flip),b,22345,a),flip(a)].">
      <j1 rule="hyper" parents="373 17138 22345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22348">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (K(y,y \ K(z,u)) * v6)) = K(x,T(L(y \ K(z,u),w,v5),y) * v6)
    ]]></literal>
    <justification jstring="[para(22346(a,1),15785(a,1,2,2,1))].">
      <j1 rule="para" parents="22346 15785"/>
    </justification>
  </clause>

  <clause id="22349">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (K(y,K(z,u)) * v6)) = K(x,T(L(y \ K(z,u),w,v5),y) * v6)
    ]]></literal>
    <justification jstring="[hyper(18405,a,22348,a)].">
      <j1 rule="hyper" parents="18405 22348"/>
    </justification>
  </clause>

  <clause id="22350">
    <literal><![CDATA[
      K(x,T(L(y \ K(z,u),w,v5),y) * v6) = K(x,L(y \ K(z,u),w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(18176,a,22349,a),flip(a)].">
      <j1 rule="hyper" parents="18176 22349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22352">
    <literal><![CDATA[
      K(x,L(K(y,z) / u,w,v5) * v6) = K(x,L(u \ K(y,z),w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,15790,a(flip),b,22350,a)].">
      <j1 rule="hyper" parents="64 15790 22350"/>
    </justification>
  </clause>

  <clause id="22353">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5))) = K(x,L(u \ K(y,z),w,v5) * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,21649,a,b,22352,a)].">
      <j1 rule="hyper" parents="64 21649 22352"/>
    </justification>
  </clause>

  <clause id="22354">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5))) = a(x,w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,22234,a(flip),b,22353,a),flip(a)].">
      <j1 rule="hyper" parents="373 22234 22353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22356">
    <literal><![CDATA[
      T(K(x,K(y,z) * ((u * w) * v5)),v5 \ T(v5 * ((u * K(z,y)) * w),x)) = (v5 \ T(v5 * ((u * K(z,y)) * w),x)) \ T((u * K(z,y)) * w,K(u,w))
    ]]></literal>
    <justification jstring="[para(20158(a,1),17607(a,1,1))].">
      <j1 rule="para" parents="20158 17607"/>
    </justification>
  </clause>

  <clause id="22357">
    <literal><![CDATA[
      T(K(x,T(y,z / u) * w),w \ T(w * T(y,T(z / u,v5)),x)) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[para(17938(a,1),19763(a,1,1))].">
      <j1 rule="para" parents="17938 19763"/>
    </justification>
  </clause>

  <clause id="22359">
    <literal><![CDATA[
      T(K(x,T(y,z * u) * w),w \ T(w * T(y,T(z / u,v5)),x)) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[para(21577(a,1),22357(a,1,1))].">
      <j1 rule="para" parents="21577 22357"/>
    </justification>
  </clause>

  <clause id="22360">
    <literal><![CDATA[
      T(K(x,T(y,z * u) * w),w * T(w \ T(y,T(z / u,v5)),x)) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,21436,a(flip),b,22359,a)].">
      <j1 rule="hyper" parents="64 21436 22359"/>
    </justification>
  </clause>

  <clause id="22361">
    <literal><![CDATA[
      T(K(x,T(y,z * u) * w),T(w * T(w \ y,x),T(z / u,v5))) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,21149,a,b,22360,a)].">
      <j1 rule="hyper" parents="64 21149 22360"/>
    </justification>
  </clause>

  <clause id="22362">
    <literal><![CDATA[
      K(x,T(T(y,z * u) * w,w * T(w \ y,x))) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[hyper(17130,a,22361,a)].">
      <j1 rule="hyper" parents="17130 22361"/>
    </justification>
  </clause>

  <clause id="22363">
    <literal><![CDATA[
      (x \ T(x * T(y,T(z / u,w)),v5)) \ T(y,T((u * z) \ (z * z),w)) = K(v5,T(T(y,z * u) * x,y))
    ]]></literal>
    <justification jstring="[hyper(18276,a,22362,a),flip(a)].">
      <j1 rule="hyper" parents="18276 22362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22365">
    <literal><![CDATA[
      (x \ T(x * T(y,T(z / u,w)),v5)) \ T(y,T((u * z) \ (z * z),w)) = K(v5,x * T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17095,a(flip),b,22363,a),flip(a)].">
      <j1 rule="hyper" parents="373 17095 22363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22366">
    <literal><![CDATA[
      (x \ T(x * T(y,T(z / u,w)),v5)) \ T(y,T(z / u,w)) = K(v5,x * T(y,z * u))
    ]]></literal>
    <justification jstring="[para(19762(a,1),22365(a,1,2))].">
      <j1 rule="para" parents="19762 22365"/>
    </justification>
  </clause>

  <clause id="22367">
    <literal><![CDATA[
      K(x,y * T(z,T(u / w,v5))) = K(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(14651,a,22366,a)].">
      <j1 rule="hyper" parents="14651 22366"/>
    </justification>
  </clause>

  <clause id="22368">
    <literal><![CDATA[
      K(x,y * T(z,u \ w)) = K(x,y * T(z,w * u))
    ]]></literal>
    <justification jstring="[para(117(a,1),22367(a,1,2,2,2))].">
      <j1 rule="para" parents="117 22367"/>
    </justification>
  </clause>

  <clause id="22369">
    <literal><![CDATA[
      K(x,y * T(z,u \ (w \ v5))) = K(x,y * T(z,v5 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(21235,a,22368,a)].">
      <j1 rule="hyper" parents="21235 22368"/>
    </justification>
  </clause>

  <clause id="22370">
    <literal><![CDATA[
      K(x,y * T(z,u * u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(379(a,1),22368(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="379 22368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22371">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (y \ z)) = w
    ]]></literal>
    <justification jstring="[para(22368(a,1),17537(a,1))].">
      <j1 rule="para" parents="22368 17537"/>
    </justification>
  </clause>

  <clause id="22372">
    <literal><![CDATA[
      T(x,y * T(z,u * u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(143,a,22370,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 22370 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22373">
    <literal><![CDATA[
      T(x,(y / z) * T(z,u * u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),22372(a,2,2))].">
      <j1 rule="para" parents="12 22372"/>
    </justification>
  </clause>

  <clause id="22374">
    <literal><![CDATA[
      T(x,y * K(z,u * u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6840(a,1),22373(a,1,2))].">
      <j1 rule="para" parents="6840 22373"/>
    </justification>
  </clause>

  <clause id="22375">
    <literal><![CDATA[
      T(x,y * K(z * z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(17511,a,22374,a)].">
      <j1 rule="hyper" parents="17511 22374"/>
    </justification>
  </clause>

  <clause id="22376">
    <literal><![CDATA[
      T(x,K(y * y,z) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(17353,a,22374,a)].">
      <j1 rule="hyper" parents="17353 22374"/>
    </justification>
  </clause>

  <clause id="22377">
    <literal><![CDATA[
      K(x * K(y * y,z),u) = u / T(u,x)
    ]]></literal>
    <justification jstring="[para(22374(a,1),16273(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22374 16273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22379">
    <literal><![CDATA[
      T(x,T(y * y,z) * u) = T(x,(y * y) * u)
    ]]></literal>
    <justification jstring="[para(8047(a,1),22375(a,1,2))].">
      <j1 rule="para" parents="8047 22375"/>
    </justification>
  </clause>

  <clause id="22380">
    <literal><![CDATA[
      T(x,((y * y) \ z) * u) = T(x,z * ((y * y) \ u))
    ]]></literal>
    <justification jstring="[para(6215(a,1),22376(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6215 22376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22381">
    <literal><![CDATA[
      K(x * K(y * y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5787,a,b,22377,a),flip(a)].">
      <j1 rule="hyper" parents="373 5787 22377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22382">
    <literal><![CDATA[
      K(x * T(y * y,z),u) = K(x * (y * y),u)
    ]]></literal>
    <justification jstring="[para(6852(a,1),22381(a,1,1))].">
      <j1 rule="para" parents="6852 22381"/>
    </justification>
  </clause>

  <clause id="22384">
    <literal><![CDATA[
      T(x,T(y * y,z) * u) = T(x,y * (y * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,15742,a(flip),b,22379,a),flip(a)].">
      <j1 rule="hyper" parents="373 15742 22379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22385">
    <literal><![CDATA[
      T(x,(y / (z * (u * u))) \ w) = T(x,u * (u * ((y / z) \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20217,a(flip),b,22384,a)].">
      <j1 rule="hyper" parents="64 20217 22384"/>
    </justification>
  </clause>

  <clause id="22386">
    <literal><![CDATA[
      T(x,y \ (y \ (z * u))) = T(x,z * ((y * y) \ u))
    ]]></literal>
    <justification jstring="[hyper(14911,a,22380,a)].">
      <j1 rule="hyper" parents="14911 22380"/>
    </justification>
  </clause>

  <clause id="22387">
    <literal><![CDATA[
      T(x,(y * z) * ((y * y) \ u)) = T(x,((1 / y) * z) * u)
    ]]></literal>
    <justification jstring="[para(535(a,1),22380(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="535 22380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22388">
    <literal><![CDATA[
      T(T(x,y * ((z * z) \ u)),w) = T(T(x,y * u),z \ (z \ w))
    ]]></literal>
    <justification jstring="[para(22386(a,1),15875(a,1,1))].">
      <j1 rule="para" parents="22386 15875"/>
    </justification>
  </clause>

  <clause id="22389">
    <literal><![CDATA[
      T(x,(y * z) * ((y * y) \ u)) = T(x,((y \ 1) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5114,a(flip),b,22387,a),flip(a)].">
      <j1 rule="hyper" parents="373 5114 22387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22390">
    <literal><![CDATA[
      T(x,((y \ 1) * z) * (y * y)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(191(a,1),22389(a,1,2)),flip(a)].">
      <j1 rule="para" parents="191 22389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22391">
    <literal><![CDATA[
      T(x,y * ((y \ 1) \ z)) = T(x,z * (y * y))
    ]]></literal>
    <justification jstring="[para(10(a,1),22390(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 22390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22392">
    <literal><![CDATA[
      T(x,(y / (z * u)) * (z * z)) = T(x,y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17056,a(flip),b,22391,a),flip(a)].">
      <j1 rule="hyper" parents="64 17056 22391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22393">
    <literal><![CDATA[
      T(x,y * ((z * u) \ (z * z))) = T(x,y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14943,a(flip),b,22392,a)].">
      <j1 rule="hyper" parents="64 14943 22392"/>
    </justification>
  </clause>

  <clause id="22394">
    <literal><![CDATA[
      T(x,y / ((1 / z) * u)) = T(x,y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(901(a,1),22392(a,1,2))].">
      <j1 rule="para" parents="901 22392"/>
    </justification>
  </clause>

  <clause id="22395">
    <literal><![CDATA[
      T(x,y / (((z \ y) \ 1) * z)) = T(x,(z \ y) * (y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17861,a(flip),b,22394,a),flip(a)].">
      <j1 rule="hyper" parents="64 17861 22394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22396">
    <literal><![CDATA[
      T(x,y / ((z \ 1) * (u / z))) = T(x,y * T(u \ (z * z),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,20302,a(flip),b,22393,a),flip(a)].">
      <j1 rule="hyper" parents="64 20302 22393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22397">
    <literal><![CDATA[
      K(x,L(y,z,u) * (y \ T(w,y * L(y,z,u)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * (y \ L(y,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(21776(a,1),22371(a,1))].">
      <j1 rule="para" parents="21776 22371"/>
    </justification>
  </clause>

  <clause id="22398">
    <literal><![CDATA[
      K(x,y * T(z,(u \ w) * v5)) = K(x,y * T(z,w * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22368,a(flip),b,22369,a)].">
      <j1 rule="hyper" parents="64 22368 22369"/>
    </justification>
  </clause>

  <clause id="22400">
    <literal><![CDATA[
      T(x,y * (y * ((z / (z / u)) \ w))) = T(x,T((y * y) \ u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15834,a(flip),b,22385,a),flip(a)].">
      <j1 rule="hyper" parents="64 15834 22385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22401">
    <literal><![CDATA[
      K(x,T(y,T(z * (u \ w),v5)) * v6) = K(x,T(v6,y) * T(y,w * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18145,a,b,22398,a)].">
      <j1 rule="hyper" parents="64 18145 22398"/>
    </justification>
  </clause>

  <clause id="22402">
    <literal><![CDATA[
      K(T(x,y),(z \ u) * T(w,u * (x * z))) = K(T(x,y),w * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,18540,a(flip),b,22398,a),flip(a)].">
      <j1 rule="hyper" parents="64 18540 22398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22403">
    <literal><![CDATA[
      T(x,T((y * y) \ z,u) \ w) = T(x,y * (y * (T(z,u) \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16197,a(flip),b,22400,a),flip(a)].">
      <j1 rule="hyper" parents="64 16197 22400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22404">
    <literal><![CDATA[
      K(x,T((y \ z) * T(u,z * (x * y)),w)) = K(T(x,w),u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(8019,a,22402,a)].">
      <j1 rule="hyper" parents="8019 22402"/>
    </justification>
  </clause>

  <clause id="22405">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(T(x,z * u),y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(17069,a,22404,a)].">
      <j1 rule="hyper" parents="17069 22404"/>
    </justification>
  </clause>

  <clause id="22406">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,T(y * (u \ z),z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,7869,a(flip),b,22405,a),flip(a)].">
      <j1 rule="hyper" parents="373 7869 22405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22407">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ z) * y) = w
    ]]></literal>
    <justification jstring="[para(22406(a,2),17068(a,1))].">
      <j1 rule="para" parents="22406 17068"/>
    </justification>
  </clause>

  <clause id="22408">
    <literal><![CDATA[
      K(x,T(y,T(z * (u \ w),v5)) * v6) = K(x,T(y,w * (z * u)) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,18035,a(flip),b,22401,a),flip(a)].">
      <j1 rule="hyper" parents="373 18035 22401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22409">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w) * v5) = K(x,T(y,u * (w * z)) * v5)
    ]]></literal>
    <justification jstring="[para(11103(a,1),22408(a,1,2,1))].">
      <j1 rule="para" parents="11103 22408"/>
    </justification>
  </clause>

  <clause id="22410">
    <literal><![CDATA[
      K(x,(y / z) * T(L(z,u,w),z)) = K(x,y * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(22397,a,22271,a),flip(a)].">
      <j1 rule="hyper" parents="22397 22271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22411">
    <literal><![CDATA[
      K(x,(y / z) * L(z,u,w)) = K(x,y * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(201(a,1),22410(a,1,2,2))].">
      <j1 rule="para" parents="201 22410"/>
    </justification>
  </clause>

  <clause id="22412">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,w)) \ L(z \ T(u,w),v5,v5 \ 1))) = K(x,(y / (z \ T(u,w))) * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22337,a(flip),b,22411,a),flip(a)].">
      <j1 rule="hyper" parents="64 22337 22411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22413">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,w)) \ L(z \ T(u,w),v5,v5 \ 1))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),22412(a,2,2))].">
      <j1 rule="para" parents="12 22412"/>
    </justification>
  </clause>

  <clause id="22414">
    <literal><![CDATA[
      K(x,y * a(z \ T(u,w),v5,v5 \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(16944,a,22413,a)].">
      <j1 rule="hyper" parents="16944 22413"/>
    </justification>
  </clause>

  <clause id="22417">
    <literal><![CDATA[
      K(x,y * a(z,u,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(82(a,1),22414(a,1,2,2,1))].">
      <j1 rule="para" parents="82 22414"/>
    </justification>
  </clause>

  <clause id="22418">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(21780,a,22417,a)].">
      <j1 rule="hyper" parents="21780 22417"/>
    </justification>
  </clause>

  <clause id="22419">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(17749,a,22418,a)].">
      <j1 rule="hyper" parents="17749 22418"/>
    </justification>
  </clause>

  <clause id="22420">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,14413,a,b,22418,a),flip(a)].">
      <j1 rule="hyper" parents="373 14413 22418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22422">
    <literal><![CDATA[
      K(x,(L(y,z,z \ 1) \ u) * ((u \ y) * u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,22128,a(flip),b,22418,a),flip(a)].">
      <j1 rule="hyper" parents="64 22128 22418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22423">
    <literal><![CDATA[
      K(x,y * L(z,u,u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(1631(a,1),22418(a,1,2,2))].">
      <j1 rule="para" parents="1631 22418"/>
    </justification>
  </clause>

  <clause id="22425">
    <literal><![CDATA[
      T(x,y * L(z,u,u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(143,a,22423,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 22423 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22427">
    <literal><![CDATA[
      T(x,y * ((z * z) \ u)) = T(x,y * (z \ (z \ u)))
    ]]></literal>
    <justification jstring="[para(346(a,1),22425(a,1,2,2))].">
      <j1 rule="para" parents="346 22425"/>
    </justification>
  </clause>

  <clause id="22429">
    <literal><![CDATA[
      K(x,y * (z / (u \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,6637,a(flip),b,22419,a),flip(a)].">
      <j1 rule="hyper" parents="64 6637 22419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22430">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(22420(a,2),14641(a,1))].">
      <j1 rule="para" parents="22420 14641"/>
    </justification>
  </clause>

  <clause id="22431">
    <literal><![CDATA[
      T(T(x,y * (z \ (z \ u))),w) = T(T(x,y * u),z \ (z \ w))
    ]]></literal>
    <justification jstring="[para(22427(a,1),22388(a,1,1))].">
      <j1 rule="para" parents="22427 22388"/>
    </justification>
  </clause>

  <clause id="22432">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / u)) = w
    ]]></literal>
    <justification jstring="[para(17748(a,1),22430(a,1))].">
      <j1 rule="para" parents="17748 22430"/>
    </justification>
  </clause>

  <clause id="22433">
    <literal><![CDATA[
      K(x,(L(y,z,z \ 1) \ u) * T(y,u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(17669,a,22422,a)].">
      <j1 rule="hyper" parents="17669 22422"/>
    </justification>
  </clause>

  <clause id="22434">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u \ z) / w)) = v5
    ]]></literal>
    <justification jstring="[para(18684(a,2),22432(a,1))].">
      <j1 rule="para" parents="18684 22432"/>
    </justification>
  </clause>

  <clause id="22435">
    <literal><![CDATA[
      K(x,T(K(y,z) * ((u * w) * v5),v5 \ T(v5 * ((u * K(z,y)) * w),x))) = (v5 \ T(v5 * ((u * K(z,y)) * w),x)) \ T((u * K(z,y)) * w,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(7964,a,22356,a)].">
      <j1 rule="hyper" parents="7964 22356"/>
    </justification>
  </clause>

  <clause id="22436">
    <literal><![CDATA[
      K(x,T(K(y,z) * ((u * w) * v5),v5 \ (v5 * ((u * K(z,y)) * w)))) = (v5 \ T(v5 * ((u * K(z,y)) * w),x)) \ T((u * K(z,y)) * w,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(18278,a,22435,a)].">
      <j1 rule="hyper" parents="18278 22435"/>
    </justification>
  </clause>

  <clause id="22438">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ T((y * K(z,u)) * w,K(y,w)) = K(v5,T(K(u,z) * ((y * w) * x),(y * K(z,u)) * w))
    ]]></literal>
    <justification jstring="[para(9(a,1),22436(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 22436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22439">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ T((y * K(z,u)) * w,K(y,w)) = K(v5,T(K(u,z) * ((y * w) * x),y * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,18256,a(flip),b,22438,a),flip(a)].">
      <j1 rule="hyper" parents="373 18256 22438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22442">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ T((y * K(z,u)) * w,K(y,w)) = K(v5,x * (K(z,u) * (y * w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,22256,a(flip),b,22439,a),flip(a)].">
      <j1 rule="hyper" parents="373 22256 22439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22443">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ ((y * K(z,u)) * w) = K(v5,x * (K(z,u) * (y * w)))
    ]]></literal>
    <justification jstring="[para(17324(a,1),22442(a,1,2))].">
      <j1 rule="para" parents="17324 22442"/>
    </justification>
  </clause>

  <clause id="22444">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * v5)) = K(x,y * (K(u,w) * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(14651,a,22443,a)].">
      <j1 rule="hyper" parents="14651 22443"/>
    </justification>
  </clause>

  <clause id="22445">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * ((v5 \ w) / w)))) = K(x,y * (w / (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20398,a(flip),b,22444,a),flip(a)].">
      <j1 rule="hyper" parents="64 20398 22444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22446">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w * z) * v5))) = K(x,y * ((w * T(z,u)) * v5))
    ]]></literal>
    <justification jstring="[para(6852(a,1),22444(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6852 22444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22447">
    <literal><![CDATA[
      K(x,y * ((z * T(u,x)) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(19594,a,22446,a),flip(a)].">
      <j1 rule="hyper" parents="19594 22446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22448">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * (u \ (w \ u))) * v5)) = K(x,(w \ (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,20221,a(flip),b,22447,a),flip(a)].">
      <j1 rule="hyper" parents="64 20221 22447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22449">
    <literal><![CDATA[
      K(x,y * (K(z,u) * T(w \ v5,v5))) = K(x,y * (v5 / (K(u,z) * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18454,a(flip),b,22445,a)].">
      <j1 rule="hyper" parents="64 18454 22445"/>
    </justification>
  </clause>

  <clause id="22450">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * v5))) = K(x,y * (K(w,u) * (z / v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15945,a(flip),b,22449,a),flip(a)].">
      <j1 rule="hyper" parents="64 15945 22449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22451">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) / v5)) = K(x,y * (K(z,u) * (w / v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20146,a,b,22450,a)].">
      <j1 rule="hyper" parents="64 20146 22450"/>
    </justification>
  </clause>

  <clause id="22452">
    <literal><![CDATA[
      K(x,y * (K(z,L(y \ 1,u,w)) * (v5 / L(y,u,w)))) = K(x,(L(y,u,w) \ v5) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,21881,a(flip),b,22451,a),flip(a)].">
      <j1 rule="hyper" parents="64 21881 22451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22453">
    <literal><![CDATA[
      K(x,y * (K(z,L(y,u,w)) * (v5 / L(y,u,w)))) = K(x,(L(T(y,z),u,w) \ v5) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,19849,a(flip),b,22451,a),flip(a)].">
      <j1 rule="hyper" parents="64 19849 22451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22454">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / T(v5,w)))) = K(x,y * (v5 \ (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19775,a(flip),b,22451,a),flip(a)].">
      <j1 rule="hyper" parents="64 19775 22451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22455">
    <literal><![CDATA[
      K(x,y * (z \ (K(u,w) * v5))) = K(x,y * (K(u,w) * (z \ v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13602,a(flip),b,22454,a),flip(a)].">
      <j1 rule="hyper" parents="64 13602 22454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22456">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ (v5 \ 1)))) = K(x,y * (w \ (v5 \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(18413,a,22455,a),flip(a)].">
      <j1 rule="hyper" parents="18413 22455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22457">
    <literal><![CDATA[
      K(x,y * (z \ (u * K(w,v5)))) = K(x,y * (K(w,v5) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(18411,a,22455,a)].">
      <j1 rule="hyper" parents="18411 22455"/>
    </justification>
  </clause>

  <clause id="22458">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w * K(v5,v6))))) = K(x,y * (K(v5,v6) * (z \ (u * w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,21888,a(flip),b,22457,a)].">
      <j1 rule="hyper" parents="64 21888 22457"/>
    </justification>
  </clause>

  <clause id="22459">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) \ (w * v5)))) = K(x,y * (v5 * K(w * v5,K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(64,a,19876,a(flip),b,22457,a),flip(a)].">
      <j1 rule="hyper" parents="64 19876 22457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22460">
    <literal><![CDATA[
      K(x,y * ((T(z,u) \ u) \ (w \ K(u,z)))) = K(x,y * ((z \ u) \ (w \ 1)))
    ]]></literal>
    <justification jstring="[para(14225(a,1),22456(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14225 22456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22461">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) * v5) = K(x,K(w,u) * ((y \ z) * v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),22448(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 22448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22462">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w) * ((v5 \ y) * v6)) = K(x,(v5 \ ((K(z,u) * (w * y)) / (K(z,u) * w))) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,19967,a,b,22461,a),flip(a)].">
      <j1 rule="hyper" parents="64 19967 22461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22464">
    <literal><![CDATA[
      K(x,y * (z \ (L(K(u,w) * v5,K(w,u),v6) * v6))) = K(x,y * (K(u,w) * (z \ (v5 * v6))))
    ]]></literal>
    <justification jstring="[hyper(64,a,22039,a,b,22458,a)].">
      <j1 rule="hyper" parents="64 22039 22458"/>
    </justification>
  </clause>

  <clause id="22465">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / z) \ (w \ K(u,z)))) = v5
    ]]></literal>
    <justification jstring="[para(22460(a,1),21292(a,1))].">
      <j1 rule="para" parents="22460 21292"/>
    </justification>
  </clause>

  <clause id="22466">
    <literal><![CDATA[
      K(x,(L(T(y,z),u,w) \ v5) * y) = K(x,y * (v5 / T(L(y,u,w),z)))
    ]]></literal>
    <justification jstring="[hyper(18094,a,22453,a),flip(a)].">
      <j1 rule="hyper" parents="18094 22453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22467">
    <literal><![CDATA[
      K(x,(L(T(y,z),u,w) \ v5) * y) = K(x,y * (v5 / L(T(y,z),u,w)))
    ]]></literal>
    <justification jstring="[para(25(a,2),22466(a,2,2,2,2))].">
      <j1 rule="para" parents="25 22466"/>
    </justification>
  </clause>

  <clause id="22468">
    <literal><![CDATA[
      K(x,y * ((K(z,z \ L(y,u,w)) * v5) / L(y,u,w))) = K(x,y * (v5 / L(T(y,z),u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20468,a,b,22467,a)].">
      <j1 rule="hyper" parents="64 20468 22467"/>
    </justification>
  </clause>

  <clause id="22469">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ ((K(u,z) * w) * v5)))) = K(x,y * (v5 * K(w * v5,K(z,u))))
    ]]></literal>
    <justification jstring="[para(20406(a,1),22459(a,1,2,2,2))].">
      <j1 rule="para" parents="20406 22459"/>
    </justification>
  </clause>

  <clause id="22470">
    <literal><![CDATA[
      K(x,y * L(z * K(u,K(w,v5)),K(u,w),v5)) = K(x,y * (z * K(v5 * z,K(u,w))))
    ]]></literal>
    <justification jstring="[para(21620(a,1),22469(a,1,2,2))].">
      <j1 rule="para" parents="21620 22469"/>
    </justification>
  </clause>

  <clause id="22471">
    <literal><![CDATA[
      K(x,y * (z * K(u * z,K(w,v5)))) = K(x,y * L(z,K(w,v5),u))
    ]]></literal>
    <justification jstring="[hyper(21825,a,22470,a),flip(a)].">
      <j1 rule="hyper" parents="21825 22470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22472">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(18011,a,22471,a),flip(a)].">
      <j1 rule="hyper" parents="18011 22471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22473">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(22471(a,1),18011(a,1))].">
      <j1 rule="para" parents="22471 18011"/>
    </justification>
  </clause>

  <clause id="22475">
    <literal><![CDATA[
      K(x,y * L((z * K(u,w)) \ v5,v6,v7)) = K(x,y * L(K(u,w) \ (z \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(709(a,1),22472(a,1,2,2))].">
      <j1 rule="para" parents="709 22472"/>
    </justification>
  </clause>

  <clause id="22476">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * (K(u,z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(6893(a,1),22473(a,1,2))].">
      <j1 rule="para" parents="6893 22473"/>
    </justification>
  </clause>

  <clause id="22477">
    <literal><![CDATA[
      K(x,y * L((z * K(u,w)) \ v5,v6,v7)) = K(x,y * L(K(w,u) * (z \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(6156(a,1),22475(a,2,2,2,1))].">
      <j1 rule="para" parents="6156 22475"/>
    </justification>
  </clause>

  <clause id="22478">
    <literal><![CDATA[
      K(x,y * L((K(z,u) \ w) \ v5,v6,v7)) = K(x,y * L(K(z,u) * (w \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,21829,a,b,22477,a)].">
      <j1 rule="hyper" parents="64 21829 22477"/>
    </justification>
  </clause>

  <clause id="22479">
    <literal><![CDATA[
      K(x,y * L((K(z,u) * w) \ v5,v6,v7)) = K(x,y * L(K(u,z) * (w \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(6156(a,1),22478(a,1,2,2,1,1))].">
      <j1 rule="para" parents="6156 22478"/>
    </justification>
  </clause>

  <clause id="22480">
    <literal><![CDATA[
      K(x,y * L(z \ (K(u,w) * v5),v6,v7)) = K(x,y * L(K(u,w) * (z \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,20159,a(flip),b,22479,a)].">
      <j1 rule="hyper" parents="64 20159 22479"/>
    </justification>
  </clause>

  <clause id="22481">
    <literal><![CDATA[
      K(x,y * L(K(z,u) * (w \ v5),w,v6)) = K(x,y * ((v6 * w) \ (v6 * (K(z,u) * v5))))
    ]]></literal>
    <justification jstring="[hyper(17267,a,22480,a),flip(a)].">
      <j1 rule="hyper" parents="17267 22480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22482">
    <literal><![CDATA[
      K(x,y * ((z * u) \ (z * (K(w,v5) * (u * v6))))) = K(x,y * L(K(w,v5) * v6,u,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),22481(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 22481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22483">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * (y * (u / L(y,w,v5)))) = K(x,(L(y,w,v5) \ u) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19891,a(flip),b,22452,a)].">
      <j1 rule="hyper" parents="64 19891 22452"/>
    </justification>
  </clause>

  <clause id="22485">
    <literal><![CDATA[
      K(x,y * (K(y \ 1,z) * (u / L(y,w,v5)))) = K(x,(L(y,w,v5) \ u) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19586,a(flip),b,22483,a)].">
      <j1 rule="hyper" parents="64 19586 22483"/>
    </justification>
  </clause>

  <clause id="22486">
    <literal><![CDATA[
      K(x,T(y,z) * (u / L(y,w,v5))) = K(x,(L(y,w,v5) \ u) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(19607,a,22485,a)].">
      <j1 rule="hyper" parents="19607 22485"/>
    </justification>
  </clause>

  <clause id="22487">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,K(w,v5)) * (K(v5,w) * v6)))) = K(x,y * (K(v5,w) * (z \ (u * v6))))
    ]]></literal>
    <justification jstring="[para(20416(a,1),22464(a,1,2,2,2))].">
      <j1 rule="para" parents="20416 22464"/>
    </justification>
  </clause>

  <clause id="22488">
    <literal><![CDATA[
      K(x,y * (z \ (u * (K(w,v5) * v6)))) = K(x,y * (K(w,v5) * (z \ (u * v6))))
    ]]></literal>
    <justification jstring="[hyper(19470,a,22487,a)].">
      <j1 rule="hyper" parents="19470 22487"/>
    </justification>
  </clause>

  <clause id="22489">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w * v5) \ (w * (v5 * v6))))) = K(x,y * L(K(z,u) * v6,v5,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,22482,a(flip),b,22488,a),flip(a)].">
      <j1 rule="hyper" parents="64 22482 22488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22490">
    <literal><![CDATA[
      K(x,y * L(K(z,u) * w,v5,v6)) = K(x,y * (K(z,u) * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(18(a,2),22489(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="18 22489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22491">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * L(K(u,z) * w,v5,v6)) = K(x,y * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(22476,a,22490,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="22476 22490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22492">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * w,v5,v6))) = K(x,u * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19997,a,22491,a)].">
      <j1 rule="hyper" parents="19997 22491"/>
    </justification>
  </clause>

  <clause id="22493">
    <literal><![CDATA[
      K(x,y * L(y \ 1,z,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22354,a(flip),b,22492,a),flip(a)].">
      <j1 rule="hyper" parents="64 22354 22492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22494">
    <literal><![CDATA[
      K(x,y * L(((z * u) / z) \ z,w,v5)) = K(x,y * L(z / u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,21663,a(flip),b,22492,a)].">
      <j1 rule="hyper" parents="64 21663 22492"/>
    </justification>
  </clause>

  <clause id="22495">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(T(1 / (y / z),y),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19059,a(flip),b,22493,a)].">
      <j1 rule="hyper" parents="64 19059 22493"/>
    </justification>
  </clause>

  <clause id="22496">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(y / (z * y),u,w)) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(17005,a,22494,a),flip(a)].">
      <j1 rule="hyper" parents="17005 22494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22498">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(1 / (y / z),T(w,y)))
    ]]></literal>
    <justification jstring="[para(7869(a,1),22495(a,2,3))].">
      <j1 rule="para" parents="7869 22495"/>
    </justification>
  </clause>

  <clause id="22499">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(z / y,T(w,y)))
    ]]></literal>
    <justification jstring="[para(6581(a,1),22498(a,2,3))].">
      <j1 rule="para" parents="6581 22498"/>
    </justification>
  </clause>

  <clause id="22500">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[para(7917(a,1),22499(a,2,3))].">
      <j1 rule="para" parents="7917 22499"/>
    </justification>
  </clause>

  <clause id="22501">
    <literal><![CDATA[
      K(x,y * (K(z,z \ L(y,u,w)) * (v5 / L(y,u,w)))) = K(x,y * (v5 / L(T(y,z),u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22451,a(flip),b,22468,a)].">
      <j1 rule="hyper" parents="64 22451 22468"/>
    </justification>
  </clause>

  <clause id="22502">
    <literal><![CDATA[
      K(x,y * (K(z,L(y,u,w) * z) * (v5 / L(y,u,w)))) = K(x,y * (v5 / L(T(y,z),u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,21596,a(flip),b,22501,a)].">
      <j1 rule="hyper" parents="64 21596 22501"/>
    </justification>
  </clause>

  <clause id="22503">
    <literal><![CDATA[
      K(x,y * (K(z,z * L(y,u,w)) * (v5 / L(y,u,w)))) = K(x,y * (v5 / L(T(y,z),u,w)))
    ]]></literal>
    <justification jstring="[para(6142(a,1),22502(a,1,2,2,1))].">
      <j1 rule="para" parents="6142 22502"/>
    </justification>
  </clause>

  <clause id="22504">
    <literal><![CDATA[
      K(x,y * (K(z,L(z * y,u,w)) * (v5 / L(y,u,w)))) = K(x,y * (v5 / L(T(y,z),u,w)))
    ]]></literal>
    <justification jstring="[para(21627(a,2),22503(a,1,2,2,1))].">
      <j1 rule="para" parents="21627 22503"/>
    </justification>
  </clause>

  <clause id="22505">
    <literal><![CDATA[
      K(x,K(y * z,y) * (z * (u / L(z,w,v5)))) = K(x,z * (u / L(T(z,y),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19891,a(flip),b,22504,a)].">
      <j1 rule="hyper" parents="64 19891 22504"/>
    </justification>
  </clause>

  <clause id="22507">
    <literal><![CDATA[
      K(x,y * (K(z * y,z) * (u / L(y,w,v5)))) = K(x,y * (u / L(T(y,z),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,19586,a(flip),b,22505,a)].">
      <j1 rule="hyper" parents="64 19586 22505"/>
    </justification>
  </clause>

  <clause id="22508">
    <literal><![CDATA[
      K(x,y * (K(z,y) * (u / L(y,w,v5)))) = K(x,y * (u / L(T(y,z),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16335,a(flip),b,22507,a)].">
      <j1 rule="hyper" parents="64 16335 22507"/>
    </justification>
  </clause>

  <clause id="22509">
    <literal><![CDATA[
      K(x,T(y,z) * (u / L(y,w,v5))) = K(x,y * (u / L(T(y,z),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(18151,a,22508,a)].">
      <j1 rule="hyper" parents="18151 22508"/>
    </justification>
  </clause>

  <clause id="22510">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ w) * T(y,v5)) = K(x,y * (w / L(T(y,v5),z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22486,a(flip),b,22509,a)].">
      <j1 rule="hyper" parents="64 22486 22509"/>
    </justification>
  </clause>

  <clause id="22511">
    <literal><![CDATA[
      K(x,y * (z / L(T(y,z),u,u \ 1))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,22433,a(flip),b,22510,a),flip(a)].">
      <j1 rule="hyper" parents="64 22433 22510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22512">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13490,a(flip),b,22511,a)].">
      <j1 rule="hyper" parents="64 13490 22511"/>
    </justification>
  </clause>

  <clause id="22513">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,22115,a(flip),b,22512,a),flip(a)].">
      <j1 rule="hyper" parents="64 22115 22512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22514">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,20931,a(flip),b,22512,a)].">
      <j1 rule="hyper" parents="64 20931 22512"/>
    </justification>
  </clause>

  <clause id="22515">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),22512(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 22512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22516">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ u) = K(x,w * (L(w,v5,v5 \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,22512,a,b,22514,a),flip(a)].">
      <j1 rule="hyper" parents="373 22512 22514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22517">
    <literal><![CDATA[
      K(x,L(y,z,z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(1631(a,1),22515(a,1,2,1))].">
      <j1 rule="para" parents="1631 22515"/>
    </justification>
  </clause>

  <clause id="22518">
    <literal><![CDATA[
      T(x,L(y,z,z) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[hyper(143,a,22517,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 22517 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22519">
    <literal><![CDATA[
      T(x,((y \ 1) \ z) * u) = T(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(576(a,1),22518(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="576 22518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22520">
    <literal><![CDATA[
      T(x,((y / z) * y) * (z \ u)) = T(x,(z \ y) * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16187,a(flip),b,22519,a),flip(a)].">
      <j1 rule="hyper" parents="64 16187 22519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22521">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,a(w,v5,v5 \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(2329(a,2),22516(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2329 22516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22522">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,(u / T(a(v5 \ 1,v5,w),L(w,v5,v5 \ 1))) \ L(w,v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,21317,a,b,22521,a),flip(a)].">
      <j1 rule="hyper" parents="64 21317 22521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22524">
    <literal><![CDATA[
      K(x,(y \ T(z * y,y)) * L(y / (z * y),u,w)) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17911,a(flip),b,22496,a)].">
      <j1 rule="hyper" parents="64 17911 22496"/>
    </justification>
  </clause>

  <clause id="22525">
    <literal><![CDATA[
      K(x,((y * z) / z) * L(z / (y * z),u,w)) = K(x,y * L((z * y) \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(16361,a,22524,a)].">
      <j1 rule="hyper" parents="16361 22524"/>
    </justification>
  </clause>

  <clause id="22526">
    <literal><![CDATA[
      K(x,y * L(z / (y * z),u,w)) = K(x,y * L((z * y) \ z,u,w))
    ]]></literal>
    <justification jstring="[para(11(a,1),22525(a,1,2,1))].">
      <j1 rule="para" parents="11 22525"/>
    </justification>
  </clause>

  <clause id="22527">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) * z) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16224,a,b,22526,a)].">
      <j1 rule="hyper" parents="64 16224 22526"/>
    </justification>
  </clause>

  <clause id="22528">
    <literal><![CDATA[
      K(x,(y \ ((K(z,u) * (w * v5)) / (K(z,u) * w))) * v6) = K(x,(y \ T(v5,K(z,u) * w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,19975,a(flip),b,22462,a),flip(a)].">
      <j1 rule="hyper" parents="64 19975 22462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22529">
    <literal><![CDATA[
      K(x,(y \ ((z * u) / (K(w,v5) * (K(v5,w) * z)))) * v6) = K(x,(y \ T(u,K(v5,w) * z)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,20507,a(flip),b,22528,a)].">
      <j1 rule="hyper" parents="64 20507 22528"/>
    </justification>
  </clause>

  <clause id="22530">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ ((v5 * z) / v5)) * v6)
    ]]></literal>
    <justification jstring="[para(6161(a,1),22529(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6161 22529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22531">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ T(z,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,17911,a(flip),b,22530,a),flip(a)].">
      <j1 rule="hyper" parents="373 17911 22530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22532">
    <literal><![CDATA[
      K(x,(y \ T(z,u * K(w,v5))) * v6) = K(x,(y \ T(z,u)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,17884,a(flip),b,22531,a)].">
      <j1 rule="hyper" parents="64 17884 22531"/>
    </justification>
  </clause>

  <clause id="22535">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,(u / a(v5 \ 1,v5,w)) \ L(w,v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[para(5633(a,1),22522(a,2,2,1,2))].">
      <j1 rule="para" parents="5633 22522"/>
    </justification>
  </clause>

  <clause id="22536">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,(a(v5 \ 1,v5,w) \ u) \ L(w,v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[para(14435(a,1),22535(a,2,2,1))].">
      <j1 rule="para" parents="14435 22535"/>
    </justification>
  </clause>

  <clause id="22537">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,u \ (a(v5 \ 1,v5,w) * L(w,v5,v5 \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,16179,a(flip),b,22536,a),flip(a)].">
      <j1 rule="hyper" parents="373 16179 22536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22538">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(5564(a,1),22537(a,2,2,2))].">
      <j1 rule="para" parents="5564 22537"/>
    </justification>
  </clause>

  <clause id="22539">
    <literal><![CDATA[
      K(x,y \ L(z,u,u \ 1)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,22514,a(flip),b,22538,a)].">
      <j1 rule="hyper" parents="64 22514 22538"/>
    </justification>
  </clause>

  <clause id="22540">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16946,a(flip),b,22539,a),flip(a)].">
      <j1 rule="hyper" parents="64 16946 22539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22541">
    <literal><![CDATA[
      K(x,y \ (z * (u \ 1))) = K(x,y \ (z / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16941,a(flip),b,22539,a)].">
      <j1 rule="hyper" parents="64 16941 22539"/>
    </justification>
  </clause>

  <clause id="22542">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16518,a(flip),b,22539,a),flip(a)].">
      <j1 rule="hyper" parents="64 16518 22539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22543">
    <literal><![CDATA[
      K(x,y \ L(z,u,u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(1631(a,1),22539(a,1,2,2))].">
      <j1 rule="para" parents="1631 22539"/>
    </justification>
  </clause>

  <clause id="22544">
    <literal><![CDATA[
      T(x,y \ L(z,u,u)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(143,a,22543,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 22543 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22545">
    <literal><![CDATA[
      T(x,y \ L(y,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,379,a(flip),b,22544,a),flip(a)].">
      <j1 rule="hyper" parents="373 379 22544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22546">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ u)) = T(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(576(a,1),22544(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="576 22544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22547">
    <literal><![CDATA[
      T(x,((y \ 1) \ z) \ (y * z)) = x
    ]]></literal>
    <justification jstring="[para(576(a,1),22545(a,1,2,2))].">
      <j1 rule="para" parents="576 22545"/>
    </justification>
  </clause>

  <clause id="22548">
    <literal><![CDATA[
      (((x \ 1) \ y) \ (x * y)) * z = z * (((x \ 1) \ y) \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(2149,a,22547,a),flip(a)].">
      <j1 rule="hyper" parents="2149 22547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22549">
    <literal><![CDATA[
      (x * y) / ((x \ 1) \ y) = ((x \ 1) \ y) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(225,a,22547,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 22547 116"/>
    </justification>
  </clause>

  <clause id="22553">
    <literal><![CDATA[
      K(x,(K(y,z) * (u \ 1)) \ w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,19929,a(flip),b,22542,a),flip(a)].">
      <j1 rule="hyper" parents="373 19929 22542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22554">
    <literal><![CDATA[
      K(x,((y * z) / y) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22034,a(flip),b,22542,a),flip(a)].">
      <j1 rule="hyper" parents="64 22034 22542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22555">
    <literal><![CDATA[
      K(x,(K(y \ z,u) * (w \ 1)) \ v5) = K(x,K(y * z,u) * (w * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,21552,a(flip),b,22553,a),flip(a)].">
      <j1 rule="hyper" parents="373 21552 22553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22556">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((T(y,z) * z) * u))
    ]]></literal>
    <justification jstring="[para(10789(a,1),22554(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10789 22554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22557">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,20535,a(flip),b,22556,a),flip(a)].">
      <j1 rule="hyper" parents="373 20535 22556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22558">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,20144,a,b,22557,a)].">
      <j1 rule="hyper" parents="64 20144 22557"/>
    </justification>
  </clause>

  <clause id="22559">
    <literal><![CDATA[
      K(x,(K(y \ z,u) * (w \ 1)) \ v5) = K(x,w * (K(y * z,u) * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,19586,a(flip),b,22555,a),flip(a)].">
      <j1 rule="hyper" parents="373 19586 22555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22560">
    <literal><![CDATA[
      K(x,(y \ z) * (K(z * y,u) * w)) = K(x,T((y \ z) \ 1,u) \ w)
    ]]></literal>
    <justification jstring="[para(6764(a,1),22559(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6764 22559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22561">
    <literal><![CDATA[
      K(x,(y \ z) * (K(z * y,u) * w)) = K(x,T(y \ z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,16837,a(flip),b,22560,a),flip(a)].">
      <j1 rule="hyper" parents="373 16837 22560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22562">
    <literal><![CDATA[
      T(K(x,(y * z) * (u / w)) * a(z,y,K(x,((u / w) \ 1) \ y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[para(14463(a,1),20316(a,1,1,1))].">
      <j1 rule="para" parents="14463 20316"/>
    </justification>
  </clause>

  <clause id="22563">
    <literal><![CDATA[
      T(K(x,(y * z) * (u / w)) * a(z,y,K(x,(u / w) * y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[para(14413(a,1),22562(a,1,1,2,3))].">
      <j1 rule="para" parents="14413 22562"/>
    </justification>
  </clause>

  <clause id="22564">
    <literal><![CDATA[
      T(K(x,(y * z) * (u / w)) * a(z,y,K(x,(w \ u) * y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[para(20941(a,1),22563(a,1,1,2))].">
      <j1 rule="para" parents="20941 22563"/>
    </justification>
  </clause>

  <clause id="22565">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) * (w / u)) = K(z,y / (T((u \ w) \ 1,w) / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,21266,a(flip),b,22564,a)].">
      <j1 rule="hyper" parents="64 21266 22564"/>
    </justification>
  </clause>

  <clause id="22566">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) * (w / u)) = K(z,y / (((w / u) \ 1) / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,20315,a(flip),b,22565,a),flip(a)].">
      <j1 rule="hyper" parents="373 20315 22565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22568">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[para(20021(a,1),14673(a,1,1))].">
      <j1 rule="para" parents="20021 14673"/>
    </justification>
  </clause>

  <clause id="22569">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),v5 * T(v5 \ K(w \ (u * (z \ 1)),y),x)) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,21436,a(flip),b,22568,a)].">
      <j1 rule="hyper" parents="64 21436 22568"/>
    </justification>
  </clause>

  <clause id="22570">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),K(v5,x) * K(y,w \ (u * (z \ 1)))) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[hyper(18794,a,22569,a)].">
      <j1 rule="hyper" parents="18794 22569"/>
    </justification>
  </clause>

  <clause id="22571">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),K(y,z * (u \ w)) * K(v5,x)) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,20111,a(flip),b,22570,a)].">
      <j1 rule="hyper" parents="64 20111 22570"/>
    </justification>
  </clause>

  <clause id="22572">
    <literal><![CDATA[
      (x \ T(x * K(y \ (z * (u \ 1)),w),v5)) \ K(y \ (z * (1 / u)),w) = K(v5,T(K(w,u * (z \ y)) * x,K(w,u * (z \ y))))
    ]]></literal>
    <justification jstring="[hyper(18283,a,22571,a),flip(a)].">
      <j1 rule="hyper" parents="18283 22571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22574">
    <literal><![CDATA[
      (x \ T(x * K(y \ (z * (u \ 1)),w),v5)) \ K(y \ (z * (1 / u)),w) = K(v5,x * K(w,u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,11113,a(flip),b,22572,a),flip(a)].">
      <j1 rule="hyper" parents="373 11113 22572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22575">
    <literal><![CDATA[
      (x \ T(x * K(y \ (z * (u \ 1)),w),v5)) \ K(y \ (z * (u \ 1)),w) = K(v5,x * K(w,u * (z \ y)))
    ]]></literal>
    <justification jstring="[para(5267(a,1),22574(a,1,2))].">
      <j1 rule="para" parents="5267 22574"/>
    </justification>
  </clause>

  <clause id="22576">
    <literal><![CDATA[
      K(x,y * K(z \ (u * (w \ 1)),v5)) = K(x,y * K(v5,w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(14651,a,22575,a)].">
      <j1 rule="hyper" parents="14651 22575"/>
    </justification>
  </clause>

  <clause id="22577">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,(y \ z) * K(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(17665,a,22576,a)].">
      <j1 rule="hyper" parents="17665 22576"/>
    </justification>
  </clause>

  <clause id="22578">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(15021(a,1),22577(a,2,2))].">
      <j1 rule="para" parents="15021 22577"/>
    </justification>
  </clause>

  <clause id="22579">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(7036(a,1),22578(a,1,2,2))].">
      <j1 rule="para" parents="7036 22578"/>
    </justification>
  </clause>

  <clause id="22580">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,21453,a(flip),b,22579,a)].">
      <j1 rule="hyper" parents="64 21453 22579"/>
    </justification>
  </clause>

  <clause id="22581">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,22000,a(flip),b,22580,a),flip(a)].">
      <j1 rule="hyper" parents="373 22000 22580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22582">
    <literal><![CDATA[
      K(T(x,y / z),((z \ 1) * y) \ T(u,z * (x * y))) = K(T(x,y / z),u / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,22311,a(flip),b,22581,a),flip(a)].">
      <j1 rule="hyper" parents="64 22311 22581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22583">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ T(u,y * (x * z)),z / y)) = K(T(x,z / y),u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(8019,a,22582,a)].">
      <j1 rule="hyper" parents="8019 22582"/>
    </justification>
  </clause>

  <clause id="22584">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ T(u,y * (x * z)),z * y)) = K(T(x,z / y),u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(17525,a,22583,a)].">
      <j1 rule="hyper" parents="17525 22583"/>
    </justification>
  </clause>

  <clause id="22585">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) = K(T(x,u / z),y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(17071,a,22584,a)].">
      <j1 rule="hyper" parents="17071 22584"/>
    </justification>
  </clause>

  <clause id="22586">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) = K(x,T(y / ((z \ 1) * u),u / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7869,a(flip),b,22585,a),flip(a)].">
      <j1 rule="hyper" parents="373 7869 22585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22587">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) = K(x,T(((z \ 1) * u) \ y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(14959(a,1),22586(a,2,2))].">
      <j1 rule="para" parents="14959 22586"/>
    </justification>
  </clause>

  <clause id="22588">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z \ 1) * u) \ y) = w
    ]]></literal>
    <justification jstring="[para(22587(a,2),17156(a,1))].">
      <j1 rule="para" parents="22587 17156"/>
    </justification>
  </clause>

  <clause id="22589">
    <literal><![CDATA[
      (L(x * K(y,z),K(z,T(y,x)),K(z,T(y,x))) \ L(K(z,T(y,x)) \ (x * u),K(z,T(y,x)),K(z,T(y,x)))) * (K(z,y) * x) = (u * x) * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(8224(a,1),16682(a,1,1,1,1))].">
      <j1 rule="para" parents="8224 16682"/>
    </justification>
  </clause>

  <clause id="22590">
    <literal><![CDATA[
      ((x * K(y,z)) \ L(K(z,T(y,x)) \ (x * u),K(z,T(y,x)),K(z,T(y,x)))) * (K(z,y) * x) = (u * x) * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9981(a,1),22589(a,1,1,1))].">
      <j1 rule="para" parents="9981 22589"/>
    </justification>
  </clause>

  <clause id="22591">
    <literal><![CDATA[
      ((x * K(y,z)) \ L(K(y,T(z,x)) * (x * u),K(z,T(y,x)),K(z,T(y,x)))) * (K(z,y) * x) = (u * x) * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(7914(a,1),22590(a,1,1,2,1))].">
      <j1 rule="para" parents="7914 22590"/>
    </justification>
  </clause>

  <clause id="22594">
    <literal><![CDATA[
      ((x * K(y,z)) \ (K(y,T(z,x)) * (x * u))) * (K(z,y) * x) = (u * x) * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9981(a,1),22591(a,1,1,2))].">
      <j1 rule="para" parents="9981 22591"/>
    </justification>
  </clause>

  <clause id="22595">
    <literal><![CDATA[
      L(x,y,K(z,T(u,y))) * (K(u,z) * y) = (x * y) * K(u,T(z,y))
    ]]></literal>
    <justification jstring="[para(8260(a,1),22594(a,1,1))].">
      <j1 rule="para" parents="8260 22594"/>
    </justification>
  </clause>

  <clause id="22598">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (K(u,z) * y) = (x * y) * K(u,T(z,y))
    ]]></literal>
    <justification jstring="[para(21808(a,1),22595(a,1,1))].">
      <j1 rule="para" parents="21808 22595"/>
    </justification>
  </clause>

  <clause id="22600">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),((z * u) * (1 / u)) * K(y \ L(z,u,u \ 1),x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18040,a(flip),b,20066,a)].">
      <j1 rule="hyper" parents="64 18040 20066"/>
    </justification>
  </clause>

  <clause id="22601">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),(z * u) * ((1 / u) * K(y \ L(z,u,u \ 1),x))) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(19502,a,22600,a)].">
      <j1 rule="hyper" parents="19502 22600"/>
    </justification>
  </clause>

  <clause id="22602">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),(z * u) * (u \ K(y \ L(z,u,u \ 1),x))) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14531,a(flip),b,22601,a)].">
      <j1 rule="hyper" parents="64 14531 22601"/>
    </justification>
  </clause>

  <clause id="22603">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),K(y \ L(z,u,u \ 1),x) * z) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(20865,a,22602,a)].">
      <j1 rule="hyper" parents="20865 22602"/>
    </justification>
  </clause>

  <clause id="22604">
    <literal><![CDATA[
      (((x * y) * (1 / y)) * K(((x * y) * (1 / y)) / z,u)) \ T((y * x) * (1 / y),y) = K(u,T(z \ R(x,y,y \ 1),x))
    ]]></literal>
    <justification jstring="[hyper(18279,a,22603,a),flip(a)].">
      <j1 rule="hyper" parents="18279 22603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22605">
    <literal><![CDATA[
      (((x * y) * (1 / y)) * K(((x * y) * (1 / y)) / z,u)) \ T((y * x) * (1 / y),y) = K(u,R(x,y,y \ 1) / z)
    ]]></literal>
    <justification jstring="[hyper(373,a,19268,a(flip),b,22604,a),flip(a)].">
      <j1 rule="hyper" parents="373 19268 22604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22606">
    <literal><![CDATA[
      (((x * y) * (1 / y)) * K(L(x,y,y \ 1) / z,u)) \ T((y * x) * (1 / y),y) = K(u,R(x,y,y \ 1) / z)
    ]]></literal>
    <justification jstring="[para(20065(a,1),22605(a,1,1,2))].">
      <j1 rule="para" parents="20065 22605"/>
    </justification>
  </clause>

  <clause id="22607">
    <literal><![CDATA[
      (((x * y) * (1 / y)) * K(L(x,y,y \ 1) / z,u)) \ ((x * y) * (1 / y)) = K(u,R(x,y,y \ 1) / z)
    ]]></literal>
    <justification jstring="[para(2135(a,1),22606(a,1,2))].">
      <j1 rule="para" parents="2135 22606"/>
    </justification>
  </clause>

  <clause id="22608">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) / u) = K(x,L(y,z,z \ 1) / u)
    ]]></literal>
    <justification jstring="[hyper(6899,a,22607,a),flip(a)].">
      <j1 rule="hyper" parents="6899 22607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22610">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,L(y,z,z \ 1) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16396,a,b,22608,a)].">
      <j1 rule="hyper" parents="64 16396 22608"/>
    </justification>
  </clause>

  <clause id="22611">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / (u * (z \ 1))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19831,a(flip),b,22610,a),flip(a)].">
      <j1 rule="hyper" parents="64 19831 22610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22612">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22513,a(flip),b,22611,a)].">
      <j1 rule="hyper" parents="64 22513 22611"/>
    </justification>
  </clause>

  <clause id="22613">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / ((z \ 1) * u)) = K(x,y / (T(u,z) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,20244,a(flip),b,22611,a)].">
      <j1 rule="hyper" parents="64 20244 22611"/>
    </justification>
  </clause>

  <clause id="22615">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,20201,a(flip),b,22613,a),flip(a)].">
      <j1 rule="hyper" parents="373 20201 22613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22616">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22513,a(flip),b,22615,a)].">
      <j1 rule="hyper" parents="64 22513 22615"/>
    </justification>
  </clause>

  <clause id="22618">
    <literal><![CDATA[
      T(x,y / ((z \ 1) * u)) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(143,a,22616,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 22616 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22620">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,u / ((u \ z) \ (y \ u))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(22616(a,1),20469(a,1,2))].">
      <j1 rule="para" parents="22616 20469"/>
    </justification>
  </clause>

  <clause id="22621">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z \ 1) * u) \ y) = w
    ]]></literal>
    <justification jstring="[para(22616(a,1),22588(a,1))].">
      <j1 rule="para" parents="22616 22588"/>
    </justification>
  </clause>

  <clause id="22622">
    <literal><![CDATA[
      T(x,y * T(z \ (u * u),u)) = T(x,y / (u \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22396,a(flip),b,22618,a)].">
      <j1 rule="hyper" parents="64 22396 22618"/>
    </justification>
  </clause>

  <clause id="22623">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,u / ((z \ u) * (y \ u))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(21322(a,1),22620(a,1,2))].">
      <j1 rule="para" parents="21322 22620"/>
    </justification>
  </clause>

  <clause id="22624">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,(y * T(z,u)) / u) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(21756(a,1),22623(a,1,2))].">
      <j1 rule="para" parents="21756 22623"/>
    </justification>
  </clause>

  <clause id="22625">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19674,a(flip),b,22624,a)].">
      <j1 rule="hyper" parents="64 19674 22624"/>
    </justification>
  </clause>

  <clause id="22626">
    <literal><![CDATA[
      K(x,y / (z \ u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,20199,a(flip),b,22625,a)].">
      <j1 rule="hyper" parents="64 20199 22625"/>
    </justification>
  </clause>

  <clause id="22627">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,((z \ 1) * u) \ y)
    ]]></literal>
    <justification jstring="[hyper(22621,a,22626,a),flip(a)].">
      <j1 rule="hyper" parents="22621 22626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22628">
    <literal><![CDATA[
      T(x,y / (z \ u)) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(143,a,22626,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 22626 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22629">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,22616,a,b,22626,a)].">
      <j1 rule="hyper" parents="64 22616 22626"/>
    </justification>
  </clause>

  <clause id="22630">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) * (y \ z)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,22500,a(flip),b,22626,a),flip(a)].">
      <j1 rule="hyper" parents="64 22500 22626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22631">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,y \ ((y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,21801,a(flip),b,22626,a),flip(a)].">
      <j1 rule="hyper" parents="64 21801 22626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22632">
    <literal><![CDATA[
      K(x,y \ ((y * (z * u)) / z)) = K(x,y * ((z * y) \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,21800,a(flip),b,22626,a)].">
      <j1 rule="hyper" parents="64 21800 22626"/>
    </justification>
  </clause>

  <clause id="22633">
    <literal><![CDATA[
      K(x,y * (z \ (u \ z))) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16346,a(flip),b,22626,a),flip(a)].">
      <j1 rule="hyper" parents="64 16346 22626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22634">
    <literal><![CDATA[
      x * K(y,x * ((z * x) \ (u * z))) = (x * z) / (z * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,22626,a(flip),b,21613,a(flip))].">
      <j1 rule="hyper" parents="145 22626 21613"/>
    </justification>
  </clause>

  <clause id="22636">
    <literal><![CDATA[
      T(x / (y / (z \ u)),y * (u \ z)) = (y / (z \ u)) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,22628,a),flip(a)].">
      <j1 rule="hyper" parents="467 22628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22637">
    <literal><![CDATA[
      T(x,y / ((z \ 1) * u)) = T(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,22618,a,b,22628,a)].">
      <j1 rule="hyper" parents="64 22618 22628"/>
    </justification>
  </clause>

  <clause id="22638">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (T(z,u) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,20243,a(flip),b,22629,a)].">
      <j1 rule="hyper" parents="64 20243 22629"/>
    </justification>
  </clause>

  <clause id="22639">
    <literal><![CDATA[
      K(x,y * (z \ (u \ 1))) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7104,a(flip),b,22629,a),flip(a)].">
      <j1 rule="hyper" parents="64 7104 22629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22640">
    <literal><![CDATA[
      K(x,y * (z \ (1 / u))) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(82(a,1),22629(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="82 22629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22641">
    <literal><![CDATA[
      K(x,y * (z \ (y \ z))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(5787(a,2),22633(a,2,2))].">
      <j1 rule="para" parents="5787 22633"/>
    </justification>
  </clause>

  <clause id="22642">
    <literal><![CDATA[
      T(x,y * (z \ (y \ z))) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(143,a,22641,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 22641 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22643">
    <literal><![CDATA[
      (x \ ((y \ (x \ y)) \ 1)) \ K(x \ ((y \ (x \ y)) \ 1),K(y,x)) = 1 / (x \ ((y \ (x \ y)) \ 1))
    ]]></literal>
    <justification jstring="[para(22641(a,1),14028(a,1,2))].">
      <j1 rule="para" parents="22641 14028"/>
    </justification>
  </clause>

  <clause id="22644">
    <literal><![CDATA[
      T(x,(y \ (z \ y)) * z) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5125,a,b,22642,a)].">
      <j1 rule="hyper" parents="64 5125 22642"/>
    </justification>
  </clause>

  <clause id="22645">
    <literal><![CDATA[
      T(x,(y \ z) * (z / y)) = T(x,z * (y \ (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22395,a(flip),b,22637,a)].">
      <j1 rule="hyper" parents="64 22395 22637"/>
    </justification>
  </clause>

  <clause id="22646">
    <literal><![CDATA[
      K(x,y * ((z / u) \ (w \ K(z,u)))) = K(x,y / (w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(22465,a,22639,a)].">
      <j1 rule="hyper" parents="22465 22639"/>
    </justification>
  </clause>

  <clause id="22647">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,16325,a(flip),b,22638,a),flip(a)].">
      <j1 rule="hyper" parents="373 16325 22638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22648">
    <literal><![CDATA[
      T(x,y / (z * (u \ 1))) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(143,a,22647,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 22647 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22649">
    <literal><![CDATA[
      K(x,y / (z / u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,22612,a(flip),b,22647,a)].">
      <j1 rule="hyper" parents="64 22612 22647"/>
    </justification>
  </clause>

  <clause id="22650">
    <literal><![CDATA[
      x * K(y,z / (u / w)) = x * K(y,z * (w / u))
    ]]></literal>
    <justification jstring="[hyper(145,a,22649,a,b,9,a)].">
      <j1 rule="hyper" parents="145 22649 9"/>
    </justification>
  </clause>

  <clause id="22651">
    <literal><![CDATA[
      T(x,y / (z / u)) = T(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(143,a,22649,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 22649 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22652">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,21491,a,b,22649,a)].">
      <j1 rule="hyper" parents="64 21491 22649"/>
    </justification>
  </clause>

  <clause id="22654">
    <literal><![CDATA[
      K(x,y \ ((y * z) / u)) = K(x,(z / (y * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17797,a(flip),b,22631,a),flip(a)].">
      <j1 rule="hyper" parents="64 17797 22631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22655">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(22407,a,22627,a),flip(a)].">
      <j1 rule="hyper" parents="22407 22627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22656">
    <literal><![CDATA[
      K(x,(y \ z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,22540,a(flip),b,22655,a)].">
      <j1 rule="hyper" parents="64 22540 22655"/>
    </justification>
  </clause>

  <clause id="22657">
    <literal><![CDATA[
      T(x,(y \ z) \ u) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(143,a,22656,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 22656 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22658">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (u \ (y * z))) = K(x,L(T(z,y),y,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,22075,a(flip),b,22656,a),flip(a)].">
      <j1 rule="hyper" parents="64 22075 22656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22659">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) / (u / w)) = K(z,y / ((u / w) / x))
    ]]></literal>
    <justification jstring="[para(22656(a,1),22070(a,1,1,3))].">
      <j1 rule="para" parents="22656 22070"/>
    </justification>
  </clause>

  <clause id="22660">
    <literal><![CDATA[
      T(x,(T(y,z) / z) * u) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,13606,a,b,22657,a)].">
      <j1 rule="hyper" parents="373 13606 22657"/>
    </justification>
  </clause>

  <clause id="22661">
    <literal><![CDATA[
      T(x,(y \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * u) = w
    ]]></literal>
    <justification jstring="[para(22660(a,1),17811(a,1))].">
      <j1 rule="para" parents="22660 17811"/>
    </justification>
  </clause>

  <clause id="22662">
    <literal><![CDATA[
      K(x,((y * z) / (u * y)) * u) = K(x,u * ((y * u) \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22654,a(flip),b,22632,a)].">
      <j1 rule="hyper" parents="64 22654 22632"/>
    </justification>
  </clause>

  <clause id="22663">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,22429,a(flip),b,22652,a),flip(a)].">
      <j1 rule="hyper" parents="373 22429 22652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22664">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ (u * y))) = K(x,L(T(u,y),y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,19988,a(flip),b,22658,a)].">
      <j1 rule="hyper" parents="64 19988 22658"/>
    </justification>
  </clause>

  <clause id="22665">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,L(T(z,y),y,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,21662,a,b,22664,a)].">
      <j1 rule="hyper" parents="64 21662 22664"/>
    </justification>
  </clause>

  <clause id="22666">
    <literal><![CDATA[
      K(x,(y \ z) * L((y * (y \ z)) \ y,u,w)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,22527,a(flip),b,22630,a)].">
      <j1 rule="hyper" parents="64 22527 22630"/>
    </justification>
  </clause>

  <clause id="22667">
    <literal><![CDATA[
      K(x,(y \ z) * L(z \ y,u,w)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[para(10(a,1),22666(a,1,2,2,1,1))].">
      <j1 rule="para" parents="10 22666"/>
    </justification>
  </clause>

  <clause id="22668">
    <literal><![CDATA[
      K(x,L(y / z,u,w) * (z / y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,20162,a,b,22667,a)].">
      <j1 rule="hyper" parents="64 20162 22667"/>
    </justification>
  </clause>

  <clause id="22670">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) * (w / u)) = K(z,y / ((u / w) / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,22650,a(flip),b,22659,a)].">
      <j1 rule="hyper" parents="64 22650 22659"/>
    </justification>
  </clause>

  <clause id="22671">
    <literal><![CDATA[
      K(x,y / (((z / u) \ 1) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,22566,a(flip),b,22670,a)].">
      <j1 rule="hyper" parents="64 22566 22670"/>
    </justification>
  </clause>

  <clause id="22672">
    <literal><![CDATA[
      K(x,y * (z / ((u / w) \ 1))) = K(x,y / ((w / u) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,22649,a(flip),b,22671,a)].">
      <j1 rule="hyper" parents="64 22649 22671"/>
    </justification>
  </clause>

  <clause id="22673">
    <literal><![CDATA[
      K(x,y / ((z / u) / w)) = K(x,y * (w * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22429,a(flip),b,22672,a),flip(a)].">
      <j1 rule="hyper" parents="64 22429 22672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22674">
    <literal><![CDATA[
      K(x,y * (z / (u / w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22649,a(flip),b,22673,a)].">
      <j1 rule="hyper" parents="64 22649 22673"/>
    </justification>
  </clause>

  <clause id="22675">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,y \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,21604,a(flip),b,22673,a),flip(a)].">
      <j1 rule="hyper" parents="64 21604 22673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22676">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) = K(x,y * ((w / u) \ z))
    ]]></literal>
    <justification jstring="[hyper(21582,a,22674,a),flip(a)].">
      <j1 rule="hyper" parents="21582 22674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22677">
    <literal><![CDATA[
      T(x,y * (z / (u / w))) = T(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(143,a,22674,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 22674 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22678">
    <literal><![CDATA[
      K(x,y \ ((y * z) * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,20042,a(flip),b,22675,a),flip(a)].">
      <j1 rule="hyper" parents="64 20042 22675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22679">
    <literal><![CDATA[
      K(x,y \ ((T(z,y * K(u,w)) * y) * v5)) = K(x,(z * (v5 / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,20533,a,b,22678,a)].">
      <j1 rule="hyper" parents="64 20533 22678"/>
    </justification>
  </clause>

  <clause id="22680">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,u \ ((u * y) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,22541,a(flip),b,22678,a),flip(a)].">
      <j1 rule="hyper" parents="64 22541 22678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22681">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,(y / (u * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,22654,a(flip),b,22680,a),flip(a)].">
      <j1 rule="hyper" parents="373 22654 22680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22682">
    <literal><![CDATA[
      K(x,y * ((z / u) \ w)) = K(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,22309,a(flip),b,22676,a),flip(a)].">
      <j1 rule="hyper" parents="64 22309 22676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22683">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) = K(x,y / (w * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22646,a(flip),b,22682,a),flip(a)].">
      <j1 rule="hyper" parents="64 22646 22682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22684">
    <literal><![CDATA[
      K(x,y / (z * (u \ w))) = K(x,y * ((w \ u) / z))
    ]]></literal>
    <justification jstring="[hyper(22434,a,22683,a),flip(a)].">
      <j1 rule="hyper" parents="22434 22683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22685">
    <literal><![CDATA[
      K(x,L(y / (z \ u),z \ u,z) * ((z \ u) / y)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22139,a(flip),b,22684,a),flip(a)].">
      <j1 rule="hyper" parents="64 22139 22684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22686">
    <literal><![CDATA[
      a(x,y \ z,K(u \ (y \ z),y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,22668,a(flip),b,22685,a)].">
      <j1 rule="hyper" parents="64 22668 22685"/>
    </justification>
  </clause>

  <clause id="22687">
    <literal><![CDATA[
      a(x,y \ z,K(u \ z,y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(15487,a,22686,a)].">
      <j1 rule="hyper" parents="15487 22686"/>
    </justification>
  </clause>

  <clause id="22688">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) = a(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(12163,a,22687,a)].">
      <j1 rule="hyper" parents="12163 22687"/>
    </justification>
  </clause>

  <clause id="22689">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22686,a(flip),b,22688,a),flip(a)].">
      <j1 rule="hyper" parents="64 22686 22688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22690">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(22688(a,1),21152(a,2,2))].">
      <j1 rule="para" parents="22688 21152"/>
    </justification>
  </clause>

  <clause id="22691">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(22688(a,1),21517(a,2,2))].">
      <j1 rule="para" parents="22688 21517"/>
    </justification>
  </clause>

  <clause id="22692">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,16609,a(flip),b,22691,a),flip(a)].">
      <j1 rule="hyper" parents="373 16609 22691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22693">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,21515,a(flip),b,22692,a)].">
      <j1 rule="hyper" parents="64 21515 22692"/>
    </justification>
  </clause>

  <clause id="22694">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(22689(a,1),22693(a,1,2))].">
      <j1 rule="para" parents="22689 22693"/>
    </justification>
  </clause>

  <clause id="22695">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,16609,a,b,22694,a)].">
      <j1 rule="hyper" parents="35 16609 22694"/>
    </justification>
  </clause>

  <clause id="22696">
    <literal><![CDATA[
      x \ (K(y,z) * ((K(z,y) * u) * x)) = T(L(u,y,K(x,z)),x)
    ]]></literal>
    <justification jstring="[para(22694(a,1),21056(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22694 21056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22697">
    <literal><![CDATA[
      x \ (K(y,z) * ((K(z,y) * u) * x)) = T(L(u,z,K(y,x)),x)
    ]]></literal>
    <justification jstring="[para(22694(a,1),21058(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22694 21058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22698">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(22695(a,1),15375(a,1,2))].">
      <j1 rule="para" parents="22695 15375"/>
    </justification>
  </clause>

  <clause id="22699">
    <literal><![CDATA[
      K(x,L(y,z,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(15339,a,22698,a)].">
      <j1 rule="hyper" parents="15339 22698"/>
    </justification>
  </clause>

  <clause id="22702">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,20593,a(flip),b,22699,a),flip(a)].">
      <j1 rule="hyper" parents="373 20593 22699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22704">
    <literal><![CDATA[
      T(x,L(y,z,u)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(143,a,22699,a,b,6406,a)].">
      <j1 rule="hyper" parents="143 22699 6406"/>
    </justification>
  </clause>

  <clause id="22705">
    <literal><![CDATA[
      L(T(x,y),z,K(y,u)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,16636,a,b,22704,a)].">
      <j1 rule="hyper" parents="373 16636 22704"/>
    </justification>
  </clause>

  <clause id="22706">
    <literal><![CDATA[
      T(x,L((y * z) \ u,y,z)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,16161,a(flip),b,22704,a),flip(a)].">
      <j1 rule="hyper" parents="373 16161 22704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22707">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(20602,a,22702,a)].">
      <j1 rule="hyper" parents="20602 22702"/>
    </justification>
  </clause>

  <clause id="22709">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,L(T(z,y),u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,22665,a,b,22702,a)].">
      <j1 rule="hyper" parents="64 22665 22702"/>
    </justification>
  </clause>

  <clause id="22710">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22663,a(flip),b,22702,a),flip(a)].">
      <j1 rule="hyper" parents="64 22663 22702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22711">
    <literal><![CDATA[
      K(x,L(y,z,u * z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22702,a(flip),b,22707,a),flip(a)].">
      <j1 rule="hyper" parents="64 22702 22707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22712">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22558,a(flip),b,22711,a),flip(a)].">
      <j1 rule="hyper" parents="64 22558 22711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22713">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = x * K(z,L(T(u,y),x,y))
    ]]></literal>
    <justification jstring="[para(22711(a,1),21833(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22711 21833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22714">
    <literal><![CDATA[
      T(x,y \ (z \ (y * u))) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16162,a(flip),b,22706,a),flip(a)].">
      <j1 rule="hyper" parents="64 16162 22706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22715">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(10(a,1),22714(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 22714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22716">
    <literal><![CDATA[
      T(x,((y \ 1) * (y \ T(z,y))) \ u) = T(x,y \ (((y * y) \ z) \ (y * u)))
    ]]></literal>
    <justification jstring="[para(1146(a,2),22714(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1146 22714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22717">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,(z \ 1) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,14479,a,b,22715,a),flip(a)].">
      <j1 rule="hyper" parents="373 14479 22715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22718">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19983,a(flip),b,22715,a)].">
      <j1 rule="hyper" parents="64 19983 22715"/>
    </justification>
  </clause>

  <clause id="22719">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ u)) = T(x,T(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16840,a(flip),b,22715,a),flip(a)].">
      <j1 rule="hyper" parents="64 16840 22715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22720">
    <literal><![CDATA[
      T(x,L(T(y,z),u,w) \ (z \ v5)) = T(x,z \ (L(y,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(25(a,2),22715(a,1,2,1))].">
      <j1 rule="para" parents="25 22715"/>
    </justification>
  </clause>

  <clause id="22721">
    <literal><![CDATA[
      T(x,L(y,z,u) \ (y \ w)) = T(x,y \ (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(198(a,1),22715(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="198 22715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22722">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(22717(a,2),14732(a,1))].">
      <j1 rule="para" parents="22717 14732"/>
    </justification>
  </clause>

  <clause id="22723">
    <literal><![CDATA[
      T(x,T(y,z) * (z \ u)) = T(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22546,a(flip),b,22719,a),flip(a)].">
      <j1 rule="hyper" parents="64 22546 22719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22724">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,z * y) \ w)) = T(x,u \ ((y \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,20290,a(flip),b,22723,a)].">
      <j1 rule="hyper" parents="64 20290 22723"/>
    </justification>
  </clause>

  <clause id="22725">
    <literal><![CDATA[
      K(x,y \ ((z * y) * u)) = K(x,(y \ z) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22710,a(flip),b,22712,a),flip(a)].">
      <j1 rule="hyper" parents="64 22710 22712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22726">
    <literal><![CDATA[
      K(x,(y \ T(z,y * K(u,w))) * (y * v5)) = K(x,(z * (v5 / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,22679,a(flip),b,22725,a),flip(a)].">
      <j1 rule="hyper" parents="64 22679 22725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22727">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(19983(a,1),22722(a,1))].">
      <j1 rule="para" parents="19983 22722"/>
    </justification>
  </clause>

  <clause id="22728">
    <literal><![CDATA[
      T(x,(y \ z) \ (T(u,y * z) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ ((y \ z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(20289(a,1),22727(a,1))].">
      <j1 rule="para" parents="20289 22727"/>
    </justification>
  </clause>

  <clause id="22729">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(22690(a,2),16641(a,1))].">
      <j1 rule="para" parents="22690 16641"/>
    </justification>
  </clause>

  <clause id="22730">
    <literal><![CDATA[
      L(x,y,K(z,u)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(41,a,22696,a(flip),b,22697,a(flip))].">
      <j1 rule="hyper" parents="41 22696 22697"/>
    </justification>
  </clause>

  <clause id="22731">
    <literal><![CDATA[
      L(T(x,y),y,K(z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,22705,a(flip),b,22730,a),flip(a)].">
      <j1 rule="hyper" parents="373 22705 22730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22732">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * (y * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,22532,a(flip),b,22726,a)].">
      <j1 rule="hyper" parents="64 22532 22726"/>
    </justification>
  </clause>

  <clause id="22733">
    <literal><![CDATA[
      K(x,(y * (z / u)) * u) = K(x,(y / u) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(16361,a,22732,a),flip(a)].">
      <j1 rule="hyper" parents="16361 22732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22734">
    <literal><![CDATA[
      K(x,(y / z) * (z * (u \ 1))) = K(x,(y / (z * u)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,22681,a(flip),b,22733,a),flip(a)].">
      <j1 rule="hyper" parents="64 22681 22733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22735">
    <literal><![CDATA[
      K(x,(y / (z * u)) * z) = K(x,(y / z) * (z / u))
    ]]></literal>
    <justification jstring="[hyper(22432,a,22734,a),flip(a)].">
      <j1 rule="hyper" parents="22432 22734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22736">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,u * ((y * u) \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22662,a(flip),b,22735,a),flip(a)].">
      <j1 rule="hyper" parents="64 22662 22735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22737">
    <literal><![CDATA[
      K(x,y * ((z * y) \ (u * z))) = K(x,L(T(u,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,22709,a(flip),b,22736,a),flip(a)].">
      <j1 rule="hyper" parents="64 22709 22736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22738">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u)) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(22737(a,1),22634(a,1,2))].">
      <j1 rule="para" parents="22737 22634"/>
    </justification>
  </clause>

  <clause id="22739">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,22713,a,b,22738,a)].">
      <j1 rule="hyper" parents="64 22713 22738"/>
    </justification>
  </clause>

  <clause id="22740">
    <literal><![CDATA[
      (x * y) / (y * K(T(z,y),u)) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,21293,a(flip),b,22739,a),flip(a)].">
      <j1 rule="hyper" parents="64 21293 22739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22741">
    <literal><![CDATA[
      (x / (y \ 1)) * (y \ K(z,u)) = (x * y) / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(7437(a,1),22740(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7437 22740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22742">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x / z) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(21942,a,22741,a),flip(a)].">
      <j1 rule="hyper" parents="21942 22741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22743">
    <literal><![CDATA[
      (x * (T(y,z) / u)) / (y / u) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,22046,a(flip),b,22742,a)].">
      <j1 rule="hyper" parents="64 22046 22742"/>
    </justification>
  </clause>

  <clause id="22744">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = L(x,K(u,z),y \ z)
    ]]></literal>
    <justification jstring="[para(22743(a,1),22060(a,1,1))].">
      <j1 rule="para" parents="22743 22060"/>
    </justification>
  </clause>

  <clause id="22745">
    <literal><![CDATA[
      L(x,K(y,z),u \ z) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(22729,a,22744,a),flip(a)].">
      <j1 rule="hyper" parents="22729 22744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22746">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,20983,a(flip),b,22745,a),flip(a)].">
      <j1 rule="hyper" parents="64 20983 22745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22747">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(13062,a,22746,a),flip(a)].">
      <j1 rule="hyper" parents="13062 22746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22750">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,22730,a,b,22747,a),flip(a)].">
      <j1 rule="hyper" parents="373 22730 22747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22751">
    <literal><![CDATA[
      L(x,K(y,z),u) = T(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,16603,a(flip),b,22747,a),flip(a)].">
      <j1 rule="hyper" parents="373 16603 22747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22752">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,K(y,x),z) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,22750,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="145 22750 18"/>
    </justification>
  </clause>

  <clause id="22753">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (K(u,z) * y) = (x * K(u,z)) * y
    ]]></literal>
    <justification jstring="[para(22750(a,1),18812(a,1,1))].">
      <j1 rule="para" parents="22750 18812"/>
    </justification>
  </clause>

  <clause id="22754">
    <literal><![CDATA[
      T(x,y * (z * L(u,K(w,v5),v6))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(22751(a,2),19562(a,1,2,2,2))].">
      <j1 rule="para" parents="22751 19562"/>
    </justification>
  </clause>

  <clause id="22755">
    <literal><![CDATA[
      x * (K(y,T(z,x)) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11841,a(flip),b,22752,a)].">
      <j1 rule="hyper" parents="64 11841 22752"/>
    </justification>
  </clause>

  <clause id="22756">
    <literal><![CDATA[
      x \ (K(y,z) * (x * u)) = K(y,T(z,x)) * u
    ]]></literal>
    <justification jstring="[hyper(139,a,22752,a(flip),b,11841,a(flip))].">
      <j1 rule="hyper" parents="139 22752 11841"/>
    </justification>
  </clause>

  <clause id="22757">
    <literal><![CDATA[
      x * (K(y,z) * K(u,T(w,x))) = K(u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(17149,a,22755,a)].">
      <j1 rule="hyper" parents="17149 22755"/>
    </justification>
  </clause>

  <clause id="22758">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ u) = z \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,22755,a),flip(a)].">
      <j1 rule="hyper" parents="139 168 22755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22759">
    <literal><![CDATA[
      K(x / y,z) * (y * u) = y * (K(y \ x,z) * u)
    ]]></literal>
    <justification jstring="[para(7917(a,1),22755(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7917 22755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22760">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(8203(a,1),22755(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8203 22755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22761">
    <literal><![CDATA[
      K(x,y) * (z * z) = z * (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(8193(a,1),22755(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8193 22755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22762">
    <literal><![CDATA[
      K(x,y \ z) * (y * u) = y * (K(x,z / y) * u)
    ]]></literal>
    <justification jstring="[para(8216(a,1),22755(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8216 22755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22763">
    <literal><![CDATA[
      K(x * y,z) * (x * u) = x * (K(y * x,z) * u)
    ]]></literal>
    <justification jstring="[para(11177(a,1),22755(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11177 22755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22764">
    <literal><![CDATA[
      K(x * y,z) * (y * u) = y * (K(y * x,z) * u)
    ]]></literal>
    <justification jstring="[para(11180(a,1),22755(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11180 22755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22765">
    <literal><![CDATA[
      K(x,y) * ((z \ (z \ 1)) * u) = (z \ (z \ 1)) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(17032(a,1),22755(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17032 22755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22766">
    <literal><![CDATA[
      K(x,y) * (z * T(z,u)) = z * (T(z,u) * K(x,y))
    ]]></literal>
    <justification jstring="[para(17108(a,1),22755(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17108 22755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22767">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) * v5) = a(z,u,w) * (K(x,y) * v5)
    ]]></literal>
    <justification jstring="[para(19211(a,1),22755(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19211 22755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22768">
    <literal><![CDATA[
      x * (K(y,z) * (u * u)) = x * (u * (u * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(145,a,22761,a,b,9,a)].">
      <j1 rule="hyper" parents="145 22761 9"/>
    </justification>
  </clause>

  <clause id="22769">
    <literal><![CDATA[
      K(x,T(y,z)) * (L(z,u,w) * (z \ v5)) = z \ (K(x,y) * (L(z,u,w) * v5))
    ]]></literal>
    <justification jstring="[para(2327(a,1),22756(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2327 22756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22770">
    <literal><![CDATA[
      T(x,y) \ (K(x,z) * u) = K(x,z) * (T(x,y) \ u)
    ]]></literal>
    <justification jstring="[para(7467(a,1),22758(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7467 22758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22771">
    <literal><![CDATA[
      x \ (K(y,T(z,x)) * u) = K(y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(8203(a,1),22758(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8203 22758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22772">
    <literal><![CDATA[
      x \ (K(y,x * z) * u) = K(y,z * x) * (x \ u)
    ]]></literal>
    <justification jstring="[para(11113(a,1),22758(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11113 22758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22773">
    <literal><![CDATA[
      K(x,T(y,z)) * ((1 / z) \ u) = (1 / z) \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(11167(a,1),22758(a,1,1))].">
      <j1 rule="para" parents="11167 22758"/>
    </justification>
  </clause>

  <clause id="22774">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * v5) = K(u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(19211(a,1),22758(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19211 22758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22775">
    <literal><![CDATA[
      K(x,T(y,z)) * (L(z,u,w) \ v5) = L(z,u,w) \ (K(x,y) * v5)
    ]]></literal>
    <justification jstring="[para(19254(a,1),22758(a,1,1))].">
      <j1 rule="para" parents="19254 22758"/>
    </justification>
  </clause>

  <clause id="22776">
    <literal><![CDATA[
      x * (K(y,z) * (x \ u)) = K(y,T(z,x)) * u
    ]]></literal>
    <justification jstring="[hyper(397,a,22760,a),flip(a)].">
      <j1 rule="hyper" parents="397 22760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22777">
    <literal><![CDATA[
      K(x,y) * (T(z,K(y,x)) * u) = z * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,9249,a(flip),b,22760,a)].">
      <j1 rule="hyper" parents="64 9249 22760"/>
    </justification>
  </clause>

  <clause id="22778">
    <literal><![CDATA[
      K(x,T(y,1 / T(z,u))) * K(u,z) = (1 / T(z,u)) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(5788(a,2),22760(a,1,2))].">
      <j1 rule="para" parents="5788 22760"/>
    </justification>
  </clause>

  <clause id="22779">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * (u \ K(u,K(x,y) * z)) = (K(x,T(y,u)) * (u * z)) * (u \ 1)
    ]]></literal>
    <justification jstring="[para(22760(a,2),10839(a,2,1))].">
      <j1 rule="para" parents="22760 10839"/>
    </justification>
  </clause>

  <clause id="22780">
    <literal><![CDATA[
      K(x,T(y,z)) * (L(z,u,w) * v5) = L(z,u,w) * (K(x,y) * v5)
    ]]></literal>
    <justification jstring="[para(19254(a,1),22760(a,1,1))].">
      <j1 rule="para" parents="19254 22760"/>
    </justification>
  </clause>

  <clause id="22781">
    <literal><![CDATA[
      K(x,y) * (z \ (z \ 1)) = z \ (z \ K(x,y))
    ]]></literal>
    <justification jstring="[para(14665(a,1),22771(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14665 22771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22782">
    <literal><![CDATA[
      R(x,y,z) \ (K(u,T(w,x)) * v5) = K(u,w) * (R(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(19277(a,1),22771(a,1,2,1))].">
      <j1 rule="para" parents="19277 22771"/>
    </justification>
  </clause>

  <clause id="22784">
    <literal><![CDATA[
      K(x,y) * ((z \ (z \ 1)) * u) = (z \ (z \ K(x,y))) * u
    ]]></literal>
    <justification jstring="[para(22781(a,1),1610(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22781 1610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22785">
    <literal><![CDATA[
      K(x,y \ (T(y,z) \ 1)) = K(x,y \ (y \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(22781(a,1),19941(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22781 19941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22786">
    <literal><![CDATA[
      T(x * y,z) \ (x * (K(y * x,z) * u)) = L(y \ u,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,22763,a(flip),b,6134,a)].">
      <j1 rule="hyper" parents="139 22763 6134"/>
    </justification>
  </clause>

  <clause id="22787">
    <literal><![CDATA[
      x * (K(x * y,z) * K(y,x)) = T(y * x,z) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,14826,a(flip),b,22764,a),flip(a)].">
      <j1 rule="hyper" parents="64 14826 22764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22788">
    <literal><![CDATA[
      K(x,y) * (z * (K(y,x) * u)) = T(z,K(x,y)) * u
    ]]></literal>
    <justification jstring="[hyper(6187,a,22777,a)].">
      <j1 rule="hyper" parents="6187 22777"/>
    </justification>
  </clause>

  <clause id="22789">
    <literal><![CDATA[
      K(x,y) * (T(z,K(y,x)) \ u) = z \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(759,a,22777,a),flip(a)].">
      <j1 rule="hyper" parents="759 22777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22790">
    <literal><![CDATA[
      T(x,K(y,z)) * (K(y,z) * u) = K(y,z) * (x * u)
    ]]></literal>
    <justification jstring="[para(7825(a,1),22777(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7825 22777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22792">
    <literal><![CDATA[
      x * (K(y,x) * K(x * y,z)) = T(y * x,z) / y
    ]]></literal>
    <justification jstring="[hyper(17149,a,22787,a)].">
      <j1 rule="hyper" parents="17149 22787"/>
    </justification>
  </clause>

  <clause id="22793">
    <literal><![CDATA[
      K(x,y) * ((1 / T(z,u)) * (K(y,x) * z)) = z * T(T(z,u) \ 1,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,3990,a(flip),b,22788,a),flip(a)].">
      <j1 rule="hyper" parents="373 3990 22788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22795">
    <literal><![CDATA[
      T(x,K(y,z)) \ (K(y,z) * u) = K(y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(7825(a,1),22789(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7825 22789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22796">
    <literal><![CDATA[
      K(x,y) * (T(z,K(x,y)) \ u) = z \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(8153(a,1),22789(a,1,2,1))].">
      <j1 rule="para" parents="8153 22789"/>
    </justification>
  </clause>

  <clause id="22797">
    <literal><![CDATA[
      K(x \ y,x) * (T(z,K(x,y)) \ u) = z \ (K(x \ y,x) * u)
    ]]></literal>
    <justification jstring="[para(8706(a,1),22789(a,1,2,1))].">
      <j1 rule="para" parents="8706 22789"/>
    </justification>
  </clause>

  <clause id="22798">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z) * u) = L(T(x,u),u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(269,a,22790,a,b,588,a)].">
      <j1 rule="hyper" parents="269 22790 588"/>
    </justification>
  </clause>

  <clause id="22799">
    <literal><![CDATA[
      T(x,T(K(y,z) * (u * w),v5)) = T(x,T(u * (K(y,z) * w),v5))
    ]]></literal>
    <justification jstring="[para(22790(a,1),18042(a,1,2,1))].">
      <j1 rule="para" parents="22790 18042"/>
    </justification>
  </clause>

  <clause id="22800">
    <literal><![CDATA[
      T(x * (K((y \ z) \ 1,x) * K(x * ((y \ z) \ 1),u)),z \ y) = ((y \ z) \ 1) \ T(((y \ z) \ 1) * x,u)
    ]]></literal>
    <justification jstring="[para(22792(a,2),6725(a,1,1))].">
      <j1 rule="para" parents="22792 6725"/>
    </justification>
  </clause>

  <clause id="22801">
    <literal><![CDATA[
      x \ (K(y,z) * (K(y,z) * u)) = K(y,z) * (K(y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[para(22795(a,1),22796(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22795 22796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22802">
    <literal><![CDATA[
      (x * y) * K(z,T(u,y)) = (x * K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,22598,a(flip),b,22753,a)].">
      <j1 rule="hyper" parents="64 22598 22753"/>
    </justification>
  </clause>

  <clause id="22803">
    <literal><![CDATA[
      K(x,(y * z) \ (u * z)) = K(x,T(y \ u,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,16218,a,b,22802,a)].">
      <j1 rule="hyper" parents="35 16218 22802"/>
    </justification>
  </clause>

  <clause id="22806">
    <literal><![CDATA[
      T(x,T(y,(z * K(u,w)) * v5) * ((z * v5) / (1 / K(u,T(w,v5))))) = T(x,((z * v5) / (1 / K(u,T(w,v5)))) * y)
    ]]></literal>
    <justification jstring="[para(22802(a,1),14612(a,1,2,1,2))].">
      <j1 rule="para" parents="22802 14612"/>
    </justification>
  </clause>

  <clause id="22808">
    <literal><![CDATA[
      K(x * x,(y * z) \ (u * z)) = K(x * x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,17051,a(flip),b,22803,a),flip(a)].">
      <j1 rule="hyper" parents="373 17051 22803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22809">
    <literal><![CDATA[
      K(x,T((y / z) \ u,z)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(12(a,1),22803(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 22803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22811">
    <literal><![CDATA[
      K(x / y,(z / y) \ u) = K(y \ x,z \ (u * y))
    ]]></literal>
    <justification jstring="[hyper(8322,a,22809,a)].">
      <j1 rule="hyper" parents="8322 22809"/>
    </justification>
  </clause>

  <clause id="22812">
    <literal><![CDATA[
      K(x * x,x \ y) = K(x * x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7726,a(flip),b,22808,a),flip(a)].">
      <j1 rule="hyper" parents="64 7726 22808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22813">
    <literal><![CDATA[
      (x \ y) * K(x * x,y * x) = T(x \ y,x \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(22812(a,1),15870(a,2,2)),flip(a)].">
      <j1 rule="para" parents="22812 15870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22814">
    <literal><![CDATA[
      x * K(y \ z,z \ (x * y)) = (z / y) * (x / (z / y))
    ]]></literal>
    <justification jstring="[hyper(145,a,22811,a(flip),b,5961,a)].">
      <j1 rule="hyper" parents="145 22811 5961"/>
    </justification>
  </clause>

  <clause id="22816">
    <literal><![CDATA[
      x * ((y * T(y \ z,(u / y) \ w)) / z) = x * K(y \ z,u \ (w * y))
    ]]></literal>
    <justification jstring="[para(22811(a,1),6357(a,2,2))].">
      <j1 rule="para" parents="22811 6357"/>
    </justification>
  </clause>

  <clause id="22817">
    <literal><![CDATA[
      T(x,y * ((z * K(u,w)) * v5)) = T(x,y * (z * (K(u,w) * v5)))
    ]]></literal>
    <justification jstring="[para(100(a,1),22754(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="100 22754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22818">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z) * u) = T(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,22731,a(flip),b,22798,a),flip(a)].">
      <j1 rule="hyper" parents="373 22731 22798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22820">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(8153(a,1),22818(a,1,1))].">
      <j1 rule="para" parents="8153 22818"/>
    </justification>
  </clause>

  <clause id="22821">
    <literal><![CDATA[
      T(T(x,K(y,z)),L(u,y,z)) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(8157(a,1),22818(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8157 22818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22822">
    <literal><![CDATA[
      T(T(T(x,L(y,z,u)),K(u,z)),K(z,u) * y) \ w = K(L(y,z,u),x) * (T(x,L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(22820(a,2),6299(a,2,1)),flip(a)].">
      <j1 rule="para" parents="22820 6299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22823">
    <literal><![CDATA[
      x * (K(x \ y,x) * K(y,T(z,x))) = T(y,z) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,14827,a(flip),b,22757,a),flip(a)].">
      <j1 rule="hyper" parents="373 14827 22757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22824">
    <literal><![CDATA[
      x * (a(y,z,u) * (K(x,w) * v5)) = T(x,w) * (a(y,z,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(145,a,22767,a(flip),b,6071,a)].">
      <j1 rule="hyper" parents="145 22767 6071"/>
    </justification>
  </clause>

  <clause id="22825">
    <literal><![CDATA[
      (x \ y) * K(x * x,y * x) = T(y / x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,14817,a(flip),b,22813,a),flip(a)].">
      <j1 rule="hyper" parents="373 14817 22813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22826">
    <literal><![CDATA[
      x * (y \ T((x \ y) * x,z)) = T(y,z) / (y / x)
    ]]></literal>
    <justification jstring="[para(11296(a,1),22823(a,1,2))].">
      <j1 rule="para" parents="11296 22823"/>
    </justification>
  </clause>

  <clause id="22827">
    <literal><![CDATA[
      (x \ 1) * (y \ (x \ T(y * x,x \ 1))) = T(y,x) / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(5475(a,1),22826(a,1,2,2))].">
      <j1 rule="para" parents="5475 22826"/>
    </justification>
  </clause>

  <clause id="22828">
    <literal><![CDATA[
      T(x * y,z) \ (x * K(y * x,z)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(8(a,1),22786(a,1,2,2))].">
      <j1 rule="para" parents="8 22786"/>
    </justification>
  </clause>

  <clause id="22829">
    <literal><![CDATA[
      (((x \ 1) \ x) * y) \ (K(z,u) * w) = y \ (K(z,u) * ((x \ (x \ 1)) * w))
    ]]></literal>
    <justification jstring="[hyper(139,a,22765,a,b,1553,a),flip(a)].">
      <j1 rule="hyper" parents="139 22765 1553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22830">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ (L(z,u,w) \ v5)) = L(z,u,w) \ (K(x,y) * (z \ v5))
    ]]></literal>
    <justification jstring="[para(2339(a,1),22775(a,1,2))].">
      <j1 rule="para" parents="2339 22775"/>
    </justification>
  </clause>

  <clause id="22832">
    <literal><![CDATA[
      R(T(x,y),z,u) \ (K(w,T(v5,T(x,y))) * x) = K(w,v5) * (x / R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(11430(a,2),22782(a,2,2))].">
      <j1 rule="para" parents="11430 22782"/>
    </justification>
  </clause>

  <clause id="22833">
    <literal><![CDATA[
      T(x,T(y * (K(z \ u,z) * w),v5)) = T(x,T(K(z,u) * (y * w),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18525,a(flip),b,22799,a),flip(a)].">
      <j1 rule="hyper" parents="64 18525 22799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22834">
    <literal><![CDATA[
      x \ (y * (T(T(y,z),z) \ u)) = K(z,y) * (K(z,y) * (x \ u))
    ]]></literal>
    <justification jstring="[para(7247(a,1),22801(a,1,2))].">
      <j1 rule="para" parents="7247 22801"/>
    </justification>
  </clause>

  <clause id="22835">
    <literal><![CDATA[
      x \ (y * (T(T(y,z),z) \ u)) = y * (T(T(y,z),z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,7247,a(flip),b,22834,a),flip(a)].">
      <j1 rule="hyper" parents="373 7247 22834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22836">
    <literal><![CDATA[
      K(x,T(y,T(z,u) \ 1)) * K(u,z) = (1 / T(z,u)) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(3870(a,1),22778(a,1,1,2))].">
      <j1 rule="para" parents="3870 22778"/>
    </justification>
  </clause>

  <clause id="22837">
    <literal><![CDATA[
      (x \ 1) * (K(y,x) * K(y * x,x \ 1)) = T(y,x) / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(15096(a,1),22827(a,1,2))].">
      <j1 rule="para" parents="15096 22827"/>
    </justification>
  </clause>

  <clause id="22838">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) * K(u,z) = (1 / T(z,u)) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(18244(a,1),22836(a,1,1))].">
      <j1 rule="para" parents="18244 22836"/>
    </justification>
  </clause>

  <clause id="22839">
    <literal><![CDATA[
      (1 / T(x,y)) * (K(z,u) * x) = K(z,T(u,x)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(11157(a,1),22838(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11157 22838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22841">
    <literal><![CDATA[
      (1 / T(x,y)) * (K(z,u) * x) = T(K(z,u) * K(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,7900,a,b,22839,a),flip(a)].">
      <j1 rule="hyper" parents="373 7900 22839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22842">
    <literal><![CDATA[
      ((x * y) * (y \ 1)) / (y * x) = T(x,y) / (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,17318,a(flip),b,22837,a)].">
      <j1 rule="hyper" parents="64 17318 22837"/>
    </justification>
  </clause>

  <clause id="22843">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y * x) = T(x,y) / (x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(297(a,1),22842(a,1,1))].">
      <j1 rule="para" parents="297 22842"/>
    </justification>
  </clause>

  <clause id="22844">
    <literal><![CDATA[
      T(x,(y \ z) * (T(u,z * y) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ ((z \ y) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(22657(a,1),22728(a,1))].">
      <j1 rule="para" parents="22657 22728"/>
    </justification>
  </clause>

  <clause id="22845">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ w)) = T(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(22844,a,22724,a)].">
      <j1 rule="hyper" parents="22844 22724"/>
    </justification>
  </clause>

  <clause id="22846">
    <literal><![CDATA[
      T(x,(y \ z) \ ((u \ w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,(z \ y) * ((w \ u) * v5)) = v6
    ]]></literal>
    <justification jstring="[para(22845(a,2),22661(a,1))].">
      <j1 rule="para" parents="22845 22661"/>
    </justification>
  </clause>

  <clause id="22847">
    <literal><![CDATA[
      T(x,((y \ 1) * (y \ T(z,y))) \ u) = T(x,y \ (z \ ((y * y) * (y * u))))
    ]]></literal>
    <justification jstring="[para(804(a,1),22716(a,2,2,2))].">
      <j1 rule="para" parents="804 22716"/>
    </justification>
  </clause>

  <clause id="22848">
    <literal><![CDATA[
      x \ (K(y,z) * (L(x,u,w) * v5)) = L(x,u,w) * (K(y,z) * (x \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,22780,a(flip),b,22769,a),flip(a)].">
      <j1 rule="hyper" parents="64 22780 22769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22849">
    <literal><![CDATA[
      K(x,y) * T(K(y,x) * K(z,u),u) = u * T(T(u,z) \ 1,K(x,y))
    ]]></literal>
    <justification jstring="[para(22841(a,1),22793(a,1,2))].">
      <j1 rule="para" parents="22841 22793"/>
    </justification>
  </clause>

  <clause id="22850">
    <literal><![CDATA[
      L(x,y,z) \ (K(u,w) * (x \ v5)) = x \ (K(u,w) * (L(x,y,z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,22758,a(flip),b,22830,a),flip(a)].">
      <j1 rule="hyper" parents="64 22758 22830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22851">
    <literal><![CDATA[
      T(x,((y \ 1) * (y \ T(z,y))) \ u) = T(x,y * (y * (y \ (z \ (y * u)))))
    ]]></literal>
    <justification jstring="[hyper(373,a,20304,a(flip),b,22847,a),flip(a)].">
      <j1 rule="hyper" parents="373 20304 22847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22852">
    <literal><![CDATA[
      T(x,((y \ 1) * (y \ T(z,y))) \ u) = T(x,y * (z \ (y * u)))
    ]]></literal>
    <justification jstring="[para(10(a,1),22851(a,2,2,2))].">
      <j1 rule="para" parents="10 22851"/>
    </justification>
  </clause>

  <clause id="22854">
    <literal><![CDATA[
      T(x,T((y * y) \ z,y) \ u) = T(x,y * (z \ (y * u)))
    ]]></literal>
    <justification jstring="[para(1146(a,1),22852(a,1,2,1))].">
      <j1 rule="para" parents="1146 22852"/>
    </justification>
  </clause>

  <clause id="22855">
    <literal><![CDATA[
      T(x,y * (y * (T(z,y) \ u))) = T(x,y * (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22403,a(flip),b,22854,a)].">
      <j1 rule="hyper" parents="64 22403 22854"/>
    </justification>
  </clause>

  <clause id="22856">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z \ (u * u),u)) = T(x,u * (z \ (u * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,21646,a,b,22855,a)].">
      <j1 rule="hyper" parents="64 21646 22855"/>
    </justification>
  </clause>

  <clause id="22857">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / (u \ (z / u))) = T(x,u * (z \ (u * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22622,a(flip),b,22856,a)].">
      <j1 rule="hyper" parents="64 22622 22856"/>
    </justification>
  </clause>

  <clause id="22858">
    <literal><![CDATA[
      T(x,(y \ (z / y)) \ u) = T(x,y * (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,20204,a(flip),b,22857,a)].">
      <j1 rule="hyper" parents="64 20204 22857"/>
    </justification>
  </clause>

  <clause id="22859">
    <literal><![CDATA[
      T(x,((y / z) \ z) * u) = T(x,z * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(22661,a,22858,a)].">
      <j1 rule="hyper" parents="22661 22858"/>
    </justification>
  </clause>

  <clause id="22860">
    <literal><![CDATA[
      R(T(x,y),z,u) \ (K(w,T(v5,x)) * x) = K(w,v5) * (x / R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(17093(a,1),22832(a,1,2,1))].">
      <j1 rule="para" parents="17093 22832"/>
    </justification>
  </clause>

  <clause id="22861">
    <literal><![CDATA[
      R(T(x,y),z,u) \ (x * K(w,v5)) = K(w,v5) * (x / R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(8193(a,1),22860(a,1,2))].">
      <j1 rule="para" parents="8193 22860"/>
    </justification>
  </clause>

  <clause id="22863">
    <literal><![CDATA[
      T(T(T(x,L(y,z,u)),K(u,z)),K(z,u) * y) \ w = K(y,L(x,z,u)) * (T(x,L(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(12093(a,1),22822(a,2,1))].">
      <j1 rule="para" parents="12093 22822"/>
    </justification>
  </clause>

  <clause id="22864">
    <literal><![CDATA[
      T(T(T(x,L(y,z,u)),K(u,z)),K(z,u) * y) \ w = T(T(x,y),y) \ w
    ]]></literal>
    <justification jstring="[hyper(373,a,16713,a(flip),b,22863,a),flip(a)].">
      <j1 rule="hyper" parents="373 16713 22863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22866">
    <literal><![CDATA[
      T(T(T(x,K(y,z)),L(u,y,z)),K(y,z) * u) \ w = T(T(x,u),u) \ w
    ]]></literal>
    <justification jstring="[para(8159(a,2),22864(a,1,1,1))].">
      <j1 rule="para" parents="8159 22864"/>
    </justification>
  </clause>

  <clause id="22867">
    <literal><![CDATA[
      T(T(x,K(y,z) * u),K(y,z) * u) \ w = T(T(x,u),u) \ w
    ]]></literal>
    <justification jstring="[para(22821(a,1),22866(a,1,1,1))].">
      <j1 rule="para" parents="22821 22866"/>
    </justification>
  </clause>

  <clause id="22868">
    <literal><![CDATA[
      K(K(x,y) * z,u) * K(K(x,y) * z,u) = T(T(u,z),z) \ u
    ]]></literal>
    <justification jstring="[hyper(7565,a,22867,a)].">
      <j1 rule="hyper" parents="7565 22867"/>
    </justification>
  </clause>

  <clause id="22869">
    <literal><![CDATA[
      K(K(x,y) * z,u) * K(K(x,y) * z,u) = K(z,u) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6606,a(flip),b,22868,a),flip(a)].">
      <j1 rule="hyper" parents="373 6606 22868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22870">
    <literal><![CDATA[
      K(x,y) * (z * (K(z,u) * K(z,u))) = T(T(K(x,y) * z,u),u)
    ]]></literal>
    <justification jstring="[para(22869(a,1),16771(a,1,2,2))].">
      <j1 rule="para" parents="22869 16771"/>
    </justification>
  </clause>

  <clause id="22871">
    <literal><![CDATA[
      K(x,y) * (T(z,u) * K(z,u)) = T(T(K(x,y) * z,u),u)
    ]]></literal>
    <justification jstring="[para(5776(a,1),22870(a,1,2))].">
      <j1 rule="para" parents="5776 22870"/>
    </justification>
  </clause>

  <clause id="22873">
    <literal><![CDATA[
      T(T(K(x,y) * z,u),u) = K(x,y) * T(T(z,u),u)
    ]]></literal>
    <justification jstring="[para(6113(a,1),22871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6113 22871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22874">
    <literal><![CDATA[
      T(x,(y \ z) * T(T(K(y,T(y \ z,u)) * (y \ z),u),u)) = T(x,T(y \ z,u) * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(22873(a,2),18837(a,1,2,2))].">
      <j1 rule="para" parents="22873 18837"/>
    </justification>
  </clause>

  <clause id="22875">
    <literal><![CDATA[
      (x \ ((y \ (x \ y)) \ 1)) \ K(y,K(x \ ((y \ (x \ y)) \ 1),x)) = 1 / (x \ ((y \ (x \ y)) \ 1))
    ]]></literal>
    <justification jstring="[para(8108(a,1),22643(a,1,2))].">
      <j1 rule="para" parents="8108 22643"/>
    </justification>
  </clause>

  <clause id="22876">
    <literal><![CDATA[
      T(x,(y \ z) * T(T((y \ z) * K(y,T(y \ z,u)),u),u)) = T(x,T(y \ z,u) * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(4011(a,1),22874(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4011 22874"/>
    </justification>
  </clause>

  <clause id="22877">
    <literal><![CDATA[
      T(x,(y \ z) * T(T(T(z / y,K(z,u)),u),u)) = T(x,T(y \ z,u) * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(21106(a,1),22876(a,1,2,2,1,1))].">
      <j1 rule="para" parents="21106 22876"/>
    </justification>
  </clause>

  <clause id="22878">
    <literal><![CDATA[
      T(x,(y \ z) * T(T(T(z / y,u),K(z,u)),u)) = T(x,T(y \ z,u) * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(23(a,1),22877(a,1,2,2,1))].">
      <j1 rule="para" parents="23 22877"/>
    </justification>
  </clause>

  <clause id="22879">
    <literal><![CDATA[
      T(x,T(y \ z,u) * T(z / y,u)) = T(x,(y \ z) * T(T(z / y,u),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17989,a(flip),b,22878,a),flip(a)].">
      <j1 rule="hyper" parents="64 17989 22878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22881">
    <literal><![CDATA[
      T(x,T(y \ z,u) * T(z / y,u)) = T(x,(y \ z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(373,a,15806,a(flip),b,22879,a),flip(a)].">
      <j1 rule="hyper" parents="373 15806 22879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22883">
    <literal><![CDATA[
      T(x,T(y \ z,u) * T(z / y,u)) = T(x,z * (y \ (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,22645,a(flip),b,22881,a),flip(a)].">
      <j1 rule="hyper" parents="373 22645 22881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22884">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(T(x,z * (y \ (y \ z))),(y \ z) \ ((y \ z) \ w))
    ]]></literal>
    <justification jstring="[para(22883(a,1),20029(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22883 20029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22885">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(T(x,z * (y \ (y \ z))),(z \ y) * ((z \ y) * w))
    ]]></literal>
    <justification jstring="[hyper(22846,a,22884,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="22846 22884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22887">
    <literal><![CDATA[
      T(x * (K(y \ z,x) * K(x * ((z \ y) \ 1),u)),y \ z) = ((z \ y) \ 1) \ T(((z \ y) \ 1) * x,u)
    ]]></literal>
    <justification jstring="[para(6756(a,1),22800(a,1,1,2,1))].">
      <j1 rule="para" parents="6756 22800"/>
    </justification>
  </clause>

  <clause id="22888">
    <literal><![CDATA[
      T(x * (K(y \ z,x) * K(x / (z \ y),u)),y \ z) = ((z \ y) \ 1) \ T(((z \ y) \ 1) * x,u)
    ]]></literal>
    <justification jstring="[para(14675(a,1),22887(a,1,1,2,2))].">
      <j1 rule="para" parents="14675 22887"/>
    </justification>
  </clause>

  <clause id="22889">
    <literal><![CDATA[
      T(x,T(y,z * (K(u,w) * v5)) * ((z * v5) / (1 / K(u,T(w,v5))))) = T(x,((z * v5) / (1 / K(u,T(w,v5)))) * y)
    ]]></literal>
    <justification jstring="[para(19623(a,1),22806(a,1,2,1))].">
      <j1 rule="para" parents="19623 22806"/>
    </justification>
  </clause>

  <clause id="22890">
    <literal><![CDATA[
      T(x,T(y,z * (K(u,w) * v5)) * ((z * v5) / (1 * K(w,T(u,v5))))) = T(x,((z * v5) / (1 / K(u,T(w,v5)))) * y)
    ]]></literal>
    <justification jstring="[para(7908(a,1),22889(a,1,2,2,2))].">
      <j1 rule="para" parents="7908 22889"/>
    </justification>
  </clause>

  <clause id="22891">
    <literal><![CDATA[
      T(x,T(y,z * (K(u,w) * v5)) * ((z * v5) / K(w,T(u,v5)))) = T(x,((z * v5) / (1 / K(u,T(w,v5)))) * y)
    ]]></literal>
    <justification jstring="[para(7(a,1),22890(a,1,2,2,2))].">
      <j1 rule="para" parents="7 22890"/>
    </justification>
  </clause>

  <clause id="22892">
    <literal><![CDATA[
      T(x,T(y,z * (K(u,w) * v5)) * ((z * v5) * K(u,T(w,v5)))) = T(x,((z * v5) / (1 / K(u,T(w,v5)))) * y)
    ]]></literal>
    <justification jstring="[para(7908(a,1),22891(a,1,2,2))].">
      <j1 rule="para" parents="7908 22891"/>
    </justification>
  </clause>

  <clause id="22893">
    <literal><![CDATA[
      T(x,T(y,z * (K(u,w) * v5)) * ((z * K(u,w)) * v5)) = T(x,((z * v5) / (1 / K(u,T(w,v5)))) * y)
    ]]></literal>
    <justification jstring="[para(22802(a,1),22892(a,1,2,2))].">
      <j1 rule="para" parents="22802 22892"/>
    </justification>
  </clause>

  <clause id="22894">
    <literal><![CDATA[
      T(x,T(y,z * (K(u,w) * v5)) * (z * (K(u,w) * v5))) = T(x,((z * v5) / (1 / K(u,T(w,v5)))) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,22817,a(flip),b,22893,a)].">
      <j1 rule="hyper" parents="64 22817 22893"/>
    </justification>
  </clause>

  <clause id="22895">
    <literal><![CDATA[
      T(x,((y * z) / (1 / K(u,T(w,z)))) * v5) = T(x,(y * (K(u,w) * z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(11200,a,22894,a),flip(a)].">
      <j1 rule="hyper" parents="11200 22894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22896">
    <literal><![CDATA[
      T(x,((y * z) / (1 * K(u,T(w,z)))) * v5) = T(x,(y * (K(w,u) * z)) * v5)
    ]]></literal>
    <justification jstring="[para(7908(a,1),22895(a,1,2,1,2))].">
      <j1 rule="para" parents="7908 22895"/>
    </justification>
  </clause>

  <clause id="22897">
    <literal><![CDATA[
      T(x,((y * z) / K(u,T(w,z))) * v5) = T(x,(y * (K(w,u) * z)) * v5)
    ]]></literal>
    <justification jstring="[para(7(a,1),22896(a,1,2,1,2))].">
      <j1 rule="para" parents="7 22896"/>
    </justification>
  </clause>

  <clause id="22898">
    <literal><![CDATA[
      T(x,((y * z) * K(u,T(w,z))) * v5) = T(x,(y * (K(u,w) * z)) * v5)
    ]]></literal>
    <justification jstring="[para(7908(a,1),22897(a,1,2,1))].">
      <j1 rule="para" parents="7908 22897"/>
    </justification>
  </clause>

  <clause id="22899">
    <literal><![CDATA[
      T(x,(y * (K(z,u) * w)) * v5) = T(x,K(u,z) * ((y * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(19671,a,22898,a),flip(a)].">
      <j1 rule="hyper" parents="19671 22898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22901">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * T(z,w)) * v5)) = T(x,(u * T(T(z,y),w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,22107,a(flip),b,22899,a),flip(a)].">
      <j1 rule="hyper" parents="64 22107 22899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22902">
    <literal><![CDATA[
      T(x,(y * T(T(z,u),u)) * w) = T(x,(y * R(z,u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19731,a(flip),b,22901,a),flip(a)].">
      <j1 rule="hyper" parents="64 19731 22901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22903">
    <literal><![CDATA[
      T(x,(y * R(z,u,z)) * w) = T(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16248,a(flip),b,22902,a),flip(a)].">
      <j1 rule="hyper" parents="64 16248 22902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22905">
    <literal><![CDATA[
      T(x,(y * (T(z,u \ z) / u)) * w) = T(x,(y * (u \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16252,a(flip),b,22903,a)].">
      <j1 rule="hyper" parents="64 16252 22903"/>
    </justification>
  </clause>

  <clause id="22907">
    <literal><![CDATA[
      T(x,((y / z) * y) * u) = T(x,(y * (z \ y)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15826,a(flip),b,22905,a)].">
      <j1 rule="hyper" parents="64 15826 22905"/>
    </justification>
  </clause>

  <clause id="22908">
    <literal><![CDATA[
      T(x,((y / z) \ z) * u) = T(x,(z * (y \ z)) * u)
    ]]></literal>
    <justification jstring="[hyper(18576,a,22907,a)].">
      <j1 rule="hyper" parents="18576 22907"/>
    </justification>
  </clause>

  <clause id="22909">
    <literal><![CDATA[
      T(x,(y * (z \ y)) * (z \ u)) = T(x,(z \ y) * ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22520,a(flip),b,22907,a),flip(a)].">
      <j1 rule="hyper" parents="64 22520 22907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22910">
    <literal><![CDATA[
      T(x,(y * (z \ y)) * u) = T(x,y * (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22859,a(flip),b,22908,a),flip(a)].">
      <j1 rule="hyper" parents="64 22859 22908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22911">
    <literal><![CDATA[
      T(x,(y \ z) * ((y \ z) * u)) = T(x,z * (y \ (z * (y \ u))))
    ]]></literal>
    <justification jstring="[hyper(64,a,22910,a(flip),b,22909,a),flip(a)].">
      <j1 rule="hyper" parents="64 22910 22909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22912">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(T(x,z * (y \ (y \ z))),y * (z \ (y * (z \ w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,22885,a,b,22911,a)].">
      <j1 rule="hyper" parents="64 22885 22911"/>
    </justification>
  </clause>

  <clause id="22913">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(T(x,z * z),y \ (y \ (y * (z \ (y * (z \ w))))))
    ]]></literal>
    <justification jstring="[hyper(373,a,22431,a(flip),b,22912,a),flip(a)].">
      <j1 rule="hyper" parents="373 22431 22912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22914">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(T(x,z * z),y \ (z \ (y * (z \ w))))
    ]]></literal>
    <justification jstring="[para(9(a,1),22913(a,2,2,2))].">
      <j1 rule="para" parents="9 22913"/>
    </justification>
  </clause>

  <clause id="22915">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(T(x,z * z),T(z,y) \ (z \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,22714,a(flip),b,22914,a),flip(a)].">
      <j1 rule="hyper" parents="373 22714 22914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22917">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(T(x,z * z),z \ (T(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,19980,a(flip),b,22915,a),flip(a)].">
      <j1 rule="hyper" parents="373 19980 22915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22918">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(x,z * (z * (z \ (T(z,y) \ w))))
    ]]></literal>
    <justification jstring="[hyper(373,a,15741,a(flip),b,22917,a),flip(a)].">
      <j1 rule="hyper" parents="373 15741 22917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22919">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(x,z * (T(z,y) \ w))
    ]]></literal>
    <justification jstring="[para(10(a,1),22918(a,2,2,2))].">
      <j1 rule="para" parents="10 22918"/>
    </justification>
  </clause>

  <clause id="22920">
    <literal><![CDATA[
      T(T(x,K(y,T(y \ z,u))),w) = T(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,13677,a(flip),b,22919,a),flip(a)].">
      <j1 rule="hyper" parents="373 13677 22919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22922">
    <literal><![CDATA[
      T(T(x,K(y,y \ z)),u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(114(a,1),22920(a,1,1,2,2))].">
      <j1 rule="para" parents="114 22920"/>
    </justification>
  </clause>

  <clause id="22924">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(8706(a,1),22922(a,1,1))].">
      <j1 rule="para" parents="8706 22922"/>
    </justification>
  </clause>

  <clause id="22925">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(8707(a,1),22922(a,1,1))].">
      <j1 rule="para" parents="8707 22922"/>
    </justification>
  </clause>

  <clause id="22928">
    <literal><![CDATA[
      T(x / y,K(z,u) * y) = T(y \ x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(913,a,22924,a),flip(a)].">
      <j1 rule="hyper" parents="913 22924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22929">
    <literal><![CDATA[
      T(T(x,y),K(z,u)) = T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(481,a,22924,a)].">
      <j1 rule="hyper" parents="481 22924"/>
    </justification>
  </clause>

  <clause id="22932">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17165,a(flip),b,22924,a),flip(a)].">
      <j1 rule="hyper" parents="373 17165 22924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22933">
    <literal><![CDATA[
      x \ T(T(x,K(y,z)),u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,22924,a,b,5753,a(flip))].">
      <j1 rule="hyper" parents="139 22924 5753"/>
    </justification>
  </clause>

  <clause id="22934">
    <literal><![CDATA[
      T(T(x / (y / z),u),z \ y) = T((y / z) \ x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,8907,a(flip),b,22924,a)].">
      <j1 rule="hyper" parents="64 8907 22924"/>
    </justification>
  </clause>

  <clause id="22936">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y) * u) = T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(6881(a,1),22924(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6881 22924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22937">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y) * u) = T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(7785(a,1),22924(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7785 22924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22938">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x) * u) = T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(8163(a,1),22924(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8163 22924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22939">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z) * u) = T(K(y,z) * (x * y),u)
    ]]></literal>
    <justification jstring="[para(8165(a,1),22924(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8165 22924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22940">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y) * u) = T((1 / z) * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(14396(a,1),22924(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14396 22924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22941">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y) * u) = T(K(y,z) * (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(14535(a,1),22924(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14535 22924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22945">
    <literal><![CDATA[
      T(T(x,K(y,z)),u * K(y,z)) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,17209,a(flip),b,22925,a),flip(a)].">
      <j1 rule="hyper" parents="373 17209 22925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22946">
    <literal><![CDATA[
      x * T(y,K(z,u) * x) = T(y,K(u,z)) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,22925,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 22925 22"/>
    </justification>
  </clause>

  <clause id="22949">
    <literal><![CDATA[
      T(T(x,y),K(z,u)) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17165,a(flip),b,22929,a),flip(a)].">
      <j1 rule="hyper" parents="373 17165 22929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22951">
    <literal><![CDATA[
      T(x,K(y,z) * (y * (u * u))) = T(x,T(y * (u * u),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17575,a(flip),b,22929,a),flip(a)].">
      <j1 rule="hyper" parents="64 17575 22929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22953">
    <literal><![CDATA[
      T(x * K(y,x),y * K(z,u)) = T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(6240,a,22932,a)].">
      <j1 rule="hyper" parents="6240 22932"/>
    </justification>
  </clause>

  <clause id="22958">
    <literal><![CDATA[
      T(T(x,K(y,z)),u * K(y,z)) = K(x,u) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,5756,a(flip),b,22945,a),flip(a)].">
      <j1 rule="hyper" parents="373 5756 22945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22959">
    <literal><![CDATA[
      (((x \ y) \ 1) \ K(x,y)) \ K(x,y) = T((x \ y) \ 1,x \ y)
    ]]></literal>
    <justification jstring="[hyper(41,a,8731,a,b,22949,a)].">
      <j1 rule="hyper" parents="41 8731 22949"/>
    </justification>
  </clause>

  <clause id="22961">
    <literal><![CDATA[
      R(T(x \ (y / (z \ u)),K(z,u)),x,K(z \ u,z)) = (x * K(z \ u,z)) \ (y / (u / z))
    ]]></literal>
    <justification jstring="[para(22928(a,1),17493(a,1,1))].">
      <j1 rule="para" parents="22928 17493"/>
    </justification>
  </clause>

  <clause id="22962">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17191,a(flip),b,22933,a)].">
      <j1 rule="hyper" parents="64 17191 22933"/>
    </justification>
  </clause>

  <clause id="22963">
    <literal><![CDATA[
      K(x,y) * (z * (K(y,x) * u)) = u * T(z,K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,22788,a,b,22946,a)].">
      <j1 rule="hyper" parents="373 22788 22946"/>
    </justification>
  </clause>

  <clause id="22964">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,u)) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,16799,a,b,22946,a)].">
      <j1 rule="hyper" parents="64 16799 22946"/>
    </justification>
  </clause>

  <clause id="22966">
    <literal><![CDATA[
      T(x * K(y * K(z,u),x),K(z,u)) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(6240,a,22953,a)].">
      <j1 rule="hyper" parents="6240 22953"/>
    </justification>
  </clause>

  <clause id="22967">
    <literal><![CDATA[
      K(x * x,y * K(z,u)) = K(x * x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,17456,a(flip),b,22958,a(flip))].">
      <j1 rule="hyper" parents="36 17456 22958"/>
    </justification>
  </clause>

  <clause id="22969">
    <literal><![CDATA[
      T(x \ K(x,y),K(z,u)) = x \ K(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,22962,a(flip),b,18324,a),flip(a)].">
      <j1 rule="hyper" parents="139 22962 18324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22973">
    <literal><![CDATA[
      T(K(x,y) * z,u * (w \ K(x,y))) = T(z * K(x,y),u / w)
    ]]></literal>
    <justification jstring="[hyper(64,a,20784,a(flip),b,22937,a)].">
      <j1 rule="hyper" parents="64 20784 22937"/>
    </justification>
  </clause>

  <clause id="22974">
    <literal><![CDATA[
      T(K(x,y) * z,u \ K(y,x)) = T(z * K(x,y),u \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,17413,a(flip),b,22937,a)].">
      <j1 rule="hyper" parents="64 17413 22937"/>
    </justification>
  </clause>

  <clause id="22976">
    <literal><![CDATA[
      T(x * ((y \ z) * y),K(z,u)) = T(x,K(z,u)) * ((y \ z) * y)
    ]]></literal>
    <justification jstring="[para(5458(a,1),22964(a,1,1,2))].">
      <j1 rule="para" parents="5458 22964"/>
    </justification>
  </clause>

  <clause id="22977">
    <literal><![CDATA[
      T(x * (K(y,z) * (u \ 1)),K(y,z)) = T(x,K(y,z)) * (u \ K(y,z))
    ]]></literal>
    <justification jstring="[para(14537(a,1),22964(a,1,1,2))].">
      <j1 rule="para" parents="14537 22964"/>
    </justification>
  </clause>

  <clause id="22978">
    <literal><![CDATA[
      T(x * K(y,x),K(z,u)) = x * K(y * K(z,u),x)
    ]]></literal>
    <justification jstring="[hyper(8182,a,22966,a)].">
      <j1 rule="hyper" parents="8182 22966"/>
    </justification>
  </clause>

  <clause id="22979">
    <literal><![CDATA[
      T(x,K(y,z)) * K(u,x) = x * K(u * K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18372,a(flip),b,22978,a)].">
      <j1 rule="hyper" parents="64 18372 22978"/>
    </justification>
  </clause>

  <clause id="22980">
    <literal><![CDATA[
      K(x,K(y,z)) * K(u,x) = K(u * K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(6085,a,22979,a)].">
      <j1 rule="hyper" parents="6085 22979"/>
    </justification>
  </clause>

  <clause id="22981">
    <literal><![CDATA[
      K(x,y) * K(z,K(u,y)) = K(x * K(z,u),y)
    ]]></literal>
    <justification jstring="[hyper(35,a,17342,a,b,22979,a(flip))].">
      <j1 rule="hyper" parents="35 17342 22979"/>
    </justification>
  </clause>

  <clause id="22982">
    <literal><![CDATA[
      K(x,K(y,z)) * K(u,z) = K(u * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(35,a,8130,a,b,22979,a(flip))].">
      <j1 rule="hyper" parents="35 8130 22979"/>
    </justification>
  </clause>

  <clause id="22983">
    <literal><![CDATA[
      K(x,K(y,z)) * K(u,y) = K(u * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(35,a,8117,a,b,22979,a(flip))].">
      <j1 rule="hyper" parents="35 8117 22979"/>
    </justification>
  </clause>

  <clause id="22984">
    <literal><![CDATA[
      x * T(T(x,y) \ 1,K(z,u)) = K(y * K(z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,18394,a,b,22980,a)].">
      <j1 rule="hyper" parents="64 18394 22980"/>
    </justification>
  </clause>

  <clause id="22985">
    <literal><![CDATA[
      K(x,y) * K(z,K(u,y)) = K(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,17178,a,b,22981,a),flip(a)].">
      <j1 rule="hyper" parents="373 17178 22981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22986">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(z,z \ u) = K(K(x,y) * z,u / z)
    ]]></literal>
    <justification jstring="[hyper(373,a,11187,a(flip),b,22982,a),flip(a)].">
      <j1 rule="hyper" parents="373 11187 22982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22987">
    <literal><![CDATA[
      K((x * (y * y)) * K(z,u),T(x,w)) = K(z,K(T(x,w),u)) * K(y * y,x)
    ]]></literal>
    <justification jstring="[para(17061(a,1),22983(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17061 22983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22988">
    <literal><![CDATA[
      a(x,x,x) * K(y,K(z,x)) = K(K(y,z) * (x * x),x)
    ]]></literal>
    <justification jstring="[para(98(a,1),22985(a,1,1))].">
      <j1 rule="para" parents="98 22985"/>
    </justification>
  </clause>

  <clause id="22989">
    <literal><![CDATA[
      K(x,y) * T(K(y,x) * K(z,u),u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,22849,a,b,22984,a)].">
      <j1 rule="hyper" parents="64 22849 22984"/>
    </justification>
  </clause>

  <clause id="22990">
    <literal><![CDATA[
      a(x,x,x) * K(x,K(y,z)) = K(K(y,z) * (x * x),x)
    ]]></literal>
    <justification jstring="[para(8110(a,1),22988(a,1,2))].">
      <j1 rule="para" parents="8110 22988"/>
    </justification>
  </clause>

  <clause id="22991">
    <literal><![CDATA[
      K(K(x,y) * (z * z),z) = T(z,K(x,y)) * (1 / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11028,a(flip),b,22990,a),flip(a)].">
      <j1 rule="hyper" parents="64 11028 22990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22992">
    <literal><![CDATA[
      K(K(x,y) * (z * z),z) = K(z,z \ K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,14965,a(flip),b,22991,a),flip(a)].">
      <j1 rule="hyper" parents="373 14965 22991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22993">
    <literal><![CDATA[
      T(x * ((y \ K(z,u)) * K(K(z,u) * (y * y),y)),y) = L(y,y \ K(z,u),x) \ (x * (y * (y \ K(z,u))))
    ]]></literal>
    <justification jstring="[para(22992(a,2),15293(a,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="22992 15293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22994">
    <literal><![CDATA[
      T(K(x,y) * (z * x),u) \ (T(z * T(x,y),K(x,y) * u) / w) = (z * T(x,y)) \ ((z * T(x,y)) / w)
    ]]></literal>
    <justification jstring="[para(22939(a,1),14846(a,1,1))].">
      <j1 rule="para" parents="22939 14846"/>
    </justification>
  </clause>

  <clause id="22995">
    <literal><![CDATA[
      (K(x,y) * K(x,y)) \ ((z \ K(y,x)) \ ((K(x,y) * K(x,y)) * u)) = T(K(y,x) * (z \ 1),K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(22941(a,1),1458(a,2,1))].">
      <j1 rule="para" parents="22941 1458"/>
    </justification>
  </clause>

  <clause id="22996">
    <literal><![CDATA[
      T(x,T(y * (z * z),u)) = T(x,T(y,u) * (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13678,a(flip),b,22951,a),flip(a)].">
      <j1 rule="hyper" parents="64 13678 22951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22997">
    <literal><![CDATA[
      T(x,T(y * (z * z),u)) = T(x,(z * z) * T(y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17048,a,b,22996,a),flip(a)].">
      <j1 rule="hyper" parents="373 17048 22996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="22998">
    <literal><![CDATA[
      T(x,T((y * y) * z,u)) = T(x,(y * y) * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17055,a,b,22997,a)].">
      <j1 rule="hyper" parents="64 17055 22997"/>
    </justification>
  </clause>

  <clause id="23000">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,16115,a,b,22963,a)].">
      <j1 rule="hyper" parents="36 16115 22963"/>
    </justification>
  </clause>

  <clause id="23001">
    <literal><![CDATA[
      K(x,L(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12091,a,23000,a)].">
      <j1 rule="hyper" parents="12091 23000"/>
    </justification>
  </clause>

  <clause id="23002">
    <literal><![CDATA[
      K(x,(y * z) \ u) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(9535,a,23000,a)].">
      <j1 rule="hyper" parents="9535 23000"/>
    </justification>
  </clause>

  <clause id="23004">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(7562,a,23000,a)].">
      <j1 rule="hyper" parents="7562 23000"/>
    </justification>
  </clause>

  <clause id="23005">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,u) = K(x \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(7304,a,23000,a)].">
      <j1 rule="hyper" parents="7304 23000"/>
    </justification>
  </clause>

  <clause id="23037">
    <literal><![CDATA[
      a(x,y,K(z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,23000,a,b,10419,a),flip(a)].">
      <j1 rule="hyper" parents="138 23000 10419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23039">
    <literal><![CDATA[
      K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15603,a(flip),b,23000,a)].">
      <j1 rule="hyper" parents="64 15603 23000"/>
    </justification>
  </clause>

  <clause id="23040">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(x \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15593,a(flip),b,23000,a)].">
      <j1 rule="hyper" parents="64 15593 23000"/>
    </justification>
  </clause>

  <clause id="23041">
    <literal><![CDATA[
      K((x * y) / z,u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15592,a(flip),b,23000,a)].">
      <j1 rule="hyper" parents="64 15592 23000"/>
    </justification>
  </clause>

  <clause id="23042">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15582,a(flip),b,23000,a)].">
      <j1 rule="hyper" parents="64 15582 23000"/>
    </justification>
  </clause>

  <clause id="23043">
    <literal><![CDATA[
      K(x,(y \ z) \ u) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12081,a(flip),b,23000,a),flip(a)].">
      <j1 rule="hyper" parents="64 12081 23000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23044">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,w)) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,9178,a(flip),b,23000,a),flip(a)].">
      <j1 rule="hyper" parents="64 9178 23000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23045">
    <literal><![CDATA[
      K((x \ y) \ z,u) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7529,a(flip),b,23000,a),flip(a)].">
      <j1 rule="hyper" parents="64 7529 23000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23046">
    <literal><![CDATA[
      K((x * y) \ z,u) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7528,a(flip),b,23000,a)].">
      <j1 rule="hyper" parents="64 7528 23000"/>
    </justification>
  </clause>

  <clause id="23047">
    <literal><![CDATA[
      K(x,L(y,z,u) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,6666,a(flip),b,23000,a)].">
      <j1 rule="hyper" parents="64 6666 23000"/>
    </justification>
  </clause>

  <clause id="23048">
    <literal><![CDATA[
      (x * (y * K(z,u))) / K(z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(225,a,23000,a(flip),b,5027,a)].">
      <j1 rule="hyper" parents="225 23000 5027"/>
    </justification>
  </clause>

  <clause id="23049">
    <literal><![CDATA[
      (x / (y * K(z,u))) * y = x / K(z,u)
    ]]></literal>
    <justification jstring="[hyper(225,a,23000,a(flip),b,15006,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 23000 15006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23050">
    <literal><![CDATA[
      (x / y) * (y * K(z,u)) = x * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,23000,a(flip),b,11067,a),flip(a)].">
      <j1 rule="hyper" parents="145 23000 11067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23051">
    <literal><![CDATA[
      (x * (y * K(z,u))) * K(u,z) = x * y
    ]]></literal>
    <justification jstring="[hyper(145,a,23000,a(flip),b,7320,a)].">
      <j1 rule="hyper" parents="145 23000 7320"/>
    </justification>
  </clause>

  <clause id="23052">
    <literal><![CDATA[
      (x * (y * z)) * K(z,u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,23000,a(flip),b,6923,a)].">
      <j1 rule="hyper" parents="145 23000 6923"/>
    </justification>
  </clause>

  <clause id="23053">
    <literal><![CDATA[
      (x * y) * K(z,u) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,23000,a(flip),b,5027,a)].">
      <j1 rule="hyper" parents="145 23000 5027"/>
    </justification>
  </clause>

  <clause id="23054">
    <literal><![CDATA[
      x * (T(y,x) * K(z,u)) = (y * x) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,23000,a(flip),b,261,a),flip(a)].">
      <j1 rule="hyper" parents="145 23000 261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23055">
    <literal><![CDATA[
      x * ((x \ y) * K(z,u)) = y * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,23000,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 23000 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23058">
    <literal><![CDATA[
      x \ (y * K(z,u)) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(23000(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="23000 598"/>
    </justification>
  </clause>

  <clause id="23059">
    <literal><![CDATA[
      (x * y) * K(z,u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(23000(a,1),334(a,1,2))].">
      <j1 rule="para" parents="23000 334"/>
    </justification>
  </clause>

  <clause id="23064">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(u,w) = L(x,y,z) * (x \ K(u,w))
    ]]></literal>
    <justification jstring="[para(23000(a,1),2338(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23000 2338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23065">
    <literal><![CDATA[
      (x * y) * ((z \ K(u,w)) * z) = x * (y * ((z \ K(u,w)) * z))
    ]]></literal>
    <justification jstring="[para(23000(a,1),5549(a,1,2,1,2))].">
      <j1 rule="para" parents="23000 5549"/>
    </justification>
  </clause>

  <clause id="23067">
    <literal><![CDATA[
      x * (y * K(z,T(u,x * y))) = K(z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(23000(a,1),7894(a,2,1))].">
      <j1 rule="para" parents="23000 7894"/>
    </justification>
  </clause>

  <clause id="23073">
    <literal><![CDATA[
      (K(x,y) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(23000(a,1),15594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23000 15594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23078">
    <literal><![CDATA[
      K(x,a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(13969,a,23037,a)].">
      <j1 rule="hyper" parents="13969 23037"/>
    </justification>
  </clause>

  <clause id="23081">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,23037,a,b,68,a)].">
      <j1 rule="hyper" parents="145 23037 68"/>
    </justification>
  </clause>

  <clause id="23084">
    <literal><![CDATA[
      a(K(x,y),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,15371,a,b,23037,a)].">
      <j1 rule="hyper" parents="64 15371 23037"/>
    </justification>
  </clause>

  <clause id="23085">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,15303,a,b,23037,a)].">
      <j1 rule="hyper" parents="64 15303 23037"/>
    </justification>
  </clause>

  <clause id="23086">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,13792,a,b,23037,a)].">
      <j1 rule="hyper" parents="64 13792 23037"/>
    </justification>
  </clause>

  <clause id="23087">
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,13786,a,b,23037,a)].">
      <j1 rule="hyper" parents="64 13786 23037"/>
    </justification>
  </clause>

  <clause id="23088">
    <literal><![CDATA[
      K(a(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,13977,a(flip),b,23037,a)].">
      <j1 rule="hyper" parents="64 13977 23037"/>
    </justification>
  </clause>

  <clause id="23103">
    <literal><![CDATA[
      x * K(y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,23078,a,b,68,a)].">
      <j1 rule="hyper" parents="145 23078 68"/>
    </justification>
  </clause>

  <clause id="23104">
    <literal><![CDATA[
      K(x,a(y,z,u)) * w = w
    ]]></literal>
    <justification jstring="[hyper(144,a,23078,a,b,76,a)].">
      <j1 rule="hyper" parents="144 23078 76"/>
    </justification>
  </clause>

  <clause id="23105">
    <literal><![CDATA[
      T(x,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,23078,a)].">
      <j1 rule="hyper" parents="57 23078"/>
    </justification>
  </clause>

  <clause id="23106">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),u) \ u = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(23078(a,1),14983(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23078 14983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23115">
    <literal><![CDATA[
      L(x,y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,23084,a)].">
      <j1 rule="hyper" parents="53 23084"/>
    </justification>
  </clause>

  <clause id="23125">
    <literal><![CDATA[
      x * K(a(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,23088,a,b,68,a)].">
      <j1 rule="hyper" parents="145 23088 68"/>
    </justification>
  </clause>

  <clause id="23126">
    <literal><![CDATA[
      K(a(x,y,z),u) * w = w
    ]]></literal>
    <justification jstring="[hyper(144,a,23088,a,b,76,a)].">
      <j1 rule="hyper" parents="144 23088 76"/>
    </justification>
  </clause>

  <clause id="23127">
    <literal><![CDATA[
      T(a(x,y,z),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(57,a,23088,a)].">
      <j1 rule="hyper" parents="57 23088"/>
    </justification>
  </clause>

  <clause id="23128">
    <literal><![CDATA[
      T(x,y \ (a(z,u,w) \ y)) = T(x,a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(23088(a,1),9240(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23088 9240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23129">
    <literal><![CDATA[
      (x * a(y,z,u)) * (x \ 1) = R(a(y,z,u),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(23088(a,1),9340(a,1,2,2))].">
      <j1 rule="para" parents="23088 9340"/>
    </justification>
  </clause>

  <clause id="23130">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ u) / u = u \ ((a(x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(23088(a,1),9507(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="23088 9507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23133">
    <literal><![CDATA[
      x / a(y,z,u) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(8638,a,23105,a),flip(a)].">
      <j1 rule="hyper" parents="8638 23105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23134">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ u = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4722,a,23105,a)].">
      <j1 rule="hyper" parents="4722 23105"/>
    </justification>
  </clause>

  <clause id="23135">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(x,y,z) = u
    ]]></literal>
    <justification jstring="[hyper(2159,a,23105,a)].">
      <j1 rule="hyper" parents="2159 23105"/>
    </justification>
  </clause>

  <clause id="23136">
    <literal><![CDATA[
      a(x,y,z) * u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2149,a,23105,a),flip(a)].">
      <j1 rule="hyper" parents="2149 23105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23137">
    <literal><![CDATA[
      ((a(x,y,z) * u) * w) / (a(x,y,z) * w) = R(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(1054,a,23105,a)].">
      <j1 rule="hyper" parents="1054 23105"/>
    </justification>
  </clause>

  <clause id="23138">
    <literal><![CDATA[
      a(x,y,z) \ (u * a(x,y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(477,a,23105,a)].">
      <j1 rule="hyper" parents="477 23105"/>
    </justification>
  </clause>

  <clause id="23139">
    <literal><![CDATA[
      (a(x,y,z) * u) / a(x,y,z) = u
    ]]></literal>
    <justification jstring="[hyper(399,a,23105,a),flip(a)].">
      <j1 rule="hyper" parents="399 23105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23144">
    <literal><![CDATA[
      T(x / (y \ x),a(z,u,w)) = y
    ]]></literal>
    <justification jstring="[hyper(373,a,79,a(flip),b,23105,a),flip(a)].">
      <j1 rule="hyper" parents="373 79 23105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23146">
    <literal><![CDATA[
      L(x,K(y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,22751,a,b,23105,a)].">
      <j1 rule="hyper" parents="64 22751 23105"/>
    </justification>
  </clause>

  <clause id="23147">
    <literal><![CDATA[
      R(x,y,K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,15982,a,b,23105,a)].">
      <j1 rule="hyper" parents="64 15982 23105"/>
    </justification>
  </clause>

  <clause id="23148">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13809,a,b,23105,a)].">
      <j1 rule="hyper" parents="64 13809 23105"/>
    </justification>
  </clause>

  <clause id="23149">
    <literal><![CDATA[
      L(x,y,z) * T(u,x) = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,19821,a(flip),b,23105,a)].">
      <j1 rule="hyper" parents="64 19821 23105"/>
    </justification>
  </clause>

  <clause id="23151">
    <literal><![CDATA[
      T(x,y \ (y \ a(z,u,w))) = T(x,y \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,15873,a(flip),b,23105,a)].">
      <j1 rule="hyper" parents="64 15873 23105"/>
    </justification>
  </clause>

  <clause id="23152">
    <literal><![CDATA[
      x * T(y,L(x,z,u)) = y * x
    ]]></literal>
    <justification jstring="[hyper(64,a,15719,a(flip),b,23105,a)].">
      <j1 rule="hyper" parents="64 15719 23105"/>
    </justification>
  </clause>

  <clause id="23153">
    <literal><![CDATA[
      T(x,L(y,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15395,a(flip),b,23105,a)].">
      <j1 rule="hyper" parents="64 15395 23105"/>
    </justification>
  </clause>

  <clause id="23155">
    <literal><![CDATA[
      ((x / a(y,z,u)) * x) \ x = a(y,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,5149,a(flip),b,23105,a)].">
      <j1 rule="hyper" parents="64 5149 23105"/>
    </justification>
  </clause>

  <clause id="23156">
    <literal><![CDATA[
      (((a(x,y,z) / u) \ 1) \ u) \ u = (a(x,y,z) / u) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,4918,a(flip),b,23105,a)].">
      <j1 rule="hyper" parents="64 4918 23105"/>
    </justification>
  </clause>

  <clause id="23157">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) / (x * y) = L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(225,a,23105,a(flip),b,14658,a)].">
      <j1 rule="hyper" parents="225 23105 14658"/>
    </justification>
  </clause>

  <clause id="23158">
    <literal><![CDATA[
      x / ((a(y,z,u) / x) \ 1) = ((a(y,z,u) / x) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,23105,a(flip),b,4918,a(flip))].">
      <j1 rule="hyper" parents="225 23105 4918"/>
    </justification>
  </clause>

  <clause id="23159">
    <literal><![CDATA[
      x / ((a(y,z,u) \ 1) * x) = ((a(y,z,u) \ 1) * x) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,23105,a(flip),b,4593,a(flip))].">
      <j1 rule="hyper" parents="225 23105 4593"/>
    </justification>
  </clause>

  <clause id="23160">
    <literal><![CDATA[
      x / (x / a(y,z,u)) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(225,a,23105,a(flip),b,117,a(flip))].">
      <j1 rule="hyper" parents="225 23105 117"/>
    </justification>
  </clause>

  <clause id="23161">
    <literal><![CDATA[
      (x * a(y,z,u)) / x = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(225,a,23105,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="225 23105 22"/>
    </justification>
  </clause>

  <clause id="23162">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (w * u) = w * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,23105,a(flip),b,14658,a)].">
      <j1 rule="hyper" parents="145 23105 14658"/>
    </justification>
  </clause>

  <clause id="23163">
    <literal><![CDATA[
      a(x,y,z) * R(u,w,w \ a(x,y,z)) = (u * w) * (w \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,23105,a(flip),b,894,a)].">
      <j1 rule="hyper" parents="145 23105 894"/>
    </justification>
  </clause>

  <clause id="23164">
    <literal><![CDATA[
      ((a(x,y,z) \ u) / u) * (a(x,y,z) * u) = u
    ]]></literal>
    <justification jstring="[hyper(144,a,3007,a(flip),b,23105,a(flip))].">
      <j1 rule="hyper" parents="144 3007 23105"/>
    </justification>
  </clause>

  <clause id="23165">
    <literal><![CDATA[
      T(x / L(y,z,u),y) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,23105,a(flip),b,19820,a),flip(a)].">
      <j1 rule="hyper" parents="139 23105 19820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23167">
    <literal><![CDATA[
      T(x,L(y,z,u)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,23105,a(flip),b,15719,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 23105 15719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23168">
    <literal><![CDATA[
      (a(x,y,z) * u) * w = (u * a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(39,a,1755,a(flip),b,23105,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 1755 23105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23169">
    <literal><![CDATA[
      x * (a(y,z,u) * w) = x * (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(38,a,2873,a(flip),b,23105,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 2873 23105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23170">
    <literal><![CDATA[
      x \ (y / a(z,u,w)) = x \ (a(z,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(36,a,5456,a(flip),b,23105,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 5456 23105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23171">
    <literal><![CDATA[
      (a(x,y,z) * u) \ ((u * w) * a(x,y,z)) = L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,11292,a,b,23105,a(flip))].">
      <j1 rule="hyper" parents="35 11292 23105"/>
    </justification>
  </clause>

  <clause id="23172">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,w)) = (a(z,u,w) * x) \ (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(35,a,11290,a(flip),b,23105,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 11290 23105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23173">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(23105(a,1),50(a,2))].">
      <j1 rule="para" parents="23105 50"/>
    </justification>
  </clause>

  <clause id="23174">
    <literal><![CDATA[
      x \ (a(y,z,u) * x) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(23105(a,1),257(a,1,2,2))].">
      <j1 rule="para" parents="23105 257"/>
    </justification>
  </clause>

  <clause id="23175">
    <literal><![CDATA[
      a(x,y,z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      w * a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(23105(a,1),158(a,1)),flip(a)].">
      <j1 rule="para" parents="23105 158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23176">
    <literal><![CDATA[
      a(x,y,z) * u != u * w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(23105(a,1),271(a,1,2)),flip(b)].">
      <j1 rule="para" parents="23105 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23177">
    <literal><![CDATA[
      a(x,y,z) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(23105(a,1),328(a,1,2))].">
      <j1 rule="para" parents="23105 328"/>
    </justification>
  </clause>

  <clause id="23178">
    <literal><![CDATA[
      x \ (a(y,z,u) * x) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(23105(a,1),337(a,1,2,2)),flip(b)].">
      <j1 rule="para" parents="23105 337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23179">
    <literal><![CDATA[
      x / a(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(23105(a,1),467(a,1))].">
      <j1 rule="para" parents="23105 467"/>
    </justification>
  </clause>

  <clause id="23180">
    <literal><![CDATA[
      x \ (a(y,z,u) * w) = x \ (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(23105(a,1),249(a,1,2,2))].">
      <j1 rule="para" parents="23105 249"/>
    </justification>
  </clause>

  <clause id="23181">
    <literal><![CDATA[
      (a(x,y,z) * u) / w = (u * a(x,y,z)) / w
    ]]></literal>
    <justification jstring="[para(23105(a,1),250(a,1,1,2))].">
      <j1 rule="para" parents="23105 250"/>
    </justification>
  </clause>

  <clause id="23182">
    <literal><![CDATA[
      a(x,y,z) * (u * (u \ w)) = w * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(23105(a,1),258(a,1,2,2,2))].">
      <j1 rule="para" parents="23105 258"/>
    </justification>
  </clause>

  <clause id="23183">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,v5) = a(u,w,v5) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(23105(a,1),266(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23105 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23184">
    <literal><![CDATA[
      L(T(x,a(y,z,u)),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(23105(a,1),162(a,1)),flip(a)].">
      <j1 rule="para" parents="23105 162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23185">
    <literal><![CDATA[
      x * (a(y,z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (w * a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(23105(a,1),737(a,1,2,2))].">
      <j1 rule="para" parents="23105 737"/>
    </justification>
  </clause>

  <clause id="23186">
    <literal><![CDATA[
      (x * a(y,z,u)) \ (a(y,z,u) * (x * w)) = L(w,T(x,a(y,z,u)),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(23105(a,1),261(a,1,2,2,1))].">
      <j1 rule="para" parents="23105 261"/>
    </justification>
  </clause>

  <clause id="23187">
    <literal><![CDATA[
      L(x,y \ a(z,u,w),y) * a(z,u,w) = y * ((y \ a(z,u,w)) * x)
    ]]></literal>
    <justification jstring="[para(23105(a,1),964(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23105 964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23188">
    <literal><![CDATA[
      a(x,y,z) * R(u,u,a(x,y,z)) = (1 / u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(23105(a,1),1914(a,1,2,1))].">
      <j1 rule="para" parents="23105 1914"/>
    </justification>
  </clause>

  <clause id="23189">
    <literal><![CDATA[
      x \ (x * (a(y,z,u) * w)) = T(a(y,z,u),x) * w
    ]]></literal>
    <justification jstring="[para(23105(a,1),5026(a,1,1))].">
      <j1 rule="para" parents="23105 5026"/>
    </justification>
  </clause>

  <clause id="23190">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,w)) = (x * a(z,u,w)) \ (a(z,u,w) * y)
    ]]></literal>
    <justification jstring="[para(23105(a,1),10979(a,1,1,1))].">
      <j1 rule="para" parents="23105 10979"/>
    </justification>
  </clause>

  <clause id="23191">
    <literal><![CDATA[
      (x * a(y,z,u)) \ (a(y,z,u) * (x * w)) = L(w,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(23105(a,1),10980(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="23105 10980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23193">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,v5) = L(x,w * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[para(23105(a,1),14165(a,1,2))].">
      <j1 rule="para" parents="23105 14165"/>
    </justification>
  </clause>

  <clause id="23198">
    <literal><![CDATA[
      R(x,y,T(z,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(16606,a,23115,a)].">
      <j1 rule="hyper" parents="16606 23115"/>
    </justification>
  </clause>

  <clause id="23199">
    <literal><![CDATA[
      (K(x,y) * z) \ u = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(7120,a,23115,a),flip(a)].">
      <j1 rule="hyper" parents="7120 23115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23215">
    <literal><![CDATA[
      L(x,y,T(z,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,21680,a(flip),b,23115,a)].">
      <j1 rule="hyper" parents="64 21680 23115"/>
    </justification>
  </clause>

  <clause id="23216">
    <literal><![CDATA[
      L(x,y,z / u) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,20980,a(flip),b,23115,a)].">
      <j1 rule="hyper" parents="64 20980 23115"/>
    </justification>
  </clause>

  <clause id="23218">
    <literal><![CDATA[
      (x * K(y,z)) / u = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16599,a(flip),b,23115,a),flip(a)].">
      <j1 rule="hyper" parents="64 16599 23115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23222">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * u) = z \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,23115,a)].">
      <j1 rule="hyper" parents="64 102 23115"/>
    </justification>
  </clause>

  <clause id="23223">
    <literal><![CDATA[
      x / (y * L(y \ x,z,u)) = (y * L(y \ x,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,23115,a(flip),b,16635,a(flip))].">
      <j1 rule="hyper" parents="225 23115 16635"/>
    </justification>
  </clause>

  <clause id="23224">
    <literal><![CDATA[
      (K(x,y) * z) / u = K(x,y) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(225,a,23115,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 23115 10262"/>
    </justification>
  </clause>

  <clause id="23225">
    <literal><![CDATA[
      (K(x,y) * (z * u)) / u = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(225,a,23115,a(flip),b,5318,a(flip))].">
      <j1 rule="hyper" parents="225 23115 5318"/>
    </justification>
  </clause>

  <clause id="23228">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) = K(x,y) * u
    ]]></literal>
    <justification jstring="[hyper(145,a,23115,a(flip),b,102,a(flip))].">
      <j1 rule="hyper" parents="145 23115 102"/>
    </justification>
  </clause>

  <clause id="23229">
    <literal><![CDATA[
      (x / (y * K(z,u))) * y = x * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,16599,a(flip),b,23115,a(flip))].">
      <j1 rule="hyper" parents="144 16599 23115"/>
    </justification>
  </clause>

  <clause id="23232">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(23115(a,1),51(a,2))].">
      <j1 rule="para" parents="23115 51"/>
    </justification>
  </clause>

  <clause id="23238">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,K(y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(23115(a,1),602(a,2,1))].">
      <j1 rule="para" parents="23115 602"/>
    </justification>
  </clause>

  <clause id="23239">
    <literal><![CDATA[
      (K(x,y) * ((z * u) * w)) / (u * w) = K(x,y) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(23115(a,1),693(a,1,2))].">
      <j1 rule="para" parents="23115 693"/>
    </justification>
  </clause>

  <clause id="23246">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) * z) * u) = z * u
    ]]></literal>
    <justification jstring="[para(23115(a,1),6201(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23115 6201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23247">
    <literal><![CDATA[
      K(x,y) * (((x * y) \ z) * u) = ((y * x) \ z) * u
    ]]></literal>
    <justification jstring="[para(23115(a,1),10847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23115 10847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23249">
    <literal><![CDATA[
      x \ (K(y,z) * (u * x)) = T(K(y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(23115(a,1),14658(a,1,1))].">
      <j1 rule="para" parents="23115 14658"/>
    </justification>
  </clause>

  <clause id="23252">
    <literal><![CDATA[
      (x * y) * K(z,T(u,y)) = x * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(23115(a,1),16660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23115 16660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23253">
    <literal><![CDATA[
      L(x,y,z * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(23115(a,1),21686(a,1,1))].">
      <j1 rule="para" parents="23115 21686"/>
    </justification>
  </clause>

  <clause id="23256">
    <literal><![CDATA[
      (x * K(y,z)) * u = x * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(23115(a,1),22753(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23115 22753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23257">
    <literal><![CDATA[
      (x * K(y,z)) \ u = K(y,z) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(710,a,23146,a),flip(a)].">
      <j1 rule="hyper" parents="710 23146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23270">
    <literal><![CDATA[
      R(x,K(y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,18806,a,b,23146,a)].">
      <j1 rule="hyper" parents="64 18806 23146"/>
    </justification>
  </clause>

  <clause id="23271">
    <literal><![CDATA[
      x / (K(y,z) * u) = (x / u) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,18807,a(flip),b,23146,a)].">
      <j1 rule="hyper" parents="64 18807 23146"/>
    </justification>
  </clause>

  <clause id="23272">
    <literal><![CDATA[
      (x * K(y,z)) \ u = K(z,y) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,6191,a(flip),b,23146,a)].">
      <j1 rule="hyper" parents="64 6191 23146"/>
    </justification>
  </clause>

  <clause id="23274">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * u) = K(y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,23146,a)].">
      <j1 rule="hyper" parents="64 102 23146"/>
    </justification>
  </clause>

  <clause id="23276">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * K(y,z) = x / u
    ]]></literal>
    <justification jstring="[hyper(225,a,23146,a(flip),b,15006,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 23146 15006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23278">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / u = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,23146,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="225 23146 18"/>
    </justification>
  </clause>

  <clause id="23279">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * u) = K(y,z) * u
    ]]></literal>
    <justification jstring="[hyper(145,a,596,a(flip),b,23146,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 596 23146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23280">
    <literal><![CDATA[
      K(x,y) * ((z * K(x,y)) \ u) = z \ u
    ]]></literal>
    <justification jstring="[hyper(145,a,346,a(flip),b,23146,a(flip))].">
      <j1 rule="hyper" parents="145 346 23146"/>
    </justification>
  </clause>

  <clause id="23281">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * u) = x * u
    ]]></literal>
    <justification jstring="[hyper(145,a,23146,a(flip),b,20409,a),flip(a)].">
      <j1 rule="hyper" parents="145 23146 20409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23282">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * u = x * (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(144,a,23146,a(flip),b,20412,a(flip))].">
      <j1 rule="hyper" parents="144 23146 20412"/>
    </justification>
  </clause>

  <clause id="23283">
    <literal><![CDATA[
      L(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(23146(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="23146 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23285">
    <literal><![CDATA[
      (x * K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(23146(a,1),334(a,1,2))].">
      <j1 rule="para" parents="23146 334"/>
    </justification>
  </clause>

  <clause id="23296">
    <literal><![CDATA[
      x \ (y * (K(z,u) * x)) = T(y * K(z,u),x)
    ]]></literal>
    <justification jstring="[para(23146(a,1),14658(a,1,1))].">
      <j1 rule="para" parents="23146 14658"/>
    </justification>
  </clause>

  <clause id="23313">
    <literal><![CDATA[
      R(x,y,(z \ u) \ u) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10095,a(flip),b,23147,a),flip(a)].">
      <j1 rule="hyper" parents="64 10095 23147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23314">
    <literal><![CDATA[
      ((x * y) * T(z,u)) / (y * T(z,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9561,a(flip),b,23147,a)].">
      <j1 rule="hyper" parents="64 9561 23147"/>
    </justification>
  </clause>

  <clause id="23316">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(23147(a,1),52(a,2))].">
      <j1 rule="para" parents="23147 52"/>
    </justification>
  </clause>

  <clause id="23318">
    <literal><![CDATA[
      x * K(y,z) != u * (w * K(y,z))
    ]]></literal>
    <literal><![CDATA[
      u * w = x
    ]]></literal>
    <justification jstring="[para(23147(a,1),665(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23147 665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23319">
    <literal><![CDATA[
      R(x,y,z \ T(z,u)) = x
    ]]></literal>
    <justification jstring="[para(1885(a,1),23147(a,1,3))].">
      <j1 rule="para" parents="1885 23147"/>
    </justification>
  </clause>

  <clause id="23362">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,23000,a,b,23001,a)].">
      <j1 rule="hyper" parents="373 23000 23001"/>
    </justification>
  </clause>

  <clause id="23380">
    <literal><![CDATA[
      K(x,L(L(y,z,u),w,v5)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,23001,a(flip),b,23001,a),flip(a)].">
      <j1 rule="hyper" parents="373 23001 23001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23383">
    <literal><![CDATA[
      K(x,L(y,z,u)) * w = K(x,y) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,23001,a,b,11,a)].">
      <j1 rule="hyper" parents="144 23001 11"/>
    </justification>
  </clause>

  <clause id="23384">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[hyper(144,a,23001,a,b,5786,a(flip))].">
      <j1 rule="hyper" parents="144 23001 5786"/>
    </justification>
  </clause>

  <clause id="23385">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15572,a,b,23001,a)].">
      <j1 rule="hyper" parents="64 15572 23001"/>
    </justification>
  </clause>

  <clause id="23386">
    <literal><![CDATA[
      K(x,(y \ z) * (y * u)) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,22710,a(flip),b,23001,a)].">
      <j1 rule="hyper" parents="64 22710 23001"/>
    </justification>
  </clause>

  <clause id="23387">
    <literal><![CDATA[
      K(x,(y / z) / u) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15587,a(flip),b,23001,a),flip(a)].">
      <j1 rule="hyper" parents="64 15587 23001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23389">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) * z) * u) = (y * z) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,23001,a(flip),b,15584,a)].">
      <j1 rule="hyper" parents="144 23001 15584"/>
    </justification>
  </clause>

  <clause id="23390">
    <literal><![CDATA[
      K(x,y) * T(L(y,z,u),x) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,23001,a(flip),b,5787,a(flip))].">
      <j1 rule="hyper" parents="144 23001 5787"/>
    </justification>
  </clause>

  <clause id="23391">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) * x) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,23001,a(flip),b,5786,a(flip))].">
      <j1 rule="hyper" parents="144 23001 5786"/>
    </justification>
  </clause>

  <clause id="23394">
    <literal><![CDATA[
      K(x,T((y * z) \ u,w)) = K(x,T(z \ (y \ u),w))
    ]]></literal>
    <justification jstring="[para(708(a,1),23001(a,1,2))].">
      <j1 rule="para" parents="708 23001"/>
    </justification>
  </clause>

  <clause id="23401">
    <literal><![CDATA[
      (x \ y) * K(z,T(u,y)) = x \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(23001(a,1),15548(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23001 15548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23408">
    <literal><![CDATA[
      (x * (y / z)) * K(u,z) = x * (y / T(z,u))
    ]]></literal>
    <justification jstring="[para(23001(a,1),19655(a,1,2))].">
      <j1 rule="para" parents="23001 19655"/>
    </justification>
  </clause>

  <clause id="23429">
    <literal><![CDATA[
      K((x * y) / (z * y),u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15614,a(flip),b,23004,a)].">
      <j1 rule="hyper" parents="64 15614 23004"/>
    </justification>
  </clause>

  <clause id="23430">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,23004,a(flip),b,5764,a)].">
      <j1 rule="hyper" parents="145 23004 5764"/>
    </justification>
  </clause>

  <clause id="23431">
    <literal><![CDATA[
      K(x,y) * (y * L(x,z,u)) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,23004,a(flip),b,5786,a(flip))].">
      <j1 rule="hyper" parents="144 23004 5786"/>
    </justification>
  </clause>

  <clause id="23436">
    <literal><![CDATA[
      K((x * (y * z)) \ ((x * y) * u),w) = K(L(z,y,x) \ u,w)
    ]]></literal>
    <justification jstring="[para(645(a,1),23004(a,1,1))].">
      <j1 rule="para" parents="645 23004"/>
    </justification>
  </clause>

  <clause id="23442">
    <literal><![CDATA[
      (x \ L(y,z,u)) * K(y,w) = x \ L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(23004(a,1),15043(a,1,2))].">
      <j1 rule="para" parents="23004 15043"/>
    </justification>
  </clause>

  <clause id="23444">
    <literal><![CDATA[
      K(x,y) * ((x * z) * u) = (T(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(23004(a,1),15613(a,1,1))].">
      <j1 rule="para" parents="23004 15613"/>
    </justification>
  </clause>

  <clause id="23495">
    <literal><![CDATA[
      K(x,R(y,z,u)) * w = K(x,y) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,23042,a,b,11,a)].">
      <j1 rule="hyper" parents="144 23042 11"/>
    </justification>
  </clause>

  <clause id="23496">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(143,a,23042,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 23042 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23499">
    <literal><![CDATA[
      R(T(x,y),z,u) * K(y,x) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,23042,a(flip),b,5802,a)].">
      <j1 rule="hyper" parents="145 23042 5802"/>
    </justification>
  </clause>

  <clause id="23500">
    <literal><![CDATA[
      T(x,R(y,z,u)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,23042,a(flip),b,5726,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 23042 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23501">
    <literal><![CDATA[
      (R(x,y,z) * u) * K(u,x) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,23042,a(flip),b,16,a(flip))].">
      <j1 rule="hyper" parents="145 23042 16"/>
    </justification>
  </clause>

  <clause id="23503">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * x) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,23042,a(flip),b,5786,a(flip))].">
      <j1 rule="hyper" parents="144 23042 5786"/>
    </justification>
  </clause>

  <clause id="23505">
    <literal><![CDATA[
      K(x,T((y / z) / u,w)) = K(x,T(y / (u * z),w))
    ]]></literal>
    <justification jstring="[para(714(a,1),23042(a,1,2)),flip(a)].">
      <j1 rule="para" parents="714 23042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23506">
    <literal><![CDATA[
      K(x,T((y * z) / u,w)) = K(x,T(y / (u / z),w))
    ]]></literal>
    <justification jstring="[para(1033(a,1),23042(a,1,2))].">
      <j1 rule="para" parents="1033 23042"/>
    </justification>
  </clause>

  <clause id="23508">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) \ w) = T(R(y,z,u),x) \ w
    ]]></literal>
    <justification jstring="[para(23042(a,1),6157(a,1,1))].">
      <j1 rule="para" parents="23042 6157"/>
    </justification>
  </clause>

  <clause id="23518">
    <literal><![CDATA[
      K(x,y) * ((R(y,z,u) * x) / w) = (x * R(y,z,u)) / w
    ]]></literal>
    <justification jstring="[para(23042(a,1),14887(a,1,1))].">
      <j1 rule="para" parents="23042 14887"/>
    </justification>
  </clause>

  <clause id="23532">
    <literal><![CDATA[
      K(x,y \ L(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,22227,a,b,23081,a)].">
      <j1 rule="hyper" parents="64 22227 23081"/>
    </justification>
  </clause>

  <clause id="23533">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,15343,a,b,23081,a)].">
      <j1 rule="hyper" parents="64 15343 23081"/>
    </justification>
  </clause>

  <clause id="23534">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13797,a,b,23081,a)].">
      <j1 rule="hyper" parents="64 13797 23081"/>
    </justification>
  </clause>

  <clause id="23538">
    <literal><![CDATA[
      x * K(y,L(z,u,w) \ z) = x
    ]]></literal>
    <justification jstring="[para(13953(a,2),23081(a,1,2))].">
      <j1 rule="para" parents="13953 23081"/>
    </justification>
  </clause>

  <clause id="23544">
    <literal><![CDATA[
      T(x,y \ R(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,23085,a)].">
      <j1 rule="hyper" parents="57 23085"/>
    </justification>
  </clause>

  <clause id="23552">
    <literal><![CDATA[
      L(x \ R(x,y,z),x \ R(x,y,z),u) \ u = u * (1 / (x \ R(x,y,z)))
    ]]></literal>
    <justification jstring="[para(23085(a,1),14981(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23085 14981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23554">
    <literal><![CDATA[
      x / (a(y,z,u) * w) = x / (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,10595,a(flip),b,23103,a)].">
      <j1 rule="hyper" parents="64 10595 23103"/>
    </justification>
  </clause>

  <clause id="23556">
    <literal><![CDATA[
      T(a(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(23103(a,1),5892(a,1,1)),flip(b)].">
      <j1 rule="para" parents="23103 5892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23557">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * v5 = v5 * L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23103(a,1),5862(a,1,1,1))].">
      <j1 rule="para" parents="23103 5862"/>
    </justification>
  </clause>

  <clause id="23558">
    <literal><![CDATA[
      R(x / y,y,a(z,u,w)) = (x * a(z,u,w)) / (a(z,u,w) * y)
    ]]></literal>
    <justification jstring="[para(23103(a,1),10305(a,1,1))].">
      <j1 rule="para" parents="23103 10305"/>
    </justification>
  </clause>

  <clause id="23560">
    <literal><![CDATA[
      (a(x,y,z) * u) \ w = (u * a(x,y,z)) \ w
    ]]></literal>
    <justification jstring="[hyper(64,a,10833,a(flip),b,23104,a)].">
      <j1 rule="hyper" parents="64 10833 23104"/>
    </justification>
  </clause>

  <clause id="23576">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ w) * w = (w / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16111,a(flip),b,23126,a)].">
      <j1 rule="hyper" parents="64 16111 23126"/>
    </justification>
  </clause>

  <clause id="23577">
    <literal><![CDATA[
      (x * x) * (a(y,z,u) \ 1) = a(y,z,u) \ (x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6629,a(flip),b,23126,a)].">
      <j1 rule="hyper" parents="64 6629 23126"/>
    </justification>
  </clause>

  <clause id="23578">
    <literal><![CDATA[
      a(x,y,z) * ((u * u) * (a(x,y,z) \ w)) = (u * u) * w
    ]]></literal>
    <justification jstring="[hyper(145,a,6626,a(flip),b,23126,a(flip))].">
      <j1 rule="hyper" parents="145 6626 23126"/>
    </justification>
  </clause>

  <clause id="23579">
    <literal><![CDATA[
      x / (L(y,z,u) \ y) = (L(y,z,u) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(8638,a,23148,a),flip(a)].">
      <j1 rule="hyper" parents="8638 23148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23580">
    <literal><![CDATA[
      ((L(x,y,z) \ x) \ u) \ u = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(4722,a,23148,a)].">
      <j1 rule="hyper" parents="4722 23148"/>
    </justification>
  </clause>

  <clause id="23581">
    <literal><![CDATA[
      (L(x,y,z) \ x) * u = u * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(2149,a,23148,a),flip(a)].">
      <j1 rule="hyper" parents="2149 23148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23584">
    <literal><![CDATA[
      (((x / y) * L(y,z,u)) \ x) \ x = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14974,a(flip),b,23148,a)].">
      <j1 rule="hyper" parents="64 14974 23148"/>
    </justification>
  </clause>

  <clause id="23586">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(55,a,23148,a)].">
      <j1 rule="hyper" parents="55 23148"/>
    </justification>
  </clause>

  <clause id="23587">
    <literal><![CDATA[
      x / ((x / y) * L(y,z,u)) = ((x / y) * L(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,23148,a(flip),b,14974,a(flip))].">
      <j1 rule="hyper" parents="225 23148 14974"/>
    </justification>
  </clause>

  <clause id="23588">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (u / (L(x,y,z) \ x)) = u
    ]]></literal>
    <justification jstring="[hyper(145,a,23148,a(flip),b,117,a(flip))].">
      <j1 rule="hyper" parents="145 23148 117"/>
    </justification>
  </clause>

  <clause id="23589">
    <literal><![CDATA[
      (L(x,y,z) \ x) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * (L(x,y,z) \ x) = w
    ]]></literal>
    <justification jstring="[para(23148(a,1),328(a,1,2))].">
      <j1 rule="para" parents="23148 328"/>
    </justification>
  </clause>

  <clause id="23590">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) / w = (u * (L(x,y,z) \ x)) / w
    ]]></literal>
    <justification jstring="[para(23148(a,1),250(a,1,1,2))].">
      <j1 rule="para" parents="23148 250"/>
    </justification>
  </clause>

  <clause id="23591">
    <literal><![CDATA[
      T(x,y / L(y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(5558(a,2),23148(a,1,2))].">
      <j1 rule="para" parents="5558 23148"/>
    </justification>
  </clause>

  <clause id="23592">
    <literal><![CDATA[
      x / ((y \ L(y,z,u)) * x) = ((y \ L(y,z,u)) * x) \ x
    ]]></literal>
    <justification jstring="[para(23148(a,1),6728(a,1,2))].">
      <j1 rule="para" parents="23148 6728"/>
    </justification>
  </clause>

  <clause id="23593">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) / u = u \ ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(23148(a,1),6735(a,1,2))].">
      <j1 rule="para" parents="23148 6735"/>
    </justification>
  </clause>

  <clause id="23605">
    <literal><![CDATA[
      T(x,L(a(y,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,23105,a(flip),b,23153,a),flip(a)].">
      <j1 rule="hyper" parents="373 23105 23153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23610">
    <literal><![CDATA[
      T(x / y,L(y,z,u)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,117,a(flip),b,23153,a),flip(a)].">
      <j1 rule="hyper" parents="373 117 23153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23614">
    <literal><![CDATA[
      x * R(L(y,z,u),x,L(y,z,u)) = T(L(y,z,u) * x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4741,a,b,23153,a)].">
      <j1 rule="hyper" parents="64 4741 23153"/>
    </justification>
  </clause>

  <clause id="23615">
    <literal><![CDATA[
      T(x,(y * z) \ u) = T(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22706,a(flip),b,23153,a),flip(a)].">
      <j1 rule="hyper" parents="64 22706 23153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23616">
    <literal><![CDATA[
      T(x,(y * z) / u) = T(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,15682,a(flip),b,23153,a)].">
      <j1 rule="hyper" parents="64 15682 23153"/>
    </justification>
  </clause>

  <clause id="23618">
    <literal><![CDATA[
      (x * L(y,z,u)) \ T(x,y) = (L(y,z,u) * x) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,23153,a(flip),b,6982,a(flip))].">
      <j1 rule="hyper" parents="139 23153 6982"/>
    </justification>
  </clause>

  <clause id="23619">
    <literal><![CDATA[
      T(x,T(L(y,z,u),w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(25(a,1),23153(a,1,2))].">
      <j1 rule="para" parents="25 23153"/>
    </justification>
  </clause>

  <clause id="23620">
    <literal><![CDATA[
      T(x,(y * z) \ (y * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(102(a,1),23153(a,1,2))].">
      <j1 rule="para" parents="102 23153"/>
    </justification>
  </clause>

  <clause id="23621">
    <literal><![CDATA[
      T(x,(y \ z) \ u) = T(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(630(a,1),23153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="630 23153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23622">
    <literal><![CDATA[
      T(x,y \ ((y / z) * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(633(a,1),23153(a,1,2))].">
      <j1 rule="para" parents="633 23153"/>
    </justification>
  </clause>

  <clause id="23623">
    <literal><![CDATA[
      T(x,T((y * z) \ u,w)) = T(x,T(z \ (y \ u),w))
    ]]></literal>
    <justification jstring="[para(708(a,1),23153(a,1,2))].">
      <j1 rule="para" parents="708 23153"/>
    </justification>
  </clause>

  <clause id="23624">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ L(z,u,w)) = L(z,u,w) \ (x * (y \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(23153(a,1),1379(a,1,1))].">
      <j1 rule="para" parents="23153 1379"/>
    </justification>
  </clause>

  <clause id="23627">
    <literal><![CDATA[
      T(x,((y * z) * u) \ ((y * (z * u)) * w)) = T(x,a(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(961(a,1),23153(a,1,2))].">
      <j1 rule="para" parents="961 23153"/>
    </justification>
  </clause>

  <clause id="23628">
    <literal><![CDATA[
      L(x,y,z) * (T(u * u,x) * w) = (u * u) * (L(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(23153(a,1),6625(a,1,2,1))].">
      <j1 rule="para" parents="23153 6625"/>
    </justification>
  </clause>

  <clause id="23629">
    <literal><![CDATA[
      T(L(x,y,z) \ 1,T(u,x)) = T(L(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(23153(a,1),7227(a,1,2))].">
      <j1 rule="para" parents="23153 7227"/>
    </justification>
  </clause>

  <clause id="23632">
    <literal><![CDATA[
      L(x,y,z) * (T(x \ 1,x) * u) = (x \ 1) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(23153(a,1),11926(a,1,2,1))].">
      <j1 rule="para" parents="23153 11926"/>
    </justification>
  </clause>

  <clause id="23637">
    <literal><![CDATA[
      T(x,y) / (z \ (x * L(y,u,w))) = x / (z \ (L(y,u,w) * x))
    ]]></literal>
    <justification jstring="[para(23153(a,1),15227(a,1,1))].">
      <j1 rule="para" parents="23153 15227"/>
    </justification>
  </clause>

  <clause id="23640">
    <literal><![CDATA[
      K(x,T(L(y \ z,y,z \ u) \ T(u,y \ z),w) * v5) = K(x,T((u / z) * y,w) * v5)
    ]]></literal>
    <justification jstring="[para(23153(a,1),18572(a,1,2,1,1,2))].">
      <j1 rule="para" parents="23153 18572"/>
    </justification>
  </clause>

  <clause id="23656">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7356,a,b,23385,a)].">
      <j1 rule="hyper" parents="64 7356 23385"/>
    </justification>
  </clause>

  <clause id="23657">
    <literal><![CDATA[
      R(x,y,z) * K(x,u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,23385,a(flip),b,5765,a)].">
      <j1 rule="hyper" parents="145 23385 5765"/>
    </justification>
  </clause>

  <clause id="23658">
    <literal><![CDATA[
      (R(x,y,z) * u) / R(x,y,z) = u * K(x,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,23385,a(flip),b,5719,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 23385 5719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23659">
    <literal><![CDATA[
      K(x,y) * R(x,z,u) = R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,23385,a(flip),b,5815,a)].">
      <j1 rule="hyper" parents="144 23385 5815"/>
    </justification>
  </clause>

  <clause id="23660">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) \ w = K(y,x) * (R(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(23385(a,1),6077(a,2,1))].">
      <j1 rule="para" parents="23385 6077"/>
    </justification>
  </clause>

  <clause id="23661">
    <literal><![CDATA[
      K(x,y) * (R(x,z,u) * w) = R(T(x,y),z,u) * w
    ]]></literal>
    <justification jstring="[para(23385(a,1),6028(a,1,1))].">
      <j1 rule="para" parents="23385 6028"/>
    </justification>
  </clause>

  <clause id="23662">
    <literal><![CDATA[
      ((x * y) * z) / R(x,y,z) = (y * z) * K(x,y * z)
    ]]></literal>
    <justification jstring="[para(23385(a,1),5896(a,2,2))].">
      <j1 rule="para" parents="23385 5896"/>
    </justification>
  </clause>

  <clause id="23663">
    <literal><![CDATA[
      K(x,y) * (x \ R(x,z,u)) = x \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(23385(a,1),10123(a,1,1))].">
      <j1 rule="para" parents="23385 10123"/>
    </justification>
  </clause>

  <clause id="23678">
    <literal><![CDATA[
      T(((x \ y) / y) \ z,x * x) = T(z / ((x \ y) / y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,15751,a(flip),b,23496,a)].">
      <j1 rule="hyper" parents="64 15751 23496"/>
    </justification>
  </clause>

  <clause id="23680">
    <literal><![CDATA[
      (x * R(y,z,u)) / T(x,y) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(225,a,23496,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="225 23496 22"/>
    </justification>
  </clause>

  <clause id="23681">
    <literal><![CDATA[
      R(x,y,z) * T(u,x) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,23496,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 23496 22"/>
    </justification>
  </clause>

  <clause id="23682">
    <literal><![CDATA[
      R(R(x,y,z),u,R(x,y,z)) = u \ T(R(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,23496,a(flip),b,4741,a),flip(a)].">
      <j1 rule="hyper" parents="139 23496 4741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23683">
    <literal><![CDATA[
      T(x,y / (z * (u \ y))) = T(x,u / z)
    ]]></literal>
    <justification jstring="[para(676(a,1),23496(a,1,2))].">
      <j1 rule="para" parents="676 23496"/>
    </justification>
  </clause>

  <clause id="23684">
    <literal><![CDATA[
      T(x,T(y / (z * u),z)) = T(x,z \ (y / u))
    ]]></literal>
    <justification jstring="[para(856(a,1),23496(a,1,2))].">
      <j1 rule="para" parents="856 23496"/>
    </justification>
  </clause>

  <clause id="23688">
    <literal><![CDATA[
      T(x * x,y) * (R(y,z,u) \ w) = R(y,z,u) \ ((x * x) * w)
    ]]></literal>
    <justification jstring="[para(23496(a,1),6431(a,1,1))].">
      <j1 rule="para" parents="23496 6431"/>
    </justification>
  </clause>

  <clause id="23689">
    <literal><![CDATA[
      L(T(x,y) \ z,x,R(y,u,w)) = (x * R(y,u,w)) \ (R(y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(23496(a,1),10979(a,1,1,1))].">
      <j1 rule="para" parents="23496 10979"/>
    </justification>
  </clause>

  <clause id="23691">
    <literal><![CDATA[
      T(x,R(y,z,u) \ (T(w,y) \ v5)) = T(x,w \ (R(y,z,u) \ v5))
    ]]></literal>
    <justification jstring="[para(23496(a,1),22718(a,1,2,2,1))].">
      <j1 rule="para" parents="23496 22718"/>
    </justification>
  </clause>

  <clause id="23693">
    <literal><![CDATA[
      x * K(y,z \ L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,23532,a,b,68,a)].">
      <j1 rule="hyper" parents="145 23532 68"/>
    </justification>
  </clause>

  <clause id="23694">
    <literal><![CDATA[
      K(x,y \ L(y,z,u)) * w = w
    ]]></literal>
    <justification jstring="[hyper(144,a,23532,a,b,76,a)].">
      <j1 rule="hyper" parents="144 23532 76"/>
    </justification>
  </clause>

  <clause id="23695">
    <literal><![CDATA[
      K(x \ L(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,23532,a,b,6076,a),flip(a)].">
      <j1 rule="hyper" parents="140 23532 6076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23696">
    <literal><![CDATA[
      K(x,a(y,z,u) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,13889,a,b,23532,a)].">
      <j1 rule="hyper" parents="64 13889 23532"/>
    </justification>
  </clause>

  <clause id="23697">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,23532,a)].">
      <j1 rule="hyper" parents="57 23532"/>
    </justification>
  </clause>

  <clause id="23700">
    <literal><![CDATA[
      (a(x,y,z) \ u) * u = u * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(145,a,23533,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 23533 22"/>
    </justification>
  </clause>

  <clause id="23701">
    <literal><![CDATA[
      T(a(x,y,z) * u,u) = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(9(a,1),23533(a,1,2))].">
      <j1 rule="para" parents="9 23533"/>
    </justification>
  </clause>

  <clause id="23702">
    <literal><![CDATA[
      (1 / (1 / x)) \ (a(y,z,u) \ 1) = (a(y,z,u) \ 1) / x
    ]]></literal>
    <justification jstring="[para(23533(a,1),5142(a,2,2))].">
      <j1 rule="para" parents="23533 5142"/>
    </justification>
  </clause>

  <clause id="23703">
    <literal><![CDATA[
      T((x * y) * z,x * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(15467(a,1),23533(a,1,2))].">
      <j1 rule="para" parents="15467 23533"/>
    </justification>
  </clause>

  <clause id="23705">
    <literal><![CDATA[
      x / (y \ R(y,z,u)) = (y \ R(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(8638,a,23544,a),flip(a)].">
      <j1 rule="hyper" parents="8638 23544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23706">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ u) \ u = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4722,a,23544,a)].">
      <j1 rule="hyper" parents="4722 23544"/>
    </justification>
  </clause>

  <clause id="23708">
    <literal><![CDATA[
      (x \ R(x,y,z)) * u = u * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(2149,a,23544,a),flip(a)].">
      <j1 rule="hyper" parents="2149 23544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23709">
    <literal><![CDATA[
      T(x,(y \ 1) * R(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,14479,a,b,23544,a)].">
      <j1 rule="hyper" parents="64 14479 23544"/>
    </justification>
  </clause>

  <clause id="23710">
    <literal><![CDATA[
      (((R(x,y,z) \ 1) * x) \ 1) \ 1 = (R(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,14972,a(flip),b,23544,a)].">
      <j1 rule="hyper" parents="64 14972 23544"/>
    </justification>
  </clause>

  <clause id="23711">
    <literal><![CDATA[
      R(x,y,z) \ (x * (u * (x \ R(x,y,z)))) = L(u,x \ R(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1049,a(flip),b,23544,a)].">
      <j1 rule="hyper" parents="64 1049 23544"/>
    </justification>
  </clause>

  <clause id="23712">
    <literal><![CDATA[
      T(x \ R(x,y,z),u) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(55,a,23544,a)].">
      <j1 rule="hyper" parents="55 23544"/>
    </justification>
  </clause>

  <clause id="23713">
    <literal><![CDATA[
      (x * (y * (z \ R(z,u,w)))) / (x * y) = L(z \ R(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(225,a,23544,a(flip),b,14658,a)].">
      <j1 rule="hyper" parents="225 23544 14658"/>
    </justification>
  </clause>

  <clause id="23714">
    <literal><![CDATA[
      (x \ R(y,z,u)) / (x \ y) = (x \ y) \ (x \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(225,a,23544,a(flip),b,12200,a(flip))].">
      <j1 rule="hyper" parents="225 23544 12200"/>
    </justification>
  </clause>

  <clause id="23715">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) / x = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(225,a,23544,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="225 23544 22"/>
    </justification>
  </clause>

  <clause id="23717">
    <literal><![CDATA[
      T(x,(y / (z * y)) * z) = x
    ]]></literal>
    <justification jstring="[para(1786(a,1),23544(a,1,2))].">
      <j1 rule="para" parents="1786 23544"/>
    </justification>
  </clause>

  <clause id="23719">
    <literal><![CDATA[
      T(x,((y \ z) / z) * y) = x
    ]]></literal>
    <justification jstring="[para(1992(a,1),23544(a,1,2))].">
      <j1 rule="para" parents="1992 23544"/>
    </justification>
  </clause>

  <clause id="23720">
    <literal><![CDATA[
      T(x,R(y,z,u) / y) = x
    ]]></literal>
    <justification jstring="[para(2071(a,2),23544(a,1,2))].">
      <j1 rule="para" parents="2071 23544"/>
    </justification>
  </clause>

  <clause id="23721">
    <literal><![CDATA[
      T(x,y \ (z * R(z \ y,u,w))) = x
    ]]></literal>
    <justification jstring="[para(2744(a,1),23544(a,1,2))].">
      <j1 rule="para" parents="2744 23544"/>
    </justification>
  </clause>

  <clause id="23722">
    <literal><![CDATA[
      T(x,y * ((y \ z) / z)) = x
    ]]></literal>
    <justification jstring="[para(3008(a,1),23544(a,1,2))].">
      <j1 rule="para" parents="3008 23544"/>
    </justification>
  </clause>

  <clause id="23723">
    <literal><![CDATA[
      T(x,y * (z / (y * z))) = x
    ]]></literal>
    <justification jstring="[para(3015(a,1),23544(a,1,2))].">
      <j1 rule="para" parents="3015 23544"/>
    </justification>
  </clause>

  <clause id="23725">
    <literal><![CDATA[
      ((x \ R(x,y,z)) / u) / (1 / u) = (1 / u) \ ((x \ R(x,y,z)) / u)
    ]]></literal>
    <justification jstring="[para(23544(a,1),10799(a,1,2))].">
      <j1 rule="para" parents="23544 10799"/>
    </justification>
  </clause>

  <clause id="23726">
    <literal><![CDATA[
      (x * R(y,z,u)) / (x * y) = (x * y) \ (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(23544(a,1),14915(a,1,2))].">
      <j1 rule="para" parents="23544 14915"/>
    </justification>
  </clause>

  <clause id="23727">
    <literal><![CDATA[
      T(x,(y / z) * (z / y)) = x
    ]]></literal>
    <justification jstring="[para(15122(a,1),23591(a,1,2))].">
      <j1 rule="para" parents="15122 23591"/>
    </justification>
  </clause>

  <clause id="23730">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),u) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(23695(a,1),14980(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23695 14980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23733">
    <literal><![CDATA[
      K(a(x,y,z) \ 1,u) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,23696,a,b,6076,a),flip(a)].">
      <j1 rule="hyper" parents="140 23696 6076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23734">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,23696,a)].">
      <j1 rule="hyper" parents="57 23696"/>
    </justification>
  </clause>

  <clause id="23735">
    <literal><![CDATA[
      T(a(x,y,z) \ 1,u) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(23696(a,1),5866(a,1,1,2))].">
      <j1 rule="para" parents="23696 5866"/>
    </justification>
  </clause>

  <clause id="23736">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u = u * (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(23696(a,1),5887(a,1,1,2))].">
      <j1 rule="para" parents="23696 5887"/>
    </justification>
  </clause>

  <clause id="23737">
    <literal><![CDATA[
      x / (a(y,z,u) \ 1) = (a(y,z,u) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(23696(a,1),8738(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="23696 8738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23739">
    <literal><![CDATA[
      T(x,y * L(y \ 1,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(14642,a,23697,a)].">
      <j1 rule="hyper" parents="14642 23697"/>
    </justification>
  </clause>

  <clause id="23740">
    <literal><![CDATA[
      x / (y \ L(y,z,u)) = (y \ L(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(8638,a,23697,a),flip(a)].">
      <j1 rule="hyper" parents="8638 23697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23741">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ u) * (x \ L(x,y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(2159,a,23697,a)].">
      <j1 rule="hyper" parents="2159 23697"/>
    </justification>
  </clause>

  <clause id="23742">
    <literal><![CDATA[
      (x \ L(x,y,z)) * u = u * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(2149,a,23697,a),flip(a)].">
      <j1 rule="hyper" parents="2149 23697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23743">
    <literal><![CDATA[
      (((x \ L(x,y,z)) * u) * w) / ((x \ L(x,y,z)) * w) = R(u,x \ L(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(1054,a,23697,a)].">
      <j1 rule="hyper" parents="1054 23697"/>
    </justification>
  </clause>

  <clause id="23744">
    <literal><![CDATA[
      L(x,y,z) \ (x * (u * (x \ L(x,y,z)))) = L(u,x \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1049,a(flip),b,23697,a)].">
      <j1 rule="hyper" parents="64 1049 23697"/>
    </justification>
  </clause>

  <clause id="23745">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * (w * u) = w * (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(145,a,23697,a(flip),b,14658,a)].">
      <j1 rule="hyper" parents="145 23697 14658"/>
    </justification>
  </clause>

  <clause id="23746">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) * w = (u * (x \ L(x,y,z))) * w
    ]]></literal>
    <justification jstring="[hyper(39,a,1755,a(flip),b,23697,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 1755 23697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23747">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(23697(a,1),50(a,2))].">
      <j1 rule="para" parents="23697 50"/>
    </justification>
  </clause>

  <clause id="23749">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1807(a,2),23697(a,1,2))].">
      <j1 rule="para" parents="1807 23697"/>
    </justification>
  </clause>

  <clause id="23751">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ ((u * u) * w) = (u * u) * ((x \ L(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(23697(a,1),6431(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23697 6431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23752">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((u * u) * w) = (u * u) * ((x \ L(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[para(23697(a,1),6625(a,1,2,1))].">
      <j1 rule="para" parents="23697 6625"/>
    </justification>
  </clause>

  <clause id="23753">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) / T(x,w) = K(w,x) * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(23697(a,1),7947(a,1,2,1))].">
      <j1 rule="para" parents="23697 7947"/>
    </justification>
  </clause>

  <clause id="23754">
    <literal><![CDATA[
      T(L(x,1 / y,L(y,z,u)) * (1 / y),L(y,z,u)) = (y \ 1) * R(x,1 / y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(23697(a,1),16431(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23697 16431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23757">
    <literal><![CDATA[
      T(x \ (a(x,y,y) \ 1),a(z,u,w) \ 1) = R(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,16021,a(flip),b,23734,a),flip(a)].">
      <j1 rule="hyper" parents="373 16021 23734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23758">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,y,z) \ (z * L(y,x,x)) = z * y
    ]]></literal>
    <justification jstring="[hyper(64,a,14742,a,b,23734,a)].">
      <j1 rule="hyper" parents="64 14742 23734"/>
    </justification>
  </clause>

  <clause id="23759">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ 1)) = L(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1178,a(flip),b,23734,a)].">
      <j1 rule="hyper" parents="64 1178 23734"/>
    </justification>
  </clause>

  <clause id="23760">
    <literal><![CDATA[
      (x \ 1) / (x \ a(y,z,u)) = (x \ a(y,z,u)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(225,a,23734,a(flip),b,12200,a(flip))].">
      <j1 rule="hyper" parents="225 23734 12200"/>
    </justification>
  </clause>

  <clause id="23761">
    <literal><![CDATA[
      x / (x * a(y,z,u)) = (x * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,23734,a(flip),b,6745,a(flip))].">
      <j1 rule="hyper" parents="225 23734 6745"/>
    </justification>
  </clause>

  <clause id="23762">
    <literal><![CDATA[
      ((a(x,y,z) * u) \ u) * (a(x,y,z) * u) = u
    ]]></literal>
    <justification jstring="[hyper(145,a,23734,a(flip),b,4590,a(flip))].">
      <j1 rule="hyper" parents="145 23734 4590"/>
    </justification>
  </clause>

  <clause id="23763">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * R(u \ 1,u,a(x,y,z) \ 1) = u \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,23734,a(flip),b,2997,a(flip))].">
      <j1 rule="hyper" parents="145 23734 2997"/>
    </justification>
  </clause>

  <clause id="23764">
    <literal><![CDATA[
      x * ((a(y,z,u) \ 1) * w) = x * (w * (a(y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(38,a,2873,a(flip),b,23734,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 2873 23734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23765">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * (a(x,y,z) \ 1) = w
    ]]></literal>
    <justification jstring="[para(23734(a,1),328(a,1,2))].">
      <j1 rule="para" parents="23734 328"/>
    </justification>
  </clause>

  <clause id="23766">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * R(u,u,a(x,y,z) \ 1) = (1 / u) \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(23734(a,1),1914(a,1,2,1))].">
      <j1 rule="para" parents="23734 1914"/>
    </justification>
  </clause>

  <clause id="23767">
    <literal><![CDATA[
      (a(x,y,z) \ u) / u = u \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(23734(a,1),4409(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23734 4409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23768">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ x)) * x = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(23734(a,1),4577(a,1,2))].">
      <j1 rule="para" parents="23734 4577"/>
    </justification>
  </clause>

  <clause id="23769">
    <literal><![CDATA[
      L((x * a(y,z,u)) \ x,x * a(y,z,u),w) = (w * x) / (w * (x * a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(23734(a,1),14916(a,2,2))].">
      <j1 rule="para" parents="23734 14916"/>
    </justification>
  </clause>

  <clause id="23776">
    <literal><![CDATA[
      a(x,y,z) != u \ w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) * u = w
    ]]></literal>
    <justification jstring="[para(23127(a,1),158(a,1))].">
      <j1 rule="para" parents="23127 158"/>
    </justification>
  </clause>

  <clause id="23777">
    <literal><![CDATA[
      x * a(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(23127(a,1),328(a,1,2))].">
      <j1 rule="para" parents="23127 328"/>
    </justification>
  </clause>

  <clause id="23778">
    <literal><![CDATA[
      (1 / x) * (a(y,z,u) * x) = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(23127(a,1),567(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23127 567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23780">
    <literal><![CDATA[
      (x * a(y,z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) * x) * w = v5
    ]]></literal>
    <justification jstring="[para(23127(a,1),718(a,1,1,2))].">
      <j1 rule="para" parents="23127 718"/>
    </justification>
  </clause>

  <clause id="23782">
    <literal><![CDATA[
      x * (a(y,z,u) * (x \ 1)) = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(23127(a,1),1140(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23127 1140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23783">
    <literal><![CDATA[
      L(a(x,y,z),u \ w,u) * w = u * ((u \ w) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(23127(a,1),964(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23127 964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23784">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) \ u,w) = (w * (a(x,y,z) \ u)) \ (w * u)
    ]]></literal>
    <justification jstring="[para(23127(a,1),409(a,1,1))].">
      <j1 rule="para" parents="23127 409"/>
    </justification>
  </clause>

  <clause id="23785">
    <literal><![CDATA[
      x / L(a(y,z,u),w,v5) = L(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[para(23127(a,1),419(a,1,2,1))].">
      <j1 rule="para" parents="23127 419"/>
    </justification>
  </clause>

  <clause id="23787">
    <literal><![CDATA[
      (x * x) \ (a(y,z,u) \ (x * w)) = a(y,z,u) \ ((1 / x) * w)
    ]]></literal>
    <justification jstring="[para(23127(a,1),1528(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23127 1528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23790">
    <literal><![CDATA[
      T(x * a(y,z,u),K(x,w)) = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(23127(a,1),8062(a,2,2))].">
      <j1 rule="para" parents="23127 8062"/>
    </justification>
  </clause>

  <clause id="23791">
    <literal><![CDATA[
      T(a(x,y,z) * (u \ w),K(u,w)) = (u \ w) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(23127(a,1),9168(a,2,2))].">
      <j1 rule="para" parents="23127 9168"/>
    </justification>
  </clause>

  <clause id="23792">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) \ v5 = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23127(a,1),10457(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23127 10457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23793">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),w) = (a(x,y,z) * w) \ (w * u)
    ]]></literal>
    <justification jstring="[para(23127(a,1),10979(a,1,1,1))].">
      <j1 rule="para" parents="23127 10979"/>
    </justification>
  </clause>

  <clause id="23794">
    <literal><![CDATA[
      x \ ((x / y) * (a(z,u,w) * y)) = L(a(z,u,w),y,y \ x)
    ]]></literal>
    <justification jstring="[para(23127(a,1),11069(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23127 11069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23797">
    <literal><![CDATA[
      a(x,y,z) \ (u * a(x,y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(22(a,1),23173(a,1))].">
      <j1 rule="para" parents="22 23173"/>
    </justification>
  </clause>

  <clause id="23798">
    <literal><![CDATA[
      R(x,y,T(z,u)) = R(x,y,T(z,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,23198,a,b,23198,a)].">
      <j1 rule="hyper" parents="373 23198 23198"/>
    </justification>
  </clause>

  <clause id="23810">
    <literal><![CDATA[
      R(x,T(y,z),y) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2542,a,b,23198,a)].">
      <j1 rule="hyper" parents="64 2542 23198"/>
    </justification>
  </clause>

  <clause id="23811">
    <literal><![CDATA[
      R(x,y,L(T(z,u),w,v5)) = R(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(25(a,2),23198(a,1,3))].">
      <j1 rule="para" parents="25 23198"/>
    </justification>
  </clause>

  <clause id="23812">
    <literal><![CDATA[
      R(x,y,R(T(z,u),w,v5)) = R(x,y,R(z,w,v5))
    ]]></literal>
    <justification jstring="[para(27(a,2),23198(a,1,3))].">
      <j1 rule="para" parents="27 23198"/>
    </justification>
  </clause>

  <clause id="23813">
    <literal><![CDATA[
      R(x,y,z / u) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(117(a,1),23198(a,1,3)),flip(a)].">
      <j1 rule="para" parents="117 23198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23814">
    <literal><![CDATA[
      R(x,y,z / (z / u)) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(276(a,1),23198(a,1,3)),flip(a)].">
      <j1 rule="para" parents="276 23198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23815">
    <literal><![CDATA[
      R(x,y,(z * z) \ 1) = R(x,y,z \ (1 / z))
    ]]></literal>
    <justification jstring="[para(555(a,1),23198(a,1,3)),flip(a)].">
      <j1 rule="para" parents="555 23198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23824">
    <literal><![CDATA[
      L(x,K(y,z) * u,y) = L(x,u,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,21719,a,b,23215,a)].">
      <j1 rule="hyper" parents="373 21719 23215"/>
    </justification>
  </clause>

  <clause id="23826">
    <literal><![CDATA[
      L(x,y,T(T(z,u),w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,23215,a(flip),b,23215,a),flip(a)].">
      <j1 rule="hyper" parents="373 23215 23215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23827">
    <literal><![CDATA[
      L(x,T(y,z),T(y,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,21717,a(flip),b,23215,a),flip(a)].">
      <j1 rule="hyper" parents="373 21717 23215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23833">
    <literal><![CDATA[
      L(x,y,(z \ u) * z) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13006,a,b,23215,a)].">
      <j1 rule="hyper" parents="64 13006 23215"/>
    </justification>
  </clause>

  <clause id="23835">
    <literal><![CDATA[
      L(x,y,(z * u) / z) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,6433,a,b,23215,a)].">
      <j1 rule="hyper" parents="64 6433 23215"/>
    </justification>
  </clause>

  <clause id="23837">
    <literal><![CDATA[
      L((x * y) \ y,a(z,u,w),x) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,14049,a(flip),b,23215,a),flip(a)].">
      <j1 rule="hyper" parents="64 14049 23215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23838">
    <literal><![CDATA[
      L(x \ T(y,T(z,u)),x,z) = (T(z,u) * x) \ (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,521,a(flip),b,23215,a),flip(a)].">
      <j1 rule="hyper" parents="64 521 23215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23839">
    <literal><![CDATA[
      L(x \ (T(y,z) \ u),x,y) = (T(y,z) * x) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,346,a(flip),b,23215,a),flip(a)].">
      <j1 rule="hyper" parents="64 346 23215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23840">
    <literal><![CDATA[
      L(x \ y,x,z) = (T(z,u) * x) \ (T(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,23215,a),flip(a)].">
      <j1 rule="hyper" parents="64 102 23215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23841">
    <literal><![CDATA[
      (T(x,y) * z) * L(u,z,x) = T(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,23215,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 23215 18"/>
    </justification>
  </clause>

  <clause id="23842">
    <literal><![CDATA[
      L(x,y,z \ (u * z)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(22(a,1),23215(a,1,3))].">
      <j1 rule="para" parents="22 23215"/>
    </justification>
  </clause>

  <clause id="23843">
    <literal><![CDATA[
      L(x,y,L(T(z,u),w,v5)) = L(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(25(a,2),23215(a,1,3))].">
      <j1 rule="para" parents="25 23215"/>
    </justification>
  </clause>

  <clause id="23844">
    <literal><![CDATA[
      L(x,y,R(T(z,u),w,v5)) = L(x,y,R(z,w,v5))
    ]]></literal>
    <justification jstring="[para(27(a,2),23215(a,1,3))].">
      <j1 rule="para" parents="27 23215"/>
    </justification>
  </clause>

  <clause id="23845">
    <literal><![CDATA[
      L(x,y,z / (z / u)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(276(a,1),23215(a,1,3)),flip(a)].">
      <j1 rule="para" parents="276 23215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23846">
    <literal><![CDATA[
      L(x,y,L(z / u,w,v5)) = L(x,y,L(u \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(279(a,1),23215(a,1,3)),flip(a)].">
      <j1 rule="para" parents="279 23215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23847">
    <literal><![CDATA[
      L(x,y,R(z / u,w,v5)) = L(x,y,R(u \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(280(a,1),23215(a,1,3)),flip(a)].">
      <j1 rule="para" parents="280 23215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23848">
    <literal><![CDATA[
      L(x,y,L((z \ u) \ u,w,v5)) = L(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(368(a,1),23215(a,1,3))].">
      <j1 rule="para" parents="368 23215"/>
    </justification>
  </clause>

  <clause id="23849">
    <literal><![CDATA[
      L(x,y,z \ ((u * u) * w)) = L(x,y,(u * u) * (w / z))
    ]]></literal>
    <justification jstring="[para(946(a,1),23215(a,1,3))].">
      <j1 rule="para" parents="946 23215"/>
    </justification>
  </clause>

  <clause id="23850">
    <literal><![CDATA[
      L(x,y,z \ (u * (z * z))) = L(x,y,u * L(z,z,u))
    ]]></literal>
    <justification jstring="[para(2848(a,1),23215(a,1,3))].">
      <j1 rule="para" parents="2848 23215"/>
    </justification>
  </clause>

  <clause id="23853">
    <literal><![CDATA[
      L(x,y,L(z,u,K(w,v5))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(16603(a,2),23215(a,1,3))].">
      <j1 rule="para" parents="16603 23215"/>
    </justification>
  </clause>

  <clause id="23856">
    <literal><![CDATA[
      L(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(11758(a,1),23232(a,1))].">
      <j1 rule="para" parents="11758 23232"/>
    </justification>
  </clause>

  <clause id="23857">
    <literal><![CDATA[
      L(x,y,z / u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(13684(a,1),23232(a,1))].">
      <j1 rule="para" parents="13684 23232"/>
    </justification>
  </clause>

  <clause id="23864">
    <literal><![CDATA[
      x / ((y / (x * y)) \ 1) = ((y / (x * y)) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,23717,a(flip),b,4916,a(flip))].">
      <j1 rule="hyper" parents="225 23717 4916"/>
    </justification>
  </clause>

  <clause id="23865">
    <literal><![CDATA[
      (1 / (1 / (x / (y * x)))) \ y = y / (x / (y * x))
    ]]></literal>
    <justification jstring="[para(23717(a,1),5139(a,2,2))].">
      <j1 rule="para" parents="23717 5139"/>
    </justification>
  </clause>

  <clause id="23866">
    <literal><![CDATA[
      x / (((y \ z) / z) * y) = (((y \ z) / z) * y) \ x
    ]]></literal>
    <justification jstring="[hyper(8638,a,23719,a),flip(a)].">
      <j1 rule="hyper" parents="8638 23719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23867">
    <literal><![CDATA[
      ((((x \ y) / y) * x) \ z) \ z = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(4722,a,23719,a)].">
      <j1 rule="hyper" parents="4722 23719"/>
    </justification>
  </clause>

  <clause id="23868">
    <literal><![CDATA[
      x / (y * ((y \ z) / z)) = (y * ((y \ z) / z)) \ x
    ]]></literal>
    <justification jstring="[hyper(8638,a,23722,a),flip(a)].">
      <j1 rule="hyper" parents="8638 23722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23871">
    <literal><![CDATA[
      x / ((x \ y) / y) = (y / (x * y)) \ x
    ]]></literal>
    <justification jstring="[para(23722(a,1),5137(a,1,2))].">
      <j1 rule="para" parents="23722 5137"/>
    </justification>
  </clause>

  <clause id="23872">
    <literal><![CDATA[
      x / (y * (z / (y * z))) = (y * (z / (y * z))) \ x
    ]]></literal>
    <justification jstring="[hyper(8638,a,23723,a),flip(a)].">
      <j1 rule="hyper" parents="8638 23723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23873">
    <literal><![CDATA[
      ((x * (y / (x * y))) \ z) \ z = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(4722,a,23723,a)].">
      <j1 rule="hyper" parents="4722 23723"/>
    </justification>
  </clause>

  <clause id="23874">
    <literal><![CDATA[
      (x * (y / (x * y))) * z = z * (x * (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(2149,a,23723,a),flip(a)].">
      <j1 rule="hyper" parents="2149 23723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23875">
    <literal><![CDATA[
      K(x * (y / (x * y)),z) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,23723,a,b,5797,a),flip(a)].">
      <j1 rule="hyper" parents="140 23723 5797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23876">
    <literal><![CDATA[
      ((x * (y / (x * y))) \ z) / z = z / ((x * (y / (x * y))) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3007,a(flip),b,23723,a)].">
      <j1 rule="hyper" parents="64 3007 23723"/>
    </justification>
  </clause>

  <clause id="23877">
    <literal><![CDATA[
      ((x / y) * (y / x)) * z = z * ((x / y) * (y / x))
    ]]></literal>
    <justification jstring="[hyper(2149,a,23727,a),flip(a)].">
      <j1 rule="hyper" parents="2149 23727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23879">
    <literal><![CDATA[
      R(x,T(y,z),T(y,u)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,23198,a,b,23810,a)].">
      <j1 rule="hyper" parents="64 23198 23810"/>
    </justification>
  </clause>

  <clause id="23880">
    <literal><![CDATA[
      T(x \ (y / (x * y)),x * x) = (x \ (y / (x * y))) * 1
    ]]></literal>
    <justification jstring="[para(23875(a,1),14719(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23875 14719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23882">
    <literal><![CDATA[
      T(x * (y \ L(y,z,u)),x) = x * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(57,a,23086,a)].">
      <j1 rule="hyper" parents="57 23086"/>
    </justification>
  </clause>

  <clause id="23886">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * L(x,y,z))) = u * x
    ]]></literal>
    <justification jstring="[para(22(a,1),23152(a,1,2))].">
      <j1 rule="para" parents="22 23152"/>
    </justification>
  </clause>

  <clause id="23887">
    <literal><![CDATA[
      (x / L(y,z,u)) * y = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(117(a,1),23152(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 23152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23888">
    <literal><![CDATA[
      ((x * y) \ z) * T(u,y \ (x \ z)) = u * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(16161(a,1),23152(a,1,2))].">
      <j1 rule="para" parents="16161 23152"/>
    </justification>
  </clause>

  <clause id="23889">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u * x)) = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,23167,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 23167 22"/>
    </justification>
  </clause>

  <clause id="23890">
    <literal><![CDATA[
      T(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(23500(a,2),5767(a,1))].">
      <j1 rule="para" parents="23500 5767"/>
    </justification>
  </clause>

  <clause id="23891">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) = T(x,x * (w \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,23697,a,b,23534,a)].">
      <j1 rule="hyper" parents="373 23697 23534"/>
    </justification>
  </clause>

  <clause id="23893">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * x = x * (x * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(145,a,23534,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 23534 22"/>
    </justification>
  </clause>

  <clause id="23896">
    <literal><![CDATA[
      L(x,y,z) * T(L(x,y,z) \ x,u) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,23538,a(flip),b,5748,a(flip))].">
      <j1 rule="hyper" parents="145 23538 5748"/>
    </justification>
  </clause>

  <clause id="23897">
    <literal><![CDATA[
      x \ ((1 / (1 / L(x,y,z))) \ x) = (L(x,y,z) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(41,a,3735,a,b,23610,a)].">
      <j1 rule="hyper" parents="41 3735 23610"/>
    </justification>
  </clause>

  <clause id="23898">
    <literal><![CDATA[
      L(x,y,z) * (x \ u) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,23610,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 23610 22"/>
    </justification>
  </clause>

  <clause id="23899">
    <literal><![CDATA[
      x \ (L(y,z,u) * (y \ w)) = x \ ((w / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(23610(a,1),249(a,1,2,2))].">
      <j1 rule="para" parents="23610 249"/>
    </justification>
  </clause>

  <clause id="23900">
    <literal><![CDATA[
      x * (L(y,z,u) * (y \ w)) = x * ((w / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(23610(a,1),251(a,1,2,2))].">
      <j1 rule="para" parents="23610 251"/>
    </justification>
  </clause>

  <clause id="23901">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * v5 = v5 * L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23693(a,1),5862(a,1,1,1))].">
      <j1 rule="para" parents="23693 5862"/>
    </justification>
  </clause>

  <clause id="23903">
    <literal><![CDATA[
      x \ (((y \ 1) * R(y,z,u)) * x) = (y \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(23709(a,1),257(a,1,2,2))].">
      <j1 rule="para" parents="23709 257"/>
    </justification>
  </clause>

  <clause id="23905">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * u = u * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(2149,a,23739,a),flip(a)].">
      <j1 rule="hyper" parents="2149 23739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23906">
    <literal><![CDATA[
      (x * (x \ y)) * a(z,u,w) = a(z,u,w) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,182,a(flip),b,23133,a)].">
      <j1 rule="hyper" parents="144 182 23133"/>
    </justification>
  </clause>

  <clause id="23908">
    <literal><![CDATA[
      x / (a(y,z,u) * K(w,w \ x)) = a(y,z,u) \ ((w \ x) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15236,a,b,23133,a)].">
      <j1 rule="hyper" parents="64 15236 23133"/>
    </justification>
  </clause>

  <clause id="23909">
    <literal><![CDATA[
      (x \ 1) * (x \ (a(y,z,u) \ 1)) = a(y,z,u) \ (x \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,13949,a,b,23133,a)].">
      <j1 rule="hyper" parents="64 13949 23133"/>
    </justification>
  </clause>

  <clause id="23910">
    <literal><![CDATA[
      L(a(x,y,z) * u,w,v5) = L(u * a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(38,a,5543,a,b,23133,a),flip(a)].">
      <j1 rule="hyper" parents="38 5543 23133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23911">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(x,y,z) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(23133(a,1),286(a,1,1))].">
      <j1 rule="para" parents="23133 286"/>
    </justification>
  </clause>

  <clause id="23914">
    <literal><![CDATA[
      (1 / x) * (a(y,z,u) \ x) = x * ((x \ 1) / a(y,z,u))
    ]]></literal>
    <justification jstring="[para(23133(a,1),1217(a,1,2))].">
      <j1 rule="para" parents="23133 1217"/>
    </justification>
  </clause>

  <clause id="23915">
    <literal><![CDATA[
      L(a(x,y,z) \ (u \ w),a(x,y,z),u) \ (u \ w) = (u \ w) / ((u * a(x,y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(23133(a,1),10471(a,1,1,1))].">
      <j1 rule="para" parents="23133 10471"/>
    </justification>
  </clause>

  <clause id="23916">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),a(x,y,z) \ w) = w \ ((a(x,y,z) \ w) * u)
    ]]></literal>
    <justification jstring="[para(23133(a,1),11070(a,2,2,1))].">
      <j1 rule="para" parents="23133 11070"/>
    </justification>
  </clause>

  <clause id="23918">
    <literal><![CDATA[
      x / T(a(y,z,u),w) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(23127(a,2),23133(a,1,2))].">
      <j1 rule="para" parents="23127 23133"/>
    </justification>
  </clause>

  <clause id="23919">
    <literal><![CDATA[
      a(x,y,z) != u \ w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) \ w = u
    ]]></literal>
    <justification jstring="[para(23134(a,1),49(a,1))].">
      <j1 rule="para" parents="23134 49"/>
    </justification>
  </clause>

  <clause id="23920">
    <literal><![CDATA[
      x * a(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ w = x
    ]]></literal>
    <justification jstring="[para(23134(a,1),153(a,1,2)),flip(b)].">
      <j1 rule="para" parents="23134 153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23921">
    <literal><![CDATA[
      T((a(x,y,z) \ u) / w,w * a(x,y,z)) = (((a(x,y,z) \ u) / w) \ u) \ u
    ]]></literal>
    <justification jstring="[para(23134(a,1),11412(a,1,2,2))].">
      <j1 rule="para" parents="23134 11412"/>
    </justification>
  </clause>

  <clause id="23922">
    <literal><![CDATA[
      a(x,y,z) = (L(z,y,x) * (y * x)) \ (z * (y * x))
    ]]></literal>
    <justification jstring="[para(21981(a,1),23134(a,1,1)),flip(a)].">
      <j1 rule="para" parents="21981 23134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23924">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ T(u,a(w,v5,v6)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,23105,a,b,23135,a)].">
      <j1 rule="hyper" parents="139 23105 23135"/>
    </justification>
  </clause>

  <clause id="23925">
    <literal><![CDATA[
      a(x,y,z) \ (z \ a(x,y,z)) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,9433,a,b,23135,a),flip(a)].">
      <j1 rule="hyper" parents="36 9433 23135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23926">
    <literal><![CDATA[
      ((x * y) * z) \ ((z * x) * y) = a(z,x,y) * K(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,10832,a,b,23136,a)].">
      <j1 rule="hyper" parents="373 10832 23136"/>
    </justification>
  </clause>

  <clause id="23927">
    <literal><![CDATA[
      R(x * y,L(z,y,x),a(u,w,v5)) \ ((x * (y * z)) * a(u,w,v5)) = a(u,w,v5) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,691,a,b,23136,a)].">
      <j1 rule="hyper" parents="373 691 23136"/>
    </justification>
  </clause>

  <clause id="23928">
    <literal><![CDATA[
      x * (y \ (y * a(z,u,w))) = a(z,u,w) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,169,a,b,23136,a)].">
      <j1 rule="hyper" parents="373 169 23136"/>
    </justification>
  </clause>

  <clause id="23929">
    <literal><![CDATA[
      a(x,y,z) * (x \ 1) = x \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,16059,a(flip),b,23136,a),flip(a)].">
      <j1 rule="hyper" parents="373 16059 23136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23930">
    <literal><![CDATA[
      a(x,y,z) * ((y * z) * x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,15980,a(flip),b,23136,a),flip(a)].">
      <j1 rule="hyper" parents="373 15980 23136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23931">
    <literal><![CDATA[
      a(x,y,z) * (z \ 1) = z \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,9433,a(flip),b,23136,a),flip(a)].">
      <j1 rule="hyper" parents="373 9433 23136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23932">
    <literal><![CDATA[
      a(x,y,z) * ((1 / u) \ u) = u * ((u \ 1) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,1175,a(flip),b,23136,a),flip(a)].">
      <j1 rule="hyper" parents="373 1175 23136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23933">
    <literal><![CDATA[
      a(x,y,z) / (a(x,y,z) * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(225,a,23136,a,b,16060,a)].">
      <j1 rule="hyper" parents="225 23136 16060"/>
    </justification>
  </clause>

  <clause id="23937">
    <literal><![CDATA[
      T(x * a(y,z,u),x) = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13930,a,b,23136,a)].">
      <j1 rule="hyper" parents="64 13930 23136"/>
    </justification>
  </clause>

  <clause id="23938">
    <literal><![CDATA[
      (a(x,y,z) * u) * T(w,a(x,y,z) * u) = w * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,23136,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="145 23136 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23939">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ ((x * a(z,u,w)) * y) = a(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(23136(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="23136 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23940">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) \ ((a(y,z,u) * x) * w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(23136(a,2),14(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="23136 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23941">
    <literal><![CDATA[
      L(x \ (a(y,z,u) \ w),x,a(y,z,u)) = (x * a(y,z,u)) \ w
    ]]></literal>
    <justification jstring="[para(23136(a,1),346(a,2,1))].">
      <j1 rule="para" parents="23136 346"/>
    </justification>
  </clause>

  <clause id="23942">
    <literal><![CDATA[
      L(a(x,y,z) \ T(u,w),a(x,y,z),w) = (a(x,y,z) * w) \ (u * w)
    ]]></literal>
    <justification jstring="[para(23136(a,2),521(a,2,1))].">
      <j1 rule="para" parents="23136 521"/>
    </justification>
  </clause>

  <clause id="23943">
    <literal><![CDATA[
      L(L((a(x,y,z) \ 1) \ u,w,v5),a(x,y,z),a(x,y,z)) = L(u * a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(23136(a,1),1143(a,2,1))].">
      <j1 rule="para" parents="23136 1143"/>
    </justification>
  </clause>

  <clause id="23945">
    <literal><![CDATA[
      (x / (y \ 1)) * (a(z,u,w) * (y \ 1)) = (x / y) * (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(23136(a,2),1627(a,1,2))].">
      <j1 rule="para" parents="23136 1627"/>
    </justification>
  </clause>

  <clause id="23946">
    <literal><![CDATA[
      (a(x,y,z) * (u \ (1 / u))) \ w = a(x,y,z) \ (u * ((u \ 1) \ w))
    ]]></literal>
    <justification jstring="[para(23136(a,2),1687(a,1,1))].">
      <j1 rule="para" parents="23136 1687"/>
    </justification>
  </clause>

  <clause id="23949">
    <literal><![CDATA[
      a(x * a(y,y,x),z,u) = a(L(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[para(23136(a,1),5678(a,1,1))].">
      <j1 rule="para" parents="23136 5678"/>
    </justification>
  </clause>

  <clause id="23950">
    <literal><![CDATA[
      (x * x) * a(y,z,x) = x * (a(y,z,x) * x)
    ]]></literal>
    <justification jstring="[para(23136(a,2),9439(a,2,2))].">
      <j1 rule="para" parents="23136 9439"/>
    </justification>
  </clause>

  <clause id="23952">
    <literal><![CDATA[
      (x \ y) \ (a(z,u,w) * ((x \ y) * x)) = (y / x) \ (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(23136(a,2),10971(a,1,2))].">
      <j1 rule="para" parents="23136 10971"/>
    </justification>
  </clause>

  <clause id="23953">
    <literal><![CDATA[
      a(x,1 / y,z) * u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(11966(a,1),23136(a,2,2))].">
      <j1 rule="para" parents="11966 23136"/>
    </justification>
  </clause>

  <clause id="23954">
    <literal><![CDATA[
      (a(x,y,z) * z) \ (a(x,y,z) * u) = L(z \ u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(23136(a,2),13811(a,1,1))].">
      <j1 rule="para" parents="23136 13811"/>
    </justification>
  </clause>

  <clause id="23955">
    <literal><![CDATA[
      (a(x,y,z) * u) * R(u,w,v5) = u * (a(x,y,z) * R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(23136(a,2),13929(a,1,1))].">
      <j1 rule="para" parents="23136 13929"/>
    </justification>
  </clause>

  <clause id="23956">
    <literal><![CDATA[
      (a(x,y,z) * (u \ w)) \ ((u \ w) * u) = ((w / u) * a(x,y,z)) \ w
    ]]></literal>
    <justification jstring="[para(23136(a,2),15004(a,1,1))].">
      <j1 rule="para" parents="23136 15004"/>
    </justification>
  </clause>

  <clause id="23957">
    <literal><![CDATA[
      x / T((x / (a(y,z,u) * w)) * w,a(y,z,u)) = ((x / (w * a(y,z,u))) * w) \ x
    ]]></literal>
    <justification jstring="[para(23136(a,2),14662(a,1,2,1,1,2))].">
      <j1 rule="para" parents="23136 14662"/>
    </justification>
  </clause>

  <clause id="23958">
    <literal><![CDATA[
      ((a(x,y,z) * u) * w) / T(u,a(x,y,z) * w) = u \ ((u * a(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[para(23136(a,2),15270(a,1,1,1))].">
      <j1 rule="para" parents="23136 15270"/>
    </justification>
  </clause>

  <clause id="23959">
    <literal><![CDATA[
      (x * (y * a(x,z,z))) \ (R(x,z,z) * y) = a(x,a(x,z,z),y)
    ]]></literal>
    <justification jstring="[para(23136(a,1),15992(a,1,1,2))].">
      <j1 rule="para" parents="23136 15992"/>
    </justification>
  </clause>

  <clause id="23960">
    <literal><![CDATA[
      T(a(x,y,z),u) * w = w * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(23127(a,2),23136(a,1,1))].">
      <j1 rule="para" parents="23127 23136"/>
    </justification>
  </clause>

  <clause id="23961">
    <literal><![CDATA[
      x * T(a(y,z,u),w) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(23127(a,2),23136(a,2,2)),flip(a)].">
      <j1 rule="para" parents="23127 23136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23963">
    <literal><![CDATA[
      (a(x,y,z) * u) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      (u * a(x,y,z)) \ w = v5
    ]]></literal>
    <justification jstring="[para(23138(a,1),402(a,1,1,2))].">
      <j1 rule="para" parents="23138 402"/>
    </justification>
  </clause>

  <clause id="23965">
    <literal><![CDATA[
      (a(x,x,y) \ 1) \ y = a(x,x,y) * y
    ]]></literal>
    <justification jstring="[para(23160(a,1),14054(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23160 14054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23967">
    <literal><![CDATA[
      x * (y \ (a(z,u,w) * y)) = a(z,u,w) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,23174,a,b,23174,a)].">
      <j1 rule="hyper" parents="145 23174 23174"/>
    </justification>
  </clause>

  <clause id="23968">
    <literal><![CDATA[
      (x * a(y,z,u)) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,u) * x) \ w = v5
    ]]></literal>
    <justification jstring="[para(23174(a,1),402(a,1,1,2))].">
      <j1 rule="para" parents="23174 402"/>
    </justification>
  </clause>

  <clause id="23969">
    <literal><![CDATA[
      L(x,y,(z / u) \ 1) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(2274,a,23216,a)].">
      <j1 rule="hyper" parents="2274 23216"/>
    </justification>
  </clause>

  <clause id="23972">
    <literal><![CDATA[
      L(x,y,T(z / u,w)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23215,a,b,23216,a)].">
      <j1 rule="hyper" parents="64 23215 23216"/>
    </justification>
  </clause>

  <clause id="23973">
    <literal><![CDATA[
      L(x,y,(z * z) * (u / w)) = L(x,y,w \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2184,a,b,23216,a)].">
      <j1 rule="hyper" parents="64 2184 23216"/>
    </justification>
  </clause>

  <clause id="23975">
    <literal><![CDATA[
      L(x \ ((y / z) * R((y / z) \ u,w,v5)),x,z \ y) = ((y / z) * x) \ R((y / z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,2134,a(flip),b,23216,a),flip(a)].">
      <j1 rule="hyper" parents="64 2134 23216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23976">
    <literal><![CDATA[
      L(x \ ((y / z) \ u),x,z \ y) = ((y / z) * x) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,346,a(flip),b,23216,a),flip(a)].">
      <j1 rule="hyper" parents="64 346 23216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23977">
    <literal><![CDATA[
      x / L(y,y \ ((z / u) \ x),u \ z) = (z / u) * (((z / u) \ x) / y)
    ]]></literal>
    <justification jstring="[hyper(225,a,23216,a(flip),b,10261,a(flip))].">
      <j1 rule="hyper" parents="225 23216 10261"/>
    </justification>
  </clause>

  <clause id="23978">
    <literal><![CDATA[
      ((x / y) * z) * L(u,z,y \ x) = (x / y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,23216,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 23216 18"/>
    </justification>
  </clause>

  <clause id="23979">
    <literal><![CDATA[
      L(x,y,R(z / (z * z),z,z \ u)) = L(x,y,u \ (L(z,z,z) \ u))
    ]]></literal>
    <justification jstring="[para(3037(a,2),23216(a,1,3))].">
      <j1 rule="para" parents="3037 23216"/>
    </justification>
  </clause>

  <clause id="23980">
    <literal><![CDATA[
      (1 / (x / y)) * (((1 / (x / y)) \ (y / x)) * z) = (y / x) * L(z,(y / x) * (x / y),y \ x)
    ]]></literal>
    <justification jstring="[para(23216(a,1),3526(a,2,2))].">
      <j1 rule="para" parents="23216 3526"/>
    </justification>
  </clause>

  <clause id="23981">
    <literal><![CDATA[
      ((x / y) * (z \ 1)) * L(u,z,y \ x) = (x / y) * ((z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(23216(a,1),11815(a,1,2))].">
      <j1 rule="para" parents="23216 11815"/>
    </justification>
  </clause>

  <clause id="23982">
    <literal><![CDATA[
      L(L(x,y,z * u),w,v5) = L(L(x,w,v5),y,u * z)
    ]]></literal>
    <justification jstring="[hyper(1435,a,23253,a)].">
      <j1 rule="hyper" parents="1435 23253"/>
    </justification>
  </clause>

  <clause id="23983">
    <literal><![CDATA[
      L(((x * y) \ z) \ u,(x * y) \ z,y * x) = z \ ((x * y) * u)
    ]]></literal>
    <justification jstring="[hyper(743,a,23253,a),flip(a)].">
      <j1 rule="hyper" parents="743 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23984">
    <literal><![CDATA[
      L((x * y) \ z,x * y,y * x) = (1 / (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(742,a,23253,a),flip(a)].">
      <j1 rule="hyper" parents="742 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23986">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,16031,a,b,23253,a)].">
      <j1 rule="hyper" parents="373 16031 23253"/>
    </justification>
  </clause>

  <clause id="23987">
    <literal><![CDATA[
      L(x,y,z * (a(u,w,u) \ v5)) = L(x,y,v5 * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,13256,a,b,23253,a)].">
      <j1 rule="hyper" parents="373 13256 23253"/>
    </justification>
  </clause>

  <clause id="23988">
    <literal><![CDATA[
      L(x,y,z * R(u,w,u)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,12986,a,b,23253,a)].">
      <j1 rule="hyper" parents="373 12986 23253"/>
    </justification>
  </clause>

  <clause id="23989">
    <literal><![CDATA[
      L(x,y,((z * z) / u) * w) = L(x,y,w * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2248,a,b,23253,a)].">
      <j1 rule="hyper" parents="373 2248 23253"/>
    </justification>
  </clause>

  <clause id="23990">
    <literal><![CDATA[
      L(x,y,(z \ 1) * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2211,a,b,23253,a)].">
      <j1 rule="hyper" parents="373 2211 23253"/>
    </justification>
  </clause>

  <clause id="23991">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),L(x,u,w),z * y) = a(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,16038,a(flip),b,23253,a),flip(a)].">
      <j1 rule="hyper" parents="373 16038 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23992">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),x,z * y) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,16033,a(flip),b,23253,a),flip(a)].">
      <j1 rule="hyper" parents="373 16033 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23993">
    <literal><![CDATA[
      L(x,y,z * (((u \ 1) * w) * v5)) = L(x,y,((u * w) * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2478,a(flip),b,23253,a),flip(a)].">
      <j1 rule="hyper" parents="373 2478 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23994">
    <literal><![CDATA[
      L(x,y,z * (((u \ 1) \ w) * v5)) = L(x,y,((u \ w) * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2316,a(flip),b,23253,a),flip(a)].">
      <j1 rule="hyper" parents="373 2316 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23995">
    <literal><![CDATA[
      L(x,y,z * ((u \ 1) * w)) = L(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2271,a(flip),b,23253,a),flip(a)].">
      <j1 rule="hyper" parents="373 2271 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23996">
    <literal><![CDATA[
      L(x,y,z * ((1 / u) \ w)) = L(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2270,a(flip),b,23253,a),flip(a)].">
      <j1 rule="hyper" parents="373 2270 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23997">
    <literal><![CDATA[
      L(x,y,z * (u \ 1)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2211,a(flip),b,23253,a),flip(a)].">
      <j1 rule="hyper" parents="373 2211 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23998">
    <literal><![CDATA[
      L(x,y,z * ((u * u) * w)) = L(x,y,w * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2202,a(flip),b,23253,a),flip(a)].">
      <j1 rule="hyper" parents="373 2202 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="23999">
    <literal><![CDATA[
      L(x,y,z * (1 / u)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2186,a(flip),b,23253,a),flip(a)].">
      <j1 rule="hyper" parents="373 2186 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24000">
    <literal><![CDATA[
      L(x,y,(z * u) * z) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,2185,a(flip),b,23253,a),flip(a)].">
      <j1 rule="hyper" parents="373 2185 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24001">
    <literal><![CDATA[
      L(x \ L(y \ z,y,u),x,y * u) = ((u * y) * x) \ (u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,713,a(flip),b,23253,a),flip(a)].">
      <j1 rule="hyper" parents="373 713 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24002">
    <literal><![CDATA[
      x * L(y,z,u * w) = x * L(y,z,w * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,23253,a,b,9,a)].">
      <j1 rule="hyper" parents="145 23253 9"/>
    </justification>
  </clause>

  <clause id="24003">
    <literal><![CDATA[
      L(x,y,z * u) \ w = L(x,y,u * z) \ w
    ]]></literal>
    <justification jstring="[hyper(62,a,23253,a)].">
      <j1 rule="hyper" parents="62 23253"/>
    </justification>
  </clause>

  <clause id="24004">
    <literal><![CDATA[
      L(x,y,z * (u / z)) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),23253(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24005">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * (w * u)) = L(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[para(100(a,1),23253(a,1,3)),flip(a)].">
      <j1 rule="para" parents="100 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24006">
    <literal><![CDATA[
      ((x * y) * (z * z)) / z = (x * y) * L(z,z,y * x)
    ]]></literal>
    <justification jstring="[para(23253(a,1),2849(a,2,2))].">
      <j1 rule="para" parents="23253 2849"/>
    </justification>
  </clause>

  <clause id="24007">
    <literal><![CDATA[
      L(x,y,y) * L(z,y,x * y) = (L(x,y,y) / y) * (y * z)
    ]]></literal>
    <justification jstring="[para(23253(a,1),11300(a,1,2))].">
      <j1 rule="para" parents="23253 11300"/>
    </justification>
  </clause>

  <clause id="24008">
    <literal><![CDATA[
      a(x,y,L(z * u,w,u * z)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(23253(a,1),13865(a,1,3))].">
      <j1 rule="para" parents="23253 13865"/>
    </justification>
  </clause>

  <clause id="24009">
    <literal><![CDATA[
      L(1 / x,y,y * x) \ 1 = (1 / (y * (x \ 1))) * y
    ]]></literal>
    <justification jstring="[para(23253(a,1),21699(a,1,1))].">
      <j1 rule="para" parents="23253 21699"/>
    </justification>
  </clause>

  <clause id="24013">
    <literal><![CDATA[
      R(1 / (x \ (y \ x)),x \ (y \ x),y) = (x \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,3809,a(flip),b,23313,a),flip(a)].">
      <j1 rule="hyper" parents="64 3809 23313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24015">
    <literal><![CDATA[
      R(x,x \ (y \ z),y) \ z = (x \ (y \ z)) * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[para(23313(a,1),974(a,1,1))].">
      <j1 rule="para" parents="23313 974"/>
    </justification>
  </clause>

  <clause id="24064">
    <literal><![CDATA[
      (x * y) * K(z,L(u,w,v5)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,23362,a(flip),b,5027,a)].">
      <j1 rule="hyper" parents="145 23362 5027"/>
    </justification>
  </clause>

  <clause id="24069">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,(w * ((w \ v5) / y)) \ v5)
    ]]></literal>
    <justification jstring="[para(711(a,1),23362(a,2,2))].">
      <j1 rule="para" parents="711 23362"/>
    </justification>
  </clause>

  <clause id="24117">
    <literal><![CDATA[
      T(x,L(y \ L(y,z,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      x = v6
    ]]></literal>
    <justification jstring="[para(23153(a,2),23747(a,1))].">
      <j1 rule="para" parents="23153 23747"/>
    </justification>
  </clause>

  <clause id="24131">
    <literal><![CDATA[
      R(x,y,T(z / u,w)) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(117(a,1),23798(a,1,3)),flip(a)].">
      <j1 rule="para" parents="117 23798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24151">
    <literal><![CDATA[
      R(R(x,y,z \ u),w,K(v5,v6)) = R(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(373,a,23147,a,b,23813,a)].">
      <j1 rule="hyper" parents="373 23147 23813"/>
    </justification>
  </clause>

  <clause id="24152">
    <literal><![CDATA[
      L(x \ R(x,y,z \ u),x,y * (u / z)) = a(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(23813(a,1),16031(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="23813 16031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24153">
    <literal><![CDATA[
      R(x,y,z) * (y * (u / (u / z))) = (x * y) * (u / (u / z))
    ]]></literal>
    <justification jstring="[hyper(144,a,23814,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 23814 20"/>
    </justification>
  </clause>

  <clause id="24157">
    <literal><![CDATA[
      L(x,y,T(T(z,u),w)) = L(x,y,L(z,v5,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,12978,a,b,23826,a),flip(a)].">
      <j1 rule="hyper" parents="373 12978 23826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24163">
    <literal><![CDATA[
      T(x,y) \ L(z,x,x) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,23827,a(flip),b,1139,a)].">
      <j1 rule="hyper" parents="139 23827 1139"/>
    </justification>
  </clause>

  <clause id="24165">
    <literal><![CDATA[
      L(x \ L(y \ z,y,y \ u),x,u) = (((y \ u) * y) * x) \ ((y \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,713,a(flip),b,23833,a),flip(a)].">
      <j1 rule="hyper" parents="64 713 23833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24166">
    <literal><![CDATA[
      x \ R(x,y \ x,y) = a(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,16055,a,b,23833,a)].">
      <j1 rule="hyper" parents="42 16055 23833"/>
    </justification>
  </clause>

  <clause id="24167">
    <literal><![CDATA[
      L(x,y,L(z * u,w,v5)) = L(x,y,L(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(5545(a,1),23833(a,1,3))].">
      <j1 rule="para" parents="5545 23833"/>
    </justification>
  </clause>

  <clause id="24168">
    <literal><![CDATA[
      L(x,(x \ y) * x,y) * L(z,(y / (y / x)) * y,(x \ y) * x) = ((x \ y) * x) * (((((x \ y) * x) \ 1) * x) * z)
    ]]></literal>
    <justification jstring="[para(23833(a,1),14212(a,1,1))].">
      <j1 rule="para" parents="23833 14212"/>
    </justification>
  </clause>

  <clause id="24171">
    <literal><![CDATA[
      x / L((y * (x \ y)) / y,x,x \ y) = (x / T(y,x \ y)) * x
    ]]></literal>
    <justification jstring="[para(23835(a,1),5154(a,1,2))].">
      <j1 rule="para" parents="23835 5154"/>
    </justification>
  </clause>

  <clause id="24172">
    <literal><![CDATA[
      ((x * y) / x) / L(z,z,y) = y * (K(x,y) * (1 / z))
    ]]></literal>
    <justification jstring="[para(23835(a,1),11820(a,1,2))].">
      <j1 rule="para" parents="23835 11820"/>
    </justification>
  </clause>

  <clause id="24173">
    <literal><![CDATA[
      L(x,1 / (y \ z),z \ y) = L(x,z \ y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5330,a(flip),b,23845,a),flip(a)].">
      <j1 rule="hyper" parents="64 5330 23845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24180">
    <literal><![CDATA[
      L(x,y,z) \ K(x \ 1,u) = T(L(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,23005,a(flip),b,5743,a)].">
      <j1 rule="hyper" parents="139 23005 5743"/>
    </justification>
  </clause>

  <clause id="24185">
    <literal><![CDATA[
      R(x,y,z) \ K(x \ 1,u) = T(R(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,23040,a(flip),b,5743,a)].">
      <j1 rule="hyper" parents="139 23040 5743"/>
    </justification>
  </clause>

  <clause id="24189">
    <literal><![CDATA[
      T(x,L(y,z,u) \ 1) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(143,a,23047,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 23047 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24191">
    <literal><![CDATA[
      (x * y) \ (K(z,x) * u) = (T(x,z) * y) \ u
    ]]></literal>
    <justification jstring="[hyper(139,a,23383,a(flip),b,19735,a(flip))].">
      <j1 rule="hyper" parents="139 23383 19735"/>
    </justification>
  </clause>

  <clause id="24192">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (x * u) = (u * L(x,y,z)) \ (u * x)
    ]]></literal>
    <justification jstring="[hyper(139,a,23384,a(flip),b,10853,a),flip(a)].">
      <j1 rule="hyper" parents="139 23384 10853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24195">
    <literal><![CDATA[
      T(x * L(y,z,u),K(L(y,z,u),w)) = L(y,z,u) * T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(23619(a,1),6998(a,2,2))].">
      <j1 rule="para" parents="23619 6998"/>
    </justification>
  </clause>

  <clause id="24196">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) / y = y \ (x * R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(225,a,23721,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 23721 116"/>
    </justification>
  </clause>

  <clause id="24197">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ (z \ y))) = x
    ]]></literal>
    <justification jstring="[para(1935(a,1),23721(a,1,2,2))].">
      <j1 rule="para" parents="1935 23721"/>
    </justification>
  </clause>

  <clause id="24198">
    <literal><![CDATA[
      (x \ y) / ((x \ 1) * y) = ((x \ 1) * y) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(225,a,24197,a(flip),b,14969,a(flip))].">
      <j1 rule="hyper" parents="225 24197 14969"/>
    </justification>
  </clause>

  <clause id="24199">
    <literal><![CDATA[
      L(x,y,z \ (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(22(a,1),23856(a,1,3))].">
      <j1 rule="para" parents="22 23856"/>
    </justification>
  </clause>

  <clause id="24200">
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(116(a,1),23856(a,1,3))].">
      <j1 rule="para" parents="116 23856"/>
    </justification>
  </clause>

  <clause id="24201">
    <literal><![CDATA[
      L(x,y,z * u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(12985(a,1),23856(a,1))].">
      <j1 rule="para" parents="12985 23856"/>
    </justification>
  </clause>

  <clause id="24202">
    <literal><![CDATA[
      L(x,y,T(T(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(23215(a,2),23856(a,1))].">
      <j1 rule="para" parents="23215 23856"/>
    </justification>
  </clause>

  <clause id="24203">
    <literal><![CDATA[
      T(x,L(y \ 1,z,u) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,3871,a(flip),b,24189,a),flip(a)].">
      <j1 rule="hyper" parents="373 3871 24189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24204">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * T(u,x \ 1) = u * (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,24189,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 24189 22"/>
    </justification>
  </clause>

  <clause id="24205">
    <literal><![CDATA[
      (L(x,y,z) \ u) / T(u,x \ 1) = u \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(24189(a,1),4576(a,1,2))].">
      <j1 rule="para" parents="24189 4576"/>
    </justification>
  </clause>

  <clause id="24208">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ w) = K(x,u \ (z \ (y \ w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,23002,a(flip),b,23002,a),flip(a)].">
      <j1 rule="hyper" parents="373 23002 23002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24210">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15897,a,b,23002,a)].">
      <j1 rule="hyper" parents="64 15897 23002"/>
    </justification>
  </clause>

  <clause id="24212">
    <literal><![CDATA[
      K(x,(y / z) \ (z \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15899,a(flip),b,23002,a),flip(a)].">
      <j1 rule="hyper" parents="64 15899 23002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24214">
    <literal><![CDATA[
      K(x,(y \ z) \ (y \ u)) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),23002(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 23002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24216">
    <literal><![CDATA[
      T(((x * y) \ z) * K(u,y \ (x \ z)),u) = (x * y) \ z
    ]]></literal>
    <justification jstring="[para(23002(a,1),5785(a,1,1,2))].">
      <j1 rule="para" parents="23002 5785"/>
    </justification>
  </clause>

  <clause id="24223">
    <literal><![CDATA[
      K(x / y,z / (x / u)) = K(y \ x,x \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8266,a(flip),b,23039,a),flip(a)].">
      <j1 rule="hyper" parents="64 8266 23039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24226">
    <literal><![CDATA[
      K(x / (((x * y) * z) / (y * z)),u) = K(a(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15478,a(flip),b,23041,a),flip(a)].">
      <j1 rule="hyper" parents="64 15478 23041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24234">
    <literal><![CDATA[
      K(x,y \ (z * u)) = K(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,22656,a(flip),b,23043,a),flip(a)].">
      <j1 rule="hyper" parents="64 22656 23043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24236">
    <literal><![CDATA[
      K(x,(y \ z) \ T(T(u,y),w)) = K(x,z \ (T(u,w) * y))
    ]]></literal>
    <justification jstring="[para(265(a,1),23043(a,2,2,2))].">
      <j1 rule="para" parents="265 23043"/>
    </justification>
  </clause>

  <clause id="24237">
    <literal><![CDATA[
      K(x,y \ (L(y,z,z) * u)) = K(x,a(z,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(1243(a,1),23043(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1243 23043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24245">
    <literal><![CDATA[
      K((x * y) \ (R(z,z \ x,y) * u),w) = K(((z \ x) * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(649(a,1),23045(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="649 23045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24246">
    <literal><![CDATA[
      (x \ (y \ z)) * K(z \ (y * x),x \ (y \ z)) = 1 / (1 / (x \ (y \ z)))
    ]]></literal>
    <justification jstring="[para(23045(a,1),4309(a,1,2))].">
      <j1 rule="para" parents="23045 4309"/>
    </justification>
  </clause>

  <clause id="24248">
    <literal><![CDATA[
      K((x * (y * z)) \ u,w) = K(z \ (y \ (x \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,23046,a(flip),b,23046,a),flip(a)].">
      <j1 rule="hyper" parents="373 23046 23046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24251">
    <literal><![CDATA[
      K((x / y) \ (y \ z),u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15927,a(flip),b,23046,a),flip(a)].">
      <j1 rule="hyper" parents="64 15927 23046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24253">
    <literal><![CDATA[
      K(x \ ((y / x) \ z),u) = K(y \ z,u)
    ]]></literal>
    <justification jstring="[para(12(a,1),23046(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 23046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24254">
    <literal><![CDATA[
      K(T(x,y) \ (y \ z),u) = K((x * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(115(a,1),23046(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="115 23046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24255">
    <literal><![CDATA[
      K((x * T(x,y)) \ z,u) = K(x \ (T(x,y) \ z),u)
    ]]></literal>
    <justification jstring="[para(273(a,1),23046(a,1,1,1))].">
      <j1 rule="para" parents="273 23046"/>
    </justification>
  </clause>

  <clause id="24259">
    <literal><![CDATA[
      (x * a(y,z,u)) * K(w,v5) = a(y,z,u) * (x * K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(144,a,23136,a(flip),b,23048,a)].">
      <j1 rule="hyper" parents="144 23136 23048"/>
    </justification>
  </clause>

  <clause id="24260">
    <literal><![CDATA[
      x * (R(y,x,y) * K(z,u)) = T(y * x,y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,4741,a(flip),b,23048,a),flip(a)].">
      <j1 rule="hyper" parents="144 4741 23048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24262">
    <literal><![CDATA[
      (x * (y * K(z,u))) * z = (x * y) * T(z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,23048,a(flip),b,6860,a),flip(a)].">
      <j1 rule="hyper" parents="144 23048 6860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24263">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(z,u) = (x * y) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,23048,a(flip),b,6903,a),flip(a)].">
      <j1 rule="hyper" parents="142 23048 6903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24265">
    <literal><![CDATA[
      K(x,y) * (z * (u * K(y,x))) = T(z * u,K(y,x))
    ]]></literal>
    <justification jstring="[para(23048(a,1),6181(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23048 6181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24268">
    <literal><![CDATA[
      ((x * y) / T(y,z)) / u = x / (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(142,a,6860,a,b,23049,a)].">
      <j1 rule="hyper" parents="142 6860 23049"/>
    </justification>
  </clause>

  <clause id="24270">
    <literal><![CDATA[
      (K(x,y) * z) / (u * K(x,y)) = T(z,K(x,y)) / u
    ]]></literal>
    <justification jstring="[hyper(142,a,8177,a(flip),b,23049,a),flip(a)].">
      <j1 rule="hyper" parents="142 8177 23049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24271">
    <literal><![CDATA[
      (x * y) / (z * K(u,y)) = (x * T(y,u)) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,6322,a(flip),b,23049,a),flip(a)].">
      <j1 rule="hyper" parents="142 6322 23049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24273">
    <literal><![CDATA[
      (x \ y) / (z * K(u,y)) = (x \ T(y,u)) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,15017,a(flip),b,23050,a)].">
      <j1 rule="hyper" parents="142 15017 23050"/>
    </justification>
  </clause>

  <clause id="24274">
    <literal><![CDATA[
      T(x,K(y,z)) / (u * K(z,y)) = (K(y,z) * x) / u
    ]]></literal>
    <justification jstring="[hyper(142,a,8160,a(flip),b,23050,a)].">
      <j1 rule="hyper" parents="142 8160 23050"/>
    </justification>
  </clause>

  <clause id="24275">
    <literal><![CDATA[
      (x / (x / y)) / z = y / (z * K(y,y \ x))
    ]]></literal>
    <justification jstring="[hyper(142,a,6596,a(flip),b,23050,a),flip(a)].">
      <j1 rule="hyper" parents="142 6596 23050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24276">
    <literal><![CDATA[
      (x / y) \ (K(z,u) * x) = y * K(z,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(139,a,7879,a(flip),b,23050,a)].">
      <j1 rule="hyper" parents="139 7879 23050"/>
    </justification>
  </clause>

  <clause id="24277">
    <literal><![CDATA[
      ((1 / T(x,y)) / z) \ (x \ K(y,x)) = z * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,5940,a(flip),b,23050,a)].">
      <j1 rule="hyper" parents="139 5940 23050"/>
    </justification>
  </clause>

  <clause id="24279">
    <literal><![CDATA[
      1 / (x * (y * K(z,u))) = K(u,z) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(225,a,23051,a(flip),b,14443,a),flip(a)].">
      <j1 rule="hyper" parents="225 23051 14443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24285">
    <literal><![CDATA[
      K(x,y) * (z * (u * K(y,x))) = T(z * u,K(x,y))
    ]]></literal>
    <justification jstring="[para(23051(a,1),8164(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23051 8164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24286">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,u) = x * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[para(14520(a,1),23051(a,1,1,2))].">
      <j1 rule="para" parents="14520 23051"/>
    </justification>
  </clause>

  <clause id="24291">
    <literal><![CDATA[
      ((x * y) / z) * (z * K(u,w)) = x * (y * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,23050,a,b,23053,a)].">
      <j1 rule="hyper" parents="64 23050 23053"/>
    </justification>
  </clause>

  <clause id="24292">
    <literal><![CDATA[
      K(x * x,y) * (z * u) = z * (u * K(x * x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17045,a,b,23053,a)].">
      <j1 rule="hyper" parents="64 17045 23053"/>
    </justification>
  </clause>

  <clause id="24293">
    <literal><![CDATA[
      (x / (y * z)) \ T(x,u) = y * (z * K(x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15034,a,b,23053,a)].">
      <j1 rule="hyper" parents="64 15034 23053"/>
    </justification>
  </clause>

  <clause id="24300">
    <literal><![CDATA[
      T(x / ((y \ z) * y),z) = (z \ x) * K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(269,a,10226,a,b,23055,a)].">
      <j1 rule="hyper" parents="269 10226 23055"/>
    </justification>
  </clause>

  <clause id="24302">
    <literal><![CDATA[
      x \ T(y * K(z,u),u) = (x \ T(y,u)) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,7797,a,b,23055,a)].">
      <j1 rule="hyper" parents="139 7797 23055"/>
    </justification>
  </clause>

  <clause id="24304">
    <literal><![CDATA[
      x \ (y * (z * K(u,w))) = (x \ (y * z)) * K(u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,23053,a(flip),b,23055,a)].">
      <j1 rule="hyper" parents="139 23053 23055"/>
    </justification>
  </clause>

  <clause id="24305">
    <literal><![CDATA[
      (x \ (y \ z)) * K(u,u \ z) = x \ (y \ (u * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(139,a,16688,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 16688 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24306">
    <literal><![CDATA[
      (x \ (y \ z)) * K(u \ z,u) = x \ (y \ ((u \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(139,a,15230,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 15230 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24307">
    <literal><![CDATA[
      (x \ (y \ (z \ u))) * K(z,z \ u) = x \ (y \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(139,a,15092,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 15092 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24309">
    <literal><![CDATA[
      (x \ (y \ T(z,u))) * K(u,z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,15017,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 15017 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24310">
    <literal><![CDATA[
      (x \ (y \ 1)) * K(z,u) = x \ (y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,14444,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 14444 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24311">
    <literal><![CDATA[
      (x \ (y * z)) * K(u \ z,u) = x \ (y * ((u \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(139,a,10196,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 10196 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24312">
    <literal><![CDATA[
      (x \ (y * z)) * K(y,T(u,z)) = x \ (T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,8047,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 8047 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24313">
    <literal><![CDATA[
      (x \ (y / (z \ u))) * K(z \ u,z) = x \ (y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(139,a,6887,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 6887 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24314">
    <literal><![CDATA[
      (x \ (y * (z / u))) * K(u \ z,u) = x \ (y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(139,a,6886,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 6886 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24315">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,u) = x \ (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,6852,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 6852 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24316">
    <literal><![CDATA[
      (x \ (y / T(z,u))) * K(z,u) = x \ (y / z)
    ]]></literal>
    <justification jstring="[hyper(139,a,6848,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 6848 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24317">
    <literal><![CDATA[
      (x \ (y * ((z \ u) \ u))) * K(z \ u,z) = x \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,6326,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 6326 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24318">
    <literal><![CDATA[
      T(x,y) * ((x \ z) * K(u,w)) = K(x,y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,23055,a(flip),b,5779,a),flip(a)].">
      <j1 rule="hyper" parents="145 23055 5779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24319">
    <literal><![CDATA[
      x * K(y * (z \ x),u) = z * (y \ T(y * (z \ x),u))
    ]]></literal>
    <justification jstring="[para(14494(a,2),23055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14494 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24322">
    <literal><![CDATA[
      x \ (y * K(z * z,u)) = K(z * z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,17045,a,b,23058,a),flip(a)].">
      <j1 rule="hyper" parents="373 17045 23058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24323">
    <literal><![CDATA[
      x \ (y * K(z,T(u,w))) = (x \ y) * T(K(z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,7878,a(flip),b,23058,a),flip(a)].">
      <j1 rule="hyper" parents="373 7878 23058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24325">
    <literal><![CDATA[
      K(x,y) * (z / R(T(z,u),w,v5)) = (R(T(z,u),w,v5) \ z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,22861,a(flip),b,23058,a)].">
      <j1 rule="hyper" parents="64 22861 23058"/>
    </justification>
  </clause>

  <clause id="24326">
    <literal><![CDATA[
      (T(x * y,z) \ x) * K(y * x,z) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,22828,a(flip),b,23058,a),flip(a)].">
      <j1 rule="hyper" parents="64 22828 23058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24327">
    <literal><![CDATA[
      (R(x,y,z) \ x) * K(u,w) = x * (R(x,y,z) \ K(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,1907,a(flip),b,23058,a),flip(a)].">
      <j1 rule="hyper" parents="64 1907 23058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24329">
    <literal><![CDATA[
      L((x \ y) * K(z,u),x,z / y) = ((z / y) * x) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(23058(a,1),15068(a,1,1))].">
      <j1 rule="para" parents="23058 15068"/>
    </justification>
  </clause>

  <clause id="24335">
    <literal><![CDATA[
      (K(x,y) * z) * (u \ T(x,K(y,w))) = K(x,T(y,w)) * (z * (u \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,19466,a(flip),b,23073,a),flip(a)].">
      <j1 rule="hyper" parents="373 19466 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24336">
    <literal><![CDATA[
      (x \ y) * ((K(x,x \ y) * z) * u) = (y / x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,23073,a,b,6442,a)].">
      <j1 rule="hyper" parents="145 23073 6442"/>
    </justification>
  </clause>

  <clause id="24339">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (K(x,y) * (z * (u * w))) = L(w,u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,23073,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="139 23073 100"/>
    </justification>
  </clause>

  <clause id="24340">
    <literal><![CDATA[
      (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(23073(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="23073 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24345">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(4097(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4097 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24346">
    <literal><![CDATA[
      K(x,x \ y) * (y * z) = (x * (y / x)) * z
    ]]></literal>
    <justification jstring="[para(5781(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5781 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24347">
    <literal><![CDATA[
      K(x,y) * ((T(x,y) \ z) * u) = (x \ z) * u
    ]]></literal>
    <justification jstring="[para(6075(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6075 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24348">
    <literal><![CDATA[
      K(x,y) * ((y \ z) * u) = (T(y,x) \ z) * u
    ]]></literal>
    <justification jstring="[para(6157(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6157 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24349">
    <literal><![CDATA[
      K(x * y,x) * (T(x,y) * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[para(6081(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6081 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24351">
    <literal><![CDATA[
      K(x,x \ y) * (((x \ y) * z) * u) = ((y / x) * z) * u
    ]]></literal>
    <justification jstring="[para(5982(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5982 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24352">
    <literal><![CDATA[
      K(x \ y,x) * (((x \ y) \ z) * u) = ((y / x) \ z) * u
    ]]></literal>
    <justification jstring="[para(6292(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6292 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24353">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ z) * u) = ((y / (y / x)) \ z) * u
    ]]></literal>
    <justification jstring="[para(6413(a,2),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6413 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24354">
    <literal><![CDATA[
      K(x,y) * ((z * K(y,x)) * u) = T(z,K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(8158(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8158 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24355">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z * x) * u) = (z * T(x,y)) * u
    ]]></literal>
    <justification jstring="[para(8245(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8245 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24357">
    <literal><![CDATA[
      T(x * (y * z),K(y,z)) * u = K(y,z) * ((x * (z * y)) * u)
    ]]></literal>
    <justification jstring="[para(10194(a,2),23073(a,1,1))].">
      <j1 rule="para" parents="10194 23073"/>
    </justification>
  </clause>

  <clause id="24358">
    <literal><![CDATA[
      K(x,y) * (((y * x) * z) * u) = ((x * y) * z) * u
    ]]></literal>
    <justification jstring="[para(10834(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10834 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24359">
    <literal><![CDATA[
      K(x,x \ y) * ((y \ z) * u) = (((x \ y) * x) \ z) * u
    ]]></literal>
    <justification jstring="[para(10843(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10843 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24360">
    <literal><![CDATA[
      K(x \ y,x) * ((y * z) * u) = (((x \ y) * x) * z) * u
    ]]></literal>
    <justification jstring="[para(10858(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10858 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24361">
    <literal><![CDATA[
      K(x,y) * ((1 / z) * u) = (K(x,y) / z) * u
    ]]></literal>
    <justification jstring="[para(14366(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14366 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24362">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z \ 1) * u) = (z \ K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(14665(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14665 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24363">
    <literal><![CDATA[
      K(x,x \ y) * (((x \ y) / z) * u) = ((y / x) / z) * u
    ]]></literal>
    <justification jstring="[para(14696(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14696 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24364">
    <literal><![CDATA[
      K(x,y) * ((x / z) * u) = (T(x,y) / z) * u
    ]]></literal>
    <justification jstring="[para(14825(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14825 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24365">
    <literal><![CDATA[
      K(x \ 1,y) * (a(y,x,x) * z) = (y \ (((1 / x) * y) * x)) * z
    ]]></literal>
    <justification jstring="[para(16209(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16209 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24366">
    <literal><![CDATA[
      K(x,y) * ((a(z,u,w) \ 1) * v5) = (a(z,u,w) \ K(x,y)) * v5
    ]]></literal>
    <justification jstring="[para(19253(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19253 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24368">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z * u) * w) = (z * (K(x,y) * u)) * w
    ]]></literal>
    <justification jstring="[para(22760(a,1),23073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22760 23073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24369">
    <literal><![CDATA[
      (K(x,y) * (z * u)) * (u \ K(u,K(x,y) * z)) = (K(x,T(y,u)) * (u * z)) * (u \ 1)
    ]]></literal>
    <justification jstring="[para(23073(a,1),22779(a,1,1))].">
      <j1 rule="para" parents="23073 22779"/>
    </justification>
  </clause>

  <clause id="24373">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * w = K(x,y) * ((z * u) * w)
    ]]></literal>
    <justification jstring="[para(23073(a,2),23073(a,1,1))].">
      <j1 rule="para" parents="23073 23073"/>
    </justification>
  </clause>

  <clause id="24375">
    <literal><![CDATA[
      L(x,y,y) \ (y * x) = T(R(y,y,x),x)
    ]]></literal>
    <justification jstring="[hyper(139,a,2001,a(flip),b,23149,a)].">
      <j1 rule="hyper" parents="139 2001 23149"/>
    </justification>
  </clause>

  <clause id="24376">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12217,a,b,23149,a)].">
      <j1 rule="hyper" parents="64 12217 23149"/>
    </justification>
  </clause>

  <clause id="24377">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = u * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12216,a,b,23149,a)].">
      <j1 rule="hyper" parents="64 12216 23149"/>
    </justification>
  </clause>

  <clause id="24378">
    <literal><![CDATA[
      (x * L(y,z,u)) / y = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(142,a,23149,a(flip),b,12217,a)].">
      <j1 rule="hyper" parents="142 23149 12217"/>
    </justification>
  </clause>

  <clause id="24379">
    <literal><![CDATA[
      ((x * y) / x) * L(x,z,u) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[para(255(a,1),23149(a,1,2)),flip(a)].">
      <j1 rule="para" parents="255 23149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24381">
    <literal><![CDATA[
      R(x \ 1,x,y) * L(y,z,u) = L(y,z,u) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(2997(a,1),23149(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2997 23149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24382">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * T(v5,x) = v5 * L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23496(a,1),23149(a,1,2))].">
      <j1 rule="para" parents="23496 23149"/>
    </justification>
  </clause>

  <clause id="24383">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) * v5 = v5 * L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23544(a,1),23149(a,1,2))].">
      <j1 rule="para" parents="23544 23149"/>
    </justification>
  </clause>

  <clause id="24384">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) / x = u / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(313,a,23165,a)].">
      <j1 rule="hyper" parents="313 23165"/>
    </justification>
  </clause>

  <clause id="24385">
    <literal><![CDATA[
      x / L(a(y,z,u) \ 1,w,v5) = L(a(y,z,u) \ 1,w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,23734,a(flip),b,23165,a)].">
      <j1 rule="hyper" parents="64 23734 23165"/>
    </justification>
  </clause>

  <clause id="24386">
    <literal><![CDATA[
      T(x / L(L(y,z,u),w,v5),y) = L(L(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,23153,a(flip),b,23165,a)].">
      <j1 rule="hyper" parents="64 23153 23165"/>
    </justification>
  </clause>

  <clause id="24387">
    <literal><![CDATA[
      T(x / L(y / z,u,w),z \ y) = T(L(y / z,u,w) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(23165(a,1),8711(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23165 8711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24388">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) \ z = T((z / (y * x)) * y,x)
    ]]></literal>
    <justification jstring="[para(15007(a,1),23165(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15007 23165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24389">
    <literal><![CDATA[
      L(x,y,z) * (L(x,u,w) \ v5) = (v5 / L(x,u,w)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(23165(a,1),23149(a,1,2))].">
      <j1 rule="para" parents="23165 23149"/>
    </justification>
  </clause>

  <clause id="24391">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ u) = (K(y,x) * z) \ u
    ]]></literal>
    <justification jstring="[hyper(373,a,22758,a,b,23199,a)].">
      <j1 rule="hyper" parents="373 22758 23199"/>
    </justification>
  </clause>

  <clause id="24392">
    <literal><![CDATA[
      (K(x,y) * a(z,u,w)) \ v5 = K(y,x) * (a(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,22774,a(flip),b,23199,a),flip(a)].">
      <j1 rule="hyper" parents="373 22774 23199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24394">
    <literal><![CDATA[
      ((x * x) \ y) \ (K(z,u) * (y * ((x * x) \ K(u,z)))) = K(y,(x * x) \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17589,a(flip),b,23199,a),flip(a)].">
      <j1 rule="hyper" parents="64 17589 23199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24395">
    <literal><![CDATA[
      (x \ 1) \ (K(y,x) * z) = (x \ K(x,y)) \ z
    ]]></literal>
    <justification jstring="[para(4097(a,1),23199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4097 23199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24396">
    <literal><![CDATA[
      (K(x,y) * z) \ (y * u) = z \ (T(y,x) * u)
    ]]></literal>
    <justification jstring="[para(5755(a,1),23199(a,2,2))].">
      <j1 rule="para" parents="5755 23199"/>
    </justification>
  </clause>

  <clause id="24397">
    <literal><![CDATA[
      (T(x,y) \ z) \ (K(y,x) * u) = (x \ z) \ u
    ]]></literal>
    <justification jstring="[para(6075(a,1),23199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6075 23199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24399">
    <literal><![CDATA[
      (x * (y / x)) \ (K(x,x \ y) * z) = y \ z
    ]]></literal>
    <justification jstring="[para(6179(a,1),23199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6179 23199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24400">
    <literal><![CDATA[
      ((x \ y) * z) \ (K(x \ y,x) * u) = ((y / x) * z) \ u
    ]]></literal>
    <justification jstring="[para(5982(a,1),23199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5982 23199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24402">
    <literal><![CDATA[
      ((x / y) \ z) \ (K(y \ x,y) * u) = ((y \ x) \ z) \ u
    ]]></literal>
    <justification jstring="[para(6270(a,1),23199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6270 23199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24403">
    <literal><![CDATA[
      (x / (y \ z)) \ (K(y,y \ z) * u) = T(x / (z / y),K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(8906(a,1),23199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8906 23199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24404">
    <literal><![CDATA[
      ((x * y) * z) \ (K(x,y) * u) = ((y * x) * z) \ u
    ]]></literal>
    <justification jstring="[para(10834(a,1),23199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10834 23199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24405">
    <literal><![CDATA[
      (x \ y) \ (K(z \ x,z) * u) = (((z \ x) * z) \ y) \ u
    ]]></literal>
    <justification jstring="[para(10843(a,1),23199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10843 23199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24406">
    <literal><![CDATA[
      (1 / x) \ (K(y,z) * u) = (K(z,y) / x) \ u
    ]]></literal>
    <justification jstring="[para(14366(a,1),23199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14366 23199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24414">
    <literal><![CDATA[
      ((1 / (1 / (x \ y))) \ y) / (1 / (x \ y)) = x / ((1 / (y / x)) * K(y \ x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16984,a,b,23218,a)].">
      <j1 rule="hyper" parents="64 16984 23218"/>
    </justification>
  </clause>

  <clause id="24415">
    <literal><![CDATA[
      K(x,y) / (x * K(z,u)) = (K(u,z) / x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17317,a(flip),b,23218,a),flip(a)].">
      <j1 rule="hyper" parents="64 17317 23218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24416">
    <literal><![CDATA[
      x / (L(x,x \ (y \ x),y) * K(x,y \ 1)) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,6693,a(flip),b,23218,a),flip(a)].">
      <j1 rule="hyper" parents="64 6693 23218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24419">
    <literal><![CDATA[
      (((x \ y) \ y) \ z) \ u = (x \ z) \ (K(x,x \ y) * u)
    ]]></literal>
    <justification jstring="[para(6073(a,1),23222(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6073 23222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24420">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (K(x,y) * w) = (z * u) \ w
    ]]></literal>
    <justification jstring="[para(23073(a,2),23222(a,1,1))].">
      <j1 rule="para" parents="23073 23222"/>
    </justification>
  </clause>

  <clause id="24421">
    <literal><![CDATA[
      R(K(x,y) / z,z,u) = K(x,y) * (u / (z * u))
    ]]></literal>
    <justification jstring="[hyper(776,a,23224,a)].">
      <j1 rule="hyper" parents="776 23224"/>
    </justification>
  </clause>

  <clause id="24423">
    <literal><![CDATA[
      x * ((K(y,z) * u) / w) = x * (K(y,z) * (u / w))
    ]]></literal>
    <justification jstring="[hyper(145,a,23224,a,b,9,a)].">
      <j1 rule="hyper" parents="145 23224 9"/>
    </justification>
  </clause>

  <clause id="24425">
    <literal><![CDATA[
      R(K(x,y) / z,z,z \ u) = K(x,y) * ((z \ u) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,677,a,b,23224,a)].">
      <j1 rule="hyper" parents="64 677 23224"/>
    </justification>
  </clause>

  <clause id="24427">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) * z) / u) = (y * z) / u
    ]]></literal>
    <justification jstring="[para(5811(a,1),23224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5811 23224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24429">
    <literal><![CDATA[
      K(x,y) * ((K(z,T(y,x)) * u) / w) = (y * (T(T(y,x),z) \ u)) / w
    ]]></literal>
    <justification jstring="[para(6216(a,1),23224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6216 23224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24430">
    <literal><![CDATA[
      K(x,y) * (((y * x) * z) / u) = ((x * y) * z) / u
    ]]></literal>
    <justification jstring="[para(10834(a,1),23224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10834 23224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24432">
    <literal><![CDATA[
      K(x,y) * ((x / z) / u) = (T(x,y) / z) / u
    ]]></literal>
    <justification jstring="[para(14825(a,1),23224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14825 23224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24433">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z \ u) / w) = (z \ (K(x,y) * u)) / w
    ]]></literal>
    <justification jstring="[para(22758(a,1),23224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="22758 23224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24439">
    <literal><![CDATA[
      x * ((y * (x / y)) \ z) = K(y \ x,y) * z
    ]]></literal>
    <justification jstring="[para(6179(a,1),23228(a,1,1))].">
      <j1 rule="para" parents="6179 23228"/>
    </justification>
  </clause>

  <clause id="24440">
    <literal><![CDATA[
      (x / T(y,z)) * ((x / y) \ u) = K(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(8676(a,1),23228(a,1,1))].">
      <j1 rule="para" parents="8676 23228"/>
    </justification>
  </clause>

  <clause id="24442">
    <literal><![CDATA[
      T(x / (y * K(z,u)),y) = (y \ x) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(269,a,23229,a,b,23055,a)].">
      <j1 rule="hyper" parents="269 23229 23055"/>
    </justification>
  </clause>

  <clause id="24443">
    <literal><![CDATA[
      x / (y * K(y \ 1,y * x)) = ((y \ 1) \ x) * (y \ (1 / y))
    ]]></literal>
    <justification jstring="[hyper(36,a,7019,a,b,23229,a),flip(a)].">
      <j1 rule="hyper" parents="36 7019 23229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24447">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ z) * u) = (((x \ y) \ y) \ z) * u
    ]]></literal>
    <justification jstring="[para(6073(a,1),23246(a,1,2,1))].">
      <j1 rule="para" parents="6073 23246"/>
    </justification>
  </clause>

  <clause id="24448">
    <literal><![CDATA[
      K(x,y) * ((z \ K(y,x)) * u) = T(z \ 1,K(y,x)) * u
    ]]></literal>
    <justification jstring="[para(14521(a,1),23246(a,1,2,1))].">
      <j1 rule="para" parents="14521 23246"/>
    </justification>
  </clause>

  <clause id="24449">
    <literal><![CDATA[
      K(K(x,y),z) * ((u \ K(z,K(x,y))) * w) = (u \ 1) * w
    ]]></literal>
    <justification jstring="[para(17158(a,1),23246(a,1,2,1))].">
      <j1 rule="para" parents="17158 23246"/>
    </justification>
  </clause>

  <clause id="24451">
    <literal><![CDATA[
      a(x,y,z) * (u * K(w,v5)) = u * (K(w,v5) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,23136,a,b,23256,a)].">
      <j1 rule="hyper" parents="64 23136 23256"/>
    </justification>
  </clause>

  <clause id="24453">
    <literal><![CDATA[
      x * (K(y \ z,y) * (T(z \ x,K(y,z)) \ u)) = (((y \ z) * y) * (x / z)) * ((x / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11728,a(flip),b,23256,a),flip(a)].">
      <j1 rule="hyper" parents="64 11728 23256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24455">
    <literal><![CDATA[
      (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y * K(z,u),w)
    ]]></literal>
    <justification jstring="[para(23256(a,1),14(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="23256 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24456">
    <literal><![CDATA[
      (x * (K(y,z) * (u * w))) \ (((x * K(y,z)) * u) * w) = a(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23256(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="23256 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24457">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ ((x * K(y,z)) * (u * w)) = L(w,u,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(23256(a,1),18(a,2,1)),flip(a)].">
      <j1 rule="para" parents="23256 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24461">
    <literal><![CDATA[
      (x * K(y,z)) * (y * u) = x * (T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5755(a,1),23256(a,2,2))].">
      <j1 rule="para" parents="5755 23256"/>
    </justification>
  </clause>

  <clause id="24462">
    <literal><![CDATA[
      (x * K(y,y \ z)) * z = x * (y * (z / y))
    ]]></literal>
    <justification jstring="[para(5781(a,1),23256(a,2,2))].">
      <j1 rule="para" parents="5781 23256"/>
    </justification>
  </clause>

  <clause id="24464">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ u) = x * (T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(6157(a,1),23256(a,2,2))].">
      <j1 rule="para" parents="6157 23256"/>
    </justification>
  </clause>

  <clause id="24465">
    <literal><![CDATA[
      (x / y) * (K(z,y) * u) = (x / T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6245(a,1),23256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6245 23256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24466">
    <literal><![CDATA[
      (x * T(y,z)) * (K(z,y) * u) = (x * y) * u
    ]]></literal>
    <justification jstring="[para(6249(a,1),23256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6249 23256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24467">
    <literal><![CDATA[
      (x * (y / (y / z))) * u = (x * z) * (K(z \ y,z) * u)
    ]]></literal>
    <justification jstring="[para(6472(a,1),23256(a,1,1))].">
      <j1 rule="para" parents="6472 23256"/>
    </justification>
  </clause>

  <clause id="24468">
    <literal><![CDATA[
      (x * y) * (K(y,z) * u) = (x * T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(6852(a,1),23256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6852 23256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24469">
    <literal><![CDATA[
      (x / (y \ z)) * (K(y \ z,y) * u) = (x / (z / y)) * u
    ]]></literal>
    <justification jstring="[para(6887(a,1),23256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6887 23256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24471">
    <literal><![CDATA[
      (x * y) * (K(z,z \ y) * u) = (x * (z * (y / z))) * u
    ]]></literal>
    <justification jstring="[para(10173(a,1),23256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10173 23256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24472">
    <literal><![CDATA[
      (x \ 1) * (K(y,z) * u) = (x \ K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(14444(a,1),23256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14444 23256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24474">
    <literal><![CDATA[
      (x \ y) * (K(y,z) * u) = (x \ T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(15021(a,1),23256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15021 23256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24475">
    <literal><![CDATA[
      (x \ (y \ z)) * (K(y,z / y) * u) = (x \ (z / y)) * u
    ]]></literal>
    <justification jstring="[para(15028(a,1),23256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15028 23256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24476">
    <literal><![CDATA[
      (x \ (y \ z)) * (K(y,y \ z) * u) = (x \ (z / y)) * u
    ]]></literal>
    <justification jstring="[para(15092(a,1),23256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15092 23256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24477">
    <literal><![CDATA[
      (K(x,y * y) * z) * u = z * (K(x,y * y) * u)
    ]]></literal>
    <justification jstring="[para(17047(a,2),23256(a,1,1))].">
      <j1 rule="para" parents="17047 23256"/>
    </justification>
  </clause>

  <clause id="24480">
    <literal><![CDATA[
      (x * (y * K(z,u))) * w = (x * y) * (K(z,u) * w)
    ]]></literal>
    <justification jstring="[para(23053(a,1),23256(a,1,1))].">
      <j1 rule="para" parents="23053 23256"/>
    </justification>
  </clause>

  <clause id="24481">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ w = K(z,T(y,u)) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,7914,a(flip),b,23257,a),flip(a)].">
      <j1 rule="hyper" parents="373 7914 23257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24485">
    <literal><![CDATA[
      x / (K(y,T(z,u)) * w) = (x / w) * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,7904,a(flip),b,23271,a),flip(a)].">
      <j1 rule="hyper" parents="373 7904 23271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24486">
    <literal><![CDATA[
      (x / (y * z)) * K(u,y) = x / (T(y,u) * z)
    ]]></literal>
    <justification jstring="[para(5755(a,1),23271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5755 23271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24488">
    <literal><![CDATA[
      x / ((y / (y / z)) * u) = (x / (z * u)) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(5984(a,1),23271(a,1,2))].">
      <j1 rule="para" parents="5984 23271"/>
    </justification>
  </clause>

  <clause id="24489">
    <literal><![CDATA[
      (x / ((y \ z) \ u)) * K(y,y \ z) = x / ((z / y) \ u)
    ]]></literal>
    <justification jstring="[para(6292(a,1),23271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6292 23271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24490">
    <literal><![CDATA[
      (x / (y * K(z,u))) * K(z,u) = x / T(y,K(u,z))
    ]]></literal>
    <justification jstring="[para(8158(a,1),23271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8158 23271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24491">
    <literal><![CDATA[
      (x / (y * (z / u))) * K(u,u \ z) = x / T(y * (u \ z),K(u,z))
    ]]></literal>
    <justification jstring="[para(8905(a,1),23271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8905 23271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24494">
    <literal><![CDATA[
      L(x / ((x / y) * K(z,u)),w,v5) \ x = x / L(K(u,z) * y,w,v5)
    ]]></literal>
    <justification jstring="[para(23271(a,1),10468(a,1,1,1,2))].">
      <j1 rule="para" parents="23271 10468"/>
    </justification>
  </clause>

  <clause id="24495">
    <literal><![CDATA[
      (x / ((y * z) * u)) * K(y,z) = x / ((z * y) * u)
    ]]></literal>
    <justification jstring="[para(10834(a,1),23271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10834 23271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24496">
    <literal><![CDATA[
      x / (y * K(z,y * u)) = (x / y) * K(u * y,z)
    ]]></literal>
    <justification jstring="[para(11119(a,1),23271(a,1,2))].">
      <j1 rule="para" parents="11119 23271"/>
    </justification>
  </clause>

  <clause id="24497">
    <literal><![CDATA[
      (x / (K(y,z) / u)) * K(y,z) = x / (1 / u)
    ]]></literal>
    <justification jstring="[para(14383(a,1),23271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14383 23271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24498">
    <literal><![CDATA[
      (x / (T(y,z) / u)) * K(y,z) = x / (y / u)
    ]]></literal>
    <justification jstring="[para(14842(a,1),23271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14842 23271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24499">
    <literal><![CDATA[
      K(x,T((y / z) * K(u,w),v5)) = K(x,T(y * (z \ K(u,w)),v5))
    ]]></literal>
    <justification jstring="[para(23271(a,1),14806(a,1,2,1))].">
      <j1 rule="para" parents="23271 14806"/>
    </justification>
  </clause>

  <clause id="24500">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * w = (x / u) * (K(z,y) * w)
    ]]></literal>
    <justification jstring="[para(23271(a,2),23256(a,1,1))].">
      <j1 rule="para" parents="23271 23256"/>
    </justification>
  </clause>

  <clause id="24503">
    <literal><![CDATA[
      (x \ y) * ((z * K(x \ y,x)) \ u) = (y / x) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(145,a,23272,a,b,6442,a)].">
      <j1 rule="hyper" parents="145 23272 6442"/>
    </justification>
  </clause>

  <clause id="24505">
    <literal><![CDATA[
      K(x,y) * ((z / x) \ u) = (z / T(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(6245(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6245 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24506">
    <literal><![CDATA[
      K(x,y) * ((z * T(x,y)) \ u) = (z * x) \ u
    ]]></literal>
    <justification jstring="[para(6249(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6249 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24507">
    <literal><![CDATA[
      K(x \ y,x) * ((z * (x \ y)) \ u) = (z * (y / x)) \ u
    ]]></literal>
    <justification jstring="[para(6471(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6471 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24508">
    <literal><![CDATA[
      (x * (y / (y / z))) \ u = K(z,z \ y) * ((x * z) \ u)
    ]]></literal>
    <justification jstring="[para(6472(a,1),23272(a,1,1))].">
      <j1 rule="para" parents="6472 23272"/>
    </justification>
  </clause>

  <clause id="24509">
    <literal><![CDATA[
      K(x,y) * ((z * y) \ u) = (z * T(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(6852(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6852 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24510">
    <literal><![CDATA[
      K(x,x \ y) * ((z / (x \ y)) \ u) = (z / (y / x)) \ u
    ]]></literal>
    <justification jstring="[para(6887(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6887 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24511">
    <literal><![CDATA[
      (x * ((y \ z) \ z)) \ u = K(y \ z,y) * ((x * y) \ u)
    ]]></literal>
    <justification jstring="[para(6889(a,1),23272(a,1,1))].">
      <j1 rule="para" parents="6889 23272"/>
    </justification>
  </clause>

  <clause id="24513">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) * z) \ u) = T(z,K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(8160(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8160 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24514">
    <literal><![CDATA[
      K(x,x \ y) * ((z * y) \ u) = (z * ((x \ y) * x)) \ u
    ]]></literal>
    <justification jstring="[para(10196(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10196 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24515">
    <literal><![CDATA[
      K(x,y) * ((z / (y * x)) \ u) = (z / (x * y)) \ u
    ]]></literal>
    <justification jstring="[para(10595(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10595 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24516">
    <literal><![CDATA[
      K(x,y) * ((z \ 1) \ u) = (z \ K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(14444(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14444 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24517">
    <literal><![CDATA[
      K(x,y) * ((z \ K(x,y)) \ u) = (z \ 1) \ u
    ]]></literal>
    <justification jstring="[para(14520(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14520 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24519">
    <literal><![CDATA[
      K(x,y) * ((z \ T(x,y)) \ u) = (z \ x) \ u
    ]]></literal>
    <justification jstring="[para(15017(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15017 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24520">
    <literal><![CDATA[
      K(x,y) * ((z \ y) \ u) = (z \ T(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(15021(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15021 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24521">
    <literal><![CDATA[
      K(x,y) * (((z \ y) / y) \ u) = ((z \ T(y,x)) / y) \ u
    ]]></literal>
    <justification jstring="[para(15049(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15049 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24522">
    <literal><![CDATA[
      K(x,x \ y) * ((z \ (y / x)) \ u) = (z \ (x \ y)) \ u
    ]]></literal>
    <justification jstring="[para(15097(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15097 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24523">
    <literal><![CDATA[
      K(x,x \ y) * ((z \ y) \ u) = (z \ ((x \ y) * x)) \ u
    ]]></literal>
    <justification jstring="[para(15230(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15230 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24524">
    <literal><![CDATA[
      T((x * K(y,z)) \ u,K(y,z) * w) = T((x \ u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[para(23272(a,2),22938(a,1,1))].">
      <j1 rule="para" parents="23272 22938"/>
    </justification>
  </clause>

  <clause id="24525">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ w = K(u,z) * ((x * y) \ w)
    ]]></literal>
    <justification jstring="[para(23053(a,1),23272(a,1,1))].">
      <j1 rule="para" parents="23053 23272"/>
    </justification>
  </clause>

  <clause id="24528">
    <literal><![CDATA[
      (x * (y \ z)) / (T(y,u) \ z) = x * K(y,u)
    ]]></literal>
    <justification jstring="[hyper(225,a,6066,a(flip),b,23274,a)].">
      <j1 rule="hyper" parents="225 6066 23274"/>
    </justification>
  </clause>

  <clause id="24531">
    <literal><![CDATA[
      (x / T(y,T(z,u))) * K(y,u) = x / T(y * K(u,y),z)
    ]]></literal>
    <justification jstring="[para(9454(a,1),23276(a,1,1,2))].">
      <j1 rule="para" parents="9454 23276"/>
    </justification>
  </clause>

  <clause id="24533">
    <literal><![CDATA[
      (x \ T(y,z)) \ ((x \ y) * u) = K(z,y) * u
    ]]></literal>
    <justification jstring="[para(15017(a,1),23279(a,1,2,1))].">
      <j1 rule="para" parents="15017 23279"/>
    </justification>
  </clause>

  <clause id="24535">
    <literal><![CDATA[
      K(x,y) * ((1 / T(z,K(y,x))) \ u) = (K(y,x) / z) \ u
    ]]></literal>
    <justification jstring="[para(14775(a,1),23280(a,1,2,1))].">
      <j1 rule="para" parents="14775 23280"/>
    </justification>
  </clause>

  <clause id="24536">
    <literal><![CDATA[
      K(x,x \ y) * ((z \ ((x \ y) \ y)) \ u) = (z \ x) \ u
    ]]></literal>
    <justification jstring="[para(15035(a,2),23280(a,1,2,1))].">
      <j1 rule="para" parents="15035 23280"/>
    </justification>
  </clause>

  <clause id="24540">
    <literal><![CDATA[
      (x * K(y,y \ z)) * ((z / (z / y)) * u) = x * (y * u)
    ]]></literal>
    <justification jstring="[para(5984(a,1),23281(a,1,2))].">
      <j1 rule="para" parents="5984 23281"/>
    </justification>
  </clause>

  <clause id="24541">
    <literal><![CDATA[
      (x \ ((y \ z) \ z)) * (K(y \ z,y) * u) = (x \ y) * u
    ]]></literal>
    <justification jstring="[para(15035(a,2),23281(a,1,1))].">
      <j1 rule="para" parents="15035 23281"/>
    </justification>
  </clause>

  <clause id="24542">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,(y / u) * z)
    ]]></literal>
    <justification jstring="[hyper(17535,a,23387,a),flip(a)].">
      <j1 rule="hyper" parents="17535 23387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24546">
    <literal><![CDATA[
      K(x,1 / (T(y,z) * u)) = K(x,u \ T(1 / y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17790,a(flip),b,23387,a),flip(a)].">
      <j1 rule="hyper" parents="64 17790 23387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24547">
    <literal><![CDATA[
      K(x,y / (T(z \ u,z) * w)) = K(x,(y / w) / (u / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16279,a(flip),b,23387,a),flip(a)].">
      <j1 rule="hyper" parents="64 16279 23387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24548">
    <literal><![CDATA[
      K(x,y / (z * L(u \ w,u,w \ y))) = K(x,((y / w) * u) / z)
    ]]></literal>
    <justification jstring="[para(15003(a,1),23387(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15003 23387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24550">
    <literal><![CDATA[
      K(x,y) * L(T(y,x),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(25(a,2),23390(a,1,2))].">
      <j1 rule="para" parents="25 23390"/>
    </justification>
  </clause>

  <clause id="24553">
    <literal><![CDATA[
      K(R(x,y,y \ 1) / (z * (y \ 1)),u) = K((x * y) / z,u)
    ]]></literal>
    <justification jstring="[para(297(a,1),23429(a,1,1,1))].">
      <j1 rule="para" parents="297 23429"/>
    </justification>
  </clause>

  <clause id="24555">
    <literal><![CDATA[
      L(T(x,y),z,u) * T(y,x) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,23430,a(flip),b,6243,a)].">
      <j1 rule="hyper" parents="144 23430 6243"/>
    </justification>
  </clause>

  <clause id="24556">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) = L(x,z,u) * K(x,y / x)
    ]]></literal>
    <justification jstring="[para(4666(a,1),23430(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4666 23430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24557">
    <literal><![CDATA[
      K(x,y) * (L(y,z,u) \ w) = L(T(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(23430(a,1),7068(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23430 7068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24560">
    <literal><![CDATA[
      (x / L(T(y,z),u,w)) * L(y,u,w) = x * K(z,y)
    ]]></literal>
    <justification jstring="[para(23430(a,1),23229(a,1,1,2))].">
      <j1 rule="para" parents="23430 23229"/>
    </justification>
  </clause>

  <clause id="24564">
    <literal><![CDATA[
      K(x,y) * (R(T(x,y),z,u) \ w) = R(x,z,u) \ w
    ]]></literal>
    <justification jstring="[para(23499(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23499 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24565">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) \ w) = R(T(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(23499(a,1),23280(a,1,2,1))].">
      <j1 rule="para" parents="23499 23280"/>
    </justification>
  </clause>

  <clause id="24566">
    <literal><![CDATA[
      R(x,y,z) * (K(x,u) * w) = R(T(x,u),y,z) * w
    ]]></literal>
    <justification jstring="[para(23499(a,1),23281(a,1,1))].">
      <j1 rule="para" parents="23499 23281"/>
    </justification>
  </clause>

  <clause id="24567">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * (u * w) = w * (T(u,w) * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(23586(a,1),10990(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23586 10990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24568">
    <literal><![CDATA[
      T(x,y \ (z \ L(z * y,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(23747,a,23615,a),flip(a)].">
      <j1 rule="hyper" parents="23747 23615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24569">
    <literal><![CDATA[
      T(x,(y * (z * u)) \ w) = T(x,u \ (z \ (y \ w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,23615,a(flip),b,23615,a),flip(a)].">
      <j1 rule="hyper" parents="373 23615 23615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24571">
    <literal><![CDATA[
      T(x,(y \ z) \ (y \ u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),23615(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 23615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24572">
    <literal><![CDATA[
      x / (y \ (z \ L(z * y,u,w))) = (y \ (z \ L(z * y,u,w))) \ x
    ]]></literal>
    <justification jstring="[hyper(8638,a,24568,a),flip(a)].">
      <j1 rule="hyper" parents="8638 24568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24573">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) / y = y \ (x \ L(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(225,a,24568,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 24568 116"/>
    </justification>
  </clause>

  <clause id="24575">
    <literal><![CDATA[
      T(x,(y * z) / u) = T(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(373,a,22651,a(flip),b,23616,a),flip(a)].">
      <j1 rule="hyper" parents="373 22651 23616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24576">
    <literal><![CDATA[
      T(x,T(y,z) / (y / z)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16096,a(flip),b,23616,a),flip(a)].">
      <j1 rule="hyper" parents="64 16096 23616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24577">
    <literal><![CDATA[
      T(x,y \ (((z * y) \ z) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13988,a(flip),b,23620,a),flip(a)].">
      <j1 rule="hyper" parents="64 13988 23620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24578">
    <literal><![CDATA[
      ((x \ (((y * x) \ y) \ 1)) \ z) \ z = x \ (((y * x) \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(4722,a,24577,a)].">
      <j1 rule="hyper" parents="4722 24577"/>
    </justification>
  </clause>

  <clause id="24579">
    <literal><![CDATA[
      T(x,y \ (z * u)) = T(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(22661,a,23621,a),flip(a)].">
      <j1 rule="hyper" parents="22661 23621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24581">
    <literal><![CDATA[
      T(x \ y,z / (y / x)) = T(x \ y,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16318,a,b,23621,a)].">
      <j1 rule="hyper" parents="64 16318 23621"/>
    </justification>
  </clause>

  <clause id="24582">
    <literal><![CDATA[
      T(x \ y,(y / x) \ z) = T(x \ y,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8492,a,b,23621,a)].">
      <j1 rule="hyper" parents="64 8492 23621"/>
    </justification>
  </clause>

  <clause id="24583">
    <literal><![CDATA[
      T(x / y,(x / y) \ z) = T(x / y,x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8480,a,b,23621,a)].">
      <j1 rule="hyper" parents="64 8480 23621"/>
    </justification>
  </clause>

  <clause id="24587">
    <literal><![CDATA[
      ((x / y) * z) / T(x,y \ z) = x \ ((x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(225,a,23622,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 23622 116"/>
    </justification>
  </clause>

  <clause id="24588">
    <literal><![CDATA[
      (x \ R(y,z,u)) * K(y,w) = x \ R(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,23657,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 23657 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24589">
    <literal><![CDATA[
      R(x,y,z) * (x \ K(x,u)) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,23657,a(flip),b,1902,a),flip(a)].">
      <j1 rule="hyper" parents="139 23657 1902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24591">
    <literal><![CDATA[
      K(x,y) * R(T(y,x),z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(6187,a,23659,a)].">
      <j1 rule="hyper" parents="6187 23659"/>
    </justification>
  </clause>

  <clause id="24593">
    <literal><![CDATA[
      T(x,y) * R(x,z,u) = x * R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,23659,a(flip),b,6071,a),flip(a)].">
      <j1 rule="hyper" parents="145 23659 6071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24594">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,u) = x \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,23659,a(flip),b,5778,a)].">
      <j1 rule="hyper" parents="139 23659 5778"/>
    </justification>
  </clause>

  <clause id="24596">
    <literal><![CDATA[
      R(T(x,y),z,u) \ 1 = R(x,z,u) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(23659(a,1),14450(a,1,1))].">
      <j1 rule="para" parents="23659 14450"/>
    </justification>
  </clause>

  <clause id="24597">
    <literal><![CDATA[
      R(T(x,y),z,u) \ y = R(x,z,u) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(23659(a,1),14833(a,1,1))].">
      <j1 rule="para" parents="23659 14833"/>
    </justification>
  </clause>

  <clause id="24598">
    <literal><![CDATA[
      K(x,y) * (T(x,z) \ R(x,u,w)) = T(x,z) \ R(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(23659(a,1),22770(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23659 22770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24599">
    <literal><![CDATA[
      R(x,y,z) \ (K(u,x) * w) = R(T(x,u),y,z) \ w
    ]]></literal>
    <justification jstring="[para(23659(a,1),23199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23659 23199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24600">
    <literal><![CDATA[
      R(x \ y,z,u) * ((x \ y) \ y) = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,23680,a(flip),b,363,a(flip))].">
      <j1 rule="hyper" parents="144 23680 363"/>
    </justification>
  </clause>

  <clause id="24601">
    <literal><![CDATA[
      T(x * R(y,z,u),x * y) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12958,a,b,23681,a)].">
      <j1 rule="hyper" parents="64 12958 23681"/>
    </justification>
  </clause>

  <clause id="24602">
    <literal><![CDATA[
      (1 / x) \ T(y,x) = y * R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10209,a(flip),b,23681,a)].">
      <j1 rule="hyper" parents="64 10209 23681"/>
    </justification>
  </clause>

  <clause id="24603">
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = (u / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(117(a,1),23681(a,1,2))].">
      <j1 rule="para" parents="117 23681"/>
    </justification>
  </clause>

  <clause id="24604">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,u) = R(x,z,u) * y
    ]]></literal>
    <justification jstring="[para(255(a,1),23681(a,1,2)),flip(a)].">
      <j1 rule="para" parents="255 23681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24605">
    <literal><![CDATA[
      R(x,y,z) * (u * x) = x * (u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(23681(a,1),1900(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23681 1900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24606">
    <literal><![CDATA[
      R(x \ 1,y,z) * (u * x) = (x \ 1) * (u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(23681(a,1),2764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23681 2764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24608">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u) * R(y,w,v5) = R(y,w,v5) * T(T(x,z),u)
    ]]></literal>
    <justification jstring="[para(5861(a,1),23681(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5861 23681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24609">
    <literal><![CDATA[
      (R(x,y,z) * u) / T(x,u) = (u * R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[para(23681(a,1),6846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23681 6846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24611">
    <literal><![CDATA[
      R(x,y,z) * (L(x,u,w) \ v5) = (v5 / L(x,u,w)) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(23165(a,1),23681(a,1,2))].">
      <j1 rule="para" parents="23165 23681"/>
    </justification>
  </clause>

  <clause id="24612">
    <literal><![CDATA[
      (K(x,y) / x) \ y = y * R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14840,a,b,24602,a)].">
      <j1 rule="hyper" parents="64 14840 24602"/>
    </justification>
  </clause>

  <clause id="24613">
    <literal><![CDATA[
      L(x,y,z) * R(u,u,L(x,y,z)) = (1 / u) \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(25(a,2),24602(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25 24602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24614">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) * R(y \ 1,y \ 1,x * ((1 / y) \ y)) = (1 / (y \ 1)) \ ((y \ 1) \ (x * y))
    ]]></literal>
    <justification jstring="[para(1593(a,1),24602(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1593 24602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24615">
    <literal><![CDATA[
      T(x,y) * K(y \ T(x,y),y \ 1) = (x * R(y,y,x)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(24602(a,1),6332(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24602 6332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24616">
    <literal><![CDATA[
      T(x,(y * (z \ x)) \ x) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4461,a(flip),b,23683,a)].">
      <j1 rule="hyper" parents="64 4461 23683"/>
    </justification>
  </clause>

  <clause id="24619">
    <literal><![CDATA[
      T(x \ R(x,y,z),u) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,23712,a,b,2071,a)].">
      <j1 rule="hyper" parents="144 23712 2071"/>
    </justification>
  </clause>

  <clause id="24620">
    <literal><![CDATA[
      T(R(x,y,z) / x,u) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2071(a,2),23712(a,1,1))].">
      <j1 rule="para" parents="2071 23712"/>
    </justification>
  </clause>

  <clause id="24622">
    <literal><![CDATA[
      (L(x \ R(x,y,z),u,w) \ v5) \ v5 = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23712(a,1),10457(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23712 10457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24623">
    <literal><![CDATA[
      (a(x,y,z) * u) * (a(x,y,z) \ 1) = L(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(23735(a,1),5134(a,1,2))].">
      <j1 rule="para" parents="23735 5134"/>
    </justification>
  </clause>

  <clause id="24624">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * u) * (1 / u) = u * ((a(x,y,z) \ 1) * (1 / u))
    ]]></literal>
    <justification jstring="[para(23735(a,1),13944(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23735 13944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24625">
    <literal><![CDATA[
      L(x,K(y,z) * u,y) = (T(y,w) * u) \ (T(y,w) * (u * x))
    ]]></literal>
    <attribute><![CDATA[
      label(flip_matches_hint)
    ]]></attribute>
    <justification jstring="[hyper(373,a,18,a(flip),b,23824,a),flip(a)].">
      <j1 rule="hyper" parents="373 18 23824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24626">
    <literal><![CDATA[
      L(x,T(y,z) \ u,T(y,w)) = L(x,y \ u,y)
    ]]></literal>
    <justification jstring="[para(6075(a,1),23824(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6075 23824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24627">
    <literal><![CDATA[
      (x / (((y \ x) / x) * x)) \ ((y \ x) / x) = ((y \ x) / x) / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2041(a,1),23871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2041 23871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24628">
    <literal><![CDATA[
      (((x \ y) / y) \ 1) * (((x \ y) / y) * ((y / (x * y)) \ x)) = L(x,(x \ y) / y,(x \ y) / y) / ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(23871(a,1),3444(a,1,2,2))].">
      <j1 rule="para" parents="23871 3444"/>
    </justification>
  </clause>

  <clause id="24629">
    <literal><![CDATA[
      x / ((y * y) * L(x,z,u)) = (y * y) \ (L(x,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(142,a,23896,a(flip),b,1265,a)].">
      <j1 rule="hyper" parents="142 23896 1265"/>
    </justification>
  </clause>

  <clause id="24631">
    <literal><![CDATA[
      (x \ a(x,y,z)) \ (a(x,y,z) * u) = L((x \ 1) \ u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(23929(a,1),11813(a,2,1)),flip(a)].">
      <j1 rule="para" parents="23929 11813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24632">
    <literal><![CDATA[
      (x \ a(y,z,x)) \ (a(y,z,x) * u) = L((x \ 1) \ u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(23931(a,1),11813(a,2,1)),flip(a)].">
      <j1 rule="para" parents="23931 11813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24633">
    <literal><![CDATA[
      T(x,x * a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(55,a,23937,a)].">
      <j1 rule="hyper" parents="55 23937"/>
    </justification>
  </clause>

  <clause id="24634">
    <literal><![CDATA[
      T(x * ((y * y) * a(z,u,w)),x) = (y * y) * (x * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(23937(a,1),4889(a,2,2))].">
      <j1 rule="para" parents="23937 4889"/>
    </justification>
  </clause>

  <clause id="24635">
    <literal><![CDATA[
      T(x \ 1,x \ a(y,z,u)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(14732,a,24633,a)].">
      <j1 rule="hyper" parents="14732 24633"/>
    </justification>
  </clause>

  <clause id="24636">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ 1),x) = x * (a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,14609,a(flip),b,24633,a)].">
      <j1 rule="hyper" parents="64 14609 24633"/>
    </justification>
  </clause>

  <clause id="24637">
    <literal><![CDATA[
      L(a(x,y,z),u,u) / u = (1 / u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,24633,a(flip),b,8886,a)].">
      <j1 rule="hyper" parents="225 24633 8886"/>
    </justification>
  </clause>

  <clause id="24638">
    <literal><![CDATA[
      (1 / (1 / x)) \ a(y,z,u) = a(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(24633(a,1),5139(a,2,2))].">
      <j1 rule="para" parents="24633 5139"/>
    </justification>
  </clause>

  <clause id="24639">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ a(y,z,u) = a(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(24633(a,1),14986(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="24633 14986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24640">
    <literal><![CDATA[
      T((a(x,y,z) * u) \ 1,u \ 1) = (a(x,y,z) * u) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,6729,a(flip),b,24635,a)].">
      <j1 rule="hyper" parents="64 6729 24635"/>
    </justification>
  </clause>

  <clause id="24641">
    <literal><![CDATA[
      a(x,y,z) / (u \ 1) = (1 / u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(24635(a,1),1691(a,1,2))].">
      <j1 rule="para" parents="24635 1691"/>
    </justification>
  </clause>

  <clause id="24642">
    <literal><![CDATA[
      (x * a(y,z,u)) * (x \ 1) = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(24635(a,1),5134(a,1,2))].">
      <j1 rule="para" parents="24635 5134"/>
    </justification>
  </clause>

  <clause id="24645">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (w * a(x,y,z))) = L(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(23960(a,1),10980(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="23960 10980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24647">
    <literal><![CDATA[
      ((a(x,y,z) * u) * w) / (u * (w * a(x,y,z))) = a(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(23960(a,1),20987(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="23960 20987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24648">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4696,a,23961,a)].">
      <j1 rule="hyper" parents="4696 23961"/>
    </justification>
  </clause>

  <clause id="24650">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) / (a(x,y,z) * w) = R(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(225,a,23961,a(flip),b,15245,a)].">
      <j1 rule="hyper" parents="225 23961 15245"/>
    </justification>
  </clause>

  <clause id="24651">
    <literal><![CDATA[
      R(a(x,y,z),u,a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,10206,a,b,23961,a(flip))].">
      <j1 rule="hyper" parents="36 10206 23961"/>
    </justification>
  </clause>

  <clause id="24653">
    <literal><![CDATA[
      (x \ L(x,y,y)) \ x = a(y,y,x) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,5670,a(flip),b,23965,a)].">
      <j1 rule="hyper" parents="64 5670 23965"/>
    </justification>
  </clause>

  <clause id="24657">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((z * w) * u)) = L(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[para(1039(a,2),23972(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1039 23972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24659">
    <literal><![CDATA[
      L(x,y,z * (u \ 1)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23253,a,b,23990,a)].">
      <j1 rule="hyper" parents="64 23253 23990"/>
    </justification>
  </clause>

  <clause id="24660">
    <literal><![CDATA[
      L(x,y,z * a(u,u,z)) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[para(5669(a,1),23990(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5669 23990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24661">
    <literal><![CDATA[
      L(x,y,z \ a(u,w,z)) = L(x,y,a(u,w,z) * z)
    ]]></literal>
    <justification jstring="[para(9433(a,1),23990(a,1,3))].">
      <j1 rule="para" parents="9433 23990"/>
    </justification>
  </clause>

  <clause id="24662">
    <literal><![CDATA[
      L(x,y,z \ a(z,u,w)) = L(x,y,a(z,u,w) * z)
    ]]></literal>
    <justification jstring="[para(16059(a,1),23990(a,1,3))].">
      <j1 rule="para" parents="16059 23990"/>
    </justification>
  </clause>

  <clause id="24663">
    <literal><![CDATA[
      L(x \ R(x,y,z \ 1),x,z * y) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,16031,a,b,23997,a),flip(a)].">
      <j1 rule="hyper" parents="64 16031 23997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24664">
    <literal><![CDATA[
      L(x,y,R(z,u,u \ 1)) = L(x,y,u * (z * u))
    ]]></literal>
    <justification jstring="[para(297(a,1),23997(a,1,3))].">
      <j1 rule="para" parents="297 23997"/>
    </justification>
  </clause>

  <clause id="24665">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ L(z,v5,v6)) = L(x,y,L(z,u,w) * L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(1850(a,1),23997(a,1,3))].">
      <j1 rule="para" parents="1850 23997"/>
    </justification>
  </clause>

  <clause id="24666">
    <literal><![CDATA[
      L(x \ L(y,y,z),x,y * z) = ((z * (1 / y)) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,11817,a(flip),b,23999,a),flip(a)].">
      <j1 rule="hyper" parents="64 11817 23999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24667">
    <literal><![CDATA[
      R(x,y,(z * u) \ u) = R(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[para(5144(a,1),24131(a,1,3))].">
      <j1 rule="para" parents="5144 24131"/>
    </justification>
  </clause>

  <clause id="24668">
    <literal><![CDATA[
      x * a(x,y \ x,y) = R(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(157,a,24166,a)].">
      <j1 rule="hyper" parents="157 24166"/>
    </justification>
  </clause>

  <clause id="24669">
    <literal><![CDATA[
      a(x,y \ x,y) * x = R(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,23174,a,b,24166,a)].">
      <j1 rule="hyper" parents="39 23174 24166"/>
    </justification>
  </clause>

  <clause id="24671">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,22656,a(flip),b,24214,a)].">
      <j1 rule="hyper" parents="64 22656 24214"/>
    </justification>
  </clause>

  <clause id="24672">
    <literal><![CDATA[
      (x \ y) * ((x \ 1) / (x \ y)) = x \ K(x \ y,y \ 1)
    ]]></literal>
    <justification jstring="[para(24214(a,1),10166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24214 10166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24674">
    <literal><![CDATA[
      K(x,y \ (z \ (u * w))) = K(x,((z * y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,23002,a(flip),b,24234,a)].">
      <j1 rule="hyper" parents="64 23002 24234"/>
    </justification>
  </clause>

  <clause id="24675">
    <literal><![CDATA[
      K(x,((y \ z) \ u) * w) = K(x,(z \ y) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,22656,a(flip),b,24234,a),flip(a)].">
      <j1 rule="hyper" parents="64 22656 24234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24677">
    <literal><![CDATA[
      ((x * y) / z) * K((x * y) \ z,(z \ x) * y) = 1 / (1 / ((x * y) / z))
    ]]></literal>
    <justification jstring="[para(24234(a,1),4325(a,1,2))].">
      <j1 rule="para" parents="24234 4325"/>
    </justification>
  </clause>

  <clause id="24678">
    <literal><![CDATA[
      L(x,y,y) \ (y * x) = R(T(y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,27,a,b,24375,a),flip(a)].">
      <j1 rule="hyper" parents="373 27 24375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24679">
    <literal><![CDATA[
      (x * y) * L(T(y,x),z,u) = (y * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,24550,a(flip),b,10824,a),flip(a)].">
      <j1 rule="hyper" parents="145 24550 10824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24680">
    <literal><![CDATA[
      K(x,y) * (L(T(y,x),z,u) * w) = L(y,z,u) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,24550,a(flip),b,23225,a),flip(a)].">
      <j1 rule="hyper" parents="144 24550 23225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24681">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,u) = x \ L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,24550,a(flip),b,5810,a),flip(a)].">
      <j1 rule="hyper" parents="139 24550 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24682">
    <literal><![CDATA[
      (x / (x / y)) \ L(y,z,u) = y \ L(T(y,y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(24550(a,1),6560(a,1,2))].">
      <j1 rule="para" parents="24550 6560"/>
    </justification>
  </clause>

  <clause id="24683">
    <literal><![CDATA[
      L(T(x,y),z,u) \ 1 = L(x,z,u) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(24550(a,1),14403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24550 14403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24684">
    <literal><![CDATA[
      L(T(x,y),z,u) \ T(x,y) = L(x,z,u) \ x
    ]]></literal>
    <justification jstring="[para(24550(a,1),14833(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24550 14833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24685">
    <literal><![CDATA[
      K(x,y) * (L(T(y,x),z,u) / w) = L(y,z,u) / w
    ]]></literal>
    <justification jstring="[para(24550(a,1),23224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24550 23224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24686">
    <literal><![CDATA[
      (x / L(y,z,u)) * K(w,y) = x / L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(24550(a,1),23276(a,1,1,2))].">
      <j1 rule="para" parents="24550 23276"/>
    </justification>
  </clause>

  <clause id="24687">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ u)) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(22661,a,24571,a)].">
      <j1 rule="hyper" parents="22661 24571"/>
    </justification>
  </clause>

  <clause id="24688">
    <literal><![CDATA[
      T(x,(y \ a(z,u,w)) \ (y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,23734,a(flip),b,24571,a),flip(a)].">
      <j1 rule="hyper" parents="373 23734 24571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24689">
    <literal><![CDATA[
      (x \ 1) / (a(y,z,u) / x) = (a(y,z,u) / x) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(24688(a,1),8473(a,1,2))].">
      <j1 rule="para" parents="24688 8473"/>
    </justification>
  </clause>

  <clause id="24690">
    <literal><![CDATA[
      T(x,(y * z) * (u \ w)) = T(x,y * (z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22628,a(flip),b,24575,a)].">
      <j1 rule="hyper" parents="64 22628 24575"/>
    </justification>
  </clause>

  <clause id="24692">
    <literal><![CDATA[
      T(x,T(y,z) * (z \ u)) = T(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,22723,a,b,24579,a)].">
      <j1 rule="hyper" parents="64 22723 24579"/>
    </justification>
  </clause>

  <clause id="24693">
    <literal><![CDATA[
      T(x,(R(y,z,u) \ y) * w) = T(x,y * (R(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(1907(a,1),24579(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1907 24579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24694">
    <literal><![CDATA[
      T(x,(x \ y) * z) / (y * z) = x / ((x \ (y * z)) * x)
    ]]></literal>
    <justification jstring="[para(24579(a,1),4715(a,1,1))].">
      <j1 rule="para" parents="24579 4715"/>
    </justification>
  </clause>

  <clause id="24695">
    <literal><![CDATA[
      (x \ ((x * y) * z)) * T(u,(x \ (x * y)) * z) = u * (T(x \ ((y * x) * z),K(x,y)) * K(x,y))
    ]]></literal>
    <justification jstring="[para(24579(a,1),12645(a,1,2))].">
      <j1 rule="para" parents="24579 12645"/>
    </justification>
  </clause>

  <clause id="24696">
    <literal><![CDATA[
      T(x,(y \ x) \ (z \ x)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23615,a(flip),b,24616,a)].">
      <j1 rule="hyper" parents="64 23615 24616"/>
    </justification>
  </clause>

  <clause id="24697">
    <literal><![CDATA[
      T((x * R(y,z,u)) / (x * y),w) = (x * R(y,z,u)) / (x * y)
    ]]></literal>
    <justification jstring="[para(24619(a,1),2877(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="24619 2877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24698">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,u) = (x * u) \ (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(24620(a,1),1326(a,1,1))].">
      <j1 rule="para" parents="24620 1326"/>
    </justification>
  </clause>

  <clause id="24699">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),v5,a(x,y,z)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(24648(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24648 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24700">
    <literal><![CDATA[
      L(x \ R(x,y,z \ 1),x,y * z) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,16031,a,b,24659,a),flip(a)].">
      <j1 rule="hyper" parents="64 16031 24659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24701">
    <literal><![CDATA[
      L(x,y,R(z,u,w) \ z) = L(x,y,z * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(1909(a,1),24659(a,1,3))].">
      <j1 rule="para" parents="1909 24659"/>
    </justification>
  </clause>

  <clause id="24703">
    <literal><![CDATA[
      K(x,(y / z) \ u) = K(x,z * (y \ u))
    ]]></literal>
    <justification jstring="[para(82(a,1),24671(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 24671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24705">
    <literal><![CDATA[
      R(T(x \ 1,y),x \ 1,y) = L(y,x,x) \ ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1151(a,1),24678(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1151 24678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24706">
    <literal><![CDATA[
      T(x,y * ((z * y) \ u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),24687(a,1,2,1))].">
      <j1 rule="para" parents="9 24687"/>
    </justification>
  </clause>

  <clause id="24707">
    <literal><![CDATA[
      T(x,(y / z) \ u) = T(x,z * (y \ u))
    ]]></literal>
    <justification jstring="[para(82(a,1),24687(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 24687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24708">
    <literal><![CDATA[
      ((x \ y) * z) / T(y,x \ z) = y \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(24687(a,1),10154(a,1,2))].">
      <j1 rule="para" parents="24687 10154"/>
    </justification>
  </clause>

  <clause id="24709">
    <literal><![CDATA[
      T(x,x \ (y * (z \ x))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23621,a(flip),b,24696,a)].">
      <j1 rule="hyper" parents="64 23621 24696"/>
    </justification>
  </clause>

  <clause id="24710">
    <literal><![CDATA[
      K(x,y / (z \ u)) = K(x,(u / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,22626,a,b,24703,a)].">
      <j1 rule="hyper" parents="373 22626 24703"/>
    </justification>
  </clause>

  <clause id="24711">
    <literal><![CDATA[
      ((x / y) / z) \ K(z \ (x / y),y * (x \ z)) = 1 / ((x / y) / z)
    ]]></literal>
    <justification jstring="[para(24703(a,1),4323(a,1,2))].">
      <j1 rule="para" parents="24703 4323"/>
    </justification>
  </clause>

  <clause id="24713">
    <literal><![CDATA[
      (x * y) / T(z * x,z \ y) = (z * x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(24706(a,1),10154(a,1,2))].">
      <j1 rule="para" parents="24706 10154"/>
    </justification>
  </clause>

  <clause id="24714">
    <literal><![CDATA[
      T(x,y / (z \ u)) = T(x,(u / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,22628,a,b,24707,a)].">
      <j1 rule="hyper" parents="373 22628 24707"/>
    </justification>
  </clause>

  <clause id="24716">
    <literal><![CDATA[
      T(x,((y / z) \ u) * w) = T(x,z * (y \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,24579,a(flip),b,24707,a)].">
      <j1 rule="hyper" parents="64 24579 24707"/>
    </justification>
  </clause>

  <clause id="24718">
    <literal><![CDATA[
      T(x \ (y / z),z * (y \ x)) = ((x \ (y / z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,3799,a(flip),b,24707,a),flip(a)].">
      <j1 rule="hyper" parents="64 3799 24707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24719">
    <literal><![CDATA[
      T(x / (y / z),z * (y \ x)) = x / (y / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,282,a(flip),b,24707,a),flip(a)].">
      <j1 rule="hyper" parents="64 282 24707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24720">
    <literal><![CDATA[
      ((x / y) \ z) * T(u,y * (x \ z)) = u * ((x / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,24707,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 24707 22"/>
    </justification>
  </clause>

  <clause id="24721">
    <literal><![CDATA[
      (x * (y \ z)) / T(z,x / y) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(225,a,24709,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 24709 116"/>
    </justification>
  </clause>

  <clause id="24722">
    <literal><![CDATA[
      K(x,y / ((z \ u) * w)) = K(x,(u / (y / w)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23387,a(flip),b,24710,a)].">
      <j1 rule="hyper" parents="64 23387 24710"/>
    </justification>
  </clause>

  <clause id="24724">
    <literal><![CDATA[
      K(x,(y / z) \ (y / u)) = K(x,z / u)
    ]]></literal>
    <justification jstring="[para(82(a,1),24710(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 24710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24726">
    <literal><![CDATA[
      T(x,y / ((z \ u) / w)) = T(x,(u / (y * w)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23616,a(flip),b,24714,a)].">
      <j1 rule="hyper" parents="64 23616 24714"/>
    </justification>
  </clause>

  <clause id="24729">
    <literal><![CDATA[
      K(x,(y \ z) / u) = K(x,y \ (z / u))
    ]]></literal>
    <justification jstring="[para(79(a,1),24724(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 24724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24730">
    <literal><![CDATA[
      K(x,T(y,z) \ (z / u)) = K(x,(y \ T(z,y)) / u)
    ]]></literal>
    <justification jstring="[para(4660(a,1),24724(a,1,2,1))].">
      <j1 rule="para" parents="4660 24724"/>
    </justification>
  </clause>

  <clause id="24732">
    <literal><![CDATA[
      K(x,y \ (z / (u \ w))) = K(x,(y \ z) * (w \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22626,a(flip),b,24729,a),flip(a)].">
      <j1 rule="hyper" parents="64 22626 24729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24736">
    <literal><![CDATA[
      L(x * a(y,z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(a(y,z,u) * x,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(5545(a,1),23911(a,1))].">
      <j1 rule="para" parents="5545 23911"/>
    </justification>
  </clause>

  <clause id="24737">
    <literal><![CDATA[
      L(x \ R(x,y,z),u \ (u * x),z * y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,11871,a,b,23986,a)].">
      <j1 rule="hyper" parents="373 11871 23986"/>
    </justification>
  </clause>

  <clause id="24738">
    <literal><![CDATA[
      L(x \ R(x,y,(z * z) * u),x,u * y) = a(x,y,(z * z) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2202,a(flip),b,23986,a)].">
      <j1 rule="hyper" parents="373 2202 23986"/>
    </justification>
  </clause>

  <clause id="24739">
    <literal><![CDATA[
      L(x \ R(x,y,(z * z) \ u),x,u * y) = a(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2188,a(flip),b,23986,a)].">
      <j1 rule="hyper" parents="373 2188 23986"/>
    </justification>
  </clause>

  <clause id="24740">
    <literal><![CDATA[
      L(R(x \ R(x,y,z),u,w),x,z * y) = R(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23986(a,2),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23986 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24741">
    <literal><![CDATA[
      L(L(L(x \ R(x,y,z),u,w),v5,v6),x,z * y) = L(L(a(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(23986(a,2),124(a,2,1,1))].">
      <j1 rule="para" parents="23986 124"/>
    </justification>
  </clause>

  <clause id="24742">
    <literal><![CDATA[
      (T(x,y) \ 1) * (T(x,z) \ 1) = T(x,y) \ (1 / T(x,z))
    ]]></literal>
    <justification jstring="[para(3175(a,1),24163(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3175 24163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24743">
    <literal><![CDATA[
      L(x,y,z * (u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * u) = w
    ]]></literal>
    <justification jstring="[para(23997(a,2),24201(a,1))].">
      <j1 rule="para" parents="23997 24201"/>
    </justification>
  </clause>

  <clause id="24744">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(24157(a,1),24202(a,1))].">
      <j1 rule="para" parents="24157 24202"/>
    </justification>
  </clause>

  <clause id="24745">
    <literal><![CDATA[
      L(x,L(y,z,y),L(u,w,u)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = v5
    ]]></literal>
    <justification jstring="[para(14160(a,2),24744(a,1))].">
      <j1 rule="para" parents="14160 24744"/>
    </justification>
  </clause>

  <clause id="24746">
    <literal><![CDATA[
      (x * (y * z)) * (K(z,u) * w) = (x * (y * T(z,u))) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,23052,a(flip),b,23278,a),flip(a)].">
      <j1 rule="hyper" parents="144 23052 23278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24747">
    <literal><![CDATA[
      (x * (y * T(z,z \ u))) / z = (x * (y * z)) / (u / (u / z))
    ]]></literal>
    <justification jstring="[para(23052(a,1),6894(a,1,1))].">
      <j1 rule="para" parents="23052 6894"/>
    </justification>
  </clause>

  <clause id="24749">
    <literal><![CDATA[
      x * (T(y,x) * K(z,u)) = y * (x * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,23053,a(flip),b,23054,a),flip(a)].">
      <j1 rule="hyper" parents="373 23053 23054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24750">
    <literal><![CDATA[
      T(x * K(y,z \ 1),z) = T(x,z) * K(y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(269,a,9321,a,b,23054,a)].">
      <j1 rule="hyper" parents="269 9321 23054"/>
    </justification>
  </clause>

  <clause id="24751">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,y)) = T(x * K(z,u),y)
    ]]></literal>
    <justification jstring="[hyper(269,a,22802,a(flip),b,23054,a),flip(a)].">
      <j1 rule="hyper" parents="269 22802 23054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24753">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * u) \ u = a(x,y,z) / u
    ]]></literal>
    <justification jstring="[para(23133(a,1),23155(a,1,1,1))].">
      <j1 rule="para" parents="23133 23155"/>
    </justification>
  </clause>

  <clause id="24755">
    <literal><![CDATA[
      x \ ((a(y,z,u) * w) * v5) = x \ ((w * a(y,z,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(139,a,23168,a,b,10,a)].">
      <j1 rule="hyper" parents="139 23168 10"/>
    </justification>
  </clause>

  <clause id="24756">
    <literal><![CDATA[
      ((x * a(y,z,u)) * (w * w)) \ v5 = (w * w) \ ((a(y,z,u) * x) \ v5)
    ]]></literal>
    <justification jstring="[para(23168(a,1),486(a,1,1))].">
      <j1 rule="para" parents="23168 486"/>
    </justification>
  </clause>

  <clause id="24758">
    <literal><![CDATA[
      x \ (y * (a(z,u,w) * v5)) = x \ (y * (v5 * a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(139,a,23169,a,b,10,a)].">
      <j1 rule="hyper" parents="139 23169 10"/>
    </justification>
  </clause>

  <clause id="24759">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) \ v5 = (x * (w * a(y,z,u))) \ v5
    ]]></literal>
    <justification jstring="[hyper(62,a,23169,a)].">
      <j1 rule="hyper" parents="62 23169"/>
    </justification>
  </clause>

  <clause id="24760">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) / a(v5,v6,v7) = a(v5,v6,v7) \ (x * (a(z,u,w) * y))
    ]]></literal>
    <justification jstring="[hyper(142,a,23169,a(flip),b,23135,a)].">
      <j1 rule="hyper" parents="142 23169 23135"/>
    </justification>
  </clause>

  <clause id="24761">
    <literal><![CDATA[
      (x \ (a(y,z,u) * w)) * v5 = (x \ (w * a(y,z,u))) * v5
    ]]></literal>
    <justification jstring="[hyper(144,a,23180,a,b,11,a)].">
      <j1 rule="hyper" parents="144 23180 11"/>
    </justification>
  </clause>

  <clause id="24763">
    <literal><![CDATA[
      (K(x,y) * z) \ (u * z) = T(K(y,x) * u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23199,a,b,23249,a)].">
      <j1 rule="hyper" parents="64 23199 23249"/>
    </justification>
  </clause>

  <clause id="24767">
    <literal><![CDATA[
      (x * y) * (y * K(x,z)) = (T(x,z) * y) * y
    ]]></literal>
    <justification jstring="[para(8047(a,1),23282(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8047 23282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24768">
    <literal><![CDATA[
      x \ (y * (T(z / x,u) \ z)) = T(y * K(u,z / x),x)
    ]]></literal>
    <justification jstring="[para(6229(a,2),23296(a,1,2,2))].">
      <j1 rule="para" parents="6229 23296"/>
    </justification>
  </clause>

  <clause id="24773">
    <literal><![CDATA[
      T(x,y) \ ((T(x,y) * z) * u) = x \ ((x * z) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,23389,a(flip),b,5810,a),flip(a)].">
      <j1 rule="hyper" parents="139 23389 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24774">
    <literal><![CDATA[
      K(x,y) * (((1 / T(y,x)) \ T(y,x)) * z) = (y * ((T(y,x) \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(1134(a,1),23389(a,1,2,1))].">
      <j1 rule="para" parents="1134 23389"/>
    </justification>
  </clause>

  <clause id="24775">
    <literal><![CDATA[
      K(x,y) * (K(T(y,x) \ 1,z) * u) = (y * T(T(y,x) \ 1,z)) * u
    ]]></literal>
    <justification jstring="[para(5743(a,1),23389(a,1,2,1))].">
      <j1 rule="para" parents="5743 23389"/>
    </justification>
  </clause>

  <clause id="24776">
    <literal><![CDATA[
      T((T(x,y) * z) * u,K(x,y)) = ((x * z) * u) * K(x,y)
    ]]></literal>
    <justification jstring="[para(23389(a,1),7808(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23389 7808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24777">
    <literal><![CDATA[
      T(x,y) \ (L(x,z,u) * y) = x \ (y * L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,23391,a(flip),b,5810,a),flip(a)].">
      <j1 rule="hyper" parents="139 23391 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24778">
    <literal><![CDATA[
      (x \ y) * (K(z,T(u,y)) * w) = (x \ (K(z,u) * y)) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,23401,a(flip),b,23278,a),flip(a)].">
      <j1 rule="hyper" parents="144 23401 23278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24779">
    <literal><![CDATA[
      (x \ (y \ z)) * K(u,T(w,z)) = x \ (y \ (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(139,a,23401,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 23401 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24781">
    <literal><![CDATA[
      (x * x) * (y / T(x * y,z)) = R(x,x,y) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(944(a,1),23408(a,1,1)),flip(a)].">
      <j1 rule="para" parents="944 23408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24782">
    <literal><![CDATA[
      T(x,y * ((z / u) * K(u,w))) = T(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(23408(a,1),19538(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23408 19538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24785">
    <literal><![CDATA[
      K(x,y * z) * (y * (z * x)) = L(x,z,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(100(a,1),23431(a,1,2))].">
      <j1 rule="para" parents="100 23431"/>
    </justification>
  </clause>

  <clause id="24786">
    <literal><![CDATA[
      K(x,y) * (z * ((z \ y) * x)) = L(x,z \ y,z) * y
    ]]></literal>
    <justification jstring="[para(515(a,1),23431(a,1,2))].">
      <j1 rule="para" parents="515 23431"/>
    </justification>
  </clause>

  <clause id="24787">
    <literal><![CDATA[
      T((T(x,y) * z) * u,K(x,y)) = (x * z) * (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(269,a,23053,a,b,23444,a)].">
      <j1 rule="hyper" parents="269 23053 23444"/>
    </justification>
  </clause>

  <clause id="24788">
    <literal><![CDATA[
      K(x,y) * ((x * x) * z) = (x * T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(273(a,1),23444(a,2,1))].">
      <j1 rule="para" parents="273 23444"/>
    </justification>
  </clause>

  <clause id="24791">
    <literal><![CDATA[
      (R(x,y,z) * (x \ u)) / R(x,y,z) = u / x
    ]]></literal>
    <justification jstring="[hyper(142,a,6872,a(flip),b,23501,a(flip))].">
      <j1 rule="hyper" parents="142 6872 23501"/>
    </justification>
  </clause>

  <clause id="24793">
    <literal><![CDATA[
      K(x,y) * ((y * z) * (z \ x)) = x * R(y,z,z \ x)
    ]]></literal>
    <justification jstring="[para(421(a,1),23503(a,1,2))].">
      <j1 rule="para" parents="421 23503"/>
    </justification>
  </clause>

  <clause id="24794">
    <literal><![CDATA[
      K(x,y) * ((y * (x / z)) * z) = x * R(y,x / z,z)
    ]]></literal>
    <justification jstring="[para(657(a,1),23503(a,1,2))].">
      <j1 rule="para" parents="657 23503"/>
    </justification>
  </clause>

  <clause id="24795">
    <literal><![CDATA[
      x * (y / (a(z,u,w) * v5)) = x * (y / (v5 * a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(145,a,23554,a,b,9,a)].">
      <j1 rule="hyper" parents="145 23554 9"/>
    </justification>
  </clause>

  <clause id="24796">
    <literal><![CDATA[
      x / (a(y,z,u) * ((w / v5) \ w)) = x / (v5 * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(220(a,2),23554(a,1,2))].">
      <j1 rule="para" parents="220 23554"/>
    </justification>
  </clause>

  <clause id="24797">
    <literal><![CDATA[
      x * ((a(y,z,u) * w) \ v5) = x * ((w * a(y,z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(145,a,23560,a,b,9,a)].">
      <j1 rule="hyper" parents="145 23560 9"/>
    </justification>
  </clause>

  <clause id="24798">
    <literal><![CDATA[
      L(x,y,L(y,z,u)) * (L(y,z,u) \ y) = y * ((L(y,z,u) \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11934,a(flip),b,23581,a),flip(a)].">
      <j1 rule="hyper" parents="64 11934 23581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24799">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) \ w = (u * (L(x,y,z) \ x)) \ w
    ]]></literal>
    <justification jstring="[hyper(62,a,23581,a)].">
      <j1 rule="hyper" parents="62 23581"/>
    </justification>
  </clause>

  <clause id="24800">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,y,z) \ x) = (L(x,y,z) \ x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(35,a,9383,a(flip),b,23581,a)].">
      <j1 rule="hyper" parents="35 9383 23581"/>
    </justification>
  </clause>

  <clause id="24801">
    <literal><![CDATA[
      (x * y) \ ((x * (L(z,u,w) \ z)) * y) = R(T(L(z,u,w) \ z,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(23581(a,1),796(a,1,2,1))].">
      <j1 rule="para" parents="23581 796"/>
    </justification>
  </clause>

  <clause id="24802">
    <literal><![CDATA[
      (1 / x) * (((L(y,z,u) \ y) * x) * w) = x * (((x \ 1) * (L(y,z,u) \ y)) * w)
    ]]></literal>
    <justification jstring="[para(23581(a,2),1603(a,1,2,1))].">
      <j1 rule="para" parents="23581 1603"/>
    </justification>
  </clause>

  <clause id="24803">
    <literal><![CDATA[
      T(((L(x,y,z) \ x) * (u * w)) / ((L(x,y,z) \ x) * u),u) = ((w * u) * (L(x,y,z) \ x)) / ((L(x,y,z) \ x) * u)
    ]]></literal>
    <justification jstring="[para(23581(a,1),2873(a,2,1))].">
      <j1 rule="para" parents="23581 2873"/>
    </justification>
  </clause>

  <clause id="24804">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ 1 = x \ (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(23581(a,1),9397(a,1,1))].">
      <j1 rule="para" parents="23581 9397"/>
    </justification>
  </clause>

  <clause id="24806">
    <literal><![CDATA[
      ((T(x,y * T(T(z,T(u,w)),v5)) * v6) * v7) / ((x * v6) * v7) = K(x,y * T(T(z,v5),u))
    ]]></literal>
    <justification jstring="[hyper(373,a,18054,a(flip),b,23656,a),flip(a)].">
      <j1 rule="hyper" parents="373 18054 23656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24807">
    <literal><![CDATA[
      (R(x,y,z) * u) / R(x,y,z) = (x * u) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,5721,a,b,23658,a),flip(a)].">
      <j1 rule="hyper" parents="373 5721 23658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24808">
    <literal><![CDATA[
      T(R(x \ 1,x,y),R(x \ 1,x,y) * y) = ((x \ y) * K(x \ 1,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(23658(a,1),4513(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23658 4513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24809">
    <literal><![CDATA[
      T((x * y) * z,K(x,y * z)) = T((x * y) * z,(y * z) * x)
    ]]></literal>
    <justification jstring="[para(23703(a,1),11151(a,1,1))].">
      <j1 rule="para" parents="23703 11151"/>
    </justification>
  </clause>

  <clause id="24810">
    <literal><![CDATA[
      1 / (x \ R(x,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,5382,a(flip),b,23705,a),flip(a)].">
      <j1 rule="hyper" parents="373 5382 23705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24812">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x * u) = x * (u / (x \ R(x,y,z)))
    ]]></literal>
    <justification jstring="[para(23705(a,2),2795(a,2,2))].">
      <j1 rule="para" parents="23705 2795"/>
    </justification>
  </clause>

  <clause id="24813">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(215,a,24810,a)].">
      <j1 rule="hyper" parents="215 24810"/>
    </justification>
  </clause>

  <clause id="24814">
    <literal><![CDATA[
      x \ R(x,x \ y,y \ x) = ((x \ y) * (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(974(a,1),24813(a,1,1)),flip(a)].">
      <j1 rule="para" parents="974 24813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24815">
    <literal><![CDATA[
      (x / (1 / y)) \ R(x / (1 / y),y,y) = ((x * y) \ (x / (1 / y))) \ 1
    ]]></literal>
    <justification jstring="[para(1407(a,1),24813(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1407 24813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24816">
    <literal><![CDATA[
      (x \ R(x,y,z)) * ((u * u) \ x) = (u * u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,802,a(flip),b,23708,a),flip(a)].">
      <j1 rule="hyper" parents="373 802 23708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24817">
    <literal><![CDATA[
      T(((a(x,y,z) \ 1) * (u * w)) / ((a(x,y,z) \ 1) * u),u) = ((w * u) * (a(x,y,z) \ 1)) / ((a(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(23736(a,1),2873(a,2,1))].">
      <j1 rule="para" parents="23736 2873"/>
    </justification>
  </clause>

  <clause id="24818">
    <literal><![CDATA[
      (x \ L(x,y,y)) * z = z * (a(y,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(5665(a,1),23736(a,1,1))].">
      <j1 rule="para" parents="5665 23736"/>
    </justification>
  </clause>

  <clause id="24820">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) / L(x,y,z) = R(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(142,a,23742,a,b,421,a)].">
      <j1 rule="hyper" parents="142 23742 421"/>
    </justification>
  </clause>

  <clause id="24822">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((y \ L(y,z,u)) * (x * y)) = a(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,23742,a,b,957,a)].">
      <j1 rule="hyper" parents="139 23742 957"/>
    </justification>
  </clause>

  <clause id="24823">
    <literal><![CDATA[
      L(x,y,z) * L(u,x,x \ L(x,y,z)) = (x * u) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5576,a,b,23742,a)].">
      <j1 rule="hyper" parents="64 5576 23742"/>
    </justification>
  </clause>

  <clause id="24824">
    <literal><![CDATA[
      T(((x \ L(x,y,z)) * (u * w)) / ((x \ L(x,y,z)) * u),u) = ((w * u) * (x \ L(x,y,z))) / ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(23742(a,1),2873(a,2,1))].">
      <j1 rule="para" parents="23742 2873"/>
    </justification>
  </clause>

  <clause id="24825">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ (u * L(x,y,z)) = L(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(23742(a,2),5579(a,1,1))].">
      <j1 rule="para" parents="23742 5579"/>
    </justification>
  </clause>

  <clause id="24826">
    <literal><![CDATA[
      L(x,y,y) \ (z * (x \ L(x,y,y))) = L(x \ z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(23742(a,1),9389(a,1,2))].">
      <j1 rule="para" parents="23742 9389"/>
    </justification>
  </clause>

  <clause id="24827">
    <literal><![CDATA[
      (a(x,y,z) \ u) / u = (a(x,y,z) * u) \ u
    ]]></literal>
    <justification jstring="[hyper(36,a,23164,a,b,23762,a)].">
      <j1 rule="hyper" parents="36 23164 23762"/>
    </justification>
  </clause>

  <clause id="24828">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ x)) * (a(y,z,u) * x) = x
    ]]></literal>
    <justification jstring="[para(23767(a,1),23164(a,1,1))].">
      <j1 rule="para" parents="23767 23164"/>
    </justification>
  </clause>

  <clause id="24829">
    <literal><![CDATA[
      T((x * a(y,z,u)) * (w * x),K(x,w)) = (x * a(y,z,u)) * (w * x)
    ]]></literal>
    <justification jstring="[para(23790(a,1),11258(a,2,1))].">
      <j1 rule="para" parents="23790 11258"/>
    </justification>
  </clause>

  <clause id="24831">
    <literal><![CDATA[
      T(x * K(R(x,y,z) * u,x),u) = R(x,u,R(T(x,w),y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,9693,a,b,23812,a)].">
      <j1 rule="hyper" parents="373 9693 23812"/>
    </justification>
  </clause>

  <clause id="24833">
    <literal><![CDATA[
      (x * a(y,z,u)) \ a(y,z,u) = a(y,z,u) \ (x \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(710,a,23837,a),flip(a)].">
      <j1 rule="hyper" parents="710 23837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24835">
    <literal><![CDATA[
      L(x,y,z * (u * z)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,2189,a(flip),b,23843,a)].">
      <j1 rule="hyper" parents="64 2189 23843"/>
    </justification>
  </clause>

  <clause id="24836">
    <literal><![CDATA[
      L(x,y,L(L(T(z,u),w,v5),v6,v7)) = L(x,y,L(L(z,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(25(a,2),23843(a,1,3,1))].">
      <j1 rule="para" parents="25 23843"/>
    </justification>
  </clause>

  <clause id="24837">
    <literal><![CDATA[
      L(x,y,L(((1 / z) \ u) * K(w,z),v5,v6)) = L(x,y,L((z * z) * (u / T(z,w)),v5,v6))
    ]]></literal>
    <justification jstring="[para(7295(a,1),23843(a,1,3,1))].">
      <j1 rule="para" parents="7295 23843"/>
    </justification>
  </clause>

  <clause id="24838">
    <literal><![CDATA[
      L(x,y,(z * u) * u) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(24201,a,24835,a)].">
      <j1 rule="hyper" parents="24201 24835"/>
    </justification>
  </clause>

  <clause id="24840">
    <literal><![CDATA[
      ((1 / x) \ y) \ (((1 / x) \ y) / (1 / y)) = L(y,y,R(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,11082,a(flip),b,23844,a)].">
      <j1 rule="hyper" parents="64 11082 23844"/>
    </justification>
  </clause>

  <clause id="24841">
    <literal><![CDATA[
      L(x,y,R(z,z,z * u)) = L(x,y,R(z,z,u))
    ]]></literal>
    <justification jstring="[para(11443(a,1),23844(a,1,3))].">
      <j1 rule="para" parents="11443 23844"/>
    </justification>
  </clause>

  <clause id="24842">
    <literal><![CDATA[
      L(x,y,z) * (u * x) = x * (u * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,23886,a(flip),b,2329,a)].">
      <j1 rule="hyper" parents="145 23886 2329"/>
    </justification>
  </clause>

  <clause id="24843">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3190,a,b,23887,a)].">
      <j1 rule="hyper" parents="64 3190 23887"/>
    </justification>
  </clause>

  <clause id="24844">
    <literal><![CDATA[
      (x * x) * ((1 / L(y,z,u)) * y) = y * (L(y,z,u) \ (x * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,556,a,b,23887,a)].">
      <j1 rule="hyper" parents="64 556 23887"/>
    </justification>
  </clause>

  <clause id="24845">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * L(x,y,z) = u * x
    ]]></literal>
    <justification jstring="[hyper(144,a,23887,a(flip),b,3190,a)].">
      <j1 rule="hyper" parents="144 23887 3190"/>
    </justification>
  </clause>

  <clause id="24846">
    <literal><![CDATA[
      x * (L(x,y,y * x) \ 1) = ((1 / (y * x)) * y) * x
    ]]></literal>
    <justification jstring="[para(920(a,1),23887(a,1,1)),flip(a)].">
      <j1 rule="para" parents="920 23887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24847">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ (u * x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(23887(a,1),3191(a,1,1))].">
      <j1 rule="para" parents="23887 3191"/>
    </justification>
  </clause>

  <clause id="24849">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u / L(x,y,z))) = u / x
    ]]></literal>
    <justification jstring="[hyper(373,a,3197,a(flip),b,23898,a),flip(a)].">
      <j1 rule="hyper" parents="373 3197 23898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24850">
    <literal><![CDATA[
      L(x * x,y,z) * ((x * x) \ u) = u * ((x * x) \ L(x * x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,897,a(flip),b,23898,a),flip(a)].">
      <j1 rule="hyper" parents="373 897 23898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24852">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = (u / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2325,a,b,23898,a)].">
      <j1 rule="hyper" parents="64 2325 23898"/>
    </justification>
  </clause>

  <clause id="24853">
    <literal><![CDATA[
      ((L(x,y,z) \ u) / x) * L(x,y,z) = x \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,2326,a(flip),b,23898,a),flip(a)].">
      <j1 rule="hyper" parents="64 2326 23898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24854">
    <literal><![CDATA[
      x * ((y / x) * L(x,z,u)) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,23898,a(flip),b,2325,a)].">
      <j1 rule="hyper" parents="145 23898 2325"/>
    </justification>
  </clause>

  <clause id="24855">
    <literal><![CDATA[
      L(x,y,R(z,z,u)) = L(x,y,(z * u) \ u)
    ]]></literal>
    <justification jstring="[para(944(a,1),23973(a,1,3))].">
      <j1 rule="para" parents="944 23973"/>
    </justification>
  </clause>

  <clause id="24856">
    <literal><![CDATA[
      L(x,y,z * ((u * u) * w)) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,23998,a),flip(a)].">
      <j1 rule="hyper" parents="373 23253 23998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24857">
    <literal><![CDATA[
      L(x,y,((z * u) * u) * w) = L(x,y,w * R(z,u,u))
    ]]></literal>
    <justification jstring="[para(662(a,1),23998(a,1,3))].">
      <j1 rule="para" parents="662 23998"/>
    </justification>
  </clause>

  <clause id="24858">
    <literal><![CDATA[
      (x * x) \ (K(y,x) * z) = (x * T(x,y)) \ z
    ]]></literal>
    <justification jstring="[para(273(a,1),24191(a,2,1))].">
      <j1 rule="para" parents="273 24191"/>
    </justification>
  </clause>

  <clause id="24859">
    <literal><![CDATA[
      (T(x,y) * z) \ ((x * y) / x) = (x * z) \ y
    ]]></literal>
    <justification jstring="[para(5807(a,1),24191(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5807 24191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24860">
    <literal><![CDATA[
      (T(x,y) * z) \ ((T(x,y) * u) * w) = (x * z) \ ((x * u) * w)
    ]]></literal>
    <justification jstring="[para(23389(a,1),24191(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23389 24191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24861">
    <literal><![CDATA[
      K(x,y * (z \ (y \ u))) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,24703,a(flip),b,24212,a)].">
      <j1 rule="hyper" parents="64 24703 24212"/>
    </justification>
  </clause>

  <clause id="24862">
    <literal><![CDATA[
      K(T(x,y) \ (y \ z),u) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23046,a(flip),b,24254,a),flip(a)].">
      <j1 rule="hyper" parents="373 23046 24254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24863">
    <literal><![CDATA[
      (T(T(x,y),z) * y) * x = (T(x,y) * y) * T(x,z)
    ]]></literal>
    <justification jstring="[para(8239(a,1),24262(a,1,1))].">
      <j1 rule="para" parents="8239 24262"/>
    </justification>
  </clause>

  <clause id="24870">
    <literal><![CDATA[
      (x * (y \ T(z,u))) / T(z,u) = (x * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(15021(a,1),24263(a,1,1,2))].">
      <j1 rule="para" parents="15021 24263"/>
    </justification>
  </clause>

  <clause id="24871">
    <literal><![CDATA[
      R(x / (y * K(z,u)),y,T(z,u)) = (x * z) / (y * T(z,u))
    ]]></literal>
    <justification jstring="[para(24268(a,1),351(a,1,1))].">
      <j1 rule="para" parents="24268 351"/>
    </justification>
  </clause>

  <clause id="24873">
    <literal><![CDATA[
      (x * T(y,z)) / (u * T(y,z)) = (x * y) / (u * y)
    ]]></literal>
    <justification jstring="[para(6249(a,1),24271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6249 24271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24874">
    <literal><![CDATA[
      (x * T(y,z)) / (u * (y * z)) = (x * y) / (u * (z * y))
    ]]></literal>
    <justification jstring="[para(10181(a,1),24271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10181 24271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24875">
    <literal><![CDATA[
      (x \ y) / T(y,z \ (z \ 1)) = (x \ T(y,z * z)) / y
    ]]></literal>
    <justification jstring="[para(15870(a,2),24273(a,1,2))].">
      <j1 rule="para" parents="15870 24273"/>
    </justification>
  </clause>

  <clause id="24876">
    <literal><![CDATA[
      (1 / (1 / x)) / ((x \ y) / y) = x / (1 / (1 / ((x \ y) / y)))
    ]]></literal>
    <justification jstring="[para(7301(a,1),24275(a,2,2))].">
      <j1 rule="para" parents="7301 24275"/>
    </justification>
  </clause>

  <clause id="24877">
    <literal><![CDATA[
      x / (y * K(z,T(u,x))) = K(u,z) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(225,a,24276,a(flip),b,23199,a)].">
      <j1 rule="hyper" parents="225 24276 23199"/>
    </justification>
  </clause>

  <clause id="24878">
    <literal><![CDATA[
      K(x,x \ 1) / (x * y) = 1 / (T(x,x * x) * y)
    ]]></literal>
    <justification jstring="[para(17441(a,1),24279(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17441 24279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24879">
    <literal><![CDATA[
      K(x,y) * (z * (u \ K(y,x))) = T(z * (u \ 1),K(y,x))
    ]]></literal>
    <justification jstring="[hyper(269,a,24286,a,b,6161,a),flip(a)].">
      <j1 rule="hyper" parents="269 24286 6161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24880">
    <literal><![CDATA[
      T(T(T(x,y \ 1) * (y \ 1),z),K(T(x,y \ 1),y)) = T(x,y \ 1) * (y \ K(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16989,a,b,24286,a)].">
      <j1 rule="hyper" parents="64 16989 24286"/>
    </justification>
  </clause>

  <clause id="24881">
    <literal><![CDATA[
      R(x / y,y,x \ 1) \ K(z,u) = y * (x \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,14513,a,b,24286,a)].">
      <j1 rule="hyper" parents="64 14513 24286"/>
    </justification>
  </clause>

  <clause id="24882">
    <literal><![CDATA[
      x * (y \ K(x / y,z)) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14682,a(flip),b,24286,a),flip(a)].">
      <j1 rule="hyper" parents="64 14682 24286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24883">
    <literal><![CDATA[
      (x * (y \ 1)) * (K(z,u) * w) = (x * (y \ K(z,u))) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,24286,a(flip),b,23278,a),flip(a)].">
      <j1 rule="hyper" parents="144 24286 23278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24884">
    <literal><![CDATA[
      x \ T(x * (y \ 1),z) = y \ K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,14682,a(flip),b,24286,a(flip))].">
      <j1 rule="hyper" parents="139 14682 24286"/>
    </justification>
  </clause>

  <clause id="24885">
    <literal><![CDATA[
      (x \ (y * (z \ 1))) * K(u,w) = x \ (y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(139,a,24286,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 24286 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24886">
    <literal><![CDATA[
      K(x,y) * ((z * (u \ 1)) \ w) = (z * (u \ K(y,x))) \ w
    ]]></literal>
    <justification jstring="[para(24286(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24286 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24890">
    <literal><![CDATA[
      R((x * x) \ (x \ K(x,y)),x,y) = ((x \ (1 / x)) * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(24310(a,1),10312(a,1,1))].">
      <j1 rule="para" parents="24310 10312"/>
    </justification>
  </clause>

  <clause id="24892">
    <literal><![CDATA[
      (x \ (y * z)) * (K(z,u) * w) = (x \ (y * T(z,u))) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,24315,a(flip),b,23278,a),flip(a)].">
      <j1 rule="hyper" parents="144 24315 23278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24893">
    <literal><![CDATA[
      (x \ (y \ (z * u))) * K(u,w) = x \ (y \ (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(139,a,24315,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 24315 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24894">
    <literal><![CDATA[
      K(x,y) * ((z \ (u / x)) \ w) = (z \ (u / T(x,y))) \ w
    ]]></literal>
    <justification jstring="[para(24316(a,1),23280(a,1,2,1))].">
      <j1 rule="para" parents="24316 23280"/>
    </justification>
  </clause>

  <clause id="24895">
    <literal><![CDATA[
      (x / y) \ ((y \ K(y,y \ x)) * z) = (y \ x) \ ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,24345,a(flip),b,6062,a)].">
      <j1 rule="hyper" parents="139 24345 6062"/>
    </justification>
  </clause>

  <clause id="24896">
    <literal><![CDATA[
      K(x,x \ y) * (x \ (y * z)) = x \ ((x * (y / x)) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,24346,a(flip),b,6133,a),flip(a)].">
      <j1 rule="hyper" parents="139 24346 6133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24898">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ z) * u) = x * ((x \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,24347,a(flip),b,6071,a),flip(a)].">
      <j1 rule="hyper" parents="145 24347 6071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24899">
    <literal><![CDATA[
      T(x,y) \ ((x \ z) * u) = x \ ((T(x,y) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,24347,a(flip),b,5778,a)].">
      <j1 rule="hyper" parents="139 24347 5778"/>
    </justification>
  </clause>

  <clause id="24900">
    <literal><![CDATA[
      K(x,y) * (K(T(x,y),z) * u) = (x \ T(T(x,y),z)) * u
    ]]></literal>
    <justification jstring="[para(5726(a,2),24347(a,1,2,1))].">
      <j1 rule="para" parents="5726 24347"/>
    </justification>
  </clause>

  <clause id="24901">
    <literal><![CDATA[
      K(x,y) * ((x \ (x / z)) * u) = (x \ (T(x,y) / z)) * u
    ]]></literal>
    <justification jstring="[para(14846(a,1),24347(a,1,2,1))].">
      <j1 rule="para" parents="14846 24347"/>
    </justification>
  </clause>

  <clause id="24902">
    <literal><![CDATA[
      ((x \ y) * z) \ (K(x,u) * w) = ((T(x,u) \ y) * z) \ w
    ]]></literal>
    <justification jstring="[para(24347(a,1),23222(a,1,1))].">
      <j1 rule="para" parents="24347 23222"/>
    </justification>
  </clause>

  <clause id="24903">
    <literal><![CDATA[
      K(x,y) * (((y \ z) * u) * w) = ((T(y,x) \ z) * u) * w
    ]]></literal>
    <justification jstring="[para(24347(a,1),23246(a,1,2,1))].">
      <j1 rule="para" parents="24347 23246"/>
    </justification>
  </clause>

  <clause id="24905">
    <literal><![CDATA[
      K(x,y) * ((y \ 1) * (y \ z)) = (y \ 1) * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,12414,a(flip),b,24348,a),flip(a)].">
      <j1 rule="hyper" parents="373 12414 24348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24906">
    <literal><![CDATA[
      (K(x,x \ y) / (x / y)) * x = (1 / (x / y)) * T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,9419,a(flip),b,24361,a),flip(a)].">
      <j1 rule="hyper" parents="64 9419 24361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24907">
    <literal><![CDATA[
      (K(x,y) / z) * (z * u) = K(x,y) * L(u,z,z)
    ]]></literal>
    <justification jstring="[para(559(a,1),24361(a,1,2)),flip(a)].">
      <j1 rule="para" parents="559 24361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24908">
    <literal><![CDATA[
      K(x,y) * (((1 / z) * u) / w) = ((K(x,y) / z) * u) / w
    ]]></literal>
    <justification jstring="[para(24361(a,1),23224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24361 23224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24910">
    <literal><![CDATA[
      (T(x,y) / (x / (z \ 1))) * z = K(x,y) * K(z \ x,z \ 1)
    ]]></literal>
    <justification jstring="[para(15278(a,1),24364(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15278 24364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24911">
    <literal><![CDATA[
      L(x,y,z) * (x \ (y * z)) = (z * (T(y,z) * x)) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,10989,a(flip),b,24376,a),flip(a)].">
      <j1 rule="hyper" parents="142 10989 24376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24912">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(x,u,w)) = L(x,u,w) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,12218,a,b,24376,a)].">
      <j1 rule="hyper" parents="36 12218 24376"/>
    </justification>
  </clause>

  <clause id="24913">
    <literal><![CDATA[
      (L(x,y,z) * u) * x = (x * u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),24376(a,1,1,2))].">
      <j1 rule="para" parents="9 24376"/>
    </justification>
  </clause>

  <clause id="24914">
    <literal><![CDATA[
      (L(x,y,z) \ u) * L(x,y,z) = (x \ u) * x
    ]]></literal>
    <justification jstring="[para(2326(a,1),24376(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2326 24376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24915">
    <literal><![CDATA[
      ((x \ 1) * (L(x,y,z) * u)) * x = L(u * L(x,y,z),x,x)
    ]]></literal>
    <justification jstring="[para(24377(a,1),3442(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24377 3442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24916">
    <literal><![CDATA[
      (x * (x * (L(x,y,z) \ u))) / x = (x * u) / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,2328,a(flip),b,24379,a),flip(a)].">
      <j1 rule="hyper" parents="142 2328 24379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24917">
    <literal><![CDATA[
      (x / (x * x)) * L(x,y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(813(a,1),24379(a,1,1))].">
      <j1 rule="para" parents="813 24379"/>
    </justification>
  </clause>

  <clause id="24918">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) = (x * u) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(24379(a,1),11086(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24379 11086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24919">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u / x)) = u / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,3201,a,b,24384,a),flip(a)].">
      <j1 rule="hyper" parents="38 3201 24384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24920">
    <literal><![CDATA[
      (K(x,y) * z) \ (u * z) = K(y,T(x,z)) * T(u,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),24391(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22 24391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24921">
    <literal><![CDATA[
      (x \ K(x,x \ y)) \ (y * z) = (x \ 1) \ (((x \ y) * x) * z)
    ]]></literal>
    <justification jstring="[para(10858(a,1),24395(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10858 24395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24922">
    <literal><![CDATA[
      (T(x,y) / z) \ (T(x,y) * u) = (x / z) \ (x * u)
    ]]></literal>
    <justification jstring="[para(14842(a,1),24396(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14842 24396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24923">
    <literal><![CDATA[
      (T(x,y) \ z) \ (K(y,x) * (((x \ z) * x) * u)) = (z / x) \ (z * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,10971,a(flip),b,24397,a),flip(a)].">
      <j1 rule="hyper" parents="373 10971 24397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24924">
    <literal><![CDATA[
      (T(x * y,z) \ u) \ (y \ K(z,y * x)) = ((x * y) \ u) \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(14666(a,1),24397(a,1,2))].">
      <j1 rule="para" parents="14666 24397"/>
    </justification>
  </clause>

  <clause id="24925">
    <literal><![CDATA[
      (x * (y / x)) \ (y / x) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(5720(a,1),24399(a,1,2))].">
      <j1 rule="para" parents="5720 24399"/>
    </justification>
  </clause>

  <clause id="24926">
    <literal><![CDATA[
      (x * (y / x)) \ ((y / x) * z) = y \ ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(5982(a,1),24399(a,1,2))].">
      <j1 rule="para" parents="5982 24399"/>
    </justification>
  </clause>

  <clause id="24927">
    <literal><![CDATA[
      T(x,x \ y) * (y \ (x \ y)) = x * (y \ (y / x))
    ]]></literal>
    <justification jstring="[para(24925(a,1),11894(a,1,2))].">
      <j1 rule="para" parents="24925 11894"/>
    </justification>
  </clause>

  <clause id="24928">
    <literal><![CDATA[
      (T(x \ (y \ x),y * (x / y)) \ z) * T((y * (x / y)) \ (x / y),y * (x / y)) = (R(1 / y,y,y \ x) \ z) * ((x / y) / (y * (x / y)))
    ]]></literal>
    <justification jstring="[para(24925(a,1),16184(a,1,1,1,1))].">
      <j1 rule="para" parents="24925 16184"/>
    </justification>
  </clause>

  <clause id="24929">
    <literal><![CDATA[
      K(x,T(y,z)) * ((1 / z) \ u) = (K(y,x) / z) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,22773,a,b,24406,a)].">
      <j1 rule="hyper" parents="64 22773 24406"/>
    </justification>
  </clause>

  <clause id="24930">
    <literal><![CDATA[
      (x * x) * (K(y,z) * u) = x * ((K(z,y) / x) \ u)
    ]]></literal>
    <justification jstring="[hyper(145,a,24406,a(flip),b,539,a),flip(a)].">
      <j1 rule="hyper" parents="145 24406 539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24931">
    <literal><![CDATA[
      (1 / x) \ (y * K(z,y * u)) = (K(u * y,z) / x) \ y
    ]]></literal>
    <justification jstring="[para(11119(a,1),24406(a,1,2))].">
      <j1 rule="para" parents="11119 24406"/>
    </justification>
  </clause>

  <clause id="24933">
    <literal><![CDATA[
      K(x,y) * ((y * (x * z)) / u) = (y * (T(x,y) * z)) / u
    ]]></literal>
    <justification jstring="[para(5017(a,1),24427(a,1,2,1))].">
      <j1 rule="para" parents="5017 24427"/>
    </justification>
  </clause>

  <clause id="24935">
    <literal><![CDATA[
      (x * (y / x)) \ (y \ z) = y \ ((x * (y / x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,11892,a(flip),b,24439,a),flip(a)].">
      <j1 rule="hyper" parents="139 11892 24439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24936">
    <literal><![CDATA[
      (x * ((x \ y) / x)) \ y = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,17528,a(flip),b,24439,a),flip(a)].">
      <j1 rule="hyper" parents="35 17528 24439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24937">
    <literal><![CDATA[
      ((x \ y) / x) * K(x * ((x \ y) / x),((x \ y) / x) \ (x \ y)) = x \ (L(x,y,x) \ y)
    ]]></literal>
    <justification jstring="[para(24936(a,1),14973(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="24936 14973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24938">
    <literal><![CDATA[
      x / (a(y,z,u) * K(w,v5)) = (a(y,z,u) \ x) * K(v5,w)
    ]]></literal>
    <justification jstring="[hyper(23173,a,24442,a)].">
      <j1 rule="hyper" parents="23173 24442"/>
    </justification>
  </clause>

  <clause id="24939">
    <literal><![CDATA[
      T(x / (y * (z / y)),z) = (z \ x) * K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5963(a,1),24442(a,1,1,2))].">
      <j1 rule="para" parents="5963 24442"/>
    </justification>
  </clause>

  <clause id="24940">
    <literal><![CDATA[
      T(x / (y \ K(z,u)),y \ 1) = ((y \ 1) \ x) * K(u,z)
    ]]></literal>
    <justification jstring="[para(14444(a,1),24442(a,1,1,2))].">
      <j1 rule="para" parents="14444 24442"/>
    </justification>
  </clause>

  <clause id="24941">
    <literal><![CDATA[
      R(x,y,(z * K(u,w)) \ v5) = R(x,y,(z \ v5) * K(w,u))
    ]]></literal>
    <justification jstring="[para(24442(a,1),24131(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24442 24131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24942">
    <literal><![CDATA[
      (x \ K(y,z)) * (y * u) = (x \ 1) * (T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(14444(a,1),24461(a,1,1))].">
      <j1 rule="para" parents="14444 24461"/>
    </justification>
  </clause>

  <clause id="24943">
    <literal><![CDATA[
      (x / (y / z)) * (z * (y / z)) = (x / (z \ y)) * y
    ]]></literal>
    <justification jstring="[para(6455(a,1),24462(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6455 24462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24944">
    <literal><![CDATA[
      (x * (y \ z)) * (y * (z / y)) = (x * (z / y)) * z
    ]]></literal>
    <justification jstring="[para(6471(a,1),24462(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6471 24462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24945">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * (y \ w)) = K(z,u) * (T(y,x) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,20728,a(flip),b,24464,a)].">
      <j1 rule="hyper" parents="64 20728 24464"/>
    </justification>
  </clause>

  <clause id="24946">
    <literal><![CDATA[
      (x * T(y,z)) * (T(y,z) \ u) = (x * y) * (y \ u)
    ]]></literal>
    <justification jstring="[para(6249(a,1),24464(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6249 24464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24947">
    <literal><![CDATA[
      R(T(x,y),z,u) * (T(x,y) \ w) = R(x,z,u) * (x \ w)
    ]]></literal>
    <justification jstring="[para(23499(a,1),24464(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23499 24464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24948">
    <literal><![CDATA[
      (x / T(y,z)) * (T(y,z) / u) = (x / y) * (y / u)
    ]]></literal>
    <justification jstring="[para(14842(a,1),24465(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14842 24465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24949">
    <literal><![CDATA[
      (x / T(y,z)) * L(T(y,z),u,w) = (x / y) * L(y,u,w)
    ]]></literal>
    <justification jstring="[para(24550(a,1),24465(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24550 24465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24950">
    <literal><![CDATA[
      (x * (y / z)) * (K(z \ y,u) * w) = (x * T(y / z,T(u,z))) * w
    ]]></literal>
    <justification jstring="[para(7917(a,1),24468(a,1,2,1))].">
      <j1 rule="para" parents="7917 24468"/>
    </justification>
  </clause>

  <clause id="24951">
    <literal><![CDATA[
      (x * (y / z)) * T(z \ y,T(u,z)) = (x * T(y / z,u)) * (z \ y)
    ]]></literal>
    <justification jstring="[para(8283(a,1),24468(a,1,2))].">
      <j1 rule="para" parents="8283 24468"/>
    </justification>
  </clause>

  <clause id="24952">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * y) * w)) = T(x,(u * T(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(24468(a,1),19545(a,2,2))].">
      <j1 rule="para" parents="24468 19545"/>
    </justification>
  </clause>

  <clause id="24953">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y * x) \ (y * z)) = (y \ K(x,y \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,11326,a,b,24472,a)].">
      <j1 rule="hyper" parents="64 11326 24472"/>
    </justification>
  </clause>

  <clause id="24954">
    <literal><![CDATA[
      x * ((x \ K(y,z)) * u) = L(K(y,z) * u,x,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,24472,a(flip),b,1148,a)].">
      <j1 rule="hyper" parents="145 24472 1148"/>
    </justification>
  </clause>

  <clause id="24955">
    <literal><![CDATA[
      x * (K(y,z) * K(x,x \ 1)) = (x \ 1) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,3648,a,b,24472,a(flip))].">
      <j1 rule="hyper" parents="36 3648 24472"/>
    </justification>
  </clause>

  <clause id="24956">
    <literal><![CDATA[
      ((x \ y) \ 1) * (K(x \ y,x) * z) = ((y / x) \ 1) * z
    ]]></literal>
    <justification jstring="[para(6256(a,1),24472(a,2,1))].">
      <j1 rule="para" parents="6256 24472"/>
    </justification>
  </clause>

  <clause id="24957">
    <literal><![CDATA[
      (x \ T(y,z)) * T(y,z) = (x \ y) * T(T(y,z),z)
    ]]></literal>
    <justification jstring="[para(6114(a,1),24474(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6114 24474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24959">
    <literal><![CDATA[
      (x / (T(y,z) * u)) * T(y,z) = (x / (y * u)) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,24486,a(flip),b,6243,a)].">
      <j1 rule="hyper" parents="144 24486 6243"/>
    </justification>
  </clause>

  <clause id="24960">
    <literal><![CDATA[
      K(x \ 1,x) * (y * (z / (x * u))) = y * (z / (T(x,x \ 1) * u))
    ]]></literal>
    <justification jstring="[para(24486(a,1),5176(a,2,2))].">
      <j1 rule="para" parents="24486 5176"/>
    </justification>
  </clause>

  <clause id="24961">
    <literal><![CDATA[
      x * ((x \ K(y,z)) * x) = K(y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4804,a(flip),b,24497,a)].">
      <j1 rule="hyper" parents="64 4804 24497"/>
    </justification>
  </clause>

  <clause id="24962">
    <literal><![CDATA[
      K(x,y) * ((z / (1 / u)) \ w) = (z / (K(x,y) / u)) \ w
    ]]></literal>
    <justification jstring="[para(24497(a,1),23280(a,1,2,1))].">
      <j1 rule="para" parents="24497 23280"/>
    </justification>
  </clause>

  <clause id="24963">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) * w) = (x / (K(u,z) / y)) * w
    ]]></literal>
    <justification jstring="[para(24497(a,1),23281(a,1,1))].">
      <j1 rule="para" parents="24497 23281"/>
    </justification>
  </clause>

  <clause id="24964">
    <literal><![CDATA[
      (x / (T(y,z) / u)) * T(y,z) = (x / (y / u)) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,24498,a(flip),b,6847,a),flip(a)].">
      <j1 rule="hyper" parents="144 24498 6847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24965">
    <literal><![CDATA[
      K(x,T(y,z)) * ((u * y) \ w) = (u * T(y,T(x,z))) \ w
    ]]></literal>
    <justification jstring="[hyper(145,a,24506,a(flip),b,7914,a)].">
      <j1 rule="hyper" parents="145 24506 7914"/>
    </justification>
  </clause>

  <clause id="24966">
    <literal><![CDATA[
      T(x,y) * ((z * T(x,y)) \ u) = x * ((z * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(145,a,24506,a(flip),b,6071,a),flip(a)].">
      <j1 rule="hyper" parents="145 24506 6071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24967">
    <literal><![CDATA[
      ((x * y) \ z) \ (K(y,u) * w) = ((x * T(y,u)) \ z) \ w
    ]]></literal>
    <justification jstring="[para(24506(a,1),23222(a,1,1))].">
      <j1 rule="para" parents="24506 23222"/>
    </justification>
  </clause>

  <clause id="24968">
    <literal><![CDATA[
      K(x,y) * (((z * y) \ u) * w) = ((z * T(y,x)) \ u) * w
    ]]></literal>
    <justification jstring="[para(24506(a,1),23246(a,1,2,1))].">
      <j1 rule="para" parents="24506 23246"/>
    </justification>
  </clause>

  <clause id="24969">
    <literal><![CDATA[
      K(x,y) * (((z \ 1) \ u) * w) = ((z \ K(y,x)) \ u) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,24516,a(flip),b,23225,a),flip(a)].">
      <j1 rule="hyper" parents="144 24516 23225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24970">
    <literal><![CDATA[
      K(x,y) * (x \ ((z \ 1) \ u)) = x \ ((z \ K(y,x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,24516,a(flip),b,6133,a),flip(a)].">
      <j1 rule="hyper" parents="139 24516 6133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24971">
    <literal><![CDATA[
      T(x,y) \ ((z \ K(y,x)) \ u) = x \ ((z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,24516,a(flip),b,5778,a)].">
      <j1 rule="hyper" parents="139 24516 5778"/>
    </justification>
  </clause>

  <clause id="24975">
    <literal><![CDATA[
      K(x,y) * (((y * x) \ x) \ z) = ((x * y) \ x) \ z
    ]]></literal>
    <justification jstring="[para(6981(a,1),24519(a,1,2,1))].">
      <j1 rule="para" parents="6981 24519"/>
    </justification>
  </clause>

  <clause id="24976">
    <literal><![CDATA[
      T((x \ T(y,z)) \ u,K(y,z)) = ((x \ y) \ u) * K(z,y)
    ]]></literal>
    <justification jstring="[para(24519(a,1),8160(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24519 8160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24978">
    <literal><![CDATA[
      ((x \ y) \ z) \ (K(y,u) * w) = ((x \ T(y,u)) \ z) \ w
    ]]></literal>
    <justification jstring="[para(24519(a,1),23222(a,1,1))].">
      <j1 rule="para" parents="24519 23222"/>
    </justification>
  </clause>

  <clause id="24979">
    <literal><![CDATA[
      K(x,y) * (((z \ y) \ u) * w) = ((z \ T(y,x)) \ u) * w
    ]]></literal>
    <justification jstring="[para(24519(a,1),23246(a,1,2,1))].">
      <j1 rule="para" parents="24519 23246"/>
    </justification>
  </clause>

  <clause id="24980">
    <literal><![CDATA[
      (x * T(y,z)) * ((u \ T(y,z)) \ w) = (x * y) * ((u \ y) \ w)
    ]]></literal>
    <justification jstring="[para(24519(a,1),24468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24519 24468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24981">
    <literal><![CDATA[
      (x * y) \ (((y \ 1) \ x) \ (y * x)) = ((y \ 1) \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,10829,a,b,24520,a)].">
      <j1 rule="hyper" parents="64 10829 24520"/>
    </justification>
  </clause>

  <clause id="24982">
    <literal><![CDATA[
      (x / T(y,y \ z)) * K(y \ z,u) = x / (T(y \ z,u) \ z)
    ]]></literal>
    <justification jstring="[para(423(a,1),24528(a,1,1)),flip(a)].">
      <j1 rule="para" parents="423 24528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24983">
    <literal><![CDATA[
      (x \ T(y,z)) \ (x \ ((1 / x) \ y)) = K(z,y) * (((x \ 1) * y) \ y)
    ]]></literal>
    <justification jstring="[para(11452(a,1),24533(a,1,2))].">
      <j1 rule="para" parents="11452 24533"/>
    </justification>
  </clause>

  <clause id="24984">
    <literal><![CDATA[
      K(x,(y / z) * u) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22629,a(flip),b,24542,a),flip(a)].">
      <j1 rule="hyper" parents="64 22629 24542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24986">
    <literal><![CDATA[
      K(x,((y / z) / u) * w) = K(x,y * (z \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,24984,a(flip),b,24984,a),flip(a)].">
      <j1 rule="hyper" parents="373 24984 24984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24987">
    <literal><![CDATA[
      T(x,(y / z) * u) = T(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(143,a,24984,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 24984 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24988">
    <literal><![CDATA[
      K(x,y * (T(z,y) \ u)) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17913,a(flip),b,24984,a),flip(a)].">
      <j1 rule="hyper" parents="64 17913 24984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24989">
    <literal><![CDATA[
      K(x,(y * z) * (z \ u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),24984(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 24984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24990">
    <literal><![CDATA[
      K(x,R(y / z,z,u) * w) = K(x,(y * u) * ((z * u) \ w))
    ]]></literal>
    <justification jstring="[para(112(a,2),24984(a,1,2,1))].">
      <j1 rule="para" parents="112 24984"/>
    </justification>
  </clause>

  <clause id="24991">
    <literal><![CDATA[
      T(x / y,x) * ((y / x) * y) = y * K(((y / x) * y) \ y,y * (x \ y))
    ]]></literal>
    <justification jstring="[para(24984(a,1),5152(a,2,2))].">
      <j1 rule="para" parents="24984 5152"/>
    </justification>
  </clause>

  <clause id="24992">
    <literal><![CDATA[
      (x \ ((y / z) \ 1)) \ K(x \ ((y / z) \ 1),y * (z \ x)) = 1 / (x \ ((y / z) \ 1))
    ]]></literal>
    <justification jstring="[para(24984(a,1),14471(a,1,2))].">
      <j1 rule="para" parents="24984 14471"/>
    </justification>
  </clause>

  <clause id="24994">
    <literal><![CDATA[
      T(x,(y / z) \ u) = T(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,24707,a,b,24987,a)].">
      <j1 rule="hyper" parents="373 24707 24987"/>
    </justification>
  </clause>

  <clause id="24995">
    <literal><![CDATA[
      T(x,((y \ z) / z) * u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,24687,a(flip),b,24987,a),flip(a)].">
      <j1 rule="hyper" parents="373 24687 24987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24996">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) * u) = T(x,z * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16363,a,b,24987,a)].">
      <j1 rule="hyper" parents="64 16363 24987"/>
    </justification>
  </clause>

  <clause id="24997">
    <literal><![CDATA[
      T(x * K(y \ z,x),z \ y) = T(x,y * (z \ (y / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,15849,a,b,24987,a)].">
      <j1 rule="hyper" parents="64 15849 24987"/>
    </justification>
  </clause>

  <clause id="24998">
    <literal><![CDATA[
      T(x,(y * z) * (z \ u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(11(a,1),24987(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 24987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="24999">
    <literal><![CDATA[
      T(x,y * ((z \ y) \ u)) = T(x,z * u)
    ]]></literal>
    <justification jstring="[para(79(a,1),24987(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 24987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25000">
    <literal><![CDATA[
      R(T(T(x / y,z),x * (y \ u)),u,T(x / y,z)) = T(T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(24987(a,1),8745(a,1,1))].">
      <j1 rule="para" parents="24987 8745"/>
    </justification>
  </clause>

  <clause id="25001">
    <literal><![CDATA[
      K(x,R(T(y / z,(y * u) * ((z * u) \ w)),z,u) * v5) = K(x,T((y * u) / (z * u),w) * v5)
    ]]></literal>
    <justification jstring="[para(24987(a,1),13439(a,1,2,1,1))].">
      <j1 rule="para" parents="24987 13439"/>
    </justification>
  </clause>

  <clause id="25003">
    <literal><![CDATA[
      K(x,(y * z) * u) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),24989(a,1,2,2))].">
      <j1 rule="para" parents="9 24989"/>
    </justification>
  </clause>

  <clause id="25004">
    <literal><![CDATA[
      K(x,a(y,z,u) * (w * v5)) = K(x,w * (a(y,z,u) * v5))
    ]]></literal>
    <justification jstring="[para(23967(a,1),24989(a,1,2))].">
      <j1 rule="para" parents="23967 24989"/>
    </justification>
  </clause>

  <clause id="25007">
    <literal><![CDATA[
      T(x,(y / (y * z)) * u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15781,a(flip),b,24994,a),flip(a)].">
      <j1 rule="hyper" parents="64 15781 24994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25009">
    <literal><![CDATA[
      T(x,(y * z) * u) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),24998(a,1,2,2))].">
      <j1 rule="para" parents="9 24998"/>
    </justification>
  </clause>

  <clause id="25010">
    <literal><![CDATA[
      T(x,(y * z) * (z \ (y \ u))) = T(x,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),24998(a,2,2))].">
      <j1 rule="para" parents="10 24998"/>
    </justification>
  </clause>

  <clause id="25011">
    <literal><![CDATA[
      T(x,a(y,z,u) * (w * v5)) = T(x,w * (v5 * a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(23928(a,1),24998(a,1,2))].">
      <j1 rule="para" parents="23928 24998"/>
    </justification>
  </clause>

  <clause id="25012">
    <literal><![CDATA[
      T(x,y * ((y \ z) * u)) = T(x,z * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),24999(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 24999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25014">
    <literal><![CDATA[
      K(x \ (y * z),T(u * (y * z),K(w,v5))) = K((y * z) / x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17179,a,b,25003,a)].">
      <j1 rule="hyper" parents="64 17179 25003"/>
    </justification>
  </clause>

  <clause id="25015">
    <literal><![CDATA[
      K(x,y * ((y \ z) * u)) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),25003(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 25003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25017">
    <literal><![CDATA[
      ((x * y) \ z) * K(u,K(w,x * (y * z))) = T((x * y) \ z,K(u,w))
    ]]></literal>
    <justification jstring="[para(25003(a,1),17555(a,1,2,2))].">
      <j1 rule="para" parents="25003 17555"/>
    </justification>
  </clause>

  <clause id="25018">
    <literal><![CDATA[
      K(x,K(y,z * (u \ w))) = K(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(25003(a,1),19449(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25003 19449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25019">
    <literal><![CDATA[
      T(x / ((y * z) * u),y * (z * u)) = ((y * z) * u) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,25009,a),flip(a)].">
      <j1 rule="hyper" parents="467 25009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25020">
    <literal><![CDATA[
      T(x,((y * z) / u) * w) = T(x,y * (z * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,24987,a,b,25009,a)].">
      <j1 rule="hyper" parents="64 24987 25009"/>
    </justification>
  </clause>

  <clause id="25021">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (((x \ 1) * y) * z)) = T(1 / x,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1670,a,b,25009,a)].">
      <j1 rule="hyper" parents="64 1670 25009"/>
    </justification>
  </clause>

  <clause id="25023">
    <literal><![CDATA[
      K(x,y * T(z,u * (w * v5))) = K(x,y * T(z,v5 * (u * w)))
    ]]></literal>
    <justification jstring="[para(25009(a,1),17966(a,1,2,2))].">
      <j1 rule="para" parents="25009 17966"/>
    </justification>
  </clause>

  <clause id="25024">
    <literal><![CDATA[
      K(x,y * T(z,(u * w) * v5)) = K(x,y * T(z,u * (v5 * w)))
    ]]></literal>
    <justification jstring="[para(25009(a,2),18536(a,1,2,2))].">
      <j1 rule="para" parents="25009 18536"/>
    </justification>
  </clause>

  <clause id="25026">
    <literal><![CDATA[
      (x * x) \ (T(y,x \ (x \ z)) \ u) = T(y,z) \ ((x * x) \ u)
    ]]></literal>
    <justification jstring="[para(25010(a,1),1776(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25010 1776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25027">
    <literal><![CDATA[
      T(x,x \ ((x \ y) * z)) = R(T(x,y * z),x,x)
    ]]></literal>
    <justification jstring="[para(25012(a,1),8871(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25012 8871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25028">
    <literal><![CDATA[
      K(x,y) * ((L(y,z,u) * x) \ w) = (L(T(y,x),z,u) * x) \ w
    ]]></literal>
    <justification jstring="[para(24555(a,1),24506(a,1,2,1))].">
      <j1 rule="para" parents="24555 24506"/>
    </justification>
  </clause>

  <clause id="25029">
    <literal><![CDATA[
      x * R(T(x,y),x,x) = T(x * T(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13179,a(flip),b,24593,a),flip(a)].">
      <j1 rule="hyper" parents="64 13179 24593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25030">
    <literal><![CDATA[
      R(x,y,z) * T(x,u) = x * R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,524,a(flip),b,24593,a)].">
      <j1 rule="hyper" parents="64 524 24593"/>
    </justification>
  </clause>

  <clause id="25031">
    <literal><![CDATA[
      (x / y) * T(y * T(y,z),y) = (x / (y \ 1)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(25029(a,1),6366(a,1,2))].">
      <j1 rule="para" parents="25029 6366"/>
    </justification>
  </clause>

  <clause id="25032">
    <literal><![CDATA[
      L(R(T(x,y),x,x) * K(z,R(T(x,y),x,x)),x,x \ z) = ((z / x) * T(x * T(x,y),x)) / z
    ]]></literal>
    <justification jstring="[para(25029(a,1),11072(a,2,1,2))].">
      <j1 rule="para" parents="25029 11072"/>
    </justification>
  </clause>

  <clause id="25033">
    <literal><![CDATA[
      (x * ((y * y) * R(T(x,y * y) \ 1,z,u))) / w = (y * y) * ((x \ R(x,z,u)) / w)
    ]]></literal>
    <justification jstring="[para(24594(a,1),2315(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="24594 2315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25034">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),(x * u) \ u,y * z),x,u) = a((x * u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(24594(a,1),16722(a,1,1,1))].">
      <j1 rule="para" parents="24594 16722"/>
    </justification>
  </clause>

  <clause id="25035">
    <literal><![CDATA[
      R(x,y,z) \ K(x \ 1,x) = R(R(x,x,x),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1417(a,1),24596(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1417 24596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25036">
    <literal><![CDATA[
      R(x,x,x) \ T(y,x) = (x \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,8876,a(flip),b,24597,a),flip(a)].">
      <j1 rule="hyper" parents="64 8876 24597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25037">
    <literal><![CDATA[
      T(x,x \ 1) \ T(y,x) = (x \ (x \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,1419,a,b,25036,a)].">
      <j1 rule="hyper" parents="64 1419 25036"/>
    </justification>
  </clause>

  <clause id="25038">
    <literal><![CDATA[
      R(x,x,x) \ T(x * y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(9(a,1),25036(a,2,1,2))].">
      <j1 rule="para" parents="9 25036"/>
    </justification>
  </clause>

  <clause id="25039">
    <literal><![CDATA[
      a(x,x,x) * ((x \ y) * x) = x \ T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,25038,a(flip),b,11371,a)].">
      <j1 rule="hyper" parents="145 25038 11371"/>
    </justification>
  </clause>

  <clause id="25040">
    <literal><![CDATA[
      (x * R(y,z,u)) * (x * y) = (x * y) * (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,24601,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 24601 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25041">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),y) = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),24601(a,1,2))].">
      <j1 rule="para" parents="10 24601"/>
    </justification>
  </clause>

  <clause id="25042">
    <literal><![CDATA[
      (x * R(y,z,u)) / y = R(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2828,a,b,24603,a)].">
      <j1 rule="hyper" parents="373 2828 24603"/>
    </justification>
  </clause>

  <clause id="25043">
    <literal><![CDATA[
      (x / y) * R(y,y,x) = y \ ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1933,a(flip),b,24603,a),flip(a)].">
      <j1 rule="hyper" parents="64 1933 24603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25044">
    <literal><![CDATA[
      (a(x,x,y) / y) * R(y,z,u) = L(y,x,x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1881,a(flip),b,24603,a),flip(a)].">
      <j1 rule="hyper" parents="64 1881 24603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25045">
    <literal><![CDATA[
      x * ((y / x) * R(x,z,u)) = R(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,24603,a(flip),b,1898,a)].">
      <j1 rule="hyper" parents="145 24603 1898"/>
    </justification>
  </clause>

  <clause id="25046">
    <literal><![CDATA[
      (x * (R(x,y,z) \ u)) / x = u / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,74,a(flip),b,24603,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="142 74 24603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25047">
    <literal><![CDATA[
      R(x \ (x \ y),z,u) * ((x \ (x \ y)) \ (y / x)) = T(x,x \ y) * R(x \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[para(4472(a,1),24603(a,2,1))].">
      <j1 rule="para" parents="4472 24603"/>
    </justification>
  </clause>

  <clause id="25049">
    <literal><![CDATA[
      L(x,y,L(R(z,z,u),u / z,u / z)) = L(x,y,(u / z) * (z \ ((1 / z) \ u)))
    ]]></literal>
    <justification jstring="[para(25043(a,1),2185(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="25043 2185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25050">
    <literal><![CDATA[
      (R(x,y,z) * u) * x = (x * u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,24604,a(flip),b,2828,a)].">
      <j1 rule="hyper" parents="144 24604 2828"/>
    </justification>
  </clause>

  <clause id="25051">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u) = (x * u) \ (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(24604(a,1),11086(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24604 11086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25052">
    <literal><![CDATA[
      x * ((y * K(x,z)) * R(x,u,w)) = R(x,u,w) * (y * T(x,z))
    ]]></literal>
    <justification jstring="[para(6850(a,1),24605(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6850 24605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25053">
    <literal><![CDATA[
      L((T(x,y) \ z) \ u,x \ z,x) = z \ (T(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(743,a,24626,a),flip(a)].">
      <j1 rule="hyper" parents="743 24626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25056">
    <literal><![CDATA[
      a(x,y,y \ (x \ 1)) / (x * y) = 1 / (1 / (y \ (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(225,a,1283,a(flip),b,24638,a)].">
      <j1 rule="hyper" parents="225 1283 24638"/>
    </justification>
  </clause>

  <clause id="25057">
    <literal><![CDATA[
      (x * x) * (a(y,z,u) / x) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,24638,a(flip),b,876,a)].">
      <j1 rule="hyper" parents="145 24638 876"/>
    </justification>
  </clause>

  <clause id="25058">
    <literal><![CDATA[
      a(x,y,z) / ((u \ 1) \ 1) = u \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(216(a,1),24638(a,1,1)),flip(a)].">
      <j1 rule="para" parents="216 24638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25059">
    <literal><![CDATA[
      a(x,y,z) * K(u,u \ 1) = u * (a(x,y,z) / u)
    ]]></literal>
    <justification jstring="[para(24638(a,1),3649(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24638 3649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25060">
    <literal><![CDATA[
      T(a(x,y,z) \ (a(x,y,z) / u),u) = a(x,y,z) \ (u \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(24638(a,1),3735(a,1,1,2))].">
      <j1 rule="para" parents="24638 3735"/>
    </justification>
  </clause>

  <clause id="25061">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ a(u,w,v5) = a(u,w,v5) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4300(a,2),24638(a,1,1))].">
      <j1 rule="para" parents="4300 24638"/>
    </justification>
  </clause>

  <clause id="25062">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) \ a(z,u,w)),T(1 / (1 / y),a(z,u,w))) = x * (T(1 / (1 / y),x * (a(z,u,w) / y)) \ a(z,u,w))
    ]]></literal>
    <justification jstring="[para(24638(a,1),14644(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="24638 14644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25063">
    <literal><![CDATA[
      a(x,y,z) / (x \ 1) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,16060,a(flip),b,24641,a),flip(a)].">
      <j1 rule="hyper" parents="373 16060 24641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25064">
    <literal><![CDATA[
      (x * a(x,y,z)) \ a(x,y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,25063,a)].">
      <j1 rule="hyper" parents="215 25063"/>
    </justification>
  </clause>

  <clause id="25065">
    <literal><![CDATA[
      L(x * a(x,y,z),x,x) = a(x,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(25063(a,1),16064(a,1,1))].">
      <j1 rule="para" parents="25063 16064"/>
    </justification>
  </clause>

  <clause id="25066">
    <literal><![CDATA[
      L(x / y,z,u) \ K(y,x / y) = L(y \ x,z,u) \ 1
    ]]></literal>
    <justification jstring="[para(117(a,1),24683(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="117 24683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25067">
    <literal><![CDATA[
      L(x,y,z) \ K(x \ 1,x) = L(R(x,x,x),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1417(a,1),24683(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1417 24683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25068">
    <literal><![CDATA[
      T(x,x \ y) / L((x \ y) \ y,z,u) = L(x,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,5585,a(flip),b,24684,a)].">
      <j1 rule="hyper" parents="64 5585 24684"/>
    </justification>
  </clause>

  <clause id="25069">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(T(x,u),y,z) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,24684,a(flip),b,5558,a)].">
      <j1 rule="hyper" parents="144 24684 5558"/>
    </justification>
  </clause>

  <clause id="25070">
    <literal><![CDATA[
      L(x \ y,z,u) \ T(y / x,x) = L(y / x,z,u) \ (y / x)
    ]]></literal>
    <justification jstring="[para(117(a,1),24684(a,1,1,1))].">
      <j1 rule="para" parents="117 24684"/>
    </justification>
  </clause>

  <clause id="25071">
    <literal><![CDATA[
      x * (L(T(y,z),u,w) \ T(y,z)) = (L(y,u,w) \ y) * x
    ]]></literal>
    <justification jstring="[para(24684(a,1),23581(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24684 23581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25072">
    <literal><![CDATA[
      T(x,(y \ (z \ y)) * u) = T(x,(y / z) * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,15827,a(flip),b,24692,a),flip(a)].">
      <j1 rule="hyper" parents="64 15827 24692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25073">
    <literal><![CDATA[
      T(x,(y \ a(z,u,w)) * v5) = T(x,a(z,u,w) * (y \ v5))
    ]]></literal>
    <justification jstring="[para(23127(a,1),24692(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23127 24692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25074">
    <literal><![CDATA[
      T(x / ((x / y) / z),z * y) = x / ((x / y) / z)
    ]]></literal>
    <justification jstring="[para(82(a,1),24719(a,1,2,2))].">
      <j1 rule="para" parents="82 24719"/>
    </justification>
  </clause>

  <clause id="25076">
    <literal><![CDATA[
      x * (K(y,z * u) * T(u,x)) = u * (x * K(y,u * z))
    ]]></literal>
    <justification jstring="[para(17449(a,1),24749(a,1,2))].">
      <j1 rule="para" parents="17449 24749"/>
    </justification>
  </clause>

  <clause id="25081">
    <literal><![CDATA[
      T(x * K(y,T(z,u)),z) = T(x,z) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(200(a,1),24751(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="200 24751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25085">
    <literal><![CDATA[
      T(x * K(y \ z,u),y) = T(x,y) * K(z / y,u)
    ]]></literal>
    <justification jstring="[para(8215(a,1),24751(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8215 24751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25088">
    <literal><![CDATA[
      L(T(((x \ 1) \ 1) * K(y,x),z),x,x \ y) = ((y / x) * ((1 / x) \ T(x,z))) / y
    ]]></literal>
    <justification jstring="[para(24751(a,1),16726(a,1,1))].">
      <j1 rule="para" parents="24751 16726"/>
    </justification>
  </clause>

  <clause id="25089">
    <literal><![CDATA[
      T(x * K(y,z),u * u) = T(x,u * u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(17031(a,1),24751(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17031 24751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25090">
    <literal><![CDATA[
      (x * (a(y,z,u) \ x)) \ x = a(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(23700(a,1),24753(a,1,1))].">
      <j1 rule="para" parents="23700 24753"/>
    </justification>
  </clause>

  <clause id="25094">
    <literal><![CDATA[
      (T(x,y) * (z \ x)) * (z \ x) = (x * (z \ x)) * (z \ T(x,y))
    ]]></literal>
    <justification jstring="[para(15021(a,1),24767(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15021 24767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25095">
    <literal><![CDATA[
      L(x,(T((T(y,z) * z) * z,y) * u) * w,v5) = L(x,(L(y,z,y * z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(24767(a,1),15294(a,1,2,1,1,1))].">
      <j1 rule="para" parents="24767 15294"/>
    </justification>
  </clause>

  <clause id="25096">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (x \ v5) = (v5 / x) * L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(24791(a,1),24379(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24791 24379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25097">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (x \ v5) = (v5 / x) * R(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(24791(a,1),24604(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24791 24604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25098">
    <literal><![CDATA[
      (x / R(y,z,u)) * y = y * (R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(144,a,171,a(flip),b,24807,a(flip))].">
      <j1 rule="hyper" parents="144 171 24807"/>
    </justification>
  </clause>

  <clause id="25099">
    <literal><![CDATA[
      L(R(x,y,z),u,R(x,y,z)) = ((x * (u * R(x,y,z))) / x) / u
    ]]></literal>
    <justification jstring="[hyper(142,a,24807,a(flip),b,4725,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="142 24807 4725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25100">
    <literal><![CDATA[
      (a(x,y,z) \ u) / u = (u * a(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(373,a,23560,a(flip),b,24827,a),flip(a)].">
      <j1 rule="hyper" parents="373 23560 24827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25101">
    <literal><![CDATA[
      (a(x,y,z) * u) \ u = u \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23767,a(flip),b,24827,a),flip(a)].">
      <j1 rule="hyper" parents="64 23767 24827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25102">
    <literal><![CDATA[
      (a(x,y,y \ 1) \ x) / x = R(x,y,y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(2080(a,1),24827(a,2,1))].">
      <j1 rule="para" parents="2080 24827"/>
    </justification>
  </clause>

  <clause id="25103">
    <literal><![CDATA[
      x / (a(y,z,u) * x) = x \ (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(154,a,24828,a)].">
      <j1 rule="hyper" parents="154 24828"/>
    </justification>
  </clause>

  <clause id="25104">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ x)) \ x = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,24828,a(flip),b,23169,a(flip))].">
      <j1 rule="hyper" parents="139 24828 23169"/>
    </justification>
  </clause>

  <clause id="25105">
    <literal><![CDATA[
      L(x,y,R(z,z,z \ u)) = L(x,y,R(z,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),24841(a,1,3,3)),flip(a)].">
      <j1 rule="para" parents="10 24841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25106">
    <literal><![CDATA[
      (x \ y) * (x * L(x \ y,z,u)) = L(x \ y,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(397,a,24842,a),flip(a)].">
      <j1 rule="hyper" parents="397 24842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25108">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,z,u) \ x) = y / L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(393,a,24843,a),flip(a)].">
      <j1 rule="hyper" parents="393 24843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25109">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = L(y,z,u) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2329,a,b,24843,a),flip(a)].">
      <j1 rule="hyper" parents="373 2329 24843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25110">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * x = x * (L(x,y,z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(144,a,24843,a(flip),b,24384,a)].">
      <j1 rule="hyper" parents="144 24843 24384"/>
    </justification>
  </clause>

  <clause id="25111">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * (1 / x))) = R(u,x,x) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1405(a,1),24843(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1405 24843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25112">
    <literal><![CDATA[
      R(x,y,L(z,u,w) \ (v5 * z)) = R(x,y,z * (L(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(24843(a,1),23813(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24843 23813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25113">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ u),x) = L(x,y,z) \ (u * x)
    ]]></literal>
    <justification jstring="[para(24843(a,1),23165(a,1,1))].">
      <j1 rule="para" parents="24843 23165"/>
    </justification>
  </clause>

  <clause id="25114">
    <literal><![CDATA[
      x * (L(x,y,y) \ y) = R(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,2001,a,b,24845,a),flip(a)].">
      <j1 rule="hyper" parents="36 2001 24845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25115">
    <literal><![CDATA[
      R(R(x \ 1,1 / x,y),x,x) = y * (L(y,1 / x,1 / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,1044,a,b,25114,a)].">
      <j1 rule="hyper" parents="373 1044 25114"/>
    </justification>
  </clause>

  <clause id="25116">
    <literal><![CDATA[
      L(x,y,y) \ (x * y) = R(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2329,a,b,25114,a)].">
      <j1 rule="hyper" parents="64 2329 25114"/>
    </justification>
  </clause>

  <clause id="25117">
    <literal><![CDATA[
      L(x,y,y) * R(y,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(145,a,25114,a(flip),b,2329,a)].">
      <j1 rule="hyper" parents="145 25114 2329"/>
    </justification>
  </clause>

  <clause id="25118">
    <literal><![CDATA[
      L(L(x,y,y) \ y,x,x) = (1 / x) * R(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,25114,a(flip),b,561,a),flip(a)].">
      <j1 rule="hyper" parents="145 25114 561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25119">
    <literal><![CDATA[
      L(x,y,z) * (L(L(x,u,u),y,z) \ u) = R(u,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(30(a,1),25114(a,1,2,1))].">
      <j1 rule="para" parents="30 25114"/>
    </justification>
  </clause>

  <clause id="25120">
    <literal><![CDATA[
      x / R(y,y,x / y) = L(x / y,y,y)
    ]]></literal>
    <justification jstring="[para(25116(a,1),386(a,1,2))].">
      <j1 rule="para" parents="25116 386"/>
    </justification>
  </clause>

  <clause id="25121">
    <literal><![CDATA[
      L(x,(y / z) \ 1,z \ y) * R((y / z) \ 1,(y / z) \ 1,x) = x * ((y / z) \ 1)
    ]]></literal>
    <justification jstring="[para(23969(a,1),25117(a,1,1))].">
      <j1 rule="para" parents="23969 25117"/>
    </justification>
  </clause>

  <clause id="25122">
    <literal><![CDATA[
      x / L(R(y,y,x),y,y) = L(x / y,y,y)
    ]]></literal>
    <justification jstring="[para(10220(a,2),25120(a,1,2))].">
      <j1 rule="para" parents="10220 25120"/>
    </justification>
  </clause>

  <clause id="25123">
    <literal><![CDATA[
      (((L(x,y,z) \ x) * u) / x) * L(x,y,z) = L(u,L(x,y,z) \ x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1012,a,24852,a),flip(a)].">
      <j1 rule="hyper" parents="1012 24852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25124">
    <literal><![CDATA[
      x * (y \ (L(y,z,u) * w)) = x * ((w / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,24852,a,b,9,a)].">
      <j1 rule="hyper" parents="145 24852 9"/>
    </justification>
  </clause>

  <clause id="25125">
    <literal><![CDATA[
      L((x / y) * L(y,z,u),y,y) = (1 / y) * (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(24852(a,1),569(a,1,1))].">
      <j1 rule="para" parents="24852 569"/>
    </justification>
  </clause>

  <clause id="25126">
    <literal><![CDATA[
      x \ ((y / x) * L(x,z,u)) = ((x \ y) / x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(23898(a,1),24852(a,1,2))].">
      <j1 rule="para" parents="23898 24852"/>
    </justification>
  </clause>

  <clause id="25127">
    <literal><![CDATA[
      ((a(x,x,y) * z) / y) * L(y,x,x) = L(z,a(x,x,y),L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,1248,a,b,24854,a),flip(a)].">
      <j1 rule="hyper" parents="35 1248 24854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25128">
    <literal><![CDATA[
      ((L(x,y,z) * u) \ ((u / x) * L(x,y,z))) * T(x,(u / x) * L(x,y,z)) = ((((u / x) * L(x,y,z)) * x) \ ((u / x) * L(x,y,z))) * x
    ]]></literal>
    <justification jstring="[para(24854(a,1),15070(a,1,1,1))].">
      <j1 rule="para" parents="24854 15070"/>
    </justification>
  </clause>

  <clause id="25129">
    <literal><![CDATA[
      L(x \ R(x,y,(z * z) * u),x,y * u) = a(x,y,(z * z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16031,a,b,24856,a),flip(a)].">
      <j1 rule="hyper" parents="64 16031 24856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25130">
    <literal><![CDATA[
      L(x,y,z * ((u * u) \ w)) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),24856(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 24856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25131">
    <literal><![CDATA[
      L(x,y,z * ((1 / u) * w)) = L(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(310(a,1),24856(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="310 24856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25132">
    <literal><![CDATA[
      L(x,y,z * (((u * w) * u) * w)) = L(x,y,z * a(u * w,u,w))
    ]]></literal>
    <justification jstring="[para(88(a,1),24856(a,1,3,2))].">
      <j1 rule="para" parents="88 24856"/>
    </justification>
  </clause>

  <clause id="25133">
    <literal><![CDATA[
      L(x,y,z * ((u * w) * (w \ u))) = L(x,y,z * a(u,w,w \ u))
    ]]></literal>
    <justification jstring="[para(957(a,1),24856(a,1,3,2))].">
      <j1 rule="para" parents="957 24856"/>
    </justification>
  </clause>

  <clause id="25134">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * (z * z) = x / ((z * T(z,y)) \ u)
    ]]></literal>
    <justification jstring="[para(24858(a,1),900(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24858 900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25135">
    <literal><![CDATA[
      (x * (x * y)) \ ((x * y) / x) = (x * (y * x)) \ y
    ]]></literal>
    <justification jstring="[para(4645(a,1),24859(a,1,1))].">
      <j1 rule="para" parents="4645 24859"/>
    </justification>
  </clause>

  <clause id="25136">
    <literal><![CDATA[
      K(a(x,y,z) \ (u \ w),v5) = K(u \ (a(x,y,z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(23105(a,1),24862(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="23105 24862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25137">
    <literal><![CDATA[
      x / (y * (K(z,u) * x)) = K(u,z) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(23252(a,1),24877(a,1,2))].">
      <j1 rule="para" parents="23252 24877"/>
    </justification>
  </clause>

  <clause id="25138">
    <literal><![CDATA[
      x * (y \ K(y \ x,z * y)) = T(x * (y \ 1),y * z)
    ]]></literal>
    <justification jstring="[para(11114(a,1),24882(a,1,2,2))].">
      <j1 rule="para" parents="11114 24882"/>
    </justification>
  </clause>

  <clause id="25139">
    <literal><![CDATA[
      x * T(L(x,y,z) * u,x) = (x * u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(329,a,24913,a)].">
      <j1 rule="hyper" parents="329 24913"/>
    </justification>
  </clause>

  <clause id="25140">
    <literal><![CDATA[
      (L(x,y,z) * (T(x \ 1,x) * u)) * x = ((x \ 1) * (x * u)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(7063(a,1),24913(a,2,1))].">
      <j1 rule="para" parents="7063 24913"/>
    </justification>
  </clause>

  <clause id="25141">
    <literal><![CDATA[
      (L(x,y,z) \ L(x * u,w,v5)) * L(x,y,z) = L(u * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,5545,a(flip),b,24914,a),flip(a)].">
      <j1 rule="hyper" parents="373 5545 24914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25142">
    <literal><![CDATA[
      L(x,y,z) \ (x * (u / x)) = u / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,84,a(flip),b,24914,a),flip(a)].">
      <j1 rule="hyper" parents="142 84 24914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25143">
    <literal><![CDATA[
      (x * y) * (z / L((x \ 1) \ y,x,x)) = ((x \ 1) \ y) * (z / ((x \ 1) \ y))
    ]]></literal>
    <justification jstring="[hyper(145,a,24919,a(flip),b,2343,a(flip))].">
      <j1 rule="hyper" parents="145 24919 2343"/>
    </justification>
  </clause>

  <clause id="25144">
    <literal><![CDATA[
      x * ((x \ K(y,x)) * x) = 1 / (K(x,y) / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,14598,a(flip),b,24961,a),flip(a)].">
      <j1 rule="hyper" parents="373 14598 24961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25145">
    <literal><![CDATA[
      K(x,T(y,T(z,u) \ w)) / (w / (u / (u * z))) = (1 / (w / (u / (u * z)))) * K(x,y)
    ]]></literal>
    <justification jstring="[para(25007(a,1),17395(a,1,1,2))].">
      <j1 rule="para" parents="25007 17395"/>
    </justification>
  </clause>

  <clause id="25146">
    <literal><![CDATA[
      T((x \ (y / x)) * x,x) = T(x,x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5456,a,b,25037,a)].">
      <j1 rule="hyper" parents="373 5456 25037"/>
    </justification>
  </clause>

  <clause id="25147">
    <literal><![CDATA[
      T(1 / (1 / x),(1 / (1 / x)) \ 1) \ T(y,1 / (1 / x)) = K(x \ 1,x) * (((1 / (1 / x)) \ ((1 / (1 / x)) \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,3866,a,b,25037,a),flip(a)].">
      <j1 rule="hyper" parents="373 3866 25037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25148">
    <literal><![CDATA[
      R(x,y,z) * (x \ (u / R(x,y,z))) = u / x
    ]]></literal>
    <justification jstring="[hyper(466,a,25042,a),flip(a)].">
      <j1 rule="hyper" parents="466 25042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25149">
    <literal><![CDATA[
      (R(x,y,z) \ u) * R(x,y,z) = (x \ u) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,1899,a(flip),b,25042,a),flip(a)].">
      <j1 rule="hyper" parents="144 1899 25042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25150">
    <literal><![CDATA[
      (x * (R(x,y,z) \ u)) * R(x,y,z) = u * x
    ]]></literal>
    <justification jstring="[hyper(144,a,74,a(flip),b,25042,a),flip(a)].">
      <j1 rule="hyper" parents="144 74 25042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25151">
    <literal><![CDATA[
      R(R(x,x,y),R(x,x,y),y) = R(x,x,y) * (x \ R(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,3143,a,b,25042,a)].">
      <j1 rule="hyper" parents="64 3143 25042"/>
    </justification>
  </clause>

  <clause id="25152">
    <literal><![CDATA[
      T(R(x,y,z) * (x \ u),x) = x \ (u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(25042(a,1),117(a,1,1))].">
      <j1 rule="para" parents="25042 117"/>
    </justification>
  </clause>

  <clause id="25153">
    <literal><![CDATA[
      (R(x,y,z) * (x \ u)) / x = R(x,y,z) * (x \ (u / x))
    ]]></literal>
    <justification jstring="[para(24603(a,2),25042(a,1,1))].">
      <j1 rule="para" parents="24603 25042"/>
    </justification>
  </clause>

  <clause id="25154">
    <literal><![CDATA[
      (x \ y) * (x * R(y / x,z,u)) = R(y / x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,6649,a(flip),b,25045,a)].">
      <j1 rule="hyper" parents="64 6649 25045"/>
    </justification>
  </clause>

  <clause id="25155">
    <literal><![CDATA[
      (x * (R(x,y,z) \ x)) / x = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,2156,a(flip),b,25046,a),flip(a)].">
      <j1 rule="hyper" parents="373 2156 25046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25156">
    <literal><![CDATA[
      T(x,R(x,y,z) \ u) * (R(x,y,z) \ u) = x * (u / R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,25046,a(flip),b,4453,a),flip(a)].">
      <j1 rule="hyper" parents="145 25046 4453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25157">
    <literal><![CDATA[
      (x * (R(x,y,z) \ u)) \ (u * x) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(783,a,25050,a)].">
      <j1 rule="hyper" parents="783 25050"/>
    </justification>
  </clause>

  <clause id="25160">
    <literal><![CDATA[
      (x \ a(y,z,u)) \ a(y,z,u) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,25058,a)].">
      <j1 rule="hyper" parents="215 25058"/>
    </justification>
  </clause>

  <clause id="25161">
    <literal><![CDATA[
      a(x,y,z) / R(u \ 1,w,v5) = R(1 / u,w,v5) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(11418(a,1),25058(a,1,2))].">
      <j1 rule="para" parents="11418 25058"/>
    </justification>
  </clause>

  <clause id="25162">
    <literal><![CDATA[
      a(x,x,y) * L(T(y,z),x,x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(1243(a,1),25069(a,1,1))].">
      <j1 rule="para" parents="1243 25069"/>
    </justification>
  </clause>

  <clause id="25163">
    <literal><![CDATA[
      a(x,x,T(y,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,5563,a,b,25162,a)].">
      <j1 rule="hyper" parents="36 5563 25162"/>
    </justification>
  </clause>

  <clause id="25164">
    <literal><![CDATA[
      ((x \ 1) * R(y,x,x)) \ T(y * (x \ 1),x) = a(x,x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,3953,a,b,25163,a)].">
      <j1 rule="hyper" parents="64 3953 25163"/>
    </justification>
  </clause>

  <clause id="25165">
    <literal><![CDATA[
      (x \ 1) / (a(y,z,u) / x) = (x \ 1) * (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(225,a,25090,a(flip),b,1228,a)].">
      <j1 rule="hyper" parents="225 25090 1228"/>
    </justification>
  </clause>

  <clause id="25168">
    <literal><![CDATA[
      K(x,y) * ((x / R(z,u,w)) * z) = z * (R(z,u,w) \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,24364,a,b,25098,a)].">
      <j1 rule="hyper" parents="64 24364 25098"/>
    </justification>
  </clause>

  <clause id="25169">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * u) = a(x,y,z) \ (u * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,489,a(flip),b,25100,a)].">
      <j1 rule="hyper" parents="144 489 25100"/>
    </justification>
  </clause>

  <clause id="25170">
    <literal><![CDATA[
      (x * a(y,z,u)) \ x = x \ (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,23767,a(flip),b,25100,a),flip(a)].">
      <j1 rule="hyper" parents="64 23767 25100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25171">
    <literal><![CDATA[
      x \ (a(x,y,y) \ x) = R(x,y,y) \ x
    ]]></literal>
    <justification jstring="[para(15998(a,1),25101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15998 25101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25172">
    <literal><![CDATA[
      x * (R(x,y,y) \ x) = a(x,y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(157,a,25171,a)].">
      <j1 rule="hyper" parents="157 25171"/>
    </justification>
  </clause>

  <clause id="25173">
    <literal><![CDATA[
      x * (a(x,y,y) \ 1) = a(x,y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,16007,a(flip),b,25171,a)].">
      <j1 rule="hyper" parents="145 16007 25171"/>
    </justification>
  </clause>

  <clause id="25174">
    <literal><![CDATA[
      T(x / y,y * y) \ (a(T(x / y,y * y),y,y) \ T(x / y,y * y)) = ((y * y) \ (x * y)) \ T(x / y,y * y)
    ]]></literal>
    <justification jstring="[para(1326(a,1),25171(a,2,1))].">
      <j1 rule="para" parents="1326 25171"/>
    </justification>
  </clause>

  <clause id="25175">
    <literal><![CDATA[
      1 / (a(x,y,y) \ x) = R(1 / x,y,y)
    ]]></literal>
    <justification jstring="[hyper(225,a,25172,a(flip),b,2468,a)].">
      <j1 rule="hyper" parents="225 25172 2468"/>
    </justification>
  </clause>

  <clause id="25176">
    <literal><![CDATA[
      (a(x,y,y) \ 1) * x = a(x,y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,23736,a,b,25173,a)].">
      <j1 rule="hyper" parents="64 23736 25173"/>
    </justification>
  </clause>

  <clause id="25177">
    <literal><![CDATA[
      L((a(x,y,y) \ 1) \ z,a(x,y,y),x) = (a(x,y,y) \ x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(25173(a,1),11813(a,2,1))].">
      <j1 rule="para" parents="25173 11813"/>
    </justification>
  </clause>

  <clause id="25178">
    <literal><![CDATA[
      R((a(x,y,y) * a(x,y,y)) \ x,y,y) = a(x,y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,16097,a,b,25176,a)].">
      <j1 rule="hyper" parents="64 16097 25176"/>
    </justification>
  </clause>

  <clause id="25179">
    <literal><![CDATA[
      ((x \ 1) \ (a(y,z,u) \ (x \ 1))) \ (1 / x) = (1 / x) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(5194(a,1),25104(a,1,1))].">
      <j1 rule="para" parents="5194 25104"/>
    </justification>
  </clause>

  <clause id="25180">
    <literal><![CDATA[
      L(x,y,z) \ (x * (u * (x \ L(x,y,z)))) = R(u,x \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5575,a(flip),b,25109,a),flip(a)].">
      <j1 rule="hyper" parents="64 5575 25109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25181">
    <literal><![CDATA[
      L(x \ R(x,y,(z * z) \ u),x,y * u) = a(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16031,a,b,25130,a),flip(a)].">
      <j1 rule="hyper" parents="64 16031 25130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25182">
    <literal><![CDATA[
      L(x,y,z * R((u * u) \ w,v5,v6)) = L(x,y,z * R(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(2051(a,2),25130(a,1,3,2))].">
      <j1 rule="para" parents="2051 25130"/>
    </justification>
  </clause>

  <clause id="25183">
    <literal><![CDATA[
      (L(x,y,z) \ u) * K(x,x \ u) = u / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16688,a,b,25142,a)].">
      <j1 rule="hyper" parents="64 16688 25142"/>
    </justification>
  </clause>

  <clause id="25184">
    <literal><![CDATA[
      x * K(x \ (x \ y),x) = 1 / (K(x,y) / x)
    ]]></literal>
    <justification jstring="[para(8885(a,2),25144(a,1,2))].">
      <j1 rule="para" parents="8885 25144"/>
    </justification>
  </clause>

  <clause id="25185">
    <literal><![CDATA[
      R(x,y,z) * (u / R(x,y,z)) = x * (u / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,25148,a(flip),b,1898,a),flip(a)].">
      <j1 rule="hyper" parents="145 25148 1898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25186">
    <literal><![CDATA[
      ((x \ y) * x) / R(x,z,u) = R(x,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(154,a,25149,a)].">
      <j1 rule="hyper" parents="154 25149"/>
    </justification>
  </clause>

  <clause id="25187">
    <literal><![CDATA[
      R(x,y,z) \ (x * (u / x)) = u / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,84,a(flip),b,25149,a),flip(a)].">
      <j1 rule="hyper" parents="142 84 25149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25188">
    <literal><![CDATA[
      x / R(T(R(y,z,u),x),R(y,z,u),R(y,z,u)) = (y \ (x / R(y,z,u))) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,8877,a,b,25149,a)].">
      <j1 rule="hyper" parents="64 8877 25149"/>
    </justification>
  </clause>

  <clause id="25190">
    <literal><![CDATA[
      (x * L(y,x,z)) * R(z,x,L(y,x,z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(1938(a,1),25150(a,1,1))].">
      <j1 rule="para" parents="1938 25150"/>
    </justification>
  </clause>

  <clause id="25191">
    <literal><![CDATA[
      (L(x,y,z) * y) \ ((x * y) * z) = R(z,y,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(10303(a,1),25157(a,1,1))].">
      <j1 rule="para" parents="10303 25157"/>
    </justification>
  </clause>

  <clause id="25192">
    <literal><![CDATA[
      R(x,y,R(z,u,w) \ (v5 * z)) = R(x,y,z * (R(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(25157(a,1),23313(a,1,3,1))].">
      <j1 rule="para" parents="25157 23313"/>
    </justification>
  </clause>

  <clause id="25193">
    <literal><![CDATA[
      ((a(x,y,z) / u) \ 1) \ 1 = u \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,219,a(flip),b,25160,a),flip(a)].">
      <j1 rule="hyper" parents="64 219 25160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25194">
    <literal><![CDATA[
      (a(x,y,z) / (a(x,y,z) / u)) \ 1 = 1 / u
    ]]></literal>
    <justification jstring="[hyper(225,a,224,a(flip),b,25160,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 224 25160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25195">
    <literal><![CDATA[
      1 / (x \ a(y,z,u)) = (a(y,z,u) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(225,a,219,a(flip),b,25160,a(flip))].">
      <j1 rule="hyper" parents="225 219 25160"/>
    </justification>
  </clause>

  <clause id="25196">
    <literal><![CDATA[
      ((x * a(x,y,z)) \ 1) \ 1 = (x \ 1) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(25064(a,1),25160(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25064 25160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25198">
    <literal><![CDATA[
      x * L(a(y,z,u) \ 1,a(y,z,u),x) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(788,a,25170,a)].">
      <j1 rule="hyper" parents="788 25170"/>
    </justification>
  </clause>

  <clause id="25199">
    <literal><![CDATA[
      (x \ y) / ((x \ y) / x) = 1 / (K(x,y) / x)
    ]]></literal>
    <justification jstring="[hyper(6145,a,25184,a)].">
      <j1 rule="hyper" parents="6145 25184"/>
    </justification>
  </clause>

  <clause id="25200">
    <literal><![CDATA[
      x \ K(x,x \ (x \ y)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(37,a,6094,a,b,25184,a(flip))].">
      <j1 rule="hyper" parents="37 6094 25184"/>
    </justification>
  </clause>

  <clause id="25201">
    <literal><![CDATA[
      K(x,x \ (x \ y)) = x * (K(x,y) / x)
    ]]></literal>
    <justification jstring="[hyper(157,a,25200,a),flip(a)].">
      <j1 rule="hyper" parents="157 25200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25202">
    <literal><![CDATA[
      x \ R(T(x,x \ (x \ y)),z,u) = x * R(K(x,y) / x,z,u)
    ]]></literal>
    <justification jstring="[para(25200(a,1),5770(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="25200 5770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25203">
    <literal><![CDATA[
      K(x,x \ (x \ (x * (L(y,z,u) \ y)))) = x * (1 / x)
    ]]></literal>
    <justification jstring="[para(23087(a,1),25201(a,2,2,1))].">
      <j1 rule="para" parents="23087 25201"/>
    </justification>
  </clause>

  <clause id="25204">
    <literal><![CDATA[
      R(x \ y,z,u) \ ((x \ y) * x) = y / R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,208,a(flip),b,25185,a)].">
      <j1 rule="hyper" parents="139 208 25185"/>
    </justification>
  </clause>

  <clause id="25205">
    <literal><![CDATA[
      (x * y) / R(y,z,u) = R(y,z,u) \ (y * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),25186(a,1,1,1))].">
      <j1 rule="para" parents="9 25186"/>
    </justification>
  </clause>

  <clause id="25206">
    <literal><![CDATA[
      x \ K(x,x \ a(y,z,u)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(64,a,6258,a(flip),b,25194,a)].">
      <j1 rule="hyper" parents="64 6258 25194"/>
    </justification>
  </clause>

  <clause id="25207">
    <literal><![CDATA[
      K(x,x \ a(y,z,u)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,1727,a,b,25206,a),flip(a)].">
      <j1 rule="hyper" parents="39 1727 25206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25208">
    <literal><![CDATA[
      K(x,x \ 1) * (a(y,z,u) \ w) = ((x \ a(y,z,u)) * x) \ w
    ]]></literal>
    <justification jstring="[para(25207(a,1),10843(a,1,1))].">
      <j1 rule="para" parents="25207 10843"/>
    </justification>
  </clause>

  <clause id="25209">
    <literal><![CDATA[
      L(1 / x,x,a(y,z,u)) = a(y,z,u) / (a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(40,a,4307,a,b,25195,a(flip))].">
      <j1 rule="hyper" parents="40 4307 25195"/>
    </justification>
  </clause>

  <clause id="25210">
    <literal><![CDATA[
      R(x,y,z) \ (x * (u * (x \ R(x,y,z)))) = R(u,x \ R(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2074,a(flip),b,25205,a),flip(a)].">
      <j1 rule="hyper" parents="64 2074 25205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25215">
    <literal><![CDATA[
      L(x \ ((((y \ z) \ z) \ z) \ u),x,y \ z) = (T(y \ z,y) * x) \ u
    ]]></literal>
    <justification jstring="[para(4679(a,1),23839(a,1,1,2,1))].">
      <j1 rule="para" parents="4679 23839"/>
    </justification>
  </clause>

  <clause id="25216">
    <literal><![CDATA[
      L(x \ y,x,z) = (z * x) \ (T(z,L(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(198(a,1),23840(a,2,1,1))].">
      <j1 rule="para" parents="198 23840"/>
    </justification>
  </clause>

  <clause id="25217">
    <literal><![CDATA[
      (x * (x * y)) \ (T(x,y) * z) = L((y * x) \ z,y * x,x)
    ]]></literal>
    <justification jstring="[para(4645(a,1),23840(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4645 23840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25218">
    <literal><![CDATA[
      T(a(x,y,z),u) = (a(x,y,z) \ w) \ T(w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(373,a,23127,a,b,23924,a)].">
      <j1 rule="hyper" parents="373 23127 23924"/>
    </justification>
  </clause>

  <clause id="25219">
    <literal><![CDATA[
      L(x,y,z * L(L(u,w,u),v5,v6)) = L(x,y,L(u,v5,v6) * z)
    ]]></literal>
    <justification jstring="[para(13628(a,1),23987(a,1,3,2))].">
      <j1 rule="para" parents="13628 23987"/>
    </justification>
  </clause>

  <clause id="25230">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(w,v5,v6)) = x * (y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(24064(a,1),23053(a,2,2))].">
      <j1 rule="para" parents="24064 23053"/>
    </justification>
  </clause>

  <clause id="25231">
    <literal><![CDATA[
      (x * L(y,z,u)) * K(y,L(w,v5,v6)) = x * L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(23430(a,1),24064(a,2,2))].">
      <j1 rule="para" parents="23430 24064"/>
    </justification>
  </clause>

  <clause id="25232">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(24069(a,1),623(a,1)),flip(b)].">
      <j1 rule="para" parents="24069 623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25233">
    <literal><![CDATA[
      R(x,y,z / u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(24151(a,1),672(a,1))].">
      <j1 rule="para" parents="24151 672"/>
    </justification>
  </clause>

  <clause id="25234">
    <literal><![CDATA[
      K(x * y,x) * (x * (y * z)) = R(x,y,x) * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[para(5017(a,1),24349(a,1,2))].">
      <j1 rule="para" parents="5017 24349"/>
    </justification>
  </clause>

  <clause id="25235">
    <literal><![CDATA[
      (1 / x) * a(x,y,z) = a(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(16056(a,1),24637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16056 24637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25236">
    <literal><![CDATA[
      a(x,y,z) * (1 / x) = a(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(23777,a,25235,a)].">
      <j1 rule="hyper" parents="23777 25235"/>
    </justification>
  </clause>

  <clause id="25237">
    <literal><![CDATA[
      (x * (x * y)) \ (x * a(x,z,u)) = L(y,x,x) \ (a(x,z,u) / x)
    ]]></literal>
    <justification jstring="[para(25235(a,1),1366(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25235 1366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25238">
    <literal><![CDATA[
      T(x * a(y,z,x),x \ 1) = (x \ 1) \ a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(493,a,9435,a(flip),b,24642,a)].">
      <j1 rule="hyper" parents="493 9435 24642"/>
    </justification>
  </clause>

  <clause id="25239">
    <literal><![CDATA[
      (x * a(y,z,x)) \ a(y,z,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,9435,a(flip),b,24642,a)].">
      <j1 rule="hyper" parents="139 9435 24642"/>
    </justification>
  </clause>

  <clause id="25240">
    <literal><![CDATA[
      L((x \ 1) \ y,1 / x,(1 / x) \ a(z,u,x)) = a(z,u,x) \ (((1 / x) \ a(z,u,x)) * y)
    ]]></literal>
    <justification jstring="[para(25239(a,1),11100(a,1,1,1))].">
      <j1 rule="para" parents="25239 11100"/>
    </justification>
  </clause>

  <clause id="25241">
    <literal><![CDATA[
      L(x,y,R(z,u,u \ 1)) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,24835,a(flip),b,24664,a),flip(a)].">
      <j1 rule="hyper" parents="373 24835 24664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25242">
    <literal><![CDATA[
      L(x,y,L((z * z) \ u,w,w)) = L(x,y,R(u,w,w \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,2195,a(flip),b,25241,a),flip(a)].">
      <j1 rule="hyper" parents="64 2195 25241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25243">
    <literal><![CDATA[
      L(x,L(y,z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(593(a,1),24745(a,1,3))].">
      <j1 rule="para" parents="593 24745"/>
    </justification>
  </clause>

  <clause id="25244">
    <literal><![CDATA[
      R(L(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(R(x,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(14169(a,1),25243(a,1))].">
      <j1 rule="para" parents="14169 25243"/>
    </justification>
  </clause>

  <clause id="25245">
    <literal><![CDATA[
      L(x \ y,x,x) = K(z,u) \ ((K(z,u) / x) * y)
    ]]></literal>
    <justification jstring="[hyper(759,a,24907,a),flip(a)].">
      <j1 rule="hyper" parents="759 24907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25246">
    <literal><![CDATA[
      (x * y) \ L(K(z,u) * T(x,y),y,y) = L(T(y \ K(z,u),x),x,y)
    ]]></literal>
    <justification jstring="[para(24954(a,1),17468(a,1,2))].">
      <j1 rule="para" parents="24954 17468"/>
    </justification>
  </clause>

  <clause id="25247">
    <literal><![CDATA[
      R(T(x,y * z),x,x) \ ((x \ y) * z) = T(x \ ((x \ y) * z),x)
    ]]></literal>
    <justification jstring="[para(25027(a,1),4648(a,1,1))].">
      <j1 rule="para" parents="25027 4648"/>
    </justification>
  </clause>

  <clause id="25248">
    <literal><![CDATA[
      (x \ y) * T(x,x \ 1) = x \ T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3898,a(flip),b,25039,a)].">
      <j1 rule="hyper" parents="64 3898 25039"/>
    </justification>
  </clause>

  <clause id="25249">
    <literal><![CDATA[
      x \ T(x * (x * y),x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),25248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 25248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25250">
    <literal><![CDATA[
      x * (y * T(x,x \ 1)) = T(x * (x * y),x)
    ]]></literal>
    <justification jstring="[hyper(157,a,25249,a)].">
      <j1 rule="hyper" parents="157 25249"/>
    </justification>
  </clause>

  <clause id="25251">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * y = T((y * x) * y,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,25249,a(flip),b,5434,a)].">
      <j1 rule="hyper" parents="144 25249 5434"/>
    </justification>
  </clause>

  <clause id="25252">
    <literal><![CDATA[
      (x * y) * R(x,x * y,x) = x * (y * T(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,4741,a,b,25250,a)].">
      <j1 rule="hyper" parents="373 4741 25250"/>
    </justification>
  </clause>

  <clause id="25253">
    <literal><![CDATA[
      T(x,x \ 1) * (y * x) = T(x * (x * y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3890,a,b,25250,a)].">
      <j1 rule="hyper" parents="64 3890 25250"/>
    </justification>
  </clause>

  <clause id="25254">
    <literal><![CDATA[
      T((x * (y / x)) * x,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2510,a(flip),b,25251,a),flip(a)].">
      <j1 rule="hyper" parents="64 2510 25251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25255">
    <literal><![CDATA[
      (x * y) * T(y,y \ x) = T(y * (y * x),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8883,a(flip),b,25253,a)].">
      <j1 rule="hyper" parents="64 8883 25253"/>
    </justification>
  </clause>

  <clause id="25256">
    <literal><![CDATA[
      R(x,y,z) * (u * T(x,x \ 1)) = ((x * (u / x)) * x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(25254(a,1),23681(a,1,2))].">
      <j1 rule="para" parents="25254 23681"/>
    </justification>
  </clause>

  <clause id="25257">
    <literal><![CDATA[
      ((x * (y / x)) * x) * x = T(x * (x * y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4766,a,b,25255,a)].">
      <j1 rule="hyper" parents="64 4766 25255"/>
    </justification>
  </clause>

  <clause id="25258">
    <literal><![CDATA[
      T(x * (x * y),x) / x = (x * (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(142,a,25255,a(flip),b,4766,a)].">
      <j1 rule="hyper" parents="142 25255 4766"/>
    </justification>
  </clause>

  <clause id="25259">
    <literal><![CDATA[
      ((x * ((R(x,y,z) * (x \ u)) / x)) * x) * x = T(x * (R(x,y,z) * u),x)
    ]]></literal>
    <justification jstring="[para(1902(a,1),25257(a,2,1,2))].">
      <j1 rule="para" parents="1902 25257"/>
    </justification>
  </clause>

  <clause id="25260">
    <literal><![CDATA[
      K(x,(y * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (y \ u)) = w
    ]]></literal>
    <justification jstring="[para(79(a,1),25232(a,1,2,1,2))].">
      <j1 rule="para" parents="79 25232"/>
    </justification>
  </clause>

  <clause id="25261">
    <literal><![CDATA[
      L(((x \ 1) * y) \ z,(x \ 1) * y,x * y) = K(u,w) \ ((K(u,w) / ((x \ 1) * y)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2211,a(flip),b,25245,a)].">
      <j1 rule="hyper" parents="64 2211 25245"/>
    </justification>
  </clause>

  <clause id="25263">
    <literal><![CDATA[
      K(x,T(y \ (z * u),u)) = K(x,u / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(8699,a,23044,a),flip(a)].">
      <j1 rule="hyper" parents="8699 23044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25265">
    <literal><![CDATA[
      K(x \ ((y * z) / y),T(((y * z) / y) \ (x * z),y)) = K(x \ z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,11517,a(flip),b,23044,a),flip(a)].">
      <j1 rule="hyper" parents="64 11517 23044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25266">
    <literal><![CDATA[
      K(x,T(y \ (z * u),u)) = K(x,(y / u) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,24710,a(flip),b,25263,a),flip(a)].">
      <j1 rule="hyper" parents="373 24710 25263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25269">
    <literal><![CDATA[
      x * K(y,T(z,u * x)) = K(y,T(z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(35,a,22755,a,b,23067,a),flip(a)].">
      <j1 rule="hyper" parents="35 22755 23067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25271">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(35,a,7953,a,b,25269,a)].">
      <j1 rule="hyper" parents="35 7953 25269"/>
    </justification>
  </clause>

  <clause id="25272">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(35,a,7879,a,b,25269,a)].">
      <j1 rule="hyper" parents="35 7879 25269"/>
    </justification>
  </clause>

  <clause id="25273">
    <literal><![CDATA[
      K(x * y,T(z,u * y)) = K(y * x,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,11186,a(flip),b,25269,a),flip(a)].">
      <j1 rule="hyper" parents="35 11186 25269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25274">
    <literal><![CDATA[
      K(x,T(y,z * u)) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[hyper(269,a,25269,a(flip),b,17088,a),flip(a)].">
      <j1 rule="hyper" parents="269 25269 17088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25275">
    <literal><![CDATA[
      K(x * T(y,z),T(u,y * w)) = K(T(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(17111,a,25271,a),flip(a)].">
      <j1 rule="hyper" parents="17111 25271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25276">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17025,a,b,25271,a),flip(a)].">
      <j1 rule="hyper" parents="373 17025 25271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25277">
    <literal><![CDATA[
      T(x,T(T(y,z),u)) = T(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(143,a,25271,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 25271 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25278">
    <literal><![CDATA[
      K(x \ T(y,z),T(u,y * w)) = K(T(y,z) / x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17101,a(flip),b,25271,a),flip(a)].">
      <j1 rule="hyper" parents="64 17101 25271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25279">
    <literal><![CDATA[
      K(x,T(y \ z,z * u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8756,a(flip),b,25271,a),flip(a)].">
      <j1 rule="hyper" parents="64 8756 25271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25280">
    <literal><![CDATA[
      K(x \ y,T(z,u * x)) = K(y / x,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8284,a(flip),b,25271,a),flip(a)].">
      <j1 rule="hyper" parents="64 8284 25271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25281">
    <literal><![CDATA[
      K(x,T(y \ z,y * u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8218,a(flip),b,25271,a),flip(a)].">
      <j1 rule="hyper" parents="64 8218 25271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25282">
    <literal><![CDATA[
      K(x,T(y / z,z * u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(278(a,1),25271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="278 25271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25283">
    <literal><![CDATA[
      T(x,T(T(y,z),u)) = T(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(143,a,25272,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 25272 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25284">
    <literal><![CDATA[
      K(x,T(y * z,u * z)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11139,a(flip),b,25272,a),flip(a)].">
      <j1 rule="hyper" parents="64 11139 25272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25285">
    <literal><![CDATA[
      K(x,T(y \ z,u * y)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8218,a(flip),b,25272,a),flip(a)].">
      <j1 rule="hyper" parents="64 8218 25272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25286">
    <literal><![CDATA[
      K(x,T(y,z * (u * w))) = T(K(x,T(T(y,z),w)),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25272,a(flip),b,25274,a)].">
      <j1 rule="hyper" parents="64 25272 25274"/>
    </justification>
  </clause>

  <clause id="25287">
    <literal><![CDATA[
      K(x,T(y,z * (u * w))) = T(K(x,T(T(y,u),w)),z)
    ]]></literal>
    <justification jstring="[para(25272(a,2),25274(a,2,1))].">
      <j1 rule="para" parents="25272 25274"/>
    </justification>
  </clause>

  <clause id="25288">
    <literal><![CDATA[
      T(x,T(T(y,z),u)) = T(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(143,a,25276,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 25276 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25289">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u)) = T(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17472,a,b,25277,a)].">
      <j1 rule="hyper" parents="64 17472 25277"/>
    </justification>
  </clause>

  <clause id="25290">
    <literal><![CDATA[
      T(x,T(y * K(z,y),u)) = T(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8244,a,b,25277,a)].">
      <j1 rule="hyper" parents="64 8244 25277"/>
    </justification>
  </clause>

  <clause id="25291">
    <literal><![CDATA[
      T(x,T(y / z,u * y)) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8757,a(flip),b,25277,a),flip(a)].">
      <j1 rule="hyper" parents="64 8757 25277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25292">
    <literal><![CDATA[
      T(x,T(y / z,u * z)) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(117(a,1),25277(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="117 25277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25293">
    <literal><![CDATA[
      T((1 / x) * y,T(x,y * z)) = T((1 / x) * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17503,a(flip),b,25283,a),flip(a)].">
      <j1 rule="hyper" parents="64 17503 25283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25294">
    <literal><![CDATA[
      T(x,T(y \ z,u * y)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8243,a(flip),b,25283,a),flip(a)].">
      <j1 rule="hyper" parents="64 8243 25283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25295">
    <literal><![CDATA[
      T(x,T(y / z,y \ u)) = T(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8757,a(flip),b,25288,a),flip(a)].">
      <j1 rule="hyper" parents="64 8757 25288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25298">
    <literal><![CDATA[
      K((x / y) * z,T(u,y)) = K(z * (x / y),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,17090,a(flip),b,25273,a),flip(a)].">
      <j1 rule="hyper" parents="64 17090 25273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25300">
    <literal><![CDATA[
      K(x,T(y \ z,u * (w * z))) = K(x,T(z / y,u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,21358,a,b,25279,a)].">
      <j1 rule="hyper" parents="64 21358 25279"/>
    </justification>
  </clause>

  <clause id="25301">
    <literal><![CDATA[
      K(x,T((y * z) \ u,y * (z * w))) = K(x,T(u / (y * z),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,21356,a(flip),b,25281,a)].">
      <j1 rule="hyper" parents="64 21356 25281"/>
    </justification>
  </clause>

  <clause id="25302">
    <literal><![CDATA[
      K(x,(y * z) * R(u,y,z)) = K(x,T(z * (u * y),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,11134,a(flip),b,25284,a)].">
      <j1 rule="hyper" parents="64 11134 25284"/>
    </justification>
  </clause>

  <clause id="25303">
    <literal><![CDATA[
      T(x * K(y,x),T(y,z * u)) = T(T(x,K(y,u)),K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7847,a(flip),b,25289,a),flip(a)].">
      <j1 rule="hyper" parents="64 7847 25289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25304">
    <literal><![CDATA[
      T(x,T(T(y,z) / u,y * w)) = T(x,T(u \ T(y,z),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18270,a(flip),b,25295,a)].">
      <j1 rule="hyper" parents="64 18270 25295"/>
    </justification>
  </clause>

  <clause id="25305">
    <literal><![CDATA[
      T(x,y \ (a(z,u,w) \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,23734,a(flip),b,23128,a),flip(a)].">
      <j1 rule="hyper" parents="373 23734 23128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25307">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(y,z,u) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,23151,a(flip),b,25305,a)].">
      <j1 rule="hyper" parents="64 23151 25305"/>
    </justification>
  </clause>

  <clause id="25308">
    <literal><![CDATA[
      T(x \ (a(y,z,u) \ x),w) = x \ (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(55,a,25305,a)].">
      <j1 rule="hyper" parents="55 25305"/>
    </justification>
  </clause>

  <clause id="25309">
    <literal><![CDATA[
      T(x,a(y,z,u) \ (a(y,z,u) \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15869,a(flip),b,25307,a)].">
      <j1 rule="hyper" parents="64 15869 25307"/>
    </justification>
  </clause>

  <clause id="25310">
    <literal><![CDATA[
      x / (a(y,z,u) * a(y,z,u)) = (a(y,z,u) * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,25307,a(flip),b,18765,a),flip(a)].">
      <j1 rule="hyper" parents="139 25307 18765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25311">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * u = u * (a(x,y,z) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(25307(a,1),15867(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25307 15867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25312">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * (u \ (a(x,y,z) \ 1)) = u \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(25307(a,1),18776(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25307 18776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25313">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(41,a,15893,a,b,25309,a),flip(a)].">
      <j1 rule="hyper" parents="41 15893 25309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25314">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(23138(a,1),25309(a,1,2,2))].">
      <j1 rule="para" parents="23138 25309"/>
    </justification>
  </clause>

  <clause id="25315">
    <literal><![CDATA[
      T(x / (a(y,z,u) \ w),a(y,z,u) * w) = (a(y,z,u) \ w) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,25313,a),flip(a)].">
      <j1 rule="hyper" parents="467 25313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25316">
    <literal><![CDATA[
      T(x,a(y,z,u) * a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,379,a(flip),b,25313,a),flip(a)].">
      <j1 rule="hyper" parents="64 379 25313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25317">
    <literal><![CDATA[
      (a(x,y,z) \ u) * T(w,a(x,y,z) * u) = w * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(145,a,25313,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 25313 22"/>
    </justification>
  </clause>

  <clause id="25318">
    <literal><![CDATA[
      T(a(x,y,z) * a(x,y,z),u) = a(x,y,z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(55,a,25316,a)].">
      <j1 rule="hyper" parents="55 25316"/>
    </justification>
  </clause>

  <clause id="25319">
    <literal><![CDATA[
      ((a(x,y,z) * a(x,y,z)) \ u) * (a(x,y,z) * w) = u * ((1 / a(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[para(25316(a,1),1454(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25316 1454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25320">
    <literal><![CDATA[
      (a(x,x,y) * a(x,x,y)) \ (z \ y) = z \ ((1 / a(x,x,y)) * L(y,x,x))
    ]]></literal>
    <justification jstring="[para(25316(a,1),5569(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25316 5569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25321">
    <literal><![CDATA[
      T(x,y * a(z,u,w)) / x = K(x,y / a(z,u,w))
    ]]></literal>
    <justification jstring="[para(25314(a,1),19338(a,1,1))].">
      <j1 rule="para" parents="25314 19338"/>
    </justification>
  </clause>

  <clause id="25322">
    <literal><![CDATA[
      x \ (L(y,z,u) * a(w,v5,v6)) = x \ (a(w,v5,v6) * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,23183,a,b,10,a)].">
      <j1 rule="hyper" parents="139 23183 10"/>
    </justification>
  </clause>

  <clause id="25325">
    <literal><![CDATA[
      K(x,T((y * z) \ u,(y \ u) * w)) = K(x,T((y \ u) / z,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,25279,a(flip),b,23394,a),flip(a)].">
      <j1 rule="hyper" parents="373 25279 23394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25327">
    <literal><![CDATA[
      K(x,T(y \ (z \ u),K(w,v5))) = K(x,T(u / (z * y),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17180,a(flip),b,23394,a),flip(a)].">
      <j1 rule="hyper" parents="64 17180 23394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25328">
    <literal><![CDATA[
      (x \ L(T(y,z),u,w)) * K(z,y) = x \ L(y,u,w)
    ]]></literal>
    <justification jstring="[hyper(6897,a,23442,a)].">
      <j1 rule="hyper" parents="6897 23442"/>
    </justification>
  </clause>

  <clause id="25329">
    <literal><![CDATA[
      (x \ L(y,z,u)) * (K(y,w) * v5) = (x \ L(T(y,w),z,u)) * v5
    ]]></literal>
    <justification jstring="[hyper(144,a,23442,a(flip),b,23278,a),flip(a)].">
      <j1 rule="hyper" parents="144 23442 23278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25330">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * K(y,z) = y \ L(T(y,z),x,x)
    ]]></literal>
    <justification jstring="[para(5665(a,2),23442(a,1,1))].">
      <j1 rule="para" parents="5665 23442"/>
    </justification>
  </clause>

  <clause id="25332">
    <literal><![CDATA[
      K(x,T(y / (z * u),z * w)) = K(x,T(z \ (y / u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,25282,a(flip),b,23505,a),flip(a)].">
      <j1 rule="hyper" parents="64 25282 23505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25333">
    <literal><![CDATA[
      K(x,T(y \ (z * u),w * y)) = K(x,T(z / (y / u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,25285,a,b,23506,a)].">
      <j1 rule="hyper" parents="64 25285 23506"/>
    </justification>
  </clause>

  <clause id="25334">
    <literal><![CDATA[
      T(R(x,x \ y,z),u) \ (y * z) = K(u,x) * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(649(a,1),23508(a,1,2)),flip(a)].">
      <j1 rule="para" parents="649 23508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25335">
    <literal><![CDATA[
      T(R(x,y,(x * y) \ z),u) \ z = K(u,x) * (y * ((x * y) \ z))
    ]]></literal>
    <justification jstring="[para(420(a,1),23508(a,1,2)),flip(a)].">
      <j1 rule="para" parents="420 23508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25336">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * v5) \ v6 = (v5 * L(a(x,y,z),u,w)) \ v6
    ]]></literal>
    <justification jstring="[hyper(62,a,23557,a)].">
      <j1 rule="hyper" parents="62 23557"/>
    </justification>
  </clause>

  <clause id="25337">
    <literal><![CDATA[
      (x * x) \ (y * ((y \ x) * x)) = a(y,y \ x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,15481,a(flip),b,23577,a)].">
      <j1 rule="hyper" parents="139 15481 23577"/>
    </justification>
  </clause>

  <clause id="25338">
    <literal><![CDATA[
      (x * (a(x,x,x) \ y)) \ y = (y * L(x,x,x)) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(6494(a,2),23618(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6494 23618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25340">
    <literal><![CDATA[
      T(x,T(y \ (z \ u),z * y)) = T(x,u / (z * y))
    ]]></literal>
    <justification jstring="[hyper(8856,a,23623,a),flip(a)].">
      <j1 rule="hyper" parents="8856 23623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25342">
    <literal><![CDATA[
      x / T(y * z,T(z \ (y \ x),u)) = T((y * z) \ x,K(y * z,u))
    ]]></literal>
    <justification jstring="[para(23623(a,1),8659(a,1,2))].">
      <j1 rule="para" parents="23623 8659"/>
    </justification>
  </clause>

  <clause id="25343">
    <literal><![CDATA[
      K(x,L(y,z,u) \ 1) * (y / (L(y,z,u) \ 1)) = y / T(L(y,z,u) \ 1,x)
    ]]></literal>
    <justification jstring="[para(23629(a,1),8679(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23629 8679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25344">
    <literal><![CDATA[
      (R(x,y,z) * (u / R(x,y,z))) * T(K(x,w),T(u,R(x,y,z))) = R(T(x,w),y,z) * (u / R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11109,a,b,23661,a)].">
      <j1 rule="hyper" parents="64 11109 23661"/>
    </justification>
  </clause>

  <clause id="25345">
    <literal><![CDATA[
      K(x,y) * (x \ (R(x,z,u) * w)) = x \ (R(T(x,y),z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(139,a,23661,a(flip),b,6133,a),flip(a)].">
      <j1 rule="hyper" parents="139 23661 6133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25347">
    <literal><![CDATA[
      K(x,y) * ((R(T(y,x),z,u) * w) * v5) = (R(y,z,u) * w) * v5
    ]]></literal>
    <justification jstring="[para(23661(a,1),23246(a,1,2,1))].">
      <j1 rule="para" parents="23661 23246"/>
    </justification>
  </clause>

  <clause id="25348">
    <literal><![CDATA[
      x \ R(T(x,y),z,z) = K(x,y) * a(x,z,z)
    ]]></literal>
    <justification jstring="[para(15987(a,1),23663(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15987 23663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25350">
    <literal><![CDATA[
      L(a(x,y,z),u,u * a(x,y,z)) \ 1 = (1 / (u * a(x,y,z))) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,920,a(flip),b,23785,a),flip(a)].">
      <j1 rule="hyper" parents="64 920 23785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25351">
    <literal><![CDATA[
      L(x * a(R(y \ z,u,w),x,x),x,R(z / y,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,9445,a(flip),b,23847,a),flip(a)].">
      <j1 rule="hyper" parents="373 9445 23847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25352">
    <literal><![CDATA[
      L(x,y,L(z,z \ u,u)) = L(x,y,u * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,2198,a(flip),b,23848,a),flip(a)].">
      <j1 rule="hyper" parents="64 2198 23848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25353">
    <literal><![CDATA[
      ((x / (y * x)) \ 1) \ y = y * ((y \ x) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3278,a(flip),b,23864,a),flip(a)].">
      <j1 rule="hyper" parents="64 3278 23864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25354">
    <literal><![CDATA[
      (x / (x * ((x \ y) / y))) * x = x / (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,3027,a(flip),b,23865,a)].">
      <j1 rule="hyper" parents="64 3027 23865"/>
    </justification>
  </clause>

  <clause id="25355">
    <literal><![CDATA[
      (x * x) * (1 / (((y \ z) / z) * y)) = (((y \ z) / z) * y) \ (x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,497,a,b,23866,a)].">
      <j1 rule="hyper" parents="64 497 23866"/>
    </justification>
  </clause>

  <clause id="25356">
    <literal><![CDATA[
      ((((x \ y) / y) * x) \ x) * x = (y / (x * y)) \ x
    ]]></literal>
    <justification jstring="[para(23866(a,1),2034(a,1,1))].">
      <j1 rule="para" parents="23866 2034"/>
    </justification>
  </clause>

  <clause id="25357">
    <literal><![CDATA[
      x / T((y * (z / (y * z))) * x,(z / (y * z)) \ (y \ 1)) = (x * (y * (z / (y * z)))) \ x
    ]]></literal>
    <justification jstring="[para(23874(a,2),14698(a,1,2,1))].">
      <j1 rule="para" parents="23874 14698"/>
    </justification>
  </clause>

  <clause id="25358">
    <literal><![CDATA[
      T((x / (y * x)) * (y * (x / (y * x))),K(y,z)) = (y * (x / (y * x))) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(23874(a,1),17574(a,1,1))].">
      <j1 rule="para" parents="23874 17574"/>
    </justification>
  </clause>

  <clause id="25359">
    <literal><![CDATA[
      ((x / y) \ 1) \ (y / x) = (x / y) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(139,a,2305,a(flip),b,23877,a(flip))].">
      <j1 rule="hyper" parents="139 2305 23877"/>
    </justification>
  </clause>

  <clause id="25360">
    <literal><![CDATA[
      R(1 / (x / y),x / y,x \ y) = (x / y) \ 1
    ]]></literal>
    <justification jstring="[hyper(40,a,15113,a,b,25359,a)].">
      <j1 rule="hyper" parents="40 15113 25359"/>
    </justification>
  </clause>

  <clause id="25361">
    <literal><![CDATA[
      R(1 / ((x \ y) / y),(x \ y) / y,x) = ((x \ y) / y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,23313,a(flip),b,25360,a)].">
      <j1 rule="hyper" parents="64 23313 25360"/>
    </justification>
  </clause>

  <clause id="25362">
    <literal><![CDATA[
      ((x \ 1) * (y \ L(y,z,u))) * x = (x \ 1) * (x * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(23882(a,1),1629(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23882 1629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25363">
    <literal><![CDATA[
      T(x * (((x \ 1) * (y \ L(y,z,u))) * x),x \ (x \ 1)) = x * (x * ((x \ 1) * (y \ L(y,z,u))))
    ]]></literal>
    <justification jstring="[para(23882(a,1),18778(a,2,2,2))].">
      <j1 rule="para" parents="23882 18778"/>
    </justification>
  </clause>

  <clause id="25364">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(4686,a,23891,a(flip))].">
      <j1 rule="hyper" parents="4686 23891"/>
    </justification>
  </clause>

  <clause id="25365">
    <literal><![CDATA[
      R(x,y * L(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13733,a(flip),b,25364,a)].">
      <j1 rule="hyper" parents="64 13733 25364"/>
    </justification>
  </clause>

  <clause id="25366">
    <literal><![CDATA[
      R(x,L(y,z,u) * y,x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13764,a,b,25365,a)].">
      <j1 rule="hyper" parents="64 13764 25365"/>
    </justification>
  </clause>

  <clause id="25367">
    <literal><![CDATA[
      a(x,y,z) * ((y * z) * (x \ 1)) = (y * z) * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2653(a,1),23930(a,1,1))].">
      <j1 rule="para" parents="2653 23930"/>
    </justification>
  </clause>

  <clause id="25369">
    <literal><![CDATA[
      L(x,y,z * ((u \ 1) * w)) = L(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,23995,a),flip(a)].">
      <j1 rule="hyper" parents="373 23253 23995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25371">
    <literal><![CDATA[
      L(x,y \ z,z \ y) = L(x,z \ y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11776,a(flip),b,24173,a)].">
      <j1 rule="hyper" parents="64 11776 24173"/>
    </justification>
  </clause>

  <clause id="25372">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((x \ y) * z) = L((y \ x) \ z,x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,102,a(flip),b,25371,a)].">
      <j1 rule="hyper" parents="373 102 25371"/>
    </justification>
  </clause>

  <clause id="25373">
    <literal><![CDATA[
      ((1 / (x \ y)) * (y \ x)) * L(z,x \ y,y \ x) = (1 / (x \ y)) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[para(25371(a,1),1651(a,1,2))].">
      <j1 rule="para" parents="25371 1651"/>
    </justification>
  </clause>

  <clause id="25374">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(x \ 1,u) = x * T(L(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(24180(a,1),16432(a,2,2))].">
      <j1 rule="para" parents="24180 16432"/>
    </justification>
  </clause>

  <clause id="25375">
    <literal><![CDATA[
      (x \ y) / ((x \ 1) * y) = (x * y) \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1682,a(flip),b,24198,a),flip(a)].">
      <j1 rule="hyper" parents="373 1682 24198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25376">
    <literal><![CDATA[
      K(x,y / (z * (z * y))) = K(x,y \ (z \ (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,21457,a,b,24208,a)].">
      <j1 rule="hyper" parents="64 21457 24208"/>
    </justification>
  </clause>

  <clause id="25377">
    <literal><![CDATA[
      K(x \ (T(x,y) \ 1),z) * a(z,(x * T(x,y)) \ 1,z) = K(z / (x * T(x,y)),z)
    ]]></literal>
    <justification jstring="[para(24255(a,1),14677(a,1,1))].">
      <j1 rule="para" parents="24255 14677"/>
    </justification>
  </clause>

  <clause id="25378">
    <literal><![CDATA[
      T(x * R(T(y,z),u,w),K(z,y)) = K(y,z) * (x * R(y,u,w))
    ]]></literal>
    <justification jstring="[para(23499(a,1),24265(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23499 24265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25379">
    <literal><![CDATA[
      K(x,y) * (z / (u * K(x,y))) = T(z,K(x,y)) / u
    ]]></literal>
    <justification jstring="[hyper(64,a,23224,a(flip),b,24270,a)].">
      <j1 rule="hyper" parents="64 23224 24270"/>
    </justification>
  </clause>

  <clause id="25380">
    <literal><![CDATA[
      T(x,K(y,z)) / (u * K(z,y)) = K(y,z) * (x / u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23224,a(flip),b,24274,a),flip(a)].">
      <j1 rule="hyper" parents="373 23224 24274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25383">
    <literal><![CDATA[
      T(x * (K(y,z) * u),K(y,z)) = K(y,z) * (x * T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(8160(a,1),24285(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8160 24285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25385">
    <literal><![CDATA[
      K(x,y) * (z * (u * (w \ K(y,x)))) = T(z * (u * (w \ 1)),K(x,y))
    ]]></literal>
    <justification jstring="[para(24286(a,1),24285(a,1,2,2))].">
      <j1 rule="para" parents="24286 24285"/>
    </justification>
  </clause>

  <clause id="25386">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * K(u,w)) = x * ((y * z) * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,403,a(flip),b,24291,a)].">
      <j1 rule="hyper" parents="64 403 24291"/>
    </justification>
  </clause>

  <clause id="25388">
    <literal><![CDATA[
      R(x,y,z) * ((y * z) * K(u,w)) = (x * y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[para(20(a,2),24291(a,1,1))].">
      <j1 rule="para" parents="20 24291"/>
    </justification>
  </clause>

  <clause id="25389">
    <literal><![CDATA[
      (x * (y * z)) * (a(x,y,z) * K(u,w)) = (x * y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[para(212(a,1),24291(a,1,1))].">
      <j1 rule="para" parents="212 24291"/>
    </justification>
  </clause>

  <clause id="25390">
    <literal><![CDATA[
      (x \ y) * (z * K(u * u,x)) = (T(x,u * u) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,24348,a(flip),b,24292,a),flip(a)].">
      <j1 rule="hyper" parents="64 24348 24292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25391">
    <literal><![CDATA[
      T(x,y \ (z * (u / T(z,w)))) = T(x,(y \ T(u,z)) * K(w,z))
    ]]></literal>
    <justification jstring="[para(24302(a,1),15952(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24302 15952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25392">
    <literal><![CDATA[
      x \ (y * (z * (u * K(w,v5)))) = (x \ (y * (z * u))) * K(w,v5)
    ]]></literal>
    <justification jstring="[para(23053(a,1),24304(a,1,2,2))].">
      <j1 rule="para" parents="23053 24304"/>
    </justification>
  </clause>

  <clause id="25393">
    <literal><![CDATA[
      (x \ (y * (z * (u \ 1)))) * K(w,v5) = x \ (y * (z * (u \ K(w,v5))))
    ]]></literal>
    <justification jstring="[para(24286(a,1),24304(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="24286 24304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25394">
    <literal><![CDATA[
      K(x * x,y) * (z \ T(y,u)) = z \ T(y,x \ (x \ u))
    ]]></literal>
    <justification jstring="[para(17576(a,1),24322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17576 24322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25396">
    <literal><![CDATA[
      (x \ y) * T(x,K(y,z)) = y * K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,9126,a(flip),b,24323,a)].">
      <j1 rule="hyper" parents="145 9126 24323"/>
    </justification>
  </clause>

  <clause id="25398">
    <literal><![CDATA[
      T(x \ (y * z),K(y,z)) * u = K(y,z) * ((x \ (z * y)) * u)
    ]]></literal>
    <justification jstring="[para(15222(a,1),24354(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15222 24354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25400">
    <literal><![CDATA[
      K(x,y) * ((L(x,z,u) \ 1) * w) = (L(x,z,u) \ K(x,y)) * w
    ]]></literal>
    <justification jstring="[para(7877(a,1),24362(a,1,1))].">
      <j1 rule="para" parents="7877 24362"/>
    </justification>
  </clause>

  <clause id="25402">
    <literal><![CDATA[
      (K(x,y) * ((z * u) * w)) / (u * w) = R(K(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(142,a,24373,a(flip),b,111,a)].">
      <j1 rule="hyper" parents="142 24373 111"/>
    </justification>
  </clause>

  <clause id="25403">
    <literal><![CDATA[
      K(x,T(y * z,z)) * (y \ R(y,y,z)) = (z / T(y * z,x)) * y
    ]]></literal>
    <justification jstring="[para(1989(a,1),24440(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1989 24440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25404">
    <literal><![CDATA[
      (x * (y * K(x,z))) * T(x,y) = (T(x,y) * y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,11912,a(flip),b,24480,a),flip(a)].">
      <j1 rule="hyper" parents="373 11912 24480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25405">
    <literal><![CDATA[
      (x * (y * (K(z,u) * w))) \ ((x * (y * K(z,u))) * w) = a(x,y,K(z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(139,a,24480,a,b,88,a)].">
      <j1 rule="hyper" parents="139 24480 88"/>
    </justification>
  </clause>

  <clause id="25406">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (K(u,w) * v5)) = K(x,(y * (K(u,w) / z)) * v5)
    ]]></literal>
    <justification jstring="[para(24480(a,1),19955(a,1,2))].">
      <j1 rule="para" parents="24480 19955"/>
    </justification>
  </clause>

  <clause id="25407">
    <literal><![CDATA[
      (x * (y * (z * K(u,w)))) * v5 = (x * (y * z)) * (K(u,w) * v5)
    ]]></literal>
    <justification jstring="[para(23053(a,1),24480(a,1,1,2))].">
      <j1 rule="para" parents="23053 24480"/>
    </justification>
  </clause>

  <clause id="25409">
    <literal><![CDATA[
      (x * L(y,z,u)) * (K(y,w) * v5) = (x * L(T(y,w),z,u)) * v5
    ]]></literal>
    <justification jstring="[para(23430(a,1),24480(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="23430 24480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25410">
    <literal><![CDATA[
      K(x,T(y,z)) * ((x \ z) \ u) = (T(x,y) \ z) \ u
    ]]></literal>
    <justification jstring="[para(8643(a,1),24481(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8643 24481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25411">
    <literal><![CDATA[
      K(x,T(y,z)) * ((u * z) \ w) = (u * (K(y,x) * z)) \ w
    ]]></literal>
    <justification jstring="[para(23252(a,1),24481(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23252 24481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25412">
    <literal><![CDATA[
      K(x,T(y,z)) * ((u \ z) \ w) = (u \ (K(y,x) * z)) \ w
    ]]></literal>
    <justification jstring="[para(23401(a,1),24481(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23401 24481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25413">
    <literal><![CDATA[
      (x / (y \ z)) * K(u,T(w,y)) = x / (y \ (K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(22758(a,1),24485(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22758 24485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25414">
    <literal><![CDATA[
      K(x,y) / T(z,K(y,x)) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(14442(a,1),24490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14442 24490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25415">
    <literal><![CDATA[
      K(x,y) / T(z,K(x,y)) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8153(a,1),25414(a,1,2))].">
      <j1 rule="para" parents="8153 25414"/>
    </justification>
  </clause>

  <clause id="25418">
    <literal><![CDATA[
      (x / y) * (K(z,T(u,y)) * w) = (x / (y * K(u,z))) * w
    ]]></literal>
    <justification jstring="[para(8194(a,1),24500(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8194 24500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25419">
    <literal><![CDATA[
      T((x * y) \ z,K(x,y)) \ u = K(x,y) * (((y * x) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(10833(a,1),24513(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10833 24513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25421">
    <literal><![CDATA[
      K(x \ y,x) * ((z * (u \ (x \ y))) \ w) = (z * (u \ (y / x))) \ w
    ]]></literal>
    <justification jstring="[para(15092(a,1),24525(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15092 24525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25422">
    <literal><![CDATA[
      (K(x,y) * (z * T(z,u))) \ w = K(y,x) * ((z * T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(22766(a,2),24525(a,1,1))].">
      <j1 rule="para" parents="22766 24525"/>
    </justification>
  </clause>

  <clause id="25423">
    <literal><![CDATA[
      K(x,y \ T(1 / z,u)) = K(x,y \ (T(z,u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,14627,a(flip),b,24546,a),flip(a)].">
      <j1 rule="hyper" parents="64 14627 24546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25425">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,u) \ w) = x * (L(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(145,a,24557,a(flip),b,6155,a)].">
      <j1 rule="hyper" parents="145 24557 6155"/>
    </justification>
  </clause>

  <clause id="25426">
    <literal><![CDATA[
      K(x,y) * ((L(y,z,u) \ w) * v5) = (L(T(y,x),z,u) \ w) * v5
    ]]></literal>
    <justification jstring="[hyper(144,a,24557,a(flip),b,23225,a),flip(a)].">
      <j1 rule="hyper" parents="144 24557 23225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25427">
    <literal><![CDATA[
      L(T(x,y),z,z) \ x = K(y,x) * a(z,z,x)
    ]]></literal>
    <justification jstring="[para(1243(a,1),24557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1243 24557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25428">
    <literal><![CDATA[
      K(x,y * (x \ 1)) * a(x,x,y * (x \ 1)) = ((x \ 1) * R(y,x,x)) \ (y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(3952(a,1),25427(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3952 25427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25429">
    <literal><![CDATA[
      T(x,y) * (a(z,u,w) * (R(T(x,y),v5,v6) \ v7)) = x * (a(z,u,w) * (R(x,v5,v6) \ v7))
    ]]></literal>
    <justification jstring="[para(24564(a,1),22824(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="24564 22824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25430">
    <literal><![CDATA[
      (R(x,y,z) \ u) \ (K(x,w) * v5) = (R(T(x,w),y,z) \ u) \ v5
    ]]></literal>
    <justification jstring="[para(24564(a,1),23222(a,1,1))].">
      <j1 rule="para" parents="24564 23222"/>
    </justification>
  </clause>

  <clause id="25431">
    <literal><![CDATA[
      K(x,y) * (x \ (R(y,z,u) \ w)) = x \ (R(T(y,x),z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(139,a,24565,a(flip),b,6133,a),flip(a)].">
      <j1 rule="hyper" parents="139 24565 6133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25433">
    <literal><![CDATA[
      R(x,y,z) \ (R(T(T(x,u),w),y,z) * v5) = K(x,u) * (K(T(x,u),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(139,a,24566,a(flip),b,24566,a)].">
      <j1 rule="hyper" parents="139 24566 24566"/>
    </justification>
  </clause>

  <clause id="25434">
    <literal><![CDATA[
      T(x,y / (z * (z * y))) = T(x,y \ (z \ (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,21459,a,b,24569,a)].">
      <j1 rule="hyper" parents="64 21459 24569"/>
    </justification>
  </clause>

  <clause id="25435">
    <literal><![CDATA[
      (x * T(x \ y,y \ (x * z))) / y = K(y / x,z / (y / x))
    ]]></literal>
    <justification jstring="[para(24581(a,1),5732(a,1,1,2))].">
      <j1 rule="para" parents="24581 5732"/>
    </justification>
  </clause>

  <clause id="25436">
    <literal><![CDATA[
      T(x \ y,(y / x) \ z) = T(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,18941,a(flip),b,24582,a),flip(a)].">
      <j1 rule="hyper" parents="373 18941 24582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25437">
    <literal><![CDATA[
      T(T(x / y,x \ y),z * (y \ x)) = T(x / y,x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,9631,a,b,24583,a)].">
      <j1 rule="hyper" parents="64 9631 24583"/>
    </justification>
  </clause>

  <clause id="25438">
    <literal><![CDATA[
      ((x / y) * R(y,z,u)) / x = x \ ((x / y) * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(23544(a,1),24587(a,1,2))].">
      <j1 rule="para" parents="23544 24587"/>
    </justification>
  </clause>

  <clause id="25439">
    <literal><![CDATA[
      R(x \ R(T(x,y),z,u),x,y) = (R(x,z,u) * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(24588(a,1),10307(a,1,1))].">
      <j1 rule="para" parents="24588 10307"/>
    </justification>
  </clause>

  <clause id="25441">
    <literal><![CDATA[
      (R(x,y,z) * u) / T(x,u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,25042,a(flip),b,24609,a),flip(a)].">
      <j1 rule="hyper" parents="373 25042 24609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25443">
    <literal><![CDATA[
      (x * (a(y,z,u) \ 1)) * x = x * (x * (a(y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(145,a,24636,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 24636 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25445">
    <literal><![CDATA[
      a(x,y,z) * L(u,z,a(x,y,z) * z) = (a(x,y,z) / z) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,24661,a(flip),b,11067,a)].">
      <j1 rule="hyper" parents="145 24661 11067"/>
    </justification>
  </clause>

  <clause id="25446">
    <literal><![CDATA[
      (K(x,y) * (z \ 1)) * ((x * z) \ T(x,K(z,y))) = ((z \ 1) * K(x,y)) * L(z \ 1,z,x)
    ]]></literal>
    <justification jstring="[para(9044(a,1),24679(a,1,2))].">
      <j1 rule="para" parents="9044 24679"/>
    </justification>
  </clause>

  <clause id="25447">
    <literal><![CDATA[
      K(x,y / x) * (L(x \ y,z,u) * w) = L(y / x,z,u) * w
    ]]></literal>
    <justification jstring="[para(117(a,1),24680(a,1,2,1,1))].">
      <j1 rule="para" parents="117 24680"/>
    </justification>
  </clause>

  <clause id="25448">
    <literal><![CDATA[
      (L(T(x,y),z,u) * w) \ (x * y) = (L(x,z,u) * w) \ (y * x)
    ]]></literal>
    <justification jstring="[para(24680(a,1),14885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24680 14885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25449">
    <literal><![CDATA[
      (L(T(x,y),z,u) / w) \ T(x,y) = (L(x,z,u) / w) \ x
    ]]></literal>
    <justification jstring="[para(24685(a,1),14833(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24685 14833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25450">
    <literal><![CDATA[
      T((x / L(y,z,u)) * a(y,x / L(y,z,u),y),y) = x / L(T(y,(x / L(y,z,u)) * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15566,a,b,24686,a)].">
      <j1 rule="hyper" parents="64 15566 24686"/>
    </justification>
  </clause>

  <clause id="25452">
    <literal><![CDATA[
      T(x,y * (z / (u \ w))) = T(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,25009,a(flip),b,24690,a),flip(a)].">
      <j1 rule="hyper" parents="64 25009 24690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25453">
    <literal><![CDATA[
      (x * (y * z)) / T(y * x,z) = (y * x) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(9(a,1),24713(a,1,2,2))].">
      <j1 rule="para" parents="9 24713"/>
    </justification>
  </clause>

  <clause id="25454">
    <literal><![CDATA[
      (x * y) / T((z \ u) * x,(u \ z) * y) = ((z \ u) * x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(22657(a,1),24713(a,1,2))].">
      <j1 rule="para" parents="22657 24713"/>
    </justification>
  </clause>

  <clause id="25455">
    <literal><![CDATA[
      (x * L(y,z,u)) / (y * x) = (y * x) \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(23697(a,1),24713(a,1,2))].">
      <j1 rule="para" parents="23697 24713"/>
    </justification>
  </clause>

  <clause id="25456">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) / u = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(23591(a,1),24721(a,1,2))].">
      <j1 rule="para" parents="23591 24721"/>
    </justification>
  </clause>

  <clause id="25457">
    <literal><![CDATA[
      (R(x,y,z) * (x \ u)) / u = u \ (R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[para(23720(a,1),24721(a,1,2))].">
      <j1 rule="para" parents="23720 24721"/>
    </justification>
  </clause>

  <clause id="25459">
    <literal><![CDATA[
      K(x,y / ((z \ y) * u)) = K(x,T(u,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,15828,a(flip),b,24722,a),flip(a)].">
      <j1 rule="hyper" parents="373 15828 24722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25460">
    <literal><![CDATA[
      K(x,y / T(T(z \ u,z) * w,K(z,u))) = K(x,(u / (y / (w * K(z \ u,z)))) \ z)
    ]]></literal>
    <justification jstring="[para(8730(a,2),24722(a,1,2,2))].">
      <j1 rule="para" parents="8730 24722"/>
    </justification>
  </clause>

  <clause id="25461">
    <literal><![CDATA[
      K(x,T(y,z) \ (z / u)) = K(x,z / (u * y))
    ]]></literal>
    <justification jstring="[para(82(a,1),25459(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="82 25459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25462">
    <literal><![CDATA[
      K(x,y / (z * (u * y))) = K(x,u \ (y \ (y / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,24210,a(flip),b,25461,a),flip(a)].">
      <j1 rule="hyper" parents="64 24210 25461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25463">
    <literal><![CDATA[
      T(((x \ y) / z) \ u,(y / (u * z)) \ x) = ((x \ y) / z) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,319,a(flip),b,24726,a),flip(a)].">
      <j1 rule="hyper" parents="64 319 24726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25464">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) / u) = K(x,z / (u * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,25461,a(flip),b,24730,a),flip(a)].">
      <j1 rule="hyper" parents="64 25461 24730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25465">
    <literal><![CDATA[
      K(x,y \ (T(z,y) / u)) = K(x,z / (u * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,24729,a(flip),b,25464,a)].">
      <j1 rule="hyper" parents="64 24729 25464"/>
    </justification>
  </clause>

  <clause id="25466">
    <literal><![CDATA[
      K(x,y / (z * z)) = K(x,z \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,21286,a(flip),b,25465,a),flip(a)].">
      <j1 rule="hyper" parents="64 21286 25465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25467">
    <literal><![CDATA[
      K(x,L(y,z,u) \ (T(w,y) / v5)) = K(x,w / (v5 * L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(23153(a,1),25465(a,1,2,2,1))].">
      <j1 rule="para" parents="23153 25465"/>
    </justification>
  </clause>

  <clause id="25469">
    <literal><![CDATA[
      K(x,(y \ T(z,u \ w)) * (w \ u)) = K(x,y \ ((u \ w) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,21286,a(flip),b,24732,a),flip(a)].">
      <j1 rule="hyper" parents="64 21286 24732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25470">
    <literal><![CDATA[
      T(x \ (y * L(x,z,u)),K(w,x * (L(x,z,u) * y))) = T(x,y) \ (L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(24777(a,1),18272(a,1,1))].">
      <j1 rule="para" parents="24777 18272"/>
    </justification>
  </clause>

  <clause id="25471">
    <literal><![CDATA[
      R(x,y,y \ z) * T(z,u) = (x * y) * (y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(144,a,110,a(flip),b,24870,a)].">
      <j1 rule="hyper" parents="144 110 24870"/>
    </justification>
  </clause>

  <clause id="25472">
    <literal><![CDATA[
      (x * (L(T(y,z),u,w) \ y)) / y = (x * (L(y,u,w) \ y)) / T(y,z)
    ]]></literal>
    <justification jstring="[para(24684(a,1),24870(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="24684 24870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25473">
    <literal><![CDATA[
      K(x,x \ 1) / (x * y) = 1 / (L(x,x,x) * y)
    ]]></literal>
    <justification jstring="[para(118(a,1),24878(a,2,2,1))].">
      <j1 rule="para" parents="118 24878"/>
    </justification>
  </clause>

  <clause id="25474">
    <literal><![CDATA[
      T(x,x \ y) * ((x \ (x \ y)) * z) = x * ((x \ (y / x)) * z)
    ]]></literal>
    <justification jstring="[para(4473(a,1),24898(a,1,2,1))].">
      <j1 rule="para" parents="4473 24898"/>
    </justification>
  </clause>

  <clause id="25475">
    <literal><![CDATA[
      x * ((x * x) \ L(x,y,z)) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,897,a(flip),b,24917,a)].">
      <j1 rule="hyper" parents="64 897 24917"/>
    </justification>
  </clause>

  <clause id="25476">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u,z) = T(K(x,y) * u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,24763,a(flip),b,24920,a),flip(a)].">
      <j1 rule="hyper" parents="64 24763 24920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25477">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,z) = K(x,y) * T(u,z)
    ]]></literal>
    <justification jstring="[hyper(41,a,22873,a,b,25476,a(flip))].">
      <j1 rule="hyper" parents="41 22873 25476"/>
    </justification>
  </clause>

  <clause id="25479">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,u)) = K(x,y) * T(z,T(x,u))
    ]]></literal>
    <justification jstring="[para(7467(a,1),25476(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7467 25476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25480">
    <literal><![CDATA[
      T(K(x,y) * z,u * u) = K(x,y) * T(z,u * u)
    ]]></literal>
    <justification jstring="[para(17031(a,1),25476(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17031 25476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25482">
    <literal><![CDATA[
      K(x,y) * T(z \ 1,z) = T(z \ K(x,y),z)
    ]]></literal>
    <justification jstring="[para(14665(a,1),25477(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14665 25477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25483">
    <literal><![CDATA[
      (x * (y / x)) \ ((y / x) * R((x \ y) \ y,z,u)) = y \ (R(x,z,u) * (x \ y))
    ]]></literal>
    <justification jstring="[para(845(a,1),24926(a,2,2))].">
      <j1 rule="para" parents="845 24926"/>
    </justification>
  </clause>

  <clause id="25484">
    <literal><![CDATA[
      ((x \ y) \ y) * (y \ (x \ y)) = x * (y \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(869,a,24927,a)].">
      <j1 rule="hyper" parents="869 24927"/>
    </justification>
  </clause>

  <clause id="25485">
    <literal><![CDATA[
      K(x,y * z) * ((1 / y) \ u) = (K(z * y,x) / y) \ u
    ]]></literal>
    <justification jstring="[para(11127(a,1),24929(a,1,1))].">
      <j1 rule="para" parents="11127 24929"/>
    </justification>
  </clause>

  <clause id="25486">
    <literal><![CDATA[
      (x / y) * (y * ((K(z,u) / y) \ w)) = (x / (1 / y)) * (K(u,z) * w)
    ]]></literal>
    <justification jstring="[para(24930(a,1),819(a,1,2))].">
      <j1 rule="para" parents="24930 819"/>
    </justification>
  </clause>

  <clause id="25488">
    <literal><![CDATA[
      T((x * (y / x)) \ z,K(x,y)) = T(z / (x * (y / x)),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11896,a,b,24939,a)].">
      <j1 rule="hyper" parents="373 11896 24939"/>
    </justification>
  </clause>

  <clause id="25489">
    <literal><![CDATA[
      (x \ K(y,y \ 1)) * (y * z) = (x \ 1) * (R(y,y,y) * z)
    ]]></literal>
    <justification jstring="[para(1417(a,1),24942(a,2,2,1))].">
      <j1 rule="para" parents="1417 24942"/>
    </justification>
  </clause>

  <clause id="25490">
    <literal><![CDATA[
      (x * ((y * z) / y)) * (y * z) = (x * z) * (y * ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(9(a,1),24944(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 24944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25491">
    <literal><![CDATA[
      R(x,T(y,z),T(y,z) \ u) = ((x * y) * (y \ u)) / u
    ]]></literal>
    <justification jstring="[hyper(142,a,24946,a(flip),b,421,a),flip(a)].">
      <j1 rule="hyper" parents="142 24946 421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25492">
    <literal><![CDATA[
      x * (x * (K(y,x) / x)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(6369(a,1),24955(a,1,2))].">
      <j1 rule="para" parents="6369 24955"/>
    </justification>
  </clause>

  <clause id="25493">
    <literal><![CDATA[
      x * (x * (1 / T(x,y))) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5799(a,1),25492(a,1,2,2))].">
      <j1 rule="para" parents="5799 25492"/>
    </justification>
  </clause>

  <clause id="25494">
    <literal><![CDATA[
      (x \ 1) \ K(x \ y,x) = x * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(8880(a,1),25493(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8880 25493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25495">
    <literal><![CDATA[
      ((x / (x / y)) \ 1) \ 1 = y * K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14456,a,b,25494,a)].">
      <j1 rule="hyper" parents="64 14456 25494"/>
    </justification>
  </clause>

  <clause id="25496">
    <literal><![CDATA[
      1 / (x \ T(x * y,y)) = (x / (x / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(225,a,6347,a,b,25495,a)].">
      <j1 rule="hyper" parents="225 6347 25495"/>
    </justification>
  </clause>

  <clause id="25497">
    <literal><![CDATA[
      T(x / (x / y),y \ 1) = x \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,8474,a,b,25496,a)].">
      <j1 rule="hyper" parents="37 8474 25496"/>
    </justification>
  </clause>

  <clause id="25498">
    <literal><![CDATA[
      T(x / (x / (y \ z)),z \ y) = x \ T(x * (y \ z),y \ z)
    ]]></literal>
    <justification jstring="[hyper(6757,a,25497,a)].">
      <j1 rule="hyper" parents="6757 25497"/>
    </justification>
  </clause>

  <clause id="25499">
    <literal><![CDATA[
      ((x * y) \ x) * T(T(x,y),y) = ((y * x) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(6981(a,1),24957(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6981 24957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25500">
    <literal><![CDATA[
      (x / (y * T(z,u))) * T((y * z) / y,u) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,10626,a,b,24959,a)].">
      <j1 rule="hyper" parents="64 10626 24959"/>
    </justification>
  </clause>

  <clause id="25501">
    <literal><![CDATA[
      T(x * x,y) * ((z * T(x * x,y)) \ u) = z \ u
    ]]></literal>
    <justification jstring="[hyper(373,a,491,a(flip),b,24966,a),flip(a)].">
      <j1 rule="hyper" parents="373 491 24966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25503">
    <literal><![CDATA[
      K(x,K(y,z * (u * (u * w)))) = K(x,K(y,z * w))
    ]]></literal>
    <justification jstring="[para(9(a,1),25018(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 25018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25504">
    <literal><![CDATA[
      ((x * x) \ (y * R(y \ x,z,u))) * x = (1 / x) * (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(25041(a,1),1051(a,2,2))].">
      <j1 rule="para" parents="25041 1051"/>
    </justification>
  </clause>

  <clause id="25505">
    <literal><![CDATA[
      (x * x) * ((a(y,z,u) / x) / w) = ((1 / x) \ a(y,z,u)) / w
    ]]></literal>
    <justification jstring="[para(25057(a,1),807(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25057 807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25506">
    <literal><![CDATA[
      x * (x * (a(y,z,u) / x)) = R(x,x,x) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(25059(a,1),3684(a,1,2))].">
      <j1 rule="para" parents="25059 3684"/>
    </justification>
  </clause>

  <clause id="25507">
    <literal><![CDATA[
      T(x,((y / z) / y) * u) = T(x,(y \ (z \ y)) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,24987,a,b,25072,a)].">
      <j1 rule="hyper" parents="373 24987 25072"/>
    </justification>
  </clause>

  <clause id="25508">
    <literal><![CDATA[
      T(T(x,y) * K(z,T(x \ 1,y)),x \ 1) = T(T(x,y) \ 1,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,9409,a(flip),b,25081,a),flip(a)].">
      <j1 rule="hyper" parents="373 9409 25081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25509">
    <literal><![CDATA[
      x / T(y * K(z,y),u * u) = (x / T(y,u * u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(25089(a,2),7099(a,1,2))].">
      <j1 rule="para" parents="25089 7099"/>
    </justification>
  </clause>

  <clause id="25510">
    <literal><![CDATA[
      T(x * K(y,z),u * u) \ w = K(z,y) * (T(x,u * u) \ w)
    ]]></literal>
    <justification jstring="[para(25089(a,2),23272(a,1,1))].">
      <j1 rule="para" parents="25089 23272"/>
    </justification>
  </clause>

  <clause id="25511">
    <literal><![CDATA[
      x * (R(x,y,y \ 1) \ x) = a(x,y,y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(38,a,25155,a,b,25102,a)].">
      <j1 rule="hyper" parents="38 25155 25102"/>
    </justification>
  </clause>

  <clause id="25512">
    <literal><![CDATA[
      L(x,y,(K(z,u) / w) * v5) = L(x,y,K(z,u) * (w * v5))
    ]]></literal>
    <justification jstring="[para(24361(a,1),25131(a,1,3))].">
      <j1 rule="para" parents="24361 25131"/>
    </justification>
  </clause>

  <clause id="25513">
    <literal><![CDATA[
      R(K(x,y) / z,z,u) = u / (z * (K(y,x) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,24421,a,b,25137,a)].">
      <j1 rule="hyper" parents="373 24421 25137"/>
    </justification>
  </clause>

  <clause id="25514">
    <literal><![CDATA[
      R(K(x,y * z) / z,z,y) = y / T(z * y,x)
    ]]></literal>
    <justification jstring="[para(14643(a,1),25513(a,2,2))].">
      <j1 rule="para" parents="14643 25513"/>
    </justification>
  </clause>

  <clause id="25515">
    <literal><![CDATA[
      R(K(x,y) / z,z,z \ u) = (z \ u) / (K(y,T(x,z)) * u)
    ]]></literal>
    <justification jstring="[para(22776(a,1),25513(a,2,2))].">
      <j1 rule="para" parents="22776 25513"/>
    </justification>
  </clause>

  <clause id="25516">
    <literal><![CDATA[
      R(x \ K(x,x \ y),x,y) = y / T(x * y,x)
    ]]></literal>
    <justification jstring="[para(14978(a,1),25514(a,1,1))].">
      <j1 rule="para" parents="14978 25514"/>
    </justification>
  </clause>

  <clause id="25517">
    <literal><![CDATA[
      T(x,y) / T(y,y \ 1) = (y \ (x / y)) * y
    ]]></literal>
    <justification jstring="[hyper(41,a,3878,a,b,25146,a)].">
      <j1 rule="hyper" parents="41 3878 25146"/>
    </justification>
  </clause>

  <clause id="25518">
    <literal><![CDATA[
      T(x,y) / R(y,y,y) = (y \ (x / y)) * y
    ]]></literal>
    <justification jstring="[para(1417(a,1),25517(a,1,2))].">
      <j1 rule="para" parents="1417 25517"/>
    </justification>
  </clause>

  <clause id="25519">
    <literal><![CDATA[
      (R(x,y,y) \ x) * (z * z) = a(x,y,y) \ (z * z)
    ]]></literal>
    <justification jstring="[para(16007(a,2),25169(a,1,1))].">
      <j1 rule="para" parents="16007 25169"/>
    </justification>
  </clause>

  <clause id="25520">
    <literal><![CDATA[
      (L(x,y,z) \ u) * (K(x,x \ u) * w) = (u / L(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,25183,a(flip),b,23278,a),flip(a)].">
      <j1 rule="hyper" parents="144 25183 23278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25521">
    <literal><![CDATA[
      (x / L(y,z,u)) \ T(L(y,z,u) \ x,w) = K(y \ x,y) * K(L(y,z,u) \ x,w)
    ]]></literal>
    <justification jstring="[para(25183(a,1),15048(a,1,1))].">
      <j1 rule="para" parents="25183 15048"/>
    </justification>
  </clause>

  <clause id="25522">
    <literal><![CDATA[
      K(x,T(y,z * (u * w))) = K(x,T(y,u * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,25286,a,b,25287,a)].">
      <j1 rule="hyper" parents="373 25286 25287"/>
    </justification>
  </clause>

  <clause id="25523">
    <literal><![CDATA[
      (x * y) \ (y * ((z \ (a(u,w,v5) \ z)) * T(x,y))) = L(z \ (a(u,w,v5) \ z),x,y)
    ]]></literal>
    <justification jstring="[para(25308(a,1),10981(a,2,1))].">
      <j1 rule="para" parents="25308 10981"/>
    </justification>
  </clause>

  <clause id="25524">
    <literal><![CDATA[
      K(x,y / a(z,u,w)) = K(x,y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(5849,a,25321,a),flip(a)].">
      <j1 rule="hyper" parents="5849 25321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25525">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) = K(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(19286,a,25524,a)].">
      <j1 rule="hyper" parents="19286 25524"/>
    </justification>
  </clause>

  <clause id="25526">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) = K(x,a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,19247,a,b,25525,a),flip(a)].">
      <j1 rule="hyper" parents="373 19247 25525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25527">
    <literal><![CDATA[
      K(x,a(y,z,u) * (w * a(y,z,u))) = K(x,w)
    ]]></literal>
    <justification jstring="[para(23138(a,1),25526(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23138 25526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25528">
    <literal><![CDATA[
      a(x,x,y) \ K(y,z) = y \ L(T(y,z),x,x)
    ]]></literal>
    <justification jstring="[hyper(14603,a,25330,a)].">
      <j1 rule="hyper" parents="14603 25330"/>
    </justification>
  </clause>

  <clause id="25529">
    <literal><![CDATA[
      T(x,T((y \ z) / u,y)) = T(x,z / (y * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,25294,a(flip),b,25340,a)].">
      <j1 rule="hyper" parents="64 25294 25340"/>
    </justification>
  </clause>

  <clause id="25530">
    <literal><![CDATA[
      T(x,y / (z * (z * u))) = T(x,z \ ((z \ y) / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,23684,a(flip),b,25529,a),flip(a)].">
      <j1 rule="hyper" parents="64 23684 25529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25531">
    <literal><![CDATA[
      T(x,T((y \ z) * u,y)) = T(x,z / (y * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14950,a(flip),b,25529,a)].">
      <j1 rule="hyper" parents="64 14950 25529"/>
    </justification>
  </clause>

  <clause id="25532">
    <literal><![CDATA[
      ((x * ((x \ y) / y)) \ x) * x = x / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(23868(a,1),25354(a,1,1))].">
      <j1 rule="para" parents="23868 25354"/>
    </justification>
  </clause>

  <clause id="25533">
    <literal><![CDATA[
      (((x \ y) / y) \ 1) * x = (y / (x * y)) \ x
    ]]></literal>
    <justification jstring="[para(2311(a,1),25356(a,1,1))].">
      <j1 rule="para" parents="2311 25356"/>
    </justification>
  </clause>

  <clause id="25534">
    <literal><![CDATA[
      ((x * y) \ ((1 / x) \ y)) \ (x \ y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(215,a,25375,a)].">
      <j1 rule="hyper" parents="215 25375"/>
    </justification>
  </clause>

  <clause id="25535">
    <literal><![CDATA[
      K(x,y) * (z / (u / T(y,x))) = T(z,K(x,y)) / (u / y)
    ]]></literal>
    <justification jstring="[para(6245(a,1),25379(a,1,2,2))].">
      <j1 rule="para" parents="6245 25379"/>
    </justification>
  </clause>

  <clause id="25536">
    <literal><![CDATA[
      T(x,K(y,z)) / T(u,K(y,z)) = (K(y,z) * (x / u)) * K(z,y)
    ]]></literal>
    <justification jstring="[para(25380(a,1),24490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25380 24490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25537">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) * T((x * K(y,z)) \ y,K(y,z) * x) = y * K((x * K(y,z)) \ y,T(x * K(y,z),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11106,a,b,25396,a)].">
      <j1 rule="hyper" parents="64 11106 25396"/>
    </justification>
  </clause>

  <clause id="25538">
    <literal><![CDATA[
      T(x,y * (z * (u \ (u / w)))) = T(x,y * (z / w))
    ]]></literal>
    <justification jstring="[para(82(a,1),25452(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="82 25452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25539">
    <literal><![CDATA[
      K(x,y \ (z \ (z \ y))) = K(x,z \ (y \ (y / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,25376,a(flip),b,25462,a)].">
      <j1 rule="hyper" parents="64 25376 25462"/>
    </justification>
  </clause>

  <clause id="25540">
    <literal><![CDATA[
      K(x,(x * x) \ L(x,y,z)) * (x \ ((((x * x) \ L(x,y,z)) * x) * u)) = x \ ((L(x,y,z) * (1 / x)) * u)
    ]]></literal>
    <justification jstring="[para(25475(a,1),10856(a,2,2,1))].">
      <j1 rule="para" parents="25475 10856"/>
    </justification>
  </clause>

  <clause id="25541">
    <literal><![CDATA[
      T(K(x,y) \ z,u * u) = K(y,x) * T(z,u * u)
    ]]></literal>
    <justification jstring="[para(6156(a,2),25480(a,1,1))].">
      <j1 rule="para" parents="6156 25480"/>
    </justification>
  </clause>

  <clause id="25542">
    <literal><![CDATA[
      (x / T(y * y,z)) \ u = T(y * y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(12(a,1),25501(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12 25501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25543">
    <literal><![CDATA[
      ((x / y) / x) / T(1 / z,(x \ (y \ x)) * z) = (1 / z) \ ((x / y) / x)
    ]]></literal>
    <justification jstring="[para(25507(a,1),10797(a,1,2))].">
      <j1 rule="para" parents="25507 10797"/>
    </justification>
  </clause>

  <clause id="25544">
    <literal><![CDATA[
      R(1 / x,y,y \ 1) \ 1 = a(x,y,y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,2468,a,b,25511,a)].">
      <j1 rule="hyper" parents="64 2468 25511"/>
    </justification>
  </clause>

  <clause id="25545">
    <literal><![CDATA[
      (R(x,y,y) \ x) * ((z * z) * u) = (a(x,y,y) \ (z * z)) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,25519,a(flip),b,133,a),flip(a)].">
      <j1 rule="hyper" parents="144 25519 133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25546">
    <literal><![CDATA[
      K(x,T(y \ z,u * (y * w))) = K(x,T(z / y,u * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,25281,a(flip),b,25522,a),flip(a)].">
      <j1 rule="hyper" parents="373 25281 25522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25547">
    <literal><![CDATA[
      T(x,y \ (z \ (z \ y))) = T(x,z \ ((z \ y) / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,25434,a(flip),b,25530,a)].">
      <j1 rule="hyper" parents="64 25434 25530"/>
    </justification>
  </clause>

  <clause id="25548">
    <literal><![CDATA[
      T(x,T((y \ z) * u,y)) = T(x,z * (u / y))
    ]]></literal>
    <justification jstring="[hyper(373,a,22648,a(flip),b,25531,a),flip(a)].">
      <j1 rule="hyper" parents="373 22648 25531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25549">
    <literal><![CDATA[
      T(x \ 1,(x \ y) * z) = T(x \ 1,y * (z / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,7227,a(flip),b,25548,a)].">
      <j1 rule="hyper" parents="64 7227 25548"/>
    </justification>
  </clause>

  <clause id="25550">
    <literal><![CDATA[
      ((x / (y * x)) \ 1) * y = y / (x / (y * x))
    ]]></literal>
    <justification jstring="[para(3277(a,1),25532(a,1,1))].">
      <j1 rule="para" parents="3277 25532"/>
    </justification>
  </clause>

  <clause id="25551">
    <literal><![CDATA[
      R((x / (y * x)) \ 1,y,y) * (1 / (1 / y)) = R(y / (x / (y * x)),y,y \ 1)
    ]]></literal>
    <justification jstring="[para(25550(a,1),2021(a,2,1))].">
      <j1 rule="para" parents="25550 2021"/>
    </justification>
  </clause>

  <clause id="25552">
    <literal><![CDATA[
      K(x,y * y) * (K(z,u) * x) = T(K(u,z) \ x,y * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,17185,a,b,25541,a)].">
      <j1 rule="hyper" parents="373 17185 25541"/>
    </justification>
  </clause>

  <clause id="25553">
    <literal><![CDATA[
      (x / T(y * y,z)) * u = x * (T(y * y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(733,a,25542,a)].">
      <j1 rule="hyper" parents="733 25542"/>
    </justification>
  </clause>

  <clause id="25554">
    <literal><![CDATA[
      T(x \ 1,(x \ y) * z) = T(x \ 1,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,7228,a(flip),b,25549,a),flip(a)].">
      <j1 rule="hyper" parents="373 7228 25549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25555">
    <literal><![CDATA[
      R(a(x,y,z),u,u \ 1) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,24642,a(flip),b,23129,a),flip(a)].">
      <j1 rule="hyper" parents="64 24642 23129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25556">
    <literal><![CDATA[
      R(a(x,y,z),x,x \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,16056,a(flip),b,25555,a),flip(a)].">
      <j1 rule="hyper" parents="373 16056 25555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25557">
    <literal><![CDATA[
      a(x,y,z) * (1 / (1 / x)) = a(x,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(25556(a,1),3868(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25556 3868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25558">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * w) * u = w * (u * R(a(x,y,z),w,u))
    ]]></literal>
    <justification jstring="[para(23157(a,1),2736(a,1,1,1))].">
      <j1 rule="para" parents="23157 2736"/>
    </justification>
  </clause>

  <clause id="25559">
    <literal><![CDATA[
      (x * y) * K(1 / x,x * y) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,243,a(flip),b,23662,a),flip(a)].">
      <j1 rule="hyper" parents="64 243 23662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25562">
    <literal><![CDATA[
      (1 / (x \ y)) * ((y / x) \ z) = ((y / x) * (x \ y)) \ z
    ]]></literal>
    <justification jstring="[hyper(742,a,23976,a)].">
      <j1 rule="hyper" parents="742 23976"/>
    </justification>
  </clause>

  <clause id="25563">
    <literal><![CDATA[
      (x \ R(x,x,y)) * L(z,x,(x * y) \ y) = (y / (x * y)) * (x * z)
    ]]></literal>
    <justification jstring="[para(1986(a,2),23978(a,1,1))].">
      <j1 rule="para" parents="1986 23978"/>
    </justification>
  </clause>

  <clause id="25564">
    <literal><![CDATA[
      (x * y) * L(y,y,y * x) = (x / (1 / y)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1416,a(flip),b,24006,a),flip(a)].">
      <j1 rule="hyper" parents="64 1416 24006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25565">
    <literal><![CDATA[
      x * L(y,y,y * x) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(36,a,3184,a,b,25564,a(flip))].">
      <j1 rule="hyper" parents="36 3184 25564"/>
    </justification>
  </clause>

  <clause id="25566">
    <literal><![CDATA[
      L(x,x,x * y) = y \ (y / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(149,a,25565,a),flip(a)].">
      <j1 rule="hyper" parents="149 25565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25567">
    <literal><![CDATA[
      L(x,x,x * a(x,y,z)) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(35,a,25557,a,b,25565,a),flip(a)].">
      <j1 rule="hyper" parents="35 25557 25565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25568">
    <literal><![CDATA[
      L(x,x,x * ((x \ y) / y)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,3363,a(flip),b,25565,a),flip(a)].">
      <j1 rule="hyper" parents="35 3363 25565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25569">
    <literal><![CDATA[
      L(x * K(y,x),x,x * y) = (y / (1 / x)) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,25565,a(flip),b,5862,a),flip(a)].">
      <j1 rule="hyper" parents="142 25565 5862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25570">
    <literal><![CDATA[
      (x \ y) * L(x,x,y) = (x \ y) / (1 / x)
    ]]></literal>
    <justification jstring="[para(10(a,1),25565(a,1,2,3))].">
      <j1 rule="para" parents="10 25565"/>
    </justification>
  </clause>

  <clause id="25571">
    <literal><![CDATA[
      x * L(x \ y,x \ y,y) = x / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(23833(a,1),25565(a,1,2))].">
      <j1 rule="para" parents="23833 25565"/>
    </justification>
  </clause>

  <clause id="25572">
    <literal><![CDATA[
      (x / y) * L(y,y,x) = (x / y) / (1 / y)
    ]]></literal>
    <justification jstring="[para(24004(a,1),25565(a,1,2))].">
      <j1 rule="para" parents="24004 25565"/>
    </justification>
  </clause>

  <clause id="25573">
    <literal><![CDATA[
      L(x \ y,x \ y,(y / x) * (x / y)) = x \ y
    ]]></literal>
    <justification jstring="[para(14901(a,1),25568(a,1,3))].">
      <j1 rule="para" parents="14901 25568"/>
    </justification>
  </clause>

  <clause id="25574">
    <literal><![CDATA[
      L(x,x,x \ y) = L(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11068,a,b,25566,a)].">
      <j1 rule="hyper" parents="373 11068 25566"/>
    </justification>
  </clause>

  <clause id="25575">
    <literal><![CDATA[
      L(x * y,x * y,L(x,y,y)) = y \ (y / (1 / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,24838,a(flip),b,25566,a)].">
      <j1 rule="hyper" parents="64 24838 25566"/>
    </justification>
  </clause>

  <clause id="25576">
    <literal><![CDATA[
      x \ ((y \ (y / (1 / x))) \ x) = L(x,x,x * y) \ 1
    ]]></literal>
    <justification jstring="[para(25566(a,1),1848(a,1,2,1))].">
      <j1 rule="para" parents="25566 1848"/>
    </justification>
  </clause>

  <clause id="25577">
    <literal><![CDATA[
      T(L(x,x,x * y) \ 1,y / (1 / x)) = (y \ ((1 / x) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(25566(a,2),7658(a,1,1,1))].">
      <j1 rule="para" parents="25566 7658"/>
    </justification>
  </clause>

  <clause id="25578">
    <literal><![CDATA[
      (x \ L(x,x,x * y)) * ((y \ (y / (1 / x))) \ x) = 1
    ]]></literal>
    <justification jstring="[para(25566(a,1),9376(a,1,2,1))].">
      <j1 rule="para" parents="25566 9376"/>
    </justification>
  </clause>

  <clause id="25579">
    <literal><![CDATA[
      (K(x,(x * a(x,y,z)) \ 1) / (x * a(x,y,z))) * (x * x) = (x * (1 / (x * a(x,y,z)))) * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(25567(a,1),11336(a,2,2))].">
      <j1 rule="para" parents="25567 11336"/>
    </justification>
  </clause>

  <clause id="25580">
    <literal><![CDATA[
      L(x,L(L(y,y,z),y \ z,y \ z),u) = L(x,(y \ z) * ((y \ z) / (1 / y)),u)
    ]]></literal>
    <justification jstring="[para(25570(a,1),11778(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="25570 11778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25581">
    <literal><![CDATA[
      (x * y) / ((x * y) * (1 / x)) = (y / (1 / x)) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,11883,a(flip),b,25569,a)].">
      <j1 rule="hyper" parents="64 11883 25569"/>
    </justification>
  </clause>

  <clause id="25582">
    <literal><![CDATA[
      L(1 / x,y,y * x) \ (1 * R(1 \ L(1 / x,y,y * x),z,u)) = ((1 / (y * (x \ 1))) * y) \ R(L(1 / x,y,y * x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(24009(a,1),2744(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24009 2744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25583">
    <literal><![CDATA[
      ((x * y) / x) / L(z,z,y) = y * (K(x,y) / z)
    ]]></literal>
    <justification jstring="[hyper(373,a,14386,a(flip),b,24172,a),flip(a)].">
      <j1 rule="hyper" parents="373 14386 24172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25585">
    <literal><![CDATA[
      ((x * (x \ 1)) / x) / L(y \ (x \ y),y \ (x \ y),x \ 1) = (x \ 1) * ((y \ (x \ y)) \ 1)
    ]]></literal>
    <justification jstring="[para(7298(a,1),25583(a,2,2))].">
      <j1 rule="para" parents="7298 25583"/>
    </justification>
  </clause>

  <clause id="25586">
    <literal><![CDATA[
      T(x * y,x) * K(x,z) = y * R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(23657(a,1),24260(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23657 24260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25587">
    <literal><![CDATA[
      T((x * y) * K(x,z),x) = y * R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7812,a,b,25586,a)].">
      <j1 rule="hyper" parents="64 7812 25586"/>
    </justification>
  </clause>

  <clause id="25588">
    <literal><![CDATA[
      x * R(T(y,T(z,x)),x,y) = T(T(y,z) * x,y)
    ]]></literal>
    <justification jstring="[para(8047(a,1),25587(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8047 25587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25589">
    <literal><![CDATA[
      R(T((T(x * y,z) \ x) \ 1,(T(x * y,z) \ x) \ K(y * x,z)),T(x * y,z) \ x,K(y * x,z)) = L(y \ 1,y,x) \ K(y * x,z)
    ]]></literal>
    <justification jstring="[para(24326(a,1),5136(a,2,1))].">
      <j1 rule="para" parents="24326 5136"/>
    </justification>
  </clause>

  <clause id="25590">
    <literal><![CDATA[
      (K(x,y) * ((z \ u) / u)) * z = z * R(z \ K(x,y),z,z \ u)
    ]]></literal>
    <justification jstring="[hyper(144,a,24425,a(flip),b,853,a)].">
      <j1 rule="hyper" parents="144 24425 853"/>
    </justification>
  </clause>

  <clause id="25591">
    <literal><![CDATA[
      (x * (y * z)) \ (L(x,z,y) * (y * z)) = ((y * z) * x) \ (y * (z * x))
    ]]></literal>
    <justification jstring="[hyper(139,a,24785,a(flip),b,10853,a)].">
      <j1 rule="hyper" parents="139 24785 10853"/>
    </justification>
  </clause>

  <clause id="25592">
    <literal><![CDATA[
      L(x,y \ L(z,u,w),y) * L(z,u,w) = K(x,z) * (y * ((y \ L(z,u,w)) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,23383,a(flip),b,24786,a),flip(a)].">
      <j1 rule="hyper" parents="64 23383 24786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25593">
    <literal><![CDATA[
      (x * y) \ (x * R(y,x / z,z)) = a(y,x / z,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,24794,a(flip),b,10860,a(flip))].">
      <j1 rule="hyper" parents="139 24794 10860"/>
    </justification>
  </clause>

  <clause id="25594">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z \ x,z)) = a(y,x / z,z)
    ]]></literal>
    <justification jstring="[para(10204(a,1),25593(a,1,2,2))].">
      <j1 rule="para" parents="10204 25593"/>
    </justification>
  </clause>

  <clause id="25595">
    <literal><![CDATA[
      x * (L(x,y,y * x) \ 1) = a(y * x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1949,a(flip),b,24846,a),flip(a)].">
      <j1 rule="hyper" parents="373 1949 24846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25596">
    <literal><![CDATA[
      L(x,y,y * x) \ x = a(y * x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1846,a(flip),b,25595,a)].">
      <j1 rule="hyper" parents="64 1846 25595"/>
    </justification>
  </clause>

  <clause id="25597">
    <literal><![CDATA[
      a(x,y,x) * (L(R(x,y,x),z,z * R(x,y,x)) \ x) = a(z * R(x,y,x),z,R(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,13229,a,b,25596,a)].">
      <j1 rule="hyper" parents="64 13229 25596"/>
    </justification>
  </clause>

  <clause id="25598">
    <literal><![CDATA[
      a(x * y,x,y) \ y = L(y,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,25596,a)].">
      <j1 rule="hyper" parents="40 23134 25596"/>
    </justification>
  </clause>

  <clause id="25599">
    <literal><![CDATA[
      L(x \ 1,y,x * y) \ (x \ 1) = a(y * (x \ 1),y,x \ 1)
    ]]></literal>
    <justification jstring="[para(23997(a,1),25596(a,1,1))].">
      <j1 rule="para" parents="23997 25596"/>
    </justification>
  </clause>

  <clause id="25600">
    <literal><![CDATA[
      a((x * y) * x,x * y,x) \ x = L(x,x * y,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,24000,a(flip),b,25598,a),flip(a)].">
      <j1 rule="hyper" parents="373 24000 25598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25601">
    <literal><![CDATA[
      R(x,x \ y,y \ 1) \ K(z,u) = (x \ y) * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[para(79(a,1),24881(a,1,1,1))].">
      <j1 rule="para" parents="79 24881"/>
    </justification>
  </clause>

  <clause id="25602">
    <literal><![CDATA[
      R(T(L(x,y,z) / x,x * u),x,u) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,1326,a,b,24918,a)].">
      <j1 rule="hyper" parents="373 1326 24918"/>
    </justification>
  </clause>

  <clause id="25603">
    <literal><![CDATA[
      L(x,y,z) * R(u,x,x \ L(x,y,z)) = (x * u) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(39,a,11325,a,b,24918,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 11325 24918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25604">
    <literal><![CDATA[
      R(R(x,x,x),y,z) \ 1 = T(R(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24185,a(flip),b,25035,a),flip(a)].">
      <j1 rule="hyper" parents="64 24185 25035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25605">
    <literal><![CDATA[
      T(R(x,y,z) \ 1,x) = R((x \ 1) \ 1,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1418(a,1),25604(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1418 25604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25606">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,u) = L(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,24698,a,b,25051,a)].">
      <j1 rule="hyper" parents="373 24698 25051"/>
    </justification>
  </clause>

  <clause id="25607">
    <literal><![CDATA[
      (x * y) \ (R(x,z,z) * y) = L(a(x,z,z),x,y)
    ]]></literal>
    <justification jstring="[para(15987(a,1),25051(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15987 25051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25608">
    <literal><![CDATA[
      L(a(x,y,y),x,z) \ (R(x,y,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(40,a,23792,a,b,25607,a)].">
      <j1 rule="hyper" parents="40 23792 25607"/>
    </justification>
  </clause>

  <clause id="25609">
    <literal><![CDATA[
      L(a(x,y,y),x,R(x,y,y) \ z) \ z = x * (R(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),25608(a,1,2))].">
      <j1 rule="para" parents="10 25608"/>
    </justification>
  </clause>

  <clause id="25610">
    <literal><![CDATA[
      a(x,y,z) = R(x \ R(x,y,z),x,z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,23986,a,b,25606,a)].">
      <j1 rule="hyper" parents="373 23986 25606"/>
    </justification>
  </clause>

  <clause id="25611">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,u) = (u * x) \ (u * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,102,a(flip),b,25606,a),flip(a)].">
      <j1 rule="hyper" parents="373 102 25606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25612">
    <literal><![CDATA[
      R(x \ R(x,y \ z,y),x,z) = a(x,y \ z,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),25610(a,2,3)),flip(a)].">
      <j1 rule="para" parents="10 25610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25613">
    <literal><![CDATA[
      L((T(T(x,y),z) \ u) \ w,x \ u,x) = u \ (T(T(x,y),z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24626,a(flip),b,25053,a)].">
      <j1 rule="hyper" parents="64 24626 25053"/>
    </justification>
  </clause>

  <clause id="25614">
    <literal><![CDATA[
      L((((x * x) / y) \ z) \ u,((x * x) / y) \ z,(x * x) / y) = z \ (T((x * x) / y,K(y,w)) * u)
    ]]></literal>
    <justification jstring="[para(17052(a,1),25053(a,1,1,1,1))].">
      <j1 rule="para" parents="17052 25053"/>
    </justification>
  </clause>

  <clause id="25615">
    <literal><![CDATA[
      L(R(x,x,x),y,z) \ 1 = T(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24180,a(flip),b,25067,a),flip(a)].">
      <j1 rule="hyper" parents="64 24180 25067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25616">
    <literal><![CDATA[
      (L(R(x,x,x),y,z) \ u) \ K(T(L(x,y,z) \ 1,x),L(R(x,x,x),y,z)) = (L(L(R(x,x,x),y,z),L(R(x,x,x),y,z),L(R(x,x,x),y,z)) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(25615(a,1),14929(a,1,2,1))].">
      <j1 rule="para" parents="25615 14929"/>
    </justification>
  </clause>

  <clause id="25617">
    <literal><![CDATA[
      (x \ L(x,x,y)) \ y = R(y,x,L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,5635,a,b,25190,a)].">
      <j1 rule="hyper" parents="35 5635 25190"/>
    </justification>
  </clause>

  <clause id="25618">
    <literal><![CDATA[
      R(x,y,L(y,y,x)) \ x = y \ L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,2157,a,b,25617,a)].">
      <j1 rule="hyper" parents="40 2157 25617"/>
    </justification>
  </clause>

  <clause id="25619">
    <literal><![CDATA[
      K(x,x \ (x \ (x * (L(y,z,u) \ y)))) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,1724,a,b,25203,a),flip(a)].">
      <j1 rule="hyper" parents="373 1724 25203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25620">
    <literal><![CDATA[
      T((x * a(y,z,u)) / x,w) = (a(y,z,u) \ v5) \ T(v5,a(v6,v7,v8))
    ]]></literal>
    <justification jstring="[para(23161(a,2),25218(a,1,1))].">
      <j1 rule="para" parents="23161 25218"/>
    </justification>
  </clause>

  <clause id="25621">
    <literal><![CDATA[
      L(T(x,x \ 1),y,x) = R(x,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(606,a,25252,a)].">
      <j1 rule="hyper" parents="606 25252"/>
    </justification>
  </clause>

  <clause id="25622">
    <literal><![CDATA[
      R(x,x * ((y * x) \ y),x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,3801,a(flip),b,25621,a),flip(a)].">
      <j1 rule="hyper" parents="64 3801 25621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25623">
    <literal><![CDATA[
      L(R(x,x,x),y,x) = R(x,x * y,x)
    ]]></literal>
    <justification jstring="[para(1417(a,1),25621(a,1,1))].">
      <j1 rule="para" parents="1417 25621"/>
    </justification>
  </clause>

  <clause id="25624">
    <literal><![CDATA[
      L(R(x,x,x),x \ y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),25623(a,2,2))].">
      <j1 rule="para" parents="10 25623"/>
    </justification>
  </clause>

  <clause id="25625">
    <literal><![CDATA[
      L(R(x,y,x),x,x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(25624(a,1),4739(a,1,1))].">
      <j1 rule="para" parents="25624 4739"/>
    </justification>
  </clause>

  <clause id="25626">
    <literal><![CDATA[
      L(R(x,y,x),x,x) = y \ (x * ((x \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,101,a,b,25625,a),flip(a)].">
      <j1 rule="hyper" parents="373 101 25625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25627">
    <literal><![CDATA[
      (1 / x) * L(x,y \ x,y) = a(y,y \ x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,965,a(flip),b,25337,a)].">
      <j1 rule="hyper" parents="64 965 25337"/>
    </justification>
  </clause>

  <clause id="25628">
    <literal><![CDATA[
      a(x,x \ y,y) \ 1 = y \ L(y,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5590,a(flip),b,25627,a),flip(a)].">
      <j1 rule="hyper" parents="64 5590 25627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25629">
    <literal><![CDATA[
      L(x,y \ x,y) \ x = a(y,y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,5658,a,b,25628,a)].">
      <j1 rule="hyper" parents="40 5658 25628"/>
    </justification>
  </clause>

  <clause id="25630">
    <literal><![CDATA[
      a(x,x \ y,y) \ y = L(y,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,25629,a)].">
      <j1 rule="hyper" parents="40 23134 25629"/>
    </justification>
  </clause>

  <clause id="25631">
    <literal><![CDATA[
      L(x * y,x \ (x * y),x) = a(x,y,x * y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),25630(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 25630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25632">
    <literal><![CDATA[
      a(x,T(y,x),y * x) \ (y * x) = L(y * x,x \ (y * x),x)
    ]]></literal>
    <justification jstring="[para(22(a,2),25630(a,1,1,2))].">
      <j1 rule="para" parents="22 25630"/>
    </justification>
  </clause>

  <clause id="25633">
    <literal><![CDATA[
      (x * y) * (y \ T(z,x)) = z * R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23681,a(flip),b,25471,a),flip(a)].">
      <j1 rule="hyper" parents="64 23681 25471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25634">
    <literal><![CDATA[
      R(T(x / y,T(z,u)),y,y \ z) = T(z,u) \ (x * (y \ T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(36,a,1398,a,b,25471,a),flip(a)].">
      <j1 rule="hyper" parents="36 1398 25471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25635">
    <literal><![CDATA[
      (x * x) * (T(x,y) \ y) = y * R(x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(4632(a,2),25633(a,1,2))].">
      <j1 rule="para" parents="4632 25633"/>
    </justification>
  </clause>

  <clause id="25637">
    <literal><![CDATA[
      R(x,T(y,z),T(y,z) \ u) = R(x,y,y \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,110,a(flip),b,25491,a),flip(a)].">
      <j1 rule="hyper" parents="373 110 25491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25638">
    <literal><![CDATA[
      x * (x * (a(y,z,x) / x)) = (x \ 1) \ a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,9441,a(flip),b,25506,a),flip(a)].">
      <j1 rule="hyper" parents="373 9441 25506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25639">
    <literal><![CDATA[
      L(x,y,y) / (1 / y) = x / R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5894,a(flip),b,25559,a)].">
      <j1 rule="hyper" parents="64 5894 25559"/>
    </justification>
  </clause>

  <clause id="25640">
    <literal><![CDATA[
      L(x,1 / y,1 / y) / (1 / (1 / y)) = x / R(L(y,y,y),1 / y,x)
    ]]></literal>
    <justification jstring="[para(818(a,2),25639(a,2,2,1))].">
      <j1 rule="para" parents="818 25639"/>
    </justification>
  </clause>

  <clause id="25641">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z \ x,z)) = a(y,z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,25612,a(flip),b,25611,a),flip(a)].">
      <j1 rule="hyper" parents="64 25612 25611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25642">
    <literal><![CDATA[
      a(x,y / z,z) = a(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,25594,a(flip),b,25641,a)].">
      <j1 rule="hyper" parents="64 25594 25641"/>
    </justification>
  </clause>

  <clause id="25643">
    <literal><![CDATA[
      L(x \ (x / y),x,x) * y = a(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1394,a,b,25642,a)].">
      <j1 rule="hyper" parents="64 1394 25642"/>
    </justification>
  </clause>

  <clause id="25644">
    <literal><![CDATA[
      (x * y) \ ((x * (y / z)) * z) = a(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,92,a,b,25642,a)].">
      <j1 rule="hyper" parents="64 92 25642"/>
    </justification>
  </clause>

  <clause id="25645">
    <literal><![CDATA[
      x * a(x / y,z \ y,z) = ((x / y) * (y / z)) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,25642,a(flip),b,1289,a)].">
      <j1 rule="hyper" parents="145 25642 1289"/>
    </justification>
  </clause>

  <clause id="25646">
    <literal><![CDATA[
      (x * y) * a(x,z \ y,z) = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,25642,a(flip),b,92,a)].">
      <j1 rule="hyper" parents="145 25642 92"/>
    </justification>
  </clause>

  <clause id="25647">
    <literal><![CDATA[
      ((1 / x) * (x / y)) * y = a(x,y \ x,y)
    ]]></literal>
    <justification jstring="[para(569(a,1),25643(a,1,1))].">
      <j1 rule="para" parents="569 25643"/>
    </justification>
  </clause>

  <clause id="25648">
    <literal><![CDATA[
      a(x,y \ x,y) / y = (1 / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(154,a,25647,a)].">
      <j1 rule="hyper" parents="154 25647"/>
    </justification>
  </clause>

  <clause id="25649">
    <literal><![CDATA[
      L(x,y,(z * (z / u)) * u) = L(x,y,a(z,u \ z,u))
    ]]></literal>
    <justification jstring="[para(25647(a,1),2238(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25647 2238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25650">
    <literal><![CDATA[
      L(x,(y * (y / z)) * z,u) = L(x,a(y,z \ y,z),u)
    ]]></literal>
    <justification jstring="[para(25647(a,1),11889(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25647 11889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25651">
    <literal><![CDATA[
      a(x,y \ x,y) / y = x * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1217,a(flip),b,25648,a),flip(a)].">
      <j1 rule="hyper" parents="373 1217 25648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25652">
    <literal><![CDATA[
      x * (x * (y * ((y \ 1) / x))) = (x \ 1) \ a(y,x \ y,x)
    ]]></literal>
    <justification jstring="[para(25651(a,1),25638(a,1,2,2))].">
      <j1 rule="para" parents="25651 25638"/>
    </justification>
  </clause>

  <clause id="25653">
    <literal><![CDATA[
      a(x,y \ (x \ y),y) = x * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(36,a,23906,a(flip),b,25646,a(flip))].">
      <j1 rule="hyper" parents="36 23906 25646"/>
    </justification>
  </clause>

  <clause id="25654">
    <literal><![CDATA[
      K(x,x \ (L(y,z,u) \ y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,10168,a(flip),b,25619,a)].">
      <j1 rule="hyper" parents="64 10168 25619"/>
    </justification>
  </clause>

  <clause id="25656">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,u \ 1) = u * ((L(x,y,z) \ x) / u)
    ]]></literal>
    <justification jstring="[hyper(145,a,25654,a(flip),b,5961,a)].">
      <j1 rule="hyper" parents="145 25654 5961"/>
    </justification>
  </clause>

  <clause id="25659">
    <literal><![CDATA[
      T(x * K(y,z),x \ 1) = (x \ K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,14541,a(flip),b,22974,a),flip(a)].">
      <j1 rule="hyper" parents="64 14541 22974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25660">
    <literal><![CDATA[
      T(T(x * K(y,z),u),x \ 1) = T((x \ K(z,y)) \ 1,u)
    ]]></literal>
    <justification jstring="[para(25659(a,1),23(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25659 23"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25662">
    <literal><![CDATA[
      L(x,y,z) * (x \ K(u,w)) = K(u,w) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,19280,a,b,23064,a),flip(a)].">
      <j1 rule="hyper" parents="64 19280 23064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25663">
    <literal><![CDATA[
      L(a(x,x,y),a(x,x,y),z) \ z = (y \ L(y,x,x)) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,24818,a,b,23106,a),flip(a)].">
      <j1 rule="hyper" parents="373 24818 23106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25664">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ 1)) = R(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,23106,a(flip),b,11856,a(flip))].">
      <j1 rule="hyper" parents="145 23106 11856"/>
    </justification>
  </clause>

  <clause id="25666">
    <literal><![CDATA[
      (x * L(x \ y,x,y \ z)) \ y = y / (x * (((z / y) * x) \ z))
    ]]></literal>
    <justification jstring="[para(15002(a,1),23223(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15002 23223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25667">
    <literal><![CDATA[
      K(x,y) * ((R(y,z,u) * x) / y) = R(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25042,a(flip),b,23518,a),flip(a)].">
      <j1 rule="hyper" parents="373 25042 23518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25668">
    <literal><![CDATA[
      ((((x * y) / z) * L(z,y,x)) \ (x * y)) \ (x * y) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(373,a,3205,a(flip),b,23584,a),flip(a)].">
      <j1 rule="hyper" parents="373 3205 23584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25669">
    <literal><![CDATA[
      x / (((L(y,z,u) \ y) \ 1) * x) = x \ ((y \ L(y,z,u)) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9379,a,b,23593,a)].">
      <j1 rule="hyper" parents="64 9379 23593"/>
    </justification>
  </clause>

  <clause id="25670">
    <literal><![CDATA[
      x * L(R(y,x,y),z,u) = T(L(y,z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(11556(a,1),23614(a,1,2))].">
      <j1 rule="para" parents="11556 23614"/>
    </justification>
  </clause>

  <clause id="25671">
    <literal><![CDATA[
      x \ T(L(y,z,u) * x,y) = L(R(y,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(149,a,25670,a)].">
      <j1 rule="hyper" parents="149 25670"/>
    </justification>
  </clause>

  <clause id="25672">
    <literal><![CDATA[
      T(L(x,x,x) * y,x) = x * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(39,a,25626,a(flip),b,25671,a),flip(a)].">
      <j1 rule="hyper" parents="39 25626 25671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25673">
    <literal><![CDATA[
      x * (x * ((x \ y) * x)) = (x * y) * L(x,x,x)
    ]]></literal>
    <justification jstring="[para(25672(a,1),25139(a,1,2))].">
      <j1 rule="para" parents="25672 25139"/>
    </justification>
  </clause>

  <clause id="25674">
    <literal><![CDATA[
      K(x \ y,x) * (R(x \ y,z,u) \ w) = R(y / x,z,u) \ w
    ]]></literal>
    <justification jstring="[para(853(a,1),23660(a,1,1)),flip(a)].">
      <j1 rule="para" parents="853 23660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25676">
    <literal><![CDATA[
      x \ T(R(y,z,u) * x,y) = R(R(y,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11592,a(flip),b,23682,a),flip(a)].">
      <j1 rule="hyper" parents="64 11592 23682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25677">
    <literal><![CDATA[
      x * R(R(y,x,y),z,u) = T(R(y,z,u) * x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,11592,a(flip),b,23682,a(flip))].">
      <j1 rule="hyper" parents="145 11592 23682"/>
    </justification>
  </clause>

  <clause id="25678">
    <literal><![CDATA[
      x * R(T(x,x \ 1),y,z) = T(R(x,y,z) * x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1763,a,b,25677,a)].">
      <j1 rule="hyper" parents="64 1763 25677"/>
    </justification>
  </clause>

  <clause id="25679">
    <literal><![CDATA[
      x * R(T(x,x \ 1),y,z) = T(x * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(274(a,1),25678(a,2,1))].">
      <j1 rule="para" parents="274 25678"/>
    </justification>
  </clause>

  <clause id="25680">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) / u) / (1 / u) = (u \ (a(x,y,z) \ 1)) / (u \ 1)
    ]]></literal>
    <justification jstring="[para(23702(a,1),3691(a,1,1))].">
      <j1 rule="para" parents="23702 3691"/>
    </justification>
  </clause>

  <clause id="25681">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,u) = (u * R(x,y,z)) / (u * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25611,a,b,23726,a)].">
      <j1 rule="hyper" parents="373 25611 23726"/>
    </justification>
  </clause>

  <clause id="25682">
    <literal><![CDATA[
      a(x,y,z) * ((z * y) * x) = (z * y) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,25610,a,b,25681,a(flip))].">
      <j1 rule="hyper" parents="144 25610 25681"/>
    </justification>
  </clause>

  <clause id="25683">
    <literal><![CDATA[
      L(x,y,z \ ((u * u) * w)) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,23973,a(flip),b,23849,a),flip(a)].">
      <j1 rule="hyper" parents="373 23973 23849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25685">
    <literal><![CDATA[
      L(x,y,z \ ((u * u) * w)) = L(x,y,(v5 * v5) * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,2184,a,b,25683,a),flip(a)].">
      <j1 rule="hyper" parents="373 2184 25683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25686">
    <literal><![CDATA[
      L(x,y,z \ (1 / u)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(245(a,1),25683(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="245 25683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25687">
    <literal><![CDATA[
      L(x,y,z \ ((1 / u) * w)) = L(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(310(a,1),25683(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="310 25683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25688">
    <literal><![CDATA[
      L(x,y,z \ (u * (u * w))) = L(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[para(100(a,1),25683(a,1,3,2))].">
      <j1 rule="para" parents="100 25683"/>
    </justification>
  </clause>

  <clause id="25689">
    <literal><![CDATA[
      L(x,y,z \ (((u * u) \ w) * v5)) = L(x,y,z \ (w * v5))
    ]]></literal>
    <justification jstring="[para(126(a,1),25683(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="126 25683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25690">
    <literal><![CDATA[
      L(x,y,z \ (((u * u) / w) * v5)) = L(x,y,z \ ((1 / w) * v5))
    ]]></literal>
    <justification jstring="[para(556(a,1),25683(a,1,3,2))].">
      <j1 rule="para" parents="556 25683"/>
    </justification>
  </clause>

  <clause id="25691">
    <literal><![CDATA[
      L(x,y,z \ ((u / (1 / w)) \ v5)) = L(x,y,z \ ((u / w) \ v5))
    ]]></literal>
    <justification jstring="[para(891(a,1),25683(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="891 25683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25692">
    <literal><![CDATA[
      L(x,y,((1 / z) * u) \ w) = L(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[para(941(a,1),25683(a,1,3))].">
      <j1 rule="para" parents="941 25683"/>
    </justification>
  </clause>

  <clause id="25694">
    <literal><![CDATA[
      L(x,y,(z \ ((z * u) * u)) \ w) = L(x,y,a(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[para(1047(a,1),25683(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1047 25683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25695">
    <literal><![CDATA[
      L(x,y,(((1 / z) * u) * w) \ v5) = L(x,y,((z * u) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(1462(a,1),25683(a,1,3))].">
      <j1 rule="para" parents="1462 25683"/>
    </justification>
  </clause>

  <clause id="25696">
    <literal><![CDATA[
      L(x,y,z \ (u \ 1)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(79(a,1),25686(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="79 25686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25697">
    <literal><![CDATA[
      L(x,y,z \ ((u / (w * u)) \ 1)) = L(x,y,z \ ((w \ u) / u))
    ]]></literal>
    <justification jstring="[para(2032(a,1),25686(a,1,3,2))].">
      <j1 rule="para" parents="2032 25686"/>
    </justification>
  </clause>

  <clause id="25698">
    <literal><![CDATA[
      L(x,y,z \ ((u \ 1) * w)) = L(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(79(a,1),25687(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="79 25687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25699">
    <literal><![CDATA[
      L(x,y,((z \ 1) * u) \ w) = L(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[para(79(a,1),25692(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="79 25692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25700">
    <literal><![CDATA[
      L(x,y,(z * (z * u)) \ w) = L(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(559(a,1),25692(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="559 25692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25701">
    <literal><![CDATA[
      x / L(1 / y,z,(y * z) \ x) = (x / (z * (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(25692(a,1),21689(a,1,2))].">
      <j1 rule="para" parents="25692 21689"/>
    </justification>
  </clause>

  <clause id="25702">
    <literal><![CDATA[
      T(x \ (y / (x * y)),x * x) = x \ (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a(flip),b,23880,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 23880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25703">
    <literal><![CDATA[
      (((1 / x) \ y) \ z) * T(u,y \ (R(x,x,y) \ z)) = u * ((R(x,x,y) * y) \ z)
    ]]></literal>
    <justification jstring="[para(1913(a,1),23888(a,1,1,1))].">
      <j1 rule="para" parents="1913 23888"/>
    </justification>
  </clause>

  <clause id="25704">
    <literal><![CDATA[
      (1 / (1 / L(x,y,z))) \ x = x * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,5584,a(flip),b,23897,a),flip(a)].">
      <j1 rule="hyper" parents="145 5584 23897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25705">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ x = x * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4300(a,2),25704(a,1,1))].">
      <j1 rule="para" parents="4300 25704"/>
    </justification>
  </clause>

  <clause id="25706">
    <literal><![CDATA[
      a(R(1 / x,x,x \ y),x,x \ y) = (x \ 1) * R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3529,a(flip),b,23903,a)].">
      <j1 rule="hyper" parents="64 3529 23903"/>
    </justification>
  </clause>

  <clause id="25708">
    <literal><![CDATA[
      (x / y) * L((x / y) \ 1,z,u) = y \ (x * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,3089,a(flip),b,23905,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 3089 23905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25709">
    <literal><![CDATA[
      (1 / x) * (a(y,z,u) \ x) = x * (a(y,z,u) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(23133(a,1),23914(a,2,2))].">
      <j1 rule="para" parents="23133 23914"/>
    </justification>
  </clause>

  <clause id="25710">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,y,z),u) = (L(x,y,z) * u) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,102,a,b,24192,a)].">
      <j1 rule="hyper" parents="373 102 24192"/>
    </justification>
  </clause>

  <clause id="25711">
    <literal><![CDATA[
      (L(x \ y,z,u) * x) \ ((x \ y) * x) = (x * L(x \ y,z,u)) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),24192(a,2,2))].">
      <j1 rule="para" parents="10 24192"/>
    </justification>
  </clause>

  <clause id="25712">
    <literal><![CDATA[
      (((x * L(x,x,x)) \ y) * R(((x * L(x,x,x)) \ y) \ x,z,u)) / x = (x * x) \ (x \ (y * R(((x * L(x,x,x)) \ y) \ x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,11472,a(flip),b,24196,a),flip(a)].">
      <j1 rule="hyper" parents="373 11472 24196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25713">
    <literal><![CDATA[
      1 \ (((1 / (x * y)) * x) * R(((1 / (x * y)) * x) \ 1,z,u)) = (((1 / (x * y)) * x) * R(L(y,x,x * y),z,u)) / 1
    ]]></literal>
    <justification jstring="[para(918(a,2),24196(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="918 24196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25714">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ 1) * v5 = v5 * (L(a(x,y,z),u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(23734(a,1),24204(a,1,2))].">
      <j1 rule="para" parents="23734 24204"/>
    </justification>
  </clause>

  <clause id="25715">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) / v5 = v5 \ (L(a(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(23734(a,1),24205(a,1,2))].">
      <j1 rule="para" parents="23734 24205"/>
    </justification>
  </clause>

  <clause id="25716">
    <literal><![CDATA[
      T((x * L(x \ y,z,u)) \ y,w) = (x * L(x \ y,z,u)) \ y
    ]]></literal>
    <justification jstring="[para(23538(a,1),24216(a,1,1))].">
      <j1 rule="para" parents="23538 24216"/>
    </justification>
  </clause>

  <clause id="25717">
    <literal><![CDATA[
      a(x,y,z) * (u * K(u * (w \ a(x,y,z)),w)) = (w \ (u * a(x,y,z))) * w
    ]]></literal>
    <justification jstring="[hyper(64,a,10240,a(flip),b,24259,a),flip(a)].">
      <j1 rule="hyper" parents="64 10240 24259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25718">
    <literal><![CDATA[
      (x \ (y / (z / u))) * (z / u) = (x \ (y / (u \ z))) * (u \ z)
    ]]></literal>
    <justification jstring="[hyper(144,a,24313,a(flip),b,6971,a)].">
      <j1 rule="hyper" parents="144 24313 6971"/>
    </justification>
  </clause>

  <clause id="25719">
    <literal><![CDATA[
      K(x,T(T(y,z),u) * (y \ w)) = K(x,K(y,z) * (w * K(u,y)))
    ]]></literal>
    <justification jstring="[para(24318(a,1),18210(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24318 18210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25720">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ K(u,w) = x * (R(x,y,z) \ K(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14524,a,b,24327,a)].">
      <j1 rule="hyper" parents="64 14524 24327"/>
    </justification>
  </clause>

  <clause id="25723">
    <literal><![CDATA[
      (x / y) * (((x / y) \ z) * u) = (y \ x) * (((y \ x) \ z) * u)
    ]]></literal>
    <justification jstring="[para(6270(a,1),24336(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6270 24336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25724">
    <literal><![CDATA[
      (x \ y) * (((y / (y / x)) \ z) * u) = (y / x) * ((x \ z) * u)
    ]]></literal>
    <justification jstring="[para(6413(a,2),24336(a,1,2,1))].">
      <j1 rule="para" parents="6413 24336"/>
    </justification>
  </clause>

  <clause id="25725">
    <literal><![CDATA[
      (x / y) \ (((x / y) * z) * u) = (y \ x) \ (((y \ x) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,24351,a(flip),b,6062,a)].">
      <j1 rule="hyper" parents="139 24351 6062"/>
    </justification>
  </clause>

  <clause id="25726">
    <literal><![CDATA[
      (x \ y) * (z * K(x,x \ 1)) = ((1 / (1 / x)) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,5170,a(flip),b,24353,a)].">
      <j1 rule="hyper" parents="64 5170 24353"/>
    </justification>
  </clause>

  <clause id="25727">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((x \ z) * u)) = y * (((1 / (1 / x)) \ z) * u)
    ]]></literal>
    <justification jstring="[para(24353(a,1),5183(a,2,2))].">
      <j1 rule="para" parents="24353 5183"/>
    </justification>
  </clause>

  <clause id="25728">
    <literal><![CDATA[
      ((x \ y) * x) * ((((x \ y) * x) \ z) * u) = y * ((y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,24359,a(flip),b,10831,a)].">
      <j1 rule="hyper" parents="145 24359 10831"/>
    </justification>
  </clause>

  <clause id="25729">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (L(x,x,v5) \ v5) = (v5 * (1 / x)) * L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(11819(a,1),24382(a,1,2))].">
      <j1 rule="para" parents="11819 24382"/>
    </justification>
  </clause>

  <clause id="25730">
    <literal><![CDATA[
      ((x / y) * z) \ (y * (x / y)) = ((y \ x) * z) \ x
    ]]></literal>
    <justification jstring="[para(6179(a,1),24400(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6179 24400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25731">
    <literal><![CDATA[
      ((x / y) * L((y \ x) \ x,z,u)) \ (y * (x / y)) = (L(y,z,u) * (y \ x)) \ x
    ]]></literal>
    <justification jstring="[para(839(a,1),25730(a,2,1))].">
      <j1 rule="para" parents="839 25730"/>
    </justification>
  </clause>

  <clause id="25732">
    <literal><![CDATA[
      ((x \ y) \ z) \ ((y / (y / x)) \ u) = ((y / x) \ z) \ (x \ u)
    ]]></literal>
    <justification jstring="[para(6599(a,1),24402(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6599 24402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25733">
    <literal><![CDATA[
      K(x,T(y,z)) * (((x * z) \ u) / w) = ((x * z) \ (K(x,y) * u)) / w
    ]]></literal>
    <justification jstring="[para(8003(a,1),24433(a,1,1))].">
      <j1 rule="para" parents="8003 24433"/>
    </justification>
  </clause>

  <clause id="25736">
    <literal><![CDATA[
      T(x,(y * (z / (z / u))) * T(w,v5)) = T(x,(y * u) * T(K(u \ z,u) * w,v5))
    ]]></literal>
    <justification jstring="[para(24467(a,2),19563(a,2,2)),flip(a)].">
      <j1 rule="para" parents="24467 19563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25737">
    <literal><![CDATA[
      (x / (y \ z)) * (((y \ z) * y) * u) = (x / (z / y)) * (z * u)
    ]]></literal>
    <justification jstring="[para(10858(a,1),24469(a,1,2))].">
      <j1 rule="para" parents="10858 24469"/>
    </justification>
  </clause>

  <clause id="25738">
    <literal><![CDATA[
      (x \ (y / z)) * ((y / z) \ u) = (x \ (z \ y)) * ((z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(6270(a,1),24476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 24476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25739">
    <literal><![CDATA[
      (((x \ 1) \ y) \ (x * y)) * K(x,x \ 1) = (x * y) / ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(22549(a,1),24489(a,1,1))].">
      <j1 rule="para" parents="22549 24489"/>
    </justification>
  </clause>

  <clause id="25740">
    <literal><![CDATA[
      (x / y) * ((z * (x / y)) \ u) = (y \ x) * ((z * (y \ x)) \ u)
    ]]></literal>
    <justification jstring="[para(6886(a,1),24503(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6886 24503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25741">
    <literal><![CDATA[
      (x / y) * ((z \ (x / y)) \ u) = (y \ x) * ((z \ (y \ x)) \ u)
    ]]></literal>
    <justification jstring="[para(15097(a,1),24503(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15097 24503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25742">
    <literal><![CDATA[
      ((x \ y) \ y) \ ((z * (x \ y)) \ u) = x \ ((z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[para(24507(a,1),6291(a,2,2))].">
      <j1 rule="para" parents="24507 6291"/>
    </justification>
  </clause>

  <clause id="25743">
    <literal><![CDATA[
      (x / (x / y)) \ ((z * y) \ u) = y \ ((z * (x / (x / y))) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,24508,a,b,6373,a),flip(a)].">
      <j1 rule="hyper" parents="139 24508 6373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25744">
    <literal><![CDATA[
      ((x \ y) \ y) * ((z * ((x \ y) \ y)) \ u) = x * ((z * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(145,a,24511,a,b,6230,a)].">
      <j1 rule="hyper" parents="145 24511 6230"/>
    </justification>
  </clause>

  <clause id="25745">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * ((w / y) * K(y,u))) = T(x,w / T(y * K(u,y),z))
    ]]></literal>
    <justification jstring="[para(24531(a,1),19525(a,2,2))].">
      <j1 rule="para" parents="24531 19525"/>
    </justification>
  </clause>

  <clause id="25746">
    <literal><![CDATA[
      K(x,y) * ((1 / (z \ (z / x))) \ u) = (K(y,x) / (z \ (z / x))) \ u
    ]]></literal>
    <justification jstring="[para(3354(a,1),24535(a,1,2,1,2))].">
      <j1 rule="para" parents="3354 24535"/>
    </justification>
  </clause>

  <clause id="25747">
    <literal><![CDATA[
      ((x \ y) \ y) * ((z \ ((x \ y) \ y)) \ u) = x * ((z \ x) \ u)
    ]]></literal>
    <justification jstring="[para(24536(a,1),6070(a,2,2))].">
      <j1 rule="para" parents="24536 6070"/>
    </justification>
  </clause>

  <clause id="25748">
    <literal><![CDATA[
      (x / L(y,z,u)) * ((x / (x / y)) * w) = (L(y,z,u) \ x) * (y * w)
    ]]></literal>
    <justification jstring="[para(25183(a,1),24540(a,1,1))].">
      <j1 rule="para" parents="25183 24540"/>
    </justification>
  </clause>

  <clause id="25749">
    <literal><![CDATA[
      K(x,y / (T(z \ u,z) * w)) = K(x,y / ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,23387,a(flip),b,24547,a),flip(a)].">
      <j1 rule="hyper" parents="373 23387 24547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25750">
    <literal><![CDATA[
      R(x \ (x \ y),z,u) * ((((x \ y) \ y) \ (y / x)) \ (y / x)) = ((x \ y) \ y) * R(((x \ y) \ y) \ (y / x),z,u)
    ]]></literal>
    <justification jstring="[para(4511(a,1),24600(a,1,1,1))].">
      <j1 rule="para" parents="4511 24600"/>
    </justification>
  </clause>

  <clause id="25751">
    <literal><![CDATA[
      K(x * y,y \ 1) * ((y \ 1) * (x * R(y,z,u))) = (x * y) * R(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(24606(a,1),23503(a,1,2))].">
      <j1 rule="para" parents="24606 23503"/>
    </justification>
  </clause>

  <clause id="25752">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ a(y,z,u) = (x \ 1) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a(flip),b,24639,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 24639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25753">
    <literal><![CDATA[
      L(x,x,a(y,z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,23931,a(flip),b,24639,a),flip(a)].">
      <j1 rule="hyper" parents="40 23931 24639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25754">
    <literal><![CDATA[
      a(x,y,z) * (1 / z) = a(x,y,z) / z
    ]]></literal>
    <justification jstring="[hyper(225,a,25753,a(flip),b,11792,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 25753 11792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25755">
    <literal><![CDATA[
      L(R(x,y,z),x,a(u,w,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(25753(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25753 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25756">
    <literal><![CDATA[
      a(x,y,z \ 1) / (z \ 1) = a(x,y,z \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(740,a,25754,a),flip(a)].">
      <j1 rule="hyper" parents="740 25754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25757">
    <literal><![CDATA[
      R(a(x,y,z),1 / z,((1 / z) \ 1) * u) * L(u,1 / z,1 / z) = (a(x,y,z) / z) * (((1 / z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(25754(a,1),1153(a,2,1))].">
      <j1 rule="para" parents="25754 1153"/>
    </justification>
  </clause>

  <clause id="25758">
    <literal><![CDATA[
      (a(x,y,z) / z) * L(u,z,a(x,y,z)) = a(x,y,z) * ((1 / z) * u)
    ]]></literal>
    <justification jstring="[para(25754(a,1),11796(a,1,1))].">
      <j1 rule="para" parents="25754 11796"/>
    </justification>
  </clause>

  <clause id="25762">
    <literal><![CDATA[
      L(x \ L(y,y,z),x,z * y) = ((z * (1 / y)) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(24201,a,24666,a)].">
      <j1 rule="hyper" parents="24201 24666"/>
    </justification>
  </clause>

  <clause id="25763">
    <literal><![CDATA[
      T(x,x \ y) \ ((x \ y) \ K((x \ y) \ y,y \ 1)) = ((x \ y) \ 1) / ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,422,a,b,24672,a)].">
      <j1 rule="hyper" parents="35 422 24672"/>
    </justification>
  </clause>

  <clause id="25764">
    <literal><![CDATA[
      T(x \ y,((x \ y) \ y) * x) / (y * x) = (x \ y) / T(y * x,x \ y)
    ]]></literal>
    <justification jstring="[para(13941(a,1),24694(a,2,2))].">
      <j1 rule="para" parents="13941 24694"/>
    </justification>
  </clause>

  <clause id="25765">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(a(x,y,z),w,v5)) = (a(x,y,z) \ u) * L(a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(24699(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="24699 598"/>
    </justification>
  </clause>

  <clause id="25766">
    <literal><![CDATA[
      L(x,y,y) \ ((y \ 1) * x) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1921,a(flip),b,24705,a),flip(a)].">
      <j1 rule="hyper" parents="64 1921 24705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25767">
    <literal><![CDATA[
      T(R(T(1 / x,y),x,y),x) = L(y,x,x) \ ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11464,a,b,25766,a)].">
      <j1 rule="hyper" parents="373 11464 25766"/>
    </justification>
  </clause>

  <clause id="25768">
    <literal><![CDATA[
      (x * (x \ (y \ x))) * L(x,y,y) = ((y \ 1) * x) * x
    ]]></literal>
    <justification jstring="[para(25766(a,1),24845(a,1,1,2))].">
      <j1 rule="para" parents="25766 24845"/>
    </justification>
  </clause>

  <clause id="25769">
    <literal><![CDATA[
      (x \ y) * L(y,x,x) = ((x \ 1) * y) * y
    ]]></literal>
    <justification jstring="[hyper(717,a,25768,a)].">
      <j1 rule="hyper" parents="717 25768"/>
    </justification>
  </clause>

  <clause id="25771">
    <literal><![CDATA[
      L(x,y,L(z,u,u) * (u \ z)) = L(x,y,((u \ 1) * z) * z)
    ]]></literal>
    <justification jstring="[para(25769(a,1),23253(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25769 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25772">
    <literal><![CDATA[
      1 / T(x \ (y / (z * y)),z * x) = (x \ (y / (z * y))) \ 1
    ]]></literal>
    <justification jstring="[hyper(225,a,24998,a(flip),b,24718,a(flip))].">
      <j1 rule="hyper" parents="225 24998 24718"/>
    </justification>
  </clause>

  <clause id="25773">
    <literal><![CDATA[
      T(x \ ((x / y) / z),z * y) = ((x \ ((x / y) / z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),24718(a,1,2,2))].">
      <j1 rule="para" parents="82 24718"/>
    </justification>
  </clause>

  <clause id="25774">
    <literal><![CDATA[
      ((x / y) \ (x * z)) * T(u,y * z) = u * ((x / y) \ (x * z))
    ]]></literal>
    <justification jstring="[para(9(a,1),24720(a,1,2,2,2))].">
      <j1 rule="para" parents="9 24720"/>
    </justification>
  </clause>

  <clause id="25775">
    <literal><![CDATA[
      (((x \ y) / y) \ 1) * x = x * (((x \ y) / y) \ 1)
    ]]></literal>
    <justification jstring="[para(1331(a,1),24720(a,1,2))].">
      <j1 rule="para" parents="1331 24720"/>
    </justification>
  </clause>

  <clause id="25776">
    <literal><![CDATA[
      x * (((x \ y) / y) \ 1) = (y / (x * y)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,25533,a(flip),b,25775,a),flip(a)].">
      <j1 rule="hyper" parents="64 25533 25775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25777">
    <literal><![CDATA[
      (a(x,y,z) * L(u,w,v5)) / u = u \ (a(x,y,z) * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(142,a,24377,a(flip),b,24761,a)].">
      <j1 rule="hyper" parents="142 24377 24761"/>
    </justification>
  </clause>

  <clause id="25778">
    <literal><![CDATA[
      (x \ (K(y,z) * u)) * (u \ w) = (x \ u) * (u \ (K(y,z) * w))
    ]]></literal>
    <justification jstring="[para(22758(a,1),24778(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22758 24778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25779">
    <literal><![CDATA[
      x \ ((y / (y / z)) \ u) = (x \ (z \ u)) * K(z,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(6616(a,2),24779(a,2,2)),flip(a)].">
      <j1 rule="para" parents="6616 24779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25780">
    <literal><![CDATA[
      x * ((a(y,y,z) * (1 / z)) \ u) = x * ((1 / L(z,y,y)) \ u)
    ]]></literal>
    <justification jstring="[para(7687(a,1),24797(a,2,2,1))].">
      <j1 rule="para" parents="7687 24797"/>
    </justification>
  </clause>

  <clause id="25781">
    <literal><![CDATA[
      (x * y) / (x \ R(x,z,u)) = x * (y / (x \ R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,23705,a,b,24812,a)].">
      <j1 rule="hyper" parents="64 23705 24812"/>
    </justification>
  </clause>

  <clause id="25782">
    <literal><![CDATA[
      (x \ R(x,y,z)) * ((u * u) \ x) = R((u * u) \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2051,a,b,24816,a),flip(a)].">
      <j1 rule="hyper" parents="373 2051 24816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25783">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * T(z,y)) / (x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,15462,a,b,24874,a)].">
      <j1 rule="hyper" parents="373 15462 24874"/>
    </justification>
  </clause>

  <clause id="25784">
    <literal><![CDATA[
      a(x,y,z) * (x * (z * y)) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,15462,a,b,24874,a)].">
      <j1 rule="hyper" parents="144 15462 24874"/>
    </justification>
  </clause>

  <clause id="25785">
    <literal><![CDATA[
      a(x,y,T(z,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,15473,a(flip),b,25783,a)].">
      <j1 rule="hyper" parents="373 15473 25783"/>
    </justification>
  </clause>

  <clause id="25786">
    <literal><![CDATA[
      (x * (y * z)) * a(x,z,y) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,23161,a,b,25783,a(flip))].">
      <j1 rule="hyper" parents="38 23161 25783"/>
    </justification>
  </clause>

  <clause id="25787">
    <literal><![CDATA[
      L(x,y,((z * u) * u) * T(z,u)) = L(x,y,a(z * u,u,z))
    ]]></literal>
    <justification jstring="[para(25783(a,2),11831(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25783 11831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25788">
    <literal><![CDATA[
      a(x,y,y \ (z * y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(22(a,1),25785(a,1,3))].">
      <j1 rule="para" parents="22 25785"/>
    </justification>
  </clause>

  <clause id="25790">
    <literal><![CDATA[
      R(T(x,y * y),y,y) \ (y \ (x * y)) = K(y,y * x) * a(y,y,x)
    ]]></literal>
    <justification jstring="[para(25788(a,1),11505(a,2,2))].">
      <j1 rule="para" parents="25788 11505"/>
    </justification>
  </clause>

  <clause id="25791">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) \ (a(y,z,u) * (x * w)) = a(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,23961,a(flip),b,25786,a)].">
      <j1 rule="hyper" parents="139 23961 25786"/>
    </justification>
  </clause>

  <clause id="25792">
    <literal><![CDATA[
      a(x,((y * z) * z) * T(y,z),u) = a(x,a(y * z,z,y),u)
    ]]></literal>
    <justification jstring="[para(25786(a,1),11960(a,1,2))].">
      <j1 rule="para" parents="25786 11960"/>
    </justification>
  </clause>

  <clause id="25793">
    <literal><![CDATA[
      (x \ T(y,x * x)) / y = y \ (x \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,16229,a(flip),b,24875,a),flip(a)].">
      <j1 rule="hyper" parents="64 16229 24875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25794">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * (u * K(w,v5))) = K(x,(y * (z \ K(w,v5))) * u)
    ]]></literal>
    <justification jstring="[para(24883(a,1),17932(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24883 17932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25795">
    <literal><![CDATA[
      K(x,(y * (z \ K(u,y / z))) \ w) = K(x,T(y * (z \ 1),u) \ w)
    ]]></literal>
    <justification jstring="[para(24886(a,1),15797(a,1,2))].">
      <j1 rule="para" parents="24886 15797"/>
    </justification>
  </clause>

  <clause id="25796">
    <literal><![CDATA[
      (x / y) \ (y \ ((y * (x / y)) * z)) = (y \ x) \ (y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(139,a,24896,a(flip),b,6062,a)].">
      <j1 rule="hyper" parents="139 24896 6062"/>
    </justification>
  </clause>

  <clause id="25797">
    <literal><![CDATA[
      x \ (K(y \ 1,z) * ((y \ (y \ 1)) * u)) = ((T(y \ 1,z) \ y) * x) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,22829,a(flip),b,24902,a)].">
      <j1 rule="hyper" parents="64 22829 24902"/>
    </justification>
  </clause>

  <clause id="25798">
    <literal><![CDATA[
      T(x,y) * (((T(x,y) \ z) * u) * w) = x * (((x \ z) * u) * w)
    ]]></literal>
    <justification jstring="[hyper(145,a,24903,a(flip),b,6155,a)].">
      <j1 rule="hyper" parents="145 24903 6155"/>
    </justification>
  </clause>

  <clause id="25799">
    <literal><![CDATA[
      K(x,y) * (((1 / y) \ y) \ z) = (y \ 1) * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(1168(a,2),24905(a,1,2))].">
      <j1 rule="para" parents="1168 24905"/>
    </justification>
  </clause>

  <clause id="25800">
    <literal><![CDATA[
      ((1 / x) \ y) * K(z,y * u) = (K(u * y,z) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,23058,a(flip),b,24931,a)].">
      <j1 rule="hyper" parents="64 23058 24931"/>
    </justification>
  </clause>

  <clause id="25801">
    <literal><![CDATA[
      (x * y) \ ((y * (T(x,y) * z)) / u) = (y * x) \ ((y * (x * z)) / u)
    ]]></literal>
    <justification jstring="[hyper(139,a,24933,a(flip),b,10853,a)].">
      <j1 rule="hyper" parents="139 24933 10853"/>
    </justification>
  </clause>

  <clause id="25802">
    <literal><![CDATA[
      x / (a(y,z,u) * K(w,a(y,z,u) \ (w \ x))) = (w \ (a(y,z,u) \ x)) * w
    ]]></literal>
    <justification jstring="[hyper(373,a,10229,a(flip),b,24938,a),flip(a)].">
      <j1 rule="hyper" parents="373 10229 24938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25803">
    <literal><![CDATA[
      (x * y) * (K(z,u) * (T(x,y) \ w)) = (y * x) * (K(z,u) * (x \ w))
    ]]></literal>
    <justification jstring="[hyper(145,a,24945,a(flip),b,10824,a)].">
      <j1 rule="hyper" parents="145 24945 10824"/>
    </justification>
  </clause>

  <clause id="25804">
    <literal><![CDATA[
      (x / T(y,z)) * R(T(y,z),u,w) = R(y,u,w) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24603,a(flip),b,24947,a)].">
      <j1 rule="hyper" parents="64 24603 24947"/>
    </justification>
  </clause>

  <clause id="25805">
    <literal><![CDATA[
      R((x \ y) \ y,z,u) * (T(x,x \ y) \ w) = R(x,z,u) * (x \ w)
    ]]></literal>
    <justification jstring="[para(116(a,1),24947(a,1,1,1))].">
      <j1 rule="para" parents="116 24947"/>
    </justification>
  </clause>

  <clause id="25806">
    <literal><![CDATA[
      (L(x,y,z) \ u) / T(x,w) = (x \ u) / L(T(x,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,24853,a(flip),b,24949,a),flip(a)].">
      <j1 rule="hyper" parents="142 24853 24949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25807">
    <literal><![CDATA[
      T(x,(y * z) * (K(z \ u,z) * w)) = T(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19548,a,b,24952,a)].">
      <j1 rule="hyper" parents="64 19548 24952"/>
    </justification>
  </clause>

  <clause id="25808">
    <literal><![CDATA[
      ((x \ y) \ 1) * ((x \ y) * x) = ((y / x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(5919(a,1),24956(a,1,2))].">
      <j1 rule="para" parents="5919 24956"/>
    </justification>
  </clause>

  <clause id="25809">
    <literal><![CDATA[
      L(x * (x \ y),x \ y,x \ y) = (((y / x) \ 1) * y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(25808(a,1),3440(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25808 3440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25810">
    <literal><![CDATA[
      L(x,(L(y \ z,K(y,y \ 1),K(y,y \ 1)) * u) * w,v5) = L(x,(((1 / (K(y,y \ 1) / y)) \ z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(24962(a,1),11952(a,2,2,1,1))].">
      <j1 rule="para" parents="24962 11952"/>
    </justification>
  </clause>

  <clause id="25812">
    <literal><![CDATA[
      T(x / T(y,y * (x \ (y / x))),y) = (x / y) * K(y / x,y)
    ]]></literal>
    <justification jstring="[para(24997(a,1),17609(a,1,1,2))].">
      <j1 rule="para" parents="24997 17609"/>
    </justification>
  </clause>

  <clause id="25813">
    <literal><![CDATA[
      T(x / ((y * z) * z),z * (z * y)) = ((y * z) * z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,17078,a(flip),b,25019,a)].">
      <j1 rule="hyper" parents="64 17078 25019"/>
    </justification>
  </clause>

  <clause id="25814">
    <literal><![CDATA[
      (x / y) * T(y * T(y,z),y) = x / (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,9330,a(flip),b,25031,a),flip(a)].">
      <j1 rule="hyper" parents="373 9330 25031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25815">
    <literal><![CDATA[
      (x * (R(y,z,u) * (x * y))) \ ((x * y) * (x * R(y,z,u))) = a(x,R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,25040,a(flip),b,88,a)].">
      <j1 rule="hyper" parents="139 25040 88"/>
    </justification>
  </clause>

  <clause id="25816">
    <literal><![CDATA[
      L(x / y,z,u) \ K(y,y \ x) = L(y \ x,z,u) \ 1
    ]]></literal>
    <justification jstring="[para(5926(a,1),25066(a,1,2))].">
      <j1 rule="para" parents="5926 25066"/>
    </justification>
  </clause>

  <clause id="25818">
    <literal><![CDATA[
      R(L(x,y,z),u,w) * (T(x,x \ v5) / L((x \ v5) \ v5,y,z)) = L(x,y,z) \ (R(L(x,y,z),u,w) * x)
    ]]></literal>
    <justification jstring="[para(25068(a,2),1898(a,2,2)),flip(a)].">
      <j1 rule="para" parents="25068 1898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25819">
    <literal><![CDATA[
      x * R(y,L(T(x,y),z,u),L(T(x,y),z,u) \ x) = (L(x,z,u) \ x) * (y * L(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,25633,a(flip),b,25071,a)].">
      <j1 rule="hyper" parents="64 25633 25071"/>
    </justification>
  </clause>

  <clause id="25820">
    <literal><![CDATA[
      (x \ y) * (L(x \ y,z,u) \ x) = L(y / x,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,10467,a(flip),b,25108,a),flip(a)].">
      <j1 rule="hyper" parents="373 10467 25108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25821">
    <literal><![CDATA[
      (x / y) * (K(z,u) * (z * z)) = x / ((z * T(z,u)) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,24500,a(flip),b,25134,a)].">
      <j1 rule="hyper" parents="64 24500 25134"/>
    </justification>
  </clause>

  <clause id="25822">
    <literal><![CDATA[
      (x \ 1) \ R(1 / x,y,z) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,8,a(flip),b,25154,a)].">
      <j1 rule="hyper" parents="139 8 25154"/>
    </justification>
  </clause>

  <clause id="25823">
    <literal><![CDATA[
      (x * (x * R(1 / x,y,z))) \ x = R(1 / x,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(25822(a,1),1229(a,1,1,2))].">
      <j1 rule="para" parents="25822 1229"/>
    </justification>
  </clause>

  <clause id="25824">
    <literal><![CDATA[
      (a(x,y,z) / u) * ((u \ 1) * (a(x,y,z) \ u)) = u \ 1
    ]]></literal>
    <justification jstring="[hyper(145,a,25165,a(flip),b,24689,a(flip))].">
      <j1 rule="hyper" parents="145 25165 24689"/>
    </justification>
  </clause>

  <clause id="25825">
    <literal><![CDATA[
      R(x \ y,z,u) \ ((x \ y) * x) = R(y / x,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,11425,a(flip),b,25204,a),flip(a)].">
      <j1 rule="hyper" parents="373 11425 25204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25826">
    <literal><![CDATA[
      L(1 / x,x,a(y,z,u)) \ a(y,z,u) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(143,a,25209,a,b,171,a)].">
      <j1 rule="hyper" parents="143 25209 171"/>
    </justification>
  </clause>

  <clause id="25827">
    <literal><![CDATA[
      L(x,y,L((z * z) \ u,w,w)) = L(x,y,L(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,25241,a(flip),b,25242,a),flip(a)].">
      <j1 rule="hyper" parents="373 25241 25242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25828">
    <literal><![CDATA[
      L(x,y,L(1 / z,u,u)) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[para(309(a,1),25827(a,1,3,1))].">
      <j1 rule="para" parents="309 25827"/>
    </justification>
  </clause>

  <clause id="25829">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,u)) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,23846,a(flip),b,25828,a)].">
      <j1 rule="hyper" parents="64 23846 25828"/>
    </justification>
  </clause>

  <clause id="25830">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,7846,a(flip),b,25303,a),flip(a)].">
      <j1 rule="hyper" parents="64 7846 25303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25831">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,u)) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22932,a(flip),b,25830,a)].">
      <j1 rule="hyper" parents="64 22932 25830"/>
    </justification>
  </clause>

  <clause id="25832">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u) * w) = T(T(x,K(y,u * z)),w)
    ]]></literal>
    <justification jstring="[para(25830(a,1),22924(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25830 22924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25833">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y * u)) = T(K(y,z) * x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22936,a(flip),b,25831,a),flip(a)].">
      <j1 rule="hyper" parents="64 22936 25831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25834">
    <literal><![CDATA[
      T(x,T(T(y,z) / u,w * (v5 * y))) = T(x,T(u \ T(y,z),w * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,21362,a,b,25304,a)].">
      <j1 rule="hyper" parents="64 21362 25304"/>
    </justification>
  </clause>

  <clause id="25835">
    <literal><![CDATA[
      L(T(a(x,y,z) * a(x,y,z),u),u,w) = T(a(x,y,z) * a(x,y,z),w * u)
    ]]></literal>
    <justification jstring="[para(25318(a,1),6653(a,1,1,1))].">
      <j1 rule="para" parents="25318 6653"/>
    </justification>
  </clause>

  <clause id="25836">
    <literal><![CDATA[
      K(x,T(y \ (z \ u),K(w,v5))) = K(x,T((u / y) / z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,23505,a,b,25327,a),flip(a)].">
      <j1 rule="hyper" parents="373 23505 25327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25837">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,w * z)) = K(x,T(y / (z / u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,23044,a,b,25333,a)].">
      <j1 rule="hyper" parents="64 23044 25333"/>
    </justification>
  </clause>

  <clause id="25838">
    <literal><![CDATA[
      L(K(x,T(y,y)) / y,y,x) = (y * (a(y,y,y) \ x)) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,15172,a,b,25338,a)].">
      <j1 rule="hyper" parents="373 15172 25338"/>
    </justification>
  </clause>

  <clause id="25839">
    <literal><![CDATA[
      (T(x,y * y) \ z) * K(x,u) = (x \ z) * K(x,y \ (y \ u))
    ]]></literal>
    <justification jstring="[para(17635(a,1),25390(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17635 25390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25840">
    <literal><![CDATA[
      R(T(x,y * y),z,u) \ T(x,w) = R(x,z,u) \ T(x,y \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,24565,a(flip),b,25394,a)].">
      <j1 rule="hyper" parents="64 24565 25394"/>
    </justification>
  </clause>

  <clause id="25841">
    <literal><![CDATA[
      (x * (y * K(x,z))) * T(x,y) = (T(T(x,y),z) * y) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,24863,a,b,25404,a),flip(a)].">
      <j1 rule="hyper" parents="373 24863 25404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25842">
    <literal><![CDATA[
      x / (y / (x \ (K(z,u) * w))) = K(z,u) * (x / (y / (x \ w)))
    ]]></literal>
    <justification jstring="[para(25413(a,1),24877(a,1,2))].">
      <j1 rule="para" parents="25413 24877"/>
    </justification>
  </clause>

  <clause id="25843">
    <literal><![CDATA[
      (x / (y * K(z,u))) * (y * w) = (x / y) * (y * (K(u,z) * w))
    ]]></literal>
    <justification jstring="[para(22760(a,1),25418(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22760 25418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25844">
    <literal><![CDATA[
      (x \ ((x / y) * R(y,z,u))) * x = (x / y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(156,a,25438,a)].">
      <j1 rule="hyper" parents="156 25438"/>
    </justification>
  </clause>

  <clause id="25845">
    <literal><![CDATA[
      T(((a(x,y,z) \ 1) / u) \ 1,u) = ((a(x,y,z) \ 1) / u) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,14960,a,b,25443,a)].">
      <j1 rule="hyper" parents="35 14960 25443"/>
    </justification>
  </clause>

  <clause id="25846">
    <literal><![CDATA[
      (L(T(x,x \ y),z,u) / w) \ ((x \ y) \ y) = (L(x,z,u) / w) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,361,a(flip),b,25449,a)].">
      <j1 rule="hyper" parents="64 361 25449"/>
    </justification>
  </clause>

  <clause id="25847">
    <literal><![CDATA[
      (x * (y * z)) / T(y * x,z) = L(K(x,y) * z,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10985,a(flip),b,25453,a),flip(a)].">
      <j1 rule="hyper" parents="373 10985 25453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25848">
    <literal><![CDATA[
      ((x * y) * L(z,y,x)) / (z * (x * y)) = (z * (x * y)) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(100(a,1),25455(a,2,2))].">
      <j1 rule="para" parents="100 25455"/>
    </justification>
  </clause>

  <clause id="25849">
    <literal><![CDATA[
      ((1 / x) \ y) * K(z,x * y) = (K(y * x,z) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,14957,a(flip),b,25485,a)].">
      <j1 rule="hyper" parents="64 14957 25485"/>
    </justification>
  </clause>

  <clause id="25850">
    <literal><![CDATA[
      K(x,y * T(z / (u * (w / u)),w)) = K(x,y * ((u * (w / u)) \ z))
    ]]></literal>
    <justification jstring="[para(25488(a,1),17930(a,1,2,2))].">
      <j1 rule="para" parents="25488 17930"/>
    </justification>
  </clause>

  <clause id="25851">
    <literal><![CDATA[
      K(x,y * y) * (K(z,u) \ x) = T(K(z,u) \ x,y * y)
    ]]></literal>
    <justification jstring="[para(6156(a,2),25552(a,1,2))].">
      <j1 rule="para" parents="6156 25552"/>
    </justification>
  </clause>

  <clause id="25852">
    <literal><![CDATA[
      (1 / (x \ y)) * ((y / x) \ z) = ((x \ y) * (y / x)) \ z
    ]]></literal>
    <justification jstring="[para(413(a,1),25562(a,2,1))].">
      <j1 rule="para" parents="413 25562"/>
    </justification>
  </clause>

  <clause id="25853">
    <literal><![CDATA[
      a(x,y,x * y) \ (x * y) = L(x * y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11871,a(flip),b,25631,a),flip(a)].">
      <j1 rule="hyper" parents="64 11871 25631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25855">
    <literal><![CDATA[
      L(x * y,y,x) \ (x * y) = a(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(40,a,5559,a,b,25853,a)].">
      <j1 rule="hyper" parents="40 5559 25853"/>
    </justification>
  </clause>

  <clause id="25856">
    <literal><![CDATA[
      L(x,y,y) * (x \ K(z,u)) = a(y,y,x) \ K(z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,19399,a(flip),b,25662,a),flip(a)].">
      <j1 rule="hyper" parents="373 19399 25662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25857">
    <literal><![CDATA[
      T(x,y) \ (R(y,z,u) * (y \ x)) = x \ ((R(y,z,u) * x) / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,25667,a(flip),b,5778,a)].">
      <j1 rule="hyper" parents="139 25667 5778"/>
    </justification>
  </clause>

  <clause id="25858">
    <literal><![CDATA[
      L(x,y,(z * z) * ((u / w) \ v5)) = L(x,y,((1 / u) / w) \ v5)
    ]]></literal>
    <justification jstring="[para(943(a,1),25685(a,1,3)),flip(a)].">
      <j1 rule="para" parents="943 25685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25859">
    <literal><![CDATA[
      L(x,y,z \ (((1 / u) * w) * v5)) = L(x,y,z \ ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(535(a,1),25689(a,1,3,2,1))].">
      <j1 rule="para" parents="535 25689"/>
    </justification>
  </clause>

  <clause id="25860">
    <literal><![CDATA[
      (x \ 1) * (x \ (a(y,z,u) \ x)) = a(y,z,u) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,1127,a,b,25709,a(flip))].">
      <j1 rule="hyper" parents="35 1127 25709"/>
    </justification>
  </clause>

  <clause id="25861">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (y * y)) = ((x * (1 / y)) * z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,646,a(flip),b,25762,a)].">
      <j1 rule="hyper" parents="64 646 25762"/>
    </justification>
  </clause>

  <clause id="25862">
    <literal><![CDATA[
      (x * (x * y)) \ (x * y) = R(T(1 / x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,3156,a,b,25767,a)].">
      <j1 rule="hyper" parents="41 3156 25767"/>
    </justification>
  </clause>

  <clause id="25863">
    <literal><![CDATA[
      x * (T(y,x) / (x \ R(x,z,u))) = (y * x) / (x \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,250,a(flip),b,25781,a),flip(a)].">
      <j1 rule="hyper" parents="64 250 25781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25864">
    <literal><![CDATA[
      ((1 / x) \ T(x,y)) \ z = (x \ 1) * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,24520,a(flip),b,25799,a)].">
      <j1 rule="hyper" parents="64 24520 25799"/>
    </justification>
  </clause>

  <clause id="25865">
    <literal><![CDATA[
      (T(x,y) \ 1) * (T(T(x,y),z) \ K(x,y)) = (x * T((T(x,y) \ 1) \ 1,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,14636,a(flip),b,25864,a),flip(a)].">
      <j1 rule="hyper" parents="64 14636 25864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25866">
    <literal><![CDATA[
      ((1 / x) \ y) / (z * K(y * u,w)) = ((K(u * y,w) / x) \ y) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,25800,a(flip),b,23229,a),flip(a)].">
      <j1 rule="hyper" parents="142 25800 23229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25867">
    <literal><![CDATA[
      R(x,y,z) * (x \ K(x,u)) = (1 / x) * R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(5757(a,1),25804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5757 25804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25868">
    <literal><![CDATA[
      T((x * y) / ((x * y) * y),y * (y * x)) = ((((x * y) \ z) \ z) * y) \ T(x * y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,14836,a,b,25813,a),flip(a)].">
      <j1 rule="hyper" parents="373 14836 25813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25869">
    <literal><![CDATA[
      L(x / y,z,z) \ K(y,y \ x) = (y \ x) \ a(z,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1851,a(flip),b,25816,a),flip(a)].">
      <j1 rule="hyper" parents="373 1851 25816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25870">
    <literal><![CDATA[
      x / ((y * T(y,z)) \ u) = (x / u) * (T(y,z) * y)
    ]]></literal>
    <justification jstring="[para(5755(a,1),25821(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5755 25821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25871">
    <literal><![CDATA[
      x / ((y * T(y,z)) \ u) = (x / u) * (y * T(y,z))
    ]]></literal>
    <justification jstring="[para(273(a,1),25870(a,2,2))].">
      <j1 rule="para" parents="273 25870"/>
    </justification>
  </clause>

  <clause id="25872">
    <literal><![CDATA[
      R(x / y,y,y) \ x = L(y,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,16070,a(flip),b,25825,a),flip(a)].">
      <j1 rule="hyper" parents="64 16070 25825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25873">
    <literal><![CDATA[
      R(x / y,y,y) \ x = L(y,y,y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25574,a(flip),b,25872,a),flip(a)].">
      <j1 rule="hyper" parents="373 25574 25872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25874">
    <literal><![CDATA[
      R(x / y,y,y) \ x = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(373,a,11068,a(flip),b,25872,a),flip(a)].">
      <j1 rule="hyper" parents="373 11068 25872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25875">
    <literal><![CDATA[
      x / L(y,y,y * x) = R(x / y,y,y)
    ]]></literal>
    <justification jstring="[hyper(225,a,25574,a(flip),b,25872,a)].">
      <j1 rule="hyper" parents="225 25574 25872"/>
    </justification>
  </clause>

  <clause id="25876">
    <literal><![CDATA[
      R((x * y) / z,z,z) \ (y * x) = L(z,z,z * (x * y)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(25873(a,1),15222(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25873 15222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25877">
    <literal><![CDATA[
      L(x,x,x * y) \ (x * (y / x)) = R(y / x,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25142,a,b,25875,a)].">
      <j1 rule="hyper" parents="64 25142 25875"/>
    </justification>
  </clause>

  <clause id="25878">
    <literal><![CDATA[
      (x \ (x / (1 / y))) \ (y * z) = ((x * y) \ x) \ ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(25874(a,1),1973(a,1,1))].">
      <j1 rule="para" parents="25874 1973"/>
    </justification>
  </clause>

  <clause id="25879">
    <literal><![CDATA[
      L(x,x,x * (y / x)) \ (x * ((y / x) / x)) = y / (x * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,351,a(flip),b,25877,a),flip(a)].">
      <j1 rule="hyper" parents="373 351 25877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25880">
    <literal><![CDATA[
      L(1 / x,x,a(y,z,u)) \ a(y,z,u) = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a(flip),b,25826,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 25826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25881">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u) * w) = T(x,K(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,22924,a(flip),b,25832,a),flip(a)].">
      <j1 rule="hyper" parents="373 22924 25832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25882">
    <literal><![CDATA[
      K(x * T(x,y),z) * u = u * K(x * T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(41,a,18344,a,b,25833,a)].">
      <j1 rule="hyper" parents="41 18344 25833"/>
    </justification>
  </clause>

  <clause id="25883">
    <literal><![CDATA[
      K(x * T(x,y),T(z,u)) = K(x * T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(8656,a,25882,a)].">
      <j1 rule="hyper" parents="8656 25882"/>
    </justification>
  </clause>

  <clause id="25884">
    <literal><![CDATA[
      (x * (a(x,x,x) \ y)) \ y = L(K(y,x) / x,x,y)
    ]]></literal>
    <justification jstring="[para(114(a,1),25838(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="114 25838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25885">
    <literal><![CDATA[
      L(K(x,y) / y,y,x) = (L(y,y,y) * x) \ x
    ]]></literal>
    <justification jstring="[para(6494(a,1),25884(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6494 25884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25886">
    <literal><![CDATA[
      R((x * y) \ y,x,x) = L(K(y,x) / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,13596,a,b,25885,a)].">
      <j1 rule="hyper" parents="373 13596 25885"/>
    </justification>
  </clause>

  <clause id="25887">
    <literal><![CDATA[
      T(T(x,y),z) * T(y,x) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,6858,a,b,25841,a)].">
      <j1 rule="hyper" parents="36 6858 25841"/>
    </justification>
  </clause>

  <clause id="25888">
    <literal><![CDATA[
      T(x * (T(T(y,z),u) * T(z,y)),K(y,z * K(y,u))) = K(y,z * K(y,u)) * (x * ((z * K(y,u)) * y))
    ]]></literal>
    <justification jstring="[para(25887(a,2),10194(a,1,1,2))].">
      <j1 rule="para" parents="25887 10194"/>
    </justification>
  </clause>

  <clause id="25889">
    <literal><![CDATA[
      (K(x * y,y) / y) \ x = (y * y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14565,a(flip),b,25849,a),flip(a)].">
      <j1 rule="hyper" parents="64 14565 25849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25890">
    <literal><![CDATA[
      (x \ ((1 / y) \ z)) * K(u,y * z) = x \ ((K(z * y,u) / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,25849,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 25849 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25891">
    <literal><![CDATA[
      (K(x * y,x) / x) \ y = (x * x) * (y / x)
    ]]></literal>
    <justification jstring="[para(8516(a,1),25889(a,1,1,1))].">
      <j1 rule="para" parents="8516 25889"/>
    </justification>
  </clause>

  <clause id="25892">
    <literal><![CDATA[
      (x * x) * ((y \ L(y,z,u)) / x) = (1 / x) \ (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(23086(a,1),25891(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="23086 25891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25893">
    <literal><![CDATA[
      K(x * K(y,z),u * u) = K(x,u * u)
    ]]></literal>
    <justification jstring="[hyper(36,a,17375,a,b,25851,a)].">
      <j1 rule="hyper" parents="36 17375 25851"/>
    </justification>
  </clause>

  <clause id="25894">
    <literal><![CDATA[
      ((x \ y) * (y / x)) \ y = (1 / (x \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(741,a,25852,a),flip(a)].">
      <j1 rule="hyper" parents="741 25852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25895">
    <literal><![CDATA[
      (x \ 1) \ (a(y,z,u) \ (x \ 1)) = x \ (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(149,a,25860,a)].">
      <j1 rule="hyper" parents="149 25860"/>
    </justification>
  </clause>

  <clause id="25896">
    <literal><![CDATA[
      (1 / x) * R(T(x,y),z,u) = x \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,24589,a(flip),b,25867,a),flip(a)].">
      <j1 rule="hyper" parents="64 24589 25867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25897">
    <literal><![CDATA[
      (x \ 1) \ R(T(x \ 1,y),z,u) = x * R(T(x \ 1,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(400,a,25896,a),flip(a)].">
      <j1 rule="hyper" parents="400 25896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25898">
    <literal><![CDATA[
      L(1 / x,x,a(y,z,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(40,a,9440,a,b,25880,a),flip(a)].">
      <j1 rule="hyper" parents="40 9440 25880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25899">
    <literal><![CDATA[
      a(x,y,z) * (1 / (1 / z)) = a(x,y,z) / (1 / z)
    ]]></literal>
    <justification jstring="[para(25898(a,1),4308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25898 4308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25900">
    <literal><![CDATA[
      T(x,K(y,z) * (K(y,u) * w)) = T(x,K(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,22924,a(flip),b,25881,a)].">
      <j1 rule="hyper" parents="64 22924 25881"/>
    </justification>
  </clause>

  <clause id="25901">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ x)) * (x \ 1) = a(y,z,u) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(144,a,25895,a(flip),b,23767,a)].">
      <j1 rule="hyper" parents="144 25895 23767"/>
    </justification>
  </clause>

  <clause id="25902">
    <literal><![CDATA[
      T(x,K(y,z) * (u * K(y,w))) = T(x,K(y,z * w) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,19541,a(flip),b,25900,a)].">
      <j1 rule="hyper" parents="64 19541 25900"/>
    </justification>
  </clause>

  <clause id="25903">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ x)) * (x \ K(w,v5)) = (a(y,z,u) \ (x \ 1)) * K(w,v5)
    ]]></literal>
    <justification jstring="[para(25901(a,1),24286(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25901 24286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25904">
    <literal><![CDATA[
      T(x,K(y,z) * (u * K(y,w))) = T(x,K(w * z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,18075,a,b,25902,a),flip(a)].">
      <j1 rule="hyper" parents="373 18075 25902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25905">
    <literal><![CDATA[
      K(x \ (y \ (z \ ((z * y) * u))),w) = K(L(x,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24248,a(flip),b,23436,a)].">
      <j1 rule="hyper" parents="64 24248 23436"/>
    </justification>
  </clause>

  <clause id="25906">
    <literal><![CDATA[
      T((x \ 1) \ (a(x,y,y) \ 1),a(z,u,w) \ 1) = R(x \ 1,y,y) \ 1
    ]]></literal>
    <justification jstring="[para(2653(a,1),23757(a,1,1,2,1))].">
      <j1 rule="para" parents="2653 23757"/>
    </justification>
  </clause>

  <clause id="25907">
    <literal><![CDATA[
      (x * T(y,z)) / L(T(y,z),u,L(u \ T(x,T(y,z)),u,y)) = ((x * T(y,z)) / (u * T(y,z))) * u
    ]]></literal>
    <justification jstring="[para(23838(a,2),21689(a,1,2,3))].">
      <j1 rule="para" parents="23838 21689"/>
    </justification>
  </clause>

  <clause id="25908">
    <literal><![CDATA[
      ((x \ (y \ x)) \ 1) \ T(y,y \ 1) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(24013(a,1),7262(a,1,1))].">
      <j1 rule="para" parents="24013 7262"/>
    </justification>
  </clause>

  <clause id="25909">
    <literal><![CDATA[
      (1 / (x \ (y \ x))) \ y = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,14878,a(flip),b,25908,a)].">
      <j1 rule="hyper" parents="64 14878 25908"/>
    </justification>
  </clause>

  <clause id="25910">
    <literal><![CDATA[
      a((x \ (y \ x)) \ y,z,u) = a(y * (x \ (y \ x)),z,u)
    ]]></literal>
    <justification jstring="[para(25909(a,1),2671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25909 2671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25911">
    <literal><![CDATA[
      R(x,(y \ (z \ y)) \ z,u) = R(x,z * (y \ (z \ y)),u)
    ]]></literal>
    <justification jstring="[para(25909(a,1),3023(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25909 3023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25912">
    <literal><![CDATA[
      R(x,x \ (y \ z),y) \ z = (x \ (z / y)) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,15106,a(flip),b,24015,a),flip(a)].">
      <j1 rule="hyper" parents="373 15106 24015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25913">
    <literal><![CDATA[
      R(x,x \ (y / z),z) = R(x,x \ (z \ y),z)
    ]]></literal>
    <justification jstring="[hyper(40,a,975,a,b,25912,a)].">
      <j1 rule="hyper" parents="40 975 25912"/>
    </justification>
  </clause>

  <clause id="25914">
    <literal><![CDATA[
      ((x \ (x / y)) * y) \ x = R(x,x \ (y \ x),y)
    ]]></literal>
    <justification jstring="[para(25912(a,1),2157(a,1,1))].">
      <j1 rule="para" parents="25912 2157"/>
    </justification>
  </clause>

  <clause id="25915">
    <literal><![CDATA[
      R(x,y \ (z / u),u) * ((y \ (((z / u) \ z) \ z)) * ((z / u) \ z)) = (x * (y \ (z / u))) * (z / (z / u))
    ]]></literal>
    <justification jstring="[para(15093(a,2),24153(a,1,2))].">
      <j1 rule="para" parents="15093 24153"/>
    </justification>
  </clause>

  <clause id="25916">
    <literal><![CDATA[
      K(a(x,y,z) \ 1,u) = K(x / R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(20(a,2),24226(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="20 24226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25917">
    <literal><![CDATA[
      K(R(x,y,z) \ x,u) = K(a(x,y,z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(2156(a,1),25916(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2156 25916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25918">
    <literal><![CDATA[
      K(R(x,y,z) \ x,u) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,23733,a(flip),b,25917,a),flip(a)].">
      <j1 rule="hyper" parents="373 23733 25917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25920">
    <literal><![CDATA[
      K(x,R(y,z,u) \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,25918,a,b,6076,a),flip(a)].">
      <j1 rule="hyper" parents="140 25918 6076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25921">
    <literal><![CDATA[
      T(R(x,y,z) \ x,u) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(57,a,25918,a)].">
      <j1 rule="hyper" parents="57 25918"/>
    </justification>
  </clause>

  <clause id="25923">
    <literal><![CDATA[
      T(x,R(y,z,u) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(57,a,25920,a)].">
      <j1 rule="hyper" parents="57 25920"/>
    </justification>
  </clause>

  <clause id="25924">
    <literal><![CDATA[
      T(x,(y / (z * y)) \ (z \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(14918,a,25923,a)].">
      <j1 rule="hyper" parents="14918 25923"/>
    </justification>
  </clause>

  <clause id="25925">
    <literal><![CDATA[
      x / (R(y,z,u) \ y) = (R(y,z,u) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(8638,a,25923,a),flip(a)].">
      <j1 rule="hyper" parents="8638 25923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25926">
    <literal><![CDATA[
      (R(x,y,z) \ x) * u = u * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(2149,a,25923,a),flip(a)].">
      <j1 rule="hyper" parents="2149 25923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25928">
    <literal><![CDATA[
      L(x,y,R(y,z,u)) * ((1 / R(y,z,u)) * y) = (1 / R(y,z,u)) * (y * x)
    ]]></literal>
    <justification jstring="[para(25923(a,1),15292(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="25923 15292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25929">
    <literal><![CDATA[
      x / ((y / (z * y)) \ (z \ 1)) = ((y / (z * y)) \ (z \ 1)) \ x
    ]]></literal>
    <justification jstring="[hyper(8638,a,25924,a),flip(a)].">
      <j1 rule="hyper" parents="8638 25924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25930">
    <literal><![CDATA[
      ((x * (y / (x * y))) \ z) / z = z \ ((x * (y / (x * y))) \ z)
    ]]></literal>
    <justification jstring="[para(25924(a,1),14699(a,1,2))].">
      <j1 rule="para" parents="25924 14699"/>
    </justification>
  </clause>

  <clause id="25931">
    <literal><![CDATA[
      (R(x,y,z) \ x) * K(u,x) = R(T(x,u),y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,24565,a(flip),b,25926,a),flip(a)].">
      <j1 rule="hyper" parents="373 24565 25926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25932">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ (R(1 / x,y,z) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,2468,a,b,25926,a)].">
      <j1 rule="hyper" parents="139 2468 25926"/>
    </justification>
  </clause>

  <clause id="25933">
    <literal><![CDATA[
      L(((R(x,y,z) \ x) \ 1) \ u,R(x,y,z) \ x,R(x,y,z) \ x) = u * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1137,a,b,25926,a)].">
      <j1 rule="hyper" parents="64 1137 25926"/>
    </justification>
  </clause>

  <clause id="25934">
    <literal><![CDATA[
      K(x,y) * (R(z,u,w) \ z) = z * (R(z,u,w) \ K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,24327,a(flip),b,25926,a),flip(a)].">
      <j1 rule="hyper" parents="64 24327 25926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25935">
    <literal><![CDATA[
      L(x,y,R(y,z,u)) * (R(y,z,u) \ y) = y * ((R(y,z,u) \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,12026,a(flip),b,25926,a),flip(a)].">
      <j1 rule="hyper" parents="64 12026 25926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25936">
    <literal><![CDATA[
      (x * y) \ ((x * (R(z,u,w) \ z)) * y) = R(T(R(z,u,w) \ z,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(25926(a,1),796(a,1,2,1))].">
      <j1 rule="para" parents="25926 796"/>
    </justification>
  </clause>

  <clause id="25937">
    <literal><![CDATA[
      ((R(x,y,z) \ x) * (u * w)) / T(u,w * (R(x,y,z) \ x)) = u \ ((u * w) * (R(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(25926(a,2),15270(a,1,1))].">
      <j1 rule="para" parents="25926 15270"/>
    </justification>
  </clause>

  <clause id="25938">
    <literal><![CDATA[
      x * T(R(y,z,u) \ y,w) = (R(y,z,u) \ y) * x
    ]]></literal>
    <justification jstring="[para(25921(a,2),25926(a,2,2)),flip(a)].">
      <j1 rule="para" parents="25921 25926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25939">
    <literal><![CDATA[
      x * (R(x,y,z) \ K(u,x)) = R(T(x,u),y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,24327,a(flip),b,25931,a)].">
      <j1 rule="hyper" parents="64 24327 25931"/>
    </justification>
  </clause>

  <clause id="25940">
    <literal><![CDATA[
      R(T(x,y),z,z) \ x = a(x,z,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,16011,a(flip),b,25931,a),flip(a)].">
      <j1 rule="hyper" parents="64 16011 25931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25941">
    <literal><![CDATA[
      K(x,y) * ((R(x,z,u) \ x) \ w) = (R(T(x,y),z,u) \ x) \ w
    ]]></literal>
    <justification jstring="[para(25931(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25931 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25942">
    <literal><![CDATA[
      L(R(x,y,z) \ x,u,R(x,y,z) \ x) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(4696,a,25938,a)].">
      <j1 rule="hyper" parents="4696 25938"/>
    </justification>
  </clause>

  <clause id="25943">
    <literal><![CDATA[
      x * (R(T(x,y),z,u) \ 1) = R(T(x,y),z,u) \ x
    ]]></literal>
    <justification jstring="[para(24596(a,2),25939(a,1,2))].">
      <j1 rule="para" parents="24596 25939"/>
    </justification>
  </clause>

  <clause id="25944">
    <literal><![CDATA[
      (R(T(x,y),z,u) \ x) * K(w,v5) = x * (R(T(x,y),z,u) \ K(w,v5))
    ]]></literal>
    <justification jstring="[para(25943(a,1),24286(a,1,1))].">
      <j1 rule="para" parents="25943 24286"/>
    </justification>
  </clause>

  <clause id="25945">
    <literal><![CDATA[
      x * (y * (R(y,z,u) \ K(x,w))) = T(x,w) * (R(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,25934,a(flip),b,6071,a)].">
      <j1 rule="hyper" parents="145 25934 6071"/>
    </justification>
  </clause>

  <clause id="25946">
    <literal><![CDATA[
      L(R(x,y,z) \ x,u,x * R(x,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,24701,a(flip),b,25942,a)].">
      <j1 rule="hyper" parents="64 24701 25942"/>
    </justification>
  </clause>

  <clause id="25947">
    <literal><![CDATA[
      L((x \ y) * K(z,u),x,y \ z) = ((z / y) * x) \ T(z,u)
    ]]></literal>
    <justification jstring="[hyper(23857,a,24329,a)].">
      <j1 rule="hyper" parents="23857 24329"/>
    </justification>
  </clause>

  <clause id="25948">
    <literal><![CDATA[
      K(R(x,y,y \ 1) / (z * (y \ 1)),u) = K(x / (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23041,a(flip),b,24553,a),flip(a)].">
      <j1 rule="hyper" parents="373 23041 24553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25950">
    <literal><![CDATA[
      (x * x) * (y / T(x * y,x)) = R(T(x,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,23657,a(flip),b,24781,a),flip(a)].">
      <j1 rule="hyper" parents="373 23657 24781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25951">
    <literal><![CDATA[
      T(x * y,x * x) \ y = y / T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1531,a,b,25950,a)].">
      <j1 rule="hyper" parents="35 1531 25950"/>
    </justification>
  </clause>

  <clause id="25952">
    <literal><![CDATA[
      L(R(x,y,R(T(x,z),u,w)),y,R(x,u,w)) = (R(x,u,w) * (x * y)) / (R(x,u,w) * y)
    ]]></literal>
    <justification jstring="[para(24831(a,1),5908(a,1,1))].">
      <j1 rule="para" parents="24831 5908"/>
    </justification>
  </clause>

  <clause id="25954">
    <literal><![CDATA[
      R(x / (y * K(z,u)),y,z) = (x * z) / (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,23198,a(flip),b,24871,a)].">
      <j1 rule="hyper" parents="64 23198 24871"/>
    </justification>
  </clause>

  <clause id="25955">
    <literal><![CDATA[
      R(x / (y * K(z,K(u,w))),y,T(z,K(u,w))) = (x * z) / (y * (K(u,K(z,w)) * z))
    ]]></literal>
    <justification jstring="[para(8115(a,2),24871(a,2,2,2))].">
      <j1 rule="para" parents="8115 24871"/>
    </justification>
  </clause>

  <clause id="25956">
    <literal><![CDATA[
      R(x / (y \ T(z,u)),y \ z,z) = (x * z) / ((y \ z) * T(z,u))
    ]]></literal>
    <justification jstring="[para(15021(a,1),25954(a,1,1,2))].">
      <j1 rule="para" parents="15021 25954"/>
    </justification>
  </clause>

  <clause id="25957">
    <literal><![CDATA[
      K(x,R(y / z,z,u) * w) = K(x,y * (u * ((z * u) \ w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,25003,a(flip),b,24990,a),flip(a)].">
      <j1 rule="hyper" parents="373 25003 24990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25958">
    <literal><![CDATA[
      a(x \ (y \ x),y,y \ ((x \ (y \ x)) \ 1)) / T((x \ (y \ x)) * y,y) = 1 / (1 / (y \ ((x \ (y \ x)) \ 1)))
    ]]></literal>
    <justification jstring="[para(15653(a,2),25056(a,1,2))].">
      <j1 rule="para" parents="15653 25056"/>
    </justification>
  </clause>

  <clause id="25959">
    <literal><![CDATA[
      T(x * y,x) * L(z,y,x) = R(x,y,x) * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6029,a(flip),b,25234,a)].">
      <j1 rule="hyper" parents="64 6029 25234"/>
    </justification>
  </clause>

  <clause id="25960">
    <literal><![CDATA[
      T(R(x,x \ y,z),u) \ (y * z) = (T(x,u) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,24348,a(flip),b,25334,a),flip(a)].">
      <j1 rule="hyper" parents="373 24348 25334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25961">
    <literal><![CDATA[
      T(x \ 1,y) \ (x * z) = (T(x \ 1,y) \ x) * z
    ]]></literal>
    <justification jstring="[para(1112(a,1),25960(a,1,1,1))].">
      <j1 rule="para" parents="1112 25960"/>
    </justification>
  </clause>

  <clause id="25962">
    <literal><![CDATA[
      (x * y) * (L(z,y,x) * K(u,w)) = x * (y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(23053(a,1),25386(a,2,2))].">
      <j1 rule="para" parents="23053 25386"/>
    </justification>
  </clause>

  <clause id="25963">
    <literal><![CDATA[
      R(x,y,z) * (y * (z * K(u,w))) = (x * y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[para(23053(a,1),25388(a,1,2))].">
      <j1 rule="para" parents="23053 25388"/>
    </justification>
  </clause>

  <clause id="25964">
    <literal><![CDATA[
      R(K(x,y) * z,u,w) = K(x,y) * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,23239,a(flip),b,25402,a),flip(a)].">
      <j1 rule="hyper" parents="64 23239 25402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25966">
    <literal><![CDATA[
      (x \ y) * R(K(x,x \ y) * z,u,w) = (y / x) * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,25964,a,b,6442,a)].">
      <j1 rule="hyper" parents="145 25964 6442"/>
    </justification>
  </clause>

  <clause id="25967">
    <literal><![CDATA[
      x * R(K(x,y) * z,u,w) = T(x,y) * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,25964,a,b,6071,a)].">
      <j1 rule="hyper" parents="145 25964 6071"/>
    </justification>
  </clause>

  <clause id="25968">
    <literal><![CDATA[
      R(K(x,y) * z,u,w) * v5 = K(x,y) * (R(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(144,a,25964,a,b,23225,a)].">
      <j1 rule="hyper" parents="144 25964 23225"/>
    </justification>
  </clause>

  <clause id="25969">
    <literal><![CDATA[
      (x * y) \ R(K(x,y) * z,u,w) = (y * x) \ R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,25964,a,b,10853,a)].">
      <j1 rule="hyper" parents="139 25964 10853"/>
    </justification>
  </clause>

  <clause id="25970">
    <literal><![CDATA[
      x \ R(K(x,y) * z,u,w) = K(x,y) * (x \ R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,25964,a,b,6133,a)].">
      <j1 rule="hyper" parents="139 25964 6133"/>
    </justification>
  </clause>

  <clause id="25971">
    <literal><![CDATA[
      (x / y) \ R(K(y,y \ x) * z,u,w) = (y \ x) \ R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,25964,a,b,6062,a)].">
      <j1 rule="hyper" parents="139 25964 6062"/>
    </justification>
  </clause>

  <clause id="25972">
    <literal><![CDATA[
      x \ R(K(y,x) * z,u,w) = T(x,y) \ R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,25964,a,b,5810,a)].">
      <j1 rule="hyper" parents="139 25964 5810"/>
    </justification>
  </clause>

  <clause id="25973">
    <literal><![CDATA[
      R(x * K(y,z),u,w) = R(x,u,w) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,2140,a(flip),b,25964,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 2140 25964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25975">
    <literal><![CDATA[
      K(x,x \ y) * R(x \ y,z,u) = R(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(5720(a,1),25964(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5720 25964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25976">
    <literal><![CDATA[
      R(K(x,y) * z,u,w) \ v5 = R(z,u,w) \ (K(y,x) * v5)
    ]]></literal>
    <justification jstring="[para(25964(a,2),23199(a,1,1))].">
      <j1 rule="para" parents="25964 23199"/>
    </justification>
  </clause>

  <clause id="25977">
    <literal><![CDATA[
      K(x,y) * R(x \ R(x,z,u),w,v5) = R(x \ R(T(x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(23663(a,1),25964(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23663 25964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25978">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (u / (u / x)) = R(x * K(x \ u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6635,a,b,25973,a)].">
      <j1 rule="hyper" parents="373 6635 25973"/>
    </justification>
  </clause>

  <clause id="25980">
    <literal><![CDATA[
      R((x \ 1) * K(y,z),x,y) = (x \ T(y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,15098,a(flip),b,25973,a),flip(a)].">
      <j1 rule="hyper" parents="373 15098 25973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25981">
    <literal><![CDATA[
      R((x \ 1) * K(y,y \ z),x,z) = (x \ z) / ((y \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,10619,a(flip),b,25973,a),flip(a)].">
      <j1 rule="hyper" parents="373 10619 25973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25982">
    <literal><![CDATA[
      R((x \ 1) * K(y,z),x,z) = (x \ z) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,6244,a(flip),b,25973,a),flip(a)].">
      <j1 rule="hyper" parents="373 6244 25973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25983">
    <literal><![CDATA[
      R(x * K(y,z),u,w) * v5 = R(x,u,w) * (K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(144,a,25973,a,b,23278,a)].">
      <j1 rule="hyper" parents="144 25973 23278"/>
    </justification>
  </clause>

  <clause id="25984">
    <literal><![CDATA[
      x \ R(y * K(z,u),w,v5) = (x \ R(y,w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,25973,a,b,23055,a)].">
      <j1 rule="hyper" parents="139 25973 23055"/>
    </justification>
  </clause>

  <clause id="25990">
    <literal><![CDATA[
      R(x \ K(y,z),x,y) = (x \ T(y,z)) / y
    ]]></literal>
    <justification jstring="[para(14444(a,1),25980(a,1,1))].">
      <j1 rule="para" parents="14444 25980"/>
    </justification>
  </clause>

  <clause id="25991">
    <literal><![CDATA[
      R(x \ K(y,z),x,z) = (x \ z) / T(z,y)
    ]]></literal>
    <justification jstring="[para(14444(a,1),25982(a,1,1))].">
      <j1 rule="para" parents="14444 25982"/>
    </justification>
  </clause>

  <clause id="25992">
    <literal><![CDATA[
      (x \ y) / T(y,x) = T(y / (y * x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,14266,a(flip),b,25991,a),flip(a)].">
      <j1 rule="hyper" parents="64 14266 25991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25993">
    <literal><![CDATA[
      (L(x \ 1,y,z) \ (x \ 1)) / T(x \ 1,L(x \ 1,y,z)) = T((x \ 1) / (x \ L(1 / x,y,z)),L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(1391(a,1),25992(a,2,1,2))].">
      <j1 rule="para" parents="1391 25992"/>
    </justification>
  </clause>

  <clause id="25994">
    <literal><![CDATA[
      T((x * y) / T((x * y) * (1 / x),K(y,z)),1 / x) = ((1 / x) \ (x * y)) / T(x * y,1 / x)
    ]]></literal>
    <justification jstring="[para(14996(a,2),25992(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="14996 25992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25995">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ z,u,w) = x * R(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(6075(a,1),25967(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6075 25967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25996">
    <literal><![CDATA[
      T(x,y) * R(x \ y,z,u) = x * R(x \ ((x * y) / x),z,u)
    ]]></literal>
    <justification jstring="[para(6072(a,2),25967(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6072 25967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25997">
    <literal><![CDATA[
      T(x,y) * R(T(x,z) \ 1,u,w) = x * R(T(x,z) \ K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(14664(a,1),25967(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14664 25967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="25998">
    <literal><![CDATA[
      T(x,y) \ R(R(T(x,y),z,u),w,v5) = x \ R(R(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(24591(a,1),25972(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="24591 25972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26000">
    <literal><![CDATA[
      K(x,x \ y) * (R(x \ y,z,u) * w) = R(y / x,z,u) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,25975,a(flip),b,23225,a),flip(a)].">
      <j1 rule="hyper" parents="144 25975 23225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26001">
    <literal><![CDATA[
      (x / y) \ R(x / y,z,u) = (y \ x) \ R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,25975,a(flip),b,6062,a)].">
      <j1 rule="hyper" parents="139 25975 6062"/>
    </justification>
  </clause>

  <clause id="26002">
    <literal><![CDATA[
      R(x \ y,z,u) * (K(x,x \ y) * w) = R(y / x,z,u) * w
    ]]></literal>
    <justification jstring="[para(25975(a,1),4607(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25975 4607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26003">
    <literal><![CDATA[
      (x * y) \ R(x * y,z,u) = (y * x) \ R(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(5796(a,1),25969(a,1,2,1))].">
      <j1 rule="para" parents="5796 25969"/>
    </justification>
  </clause>

  <clause id="26004">
    <literal><![CDATA[
      K(x,x \ y) * (x \ R(y,z,u)) = x \ R(x * (y / x),z,u)
    ]]></literal>
    <justification jstring="[para(5781(a,1),25970(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5781 25970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26005">
    <literal><![CDATA[
      R(x,y,z) * (K(u,w) * (y * z)) = ((x * K(u,w)) * y) * z
    ]]></literal>
    <justification jstring="[hyper(327,a,25983,a),flip(a)].">
      <j1 rule="hyper" parents="327 25983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26006">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(u,w) = x * R(x \ K(u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2124,a(flip),b,25984,a),flip(a)].">
      <j1 rule="hyper" parents="64 2124 25984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26009">
    <literal><![CDATA[
      x * R(x \ (y / T(x,z)),u,w) = R(y,u,w) / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2115,a(flip),b,25995,a),flip(a)].">
      <j1 rule="hyper" parents="64 2115 25995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26010">
    <literal><![CDATA[
      T(x,y) * (x * R(x \ z,u,w)) = R(T(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,25995,a(flip),b,2124,a)].">
      <j1 rule="hyper" parents="145 25995 2124"/>
    </justification>
  </clause>

  <clause id="26011">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (y * z),u,w) = y * (x * R(x \ z,u,w))
    ]]></literal>
    <justification jstring="[para(25995(a,1),2614(a,2,2))].">
      <j1 rule="para" parents="25995 2614"/>
    </justification>
  </clause>

  <clause id="26012">
    <literal><![CDATA[
      (x / y) \ R(x / y,z,u) = y \ (x * R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,2744,a(flip),b,26001,a),flip(a)].">
      <j1 rule="hyper" parents="373 2744 26001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26014">
    <literal><![CDATA[
      ((x * y) * x) \ R((x * y) * x,z,u) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,4290,a(flip),b,26003,a),flip(a)].">
      <j1 rule="hyper" parents="373 4290 26003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26015">
    <literal><![CDATA[
      (x * y) * a(y * x,z,z) = R(x * y,z,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,15987,a(flip),b,26003,a)].">
      <j1 rule="hyper" parents="145 15987 26003"/>
    </justification>
  </clause>

  <clause id="26016">
    <literal><![CDATA[
      a(x * y,z,z) = a(y * x,z,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,15984,a,b,26015,a)].">
      <j1 rule="hyper" parents="35 15984 26015"/>
    </justification>
  </clause>

  <clause id="26017">
    <literal><![CDATA[
      a(x * y,z,z) / (y * x) = R(1 / (y * x),z,z)
    ]]></literal>
    <justification jstring="[para(26016(a,1),16000(a,2,1)),flip(a)].">
      <j1 rule="para" parents="26016 16000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26018">
    <literal><![CDATA[
      x * R(x \ K(y,x),z,u) = T(x,y) \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,8641,a(flip),b,26006,a),flip(a)].">
      <j1 rule="hyper" parents="64 8641 26006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26019">
    <literal><![CDATA[
      x * R(T(x,y) \ 1,z,u) = T(x,y) \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,7214,a,b,26018,a)].">
      <j1 rule="hyper" parents="64 7214 26018"/>
    </justification>
  </clause>

  <clause id="26020">
    <literal><![CDATA[
      T(x,y) * R(T(x,z) \ 1,u,w) = K(x,y) * (T(x,z) \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,26019,a(flip),b,5779,a),flip(a)].">
      <j1 rule="hyper" parents="145 26019 5779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26021">
    <literal><![CDATA[
      R(x * (y / T(x,z)),u,w) = x * (R(y,u,w) / T(x,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,26009,a(flip),b,2124,a),flip(a)].">
      <j1 rule="hyper" parents="145 26009 2124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26022">
    <literal><![CDATA[
      x \ R(T(x,y) * z,u,w) = T(x,y) * R(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,26010,a(flip),b,2403,a(flip))].">
      <j1 rule="hyper" parents="139 26010 2403"/>
    </justification>
  </clause>

  <clause id="26023">
    <literal><![CDATA[
      (x / (1 / y)) \ R(x / (1 / y),z,u) = y \ (x * R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,3507,a,b,26012,a)].">
      <j1 rule="hyper" parents="64 3507 26012"/>
    </justification>
  </clause>

  <clause id="26024">
    <literal><![CDATA[
      (x \ (y * R(y \ x,x,y \ 1))) * (x * (y \ 1)) = (y / x) \ 1
    ]]></literal>
    <justification jstring="[para(26012(a,1),5367(a,1,1))].">
      <j1 rule="para" parents="26012 5367"/>
    </justification>
  </clause>

  <clause id="26025">
    <literal><![CDATA[
      R(x / T(y * y,z),u,w) = R(x,u,w) / T(y * y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,1981,a(flip),b,26021,a(flip))].">
      <j1 rule="hyper" parents="35 1981 26021"/>
    </justification>
  </clause>

  <clause id="26026">
    <literal><![CDATA[
      T(x,y) * R(x \ 1,z,u) = x \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8(a,1),26022(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8 26022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26027">
    <literal><![CDATA[
      x \ R(T(x,y),x,y) = (y / (y * x)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,10635,a(flip),b,26026,a),flip(a)].">
      <j1 rule="hyper" parents="64 10635 26026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26028">
    <literal><![CDATA[
      R(1 / x,y,z) * T(x,u) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4091,a(flip),b,26026,a)].">
      <j1 rule="hyper" parents="64 4091 26026"/>
    </justification>
  </clause>

  <clause id="26029">
    <literal><![CDATA[
      ((x * y) * R((x * y) \ x,z,u)) * T(y,w) = (x * y) * (y \ R(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[para(26026(a,1),11678(a,2,2))].">
      <j1 rule="para" parents="26026 11678"/>
    </justification>
  </clause>

  <clause id="26030">
    <literal><![CDATA[
      x \ (y \ ((1 / x) \ y)) = (y / (y * x)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,1922,a(flip),b,26027,a)].">
      <j1 rule="hyper" parents="64 1922 26027"/>
    </justification>
  </clause>

  <clause id="26031">
    <literal><![CDATA[
      x * (x * T(y / (y * x),x)) = y \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,115,a,b,26030,a)].">
      <j1 rule="hyper" parents="145 115 26030"/>
    </justification>
  </clause>

  <clause id="26033">
    <literal><![CDATA[
      (x \ 1) \ R(T(x \ 1,y),z,u) = R(x,z,u) * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),26028(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 26028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26034">
    <literal><![CDATA[
      (x / (x * y)) \ ((y * y) \ z) = (x \ ((1 / y) \ x)) \ z
    ]]></literal>
    <justification jstring="[para(26031(a,1),14271(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26031 14271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26035">
    <literal><![CDATA[
      R(T(x * x,y) * z,u,w) = T(x * x,y) * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(38,a,1203,a(flip),b,26025,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 1203 26025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26036">
    <literal><![CDATA[
      (x \ ((1 / y) \ x)) \ (y * z) = (x / (x * y)) \ ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(535(a,1),26034(a,1,2)),flip(a)].">
      <j1 rule="para" parents="535 26034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26037">
    <literal><![CDATA[
      R(K(x,y) / z,z,z \ y) = (z \ y) / T(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(5756(a,2),25515(a,2,2))].">
      <j1 rule="para" parents="5756 25515"/>
    </justification>
  </clause>

  <clause id="26038">
    <literal><![CDATA[
      (x \ y) / T(y,T(x,x)) = T(y,x * x) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6944,a(flip),b,26037,a),flip(a)].">
      <j1 rule="hyper" parents="64 6944 26037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26039">
    <literal><![CDATA[
      T(x,y * y) \ (y \ x) = (y \ x) / T(x,y)
    ]]></literal>
    <justification jstring="[para(114(a,1),26038(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="114 26038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26040">
    <literal><![CDATA[
      T(x,y * y) \ (y \ x) = T(x / (x * y),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,25992,a(flip),b,26039,a),flip(a)].">
      <j1 rule="hyper" parents="373 25992 26039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26041">
    <literal><![CDATA[
      (x \ y) * (y \ K(x,x \ 1)) = 1 / R(x,x \ y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3760,a(flip),b,25601,a),flip(a)].">
      <j1 rule="hyper" parents="64 3760 25601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26042">
    <literal><![CDATA[
      T(x * a(y,x \ y,x),x \ 1) = x * (x * (y * ((y \ 1) / x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,25238,a,b,25652,a)].">
      <j1 rule="hyper" parents="373 25238 25652"/>
    </justification>
  </clause>

  <clause id="26044">
    <literal><![CDATA[
      a(R(x \ 1,x,y),x,x \ y) = (x \ 1) * R(x,x,y)
    ]]></literal>
    <justification jstring="[para(3005(a,1),25706(a,1,1))].">
      <j1 rule="para" parents="3005 25706"/>
    </justification>
  </clause>

  <clause id="26045">
    <literal><![CDATA[
      a(R(x,x,y),x,x \ y) = (x \ 1) * R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2697,a(flip),b,26044,a)].">
      <j1 rule="hyper" parents="64 2697 26044"/>
    </justification>
  </clause>

  <clause id="26046">
    <literal><![CDATA[
      L(x,y,L(z,u,u) * (u \ z)) = L(x,y,L(u \ 1,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,24838,a(flip),b,25771,a),flip(a)].">
      <j1 rule="hyper" parents="373 24838 25771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26047">
    <literal><![CDATA[
      L(x,y,L(z,u,u) * (u \ z)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,25829,a(flip),b,26046,a),flip(a)].">
      <j1 rule="hyper" parents="373 25829 26046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26048">
    <literal><![CDATA[
      L(x,x,y) \ (x * ((y / x) / x)) = y / (x * x)
    ]]></literal>
    <justification jstring="[para(24004(a,1),25879(a,1,1))].">
      <j1 rule="para" parents="24004 25879"/>
    </justification>
  </clause>

  <clause id="26049">
    <literal><![CDATA[
      (x / y) / L(y,y,x) = x / (y * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,25142,a(flip),b,26048,a)].">
      <j1 rule="hyper" parents="64 25142 26048"/>
    </justification>
  </clause>

  <clause id="26051">
    <literal><![CDATA[
      (x * x) * (y \ (y / x)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,895,a,b,26049,a)].">
      <j1 rule="hyper" parents="37 895 26049"/>
    </justification>
  </clause>

  <clause id="26052">
    <literal><![CDATA[
      (x * x) * ((y \ (y / x)) * z) = L(x,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,26051,a(flip),b,127,a),flip(a)].">
      <j1 rule="hyper" parents="144 26051 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26053">
    <literal><![CDATA[
      (1 / x) \ (y \ (y / x)) = x \ L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,26051,a(flip),b,538,a),flip(a)].">
      <j1 rule="hyper" parents="139 26051 538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26054">
    <literal><![CDATA[
      R(x,x,y \ (y / x)) \ L(x,x,y) = x * (y \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(139,a,26051,a(flip),b,111,a)].">
      <j1 rule="hyper" parents="139 26051 111"/>
    </justification>
  </clause>

  <clause id="26055">
    <literal><![CDATA[
      ((x \ y) * (x \ y)) * (y \ x) = L(x \ y,x \ y,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),26051(a,1,2,2))].">
      <j1 rule="para" parents="79 26051"/>
    </justification>
  </clause>

  <clause id="26056">
    <literal><![CDATA[
      L(x,x,y) \ (x * x) = (y \ (y / x)) \ 1
    ]]></literal>
    <justification jstring="[para(26051(a,1),489(a,1,1))].">
      <j1 rule="para" parents="26051 489"/>
    </justification>
  </clause>

  <clause id="26057">
    <literal><![CDATA[
      L(x,x,y) \ x = (y \ (y / x)) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(26051(a,1),878(a,1,1))].">
      <j1 rule="para" parents="26051 878"/>
    </justification>
  </clause>

  <clause id="26058">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = a(y \ (y / x),z,u)
    ]]></literal>
    <justification jstring="[para(26051(a,1),2639(a,1,1))].">
      <j1 rule="para" parents="26051 2639"/>
    </justification>
  </clause>

  <clause id="26059">
    <literal><![CDATA[
      R(x,L(y,y,z),u) = R(x,z \ (z / y),u)
    ]]></literal>
    <justification jstring="[para(26051(a,1),2965(a,1,2))].">
      <j1 rule="para" parents="26051 2965"/>
    </justification>
  </clause>

  <clause id="26060">
    <literal><![CDATA[
      (L(x,x,y) * L(x,x,y)) * (y \ (y * (1 / x))) = L(L(x,x,y),L(x,x,y),y)
    ]]></literal>
    <justification jstring="[para(11795(a,1),26051(a,1,2,2))].">
      <j1 rule="para" parents="11795 26051"/>
    </justification>
  </clause>

  <clause id="26061">
    <literal><![CDATA[
      (x \ (x / y)) \ 1 = y * (L(y,y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(2342,a,26056,a),flip(a)].">
      <j1 rule="hyper" parents="2342 26056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26062">
    <literal><![CDATA[
      a(L(a(x,y,z),a(x,y,z),u),w,v5) = a(u \ (a(x,y,z) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(23133(a,1),26058(a,2,1,2))].">
      <j1 rule="para" parents="23133 26058"/>
    </justification>
  </clause>

  <clause id="26063">
    <literal><![CDATA[
      R(x,L(y \ z,y \ z,z),u) = R(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),26059(a,2,2,2))].">
      <j1 rule="para" parents="79 26059"/>
    </justification>
  </clause>

  <clause id="26064">
    <literal><![CDATA[
      ((x \ y) * (x \ y)) * ((y \ x) * z) = L(x \ y,x \ y,y) * z
    ]]></literal>
    <justification jstring="[para(79(a,1),26052(a,1,2,1,2))].">
      <j1 rule="para" parents="79 26052"/>
    </justification>
  </clause>

  <clause id="26065">
    <literal><![CDATA[
      L(x,y,L(z \ u,z \ u,u)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(26055(a,1),2184(a,1,3))].">
      <j1 rule="para" parents="26055 2184"/>
    </justification>
  </clause>

  <clause id="26066">
    <literal><![CDATA[
      L(x,L(y \ z,y \ z,z),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(26055(a,1),11772(a,1,2))].">
      <j1 rule="para" parents="26055 11772"/>
    </justification>
  </clause>

  <clause id="26067">
    <literal><![CDATA[
      a(x,L(y \ z,y \ z,z),u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(26055(a,1),11960(a,1,2))].">
      <j1 rule="para" parents="26055 11960"/>
    </justification>
  </clause>

  <clause id="26068">
    <literal><![CDATA[
      K(L(x,y,z) \ L(u,y,z),w) = K(x \ (y \ (y * u)),w)
    ]]></literal>
    <justification jstring="[para(344(a,1),25905(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="344 25905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26069">
    <literal><![CDATA[
      K(L(x,y,z) \ L(u,y,z),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),26068(a,2,1,2))].">
      <j1 rule="para" parents="9 26068"/>
    </justification>
  </clause>

  <clause id="26070">
    <literal><![CDATA[
      L(x * K(y,z),u,w) = L(x,u,w) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(606,a,25962,a)].">
      <j1 rule="hyper" parents="606 25962"/>
    </justification>
  </clause>

  <clause id="26072">
    <literal><![CDATA[
      L(x * K(y,T(z,x)),u,w) = K(y,z) * L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,19274,a(flip),b,26070,a),flip(a)].">
      <j1 rule="hyper" parents="373 19274 26070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26073">
    <literal><![CDATA[
      1 / L(x * K(y,z),u,w) = K(z,y) / L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(225,a,26070,a,b,14592,a)].">
      <j1 rule="hyper" parents="225 26070 14592"/>
    </justification>
  </clause>

  <clause id="26075">
    <literal><![CDATA[
      L(x * K(y,z),u,w) * v5 = L(x,u,w) * (K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(144,a,26070,a,b,23278,a)].">
      <j1 rule="hyper" parents="144 26070 23278"/>
    </justification>
  </clause>

  <clause id="26076">
    <literal><![CDATA[
      x \ L(y * K(z,u),w,v5) = (x \ L(y,w,v5)) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,26070,a,b,23055,a)].">
      <j1 rule="hyper" parents="139 26070 23055"/>
    </justification>
  </clause>

  <clause id="26077">
    <literal><![CDATA[
      L(x \ y,z,u) * K(x,x \ y) = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(5774(a,1),26070(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5774 26070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26078">
    <literal><![CDATA[
      L(x * y,z,u) * K(y,w) = L(x * T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(6852(a,1),26070(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6852 26070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26080">
    <literal><![CDATA[
      L(x \ 1,y,z) * K(u,w) = L(x \ K(u,w),y,z)
    ]]></literal>
    <justification jstring="[para(14444(a,1),26070(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14444 26070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26081">
    <literal><![CDATA[
      L(x * K(y \ 1,z * (y * y)),u,w) = L(x,u,w) * (T(y \ 1,z) * y)
    ]]></literal>
    <justification jstring="[para(17393(a,1),26070(a,2,2))].">
      <j1 rule="para" parents="17393 26070"/>
    </justification>
  </clause>

  <clause id="26082">
    <literal><![CDATA[
      K(x \ K(y,z),x) * L(u * K(y,z),w,v5) = L(u,w,v5) * ((x \ K(y,z)) * x)
    ]]></literal>
    <justification jstring="[para(26070(a,2),17172(a,1,2))].">
      <j1 rule="para" parents="26070 17172"/>
    </justification>
  </clause>

  <clause id="26084">
    <literal><![CDATA[
      L(x * K(y,z),u,w) \ v5 = K(z,y) * (L(x,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(26070(a,2),23272(a,1,1))].">
      <j1 rule="para" parents="26070 23272"/>
    </justification>
  </clause>

  <clause id="26085">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) = K(x,y) * L(z,u,w)
    ]]></literal>
    <justification jstring="[para(7879(a,1),26072(a,1,1))].">
      <j1 rule="para" parents="7879 26072"/>
    </justification>
  </clause>

  <clause id="26086">
    <literal><![CDATA[
      K(x,y) * L(x * z,u,w) = L(T(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(7949(a,1),26072(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7949 26072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26087">
    <literal><![CDATA[
      (K(x,y) / z) * (z * u) = L(K(x,y) * u,z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,24907,a,b,26085,a)].">
      <j1 rule="hyper" parents="373 24907 26085"/>
    </justification>
  </clause>

  <clause id="26088">
    <literal><![CDATA[
      T(((1 / x) * y) \ y,K(y,1 / x)) = L(K(y,x \ 1) * x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,16487,a,b,26085,a)].">
      <j1 rule="hyper" parents="373 16487 26085"/>
    </justification>
  </clause>

  <clause id="26089">
    <literal><![CDATA[
      ((x * y) * z) / T(z * x,y) = L(K(x * y,z) * y,x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,14890,a,b,26085,a)].">
      <j1 rule="hyper" parents="373 14890 26085"/>
    </justification>
  </clause>

  <clause id="26090">
    <literal><![CDATA[
      T(x * y,z) \ (x * (y * u)) = L(K(z,x * y) * u,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6228,a,b,26085,a)].">
      <j1 rule="hyper" parents="373 6228 26085"/>
    </justification>
  </clause>

  <clause id="26091">
    <literal><![CDATA[
      L(K(x,y) * z,x,x) = T(x,y) * ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6033,a,b,26085,a),flip(a)].">
      <j1 rule="hyper" parents="373 6033 26085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26092">
    <literal><![CDATA[
      L(K(x * x,y) * x,x,y) = y \ (((x * x) * y) / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,15194,a(flip),b,26085,a),flip(a)].">
      <j1 rule="hyper" parents="373 15194 26085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26093">
    <literal><![CDATA[
      x * L(K(x,y) * z,u,w) = T(x,y) * L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,26085,a,b,6071,a)].">
      <j1 rule="hyper" parents="145 26085 6071"/>
    </justification>
  </clause>

  <clause id="26094">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) * v5 = K(x,y) * (L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(144,a,26085,a,b,23225,a)].">
      <j1 rule="hyper" parents="144 26085 23225"/>
    </justification>
  </clause>

  <clause id="26095">
    <literal><![CDATA[
      ((x \ y) * x) \ L(K(x \ y,x) * z,u,w) = y \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,26085,a,b,10873,a)].">
      <j1 rule="hyper" parents="139 26085 10873"/>
    </justification>
  </clause>

  <clause id="26096">
    <literal><![CDATA[
      (x / y) \ L(K(y,y \ x) * z,u,w) = (y \ x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,26085,a,b,6062,a)].">
      <j1 rule="hyper" parents="139 26085 6062"/>
    </justification>
  </clause>

  <clause id="26097">
    <literal><![CDATA[
      x \ L(K(y,x) * z,u,w) = T(x,y) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,26085,a,b,5810,a)].">
      <j1 rule="hyper" parents="139 26085 5810"/>
    </justification>
  </clause>

  <clause id="26098">
    <literal><![CDATA[
      K(x,y) * L(K(x,y) \ z,u,w) = L(z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),26085(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 26085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26099">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),z,z) = K(x,y) * ((1 / z) * u)
    ]]></literal>
    <justification jstring="[para(569(a,1),26085(a,2,2))].">
      <j1 rule="para" parents="569 26085"/>
    </justification>
  </clause>

  <clause id="26100">
    <literal><![CDATA[
      K(x,y) * L(T(x,y) \ z,u,w) = L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(6075(a,1),26085(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6075 26085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26101">
    <literal><![CDATA[
      L(L(K(x \ 1,y) * T(z,T(x \ 1,y)),u,w),x,x) = x * (L(z,u,w) * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(26085(a,2),7062(a,1,1))].">
      <j1 rule="para" parents="26085 7062"/>
    </justification>
  </clause>

  <clause id="26103">
    <literal><![CDATA[
      T(x,y) \ L(K(x,z) * u,w,v5) = K(x,z) * (T(x,y) \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(26085(a,2),22770(a,1,2))].">
      <j1 rule="para" parents="26085 22770"/>
    </justification>
  </clause>

  <clause id="26104">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) \ v5 = L(z,u,w) \ (K(y,x) * v5)
    ]]></literal>
    <justification jstring="[para(26085(a,2),23199(a,1,1))].">
      <j1 rule="para" parents="26085 23199"/>
    </justification>
  </clause>

  <clause id="26105">
    <literal><![CDATA[
      L(K(x,y) * z,u,w) / v5 = K(x,y) * (L(z,u,w) / v5)
    ]]></literal>
    <justification jstring="[para(26085(a,2),23224(a,1,1))].">
      <j1 rule="para" parents="26085 23224"/>
    </justification>
  </clause>

  <clause id="26106">
    <literal><![CDATA[
      (x \ 1) * L(K(y,z) * u,w,v5) = (x \ K(y,z)) * L(u,w,v5)
    ]]></literal>
    <justification jstring="[para(26085(a,2),24472(a,1,2))].">
      <j1 rule="para" parents="26085 24472"/>
    </justification>
  </clause>

  <clause id="26107">
    <literal><![CDATA[
      K(x,y) * L(T(z \ 1,z),u,w) = L(T(z \ K(x,y),z),u,w)
    ]]></literal>
    <justification jstring="[para(25482(a,1),26085(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25482 26085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26108">
    <literal><![CDATA[
      (K(x,y) / z) \ L(K(x,y) / z,u,w) = z * L(z \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,26098,a(flip),b,1719,a)].">
      <j1 rule="hyper" parents="139 26098 1719"/>
    </justification>
  </clause>

  <clause id="26110">
    <literal><![CDATA[
      L(K(x,y) * T(z,u),u,u) = (K(x,y) / u) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(737,a,26087,a),flip(a)].">
      <j1 rule="hyper" parents="737 26087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26111">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),z,z) = (K(x,y) / z) * u
    ]]></literal>
    <justification jstring="[hyper(397,a,26087,a),flip(a)].">
      <j1 rule="hyper" parents="397 26087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26112">
    <literal><![CDATA[
      (K(x,y) / z) * (z * u) = z * ((z \ K(x,y)) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,24954,a,b,26087,a),flip(a)].">
      <j1 rule="hyper" parents="373 24954 26087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26113">
    <literal><![CDATA[
      L(K(x,y) * (z \ 1),z,z) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(236,a,26087,a),flip(a)].">
      <j1 rule="hyper" parents="236 26087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26114">
    <literal><![CDATA[
      (x \ 1) * L(K(y,z) * (x \ 1),u,w) = x \ L(K(y,z) / x,u,w)
    ]]></literal>
    <justification jstring="[para(26113(a,1),1149(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="26113 1149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26115">
    <literal><![CDATA[
      L(K(x,y) * (x \ 1),x,x) \ z = ((x \ 1) * (x \ 1)) \ (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[para(26091(a,2),486(a,1,1))].">
      <j1 rule="para" parents="26091 486"/>
    </justification>
  </clause>

  <clause id="26116">
    <literal><![CDATA[
      K(x \ y,x) / L(x \ y,z,u) = 1 / L(y / x,z,u)
    ]]></literal>
    <justification jstring="[para(5774(a,1),26073(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5774 26073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26117">
    <literal><![CDATA[
      L(x \ y,z,u) * (K(x,x \ y) * w) = L(y / x,z,u) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,26077,a(flip),b,23278,a),flip(a)].">
      <j1 rule="hyper" parents="144 26077 23278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26118">
    <literal><![CDATA[
      (x \ L(y \ z,u,w)) * K(y,y \ z) = x \ L(z / y,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,26077,a(flip),b,23055,a),flip(a)].">
      <j1 rule="hyper" parents="139 26077 23055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26119">
    <literal><![CDATA[
      K(x \ y,x) * (L(x \ y,z,u) \ w) = L(y / x,z,u) \ w
    ]]></literal>
    <justification jstring="[para(26077(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26077 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26120">
    <literal><![CDATA[
      a(x * y,z,x * y) \ (y * x) = L(x * T(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11040,a,b,26078,a)].">
      <j1 rule="hyper" parents="64 11040 26078"/>
    </justification>
  </clause>

  <clause id="26121">
    <literal><![CDATA[
      K(x,y) * (L(z \ 1,u,w) \ v5) = L(z \ K(y,x),u,w) \ v5
    ]]></literal>
    <justification jstring="[para(26080(a,1),23272(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26080 23272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26122">
    <literal><![CDATA[
      T(x,x \ 1) * L(y,x,x) = x * (x * ((1 / x) * y))
    ]]></literal>
    <justification jstring="[para(2451(a,1),26093(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2451 26093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26123">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ z,u,w) = x * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(6075(a,1),26093(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6075 26093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26124">
    <literal><![CDATA[
      T(x,y) * L(L(T(y,x),z,u),w,v5) = x * L(L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(24550(a,1),26093(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="24550 26093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26125">
    <literal><![CDATA[
      x * L(x \ (T(x \ 1,y) \ z),u,w) = T(x \ 1,y) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,6170,a(flip),b,26097,a)].">
      <j1 rule="hyper" parents="64 6170 26097"/>
    </justification>
  </clause>

  <clause id="26127">
    <literal><![CDATA[
      (K(x,y) / z) \ (z * u) = z * ((z \ K(x,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,26112,a)].">
      <j1 rule="hyper" parents="139 168 26112"/>
    </justification>
  </clause>

  <clause id="26128">
    <literal><![CDATA[
      L(x * K(x * x,y),x,y) = y \ (((x * x) * y) / x)
    ]]></literal>
    <justification jstring="[para(11186(a,1),26092(a,1,1))].">
      <j1 rule="para" parents="11186 26092"/>
    </justification>
  </clause>

  <clause id="26129">
    <literal><![CDATA[
      L(K(x \ 1,y) * (x \ z),x,x) = T(1 / x,T(y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,7979,a(flip),b,26099,a),flip(a)].">
      <j1 rule="hyper" parents="373 7979 26099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26130">
    <literal><![CDATA[
      L(x,y,y) * K(y,y \ 1) = y * ((1 / y) * x)
    ]]></literal>
    <justification jstring="[hyper(35,a,3661,a,b,26122,a(flip))].">
      <j1 rule="hyper" parents="35 3661 26122"/>
    </justification>
  </clause>

  <clause id="26131">
    <literal><![CDATA[
      (x * y) \ ((y * y) * x) = x \ (((y * y) * x) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14648,a(flip),b,26128,a)].">
      <j1 rule="hyper" parents="64 14648 26128"/>
    </justification>
  </clause>

  <clause id="26132">
    <literal><![CDATA[
      (x * y) \ ((y * y) * x) = x \ ((y * y) * (x / y))
    ]]></literal>
    <justification jstring="[para(807(a,1),26131(a,2,2))].">
      <j1 rule="para" parents="807 26131"/>
    </justification>
  </clause>

  <clause id="26133">
    <literal><![CDATA[
      L(x,y,z) * (K(u \ x,u) * w) = L((u \ x) * u,y,z) * w
    ]]></literal>
    <justification jstring="[para(354(a,1),26075(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="354 26075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26136">
    <literal><![CDATA[
      (x \ L(y,z,z)) * K(y * z,z) = x \ (((1 / z) * y) * z)
    ]]></literal>
    <justification jstring="[para(15142(a,1),26076(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15142 26076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26137">
    <literal><![CDATA[
      K(x,y) * (L(x * y,z,u) \ w) = L(y * x,z,u) \ w
    ]]></literal>
    <justification jstring="[para(94(a,1),26084(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="94 26084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26138">
    <literal><![CDATA[
      K(x,x \ y) * (L(y,z,u) \ w) = L((x \ y) * x,z,u) \ w
    ]]></literal>
    <justification jstring="[para(354(a,1),26084(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="354 26084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26139">
    <literal><![CDATA[
      L(x / (x / y),z,u) \ w = K(y,y \ x) * (L(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(5793(a,2),26084(a,1,1,1))].">
      <j1 rule="para" parents="5793 26084"/>
    </justification>
  </clause>

  <clause id="26140">
    <literal><![CDATA[
      K(x,y) * (L(y * x,z,u) * w) = L(x * y,z,u) * w
    ]]></literal>
    <justification jstring="[para(5796(a,1),26094(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5796 26094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26141">
    <literal><![CDATA[
      L(x,y,z) \ (K(u,T(w,x)) * v5) = L(x * K(w,u),y,z) \ v5
    ]]></literal>
    <justification jstring="[para(8194(a,1),26104(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8194 26104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26142">
    <literal><![CDATA[
      (K(x,y) * (L(z,x,x) / u)) \ (((1 / x) * ((T(x,y) * z) * u)) / u) = L(u,T(x,y) * z,1 / x)
    ]]></literal>
    <justification jstring="[para(26105(a,1),6658(a,1,1))].">
      <j1 rule="para" parents="26105 6658"/>
    </justification>
  </clause>

  <clause id="26143">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,u),w) = L(x \ T(y,w),z,u)
    ]]></literal>
    <justification jstring="[hyper(3288,a,26123,a)].">
      <j1 rule="hyper" parents="3288 26123"/>
    </justification>
  </clause>

  <clause id="26147">
    <literal><![CDATA[
      T(x * L(x \ y,z,u),w) = x * L(x \ T(y,w),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,3285,a(flip),b,26123,a)].">
      <j1 rule="hyper" parents="64 3285 26123"/>
    </justification>
  </clause>

  <clause id="26149">
    <literal><![CDATA[
      L(x * y,z,u) \ K(x,y) = L(y * x,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(721,a,26140,a)].">
      <j1 rule="hyper" parents="721 26140"/>
    </justification>
  </clause>

  <clause id="26151">
    <literal><![CDATA[
      L(x \ T(x * y,z),u,w) = x \ T(x * L(y,u,w),z)
    ]]></literal>
    <justification jstring="[para(9(a,1),26143(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 26143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26156">
    <literal><![CDATA[
      x * L(x \ T(y * x,z),u,w) = T(L(y,u,w) * x,z)
    ]]></literal>
    <justification jstring="[para(833(a,1),26147(a,1,1)),flip(a)].">
      <j1 rule="para" parents="833 26147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26158">
    <literal><![CDATA[
      L(x \ T(x * y,z),u,w) = T(L(y,u,w) * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,5434,a,b,26151,a),flip(a)].">
      <j1 rule="hyper" parents="373 5434 26151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26160">
    <literal><![CDATA[
      x * L(L(R(y,x,y),z,u),w,v5) = T(L(L(y,z,u),w,v5) * x,y)
    ]]></literal>
    <justification jstring="[para(25671(a,1),26156(a,1,2,1))].">
      <j1 rule="para" parents="25671 26156"/>
    </justification>
  </clause>

  <clause id="26161">
    <literal><![CDATA[
      x * L(R(R(y,x,y),z,u),w,v5) = T(L(R(y,z,u),w,v5) * x,y)
    ]]></literal>
    <justification jstring="[para(25676(a,1),26156(a,1,2,1))].">
      <j1 rule="para" parents="25676 26156"/>
    </justification>
  </clause>

  <clause id="26162">
    <literal><![CDATA[
      R(x,y,z * K(u,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,111,a,b,25963,a)].">
      <j1 rule="hyper" parents="36 111 25963"/>
    </justification>
  </clause>

  <clause id="26163">
    <literal><![CDATA[
      R(x,y,(z * K(u,w)) \ v5) = R(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,24941,a,b,26162,a)].">
      <j1 rule="hyper" parents="64 24941 26162"/>
    </justification>
  </clause>

  <clause id="26164">
    <literal><![CDATA[
      R(x,y,z * u) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(94(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="94 26162"/>
    </justification>
  </clause>

  <clause id="26165">
    <literal><![CDATA[
      R(x,y,(z \ u) * z) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(353(a,1),26162(a,1,3)),flip(a)].">
      <j1 rule="para" parents="353 26162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26166">
    <literal><![CDATA[
      R(x,y,z * (u / z)) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(355(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="355 26162"/>
    </justification>
  </clause>

  <clause id="26167">
    <literal><![CDATA[
      R(x,y,L(z,u,w) * (w * u)) = R(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[para(609(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="609 26162"/>
    </justification>
  </clause>

  <clause id="26168">
    <literal><![CDATA[
      R(x,y,z \ T(u,w)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(2433(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="2433 26162"/>
    </justification>
  </clause>

  <clause id="26169">
    <literal><![CDATA[
      R(x,y,(L(z,u,w) \ 1) * z) = R(x,y,L(z,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(5207(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="5207 26162"/>
    </justification>
  </clause>

  <clause id="26170">
    <literal><![CDATA[
      R(x,y,z * T(u,w)) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(6249(a,1),26162(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6249 26162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26171">
    <literal><![CDATA[
      R(x,y,z * (u / w)) = R(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[para(6471(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="6471 26162"/>
    </justification>
  </clause>

  <clause id="26172">
    <literal><![CDATA[
      R(x,y,K(z,u) * w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[para(6576(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="6576 26162"/>
    </justification>
  </clause>

  <clause id="26173">
    <literal><![CDATA[
      R(x,y,T(z,u) * w) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(6570(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="6570 26162"/>
    </justification>
  </clause>

  <clause id="26174">
    <literal><![CDATA[
      R(x,y,z * (u * (w / u))) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(7201(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="7201 26162"/>
    </justification>
  </clause>

  <clause id="26175">
    <literal><![CDATA[
      R(x,y,(z * z) * (u / z)) = R(x,y,(1 / z) \ u)
    ]]></literal>
    <justification jstring="[para(7211(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="7211 26162"/>
    </justification>
  </clause>

  <clause id="26177">
    <literal><![CDATA[
      R(x,y,z * (u * T(w,v5))) = R(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(7368(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="7368 26162"/>
    </justification>
  </clause>

  <clause id="26178">
    <literal><![CDATA[
      R(x,y,z * (u * w)) = R(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[para(7591(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="7591 26162"/>
    </justification>
  </clause>

  <clause id="26179">
    <literal><![CDATA[
      R(x,y,T(z,u) \ w) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(7948(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="7948 26162"/>
    </justification>
  </clause>

  <clause id="26180">
    <literal><![CDATA[
      R(x,y,(z / u) * w) = R(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(8651(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="8651 26162"/>
    </justification>
  </clause>

  <clause id="26181">
    <literal><![CDATA[
      R(x,y,z * ((u \ w) * u)) = R(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(10196(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="10196 26162"/>
    </justification>
  </clause>

  <clause id="26182">
    <literal><![CDATA[
      R(x,y,z * (u * K(w,v5))) = R(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(12078(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="12078 26162"/>
    </justification>
  </clause>

  <clause id="26183">
    <literal><![CDATA[
      R(x,y,z \ (u / w)) = R(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(15028(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="15028 26162"/>
    </justification>
  </clause>

  <clause id="26184">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) \ w)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(15035(a,2),26162(a,1,3))].">
      <j1 rule="para" parents="15035 26162"/>
    </justification>
  </clause>

  <clause id="26185">
    <literal><![CDATA[
      R(x,y,z \ (u * w)) = R(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[para(14934(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="14934 26162"/>
    </justification>
  </clause>

  <clause id="26186">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) * u)) = R(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(15230(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="15230 26162"/>
    </justification>
  </clause>

  <clause id="26187">
    <literal><![CDATA[
      R(x,y,z \ (u * K(w,v5))) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(16164(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="16164 26162"/>
    </justification>
  </clause>

  <clause id="26188">
    <literal><![CDATA[
      R(x,y,z * (K(u,w) * v5)) = R(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(23252(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="23252 26162"/>
    </justification>
  </clause>

  <clause id="26189">
    <literal><![CDATA[
      R(x,y,z \ (K(u,w) * v5)) = R(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(23401(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="23401 26162"/>
    </justification>
  </clause>

  <clause id="26192">
    <literal><![CDATA[
      R(x,y,z * (u * (w * K(v5,v6)))) = R(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(25230(a,1),26162(a,1,3))].">
      <j1 rule="para" parents="25230 26162"/>
    </justification>
  </clause>

  <clause id="26193">
    <literal><![CDATA[
      R(x,y,L(z * K(u,w),v5,v6)) = R(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(26070(a,2),26162(a,1,3))].">
      <j1 rule="para" parents="26070 26162"/>
    </justification>
  </clause>

  <clause id="26194">
    <literal><![CDATA[
      R(T(x,x \ 1),x,y) = R(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,11443,a,b,26164,a)].">
      <j1 rule="hyper" parents="373 11443 26164"/>
    </justification>
  </clause>

  <clause id="26195">
    <literal><![CDATA[
      R(R(x,x,x),x,y) = R(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,11442,a,b,26164,a)].">
      <j1 rule="hyper" parents="373 11442 26164"/>
    </justification>
  </clause>

  <clause id="26196">
    <literal><![CDATA[
      R(1 / (1 / x),x,y * z) = R(x,x,x \ (z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,3021,a(flip),b,26164,a),flip(a)].">
      <j1 rule="hyper" parents="373 3021 26164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26197">
    <literal><![CDATA[
      R(T(x \ 1,y * z),x,z * y) = (y * z) \ (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,2985,a(flip),b,26164,a),flip(a)].">
      <j1 rule="hyper" parents="373 2985 26164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26198">
    <literal><![CDATA[
      R(x,y,z * u) * (y * (u * z)) = (x * y) * (u * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,26164,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="144 26164 20"/>
    </justification>
  </clause>

  <clause id="26199">
    <literal><![CDATA[
      x \ R(y,z,u * w) = x \ R(y,z,w * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,26164,a,b,10,a)].">
      <j1 rule="hyper" parents="139 26164 10"/>
    </justification>
  </clause>

  <clause id="26200">
    <literal><![CDATA[
      R(x,y,((1 / z) * u) * (w * w)) = R(x,y,((w * w) / z) * u)
    ]]></literal>
    <justification jstring="[para(556(a,1),26164(a,1,3)),flip(a)].">
      <j1 rule="para" parents="556 26164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26201">
    <literal><![CDATA[
      R(x,x,y * x) * y = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(26164(a,1),2044(a,1,1))].">
      <j1 rule="para" parents="26164 2044"/>
    </justification>
  </clause>

  <clause id="26202">
    <literal><![CDATA[
      R(x,y,z * (y \ 1)) * L(z,y,y) = (x * y) * ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(26164(a,1),1153(a,1,1))].">
      <j1 rule="para" parents="26164 1153"/>
    </justification>
  </clause>

  <clause id="26203">
    <literal><![CDATA[
      R(x,y,(z \ (u * w)) * z) = R(x,y,w * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26164,a,b,26165,a),flip(a)].">
      <j1 rule="hyper" parents="373 26164 26165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26204">
    <literal><![CDATA[
      R(x,y,L((z \ u) * z,w,v5)) = R(x,y,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(5544(a,2),26165(a,1,3))].">
      <j1 rule="para" parents="5544 26165"/>
    </justification>
  </clause>

  <clause id="26206">
    <literal><![CDATA[
      R(x,y,K(z,u) * (w * v5)) = R(x,y,v5 * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26164,a,b,26172,a),flip(a)].">
      <j1 rule="hyper" parents="373 26164 26172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26209">
    <literal><![CDATA[
      R(x,y,(z / u) \ w) = R(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),26172(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6270 26172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26210">
    <literal><![CDATA[
      R(x,y,((z * z) \ u) * w) = R(x,y,u * ((z * z) \ w))
    ]]></literal>
    <justification jstring="[para(6024(a,1),26172(a,1,3))].">
      <j1 rule="para" parents="6024 26172"/>
    </justification>
  </clause>

  <clause id="26211">
    <literal><![CDATA[
      R(x,y,z \ ((u * u) * w)) = R(x,y,(u * u) * (z \ w))
    ]]></literal>
    <justification jstring="[para(6626(a,1),26172(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6626 26172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26212">
    <literal><![CDATA[
      R(x,y,(z * u) \ w) = R(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[para(10833(a,1),26172(a,1,3))].">
      <j1 rule="para" parents="10833 26172"/>
    </justification>
  </clause>

  <clause id="26213">
    <literal><![CDATA[
      R(x,y,(z * u) * w) = R(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[para(10834(a,1),26172(a,1,3))].">
      <j1 rule="para" parents="10834 26172"/>
    </justification>
  </clause>

  <clause id="26214">
    <literal><![CDATA[
      R(x,y,((z \ u) * z) \ w) = R(x,y,u \ w)
    ]]></literal>
    <justification jstring="[para(10843(a,1),26172(a,1,3))].">
      <j1 rule="para" parents="10843 26172"/>
    </justification>
  </clause>

  <clause id="26216">
    <literal><![CDATA[
      R(x,y,(T(z,u) \ w) * v5) = R(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[para(24347(a,1),26172(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24347 26172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26217">
    <literal><![CDATA[
      R(x,y,(z * T(u,w)) \ v5) = R(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(24506(a,1),26172(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24506 26172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26218">
    <literal><![CDATA[
      R(x,y,L(T(z,u),w,v5) \ v6) = R(x,y,L(z,w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(24557(a,1),26172(a,1,3))].">
      <j1 rule="para" parents="24557 26172"/>
    </justification>
  </clause>

  <clause id="26219">
    <literal><![CDATA[
      R(x,y,(T(z,u) \ w) \ v5) = R(x,y,(z \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(25410(a,1),26172(a,1,3))].">
      <j1 rule="para" parents="25410 26172"/>
    </justification>
  </clause>

  <clause id="26220">
    <literal><![CDATA[
      R(x,y,((z / u) * w) * v5) = R(x,y,((u \ z) * w) * v5)
    ]]></literal>
    <justification jstring="[para(24351(a,1),26172(a,1,3))].">
      <j1 rule="para" parents="24351 26172"/>
    </justification>
  </clause>

  <clause id="26221">
    <literal><![CDATA[
      R(x,y,(z * (u / w)) \ v5) = R(x,y,(z * (w \ u)) \ v5)
    ]]></literal>
    <justification jstring="[para(24507(a,1),26172(a,1,3))].">
      <j1 rule="para" parents="24507 26172"/>
    </justification>
  </clause>

  <clause id="26222">
    <literal><![CDATA[
      R(x,y,(z \ (u / w)) \ v5) = R(x,y,(z \ (w \ u)) \ v5)
    ]]></literal>
    <justification jstring="[para(24522(a,1),26172(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24522 26172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26223">
    <literal><![CDATA[
      R(x,y,(z \ ((u \ w) \ w)) \ v5) = R(x,y,(z \ u) \ v5)
    ]]></literal>
    <justification jstring="[para(24536(a,1),26172(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24536 26172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26224">
    <literal><![CDATA[
      R(x,y,((z * T(u,w)) \ v5) * v6) = R(x,y,((z * u) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(24968(a,1),26172(a,1,3))].">
      <j1 rule="para" parents="24968 26172"/>
    </justification>
  </clause>

  <clause id="26225">
    <literal><![CDATA[
      R(x,y,(z * (K(u,w) * v5)) \ v6) = R(x,y,(z * v5) \ v6)
    ]]></literal>
    <justification jstring="[para(25411(a,1),26172(a,1,3))].">
      <j1 rule="para" parents="25411 26172"/>
    </justification>
  </clause>

  <clause id="26226">
    <literal><![CDATA[
      R(x,y,R(K(z,u) * w,v5,v6) * v7) = R(x,y,R(w,v5,v6) * v7)
    ]]></literal>
    <justification jstring="[para(25968(a,2),26172(a,1,3))].">
      <j1 rule="para" parents="25968 26172"/>
    </justification>
  </clause>

  <clause id="26227">
    <literal><![CDATA[
      R(R(x,x,y),x,x) = R(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,31,a,b,26195,a)].">
      <j1 rule="hyper" parents="64 31 26195"/>
    </justification>
  </clause>

  <clause id="26228">
    <literal><![CDATA[
      R(T(x,x \ (x \ 1)),x,y) = R(x,x,y * x)
    ]]></literal>
    <justification jstring="[para(1561(a,2),26195(a,1,1))].">
      <j1 rule="para" parents="1561 26195"/>
    </justification>
  </clause>

  <clause id="26229">
    <literal><![CDATA[
      T(R(x,x,y) \ 1,x) = R(x,x,y * x) \ 1
    ]]></literal>
    <justification jstring="[para(26195(a,1),25604(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26195 25604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26230">
    <literal><![CDATA[
      R((x * y) * y,x,y * x) = ((x \ 1) \ y) * y
    ]]></literal>
    <justification jstring="[para(26201(a,1),2106(a,2,1))].">
      <j1 rule="para" parents="26201 2106"/>
    </justification>
  </clause>

  <clause id="26234">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) / w)) = R(x,y,z \ (w / (u * w)))
    ]]></literal>
    <justification jstring="[para(3007(a,1),26168(a,1,3,2))].">
      <j1 rule="para" parents="3007 26168"/>
    </justification>
  </clause>

  <clause id="26235">
    <literal><![CDATA[
      R(x,x \ y,z \ T(u,w)) \ (y * (z \ T(T(u,w),v5))) = (x \ y) * (z \ T(T(u,v5),w))
    ]]></literal>
    <justification jstring="[para(26168(a,1),1449(a,1,1))].">
      <j1 rule="para" parents="26168 1449"/>
    </justification>
  </clause>

  <clause id="26236">
    <literal><![CDATA[
      R(x,y,z * T(u,w)) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,26164,a,b,26170,a),flip(a)].">
      <j1 rule="hyper" parents="373 26164 26170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26237">
    <literal><![CDATA[
      R(x,y,(z / u) \ u) = R(x,y,(u / z) * u)
    ]]></literal>
    <justification jstring="[para(3818(a,1),26173(a,1,3))].">
      <j1 rule="para" parents="3818 26173"/>
    </justification>
  </clause>

  <clause id="26238">
    <literal><![CDATA[
      R(x,y,(z * z) \ (u \ z)) = R(x,y,u \ (1 / z))
    ]]></literal>
    <justification jstring="[para(1527(a,1),26179(a,1,3))].">
      <j1 rule="para" parents="1527 26179"/>
    </justification>
  </clause>

  <clause id="26239">
    <literal><![CDATA[
      R(x,y,T(z * u,z) \ ((w * w) * v5)) = R(x,y,(z * ((w * w) \ u)) \ v5)
    ]]></literal>
    <justification jstring="[para(4860(a,1),26179(a,1,3))].">
      <j1 rule="para" parents="4860 26179"/>
    </justification>
  </clause>

  <clause id="26240">
    <literal><![CDATA[
      R(x,y,R(z,z,u * z)) = R(x,y,R(z,z,u))
    ]]></literal>
    <justification jstring="[para(26194(a,1),23812(a,1,3))].">
      <j1 rule="para" parents="26194 23812"/>
    </justification>
  </clause>

  <clause id="26241">
    <literal><![CDATA[
      R(x,y,(z / u) * w) = R(x,y,w * (u \ z))
    ]]></literal>
    <justification jstring="[para(117(a,1),26236(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="117 26236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26242">
    <literal><![CDATA[
      R(x,y,z * ((1 / u) \ u)) = R(x,y,(u * u) * z)
    ]]></literal>
    <justification jstring="[para(562(a,1),26236(a,1,3,2))].">
      <j1 rule="para" parents="562 26236"/>
    </justification>
  </clause>

  <clause id="26244">
    <literal><![CDATA[
      R(x,y,(T(z,u) * w) \ v5) = R(x,y,(z * w) \ v5)
    ]]></literal>
    <justification jstring="[para(6570(a,1),26163(a,1,3,1))].">
      <j1 rule="para" parents="6570 26163"/>
    </justification>
  </clause>

  <clause id="26245">
    <literal><![CDATA[
      R(x,y,((z / u) * w) \ v5) = R(x,y,((u \ z) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(8651(a,1),26163(a,1,3,1))].">
      <j1 rule="para" parents="8651 26163"/>
    </justification>
  </clause>

  <clause id="26246">
    <literal><![CDATA[
      R(x,y,(z \ u) * w) = R(x,y,w * (u / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,26164,a,b,26171,a)].">
      <j1 rule="hyper" parents="373 26164 26171"/>
    </justification>
  </clause>

  <clause id="26247">
    <literal><![CDATA[
      R(x,y,(z * u) * w) = R(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,26164,a,b,26178,a)].">
      <j1 rule="hyper" parents="373 26164 26178"/>
    </justification>
  </clause>

  <clause id="26248">
    <literal><![CDATA[
      R(1 / x,x,(y \ z) * u) = ((z / y) * u) / (x * ((z / y) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,244,a(flip),b,26180,a),flip(a)].">
      <j1 rule="hyper" parents="64 244 26180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26249">
    <literal><![CDATA[
      R(x,y,((z \ u) * z) * w) = R(x,y,w * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26164,a,b,26181,a)].">
      <j1 rule="hyper" parents="64 26164 26181"/>
    </justification>
  </clause>

  <clause id="26250">
    <literal><![CDATA[
      R(x,y,(z * K(u,w)) * v5) = R(x,y,v5 * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26164,a,b,26182,a)].">
      <j1 rule="hyper" parents="64 26164 26182"/>
    </justification>
  </clause>

  <clause id="26251">
    <literal><![CDATA[
      R(x,y,z * (K(u,w) \ v5)) = R(x,y,z * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26181,a(flip),b,26182,a),flip(a)].">
      <j1 rule="hyper" parents="64 26181 26182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26252">
    <literal><![CDATA[
      R(x,y,z * (u * ((w \ v5) \ v5))) = R(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(6326(a,1),26182(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6326 26182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26253">
    <literal><![CDATA[
      R(x,y,z * (u * (w / v5))) = R(x,y,z * (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(6471(a,1),26182(a,1,3,2))].">
      <j1 rule="para" parents="6471 26182"/>
    </justification>
  </clause>

  <clause id="26254">
    <literal><![CDATA[
      R(x,y,z * (u \ (w / v5))) = R(x,y,z * (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(15028(a,1),26182(a,1,3,2))].">
      <j1 rule="para" parents="15028 26182"/>
    </justification>
  </clause>

  <clause id="26255">
    <literal><![CDATA[
      R(x,y,z * L(u \ K(w,v5),v6,v7)) = R(x,y,z * L(u \ 1,v6,v7))
    ]]></literal>
    <justification jstring="[para(26080(a,1),26182(a,1,3,2))].">
      <j1 rule="para" parents="26080 26182"/>
    </justification>
  </clause>

  <clause id="26256">
    <literal><![CDATA[
      R(x,y,(z * z) \ 1) = R(x,y,z \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,23815,a,b,26183,a)].">
      <j1 rule="hyper" parents="64 23815 26183"/>
    </justification>
  </clause>

  <clause id="26257">
    <literal><![CDATA[
      R(1 / x,x,y \ (x \ y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,3810,a(flip),b,26183,a),flip(a)].">
      <j1 rule="hyper" parents="64 3810 26183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26258">
    <literal><![CDATA[
      R(x,y,(z / u) \ ((1 / u) \ z)) = R(x,y,u * u)
    ]]></literal>
    <justification jstring="[para(814(a,1),26183(a,1,3)),flip(a)].">
      <j1 rule="para" parents="814 26183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26259">
    <literal><![CDATA[
      R(x,x,y \ (x \ y)) \ L(x,x,y) = x * (y \ (y / x))
    ]]></literal>
    <justification jstring="[para(26183(a,1),26054(a,1,1))].">
      <j1 rule="para" parents="26183 26054"/>
    </justification>
  </clause>

  <clause id="26260">
    <literal><![CDATA[
      R(1 / x,x,(x * y) \ y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,24667,a,b,26257,a)].">
      <j1 rule="hyper" parents="64 24667 26257"/>
    </justification>
  </clause>

  <clause id="26261">
    <literal><![CDATA[
      (x \ 1) * (x * (y \ (x \ y))) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(144,a,26257,a(flip),b,244,a(flip))].">
      <j1 rule="hyper" parents="144 26257 244"/>
    </justification>
  </clause>

  <clause id="26262">
    <literal><![CDATA[
      (x \ 1) \ (y \ (x \ y)) = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(26257(a,1),452(a,1,1))].">
      <j1 rule="para" parents="26257 452"/>
    </justification>
  </clause>

  <clause id="26263">
    <literal><![CDATA[
      (x \ 1) \ T(y \ (x \ y),z) = x * T(y \ (x \ y),z)
    ]]></literal>
    <justification jstring="[para(26257(a,1),15091(a,1,1))].">
      <j1 rule="para" parents="26257 15091"/>
    </justification>
  </clause>

  <clause id="26264">
    <literal><![CDATA[
      (x \ 1) \ ((x * y) \ y) = x * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(26260(a,1),452(a,1,1))].">
      <j1 rule="para" parents="26260 452"/>
    </justification>
  </clause>

  <clause id="26265">
    <literal><![CDATA[
      (x \ 1) \ (y / (x * y)) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(26260(a,1),15113(a,1,1))].">
      <j1 rule="para" parents="26260 15113"/>
    </justification>
  </clause>

  <clause id="26268">
    <literal><![CDATA[
      R(x,y,z \ (u * (w * v5))) = R(x,y,z \ (u * (v5 * w)))
    ]]></literal>
    <justification jstring="[para(7591(a,1),26187(a,1,3,2))].">
      <j1 rule="para" parents="7591 26187"/>
    </justification>
  </clause>

  <clause id="26269">
    <literal><![CDATA[
      R(x,y,z \ (T(u,w) \ v5)) = R(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(7948(a,1),26187(a,1,3,2))].">
      <j1 rule="para" parents="7948 26187"/>
    </justification>
  </clause>

  <clause id="26270">
    <literal><![CDATA[
      R(x,y,z \ ((u / w) * v5)) = R(x,y,z \ ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(8651(a,1),26187(a,1,3,2))].">
      <j1 rule="para" parents="8651 26187"/>
    </justification>
  </clause>

  <clause id="26271">
    <literal><![CDATA[
      R(x,y,z \ (u \ (w * v5))) = R(x,y,z \ (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[para(14934(a,1),26187(a,1,3,2))].">
      <j1 rule="para" parents="14934 26187"/>
    </justification>
  </clause>

  <clause id="26273">
    <literal><![CDATA[
      R(x,y,(K(z,u) * w) * v5) = R(x,y,v5 * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26164,a,b,26188,a)].">
      <j1 rule="hyper" parents="64 26164 26188"/>
    </justification>
  </clause>

  <clause id="26274">
    <literal><![CDATA[
      R(x,y,z * ((u / (u / w)) * v5)) = R(x,y,z * (w * v5))
    ]]></literal>
    <justification jstring="[para(5984(a,1),26188(a,1,3,2))].">
      <j1 rule="para" parents="5984 26188"/>
    </justification>
  </clause>

  <clause id="26275">
    <literal><![CDATA[
      R(x,y,z * ((u / w) \ v5)) = R(x,y,z * ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(6270(a,1),26188(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6270 26188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26277">
    <literal><![CDATA[
      R(x,y,z \ (((u \ w) \ w) \ v5)) = R(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(6073(a,1),26189(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6073 26189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26278">
    <literal><![CDATA[
      R(x,y,z \ ((u / w) \ v5)) = R(x,y,z \ ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(6270(a,1),26189(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6270 26189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26279">
    <literal><![CDATA[
      R(x,y,z \ ((u * T(w,v5)) \ v6)) = R(x,y,z \ ((u * w) \ v6))
    ]]></literal>
    <justification jstring="[para(24506(a,1),26189(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="24506 26189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26280">
    <literal><![CDATA[
      R(x,y,((z / u) \ w) \ v5) = R(x,y,((u \ z) \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(24402(a,1),26189(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24402 26189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26281">
    <literal><![CDATA[
      R(x,y,((z * T(u,w)) \ v5) \ v6) = R(x,y,((z * u) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[para(24967(a,1),26189(a,1,3))].">
      <j1 rule="para" parents="24967 26189"/>
    </justification>
  </clause>

  <clause id="26282">
    <literal><![CDATA[
      R(x,y,z \ R(K(u,w) * v5,v6,v7)) = R(x,y,z \ R(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(25964(a,2),26189(a,1,3,2))].">
      <j1 rule="para" parents="25964 26189"/>
    </justification>
  </clause>

  <clause id="26283">
    <literal><![CDATA[
      x * (x * (y / (x * y))) = R(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,3015,a(flip),b,26199,a)].">
      <j1 rule="hyper" parents="145 3015 26199"/>
    </justification>
  </clause>

  <clause id="26284">
    <literal><![CDATA[
      R(x,y,(z * u) * (w * w)) = R(x,y,u * ((w * w) * z))
    ]]></literal>
    <justification jstring="[para(125(a,1),26203(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="125 26203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26285">
    <literal><![CDATA[
      R(x,y,((z \ u) \ u) * w) = R(x,y,w * z)
    ]]></literal>
    <justification jstring="[para(6025(a,1),26206(a,1,3))].">
      <j1 rule="para" parents="6025 26206"/>
    </justification>
  </clause>

  <clause id="26286">
    <literal><![CDATA[
      R(x,y,z * (T(u,w) \ v5)) = R(x,y,(u \ v5) * z)
    ]]></literal>
    <justification jstring="[para(24347(a,1),26206(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24347 26206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26287">
    <literal><![CDATA[
      R(x,y,((z * u) \ w) * v5) = R(x,y,v5 * ((u * z) \ w))
    ]]></literal>
    <justification jstring="[para(23247(a,1),26206(a,1,3))].">
      <j1 rule="para" parents="23247 26206"/>
    </justification>
  </clause>

  <clause id="26288">
    <literal><![CDATA[
      R(x,y,(z * T(u,w)) * v5) = R(x,y,v5 * (z * u))
    ]]></literal>
    <justification jstring="[para(24355(a,1),26206(a,1,3))].">
      <j1 rule="para" parents="24355 26206"/>
    </justification>
  </clause>

  <clause id="26289">
    <literal><![CDATA[
      R(x,y,((z / u) * w) * v5) = R(x,y,v5 * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(24351(a,1),26206(a,1,3))].">
      <j1 rule="para" parents="24351 26206"/>
    </justification>
  </clause>

  <clause id="26290">
    <literal><![CDATA[
      R(x,y,z / (u * w)) = R(x,y,(w * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,23813,a,b,26212,a)].">
      <j1 rule="hyper" parents="373 23813 26212"/>
    </justification>
  </clause>

  <clause id="26291">
    <literal><![CDATA[
      R(x,y,(z * u) \ z) = R(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,24667,a(flip),b,26212,a),flip(a)].">
      <j1 rule="hyper" parents="373 24667 26212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26292">
    <literal><![CDATA[
      R(x,y,((z \ u) * (1 / z)) \ w) = R(x,y,((z * z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(536(a,1),26212(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="536 26212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26293">
    <literal><![CDATA[
      R(x,y,L(z \ u,z,w)) = R(x,y,(z * w) \ (w * u))
    ]]></literal>
    <justification jstring="[para(102(a,2),26212(a,1,3))].">
      <j1 rule="para" parents="102 26212"/>
    </justification>
  </clause>

  <clause id="26294">
    <literal><![CDATA[
      R(x,y,(y * x) \ z) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(26212(a,1),420(a,1,1))].">
      <j1 rule="para" parents="26212 420"/>
    </justification>
  </clause>

  <clause id="26295">
    <literal><![CDATA[
      R((x \ 1) \ y,x,y \ z) \ z = (x \ 1) * ((((x \ 1) \ y) * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[para(26214(a,1),2986(a,1,1))].">
      <j1 rule="para" parents="26214 2986"/>
    </justification>
  </clause>

  <clause id="26296">
    <literal><![CDATA[
      T(R(x,x,y),x \ (x \ 1)) = R(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(795,a,26228,a)].">
      <j1 rule="hyper" parents="795 26228"/>
    </justification>
  </clause>

  <clause id="26297">
    <literal><![CDATA[
      T(R(x,x,y) \ 1,x) \ R(R(x,x,y * x) \ 1,z,u) = R(x,x,y * x) \ (1 * R(1 \ R(x,x,y * x),z,u))
    ]]></literal>
    <justification jstring="[para(26229(a,2),2744(a,1,1))].">
      <j1 rule="para" parents="26229 2744"/>
    </justification>
  </clause>

  <clause id="26298">
    <literal><![CDATA[
      R(x,y,(z \ u) \ z) = R(x,y,(z / u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26209,a(flip),b,26237,a)].">
      <j1 rule="hyper" parents="64 26209 26237"/>
    </justification>
  </clause>

  <clause id="26299">
    <literal><![CDATA[
      R(x,y,R(z,z,z \ u)) = R(x,y,R(z,z,u))
    ]]></literal>
    <justification jstring="[para(26165(a,1),26240(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26165 26240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26300">
    <literal><![CDATA[
      R(x,y,L(z * (u \ 1),u,u)) = R(x,y,(u \ 1) * L(z,u,u))
    ]]></literal>
    <justification jstring="[para(3747(a,2),26246(a,2,3)),flip(a)].">
      <j1 rule="para" parents="3747 26246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26301">
    <literal><![CDATA[
      R(x,y,(z * L(T(u,w),v5,v6)) * v7) = R(x,y,v7 * (z * L(u,v5,v6)))
    ]]></literal>
    <justification jstring="[para(25231(a,1),26250(a,1,3,1))].">
      <j1 rule="para" parents="25231 26250"/>
    </justification>
  </clause>

  <clause id="26302">
    <literal><![CDATA[
      R(x,y,L(z \ K(u,w),v5,v6) * v7) = R(x,y,v7 * L(z \ 1,v5,v6))
    ]]></literal>
    <justification jstring="[para(26080(a,1),26250(a,1,3,1))].">
      <j1 rule="para" parents="26080 26250"/>
    </justification>
  </clause>

  <clause id="26303">
    <literal><![CDATA[
      L(x * (y \ (x \ y)),x,x) = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(145,a,26261,a(flip),b,1148,a),flip(a)].">
      <j1 rule="hyper" parents="145 26261 1148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26304">
    <literal><![CDATA[
      L(x,y,z \ (u \ (z \ u))) = L(x,y,z * (u \ (z \ u)))
    ]]></literal>
    <justification jstring="[para(26262(a,1),2234(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26262 2234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26305">
    <literal><![CDATA[
      R(x,y \ (z \ (y \ z)),u) = R(x,y * (z \ (y \ z)),u)
    ]]></literal>
    <justification jstring="[para(26262(a,1),3028(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26262 3028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26306">
    <literal><![CDATA[
      (1 / x) * (((1 / x) * y) \ y) = x \ (((1 / x) * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,219,a(flip),b,26264,a),flip(a)].">
      <j1 rule="hyper" parents="64 219 26264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26307">
    <literal><![CDATA[
      (x * (y / (x * y))) \ (y / (x * y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(40,a,23873,a,b,26265,a)].">
      <j1 rule="hyper" parents="40 23873 26265"/>
    </justification>
  </clause>

  <clause id="26308">
    <literal><![CDATA[
      R(x,y,z * (((u \ w) \ w) * v5)) = R(x,y,(u * v5) * z)
    ]]></literal>
    <justification jstring="[para(6168(a,1),26273(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="6168 26273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26309">
    <literal><![CDATA[
      R(x,y,((z \ u) * w) * v5) = R(x,y,v5 * ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(6553(a,1),26273(a,1,3,1))].">
      <j1 rule="para" parents="6553 26273"/>
    </justification>
  </clause>

  <clause id="26310">
    <literal><![CDATA[
      R(R(x,(x \ 1) \ 1,y * x),x,x) * y = (((x \ 1) \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(26285(a,1),2045(a,1,1,1))].">
      <j1 rule="para" parents="26285 2045"/>
    </justification>
  </clause>

  <clause id="26311">
    <literal><![CDATA[
      R(x,y,(z * u) \ ((w * u) * z)) = R(x,y,R(w,u,z))
    ]]></literal>
    <justification jstring="[para(20(a,2),26290(a,1,3)),flip(a)].">
      <j1 rule="para" parents="20 26290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26312">
    <literal><![CDATA[
      R(x,y,x \ (y \ x)) \ x = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(26291(a,1),420(a,1,1))].">
      <j1 rule="para" parents="26291 420"/>
    </justification>
  </clause>

  <clause id="26313">
    <literal><![CDATA[
      R(x,y,(z * ((u \ z) * (z / u))) \ z) = R(x,y,z \ ((1 / (u \ z)) * u))
    ]]></literal>
    <justification jstring="[para(25894(a,1),26291(a,2,3,2))].">
      <j1 rule="para" parents="25894 26291"/>
    </justification>
  </clause>

  <clause id="26314">
    <literal><![CDATA[
      R(x,y,(z \ u) \ z) = R(x,y,(u \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,26180,a(flip),b,26298,a),flip(a)].">
      <j1 rule="hyper" parents="373 26180 26298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26315">
    <literal><![CDATA[
      (x * (y / (x * y))) * (x \ 1) = y / (x * y)
    ]]></literal>
    <justification jstring="[hyper(157,a,26307,a)].">
      <j1 rule="hyper" parents="157 26307"/>
    </justification>
  </clause>

  <clause id="26316">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,x,y * x) = (x * y) \ (((x \ 1) \ y) * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,26230,a(flip),b,2125,a),flip(a)].">
      <j1 rule="hyper" parents="139 26230 2125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26317">
    <literal><![CDATA[
      (1 / (1 / x)) * L(y \ (x \ y),x,x) = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,1260,a,b,26303,a)].">
      <j1 rule="hyper" parents="64 1260 26303"/>
    </justification>
  </clause>

  <clause id="26318">
    <literal><![CDATA[
      (x \ y) * ((y * (x \ y)) \ y) = R(y,x \ y,y \ x) \ y
    ]]></literal>
    <justification jstring="[para(26184(a,1),26312(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26184 26312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26319">
    <literal><![CDATA[
      R(x,y,(z * z) * (z \ u)) = R(x,y,(1 / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26171,a(flip),b,26175,a)].">
      <j1 rule="hyper" parents="64 26171 26175"/>
    </justification>
  </clause>

  <clause id="26320">
    <literal><![CDATA[
      R(x,y,z * (u * R(T(w,v5),v6,v7))) = R(x,y,z * (u * R(w,v6,v7)))
    ]]></literal>
    <justification jstring="[para(27(a,2),26177(a,1,3,2,2))].">
      <j1 rule="para" parents="27 26177"/>
    </justification>
  </clause>

  <clause id="26321">
    <literal><![CDATA[
      R(x,y,L(z \ T(u,w),v5,v6)) = R(x,y,L(z \ u,v5,v6))
    ]]></literal>
    <justification jstring="[para(2433(a,1),26193(a,1,3,1))].">
      <j1 rule="para" parents="2433 26193"/>
    </justification>
  </clause>

  <clause id="26322">
    <literal><![CDATA[
      R(x,y,(L(T(z,u),w,v5) \ v6) * v7) = R(x,y,(L(z,w,v5) \ v6) * v7)
    ]]></literal>
    <justification jstring="[para(25(a,2),26216(a,1,3,1,1))].">
      <j1 rule="para" parents="25 26216"/>
    </justification>
  </clause>

  <clause id="26323">
    <literal><![CDATA[
      R(x,y,(T(z,u) * w) \ v5) = R(x,y,(w * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26212,a,b,26217,a)].">
      <j1 rule="hyper" parents="64 26212 26217"/>
    </justification>
  </clause>

  <clause id="26324">
    <literal><![CDATA[
      R(T(x,y),z,(z * x) \ u) \ u = z * ((T(x,y) * z) \ u)
    ]]></literal>
    <justification jstring="[para(26217(a,1),26294(a,1,1))].">
      <j1 rule="para" parents="26217 26294"/>
    </justification>
  </clause>

  <clause id="26325">
    <literal><![CDATA[
      R(x,y,(z * z) \ (u \ z)) = R(x,y,u \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,26183,a(flip),b,26238,a),flip(a)].">
      <j1 rule="hyper" parents="373 26183 26238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26326">
    <literal><![CDATA[
      R(T(x,y),z,(x * z) \ u) \ u = z * ((T(x,y) * z) \ u)
    ]]></literal>
    <justification jstring="[para(26244(a,1),420(a,1,1))].">
      <j1 rule="para" parents="26244 420"/>
    </justification>
  </clause>

  <clause id="26327">
    <literal><![CDATA[
      R(x,y,(z \ u) \ ((1 / z) \ u)) = R(x,y,z * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26209,a(flip),b,26258,a)].">
      <j1 rule="hyper" parents="64 26209 26258"/>
    </justification>
  </clause>

  <clause id="26330">
    <literal><![CDATA[
      L(x \ R(x,y,z * (u * w)),x,y * ((u * T(w,v5)) * z)) = a(x,y,(u * T(w,v5)) * z)
    ]]></literal>
    <justification jstring="[para(26288(a,1),16031(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="26288 16031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26331">
    <literal><![CDATA[
      R(x,y,(z * z) * (z \ u)) = R(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26209,a(flip),b,26319,a),flip(a)].">
      <j1 rule="hyper" parents="373 26209 26319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26332">
    <literal><![CDATA[
      R(x,y,((z \ u) * w) \ v5) = R(x,y,(w * (u / z)) \ v5)
    ]]></literal>
    <justification jstring="[para(117(a,1),26323(a,1,3,1,1))].">
      <j1 rule="para" parents="117 26323"/>
    </justification>
  </clause>

  <clause id="26333">
    <literal><![CDATA[
      R(x,y,(((z * u) \ w) * z) \ v5) = R(x,y,(z * ((u * z) \ w)) \ v5)
    ]]></literal>
    <justification jstring="[para(10844(a,1),26323(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10844 26323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26334">
    <literal><![CDATA[
      R(x,y,L(a(z,u,w) \ v5,a(z,u,w) * a(z,u,w),v6) * (v6 * (a(z,u,w) * a(z,u,w)))) = R(x,y,v6 * ((a(z,u,w) \ 1) \ v5))
    ]]></literal>
    <justification jstring="[para(14002(a,1),26167(a,2,3,2))].">
      <j1 rule="para" parents="14002 26167"/>
    </justification>
  </clause>

  <clause id="26335">
    <literal><![CDATA[
      R(x,T(y * z,u),y * z) * ((z * y) * T(y * z,u)) = (x * T(y * z,u)) * (z * y)
    ]]></literal>
    <justification jstring="[para(5462(a,1),26198(a,1,2))].">
      <j1 rule="para" parents="5462 26198"/>
    </justification>
  </clause>

  <clause id="26336">
    <literal><![CDATA[
      R(x,y,z * (u * (w \ T(v5,v6)))) = R(x,y,z * (u * (w \ v5)))
    ]]></literal>
    <justification jstring="[para(2433(a,1),26192(a,1,3,2,2))].">
      <j1 rule="para" parents="2433 26192"/>
    </justification>
  </clause>

  <clause id="26337">
    <literal><![CDATA[
      R(x,y,(z * u) * ((z * z) \ w)) = R(x,y,((1 / z) * u) * w)
    ]]></literal>
    <justification jstring="[para(535(a,1),26210(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="535 26210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26338">
    <literal><![CDATA[
      R(x,y,z \ (u * (w * w))) = R(x,y,(w * w) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26185,a,b,26211,a)].">
      <j1 rule="hyper" parents="64 26185 26211"/>
    </justification>
  </clause>

  <clause id="26339">
    <literal><![CDATA[
      R(x,y,((z / (u / w)) * v5) \ v6) = R(x,y,((z / (w \ u)) * v5) \ v6)
    ]]></literal>
    <justification jstring="[para(24469(a,1),26225(a,1,3,1))].">
      <j1 rule="para" parents="24469 26225"/>
    </justification>
  </clause>

  <clause id="26340">
    <literal><![CDATA[
      R(x,y,z \ (u / (w * u))) = R(x,y,z \ (u \ (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,26183,a(flip),b,26234,a),flip(a)].">
      <j1 rule="hyper" parents="64 26183 26234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26341">
    <literal><![CDATA[
      R(x,y,z * (R(T(u * K((w \ v5) \ v5,u),v6),v7,v8) * w)) = R(x,y,z * (((w \ v5) \ v5) * R(T(u,v6),v7,v8)))
    ]]></literal>
    <justification jstring="[para(5864(a,1),26252(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5864 26252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26342">
    <literal><![CDATA[
      R(x,y,z * ((u / w) * v5)) = R(x,y,z * (v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,26178,a,b,26253,a)].">
      <j1 rule="hyper" parents="64 26178 26253"/>
    </justification>
  </clause>

  <clause id="26343">
    <literal><![CDATA[
      (1 / x) \ (y \ (x \ y)) = x * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,7588,a(flip),b,26263,a)].">
      <j1 rule="hyper" parents="64 7588 26263"/>
    </justification>
  </clause>

  <clause id="26344">
    <literal><![CDATA[
      L(T(x \ (y \ x),y),y,y) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(39,a,561,a,b,26343,a)].">
      <j1 rule="hyper" parents="39 561 26343"/>
    </justification>
  </clause>

  <clause id="26345">
    <literal><![CDATA[
      L(x \ (y \ x),y,y) * y = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(145,a,26344,a(flip),b,121,a),flip(a)].">
      <j1 rule="hyper" parents="145 26344 121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26346">
    <literal><![CDATA[
      L((x \ (y \ x)) \ z,L(x \ (y \ x),y,y),y) = (L(x \ (y \ x),y,y) * y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(26344(a,1),10982(a,1,1,1))].">
      <j1 rule="para" parents="26344 10982"/>
    </justification>
  </clause>

  <clause id="26347">
    <literal><![CDATA[
      R(x,y,z \ ((u * w) * v5)) = R(x,y,z \ (v5 * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,26185,a,b,26268,a)].">
      <j1 rule="hyper" parents="373 26185 26268"/>
    </justification>
  </clause>

  <clause id="26348">
    <literal><![CDATA[
      R(x,y,z \ ((u * w) \ ((w * v5) * u))) = R(x,y,z \ L(v5,w,u))
    ]]></literal>
    <justification jstring="[para(18(a,2),26271(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="18 26271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26349">
    <literal><![CDATA[
      R(x,x,x * ((x \ 1) \ y)) = R(x,x,x * (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7606,a(flip),b,26274,a)].">
      <j1 rule="hyper" parents="64 7606 26274"/>
    </justification>
  </clause>

  <clause id="26351">
    <literal><![CDATA[
      R(x,y,z * ((z \ 1) \ u)) = R(x,y,(z * z) * u)
    ]]></literal>
    <justification jstring="[para(538(a,1),26275(a,1,3)),flip(a)].">
      <j1 rule="para" parents="538 26275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26352">
    <literal><![CDATA[
      R(x,x,(x * x) * y) = R(x,x,x * (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,26349,a(flip),b,26351,a),flip(a)].">
      <j1 rule="hyper" parents="64 26349 26351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26353">
    <literal><![CDATA[
      R(x,y,(z * u) * (w * w)) = R(x,y,z * ((w * w) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26213,a,b,26284,a)].">
      <j1 rule="hyper" parents="64 26213 26284"/>
    </justification>
  </clause>

  <clause id="26354">
    <literal><![CDATA[
      R(x,y,((z * u) \ w) * ((z \ 1) * u)) = R(x,y,(z * z) \ w)
    ]]></literal>
    <justification jstring="[para(892(a,1),26289(a,1,3)),flip(a)].">
      <j1 rule="para" parents="892 26289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26355">
    <literal><![CDATA[
      (x \ 1) * (((x \ 1) * y) \ y) = x \ (((1 / x) * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5238,a(flip),b,26306,a)].">
      <j1 rule="hyper" parents="64 5238 26306"/>
    </justification>
  </clause>

  <clause id="26356">
    <literal><![CDATA[
      R(x,y,z * (R(T(u,w),v5,v6) * v7)) = R(x,y,(R(u,v5,v6) * v7) * z)
    ]]></literal>
    <justification jstring="[para(11417(a,1),26308(a,1,3,2,1))].">
      <j1 rule="para" parents="11417 26308"/>
    </justification>
  </clause>

  <clause id="26357">
    <literal><![CDATA[
      R(x,y,(z * z) * (u \ (w / z))) = R(x,y,u \ (w / (1 / z)))
    ]]></literal>
    <justification jstring="[para(809(a,1),26338(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="809 26338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26358">
    <literal><![CDATA[
      R(x,y,z \ ((u * w) \ w)) = R(x,y,z \ (w \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,26183,a(flip),b,26340,a)].">
      <j1 rule="hyper" parents="64 26183 26340"/>
    </justification>
  </clause>

  <clause id="26359">
    <literal><![CDATA[
      R(x,y,(z * u) \ ((w * u) * z)) = R(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(18(a,2),26347(a,2,3))].">
      <j1 rule="para" parents="18 26347"/>
    </justification>
  </clause>

  <clause id="26360">
    <literal><![CDATA[
      R(x,y,R(z,u,w)) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,26311,a(flip),b,26359,a)].">
      <j1 rule="hyper" parents="64 26311 26359"/>
    </justification>
  </clause>

  <clause id="26361">
    <literal><![CDATA[
      R(x,y,L(z * z,u,w)) = R(x,y,z * z)
    ]]></literal>
    <justification jstring="[para(655(a,1),26360(a,1,3)),flip(a)].">
      <j1 rule="para" parents="655 26360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26362">
    <literal><![CDATA[
      R(x,x,L(y,z,u)) * R(y,z,u) = (1 / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(26360(a,1),1913(a,1,1))].">
      <j1 rule="para" parents="26360 1913"/>
    </justification>
  </clause>

  <clause id="26363">
    <literal><![CDATA[
      R(x,y,L(z,T(u,w),T(u,w) \ v5)) = R(x,y,R(z,u,u \ v5))
    ]]></literal>
    <justification jstring="[para(25637(a,1),26360(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25637 26360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26364">
    <literal><![CDATA[
      L(((x \ 1) * y) \ y,x,x) = ((1 / x) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(39,a,1148,a,b,26355,a(flip))].">
      <j1 rule="hyper" parents="39 1148 26355"/>
    </justification>
  </clause>

  <clause id="26365">
    <literal><![CDATA[
      R(x \ K(y,y \ z),x,z) = (x \ z) / ((y \ z) * y)
    ]]></literal>
    <justification jstring="[para(14444(a,1),25981(a,1,1))].">
      <j1 rule="para" parents="14444 25981"/>
    </justification>
  </clause>

  <clause id="26366">
    <literal><![CDATA[
      (x \ y) / ((x \ y) * x) = y / T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25516,a(flip),b,26365,a),flip(a)].">
      <j1 rule="hyper" parents="64 25516 26365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26367">
    <literal><![CDATA[
      x / T(y * x,y) = (x / y) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,10252,a(flip),b,26366,a),flip(a)].">
      <j1 rule="hyper" parents="64 10252 26366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26368">
    <literal><![CDATA[
      ((x / y) / x) * T(y * x,y) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,10252,a(flip),b,26366,a(flip))].">
      <j1 rule="hyper" parents="144 10252 26366"/>
    </justification>
  </clause>

  <clause id="26369">
    <literal><![CDATA[
      T(x * y,x * x) \ y = (y / x) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,25951,a,b,26367,a)].">
      <j1 rule="hyper" parents="64 25951 26367"/>
    </justification>
  </clause>

  <clause id="26370">
    <literal><![CDATA[
      ((x \ y) / x) / (x \ y) = (x \ y) / T(y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),26367(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 26367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26371">
    <literal><![CDATA[
      L(T(x * y,x) \ 1,T(x * y,x),T(x * y,x) \ y) = y \ ((y / x) / y)
    ]]></literal>
    <justification jstring="[para(26367(a,1),10975(a,2,2))].">
      <j1 rule="para" parents="26367 10975"/>
    </justification>
  </clause>

  <clause id="26372">
    <literal><![CDATA[
      (a(x,y,z) / u) / a(x,y,z) = a(x,y,z) / (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(13930(a,1),26367(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13930 26367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26373">
    <literal><![CDATA[
      (x / (a(y,z,u) \ 1)) / x = x / ((a(y,z,u) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(23734(a,1),26367(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23734 26367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26374">
    <literal><![CDATA[
      ((T(x,y) / y) / T(x,y)) * T(x * y,y) = T(x,y)
    ]]></literal>
    <justification jstring="[para(115(a,1),26368(a,1,2,1))].">
      <j1 rule="para" parents="115 26368"/>
    </justification>
  </clause>

  <clause id="26375">
    <literal><![CDATA[
      (x \ 1) \ ((y / x) / y) = x \ (((x \ 1) * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,26369,a(flip),b,15136,a)].">
      <j1 rule="hyper" parents="139 26369 15136"/>
    </justification>
  </clause>

  <clause id="26376">
    <literal><![CDATA[
      ((x \ y) / x) / (x \ y) = T(y / (y * x),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25992,a(flip),b,26370,a),flip(a)].">
      <j1 rule="hyper" parents="373 25992 26370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26377">
    <literal><![CDATA[
      ((x / y) / x) * T(x * y,y) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6845(a,1),26374(a,1,1))].">
      <j1 rule="para" parents="6845 26374"/>
    </justification>
  </clause>

  <clause id="26379">
    <literal><![CDATA[
      (x \ 1) \ (((y / x) / y) * x) = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(39,a,7057,a,b,26375,a(flip))].">
      <j1 rule="hyper" parents="39 7057 26375"/>
    </justification>
  </clause>

  <clause id="26380">
    <literal><![CDATA[
      (x \ 1) * (((x \ 1) * y) \ y) = ((y / x) / y) * x
    ]]></literal>
    <justification jstring="[hyper(157,a,26379,a)].">
      <j1 rule="hyper" parents="157 26379"/>
    </justification>
  </clause>

  <clause id="26381">
    <literal><![CDATA[
      L((((x / y) / x) * y) \ z,y * (((y \ 1) * x) \ x),y) = L(((y \ 1) * x) \ x,y,y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(26380(a,1),1870(a,1,1,1))].">
      <j1 rule="para" parents="26380 1870"/>
    </justification>
  </clause>

  <clause id="26382">
    <literal><![CDATA[
      (x / (a(y,z,u) \ 1)) / x = ((a(y,z,u) \ 1) * x) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,23159,a(flip),b,26373,a),flip(a)].">
      <j1 rule="hyper" parents="373 23159 26373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26383">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ u) / u = ((a(x,y,z) \ 1) * u) \ u
    ]]></literal>
    <justification jstring="[para(23737(a,1),26382(a,1,1))].">
      <j1 rule="para" parents="23737 26382"/>
    </justification>
  </clause>

  <clause id="26384">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * u) \ u = u \ ((a(x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23130,a(flip),b,26383,a),flip(a)].">
      <j1 rule="hyper" parents="64 23130 26383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26385">
    <literal><![CDATA[
      x / ((a(y,z,u) \ 1) * x) = x \ ((a(y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,23159,a,b,26384,a)].">
      <j1 rule="hyper" parents="64 23159 26384"/>
    </justification>
  </clause>

  <clause id="26386">
    <literal><![CDATA[
      (x \ ((a(y,z,u) \ 1) \ x)) \ x = (a(y,z,u) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(215,a,26385,a)].">
      <j1 rule="hyper" parents="215 26385"/>
    </justification>
  </clause>

  <clause id="26387">
    <literal><![CDATA[
      R(x,y,z) * (K(u,w) * (y * z)) = (x * (K(u,w) * y)) * z
    ]]></literal>
    <justification jstring="[para(23256(a,1),26005(a,2,1))].">
      <j1 rule="para" parents="23256 26005"/>
    </justification>
  </clause>

  <clause id="26388">
    <literal><![CDATA[
      (x \ (1 / y)) * ((1 / y) \ K(x,x \ 1)) = 1 / R(x,x \ (1 / y),y)
    ]]></literal>
    <justification jstring="[para(82(a,1),26041(a,2,2,3))].">
      <j1 rule="para" parents="82 26041"/>
    </justification>
  </clause>

  <clause id="26389">
    <literal><![CDATA[
      ((x * y) * z) / T(z * x,y) = L(y * K(y * x,z),x,z)
    ]]></literal>
    <justification jstring="[para(11186(a,1),26089(a,2,1))].">
      <j1 rule="para" parents="11186 26089"/>
    </justification>
  </clause>

  <clause id="26390">
    <literal><![CDATA[
      x * (T(x \ 1,y) * (x \ z)) = T(1 / x,T(y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,6082,a(flip),b,26129,a)].">
      <j1 rule="hyper" parents="64 6082 26129"/>
    </justification>
  </clause>

  <clause id="26391">
    <literal><![CDATA[
      x * (T(x \ 1,y) * (x \ z)) = T(1 / x,y) * z
    ]]></literal>
    <justification jstring="[para(7850(a,1),26390(a,2,1))].">
      <j1 rule="para" parents="7850 26390"/>
    </justification>
  </clause>

  <clause id="26392">
    <literal><![CDATA[
      L(x,y,y) * (x \ K(x * y,y)) = x \ (((1 / y) * x) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,23064,a(flip),b,26136,a)].">
      <j1 rule="hyper" parents="64 23064 26136"/>
    </justification>
  </clause>

  <clause id="26393">
    <literal><![CDATA[
      R(x,x,y \ (x \ y)) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(36,a,2001,a,b,26317,a)].">
      <j1 rule="hyper" parents="36 2001 26317"/>
    </justification>
  </clause>

  <clause id="26394">
    <literal><![CDATA[
      (1 / (1 / x)) \ L(x,x,y) = x * (y \ (y / x))
    ]]></literal>
    <justification jstring="[para(26393(a,1),26259(a,1,1))].">
      <j1 rule="para" parents="26393 26259"/>
    </justification>
  </clause>

  <clause id="26395">
    <literal><![CDATA[
      L(x,x,y) * (1 / x) = x * (y \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,3680,a(flip),b,26394,a)].">
      <j1 rule="hyper" parents="64 3680 26394"/>
    </justification>
  </clause>

  <clause id="26396">
    <literal><![CDATA[
      x * (x * (y \ (y / x))) = L(T(x,x \ 1),x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,26394,a(flip),b,24682,a(flip))].">
      <j1 rule="hyper" parents="145 26394 24682"/>
    </justification>
  </clause>

  <clause id="26398">
    <literal><![CDATA[
      x \ (y * L(y \ x,x \ y,y)) = R(y,x \ y,y \ x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,1778,a,b,26318,a)].">
      <j1 rule="hyper" parents="64 1778 26318"/>
    </justification>
  </clause>

  <clause id="26399">
    <literal><![CDATA[
      R(x \ R(x,y,z),u,(u * (x \ R(x,y,z))) \ w) \ w = u * ((T(x \ R(x,y,z),v5) * u) \ w)
    ]]></literal>
    <justification jstring="[para(23712(a,1),26324(a,1,1,1))].">
      <j1 rule="para" parents="23712 26324"/>
    </justification>
  </clause>

  <clause id="26400">
    <literal><![CDATA[
      T(R(x,y,(x * y) \ z),u) \ z = y * ((T(x,u) * y) \ z)
    ]]></literal>
    <justification jstring="[para(27(a,1),26326(a,1,1))].">
      <j1 rule="para" parents="27 26326"/>
    </justification>
  </clause>

  <clause id="26401">
    <literal><![CDATA[
      R(x,y,z) * ((K(u,w) * y) * z) = (x * (K(u,w) * y)) * z
    ]]></literal>
    <justification jstring="[para(23073(a,2),26387(a,1,2))].">
      <j1 rule="para" parents="23073 26387"/>
    </justification>
  </clause>

  <clause id="26402">
    <literal><![CDATA[
      R(x,y,(T(z * u,w) \ ((u * w) * z)) \ v5) = R(x,y,L(w * K(w * u,z),u,z) \ v5)
    ]]></literal>
    <justification jstring="[para(26389(a,1),26209(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="26389 26209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26403">
    <literal><![CDATA[
      a(x,x,y) \ K(y * x,x) = y \ (((1 / x) * y) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25856,a(flip),b,26392,a)].">
      <j1 rule="hyper" parents="64 25856 26392"/>
    </justification>
  </clause>

  <clause id="26404">
    <literal><![CDATA[
      R(x,K(y,z) * u,w) = R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,111,a,b,26401,a)].">
      <j1 rule="hyper" parents="36 111 26401"/>
    </justification>
  </clause>

  <clause id="26406">
    <literal><![CDATA[
      R(x,T(y,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(1886(a,2),26404(a,1,2))].">
      <j1 rule="para" parents="1886 26404"/>
    </justification>
  </clause>

  <clause id="26408">
    <literal><![CDATA[
      R(x,(y * z) / y,u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(5718(a,2),26404(a,1,2))].">
      <j1 rule="para" parents="5718 26404"/>
    </justification>
  </clause>

  <clause id="26409">
    <literal><![CDATA[
      R(x,y * z,u) = R(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(5796(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="5796 26404"/>
    </justification>
  </clause>

  <clause id="26410">
    <literal><![CDATA[
      R(x,y / z,u) = R(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(5720(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="5720 26404"/>
    </justification>
  </clause>

  <clause id="26411">
    <literal><![CDATA[
      R(x,y / (y / z),u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(5723(a,2),26404(a,1,2))].">
      <j1 rule="para" parents="5723 26404"/>
    </justification>
  </clause>

  <clause id="26412">
    <literal><![CDATA[
      R(x,T(y,z) * u,w) = R(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(5755(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="5755 26404"/>
    </justification>
  </clause>

  <clause id="26413">
    <literal><![CDATA[
      R(x,y * (z / y),u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(5781(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="5781 26404"/>
    </justification>
  </clause>

  <clause id="26414">
    <literal><![CDATA[
      R(x,(y \ z) \ z,u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(5842(a,2),26404(a,1,2))].">
      <j1 rule="para" parents="5842 26404"/>
    </justification>
  </clause>

  <clause id="26415">
    <literal><![CDATA[
      R(x,(y \ z) * y,u) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(5919(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="5919 26404"/>
    </justification>
  </clause>

  <clause id="26416">
    <literal><![CDATA[
      R(x,T(y,z) \ u,w) = R(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(6075(a,1),26404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6075 26404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26417">
    <literal><![CDATA[
      R(x,(y / z) * u,w) = R(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(5982(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="5982 26404"/>
    </justification>
  </clause>

  <clause id="26419">
    <literal><![CDATA[
      R(x,(y / z) \ u,w) = R(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),26404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 26404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26420">
    <literal><![CDATA[
      R(x,y * T(z,u),w) = R(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(6367(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="6367 26404"/>
    </justification>
  </clause>

  <clause id="26421">
    <literal><![CDATA[
      R(x,y * K(z,u),w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[para(6823(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="6823 26404"/>
    </justification>
  </clause>

  <clause id="26422">
    <literal><![CDATA[
      R(x,y \ T(z,u),w) = R(x,y \ z,w)
    ]]></literal>
    <justification jstring="[para(6417(a,1),26404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6417 26404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26424">
    <literal><![CDATA[
      R(x,y * (K(z,u) * w),v5) = R(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(10720(a,1),26404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10720 26404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26425">
    <literal><![CDATA[
      R(x,(y * z) \ u,w) = R(x,(z * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(10833(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="10833 26404"/>
    </justification>
  </clause>

  <clause id="26426">
    <literal><![CDATA[
      R(x,((y \ z) * y) \ u,w) = R(x,z \ u,w)
    ]]></literal>
    <justification jstring="[para(10843(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="10843 26404"/>
    </justification>
  </clause>

  <clause id="26428">
    <literal><![CDATA[
      R(x,y \ K(z,u),w) = R(x,y \ 1,w)
    ]]></literal>
    <justification jstring="[para(14665(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="14665 26404"/>
    </justification>
  </clause>

  <clause id="26429">
    <literal><![CDATA[
      R(x,y \ (K(z,u) * w),v5) = R(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(22758(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="22758 26404"/>
    </justification>
  </clause>

  <clause id="26430">
    <literal><![CDATA[
      R(x,L(T(y,z),u,w),v5) = R(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(24550(a,1),26404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24550 26404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26431">
    <literal><![CDATA[
      R(x,(T(y,z) \ u) * w,v5) = R(x,(y \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(24347(a,1),26404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24347 26404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26432">
    <literal><![CDATA[
      R(x,(y \ T(z,u)) \ w,v5) = R(x,(y \ z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(24519(a,1),26404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24519 26404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26433">
    <literal><![CDATA[
      R(x,((y * z) * u) * w,v5) = R(x,((z * y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(24358(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="24358 26404"/>
    </justification>
  </clause>

  <clause id="26434">
    <literal><![CDATA[
      R(x,R(T(y,z),u,w) \ v5,v6) = R(x,R(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(24564(a,1),26404(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24564 26404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26435">
    <literal><![CDATA[
      R(x,((y / z) \ u) * w,v5) = R(x,((z \ y) \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(24352(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="24352 26404"/>
    </justification>
  </clause>

  <clause id="26436">
    <literal><![CDATA[
      R(x,((y / z) / u) * w,v5) = R(x,((z \ y) / u) * w,v5)
    ]]></literal>
    <justification jstring="[para(24363(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="24363 26404"/>
    </justification>
  </clause>

  <clause id="26437">
    <literal><![CDATA[
      R(x,((y * T(z,u)) \ w) * v5,v6) = R(x,((y * z) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(24968(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="24968 26404"/>
    </justification>
  </clause>

  <clause id="26438">
    <literal><![CDATA[
      R(x,R(y / z,u,w),v5) = R(x,R(z \ y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(25975(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="25975 26404"/>
    </justification>
  </clause>

  <clause id="26439">
    <literal><![CDATA[
      R(x,R(K(y,z) * u,w,v5) * v6,v7) = R(x,R(u,w,v5) * v6,v7)
    ]]></literal>
    <justification jstring="[para(25968(a,2),26404(a,1,2))].">
      <j1 rule="para" parents="25968 26404"/>
    </justification>
  </clause>

  <clause id="26440">
    <literal><![CDATA[
      R(x,L(K(y,z) * u,w,v5),v6) = R(x,L(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(26085(a,2),26404(a,1,2))].">
      <j1 rule="para" parents="26085 26404"/>
    </justification>
  </clause>

  <clause id="26441">
    <literal><![CDATA[
      R(x,L(y * z,u,w) * v5,v6) = R(x,L(z * y,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(26140(a,1),26404(a,1,2))].">
      <j1 rule="para" parents="26140 26404"/>
    </justification>
  </clause>

  <clause id="26450">
    <literal><![CDATA[
      ((x * y) * z) / (z * T(x,y)) = R(K(x,z) * y,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10392,a,b,26406,a)].">
      <j1 rule="hyper" parents="64 10392 26406"/>
    </justification>
  </clause>

  <clause id="26451">
    <literal><![CDATA[
      R(R(T(x,y),T(x,y),T(x,y)),x,z) = R(T(x,y),T(x,y),z * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,26195,a(flip),b,26406,a),flip(a)].">
      <j1 rule="hyper" parents="64 26195 26406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26453">
    <literal><![CDATA[
      R(x,y,z) * (T(y,u) * z) = (x * T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,26406,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 26406 20"/>
    </justification>
  </clause>

  <clause id="26454">
    <literal><![CDATA[
      R(x,L(y / z,u,w),v5) = R(x,L(z \ y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(279(a,1),26406(a,1,2)),flip(a)].">
      <j1 rule="para" parents="279 26406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26455">
    <literal><![CDATA[
      R(x,(y \ 1) \ (z * z),u) = R(x,(z * z) * y,u)
    ]]></literal>
    <justification jstring="[para(558(a,1),26406(a,1,2))].">
      <j1 rule="para" parents="558 26406"/>
    </justification>
  </clause>

  <clause id="26456">
    <literal><![CDATA[
      R(x,y \ ((z * z) * u),w) = R(x,(z * z) * (u / y),w)
    ]]></literal>
    <justification jstring="[para(946(a,1),26406(a,1,2))].">
      <j1 rule="para" parents="946 26406"/>
    </justification>
  </clause>

  <clause id="26457">
    <literal><![CDATA[
      R(x,R(y / z,z,u),w) = R(x,(z * u) \ (y * u),w)
    ]]></literal>
    <justification jstring="[para(681(a,1),26406(a,1,2)),flip(a)].">
      <j1 rule="para" parents="681 26406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26458">
    <literal><![CDATA[
      R(T(x,y),x,z) * z = (1 / T(x,y)) \ z
    ]]></literal>
    <justification jstring="[para(26406(a,1),1913(a,1,1))].">
      <j1 rule="para" parents="26406 1913"/>
    </justification>
  </clause>

  <clause id="26459">
    <literal><![CDATA[
      R(x,y \ (z * (y * y)),u) = R(x,z * L(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(2848(a,1),26406(a,1,2))].">
      <j1 rule="para" parents="2848 26406"/>
    </justification>
  </clause>

  <clause id="26462">
    <literal><![CDATA[
      R(x,L(y,y,z) \ z,u) = R(x,z * (1 / y),u)
    ]]></literal>
    <justification jstring="[para(11819(a,1),26406(a,1,2))].">
      <j1 rule="para" parents="11819 26406"/>
    </justification>
  </clause>

  <clause id="26465">
    <literal><![CDATA[
      R(x,R(y,y,z * y),u) = R(x,R(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(26296(a,1),26406(a,1,2))].">
      <j1 rule="para" parents="26296 26406"/>
    </justification>
  </clause>

  <clause id="26469">
    <literal><![CDATA[
      R(x,((y * y) \ z) / u,w) = R(x,((y * y) * u) \ z,w)
    ]]></literal>
    <justification jstring="[para(492(a,1),26408(a,1,2,1))].">
      <j1 rule="para" parents="492 26408"/>
    </justification>
  </clause>

  <clause id="26470">
    <literal><![CDATA[
      R(x,K(y,z) * (u * w),v5) = R(x,w * u,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26404,a,b,26409,a)].">
      <j1 rule="hyper" parents="373 26404 26409"/>
    </justification>
  </clause>

  <clause id="26471">
    <literal><![CDATA[
      R(x,(y \ 1) * z,u) = R(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,3018,a,b,26409,a)].">
      <j1 rule="hyper" parents="373 3018 26409"/>
    </justification>
  </clause>

  <clause id="26472">
    <literal><![CDATA[
      R(x,y * (z \ 1),u) = R(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,3018,a(flip),b,26409,a),flip(a)].">
      <j1 rule="hyper" parents="373 3018 26409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26473">
    <literal><![CDATA[
      R(x,y * (z * (z * u)),w) = R(x,L(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2973,a(flip),b,26409,a),flip(a)].">
      <j1 rule="hyper" parents="373 2973 26409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26474">
    <literal><![CDATA[
      R(x,(y * z) * y,u) = R(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2970,a(flip),b,26409,a),flip(a)].">
      <j1 rule="hyper" parents="373 2970 26409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26475">
    <literal><![CDATA[
      R(x,y * (z * z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2965,a(flip),b,26409,a),flip(a)].">
      <j1 rule="hyper" parents="373 2965 26409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26476">
    <literal><![CDATA[
      R(x,y * z,u) * ((z * y) * T(u,w)) = (x * (z * y)) * T(u,w)
    ]]></literal>
    <justification jstring="[hyper(144,a,26409,a,b,23314,a)].">
      <j1 rule="hyper" parents="144 26409 23314"/>
    </justification>
  </clause>

  <clause id="26477">
    <literal><![CDATA[
      R(x,((y * y) * z) * R(u,y,y),w) = R(x,((u * y) * y) * z,w)
    ]]></literal>
    <justification jstring="[para(662(a,1),26409(a,1,2)),flip(a)].">
      <j1 rule="para" parents="662 26409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26478">
    <literal><![CDATA[
      R(x / (y / z),z \ y,u) = (x * u) / ((y / z) * u)
    ]]></literal>
    <justification jstring="[hyper(1084,a,26410,a),flip(a)].">
      <j1 rule="hyper" parents="1084 26410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26480">
    <literal><![CDATA[
      R(x,y / z,(u / w) \ v5) = R(x,z \ y,(w \ u) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26209,a(flip),b,26410,a),flip(a)].">
      <j1 rule="hyper" parents="373 26209 26410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26481">
    <literal><![CDATA[
      R(x,y / (z \ 1),u) = R(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,3028,a(flip),b,26410,a),flip(a)].">
      <j1 rule="hyper" parents="373 3028 26410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26482">
    <literal><![CDATA[
      (x * y) / ((y / (z * z)) * ((x * (y / (z * z))) \ (x * y))) = R(x,(z * z) \ y,L(z * z,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,11903,a,b,26410,a)].">
      <j1 rule="hyper" parents="64 11903 26410"/>
    </justification>
  </clause>

  <clause id="26483">
    <literal><![CDATA[
      R(1 / ((x \ y) / y),y \ (x \ y),x) = ((x \ y) / y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,25361,a(flip),b,26410,a),flip(a)].">
      <j1 rule="hyper" parents="64 25361 26410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26484">
    <literal><![CDATA[
      R(T(x \ 1,y) * (x * x),(x * x) \ x,y) = (1 * y) / (y * (x / (x * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17440,a(flip),b,26410,a),flip(a)].">
      <j1 rule="hyper" parents="64 17440 26410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26485">
    <literal><![CDATA[
      R(R(x,y,(z * z) \ 1),(z * z) \ y,u) = R(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,3544,a(flip),b,26410,a),flip(a)].">
      <j1 rule="hyper" parents="64 3544 26410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26486">
    <literal><![CDATA[
      R(x,y \ (1 / z),u) = R(x,z / y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2972,a(flip),b,26410,a),flip(a)].">
      <j1 rule="hyper" parents="64 2972 26410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26488">
    <literal><![CDATA[
      R(x,y \ z,u) * ((z / y) * u) = (x * (z / y)) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,26410,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 26410 20"/>
    </justification>
  </clause>

  <clause id="26489">
    <literal><![CDATA[
      R(x,(y * z) / (y * ((u * u) \ z)),w) = R(x,L(T(u * u,z),z,y),w)
    ]]></literal>
    <justification jstring="[para(11835(a,1),26410(a,2,2))].">
      <j1 rule="para" parents="11835 26410"/>
    </justification>
  </clause>

  <clause id="26490">
    <literal><![CDATA[
      R(x,R(1 / y,z,z),u) = R(x,y \ a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(16000(a,2),26410(a,1,2))].">
      <j1 rule="para" parents="16000 26410"/>
    </justification>
  </clause>

  <clause id="26491">
    <literal><![CDATA[
      R(x,T(y * z,y) \ z,u) = R(x,(z / y) / z,u)
    ]]></literal>
    <justification jstring="[para(26367(a,1),26410(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26367 26410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26494">
    <literal><![CDATA[
      R(x,y \ (z / y),x) = R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13733,a,b,26413,a)].">
      <j1 rule="hyper" parents="64 13733 26413"/>
    </justification>
  </clause>

  <clause id="26495">
    <literal><![CDATA[
      R(x * ((y \ K(z,u)) * y),K(u,z),x \ w) \ w = (y * (K(u,z) / y)) * (x \ w)
    ]]></literal>
    <justification jstring="[para(26413(a,1),20909(a,1,1))].">
      <j1 rule="para" parents="26413 20909"/>
    </justification>
  </clause>

  <clause id="26496">
    <literal><![CDATA[
      R(x,L(y * z,u,w),v5) = R(x,L(z * y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(5545(a,1),26415(a,1,2))].">
      <j1 rule="para" parents="5545 26415"/>
    </justification>
  </clause>

  <clause id="26497">
    <literal><![CDATA[
      R(x \ y,y,x \ y) * x = x * T(x \ y,(x \ y) \ x)
    ]]></literal>
    <justification jstring="[para(26415(a,1),13753(a,1,1))].">
      <j1 rule="para" parents="26415 13753"/>
    </justification>
  </clause>

  <clause id="26500">
    <literal><![CDATA[
      R(x,y * (z / u),w) = R(x,y * (u \ z),w)
    ]]></literal>
    <justification jstring="[para(6471(a,1),26421(a,1,2))].">
      <j1 rule="para" parents="6471 26421"/>
    </justification>
  </clause>

  <clause id="26501">
    <literal><![CDATA[
      R(x,y * (z * u),w) = R(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(7591(a,1),26421(a,1,2))].">
      <j1 rule="para" parents="7591 26421"/>
    </justification>
  </clause>

  <clause id="26503">
    <literal><![CDATA[
      R(x,y * ((z \ u) * z),w) = R(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(10196(a,1),26421(a,1,2))].">
      <j1 rule="para" parents="10196 26421"/>
    </justification>
  </clause>

  <clause id="26505">
    <literal><![CDATA[
      R(x,y * (z * K(u,w)),v5) = R(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(12078(a,1),26421(a,1,2))].">
      <j1 rule="para" parents="12078 26421"/>
    </justification>
  </clause>

  <clause id="26506">
    <literal><![CDATA[
      R(x,y \ (z / u),w) = R(x,y \ (u \ z),w)
    ]]></literal>
    <justification jstring="[para(15028(a,1),26421(a,1,2))].">
      <j1 rule="para" parents="15028 26421"/>
    </justification>
  </clause>

  <clause id="26507">
    <literal><![CDATA[
      R(x,y \ (z * u),w) = R(x,y \ (u * z),w)
    ]]></literal>
    <justification jstring="[para(14934(a,1),26421(a,1,2))].">
      <j1 rule="para" parents="14934 26421"/>
    </justification>
  </clause>

  <clause id="26508">
    <literal><![CDATA[
      R(x,y \ (z \ T(u,w)),v5) = R(x,y \ (z \ u),v5)
    ]]></literal>
    <justification jstring="[para(24309(a,1),26421(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24309 26421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26509">
    <literal><![CDATA[
      R(x,y \ (T(z,u) * w),v5) = R(x,y \ (z * w),v5)
    ]]></literal>
    <justification jstring="[para(24312(a,1),26421(a,1,2))].">
      <j1 rule="para" parents="24312 26421"/>
    </justification>
  </clause>

  <clause id="26510">
    <literal><![CDATA[
      R(x,y \ (z \ (u / w)),v5) = R(x,y \ (z \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(24307(a,1),26421(a,1,2))].">
      <j1 rule="para" parents="24307 26421"/>
    </justification>
  </clause>

  <clause id="26511">
    <literal><![CDATA[
      R(x,y \ (z * (u / w)),v5) = R(x,y \ (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(24314(a,1),26421(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24314 26421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26512">
    <literal><![CDATA[
      R(R(x,y,z * z),y,u) = R(x,y,(z * z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,3466,a(flip),b,26475,a),flip(a)].">
      <j1 rule="hyper" parents="64 3466 26475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26513">
    <literal><![CDATA[
      (x \ (y / x)) \ (x \ y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4762,a(flip),b,26494,a)].">
      <j1 rule="hyper" parents="64 4762 26494"/>
    </justification>
  </clause>

  <clause id="26515">
    <literal><![CDATA[
      (x \ (x * ((y * x) \ y))) / x = x \ ((x * ((y * x) \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(225,a,25622,a(flip),b,26513,a)].">
      <j1 rule="hyper" parents="225 25622 26513"/>
    </justification>
  </clause>

  <clause id="26516">
    <literal><![CDATA[
      R(x,y * T(y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(672,a,26412,a),flip(a)].">
      <j1 rule="hyper" parents="672 26412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26517">
    <literal><![CDATA[
      R(x,(y / z) \ z,u) = R(x,(z / y) * z,u)
    ]]></literal>
    <justification jstring="[para(3818(a,1),26412(a,1,2))].">
      <j1 rule="para" parents="3818 26412"/>
    </justification>
  </clause>

  <clause id="26518">
    <literal><![CDATA[
      (x * (y * T(y,z))) * u = x * ((y * T(y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,26516,a(flip),b,14095,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 26516 14095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26519">
    <literal><![CDATA[
      (x / (y * T(y,z))) * u = x * ((y * T(y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(144,a,26516,a(flip),b,677,a(flip))].">
      <j1 rule="hyper" parents="144 26516 677"/>
    </justification>
  </clause>

  <clause id="26520">
    <literal><![CDATA[
      K(x * (y * T(y,z)),x) = K(y * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(35,a,6387,a(flip),b,26516,a(flip))].">
      <j1 rule="hyper" parents="35 6387 26516"/>
    </justification>
  </clause>

  <clause id="26521">
    <literal><![CDATA[
      R(x,(y / (y / z)) * z,u) = x
    ]]></literal>
    <justification jstring="[para(276(a,1),26516(a,1,2,2))].">
      <j1 rule="para" parents="276 26516"/>
    </justification>
  </clause>

  <clause id="26522">
    <literal><![CDATA[
      R(x,y * (z / (z / y)),u) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,26409,a,b,26521,a)].">
      <j1 rule="hyper" parents="64 26409 26521"/>
    </justification>
  </clause>

  <clause id="26523">
    <literal><![CDATA[
      1 / (x * (y / (y / x))) = (x * (y / (y / x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,26260,a(flip),b,26522,a),flip(a)].">
      <j1 rule="hyper" parents="64 26260 26522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26527">
    <literal><![CDATA[
      R(x,((y * z) * (u * K(y,w))) \ v5,v6) = R(x,((T(y,w) * z) * u) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(24787(a,1),26416(a,1,2,1))].">
      <j1 rule="para" parents="24787 26416"/>
    </justification>
  </clause>

  <clause id="26531">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) * u) / T(y,z) = R(x,u \ y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10215,a,b,26422,a)].">
      <j1 rule="hyper" parents="64 10215 26422"/>
    </justification>
  </clause>

  <clause id="26533">
    <literal><![CDATA[
      R(x,y \ K(z,u),w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2975,a(flip),b,26428,a),flip(a)].">
      <j1 rule="hyper" parents="373 2975 26428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26535">
    <literal><![CDATA[
      R(x,y \ K(z,u),R(w,v5,v6)) = R(x,y,L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,26360,a(flip),b,26533,a),flip(a)].">
      <j1 rule="hyper" parents="373 26360 26533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26536">
    <literal><![CDATA[
      R(x,y * a(z,z,y),u) = R(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(5669(a,1),26471(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5669 26471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26537">
    <literal><![CDATA[
      (x \ 1) / R(y \ (x \ y),(y \ (x \ y)) * x,y \ (x \ y)) = (y \ (x \ y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(26471(a,1),13767(a,1,2))].">
      <j1 rule="para" parents="26471 13767"/>
    </justification>
  </clause>

  <clause id="26538">
    <literal><![CDATA[
      R(x,L(y,z,z) * y,u) = R(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(1847(a,1),26472(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1847 26472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26539">
    <literal><![CDATA[
      R(T(T(x,y),z),x,u) * u = (1 / T(T(x,y),z)) \ u
    ]]></literal>
    <justification jstring="[para(26406(a,1),26458(a,1,1))].">
      <j1 rule="para" parents="26406 26458"/>
    </justification>
  </clause>

  <clause id="26540">
    <literal><![CDATA[
      R(x,L(y * z,y,y),u) = R(x,L(z,y,y) * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2973,a(flip),b,26474,a),flip(a)].">
      <j1 rule="hyper" parents="64 2973 26474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26541">
    <literal><![CDATA[
      R(x,(y / z) * u,w) = R(x,u * (z \ y),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26409,a,b,26417,a),flip(a)].">
      <j1 rule="hyper" parents="373 26409 26417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26542">
    <literal><![CDATA[
      R(x,(y \ z) * (z * (y \ 1)),x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13934,a(flip),b,26417,a),flip(a)].">
      <j1 rule="hyper" parents="64 13934 26417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26543">
    <literal><![CDATA[
      R(x,(y \ (1 / z)) * u,w) = R(x,(z / y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,3034,a(flip),b,26417,a),flip(a)].">
      <j1 rule="hyper" parents="64 3034 26417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26544">
    <literal><![CDATA[
      R(x,y * ((z * u) \ w),v5) = R(x,y * ((u * z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(10833(a,1),26424(a,1,2,2))].">
      <j1 rule="para" parents="10833 26424"/>
    </justification>
  </clause>

  <clause id="26546">
    <literal><![CDATA[
      R((x \ y) * x,y \ x,x \ y) \ y = (y \ x) * (y / x)
    ]]></literal>
    <justification jstring="[para(26426(a,1),15137(a,1,1))].">
      <j1 rule="para" parents="26426 15137"/>
    </justification>
  </clause>

  <clause id="26547">
    <literal><![CDATA[
      R(x,y \ ((z / u) \ w),v5) = R(x,y \ ((u \ z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(6270(a,1),26429(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6270 26429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26548">
    <literal><![CDATA[
      R(x,y * ((z \ u) \ u),w) = R(x,z * y,w)
    ]]></literal>
    <justification jstring="[para(6168(a,1),26470(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6168 26470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26549">
    <literal><![CDATA[
      R(x,(y * z) * u,w) = R(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[para(10834(a,1),26470(a,1,2))].">
      <j1 rule="para" parents="10834 26470"/>
    </justification>
  </clause>

  <clause id="26550">
    <literal><![CDATA[
      R(x,y * (T(z,u) \ w),v5) = R(x,(z \ w) * y,v5)
    ]]></literal>
    <justification jstring="[para(24347(a,1),26470(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24347 26470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26551">
    <literal><![CDATA[
      R(x,y * (y / z),x) = R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13744,a(flip),b,26500,a),flip(a)].">
      <j1 rule="hyper" parents="373 13744 26500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26552">
    <literal><![CDATA[
      (x \ (y / z)) * R(x,x * (z \ y),x) = T(y / z,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,26500,a(flip),b,13734,a(flip))].">
      <j1 rule="hyper" parents="145 26500 13734"/>
    </justification>
  </clause>

  <clause id="26553">
    <literal><![CDATA[
      (1 / (x \ (y / z))) * R(u,x * (z \ y),u) = T(u * (1 / (x \ (y / z))),u)
    ]]></literal>
    <justification jstring="[para(26500(a,1),13738(a,1,2))].">
      <j1 rule="para" parents="26500 13738"/>
    </justification>
  </clause>

  <clause id="26554">
    <literal><![CDATA[
      ((x / y) / x) / R(y,y * (x \ (x / y)),y) = y \ (1 / (1 / ((x / y) / x)))
    ]]></literal>
    <justification jstring="[para(26500(a,1),13885(a,1,2))].">
      <j1 rule="para" parents="26500 13885"/>
    </justification>
  </clause>

  <clause id="26555">
    <literal><![CDATA[
      T(x * T(y \ (y / z),K(z,u)),x) = (y \ (y / z)) * R(x,z,x)
    ]]></literal>
    <justification jstring="[para(26551(a,1),13740(a,2,2))].">
      <j1 rule="para" parents="26551 13740"/>
    </justification>
  </clause>

  <clause id="26556">
    <literal><![CDATA[
      R(x,y \ (z * u),x) = R(x,y * (u * z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13733,a,b,26501,a)].">
      <j1 rule="hyper" parents="373 13733 26501"/>
    </justification>
  </clause>

  <clause id="26557">
    <literal><![CDATA[
      R(x,y * (z * (u / w)),v5) = R(x,y * (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(6471(a,1),26505(a,1,2,2))].">
      <j1 rule="para" parents="6471 26505"/>
    </justification>
  </clause>

  <clause id="26558">
    <literal><![CDATA[
      R(x,y * (z * (u * w)),v5) = R(x,y * (z * (w * u)),v5)
    ]]></literal>
    <justification jstring="[para(7591(a,1),26505(a,1,2,2))].">
      <j1 rule="para" parents="7591 26505"/>
    </justification>
  </clause>

  <clause id="26559">
    <literal><![CDATA[
      R(x,y * (z \ (u / w)),v5) = R(x,y * (z \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(15028(a,1),26505(a,1,2,2))].">
      <j1 rule="para" parents="15028 26505"/>
    </justification>
  </clause>

  <clause id="26560">
    <literal><![CDATA[
      R(x,y \ T(z / u,w),v5) = R(x,y \ (u \ z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26422,a,b,26506,a)].">
      <j1 rule="hyper" parents="64 26422 26506"/>
    </justification>
  </clause>

  <clause id="26561">
    <literal><![CDATA[
      R(x,L(y,y,z),u) = R(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26059,a,b,26506,a)].">
      <j1 rule="hyper" parents="64 26059 26506"/>
    </justification>
  </clause>

  <clause id="26562">
    <literal><![CDATA[
      R(x,y \ (z \ 1),u) = R(x,z / y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26486,a(flip),b,26506,a),flip(a)].">
      <j1 rule="hyper" parents="64 26486 26506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26563">
    <literal><![CDATA[
      R(x,y \ (z \ 1),u) = R(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26410,a(flip),b,26562,a),flip(a)].">
      <j1 rule="hyper" parents="373 26410 26562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26564">
    <literal><![CDATA[
      L(R(x,y \ (x \ y),z),x,y) * z = (1 / L(x,x,y)) \ z
    ]]></literal>
    <justification jstring="[para(26561(a,1),1919(a,1,1,1))].">
      <j1 rule="para" parents="26561 1919"/>
    </justification>
  </clause>

  <clause id="26565">
    <literal><![CDATA[
      R(x,(y * z) \ ((z * u) * y),w) = R(x,L(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(18(a,2),26507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18 26507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26566">
    <literal><![CDATA[
      R(x,(y \ z) \ y,u) = R(x,(y / z) * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26419,a(flip),b,26517,a)].">
      <j1 rule="hyper" parents="64 26419 26517"/>
    </justification>
  </clause>

  <clause id="26567">
    <literal><![CDATA[
      K(x * (y * T(y,z)),T(x,u)) = K(y * T(y,z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,8606,a(flip),b,26520,a)].">
      <j1 rule="hyper" parents="64 8606 26520"/>
    </justification>
  </clause>

  <clause id="26568">
    <literal><![CDATA[
      R(x,y \ R(y,y,z),u) = R(x,y * ((y * z) \ z),u)
    ]]></literal>
    <justification jstring="[para(1986(a,2),26541(a,1,2))].">
      <j1 rule="para" parents="1986 26541"/>
    </justification>
  </clause>

  <clause id="26569">
    <literal><![CDATA[
      R(x,y * (z * (y \ z)),x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13935,a(flip),b,26548,a),flip(a)].">
      <j1 rule="hyper" parents="64 13935 26548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26570">
    <literal><![CDATA[
      R(x,(y * z) * z,u) = R(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2970,a(flip),b,26549,a),flip(a)].">
      <j1 rule="hyper" parents="373 2970 26549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26571">
    <literal><![CDATA[
      R(x,y * ((z * u) * z),w) = R(x,L(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2973,a(flip),b,26549,a),flip(a)].">
      <j1 rule="hyper" parents="64 2973 26549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26572">
    <literal><![CDATA[
      T(((x * y) * y) * z,z) / R(z,L(x,y,y),z) = T((x * y) * y,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,26570,a(flip),b,4792,a)].">
      <j1 rule="hyper" parents="225 26570 4792"/>
    </justification>
  </clause>

  <clause id="26573">
    <literal><![CDATA[
      R(x,(y \ z) \ u,x) = R(x,z * (u * y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13716,a,b,26556,a)].">
      <j1 rule="hyper" parents="64 13716 26556"/>
    </justification>
  </clause>

  <clause id="26574">
    <literal><![CDATA[
      R(x,(y \ z) \ y,u) = R(x,(z \ y) * y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26417,a(flip),b,26566,a),flip(a)].">
      <j1 rule="hyper" parents="373 26417 26566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26575">
    <literal><![CDATA[
      R(x,(y \ z) * u,x) = R(x,z * (u * y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13733,a(flip),b,26573,a)].">
      <j1 rule="hyper" parents="64 13733 26573"/>
    </justification>
  </clause>

  <clause id="26576">
    <literal><![CDATA[
      R(x,y * ((y * (z \ 1)) * z),x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,26542,a(flip),b,26575,a),flip(a)].">
      <j1 rule="hyper" parents="64 26542 26575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26577">
    <literal><![CDATA[
      R(x,y * (z * (y * (z \ 1))),x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,26501,a,b,26576,a)].">
      <j1 rule="hyper" parents="64 26501 26576"/>
    </justification>
  </clause>

  <clause id="26578">
    <literal><![CDATA[
      (x * (y * (x \ 1))) / y = y \ (x * (y * (x \ 1)))
    ]]></literal>
    <justification jstring="[para(26577(a,1),14805(a,1,2))].">
      <j1 rule="para" parents="26577 14805"/>
    </justification>
  </clause>

  <clause id="26581">
    <literal><![CDATA[
      R(x,y,z) * (T(y \ 1,u) * z) = (x * T(y \ 1,u)) * z
    ]]></literal>
    <justification jstring="[para(2975(a,1),26453(a,1,1))].">
      <j1 rule="para" parents="2975 26453"/>
    </justification>
  </clause>

  <clause id="26582">
    <literal><![CDATA[
      R(x,L(y,y,z) \ z,u) = R(x,z * (y \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26500,a(flip),b,26462,a),flip(a)].">
      <j1 rule="hyper" parents="373 26500 26462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26584">
    <literal><![CDATA[
      R(x,L(y,y,z) \ z,u) = R(x,y * z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26472,a(flip),b,26582,a),flip(a)].">
      <j1 rule="hyper" parents="373 26472 26582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26585">
    <literal><![CDATA[
      R(x,y * z,L(y,y,z)) * z = (x * (z * (1 / y))) * L(y,y,z)
    ]]></literal>
    <justification jstring="[para(26584(a,1),11823(a,1,1))].">
      <j1 rule="para" parents="26584 11823"/>
    </justification>
  </clause>

  <clause id="26586">
    <literal><![CDATA[
      R(x,(R(T(y,z),u,w) \ v5) * v6,v7) = R(x,(R(y,u,w) \ v5) * v6,v7)
    ]]></literal>
    <justification jstring="[para(27(a,2),26431(a,1,2,1,1))].">
      <j1 rule="para" parents="27 26431"/>
    </justification>
  </clause>

  <clause id="26587">
    <literal><![CDATA[
      R(x,L((y / z) \ u,w,v5),v6) = R(x,L((z \ y) \ u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(6270(a,1),26440(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6270 26440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26588">
    <literal><![CDATA[
      R(x,L(y \ T(z,u),w,v5),v6) = R(x,L(y \ z,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(6417(a,1),26440(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6417 26440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26589">
    <literal><![CDATA[
      R(x,(y \ 1) \ (z * z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2965,a(flip),b,26455,a),flip(a)].">
      <j1 rule="hyper" parents="373 2965 26455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26591">
    <literal><![CDATA[
      R(x,y \ (z * z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,3028,a(flip),b,26589,a)].">
      <j1 rule="hyper" parents="64 3028 26589"/>
    </justification>
  </clause>

  <clause id="26592">
    <literal><![CDATA[
      R(x,y * (z * (y * z)),u) = R(x,a(y,z,y * z),u)
    ]]></literal>
    <justification jstring="[para(14(a,2),26591(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 26591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26593">
    <literal><![CDATA[
      R(x,y * ((y \ z) * z),u) = R(x,a(y,y \ z,z),u)
    ]]></literal>
    <justification jstring="[para(90(a,1),26591(a,1,2)),flip(a)].">
      <j1 rule="para" parents="90 26591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26594">
    <literal><![CDATA[
      R(x,y \ (K(z,u) * (z * T(z,u))),w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[para(5755(a,2),26591(a,1,2,2))].">
      <j1 rule="para" parents="5755 26591"/>
    </justification>
  </clause>

  <clause id="26595">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,w) = R(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(9377(a,1),26591(a,1,2))].">
      <j1 rule="para" parents="9377 26591"/>
    </justification>
  </clause>

  <clause id="26596">
    <literal><![CDATA[
      R(x,T(y * z,y) \ z,u) = R(x,z \ (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26410,a(flip),b,26491,a),flip(a)].">
      <j1 rule="hyper" parents="373 26410 26491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26597">
    <literal><![CDATA[
      (x * (y * T(y,z))) \ u = (y * T(y,z)) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,75,a(flip),b,26518,a)].">
      <j1 rule="hyper" parents="139 75 26518"/>
    </justification>
  </clause>

  <clause id="26598">
    <literal><![CDATA[
      a(x,y * T(y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,26518,a(flip),b,15463,a),flip(a)].">
      <j1 rule="hyper" parents="140 26518 15463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26599">
    <literal><![CDATA[
      ((x * (y / (y / x))) * T((x * (y / (y / x))) \ 1,z)) \ (x * (y / (y / x))) = 1 / T(1 / (x * (y / (y / x))),z)
    ]]></literal>
    <justification jstring="[para(26523(a,1),14874(a,1,1,2,1))].">
      <j1 rule="para" parents="26523 14874"/>
    </justification>
  </clause>

  <clause id="26600">
    <literal><![CDATA[
      R(x,K(y,z) / u,R(w,v5,v6)) = R(x,u,L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,26410,a,b,26535,a)].">
      <j1 rule="hyper" parents="64 26410 26535"/>
    </justification>
  </clause>

  <clause id="26601">
    <literal><![CDATA[
      R(x,(y \ (1 / z)) * u,w) = R(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26417,a(flip),b,26543,a),flip(a)].">
      <j1 rule="hyper" parents="373 26417 26543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26602">
    <literal><![CDATA[
      R(x,y \ ((z * u) \ u),w) = R(x,y \ (u \ (z \ u)),w)
    ]]></literal>
    <justification jstring="[para(5144(a,1),26560(a,1,2,2))].">
      <j1 rule="para" parents="5144 26560"/>
    </justification>
  </clause>

  <clause id="26603">
    <literal><![CDATA[
      T(x,y * y) \ ((y \ 1) * (x * (((y \ 1) \ y) * (y \ 1)))) = (y * (T(x,y * y) * (y \ 1))) / T(x,y * y)
    ]]></literal>
    <justification jstring="[para(16468(a,2),26578(a,2,2)),flip(a)].">
      <j1 rule="para" parents="16468 26578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26604">
    <literal><![CDATA[
      R(x,y \ (K(z,z \ 1) * ((1 / z) \ z)),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(1160(a,1),26594(a,1,2,2,2))].">
      <j1 rule="para" parents="1160 26594"/>
    </justification>
  </clause>

  <clause id="26605">
    <literal><![CDATA[
      R(x,T(y * z,y) \ z,u) = R(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26506,a(flip),b,26596,a),flip(a)].">
      <j1 rule="hyper" parents="373 26506 26596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26606">
    <literal><![CDATA[
      ((x / y) * T(x / y,y)) \ (z \ u) = (z * ((x / y) * (y \ x))) \ u
    ]]></literal>
    <justification jstring="[para(117(a,1),26597(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 26597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26607">
    <literal><![CDATA[
      R(x,T(K(y,z) / u,w),R(v5,v6,v7)) = R(x,u,L(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,26406,a,b,26600,a)].">
      <j1 rule="hyper" parents="64 26406 26600"/>
    </justification>
  </clause>

  <clause id="26608">
    <literal><![CDATA[
      R(x,(y \ (z \ 1)) * u,w) = R(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),26601(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 26601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26609">
    <literal><![CDATA[
      R(x,(y * z) \ z,u) = R(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26416,a(flip),b,26605,a)].">
      <j1 rule="hyper" parents="64 26416 26605"/>
    </justification>
  </clause>

  <clause id="26610">
    <literal><![CDATA[
      R(x,(y * z) \ y,u) = R(x,y \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26425,a,b,26609,a)].">
      <j1 rule="hyper" parents="64 26425 26609"/>
    </justification>
  </clause>

  <clause id="26613">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * (v5 * v6)) / (L(a(x,y,z),u,w) * T(v5,v6)) = R(K(v5,L(a(x,y,z),u,w)) * v6,v5,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(23557(a,2),26450(a,1,1))].">
      <j1 rule="para" parents="23557 26450"/>
    </justification>
  </clause>

  <clause id="26614">
    <literal><![CDATA[
      R(x,y,((z * T(u,w)) \ ((u * w) * z)) * v5) = R(x,y,R(K(u,z) * w,u,z) * v5)
    ]]></literal>
    <justification jstring="[para(26450(a,1),26180(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="26450 26180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26615">
    <literal><![CDATA[
      R(x,y,z \ ((u * T(w,v5)) \ ((w * v5) * u))) = R(x,y,z \ R(K(w,u) * v5,w,u))
    ]]></literal>
    <justification jstring="[para(26450(a,1),26183(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="26450 26183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26616">
    <literal><![CDATA[
      R(x,y,((z * T(u,w)) \ ((u * w) * z)) \ v5) = R(x,y,R(K(u,z) * w,u,z) \ v5)
    ]]></literal>
    <justification jstring="[para(26450(a,1),26209(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="26450 26209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26617">
    <literal><![CDATA[
      R(x,((y * T(z,u)) \ ((z * u) * y)) * w,v5) = R(x,R(K(z,y) * u,z,y) * w,v5)
    ]]></literal>
    <justification jstring="[para(26450(a,1),26417(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="26450 26417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26618">
    <literal><![CDATA[
      R(x,R(y \ z,y,u),w) = R(x,(y * u) \ (z * u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26438,a(flip),b,26457,a)].">
      <j1 rule="hyper" parents="64 26438 26457"/>
    </justification>
  </clause>

  <clause id="26619">
    <literal><![CDATA[
      T(x,y * y) / R(y * (y * x),L(x,y,y) * x,y * (y * x)) = (y * (y * x)) \ x
    ]]></literal>
    <justification jstring="[para(26473(a,1),13769(a,1,2))].">
      <j1 rule="para" parents="26473 13769"/>
    </justification>
  </clause>

  <clause id="26620">
    <literal><![CDATA[
      R(1 / (x / y),y \ x,x) \ 1 = 1 / (y / x)
    ]]></literal>
    <justification jstring="[para(26478(a,2),2036(a,1,1))].">
      <j1 rule="para" parents="26478 2036"/>
    </justification>
  </clause>

  <clause id="26621">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,R(y,z,u)) = (x * R(y,z,u)) / (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(2067(a,1),26478(a,2,2))].">
      <j1 rule="para" parents="2067 26478"/>
    </justification>
  </clause>

  <clause id="26622">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,L(y,z,u)) = (x * L(y,z,u)) / (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5590(a,1),26478(a,2,2))].">
      <j1 rule="para" parents="5590 26478"/>
    </justification>
  </clause>

  <clause id="26623">
    <literal><![CDATA[
      R((x / y) \ 1,y \ x,x) = y / x
    ]]></literal>
    <justification jstring="[hyper(37,a,11425,a,b,26620,a(flip))].">
      <j1 rule="hyper" parents="37 11425 26620"/>
    </justification>
  </clause>

  <clause id="26624">
    <literal><![CDATA[
      ((x / y) \ 1) * (R((x / y) \ 1,y \ x,x) * z) = (y / x) * (((x / y) \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,26623,a(flip),b,1904,a),flip(a)].">
      <j1 rule="hyper" parents="144 26623 1904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26625">
    <literal><![CDATA[
      R(((x * x) \ y) \ 1,(y \ x) \ (1 / x),1 / x) = (y \ x) / (1 / x)
    ]]></literal>
    <justification jstring="[para(884(a,1),26623(a,1,1,1))].">
      <j1 rule="para" parents="884 26623"/>
    </justification>
  </clause>

  <clause id="26626">
    <literal><![CDATA[
      R(x,y \ 1,y * z) * L(z,y,y) = (x * (1 / y)) * (y * z)
    ]]></literal>
    <justification jstring="[para(559(a,1),26488(a,1,2))].">
      <j1 rule="para" parents="559 26488"/>
    </justification>
  </clause>

  <clause id="26627">
    <literal><![CDATA[
      (x * (T(y,x) / z)) * z = y * R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(38,a,23680,a,b,26531,a),flip(a)].">
      <j1 rule="hyper" parents="38 23680 26531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26628">
    <literal><![CDATA[
      R(x,(y * z) \ ((y * u) * z),w) = R(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26425,a,b,26565,a)].">
      <j1 rule="hyper" parents="64 26425 26565"/>
    </justification>
  </clause>

  <clause id="26629">
    <literal><![CDATA[
      R(x,y * ((y * z) \ z),x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13916,a(flip),b,26568,a),flip(a)].">
      <j1 rule="hyper" parents="64 13916 26568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26630">
    <literal><![CDATA[
      R(x,y * (z \ (y \ z)),x) = x
    ]]></literal>
    <justification jstring="[para(10(a,1),26629(a,1,2,2,1))].">
      <j1 rule="para" parents="10 26629"/>
    </justification>
  </clause>

  <clause id="26631">
    <literal><![CDATA[
      T(x / (y * (z \ (y \ z))),x) = (y * (z \ (y \ z))) \ x
    ]]></literal>
    <justification jstring="[hyper(1382,a,26630,a)].">
      <j1 rule="hyper" parents="1382 26630"/>
    </justification>
  </clause>

  <clause id="26632">
    <literal><![CDATA[
      R(x,(y \ (z \ y)) * z,x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,26409,a,b,26630,a)].">
      <j1 rule="hyper" parents="64 26409 26630"/>
    </justification>
  </clause>

  <clause id="26633">
    <literal><![CDATA[
      1 / (x * (y \ (x \ y))) = (x * (y \ (x \ y))) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,2445,a(flip),b,26630,a),flip(a)].">
      <j1 rule="hyper" parents="64 2445 26630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26634">
    <literal><![CDATA[
      T(x,y * y) / R(y * (x * y),a(x,y,x * y),y * (x * y)) = (y * (x * y)) \ x
    ]]></literal>
    <justification jstring="[para(26592(a,1),13770(a,1,2))].">
      <j1 rule="para" parents="26592 13770"/>
    </justification>
  </clause>

  <clause id="26635">
    <literal><![CDATA[
      R(x,(y * z) \ ((y * u) * z),w) = R(x,R(u,y,z),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),26618(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 26618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26636">
    <literal><![CDATA[
      R(x,R(y,z,u),w) = R(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26628,a(flip),b,26635,a),flip(a)].">
      <j1 rule="hyper" parents="64 26628 26635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26637">
    <literal><![CDATA[
      R(x,R(y,z,u),R(w,v5,v6)) = R(x,L(y,z,u),L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,26360,a(flip),b,26636,a),flip(a)].">
      <j1 rule="hyper" parents="373 26360 26636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26638">
    <literal><![CDATA[
      R(x,R(y,z,u),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13712,a(flip),b,26636,a),flip(a)].">
      <j1 rule="hyper" parents="373 13712 26636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26639">
    <literal><![CDATA[
      R(x,L(1 / y,z,z),u) = R(x,y \ a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26490,a(flip),b,26636,a),flip(a)].">
      <j1 rule="hyper" parents="64 26490 26636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26640">
    <literal><![CDATA[
      R(x,L(y,y,z * y),u) = R(x,R(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26465,a(flip),b,26636,a),flip(a)].">
      <j1 rule="hyper" parents="64 26465 26636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26641">
    <literal><![CDATA[
      R(x / R(y \ 1,y,z),L(y,y,z),z) = (x * z) / (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,3053,a(flip),b,26636,a),flip(a)].">
      <j1 rule="hyper" parents="64 3053 26636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26642">
    <literal><![CDATA[
      R(x,L(1 / y,z,u),w) = R(x,R(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,3043,a(flip),b,26636,a),flip(a)].">
      <j1 rule="hyper" parents="64 3043 26636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26643">
    <literal><![CDATA[
      R(x,L(y,z,u),y) = R(x,y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,2838,a(flip),b,26636,a),flip(a)].">
      <j1 rule="hyper" parents="64 2838 26636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26645">
    <literal><![CDATA[
      R(x,(y / z) / u,x) = R(x,y / (u * z),x)
    ]]></literal>
    <justification jstring="[para(351(a,1),26638(a,1,2)),flip(a)].">
      <j1 rule="para" parents="351 26638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26646">
    <literal><![CDATA[
      R(x,L(y,z,u),y) = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,26360,a(flip),b,26643,a),flip(a)].">
      <j1 rule="hyper" parents="373 26360 26643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26647">
    <literal><![CDATA[
      R(x,y \ (z \ y),z) = R(x,z,L(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,26561,a(flip),b,26646,a)].">
      <j1 rule="hyper" parents="64 26561 26646"/>
    </justification>
  </clause>

  <clause id="26648">
    <literal><![CDATA[
      R(x,(y \ z) \ u,L((y \ z) \ u,y \ z,y)) = R(x,z \ (y * u),(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(630(a,1),26646(a,1,2)),flip(a)].">
      <j1 rule="para" parents="630 26646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26649">
    <literal><![CDATA[
      R(x,1 / (y \ z),L(1 / (y \ z),y \ z,y)) = R(x,1 / (1 / (z \ y)),1 / (y \ z))
    ]]></literal>
    <justification jstring="[para(4305(a,1),26646(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4305 26646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26650">
    <literal><![CDATA[
      R(x,x \ (y \ x),y) = (y \ L(y,y,x)) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,25617,a,b,26647,a),flip(a)].">
      <j1 rule="hyper" parents="373 25617 26647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26651">
    <literal><![CDATA[
      R(x,L(y,y,z * y),u) = R(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26636,a(flip),b,26640,a),flip(a)].">
      <j1 rule="hyper" parents="373 26636 26640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26652">
    <literal><![CDATA[
      R(x,L(1 / y,z,u),w) = R(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26636,a(flip),b,26642,a),flip(a)].">
      <j1 rule="hyper" parents="373 26636 26642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26653">
    <literal><![CDATA[
      R(x,(y / z) / u,x) = R(x,(u * z) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,26410,a(flip),b,26645,a),flip(a)].">
      <j1 rule="hyper" parents="373 26410 26645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26654">
    <literal><![CDATA[
      x \ L(x,x,y) = (y \ (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(40,a,25914,a,b,26650,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 25914 26650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26655">
    <literal><![CDATA[
      x * ((y \ (y / x)) * x) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(157,a,26654,a)].">
      <j1 rule="hyper" parents="157 26654"/>
    </justification>
  </clause>

  <clause id="26656">
    <literal><![CDATA[
      (1 / x) \ (y \ (y / x)) = (y \ (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,26053,a,b,26654,a)].">
      <j1 rule="hyper" parents="64 26053 26654"/>
    </justification>
  </clause>

  <clause id="26657">
    <literal><![CDATA[
      (1 / x) * ((y \ (y / x)) * x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,26654,a(flip),b,26053,a)].">
      <j1 rule="hyper" parents="145 26654 26053"/>
    </justification>
  </clause>

  <clause id="26658">
    <literal><![CDATA[
      ((x \ (x / y)) * y) * y = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,26654,a(flip),b,5572,a)].">
      <j1 rule="hyper" parents="144 26654 5572"/>
    </justification>
  </clause>

  <clause id="26659">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,x \ y,y) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),26654(a,2,1,2))].">
      <j1 rule="para" parents="79 26654"/>
    </justification>
  </clause>

  <clause id="26660">
    <literal><![CDATA[
      ((x * (y \ x)) \ (y \ T(x,y \ x))) * x = x \ L(x,x,x * (y \ x))
    ]]></literal>
    <justification jstring="[para(4464(a,2),26654(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4464 26654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26661">
    <literal><![CDATA[
      x \ L(x,x,x * y) = ((y * x) \ y) * x
    ]]></literal>
    <justification jstring="[para(5888(a,1),26654(a,2,1))].">
      <j1 rule="para" parents="5888 26654"/>
    </justification>
  </clause>

  <clause id="26662">
    <literal><![CDATA[
      (x \ L(x,x,y)) \ K(y \ (y / x),y) = (((y / x) / y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(26654(a,2),14455(a,1,1))].">
      <j1 rule="para" parents="26654 14455"/>
    </justification>
  </clause>

  <clause id="26663">
    <literal><![CDATA[
      K(x,y) * (z \ L(z,z,x)) = (x \ (T(x,y) / z)) * z
    ]]></literal>
    <justification jstring="[para(26654(a,2),24901(a,1,2))].">
      <j1 rule="para" parents="26654 24901"/>
    </justification>
  </clause>

  <clause id="26664">
    <literal><![CDATA[
      x * (L(x \ 1,x,y) * x) = L(x,x,x * y)
    ]]></literal>
    <justification jstring="[para(6390(a,1),26655(a,1,2,1))].">
      <j1 rule="para" parents="6390 26655"/>
    </justification>
  </clause>

  <clause id="26665">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) * (y \ x) = L(y \ x,y \ x,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),26658(a,1,1,1,2))].">
      <j1 rule="para" parents="79 26658"/>
    </justification>
  </clause>

  <clause id="26666">
    <literal><![CDATA[
      L((x * y) \ x,(x * y) \ x,x) = (y * ((x * y) \ x)) * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(211(a,1),26658(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="211 26658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26667">
    <literal><![CDATA[
      (((x * y) \ x) * y) * y = L(y,y,y * x)
    ]]></literal>
    <justification jstring="[para(5888(a,1),26658(a,1,1,1))].">
      <j1 rule="para" parents="5888 26658"/>
    </justification>
  </clause>

  <clause id="26668">
    <literal><![CDATA[
      (x \ L(x,x,x * y)) * ((((y * x) \ y) * x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(144,a,26661,a,b,79,a)].">
      <j1 rule="hyper" parents="144 26661 79"/>
    </justification>
  </clause>

  <clause id="26670">
    <literal><![CDATA[
      (x \ L(x,x,x * y)) \ K(x \ 1,y * x) = ((y / (y * x)) * x) \ 1
    ]]></literal>
    <justification jstring="[para(26661(a,2),14928(a,1,1))].">
      <j1 rule="para" parents="26661 14928"/>
    </justification>
  </clause>

  <clause id="26671">
    <literal><![CDATA[
      (((((x * y) \ z) * y) \ ((x * y) \ z)) * y) * y = L(y,y,T(y,x) * ((y * x) \ z))
    ]]></literal>
    <justification jstring="[para(10844(a,2),26667(a,2,3))].">
      <j1 rule="para" parents="10844 26667"/>
    </justification>
  </clause>

  <clause id="26672">
    <literal><![CDATA[
      (((((x \ y) * L(x,z,u)) * x) \ ((x \ y) * L(x,z,u))) * x) * x = L(x,x,y * L(L(x,y * x,x),z,u))
    ]]></literal>
    <justification jstring="[para(13725(a,2),26667(a,2,3))].">
      <j1 rule="para" parents="13725 26667"/>
    </justification>
  </clause>

  <clause id="26673">
    <literal><![CDATA[
      R(x,L(y,y,y * z),u) = R(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(23253(a,1),26651(a,1,2))].">
      <j1 rule="para" parents="23253 26651"/>
    </justification>
  </clause>

  <clause id="26674">
    <literal><![CDATA[
      R(x,L(y \ 1,z,u),w) = R(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26454,a(flip),b,26652,a)].">
      <j1 rule="hyper" parents="64 26454 26652"/>
    </justification>
  </clause>

  <clause id="26675">
    <literal><![CDATA[
      R(x,(y / z) / u,x) = R(x,(u * z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13733,a(flip),b,26653,a),flip(a)].">
      <j1 rule="hyper" parents="373 13733 26653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26676">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * (y \ 1) = y \ (x \ (x / (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,207,a(flip),b,26656,a),flip(a)].">
      <j1 rule="hyper" parents="64 207 26656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26677">
    <literal><![CDATA[
      L(T(x \ (x / y),y),y,y) = x \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,567,a,b,26657,a)].">
      <j1 rule="hyper" parents="64 567 26657"/>
    </justification>
  </clause>

  <clause id="26678">
    <literal><![CDATA[
      (x * x) \ L(x,x,x * y) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,26664,a(flip),b,1830,a)].">
      <j1 rule="hyper" parents="139 26664 1830"/>
    </justification>
  </clause>

  <clause id="26679">
    <literal><![CDATA[
      R(x,y \ (z / u),x) = R(x,(y * u) * z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26410,a(flip),b,26675,a)].">
      <j1 rule="hyper" parents="64 26410 26675"/>
    </justification>
  </clause>

  <clause id="26680">
    <literal><![CDATA[
      L(x,x,x * y) \ ((x * x) * z) = L(x \ 1,x,y) \ z
    ]]></literal>
    <justification jstring="[para(26678(a,1),804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26678 804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26681">
    <literal><![CDATA[
      ((1 / x) * L(x,x,x * y)) \ ((x * x) * z) = ((x \ 1) * L(x \ 1,x,y)) \ z
    ]]></literal>
    <justification jstring="[para(26678(a,1),4928(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="26678 4928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26682">
    <literal><![CDATA[
      R(x,(y * z) * u,x) = R(x,y * (u / z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13733,a(flip),b,26679,a),flip(a)].">
      <j1 rule="hyper" parents="64 13733 26679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26683">
    <literal><![CDATA[
      R(x,(y * z) * u,x) = R(x,y * (z \ u),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,26500,a(flip),b,26682,a),flip(a)].">
      <j1 rule="hyper" parents="373 26500 26682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26684">
    <literal><![CDATA[
      R(x,y * (z \ (z \ y)),x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,13935,a(flip),b,26683,a),flip(a)].">
      <j1 rule="hyper" parents="64 13935 26683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26685">
    <literal><![CDATA[
      L(x,y * (z \ (z \ y)),x) = x
    ]]></literal>
    <justification jstring="[hyper(4734,a,26684,a)].">
      <j1 rule="hyper" parents="4734 26684"/>
    </justification>
  </clause>

  <clause id="26686">
    <literal><![CDATA[
      T(x \ (x \ y),y) / y = y \ (x \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(225,a,26684,a(flip),b,13734,a(flip))].">
      <j1 rule="hyper" parents="225 26684 13734"/>
    </justification>
  </clause>

  <clause id="26687">
    <literal><![CDATA[
      (x \ ((y \ x) / y)) * x = T((y \ x) / y,x)
    ]]></literal>
    <justification jstring="[para(26684(a,1),26552(a,1,2))].">
      <j1 rule="para" parents="26684 26552"/>
    </justification>
  </clause>

  <clause id="26688">
    <literal><![CDATA[
      L(x,a(y,z,u),x) = L(x,w * (v5 \ (v5 \ w)),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13919,a,b,26685,a)].">
      <j1 rule="hyper" parents="373 13919 26685"/>
    </justification>
  </clause>

  <clause id="26689">
    <literal><![CDATA[
      K(x * x,y) * (y \ (x \ (x \ y))) = (x \ (x \ y)) / y
    ]]></literal>
    <justification jstring="[para(26686(a,1),17580(a,1,2))].">
      <j1 rule="para" parents="26686 17580"/>
    </justification>
  </clause>

  <clause id="26690">
    <literal><![CDATA[
      T((x \ y) / x,y) / y = y \ ((x \ y) / x)
    ]]></literal>
    <justification jstring="[hyper(154,a,26687,a)].">
      <j1 rule="hyper" parents="154 26687"/>
    </justification>
  </clause>

  <clause id="26691">
    <literal><![CDATA[
      R(x,y \ a(y,z,z),u) = R(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26652,a(flip),b,26639,a),flip(a)].">
      <j1 rule="hyper" parents="64 26652 26639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26692">
    <literal><![CDATA[
      (a(x,y,y) * z) / (R(x \ 1,y,y) * z) = R(x,L(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16020,a(flip),b,26691,a)].">
      <j1 rule="hyper" parents="64 16020 26691"/>
    </justification>
  </clause>

  <clause id="26693">
    <literal><![CDATA[
      R(x,(y \ z) * (z \ y),x) = x
    ]]></literal>
    <justification jstring="[para(26659(a,1),25364(a,1,2))].">
      <j1 rule="para" parents="26659 25364"/>
    </justification>
  </clause>

  <clause id="26694">
    <literal><![CDATA[
      ((x \ y) \ (y \ x)) * (x \ y) = T(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,26693,a(flip),b,13765,a(flip))].">
      <j1 rule="hyper" parents="145 26693 13765"/>
    </justification>
  </clause>

  <clause id="26696">
    <literal><![CDATA[
      x * T(x \ ((y \ z) * ((z \ y) \ x)),z \ y) = T(y \ z,z \ y) * ((z \ y) \ x)
    ]]></literal>
    <justification jstring="[para(26694(a,1),1764(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26694 1764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26697">
    <literal><![CDATA[
      R(x,((y / z) / u) * w,v5) = R(x,(u \ (z \ y)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26417,a(flip),b,26436,a),flip(a)].">
      <j1 rule="hyper" parents="373 26417 26436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26698">
    <literal><![CDATA[
      R(x,y \ ((z * z) * u),w) = R(x,u / y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2965,a(flip),b,26456,a),flip(a)].">
      <j1 rule="hyper" parents="373 2965 26456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26700">
    <literal><![CDATA[
      R(x,y \ ((z * z) * u),w) = R(x,y \ u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26410,a(flip),b,26698,a),flip(a)].">
      <j1 rule="hyper" parents="373 26410 26698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26701">
    <literal><![CDATA[
      R(x,y \ (z * (u * u)),w) = R(x,y \ z,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26507,a,b,26700,a)].">
      <j1 rule="hyper" parents="64 26507 26700"/>
    </justification>
  </clause>

  <clause id="26702">
    <literal><![CDATA[
      R(x,y \ ((z * z) / u),w) = R(x,y \ (1 / u),w)
    ]]></literal>
    <justification jstring="[para(497(a,1),26700(a,1,2,2))].">
      <j1 rule="para" parents="497 26700"/>
    </justification>
  </clause>

  <clause id="26703">
    <literal><![CDATA[
      R(x,((1 / y) * z) \ u,w) = R(x,(y * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(941(a,1),26700(a,1,2))].">
      <j1 rule="para" parents="941 26700"/>
    </justification>
  </clause>

  <clause id="26704">
    <literal><![CDATA[
      R(x,y \ (T(z,u * u) * w),v5) = R(x,y \ (z * ((u * u) * w)),v5)
    ]]></literal>
    <justification jstring="[para(1434(a,1),26700(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1434 26700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26705">
    <literal><![CDATA[
      R(x,y * L(z,z,y),u) = R(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26459,a(flip),b,26701,a)].">
      <j1 rule="hyper" parents="64 26459 26701"/>
    </justification>
  </clause>

  <clause id="26707">
    <literal><![CDATA[
      R(x,y \ ((z * z) / u),w) = R(x,y \ (u \ 1),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26506,a(flip),b,26702,a),flip(a)].">
      <j1 rule="hyper" parents="373 26506 26702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26708">
    <literal><![CDATA[
      R(x,((1 / y) * z) \ z,u) = R(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26609,a(flip),b,26703,a),flip(a)].">
      <j1 rule="hyper" parents="373 26609 26703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26709">
    <literal><![CDATA[
      R(x,y \ ((z * z) / u),w) = R(x,y \ u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26563,a(flip),b,26707,a),flip(a)].">
      <j1 rule="hyper" parents="373 26563 26707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26710">
    <literal><![CDATA[
      R(x,y \ (z \ (u * u)),w) = R(x,y \ z,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26506,a(flip),b,26709,a)].">
      <j1 rule="hyper" parents="64 26506 26709"/>
    </justification>
  </clause>

  <clause id="26711">
    <literal><![CDATA[
      R(x,y \ ((1 / z) \ y),u) = R(x,y \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26609,a(flip),b,26708,a)].">
      <j1 rule="hyper" parents="64 26609 26708"/>
    </justification>
  </clause>

  <clause id="26712">
    <literal><![CDATA[
      R(x,((y * y) * z) \ u,w) = R(x,(y * y) \ (u / z),w)
    ]]></literal>
    <justification jstring="[para(933(a,1),26469(a,1,2)),flip(a)].">
      <j1 rule="para" parents="933 26469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26713">
    <literal><![CDATA[
      R(x,y \ z,(y \ z) \ u) * u = (x * (z / y)) * ((z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(144,a,26480,a(flip),b,110,a)].">
      <j1 rule="hyper" parents="144 26480 110"/>
    </justification>
  </clause>

  <clause id="26714">
    <literal><![CDATA[
      R(x,(y / (z * u)) * w,v5) = R(x,w * ((u * z) \ y),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26541,a,b,26544,a)].">
      <j1 rule="hyper" parents="373 26541 26544"/>
    </justification>
  </clause>

  <clause id="26715">
    <literal><![CDATA[
      R(x,y * (z * (z / y)),x) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,26569,a(flip),b,26557,a),flip(a)].">
      <j1 rule="hyper" parents="373 26569 26557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26716">
    <literal><![CDATA[
      R(x,y * ((z * u) * w),v5) = R(x,y * (w * (u * z)),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26501,a,b,26558,a)].">
      <j1 rule="hyper" parents="373 26501 26558"/>
    </justification>
  </clause>

  <clause id="26717">
    <literal><![CDATA[
      R(x,y * (z * (u * z)),w) = R(x,L(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26473,a(flip),b,26558,a),flip(a)].">
      <j1 rule="hyper" parents="373 26473 26558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26718">
    <literal><![CDATA[
      R(x,a(y,z,y * z),u) = R(x,L(y,z,z) * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26592,a(flip),b,26717,a)].">
      <j1 rule="hyper" parents="64 26592 26717"/>
    </justification>
  </clause>

  <clause id="26719">
    <literal><![CDATA[
      R(x,a(y,z,y * z),u) = R(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26538,a(flip),b,26718,a),flip(a)].">
      <j1 rule="hyper" parents="373 26538 26718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26720">
    <literal><![CDATA[
      K(x * (y * T(y,z)),T(x,u)) = K(y * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25883,a(flip),b,26567,a),flip(a)].">
      <j1 rule="hyper" parents="373 25883 26567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26722">
    <literal><![CDATA[
      R(x,y \ ((z \ 1) \ z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[para(2450(a,1),26604(a,1,2,2))].">
      <j1 rule="para" parents="2450 26604"/>
    </justification>
  </clause>

  <clause id="26723">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y,z,u)) / R(y,z,u) = x * (1 / R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(142,a,26637,a(flip),b,1405,a)].">
      <j1 rule="hyper" parents="142 26637 1405"/>
    </justification>
  </clause>

  <clause id="26724">
    <literal><![CDATA[
      (((x * x) * y) / L(x,x,x * z)) * x = x * (L(x \ 1,x,z) \ y)
    ]]></literal>
    <justification jstring="[para(26680(a,1),23887(a,2,2))].">
      <j1 rule="para" parents="26680 23887"/>
    </justification>
  </clause>

  <clause id="26725">
    <literal><![CDATA[
      (x \ (y \ (y \ x))) \ K(x,y * y) = ((y \ (y \ x)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(26689(a,1),14450(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26689 14450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26726">
    <literal><![CDATA[
      R(x,((y * y) * z) \ u,w) = R(x,u / z,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2967,a(flip),b,26712,a),flip(a)].">
      <j1 rule="hyper" parents="373 2967 26712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26728">
    <literal><![CDATA[
      R(x,((y * y) * z) \ u,w) = R(x,z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26410,a(flip),b,26726,a),flip(a)].">
      <j1 rule="hyper" parents="373 26410 26726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26729">
    <literal><![CDATA[
      R(x,((T(y,z * z) * u) * w) \ v5,v6) = R(x,((y * ((z * z) * u)) * w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(1455(a,1),26728(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1455 26728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26731">
    <literal><![CDATA[
      R(x,y * ((z * y) \ ((y * u) * z)),w) = R(x,y * R(u,y,z),w)
    ]]></literal>
    <justification jstring="[para(1053(a,1),26714(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1053 26714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26732">
    <literal><![CDATA[
      R(x \ y,y,x \ y) * x = x * (((x \ y) \ x) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,364,a(flip),b,26497,a),flip(a)].">
      <j1 rule="hyper" parents="373 364 26497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26734">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (T(y \ 1,v5) * z) = (L(x,u,w) * T(y \ 1,v5)) * z
    ]]></literal>
    <justification jstring="[para(29(a,1),26581(a,1,1))].">
      <j1 rule="para" parents="29 26581"/>
    </justification>
  </clause>

  <clause id="26735">
    <literal><![CDATA[
      T((1 / x) \ ((x \ 1) \ y),K(1,x) * x) = (x \ 1) \ ((x \ 1) \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,7604,a(flip),b,22934,a),flip(a)].">
      <j1 rule="hyper" parents="64 7604 22934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26736">
    <literal><![CDATA[
      (((x \ (y \ (y \ x))) \ 1) \ K(y * y,x)) \ K(x,y \ (y \ x)) = T((x \ (y \ (y \ x))) \ 1,x \ (y \ (y \ x)))
    ]]></literal>
    <justification jstring="[para(17579(a,1),22959(a,1,1,2))].">
      <j1 rule="para" parents="17579 22959"/>
    </justification>
  </clause>

  <clause id="26737">
    <literal><![CDATA[
      T(1 / x,K(y,z)) * ((x \ y) * x) = (1 / x) * (T(x \ y,K(y,z)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1468,a(flip),b,22976,a),flip(a)].">
      <j1 rule="hyper" parents="64 1468 22976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26738">
    <literal><![CDATA[
      K(x,K(y,z * u)) * K(z,z \ u) = K(K(x,y) * z,u / z)
    ]]></literal>
    <justification jstring="[para(17551(a,1),22986(a,1,1))].">
      <j1 rule="para" parents="17551 22986"/>
    </justification>
  </clause>

  <clause id="26739">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((x * w) * a(y,z,u)) = L(w,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(23963,a,23171,a)].">
      <j1 rule="hyper" parents="23963 23171"/>
    </justification>
  </clause>

  <clause id="26740">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,w)) = (x * a(z,u,w)) \ (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,23560,a(flip),b,23172,a),flip(a)].">
      <j1 rule="hyper" parents="373 23560 23172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26741">
    <literal><![CDATA[
      L(x \ y,x,a(y,z,z)) = (x * a(y,z,z)) \ R(y,z,z)
    ]]></literal>
    <justification jstring="[para(15998(a,1),23190(a,2,2))].">
      <j1 rule="para" parents="15998 23190"/>
    </justification>
  </clause>

  <clause id="26742">
    <literal><![CDATA[
      (x * a(x,y,z)) \ ((x * y) * T(z,y)) = L(z * y,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(25784(a,1),23191(a,1,2))].">
      <j1 rule="para" parents="25784 23191"/>
    </justification>
  </clause>

  <clause id="26743">
    <literal><![CDATA[
      L(x,y,z) * (((1 / x) \ x) * u) = (x * x) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(562(a,1),23628(a,1,2,1))].">
      <j1 rule="para" parents="562 23628"/>
    </justification>
  </clause>

  <clause id="26745">
    <literal><![CDATA[
      x \ (R(x,y,z) \ ((x * x) * u)) = (x \ 1) \ (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(23688(a,1),1167(a,1,2))].">
      <j1 rule="para" parents="23688 1167"/>
    </justification>
  </clause>

  <clause id="26746">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * (u * w) = w * (T(u,w) * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,10989,a(flip),b,23901,a),flip(a)].">
      <j1 rule="hyper" parents="373 10989 23901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26747">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) * w = w * L(y \ L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(5665(a,2),23901(a,1,1,1))].">
      <j1 rule="para" parents="5665 23901"/>
    </justification>
  </clause>

  <clause id="26748">
    <literal><![CDATA[
      K(x,y) * (z * (a(u,w,v5) \ 1)) = (a(u,w,v5) \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,23764,a(flip),b,24366,a)].">
      <j1 rule="hyper" parents="64 23764 24366"/>
    </justification>
  </clause>

  <clause id="26749">
    <literal><![CDATA[
      (1 / L(x,y,z)) * L(x,u,w) = L(x,y,z) \ L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,1850,a(flip),b,24389,a),flip(a)].">
      <j1 rule="hyper" parents="64 1850 24389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26750">
    <literal><![CDATA[
      R(L(x,y,z),L(x,y,z),L(x,y,z) \ L(x,u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,2016,a,b,26749,a(flip))].">
      <j1 rule="hyper" parents="40 2016 26749"/>
    </justification>
  </clause>

  <clause id="26751">
    <literal><![CDATA[
      a(1 / L(x,y,z),L(x,u,w),L(x,u,w) \ ((1 / L(x,y,z)) \ 1)) / (L(x,y,z) \ L(x,u,w)) = 1 / (1 / (L(x,u,w) \ ((1 / L(x,y,z)) \ 1)))
    ]]></literal>
    <justification jstring="[para(26749(a,1),25056(a,1,2))].">
      <j1 rule="para" parents="26749 25056"/>
    </justification>
  </clause>

  <clause id="26752">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ (1 / x)) = (y / x) * K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,24496,a(flip),b,24443,a),flip(a)].">
      <j1 rule="hyper" parents="64 24496 24443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26753">
    <literal><![CDATA[
      K(x,T(y * (z \ K(u,u \ w)),v5)) = K(x,T(K(w,u) * (y / z),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18231,a(flip),b,24499,a),flip(a)].">
      <j1 rule="hyper" parents="64 18231 24499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26754">
    <literal><![CDATA[
      K(x,T(y * (z \ K(z,u)),w)) = K(x,T(y / T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18174,a(flip),b,24499,a),flip(a)].">
      <j1 rule="hyper" parents="64 18174 24499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26758">
    <literal><![CDATA[
      (1 / L(x,y,z)) * R(x,u,w) = L(x,y,z) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,1879,a(flip),b,24611,a),flip(a)].">
      <j1 rule="hyper" parents="64 1879 24611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26759">
    <literal><![CDATA[
      K(R(x,y,z),u) * T((u * R(x,y,z)) / (u * x),w) = (R(x,y,z) * u) / (u * x)
    ]]></literal>
    <justification jstring="[para(24697(a,2),14887(a,1,2))].">
      <j1 rule="para" parents="24697 14887"/>
    </justification>
  </clause>

  <clause id="26761">
    <literal><![CDATA[
      T(x * (x * y),x) / x = (x * (y * x)) / (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(25250(a,1),24747(a,1,1))].">
      <j1 rule="para" parents="25250 24747"/>
    </justification>
  </clause>

  <clause id="26762">
    <literal><![CDATA[
      (x * (y * x)) / (1 / (1 / x)) = (x * (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,25258,a(flip),b,26761,a),flip(a)].">
      <j1 rule="hyper" parents="64 25258 26761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26763">
    <literal><![CDATA[
      (x * ((y \ (x \ y)) / x)) * x = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,11398,a(flip),b,26762,a),flip(a)].">
      <j1 rule="hyper" parents="64 11398 26762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26764">
    <literal><![CDATA[
      x * ((y \ (x \ y)) / x) = L(y \ (x \ y),x,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,26345,a,b,26763,a),flip(a)].">
      <j1 rule="hyper" parents="36 26345 26763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26765">
    <literal><![CDATA[
      (x \ 1) * (y \ (x \ y)) = (y \ (x \ y)) / x
    ]]></literal>
    <justification jstring="[hyper(35,a,1139,a,b,26764,a)].">
      <j1 rule="hyper" parents="35 1139 26764"/>
    </justification>
  </clause>

  <clause id="26766">
    <literal><![CDATA[
      (x \ (y \ x)) * (y \ 1) = (x \ (y \ x)) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,1928,a,b,26765,a)].">
      <j1 rule="hyper" parents="64 1928 26765"/>
    </justification>
  </clause>

  <clause id="26767">
    <literal><![CDATA[
      T((x * y) * z,(y * z) * x) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,14017,a(flip),b,24809,a),flip(a)].">
      <j1 rule="hyper" parents="64 14017 24809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26768">
    <literal><![CDATA[
      T((x * y) * z,y * (z * x)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,25009,a(flip),b,26767,a)].">
      <j1 rule="hyper" parents="64 25009 26767"/>
    </justification>
  </clause>

  <clause id="26769">
    <literal><![CDATA[
      (a(x,y,z) * u) \ a(x,y,z) = a(x,y,z) \ (u \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(23968,a,24833,a)].">
      <j1 rule="hyper" parents="23968 24833"/>
    </justification>
  </clause>

  <clause id="26770">
    <literal><![CDATA[
      L(x,y,L(L(T(z,u),w,v5),v6,v7)) = L(x,y,L(L(z,v6,v7),w,v5))
    ]]></literal>
    <justification jstring="[para(30(a,1),24836(a,1,3))].">
      <j1 rule="para" parents="30 24836"/>
    </justification>
  </clause>

  <clause id="26772">
    <literal><![CDATA[
      L(x,x,R(y,y,x)) = L(x,x,x * ((1 / y) \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,25566,a,b,24840,a),flip(a)].">
      <j1 rule="hyper" parents="64 25566 24840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26773">
    <literal><![CDATA[
      L(x,x,R(y,y,x)) = L(x,x,(y \ x) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,23996,a(flip),b,26772,a),flip(a)].">
      <j1 rule="hyper" parents="373 23996 26772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26774">
    <literal><![CDATA[
      (x * x) * (L(y,z,u) \ y) = y * (L(y,z,u) \ (x * x))
    ]]></literal>
    <justification jstring="[para(5556(a,1),24844(a,1,2))].">
      <j1 rule="para" parents="5556 24844"/>
    </justification>
  </clause>

  <clause id="26775">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (u * u) = x * (L(x,y,z) \ (u * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,23581,a,b,26774,a)].">
      <j1 rule="hyper" parents="64 23581 26774"/>
    </justification>
  </clause>

  <clause id="26776">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,y,z) * L(x,y,z))) = x / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5562,a(flip),b,26775,a),flip(a)].">
      <j1 rule="hyper" parents="64 5562 26775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26777">
    <literal><![CDATA[
      a(T(x,y),z,u) = (x * (z * u)) \ ((x * z) * u)
    ]]></literal>
    <justification jstring="[hyper(959,a,24860,a)].">
      <j1 rule="hyper" parents="959 24860"/>
    </justification>
  </clause>

  <clause id="26779">
    <literal><![CDATA[
      a(T(x,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,14,a,b,26777,a),flip(a)].">
      <j1 rule="hyper" parents="373 14 26777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26780">
    <literal><![CDATA[
      a(T(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(26777(a,2),959(a,1))].">
      <j1 rule="para" parents="26777 959"/>
    </justification>
  </clause>

  <clause id="26781">
    <literal><![CDATA[
      a(T(x,y),z,u) = a(x,(w * w) * z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11960,a,b,26779,a),flip(a)].">
      <j1 rule="hyper" parents="373 11960 26779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26783">
    <literal><![CDATA[
      a(T(x \ 1,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2653,a(flip),b,26779,a),flip(a)].">
      <j1 rule="hyper" parents="373 2653 26779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26784">
    <literal><![CDATA[
      a((x \ y) \ y,z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13111,a,b,26779,a)].">
      <j1 rule="hyper" parents="64 13111 26779"/>
    </justification>
  </clause>

  <clause id="26785">
    <literal><![CDATA[
      a(x / y,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13118,a(flip),b,26779,a),flip(a)].">
      <j1 rule="hyper" parents="64 13118 26779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26787">
    <literal><![CDATA[
      a(x * y,z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13107,a(flip),b,26779,a)].">
      <j1 rule="hyper" parents="64 13107 26779"/>
    </justification>
  </clause>

  <clause id="26791">
    <literal><![CDATA[
      a(x \ (y * x),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(22(a,1),26779(a,1,1))].">
      <j1 rule="para" parents="22 26779"/>
    </justification>
  </clause>

  <clause id="26792">
    <literal><![CDATA[
      a(L(T(x,y),z,u),w,v5) = a(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(25(a,2),26779(a,1,1))].">
      <j1 rule="para" parents="25 26779"/>
    </justification>
  </clause>

  <clause id="26793">
    <literal><![CDATA[
      a(R(T(x,y),z,u),w,v5) = a(R(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(27(a,2),26779(a,1,1))].">
      <j1 rule="para" parents="27 26779"/>
    </justification>
  </clause>

  <clause id="26794">
    <literal><![CDATA[
      a(L(x / y,z,u),w,v5) = a(L(y \ x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(279(a,1),26779(a,1,1)),flip(a)].">
      <j1 rule="para" parents="279 26779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26795">
    <literal><![CDATA[
      a(R(x \ y,x,z),u,w) = a((y * z) / (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(855(a,1),26779(a,1,1))].">
      <j1 rule="para" parents="855 26779"/>
    </justification>
  </clause>

  <clause id="26796">
    <literal><![CDATA[
      a(L((x \ y) \ y,z,u),w,v5) = a(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(368(a,1),26779(a,1,1))].">
      <j1 rule="para" parents="368 26779"/>
    </justification>
  </clause>

  <clause id="26797">
    <literal><![CDATA[
      a(x * (y * (x \ 1)),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(1178(a,1),26779(a,1,1))].">
      <j1 rule="para" parents="1178 26779"/>
    </justification>
  </clause>

  <clause id="26798">
    <literal><![CDATA[
      a(x \ ((y * y) * z),u,w) = a((y * y) * (z / x),u,w)
    ]]></literal>
    <justification jstring="[para(946(a,1),26779(a,1,1))].">
      <j1 rule="para" parents="946 26779"/>
    </justification>
  </clause>

  <clause id="26799">
    <literal><![CDATA[
      a(x \ (y * (x * x)),z,u) = a(y * L(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2848(a,1),26779(a,1,1))].">
      <j1 rule="para" parents="2848 26779"/>
    </justification>
  </clause>

  <clause id="26802">
    <literal><![CDATA[
      a(L(x,K(y,z),u),w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(22751(a,2),26779(a,1,1))].">
      <j1 rule="para" parents="22751 26779"/>
    </justification>
  </clause>

  <clause id="26803">
    <literal><![CDATA[
      a(((x * y) * z) * K(x,u),w,v5) = a((T(x,u) * y) * z,w,v5)
    ]]></literal>
    <justification jstring="[para(24776(a,1),26779(a,1,1))].">
      <j1 rule="para" parents="24776 26779"/>
    </justification>
  </clause>

  <clause id="26805">
    <literal><![CDATA[
      a(R(x,y,(x * y) \ z),u,w) = a((y * ((x * y) \ z)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(420(a,1),26784(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="420 26784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26807">
    <literal><![CDATA[
      (x * y) / ((x / z) * (z * y)) = a(z \ x,z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15470,a,b,26785,a)].">
      <j1 rule="hyper" parents="64 15470 26785"/>
    </justification>
  </clause>

  <clause id="26808">
    <literal><![CDATA[
      (((x \ 1) / y) * (y * x)) \ K(x \ 1,x) = a(y \ (x \ 1),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1291,a,b,26785,a)].">
      <j1 rule="hyper" parents="64 1291 26785"/>
    </justification>
  </clause>

  <clause id="26809">
    <literal><![CDATA[
      x \ (((x / y) * z) * (z \ y)) = a(y \ x,z,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1285,a,b,26785,a)].">
      <j1 rule="hyper" parents="64 1285 26785"/>
    </justification>
  </clause>

  <clause id="26810">
    <literal><![CDATA[
      a(x \ (1 / y),z,u) = a(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2646,a(flip),b,26785,a),flip(a)].">
      <j1 rule="hyper" parents="64 2646 26785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26811">
    <literal><![CDATA[
      a(x \ y,x,x \ z) = ((y / x) * z) \ (y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1286,a(flip),b,26785,a),flip(a)].">
      <j1 rule="hyper" parents="64 1286 26785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26812">
    <literal><![CDATA[
      a((x * y) \ z,x,y) * z = ((z / (x * y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,26785,a(flip),b,15471,a)].">
      <j1 rule="hyper" parents="144 26785 15471"/>
    </justification>
  </clause>

  <clause id="26814">
    <literal><![CDATA[
      a((1 / x) \ y,x,x) / (y * x) = 1 / (y / (1 / x))
    ]]></literal>
    <justification jstring="[para(26785(a,1),16018(a,1,1))].">
      <j1 rule="para" parents="26785 16018"/>
    </justification>
  </clause>

  <clause id="26815">
    <literal><![CDATA[
      T(a(x / y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,z,u) = v5
    ]]></literal>
    <justification jstring="[para(26785(a,2),23556(a,1,1))].">
      <j1 rule="para" parents="26785 23556"/>
    </justification>
  </clause>

  <clause id="26816">
    <literal><![CDATA[
      x * a(y \ x,z \ y,z) = ((x / y) * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(26785(a,1),25645(a,1,2))].">
      <j1 rule="para" parents="26785 25645"/>
    </justification>
  </clause>

  <clause id="26818">
    <literal><![CDATA[
      L(a(x * y,z,u),w,K(v5,v6)) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23115,a,b,26787,a)].">
      <j1 rule="hyper" parents="373 23115 26787"/>
    </justification>
  </clause>

  <clause id="26819">
    <literal><![CDATA[
      a(x * (a(y,z,y) * u),w,v5) = a(u * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,13238,a,b,26787,a)].">
      <j1 rule="hyper" parents="373 13238 26787"/>
    </justification>
  </clause>

  <clause id="26820">
    <literal><![CDATA[
      a(x * ((y * y) \ z),u,w) = a(z * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11955,a,b,26787,a)].">
      <j1 rule="hyper" parents="373 11955 26787"/>
    </justification>
  </clause>

  <clause id="26821">
    <literal><![CDATA[
      a(((x \ 1) * y) * z,u,w) = a(z * (x * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2690,a,b,26787,a)].">
      <j1 rule="hyper" parents="373 2690 26787"/>
    </justification>
  </clause>

  <clause id="26822">
    <literal><![CDATA[
      a(((x * x) / y) * z,u,w) = a(z * y,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2688,a,b,26787,a)].">
      <j1 rule="hyper" parents="373 2688 26787"/>
    </justification>
  </clause>

  <clause id="26823">
    <literal><![CDATA[
      a((x \ 1) * y,z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2662,a,b,26787,a)].">
      <j1 rule="hyper" parents="373 2662 26787"/>
    </justification>
  </clause>

  <clause id="26824">
    <literal><![CDATA[
      a((x * (x * y)) * z,u,w) = a(z * L(y,x,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2657,a,b,26787,a)].">
      <j1 rule="hyper" parents="373 2657 26787"/>
    </justification>
  </clause>

  <clause id="26825">
    <literal><![CDATA[
      a(((x * x) * y) * z,u,w) = a(z * y,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2655,a,b,26787,a)].">
      <j1 rule="hyper" parents="373 2655 26787"/>
    </justification>
  </clause>

  <clause id="26826">
    <literal><![CDATA[
      a(x * R(y,z,y),u,w) = a(y * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,13108,a(flip),b,26787,a),flip(a)].">
      <j1 rule="hyper" parents="373 13108 26787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26827">
    <literal><![CDATA[
      a(x * (L(y * y,z,u) \ w),v5,v6) = a(w * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,4184,a(flip),b,26787,a),flip(a)].">
      <j1 rule="hyper" parents="373 4184 26787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26828">
    <literal><![CDATA[
      a(x * R((y \ 1) * z,u,w),v5,v6) = a(R(y * z,u,w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,2783,a(flip),b,26787,a),flip(a)].">
      <j1 rule="hyper" parents="373 2783 26787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26829">
    <literal><![CDATA[
      a(x * R(1 / y,z,u),w,v5) = a(R(y,z,u) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,2703,a(flip),b,26787,a),flip(a)].">
      <j1 rule="hyper" parents="373 2703 26787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26830">
    <literal><![CDATA[
      a(x * ((y \ 1) * z),u,w) = a((y * z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2690,a(flip),b,26787,a),flip(a)].">
      <j1 rule="hyper" parents="373 2690 26787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26831">
    <literal><![CDATA[
      a(x * (y \ 1),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2662,a(flip),b,26787,a),flip(a)].">
      <j1 rule="hyper" parents="373 2662 26787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26832">
    <literal><![CDATA[
      a(x * (y * (y * z)),u,w) = a(L(z,y,y) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2657,a(flip),b,26787,a),flip(a)].">
      <j1 rule="hyper" parents="373 2657 26787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26833">
    <literal><![CDATA[
      a((x \ y) * (y * x),z,u) = a(a(y,x,x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2649,a(flip),b,26787,a),flip(a)].">
      <j1 rule="hyper" parents="373 2649 26787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26834">
    <literal><![CDATA[
      a((x * y) * x,z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2640,a(flip),b,26787,a),flip(a)].">
      <j1 rule="hyper" parents="373 2640 26787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26835">
    <literal><![CDATA[
      a(x * y,z,u) \ w = a(y * x,z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(62,a,26787,a)].">
      <j1 rule="hyper" parents="62 26787"/>
    </justification>
  </clause>

  <clause id="26836">
    <literal><![CDATA[
      a((x \ y) * x,z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),26787(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 26787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26837">
    <literal><![CDATA[
      a(L(x,y,z) * (z * y),u,w) = a(z * (y * x),u,w)
    ]]></literal>
    <justification jstring="[para(100(a,1),26787(a,1,1)),flip(a)].">
      <j1 rule="para" parents="100 26787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26838">
    <literal><![CDATA[
      a((x * y) * L(y,z,u),w,v5) = a(y * (x * L(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(3184(a,1),26787(a,1,1))].">
      <j1 rule="para" parents="3184 26787"/>
    </justification>
  </clause>

  <clause id="26839">
    <literal><![CDATA[
      a(L(x,y,z) * (y * z),u,w) = a(z * (T(y,z) * x),u,w)
    ]]></literal>
    <justification jstring="[para(10989(a,1),26787(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10989 26787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26840">
    <literal><![CDATA[
      a((x * y) * K(z,z \ x),u,w) = a((z * (x / z)) * y,u,w)
    ]]></literal>
    <justification jstring="[para(24346(a,1),26787(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24346 26787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26841">
    <literal><![CDATA[
      a(x * y,y,x) \ x = L(x,y,y * x)
    ]]></literal>
    <justification jstring="[para(26787(a,1),25598(a,1,1))].">
      <j1 rule="para" parents="26787 25598"/>
    </justification>
  </clause>

  <clause id="26842">
    <literal><![CDATA[
      a(x \ (y * (x \ 1)),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2675,a(flip),b,26791,a)].">
      <j1 rule="hyper" parents="64 2675 26791"/>
    </justification>
  </clause>

  <clause id="26843">
    <literal><![CDATA[
      a(R(x * y,z,u),w,v5) = a(R(y * x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(2131(a,1),26836(a,1,1))].">
      <j1 rule="para" parents="2131 26836"/>
    </justification>
  </clause>

  <clause id="26844">
    <literal><![CDATA[
      a(L((x \ y) * x,z,u),w,v5) = a(L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(5544(a,2),26836(a,1,1))].">
      <j1 rule="para" parents="5544 26836"/>
    </justification>
  </clause>

  <clause id="26845">
    <literal><![CDATA[
      a(L(x * y,z,u),w,v5) = a(L(y * x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(5545(a,1),26836(a,1,1))].">
      <j1 rule="para" parents="5545 26836"/>
    </justification>
  </clause>

  <clause id="26846">
    <literal><![CDATA[
      a((x \ y) \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(116(a,1),26780(a,1,1))].">
      <j1 rule="para" parents="116 26780"/>
    </justification>
  </clause>

  <clause id="26847">
    <literal><![CDATA[
      a(x * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y * x,z,u) = w
    ]]></literal>
    <justification jstring="[para(13107(a,1),26780(a,1))].">
      <j1 rule="para" parents="13107 26780"/>
    </justification>
  </clause>

  <clause id="26848">
    <literal><![CDATA[
      a(x,(y * y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(26781(a,1),26780(a,1))].">
      <j1 rule="para" parents="26781 26780"/>
    </justification>
  </clause>

  <clause id="26849">
    <literal><![CDATA[
      a(x \ (1 / y),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26785,a(flip),b,26810,a),flip(a)].">
      <j1 rule="hyper" parents="373 26785 26810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26850">
    <literal><![CDATA[
      a(x * (y \ 1),z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26787,a,b,26823,a)].">
      <j1 rule="hyper" parents="64 26787 26823"/>
    </justification>
  </clause>

  <clause id="26851">
    <literal><![CDATA[
      a(x * y,y,x \ 1) * (y * (x \ 1)) = R(y * (x \ 1),y,x \ 1)
    ]]></literal>
    <justification jstring="[para(26831(a,1),16047(a,1,1))].">
      <j1 rule="para" parents="26831 16047"/>
    </justification>
  </clause>

  <clause id="26852">
    <literal><![CDATA[
      L(x * y,L(y \ 1,y,x),L(y \ 1,y,x) * (x * y)) = a(x,L(y \ 1,y,x),x * y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(442(a,1),26841(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="442 26841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26853">
    <literal><![CDATA[
      a(x \ (x \ L(x * y,z,u)),w,v5) = a(L(y / (x \ 1),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(1801(a,1),26842(a,1,1,2))].">
      <j1 rule="para" parents="1801 26842"/>
    </justification>
  </clause>

  <clause id="26854">
    <literal><![CDATA[
      a((x / (y * x)) \ y,z,u) = a((x / (y * x)) * y,z,u)
    ]]></literal>
    <justification jstring="[para(3281(a,1),26842(a,1,1,2))].">
      <j1 rule="para" parents="3281 26842"/>
    </justification>
  </clause>

  <clause id="26855">
    <literal><![CDATA[
      a(x \ (y \ 1),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),26849(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 26849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26856">
    <literal><![CDATA[
      a(R(x * (x * y),z,u) * x,w,v5) = a(L(x * R(y,z,u),x,x),w,v5)
    ]]></literal>
    <justification jstring="[para(2137(a,2),26834(a,1,1,1))].">
      <j1 rule="para" parents="2137 26834"/>
    </justification>
  </clause>

  <clause id="26857">
    <literal><![CDATA[
      a(L(x,y,y),y * x,y) \ y = L(y,y * x,L(x,y,y))
    ]]></literal>
    <justification jstring="[para(26834(a,1),25600(a,1,1))].">
      <j1 rule="para" parents="26834 25600"/>
    </justification>
  </clause>

  <clause id="26858">
    <literal><![CDATA[
      a(x * (y * y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(3177(a,2),26848(a,1))].">
      <j1 rule="para" parents="3177 26848"/>
    </justification>
  </clause>

  <clause id="26860">
    <literal><![CDATA[
      a(L(x,y,x * y),z,u) = a((x * y) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2669,a(flip),b,26792,a),flip(a)].">
      <j1 rule="hyper" parents="64 2669 26792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26861">
    <literal><![CDATA[
      a(x * (y * x),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2647,a(flip),b,26792,a)].">
      <j1 rule="hyper" parents="64 2647 26792"/>
    </justification>
  </clause>

  <clause id="26862">
    <literal><![CDATA[
      a(L(L(T(x,y),z,u),w,v5),v6,v7) = a(L(L(x,z,u),w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(25(a,2),26792(a,1,1,1))].">
      <j1 rule="para" parents="25 26792"/>
    </justification>
  </clause>

  <clause id="26863">
    <literal><![CDATA[
      a(L(L(x / y,z,u),w,v5),v6,v7) = a(L(L(y \ x,z,u),w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(279(a,1),26792(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="279 26792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26864">
    <literal><![CDATA[
      a(L(L((x \ y) \ y,z,u),w,v5),v6,v7) = a(L(L(x,z,u),w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(368(a,1),26792(a,1,1,1))].">
      <j1 rule="para" parents="368 26792"/>
    </justification>
  </clause>

  <clause id="26865">
    <literal><![CDATA[
      a(L(R(x * y,x,x),z,u),w,v5) = a(L(L(y,x,x) * x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(3884(a,1),26792(a,1,1,1))].">
      <j1 rule="para" parents="3884 26792"/>
    </justification>
  </clause>

  <clause id="26866">
    <literal><![CDATA[
      a(L(R(x,x,y * x),z,u),w,v5) = a(L(R(x,x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(26296(a,1),26792(a,1,1,1))].">
      <j1 rule="para" parents="26296 26792"/>
    </justification>
  </clause>

  <clause id="26867">
    <literal><![CDATA[
      a((x * y) * y,z,u) = a(L(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(26847,a,26861,a)].">
      <j1 rule="hyper" parents="26847 26861"/>
    </justification>
  </clause>

  <clause id="26869">
    <literal><![CDATA[
      a(L(R(x,x,y),y,y),z,u) = a(y * ((1 / x) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(1913(a,1),26861(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1913 26861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26870">
    <literal><![CDATA[
      a(L(R(x \ 1,x,y),y,y),z,u) = a(y * (x \ y),z,u)
    ]]></literal>
    <justification jstring="[para(2998(a,1),26861(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2998 26861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26871">
    <literal><![CDATA[
      a(R(x,y,y),z,u) = a(L(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11962,a(flip),b,26867,a)].">
      <j1 rule="hyper" parents="64 11962 26867"/>
    </justification>
  </clause>

  <clause id="26872">
    <literal><![CDATA[
      a(R(R(x,y,y),z,u),w,v5) = a(L(R(x,z,u),y,y),w,v5)
    ]]></literal>
    <justification jstring="[para(31(a,1),26871(a,1,1))].">
      <j1 rule="para" parents="31 26871"/>
    </justification>
  </clause>

  <clause id="26873">
    <literal><![CDATA[
      a(R(x,y,z),u,u) = R(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16742,a(flip),b,26793,a),flip(a)].">
      <j1 rule="hyper" parents="64 16742 26793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26875">
    <literal><![CDATA[
      a(x * (y \ (z * z)),u,w) = a(y * x,u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),26822(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 26822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26876">
    <literal><![CDATA[
      a((x * ((x \ y) * y)) * z,u,w) = a(z * a(x,x \ y,y),u,w)
    ]]></literal>
    <justification jstring="[para(954(a,1),26822(a,1,1,1))].">
      <j1 rule="para" parents="954 26822"/>
    </justification>
  </clause>

  <clause id="26877">
    <literal><![CDATA[
      a(x * R(x \ (y * y),z,u),w,v5) = a(x * R(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(2132(a,1),26875(a,1,1))].">
      <j1 rule="para" parents="2132 26875"/>
    </justification>
  </clause>

  <clause id="26878">
    <literal><![CDATA[
      a((x * (y \ 1)) * y,z,u) = a(L(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(26847,a,26797,a)].">
      <j1 rule="hyper" parents="26847 26797"/>
    </justification>
  </clause>

  <clause id="26879">
    <literal><![CDATA[
      a(x \ (y / z),x,z) \ y = ((y / z) / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(26807(a,1),387(a,1,1))].">
      <j1 rule="para" parents="26807 387"/>
    </justification>
  </clause>

  <clause id="26880">
    <literal><![CDATA[
      a(x / y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(114(a,1),26815(a,1))].">
      <j1 rule="para" parents="114 26815"/>
    </justification>
  </clause>

  <clause id="26881">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) = a(x,y,a(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(26818(a,1),13876(a,1,3))].">
      <j1 rule="para" parents="26818 13876"/>
    </justification>
  </clause>

  <clause id="26882">
    <literal><![CDATA[
      a(L(x,y,x * y),z,u) = a(L(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26867,a(flip),b,26860,a),flip(a)].">
      <j1 rule="hyper" parents="373 26867 26860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26884">
    <literal><![CDATA[
      a(L(x,x * y,L(y,x,x)),z,u) = a(L(x,x * y,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(2185(a,1),26882(a,1,1))].">
      <j1 rule="para" parents="2185 26882"/>
    </justification>
  </clause>

  <clause id="26885">
    <literal><![CDATA[
      a(L(L(x,y,y * x) \ 1,z,u),w,v5) = a(L((1 / (y * x)) * y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(920(a,1),26794(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="920 26794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26886">
    <literal><![CDATA[
      a(x * ((y \ 1) * z),u,w) = a(x * (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,26821,a)].">
      <j1 rule="hyper" parents="26847 26821"/>
    </justification>
  </clause>

  <clause id="26887">
    <literal><![CDATA[
      a(R((x \ 1) * y,z,u),w,v5) = a(R(y * x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,2696,a,b,26843,a)].">
      <j1 rule="hyper" parents="373 2696 26843"/>
    </justification>
  </clause>

  <clause id="26888">
    <literal><![CDATA[
      a(L((R(x,y,z) \ 1) * (x * x),u,w),v5,v6) = a(L(1 / R(1 / x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(11454(a,1),26845(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11454 26845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26889">
    <literal><![CDATA[
      a(R(x \ y,x,z),u,w) = a((x * z) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26785,a(flip),b,26795,a),flip(a)].">
      <j1 rule="hyper" parents="373 26785 26795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26890">
    <literal><![CDATA[
      ((L(x,y,z) / x) * u) \ ((u / x) * L(x,y,z)) = a(x \ L(x,y,z),x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23899,a(flip),b,26811,a)].">
      <j1 rule="hyper" parents="373 23899 26811"/>
    </justification>
  </clause>

  <clause id="26891">
    <literal><![CDATA[
      (a((x * (y / (y / z))) \ u,x,y / (y / z)) * u) / z = ((u / (x * (y / (y / z)))) * x) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[para(26812(a,2),6152(a,1,1))].">
      <j1 rule="para" parents="26812 6152"/>
    </justification>
  </clause>

  <clause id="26892">
    <literal><![CDATA[
      a(T(x,y) \ 1,x,y) * R(y,x,x \ 1) = ((R(y,x,x \ 1) / (x * y)) * x) * y
    ]]></literal>
    <justification jstring="[para(9341(a,1),26812(a,1,1,1))].">
      <j1 rule="para" parents="9341 26812"/>
    </justification>
  </clause>

  <clause id="26893">
    <literal><![CDATA[
      a(x \ y,x,x) / (y * x) = 1 / (y / (1 / x))
    ]]></literal>
    <justification jstring="[para(2671(a,1),26814(a,1,1))].">
      <j1 rule="para" parents="2671 26814"/>
    </justification>
  </clause>

  <clause id="26894">
    <literal><![CDATA[
      a(x \ y,y \ x,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(35,a,23877,a(flip),b,26816,a),flip(a)].">
      <j1 rule="hyper" parents="35 23877 26816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26895">
    <literal><![CDATA[
      a((x * y) \ ((x * z) * y),u,w) = a(R(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),26889(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 26889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26896">
    <literal><![CDATA[
      a(x \ ((y * y) * z),u,w) = a(z / x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2639,a(flip),b,26798,a),flip(a)].">
      <j1 rule="hyper" parents="373 2639 26798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26898">
    <literal><![CDATA[
      a(x \ ((y * y) * z),u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26785,a(flip),b,26896,a),flip(a)].">
      <j1 rule="hyper" parents="373 26785 26896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26899">
    <literal><![CDATA[
      a(x \ ((y * y) \ z),u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),26898(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 26898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26900">
    <literal><![CDATA[
      a(x \ (((y * y) * z) * u),w,v5) = a(x \ (z * u),w,v5)
    ]]></literal>
    <justification jstring="[para(33(a,2),26898(a,1,1,2))].">
      <j1 rule="para" parents="33 26898"/>
    </justification>
  </clause>

  <clause id="26901">
    <literal><![CDATA[
      a(x \ ((1 / y) * z),u,w) = a(x \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(310(a,1),26898(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="310 26898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26902">
    <literal><![CDATA[
      a(x \ (y * (y * z)),u,w) = a(x \ L(z,y,y),u,w)
    ]]></literal>
    <justification jstring="[para(100(a,1),26898(a,1,1,2))].">
      <j1 rule="para" parents="100 26898"/>
    </justification>
  </clause>

  <clause id="26903">
    <literal><![CDATA[
      a(x \ (((y * y) \ z) * u),w,v5) = a(x \ (z * u),w,v5)
    ]]></literal>
    <justification jstring="[para(126(a,1),26898(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="126 26898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26904">
    <literal><![CDATA[
      a(x \ ((1 / y) / z),u,w) = a(x \ (y / z),u,w)
    ]]></literal>
    <justification jstring="[para(883(a,1),26898(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="883 26898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26905">
    <literal><![CDATA[
      a(((1 / x) * y) \ z,u,w) = a((x * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(941(a,1),26898(a,1,1))].">
      <j1 rule="para" parents="941 26898"/>
    </justification>
  </clause>

  <clause id="26906">
    <literal><![CDATA[
      a((L(x * x,y,z) \ (u * u)) * w,v5,v6) = a(L(x * x,y,z) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(1822(a,1),26898(a,1,1))].">
      <j1 rule="para" parents="1822 26898"/>
    </justification>
  </clause>

  <clause id="26908">
    <literal><![CDATA[
      a((T(x,y * y) * z) \ u,w,v5) = a((x * ((y * y) * z)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(1463(a,1),26898(a,1,1))].">
      <j1 rule="para" parents="1463 26898"/>
    </justification>
  </clause>

  <clause id="26909">
    <literal><![CDATA[
      a(x \ ((T(y,z * z) * u) / w),v5,v6) = a(x \ ((y * ((z * z) * u)) / w),v5,v6)
    ]]></literal>
    <justification jstring="[para(1523(a,1),26898(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1523 26898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26910">
    <literal><![CDATA[
      a(x \ ((y * T(z,y \ 1)) / u),w,v5) = a(x \ ((z * (1 / y)) / u),w,v5)
    ]]></literal>
    <justification jstring="[para(3888(a,1),26898(a,1,1,2))].">
      <j1 rule="para" parents="3888 26898"/>
    </justification>
  </clause>

  <clause id="26911">
    <literal><![CDATA[
      a(x \ (y \ L(y,z,u)),w,v5) = a(x \ (y * L(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(5602(a,1),26898(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5602 26898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26912">
    <literal><![CDATA[
      a((x \ 1) \ ((y * y) \ z),u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2675,a(flip),b,26899,a),flip(a)].">
      <j1 rule="hyper" parents="373 2675 26899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26913">
    <literal><![CDATA[
      a(x \ (y * ((y \ 1) \ z)),u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(582(a,1),26899(a,1,1,2))].">
      <j1 rule="para" parents="582 26899"/>
    </justification>
  </clause>

  <clause id="26914">
    <literal><![CDATA[
      a((x * (x * y)) \ z,u,w) = a(L(y,x,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(881(a,1),26899(a,1,1))].">
      <j1 rule="para" parents="881 26899"/>
    </justification>
  </clause>

  <clause id="26915">
    <literal><![CDATA[
      a(R(x \ 1,y,z) \ u,w,v5) = a(R(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(2770(a,1),26899(a,1,1))].">
      <j1 rule="para" parents="2770 26899"/>
    </justification>
  </clause>

  <clause id="26916">
    <literal><![CDATA[
      a(x \ ((y \ 1) * z),u,w) = a(x \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),26901(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 26901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26917">
    <literal><![CDATA[
      a(((1 / (1 / x)) * y) \ z,u,w) = a((x * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26905,a(flip),b,26905,a),flip(a)].">
      <j1 rule="hyper" parents="373 26905 26905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26918">
    <literal><![CDATA[
      a(((x \ 1) * y) \ z,u,w) = a((x * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),26905(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 26905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26919">
    <literal><![CDATA[
      a(a(x \ y,x \ y,x),z,u) = a(((y / x) * y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(10628(a,2),26905(a,1,1))].">
      <j1 rule="para" parents="10628 26905"/>
    </justification>
  </clause>

  <clause id="26920">
    <literal><![CDATA[
      a(((x * x) * (y \ 1)) \ z,u,w) = a(y \ z,u,w)
    ]]></literal>
    <justification jstring="[para(487(a,2),26912(a,1,1))].">
      <j1 rule="para" parents="487 26912"/>
    </justification>
  </clause>

  <clause id="26921">
    <literal><![CDATA[
      a(x \ ((1 / y) \ z),u,w) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[para(1138(a,1),26913(a,1,1,2))].">
      <j1 rule="para" parents="1138 26913"/>
    </justification>
  </clause>

  <clause id="26922">
    <literal><![CDATA[
      a(x \ (y \ a(y,z,u)),w,v5) = a(x \ (y * a(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(16065(a,1),26913(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="16065 26913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26923">
    <literal><![CDATA[
      a(x \ (a(y,y,z) * z),u,w) = a(x \ L(z,y,y),u,w)
    ]]></literal>
    <justification jstring="[para(5669(a,1),26916(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5669 26916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26924">
    <literal><![CDATA[
      a(((x / (y * y)) \ 1) \ z,u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(890(a,2),26920(a,1,1,1))].">
      <j1 rule="para" parents="890 26920"/>
    </justification>
  </clause>

  <clause id="26925">
    <literal><![CDATA[
      a(x \ ((y \ 1) \ z),u,w) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),26921(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 26921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26926">
    <literal><![CDATA[
      a(x \ ((y \ 1) * R((y \ 1) * (y * z),u,w)),v5,v6) = a(x \ L(y * R(z,u,w),y \ 1,y \ 1),v5,v6)
    ]]></literal>
    <justification jstring="[para(2164(a,2),26902(a,1,1,2,2))].">
      <j1 rule="para" parents="2164 26902"/>
    </justification>
  </clause>

  <clause id="26927">
    <literal><![CDATA[
      a(x / ((x \ y) / y),z,u) = a((y / (x * y)) * x,z,u)
    ]]></literal>
    <justification jstring="[para(23871(a,2),26854(a,1,1))].">
      <j1 rule="para" parents="23871 26854"/>
    </justification>
  </clause>

  <clause id="26928">
    <literal><![CDATA[
      a(R(x \ a(x,y,y),z,u),w,v5) = a(L(R(x,z,u),y,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,16019,a,b,26872,a)].">
      <j1 rule="hyper" parents="64 16019 26872"/>
    </justification>
  </clause>

  <clause id="26929">
    <literal><![CDATA[
      a(x \ (((1 / y) / z) * u),w,v5) = a(x \ ((y / z) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(883(a,1),26900(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="883 26900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26930">
    <literal><![CDATA[
      a(x \ (((y * y) * L((z * z) \ 1,u,w)) * v5),v6,v7) = a(x \ (v5 * L(v5 \ ((z * z) \ v5),u,w)),v6,v7)
    ]]></literal>
    <justification jstring="[para(1188(a,2),26900(a,2,1,2))].">
      <j1 rule="para" parents="1188 26900"/>
    </justification>
  </clause>

  <clause id="26931">
    <literal><![CDATA[
      a(L(x * y,x,x) \ z,u,w) = a((x * L(y,x,x)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(1260(a,1),26917(a,1,1,1))].">
      <j1 rule="para" parents="1260 26917"/>
    </justification>
  </clause>

  <clause id="26932">
    <literal><![CDATA[
      a(x / ((x \ y) / y),z,u) = a(x * ((x \ y) / y),z,u)
    ]]></literal>
    <justification jstring="[para(3009(a,1),26927(a,2,1))].">
      <j1 rule="para" parents="3009 26927"/>
    </justification>
  </clause>

  <clause id="26933">
    <literal><![CDATA[
      (1 / (1 / x)) / ((x \ y) / y) = x / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(2027(a,1),24876(a,2,2))].">
      <j1 rule="para" parents="2027 24876"/>
    </justification>
  </clause>

  <clause id="26934">
    <literal><![CDATA[
      (a(x,y,z) / u) \ ((1 / u) * w) = (u \ a(x,y,z)) \ ((u \ 1) * w)
    ]]></literal>
    <justification jstring="[para(25206(a,1),24895(a,1,2,1))].">
      <j1 rule="para" parents="25206 24895"/>
    </justification>
  </clause>

  <clause id="26935">
    <literal><![CDATA[
      (K(x,x \ y) / (x / y)) * x = x * (1 / (x / y))
    ]]></literal>
    <justification jstring="[hyper(373,a,4582,a(flip),b,24906,a),flip(a)].">
      <j1 rule="hyper" parents="373 4582 24906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26936">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(x,u,w) = L(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,23742,a,b,24912,a)].">
      <j1 rule="hyper" parents="373 23742 24912"/>
    </justification>
  </clause>

  <clause id="26937">
    <literal><![CDATA[
      (x \ 1) \ (((x \ y) * x) * x) = (1 / x) \ T(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,14979,a(flip),b,24921,a),flip(a)].">
      <j1 rule="hyper" parents="64 14979 24921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26938">
    <literal><![CDATA[
      T(((1 / x) \ y) * x,x) = (1 / x) \ T(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2318,a(flip),b,26937,a)].">
      <j1 rule="hyper" parents="64 2318 26937"/>
    </justification>
  </clause>

  <clause id="26939">
    <literal><![CDATA[
      (1 / x) \ T((y * R(y \ (1 / x),z,z)) * x,x) = T(a((1 / x) \ y,z,z) * x,x)
    ]]></literal>
    <justification jstring="[para(15997(a,1),26938(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="15997 26938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26940">
    <literal><![CDATA[
      x * T(x \ (x / T(y,y \ 1)),z) = x / (T(y \ 1,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,6688,a(flip),b,24982,a)].">
      <j1 rule="hyper" parents="64 6688 24982"/>
    </justification>
  </clause>

  <clause id="26941">
    <literal><![CDATA[
      K(x,y * T(z,(z * u) * (w * v5))) = K(x,y * T(z,w * (u * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18123,a,b,25024,a)].">
      <j1 rule="hyper" parents="64 18123 25024"/>
    </justification>
  </clause>

  <clause id="26942">
    <literal><![CDATA[
      T(x,y) \ ((z * z) \ ((T(x,z \ (z \ y)) * u) * w)) = (z * z) \ (x \ ((x * u) * w))
    ]]></literal>
    <justification jstring="[para(24773(a,1),25026(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24773 25026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26943">
    <literal><![CDATA[
      x * (y * (K(x,z) * R(x,u,w))) = R(x,u,w) * (y * T(x,z))
    ]]></literal>
    <justification jstring="[para(23256(a,1),25052(a,1,2))].">
      <j1 rule="para" parents="23256 25052"/>
    </justification>
  </clause>

  <clause id="26944">
    <literal><![CDATA[
      L(L(x,x,x),y,z) \ a(u,w,v5) = a(u,w,v5) / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(818(a,2),25061(a,1,1,1))].">
      <j1 rule="para" parents="818 25061"/>
    </justification>
  </clause>

  <clause id="26945">
    <literal><![CDATA[
      L(x / y,z,u) \ (x / y) = L(y \ x,z,u) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(117(a,1),25070(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 25070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26946">
    <literal><![CDATA[
      (1 / x) * L(R(x,y,z),u,w) = x \ L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,1844,a(flip),b,25096,a),flip(a)].">
      <j1 rule="hyper" parents="64 1844 25096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26947">
    <literal><![CDATA[
      (1 / x) * R(R(x,y,z),u,w) = x \ R(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,1878,a(flip),b,25097,a),flip(a)].">
      <j1 rule="hyper" parents="64 1878 25097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26948">
    <literal><![CDATA[
      L(L(x,y,z),z * y,z) * L(y,z,z) = L(x * y,z,z)
    ]]></literal>
    <justification jstring="[para(2290(a,1),25141(a,1,1))].">
      <j1 rule="para" parents="2290 25141"/>
    </justification>
  </clause>

  <clause id="26949">
    <literal><![CDATA[
      K(x,y) * (z * (R(z,u,w) \ x)) = z * (R(z,u,w) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(25098(a,1),25168(a,1,2))].">
      <j1 rule="para" parents="25098 25168"/>
    </justification>
  </clause>

  <clause id="26950">
    <literal><![CDATA[
      x \ R(R(T(x,y),x,x),z,u) = x * R(K(x,y) / x,z,u)
    ]]></literal>
    <justification jstring="[para(8874(a,1),25202(a,1,2,1))].">
      <j1 rule="para" parents="8874 25202"/>
    </justification>
  </clause>

  <clause id="26951">
    <literal><![CDATA[
      K(x \ 1,x) * a(y,z,u) = (x \ a(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(40,a,24392,a,b,25208,a(flip))].">
      <j1 rule="hyper" parents="40 24392 25208"/>
    </justification>
  </clause>

  <clause id="26952">
    <literal><![CDATA[
      a(x,y,z) * K(u \ 1,u) = (u \ a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(40,a,23272,a,b,25208,a(flip))].">
      <j1 rule="hyper" parents="40 23272 25208"/>
    </justification>
  </clause>

  <clause id="26953">
    <literal><![CDATA[
      a(x,y,z) * (1 / (1 / u)) = ((u \ a(x,y,z)) * u) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,26952,a(flip),b,6152,a),flip(a)].">
      <j1 rule="hyper" parents="144 26952 6152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26954">
    <literal><![CDATA[
      ((x / y) \ a(z,u,w)) * (x / y) = a(z,u,w) * K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(4322(a,1),26952(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4322 26952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26955">
    <literal><![CDATA[
      K(x,T(y \ (z \ u),z * (y * w))) = K(x,T(u / (z * y),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,23394,a(flip),b,25301,a)].">
      <j1 rule="hyper" parents="64 23394 25301"/>
    </justification>
  </clause>

  <clause id="26956">
    <literal><![CDATA[
      x * (a(y,z,u) \ (a(y,z,u) \ 1)) = (a(y,z,u) * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,14004,a,b,25310,a)].">
      <j1 rule="hyper" parents="64 14004 25310"/>
    </justification>
  </clause>

  <clause id="26957">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (a(x,y,z) * a(x,y,z)) = (a(x,y,z) \ 1) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,14002,a(flip),b,25311,a),flip(a)].">
      <j1 rule="hyper" parents="64 14002 25311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26958">
    <literal><![CDATA[
      x * ((x * (a(y,z,u) * a(y,z,u))) \ w) = (a(y,z,u) * a(y,z,u)) \ w
    ]]></literal>
    <justification jstring="[para(25311(a,1),492(a,1,2,1))].">
      <j1 rule="para" parents="25311 492"/>
    </justification>
  </clause>

  <clause id="26959">
    <literal><![CDATA[
      K(x,T((y * z) \ u,y * (w * u))) = K(x,T((y \ u) / z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,21363,a(flip),b,25325,a)].">
      <j1 rule="hyper" parents="64 21363 25325"/>
    </justification>
  </clause>

  <clause id="26960">
    <literal><![CDATA[
      K(x,y) * (R(x,z,u) * (x \ w)) = x \ (R(T(x,y),z,u) * w)
    ]]></literal>
    <justification jstring="[para(1898(a,1),25345(a,1,2))].">
      <j1 rule="para" parents="1898 25345"/>
    </justification>
  </clause>

  <clause id="26961">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ L(a(x,y,z),a(x,y,z),(y * z) * R(x \ 1,y,z)) = L(a(x,y,z) \ 1,a(x,y,z),(y * z) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(25367(a,1),26678(a,1,2,3))].">
      <j1 rule="para" parents="25367 26678"/>
    </justification>
  </clause>

  <clause id="26962">
    <literal><![CDATA[
      K(x \ 1,y) * (L(x,z,u) \ x) = x * T(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(23589,a,25374,a)].">
      <j1 rule="hyper" parents="23589 25374"/>
    </justification>
  </clause>

  <clause id="26963">
    <literal><![CDATA[
      R(x,y,z * (K(u,w) * (v5 * R(u,v6,v7)))) = R(x,y,(v5 * R(T(u,w),v6,v7)) * z)
    ]]></literal>
    <justification jstring="[para(25378(a,1),26236(a,1,3,2))].">
      <j1 rule="para" parents="25378 26236"/>
    </justification>
  </clause>

  <clause id="26964">
    <literal><![CDATA[
      T(x,(y \ T(z,u)) * K(w,u)) = T(x,(y \ u) * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,24579,a(flip),b,25391,a),flip(a)].">
      <j1 rule="hyper" parents="64 24579 25391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26965">
    <literal><![CDATA[
      (L(x,y,z) \ K(x,x \ 1)) * R(x,u,w) = (L(x,y,z) \ 1) * R((x \ 1) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,5216,a(flip),b,25400,a),flip(a)].">
      <j1 rule="hyper" parents="64 5216 25400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26966">
    <literal><![CDATA[
      (x * L(T(y,z),u,w)) * (L(y,v5,v6) \ y) = (x * L(y,u,w)) * (L(y,v5,v6) \ T(y,z))
    ]]></literal>
    <justification jstring="[para(14828(a,1),25409(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14828 25409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26967">
    <literal><![CDATA[
      K(x,y) * ((z * T(z,u)) \ (K(y,x) * ((w * (z * T(z,u))) / w))) = K(w,z * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,6463,a(flip),b,25422,a),flip(a)].">
      <j1 rule="hyper" parents="64 6463 25422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26968">
    <literal><![CDATA[
      K(x / y,z / (x / y)) = K(x / y,x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5732,a(flip),b,25435,a),flip(a)].">
      <j1 rule="hyper" parents="64 5732 25435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26969">
    <literal><![CDATA[
      K(x / y,z / (x / y)) = K(y \ x,(y * z) / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,7938,a(flip),b,26968,a),flip(a)].">
      <j1 rule="hyper" parents="373 7938 26968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26970">
    <literal><![CDATA[
      K(x \ y,(x * z) / y) = K(x \ y,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,24223,a(flip),b,26969,a),flip(a)].">
      <j1 rule="hyper" parents="64 24223 26969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26971">
    <literal><![CDATA[
      K(x \ y,x / (y / z)) = K(x \ y,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,23039,a(flip),b,26970,a)].">
      <j1 rule="hyper" parents="64 23039 26970"/>
    </justification>
  </clause>

  <clause id="26972">
    <literal><![CDATA[
      x * K(y \ z,z \ (u * y)) = x * K(y \ z,y * (u / z))
    ]]></literal>
    <justification jstring="[para(26971(a,1),22650(a,1,2))].">
      <j1 rule="para" parents="26971 22650"/>
    </justification>
  </clause>

  <clause id="26974">
    <literal><![CDATA[
      K(x,y) * ((L(y,z,u) * x) \ (y * x)) = (L(y,z,u) * x) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,25028,a,b,25448,a)].">
      <j1 rule="hyper" parents="64 25028 25448"/>
    </justification>
  </clause>

  <clause id="26975">
    <literal><![CDATA[
      T(((x \ y) / z) \ u,(u * z) * (y \ x)) = ((x \ y) / z) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,24707,a(flip),b,25463,a)].">
      <j1 rule="hyper" parents="64 24707 25463"/>
    </justification>
  </clause>

  <clause id="26977">
    <literal><![CDATA[
      x / T(y * K(z,y),u * u) = (x / y) * K(y,u \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17636,a(flip),b,25509,a),flip(a)].">
      <j1 rule="hyper" parents="373 17636 25509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26978">
    <literal><![CDATA[
      (L(x,y,z) \ u) \ (w * (u / L(x,y,z))) = K(x,x \ u) * T(w,u / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,115,a(flip),b,25520,a)].">
      <j1 rule="hyper" parents="139 115 25520"/>
    </justification>
  </clause>

  <clause id="26979">
    <literal><![CDATA[
      K(x,x \ y) * (L(x,z,u) \ y) = y / L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,413,a(flip),b,25520,a),flip(a)].">
      <j1 rule="hyper" parents="35 413 25520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26980">
    <literal><![CDATA[
      (x / L(y,z,u)) * ((x / y) \ w) = (L(y,z,u) \ x) * ((y \ x) \ w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),25520(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 25520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26981">
    <literal><![CDATA[
      T(x,x \ y) * (L(x,z,u) \ y) = x * (y / L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,26979,a(flip),b,6071,a),flip(a)].">
      <j1 rule="hyper" parents="145 26979 6071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26982">
    <literal><![CDATA[
      (x / y) \ (x / L(y,z,u)) = (y \ x) \ (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,26979,a(flip),b,6062,a)].">
      <j1 rule="hyper" parents="139 26979 6062"/>
    </justification>
  </clause>

  <clause id="26983">
    <literal><![CDATA[
      K(R(x,x,x),R(x,x,x) \ ((x \ 1) \ y)) * ((x \ 1) \ (L(x,z,u) \ y)) = ((x \ 1) \ y) / L(R(x,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(3475(a,1),26979(a,1,2))].">
      <j1 rule="para" parents="3475 26979"/>
    </justification>
  </clause>

  <clause id="26984">
    <literal><![CDATA[
      K(x,y) * (L(x,z,u) \ ((1 / x) \ y)) = ((1 / x) \ y) / L(x,z,u)
    ]]></literal>
    <justification jstring="[para(14475(a,1),26979(a,1,1))].">
      <j1 rule="para" parents="14475 26979"/>
    </justification>
  </clause>

  <clause id="26985">
    <literal><![CDATA[
      (x / L(y,z,u)) \ (K(y,y \ x) * w) = (L(y,z,u) \ x) \ w
    ]]></literal>
    <justification jstring="[para(26979(a,1),23222(a,1,1))].">
      <j1 rule="para" parents="26979 23222"/>
    </justification>
  </clause>

  <clause id="26986">
    <literal><![CDATA[
      L(x,y,z) \ T(x,x \ 1) = x * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1849,a(flip),b,26981,a)].">
      <j1 rule="hyper" parents="64 1849 26981"/>
    </justification>
  </clause>

  <clause id="26987">
    <literal><![CDATA[
      T(x,K(y,z)) / T(u,K(y,z)) = T(x / u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8160,a(flip),b,25536,a),flip(a)].">
      <j1 rule="hyper" parents="373 8160 25536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26988">
    <literal><![CDATA[
      R(T(x,K(y,z)),u,w) / T(v5,K(y,z)) = T(R(x,u,w) / v5,K(y,z))
    ]]></literal>
    <justification jstring="[para(27(a,2),26987(a,1,1))].">
      <j1 rule="para" parents="27 26987"/>
    </justification>
  </clause>

  <clause id="26989">
    <literal><![CDATA[
      T(x,K(y,z)) / (y \ z) = T(x / (y \ z),K(y,z))
    ]]></literal>
    <justification jstring="[para(7133(a,1),26987(a,1,2))].">
      <j1 rule="para" parents="7133 26987"/>
    </justification>
  </clause>

  <clause id="26990">
    <literal><![CDATA[
      K(x,x \ y) * (z / (y / x)) = T(z,K(x,y)) / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8903,a,b,26989,a)].">
      <j1 rule="hyper" parents="373 8903 26989"/>
    </justification>
  </clause>

  <clause id="26991">
    <literal><![CDATA[
      K(x,x \ y) * (z / (y / x)) = T(z,K(y,x)) / (x \ y)
    ]]></literal>
    <justification jstring="[para(8153(a,1),26990(a,2,1))].">
      <j1 rule="para" parents="8153 26990"/>
    </justification>
  </clause>

  <clause id="26992">
    <literal><![CDATA[
      (x \ y) \ ((y / x) * (z / (y / x))) = T(z,K(y,x)) / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6442,a,b,26991,a)].">
      <j1 rule="hyper" parents="64 6442 26991"/>
    </justification>
  </clause>

  <clause id="26993">
    <literal><![CDATA[
      x \ (L(1 / x,y,x * y) \ 1) = a(y * (x \ 1),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,9392,a(flip),b,25599,a)].">
      <j1 rule="hyper" parents="64 9392 25599"/>
    </justification>
  </clause>

  <clause id="26994">
    <literal><![CDATA[
      R(T(x \ L(x,y,z),x * u),x,u) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(5572(a,1),25602(a,1,1,1))].">
      <j1 rule="para" parents="5572 25602"/>
    </justification>
  </clause>

  <clause id="26995">
    <literal><![CDATA[
      L(x * y,y \ (x * y),y) = a(y,x,x * y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(20986(a,1),25632(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20986 25632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26996">
    <literal><![CDATA[
      a(x,y,y * x) \ (y * x) = L(y * x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10995,a(flip),b,26995,a),flip(a)].">
      <j1 rule="hyper" parents="64 10995 26995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26997">
    <literal><![CDATA[
      (1 / (1 / x)) \ (L(y,z,u) \ y) = (L(y,z,u) \ y) / x
    ]]></literal>
    <justification jstring="[hyper(35,a,3649,a,b,25656,a(flip))].">
      <j1 rule="hyper" parents="35 3649 25656"/>
    </justification>
  </clause>

  <clause id="26998">
    <literal><![CDATA[
      (L(x,y,z) \ x) / (u \ 1) = (1 / u) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(79(a,1),26997(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 26997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="26999">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * ((x \ 1) \ u)) = ((1 / x) \ (L(x,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[para(26998(a,1),12290(a,2,1))].">
      <j1 rule="para" parents="26998 12290"/>
    </justification>
  </clause>

  <clause id="27000">
    <literal><![CDATA[
      x / ((y \ L(y,z,u)) * x) = x \ ((y \ L(y,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(5658(a,1),25669(a,1,2,1))].">
      <j1 rule="para" parents="5658 25669"/>
    </justification>
  </clause>

  <clause id="27001">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ u = u \ ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23592,a(flip),b,27000,a)].">
      <j1 rule="hyper" parents="64 23592 27000"/>
    </justification>
  </clause>

  <clause id="27002">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) \ x = x \ ((y \ L(y,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(23742(a,1),27001(a,1,1))].">
      <j1 rule="para" parents="23742 27001"/>
    </justification>
  </clause>

  <clause id="27003">
    <literal><![CDATA[
      x \ ((T(y,z) \ L(T(y,z),u,w)) \ x) = ((y \ L(y,u,w)) * x) \ x
    ]]></literal>
    <justification jstring="[para(24681(a,1),27001(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="24681 27001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27004">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ x = x * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,174,a(flip),b,27002,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 174 27002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27005">
    <literal><![CDATA[
      (x * ((1 / y) * L(y,z,u))) \ x = x \ ((y \ L(y,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(5590(a,2),27002(a,1,1,2))].">
      <j1 rule="para" parents="5590 27002"/>
    </justification>
  </clause>

  <clause id="27006">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ x = L(x,y,z) \ (x * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2329,a,b,27004,a),flip(a)].">
      <j1 rule="hyper" parents="373 2329 27004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27007">
    <literal><![CDATA[
      L(x,y,y) \ (x * x) = a(y,y,x) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,24653,a(flip),b,27006,a),flip(a)].">
      <j1 rule="hyper" parents="64 24653 27006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27008">
    <literal><![CDATA[
      L(x,y,z \ (((u * u) / w) * v5)) = L(x,y,z \ (w * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,25687,a(flip),b,25690,a),flip(a)].">
      <j1 rule="hyper" parents="373 25687 25690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27009">
    <literal><![CDATA[
      L(x,y,(((z \ 1) * u) * w) \ v5) = L(x,y,((z * u) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),25695(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 25695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27010">
    <literal><![CDATA[
      (x \ (L(a(y,z,u),w,v5) \ x)) * x = L(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(156,a,25715,a)].">
      <j1 rule="hyper" parents="156 25715"/>
    </justification>
  </clause>

  <clause id="27011">
    <literal><![CDATA[
      T((x \ L(x * y,z,u)) \ y,w) = ((x \ 1) * L((x \ 1) \ y,z,u)) \ y
    ]]></literal>
    <justification jstring="[para(1389(a,1),25716(a,1,1,1))].">
      <j1 rule="para" parents="1389 25716"/>
    </justification>
  </clause>

  <clause id="27012">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ K(x \ y,y \ x)) * z) = (y / x) * ((1 / (y / x)) * z)
    ]]></literal>
    <justification jstring="[para(4323(a,1),25723(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4323 25723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27013">
    <literal><![CDATA[
      (a(x,y,z) / u) * ((u \ 1) * w) = (u \ a(x,y,z)) * ((1 / u) * w)
    ]]></literal>
    <justification jstring="[para(25194(a,1),25724(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="25194 25724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27014">
    <literal><![CDATA[
      (1 / x) \ (((1 / x) * y) * z) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1600,a(flip),b,25725,a),flip(a)].">
      <j1 rule="hyper" parents="373 1600 25725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27015">
    <literal><![CDATA[
      (x \ 1) \ (((x \ 1) * (L(x,y,z) \ x)) * u) = (1 / x) \ ((1 / L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(7685(a,1),25725(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7685 25725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27016">
    <literal><![CDATA[
      (x \ y) * ((((x \ y) \ 1) * x) * z) = (1 / (y / x)) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1603,a(flip),b,25737,a)].">
      <j1 rule="hyper" parents="64 1603 25737"/>
    </justification>
  </clause>

  <clause id="27017">
    <literal><![CDATA[
      x * ((R(y,x,x) / (x \ 1)) \ z) = (x \ 1) * ((y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1694,a,b,25740,a)].">
      <j1 rule="hyper" parents="64 1694 25740"/>
    </justification>
  </clause>

  <clause id="27018">
    <literal><![CDATA[
      (x \ 1) * ((y * (x \ 1)) \ y) = x \ ((y * (1 / x)) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3793,a(flip),b,25742,a)].">
      <j1 rule="hyper" parents="64 3793 25742"/>
    </justification>
  </clause>

  <clause id="27019">
    <literal><![CDATA[
      ((x * y) \ 1) / T(y,(1 / (x * y)) * y) = y \ ((x * (1 / (1 / y))) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5141,a,b,25743,a)].">
      <j1 rule="hyper" parents="64 5141 25743"/>
    </justification>
  </clause>

  <clause id="27020">
    <literal><![CDATA[
      1 / (x \ (y / (x * y))) = (x \ (y / (x * y))) \ 1
    ]]></literal>
    <justification jstring="[para(25702(a,1),25772(a,1,2))].">
      <j1 rule="para" parents="25702 25772"/>
    </justification>
  </clause>

  <clause id="27021">
    <literal><![CDATA[
      (x \ (a(y,z,u) * L(R(x,w,v5),v6,v7))) * x = a(y,z,u) * L(R(x,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(38,a,25186,a,b,25777,a)].">
      <j1 rule="hyper" parents="38 25186 25777"/>
    </justification>
  </clause>

  <clause id="27022">
    <literal><![CDATA[
      K(x \ ((y / (y / z)) \ u),w) = K(K(z,y) * (x \ (z \ u)),w)
    ]]></literal>
    <justification jstring="[para(25779(a,2),18082(a,1,1))].">
      <j1 rule="para" parents="25779 18082"/>
    </justification>
  </clause>

  <clause id="27023">
    <literal><![CDATA[
      x * ((a(y,y,z) / z) \ u) = x * ((1 / L(z,y,y)) \ u)
    ]]></literal>
    <justification jstring="[para(25754(a,1),25780(a,1,2,1))].">
      <j1 rule="para" parents="25754 25780"/>
    </justification>
  </clause>

  <clause id="27024">
    <literal><![CDATA[
      (1 / x) * ((1 / L(x,y,y)) \ z) = x * ((a(y,y,x) / (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1693,a(flip),b,27023,a),flip(a)].">
      <j1 rule="hyper" parents="64 1693 27023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27025">
    <literal><![CDATA[
      x * ((R(x,y,z) / x) \ (x \ ((x * (R(x,y,z) / x)) * u))) = (x \ R(x,y,z)) \ (x * (x \ (R(x,y,z) * u)))
    ]]></literal>
    <justification jstring="[para(25796(a,2),2795(a,2,2)),flip(a)].">
      <j1 rule="para" parents="25796 2795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27026">
    <literal><![CDATA[
      (K(x,y) / y) * ((T(y,x) * z) * u) = y * (((y \ 1) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5953,a(flip),b,25798,a)].">
      <j1 rule="hyper" parents="64 5953 25798"/>
    </justification>
  </clause>

  <clause id="27027">
    <literal><![CDATA[
      T(x,(y * (z / (z / u))) * w) = T(x,(y * T(u,z)) * w)
    ]]></literal>
    <justification jstring="[para(24467(a,2),25807(a,1,2))].">
      <j1 rule="para" parents="24467 25807"/>
    </justification>
  </clause>

  <clause id="27028">
    <literal><![CDATA[
      T(x,(y * (z / (z / u))) * w) = T(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,25009,a(flip),b,27027,a),flip(a)].">
      <j1 rule="hyper" parents="373 25009 27027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27029">
    <literal><![CDATA[
      T(x / T(y,y * (x \ (x \ y))),y) = (x / y) * K(y / x,y)
    ]]></literal>
    <justification jstring="[para(15661(a,1),25812(a,1,1,2))].">
      <j1 rule="para" parents="15661 25812"/>
    </justification>
  </clause>

  <clause id="27030">
    <literal><![CDATA[
      R(T(x,x \ 1),y,z) \ x = R(1 / x,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2150(a,1),25823(a,1,1))].">
      <j1 rule="para" parents="2150 25823"/>
    </justification>
  </clause>

  <clause id="27031">
    <literal><![CDATA[
      R(1 / x,y,z) \ (x \ 1) = (R(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,15132,a(flip),b,27030,a),flip(a)].">
      <j1 rule="hyper" parents="64 15132 27030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27032">
    <literal><![CDATA[
      (x / (y * x)) \ (y \ 1) = (R(y,y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,449,a(flip),b,27031,a)].">
      <j1 rule="hyper" parents="64 449 27031"/>
    </justification>
  </clause>

  <clause id="27033">
    <literal><![CDATA[
      x / (((y / (z * y)) \ (z \ 1)) \ x) = (R(z,z,y) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(730,a,27032,a)].">
      <j1 rule="hyper" parents="730 27032"/>
    </justification>
  </clause>

  <clause id="27034">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(x,u \ (u \ w)) = T(x,u * u) \ L(T(x,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23442,a(flip),b,25839,a),flip(a)].">
      <j1 rule="hyper" parents="64 23442 25839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27035">
    <literal><![CDATA[
      (T(x,y) / z) * (z * (K(y,x) * u)) = (x / z) * (z * u)
    ]]></literal>
    <justification jstring="[para(15038(a,1),25843(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15038 25843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27036">
    <literal><![CDATA[
      (T(x,y) / z) * (z * (T(x,y) \ u)) = (x / z) * (z * (x \ u))
    ]]></literal>
    <justification jstring="[para(6157(a,1),27035(a,1,2,2))].">
      <j1 rule="para" parents="6157 27035"/>
    </justification>
  </clause>

  <clause id="27037">
    <literal><![CDATA[
      (x \ y) \ a(z,z,x \ y) = L(x \ y,z,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,25816,a(flip),b,25869,a),flip(a)].">
      <j1 rule="hyper" parents="64 25816 25869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27038">
    <literal><![CDATA[
      ((x * y) \ x) \ ((1 / y) * 1) = (x \ (x / (1 / y))) \ y
    ]]></literal>
    <justification jstring="[hyper(341,a,25878,a),flip(a)].">
      <j1 rule="hyper" parents="341 25878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27039">
    <literal><![CDATA[
      (x \ (x / (1 / y))) \ y = ((x * y) \ x) \ (1 / y)
    ]]></literal>
    <justification jstring="[hyper(341,a,27038,a),flip(a)].">
      <j1 rule="hyper" parents="341 27038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27040">
    <literal><![CDATA[
      x / (x / ((y / (z * y)) \ (z \ 1))) = (R(z,z,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(25929(a,2),27033(a,1,2))].">
      <j1 rule="para" parents="25929 27033"/>
    </justification>
  </clause>

  <clause id="27041">
    <literal><![CDATA[
      x / ((y * (z / (y * z))) * x) = x \ ((y * (z / (y * z))) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,23876,a(flip),b,25930,a)].">
      <j1 rule="hyper" parents="64 23876 25930"/>
    </justification>
  </clause>

  <clause id="27042">
    <literal><![CDATA[
      (R(T(x,y),z,u) \ x) \ 1 = K(x,y) * (x \ R(x,z,u))
    ]]></literal>
    <justification jstring="[para(24813(a,1),25941(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24813 25941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27043">
    <literal><![CDATA[
      (R(T(x,y),z,u) \ x) \ 1 = x \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23663,a(flip),b,27042,a),flip(a)].">
      <j1 rule="hyper" parents="373 23663 27042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27044">
    <literal><![CDATA[
      ((R(x,y,z) \ 1) * x) \ 1 = x \ R(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(15132(a,1),27043(a,1,1))].">
      <j1 rule="para" parents="15132 27043"/>
    </justification>
  </clause>

  <clause id="27045">
    <literal><![CDATA[
      ((R(x,y,z) \ 1) * x) \ 1 = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2160,a(flip),b,27044,a),flip(a)].">
      <j1 rule="hyper" parents="373 2160 27044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27046">
    <literal><![CDATA[
      (x * R(1 / x,y,z)) \ 1 = (R(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(27045(a,1),23710(a,1,1))].">
      <j1 rule="para" parents="27045 23710"/>
    </justification>
  </clause>

  <clause id="27047">
    <literal><![CDATA[
      (x / y) * R((x / y) \ z,u,w) = (y \ x) * R((y \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),25966(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6270 25966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27048">
    <literal><![CDATA[
      (x \ y) \ R((x \ y) * x,z,u) = (y / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(5947(a,1),25971(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5947 25971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27049">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ x,z,u) = (y / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2124,a(flip),b,27048,a)].">
      <j1 rule="hyper" parents="64 2124 27048"/>
    </justification>
  </clause>

  <clause id="27050">
    <literal><![CDATA[
      R(x,y,z) / (u \ x) = (x / u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2114,a(flip),b,27049,a)].">
      <j1 rule="hyper" parents="64 2114 27049"/>
    </justification>
  </clause>

  <clause id="27051">
    <literal><![CDATA[
      x * R(x \ (y * y),z,u) = y * ((x / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,27049,a(flip),b,1956,a),flip(a)].">
      <j1 rule="hyper" parents="145 27049 1956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27052">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ (1 / x),z,u) = (x * x) \ ((y / x) \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(27050(a,1),3088(a,2,2))].">
      <j1 rule="para" parents="27050 3088"/>
    </justification>
  </clause>

  <clause id="27053">
    <literal><![CDATA[
      x * ((y / x) \ R(y,z,z)) = (x * x) * a(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16028,a(flip),b,27051,a),flip(a)].">
      <j1 rule="hyper" parents="64 16028 27051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27054">
    <literal><![CDATA[
      (x / y) \ R(x,y,y) = a(x,y,y) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,23950,a(flip),b,27053,a),flip(a)].">
      <j1 rule="hyper" parents="35 23950 27053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27055">
    <literal><![CDATA[
      (x / y) * (a(x,y,y) * y) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(157,a,27054,a)].">
      <j1 rule="hyper" parents="157 27054"/>
    </justification>
  </clause>

  <clause id="27056">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) * (a(x \ 1,y \ x,y \ x) * (y \ x)) = R(x \ 1,y \ x,y \ x)
    ]]></literal>
    <justification jstring="[para(1218(a,1),27055(a,1,1))].">
      <j1 rule="para" parents="1218 27055"/>
    </justification>
  </clause>

  <clause id="27057">
    <literal><![CDATA[
      (K(x \ y,x) * z) * (a((x \ y) * x,z \ y,z \ y) * (z \ y)) = R((x \ y) * x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[para(14886(a,1),27055(a,1,1))].">
      <j1 rule="para" parents="14886 27055"/>
    </justification>
  </clause>

  <clause id="27058">
    <literal><![CDATA[
      R(x \ R(x,y,z),u / (u / x),(u / (u / x)) \ w) * w = R(x * K(x \ u,x),y,z) * ((u / (u / x)) \ w)
    ]]></literal>
    <justification jstring="[para(25978(a,1),421(a,2,1))].">
      <j1 rule="para" parents="25978 421"/>
    </justification>
  </clause>

  <clause id="27059">
    <literal><![CDATA[
      T(x,y) * R(x \ y,z,u) = R(x * y,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,2115,a(flip),b,25996,a),flip(a)].">
      <j1 rule="hyper" parents="373 2115 25996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27060">
    <literal><![CDATA[
      ((x \ y) \ y) * (R(x \ y,z,u) * w) = x * (R(y / x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(26000(a,1),6070(a,2,2))].">
      <j1 rule="para" parents="26000 6070"/>
    </justification>
  </clause>

  <clause id="27061">
    <literal><![CDATA[
      R(x / y,z,u) * ((x / y) \ w) = R(y \ x,z,u) * ((y \ x) \ w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),26002(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 26002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27062">
    <literal><![CDATA[
      K(x,x \ y) * (x \ R(y,z,u)) = R(y,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,2127,a(flip),b,26004,a),flip(a)].">
      <j1 rule="hyper" parents="373 2127 26004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27063">
    <literal><![CDATA[
      K(x,x \ R(y,z,u)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(36,a,5720,a,b,27062,a)].">
      <j1 rule="hyper" parents="36 5720 27062"/>
    </justification>
  </clause>

  <clause id="27064">
    <literal><![CDATA[
      (x / y) \ (R(x,z,u) / y) = (y \ x) \ (y \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,27062,a(flip),b,6062,a)].">
      <j1 rule="hyper" parents="139 27062 6062"/>
    </justification>
  </clause>

  <clause id="27065">
    <literal><![CDATA[
      T(x,x \ R(y,z,u)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(143,a,27063,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 27063 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27066">
    <literal><![CDATA[
      T(x,x \ y) = (x \ R(y,z,u)) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(478,a,27065,a),flip(a)].">
      <j1 rule="hyper" parents="478 27065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27067">
    <literal><![CDATA[
      R(x,y,z) / T(u,u \ x) = u \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,27065,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 27065 116"/>
    </justification>
  </clause>

  <clause id="27068">
    <literal><![CDATA[
      (x \ R(y,z,u)) \ R(y,z,u) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(478,a,27066,a),flip(a)].">
      <j1 rule="hyper" parents="478 27066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27069">
    <literal><![CDATA[
      (R(x,y,z) / u) / (x / u) = (u \ R(x,y,z)) / (u \ x)
    ]]></literal>
    <justification jstring="[para(27067(a,1),6866(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27067 6866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27071">
    <literal><![CDATA[
      (R(x,y,z) / u) / (x / u) = (u \ x) \ (u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,23714,a(flip),b,27069,a),flip(a)].">
      <j1 rule="hyper" parents="373 23714 27069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27072">
    <literal><![CDATA[
      R(x,y,z) * T(x \ 1,u) = x * R(T(x \ 1,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,25897,a(flip),b,26033,a),flip(a)].">
      <j1 rule="hyper" parents="64 25897 26033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27073">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ R(x,z,u)) = x * R(T(x \ 1,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,6689,a,b,27072,a)].">
      <j1 rule="hyper" parents="64 6689 27072"/>
    </justification>
  </clause>

  <clause id="27074">
    <literal><![CDATA[
      R(T(x,y),x,y) \ (x * z) = (y / (y * x)) \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1923,a,b,26036,a)].">
      <j1 rule="hyper" parents="64 1923 26036"/>
    </justification>
  </clause>

  <clause id="27075">
    <literal><![CDATA[
      L((x / (x * y)) \ ((1 / y) * z),u,w * w) = R(T(y,x),y,x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,594,a,b,27074,a)].">
      <j1 rule="hyper" parents="373 594 27074"/>
    </justification>
  </clause>

  <clause id="27076">
    <literal><![CDATA[
      ((x \ y) * x) \ L(((x \ y) * x) * z,u,w) = y \ L(y * z,u,w)
    ]]></literal>
    <justification jstring="[para(10858(a,1),26095(a,1,2,1))].">
      <j1 rule="para" parents="10858 26095"/>
    </justification>
  </clause>

  <clause id="27077">
    <literal><![CDATA[
      (x / y) \ L(x / y,z,u) = (y \ x) \ L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(5720(a,1),26096(a,1,2,1))].">
      <j1 rule="para" parents="5720 26096"/>
    </justification>
  </clause>

  <clause id="27078">
    <literal><![CDATA[
      x * ((x \ K(y,z)) * L(u,w,v5)) = L(L(K(y,z) * u,x,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(145,a,26106,a(flip),b,1149,a)].">
      <j1 rule="hyper" parents="145 26106 1149"/>
    </justification>
  </clause>

  <clause id="27079">
    <literal><![CDATA[
      K(x,y) * T(L(z \ 1,u,w),z) = L(T(z \ K(x,y),z),u,w)
    ]]></literal>
    <justification jstring="[para(25(a,1),26107(a,1,2))].">
      <j1 rule="para" parents="25 26107"/>
    </justification>
  </clause>

  <clause id="27080">
    <literal><![CDATA[
      (x \ K(y,z)) \ L(x \ K(y,z),u,w) = x * L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27077,a(flip),b,26108,a)].">
      <j1 rule="hyper" parents="64 27077 26108"/>
    </justification>
  </clause>

  <clause id="27081">
    <literal><![CDATA[
      L(x \ y,z,u) * (((x \ y) \ y) * w) = L(y / x,z,u) * (x * w)
    ]]></literal>
    <justification jstring="[para(6025(a,1),26117(a,1,2))].">
      <j1 rule="para" parents="6025 26117"/>
    </justification>
  </clause>

  <clause id="27082">
    <literal><![CDATA[
      L(x / y,z,u) * ((x / y) \ w) = L(y \ x,z,u) * ((y \ x) \ w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),26117(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 26117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27083">
    <literal><![CDATA[
      (L(1 / x,y,z) \ u) * K(x,x \ 1) = L(x \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(3668,a,26119,a)].">
      <j1 rule="hyper" parents="3668 26119"/>
    </justification>
  </clause>

  <clause id="27084">
    <literal><![CDATA[
      T(x,x \ y) \ (L(x \ y,z,u) \ w) = x \ (L(y / x,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(139,a,26119,a(flip),b,5810,a),flip(a)].">
      <j1 rule="hyper" parents="139 26119 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27085">
    <literal><![CDATA[
      a(x * y,z,x * y) \ (y * x) = L(y * x,z,x * y)
    ]]></literal>
    <justification jstring="[para(115(a,1),26120(a,2,1))].">
      <j1 rule="para" parents="115 26120"/>
    </justification>
  </clause>

  <clause id="27086">
    <literal><![CDATA[
      x * (a(y * x,z,y * x) \ y) = L(x * y,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(13255,a,27085,a)].">
      <j1 rule="hyper" parents="13255 27085"/>
    </justification>
  </clause>

  <clause id="27087">
    <literal><![CDATA[
      (x * y) * L(L(L(T(y,x),z,u),w,v5),x,y) = y * (x * L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(26124(a,1),10989(a,2,2))].">
      <j1 rule="para" parents="26124 10989"/>
    </justification>
  </clause>

  <clause id="27088">
    <literal><![CDATA[
      L((x \ y) * x,z,u) * L(K(x \ y,x) \ (L(y,z,u) \ 1),w,w) = a(w,w,(L(y,z,u) * K(x \ y,x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,5682,a(flip),b,26133,a),flip(a)].">
      <j1 rule="hyper" parents="64 5682 26133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27089">
    <literal><![CDATA[
      L(x * K(y,z),u,w) \ (x * K(y,z)) = L(x,u,w) \ x
    ]]></literal>
    <justification jstring="[para(8258(a,1),26141(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8258 26141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27090">
    <literal><![CDATA[
      (x * K(y,z)) \ L(x * K(y,z),u,w) = (L(x,u,w) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(27089(a,1),5658(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27089 5658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27091">
    <literal><![CDATA[
      R(x,y,((1 / z) * u) * (w * w)) = R(x,y,(z \ (w * w)) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26180,a(flip),b,26200,a),flip(a)].">
      <j1 rule="hyper" parents="373 26180 26200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27092">
    <literal><![CDATA[
      R(x,y,((z \ u) * (1 / z)) \ w) = R(x,y,u \ ((z * z) * w))
    ]]></literal>
    <justification jstring="[para(804(a,1),26292(a,2,3))].">
      <j1 rule="para" parents="804 26292"/>
    </justification>
  </clause>

  <clause id="27093">
    <literal><![CDATA[
      R(x,y,z * ((T(u,w) / v5) * v6)) = R(x,y,z * (v6 * (v5 \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,26342,a,b,26336,a)].">
      <j1 rule="hyper" parents="64 26342 26336"/>
    </justification>
  </clause>

  <clause id="27094">
    <literal><![CDATA[
      R(x,y,(z * u) * ((z * z) \ w)) = R(x,y,((z \ 1) * u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26220,a(flip),b,26337,a),flip(a)].">
      <j1 rule="hyper" parents="373 26220 26337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27095">
    <literal><![CDATA[
      R(x,y,(L(T(z,z \ 1),z,u) \ w) * ((z \ 1) * (z * (u \ (u / z))))) = R(x,y,(z * z) \ w)
    ]]></literal>
    <justification jstring="[para(26396(a,1),26354(a,1,3,1,1))].">
      <j1 rule="para" parents="26396 26354"/>
    </justification>
  </clause>

  <clause id="27096">
    <literal><![CDATA[
      R(x,y,(z * z) * (u \ (w / z))) = R(x,y,u \ ((1 / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,26183,a(flip),b,26357,a),flip(a)].">
      <j1 rule="hyper" parents="373 26183 26357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27097">
    <literal><![CDATA[
      R(x,y,L(T(z,u),T(w,v5),T(w,v5) \ v6)) = R(x,y,R(z,w,w \ v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,23812,a(flip),b,26363,a),flip(a)].">
      <j1 rule="hyper" parents="373 23812 26363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27098">
    <literal><![CDATA[
      a(x,y,z) / (a(x,y,z) * u) = a(x,y,z) \ (a(x,y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(23179,a,26372,a),flip(a)].">
      <j1 rule="hyper" parents="23179 26372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27099">
    <literal><![CDATA[
      (a(x,y,z) / (a(x,y,z) \ u)) / a(x,y,z) = a(x,y,z) / u
    ]]></literal>
    <justification jstring="[para(10(a,1),26372(a,2,2))].">
      <j1 rule="para" parents="10 26372"/>
    </justification>
  </clause>

  <clause id="27100">
    <literal><![CDATA[
      R(x,L(K(y * z,u) * z,y,u) * w,v5) = R(x,((u * y) \ ((y * z) * u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(14648(a,1),26441(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14648 26441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27101">
    <literal><![CDATA[
      x \ ((x * ((y * x) \ y)) / x) = ((y * x) \ y) / x
    ]]></literal>
    <justification jstring="[para(9(a,1),26515(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 26515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27103">
    <literal><![CDATA[
      x \ L(1 / x,x,y) = ((y * x) \ y) / x
    ]]></literal>
    <justification jstring="[para(1190(a,1),27101(a,1,2))].">
      <j1 rule="para" parents="1190 27101"/>
    </justification>
  </clause>

  <clause id="27104">
    <literal><![CDATA[
      R(x,y,y * z) * L(z,y,y) = (x * (1 / y)) * (y * z)
    ]]></literal>
    <justification jstring="[para(2975(a,1),26626(a,1,1))].">
      <j1 rule="para" parents="2975 26626"/>
    </justification>
  </clause>

  <clause id="27105">
    <literal><![CDATA[
      R(x,y,z * y) * L(z,y,y) = (x * (1 / y)) * (y * z)
    ]]></literal>
    <justification jstring="[para(26164(a,1),27104(a,1,1))].">
      <j1 rule="para" parents="26164 27104"/>
    </justification>
  </clause>

  <clause id="27106">
    <literal><![CDATA[
      R(1 / (1 / (x / y)),1 / (y / x),z * (1 / (y / x))) * L(z,1 / (y / x),1 / (y / x)) = ((x / y) * (y / x)) * ((1 / (y / x)) * z)
    ]]></literal>
    <justification jstring="[para(4344(a,1),27105(a,2,1))].">
      <j1 rule="para" parents="4344 27105"/>
    </justification>
  </clause>

  <clause id="27107">
    <literal><![CDATA[
      (x \ y) \ T(y / x,K(z,u)) = K(K(z,u) * x,y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,17853,a(flip),b,26738,a)].">
      <j1 rule="hyper" parents="64 17853 26738"/>
    </justification>
  </clause>

  <clause id="27108">
    <literal><![CDATA[
      (x \ y) \ T(y / x,K(z,u)) = K(K(z,u) * x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,17360,a(flip),b,27107,a),flip(a)].">
      <j1 rule="hyper" parents="373 17360 27107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27110">
    <literal><![CDATA[
      L(a(x,y,z) \ (u \ ((u * w) * a(x,y,z))),a(x,y,z),u) = L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1080,a,26739,a)].">
      <j1 rule="hyper" parents="1080 26739"/>
    </justification>
  </clause>

  <clause id="27111">
    <literal><![CDATA[
      L(x,y,z) * (x * ((x \ 1) \ u)) = (x * x) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(1175(a,1),26743(a,1,2))].">
      <j1 rule="para" parents="1175 26743"/>
    </justification>
  </clause>

  <clause id="27112">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ u) = x \ (R(1 / x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(2118(a,1),26745(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2118 26745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27113">
    <literal><![CDATA[
      x * ((x \ 1) \ (R(x,y,z) \ u)) = R(1 / x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(145,a,27112,a,b,xx)].">
      <j1 rule="hyper" parents="145 27112"/>
    </justification>
  </clause>

  <clause id="27114">
    <literal><![CDATA[
      (R(1 / x,y,z) \ u) \ x = (R(x,y,z) \ u) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(27113(a,1),1229(a,1,1))].">
      <j1 rule="para" parents="27113 1229"/>
    </justification>
  </clause>

  <clause id="27115">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) * w = L(y \ L(y,x,x),z,u) * w
    ]]></literal>
    <justification jstring="[hyper(373,a,23901,a,b,26747,a),flip(a)].">
      <j1 rule="hyper" parents="373 23901 26747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27116">
    <literal><![CDATA[
      R(x,L(x,y,z),L(x,y,z) \ L(x,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,29,a(flip),b,26750,a(flip))].">
      <j1 rule="hyper" parents="42 29 26750"/>
    </justification>
  </clause>

  <clause id="27118">
    <literal><![CDATA[
      a(L(x,y,z),L(x,u,w),L(x,u,w) \ L(x,y,z)) = L(x,y,z) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(27116(a,1),2098(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="27116 2098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27119">
    <literal><![CDATA[
      (x / y) * K(x * y,y \ 1) = ((1 / y) \ x) / (y * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3771,a(flip),b,26752,a),flip(a)].">
      <j1 rule="hyper" parents="64 3771 26752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27121">
    <literal><![CDATA[
      L(x \ 1,x,a(y,z,u)) = a(y,z,u) \ (x \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(472,a,26769,a)].">
      <j1 rule="hyper" parents="472 26769"/>
    </justification>
  </clause>

  <clause id="27122">
    <literal><![CDATA[
      a(x,y,z) * L(u,u,a(x,y,z)) = (1 / u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,11792,a,b,26769,a(flip))].">
      <j1 rule="hyper" parents="145 11792 26769"/>
    </justification>
  </clause>

  <clause id="27123">
    <literal><![CDATA[
      L(x \ 1,x,a(y,z,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,23925,a(flip),b,27121,a),flip(a)].">
      <j1 rule="hyper" parents="373 23925 27121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27124">
    <literal><![CDATA[
      L(x \ 1,x,a(y,z,u)) * a(y,z,u) = x \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,27121,a,b,23133,a)].">
      <j1 rule="hyper" parents="144 27121 23133"/>
    </justification>
  </clause>

  <clause id="27125">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,(y * x) * (x \ y)) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,2193,a,b,27123,a)].">
      <j1 rule="hyper" parents="64 2193 27123"/>
    </justification>
  </clause>

  <clause id="27126">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) * a(y,z,u) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(23177,a,27122,a)].">
      <j1 rule="hyper" parents="23177 27122"/>
    </justification>
  </clause>

  <clause id="27127">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w),v5,v6)) = L(x,y,L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,24836,a(flip),b,26770,a)].">
      <j1 rule="hyper" parents="64 24836 26770"/>
    </justification>
  </clause>

  <clause id="27128">
    <literal><![CDATA[
      a(L(L(T(x,y),z,u),w,v5),v6,v7) = a(L(L(x,w,v5),z,u),v6,v7)
    ]]></literal>
    <justification jstring="[para(30(a,1),26862(a,1,1))].">
      <j1 rule="para" parents="30 26862"/>
    </justification>
  </clause>

  <clause id="27129">
    <literal><![CDATA[
      x * T(T(x \ (x / y),y),z) = x / (T(y \ 1,z) \ 1)
    ]]></literal>
    <justification jstring="[para(3927(a,1),26940(a,1,2,1))].">
      <j1 rule="para" parents="3927 26940"/>
    </justification>
  </clause>

  <clause id="27130">
    <literal><![CDATA[
      a(x,y,z) / (a(x,y,z) * T(T(a(x,y,z) \ (a(x,y,z) / u),u),w)) = 1 / (1 / (T(u \ 1,w) \ 1))
    ]]></literal>
    <justification jstring="[hyper(225,a,27129,a,b,24638,a)].">
      <j1 rule="hyper" parents="225 27129 24638"/>
    </justification>
  </clause>

  <clause id="27131">
    <literal><![CDATA[
      R(x,y,z) * (u * T(x,w)) = x * (u * R(T(x,w),y,z))
    ]]></literal>
    <justification jstring="[para(23659(a,1),26943(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23659 26943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27132">
    <literal><![CDATA[
      K(x,T(y \ T(z,u),u * (y * w))) = K(x,T((z * u) / (u * y),w))
    ]]></literal>
    <justification jstring="[para(22(a,2),26955(a,1,2,1,2))].">
      <j1 rule="para" parents="22 26955"/>
    </justification>
  </clause>

  <clause id="27133">
    <literal><![CDATA[
      K(x,T(y / (z * u),z * w)) = K(x,T((z \ y) / u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,25300,a(flip),b,26959,a)].">
      <j1 rule="hyper" parents="64 25300 26959"/>
    </justification>
  </clause>

  <clause id="27134">
    <literal><![CDATA[
      K(x,T((y \ z) / u,w)) = K(x,T(y \ (z / u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,25332,a(flip),b,27133,a),flip(a)].">
      <j1 rule="hyper" parents="64 25332 27133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27135">
    <literal><![CDATA[
      K(x,T((y \ z) \ (u / w),z * (y * u))) = K(x,w \ ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,21365,a(flip),b,27134,a),flip(a)].">
      <j1 rule="hyper" parents="64 21365 27134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27136">
    <literal><![CDATA[
      x \ (R(T(x,y),z,u) * w) = R(T(x,y),z,u) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,23661,a(flip),b,26960,a),flip(a)].">
      <j1 rule="hyper" parents="64 23661 26960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27137">
    <literal><![CDATA[
      x \ R(T(x,y) * (z * z),u,w) = R(T(x,y),u,w) * (x \ (z * z))
    ]]></literal>
    <justification jstring="[para(2102(a,2),27136(a,1,2))].">
      <j1 rule="para" parents="2102 27136"/>
    </justification>
  </clause>

  <clause id="27138">
    <literal><![CDATA[
      x * K(y \ z,y * (x / z)) = (z / y) * (x / (z / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,22814,a(flip),b,26972,a),flip(a)].">
      <j1 rule="hyper" parents="64 22814 26972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27139">
    <literal><![CDATA[
      (x * T(x \ y,(y / x) \ z)) / y = K(x \ y,x * (z / y))
    ]]></literal>
    <justification jstring="[hyper(35,a,22816,a,b,26972,a(flip))].">
      <j1 rule="hyper" parents="35 22816 26972"/>
    </justification>
  </clause>

  <clause id="27140">
    <literal><![CDATA[
      T(((x \ y) / y) \ z,z * x) = ((x \ y) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,24998,a(flip),b,26975,a)].">
      <j1 rule="hyper" parents="64 24998 26975"/>
    </justification>
  </clause>

  <clause id="27141">
    <literal><![CDATA[
      T(x / ((x \ y) / y),x) = ((x \ y) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,23678,a(flip),b,27140,a)].">
      <j1 rule="hyper" parents="64 23678 27140"/>
    </justification>
  </clause>

  <clause id="27142">
    <literal><![CDATA[
      T(((x \ y) / y) \ x,x * (x * z)) = T(((x \ y) / y) \ x,z)
    ]]></literal>
    <justification jstring="[para(27140(a,1),15741(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27140 15741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27143">
    <literal><![CDATA[
      T((x / (y * x)) \ y,y) = ((y \ x) / x) \ y
    ]]></literal>
    <justification jstring="[para(23871(a,1),27141(a,1,1))].">
      <j1 rule="para" parents="23871 27141"/>
    </justification>
  </clause>

  <clause id="27144">
    <literal><![CDATA[
      T(x * K(y,x),z * z) = x * K(z \ (z \ y),x)
    ]]></literal>
    <justification jstring="[hyper(37,a,24415,a,b,26977,a),flip(a)].">
      <j1 rule="hyper" parents="37 24415 26977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27145">
    <literal><![CDATA[
      T(x * K(y * z,x),y * y) = x * K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),27144(a,2,2,1,2))].">
      <j1 rule="para" parents="9 27144"/>
    </justification>
  </clause>

  <clause id="27146">
    <literal><![CDATA[
      (x / L(y,z,u)) \ ((x / y) * w) = (L(y,z,u) \ x) \ ((y \ x) * w)
    ]]></literal>
    <justification jstring="[para(5982(a,1),26985(a,1,2))].">
      <j1 rule="para" parents="5982 26985"/>
    </justification>
  </clause>

  <clause id="27147">
    <literal><![CDATA[
      T((x \ y) * (z / (x \ y)),K(x,y)) = (y / x) * (z / (y / x))
    ]]></literal>
    <justification jstring="[hyper(39,a,8168,a,b,26992,a)].">
      <j1 rule="hyper" parents="39 8168 26992"/>
    </justification>
  </clause>

  <clause id="27148">
    <literal><![CDATA[
      x \ ((1 / (y * (x \ 1))) * y) = a(y * (x \ 1),y,x \ 1)
    ]]></literal>
    <justification jstring="[para(21699(a,1),26993(a,1,2))].">
      <j1 rule="para" parents="21699 26993"/>
    </justification>
  </clause>

  <clause id="27149">
    <literal><![CDATA[
      (x * (y * L(y,z,u))) \ (x * (y * y)) = x \ ((y \ L(y,z,u)) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,15291,a,b,27005,a)].">
      <j1 rule="hyper" parents="64 15291 27005"/>
    </justification>
  </clause>

  <clause id="27150">
    <literal><![CDATA[
      K(x \ ((y / (y / z)) \ u),w) = K(x \ (T(z,y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,20821,a(flip),b,27022,a),flip(a)].">
      <j1 rule="hyper" parents="373 20821 27022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27151">
    <literal><![CDATA[
      K(x \ (T(y,z) \ z),u) = K(x \ (z / y),u)
    ]]></literal>
    <justification jstring="[para(82(a,1),27150(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="82 27150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27152">
    <literal><![CDATA[
      K(x \ (y / (y * z)),u) = K(x \ ((z * y) \ y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13404,a(flip),b,27151,a),flip(a)].">
      <j1 rule="hyper" parents="64 13404 27151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27154">
    <literal><![CDATA[
      T(x,(y \ x) * (y \ x)) \ y = (y / x) * K(x / y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,15173,a(flip),b,27029,a)].">
      <j1 rule="hyper" parents="64 15173 27029"/>
    </justification>
  </clause>

  <clause id="27155">
    <literal><![CDATA[
      T(x,x * (y \ (y \ x))) \ y = (y / x) * K(x / y,x)
    ]]></literal>
    <justification jstring="[para(15649(a,1),27154(a,1,1))].">
      <j1 rule="para" parents="15649 27154"/>
    </justification>
  </clause>

  <clause id="27156">
    <literal><![CDATA[
      (x \ K(y,z)) \ L(x \ K(y,z),x,u) = x * ((u * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,439,a(flip),b,27080,a),flip(a)].">
      <j1 rule="hyper" parents="373 439 27080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27157">
    <literal><![CDATA[
      L(x \ K(y,z),x,u) \ (x \ K(y,z)) = (x * ((u * x) \ u)) \ 1
    ]]></literal>
    <justification jstring="[para(27156(a,1),9374(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27156 9374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27158">
    <literal><![CDATA[
      (x * K(y,z)) \ L(x * K(y,z),u,w) = x \ L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,5658,a(flip),b,27090,a),flip(a)].">
      <j1 rule="hyper" parents="373 5658 27090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27159">
    <literal><![CDATA[
      (x * K(y * x,z)) \ ((z * y) \ ((y * x) * z)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(14648(a,1),27158(a,1,2))].">
      <j1 rule="para" parents="14648 27158"/>
    </justification>
  </clause>

  <clause id="27160">
    <literal><![CDATA[
      R(x,y,(1 / z) * ((u * u) * w)) = R(x,y,(z \ (u * u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26353,a(flip),b,27091,a)].">
      <j1 rule="hyper" parents="64 26353 27091"/>
    </justification>
  </clause>

  <clause id="27161">
    <literal><![CDATA[
      R(x,y,((z \ u) * (1 / z)) \ w) = R(x,y,(z * z) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,26211,a(flip),b,27092,a),flip(a)].">
      <j1 rule="hyper" parents="373 26211 27092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27162">
    <literal><![CDATA[
      R(x,y,z * ((T(u,w) / v5) * v6)) = R(x,y,((v5 \ u) * v6) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,26247,a,b,27093,a),flip(a)].">
      <j1 rule="hyper" parents="373 26247 27093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27163">
    <literal><![CDATA[
      R(x,y,((z \ 1) * u) * ((z * z) * w)) = R(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[para(9(a,1),27094(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 27094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27164">
    <literal><![CDATA[
      R(x,y,(z * z) * (u \ (w / z))) = R(x,y,u \ ((z \ 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,26278,a(flip),b,27096,a),flip(a)].">
      <j1 rule="hyper" parents="373 26278 27096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27165">
    <literal><![CDATA[
      L(1 / x,x,a(y,z,u)) = a(y,z,u) \ (a(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25209,a,b,27098,a)].">
      <j1 rule="hyper" parents="64 25209 27098"/>
    </justification>
  </clause>

  <clause id="27166">
    <literal><![CDATA[
      a(x,y,z) / (a(x,y,z) \ u) = a(x,y,z) * (a(x,y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(38,a,23139,a,b,27099,a),flip(a)].">
      <j1 rule="hyper" parents="38 23139 27099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27167">
    <literal><![CDATA[
      x * ((x \ 1) \ (L(x,y,z) \ u)) = L(x,y,z) \ ((x * x) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,27111,a),flip(a)].">
      <j1 rule="hyper" parents="139 168 27111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27168">
    <literal><![CDATA[
      x * (L(x,y,z) * ((x \ 1) \ u)) = (x * x) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2323,a(flip),b,27111,a)].">
      <j1 rule="hyper" parents="64 2323 27111"/>
    </justification>
  </clause>

  <clause id="27169">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) \ w = L(y \ L(y,x,x),z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(462,a,27115,a),flip(a)].">
      <j1 rule="hyper" parents="462 27115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27170">
    <literal><![CDATA[
      a(L(L(x,y,z),u,w),v5,v6) = a(L(L(x,u,w),y,z),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26862,a(flip),b,27128,a)].">
      <j1 rule="hyper" parents="64 26862 27128"/>
    </justification>
  </clause>

  <clause id="27171">
    <literal><![CDATA[
      a(L(L(x \ 1,x,y),y * x,z),u,w) = a((z * (y * x)) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(1301(a,1),27170(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1301 27170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27172">
    <literal><![CDATA[
      (x * T(x \ y,z * (y \ x))) / y = K(x \ y,x * (z / y))
    ]]></literal>
    <justification jstring="[para(25436(a,1),27139(a,1,1,2))].">
      <j1 rule="para" parents="25436 27139"/>
    </justification>
  </clause>

  <clause id="27173">
    <literal><![CDATA[
      (x / y) * ((x * y) / (x / y)) = (y \ x) * ((x * y) / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,5964,a(flip),b,27147,a),flip(a)].">
      <j1 rule="hyper" parents="64 5964 27147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27174">
    <literal><![CDATA[
      R(x,y,(z \ 1) * ((u * u) * w)) = R(x,y,(z \ (u * u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26180,a(flip),b,27160,a)].">
      <j1 rule="hyper" parents="64 26180 27160"/>
    </justification>
  </clause>

  <clause id="27175">
    <literal><![CDATA[
      R(x,y,((z \ 1) * (z \ u)) \ w) = R(x,y,(z * z) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,26332,a,b,27161,a)].">
      <j1 rule="hyper" parents="64 26332 27161"/>
    </justification>
  </clause>

  <clause id="27176">
    <literal><![CDATA[
      R(x,y,((z \ u) * (z \ 1)) \ w) = R(x,y,(z * z) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,26221,a(flip),b,27161,a)].">
      <j1 rule="hyper" parents="64 26221 27161"/>
    </justification>
  </clause>

  <clause id="27177">
    <literal><![CDATA[
      R(x,y,((z \ T(u,w)) * v5) * v6) = R(x,y,((z \ u) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26309,a,b,27162,a)].">
      <j1 rule="hyper" parents="64 26309 27162"/>
    </justification>
  </clause>

  <clause id="27178">
    <literal><![CDATA[
      R(x,y,L(z,z,u)) = R(x,y,u \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(26051(a,1),27164(a,1,3))].">
      <j1 rule="para" parents="26051 27164"/>
    </justification>
  </clause>

  <clause id="27179">
    <literal><![CDATA[
      R(x,L(y,y,z),L(u,u,w)) = R(x,z \ (y \ z),w \ ((u \ 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,26561,a(flip),b,27178,a),flip(a)].">
      <j1 rule="hyper" parents="373 26561 27178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27180">
    <literal><![CDATA[
      (L(x,y,z) \ ((x * x) * u)) / T(x,(x \ 1) \ (L(x,y,z) \ u)) = (x \ 1) \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(142,a,27167,a(flip),b,115,a)].">
      <j1 rule="hyper" parents="142 27167 115"/>
    </justification>
  </clause>

  <clause id="27181">
    <literal><![CDATA[
      (1 / x) \ (L(x,y,z) * u) = L(x,y,z) * ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(35,a,538,a,b,27168,a)].">
      <j1 rule="hyper" parents="35 538 27168"/>
    </justification>
  </clause>

  <clause id="27182">
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) * ((x \ 1) \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(35,a,310,a,b,27168,a(flip))].">
      <j1 rule="hyper" parents="35 310 27168"/>
    </justification>
  </clause>

  <clause id="27183">
    <literal><![CDATA[
      L(x,y,z) * ((x \ 1) * u) = (1 / x) * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(1335,a,27181,a),flip(a)].">
      <j1 rule="hyper" parents="1335 27181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27184">
    <literal><![CDATA[
      (1 / L(x,y,z)) * (T(x \ 1,L(x,y,z) \ (L(x,y,z) \ 1)) \ u) = (1 / x) \ (L(x,y,z) * ((L(x,y,z) \ 1) * (L(x,y,z) \ u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,16437,a,b,27181,a)].">
      <j1 rule="hyper" parents="373 16437 27181"/>
    </justification>
  </clause>

  <clause id="27185">
    <literal><![CDATA[
      x * ((1 / x) * (L(x,y,z) * u)) = L(x,y,z) * L(u,x,x)
    ]]></literal>
    <justification jstring="[para(27183(a,1),2335(a,1,2))].">
      <j1 rule="para" parents="27183 2335"/>
    </justification>
  </clause>

  <clause id="27186">
    <literal><![CDATA[
      K(x / y,z * (x \ y)) = K(y \ x,y * (z / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,5732,a(flip),b,27172,a)].">
      <j1 rule="hyper" parents="64 5732 27172"/>
    </justification>
  </clause>

  <clause id="27187">
    <literal><![CDATA[
      ((x / y) \ 1) * (z / ((x / y) \ 1)) = z * K(x \ y,x * (z / y))
    ]]></literal>
    <justification jstring="[para(27186(a,1),10393(a,2,2))].">
      <j1 rule="para" parents="27186 10393"/>
    </justification>
  </clause>

  <clause id="27188">
    <literal><![CDATA[
      (x / y) * ((x * y) / (x / y)) = T(x * y,y * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,15212,a(flip),b,27173,a),flip(a)].">
      <j1 rule="hyper" parents="373 15212 27173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27189">
    <literal><![CDATA[
      ((x / y) \ (x * y)) * T(x * y,y * y) = ((x * y) / (x / y)) * (x * y)
    ]]></literal>
    <justification jstring="[para(27188(a,1),6591(a,1,2))].">
      <j1 rule="para" parents="27188 6591"/>
    </justification>
  </clause>

  <clause id="27190">
    <literal><![CDATA[
      R(x,y,((z \ R(z,u,w)) * ((R(z,u,w) \ z) \ v5)) \ v6) = R(x,y,((R(z,u,w) \ z) * (R(z,u,w) \ z)) * (v5 \ v6))
    ]]></literal>
    <justification jstring="[para(24813(a,1),27175(a,1,3,1,1))].">
      <j1 rule="para" parents="24813 27175"/>
    </justification>
  </clause>

  <clause id="27191">
    <literal><![CDATA[
      R(x,y,((R(z,u,w) \ z) * (R(z,u,w) \ z)) * ((R(1 / z,u,w) \ 1) \ v5)) = R(x,y,(z * ((R(z,u,w) \ z) \ 1)) \ v5)
    ]]></literal>
    <justification jstring="[para(25932(a,1),27176(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="25932 27176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27192">
    <literal><![CDATA[
      R(x,y,((z \ (u / w)) * v5) * v6) = R(x,y,((z \ (w \ u)) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(117(a,1),27177(a,1,3,1,1,2)),flip(a)].">
      <j1 rule="para" parents="117 27177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27193">
    <literal><![CDATA[
      T(x,y \ ((z * u) \ ((z * (u * y)) * w))) = T(x,a(z,u,y) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,23615,a(flip),b,23627,a)].">
      <j1 rule="hyper" parents="64 23615 23627"/>
    </justification>
  </clause>

  <clause id="27194">
    <literal><![CDATA[
      x / (((y / x) * (x * (x \ y))) / y) = (x / T(y,x \ y)) * x
    ]]></literal>
    <justification jstring="[para(11073(a,1),24171(a,1,2))].">
      <j1 rule="para" parents="11073 24171"/>
    </justification>
  </clause>

  <clause id="27196">
    <literal><![CDATA[
      x / (((y / x) * y) / y) = (x / T(y,x \ y)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),27194(a,1,2,1,2))].">
      <j1 rule="para" parents="10 27194"/>
    </justification>
  </clause>

  <clause id="27197">
    <literal><![CDATA[
      (x / T(y,x \ y)) * x = x / (y / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),27196(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 27196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27199">
    <literal><![CDATA[
      x / T(x * y,x \ (x * y)) = (K(y,x) * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,7165,a(flip),b,27197,a),flip(a)].">
      <j1 rule="hyper" parents="142 7165 27197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27201">
    <literal><![CDATA[
      (K(x,y) * (y / x)) / y = y / T(y * x,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),27199(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 27199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27202">
    <literal><![CDATA[
      (x / y) / T(x,y) = x / T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7166,a(flip),b,27201,a)].">
      <j1 rule="hyper" parents="64 7166 27201"/>
    </justification>
  </clause>

  <clause id="27203">
    <literal><![CDATA[
      T((x / y) / ((x / y) / x),y) \ (x / y) = x / T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,8331,a,b,27202,a)].">
      <j1 rule="hyper" parents="64 8331 27202"/>
    </justification>
  </clause>

  <clause id="27204">
    <literal><![CDATA[
      ((x * x) \ y) / T((1 / x) * T(y,x),x) = (((x * x) \ y) / x) / T((x * x) \ y,x)
    ]]></literal>
    <justification jstring="[para(1051(a,1),27202(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1051 27202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27205">
    <literal><![CDATA[
      T((x / T(x * y,y)) \ 1,T(x,y) / (x / y)) = ((x / y) / T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(27202(a,1),4825(a,1,1,1))].">
      <j1 rule="para" parents="27202 4825"/>
    </justification>
  </clause>

  <clause id="27206">
    <literal><![CDATA[
      T(x * K(y \ 1,x),y) \ (x / y) = x / T(x * y,y)
    ]]></literal>
    <justification jstring="[para(6797(a,1),27203(a,1,1,1))].">
      <j1 rule="para" parents="6797 27203"/>
    </justification>
  </clause>

  <clause id="27207">
    <literal><![CDATA[
      T(x,y * y) \ (x / y) = x / T(x * y,y)
    ]]></literal>
    <justification jstring="[para(7577(a,1),27206(a,1,1))].">
      <j1 rule="para" parents="7577 27206"/>
    </justification>
  </clause>

  <clause id="27208">
    <literal><![CDATA[
      T(x * L(y,z,u),K(y,w)) = L(y,z,u) * T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(23004(a,1),24195(a,1,2))].">
      <j1 rule="para" parents="23004 24195"/>
    </justification>
  </clause>

  <clause id="27210">
    <literal><![CDATA[
      K((x * y) \ (R(z,z \ x,y) * u),w) = K(y \ ((z \ x) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,23046,a(flip),b,24245,a),flip(a)].">
      <j1 rule="hyper" parents="373 23046 24245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27211">
    <literal><![CDATA[
      x / L(T(x,y \ 1),x \ (y \ x),y) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(23430(a,1),24416(a,1,2))].">
      <j1 rule="para" parents="23430 24416"/>
    </justification>
  </clause>

  <clause id="27212">
    <literal><![CDATA[
      L(T(x,y \ 1),x \ (y \ x),y) \ x = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,10474,a(flip),b,27211,a)].">
      <j1 rule="hyper" parents="64 10474 27211"/>
    </justification>
  </clause>

  <clause id="27213">
    <literal><![CDATA[
      K(x,y / (z * L(u \ w,u,w \ y))) = K(x,(y / w) / (z / u))
    ]]></literal>
    <justification jstring="[hyper(373,a,23039,a(flip),b,24548,a),flip(a)].">
      <j1 rule="hyper" parents="373 23039 24548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27214">
    <literal><![CDATA[
      (a(x,y,z) * (u / (u / (a(x,y,z) \ w)))) * (a(x,y,z) \ 1) = u / (u / ((1 / a(x,y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,10475,a(flip),b,24623,a),flip(a)].">
      <j1 rule="hyper" parents="373 10475 24623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27215">
    <literal><![CDATA[
      (x * a(y,z,u)) * (a(y,z,u) \ 1) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,23168,a(flip),b,24623,a)].">
      <j1 rule="hyper" parents="64 23168 24623"/>
    </justification>
  </clause>

  <clause id="27216">
    <literal><![CDATA[
      L(x \ R(x,y,((z \ u) * (u / z)) \ w),x,w * y) = a(x,y,((u / z) * (u / z)) \ w)
    ]]></literal>
    <justification jstring="[para(26245(a,1),24739(a,1,1,2))].">
      <j1 rule="para" parents="26245 24739"/>
    </justification>
  </clause>

  <clause id="27217">
    <literal><![CDATA[
      R((x * x) \ (x \ K(x,y)),x,y) = ((x \ 1) * (x \ y)) / (y * x)
    ]]></literal>
    <justification jstring="[para(1098(a,1),24890(a,2,1))].">
      <j1 rule="para" parents="1098 24890"/>
    </justification>
  </clause>

  <clause id="27218">
    <literal><![CDATA[
      T(x,y * (x \ y)) \ ((x \ y) * y) = T(x \ ((x \ y) * y),x)
    ]]></literal>
    <justification jstring="[para(10297(a,1),25247(a,1,1))].">
      <j1 rule="para" parents="10297 25247"/>
    </justification>
  </clause>

  <clause id="27219">
    <literal><![CDATA[
      x \ ((T(x,y * (x \ y)) \ y) * y) = T(x \ ((x \ y) * y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24899,a(flip),b,27218,a)].">
      <j1 rule="hyper" parents="64 24899 27218"/>
    </justification>
  </clause>

  <clause id="27220">
    <literal><![CDATA[
      T(x \ ((x \ y) * y),x) = x \ T((x \ y) * y,x)
    ]]></literal>
    <justification jstring="[para(14992(a,1),27219(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14992 27219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27221">
    <literal><![CDATA[
      (x \ ((x \ y) * y)) * x = T((x \ y) * y,x)
    ]]></literal>
    <justification jstring="[hyper(158,a,27220,a)].">
      <j1 rule="hyper" parents="158 27220"/>
    </justification>
  </clause>

  <clause id="27222">
    <literal><![CDATA[
      T((x \ y) * y,T(x,z)) = (x \ ((x \ y) * y)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,17645,a,b,27221,a)].">
      <j1 rule="hyper" parents="373 17645 27221"/>
    </justification>
  </clause>

  <clause id="27223">
    <literal><![CDATA[
      K(x * (y \ x),y) * ((y \ x) * x) = (y \ ((y \ x) * x)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,11237,a,b,27222,a)].">
      <j1 rule="hyper" parents="64 11237 27222"/>
    </justification>
  </clause>

  <clause id="27224">
    <literal><![CDATA[
      K(x * (y \ (y \ x)),y) = K(x * (y \ x),y)
    ]]></literal>
    <justification jstring="[hyper(36,a,15155,a,b,27223,a)].">
      <j1 rule="hyper" parents="36 15155 27223"/>
    </justification>
  </clause>

  <clause id="27225">
    <literal><![CDATA[
      K(x,y) * (z * ((y * z) \ u)) = z * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26400,a(flip),b,25335,a),flip(a)].">
      <j1 rule="hyper" parents="64 26400 25335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27226">
    <literal><![CDATA[
      x * ((T(y,x * ((y * x) \ z)) * x) \ z) = T(x * ((y * x) \ z),y)
    ]]></literal>
    <justification jstring="[hyper(5816,a,27225,a),flip(a)].">
      <j1 rule="hyper" parents="5816 27225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27227">
    <literal><![CDATA[
      (x * (y * z)) * (K(u,w) * a(x,y,z)) = (x * y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(23185,a,25389,a)].">
      <j1 rule="hyper" parents="23185 25389"/>
    </justification>
  </clause>

  <clause id="27228">
    <literal><![CDATA[
      K(x,y * z) * (z \ R(z,z,y)) = (y / T(z * y,x)) * z
    ]]></literal>
    <justification jstring="[para(11127(a,1),25403(a,1,1))].">
      <j1 rule="para" parents="11127 25403"/>
    </justification>
  </clause>

  <clause id="27229">
    <literal><![CDATA[
      T(L(x,x,x * y) \ 1,y * x) = (y \ ((1 / x) \ y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,14549,a(flip),b,25577,a)].">
      <j1 rule="hyper" parents="64 14549 25577"/>
    </justification>
  </clause>

  <clause id="27230">
    <literal><![CDATA[
      x * R(x \ K(x,y),x,x \ y) = ((x \ y) / T(y,x)) * x
    ]]></literal>
    <justification jstring="[para(8681(a,1),25590(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8681 25590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27231">
    <literal><![CDATA[
      x \ R(T(x,y),x,x \ y) = ((x \ y) / T(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,5770,a(flip),b,27230,a)].">
      <j1 rule="hyper" parents="64 5770 27230"/>
    </justification>
  </clause>

  <clause id="27232">
    <literal><![CDATA[
      x \ R(T(x,y),x,x \ y) = T(y / (y * x),x) * x
    ]]></literal>
    <justification jstring="[para(25992(a,1),27231(a,2,1))].">
      <j1 rule="para" parents="25992 27231"/>
    </justification>
  </clause>

  <clause id="27233">
    <literal><![CDATA[
      (T(T(x,y),z) \ (1 / x)) \ u = (1 / x) \ (T(T(x,y),z) * u)
    ]]></literal>
    <justification jstring="[hyper(1095,a,25613,a)].">
      <j1 rule="hyper" parents="1095 25613"/>
    </justification>
  </clause>

  <clause id="27234">
    <literal><![CDATA[
      (x \ (1 / T(T(x,y),z))) \ u = (1 / x) \ (T(T(x,y),z) * u)
    ]]></literal>
    <justification jstring="[para(20238(a,1),27233(a,1,1))].">
      <j1 rule="para" parents="20238 27233"/>
    </justification>
  </clause>

  <clause id="27235">
    <literal><![CDATA[
      (x * (y / x)) \ (z * (y / x)) = T(y,x) \ (z * (x \ T(y,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11302,a(flip),b,25634,a)].">
      <j1 rule="hyper" parents="64 11302 25634"/>
    </justification>
  </clause>

  <clause id="27236">
    <literal><![CDATA[
      R(T(x / y,T(z,x)),y,y \ z) = T(z,y) \ (x * (y \ T(z,y)))
    ]]></literal>
    <justification jstring="[para(8013(a,1),25634(a,1,1))].">
      <j1 rule="para" parents="8013 25634"/>
    </justification>
  </clause>

  <clause id="27237">
    <literal><![CDATA[
      R(x,a(y,z,u),a(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,23759,a(flip),b,25664,a),flip(a)].">
      <j1 rule="hyper" parents="64 23759 25664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27238">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),a(y,z,u)) = a(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,27237,a(flip),b,15984,a)].">
      <j1 rule="hyper" parents="139 27237 15984"/>
    </justification>
  </clause>

  <clause id="27239">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z),u) \ 1 = a(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,5665,a,b,27238,a)].">
      <j1 rule="hyper" parents="64 5665 27238"/>
    </justification>
  </clause>

  <clause id="27240">
    <literal><![CDATA[
      (((x / y) \ 1) * x) * (y \ x) = L(x,y \ x,y \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),25809(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 25809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27241">
    <literal><![CDATA[
      T(x * a(y,x \ y,x),x \ 1) = x * (x * (1 / L(x,x \ y,y)))
    ]]></literal>
    <justification jstring="[para(10275(a,2),26042(a,2,2,2))].">
      <j1 rule="para" parents="10275 26042"/>
    </justification>
  </clause>

  <clause id="27242">
    <literal><![CDATA[
      T(((1 / x) * y) \ y,K(y,1 / x)) = L(x * K(y,x \ 1),x,y)
    ]]></literal>
    <justification jstring="[para(3348(a,1),26088(a,2,1))].">
      <j1 rule="para" parents="3348 26088"/>
    </justification>
  </clause>

  <clause id="27243">
    <literal><![CDATA[
      x * T(L(L(x,y,z),u,w) * v5,x) = (x * v5) * L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(26160(a,1),4780(a,1,2))].">
      <j1 rule="para" parents="26160 4780"/>
    </justification>
  </clause>

  <clause id="27244">
    <literal><![CDATA[
      R(1 / x,x,(x \ y) * R(x,z,u)) = ((y / x) * R(x,z,u)) / (R(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(25045(a,1),26248(a,2,2))].">
      <j1 rule="para" parents="25045 26248"/>
    </justification>
  </clause>

  <clause id="27245">
    <literal><![CDATA[
      R(x,(y * y) * (z * R(u,y,y)),w) = R(x,((u * y) * y) * z,w)
    ]]></literal>
    <justification jstring="[para(33(a,1),26477(a,1,2))].">
      <j1 rule="para" parents="33 26477"/>
    </justification>
  </clause>

  <clause id="27246">
    <literal><![CDATA[
      R(R(x,y,(z * z) \ 1),y,u) = R(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2967,a(flip),b,26485,a)].">
      <j1 rule="hyper" parents="64 2967 26485"/>
    </justification>
  </clause>

  <clause id="27248">
    <literal><![CDATA[
      R(R(x,y,z \ (z \ 1)),y,u) = R(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[para(26256(a,1),27246(a,1,1))].">
      <j1 rule="para" parents="26256 27246"/>
    </justification>
  </clause>

  <clause id="27249">
    <literal><![CDATA[
      R(R(x,y,(z \ u) \ ((z \ u) \ 1)),y,w) = R(x,y,((z \ u) * (u / z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26221,a,b,27248,a),flip(a)].">
      <j1 rule="hyper" parents="373 26221 27248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27250">
    <literal><![CDATA[
      (x \ (x / y)) * R(z,y,z) = T(z * (x \ (x / y)),z)
    ]]></literal>
    <justification jstring="[para(3347(a,1),26555(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3347 26555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27252">
    <literal><![CDATA[
      T(x * ((y * z) \ ((y * z) / z)),x) = ((y * z) \ y) * R(x,z,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),27250(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 27250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27253">
    <literal><![CDATA[
      (x \ L(x,x,y)) \ K(x \ 1,y) = (((y / x) / y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(6767(a,1),26662(a,1,2))].">
      <j1 rule="para" parents="6767 26662"/>
    </justification>
  </clause>

  <clause id="27254">
    <literal><![CDATA[
      (L(x,x,y) \ x) * K(x \ 1,y) = (((y / x) / y) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,14517,a(flip),b,27253,a)].">
      <j1 rule="hyper" parents="64 14517 27253"/>
    </justification>
  </clause>

  <clause id="27256">
    <literal><![CDATA[
      x * T(L(x,x,y) \ 1,y) = (((y / x) / y) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,25374,a(flip),b,27254,a)].">
      <j1 rule="hyper" parents="64 25374 27254"/>
    </justification>
  </clause>

  <clause id="27257">
    <literal><![CDATA[
      (x * (y / z)) * ((y / z) \ u) = (x * (z \ y)) * ((z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(977,a,26713,a),flip(a)].">
      <j1 rule="hyper" parents="977 26713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27258">
    <literal><![CDATA[
      R(x,T(y * L(z,y,u),u),w) = R(x,y * R(z,y,u),w)
    ]]></literal>
    <justification jstring="[para(11292(a,1),26731(a,1,2))].">
      <j1 rule="para" parents="11292 26731"/>
    </justification>
  </clause>

  <clause id="27259">
    <literal><![CDATA[
      R(x,y * R(z,y,u),w) = R(x,y * L(z,y,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26406,a(flip),b,27258,a),flip(a)].">
      <j1 rule="hyper" parents="64 26406 27258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27261">
    <literal><![CDATA[
      R(x,((y \ z) / z) * y,u) = R(x,y * L(y,y,y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,3046,a,b,27259,a)].">
      <j1 rule="hyper" parents="64 3046 27259"/>
    </justification>
  </clause>

  <clause id="27262">
    <literal><![CDATA[
      R(x,((y \ z) / z) * y,u) = R(x,y * L(y,y,y * z),u)
    ]]></literal>
    <justification jstring="[para(25574(a,1),27261(a,2,2,2))].">
      <j1 rule="para" parents="25574 27261"/>
    </justification>
  </clause>

  <clause id="27263">
    <literal><![CDATA[
      R(x,(y \ (z \ y)) * z,u) = R(x,z * L(z,z,z * y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26417,a(flip),b,27262,a)].">
      <j1 rule="hyper" parents="64 26417 27262"/>
    </justification>
  </clause>

  <clause id="27264">
    <literal><![CDATA[
      (((x \ 1) / y) * (y * x)) \ K(x \ 1,x) = a(y \ x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,26855,a(flip),b,26808,a),flip(a)].">
      <j1 rule="hyper" parents="373 26855 26808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27265">
    <literal><![CDATA[
      (L(x,y,y \ (x \ 1)) * (x \ 1)) \ 1 = a(y \ x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,16112,a(flip),b,27264,a)].">
      <j1 rule="hyper" parents="64 16112 27264"/>
    </justification>
  </clause>

  <clause id="27266">
    <literal><![CDATA[
      (L(x,y,y \ x) * (x \ 1)) \ 1 = a(y \ x,y,x)
    ]]></literal>
    <justification jstring="[para(25696(a,1),27265(a,1,1,1))].">
      <j1 rule="para" parents="25696 27265"/>
    </justification>
  </clause>

  <clause id="27267">
    <literal><![CDATA[
      (x \ L(x,y,y \ x)) \ 1 = a(y \ x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1810,a(flip),b,27266,a)].">
      <j1 rule="hyper" parents="64 1810 27266"/>
    </justification>
  </clause>

  <clause id="27268">
    <literal><![CDATA[
      L(x,y,y \ x) \ x = a(y \ x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9374,a(flip),b,27267,a)].">
      <j1 rule="hyper" parents="64 9374 27267"/>
    </justification>
  </clause>

  <clause id="27269">
    <literal><![CDATA[
      x * ((x \ K(x,x \ 1)) * L(y,z,u)) = L(x * ((1 / x) * y),z,u)
    ]]></literal>
    <justification jstring="[para(2451(a,1),27078(a,2,1))].">
      <j1 rule="para" parents="2451 27078"/>
    </justification>
  </clause>

  <clause id="27270">
    <literal><![CDATA[
      (T(x * y,z) \ x) \ (y \ K(z,y * x)) = (y * ((x * y) \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(11247(a,1),27157(a,1,1))].">
      <j1 rule="para" parents="11247 27157"/>
    </justification>
  </clause>

  <clause id="27271">
    <literal><![CDATA[
      K(x,y * z) * (z \ ((x * y) \ ((y * z) * x))) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,23272,a(flip),b,27159,a)].">
      <j1 rule="hyper" parents="64 23272 27159"/>
    </justification>
  </clause>

  <clause id="27272">
    <literal><![CDATA[
      T(x,y \ ((z * u) \ ((z * (u * y)) * w))) = T(x,a(z,u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,25313,a(flip),b,27193,a),flip(a)].">
      <j1 rule="hyper" parents="373 25313 27193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27273">
    <literal><![CDATA[
      K(x,y / (z * L(u \ w,u,w \ y))) = K(x,y / ((z / u) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,23387,a(flip),b,27213,a),flip(a)].">
      <j1 rule="hyper" parents="373 23387 27213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27274">
    <literal><![CDATA[
      R((x * x) \ (x \ K(x,y)),x,y) = (x \ 1) * (x \ (y / (y * x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,1686,a(flip),b,27217,a),flip(a)].">
      <j1 rule="hyper" parents="373 1686 27217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27275">
    <literal><![CDATA[
      (x * (y * (z * K(u,w)))) * a(x,y,z) = (x * y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,25407,a,b,27227,a)].">
      <j1 rule="hyper" parents="64 25407 27227"/>
    </justification>
  </clause>

  <clause id="27276">
    <literal><![CDATA[
      R(T(x / y,T((y \ z) * T(y,z),x)),y,y \ ((y \ z) * T(y,z))) = ((y \ z) * y) \ (x * (y \ T((y \ z) * T(y,z),y)))
    ]]></literal>
    <justification jstring="[para(4701(a,1),27236(a,2,1))].">
      <j1 rule="para" parents="4701 27236"/>
    </justification>
  </clause>

  <clause id="27277">
    <literal><![CDATA[
      L(x * K(y,x \ 1),x,y) = ((1 / x) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,7829,a(flip),b,27242,a),flip(a)].">
      <j1 rule="hyper" parents="64 7829 27242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27279">
    <literal><![CDATA[
      R(x,((y * z) * z) * u,w) = R(x,u * R(y,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2965,a(flip),b,27245,a),flip(a)].">
      <j1 rule="hyper" parents="64 2965 27245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27281">
    <literal><![CDATA[
      R(x,((y * z) * y) * u,w) = R(x,u * R(z,y,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26433,a,b,27279,a)].">
      <j1 rule="hyper" parents="64 26433 27279"/>
    </justification>
  </clause>

  <clause id="27282">
    <literal><![CDATA[
      R(x,y * ((z * u) * z),w) = R(x,y * R(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26409,a,b,27281,a)].">
      <j1 rule="hyper" parents="64 26409 27281"/>
    </justification>
  </clause>

  <clause id="27283">
    <literal><![CDATA[
      R(x,y * ((z * u) * z),w) = R(x,R(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26409,a,b,27282,a),flip(a)].">
      <j1 rule="hyper" parents="373 26409 27282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27284">
    <literal><![CDATA[
      R(x,y * ((z * y) * z),u) = R(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,16006,a(flip),b,27282,a),flip(a)].">
      <j1 rule="hyper" parents="373 16006 27282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27285">
    <literal><![CDATA[
      R(x,y * (z * (y * z)),u) = R(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26716,a(flip),b,27284,a)].">
      <j1 rule="hyper" parents="64 26716 27284"/>
    </justification>
  </clause>

  <clause id="27286">
    <literal><![CDATA[
      R(x,a(y,z,y * z),u) = R(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26592,a(flip),b,27285,a)].">
      <j1 rule="hyper" parents="64 26592 27285"/>
    </justification>
  </clause>

  <clause id="27287">
    <literal><![CDATA[
      R(x,a(y,z,z),u) = R(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26719,a(flip),b,27286,a),flip(a)].">
      <j1 rule="hyper" parents="64 26719 27286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27288">
    <literal><![CDATA[
      R(x,R(y,z,z) * u,w) = R(x,L(y,z,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26571,a(flip),b,27283,a),flip(a)].">
      <j1 rule="hyper" parents="64 26571 27283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27289">
    <literal><![CDATA[
      R(x,(a(y,z,z) \ y) * u,w) = R(x,L(y,z,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16026,a,b,27288,a)].">
      <j1 rule="hyper" parents="64 16026 27288"/>
    </justification>
  </clause>

  <clause id="27290">
    <literal><![CDATA[
      ((x * y) \ x) * R(z,y,z) = T(z * ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[para(11(a,1),27252(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 27252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27291">
    <literal><![CDATA[
      ((x \ (y \ x)) \ (y \ 1)) * R(z,y * (x \ (y \ x)),z) = T(z * (((y \ 1) * (y * (x \ (y \ x)))) \ (y \ 1)),z)
    ]]></literal>
    <justification jstring="[para(26261(a,1),27290(a,1,1,1))].">
      <j1 rule="para" parents="26261 27290"/>
    </justification>
  </clause>

  <clause id="27292">
    <literal><![CDATA[
      L(x,y,z) = K(z,x * y) * ((z * y) \ ((y * x) * z))
    ]]></literal>
    <justification jstring="[hyper(39,a,22772,a,b,27271,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 22772 27271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27293">
    <literal><![CDATA[
      K(x,y * z) * (((x * z) \ ((z * y) * x)) * u) = L(y,z,x) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,27292,a,b,23225,a),flip(a)].">
      <j1 rule="hyper" parents="144 27292 23225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27294">
    <literal><![CDATA[
      (x * x) \ T(y / (y * x),x) = (x \ 1) * (x \ (y / (y * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14267,a(flip),b,27274,a)].">
      <j1 rule="hyper" parents="64 14267 27274"/>
    </justification>
  </clause>

  <clause id="27295">
    <literal><![CDATA[
      (x * x) \ T(y / (y * x),x) = (x \ (y / (y * x))) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,14272,a(flip),b,27294,a),flip(a)].">
      <j1 rule="hyper" parents="373 14272 27294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27296">
    <literal><![CDATA[
      a(x,y,z * K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,88,a,b,27275,a)].">
      <j1 rule="hyper" parents="35 88 27275"/>
    </justification>
  </clause>

  <clause id="27297">
    <literal><![CDATA[
      L(a(x,y,z),u,K(w,v5)) = a(x,y,z * K(v6,v7))
    ]]></literal>
    <justification jstring="[hyper(373,a,23115,a,b,27296,a)].">
      <j1 rule="hyper" parents="373 23115 27296"/>
    </justification>
  </clause>

  <clause id="27298">
    <literal><![CDATA[
      a(x,y,z * u) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(94(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="94 27296"/>
    </justification>
  </clause>

  <clause id="27299">
    <literal><![CDATA[
      a(x,y,(z \ u) * z) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(353(a,1),27296(a,1,3)),flip(a)].">
      <j1 rule="para" parents="353 27296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27300">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * (w * u)) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[para(609(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="609 27296"/>
    </justification>
  </clause>

  <clause id="27301">
    <literal><![CDATA[
      a(x,y,z \ T(u,w)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(2433(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="2433 27296"/>
    </justification>
  </clause>

  <clause id="27302">
    <literal><![CDATA[
      a(x,y,((1 / z) * u) \ w) = a(x,y,((z \ 1) * u) \ w)
    ]]></literal>
    <justification jstring="[para(5225(a,1),27296(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5225 27296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27303">
    <literal><![CDATA[
      a(x,y,(z \ 1) * L(z,u,w)) = a(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(5613(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="5613 27296"/>
    </justification>
  </clause>

  <clause id="27304">
    <literal><![CDATA[
      a(x,y,T(z,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(5748(a,1),27296(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5748 27296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27306">
    <literal><![CDATA[
      a(x,y,z / (z / u)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(5751(a,2),27296(a,1,3))].">
      <j1 rule="para" parents="5751 27296"/>
    </justification>
  </clause>

  <clause id="27307">
    <literal><![CDATA[
      a(x,y,(z \ u) \ u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(5752(a,2),27296(a,1,3))].">
      <j1 rule="para" parents="5752 27296"/>
    </justification>
  </clause>

  <clause id="27308">
    <literal><![CDATA[
      a(x,y,z / u) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(5774(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="5774 27296"/>
    </justification>
  </clause>

  <clause id="27309">
    <literal><![CDATA[
      a(x,y,z * T(u,w)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(6249(a,1),27296(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6249 27296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27310">
    <literal><![CDATA[
      a(x,y,z * (u / w)) = a(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[para(6471(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="6471 27296"/>
    </justification>
  </clause>

  <clause id="27311">
    <literal><![CDATA[
      a(x,y,K(z,u) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(6576(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="6576 27296"/>
    </justification>
  </clause>

  <clause id="27312">
    <literal><![CDATA[
      a(x,y,T(z,u) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(6570(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="6570 27296"/>
    </justification>
  </clause>

  <clause id="27313">
    <literal><![CDATA[
      a(x,y,(z * z) * (u / z)) = a(x,y,(1 / z) \ u)
    ]]></literal>
    <justification jstring="[para(7211(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="7211 27296"/>
    </justification>
  </clause>

  <clause id="27314">
    <literal><![CDATA[
      a(x,y,z * (u * T(w,v5))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(7368(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="7368 27296"/>
    </justification>
  </clause>

  <clause id="27315">
    <literal><![CDATA[
      a(x,y,z * (u * w)) = a(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[para(7591(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="7591 27296"/>
    </justification>
  </clause>

  <clause id="27316">
    <literal><![CDATA[
      a(x,y,T(z,u) \ w) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(7948(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="7948 27296"/>
    </justification>
  </clause>

  <clause id="27317">
    <literal><![CDATA[
      a(x,y,(z / u) * w) = a(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(8651(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="8651 27296"/>
    </justification>
  </clause>

  <clause id="27318">
    <literal><![CDATA[
      a(x,y,(z * K(u,w)) * v5) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(9345(a,1),27296(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9345 27296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27319">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) * u)) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(10196(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="10196 27296"/>
    </justification>
  </clause>

  <clause id="27320">
    <literal><![CDATA[
      a(x,y,z * (u * K(w,v5))) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(12078(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="12078 27296"/>
    </justification>
  </clause>

  <clause id="27321">
    <literal><![CDATA[
      a(x,y,z \ K(u,w)) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(14444(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="14444 27296"/>
    </justification>
  </clause>

  <clause id="27322">
    <literal><![CDATA[
      a(x,y,z \ (u / w)) = a(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(15028(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="15028 27296"/>
    </justification>
  </clause>

  <clause id="27323">
    <literal><![CDATA[
      a(x,y,z \ ((u \ w) \ w)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(15035(a,2),27296(a,1,3))].">
      <j1 rule="para" parents="15035 27296"/>
    </justification>
  </clause>

  <clause id="27324">
    <literal><![CDATA[
      a(x,y,z \ L(T(u,w),v5,v6)) = a(x,y,z \ L(u,v5,v6))
    ]]></literal>
    <justification jstring="[para(15043(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="15043 27296"/>
    </justification>
  </clause>

  <clause id="27325">
    <literal><![CDATA[
      a(x,y,z \ (u * w)) = a(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[para(14934(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="14934 27296"/>
    </justification>
  </clause>

  <clause id="27326">
    <literal><![CDATA[
      a(x,y,(z * u) * R(w,z,u)) = a(x,y,(w * z) * u)
    ]]></literal>
    <justification jstring="[para(15979(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="15979 27296"/>
    </justification>
  </clause>

  <clause id="27327">
    <literal><![CDATA[
      a(x,y,z \ (u * K(w,v5))) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(16164(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="16164 27296"/>
    </justification>
  </clause>

  <clause id="27328">
    <literal><![CDATA[
      a(x,y,L(T(z,u),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(23430(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="23430 27296"/>
    </justification>
  </clause>

  <clause id="27330">
    <literal><![CDATA[
      a(x,y,z * (K(u,w) * v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(23252(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="23252 27296"/>
    </justification>
  </clause>

  <clause id="27331">
    <literal><![CDATA[
      a(x,y,z \ (K(u,w) * v5)) = a(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(23401(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="23401 27296"/>
    </justification>
  </clause>

  <clause id="27332">
    <literal><![CDATA[
      a(x,y,z \ (u \ T(w,v5))) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(24309(a,1),27296(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24309 27296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27333">
    <literal><![CDATA[
      a(x,y,z \ (u * T(w,v5))) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(24315(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="24315 27296"/>
    </justification>
  </clause>

  <clause id="27334">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * K(v5,v6)))) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(24304(a,2),27296(a,1,3))].">
      <j1 rule="para" parents="24304 27296"/>
    </justification>
  </clause>

  <clause id="27335">
    <literal><![CDATA[
      a(x,y,z \ (T(u,w) * v5)) = a(x,y,z \ (u * v5))
    ]]></literal>
    <justification jstring="[para(24312(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="24312 27296"/>
    </justification>
  </clause>

  <clause id="27336">
    <literal><![CDATA[
      a(x,y,L((z \ u) \ u,w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(24556(a,2),27296(a,1,3))].">
      <j1 rule="para" parents="24556 27296"/>
    </justification>
  </clause>

  <clause id="27337">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w \ v5) * w))) = a(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(24306(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="24306 27296"/>
    </justification>
  </clause>

  <clause id="27338">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w / v5))) = a(x,y,z \ (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(24307(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="24307 27296"/>
    </justification>
  </clause>

  <clause id="27339">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w \ v5) \ v5))) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[para(24317(a,1),27296(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24317 27296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27340">
    <literal><![CDATA[
      a(x,y,z \ (u \ (K(w,v5) * v6))) = a(x,y,z \ (u \ v6))
    ]]></literal>
    <justification jstring="[para(24779(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="24779 27296"/>
    </justification>
  </clause>

  <clause id="27341">
    <literal><![CDATA[
      a(x,y,z * (u * (w * K(v5,v6)))) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(25230(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="25230 27296"/>
    </justification>
  </clause>

  <clause id="27342">
    <literal><![CDATA[
      a(x,y,z * L(T(u,w),v5,v6)) = a(x,y,z * L(u,v5,v6))
    ]]></literal>
    <justification jstring="[para(25231(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="25231 27296"/>
    </justification>
  </clause>

  <clause id="27343">
    <literal><![CDATA[
      a(x,y,L(z * K(u,w),v5,v6)) = a(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(26070(a,2),27296(a,1,3))].">
      <j1 rule="para" parents="26070 27296"/>
    </justification>
  </clause>

  <clause id="27344">
    <literal><![CDATA[
      a(x,y,L(z / u,w,v5)) = a(x,y,L(u \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(26077(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="26077 27296"/>
    </justification>
  </clause>

  <clause id="27345">
    <literal><![CDATA[
      a(x,y,z \ L(u / w,v5,v6)) = a(x,y,z \ L(w \ u,v5,v6))
    ]]></literal>
    <justification jstring="[para(26118(a,1),27296(a,1,3))].">
      <j1 rule="para" parents="26118 27296"/>
    </justification>
  </clause>

  <clause id="27355">
    <literal><![CDATA[
      a(x,y,T(z * z,z)) = a(x,y,(z \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(1176(a,1),27304(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1176 27304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27356">
    <literal><![CDATA[
      a(x,y,z) \ (T(z,u) * (x * y)) = L(T(z,u),y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(27304(a,1),15715(a,1,1))].">
      <j1 rule="para" parents="27304 15715"/>
    </justification>
  </clause>

  <clause id="27359">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ (v5 * z)) = a(x,y,z * (L(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(25113(a,1),27304(a,1,3))].">
      <j1 rule="para" parents="25113 27304"/>
    </justification>
  </clause>

  <clause id="27360">
    <literal><![CDATA[
      a(x,y,T(z * u,w)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27304,a,b,27298,a)].">
      <j1 rule="hyper" parents="373 27304 27298"/>
    </justification>
  </clause>

  <clause id="27361">
    <literal><![CDATA[
      a(x,y,z * L(L(u,w,u),v5,v6)) = a(x,y,L(u,v5,v6) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,13882,a,b,27298,a)].">
      <j1 rule="hyper" parents="373 13882 27298"/>
    </justification>
  </clause>

  <clause id="27362">
    <literal><![CDATA[
      a(x,y,L(z,u,z) * w) = a(x,y,w * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,13866,a,b,27298,a)].">
      <j1 rule="hyper" parents="373 13866 27298"/>
    </justification>
  </clause>

  <clause id="27363">
    <literal><![CDATA[
      a(x,y,(z * u) * (z \ 1)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,13880,a(flip),b,27298,a),flip(a)].">
      <j1 rule="hyper" parents="373 13880 27298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27364">
    <literal><![CDATA[
      a(x,y,z * u) * w = w * a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,27298,a,b,23174,a),flip(a)].">
      <j1 rule="hyper" parents="145 27298 23174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27365">
    <literal><![CDATA[
      (x * (y * (z * u))) * a(x,y,u * z) = (x * y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,27298,a,b,14,a(flip))].">
      <j1 rule="hyper" parents="145 27298 14"/>
    </justification>
  </clause>

  <clause id="27366">
    <literal><![CDATA[
      a(x,y,z * u) \ w = a(x,y,u * z) \ w
    ]]></literal>
    <justification jstring="[hyper(62,a,27298,a)].">
      <j1 rule="hyper" parents="62 27298"/>
    </justification>
  </clause>

  <clause id="27367">
    <literal><![CDATA[
      a(x,y,(z * z) * (u * w)) = a(x,y,w * ((z * z) * u))
    ]]></literal>
    <justification jstring="[para(33(a,1),27298(a,1,3))].">
      <j1 rule="para" parents="33 27298"/>
    </justification>
  </clause>

  <clause id="27368">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) * z) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(1139(a,1),27298(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1139 27298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27369">
    <literal><![CDATA[
      a(x,y,((z * z) * u) * (w / z)) = a(x,y,(w / (1 / z)) * u)
    ]]></literal>
    <justification jstring="[para(819(a,1),27298(a,1,3)),flip(a)].">
      <j1 rule="para" parents="819 27298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27370">
    <literal><![CDATA[
      a(x,y,(z * u) * ((w * w) / z)) = a(x,y,(w * w) * L(u,z,z))
    ]]></literal>
    <justification jstring="[para(1076(a,1),27298(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1076 27298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27371">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),v5,v6) * (w * u)) = a(x,y,w * (u * L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(513(a,1),27298(a,1,3)),flip(a)].">
      <j1 rule="para" parents="513 27298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27372">
    <literal><![CDATA[
      a(x,y,(z \ ((u * (z \ 1)) \ w)) * (z \ 1)) = a(x,y,(R(u,z,z) / (1 / z)) \ w)
    ]]></literal>
    <justification jstring="[para(3122(a,1),27298(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3122 27298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27373">
    <literal><![CDATA[
      a(x,y,(T(z,u) * L(w,u,z)) * u) = a(x,y,z * (u * L(w,z,u)))
    ]]></literal>
    <justification jstring="[para(11002(a,1),27298(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11002 27298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27374">
    <literal><![CDATA[
      a(x,y,((z / u) * w) * R(v5,u \ z,w)) = a(x,y,(v5 * (z / u)) * w)
    ]]></literal>
    <justification jstring="[para(26488(a,1),27298(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26488 27298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27375">
    <literal><![CDATA[
      (a(x,y,z * u) * w) \ (w * (v5 * a(x,y,z * u))) = L(v5,a(x,y,u * z),w)
    ]]></literal>
    <justification jstring="[para(27298(a,1),24645(a,2,2))].">
      <j1 rule="para" parents="27298 24645"/>
    </justification>
  </clause>

  <clause id="27376">
    <literal><![CDATA[
      a(x,y,((1 / z) / u) * (w * w)) = a(x,y,((w * w) / z) / u)
    ]]></literal>
    <justification jstring="[para(936(a,1),27299(a,1,3,1))].">
      <j1 rule="para" parents="936 27299"/>
    </justification>
  </clause>

  <clause id="27377">
    <literal><![CDATA[
      a(x,y,L(z * u,w,v5)) = a(x,y,L(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(5545(a,1),27299(a,1,3))].">
      <j1 rule="para" parents="5545 27299"/>
    </justification>
  </clause>

  <clause id="27378">
    <literal><![CDATA[
      a(x,y,R(z,u,w) \ (v5 * z)) = a(x,y,z * (R(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(25157(a,1),27307(a,1,3,1))].">
      <j1 rule="para" parents="25157 27307"/>
    </justification>
  </clause>

  <clause id="27380">
    <literal><![CDATA[
      a(x,y,T(z / u,w)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27304,a,b,27308,a)].">
      <j1 rule="hyper" parents="64 27304 27308"/>
    </justification>
  </clause>

  <clause id="27381">
    <literal><![CDATA[
      a(x \ (y / z),(y / z) \ x,z \ y) = ((y / z) / x) * (x / (y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26894,a(flip),b,27308,a),flip(a)].">
      <j1 rule="hyper" parents="64 26894 27308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27382">
    <literal><![CDATA[
      a(x,y,(1 / z) \ (u * z)) = a(x,y,u * (z * z))
    ]]></literal>
    <justification jstring="[para(808(a,1),27308(a,1,3)),flip(a)].">
      <j1 rule="para" parents="808 27308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27383">
    <literal><![CDATA[
      a(x,y,K(z,u) * (w * v5)) = a(x,y,v5 * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,27311,a),flip(a)].">
      <j1 rule="hyper" parents="373 27298 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27387">
    <literal><![CDATA[
      a(x,y,((z \ u) \ u) * w) = a(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(6025(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="6025 27311"/>
    </justification>
  </clause>

  <clause id="27388">
    <literal><![CDATA[
      a(x,y,((z \ u) \ u) \ w) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(6073(a,1),27311(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6073 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27389">
    <literal><![CDATA[
      a(x,y,(z / u) \ w) = a(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),27311(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6270 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27390">
    <literal><![CDATA[
      a(x,y,(z * z) * (u \ 1)) = a(x,y,u \ (z * z))
    ]]></literal>
    <justification jstring="[para(6629(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="6629 27311"/>
    </justification>
  </clause>

  <clause id="27391">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) * w) = a(x,y,u * ((z * z) \ w))
    ]]></literal>
    <justification jstring="[para(6024(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="6024 27311"/>
    </justification>
  </clause>

  <clause id="27392">
    <literal><![CDATA[
      a(x,y,z \ ((u * u) * w)) = a(x,y,(u * u) * (z \ w))
    ]]></literal>
    <justification jstring="[para(6626(a,1),27311(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6626 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27393">
    <literal><![CDATA[
      a(x,y,(K(z,u) * w) * v5) = a(x,y,w * v5)
    ]]></literal>
    <justification jstring="[para(7760(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="7760 27311"/>
    </justification>
  </clause>

  <clause id="27394">
    <literal><![CDATA[
      a(x,y,(z * u) \ w) = a(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[para(10833(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="10833 27311"/>
    </justification>
  </clause>

  <clause id="27395">
    <literal><![CDATA[
      a(x,y,(z * u) * w) = a(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[para(10834(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="10834 27311"/>
    </justification>
  </clause>

  <clause id="27396">
    <literal><![CDATA[
      a(x,y,((z \ u) * z) \ w) = a(x,y,u \ w)
    ]]></literal>
    <justification jstring="[para(10843(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="10843 27311"/>
    </justification>
  </clause>

  <clause id="27397">
    <literal><![CDATA[
      a(x,y,((z \ u) * z) * w) = a(x,y,u * w)
    ]]></literal>
    <justification jstring="[para(10858(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="10858 27311"/>
    </justification>
  </clause>

  <clause id="27398">
    <literal><![CDATA[
      a(x,y,(T(z,u) * w) * v5) = a(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[para(15613(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="15613 27311"/>
    </justification>
  </clause>

  <clause id="27400">
    <literal><![CDATA[
      a(x,y,(z * K(u,w)) \ v5) = a(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(23272(a,2),27311(a,1,3))].">
      <j1 rule="para" parents="23272 27311"/>
    </justification>
  </clause>

  <clause id="27401">
    <literal><![CDATA[
      a(x,y,(T(z,u) \ w) * v5) = a(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[para(24347(a,1),27311(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24347 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27402">
    <literal><![CDATA[
      a(x,y,(T(z,u) / w) * v5) = a(x,y,(z / w) * v5)
    ]]></literal>
    <justification jstring="[para(24364(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="24364 27311"/>
    </justification>
  </clause>

  <clause id="27403">
    <literal><![CDATA[
      a(x,y,(K(z,u) * w) \ v5) = a(x,y,w \ v5)
    ]]></literal>
    <justification jstring="[para(24391(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="24391 27311"/>
    </justification>
  </clause>

  <clause id="27404">
    <literal><![CDATA[
      a(x,y,(z * T(u,w)) \ v5) = a(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(24506(a,1),27311(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24506 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27405">
    <literal><![CDATA[
      a(x,y,(z \ T(u,w)) \ v5) = a(x,y,(z \ u) \ v5)
    ]]></literal>
    <justification jstring="[para(24519(a,1),27311(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24519 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27406">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * v5) = a(x,y,((u * z) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(23247(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="23247 27311"/>
    </justification>
  </clause>

  <clause id="27407">
    <literal><![CDATA[
      a(x,y,(z * T(u,w)) * v5) = a(x,y,(z * u) * v5)
    ]]></literal>
    <justification jstring="[para(24355(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="24355 27311"/>
    </justification>
  </clause>

  <clause id="27408">
    <literal><![CDATA[
      a(x,y,R(T(z,u),w,v5) \ v6) = a(x,y,R(z,w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(24564(a,1),27311(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24564 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27409">
    <literal><![CDATA[
      a(x,y,L(T(z,u),w,v5) * v6) = a(x,y,L(z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(24680(a,1),27311(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24680 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27410">
    <literal><![CDATA[
      a(x,y,(T(z,u) \ w) \ v5) = a(x,y,(z \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(25410(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="25410 27311"/>
    </justification>
  </clause>

  <clause id="27411">
    <literal><![CDATA[
      a(x,y,((z / u) * w) * v5) = a(x,y,((u \ z) * w) * v5)
    ]]></literal>
    <justification jstring="[para(24351(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="24351 27311"/>
    </justification>
  </clause>

  <clause id="27412">
    <literal><![CDATA[
      a(x,y,((z / u) \ w) * v5) = a(x,y,((u \ z) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(24352(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="24352 27311"/>
    </justification>
  </clause>

  <clause id="27413">
    <literal><![CDATA[
      a(x,y,(((z \ u) * z) \ w) * v5) = a(x,y,(u \ w) * v5)
    ]]></literal>
    <justification jstring="[para(24359(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="24359 27311"/>
    </justification>
  </clause>

  <clause id="27414">
    <literal><![CDATA[
      a(x,y,(((z \ u) * z) * w) * v5) = a(x,y,(u * w) * v5)
    ]]></literal>
    <justification jstring="[para(24360(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="24360 27311"/>
    </justification>
  </clause>

  <clause id="27415">
    <literal><![CDATA[
      a(x,y,(z * (K(u,w) * v5)) * v6) = a(x,y,(z * v5) * v6)
    ]]></literal>
    <justification jstring="[para(24368(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="24368 27311"/>
    </justification>
  </clause>

  <clause id="27416">
    <literal><![CDATA[
      a(x,y,(((z \ u) \ u) \ w) * v5) = a(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[para(24447(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="24447 27311"/>
    </justification>
  </clause>

  <clause id="27417">
    <literal><![CDATA[
      a(x,y,(z * (u / w)) \ v5) = a(x,y,(z * (w \ u)) \ v5)
    ]]></literal>
    <justification jstring="[para(24507(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="24507 27311"/>
    </justification>
  </clause>

  <clause id="27418">
    <literal><![CDATA[
      a(x,y,(z * ((u \ w) * u)) \ v5) = a(x,y,(z * w) \ v5)
    ]]></literal>
    <justification jstring="[para(24514(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="24514 27311"/>
    </justification>
  </clause>

  <clause id="27419">
    <literal><![CDATA[
      a(x,y,(z \ (u / w)) \ v5) = a(x,y,(z \ (w \ u)) \ v5)
    ]]></literal>
    <justification jstring="[para(24522(a,1),27311(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24522 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27420">
    <literal><![CDATA[
      a(x,y,(z \ ((u \ w) \ w)) \ v5) = a(x,y,(z \ u) \ v5)
    ]]></literal>
    <justification jstring="[para(24536(a,1),27311(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24536 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27421">
    <literal><![CDATA[
      a(x,y,(z * (u \ K(w,v5))) \ v6) = a(x,y,(z * (u \ 1)) \ v6)
    ]]></literal>
    <justification jstring="[para(24886(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="24886 27311"/>
    </justification>
  </clause>

  <clause id="27422">
    <literal><![CDATA[
      a(x,y,((z * T(u,w)) \ v5) * v6) = a(x,y,((z * u) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(24968(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="24968 27311"/>
    </justification>
  </clause>

  <clause id="27423">
    <literal><![CDATA[
      a(x,y,(z * (K(u,w) * v5)) \ v6) = a(x,y,(z * v5) \ v6)
    ]]></literal>
    <justification jstring="[para(25411(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="25411 27311"/>
    </justification>
  </clause>

  <clause id="27424">
    <literal><![CDATA[
      a(x,y,(z \ (K(u,w) * v5)) \ v6) = a(x,y,(z \ v5) \ v6)
    ]]></literal>
    <justification jstring="[para(25412(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="25412 27311"/>
    </justification>
  </clause>

  <clause id="27425">
    <literal><![CDATA[
      a(x,y,L(K(z,u) * w,v5,v6)) = a(x,y,L(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(26085(a,2),27311(a,1,3))].">
      <j1 rule="para" parents="26085 27311"/>
    </justification>
  </clause>

  <clause id="27426">
    <literal><![CDATA[
      a(x,y,L(T(z,u) * w,v5,v6)) = a(x,y,L(z * w,v5,v6))
    ]]></literal>
    <justification jstring="[para(26086(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="26086 27311"/>
    </justification>
  </clause>

  <clause id="27427">
    <literal><![CDATA[
      a(x,y,L(T(z,u) \ w,v5,v6)) = a(x,y,L(z \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(26100(a,1),27311(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26100 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27428">
    <literal><![CDATA[
      a(x,y,(R(T(z,u),w,v5) * v6) * v7) = a(x,y,(R(z,w,v5) * v6) * v7)
    ]]></literal>
    <justification jstring="[para(25347(a,1),27311(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25347 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27429">
    <literal><![CDATA[
      a(x,y,L(z / u,w,v5) * v6) = a(x,y,L(u \ z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(25447(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="25447 27311"/>
    </justification>
  </clause>

  <clause id="27430">
    <literal><![CDATA[
      a(x,y,R(z / u,w,v5) \ v6) = a(x,y,R(u \ z,w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(25674(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="25674 27311"/>
    </justification>
  </clause>

  <clause id="27431">
    <literal><![CDATA[
      a(x,y,L(z / u,w,v5) \ v6) = a(x,y,L(u \ z,w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(26119(a,1),27311(a,1,3))].">
      <j1 rule="para" parents="26119 27311"/>
    </justification>
  </clause>

  <clause id="27432">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((u * w) * z)) = a(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(27292(a,2),27311(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27292 27311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27433">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ (w * w))) = a(x,y,z \ ((w * w) * u))
    ]]></literal>
    <justification jstring="[para(558(a,1),27301(a,1,3,2))].">
      <j1 rule="para" parents="558 27301"/>
    </justification>
  </clause>

  <clause id="27434">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ (w * u))) = a(x,y,z \ (w * ((1 / u) \ u)))
    ]]></literal>
    <justification jstring="[para(1593(a,1),27301(a,1,3,2))].">
      <j1 rule="para" parents="1593 27301"/>
    </justification>
  </clause>

  <clause id="27435">
    <literal><![CDATA[
      a(x,y,z \ ((u \ w) / w)) = a(x,y,z \ ((u * w) \ w))
    ]]></literal>
    <justification jstring="[para(5144(a,1),27301(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5144 27301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27436">
    <literal><![CDATA[
      a(x,y,z \ (u * ((u \ 1) \ w))) = a(x,y,z \ (w * ((1 / u) \ u)))
    ]]></literal>
    <justification jstring="[para(14955(a,1),27301(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="14955 27301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27437">
    <literal><![CDATA[
      a(x,y,z \ (T(u * w,u) * (v5 * v5))) = a(x,y,z \ (u * ((v5 * v5) * w)))
    ]]></literal>
    <justification jstring="[para(17283(a,1),27301(a,1,3,2))].">
      <j1 rule="para" parents="17283 27301"/>
    </justification>
  </clause>

  <clause id="27438">
    <literal><![CDATA[
      a(x,y,z * T(u,w)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,27309,a),flip(a)].">
      <j1 rule="hyper" parents="373 27298 27309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27439">
    <literal><![CDATA[
      a(x,y,z * (u \ R(w,u,u))) = a(x,y,z * (w * (1 / u)))
    ]]></literal>
    <justification jstring="[para(1406(a,1),27309(a,1,3,2))].">
      <j1 rule="para" parents="1406 27309"/>
    </justification>
  </clause>

  <clause id="27440">
    <literal><![CDATA[
      a(x,y,z * (((1 / u) * w) * u)) = a(x,y,z * R(w,u,u))
    ]]></literal>
    <justification jstring="[para(3883(a,1),27309(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3883 27309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27441">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) / w)) = a(x,y,z * ((u * w) \ w))
    ]]></literal>
    <justification jstring="[para(5144(a,1),27309(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5144 27309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27443">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (z \ u)) = a(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[para(1132(a,1),27316(a,1,3))].">
      <j1 rule="para" parents="1132 27316"/>
    </justification>
  </clause>

  <clause id="27444">
    <literal><![CDATA[
      a(x,y,((z * z) \ (u / w)) \ v5) = a(x,y,(w \ ((z * z) \ u)) \ v5)
    ]]></literal>
    <justification jstring="[para(932(a,1),27316(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="932 27316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27445">
    <literal><![CDATA[
      a(x,y,(z * z) \ (u \ w)) = a(x,y,u \ ((z * z) \ w))
    ]]></literal>
    <justification jstring="[para(1452(a,1),27316(a,1,3))].">
      <j1 rule="para" parents="1452 27316"/>
    </justification>
  </clause>

  <clause id="27446">
    <literal><![CDATA[
      a(x,y,(z * z) \ (u \ (z * w))) = a(x,y,u \ ((1 / z) * w))
    ]]></literal>
    <justification jstring="[para(1528(a,1),27316(a,1,3))].">
      <j1 rule="para" parents="1528 27316"/>
    </justification>
  </clause>

  <clause id="27447">
    <literal><![CDATA[
      a(x,y,(((1 / z) * u) * z) \ w) = a(x,y,R(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(3883(a,1),27316(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="3883 27316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27448">
    <literal><![CDATA[
      a(x,y,(R(z,u,u) / (1 / u)) \ w) = a(x,y,(u * T(z,u \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(3875(a,1),27316(a,1,3,1))].">
      <j1 rule="para" parents="3875 27316"/>
    </justification>
  </clause>

  <clause id="27449">
    <literal><![CDATA[
      a(x,y,((z * z) \ T(u * w,u)) \ v5) = a(x,y,(u * ((z * z) \ w)) \ v5)
    ]]></literal>
    <justification jstring="[para(4859(a,1),27316(a,1,3,1))].">
      <j1 rule="para" parents="4859 27316"/>
    </justification>
  </clause>

  <clause id="27450">
    <literal><![CDATA[
      a(x,y,((z \ u) / u) \ w) = a(x,y,((z * u) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(5144(a,1),27316(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5144 27316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27451">
    <literal><![CDATA[
      a(x,y,z \ (u * (z * z))) = a(x,y,L(z,z,u) * u)
    ]]></literal>
    <justification jstring="[para(2848(a,1),27360(a,1,3))].">
      <j1 rule="para" parents="2848 27360"/>
    </justification>
  </clause>

  <clause id="27453">
    <literal><![CDATA[
      a(x,y,z * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u * z) = w
    ]]></literal>
    <justification jstring="[para(27360(a,1),16107(a,1))].">
      <j1 rule="para" parents="27360 16107"/>
    </justification>
  </clause>

  <clause id="27454">
    <literal><![CDATA[
      a(x,y,K(z,u) * (w * R(z,v5,v6))) = a(x,y,R(T(z,u),v5,v6) * w)
    ]]></literal>
    <justification jstring="[para(25378(a,1),27360(a,1,3))].">
      <j1 rule="para" parents="25378 27360"/>
    </justification>
  </clause>

  <clause id="27455">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z * w) * u)) = a(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[para(1039(a,2),27380(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1039 27380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27456">
    <literal><![CDATA[
      a(x,y,(1 / z) * (u * u)) = a(x,y,z \ (u * u))
    ]]></literal>
    <justification jstring="[para(829(a,1),27380(a,1,3))].">
      <j1 rule="para" parents="829 27380"/>
    </justification>
  </clause>

  <clause id="27457">
    <literal><![CDATA[
      a(x,y,(z * u) \ u) = a(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[para(5144(a,1),27380(a,1,3))].">
      <j1 rule="para" parents="5144 27380"/>
    </justification>
  </clause>

  <clause id="27458">
    <literal><![CDATA[
      a(x,y,(z / u) * w) = a(x,y,w * (u \ z))
    ]]></literal>
    <justification jstring="[para(117(a,1),27438(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="117 27438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27459">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ w)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(116(a,1),27438(a,1,3,2))].">
      <j1 rule="para" parents="116 27438"/>
    </justification>
  </clause>

  <clause id="27460">
    <literal><![CDATA[
      a(x,y,(z \ u) * w) = a(x,y,w * (u / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,27310,a)].">
      <j1 rule="hyper" parents="373 27298 27310"/>
    </justification>
  </clause>

  <clause id="27461">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ (w \ 1))) = a(x,y,z * ((w \ 1) * (w \ u)))
    ]]></literal>
    <justification jstring="[para(1218(a,1),27310(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="1218 27310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27462">
    <literal><![CDATA[
      a(x,y,(z * u) * w) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(27453,a,27315,a)].">
      <j1 rule="hyper" parents="27453 27315"/>
    </justification>
  </clause>

  <clause id="27463">
    <literal><![CDATA[
      a(x,y,(z * u) * T(w,v5)) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27438,a,b,27315,a)].">
      <j1 rule="hyper" parents="373 27438 27315"/>
    </justification>
  </clause>

  <clause id="27464">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (u * z)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,13880,a(flip),b,27315,a),flip(a)].">
      <j1 rule="hyper" parents="373 13880 27315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27465">
    <literal><![CDATA[
      a(x,y,(z * z) * (u * (1 / w))) = a(x,y,((z * z) / w) * u)
    ]]></literal>
    <justification jstring="[para(556(a,1),27315(a,1,3)),flip(a)].">
      <j1 rule="para" parents="556 27315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27466">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u) \ 1) = a(x,y,(u \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5344,a,b,27317,a)].">
      <j1 rule="hyper" parents="64 5344 27317"/>
    </justification>
  </clause>

  <clause id="27467">
    <literal><![CDATA[
      a(x,y,(z * K(u,w)) * v5) = a(x,y,v5 * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,27318,a),flip(a)].">
      <j1 rule="hyper" parents="373 27298 27318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27468">
    <literal><![CDATA[
      a(x,y,(z \ T(u,w)) * v5) = a(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[para(2433(a,1),27318(a,1,3,1))].">
      <j1 rule="para" parents="2433 27318"/>
    </justification>
  </clause>

  <clause id="27469">
    <literal><![CDATA[
      a(x,y,(z * (u / w)) * v5) = a(x,y,(z * (w \ u)) * v5)
    ]]></literal>
    <justification jstring="[para(6471(a,1),27318(a,1,3,1))].">
      <j1 rule="para" parents="6471 27318"/>
    </justification>
  </clause>

  <clause id="27470">
    <literal><![CDATA[
      a(x,y,(z \ (u / w)) * v5) = a(x,y,(z \ (w \ u)) * v5)
    ]]></literal>
    <justification jstring="[para(15028(a,1),27318(a,1,3,1))].">
      <j1 rule="para" parents="15028 27318"/>
    </justification>
  </clause>

  <clause id="27471">
    <literal><![CDATA[
      a(x,y,(z \ ((u \ w) \ w)) * v5) = a(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[para(15035(a,2),27318(a,1,3,1))].">
      <j1 rule="para" parents="15035 27318"/>
    </justification>
  </clause>

  <clause id="27472">
    <literal><![CDATA[
      a(x,y,(z \ (K(u,w) * v5)) * v6) = a(x,y,(z \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(23401(a,1),27318(a,1,3,1))].">
      <j1 rule="para" parents="23401 27318"/>
    </justification>
  </clause>

  <clause id="27473">
    <literal><![CDATA[
      a(x,y,z * (T(u,w) * v5)) = a(x,y,z * (u * v5))
    ]]></literal>
    <justification jstring="[para(24461(a,1),27318(a,1,3))].">
      <j1 rule="para" parents="24461 27318"/>
    </justification>
  </clause>

  <clause id="27474">
    <literal><![CDATA[
      a(x,y,z * (T(u,w) \ v5)) = a(x,y,z * (u \ v5))
    ]]></literal>
    <justification jstring="[para(24464(a,1),27318(a,1,3))].">
      <j1 rule="para" parents="24464 27318"/>
    </justification>
  </clause>

  <clause id="27475">
    <literal><![CDATA[
      a(x,y,(z \ (u * (w / v5))) * v6) = a(x,y,(z \ (u * (v5 \ w))) * v6)
    ]]></literal>
    <justification jstring="[para(24314(a,1),27318(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="24314 27318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27476">
    <literal><![CDATA[
      a(x,y,((z \ u) * z) * w) = a(x,y,w * u)
    ]]></literal>
    <justification jstring="[hyper(27453,a,27319,a)].">
      <j1 rule="hyper" parents="27453 27319"/>
    </justification>
  </clause>

  <clause id="27477">
    <literal><![CDATA[
      a(x,y,z * (u \ T(w,v5))) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[para(2433(a,1),27320(a,1,3,2))].">
      <j1 rule="para" parents="2433 27320"/>
    </justification>
  </clause>

  <clause id="27478">
    <literal><![CDATA[
      a(x,y,z * (u * (w / v5))) = a(x,y,z * (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(6471(a,1),27320(a,1,3,2))].">
      <j1 rule="para" parents="6471 27320"/>
    </justification>
  </clause>

  <clause id="27480">
    <literal><![CDATA[
      a(x,y,z * ((u / w) * v5)) = a(x,y,z * ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(8651(a,1),27320(a,1,3,2))].">
      <j1 rule="para" parents="8651 27320"/>
    </justification>
  </clause>

  <clause id="27481">
    <literal><![CDATA[
      a(x,y,z * (u \ R(T(w,v5),v6,v7))) = a(x,y,z * (u \ R(w,v6,v7)))
    ]]></literal>
    <justification jstring="[para(7270(a,1),27320(a,1,3,2))].">
      <j1 rule="para" parents="7270 27320"/>
    </justification>
  </clause>

  <clause id="27482">
    <literal><![CDATA[
      a(x,y,z * (u \ (w / v5))) = a(x,y,z * (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(15028(a,1),27320(a,1,3,2))].">
      <j1 rule="para" parents="15028 27320"/>
    </justification>
  </clause>

  <clause id="27483">
    <literal><![CDATA[
      a(x,y,z * (u * (K(w,v5) * v6))) = a(x,y,z * (u * v6))
    ]]></literal>
    <justification jstring="[para(23252(a,1),27320(a,1,3,2))].">
      <j1 rule="para" parents="23252 27320"/>
    </justification>
  </clause>

  <clause id="27484">
    <literal><![CDATA[
      a(x,y,z * (u \ (K(w,v5) * v6))) = a(x,y,z * (u \ v6))
    ]]></literal>
    <justification jstring="[para(23401(a,1),27320(a,1,3,2))].">
      <j1 rule="para" parents="23401 27320"/>
    </justification>
  </clause>

  <clause id="27485">
    <literal><![CDATA[
      a(x,y,z * (u \ (w * (v5 / v6)))) = a(x,y,z * (u \ (w * (v6 \ v5))))
    ]]></literal>
    <justification jstring="[para(24314(a,1),27320(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="24314 27320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27486">
    <literal><![CDATA[
      a(x,y,z * (u * L(T(w,v5),v6,v7))) = a(x,y,z * (u * L(w,v6,v7)))
    ]]></literal>
    <justification jstring="[para(25231(a,1),27320(a,1,3,2))].">
      <j1 rule="para" parents="25231 27320"/>
    </justification>
  </clause>

  <clause id="27487">
    <literal><![CDATA[
      a(x,y,(z / u) / w) = a(x,y,w \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27308,a,b,27322,a)].">
      <j1 rule="hyper" parents="64 27308 27322"/>
    </justification>
  </clause>

  <clause id="27488">
    <literal><![CDATA[
      a(x,y,z \ (((u \ w) / w) \ 1)) = a(x,y,z \ ((w / (u * w)) \ 1))
    ]]></literal>
    <justification jstring="[para(2032(a,1),27322(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2032 27322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27489">
    <literal><![CDATA[
      a(x,y,z \ (u * (R(w,v5,w) * v6))) = a(x,y,z \ ((w * v6) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13873,a(flip),b,27325,a),flip(a)].">
      <j1 rule="hyper" parents="373 13873 27325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27490">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((w \ u) * (z * w))) = a(x,y,a(z,w,w \ u))
    ]]></literal>
    <justification jstring="[para(89(a,1),27325(a,1,3)),flip(a)].">
      <j1 rule="para" parents="89 27325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27491">
    <literal><![CDATA[
      a(x,y,z \ (T(u,w) \ v5)) = a(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(7948(a,1),27327(a,1,3,2))].">
      <j1 rule="para" parents="7948 27327"/>
    </justification>
  </clause>

  <clause id="27492">
    <literal><![CDATA[
      a(x,y,z \ ((u / w) * v5)) = a(x,y,z \ ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(8651(a,1),27327(a,1,3,2))].">
      <j1 rule="para" parents="8651 27327"/>
    </justification>
  </clause>

  <clause id="27493">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * v5))) = a(x,y,z \ (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[para(14934(a,1),27327(a,1,3,2))].">
      <j1 rule="para" parents="14934 27327"/>
    </justification>
  </clause>

  <clause id="27494">
    <literal><![CDATA[
      a(x,y,z \ (u * (K(w,v5) * v6))) = a(x,y,z \ (u * v6))
    ]]></literal>
    <justification jstring="[para(23252(a,1),27327(a,1,3,2))].">
      <j1 rule="para" parents="23252 27327"/>
    </justification>
  </clause>

  <clause id="27495">
    <literal><![CDATA[
      a(x,y,z \ (u \ (T(w,v5) * v6))) = a(x,y,z \ (u \ (w * v6)))
    ]]></literal>
    <justification jstring="[para(24312(a,1),27327(a,1,3,2))].">
      <j1 rule="para" parents="24312 27327"/>
    </justification>
  </clause>

  <clause id="27497">
    <literal><![CDATA[
      a(x,y,L(L(T(z,u),w,v5),v6,v7)) = a(x,y,L(L(z,w,v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(25(a,2),27328(a,1,3,1))].">
      <j1 rule="para" parents="25 27328"/>
    </justification>
  </clause>

  <clause id="27498">
    <literal><![CDATA[
      a(x,y,L(z,z \ u,w)) = a(x,y,(w * (z \ u)) \ (w * u))
    ]]></literal>
    <justification jstring="[para(409(a,1),27328(a,1,3)),flip(a)].">
      <j1 rule="para" parents="409 27328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27499">
    <literal><![CDATA[
      a(x,y,(K(z,u) * w) * v5) = a(x,y,v5 * w)
    ]]></literal>
    <justification jstring="[hyper(27453,a,27330,a)].">
      <j1 rule="hyper" parents="27453 27330"/>
    </justification>
  </clause>

  <clause id="27500">
    <literal><![CDATA[
      a(x,y,z * ((u / w) \ v5)) = a(x,y,z * ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(6270(a,1),27330(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6270 27330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27501">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * (w \ 1))) = a(x,y,z * (w \ (u * u)))
    ]]></literal>
    <justification jstring="[para(6629(a,1),27330(a,1,3,2))].">
      <j1 rule="para" parents="6629 27330"/>
    </justification>
  </clause>

  <clause id="27502">
    <literal><![CDATA[
      a(x,y,(z * z) * (u * w)) = a(x,y,u * ((z * z) * w))
    ]]></literal>
    <justification jstring="[para(6650(a,1),27330(a,1,3))].">
      <j1 rule="para" parents="6650 27330"/>
    </justification>
  </clause>

  <clause id="27503">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ v5)) = a(x,y,z * ((w * u) \ v5))
    ]]></literal>
    <justification jstring="[para(10833(a,1),27330(a,1,3,2))].">
      <j1 rule="para" parents="10833 27330"/>
    </justification>
  </clause>

  <clause id="27504">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) * u) \ v5)) = a(x,y,z * (w \ v5))
    ]]></literal>
    <justification jstring="[para(10843(a,1),27330(a,1,3,2))].">
      <j1 rule="para" parents="10843 27330"/>
    </justification>
  </clause>

  <clause id="27505">
    <literal><![CDATA[
      a(x,y,z * ((u * T(w,v5)) \ v6)) = a(x,y,z * ((u * w) \ v6))
    ]]></literal>
    <justification jstring="[para(24506(a,1),27330(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="24506 27330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27506">
    <literal><![CDATA[
      a(x,y,z * (L(T(u,w),v5,v6) \ v7)) = a(x,y,z * (L(u,v5,v6) \ v7))
    ]]></literal>
    <justification jstring="[para(24557(a,1),27330(a,1,3,2))].">
      <j1 rule="para" parents="24557 27330"/>
    </justification>
  </clause>

  <clause id="27507">
    <literal><![CDATA[
      a(x,y,z * (R(T(u,w),v5,v6) \ v7)) = a(x,y,z * (R(u,v5,v6) \ v7))
    ]]></literal>
    <justification jstring="[para(24564(a,1),27330(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="24564 27330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27508">
    <literal><![CDATA[
      a(x,y,z * (((u * w) \ w) \ v5)) = a(x,y,z * (((w * u) \ w) \ v5))
    ]]></literal>
    <justification jstring="[para(24975(a,1),27330(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="24975 27330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27509">
    <literal><![CDATA[
      a(x,y,z * (((u / w) * v5) * v6)) = a(x,y,z * (((w \ u) * v5) * v6))
    ]]></literal>
    <justification jstring="[para(24351(a,1),27330(a,1,3,2))].">
      <j1 rule="para" parents="24351 27330"/>
    </justification>
  </clause>

  <clause id="27510">
    <literal><![CDATA[
      a(x,y,z \ (((u \ w) \ w) \ v5)) = a(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(6073(a,1),27331(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6073 27331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27511">
    <literal><![CDATA[
      a(x,y,z \ ((u / w) \ v5)) = a(x,y,z \ ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(6270(a,1),27331(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6270 27331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27512">
    <literal><![CDATA[
      a(x,y,z \ (R(T(u,w),v5,v6) * v7)) = a(x,y,z \ (R(u,v5,v6) * v7))
    ]]></literal>
    <justification jstring="[para(6028(a,1),27331(a,1,3,2))].">
      <j1 rule="para" parents="6028 27331"/>
    </justification>
  </clause>

  <clause id="27513">
    <literal><![CDATA[
      a(x,y,(T(z,u) * w) \ v5) = a(x,y,(z * w) \ v5)
    ]]></literal>
    <justification jstring="[para(24191(a,1),27331(a,1,3))].">
      <j1 rule="para" parents="24191 27331"/>
    </justification>
  </clause>

  <clause id="27514">
    <literal><![CDATA[
      a(x,y,z \ ((T(u,w) \ v5) * v6)) = a(x,y,z \ ((u \ v5) * v6))
    ]]></literal>
    <justification jstring="[para(24347(a,1),27331(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="24347 27331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27515">
    <literal><![CDATA[
      a(x,y,z \ (L(T(u,w),v5,v6) * v7)) = a(x,y,z \ (L(u,v5,v6) * v7))
    ]]></literal>
    <justification jstring="[para(24680(a,1),27331(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="24680 27331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27516">
    <literal><![CDATA[
      a(x,y,z \ ((T(u,w) \ v5) \ v6)) = a(x,y,z \ ((u \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(25410(a,1),27331(a,1,3,2))].">
      <j1 rule="para" parents="25410 27331"/>
    </justification>
  </clause>

  <clause id="27517">
    <literal><![CDATA[
      a(x,y,z \ (((u / w) * v5) * v6)) = a(x,y,z \ (((w \ u) * v5) * v6))
    ]]></literal>
    <justification jstring="[para(24351(a,1),27331(a,1,3,2))].">
      <j1 rule="para" parents="24351 27331"/>
    </justification>
  </clause>

  <clause id="27518">
    <literal><![CDATA[
      a(x,y,z \ ((((u \ w) * u) \ v5) * v6)) = a(x,y,z \ ((w \ v5) * v6))
    ]]></literal>
    <justification jstring="[para(24359(a,1),27331(a,1,3,2))].">
      <j1 rule="para" parents="24359 27331"/>
    </justification>
  </clause>

  <clause id="27519">
    <literal><![CDATA[
      a(x,y,((z / u) * w) \ v5) = a(x,y,((u \ z) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(24400(a,1),27331(a,1,3))].">
      <j1 rule="para" parents="24400 27331"/>
    </justification>
  </clause>

  <clause id="27520">
    <literal><![CDATA[
      a(x,y,((z / u) \ w) \ v5) = a(x,y,((u \ z) \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(24402(a,1),27331(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24402 27331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27521">
    <literal><![CDATA[
      a(x,y,(((z \ u) * z) \ w) \ v5) = a(x,y,(u \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(24405(a,1),27331(a,1,3))].">
      <j1 rule="para" parents="24405 27331"/>
    </justification>
  </clause>

  <clause id="27522">
    <literal><![CDATA[
      a(x,y,(((z \ u) \ u) \ w) \ v5) = a(x,y,(z \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(24419(a,2),27331(a,1,3))].">
      <j1 rule="para" parents="24419 27331"/>
    </justification>
  </clause>

  <clause id="27523">
    <literal><![CDATA[
      a(x,y,((z * T(u,w)) \ v5) \ v6) = a(x,y,((z * u) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[para(24967(a,1),27331(a,1,3))].">
      <j1 rule="para" parents="24967 27331"/>
    </justification>
  </clause>

  <clause id="27524">
    <literal><![CDATA[
      a(x,y,((z \ T(u,w)) \ v5) \ v6) = a(x,y,((z \ u) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[para(24978(a,1),27331(a,1,3))].">
      <j1 rule="para" parents="24978 27331"/>
    </justification>
  </clause>

  <clause id="27525">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ z) = a(x,y,z * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27360,a(flip),b,27355,a),flip(a)].">
      <j1 rule="hyper" parents="64 27360 27355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27527">
    <literal><![CDATA[
      a(x,y,(a(z,u,w * v5) \ v6) \ v6) = a(x,y,a(z,u,v5 * w))
    ]]></literal>
    <justification jstring="[para(27366(a,1),27307(a,1,3,1))].">
      <j1 rule="para" parents="27366 27307"/>
    </justification>
  </clause>

  <clause id="27528">
    <literal><![CDATA[
      a(x,y,((z \ u) \ u) * w) = a(x,y,w * z)
    ]]></literal>
    <justification jstring="[para(6025(a,1),27383(a,1,3))].">
      <j1 rule="para" parents="6025 27383"/>
    </justification>
  </clause>

  <clause id="27529">
    <literal><![CDATA[
      a(x,y,R(T(z,u),w,v5) * v6) = a(x,y,v6 * R(z,w,v5))
    ]]></literal>
    <justification jstring="[para(6028(a,1),27383(a,1,3))].">
      <j1 rule="para" parents="6028 27383"/>
    </justification>
  </clause>

  <clause id="27530">
    <literal><![CDATA[
      a(x,y,(T(z,u) * w) * v5) = a(x,y,v5 * (z * w))
    ]]></literal>
    <justification jstring="[para(15613(a,1),27383(a,1,3))].">
      <j1 rule="para" parents="15613 27383"/>
    </justification>
  </clause>

  <clause id="27531">
    <literal><![CDATA[
      a(x,y,z * (T(u,w) \ v5)) = a(x,y,(u \ v5) * z)
    ]]></literal>
    <justification jstring="[para(24347(a,1),27383(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24347 27383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27532">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * v5) = a(x,y,v5 * ((u * z) \ w))
    ]]></literal>
    <justification jstring="[para(23247(a,1),27383(a,1,3))].">
      <j1 rule="para" parents="23247 27383"/>
    </justification>
  </clause>

  <clause id="27533">
    <literal><![CDATA[
      a(x,y,(z * T(u,w)) * v5) = a(x,y,v5 * (z * u))
    ]]></literal>
    <justification jstring="[para(24355(a,1),27383(a,1,3))].">
      <j1 rule="para" parents="24355 27383"/>
    </justification>
  </clause>

  <clause id="27534">
    <literal><![CDATA[
      a(x,y,((z / u) * w) * v5) = a(x,y,v5 * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(24351(a,1),27383(a,1,3))].">
      <j1 rule="para" parents="24351 27383"/>
    </justification>
  </clause>

  <clause id="27535">
    <literal><![CDATA[
      a(x,y,(z * (K(u,w) * v5)) * v6) = a(x,y,v6 * (z * v5))
    ]]></literal>
    <justification jstring="[para(24368(a,1),27383(a,1,3))].">
      <j1 rule="para" parents="24368 27383"/>
    </justification>
  </clause>

  <clause id="27536">
    <literal><![CDATA[
      a(x,y,L(z * u,w,v5) * v6) = a(x,y,v6 * L(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(26140(a,1),27383(a,1,3))].">
      <j1 rule="para" parents="26140 27383"/>
    </justification>
  </clause>

  <clause id="27537">
    <literal><![CDATA[
      a(x,y,(L(T(z,u),w,v5) \ v6) * v7) = a(x,y,v7 * (L(z,w,v5) \ v6))
    ]]></literal>
    <justification jstring="[para(25426(a,1),27383(a,1,3))].">
      <j1 rule="para" parents="25426 27383"/>
    </justification>
  </clause>

  <clause id="27538">
    <literal><![CDATA[
      a(x,y,(z / u) \ (w * v5)) = a(x,y,(u \ z) \ (v5 * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27325,a,b,27389,a),flip(a)].">
      <j1 rule="hyper" parents="373 27325 27389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27539">
    <literal><![CDATA[
      a(x,y,K(z,u) * ((w / v5) \ v6)) = a(x,y,(v5 \ w) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,27311,a,b,27389,a)].">
      <j1 rule="hyper" parents="64 27311 27389"/>
    </justification>
  </clause>

  <clause id="27540">
    <literal><![CDATA[
      a(x,y,(z \ u) \ z) = a(x,y,(z / u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5346,a(flip),b,27389,a),flip(a)].">
      <j1 rule="hyper" parents="64 5346 27389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27541">
    <literal><![CDATA[
      a(x,y,((z * z) \ u) \ w) = a(x,y,(z * z) * (u \ w))
    ]]></literal>
    <justification jstring="[para(890(a,1),27389(a,1,3)),flip(a)].">
      <j1 rule="para" parents="890 27389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27542">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ (u * u)) \ w) = a(x,y,z \ ((u * u) \ w))
    ]]></literal>
    <justification jstring="[para(880(a,1),27389(a,1,3)),flip(a)].">
      <j1 rule="para" parents="880 27389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27543">
    <literal><![CDATA[
      a(x,y,(L(z,u,z) \ u) \ w) = a(x,y,((u / (u * z)) * u) \ w)
    ]]></literal>
    <justification jstring="[para(5151(a,1),27389(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5151 27389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27544">
    <literal><![CDATA[
      a(x,y,(((z * u) \ w) * v5) * v6) = a(x,y,(((u * z) \ w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(23247(a,1),27393(a,1,3,1))].">
      <j1 rule="para" parents="23247 27393"/>
    </justification>
  </clause>

  <clause id="27545">
    <literal><![CDATA[
      a(x,y,((T(z,u) \ w) \ v5) * v6) = a(x,y,((z \ w) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(25410(a,1),27393(a,1,3,1))].">
      <j1 rule="para" parents="25410 27393"/>
    </justification>
  </clause>

  <clause id="27546">
    <literal><![CDATA[
      a(x,y,(((z / u) * w) * v5) * v6) = a(x,y,(((u \ z) * w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(24351(a,1),27393(a,1,3,1))].">
      <j1 rule="para" parents="24351 27393"/>
    </justification>
  </clause>

  <clause id="27547">
    <literal><![CDATA[
      a(x,y,(((z / u) / w) * v5) * v6) = a(x,y,(((u \ z) / w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(24363(a,1),27393(a,1,3,1))].">
      <j1 rule="para" parents="24363 27393"/>
    </justification>
  </clause>

  <clause id="27548">
    <literal><![CDATA[
      a(x,y,((z * (u / w)) \ v5) * v6) = a(x,y,((z * (w \ u)) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(24507(a,1),27393(a,1,3,1))].">
      <j1 rule="para" parents="24507 27393"/>
    </justification>
  </clause>

  <clause id="27549">
    <literal><![CDATA[
      a(x,y,((z * u) \ ((u * w) * z)) * v5) = a(x,y,L(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[para(27292(a,2),27393(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="27292 27393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27550">
    <literal><![CDATA[
      a(x,y,(z * R(u,w,u)) \ v5) = a(x,y,(u * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,13879,a,b,27394,a)].">
      <j1 rule="hyper" parents="373 13879 27394"/>
    </justification>
  </clause>

  <clause id="27551">
    <literal><![CDATA[
      a(x,y,((z \ u) * (1 / z)) \ w) = a(x,y,((z * z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(536(a,1),27394(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="536 27394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27552">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,w)) = a(x,y,(z * w) \ (w * u))
    ]]></literal>
    <justification jstring="[para(102(a,2),27394(a,1,3))].">
      <j1 rule="para" parents="102 27394"/>
    </justification>
  </clause>

  <clause id="27553">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) \ ((u \ 1) * w)) = a(x,y,(u * z) \ (u * w))
    ]]></literal>
    <justification jstring="[para(1658(a,1),27394(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1658 27394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27554">
    <literal><![CDATA[
      a(x,y,(z * u) * (w * v5)) = a(x,y,(u * z) * (v5 * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27315,a,b,27395,a)].">
      <j1 rule="hyper" parents="373 27315 27395"/>
    </justification>
  </clause>

  <clause id="27555">
    <literal><![CDATA[
      a(x,y,(((z * z) / u) * w) * u) = a(x,y,R(w * (z * z),u,u))
    ]]></literal>
    <justification jstring="[para(1762(a,1),27395(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1762 27395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27556">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (z * u)) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(3677(a,1),27400(a,1,3,1))].">
      <j1 rule="para" parents="3677 27400"/>
    </justification>
  </clause>

  <clause id="27557">
    <literal><![CDATA[
      a(x,y,(z * (u * w)) \ v5) = a(x,y,(z * (w * u)) \ v5)
    ]]></literal>
    <justification jstring="[para(7591(a,1),27400(a,1,3,1))].">
      <j1 rule="para" parents="7591 27400"/>
    </justification>
  </clause>

  <clause id="27558">
    <literal><![CDATA[
      a(x,y,(z * ((1 / z) * u)) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(26130(a,1),27400(a,1,3,1))].">
      <j1 rule="para" parents="26130 27400"/>
    </justification>
  </clause>

  <clause id="27559">
    <literal><![CDATA[
      a(x,y,(K(z,u) * (w * v5)) \ v6) = a(x,y,(v5 * w) \ v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,27394,a,b,27403,a),flip(a)].">
      <j1 rule="hyper" parents="373 27394 27403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27560">
    <literal><![CDATA[
      a(x,y,(z \ ((z \ 1) \ (u * z))) \ w) = a(x,y,((z \ 1) \ T(u,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6297(a,1),27403(a,1,3,1))].">
      <j1 rule="para" parents="6297 27403"/>
    </justification>
  </clause>

  <clause id="27561">
    <literal><![CDATA[
      a(x,y,(((z / u) \ w) * v5) \ v6) = a(x,y,(((u \ z) \ w) * v5) \ v6)
    ]]></literal>
    <justification jstring="[para(24352(a,1),27403(a,1,3,1))].">
      <j1 rule="para" parents="24352 27403"/>
    </justification>
  </clause>

  <clause id="27562">
    <literal><![CDATA[
      a(x,y,L(T(z,u) \ w,v5,v6) \ v7) = a(x,y,L(z \ w,v5,v6) \ v7)
    ]]></literal>
    <justification jstring="[para(26100(a,1),27403(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="26100 27403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27563">
    <literal><![CDATA[
      a(x,y,((z * u) \ ((u * w) * z)) \ v5) = a(x,y,L(w,u,z) \ v5)
    ]]></literal>
    <justification jstring="[para(27292(a,2),27403(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="27292 27403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27564">
    <literal><![CDATA[
      a(x,y,(z * u) \ z) = a(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27394,a,b,27457,a)].">
      <j1 rule="hyper" parents="64 27394 27457"/>
    </justification>
  </clause>

  <clause id="27565">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,z)) = a(x,y,u * (z \ 1))
    ]]></literal>
    <justification jstring="[para(569(a,2),27458(a,1,3))].">
      <j1 rule="para" parents="569 27458"/>
    </justification>
  </clause>

  <clause id="27566">
    <literal><![CDATA[
      a(x,y,(z \ u) * (z \ 1)) = a(x,y,(z * z) \ u)
    ]]></literal>
    <justification jstring="[para(536(a,1),27458(a,1,3)),flip(a)].">
      <j1 rule="para" parents="536 27458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27567">
    <literal><![CDATA[
      a(x,y,(z * u) * (w * v5)) = a(x,y,(v5 * w) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27395,a,b,27462,a)].">
      <j1 rule="hyper" parents="373 27395 27462"/>
    </justification>
  </clause>

  <clause id="27568">
    <literal><![CDATA[
      a(x,y,(z * u) * (u \ 1)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13880,a(flip),b,27462,a),flip(a)].">
      <j1 rule="hyper" parents="373 13880 27462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27569">
    <literal><![CDATA[
      a(x,y,(a(z,u,z) * w) * v5) = a(x,y,v5 * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,13872,a(flip),b,27462,a),flip(a)].">
      <j1 rule="hyper" parents="373 13872 27462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27570">
    <literal><![CDATA[
      a(x,y,(K(z,u) * (w * v5)) * v6) = a(x,y,v6 * (v5 * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27393,a,b,27462,a)].">
      <j1 rule="hyper" parents="64 27393 27462"/>
    </justification>
  </clause>

  <clause id="27571">
    <literal><![CDATA[
      a(x,y,(z * z) * (u * w)) = a(x,y,w * (u * (z * z)))
    ]]></literal>
    <justification jstring="[para(33(a,1),27462(a,1,3))].">
      <j1 rule="para" parents="33 27462"/>
    </justification>
  </clause>

  <clause id="27572">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * (u * w)) = a(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[para(100(a,1),27462(a,1,3)),flip(a)].">
      <j1 rule="para" parents="100 27462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27573">
    <literal><![CDATA[
      a(x,y,z * (u \ T(w,v5))) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[para(7026(a,1),27467(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="7026 27467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27574">
    <literal><![CDATA[
      a(x,y,z * (u \ K(w,v5))) = a(x,y,(u \ 1) * z)
    ]]></literal>
    <justification jstring="[para(14520(a,1),27467(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="14520 27467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27575">
    <literal><![CDATA[
      a(x,y,z * (u * (w * K(v5,v6)))) = a(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[para(23051(a,1),27467(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="23051 27467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27576">
    <literal><![CDATA[
      a(x,y,L((z \ u) \ u,w,v5) * v6) = a(x,y,v6 * L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(24556(a,2),27467(a,1,3,1))].">
      <j1 rule="para" parents="24556 27467"/>
    </justification>
  </clause>

  <clause id="27577">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) \ w) \ v5)) = a(x,y,(u \ v5) * z)
    ]]></literal>
    <justification jstring="[para(6073(a,1),27499(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="6073 27499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27578">
    <literal><![CDATA[
      a(x,y,L(T(z,u) * w,v5,v6) * v7) = a(x,y,v7 * L(z * w,v5,v6))
    ]]></literal>
    <justification jstring="[para(26086(a,1),27499(a,1,3,1))].">
      <j1 rule="para" parents="26086 27499"/>
    </justification>
  </clause>

  <clause id="27579">
    <literal><![CDATA[
      a(x,y,(z \ u) \ z) = a(x,y,(u \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27317,a(flip),b,27540,a),flip(a)].">
      <j1 rule="hyper" parents="373 27317 27540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27580">
    <literal><![CDATA[
      a(x,y,L(z \ 1,z,u)) = a(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[para(241(a,2),27564(a,1,3))].">
      <j1 rule="para" parents="241 27564"/>
    </justification>
  </clause>

  <clause id="27581">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) = a(x,y,u \ ((1 / z) \ u))
    ]]></literal>
    <justification jstring="[para(11792(a,2),27564(a,1,3))].">
      <j1 rule="para" parents="11792 27564"/>
    </justification>
  </clause>

  <clause id="27583">
    <literal><![CDATA[
      a(x,y,z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(27297(a,1),616(a,1))].">
      <j1 rule="para" parents="27297 616"/>
    </justification>
  </clause>

  <clause id="27584">
    <literal><![CDATA[
      a(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(5753(a,2),27583(a,1,3))].">
      <j1 rule="para" parents="5753 27583"/>
    </justification>
  </clause>

  <clause id="27585">
    <literal><![CDATA[
      a(x,y,(z \ u) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(5752(a,2),27583(a,1,3))].">
      <j1 rule="para" parents="5752 27583"/>
    </justification>
  </clause>

  <clause id="27586">
    <literal><![CDATA[
      a(x,y,z / u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u \ z) = w
    ]]></literal>
    <justification jstring="[para(5774(a,1),27583(a,1,3))].">
      <j1 rule="para" parents="5774 27583"/>
    </justification>
  </clause>

  <clause id="27587">
    <literal><![CDATA[
      a(x,y,K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(6576(a,1),27583(a,1,3))].">
      <j1 rule="para" parents="6576 27583"/>
    </justification>
  </clause>

  <clause id="27588">
    <literal><![CDATA[
      a(x,y,T(z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ w) = v5
    ]]></literal>
    <justification jstring="[para(7948(a,1),27583(a,1,3))].">
      <j1 rule="para" parents="7948 27583"/>
    </justification>
  </clause>

  <clause id="27589">
    <literal><![CDATA[
      a(x,y,z \ (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z \ (w * u)) = v5
    ]]></literal>
    <justification jstring="[para(14934(a,1),27583(a,1,3))].">
      <j1 rule="para" parents="14934 27583"/>
    </justification>
  </clause>

  <clause id="27591">
    <literal><![CDATA[
      a(x,y,(z * u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,(u * z) \ w) = v5
    ]]></literal>
    <justification jstring="[para(10833(a,1),27587(a,1,3))].">
      <j1 rule="para" parents="10833 27587"/>
    </justification>
  </clause>

  <clause id="27594">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),u,u)) = a(x,y,((u * (z * z)) / z) * (u \ 1))
    ]]></literal>
    <justification jstring="[para(2849(a,2),27363(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2849 27363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27595">
    <literal><![CDATA[
      a(x,y,L(z * (u \ (1 / u)),u,u)) = a(x,y,(u \ 1) * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(1123(a,1),27464(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="1123 27464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27596">
    <literal><![CDATA[
      a(x,y,R(z,u,u \ 1)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[para(297(a,1),27568(a,1,3))].">
      <j1 rule="para" parents="297 27568"/>
    </justification>
  </clause>

  <clause id="27597">
    <literal><![CDATA[
      a(x,y,z * ((u \ a(w,v5,w)) \ v6)) = a(x,y,((u \ 1) \ v6) * z)
    ]]></literal>
    <justification jstring="[para(13286(a,1),27569(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="13286 27569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27598">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) = a(x,y,u \ (u / (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27322,a,b,27581,a),flip(a)].">
      <j1 rule="hyper" parents="373 27322 27581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27599">
    <literal><![CDATA[
      a(x,y,L(z,z,z * u)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[para(10992(a,1),27598(a,2,3))].">
      <j1 rule="para" parents="10992 27598"/>
    </justification>
  </clause>

  <clause id="27600">
    <literal><![CDATA[
      a(x,y,L(z,z,z \ u)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[para(11068(a,2),27598(a,2,3)),flip(a)].">
      <j1 rule="para" parents="11068 27598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27601">
    <literal><![CDATA[
      a(x,y,(z * z) * (z \ u)) = a(x,y,(1 / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27310,a(flip),b,27313,a)].">
      <j1 rule="hyper" parents="64 27310 27313"/>
    </justification>
  </clause>

  <clause id="27602">
    <literal><![CDATA[
      a(x,y,z \ (T(u,w) / v5)) = a(x,y,z \ (v5 \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27322,a,b,27332,a)].">
      <j1 rule="hyper" parents="64 27322 27332"/>
    </justification>
  </clause>

  <clause id="27603">
    <literal><![CDATA[
      a(x,y,L(z \ T(u,w),v5,v6)) = a(x,y,L(z \ u,v5,v6))
    ]]></literal>
    <justification jstring="[para(2433(a,1),27343(a,1,3,1))].">
      <j1 rule="para" parents="2433 27343"/>
    </justification>
  </clause>

  <clause id="27604">
    <literal><![CDATA[
      a(x,y,L((z \ 1) * (z * u),w,v5)) = a(x,y,L(L(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[para(3677(a,1),27343(a,1,3,1))].">
      <j1 rule="para" parents="3677 27343"/>
    </justification>
  </clause>

  <clause id="27605">
    <literal><![CDATA[
      a(x,y,L(z * (u / w),v5,v6)) = a(x,y,L(z * (w \ u),v5,v6))
    ]]></literal>
    <justification jstring="[para(6471(a,1),27343(a,1,3,1))].">
      <j1 rule="para" parents="6471 27343"/>
    </justification>
  </clause>

  <clause id="27606">
    <literal><![CDATA[
      a(x,y,L(z * (u * w),v5,v6)) = a(x,y,L(z * (w * u),v5,v6))
    ]]></literal>
    <justification jstring="[para(7591(a,1),27343(a,1,3,1))].">
      <j1 rule="para" parents="7591 27343"/>
    </justification>
  </clause>

  <clause id="27607">
    <literal><![CDATA[
      a(x,y,L((z / u) * w,v5,v6)) = a(x,y,L((u \ z) * w,v5,v6))
    ]]></literal>
    <justification jstring="[para(8651(a,1),27343(a,1,3,1))].">
      <j1 rule="para" parents="8651 27343"/>
    </justification>
  </clause>

  <clause id="27608">
    <literal><![CDATA[
      a(x,y,L(z * ((u \ w) * u),v5,v6)) = a(x,y,L(z * w,v5,v6))
    ]]></literal>
    <justification jstring="[para(10196(a,1),27343(a,1,3,1))].">
      <j1 rule="para" parents="10196 27343"/>
    </justification>
  </clause>

  <clause id="27609">
    <literal><![CDATA[
      a(x,y,L(z \ (u / w),v5,v6)) = a(x,y,L(z \ (w \ u),v5,v6))
    ]]></literal>
    <justification jstring="[para(15028(a,1),27343(a,1,3,1))].">
      <j1 rule="para" parents="15028 27343"/>
    </justification>
  </clause>

  <clause id="27610">
    <literal><![CDATA[
      a(x,y,L(z \ (u \ T(w,v5)),v6,v7)) = a(x,y,L(z \ (u \ w),v6,v7))
    ]]></literal>
    <justification jstring="[para(24309(a,1),27343(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="24309 27343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27611">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,u),w,v5)) = a(x,y,L(1 / a(u,u,z),w,v5))
    ]]></literal>
    <justification jstring="[para(5665(a,1),27344(a,2,3,1)),flip(a)].">
      <j1 rule="para" parents="5665 27344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27612">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ (u * z)) = a(x,y,u * (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27389,a(flip),b,27382,a)].">
      <j1 rule="hyper" parents="64 27389 27382"/>
    </justification>
  </clause>

  <clause id="27613">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (u * u)) = a(x,y,z \ (u * u))
    ]]></literal>
    <justification jstring="[hyper(27453,a,27390,a)].">
      <j1 rule="hyper" parents="27453 27390"/>
    </justification>
  </clause>

  <clause id="27614">
    <literal><![CDATA[
      a(x,y,(z / ((u * u) / w)) \ 1) = a(x,y,(z / (1 / w)) \ (u * u))
    ]]></literal>
    <justification jstring="[para(1235(a,1),27390(a,1,3))].">
      <j1 rule="para" parents="1235 27390"/>
    </justification>
  </clause>

  <clause id="27615">
    <literal><![CDATA[
      a(x,y,(((z \ u) / u) * w) * v5) = a(x,y,((u / (z * u)) * w) * v5)
    ]]></literal>
    <justification jstring="[para(3007(a,1),27398(a,1,3,1,1))].">
      <j1 rule="para" parents="3007 27398"/>
    </justification>
  </clause>

  <clause id="27616">
    <literal><![CDATA[
      a(x,y,(T(z,u) * w) * a(L(v5,w,z),v6,v6 \ 1)) = a(x,y,z * (w * a(v5,v6,v6 \ 1)))
    ]]></literal>
    <justification jstring="[para(4249(a,1),27398(a,2,3))].">
      <j1 rule="para" parents="4249 27398"/>
    </justification>
  </clause>

  <clause id="27617">
    <literal><![CDATA[
      a(x,y,(T(z,u) / w) * v5) = a(x,y,(w \ z) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,27317,a(flip),b,27402,a),flip(a)].">
      <j1 rule="hyper" parents="373 27317 27402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27618">
    <literal><![CDATA[
      a(x,y,((z * u) * (z \ 1)) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(5134(a,1),27404(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5134 27404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27619">
    <literal><![CDATA[
      a(x,y,(((1 / z) * u) * z) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(8887(a,1),27404(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="8887 27404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27620">
    <literal><![CDATA[
      a(x,y,((z * z) * (u * (z \ 1))) * w) = a(x,y,(L(z,z,z) * u) * w)
    ]]></literal>
    <justification jstring="[para(12005(a,1),27407(a,1,3,1))].">
      <j1 rule="para" parents="12005 27407"/>
    </justification>
  </clause>

  <clause id="27621">
    <literal><![CDATA[
      a(x,y,(z \ ((u / z) \ w)) \ v5) = a(x,y,(z \ ((z \ u) \ w)) \ v5)
    ]]></literal>
    <justification jstring="[para(5029(a,1),27410(a,1,3,1))].">
      <j1 rule="para" parents="5029 27410"/>
    </justification>
  </clause>

  <clause id="27622">
    <literal><![CDATA[
      a(x,y,(z \ (u \ 1)) \ ((u \ 1) * (u \ w))) = a(x,y,(z \ u) \ w)
    ]]></literal>
    <justification jstring="[para(18777(a,2),27410(a,1,3))].">
      <j1 rule="para" parents="18777 27410"/>
    </justification>
  </clause>

  <clause id="27623">
    <literal><![CDATA[
      (x * (y * L(z,x,y))) \ (x * (y * z)) = a(y,x,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,11331,a,b,27425,a)].">
      <j1 rule="hyper" parents="64 11331 27425"/>
    </justification>
  </clause>

  <clause id="27624">
    <literal><![CDATA[
      a(x,y,L(((z \ u) \ u) \ w,v5,v6)) = a(x,y,L(z \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(6073(a,1),27425(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="6073 27425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27625">
    <literal><![CDATA[
      a(x,y,L((z / u) \ w,v5,v6)) = a(x,y,L((u \ z) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(6270(a,1),27425(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="6270 27425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27626">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,v5,v6)) = a(x,y,L((u * z) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(10833(a,1),27425(a,1,3,1))].">
      <j1 rule="para" parents="10833 27425"/>
    </justification>
  </clause>

  <clause id="27627">
    <literal><![CDATA[
      a(x,y,L((z * T(u,w)) \ v5,v6,v7)) = a(x,y,L((z * u) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(24506(a,1),27425(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="24506 27425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27628">
    <literal><![CDATA[
      a(x,y,(z * z) \ ((z * u) * w)) = a(x,y,((z \ 1) * u) * w)
    ]]></literal>
    <justification jstring="[para(1596(a,1),27443(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1596 27443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27629">
    <literal><![CDATA[
      a(x,y,(1 / (z / u)) * (w * w)) = a(x,y,(u \ z) \ (w * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27389,a(flip),b,27456,a),flip(a)].">
      <j1 rule="hyper" parents="373 27389 27456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27630">
    <literal><![CDATA[
      a(x,y,(z \ u) * (w * v5)) = a(x,y,(v5 * w) * (z \ u))
    ]]></literal>
    <justification jstring="[para(319(a,1),27463(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="319 27463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27631">
    <literal><![CDATA[
      a(x,y,z * (((u \ w) / w) \ v5)) = a(x,y,z * (((u * w) \ w) \ v5))
    ]]></literal>
    <justification jstring="[para(5144(a,1),27474(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="5144 27474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27633">
    <literal><![CDATA[
      a(x,y,(L(z,z,z) * u) * w) = a(x,y,w * (z * u))
    ]]></literal>
    <justification jstring="[para(118(a,1),27530(a,1,3,1,1))].">
      <j1 rule="para" parents="118 27530"/>
    </justification>
  </clause>

  <clause id="27634">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) * (u \ w))) = a(x,y,((u * u) \ w) * z)
    ]]></literal>
    <justification jstring="[para(1132(a,1),27531(a,1,3,2))].">
      <j1 rule="para" parents="1132 27531"/>
    </justification>
  </clause>

  <clause id="27635">
    <literal><![CDATA[
      a(x,y,(z * z) * (z \ u)) = a(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,27389,a(flip),b,27601,a),flip(a)].">
      <j1 rule="hyper" parents="373 27389 27601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27636">
    <literal><![CDATA[
      a(x,y,(R(T(z,u),w,v5) \ 1) \ R(z,w,v5)) = a(x,y,K(z,u) * (R(z,w,v5) * R(z,w,v5)))
    ]]></literal>
    <justification jstring="[para(25430(a,1),27612(a,1,3))].">
      <j1 rule="para" parents="25430 27612"/>
    </justification>
  </clause>

  <clause id="27637">
    <literal><![CDATA[
      a(x,y,(z \ u) * (z * z)) = a(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(27453,a,27635,a)].">
      <j1 rule="hyper" parents="27453 27635"/>
    </justification>
  </clause>

  <clause id="27638">
    <literal><![CDATA[
      a(x,y,L(z,u * w,u \ w) * ((u * w) * (u \ w))) = a(x,y,(u * w) * ((u \ w) * z))
    ]]></literal>
    <justification jstring="[para(11928(a,1),27300(a,1,3,1))].">
      <j1 rule="para" parents="11928 27300"/>
    </justification>
  </clause>

  <clause id="27639">
    <literal><![CDATA[
      a(x,y,(z * u) \ ((z * w) * u)) = a(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27394,a,b,27432,a)].">
      <j1 rule="hyper" parents="64 27394 27432"/>
    </justification>
  </clause>

  <clause id="27640">
    <literal><![CDATA[
      a(x,y,R(z,u,u)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27432,a(flip),b,27455,a),flip(a)].">
      <j1 rule="hyper" parents="64 27432 27455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27641">
    <literal><![CDATA[
      a(x,y,R(z * u,w,w)) = a(x,y,L(u * z,w,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27377,a,b,27640,a),flip(a)].">
      <j1 rule="hyper" parents="373 27377 27640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27642">
    <literal><![CDATA[
      a(x,y,L((z * z) * u,z,z)) = a(x,y,(u * z) * z)
    ]]></literal>
    <justification jstring="[para(1403(a,1),27641(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1403 27641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27643">
    <literal><![CDATA[
      a(x,y,L(z,u,u * z) \ 1) = a(x,y,((u * z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),27466(a,1,3,1,1))].">
      <j1 rule="para" parents="9 27466"/>
    </justification>
  </clause>

  <clause id="27644">
    <literal><![CDATA[
      a(x,y,R(z,u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27455,a(flip),b,27639,a)].">
      <j1 rule="hyper" parents="64 27455 27639"/>
    </justification>
  </clause>

  <clause id="27645">
    <literal><![CDATA[
      a(x,y,L(z,u,L(z,w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(3183(a,1),27639(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3183 27639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27647">
    <literal><![CDATA[
      a(x,R(y,z,u),y) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,2861,a,b,27644,a)].">
      <j1 rule="hyper" parents="64 2861 27644"/>
    </justification>
  </clause>

  <clause id="27648">
    <literal><![CDATA[
      a(x,y,R(L(z,u,w),v5,v6)) = a(x,y,L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(30(a,1),27644(a,2,3))].">
      <j1 rule="para" parents="30 27644"/>
    </justification>
  </clause>

  <clause id="27650">
    <literal><![CDATA[
      ((x * (1 / y)) * R(y,z,u)) / L(y \ R(y,z,u),x,a(x,1 / y,L(y,z,u))) = a(x,1 / y,R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(27644(a,1),15717(a,1,2,3))].">
      <j1 rule="para" parents="27644 15717"/>
    </justification>
  </clause>

  <clause id="27651">
    <literal><![CDATA[
      a(x,y,L((z * z) * u,z,z)) = a(x,y,z * (z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27462,a(flip),b,27642,a),flip(a)].">
      <j1 rule="hyper" parents="373 27462 27642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27652">
    <literal><![CDATA[
      a(x,y,L((z * z) / u,z,z)) = a(x,y,((1 / u) * z) * z)
    ]]></literal>
    <justification jstring="[para(497(a,1),27642(a,1,3,1))].">
      <j1 rule="para" parents="497 27642"/>
    </justification>
  </clause>

  <clause id="27653">
    <literal><![CDATA[
      a(x,y,z * (z * (T(u,z * z) * w))) = a(x,y,L(u * ((z * z) * w),z,z))
    ]]></literal>
    <justification jstring="[para(1434(a,1),27651(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1434 27651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27654">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,z) \ w) = a(x,y,((z \ 1) * u) \ w)
    ]]></literal>
    <justification jstring="[para(569(a,2),27302(a,1,3,1))].">
      <j1 rule="para" parents="569 27302"/>
    </justification>
  </clause>

  <clause id="27655">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) \ 1) = a(x,y,(z * u) \ (z * z))
    ]]></literal>
    <justification jstring="[para(552(a,1),27302(a,1,3)),flip(a)].">
      <j1 rule="para" parents="552 27302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27656">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u)) = a(x,y,((u \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[para(917(a,2),27302(a,1,3))].">
      <j1 rule="para" parents="917 27302"/>
    </justification>
  </clause>

  <clause id="27657">
    <literal><![CDATA[
      a(x,y,L(z \ ((u * u) / w),z,(u * u) / w)) = a(x,y,(((1 / w) \ ((u * u) \ 1)) * z) \ 1)
    ]]></literal>
    <justification jstring="[para(879(a,2),27656(a,2,3,1,1))].">
      <j1 rule="para" parents="879 27656"/>
    </justification>
  </clause>

  <clause id="27658">
    <literal><![CDATA[
      a(x,y,z \ (u * (T(w,v5) \ v6))) = a(x,y,z \ (u * (w \ v6)))
    ]]></literal>
    <justification jstring="[para(7948(a,1),27334(a,1,3,2,2))].">
      <j1 rule="para" parents="7948 27334"/>
    </justification>
  </clause>

  <clause id="27659">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w / v5) \ v6))) = a(x,y,z \ (u \ ((v5 \ w) \ v6)))
    ]]></literal>
    <justification jstring="[para(6270(a,1),27340(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="6270 27340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27660">
    <literal><![CDATA[
      a(x,y,z \ ((((u \ w) \ w) \ v5) \ v6)) = a(x,y,z \ ((u \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(24419(a,2),27340(a,1,3,2))].">
      <j1 rule="para" parents="24419 27340"/>
    </justification>
  </clause>

  <clause id="27661">
    <literal><![CDATA[
      a(x,y,z * ((u * K(w,v5)) * v6)) = a(x,y,z * (v6 * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27315,a,b,27341,a)].">
      <j1 rule="hyper" parents="64 27315 27341"/>
    </justification>
  </clause>

  <clause id="27662">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ T(v5,v6)))) = a(x,y,z * (u * (w \ v5)))
    ]]></literal>
    <justification jstring="[para(2433(a,1),27341(a,1,3,2,2))].">
      <j1 rule="para" parents="2433 27341"/>
    </justification>
  </clause>

  <clause id="27663">
    <literal><![CDATA[
      a(x,y,z * (u * (w * (v5 / v6)))) = a(x,y,z * (u * (w * (v6 \ v5))))
    ]]></literal>
    <justification jstring="[para(6471(a,1),27341(a,1,3,2,2))].">
      <j1 rule="para" parents="6471 27341"/>
    </justification>
  </clause>

  <clause id="27664">
    <literal><![CDATA[
      a(x,y,z * (u * ((w / v5) * v6))) = a(x,y,z * (u * ((v5 \ w) * v6)))
    ]]></literal>
    <justification jstring="[para(8651(a,1),27341(a,1,3,2,2))].">
      <j1 rule="para" parents="8651 27341"/>
    </justification>
  </clause>

  <clause id="27665">
    <literal><![CDATA[
      a(x,y,z * ((z * z) \ u)) = a(x,y,(1 / z) * u)
    ]]></literal>
    <justification jstring="[para(309(a,1),27391(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="309 27391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27666">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z * z) \ w)) = a(x,y,((1 / z) * u) * w)
    ]]></literal>
    <justification jstring="[para(535(a,1),27391(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="535 27391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27667">
    <literal><![CDATA[
      a(x,y,z * ((z * z) \ u)) = a(x,y,(z \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,27317,a(flip),b,27665,a),flip(a)].">
      <j1 rule="hyper" parents="373 27317 27665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27668">
    <literal><![CDATA[
      a(x,y,z \ (u * (w * w))) = a(x,y,(w * w) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(27589,a,27392,a)].">
      <j1 rule="hyper" parents="27589 27392"/>
    </justification>
  </clause>

  <clause id="27669">
    <literal><![CDATA[
      a(x,y,(z * z) * ((z * u) \ w)) = a(x,y,((1 / z) * u) \ w)
    ]]></literal>
    <justification jstring="[para(941(a,1),27392(a,1,3)),flip(a)].">
      <j1 rule="para" parents="941 27392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27670">
    <literal><![CDATA[
      a(x,y,(z / (u * w)) * v5) = a(x,y,((w * u) \ z) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,27317,a,b,27406,a)].">
      <j1 rule="hyper" parents="373 27317 27406"/>
    </justification>
  </clause>

  <clause id="27671">
    <literal><![CDATA[
      a(x,y,(z / (u / w)) * v5) = a(x,y,((w \ u) \ z) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27317,a,b,27412,a)].">
      <j1 rule="hyper" parents="64 27317 27412"/>
    </justification>
  </clause>

  <clause id="27672">
    <literal><![CDATA[
      a(x,y,((z \ u) * w) \ v5) = a(x,y,(w * (u / z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,27394,a,b,27417,a)].">
      <j1 rule="hyper" parents="373 27394 27417"/>
    </justification>
  </clause>

  <clause id="27673">
    <literal><![CDATA[
      a(x,y,((z / u) / w) \ v5) = a(x,y,(w \ (u \ z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27389,a,b,27419,a)].">
      <j1 rule="hyper" parents="64 27389 27419"/>
    </justification>
  </clause>

  <clause id="27674">
    <literal><![CDATA[
      a(x,y,((z \ (u / w)) * v5) \ v6) = a(x,y,((z \ (w \ u)) * v5) \ v6)
    ]]></literal>
    <justification jstring="[para(24475(a,1),27423(a,1,3,1))].">
      <j1 rule="para" parents="24475 27423"/>
    </justification>
  </clause>

  <clause id="27676">
    <literal><![CDATA[
      a(x,y,(((z / u) * w) \ v5) \ v6) = a(x,y,(((u \ z) * w) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[para(24400(a,1),27424(a,1,3,1))].">
      <j1 rule="para" parents="24400 27424"/>
    </justification>
  </clause>

  <clause id="27677">
    <literal><![CDATA[
      a(x,y,L(z / T(u,w),v5,v6)) = a(x,y,L(u \ z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,27344,a,b,27427,a)].">
      <j1 rule="hyper" parents="64 27344 27427"/>
    </justification>
  </clause>

  <clause id="27678">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) \ w)) = a(x,y,z \ (w \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27322,a(flip),b,27435,a),flip(a)].">
      <j1 rule="hyper" parents="64 27322 27435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27679">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ w)) = a(x,y,z * (w \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27310,a(flip),b,27441,a),flip(a)].">
      <j1 rule="hyper" parents="64 27310 27441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27680">
    <literal><![CDATA[
      a(x,y,((z * u) \ u) \ w) = a(x,y,(u \ (z \ u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27389,a(flip),b,27450,a),flip(a)].">
      <j1 rule="hyper" parents="64 27389 27450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27681">
    <literal><![CDATA[
      a(x,y,((z / u) / w) * v5) = a(x,y,(w \ (u \ z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27317,a,b,27470,a)].">
      <j1 rule="hyper" parents="64 27317 27470"/>
    </justification>
  </clause>

  <clause id="27682">
    <literal><![CDATA[
      a(x,y,z * (u \ (K(w,v5) * v6))) = a(x,y,(u \ v6) * z)
    ]]></literal>
    <justification jstring="[hyper(27453,a,27472,a)].">
      <j1 rule="hyper" parents="27453 27472"/>
    </justification>
  </clause>

  <clause id="27683">
    <literal><![CDATA[
      a(x,y,(z \ (((u \ w) \ w) \ v5)) * v6) = a(x,y,(z \ (u \ v5)) * v6)
    ]]></literal>
    <justification jstring="[para(6073(a,1),27472(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="6073 27472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27684">
    <literal><![CDATA[
      a(x,y,(z \ ((u / w) \ v5)) * v6) = a(x,y,(z \ ((w \ u) \ v5)) * v6)
    ]]></literal>
    <justification jstring="[para(6270(a,1),27472(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 27472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27685">
    <literal><![CDATA[
      a(x,y,(((z / u) \ w) \ v5) * v6) = a(x,y,(((u \ z) \ w) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(24402(a,1),27472(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="24402 27472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27686">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) * v5)) = a(x,y,z * (v5 * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27315,a,b,27478,a)].">
      <j1 rule="hyper" parents="373 27315 27478"/>
    </justification>
  </clause>

  <clause id="27687">
    <literal><![CDATA[
      a(x,y,z * (u * ((w / v5) \ v6))) = a(x,y,z * (u * ((v5 \ w) \ v6)))
    ]]></literal>
    <justification jstring="[para(6270(a,1),27483(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="6270 27483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27688">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w / v5) \ v6))) = a(x,y,z * (u \ ((v5 \ w) \ v6)))
    ]]></literal>
    <justification jstring="[para(6270(a,1),27484(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="6270 27484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27690">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (w / v5)) * v6)) = a(x,y,z \ ((u \ (v5 \ w)) * v6))
    ]]></literal>
    <justification jstring="[para(24475(a,1),27494(a,1,3,2))].">
      <j1 rule="para" parents="24475 27494"/>
    </justification>
  </clause>

  <clause id="27691">
    <literal><![CDATA[
      a(x,y,(T(z,u * u) / w) * ((u * u) * v5)) = a(x,y,((z * (u * u)) / w) * v5)
    ]]></literal>
    <justification jstring="[para(1459(a,1),27502(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1459 27502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27692">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) = a(x,y,u \ ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27581,a,b,27511,a)].">
      <j1 rule="hyper" parents="64 27581 27511"/>
    </justification>
  </clause>

  <clause id="27693">
    <literal><![CDATA[
      a(x,y,(T(z / u,w) \ v5) \ v6) = a(x,y,((u \ z) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,27410,a,b,27520,a)].">
      <j1 rule="hyper" parents="64 27410 27520"/>
    </justification>
  </clause>

  <clause id="27694">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ (z \ u)) \ w) = a(x,y,(z \ ((z \ 1) \ u)) \ w)
    ]]></literal>
    <justification jstring="[para(1612(a,1),27522(a,1,3,1))].">
      <j1 rule="para" parents="1612 27522"/>
    </justification>
  </clause>

  <clause id="27696">
    <literal><![CDATA[
      a(x,y,(z / (u * w)) \ v5) = a(x,y,((w * u) \ z) \ v5)
    ]]></literal>
    <justification jstring="[para(24515(a,1),27539(a,1,3))].">
      <j1 rule="para" parents="24515 27539"/>
    </justification>
  </clause>

  <clause id="27697">
    <literal><![CDATA[
      a(x,y,((z \ (u * u)) \ 1) \ w) = a(x,y,(u * u) * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,5347,a,b,27541,a)].">
      <j1 rule="hyper" parents="64 5347 27541"/>
    </justification>
  </clause>

  <clause id="27698">
    <literal><![CDATA[
      a(x,y,((z * u) * w) \ v5) = a(x,y,(w * (u * z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(27591,a,27557,a)].">
      <j1 rule="hyper" parents="27591 27557"/>
    </justification>
  </clause>

  <clause id="27699">
    <literal><![CDATA[
      a(x,y,(z * (T(u,w) \ v5)) \ v6) = a(x,y,((u \ v5) * z) \ v6)
    ]]></literal>
    <justification jstring="[para(24347(a,1),27559(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="24347 27559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27700">
    <literal><![CDATA[
      a(x,y,z * (u * (T(w,v5) * v6))) = a(x,y,((w * v6) * u) * z)
    ]]></literal>
    <justification jstring="[para(23389(a,1),27570(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="23389 27570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27701">
    <literal><![CDATA[
      a(x,y,L(z \ ((1 / u) \ u),w,v5)) = a(x,y,L(z \ (u * u),w,v5))
    ]]></literal>
    <justification jstring="[para(562(a,1),27603(a,1,3,1,2))].">
      <j1 rule="para" parents="562 27603"/>
    </justification>
  </clause>

  <clause id="27702">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),v5,v6)) = a(x,y,L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27644,a(flip),b,27648,a)].">
      <j1 rule="hyper" parents="64 27644 27648"/>
    </justification>
  </clause>

  <clause id="27703">
    <literal><![CDATA[
      a(x,y,L(R(z,u,w),v5,v6)) = a(x,y,L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(29(a,1),27648(a,1,3))].">
      <j1 rule="para" parents="29 27648"/>
    </justification>
  </clause>

  <clause id="27704">
    <literal><![CDATA[
      a(x,y,z * ((u * T(u \ w,v5)) * v6)) = a(x,y,z * (v6 * w))
    ]]></literal>
    <justification jstring="[para(2430(a,2),27661(a,1,3,2,1))].">
      <j1 rule="para" parents="2430 27661"/>
    </justification>
  </clause>

  <clause id="27705">
    <literal><![CDATA[
      a(x,y,z * (((u / w) * v5) * v6)) = a(x,y,z * (v6 * ((w \ u) * v5)))
    ]]></literal>
    <justification jstring="[para(8651(a,1),27661(a,1,3,2,1))].">
      <j1 rule="para" parents="8651 27661"/>
    </justification>
  </clause>

  <clause id="27706">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w / v5)) * v6)) = a(x,y,z * (v6 * (u \ (v5 \ w))))
    ]]></literal>
    <justification jstring="[para(15028(a,1),27661(a,1,3,2,1))].">
      <j1 rule="para" parents="15028 27661"/>
    </justification>
  </clause>

  <clause id="27707">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * u) = a(x,y,(z * z) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27451,a(flip),b,27668,a)].">
      <j1 rule="hyper" parents="64 27451 27668"/>
    </justification>
  </clause>

  <clause id="27708">
    <literal><![CDATA[
      a(x,y,L(z,z,u) * u) = a(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,27635,a(flip),b,27707,a),flip(a)].">
      <j1 rule="hyper" parents="373 27635 27707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27709">
    <literal><![CDATA[
      a(x,y,z * L(u,u,z)) = a(x,y,(u \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(27453,a,27708,a)].">
      <j1 rule="hyper" parents="27453 27708"/>
    </justification>
  </clause>

  <clause id="27710">
    <literal><![CDATA[
      a(x,y,((z * T(u,w)) \ ((u * w) * z)) * v5) = a(x,y,R(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[para(14083(a,2),27670(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="14083 27670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27711">
    <literal><![CDATA[
      a(x,y,L(z * (u \ (1 / u)),w,v5)) = a(x,y,L((u * u) \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(1535(a,1),27677(a,1,3,1))].">
      <j1 rule="para" parents="1535 27677"/>
    </justification>
  </clause>

  <clause id="27712">
    <literal><![CDATA[
      a(x,y,R(z / u,u,z \ ((w * v5) \ v5)) \ (v5 \ (w \ v5))) = a(x,y,u * (z \ ((w * v5) \ v5)))
    ]]></literal>
    <justification jstring="[para(684(a,1),27678(a,1,3)),flip(a)].">
      <j1 rule="para" parents="684 27678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27713">
    <literal><![CDATA[
      a(x,y,((z * u) \ z) * w) = a(x,y,w * (z \ (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27532,a,b,27679,a)].">
      <j1 rule="hyper" parents="64 27532 27679"/>
    </justification>
  </clause>

  <clause id="27714">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ u)) = a(x,y,z * (u \ (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27503,a,b,27679,a)].">
      <j1 rule="hyper" parents="64 27503 27679"/>
    </justification>
  </clause>

  <clause id="27715">
    <literal><![CDATA[
      a(x,y,z * (u \ (T(w,v5) \ v6))) = a(x,y,(u \ (w \ v6)) * z)
    ]]></literal>
    <justification jstring="[para(6157(a,1),27682(a,1,3,2,2))].">
      <j1 rule="para" parents="6157 27682"/>
    </justification>
  </clause>

  <clause id="27716">
    <literal><![CDATA[
      a(x,y,z * ((u * K(w,v5)) * (v6 / v7))) = a(x,y,((v7 \ v6) * u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27575,a(flip),b,27686,a),flip(a)].">
      <j1 rule="hyper" parents="64 27575 27686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27717">
    <literal><![CDATA[
      a(x,y,((z * T(u,w)) \ ((u * w) * z)) \ v5) = a(x,y,R(w,u,z) \ v5)
    ]]></literal>
    <justification jstring="[para(14083(a,2),27696(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="14083 27696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27718">
    <literal><![CDATA[
      a(x,y,L(L(z \ u,w,v5),z,v6)) = a(x,y,L((v6 * z) \ (v6 * u),w,v5))
    ]]></literal>
    <justification jstring="[para(102(a,1),27702(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="102 27702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27719">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w * v5),v6,v7)) = a(x,y,L(L(z,u,v5 * w),v6,v7))
    ]]></literal>
    <justification jstring="[para(23982(a,2),27702(a,1,3))].">
      <j1 rule="para" parents="23982 27702"/>
    </justification>
  </clause>

  <clause id="27720">
    <literal><![CDATA[
      a(x,y,L(R(z \ K(u,w),z,u),v5,v6)) = a(x,y,L((u * z) \ T(u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(5768(a,1),27703(a,2,3,1))].">
      <j1 rule="para" parents="5768 27703"/>
    </justification>
  </clause>

  <clause id="27721">
    <literal><![CDATA[
      a(x,y,((z * u) \ z) * w) = a(x,y,(z \ (u \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,27713,a),flip(a)].">
      <j1 rule="hyper" parents="373 27298 27713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27722">
    <literal><![CDATA[
      a(x,y,(z / (u * z)) * w) = a(x,y,(z \ (u \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27670,a,b,27721,a)].">
      <j1 rule="hyper" parents="64 27670 27721"/>
    </justification>
  </clause>

  <clause id="27723">
    <literal><![CDATA[
      a(x,y,((z * u) \ u) * w) = a(x,y,(u \ (z \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27406,a,b,27721,a)].">
      <j1 rule="hyper" parents="64 27406 27721"/>
    </justification>
  </clause>

  <clause id="27724">
    <literal><![CDATA[
      a(x,y,L(z \ 1,z,u) * w) = a(x,y,(u \ (z \ u)) * w)
    ]]></literal>
    <justification jstring="[para(241(a,2),27721(a,1,3,1))].">
      <j1 rule="para" parents="241 27721"/>
    </justification>
  </clause>

  <clause id="27725">
    <literal><![CDATA[
      (x * (y * (z * (u / z)))) * a(x,y,u) = (x * y) * (z * (u / z))
    ]]></literal>
    <justification jstring="[para(12(a,1),27365(a,1,2,3))].">
      <j1 rule="para" parents="12 27365"/>
    </justification>
  </clause>

  <clause id="27726">
    <literal><![CDATA[
      a(x,y,z * (u \ R(w,u,u))) = a(x,y,z * (w * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27478,a(flip),b,27439,a),flip(a)].">
      <j1 rule="hyper" parents="373 27478 27439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27727">
    <literal><![CDATA[
      a(x,y,L(z,(u * u) / w,(u * u) / w) \ (u * u)) = a(x,y,((1 / w) * ((1 / ((u * u) / w)) * z)) \ 1)
    ]]></literal>
    <justification jstring="[para(1075(a,1),27558(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1075 27558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27728">
    <literal><![CDATA[
      a(x,y,R(z,u,u) \ w) = a(x,y,L(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27447,a(flip),b,27619,a)].">
      <j1 rule="hyper" parents="64 27447 27619"/>
    </justification>
  </clause>

  <clause id="27729">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z) \ w) = a(x,y,(L(u,z,z) * z) \ w)
    ]]></literal>
    <justification jstring="[para(559(a,1),27619(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="559 27619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27730">
    <literal><![CDATA[
      a(x,y,R(z,u,u) \ z) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(1243(a,1),27728(a,2,3))].">
      <j1 rule="para" parents="1243 27728"/>
    </justification>
  </clause>

  <clause id="27731">
    <literal><![CDATA[
      a(x,y,a(z,u,u) \ 1) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(16007(a,1),27730(a,1,3))].">
      <j1 rule="para" parents="16007 27730"/>
    </justification>
  </clause>

  <clause id="27733">
    <literal><![CDATA[
      a(x,y,L(z,u,u * z) \ 1) = a(x,y,u * ((z * u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,27532,a(flip),b,27643,a),flip(a)].">
      <j1 rule="hyper" parents="373 27532 27643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27734">
    <literal><![CDATA[
      a(x,y,L(z \ (u * u),u,u)) = a(x,y,((1 / z) * u) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27344,a(flip),b,27652,a)].">
      <j1 rule="hyper" parents="64 27344 27652"/>
    </justification>
  </clause>

  <clause id="27735">
    <literal><![CDATA[
      a(x,y,R(z \ u,z,z) \ w) = a(x,y,((z \ 1) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27728,a,b,27654,a)].">
      <j1 rule="hyper" parents="64 27728 27654"/>
    </justification>
  </clause>

  <clause id="27736">
    <literal><![CDATA[
      a(x,y,L(z \ 1,z,u) * u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,27299,a(flip),b,27724,a),flip(a)].">
      <j1 rule="hyper" parents="373 27299 27724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27737">
    <literal><![CDATA[
      a(x,y,z * L(u \ 1,u,z)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(27453,a,27736,a)].">
      <j1 rule="hyper" parents="27453 27736"/>
    </justification>
  </clause>

  <clause id="27738">
    <literal><![CDATA[
      a(x,y,(z * u) * L(w \ 1,w,u * z)) = a(x,y,w \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27462,a,b,27736,a)].">
      <j1 rule="hyper" parents="64 27462 27736"/>
    </justification>
  </clause>

  <clause id="27739">
    <literal><![CDATA[
      a(x,y,L((((z * z) / u) \ w) \ 1,((z * z) / u) \ w,u) * u) = a(x,y,(u \ w) \ (u \ (z * z)))
    ]]></literal>
    <justification jstring="[para(7647(a,1),27736(a,2,3))].">
      <j1 rule="para" parents="7647 27736"/>
    </justification>
  </clause>

  <clause id="27740">
    <literal><![CDATA[
      a(x,y,(z \ u) * (((z \ a(w,v5,z)) * ((z * a(w,v5,z)) \ u)) \ 1)) = a(x,y,L(z \ 1,z \ u,(z \ u) * (z \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(9436(a,2),27733(a,2,3,2,1)),flip(a)].">
      <j1 rule="para" parents="9436 27733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27741">
    <literal><![CDATA[
      a(x,y,L(z \ (u * u),u,u)) = a(x,y,u * (u * (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27462,a(flip),b,27734,a),flip(a)].">
      <j1 rule="hyper" parents="373 27462 27734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27742">
    <literal><![CDATA[
      a(x,y,L(z \ (u * u),u,u)) = a(x,y,u * (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27478,a(flip),b,27741,a),flip(a)].">
      <j1 rule="hyper" parents="373 27478 27741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27743">
    <literal><![CDATA[
      a(x,y,((z * z) * u) * (w / z)) = a(x,y,((z \ 1) \ w) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,27671,a(flip),b,27369,a),flip(a)].">
      <j1 rule="hyper" parents="373 27671 27369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27744">
    <literal><![CDATA[
      a(x,y,((1 / z) / u) * (w * w)) = a(x,y,u \ (z \ (w * w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27487,a(flip),b,27376,a),flip(a)].">
      <j1 rule="hyper" parents="373 27487 27376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27745">
    <literal><![CDATA[
      a(x,y,T(((1 / (z \ K(u,w))) * (v5 * (z \ K(u,w)))) * (z \ K(u,w)),z \ K(u,w)) \ v6) = a(x,y,(T(((1 / (z \ K(u,w))) * v5) * (z \ K(u,w)),z \ K(u,w)) * (z \ 1)) \ v6)
    ]]></literal>
    <justification jstring="[para(1620(a,2),27421(a,1,3,1))].">
      <j1 rule="para" parents="1620 27421"/>
    </justification>
  </clause>

  <clause id="27746">
    <literal><![CDATA[
      a(x,y,R(z / u,u,u) \ w) = a(x,y,((u \ 1) * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27735,a(flip),b,27430,a),flip(a)].">
      <j1 rule="hyper" parents="373 27735 27430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27747">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ (w * w))) = a(x,y,(w * w) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27392,a(flip),b,27433,a),flip(a)].">
      <j1 rule="hyper" parents="373 27392 27433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27748">
    <literal><![CDATA[
      a(x,y,(z * z) \ (u \ (z * w))) = a(x,y,u \ ((z \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27492,a(flip),b,27446,a),flip(a)].">
      <j1 rule="hyper" parents="373 27492 27446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27749">
    <literal><![CDATA[
      a(x,y,(z * z) * (u * (1 / w))) = a(x,y,(w \ (z * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,27317,a(flip),b,27465,a),flip(a)].">
      <j1 rule="hyper" parents="373 27317 27465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27750">
    <literal><![CDATA[
      a(x,y,z \ (((u / w) / u) * v5)) = a(x,y,z \ (((w * u) \ u) * v5))
    ]]></literal>
    <justification jstring="[para(26369(a,1),27514(a,1,3,2,1))].">
      <j1 rule="para" parents="26369 27514"/>
    </justification>
  </clause>

  <clause id="27751">
    <literal><![CDATA[
      a(x,y,z \ (T(u / (u * w),w) \ v5)) = a(x,y,z \ ((u \ (w \ u)) \ v5))
    ]]></literal>
    <justification jstring="[para(26040(a,1),27516(a,1,3,2,1))].">
      <j1 rule="para" parents="26040 27516"/>
    </justification>
  </clause>

  <clause id="27752">
    <literal><![CDATA[
      a(x,y,a(z,u,w * v5)) = a(x,y,a(z,u,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(27585,a,27527,a)].">
      <j1 rule="hyper" parents="27585 27527"/>
    </justification>
  </clause>

  <clause id="27753">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ ((u * u) \ w)) = a(x,y,(z \ (u * u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27522,a(flip),b,27542,a),flip(a)].">
      <j1 rule="hyper" parents="64 27522 27542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27754">
    <literal><![CDATA[
      a(x,y,((z \ u) * (1 / z)) \ w) = a(x,y,(z * z) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27541,a(flip),b,27551,a),flip(a)].">
      <j1 rule="hyper" parents="373 27541 27551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27755">
    <literal><![CDATA[
      a(x,y,L((z * u) * w,v5,v6)) = a(x,y,L(w * (u * z),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,27377,a,b,27606,a)].">
      <j1 rule="hyper" parents="373 27377 27606"/>
    </justification>
  </clause>

  <clause id="27756">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (u * u)) = a(x,y,1 / ((1 / u) / z))
    ]]></literal>
    <justification jstring="[para(904(a,1),27629(a,1,3)),flip(a)].">
      <j1 rule="para" parents="904 27629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27757">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (u * u)) = a(x,y,((1 / u) / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,27308,a(flip),b,27756,a),flip(a)].">
      <j1 rule="hyper" parents="373 27308 27756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27758">
    <literal><![CDATA[
      a(x,y,(z \ (u \ 1)) \ 1) = a(x,y,(z \ u) \ (u * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27673,a(flip),b,27757,a)].">
      <j1 rule="hyper" parents="373 27673 27757"/>
    </justification>
  </clause>

  <clause id="27759">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) * (u \ w))) = a(x,y,w * ((u * u) \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27391,a(flip),b,27634,a),flip(a)].">
      <j1 rule="hyper" parents="373 27391 27634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27760">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z * z) \ w)) = a(x,y,((z \ 1) * u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27411,a(flip),b,27666,a),flip(a)].">
      <j1 rule="hyper" parents="373 27411 27666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27761">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * (z * z)) = a(x,y,((1 / z) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(27453,a,27669,a)].">
      <j1 rule="hyper" parents="27453 27669"/>
    </justification>
  </clause>

  <clause id="27762">
    <literal><![CDATA[
      a(x,y,(T(((z / u) \ 1) \ 1,w) \ v5) \ v6) = a(x,y,((z \ ((u / z) \ z)) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[para(2037(a,2),27693(a,1,3,1,1,1))].">
      <j1 rule="para" parents="2037 27693"/>
    </justification>
  </clause>

  <clause id="27763">
    <literal><![CDATA[
      a(x,y,((z \ (u * u)) \ 1) \ w) = a(x,y,(z \ w) * (u * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27630,a,b,27697,a),flip(a)].">
      <j1 rule="hyper" parents="373 27630 27697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27764">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((z * z) * w)) = a(x,y,((z \ 1) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27460,a,b,27743,a)].">
      <j1 rule="hyper" parents="64 27460 27743"/>
    </justification>
  </clause>

  <clause id="27765">
    <literal><![CDATA[
      a(x,y,(z \ (u \ 1)) * (w * w)) = a(x,y,z \ (u \ (w * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27681,a(flip),b,27744,a)].">
      <j1 rule="hyper" parents="64 27681 27744"/>
    </justification>
  </clause>

  <clause id="27766">
    <literal><![CDATA[
      a(x,y,(z * z) * (u \ (w \ 1))) = a(x,y,u \ (w \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27510,a(flip),b,27747,a),flip(a)].">
      <j1 rule="hyper" parents="64 27510 27747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27767">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) * (u \ w))) = a(x,y,(u * u) \ (z \ w))
    ]]></literal>
    <justification jstring="[para(10(a,1),27748(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="10 27748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27768">
    <literal><![CDATA[
      a(x,y,(z * z) * (u * (w \ 1))) = a(x,y,(w \ (z * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27478,a(flip),b,27749,a)].">
      <j1 rule="hyper" parents="64 27478 27749"/>
    </justification>
  </clause>

  <clause id="27769">
    <literal><![CDATA[
      a(x,y,(1 / z) * ((u * u) * w)) = a(x,y,(z \ (u * u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27367,a(flip),b,27749,a)].">
      <j1 rule="hyper" parents="64 27367 27749"/>
    </justification>
  </clause>

  <clause id="27770">
    <literal><![CDATA[
      a(x,y,(z * z) \ ((u \ 1) \ w)) = a(x,y,(u \ (z * z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27445,a,b,27753,a)].">
      <j1 rule="hyper" parents="64 27445 27753"/>
    </justification>
  </clause>

  <clause id="27771">
    <literal><![CDATA[
      a(x,y,((z \ u) * (z \ 1)) \ w) = a(x,y,(z * z) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27417,a(flip),b,27754,a)].">
      <j1 rule="hyper" parents="64 27417 27754"/>
    </justification>
  </clause>

  <clause id="27772">
    <literal><![CDATA[
      a(x,y,L((z * (1 / u)) * (u * u),w,v5)) = a(x,y,L(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(310(a,1),27755(a,2,3,1))].">
      <j1 rule="para" parents="310 27755"/>
    </justification>
  </clause>

  <clause id="27773">
    <literal><![CDATA[
      a(x,y,((z \ u) * (z \ 1)) * w) = a(x,y,u * ((z * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27462,a,b,27759,a)].">
      <j1 rule="hyper" parents="64 27462 27759"/>
    </justification>
  </clause>

  <clause id="27774">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) * (z / w)) = a(x,y,(z * u) * ((1 / z) / w))
    ]]></literal>
    <justification jstring="[para(887(a,1),27760(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="887 27760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27775">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * (z * z)) = a(x,y,((z \ 1) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27519,a(flip),b,27761,a),flip(a)].">
      <j1 rule="hyper" parents="373 27519 27761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27776">
    <literal><![CDATA[
      a(x,y,(z * z) * (u * (z \ w))) = a(x,y,((z \ 1) \ w) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27367,a,b,27764,a)].">
      <j1 rule="hyper" parents="64 27367 27764"/>
    </justification>
  </clause>

  <clause id="27777">
    <literal><![CDATA[
      a(x,y,(z \ 1) * ((u * u) * w)) = a(x,y,(z \ (u * u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27367,a(flip),b,27768,a)].">
      <j1 rule="hyper" parents="64 27367 27768"/>
    </justification>
  </clause>

  <clause id="27778">
    <literal><![CDATA[
      a(x,y,(((z / u) * (u / z)) * ((1 / (u / z)) \ 1)) \ w) = a(x,y,((1 / (u / z)) * (1 / (u / z))) * ((z / u) \ w))
    ]]></literal>
    <justification jstring="[para(2719(a,1),27771(a,1,3,1,1))].">
      <j1 rule="para" parents="2719 27771"/>
    </justification>
  </clause>

  <clause id="27779">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * ((z * z) \ v5)) = a(x,y,R(z \ 1,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(2083(a,1),27773(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2083 27773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27780">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (z \ u)) \ w) = a(x,y,(u \ w) * (z * z))
    ]]></literal>
    <justification jstring="[para(10(a,1),27775(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="10 27775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27781">
    <literal><![CDATA[
      a(x,y,(z \ (u * u)) * (w \ 1)) = a(x,y,(z \ 1) * (w \ (u * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27501,a(flip),b,27777,a),flip(a)].">
      <j1 rule="hyper" parents="64 27501 27777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27782">
    <literal><![CDATA[
      a(x,y,z \ (u * ((u \ 1) \ w))) = a(x,y,(z \ w) * (u * u))
    ]]></literal>
    <justification jstring="[para(1660(a,1),27780(a,1,3))].">
      <j1 rule="para" parents="1660 27780"/>
    </justification>
  </clause>

  <clause id="27783">
    <literal><![CDATA[
      a(x,y,z \ (u * ((u \ 1) \ w))) = a(x,y,(u * u) * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27462,a,b,27782,a),flip(a)].">
      <j1 rule="hyper" parents="373 27462 27782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27784">
    <literal><![CDATA[
      a(x,y,(z * z) * (u \ ((z \ 1) * w))) = a(x,y,u \ (z * w))
    ]]></literal>
    <justification jstring="[para(9(a,1),27783(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="9 27783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27785">
    <literal><![CDATA[
      R(x,y,((z * u) \ ((u * w) * z)) * v5) = R(x,y,L(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[para(27293(a,1),26172(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27293 26172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27786">
    <literal><![CDATA[
      a(x,y,((z * L(z,z,z)) * u) \ ((w \ ((z * z) * (z \ u))) * (z * w))) = a(x,y,a(z,w,w \ ((z * z) * (z \ u))))
    ]]></literal>
    <justification jstring="[para(11461(a,1),27490(a,1,3,1))].">
      <j1 rule="para" parents="11461 27490"/>
    </justification>
  </clause>

  <clause id="27787">
    <literal><![CDATA[
      a(x,y,((z / (z * u)) * z) \ w) = a(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13881,a(flip),b,27543,a),flip(a)].">
      <j1 rule="hyper" parents="64 13881 27543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27789">
    <literal><![CDATA[
      a(x,y,(((z * u) \ z) * z) \ w) = a(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27519,a(flip),b,27787,a)].">
      <j1 rule="hyper" parents="64 27519 27787"/>
    </justification>
  </clause>

  <clause id="27790">
    <literal><![CDATA[
      a(x,y,((z \ u) \ z) \ w) = a(x,y,((u \ z) * z) \ w)
    ]]></literal>
    <justification jstring="[para(10(a,1),27789(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 27789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27791">
    <literal><![CDATA[
      a(x,y,(((z * z) / u) * w) * u) = a(x,y,L(w * (z * z),u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27644,a(flip),b,27555,a),flip(a)].">
      <j1 rule="hyper" parents="373 27644 27555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27792">
    <literal><![CDATA[
      a(x,y,L((z \ 1) * (u * z),w,v5)) = a(x,y,L(L(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27606,a,b,27604,a)].">
      <j1 rule="hyper" parents="64 27606 27604"/>
    </justification>
  </clause>

  <clause id="27793">
    <literal><![CDATA[
      (x * y) * (z * (K(u,w) / z)) = x * (y * (z * (K(u,w) / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,23081,a(flip),b,27725,a),flip(a)].">
      <j1 rule="hyper" parents="64 23081 27725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27794">
    <literal><![CDATA[
      a(x,y,z * ((z \ (u * u)) * w)) = a(x,y,L(w * (u * u),z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27534,a(flip),b,27791,a)].">
      <j1 rule="hyper" parents="64 27534 27791"/>
    </justification>
  </clause>

  <clause id="27795">
    <literal><![CDATA[
      a(x,y,L(z * (u * u),w,w)) = a(x,y,(u * u) * L(z,w,w))
    ]]></literal>
    <justification jstring="[para(11869(a,1),27794(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11869 27794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27796">
    <literal><![CDATA[
      a(x,y,(z * u) * ((w * w) / z)) = a(x,y,L(u * (w * w),z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27370,a,b,27795,a)].">
      <j1 rule="hyper" parents="373 27370 27795"/>
    </justification>
  </clause>

  <clause id="27797">
    <literal><![CDATA[
      a(x,y,(z * u) * (z \ (w * w))) = a(x,y,L(u * (w * w),z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27310,a(flip),b,27796,a)].">
      <j1 rule="hyper" parents="64 27310 27796"/>
    </justification>
  </clause>

  <clause id="27798">
    <literal><![CDATA[
      a(x,y,L((z \ u) * (w * w),z,z)) = a(x,y,u * (z \ (w * w)))
    ]]></literal>
    <justification jstring="[para(10(a,1),27797(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 27797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27799">
    <literal><![CDATA[
      a(x,y * ((z * u) * (u \ a(w,v5,w))),v6) = a(x,y * R(z,u,u \ a(w,v5,w)),v6)
    ]]></literal>
    <justification jstring="[para(23163(a,1),13834(a,1,2,2))].">
      <j1 rule="para" parents="23163 13834"/>
    </justification>
  </clause>

  <clause id="27801">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x * x) * u) = (x * L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,5621,a(flip),b,23752,a),flip(a)].">
      <j1 rule="hyper" parents="373 5621 23752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27802">
    <literal><![CDATA[
      (x * L(x,y,z)) * ((1 / x) * u) = (x \ L(x,y,z)) * (x * u)
    ]]></literal>
    <justification jstring="[para(310(a,1),27801(a,1,2)),flip(a)].">
      <j1 rule="para" parents="310 27801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27803">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ L(z,u,w)) * v5) = a(x,y,(z * L(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(27801(a,1),27764(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27801 27764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27804">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) \ u,w) \ (w * u) = w * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(40,a,23792,a,b,23784,a(flip))].">
      <j1 rule="hyper" parents="40 23792 23784"/>
    </justification>
  </clause>

  <clause id="27806">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ ((a(z,u,w) * x) * y) = a(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,24755,a,b,23939,a)].">
      <j1 rule="hyper" parents="64 24755 23939"/>
    </justification>
  </clause>

  <clause id="27807">
    <literal><![CDATA[
      a(x,y,z) \ (u * ((u \ 1) \ w)) = u * ((u \ 1) \ (a(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,1471,a(flip),b,23946,a),flip(a)].">
      <j1 rule="hyper" parents="64 1471 23946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27808">
    <literal><![CDATA[
      x \ (a(y,z,u) * (((w / x) \ w) * (w / x))) = (w / (w / x)) \ (w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,219,a(flip),b,23952,a)].">
      <j1 rule="hyper" parents="64 219 23952"/>
    </justification>
  </clause>

  <clause id="27809">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (((w / u) \ w) * (w / u)) = ((w / (w / u)) * a(x,y,z)) \ w
    ]]></literal>
    <justification jstring="[para(82(a,1),23956(a,1,1,2))].">
      <j1 rule="para" parents="82 23956"/>
    </justification>
  </clause>

  <clause id="27810">
    <literal><![CDATA[
      L(x,y,R((z * z) \ z,z,z \ u)) = L(x,y,u \ (L(z,z,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,23847,a(flip),b,23979,a)].">
      <j1 rule="hyper" parents="64 23847 23979"/>
    </justification>
  </clause>

  <clause id="27811">
    <literal><![CDATA[
      K(x,y) * (R(T(z,u),w,v5) \ z) = (R(T(z,u),w,v5) \ z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(11430(a,1),24325(a,1,2))].">
      <j1 rule="para" parents="11430 24325"/>
    </justification>
  </clause>

  <clause id="27812">
    <literal><![CDATA[
      (K(x,y) * z) * (u \ T(x,K(w,y))) = K(x,T(y,w)) * (z * (u \ x))
    ]]></literal>
    <justification jstring="[para(8153(a,1),24335(a,1,2,2))].">
      <j1 rule="para" parents="8153 24335"/>
    </justification>
  </clause>

  <clause id="27813">
    <literal><![CDATA[
      R(x,y,((K(z,z \ u) * w) / (v5 / (z \ u))) \ v6) = R(x,y,(T(v5 / (u / z),K(z,u)) \ w) \ v6)
    ]]></literal>
    <justification jstring="[para(24403(a,1),26209(a,2,3,1))].">
      <j1 rule="para" parents="24403 26209"/>
    </justification>
  </clause>

  <clause id="27814">
    <literal><![CDATA[
      K(x,y) * (K(z,T(y,x)) * (u / w)) = (y * (T(T(y,x),z) \ u)) / w
    ]]></literal>
    <justification jstring="[hyper(64,a,24423,a(flip),b,24429,a)].">
      <j1 rule="hyper" parents="64 24423 24429"/>
    </justification>
  </clause>

  <clause id="27815">
    <literal><![CDATA[
      (x / (y * (z / u))) * K(u,u \ z) = x / T(y * (u \ z),K(z,u))
    ]]></literal>
    <justification jstring="[para(8153(a,1),24491(a,2,2))].">
      <j1 rule="para" parents="8153 24491"/>
    </justification>
  </clause>

  <clause id="27816">
    <literal><![CDATA[
      L(x / ((x / y) * K(z,z \ 1)),z,z) \ x = x / ((z \ 1) * (z * y))
    ]]></literal>
    <justification jstring="[para(2392(a,1),24494(a,2,2))].">
      <j1 rule="para" parents="2392 24494"/>
    </justification>
  </clause>

  <clause id="27817">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u) * R(y,y,T(T(x,z),u)) = (1 / y) \ T(T(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,1913,a(flip),b,24608,a),flip(a)].">
      <j1 rule="hyper" parents="373 1913 24608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27818">
    <literal><![CDATA[
      R(x \ (a(y,z,u) \ 1),x,x) = (a(y,z,u) \ 1) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1386,a,b,24624,a(flip))].">
      <j1 rule="hyper" parents="35 1386 24624"/>
    </justification>
  </clause>

  <clause id="27820">
    <literal><![CDATA[
      (x \ a(y,z,x)) \ (u * a(y,z,x)) = L((x \ 1) \ u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,23180,a(flip),b,24632,a)].">
      <j1 rule="hyper" parents="64 23180 24632"/>
    </justification>
  </clause>

  <clause id="27821">
    <literal><![CDATA[
      ((x / (y * x)) / z) \ K(z \ (x / (y * x)),y * z) = 1 / ((x / (y * x)) / z)
    ]]></literal>
    <justification jstring="[para(24989(a,1),24711(a,1,2))].">
      <j1 rule="para" parents="24989 24711"/>
    </justification>
  </clause>

  <clause id="27822">
    <literal><![CDATA[
      ((x / (y * z)) / u) \ K(u \ (x / (y * z)),y * (z * (x \ u))) = 1 / ((x / (y * z)) / u)
    ]]></literal>
    <justification jstring="[para(25003(a,1),24711(a,1,2))].">
      <j1 rule="para" parents="25003 24711"/>
    </justification>
  </clause>

  <clause id="27823">
    <literal><![CDATA[
      K(x,y) * (K(y \ 1,T(z,x)) * u) = (y * T(T(y,x) \ 1,z)) * u
    ]]></literal>
    <justification jstring="[para(7872(a,1),24775(a,1,2,1))].">
      <j1 rule="para" parents="7872 24775"/>
    </justification>
  </clause>

  <clause id="27824">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ (u * L(x,y,z)) = L(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11786,a(flip),b,24825,a),flip(a)].">
      <j1 rule="hyper" parents="373 11786 24825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27825">
    <literal><![CDATA[
      (T(x,y) \ z) \ (((T(x,y) \ z) * x) * u) = (z / x) \ (z * u)
    ]]></literal>
    <justification jstring="[para(24903(a,1),24923(a,1,2))].">
      <j1 rule="para" parents="24903 24923"/>
    </justification>
  </clause>

  <clause id="27826">
    <literal><![CDATA[
      (x / T(y,z)) \ (x * y) = (x / y) \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11065,a(flip),b,27825,a)].">
      <j1 rule="hyper" parents="64 11065 27825"/>
    </justification>
  </clause>

  <clause id="27828">
    <literal><![CDATA[
      (x * T(y / z,T(z,z))) * T(y / z,u) = (x * (y / z)) * T(z \ y,T(u,z))
    ]]></literal>
    <justification jstring="[para(9456(a,1),24950(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9456 24950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27829">
    <literal><![CDATA[
      (x / (y * x)) * ((1 / y) \ (z * (y \ 1))) = z * (x / (T(y,y \ 1) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,9969,a,b,24960,a)].">
      <j1 rule="hyper" parents="64 9969 24960"/>
    </justification>
  </clause>

  <clause id="27830">
    <literal><![CDATA[
      (x \ T(y,z)) \ (x \ ((1 / x) \ y)) = ((x \ 1) * T(y,z)) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,24509,a(flip),b,24983,a),flip(a)].">
      <j1 rule="hyper" parents="373 24509 24983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27831">
    <literal><![CDATA[
      (((x * y) * z) \ u) * K(w,K(v5,x * (y * (z * u)))) = T(((x * y) * z) \ u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(25003(a,1),25017(a,1,2,2))].">
      <j1 rule="para" parents="25003 25017"/>
    </justification>
  </clause>

  <clause id="27832">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (((x \ 1) * y) * z)) = T(x \ 1,x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,5131,a(flip),b,25021,a),flip(a)].">
      <j1 rule="hyper" parents="373 5131 25021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27834">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ x)) \ (1 / x) = (1 / x) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(25895(a,1),25179(a,1,1))].">
      <j1 rule="para" parents="25895 25179"/>
    </justification>
  </clause>

  <clause id="27835">
    <literal><![CDATA[
      (x * x) * (x \ (a(y,z,u) \ x)) = x / ((1 / x) * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(225,a,27834,a(flip),b,878,a),flip(a)].">
      <j1 rule="hyper" parents="225 27834 878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27836">
    <literal><![CDATA[
      (1 / x) \ (x \ (a(y,z,u) \ x)) = x \ (x / ((1 / x) * a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(139,a,27835,a(flip),b,538,a),flip(a)].">
      <j1 rule="hyper" parents="139 27835 538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27837">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),y) = L(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,23744,a(flip),b,25180,a),flip(a)].">
      <j1 rule="hyper" parents="64 23744 25180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27838">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),y) = L(x,y \ R(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,23711,a(flip),b,25210,a),flip(a)].">
      <j1 rule="hyper" parents="64 23711 25210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27839">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ x) / x = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(43,a,3051,a(flip),b,27838,a),flip(a)].">
      <j1 rule="hyper" parents="43 3051 27838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27841">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ x = x * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(38,a,25155,a,b,27839,a),flip(a)].">
      <j1 rule="hyper" parents="38 25155 27839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27842">
    <literal><![CDATA[
      R(1 / x,y,z) \ 1 = (x \ R(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,2468,a,b,27841,a)].">
      <j1 rule="hyper" parents="373 2468 27841"/>
    </justification>
  </clause>

  <clause id="27843">
    <literal><![CDATA[
      (x * y) \ ((K(z,u) / y) * (x * y)) = L(T(y \ K(z,u),x),x,y)
    ]]></literal>
    <justification jstring="[para(26110(a,1),25246(a,1,2))].">
      <j1 rule="para" parents="26110 25246"/>
    </justification>
  </clause>

  <clause id="27844">
    <literal><![CDATA[
      L(T(x \ K(y,z),u),u,x) = T(K(y,z) / x,u * x)
    ]]></literal>
    <justification jstring="[hyper(336,a,27843,a),flip(a)].">
      <j1 rule="hyper" parents="336 27843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27845">
    <literal><![CDATA[
      ((x * (y / x)) * x) * R(x,z,u) = x * (y * R(T(x,x \ 1),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27131,a(flip),b,25256,a),flip(a)].">
      <j1 rule="hyper" parents="64 27131 25256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27846">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ (u \ a(x,y,z)) = u \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(149,a,25312,a)].">
      <j1 rule="hyper" parents="149 25312"/>
    </justification>
  </clause>

  <clause id="27847">
    <literal><![CDATA[
      (x \ a(y,z,u)) \ (a(y,z,u) * a(y,z,u)) = (x \ (a(y,z,u) \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(25312(a,1),489(a,1,1))].">
      <j1 rule="para" parents="25312 489"/>
    </justification>
  </clause>

  <clause id="27848">
    <literal><![CDATA[
      (x * x) * ((((y \ z) / z) * y) \ 1) = (((y \ z) / z) * y) \ (x * x)
    ]]></literal>
    <justification jstring="[para(23866(a,1),25355(a,1,2))].">
      <j1 rule="para" parents="23866 25355"/>
    </justification>
  </clause>

  <clause id="27849">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u * K(w,v5))) = K(x,(y * (K(w,v5) / z)) * u)
    ]]></literal>
    <justification jstring="[hyper(18093,a,25406,a)].">
      <j1 rule="hyper" parents="18093 25406"/>
    </justification>
  </clause>

  <clause id="27850">
    <literal><![CDATA[
      K(x,(y * (K(z,u * y) / u)) * w) = K(x,T(y * (1 / u),z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,21569,a(flip),b,25406,a),flip(a)].">
      <j1 rule="hyper" parents="64 21569 25406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27851">
    <literal><![CDATA[
      (x * (y \ (1 / z))) \ (1 / z) = (x * (y \ (z \ 1))) \ (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5192,a(flip),b,25421,a),flip(a)].">
      <j1 rule="hyper" parents="64 5192 25421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27852">
    <literal><![CDATA[
      ((x * x) * (y * (z \ (1 / x)))) \ x = (y * (z \ (x \ 1))) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,878,a,b,27851,a)].">
      <j1 rule="hyper" parents="64 878 27851"/>
    </justification>
  </clause>

  <clause id="27854">
    <literal><![CDATA[
      ((x * L(T(y,z),u,w)) * (L(y,u,w) \ y)) / T(y,z) = R(x,L(T(y,z),u,w),L(T(y,z),u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,110,a(flip),b,25472,a),flip(a)].">
      <j1 rule="hyper" parents="64 110 25472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27855">
    <literal><![CDATA[
      (x / y) * (y * ((K(z,u) / y) \ w)) = (x / (K(z,u) / y)) * w
    ]]></literal>
    <justification jstring="[hyper(373,a,24963,a(flip),b,25486,a),flip(a)].">
      <j1 rule="hyper" parents="373 24963 25486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27856">
    <literal><![CDATA[
      L((K(x,y) / z) \ u,z,z) = (1 / (K(x,y) / z)) * u
    ]]></literal>
    <justification jstring="[hyper(573,a,27855,a)].">
      <j1 rule="hyper" parents="573 27855"/>
    </justification>
  </clause>

  <clause id="27857">
    <literal><![CDATA[
      T(T(x * K(y,x \ 1),z),x \ 1) = T(T(x,z) \ 1,y) \ 1
    ]]></literal>
    <justification jstring="[para(24751(a,1),25508(a,1,1))].">
      <j1 rule="para" parents="24751 25508"/>
    </justification>
  </clause>

  <clause id="27858">
    <literal><![CDATA[
      T((x \ K(x \ 1,y)) \ 1,z) = T(T(x,z) \ 1,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,25660,a(flip),b,27857,a)].">
      <j1 rule="hyper" parents="64 25660 27857"/>
    </justification>
  </clause>

  <clause id="27859">
    <literal><![CDATA[
      T(T(x \ 1,y) \ 1,z) = T(T(x,z) \ 1,y) \ 1
    ]]></literal>
    <justification jstring="[para(5762(a,1),27858(a,1,1,1))].">
      <j1 rule="para" parents="5762 27858"/>
    </justification>
  </clause>

  <clause id="27860">
    <literal><![CDATA[
      T(x \ 1,T(y,z)) \ K(x,z) = T(T(x \ 1,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,15272,a,b,27859,a)].">
      <j1 rule="hyper" parents="373 15272 27859"/>
    </justification>
  </clause>

  <clause id="27861">
    <literal><![CDATA[
      T(x,y / T(z \ K(u,z),w)) = T(x,y * T(T(z \ 1,w) \ 1,u))
    ]]></literal>
    <justification jstring="[para(27860(a,1),15118(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="27860 15118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27862">
    <literal><![CDATA[
      (x \ R(x,x,y)) * L(z,x,y \ (x \ y)) = (y / (x * y)) * (x * z)
    ]]></literal>
    <justification jstring="[para(13011(a,1),25563(a,1,2))].">
      <j1 rule="para" parents="13011 25563"/>
    </justification>
  </clause>

  <clause id="27863">
    <literal><![CDATA[
      R(x,y,y \ L(y,z,u)) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,24823,a,b,25603,a),flip(a)].">
      <j1 rule="hyper" parents="35 24823 25603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27864">
    <literal><![CDATA[
      L(x \ L(x,y,y \ L(y,z,u)),x,L(y,z,u)) = a(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(27863(a,1),16036(a,1,1,2))].">
      <j1 rule="para" parents="27863 16036"/>
    </justification>
  </clause>

  <clause id="27865">
    <literal><![CDATA[
      x * (((y \ 1) * z) \ ((((1 / y) \ 1) \ z) * u)) = x * (((1 / (1 / y)) \ z) * (((1 / y) * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5357,a(flip),b,25727,a)].">
      <j1 rule="hyper" parents="64 5357 25727"/>
    </justification>
  </clause>

  <clause id="27866">
    <literal><![CDATA[
      (x * y) / ((1 / x) \ y) = ((1 / x) \ y) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5226,a(flip),b,25739,a),flip(a)].">
      <j1 rule="hyper" parents="64 5226 25739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27867">
    <literal><![CDATA[
      (x * y) / ((1 / x) \ y) = (x \ y) \ ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1692,a(flip),b,27866,a),flip(a)].">
      <j1 rule="hyper" parents="373 1692 27866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27868">
    <literal><![CDATA[
      (1 / (1 / x)) * ((L(x,y,z) \ 1) \ u) = x * ((1 / L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(35,a,5237,a,b,25748,a),flip(a)].">
      <j1 rule="hyper" parents="35 5237 25748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27869">
    <literal><![CDATA[
      a(x,y,z) * ((1 / z) * R(z,u,w)) = (a(x,y,z) / z) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(25755(a,1),25758(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25755 25758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27870">
    <literal><![CDATA[
      R(T(x,y * y),y,y) \ (y \ (x * y)) = a(y,y,x) * K(y,y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a,b,25790,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 25790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27871">
    <literal><![CDATA[
      K(x,(y * (z \ K(u,z * y))) * w) = K(x,T(y * (z \ 1),u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,21573,a(flip),b,25794,a),flip(a)].">
      <j1 rule="hyper" parents="64 21573 25794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27872">
    <literal><![CDATA[
      K(x,(y \ K(z,u / y)) \ (u \ w)) = K(x,T(u * (y \ 1),z) \ w)
    ]]></literal>
    <justification jstring="[hyper(25260,a,25795,a)].">
      <j1 rule="hyper" parents="25260 25795"/>
    </justification>
  </clause>

  <clause id="27873">
    <literal><![CDATA[
      (x * y) * (K(z,u) * (y \ K(y,x))) = (y * x) * (K(z,u) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(5761(a,1),25803(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5761 25803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27874">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) * ((x \ 1) * R(x,u,w)) = R(x,y,z) * (x \ R(x,u,w))
    ]]></literal>
    <justification jstring="[para(8892(a,1),25805(a,1,2))].">
      <j1 rule="para" parents="8892 25805"/>
    </justification>
  </clause>

  <clause id="27875">
    <literal><![CDATA[
      (L(x,x,y) / z) \ x = (((y * (x \ 1)) \ y) / z) \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(11811(a,1),25846(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11811 25846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27876">
    <literal><![CDATA[
      K(x,y * T(z / (u * (w / u)),w)) = K(x,y * (T(w,u) \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,18468,a(flip),b,25850,a),flip(a)].">
      <j1 rule="hyper" parents="373 18468 25850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27877">
    <literal><![CDATA[
      (K(x * y,x \ 1) / x) \ y = y / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(38,a,15103,a(flip),b,25866,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 15103 25866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27878">
    <literal><![CDATA[
      (K((x \ y) * z,y \ x) / (x \ y)) \ z = z / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(6700(a,1),27877(a,1,1,1))].">
      <j1 rule="para" parents="6700 27877"/>
    </justification>
  </clause>

  <clause id="27879">
    <literal><![CDATA[
      (K(x * y,y \ 1) / y) \ x = x / (1 / y)
    ]]></literal>
    <justification jstring="[para(7520(a,2),27877(a,1,1,1))].">
      <j1 rule="para" parents="7520 27877"/>
    </justification>
  </clause>

  <clause id="27880">
    <literal><![CDATA[
      (K((x \ y) * K(x \ 1,y),(x \ y) \ y) / (y \ (x \ y))) \ y = y / (1 / (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(6328(a,1),27878(a,1,1,1,1))].">
      <j1 rule="para" parents="6328 27878"/>
    </justification>
  </clause>

  <clause id="27881">
    <literal><![CDATA[
      L(x * K(y,z),x,x * (z * y)) = R((z * y) / x,x,x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,26070,a,b,25876,a)].">
      <j1 rule="hyper" parents="373 26070 25876"/>
    </justification>
  </clause>

  <clause id="27882">
    <literal><![CDATA[
      (x \ ((1 / y) \ z)) * K(u,(1 / y) \ z) = x \ ((K(z * y,u) / y) \ z)
    ]]></literal>
    <justification jstring="[para(14469(a,2),25890(a,1,2))].">
      <j1 rule="para" parents="14469 25890"/>
    </justification>
  </clause>

  <clause id="27883">
    <literal><![CDATA[
      (R(K(x,y) * (y / z),u,w) * z) * x = x * (z * R(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14713,a,b,26011,a)].">
      <j1 rule="hyper" parents="64 14713 26011"/>
    </justification>
  </clause>

  <clause id="27885">
    <literal><![CDATA[
      T(x,y) * R(T(x,z) \ 1,u,w) = T(x,z) \ R(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,24598,a(flip),b,26020,a),flip(a)].">
      <j1 rule="hyper" parents="373 24598 26020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27886">
    <literal><![CDATA[
      x * R(T(x,y) \ K(x,z),u,w) = T(x,y) \ R(T(x,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,25997,a(flip),b,27885,a)].">
      <j1 rule="hyper" parents="64 25997 27885"/>
    </justification>
  </clause>

  <clause id="27888">
    <literal><![CDATA[
      T(x,y) \ R(T(x,x \ 1),z,u) = x * R(K(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[para(5803(a,1),27886(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5803 27886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27889">
    <literal><![CDATA[
      T(x,y) \ R(x,x,z * x) = x * R(K(y,x) / x,x,z)
    ]]></literal>
    <justification jstring="[para(26194(a,1),27888(a,1,2))].">
      <j1 rule="para" parents="26194 27888"/>
    </justification>
  </clause>

  <clause id="27890">
    <literal><![CDATA[
      (1 / x) \ (y * R(y \ (1 / x),z,u)) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26012,a(flip),b,26023,a)].">
      <j1 rule="hyper" parents="64 26012 26023"/>
    </justification>
  </clause>

  <clause id="27891">
    <literal><![CDATA[
      (K(x,y) * (T(x,y) \ L(z,u,w))) / (T(x,y) \ 1) = L((x \ z) / (T(x,y) \ 1),u,w)
    ]]></literal>
    <justification jstring="[para(26103(a,1),6138(a,1,1))].">
      <j1 rule="para" parents="26103 6138"/>
    </justification>
  </clause>

  <clause id="27892">
    <literal><![CDATA[
      (x \ K(y,z)) * L(x \ 1,u,w) = x \ L(K(y,z) / x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26106,a(flip),b,26114,a)].">
      <j1 rule="hyper" parents="64 26106 26114"/>
    </justification>
  </clause>

  <clause id="27893">
    <literal><![CDATA[
      R(R(x,x,y * x),x,x) * y = (((x \ 1) \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(2981(a,1),26310(a,1,1,1))].">
      <j1 rule="para" parents="2981 26310"/>
    </justification>
  </clause>

  <clause id="27895">
    <literal><![CDATA[
      R(x,x,(y * x) * x) * y = (((x \ 1) \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(26227(a,1),27893(a,1,1))].">
      <j1 rule="para" parents="26227 27893"/>
    </justification>
  </clause>

  <clause id="27897">
    <literal><![CDATA[
      R(x,x,x * (x * y)) * y = (((x \ 1) \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(26247(a,1),27895(a,1,1))].">
      <j1 rule="para" parents="26247 27895"/>
    </justification>
  </clause>

  <clause id="27898">
    <literal><![CDATA[
      R(x,y,((z / (u / w)) * v5) \ v6) = R(x,y,(((w \ u) \ z) * v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,26245,a(flip),b,26339,a),flip(a)].">
      <j1 rule="hyper" parents="373 26245 26339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27899">
    <literal><![CDATA[
      T(((x * y) * y) * z,z) / R(z,x,z) = T((x * y) * y,z)
    ]]></literal>
    <justification jstring="[para(13712(a,1),26572(a,1,2))].">
      <j1 rule="para" parents="13712 26572"/>
    </justification>
  </clause>

  <clause id="27900">
    <literal><![CDATA[
      (x \ ((((x * y) * y) * x) / x)) * x = T((x * y) * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25518,a(flip),b,27899,a)].">
      <j1 rule="hyper" parents="64 25518 27899"/>
    </justification>
  </clause>

  <clause id="27902">
    <literal><![CDATA[
      (x \ ((x * y) * y)) * x = T((x * y) * y,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),27900(a,1,1,2))].">
      <j1 rule="para" parents="11 27900"/>
    </justification>
  </clause>

  <clause id="27904">
    <literal><![CDATA[
      R(x,R(T(y,z),u,w) \ (L(v5,R(T(y,z),u,w) \ v6,R(T(y,z),u,w)) * v6),v7) = R(x,(R(y,u,w) \ v6) * T(v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(1010(a,2),26586(a,1,2))].">
      <j1 rule="para" parents="1010 26586"/>
    </justification>
  </clause>

  <clause id="27905">
    <literal><![CDATA[
      ((x / y) * T(x / y,y)) \ (z \ u) = (z * ((y \ x) * (x / y))) \ u
    ]]></literal>
    <justification jstring="[para(413(a,1),26606(a,2,1,2))].">
      <j1 rule="para" parents="413 26606"/>
    </justification>
  </clause>

  <clause id="27906">
    <literal><![CDATA[
      R(x,y \ (z * ((u * u) * w)),v5) = R(x,y \ (z * w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26509,a(flip),b,26704,a),flip(a)].">
      <j1 rule="hyper" parents="64 26509 26704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27908">
    <literal><![CDATA[
      R(x,(y * (z * ((u * u) * w))) \ ((y * z) * w),v5) = R(x,a(y,z,(u * u) * w),v5)
    ]]></literal>
    <justification jstring="[para(14(a,2),27906(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 27906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27909">
    <literal><![CDATA[
      ((x * x) * (y / L(x,x,x * z))) * x = x * (L(x \ 1,x,z) \ y)
    ]]></literal>
    <justification jstring="[para(807(a,1),26724(a,1,1))].">
      <j1 rule="para" parents="807 26724"/>
    </justification>
  </clause>

  <clause id="27910">
    <literal><![CDATA[
      K(x,T(((y \ z) \ z) / u,w)) = K(x,T(K(z,y) * (y / u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,19647,a,b,26753,a)].">
      <j1 rule="hyper" parents="64 19647 26753"/>
    </justification>
  </clause>

  <clause id="27911">
    <literal><![CDATA[
      K(x,T((y \ z) \ (z / u),w)) = K(x,T(K(z,y) * (y / u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27134,a(flip),b,27910,a)].">
      <j1 rule="hyper" parents="64 27134 27910"/>
    </justification>
  </clause>

  <clause id="27912">
    <literal><![CDATA[
      K(x,T((y \ z) \ (z / u),w)) = K(x,T(T(y,z) / u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,18173,a(flip),b,27911,a),flip(a)].">
      <j1 rule="hyper" parents="373 18173 27911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27913">
    <literal><![CDATA[
      K(x,T(y / (z / (z / u)),w)) = K(x,T(T(y,z) / u,w * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,25837,a(flip),b,27912,a)].">
      <j1 rule="hyper" parents="64 25837 27912"/>
    </justification>
  </clause>

  <clause id="27915">
    <literal><![CDATA[
      x / (1 / L(x,y,z)) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(739,a,26776,a),flip(a)].">
      <j1 rule="hyper" parents="739 26776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27917">
    <literal><![CDATA[
      (x * L(x,y,z)) \ x = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(215,a,27915,a)].">
      <j1 rule="hyper" parents="215 27915"/>
    </justification>
  </clause>

  <clause id="27918">
    <literal><![CDATA[
      a(x \ (x \ L(x * y,z,u)),w,v5) = a(L((x \ 1) \ y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26794,a(flip),b,26853,a),flip(a)].">
      <j1 rule="hyper" parents="373 26794 26853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27919">
    <literal><![CDATA[
      a(x,x,y) \ (a(x,x,y) \ 1) = y \ (a(x,x,y) \ L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(139,a,14102,a(flip),b,26956,a),flip(a)].">
      <j1 rule="hyper" parents="139 14102 26956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27920">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u * a(x,y,z)) = u * (a(x,y,z) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(23138(a,1),26957(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23138 26957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27921">
    <literal><![CDATA[
      (x \ a(y,z,u)) * ((1 / x) * (a(y,z,u) \ x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,25824,a(flip),b,27013,a),flip(a)].">
      <j1 rule="hyper" parents="64 25824 27013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27922">
    <literal><![CDATA[
      (1 / x) * ((1 / L(x,y,y)) \ z) = x * (((1 / x) \ a(y,y,x)) \ z)
    ]]></literal>
    <justification jstring="[para(24641(a,1),27024(a,2,2,1))].">
      <j1 rule="para" parents="24641 27024"/>
    </justification>
  </clause>

  <clause id="27924">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ (z / x),u,w) = (y * R(y \ z,u,w)) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,2864,a(flip),b,27047,a),flip(a)].">
      <j1 rule="hyper" parents="64 2864 27047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27925">
    <literal><![CDATA[
      R(x \ 1,x,y) * ((x \ 1) \ z) = (y / (x * y)) * ((1 / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,451,a(flip),b,27061,a),flip(a)].">
      <j1 rule="hyper" parents="64 451 27061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27926">
    <literal><![CDATA[
      R(x,x,y) * (x \ z) = (y / (x * y)) * ((1 / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2760,a(flip),b,27925,a)].">
      <j1 rule="hyper" parents="64 2760 27925"/>
    </justification>
  </clause>

  <clause id="27927">
    <literal><![CDATA[
      (1 / (x \ 1)) * (L(x \ 1,y,z) * u) = L(1 / x,y,z) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27183,a(flip),b,27081,a)].">
      <j1 rule="hyper" parents="64 27183 27081"/>
    </justification>
  </clause>

  <clause id="27928">
    <literal><![CDATA[
      R(x,y,L(T(z,u),T(z,w),T(z,w) \ v5)) = R(x,y,R(z,z,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,26299,a(flip),b,27097,a),flip(a)].">
      <j1 rule="hyper" parents="373 26299 27097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27929">
    <literal><![CDATA[
      R(x,T(y,z),L(T(u,w),T(u,v5),T(u,v5) \ v6)) = R(x,y,R(u,u,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,26406,a(flip),b,27928,a),flip(a)].">
      <j1 rule="hyper" parents="373 26406 27928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27930">
    <literal><![CDATA[
      K(x,T((y * z) / (z * u),w)) = K(x,T(T(y,z) / u,z * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,25546,a(flip),b,27132,a),flip(a)].">
      <j1 rule="hyper" parents="64 25546 27132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27931">
    <literal><![CDATA[
      K(x,T(y / ((z * u) / z),w)) = K(x,T(T(y,z) / u,z * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,23506,a(flip),b,27930,a)].">
      <j1 rule="hyper" parents="64 23506 27930"/>
    </justification>
  </clause>

  <clause id="27932">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,z * w)) = K(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18233,a(flip),b,27931,a),flip(a)].">
      <j1 rule="hyper" parents="64 18233 27931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27933">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,w * z)) = K(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(17266,a,27932,a)].">
      <j1 rule="hyper" parents="17266 27932"/>
    </justification>
  </clause>

  <clause id="27934">
    <literal><![CDATA[
      T(x,T(T(y,z) / u,z * w)) = T(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(143,a,27932,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 27932 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27935">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,w * (z * v5))) = K(x,T(y / T(u,z),w * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,25522,a,b,27932,a)].">
      <j1 rule="hyper" parents="64 25522 27932"/>
    </justification>
  </clause>

  <clause id="27936">
    <literal><![CDATA[
      K(x,T(y / (z / (z / u)),w)) = K(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27913,a,b,27933,a)].">
      <j1 rule="hyper" parents="64 27913 27933"/>
    </justification>
  </clause>

  <clause id="27937">
    <literal><![CDATA[
      T(x,T(y \ T(z,u),u * w)) = T(x,T(z / T(y,u),w * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,25834,a(flip),b,27934,a)].">
      <j1 rule="hyper" parents="64 25834 27934"/>
    </justification>
  </clause>

  <clause id="27938">
    <literal><![CDATA[
      K(x,T(y / (1 / (K(z,u) / z)),w)) = K(x,T(y / T(z,z \ u),w))
    ]]></literal>
    <justification jstring="[para(25199(a,1),27936(a,1,2,1,2))].">
      <j1 rule="para" parents="25199 27936"/>
    </justification>
  </clause>

  <clause id="27939">
    <literal><![CDATA[
      T(x,T(y \ T(z,u),u * w)) = T(x,T(T(y,u) \ z,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,25291,a(flip),b,27937,a),flip(a)].">
      <j1 rule="hyper" parents="373 25291 27937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27940">
    <literal><![CDATA[
      T(x,T(T(y,z) \ 1,u)) = T(x,T(y \ 1,z * u))
    ]]></literal>
    <justification jstring="[para(376(a,1),27939(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="376 27939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27941">
    <literal><![CDATA[
      T(x,T(T(y,z) \ 1,u)) = T(x,T(y \ 1,u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,17089,a,b,27940,a),flip(a)].">
      <j1 rule="hyper" parents="373 17089 27940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27942">
    <literal><![CDATA[
      T(x,T(y \ 1,z * u)) = T(x,z \ (T(y,u) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,8083,a(flip),b,27941,a),flip(a)].">
      <j1 rule="hyper" parents="64 8083 27941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27943">
    <literal><![CDATA[
      T(x,y \ (T(1 / z,u) \ y)) = T(x,T(z,y * u))
    ]]></literal>
    <justification jstring="[para(82(a,1),27942(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 27942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27944">
    <literal><![CDATA[
      T(x,T(y \ ((1 / z) \ y),u)) = T(x,T(z,y * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19645,a,b,27943,a)].">
      <j1 rule="hyper" parents="64 19645 27943"/>
    </justification>
  </clause>

  <clause id="27945">
    <literal><![CDATA[
      T(((1 / x) * y) \ y,K((1 / x) * y,z)) = y / T((1 / x) * y,T(x,y * z))
    ]]></literal>
    <justification jstring="[para(27944(a,1),25342(a,1,2)),flip(a)].">
      <j1 rule="para" parents="27944 25342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27946">
    <literal><![CDATA[
      K(x,T(y \ (z * (u / w)),y * (z * u))) = K(x,w \ ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,23044,a(flip),b,27135,a)].">
      <j1 rule="hyper" parents="64 23044 27135"/>
    </justification>
  </clause>

  <clause id="27947">
    <literal><![CDATA[
      R(T(x,y),z,u) * (x \ (w * w)) = T(x,y) * R(x \ (w * w),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26022,a(flip),b,27137,a),flip(a)].">
      <j1 rule="hyper" parents="64 26022 27137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27948">
    <literal><![CDATA[
      (L(x,x,y) \ y) \ ((x \ y) * z) = (y * (1 / x)) \ ((y / x) * z)
    ]]></literal>
    <justification jstring="[para(11795(a,1),27146(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11795 27146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27949">
    <literal><![CDATA[
      x \ ((y \ L(y,y,x)) \ x) = a(x,y,L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,600,a(flip),b,27149,a),flip(a)].">
      <j1 rule="hyper" parents="64 600 27149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27950">
    <literal><![CDATA[
      (x * (y \ L(y,y,x))) \ x = a(x,y,L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,27002,a,b,27949,a)].">
      <j1 rule="hyper" parents="64 27002 27949"/>
    </justification>
  </clause>

  <clause id="27951">
    <literal><![CDATA[
      a(x,y,L(y,y,x)) \ x = x * (y \ L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,27950,a)].">
      <j1 rule="hyper" parents="40 23134 27950"/>
    </justification>
  </clause>

  <clause id="27952">
    <literal><![CDATA[
      ((x / y) \ 1) * (z / ((x / y) \ 1)) = (y / x) * (z / (y / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,27138,a(flip),b,27187,a),flip(a)].">
      <j1 rule="hyper" parents="373 27138 27187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27953">
    <literal><![CDATA[
      R(x,y,((z \ (u / w)) * v5) * v6) = R(x,y,(v5 * (z \ (w \ u))) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,26213,a,b,27192,a),flip(a)].">
      <j1 rule="hyper" parents="373 26213 27192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27954">
    <literal><![CDATA[
      x * ((T(y,y \ z) * x) \ z) = T(x * ((y * x) \ z),y)
    ]]></literal>
    <justification jstring="[para(24706(a,1),27226(a,1,2,1,1))].">
      <j1 rule="para" parents="24706 27226"/>
    </justification>
  </clause>

  <clause id="27956">
    <literal><![CDATA[
      x * (L(x,x \ y,y) \ T(x,x \ 1)) = T(x * a(y,x \ y,x),x \ 1)
    ]]></literal>
    <justification jstring="[para(26986(a,2),27241(a,2,2)),flip(a)].">
      <j1 rule="para" parents="26986 27241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27957">
    <literal><![CDATA[
      (L(L(x,y,z),u,w) * v5) * x = (x * v5) * L(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(328,a,27243,a)].">
      <j1 rule="hyper" parents="328 27243"/>
    </justification>
  </clause>

  <clause id="27958">
    <literal><![CDATA[
      (x * (L(x,y,z) \ 1)) * L(L(x,y,z),u,w) = (L(x,y,z) \ L(L(x,y,z),u,w)) * x
    ]]></literal>
    <justification jstring="[para(1807(a,1),27957(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1807 27957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27959">
    <literal><![CDATA[
      L(x * ((1 / x) * y),z,u) = x * ((1 / x) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1727(a,1),27269(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1727 27269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27960">
    <literal><![CDATA[
      x \ L(x * ((1 / x) * y),z,u) = (1 / x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,27959,a,b,xx)].">
      <j1 rule="hyper" parents="139 27959"/>
    </justification>
  </clause>

  <clause id="27961">
    <literal><![CDATA[
      L(((1 / x) * y) * x,z,u) = ((1 / x) * L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,27960,a(flip),b,5543,a),flip(a)].">
      <j1 rule="hyper" parents="144 27960 5543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27962">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ 1 = ((y * x) \ y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,24924,a(flip),b,27270,a),flip(a)].">
      <j1 rule="hyper" parents="64 24924 27270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27963">
    <literal><![CDATA[
      a(x,y,(z * L(u,w,z)) * w) = a(x,y,z * (w * L(u,z,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27398,a(flip),b,27373,a)].">
      <j1 rule="hyper" parents="64 27398 27373"/>
    </justification>
  </clause>

  <clause id="27965">
    <literal><![CDATA[
      a(x,y,z \ (u * ((1 / w) \ w))) = a(x,y,(z \ u) * (w * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27782,a(flip),b,27436,a),flip(a)].">
      <j1 rule="hyper" parents="64 27782 27436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27966">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ (w * u))) = a(x,y,(z \ w) * (u * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27434,a,b,27965,a)].">
      <j1 rule="hyper" parents="64 27434 27965"/>
    </justification>
  </clause>

  <clause id="27967">
    <literal><![CDATA[
      a(x,y,(z \ (u \ w)) * (u * u)) = a(x,y,z \ ((u \ 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27337,a(flip),b,27966,a),flip(a)].">
      <j1 rule="hyper" parents="64 27337 27966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27968">
    <literal><![CDATA[
      a(x,y,(z * z) * (u \ (z \ w))) = a(x,y,u \ ((z \ 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(27453,a,27967,a)].">
      <j1 rule="hyper" parents="27453 27967"/>
    </justification>
  </clause>

  <clause id="27969">
    <literal><![CDATA[
      a(x,y,(z \ ((u * u) \ w)) \ v5) = a(x,y,(u * u) * ((w / z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27541,a(flip),b,27444,a),flip(a)].">
      <j1 rule="hyper" parents="64 27541 27444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27970">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ (w \ 1))) = a(x,y,u * ((w * w) \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27759,a(flip),b,27461,a),flip(a)].">
      <j1 rule="hyper" parents="373 27759 27461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27971">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((u * u) \ w)) = a(x,y,(z \ (u \ 1)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27577,a(flip),b,27970,a),flip(a)].">
      <j1 rule="hyper" parents="64 27577 27970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27972">
    <literal><![CDATA[
      a(x,y,z \ ((u / (w * u)) \ 1)) = a(x,y,z \ ((u \ (w \ u)) \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,27511,a(flip),b,27488,a),flip(a)].">
      <j1 rule="hyper" parents="64 27511 27488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27973">
    <literal><![CDATA[
      a(x,y,(L(T(z,u),w,v5) \ v6) * ((v7 * v7) \ L(z,w,v5))) = a(x,y,(v7 * v7) \ v6)
    ]]></literal>
    <justification jstring="[para(802(a,1),27537(a,2,3))].">
      <j1 rule="para" parents="802 27537"/>
    </justification>
  </clause>

  <clause id="27974">
    <literal><![CDATA[
      a(x,y,(((z / u) / w) * v5) * v6) = a(x,y,((w \ (u \ z)) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,27411,a(flip),b,27547,a),flip(a)].">
      <j1 rule="hyper" parents="373 27411 27547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27975">
    <literal><![CDATA[
      a(x,y,(z / (u * (w / v5))) * v6) = a(x,y,((u * (v5 \ w)) \ z) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,27317,a,b,27548,a)].">
      <j1 rule="hyper" parents="64 27317 27548"/>
    </justification>
  </clause>

  <clause id="27976">
    <literal><![CDATA[
      a(x,y,(R(1 / z,u,w) * R(z,u,w)) \ (R(1 / z,u,w) * v5)) = a(x,y,((z * z) * 1) \ ((R(1 / z,u,w) \ 1) * v5))
    ]]></literal>
    <justification jstring="[para(2119(a,1),27553(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2119 27553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27977">
    <literal><![CDATA[
      a(x,y,L(a(z,z,u) \ 1,w,v5)) = a(x,y,L(u \ L(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,27344,a(flip),b,27611,a)].">
      <j1 rule="hyper" parents="373 27344 27611"/>
    </justification>
  </clause>

  <clause id="27978">
    <literal><![CDATA[
      a(x,y,(((z * z) / u) \ w) \ 1) = a(x,y,(w / (1 / u)) \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27389,a(flip),b,27614,a)].">
      <j1 rule="hyper" parents="64 27389 27614"/>
    </justification>
  </clause>

  <clause id="27979">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) * w) * v5) = a(x,y,((z \ (u \ z)) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27411,a(flip),b,27615,a),flip(a)].">
      <j1 rule="hyper" parents="64 27411 27615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27980">
    <literal><![CDATA[
      a(x,y,(z * z) \ ((u \ (z \ 1)) \ w)) = a(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27767,a(flip),b,27622,a)].">
      <j1 rule="hyper" parents="64 27767 27622"/>
    </justification>
  </clause>

  <clause id="27981">
    <literal><![CDATA[
      a(x,y,(R(z,u,u) * R(z,u,u)) \ ((((z * u) * u) \ 1) \ w)) = a(x,y,((u * u) \ R(z,u,u)) \ w)
    ]]></literal>
    <justification jstring="[para(875(a,1),27980(a,1,3,2,1))].">
      <j1 rule="para" parents="875 27980"/>
    </justification>
  </clause>

  <clause id="27982">
    <literal><![CDATA[
      a(x,y,z * (((u * w) \ w) \ v5)) = a(x,y,z * ((w \ (u \ w)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27500,a(flip),b,27631,a),flip(a)].">
      <j1 rule="hyper" parents="64 27500 27631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27983">
    <literal><![CDATA[
      a(x,y,(z \ (u / (w \ v5))) * v6) = a(x,y,(z \ ((v5 / w) \ u)) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,27470,a,b,27684,a)].">
      <j1 rule="hyper" parents="373 27470 27684"/>
    </justification>
  </clause>

  <clause id="27984">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ (u \ w))) = a(x,y,z * (u \ ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[para(1166(a,2),27688(a,1,3,2))].">
      <j1 rule="para" parents="1166 27688"/>
    </justification>
  </clause>

  <clause id="27985">
    <literal><![CDATA[
      a(x,y,z * (u * ((w \ v5) * T((v5 / w) \ v6,v7)))) = a(x,y,z * (u * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,27704,a(flip),b,27705,a),flip(a)].">
      <j1 rule="hyper" parents="64 27704 27705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27986">
    <literal><![CDATA[
      a(x,y,z * (u * ((u \ 1) * w))) = a(x,y,z * R(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27440,a(flip),b,27705,a),flip(a)].">
      <j1 rule="hyper" parents="64 27440 27705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27987">
    <literal><![CDATA[
      a(x,y,z * R(u,w,w)) = a(x,y,z * L(u,w,w))
    ]]></literal>
    <justification jstring="[para(1139(a,1),27986(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="1139 27986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27988">
    <literal><![CDATA[
      a(x,y,(1 / z) * ((u * u) * R(w,v5,v5))) = a(x,y,(z \ (u * u)) * L(w,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27769,a,b,27987,a)].">
      <j1 rule="hyper" parents="64 27769 27987"/>
    </justification>
  </clause>

  <clause id="27989">
    <literal><![CDATA[
      a(x,y,z \ (((u * w) \ w) * v5)) = a(x,y,z \ ((w \ (w / u)) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27492,a(flip),b,27750,a),flip(a)].">
      <j1 rule="hyper" parents="64 27492 27750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27990">
    <literal><![CDATA[
      a(x,y,L(R(z,u,u) / (1 / u),w,v5)) = a(x,y,L(u * z,w,v5))
    ]]></literal>
    <justification jstring="[para(1413(a,1),27772(a,1,3,1))].">
      <j1 rule="para" parents="1413 27772"/>
    </justification>
  </clause>

  <clause id="27991">
    <literal><![CDATA[
      a(x,y,L((1 / z) \ R(u,z,z),w,v5)) = a(x,y,L(z * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27344,a(flip),b,27990,a)].">
      <j1 rule="hyper" parents="64 27344 27990"/>
    </justification>
  </clause>

  <clause id="27992">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) * (z / w)) = a(x,y,(z * u) * (w \ (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27310,a(flip),b,27774,a),flip(a)].">
      <j1 rule="hyper" parents="373 27310 27774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27993">
    <literal><![CDATA[
      L(x,y,z \ (L(u,u,u) \ z)) = L(x,y,R(u,u,u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,2195,a(flip),b,27810,a),flip(a)].">
      <j1 rule="hyper" parents="64 2195 27810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27995">
    <literal><![CDATA[
      L(x,y,L(z \ (u \ z),u,u)) = L(x,y,R(u,u,u \ z))
    ]]></literal>
    <justification jstring="[para(12019(a,2),27993(a,1,3))].">
      <j1 rule="para" parents="12019 27993"/>
    </justification>
  </clause>

  <clause id="27996">
    <literal><![CDATA[
      L(x,y,L(z \ (u \ z),u,u)) = L(x,y,R(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,25105,a(flip),b,27995,a),flip(a)].">
      <j1 rule="hyper" parents="373 25105 27995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27997">
    <literal><![CDATA[
      K(x,y) * (R(T(z,u),w,v5) \ z) = z * (R(T(z,u),w,v5) \ K(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,25944,a(flip),b,27811,a),flip(a)].">
      <j1 rule="hyper" parents="373 25944 27811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27998">
    <literal><![CDATA[
      (x * (T(T(x,y),z) \ u)) / w = x * (T(T(x,y),z) \ (u / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,6216,a(flip),b,27814,a),flip(a)].">
      <j1 rule="hyper" parents="64 6216 27814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="27999">
    <literal><![CDATA[
      T(x,y * (z * (T(T(z,u),w) \ (v5 / z)))) = T(x,y * T(T(T(z,u),w) \ v5,z))
    ]]></literal>
    <justification jstring="[para(27998(a,1),15808(a,1,2,2))].">
      <j1 rule="para" parents="27998 15808"/>
    </justification>
  </clause>

  <clause id="28000">
    <literal><![CDATA[
      (x / (y \ R(y,y,z))) * K(z,z \ (y \ z)) = x / T(y * (z \ (y \ z)),K(y \ z,z))
    ]]></literal>
    <justification jstring="[para(3008(a,2),27815(a,1,1,2))].">
      <j1 rule="para" parents="3008 27815"/>
    </justification>
  </clause>

  <clause id="28001">
    <literal><![CDATA[
      K(x,K(y \ 1,T(z,u)) * (w * K(u,y))) = K(x,(y * T(T(y,u) \ 1,z)) * w)
    ]]></literal>
    <justification jstring="[para(27823(a,1),19582(a,1,2)),flip(a)].">
      <j1 rule="para" parents="27823 19582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28002">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (((x \ 1) * y) * z)) = T(x \ 1,(x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,24579,a(flip),b,27832,a),flip(a)].">
      <j1 rule="hyper" parents="373 24579 27832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28003">
    <literal><![CDATA[
      x * ((x \ 1) \ (y * (z \ (x \ 1)))) = (x * x) * (y * (z \ (1 / x)))
    ]]></literal>
    <justification jstring="[hyper(40,a,1229,a,b,27852,a)].">
      <j1 rule="hyper" parents="40 1229 27852"/>
    </justification>
  </clause>

  <clause id="28004">
    <literal><![CDATA[
      T(x,y / T(T(z \ 1,u),w)) = T(x,y / T(z \ K(w,z),u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17712,a(flip),b,27861,a)].">
      <j1 rule="hyper" parents="373 17712 27861"/>
    </justification>
  </clause>

  <clause id="28005">
    <literal><![CDATA[
      T(x,y / T(T(z \ 1,u),w)) = T(x,y * T(T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17718,a(flip),b,28004,a),flip(a)].">
      <j1 rule="hyper" parents="373 17718 28004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28006">
    <literal><![CDATA[
      (x * x) * ((x \ 1) * ((L(x,y,z) \ 1) \ u)) = x * ((1 / L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2020,a,b,27868,a)].">
      <j1 rule="hyper" parents="64 2020 27868"/>
    </justification>
  </clause>

  <clause id="28007">
    <literal><![CDATA[
      (a(x,y,z) / z) * R(z,u,w) = a(x,y,z) * (z \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(2067(a,1),27869(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2067 27869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28008">
    <literal><![CDATA[
      a(x,x,y) * (y \ R(y,z,u)) = L(y,x,x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25044,a(flip),b,28007,a),flip(a)].">
      <j1 rule="hyper" parents="64 25044 28007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28009">
    <literal><![CDATA[
      R(T(x,y * y),y,y) \ T(x,y) = a(y,y,x) * K(y,y * x)
    ]]></literal>
    <justification jstring="[para(22(a,2),27870(a,1,2))].">
      <j1 rule="para" parents="22 27870"/>
    </justification>
  </clause>

  <clause id="28010">
    <literal><![CDATA[
      R(x,y,y) \ T(x,y \ (y \ y)) = a(y,y,x) * K(y,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25840,a(flip),b,28009,a)].">
      <j1 rule="hyper" parents="64 25840 28009"/>
    </justification>
  </clause>

  <clause id="28011">
    <literal><![CDATA[
      R(x,y,y) \ T(x,y \ 1) = a(y,y,x) * K(y,y * x)
    ]]></literal>
    <justification jstring="[para(68(a,1),28010(a,1,2,2,2))].">
      <j1 rule="para" parents="68 28010"/>
    </justification>
  </clause>

  <clause id="28012">
    <literal><![CDATA[
      a(x,y,y) \ K(x,y \ 1) = a(y,y,x) * K(y,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,16048,a,b,28011,a)].">
      <j1 rule="hyper" parents="64 16048 28011"/>
    </justification>
  </clause>

  <clause id="28014">
    <literal><![CDATA[
      K(x,K(y,z / u) \ (u * (z \ w))) = K(x,T(z * (u \ 1),y) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,23043,a(flip),b,27872,a)].">
      <j1 rule="hyper" parents="64 23043 27872"/>
    </justification>
  </clause>

  <clause id="28015">
    <literal><![CDATA[
      (K(x,y) * (R(y / z,u,w) * z)) * x = x * (z * R(z \ y,u,w))
    ]]></literal>
    <justification jstring="[para(25968(a,1),27883(a,1,1))].">
      <j1 rule="para" parents="25968 27883"/>
    </justification>
  </clause>

  <clause id="28016">
    <literal><![CDATA[
      (x * ((y \ z) * (z / y))) \ u = ((z / y) * (y \ z)) \ (x \ u)
    ]]></literal>
    <justification jstring="[para(117(a,1),27905(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="117 27905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28017">
    <literal><![CDATA[
      (x * ((y \ z) * (z / y))) \ u = ((y \ z) * (z / y)) \ (x \ u)
    ]]></literal>
    <justification jstring="[para(413(a,1),28016(a,2,1))].">
      <j1 rule="para" parents="413 28016"/>
    </justification>
  </clause>

  <clause id="28018">
    <literal><![CDATA[
      (x * x) * ((y / L(x,x,x * z)) * x) = x * (L(x \ 1,x,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,33,a(flip),b,27909,a)].">
      <j1 rule="hyper" parents="64 33 27909"/>
    </justification>
  </clause>

  <clause id="28019">
    <literal><![CDATA[
      (1 / x) * ((1 / L(x,y,y)) \ z) = x * ((x * a(y,y,x)) \ z)
    ]]></literal>
    <justification jstring="[para(9440(a,1),27922(a,2,2,1))].">
      <j1 rule="para" parents="9440 27922"/>
    </justification>
  </clause>

  <clause id="28020">
    <literal><![CDATA[
      (x \ y) * (x * R(x \ ((x \ y) \ z),u,w)) = y * R(y \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(38,a,2840,a,b,27924,a(flip))].">
      <j1 rule="hyper" parents="38 2840 27924"/>
    </justification>
  </clause>

  <clause id="28021">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ (1 / x),z,u) = (y \ R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[para(1987(a,1),27924(a,2,1))].">
      <j1 rule="para" parents="1987 27924"/>
    </justification>
  </clause>

  <clause id="28022">
    <literal><![CDATA[
      L(1 / x,y,z) * (x * u) = x * (L(x \ 1,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(400,a,27927,a),flip(a)].">
      <j1 rule="hyper" parents="400 27927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28023">
    <literal><![CDATA[
      x \ (L(1 / x,y,z) * u) = L(x \ 1,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(759,a,28022,a)].">
      <j1 rule="hyper" parents="759 28022"/>
    </justification>
  </clause>

  <clause id="28024">
    <literal><![CDATA[
      L(x \ 1,y,z) * (x \ (L(1 / x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(757,a,28022,a),flip(a)].">
      <j1 rule="hyper" parents="757 28022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28026">
    <literal><![CDATA[
      x * (L(x \ 1,y,z) \ 1) = L(1 / x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,72,a(flip),b,28022,a),flip(a)].">
      <j1 rule="hyper" parents="139 72 28022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28027">
    <literal><![CDATA[
      (x \ y) \ (L(1 / (x \ y),x \ y,x) * z) = (y \ (x * 1)) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(630(a,1),28023(a,2,1))].">
      <j1 rule="para" parents="630 28023"/>
    </justification>
  </clause>

  <clause id="28028">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ u) = x \ (L(1 / x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(149,a,28024,a)].">
      <j1 rule="hyper" parents="149 28024"/>
    </justification>
  </clause>

  <clause id="28029">
    <literal><![CDATA[
      R(x,T(y,z),L(T(u,w),T(u,v5),T(u,v5) \ v6)) = R(x,y,L(u,u,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,26360,a(flip),b,27929,a),flip(a)].">
      <j1 rule="hyper" parents="373 26360 27929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28030">
    <literal><![CDATA[
      K(x,T((y * (z / u)) / T(w,u),y * z)) = K(x,w \ T(y * (z / u),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,21400,a(flip),b,27935,a),flip(a)].">
      <j1 rule="hyper" parents="64 21400 27935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28031">
    <literal><![CDATA[
      K(x,T(y / T(z,z \ u),w)) = K(x,T(y * (K(z,u) / z),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,14621,a(flip),b,27938,a),flip(a)].">
      <j1 rule="hyper" parents="64 14621 27938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28032">
    <literal><![CDATA[
      K(x,T(y / T(z,z \ u),w)) = K(x,T(y * (z \ K(z,u)),w))
    ]]></literal>
    <justification jstring="[hyper(373,a,19617,a(flip),b,28031,a),flip(a)].">
      <j1 rule="hyper" parents="373 19617 28031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28033">
    <literal><![CDATA[
      K(x,T(y / T(z,z \ u),w)) = K(x,T(y / T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(373,a,26754,a(flip),b,28032,a),flip(a)].">
      <j1 rule="hyper" parents="373 26754 28032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28034">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) \ u),w)) = K(x,T(y / T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18131,a(flip),b,28033,a)].">
      <j1 rule="hyper" parents="64 18131 28033"/>
    </justification>
  </clause>

  <clause id="28035">
    <literal><![CDATA[
      K(x,T(y \ (((z \ u) \ u) \ w),K(v5,v6))) = K(x,T((w / y) / T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,25836,a,b,28034,a)].">
      <j1 rule="hyper" parents="64 25836 28034"/>
    </justification>
  </clause>

  <clause id="28036">
    <literal><![CDATA[
      K(x,T((y * (z / u)) / w,y * z)) = K(x,u \ ((y \ w) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,25281,a(flip),b,27946,a)].">
      <j1 rule="hyper" parents="64 25281 27946"/>
    </justification>
  </clause>

  <clause id="28037">
    <literal><![CDATA[
      R(x,y,((z \ (u / w)) * v5) * (K(v6,v7) \ v8)) = R(x,y,(v5 * (z \ (w \ u))) * v8)
    ]]></literal>
    <justification jstring="[hyper(373,a,26251,a(flip),b,27953,a),flip(a)].">
      <j1 rule="hyper" parents="373 26251 27953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28038">
    <literal><![CDATA[
      L(x \ R(x,y,((z \ (u / w)) * (z \ (w \ u))) * v5),x,y * v5) = a(x,y,((z \ (u / w)) * (z \ (u / w))) * v5)
    ]]></literal>
    <justification jstring="[para(27953(a,1),25129(a,1,1,2))].">
      <j1 rule="para" parents="27953 25129"/>
    </justification>
  </clause>

  <clause id="28039">
    <literal><![CDATA[
      a(x,y,(z \ ((u * u) \ w)) \ v5) = a(x,y,(u * u) * ((z \ w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,27500,a(flip),b,27969,a),flip(a)].">
      <j1 rule="hyper" parents="373 27500 27969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28040">
    <literal><![CDATA[
      a(x,y,((z \ (u * u)) \ w) \ 1) = a(x,y,(w / (1 / z)) \ (u * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27520,a(flip),b,27978,a)].">
      <j1 rule="hyper" parents="64 27520 27978"/>
    </justification>
  </clause>

  <clause id="28041">
    <literal><![CDATA[
      a(x,y,(((z * u) \ u) * w) * v5) = a(x,y,((u \ (z \ u)) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27411,a(flip),b,27979,a)].">
      <j1 rule="hyper" parents="64 27411 27979"/>
    </justification>
  </clause>

  <clause id="28042">
    <literal><![CDATA[
      a(x,y,z * (((u * w) \ u) \ v5)) = a(x,y,z * ((u \ (w \ u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27508,a(flip),b,27982,a)].">
      <j1 rule="hyper" parents="64 27508 27982"/>
    </justification>
  </clause>

  <clause id="28043">
    <literal><![CDATA[
      a(x,y,z \ (((u * w) \ w) * v5)) = a(x,y,z \ ((w \ (u \ w)) * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,27690,a(flip),b,27989,a),flip(a)].">
      <j1 rule="hyper" parents="373 27690 27989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28044">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) * (z / w)) = a(x,y,(z * u) * (w \ (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27482,a(flip),b,27992,a),flip(a)].">
      <j1 rule="hyper" parents="373 27482 27992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28045">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (((x \ 1) * y) * z)) = T(x \ 1,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,25554,a(flip),b,28002,a),flip(a)].">
      <j1 rule="hyper" parents="373 25554 28002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28046">
    <literal><![CDATA[
      K(x,K(y / z,u) * (z * (y \ w))) = K(x,T(y * (z \ 1),u) \ w)
    ]]></literal>
    <justification jstring="[para(6156(a,1),28014(a,1,2))].">
      <j1 rule="para" parents="6156 28014"/>
    </justification>
  </clause>

  <clause id="28047">
    <literal><![CDATA[
      (K(x,y) * (z * R(z \ y,u,w))) * x = x * (z * R(z \ y,u,w))
    ]]></literal>
    <justification jstring="[para(843(a,1),28015(a,1,1,2))].">
      <j1 rule="para" parents="843 28015"/>
    </justification>
  </clause>

  <clause id="28048">
    <literal><![CDATA[
      (x * x) * (x * (L(x,x,x * y) \ z)) = x * (L(x \ 1,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(23887(a,1),28018(a,1,2))].">
      <j1 rule="para" parents="23887 28018"/>
    </justification>
  </clause>

  <clause id="28049">
    <literal><![CDATA[
      ((x \ y) * x) * R(((x \ y) * x) \ z,u,w) = y * R(y \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,1709,a,b,28020,a)].">
      <j1 rule="hyper" parents="64 1709 28020"/>
    </justification>
  </clause>

  <clause id="28050">
    <literal><![CDATA[
      R(x,T(y,z),L(T(u,w),T(u,w),T(u,w) * v5)) = R(x,y,L(u,u,v5))
    ]]></literal>
    <justification jstring="[para(25574(a,1),28029(a,1,3))].">
      <j1 rule="para" parents="25574 28029"/>
    </justification>
  </clause>

  <clause id="28051">
    <literal><![CDATA[
      a(x,y,((z \ (u * u)) \ w) \ 1) = a(x,y,((1 / z) \ w) \ (u * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27538,a(flip),b,28040,a),flip(a)].">
      <j1 rule="hyper" parents="373 27538 28040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28052">
    <literal><![CDATA[
      a(x,y,(((z * u) \ z) * w) * v5) = a(x,y,((z \ (u \ z)) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27544,a,b,28041,a)].">
      <j1 rule="hyper" parents="64 27544 28041"/>
    </justification>
  </clause>

  <clause id="28053">
    <literal><![CDATA[
      a(x,y,(((z * u) \ z) \ w) * v5) = a(x,y,v5 * ((z \ (u \ z)) \ w))
    ]]></literal>
    <justification jstring="[hyper(27453,a,28042,a)].">
      <j1 rule="hyper" parents="27453 28042"/>
    </justification>
  </clause>

  <clause id="28054">
    <literal><![CDATA[
      a(x,y,z \ ((u \ ((u \ w) \ u)) * v5)) = a(x,y,z \ ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27518,a(flip),b,28043,a),flip(a)].">
      <j1 rule="hyper" parents="64 27518 28043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28055">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) * (w \ z)) = a(x,y,(z * u) * (w \ (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27310,a(flip),b,28044,a)].">
      <j1 rule="hyper" parents="64 27310 28044"/>
    </justification>
  </clause>

  <clause id="28056">
    <literal><![CDATA[
      K(x,y * (K(y \ z,u) * (z \ w))) = K(x,T(z * (y \ 1),u) \ w)
    ]]></literal>
    <justification jstring="[para(22759(a,1),28046(a,1,2))].">
      <j1 rule="para" parents="22759 28046"/>
    </justification>
  </clause>

  <clause id="28057">
    <literal><![CDATA[
      K(x,y) * ((z * R(z \ y,u,w)) * x) = x * (z * R(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,23073,a(flip),b,28047,a)].">
      <j1 rule="hyper" parents="64 23073 28047"/>
    </justification>
  </clause>

  <clause id="28058">
    <literal><![CDATA[
      (x \ y) * (x \ R(x,z,u)) = y * R(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2299,a(flip),b,28049,a)].">
      <j1 rule="hyper" parents="64 2299 28049"/>
    </justification>
  </clause>

  <clause id="28059">
    <literal><![CDATA[
      x \ ((y \ x) * (y \ R(y,z,u))) = R(x \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,2299,a(flip),b,28049,a(flip))].">
      <j1 rule="hyper" parents="139 2299 28049"/>
    </justification>
  </clause>

  <clause id="28060">
    <literal><![CDATA[
      (x \ y) \ (y * R(y \ (x \ y),z,u)) = x \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,28049,a(flip),b,2299,a(flip))].">
      <j1 rule="hyper" parents="139 28049 2299"/>
    </justification>
  </clause>

  <clause id="28061">
    <literal><![CDATA[
      (x \ y) \ ((y * (y \ (x \ y))) * a(y \ (x \ y),z,(z \ 1) \ y)) = x \ R(x,z,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,16186,a,b,28058,a)].">
      <j1 rule="hyper" parents="139 16186 28058"/>
    </justification>
  </clause>

  <clause id="28062">
    <literal><![CDATA[
      (x \ y) \ ((((x \ y) / y) * z) * (z \ y)) = x \ R(x,z,z \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,1198,a(flip),b,28058,a)].">
      <j1 rule="hyper" parents="139 1198 28058"/>
    </justification>
  </clause>

  <clause id="28063">
    <literal><![CDATA[
      L(x \ R(x,y,z),x \ u,x \ u) = (1 / (x \ u)) * (u * R(u \ (x \ u),y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,28058,a(flip),b,561,a),flip(a)].">
      <j1 rule="hyper" parents="145 28058 561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28064">
    <literal><![CDATA[
      x \ ((y \ R(y,z,u)) * (y \ x)) = R(x \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,23708,a,b,28058,a(flip))].">
      <j1 rule="hyper" parents="139 23708 28058"/>
    </justification>
  </clause>

  <clause id="28065">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (x \ R(x,u,w)) = R(x,y,z) * R(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(1796(a,1),28058(a,2,2,1))].">
      <j1 rule="para" parents="1796 28058"/>
    </justification>
  </clause>

  <clause id="28066">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ R(x,u,w)) = L(x,y,z) * R(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(1808(a,1),28058(a,2,2,1))].">
      <j1 rule="para" parents="1808 28058"/>
    </justification>
  </clause>

  <clause id="28067">
    <literal><![CDATA[
      L(x \ R(x,y,z),x \ u,u) = (u * (x \ u)) \ R(u * (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(28060(a,1),2134(a,1,1))].">
      <j1 rule="para" parents="28060 2134"/>
    </justification>
  </clause>

  <clause id="28068">
    <literal><![CDATA[
      R(T(x / (y * x),z),y,y \ z) = R(z \ (y \ z),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1993,a,b,28064,a)].">
      <j1 rule="hyper" parents="64 1993 28064"/>
    </justification>
  </clause>

  <clause id="28069">
    <literal><![CDATA[
      R(T(x / (y * x),z),y,y \ z) = (z \ ((y \ z) * R((y \ z) \ z,y,x))) * (z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,2745,a,b,28068,a),flip(a)].">
      <j1 rule="hyper" parents="373 2745 28068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28070">
    <literal><![CDATA[
      a(x \ (y \ x),z,z \ x) = y \ R(y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26809,a(flip),b,28062,a)].">
      <j1 rule="hyper" parents="64 26809 28062"/>
    </justification>
  </clause>

  <clause id="28071">
    <literal><![CDATA[
      a((x * y) \ (z \ (x * y)),y,x) = z \ R(z,y,y \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,25788,a(flip),b,28070,a)].">
      <j1 rule="hyper" parents="64 25788 28070"/>
    </justification>
  </clause>

  <clause id="28072">
    <literal><![CDATA[
      a((x * y) \ (z \ (x * y)),y,x) = z \ R(z,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(22(a,2),28071(a,2,2,3))].">
      <j1 rule="para" parents="22 28071"/>
    </justification>
  </clause>

  <clause id="28073">
    <literal><![CDATA[
      a((x * y) \ (z \ (x * y)),y,x) = z \ R(z,y,x)
    ]]></literal>
    <justification jstring="[para(10200(a,1),28072(a,2,2))].">
      <j1 rule="para" parents="10200 28072"/>
    </justification>
  </clause>

  <clause id="28076">
    <literal><![CDATA[
      R(x,y,z) \ a((z * y) \ (x \ (z * y)),y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,28073,a,b,1794,a)].">
      <j1 rule="hyper" parents="139 28073 1794"/>
    </justification>
  </clause>

  <clause id="28077">
    <literal><![CDATA[
      K(x,x \ (y \ R(y,z,u))) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(28073(a,1),25207(a,1,2,2))].">
      <j1 rule="para" parents="28073 25207"/>
    </justification>
  </clause>

  <clause id="28078">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(u,u \ 1) = u * (1 * ((x \ R(x,y,z)) / u))
    ]]></literal>
    <justification jstring="[para(28077(a,1),6264(a,1,2))].">
      <j1 rule="para" parents="28077 6264"/>
    </justification>
  </clause>

  <clause id="28079">
    <literal><![CDATA[
      R(x,y,z) \ (u * ((x \ R(x,y,z)) / u)) = (x \ 1) * K(u,u \ 1)
    ]]></literal>
    <justification jstring="[para(28077(a,1),16690(a,2,2))].">
      <j1 rule="para" parents="28077 16690"/>
    </justification>
  </clause>

  <clause id="28080">
    <literal><![CDATA[
      a((x * y) \ ((a(z,u,w) \ 1) \ (x * y)),y,x) = R(a(z,u,w) \ 1,y,x) * a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,23134,a(flip),b,28076,a),flip(a)].">
      <j1 rule="hyper" parents="145 23134 28076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28081">
    <literal><![CDATA[
      a(x,y,((z \ (u * u)) \ w) \ 1) = a(x,y,((z \ 1) \ w) \ (u * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27520,a(flip),b,28051,a),flip(a)].">
      <j1 rule="hyper" parents="373 27520 28051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28082">
    <literal><![CDATA[
      a(x,y,(((z * u) \ z) * z) * w) = a(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27397,a(flip),b,28052,a),flip(a)].">
      <j1 rule="hyper" parents="373 27397 28052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28083">
    <literal><![CDATA[
      a(x,y,z * ((u * K(w,v5)) * (u / (u * v6)))) = a(x,y,(v6 \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27716,a,b,28082,a)].">
      <j1 rule="hyper" parents="64 27716 28082"/>
    </justification>
  </clause>

  <clause id="28084">
    <literal><![CDATA[
      a(x,y,(((z * u) \ z) \ w) * v5) = a(x,y,((z \ (u \ z)) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,28053,a),flip(a)].">
      <j1 rule="hyper" parents="373 27298 28053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28085">
    <literal><![CDATA[
      K(x,y * (K(y * z,u) * (z \ w))) = K(x,T(z * (y \ 1),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,21570,a(flip),b,28056,a)].">
      <j1 rule="hyper" parents="64 21570 28056"/>
    </justification>
  </clause>

  <clause id="28086">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(y * z,w))) = K(x,T(z * (y \ 1),w) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,21563,a(flip),b,28056,a)].">
      <j1 rule="hyper" parents="64 21563 28056"/>
    </justification>
  </clause>

  <clause id="28087">
    <literal><![CDATA[
      K(x,y * R(y \ z,u,w)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,5796,a,b,28057,a)].">
      <j1 rule="hyper" parents="36 5796 28057"/>
    </justification>
  </clause>

  <clause id="28088">
    <literal><![CDATA[
      T(x,y * R(y \ z,u,w)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(143,a,28087,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 28087 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28089">
    <literal><![CDATA[
      K(x,y * R(z,u,w)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),28087(a,1,2,2,1))].">
      <j1 rule="para" parents="9 28087"/>
    </justification>
  </clause>

  <clause id="28090">
    <literal><![CDATA[
      K(x,y \ R(y * z,u,w)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1387(a,1),28087(a,1,2))].">
      <j1 rule="para" parents="1387 28087"/>
    </justification>
  </clause>

  <clause id="28091">
    <literal><![CDATA[
      K(x,y \ R(z,u,w)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2133(a,1),28087(a,1,2))].">
      <j1 rule="para" parents="2133 28087"/>
    </justification>
  </clause>

  <clause id="28092">
    <literal><![CDATA[
      K(x,(y * R(z,u,w)) * v5) = K(x,(y * z) * v5)
    ]]></literal>
    <justification jstring="[para(2790(a,1),28087(a,1,2))].">
      <j1 rule="para" parents="2790 28087"/>
    </justification>
  </clause>

  <clause id="28093">
    <literal><![CDATA[
      K(x * R(x \ y,z,u),w) = w / T(w,y)
    ]]></literal>
    <justification jstring="[hyper(225,a,28088,a(flip),b,5804,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 28088 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28094">
    <literal><![CDATA[
      T(x,y * R(z,u,w)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),28088(a,1,2,2,1))].">
      <j1 rule="para" parents="9 28088"/>
    </justification>
  </clause>

  <clause id="28095">
    <literal><![CDATA[
      T(x,y \ R(z,u,w)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2133(a,1),28088(a,1,2))].">
      <j1 rule="para" parents="2133 28088"/>
    </justification>
  </clause>

  <clause id="28096">
    <literal><![CDATA[
      T(x,y * (z \ R(z,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2299(a,1),28088(a,1,2))].">
      <j1 rule="para" parents="2299 28088"/>
    </justification>
  </clause>

  <clause id="28097">
    <literal><![CDATA[
      T(x,(y \ R(y,z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[para(2480(a,1),28088(a,1,2))].">
      <j1 rule="para" parents="2480 28088"/>
    </justification>
  </clause>

  <clause id="28099">
    <literal><![CDATA[
      K(x,(y * z) * R(u,w,v5)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,25003,a(flip),b,28089,a),flip(a)].">
      <j1 rule="hyper" parents="373 25003 28089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28101">
    <literal><![CDATA[
      K(x,T(y * (z * u),u)) = K(x,(u * y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,25302,a(flip),b,28089,a)].">
      <j1 rule="hyper" parents="64 25302 28089"/>
    </justification>
  </clause>

  <clause id="28102">
    <literal><![CDATA[
      K(x * (y * R(z,u,w)),x) * K(x,y * z) = a(x,y * R(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(28089(a,1),10886(a,1,2))].">
      <j1 rule="para" parents="28089 10886"/>
    </justification>
  </clause>

  <clause id="28103">
    <literal><![CDATA[
      K(x,R(y,z,u) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(2139(a,1),28090(a,1,2))].">
      <j1 rule="para" parents="2139 28090"/>
    </justification>
  </clause>

  <clause id="28108">
    <literal><![CDATA[
      K(x,y \ ((z / u) / w)) = K(x,y \ (z / (w * u)))
    ]]></literal>
    <justification jstring="[para(351(a,1),28091(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="351 28091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28109">
    <literal><![CDATA[
      K(x,y \ T(1 / z,u)) = K(x,y \ T(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(1004(a,1),28091(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1004 28091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28113">
    <literal><![CDATA[
      (x * R(y,z,u)) * T(w,x * y) = w * (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,28094,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 28094 22"/>
    </justification>
  </clause>

  <clause id="28114">
    <literal><![CDATA[
      T(x,y * ((z * u) / w)) = T(x,y * (z / (w / u)))
    ]]></literal>
    <justification jstring="[para(678(a,1),28094(a,1,2,2))].">
      <j1 rule="para" parents="678 28094"/>
    </justification>
  </clause>

  <clause id="28115">
    <literal><![CDATA[
      R(x * (y * x),z,u) / T(x,x * y) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(28094(a,1),4698(a,1,2))].">
      <j1 rule="para" parents="28094 4698"/>
    </justification>
  </clause>

  <clause id="28117">
    <literal><![CDATA[
      T(x,y \ ((z \ u) / u)) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(3001(a,1),28095(a,1,2,2))].">
      <j1 rule="para" parents="3001 28095"/>
    </justification>
  </clause>

  <clause id="28118">
    <literal><![CDATA[
      T(x,R(y,z,u) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24687,a(flip),b,28097,a),flip(a)].">
      <j1 rule="hyper" parents="64 24687 28097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28119">
    <literal><![CDATA[
      T(x,a(y,z,z) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(15987(a,1),28097(a,1,2,1))].">
      <j1 rule="para" parents="15987 28097"/>
    </justification>
  </clause>

  <clause id="28120">
    <literal><![CDATA[
      T(x,a(y,z,z) \ u) = T(x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25313,a,b,28119,a)].">
      <j1 rule="hyper" parents="64 25313 28119"/>
    </justification>
  </clause>

  <clause id="28121">
    <literal><![CDATA[
      T(((x * y) * y) / x,y * y) = ((x * y) * y) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,1754,a(flip),b,28119,a),flip(a)].">
      <j1 rule="hyper" parents="64 1754 28119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28124">
    <literal><![CDATA[
      T(x,R(y,z,u) * w) = T(x,y * w)
    ]]></literal>
    <justification jstring="[hyper(143,a,28103,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 28103 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28126">
    <literal><![CDATA[
      K(x,y * (z * ((u * z) \ w))) = K(x,(y / u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,25957,a(flip),b,28103,a)].">
      <j1 rule="hyper" parents="64 25957 28103"/>
    </justification>
  </clause>

  <clause id="28127">
    <literal><![CDATA[
      K(x,y * (R(y,z,u) \ w)) = K(x,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),28103(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 28103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28128">
    <literal><![CDATA[
      K(x,((y / z) / u) * w) = K(x,(y / (u * z)) * w)
    ]]></literal>
    <justification jstring="[para(351(a,1),28103(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="351 28103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28129">
    <literal><![CDATA[
      K(x,T((y / z) / u,w) * v5) = K(x,T(y / (u * z),w) * v5)
    ]]></literal>
    <justification jstring="[para(714(a,1),28103(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="714 28103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28130">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),u) * w) = K(x,T(y / z,u) * w)
    ]]></literal>
    <justification jstring="[para(779(a,1),28103(a,1,2,1))].">
      <j1 rule="para" parents="779 28103"/>
    </justification>
  </clause>

  <clause id="28131">
    <literal><![CDATA[
      K(x,T((y * z) / u,w) * v5) = K(x,T(y / (u / z),w) * v5)
    ]]></literal>
    <justification jstring="[para(1033(a,1),28103(a,1,2,1))].">
      <j1 rule="para" parents="1033 28103"/>
    </justification>
  </clause>

  <clause id="28132">
    <literal><![CDATA[
      T(x,y \ (T(z,y) \ u)) = T(x,z \ (R(y,w,v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,23691,a(flip),b,28118,a),flip(a)].">
      <j1 rule="hyper" parents="64 23691 28118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28133">
    <literal><![CDATA[
      T(x,(((y * z) * u) / (w * (z * u))) \ v5) = T(x,(R(y,z,u) / w) \ v5)
    ]]></literal>
    <justification jstring="[para(686(a,1),28118(a,1,2,1))].">
      <j1 rule="para" parents="686 28118"/>
    </justification>
  </clause>

  <clause id="28134">
    <literal><![CDATA[
      T(x,x \ y) * (R(x,z,u) \ y) = x * (y / R(x,z,u))
    ]]></literal>
    <justification jstring="[para(28118(a,1),25156(a,1,1))].">
      <j1 rule="para" parents="28118 25156"/>
    </justification>
  </clause>

  <clause id="28135">
    <literal><![CDATA[
      T(x,R(y,z,u) * R(w,v5,v6)) = T(x,y * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,28094,a(flip),b,28124,a),flip(a)].">
      <j1 rule="hyper" parents="373 28094 28124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28136">
    <literal><![CDATA[
      T(x,R(y / z,u,w) * v5) = T(x,y * (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,24987,a(flip),b,28124,a),flip(a)].">
      <j1 rule="hyper" parents="373 24987 28124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28137">
    <literal><![CDATA[
      T(x,y * (R(y,z,u) \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),28124(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 28124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28140">
    <literal><![CDATA[
      K(x,R(y,z,u) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(1908(a,1),28127(a,1,2))].">
      <j1 rule="para" parents="1908 28127"/>
    </justification>
  </clause>

  <clause id="28141">
    <literal><![CDATA[
      x * T(y,z * (R(z,u,w) \ x)) = y * x
    ]]></literal>
    <justification jstring="[hyper(145,a,28137,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="145 28137 22"/>
    </justification>
  </clause>

  <clause id="28145">
    <literal><![CDATA[
      K(x,R(y,z,u) \ (w * v5)) = K(x,(y \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,24234,a(flip),b,28140,a),flip(a)].">
      <j1 rule="hyper" parents="373 24234 28140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28149">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),u) \ w) = K(x,T(y / z,u) \ w)
    ]]></literal>
    <justification jstring="[para(779(a,1),28140(a,1,2,1))].">
      <j1 rule="para" parents="779 28140"/>
    </justification>
  </clause>

  <clause id="28153">
    <literal><![CDATA[
      K(x * R(x \ y,z,u),w) = K(y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,5787,a,b,28093,a),flip(a)].">
      <j1 rule="hyper" parents="373 5787 28093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28154">
    <literal><![CDATA[
      K(x * R(y,z,u),w) = K(x * y,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),28153(a,1,1,2,1))].">
      <j1 rule="para" parents="9 28153"/>
    </justification>
  </clause>

  <clause id="28155">
    <literal><![CDATA[
      K(R(x,y,z) / u,w) = K(x / u,w)
    ]]></literal>
    <justification jstring="[para(2115(a,1),28153(a,1,1))].">
      <j1 rule="para" parents="2115 28153"/>
    </justification>
  </clause>

  <clause id="28156">
    <literal><![CDATA[
      K(x \ R(y,z,u),w) = K(x \ y,w)
    ]]></literal>
    <justification jstring="[para(2133(a,1),28153(a,1,1))].">
      <j1 rule="para" parents="2133 28153"/>
    </justification>
  </clause>

  <clause id="28157">
    <literal><![CDATA[
      K(x * (y \ R(y,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(2299(a,1),28153(a,1,1))].">
      <j1 rule="para" parents="2299 28153"/>
    </justification>
  </clause>

  <clause id="28158">
    <literal><![CDATA[
      K((x * R(x \ y,z,u)) * w,v5) = K(y * w,v5)
    ]]></literal>
    <justification jstring="[para(2789(a,1),28153(a,1,1))].">
      <j1 rule="para" parents="2789 28153"/>
    </justification>
  </clause>

  <clause id="28163">
    <literal><![CDATA[
      K((x * y) * z,u) = K(x * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17904,a(flip),b,28154,a),flip(a)].">
      <j1 rule="hyper" parents="64 17904 28154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28164">
    <literal><![CDATA[
      K(x / (y * (z \ 1)),u) = K(x * (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14684,a(flip),b,28154,a)].">
      <j1 rule="hyper" parents="64 14684 28154"/>
    </justification>
  </clause>

  <clause id="28165">
    <literal><![CDATA[
      K((x / R(y,z,u)) * y,w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),28154(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 28154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28166">
    <literal><![CDATA[
      K(x * ((y / z) / u),w) = K(x * (y / (u * z)),w)
    ]]></literal>
    <justification jstring="[para(351(a,1),28154(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="351 28154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28167">
    <literal><![CDATA[
      K(x * (y / (1 / z)),u) = K(x * (y * z),u)
    ]]></literal>
    <justification jstring="[para(674(a,1),28154(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="674 28154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28168">
    <literal><![CDATA[
      K((x * y) * (y \ x),z) = K(x * x,z)
    ]]></literal>
    <justification jstring="[para(995(a,1),28154(a,1,1))].">
      <j1 rule="para" parents="995 28154"/>
    </justification>
  </clause>

  <clause id="28169">
    <literal><![CDATA[
      R(x,y,z) * K(u * R(w,v5,v6),v7) = R(x * K(u * w,v7),y,z)
    ]]></literal>
    <justification jstring="[para(28154(a,1),25973(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="28154 25973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28171">
    <literal><![CDATA[
      (K(x * y,x \ 1) / x) \ R(y,z,u) = R(y,z,u) / (1 / x)
    ]]></literal>
    <justification jstring="[para(28154(a,1),27877(a,1,1,1))].">
      <j1 rule="para" parents="28154 27877"/>
    </justification>
  </clause>

  <clause id="28172">
    <literal><![CDATA[
      K(x / (y * (z \ 1)),u) = K(x / (y / z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25948,a(flip),b,28155,a),flip(a)].">
      <j1 rule="hyper" parents="64 25948 28155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28174">
    <literal><![CDATA[
      K(x \ ((y * z) \ (u * z)),u * z) = K(x \ (u / y),u * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13453,a(flip),b,28156,a)].">
      <j1 rule="hyper" parents="64 13453 28156"/>
    </justification>
  </clause>

  <clause id="28176">
    <literal><![CDATA[
      K(x \ ((y / z) / u),w) = K(x \ (y / (u * z)),w)
    ]]></literal>
    <justification jstring="[para(351(a,1),28156(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="351 28156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28177">
    <literal><![CDATA[
      K(x \ T(1 / y,z),u) = K(x \ T(y \ 1,z),u)
    ]]></literal>
    <justification jstring="[para(1004(a,1),28156(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1004 28156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28178">
    <literal><![CDATA[
      K(x \ ((y / z) \ 1),u) = K(x \ (z / y),u)
    ]]></literal>
    <justification jstring="[para(26623(a,1),28156(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="26623 28156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28179">
    <literal><![CDATA[
      (x \ K(x,x \ 1)) \ (y \ R(y,z,u)) = (y \ R(y,z,u)) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(28157(a,1),8738(a,1,1,2))].">
      <j1 rule="para" parents="28157 8738"/>
    </justification>
  </clause>

  <clause id="28181">
    <literal><![CDATA[
      K(x * (R(x,y,z) \ u),w) = K(u,w)
    ]]></literal>
    <justification jstring="[para(25098(a,1),28165(a,1,1))].">
      <j1 rule="para" parents="25098 28165"/>
    </justification>
  </clause>

  <clause id="28182">
    <literal><![CDATA[
      K(x,y) * (z * (R(z,u,w) \ x)) = T(z * (R(z,u,w) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(144,a,28181,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 28181 5739"/>
    </justification>
  </clause>

  <clause id="28183">
    <literal><![CDATA[
      K(R(x,y,z) * u,w) = K(x * u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),28181(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 28181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28184">
    <literal><![CDATA[
      K(x * ((x \ y) * z),u) = K(y * z,u)
    ]]></literal>
    <justification jstring="[para(649(a,1),28181(a,1,1,2))].">
      <j1 rule="para" parents="649 28181"/>
    </justification>
  </clause>

  <clause id="28185">
    <literal><![CDATA[
      K(R(x,y,z) \ u,w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(1908(a,1),28181(a,1,1))].">
      <j1 rule="para" parents="1908 28181"/>
    </justification>
  </clause>

  <clause id="28186">
    <literal><![CDATA[
      K(((x / y) / z) * u,w) = K((x / (z * y)) * u,w)
    ]]></literal>
    <justification jstring="[para(351(a,1),28183(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="351 28183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28188">
    <literal><![CDATA[
      R(x,y,z) * (u * K(x * u,w)) = T(R(x,y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(28183(a,1),14495(a,1,2,2))].">
      <j1 rule="para" parents="28183 14495"/>
    </justification>
  </clause>

  <clause id="28189">
    <literal><![CDATA[
      K(x,(R(y,z,u) \ w) * (v5 * K(y * w,v6))) = K(x,T(R(y,z,u) \ w,v6) * v5)
    ]]></literal>
    <justification jstring="[para(28183(a,1),21564(a,1,2,2,2))].">
      <j1 rule="para" parents="28183 21564"/>
    </justification>
  </clause>

  <clause id="28195">
    <literal><![CDATA[
      K(((x \ (1 / y)) * y) * z,u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14581,a(flip),b,28185,a)].">
      <j1 rule="hyper" parents="64 14581 28185"/>
    </justification>
  </clause>

  <clause id="28196">
    <literal><![CDATA[
      K(x \ ((x * y) * z),u) = K(y * z,u)
    ]]></literal>
    <justification jstring="[para(210(a,1),28185(a,1,1)),flip(a)].">
      <j1 rule="para" parents="210 28185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28197">
    <literal><![CDATA[
      K(x \ (y * z),u) = K((x \ y) * z,u)
    ]]></literal>
    <justification jstring="[para(649(a,1),28185(a,1,1)),flip(a)].">
      <j1 rule="para" parents="649 28185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28198">
    <literal><![CDATA[
      K((x / y) \ z,u) = K(y * (x \ z),u)
    ]]></literal>
    <justification jstring="[para(684(a,1),28185(a,1,1)),flip(a)].">
      <j1 rule="para" parents="684 28185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28203">
    <literal><![CDATA[
      K(x * (y * z),T(u,z)) = K(z * (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(11189,a,28163,a),flip(a)].">
      <j1 rule="hyper" parents="11189 28163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28204">
    <literal><![CDATA[
      K((x * y) * R(z,u,w),v5) = K(x * (y * z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28154,a,b,28163,a)].">
      <j1 rule="hyper" parents="64 28154 28163"/>
    </justification>
  </clause>

  <clause id="28205">
    <literal><![CDATA[
      K(x * ((y \ x) \ z),u) = K(y * z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),28184(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 28184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28206">
    <literal><![CDATA[
      K((x / y) * z,u) = K(x * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(405(a,1),28184(a,1,1,2))].">
      <j1 rule="para" parents="405 28184"/>
    </justification>
  </clause>

  <clause id="28209">
    <literal><![CDATA[
      K((x \ y) \ z,u) = K((y \ x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23045,a,b,28197,a)].">
      <j1 rule="hyper" parents="64 23045 28197"/>
    </justification>
  </clause>

  <clause id="28210">
    <literal><![CDATA[
      K(x \ (y \ (z * u)),w) = K(((y * x) \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,23046,a(flip),b,28197,a)].">
      <j1 rule="hyper" parents="64 23046 28197"/>
    </justification>
  </clause>

  <clause id="28212">
    <literal><![CDATA[
      K(R(x / y,z,u) \ w,v5) = K(y * (x \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28185,a,b,28198,a)].">
      <j1 rule="hyper" parents="64 28185 28198"/>
    </justification>
  </clause>

  <clause id="28213">
    <literal><![CDATA[
      K(x,(x / y) * (x / y)) = K(y * (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,15890,a,b,28198,a)].">
      <j1 rule="hyper" parents="64 15890 28198"/>
    </justification>
  </clause>

  <clause id="28214">
    <literal><![CDATA[
      K(((x / y) \ z) * u,w) = K(y * (x \ (z * u)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28197,a(flip),b,28198,a)].">
      <j1 rule="hyper" parents="64 28197 28198"/>
    </justification>
  </clause>

  <clause id="28215">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,24251,a(flip),b,28198,a),flip(a)].">
      <j1 rule="hyper" parents="64 24251 28198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28217">
    <literal><![CDATA[
      K(((x / y) / z) * u,w) = K(x * (y \ (z \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,28206,a(flip),b,28206,a),flip(a)].">
      <j1 rule="hyper" parents="373 28206 28206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28218">
    <literal><![CDATA[
      K(T(x \ y,x) * z,u) = K(y * (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16854,a,b,28206,a)].">
      <j1 rule="hyper" parents="64 16854 28206"/>
    </justification>
  </clause>

  <clause id="28219">
    <literal><![CDATA[
      K(x * (y \ z),T(u,y)) = K(z * (x / y),T(u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,25298,a(flip),b,28206,a),flip(a)].">
      <j1 rule="hyper" parents="64 25298 28206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28220">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,w) = K((y \ x) * (z * u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28197,a(flip),b,28209,a)].">
      <j1 rule="hyper" parents="64 28197 28209"/>
    </justification>
  </clause>

  <clause id="28221">
    <literal><![CDATA[
      K((x \ (x / y)) \ z,u) = K(y * z,u)
    ]]></literal>
    <justification jstring="[para(82(a,1),28209(a,2,1,1))].">
      <j1 rule="para" parents="82 28209"/>
    </justification>
  </clause>

  <clause id="28222">
    <literal><![CDATA[
      (((x \ (x \ y)) \ y) \ z) * K(((x \ y) \ x) * y,x \ (x \ y)) = T((y / (x \ (x \ y))) \ z,K(y,x * x))
    ]]></literal>
    <justification jstring="[para(28209(a,1),15891(a,1,2))].">
      <j1 rule="para" parents="28209 15891"/>
    </justification>
  </clause>

  <clause id="28223">
    <literal><![CDATA[
      T(K(x * (y \ (y / z)),(y \ (y / z)) \ 1) / (y \ (y / z)),z \ 1) = K(z * x,z) / (y \ (y / z))
    ]]></literal>
    <justification jstring="[para(28221(a,1),17006(a,2,1))].">
      <j1 rule="para" parents="28221 17006"/>
    </justification>
  </clause>

  <clause id="28224">
    <literal><![CDATA[
      x * T(y,(R(z,u,w) \ z) * x) = y * x
    ]]></literal>
    <justification jstring="[para(24693(a,2),28141(a,1,2))].">
      <j1 rule="para" parents="24693 28141"/>
    </justification>
  </clause>

  <clause id="28227">
    <literal><![CDATA[
      T(x,y \ (z \ (z \ y))) = T(x,z \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,25547,a,b,28117,a)].">
      <j1 rule="hyper" parents="64 25547 28117"/>
    </justification>
  </clause>

  <clause id="28229">
    <literal><![CDATA[
      K(x * (y / (1 / z)),u / (1 / w)) = K(x * (y * z),u * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,14464,a(flip),b,28167,a),flip(a)].">
      <j1 rule="hyper" parents="373 14464 28167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28231">
    <literal><![CDATA[
      K(x / (y / z),u) = K(x * (z / y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28164,a(flip),b,28172,a),flip(a)].">
      <j1 rule="hyper" parents="64 28164 28172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28232">
    <literal><![CDATA[
      K((x * y) / z,u) = K(x * (y / z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23041,a,b,28231,a)].">
      <j1 rule="hyper" parents="64 23041 28231"/>
    </justification>
  </clause>

  <clause id="28233">
    <literal><![CDATA[
      K(x * (y / (y * z)),u) = K(x / T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16312,a(flip),b,28231,a),flip(a)].">
      <j1 rule="hyper" parents="64 16312 28231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28235">
    <literal><![CDATA[
      K((x \ (1 / y)) * (y * z),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28163,a(flip),b,28195,a)].">
      <j1 rule="hyper" parents="64 28163 28195"/>
    </justification>
  </clause>

  <clause id="28236">
    <literal><![CDATA[
      K(x * (y * (z / x)),u) = K(y * z,T(u,x))
    ]]></literal>
    <justification jstring="[para(12(a,1),28203(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 28203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28237">
    <literal><![CDATA[
      K(x,(y \ x) * (y \ x)) = K(y * (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,15859,a(flip),b,28213,a)].">
      <j1 rule="hyper" parents="64 15859 28213"/>
    </justification>
  </clause>

  <clause id="28238">
    <literal><![CDATA[
      x * ((y \ (x \ z)) * K(T(y,x) \ z,u)) = T(x * (y \ (x \ z)),u)
    ]]></literal>
    <justification jstring="[para(28215(a,1),14495(a,1,2,2))].">
      <j1 rule="para" parents="28215 14495"/>
    </justification>
  </clause>

  <clause id="28240">
    <literal><![CDATA[
      (x \ (1 / x)) * K(x \ y,x * y) = (x * y) \ ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(28235(a,1),16127(a,1,2))].">
      <j1 rule="para" parents="28235 16127"/>
    </justification>
  </clause>

  <clause id="28241">
    <literal><![CDATA[
      K((x \ y) * z,T(u,x)) = K(y * (z / x),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28184,a(flip),b,28236,a),flip(a)].">
      <j1 rule="hyper" parents="64 28184 28236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28242">
    <literal><![CDATA[
      T(x,(y \ x) * (y \ x)) * z = x * (z * K(y * (x \ y),x))
    ]]></literal>
    <justification jstring="[para(28237(a,1),17044(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28237 17044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28243">
    <literal><![CDATA[
      K((x \ y) * z,u \ x) = K(y * (z / x),x / u)
    ]]></literal>
    <justification jstring="[hyper(8456,a,28241,a)].">
      <j1 rule="hyper" parents="8456 28241"/>
    </justification>
  </clause>

  <clause id="28244">
    <literal><![CDATA[
      K(x * (y / z),T(u,z)) = K((z \ x) * y,u)
    ]]></literal>
    <justification jstring="[hyper(8313,a,28241,a),flip(a)].">
      <j1 rule="hyper" parents="8313 28241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28245">
    <literal><![CDATA[
      K(x * (y / R(z,u,w)),T(v5,z)) = K((R(z,u,w) \ x) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,19277,a(flip),b,28244,a)].">
      <j1 rule="hyper" parents="64 19277 28244"/>
    </justification>
  </clause>

  <clause id="28246">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * u) = K(x,(y * (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(1043(a,1),28092(a,1,2,1,2))].">
      <j1 rule="para" parents="1043 28092"/>
    </justification>
  </clause>

  <clause id="28247">
    <literal><![CDATA[
      K(x,T(y,z) * (z * u)) = K(x,(z * y) * R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,15821,a(flip),b,28099,a),flip(a)].">
      <j1 rule="hyper" parents="64 15821 28099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28250">
    <literal><![CDATA[
      T(x,((y * (z \ u)) / u) * w) = T(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[para(677(a,1),28136(a,1,2,1))].">
      <j1 rule="para" parents="677 28136"/>
    </justification>
  </clause>

  <clause id="28251">
    <literal><![CDATA[
      K(x,(R(y,z,u) \ w) * v5) = K(x,(y \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,24234,a(flip),b,28145,a)].">
      <j1 rule="hyper" parents="64 24234 28145"/>
    </justification>
  </clause>

  <clause id="28252">
    <literal><![CDATA[
      K((x \ R(y,z,u)) * w,v5) = K((x \ y) * w,v5)
    ]]></literal>
    <justification jstring="[para(2133(a,1),28158(a,1,1,1))].">
      <j1 rule="para" parents="2133 28158"/>
    </justification>
  </clause>

  <clause id="28254">
    <literal><![CDATA[
      K(x * (y * R(z,u,w)),v5) = K(x * (y * z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28163,a(flip),b,28204,a)].">
      <j1 rule="hyper" parents="64 28163 28204"/>
    </justification>
  </clause>

  <clause id="28259">
    <literal><![CDATA[
      K((x / (y * (z \ x))) \ u,w) = K(y * (z \ u),w)
    ]]></literal>
    <justification jstring="[para(676(a,1),28212(a,1,1,1))].">
      <j1 rule="para" parents="676 28212"/>
    </justification>
  </clause>

  <clause id="28260">
    <literal><![CDATA[
      K(x \ (R(y,z,u) * w),v5) = K((x \ y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28197,a,b,28252,a)].">
      <j1 rule="hyper" parents="64 28197 28252"/>
    </justification>
  </clause>

  <clause id="28261">
    <literal><![CDATA[
      K(x * (y * T(z,z \ u)),w) = K(x * (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[para(1322(a,1),28254(a,1,1,2,2))].">
      <j1 rule="para" parents="1322 28254"/>
    </justification>
  </clause>

  <clause id="28262">
    <literal><![CDATA[
      K(x \ ((y \ z) \ u),w) = K(((z * x) \ y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27210,a(flip),b,28260,a)].">
      <j1 rule="hyper" parents="64 27210 28260"/>
    </justification>
  </clause>

  <clause id="28263">
    <literal><![CDATA[
      K(x,y \ T(z \ 1,u)) = K(x,y \ (T(z,u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,25423,a(flip),b,28109,a),flip(a)].">
      <j1 rule="hyper" parents="64 25423 28109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28264">
    <literal><![CDATA[
      T(x,y * ((z * u) / w)) = T(x,y * (z * (u / w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,22677,a(flip),b,28114,a),flip(a)].">
      <j1 rule="hyper" parents="373 22677 28114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28266">
    <literal><![CDATA[
      (x * x) \ (a(y,x,x) \ K(x * x,y)) = (((y * x) * x) / y) \ 1
    ]]></literal>
    <justification jstring="[para(28121(a,1),17060(a,2,1))].">
      <j1 rule="para" parents="28121 17060"/>
    </justification>
  </clause>

  <clause id="28268">
    <literal><![CDATA[
      K(x,y * (z * ((u * z) \ w))) = K(x,y * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,24984,a(flip),b,28126,a),flip(a)].">
      <j1 rule="hyper" parents="373 24984 28126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28269">
    <literal><![CDATA[
      K(x,((y / z) / u) * w) = K(x,y * ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,24984,a(flip),b,28128,a),flip(a)].">
      <j1 rule="hyper" parents="373 24984 28128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28270">
    <literal><![CDATA[
      K((x \ y) * (z / u),T(w,x)) = K(y * (z / (x * u)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28241,a,b,28166,a)].">
      <j1 rule="hyper" parents="64 28241 28166"/>
    </justification>
  </clause>

  <clause id="28271">
    <literal><![CDATA[
      K(x \ T(y \ 1,z),u) = K(x \ (T(y,z) \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17720,a(flip),b,28177,a),flip(a)].">
      <j1 rule="hyper" parents="64 17720 28177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28272">
    <literal><![CDATA[
      K(((x / y) / z) * u,w) = K(x * ((z * y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,28206,a(flip),b,28186,a),flip(a)].">
      <j1 rule="hyper" parents="373 28206 28186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28273">
    <literal><![CDATA[
      K(x * (R(y,z,u) \ w),T(v5,y)) = K(w * (x / R(y,z,u)),T(v5,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,19277,a(flip),b,28219,a)].">
      <j1 rule="hyper" parents="64 19277 28219"/>
    </justification>
  </clause>

  <clause id="28274">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) * (u * K(w,v5))) = K(x,(y * (K(w,v5) / z)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27849,a(flip),b,28246,a),flip(a)].">
      <j1 rule="hyper" parents="64 27849 28246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28275">
    <literal><![CDATA[
      T(x,y * ((z \ u) * (u \ w))) = T(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,25020,a(flip),b,28250,a)].">
      <j1 rule="hyper" parents="64 25020 28250"/>
    </justification>
  </clause>

  <clause id="28276">
    <literal><![CDATA[
      K((x * (y \ z)) * (z \ u),w) = K(x * (y \ u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28198,a(flip),b,28259,a)].">
      <j1 rule="hyper" parents="64 28198 28259"/>
    </justification>
  </clause>

  <clause id="28278">
    <literal><![CDATA[
      K(x,y \ T(y \ 1,z)) = K(x,y \ (y \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,22785,a(flip),b,28263,a),flip(a)].">
      <j1 rule="hyper" parents="373 22785 28263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28279">
    <literal><![CDATA[
      T(x,y * ((z * u) / T(w,u))) = T(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,13603,a(flip),b,28264,a),flip(a)].">
      <j1 rule="hyper" parents="373 13603 28264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28280">
    <literal><![CDATA[
      T(x,y * (z * ((u * z) \ w))) = T(x,y * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(143,a,28268,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 28268 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28281">
    <literal><![CDATA[
      K(x,y * ((z / u) \ w)) = K(x,y * (u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(12(a,1),28268(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12 28268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28282">
    <literal><![CDATA[
      K(x,y * ((z * u) \ w)) = K(x,y * (u \ (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,24986,a(flip),b,28269,a),flip(a)].">
      <j1 rule="hyper" parents="64 24986 28269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28283">
    <literal><![CDATA[
      K(x * ((y * z) \ u),w) = K(x * (z \ (y \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28217,a(flip),b,28272,a),flip(a)].">
      <j1 rule="hyper" parents="64 28217 28272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28284">
    <literal><![CDATA[
      T(x,y * ((z \ u) / w)) = T(x,y * (z \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,25538,a(flip),b,28275,a)].">
      <j1 rule="hyper" parents="64 25538 28275"/>
    </justification>
  </clause>

  <clause id="28285">
    <literal><![CDATA[
      T(x,y * (z \ (u * w))) = T(x,y * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[para(9(a,1),28275(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 28275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28286">
    <literal><![CDATA[
      T(x,y * ((z / u) \ w)) = T(x,y * (u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(82(a,1),28275(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="82 28275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28287">
    <literal><![CDATA[
      K(x * ((y \ z) * (z \ u)),w) = K(x * (y \ u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28163,a(flip),b,28276,a)].">
      <j1 rule="hyper" parents="64 28163 28276"/>
    </justification>
  </clause>

  <clause id="28288">
    <literal><![CDATA[
      K(x,y * (T(z \ u,z) \ w)) = K(x,y * (z * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16353,a,b,28281,a)].">
      <j1 rule="hyper" parents="64 16353 28281"/>
    </justification>
  </clause>

  <clause id="28289">
    <literal><![CDATA[
      T(x,y * ((z * u) \ w)) = T(x,y * (u \ (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(143,a,28282,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 28282 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28290">
    <literal><![CDATA[
      K(x,y * ((z * u) \ (z * w))) = K(x,y * (u \ w))
    ]]></literal>
    <justification jstring="[para(9(a,1),28282(a,2,2,2,2))].">
      <j1 rule="para" parents="9 28282"/>
    </justification>
  </clause>

  <clause id="28291">
    <literal><![CDATA[
      K(x * (y \ (z \ 1)),u) = K(x / (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(14676,a,28283,a),flip(a)].">
      <j1 rule="hyper" parents="14676 28283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28292">
    <literal><![CDATA[
      K(x * ((y * a(z,u,w)) \ v5),v6) = K(x * (y \ (a(z,u,w) \ v5)),v6)
    ]]></literal>
    <justification jstring="[para(23136(a,1),28283(a,1,1,2,1))].">
      <j1 rule="para" parents="23136 28283"/>
    </justification>
  </clause>

  <clause id="28294">
    <literal><![CDATA[
      T(x,((y / z) \ u) * w) = T(x,z * ((y \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,24716,a,b,28285,a)].">
      <j1 rule="hyper" parents="64 24716 28285"/>
    </justification>
  </clause>

  <clause id="28295">
    <literal><![CDATA[
      T(x,y * (((z \ y) \ u) * w)) = T(x,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,24999,a(flip),b,28285,a),flip(a)].">
      <j1 rule="hyper" parents="64 24999 28285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28297">
    <literal><![CDATA[
      T((x / y) / z,z * (y * (x \ u))) = (((x / y) / z) \ u) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,11412,a(flip),b,28286,a),flip(a)].">
      <j1 rule="hyper" parents="64 11412 28286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28298">
    <literal><![CDATA[
      K(x * (y \ (z * u)),w) = K(x * ((y \ z) * u),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),28287(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 28287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28300">
    <literal><![CDATA[
      K(x,y * L(z,u,w)) = K(x,y * (u \ (u * z)))
    ]]></literal>
    <justification jstring="[para(18(a,2),28290(a,1,2,2))].">
      <j1 rule="para" parents="18 28290"/>
    </justification>
  </clause>

  <clause id="28301">
    <literal><![CDATA[
      K(x,y * L(z,u,w)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),28300(a,2,2,2))].">
      <j1 rule="para" parents="9 28300"/>
    </justification>
  </clause>

  <clause id="28308">
    <literal><![CDATA[
      T(x,y * L(z,u,w)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(143,a,28301,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 28301 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28312">
    <literal><![CDATA[
      K(x,(y / z) * L(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),28301(a,2,2))].">
      <j1 rule="para" parents="12 28301"/>
    </justification>
  </clause>

  <clause id="28319">
    <literal><![CDATA[
      K(x,y * z) * ((x * L(z,u,w)) \ ((L(z,u,w) * y) * x)) = L(y,L(z,u,w),x)
    ]]></literal>
    <justification jstring="[para(28301(a,1),27292(a,2,1)),flip(a)].">
      <j1 rule="para" parents="28301 27292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28320">
    <literal><![CDATA[
      T(x,y * R(z,u,w)) = T(x,y * L(z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,28094,a,b,28308,a)].">
      <j1 rule="hyper" parents="373 28094 28308"/>
    </justification>
  </clause>

  <clause id="28322">
    <literal><![CDATA[
      T(x,y * (z * L(u,w,v5))) = T(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25009,a(flip),b,28308,a)].">
      <j1 rule="hyper" parents="64 25009 28308"/>
    </justification>
  </clause>

  <clause id="28323">
    <literal><![CDATA[
      (x * L(y,z,u)) * T(w,x * y) = w * (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,28308,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 28308 22"/>
    </justification>
  </clause>

  <clause id="28324">
    <literal><![CDATA[
      T(x,(y / z) * L(z,u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),28308(a,2,2))].">
      <j1 rule="para" parents="12 28308"/>
    </justification>
  </clause>

  <clause id="28325">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ w)) = T(x,y * (u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(630(a,1),28308(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="630 28308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28326">
    <literal><![CDATA[
      (1 / (1 / x)) \ L(y,z,u) = L(y,z,u) / T(x,x * y)
    ]]></literal>
    <justification jstring="[para(28308(a,1),5139(a,2,2))].">
      <j1 rule="para" parents="28308 5139"/>
    </justification>
  </clause>

  <clause id="28327">
    <literal><![CDATA[
      K(x,y * (z \ L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,24984,a(flip),b,28312,a)].">
      <j1 rule="hyper" parents="64 24984 28312"/>
    </justification>
  </clause>

  <clause id="28329">
    <literal><![CDATA[
      K(x,L(y,z,u) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(24379(a,1),28312(a,1,2))].">
      <j1 rule="para" parents="24379 28312"/>
    </justification>
  </clause>

  <clause id="28330">
    <literal><![CDATA[
      K(x,y \ (L(y,z,u) * w)) = K(x,w)
    ]]></literal>
    <justification jstring="[para(24852(a,2),28312(a,1,2))].">
      <j1 rule="para" parents="24852 28312"/>
    </justification>
  </clause>

  <clause id="28331">
    <literal><![CDATA[
      K(x,L(y,z,u) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(24853(a,1),28312(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24853 28312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28332">
    <literal><![CDATA[
      T(x,y \ L(z,u,w)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,24995,a(flip),b,28324,a)].">
      <j1 rule="hyper" parents="64 24995 28324"/>
    </justification>
  </clause>

  <clause id="28333">
    <literal><![CDATA[
      T(x,y / L(z,u,w)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(3197(a,1),28324(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3197 28324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28334">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ w)) = T(x,w)
    ]]></literal>
    <justification jstring="[para(23898(a,2),28324(a,1,2))].">
      <j1 rule="para" parents="23898 28324"/>
    </justification>
  </clause>

  <clause id="28335">
    <literal><![CDATA[
      T(x,L(y,z,u) * w) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(24379(a,1),28324(a,1,2))].">
      <j1 rule="para" parents="24379 28324"/>
    </justification>
  </clause>

  <clause id="28336">
    <literal><![CDATA[
      T(x,L(y,z,u) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[para(24853(a,1),28324(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24853 28324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28338">
    <literal><![CDATA[
      K(x,y \ L(z,u,w)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,24671,a(flip),b,28327,a)].">
      <j1 rule="hyper" parents="64 24671 28327"/>
    </justification>
  </clause>

  <clause id="28345">
    <literal><![CDATA[
      x * K(y,L(z,u,w) * v5) = x * K(y,z * v5)
    ]]></literal>
    <justification jstring="[hyper(145,a,28329,a,b,9,a)].">
      <j1 rule="hyper" parents="145 28329 9"/>
    </justification>
  </clause>

  <clause id="28347">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ w)) = K(x,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),28329(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 28329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28348">
    <literal><![CDATA[
      K(x,((y * z) \ u) * w) = K(x,(z \ (y \ u)) * w)
    ]]></literal>
    <justification jstring="[para(346(a,1),28329(a,1,2,1))].">
      <j1 rule="para" parents="346 28329"/>
    </justification>
  </clause>

  <clause id="28349">
    <literal><![CDATA[
      K(x,((y \ z) \ u) * w) = K(x,(z \ (y * u)) * w)
    ]]></literal>
    <justification jstring="[para(630(a,1),28329(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="630 28329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28350">
    <literal><![CDATA[
      K(x,T((y * z) \ u,w) * v5) = K(x,T(z \ (y \ u),w) * v5)
    ]]></literal>
    <justification jstring="[para(708(a,1),28329(a,1,2,1))].">
      <j1 rule="para" parents="708 28329"/>
    </justification>
  </clause>

  <clause id="28351">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,w) * v5) = K(x,T(z \ (y * u),w) * v5)
    ]]></literal>
    <justification jstring="[para(1024(a,1),28329(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1024 28329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28352">
    <literal><![CDATA[
      K(x,a(y,y,z) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,24237,a(flip),b,28330,a)].">
      <j1 rule="hyper" parents="64 24237 28330"/>
    </justification>
  </clause>

  <clause id="28363">
    <literal><![CDATA[
      K(x,y \ (T(z,y) / u)) = K(x,z / (u * L(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,25467,a(flip),b,28331,a),flip(a)].">
      <j1 rule="hyper" parents="64 25467 28331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28364">
    <literal><![CDATA[
      T(x,L(y,z,u) \ w) = x * K(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(145,a,28331,a(flip),b,5726,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 28331 5726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28367">
    <literal><![CDATA[
      T(x,L(y,z,u) \ L(y,w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,23148,a(flip),b,28332,a),flip(a)].">
      <j1 rule="hyper" parents="373 23148 28332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28368">
    <literal><![CDATA[
      T(x \ L(y,z,u),x \ y) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(339,a,28332,a)].">
      <j1 rule="hyper" parents="339 28332"/>
    </justification>
  </clause>

  <clause id="28369">
    <literal><![CDATA[
      L(x,y,z) / L(T(u,u \ x),w,v5) = L(u,w,v5) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(28332(a,1),10458(a,1,2,1))].">
      <j1 rule="para" parents="28332 10458"/>
    </justification>
  </clause>

  <clause id="28370">
    <literal><![CDATA[
      x / (L(y,z,u) \ L(y,w,v5)) = (L(y,z,u) \ L(y,w,v5)) \ x
    ]]></literal>
    <justification jstring="[hyper(8638,a,28367,a),flip(a)].">
      <j1 rule="hyper" parents="8638 28367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28372">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,21778,a,b,28334,a)].">
      <j1 rule="hyper" parents="64 21778 28334"/>
    </justification>
  </clause>

  <clause id="28376">
    <literal><![CDATA[
      T(L(x,y,z) \ 1,x * L(x,y,z)) = T(L(x,y,z) \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,4917,a(flip),b,28335,a),flip(a)].">
      <j1 rule="hyper" parents="64 4917 28335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28379">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ w) * v5) = T(x,y \ (w * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,24579,a(flip),b,28336,a)].">
      <j1 rule="hyper" parents="64 24579 28336"/>
    </justification>
  </clause>

  <clause id="28380">
    <literal><![CDATA[
      T(x,y \ (L(y,z,u) \ w)) = T(x,y \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,22721,a(flip),b,28336,a)].">
      <j1 rule="hyper" parents="64 22721 28336"/>
    </justification>
  </clause>

  <clause id="28381">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ u)) = T(x,z \ (L(y,w,v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,22720,a(flip),b,28336,a),flip(a)].">
      <j1 rule="hyper" parents="64 22720 28336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28382">
    <literal><![CDATA[
      (L(x,y,z) \ u) * T(w,x \ u) = w * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(145,a,28336,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 28336 22"/>
    </justification>
  </clause>

  <clause id="28383">
    <literal><![CDATA[
      K(x,T(y,z \ u) * (L(z,w,v5) \ u)) = K(x,(L(z,w,v5) \ u) * y)
    ]]></literal>
    <justification jstring="[para(28336(a,1),11142(a,1,2,1))].">
      <j1 rule="para" parents="28336 11142"/>
    </justification>
  </clause>

  <clause id="28389">
    <literal><![CDATA[
      K(x,y \ ((z * u) \ w)) = K(x,y \ (u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(346(a,1),28338(a,1,2,2))].">
      <j1 rule="para" parents="346 28338"/>
    </justification>
  </clause>

  <clause id="28390">
    <literal><![CDATA[
      K(x,y \ (z \ (z / u))) = K(x,y \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(443(a,1),28338(a,1,2,2))].">
      <j1 rule="para" parents="443 28338"/>
    </justification>
  </clause>

  <clause id="28391">
    <literal><![CDATA[
      (K(x,x \ y) / (x / L(y,z,u))) * x = x * (1 / (x / L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(28338(a,1),26935(a,1,1,1))].">
      <j1 rule="para" parents="28338 26935"/>
    </justification>
  </clause>

  <clause id="28395">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),w) = K(w,u) \ 1
    ]]></literal>
    <justification jstring="[para(28347(a,1),6092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28347 6092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28396">
    <literal><![CDATA[
      T(x / ((y \ L(y,z,u)) * w),w) = ((y \ L(y,z,u)) * w) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,28372,a),flip(a)].">
      <j1 rule="hyper" parents="467 28372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28398">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * (w \ L(w,v5,v6))) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,23697,a(flip),b,28372,a),flip(a)].">
      <j1 rule="hyper" parents="373 23697 28372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28399">
    <literal><![CDATA[
      T(x,L(y,z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(28364(a,2),5767(a,1))].">
      <j1 rule="para" parents="28364 5767"/>
    </justification>
  </clause>

  <clause id="28400">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,6092,a(flip),b,28395,a),flip(a)].">
      <j1 rule="hyper" parents="373 6092 28395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28401">
    <literal><![CDATA[
      x * K(y * (L(y,z,u) \ x),w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,28400,a,b,5726,a(flip))].">
      <j1 rule="hyper" parents="145 28400 5726"/>
    </justification>
  </clause>

  <clause id="28402">
    <literal><![CDATA[
      K(x,y) * (z * (L(z,u,w) \ x)) = T(z * (L(z,u,w) \ x),y)
    ]]></literal>
    <justification jstring="[hyper(144,a,28400,a(flip),b,5739,a(flip))].">
      <j1 rule="hyper" parents="144 28400 5739"/>
    </justification>
  </clause>

  <clause id="28403">
    <literal><![CDATA[
      K(L(x,y,z) * u,w) = K(x * u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),28400(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 28400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28404">
    <literal><![CDATA[
      K(L(x,y,z) \ u,w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(2330(a,1),28400(a,1,1))].">
      <j1 rule="para" parents="2330 28400"/>
    </justification>
  </clause>

  <clause id="28406">
    <literal><![CDATA[
      K(x * L(y,z,u),w) = K(x * y,w)
    ]]></literal>
    <justification jstring="[para(23886(a,1),28400(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23886 28400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28407">
    <literal><![CDATA[
      K(x / L(y,z,u),w) = K(x / y,w)
    ]]></literal>
    <justification jstring="[para(24919(a,1),28400(a,1,1))].">
      <j1 rule="para" parents="24919 28400"/>
    </justification>
  </clause>

  <clause id="28409">
    <literal><![CDATA[
      K(((x * y) \ z) * u,w) = K((y \ (x \ z)) * u,w)
    ]]></literal>
    <justification jstring="[para(346(a,1),28403(a,1,1,1))].">
      <j1 rule="para" parents="346 28403"/>
    </justification>
  </clause>

  <clause id="28410">
    <literal><![CDATA[
      L(x,y,z) * (u * K(x * u,w)) = T(L(x,y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(28403(a,1),14495(a,1,2,2))].">
      <j1 rule="para" parents="28403 14495"/>
    </justification>
  </clause>

  <clause id="28413">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ w) * (v5 * K(y * w,v6))) = K(x,T(L(y,z,u) \ w,v6) * v5)
    ]]></literal>
    <justification jstring="[para(28403(a,1),21564(a,1,2,2,2))].">
      <j1 rule="para" parents="28403 21564"/>
    </justification>
  </clause>

  <clause id="28418">
    <literal><![CDATA[
      K(x \ L(y,z,u),w) = K(x \ y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26069,a(flip),b,28404,a),flip(a)].">
      <j1 rule="hyper" parents="64 26069 28404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28422">
    <literal><![CDATA[
      K(x * (y \ ((y / z) * u)),w) = K(x * (z \ u),w)
    ]]></literal>
    <justification jstring="[para(633(a,1),28406(a,1,1,2))].">
      <j1 rule="para" parents="633 28406"/>
    </justification>
  </clause>

  <clause id="28428">
    <literal><![CDATA[
      K(x,K(y / z,u) * ((y / L(z,w,v5)) \ v6)) = K(x,T(y / L(z,w,v5),u) \ v6)
    ]]></literal>
    <justification jstring="[para(28407(a,1),15774(a,1,2,1))].">
      <j1 rule="para" parents="28407 15774"/>
    </justification>
  </clause>

  <clause id="28431">
    <literal><![CDATA[
      K(x \ ((y * z) \ u),w) = K(x \ (z \ (y \ u)),w)
    ]]></literal>
    <justification jstring="[para(346(a,1),28418(a,1,1,2))].">
      <j1 rule="para" parents="346 28418"/>
    </justification>
  </clause>

  <clause id="28433">
    <literal><![CDATA[
      L(x,y,z) * (x \ T(x * (L(x,y,z) \ u),w)) = T(u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24319,a(flip),b,28401,a)].">
      <j1 rule="hyper" parents="64 24319 28401"/>
    </justification>
  </clause>

  <clause id="28435">
    <literal><![CDATA[
      x / (L(y,z,u) \ R(y,w,v5)) = (L(y,z,u) \ R(y,w,v5)) \ x
    ]]></literal>
    <justification jstring="[hyper(41,a,15750,a(flip),b,28320,a)].">
      <j1 rule="hyper" parents="41 15750 28320"/>
    </justification>
  </clause>

  <clause id="28439">
    <literal><![CDATA[
      K(x,y \ (z \ (z / y))) = K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,15871,a(flip),b,28390,a),flip(a)].">
      <j1 rule="hyper" parents="373 15871 28390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28441">
    <literal><![CDATA[
      K(x,y \ (z \ (z \ y))) = K(z * z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25539,a,b,28439,a)].">
      <j1 rule="hyper" parents="64 25539 28439"/>
    </justification>
  </clause>

  <clause id="28443">
    <literal><![CDATA[
      ((x \ (x \ y)) \ y) \ K(x * x,(x \ (x \ y)) \ y) = 1 / ((x \ (x \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,28441,a(flip),b,4338,a)].">
      <j1 rule="hyper" parents="139 28441 4338"/>
    </justification>
  </clause>

  <clause id="28444">
    <literal><![CDATA[
      ((x \ (x \ y)) / y) \ K(x * x,x \ (x \ y)) = T((x \ (x \ y)) / y,x \ (x \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(28441(a,1),6127(a,1,2))].">
      <j1 rule="para" parents="28441 6127"/>
    </justification>
  </clause>

  <clause id="28445">
    <literal><![CDATA[
      T(x \ (y \ (y \ x)),z) * K(y * y,x) = T((y \ (y \ x)) / x,T(z,x))
    ]]></literal>
    <justification jstring="[para(28441(a,1),8384(a,1,2))].">
      <j1 rule="para" parents="28441 8384"/>
    </justification>
  </clause>

  <clause id="28446">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (x \ L(x,y,z))) \ (x \ 1) = L(x,y,z) \ (1 / (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(28398(a,1),1816(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28398 1816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28447">
    <literal><![CDATA[
      T(x,y * (z * L(u,w,v5))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,25009,a(flip),b,28322,a),flip(a)].">
      <j1 rule="hyper" parents="373 25009 28322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28448">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ w) * v5) = T(x,(y \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,24579,a(flip),b,28379,a),flip(a)].">
      <j1 rule="hyper" parents="373 24579 28379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28449">
    <literal><![CDATA[
      T(x,(L(y,z,u) \ y) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),28379(a,2,2))].">
      <j1 rule="para" parents="9 28379"/>
    </justification>
  </clause>

  <clause id="28450">
    <literal><![CDATA[
      T(x / ((L(y,z,u) \ y) * w),w) = ((L(y,z,u) \ y) * w) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,28449,a),flip(a)].">
      <j1 rule="hyper" parents="467 28449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28451">
    <literal><![CDATA[
      (x * y) / T((z \ L(z,u,w)) * x,y) = ((z \ L(z,u,w)) * x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(28449(a,1),25454(a,1,2))].">
      <j1 rule="para" parents="28449 25454"/>
    </justification>
  </clause>

  <clause id="28453">
    <literal><![CDATA[
      T(x,L(y,z,u) \ (L(y,w,v5) \ v6)) = T(x,y \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,28336,a,b,28380,a)].">
      <j1 rule="hyper" parents="64 28336 28380"/>
    </justification>
  </clause>

  <clause id="28454">
    <literal><![CDATA[
      T(x,y * ((z * u) * w)) = T(x,y * (z * (u * w)))
    ]]></literal>
    <justification jstring="[para(100(a,1),28447(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="100 28447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28455">
    <literal><![CDATA[
      T(x,y * ((z / u) * (u * w))) = T(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(592(a,1),28447(a,1,2,2))].">
      <j1 rule="para" parents="592 28447"/>
    </justification>
  </clause>

  <clause id="28457">
    <literal><![CDATA[
      T(x,(y \ z) * ((z \ u) * w)) = T(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[para(79(a,1),28294(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 28294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28458">
    <literal><![CDATA[
      K(((x / y) \ z) * u,w) = K(y * ((x \ z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28214,a,b,28298,a)].">
      <j1 rule="hyper" parents="64 28214 28298"/>
    </justification>
  </clause>

  <clause id="28459">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ w)) = T(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,28285,a(flip),b,28325,a),flip(a)].">
      <j1 rule="hyper" parents="373 28285 28325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28460">
    <literal><![CDATA[
      K(x,y \ (z \ (u * w))) = K(x,(y \ (z \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24674,a,b,28348,a)].">
      <j1 rule="hyper" parents="64 24674 28348"/>
    </justification>
  </clause>

  <clause id="28461">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * w) = K(x,(y \ z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,24675,a(flip),b,28349,a),flip(a)].">
      <j1 rule="hyper" parents="64 24675 28349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28462">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * K(z * y,w)) = K(x,T(z \ y,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,21554,a(flip),b,28349,a),flip(a)].">
      <j1 rule="hyper" parents="64 21554 28349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28464">
    <literal><![CDATA[
      K(x,((y * z) * u) \ w) = K(x,u \ (z \ (y \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,23002,a,b,28389,a)].">
      <j1 rule="hyper" parents="64 23002 28389"/>
    </justification>
  </clause>

  <clause id="28465">
    <literal><![CDATA[
      K(x \ ((y \ z) \ u),w) = K((x \ (z \ y)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28262,a,b,28409,a)].">
      <j1 rule="hyper" parents="64 28262 28409"/>
    </justification>
  </clause>

  <clause id="28466">
    <literal><![CDATA[
      K(x \ (y \ (z * u)),w) = K((x \ (y \ z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28210,a,b,28409,a)].">
      <j1 rule="hyper" parents="64 28210 28409"/>
    </justification>
  </clause>

  <clause id="28467">
    <literal><![CDATA[
      K(x * ((y \ (y / z)) * u),w) = K(x * (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28298,a(flip),b,28422,a)].">
      <j1 rule="hyper" parents="64 28298 28422"/>
    </justification>
  </clause>

  <clause id="28468">
    <literal><![CDATA[
      K(x \ (y / (y * z)),u) = K(x \ (y \ (z \ y)),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27152,a,b,28431,a)].">
      <j1 rule="hyper" parents="64 27152 28431"/>
    </justification>
  </clause>

  <clause id="28469">
    <literal><![CDATA[
      K(x \ (y \ (y \ x)),z) = K(z,y * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17587,a(flip),b,28431,a),flip(a)].">
      <j1 rule="hyper" parents="64 17587 28431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28470">
    <literal><![CDATA[
      ((x \ (x \ y)) / y) \ K((x \ (x \ y)) \ y,z) = K(y,x * x) * T((y \ (x \ (x \ y))) \ 1,z)
    ]]></literal>
    <justification jstring="[para(28469(a,1),6838(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28469 6838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28471">
    <literal><![CDATA[
      T((x \ (x \ y)) / y,T(z,y)) = ((x \ (x \ y)) / y) * K(z,x * x)
    ]]></literal>
    <justification jstring="[para(28469(a,1),7975(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28469 7975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28472">
    <literal><![CDATA[
      T(T((x \ (x \ y)) / y,x \ (x \ y)),T(z,x \ (x \ y))) = K(x \ (x \ y),x * x) * T((x \ (x \ y)) / y,z)
    ]]></literal>
    <justification jstring="[para(28469(a,1),8366(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28469 8366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28473">
    <literal><![CDATA[
      T(x,y * ((z / u) * w)) = T(x,y * (z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(10(a,1),28455(a,1,2,2,2))].">
      <j1 rule="para" parents="10 28455"/>
    </justification>
  </clause>

  <clause id="28474">
    <literal><![CDATA[
      T(x,y * (z \ ((y \ u) * w))) = T(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24996,a(flip),b,28457,a)].">
      <j1 rule="hyper" parents="64 24996 28457"/>
    </justification>
  </clause>

  <clause id="28476">
    <literal><![CDATA[
      K((x \ y) * ((y \ z) * u),w) = K((x \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),28458(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 28458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28477">
    <literal><![CDATA[
      T(x,y \ (z \ (u * w))) = T(x,(y \ (z \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(143,a,28460,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="143 28460 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28478">
    <literal><![CDATA[
      K(x,(y \ z) * (u * y)) = K(x,T(z * u,y))
    ]]></literal>
    <justification jstring="[hyper(11219,a,28461,a),flip(a)].">
      <j1 rule="hyper" parents="11219 28461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28479">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * K(w,v5)) = K(x,(y \ z) * (K(w,v5) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17932,a,b,28461,a),flip(a)].">
      <j1 rule="hyper" parents="373 17932 28461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28481">
    <literal><![CDATA[
      K(x,(y \ z) * (u * (y * w))) = K(x,T(z * u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,23386,a(flip),b,28461,a),flip(a)].">
      <j1 rule="hyper" parents="64 23386 28461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28484">
    <literal><![CDATA[
      K(R(x * (y * y),z,z),a(x,z,z) \ (y \ (y \ 1))) * ((x * ((y * y) * a(x,z,z))) \ x) = x / (x * ((y * y) * a(x,z,z)))
    ]]></literal>
    <justification jstring="[para(28464(a,1),16052(a,1,1))].">
      <j1 rule="para" parents="28464 16052"/>
    </justification>
  </clause>

  <clause id="28485">
    <literal><![CDATA[
      (x \ ((y \ (x \ y)) \ 1)) \ K(y,K((x \ ((x \ y) \ y)) * 1,x)) = 1 / (x \ ((y \ (x \ y)) \ 1))
    ]]></literal>
    <justification jstring="[para(28465(a,1),22875(a,1,2,2))].">
      <j1 rule="para" parents="28465 22875"/>
    </justification>
  </clause>

  <clause id="28486">
    <literal><![CDATA[
      K(x \ (y \ (z * u)),w) = K(x \ ((y \ z) * u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,28197,a,b,28466,a),flip(a)].">
      <j1 rule="hyper" parents="373 28197 28466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28487">
    <literal><![CDATA[
      K(x \ (y \ (z * x)),u) = K(y \ z,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,11175,a(flip),b,28466,a),flip(a)].">
      <j1 rule="hyper" parents="373 11175 28466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28488">
    <literal><![CDATA[
      K((x \ (y \ z)) * (z \ u),w) = K(x \ (y \ u),w)
    ]]></literal>
    <justification jstring="[para(10(a,1),28466(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 28466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28489">
    <literal><![CDATA[
      K((x / y) \ z,T(u,y)) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,24253,a(flip),b,28487,a),flip(a)].">
      <j1 rule="hyper" parents="64 24253 28487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28490">
    <literal><![CDATA[
      K(x \ (y / z),T(u,z)) = K(z \ (x \ y),u)
    ]]></literal>
    <justification jstring="[para(12(a,1),28487(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 28487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28491">
    <literal><![CDATA[
      K(x \ (y * z),T(u,z)) = K((x / z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(8313,a,28489,a),flip(a)].">
      <j1 rule="hyper" parents="8313 28489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28492">
    <literal><![CDATA[
      K(x \ (y / z),u) * z = z * K(z \ (x \ y),u)
    ]]></literal>
    <justification jstring="[para(28490(a,1),7879(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28490 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28493">
    <literal><![CDATA[
      K(((x / y) / y) \ z,u) = K(x \ ((z * y) * y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28489,a(flip),b,28491,a),flip(a)].">
      <j1 rule="hyper" parents="64 28489 28491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28494">
    <literal><![CDATA[
      K((x / y) \ (y \ z),u) = K(x \ T(z,y),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,13472,a(flip),b,28491,a),flip(a)].">
      <j1 rule="hyper" parents="64 13472 28491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28495">
    <literal><![CDATA[
      K(x * ((y \ z) \ u),w) = K(x * ((z \ y) * u),w)
    ]]></literal>
    <justification jstring="[para(79(a,1),28467(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 28467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28496">
    <literal><![CDATA[
      K((x \ (y * z)) * u,w) = K((x \ y) * (z * u),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),28476(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 28476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28497">
    <literal><![CDATA[
      T(x,(y \ ((z * u) \ (z * (u * y)))) * w) = T(x,a(z,u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27272,a(flip),b,28477,a),flip(a)].">
      <j1 rule="hyper" parents="64 27272 28477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28498">
    <literal><![CDATA[
      K(x \ ((y / z) \ u),w) = K((x \ z) * (y \ u),w)
    ]]></literal>
    <justification jstring="[para(82(a,1),28488(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="82 28488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28499">
    <literal><![CDATA[
      K((x \ y) / z,u) = K(x \ (y / z),u)
    ]]></literal>
    <justification jstring="[hyper(36,a,7457,a,b,28492,a)].">
      <j1 rule="hyper" parents="36 7457 28492"/>
    </justification>
  </clause>

  <clause id="28500">
    <literal><![CDATA[
      K((1 / x) \ (x / y),z) = K(y \ T(x * x,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,17616,a,b,28499,a),flip(a)].">
      <j1 rule="hyper" parents="64 17616 28499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28501">
    <literal><![CDATA[
      K(x \ ((x * y) / z),u) = K(y / z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),28499(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 28499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28502">
    <literal><![CDATA[
      K((x \ y) / (z \ y),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),28499(a,2,1,2))].">
      <j1 rule="para" parents="79 28499"/>
    </justification>
  </clause>

  <clause id="28503">
    <literal><![CDATA[
      K((x / y) \ (x / z),u) = K(y / z,u)
    ]]></literal>
    <justification jstring="[para(82(a,1),28499(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 28499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28504">
    <literal><![CDATA[
      K(x / (y \ (z * x)),u) = K(z \ y,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),28501(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 28501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28505">
    <literal><![CDATA[
      K(x / (y \ z),u) = K((z / x) \ y,u)
    ]]></literal>
    <justification jstring="[para(82(a,1),28502(a,1,1,1))].">
      <j1 rule="para" parents="82 28502"/>
    </justification>
  </clause>

  <clause id="28506">
    <literal><![CDATA[
      K(x * (y \ (y / z)),u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28198,a(flip),b,28503,a)].">
      <j1 rule="hyper" parents="64 28198 28503"/>
    </justification>
  </clause>

  <clause id="28508">
    <literal><![CDATA[
      K(x / (y \ z),u) = K(x * (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,28198,a(flip),b,28505,a),flip(a)].">
      <j1 rule="hyper" parents="373 28198 28505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28509">
    <literal><![CDATA[
      K((x / (y \ z)) \ u,w) = K(y \ (z / (u \ x)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28499,a(flip),b,28505,a),flip(a)].">
      <j1 rule="hyper" parents="64 28499 28505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28510">
    <literal><![CDATA[
      K(x / ((y \ z) / u),w) = K((z / (x * u)) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,23041,a(flip),b,28505,a)].">
      <j1 rule="hyper" parents="64 23041 28505"/>
    </justification>
  </clause>

  <clause id="28511">
    <literal><![CDATA[
      K(x * (y \ z),u) * (u / T(x / (z \ y),u)) = u / (x / (z \ y))
    ]]></literal>
    <justification jstring="[para(28508(a,1),6079(a,1,1))].">
      <j1 rule="para" parents="28508 6079"/>
    </justification>
  </clause>

  <clause id="28512">
    <literal><![CDATA[
      T(x * (K(y \ z,x) * K(x * (y \ z),u)),y \ z) = ((z \ y) \ 1) \ T(((z \ y) \ 1) * x,u)
    ]]></literal>
    <justification jstring="[para(28508(a,1),22888(a,1,1,2,2))].">
      <j1 rule="para" parents="28508 22888"/>
    </justification>
  </clause>

  <clause id="28513">
    <literal><![CDATA[
      ((x \ ((y / z) / z)) \ 1) \ K(y \ ((x * z) * z),x \ ((y / z) / z)) = x \ ((y / z) / z)
    ]]></literal>
    <justification jstring="[para(28493(a,1),4318(a,1,2))].">
      <j1 rule="para" parents="28493 4318"/>
    </justification>
  </clause>

  <clause id="28514">
    <literal><![CDATA[
      K(x \ ((y * z) * z),(x / z) / z) / (((x / z) / z) \ y) = 1 / (y / ((x / z) / z))
    ]]></literal>
    <justification jstring="[para(28493(a,1),6450(a,1,1))].">
      <j1 rule="para" parents="28493 6450"/>
    </justification>
  </clause>

  <clause id="28515">
    <literal><![CDATA[
      K(x \ T(y,z),T(u,z)) = K(T(x,z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,24251,a(flip),b,28494,a),flip(a)].">
      <j1 rule="hyper" parents="64 24251 28494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28516">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(x * T(z,y),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(14763,a,28515,a),flip(a)].">
      <j1 rule="hyper" parents="14763 28515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28517">
    <literal><![CDATA[
      K(x \ T(y * y,y),z) = K(y * (y / x),z)
    ]]></literal>
    <justification jstring="[hyper(14764,a,28500,a),flip(a)].">
      <j1 rule="hyper" parents="14764 28500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28518">
    <literal><![CDATA[
      K(x \ (y * y),z) = K(y * (y / x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,18519,a(flip),b,28517,a)].">
      <j1 rule="hyper" parents="64 18519 28517"/>
    </justification>
  </clause>

  <clause id="28519">
    <literal><![CDATA[
      (x * K(y * (y / z),u)) \ x = K(u,z \ (y * y))
    ]]></literal>
    <justification jstring="[para(28518(a,1),6882(a,1,1,2))].">
      <j1 rule="para" parents="28518 6882"/>
    </justification>
  </clause>

  <clause id="28520">
    <literal><![CDATA[
      (x / (y \ z)) / ((x / (y \ z)) / u) = u * K((z / (u \ x)) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,28509,a,b,5790,a),flip(a)].">
      <j1 rule="hyper" parents="145 28509 5790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28521">
    <literal><![CDATA[
      ((x \ y) / z) \ K((y / (u * z)) \ x,w) = u \ T(u * (((x \ y) / z) \ 1),w)
    ]]></literal>
    <justification jstring="[para(28510(a,1),24884(a,2,2)),flip(a)].">
      <j1 rule="para" parents="28510 24884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28522">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z)) = K(T(x,z) * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16851,a(flip),b,28516,a),flip(a)].">
      <j1 rule="hyper" parents="64 16851 28516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28523">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,y)) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(8313,a,28522,a),flip(a)].">
      <j1 rule="hyper" parents="8313 28522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28524">
    <literal><![CDATA[
      K(T(x,x * y) * z,T(u,y)) = K(T(z,x * y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25275,a(flip),b,28522,a)].">
      <j1 rule="hyper" parents="64 25275 28522"/>
    </justification>
  </clause>

  <clause id="28526">
    <literal><![CDATA[
      K(T(x,y) * (z * z),u) = K(x * (z * z),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,22382,a(flip),b,28522,a),flip(a)].">
      <j1 rule="hyper" parents="64 22382 28522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28527">
    <literal><![CDATA[
      K(x,y \ (z * z)) = K(x,z * (z / y))
    ]]></literal>
    <justification jstring="[hyper(6899,a,28519,a),flip(a)].">
      <j1 rule="hyper" parents="6899 28519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28528">
    <literal><![CDATA[
      K(x * (y / x),z * (z / u)) = K(y,T(u \ (z * z),x))
    ]]></literal>
    <justification jstring="[hyper(64,a,11193,a(flip),b,28527,a),flip(a)].">
      <j1 rule="hyper" parents="64 11193 28527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28529">
    <literal><![CDATA[
      K((x \ y) * (z * z),T(u,x)) = K(y * (x \ (z * z)),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28218,a(flip),b,28526,a),flip(a)].">
      <j1 rule="hyper" parents="64 28218 28526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28530">
    <literal><![CDATA[
      T(x,y \ (R(z,u,w) \ v5)) = T(x,y \ (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(22727,a,28132,a),flip(a)].">
      <j1 rule="hyper" parents="22727 28132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28532">
    <literal><![CDATA[
      K(x,T(y,z) * (z * u)) = K(x,z * (y * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,28099,a(flip),b,28247,a),flip(a)].">
      <j1 rule="hyper" parents="373 28099 28247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28533">
    <literal><![CDATA[
      K(x,y * (z * (y \ u))) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),28532(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 28532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28534">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) * (z * v5)) = K(x,z * (L(y,u,w) * v5))
    ]]></literal>
    <justification jstring="[para(25(a,2),28532(a,1,2,1))].">
      <j1 rule="para" parents="25 28532"/>
    </justification>
  </clause>

  <clause id="28536">
    <literal><![CDATA[
      K(x,y / (z * L(u,w,v5))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,25465,a(flip),b,28363,a),flip(a)].">
      <j1 rule="hyper" parents="64 25465 28363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28539">
    <literal><![CDATA[
      T(x,y \ (L(z,u,w) \ v5)) = T(x,y \ (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(22722,a,28381,a),flip(a)].">
      <j1 rule="hyper" parents="22722 28381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28543">
    <literal><![CDATA[
      T(x,(y \ z) \ (L(y,u,w) \ z)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,379,a(flip),b,28539,a),flip(a)].">
      <j1 rule="hyper" parents="373 379 28539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28544">
    <literal><![CDATA[
      ((x \ y) \ (L(x,z,u) \ y)) * (x \ y) = L(x,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(145,a,28543,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="145 28543 116"/>
    </justification>
  </clause>

  <clause id="28545">
    <literal><![CDATA[
      T(x,y \ (L(z / y,u,w) \ z)) = x
    ]]></literal>
    <justification jstring="[para(82(a,1),28543(a,1,2,1))].">
      <j1 rule="para" parents="82 28543"/>
    </justification>
  </clause>

  <clause id="28546">
    <literal><![CDATA[
      T(x \ (L(y / x,z,u) \ y),w) = x \ (L(y / x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(55,a,28545,a)].">
      <j1 rule="hyper" parents="55 28545"/>
    </justification>
  </clause>

  <clause id="28547">
    <literal><![CDATA[
      (x / (y * z)) * (y * R(z,u,w)) = (y * R(z,u,w)) * ((y * z) \ x)
    ]]></literal>
    <justification jstring="[para(117(a,1),28113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 28113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28549">
    <literal><![CDATA[
      R(x,y,z) \ T(x,x \ 1) = x * (1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,3239,a(flip),b,28134,a)].">
      <j1 rule="hyper" parents="64 3239 28134"/>
    </justification>
  </clause>

  <clause id="28551">
    <literal><![CDATA[
      R(x,y,z) * ((x \ u) * K(u,w)) = T(R(x,y,z) * (x \ u),w)
    ]]></literal>
    <justification jstring="[para(10(a,1),28188(a,1,2,2,1))].">
      <j1 rule="para" parents="10 28188"/>
    </justification>
  </clause>

  <clause id="28552">
    <literal><![CDATA[
      K(x * (y * (z * K(z \ u,z))),w) = K(x * (y * T(z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,19578,a,b,28261,a)].">
      <j1 rule="hyper" parents="64 19578 28261"/>
    </justification>
  </clause>

  <clause id="28553">
    <literal><![CDATA[
      K(x,((y \ z) \ y) * u) = K(x,y * (y * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,24988,a(flip),b,28288,a)].">
      <j1 rule="hyper" parents="64 24988 28288"/>
    </justification>
  </clause>

  <clause id="28554">
    <literal><![CDATA[
      (1 / (1 / x)) \ L(a(y,z,u),w,v5) = L(a(y,z,u),w,v5) / x
    ]]></literal>
    <justification jstring="[para(24633(a,1),28326(a,2,2))].">
      <j1 rule="para" parents="24633 28326"/>
    </justification>
  </clause>

  <clause id="28555">
    <literal><![CDATA[
      (L(x,y,z) \ u) * ((x \ u) \ w) = (w / (x \ u)) * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(117(a,1),28382(a,1,2))].">
      <j1 rule="para" parents="117 28382"/>
    </justification>
  </clause>

  <clause id="28556">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) * v5 = v5 * (L(a(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(23533(a,1),28382(a,1,2))].">
      <j1 rule="para" parents="23533 28382"/>
    </justification>
  </clause>

  <clause id="28557">
    <literal><![CDATA[
      T(x,(y \ z) * T(u,y \ z)) = T(x,u * (L(y,w,v5) \ z))
    ]]></literal>
    <justification jstring="[para(28382(a,1),28448(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28382 28448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28558">
    <literal><![CDATA[
      L(x,y,z) * (x \ T(x * u,w)) = T(L(x,y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(14494(a,2),28410(a,1,2))].">
      <j1 rule="para" parents="14494 28410"/>
    </justification>
  </clause>

  <clause id="28559">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ u),w) = x * (L(x,y,z) \ T(u,w))
    ]]></literal>
    <justification jstring="[para(28433(a,1),74(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28433 74"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28560">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ u),w) = L(x,y,z) * (x \ T(u,w))
    ]]></literal>
    <justification jstring="[para(74(a,1),28433(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="74 28433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28561">
    <literal><![CDATA[
      T(x,y * ((z \ (y \ u)) * w)) = T(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28285,a(flip),b,28474,a)].">
      <j1 rule="hyper" parents="64 28285 28474"/>
    </justification>
  </clause>

  <clause id="28562">
    <literal><![CDATA[
      K(x,y \ (z * (u * (y * w)))) = K(x,T(z * u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24234,a,b,28481,a)].">
      <j1 rule="hyper" parents="64 24234 28481"/>
    </justification>
  </clause>

  <clause id="28563">
    <literal><![CDATA[
      K(T(x,y * z) * y,u) = K(T(y,z) * x,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13369,a(flip),b,28524,a),flip(a)].">
      <j1 rule="hyper" parents="64 13369 28524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28564">
    <literal><![CDATA[
      K(T(x,y * z) * y,u) = K(y * T(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,28523,a(flip),b,28563,a),flip(a)].">
      <j1 rule="hyper" parents="373 28523 28563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28565">
    <literal><![CDATA[
      K(T(x,y * z) * z,u) = K(z * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18001,a,b,28564,a)].">
      <j1 rule="hyper" parents="64 18001 28564"/>
    </justification>
  </clause>

  <clause id="28566">
    <literal><![CDATA[
      K(x * T(y,z),x * z) = K(x * y,z * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11210,a(flip),b,28565,a),flip(a)].">
      <j1 rule="hyper" parents="64 11210 28565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28567">
    <literal><![CDATA[
      K(x * (y / z),x * y) = K(x * (z \ y),y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,17507,a(flip),b,28566,a)].">
      <j1 rule="hyper" parents="64 17507 28566"/>
    </justification>
  </clause>

  <clause id="28568">
    <literal><![CDATA[
      K(x,T(y \ (z * z),u)) = K(x,T(z * (z / y),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11193,a(flip),b,28528,a),flip(a)].">
      <j1 rule="hyper" parents="64 11193 28528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28569">
    <literal><![CDATA[
      K(x,T(y * (y / x),z)) = K(x,x \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17442,a(flip),b,28568,a),flip(a)].">
      <j1 rule="hyper" parents="64 17442 28568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28570">
    <literal><![CDATA[
      K(x,T(y * (y / x),z)) = K(x,y * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,10143,a(flip),b,28569,a),flip(a)].">
      <j1 rule="hyper" parents="373 10143 28569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28571">
    <literal><![CDATA[
      K(x,T(y * (x \ y),z)) = K(x,y * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,8627,a(flip),b,28570,a)].">
      <j1 rule="hyper" parents="64 8627 28570"/>
    </justification>
  </clause>

  <clause id="28572">
    <literal><![CDATA[
      T(K(x,y * (x \ y)) * z,u) = K(x,y * (x \ y)) * T(z,u)
    ]]></literal>
    <justification jstring="[para(28571(a,1),25476(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28571 25476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28573">
    <literal><![CDATA[
      K((x \ y) * (z * z),T(u,w * x)) = K(y * (x \ (z * z)),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,25272,a(flip),b,28529,a)].">
      <j1 rule="hyper" parents="64 25272 28529"/>
    </justification>
  </clause>

  <clause id="28574">
    <literal><![CDATA[
      L(x,y,z) \ T(L(x,y,z) * u,w) = x \ T(x * u,w)
    ]]></literal>
    <justification jstring="[hyper(149,a,28558,a)].">
      <j1 rule="hyper" parents="149 28558"/>
    </justification>
  </clause>

  <clause id="28576">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ u),w) = x \ (L(x,y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,2325,a,b,28560,a),flip(a)].">
      <j1 rule="hyper" parents="373 2325 28560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28577">
    <literal><![CDATA[
      T(x,T(L(y,z,u) * (y \ w),v5)) = T(x,T(w,v5))
    ]]></literal>
    <justification jstring="[para(28560(a,2),28334(a,1,2))].">
      <j1 rule="para" parents="28560 28334"/>
    </justification>
  </clause>

  <clause id="28578">
    <literal><![CDATA[
      T(x,T(y / L(z,u,w),v5)) = T(x,T(y / z,v5))
    ]]></literal>
    <justification jstring="[para(24849(a,1),28577(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="24849 28577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28579">
    <literal><![CDATA[
      T(x,T((y * z) / u,w)) = T(x,T(y * (z / u),w))
    ]]></literal>
    <justification jstring="[para(692(a,1),28578(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="692 28578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28580">
    <literal><![CDATA[
      T(x,T(y * (z / u),w * u)) = T(x,T(u \ (y * z),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,25292,a(flip),b,28579,a),flip(a)].">
      <j1 rule="hyper" parents="64 25292 28579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28581">
    <literal><![CDATA[
      K(x,(y \ 1) * (z * (u * (y * w)))) = K(x,T(z * u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,14466,a,b,28562,a)].">
      <j1 rule="hyper" parents="64 14466 28562"/>
    </justification>
  </clause>

  <clause id="28582">
    <literal><![CDATA[
      x \ T(x * ((L(x,y,z) \ 1) * u),w) = (L(x,y,z) \ 1) * T(u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,1485,a(flip),b,28574,a),flip(a)].">
      <j1 rule="hyper" parents="64 1485 28574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28583">
    <literal><![CDATA[
      T(x \ (L(x,y,z) * u),w) = x \ (L(x,y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[para(2325(a,2),28576(a,1,1))].">
      <j1 rule="para" parents="2325 28576"/>
    </justification>
  </clause>

  <clause id="28585">
    <literal><![CDATA[
      T(x,y * (L(z,u,w) \ v5)) = T(x,y * (z \ v5))
    ]]></literal>
    <justification jstring="[para(115(a,1),28557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="115 28557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28586">
    <literal><![CDATA[
      T(x,y * (L(z,u,w) \ (v5 * v6))) = T(x,y * ((z \ v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,28285,a(flip),b,28585,a),flip(a)].">
      <j1 rule="hyper" parents="373 28285 28585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28587">
    <literal><![CDATA[
      x / ((L(y,z,u) \ w) \ (y \ w)) = ((L(y,z,u) \ w) \ (y \ w)) \ x
    ]]></literal>
    <justification jstring="[hyper(41,a,15750,a,b,28585,a),flip(a)].">
      <j1 rule="hyper" parents="41 15750 28585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28588">
    <literal><![CDATA[
      K(x,y * (L(z,u,w) \ v5)) = x \ T(x,y * (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(139,a,28585,a(flip),b,5753,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 28585 5753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28589">
    <literal><![CDATA[
      K(x,y * (L(z,u,w) \ v5)) = K(x,y * (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,5726,a,b,28588,a),flip(a)].">
      <j1 rule="hyper" parents="373 5726 28588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28591">
    <literal><![CDATA[
      T(x,y * ((L(z,u,w) \ v5) * v6)) = T(x,y * ((z \ v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,28285,a(flip),b,28586,a)].">
      <j1 rule="hyper" parents="64 28285 28586"/>
    </justification>
  </clause>

  <clause id="28592">
    <literal><![CDATA[
      T(x,y * ((z / T(u,z)) * w)) = T(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(4885(a,1),28591(a,1,2,2,1))].">
      <j1 rule="para" parents="4885 28591"/>
    </justification>
  </clause>

  <clause id="28593">
    <literal><![CDATA[
      T(x,y * (z * (T(u,z) \ w))) = T(x,y * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,28473,a(flip),b,28592,a)].">
      <j1 rule="hyper" parents="64 28473 28592"/>
    </justification>
  </clause>

  <clause id="28595">
    <literal><![CDATA[
      (K(x * y,x \ 1) / x) \ R(R(y,z,u),w,v5) = R(R(y,z,u),w,v5) / (1 / x)
    ]]></literal>
    <justification jstring="[para(28154(a,1),28171(a,1,1,1))].">
      <j1 rule="para" parents="28154 28171"/>
    </justification>
  </clause>

  <clause id="28597">
    <literal><![CDATA[
      K(x \ (((y * z) \ u) * z),u * z) = K(x \ (u / y),u * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,28486,a(flip),b,28174,a)].">
      <j1 rule="hyper" parents="64 28486 28174"/>
    </justification>
  </clause>

  <clause id="28598">
    <literal><![CDATA[
      x \ T(x * (R(x,y,z) \ u),w) = R(x,y,z) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,28182,a(flip),b,26949,a(flip))].">
      <j1 rule="hyper" parents="139 28182 26949"/>
    </justification>
  </clause>

  <clause id="28599">
    <literal><![CDATA[
      R(x,y,z) \ T(R(x,y,z) * u,w) = x \ T(x * u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),28598(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 28598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28600">
    <literal><![CDATA[
      K(x * (y * z),y * z) * K(y * z,x) = a(y / (1 / z),x,y / (1 / z))
    ]]></literal>
    <justification jstring="[para(28229(a,1),14688(a,1,1))].">
      <j1 rule="para" parents="28229 14688"/>
    </justification>
  </clause>

  <clause id="28601">
    <literal><![CDATA[
      ((x \ 1) \ y) \ ((1 / (1 / x)) \ y) = (x * y) \ ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16778,a,b,28240,a)].">
      <j1 rule="hyper" parents="64 16778 28240"/>
    </justification>
  </clause>

  <clause id="28603">
    <literal><![CDATA[
      T(x,x * (y \ (y \ x))) * z = x * (z * K(y * (x \ y),x))
    ]]></literal>
    <justification jstring="[para(15649(a,1),28242(a,1,1))].">
      <j1 rule="para" parents="15649 28242"/>
    </justification>
  </clause>

  <clause id="28604">
    <literal><![CDATA[
      T(((x / y) / z) / u,u * (z * y)) = ((((x / y) / z) / u) \ x) \ x
    ]]></literal>
    <justification jstring="[para(82(a,1),28297(a,1,2,2,2))].">
      <j1 rule="para" parents="82 28297"/>
    </justification>
  </clause>

  <clause id="28605">
    <literal><![CDATA[
      L(R(x,y,z),u,w) / L(x,v5,v6) = L(x,v5,v6) \ L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(2070(a,1),28369(a,1,2,1))].">
      <j1 rule="para" parents="2070 28369"/>
    </justification>
  </clause>

  <clause id="28606">
    <literal><![CDATA[
      T(x,y) \ T(z * (L(z,u,w) \ x),y) = x \ (z * (L(z,u,w) \ x))
    ]]></literal>
    <justification jstring="[hyper(139,a,28402,a(flip),b,5778,a)].">
      <j1 rule="hyper" parents="139 28402 5778"/>
    </justification>
  </clause>

  <clause id="28607">
    <literal><![CDATA[
      ((L(x,y,z) \ R(x,u,w)) \ v5) \ v5 = L(x,y,z) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(215,a,28435,a)].">
      <j1 rule="hyper" parents="215 28435"/>
    </justification>
  </clause>

  <clause id="28608">
    <literal><![CDATA[
      K(x,(y \ z) * (K(z * y,u) * w)) = K(x,T(z \ y,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28462,a(flip),b,28479,a),flip(a)].">
      <j1 rule="hyper" parents="64 28462 28479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28609">
    <literal><![CDATA[
      K(x,T(y,z) * (z * u)) = K(x,z * (L(y,w,v5) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,28329,a(flip),b,28534,a)].">
      <j1 rule="hyper" parents="64 28329 28534"/>
    </justification>
  </clause>

  <clause id="28611">
    <literal><![CDATA[
      K(x,y * (L(z,u,w) * v5)) = K(x,y * (z * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,28532,a(flip),b,28609,a),flip(a)].">
      <j1 rule="hyper" parents="64 28532 28609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28612">
    <literal><![CDATA[
      T(L(x / y,z,u) \ x,K(w,y)) = L(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(39,a,8406,a(flip),b,28546,a(flip))].">
      <j1 rule="hyper" parents="39 8406 28546"/>
    </justification>
  </clause>

  <clause id="28613">
    <literal><![CDATA[
      T(R(x,y,z) * (x \ u),w) = R(x,y,z) * (x \ T(u,w))
    ]]></literal>
    <justification jstring="[para(15021(a,1),28551(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15021 28551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28614">
    <literal><![CDATA[
      L(a(x,y,z),u,w) / (v5 \ 1) = (1 / v5) \ L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),28554(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 28554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28615">
    <literal><![CDATA[
      x * T(K(y,z * (y \ z)) * (y \ z),x) = (y \ z) * (x * K(y,(y \ z) * z))
    ]]></literal>
    <justification jstring="[para(28572(a,2),25076(a,1,2))].">
      <j1 rule="para" parents="28572 25076"/>
    </justification>
  </clause>

  <clause id="28616">
    <literal><![CDATA[
      K(x,(y \ (z \ z)) * (u * (w * (y * v5)))) = K(x,T(u * w,y) * v5)
    ]]></literal>
    <justification jstring="[para(68(a,2),28581(a,1,2,1,2))].">
      <j1 rule="para" parents="68 28581"/>
    </justification>
  </clause>

  <clause id="28617">
    <literal><![CDATA[
      ((1 / x) \ y) \ (x \ y) = (x * y) \ ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,25732,a(flip),b,28601,a)].">
      <j1 rule="hyper" parents="64 25732 28601"/>
    </justification>
  </clause>

  <clause id="28618">
    <literal><![CDATA[
      T(x,x * (y \ (y \ x))) = x * K(y * (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(23318,a,28603,a),flip(a)].">
      <j1 rule="hyper" parents="23318 28603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28619">
    <literal><![CDATA[
      T(x,x * (y \ (y \ x))) \ z = K(x,y * (x \ y)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(28618(a,2),6414(a,1,1))].">
      <j1 rule="para" parents="28618 6414"/>
    </justification>
  </clause>

  <clause id="28620">
    <literal><![CDATA[
      T(x,x * (y \ (y \ x))) / z = K(y * (x \ y),x) * (x / z)
    ]]></literal>
    <justification jstring="[para(28618(a,2),14622(a,1,1))].">
      <j1 rule="para" parents="28618 14622"/>
    </justification>
  </clause>

  <clause id="28621">
    <literal><![CDATA[
      K(x,T(y \ z,u) \ w) = K(x,T(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,22561,a(flip),b,28608,a),flip(a)].">
      <j1 rule="hyper" parents="64 22561 28608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28623">
    <literal><![CDATA[
      K(x,y * (x \ y)) * (x \ y) = (y / x) * K(x / y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27155,a(flip),b,28619,a),flip(a)].">
      <j1 rule="hyper" parents="64 27155 28619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28624">
    <literal><![CDATA[
      (x \ y) * K(x,(x \ y) * y) = (y / x) * K(x / y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11119,a(flip),b,28623,a)].">
      <j1 rule="hyper" parents="64 11119 28623"/>
    </justification>
  </clause>

  <clause id="28625">
    <literal><![CDATA[
      (x \ y) * K(x,y * (x \ y)) = (y / x) * K(x / y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,14021,a(flip),b,28624,a)].">
      <j1 rule="hyper" parents="64 14021 28624"/>
    </justification>
  </clause>

  <clause id="28626">
    <literal><![CDATA[
      (x \ y) * K(x,y * (x \ y)) = (y / x) * K(y \ x,x)
    ]]></literal>
    <justification jstring="[para(6778(a,1),28625(a,2,2))].">
      <j1 rule="para" parents="6778 28625"/>
    </justification>
  </clause>

  <clause id="28627">
    <literal><![CDATA[
      (x \ y) * K(x,y * (x \ y)) = y / T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6245,a(flip),b,28626,a),flip(a)].">
      <j1 rule="hyper" parents="373 6245 28626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28628">
    <literal><![CDATA[
      x * R(y * K(x * y,z),u,w) = T(x * R(y,u,w),z)
    ]]></literal>
    <justification jstring="[hyper(145,a,28169,a(flip),b,14494,a)].">
      <j1 rule="hyper" parents="145 28169 14494"/>
    </justification>
  </clause>

  <clause id="28629">
    <literal><![CDATA[
      x * R(y * K(y * x,z),u,w) = T(x * R(y,u,w),T(z,y))
    ]]></literal>
    <justification jstring="[para(11180(a,1),28628(a,1,2,1,2))].">
      <j1 rule="para" parents="11180 28628"/>
    </justification>
  </clause>

  <clause id="28630">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * w) = T(x,a(u,z,y) * w)
    ]]></literal>
    <justification jstring="[para(18(a,2),28497(a,1,2,1,2))].">
      <j1 rule="para" parents="18 28497"/>
    </justification>
  </clause>

  <clause id="28631">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28372,a(flip),b,28630,a),flip(a)].">
      <j1 rule="hyper" parents="64 28372 28630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28632">
    <literal><![CDATA[
      T(x / (a(y,z,u) * w),w) = (a(y,z,u) * w) \ x
    ]]></literal>
    <justification jstring="[hyper(467,a,28631,a),flip(a)].">
      <j1 rule="hyper" parents="467 28631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28636">
    <literal><![CDATA[
      x * T(y,a(z,u,w) * x) = y * x
    ]]></literal>
    <justification jstring="[hyper(145,a,28631,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="145 28631 22"/>
    </justification>
  </clause>

  <clause id="28638">
    <literal><![CDATA[
      T(x,a(y,z,u) \ w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,25313,a,b,28631,a)].">
      <j1 rule="hyper" parents="64 25313 28631"/>
    </justification>
  </clause>

  <clause id="28639">
    <literal><![CDATA[
      T(x,(y \ a(z,u,w)) * v5) = T(x,y \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,25073,a,b,28631,a)].">
      <j1 rule="hyper" parents="64 25073 28631"/>
    </justification>
  </clause>

  <clause id="28640">
    <literal><![CDATA[
      T(x / (a(y,z,u) \ w),w) = (a(y,z,u) \ w) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,25315,a(flip),b,28631,a),flip(a)].">
      <j1 rule="hyper" parents="64 25315 28631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28641">
    <literal><![CDATA[
      T(x,(a(y,z,u) \ w) * v5) = T(x,w * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,25012,a(flip),b,28631,a),flip(a)].">
      <j1 rule="hyper" parents="64 25012 28631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28642">
    <literal><![CDATA[
      T(x,y * (z * a(u,w,v5))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,25011,a(flip),b,28631,a)].">
      <j1 rule="hyper" parents="64 25011 28631"/>
    </justification>
  </clause>

  <clause id="28643">
    <literal><![CDATA[
      T(x / (a(y,z,u) / (w \ v5)),v5 \ w) = (a(y,z,u) / (w \ v5)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,22636,a(flip),b,28631,a),flip(a)].">
      <j1 rule="hyper" parents="64 22636 28631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28644">
    <literal><![CDATA[
      T(x,y * a(z,u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,19215,a(flip),b,28631,a)].">
      <j1 rule="hyper" parents="64 19215 28631"/>
    </justification>
  </clause>

  <clause id="28645">
    <literal><![CDATA[
      K(a(x,y,z) * u,w) = w / T(w,u)
    ]]></literal>
    <justification jstring="[hyper(225,a,28631,a(flip),b,5804,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 28631 5804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28646">
    <literal><![CDATA[
      (a(x,y,z) * u) * T(w,u) = w * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,28631,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 28631 22"/>
    </justification>
  </clause>

  <clause id="28647">
    <literal><![CDATA[
      K(x,a(y,z,u) * w) = T(x,w) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,28631,a(flip),b,5756,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="142 28631 5756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28648">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ u) * T(w,u) = w * ((a(x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(28631(a,1),14486(a,1,2))].">
      <j1 rule="para" parents="28631 14486"/>
    </justification>
  </clause>

  <clause id="28650">
    <literal><![CDATA[
      (a(x,y,z) * u) * T(w,u) = w * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28631(a,1),23938(a,1,2))].">
      <j1 rule="para" parents="28631 23938"/>
    </justification>
  </clause>

  <clause id="28651">
    <literal><![CDATA[
      (a(x,y,z) \ u) * T(w,u) = w * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(28631(a,1),25317(a,1,2))].">
      <j1 rule="para" parents="28631 25317"/>
    </justification>
  </clause>

  <clause id="28655">
    <literal><![CDATA[
      T(x / ((a(y,z,u) \ 1) * w),w) = ((a(y,z,u) \ 1) * w) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,14569,a(flip),b,28638,a),flip(a)].">
      <j1 rule="hyper" parents="64 14569 28638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28656">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(T(w,u),v5,v6) = L(w,v5,v6) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(28638(a,1),266(a,1,2,1))].">
      <j1 rule="para" parents="28638 266"/>
    </justification>
  </clause>

  <clause id="28657">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * w) / T(u,w) = u \ ((a(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(28638(a,1),24708(a,1,2))].">
      <j1 rule="para" parents="28638 24708"/>
    </justification>
  </clause>

  <clause id="28658">
    <literal><![CDATA[
      T(x,y \ a(z,u,w)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(14732,a,28644,a)].">
      <j1 rule="hyper" parents="14732 28644"/>
    </justification>
  </clause>

  <clause id="28662">
    <literal><![CDATA[
      T(x,y \ (z * a(u,w,v5))) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,24579,a,b,28644,a)].">
      <j1 rule="hyper" parents="64 24579 28644"/>
    </justification>
  </clause>

  <clause id="28663">
    <literal><![CDATA[
      T((x * a(y,z,u)) * (w * w),x) = (w * w) * (x * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,253,a(flip),b,28644,a),flip(a)].">
      <j1 rule="hyper" parents="64 253 28644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28667">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) * y) = a(z,u,w) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,28636,a(flip),b,831,a),flip(a)].">
      <j1 rule="hyper" parents="145 28636 831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28668">
    <literal><![CDATA[
      (x / (a(y,z,u) * w)) * w = w * ((a(y,z,u) * w) \ x)
    ]]></literal>
    <justification jstring="[para(117(a,1),28636(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 28636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28669">
    <literal><![CDATA[
      (x / ((a(y,z,u) \ 1) \ w)) * w = w * (((a(y,z,u) \ 1) \ w) \ x)
    ]]></literal>
    <justification jstring="[para(14485(a,1),28636(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14485 28636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28670">
    <literal><![CDATA[
      (x / (a(y,z,u) \ w)) * w = w * ((a(y,z,u) \ w) \ x)
    ]]></literal>
    <justification jstring="[para(25315(a,1),28636(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25315 28636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28671">
    <literal><![CDATA[
      K(a(x,y,z) * u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,5787,a,b,28645,a),flip(a)].">
      <j1 rule="hyper" parents="373 5787 28645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28673">
    <literal><![CDATA[
      K(a(x,y,z) / u,w) = K(u \ 1,w)
    ]]></literal>
    <justification jstring="[hyper(14676,a,28671,a)].">
      <j1 rule="hyper" parents="14676 28671"/>
    </justification>
  </clause>

  <clause id="28676">
    <literal><![CDATA[
      K(a(x,y,z) \ u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),28671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 28671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28677">
    <literal><![CDATA[
      K(x * a(y,z,u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(23136(a,1),28671(a,1,1))].">
      <j1 rule="para" parents="23136 28671"/>
    </justification>
  </clause>

  <clause id="28678">
    <literal><![CDATA[
      K(a(x,y,z) \ u,u \ a(w,v5,v6)) = K(u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,25207,a(flip),b,28676,a),flip(a)].">
      <j1 rule="hyper" parents="373 25207 28676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28679">
    <literal><![CDATA[
      K(x \ (a(y,z,u) \ w),v5) = K(x \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,25136,a(flip),b,28676,a)].">
      <j1 rule="hyper" parents="64 25136 28676"/>
    </justification>
  </clause>

  <clause id="28680">
    <literal><![CDATA[
      K(x \ a(y,z,u),w) = K(x \ 1,w)
    ]]></literal>
    <justification jstring="[hyper(14674,a,28677,a)].">
      <j1 rule="hyper" parents="14674 28677"/>
    </justification>
  </clause>

  <clause id="28681">
    <literal><![CDATA[
      K(x * (y \ a(z,u,w)),v5) = K(x / y,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28206,a(flip),b,28677,a)].">
      <j1 rule="hyper" parents="64 28206 28677"/>
    </justification>
  </clause>

  <clause id="28682">
    <literal><![CDATA[
      K(x * (y * a(z,u,w)),v5) = K(x * y,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28163,a(flip),b,28677,a)].">
      <j1 rule="hyper" parents="64 28163 28677"/>
    </justification>
  </clause>

  <clause id="28683">
    <literal><![CDATA[
      T(T(x * K(y,x),z),x * (y * a(u,w,v5))) = L(T(x,z),y * a(u,w,v5),x)
    ]]></literal>
    <justification jstring="[para(28677(a,1),6661(a,1,1,1,2))].">
      <j1 rule="para" parents="28677 6661"/>
    </justification>
  </clause>

  <clause id="28684">
    <literal><![CDATA[
      K(x,a(y,z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,5739,a,b,28647,a),flip(a)].">
      <j1 rule="hyper" parents="373 5739 28647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28686">
    <literal><![CDATA[
      K(x,a(y,z,u) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,25526,a,b,28684,a)].">
      <j1 rule="hyper" parents="64 25526 28684"/>
    </justification>
  </clause>

  <clause id="28688">
    <literal><![CDATA[
      K(x,y * a(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,25527,a(flip),b,28684,a),flip(a)].">
      <j1 rule="hyper" parents="64 25527 28684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28689">
    <literal><![CDATA[
      K(x,(a(y,z,u) \ w) * v5) = K(x,w * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,25015,a(flip),b,28684,a),flip(a)].">
      <j1 rule="hyper" parents="64 25015 28684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28690">
    <literal><![CDATA[
      K(x,y * (a(z,u,w) * v5)) = K(x,y * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,25004,a(flip),b,28684,a)].">
      <j1 rule="hyper" parents="64 25004 28684"/>
    </justification>
  </clause>

  <clause id="28692">
    <literal><![CDATA[
      K(x * (a(y,z,u) * w),x) * K(x,w) = a(x,a(y,z,u) * w,x)
    ]]></literal>
    <justification jstring="[para(28684(a,1),10886(a,1,2))].">
      <j1 rule="para" parents="28684 10886"/>
    </justification>
  </clause>

  <clause id="28699">
    <literal><![CDATA[
      x * ((a(y,z,u) \ w) \ K(x * (a(y,z,u) \ w),w)) = L(a(y,z,u) \ w,a(y,z,u) \ w,x) \ x
    ]]></literal>
    <justification jstring="[para(28686(a,1),14988(a,1,2,2))].">
      <j1 rule="para" parents="28686 14988"/>
    </justification>
  </clause>

  <clause id="28706">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,25003,a(flip),b,28688,a)].">
      <j1 rule="hyper" parents="64 25003 28688"/>
    </justification>
  </clause>

  <clause id="28713">
    <literal><![CDATA[
      L(T(x \ a(y,z,u),(x \ a(y,z,u)) \ w),x \ a(y,z,u),x \ a(y,z,u)) = T(x \ a(y,z,u),x \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,8869,a,b,28639,a)].">
      <j1 rule="hyper" parents="64 8869 28639"/>
    </justification>
  </clause>

  <clause id="28716">
    <literal><![CDATA[
      (x * a(y,z,u)) / T(w,w \ x) = w \ (x * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(225,a,28662,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 28662 116"/>
    </justification>
  </clause>

  <clause id="28719">
    <literal><![CDATA[
      x * T(x \ (a(y,z,u) \ 1),w) = a(y,z,u) \ K(x \ 1,w)
    ]]></literal>
    <justification jstring="[para(28679(a,1),14523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28679 14523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28720">
    <literal><![CDATA[
      K(x * (T(y,z) / z),u) = K(x * (z \ y),u)
    ]]></literal>
    <justification jstring="[para(10928(a,1),28682(a,1,1,2))].">
      <j1 rule="para" parents="10928 28682"/>
    </justification>
  </clause>

  <clause id="28721">
    <literal><![CDATA[
      K(x * (a(y,z,u) \ w),v5) = K(x * w,v5)
    ]]></literal>
    <justification jstring="[para(23135(a,1),28682(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="23135 28682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28722">
    <literal><![CDATA[
      K(x * (a(y,z,u) * w),v5) = K(x * w,v5)
    ]]></literal>
    <justification jstring="[para(23136(a,2),28682(a,1,1,2))].">
      <j1 rule="para" parents="23136 28682"/>
    </justification>
  </clause>

  <clause id="28729">
    <literal><![CDATA[
      K(x * ((y \ R(y,z,u)) \ w),v5) = K(x * w,v5)
    ]]></literal>
    <justification jstring="[para(28073(a,1),28721(a,1,1,2,1))].">
      <j1 rule="para" parents="28073 28721"/>
    </justification>
  </clause>

  <clause id="28730">
    <literal><![CDATA[
      K(x * (y / T(z,y)),u) = K(x * (z \ y),u)
    ]]></literal>
    <justification jstring="[para(4630(a,1),28720(a,1,1,2))].">
      <j1 rule="para" parents="4630 28720"/>
    </justification>
  </clause>

  <clause id="28731">
    <literal><![CDATA[
      K(x * ((1 / y) / T(z,y \ 1)),u) = K(x * (z \ (1 / y)),u)
    ]]></literal>
    <justification jstring="[para(3870(a,1),28730(a,1,1,2,2))].">
      <j1 rule="para" parents="3870 28730"/>
    </justification>
  </clause>

  <clause id="28732">
    <literal><![CDATA[
      K(x * ((R(y,z,u) \ y) * w),v5) = K(x * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28495,a(flip),b,28729,a)].">
      <j1 rule="hyper" parents="64 28495 28729"/>
    </justification>
  </clause>

  <clause id="28734">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) / (a(x,y,z) * w) = L(u,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(41,a,987,a(flip),b,28632,a),flip(a)].">
      <j1 rule="hyper" parents="41 987 28632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28735">
    <literal><![CDATA[
      T(x / (y * a(z,u,w)),y) = (a(z,u,w) * y) \ x
    ]]></literal>
    <justification jstring="[para(23136(a,1),28632(a,1,1,2))].">
      <j1 rule="para" parents="23136 28632"/>
    </justification>
  </clause>

  <clause id="28738">
    <literal><![CDATA[
      (x / y) * (a(z,u,w) * y) = (a(z,u,w) * y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(117(a,1),28646(a,1,2)),flip(a)].">
      <j1 rule="para" parents="117 28646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28739">
    <literal><![CDATA[
      ((a(x,y,z) * u) * w) / T(u,w) = (w * (a(x,y,z) * u)) / u
    ]]></literal>
    <justification jstring="[para(28646(a,1),6846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28646 6846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28741">
    <literal><![CDATA[
      x * (T(y,x) * a(z,u,w)) = (a(z,u,w) * y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,6951,a(flip),b,28650,a),flip(a)].">
      <j1 rule="hyper" parents="64 6951 28650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28742">
    <literal><![CDATA[
      (a(x,y,z) * (u / w)) * w = w * ((w \ u) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,6855,a(flip),b,28650,a)].">
      <j1 rule="hyper" parents="64 6855 28650"/>
    </justification>
  </clause>

  <clause id="28743">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (y * a(z,u,w)) = a(z,u,w) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,988,a(flip),b,28650,a),flip(a)].">
      <j1 rule="hyper" parents="64 988 28650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28744">
    <literal><![CDATA[
      T(a(x,y,z) * u,w) = T(u,w) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(269,a,6951,a(flip),b,28650,a(flip))].">
      <j1 rule="hyper" parents="269 6951 28650"/>
    </justification>
  </clause>

  <clause id="28745">
    <literal><![CDATA[
      T(a(x,y,z) * (u / w),w) = (w \ u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(269,a,6855,a(flip),b,28650,a(flip))].">
      <j1 rule="hyper" parents="269 6855 28650"/>
    </justification>
  </clause>

  <clause id="28748">
    <literal><![CDATA[
      T(a(x,y,z) * a(u,w,v5),v6) = a(x,y,z) * a(u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,23960,a(flip),b,28744,a),flip(a)].">
      <j1 rule="hyper" parents="373 23960 28744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28750">
    <literal><![CDATA[
      T(x * a(y,z,u),w) = T(x,w) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(23136(a,1),28744(a,1,1))].">
      <j1 rule="para" parents="23136 28744"/>
    </justification>
  </clause>

  <clause id="28751">
    <literal><![CDATA[
      T(x,T(a(y,z,u) * w,v5)) = T(x,T(w,v5))
    ]]></literal>
    <justification jstring="[para(28744(a,2),28644(a,1,2))].">
      <j1 rule="para" parents="28744 28644"/>
    </justification>
  </clause>

  <clause id="28752">
    <literal><![CDATA[
      T(x,T((y * z) * u,w)) = T(x,T(y * (z * u),w))
    ]]></literal>
    <justification jstring="[para(15463(a,1),28751(a,1,2,1))].">
      <j1 rule="para" parents="15463 28751"/>
    </justification>
  </clause>

  <clause id="28753">
    <literal><![CDATA[
      T(x * a(y,z,u),w) = a(y,z,u) * T(x,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a,b,28750,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 28750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28755">
    <literal><![CDATA[
      T(a(x,y,z) \ (u / w),w) = a(x,y,z) \ (w \ u)
    ]]></literal>
    <justification jstring="[hyper(36,a,5456,a(flip),b,28750,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 5456 28750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28756">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ 1),w) = T(x,w) * (a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,5444,a(flip),b,28750,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 5444 28750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28757">
    <literal><![CDATA[
      T(a(x,y,z) \ u,w) = a(x,y,z) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,5432,a(flip),b,28750,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 5432 28750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28759">
    <literal><![CDATA[
      T(x,T((y \ z) * a(u,w,v5),y)) = T(x,a(u,w,v5) * (z / y))
    ]]></literal>
    <justification jstring="[para(28753(a,2),15807(a,1,2))].">
      <j1 rule="para" parents="28753 15807"/>
    </justification>
  </clause>

  <clause id="28761">
    <literal><![CDATA[
      x * (a(y,z,u) \ T(w,x)) = (a(y,z,u) \ w) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,28757,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 28757 22"/>
    </justification>
  </clause>

  <clause id="28762">
    <literal><![CDATA[
      T((a(x,y,z) \ 1) \ u,w) = (a(x,y,z) \ 1) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(39,a,5469,a(flip),b,28757,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 5469 28757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28763">
    <literal><![CDATA[
      L(T(a(x,y,z) \ u,w),a(x,y,z),w) = (a(x,y,z) * w) \ (u * w)
    ]]></literal>
    <justification jstring="[para(28757(a,2),23942(a,1,1))].">
      <j1 rule="para" parents="28757 23942"/>
    </justification>
  </clause>

  <clause id="28764">
    <literal><![CDATA[
      L(x,a(y,z,u) \ w,a(y,z,u)) * w = a(y,z,u) * (x * (a(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(145,a,28651,a(flip),b,1010,a),flip(a)].">
      <j1 rule="hyper" parents="145 28651 1010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28765">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (u \ w) = (w / u) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(117(a,1),28651(a,1,2))].">
      <j1 rule="para" parents="117 28651"/>
    </justification>
  </clause>

  <clause id="28766">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * w) / T(u,w) = (w * (a(x,y,z) \ u)) / u
    ]]></literal>
    <justification jstring="[para(28651(a,1),6846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28651 6846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28768">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ K(u,u \ 1) = 1 / (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,28678,a(flip),b,4338,a)].">
      <j1 rule="hyper" parents="139 28678 4338"/>
    </justification>
  </clause>

  <clause id="28773">
    <literal><![CDATA[
      (x * ((a(y,z,u) * x) \ w)) / x = w / (x * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(313,a,28735,a)].">
      <j1 rule="hyper" parents="313 28735"/>
    </justification>
  </clause>

  <clause id="28774">
    <literal><![CDATA[
      (x / (y * a(z,u,w))) * y = y * ((a(z,u,w) * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,28735,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 28735 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28775">
    <literal><![CDATA[
      (x * y) * L(a(z,u,w),x,y) = (a(z,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,10989,a,b,28741,a)].">
      <j1 rule="hyper" parents="64 10989 28741"/>
    </justification>
  </clause>

  <clause id="28776">
    <literal><![CDATA[
      x * L(a(y,z,u),w,w \ x) = (a(y,z,u) * w) * (w \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10988,a(flip),b,28741,a)].">
      <j1 rule="hyper" parents="64 10988 28741"/>
    </justification>
  </clause>

  <clause id="28777">
    <literal><![CDATA[
      T(x,T(y * (z * u),u)) = T(x,u * (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11103,a(flip),b,28752,a),flip(a)].">
      <j1 rule="hyper" parents="64 11103 28752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28778">
    <literal><![CDATA[
      T(x,T(K(y,z) * (u * w),w)) = T(x,w * (u * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,17948,a(flip),b,28777,a),flip(a)].">
      <j1 rule="hyper" parents="373 17948 28777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28779">
    <literal><![CDATA[
      T(x,T(y * (z * (u \ w)),u * w)) = T(x,(u \ w) * (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,17029,a(flip),b,28777,a)].">
      <j1 rule="hyper" parents="64 17029 28777"/>
    </justification>
  </clause>

  <clause id="28780">
    <literal><![CDATA[
      T(x,T((T(T(y,z),u) \ y) * (w * v5),v5)) = T(x,v5 * (y * (T(T(y,z),u) \ w)))
    ]]></literal>
    <justification jstring="[para(20810(a,1),28777(a,2,2,2))].">
      <j1 rule="para" parents="20810 28777"/>
    </justification>
  </clause>

  <clause id="28781">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * w) \ (u * w) = (w * (a(x,y,z) \ u)) \ (w * u)
    ]]></literal>
    <justification jstring="[para(28761(a,1),21648(a,1,1))].">
      <j1 rule="para" parents="28761 21648"/>
    </justification>
  </clause>

  <clause id="28783">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,w)) * y) = L(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,23168,a(flip),b,28775,a)].">
      <j1 rule="hyper" parents="139 23168 28775"/>
    </justification>
  </clause>

  <clause id="28784">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (u * w) = (a(x,y,z) * u) * w
    ]]></literal>
    <justification jstring="[hyper(64,a,23557,a,b,28775,a)].">
      <j1 rule="hyper" parents="64 23557 28775"/>
    </justification>
  </clause>

  <clause id="28785">
    <literal><![CDATA[
      (x * L(a(y,z,u),w,x)) * w = x * (w * L(a(y,z,u),x,w))
    ]]></literal>
    <justification jstring="[para(28783(a,1),2845(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28783 2845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28786">
    <literal><![CDATA[
      ((x * a(y,z,u)) * w) / (x * w) = L(a(y,z,u),x,w)
    ]]></literal>
    <justification jstring="[hyper(142,a,23168,a(flip),b,28784,a)].">
      <j1 rule="hyper" parents="142 23168 28784"/>
    </justification>
  </clause>

  <clause id="28787">
    <literal><![CDATA[
      R(a(x,y,z),u,w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,111,a,b,28784,a)].">
      <j1 rule="hyper" parents="36 111 28784"/>
    </justification>
  </clause>

  <clause id="28789">
    <literal><![CDATA[
      (x * y) \ (x * (y * a(z,u,w))) = R(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,18,a(flip),b,28787,a)].">
      <j1 rule="hyper" parents="373 18 28787"/>
    </justification>
  </clause>

  <clause id="28790">
    <literal><![CDATA[
      L(R(x \ R(x,y,z),u,w),x,z * y) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24740,a,b,28787,a)].">
      <j1 rule="hyper" parents="64 24740 28787"/>
    </justification>
  </clause>

  <clause id="28791">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u,u) = a(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,28787,a(flip),b,15984,a)].">
      <j1 rule="hyper" parents="139 28787 15984"/>
    </justification>
  </clause>

  <clause id="28792">
    <literal><![CDATA[
      L((x * (y * z)) \ ((x * y) * z),u,w) = R(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14(a,1),28787(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14 28787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28793">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (1 / a(x,y,z)) = a(x,y,z) * R(1 / a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(28787(a,1),2169(a,1,1))].">
      <j1 rule="para" parents="28787 2169"/>
    </justification>
  </clause>

  <clause id="28794">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),u,w) \ a(x,y,z)) = 1 / R(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(28787(a,1),11435(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="28787 11435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28795">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),u) * u = (a(x,y,z) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(28787(a,1),13950(a,1,1))].">
      <j1 rule="para" parents="28787 13950"/>
    </justification>
  </clause>

  <clause id="28796">
    <literal><![CDATA[
      ((x * y) * a(z,u,w)) \ ((x * y) * L(a(z,u,w),x,y)) = a(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[para(28787(a,1),15981(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="28787 15981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28797">
    <literal><![CDATA[
      L(a(x,y,z),u,u) \ u = a(x,y,z) \ L(u,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28787(a,1),16075(a,1,1))].">
      <j1 rule="para" parents="28787 16075"/>
    </justification>
  </clause>

  <clause id="28798">
    <literal><![CDATA[
      R(T(a(x,y,z),u),w,v5) = L(a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(23127(a,2),28787(a,1,1))].">
      <j1 rule="para" parents="23127 28787"/>
    </justification>
  </clause>

  <clause id="28799">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ a((w * u) \ (a(x,y,z) \ (w * u)),u,w) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(28787(a,1),28076(a,1,1))].">
      <j1 rule="para" parents="28787 28076"/>
    </justification>
  </clause>

  <clause id="28800">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (y * a(z,u,w)) = (x * y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(39,a,25191,a,b,28789,a),flip(a)].">
      <j1 rule="hyper" parents="39 25191 28789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28801">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) \ 1 = a(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5665,a,b,28791,a)].">
      <j1 rule="hyper" parents="64 5665 28791"/>
    </justification>
  </clause>

  <clause id="28802">
    <literal><![CDATA[
      a(a(x,y,z),u,u) \ 1 = a(u,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,28801,a)].">
      <j1 rule="hyper" parents="40 23134 28801"/>
    </justification>
  </clause>

  <clause id="28803">
    <literal><![CDATA[
      (x / (y / a(z,u,w))) * y = y * ((a(z,u,w) \ y) \ x)
    ]]></literal>
    <justification jstring="[para(23133(a,2),28670(a,1,1,2))].">
      <j1 rule="para" parents="23133 28670"/>
    </justification>
  </clause>

  <clause id="28804">
    <literal><![CDATA[
      (x * a(y,z,u)) / (w \ x) = (x / w) \ (x * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(848(a,1),28716(a,1,2))].">
      <j1 rule="para" parents="848 28716"/>
    </justification>
  </clause>

  <clause id="28805">
    <literal><![CDATA[
      (x / y) * (a(z,u,w) * y) = (y * a(z,u,w)) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,23168,a(flip),b,28738,a),flip(a)].">
      <j1 rule="hyper" parents="373 23168 28738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28806">
    <literal><![CDATA[
      (a(x,y,z) * (u \ 1)) * ((u \ 1) \ w) = (w / u) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,23945,a(flip),b,28738,a),flip(a)].">
      <j1 rule="hyper" parents="64 23945 28738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28807">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (u \ 1) = u * (a(x,y,z) \ (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,25709,a(flip),b,28765,a),flip(a)].">
      <j1 rule="hyper" parents="373 25709 28765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28808">
    <literal><![CDATA[
      (a(x,y,z) \ L(u,u,u)) \ 1 = 1 / (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14727,a(flip),b,28768,a)].">
      <j1 rule="hyper" parents="64 14727 28768"/>
    </justification>
  </clause>

  <clause id="28809">
    <literal><![CDATA[
      (a(x,y,z) \ (1 / (1 / u))) \ 1 = 1 / (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(818(a,1),28808(a,1,1,2))].">
      <j1 rule="para" parents="818 28808"/>
    </justification>
  </clause>

  <clause id="28810">
    <literal><![CDATA[
      L((a(x,y,z) \ u) / w,w,a(x,y,z)) = u / (w * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1208,a,b,28773,a)].">
      <j1 rule="hyper" parents="64 1208 28773"/>
    </justification>
  </clause>

  <clause id="28811">
    <literal><![CDATA[
      L(x / y,y,a(z,u,w)) = (a(z,u,w) * x) / (y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,1207,a(flip),b,28773,a)].">
      <j1 rule="hyper" parents="64 1207 28773"/>
    </justification>
  </clause>

  <clause id="28812">
    <literal><![CDATA[
      L(a(x,y,z),u,u * a(x,y,z)) \ 1 = u * ((a(x,y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,25350,a,b,28774,a)].">
      <j1 rule="hyper" parents="64 25350 28774"/>
    </justification>
  </clause>

  <clause id="28813">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,y,z) * u) = (u * ((a(x,y,z) * u) \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(28774(a,1),21692(a,2,1))].">
      <j1 rule="para" parents="28774 21692"/>
    </justification>
  </clause>

  <clause id="28814">
    <literal><![CDATA[
      x * L(a(y,z,u),a(y,z,u),x) = (a(y,z,u) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,23557,a(flip),b,28795,a)].">
      <j1 rule="hyper" parents="64 23557 28795"/>
    </justification>
  </clause>

  <clause id="28815">
    <literal><![CDATA[
      (a(x,y,z) * u) / (w \ u) = (u / w) \ (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,23181,a,b,28804,a)].">
      <j1 rule="hyper" parents="64 23181 28804"/>
    </justification>
  </clause>

  <clause id="28816">
    <literal><![CDATA[
      (a(x,y,z) * (u * (u \ w))) / (v5 \ w) = (w / v5) \ (w * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(23182(a,2),28804(a,1,1))].">
      <j1 rule="para" parents="23182 28804"/>
    </justification>
  </clause>

  <clause id="28817">
    <literal><![CDATA[
      1 / (a(x,y,z) \ (u \ 1)) = (a(x,y,z) \ (1 / u)) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),28809(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="79 28809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28818">
    <literal><![CDATA[
      (x / (x / y)) \ (x * a(z,u,w)) = (a(z,u,w) * x) / y
    ]]></literal>
    <justification jstring="[para(82(a,1),28815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="82 28815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28819">
    <literal><![CDATA[
      ((a(x,y,z) \ (1 / u)) \ 1) \ 1 = a(x,y,z) \ (u \ 1)
    ]]></literal>
    <justification jstring="[hyper(215,a,28817,a)].">
      <j1 rule="hyper" parents="215 28817"/>
    </justification>
  </clause>

  <clause id="28820">
    <literal><![CDATA[
      ((a(x,y,z) \ u) \ 1) \ 1 = a(x,y,z) \ ((u \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(79(a,1),28819(a,1,1,1,2))].">
      <j1 rule="para" parents="79 28819"/>
    </justification>
  </clause>

  <clause id="28821">
    <literal><![CDATA[
      R(x \ R(x,y,z),u,w) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(42,a,23992,a,b,28790,a),flip(a)].">
      <j1 rule="hyper" parents="42 23992 28790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28822">
    <literal><![CDATA[
      K(x,y) * L(x \ R(x,z,u),w,v5) = R(x \ R(T(x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(28821(a,1),25977(a,1,2))].">
      <j1 rule="para" parents="28821 25977"/>
    </justification>
  </clause>

  <clause id="28823">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),L(x,y,z),z * y) = R(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,1711,a,b,28792,a)].">
      <j1 rule="hyper" parents="64 1711 28792"/>
    </justification>
  </clause>

  <clause id="28824">
    <literal><![CDATA[
      (x / ((a(y,z,u) \ 1) * w)) * w = w * (((a(y,z,u) \ 1) * w) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,28655,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 28655 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28825">
    <literal><![CDATA[
      (x * a(y,z,u)) * (w * w) = x * ((w * w) * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(41,a,24634,a,b,28663,a),flip(a)].">
      <j1 rule="hyper" parents="41 24634 28663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28826">
    <literal><![CDATA[
      (x * ((y * y) * a(z,u,w))) * v5 = (x * a(z,u,w)) * ((y * y) * v5)
    ]]></literal>
    <justification jstring="[hyper(144,a,28825,a(flip),b,133,a)].">
      <j1 rule="hyper" parents="144 28825 133"/>
    </justification>
  </clause>

  <clause id="28827">
    <literal><![CDATA[
      (x * ((y * y) * a(z,u,w))) \ v5 = (y * y) \ ((x * a(z,u,w)) \ v5)
    ]]></literal>
    <justification jstring="[para(28825(a,1),486(a,1,1))].">
      <j1 rule="para" parents="28825 486"/>
    </justification>
  </clause>

  <clause id="28828">
    <literal><![CDATA[
      (x * ((y * y) * a(z,u,w))) \ v5 = (y * y) \ ((a(z,u,w) * x) \ v5)
    ]]></literal>
    <justification jstring="[para(28825(a,1),24756(a,1,1))].">
      <j1 rule="para" parents="28825 24756"/>
    </justification>
  </clause>

  <clause id="28829">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) * (1 / y)) = a(z,u,w) * (x * (1 / y))
    ]]></literal>
    <justification jstring="[para(11776(a,1),28667(a,1,1))].">
      <j1 rule="para" parents="11776 28667"/>
    </justification>
  </clause>

  <clause id="28830">
    <literal><![CDATA[
      a(x,y,z) \ K(u \ 1,u) = (u \ (a(x,y,z) \ 1)) * u
    ]]></literal>
    <justification jstring="[hyper(328,a,28719,a),flip(a)].">
      <j1 rule="hyper" parents="328 28719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28831">
    <literal><![CDATA[
      K(x * ((y \ 1) / T(z,y \ 1)),u) = K(x * (z \ (1 / y)),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,19706,a(flip),b,28731,a)].">
      <j1 rule="hyper" parents="64 19706 28731"/>
    </justification>
  </clause>

  <clause id="28832">
    <literal><![CDATA[
      R(x,y,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,24650,a(flip),b,28734,a)].">
      <j1 rule="hyper" parents="64 24650 28734"/>
    </justification>
  </clause>

  <clause id="28833">
    <literal><![CDATA[
      (a(x,y,y) * (z * x)) / R(x,y,y) = L(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(15998(a,1),28734(a,1,2))].">
      <j1 rule="para" parents="15998 28734"/>
    </justification>
  </clause>

  <clause id="28834">
    <literal><![CDATA[
      x * (x \ L(y,z,a(u,w,v5))) = R(y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,10,a,b,28832,a)].">
      <j1 rule="hyper" parents="373 10 28832"/>
    </justification>
  </clause>

  <clause id="28835">
    <literal><![CDATA[
      L(x / y,y,a(z,u,w)) = (x * a(z,u,w)) / (a(z,u,w) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,23558,a(flip),b,28832,a),flip(a)].">
      <j1 rule="hyper" parents="64 23558 28832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28836">
    <literal><![CDATA[
      L((x \ y) / x,z,a(u,w,v5)) = (x \ R(y,z,a(u,w,v5))) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,2147,a(flip),b,28832,a),flip(a)].">
      <j1 rule="hyper" parents="64 2147 28832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28837">
    <literal><![CDATA[
      x * L(x \ 1,y,a(z,u,w)) = x \ R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,28832,a(flip),b,1990,a)].">
      <j1 rule="hyper" parents="145 28832 1990"/>
    </justification>
  </clause>

  <clause id="28838">
    <literal><![CDATA[
      x \ L(x * y,z,a(u,w,v5)) = x * R(x \ y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(139,a,28832,a(flip),b,2125,a)].">
      <j1 rule="hyper" parents="139 28832 2125"/>
    </justification>
  </clause>

  <clause id="28839">
    <literal><![CDATA[
      L(x,y,a(z,z \ u,(z \ u) \ 1)) = R(x,y,z \ (u * ((z \ u) \ 1)))
    ]]></literal>
    <justification jstring="[para(980(a,1),28832(a,1,3)),flip(a)].">
      <j1 rule="para" parents="980 28832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28840">
    <literal><![CDATA[
      x \ (L(1 / x,y,a(z,u,w)) \ 1) = R(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(28832(a,1),2467(a,1,2,1))].">
      <j1 rule="para" parents="28832 2467"/>
    </justification>
  </clause>

  <clause id="28841">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,y * a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(28832(a,1),16031(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="28832 16031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28842">
    <literal><![CDATA[
      (R(x,y,y) * z) \ (R(x,y,y) * L(z,x,a(x,y,y))) = a(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(28832(a,1),16455(a,1,2,2))].">
      <j1 rule="para" parents="28832 16455"/>
    </justification>
  </clause>

  <clause id="28843">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,a(z,u,w) * y) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(28832(a,1),23986(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="28832 23986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28844">
    <literal><![CDATA[
      R(x,y,a(z,u,w * v5)) = L(x,y,a(z,u,v5 * w))
    ]]></literal>
    <justification jstring="[para(27298(a,1),28832(a,1,3))].">
      <j1 rule="para" parents="27298 28832"/>
    </justification>
  </clause>

  <clause id="28845">
    <literal><![CDATA[
      R(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(28834(a,1),228(a,1)),flip(b)].">
      <j1 rule="para" parents="28834 228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28846">
    <literal><![CDATA[
      L(x,y,a(z,u,w * v5)) = L(x,y,a(z,u,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(28845,a,28844,a)].">
      <j1 rule="hyper" parents="28845 28844"/>
    </justification>
  </clause>

  <clause id="28847">
    <literal><![CDATA[
      L(x,y,a(z,u,(w * v5) * v6)) = L(x,y,a(z,u,v6 * (v5 * w)))
    ]]></literal>
    <justification jstring="[para(27315(a,1),28846(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27315 28846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28848">
    <literal><![CDATA[
      x * L(x \ 1,y,a(z,u,w)) = x \ L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(28832(a,1),28837(a,2,2))].">
      <j1 rule="para" parents="28832 28837"/>
    </justification>
  </clause>

  <clause id="28849">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),u,a(w,v5,v6)) = L(x * L(x \ 1,u,a(w,v5,v6)),y,z)
    ]]></literal>
    <justification jstring="[hyper(4274,a,28848,a),flip(a)].">
      <j1 rule="hyper" parents="4274 28848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28850">
    <literal><![CDATA[
      T(x,a(y,z,u) * (w / v5)) = T(x,w * (a(y,z,u) / v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,25548,a(flip),b,28759,a),flip(a)].">
      <j1 rule="hyper" parents="64 25548 28759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28851">
    <literal><![CDATA[
      T(x,y * (a(z,u,w) / v5)) = T(x,y / v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28631,a(flip),b,28850,a),flip(a)].">
      <j1 rule="hyper" parents="64 28631 28850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28853">
    <literal><![CDATA[
      (x \ ((a(y,z,u) \ x) * w)) * x = w * (a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(144,a,28657,a(flip),b,28766,a(flip))].">
      <j1 rule="hyper" parents="144 28657 28766"/>
    </justification>
  </clause>

  <clause id="28854">
    <literal><![CDATA[
      ((a(x,y,z) \ u) \ w) * (a(x,y,z) \ u) = (u \ w) * u
    ]]></literal>
    <justification jstring="[para(10(a,1),28853(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 28853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28855">
    <literal><![CDATA[
      ((a(x,y,z) \ u) \ (u / w)) * (a(x,y,z) \ u) = (u / w) * K(w \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6425,a(flip),b,28854,a),flip(a)].">
      <j1 rule="hyper" parents="373 6425 28854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28856">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (u * (w / u)) = w / (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(142,a,84,a(flip),b,28854,a),flip(a)].">
      <j1 rule="hyper" parents="142 84 28854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28857">
    <literal><![CDATA[
      (x * y) / (a(z,u,w) \ y) = (a(z,u,w) \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),28856(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 28856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28858">
    <literal><![CDATA[
      ((a(x,y,z) \ u) \ (u * w)) \ (w * u) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(215,a,28857,a)].">
      <j1 rule="hyper" parents="215 28857"/>
    </justification>
  </clause>

  <clause id="28859">
    <literal><![CDATA[
      T(x,T(K(y,z) * (u * (y \ w)),y * w)) = T(x,(T(y,z) \ w) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,19557,a(flip),b,28779,a),flip(a)].">
      <j1 rule="hyper" parents="373 19557 28779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28860">
    <literal><![CDATA[
      (x * y) * a(z,u,w) != v5 * (y * a(z,u,w))
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(28800(a,1),45(a,1))].">
      <j1 rule="para" parents="28800 45"/>
    </justification>
  </clause>

  <clause id="28862">
    <literal><![CDATA[
      K(x * (y \ (1 / z)),u) = K(x * (y \ (z \ 1)),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28730,a(flip),b,28831,a),flip(a)].">
      <j1 rule="hyper" parents="64 28730 28831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28863">
    <literal><![CDATA[
      K(x * (y \ (1 / z)),u) = K(x / (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,28291,a(flip),b,28862,a),flip(a)].">
      <j1 rule="hyper" parents="373 28291 28862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28864">
    <literal><![CDATA[
      L((x \ y) / x,z,a(u,w,v5)) = (x \ L(y,z,a(u,w,v5))) / x
    ]]></literal>
    <justification jstring="[para(28832(a,1),28836(a,2,1,2))].">
      <j1 rule="para" parents="28832 28836"/>
    </justification>
  </clause>

  <clause id="28865">
    <literal><![CDATA[
      x \ L(x * y,z,a(u,w,v5)) = x * L(x \ y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(28832(a,1),28838(a,2,2))].">
      <j1 rule="para" parents="28832 28838"/>
    </justification>
  </clause>

  <clause id="28866">
    <literal><![CDATA[
      x \ (L(1 / x,y,a(z,u,w)) \ 1) = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(28832(a,1),28840(a,2,1))].">
      <j1 rule="para" parents="28832 28840"/>
    </justification>
  </clause>

  <clause id="28867">
    <literal><![CDATA[
      x \ L(x * a(y,z,u),x,a(y,z,u)) = x * (((a(y,z,u) \ 1) * x) \ 1)
    ]]></literal>
    <justification jstring="[para(13948(a,1),28865(a,2,2))].">
      <j1 rule="para" parents="13948 28865"/>
    </justification>
  </clause>

  <clause id="28868">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,x) = K(x * w,x) * K(x,w)
    ]]></literal>
    <justification jstring="[para(28722(a,1),28692(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28722 28692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28869">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,x) = a(x,w,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10886,a(flip),b,28868,a),flip(a)].">
      <j1 rule="hyper" parents="373 10886 28868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28872">
    <literal><![CDATA[
      R(x,a(y,z,u) * w,x) = x * a(x,w,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,28869,a(flip),b,10884,a),flip(a)].">
      <j1 rule="hyper" parents="145 28869 10884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28873">
    <literal><![CDATA[
      R(x,a(y,z,u) * w,x) = R(x,w,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10889,a(flip),b,28872,a),flip(a)].">
      <j1 rule="hyper" parents="373 10889 28872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28874">
    <literal><![CDATA[
      R(x,(y * z) * u,x) = R(x,y * (z * u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,15484,a(flip),b,28873,a),flip(a)].">
      <j1 rule="hyper" parents="64 15484 28873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28876">
    <literal><![CDATA[
      R(x,y * (z \ u),x) = R(x,y * (z * u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26683,a(flip),b,28874,a)].">
      <j1 rule="hyper" parents="64 26683 28874"/>
    </justification>
  </clause>

  <clause id="28877">
    <literal><![CDATA[
      x * R(x \ K(y,y \ 1),z,u) = y * (1 * ((x \ R(x,z,u)) / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,26006,a(flip),b,28078,a)].">
      <j1 rule="hyper" parents="64 26006 28078"/>
    </justification>
  </clause>

  <clause id="28878">
    <literal><![CDATA[
      R(x,y,z) \ (u * ((x \ R(x,y,z)) / u)) = x \ K(u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,14444,a(flip),b,28079,a),flip(a)].">
      <j1 rule="hyper" parents="373 14444 28079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28880">
    <literal><![CDATA[
      a(x,y,z * (u * (K(w,v5) * (u / (u * v6))))) = a(x,y,(v6 \ u) * z)
    ]]></literal>
    <justification jstring="[para(23256(a,1),28083(a,1,3,2))].">
      <j1 rule="para" parents="23256 28083"/>
    </justification>
  </clause>

  <clause id="28881">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(z * y,w))) = K(x,T(z * (y \ 1),w) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,18211,a,b,28086,a)].">
      <j1 rule="hyper" parents="64 18211 28086"/>
    </justification>
  </clause>

  <clause id="28882">
    <literal><![CDATA[
      (x \ R(x,y,z)) / (u \ 1) = (1 / u) \ (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1727(a,1),28179(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1727 28179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28883">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * K(K(x,y),z)) = T(x * (y \ (x \ y)),z)
    ]]></literal>
    <justification jstring="[para(5731(a,2),28238(a,1,2,2,1))].">
      <j1 rule="para" parents="5731 28238"/>
    </justification>
  </clause>

  <clause id="28884">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * K(x,K(y,z))) = T(x * (y \ (x \ y)),z)
    ]]></literal>
    <justification jstring="[para(8092(a,1),28883(a,1,2,2))].">
      <j1 rule="para" parents="8092 28883"/>
    </justification>
  </clause>

  <clause id="28885">
    <literal><![CDATA[
      x * (T(y,K(x,z)) \ (x \ y)) = T(x * (y \ (x \ y)),z)
    ]]></literal>
    <justification jstring="[para(17339(a,1),28884(a,1,2))].">
      <j1 rule="para" parents="17339 28884"/>
    </justification>
  </clause>

  <clause id="28886">
    <literal><![CDATA[
      T(x * (y \ (x \ y)),z * z) = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(17041(a,1),28885(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17041 28885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28887">
    <literal><![CDATA[
      T(x * (y \ (x \ y)),K(z,u)) = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(17163(a,1),28885(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17163 28885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28888">
    <literal><![CDATA[
      (1 / (x * (y \ (x \ y)))) * K(z,u) = K(z,u) / (x * (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(28887(a,1),25414(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28887 25414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28889">
    <literal><![CDATA[
      K((x * y) * (z / R(u,w,v5)),T(v6,z)) = K(z * ((R(u,w,v5) \ x) * y),T(v6,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,28298,a(flip),b,28273,a),flip(a)].">
      <j1 rule="hyper" parents="64 28298 28273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28890">
    <literal><![CDATA[
      K((x * (y / x)) * (z / R(x,u,w)),T(v5,z)) = K(z * (y / R(x,u,w)),T(v5,x))
    ]]></literal>
    <justification jstring="[para(25187(a,1),28273(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="25187 28273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28891">
    <literal><![CDATA[
      K(x,(y * (K(z,u) / w)) * v5) = K(x,(y * (w \ K(z,u))) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,25794,a(flip),b,28274,a),flip(a)].">
      <j1 rule="hyper" parents="64 25794 28274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28892">
    <literal><![CDATA[
      K(x,(y * (z \ K(u,z * y))) * w) = K(x,T(y * (1 / z),u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27850,a(flip),b,28891,a),flip(a)].">
      <j1 rule="hyper" parents="64 27850 28891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28893">
    <literal><![CDATA[
      x * (((y * a(z,u,w)) \ v5) * K(x * (y \ (a(z,u,w) \ v5)),v6)) = T(x * ((y * a(z,u,w)) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(28292(a,1),14495(a,1,2,2))].">
      <j1 rule="para" parents="28292 14495"/>
    </justification>
  </clause>

  <clause id="28894">
    <literal><![CDATA[
      T(L(x,y,z) \ 1,x * L(x,y,z)) = T(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,23153,a(flip),b,28376,a),flip(a)].">
      <j1 rule="hyper" parents="373 23153 28376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28896">
    <literal><![CDATA[
      x / T(L(x,y,z) \ 1,x) = (L(x,y,z) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,28894,a(flip),b,7229,a(flip))].">
      <j1 rule="hyper" parents="225 28894 7229"/>
    </justification>
  </clause>

  <clause id="28897">
    <literal><![CDATA[
      K(x,T(y,z \ u) * (z \ u)) = K(x,(L(z,w,v5) \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,28589,a(flip),b,28383,a)].">
      <j1 rule="hyper" parents="64 28589 28383"/>
    </justification>
  </clause>

  <clause id="28898">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ w) * v5) = K(x,(y \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(11231,a,28897,a),flip(a)].">
      <j1 rule="hyper" parents="11231 28897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28900">
    <literal><![CDATA[
      (1 / (R(x,y,z) / L(x,u,w))) * R(x,y,z) = R(x,y,z) * (1 / (R(x,y,z) / L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(25920(a,1),28391(a,1,1,1))].">
      <j1 rule="para" parents="25920 28391"/>
    </justification>
  </clause>

  <clause id="28901">
    <literal><![CDATA[
      T(x,x * (y \ (y \ x))) / T(y / (y \ x),x) = x / (y / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,28620,a,b,28511,a)].">
      <j1 rule="hyper" parents="64 28620 28511"/>
    </justification>
  </clause>

  <clause id="28902">
    <literal><![CDATA[
      (x / (y \ z)) / ((x / (y \ z)) / u) = u * K((u \ x) * (z \ y),u)
    ]]></literal>
    <justification jstring="[para(28198(a,1),28520(a,2,2))].">
      <j1 rule="para" parents="28198 28520"/>
    </justification>
  </clause>

  <clause id="28903">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ u) = (u / x) * (x * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,9368,a(flip),b,28555,a),flip(a)].">
      <j1 rule="hyper" parents="373 9368 28555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28904">
    <literal><![CDATA[
      K(x * (y \ (z * z)),T(u,x)) = K((z * z) * (y \ x),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,17065,a(flip),b,28573,a),flip(a)].">
      <j1 rule="hyper" parents="64 17065 28573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28905">
    <literal><![CDATA[
      K((x \ (y * y)) * z,u) = K((y * y) * (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(11195,a,28904,a)].">
      <j1 rule="hyper" parents="11195 28904"/>
    </justification>
  </clause>

  <clause id="28906">
    <literal><![CDATA[
      K((x \ (y * y)) * z,u) = K(y * (y * (x \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,28163,a(flip),b,28905,a),flip(a)].">
      <j1 rule="hyper" parents="373 28163 28905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28907">
    <literal><![CDATA[
      K((x \ y) * (y * z),u) = K(y * (y * (x \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28496,a(flip),b,28906,a)].">
      <j1 rule="hyper" parents="64 28496 28906"/>
    </justification>
  </clause>

  <clause id="28908">
    <literal><![CDATA[
      T(x * ((L(x,y,z) \ 1) * u),x \ 1) = x * (u * (L(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(145,a,28382,a(flip),b,28582,a),flip(a)].">
      <j1 rule="hyper" parents="145 28382 28582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28909">
    <literal><![CDATA[
      T(x \ ((y / z) / z),z * z) = ((((y / z) / z) / x) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,17280,a(flip),b,28604,a)].">
      <j1 rule="hyper" parents="64 17280 28604"/>
    </justification>
  </clause>

  <clause id="28910">
    <literal><![CDATA[
      L(x,y,z) \ L(R(x,x,x),u,w) = L(x,u,w) * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13717,a(flip),b,28605,a),flip(a)].">
      <j1 rule="hyper" parents="64 13717 28605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28912">
    <literal><![CDATA[
      T(x,y) \ (L(y,z,u) \ (x * y)) = x \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(25113(a,1),28606(a,1,2))].">
      <j1 rule="para" parents="25113 28606"/>
    </justification>
  </clause>

  <clause id="28913">
    <literal><![CDATA[
      K(x,y) * (x \ (y * (L(y,z,u) \ x))) = x \ (L(y,z,u) \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(145,a,28912,a(flip),b,6066,a)].">
      <j1 rule="hyper" parents="145 28912 6066"/>
    </justification>
  </clause>

  <clause id="28914">
    <literal><![CDATA[
      K(x,((y * z) \ y) * (u * (w * (z * v5)))) = K(x,T(u * w,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28348,a,b,28616,a)].">
      <j1 rule="hyper" parents="64 28348 28616"/>
    </justification>
  </clause>

  <clause id="28916">
    <literal><![CDATA[
      (x \ a(y,z,x)) * ((x \ 1) \ u) = (u / x) * (x * a(y,z,x))
    ]]></literal>
    <justification jstring="[para(23931(a,1),28806(a,1,1))].">
      <j1 rule="para" parents="23931 28806"/>
    </justification>
  </clause>

  <clause id="28917">
    <literal><![CDATA[
      a(x,y,z) \ (z * ((u / z) * (z * a(x,y,z)))) = L((z \ 1) \ u,z \ a(x,y,z),z)
    ]]></literal>
    <justification jstring="[para(28916(a,1),101(a,1,2,2))].">
      <j1 rule="para" parents="28916 101"/>
    </justification>
  </clause>

  <clause id="28918">
    <literal><![CDATA[
      L(K(x,y) * (x \ R(x,z,u)),w,v5) = R(x \ R(T(x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26085,a,b,28822,a)].">
      <j1 rule="hyper" parents="64 26085 28822"/>
    </justification>
  </clause>

  <clause id="28919">
    <literal><![CDATA[
      R(L(x,y,z) \ x,u,w) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(42,a,2870,a,b,28823,a)].">
      <j1 rule="hyper" parents="42 2870 28823"/>
    </justification>
  </clause>

  <clause id="28920">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * (u * w) = ((L(x,y,z) \ x) * u) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,28919,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 28919 20"/>
    </justification>
  </clause>

  <clause id="28921">
    <literal><![CDATA[
      L(x,y,R(z * L(z,u,w),v5,v6)) = L(x,y,L(L(z,u,w) \ z,v5,v6))
    ]]></literal>
    <justification jstring="[para(28919(a,1),9386(a,1,3)),flip(a)].">
      <j1 rule="para" parents="28919 9386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28922">
    <literal><![CDATA[
      R(T(L(x,y,z) \ x,u),w,v5) = L(L(x,y,z) \ x,w,v5)
    ]]></literal>
    <justification jstring="[para(23586(a,2),28919(a,1,1))].">
      <j1 rule="para" parents="23586 28919"/>
    </justification>
  </clause>

  <clause id="28923">
    <literal><![CDATA[
      x * L(L(y,z,u) \ y,w,w \ x) = ((L(y,z,u) \ y) * w) * (w \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,28922,a(flip),b,996,a)].">
      <j1 rule="hyper" parents="145 28922 996"/>
    </justification>
  </clause>

  <clause id="28924">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) * (u * w) = (u * (L(x,y,z) \ x)) * w
    ]]></literal>
    <justification jstring="[para(23581(a,1),28920(a,2,1))].">
      <j1 rule="para" parents="23581 28920"/>
    </justification>
  </clause>

  <clause id="28925">
    <literal><![CDATA[
      x * L(x \ a(y,z,u),x,a(y,z,u)) = (1 / ((a(y,z,u) \ 1) * x)) * x
    ]]></literal>
    <justification jstring="[para(13948(a,2),28824(a,2,2)),flip(a)].">
      <j1 rule="para" parents="13948 28824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28926">
    <literal><![CDATA[
      (x / (y * (a(z,u,w) \ 1))) * y = y * (((a(z,u,w) \ 1) * y) \ x)
    ]]></literal>
    <justification jstring="[para(23736(a,1),28824(a,1,1,2))].">
      <j1 rule="para" parents="23736 28824"/>
    </justification>
  </clause>

  <clause id="28927">
    <literal><![CDATA[
      ((x * ((((a(y,z,u) \ 1) * x) \ w) / x)) * x) * x = T(x * ((w / ((a(y,z,u) \ 1) * x)) * x),x)
    ]]></literal>
    <justification jstring="[para(28824(a,2),25257(a,2,1,2))].">
      <j1 rule="para" parents="28824 25257"/>
    </justification>
  </clause>

  <clause id="28928">
    <literal><![CDATA[
      K(x,y * T(z,(T(u,w) \ v5) * v6)) = K(x,y * T(z,v6 * (u \ v5)))
    ]]></literal>
    <justification jstring="[para(28859(a,1),18534(a,1,2,2))].">
      <j1 rule="para" parents="28859 18534"/>
    </justification>
  </clause>

  <clause id="28929">
    <literal><![CDATA[
      x * R(x \ K(y,y \ 1),z,u) = y * ((x \ R(x,z,u)) / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),28877(a,2,2))].">
      <j1 rule="para" parents="7 28877"/>
    </justification>
  </clause>

  <clause id="28930">
    <literal><![CDATA[
      (x \ 1) * (y * ((x \ R(x,z,u)) / y)) = R((x \ 1) * K(y,y \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(28929(a,1),2138(a,1,2))].">
      <j1 rule="para" parents="28929 2138"/>
    </justification>
  </clause>

  <clause id="28931">
    <literal><![CDATA[
      a(x,y,z * (u * (K(w,v5) * ((u * v6) \ u)))) = a(x,y,(v6 \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27663,a(flip),b,28880,a)].">
      <j1 rule="hyper" parents="64 27663 28880"/>
    </justification>
  </clause>

  <clause id="28932">
    <literal><![CDATA[
      K(x,T(1 / (y * (z \ 1)),u) * w) = K(x,z * ((y \ w) * K(y * z,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,16841,a,b,28881,a)].">
      <j1 rule="hyper" parents="373 16841 28881"/>
    </justification>
  </clause>

  <clause id="28933">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u) * w) = K(x,T(y * (z \ 1),u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27871,a(flip),b,28892,a),flip(a)].">
      <j1 rule="hyper" parents="64 27871 28892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28934">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u) * w) = K(x,T(y / z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,28130,a(flip),b,28933,a),flip(a)].">
      <j1 rule="hyper" parents="373 28130 28933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28935">
    <literal><![CDATA[
      (x / (y \ z)) / ((x / (y \ z)) / u) = u * K(x * (u \ (z \ y)),u)
    ]]></literal>
    <justification jstring="[para(15153(a,1),28902(a,2,2))].">
      <j1 rule="para" parents="15153 28902"/>
    </justification>
  </clause>

  <clause id="28936">
    <literal><![CDATA[
      ((x \ 1) \ ((L(x,y,z) \ 1) * u)) * (x \ 1) = u * (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1481,a,28908,a)].">
      <j1 rule="hyper" parents="1481 28908"/>
    </justification>
  </clause>

  <clause id="28937">
    <literal><![CDATA[
      K(x,((y * z) \ (y * u)) * (w * (z * v5))) = K(x,T(u * w,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28461,a,b,28914,a)].">
      <j1 rule="hyper" parents="64 28461 28914"/>
    </justification>
  </clause>

  <clause id="28938">
    <literal><![CDATA[
      R(x \ R(T(x,y),z,u),w,v5) = L(x \ R(T(x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(23663(a,1),28918(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23663 28918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28939">
    <literal><![CDATA[
      L(x \ R(T(x,y),z,u),x,y) = (R(x,z,u) * y) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25439,a(flip),b,28938,a),flip(a)].">
      <j1 rule="hyper" parents="64 25439 28938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28940">
    <literal><![CDATA[
      (R(x,y,z) * u) / (u * x) = (u * x) \ (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,797,a(flip),b,28939,a),flip(a)].">
      <j1 rule="hyper" parents="64 797 28939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28941">
    <literal><![CDATA[
      L(x,y,R(z \ L(z,u,w),v5,v6)) = L(x,y,L(L(z,u,w) \ z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,5622,a,b,28921,a)].">
      <j1 rule="hyper" parents="64 5622 28921"/>
    </justification>
  </clause>

  <clause id="28942">
    <literal><![CDATA[
      K(x,y * T(z,u * (w * T(v5,v6)))) = K(x,y * T(z,w * (v5 \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22398,a(flip),b,28928,a)].">
      <j1 rule="hyper" parents="64 22398 28928"/>
    </justification>
  </clause>

  <clause id="28943">
    <literal><![CDATA[
      a(x,y,z * (u * L(T(w \ 1,v5),w,u))) = a(x,y,(w \ u) * z)
    ]]></literal>
    <justification jstring="[para(7048(a,1),28931(a,1,3,2,2))].">
      <j1 rule="para" parents="7048 28931"/>
    </justification>
  </clause>

  <clause id="28944">
    <literal><![CDATA[
      a(x,y,z * (u * L(w \ 1,w,u))) = a(x,y,(w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27486,a(flip),b,28943,a)].">
      <j1 rule="hyper" parents="64 27486 28943"/>
    </justification>
  </clause>

  <clause id="28945">
    <literal><![CDATA[
      (x / (x \ y)) / ((x / (x \ y)) / y) = y * K(x * (y \ x),y)
    ]]></literal>
    <justification jstring="[para(27224(a,1),28935(a,2,2))].">
      <j1 rule="para" parents="27224 28935"/>
    </justification>
  </clause>

  <clause id="28946">
    <literal><![CDATA[
      (x / (x \ y)) / ((x / (x \ y)) / y) = T(y,y * (x \ (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,28618,a,b,28945,a),flip(a)].">
      <j1 rule="hyper" parents="373 28618 28945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28947">
    <literal><![CDATA[
      T(x,x * (y \ (y \ x))) / ((x \ (y / (y \ x))) * x) = x / (y / (y \ x))
    ]]></literal>
    <justification jstring="[para(28946(a,1),10251(a,1,1))].">
      <j1 rule="para" parents="28946 10251"/>
    </justification>
  </clause>

  <clause id="28948">
    <literal><![CDATA[
      K(x,(((y * z) \ (y * u)) \ w) * (u * v5)) = K(x,T(z * w,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,24675,a,b,28937,a)].">
      <j1 rule="hyper" parents="64 24675 28937"/>
    </justification>
  </clause>

  <clause id="28949">
    <literal><![CDATA[
      K(x,(((y * z) \ (y * u)) \ (w * u)) * v5) = K(x,T(z * w,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28461,a,b,28948,a)].">
      <j1 rule="hyper" parents="64 28461 28948"/>
    </justification>
  </clause>

  <clause id="28950">
    <literal><![CDATA[
      K(x,T(y * z,y * u) * w) = K(x,T(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(13526,a,28949,a)].">
      <j1 rule="hyper" parents="13526 28949"/>
    </justification>
  </clause>

  <clause id="28951">
    <literal><![CDATA[
      K(x,T(y * z,u * y) * w) = K(x,T(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,17970,a,b,28950,a)].">
      <j1 rule="hyper" parents="64 17970 28950"/>
    </justification>
  </clause>

  <clause id="28952">
    <literal><![CDATA[
      K(x,T(y * z,u * z) * w) = K(x,T(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,21579,a(flip),b,28950,a),flip(a)].">
      <j1 rule="hyper" parents="64 21579 28950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28953">
    <literal><![CDATA[
      K(x,T((K(y,y \ z) / u) * (y \ z),w) * v5) = K(x,T((z / y) * (1 / u),w * (y \ z)) * v5)
    ]]></literal>
    <justification jstring="[para(14390(a,1),28951(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14390 28951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28954">
    <literal><![CDATA[
      K(x,T(y * (z / y),u) * w) = K(x,T(z,u * y) * w)
    ]]></literal>
    <justification jstring="[para(12(a,1),28952(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="12 28952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28955">
    <literal><![CDATA[
      K(x,T(T(y,z),u) * w) = K(x,T(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15879,a(flip),b,28954,a)].">
      <j1 rule="hyper" parents="64 15879 28954"/>
    </justification>
  </clause>

  <clause id="28956">
    <literal><![CDATA[
      K(x,T(y,z * u) * (y \ w)) = K(x,K(y,z) * (w * K(u,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,25719,a(flip),b,28955,a),flip(a)].">
      <j1 rule="hyper" parents="64 25719 28955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28957">
    <literal><![CDATA[
      K(x,T(1 / y,z * u) * w) = K(x,T(T(y,z),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,21586,a(flip),b,28955,a),flip(a)].">
      <j1 rule="hyper" parents="64 21586 28955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28958">
    <literal><![CDATA[
      K(x,T(y \ z,u * y) * w) = K(x,T(z / y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15788,a(flip),b,28955,a),flip(a)].">
      <j1 rule="hyper" parents="64 15788 28955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28959">
    <literal><![CDATA[
      K(x,T(T(y,z),u) \ w) = K(x,T(y,z * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16841,a(flip),b,28957,a),flip(a)].">
      <j1 rule="hyper" parents="64 16841 28957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28960">
    <literal><![CDATA[
      K(x,T(y / (y / z),u) \ w) = K(x,T(z,y * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15918,a,b,28959,a)].">
      <j1 rule="hyper" parents="64 15918 28959"/>
    </justification>
  </clause>

  <clause id="28961">
    <literal><![CDATA[
      K(x,T(y \ z,u * y) \ w) = K(x,T(z / y,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,15794,a(flip),b,28959,a),flip(a)].">
      <j1 rule="hyper" parents="64 15794 28959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28962">
    <literal><![CDATA[
      K(x,T(y / (y / (z / u)),u * w) \ v5) = K(x,T(y / (y / (u \ z)),w) \ v5)
    ]]></literal>
    <justification jstring="[para(8415(a,1),28959(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="8415 28959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28963">
    <literal><![CDATA[
      K(x,T(y \ z,u * (w * y)) * v5) = K(x,T(z / y,u * w) * v5)
    ]]></literal>
    <justification jstring="[para(25009(a,1),28958(a,1,2,1))].">
      <j1 rule="para" parents="25009 28958"/>
    </justification>
  </clause>

  <clause id="28964">
    <literal><![CDATA[
      K(x,T(y \ z,u * (w * y)) \ v5) = K(x,T(z / y,u * w) \ v5)
    ]]></literal>
    <justification jstring="[para(25009(a,1),28961(a,1,2,1))].">
      <j1 rule="para" parents="25009 28961"/>
    </justification>
  </clause>

  <clause id="28965">
    <literal><![CDATA[
      K(x,K(y,z) * (u * K(w,y))) = K(x,K(y,z * w) * u)
    ]]></literal>
    <justification jstring="[para(5778(a,1),28956(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5778 28956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28966">
    <literal><![CDATA[
      K(x,T(y \ z,u * (w * z)) * v5) = K(x,T(y / z,u * w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28621,a(flip),b,28964,a)].">
      <j1 rule="hyper" parents="64 28621 28964"/>
    </justification>
  </clause>

  <clause id="28968">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = (w * y) \ (w * (y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,24420,a(flip),b,24339,a),flip(a)].">
      <j1 rule="hyper" parents="64 24420 24339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28970">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,18,a,b,28968,a),flip(a)].">
      <j1 rule="hyper" parents="373 18 28968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28971">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(28968(a,2),608(a,1))].">
      <j1 rule="para" parents="28968 608"/>
    </justification>
  </clause>

  <clause id="28973">
    <literal><![CDATA[
      L(x,y,z * K(u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(24201,a,28970,a)].">
      <j1 rule="hyper" parents="24201 28970"/>
    </justification>
  </clause>

  <clause id="28975">
    <literal><![CDATA[
      L(x,y,K(z,u) * (w / v5)) = L(x,y,v5 \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,23216,a(flip),b,28970,a),flip(a)].">
      <j1 rule="hyper" parents="373 23216 28970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28976">
    <literal><![CDATA[
      L(x,y,(K(z,u) / w) * v5) = L(x,y,w * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,25512,a,b,28970,a)].">
      <j1 rule="hyper" parents="64 25512 28970"/>
    </justification>
  </clause>

  <clause id="28978">
    <literal><![CDATA[
      L(x,y,T(z,u) * w) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(5755(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="5755 28970"/>
    </justification>
  </clause>

  <clause id="28979">
    <literal><![CDATA[
      L(x,y,T(z,u) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(6075(a,1),28970(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6075 28970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28980">
    <literal><![CDATA[
      L(x,y,(z / u) * w) = L(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[para(5982(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="5982 28970"/>
    </justification>
  </clause>

  <clause id="28981">
    <literal><![CDATA[
      L(x,y,((z \ u) \ u) * w) = L(x,y,z * w)
    ]]></literal>
    <justification jstring="[para(6025(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="6025 28970"/>
    </justification>
  </clause>

  <clause id="28982">
    <literal><![CDATA[
      L(x,y,(z / u) \ w) = L(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),28970(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6270 28970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28983">
    <literal><![CDATA[
      L(x,y,z * T(u,w)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(6367(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="6367 28970"/>
    </justification>
  </clause>

  <clause id="28984">
    <literal><![CDATA[
      L(x,y,z \ T(u,w)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(6417(a,1),28970(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6417 28970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28986">
    <literal><![CDATA[
      L(x,y,(K(z,u) * w) * v5) = L(x,y,w * v5)
    ]]></literal>
    <justification jstring="[para(7760(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="7760 28970"/>
    </justification>
  </clause>

  <clause id="28987">
    <literal><![CDATA[
      L(x,y,z * (K(u,w) * v5)) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(10720(a,1),28970(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10720 28970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28988">
    <literal><![CDATA[
      L(x,y,(z * u) \ w) = L(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[para(10833(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="10833 28970"/>
    </justification>
  </clause>

  <clause id="28989">
    <literal><![CDATA[
      L(x,y,(z * u) * w) = L(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[para(10834(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="10834 28970"/>
    </justification>
  </clause>

  <clause id="28990">
    <literal><![CDATA[
      L(x,y,((z \ u) * z) \ w) = L(x,y,u \ w)
    ]]></literal>
    <justification jstring="[para(10843(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="10843 28970"/>
    </justification>
  </clause>

  <clause id="28992">
    <literal><![CDATA[
      L(x,y,(T(z,u) * w) * v5) = L(x,y,(z * w) * v5)
    ]]></literal>
    <justification jstring="[para(15613(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="15613 28970"/>
    </justification>
  </clause>

  <clause id="28993">
    <literal><![CDATA[
      L(x,y,z \ (K(u,w) * v5)) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(22758(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="22758 28970"/>
    </justification>
  </clause>

  <clause id="28994">
    <literal><![CDATA[
      L(x,y,(z * (u / z)) * w) = L(x,y,u * w)
    ]]></literal>
    <justification jstring="[para(24346(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="24346 28970"/>
    </justification>
  </clause>

  <clause id="28995">
    <literal><![CDATA[
      L(x,y,(T(z,u) \ w) * v5) = L(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[para(24347(a,1),28970(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24347 28970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28996">
    <literal><![CDATA[
      L(x,y,(z * T(u,w)) \ v5) = L(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(24506(a,1),28970(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24506 28970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="28998">
    <literal><![CDATA[
      L(x,y,(z * T(u,w)) * v5) = L(x,y,(z * u) * v5)
    ]]></literal>
    <justification jstring="[para(24355(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="24355 28970"/>
    </justification>
  </clause>

  <clause id="28999">
    <literal><![CDATA[
      L(x,y,L(T(z,u),w,v5) * v6) = L(x,y,L(z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(24680(a,1),28970(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24680 28970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29000">
    <literal><![CDATA[
      L(x,y,(T(z,u) \ w) \ v5) = L(x,y,(z \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(25410(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="25410 28970"/>
    </justification>
  </clause>

  <clause id="29001">
    <literal><![CDATA[
      L(x,y,((z / u) * w) * v5) = L(x,y,((u \ z) * w) * v5)
    ]]></literal>
    <justification jstring="[para(24351(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="24351 28970"/>
    </justification>
  </clause>

  <clause id="29002">
    <literal><![CDATA[
      L(x,y,(z * (K(u,w) * v5)) * v6) = L(x,y,(z * v5) * v6)
    ]]></literal>
    <justification jstring="[para(24368(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="24368 28970"/>
    </justification>
  </clause>

  <clause id="29003">
    <literal><![CDATA[
      L(x,y,(z * (u / w)) \ v5) = L(x,y,(z * (w \ u)) \ v5)
    ]]></literal>
    <justification jstring="[para(24507(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="24507 28970"/>
    </justification>
  </clause>

  <clause id="29004">
    <literal><![CDATA[
      L(x,y,(z \ ((u \ w) * u)) \ v5) = L(x,y,(z \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(24523(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="24523 28970"/>
    </justification>
  </clause>

  <clause id="29005">
    <literal><![CDATA[
      L(x,y,L(K(z,u) * w,v5,v6)) = L(x,y,L(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(26085(a,2),28970(a,1,3))].">
      <j1 rule="para" parents="26085 28970"/>
    </justification>
  </clause>

  <clause id="29006">
    <literal><![CDATA[
      L(x,y,L(T(z,u) \ w,v5,v6)) = L(x,y,L(z \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(26100(a,1),28970(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26100 28970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29007">
    <literal><![CDATA[
      L(x,y,L(z / u,w,v5) * v6) = L(x,y,L(u \ z,w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(25447(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="25447 28970"/>
    </justification>
  </clause>

  <clause id="29008">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((u * w) * z)) = L(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(27292(a,2),28970(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27292 28970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29009">
    <literal><![CDATA[
      L(x,y,(z * (u \ (w / v5))) \ v6) = L(x,y,(z * (u \ (v5 \ w))) \ v6)
    ]]></literal>
    <justification jstring="[para(25421(a,1),28970(a,1,3))].">
      <j1 rule="para" parents="25421 28970"/>
    </justification>
  </clause>

  <clause id="29018">
    <literal><![CDATA[
      L(x,y,z * (u / w)) = L(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[para(6471(a,1),28973(a,1,3))].">
      <j1 rule="para" parents="6471 28973"/>
    </justification>
  </clause>

  <clause id="29019">
    <literal><![CDATA[
      L(x,y,z * (u * T(w,v5))) = L(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[para(7368(a,1),28973(a,1,3))].">
      <j1 rule="para" parents="7368 28973"/>
    </justification>
  </clause>

  <clause id="29020">
    <literal><![CDATA[
      L(x,y,z * (u * w)) = L(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[para(7591(a,1),28973(a,1,3))].">
      <j1 rule="para" parents="7591 28973"/>
    </justification>
  </clause>

  <clause id="29022">
    <literal><![CDATA[
      L(x,y,z * (u * K(w,v5))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(12078(a,1),28973(a,1,3))].">
      <j1 rule="para" parents="12078 28973"/>
    </justification>
  </clause>

  <clause id="29023">
    <literal><![CDATA[
      L(x,y,z \ (u / w)) = L(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[para(15028(a,1),28973(a,1,3))].">
      <j1 rule="para" parents="15028 28973"/>
    </justification>
  </clause>

  <clause id="29024">
    <literal><![CDATA[
      L(x,y,z \ L(T(u,w),v5,v6)) = L(x,y,z \ L(u,v5,v6))
    ]]></literal>
    <justification jstring="[para(15043(a,1),28973(a,1,3))].">
      <j1 rule="para" parents="15043 28973"/>
    </justification>
  </clause>

  <clause id="29025">
    <literal><![CDATA[
      L(x,y,z \ (u * w)) = L(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[para(14934(a,1),28973(a,1,3))].">
      <j1 rule="para" parents="14934 28973"/>
    </justification>
  </clause>

  <clause id="29026">
    <literal><![CDATA[
      L(x,y,z \ ((u \ w) * u)) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(15230(a,1),28973(a,1,3))].">
      <j1 rule="para" parents="15230 28973"/>
    </justification>
  </clause>

  <clause id="29027">
    <literal><![CDATA[
      L(x,y,z \ (u * K(w,v5))) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(16164(a,1),28973(a,1,3))].">
      <j1 rule="para" parents="16164 28973"/>
    </justification>
  </clause>

  <clause id="29029">
    <literal><![CDATA[
      L(x,y,z \ (u \ (w / v5))) = L(x,y,z \ (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(24307(a,1),28973(a,1,3))].">
      <j1 rule="para" parents="24307 28973"/>
    </justification>
  </clause>

  <clause id="29030">
    <literal><![CDATA[
      L(x,y,z \ (u / (w / v5))) = L(x,y,z \ (u / (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(24313(a,1),28973(a,1,3))].">
      <j1 rule="para" parents="24313 28973"/>
    </justification>
  </clause>

  <clause id="29031">
    <literal><![CDATA[
      L(x,y,z * L(T(u,w),v5,v6)) = L(x,y,z * L(u,v5,v6))
    ]]></literal>
    <justification jstring="[para(25231(a,1),28973(a,1,3))].">
      <j1 rule="para" parents="25231 28973"/>
    </justification>
  </clause>

  <clause id="29032">
    <literal><![CDATA[
      L(x,y,R(z * K(u,w),v5,v6)) = L(x,y,R(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(25973(a,2),28973(a,1,3))].">
      <j1 rule="para" parents="25973 28973"/>
    </justification>
  </clause>

  <clause id="29033">
    <literal><![CDATA[
      L(x,y,z \ R(u * K(w,v5),v6,v7)) = L(x,y,z \ R(u,v6,v7))
    ]]></literal>
    <justification jstring="[para(25984(a,2),28973(a,1,3))].">
      <j1 rule="para" parents="25984 28973"/>
    </justification>
  </clause>

  <clause id="29034">
    <literal><![CDATA[
      L(x,y,L(z * K(u,w),v5,v6)) = L(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(26070(a,2),28973(a,1,3))].">
      <j1 rule="para" parents="26070 28973"/>
    </justification>
  </clause>

  <clause id="29035">
    <literal><![CDATA[
      L(x,y,L(z * T(u,w),v5,v6)) = L(x,y,L(z * u,v5,v6))
    ]]></literal>
    <justification jstring="[para(26078(a,1),28973(a,1,3))].">
      <j1 rule="para" parents="26078 28973"/>
    </justification>
  </clause>

  <clause id="29036">
    <literal><![CDATA[
      L(x,y,L(z \ K(u,w),v5,v6)) = L(x,y,L(z \ 1,v5,v6))
    ]]></literal>
    <justification jstring="[para(26080(a,1),28973(a,1,3))].">
      <j1 rule="para" parents="26080 28973"/>
    </justification>
  </clause>

  <clause id="29037">
    <literal><![CDATA[
      L(x,y,z * T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(622,a,28978,a),flip(a)].">
      <j1 rule="hyper" parents="622 28978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29039">
    <literal><![CDATA[
      L(x,y,T(z,u) * w) = L(x,y,w * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,28978,a),flip(a)].">
      <j1 rule="hyper" parents="373 23253 28978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29040">
    <literal><![CDATA[
      L(x,y,z * (1 / T(u,w))) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23999,a,b,28978,a)].">
      <j1 rule="hyper" parents="64 23999 28978"/>
    </justification>
  </clause>

  <clause id="29041">
    <literal><![CDATA[
      L(x,y,(z \ (u * (z * z))) * w) = L(x,y,(u * L(z,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(2848(a,1),28978(a,1,3,1))].">
      <j1 rule="para" parents="2848 28978"/>
    </justification>
  </clause>

  <clause id="29042">
    <literal><![CDATA[
      L(x,y,(z / u) \ u) = L(x,y,(u / z) * u)
    ]]></literal>
    <justification jstring="[para(3818(a,1),28978(a,1,3))].">
      <j1 rule="para" parents="3818 28978"/>
    </justification>
  </clause>

  <clause id="29043">
    <literal><![CDATA[
      R(x,T(y,z),L(T(u,w),T(u,w),u * v5)) = R(x,y,L(u,u,v5))
    ]]></literal>
    <justification jstring="[para(28978(a,1),28050(a,1,3))].">
      <j1 rule="para" parents="28978 28050"/>
    </justification>
  </clause>

  <clause id="29044">
    <literal><![CDATA[
      ((x * T(x,y)) * z) * u = (x * T(x,y)) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(1960,a,29037,a),flip(a)].">
      <j1 rule="hyper" parents="1960 29037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29045">
    <literal><![CDATA[
      ((x * T(x,y)) \ z) \ u = z \ ((x * T(x,y)) * u)
    ]]></literal>
    <justification jstring="[hyper(743,a,29037,a),flip(a)].">
      <j1 rule="hyper" parents="743 29037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29046">
    <literal><![CDATA[
      ((x * T(x,y)) * z) \ u = z \ ((x * T(x,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(710,a,29037,a),flip(a)].">
      <j1 rule="hyper" parents="710 29037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29047">
    <literal><![CDATA[
      L(x,y,z * T(T(z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,28978,a(flip),b,29037,a)].">
      <j1 rule="hyper" parents="64 28978 29037"/>
    </justification>
  </clause>

  <clause id="29048">
    <literal><![CDATA[
      ((x * T(x,y)) * z) / u = (x * T(x,y)) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(225,a,29037,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 29037 10262"/>
    </justification>
  </clause>

  <clause id="29049">
    <literal><![CDATA[
      (x * T(x,y)) * (((x * T(x,y)) \ z) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(145,a,29037,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 29037 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29050">
    <literal><![CDATA[
      x / T(y * T(y,z),x) = (y * T(y,z)) \ x
    ]]></literal>
    <justification jstring="[para(29037(a,1),4885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29037 4885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29051">
    <literal><![CDATA[
      ((x * T(T(x,y),z)) \ u) \ w = u \ ((x * T(T(x,y),z)) * w)
    ]]></literal>
    <justification jstring="[hyper(743,a,29047,a),flip(a)].">
      <j1 rule="hyper" parents="743 29047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29052">
    <literal><![CDATA[
      L(x,y,T(z * u,w) \ u) = L(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,13011,a(flip),b,28979,a),flip(a)].">
      <j1 rule="hyper" parents="373 13011 28979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29054">
    <literal><![CDATA[
      L(x,y,((z * u) * (z \ 1)) \ w) = L(x,y,R(u,z,z \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(1042(a,1),28979(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1042 28979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29059">
    <literal><![CDATA[
      L(x,y,((z * u) * u) * z) = L(x,y,a(z * u,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,25787,a(flip),b,28983,a),flip(a)].">
      <j1 rule="hyper" parents="64 25787 28983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29060">
    <literal><![CDATA[
      L(x,y,z * (u \ ((w * w) * v5))) = L(x,y,z * ((w * w) * (v5 / u)))
    ]]></literal>
    <justification jstring="[para(946(a,1),28983(a,1,3,2))].">
      <j1 rule="para" parents="946 28983"/>
    </justification>
  </clause>

  <clause id="29062">
    <literal><![CDATA[
      L(x,x \ T(y,z),x \ y) = (1 / (T(y,z) / x)) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10627,a(flip),b,28984,a),flip(a)].">
      <j1 rule="hyper" parents="64 10627 28984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29064">
    <literal><![CDATA[
      L(x,y,z \ (((1 / u) * w) * u)) = L(x,y,z \ R(w,u,u))
    ]]></literal>
    <justification jstring="[para(3883(a,1),28984(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="3883 28984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29065">
    <literal><![CDATA[
      L(x,y,T(z,u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ w) = v5
    ]]></literal>
    <justification jstring="[para(6157(a,1),28971(a,1,3))].">
      <j1 rule="para" parents="6157 28971"/>
    </justification>
  </clause>

  <clause id="29066">
    <literal><![CDATA[
      L(x,y,(z / u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u \ z) * w) = v5
    ]]></literal>
    <justification jstring="[para(5982(a,1),28971(a,1,3))].">
      <j1 rule="para" parents="5982 28971"/>
    </justification>
  </clause>

  <clause id="29067">
    <literal><![CDATA[
      L(x,y,z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(6823(a,1),28971(a,1,3))].">
      <j1 rule="para" parents="6823 28971"/>
    </justification>
  </clause>

  <clause id="29068">
    <literal><![CDATA[
      L(x,y,z \ T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ u) = v5
    ]]></literal>
    <justification jstring="[para(6578(a,1),28971(a,1,3))].">
      <j1 rule="para" parents="6578 28971"/>
    </justification>
  </clause>

  <clause id="29069">
    <literal><![CDATA[
      L(x,y,((z / u) \ w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,((u \ z) \ w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(24352(a,1),28971(a,1,3))].">
      <j1 rule="para" parents="24352 28971"/>
    </justification>
  </clause>

  <clause id="29071">
    <literal><![CDATA[
      L(x,y,z * (u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * (w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(6471(a,1),29067(a,1,3))].">
      <j1 rule="para" parents="6471 29067"/>
    </justification>
  </clause>

  <clause id="29073">
    <literal><![CDATA[
      L(x,y,(z * u) / w) = L(x,y,w \ (u * z))
    ]]></literal>
    <justification jstring="[para(14887(a,1),28975(a,1,3))].">
      <j1 rule="para" parents="14887 28975"/>
    </justification>
  </clause>

  <clause id="29075">
    <literal><![CDATA[
      L(x,y,(z \ K(u,w)) * v5) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),28976(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="79 28976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29076">
    <literal><![CDATA[
      L(x,y,(z / u) * w) = L(x,y,w * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,28980,a),flip(a)].">
      <j1 rule="hyper" parents="373 23253 28980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29077">
    <literal><![CDATA[
      L(x,y,(z \ (u * u)) * w) = L(x,y,w * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23989,a(flip),b,28980,a),flip(a)].">
      <j1 rule="hyper" parents="64 23989 28980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29078">
    <literal><![CDATA[
      L(x,y,L(R(z,u,z) \ 1,z,u) * w) = L(x,y,(u / T(z * u,z)) * w)
    ]]></literal>
    <justification jstring="[para(14173(a,2),28980(a,2,3,1)),flip(a)].">
      <j1 rule="para" parents="14173 28980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29079">
    <literal><![CDATA[
      L(x,x,((x \ y) \ y) * z) = x * (L(x \ 1,x,z) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,26664,a,b,28981,a),flip(a)].">
      <j1 rule="hyper" parents="373 26664 28981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29081">
    <literal><![CDATA[
      L(x,y,((1 / z) \ u) \ w) = L(x,y,(u / z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2192,a(flip),b,28982,a),flip(a)].">
      <j1 rule="hyper" parents="64 2192 28982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29083">
    <literal><![CDATA[
      x / L(y,y \ (z / u),(u \ z) \ x) = ((z / u) \ x) * ((((z / u) \ x) \ x) / y)
    ]]></literal>
    <justification jstring="[para(28982(a,1),15126(a,1,2))].">
      <j1 rule="para" parents="28982 15126"/>
    </justification>
  </clause>

  <clause id="29084">
    <literal><![CDATA[
      L(x,y,z * (K(u,w) * v5)) = L(x,y,v5 * z)
    ]]></literal>
    <justification jstring="[hyper(24201,a,28986,a)].">
      <j1 rule="hyper" parents="24201 28986"/>
    </justification>
  </clause>

  <clause id="29085">
    <literal><![CDATA[
      L(x,y,(z \ T(u,w)) * v5) = L(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[para(6417(a,1),28986(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="6417 28986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29086">
    <literal><![CDATA[
      L(x,y,(z \ (K(u,w) * v5)) * v6) = L(x,y,(z \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(22758(a,1),28986(a,1,3,1))].">
      <j1 rule="para" parents="22758 28986"/>
    </justification>
  </clause>

  <clause id="29087">
    <literal><![CDATA[
      L(x,y,(L(T(z,u),w,v5) * v6) * v7) = L(x,y,(L(z,w,v5) * v6) * v7)
    ]]></literal>
    <justification jstring="[para(24680(a,1),28986(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="24680 28986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29088">
    <literal><![CDATA[
      L(x,y,z * (T(u,w) * v5)) = L(x,y,z * (u * v5))
    ]]></literal>
    <justification jstring="[para(5755(a,1),28987(a,1,3,2))].">
      <j1 rule="para" parents="5755 28987"/>
    </justification>
  </clause>

  <clause id="29089">
    <literal><![CDATA[
      L(x,y,z * ((u / w) * v5)) = L(x,y,z * ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(5982(a,1),28987(a,1,3,2))].">
      <j1 rule="para" parents="5982 28987"/>
    </justification>
  </clause>

  <clause id="29090">
    <literal><![CDATA[
      L(x,y,z * ((u / w) \ v5)) = L(x,y,z * ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(6270(a,1),28987(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6270 28987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29091">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ v5)) = L(x,y,z * ((w * u) \ v5))
    ]]></literal>
    <justification jstring="[para(10833(a,1),28987(a,1,3,2))].">
      <j1 rule="para" parents="10833 28987"/>
    </justification>
  </clause>

  <clause id="29092">
    <literal><![CDATA[
      L(x,y,z * ((u * w) * v5)) = L(x,y,z * ((w * u) * v5))
    ]]></literal>
    <justification jstring="[para(10834(a,1),28987(a,1,3,2))].">
      <j1 rule="para" parents="10834 28987"/>
    </justification>
  </clause>

  <clause id="29093">
    <literal><![CDATA[
      L(x,y,z * (u \ (K(w,v5) * v6))) = L(x,y,z * (u \ v6))
    ]]></literal>
    <justification jstring="[para(22758(a,1),28987(a,1,3,2))].">
      <j1 rule="para" parents="22758 28987"/>
    </justification>
  </clause>

  <clause id="29094">
    <literal><![CDATA[
      L(x,y,z * ((u * T(w,v5)) * v6)) = L(x,y,z * ((u * w) * v6))
    ]]></literal>
    <justification jstring="[para(24355(a,1),28987(a,1,3,2))].">
      <j1 rule="para" parents="24355 28987"/>
    </justification>
  </clause>

  <clause id="29095">
    <literal><![CDATA[
      L(x,y,(z \ (u / w)) * v5) = L(x,y,(z \ (w \ u)) * v5)
    ]]></literal>
    <justification jstring="[para(24475(a,1),28987(a,1,3))].">
      <j1 rule="para" parents="24475 28987"/>
    </justification>
  </clause>

  <clause id="29096">
    <literal><![CDATA[
      L(x,y,(z * (u * T(w,v5))) * v6) = L(x,y,(z * (u * w)) * v6)
    ]]></literal>
    <justification jstring="[para(24746(a,1),28987(a,1,3))].">
      <j1 rule="para" parents="24746 28987"/>
    </justification>
  </clause>

  <clause id="29097">
    <literal><![CDATA[
      L(x,y,(z \ (u * T(w,v5))) * v6) = L(x,y,(z \ (u * w)) * v6)
    ]]></literal>
    <justification jstring="[para(24892(a,1),28987(a,1,3))].">
      <j1 rule="para" parents="24892 28987"/>
    </justification>
  </clause>

  <clause id="29100">
    <literal><![CDATA[
      L(x,y,(z * (u \ 1)) \ w) = L(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,25699,a(flip),b,28988,a),flip(a)].">
      <j1 rule="hyper" parents="373 25699 28988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29101">
    <literal><![CDATA[
      L(x,y,(z * u) \ z) = L(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,13011,a(flip),b,28988,a),flip(a)].">
      <j1 rule="hyper" parents="373 13011 28988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29102">
    <literal><![CDATA[
      L(x,y,((z * u) * R(w,z,u)) \ v5) = L(x,y,((w * z) * u) \ v5)
    ]]></literal>
    <justification jstring="[para(111(a,1),28988(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="111 28988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29103">
    <literal><![CDATA[
      L(x,y,((z * u) * w) \ (u * (w * z))) = L(x,y,a(w,z,u) * K(u,w * z))
    ]]></literal>
    <justification jstring="[para(15232(a,1),28988(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15232 28988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29104">
    <literal><![CDATA[
      x / L(1 / y,z,(z * y) \ x) = (x / (z * (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(28988(a,1),25701(a,1,2))].">
      <j1 rule="para" parents="28988 25701"/>
    </justification>
  </clause>

  <clause id="29105">
    <literal><![CDATA[
      L(x,y,(z * u) * w) = L(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(24201,a,28989,a),flip(a)].">
      <j1 rule="hyper" parents="24201 28989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29106">
    <literal><![CDATA[
      L(x,y,z \ ((z \ u) \ z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13011,a(flip),b,28990,a)].">
      <j1 rule="hyper" parents="64 13011 28990"/>
    </justification>
  </clause>

  <clause id="29107">
    <literal><![CDATA[
      L(x,y,(z * u) \ (K(w,v5) * v6)) = L(x,y,(u * z) \ v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,28988,a,b,28993,a),flip(a)].">
      <j1 rule="hyper" parents="373 28988 28993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29108">
    <literal><![CDATA[
      L(x,y,z \ K(u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2183,a(flip),b,28993,a),flip(a)].">
      <j1 rule="hyper" parents="64 2183 28993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29109">
    <literal><![CDATA[
      L(x,y,z \ (T(u,w) \ v5)) = L(x,y,z \ (u \ v5))
    ]]></literal>
    <justification jstring="[para(6075(a,1),28993(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6075 28993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29110">
    <literal><![CDATA[
      L(x,y,z \ ((u / w) \ v5)) = L(x,y,z \ ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(6270(a,1),28993(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6270 28993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29111">
    <literal><![CDATA[
      L(x,y,((z / u) \ w) \ v5) = L(x,y,((u \ z) \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(24402(a,1),28993(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24402 28993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29114">
    <literal><![CDATA[
      T(x \ K(y,z),u * (x \ K(y,z))) = L(T(x \ K(y,z),u),u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,4690,a(flip),b,29108,a)].">
      <j1 rule="hyper" parents="64 4690 29108"/>
    </justification>
  </clause>

  <clause id="29115">
    <literal><![CDATA[
      L(x,y,z * (u * (w / u))) = L(x,y,w * z)
    ]]></literal>
    <justification jstring="[hyper(24201,a,28994,a)].">
      <j1 rule="hyper" parents="24201 28994"/>
    </justification>
  </clause>

  <clause id="29116">
    <literal><![CDATA[
      L(x,y,z * T(u / w,v5)) = L(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,28983,a,b,29018,a)].">
      <j1 rule="hyper" parents="64 28983 29018"/>
    </justification>
  </clause>

  <clause id="29117">
    <literal><![CDATA[
      L(x \ y,x \ y,(y / x) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,25573,a(flip),b,29018,a),flip(a)].">
      <j1 rule="hyper" parents="64 25573 29018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29118">
    <literal><![CDATA[
      L(x,x,x * (y \ (x \ y))) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,25568,a(flip),b,29018,a),flip(a)].">
      <j1 rule="hyper" parents="64 25568 29018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29119">
    <literal><![CDATA[
      (x / y) / L(z,z,z * (y \ x)) = R((x / y) / z,z,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,29018,a(flip),b,25873,a)].">
      <j1 rule="hyper" parents="225 29018 25873"/>
    </justification>
  </clause>

  <clause id="29120">
    <literal><![CDATA[
      L(x,y,z * (u * (w \ 1))) = L(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,25369,a(flip),b,29020,a),flip(a)].">
      <j1 rule="hyper" parents="373 25369 29020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29121">
    <literal><![CDATA[
      L(x,y,z * (u * (1 / w))) = L(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,25131,a(flip),b,29020,a),flip(a)].">
      <j1 rule="hyper" parents="373 25131 29020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29122">
    <literal><![CDATA[
      L(x,y,z * (u * (w / v5))) = L(x,y,z * (u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(6471(a,1),29022(a,1,3,2))].">
      <j1 rule="para" parents="6471 29022"/>
    </justification>
  </clause>

  <clause id="29123">
    <literal><![CDATA[
      L(x,y,z * (u \ (w / v5))) = L(x,y,z * (u \ (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(15028(a,1),29022(a,1,3,2))].">
      <j1 rule="para" parents="15028 29022"/>
    </justification>
  </clause>

  <clause id="29125">
    <literal><![CDATA[
      L(x,y,z \ ((u / (w * u)) \ 1)) = L(x,y,z \ (u \ (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,25697,a,b,29023,a)].">
      <j1 rule="hyper" parents="64 25697 29023"/>
    </justification>
  </clause>

  <clause id="29126">
    <literal><![CDATA[
      x \ ((((x / y) / z) * (z * y)) * y) = L(y,z,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,11078,a,b,29023,a)].">
      <j1 rule="hyper" parents="64 11078 29023"/>
    </justification>
  </clause>

  <clause id="29127">
    <literal><![CDATA[
      L((x \ (x / y)) \ z,x \ (x / y),x \ (y \ x)) = (1 / (T(1,y \ 1) / (T(x \ (x / y),1) \ 1))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,12540,a(flip),b,29023,a),flip(a)].">
      <j1 rule="hyper" parents="64 12540 29023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29128">
    <literal><![CDATA[
      (x / y) * L(z,u,u \ (y \ x)) = ((x / y) / u) * (u * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,29023,a(flip),b,11067,a)].">
      <j1 rule="hyper" parents="145 29023 11067"/>
    </justification>
  </clause>

  <clause id="29129">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) = L(x,y,z \ R(v5 * K(w,u),w,u))
    ]]></literal>
    <justification jstring="[para(10304(a,1),29023(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10304 29023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29130">
    <literal><![CDATA[
      L(x,y,z \ (u * ((w * w) / v5))) = L(x,y,z \ (v5 * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27008,a(flip),b,29025,a),flip(a)].">
      <j1 rule="hyper" parents="373 27008 29025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29131">
    <literal><![CDATA[
      L(x,y,z \ (u * (w \ 1))) = L(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,25698,a(flip),b,29025,a),flip(a)].">
      <j1 rule="hyper" parents="373 25698 29025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29132">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) * u)) = L(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,25688,a(flip),b,29025,a),flip(a)].">
      <j1 rule="hyper" parents="373 25688 29025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29133">
    <literal><![CDATA[
      L(x,y,z \ (u * (1 / w))) = L(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,25687,a(flip),b,29025,a),flip(a)].">
      <j1 rule="hyper" parents="373 25687 29025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29134">
    <literal><![CDATA[
      L(x,y,z \ (u * (w * w))) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,25683,a(flip),b,29025,a),flip(a)].">
      <j1 rule="hyper" parents="373 25683 29025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29135">
    <literal><![CDATA[
      L(x,y,z \ (u \ (w * v5))) = L(x,y,z \ (u \ (v5 * w)))
    ]]></literal>
    <justification jstring="[para(14934(a,1),29027(a,1,3,2))].">
      <j1 rule="para" parents="14934 29027"/>
    </justification>
  </clause>

  <clause id="29136">
    <literal><![CDATA[
      L(x,y,L(z,z,u) \ u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(14982(a,1),29040(a,1,3))].">
      <j1 rule="para" parents="14982 29040"/>
    </justification>
  </clause>

  <clause id="29137">
    <literal><![CDATA[
      L(x,y,(z \ u) \ z) = L(x,y,(z / u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,28982,a(flip),b,29042,a)].">
      <j1 rule="hyper" parents="64 28982 29042"/>
    </justification>
  </clause>

  <clause id="29138">
    <literal><![CDATA[
      L(x,y,(z / (u * z)) * z) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(11(a,1),29042(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="11 29042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29139">
    <literal><![CDATA[
      x * (y / T(z * T(z,u),y)) = (x / (z * T(z,u))) * y
    ]]></literal>
    <justification jstring="[para(29050(a,2),26519(a,2,2)),flip(a)].">
      <j1 rule="para" parents="29050 26519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29140">
    <literal><![CDATA[
      L(x,y,(z * u) \ (u * (w * z))) = L(x,y,R(w,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),29073(a,1,3)),flip(a)].">
      <j1 rule="para" parents="20 29073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29141">
    <literal><![CDATA[
      L((x / y) * z,a(u,w,v5),z * (y \ x)) = (x / y) * z
    ]]></literal>
    <justification jstring="[hyper(13955,a,29076,a)].">
      <j1 rule="hyper" parents="13955 29076"/>
    </justification>
  </clause>

  <clause id="29142">
    <literal><![CDATA[
      L(x,y,z * (u * (L(u,w,v5) \ u))) = L(x,y,L(u,w,v5) * z)
    ]]></literal>
    <justification jstring="[para(24847(a,1),29077(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="24847 29077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29143">
    <literal><![CDATA[
      L(x,y,z * ((u \ w) * u)) = L(x,y,w * z)
    ]]></literal>
    <justification jstring="[para(5919(a,1),29084(a,1,3,2))].">
      <j1 rule="para" parents="5919 29084"/>
    </justification>
  </clause>

  <clause id="29144">
    <literal><![CDATA[
      L(x,y,z * (((u \ w) \ w) * v5)) = L(x,y,(u * v5) * z)
    ]]></literal>
    <justification jstring="[para(6025(a,1),29084(a,1,3,2))].">
      <j1 rule="para" parents="6025 29084"/>
    </justification>
  </clause>

  <clause id="29145">
    <literal><![CDATA[
      L(x,y,(z \ T(u,w)) * v5) = L(x,y,v5 * (z \ u))
    ]]></literal>
    <justification jstring="[para(6417(a,1),29084(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="6417 29084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29146">
    <literal><![CDATA[
      L(x,y,z * (u \ T(w,v5))) = L(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[para(6578(a,1),29084(a,1,3,2))].">
      <j1 rule="para" parents="6578 29084"/>
    </justification>
  </clause>

  <clause id="29147">
    <literal><![CDATA[
      L(x,y,((z * u) * w) * v5) = L(x,y,v5 * ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(10834(a,1),29084(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10834 29084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29148">
    <literal><![CDATA[
      L(x,y,(z * T(u,w)) * v5) = L(x,y,v5 * (z * u))
    ]]></literal>
    <justification jstring="[para(24468(a,1),29084(a,1,3))].">
      <j1 rule="para" parents="24468 29084"/>
    </justification>
  </clause>

  <clause id="29149">
    <literal><![CDATA[
      L(x,y,(L(z * u,w,v5) \ v6) * v7) = L(x,y,v7 * (L(u * z,w,v5) \ v6))
    ]]></literal>
    <justification jstring="[para(26137(a,1),29084(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="26137 29084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29150">
    <literal><![CDATA[
      L(x,y,(z \ L(T(u,w),v5,v6)) * v7) = L(x,y,v7 * (z \ L(u,v5,v6)))
    ]]></literal>
    <justification jstring="[para(25329(a,1),29084(a,1,3))].">
      <j1 rule="para" parents="25329 29084"/>
    </justification>
  </clause>

  <clause id="29151">
    <literal><![CDATA[
      L(x,y,z \ ((z * u) \ z)) = L(x,y,L(u,z,z) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,25700,a(flip),b,29101,a),flip(a)].">
      <j1 rule="hyper" parents="64 25700 29101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29152">
    <literal><![CDATA[
      x * L(y,x * z,x \ (z \ x)) = (x / (x * z)) * ((x * z) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,29101,a(flip),b,11067,a)].">
      <j1 rule="hyper" parents="145 29101 11067"/>
    </justification>
  </clause>

  <clause id="29153">
    <literal><![CDATA[
      L(x,y,(z * (u \ 1)) * w) = L(x,y,w * (u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,25369,a(flip),b,29105,a),flip(a)].">
      <j1 rule="hyper" parents="373 25369 29105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29154">
    <literal><![CDATA[
      L(x,y,z * ((u * w) * u)) = L(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2204,a(flip),b,29105,a),flip(a)].">
      <j1 rule="hyper" parents="64 2204 29105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29155">
    <literal><![CDATA[
      L(x,y,(z * u) * R(R(w,u,z),v5,v6)) = L(x,y,(R(w,v5,v6) * u) * z)
    ]]></literal>
    <justification jstring="[para(506(a,1),29105(a,2,3))].">
      <j1 rule="para" parents="506 29105"/>
    </justification>
  </clause>

  <clause id="29156">
    <literal><![CDATA[
      L(x,y,(z * u) * L(R(w,u,z),v5,v6)) = L(x,y,(L(w,v5,v6) * u) * z)
    ]]></literal>
    <justification jstring="[para(510(a,1),29105(a,2,3))].">
      <j1 rule="para" parents="510 29105"/>
    </justification>
  </clause>

  <clause id="29157">
    <literal><![CDATA[
      L(x,y,z * (u * R(w,w,u))) = L(x,y,((1 / w) \ u) * z)
    ]]></literal>
    <justification jstring="[para(1913(a,1),29105(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1913 29105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29158">
    <literal><![CDATA[
      L(x,y,z * L(u,u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23850,a(flip),b,29134,a)].">
      <j1 rule="hyper" parents="64 23850 29134"/>
    </justification>
  </clause>

  <clause id="29159">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) * w)) = L(x,y,z \ R(u,w,w))
    ]]></literal>
    <justification jstring="[para(111(a,1),29134(a,1,3,2))].">
      <j1 rule="para" parents="111 29134"/>
    </justification>
  </clause>

  <clause id="29160">
    <literal><![CDATA[
      L(x,y,L(z,z,u) * u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(24201,a,29158,a)].">
      <j1 rule="hyper" parents="24201 29158"/>
    </justification>
  </clause>

  <clause id="29162">
    <literal><![CDATA[
      L(x,y,(R(z,u,w) * v5) * L(v6,v6,R(1 / z,u,w) * v5)) = L(x,y,v6 \ (R(1 / z,u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,3385,a(flip),b,29158,a)].">
      <j1 rule="hyper" parents="64 3385 29158"/>
    </justification>
  </clause>

  <clause id="29163">
    <literal><![CDATA[
      L(x,y,(z \ u) \ z) = L(x,y,(u \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,28980,a(flip),b,29137,a),flip(a)].">
      <j1 rule="hyper" parents="373 28980 29137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29164">
    <literal><![CDATA[
      L(x,y,((z * u) \ u) * u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28980,a(flip),b,29138,a)].">
      <j1 rule="hyper" parents="64 28980 29138"/>
    </justification>
  </clause>

  <clause id="29165">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,(y \ x) * x) = x \ ((x / (x \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11070,a(flip),b,29163,a),flip(a)].">
      <j1 rule="hyper" parents="64 11070 29163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29166">
    <literal><![CDATA[
      L(x \ y,x \ y,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,28980,a(flip),b,29117,a)].">
      <j1 rule="hyper" parents="64 28980 29117"/>
    </justification>
  </clause>

  <clause id="29168">
    <literal><![CDATA[
      L(x,y,(z \ ((u * u) * w)) * v5) = L(x,y,(z \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,2240,a(flip),b,28995,a)].">
      <j1 rule="hyper" parents="64 2240 28995"/>
    </justification>
  </clause>

  <clause id="29169">
    <literal><![CDATA[
      L(x,y,((z * u) * (z \ 1)) \ w) = L(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(5134(a,1),28996(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5134 28996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29170">
    <literal><![CDATA[
      L(x,y,(z * ((u \ w) \ w)) * v5) = L(x,y,(z * u) * v5)
    ]]></literal>
    <justification jstring="[para(116(a,1),28998(a,1,3,1,2))].">
      <j1 rule="para" parents="116 28998"/>
    </justification>
  </clause>

  <clause id="29171">
    <literal><![CDATA[
      L(x,y,(((z \ u) / u) \ w) \ v5) = L(x,y,(((z * u) \ u) \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(5144(a,1),29000(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="5144 29000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29172">
    <literal><![CDATA[
      L(x,T(x,y) \ z,(x \ z) \ y) * y = (K(x,y) * (y / (z / x))) * z
    ]]></literal>
    <justification jstring="[para(29000(a,1),16449(a,1,1))].">
      <j1 rule="para" parents="29000 16449"/>
    </justification>
  </clause>

  <clause id="29173">
    <literal><![CDATA[
      L(x,y,L(K(z,u) * (w * ((v5 * v6) \ v5)),v7,v8)) = L(x,y,L(w * L(v6 \ 1,v6,v5),v7,v8))
    ]]></literal>
    <justification jstring="[para(999(a,1),29005(a,1,3,1))].">
      <j1 rule="para" parents="999 29005"/>
    </justification>
  </clause>

  <clause id="29174">
    <literal><![CDATA[
      L(x,y,L((z / u) * w,v5,v6)) = L(x,y,L((u \ z) * w,v5,v6))
    ]]></literal>
    <justification jstring="[para(5982(a,1),29005(a,1,3,1))].">
      <j1 rule="para" parents="5982 29005"/>
    </justification>
  </clause>

  <clause id="29175">
    <literal><![CDATA[
      L(x,y,L((z / u) \ w,v5,v6)) = L(x,y,L((u \ z) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(6270(a,1),29005(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="6270 29005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29176">
    <literal><![CDATA[
      L(x,y,L(z \ T(u,w),v5,v6)) = L(x,y,L(z \ u,v5,v6))
    ]]></literal>
    <justification jstring="[para(6417(a,1),29005(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="6417 29005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29177">
    <literal><![CDATA[
      L(x,y,L(z * (K(u,w) * v5),v6,v7)) = L(x,y,L(z * v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(10720(a,1),29005(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10720 29005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29178">
    <literal><![CDATA[
      L(x,y,L((z * T(u,w)) \ v5,v6,v7)) = L(x,y,L((z * u) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(24506(a,1),29005(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="24506 29005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29179">
    <literal><![CDATA[
      L(x,y,L(z * (u / w),v5,v6)) = L(x,y,L(z * (w \ u),v5,v6))
    ]]></literal>
    <justification jstring="[para(6471(a,1),29034(a,1,3,1))].">
      <j1 rule="para" parents="6471 29034"/>
    </justification>
  </clause>

  <clause id="29180">
    <literal><![CDATA[
      T(x,y) \ ((x * T(x,z)) * u) = (K(x,y) / T(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(15130(a,1),29045(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15130 29045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29181">
    <literal><![CDATA[
      x \ ((y * T(y,y * y)) \ z) = ((y * L(y,y,y)) * x) \ z
    ]]></literal>
    <justification jstring="[para(118(a,1),29046(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="118 29046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29182">
    <literal><![CDATA[
      (x * T(x,T(x \ 1,y))) * (z / u) = ((x * ((x \ 1) \ 1)) * z) / u
    ]]></literal>
    <justification jstring="[para(4089(a,1),29048(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4089 29048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29183">
    <literal><![CDATA[
      ((x * T(x,y)) * z) \ (z * (x * T(x,y))) = K((x * T(x,y)) \ z,x * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,29049,a(flip),b,10196,a)].">
      <j1 rule="hyper" parents="139 29049 10196"/>
    </justification>
  </clause>

  <clause id="29184">
    <literal><![CDATA[
      L(x,y,((1 / z) \ u) \ w) = L(x,y,(z \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,28982,a(flip),b,29081,a),flip(a)].">
      <j1 rule="hyper" parents="373 28982 29081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29185">
    <literal><![CDATA[
      L(x,y,z \ T(u / (u * w),w)) = L(x,y,z \ (u \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(26040(a,1),29109(a,1,3,2))].">
      <j1 rule="para" parents="26040 29109"/>
    </justification>
  </clause>

  <clause id="29186">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ w)) = L(x,y,z * (w \ (u \ w)))
    ]]></literal>
    <justification jstring="[para(5144(a,1),29116(a,1,3,2))].">
      <j1 rule="para" parents="5144 29116"/>
    </justification>
  </clause>

  <clause id="29187">
    <literal><![CDATA[
      L(x,y,(z * (u * (w \ 1))) \ (w * (z * u))) = L(x,y,a(z,u,w \ 1))
    ]]></literal>
    <justification jstring="[para(14(a,2),29131(a,1,3)),flip(a)].">
      <j1 rule="para" parents="14 29131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29188">
    <literal><![CDATA[
      L(x,y,(z \ R(T(u,w),v5,v6)) * v7) = L(x,y,v7 * (z \ R(u,v5,v6)))
    ]]></literal>
    <justification jstring="[para(27(a,2),29145(a,1,3,1,2))].">
      <j1 rule="para" parents="27 29145"/>
    </justification>
  </clause>

  <clause id="29189">
    <literal><![CDATA[
      L(x,y,(z * (u \ 1)) * w) = L(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29105,a,b,29153,a),flip(a)].">
      <j1 rule="hyper" parents="373 29105 29153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29190">
    <literal><![CDATA[
      L(x,y,(z * L(z,u,u)) * w) = L(x,y,a(u,u,z) * w)
    ]]></literal>
    <justification jstring="[para(1847(a,1),29189(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1847 29189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29191">
    <literal><![CDATA[
      L(x,y,(L(z,u,w) \ z) * v5) = L(x,y,(z * L(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(1846(a,1),29189(a,1,3,1))].">
      <j1 rule="para" parents="1846 29189"/>
    </justification>
  </clause>

  <clause id="29192">
    <literal><![CDATA[
      L(x,y,(z * u) \ ((z * w) * u)) = L(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,28988,a,b,29008,a)].">
      <j1 rule="hyper" parents="64 28988 29008"/>
    </justification>
  </clause>

  <clause id="29193">
    <literal><![CDATA[
      L(x,y,R(z,u,u)) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,24657,a(flip),b,29008,a)].">
      <j1 rule="hyper" parents="64 24657 29008"/>
    </justification>
  </clause>

  <clause id="29194">
    <literal><![CDATA[
      L(x,y,a(z,u,u) \ z) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,16025,a,b,29193,a)].">
      <j1 rule="hyper" parents="64 16025 29193"/>
    </justification>
  </clause>

  <clause id="29195">
    <literal><![CDATA[
      L(x,x,L(y,x,x)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16076,a(flip),b,29193,a),flip(a)].">
      <j1 rule="hyper" parents="64 16076 29193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29196">
    <literal><![CDATA[
      1 / L(x,y * (1 / x),L(y,x,x)) = (1 / R(y,x,x)) * (y * (1 / x))
    ]]></literal>
    <justification jstring="[para(29193(a,1),1427(a,1,2))].">
      <j1 rule="para" parents="29193 1427"/>
    </justification>
  </clause>

  <clause id="29197">
    <literal><![CDATA[
      L(x,x,L((x * x) \ (x * y),z,u)) = L(x,x,L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(637(a,1),29195(a,1,3))].">
      <j1 rule="para" parents="637 29195"/>
    </justification>
  </clause>

  <clause id="29199">
    <literal><![CDATA[
      L(x,y,a(z * u,u,z)) = L(x,y,z * R(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,24857,a(flip),b,29059,a),flip(a)].">
      <j1 rule="hyper" parents="64 24857 29059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29200">
    <literal><![CDATA[
      L(x,y,a(z * u,u,z)) = L(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,16004,a(flip),b,29199,a),flip(a)].">
      <j1 rule="hyper" parents="373 16004 29199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29201">
    <literal><![CDATA[
      L(x,y,a(z,z \ u,z \ u)) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),29200(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 29200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29202">
    <literal><![CDATA[
      L(x,y,a(z * (z * u),u * z,T(z,u))) = L(x,y,a(T(z,u),u * z,u * z))
    ]]></literal>
    <justification jstring="[para(4645(a,1),29200(a,1,3,1))].">
      <j1 rule="para" parents="4645 29200"/>
    </justification>
  </clause>

  <clause id="29203">
    <literal><![CDATA[
      L(x,y,R(z,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,24657,a(flip),b,29192,a)].">
      <j1 rule="hyper" parents="64 24657 29192"/>
    </justification>
  </clause>

  <clause id="29204">
    <literal><![CDATA[
      L((R(x,y,z) \ 1) \ u,R(x,y,z),L(x,y,z)) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(1155,a,29203,a),flip(a)].">
      <j1 rule="hyper" parents="1155 29203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29205">
    <literal><![CDATA[
      L(R(x,y,z) \ u,R(x,y,z),L(x,y,z)) = (1 / R(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(742,a,29203,a),flip(a)].">
      <j1 rule="hyper" parents="742 29203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29206">
    <literal><![CDATA[
      L(x,y,R(L(z,u,w),v5,v6)) = L(x,y,L(L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27127,a,b,29203,a),flip(a)].">
      <j1 rule="hyper" parents="373 27127 29203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29207">
    <literal><![CDATA[
      L(x,y,(z * u) \ (u * (w * z))) = L(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29140,a,b,29203,a)].">
      <j1 rule="hyper" parents="64 29140 29203"/>
    </justification>
  </clause>

  <clause id="29208">
    <literal><![CDATA[
      L(x,y,L(z \ (u \ z),u,u)) = L(x,y,L(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27996,a,b,29203,a)].">
      <j1 rule="hyper" parents="64 27996 29203"/>
    </justification>
  </clause>

  <clause id="29209">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (R(x,y,z) * u) = L((x \ 1) \ u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11899,a,b,29203,a)].">
      <j1 rule="hyper" parents="64 11899 29203"/>
    </justification>
  </clause>

  <clause id="29210">
    <literal><![CDATA[
      (x * R(y,x,z)) \ ((x * y) * z) = L(z,x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11325,a,b,29203,a)].">
      <j1 rule="hyper" parents="64 11325 29203"/>
    </justification>
  </clause>

  <clause id="29211">
    <literal><![CDATA[
      L(x,R(y,z,u),y) = L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,2554,a,b,29203,a)].">
      <j1 rule="hyper" parents="64 2554 29203"/>
    </justification>
  </clause>

  <clause id="29212">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w) \ z,v5,v6)) = L(x,y,L(z \ L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,28941,a(flip),b,29203,a)].">
      <j1 rule="hyper" parents="64 28941 29203"/>
    </justification>
  </clause>

  <clause id="29213">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w) \ z,v5,v6)) = L(x,y,L(z * L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,28921,a(flip),b,29203,a)].">
      <j1 rule="hyper" parents="64 28921 29203"/>
    </justification>
  </clause>

  <clause id="29214">
    <literal><![CDATA[
      L(x,y,L(z,z,z * u)) = L(x,y,R(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,24841,a(flip),b,29203,a),flip(a)].">
      <j1 rule="hyper" parents="64 24841 29203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29215">
    <literal><![CDATA[
      L(T(x,y) \ z,x,L(y,u,w)) = (x * R(y,u,w)) \ (R(y,u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23689,a(flip),b,29203,a),flip(a)].">
      <j1 rule="hyper" parents="64 23689 29203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29216">
    <literal><![CDATA[
      L(x,y,L(z * (u \ (a(w,v5,w) / u)),v6,v7)) = L(x,y,R(z,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,13818,a(flip),b,29203,a),flip(a)].">
      <j1 rule="hyper" parents="64 13818 29203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29217">
    <literal><![CDATA[
      R(x,y,z) \ L(u,R(x,y,z),L(x,y,z)) = (R(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(139,a,29203,a(flip),b,1139,a)].">
      <j1 rule="hyper" parents="139 29203 1139"/>
    </justification>
  </clause>

  <clause id="29219">
    <literal><![CDATA[
      ((1 / x) \ y) * L(z,y,L(x,x,y)) = R(x,x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(29203(a,1),1916(a,1,2))].">
      <j1 rule="para" parents="29203 1916"/>
    </justification>
  </clause>

  <clause id="29220">
    <literal><![CDATA[
      (R(x,y,z) \ x) * L(u,x,L(x,y,z)) = x * ((R(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(29203(a,1),12026(a,1,2))].">
      <j1 rule="para" parents="29203 12026"/>
    </justification>
  </clause>

  <clause id="29221">
    <literal><![CDATA[
      L(x,y,R(z,u,T(w,v5))) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(23198(a,2),29203(a,1,3))].">
      <j1 rule="para" parents="23198 29203"/>
    </justification>
  </clause>

  <clause id="29222">
    <literal><![CDATA[
      R(x,R(y,z,u) * L(w,w,L(y,z,u)),v5) = R(x,w \ R(y,z,u),v5)
    ]]></literal>
    <justification jstring="[para(29203(a,1),26705(a,1,2,2))].">
      <j1 rule="para" parents="29203 26705"/>
    </justification>
  </clause>

  <clause id="29223">
    <literal><![CDATA[
      L(x,y,L(z,z,z * u)) = L(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,29203,a(flip),b,29214,a),flip(a)].">
      <j1 rule="hyper" parents="373 29203 29214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29224">
    <literal><![CDATA[
      L(x,y,(z * (u * z)) * w) = L(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2239,a(flip),b,28999,a)].">
      <j1 rule="hyper" parents="64 2239 28999"/>
    </justification>
  </clause>

  <clause id="29226">
    <literal><![CDATA[
      L(x,y,(z * (u * z)) * w) = L(x,y,w * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,29224,a),flip(a)].">
      <j1 rule="hyper" parents="373 23253 29224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29227">
    <literal><![CDATA[
      L(x,y,((z * u) * u) * w) = L(x,y,w * L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,28989,a,b,29226,a)].">
      <j1 rule="hyper" parents="64 28989 29226"/>
    </justification>
  </clause>

  <clause id="29228">
    <literal><![CDATA[
      L(x,y,z * ((u * w) * w)) = L(x,y,z * L(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,29105,a(flip),b,29226,a)].">
      <j1 rule="hyper" parents="64 29105 29226"/>
    </justification>
  </clause>

  <clause id="29229">
    <literal><![CDATA[
      L(x,y,z * R(u,w,w)) = L(x,y,z * L(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,24857,a(flip),b,29227,a)].">
      <j1 rule="hyper" parents="64 24857 29227"/>
    </justification>
  </clause>

  <clause id="29230">
    <literal><![CDATA[
      L(x,y,y * L(y,z,z)) = L(x,a(y,z,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16005,a(flip),b,29229,a),flip(a)].">
      <j1 rule="hyper" parents="64 16005 29229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29231">
    <literal><![CDATA[
      L(x,a(y,z,z),y) = L(x,y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,9388,a(flip),b,29230,a),flip(a)].">
      <j1 rule="hyper" parents="64 9388 29230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29232">
    <literal><![CDATA[
      R(x,y,y) \ (x * (a(x,y,y) * z)) = L(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,15993,a,b,29231,a)].">
      <j1 rule="hyper" parents="64 15993 29231"/>
    </justification>
  </clause>

  <clause id="29233">
    <literal><![CDATA[
      L((a(x,y,y) \ 1) \ z,x,a(y,y,x)) = (a(x,y,y) \ x) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,25177,a(flip),b,29231,a),flip(a)].">
      <j1 rule="hyper" parents="64 25177 29231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29234">
    <literal><![CDATA[
      L(x,y,(z * (T(u,w) * v5)) * v6) = L(x,y,(z * (u * v5)) * v6)
    ]]></literal>
    <justification jstring="[para(5755(a,1),29002(a,1,3,1,2))].">
      <j1 rule="para" parents="5755 29002"/>
    </justification>
  </clause>

  <clause id="29235">
    <literal><![CDATA[
      L(x,y,(z \ (u * w)) \ v5) = L(x,y,(z \ (w * u)) \ v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),29004(a,1,3,1,2,1))].">
      <j1 rule="para" parents="9 29004"/>
    </justification>
  </clause>

  <clause id="29236">
    <literal><![CDATA[
      L(x,y,z \ (u / (w / v5))) = L(x,y,z \ ((v5 \ w) \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,29023,a(flip),b,29030,a),flip(a)].">
      <j1 rule="hyper" parents="373 29023 29030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29237">
    <literal><![CDATA[
      L(x,y,z * L(u,u,w)) = L(x,y,z * ((w * (u \ 1)) \ w))
    ]]></literal>
    <justification jstring="[para(11811(a,1),29031(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="11811 29031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29238">
    <literal><![CDATA[
      L(x,y,(z \ (u \ T(w,v5))) * v6) = L(x,y,(z \ (u \ w)) * v6)
    ]]></literal>
    <justification jstring="[para(6417(a,1),29086(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="6417 29086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29239">
    <literal><![CDATA[
      L(x,(y / z) * u,x * ((z \ y) * u)) = ((1 / (((y / z) * u) * x)) * ((y / z) * u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,21692,a(flip),b,29089,a),flip(a)].">
      <j1 rule="hyper" parents="64 21692 29089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29240">
    <literal><![CDATA[
      L(x,y,(z * z) * ((u \ w) \ v5)) = L(x,y,((1 / w) / u) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,25858,a(flip),b,29090,a),flip(a)].">
      <j1 rule="hyper" parents="64 25858 29090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29241">
    <literal><![CDATA[
      L(x,y,z * (u \ ((w / v5) * v6))) = L(x,y,z * (u \ ((v5 \ w) * v6)))
    ]]></literal>
    <justification jstring="[para(5982(a,1),29093(a,1,3,2,2))].">
      <j1 rule="para" parents="5982 29093"/>
    </justification>
  </clause>

  <clause id="29242">
    <literal><![CDATA[
      L(x,y,z * (u \ ((w / v5) \ v6))) = L(x,y,z * (u \ ((v5 \ w) \ v6)))
    ]]></literal>
    <justification jstring="[para(6270(a,1),29093(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="6270 29093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29243">
    <literal><![CDATA[
      L(x,y,z * (((u / w) \ v5) \ v6)) = L(x,y,z * (((w \ u) \ v5) \ v6))
    ]]></literal>
    <justification jstring="[para(24402(a,1),29093(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="24402 29093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29244">
    <literal><![CDATA[
      L(x,y,((z / u) / w) * v5) = L(x,y,(w \ (u \ z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28980,a,b,29095,a)].">
      <j1 rule="hyper" parents="64 28980 29095"/>
    </justification>
  </clause>

  <clause id="29245">
    <literal><![CDATA[
      L(x,y,((z * u) * w) \ v5) = L(x,y,(w * (u * z)) \ v5)
    ]]></literal>
    <justification jstring="[para(24404(a,1),29107(a,1,3))].">
      <j1 rule="para" parents="24404 29107"/>
    </justification>
  </clause>

  <clause id="29246">
    <literal><![CDATA[
      L(x,y,(z * (K(u,w) * v5)) \ v6) = L(x,y,(v5 * z) \ v6)
    ]]></literal>
    <justification jstring="[para(24420(a,1),29107(a,1,3)),flip(a)].">
      <j1 rule="para" parents="24420 29107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29247">
    <literal><![CDATA[
      L(x,y,z \ (((1 / u) \ w) \ v5)) = L(x,y,z \ ((w / u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,25691,a(flip),b,29110,a),flip(a)].">
      <j1 rule="hyper" parents="64 25691 29110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29248">
    <literal><![CDATA[
      R((x / y) / (x \ y),x \ y,x \ y) = (x / y) / (x \ y)
    ]]></literal>
    <justification jstring="[para(29166(a,1),29119(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29166 29119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29249">
    <literal><![CDATA[
      L(x,y,(z * (u / w)) * v5) = L(x,y,v5 * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(24201,a,29122,a)].">
      <j1 rule="hyper" parents="24201 29122"/>
    </justification>
  </clause>

  <clause id="29250">
    <literal><![CDATA[
      L(x,y,z \ (((u * w) * w) * (1 / v5))) = L(x,y,z \ (v5 * R(u,w,w)))
    ]]></literal>
    <justification jstring="[para(1325(a,1),29130(a,1,3,2))].">
      <j1 rule="para" parents="1325 29130"/>
    </justification>
  </clause>

  <clause id="29251">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) = L(x,y,z \ L(T(v5,w),w,u))
    ]]></literal>
    <justification jstring="[para(262(a,1),29135(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="262 29135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29252">
    <literal><![CDATA[
      (x * (y / (z * T(z,u)))) * K(y,z * T(z,u)) = (x / (z * T(z,u))) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,23408,a,b,29139,a)].">
      <j1 rule="hyper" parents="64 23408 29139"/>
    </justification>
  </clause>

  <clause id="29253">
    <literal><![CDATA[
      L(((x / y) / z) * u,a(w,v5,v6),u * (z \ (y \ x))) = ((x / y) / z) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,29123,a(flip),b,29141,a)].">
      <j1 rule="hyper" parents="64 29123 29141"/>
    </justification>
  </clause>

  <clause id="29254">
    <literal><![CDATA[
      L(x,y,((z * u) * (z \ u)) * w) = L(x,y,w * a(u,z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,25133,a(flip),b,29147,a),flip(a)].">
      <j1 rule="hyper" parents="373 25133 29147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29255">
    <literal><![CDATA[
      L(x,y,((z * (u \ 1)) * w) * v5) = L(x,y,((u * z) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,23993,a(flip),b,29147,a),flip(a)].">
      <j1 rule="hyper" parents="373 23993 29147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29256">
    <literal><![CDATA[
      L(x,y,z * (((u * w) * u) * v5)) = L(x,y,(L(w,u,u) * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2207,a(flip),b,29147,a),flip(a)].">
      <j1 rule="hyper" parents="64 2207 29147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29258">
    <literal><![CDATA[
      L(x,y,(z \ (u * (u * w))) * v5) = L(x,y,(z \ L(w,u,u)) * v5)
    ]]></literal>
    <justification jstring="[para(100(a,1),29168(a,1,3,1,2))].">
      <j1 rule="para" parents="100 29168"/>
    </justification>
  </clause>

  <clause id="29259">
    <literal><![CDATA[
      L(x,y,(((1 / z) * u) \ w) * v5) = L(x,y,((z * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(941(a,1),29168(a,1,3,1))].">
      <j1 rule="para" parents="941 29168"/>
    </justification>
  </clause>

  <clause id="29260">
    <literal><![CDATA[
      L(x,y,(z \ (u * T(w,u \ 1))) * v5) = L(x,y,(z \ (w * (1 / u))) * v5)
    ]]></literal>
    <justification jstring="[para(3874(a,1),29168(a,1,3,1,2))].">
      <j1 rule="para" parents="3874 29168"/>
    </justification>
  </clause>

  <clause id="29261">
    <literal><![CDATA[
      L(x,y,z * ((u * w) \ u)) = L(x,y,z * (u \ (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29091,a,b,29186,a)].">
      <j1 rule="hyper" parents="64 29091 29186"/>
    </justification>
  </clause>

  <clause id="29262">
    <literal><![CDATA[
      L(x,y,z \ (u * (z \ u))) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,2244,a(flip),b,29201,a)].">
      <j1 rule="hyper" parents="64 2244 29201"/>
    </justification>
  </clause>

  <clause id="29263">
    <literal><![CDATA[
      L(x,y,z \ ((z \ u) * u)) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29025,a,b,29262,a)].">
      <j1 rule="hyper" parents="64 29025 29262"/>
    </justification>
  </clause>

  <clause id="29264">
    <literal><![CDATA[
      L(x,y,L(R(z,u,w),v5,v6)) = L(x,y,L(L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(29(a,1),29206(a,1,3))].">
      <j1 rule="para" parents="29 29206"/>
    </justification>
  </clause>

  <clause id="29265">
    <literal><![CDATA[
      x * (R(x,y,y) \ (a(x,y,y) * z)) = L(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,1907,a(flip),b,29232,a)].">
      <j1 rule="hyper" parents="64 1907 29232"/>
    </justification>
  </clause>

  <clause id="29266">
    <literal><![CDATA[
      L(x,y,((z * u) * u) \ w) = L(x,y,L(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,25700,a(flip),b,29245,a),flip(a)].">
      <j1 rule="hyper" parents="373 25700 29245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29267">
    <literal><![CDATA[
      L(x,y,((z * u) * w) \ (z * (w * u))) = L(x,y,a(w,u,z) * K(z,w * u))
    ]]></literal>
    <justification jstring="[para(15232(a,1),29245(a,2,3))].">
      <j1 rule="para" parents="15232 29245"/>
    </justification>
  </clause>

  <clause id="29268">
    <literal><![CDATA[
      L(x,y,R(z,u,u) \ w) = L(x,y,L(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2194,a(flip),b,29266,a)].">
      <j1 rule="hyper" parents="64 2194 29266"/>
    </justification>
  </clause>

  <clause id="29269">
    <literal><![CDATA[
      L(x,y,R(z,u,u) \ z) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(1243(a,1),29268(a,2,3))].">
      <j1 rule="para" parents="1243 29268"/>
    </justification>
  </clause>

  <clause id="29270">
    <literal><![CDATA[
      L(a(x,y,y),x,L(x,y,y) \ z) \ z = x * (R(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[para(29268(a,1),25609(a,1,1))].">
      <j1 rule="para" parents="29268 25609"/>
    </justification>
  </clause>

  <clause id="29271">
    <literal><![CDATA[
      L(x,y,((z \ T(u,w)) * v5) \ v6) = L(x,y,(v5 * (z \ u)) \ v6)
    ]]></literal>
    <justification jstring="[para(6417(a,1),29246(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="6417 29246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29272">
    <literal><![CDATA[
      L(x,y,z * (u * (z \ u))) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,25649,a(flip),b,29249,a),flip(a)].">
      <j1 rule="hyper" parents="64 25649 29249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29273">
    <literal><![CDATA[
      L(x \ 1,x,x * (y * (x \ y))) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,27123,a(flip),b,29272,a),flip(a)].">
      <j1 rule="hyper" parents="373 27123 29272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29274">
    <literal><![CDATA[
      L(x,y,((z \ u) * u) * z) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29105,a,b,29272,a)].">
      <j1 rule="hyper" parents="64 29105 29272"/>
    </justification>
  </clause>

  <clause id="29275">
    <literal><![CDATA[
      L(x,y,z * ((z \ u) * u)) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29020,a,b,29272,a)].">
      <j1 rule="hyper" parents="64 29020 29272"/>
    </justification>
  </clause>

  <clause id="29276">
    <literal><![CDATA[
      L(x,y,a(z,u \ z,u)) = L(x,y,a(u,u \ z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,2199,a(flip),b,29275,a),flip(a)].">
      <j1 rule="hyper" parents="64 2199 29275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29277">
    <literal><![CDATA[
      ((x * y) \ x) / L(z,z,z * (x \ (y \ x))) = R(((x * y) \ x) / z,z,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,29261,a(flip),b,25873,a)].">
      <j1 rule="hyper" parents="225 29261 25873"/>
    </justification>
  </clause>

  <clause id="29278">
    <literal><![CDATA[
      L(x,L(R(y,z,u),w,v5),y) = L(x,y,L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,3492,a,b,29264,a)].">
      <j1 rule="hyper" parents="64 3492 29264"/>
    </justification>
  </clause>

  <clause id="29279">
    <literal><![CDATA[
      x * L(x \ y,x,a(x,z,z)) = L(y,x,a(z,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,16015,a,b,29265,a)].">
      <j1 rule="hyper" parents="64 16015 29265"/>
    </justification>
  </clause>

  <clause id="29280">
    <literal><![CDATA[
      x * (R(x,y,y) \ (z * a(x,y,y))) = L(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(23136(a,1),29265(a,1,2,2))].">
      <j1 rule="para" parents="23136 29265"/>
    </justification>
  </clause>

  <clause id="29281">
    <literal><![CDATA[
      (T(R(x,y,y),z) / x) * (x * (T(R(x,y,y),z) \ (u * a(x,y,y)))) = (R(x,y,y) / x) * L(u,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(29280(a,1),27036(a,2,2))].">
      <j1 rule="para" parents="29280 27036"/>
    </justification>
  </clause>

  <clause id="29282">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) * u)) = L(x,y,z \ R(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,25859,a(flip),b,29064,a)].">
      <j1 rule="hyper" parents="64 25859 29064"/>
    </justification>
  </clause>

  <clause id="29283">
    <literal><![CDATA[
      L(x,y,z \ R(u,w,w)) = L(x,y,z \ L(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,29132,a(flip),b,29282,a),flip(a)].">
      <j1 rule="hyper" parents="64 29132 29282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29284">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) * w)) = L(x,y,z \ L(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,29159,a,b,29283,a)].">
      <j1 rule="hyper" parents="64 29159 29283"/>
    </justification>
  </clause>

  <clause id="29285">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,u)) = L(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(15987(a,1),29283(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15987 29283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29286">
    <literal><![CDATA[
      L(x,y \ 1,a(z,u,u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11855,a(flip),b,29285,a),flip(a)].">
      <j1 rule="hyper" parents="64 11855 29285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29287">
    <literal><![CDATA[
      L(x,y,a(z,u,u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(11853,a,29286,a)].">
      <j1 rule="hyper" parents="11853 29286"/>
    </justification>
  </clause>

  <clause id="29288">
    <literal><![CDATA[
      L(a(x,y,y),z,a(y,y,x)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,24648,a(flip),b,29286,a),flip(a)].">
      <j1 rule="hyper" parents="64 24648 29286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29289">
    <literal><![CDATA[
      (a(x,x,y) * (z * u)) \ (a(x,x,y) * (u * (T(z,u) * w))) = L(L(w,z,u),z * u,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,10991,a,b,29287,a)].">
      <j1 rule="hyper" parents="373 10991 29287"/>
    </justification>
  </clause>

  <clause id="29290">
    <literal><![CDATA[
      L(a(x,x,y),z,a(y,x,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,24648,a(flip),b,29287,a),flip(a)].">
      <j1 rule="hyper" parents="373 24648 29287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29291">
    <literal><![CDATA[
      R(x,y,y) * L(z,x,a(x,y,y)) = x * (a(x,y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,29287,a,b,29232,a)].">
      <j1 rule="hyper" parents="145 29287 29232"/>
    </justification>
  </clause>

  <clause id="29292">
    <literal><![CDATA[
      x * L(y,z,a(u,w,w)) = x * L(y,z,a(w,w,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,29287,a,b,9,a)].">
      <j1 rule="hyper" parents="145 29287 9"/>
    </justification>
  </clause>

  <clause id="29293">
    <literal><![CDATA[
      L(x,y,a(z,u,u)) * w = L(x,y,a(u,u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,29287,a,b,11,a)].">
      <j1 rule="hyper" parents="144 29287 11"/>
    </justification>
  </clause>

  <clause id="29294">
    <literal><![CDATA[
      L(x,y,a(z * u,u,z)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29200,a,b,29287,a)].">
      <j1 rule="hyper" parents="64 29200 29287"/>
    </justification>
  </clause>

  <clause id="29295">
    <literal><![CDATA[
      (a(x,y,y) * (z * ((a(x,y,y) * z) \ u))) / (z * a(x,y,y)) = L(u / (z * a(x,y,y)),z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,11319,a,b,29287,a)].">
      <j1 rule="hyper" parents="64 11319 29287"/>
    </justification>
  </clause>

  <clause id="29296">
    <literal><![CDATA[
      L(x,y,a(z \ u,z \ u,z)) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29201,a(flip),b,29287,a),flip(a)].">
      <j1 rule="hyper" parents="64 29201 29287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29297">
    <literal><![CDATA[
      L(x,y,a(z,z,y)) * R(y,z,z) = a(y,z,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,29287,a(flip),b,28833,a)].">
      <j1 rule="hyper" parents="144 29287 28833"/>
    </justification>
  </clause>

  <clause id="29298">
    <literal><![CDATA[
      L(x,y,a(z,z,u \ 1)) = L(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[para(2653(a,1),29287(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2653 29287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29299">
    <literal><![CDATA[
      a(x,x,y) / L(1 / z,z,a(y,x,x)) = a(x,x,y) * (1 / (1 / z))
    ]]></literal>
    <justification jstring="[para(29287(a,2),4308(a,1,2))].">
      <j1 rule="para" parents="29287 4308"/>
    </justification>
  </clause>

  <clause id="29300">
    <literal><![CDATA[
      L(x,y,y) * L(z,x,a(x,y,y)) = (a(y,y,x) \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(29287(a,2),5676(a,1,2))].">
      <j1 rule="para" parents="29287 5676"/>
    </justification>
  </clause>

  <clause id="29301">
    <literal><![CDATA[
      a(x,x,y) * L(z,z,a(y,x,x)) = (1 / z) \ a(x,x,y)
    ]]></literal>
    <justification jstring="[para(29287(a,2),27122(a,1,2))].">
      <j1 rule="para" parents="29287 27122"/>
    </justification>
  </clause>

  <clause id="29302">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,z,x)) = L(y,x,a(z,z,x))
    ]]></literal>
    <justification jstring="[para(29287(a,1),29279(a,1,2))].">
      <j1 rule="para" parents="29287 29279"/>
    </justification>
  </clause>

  <clause id="29303">
    <literal><![CDATA[
      a(x,x,y) \ (a(y,x,x) * z) = a(y,x,x) * (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(29290(a,1),27804(a,1,1))].">
      <j1 rule="para" parents="29290 27804"/>
    </justification>
  </clause>

  <clause id="29304">
    <literal><![CDATA[
      L(x,y,a(z * u,z,u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(26787(a,1),29294(a,1,3))].">
      <j1 rule="para" parents="26787 29294"/>
    </justification>
  </clause>

  <clause id="29305">
    <literal><![CDATA[
      x * (L(x,y,y) \ (z * (x \ L(x,y,y)))) = L(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(24826(a,2),29302(a,1,2))].">
      <j1 rule="para" parents="24826 29302"/>
    </justification>
  </clause>

  <clause id="29306">
    <literal><![CDATA[
      ((x * y) * y) * L(z,u,u \ L(x,y,y)) = (((x * y) * y) / u) * (u * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,29284,a(flip),b,11067,a)].">
      <j1 rule="hyper" parents="145 29284 11067"/>
    </justification>
  </clause>

  <clause id="29307">
    <literal><![CDATA[
      a(x,y,y) * (x * z) = x * (a(x,y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16012,a(flip),b,29291,a)].">
      <j1 rule="hyper" parents="64 16012 29291"/>
    </justification>
  </clause>

  <clause id="29308">
    <literal><![CDATA[
      x * (a(x,y,y) * (x \ z)) = z * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,23182,a(flip),b,29307,a),flip(a)].">
      <j1 rule="hyper" parents="64 23182 29307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29309">
    <literal><![CDATA[
      L(x,y,a(x,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,28667,a,b,29307,a(flip))].">
      <j1 rule="hyper" parents="36 28667 29307"/>
    </justification>
  </clause>

  <clause id="29310">
    <literal><![CDATA[
      (x * (a(x,y,y) * z)) \ (a(x,y,y) * (x * (z * u))) = L(L(u,z,x),x * z,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(29307(a,1),602(a,1,1))].">
      <j1 rule="para" parents="29307 602"/>
    </justification>
  </clause>

  <clause id="29311">
    <literal><![CDATA[
      (R(x,y,y) * z) / (x * (a(x,y,y) * z)) = a(a(x,y,y),x,z)
    ]]></literal>
    <justification jstring="[para(29307(a,1),16016(a,1,2))].">
      <j1 rule="para" parents="29307 16016"/>
    </justification>
  </clause>

  <clause id="29312">
    <literal><![CDATA[
      L(x,y,a(z,z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,29287,a(flip),b,29309,a)].">
      <j1 rule="hyper" parents="64 29287 29309"/>
    </justification>
  </clause>

  <clause id="29313">
    <literal><![CDATA[
      L(x,y,a(z,x \ z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,29201,a(flip),b,29309,a)].">
      <j1 rule="hyper" parents="64 29201 29309"/>
    </justification>
  </clause>

  <clause id="29315">
    <literal><![CDATA[
      (a(x,y,y) * z) * x = a(x,y,y) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,29309,a(flip),b,5318,a(flip))].">
      <j1 rule="hyper" parents="145 29309 5318"/>
    </justification>
  </clause>

  <clause id="29317">
    <literal><![CDATA[
      (a(x,x,y) * z) / y = a(x,x,y) * (z / y)
    ]]></literal>
    <justification jstring="[hyper(225,a,29312,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 29312 10262"/>
    </justification>
  </clause>

  <clause id="29318">
    <literal><![CDATA[
      (x * a(y,y,z)) * z = a(y,y,z) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,29312,a(flip),b,23191,a)].">
      <j1 rule="hyper" parents="145 29312 23191"/>
    </justification>
  </clause>

  <clause id="29319">
    <literal><![CDATA[
      (a(x,x,y) * z) * y = a(x,x,y) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,29312,a(flip),b,5318,a(flip))].">
      <j1 rule="hyper" parents="145 29312 5318"/>
    </justification>
  </clause>

  <clause id="29320">
    <literal><![CDATA[
      a(x,x,y) * (y * z) = y * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,29312,a(flip),b,28734,a),flip(a)].">
      <j1 rule="hyper" parents="144 29312 28734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29322">
    <literal><![CDATA[
      a(x,x,y) \ (z * y) = (a(x,x,y) \ z) * y
    ]]></literal>
    <justification jstring="[para(29312(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="29312 598"/>
    </justification>
  </clause>

  <clause id="29323">
    <literal><![CDATA[
      (a(x,x,y) * z) * L(y,u,w) = a(x,x,y) * (z * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(29312(a,1),513(a,1,2,1))].">
      <j1 rule="para" parents="29312 513"/>
    </justification>
  </clause>

  <clause id="29324">
    <literal><![CDATA[
      (x * y) * a(z,z,x) = x * (y * a(z,z,x))
    ]]></literal>
    <justification jstring="[para(29312(a,1),28800(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29312 28800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29325">
    <literal><![CDATA[
      a(a(x,y \ x,y),z,y) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,29313,a)].">
      <j1 rule="hyper" parents="54 29313"/>
    </justification>
  </clause>

  <clause id="29327">
    <literal><![CDATA[
      L(a(x,y,y),z,x) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,28784,a,b,29315,a(flip))].">
      <j1 rule="hyper" parents="36 28784 29315"/>
    </justification>
  </clause>

  <clause id="29328">
    <literal><![CDATA[
      x * R(T(a(y,z,z),y * x),y,x) = y \ ((a(y,z,z) * y) * x)
    ]]></literal>
    <justification jstring="[para(29327(a,1),1821(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="29327 1821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29329">
    <literal><![CDATA[
      (a(x,x,y) * (z / y)) * L(y,x,x) = L(z,a(x,x,y),L(y,x,x))
    ]]></literal>
    <justification jstring="[para(29317(a,1),25127(a,1,1))].">
      <j1 rule="para" parents="29317 25127"/>
    </justification>
  </clause>

  <clause id="29330">
    <literal><![CDATA[
      R(a(x,x,y),z,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(664,a,29319,a)].">
      <j1 rule="hyper" parents="664 29319"/>
    </justification>
  </clause>

  <clause id="29331">
    <literal><![CDATA[
      L(a(x,x,y),z,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,28784,a,b,29319,a(flip))].">
      <j1 rule="hyper" parents="36 28784 29319"/>
    </justification>
  </clause>

  <clause id="29332">
    <literal><![CDATA[
      a(x,y,a(z,z,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,29331,a)].">
      <j1 rule="hyper" parents="54 29331"/>
    </justification>
  </clause>

  <clause id="29333">
    <literal><![CDATA[
      x * R(T(a(y,y,z),z * x),z,x) = z \ ((a(y,y,z) * z) * x)
    ]]></literal>
    <justification jstring="[para(29331(a,1),1821(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="29331 1821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29334">
    <literal><![CDATA[
      x * (a(y,y,x) * (x \ z)) = a(y,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(397,a,29320,a),flip(a)].">
      <j1 rule="hyper" parents="397 29320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29335">
    <literal><![CDATA[
      x \ (a(y,y,x) * z) = (x \ z) * a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,23906,a(flip),b,29324,a(flip))].">
      <j1 rule="hyper" parents="139 23906 29324"/>
    </justification>
  </clause>

  <clause id="29336">
    <literal><![CDATA[
      a(x,x,y) * (y \ (L(y,x,x) * z)) = L(z,L(y,x,x),a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,5568,a,b,29334,a),flip(a)].">
      <j1 rule="hyper" parents="35 5568 29334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29337">
    <literal><![CDATA[
      1 / L(1 / x,y,y * x) = (1 / (y * (1 / x))) * y
    ]]></literal>
    <justification jstring="[para(1631(a,1),29104(a,1,2))].">
      <j1 rule="para" parents="1631 29104"/>
    </justification>
  </clause>

  <clause id="29338">
    <literal><![CDATA[
      1 / L(a(x,y,z) \ 1,u,u * a(x,y,z)) = (1 / (u * (1 / a(x,y,z)))) * u
    ]]></literal>
    <justification jstring="[para(13923(a,1),29337(a,1,2,1))].">
      <j1 rule="para" parents="13923 29337"/>
    </justification>
  </clause>

  <clause id="29339">
    <literal><![CDATA[
      L(x,y,z * (u * R(w,w,u))) = L(x,y,(w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2270,a(flip),b,29157,a),flip(a)].">
      <j1 rule="hyper" parents="373 2270 29157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29340">
    <literal><![CDATA[
      ((x * L(x,x,x)) * y) \ z = y \ ((x * L(x,x,x)) \ z)
    ]]></literal>
    <justification jstring="[para(118(a,1),29181(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="118 29181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29342">
    <literal><![CDATA[
      K(x,x * x) \ ((x * T(T(x,y),z)) * u) = ((R(x,x,x) * T(T(x,y),z)) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(14735(a,1),29051(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14735 29051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29343">
    <literal><![CDATA[
      L(x,y,(L(z,u,w) * (u * w)) * v5) = L(x,y,((w \ 1) * (T(u,w) * z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,11098,a(flip),b,29096,a)].">
      <j1 rule="hyper" parents="64 11098 29096"/>
    </justification>
  </clause>

  <clause id="29344">
    <literal><![CDATA[
      L(x,y,z * (u \ (w * T(v5,v6)))) = L(x,y,(u \ (w * v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(24201,a,29097,a)].">
      <j1 rule="hyper" parents="24201 29097"/>
    </justification>
  </clause>

  <clause id="29345">
    <literal><![CDATA[
      L(x,y,(z \ (u * (w / v5))) * v6) = L(x,y,(z \ (u * (v5 \ w))) * v6)
    ]]></literal>
    <justification jstring="[para(117(a,1),29097(a,1,3,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 29097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29346">
    <literal><![CDATA[
      L(x,y,z \ (u / (w * u))) = L(x,y,z \ (u \ (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,25696,a(flip),b,29125,a)].">
      <j1 rule="hyper" parents="64 25696 29125"/>
    </justification>
  </clause>

  <clause id="29347">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ w)) = L(x,y,z \ (w \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29023,a(flip),b,29346,a)].">
      <j1 rule="hyper" parents="64 29023 29346"/>
    </justification>
  </clause>

  <clause id="29348">
    <literal><![CDATA[
      L(x,y,L((z / u) * w,v5,v6)) = L(x,y,L(w * (u \ z),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,24167,a,b,29174,a),flip(a)].">
      <j1 rule="hyper" parents="373 24167 29174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29349">
    <literal><![CDATA[
      L(x,y,z \ (u / (u * w))) = L(x,y,z \ (u \ (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(29068,a,29185,a)].">
      <j1 rule="hyper" parents="29068 29185"/>
    </justification>
  </clause>

  <clause id="29351">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ u)) = L(x,y,z \ (u \ (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29023,a(flip),b,29349,a)].">
      <j1 rule="hyper" parents="64 29023 29349"/>
    </justification>
  </clause>

  <clause id="29352">
    <literal><![CDATA[
      L(x,y,z * (u \ (w \ T(v5,v6)))) = L(x,y,(u \ (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(24201,a,29238,a)].">
      <j1 rule="hyper" parents="24201 29238"/>
    </justification>
  </clause>

  <clause id="29353">
    <literal><![CDATA[
      L(x,y,((1 / z) / u) \ w) = L(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2184,a(flip),b,29240,a),flip(a)].">
      <j1 rule="hyper" parents="64 2184 29240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29354">
    <literal><![CDATA[
      L(x,y,(z \ (1 / u)) \ w) = L(x,y,(z \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28982,a(flip),b,29353,a)].">
      <j1 rule="hyper" parents="64 28982 29353"/>
    </justification>
  </clause>

  <clause id="29355">
    <literal><![CDATA[
      L(x,y,(z \ (u \ 1)) \ w) = L(x,y,(z \ u) \ w)
    ]]></literal>
    <justification jstring="[para(79(a,1),29354(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="79 29354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29356">
    <literal><![CDATA[
      L(x,y,z \ (((1 / u) \ w) \ v5)) = L(x,y,z \ ((u \ w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,29110,a(flip),b,29247,a),flip(a)].">
      <j1 rule="hyper" parents="373 29110 29247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29357">
    <literal><![CDATA[
      L(x,y,z \ ((1 / u) \ w)) = L(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[para(82(a,1),29247(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="82 29247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29358">
    <literal><![CDATA[
      L(x,y,z \ ((u \ 1) \ w)) = L(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,29110,a(flip),b,29357,a)].">
      <j1 rule="hyper" parents="64 29110 29357"/>
    </justification>
  </clause>

  <clause id="29359">
    <literal><![CDATA[
      L(x,y,z \ ((u \ a(w,w,u)) \ v5)) = L(x,y,z \ (L(u,w,w) \ v5))
    ]]></literal>
    <justification jstring="[para(1856(a,1),29357(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="1856 29357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29360">
    <literal><![CDATA[
      L(x,y,((z * (u \ 1)) * w) * v5) = L(x,y,((u * z) * (w \ 1)) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29189,a,b,29255,a),flip(a)].">
      <j1 rule="hyper" parents="373 29189 29255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29361">
    <literal><![CDATA[
      L(x,y,z * (((1 / u) * w) \ v5)) = L(x,y,((u * w) \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(24201,a,29259,a)].">
      <j1 rule="hyper" parents="24201 29259"/>
    </justification>
  </clause>

  <clause id="29362">
    <literal><![CDATA[
      L(x,y,(((z \ 1) * u) \ w) * v5) = L(x,y,((z * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),29259(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 29259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29363">
    <literal><![CDATA[
      L(x,y,(z * (u \ T(w,v5))) \ v6) = L(x,y,(z * (u \ w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,28988,a,b,29271,a)].">
      <j1 rule="hyper" parents="64 28988 29271"/>
    </justification>
  </clause>

  <clause id="29364">
    <literal><![CDATA[
      L((x \ L(x,y,y)) \ z,x,a(y,y,x)) = x * (L(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[para(23741(a,1),29305(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23741 29305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29365">
    <literal><![CDATA[
      a(a(x,y,y),x,z) = a(x,a(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,15996,a(flip),b,29311,a),flip(a)].">
      <j1 rule="hyper" parents="64 15996 29311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29367">
    <literal><![CDATA[
      L(x,y,(z \ (u * w)) * v5) = L(x,y,v5 * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[para(115(a,1),29344(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="115 29344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29368">
    <literal><![CDATA[
      L(x,y,z * (u \ (w * (v5 * v5)))) = L(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29168,a(flip),b,29367,a),flip(a)].">
      <j1 rule="hyper" parents="64 29168 29367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29369">
    <literal><![CDATA[
      L(x,y,(z \ (u * (w * w))) * v5) = L(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[hyper(24201,a,29368,a)].">
      <j1 rule="hyper" parents="24201 29368"/>
    </justification>
  </clause>

  <clause id="29370">
    <literal><![CDATA[
      L(x,y,z \ ((u \ a(w,v5,u)) \ v6)) = L(x,y,z \ ((u * a(w,v5,u)) \ v6))
    ]]></literal>
    <justification jstring="[para(9440(a,1),29356(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="9440 29356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29371">
    <literal><![CDATA[
      L(x,y,z * a(u \ w,u \ w,u)) = L(x,y,(((w / u) * w) \ u) * z)
    ]]></literal>
    <justification jstring="[para(10628(a,2),29361(a,1,3,2))].">
      <j1 rule="para" parents="10628 29361"/>
    </justification>
  </clause>

  <clause id="29372">
    <literal><![CDATA[
      L(x,y,z * (((u \ 1) * w) \ v5)) = L(x,y,((u * w) \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(24201,a,29362,a)].">
      <j1 rule="hyper" parents="24201 29362"/>
    </justification>
  </clause>

  <clause id="29373">
    <literal><![CDATA[
      L((x \ L(x,y,y)) \ z,x,a(x,y,y)) = x * (L(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29287,a,b,29364,a)].">
      <j1 rule="hyper" parents="64 29287 29364"/>
    </justification>
  </clause>

  <clause id="29374">
    <literal><![CDATA[
      L(x,y,z * ((u * (w \ 1)) \ v5)) = L(x,y,((w * u) \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29091,a,b,29372,a)].">
      <j1 rule="hyper" parents="64 29091 29372"/>
    </justification>
  </clause>

  <clause id="29375">
    <literal><![CDATA[
      L(x,y,(z * L(u,u,z)) * w) = L(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29369,a(flip),b,29041,a),flip(a)].">
      <j1 rule="hyper" parents="64 29369 29041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29377">
    <literal><![CDATA[
      L(x,y,R(z,u,u \ 1) \ w) = L(x,y,L(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29169,a(flip),b,29054,a),flip(a)].">
      <j1 rule="hyper" parents="64 29169 29054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29378">
    <literal><![CDATA[
      L(x,y,(((z \ 1) * u) * R(w,z,u)) \ v5) = L(x,y,((w * (z \ 1)) * u) \ v5)
    ]]></literal>
    <justification jstring="[para(2975(a,1),29102(a,1,3,1,2))].">
      <j1 rule="para" parents="2975 29102"/>
    </justification>
  </clause>

  <clause id="29379">
    <literal><![CDATA[
      T(x \ K(y,z),u * (x \ K(y,z))) = T(K(y,z) / x,u * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,27844,a(flip),b,29114,a),flip(a)].">
      <j1 rule="hyper" parents="373 27844 29114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29380">
    <literal><![CDATA[
      T(K(x,y) * (z \ 1),u * (z \ K(x,y))) = T(T(K(x,y) / z,u * z),K(x,y))
    ]]></literal>
    <justification jstring="[para(29379(a,1),14801(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29379 14801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29381">
    <literal><![CDATA[
      (((x \ y) * y) * (y \ x)) \ ((x \ y) * y) = y \ ((y / (y \ x)) * 1)
    ]]></literal>
    <justification jstring="[hyper(642,a,29165,a)].">
      <j1 rule="hyper" parents="642 29165"/>
    </justification>
  </clause>

  <clause id="29382">
    <literal><![CDATA[
      L(x,y,L(z * (u \ (a(w,v5,w) / u)),v6,v7)) = L(x,y,L(z,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(373,a,29203,a(flip),b,29216,a),flip(a)].">
      <j1 rule="hyper" parents="373 29203 29216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29383">
    <literal><![CDATA[
      L(x,y,z * a(u,w \ u,(w \ u) \ u)) = L(x,y,(((w \ u) * u) * w) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29170,a(flip),b,29254,a),flip(a)].">
      <j1 rule="hyper" parents="64 29170 29254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29384">
    <literal><![CDATA[
      L(x,y,(L(z,u,u) * z) * w) = L(x,y,w * a(u * z,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,25132,a(flip),b,29256,a),flip(a)].">
      <j1 rule="hyper" parents="64 25132 29256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29385">
    <literal><![CDATA[
      L(x,y,(z * L(z,u,u)) * w) = L(x,y,w * a(u * z,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,28989,a,b,29384,a)].">
      <j1 rule="hyper" parents="64 28989 29384"/>
    </justification>
  </clause>

  <clause id="29386">
    <literal><![CDATA[
      L(x,y,z * a(u * w,u,w)) = L(x,y,a(u,u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29190,a(flip),b,29385,a),flip(a)].">
      <j1 rule="hyper" parents="64 29190 29385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29387">
    <literal><![CDATA[
      L(x,y,z * a((u \ w) * u,u \ w,u)) = L(x,y,(((1 / (w / u)) * w) \ u) * z)
    ]]></literal>
    <justification jstring="[para(10628(a,1),29386(a,2,3,1))].">
      <j1 rule="para" parents="10628 29386"/>
    </justification>
  </clause>

  <clause id="29388">
    <literal><![CDATA[
      x * R(T(a(y,z,z),y * x),y,x) = y \ (R(y,z,z) * x)
    ]]></literal>
    <justification jstring="[para(15998(a,1),29328(a,2,2,1))].">
      <j1 rule="para" parents="15998 29328"/>
    </justification>
  </clause>

  <clause id="29389">
    <literal><![CDATA[
      x * R(T(a(y,z,z),y * x),y,x) = R(y,z,z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1898,a(flip),b,29388,a),flip(a)].">
      <j1 rule="hyper" parents="373 1898 29388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29390">
    <literal><![CDATA[
      x * L(a(y,z,z),y,x) = R(y,z,z) * (y \ x)
    ]]></literal>
    <justification jstring="[para(28798(a,1),29389(a,1,2))].">
      <j1 rule="para" parents="28798 29389"/>
    </justification>
  </clause>

  <clause id="29391">
    <literal><![CDATA[
      x \ (R(y,z,z) * (y \ x)) = L(a(y,z,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(149,a,29390,a)].">
      <j1 rule="hyper" parents="149 29390"/>
    </justification>
  </clause>

  <clause id="29393">
    <literal><![CDATA[
      a(x,x,y) * ((z / y) * L(y,x,x)) = L(z,a(x,x,y),L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,29323,a(flip),b,29329,a)].">
      <j1 rule="hyper" parents="64 29323 29329"/>
    </justification>
  </clause>

  <clause id="29394">
    <literal><![CDATA[
      x \ ((a(y,y,x) * x) * z) = z * L(a(y,y,x),x,z)
    ]]></literal>
    <justification jstring="[para(28798(a,1),29333(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28798 29333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29396">
    <literal><![CDATA[
      a(x,x,y) * ((z / y) * L(y,x,x)) = L(z,L(y,x,x),a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,25124,a(flip),b,29336,a)].">
      <j1 rule="hyper" parents="64 25124 29336"/>
    </justification>
  </clause>

  <clause id="29397">
    <literal><![CDATA[
      L(x,y,L(z / (u * T(w,u \ 1)),v5,v6)) = L(x,y,L(z / (w * (u \ 1)),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,14248,a(flip),b,29382,a)].">
      <j1 rule="hyper" parents="64 14248 29382"/>
    </justification>
  </clause>

  <clause id="29398">
    <literal><![CDATA[
      L(x / L(y,z,z),a(z,z,y),L(y,z,z)) = a(z,z,y) * (x / y)
    ]]></literal>
    <justification jstring="[para(3197(a,1),29393(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3197 29393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29399">
    <literal><![CDATA[
      L(x,a(y,y,z),L(z,y,y)) = L(x,L(z,y,y),a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29393,a(flip),b,29396,a)].">
      <j1 rule="hyper" parents="64 29393 29396"/>
    </justification>
  </clause>

  <clause id="29400">
    <literal><![CDATA[
      x * L(y,a(z,z,x),L(x,z,z)) = a(z,z,x) * (L(x,z,z) * y)
    ]]></literal>
    <justification jstring="[para(29399(a,2),5568(a,1,2))].">
      <j1 rule="para" parents="29399 5568"/>
    </justification>
  </clause>

  <clause id="29401">
    <literal><![CDATA[
      a(x,x,y) * (L(y,x,x) * z) = L(y,x,x) * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1248,a(flip),b,29400,a),flip(a)].">
      <j1 rule="hyper" parents="64 1248 29400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29402">
    <literal><![CDATA[
      L(L(x,a(y,y,z),L(z,y,y)),z,z) = (1 / z) * (a(y,y,z) * (L(z,y,y) * x))
    ]]></literal>
    <justification jstring="[hyper(145,a,29400,a(flip),b,561,a),flip(a)].">
      <j1 rule="hyper" parents="145 29400 561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29403">
    <literal><![CDATA[
      L(x,y,z * (u \ ((w * w) * v5))) = L(x,y,z * (v5 / u))
    ]]></literal>
    <justification jstring="[hyper(373,a,24856,a(flip),b,29060,a),flip(a)].">
      <j1 rule="hyper" parents="373 24856 29060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29405">
    <literal><![CDATA[
      L(x,y,z * (u \ ((w * w) * v5))) = L(x,y,z * (u \ v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,29018,a(flip),b,29403,a),flip(a)].">
      <j1 rule="hyper" parents="373 29018 29403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29406">
    <literal><![CDATA[
      L(x,y,z * (((1 / u) * w) / v5)) = L(x,y,z * (v5 \ (u * w)))
    ]]></literal>
    <justification jstring="[para(310(a,1),29403(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="310 29403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29407">
    <literal><![CDATA[
      L(x,y,z * (u \ ((1 / w) * v5))) = L(x,y,z * (u \ (w * v5)))
    ]]></literal>
    <justification jstring="[para(310(a,1),29405(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="310 29405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29408">
    <literal><![CDATA[
      L(x,y,z * (u \ ((w \ 1) * (w \ v5)))) = L(x,y,z * (u \ v5))
    ]]></literal>
    <justification jstring="[para(584(a,1),29405(a,1,3,2,2))].">
      <j1 rule="para" parents="584 29405"/>
    </justification>
  </clause>

  <clause id="29409">
    <literal><![CDATA[
      L(x,y,z * (u \ (T(1 / w,(1 / w) \ 1) * L(v5,1 / w,1 / w)))) = L(x,y,z * (u \ (w * ((1 / w) * ((1 / (1 / w)) * v5)))))
    ]]></literal>
    <justification jstring="[para(26122(a,2),29407(a,1,3,2,2))].">
      <j1 rule="para" parents="26122 29407"/>
    </justification>
  </clause>

  <clause id="29410">
    <literal><![CDATA[
      L(x,y,z * (u \ ((1 / (1 / w)) \ v5))) = L(x,y,z * (u \ ((w \ 1) \ v5)))
    ]]></literal>
    <justification jstring="[para(7033(a,1),29408(a,1,3,2,2))].">
      <j1 rule="para" parents="7033 29408"/>
    </justification>
  </clause>

  <clause id="29411">
    <literal><![CDATA[
      L(x,y,((z * (u * z)) * w) * v5) = L(x,y,(L(u,z,z) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,2280,a(flip),b,29087,a)].">
      <j1 rule="hyper" parents="64 2280 29087"/>
    </justification>
  </clause>

  <clause id="29413">
    <literal><![CDATA[
      L(x,y,(L(z,z \ u,z \ u) * w) * v5) = L(x,y,(((z \ u) * u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),29411(a,1,3,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 29411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29414">
    <literal><![CDATA[
      L(x,y,(((z * u) \ u) \ w) \ v5) = L(x,y,((u \ (z \ u)) \ w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29111,a(flip),b,29171,a),flip(a)].">
      <j1 rule="hyper" parents="64 29111 29171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29415">
    <literal><![CDATA[
      L(x,y,L(z / (u * T(w,v5)),v6,v7)) = L(x,y,L((u * w) \ z,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,23846,a,b,29178,a)].">
      <j1 rule="hyper" parents="64 23846 29178"/>
    </justification>
  </clause>

  <clause id="29416">
    <literal><![CDATA[
      (x * T(x,T(x \ 1,y))) * (z / u) = (((1 / x) \ x) * z) / u
    ]]></literal>
    <justification jstring="[para(1134(a,1),29182(a,2,1,1))].">
      <j1 rule="para" parents="1134 29182"/>
    </justification>
  </clause>

  <clause id="29417">
    <literal><![CDATA[
      (x * T(x,T(x \ 1,y))) * (z / u) = (x * ((x \ 1) \ z)) / u
    ]]></literal>
    <justification jstring="[para(1175(a,1),29416(a,2,1))].">
      <j1 rule="para" parents="1175 29416"/>
    </justification>
  </clause>

  <clause id="29418">
    <literal><![CDATA[
      (x * ((x \ 1) \ 1)) * (y / z) = (x * ((x \ 1) \ y)) / z
    ]]></literal>
    <justification jstring="[para(4089(a,1),29417(a,1,1,2))].">
      <j1 rule="para" parents="4089 29417"/>
    </justification>
  </clause>

  <clause id="29419">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) / z = ((1 / x) \ x) * (y / z)
    ]]></literal>
    <justification jstring="[para(1134(a,1),29418(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1134 29418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29420">
    <literal><![CDATA[
      (x * ((x \ 1) \ y)) / z = x * ((x \ 1) \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,1175,a(flip),b,29419,a),flip(a)].">
      <j1 rule="hyper" parents="373 1175 29419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29421">
    <literal><![CDATA[
      L(x,y,L(z \ L(z,u,w),v5,v6)) = L(x,y,L(z * L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,29212,a(flip),b,29213,a)].">
      <j1 rule="hyper" parents="64 29212 29213"/>
    </justification>
  </clause>

  <clause id="29422">
    <literal><![CDATA[
      L(x,y,z * ((((1 / u) \ 1) \ w) \ v5)) = L(x,y,z * (((w / (u * w)) * w) \ v5))
    ]]></literal>
    <justification jstring="[para(2014(a,1),29243(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="2014 29243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29423">
    <literal><![CDATA[
      (((x \ y) * y) * (y \ x)) \ ((x \ y) * y) = y \ (y / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,177,a(flip),b,29381,a),flip(a)].">
      <j1 rule="hyper" parents="373 177 29381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29424">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ ((x * K(y,z)) * (u * w)) = L(w,u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,28973,a(flip),b,24457,a),flip(a)].">
      <j1 rule="hyper" parents="373 28973 24457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29426">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * (K(y,z) * (u * w))) = L(w,u,x)
    ]]></literal>
    <justification jstring="[para(23256(a,1),29424(a,1,2))].">
      <j1 rule="para" parents="23256 29424"/>
    </justification>
  </clause>

  <clause id="29429">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,23238,a(flip),b,29426,a)].">
      <j1 rule="hyper" parents="64 23238 29426"/>
    </justification>
  </clause>

  <clause id="29430">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) = L(x,u,T(w,v5))
    ]]></literal>
    <justification jstring="[hyper(23856,a,29429,a)].">
      <j1 rule="hyper" parents="23856 29429"/>
    </justification>
  </clause>

  <clause id="29434">
    <literal><![CDATA[
      L(x,T(y,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(1886(a,2),29429(a,1,2))].">
      <j1 rule="para" parents="1886 29429"/>
    </justification>
  </clause>

  <clause id="29435">
    <literal><![CDATA[
      L(x,y * K(z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(3994(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="3994 29429"/>
    </justification>
  </clause>

  <clause id="29436">
    <literal><![CDATA[
      L(x,y * z,u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(5796(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="5796 29429"/>
    </justification>
  </clause>

  <clause id="29437">
    <literal><![CDATA[
      L(x,y / z,u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(5720(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="5720 29429"/>
    </justification>
  </clause>

  <clause id="29438">
    <literal><![CDATA[
      L(x,T(y,z) * u,w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(5755(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="5755 29429"/>
    </justification>
  </clause>

  <clause id="29439">
    <literal><![CDATA[
      L(x,y * (z / y),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5781(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="5781 29429"/>
    </justification>
  </clause>

  <clause id="29440">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(5842(a,2),29429(a,1,2))].">
      <j1 rule="para" parents="5842 29429"/>
    </justification>
  </clause>

  <clause id="29441">
    <literal><![CDATA[
      L(x,(y \ z) * y,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5919(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="5919 29429"/>
    </justification>
  </clause>

  <clause id="29442">
    <literal><![CDATA[
      L(x,T(y,z) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(6075(a,1),29429(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6075 29429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29443">
    <literal><![CDATA[
      L(x,(y / z) * u,w) = L(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(5982(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="5982 29429"/>
    </justification>
  </clause>

  <clause id="29444">
    <literal><![CDATA[
      L(x,((y \ z) \ z) * u,w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(6025(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="6025 29429"/>
    </justification>
  </clause>

  <clause id="29445">
    <literal><![CDATA[
      L(x,(y / z) \ u,w) = L(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),29429(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 29429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29446">
    <literal><![CDATA[
      L(x,y \ (z / y),u) = L(x,y \ (y \ z),u)
    ]]></literal>
    <justification jstring="[para(6277(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="6277 29429"/>
    </justification>
  </clause>

  <clause id="29447">
    <literal><![CDATA[
      L(x,y * T(z,u),w) = L(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(6367(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="6367 29429"/>
    </justification>
  </clause>

  <clause id="29449">
    <literal><![CDATA[
      L(x,y * K(z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(6823(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="6823 29429"/>
    </justification>
  </clause>

  <clause id="29450">
    <literal><![CDATA[
      L(x,y \ T(z,u),w) = L(x,y \ z,w)
    ]]></literal>
    <justification jstring="[para(6417(a,1),29429(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6417 29429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29453">
    <literal><![CDATA[
      L(x,y * (K(z,u) * w),v5) = L(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(10720(a,1),29429(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10720 29429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29454">
    <literal><![CDATA[
      L(x,(y * z) \ u,w) = L(x,(z * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(10833(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="10833 29429"/>
    </justification>
  </clause>

  <clause id="29455">
    <literal><![CDATA[
      L(x,(y * z) * u,w) = L(x,(z * y) * u,w)
    ]]></literal>
    <justification jstring="[para(10834(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="10834 29429"/>
    </justification>
  </clause>

  <clause id="29457">
    <literal><![CDATA[
      L(x,(T(y,z) * u) * w,v5) = L(x,(y * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(15613(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="15613 29429"/>
    </justification>
  </clause>

  <clause id="29458">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),v5) = L(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(22758(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="22758 29429"/>
    </justification>
  </clause>

  <clause id="29460">
    <literal><![CDATA[
      L(x,(T(y,z) \ u) * w,v5) = L(x,(y \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(24347(a,1),29429(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24347 29429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29462">
    <literal><![CDATA[
      L(x,((y * z) \ u) * w,v5) = L(x,((z * y) \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(23247(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="23247 29429"/>
    </justification>
  </clause>

  <clause id="29463">
    <literal><![CDATA[
      L(x,L(T(y,z),u,w) \ v5,v6) = L(x,L(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(24557(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="24557 29429"/>
    </justification>
  </clause>

  <clause id="29464">
    <literal><![CDATA[
      L(x,R(T(y,z),u,w) \ v5,v6) = L(x,R(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(24564(a,1),29429(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24564 29429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29465">
    <literal><![CDATA[
      L(x,L(T(y,z),u,w) * v5,v6) = L(x,L(y,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(24680(a,1),29429(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24680 29429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29466">
    <literal><![CDATA[
      L(x,(T(y,z) \ u) \ w,v5) = L(x,(y \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(25410(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="25410 29429"/>
    </justification>
  </clause>

  <clause id="29468">
    <literal><![CDATA[
      L(x,(y * (K(z,u) * w)) * v5,v6) = L(x,(y * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(24368(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="24368 29429"/>
    </justification>
  </clause>

  <clause id="29469">
    <literal><![CDATA[
      L(x,(y * (z / u)) \ w,v5) = L(x,(y * (u \ z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(24507(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="24507 29429"/>
    </justification>
  </clause>

  <clause id="29470">
    <literal><![CDATA[
      L(x,(y \ (K(z,u) * w)) \ v5,v6) = L(x,(y \ w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(25412(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="25412 29429"/>
    </justification>
  </clause>

  <clause id="29471">
    <literal><![CDATA[
      L(x,L(K(y,z) * u,w,v5),v6) = L(x,L(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(26085(a,2),29429(a,1,2))].">
      <j1 rule="para" parents="26085 29429"/>
    </justification>
  </clause>

  <clause id="29472">
    <literal><![CDATA[
      L(x,L(T(y,z) * u,w,v5),v6) = L(x,L(y * u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(26086(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="26086 29429"/>
    </justification>
  </clause>

  <clause id="29473">
    <literal><![CDATA[
      L(x,L(T(y,z) \ u,w,v5),v6) = L(x,L(y \ u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(26100(a,1),29429(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26100 29429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29474">
    <literal><![CDATA[
      L(x,L(y * z,u,w) * v5,v6) = L(x,L(z * y,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(26140(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="26140 29429"/>
    </justification>
  </clause>

  <clause id="29475">
    <literal><![CDATA[
      L(x,L(y / z,u,w) * v5,v6) = L(x,L(z \ y,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(25447(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="25447 29429"/>
    </justification>
  </clause>

  <clause id="29476">
    <literal><![CDATA[
      L(x,(y * z) \ ((z * u) * y),w) = L(x,L(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(27292(a,2),29429(a,1,2)),flip(a)].">
      <j1 rule="para" parents="27292 29429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29477">
    <literal><![CDATA[
      L(x,(y * (z \ (u / w))) \ v5,v6) = L(x,(y * (z \ (w \ u))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(25421(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="25421 29429"/>
    </justification>
  </clause>

  <clause id="29478">
    <literal><![CDATA[
      L(x,T(y,z),u) = L(x,y,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(23856,a,29434,a)].">
      <j1 rule="hyper" parents="23856 29434"/>
    </justification>
  </clause>

  <clause id="29491">
    <literal><![CDATA[
      (x * T(y,z)) \ ((T(y,z) * z) * x) = L(z * K(z * y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,15145,a,b,29434,a)].">
      <j1 rule="hyper" parents="64 15145 29434"/>
    </justification>
  </clause>

  <clause id="29492">
    <literal><![CDATA[
      L(T(x,y),x,L(z,T(x,y),T(x,y))) = L(T(x,y),T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29195,a(flip),b,29434,a),flip(a)].">
      <j1 rule="hyper" parents="64 29195 29434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29493">
    <literal><![CDATA[
      L(x,y \ (z * y),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(22(a,1),29434(a,1,2))].">
      <j1 rule="para" parents="22 29434"/>
    </justification>
  </clause>

  <clause id="29495">
    <literal><![CDATA[
      L(x,L(y / z,u,w),v5) = L(x,L(z \ y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(279(a,1),29434(a,1,2)),flip(a)].">
      <j1 rule="para" parents="279 29434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29496">
    <literal><![CDATA[
      L(x,y \ (z * (y * y)),u) = L(x,z * L(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(2848(a,1),29434(a,1,2))].">
      <j1 rule="para" parents="2848 29434"/>
    </justification>
  </clause>

  <clause id="29503">
    <literal><![CDATA[
      L(x,R(y,y,z * y),u) = L(x,R(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(26296(a,1),29434(a,1,2))].">
      <j1 rule="para" parents="26296 29434"/>
    </justification>
  </clause>

  <clause id="29505">
    <literal><![CDATA[
      R(x,T(y,z),L(T(u,w),u,u * v5)) = R(x,y,L(u,u,v5))
    ]]></literal>
    <justification jstring="[para(29434(a,1),29043(a,1,3))].">
      <j1 rule="para" parents="29434 29043"/>
    </justification>
  </clause>

  <clause id="29507">
    <literal><![CDATA[
      L(x,y * z,u * w) = L(x,z * y,w * u)
    ]]></literal>
    <justification jstring="[hyper(24201,a,29436,a)].">
      <j1 rule="hyper" parents="24201 29436"/>
    </justification>
  </clause>

  <clause id="29508">
    <literal><![CDATA[
      L(x,(y * z) * y,u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(11888,a,29436,a),flip(a)].">
      <j1 rule="hyper" parents="11888 29436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29509">
    <literal><![CDATA[
      L(x,y * (z * z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(11886,a,29436,a),flip(a)].">
      <j1 rule="hyper" parents="11886 29436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29510">
    <literal><![CDATA[
      L((x * y) \ z,y * x,x * y) = (1 / (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(742,a,29436,a),flip(a)].">
      <j1 rule="hyper" parents="742 29436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29512">
    <literal><![CDATA[
      L(x,K(y,z) * (u * w),v5) = L(x,w * u,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29429,a,b,29436,a)].">
      <j1 rule="hyper" parents="373 29429 29436"/>
    </justification>
  </clause>

  <clause id="29513">
    <literal><![CDATA[
      L(x,y * z,a(u,w,w)) = L(x,z * y,a(w,w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,29287,a,b,29436,a)].">
      <j1 rule="hyper" parents="373 29287 29436"/>
    </justification>
  </clause>

  <clause id="29514">
    <literal><![CDATA[
      L(L(x,y * z,u),w,K(v5,v6)) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23115,a,b,29436,a)].">
      <j1 rule="hyper" parents="373 23115 29436"/>
    </justification>
  </clause>

  <clause id="29515">
    <literal><![CDATA[
      L(x,(y \ 1) * z,u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11864,a,b,29436,a)].">
      <j1 rule="hyper" parents="373 11864 29436"/>
    </justification>
  </clause>

  <clause id="29516">
    <literal><![CDATA[
      L(x,((y * y) \ z) * u,w) = L(x,u * z,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11779,a,b,29436,a)].">
      <j1 rule="hyper" parents="373 11779 29436"/>
    </justification>
  </clause>

  <clause id="29517">
    <literal><![CDATA[
      L(x,y * (((z \ 1) * u) * w),v5) = L(x,((z * u) * w) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,11948,a(flip),b,29436,a),flip(a)].">
      <j1 rule="hyper" parents="373 11948 29436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29518">
    <literal><![CDATA[
      L(x,y * (((1 / z) * u) * w),v5) = L(x,((z * u) * w) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,11929,a(flip),b,29436,a),flip(a)].">
      <j1 rule="hyper" parents="373 11929 29436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29519">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * u),w) = L(x,(z * u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11918,a(flip),b,29436,a),flip(a)].">
      <j1 rule="hyper" parents="373 11918 29436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29520">
    <literal><![CDATA[
      L(x,y * (z \ 1),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11864,a(flip),b,29436,a),flip(a)].">
      <j1 rule="hyper" parents="373 11864 29436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29523">
    <literal><![CDATA[
      L(x,y * R(z,z,y),u) = L(x,(1 / z) \ y,u)
    ]]></literal>
    <justification jstring="[para(1913(a,1),29436(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1913 29436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29524">
    <literal><![CDATA[
      L(x,L(y,z,z) * (z \ y),u) = L(x,((z \ 1) * y) * y,u)
    ]]></literal>
    <justification jstring="[para(25769(a,1),29436(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25769 29436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29525">
    <literal><![CDATA[
      L(x,(y * T(y,z)) * (u * w),v5) = L(x,w * ((y * T(y,z)) * u),v5)
    ]]></literal>
    <justification jstring="[para(29044(a,1),29436(a,1,2))].">
      <j1 rule="para" parents="29044 29436"/>
    </justification>
  </clause>

  <clause id="29526">
    <literal><![CDATA[
      L(x,(y / z) \ 1,u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(11854,a,29437,a)].">
      <j1 rule="hyper" parents="11854 29437"/>
    </justification>
  </clause>

  <clause id="29527">
    <literal><![CDATA[
      L(x,y / z,u / w) = L(x,z \ y,w \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23216,a(flip),b,29437,a),flip(a)].">
      <j1 rule="hyper" parents="373 23216 29437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29528">
    <literal><![CDATA[
      L(x,y / (z * z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11775,a(flip),b,29437,a),flip(a)].">
      <j1 rule="hyper" parents="373 11775 29437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29529">
    <literal><![CDATA[
      x * L(y,z / u,w) = x * L(y,u \ z,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,29437,a,b,9,a)].">
      <j1 rule="hyper" parents="145 29437 9"/>
    </justification>
  </clause>

  <clause id="29530">
    <literal><![CDATA[
      L(x,T(y / z,u),w) = L(x,z \ y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29434,a,b,29437,a)].">
      <j1 rule="hyper" parents="64 29434 29437"/>
    </justification>
  </clause>

  <clause id="29531">
    <literal><![CDATA[
      L((x / y) \ z,y \ x,u) = (u * (x / y)) \ (u * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,29437,a),flip(a)].">
      <j1 rule="hyper" parents="64 102 29437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29533">
    <literal><![CDATA[
      (x \ R(x,x,y)) * L(z,y \ (x \ y),x) = x * (((x \ y) / y) * z)
    ]]></literal>
    <justification jstring="[para(29437(a,1),3014(a,1,2))].">
      <j1 rule="para" parents="29437 3014"/>
    </justification>
  </clause>

  <clause id="29534">
    <literal><![CDATA[
      L(x,(y * z) \ ((u * z) * y),w) = L(x,R(u * K(z,y),z,y),w)
    ]]></literal>
    <justification jstring="[para(10304(a,1),29437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10304 29437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29541">
    <literal><![CDATA[
      L(x,L(y * z,u,w),v5) = L(x,L(z * y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(5545(a,1),29441(a,1,2))].">
      <j1 rule="para" parents="5545 29441"/>
    </justification>
  </clause>

  <clause id="29547">
    <literal><![CDATA[
      L(x,y * (z / u),w) = L(x,y * (u \ z),w)
    ]]></literal>
    <justification jstring="[para(6471(a,1),29449(a,1,2))].">
      <j1 rule="para" parents="6471 29449"/>
    </justification>
  </clause>

  <clause id="29548">
    <literal><![CDATA[
      L(x,y * (z * u),w) = L(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(7591(a,1),29449(a,1,2))].">
      <j1 rule="para" parents="7591 29449"/>
    </justification>
  </clause>

  <clause id="29549">
    <literal><![CDATA[
      L(x,y * ((z \ u) * z),w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(10196(a,1),29449(a,1,2))].">
      <j1 rule="para" parents="10196 29449"/>
    </justification>
  </clause>

  <clause id="29551">
    <literal><![CDATA[
      L(x,y * (z * K(u,w)),v5) = L(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(12078(a,1),29449(a,1,2))].">
      <j1 rule="para" parents="12078 29449"/>
    </justification>
  </clause>

  <clause id="29552">
    <literal><![CDATA[
      L(x,y \ (z / u),w) = L(x,y \ (u \ z),w)
    ]]></literal>
    <justification jstring="[para(15028(a,1),29449(a,1,2))].">
      <j1 rule="para" parents="15028 29449"/>
    </justification>
  </clause>

  <clause id="29553">
    <literal><![CDATA[
      L(x,y \ ((z \ u) \ u),w) = L(x,y \ z,w)
    ]]></literal>
    <justification jstring="[para(15035(a,2),29449(a,1,2))].">
      <j1 rule="para" parents="15035 29449"/>
    </justification>
  </clause>

  <clause id="29554">
    <literal><![CDATA[
      L(x,y \ (z * u),w) = L(x,y \ (u * z),w)
    ]]></literal>
    <justification jstring="[para(14934(a,1),29449(a,1,2))].">
      <j1 rule="para" parents="14934 29449"/>
    </justification>
  </clause>

  <clause id="29556">
    <literal><![CDATA[
      L(x,y \ (z * K(u,w)),v5) = L(x,y \ z,v5)
    ]]></literal>
    <justification jstring="[para(16164(a,1),29449(a,1,2))].">
      <j1 rule="para" parents="16164 29449"/>
    </justification>
  </clause>

  <clause id="29557">
    <literal><![CDATA[
      L(x,y \ (T(z,u) * w),v5) = L(x,y \ (z * w),v5)
    ]]></literal>
    <justification jstring="[para(24312(a,1),29449(a,1,2))].">
      <j1 rule="para" parents="24312 29449"/>
    </justification>
  </clause>

  <clause id="29558">
    <literal><![CDATA[
      L(x,y \ (z \ (u * (w / u))),v5) = L(x,y \ (z \ w),v5)
    ]]></literal>
    <justification jstring="[para(24305(a,1),29449(a,1,2))].">
      <j1 rule="para" parents="24305 29449"/>
    </justification>
  </clause>

  <clause id="29559">
    <literal><![CDATA[
      L(x,y \ (z \ (u / w)),v5) = L(x,y \ (z \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(24307(a,1),29449(a,1,2))].">
      <j1 rule="para" parents="24307 29449"/>
    </justification>
  </clause>

  <clause id="29560">
    <literal><![CDATA[
      L(x,y \ (z / (u / w)),v5) = L(x,y \ (z / (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(24313(a,1),29449(a,1,2))].">
      <j1 rule="para" parents="24313 29449"/>
    </justification>
  </clause>

  <clause id="29561">
    <literal><![CDATA[
      L(x,y \ (z * (u / w)),v5) = L(x,y \ (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(24314(a,1),29449(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24314 29449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29563">
    <literal><![CDATA[
      L(x,R(y * K(z,u),w,v5),v6) = L(x,R(y,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(25973(a,2),29449(a,1,2))].">
      <j1 rule="para" parents="25973 29449"/>
    </justification>
  </clause>

  <clause id="29565">
    <literal><![CDATA[
      L(x,T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(29478(a,2),11765(a,1))].">
      <j1 rule="para" parents="29478 11765"/>
    </justification>
  </clause>

  <clause id="29568">
    <literal><![CDATA[
      (x * (y * (z * z))) \ (x * (y * u)) = L((z * z) \ u,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2291,a(flip),b,29509,a)].">
      <j1 rule="hyper" parents="64 2291 29509"/>
    </justification>
  </clause>

  <clause id="29569">
    <literal><![CDATA[
      (x * ((y * y) \ z)) * L(u,x,z) = z * (T(x / (y * y),z) * u)
    ]]></literal>
    <justification jstring="[para(29528(a,1),11000(a,1,2))].">
      <j1 rule="para" parents="29528 11000"/>
    </justification>
  </clause>

  <clause id="29570">
    <literal><![CDATA[
      L(x,L(T(y,z),u,w),v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y,u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(25(a,2),29565(a,1,2))].">
      <j1 rule="para" parents="25 29565"/>
    </justification>
  </clause>

  <clause id="29572">
    <literal><![CDATA[
      L(x,y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(14165(a,1),29565(a,1))].">
      <j1 rule="para" parents="14165 29565"/>
    </justification>
  </clause>

  <clause id="29576">
    <literal><![CDATA[
      L(x,K(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(29430(a,2),11765(a,1))].">
      <j1 rule="para" parents="29430 11765"/>
    </justification>
  </clause>

  <clause id="29577">
    <literal><![CDATA[
      L(x,T(y * y,z) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11772,a(flip),b,29438,a),flip(a)].">
      <j1 rule="hyper" parents="373 11772 29438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29578">
    <literal><![CDATA[
      L(x,y * T(z,u),w) = L(x,z * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29436,a,b,29438,a)].">
      <j1 rule="hyper" parents="64 29436 29438"/>
    </justification>
  </clause>

  <clause id="29581">
    <literal><![CDATA[
      L(x,y / T(z,u),w) = L(x,z \ y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29437,a,b,29442,a)].">
      <j1 rule="hyper" parents="64 29437 29442"/>
    </justification>
  </clause>

  <clause id="29582">
    <literal><![CDATA[
      L(x,R(y,z,y) \ 1,L(R(y,z,y) \ 1,y,z)) = L(x,(y * z) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14232,a,b,29442,a)].">
      <j1 rule="hyper" parents="64 14232 29442"/>
    </justification>
  </clause>

  <clause id="29583">
    <literal><![CDATA[
      L(x,T(y * z,u) \ (y * ((w * w) * (z * v5))),v6) = L(x,L(T(w * w,z) * v5,z,y),v6)
    ]]></literal>
    <justification jstring="[para(6651(a,1),29442(a,2,2))].">
      <j1 rule="para" parents="6651 29442"/>
    </justification>
  </clause>

  <clause id="29588">
    <literal><![CDATA[
      L(x,T(y,z) / u,w) = L(x,u \ y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29437,a,b,29450,a)].">
      <j1 rule="hyper" parents="64 29437 29450"/>
    </justification>
  </clause>

  <clause id="29589">
    <literal><![CDATA[
      (x * T(y,z)) / L(u,u \ y,x) = x * (T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(225,a,29450,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 29450 10262"/>
    </justification>
  </clause>

  <clause id="29591">
    <literal><![CDATA[
      L(x,y \ R(z / u,w,v5),v6) = L(x,y \ R(u \ z,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(280(a,1),29450(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="280 29450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29592">
    <literal><![CDATA[
      L(x,y \ R(z / u,u,w),v5) = L(x,y \ ((u * w) \ (z * w)),v5)
    ]]></literal>
    <justification jstring="[para(681(a,1),29450(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="681 29450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29594">
    <literal><![CDATA[
      L(x,y \ (((z \ 1) \ u) * K(w,v5)),v6) = L(x,y \ (u / (z \ K(v5,w))),v6)
    ]]></literal>
    <justification jstring="[para(24940(a,1),29450(a,1,2,2))].">
      <j1 rule="para" parents="24940 29450"/>
    </justification>
  </clause>

  <clause id="29595">
    <literal><![CDATA[
      L(x,y * (z \ 1),u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29436,a,b,29515,a)].">
      <j1 rule="hyper" parents="64 29436 29515"/>
    </justification>
  </clause>

  <clause id="29596">
    <literal><![CDATA[
      L(x,L(y \ z,y,y),u) = L(x,z * (y \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11837,a,b,29520,a)].">
      <j1 rule="hyper" parents="373 11837 29520"/>
    </justification>
  </clause>

  <clause id="29597">
    <literal><![CDATA[
      R(x,y,y) \ (((x * (1 / y)) \ R(x,y,y)) * z) = L((y \ R(x,y,y)) \ z,y * x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,12524,a,b,29520,a)].">
      <j1 rule="hyper" parents="64 12524 29520"/>
    </justification>
  </clause>

  <clause id="29598">
    <literal><![CDATA[
      L(L(x,x,y),x * (y \ 1),y) = (y * ((y \ 1) * (1 / x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,12025,a(flip),b,29520,a),flip(a)].">
      <j1 rule="hyper" parents="64 12025 29520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29599">
    <literal><![CDATA[
      L(((x \ 1) * (y \ 1)) \ z,y * x,x) = L(y \ 1,x,x) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1870,a(flip),b,29520,a),flip(a)].">
      <j1 rule="hyper" parents="64 1870 29520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29602">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * u) * z),w) = L(x,R(u,y,z),w)
    ]]></literal>
    <justification jstring="[para(1039(a,2),29530(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1039 29530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29603">
    <literal><![CDATA[
      L(x,(y * z) \ z,u) = L(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[para(5144(a,1),29530(a,1,2))].">
      <j1 rule="para" parents="5144 29530"/>
    </justification>
  </clause>

  <clause id="29604">
    <literal><![CDATA[
      L(x,y \ ((z * z) * u),w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(6431(a,1),29577(a,1,2))].">
      <j1 rule="para" parents="6431 29577"/>
    </justification>
  </clause>

  <clause id="29605">
    <literal><![CDATA[
      L(x,(y \ ((z * z) * u)) * w,v5) = L(x,(y \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(6627(a,1),29577(a,1,2))].">
      <j1 rule="para" parents="6627 29577"/>
    </justification>
  </clause>

  <clause id="29606">
    <literal><![CDATA[
      L(x,(y / z) * u,w) = L(x,u * (z \ y),w)
    ]]></literal>
    <justification jstring="[para(117(a,1),29578(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 29578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29609">
    <literal><![CDATA[
      L(x,y * (1 / z),u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5322,a,b,29595,a)].">
      <j1 rule="hyper" parents="64 5322 29595"/>
    </justification>
  </clause>

  <clause id="29610">
    <literal><![CDATA[
      L(x,R(y,z,u) \ y,w) = L(x,y * R(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(1909(a,1),29595(a,1,2))].">
      <j1 rule="para" parents="1909 29595"/>
    </justification>
  </clause>

  <clause id="29611">
    <literal><![CDATA[
      L(x,(y \ z) \ ((1 / y) * z),u) = L(x,((1 / y) * z) * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(1975(a,1),29595(a,1,2))].">
      <j1 rule="para" parents="1975 29595"/>
    </justification>
  </clause>

  <clause id="29612">
    <literal><![CDATA[
      L(x,y * (L(z,u,w) \ z),v5) = L(x,y * (z \ L(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(5658(a,1),29595(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5658 29595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29613">
    <literal><![CDATA[
      L(x,y * (1 / z),u * (w \ 1)) = L(x,y * z,u * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,24659,a(flip),b,29609,a),flip(a)].">
      <j1 rule="hyper" parents="373 24659 29609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29614">
    <literal><![CDATA[
      L(x,L(y * z,y,y),u) = L(x,L(z,y,y) * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11780,a(flip),b,29508,a),flip(a)].">
      <j1 rule="hyper" parents="64 11780 29508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29615">
    <literal><![CDATA[
      L(x,(y \ 1) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(29515(a,2),29572(a,1))].">
      <j1 rule="para" parents="29515 29572"/>
    </justification>
  </clause>

  <clause id="29616">
    <literal><![CDATA[
      L(x,y * (z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(29595(a,2),29572(a,1))].">
      <j1 rule="para" parents="29595 29572"/>
    </justification>
  </clause>

  <clause id="29617">
    <literal><![CDATA[
      L(x,y / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ y,u) = w
    ]]></literal>
    <justification jstring="[para(5720(a,1),29576(a,1,2))].">
      <j1 rule="para" parents="5720 29576"/>
    </justification>
  </clause>

  <clause id="29619">
    <literal><![CDATA[
      L(x,(y \ z) * u,w) = L(x,u * (z / y),w)
    ]]></literal>
    <justification jstring="[hyper(29572,a,29443,a),flip(a)].">
      <j1 rule="hyper" parents="29572 29443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29620">
    <literal><![CDATA[
      L(x,T(y / z,u) * w,v5) = L(x,(z \ y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29438,a,b,29443,a)].">
      <j1 rule="hyper" parents="64 29438 29443"/>
    </justification>
  </clause>

  <clause id="29621">
    <literal><![CDATA[
      L(x,(y / ((z * T(z,u)) \ w)) * v5,v6) = L(x,(w \ ((z * T(z,u)) * y)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(29045(a,1),29443(a,2,2,1))].">
      <j1 rule="para" parents="29045 29443"/>
    </justification>
  </clause>

  <clause id="29622">
    <literal><![CDATA[
      L(x,((y \ z) \ z) * u,w) = L(x,u * y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29436,a,b,29444,a),flip(a)].">
      <j1 rule="hyper" parents="373 29436 29444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29623">
    <literal><![CDATA[
      L(x,y * (K(z,u) * w),v5) = L(x,w * y,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29436,a,b,29453,a),flip(a)].">
      <j1 rule="hyper" parents="373 29436 29453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29624">
    <literal><![CDATA[
      L(x,y * (T(z,u) * w),v5) = L(x,y * (z * w),v5)
    ]]></literal>
    <justification jstring="[para(5755(a,1),29453(a,1,2,2))].">
      <j1 rule="para" parents="5755 29453"/>
    </justification>
  </clause>

  <clause id="29625">
    <literal><![CDATA[
      L(x,y * (T(z,u) \ w),v5) = L(x,y * (z \ w),v5)
    ]]></literal>
    <justification jstring="[para(6075(a,1),29453(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6075 29453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29626">
    <literal><![CDATA[
      L(x,y * ((z / u) * w),v5) = L(x,y * ((u \ z) * w),v5)
    ]]></literal>
    <justification jstring="[para(5982(a,1),29453(a,1,2,2))].">
      <j1 rule="para" parents="5982 29453"/>
    </justification>
  </clause>

  <clause id="29627">
    <literal><![CDATA[
      L(x,y * ((z / u) \ w),v5) = L(x,y * ((u \ z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(6270(a,1),29453(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6270 29453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29628">
    <literal><![CDATA[
      L(x,y * ((z * u) \ w),v5) = L(x,y * ((u * z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(10833(a,1),29453(a,1,2,2))].">
      <j1 rule="para" parents="10833 29453"/>
    </justification>
  </clause>

  <clause id="29629">
    <literal><![CDATA[
      L(x,(y \ T(z,u)) * w,v5) = L(x,(y \ z) * w,v5)
    ]]></literal>
    <justification jstring="[para(24474(a,1),29453(a,1,2))].">
      <j1 rule="para" parents="24474 29453"/>
    </justification>
  </clause>

  <clause id="29630">
    <literal><![CDATA[
      L(x,y * ((z * T(u,w)) \ v5),v6) = L(x,y * ((z * u) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(24506(a,1),29453(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="24506 29453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29631">
    <literal><![CDATA[
      L(x,y * ((K(z,u) / w) \ v5),v6) = L(x,y * ((1 / w) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(24929(a,1),29453(a,1,2,2))].">
      <j1 rule="para" parents="24929 29453"/>
    </justification>
  </clause>

  <clause id="29632">
    <literal><![CDATA[
      L(x,(y * (z * (u / z))) * w,v5) = L(x,(y * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(24471(a,1),29453(a,1,2))].">
      <j1 rule="para" parents="24471 29453"/>
    </justification>
  </clause>

  <clause id="29633">
    <literal><![CDATA[
      L(x,(y \ (z / u)) * w,v5) = L(x,(y \ (u \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(24475(a,1),29453(a,1,2))].">
      <j1 rule="para" parents="24475 29453"/>
    </justification>
  </clause>

  <clause id="29634">
    <literal><![CDATA[
      L(x,(y \ (K(z,u) * w)) * v5,v6) = L(x,(y \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(24778(a,1),29453(a,1,2))].">
      <j1 rule="para" parents="24778 29453"/>
    </justification>
  </clause>

  <clause id="29637">
    <literal><![CDATA[
      L(x,(y * z) * u,w) = L(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[hyper(29572,a,29455,a),flip(a)].">
      <j1 rule="hyper" parents="29572 29455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29638">
    <literal><![CDATA[
      L(x,T(y * z,u) * w,v5) = L(x,(z * y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29438,a,b,29455,a)].">
      <j1 rule="hyper" parents="373 29438 29455"/>
    </justification>
  </clause>

  <clause id="29639">
    <literal><![CDATA[
      L(x,(y * z) * u,(w * v5) * v6) = L(x,(z * y) * u,v6 * (v5 * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,29105,a,b,29455,a)].">
      <j1 rule="hyper" parents="373 29105 29455"/>
    </justification>
  </clause>

  <clause id="29641">
    <literal><![CDATA[
      L(x,(y * z) * z,u) = L(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29508,a(flip),b,29455,a),flip(a)].">
      <j1 rule="hyper" parents="373 29508 29455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29642">
    <literal><![CDATA[
      L(x,(y * ((z \ 1) * u)) * w,v5) = L(x,((z * u) * y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,11948,a(flip),b,29455,a),flip(a)].">
      <j1 rule="hyper" parents="373 11948 29455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29643">
    <literal><![CDATA[
      L(x,(y * (z \ 1)) * u,w) = L(x,(z * y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11918,a(flip),b,29455,a),flip(a)].">
      <j1 rule="hyper" parents="373 11918 29455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29644">
    <literal><![CDATA[
      L(x,(y * R(1 / z,u,w)) * v5,v6) = L(x,(R(z,u,w) * y) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,11784,a(flip),b,29455,a),flip(a)].">
      <j1 rule="hyper" parents="373 11784 29455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29645">
    <literal><![CDATA[
      L(x,(y * ((z * z) \ u)) * w,v5) = L(x,(u * y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,11781,a(flip),b,29455,a),flip(a)].">
      <j1 rule="hyper" parents="373 11781 29455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29646">
    <literal><![CDATA[
      L(x,((y * z) * y) * u,w) = L(x,L(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11780,a(flip),b,29455,a),flip(a)].">
      <j1 rule="hyper" parents="373 11780 29455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29647">
    <literal><![CDATA[
      L(x,(y * T(z,u)) * ((w \ T(z,u)) \ v5),v6) = L(x,(z * y) * ((w \ z) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(24980(a,2),29455(a,1,2))].">
      <j1 rule="para" parents="24980 29455"/>
    </justification>
  </clause>

  <clause id="29648">
    <literal><![CDATA[
      L(x,y * (z * y),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(29572,a,29641,a)].">
      <j1 rule="hyper" parents="29572 29641"/>
    </justification>
  </clause>

  <clause id="29649">
    <literal><![CDATA[
      L(x,(y * z) * T(z,u),w) = L(x,L(y,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29447,a,b,29641,a)].">
      <j1 rule="hyper" parents="64 29447 29641"/>
    </justification>
  </clause>

  <clause id="29650">
    <literal><![CDATA[
      L(x,R(((1 / y) * z) * y,u,w) * y,v5) = L(x,L((1 / y) * R(z,u,w),y,y),v5)
    ]]></literal>
    <justification jstring="[para(1819(a,2),29641(a,1,2,1))].">
      <j1 rule="para" parents="1819 29641"/>
    </justification>
  </clause>

  <clause id="29651">
    <literal><![CDATA[
      L(x,L(((1 / y) * z) * y,u,w) * y,v5) = L(x,L((1 / y) * L(z,u,w),y,y),v5)
    ]]></literal>
    <justification jstring="[para(27961(a,2),29641(a,1,2,1))].">
      <j1 rule="para" parents="27961 29641"/>
    </justification>
  </clause>

  <clause id="29652">
    <literal><![CDATA[
      L(x,(y * z) \ (K(u,w) * v5),v6) = L(x,(z * y) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29454,a,b,29458,a),flip(a)].">
      <j1 rule="hyper" parents="373 29454 29458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29653">
    <literal><![CDATA[
      L(x,y \ K(z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11867,a(flip),b,29458,a),flip(a)].">
      <j1 rule="hyper" parents="64 11867 29458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29654">
    <literal><![CDATA[
      L(x,y \ (T(z,u) \ w),v5) = L(x,y \ (z \ w),v5)
    ]]></literal>
    <justification jstring="[para(6075(a,1),29458(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6075 29458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29655">
    <literal><![CDATA[
      L(x,y \ ((z / u) * w),v5) = L(x,y \ ((u \ z) * w),v5)
    ]]></literal>
    <justification jstring="[para(5982(a,1),29458(a,1,2,2))].">
      <j1 rule="para" parents="5982 29458"/>
    </justification>
  </clause>

  <clause id="29656">
    <literal><![CDATA[
      L(x,y \ ((z / u) \ w),v5) = L(x,y \ ((u \ z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(6270(a,1),29458(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6270 29458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29657">
    <literal><![CDATA[
      L(x,y \ (z * (K(u,w) * v5)),v6) = L(x,y \ (z * v5),v6)
    ]]></literal>
    <justification jstring="[para(10720(a,1),29458(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10720 29458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29658">
    <literal><![CDATA[
      L(x,y \ ((z * u) * w),v5) = L(x,y \ ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[para(10834(a,1),29458(a,1,2,2))].">
      <j1 rule="para" parents="10834 29458"/>
    </justification>
  </clause>

  <clause id="29659">
    <literal><![CDATA[
      L(x,y \ (((z / u) * w) * v5),v6) = L(x,y \ (((u \ z) * w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(24351(a,1),29458(a,1,2,2))].">
      <j1 rule="para" parents="24351 29458"/>
    </justification>
  </clause>

  <clause id="29660">
    <literal><![CDATA[
      L(x,y \ ((z * (u / w)) \ v5),v6) = L(x,y \ ((z * (w \ u)) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(24507(a,1),29458(a,1,2,2))].">
      <j1 rule="para" parents="24507 29458"/>
    </justification>
  </clause>

  <clause id="29661">
    <literal><![CDATA[
      L(x,y \ ((z * u) \ ((u * w) * z)),v5) = L(x,y \ L(w,u,z),v5)
    ]]></literal>
    <justification jstring="[para(27292(a,2),29458(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="27292 29458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29662">
    <literal><![CDATA[
      (x * (y \ K(z,u))) * L(w,y,x) = x * ((y \ K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(145,a,29653,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 29653 18"/>
    </justification>
  </clause>

  <clause id="29663">
    <literal><![CDATA[
      L(x * y,y * x,y * x) = 1 / (1 / (x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,818,a(flip),b,29507,a),flip(a)].">
      <j1 rule="hyper" parents="373 818 29507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29664">
    <literal><![CDATA[
      L(L(x \ y,x,z),x * z,x * z) = (1 / (z * x)) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,644,a(flip),b,29507,a),flip(a)].">
      <j1 rule="hyper" parents="373 644 29507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29665">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u * w,u * w) = a(a(x,y,z),w * u,w * u)
    ]]></literal>
    <justification jstring="[para(29507(a,1),28791(a,1,2))].">
      <j1 rule="para" parents="29507 28791"/>
    </justification>
  </clause>

  <clause id="29666">
    <literal><![CDATA[
      L(x,((y \ z) * y) * u,w) = L(x,u * z,w)
    ]]></literal>
    <justification jstring="[para(10858(a,1),29512(a,1,2))].">
      <j1 rule="para" parents="10858 29512"/>
    </justification>
  </clause>

  <clause id="29667">
    <literal><![CDATA[
      L(x,((y * z) * u) * w,v5) = L(x,w * ((z * y) * u),v5)
    ]]></literal>
    <justification jstring="[para(24358(a,1),29512(a,1,2))].">
      <j1 rule="para" parents="24358 29512"/>
    </justification>
  </clause>

  <clause id="29668">
    <literal><![CDATA[
      L(x,L(y * z,u,w) * v5,v6) = L(x,v5 * L(z * y,u,w),v6)
    ]]></literal>
    <justification jstring="[para(26140(a,1),29512(a,1,2))].">
      <j1 rule="para" parents="26140 29512"/>
    </justification>
  </clause>

  <clause id="29669">
    <literal><![CDATA[
      L(x,y * ((z * z) \ u),w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[hyper(29572,a,29516,a)].">
      <j1 rule="hyper" parents="29572 29516"/>
    </justification>
  </clause>

  <clause id="29670">
    <literal><![CDATA[
      L(x,(y \ z) * (z * y),u) = L(x,a(z,y,y \ z),u)
    ]]></literal>
    <justification jstring="[para(1281(a,1),29516(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1281 29516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29671">
    <literal><![CDATA[
      L(((x / y) \ 1) \ z,y \ x,y \ x) = (x / y) * z
    ]]></literal>
    <justification jstring="[hyper(1155,a,29527,a),flip(a)].">
      <j1 rule="hyper" parents="1155 29527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29672">
    <literal><![CDATA[
      L(x,y * T(z / u,w),v5) = L(x,y * (u \ z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29447,a,b,29547,a)].">
      <j1 rule="hyper" parents="64 29447 29547"/>
    </justification>
  </clause>

  <clause id="29673">
    <literal><![CDATA[
      L(x,(y * z) * u,x) = L(x,y * (z \ u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13751,a,b,29547,a)].">
      <j1 rule="hyper" parents="64 13751 29547"/>
    </justification>
  </clause>

  <clause id="29674">
    <literal><![CDATA[
      L(x,y * (((z * z) \ u) / (w * (1 / z))),v5) = L(x,y * ((z * T(w,z \ 1)) \ u),v5)
    ]]></literal>
    <justification jstring="[para(3887(a,1),29547(a,2,2,2))].">
      <j1 rule="para" parents="3887 29547"/>
    </justification>
  </clause>

  <clause id="29675">
    <literal><![CDATA[
      L(x,y * (z * (u / w)),v5) = L(x,y * (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(6471(a,1),29551(a,1,2,2))].">
      <j1 rule="para" parents="6471 29551"/>
    </justification>
  </clause>

  <clause id="29676">
    <literal><![CDATA[
      L(x,y * (z \ (u / w)),v5) = L(x,y * (z \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(15028(a,1),29551(a,1,2,2))].">
      <j1 rule="para" parents="15028 29551"/>
    </justification>
  </clause>

  <clause id="29677">
    <literal><![CDATA[
      L(x,y * (z \ (u \ T(w,v5))),v6) = L(x,y * (z \ (u \ w)),v6)
    ]]></literal>
    <justification jstring="[para(24309(a,1),29551(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="24309 29551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29678">
    <literal><![CDATA[
      L(x,y * (z \ (u / (w / v5))),v6) = L(x,y * (z \ (u / (v5 \ w))),v6)
    ]]></literal>
    <justification jstring="[para(24313(a,1),29551(a,1,2,2))].">
      <j1 rule="para" parents="24313 29551"/>
    </justification>
  </clause>

  <clause id="29679">
    <literal><![CDATA[
      L(x,y * (K(z,u) * ((w * (u * z)) * K(v5,v6))),v7) = L(x,y * T(w * (z * u),K(z,u)),v7)
    ]]></literal>
    <justification jstring="[para(24357(a,1),29551(a,1,2,2))].">
      <j1 rule="para" parents="24357 29551"/>
    </justification>
  </clause>

  <clause id="29680">
    <literal><![CDATA[
      L((x \ (y / z)) \ u,x \ (z \ y),x) = (y / z) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(743,a,29552,a),flip(a)].">
      <j1 rule="hyper" parents="743 29552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29681">
    <literal><![CDATA[
      (x / y) * L(z,u \ (y \ x),u) = u * ((u \ (x / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,29552,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="145 29552 101"/>
    </justification>
  </clause>

  <clause id="29682">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * (w * v5)),v6) = L(x,y \ (v5 * w),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29458,a,b,29554,a)].">
      <j1 rule="hyper" parents="373 29458 29554"/>
    </justification>
  </clause>

  <clause id="29683">
    <literal><![CDATA[
      L(x,(y * z) \ ((u * z) * y),w) = L(x,L(T(u,z),z,y),w)
    ]]></literal>
    <justification jstring="[para(262(a,1),29554(a,1,2)),flip(a)].">
      <j1 rule="para" parents="262 29554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29685">
    <literal><![CDATA[
      L(x,y \ (z \ (u * ((w \ v5) * w))),v6) = L(x,y \ (z \ (u * v5)),v6)
    ]]></literal>
    <justification jstring="[para(24311(a,1),29556(a,1,2,2))].">
      <j1 rule="para" parents="24311 29556"/>
    </justification>
  </clause>

  <clause id="29686">
    <literal><![CDATA[
      L(((x * y) \ y) \ z,y \ (x \ y),x * y) = y \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(743,a,29603,a),flip(a)].">
      <j1 rule="hyper" parents="743 29603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29687">
    <literal><![CDATA[
      L(x,(y * z) \ y,u) = L(x,y \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29454,a,b,29603,a)].">
      <j1 rule="hyper" parents="64 29454 29603"/>
    </justification>
  </clause>

  <clause id="29688">
    <literal><![CDATA[
      x * L(y,x \ (z \ x),z * x) = (z * x) * (((z * x) \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,29603,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="145 29603 101"/>
    </justification>
  </clause>

  <clause id="29690">
    <literal><![CDATA[
      L(x,y \ (z * (u * u)),w) = L(x,y \ z,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29554,a,b,29604,a)].">
      <j1 rule="hyper" parents="64 29554 29604"/>
    </justification>
  </clause>

  <clause id="29691">
    <literal><![CDATA[
      L(x,y \ ((z * z) \ u),w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),29604(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 29604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29692">
    <literal><![CDATA[
      L(x,y \ (1 / z),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(245(a,1),29604(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="245 29604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29693">
    <literal><![CDATA[
      L(x,y \ ((1 / z) * u),w) = L(x,y \ (z * u),w)
    ]]></literal>
    <justification jstring="[para(310(a,1),29604(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="310 29604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29694">
    <literal><![CDATA[
      L(x,(1 / y) \ z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(539(a,1),29604(a,1,2))].">
      <j1 rule="para" parents="539 29604"/>
    </justification>
  </clause>

  <clause id="29695">
    <literal><![CDATA[
      L(x,y \ (z * (z * u)),w) = L(x,y \ L(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(100(a,1),29604(a,1,2,2))].">
      <j1 rule="para" parents="100 29604"/>
    </justification>
  </clause>

  <clause id="29696">
    <literal><![CDATA[
      L(x,y \ (((z * z) \ u) * w),v5) = L(x,y \ (u * w),v5)
    ]]></literal>
    <justification jstring="[para(126(a,1),29604(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="126 29604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29697">
    <literal><![CDATA[
      L(x,((y * y) \ z) \ u,w) = L(x,z \ u,w)
    ]]></literal>
    <justification jstring="[para(804(a,2),29604(a,1,2))].">
      <j1 rule="para" parents="804 29604"/>
    </justification>
  </clause>

  <clause id="29698">
    <literal><![CDATA[
      L(x,a(y,y,y \ z),u) = L(x,(y * z) \ (y \ z),u)
    ]]></literal>
    <justification jstring="[para(89(a,1),29604(a,1,2))].">
      <j1 rule="para" parents="89 29604"/>
    </justification>
  </clause>

  <clause id="29699">
    <literal><![CDATA[
      L(x,y \ ((((z * z) \ u) * w) * v5),v6) = L(x,y \ ((u * w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(805(a,1),29604(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="805 29604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29700">
    <literal><![CDATA[
      L(x,y \ R((z * z) * u,w,v5),v6) = L(x,y \ R(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(1981(a,2),29604(a,1,2,2))].">
      <j1 rule="para" parents="1981 29604"/>
    </justification>
  </clause>

  <clause id="29701">
    <literal><![CDATA[
      L(x,y \ (z \ 1),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29552,a(flip),b,29692,a)].">
      <j1 rule="hyper" parents="64 29552 29692"/>
    </justification>
  </clause>

  <clause id="29702">
    <literal><![CDATA[
      (1 / x) * L(y,z \ x,z) = z * ((z \ (1 / x)) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,29692,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="145 29692 101"/>
    </justification>
  </clause>

  <clause id="29703">
    <literal><![CDATA[
      L(x,y \ ((z / (u * z)) \ 1),w) = L(x,y \ ((u \ z) / z),w)
    ]]></literal>
    <justification jstring="[para(2032(a,1),29692(a,1,2,2))].">
      <j1 rule="para" parents="2032 29692"/>
    </justification>
  </clause>

  <clause id="29704">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29445,a(flip),b,29694,a)].">
      <j1 rule="hyper" parents="64 29445 29694"/>
    </justification>
  </clause>

  <clause id="29705">
    <literal><![CDATA[
      L(x,((y * y) \ z) \ u,w) = L(x,(z \ (y * y)) \ u,w)
    ]]></literal>
    <justification jstring="[para(551(a,1),29694(a,1,2,1))].">
      <j1 rule="para" parents="551 29694"/>
    </justification>
  </clause>

  <clause id="29706">
    <literal><![CDATA[
      L(x,(y * z) \ (z \ 1),u) = L(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29603,a(flip),b,29701,a),flip(a)].">
      <j1 rule="hyper" parents="373 29603 29701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29707">
    <literal><![CDATA[
      (x \ 1) * L(y,z \ x,z) = z * ((z \ (x \ 1)) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,29701,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="145 29701 101"/>
    </justification>
  </clause>

  <clause id="29708">
    <literal><![CDATA[
      L(x,(y \ 1) \ z,u \ 1) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(2274,a,29704,a)].">
      <j1 rule="hyper" parents="2274 29704"/>
    </justification>
  </clause>

  <clause id="29709">
    <literal><![CDATA[
      L(x,T((y \ 1) \ z,u),w) = L(x,y \ z,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29434,a,b,29704,a)].">
      <j1 rule="hyper" parents="64 29434 29704"/>
    </justification>
  </clause>

  <clause id="29710">
    <literal><![CDATA[
      L(x,(y \ z) \ (z \ y),u) = L(x,(y \ z) * (z \ y),u)
    ]]></literal>
    <justification jstring="[para(3814(a,1),29704(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3814 29704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29711">
    <literal><![CDATA[
      L(x,y \ (z \ (y \ z)),u) = L(x,y * (z \ (y \ z)),u)
    ]]></literal>
    <justification jstring="[para(26262(a,1),29704(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26262 29704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29712">
    <literal><![CDATA[
      L(x,y * L(K(z,u) * w,v5,v6),v7) = L(x,L(w,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[para(26085(a,2),29623(a,1,2,2))].">
      <j1 rule="para" parents="26085 29623"/>
    </justification>
  </clause>

  <clause id="29713">
    <literal><![CDATA[
      L(x,y * (z * (u \ 1)),w) = L(x,(u * z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11918,a(flip),b,29637,a),flip(a)].">
      <j1 rule="hyper" parents="64 11918 29637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29714">
    <literal><![CDATA[
      L(x,y * (z * ((u * u) \ w)),v5) = L(x,(w * z) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,11781,a(flip),b,29637,a),flip(a)].">
      <j1 rule="hyper" parents="64 11781 29637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29716">
    <literal><![CDATA[
      L(x,y * ((z * z) * u),w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),29669(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 29669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29717">
    <literal><![CDATA[
      L(x,y * (z * (z * u)),w) = L(x,y * L(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(18(a,2),29669(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18 29669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29718">
    <literal><![CDATA[
      L(x,y * ((1 / z) * u),w) = L(x,y * (z * u),w)
    ]]></literal>
    <justification jstring="[para(535(a,1),29669(a,1,2,2))].">
      <j1 rule="para" parents="535 29669"/>
    </justification>
  </clause>

  <clause id="29720">
    <literal><![CDATA[
      L(x,a(y,z,u),x) = L(x,(w * v5) * (v5 \ w),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,26688,a,b,29673,a)].">
      <j1 rule="hyper" parents="373 26688 29673"/>
    </justification>
  </clause>

  <clause id="29721">
    <literal><![CDATA[
      ((x * y) * (L(y \ 1,y,x) * x)) / x = L(x,x \ (y \ x),x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1050,a,b,29687,a)].">
      <j1 rule="hyper" parents="64 1050 29687"/>
    </justification>
  </clause>

  <clause id="29722">
    <literal><![CDATA[
      L(((x * y) \ x) \ z,x \ (y \ x),y * x) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23983,a(flip),b,29687,a),flip(a)].">
      <j1 rule="hyper" parents="64 23983 29687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29723">
    <literal><![CDATA[
      L(x,L(y,y,z),u) = L(x,(z * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(18(a,2),29690(a,1,2))].">
      <j1 rule="para" parents="18 29690"/>
    </justification>
  </clause>

  <clause id="29724">
    <literal><![CDATA[
      L(x,y \ ((z * u) * u),w) = L(x,y \ R(z,u,u),w)
    ]]></literal>
    <justification jstring="[para(111(a,1),29690(a,1,2,2))].">
      <j1 rule="para" parents="111 29690"/>
    </justification>
  </clause>

  <clause id="29725">
    <literal><![CDATA[
      L(x,L(y \ z,y \ z,y),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(101(a,1),29690(a,1,2))].">
      <j1 rule="para" parents="101 29690"/>
    </justification>
  </clause>

  <clause id="29726">
    <literal><![CDATA[
      L(x,L(y,y,z),u) = L(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29687,a(flip),b,29723,a),flip(a)].">
      <j1 rule="hyper" parents="373 29687 29723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29727">
    <literal><![CDATA[
      (x * y) * (((x * y) \ x) * z) = x * L(z,L(y,y,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,29723,a,b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 29723 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29728">
    <literal><![CDATA[
      L(x,L(y \ 1,y,z),u) = L(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(241(a,2),29723(a,2,2)),flip(a)].">
      <j1 rule="para" parents="241 29723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29729">
    <literal><![CDATA[
      x \ (L(y,L(z,z,x),x) * (z \ x)) = (x \ (z \ x)) * T(y,z \ x)
    ]]></literal>
    <justification jstring="[para(29726(a,2),1010(a,1,2,1))].">
      <j1 rule="para" parents="29726 1010"/>
    </justification>
  </clause>

  <clause id="29730">
    <literal><![CDATA[
      L(x,L(y * z,z * y,z),u) = L(x,z \ ((y * z) \ z),u)
    ]]></literal>
    <justification jstring="[para(14181(a,1),29726(a,1,2))].">
      <j1 rule="para" parents="14181 29726"/>
    </justification>
  </clause>

  <clause id="29731">
    <literal><![CDATA[
      L(x,L(y,y,z),u) = L(x,T(z,w) \ (y \ T(z,w)),u)
    ]]></literal>
    <justification jstring="[para(21687(a,1),29726(a,1,2))].">
      <j1 rule="para" parents="21687 29726"/>
    </justification>
  </clause>

  <clause id="29733">
    <literal><![CDATA[
      L(x,y \ T((z * z) \ u,w),v5) = L(x,y \ u,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29450,a,b,29691,a)].">
      <j1 rule="hyper" parents="64 29450 29691"/>
    </justification>
  </clause>

  <clause id="29734">
    <literal><![CDATA[
      L(x,(y * (y * z)) \ u,w) = L(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(881(a,1),29691(a,1,2))].">
      <j1 rule="para" parents="881 29691"/>
    </justification>
  </clause>

  <clause id="29735">
    <literal><![CDATA[
      L(x,R(y \ 1,z,u) \ w,v5) = L(x,R(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(2770(a,1),29691(a,1,2))].">
      <j1 rule="para" parents="2770 29691"/>
    </justification>
  </clause>

  <clause id="29736">
    <literal><![CDATA[
      L(x,(T(y * z,y * y) \ u) \ w,v5) = L(x,(((1 / y) * z) \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(1456(a,1),29697(a,1,2,1))].">
      <j1 rule="para" parents="1456 29697"/>
    </justification>
  </clause>

  <clause id="29737">
    <literal><![CDATA[
      L(x,L((y \ 1) * (y * y),z,u) * w,v5) = L(x,L(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,12027,a,b,29716,a)].">
      <j1 rule="hyper" parents="64 12027 29716"/>
    </justification>
  </clause>

  <clause id="29738">
    <literal><![CDATA[
      L(x,y * (z \ L(z,u,w)),v5) = L(x,y * (z * L(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(5602(a,1),29716(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5602 29716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29739">
    <literal><![CDATA[
      a(x,y,L(z,u * w,v5)) = a(x,y,L(z,w * u,v5))
    ]]></literal>
    <justification jstring="[para(29514(a,1),13876(a,1,3))].">
      <j1 rule="para" parents="29514 13876"/>
    </justification>
  </clause>

  <clause id="29740">
    <literal><![CDATA[
      L(x,y,L(z,u * w,v5)) = L(x,y,L(z,w * u,v5))
    ]]></literal>
    <justification jstring="[para(29514(a,1),23853(a,1,3))].">
      <j1 rule="para" parents="29514 23853"/>
    </justification>
  </clause>

  <clause id="29741">
    <literal><![CDATA[
      L(x,y * R(z,z,y),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29694,a(flip),b,29523,a),flip(a)].">
      <j1 rule="hyper" parents="373 29694 29523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29742">
    <literal><![CDATA[
      L(x,L(y \ z,y,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y * z,u) = w
    ]]></literal>
    <justification jstring="[para(29596(a,2),29616(a,1))].">
      <j1 rule="para" parents="29596 29616"/>
    </justification>
  </clause>

  <clause id="29743">
    <literal><![CDATA[
      L((x / y) * z,z * (x / y),z * (y \ x)) = 1 / (1 / ((x / y) * z))
    ]]></literal>
    <justification jstring="[hyper(29071,a,29663,a)].">
      <j1 rule="hyper" parents="29071 29663"/>
    </justification>
  </clause>

  <clause id="29744">
    <literal><![CDATA[
      L(x * y,a(z,u,w),x * y) \ (y \ x) = (y \ x) / T(x * y,y \ x)
    ]]></literal>
    <justification jstring="[para(29720(a,2),13729(a,1,1))].">
      <j1 rule="para" parents="29720 13729"/>
    </justification>
  </clause>

  <clause id="29745">
    <literal><![CDATA[
      L(x,(y * T(z,u)) * w,v5) = L(x,(z * y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29455,a,b,29457,a)].">
      <j1 rule="hyper" parents="64 29455 29457"/>
    </justification>
  </clause>

  <clause id="29746">
    <literal><![CDATA[
      L(x,((y / (y / z)) * u) * w,v5) = L(x,(z * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(276(a,1),29457(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="276 29457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29747">
    <literal><![CDATA[
      L(x,(T(y * z,u) \ (y * ((w * w) * (z * v5)))) * v6,v7) = L(x,L(T(w * w,z) * v5,z,y) * v6,v7)
    ]]></literal>
    <justification jstring="[para(6651(a,1),29460(a,2,2,1))].">
      <j1 rule="para" parents="6651 29460"/>
    </justification>
  </clause>

  <clause id="29748">
    <literal><![CDATA[
      L(x,L((y / z) * u,w,v5),v6) = L(x,L((z \ y) * u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(5982(a,1),29471(a,1,2,1))].">
      <j1 rule="para" parents="5982 29471"/>
    </justification>
  </clause>

  <clause id="29749">
    <literal><![CDATA[
      L(x,L(((y \ z) \ z) \ u,w,v5),v6) = L(x,L(y \ u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(6073(a,1),29471(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6073 29471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29750">
    <literal><![CDATA[
      L(x,L((y / z) \ u,w,v5),v6) = L(x,L((z \ y) \ u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(6270(a,1),29471(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6270 29471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29751">
    <literal><![CDATA[
      L(x,L((y * T(z,u)) \ w,v5,v6),v7) = L(x,L((y * z) \ w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(24506(a,1),29471(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="24506 29471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29752">
    <literal><![CDATA[
      L(x,L((T(y * y,y) * z) / y,u,w),v5) = L(x,L((y \ 1) \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(1167(a,1),29495(a,2,2,1))].">
      <j1 rule="para" parents="1167 29495"/>
    </justification>
  </clause>

  <clause id="29753">
    <literal><![CDATA[
      L(x,L((y \ (z * u)) \ ((z \ 1) * u),w,v5),v6) = L(x,L((z \ 1) * (z \ y),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(1659(a,1),29495(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1659 29495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29754">
    <literal><![CDATA[
      L(x,y \ ((z * T(u,w)) * L(v5,z,T(u,w))),v6) = L(x,y \ (u * (T(z,T(u,w)) * v5)),v6)
    ]]></literal>
    <justification jstring="[para(10989(a,2),29557(a,1,2,2))].">
      <j1 rule="para" parents="10989 29557"/>
    </justification>
  </clause>

  <clause id="29755">
    <literal><![CDATA[
      L(x,L((y * z) \ u,y * z,z),w) = L(x,(z * (z * y)) \ (z * u),w)
    ]]></literal>
    <justification jstring="[para(25217(a,1),29557(a,1,2))].">
      <j1 rule="para" parents="25217 29557"/>
    </justification>
  </clause>

  <clause id="29756">
    <literal><![CDATA[
      L(x,L(y * z,y,y),u) = L(x,y * L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29436,a,b,29614,a),flip(a)].">
      <j1 rule="hyper" parents="373 29436 29614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29757">
    <literal><![CDATA[
      L(x,((y * z) \ ((y * u) * z)) * w,v5) = L(x,R(u,y,z) * w,v5)
    ]]></literal>
    <justification jstring="[para(1039(a,2),29620(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1039 29620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29758">
    <literal><![CDATA[
      L(x,((y * z) \ z) * u,w) = L(x,(z \ (y \ z)) * u,w)
    ]]></literal>
    <justification jstring="[para(5144(a,1),29620(a,1,2,1))].">
      <j1 rule="para" parents="5144 29620"/>
    </justification>
  </clause>

  <clause id="29759">
    <literal><![CDATA[
      L(x,y * (T(z * z,u) \ w),v5) = L(x,y * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29669,a(flip),b,29625,a),flip(a)].">
      <j1 rule="hyper" parents="373 29669 29625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29760">
    <literal><![CDATA[
      L(x,(y \ (z * (y * y))) * u,w) = L(x,(L(y,y,z) * z) * u,w)
    ]]></literal>
    <justification jstring="[para(2848(a,1),29638(a,1,2,1))].">
      <j1 rule="para" parents="2848 29638"/>
    </justification>
  </clause>

  <clause id="29761">
    <literal><![CDATA[
      L(x,(y * (z \ 1)) * u,w) = L(x,(z * y) * (u \ 1),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29595,a,b,29643,a),flip(a)].">
      <j1 rule="hyper" parents="373 29595 29643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29763">
    <literal><![CDATA[
      L(x,y \ T(z / (z * u),u),w) = L(x,y \ (z \ (u \ z)),w)
    ]]></literal>
    <justification jstring="[para(26040(a,1),29654(a,1,2,2))].">
      <j1 rule="para" parents="26040 29654"/>
    </justification>
  </clause>

  <clause id="29764">
    <literal><![CDATA[
      L(x,y * ((z * u) \ u),w) = L(x,y * (u \ (z \ u)),w)
    ]]></literal>
    <justification jstring="[para(5144(a,1),29672(a,1,2,2))].">
      <j1 rule="para" parents="5144 29672"/>
    </justification>
  </clause>

  <clause id="29765">
    <literal><![CDATA[
      L(x,y \ ((z \ 1) * u),w) = L(x,y \ (z * u),w)
    ]]></literal>
    <justification jstring="[para(79(a,1),29693(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 29693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29766">
    <literal><![CDATA[
      L(x,(y * z) \ (z \ 1),u \ 1) = L(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(2274,a,29706,a)].">
      <j1 rule="hyper" parents="2274 29706"/>
    </justification>
  </clause>

  <clause id="29767">
    <literal><![CDATA[
      L(x,y * R(z,u,u \ 1),w) = L(x,(u * (z * u)) * y,w)
    ]]></literal>
    <justification jstring="[para(297(a,1),29713(a,1,2,2))].">
      <j1 rule="para" parents="297 29713"/>
    </justification>
  </clause>

  <clause id="29768">
    <literal><![CDATA[
      L(x,y \ T((z * z) \ (u / w),v5),v6) = L(x,y \ (w \ u),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29552,a(flip),b,29733,a),flip(a)].">
      <j1 rule="hyper" parents="373 29552 29733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29769">
    <literal><![CDATA[
      L(x,(y * R(T(z,u),w,v5)) * v6,v7) = L(x,(R(z,w,v5) * y) * v6,v7)
    ]]></literal>
    <justification jstring="[para(27(a,2),29745(a,1,2,1,2))].">
      <j1 rule="para" parents="27 29745"/>
    </justification>
  </clause>

  <clause id="29770">
    <literal><![CDATA[
      L(x,((y / z) * u) * w,v5) = L(x,(u * (z \ y)) * w,v5)
    ]]></literal>
    <justification jstring="[para(117(a,1),29745(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="117 29745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29771">
    <literal><![CDATA[
      L(x,(y * (z \ R(u,z,z))) * w,v5) = L(x,((u * (1 / z)) * y) * w,v5)
    ]]></literal>
    <justification jstring="[para(1406(a,1),29745(a,1,2,1,2))].">
      <j1 rule="para" parents="1406 29745"/>
    </justification>
  </clause>

  <clause id="29772">
    <literal><![CDATA[
      L(x,y * (z \ (u * u)),w) = L(x,y * (z \ 1),w)
    ]]></literal>
    <justification jstring="[para(6623(a,1),29759(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6623 29759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29773">
    <literal><![CDATA[
      L(x,y \ (R(1 / z,z,z * u) * w),v5) = L(x,y \ ((1 / R(1 / z,z,u)) * w),v5)
    ]]></literal>
    <justification jstring="[para(11432(a,1),29765(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="11432 29765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29774">
    <literal><![CDATA[
      L(x,y * (z \ (u * u)),w) = L(x,z * y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29520,a(flip),b,29772,a),flip(a)].">
      <j1 rule="hyper" parents="373 29520 29772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29775">
    <literal><![CDATA[
      L(x,(y \ (z * z)) * u,w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[hyper(29572,a,29774,a)].">
      <j1 rule="hyper" parents="29572 29774"/>
    </justification>
  </clause>

  <clause id="29776">
    <literal><![CDATA[
      L(x,(R(y,z,u) * (y \ R(y,z,u))) * w,v5) = L(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(1898(a,1),29775(a,1,2,1))].">
      <j1 rule="para" parents="1898 29775"/>
    </justification>
  </clause>

  <clause id="29777">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ y) * w,v5) = L(x,(y * L(y,z,u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(9377(a,1),29775(a,1,2,1))].">
      <j1 rule="para" parents="9377 29775"/>
    </justification>
  </clause>

  <clause id="29778">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * u) * z),w) = L(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29454,a,b,29476,a)].">
      <j1 rule="hyper" parents="64 29454 29476"/>
    </justification>
  </clause>

  <clause id="29779">
    <literal><![CDATA[
      L(x,y * L(z,z,y),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29690,a(flip),b,29496,a),flip(a)].">
      <j1 rule="hyper" parents="64 29690 29496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29781">
    <literal><![CDATA[
      L(x,(L(y,y,z) * z) * L(u,u,y \ z),w) = L(x,u \ (L(y,y,z) * z),w)
    ]]></literal>
    <justification jstring="[para(29160(a,1),29779(a,1,2,2))].">
      <j1 rule="para" parents="29160 29779"/>
    </justification>
  </clause>

  <clause id="29782">
    <literal><![CDATA[
      L((K(x,y) / z) \ u,z,w) = (w * (K(x,y) / z)) \ (w * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29653,a(flip),b,29531,a)].">
      <j1 rule="hyper" parents="64 29653 29531"/>
    </justification>
  </clause>

  <clause id="29784">
    <literal><![CDATA[
      (x * y) / L(z,z \ x,y) = y * (T(x,y) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,250,a(flip),b,29589,a)].">
      <j1 rule="hyper" parents="64 250 29589"/>
    </justification>
  </clause>

  <clause id="29785">
    <literal><![CDATA[
      ((x * y) * z) / L(x,y,z) = z * (T(x * y,z) / x)
    ]]></literal>
    <justification jstring="[para(9(a,1),29784(a,1,2,2))].">
      <j1 rule="para" parents="9 29784"/>
    </justification>
  </clause>

  <clause id="29786">
    <literal><![CDATA[
      (x * y) / L(z * z,x,y) = y * (T(x,y) / (z * z))
    ]]></literal>
    <justification jstring="[para(11775(a,1),29784(a,1,2))].">
      <j1 rule="para" parents="11775 29784"/>
    </justification>
  </clause>

  <clause id="29787">
    <literal><![CDATA[
      L(x,x \ y,z) \ (y * z) = T(z * (T(y,z) / x),x)
    ]]></literal>
    <justification jstring="[para(29784(a,1),23165(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29784 23165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29788">
    <literal><![CDATA[
      L(((x / y) \ 1) \ z,T(x,u) / y,y \ x) = (x / y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,29588,a,b,29671,a)].">
      <j1 rule="hyper" parents="64 29588 29671"/>
    </justification>
  </clause>

  <clause id="29789">
    <literal><![CDATA[
      x * L(y,z \ (x \ 1),z) = z * ((z \ (1 / (x \ 1))) * y)
    ]]></literal>
    <justification jstring="[hyper(400,a,29702,a)].">
      <j1 rule="hyper" parents="400 29702"/>
    </justification>
  </clause>

  <clause id="29790">
    <literal><![CDATA[
      x * ((x \ (1 / y)) * y) = a(x,x \ y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,25627,a(flip),b,29702,a),flip(a)].">
      <j1 rule="hyper" parents="64 25627 29702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29791">
    <literal><![CDATA[
      (1 / T(T(x,y),z)) * ((R(T(T(x,y),z),x,1 / u) * (1 / u)) * u) = a(1 / T(T(x,y),z),(1 / T(T(x,y),z)) \ u,u) \ 1
    ]]></literal>
    <justification jstring="[para(26539(a,2),29790(a,1,2,1))].">
      <j1 rule="para" parents="26539 29790"/>
    </justification>
  </clause>

  <clause id="29794">
    <literal><![CDATA[
      L(x,R(y,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29602,a(flip),b,29778,a)].">
      <j1 rule="hyper" parents="64 29602 29778"/>
    </justification>
  </clause>

  <clause id="29795">
    <literal><![CDATA[
      (x * R(y,y,z)) \ (x * ((1 / y) \ z)) = L(z,L(y,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1918,a,b,29794,a)].">
      <j1 rule="hyper" parents="64 1918 29794"/>
    </justification>
  </clause>

  <clause id="29796">
    <literal><![CDATA[
      L(x,L(y,y,z * y),u) = L(x,R(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29503,a(flip),b,29794,a),flip(a)].">
      <j1 rule="hyper" parents="64 29503 29794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29797">
    <literal><![CDATA[
      L(R(x,y,z) \ u,L(x,y,z),L(x,y,z)) = (1 / R(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,29205,a(flip),b,29794,a),flip(a)].">
      <j1 rule="hyper" parents="64 29205 29794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29798">
    <literal><![CDATA[
      L((R(x,y,z) \ 1) \ u,L(x,y,z),L(x,y,z)) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,29204,a(flip),b,29794,a),flip(a)].">
      <j1 rule="hyper" parents="64 29204 29794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29799">
    <literal><![CDATA[
      L(x,L((y \ 1) * z,u,w),v5) = L(x,R(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,11935,a(flip),b,29794,a),flip(a)].">
      <j1 rule="hyper" parents="64 11935 29794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29800">
    <literal><![CDATA[
      L(R(x,y,z) \ u,L(x,y,z),u) = ((1 / u) * R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,917,a(flip),b,29794,a),flip(a)].">
      <j1 rule="hyper" parents="64 917 29794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29801">
    <literal><![CDATA[
      L(x,R(L(y,z,u),w,v5),v6) = L(x,L(L(y,w,v5),z,u),v6)
    ]]></literal>
    <justification jstring="[para(30(a,1),29794(a,2,2))].">
      <j1 rule="para" parents="30 29794"/>
    </justification>
  </clause>

  <clause id="29803">
    <literal><![CDATA[
      R(x,y,z) \ L(u,L(x,y,z),L(x,y,z)) = (R(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(29794(a,1),29217(a,1,2))].">
      <j1 rule="para" parents="29794 29217"/>
    </justification>
  </clause>

  <clause id="29804">
    <literal><![CDATA[
      L(x,L(y,y,z * y),u) = L(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29794,a(flip),b,29796,a),flip(a)].">
      <j1 rule="hyper" parents="373 29794 29796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29805">
    <literal><![CDATA[
      L(x,L(y,y,y * z),u) = L(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(23253(a,1),29804(a,1,2))].">
      <j1 rule="para" parents="23253 29804"/>
    </justification>
  </clause>

  <clause id="29806">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,25863,a(flip),b,29785,a),flip(a)].">
      <j1 rule="hyper" parents="37 25863 29785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29807">
    <literal><![CDATA[
      a(x,y,x \ R(x,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,29806,a)].">
      <j1 rule="hyper" parents="54 29806"/>
    </justification>
  </clause>

  <clause id="29808">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),v5,x) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29806(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29806 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29809">
    <literal><![CDATA[
      x \ (y * (x \ R(x,z,u))) = (x \ y) * (x \ R(x,z,u))
    ]]></literal>
    <justification jstring="[para(29806(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="29806 598"/>
    </justification>
  </clause>

  <clause id="29810">
    <literal><![CDATA[
      (x * y) * L(x \ R(x,z,u),w,v5) = x * (y * L(x \ R(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(29806(a,1),513(a,1,2,1))].">
      <j1 rule="para" parents="29806 513"/>
    </justification>
  </clause>

  <clause id="29812">
    <literal><![CDATA[
      (x * y) / L(z * z,x,y) = x * (y / (z * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,18770,a(flip),b,29786,a),flip(a)].">
      <j1 rule="hyper" parents="373 18770 29786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29813">
    <literal><![CDATA[
      L(x * x,y,z) = L(x * x,z,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,11836,a,b,29812,a)].">
      <j1 rule="hyper" parents="37 11836 29812"/>
    </justification>
  </clause>

  <clause id="29814">
    <literal><![CDATA[
      ((x * x) \ y) * L(((x * x) \ y) \ y,z,u) = L(x * x,u,z) * ((x * x) \ y)
    ]]></literal>
    <justification jstring="[para(29813(a,1),839(a,2,1))].">
      <j1 rule="para" parents="29813 839"/>
    </justification>
  </clause>

  <clause id="29815">
    <literal><![CDATA[
      T(x * (T(y * z,x) / z),z) = L(z,y,x) \ ((y * z) * x)
    ]]></literal>
    <justification jstring="[para(29493(a,1),29787(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29493 29787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29816">
    <literal><![CDATA[
      a(x,L(T(y,z),u,w) \ v5,x) \ x = L(x,L(y,u,w) \ v5,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10905,a,b,29463,a)].">
      <j1 rule="hyper" parents="64 10905 29463"/>
    </justification>
  </clause>

  <clause id="29817">
    <literal><![CDATA[
      L(x,(y * (K(z,u) * w)) * v5,v6) = L(x,v5 * (w * y),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29637,a(flip),b,29468,a),flip(a)].">
      <j1 rule="hyper" parents="373 29637 29468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29818">
    <literal><![CDATA[
      L(x,(y * (z / u)) * w,v5) = L(x,(y * (u \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(5720(a,1),29468(a,1,2,1,2))].">
      <j1 rule="para" parents="5720 29468"/>
    </justification>
  </clause>

  <clause id="29819">
    <literal><![CDATA[
      L(x,(y * ((z / u) * w)) * v5,v6) = L(x,(y * ((u \ z) * w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(5982(a,1),29468(a,1,2,1,2))].">
      <j1 rule="para" parents="5982 29468"/>
    </justification>
  </clause>

  <clause id="29820">
    <literal><![CDATA[
      L(x,((y \ (z / u)) * w) * v5,v6) = L(x,((y \ (u \ z)) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(24475(a,1),29468(a,1,2,1))].">
      <j1 rule="para" parents="24475 29468"/>
    </justification>
  </clause>

  <clause id="29821">
    <literal><![CDATA[
      L(x,(y * (z / T(z * u,u))) \ w,v5) = L(x,(y * (T(z,u) \ (z / u))) \ w,v5)
    ]]></literal>
    <justification jstring="[para(27202(a,1),29469(a,1,2,1,2))].">
      <j1 rule="para" parents="27202 29469"/>
    </justification>
  </clause>

  <clause id="29822">
    <literal><![CDATA[
      L(x,(((y / z) \ u) \ w) \ v5,v6) = L(x,(((z \ y) \ u) \ w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(24402(a,1),29470(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="24402 29470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29823">
    <literal><![CDATA[
      L(x,L(T(y * (z \ 1),u) \ ((z \ 1) * (z \ w)),v5,v6),v7) = L(x,L((z * T(y,z \ 1)) \ w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(1677(a,1),29473(a,2,2,1))].">
      <j1 rule="para" parents="1677 29473"/>
    </justification>
  </clause>

  <clause id="29824">
    <literal><![CDATA[
      R(x,T(y,z),L(u,u,u * w)) = R(x,y,L(u,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,23811,a(flip),b,29505,a)].">
      <j1 rule="hyper" parents="64 23811 29505"/>
    </justification>
  </clause>

  <clause id="29826">
    <literal><![CDATA[
      R(x,y,L(z,z,z * u)) = R(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26406,a(flip),b,29824,a)].">
      <j1 rule="hyper" parents="64 26406 29824"/>
    </justification>
  </clause>

  <clause id="29827">
    <literal><![CDATA[
      R(x,y \ (z \ y),z) = R(x,z,L(z,z,z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,26647,a,b,29826,a)].">
      <j1 rule="hyper" parents="373 26647 29826"/>
    </justification>
  </clause>

  <clause id="29828">
    <literal><![CDATA[
      L(x,y \ (z / (u / w)),v5) = L(x,y \ ((w \ u) \ z),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29552,a(flip),b,29560,a),flip(a)].">
      <j1 rule="hyper" parents="373 29552 29560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29829">
    <literal><![CDATA[
      L(x,y * (z \ ((u * u) * w)),v5) = L(x,(z \ w) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(29572,a,29605,a)].">
      <j1 rule="hyper" parents="29572 29605"/>
    </justification>
  </clause>

  <clause id="29830">
    <literal><![CDATA[
      L(x,(y \ ((z * z) \ u)) * w,v5) = L(x,(y \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),29605(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 29605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29831">
    <literal><![CDATA[
      L(x,(y \ T(z,u * u)) * w,v5) = L(x,(y \ (z * (u * u))) * w,v5)
    ]]></literal>
    <justification jstring="[para(115(a,1),29605(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="115 29605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29832">
    <literal><![CDATA[
      L(x,(y \ (1 / z)) * u,w) = L(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(245(a,1),29605(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="245 29605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29833">
    <literal><![CDATA[
      L(x,(y \ (T(z,u * u) * w)) * v5,v6) = L(x,(y \ (z * ((u * u) * w))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(1434(a,1),29605(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1434 29605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29834">
    <literal><![CDATA[
      L(x,(y \ (z \ 1)) * u,w) = L(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),29832(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 29832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29835">
    <literal><![CDATA[
      L(x,y * (z \ (u \ 1)),w) = L(x,(z \ u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(29572,a,29834,a)].">
      <j1 rule="hyper" parents="29572 29834"/>
    </justification>
  </clause>

  <clause id="29836">
    <literal><![CDATA[
      L(x,(y * L(z * (u / z),w,v5)) * v6,v7) = L(x,(y * L(u,w,v5)) * v6,v7)
    ]]></literal>
    <justification jstring="[para(5618(a,2),29632(a,1,2,1,2))].">
      <j1 rule="para" parents="5618 29632"/>
    </justification>
  </clause>

  <clause id="29837">
    <literal><![CDATA[
      L(x,(y \ (T(z,u) * w)) * v5,v6) = L(x,(y \ (z * w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(5755(a,1),29634(a,1,2,1,2))].">
      <j1 rule="para" parents="5755 29634"/>
    </justification>
  </clause>

  <clause id="29838">
    <literal><![CDATA[
      L(x,(y * ((z * z) \ u)) * w,v5) = L(x,(y * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29455,a,b,29645,a),flip(a)].">
      <j1 rule="hyper" parents="373 29455 29645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29839">
    <literal><![CDATA[
      L(x,(K(y,z) * (u * w)) \ v5,v6) = L(x,(w * u) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(23199(a,2),29652(a,1,2))].">
      <j1 rule="para" parents="23199 29652"/>
    </justification>
  </clause>

  <clause id="29840">
    <literal><![CDATA[
      x / L(y,y \ ((z \ u) \ x),z \ u) = (u / z) * (((u / z) \ x) / y)
    ]]></literal>
    <justification jstring="[para(29656(a,1),23977(a,1,2))].">
      <j1 rule="para" parents="29656 23977"/>
    </justification>
  </clause>

  <clause id="29841">
    <literal><![CDATA[
      L(x,y \ (z * ((u / w) * v5)),v6) = L(x,y \ (z * ((w \ u) * v5)),v6)
    ]]></literal>
    <justification jstring="[para(5982(a,1),29657(a,1,2,2,2))].">
      <j1 rule="para" parents="5982 29657"/>
    </justification>
  </clause>

  <clause id="29842">
    <literal><![CDATA[
      L(x,(y * (z * u)) \ ((z * y) * u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(14(a,2),29658(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14 29658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29843">
    <literal><![CDATA[
      L(x,y * ((z * u) * u),w) = L(x,L(z,u,u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29646,a(flip),b,29667,a),flip(a)].">
      <j1 rule="hyper" parents="64 29646 29667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29844">
    <literal><![CDATA[
      L(x,y * (((z * u) * z) * w),v5) = L(x,(L(u,z,z) * w) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,11783,a(flip),b,29667,a),flip(a)].">
      <j1 rule="hyper" parents="64 11783 29667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29845">
    <literal><![CDATA[
      L(x,(y * (z * y)) * u,w) = L(x,L(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29637,a,b,29843,a)].">
      <j1 rule="hyper" parents="64 29637 29843"/>
    </justification>
  </clause>

  <clause id="29846">
    <literal><![CDATA[
      L(x,y \ (z * (T(u,w) * v5)),v6) = L(x,y \ ((u * v5) * z),v6)
    ]]></literal>
    <justification jstring="[para(23389(a,1),29682(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23389 29682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29847">
    <literal><![CDATA[
      L(x,y \ ((z * T(u,w)) * v5),v6) = L(x,y \ (v5 * (z * u)),v6)
    ]]></literal>
    <justification jstring="[para(24355(a,1),29682(a,1,2,2))].">
      <j1 rule="para" parents="24355 29682"/>
    </justification>
  </clause>

  <clause id="29848">
    <literal><![CDATA[
      L(x,y \ (((z * z) \ u) * w),v5) = L(x,y \ (w * u),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29554,a,b,29696,a),flip(a)].">
      <j1 rule="hyper" parents="373 29554 29696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29849">
    <literal><![CDATA[
      L(x,y \ (((1 / z) * u) * w),v5) = L(x,y \ ((z * u) * w),v5)
    ]]></literal>
    <justification jstring="[para(535(a,1),29696(a,1,2,2,1))].">
      <j1 rule="para" parents="535 29696"/>
    </justification>
  </clause>

  <clause id="29850">
    <literal><![CDATA[
      L(x,(y \ (z * z)) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29697,a(flip),b,29705,a),flip(a)].">
      <j1 rule="hyper" parents="64 29697 29705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29852">
    <literal><![CDATA[
      L(x,(y \ z) \ (z \ y),u) = L(x,(z / y) * (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29443,a,b,29710,a),flip(a)].">
      <j1 rule="hyper" parents="373 29443 29710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29853">
    <literal><![CDATA[
      L(x,L(y * z,y,y) * u,w) = L(x,(y * L(z,y,y)) * u,w)
    ]]></literal>
    <justification jstring="[para(1260(a,1),29746(a,1,2,1))].">
      <j1 rule="para" parents="1260 29746"/>
    </justification>
  </clause>

  <clause id="29854">
    <literal><![CDATA[
      L(x,((y * z) \ y) * u,w) = L(x,(y \ (z \ y)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29462,a,b,29758,a)].">
      <j1 rule="hyper" parents="64 29462 29758"/>
    </justification>
  </clause>

  <clause id="29855">
    <literal><![CDATA[
      L(x,L((y \ 1) * z,u,w),v5) = L(x,L(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29794,a(flip),b,29799,a),flip(a)].">
      <j1 rule="hyper" parents="373 29794 29799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29856">
    <literal><![CDATA[
      L(x,L(R(y,z,u),w,v5),v6) = L(x,L(L(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(29(a,1),29801(a,1,2))].">
      <j1 rule="para" parents="29 29801"/>
    </justification>
  </clause>

  <clause id="29857">
    <literal><![CDATA[
      R(T(x \ 1,y * (x \ R(x,z,u))),x,y * (x \ R(x,z,u))) = (y * (x \ R(x,z,u))) \ ((x \ y) * (x \ R(x,z,u)))
    ]]></literal>
    <justification jstring="[para(29809(a,1),2985(a,2,2))].">
      <j1 rule="para" parents="29809 2985"/>
    </justification>
  </clause>

  <clause id="29858">
    <literal><![CDATA[
      a((x * (y \ R(y,z,u))) \ ((y \ x) * (y \ R(y,z,u))),y \ R(y,z,u),x) = y \ R(y,y \ R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(29809(a,1),28073(a,1,1,2))].">
      <j1 rule="para" parents="29809 28073"/>
    </justification>
  </clause>

  <clause id="29859">
    <literal><![CDATA[
      L(x,(y * ((z * u) * w)) * v5,v6) = L(x,v5 * (((u * z) * w) * y),v6)
    ]]></literal>
    <justification jstring="[para(10834(a,1),29817(a,1,2,1,2))].">
      <j1 rule="para" parents="10834 29817"/>
    </justification>
  </clause>

  <clause id="29860">
    <literal><![CDATA[
      L(x,(y * (z \ y)) * z,u) = L(x,a(y,z \ y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25650,a(flip),b,29818,a),flip(a)].">
      <j1 rule="hyper" parents="64 25650 29818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29861">
    <literal><![CDATA[
      L(x,((y \ z) * z) * y,u) = L(x,a(z,y \ z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29455,a,b,29860,a)].">
      <j1 rule="hyper" parents="64 29455 29860"/>
    </justification>
  </clause>

  <clause id="29862">
    <literal><![CDATA[
      L(x,y * ((1 / z) \ u),w) = L(x,(z \ u) * y,w)
    ]]></literal>
    <justification jstring="[para(539(a,1),29829(a,1,2,2))].">
      <j1 rule="para" parents="539 29829"/>
    </justification>
  </clause>

  <clause id="29863">
    <literal><![CDATA[
      L(x,y * ((z \ 1) \ u),w) = L(x,(z \ u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29627,a(flip),b,29862,a)].">
      <j1 rule="hyper" parents="64 29627 29862"/>
    </justification>
  </clause>

  <clause id="29864">
    <literal><![CDATA[
      L((1 / x) \ y,(x \ y) * z,x \ y) \ z = z / T((1 / x) \ y,z)
    ]]></literal>
    <justification jstring="[para(29862(a,1),13731(a,1,1))].">
      <j1 rule="para" parents="29862 13731"/>
    </justification>
  </clause>

  <clause id="29865">
    <literal><![CDATA[
      L(x,((y \ 1) \ z) * u,w) = L(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(29572,a,29863,a)].">
      <j1 rule="hyper" parents="29572 29863"/>
    </justification>
  </clause>

  <clause id="29866">
    <literal><![CDATA[
      L(x,y * ((z \ 1) \ u),w) = L(x,y * (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29436,a,b,29863,a),flip(a)].">
      <j1 rule="hyper" parents="373 29436 29863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29867">
    <literal><![CDATA[
      L(x,(R(y \ 1,z,u) \ w) * v5,v6) = L(x,(R(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(2770(a,1),29830(a,1,2,1))].">
      <j1 rule="para" parents="2770 29830"/>
    </justification>
  </clause>

  <clause id="29868">
    <literal><![CDATA[
      L(x,(y * ((1 / z) * u)) * w,v5) = L(x,(y * (z * u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(535(a,1),29838(a,1,2,1,2))].">
      <j1 rule="para" parents="535 29838"/>
    </justification>
  </clause>

  <clause id="29869">
    <literal><![CDATA[
      L(x,(y * (((z * z) \ u) * w)) * v5,v6) = L(x,(y * (u * w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(484(a,1),29838(a,1,2,1,2))].">
      <j1 rule="para" parents="484 29838"/>
    </justification>
  </clause>

  <clause id="29870">
    <literal><![CDATA[
      L(x,(y * (T(z,u) \ w)) \ v5,v6) = L(x,((z \ w) * y) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(24347(a,1),29839(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="24347 29839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29871">
    <literal><![CDATA[
      L(x,y \ (z * ((u * u) \ w)),v5) = L(x,y \ (z * w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29554,a,b,29848,a)].">
      <j1 rule="hyper" parents="64 29554 29848"/>
    </justification>
  </clause>

  <clause id="29872">
    <literal><![CDATA[
      L(x,(y \ z) \ (z \ y),u) = L(x,(z / y) * (y / z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29547,a,b,29852,a),flip(a)].">
      <j1 rule="hyper" parents="373 29547 29852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29873">
    <literal><![CDATA[
      L(x,L((1 / y) * z,u,w),v5) = L(x,L(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(82(a,1),29855(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="82 29855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29874">
    <literal><![CDATA[
      L(x,L(L(y,z,u),w,v5),y) = L(x,y,L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,29278,a(flip),b,29856,a),flip(a)].">
      <j1 rule="hyper" parents="64 29278 29856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29875">
    <literal><![CDATA[
      L(x,y \ (z * ((u * u) * w)),v5) = L(x,y \ (z * w),v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),29871(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9 29871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29876">
    <literal><![CDATA[
      L(x,y \ (z * (((u * u) \ w) * v5)),v6) = L(x,y \ (z * (w * v5)),v6)
    ]]></literal>
    <justification jstring="[para(484(a,1),29871(a,1,2,2,2))].">
      <j1 rule="para" parents="484 29871"/>
    </justification>
  </clause>

  <clause id="29877">
    <literal><![CDATA[
      L(x,L((1 / y) * 1,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(8(a,1),29873(a,2,2,1))].">
      <j1 rule="para" parents="8 29873"/>
    </justification>
  </clause>

  <clause id="29878">
    <literal><![CDATA[
      L(x,L(y \ L(y,z,u),w,v5),v6) = L(x,L(y * L(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(5590(a,1),29873(a,1,2,1))].">
      <j1 rule="para" parents="5590 29873"/>
    </justification>
  </clause>

  <clause id="29879">
    <literal><![CDATA[
      L(x,L(1 / y,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(8(a,1),29877(a,1,2,1))].">
      <j1 rule="para" parents="8 29877"/>
    </justification>
  </clause>

  <clause id="29880">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29495,a(flip),b,29879,a)].">
      <j1 rule="hyper" parents="64 29495 29879"/>
    </justification>
  </clause>

  <clause id="29881">
    <literal><![CDATA[
      L(L(x \ 1,y,z) \ u,L(x,y,z),L(x \ 1,y,z)) = (1 / L(x \ 1,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(742,a,29880,a),flip(a)].">
      <j1 rule="hyper" parents="742 29880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29882">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u),y) = L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,2482,a(flip),b,29880,a),flip(a)].">
      <j1 rule="hyper" parents="373 2482 29880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29883">
    <literal><![CDATA[
      L(x,y \ ((z / (1 / u)) * w),v5) = L(x,y \ ((z / u) * w),v5)
    ]]></literal>
    <justification jstring="[para(819(a,1),29875(a,1,2,2))].">
      <j1 rule="para" parents="819 29875"/>
    </justification>
  </clause>

  <clause id="29884">
    <literal><![CDATA[
      L(T(x,y),T(x,y),z) = L(T(x,y),x,L(z,x,x))
    ]]></literal>
    <justification jstring="[para(23827(a,1),29492(a,1,3)),flip(a)].">
      <j1 rule="para" parents="23827 29492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29885">
    <literal><![CDATA[
      L(T(x,y),x,L(z,x,x)) = L(T(x,y),x,z)
    ]]></literal>
    <justification jstring="[hyper(29565,a,29884,a),flip(a)].">
      <j1 rule="hyper" parents="29565 29884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29888">
    <literal><![CDATA[
      L(T(x,y),x,x \ z) = L(T(x,y),x,x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2187,a(flip),b,29885,a),flip(a)].">
      <j1 rule="hyper" parents="64 2187 29885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29889">
    <literal><![CDATA[
      L(x,L(y,z,z) * (z \ y),u) = L(x,L(z \ 1,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29641,a(flip),b,29524,a),flip(a)].">
      <j1 rule="hyper" parents="373 29641 29524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29890">
    <literal><![CDATA[
      L(x,L(y,z,z) * (z \ y),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29880,a(flip),b,29889,a),flip(a)].">
      <j1 rule="hyper" parents="373 29880 29889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29892">
    <literal><![CDATA[
      (x * ((y * y) * a(z,u,w))) \ (x * (a(z,u,w) * v5)) = L((y * y) \ v5,a(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24759,a(flip),b,29568,a)].">
      <j1 rule="hyper" parents="64 24759 29568"/>
    </justification>
  </clause>

  <clause id="29893">
    <literal><![CDATA[
      L(x,(y * z) \ ((u * z) * y),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,L(u,z,y),w) = v5
    ]]></literal>
    <justification jstring="[para(29683(a,2),29570(a,1))].">
      <j1 rule="para" parents="29683 29570"/>
    </justification>
  </clause>

  <clause id="29894">
    <literal><![CDATA[
      L(x,y * R(z,u,u \ 1),w) = L(x,L(z,u,u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29845,a(flip),b,29767,a),flip(a)].">
      <j1 rule="hyper" parents="373 29845 29767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29895">
    <literal><![CDATA[
      L(x,a(y,z,z \ 1),u) = L(x,L(y,z,z) * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11915,a(flip),b,29894,a)].">
      <j1 rule="hyper" parents="64 11915 29894"/>
    </justification>
  </clause>

  <clause id="29896">
    <literal><![CDATA[
      L(x,a(y,z,z \ 1),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11917,a(flip),b,29895,a),flip(a)].">
      <j1 rule="hyper" parents="373 11917 29895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29897">
    <literal><![CDATA[
      (x * (K(y,z) / x)) \ (x * u) = (1 / (K(y,z) / x)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,27856,a(flip),b,29782,a),flip(a)].">
      <j1 rule="hyper" parents="64 27856 29782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29898">
    <literal><![CDATA[
      ((x \ K(y,z)) * x) * (x * u) = (1 / (K(z,y) / x)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,20892,a(flip),b,29897,a)].">
      <j1 rule="hyper" parents="64 20892 29897"/>
    </justification>
  </clause>

  <clause id="29899">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * ((x \ K(u,w)) * x) = (1 / (K(w,u) / x)) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23905,a,b,29898,a)].">
      <j1 rule="hyper" parents="64 23905 29898"/>
    </justification>
  </clause>

  <clause id="29900">
    <literal><![CDATA[
      x * L(y,z \ x,z) = z * ((z \ (1 / (x \ 1))) * y)
    ]]></literal>
    <justification jstring="[para(29701(a,1),29789(a,1,2))].">
      <j1 rule="para" parents="29701 29789"/>
    </justification>
  </clause>

  <clause id="29901">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),x,y * z),u,x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,16031,a,b,29808,a),flip(a)].">
      <j1 rule="hyper" parents="373 16031 29808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29902">
    <literal><![CDATA[
      L(a(x,y,z),u,x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(16031(a,2),29901(a,1,1))].">
      <j1 rule="para" parents="16031 29901"/>
    </justification>
  </clause>

  <clause id="29903">
    <literal><![CDATA[
      L(a(x,y,z),u,x \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2274,a,29902,a)].">
      <j1 rule="hyper" parents="2274 29902"/>
    </justification>
  </clause>

  <clause id="29904">
    <literal><![CDATA[
      (x * (a(x,y,z) \ u)) \ (x * u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23784,a(flip),b,29902,a)].">
      <j1 rule="hyper" parents="64 23784 29902"/>
    </justification>
  </clause>

  <clause id="29905">
    <literal><![CDATA[
      (x * L(y,x,x)) \ (x * y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1247,a(flip),b,29902,a)].">
      <j1 rule="hyper" parents="64 1247 29902"/>
    </justification>
  </clause>

  <clause id="29907">
    <literal><![CDATA[
      a(L(x,y,z),u,u \ x) = L(a(x,u,u \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(42,a,16482,a,b,29902,a),flip(a)].">
      <j1 rule="hyper" parents="42 16482 29902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29909">
    <literal><![CDATA[
      x * ((x \ y) * a(x,z,u)) = y * a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,29902,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 29902 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29910">
    <literal><![CDATA[
      (x * y) * a(x,z,u) = x * (y * a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,29902,a(flip),b,5318,a(flip))].">
      <j1 rule="hyper" parents="145 29902 5318"/>
    </justification>
  </clause>

  <clause id="29911">
    <literal><![CDATA[
      (x * a(y,z,u)) * y = a(y,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,29902,a(flip),b,28786,a),flip(a)].">
      <j1 rule="hyper" parents="144 29902 28786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29912">
    <literal><![CDATA[
      a(x,y,z) * (x * u) = x * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(144,a,29902,a(flip),b,23157,a)].">
      <j1 rule="hyper" parents="144 29902 23157"/>
    </justification>
  </clause>

  <clause id="29913">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),v5,x) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29902(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29902 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29914">
    <literal><![CDATA[
      x \ (y * a(x,z,u)) = (x \ y) * a(x,z,u)
    ]]></literal>
    <justification jstring="[para(29902(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="29902 598"/>
    </justification>
  </clause>

  <clause id="29915">
    <literal><![CDATA[
      ((x \ 1) * y) * a(x,z,u) = (x \ 1) * (y * a(x,z,u))
    ]]></literal>
    <justification jstring="[para(29902(a,1),1630(a,1,2))].">
      <j1 rule="para" parents="29902 1630"/>
    </justification>
  </clause>

  <clause id="29916">
    <literal><![CDATA[
      x * (((x \ 1) * y) * a(x,z,u)) = L(y,x,x) * a(x,z,u)
    ]]></literal>
    <justification jstring="[para(29902(a,1),1820(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29902 1820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29918">
    <literal><![CDATA[
      x * (T(y,x) * L(a(x,z,u),w,v5)) = (y * x) * L(a(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(29902(a,1),1295(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="29902 1295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29919">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(x,u,w) = L(x,y,z) * (x \ a(x,u,w))
    ]]></literal>
    <justification jstring="[para(29902(a,1),2338(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="29902 2338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29920">
    <literal><![CDATA[
      x * (y * L(a(x,z,u),x,y)) = y * (T(x,y) * a(x,z,u))
    ]]></literal>
    <justification jstring="[para(29902(a,1),11002(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="29902 11002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29921">
    <literal><![CDATA[
      x * (a(x,y,z) \ 1) = a(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(29902(a,1),23106(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29902 23106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29922">
    <literal><![CDATA[
      x * ((x \ y) * a(x,z,u)) = a(x,z,u) * y
    ]]></literal>
    <justification jstring="[para(29902(a,1),23783(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29902 23783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29923">
    <literal><![CDATA[
      a(x,y,z) \ (x * u) = x * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(29902(a,1),27804(a,1,1))].">
      <j1 rule="para" parents="29902 27804"/>
    </justification>
  </clause>

  <clause id="29924">
    <literal><![CDATA[
      (a(x,y,z) * u) * x = a(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[para(29902(a,1),28784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29902 28784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29925">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ x = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[para(29902(a,1),28795(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29902 28795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29926">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ x = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(29902(a,1),28814(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29902 28814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29927">
    <literal><![CDATA[
      x * (y * L(a(x,z,u),x,y)) = (x * a(x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(29902(a,1),28785(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="29902 28785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29929">
    <literal><![CDATA[
      (x \ 1) * (y * R(a(x,z,u),x \ 1,y)) = (a(x,z,u) * (x \ 1)) * y
    ]]></literal>
    <justification jstring="[para(29903(a,1),25558(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="29903 25558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29930">
    <literal><![CDATA[
      a(x,y,z) \ ((x \ 1) * u) = (x \ 1) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(29903(a,1),27804(a,1,1))].">
      <j1 rule="para" parents="29903 27804"/>
    </justification>
  </clause>

  <clause id="29931">
    <literal><![CDATA[
      (x * L((y / x) * L(x,z,u),x,x)) \ (L(x,z,u) * y) = a(x,x,(y / x) * L(x,z,u))
    ]]></literal>
    <justification jstring="[para(24854(a,1),29905(a,1,2))].">
      <j1 rule="para" parents="24854 29905"/>
    </justification>
  </clause>

  <clause id="29932">
    <literal><![CDATA[
      x \ (a(x,y,z) \ x) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(149,a,29921,a)].">
      <j1 rule="hyper" parents="149 29921"/>
    </justification>
  </clause>

  <clause id="29933">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * x = a(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,23736,a,b,29921,a)].">
      <j1 rule="hyper" parents="64 23736 29921"/>
    </justification>
  </clause>

  <clause id="29934">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) \ u,a(x,y,z),x) = (a(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(29921(a,1),11813(a,2,1))].">
      <j1 rule="para" parents="29921 11813"/>
    </justification>
  </clause>

  <clause id="29935">
    <literal><![CDATA[
      x * (K(y,z / x) * (a(x,u,w) \ 1)) = K(y,x \ z) * (a(x,u,w) \ x)
    ]]></literal>
    <justification jstring="[para(29921(a,1),22762(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29921 22762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29936">
    <literal><![CDATA[
      x * ((a(y,z,u) \ 1) * y) = x * (a(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(29921(a,1),23764(a,2,2))].">
      <j1 rule="para" parents="29921 23764"/>
    </justification>
  </clause>

  <clause id="29937">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) \ x = x * a(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(28801(a,1),29921(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28801 29921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29938">
    <literal><![CDATA[
      (1 / a(x,y,z)) \ x = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[para(13923(a,2),29925(a,1,1))].">
      <j1 rule="para" parents="13923 29925"/>
    </justification>
  </clause>

  <clause id="29939">
    <literal><![CDATA[
      (a(x,y,z) \ x) \ ((a(x,y,z) \ 1) * u) = L(x \ u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(29933(a,1),1632(a,2,1)),flip(a)].">
      <j1 rule="para" parents="29933 1632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29940">
    <literal><![CDATA[
      x * (a(x,y,x * y) \ y) = L(x * y,y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,25855,a,b,29904,a),flip(a)].">
      <j1 rule="hyper" parents="40 25855 29904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29941">
    <literal><![CDATA[
      x \ (a(x,y,z) * u) = (x \ u) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,23136,a,b,29909,a)].">
      <j1 rule="hyper" parents="139 23136 29909"/>
    </justification>
  </clause>

  <clause id="29942">
    <literal><![CDATA[
      (x \ (a(x,y,z) \ u)) * a(x,y,z) = x \ u
    ]]></literal>
    <justification jstring="[hyper(139,a,23135,a(flip),b,29909,a),flip(a)].">
      <j1 rule="hyper" parents="139 23135 29909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29943">
    <literal><![CDATA[
      (R(1 / x,y,z) \ 1) * a(x,u,w) = x * ((R(x,y,z) \ x) * a(x,u,w))
    ]]></literal>
    <justification jstring="[para(2467(a,1),29909(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2467 29909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29944">
    <literal><![CDATA[
      x \ ((x * y) * z) = (y * z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(758,a,29910,a)].">
      <j1 rule="hyper" parents="758 29910"/>
    </justification>
  </clause>

  <clause id="29945">
    <literal><![CDATA[
      R(x,y,a(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(664,a,29910,a)].">
      <j1 rule="hyper" parents="664 29910"/>
    </justification>
  </clause>

  <clause id="29946">
    <literal><![CDATA[
      (x * y) * a(x,z,u) = x * (a(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,23169,a,b,29910,a),flip(a)].">
      <j1 rule="hyper" parents="373 23169 29910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29947">
    <literal><![CDATA[
      x * ((y * (z * u)) * a(x,y,u * z)) = (x * y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27365,a(flip),b,29910,a),flip(a)].">
      <j1 rule="hyper" parents="64 27365 29910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29948">
    <literal><![CDATA[
      x * ((y * z) * a(x,z,y)) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,25786,a(flip),b,29910,a),flip(a)].">
      <j1 rule="hyper" parents="64 25786 29910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29949">
    <literal><![CDATA[
      x * (y * a(x,z \ y,z)) = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,25646,a(flip),b,29910,a),flip(a)].">
      <j1 rule="hyper" parents="64 25646 29910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29950">
    <literal><![CDATA[
      x * (y * a(x,z,z \ y)) = (x * z) * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,957,a(flip),b,29910,a),flip(a)].">
      <j1 rule="hyper" parents="64 957 29910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29951">
    <literal><![CDATA[
      x * ((y * z) * a(x,y,z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,88,a(flip),b,29910,a),flip(a)].">
      <j1 rule="hyper" parents="64 88 29910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29952">
    <literal><![CDATA[
      x \ ((x * y) * T(z,y)) = (z * y) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,25786,a(flip),b,29910,a(flip))].">
      <j1 rule="hyper" parents="139 25786 29910"/>
    </justification>
  </clause>

  <clause id="29953">
    <literal><![CDATA[
      x \ ((x * y) * (y \ z)) = z * a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,957,a(flip),b,29910,a(flip))].">
      <j1 rule="hyper" parents="139 957 29910"/>
    </justification>
  </clause>

  <clause id="29954">
    <literal><![CDATA[
      L(x,y,a(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,28800,a,b,29910,a(flip))].">
      <j1 rule="hyper" parents="36 28800 29910"/>
    </justification>
  </clause>

  <clause id="29955">
    <literal><![CDATA[
      (x * a(x,y,z)) \ (x * (u * a(x,y,z))) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(29910(a,1),26739(a,1,2))].">
      <j1 rule="para" parents="29910 26739"/>
    </justification>
  </clause>

  <clause id="29956">
    <literal><![CDATA[
      a(x,y,z) * (x * u) = x * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,29945,a(flip),b,24650,a),flip(a)].">
      <j1 rule="hyper" parents="144 29945 24650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29957">
    <literal><![CDATA[
      R(R(x,y,z),u,a(x,w,v5)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(29945(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29945 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29958">
    <literal><![CDATA[
      (R(x,y,z) * u) * a(x,w,v5) = R(x,y,z) * (u * a(x,w,v5))
    ]]></literal>
    <justification jstring="[para(29945(a,1),506(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="29945 506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29959">
    <literal><![CDATA[
      (L(x,y,z) * u) * a(x,w,v5) = L(x,y,z) * (u * a(x,w,v5))
    ]]></literal>
    <justification jstring="[para(29945(a,1),510(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="29945 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29960">
    <literal><![CDATA[
      L(x,y,z) \ (u * a(x,w,v5)) = (L(x,y,z) \ u) * a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(29945(a,1),1028(a,1,1,1))].">
      <j1 rule="para" parents="29945 1028"/>
    </justification>
  </clause>

  <clause id="29961">
    <literal><![CDATA[
      (x * ((y * x) \ z)) * a(y,x,(y * x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[para(29945(a,1),2608(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29945 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29962">
    <literal><![CDATA[
      L(x,y,a(z,x,x)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,29287,a,b,29954,a)].">
      <j1 rule="hyper" parents="64 29287 29954"/>
    </justification>
  </clause>

  <clause id="29963">
    <literal><![CDATA[
      L(x * y,z,a(x,x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(64,a,29304,a(flip),b,29954,a)].">
      <j1 rule="hyper" parents="64 29304 29954"/>
    </justification>
  </clause>

  <clause id="29964">
    <literal><![CDATA[
      L(x * y,z,a(y,y,x)) = x * y
    ]]></literal>
    <justification jstring="[hyper(64,a,29294,a(flip),b,29954,a)].">
      <j1 rule="hyper" parents="64 29294 29954"/>
    </justification>
  </clause>

  <clause id="29965">
    <literal><![CDATA[
      L(x * y,z,a(x,y,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(64,a,29200,a(flip),b,29954,a)].">
      <j1 rule="hyper" parents="64 29200 29954"/>
    </justification>
  </clause>

  <clause id="29966">
    <literal><![CDATA[
      (a(x,y,z) * u) / x = a(x,y,z) * (u / x)
    ]]></literal>
    <justification jstring="[hyper(225,a,29954,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 29954 10262"/>
    </justification>
  </clause>

  <clause id="29967">
    <literal><![CDATA[
      x * (a(x,y,y) * y) = R(x,y,y) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,29954,a(flip),b,29232,a),flip(a)].">
      <j1 rule="hyper" parents="145 29954 29232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29968">
    <literal><![CDATA[
      a(x,y,z) * ((a(x,y,z) \ u) * x) = u * x
    ]]></literal>
    <justification jstring="[hyper(145,a,29954,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 29954 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29969">
    <literal><![CDATA[
      L(x,y,a(L(x,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,30,a,b,29954,a(flip))].">
      <j1 rule="hyper" parents="42 30 29954"/>
    </justification>
  </clause>

  <clause id="29970">
    <literal><![CDATA[
      L(T(x,y),z,a(x,u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(29954(a,1),25(a,2,1))].">
      <j1 rule="para" parents="29954 25"/>
    </justification>
  </clause>

  <clause id="29971">
    <literal><![CDATA[
      L(R(x,y,z),u,a(x,w,v5)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(29954(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29954 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29972">
    <literal><![CDATA[
      L(L(x,y,z),u,a(x,w,v5)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(29954(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29954 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29973">
    <literal><![CDATA[
      a(x,y,z) \ (u * x) = (a(x,y,z) \ u) * x
    ]]></literal>
    <justification jstring="[para(29954(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="29954 598"/>
    </justification>
  </clause>

  <clause id="29974">
    <literal><![CDATA[
      (a(x,y,z) * u) * L(x,w,v5) = a(x,y,z) * (u * L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(29954(a,1),513(a,1,2,1))].">
      <j1 rule="para" parents="29954 513"/>
    </justification>
  </clause>

  <clause id="29975">
    <literal><![CDATA[
      (a(x,y,z) * u) * R(x,w,v5) = a(x,y,z) * (u * R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(29954(a,1),514(a,1,2,1))].">
      <j1 rule="para" parents="29954 514"/>
    </justification>
  </clause>

  <clause id="29976">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),a(y,z,u) * y,a(y,z,u)) = y \ L(y * x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(29954(a,1),2290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29954 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29977">
    <literal><![CDATA[
      L(1 / x,y,a(x,z,u)) = 1 / x
    ]]></literal>
    <justification jstring="[para(2641(a,1),29954(a,1,3))].">
      <j1 rule="para" parents="2641 29954"/>
    </justification>
  </clause>

  <clause id="29978">
    <literal><![CDATA[
      L(x \ 1,y,a(x,z,u)) = x \ 1
    ]]></literal>
    <justification jstring="[para(2653(a,1),29954(a,1,3))].">
      <j1 rule="para" parents="2653 29954"/>
    </justification>
  </clause>

  <clause id="29979">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,a(x,w,v5)) = x \ L(R(x,y,z),u,a(x,w,v5))
    ]]></literal>
    <justification jstring="[para(29954(a,1),4243(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29954 4243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29982">
    <literal><![CDATA[
      a(x,y,y) * (y * x) = y * R(x,y,y)
    ]]></literal>
    <justification jstring="[para(29954(a,1),29297(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29954 29297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29983">
    <literal><![CDATA[
      R(x,y,a(z,x,x)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,28832,a,b,29962,a)].">
      <j1 rule="hyper" parents="64 28832 29962"/>
    </justification>
  </clause>

  <clause id="29984">
    <literal><![CDATA[
      (a(x,y,y) * z) / y = a(x,y,y) * (z / y)
    ]]></literal>
    <justification jstring="[hyper(225,a,29962,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 29962 10262"/>
    </justification>
  </clause>

  <clause id="29985">
    <literal><![CDATA[
      (a(x,y,y) \ 1) * y = a(x,y,y) \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,29962,a(flip),b,1139,a),flip(a)].">
      <j1 rule="hyper" parents="139 29962 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29986">
    <literal><![CDATA[
      (a(x,y,y) \ 1) * L(y,z,u) = a(x,y,y) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(29962(a,1),1149(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="29962 1149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29987">
    <literal><![CDATA[
      (a(x,y,y) * z) * L(y,u,w) = a(x,y,y) * (z * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(29962(a,1),513(a,1,2,1))].">
      <j1 rule="para" parents="29962 513"/>
    </justification>
  </clause>

  <clause id="29988">
    <literal><![CDATA[
      (x * y) * a(z,x,x) = x * (y * a(z,x,x))
    ]]></literal>
    <justification jstring="[para(29962(a,1),28800(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29962 28800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29989">
    <literal><![CDATA[
      x \ (y * a(z,x,x)) = (x \ y) * a(z,x,x)
    ]]></literal>
    <justification jstring="[para(29983(a,1),649(a,1,1))].">
      <j1 rule="para" parents="29983 649"/>
    </justification>
  </clause>

  <clause id="29990">
    <literal><![CDATA[
      a(a(L(x,y,z),u,w),v5,x) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,29969,a)].">
      <j1 rule="hyper" parents="54 29969"/>
    </justification>
  </clause>

  <clause id="29991">
    <literal><![CDATA[
      a(L(x,y,z),u,w) * (x * v5) = x * (a(L(x,y,z),u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(144,a,29969,a(flip),b,28734,a),flip(a)].">
      <j1 rule="hyper" parents="144 29969 28734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29992">
    <literal><![CDATA[
      L(x / y,z,a(L(y \ x,u,w),v5,v6)) = x / y
    ]]></literal>
    <justification jstring="[para(26794(a,1),29969(a,1,3))].">
      <j1 rule="para" parents="26794 29969"/>
    </justification>
  </clause>

  <clause id="29993">
    <literal><![CDATA[
      (x * y) / (a(x,x,y) * (x * y)) = 1 / a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,29963,a(flip),b,1156,a)].">
      <j1 rule="hyper" parents="142 29963 1156"/>
    </justification>
  </clause>

  <clause id="29994">
    <literal><![CDATA[
      a(x,x,y) \ (z * (x * y)) = (a(x,x,y) \ z) * (x * y)
    ]]></literal>
    <justification jstring="[para(29963(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="29963 598"/>
    </justification>
  </clause>

  <clause id="29995">
    <literal><![CDATA[
      (a(x,x,y) * ((z * x) * y)) / (x * y) = a(x,x,y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[para(29963(a,1),693(a,1,2))].">
      <j1 rule="para" parents="29963 693"/>
    </justification>
  </clause>

  <clause id="29996">
    <literal><![CDATA[
      ((x * y) * z) * a(y,y,x) = (x * y) * (z * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(29964(a,1),28800(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29964 28800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29997">
    <literal><![CDATA[
      L(x,(y * z) \ a(z,z,y),u) = L(x,a(z,z,y) * (y * z),u)
    ]]></literal>
    <justification jstring="[para(29964(a,1),29779(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="29964 29779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="29998">
    <literal><![CDATA[
      a(x,y,y) \ (z * (x * y)) = (a(x,y,y) \ z) * (x * y)
    ]]></literal>
    <justification jstring="[para(29965(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="29965 598"/>
    </justification>
  </clause>

  <clause id="29999">
    <literal><![CDATA[
      a(x,y,y) * ((x * y) * z) = (x * y) * (z * a(x,y,y))
    ]]></literal>
    <justification jstring="[para(29965(a,1),28743(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29965 28743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30000">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ u) * T(T(x,w),u) = (a(x,y,z) \ 1) \ (T(x,w) * u)
    ]]></literal>
    <justification jstring="[para(29970(a,1),1614(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="29970 1614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30001">
    <literal><![CDATA[
      (x * a(y,z,u)) * (1 / y) = a(y,z,u) * (x * (1 / y))
    ]]></literal>
    <justification jstring="[hyper(145,a,29977,a(flip),b,23191,a)].">
      <j1 rule="hyper" parents="145 29977 23191"/>
    </justification>
  </clause>

  <clause id="30002">
    <literal><![CDATA[
      a(x,y,z) \ (u * (1 / x)) = (a(x,y,z) \ u) * (1 / x)
    ]]></literal>
    <justification jstring="[para(29977(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="29977 598"/>
    </justification>
  </clause>

  <clause id="30003">
    <literal><![CDATA[
      (1 / a(x,y,z)) * (u * T(x \ 1,a(x,y,z) \ u)) = (x \ 1) * ((1 / a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(29978(a,1),15292(a,2,1))].">
      <j1 rule="para" parents="29978 15292"/>
    </justification>
  </clause>

  <clause id="30004">
    <literal><![CDATA[
      L(x \ 1,y,x * ((x \ z) / z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(25653(a,1),29978(a,1,3))].">
      <j1 rule="para" parents="25653 29978"/>
    </justification>
  </clause>

  <clause id="30005">
    <literal><![CDATA[
      R(x,y,z) * (a(x,u,w) \ 1) = a(x,u,w) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,29957,a(flip),b,25664,a),flip(a)].">
      <j1 rule="hyper" parents="139 29957 25664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30006">
    <literal><![CDATA[
      R(x,y,z) \ (u * a(x,w,v5)) = (R(x,y,z) \ u) * a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(29957(a,1),649(a,1,1))].">
      <j1 rule="para" parents="29957 649"/>
    </justification>
  </clause>

  <clause id="30007">
    <literal><![CDATA[
      x * (y * a(x,y,y)) = R(x,y,y) * y
    ]]></literal>
    <justification jstring="[hyper(23185,a,29967,a)].">
      <j1 rule="hyper" parents="23185 29967"/>
    </justification>
  </clause>

  <clause id="30008">
    <literal><![CDATA[
      R(x,x,a(x \ 1,y,y) * y) = (a(x \ 1,y,y) * y) / (R(x \ 1,y,y) * y)
    ]]></literal>
    <justification jstring="[hyper(225,a,29967,a(flip),b,1997,a),flip(a)].">
      <j1 rule="hyper" parents="225 29967 1997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30009">
    <literal><![CDATA[
      x \ (R(y,y \ x,y \ x) * (y \ x)) = a(y,y \ x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,29967,a(flip),b,29308,a(flip))].">
      <j1 rule="hyper" parents="139 29967 29308"/>
    </justification>
  </clause>

  <clause id="30010">
    <literal><![CDATA[
      (R(x,y,y) * y) \ (x * ((y * a(x,y,y)) * z)) = L(K(y,a(x,y,y)) * z,a(x,y,y) * y,x)
    ]]></literal>
    <justification jstring="[para(29967(a,1),10837(a,1,1))].">
      <j1 rule="para" parents="29967 10837"/>
    </justification>
  </clause>

  <clause id="30011">
    <literal><![CDATA[
      (a(x,y,z) * u) / R(x,w,v5) = a(x,y,z) * (u / R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(225,a,29971,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 29971 10262"/>
    </justification>
  </clause>

  <clause id="30012">
    <literal><![CDATA[
      (x * a(y,z,u)) * L(y,w,v5) = a(y,z,u) * (x * L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(145,a,29972,a(flip),b,23191,a)].">
      <j1 rule="hyper" parents="145 29972 23191"/>
    </justification>
  </clause>

  <clause id="30013">
    <literal><![CDATA[
      L(x,y,z) * (a(x,u,w) \ 1) = a(x,u,w) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,29972,a(flip),b,23759,a),flip(a)].">
      <j1 rule="hyper" parents="139 29972 23759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30014">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(x,w,v5)) = (a(x,y,z) \ u) * L(x,w,v5)
    ]]></literal>
    <justification jstring="[para(29972(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="29972 598"/>
    </justification>
  </clause>

  <clause id="30015">
    <literal><![CDATA[
      x \ (a(y,x,x) \ x) = a(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,23768,a,b,29985,a)].">
      <j1 rule="hyper" parents="36 23768 29985"/>
    </justification>
  </clause>

  <clause id="30016">
    <literal><![CDATA[
      (a(x,y,y) \ y) * L(z,y,a(x,y,y)) = (a(x,y,y) \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[para(29985(a,1),1630(a,1,1))].">
      <j1 rule="para" parents="29985 1630"/>
    </justification>
  </clause>

  <clause id="30017">
    <literal><![CDATA[
      (x * y) * a(x,y,y) = R(x,y,y) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,29910,a,b,30007,a)].">
      <j1 rule="hyper" parents="64 29910 30007"/>
    </justification>
  </clause>

  <clause id="30018">
    <literal><![CDATA[
      x * (T(x \ 1,y) * (a(z,x,x) \ 1)) = T(1 / x,y) * (a(z,x,x) \ x)
    ]]></literal>
    <justification jstring="[para(30015(a,1),26391(a,1,2,2))].">
      <j1 rule="para" parents="30015 26391"/>
    </justification>
  </clause>

  <clause id="30019">
    <literal><![CDATA[
      (x * T(y,z)) \ (R(x,y,y) * y) = K(z,y) * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,30017,a(flip),b,24466,a)].">
      <j1 rule="hyper" parents="139 30017 24466"/>
    </justification>
  </clause>

  <clause id="30020">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(x,y,y),x * y) = (R(x,y,y) * y) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(30017(a,1),102(a,2,1))].">
      <j1 rule="para" parents="30017 102"/>
    </justification>
  </clause>

  <clause id="30021">
    <literal><![CDATA[
      x \ ((x * y) * z) = a(x,y,z) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a,b,29944,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 29944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30022">
    <literal><![CDATA[
      x \ ((x * a(y,z,u)) * w) = (w * a(y,z,u)) * a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,23168,a(flip),b,29944,a),flip(a)].">
      <j1 rule="hyper" parents="373 23168 29944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30023">
    <literal><![CDATA[
      x * (a(x,y,z) * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,23136,a,b,29944,a)].">
      <j1 rule="hyper" parents="145 23136 29944"/>
    </justification>
  </clause>

  <clause id="30024">
    <literal><![CDATA[
      L(x,y,a(z,x,y)) \ (z \ ((z * x) * y)) = y * a(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,29944,a,b,28800,a)].">
      <j1 rule="hyper" parents="139 29944 28800"/>
    </justification>
  </clause>

  <clause id="30025">
    <literal><![CDATA[
      (x * a(y,z,u)) \ (w \ ((w * a(y,z,u)) * x)) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(139,a,29944,a,b,23168,a(flip))].">
      <j1 rule="hyper" parents="139 29944 23168"/>
    </justification>
  </clause>

  <clause id="30026">
    <literal><![CDATA[
      x \ (y \ ((y * z) * (z \ x))) = a(y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,29944,a,b,167,a(flip))].">
      <j1 rule="hyper" parents="139 29944 167"/>
    </justification>
  </clause>

  <clause id="30027">
    <literal><![CDATA[
      a(x,y,z) = (y * z) \ (x \ ((x * y) * z))
    ]]></literal>
    <justification jstring="[hyper(139,a,29944,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="139 29944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30028">
    <literal><![CDATA[
      (x / y) \ (x * z) = (y * z) * a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10971,a(flip),b,29944,a)].">
      <j1 rule="hyper" parents="64 10971 29944"/>
    </justification>
  </clause>

  <clause id="30029">
    <literal><![CDATA[
      (x * L(y,x,z)) * a(z,x,L(y,x,z)) = x * y
    ]]></literal>
    <justification jstring="[hyper(64,a,344,a(flip),b,29944,a),flip(a)].">
      <j1 rule="hyper" parents="64 344 29944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30030">
    <literal><![CDATA[
      (x \ 1) * ((y * z) * a(x,y,z)) = ((x \ 1) * y) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,29944,a(flip),b,1600,a)].">
      <j1 rule="hyper" parents="145 29944 1600"/>
    </justification>
  </clause>

  <clause id="30031">
    <literal><![CDATA[
      (x * a(y,z,u)) \ (w \ (a(y,z,u) * (w * x))) = a(w,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,23180,a,b,29944,a(flip))].">
      <j1 rule="hyper" parents="139 23180 29944"/>
    </justification>
  </clause>

  <clause id="30032">
    <literal><![CDATA[
      (x * y) \ ((z / x) \ (z * y)) = a(x \ z,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,10971,a(flip),b,29944,a(flip))].">
      <j1 rule="hyper" parents="139 10971 29944"/>
    </justification>
  </clause>

  <clause id="30033">
    <literal><![CDATA[
      ((x \ y) * z) \ (x \ (y * z)) = a(x \ 1,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,1540,a(flip),b,29944,a(flip))].">
      <j1 rule="hyper" parents="139 1540 29944"/>
    </justification>
  </clause>

  <clause id="30034">
    <literal><![CDATA[
      (x * y) \ ((1 / x) \ y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,539,a(flip),b,29944,a(flip))].">
      <j1 rule="hyper" parents="139 539 29944"/>
    </justification>
  </clause>

  <clause id="30035">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) = (y * L(z,y,x)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,344,a(flip),b,29944,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 344 29944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30036">
    <literal><![CDATA[
      ((x \ y) * z) * a(x,x \ y,z) = x \ (y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),29944(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 29944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30038">
    <literal><![CDATA[
      x \ ((x * y) * z) = (y * z) * T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(23127(a,2),29944(a,2,2))].">
      <j1 rule="para" parents="23127 29944"/>
    </justification>
  </clause>

  <clause id="30039">
    <literal><![CDATA[
      (x * y) \ (((x * y) * z) * u) = (z * u) * a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(26787(a,1),29944(a,2,2))].">
      <j1 rule="para" parents="26787 29944"/>
    </justification>
  </clause>

  <clause id="30040">
    <literal><![CDATA[
      a(x,x,y) \ ((1 / x) \ y) = x * y
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,30034,a)].">
      <j1 rule="hyper" parents="40 23134 30034"/>
    </justification>
  </clause>

  <clause id="30041">
    <literal><![CDATA[
      a(x,x,y) * (x * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(39,a,23174,a,b,30034,a)].">
      <j1 rule="hyper" parents="39 23174 30034"/>
    </justification>
  </clause>

  <clause id="30042">
    <literal><![CDATA[
      x * a(y,y,y \ x) = (1 / y) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,30034,a(flip),b,174,a(flip))].">
      <j1 rule="hyper" parents="145 30034 174"/>
    </justification>
  </clause>

  <clause id="30043">
    <literal><![CDATA[
      a(x,x,y) * ((x \ 1) * y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(144,a,30034,a(flip),b,25375,a)].">
      <j1 rule="hyper" parents="144 30034 25375"/>
    </justification>
  </clause>

  <clause id="30044">
    <literal><![CDATA[
      a(x,x,y) \ (x \ y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(30034(a,1),25534(a,1,1))].">
      <j1 rule="para" parents="30034 25534"/>
    </justification>
  </clause>

  <clause id="30045">
    <literal><![CDATA[
      L(x,y,(z * u) \ (z \ u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(30034(a,1),29357(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30034 29357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30046">
    <literal><![CDATA[
      a(x,x,x \ y) * y = (1 / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(395,a,30040,a)].">
      <j1 rule="hyper" parents="395 30040"/>
    </justification>
  </clause>

  <clause id="30047">
    <literal><![CDATA[
      (((1 / x) \ y) \ z) * (a(x,x,y) \ ((((1 / x) \ y) \ z) \ z)) = (z / ((1 / x) \ y)) * (x * y)
    ]]></literal>
    <justification jstring="[para(30040(a,1),19692(a,2,2))].">
      <j1 rule="para" parents="30040 19692"/>
    </justification>
  </clause>

  <clause id="30048">
    <literal><![CDATA[
      a(x,x,y) * (x * y) = R(x,x,y) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,1913,a,b,30041,a),flip(a)].">
      <j1 rule="hyper" parents="373 1913 30041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30049">
    <literal><![CDATA[
      a(x / y,x / y,x) \ y = ((x / y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,82,a(flip),b,30043,a)].">
      <j1 rule="hyper" parents="139 82 30043"/>
    </justification>
  </clause>

  <clause id="30050">
    <literal><![CDATA[
      a(x,x,x * y) \ y = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,9,a(flip),b,30043,a)].">
      <j1 rule="hyper" parents="139 9 30043"/>
    </justification>
  </clause>

  <clause id="30051">
    <literal><![CDATA[
      a(x,x \ 1,y) * ((x \ 1) * y) = x \ y
    ]]></literal>
    <justification jstring="[para(5598(a,2),30043(a,1,1))].">
      <j1 rule="para" parents="5598 30043"/>
    </justification>
  </clause>

  <clause id="30052">
    <literal><![CDATA[
      R(a(x,x,y),(x \ 1) * y,z) \ ((x \ y) * z) = (a(x,x,y) \ (x \ y)) * z
    ]]></literal>
    <justification jstring="[para(30044(a,1),649(a,1,1,2))].">
      <j1 rule="para" parents="30044 649"/>
    </justification>
  </clause>

  <clause id="30053">
    <literal><![CDATA[
      a(x,x,y) * x = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,29319,a,b,30048,a(flip))].">
      <j1 rule="hyper" parents="36 29319 30048"/>
    </justification>
  </clause>

  <clause id="30054">
    <literal><![CDATA[
      x * a(x,x,y) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,29318,a,b,30048,a(flip))].">
      <j1 rule="hyper" parents="36 29318 30048"/>
    </justification>
  </clause>

  <clause id="30055">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * x = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,28832,a(flip),b,30053,a),flip(a)].">
      <j1 rule="hyper" parents="373 28832 30053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30056">
    <literal><![CDATA[
      (a(x,x,y) \ 1) \ x = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29925,a,b,30053,a)].">
      <j1 rule="hyper" parents="64 29925 30053"/>
    </justification>
  </clause>

  <clause id="30057">
    <literal><![CDATA[
      (x / (y * x)) * y = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,2082,a,b,30053,a)].">
      <j1 rule="hyper" parents="36 2082 30053"/>
    </justification>
  </clause>

  <clause id="30058">
    <literal><![CDATA[
      x \ R(x,x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,2069,a,b,30053,a)].">
      <j1 rule="hyper" parents="36 2069 30053"/>
    </justification>
  </clause>

  <clause id="30059">
    <literal><![CDATA[
      R(x,x,y) \ (a(x,x,y) * z) = L(x \ z,x,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(30053(a,1),102(a,2,1)),flip(a)].">
      <j1 rule="para" parents="30053 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30060">
    <literal><![CDATA[
      (a(x,x,y) * x) \ (x * z) = x * (R(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(30053(a,2),1907(a,1,1))].">
      <j1 rule="para" parents="30053 1907"/>
    </justification>
  </clause>

  <clause id="30061">
    <literal><![CDATA[
      a(x,x,y) / R(x,x,y) = 1 / x
    ]]></literal>
    <justification jstring="[para(30053(a,1),23933(a,1,2))].">
      <j1 rule="para" parents="30053 23933"/>
    </justification>
  </clause>

  <clause id="30062">
    <literal><![CDATA[
      x * (y \ R(y,y,z)) = a(y,y,z) * x
    ]]></literal>
    <justification jstring="[para(30053(a,1),23967(a,1,2,2))].">
      <j1 rule="para" parents="30053 23967"/>
    </justification>
  </clause>

  <clause id="30063">
    <literal><![CDATA[
      L(x,y,a(y,y,z)) * R(y,y,z) = a(y,y,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(30053(a,1),28667(a,1,2))].">
      <j1 rule="para" parents="30053 28667"/>
    </justification>
  </clause>

  <clause id="30064">
    <literal><![CDATA[
      (x \ y) * a(y,y,x) = x \ R(y,y,x)
    ]]></literal>
    <justification jstring="[para(30053(a,1),29335(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30053 29335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30065">
    <literal><![CDATA[
      x \ L(x,x,a(y,z,u)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,28832,a(flip),b,30054,a)].">
      <j1 rule="hyper" parents="139 28832 30054"/>
    </justification>
  </clause>

  <clause id="30066">
    <literal><![CDATA[
      (1 / x) \ a(x,x,y) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16060,a,b,30054,a)].">
      <j1 rule="hyper" parents="64 16060 30054"/>
    </justification>
  </clause>

  <clause id="30067">
    <literal><![CDATA[
      a(x,x,y * x) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(35,a,26283,a,b,30054,a),flip(a)].">
      <j1 rule="hyper" parents="35 26283 30054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30068">
    <literal><![CDATA[
      a(x \ y,x \ y,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(35,a,15011,a,b,30054,a),flip(a)].">
      <j1 rule="hyper" parents="35 15011 30054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30069">
    <literal><![CDATA[
      a(x \ y,x \ y,x) = (x / y) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(35,a,10631,a,b,30054,a),flip(a)].">
      <j1 rule="hyper" parents="35 10631 30054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30070">
    <literal><![CDATA[
      x * ((x \ y) / y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,3012,a,b,30054,a)].">
      <j1 rule="hyper" parents="35 3012 30054"/>
    </justification>
  </clause>

  <clause id="30071">
    <literal><![CDATA[
      x * R(x \ 1,x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1988,a,b,30054,a)].">
      <j1 rule="hyper" parents="35 1988 30054"/>
    </justification>
  </clause>

  <clause id="30072">
    <literal><![CDATA[
      T(x,y) \ R(x,x,z) = K(y,x) * a(x,x,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,30054,a(flip),b,5829,a)].">
      <j1 rule="hyper" parents="139 30054 5829"/>
    </justification>
  </clause>

  <clause id="30073">
    <literal><![CDATA[
      x * (L(x,y,z) \ a(x,x,u)) = L(x,y,z) \ R(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,30054,a(flip),b,2328,a),flip(a)].">
      <j1 rule="hyper" parents="139 30054 2328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30074">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * (a(x,x,y) \ (R(x,x,y) * z)) = ((a(x,x,y) \ 1) * T(x,a(x,x,y))) * z
    ]]></literal>
    <justification jstring="[para(30054(a,1),1597(a,1,2,2,1))].">
      <j1 rule="para" parents="30054 1597"/>
    </justification>
  </clause>

  <clause id="30075">
    <literal><![CDATA[
      L(L(a(x,x,y),x,z),z * x,z) = L(x,z,z) \ L(R(x,x,y),z,z)
    ]]></literal>
    <justification jstring="[para(30054(a,1),2290(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30054 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30076">
    <literal><![CDATA[
      (a(x,x,y) * z) / R(x,x,y) = L(z / x,x,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(30054(a,1),28811(a,2,2)),flip(a)].">
      <j1 rule="para" parents="30054 28811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30077">
    <literal><![CDATA[
      L(x \ R(x,L(x,y,z),u),y,z) = a(L(x,y,z),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,4246,a(flip),b,30058,a)].">
      <j1 rule="hyper" parents="64 4246 30058"/>
    </justification>
  </clause>

  <clause id="30078">
    <literal><![CDATA[
      (x \ 1) * R(x,x,y) = a(x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3022,a(flip),b,30058,a)].">
      <j1 rule="hyper" parents="64 3022 30058"/>
    </justification>
  </clause>

  <clause id="30079">
    <literal><![CDATA[
      a(x,x,x * y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,3015,a(flip),b,30058,a),flip(a)].">
      <j1 rule="hyper" parents="64 3015 30058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30080">
    <literal><![CDATA[
      a(x,x,x \ y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,1992,a(flip),b,30058,a),flip(a)].">
      <j1 rule="hyper" parents="64 1992 30058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30081">
    <literal><![CDATA[
      R(1 / x,x,y) = a(x,x,y) / x
    ]]></literal>
    <justification jstring="[hyper(142,a,30058,a(flip),b,2007,a),flip(a)].">
      <j1 rule="hyper" parents="142 30058 2007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30082">
    <literal><![CDATA[
      a(x,x,y) / x = y / (x * y)
    ]]></literal>
    <justification jstring="[hyper(142,a,30058,a(flip),b,1986,a(flip))].">
      <j1 rule="hyper" parents="142 30058 1986"/>
    </justification>
  </clause>

  <clause id="30083">
    <literal><![CDATA[
      R(x \ 1,x,y) = x \ a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,30058,a(flip),b,1987,a),flip(a)].">
      <j1 rule="hyper" parents="139 30058 1987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30084">
    <literal><![CDATA[
      x \ a(x,x,x * y) = y / (x * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,30058,a(flip),b,3015,a(flip))].">
      <j1 rule="hyper" parents="139 30058 3015"/>
    </justification>
  </clause>

  <clause id="30085">
    <literal><![CDATA[
      x \ a(x,x,y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(139,a,30058,a(flip),b,3008,a(flip))].">
      <j1 rule="hyper" parents="139 30058 3008"/>
    </justification>
  </clause>

  <clause id="30086">
    <literal><![CDATA[
      (x / (y * x)) \ a(y,y,x) = y
    ]]></literal>
    <justification jstring="[hyper(139,a,30058,a(flip),b,1986,a(flip))].">
      <j1 rule="hyper" parents="139 30058 1986"/>
    </justification>
  </clause>

  <clause id="30087">
    <literal><![CDATA[
      R(x,x,y) * L(z,a(x,x,y),x) = x * ((x \ R(x,x,y)) * z)
    ]]></literal>
    <justification jstring="[para(30058(a,1),515(a,1,2,2))].">
      <j1 rule="para" parents="30058 515"/>
    </justification>
  </clause>

  <clause id="30088">
    <literal><![CDATA[
      L(a(x,x,y),z,u) * L(x,z,u) = L(R(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(30058(a,1),4250(a,1,1,1))].">
      <j1 rule="para" parents="30058 4250"/>
    </justification>
  </clause>

  <clause id="30089">
    <literal><![CDATA[
      a(x,x,y) \ (x \ 1) = R(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(30058(a,1),5366(a,1,1))].">
      <j1 rule="para" parents="30058 5366"/>
    </justification>
  </clause>

  <clause id="30090">
    <literal><![CDATA[
      R(x,x,y) \ x = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(30058(a,1),5382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30058 5382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30091">
    <literal><![CDATA[
      x \ R(T(x,y),x,z) = K(x,y) * a(x,x,z)
    ]]></literal>
    <justification jstring="[para(30058(a,1),23663(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30058 23663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30092">
    <literal><![CDATA[
      a(x,x,y) * ((z * z) \ x) = R((z * z) \ x,x,y)
    ]]></literal>
    <justification jstring="[para(30058(a,1),25782(a,1,1))].">
      <j1 rule="para" parents="30058 25782"/>
    </justification>
  </clause>

  <clause id="30093">
    <literal><![CDATA[
      R(R(x,x,y),R(x,x,y),y) = R(x,x,y) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(30058(a,1),25151(a,2,2))].">
      <j1 rule="para" parents="30058 25151"/>
    </justification>
  </clause>

  <clause id="30094">
    <literal><![CDATA[
      K(x,y * z) * a(z,z,y) = (y / T(z * y,x)) * z
    ]]></literal>
    <justification jstring="[para(30058(a,1),27228(a,1,2))].">
      <j1 rule="para" parents="30058 27228"/>
    </justification>
  </clause>

  <clause id="30095">
    <literal><![CDATA[
      R(1 / x,x,y) \ 1 = a(x,x,y) \ x
    ]]></literal>
    <justification jstring="[para(30058(a,1),27842(a,2,1))].">
      <j1 rule="para" parents="30058 27842"/>
    </justification>
  </clause>

  <clause id="30096">
    <literal><![CDATA[
      x \ ((y \ x) * a(y,y,z)) = R(x \ (y \ x),y,z)
    ]]></literal>
    <justification jstring="[para(30058(a,1),28059(a,1,2,2))].">
      <j1 rule="para" parents="30058 28059"/>
    </justification>
  </clause>

  <clause id="30097">
    <literal><![CDATA[
      (x / (y * x)) * y = a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2653,a,b,30057,a),flip(a)].">
      <j1 rule="hyper" parents="373 2653 30057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30098">
    <literal><![CDATA[
      a(x,x,y) \ x = (y / (x * y)) \ 1
    ]]></literal>
    <justification jstring="[para(30057(a,1),3280(a,1,1))].">
      <j1 rule="para" parents="30057 3280"/>
    </justification>
  </clause>

  <clause id="30099">
    <literal><![CDATA[
      a(x,x,y) * ((y / (x * y)) \ 1) = x
    ]]></literal>
    <justification jstring="[para(30057(a,1),3281(a,1,1))].">
      <j1 rule="para" parents="30057 3281"/>
    </justification>
  </clause>

  <clause id="30100">
    <literal><![CDATA[
      L((x * (y / (x * y))) \ z,x * (y / (x * y)),a(x,x,y)) = (1 / (x * (y / (x * y)))) * z
    ]]></literal>
    <justification jstring="[para(30057(a,1),23984(a,1,3))].">
      <j1 rule="para" parents="30057 23984"/>
    </justification>
  </clause>

  <clause id="30101">
    <literal><![CDATA[
      R(x,y,(((z * u) \ u) * z) \ w) = R(x,y,a(z,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(30057(a,1),26245(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30057 26245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30102">
    <literal><![CDATA[
      L(x \ 1,y,(z / (x * z)) * x) = x \ 1
    ]]></literal>
    <justification jstring="[para(30057(a,2),29978(a,1,3))].">
      <j1 rule="para" parents="30057 29978"/>
    </justification>
  </clause>

  <clause id="30103">
    <literal><![CDATA[
      x * ((x \ y) / y) = a(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11980,a,b,30070,a),flip(a)].">
      <j1 rule="hyper" parents="373 11980 30070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30104">
    <literal><![CDATA[
      (x \ a(x,x,y)) * y = x \ y
    ]]></literal>
    <justification jstring="[para(30070(a,1),84(a,1,1,2))].">
      <j1 rule="para" parents="30070 84"/>
    </justification>
  </clause>

  <clause id="30105">
    <literal><![CDATA[
      a(x,x,y) \ ((x \ y) / y) = x \ 1
    ]]></literal>
    <justification jstring="[para(30070(a,1),2314(a,1,1))].">
      <j1 rule="para" parents="30070 2314"/>
    </justification>
  </clause>

  <clause id="30106">
    <literal><![CDATA[
      (x * (y \ (x \ y))) * ((x \ y) / y) = a(x,x,y) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(30070(a,1),2547(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30070 2547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30107">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ 1 = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(30070(a,1),3279(a,1,1,1))].">
      <j1 rule="para" parents="30070 3279"/>
    </justification>
  </clause>

  <clause id="30108">
    <literal><![CDATA[
      a(x,x,y) / (1 / x) = R(x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(30070(a,1),5055(a,1,1))].">
      <j1 rule="para" parents="30070 5055"/>
    </justification>
  </clause>

  <clause id="30109">
    <literal><![CDATA[
      K(x,x \ (y \ x)) / a(y,y,x) = 1 / (y * (x \ (y \ x)))
    ]]></literal>
    <justification jstring="[para(30070(a,1),14506(a,1,2))].">
      <j1 rule="para" parents="30070 14506"/>
    </justification>
  </clause>

  <clause id="30110">
    <literal><![CDATA[
      a(x,y,(z * (u \ (z \ u))) * w) = a(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[para(30070(a,1),27469(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30070 27469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30111">
    <literal><![CDATA[
      a(x,y,((z \ (u \ z)) * u) \ w) = a(x,y,a(u,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(30070(a,1),27672(a,2,3,1))].">
      <j1 rule="para" parents="30070 27672"/>
    </justification>
  </clause>

  <clause id="30112">
    <literal><![CDATA[
      L(x,y,z * (u \ (z \ u))) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(30070(a,1),29018(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30070 29018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30113">
    <literal><![CDATA[
      L(x,y,(z * (u \ (z \ u))) \ w) = L(x,y,a(z,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(30070(a,1),29003(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30070 29003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30114">
    <literal><![CDATA[
      L(x,y,z * (u * (w \ (u \ w)))) = L(x,y,z * a(u,u,w))
    ]]></literal>
    <justification jstring="[para(30070(a,1),29122(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="30070 29122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30115">
    <literal><![CDATA[
      L(x,y * (z \ (y \ z)),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(30070(a,1),29547(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30070 29547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30116">
    <literal><![CDATA[
      L(x,(y \ (z \ y)) * z,u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(30070(a,1),29619(a,2,2))].">
      <j1 rule="para" parents="30070 29619"/>
    </justification>
  </clause>

  <clause id="30117">
    <literal><![CDATA[
      L(x,y * (z * (u \ (z \ u))),w) = L(x,y * a(z,z,u),w)
    ]]></literal>
    <justification jstring="[para(30070(a,1),29675(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="30070 29675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30118">
    <literal><![CDATA[
      (a(x,x,y) / x) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(143,a,30082,a,b,171,a)].">
      <j1 rule="hyper" parents="143 30082 171"/>
    </justification>
  </clause>

  <clause id="30119">
    <literal><![CDATA[
      (a(x,x,y) / x) * y = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(30082(a,2),2014(a,2,1)),flip(a)].">
      <j1 rule="para" parents="30082 2014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30120">
    <literal><![CDATA[
      (a(x,x,T(y,z)) / x) \ K(y,z) = (y / (x * T(y,z))) \ 1
    ]]></literal>
    <justification jstring="[para(30082(a,2),14851(a,1,1))].">
      <j1 rule="para" parents="30082 14851"/>
    </justification>
  </clause>

  <clause id="30121">
    <literal><![CDATA[
      x * (y \ a(y,y,x)) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,30085,a,b,4409,a)].">
      <j1 rule="hyper" parents="145 30085 4409"/>
    </justification>
  </clause>

  <clause id="30122">
    <literal><![CDATA[
      (x \ a(x,x,L(y,z,u))) * y = y * (L(y,z,u) \ (x \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(144,a,30085,a,b,24384,a)].">
      <j1 rule="hyper" parents="144 30085 24384"/>
    </justification>
  </clause>

  <clause id="30123">
    <literal><![CDATA[
      (x \ a(x,x,y)) \ (x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(143,a,30085,a,b,171,a)].">
      <j1 rule="hyper" parents="143 30085 171"/>
    </justification>
  </clause>

  <clause id="30124">
    <literal><![CDATA[
      T(x \ a(x,x,y),y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[para(30085(a,2),117(a,1,1))].">
      <j1 rule="para" parents="30085 117"/>
    </justification>
  </clause>

  <clause id="30125">
    <literal><![CDATA[
      T(x \ a(x,x,y),x \ y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[para(30085(a,2),5144(a,1,1))].">
      <j1 rule="para" parents="30085 5144"/>
    </justification>
  </clause>

  <clause id="30126">
    <literal><![CDATA[
      T(x \ a(x,x,y * z),z * y) = (z * y) \ (x \ (z * y))
    ]]></literal>
    <justification jstring="[para(30085(a,2),15225(a,1,1))].">
      <j1 rule="para" parents="30085 15225"/>
    </justification>
  </clause>

  <clause id="30127">
    <literal><![CDATA[
      (1 / (x \ a(x,x,y))) \ L(y,x \ a(x,x,y),x \ a(x,x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,561,a,b,30104,a)].">
      <j1 rule="hyper" parents="64 561 30104"/>
    </justification>
  </clause>

  <clause id="30128">
    <literal><![CDATA[
      ((x \ a(x,x,y)) * (x \ a(x,x,y))) \ (x \ y) = (1 / (x \ a(x,x,y))) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,30104,a(flip),b,310,a)].">
      <j1 rule="hyper" parents="139 30104 310"/>
    </justification>
  </clause>

  <clause id="30129">
    <literal><![CDATA[
      (x * (y \ a(y,y,z))) \ (x * (y \ z)) = L(z,y \ a(y,y,z),x)
    ]]></literal>
    <justification jstring="[para(30104(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="30104 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30130">
    <literal><![CDATA[
      L(x,y \ a(y,y,x),y \ a(y,y,x)) \ (y \ x) = R(T(y \ a(y,y,x),x),y \ a(y,y,x),x)
    ]]></literal>
    <justification jstring="[para(30104(a,1),24678(a,1,2))].">
      <j1 rule="para" parents="30104 24678"/>
    </justification>
  </clause>

  <clause id="30131">
    <literal><![CDATA[
      (x \ a(x,x,y \ z)) * (z / y) = x \ (z / y)
    ]]></literal>
    <justification jstring="[para(27308(a,1),30104(a,1,1,2))].">
      <j1 rule="para" parents="27308 30104"/>
    </justification>
  </clause>

  <clause id="30132">
    <literal><![CDATA[
      (x \ a(x,x,(y \ z) * u)) * (u * (z / y)) = x \ (u * (z / y))
    ]]></literal>
    <justification jstring="[para(27460(a,2),30104(a,1,1,2))].">
      <j1 rule="para" parents="27460 30104"/>
    </justification>
  </clause>

  <clause id="30133">
    <literal><![CDATA[
      (a(x,x,R(R(x,y,z),u,w)) / x) \ R(R(x,y,z),u,w) = R(R(x,y,z),u,w) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,846,a,b,30118,a),flip(a)].">
      <j1 rule="hyper" parents="373 846 30118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30134">
    <literal><![CDATA[
      a(x,x,y) * ((a(x,x,y) \ x) * z) = (a(x,x,y) \ 1) * (R(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(30056(a,1),1547(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30056 1547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30135">
    <literal><![CDATA[
      a(a(x,x,y) \ x,z,u) = a(R(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(30056(a,1),2675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30056 2675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30136">
    <literal><![CDATA[
      R(x,a(y,y,z) \ y,u) = R(x,R(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(30056(a,1),3028(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30056 3028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30137">
    <literal><![CDATA[
      x * R(1 / x,x,y) = a(x,x,x * y)
    ]]></literal>
    <justification jstring="[para(3025(a,1),30071(a,1,2))].">
      <j1 rule="para" parents="3025 30071"/>
    </justification>
  </clause>

  <clause id="30138">
    <literal><![CDATA[
      R(x / (y \ a(y,y,z)),R(y,y,z),z) = (x * z) / (y \ z)
    ]]></literal>
    <justification jstring="[para(30083(a,1),3053(a,1,1,2))].">
      <j1 rule="para" parents="30083 3053"/>
    </justification>
  </clause>

  <clause id="30139">
    <literal><![CDATA[
      R(R(T(x \ 1,y),x,z),R(x,x,z),y) = y \ ((1 / (x \ a(x,x,z))) \ y)
    ]]></literal>
    <justification jstring="[para(30083(a,1),3045(a,2,2,1,2))].">
      <j1 rule="para" parents="30083 3045"/>
    </justification>
  </clause>

  <clause id="30140">
    <literal><![CDATA[
      R(x / (y \ a(y,y,z)),L(y,y,z),z) = (x * z) / (y \ z)
    ]]></literal>
    <justification jstring="[para(30083(a,1),26641(a,1,1,2))].">
      <j1 rule="para" parents="30083 26641"/>
    </justification>
  </clause>

  <clause id="30141">
    <literal><![CDATA[
      R(x,x,y) \ x = y \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5665,a(flip),b,30090,a),flip(a)].">
      <j1 rule="hyper" parents="373 5665 30090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30142">
    <literal><![CDATA[
      x * (R(y,y,z) \ y) = x * (a(y,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,30090,a,b,9,a)].">
      <j1 rule="hyper" parents="145 30090 9"/>
    </justification>
  </clause>

  <clause id="30143">
    <literal><![CDATA[
      (a(x,x,y) \ 1) / x = 1 / R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,30090,a(flip),b,2835,a)].">
      <j1 rule="hyper" parents="142 30090 2835"/>
    </justification>
  </clause>

  <clause id="30144">
    <literal><![CDATA[
      x \ (a(x,x,y) \ 1) = R(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,30090,a(flip),b,1909,a)].">
      <j1 rule="hyper" parents="139 30090 1909"/>
    </justification>
  </clause>

  <clause id="30145">
    <literal><![CDATA[
      (R(x,x,y) \ x) * z = z * (a(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(30090(a,2),23736(a,1,1))].">
      <j1 rule="para" parents="30090 23736"/>
    </justification>
  </clause>

  <clause id="30146">
    <literal><![CDATA[
      x \ (y \ L(y,x,x)) = R(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,30141,a(flip),b,1909,a)].">
      <j1 rule="hyper" parents="139 30141 1909"/>
    </justification>
  </clause>

  <clause id="30147">
    <literal><![CDATA[
      x * R(1 / x,x,y) = a(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,450,a,b,30067,a)].">
      <j1 rule="hyper" parents="373 450 30067"/>
    </justification>
  </clause>

  <clause id="30148">
    <literal><![CDATA[
      (x * y) \ (y * (x / (y * x))) = L(x * y,y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,30067,a(flip),b,1847,a)].">
      <j1 rule="hyper" parents="139 30067 1847"/>
    </justification>
  </clause>

  <clause id="30149">
    <literal><![CDATA[
      a(x,x,((y / x) * R(x,z,u)) * x) = x * (((y / x) * R(x,z,u)) / (R(x,z,u) * y))
    ]]></literal>
    <justification jstring="[para(25045(a,1),30067(a,2,2,2))].">
      <j1 rule="para" parents="25045 30067"/>
    </justification>
  </clause>

  <clause id="30150">
    <literal><![CDATA[
      L(x,(a(y,y,z * y) * u) * w,v5) = L(x,w * (((z / (y * z)) * y) * u),v5)
    ]]></literal>
    <justification jstring="[para(30067(a,2),29667(a,1,2,1,1))].">
      <j1 rule="para" parents="30067 29667"/>
    </justification>
  </clause>

  <clause id="30151">
    <literal><![CDATA[
      L((x / (y * x)) * y,z,u) \ K(x / (y * x),y) = L(a(y,y,y * x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(30079(a,2),26149(a,2,1,1))].">
      <j1 rule="para" parents="30079 26149"/>
    </justification>
  </clause>

  <clause id="30152">
    <literal><![CDATA[
      x * (a(x,x,y) / x) = a(x,x,x * y)
    ]]></literal>
    <justification jstring="[para(30082(a,2),30079(a,2,2)),flip(a)].">
      <j1 rule="para" parents="30082 30079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30153">
    <literal><![CDATA[
      (x * L(x \ y,x,x)) \ (x * (x \ y)) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,29905,a,b,30080,a)].">
      <j1 rule="hyper" parents="64 29905 30080"/>
    </justification>
  </clause>

  <clause id="30154">
    <literal><![CDATA[
      ((x * x) * (x \ y)) / (x * y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,15469,a,b,30080,a)].">
      <j1 rule="hyper" parents="64 15469 30080"/>
    </justification>
  </clause>

  <clause id="30155">
    <literal><![CDATA[
      (x \ a(x,x,y)) * x = a(x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(30085(a,2),30080(a,2,1)),flip(a)].">
      <j1 rule="para" parents="30085 30080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30156">
    <literal><![CDATA[
      (x \ a(x,x,x * y)) * x = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,30084,a,b,30082,a)].">
      <j1 rule="hyper" parents="144 30084 30082"/>
    </justification>
  </clause>

  <clause id="30157">
    <literal><![CDATA[
      a((x / y) \ 1,x / y,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),30097(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 30097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30158">
    <literal><![CDATA[
      a(x \ 1,x,y) \ ((y / (x * y)) * z) = L(x \ z,x,y / (x * y))
    ]]></literal>
    <justification jstring="[para(30097(a,1),102(a,2,1)),flip(a)].">
      <j1 rule="para" parents="30097 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30159">
    <literal><![CDATA[
      (a(x,x,y) \ x) * ((x \ y) / y) = 1
    ]]></literal>
    <justification jstring="[hyper(144,a,30098,a,b,2032,a)].">
      <j1 rule="hyper" parents="144 30098 2032"/>
    </justification>
  </clause>

  <clause id="30160">
    <literal><![CDATA[
      (a(x,x,y) \ x) * z = ((y / (x * y)) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,30098,a,b,11,a)].">
      <j1 rule="hyper" parents="144 30098 11"/>
    </justification>
  </clause>

  <clause id="30161">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ z = ((y / (x * y)) \ 1) \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,30098,a)].">
      <j1 rule="hyper" parents="62 30098"/>
    </justification>
  </clause>

  <clause id="30162">
    <literal><![CDATA[
      x \ ((y / (x * y)) \ 1) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,30098,a(flip),b,29921,a)].">
      <j1 rule="hyper" parents="139 30098 29921"/>
    </justification>
  </clause>

  <clause id="30163">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ 1 = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(30098(a,2),3004(a,2,1)),flip(a)].">
      <j1 rule="para" parents="30098 3004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30164">
    <literal><![CDATA[
      a(x,x,y) / ((y / (x * y)) \ 1) = a(x,x,y) * (a(x,x,y) / x)
    ]]></literal>
    <justification jstring="[para(30098(a,1),27166(a,1,2))].">
      <j1 rule="para" parents="30098 27166"/>
    </justification>
  </clause>

  <clause id="30165">
    <literal><![CDATA[
      (a(x,x,y) / x) \ 1 = a(x,x,y) \ x
    ]]></literal>
    <justification jstring="[para(30082(a,2),30098(a,2,1)),flip(a)].">
      <j1 rule="para" parents="30082 30098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30166">
    <literal><![CDATA[
      ((1 / ((x / (y * x)) \ 1)) \ a(y,y,x)) / (((x / (y * x)) \ 1) * ((x / (y * x)) \ 1)) = (a(y,y,x) / ((x / (y * x)) \ 1)) * K(y,((x / (y * x)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(30099(a,1),27119(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30099 27119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30167">
    <literal><![CDATA[
      L(x,x \ (y \ x),y) = a(y,y \ 1,x) \ x
    ]]></literal>
    <justification jstring="[para(30103(a,1),10261(a,2,1))].">
      <j1 rule="para" parents="30103 10261"/>
    </justification>
  </clause>

  <clause id="30168">
    <literal><![CDATA[
      a(x,x,y) \ (y \ (x \ y)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(30105(a,1),28755(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30105 28755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30169">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ 1 = x \ a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30085,a,b,30107,a),flip(a)].">
      <j1 rule="hyper" parents="373 30085 30107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30170">
    <literal><![CDATA[
      (x \ a(x,x,y)) * (a(x,x,y) * K(a(x,x,y) / x,y)) = (y \ (x \ y)) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(30124(a,1),8268(a,2,1))].">
      <j1 rule="para" parents="30124 8268"/>
    </justification>
  </clause>

  <clause id="30171">
    <literal><![CDATA[
      L(x \ R(x,a(y,y,z) \ y,z \ (y \ z)),x,1) = a(x,a(y,y,z) \ y,(y \ z) / z)
    ]]></literal>
    <justification jstring="[para(30159(a,1),24152(a,1,3))].">
      <j1 rule="para" parents="30159 24152"/>
    </justification>
  </clause>

  <clause id="30172">
    <literal><![CDATA[
      a(x,x,y) * K(x \ 1,z) = x * R(T(x \ 1,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27073,a(flip),b,30062,a),flip(a)].">
      <j1 rule="hyper" parents="64 27073 30062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30173">
    <literal><![CDATA[
      (x \ (y / x)) * a(y / x,x \ y,x) = x \ R(y / x,y / x,x)
    ]]></literal>
    <justification jstring="[para(25642(a,1),30064(a,1,2))].">
      <j1 rule="para" parents="25642 30064"/>
    </justification>
  </clause>

  <clause id="30174">
    <literal><![CDATA[
      T(x,x \ y) * (x \ R(x \ y,x \ y,x)) = x * ((x \ (y / x)) * a(x \ y,x \ y,x))
    ]]></literal>
    <justification jstring="[para(30064(a,1),25474(a,1,2))].">
      <j1 rule="para" parents="30064 25474"/>
    </justification>
  </clause>

  <clause id="30175">
    <literal><![CDATA[
      a(x,x,y) \ ((x \ 1) * y) = (R(x,x,y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(30089(a,1),29322(a,2,1))].">
      <j1 rule="para" parents="30089 29322"/>
    </justification>
  </clause>

  <clause id="30176">
    <literal><![CDATA[
      a(x,x,x * y) \ 1 = (R(x,x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(30137(a,1),27046(a,1,1))].">
      <j1 rule="para" parents="30137 27046"/>
    </justification>
  </clause>

  <clause id="30177">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) * z) / L(x,R(x,x,y) \ 1,z) = z * (T(a(x,x,y) \ 1,z) / x)
    ]]></literal>
    <justification jstring="[para(30144(a,1),29784(a,1,2,2))].">
      <j1 rule="para" parents="30144 29784"/>
    </justification>
  </clause>

  <clause id="30178">
    <literal><![CDATA[
      a(x,y,((z \ L(z,u,u)) \ w) * v5) = a(x,y,(((R(u,u,z) \ 1) * u) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(30146(a,1),27413(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="30146 27413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30179">
    <literal><![CDATA[
      R(x,x,y) * (1 / x) = a(x,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2169,a,b,30147,a)].">
      <j1 rule="hyper" parents="64 2169 30147"/>
    </justification>
  </clause>

  <clause id="30180">
    <literal><![CDATA[
      a(x,x,y * x) \ 1 = (R(x,x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(30147(a,1),27046(a,1,1))].">
      <j1 rule="para" parents="30147 27046"/>
    </justification>
  </clause>

  <clause id="30181">
    <literal><![CDATA[
      L(x,y,a(z,z,z * u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(30152(a,1),24004(a,1,3))].">
      <j1 rule="para" parents="30152 24004"/>
    </justification>
  </clause>

  <clause id="30182">
    <literal><![CDATA[
      L(x,y,a(z,z,z * u) * w) = L(x,y,a(z,z,u) * w)
    ]]></literal>
    <justification jstring="[para(30152(a,1),28994(a,1,3,1))].">
      <j1 rule="para" parents="30152 28994"/>
    </justification>
  </clause>

  <clause id="30183">
    <literal><![CDATA[
      L(x,y,a(z,z,z \ u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(30155(a,1),23833(a,1,3))].">
      <j1 rule="para" parents="30155 23833"/>
    </justification>
  </clause>

  <clause id="30184">
    <literal><![CDATA[
      a(a(x,x,x \ y),z,u) = a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(30155(a,1),26836(a,1,1))].">
      <j1 rule="para" parents="30155 26836"/>
    </justification>
  </clause>

  <clause id="30185">
    <literal><![CDATA[
      a(x,y,a(z,z,z \ u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(30155(a,1),27299(a,1,3))].">
      <j1 rule="para" parents="30155 27299"/>
    </justification>
  </clause>

  <clause id="30186">
    <literal><![CDATA[
      a(x,y,z * a(u,u,u \ w)) = a(x,y,z * a(u,u,w))
    ]]></literal>
    <justification jstring="[para(30155(a,1),27319(a,1,3,2))].">
      <j1 rule="para" parents="30155 27319"/>
    </justification>
  </clause>

  <clause id="30187">
    <literal><![CDATA[
      a(x,y,(a(z,z,z \ u) \ w) \ v5) = a(x,y,(a(z,z,u) \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(30155(a,1),27521(a,1,3,1,1))].">
      <j1 rule="para" parents="30155 27521"/>
    </justification>
  </clause>

  <clause id="30188">
    <literal><![CDATA[
      L(x,a(y,y,y \ z),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(30155(a,1),29441(a,1,2))].">
      <j1 rule="para" parents="30155 29441"/>
    </justification>
  </clause>

  <clause id="30189">
    <literal><![CDATA[
      a(x,y,a(z,z,z * u)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(30156(a,1),27299(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30156 27299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30190">
    <literal><![CDATA[
      a(x,y,(R(z \ 1,z,u) \ 1) * w) = a(x,y,(a(z,z,u) \ z) * w)
    ]]></literal>
    <justification jstring="[para(30163(a,1),5341(a,1,3,1,1))].">
      <j1 rule="para" parents="30163 5341"/>
    </justification>
  </clause>

  <clause id="30191">
    <literal><![CDATA[
      (a(x,x,y) / x) \ K(z,u) = (a(x,x,y) \ x) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,30165,a(flip),b,14511,a),flip(a)].">
      <j1 rule="hyper" parents="144 30165 14511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30192">
    <literal><![CDATA[
      ((a(x,x,y) / x) \ 1) * y = a(x,x,y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(30165(a,2),29322(a,2,1)),flip(a)].">
      <j1 rule="para" parents="30165 29322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30193">
    <literal><![CDATA[
      K(x,y) / (z \ a(z,z,u)) = K(x,y) * (a(z,z,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(225,a,30169,a(flip),b,14403,a)].">
      <j1 rule="hyper" parents="225 30169 14403"/>
    </justification>
  </clause>

  <clause id="30194">
    <literal><![CDATA[
      R(x,x,y) * (a(x,x,z) / R(x,x,z)) = a(x,x,y * x)
    ]]></literal>
    <justification jstring="[para(30061(a,2),30179(a,1,2))].">
      <j1 rule="para" parents="30061 30179"/>
    </justification>
  </clause>

  <clause id="30195">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) * (y * L(z,y,x)) = y * z
    ]]></literal>
    <justification jstring="[hyper(64,a,344,a(flip),b,30021,a),flip(a)].">
      <j1 rule="hyper" parents="64 344 30021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30196">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ (y * z) = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,344,a(flip),b,30021,a(flip))].">
      <j1 rule="hyper" parents="139 344 30021"/>
    </justification>
  </clause>

  <clause id="30197">
    <literal><![CDATA[
      a(x,x \ y,z) * ((x \ y) * z) = x \ (y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),30021(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 30021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30199">
    <literal><![CDATA[
      x \ ((x * (y \ 1)) * z) = a(x,y,z) * ((y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(11980(a,1),30021(a,2,1))].">
      <j1 rule="para" parents="11980 30021"/>
    </justification>
  </clause>

  <clause id="30200">
    <literal><![CDATA[
      (x * L(a(y,z,u),w,v5)) \ (v6 \ ((v6 * L(a(y,z,u),w,v5)) * x)) = a(v6,L(a(y,z,u),w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25336,a(flip),b,30027,a)].">
      <j1 rule="hyper" parents="373 25336 30027"/>
    </justification>
  </clause>

  <clause id="30201">
    <literal><![CDATA[
      (a(x,y,y) * z) \ (x \ ((x * a(x,y,y)) * z)) = a(a(x,y,y),x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29365,a,b,30027,a),flip(a)].">
      <j1 rule="hyper" parents="64 29365 30027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30202">
    <literal><![CDATA[
      ((x \ y) * z) \ (x \ (y * z)) = a(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),30027(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 30027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30203">
    <literal><![CDATA[
      ((x * y) \ (x * (y * z))) * L(((x * y) \ (x * (y * z))) \ z,u,w) = (x * y) \ (x * ((y * z) * L(a(x,y,z),u,w)))
    ]]></literal>
    <justification jstring="[para(30027(a,2),2747(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="30027 2747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30204">
    <literal><![CDATA[
      K(x,a(y,y,y \ x)) * (x \ (a(y,y,y \ x) * (L(a(y,y,y \ x),z,u) \ x))) = x \ (L(a(y,y,y \ x),z,u) \ ((1 / y) \ (y \ x)))
    ]]></literal>
    <justification jstring="[para(30042(a,1),28913(a,2,2,2))].">
      <j1 rule="para" parents="30042 28913"/>
    </justification>
  </clause>

  <clause id="30205">
    <literal><![CDATA[
      a(x \ y,x \ y,(x \ y) \ y) * y = (1 / (x \ y)) \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,361,a,b,30046,a),flip(a)].">
      <j1 rule="hyper" parents="373 361 30046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30206">
    <literal><![CDATA[
      (x * a(y,y,y * x)) \ x = x \ ((y \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[para(30050(a,1),25170(a,2,2))].">
      <j1 rule="para" parents="30050 25170"/>
    </justification>
  </clause>

  <clause id="30207">
    <literal><![CDATA[
      (x * (y / (x * y))) \ y = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(30079(a,1),30050(a,1,1))].">
      <j1 rule="para" parents="30079 30050"/>
    </justification>
  </clause>

  <clause id="30208">
    <literal><![CDATA[
      a(x \ y,x \ y,(x \ z) \ z) = (x / y) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27307,a,b,30069,a)].">
      <j1 rule="hyper" parents="64 27307 30069"/>
    </justification>
  </clause>

  <clause id="30209">
    <literal><![CDATA[
      L(x,y,(z / u) * (u / z)) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[para(30069(a,1),29296(a,1,3))].">
      <j1 rule="para" parents="30069 29296"/>
    </justification>
  </clause>

  <clause id="30211">
    <literal><![CDATA[
      L(x \ 1,y,x * ((x * z) \ z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,29076,a(flip),b,30102,a)].">
      <j1 rule="hyper" parents="64 29076 30102"/>
    </justification>
  </clause>

  <clause id="30212">
    <literal><![CDATA[
      a(x,x,y) / L(y \ x,y,x \ a(x,x,y)) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,15003,a,b,30119,a)].">
      <j1 rule="hyper" parents="64 15003 30119"/>
    </justification>
  </clause>

  <clause id="30213">
    <literal><![CDATA[
      T(x \ a(x,x,(y / x) * L(x,z,u)),x \ ((y / x) * L(x,z,u))) = (L(x,z,u) * y) \ ((y / x) * L(x,z,u))
    ]]></literal>
    <justification jstring="[para(24854(a,1),30125(a,2,1))].">
      <j1 rule="para" parents="24854 30125"/>
    </justification>
  </clause>

  <clause id="30214">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (z \ u)) \ 1)) = a(x,y,a(z,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(30162(a,1),27972(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30162 27972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30215">
    <literal><![CDATA[
      L(x \ 1,y,x * ((z * x) \ z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,29091,a,b,30211,a)].">
      <j1 rule="hyper" parents="64 29091 30211"/>
    </justification>
  </clause>

  <clause id="30217">
    <literal><![CDATA[
      L((x \ y) \ 1,z,(x \ y) * (y \ x)) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),30215(a,1,3,2,1))].">
      <j1 rule="para" parents="10 30215"/>
    </justification>
  </clause>

  <clause id="30218">
    <literal><![CDATA[
      (x * (a(x,y,z) * u)) / (x * u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,23169,a,b,29912,a)].">
      <j1 rule="hyper" parents="142 23169 29912"/>
    </justification>
  </clause>

  <clause id="30219">
    <literal><![CDATA[
      x * (y * a(x,x,y)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,30041,a(flip),b,29912,a),flip(a)].">
      <j1 rule="hyper" parents="64 30041 29912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30220">
    <literal><![CDATA[
      x \ ((1 / x) \ y) = y * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,30041,a(flip),b,29912,a(flip))].">
      <j1 rule="hyper" parents="139 30041 29912"/>
    </justification>
  </clause>

  <clause id="30221">
    <literal><![CDATA[
      (x * (y * a(x,z,u))) \ ((a(x,z,u) * x) * y) = a(a(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(29912(a,1),14(a,2,1)),flip(a)].">
      <j1 rule="para" parents="29912 14"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30222">
    <literal><![CDATA[
      x * ((L(x,x,y) \ y) * a(x,z,u)) = a(x,z,u) * R(y,x,x)
    ]]></literal>
    <justification jstring="[para(11857(a,1),29912(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11857 29912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30223">
    <literal><![CDATA[
      x * (a(x,y,y) * a(x,z,u)) = a(x,z,u) * R(x,y,y)
    ]]></literal>
    <justification jstring="[para(15984(a,1),29912(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15984 29912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30224">
    <literal><![CDATA[
      x * (a(x,x,y) * a(x,z,u)) = a(x,z,u) * R(x,x,y)
    ]]></literal>
    <justification jstring="[para(30054(a,1),29912(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30054 29912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30225">
    <literal><![CDATA[
      x * (a(x,x,y) * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,23169,a,b,30219,a)].">
      <j1 rule="hyper" parents="64 23169 30219"/>
    </justification>
  </clause>

  <clause id="30226">
    <literal><![CDATA[
      L(x,y,z) * a(u,u,L(x,y,z)) = L(u \ ((1 / u) \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,1779,a,b,30219,a),flip(a)].">
      <j1 rule="hyper" parents="35 1779 30219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30227">
    <literal><![CDATA[
      (x * y) * a(x,x,x * y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,1124,a(flip),b,30219,a),flip(a)].">
      <j1 rule="hyper" parents="35 1124 30219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30228">
    <literal><![CDATA[
      x \ ((1 / x) \ y) = a(x,x,y) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,30219,a(flip),b,23169,a)].">
      <j1 rule="hyper" parents="139 30219 23169"/>
    </justification>
  </clause>

  <clause id="30229">
    <literal><![CDATA[
      L(x * a(y,y,x),y,y) = x
    ]]></literal>
    <justification jstring="[hyper(39,a,561,a,b,30219,a(flip))].">
      <j1 rule="hyper" parents="39 561 30219"/>
    </justification>
  </clause>

  <clause id="30230">
    <literal><![CDATA[
      x \ (y \ ((1 / y) \ x)) = a(y,y,x)
    ]]></literal>
    <justification jstring="[para(30219(a,1),69(a,1,2,2))].">
      <j1 rule="para" parents="30219 69"/>
    </justification>
  </clause>

  <clause id="30231">
    <literal><![CDATA[
      x * (y \ ((1 / y) \ z)) = x * (z * a(y,y,z))
    ]]></literal>
    <justification jstring="[para(30219(a,1),169(a,1,2,2))].">
      <j1 rule="para" parents="30219 169"/>
    </justification>
  </clause>

  <clause id="30232">
    <literal><![CDATA[
      a(x,y,z \ ((1 / z) \ u)) = a(x,y,u * a(z,z,u))
    ]]></literal>
    <justification jstring="[para(30219(a,1),13875(a,1,3,2))].">
      <j1 rule="para" parents="30219 13875"/>
    </justification>
  </clause>

  <clause id="30233">
    <literal><![CDATA[
      L(a(x,x,y) * y,x,x) = y
    ]]></literal>
    <justification jstring="[hyper(24736,a,30229,a)].">
      <j1 rule="hyper" parents="24736 30229"/>
    </justification>
  </clause>

  <clause id="30234">
    <literal><![CDATA[
      L(R(x * a(y,y,x),z,u),y,y) = R(x,z,u)
    ]]></literal>
    <justification jstring="[para(30229(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30229 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30235">
    <literal><![CDATA[
      L(L(x * a(y,y,x),z,u),y,y) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(30229(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30229 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30236">
    <literal><![CDATA[
      (x \ 1) * L(y * a(x,x,y),z,u) = x \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(30229(a,1),1149(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30229 1149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30237">
    <literal><![CDATA[
      R(x,y * a(z,z,y),L(y * a(z,z,y),z,z)) = R(x,y,y * a(z,z,y))
    ]]></literal>
    <justification jstring="[para(30229(a,1),26646(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30229 26646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30238">
    <literal><![CDATA[
      (x \ 1) * (a(x,x,y) * y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,30233,a(flip),b,1139,a),flip(a)].">
      <j1 rule="hyper" parents="139 30233 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30239">
    <literal><![CDATA[
      a(x,x,y) \ (x \ ((1 / x) \ y)) = y
    ]]></literal>
    <justification jstring="[hyper(139,a,30220,a,b,23136,a)].">
      <j1 rule="hyper" parents="139 30220 23136"/>
    </justification>
  </clause>

  <clause id="30240">
    <literal><![CDATA[
      x * a(y \ x,y \ x,x) = ((x / y) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,15128,a(flip),b,30220,a),flip(a)].">
      <j1 rule="hyper" parents="64 15128 30220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30241">
    <literal><![CDATA[
      L(a(x,x,y \ z),y \ z,y) = z \ (y * (x \ ((1 / x) \ (y \ z))))
    ]]></literal>
    <justification jstring="[para(30220(a,2),101(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="30220 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30242">
    <literal><![CDATA[
      a(x,y,(z \ ((1 / z) \ u)) * w) = a(x,y,(a(z,z,u) * u) * w)
    ]]></literal>
    <justification jstring="[para(30220(a,2),27395(a,1,3,1))].">
      <j1 rule="para" parents="30220 27395"/>
    </justification>
  </clause>

  <clause id="30243">
    <literal><![CDATA[
      a(x,y,z \ ((z \ 1) \ u)) = a(x,y,u * a(z,z,u))
    ]]></literal>
    <justification jstring="[para(30220(a,1),27511(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30220 27511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30244">
    <literal><![CDATA[
      a(x,y,(z \ ((z \ 1) \ u)) \ w) = a(x,y,(u * a(z,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(30220(a,1),27621(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30220 27621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30245">
    <literal><![CDATA[
      a(x,x,R(y,1 / x,1 / x)) * R(y,1 / x,1 / x) = x \ (L(1 / x,1 / x,y) \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,11856,a,b,30225,a),flip(a)].">
      <j1 rule="hyper" parents="139 11856 30225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30246">
    <literal><![CDATA[
      ((1 / x) \ y) * L(z,a(x,x,y) * y,x) = x * ((a(x,x,y) * y) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,30225,a(flip),b,213,a)].">
      <j1 rule="hyper" parents="144 30225 213"/>
    </justification>
  </clause>

  <clause id="30247">
    <literal><![CDATA[
      (x / ((y \ 1) * (a(y,y,z) * z))) * (y \ 1) = (x / ((1 / y) \ z)) * y
    ]]></literal>
    <justification jstring="[para(30225(a,1),1624(a,2,1,2))].">
      <j1 rule="para" parents="30225 1624"/>
    </justification>
  </clause>

  <clause id="30248">
    <literal><![CDATA[
      a((x \ ((1 / x) \ y)) * z,u,w) = a(L(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(30228(a,2),5679(a,1,1,1))].">
      <j1 rule="para" parents="30228 5679"/>
    </justification>
  </clause>

  <clause id="30249">
    <literal><![CDATA[
      a(x,x,y \ z) * (z / y) = x \ ((1 / x) \ (z / y))
    ]]></literal>
    <justification jstring="[para(27308(a,1),30228(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27308 30228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30250">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u \ 1) \ w))) = a(x,y,z \ (a(u,u,w) * w))
    ]]></literal>
    <justification jstring="[para(30228(a,1),27659(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="30228 27659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30251">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) \ y = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(30230(a,1),9924(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30230 9924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30252">
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) * (a(x,x,u) * u)) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(30238(a,1),27183(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30238 27183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30253">
    <literal><![CDATA[
      L(x,(R(T(y,z),u,w) \ 1) * (a(R(T(y,z),u,w),R(T(y,z),u,w),v5) * v5),v6) = L(x,R(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(30238(a,2),29464(a,1,2))].">
      <j1 rule="para" parents="30238 29464"/>
    </justification>
  </clause>

  <clause id="30254">
    <literal><![CDATA[
      x * a(y,y,y * x) = y \ ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,30227,a(flip),b,29910,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 30227 29910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30255">
    <literal><![CDATA[
      a(L(x * y,x,x),z,u) = a((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(30227(a,1),23949(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30227 23949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30256">
    <literal><![CDATA[
      L(x,y,L(z * u,z,z)) = L(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(30227(a,1),24660(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30227 24660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30257">
    <literal><![CDATA[
      R(x,L(y * z,y,y),u) = R(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(30227(a,1),26536(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30227 26536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30258">
    <literal><![CDATA[
      (x * y) * (x * (y / (x * y))) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(30079(a,1),30227(a,1,2))].">
      <j1 rule="para" parents="30079 30227"/>
    </justification>
  </clause>

  <clause id="30259">
    <literal><![CDATA[
      (((x * y) / (x * (z \ ((1 / z) \ y)))) * x) * (z \ ((1 / z) \ y)) = x * ((z \ ((1 / z) \ y)) * R(a(z,z,y) \ 1,x,z \ ((1 / z) \ y)))
    ]]></literal>
    <justification jstring="[para(30251(a,1),2735(a,2,2,2,1))].">
      <j1 rule="para" parents="30251 2735"/>
    </justification>
  </clause>

  <clause id="30261">
    <literal><![CDATA[
      a(x,x,y * x) * y = x \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27364,a,b,30254,a)].">
      <j1 rule="hyper" parents="64 27364 30254"/>
    </justification>
  </clause>

  <clause id="30262">
    <literal><![CDATA[
      (x * a(y,y,y * x)) \ x = x / (y \ ((y \ 1) \ x))
    ]]></literal>
    <justification jstring="[para(30254(a,1),23761(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30254 23761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30263">
    <literal><![CDATA[
      x * (a(x,y,z) * (x \ u)) = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,23169,a,b,29922,a)].">
      <j1 rule="hyper" parents="64 23169 29922"/>
    </justification>
  </clause>

  <clause id="30264">
    <literal><![CDATA[
      x \ (a(x,y,z) * u) = a(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,29922,a(flip),b,23169,a)].">
      <j1 rule="hyper" parents="139 29922 23169"/>
    </justification>
  </clause>

  <clause id="30265">
    <literal><![CDATA[
      (a(x,y,y) * z) \ (R(x,y,y) * (x \ z)) = a(x,a(x,y,y),x \ z)
    ]]></literal>
    <justification jstring="[para(29922(a,1),23959(a,1,1))].">
      <j1 rule="para" parents="29922 23959"/>
    </justification>
  </clause>

  <clause id="30266">
    <literal><![CDATA[
      a(x,y,z) * (a(u,w,v5) * x) = x * (a(x,y,z) * a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(145,a,23928,a(flip),b,29923,a)].">
      <j1 rule="hyper" parents="145 23928 29923"/>
    </justification>
  </clause>

  <clause id="30267">
    <literal><![CDATA[
      x \ (a(x,y,z) \ (x * u)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(139,a,29923,a,b,xx)].">
      <j1 rule="hyper" parents="139 29923"/>
    </justification>
  </clause>

  <clause id="30268">
    <literal><![CDATA[
      a(x,y,z) \ ((x \ 1) \ u) = (x \ 1) \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(35,a,27807,a(flip),b,29923,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 27807 29923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30269">
    <literal><![CDATA[
      x * (a(x,y,z) \ (x \ u)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(10(a,1),29923(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 29923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30270">
    <literal><![CDATA[
      x * (((x \ y) * a(x,z,u)) / (a(x,z,u) * y)) = a(x,x,a(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(29941(a,1),30070(a,1,2,1))].">
      <j1 rule="para" parents="29941 30070"/>
    </justification>
  </clause>

  <clause id="30271">
    <literal><![CDATA[
      a(x,y,z) \ (x \ u) = x \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(23920,a,29942,a)].">
      <j1 rule="hyper" parents="23920 29942"/>
    </justification>
  </clause>

  <clause id="30272">
    <literal><![CDATA[
      x * (a(x,y,z) * (z * y)) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,25786,a(flip),b,29946,a),flip(a)].">
      <j1 rule="hyper" parents="64 25786 29946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30273">
    <literal><![CDATA[
      (x * (a(x,y,z) * x)) * u = a(x,y,z) * ((x * x) * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,29956,a(flip),b,133,a)].">
      <j1 rule="hyper" parents="144 29956 133"/>
    </justification>
  </clause>

  <clause id="30275">
    <literal><![CDATA[
      x \ (a(x,y,z) * (x * u)) = T(a(x,y,z),x) * u
    ]]></literal>
    <justification jstring="[para(29956(a,2),23189(a,1,2))].">
      <j1 rule="para" parents="29956 23189"/>
    </justification>
  </clause>

  <clause id="30276">
    <literal><![CDATA[
      (a(x,y,z) \ u) / x = a(x,y,z) \ (u / x)
    ]]></literal>
    <justification jstring="[hyper(755,a,29966,a),flip(a)].">
      <j1 rule="hyper" parents="755 29966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30277">
    <literal><![CDATA[
      (x * x) * ((a(x,y,z) * u) \ (a(x,y,z) * (u / x))) = L(x,x,a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(29966(a,1),26051(a,1,2,2))].">
      <j1 rule="para" parents="29966 26051"/>
    </justification>
  </clause>

  <clause id="30278">
    <literal><![CDATA[
      (a(x,y,y * x) \ y) * x = L(y * x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26996,a(flip),b,29973,a),flip(a)].">
      <j1 rule="hyper" parents="64 26996 29973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30279">
    <literal><![CDATA[
      L(a(x,y,y),z,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(14211,a,29988,a)].">
      <j1 rule="hyper" parents="14211 29988"/>
    </justification>
  </clause>

  <clause id="30280">
    <literal><![CDATA[
      a(x,y,a(z,x,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,29988,a(flip),b,15463,a),flip(a)].">
      <j1 rule="hyper" parents="140 29988 15463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30281">
    <literal><![CDATA[
      a(x,y,y) \ (y * z) = y * (a(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[para(30279(a,1),27804(a,1,1))].">
      <j1 rule="para" parents="30279 27804"/>
    </justification>
  </clause>

  <clause id="30282">
    <literal><![CDATA[
      (x \ y) * a(y,x,x) = x \ R(y,x,x)
    ]]></literal>
    <justification jstring="[para(15984(a,1),29989(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15984 29989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30283">
    <literal><![CDATA[
      K(x,y) * a(y,y,z * y) = y * R(K(x,y) / y,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27889,a(flip),b,30072,a),flip(a)].">
      <j1 rule="hyper" parents="64 27889 30072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30284">
    <literal><![CDATA[
      K(x,y) * a(x,x,x \ y) = T(y / (y * x),x) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,27232,a(flip),b,30091,a),flip(a)].">
      <j1 rule="hyper" parents="64 27232 30091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30285">
    <literal><![CDATA[
      K(x,y) * a(x,x,y) = (y / (y * x)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,26027,a(flip),b,30091,a),flip(a)].">
      <j1 rule="hyper" parents="64 26027 30091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30286">
    <literal><![CDATA[
      x \ ((y * (x / y)) * a(y,y,y \ x)) = ((y \ x) / ((y \ x) * y)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,11893,a,b,30285,a)].">
      <j1 rule="hyper" parents="64 11893 30285"/>
    </justification>
  </clause>

  <clause id="30287">
    <literal><![CDATA[
      ((x / (x * y)) * y) \ K(K(y,x) * a(y,y,x),a(y,y,x) \ (K(y,x) \ 1)) = 1 / (K(y,x) * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(30285(a,1),14629(a,1,1))].">
      <j1 rule="para" parents="30285 14629"/>
    </justification>
  </clause>

  <clause id="30288">
    <literal><![CDATA[
      a(x,y,z * ((u / (u * w)) * w)) = a(x,y,z * a(w,w,u))
    ]]></literal>
    <justification jstring="[para(30285(a,1),27330(a,1,3,2))].">
      <j1 rule="para" parents="30285 27330"/>
    </justification>
  </clause>

  <clause id="30289">
    <literal><![CDATA[
      a(x,y,L((z / (z * u)) * u,w,v5)) = a(x,y,L(a(u,u,z),w,v5))
    ]]></literal>
    <justification jstring="[para(30285(a,1),27425(a,1,3,1))].">
      <j1 rule="para" parents="30285 27425"/>
    </justification>
  </clause>

  <clause id="30290">
    <literal><![CDATA[
      L(x,y,L((z / (z * u)) * u,w,v5)) = L(x,y,L(a(u,u,z),w,v5))
    ]]></literal>
    <justification jstring="[para(30285(a,1),29005(a,1,3,1))].">
      <j1 rule="para" parents="30285 29005"/>
    </justification>
  </clause>

  <clause id="30291">
    <literal><![CDATA[
      L(x,x \ (y \ x),y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5587,a(flip),b,30167,a),flip(a)].">
      <j1 rule="hyper" parents="373 5587 30167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30292">
    <literal><![CDATA[
      L(T(x,y),x \ (z \ x),z) = T(L(x,z \ 1,z),y)
    ]]></literal>
    <justification jstring="[para(30291(a,1),25(a,2,1))].">
      <j1 rule="para" parents="30291 25"/>
    </justification>
  </clause>

  <clause id="30293">
    <literal><![CDATA[
      a(x,x,x * y) \ 1 = z / (z / ((y / (x * y)) \ (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27040,a,b,30176,a),flip(a)].">
      <j1 rule="hyper" parents="373 27040 30176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30294">
    <literal><![CDATA[
      L(x,y,a(z,z,z * u)) = L(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,29287,a,b,30181,a),flip(a)].">
      <j1 rule="hyper" parents="373 29287 30181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30295">
    <literal><![CDATA[
      L(a(x * y,x,x),z,a(x,x,y)) = a(x * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29288,a(flip),b,30181,a),flip(a)].">
      <j1 rule="hyper" parents="64 29288 30181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30296">
    <literal><![CDATA[
      L(x,y,a(z \ u,z \ u,u)) = L(x,y,a(z \ u,z \ u,z))
    ]]></literal>
    <justification jstring="[para(27299(a,1),30181(a,1,3))].">
      <j1 rule="para" parents="27299 30181"/>
    </justification>
  </clause>

  <clause id="30297">
    <literal><![CDATA[
      L(x,y,a(z \ u,z,z)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29287,a,b,30183,a)].">
      <j1 rule="hyper" parents="64 29287 30183"/>
    </justification>
  </clause>

  <clause id="30298">
    <literal><![CDATA[
      L(x \ y,z,a(x,x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,29312,a(flip),b,30183,a),flip(a)].">
      <j1 rule="hyper" parents="64 29312 30183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30299">
    <literal><![CDATA[
      L(x \ y,z,a(y,x,x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,29287,a,b,30298,a)].">
      <j1 rule="hyper" parents="64 29287 30298"/>
    </justification>
  </clause>

  <clause id="30300">
    <literal><![CDATA[
      a(a(x,x,y),z,x \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,30298,a)].">
      <j1 rule="hyper" parents="54 30298"/>
    </justification>
  </clause>

  <clause id="30301">
    <literal><![CDATA[
      (a(x,x,y) * y) / (x \ y) = a(x,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(225,a,30298,a(flip),b,102,a(flip))].">
      <j1 rule="hyper" parents="225 30298 102"/>
    </justification>
  </clause>

  <clause id="30302">
    <literal><![CDATA[
      a(x,x,y) * ((x \ y) * z) = (x \ y) * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,30298,a(flip),b,28734,a),flip(a)].">
      <j1 rule="hyper" parents="144 30298 28734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30303">
    <literal><![CDATA[
      L(L(x \ y,z,a(x,x,y)),x,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(30298(a,2),569(a,1,1))].">
      <j1 rule="para" parents="30298 569"/>
    </justification>
  </clause>

  <clause id="30304">
    <literal><![CDATA[
      R(a(x,x,y) \ 1,z,L(x \ y,z,a(x,x,y))) = ((a(x,x,y) \ 1) * (z * (x \ y))) / (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(30298(a,1),1634(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="30298 1634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30305">
    <literal><![CDATA[
      T(a(x,x,y) * (z / (x \ y)),x \ y) = (x \ y) \ (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(30298(a,1),14740(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30298 14740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30306">
    <literal><![CDATA[
      ((1 / a(x,x,y)) * x) * (x \ y) = ((1 / a(x,x,y)) * y) * 1
    ]]></literal>
    <justification jstring="[para(30300(a,1),2652(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30300 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30307">
    <literal><![CDATA[
      a(x,y,y) * ((y \ x) * z) = (y \ x) * (a(x,y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(144,a,30299,a(flip),b,28734,a),flip(a)].">
      <j1 rule="hyper" parents="144 30299 28734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30308">
    <literal><![CDATA[
      L(x,(a(y,z,z) * ((z \ y) * a(y,z,z))) * u,w) = L(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(30299(a,1),29845(a,2,2,1))].">
      <j1 rule="para" parents="30299 29845"/>
    </justification>
  </clause>

  <clause id="30309">
    <literal><![CDATA[
      a(a(x \ y,x \ y,y),z,u) = a(a(x \ y,x \ y,x),z,u)
    ]]></literal>
    <justification jstring="[para(27307(a,1),30184(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27307 30184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30310">
    <literal><![CDATA[
      a(x,y,a(z,z,u * z)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(25788(a,1),30185(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25788 30185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30311">
    <literal><![CDATA[
      L(x,(y * z) \ (y \ z),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29698,a(flip),b,30188,a)].">
      <j1 rule="hyper" parents="64 29698 30188"/>
    </justification>
  </clause>

  <clause id="30312">
    <literal><![CDATA[
      a(x * y,z,a(x,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,29332,a(flip),b,30189,a),flip(a)].">
      <j1 rule="hyper" parents="64 29332 30189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30313">
    <literal><![CDATA[
      L(a(x,x,y),z,x * y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,30312,a)].">
      <j1 rule="hyper" parents="53 30312"/>
    </justification>
  </clause>

  <clause id="30314">
    <literal><![CDATA[
      L(a(x,x,y),z,y * x) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(24201,a,30313,a)].">
      <j1 rule="hyper" parents="24201 30313"/>
    </justification>
  </clause>

  <clause id="30315">
    <literal><![CDATA[
      L(L(a(x,x,y),z,u),w,x * y) = L(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(30313(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30313 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30316">
    <literal><![CDATA[
      (x * y) \ (z * a(x,x,y)) = ((x * y) \ z) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(30313(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="30313 598"/>
    </justification>
  </clause>

  <clause id="30317">
    <literal><![CDATA[
      R(R(x,y,z),y * z,L(a(x,x,y),z,x * y)) = ((x * y) * (z * a(x,x,y))) / ((y * z) * a(x,x,y))
    ]]></literal>
    <justification jstring="[para(30313(a,1),2293(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="30313 2293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30318">
    <literal><![CDATA[
      (x * y) * (z * R(a(x,x,y),x * y,z)) = (a(x,x,y) * (x * y)) * z
    ]]></literal>
    <justification jstring="[para(30313(a,1),25558(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="30313 25558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30319">
    <literal><![CDATA[
      L(x,y \ ((z * u) * ((z * u) * a(z,z,u))),w) = L(x,y \ a(z,z,u),w)
    ]]></literal>
    <justification jstring="[para(30313(a,1),29695(a,2,2,2))].">
      <j1 rule="para" parents="30313 29695"/>
    </justification>
  </clause>

  <clause id="30320">
    <literal><![CDATA[
      L(x,y,(z * u) * ((z * u) * a(u,u,z))) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(30314(a,1),2185(a,2,3))].">
      <j1 rule="para" parents="30314 2185"/>
    </justification>
  </clause>

  <clause id="30321">
    <literal><![CDATA[
      a((x * y) * ((x * y) * a(y,y,x)),z,u) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(30314(a,1),2640(a,2,1))].">
      <j1 rule="para" parents="30314 2640"/>
    </justification>
  </clause>

  <clause id="30322">
    <literal><![CDATA[
      L(x,(y * z) * ((y * z) * a(z,z,y)),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(30314(a,1),11778(a,2,2))].">
      <j1 rule="para" parents="30314 11778"/>
    </justification>
  </clause>

  <clause id="30323">
    <literal><![CDATA[
      x / ((y \ 1) * (y * x)) = y * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(226,a,30207,a)].">
      <j1 rule="hyper" parents="226 30207"/>
    </justification>
  </clause>

  <clause id="30324">
    <literal><![CDATA[
      (x * y) \ ((x \ 1) \ y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(149,a,30258,a)].">
      <j1 rule="hyper" parents="149 30258"/>
    </justification>
  </clause>

  <clause id="30325">
    <literal><![CDATA[
      a(x,y,z) * (x \ (R(a(x,y,z),x,L(u,x,a(x,y,z))) \ (x * u))) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,1938,a(flip),b,30263,a),flip(a)].">
      <j1 rule="hyper" parents="35 1938 30263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30326">
    <literal><![CDATA[
      L(a(x,y,z) \ u,x,a(x,y,z)) = (a(x,y,z) * x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(30267(a,1),346(a,1,1))].">
      <j1 rule="para" parents="30267 346"/>
    </justification>
  </clause>

  <clause id="30327">
    <literal><![CDATA[
      L(a(x,y,z) \ u,x,a(x,y,z)) = (x * a(x,y,z)) \ (x * u)
    ]]></literal>
    <justification jstring="[para(30267(a,1),23941(a,1,1))].">
      <j1 rule="para" parents="30267 23941"/>
    </justification>
  </clause>

  <clause id="30328">
    <literal><![CDATA[
      (1 / x) \ (a(x,y,z) \ 1) = a(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,30269,a(flip),b,25709,a)].">
      <j1 rule="hyper" parents="139 30269 25709"/>
    </justification>
  </clause>

  <clause id="30329">
    <literal><![CDATA[
      a(x,x,y) \ (1 / x) = 1 / R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30143,a(flip),b,30276,a),flip(a)].">
      <j1 rule="hyper" parents="64 30143 30276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30330">
    <literal><![CDATA[
      ((1 / x) \ 1) * L(y,1 / R(x,x,z),a(x,x,z)) = a(x,x,z) * ((a(x,x,z) \ ((1 / x) \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(30329(a,1),29707(a,1,2,2))].">
      <j1 rule="para" parents="30329 29707"/>
    </justification>
  </clause>

  <clause id="30331">
    <literal><![CDATA[
      L(x,y,a(z * u,z,z)) = L(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29287,a,b,30294,a)].">
      <j1 rule="hyper" parents="64 29287 30294"/>
    </justification>
  </clause>

  <clause id="30332">
    <literal><![CDATA[
      L(x,y,a(z,z,u * z)) = L(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,28846,a,b,30294,a)].">
      <j1 rule="hyper" parents="64 28846 30294"/>
    </justification>
  </clause>

  <clause id="30333">
    <literal><![CDATA[
      L(x,y,a(z / u,u,u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(26785(a,2),30297(a,1,3))].">
      <j1 rule="para" parents="26785 30297"/>
    </justification>
  </clause>

  <clause id="30334">
    <literal><![CDATA[
      (x * (y / (x * y))) \ 1 = ((x \ 1) \ y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(30324(a,1),9449(a,1,1))].">
      <j1 rule="para" parents="30324 9449"/>
    </justification>
  </clause>

  <clause id="30335">
    <literal><![CDATA[
      (x \ (a(x,y,z) \ 1)) \ (x \ u) = (a(x,y,z) \ x) \ ((1 / x) \ u)
    ]]></literal>
    <justification jstring="[para(30328(a,1),1679(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30328 1679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30336">
    <literal><![CDATA[
      L(x,y,a(z * u,u,u)) = L(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(26016(a,1),30331(a,1,3))].">
      <j1 rule="para" parents="26016 30331"/>
    </justification>
  </clause>

  <clause id="30337">
    <literal><![CDATA[
      L(x / y,z,a(y,y,x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(64,a,29954,a(flip),b,30333,a),flip(a)].">
      <j1 rule="hyper" parents="64 29954 30333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30338">
    <literal><![CDATA[
      L(x / y,z,a(x,y,y)) = x / y
    ]]></literal>
    <justification jstring="[hyper(64,a,29287,a,b,30337,a)].">
      <j1 rule="hyper" parents="64 29287 30337"/>
    </justification>
  </clause>

  <clause id="30339">
    <literal><![CDATA[
      R(a(x,y,y) \ 1,z,L(x / y,z,a(x,y,y))) = ((a(x,y,y) \ 1) * (z * (x / y))) / (z * (x / y))
    ]]></literal>
    <justification jstring="[para(30338(a,1),1634(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="30338 1634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30340">
    <literal><![CDATA[
      L(x,y,a(z * u,u,u)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,29287,a(flip),b,30336,a),flip(a)].">
      <j1 rule="hyper" parents="373 29287 30336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30341">
    <literal><![CDATA[
      a(x,y,L(a(x,z,u),w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,29913,a)].">
      <j1 rule="hyper" parents="54 29913"/>
    </justification>
  </clause>

  <clause id="30342">
    <literal><![CDATA[
      (x * y) / L(a(x,z,u),w,v5) = x * (y / L(a(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(225,a,29913,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 29913 10262"/>
    </justification>
  </clause>

  <clause id="30343">
    <literal><![CDATA[
      (L(x,y,z) * y) * a(z,y,L(x,y,z)) = x * y
    ]]></literal>
    <justification jstring="[hyper(35,a,988,a(flip),b,29948,a),flip(a)].">
      <j1 rule="hyper" parents="35 988 29948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30344">
    <literal><![CDATA[
      x \ (y \ ((y * (x / z)) * z)) = a(y,z \ x,z)
    ]]></literal>
    <justification jstring="[para(29949(a,1),69(a,1,2,2))].">
      <j1 rule="para" parents="29949 69"/>
    </justification>
  </clause>

  <clause id="30345">
    <literal><![CDATA[
      x * (a(x,y,z) * a(a(x,y,z),u,u \ x)) = (a(x,y,z) * u) * (u \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29956,a(flip),b,29950,a)].">
      <j1 rule="hyper" parents="64 29956 29950"/>
    </justification>
  </clause>

  <clause id="30346">
    <literal><![CDATA[
      a(a(x,y,z) \ u,a(x,y,z),a(x,y,z) \ w) = w \ ((a(x,y,z) \ u) \ (u * (a(x,y,z) \ w)))
    ]]></literal>
    <justification jstring="[para(23135(a,1),30026(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="23135 30026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30347">
    <literal><![CDATA[
      (x * (y \ z)) * a(x \ y,x,y \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),30028(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 30028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30348">
    <literal><![CDATA[
      a(x,y,L(y \ z,y,x)) = (y * L(y \ z,y,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,30029,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 30029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30349">
    <literal><![CDATA[
      (x * (y \ z)) \ ((y / x) \ z) = a(x \ y,x,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),30032(a,1,2,2))].">
      <j1 rule="para" parents="10 30032"/>
    </justification>
  </clause>

  <clause id="30350">
    <literal><![CDATA[
      (x * (y / (y / z))) \ (((z \ R(z,u,w)) / x) \ R(z * K(z \ y,z),u,w)) = a(x \ (z \ R(z,u,w)),x,y / (y / z))
    ]]></literal>
    <justification jstring="[para(25978(a,1),30032(a,1,2,2))].">
      <j1 rule="para" parents="25978 30032"/>
    </justification>
  </clause>

  <clause id="30351">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,y,z),y) = a(z,y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,102,a,b,30035,a)].">
      <j1 rule="hyper" parents="373 102 30035"/>
    </justification>
  </clause>

  <clause id="30352">
    <literal><![CDATA[
      a(x,x,L(y,x,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,29905,a(flip),b,30035,a),flip(a)].">
      <j1 rule="hyper" parents="373 29905 30035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30353">
    <literal><![CDATA[
      a(x,y,L(y,y,x)) = L(y,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,9377,a(flip),b,30035,a),flip(a)].">
      <j1 rule="hyper" parents="373 9377 30035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30354">
    <literal><![CDATA[
      (x * L(L(R(R(y,x,y),z,u),w,v5),x,y)) \ (x * L(R(R(y,x,y),z,u),w,v5)) = a(y,x,L(R(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(4779(a,1),30035(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4779 30035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30355">
    <literal><![CDATA[
      L(L(x,y,y),y,y) \ L(x,y,y) = a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(2871,a,30352,a)].">
      <j1 rule="hyper" parents="2871 30352"/>
    </justification>
  </clause>

  <clause id="30356">
    <literal><![CDATA[
      a(x,x,y * (x \ 1)) = a(x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27565,a(flip),b,30352,a)].">
      <j1 rule="hyper" parents="64 27565 30352"/>
    </justification>
  </clause>

  <clause id="30357">
    <literal><![CDATA[
      a(x,x,(1 / x) * y) = a(x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(569(a,1),30352(a,1,3))].">
      <j1 rule="para" parents="569 30352"/>
    </justification>
  </clause>

  <clause id="30358">
    <literal><![CDATA[
      a(x,x,y) \ L(y,x,x) = L(L(y,x,x),x,x)
    ]]></literal>
    <justification jstring="[para(30352(a,1),5567(a,1,1))].">
      <j1 rule="para" parents="30352 5567"/>
    </justification>
  </clause>

  <clause id="30359">
    <literal><![CDATA[
      (L(x,x,y) \ x) \ y = y * (x \ L(x,x,y))
    ]]></literal>
    <justification jstring="[para(30353(a,1),27951(a,1,1))].">
      <j1 rule="para" parents="30353 27951"/>
    </justification>
  </clause>

  <clause id="30360">
    <literal><![CDATA[
      ((x \ 1) * R(y,x,x)) \ T(y * (x \ 1),x) = a(x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,25164,a,b,30356,a)].">
      <j1 rule="hyper" parents="64 25164 30356"/>
    </justification>
  </clause>

  <clause id="30361">
    <literal><![CDATA[
      a(x,x,x \ ((x \ 1) \ y)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27299,a(flip),b,30356,a),flip(a)].">
      <j1 rule="hyper" parents="64 27299 30356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30362">
    <literal><![CDATA[
      a(x,x,x \ (R(T(y,z),u,w) * v5)) = a(x,x,(1 / x) * (R(y,u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,27512,a,b,30357,a)].">
      <j1 rule="hyper" parents="373 27512 30357"/>
    </justification>
  </clause>

  <clause id="30363">
    <literal><![CDATA[
      L(x,y,L(L(z,u,u),u,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(30358(a,1),5685(a,1,3))].">
      <j1 rule="para" parents="30358 5685"/>
    </justification>
  </clause>

  <clause id="30364">
    <literal><![CDATA[
      a(x,L(L(y,z,z),z,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(30358(a,1),14105(a,1,2))].">
      <j1 rule="para" parents="30358 14105"/>
    </justification>
  </clause>

  <clause id="30365">
    <literal><![CDATA[
      (a(x,x,y) * a(x,x,y)) * z = y * (L(L(y,x,x),x,x) \ z)
    ]]></literal>
    <justification jstring="[para(30358(a,1),14106(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30358 14106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30366">
    <literal><![CDATA[
      a(x,x,y) \ (a(x,x,y) \ 1) = y \ L(L(y,x,x),x,x)
    ]]></literal>
    <justification jstring="[para(30358(a,1),27919(a,2,2))].">
      <j1 rule="para" parents="30358 27919"/>
    </justification>
  </clause>

  <clause id="30367">
    <literal><![CDATA[
      L(x,y,L(L(z * u,w,v5),z,z)) = L(x,y,L((z \ 1) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(1143(a,1),30363(a,1,3,1))].">
      <j1 rule="para" parents="1143 30363"/>
    </justification>
  </clause>

  <clause id="30368">
    <literal><![CDATA[
      a(x,L(y * z,y,y),u) = a(x,(y \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(1137(a,1),30364(a,1,2,1))].">
      <j1 rule="para" parents="1137 30364"/>
    </justification>
  </clause>

  <clause id="30369">
    <literal><![CDATA[
      ((x \ y) * T(z,u)) * a(x,x \ y,z) = x \ (y * T(z,u))
    ]]></literal>
    <justification jstring="[para(27304(a,1),30036(a,1,2))].">
      <j1 rule="para" parents="27304 30036"/>
    </justification>
  </clause>

  <clause id="30370">
    <literal><![CDATA[
      T(((x \ L(x,y,z)) * u) * a(x,x \ L(x,y,z),u),w) = x \ (L(x,y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[para(30036(a,2),28583(a,1,1))].">
      <j1 rule="para" parents="30036 28583"/>
    </justification>
  </clause>

  <clause id="30371">
    <literal><![CDATA[
      K(x,y * (z \ (u * w))) = K(x,y * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[para(30036(a,1),28706(a,1,2,2))].">
      <j1 rule="para" parents="30036 28706"/>
    </justification>
  </clause>

  <clause id="30372">
    <literal><![CDATA[
      L(x,y,(z * u) \ (u \ z)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,28988,a,b,30045,a)].">
      <j1 rule="hyper" parents="64 28988 30045"/>
    </justification>
  </clause>

  <clause id="30373">
    <literal><![CDATA[
      L(x,y,x * (z \ (x \ z))) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,29954,a(flip),b,30112,a),flip(a)].">
      <j1 rule="hyper" parents="373 29954 30112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30374">
    <literal><![CDATA[
      L(x,y,z \ (u \ (z \ u))) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26304,a,b,30112,a)].">
      <j1 rule="hyper" parents="64 26304 30112"/>
    </justification>
  </clause>

  <clause id="30375">
    <literal><![CDATA[
      a(x * (y \ (x \ y)),z,x) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,30373,a)].">
      <j1 rule="hyper" parents="54 30373"/>
    </justification>
  </clause>

  <clause id="30376">
    <literal><![CDATA[
      (x * (y \ (x \ y))) * (z * T(x,(x * (y \ (x \ y))) * z)) = x * ((x * (y \ (x \ y))) * z)
    ]]></literal>
    <justification jstring="[para(30373(a,1),793(a,2,1))].">
      <j1 rule="para" parents="30373 793"/>
    </justification>
  </clause>

  <clause id="30377">
    <literal><![CDATA[
      L(x,y \ (z \ (y \ z)),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29711,a,b,30115,a)].">
      <j1 rule="hyper" parents="64 29711 30115"/>
    </justification>
  </clause>

  <clause id="30378">
    <literal><![CDATA[
      a(x,y \ 1,L(y \ ((1 / y) \ z),y \ 1,x)) * (y \ L(z,y \ 1,x)) = (y \ 1) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(1863(a,1),30195(a,1,2))].">
      <j1 rule="para" parents="1863 30195"/>
    </justification>
  </clause>

  <clause id="30379">
    <literal><![CDATA[
      T(x,T(y \ (z * u),w)) = T(x,T((y \ z) * u,w))
    ]]></literal>
    <justification jstring="[para(30197(a,1),28751(a,1,2,1))].">
      <j1 rule="para" parents="30197 28751"/>
    </justification>
  </clause>

  <clause id="30380">
    <literal><![CDATA[
      x * ((x / y) * (y / x)) = ((x / y) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(30068(a,1),30240(a,1,2))].">
      <j1 rule="para" parents="30068 30240"/>
    </justification>
  </clause>

  <clause id="30381">
    <literal><![CDATA[
      ((x / y) * (y / x)) * x = ((x / y) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,23877,a,b,30380,a)].">
      <j1 rule="hyper" parents="64 23877 30380"/>
    </justification>
  </clause>

  <clause id="30382">
    <literal><![CDATA[
      a(L(x * y,x,x),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2675,a(flip),b,30255,a),flip(a)].">
      <j1 rule="hyper" parents="373 2675 30255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30383">
    <literal><![CDATA[
      a(L(x * y,y,y),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26845,a,b,30382,a)].">
      <j1 rule="hyper" parents="64 26845 30382"/>
    </justification>
  </clause>

  <clause id="30384">
    <literal><![CDATA[
      a(x \ (x \ y),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),30382(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 30382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30385">
    <literal><![CDATA[
      a(x * L((x \ 1) * y,z,u),w,v5) = a(x \ L(x \ y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(5632(a,1),30382(a,1,1))].">
      <j1 rule="para" parents="5632 30382"/>
    </justification>
  </clause>

  <clause id="30386">
    <literal><![CDATA[
      a(x \ ((x \ 1) \ y),z,u) = a(L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26925,a,b,30384,a)].">
      <j1 rule="hyper" parents="64 26925 30384"/>
    </justification>
  </clause>

  <clause id="30387">
    <literal><![CDATA[
      L(x,y,L(z * u,z,z)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2234,a(flip),b,30256,a),flip(a)].">
      <j1 rule="hyper" parents="373 2234 30256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30388">
    <literal><![CDATA[
      L(x,y,L(z * u,u,u)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,24167,a,b,30387,a)].">
      <j1 rule="hyper" parents="64 24167 30387"/>
    </justification>
  </clause>

  <clause id="30389">
    <literal><![CDATA[
      L(x,y,z * L(u,z,z)) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13027,a(flip),b,30387,a)].">
      <j1 rule="hyper" parents="64 13027 30387"/>
    </justification>
  </clause>

  <clause id="30390">
    <literal><![CDATA[
      L(x,y,z \ (z \ u)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),30387(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 30387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30391">
    <literal><![CDATA[
      L(x,y,L((K(z,u) * (L(w,v5,v6) * v7)) * w,w,w)) = L(x,y,L(w,v5,v6) * (K(z,u) * (w \ v7)))
    ]]></literal>
    <justification jstring="[para(22848(a,1),30388(a,2,3))].">
      <j1 rule="para" parents="22848 30388"/>
    </justification>
  </clause>

  <clause id="30392">
    <literal><![CDATA[
      L(x,y,L(z,u,u) * (u \ 1)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23997,a,b,30389,a)].">
      <j1 rule="hyper" parents="64 23997 30389"/>
    </justification>
  </clause>

  <clause id="30393">
    <literal><![CDATA[
      L(x,y,z \ ((z \ 1) \ u)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29358,a,b,30390,a)].">
      <j1 rule="hyper" parents="64 29358 30390"/>
    </justification>
  </clause>

  <clause id="30394">
    <literal><![CDATA[
      R(x,L(y * z,y,y),u) = R(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,3028,a(flip),b,30257,a),flip(a)].">
      <j1 rule="hyper" parents="373 3028 30257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30395">
    <literal><![CDATA[
      R(x,L(y * z,z,z),u) = R(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26496,a,b,30394,a)].">
      <j1 rule="hyper" parents="64 26496 30394"/>
    </justification>
  </clause>

  <clause id="30396">
    <literal><![CDATA[
      R(x,L(y,z,z) * z,u) = R(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26540,a(flip),b,30394,a)].">
      <j1 rule="hyper" parents="64 26540 30394"/>
    </justification>
  </clause>

  <clause id="30397">
    <literal><![CDATA[
      R(x,y \ (y \ z),u) = R(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),30394(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 30394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30398">
    <literal><![CDATA[
      (x \ y) * a(x \ y,x \ (x \ y),x) = R(x \ y,L(y,x,x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24668,a,b,30397,a)].">
      <j1 rule="hyper" parents="64 24668 30397"/>
    </justification>
  </clause>

  <clause id="30399">
    <literal><![CDATA[
      L((1 / x) * y,z,a(x,x,y)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,580,a(flip),b,30303,a)].">
      <j1 rule="hyper" parents="64 580 30303"/>
    </justification>
  </clause>

  <clause id="30400">
    <literal><![CDATA[
      a(x,x,y) * (((1 / x) * y) \ 1) = ((1 / x) * y) \ a(x,x,y)
    ]]></literal>
    <justification jstring="[para(30399(a,1),24639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30399 24639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30401">
    <literal><![CDATA[
      L(x,(y * z) \ (z \ y),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29454,a,b,30311,a)].">
      <j1 rule="hyper" parents="64 29454 30311"/>
    </justification>
  </clause>

  <clause id="30402">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ (z * y) = L(z,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(23920,a,30343,a)].">
      <j1 rule="hyper" parents="23920 30343"/>
    </justification>
  </clause>

  <clause id="30403">
    <literal><![CDATA[
      a(x,y,z) \ (x \ ((a(x,y,z) * (x / u)) * u)) = a(a(x,y,z),u \ x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30271,a,b,30344,a)].">
      <j1 rule="hyper" parents="64 30271 30344"/>
    </justification>
  </clause>

  <clause id="30404">
    <literal><![CDATA[
      x \ ((y \ R(y,z,u)) \ (R(y * K(y \ x,y),z,u) * (x / y))) = a(y \ R(y,z,u),(x / y) \ x,x / y)
    ]]></literal>
    <justification jstring="[para(25978(a,1),30344(a,1,2,2,1))].">
      <j1 rule="para" parents="25978 30344"/>
    </justification>
  </clause>

  <clause id="30405">
    <literal><![CDATA[
      a(x,(y \ 1) \ (y \ z),u) = a(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),30368(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 30368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30406">
    <literal><![CDATA[
      L((x \ (y \ (x \ y))) \ z,a(x,x,y),x) = (y \ (x \ y)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(743,a,30377,a),flip(a)].">
      <j1 rule="hyper" parents="743 30377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30407">
    <literal><![CDATA[
      a(L(x,y,y),y,y \ 1) = ((x / (y \ 1)) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,19813,a(flip),b,30386,a),flip(a)].">
      <j1 rule="hyper" parents="64 19813 30386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30408">
    <literal><![CDATA[
      a(L(x,x * y,y),y,y \ x) = (y * L(y \ x,y,x)) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,11887,a(flip),b,29907,a),flip(a)].">
      <j1 rule="hyper" parents="373 11887 29907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30410">
    <literal><![CDATA[
      (x * y) / (a(x,x,y) * (x * y)) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,23133,a(flip),b,29993,a),flip(a)].">
      <j1 rule="hyper" parents="373 23133 29993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30411">
    <literal><![CDATA[
      R((a(x,x,y) * a(x,x,y)) \ x,x,y) = (a(x,x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,14052,a(flip),b,30092,a),flip(a)].">
      <j1 rule="hyper" parents="64 14052 30092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30412">
    <literal><![CDATA[
      (x * x) * ((x \ y) / (x * y)) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,807,a(flip),b,30154,a)].">
      <j1 rule="hyper" parents="64 807 30154"/>
    </justification>
  </clause>

  <clause id="30413">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) / y) * x) = ((1 / x) * y) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,30154,a(flip),b,16113,a(flip))].">
      <j1 rule="hyper" parents="139 30154 16113"/>
    </justification>
  </clause>

  <clause id="30414">
    <literal><![CDATA[
      ((a(x,x,y) / x) \ 1) * y = x * (a(x,x,y) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,29923,a(flip),b,30192,a),flip(a)].">
      <j1 rule="hyper" parents="373 29923 30192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30415">
    <literal><![CDATA[
      L(x,a(y,z,u),y) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,11003,a(flip),b,30275,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 11003 30275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30416">
    <literal><![CDATA[
      L(x,(y \ (z \ y)) * z,z) = L(x,z,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30116,a,b,30415,a)].">
      <j1 rule="hyper" parents="64 30116 30415"/>
    </justification>
  </clause>

  <clause id="30418">
    <literal><![CDATA[
      a(x,a(x,y,z),u) * (L(u,x,a(x,y,z)) * (x * a(x,y,z))) = u * (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(30415(a,1),15714(a,1,2,1))].">
      <j1 rule="para" parents="30415 15714"/>
    </justification>
  </clause>

  <clause id="30419">
    <literal><![CDATA[
      L(T(x,y),x \ (z \ x),z) = L(T(x,y),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,25,a,b,30292,a),flip(a)].">
      <j1 rule="hyper" parents="373 25 30292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30420">
    <literal><![CDATA[
      T(x,T(y * (z / u),w * u)) = T(x,T((u \ y) * z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,28580,a,b,30379,a)].">
      <j1 rule="hyper" parents="64 28580 30379"/>
    </justification>
  </clause>

  <clause id="30421">
    <literal><![CDATA[
      (x * y) / ((1 / x) \ y) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(30041(a,1),30410(a,1,2))].">
      <j1 rule="para" parents="30041 30410"/>
    </justification>
  </clause>

  <clause id="30422">
    <literal><![CDATA[
      (x \ y) \ ((x \ 1) * y) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,27867,a(flip),b,30421,a)].">
      <j1 rule="hyper" parents="64 27867 30421"/>
    </justification>
  </clause>

  <clause id="30423">
    <literal><![CDATA[
      (x \ y) * (a(x,x,y) \ 1) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,30421,a(flip),b,27867,a(flip))].">
      <j1 rule="hyper" parents="145 30421 27867"/>
    </justification>
  </clause>

  <clause id="30424">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,x \ y,z) = (z * (x \ y)) \ (z * ((x \ 1) * y))
    ]]></literal>
    <justification jstring="[para(30422(a,1),102(a,1,1))].">
      <j1 rule="para" parents="30422 102"/>
    </justification>
  </clause>

  <clause id="30425">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * (x \ y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,23736,a,b,30423,a)].">
      <j1 rule="hyper" parents="64 23736 30423"/>
    </justification>
  </clause>

  <clause id="30426">
    <literal><![CDATA[
      (a(x,x,L(y,y,x \ 1)) \ 1) * (x \ L(y,y,x \ 1)) = ((x \ 1) * (y * y)) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,2849,a,b,30425,a),flip(a)].">
      <j1 rule="hyper" parents="373 2849 30425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30427">
    <literal><![CDATA[
      R(a(x,x,y) \ 1,x \ y,z) = (((x \ 1) * y) * z) / ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(30425(a,1),20(a,2,1,1))].">
      <j1 rule="para" parents="30425 20"/>
    </justification>
  </clause>

  <clause id="30428">
    <literal><![CDATA[
      (a(R(x,y,y),R(x,y,y),y) \ 1) * (x \ L(y,y,x)) = (R(x,y,y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(16075(a,1),30425(a,1,2))].">
      <j1 rule="para" parents="16075 30425"/>
    </justification>
  </clause>

  <clause id="30429">
    <literal><![CDATA[
      L(x,y,(z \ L(u \ w,a(u,u,w) \ 1,a(u,u,w) \ 1)) * v5) = L(x,y,(z \ ((a(u,u,w) \ 1) * ((u \ 1) * w))) * v5)
    ]]></literal>
    <justification jstring="[para(30425(a,1),29258(a,1,3,1,2,2)),flip(a)].">
      <j1 rule="para" parents="30425 29258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30430">
    <literal><![CDATA[
      ((1 / x) * y) \ (x \ y) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,15735,a(flip),b,30412,a)].">
      <j1 rule="hyper" parents="64 15735 30412"/>
    </justification>
  </clause>

  <clause id="30431">
    <literal><![CDATA[
      (((x \ y) / y) * x) \ 1 = (x \ y) \ ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(30430(a,1),5688(a,1,1))].">
      <j1 rule="para" parents="30430 5688"/>
    </justification>
  </clause>

  <clause id="30432">
    <literal><![CDATA[
      ((a(x,x,y) / x) \ 1) * y = x * L(y,x,x)
    ]]></literal>
    <justification jstring="[para(5567(a,1),30414(a,2,2))].">
      <j1 rule="para" parents="5567 30414"/>
    </justification>
  </clause>

  <clause id="30433">
    <literal><![CDATA[
      (a(x,x,y) \ x) * y = x * L(y,x,x)
    ]]></literal>
    <justification jstring="[para(30165(a,1),30432(a,1,1))].">
      <j1 rule="para" parents="30165 30432"/>
    </justification>
  </clause>

  <clause id="30434">
    <literal><![CDATA[
      L(x,y,y) * (x \ y) = a(y,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(36,a,24376,a,b,30433,a)].">
      <j1 rule="hyper" parents="36 24376 30433"/>
    </justification>
  </clause>

  <clause id="30435">
    <literal><![CDATA[
      x * (a(y,y,x) \ y) = L(x,y,y) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,30434,a(flip),b,2325,a)].">
      <j1 rule="hyper" parents="145 30434 2325"/>
    </justification>
  </clause>

  <clause id="30436">
    <literal><![CDATA[
      (a(x,x,y) \ x) * K(y,a(x,x,y) \ x) = (L(y,x,x) * x) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,30435,a(flip),b,5722,a),flip(a)].">
      <j1 rule="hyper" parents="142 30435 5722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30437">
    <literal><![CDATA[
      L(T(x,y \ 1),y \ 1,y) \ x = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(30419(a,1),27212(a,1,1))].">
      <j1 rule="para" parents="30419 27212"/>
    </justification>
  </clause>

  <clause id="30438">
    <literal><![CDATA[
      (x * x) * ((y \ z) \ ((1 / y) * z)) = (((y \ z) / z) * y) \ (x * x)
    ]]></literal>
    <justification jstring="[para(30431(a,1),27848(a,1,2))].">
      <j1 rule="para" parents="30431 27848"/>
    </justification>
  </clause>

  <clause id="30439">
    <literal><![CDATA[
      x * (y * L(a(x,z,u),x,y)) = (a(x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,23168,a,b,29927,a),flip(a)].">
      <j1 rule="hyper" parents="373 23168 29927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30440">
    <literal><![CDATA[
      L((x * y) * a(z,x,y),z,z) = z * (((z \ 1) * x) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,30030,a(flip),b,1148,a),flip(a)].">
      <j1 rule="hyper" parents="145 30030 1148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30441">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ ((u / x) * L(x,y,z)) = a(x \ 1,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(24852(a,1),30033(a,1,2))].">
      <j1 rule="para" parents="24852 30033"/>
    </justification>
  </clause>

  <clause id="30442">
    <literal><![CDATA[
      a(x,x,y) * (z * K(u,y * x)) = z * ((y / T(x * y,u)) * x)
    ]]></literal>
    <justification jstring="[para(30094(a,1),24451(a,2,2))].">
      <j1 rule="para" parents="30094 24451"/>
    </justification>
  </clause>

  <clause id="30443">
    <literal><![CDATA[
      L(x,y,(z / u) * (z \ u)) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[hyper(29071,a,30209,a)].">
      <j1 rule="hyper" parents="29071 30209"/>
    </justification>
  </clause>

  <clause id="30444">
    <literal><![CDATA[
      x / (y \ ((y \ 1) \ x)) = x \ ((y \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,30206,a(flip),b,30262,a),flip(a)].">
      <j1 rule="hyper" parents="64 30206 30262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30445">
    <literal><![CDATA[
      (x \ ((y \ 1) * (y * x))) \ x = y \ ((y \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(215,a,30444,a)].">
      <j1 rule="hyper" parents="215 30444"/>
    </justification>
  </clause>

  <clause id="30446">
    <literal><![CDATA[
      (x * x) \ (T(y / (y * x),x) * x) = T(y * x,x * x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(30284(a,1),11279(a,1,2))].">
      <j1 rule="para" parents="30284 11279"/>
    </justification>
  </clause>

  <clause id="30447">
    <literal><![CDATA[
      (x * ((y \ z) \ (y \ u))) * a(x \ ((y \ 1) \ z),x,((y \ 1) \ z) \ ((y \ 1) \ u)) = (((y \ 1) \ z) / x) \ ((y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1612(a,1),30347(a,1,1,2))].">
      <j1 rule="para" parents="1612 30347"/>
    </justification>
  </clause>

  <clause id="30448">
    <literal><![CDATA[
      (L(x,y,z) * ((x * u) \ w)) * a(x * (L(x,y,z) \ u),L(x,y,z),(x * u) \ w) = ((x * u) / L(x,y,z)) \ w
    ]]></literal>
    <justification jstring="[para(2329(a,1),30347(a,1,2,1))].">
      <j1 rule="para" parents="2329 30347"/>
    </justification>
  </clause>

  <clause id="30449">
    <literal><![CDATA[
      (x * (((y * z) * u) \ w)) * a(x \ ((y * z) * u),x,(u * (z * y)) \ w) = (((y * z) * u) / x) \ w
    ]]></literal>
    <justification jstring="[para(27698(a,1),30347(a,1,2))].">
      <j1 rule="para" parents="27698 30347"/>
    </justification>
  </clause>

  <clause id="30451">
    <literal><![CDATA[
      a(x,y,L(y \ z,y,x)) = (y * ((x * y) \ (x * z))) \ z
    ]]></literal>
    <justification jstring="[para(102(a,1),30348(a,2,1,2))].">
      <j1 rule="para" parents="102 30348"/>
    </justification>
  </clause>

  <clause id="30452">
    <literal><![CDATA[
      (x * (y * (x \ 1))) \ y = x * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(695(a,1),30437(a,1,1))].">
      <j1 rule="para" parents="695 30437"/>
    </justification>
  </clause>

  <clause id="30453">
    <literal><![CDATA[
      L(x,y,(z \ u) * (u \ z)) = L(x,y,a(z,u \ z,u))
    ]]></literal>
    <justification jstring="[hyper(29066,a,30443,a)].">
      <j1 rule="hyper" parents="29066 30443"/>
    </justification>
  </clause>

  <clause id="30454">
    <literal><![CDATA[
      (x \ 1) * (a(x,x,y) \ y) = (R(x,x,y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,30175,a(flip),b,29930,a),flip(a)].">
      <j1 rule="hyper" parents="64 30175 29930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30455">
    <literal><![CDATA[
      (R(x,x,y) \ 1) * y = (x \ 1) * L(y,x,x)
    ]]></literal>
    <justification jstring="[para(5567(a,1),30454(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5567 30454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30456">
    <literal><![CDATA[
      a(x,y,L(T(R(z,z,u) \ 1,w) * u,v5,v6)) = a(x,y,L((z \ 1) * L(u,z,z),v5,v6))
    ]]></literal>
    <justification jstring="[para(30455(a,1),27426(a,2,3,1))].">
      <j1 rule="para" parents="30455 27426"/>
    </justification>
  </clause>

  <clause id="30457">
    <literal><![CDATA[
      a(x,x,y) \ (L(z,a(x,x,y) * (x * y),a(x,x,y)) * L(x * y,a(x,x,y),a(x,x,y))) = (a(x,x,y) \ (1 * (x * y))) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(29994(a,2),14430(a,2,1))].">
      <j1 rule="para" parents="29994 14430"/>
    </justification>
  </clause>

  <clause id="30458">
    <literal><![CDATA[
      (x * y) \ (a(y,y,x) * z) = ((x * y) \ z) * a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,23906,a(flip),b,29996,a(flip))].">
      <j1 rule="hyper" parents="139 23906 29996"/>
    </justification>
  </clause>

  <clause id="30459">
    <literal><![CDATA[
      a(x,y,y) \ y = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,15715,a(flip),b,29998,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 15715 29998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30460">
    <literal><![CDATA[
      L(x,x,y) * a(y,x,x) = x
    ]]></literal>
    <justification jstring="[hyper(23175,a,30459,a)].">
      <j1 rule="hyper" parents="23175 30459"/>
    </justification>
  </clause>

  <clause id="30461">
    <literal><![CDATA[
      a(x,y,y) * L(y,y,x) = y
    ]]></literal>
    <justification jstring="[hyper(157,a,30459,a)].">
      <j1 rule="hyper" parents="157 30459"/>
    </justification>
  </clause>

  <clause id="30462">
    <literal><![CDATA[
      L(x,x,y) \ x = a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,5559,a,b,30459,a)].">
      <j1 rule="hyper" parents="40 5559 30459"/>
    </justification>
  </clause>

  <clause id="30463">
    <literal><![CDATA[
      L(L(x,x,y),a(y,x,x),z) = (a(y,x,x) * z) \ (z * x)
    ]]></literal>
    <justification jstring="[para(30459(a,1),23793(a,1,1))].">
      <j1 rule="para" parents="30459 23793"/>
    </justification>
  </clause>

  <clause id="30464">
    <literal><![CDATA[
      (x * L(y,y,x)) \ (x * y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[para(30459(a,1),29904(a,1,1,2))].">
      <j1 rule="para" parents="30459 29904"/>
    </justification>
  </clause>

  <clause id="30465">
    <literal><![CDATA[
      a(x,y,y) \ 1 = y \ L(y,y,x)
    ]]></literal>
    <justification jstring="[para(30459(a,1),30015(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30459 30015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30466">
    <literal><![CDATA[
      L(L(x,x,y) \ (a(y,x,x) \ z),L(x,x,y),a(y,x,x)) = x \ z
    ]]></literal>
    <justification jstring="[para(30460(a,1),23941(a,2,1))].">
      <j1 rule="para" parents="30460 23941"/>
    </justification>
  </clause>

  <clause id="30467">
    <literal><![CDATA[
      L(L(x,x,y) \ z,L(x,x,y),a(y,x,x)) = x \ (z * a(y,x,x))
    ]]></literal>
    <justification jstring="[para(30460(a,1),26740(a,2,1))].">
      <j1 rule="para" parents="30460 26740"/>
    </justification>
  </clause>

  <clause id="30468">
    <literal><![CDATA[
      x * L(y,L(x,x,z),a(z,x,x)) = a(z,x,x) * (L(x,x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,30461,a(flip),b,213,a)].">
      <j1 rule="hyper" parents="144 30461 213"/>
    </justification>
  </clause>

  <clause id="30469">
    <literal><![CDATA[
      (a(x,y,y) * (z * L(y,y,x))) / y = L(z,L(y,y,x),a(x,y,y))
    ]]></literal>
    <justification jstring="[para(30461(a,1),28734(a,1,2))].">
      <j1 rule="para" parents="30461 28734"/>
    </justification>
  </clause>

  <clause id="30470">
    <literal><![CDATA[
      L(x / L(y,y,z),L(y,y,z),a(z,y,y)) = (x * a(z,y,y)) / y
    ]]></literal>
    <justification jstring="[para(30461(a,1),28835(a,2,2))].">
      <j1 rule="para" parents="30461 28835"/>
    </justification>
  </clause>

  <clause id="30471">
    <literal><![CDATA[
      a(x,y,L(y,y,x)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30353,a,b,30462,a)].">
      <j1 rule="hyper" parents="64 30353 30462"/>
    </justification>
  </clause>

  <clause id="30472">
    <literal><![CDATA[
      (x \ (x / y)) \ (1 / y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26057,a(flip),b,30462,a)].">
      <j1 rule="hyper" parents="64 26057 30462"/>
    </justification>
  </clause>

  <clause id="30473">
    <literal><![CDATA[
      x * (((y * (1 / x)) \ y) \ 1) = a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11818,a(flip),b,30462,a)].">
      <j1 rule="hyper" parents="64 11818 30462"/>
    </justification>
  </clause>

  <clause id="30474">
    <literal><![CDATA[
      a(x,y,y) / y = 1 / L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,30462,a(flip),b,5556,a)].">
      <j1 rule="hyper" parents="142 30462 5556"/>
    </justification>
  </clause>

  <clause id="30475">
    <literal><![CDATA[
      L(x,x,y) \ 1 = x \ a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,30462,a(flip),b,1846,a),flip(a)].">
      <j1 rule="hyper" parents="139 30462 1846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30476">
    <literal><![CDATA[
      L(x,y,z) * (x \ a(u,x,x)) = L(x,x,u) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(30462(a,1),1880(a,1,2,2))].">
      <j1 rule="para" parents="30462 1880"/>
    </justification>
  </clause>

  <clause id="30477">
    <literal><![CDATA[
      x * (a(y,x,x) \ 1) = L(x,x,y)
    ]]></literal>
    <justification jstring="[para(30462(a,1),5662(a,1,2,1))].">
      <j1 rule="para" parents="30462 5662"/>
    </justification>
  </clause>

  <clause id="30478">
    <literal><![CDATA[
      a(x * L(x,x,y),z,u) = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(30462(a,1),9387(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30462 9387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30479">
    <literal><![CDATA[
      a(x,y,y) \ (L(y,y,x) \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[para(30462(a,1),10807(a,1,1))].">
      <j1 rule="para" parents="30462 10807"/>
    </justification>
  </clause>

  <clause id="30480">
    <literal><![CDATA[
      L(1 / x,x,y) \ (1 / x) = a(y,1 / x,1 / x)
    ]]></literal>
    <justification jstring="[para(11776(a,1),30462(a,1,1))].">
      <j1 rule="para" parents="11776 30462"/>
    </justification>
  </clause>

  <clause id="30481">
    <literal><![CDATA[
      ((x * (1 / y)) \ x) \ y = a(x,y,y)
    ]]></literal>
    <justification jstring="[para(11792(a,1),30462(a,1,1))].">
      <j1 rule="para" parents="11792 30462"/>
    </justification>
  </clause>

  <clause id="30483">
    <literal><![CDATA[
      L(x,x,x * y) \ x = a(x \ y,x,x)
    ]]></literal>
    <justification jstring="[para(25574(a,1),30462(a,1,1))].">
      <j1 rule="para" parents="25574 30462"/>
    </justification>
  </clause>

  <clause id="30484">
    <literal><![CDATA[
      (x \ (x / y)) \ 1 = y * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(30462(a,1),26061(a,2,2))].">
      <j1 rule="para" parents="30462 26061"/>
    </justification>
  </clause>

  <clause id="30485">
    <literal><![CDATA[
      R(x,y * L(y,y,z),u) = R(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(30462(a,1),26595(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30462 26595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30486">
    <literal><![CDATA[
      a(x,y,y) * K(y \ 1,z) = y * T(L(y,y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(30462(a,1),25374(a,1,1))].">
      <j1 rule="para" parents="30462 25374"/>
    </justification>
  </clause>

  <clause id="30487">
    <literal><![CDATA[
      K(x \ 1,y) * a(z,x,x) = x * T(L(x,x,z) \ 1,y)
    ]]></literal>
    <justification jstring="[para(30462(a,1),26962(a,1,2))].">
      <j1 rule="para" parents="30462 26962"/>
    </justification>
  </clause>

  <clause id="30488">
    <literal><![CDATA[
      (x * x) * (y * (L(x \ 1,x \ 1,z) \ (1 / x))) = x * ((x \ 1) \ (y * a(z,x \ 1,x \ 1)))
    ]]></literal>
    <justification jstring="[para(30462(a,1),28003(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="30462 28003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30489">
    <literal><![CDATA[
      L(x,y,(z * L(z,z,u)) * w) = L(x,y,a(u,z,z) * w)
    ]]></literal>
    <justification jstring="[para(30462(a,1),29191(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30462 29191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30490">
    <literal><![CDATA[
      x * (y \ L(y,y,x)) = a(x,y,y) \ x
    ]]></literal>
    <justification jstring="[para(30462(a,1),30359(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30462 30359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30491">
    <literal><![CDATA[
      (1 / x) \ (y \ (y / x)) = a(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,26053,a,b,30465,a)].">
      <j1 rule="hyper" parents="373 26053 30465"/>
    </justification>
  </clause>

  <clause id="30492">
    <literal><![CDATA[
      a(x,y \ x,y \ x) \ 1 = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,26659,a(flip),b,30465,a),flip(a)].">
      <j1 rule="hyper" parents="373 26659 30465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30493">
    <literal><![CDATA[
      (x \ (x / y)) * y = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,26654,a(flip),b,30465,a)].">
      <j1 rule="hyper" parents="373 26654 30465"/>
    </justification>
  </clause>

  <clause id="30494">
    <literal><![CDATA[
      R(x,y,y) \ x = y \ L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,16007,a,b,30465,a)].">
      <j1 rule="hyper" parents="64 16007 30465"/>
    </justification>
  </clause>

  <clause id="30495">
    <literal><![CDATA[
      x \ ((y * (1 / x)) \ y) = a(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[para(11792(a,1),30465(a,2,2)),flip(a)].">
      <j1 rule="para" parents="11792 30465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30496">
    <literal><![CDATA[
      K(x,y) * (z \ L(z,z,u)) = a(u,z,z) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(30465(a,1),19253(a,1,2))].">
      <j1 rule="para" parents="30465 19253"/>
    </justification>
  </clause>

  <clause id="30497">
    <literal><![CDATA[
      (a(x,y,y) \ 1) * z = z * (y \ L(y,y,x))
    ]]></literal>
    <justification jstring="[para(30465(a,1),23736(a,2,2))].">
      <j1 rule="para" parents="30465 23736"/>
    </justification>
  </clause>

  <clause id="30498">
    <literal><![CDATA[
      (L(x,x,y) * z) / L(x,a(y,x,x) \ 1,z) = z * (T(L(x,x,y),z) / x)
    ]]></literal>
    <justification jstring="[para(30465(a,2),29784(a,1,2,2))].">
      <j1 rule="para" parents="30465 29784"/>
    </justification>
  </clause>

  <clause id="30499">
    <literal><![CDATA[
      x * ((x \ 1) \ (a(y,x \ 1,x \ 1) * z)) = (x * (L(x \ 1,x \ 1,y) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(30475(a,2),1589(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="30475 1589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30500">
    <literal><![CDATA[
      a((x \ a(y,x,x)) * z,u,w) = a(L(x,x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(30475(a,1),2662(a,1,1,1))].">
      <j1 rule="para" parents="30475 2662"/>
    </justification>
  </clause>

  <clause id="30501">
    <literal><![CDATA[
      a(x,y,y) * (1 / (1 / y)) = ((L(y,y,x) \ 1) * y) * y
    ]]></literal>
    <justification jstring="[para(30475(a,2),26953(a,2,1,1))].">
      <j1 rule="para" parents="30475 26953"/>
    </justification>
  </clause>

  <clause id="30502">
    <literal><![CDATA[
      a(x * y,x,x) \ 1 = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(35,a,26664,a,b,30477,a),flip(a)].">
      <j1 rule="hyper" parents="35 26664 30477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30503">
    <literal><![CDATA[
      L(x,a(y,z,z) * z,u) = L(x,L(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(30477(a,1),29520(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30477 29520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30504">
    <literal><![CDATA[
      L(x,y * a(z,y,y),u) = L(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(30477(a,1),29595(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30477 29595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30505">
    <literal><![CDATA[
      (R(x,y,y) \ x) * y = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,30494,a,b,5572,a)].">
      <j1 rule="hyper" parents="144 30494 5572"/>
    </justification>
  </clause>

  <clause id="30506">
    <literal><![CDATA[
      R(x,y,L(y,y,x)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,25618,a,b,30494,a)].">
      <j1 rule="hyper" parents="40 25618 30494"/>
    </justification>
  </clause>

  <clause id="30507">
    <literal><![CDATA[
      L(x,y,z \ L(z,z,u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(30494(a,1),29269(a,1,3))].">
      <j1 rule="para" parents="30494 29269"/>
    </justification>
  </clause>

  <clause id="30508">
    <literal><![CDATA[
      R(x,x \ (y \ x),y) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26647,a,b,30506,a)].">
      <j1 rule="hyper" parents="64 26647 30506"/>
    </justification>
  </clause>

  <clause id="30509">
    <literal><![CDATA[
      L(x,x,y) \ ((R(y,x,x) \ y) * ((x * x) * z)) = L((1 / x) \ z,x,R(y,x,x) \ y)
    ]]></literal>
    <justification jstring="[para(30505(a,1),583(a,1,1))].">
      <j1 rule="para" parents="30505 583"/>
    </justification>
  </clause>

  <clause id="30510">
    <literal><![CDATA[
      R(x,x / y,x / y) = R(x,x \ y,x / y)
    ]]></literal>
    <justification jstring="[para(82(a,1),30508(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 30508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30511">
    <literal><![CDATA[
      R(x,y,y) \ ((y \ x) * y) = (x \ (y \ x)) * y
    ]]></literal>
    <justification jstring="[para(30508(a,1),649(a,1,1))].">
      <j1 rule="para" parents="30508 649"/>
    </justification>
  </clause>

  <clause id="30512">
    <literal><![CDATA[
      a(x,y,y) * (x \ (x / y)) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(39,a,23174,a,b,30472,a)].">
      <j1 rule="hyper" parents="39 23174 30472"/>
    </justification>
  </clause>

  <clause id="30513">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (1 / x) = a(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(6390(a,1),30472(a,1,1))].">
      <j1 rule="para" parents="6390 30472"/>
    </justification>
  </clause>

  <clause id="30514">
    <literal><![CDATA[
      (((1 / x) * ((1 / x) * (y \ L(y,z,u)))) \ ((1 / x) * (y \ L(y,z,u)))) \ x = a((1 / x) * (y \ L(y,z,u)),x,x)
    ]]></literal>
    <justification jstring="[para(23893(a,1),30481(a,1,1,1))].">
      <j1 rule="para" parents="23893 30481"/>
    </justification>
  </clause>

  <clause id="30515">
    <literal><![CDATA[
      (x \ (x / y)) \ 1 = a(x,y,y) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a,b,30484,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 30484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30516">
    <literal><![CDATA[
      x * ((y \ (y / x)) \ 1) = y \ ((y * x) * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,30484,a,b,9443,a)].">
      <j1 rule="hyper" parents="145 30484 9443"/>
    </justification>
  </clause>

  <clause id="30517">
    <literal><![CDATA[
      x \ ((y \ (y / x)) \ 1) = a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,30484,a,b,xx)].">
      <j1 rule="hyper" parents="139 30484"/>
    </justification>
  </clause>

  <clause id="30519">
    <literal><![CDATA[
      L((x \ (x / y)) \ 1,y,x) = y
    ]]></literal>
    <justification jstring="[para(30484(a,2),9445(a,1,1))].">
      <j1 rule="para" parents="30484 9445"/>
    </justification>
  </clause>

  <clause id="30520">
    <literal><![CDATA[
      R(x,y,(z \ (z / R(u,w,u))) \ 1) = R(x,y,u * a(z,R(u,w,u),R(u,w,u)))
    ]]></literal>
    <justification jstring="[para(30484(a,2),13901(a,1,3))].">
      <j1 rule="para" parents="30484 13901"/>
    </justification>
  </clause>

  <clause id="30521">
    <literal><![CDATA[
      K(x,T(y,x / z)) * (z * a(x,z,z)) = (T(x,y) \ (x / z)) \ 1
    ]]></literal>
    <justification jstring="[para(30484(a,1),25410(a,1,2))].">
      <j1 rule="para" parents="30484 25410"/>
    </justification>
  </clause>

  <clause id="30522">
    <literal><![CDATA[
      L((x / y) \ (x * 1),y,x) = L(y,x \ (x / y),x)
    ]]></literal>
    <justification jstring="[para(30519(a,1),1026(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30519 1026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30524">
    <literal><![CDATA[
      a(x,y,(z * (u \ (u / z))) * w) = a(x,y,(a(u,z,z) \ 1) * w)
    ]]></literal>
    <justification jstring="[para(30493(a,1),27395(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30493 27395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30525">
    <literal><![CDATA[
      a(x,y,((z \ (u \ z)) * u) \ w) = a(x,y,(a(z,u,u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(30493(a,1),27674(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30493 27674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30526">
    <literal><![CDATA[
      R(x \ a(x,y,y),x,x \ (x / y)) = T((1 / y) / (x / y),x)
    ]]></literal>
    <justification jstring="[para(30512(a,1),1032(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="30512 1032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30527">
    <literal><![CDATA[
      (x / y) * a(x,y,y) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(30512(a,1),29308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30512 29308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30528">
    <literal><![CDATA[
      a(x,y \ x,y \ x) * (y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),30515(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 30515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30529">
    <literal><![CDATA[
      K(x \ (x / y),x) * ((a(x,y,y) * y) * z) = (((x / y) / x) \ 1) * z
    ]]></literal>
    <justification jstring="[para(30515(a,1),24352(a,1,2,1))].">
      <j1 rule="para" parents="30515 24352"/>
    </justification>
  </clause>

  <clause id="30530">
    <literal><![CDATA[
      (x \ y) * ((y \ (x \ y)) \ 1) = (y / x) * (a(y,x,x) * x)
    ]]></literal>
    <justification jstring="[para(30515(a,1),25741(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30515 25741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30531">
    <literal><![CDATA[
      L(1 / x,x,a(y,z,u)) \ 1 = a(a(y,z,u),x,x) * x
    ]]></literal>
    <justification jstring="[para(27165(a,2),30515(a,1,1))].">
      <j1 rule="para" parents="27165 30515"/>
    </justification>
  </clause>

  <clause id="30532">
    <literal><![CDATA[
      a(x * y,y,y) = y \ (((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(11(a,1),30517(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 30517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30533">
    <literal><![CDATA[
      a(x * y,x,x) = x \ (((y * x) \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(5888(a,1),30517(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5888 30517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30534">
    <literal><![CDATA[
      x \ (L(x \ 1,x,y) \ 1) = a(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(6390(a,1),30517(a,1,2,1))].">
      <j1 rule="para" parents="6390 30517"/>
    </justification>
  </clause>

  <clause id="30535">
    <literal><![CDATA[
      (x \ (x / y)) * L(z,a(x,y,y),y) = y * ((y \ (1 / ((x \ (x / y)) \ 1))) * z)
    ]]></literal>
    <justification jstring="[para(30517(a,1),29789(a,1,2,2))].">
      <j1 rule="para" parents="30517 29789"/>
    </justification>
  </clause>

  <clause id="30536">
    <literal><![CDATA[
      (x / y) \ (x * (1 / y)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(149,a,30527,a)].">
      <j1 rule="hyper" parents="149 30527"/>
    </justification>
  </clause>

  <clause id="30537">
    <literal><![CDATA[
      x * a(x * y,y,y) = (x * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(11(a,1),30527(a,1,1))].">
      <j1 rule="para" parents="11 30527"/>
    </justification>
  </clause>

  <clause id="30538">
    <literal><![CDATA[
      1 / T((x * (1 / y)) \ (x / y),a(x,y,y)) = ((x * (1 / y)) \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(30536(a,1),3803(a,1,2,2))].">
      <j1 rule="para" parents="30536 3803"/>
    </justification>
  </clause>

  <clause id="30539">
    <literal><![CDATA[
      L(1 / a(x,y,y),(x / y) \ (x * (1 / y)),x / y) = 1 / (1 / ((x * (1 / y)) \ (x / y)))
    ]]></literal>
    <justification jstring="[para(30536(a,1),4305(a,1,1,2))].">
      <j1 rule="para" parents="30536 4305"/>
    </justification>
  </clause>

  <clause id="30540">
    <literal><![CDATA[
      L(a(x,y,y),y \ x,z) = (z * (x / y)) \ (z * (x * (1 / y)))
    ]]></literal>
    <justification jstring="[para(30536(a,1),29531(a,1,1))].">
      <j1 rule="para" parents="30536 29531"/>
    </justification>
  </clause>

  <clause id="30541">
    <literal><![CDATA[
      L(a(x,y,y),x * L(y,y,x),z) = (z * (x * L(y,y,x))) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[para(30464(a,1),102(a,1,1))].">
      <j1 rule="para" parents="30464 102"/>
    </justification>
  </clause>

  <clause id="30542">
    <literal><![CDATA[
      ((L(x,x,y) \ 1) / a(y,x,x)) * (a(y,x,x) * z) = (L(x,x,y) \ 1) * L(z,a(y,x,x),x \ 1)
    ]]></literal>
    <justification jstring="[para(30479(a,1),11064(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="30479 11064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30543">
    <literal><![CDATA[
      a(x \ y,x,x) = a(x * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30462,a(flip),b,30483,a),flip(a)].">
      <j1 rule="hyper" parents="64 30462 30483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30545">
    <literal><![CDATA[
      a(x \ y,x,x) = a(y * x,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,30543,a),flip(a)].">
      <j1 rule="hyper" parents="373 26787 30543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30546">
    <literal><![CDATA[
      a(x * y,x,x) / (y * x) = 1 / (y / (1 / x))
    ]]></literal>
    <justification jstring="[para(30543(a,1),26893(a,1,1))].">
      <j1 rule="para" parents="30543 26893"/>
    </justification>
  </clause>

  <clause id="30547">
    <literal><![CDATA[
      a(x,y \ x,y \ x) \ x = x * ((x \ y) * (y \ x))
    ]]></literal>
    <justification jstring="[para(26659(a,1),30490(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26659 30490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30548">
    <literal><![CDATA[
      (1 / x) * ((a(y,x,x) \ 1) * z) = x * ((x \ (y \ (y / x))) * z)
    ]]></literal>
    <justification jstring="[para(30491(a,1),1666(a,1,2,1))].">
      <j1 rule="para" parents="30491 1666"/>
    </justification>
  </clause>

  <clause id="30549">
    <literal><![CDATA[
      (x \ 1) * ((y * (x \ 1)) \ y) = a(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,27018,a,b,30495,a)].">
      <j1 rule="hyper" parents="64 27018 30495"/>
    </justification>
  </clause>

  <clause id="30550">
    <literal><![CDATA[
      a(x \ y,x,x) = x \ (((y * x) \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,30545,a,b,30532,a)].">
      <j1 rule="hyper" parents="64 30545 30532"/>
    </justification>
  </clause>

  <clause id="30551">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) * R(y,y,a(y * x,y,y)) = (y * y) * (T(y,((x * y) \ x) \ 1) \ (((x * y) \ x) \ 1))
    ]]></literal>
    <justification jstring="[para(30533(a,2),25635(a,2,2,3)),flip(a)].">
      <j1 rule="para" parents="30533 25635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30552">
    <literal><![CDATA[
      x \ (x \ (((y * x) \ y) \ 1)) = L(x,x,x * y) \ 1
    ]]></literal>
    <justification jstring="[para(30533(a,1),30475(a,2,2)),flip(a)].">
      <j1 rule="para" parents="30533 30475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30553">
    <literal><![CDATA[
      x * a(y * x,y,y) = (x * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(26016(a,1),30537(a,1,2))].">
      <j1 rule="para" parents="26016 30537"/>
    </justification>
  </clause>

  <clause id="30554">
    <literal><![CDATA[
      a(x,x \ y,x \ y) = (x \ y) \ (((y * (x \ y)) \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(26846,a,30550,a)].">
      <j1 rule="hyper" parents="26846 30550"/>
    </justification>
  </clause>

  <clause id="30555">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x \ y) = ((y * (x \ y)) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(145,a,26784,a(flip),b,30550,a(flip))].">
      <j1 rule="hyper" parents="145 26784 30550"/>
    </justification>
  </clause>

  <clause id="30556">
    <literal><![CDATA[
      ((x \ y) \ ((x \ y) / x)) \ 1 = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,30517,a,b,30550,a(flip))].">
      <j1 rule="hyper" parents="39 30517 30550"/>
    </justification>
  </clause>

  <clause id="30557">
    <literal><![CDATA[
      T(((x * y) * (1 / y)) / x,z) = (a(y * x,y,y) \ u) \ T(u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(30553(a,1),25620(a,1,1,1))].">
      <j1 rule="para" parents="30553 25620"/>
    </justification>
  </clause>

  <clause id="30558">
    <literal><![CDATA[
      R(x,a(y * z,y,y),u) = R(x,(z \ (y \ z)) * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27263,a,b,30485,a),flip(a)].">
      <j1 rule="hyper" parents="64 27263 30485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30559">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(x,x,u)) = a(u,x,x) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29986,a(flip),b,30497,a),flip(a)].">
      <j1 rule="hyper" parents="64 29986 30497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30560">
    <literal><![CDATA[
      a(x * y,y,y) \ 1 = L(y \ 1,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,26835,a,b,30502,a)].">
      <j1 rule="hyper" parents="64 26835 30502"/>
    </justification>
  </clause>

  <clause id="30561">
    <literal><![CDATA[
      L(a(x * y,x,x),a(x * y,x,x),z) \ z = z * (L(x \ 1,x,y) * x)
    ]]></literal>
    <justification jstring="[para(30502(a,1),23106(a,2,2))].">
      <j1 rule="para" parents="30502 23106"/>
    </justification>
  </clause>

  <clause id="30562">
    <literal><![CDATA[
      L(x,y,z * L(z,z,u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,5608,a(flip),b,30507,a)].">
      <j1 rule="hyper" parents="64 5608 30507"/>
    </justification>
  </clause>

  <clause id="30563">
    <literal><![CDATA[
      R(x,x / y,x / y) = R(x,x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,23813,a(flip),b,30510,a),flip(a)].">
      <j1 rule="hyper" parents="373 23813 30510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30564">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) * y = x \ ((x * y) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1239,a,b,30516,a)].">
      <j1 rule="hyper" parents="64 1239 30516"/>
    </justification>
  </clause>

  <clause id="30565">
    <literal><![CDATA[
      a(x,y,y) \ K(y \ x,y) = (x \ (y \ x)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,16049,a,b,30511,a)].">
      <j1 rule="hyper" parents="64 16049 30511"/>
    </justification>
  </clause>

  <clause id="30566">
    <literal><![CDATA[
      R(1 / (x * y),y,y) = 1 / (x / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,26017,a(flip),b,30546,a)].">
      <j1 rule="hyper" parents="64 26017 30546"/>
    </justification>
  </clause>

  <clause id="30567">
    <literal><![CDATA[
      1 / ((x / y) / (1 / y)) = R(1 / x,y,y)
    ]]></literal>
    <justification jstring="[para(12(a,1),30566(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 30566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30568">
    <literal><![CDATA[
      R(1 / x,y,y) \ 1 = (x / y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(215,a,30567,a)].">
      <j1 rule="hyper" parents="215 30567"/>
    </justification>
  </clause>

  <clause id="30569">
    <literal><![CDATA[
      a(x,y,y) \ x = (x / y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(37,a,25175,a,b,30567,a)].">
      <j1 rule="hyper" parents="37 25175 30567"/>
    </justification>
  </clause>

  <clause id="30570">
    <literal><![CDATA[
      ((1 / x) / y) / (1 / y) = 1 / R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,11436,a(flip),b,30567,a),flip(a)].">
      <j1 rule="hyper" parents="37 11436 30567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30571">
    <literal><![CDATA[
      (x / y) * L(y,y,x) = a(x,y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,25572,a,b,30569,a)].">
      <j1 rule="hyper" parents="373 25572 30569"/>
    </justification>
  </clause>

  <clause id="30572">
    <literal><![CDATA[
      (x \ y) / (T(x,y * x) \ 1) = a(y,x,x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,15139,a,b,30569,a)].">
      <j1 rule="hyper" parents="373 15139 30569"/>
    </justification>
  </clause>

  <clause id="30573">
    <literal><![CDATA[
      (x \ y) / (1 / T(x,x \ y)) = a(y,x,x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,15100,a,b,30569,a)].">
      <j1 rule="hyper" parents="373 15100 30569"/>
    </justification>
  </clause>

  <clause id="30574">
    <literal><![CDATA[
      (a(x,y,y) \ x) * z = ((x / y) / (1 / y)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,30569,a,b,11,a)].">
      <j1 rule="hyper" parents="144 30569 11"/>
    </justification>
  </clause>

  <clause id="30575">
    <literal><![CDATA[
      (a(x,y,y) \ x) \ (x / y) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(143,a,30569,a,b,171,a)].">
      <j1 rule="hyper" parents="143 30569 171"/>
    </justification>
  </clause>

  <clause id="30576">
    <literal><![CDATA[
      (a(x,y,y) \ x) / L(y,y,x) = x / y
    ]]></literal>
    <justification jstring="[hyper(142,a,30569,a,b,25572,a)].">
      <j1 rule="hyper" parents="142 30569 25572"/>
    </justification>
  </clause>

  <clause id="30577">
    <literal><![CDATA[
      T((1 / x) / (y / x),a(y,x,x) \ y) = T((1 / x) / (y / x),(1 / x) \ (y / x))
    ]]></literal>
    <justification jstring="[para(30569(a,2),3817(a,1,2))].">
      <j1 rule="para" parents="30569 3817"/>
    </justification>
  </clause>

  <clause id="30578">
    <literal><![CDATA[
      a(x \ y,T(x,x * y) \ 1,T(x,x * y) \ 1) \ (x \ y) = ((y / x) / (1 / x)) / (1 / (T(x,x * y) \ 1))
    ]]></literal>
    <justification jstring="[para(15135(a,1),30569(a,2,1))].">
      <j1 rule="para" parents="15135 30569"/>
    </justification>
  </clause>

  <clause id="30579">
    <literal><![CDATA[
      ((x / y) / (1 / y)) \ x = a(x,y,y)
    ]]></literal>
    <justification jstring="[para(30569(a,1),23134(a,1,1))].">
      <j1 rule="para" parents="30569 23134"/>
    </justification>
  </clause>

  <clause id="30580">
    <literal><![CDATA[
      R(x,y,(a(z,u,u) \ z) \ w) = R(x,y,((1 / u) \ (z / u)) \ w)
    ]]></literal>
    <justification jstring="[para(30569(a,2),26209(a,1,3,1))].">
      <j1 rule="para" parents="30569 26209"/>
    </justification>
  </clause>

  <clause id="30581">
    <literal><![CDATA[
      a(x * (y \ L(y,z,u)),T(x,w),T(x,w)) \ (x * (y \ L(y,z,u))) = (K(w,x) * (y \ L(y,z,u))) / (1 / T(x,w))
    ]]></literal>
    <justification jstring="[para(23753(a,1),30569(a,2,1))].">
      <j1 rule="para" parents="23753 30569"/>
    </justification>
  </clause>

  <clause id="30582">
    <literal><![CDATA[
      R(x,((y / z) / (1 / z)) * u,w) = R(x,L(y,z,z) * u,w)
    ]]></literal>
    <justification jstring="[para(30569(a,1),27289(a,1,2,1))].">
      <j1 rule="para" parents="30569 27289"/>
    </justification>
  </clause>

  <clause id="30583">
    <literal><![CDATA[
      (x / y) * (((z / y) / y) \ z) = (x / (1 / y)) * a(z,y,y)
    ]]></literal>
    <justification jstring="[para(30579(a,1),1232(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30579 1232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30584">
    <literal><![CDATA[
      x * (a(y,x,x) \ y) = L(x,x,y) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,30571,a(flip),b,24852,a)].">
      <j1 rule="hyper" parents="145 30571 24852"/>
    </justification>
  </clause>

  <clause id="30585">
    <literal><![CDATA[
      (a(x,y,y) \ x) * y = x * L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,30571,a(flip),b,3196,a)].">
      <j1 rule="hyper" parents="144 30571 3196"/>
    </justification>
  </clause>

  <clause id="30586">
    <literal><![CDATA[
      x * L(y,y,a(x,y,y) \ x) = (a(x,y,y) \ x) * y
    ]]></literal>
    <justification jstring="[para(16077(a,2),30585(a,2,2)),flip(a)].">
      <j1 rule="para" parents="16077 30585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30587">
    <literal><![CDATA[
      (1 / R(x,y,y)) * (1 / y) = (1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(144,a,11426,a(flip),b,30568,a(flip))].">
      <j1 rule="hyper" parents="144 11426 30568"/>
    </justification>
  </clause>

  <clause id="30588">
    <literal><![CDATA[
      ((x \ 1) / y) / (1 / y) = R(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),30568(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 30568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30589">
    <literal><![CDATA[
      ((x \ R(x,y,z)) / u) / (1 / u) = R(R(x,y,z) \ x,u,u) \ 1
    ]]></literal>
    <justification jstring="[para(24810(a,1),30568(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="24810 30568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30590">
    <literal><![CDATA[
      a(x,y,(1 / z) \ ((1 / u) / z)) = a(x,y,1 / R(u,z,z))
    ]]></literal>
    <justification jstring="[para(30570(a,1),27308(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30570 27308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30591">
    <literal><![CDATA[
      R(1 / R(x,y,y),y,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(38,a,1408,a,b,30587,a(flip))].">
      <j1 rule="hyper" parents="38 1408 30587"/>
    </justification>
  </clause>

  <clause id="30592">
    <literal><![CDATA[
      R(R(x,y,y),y,y) / (1 / x) = R(x,y,y) * R(x,y,y)
    ]]></literal>
    <justification jstring="[para(30591(a,1),2120(a,1,2))].">
      <j1 rule="para" parents="30591 2120"/>
    </justification>
  </clause>

  <clause id="30593">
    <literal><![CDATA[
      (R(x,y,y) \ 1) * (1 / y) = (x \ 1) / y
    ]]></literal>
    <justification jstring="[hyper(156,a,30588,a)].">
      <j1 rule="hyper" parents="156 30588"/>
    </justification>
  </clause>

  <clause id="30594">
    <literal><![CDATA[
      (x * x) * (((y * x) \ 1) * (1 / x)) = ((y / x) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,1372,a,b,30593,a)].">
      <j1 rule="hyper" parents="64 1372 30593"/>
    </justification>
  </clause>

  <clause id="30595">
    <literal><![CDATA[
      R(R(x,y,y) \ 1,y,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(38,a,1408,a,b,30593,a(flip))].">
      <j1 rule="hyper" parents="38 1408 30593"/>
    </justification>
  </clause>

  <clause id="30596">
    <literal><![CDATA[
      ((x \ 1) * (y * y)) / y = (R(x,y,y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(30595(a,1),350(a,1,1,1))].">
      <j1 rule="para" parents="30595 350"/>
    </justification>
  </clause>

  <clause id="30597">
    <literal><![CDATA[
      R((x / (y * y)) \ 1,y,y) = ((x / y) / y) \ 1
    ]]></literal>
    <justification jstring="[para(351(a,1),30595(a,1,1,1))].">
      <j1 rule="para" parents="351 30595"/>
    </justification>
  </clause>

  <clause id="30598">
    <literal><![CDATA[
      R((x * y) \ 1,y,y) = (x / (1 / y)) \ 1
    ]]></literal>
    <justification jstring="[para(1407(a,1),30595(a,1,1,1))].">
      <j1 rule="para" parents="1407 30595"/>
    </justification>
  </clause>

  <clause id="30599">
    <literal><![CDATA[
      R(x \ 1,y \ x,y \ x) = (y / (1 / (y \ x))) \ 1
    ]]></literal>
    <justification jstring="[para(10(a,1),30598(a,1,1,1))].">
      <j1 rule="para" parents="10 30598"/>
    </justification>
  </clause>

  <clause id="30600">
    <literal><![CDATA[
      R((L(1 / x,y,z) * x) \ 1,x,x) = ((1 / x) \ L(1 / x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(5572(a,1),30598(a,2,1))].">
      <j1 rule="para" parents="5572 30598"/>
    </justification>
  </clause>

  <clause id="30601">
    <literal><![CDATA[
      R(((1 / x) \ a(y,y,z)) \ 1,L(x,x,a(z,y,y)),L(x,x,a(z,y,y))) = (a(y,y,z) / (1 / L(x,x,a(z,y,y)))) \ 1
    ]]></literal>
    <justification jstring="[para(29301(a,1),30598(a,1,1,1))].">
      <j1 rule="para" parents="29301 30598"/>
    </justification>
  </clause>

  <clause id="30602">
    <literal><![CDATA[
      (x \ 1) * ((y * (x \ 1)) \ y) = (y \ (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,30493,a,b,30549,a),flip(a)].">
      <j1 rule="hyper" parents="373 30493 30549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30603">
    <literal><![CDATA[
      R(x,(y \ (z \ y)) * z,u) = R(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(30565(a,1),26533(a,1,2))].">
      <j1 rule="para" parents="30565 26533"/>
    </justification>
  </clause>

  <clause id="30604">
    <literal><![CDATA[
      L(x,y,((z \ (u \ z)) * u) * w) = L(x,y,a(z,u,u) * w)
    ]]></literal>
    <justification jstring="[para(30565(a,1),29075(a,1,3,1))].">
      <j1 rule="para" parents="30565 29075"/>
    </justification>
  </clause>

  <clause id="30605">
    <literal><![CDATA[
      R((x * x) * (y \ 1),x,x) = ((y / x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(890(a,1),30597(a,1,1))].">
      <j1 rule="para" parents="890 30597"/>
    </justification>
  </clause>

  <clause id="30606">
    <literal><![CDATA[
      R(x,y * (z \ (y \ z)),u) = R(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26409,a,b,30603,a)].">
      <j1 rule="hyper" parents="64 26409 30603"/>
    </justification>
  </clause>

  <clause id="30607">
    <literal><![CDATA[
      (x * T(y \ 1,x \ 1)) * x = ((y / x) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,3955,a(flip),b,30605,a)].">
      <j1 rule="hyper" parents="64 3955 30605"/>
    </justification>
  </clause>

  <clause id="30608">
    <literal><![CDATA[
      T(((x / y) / y) \ 1,y * y) = ((x \ 1) * y) * y
    ]]></literal>
    <justification jstring="[para(30605(a,1),1402(a,1,1))].">
      <j1 rule="para" parents="30605 1402"/>
    </justification>
  </clause>

  <clause id="30609">
    <literal><![CDATA[
      R(x,y \ (z \ (y \ z)),u) = R(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26305,a,b,30606,a)].">
      <j1 rule="hyper" parents="64 26305 30606"/>
    </justification>
  </clause>

  <clause id="30610">
    <literal><![CDATA[
      R(x,(y \ (z \ y)) \ z,u) = R(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25911,a,b,30606,a)].">
      <j1 rule="hyper" parents="64 25911 30606"/>
    </justification>
  </clause>

  <clause id="30611">
    <literal><![CDATA[
      R(x \ (y \ x),a(x,y,y),z) \ (y * z) = ((x \ (y \ x)) \ y) * z
    ]]></literal>
    <justification jstring="[para(30610(a,1),649(a,1,1))].">
      <j1 rule="para" parents="30610 649"/>
    </justification>
  </clause>

  <clause id="30612">
    <literal><![CDATA[
      a(1 / x,y,L(1 / x,x,z) \ (1 / x)) = 1
    ]]></literal>
    <justification jstring="[para(30480(a,2),30280(a,1,3))].">
      <j1 rule="para" parents="30480 30280"/>
    </justification>
  </clause>

  <clause id="30613">
    <literal><![CDATA[
      a(1 / (x \ y),z,(1 / (1 / (y \ x))) \ (1 / (x \ y))) = 1
    ]]></literal>
    <justification jstring="[para(4305(a,1),30612(a,1,3,1))].">
      <j1 rule="para" parents="4305 30612"/>
    </justification>
  </clause>

  <clause id="30614">
    <literal><![CDATA[
      (x \ (T(x,y) / z)) * z = a(x,z,z) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26663,a(flip),b,30496,a)].">
      <j1 rule="hyper" parents="64 26663 30496"/>
    </justification>
  </clause>

  <clause id="30615">
    <literal><![CDATA[
      a(x,y,y) \ K(x,y \ 1) = ((x / y) / x) * y
    ]]></literal>
    <justification jstring="[para(4402(a,1),30614(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4402 30614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30616">
    <literal><![CDATA[
      a(x,x,y) * K(x,x * y) = ((y / x) / y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,28012,a(flip),b,30615,a)].">
      <j1 rule="hyper" parents="64 28012 30615"/>
    </justification>
  </clause>

  <clause id="30617">
    <literal><![CDATA[
      a(x,x,y) * (K(x,x * y) * z) = (((y / x) / y) * x) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,30616,a(flip),b,23278,a),flip(a)].">
      <j1 rule="hyper" parents="144 30616 23278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30618">
    <literal><![CDATA[
      L((x / y) \ (x * 1),y,x) = L(y,x \ (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,29552,a(flip),b,30522,a),flip(a)].">
      <j1 rule="hyper" parents="373 29552 30522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30619">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / x) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(325,a,30556,a),flip(a)].">
      <j1 rule="hyper" parents="325 30556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30620">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / x) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,437,a,b,30556,a),flip(a)].">
      <j1 rule="hyper" parents="40 437 30556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30621">
    <literal><![CDATA[
      (x \ y) * ((y * x) \ y) = (x \ y) / x
    ]]></literal>
    <justification jstring="[hyper(157,a,30619,a)].">
      <j1 rule="hyper" parents="157 30619"/>
    </justification>
  </clause>

  <clause id="30623">
    <literal><![CDATA[
      (x * ((y \ x) \ 1)) \ x = y \ (y / ((y \ x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(35,a,15012,a,b,30621,a),flip(a)].">
      <j1 rule="hyper" parents="35 15012 30621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30624">
    <literal><![CDATA[
      ((x / y) \ 1) * L(y \ 1,y,x) = ((x / y) \ 1) / y
    ]]></literal>
    <justification jstring="[para(30620(a,1),14998(a,1,2))].">
      <j1 rule="para" parents="30620 14998"/>
    </justification>
  </clause>

  <clause id="30625">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * (y \ 1) = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25744,a(flip),b,30602,a),flip(a)].">
      <j1 rule="hyper" parents="64 25744 30602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30626">
    <literal><![CDATA[
      T((x / y) \ 1,y * y) = (((x * y) \ 1) * y) * y
    ]]></literal>
    <justification jstring="[para(11(a,1),30608(a,1,1,1,1))].">
      <j1 rule="para" parents="11 30608"/>
    </justification>
  </clause>

  <clause id="30627">
    <literal><![CDATA[
      L((x / y) \ x,y,x) = L(y,x \ (y \ x),x)
    ]]></literal>
    <justification jstring="[para(8(a,1),30618(a,1,1,2))].">
      <j1 rule="para" parents="8 30618"/>
    </justification>
  </clause>

  <clause id="30628">
    <literal><![CDATA[
      L(x,y \ (x \ y),y) = L(x,x,y)
    ]]></literal>
    <justification jstring="[para(82(a,1),30627(a,1,1)),flip(a)].">
      <j1 rule="para" parents="82 30627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30629">
    <literal><![CDATA[
      L(x,L(x,x,y),y) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29726,a,b,30628,a)].">
      <j1 rule="hyper" parents="64 29726 30628"/>
    </justification>
  </clause>

  <clause id="30630">
    <literal><![CDATA[
      L(x \ y,y \ x,y) = L(x \ y,x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29553,a(flip),b,30628,a)].">
      <j1 rule="hyper" parents="64 29553 30628"/>
    </justification>
  </clause>

  <clause id="30631">
    <literal><![CDATA[
      L(x,(y * (z / y)) \ (x \ (y * (z / y))),z) = L(x,x,y * (z / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,24004,a(flip),b,30628,a)].">
      <j1 rule="hyper" parents="64 24004 30628"/>
    </justification>
  </clause>

  <clause id="30632">
    <literal><![CDATA[
      L(x \ y,y \ x,x) = L(x \ y,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29725,a(flip),b,30629,a)].">
      <j1 rule="hyper" parents="64 29725 30629"/>
    </justification>
  </clause>

  <clause id="30633">
    <literal><![CDATA[
      L(L(x,y,z),L(x,x,u),u) = L(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(30629(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30629 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30634">
    <literal><![CDATA[
      L((x * y) \ x,(x * y) \ x,x) = L((x * y) \ x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11871,a(flip),b,30630,a),flip(a)].">
      <j1 rule="hyper" parents="64 11871 30630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30635">
    <literal><![CDATA[
      x * L(x \ y,y \ x,y) = x / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(30630(a,2),25571(a,1,2))].">
      <j1 rule="para" parents="30630 25571"/>
    </justification>
  </clause>

  <clause id="30636">
    <literal><![CDATA[
      x * ((x \ y) * (y \ x)) = y / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,515,a(flip),b,30635,a)].">
      <j1 rule="hyper" parents="64 515 30635"/>
    </justification>
  </clause>

  <clause id="30637">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) * x = y / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,9463,a,b,30636,a)].">
      <j1 rule="hyper" parents="64 9463 30636"/>
    </justification>
  </clause>

  <clause id="30638">
    <literal><![CDATA[
      x * ((x \ (K(y,z) * u)) * (u \ (K(z,y) * x))) = (K(y,z) * u) / (1 / ((K(y,z) * u) \ x))
    ]]></literal>
    <justification jstring="[para(23199(a,1),30636(a,1,2,2))].">
      <j1 rule="para" parents="23199 30636"/>
    </justification>
  </clause>

  <clause id="30639">
    <literal><![CDATA[
      (x \ (x / (1 / y))) * (1 / y) = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25718,a,b,30625,a)].">
      <j1 rule="hyper" parents="64 25718 30625"/>
    </justification>
  </clause>

  <clause id="30640">
    <literal><![CDATA[
      x * (x * ((y * x) \ y)) = y \ (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(145,a,30625,a(flip),b,26676,a(flip))].">
      <j1 rule="hyper" parents="145 30625 26676"/>
    </justification>
  </clause>

  <clause id="30641">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (x \ 1) = (y \ (y / (x \ 1))) \ x
    ]]></literal>
    <justification jstring="[para(30640(a,1),3794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30640 3794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30642">
    <literal><![CDATA[
      (x / (y \ 1)) * ((z * y) \ z) = (x / y) * (z \ (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(30640(a,1),3796(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30640 3796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30643">
    <literal><![CDATA[
      a((((x * y) \ 1) \ T((x / y) \ 1,y * y)) * z,u,w) = a(a((x * y) \ 1,y,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(30626(a,2),2683(a,1,1,1,2))].">
      <j1 rule="para" parents="30626 2683"/>
    </justification>
  </clause>

  <clause id="30644">
    <literal><![CDATA[
      (x \ (x / (1 / y))) * (1 / y) = y * L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,439,a,b,30639,a),flip(a)].">
      <j1 rule="hyper" parents="373 439 30639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30647">
    <literal><![CDATA[
      (x \ (x / (1 / y))) \ y = y \ (((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(39,a,25576,a,b,30552,a)].">
      <j1 rule="hyper" parents="39 25576 30552"/>
    </justification>
  </clause>

  <clause id="30648">
    <literal><![CDATA[
      ((x * y) \ x) \ (1 / y) = y \ (((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27039,a(flip),b,30647,a)].">
      <j1 rule="hyper" parents="64 27039 30647"/>
    </justification>
  </clause>

  <clause id="30649">
    <literal><![CDATA[
      (x \ L(x,x,x * y)) * (x \ (((y * x) \ y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(30647(a,1),25578(a,1,2))].">
      <j1 rule="para" parents="30647 25578"/>
    </justification>
  </clause>

  <clause id="30650">
    <literal><![CDATA[
      R(x,a(y * z,y,y),u) = R(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,30603,a(flip),b,30558,a),flip(a)].">
      <j1 rule="hyper" parents="373 30603 30558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30651">
    <literal><![CDATA[
      R(a(x,y,y) \ x,y,y) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,16072,a,b,30586,a)].">
      <j1 rule="hyper" parents="36 16072 30586"/>
    </justification>
  </clause>

  <clause id="30652">
    <literal><![CDATA[
      R(a(x,y,y) \ x,y,y) = L(x,z,a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,29954,a,b,30651,a),flip(a)].">
      <j1 rule="hyper" parents="373 29954 30651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30653">
    <literal><![CDATA[
      R(a(x,y,y) \ x,y,y) * ((a(x,y,y) \ x) \ z) = (a(x,y,y) \ x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(30651(a,1),1898(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30651 1898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30654">
    <literal><![CDATA[
      L(x,x,a(y,x,x) \ y) = (a(y,x,x) \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(30651(a,1),16074(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30651 16074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30655">
    <literal><![CDATA[
      R(R((a(x,y,y) * a(x,y,y)) \ x,y,y),y,y) = L(x,z,a(x,u,w))
    ]]></literal>
    <justification jstring="[para(25178(a,2),30652(a,1,1))].">
      <j1 rule="para" parents="25178 30652"/>
    </justification>
  </clause>

  <clause id="30656">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) \ y = y \ (L(1 / y,y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,28028,a(flip),b,30641,a),flip(a)].">
      <j1 rule="hyper" parents="64 28028 30641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30657">
    <literal><![CDATA[
      x * L(x \ 1,x,x * y) = L(x,x,y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(10992(a,1),30644(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10992 30644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30659">
    <literal><![CDATA[
      L(x \ 1,x,x * y) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(35,a,26395,a(flip),b,30657,a),flip(a)].">
      <j1 rule="hyper" parents="35 26395 30657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30660">
    <literal><![CDATA[
      (x \ 1) * (x \ (((x \ 1) * L(x \ 1,x,x * y)) \ z)) = T(L(x,x,y) * (1 / x),x * x) \ z
    ]]></literal>
    <justification jstring="[para(30657(a,1),15136(a,2,1,1))].">
      <j1 rule="para" parents="30657 15136"/>
    </justification>
  </clause>

  <clause id="30661">
    <literal><![CDATA[
      L(x \ 1,x,x * (y \ z)) = (z / y) \ ((z / y) / x)
    ]]></literal>
    <justification jstring="[hyper(29071,a,30659,a)].">
      <j1 rule="hyper" parents="29071 30659"/>
    </justification>
  </clause>

  <clause id="30662">
    <literal><![CDATA[
      L(x \ 1,x,y * x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(24201,a,30659,a)].">
      <j1 rule="hyper" parents="24201 30659"/>
    </justification>
  </clause>

  <clause id="30663">
    <literal><![CDATA[
      L(x \ 1,x,x \ y) = L(x \ 1,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,10975,a,b,30659,a)].">
      <j1 rule="hyper" parents="373 10975 30659"/>
    </justification>
  </clause>

  <clause id="30664">
    <literal><![CDATA[
      (x / y) * L(z \ 1,z,z * (y \ x)) = (x / y) / z
    ]]></literal>
    <justification jstring="[hyper(145,a,30659,a,b,14813,a)].">
      <j1 rule="hyper" parents="145 30659 14813"/>
    </justification>
  </clause>

  <clause id="30665">
    <literal><![CDATA[
      x * L(y \ 1,y,y * x) = x / y
    ]]></literal>
    <justification jstring="[hyper(145,a,30659,a,b,xx)].">
      <j1 rule="hyper" parents="145 30659"/>
    </justification>
  </clause>

  <clause id="30666">
    <literal><![CDATA[
      L(x \ 1,x,(y \ z) * x) = (y \ T(z,u)) \ ((y \ T(z,u)) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29146,a(flip),b,30659,a)].">
      <j1 rule="hyper" parents="64 29146 30659"/>
    </justification>
  </clause>

  <clause id="30667">
    <literal><![CDATA[
      ((x * y) * (x \ 1)) \ (x * y) = y \ (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,2232,a(flip),b,30659,a)].">
      <j1 rule="hyper" parents="64 2232 30659"/>
    </justification>
  </clause>

  <clause id="30668">
    <literal><![CDATA[
      (x * y) * L(z \ 1,z,(y * x) * z) = (x * y) / z
    ]]></literal>
    <justification jstring="[hyper(145,a,29105,a,b,30659,a(flip))].">
      <j1 rule="hyper" parents="145 29105 30659"/>
    </justification>
  </clause>

  <clause id="30669">
    <literal><![CDATA[
      (x * y) * L(z \ 1,z,z * (y * x)) = (x * y) / z
    ]]></literal>
    <justification jstring="[hyper(145,a,29020,a,b,30659,a(flip))].">
      <j1 rule="hyper" parents="145 29020 30659"/>
    </justification>
  </clause>

  <clause id="30670">
    <literal><![CDATA[
      x * L(y \ 1,y,x * y) = x / y
    ]]></literal>
    <justification jstring="[hyper(145,a,23253,a,b,30659,a(flip))].">
      <j1 rule="hyper" parents="145 23253 30659"/>
    </justification>
  </clause>

  <clause id="30671">
    <literal><![CDATA[
      (x \ y) * ((y \ x) \ 1) = (x \ y) / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,30217,a(flip),b,30659,a(flip))].">
      <j1 rule="hyper" parents="145 30217 30659"/>
    </justification>
  </clause>

  <clause id="30672">
    <literal><![CDATA[
      ((x * y) \ x) * (y \ 1) = ((x * y) \ x) / y
    ]]></literal>
    <justification jstring="[hyper(145,a,30215,a(flip),b,30659,a(flip))].">
      <j1 rule="hyper" parents="145 30215 30659"/>
    </justification>
  </clause>

  <clause id="30673">
    <literal><![CDATA[
      ((x * y) \ y) * (x \ 1) = ((x * y) \ y) / x
    ]]></literal>
    <justification jstring="[hyper(145,a,30211,a(flip),b,30659,a(flip))].">
      <j1 rule="hyper" parents="145 30211 30659"/>
    </justification>
  </clause>

  <clause id="30674">
    <literal><![CDATA[
      ((x \ y) / y) * (x \ 1) = ((x \ y) / y) / x
    ]]></literal>
    <justification jstring="[hyper(145,a,30004,a(flip),b,30659,a(flip))].">
      <j1 rule="hyper" parents="145 30004 30659"/>
    </justification>
  </clause>

  <clause id="30675">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,(x \ y) * y) = y \ x
    ]]></literal>
    <justification jstring="[para(79(a,1),30659(a,2,2))].">
      <j1 rule="para" parents="79 30659"/>
    </justification>
  </clause>

  <clause id="30676">
    <literal><![CDATA[
      x * R(L(y \ 1,y,y * x),z,u) = (x / y) * (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(30659(a,2),2470(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="30659 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30677">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u * x) = L(u \ (u / x),y,z)
    ]]></literal>
    <justification jstring="[para(30659(a,1),23982(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30659 23982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30678">
    <literal><![CDATA[
      K(x \ 1,x) / (y \ (y / x)) = 1 / L(1 / x,x,x * y)
    ]]></literal>
    <justification jstring="[para(30659(a,1),26116(a,1,2))].">
      <j1 rule="para" parents="30659 26116"/>
    </justification>
  </clause>

  <clause id="30679">
    <literal><![CDATA[
      L(x \ 1,x,x * y) * x = x \ L(x,x,y)
    ]]></literal>
    <justification jstring="[para(30659(a,2),26654(a,2,1)),flip(a)].">
      <j1 rule="para" parents="30659 26654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30680">
    <literal><![CDATA[
      L(x \ 1,x,y * x) = ((y \ z) \ z) \ (((y \ z) \ z) / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,14903,a,b,30662,a),flip(a)].">
      <j1 rule="hyper" parents="373 14903 30662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30681">
    <literal><![CDATA[
      R(T(x / (x * y),(x * y) * y),x * y,y) = x \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1395,a,b,30662,a)].">
      <j1 rule="hyper" parents="64 1395 30662"/>
    </justification>
  </clause>

  <clause id="30682">
    <literal><![CDATA[
      (x * y) / (x \ (x / y)) = (x * y) * y
    ]]></literal>
    <justification jstring="[hyper(225,a,30662,a(flip),b,241,a(flip))].">
      <j1 rule="hyper" parents="225 30662 241"/>
    </justification>
  </clause>

  <clause id="30683">
    <literal><![CDATA[
      L(x \ 1,x,y * x) * x = x \ L(x,x,y)
    ]]></literal>
    <justification jstring="[para(30662(a,2),26654(a,2,1)),flip(a)].">
      <j1 rule="para" parents="30662 26654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30684">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,z,z * (u \ 1)) \ u,L(z \ 1,z,z * (u \ 1)),u)) = a(x,y,((u \ 1) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(30665(a,1),27656(a,2,3,1))].">
      <j1 rule="para" parents="30665 27656"/>
    </justification>
  </clause>

  <clause id="30685">
    <literal><![CDATA[
      1 / (1 / L(x \ 1,x,x * y)) = L(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(30663(a,1),4301(a,1,2,2))].">
      <j1 rule="para" parents="30663 4301"/>
    </justification>
  </clause>

  <clause id="30686">
    <literal><![CDATA[
      ((x \ y) \ 1) * (y \ x) = (y \ x) / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,925,a,b,30671,a)].">
      <j1 rule="hyper" parents="64 925 30671"/>
    </justification>
  </clause>

  <clause id="30687">
    <literal><![CDATA[
      (x \ 1) * ((y * x) \ y) = ((y * x) \ y) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,7046,a(flip),b,30672,a)].">
      <j1 rule="hyper" parents="64 7046 30672"/>
    </justification>
  </clause>

  <clause id="30688">
    <literal><![CDATA[
      (x \ 1) * ((x * y) \ y) = ((x * y) \ y) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,1946,a(flip),b,30673,a)].">
      <j1 rule="hyper" parents="64 1946 30673"/>
    </justification>
  </clause>

  <clause id="30689">
    <literal><![CDATA[
      T(L(x \ 1,x,x * y),x) = x \ (x \ L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(493,a,xx,b,30679,a)].">
      <j1 rule="hyper" parents="493 30679"/>
    </justification>
  </clause>

  <clause id="30690">
    <literal><![CDATA[
      L(x \ 1,x,((y * z) \ u) * x) * x = x \ L(x,x,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(29374(a,1),30679(a,1,1))].">
      <j1 rule="para" parents="29374 30679"/>
    </justification>
  </clause>

  <clause id="30691">
    <literal><![CDATA[
      (((x \ y) * (x \ y)) \ (y \ x)) * (x \ y) = (y \ x) / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6972,a,b,30686,a)].">
      <j1 rule="hyper" parents="64 6972 30686"/>
    </justification>
  </clause>

  <clause id="30692">
    <literal><![CDATA[
      ((x \ y) \ 1) * (z * L((x \ y) \ 1,x \ y,(x \ y) * y)) = (y \ x) * (z * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(30675(a,1),24842(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30675 24842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30693">
    <literal><![CDATA[
      R(x,y,y \ 1) \ (x * y) = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,14894,a(flip),b,30667,a)].">
      <j1 rule="hyper" parents="64 14894 30667"/>
    </justification>
  </clause>

  <clause id="30694">
    <literal><![CDATA[
      L(T(x \ K(y,z),x),x,x * u) = K(y,z) * (x \ (x \ L(x,x,u)))
    ]]></literal>
    <justification jstring="[para(30689(a,1),27079(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30689 27079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30695">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ 1 = y \ (((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,26668,a,b,30649,a)].">
      <j1 rule="hyper" parents="35 26668 30649"/>
    </justification>
  </clause>

  <clause id="30696">
    <literal><![CDATA[
      (x \ (((y * x) \ y) \ 1)) \ 1 = ((y * x) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(40,a,24578,a,b,30695,a)].">
      <j1 rule="hyper" parents="40 24578 30695"/>
    </justification>
  </clause>

  <clause id="30697">
    <literal><![CDATA[
      a((x * y) \ x,y,y \ (((x * y) \ x) \ 1)) = 1
    ]]></literal>
    <justification jstring="[hyper(39,a,1284,a,b,30695,a)].">
      <j1 rule="hyper" parents="39 1284 30695"/>
    </justification>
  </clause>

  <clause id="30698">
    <literal><![CDATA[
      a(x / (x * y),y,y \ (((x * y) \ x) \ 1)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,26785,a,b,30697,a)].">
      <j1 rule="hyper" parents="64 26785 30697"/>
    </justification>
  </clause>

  <clause id="30699">
    <literal><![CDATA[
      a(x / (x * y),y,y \ ((x / (x * y)) \ 1)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,27511,a,b,30698,a)].">
      <j1 rule="hyper" parents="64 27511 30698"/>
    </justification>
  </clause>

  <clause id="30700">
    <literal><![CDATA[
      1 / (1 / (x \ ((y / (y * x)) \ 1))) = 1 / ((y / (y * x)) * x)
    ]]></literal>
    <justification jstring="[para(30699(a,1),25056(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30699 25056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30701">
    <literal><![CDATA[
      (((x * y) \ x) \ (1 / y)) \ 1 = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[para(30648(a,2),30696(a,1,1))].">
      <j1 rule="para" parents="30648 30696"/>
    </justification>
  </clause>

  <clause id="30702">
    <literal><![CDATA[
      ((x / (x * y)) \ (1 / y)) \ K(y \ 1,x * y) = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,14927,a,b,30701,a)].">
      <j1 rule="hyper" parents="64 14927 30701"/>
    </justification>
  </clause>

  <clause id="30703">
    <literal><![CDATA[
      (a(x,y,y) \ x) * (x \ y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,16077,a(flip),b,30654,a),flip(a)].">
      <j1 rule="hyper" parents="64 16077 30654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30704">
    <literal><![CDATA[
      (a(x,y,y) \ x) \ L(y,y,x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,16077,a(flip),b,30654,a(flip))].">
      <j1 rule="hyper" parents="139 16077 30654"/>
    </justification>
  </clause>

  <clause id="30705">
    <literal><![CDATA[
      ((x / y) / (1 / y)) \ L(y,y,x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,30703,a(flip),b,30574,a(flip))].">
      <j1 rule="hyper" parents="139 30703 30574"/>
    </justification>
  </clause>

  <clause id="30706">
    <literal><![CDATA[
      (x / y) * ((x \ y) \ 1) = (x / y) / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,30217,a(flip),b,30661,a(flip))].">
      <j1 rule="hyper" parents="145 30217 30661"/>
    </justification>
  </clause>

  <clause id="30707">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,(u \ w) * x) = L((w / u) \ ((w / u) / x),y,z)
    ]]></literal>
    <justification jstring="[para(30661(a,1),23982(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30661 23982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30708">
    <literal><![CDATA[
      ((x \ y) \ 1) * (x / y) = (x / y) / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,6837,a,b,30706,a)].">
      <j1 rule="hyper" parents="64 6837 30706"/>
    </justification>
  </clause>

  <clause id="30709">
    <literal><![CDATA[
      (x * y) * ((x \ y) \ 1) = (x * y) / (x \ y)
    ]]></literal>
    <justification jstring="[para(27125(a,1),30668(a,1,2))].">
      <j1 rule="para" parents="27125 30668"/>
    </justification>
  </clause>

  <clause id="30710">
    <literal><![CDATA[
      ((x \ y) * y) * (x \ 1) = ((x \ y) * y) / x
    ]]></literal>
    <justification jstring="[para(29273(a,1),30669(a,1,2))].">
      <j1 rule="para" parents="29273 30669"/>
    </justification>
  </clause>

  <clause id="30711">
    <literal><![CDATA[
      L(L(x \ 1,y \ z,y),x,(y \ z) * x) = z \ (y * ((y \ z) / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,630,a(flip),b,30677,a),flip(a)].">
      <j1 rule="hyper" parents="373 630 30677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30712">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,y * x) = (z * y) \ (z * (y / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,102,a(flip),b,30677,a),flip(a)].">
      <j1 rule="hyper" parents="373 102 30677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30713">
    <literal><![CDATA[
      L(a(x,y,y),z,x * y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,23162,a,b,29999,a)].">
      <j1 rule="hyper" parents="36 23162 29999"/>
    </justification>
  </clause>

  <clause id="30714">
    <literal><![CDATA[
      (x * y) \ (z * a(x,y,y)) = ((x * y) \ z) * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,23182,a(flip),b,29999,a(flip))].">
      <j1 rule="hyper" parents="139 23182 29999"/>
    </justification>
  </clause>

  <clause id="30715">
    <literal><![CDATA[
      L(L(a(x,y,y),z,u),w,y * x) = L(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[para(30713(a,1),23982(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30713 23982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30716">
    <literal><![CDATA[
      K(x \ 1,x) * a(y,x,x) = a(y * x,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5345,a(flip),b,30019,a),flip(a)].">
      <j1 rule="hyper" parents="64 5345 30019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30717">
    <literal><![CDATA[
      a(x * y,y,y \ 1) = (y \ a(x,y,y)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,26951,a(flip),b,30716,a),flip(a)].">
      <j1 rule="hyper" parents="64 26951 30716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30718">
    <literal><![CDATA[
      a(x * y,y,y \ 1) \ (z * (y \ 1)) = a(x,y,y) \ (z * (1 / y))
    ]]></literal>
    <justification jstring="[para(30716(a,1),3678(a,1,1))].">
      <j1 rule="para" parents="30716 3678"/>
    </justification>
  </clause>

  <clause id="30719">
    <literal><![CDATA[
      R(x,y,z * a(u * w,w,w \ 1)) = R(x,y,z * a(u,w,w))
    ]]></literal>
    <justification jstring="[para(30716(a,1),26188(a,1,3,2))].">
      <j1 rule="para" parents="30716 26188"/>
    </justification>
  </clause>

  <clause id="30720">
    <literal><![CDATA[
      a(x,y,a(z * u,u,u \ 1) * w) = a(x,y,w * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(30716(a,1),27499(a,1,3,1))].">
      <j1 rule="para" parents="30716 27499"/>
    </justification>
  </clause>

  <clause id="30721">
    <literal><![CDATA[
      L(x,a(y * z,z,z \ 1),u) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(30716(a,1),29429(a,1,2))].">
      <j1 rule="para" parents="30716 29429"/>
    </justification>
  </clause>

  <clause id="30722">
    <literal><![CDATA[
      a(x * y,y,y \ 1) = (L(y,y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(30475(a,2),30717(a,2,1))].">
      <j1 rule="para" parents="30475 30717"/>
    </justification>
  </clause>

  <clause id="30723">
    <literal><![CDATA[
      (L(x,x,y) \ 1) * (L(x,x,y) \ ((L(x,x,y) * x) * z)) = a(y * x,x,x \ 1) * z
    ]]></literal>
    <justification jstring="[para(30722(a,2),1596(a,2,1))].">
      <j1 rule="para" parents="30722 1596"/>
    </justification>
  </clause>

  <clause id="30724">
    <literal><![CDATA[
      L(x,a(y,y,z * y),u) = L(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29896,a(flip),b,30721,a)].">
      <j1 rule="hyper" parents="64 29896 30721"/>
    </justification>
  </clause>

  <clause id="30725">
    <literal><![CDATA[
      L(x,a(y,y,y * z),u) = L(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(27298(a,1),30724(a,1,2))].">
      <j1 rule="para" parents="27298 30724"/>
    </justification>
  </clause>

  <clause id="30726">
    <literal><![CDATA[
      L(x,a(y \ z,y,y),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(27299(a,1),30724(a,1,2)),flip(a)].">
      <j1 rule="para" parents="27299 30724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30727">
    <literal><![CDATA[
      L(x,y \ z,a(y \ z,y,y)) = L(x,a(y,y,z),y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30415,a(flip),b,30726,a)].">
      <j1 rule="hyper" parents="64 30415 30726"/>
    </justification>
  </clause>

  <clause id="30728">
    <literal><![CDATA[
      L(x,a(y * z,y,y),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(30543(a,1),30726(a,1,2))].">
      <j1 rule="para" parents="30543 30726"/>
    </justification>
  </clause>

  <clause id="30729">
    <literal><![CDATA[
      L(x,a(y * z,z,z),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(30545(a,1),30726(a,1,2))].">
      <j1 rule="para" parents="30545 30726"/>
    </justification>
  </clause>

  <clause id="30730">
    <literal><![CDATA[
      L(x,y * z,a(z,z,y * z)) = L(x,a(z,z,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29231,a(flip),b,30729,a)].">
      <j1 rule="hyper" parents="64 29231 30729"/>
    </justification>
  </clause>

  <clause id="30731">
    <literal><![CDATA[
      R(x,y,z * a(u,u,w * u)) = R(x,y,z * a(u,u,w))
    ]]></literal>
    <justification jstring="[para(30194(a,1),26174(a,1,3,2))].">
      <j1 rule="para" parents="30194 26174"/>
    </justification>
  </clause>

  <clause id="30732">
    <literal><![CDATA[
      a(x,x,y) * ((x * x) * z) = (x * R(x,x,y)) * z
    ]]></literal>
    <justification jstring="[para(30053(a,1),30273(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="30053 30273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30733">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * ((z * z) * (a(w,v5,w) \ v6))) = a(x,y,(z * R(z,z,u)) * v6)
    ]]></literal>
    <justification jstring="[para(30732(a,2),13878(a,1,3))].">
      <j1 rule="para" parents="30732 13878"/>
    </justification>
  </clause>

  <clause id="30734">
    <literal><![CDATA[
      a(x,x,x * y) * K(z,x) = x * R(K(z,x) / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27364,a,b,30283,a)].">
      <j1 rule="hyper" parents="64 27364 30283"/>
    </justification>
  </clause>

  <clause id="30735">
    <literal><![CDATA[
      (x * a(y,z,z)) \ (R(y,z,z) * a(x,x,a(y,z,z))) = L(x \ y,x,a(y,z,z)) * a(x,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(26741(a,2),30316(a,2,1))].">
      <j1 rule="para" parents="26741 30316"/>
    </justification>
  </clause>

  <clause id="30736">
    <literal><![CDATA[
      (x \ L(x,y,y)) * (x \ L(x,y,y)) = x \ L(L(x,y,y),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14100,a,b,30366,a)].">
      <j1 rule="hyper" parents="64 14100 30366"/>
    </justification>
  </clause>

  <clause id="30737">
    <literal><![CDATA[
      T(x,T((y \ z) * T(y,u),w)) = T(x,T(z * K(y,u),w * y))
    ]]></literal>
    <justification jstring="[para(5739(a,2),30420(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5739 30420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30738">
    <literal><![CDATA[
      (x * y) \ (a(y,y,x) * (x * (y * z))) = L(z,y,x) * a(y,y,x)
    ]]></literal>
    <justification jstring="[para(18(a,2),30458(a,2,1))].">
      <j1 rule="para" parents="18 30458"/>
    </justification>
  </clause>

  <clause id="30739">
    <literal><![CDATA[
      L(L(x,a(y,x,x),z),x,y) = (a(y,x,x) * z) \ (z * x)
    ]]></literal>
    <justification jstring="[hyper(1435,a,30463,a)].">
      <j1 rule="hyper" parents="1435 30463"/>
    </justification>
  </clause>

  <clause id="30740">
    <literal><![CDATA[
      x * T(L(x,x,y) \ 1,y) = y \ (((1 / x) * y) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,16209,a(flip),b,30487,a),flip(a)].">
      <j1 rule="hyper" parents="64 16209 30487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30741">
    <literal><![CDATA[
      1 / (x \ (((1 / y) * x) * y)) = ((x / y) / x) * y
    ]]></literal>
    <justification jstring="[hyper(225,a,30740,a(flip),b,27256,a(flip))].">
      <j1 rule="hyper" parents="225 30740 27256"/>
    </justification>
  </clause>

  <clause id="30742">
    <literal><![CDATA[
      ((L(x,x,y) \ 1) * x) * x = a(y,x,x) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25899,a(flip),b,30501,a),flip(a)].">
      <j1 rule="hyper" parents="64 25899 30501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30743">
    <literal><![CDATA[
      a(x * y,y,y \ 1) * y = a(x,y,y) / (1 / y)
    ]]></literal>
    <justification jstring="[para(30722(a,2),30742(a,1,1))].">
      <j1 rule="para" parents="30722 30742"/>
    </justification>
  </clause>

  <clause id="30744">
    <literal><![CDATA[
      x * T((y * x) \ 1,x \ 1) = ((y / x) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,3874,a(flip),b,30594,a)].">
      <j1 rule="hyper" parents="64 3874 30594"/>
    </justification>
  </clause>

  <clause id="30745">
    <literal><![CDATA[
      ((a(x,y,z) / u) \ 1) / u = u * ((a(x,y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[para(24640(a,1),30744(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24640 30744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30746">
    <literal><![CDATA[
      L(1 / x,x,x \ y) = L(1 / x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10472,a(flip),b,30685,a),flip(a)].">
      <j1 rule="hyper" parents="64 10472 30685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30747">
    <literal><![CDATA[
      (x \ (x / y)) \ K(y,y * y) = L(1 / y,y,y * x) \ 1
    ]]></literal>
    <justification jstring="[para(30746(a,1),14760(a,2,1))].">
      <j1 rule="para" parents="30746 14760"/>
    </justification>
  </clause>

  <clause id="30748">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,x * y) = (z * y) \ (z * (y / x))
    ]]></literal>
    <justification jstring="[hyper(24201,a,30712,a)].">
      <j1 rule="hyper" parents="24201 30712"/>
    </justification>
  </clause>

  <clause id="30749">
    <literal><![CDATA[
      L(x,a(y,y,z),y \ z) = L(x,y \ z,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30297,a(flip),b,30727,a),flip(a)].">
      <j1 rule="hyper" parents="64 30297 30727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30750">
    <literal><![CDATA[
      L(x,a(y,y,z),z * y) = L(x,z * y,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30332,a(flip),b,30730,a),flip(a)].">
      <j1 rule="hyper" parents="64 30332 30730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30751">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (a(x,y,z) * (u / x)) = L(x \ 1,x,x * u)
    ]]></literal>
    <justification jstring="[para(29978(a,1),30748(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29978 30748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30752">
    <literal><![CDATA[
      T(x * (y \ T(y * z,x)),y) = L(y,z,x) \ ((z * y) * x)
    ]]></literal>
    <justification jstring="[para(5434(a,1),29815(a,1,1,2))].">
      <j1 rule="para" parents="5434 29815"/>
    </justification>
  </clause>

  <clause id="30753">
    <literal><![CDATA[
      x * ((x \ 1) * (y * a(x,z,u))) = L(y,x,x) * a(x,z,u)
    ]]></literal>
    <justification jstring="[para(29915(a,1),29916(a,1,2))].">
      <j1 rule="para" parents="29915 29916"/>
    </justification>
  </clause>

  <clause id="30754">
    <literal><![CDATA[
      R(x,y,(z * ((u * z) \ u)) \ w) = R(x,y,a(z,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26333,a(flip),b,30101,a)].">
      <j1 rule="hyper" parents="64 26333 30101"/>
    </justification>
  </clause>

  <clause id="30755">
    <literal><![CDATA[
      K(x,y \ 1) / a(y,y,x) = 1 / (y * (x \ (y \ x)))
    ]]></literal>
    <justification jstring="[para(5962(a,1),30109(a,1,1))].">
      <j1 rule="para" parents="5962 30109"/>
    </justification>
  </clause>

  <clause id="30756">
    <literal><![CDATA[
      a(x,x,y) \ K(y,x \ 1) = 1 / (x * (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(23179,a,30755,a)].">
      <j1 rule="hyper" parents="23179 30755"/>
    </justification>
  </clause>

  <clause id="30757">
    <literal><![CDATA[
      x \ L(T(x,y \ 1),y,y) = 1 / (y * (x \ (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,25528,a(flip),b,30756,a)].">
      <j1 rule="hyper" parents="64 25528 30756"/>
    </justification>
  </clause>

  <clause id="30758">
    <literal><![CDATA[
      1 / (x * (y \ (x \ y))) = y \ (x * (y * (x \ 1)))
    ]]></literal>
    <justification jstring="[para(1140(a,1),30757(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1140 30757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30759">
    <literal><![CDATA[
      (x * (y \ (x \ y))) \ 1 = y \ (x * (y * (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,26633,a(flip),b,30758,a)].">
      <j1 rule="hyper" parents="64 26633 30758"/>
    </justification>
  </clause>

  <clause id="30760">
    <literal><![CDATA[
      (x \ (y * (x * (y \ 1)))) * K(z,u) = K(z,u) / (y * (x \ (y \ x)))
    ]]></literal>
    <justification jstring="[para(30758(a,1),28888(a,1,1))].">
      <j1 rule="para" parents="30758 28888"/>
    </justification>
  </clause>

  <clause id="30761">
    <literal><![CDATA[
      L(x,((y \ (z \ y)) * z) * u,w) = L(x,u * a(z,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29637,a,b,30117,a)].">
      <j1 rule="hyper" parents="64 29637 30117"/>
    </justification>
  </clause>

  <clause id="30762">
    <literal><![CDATA[
      (a(x,x,y) / x) \ K(y,z) = (y / (x * T(y,z))) \ 1
    ]]></literal>
    <justification jstring="[para(25163(a,1),30120(a,1,1,1))].">
      <j1 rule="para" parents="25163 30120"/>
    </justification>
  </clause>

  <clause id="30763">
    <literal><![CDATA[
      (a(x,x,y) \ x) * K(y,z) = (y / (x * T(y,z))) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,30191,a(flip),b,30762,a)].">
      <j1 rule="hyper" parents="64 30191 30762"/>
    </justification>
  </clause>

  <clause id="30765">
    <literal><![CDATA[
      (a(x,x,y) * y) / (x \ y) = R(x,R(x,x,y),y)
    ]]></literal>
    <justification jstring="[para(79(a,1),30138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="79 30138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30766">
    <literal><![CDATA[
      R(x,R(x,x,y),y) = a(x,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,30301,a(flip),b,30765,a),flip(a)].">
      <j1 rule="hyper" parents="64 30301 30765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30767">
    <literal><![CDATA[
      R(x,R(x,x,y),y) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30053,a(flip),b,30766,a),flip(a)].">
      <j1 rule="hyper" parents="373 30053 30766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30768">
    <literal><![CDATA[
      R(R(x,y,z),R(x,x,u),u) = R(R(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(30767(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30767 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30769">
    <literal><![CDATA[
      R(x,x,y) * a(x,x,y) = R(R(x,x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30093,a(flip),b,30768,a)].">
      <j1 rule="hyper" parents="64 30093 30768"/>
    </justification>
  </clause>

  <clause id="30770">
    <literal><![CDATA[
      a(x,x,y) * R(x,x,y) = R(R(x,x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(23777,a,30769,a)].">
      <j1 rule="hyper" parents="23777 30769"/>
    </justification>
  </clause>

  <clause id="30771">
    <literal><![CDATA[
      R((1 / x) / (y \ a(y,y,R(x,z,u))),L(y,y,R(x,z,u)),R(x,z,u)) = (x \ R(x,z,u)) / (y \ R(x,z,u))
    ]]></literal>
    <justification jstring="[para(2067(a,1),30140(a,2,1))].">
      <j1 rule="para" parents="2067 30140"/>
    </justification>
  </clause>

  <clause id="30772">
    <literal><![CDATA[
      (x * ((1 / x) * y)) \ (x * (x \ y)) = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[para(569(a,1),30153(a,1,1,2))].">
      <j1 rule="para" parents="569 30153"/>
    </justification>
  </clause>

  <clause id="30773">
    <literal><![CDATA[
      (x * ((1 / x) * y)) \ y = ((x \ y) / y) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),30772(a,1,2))].">
      <j1 rule="para" parents="10 30772"/>
    </justification>
  </clause>

  <clause id="30774">
    <literal><![CDATA[
      (((x \ y) / y) * x) \ y = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(40,a,23867,a,b,30773,a)].">
      <j1 rule="hyper" parents="40 23867 30773"/>
    </justification>
  </clause>

  <clause id="30775">
    <literal><![CDATA[
      a(x,x,x \ y) \ y = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(30080(a,2),30774(a,1,1))].">
      <j1 rule="para" parents="30080 30774"/>
    </justification>
  </clause>

  <clause id="30776">
    <literal><![CDATA[
      a(x,x,x \ ((((1 / x) \ y) \ z) \ z)) \ ((((1 / x) \ y) \ z) \ z) = x * (y * K((1 / x) \ y,z * (y \ (1 / x))))
    ]]></literal>
    <justification jstring="[para(18942(a,2),30775(a,2,2))].">
      <j1 rule="para" parents="18942 30775"/>
    </justification>
  </clause>

  <clause id="30777">
    <literal><![CDATA[
      a(L(x,y,y) * y,z,u) = a((1 / y) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26836,a(flip),b,30248,a),flip(a)].">
      <j1 rule="hyper" parents="64 26836 30248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30778">
    <literal><![CDATA[
      a(((x \ 1) \ (x \ y)) * z,u,w) = a(L(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(1166(a,2),30248(a,1,1,1))].">
      <j1 rule="para" parents="1166 30248"/>
    </justification>
  </clause>

  <clause id="30779">
    <literal><![CDATA[
      a(L(x,y,y) * y,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2671,a(flip),b,30777,a),flip(a)].">
      <j1 rule="hyper" parents="373 2671 30777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30780">
    <literal><![CDATA[
      a(x * L(y,x,x),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(26847,a,30779,a)].">
      <j1 rule="hyper" parents="26847 30779"/>
    </justification>
  </clause>

  <clause id="30781">
    <literal><![CDATA[
      a(x,y,z * (((u * w) \ u) * w)) = a(x,y,z * a(w,w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27480,a(flip),b,30288,a)].">
      <j1 rule="hyper" parents="64 27480 30288"/>
    </justification>
  </clause>

  <clause id="30782">
    <literal><![CDATA[
      x / (x / ((y / (z * y)) \ (z \ 1))) = (z * (y / (z * y))) \ 1
    ]]></literal>
    <justification jstring="[para(30079(a,1),30293(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30079 30293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30783">
    <literal><![CDATA[
      (x \ y) * ((y \ (x \ y)) \ 1) = R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,27055,a(flip),b,30530,a),flip(a)].">
      <j1 rule="hyper" parents="373 27055 30530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30784">
    <literal><![CDATA[
      R(x,y \ x,y \ x) = y * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,25747,a(flip),b,30783,a),flip(a)].">
      <j1 rule="hyper" parents="64 25747 30783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30785">
    <literal><![CDATA[
      R(x,x / y,y \ x) = y * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,26410,a,b,30784,a)].">
      <j1 rule="hyper" parents="64 26410 30784"/>
    </justification>
  </clause>

  <clause id="30786">
    <literal><![CDATA[
      a(x,y \ x,y \ x) = x \ (y * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[hyper(139,a,30784,a(flip),b,15984,a),flip(a)].">
      <j1 rule="hyper" parents="139 30784 15984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30787">
    <literal><![CDATA[
      R(x * y,x \ (x * y),y) = x * (((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),30784(a,1,3))].">
      <j1 rule="para" parents="9 30784"/>
    </justification>
  </clause>

  <clause id="30788">
    <literal><![CDATA[
      R(x,x / y,x / y) = y * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,23813,a,b,30785,a)].">
      <j1 rule="hyper" parents="64 23813 30785"/>
    </justification>
  </clause>

  <clause id="30789">
    <literal><![CDATA[
      R(x,x \ y,y \ x) = y * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,30563,a(flip),b,30788,a)].">
      <j1 rule="hyper" parents="64 30563 30788"/>
    </justification>
  </clause>

  <clause id="30790">
    <literal><![CDATA[
      R(x \ 1,(x \ 1) \ y,(x * x) \ (y \ x)) = y * (((x \ 1) \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,26325,a,b,30789,a)].">
      <j1 rule="hyper" parents="64 26325 30789"/>
    </justification>
  </clause>

  <clause id="30791">
    <literal><![CDATA[
      x \ (x \ (y * ((x \ y) \ 1))) = R(x \ 1,x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(30789(a,1),1990(a,1,2,2))].">
      <j1 rule="para" parents="30789 1990"/>
    </justification>
  </clause>

  <clause id="30792">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ 1 = x \ (y * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(30789(a,1),24814(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30789 24814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30793">
    <literal><![CDATA[
      a(x,y \ x,y \ x) \ z = (x \ (y * ((x \ y) \ 1))) \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,30786,a)].">
      <j1 rule="hyper" parents="62 30786"/>
    </justification>
  </clause>

  <clause id="30794">
    <literal><![CDATA[
      (x \ (y * ((x \ y) \ 1))) * (y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(30786(a,1),30528(a,1,1))].">
      <j1 rule="para" parents="30786 30528"/>
    </justification>
  </clause>

  <clause id="30795">
    <literal><![CDATA[
      (x \ (y * ((x \ y) \ 1))) * (((x \ y) \ 1) \ 1) = (((y \ x) * (x \ y)) \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[para(30792(a,1),14809(a,1,1))].">
      <j1 rule="para" parents="30792 14809"/>
    </justification>
  </clause>

  <clause id="30796">
    <literal><![CDATA[
      (((x \ y) * (y \ x)) \ 1) * (y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(30792(a,2),30794(a,1,1))].">
      <j1 rule="para" parents="30792 30794"/>
    </justification>
  </clause>

  <clause id="30797">
    <literal><![CDATA[
      R(x * y,y,y) = x * (((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),30787(a,1,2))].">
      <j1 rule="para" parents="9 30787"/>
    </justification>
  </clause>

  <clause id="30798">
    <literal><![CDATA[
      (x * y) \ (x * (((x * y) \ x) \ 1)) = (x * y) * R((x * y) \ 1,y,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,30797,a(flip),b,1988,a)].">
      <j1 rule="hyper" parents="139 30797 1988"/>
    </justification>
  </clause>

  <clause id="30799">
    <literal><![CDATA[
      R(x,x \ y,x \ y) * (x \ y) = x * (((y * (x \ y)) \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(30555(a,1),30007(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30555 30007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30800">
    <literal><![CDATA[
      R(x,((1 / y) \ (y \ z)) * u,w) = R(x,L(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26697,a(flip),b,30582,a)].">
      <j1 rule="hyper" parents="64 26697 30582"/>
    </justification>
  </clause>

  <clause id="30801">
    <literal><![CDATA[
      ((x / y) / y) \ x = x \ ((x * y) * y)
    ]]></literal>
    <justification jstring="[hyper(35,a,1270,a,b,30583,a),flip(a)].">
      <j1 rule="hyper" parents="35 1270 30583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30802">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) * y = ((x / y) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,30564,a,b,30801,a)].">
      <j1 rule="hyper" parents="373 30564 30801"/>
    </justification>
  </clause>

  <clause id="30803">
    <literal><![CDATA[
      (x * y) \ (((x * y) * y) * y) = (x / y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(11(a,1),30801(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 30801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30804">
    <literal><![CDATA[
      ((((x \ y) * x) / (x \ y)) / (x \ y)) \ ((x \ y) * x) = ((x \ y) * x) \ ((y * T(x \ y,x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1297(a,1),30801(a,2,2,1))].">
      <j1 rule="para" parents="1297 30801"/>
    </justification>
  </clause>

  <clause id="30805">
    <literal><![CDATA[
      T(x,y) \ ((T(x,y) * (z \ x)) * (z \ x)) = ((K(x,y) * z) / (z \ x)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(14819(a,1),30801(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14819 30801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30806">
    <literal><![CDATA[
      x / (y \ (y / x)) = ((y / x) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,9481,a(flip),b,30802,a)].">
      <j1 rule="hyper" parents="64 9481 30802"/>
    </justification>
  </clause>

  <clause id="30807">
    <literal><![CDATA[
      T(((x / y) / y) \ x,K(z,u)) = y / (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(30806(a,1),17758(a,1,1))].">
      <j1 rule="para" parents="30806 17758"/>
    </justification>
  </clause>

  <clause id="30808">
    <literal><![CDATA[
      (x * y) * ((x / y) \ (x * y)) = ((x * y) * y) * y
    ]]></literal>
    <justification jstring="[hyper(157,a,30803,a)].">
      <j1 rule="hyper" parents="157 30803"/>
    </justification>
  </clause>

  <clause id="30809">
    <literal><![CDATA[
      T(x \ ((x * y) * y),K(z,u)) = y / (x \ (x / y))
    ]]></literal>
    <justification jstring="[para(30801(a,1),30807(a,1,1))].">
      <j1 rule="para" parents="30801 30807"/>
    </justification>
  </clause>

  <clause id="30810">
    <literal><![CDATA[
      T(x \ ((x * y) * y),K(z,u)) = ((x / y) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,30806,a(flip),b,30809,a),flip(a)].">
      <j1 rule="hyper" parents="373 30806 30809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30811">
    <literal><![CDATA[
      T(x \ ((x * y) * y),K(z,u)) = x \ ((x * y) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30801,a(flip),b,30810,a),flip(a)].">
      <j1 rule="hyper" parents="373 30801 30810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30812">
    <literal><![CDATA[
      K(x,y) * ((z \ ((z * u) * u)) \ 1) = (z \ ((z * u) * u)) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(30811(a,1),18383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30811 18383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30813">
    <literal><![CDATA[
      K(x * y,y) * ((x \ (y * (x * y))) * z) = (x \ ((x * y) * y)) * z
    ]]></literal>
    <justification jstring="[para(30811(a,1),25398(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30811 25398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30814">
    <literal><![CDATA[
      a(x,y,(1 / z) \ ((1 / u) / z)) = a(x,y,R(u,z,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,27308,a(flip),b,30590,a),flip(a)].">
      <j1 rule="hyper" parents="373 27308 30590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30815">
    <literal><![CDATA[
      L(x,y,z * (u * (w \ (u \ w)))) = L(x,y,a(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29105,a(flip),b,30604,a)].">
      <j1 rule="hyper" parents="64 29105 30604"/>
    </justification>
  </clause>

  <clause id="30816">
    <literal><![CDATA[
      a(1 / (x \ y),z,(1 / (1 / (y \ x))) \ ((x \ y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,27322,a(flip),b,30613,a)].">
      <j1 rule="hyper" parents="64 27322 30613"/>
    </justification>
  </clause>

  <clause id="30817">
    <literal><![CDATA[
      a(x,y,((((z / u) / z) * u) * w) * v5) = a(x,y,(a(u,u,z) * w) * v5)
    ]]></literal>
    <justification jstring="[para(30617(a,1),27415(a,1,3,1))].">
      <j1 rule="para" parents="30617 27415"/>
    </justification>
  </clause>

  <clause id="30818">
    <literal><![CDATA[
      a(x,y,z \ ((((u / w) / u) * w) * v5)) = a(x,y,z \ (a(w,w,u) * v5))
    ]]></literal>
    <justification jstring="[para(30617(a,1),27494(a,1,3,2))].">
      <j1 rule="para" parents="30617 27494"/>
    </justification>
  </clause>

  <clause id="30819">
    <literal><![CDATA[
      ((((x * y) \ z) \ z) * y) \ T(x * y,y \ (x \ z)) = x \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16762,a(flip),b,30681,a)].">
      <j1 rule="hyper" parents="64 16762 30681"/>
    </justification>
  </clause>

  <clause id="30820">
    <literal><![CDATA[
      L(x * a(y,z,u),y,y) = L(x,y,y) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1139,a(flip),b,30753,a)].">
      <j1 rule="hyper" parents="64 1139 30753"/>
    </justification>
  </clause>

  <clause id="30821">
    <literal><![CDATA[
      L(x * a(y,z,u),y,y) = a(y,z,u) * L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a,b,30820,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 30820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30822">
    <literal><![CDATA[
      x \ L(x * a(y,z,u),y,y) = (a(y,z,u) / x) * L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,30820,a,b,24854,a)].">
      <j1 rule="hyper" parents="139 30820 24854"/>
    </justification>
  </clause>

  <clause id="30823">
    <literal><![CDATA[
      L(x,x,x) * a(x,y,z) = a(x,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25065,a(flip),b,30820,a),flip(a)].">
      <j1 rule="hyper" parents="64 25065 30820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30824">
    <literal><![CDATA[
      L(a(x,y,z) \ u,x,x) = a(x,y,z) \ L(u,x,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,5544,a(flip),b,30820,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 5544 30820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30825">
    <literal><![CDATA[
      L(L(x,a(y,z,u),y),y * a(y,z,u),y) = L(a(y,z,u) \ (a(y,z,u) * x),y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,16062,a,b,30824,a)].">
      <j1 rule="hyper" parents="373 16062 30824"/>
    </justification>
  </clause>

  <clause id="30826">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,x) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(425(a,1),30824(a,2,2))].">
      <j1 rule="para" parents="425 30824"/>
    </justification>
  </clause>

  <clause id="30827">
    <literal><![CDATA[
      R(x,y,(((z * u) \ z) * u) \ w) = R(x,y,a(u,u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26212,a,b,30754,a)].">
      <j1 rule="hyper" parents="64 26212 30754"/>
    </justification>
  </clause>

  <clause id="30828">
    <literal><![CDATA[
      R(x \ 1,x \ y,(x \ y) \ 1) = R(x \ 1,x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2012,a,b,30791,a)].">
      <j1 rule="hyper" parents="64 2012 30791"/>
    </justification>
  </clause>

  <clause id="30829">
    <literal><![CDATA[
      R(x,((y \ 1) \ (y \ z)) * u,w) = R(x,L(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26435,a(flip),b,30800,a)].">
      <j1 rule="hyper" parents="64 26435 30800"/>
    </justification>
  </clause>

  <clause id="30830">
    <literal><![CDATA[
      a(x,y,(1 / z) \ ((1 / u) / z)) = a(x,y,L(u,z,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,27728,a(flip),b,30814,a),flip(a)].">
      <j1 rule="hyper" parents="373 27728 30814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30831">
    <literal><![CDATA[
      L(x,y,a(z,u,u) * w) = L(x,y,w * a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30114,a(flip),b,30815,a),flip(a)].">
      <j1 rule="hyper" parents="64 30114 30815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30832">
    <literal><![CDATA[
      L(x,y,z * a(u,w,w)) = L(x,y,z * a(w,w,u))
    ]]></literal>
    <justification jstring="[hyper(24201,a,30831,a)].">
      <j1 rule="hyper" parents="24201 30831"/>
    </justification>
  </clause>

  <clause id="30833">
    <literal><![CDATA[
      L(x,y,a(z,u,u) * w) = L(x,y,a(u,u,z) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,30831,a),flip(a)].">
      <j1 rule="hyper" parents="373 23253 30831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30834">
    <literal><![CDATA[
      L(x,y,a(z,z,u) * a(u,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,594,a(flip),b,30832,a),flip(a)].">
      <j1 rule="hyper" parents="373 594 30832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30835">
    <literal><![CDATA[
      a(1 / (x \ y),z,((1 / (y \ x)) \ 1) \ ((x \ y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,27389,a(flip),b,30816,a)].">
      <j1 rule="hyper" parents="64 27389 30816"/>
    </justification>
  </clause>

  <clause id="30836">
    <literal><![CDATA[
      R(x,y,(L(z \ 1,z,u) * z) \ w) = R(x,y,a(z,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(241(a,2),30827(a,1,3,1,1))].">
      <j1 rule="para" parents="241 30827"/>
    </justification>
  </clause>

  <clause id="30837">
    <literal><![CDATA[
      R(x,(y \ (y \ z)) * u,w) = R(x,L(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,3029,a(flip),b,30829,a)].">
      <j1 rule="hyper" parents="64 3029 30829"/>
    </justification>
  </clause>

  <clause id="30838">
    <literal><![CDATA[
      R(x,y * (z \ (z \ u)),w) = R(x,L(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26409,a,b,30837,a)].">
      <j1 rule="hyper" parents="64 26409 30837"/>
    </justification>
  </clause>

  <clause id="30839">
    <literal><![CDATA[
      R(x,L(y * z,y,y) * u,w) = R(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),30837(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 30837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30840">
    <literal><![CDATA[
      R(x,L(y * z,z,z) * u,w) = R(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26441,a,b,30839,a)].">
      <j1 rule="hyper" parents="64 26441 30839"/>
    </justification>
  </clause>

  <clause id="30841">
    <literal><![CDATA[
      a(x,y,(1 / z) \ (z \ (1 / u))) = a(x,y,L(u,z,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27322,a(flip),b,30830,a)].">
      <j1 rule="hyper" parents="64 27322 30830"/>
    </justification>
  </clause>

  <clause id="30842">
    <literal><![CDATA[
      a(1 / (x \ y),z,(y \ x) \ ((x \ y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(82(a,1),30835(a,1,3,1))].">
      <j1 rule="para" parents="82 30835"/>
    </justification>
  </clause>

  <clause id="30843">
    <literal><![CDATA[
      a(x \ y,z,(y \ x) \ ((x \ y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,2641,a(flip),b,30842,a)].">
      <j1 rule="hyper" parents="64 2641 30842"/>
    </justification>
  </clause>

  <clause id="30845">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ 1 = (y \ x) \ ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,30843,a(flip),b,1282,a)].">
      <j1 rule="hyper" parents="139 30843 1282"/>
    </justification>
  </clause>

  <clause id="30847">
    <literal><![CDATA[
      (x \ y) \ ((y \ x) \ 1) = y \ (x * ((y \ x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,30792,a(flip),b,30845,a),flip(a)].">
      <j1 rule="hyper" parents="64 30792 30845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30848">
    <literal><![CDATA[
      (x * y) \ (x * (((x * y) \ x) \ 1)) = y \ (((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),30847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 30847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30849">
    <literal><![CDATA[
      a(x,y,(1 / z) \ (z \ (u \ 1))) = a(x,y,L(u,z,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27338,a(flip),b,30841,a)].">
      <j1 rule="hyper" parents="64 27338 30841"/>
    </justification>
  </clause>

  <clause id="30850">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ (z \ (u \ 1))) = a(x,y,L(u,z,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27389,a(flip),b,30849,a)].">
      <j1 rule="hyper" parents="64 27389 30849"/>
    </justification>
  </clause>

  <clause id="30851">
    <literal><![CDATA[
      a(x,y,z \ ((z \ 1) \ (u \ 1))) = a(x,y,L(u,z,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,5348,a(flip),b,30850,a)].">
      <j1 rule="hyper" parents="64 5348 30850"/>
    </justification>
  </clause>

  <clause id="30852">
    <literal><![CDATA[
      L(x,((y * (z \ 1)) * u) * w,v5) = L(x,((z * y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29667,a,b,29517,a)].">
      <j1 rule="hyper" parents="64 29667 29517"/>
    </justification>
  </clause>

  <clause id="30853">
    <literal><![CDATA[
      L(x,((y * (1 / z)) * u) * w,v5) = L(x,((z * y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29667,a,b,29518,a)].">
      <j1 rule="hyper" parents="64 29667 29518"/>
    </justification>
  </clause>

  <clause id="30854">
    <literal><![CDATA[
      L(L(x,x,y),y * x,y) = (y * ((y \ 1) * (1 / x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(29616,a,29598,a)].">
      <j1 rule="hyper" parents="29616 29598"/>
    </justification>
  </clause>

  <clause id="30855">
    <literal><![CDATA[
      L(L(x,x,y),y * x,y) = L(1 / x,y,y) \ 1
    ]]></literal>
    <justification jstring="[para(1139(a,1),30854(a,2,1))].">
      <j1 rule="para" parents="1139 30854"/>
    </justification>
  </clause>

  <clause id="30856">
    <literal><![CDATA[
      L(L(x,x,y),x * y,y) = L(1 / x,y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(29572,a,30855,a)].">
      <j1 rule="hyper" parents="29572 30855"/>
    </justification>
  </clause>

  <clause id="30857">
    <literal><![CDATA[
      L(x,y * ((K(z,u) / w) \ v5),v6) = L(x,(w \ v5) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29862,a(flip),b,29631,a),flip(a)].">
      <j1 rule="hyper" parents="373 29862 29631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30858">
    <literal><![CDATA[
      L(x,y * (z * R(u,u,z)),w) = L(x,(u \ z) * y,w)
    ]]></literal>
    <justification jstring="[para(24612(a,1),30857(a,1,2,2))].">
      <j1 rule="para" parents="24612 30857"/>
    </justification>
  </clause>

  <clause id="30859">
    <literal><![CDATA[
      L(x,y \ R(1 / z,u,w),v5) = L(x,y \ R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(245(a,1),29700(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="245 29700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30860">
    <literal><![CDATA[
      L(x,y \ (((z / u) / u) \ 1),w) = L(x,y \ R(z \ 1,u,u),w)
    ]]></literal>
    <justification jstring="[para(30605(a,1),29700(a,1,2,2))].">
      <j1 rule="para" parents="30605 29700"/>
    </justification>
  </clause>

  <clause id="30861">
    <literal><![CDATA[
      L(x,y \ R(z \ 1,u,w),v5) = L(x,y \ R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29591,a(flip),b,30859,a)].">
      <j1 rule="hyper" parents="64 29591 30859"/>
    </justification>
  </clause>

  <clause id="30862">
    <literal><![CDATA[
      L(x,y \ ((z / (u * z)) \ 1),w) = L(x,y \ (z \ (u \ z)),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29552,a(flip),b,29703,a),flip(a)].">
      <j1 rule="hyper" parents="373 29552 29703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30863">
    <literal><![CDATA[
      L(x,y * L(z * T(u,w),v5,v6),v7) = L(x,L(z * u,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[para(6367(a,1),29712(a,1,2,2,1))].">
      <j1 rule="para" parents="6367 29712"/>
    </justification>
  </clause>

  <clause id="30864">
    <literal><![CDATA[
      L(x,y * (L(z,u,w) \ z),v5) = L(x,y * (z * L(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29612,a,b,29738,a)].">
      <j1 rule="hyper" parents="64 29612 29738"/>
    </justification>
  </clause>

  <clause id="30865">
    <literal><![CDATA[
      L(x,L((1 / (y / z)) * u,w,v5),v6) = L(x,L((z \ y) * u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29873,a,b,29748,a)].">
      <j1 rule="hyper" parents="64 29873 29748"/>
    </justification>
  </clause>

  <clause id="30866">
    <literal><![CDATA[
      L(x,y \ (z / (z * u)),w) = L(x,y \ (z \ (u \ z)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29450,a(flip),b,29763,a)].">
      <j1 rule="hyper" parents="64 29450 29763"/>
    </justification>
  </clause>

  <clause id="30868">
    <literal><![CDATA[
      L(x,y \ ((z * u) \ z),w) = L(x,y \ (z \ (u \ z)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29552,a(flip),b,30866,a)].">
      <j1 rule="hyper" parents="64 29552 30866"/>
    </justification>
  </clause>

  <clause id="30869">
    <literal><![CDATA[
      (x / (x * y)) * L(z,u \ (x \ (y \ x)),u) = u * ((u \ (x / (x * y))) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,30866,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="145 30866 101"/>
    </justification>
  </clause>

  <clause id="30870">
    <literal><![CDATA[
      ((x * y) \ x) * L(z,u \ (x \ (y \ x)),u) = u * ((u \ (1 / (((x * y) \ x) \ 1))) * z)
    ]]></literal>
    <justification jstring="[para(30868(a,1),29900(a,1,2))].">
      <j1 rule="para" parents="30868 29900"/>
    </justification>
  </clause>

  <clause id="30871">
    <literal><![CDATA[
      L(x,y \ (z \ ((u * u) \ w)),v5) = L(x,y \ (z \ w),v5)
    ]]></literal>
    <justification jstring="[para(932(a,1),29768(a,1,2,2))].">
      <j1 rule="para" parents="932 29768"/>
    </justification>
  </clause>

  <clause id="30872">
    <literal><![CDATA[
      L(x,y \ ((1 / z) \ u),w) = L(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(540(a,1),30871(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="540 30871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30873">
    <literal><![CDATA[
      L(x,y \ ((z \ 1) \ u),w) = L(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29656,a(flip),b,30872,a)].">
      <j1 rule="hyper" parents="64 29656 30872"/>
    </justification>
  </clause>

  <clause id="30874">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (x * (y * (x \ ((x \ 1) \ y)))) = L(y,x \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5501,a,b,30873,a)].">
      <j1 rule="hyper" parents="64 5501 30873"/>
    </justification>
  </clause>

  <clause id="30875">
    <literal><![CDATA[
      L(x,(y * L(y,y,z)) * u,w) = L(x,a(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[para(30462(a,1),29777(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30462 29777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30876">
    <literal><![CDATA[
      a(x,y * L(T(z,u),w,v5),x) \ x = L(x,L(z,w,v5) \ y,x)
    ]]></literal>
    <justification jstring="[para(13566(a,1),29816(a,1,1))].">
      <j1 rule="para" parents="13566 29816"/>
    </justification>
  </clause>

  <clause id="30877">
    <literal><![CDATA[
      L(x,y \ (z * ((1 / u) * w)),v5) = L(x,y \ ((u * w) * z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29554,a,b,29849,a)].">
      <j1 rule="hyper" parents="64 29554 29849"/>
    </justification>
  </clause>

  <clause id="30878">
    <literal><![CDATA[
      L(x,L(K(y,z) * (u \ w),u,u) * v5,v6) = L(x,(K(y,z) * (u * w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(26099(a,2),29868(a,1,2,1))].">
      <j1 rule="para" parents="26099 29868"/>
    </justification>
  </clause>

  <clause id="30879">
    <literal><![CDATA[
      L(x,y \ ((z / (1 / u)) * w),v5) = L(x,y \ ((u \ z) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29655,a(flip),b,29883,a),flip(a)].">
      <j1 rule="hyper" parents="373 29655 29883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30880">
    <literal><![CDATA[
      a(x,y,z) \ ((T(x,u) \ L(T(x,u),w,v5)) \ a(x,y,z)) = (L(x,w,v5) * (x \ a(x,y,z))) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(29919(a,1),27003(a,2,1))].">
      <j1 rule="para" parents="29919 27003"/>
    </justification>
  </clause>

  <clause id="30881">
    <literal><![CDATA[
      L(a(x,y,z),u,R(x,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14211,a,29958,a)].">
      <j1 rule="hyper" parents="14211 29958"/>
    </justification>
  </clause>

  <clause id="30882">
    <literal><![CDATA[
      R(x,y,z) \ (a(x,u,w) * v5) = (R(x,y,z) \ v5) * a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,23906,a(flip),b,29958,a(flip))].">
      <j1 rule="hyper" parents="139 23906 29958"/>
    </justification>
  </clause>

  <clause id="30883">
    <literal><![CDATA[
      ((a(x,y,z) * R(x,u,w)) * v5) / (R(x,u,w) * (v5 * a(x,y,z))) = a(a(x,y,z),R(x,u,w),v5) * K(a(x,y,z),R(x,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(29958(a,1),15480(a,1,2))].">
      <j1 rule="para" parents="29958 15480"/>
    </justification>
  </clause>

  <clause id="30884">
    <literal><![CDATA[
      L(a(x,y,z),u,L(x,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29221,a(flip),b,30881,a)].">
      <j1 rule="hyper" parents="64 29221 30881"/>
    </justification>
  </clause>

  <clause id="30885">
    <literal><![CDATA[
      a(x,y,z) \ (R(x,u,w) * v5) = R(x,u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(30881(a,1),27804(a,1,1))].">
      <j1 rule="para" parents="30881 27804"/>
    </justification>
  </clause>

  <clause id="30886">
    <literal><![CDATA[
      L(a(x,y,z),u,L(x,w,v5)) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a,b,30884,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 30884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30887">
    <literal><![CDATA[
      L(a(x,y,z),u,w * (x \ w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,25352,a(flip),b,30884,a)].">
      <j1 rule="hyper" parents="64 25352 30884"/>
    </justification>
  </clause>

  <clause id="30888">
    <literal><![CDATA[
      (L(x,y,z) * L(u,x,x)) \ (L(x,y,z) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1247,a(flip),b,30884,a)].">
      <j1 rule="hyper" parents="64 1247 30884"/>
    </justification>
  </clause>

  <clause id="30889">
    <literal><![CDATA[
      a(L(x,y,z),u,a(x,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,30884,a)].">
      <j1 rule="hyper" parents="54 30884"/>
    </justification>
  </clause>

  <clause id="30890">
    <literal><![CDATA[
      a(x,y,z) \ (L(x,u,w) * v5) = L(x,u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(30884(a,1),27804(a,1,1))].">
      <j1 rule="para" parents="30884 27804"/>
    </justification>
  </clause>

  <clause id="30891">
    <literal><![CDATA[
      a(x,y,a((z \ (z / x)) \ 1,u,w)) = 1
    ]]></literal>
    <justification jstring="[para(30519(a,1),30889(a,1,1))].">
      <j1 rule="para" parents="30519 30889"/>
    </justification>
  </clause>

  <clause id="30892">
    <literal><![CDATA[
      a(x,y,a(z \ (z / x),u,w)) = 1
    ]]></literal>
    <justification jstring="[para(2653(a,1),30891(a,1,3))].">
      <j1 rule="para" parents="2653 30891"/>
    </justification>
  </clause>

  <clause id="30893">
    <literal><![CDATA[
      x \ R(x,x \ y,y) = a(x,x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,24737,a,b,30887,a)].">
      <j1 rule="hyper" parents="42 24737 30887"/>
    </justification>
  </clause>

  <clause id="30894">
    <literal><![CDATA[
      x \ R(x,y,x \ y) = a(x,y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(42,a,16031,a(flip),b,30887,a)].">
      <j1 rule="hyper" parents="42 16031 30887"/>
    </justification>
  </clause>

  <clause id="30895">
    <literal><![CDATA[
      a(x,x \ y,y) * x = R(x,x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,23174,a,b,30893,a)].">
      <j1 rule="hyper" parents="39 23174 30893"/>
    </justification>
  </clause>

  <clause id="30896">
    <literal><![CDATA[
      a(x,x * y,x \ (x * y)) = x \ R(x,x * y,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),30894(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="9 30894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30897">
    <literal><![CDATA[
      a(1 / x,L(y,x,x),(1 / x) \ L(y,x,x)) = (1 / x) \ R(1 / x,L(y,x,x),x * y)
    ]]></literal>
    <justification jstring="[para(561(a,1),30894(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="561 30894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30898">
    <literal><![CDATA[
      L(a(x,y,z),u,L(x,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(30886(a,2),152(a,1))].">
      <j1 rule="para" parents="30886 152"/>
    </justification>
  </clause>

  <clause id="30899">
    <literal><![CDATA[
      L(a(x,y,z),u,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(593(a,1),30898(a,1,3))].">
      <j1 rule="para" parents="593 30898"/>
    </justification>
  </clause>

  <clause id="30900">
    <literal><![CDATA[
      x \ R(x,x * y,y) = a(x,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13875,a(flip),b,30896,a),flip(a)].">
      <j1 rule="hyper" parents="64 13875 30896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30902">
    <literal><![CDATA[
      a(x,x * y,y) * x = R(x,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,23174,a,b,30900,a)].">
      <j1 rule="hyper" parents="39 23174 30900"/>
    </justification>
  </clause>

  <clause id="30903">
    <literal><![CDATA[
      L(x,y,z) \ (a(x,u,w) * v5) = (L(x,y,z) \ v5) * a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,23906,a(flip),b,29959,a(flip))].">
      <j1 rule="hyper" parents="139 23906 29959"/>
    </justification>
  </clause>

  <clause id="30904">
    <literal><![CDATA[
      (L(x,y,z) \ x) * a(x,u,w) = x * (L(x,y,z) \ a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(2342,a,29960,a),flip(a)].">
      <j1 rule="hyper" parents="2342 29960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30905">
    <literal><![CDATA[
      L(x,y,z) \ (u * a(x,w,v5)) = a(x,w,v5) * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a,b,29960,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 29960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30906">
    <literal><![CDATA[
      (a(x,y,z) * (u * R(x,w,v5))) / (a(x,y,z) * R(x,w,v5)) = R(u,a(x,y,z),R(x,w,v5))
    ]]></literal>
    <justification jstring="[para(29975(a,1),23137(a,1,1))].">
      <j1 rule="para" parents="29975 23137"/>
    </justification>
  </clause>

  <clause id="30907">
    <literal><![CDATA[
      (x * (a(y,z,u) * R(y,w,v5))) \ (a(y,z,u) * (x * R(y,w,v5))) = a(x,a(y,z,u),R(y,w,v5))
    ]]></literal>
    <justification jstring="[para(29975(a,1),23940(a,1,2))].">
      <j1 rule="para" parents="29975 23940"/>
    </justification>
  </clause>

  <clause id="30908">
    <literal><![CDATA[
      a(L(x,y,z),u,w) \ (x * v5) = x * (a(L(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,29991,a)].">
      <j1 rule="hyper" parents="139 168 29991"/>
    </justification>
  </clause>

  <clause id="30909">
    <literal><![CDATA[
      L(x,(y * z) \ a(z,z,y),u) = L(x,y * (a(z,z,y) * z),u)
    ]]></literal>
    <justification jstring="[para(29320(a,1),29997(a,2,2))].">
      <j1 rule="para" parents="29320 29997"/>
    </justification>
  </clause>

  <clause id="30910">
    <literal><![CDATA[
      (R(x,y,z) \ x) * a(x,u,w) = x * (R(x,y,z) \ a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,1907,a(flip),b,30006,a),flip(a)].">
      <j1 rule="hyper" parents="64 1907 30006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30911">
    <literal><![CDATA[
      a(x,x,y) * (z / R(x,x,y)) = L(z / x,x,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30076,a(flip),b,30011,a),flip(a)].">
      <j1 rule="hyper" parents="64 30076 30011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30912">
    <literal><![CDATA[
      L(a(L(x,y,z),L(x,y,z),u),x,L(x,y,z) * u) = L(a(x,L(x,y,z),u),y,z)
    ]]></literal>
    <justification jstring="[para(30077(a,1),16033(a,1,1))].">
      <j1 rule="para" parents="30077 16033"/>
    </justification>
  </clause>

  <clause id="30913">
    <literal><![CDATA[
      R(x,x,y) * L(z,x,a(x,x,y)) = x * ((x \ R(x,x,y)) * z)
    ]]></literal>
    <justification jstring="[para(30415(a,1),30087(a,1,2))].">
      <j1 rule="para" parents="30415 30087"/>
    </justification>
  </clause>

  <clause id="30914">
    <literal><![CDATA[
      a(x,y,y) * (a(x,z,u) * x) = a(x,z,u) * R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30223,a(flip),b,30266,a),flip(a)].">
      <j1 rule="hyper" parents="373 30223 30266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30915">
    <literal><![CDATA[
      L(x,a(y \ z,y \ z,z),y \ z) = L(x,y \ z,a(y \ z,y \ z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30415,a,b,30296,a)].">
      <j1 rule="hyper" parents="64 30415 30296"/>
    </justification>
  </clause>

  <clause id="30916">
    <literal><![CDATA[
      ((1 / a(x,x,y)) * x) * (x \ y) = ((a(x,x,y) \ 1) * y) * 1
    ]]></literal>
    <justification jstring="[para(13923(a,1),30306(a,2,1,1))].">
      <j1 rule="para" parents="13923 30306"/>
    </justification>
  </clause>

  <clause id="30917">
    <literal><![CDATA[
      L(x,y,(z * u) * (z * (u * a(u,u,z)))) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(29324(a,1),30320(a,1,3,2))].">
      <j1 rule="para" parents="29324 30320"/>
    </justification>
  </clause>

  <clause id="30918">
    <literal><![CDATA[
      a((x * y) * (x * (y * a(y,y,x))),z,u) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(29324(a,1),30321(a,1,1,2))].">
      <j1 rule="para" parents="29324 30321"/>
    </justification>
  </clause>

  <clause id="30919">
    <literal><![CDATA[
      L(x,(y * z) * (y * (z * a(z,z,y))),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(29324(a,1),30322(a,1,2,2))].">
      <j1 rule="para" parents="29324 30322"/>
    </justification>
  </clause>

  <clause id="30920">
    <literal><![CDATA[
      L(a(x,x,y) \ z,x,a(x,x,y)) = x * (R(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,30060,a(flip),b,30326,a),flip(a)].">
      <j1 rule="hyper" parents="373 30060 30326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30921">
    <literal><![CDATA[
      L(a(x,x,y) \ z,x,a(x,x,y)) = R(x,x,y) \ (x * z)
    ]]></literal>
    <justification jstring="[para(30053(a,1),30326(a,2,1))].">
      <j1 rule="para" parents="30053 30326"/>
    </justification>
  </clause>

  <clause id="30922">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ (x * v5) = x * (v5 / L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,23785,a(flip),b,30342,a)].">
      <j1 rule="hyper" parents="64 23785 30342"/>
    </justification>
  </clause>

  <clause id="30923">
    <literal><![CDATA[
      a(x,y,((((z \ 1) * R(u,z,z)) \ (u * (z \ 1))) \ w) \ v5) = a(x,y,(a(z,z,z \ u) \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(30360(a,1),27524(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="30360 27524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30924">
    <literal><![CDATA[
      a(x,x,y) * ((y \ L(y,x,x)) \ z) = y * (L(L(y,x,x),x,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14051,a,b,30365,a)].">
      <j1 rule="hyper" parents="64 14051 30365"/>
    </justification>
  </clause>

  <clause id="30925">
    <literal><![CDATA[
      (x \ L(x,y,y)) \ (a(y,y,x) * z) = x * (L(L(x,y,y),y,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14005,a,b,30365,a)].">
      <j1 rule="hyper" parents="64 14005 30365"/>
    </justification>
  </clause>

  <clause id="30926">
    <literal><![CDATA[
      L(L(x,y,y),y,y) \ x = a(y,y,x) * a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,25311,a(flip),b,30365,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 25311 30365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30927">
    <literal><![CDATA[
      x \ ((x / (((1 / y) * z) \ 1)) * (((1 / y) * z) \ a(y,y,z))) = L(a(y,y,z),((1 / y) * z) \ 1,(((1 / y) * z) \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(30400(a,1),23794(a,1,2,2))].">
      <j1 rule="para" parents="30400 23794"/>
    </justification>
  </clause>

  <clause id="30928">
    <literal><![CDATA[
      R((a(x,x,y) * a(x,x,y)) \ x,x,y) = a(x,x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,29933,a(flip),b,30411,a),flip(a)].">
      <j1 rule="hyper" parents="373 29933 30411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30929">
    <literal><![CDATA[
      R(x \ a(x,y,y),x,x \ (y \ x)) = T((1 / y) / (x / y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26183,a(flip),b,30526,a)].">
      <j1 rule="hyper" parents="64 26183 30526"/>
    </justification>
  </clause>

  <clause id="30930">
    <literal><![CDATA[
      L(a(x,y,y),y \ x,z) \ (z * (x * (1 / y))) = z * (x / y)
    ]]></literal>
    <justification jstring="[hyper(40,a,23792,a,b,30540,a(flip))].">
      <j1 rule="hyper" parents="40 23792 30540"/>
    </justification>
  </clause>

  <clause id="30931">
    <literal><![CDATA[
      ((x * y) \ x) * ((y \ 1) \ z) = (z / y) * (x \ (x / (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,7047,a,b,30642,a)].">
      <j1 rule="hyper" parents="64 7047 30642"/>
    </justification>
  </clause>

  <clause id="30932">
    <literal><![CDATA[
      a(((x \ y) / (y \ x)) * z,u,w) = a(((x \ y) * (y \ x)) * z,u,w)
    ]]></literal>
    <justification jstring="[para(30691(a,1),2658(a,1,1,1))].">
      <j1 rule="para" parents="30691 2658"/>
    </justification>
  </clause>

  <clause id="30933">
    <literal><![CDATA[
      1 / (1 / (x \ ((y / (y * x)) \ 1))) = 1 / (K(x,y) * a(x,x,y))
    ]]></literal>
    <justification jstring="[para(30285(a,2),30700(a,2,2))].">
      <j1 rule="para" parents="30285 30700"/>
    </justification>
  </clause>

  <clause id="30934">
    <literal><![CDATA[
      x / (x / ((y / (z * y)) \ (z \ 1))) = ((z \ 1) \ y) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30334,a(flip),b,30782,a),flip(a)].">
      <j1 rule="hyper" parents="373 30334 30782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30935">
    <literal><![CDATA[
      R(x,y,(a(z * u,u,u) \ 1) \ w) = R(x,y,a(u,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(30560(a,2),30836(a,1,3,1))].">
      <j1 rule="para" parents="30560 30836"/>
    </justification>
  </clause>

  <clause id="30936">
    <literal><![CDATA[
      L(x,y \ (z / (u * z)),w) = L(x,y \ (z \ (u \ z)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29701,a(flip),b,30862,a)].">
      <j1 rule="hyper" parents="64 29701 30862"/>
    </justification>
  </clause>

  <clause id="30937">
    <literal><![CDATA[
      L(x,y \ ((z * u) \ u),w) = L(x,y \ (u \ (z \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29552,a(flip),b,30936,a)].">
      <j1 rule="hyper" parents="64 29552 30936"/>
    </justification>
  </clause>

  <clause id="30938">
    <literal><![CDATA[
      L(x,L(y * z,z * y,z),u) = L(x,z \ (z \ (y \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29730,a,b,30937,a)].">
      <j1 rule="hyper" parents="64 29730 30937"/>
    </justification>
  </clause>

  <clause id="30939">
    <literal><![CDATA[
      L(x,y \ (z * (u / (1 / w))),v5) = L(x,y \ ((w \ u) * z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29554,a,b,30879,a)].">
      <j1 rule="hyper" parents="64 29554 30879"/>
    </justification>
  </clause>

  <clause id="30940">
    <literal><![CDATA[
      R(x,y,z) \ (a(x,u,w) * v5) = a(x,u,w) * (R(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a,b,30882,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 30882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30941">
    <literal><![CDATA[
      L(x,y,z) * (a(x,u,w) \ T(v5,x)) = a(x,u,w) \ (v5 * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(23149(a,1),30890(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23149 30890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30942">
    <literal><![CDATA[
      a(x,x,y) * (L(x,z,u) \ x) = L(x,z,u) \ R(x,x,y)
    ]]></literal>
    <justification jstring="[para(30054(a,1),30905(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30054 30905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30943">
    <literal><![CDATA[
      x * (a(L(x,y,z),u,w) \ a(x,v5,v5)) = a(L(x,y,z),u,w) \ R(x,v5,v5)
    ]]></literal>
    <justification jstring="[para(15984(a,1),30908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15984 30908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30944">
    <literal><![CDATA[
      L(x,(y * z) \ a(z,z,y),u) = L(x,y * R(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(30053(a,1),30909(a,2,2,2))].">
      <j1 rule="para" parents="30053 30909"/>
    </justification>
  </clause>

  <clause id="30945">
    <literal><![CDATA[
      L(x,(y * z) \ a(z,z,y),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29741,a(flip),b,30944,a),flip(a)].">
      <j1 rule="hyper" parents="373 29741 30944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30946">
    <literal><![CDATA[
      R(x,x,y) * L(z,x,a(x,x,y)) = x * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(30058(a,1),30913(a,2,2,1))].">
      <j1 rule="para" parents="30058 30913"/>
    </justification>
  </clause>

  <clause id="30947">
    <literal><![CDATA[
      R(x,x,y) * L(z,x,a(y,x,x)) = x * (a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29292,a,b,30946,a)].">
      <j1 rule="hyper" parents="64 29292 30946"/>
    </justification>
  </clause>

  <clause id="30948">
    <literal><![CDATA[
      ((1 / a(x,x,y)) * x) * (x \ y) = L(y,x,x) * 1
    ]]></literal>
    <justification jstring="[para(5669(a,1),30916(a,2,1))].">
      <j1 rule="para" parents="5669 30916"/>
    </justification>
  </clause>

  <clause id="30949">
    <literal><![CDATA[
      ((1 / a(x,x,y)) * x) * (x \ y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a(flip),b,30948,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 30948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30950">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) * x) * (x \ y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[para(13923(a,1),30949(a,1,1,1))].">
      <j1 rule="para" parents="13923 30949"/>
    </justification>
  </clause>

  <clause id="30951">
    <literal><![CDATA[
      (a(x,x,y) \ x) * (x \ y) = L(y,x,x)
    ]]></literal>
    <justification jstring="[para(29933(a,1),30950(a,1,1))].">
      <j1 rule="para" parents="29933 30950"/>
    </justification>
  </clause>

  <clause id="30952">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ L(y,x,x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(149,a,30951,a)].">
      <j1 rule="hyper" parents="149 30951"/>
    </justification>
  </clause>

  <clause id="30953">
    <literal><![CDATA[
      ((x * (y / (x * y))) \ x) * (x \ (x * y)) = L(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(30079(a,1),30951(a,1,1,1))].">
      <j1 rule="para" parents="30079 30951"/>
    </justification>
  </clause>

  <clause id="30954">
    <literal><![CDATA[
      (1 / (x / (y * x))) * (y \ (y * x)) = L(y * x,y,y)
    ]]></literal>
    <justification jstring="[para(3368(a,1),30953(a,1,1))].">
      <j1 rule="para" parents="3368 30953"/>
    </justification>
  </clause>

  <clause id="30955">
    <literal><![CDATA[
      L(x * y,x,x) = (1 / (y / (x * y))) * y
    ]]></literal>
    <justification jstring="[hyper(739,a,30954,a),flip(a)].">
      <j1 rule="hyper" parents="739 30954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30957">
    <literal><![CDATA[
      L((x \ 1) * y,x,x) = (1 / (y / ((x \ 1) * y))) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,11807,a(flip),b,30955,a)].">
      <j1 rule="hyper" parents="64 11807 30955"/>
    </justification>
  </clause>

  <clause id="30958">
    <literal><![CDATA[
      L(x * y,x,x) = (1 / R(1 / x,x,y)) * y
    ]]></literal>
    <justification jstring="[para(244(a,2),30955(a,2,1,2))].">
      <j1 rule="para" parents="244 30955"/>
    </justification>
  </clause>

  <clause id="30959">
    <literal><![CDATA[
      L(x,y,L(z * u,z,z) \ w) = L(x,y,((u / (z * u)) * u) \ w)
    ]]></literal>
    <justification jstring="[para(30955(a,2),25692(a,1,3,1))].">
      <j1 rule="para" parents="30955 25692"/>
    </justification>
  </clause>

  <clause id="30960">
    <literal><![CDATA[
      a(L(x * y,x,x) \ z,u,w) = a(((y / (x * y)) * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(30955(a,2),26905(a,1,1,1))].">
      <j1 rule="para" parents="30955 26905"/>
    </justification>
  </clause>

  <clause id="30961">
    <literal><![CDATA[
      L(x,y,(L(z * u,z,z) \ w) * v5) = L(x,y,v5 * ((((1 / (u / (z * u))) \ 1) * u) \ w))
    ]]></literal>
    <justification jstring="[para(30955(a,2),29372(a,2,3,1,1)),flip(a)].">
      <j1 rule="para" parents="30955 29372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30962">
    <literal><![CDATA[
      (1 / (a(x,x,y) / x)) * y = L(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(30082(a,2),30955(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="30082 30955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30963">
    <literal><![CDATA[
      L((x \ 1) * y,x,x) = (1 / R(x,x,y)) * y
    ]]></literal>
    <justification jstring="[para(1991(a,2),30957(a,2,1,2))].">
      <j1 rule="para" parents="1991 30957"/>
    </justification>
  </clause>

  <clause id="30964">
    <literal><![CDATA[
      L(x,y,(z * u) * (z * R(u,u,z))) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(30054(a,1),30917(a,1,3,2,2))].">
      <j1 rule="para" parents="30054 30917"/>
    </justification>
  </clause>

  <clause id="30965">
    <literal><![CDATA[
      L(x,y,(z \ u) * (u * z)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29339,a(flip),b,30964,a)].">
      <j1 rule="hyper" parents="64 29339 30964"/>
    </justification>
  </clause>

  <clause id="30966">
    <literal><![CDATA[
      L(x,y,(z \ u) * (z * u)) = L(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29020,a,b,30965,a)].">
      <j1 rule="hyper" parents="64 29020 30965"/>
    </justification>
  </clause>

  <clause id="30967">
    <literal><![CDATA[
      a((x * y) * (x * R(y,y,x)),z,u) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(30054(a,1),30918(a,1,1,2,2))].">
      <j1 rule="para" parents="30054 30918"/>
    </justification>
  </clause>

  <clause id="30968">
    <literal><![CDATA[
      L(x,(y * z) * (y * R(z,z,y)),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(30054(a,1),30919(a,1,2,2,2))].">
      <j1 rule="para" parents="30054 30919"/>
    </justification>
  </clause>

  <clause id="30969">
    <literal><![CDATA[
      L(x,(y \ z) * (z * y),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30858,a(flip),b,30968,a)].">
      <j1 rule="hyper" parents="64 30858 30968"/>
    </justification>
  </clause>

  <clause id="30970">
    <literal><![CDATA[
      L(x,(y \ z) * (y * z),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29548,a,b,30969,a)].">
      <j1 rule="hyper" parents="64 29548 30969"/>
    </justification>
  </clause>

  <clause id="30971">
    <literal><![CDATA[
      L(x,a(y,z,z \ y),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29670,a(flip),b,30969,a)].">
      <j1 rule="hyper" parents="64 29670 30969"/>
    </justification>
  </clause>

  <clause id="30972">
    <literal><![CDATA[
      L(x,a(y,z,z \ y),u) = L(x,a(z,z,z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,30188,a,b,30971,a),flip(a)].">
      <j1 rule="hyper" parents="373 30188 30971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30973">
    <literal><![CDATA[
      L(x,a(y \ z,y \ z,y),u) = L(x,a(z,y \ z,(y \ z) \ z),u)
    ]]></literal>
    <justification jstring="[para(27307(a,1),30972(a,2,2)),flip(a)].">
      <j1 rule="para" parents="27307 30972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30974">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ (x * v5) = x * (L(a(x,y,z),u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(23785(a,1),30922(a,2,2))].">
      <j1 rule="para" parents="23785 30922"/>
    </justification>
  </clause>

  <clause id="30975">
    <literal><![CDATA[
      x * R(x \ a(x,y,y),x,x \ (y \ x)) = ((1 / y) / (x / y)) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,30929,a,b,22,a(flip))].">
      <j1 rule="hyper" parents="145 30929 22"/>
    </justification>
  </clause>

  <clause id="30976">
    <literal><![CDATA[
      L(x \ 1,x,y) * ((x \ 1) \ z) = (z / x) * (y \ (y / (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,440,a,b,30931,a)].">
      <j1 rule="hyper" parents="64 440 30931"/>
    </justification>
  </clause>

  <clause id="30977">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (x * y) = (y / (x * y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,9270,a(flip),b,30934,a),flip(a)].">
      <j1 rule="hyper" parents="64 9270 30934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30978">
    <literal><![CDATA[
      L(x,y \ (z * ((1 / u) \ w)),v5) = L(x,y \ ((u \ w) * z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29561,a(flip),b,30939,a)].">
      <j1 rule="hyper" parents="64 29561 30939"/>
    </justification>
  </clause>

  <clause id="30979">
    <literal><![CDATA[
      a(x,y,z) * (R(x,u,w) \ (a(x,y,z) \ v5)) = R(x,u,w) \ v5
    ]]></literal>
    <justification jstring="[para(10(a,1),30940(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 30940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30980">
    <literal><![CDATA[
      x * L(y \ z,y,a(y,u,u)) = x * (a(y,u,u) * (R(y,u,u) \ z))
    ]]></literal>
    <justification jstring="[para(30940(a,1),16015(a,2,2))].">
      <j1 rule="para" parents="30940 16015"/>
    </justification>
  </clause>

  <clause id="30981">
    <literal><![CDATA[
      x * (a(x,y,y) * (R(x,y,y) \ z)) = L(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(30940(a,1),29265(a,1,2))].">
      <j1 rule="para" parents="30940 29265"/>
    </justification>
  </clause>

  <clause id="30983">
    <literal><![CDATA[
      L(x,((T(y,z) * u) \ ((T(y,z) * z) * u)) * w,v5) = L(x,L(z * K(z * y,u),y,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(29491(a,1),29462(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="29491 29462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30984">
    <literal><![CDATA[
      L(x,(y * z) \ ((u * z) * y),w) = L(x,R(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29563,a(flip),b,29534,a),flip(a)].">
      <j1 rule="hyper" parents="373 29563 29534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30986">
    <literal><![CDATA[
      L(x,R(y,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,L(y,z,u),w) = v5
    ]]></literal>
    <justification jstring="[para(30984(a,1),29893(a,1))].">
      <j1 rule="para" parents="30984 29893"/>
    </justification>
  </clause>

  <clause id="30988">
    <literal><![CDATA[
      L(x,y \ R(z \ u,z,w),v5) = L(x,y \ ((z * w) \ (u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29591,a(flip),b,29592,a)].">
      <j1 rule="hyper" parents="64 29591 29592"/>
    </justification>
  </clause>

  <clause id="30989">
    <literal><![CDATA[
      L(((a(x,y,z) * (x \ 1)) \ (x \ 1)) \ u,a(x,y,z) \ ((x \ 1) \ (x \ 1)),a(x,y,z) * (x \ 1)) = (x \ 1) \ ((a(x,y,z) * (x \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(30268(a,2),29686(a,1,2))].">
      <j1 rule="para" parents="30268 29686"/>
    </justification>
  </clause>

  <clause id="30990">
    <literal><![CDATA[
      x / (1 / L(x,x \ (y \ x),y * x)) = (y * x) * (((y * x) \ x) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27915,a,b,29688,a)].">
      <j1 rule="hyper" parents="64 27915 29688"/>
    </justification>
  </clause>

  <clause id="30991">
    <literal><![CDATA[
      L(((L(x,x,y) * (1 / x)) \ x) \ z,x \ (L(x \ 1,x,x * y) \ x),L(x \ 1,x,x * y) * x) = x \ ((x * L(x \ 1,x,x * y)) * z)
    ]]></literal>
    <justification jstring="[para(30657(a,1),29722(a,1,1,1,1))].">
      <j1 rule="para" parents="30657 29722"/>
    </justification>
  </clause>

  <clause id="30992">
    <literal><![CDATA[
      L(x,(y \ (z * (y * y))) * u,w) = L(x,u * (L(y,y,z) * z),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29436,a,b,29760,a),flip(a)].">
      <j1 rule="hyper" parents="373 29436 29760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30993">
    <literal><![CDATA[
      L(x,(((y * z) * y) * u) * w,v5) = L(x,(L(z,y,y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(29572,a,29844,a)].">
      <j1 rule="hyper" parents="29572 29844"/>
    </justification>
  </clause>

  <clause id="30994">
    <literal><![CDATA[
      (x * (y \ a(y,y,z))) \ (x * (y \ z)) = L(z,y * a(y,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,16066,a(flip),b,30129,a),flip(a)].">
      <j1 rule="hyper" parents="373 16066 30129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30995">
    <literal><![CDATA[
      (1 / (x / (y * x))) \ a(y,y,x) = a(y,y,x) * (a(y,y,x) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,24641,a(flip),b,30164,a)].">
      <j1 rule="hyper" parents="64 24641 30164"/>
    </justification>
  </clause>

  <clause id="30996">
    <literal><![CDATA[
      a(x,x,y) / L(y \ x,y,a(x,x,y) * x) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(24662(a,1),30212(a,1,2))].">
      <j1 rule="para" parents="24662 30212"/>
    </justification>
  </clause>

  <clause id="30997">
    <literal><![CDATA[
      (L(x,y,z) * (a(x,x,u) * u)) * K(1 / x,L(x,y,z) * (a(x,x,u) * u)) = (L(x,y,z) * (x \ u)) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(142,a,30252,a(flip),b,5722,a),flip(a)].">
      <j1 rule="hyper" parents="142 30252 5722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="30998">
    <literal><![CDATA[
      a(x,y,L(((z * u) \ z) * u,w,v5)) = a(x,y,L(a(u,u,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27607,a(flip),b,30289,a)].">
      <j1 rule="hyper" parents="64 27607 30289"/>
    </justification>
  </clause>

  <clause id="30999">
    <literal><![CDATA[
      L(x,y,L(z * ((u * z) \ u),w,v5)) = L(x,y,L(a(z,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,29348,a(flip),b,30290,a)].">
      <j1 rule="hyper" parents="64 29348 30290"/>
    </justification>
  </clause>

  <clause id="31000">
    <literal><![CDATA[
      (a(x,x,y) \ x) * K(y,x) = (L(y,x,x) * x) / y
    ]]></literal>
    <justification jstring="[para(28352(a,1),30436(a,1,2))].">
      <j1 rule="para" parents="28352 30436"/>
    </justification>
  </clause>

  <clause id="31001">
    <literal><![CDATA[
      (x / (y * T(x,y))) \ 1 = (L(x,y,y) * y) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,30763,a(flip),b,31000,a)].">
      <j1 rule="hyper" parents="64 30763 31000"/>
    </justification>
  </clause>

  <clause id="31004">
    <literal><![CDATA[
      (L(x,y,y) * y) / x = (x / (x * y)) \ 1
    ]]></literal>
    <justification jstring="[para(115(a,1),31001(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="115 31001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31005">
    <literal><![CDATA[
      (L(x,y / x,y / x) * (y / x)) / x = (x / (y * K(x,x \ y))) \ 1
    ]]></literal>
    <justification jstring="[para(5963(a,2),31004(a,2,1,2))].">
      <j1 rule="para" parents="5963 31004"/>
    </justification>
  </clause>

  <clause id="31006">
    <literal><![CDATA[
      L(L(x,x,y) \ z,L(x,x,y),a(y,x,x)) = (x \ z) * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,29989,a(flip),b,30467,a),flip(a)].">
      <j1 rule="hyper" parents="373 29989 30467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31007">
    <literal><![CDATA[
      a(x,y,y) * ((z * L(y,y,x)) / y) = L(z,L(y,y,x),a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29984,a(flip),b,30469,a)].">
      <j1 rule="hyper" parents="64 29984 30469"/>
    </justification>
  </clause>

  <clause id="31008">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * a(x,z,z)) = (T(x,y) \ (x / z)) \ 1
    ]]></literal>
    <justification jstring="[para(11171(a,1),30521(a,1,1))].">
      <j1 rule="para" parents="11171 30521"/>
    </justification>
  </clause>

  <clause id="31009">
    <literal><![CDATA[
      x * (K(y,z) * a(y,x,x)) = (T(y,z) \ (y / x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,22760,a(flip),b,31008,a)].">
      <j1 rule="hyper" parents="64 22760 31008"/>
    </justification>
  </clause>

  <clause id="31010">
    <literal><![CDATA[
      a(x,y,y) * (y * K(x,z)) = (T(x,z) \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,24451,a,b,31009,a)].">
      <j1 rule="hyper" parents="64 24451 31009"/>
    </justification>
  </clause>

  <clause id="31011">
    <literal><![CDATA[
      a(x,y,(a(z,u,u) \ 1) \ w) = a(x,y,a(u,u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30111,a(flip),b,30525,a),flip(a)].">
      <j1 rule="hyper" parents="64 30111 30525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31012">
    <literal><![CDATA[
      (x \ T(y,z)) \ ((x \ T(y,z)) / u) = (x \ y) \ ((x \ y) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30662,a(flip),b,30666,a),flip(a)].">
      <j1 rule="hyper" parents="64 30662 30666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31013">
    <literal><![CDATA[
      ((x * x) \ T(x / y,z)) \ (((x * x) \ T(x / y,z)) / u) = ((1 / x) / y) \ (((x * x) \ (x / y)) / u)
    ]]></literal>
    <justification jstring="[para(887(a,1),31012(a,2,1))].">
      <j1 rule="para" parents="887 31012"/>
    </justification>
  </clause>

  <clause id="31014">
    <literal><![CDATA[
      a(x,x \ y,x \ y) = y \ (x * (((y * (x \ y)) \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(30799(a,1),30009(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30799 30009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31015">
    <literal><![CDATA[
      a(a(x,x \ y,x \ y) * y,z,u) = a(x * (((y * (x \ y)) \ y) \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(31014(a,2),26836(a,1,1,1))].">
      <j1 rule="para" parents="31014 26836"/>
    </justification>
  </clause>

  <clause id="31016">
    <literal><![CDATA[
      L(x,y \ R(z \ 1,u,u),w) = L(x,y \ ((z / u) / u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29701,a(flip),b,30860,a),flip(a)].">
      <j1 rule="hyper" parents="64 29701 30860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31017">
    <literal><![CDATA[
      L(x,y \ R(z \ 1,u,u),w) = L(x,y \ (u \ (z / u)),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29552,a(flip),b,31016,a),flip(a)].">
      <j1 rule="hyper" parents="373 29552 31016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31018">
    <literal><![CDATA[
      L(x,y \ (z \ (u / z)),w) = L(x,y \ R(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30861,a(flip),b,31017,a),flip(a)].">
      <j1 rule="hyper" parents="64 30861 31017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31019">
    <literal><![CDATA[
      L(x,y,L(z * u,z,z) \ w) = L(x,y,(z \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,13561,a(flip),b,30959,a),flip(a)].">
      <j1 rule="hyper" parents="373 13561 30959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31020">
    <literal><![CDATA[
      L(x,y,(z * u) \ (K(w,v5) * (L(z * u,z,z) \ v6))) = L(x,y,(z \ u) \ (K(w,v5) * ((z * u) \ v6)))
    ]]></literal>
    <justification jstring="[para(22850(a,1),31019(a,1,3))].">
      <j1 rule="para" parents="22850 31019"/>
    </justification>
  </clause>

  <clause id="31021">
    <literal><![CDATA[
      L(x,y \ R(z \ (z * u),z,z),w) = L(x,y \ L(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29661,a(flip),b,30988,a),flip(a)].">
      <j1 rule="hyper" parents="373 29661 30988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31022">
    <literal><![CDATA[
      L(x,y \ R(z,u,u),w) = L(x,y \ L(z,u,u),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),31021(a,1,2,2,1))].">
      <j1 rule="para" parents="9 31021"/>
    </justification>
  </clause>

  <clause id="31023">
    <literal><![CDATA[
      L(x,y \ (z \ (u / z)),w) = L(x,y \ L(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31018,a,b,31022,a)].">
      <j1 rule="hyper" parents="64 31018 31022"/>
    </justification>
  </clause>

  <clause id="31024">
    <literal><![CDATA[
      L(x,y \ ((z * u) * u),w) = L(x,y \ L(z,u,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29724,a,b,31022,a)].">
      <j1 rule="hyper" parents="64 29724 31022"/>
    </justification>
  </clause>

  <clause id="31025">
    <literal><![CDATA[
      L(x,(y \ R(z,u,u)) \ L(z,u,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29440,a(flip),b,31022,a),flip(a)].">
      <j1 rule="hyper" parents="64 29440 31022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31026">
    <literal><![CDATA[
      L(x,y \ L(y,z,z),u) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(15987(a,1),31022(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15987 31022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31027">
    <literal><![CDATA[
      L(x,R(y,y,z) \ y,u) = L(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(30141(a,2),31026(a,1,2))].">
      <j1 rule="para" parents="30141 31026"/>
    </justification>
  </clause>

  <clause id="31028">
    <literal><![CDATA[
      L(x,L(y \ z,y,z \ R(u,w,w)) \ L(u,w,w),v5) = L(x,(R(u,w,w) / z) * y,v5)
    ]]></literal>
    <justification jstring="[para(15002(a,2),31025(a,1,2,1))].">
      <j1 rule="para" parents="15002 31025"/>
    </justification>
  </clause>

  <clause id="31029">
    <literal><![CDATA[
      L(x,y \ L(z * u,u,u),w) = L(x,y \ (u \ z),w)
    ]]></literal>
    <justification jstring="[para(11(a,1),31023(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 31023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31030">
    <literal><![CDATA[
      ((x * y) * y) * L(z,u \ L(x,y,y),u) = u * ((u \ ((x * y) * y)) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,31024,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="145 31024 101"/>
    </justification>
  </clause>

  <clause id="31031">
    <literal><![CDATA[
      L(x,(L(y,z,y * z) * u) * w,v5) = L(x,(L(y,z,z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,21703,a,b,30993,a)].">
      <j1 rule="hyper" parents="64 21703 30993"/>
    </justification>
  </clause>

  <clause id="31032">
    <literal><![CDATA[
      L(x,(L(L(y,z,z),a(z,z,y),a(z,z,y)) * u) * w,v5) = L(x,((y * a(z,z,y)) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(5563(a,1),30993(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5563 30993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31033">
    <literal><![CDATA[
      (x * (y \ a(y,y,z))) \ (x * (y \ z)) = L(z,R(y,y,z),x)
    ]]></literal>
    <justification jstring="[para(30054(a,1),30994(a,2,2))].">
      <j1 rule="para" parents="30054 30994"/>
    </justification>
  </clause>

  <clause id="31034">
    <literal><![CDATA[
      (x * (y \ a(y,y,z))) \ (x * (y \ z)) = L(z,L(y,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,29794,a(flip),b,31033,a),flip(a)].">
      <j1 rule="hyper" parents="373 29794 31033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31035">
    <literal><![CDATA[
      a(x,x,y) / L(y \ x,y,R(x,x,y)) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(30053(a,1),30996(a,1,2,3))].">
      <j1 rule="para" parents="30053 30996"/>
    </justification>
  </clause>

  <clause id="31036">
    <literal><![CDATA[
      a(x,x,y) / L(y \ x,y,L(x,x,y)) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(29203(a,1),31035(a,1,2))].">
      <j1 rule="para" parents="29203 31035"/>
    </justification>
  </clause>

  <clause id="31037">
    <literal><![CDATA[
      L(L(x,x,y) \ z,L(x,x,y),a(y,x,x)) = a(y,x,x) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a,b,31006,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 31006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31038">
    <literal><![CDATA[
      a(x,y,y) * ((z / y) * L(y,y,x)) = L(z,L(y,y,x),a(x,y,y))
    ]]></literal>
    <justification jstring="[para(3196(a,1),31007(a,1,2))].">
      <j1 rule="para" parents="3196 31007"/>
    </justification>
  </clause>

  <clause id="31039">
    <literal><![CDATA[
      a(x,y,y) \ (y \ z) = y \ (a(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,30466,a(flip),b,31037,a(flip))].">
      <j1 rule="hyper" parents="139 30466 31037"/>
    </justification>
  </clause>

  <clause id="31040">
    <literal><![CDATA[
      L(x,y * ((z * T(z,u)) * w),v5) = L(x,(z * z) * (w * y),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29745,a(flip),b,29525,a),flip(a)].">
      <j1 rule="hyper" parents="64 29745 29525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31042">
    <literal><![CDATA[
      L(x,y * ((z * T(z,u)) * w),v5) = L(x,w * y,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,11772,a(flip),b,31040,a),flip(a)].">
      <j1 rule="hyper" parents="373 11772 31040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31044">
    <literal><![CDATA[
      L(((L(x,y,z) \ 1) * ((R(x,y,z) \ 1) \ 1)) \ u,(R(x,y,z) \ 1) * L(x,y,z),L(x,y,z)) = (R(x,y,z) * 1) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(29798(a,1),29599(a,2,1))].">
      <j1 rule="para" parents="29798 29599"/>
    </justification>
  </clause>

  <clause id="31045">
    <literal><![CDATA[
      L(x,((1 / y) * z) * (y \ z),u) = L(x,(y \ z) \ (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29693,a(flip),b,29611,a),flip(a)].">
      <j1 rule="hyper" parents="64 29693 29611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31046">
    <literal><![CDATA[
      L(x,(y \ z) * ((1 / y) * z),u) = L(x,(y \ z) \ (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(29572,a,31045,a)].">
      <j1 rule="hyper" parents="29572 31045"/>
    </justification>
  </clause>

  <clause id="31047">
    <literal><![CDATA[
      L(x,(y \ z) \ (y * z),u) = L(x,(y \ z) * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29718,a(flip),b,31046,a),flip(a)].">
      <j1 rule="hyper" parents="64 29718 31046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31048">
    <literal><![CDATA[
      L(x,(y \ z) \ (y * z),u) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,30970,a(flip),b,31047,a),flip(a)].">
      <j1 rule="hyper" parents="373 30970 31047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31049">
    <literal><![CDATA[
      L(x,y * (z \ (u / (w / v5))),v6) = L(x,y * (z \ ((v5 \ w) \ u)),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29676,a(flip),b,29678,a),flip(a)].">
      <j1 rule="hyper" parents="373 29676 29678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31050">
    <literal><![CDATA[
      L(x,y \ ((((z * z) \ (u * u)) * (R(u,w,v5) \ 1)) * v6),v7) = L(x,y \ ((1 / R(1 / u,w,v5)) * v6),v7)
    ]]></literal>
    <justification jstring="[para(11454(a,1),29699(a,2,2,2,1))].">
      <j1 rule="para" parents="11454 29699"/>
    </justification>
  </clause>

  <clause id="31052">
    <literal><![CDATA[
      L(x,(y \ L(y,y,z)) * u,w) = L(x,((z \ (y \ z)) * y) * u,w)
    ]]></literal>
    <justification jstring="[para(26654(a,2),29820(a,1,2,1))].">
      <j1 rule="para" parents="26654 29820"/>
    </justification>
  </clause>

  <clause id="31053">
    <literal><![CDATA[
      L(x,((y \ (z \ y)) * z) * u,w) = L(x,(z * L(z,z,y)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11787,a(flip),b,31052,a),flip(a)].">
      <j1 rule="hyper" parents="64 11787 31052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31054">
    <literal><![CDATA[
      L(x,(y * L(y,y,z)) * u,w) = L(x,u * a(y,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30761,a(flip),b,31053,a),flip(a)].">
      <j1 rule="hyper" parents="64 30761 31053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31055">
    <literal><![CDATA[
      L(x,a(y,z,z) * u,w) = L(x,u * a(z,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30875,a(flip),b,31054,a)].">
      <j1 rule="hyper" parents="64 30875 31054"/>
    </justification>
  </clause>

  <clause id="31056">
    <literal><![CDATA[
      L(x,a(y,z,z) * u,w) = L(x,a(z,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29436,a,b,31055,a),flip(a)].">
      <j1 rule="hyper" parents="373 29436 31055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31057">
    <literal><![CDATA[
      L(x,a(y,y,z) * a(z,y,y),u) = x
    ]]></literal>
    <justification jstring="[hyper(616,a,31056,a),flip(a)].">
      <j1 rule="hyper" parents="616 31056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31058">
    <literal><![CDATA[
      a(x,y,z * ((a(u,u,w) * a(w,u,u)) * L(v5,z,a(u,u,w) * a(w,u,u)))) = a(x,y,(z * v5) * (a(u,u,w) * a(w,u,u)))
    ]]></literal>
    <justification jstring="[para(31057(a,1),27963(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="31057 27963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31059">
    <literal><![CDATA[
      L(x,((((1 / y) \ 1) \ z) \ u) \ w,v5) = L(x,(((z / (y * z)) * z) \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(2014(a,1),29822(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2014 29822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31060">
    <literal><![CDATA[
      L(x,(y \ (z * (u * u))) * w,v5) = L(x,(y \ z) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29629,a(flip),b,29831,a),flip(a)].">
      <j1 rule="hyper" parents="64 29629 29831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31062">
    <literal><![CDATA[
      L(x,y * (L(z,z,u) * u),w) = L(x,(z \ u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30992,a(flip),b,31060,a)].">
      <j1 rule="hyper" parents="64 30992 31060"/>
    </justification>
  </clause>

  <clause id="31063">
    <literal><![CDATA[
      L(x,(L(y,y,z) * z) * u,w) = L(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29760,a(flip),b,31060,a)].">
      <j1 rule="hyper" parents="64 29760 31060"/>
    </justification>
  </clause>

  <clause id="31064">
    <literal><![CDATA[
      L(x,(y \ (z / (1 / u))) * w,v5) = L(x,(y \ (z / u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(809(a,1),31060(a,1,2,1,2))].">
      <j1 rule="para" parents="809 31060"/>
    </justification>
  </clause>

  <clause id="31065">
    <literal><![CDATA[
      L(x,L(y,L(z,z,y),L(z,z,y)),u) = L(x,(z \ y) * L(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(11888,a,31062,a)].">
      <j1 rule="hyper" parents="11888 31062"/>
    </justification>
  </clause>

  <clause id="31067">
    <literal><![CDATA[
      L(x,y * (z * L(u,u,z)),w) = L(x,(u \ z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29548,a,b,31062,a)].">
      <j1 rule="hyper" parents="64 29548 31062"/>
    </justification>
  </clause>

  <clause id="31069">
    <literal><![CDATA[
      L(x,(y \ (R(1 / z,u,w) * v5)) * (z * z),v6) = L(x,(R(z,u,w) * v5) * L(y,y,R(1 / z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(3384(a,1),31067(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3384 31067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31070">
    <literal><![CDATA[
      L(x,y * (z * L(a(u,u,w * u),a(w,u,u),z)),v5) = L(x,(a(u,u,w * u) \ z) * y,v5)
    ]]></literal>
    <justification jstring="[para(30724(a,1),31067(a,1,2,2,2))].">
      <j1 rule="para" parents="30724 31067"/>
    </justification>
  </clause>

  <clause id="31071">
    <literal><![CDATA[
      L(x,(y \ (z / (1 / u))) * w,v5) = L(x,(y \ (u \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29633,a(flip),b,31064,a),flip(a)].">
      <j1 rule="hyper" parents="373 29633 31064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31072">
    <literal><![CDATA[
      L(x,y * (z \ (u / (1 / w))),v5) = L(x,(z \ (w \ u)) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(29572,a,31071,a)].">
      <j1 rule="hyper" parents="29572 31071"/>
    </justification>
  </clause>

  <clause id="31073">
    <literal><![CDATA[
      L(x,y * (z \ ((1 / u) \ w)),v5) = L(x,(z \ (u \ w)) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29676,a(flip),b,31072,a)].">
      <j1 rule="hyper" parents="64 29676 31072"/>
    </justification>
  </clause>

  <clause id="31074">
    <literal><![CDATA[
      L(x,y \ (z * ((u \ 1) * w)),v5) = L(x,y \ ((u * w) * z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,30877,a(flip),b,29841,a),flip(a)].">
      <j1 rule="hyper" parents="64 30877 29841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31075">
    <literal><![CDATA[
      L(x,R(y \ 1,z,u) \ (L(w,R(y \ 1,z,u) \ v5,R(y \ 1,z,u)) * v5),v6) = L(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(1010(a,2),29867(a,1,2))].">
      <j1 rule="para" parents="1010 29867"/>
    </justification>
  </clause>

  <clause id="31076">
    <literal><![CDATA[
      L(x,(y * ((z / (u * u)) * w)) * v5,v6) = L(x,(y * (z * w)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29819,a,b,29869,a)].">
      <j1 rule="hyper" parents="64 29819 29869"/>
    </justification>
  </clause>

  <clause id="31077">
    <literal><![CDATA[
      L(x,(y * (z * u)) * (T(w,y * (((v5 * v5) \ z) * u)) * K(v6,v7)),v8) = L(x,w * ((y * (((v5 * v5) \ z) * u)) * K(v6,v7)),v8)
    ]]></literal>
    <justification jstring="[para(24749(a,1),29869(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24749 29869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31078">
    <literal><![CDATA[
      L(x,L(y * L(y,z,u),y,w),v5) = L(x,(y * w) \ (L(y,z,u) * w),v5)
    ]]></literal>
    <justification jstring="[para(24918(a,1),29878(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24918 29878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31079">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) \ u,x,a(x,y,z)) = (a(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30415,a(flip),b,29934,a)].">
      <j1 rule="hyper" parents="64 30415 29934"/>
    </justification>
  </clause>

  <clause id="31080">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,a(x,w,v5)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(29971(a,1),29979(a,2,2))].">
      <j1 rule="para" parents="29971 29979"/>
    </justification>
  </clause>

  <clause id="31081">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,w,v5)) = L(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[para(31080(a,1),16033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31080 16033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31083">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,16031,a,b,31081,a),flip(a)].">
      <j1 rule="hyper" parents="373 16031 31081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31084">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,w,v5) \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2274,a,31083,a)].">
      <j1 rule="hyper" parents="2274 31083"/>
    </justification>
  </clause>

  <clause id="31085">
    <literal><![CDATA[
      L(a(x,y,z),u,a(w,x,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29287,a,b,31083,a)].">
      <j1 rule="hyper" parents="64 29287 31083"/>
    </justification>
  </clause>

  <clause id="31087">
    <literal><![CDATA[
      L(a(x * y,z,u),w,a(x,x,y)) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29304,a(flip),b,31083,a)].">
      <j1 rule="hyper" parents="64 29304 31083"/>
    </justification>
  </clause>

  <clause id="31089">
    <literal><![CDATA[
      a(a(x,y,z),u,a(x,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,31083,a)].">
      <j1 rule="hyper" parents="54 31083"/>
    </justification>
  </clause>

  <clause id="31090">
    <literal><![CDATA[
      (x * a(y,z,u)) * a(y,w,v5) = a(y,z,u) * (x * a(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(145,a,31083,a(flip),b,23191,a)].">
      <j1 rule="hyper" parents="145 31083 23191"/>
    </justification>
  </clause>

  <clause id="31091">
    <literal><![CDATA[
      a(x,y,z) * (a(x,u,w) * v5) = a(x,u,w) * (a(x,y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(144,a,31083,a(flip),b,28734,a)].">
      <j1 rule="hyper" parents="144 31083 28734"/>
    </justification>
  </clause>

  <clause id="31092">
    <literal><![CDATA[
      (a(x,y,z) / u) * L(u,x,x) = a(x,x,u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,31083,a(flip),b,29396,a),flip(a)].">
      <j1 rule="hyper" parents="139 31083 29396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31093">
    <literal><![CDATA[
      a(x,y,z) * (a(x,u,w) \ 1) = a(x,u,w) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,31083,a(flip),b,23782,a),flip(a)].">
      <j1 rule="hyper" parents="139 31083 23782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31094">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),v5,a(x,v6,v7)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(31083(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31083 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31095">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * u) * a(x,w,v5) = (a(x,y,z) \ 1) * (u * a(x,w,v5))
    ]]></literal>
    <justification jstring="[para(31083(a,1),1630(a,1,2))].">
      <j1 rule="para" parents="31083 1630"/>
    </justification>
  </clause>

  <clause id="31096">
    <literal><![CDATA[
      a(x,y,z) \ (a(x,u,w) * v5) = a(x,u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(31083(a,1),27804(a,1,1))].">
      <j1 rule="para" parents="31083 27804"/>
    </justification>
  </clause>

  <clause id="31100">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(w,x,x) = a(x,y,z) * (u * a(w,x,x))
    ]]></literal>
    <justification jstring="[para(31085(a,1),28784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31085 28784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31103">
    <literal><![CDATA[
      (a(x * y,z,u) \ 1) * a(x,x,y) = a(x * y,z,u) \ a(x,x,y)
    ]]></literal>
    <justification jstring="[para(31087(a,1),25752(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31087 25752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31104">
    <literal><![CDATA[
      x \ L(x * a(y,z,u),y,y) = a(y,y,x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30822,a,b,31092,a)].">
      <j1 rule="hyper" parents="64 30822 31092"/>
    </justification>
  </clause>

  <clause id="31106">
    <literal><![CDATA[
      a(x,y,z) * (a(x,u,w) * (a(x,y,z) \ v5)) = a(x,u,w) * v5
    ]]></literal>
    <justification jstring="[hyper(397,a,31091,a),flip(a)].">
      <j1 rule="hyper" parents="397 31091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31107">
    <literal><![CDATA[
      a(x,y,z) \ (u * a(x,w,v5)) = a(x,w,v5) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,23182,a(flip),b,31091,a)].">
      <j1 rule="hyper" parents="139 23182 31091"/>
    </justification>
  </clause>

  <clause id="31109">
    <literal><![CDATA[
      L(x,y,a(z,y,y)) * (a(z,y,y) \ y) = (a(z,y,y) \ 1) * (y * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,28656,a(flip),b,30016,a)].">
      <j1 rule="hyper" parents="64 28656 30016"/>
    </justification>
  </clause>

  <clause id="31110">
    <literal><![CDATA[
      L(L(a(x,x,y),x,z),z * x,z) = L(x \ R(x,x,y),z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,4243,a(flip),b,30075,a),flip(a)].">
      <j1 rule="hyper" parents="373 4243 30075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31111">
    <literal><![CDATA[
      L(L(a(x,x,y),x,z),z * x,z) = L(a(x,x,y),z,z)
    ]]></literal>
    <justification jstring="[para(30058(a,1),31110(a,2,1))].">
      <j1 rule="para" parents="30058 31110"/>
    </justification>
  </clause>

  <clause id="31112">
    <literal><![CDATA[
      a(x \ 1,x,y) \ ((y / (x * y)) * z) = L(x \ z,x,(x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,23216,a(flip),b,30158,a),flip(a)].">
      <j1 rule="hyper" parents="373 23216 30158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31113">
    <literal><![CDATA[
      (x \ (y / x)) * a(x \ y,x \ y,x) = x \ R(y / x,y / x,x)
    ]]></literal>
    <justification jstring="[para(26785(a,1),30173(a,1,2))].">
      <j1 rule="para" parents="26785 30173"/>
    </justification>
  </clause>

  <clause id="31114">
    <literal><![CDATA[
      (a(x,y,y) * z) \ (x \ (R(x,y,y) * z)) = a(a(x,y,y),x,z)
    ]]></literal>
    <justification jstring="[para(15984(a,1),30201(a,1,2,2,1))].">
      <j1 rule="para" parents="15984 30201"/>
    </justification>
  </clause>

  <clause id="31115">
    <literal><![CDATA[
      (a(x,y,y) * z) \ (R(x,y,y) * (x \ z)) = a(a(x,y,y),x,z)
    ]]></literal>
    <justification jstring="[para(1898(a,1),31114(a,1,2))].">
      <j1 rule="para" parents="1898 31114"/>
    </justification>
  </clause>

  <clause id="31116">
    <literal><![CDATA[
      a(a(x,y,z),x,u) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27806,a(flip),b,30221,a),flip(a)].">
      <j1 rule="hyper" parents="64 27806 30221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31118">
    <literal><![CDATA[
      a(x,a(x,y,y),x \ z) = a(a(x,y,y),x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31115,a(flip),b,30265,a),flip(a)].">
      <j1 rule="hyper" parents="64 31115 30265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31119">
    <literal><![CDATA[
      a(x,a(x,y,y),x \ z) = a(x,a(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31116,a(flip),b,31118,a),flip(a)].">
      <j1 rule="hyper" parents="373 31116 31118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31120">
    <literal><![CDATA[
      (x \ y) \ (a(x,x,y) * z) = ((x \ y) \ z) * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,28745,a(flip),b,30305,a),flip(a)].">
      <j1 rule="hyper" parents="64 28745 30305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31121">
    <literal><![CDATA[
      (a(a(x,x,y),z,u) \ a(x,x,y)) \ ((1 / a(x,x,y)) \ x) = (a(x,x,y) \ (a(a(x,x,y),z,u) \ 1)) \ (R(1 / x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(30095(a,2),30335(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30095 30335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31122">
    <literal><![CDATA[
      L((x \ (y \ (x \ y))) \ z,x,a(x,x,y)) = (y \ (x \ y)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30415,a(flip),b,30406,a)].">
      <j1 rule="hyper" parents="64 30415 30406"/>
    </justification>
  </clause>

  <clause id="31123">
    <literal><![CDATA[
      (((x \ y) / y) * x) \ (x * x) = (((1 / x) \ 1) * y) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3501,a,b,30438,a),flip(a)].">
      <j1 rule="hyper" parents="64 3501 30438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31124">
    <literal><![CDATA[
      ((x * x) \ T(y / (y * x),x)) * x = T(y * x,x * x) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(806,a,30446,a)].">
      <j1 rule="hyper" parents="806 30446"/>
    </justification>
  </clause>

  <clause id="31126">
    <literal><![CDATA[
      L(x,(y * (z / y)) \ (x \ z),z) = L(x,x,y * (z / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29558,a(flip),b,30631,a)].">
      <j1 rule="hyper" parents="64 29558 30631"/>
    </justification>
  </clause>

  <clause id="31128">
    <literal><![CDATA[
      L(x * y,(z * (y / z)) \ (y \ (x \ y)),y) = L(x * y,x * y,z * (y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30937,a(flip),b,31126,a)].">
      <j1 rule="hyper" parents="64 30937 31126"/>
    </justification>
  </clause>

  <clause id="31129">
    <literal><![CDATA[
      R((a(x,y,y) * a(x,y,y)) \ R(x,y,y),y,y) = L(x,z,a(x,u,w))
    ]]></literal>
    <justification jstring="[para(2051(a,1),30655(a,1,1))].">
      <j1 rule="para" parents="2051 30655"/>
    </justification>
  </clause>

  <clause id="31130">
    <literal><![CDATA[
      x * L(T(x \ K(y,z),x),x,x * u) = K(y,T(z,x)) * (x \ L(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,30694,a,b,22771,a)].">
      <j1 rule="hyper" parents="145 30694 22771"/>
    </justification>
  </clause>

  <clause id="31131">
    <literal><![CDATA[
      ((x / (x * y)) * y) \ 1 = (x / (x * y)) \ (1 / y)
    ]]></literal>
    <justification jstring="[hyper(40,a,16138,a,b,30702,a)].">
      <j1 rule="hyper" parents="40 16138 30702"/>
    </justification>
  </clause>

  <clause id="31132">
    <literal><![CDATA[
      K(x,y) / (z * (u \ (z \ u))) = u \ (z * (u * (z \ K(x,y))))
    ]]></literal>
    <justification jstring="[hyper(64,a,25393,a(flip),b,30760,a),flip(a)].">
      <j1 rule="hyper" parents="64 25393 30760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31133">
    <literal><![CDATA[
      x \ (y * (x * (y \ K(y,y \ 1)))) = 1 / ((x \ (y \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10212,a(flip),b,31132,a),flip(a)].">
      <j1 rule="hyper" parents="64 10212 31132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31134">
    <literal><![CDATA[
      1 / ((x \ (y \ x)) * y) = x \ (y * (x * (1 / y)))
    ]]></literal>
    <justification jstring="[para(1727(a,1),31133(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1727 31133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31135">
    <literal><![CDATA[
      ((((x * y) \ z) \ z) * y) \ T(x * y,y \ (x \ z)) = L(T(x \ (x / y),y),y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,26677,a,b,30819,a),flip(a)].">
      <j1 rule="hyper" parents="373 26677 30819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31136">
    <literal><![CDATA[
      L(x,L(T(y,z) * u,w,v5) * v6,v7) = L(x,L(u * y,w,v5) * v6,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,29668,a,b,30863,a)].">
      <j1 rule="hyper" parents="64 29668 30863"/>
    </justification>
  </clause>

  <clause id="31137">
    <literal><![CDATA[
      ((x \ L(x,y,y)) * (x \ L(x,y,y))) \ z = x * (L(L(x,y,y),y,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14111,a,b,30924,a)].">
      <j1 rule="hyper" parents="64 14111 30924"/>
    </justification>
  </clause>

  <clause id="31138">
    <literal><![CDATA[
      L(x,a(y \ z,y \ z,y),u) = L(x,a(z,y \ z,y),u)
    ]]></literal>
    <justification jstring="[para(27307(a,1),30973(a,2,2))].">
      <j1 rule="para" parents="27307 30973"/>
    </justification>
  </clause>

  <clause id="31140">
    <literal><![CDATA[
      L(x,(y / z) * (z / y),u) = L(x,a(z,y \ z,y),u)
    ]]></literal>
    <justification jstring="[para(30069(a,1),31138(a,1,2))].">
      <j1 rule="para" parents="30069 31138"/>
    </justification>
  </clause>

  <clause id="31141">
    <literal><![CDATA[
      L(x,(y \ z) \ (z \ y),u) = L(x,a(y,z \ y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29872,a,b,31140,a)].">
      <j1 rule="hyper" parents="64 29872 31140"/>
    </justification>
  </clause>

  <clause id="31142">
    <literal><![CDATA[
      L(x,(y / z) * (y \ z),u) = L(x,a(z,y \ z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29547,a(flip),b,31140,a)].">
      <j1 rule="hyper" parents="64 29547 31140"/>
    </justification>
  </clause>

  <clause id="31143">
    <literal><![CDATA[
      L(x,(y \ z) * (z \ y),u) = L(x,a(y,z \ y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29710,a(flip),b,31141,a)].">
      <j1 rule="hyper" parents="64 29710 31141"/>
    </justification>
  </clause>

  <clause id="31144">
    <literal><![CDATA[
      L(x,(y \ z) * (z \ y),u) = L(x,a(z,y \ z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29606,a(flip),b,31142,a)].">
      <j1 rule="hyper" parents="64 29606 31142"/>
    </justification>
  </clause>

  <clause id="31145">
    <literal><![CDATA[
      L(x,a(y,z \ y,z),u) = L(x,a(z,y \ z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31143,a(flip),b,31144,a)].">
      <j1 rule="hyper" parents="64 31143 31144"/>
    </justification>
  </clause>

  <clause id="31146">
    <literal><![CDATA[
      x \ R(R(x,y,y),x,x \ (y \ x)) = ((1 / y) / (x / y)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,15995,a(flip),b,30975,a)].">
      <j1 rule="hyper" parents="64 15995 30975"/>
    </justification>
  </clause>

  <clause id="31147">
    <literal><![CDATA[
      L(x,y * (z \ ((u \ 1) \ w)),v5) = L(x,(z \ (u \ w)) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31072,a(flip),b,31049,a),flip(a)].">
      <j1 rule="hyper" parents="64 31072 31049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31148">
    <literal><![CDATA[
      L(x,L(y,L(z,z,y),L(z,z,y)),u) = L(x,(z \ y) / (1 / z),u)
    ]]></literal>
    <justification jstring="[para(25570(a,1),31065(a,2,2))].">
      <j1 rule="para" parents="25570 31065"/>
    </justification>
  </clause>

  <clause id="31149">
    <literal><![CDATA[
      L(x,L(y,L(z,z,y),L(z,z,y)),u) = L(x,(1 / z) \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29437,a(flip),b,31148,a),flip(a)].">
      <j1 rule="hyper" parents="373 29437 31148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31150">
    <literal><![CDATA[
      L(x,L(y,L(z,z,y),L(z,z,y)),u) = L(x,z \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29694,a(flip),b,31149,a),flip(a)].">
      <j1 rule="hyper" parents="373 29694 31149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31151">
    <literal><![CDATA[
      L(x,(y * (z * (u * u))) * w,v5) = L(x,(y * z) * w,v5)
    ]]></literal>
    <justification jstring="[para(12(a,1),31076(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 31076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31152">
    <literal><![CDATA[
      L(x,(y * (z * ((u * u) \ w))) * v5,v6) = L(x,(y * (z * w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(897(a,1),31076(a,1,2,1,2))].">
      <j1 rule="para" parents="897 31076"/>
    </justification>
  </clause>

  <clause id="31153">
    <literal><![CDATA[
      L(x,(y * ((z * u) * u)) * w,v5) = L(x,(y * R(z,u,u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(111(a,1),31151(a,1,2,1,2))].">
      <j1 rule="para" parents="111 31151"/>
    </justification>
  </clause>

  <clause id="31154">
    <literal><![CDATA[
      L(x,(((y * z) * z) * u) * w,v5) = L(x,(u * R(y,z,z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29455,a,b,31153,a)].">
      <j1 rule="hyper" parents="64 29455 31153"/>
    </justification>
  </clause>

  <clause id="31155">
    <literal><![CDATA[
      (a(x,y,z) \ x) \ (x * ((a(x,y,z) \ 1) * u)) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),31079(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 31079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31156">
    <literal><![CDATA[
      L((R(x,x,y) \ x) \ z,x,a(x,x,y)) = (a(x,x,y) \ x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(30090(a,2),31079(a,1,1,1))].">
      <j1 rule="para" parents="30090 31079"/>
    </justification>
  </clause>

  <clause id="31157">
    <literal><![CDATA[
      a(x \ 1,x,y) \ ((y / (x * y)) * z) = L(x \ z,x,y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,13011,a(flip),b,31112,a),flip(a)].">
      <j1 rule="hyper" parents="373 13011 31112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31158">
    <literal><![CDATA[
      (x \ (y / x)) * ((x / y) * (y / x)) = x \ R(y / x,y / x,x)
    ]]></literal>
    <justification jstring="[para(30069(a,1),31113(a,1,2))].">
      <j1 rule="para" parents="30069 31113"/>
    </justification>
  </clause>

  <clause id="31159">
    <literal><![CDATA[
      (x \ (y / x)) * ((x / y) * (y / x)) = x \ R(y / x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(10204(a,1),31158(a,2,2))].">
      <j1 rule="para" parents="10204 31158"/>
    </justification>
  </clause>

  <clause id="31160">
    <literal><![CDATA[
      (((x \ y) / y) * x) \ (x * x) = (x * y) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(82(a,1),31123(a,2,1,1))].">
      <j1 rule="para" parents="82 31123"/>
    </justification>
  </clause>

  <clause id="31161">
    <literal><![CDATA[
      (((x \ y) / y) * x) \ (x * x) = (x * y) / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30709,a(flip),b,31160,a),flip(a)].">
      <j1 rule="hyper" parents="373 30709 31160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31163">
    <literal><![CDATA[
      T(x * y,y * y) \ (y \ x) = ((y \ (x / (x * y))) / y) * y
    ]]></literal>
    <justification jstring="[para(27295(a,1),31124(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27295 31124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31164">
    <literal><![CDATA[
      T(x * y,y * y) \ (y \ x) = y \ (x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,12,a(flip),b,31163,a),flip(a)].">
      <j1 rule="hyper" parents="373 12 31163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31168">
    <literal><![CDATA[
      L(x,y,a(x,z,u)) = (a(x,w,w) * a(x,w,w)) \ R(R(x,w,w),w,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2051,a(flip),b,31129,a),flip(a)].">
      <j1 rule="hyper" parents="64 2051 31129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31169">
    <literal><![CDATA[
      x * ((a(x,y,z) \ 1) * (x \ u)) = (a(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(39,a,29939,a,b,31155,a),flip(a)].">
      <j1 rule="hyper" parents="39 29939 31155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31170">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (x * u) = x * ((a(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),31169(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 31169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31171">
    <literal><![CDATA[
      x * ((a(x,y,z) \ 1) \ T(u,x)) = (a(x,y,z) \ 1) \ (u * x)
    ]]></literal>
    <justification jstring="[hyper(139,a,258,a(flip),b,31170,a),flip(a)].">
      <j1 rule="hyper" parents="139 258 31170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31172">
    <literal><![CDATA[
      x * (T(y,x) / (a(x,z,u) \ 1)) = (a(x,z,u) \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(23737(a,2),31171(a,1,2))].">
      <j1 rule="para" parents="23737 31171"/>
    </justification>
  </clause>

  <clause id="31173">
    <literal><![CDATA[
      x * (T(y,x) / (a(x,z,u) \ 1)) = (y * x) / (a(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,23737,a,b,31172,a),flip(a)].">
      <j1 rule="hyper" parents="373 23737 31172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31174">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,x) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(37,a,29785,a,b,31173,a(flip))].">
      <j1 rule="hyper" parents="37 29785 31173"/>
    </justification>
  </clause>

  <clause id="31175">
    <literal><![CDATA[
      a(x,y,y) * R(x,y,y) = R(R(x,y,y),y,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,16014,a,b,31168,a(flip))].">
      <j1 rule="hyper" parents="39 16014 31168"/>
    </justification>
  </clause>

  <clause id="31176">
    <literal><![CDATA[
      a(R(x,y,y),y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,15998,a,b,31175,a)].">
      <j1 rule="hyper" parents="36 15998 31175"/>
    </justification>
  </clause>

  <clause id="31177">
    <literal><![CDATA[
      T(x * (L(y,z,u) \ y),w) = T(x,w) * (L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(269,a,28924,a(flip),b,24567,a(flip))].">
      <j1 rule="hyper" parents="269 28924 24567"/>
    </justification>
  </clause>

  <clause id="31178">
    <literal><![CDATA[
      ((x * y) \ (x / (1 / y))) \ 1 = (x / (1 / y)) \ (x * y)
    ]]></literal>
    <justification jstring="[para(1407(a,1),24815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1407 24815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31180">
    <literal><![CDATA[
      R(T(x / y,x \ (y * x)),x,T(x / y,x \ y)) = T(T(x / y,x \ y),x)
    ]]></literal>
    <justification jstring="[para(25437(a,1),25000(a,1,1))].">
      <j1 rule="para" parents="25437 25000"/>
    </justification>
  </clause>

  <clause id="31181">
    <literal><![CDATA[
      R(R(x \ 1,1 / x,y),x,x) = y * (L(y,x,x) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(1158(a,1),25115(a,2,2,1))].">
      <j1 rule="para" parents="1158 25115"/>
    </justification>
  </clause>

  <clause id="31182">
    <literal><![CDATA[
      R(R(x \ 1,1 / x,y),x,x) = y * ((x * (x * y)) \ x)
    ]]></literal>
    <justification jstring="[para(886(a,1),31181(a,2,2))].">
      <j1 rule="para" parents="886 31181"/>
    </justification>
  </clause>

  <clause id="31183">
    <literal><![CDATA[
      R(R(x \ 1,x,y),x,x) = y * ((x * (x * y)) \ x)
    ]]></literal>
    <justification jstring="[para(2968(a,1),31182(a,1,1))].">
      <j1 rule="para" parents="2968 31182"/>
    </justification>
  </clause>

  <clause id="31184">
    <literal><![CDATA[
      (x * (x * y)) \ x = y \ R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,1044,a(flip),b,31183,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 1044 31183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31185">
    <literal><![CDATA[
      T(x,y) \ R(1 / y,y,T(x,y)) = (y * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(115(a,1),31184(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="115 31184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31186">
    <literal><![CDATA[
      T(x,y) \ R(1 / y,y,x) = (y * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(4755(a,1),31185(a,1,2))].">
      <j1 rule="para" parents="4755 31185"/>
    </justification>
  </clause>

  <clause id="31188">
    <literal><![CDATA[
      (x * (y * x)) \ x = y \ (y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,14882,a(flip),b,31186,a),flip(a)].">
      <j1 rule="hyper" parents="64 14882 31186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31189">
    <literal><![CDATA[
      x * ((y * (x * y)) \ y) = x / (x * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,31186,a(flip),b,14882,a(flip))].">
      <j1 rule="hyper" parents="145 31186 14882"/>
    </justification>
  </clause>

  <clause id="31190">
    <literal><![CDATA[
      (x / y) / ((x / y) * y) = (x / y) * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(12(a,1),31189(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12 31189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31191">
    <literal><![CDATA[
      (x / y) * ((y * x) \ y) = (x / y) / x
    ]]></literal>
    <justification jstring="[para(12(a,1),31190(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12 31190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31192">
    <literal><![CDATA[
      L(x \ 1,x,x * (y \ x)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,30664,a,b,31191,a)].">
      <j1 rule="hyper" parents="35 30664 31191"/>
    </justification>
  </clause>

  <clause id="31193">
    <literal><![CDATA[
      (x \ y) * ((x * y) \ x) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(145,a,31192,a(flip),b,30659,a(flip))].">
      <j1 rule="hyper" parents="145 31192 30659"/>
    </justification>
  </clause>

  <clause id="31194">
    <literal><![CDATA[
      (x \ y) * L(y \ 1,y,x) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,439,a,b,31193,a)].">
      <j1 rule="hyper" parents="64 439 31193"/>
    </justification>
  </clause>

  <clause id="31195">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / y) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,31193,a(flip),b,439,a)].">
      <j1 rule="hyper" parents="139 31193 439"/>
    </justification>
  </clause>

  <clause id="31196">
    <literal><![CDATA[
      (x \ y) \ R(x \ 1,x,y) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,3001,a,b,31194,a)].">
      <j1 rule="hyper" parents="139 3001 31194"/>
    </justification>
  </clause>

  <clause id="31197">
    <literal><![CDATA[
      L(x \ 1,x,y \ x) = L(x \ 1,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30680,a,b,31195,a),flip(a)].">
      <j1 rule="hyper" parents="64 30680 31195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31198">
    <literal><![CDATA[
      (x * (y \ x)) \ (y \ T(x,y \ x)) = L(x \ 1,x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6512,a,b,31197,a)].">
      <j1 rule="hyper" parents="64 6512 31197"/>
    </justification>
  </clause>

  <clause id="31199">
    <literal><![CDATA[
      ((x * (y \ x)) \ (y \ T(x,y \ x))) * x = x \ L(x,x,y)
    ]]></literal>
    <justification jstring="[para(31198(a,2),30683(a,1,1))].">
      <j1 rule="para" parents="31198 30683"/>
    </justification>
  </clause>

  <clause id="31200">
    <literal><![CDATA[
      L(x \ ((((y \ 1) \ 1) \ 1) \ z),x,y) = (T(y \ 1,y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(2275,a,25215,a)].">
      <j1 rule="hyper" parents="2275 25215"/>
    </justification>
  </clause>

  <clause id="31201">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((x \ y) * z) = L((y \ x) \ z,y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,25371,a,b,25372,a),flip(a)].">
      <j1 rule="hyper" parents="373 25371 25372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31202">
    <literal><![CDATA[
      x / R(L(y,y,y),1 / y,x) = L(x,y,y) / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(1158(a,1),25640(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1158 25640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31203">
    <literal><![CDATA[
      L(x,y,y) / (1 / (1 / y)) = x / R(L(y,y,y),y,x)
    ]]></literal>
    <justification jstring="[para(2968(a,1),31202(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2968 31202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31204">
    <literal><![CDATA[
      L(x,y,y) / (1 / (1 / y)) = x / L(R(y,y,x),y,y)
    ]]></literal>
    <justification jstring="[para(29(a,1),31203(a,2,2))].">
      <j1 rule="para" parents="29 31203"/>
    </justification>
  </clause>

  <clause id="31205">
    <literal><![CDATA[
      L(x,y,y) / (1 / (1 / y)) = L(x / y,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,25122,a(flip),b,31204,a),flip(a)].">
      <j1 rule="hyper" parents="373 25122 31204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31206">
    <literal><![CDATA[
      L(x,y,y) / L(y,y,y) = L(x / y,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,821,a,b,31205,a)].">
      <j1 rule="hyper" parents="64 821 31205"/>
    </justification>
  </clause>

  <clause id="31207">
    <literal><![CDATA[
      L(((x * x) * y) / x,x,x) = (x * (x * y)) / R(x,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10079,a(flip),b,31206,a),flip(a)].">
      <j1 rule="hyper" parents="64 10079 31206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31208">
    <literal><![CDATA[
      L((x \ (x \ y)) / x,x,x) = ((x * x) \ y) / L(x,x,x)
    ]]></literal>
    <justification jstring="[para(346(a,1),31206(a,1,1)),flip(a)].">
      <j1 rule="para" parents="346 31206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31209">
    <literal><![CDATA[
      L((x * x) * (y / x),x,x) = (x * (x * y)) / R(x,x,x)
    ]]></literal>
    <justification jstring="[para(807(a,1),31207(a,1,1))].">
      <j1 rule="para" parents="807 31207"/>
    </justification>
  </clause>

  <clause id="31210">
    <literal><![CDATA[
      L((x \ (x \ y)) / x,x,x) = (x * x) \ (y / L(x,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,933,a(flip),b,31208,a),flip(a)].">
      <j1 rule="hyper" parents="373 933 31208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31211">
    <literal><![CDATA[
      (((x * (y * z)) / z) \ (x * y)) \ (x * y) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(3205(a,1),25668(a,1,1,1))].">
      <j1 rule="para" parents="3205 25668"/>
    </justification>
  </clause>

  <clause id="31212">
    <literal><![CDATA[
      (x * (y * z)) / (z * (x * y)) = (z * (x * y)) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(100(a,1),25848(a,1,1))].">
      <j1 rule="para" parents="100 25848"/>
    </justification>
  </clause>

  <clause id="31213">
    <literal><![CDATA[
      T((a(x,y,z) \ 1) \ a(u,u,a(x,y,z)),a(w,v5,v6) \ 1) = R(a(x,y,z) \ 1,u,u) \ 1
    ]]></literal>
    <justification jstring="[para(28802(a,1),25906(a,1,1,2))].">
      <j1 rule="para" parents="28802 25906"/>
    </justification>
  </clause>

  <clause id="31214">
    <literal><![CDATA[
      ((x \ 1) * (x \ 1)) \ (T(x,y) \ z) = (K(x,y) / x) \ z
    ]]></literal>
    <justification jstring="[para(26113(a,1),26115(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26113 26115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31215">
    <literal><![CDATA[
      x * ((x \ 1) \ (T(x,y) \ z)) = (K(x,y) / x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,582,a(flip),b,31214,a)].">
      <j1 rule="hyper" parents="64 582 31214"/>
    </justification>
  </clause>

  <clause id="31216">
    <literal><![CDATA[
      x \ ((x * (((x \ 1) \ 1) \ (T(x \ 1,y) \ z))) * u) = (x \ 1) \ (((K(x \ 1,y) / (x \ 1)) \ z) * u)
    ]]></literal>
    <justification jstring="[para(31215(a,1),1600(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="31215 1600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31217">
    <literal><![CDATA[
      (x * y) \ (((x \ 1) \ y) * y) = (x \ R(x,x,y * x)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,2480,a(flip),b,26316,a),flip(a)].">
      <j1 rule="hyper" parents="64 2480 26316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31218">
    <literal><![CDATA[
      (x * y) \ (((x \ 1) \ y) * y) = a(x,x,y * x) * y
    ]]></literal>
    <justification jstring="[para(30058(a,1),31217(a,2,1))].">
      <j1 rule="para" parents="30058 31217"/>
    </justification>
  </clause>

  <clause id="31219">
    <literal><![CDATA[
      (x * y) \ (((x \ 1) \ y) * y) = x \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30261,a(flip),b,31218,a),flip(a)].">
      <j1 rule="hyper" parents="373 30261 31218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31220">
    <literal><![CDATA[
      (x \ (1 / y)) * (y * K(x,x \ 1)) = 1 / R(x,x \ (1 / y),y)
    ]]></literal>
    <justification jstring="[para(14443(a,1),26388(a,1,2))].">
      <j1 rule="para" parents="14443 26388"/>
    </justification>
  </clause>

  <clause id="31221">
    <literal><![CDATA[
      1 / R(x,x \ (1 / y),y) = ((1 / (1 / x)) \ (1 / y)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,25726,a(flip),b,31220,a),flip(a)].">
      <j1 rule="hyper" parents="64 25726 31220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31222">
    <literal><![CDATA[
      1 / (1 / ((x \ (1 / y)) * y)) = ((1 / (1 / x)) \ (1 / y)) * y
    ]]></literal>
    <justification jstring="[para(715(a,1),31221(a,1,2))].">
      <j1 rule="para" parents="715 31221"/>
    </justification>
  </clause>

  <clause id="31223">
    <literal><![CDATA[
      1 / R(x,x \ (y \ 1),y) = ((1 / (1 / x)) \ (1 / y)) * y
    ]]></literal>
    <justification jstring="[para(25913(a,1),31221(a,1,2))].">
      <j1 rule="para" parents="25913 31221"/>
    </justification>
  </clause>

  <clause id="31224">
    <literal><![CDATA[
      1 / R(x,x \ y,y) = ((1 / (1 / x)) \ (1 / y)) * y
    ]]></literal>
    <justification jstring="[para(26563(a,1),31223(a,1,2))].">
      <j1 rule="para" parents="26563 31223"/>
    </justification>
  </clause>

  <clause id="31226">
    <literal><![CDATA[
      R(T(x,y),T(x,y),z * T(x,y)) = R(R(T(x,y),x,x),x,z)
    ]]></literal>
    <justification jstring="[para(23879(a,1),26451(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23879 26451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31227">
    <literal><![CDATA[
      R(T(x,y),T(x,y),z * x) = R(R(T(x,y),x,x),x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26170,a(flip),b,31226,a)].">
      <j1 rule="hyper" parents="64 26170 31226"/>
    </justification>
  </clause>

  <clause id="31230">
    <literal><![CDATA[
      R(R(T(x,y),x,x),x,z) = R(T(x,y),x,z * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26406,a(flip),b,31227,a),flip(a)].">
      <j1 rule="hyper" parents="64 26406 31227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31232">
    <literal><![CDATA[
      x \ R(T(x,y),x,z * x) = x * R(K(x,y) / x,x,z)
    ]]></literal>
    <justification jstring="[para(31230(a,1),26950(a,1,2))].">
      <j1 rule="para" parents="31230 26950"/>
    </justification>
  </clause>

  <clause id="31233">
    <literal><![CDATA[
      x \ R(T(x,y),x,x * z) = x * R(K(x,y) / x,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26199,a,b,31232,a)].">
      <j1 rule="hyper" parents="64 26199 31232"/>
    </justification>
  </clause>

  <clause id="31234">
    <literal><![CDATA[
      K(x,y) * a(x,x,x * z) = x * R(K(x,y) / x,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30091,a(flip),b,31233,a)].">
      <j1 rule="hyper" parents="64 30091 31233"/>
    </justification>
  </clause>

  <clause id="31235">
    <literal><![CDATA[
      a(x,x,y * x) * K(x,z) = x * R(K(x,z) / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27364,a,b,31234,a)].">
      <j1 rule="hyper" parents="64 27364 31234"/>
    </justification>
  </clause>

  <clause id="31236">
    <literal><![CDATA[
      (x * R(K(x,y) / x,x,z)) \ u = K(y,x) * (a(x,x,x * z) \ u)
    ]]></literal>
    <justification jstring="[para(31234(a,1),24392(a,1,1))].">
      <j1 rule="para" parents="31234 24392"/>
    </justification>
  </clause>

  <clause id="31237">
    <literal><![CDATA[
      a(x,y,(a(z,z,u * z) * ((w \ K(z,v5)) * w)) \ v6) = a(x,y,(z * R(K(z,v5) / z,z,u)) \ v6)
    ]]></literal>
    <justification jstring="[para(31235(a,1),27418(a,2,3,1))].">
      <j1 rule="para" parents="31235 27418"/>
    </justification>
  </clause>

  <clause id="31238">
    <literal><![CDATA[
      R(x,L(T(y * y,z),z,u),w) = R(x,u / (u / (y * y)),w)
    ]]></literal>
    <justification jstring="[para(11456(a,1),26489(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11456 26489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31239">
    <literal><![CDATA[
      R(x,L(T(y * y,z),z,u),w) = R(x,y * y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26411,a(flip),b,31238,a),flip(a)].">
      <j1 rule="hyper" parents="373 26411 31238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31242">
    <literal><![CDATA[
      R(x,L(T(y * y,z),z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,654,a(flip),b,31239,a),flip(a)].">
      <j1 rule="hyper" parents="373 654 31239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31244">
    <literal><![CDATA[
      R(x,L(y * y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,26430,a(flip),b,31242,a)].">
      <j1 rule="hyper" parents="64 26430 31242"/>
    </justification>
  </clause>

  <clause id="31245">
    <literal><![CDATA[
      x * (L(y * y,z,u) \ 1) = x / L(y * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(719,a,31244,a)].">
      <j1 rule="hyper" parents="719 31244"/>
    </justification>
  </clause>

  <clause id="31247">
    <literal><![CDATA[
      (x * L(y * y,z,u)) * w = x * (L(y * y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(144,a,31244,a(flip),b,14095,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="144 31244 14095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31248">
    <literal><![CDATA[
      (x * y) \ (x * (y / (z * z))) = L(z * z,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,11836,a(flip),b,31245,a)].">
      <j1 rule="hyper" parents="139 11836 31245"/>
    </justification>
  </clause>

  <clause id="31249">
    <literal><![CDATA[
      L((x * x) \ 1,y,z) = L(x * x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,586,a(flip),b,31248,a)].">
      <j1 rule="hyper" parents="64 586 31248"/>
    </justification>
  </clause>

  <clause id="31250">
    <literal><![CDATA[
      L((x * x) \ 1,y,z) * u = L(x * x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(31249(a,2),1824(a,1,1))].">
      <j1 rule="para" parents="31249 1824"/>
    </justification>
  </clause>

  <clause id="31251">
    <literal><![CDATA[
      x * L((y * y) \ 1,z,u) = x / L(y * y,z,u)
    ]]></literal>
    <justification jstring="[para(31249(a,2),31245(a,1,2))].">
      <j1 rule="para" parents="31249 31245"/>
    </justification>
  </clause>

  <clause id="31252">
    <literal><![CDATA[
      x * L(x \ ((y * y) \ x),z,u) = L(y * y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,1188,a,b,31250,a)].">
      <j1 rule="hyper" parents="64 1188 31250"/>
    </justification>
  </clause>

  <clause id="31253">
    <literal><![CDATA[
      a(x * (((y * y) / L(y * y,z,u)) * w),v5,v6) = a(x * (w * L(w \ ((y * y) \ w),z,u)),v5,v6)
    ]]></literal>
    <justification jstring="[para(31251(a,1),11988(a,1,1,2,1))].">
      <j1 rule="para" parents="31251 11988"/>
    </justification>
  </clause>

  <clause id="31254">
    <literal><![CDATA[
      L(x,L(y * y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(606,a,31247,a)].">
      <j1 rule="hyper" parents="606 31247"/>
    </justification>
  </clause>

  <clause id="31255">
    <literal><![CDATA[
      L(x * x,y,z) \ (x * x) = a(z,y,x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2869,a,b,31254,a),flip(a)].">
      <j1 rule="hyper" parents="64 2869 31254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31256">
    <literal><![CDATA[
      (x * x) / L(x * x,y,z) = a(z,y,x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5558,a,b,31255,a)].">
      <j1 rule="hyper" parents="64 5558 31255"/>
    </justification>
  </clause>

  <clause id="31257">
    <literal><![CDATA[
      (x * x) \ L(x * x,y,z) = a(z,y,x * x) \ 1
    ]]></literal>
    <justification jstring="[para(31255(a,1),1827(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31255 1827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31258">
    <literal><![CDATA[
      a(a(x,y,z * z),u,w) = a(L(z * z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(31255(a,1),2666(a,1,1))].">
      <j1 rule="para" parents="31255 2666"/>
    </justification>
  </clause>

  <clause id="31259">
    <literal><![CDATA[
      L(x,a(y,z,u * u),w) = L(x,L(u * u,z,y),w)
    ]]></literal>
    <justification jstring="[para(31255(a,1),11867(a,1,2))].">
      <j1 rule="para" parents="31255 11867"/>
    </justification>
  </clause>

  <clause id="31260">
    <literal><![CDATA[
      L(x * x,y,z) * ((x * x) \ u) = u * (a(z,y,x * x) \ 1)
    ]]></literal>
    <justification jstring="[para(31257(a,1),24850(a,2,2))].">
      <j1 rule="para" parents="31257 24850"/>
    </justification>
  </clause>

  <clause id="31261">
    <literal><![CDATA[
      a(a(x,y,z * z),u,w) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,1825,a(flip),b,31258,a),flip(a)].">
      <j1 rule="hyper" parents="373 1825 31258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31263">
    <literal><![CDATA[
      L(x,y,a(z,u,w * w)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,31261,a)].">
      <j1 rule="hyper" parents="53 31261"/>
    </justification>
  </clause>

  <clause id="31264">
    <literal><![CDATA[
      (a(x,y,z * z) \ 1) * u = a(x,y,z * z) \ u
    ]]></literal>
    <justification jstring="[para(31261(a,1),30104(a,1,1,2))].">
      <j1 rule="para" parents="31261 30104"/>
    </justification>
  </clause>

  <clause id="31265">
    <literal><![CDATA[
      (a(x,y,z * z) \ u) \ w = u \ (a(x,y,z * z) * w)
    ]]></literal>
    <justification jstring="[hyper(743,a,31263,a),flip(a)].">
      <j1 rule="hyper" parents="743 31263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31266">
    <literal><![CDATA[
      L(x,a(y,z,u * u),w) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,31254,a(flip),b,31259,a),flip(a)].">
      <j1 rule="hyper" parents="373 31254 31259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31268">
    <literal><![CDATA[
      (x * y) / (a(z,u,w * w) \ y) = x * a(z,u,w * w)
    ]]></literal>
    <justification jstring="[hyper(225,a,31266,a(flip),b,102,a(flip))].">
      <j1 rule="hyper" parents="225 31266 102"/>
    </justification>
  </clause>

  <clause id="31269">
    <literal><![CDATA[
      (x / a(y,z,u * u)) \ w = a(y,z,u * u) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(38,a,1392,a(flip),b,31266,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 1392 31266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31270">
    <literal><![CDATA[
      (a(x,y,z * z) \ u) \ w = a(x,y,z * z) * (u \ w)
    ]]></literal>
    <justification jstring="[para(23133(a,1),31269(a,1,1))].">
      <j1 rule="para" parents="23133 31269"/>
    </justification>
  </clause>

  <clause id="31271">
    <literal><![CDATA[
      x \ (a(y,z,u * u) * w) = a(y,z,u * u) * (x \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31265,a(flip),b,31270,a)].">
      <j1 rule="hyper" parents="64 31265 31270"/>
    </justification>
  </clause>

  <clause id="31272">
    <literal><![CDATA[
      R(x \ (y * y),(x \ y) \ (1 / y),1 / y) = (x \ y) / (1 / y)
    ]]></literal>
    <justification jstring="[para(550(a,1),26625(a,1,1))].">
      <j1 rule="para" parents="550 26625"/>
    </justification>
  </clause>

  <clause id="31273">
    <literal><![CDATA[
      R(x \ (y * y),(x \ y) \ (1 / y),y \ 1) = (x \ y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(25233,a,31272,a)].">
      <j1 rule="hyper" parents="25233 31272"/>
    </justification>
  </clause>

  <clause id="31274">
    <literal><![CDATA[
      R(x \ (y * y),(x \ y) \ (y \ 1),y \ 1) = (x \ y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26506,a(flip),b,31273,a)].">
      <j1 rule="hyper" parents="64 26506 31273"/>
    </justification>
  </clause>

  <clause id="31275">
    <literal><![CDATA[
      R(x \ (y * y),(x \ y) \ y,y \ 1) = (x \ y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26563,a(flip),b,31274,a)].">
      <j1 rule="hyper" parents="64 26563 31274"/>
    </justification>
  </clause>

  <clause id="31276">
    <literal><![CDATA[
      R(x \ (y * y),x,y \ 1) = (x \ y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26414,a(flip),b,31275,a)].">
      <j1 rule="hyper" parents="64 26414 31275"/>
    </justification>
  </clause>

  <clause id="31278">
    <literal><![CDATA[
      T(x / (y * (1 / x)),y) = (y \ x) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,5156,a(flip),b,31276,a)].">
      <j1 rule="hyper" parents="64 5156 31276"/>
    </justification>
  </clause>

  <clause id="31279">
    <literal><![CDATA[
      L(x,x,x * (y \ x)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,31199,a(flip),b,26660,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 31199 26660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31280">
    <literal><![CDATA[
      L(x,x,(y \ x) * x) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(24201,a,31279,a)].">
      <j1 rule="hyper" parents="24201 31279"/>
    </justification>
  </clause>

  <clause id="31281">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / (1 / y)) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25566,a(flip),b,31279,a)].">
      <j1 rule="hyper" parents="64 25566 31279"/>
    </justification>
  </clause>

  <clause id="31282">
    <literal><![CDATA[
      (x \ y) * L(y,y,x) = (x \ y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,31279,a(flip),b,25566,a(flip))].">
      <j1 rule="hyper" parents="145 31279 25566"/>
    </justification>
  </clause>

  <clause id="31283">
    <literal><![CDATA[
      a(x * (y \ x),x,x) = L(x,x,y) \ x
    ]]></literal>
    <justification jstring="[para(31279(a,1),30462(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31279 30462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31284">
    <literal><![CDATA[
      L(x,x,R(y,y,x)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26773,a,b,31280,a)].">
      <j1 rule="hyper" parents="64 26773 31280"/>
    </justification>
  </clause>

  <clause id="31285">
    <literal><![CDATA[
      L(x * y,x * y,T(x,y) * (x * y)) = L(x * y,x * y,y)
    ]]></literal>
    <justification jstring="[para(22(a,2),31280(a,1,3,1))].">
      <j1 rule="para" parents="22 31280"/>
    </justification>
  </clause>

  <clause id="31286">
    <literal><![CDATA[
      L(x,x,L(y,y,x)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29203,a(flip),b,31284,a)].">
      <j1 rule="hyper" parents="64 29203 31284"/>
    </justification>
  </clause>

  <clause id="31287">
    <literal><![CDATA[
      a(L(x,x,y),y,y) = L(y,y,x) \ y
    ]]></literal>
    <justification jstring="[para(31286(a,1),30462(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31286 30462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31288">
    <literal><![CDATA[
      a(L(x,x,y),y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30462,a(flip),b,31287,a),flip(a)].">
      <j1 rule="hyper" parents="373 30462 31287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31289">
    <literal><![CDATA[
      a(x * (y \ x),x,x) = a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,30462,a(flip),b,31283,a),flip(a)].">
      <j1 rule="hyper" parents="373 30462 31283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31290">
    <literal><![CDATA[
      a((x \ y) * y,y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(26847,a,31289,a)].">
      <j1 rule="hyper" parents="26847 31289"/>
    </justification>
  </clause>

  <clause id="31291">
    <literal><![CDATA[
      L(x,y,a(z,z,u \ z)) = L(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[para(31290(a,1),30340(a,1,3)),flip(a)].">
      <j1 rule="para" parents="31290 30340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31292">
    <literal><![CDATA[
      L(x \ y,z,a(x,y,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,29312,a(flip),b,31291,a),flip(a)].">
      <j1 rule="hyper" parents="64 29312 31291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31293">
    <literal><![CDATA[
      L(x \ y,z,a(y,y,x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,29287,a(flip),b,31292,a)].">
      <j1 rule="hyper" parents="64 29287 31292"/>
    </justification>
  </clause>

  <clause id="31294">
    <literal><![CDATA[
      (a(x,x,y) * y) \ (a(x,x,y) * x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,23954,a,b,31293,a)].">
      <j1 rule="hyper" parents="64 23954 31293"/>
    </justification>
  </clause>

  <clause id="31295">
    <literal><![CDATA[
      (a(x,x,y) * y) \ R(x,x,y) = y \ x
    ]]></literal>
    <justification jstring="[para(30053(a,1),31294(a,1,2))].">
      <j1 rule="para" parents="30053 31294"/>
    </justification>
  </clause>

  <clause id="31296">
    <literal><![CDATA[
      R(x,x,y) / (y \ x) = a(x,x,y) * y
    ]]></literal>
    <justification jstring="[hyper(226,a,31295,a)].">
      <j1 rule="hyper" parents="226 31295"/>
    </justification>
  </clause>

  <clause id="31297">
    <literal><![CDATA[
      (x / y) \ R(x,x,y) = a(x,x,y) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,27050,a(flip),b,31296,a)].">
      <j1 rule="hyper" parents="64 27050 31296"/>
    </justification>
  </clause>

  <clause id="31298">
    <literal><![CDATA[
      a(x,x,y) * (z * a(a(x,x,y),y,y \ z)) = ((x / y) \ R(x,x,y)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(31297(a,2),29950(a,2,1))].">
      <j1 rule="para" parents="31297 29950"/>
    </justification>
  </clause>

  <clause id="31299">
    <literal><![CDATA[
      L(x * y,x * y,(x * y) * x) = L(x * y,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29039,a(flip),b,31285,a)].">
      <j1 rule="hyper" parents="64 29039 31285"/>
    </justification>
  </clause>

  <clause id="31301">
    <literal><![CDATA[
      L(x * y,x * y,y) = x \ (x / (1 / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,25566,a(flip),b,31299,a),flip(a)].">
      <j1 rule="hyper" parents="64 25566 31299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31302">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * ((y * x) \ y) = L((y * x) \ y,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30634,a(flip),b,26666,a),flip(a)].">
      <j1 rule="hyper" parents="64 30634 26666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31303">
    <literal><![CDATA[
      a(x,y,((z * u) \ z) * (((z * u) \ z) * u)) = a(x,y,L((z * u) \ z,u,z))
    ]]></literal>
    <justification jstring="[para(31302(a,1),27462(a,1,3)),flip(a)].">
      <j1 rule="para" parents="31302 27462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31304">
    <literal><![CDATA[
      x * (L(x,x,x * y) \ K(x \ 1,y * x)) = ((y / (y * x)) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,16433,a(flip),b,26670,a)].">
      <j1 rule="hyper" parents="64 16433 26670"/>
    </justification>
  </clause>

  <clause id="31305">
    <literal><![CDATA[
      a(R(x * (x * y),z,u) * x,w,v5) = a(x \ R(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,30382,a(flip),b,26856,a),flip(a)].">
      <j1 rule="hyper" parents="373 30382 26856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31306">
    <literal><![CDATA[
      a(x,y,(((z / u) / w) * v5) * R(v6,w \ (u \ z),v5)) = a(x,y,(v6 * ((z / u) / w)) * v5)
    ]]></literal>
    <justification jstring="[para(26506(a,1),27374(a,1,3,2))].">
      <j1 rule="para" parents="26506 27374"/>
    </justification>
  </clause>

  <clause id="31307">
    <literal><![CDATA[
      a(x,y,(R(z,u,u) / (1 / u)) \ w) = a(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27404,a(flip),b,27448,a),flip(a)].">
      <j1 rule="hyper" parents="373 27404 27448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31309">
    <literal><![CDATA[
      a(x,y,L((z * z) \ u,z,z)) = a(x,y,(z \ 1) * (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27711,a(flip),b,27595,a)].">
      <j1 rule="hyper" parents="64 27711 27595"/>
    </justification>
  </clause>

  <clause id="31310">
    <literal><![CDATA[
      a(x,y,((z * z) * (u * (z \ 1))) * w) = a(x,y,w * (z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27633,a(flip),b,27620,a),flip(a)].">
      <j1 rule="hyper" parents="373 27633 27620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31311">
    <literal><![CDATA[
      a(x,y,(z * z) * ((u * (z \ 1)) * w)) = a(x,y,w * (z * u))
    ]]></literal>
    <justification jstring="[para(33(a,1),31310(a,1,3))].">
      <j1 rule="para" parents="33 31310"/>
    </justification>
  </clause>

  <clause id="31312">
    <literal><![CDATA[
      a(x,y,((z * u) \ ((u * w) * z)) * v5) = a(x,y,R(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27422,a(flip),b,27710,a)].">
      <j1 rule="hyper" parents="64 27422 27710"/>
    </justification>
  </clause>

  <clause id="31314">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * v5) = a(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27549,a(flip),b,31312,a),flip(a)].">
      <j1 rule="hyper" parents="64 27549 31312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31315">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * v5) = a(x,y,v5 * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,31314,a),flip(a)].">
      <j1 rule="hyper" parents="373 27298 31314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31316">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * ((z * z) \ v5)) = a(x,y,R(z \ 1,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27779,a(flip),b,31314,a),flip(a)].">
      <j1 rule="hyper" parents="64 27779 31314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31317">
    <literal><![CDATA[
      a(x,y,z * R(u,w,v5)) = a(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(27453,a,31315,a)].">
      <j1 rule="hyper" parents="27453 31315"/>
    </justification>
  </clause>

  <clause id="31318">
    <literal><![CDATA[
      a(x,y,(z \ 1) * L(z,u,w)) = a(x,y,z \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(1794(a,1),31315(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1794 31315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31320">
    <literal><![CDATA[
      a(x,y,(z \ 1) * L(z \ ((1 / z) \ u),w,v5)) = a(x,y,z \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1789(a,1),31317(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1789 31317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31321">
    <literal><![CDATA[
      a(x,y,z * L(z \ 1,u,w)) = a(x,y,z \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(1987(a,1),31317(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1987 31317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31322">
    <literal><![CDATA[
      a(x,y,z \ R(z,u,w)) = a(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27303,a(flip),b,31318,a),flip(a)].">
      <j1 rule="hyper" parents="64 27303 31318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31323">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ L(L(z,u,w),v5,v6)) = a(x,y,L(z \ R(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(4246(a,1),31322(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4246 31322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31324">
    <literal><![CDATA[
      a(x,y,x * L(x \ 1,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,29807,a(flip),b,31321,a),flip(a)].">
      <j1 rule="hyper" parents="373 29807 31321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31325">
    <literal><![CDATA[
      L(x * L(x \ 1,y,z),u,x) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,31324,a)].">
      <j1 rule="hyper" parents="53 31324"/>
    </justification>
  </clause>

  <clause id="31327">
    <literal><![CDATA[
      L(x * ((y * x) \ y),z,x) = x * L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(241(a,1),31325(a,1,1,2))].">
      <j1 rule="para" parents="241 31325"/>
    </justification>
  </clause>

  <clause id="31328">
    <literal><![CDATA[
      L(L(x * ((y * x) \ y),z,u),w,x) = L(x * L(x \ 1,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(31327(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31327 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31329">
    <literal><![CDATA[
      L(x * L(x \ 1,x,y),z,u) \ K(x * ((y * x) \ y),(x * ((y * x) \ y)) \ 1) = 1 / L(L(x * ((y * x) \ y),z,u),w,x)
    ]]></literal>
    <justification jstring="[para(31327(a,1),5402(a,1,1,1))].">
      <j1 rule="para" parents="31327 5402"/>
    </justification>
  </clause>

  <clause id="31330">
    <literal><![CDATA[
      L(L(x * ((y * x) \ y),z,x),u,w) * v5 = K(x,L(x \ 1,x,y)) * (L(L(x \ 1,x,y) * x,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(31327(a,2),26140(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="31327 26140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31331">
    <literal><![CDATA[
      a(x,y,R(z \ 1,u,w) * T(v5,v6)) = a(x,y,((z * z) \ v5) * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27573,a(flip),b,31316,a),flip(a)].">
      <j1 rule="hyper" parents="64 27573 31316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31332">
    <literal><![CDATA[
      a(x,y,((z * u) \ ((u * w) * z)) \ v5) = a(x,y,R(w,u,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27523,a(flip),b,27717,a)].">
      <j1 rule="hyper" parents="64 27523 27717"/>
    </justification>
  </clause>

  <clause id="31334">
    <literal><![CDATA[
      a(x,y,R(z,u,w) \ v5) = a(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27563,a(flip),b,31332,a),flip(a)].">
      <j1 rule="hyper" parents="64 27563 31332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31335">
    <literal><![CDATA[
      a(x,y,R(T(z,u),w,v5) \ v6) = a(x,y,L(z,w,v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,27408,a,b,31334,a)].">
      <j1 rule="hyper" parents="64 27408 31334"/>
    </justification>
  </clause>

  <clause id="31336">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ (v5 * z)) = a(x,y,z * (R(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27378,a(flip),b,31334,a),flip(a)].">
      <j1 rule="hyper" parents="64 27378 31334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31337">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) \ 1) = a(x,y,z * (R(z,u,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11444,a(flip),b,31334,a),flip(a)].">
      <j1 rule="hyper" parents="64 11444 31334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31338">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ L(v5,L(z,u,w),L(z,u,w))) = a(x,y,(R(z,u,w) \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(29803(a,1),31334(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29803 31334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31339">
    <literal><![CDATA[
      a(x,y,z * (R(z,u,w) \ v5)) = a(x,y,z * (L(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27359,a(flip),b,31336,a),flip(a)].">
      <j1 rule="hyper" parents="64 27359 31336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31340">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) \ 1) = a(x,y,z * (L(z,u,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,31337,a,b,31339,a)].">
      <j1 rule="hyper" parents="64 31337 31339"/>
    </justification>
  </clause>

  <clause id="31341">
    <literal><![CDATA[
      a(x,y,L(z \ 1,z,u) \ 1) = a(x,y,z * a(u,z,z))
    ]]></literal>
    <justification jstring="[para(30462(a,1),31340(a,2,3,2))].">
      <j1 rule="para" parents="30462 31340"/>
    </justification>
  </clause>

  <clause id="31342">
    <literal><![CDATA[
      L((x / (x / y)) * K(z \ 1,z),z,z) \ x = x / ((z \ 1) * (z * y))
    ]]></literal>
    <justification jstring="[para(5224(a,1),27816(a,1,1,1))].">
      <j1 rule="para" parents="5224 27816"/>
    </justification>
  </clause>

  <clause id="31343">
    <literal><![CDATA[
      a(x,y * R(z,u,w),x) = K(x * (y * z),x) * K(x,y * z)
    ]]></literal>
    <justification jstring="[para(28254(a,1),28102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28254 28102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31344">
    <literal><![CDATA[
      a(x,y * R(z,u,w),x) = a(x,y * z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10886,a(flip),b,31343,a),flip(a)].">
      <j1 rule="hyper" parents="373 10886 31343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31346">
    <literal><![CDATA[
      T(x,(y * (z * u)) * (((w * z) * u) \ v5)) = T(x,(R(w,z,u) / y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,24707,a(flip),b,28133,a)].">
      <j1 rule="hyper" parents="64 24707 28133"/>
    </justification>
  </clause>

  <clause id="31347">
    <literal><![CDATA[
      R(x,y,z \ (u * ((z \ u) \ 1))) = L(x,y,z \ (u * ((z \ u) \ 1)))
    ]]></literal>
    <justification jstring="[para(980(a,1),28839(a,1,3)),flip(a)].">
      <j1 rule="para" parents="980 28839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31348">
    <literal><![CDATA[
      R(x,y,z \ (u * ((z \ u) \ 1))) = L(x,y,z \ ((z \ u) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,29131,a(flip),b,31347,a),flip(a)].">
      <j1 rule="hyper" parents="373 29131 31347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31349">
    <literal><![CDATA[
      R(x,y,z \ (u * ((z \ u) \ 1))) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,29263,a(flip),b,31348,a),flip(a)].">
      <j1 rule="hyper" parents="373 29263 31348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31350">
    <literal><![CDATA[
      (x / y) * (y * (L(z,u,w) \ z)) = ((L(z,u,w) \ z) * y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(11083,a,28923,a)].">
      <j1 rule="hyper" parents="11083 28923"/>
    </justification>
  </clause>

  <clause id="31351">
    <literal><![CDATA[
      (x / y) * (y * (L(z,u,w) \ z)) = (y * (L(z,u,w) \ z)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(23581(a,1),31350(a,2,1))].">
      <j1 rule="para" parents="23581 31350"/>
    </justification>
  </clause>

  <clause id="31353">
    <literal><![CDATA[
      L(x,x \ y,(x \ y) \ z) * z = (K(x,z) * (z / (y / x))) * y
    ]]></literal>
    <justification jstring="[para(29442(a,1),29172(a,1,1))].">
      <j1 rule="para" parents="29442 29172"/>
    </justification>
  </clause>

  <clause id="31354">
    <literal><![CDATA[
      L(x,x \ y,(x \ y) \ z) * z = (z / (y / T(x,z))) * y
    ]]></literal>
    <justification jstring="[para(15080(a,1),31353(a,2,1))].">
      <j1 rule="para" parents="15080 31353"/>
    </justification>
  </clause>

  <clause id="31356">
    <literal><![CDATA[
      L(a(x,x,y),(x \ 1) * y,(a(x,x,y) \ (x \ y)) \ z) * z = (z / ((x \ y) / T(a(x,x,y),z))) * (x \ y)
    ]]></literal>
    <justification jstring="[para(30044(a,1),31354(a,1,1,2))].">
      <j1 rule="para" parents="30044 31354"/>
    </justification>
  </clause>

  <clause id="31357">
    <literal><![CDATA[
      1 / L(x,y * (x \ 1),L(y,x,x)) = (1 / R(y,x,x)) * (y * (1 / x))
    ]]></literal>
    <justification jstring="[para(5322(a,1),29196(a,1,2))].">
      <j1 rule="para" parents="5322 29196"/>
    </justification>
  </clause>

  <clause id="31358">
    <literal><![CDATA[
      L(x,y,z \ (u * ((w * v5) * v5))) = L(x,y,z \ (u * R(w,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29133,a(flip),b,29250,a)].">
      <j1 rule="hyper" parents="64 29133 29250"/>
    </justification>
  </clause>

  <clause id="31359">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) = L(x,y,z \ L(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,29024,a(flip),b,29251,a),flip(a)].">
      <j1 rule="hyper" parents="373 29024 29251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31362">
    <literal><![CDATA[
      L(x,R(y,z,y) \ 1,T(y * z,y) \ z) = L(x,(y * z) \ z,y)
    ]]></literal>
    <justification jstring="[para(14173(a,1),29582(a,1,3))].">
      <j1 rule="para" parents="14173 29582"/>
    </justification>
  </clause>

  <clause id="31363">
    <literal><![CDATA[
      L(x,R(y,z,y) \ 1,(y * z) \ z) = L(x,(y * z) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(29065,a,31362,a)].">
      <j1 rule="hyper" parents="29065 31362"/>
    </justification>
  </clause>

  <clause id="31364">
    <literal><![CDATA[
      L(x,R(y,z,y),(y * z) \ z) = L(x,(y * z) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(11853,a,31363,a)].">
      <j1 rule="hyper" parents="11853 31363"/>
    </justification>
  </clause>

  <clause id="31366">
    <literal><![CDATA[
      L(x,(y * z) \ z,y) = L(x,y,(y * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14161,a(flip),b,31364,a),flip(a)].">
      <j1 rule="hyper" parents="64 14161 31364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31368">
    <literal><![CDATA[
      L(x,y \ (z \ y),z) = L(x,z,(z * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29603,a(flip),b,31366,a)].">
      <j1 rule="hyper" parents="64 29603 31366"/>
    </justification>
  </clause>

  <clause id="31369">
    <literal><![CDATA[
      L(x,y \ (z \ y),z) = L(x,z,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,13011,a(flip),b,31368,a),flip(a)].">
      <j1 rule="hyper" parents="373 13011 31368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31370">
    <literal><![CDATA[
      (x \ R(x,x,y)) * L(z,x,y \ (x \ y)) = x * (((x \ y) / y) * z)
    ]]></literal>
    <justification jstring="[para(31369(a,1),29533(a,1,2))].">
      <j1 rule="para" parents="31369 29533"/>
    </justification>
  </clause>

  <clause id="31371">
    <literal><![CDATA[
      (x / (y * x)) * (y * z) = y * (((y \ x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27862,a(flip),b,31370,a)].">
      <j1 rule="hyper" parents="64 27862 31370"/>
    </justification>
  </clause>

  <clause id="31372">
    <literal><![CDATA[
      ((x \ y) / y) * (x \ 1) = x \ (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(721,a,31371,a),flip(a)].">
      <j1 rule="hyper" parents="721 31371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31373">
    <literal><![CDATA[
      ((x \ y) / y) / x = x \ (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30674,a(flip),b,31372,a)].">
      <j1 rule="hyper" parents="64 30674 31372"/>
    </justification>
  </clause>

  <clause id="31374">
    <literal><![CDATA[
      (x / y) \ (x / ((x / y) * x)) = (y / x) * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(82(a,1),31372(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 31372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31375">
    <literal><![CDATA[
      (x / y) \ (x / ((x / y) * x)) = (y / x) / (x / y)
    ]]></literal>
    <justification jstring="[para(82(a,1),31373(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 31373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31376">
    <literal><![CDATA[
      T(x \ (y / (x * y)),x * x) \ 1 = (((x \ y) / y) / (1 / x)) \ (x * x)
    ]]></literal>
    <justification jstring="[para(31373(a,1),1185(a,1,1,1))].">
      <j1 rule="para" parents="31373 1185"/>
    </justification>
  </clause>

  <clause id="31377">
    <literal><![CDATA[
      (((x \ y) / y) / ((((x \ y) / y) \ x) * ((x \ y) / y))) \ 1 = T((x \ (y / (x * y))) \ 1,(x \ y) / y)
    ]]></literal>
    <justification jstring="[para(31373(a,1),7657(a,2,1,1))].">
      <j1 rule="para" parents="31373 7657"/>
    </justification>
  </clause>

  <clause id="31378">
    <literal><![CDATA[
      K(x,x \ (y \ x)) * (((x \ (y \ x)) / y) * z) = (y \ (x / (y * x))) * z
    ]]></literal>
    <justification jstring="[para(31373(a,1),24363(a,2,1))].">
      <j1 rule="para" parents="31373 24363"/>
    </justification>
  </clause>

  <clause id="31379">
    <literal><![CDATA[
      (x / y) \ ((x / y) / (y / x)) = (y / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,31375,a(flip),b,31374,a(flip))].">
      <j1 rule="hyper" parents="139 31375 31374"/>
    </justification>
  </clause>

  <clause id="31380">
    <literal><![CDATA[
      ((x / y) * (y / x)) / ((y / x) \ 1) = ((x / y) * (y / x)) * (y / x)
    ]]></literal>
    <justification jstring="[para(31379(a,1),30682(a,1,2))].">
      <j1 rule="para" parents="31379 30682"/>
    </justification>
  </clause>

  <clause id="31381">
    <literal><![CDATA[
      (x / y) * ((1 / (y / x)) \ (y / x)) = ((x / y) * (y / x)) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1592,a(flip),b,31380,a)].">
      <j1 rule="hyper" parents="64 1592 31380"/>
    </justification>
  </clause>

  <clause id="31382">
    <literal><![CDATA[
      ((x / y) * (y / x)) * (y / x) = x / (((y / x) \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1623,a(flip),b,31381,a),flip(a)].">
      <j1 rule="hyper" parents="64 1623 31381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31383">
    <literal><![CDATA[
      L(((x / y) / z) * u,u * ((x / y) / z),u * (z \ (y \ x))) = 1 / (1 / (((x / y) / z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29123,a(flip),b,29743,a)].">
      <j1 rule="hyper" parents="64 29123 29743"/>
    </justification>
  </clause>

  <clause id="31384">
    <literal><![CDATA[
      L(x,L((y * z) \ u,y * z,z),w) = L(x,L(y,z,z) \ (z * u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29734,a(flip),b,29755,a),flip(a)].">
      <j1 rule="hyper" parents="373 29734 29755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31385">
    <literal><![CDATA[
      L(x,L(y,z,z) \ (z * ((y * z) * u)),w) = L(x,L(u,y * z,z),w)
    ]]></literal>
    <justification jstring="[para(9(a,1),31384(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 31384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31386">
    <literal><![CDATA[
      L(x,(y * (z \ R(u,z,z))) * w,v5) = L(x,((z * u) * y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,30853,a(flip),b,29771,a),flip(a)].">
      <j1 rule="hyper" parents="373 30853 29771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31387">
    <literal><![CDATA[
      (x / y) * (((x / y) \ z) / u) = (y \ x) * (((y \ x) \ z) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,10263,a(flip),b,29840,a),flip(a)].">
      <j1 rule="hyper" parents="64 10263 29840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31388">
    <literal><![CDATA[
      L((1 / x) \ y,a(y,x,x \ y),x \ y) \ (y * x) = (y * x) / T((1 / x) \ y,y * x)
    ]]></literal>
    <justification jstring="[para(29670(a,1),29864(a,1,1))].">
      <j1 rule="para" parents="29670 29864"/>
    </justification>
  </clause>

  <clause id="31389">
    <literal><![CDATA[
      (x \ 1) * (y * R(a(x,z,u),x \ 1,y)) = (x \ a(x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(23929(a,1),29929(a,2,1))].">
      <j1 rule="para" parents="23929 29929"/>
    </justification>
  </clause>

  <clause id="31390">
    <literal><![CDATA[
      (x \ 1) * (y * R(a(x,z,u),x,y)) = (x \ a(x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(2975(a,1),31389(a,1,2,2))].">
      <j1 rule="para" parents="2975 31389"/>
    </justification>
  </clause>

  <clause id="31391">
    <literal><![CDATA[
      (x \ 1) * (y * L(a(x,z,u),x,y)) = (x \ a(x,z,u)) * y
    ]]></literal>
    <justification jstring="[para(28787(a,1),31390(a,1,2,2))].">
      <j1 rule="para" parents="28787 31390"/>
    </justification>
  </clause>

  <clause id="31392">
    <literal><![CDATA[
      (1 / (x \ y)) \ T(x,x \ y) = ((x / y) * (y / x)) * y
    ]]></literal>
    <justification jstring="[para(30208(a,1),30205(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30208 30205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31393">
    <literal><![CDATA[
      ((x / y) * (y / x)) * y = (1 / (y / x)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,14879,a(flip),b,31392,a),flip(a)].">
      <j1 rule="hyper" parents="64 14879 31392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31395">
    <literal><![CDATA[
      x \ ((1 / (x / y)) \ y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,31393,a(flip),b,23877,a(flip))].">
      <j1 rule="hyper" parents="139 31393 23877"/>
    </justification>
  </clause>

  <clause id="31396">
    <literal><![CDATA[
      (x * (y / (y / z))) \ ((1 / (x * K(z \ y,z))) \ z) = (z / (x * (y / (y / z)))) * ((x * (y / (y / z))) / z)
    ]]></literal>
    <justification jstring="[para(6152(a,1),31395(a,1,2,1,2))].">
      <j1 rule="para" parents="6152 31395"/>
    </justification>
  </clause>

  <clause id="31397">
    <literal><![CDATA[
      ((1 / x) \ y) * L(z,L(y,x,x),x) = x * ((a(x,x,y) * y) * z)
    ]]></literal>
    <justification jstring="[para(11878(a,1),30246(a,1,2))].">
      <j1 rule="para" parents="11878 30246"/>
    </justification>
  </clause>

  <clause id="31398">
    <literal><![CDATA[
      L((a(x,x,y) * y) \ z,L(y,x,x),x) = ((1 / x) \ y) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,31397,a),flip(a)].">
      <j1 rule="hyper" parents="139 168 31397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31399">
    <literal><![CDATA[
      L((a(x,x,y) * y) \ z,L(y,x,x),x) = (x \ y) \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1692,a(flip),b,31398,a),flip(a)].">
      <j1 rule="hyper" parents="373 1692 31398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31400">
    <literal><![CDATA[
      L((x \ ((1 / x) \ y)) \ z,L(y,x,x),x) = (x \ y) \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(30228(a,2),31399(a,1,1,1))].">
      <j1 rule="para" parents="30228 31399"/>
    </justification>
  </clause>

  <clause id="31401">
    <literal><![CDATA[
      (x / ((1 / y) \ z)) * y = (x / (y \ z)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(30238(a,1),30247(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="30238 30247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31402">
    <literal><![CDATA[
      ((x / (y \ z)) * (y \ 1)) * L(u,y,((1 / y) \ z) \ x) = (x / ((1 / y) \ z)) * (y * u)
    ]]></literal>
    <justification jstring="[para(31401(a,1),23978(a,1,1))].">
      <j1 rule="para" parents="31401 23978"/>
    </justification>
  </clause>

  <clause id="31403">
    <literal><![CDATA[
      x \ (y * (a(y,y,y \ x) * (x / y))) = ((y \ x) / ((y \ x) * y)) * y
    ]]></literal>
    <justification jstring="[para(29946(a,1),30286(a,1,2))].">
      <j1 rule="para" parents="29946 30286"/>
    </justification>
  </clause>

  <clause id="31404">
    <literal><![CDATA[
      (x * y) * (z * R(a(x,x,y),x * y,z)) = ((1 / x) \ y) * z
    ]]></literal>
    <justification jstring="[para(30041(a,1),30318(a,2,1))].">
      <j1 rule="para" parents="30041 30318"/>
    </justification>
  </clause>

  <clause id="31405">
    <literal><![CDATA[
      (x * y) * (z * L(a(x,x,y),x * y,z)) = ((1 / x) \ y) * z
    ]]></literal>
    <justification jstring="[para(28787(a,1),31404(a,1,2,2))].">
      <j1 rule="para" parents="28787 31404"/>
    </justification>
  </clause>

  <clause id="31406">
    <literal><![CDATA[
      (x * y) * (y * a(x,x,y)) = ((1 / x) \ y) * y
    ]]></literal>
    <justification jstring="[para(29330(a,1),31404(a,1,2,2))].">
      <j1 rule="para" parents="29330 31404"/>
    </justification>
  </clause>

  <clause id="31407">
    <literal><![CDATA[
      x * ((y \ x) * a(y,y,y \ x)) = ((1 / y) \ (y \ x)) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(717,a,31406,a)].">
      <j1 rule="hyper" parents="717 31406"/>
    </justification>
  </clause>

  <clause id="31408">
    <literal><![CDATA[
      ((1 / x) \ (x \ y)) * (x \ y) = y * (x \ ((1 / x) \ (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,30231,a,b,31407,a),flip(a)].">
      <j1 rule="hyper" parents="64 30231 31407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31409">
    <literal><![CDATA[
      K(x \ 1,y) * ((a(y,x,x) * x) * z) = (((y / x) / y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(6767(a,1),30529(a,1,1))].">
      <j1 rule="para" parents="6767 30529"/>
    </justification>
  </clause>

  <clause id="31411">
    <literal><![CDATA[
      R((x * L(x \ 1,y,z)) \ 1,x,x) = ((1 / x) \ L(1 / x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(836(a,1),30600(a,1,1,1))].">
      <j1 rule="para" parents="836 30600"/>
    </justification>
  </clause>

  <clause id="31412">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,(u \ w) * x) = L((w / (1 / u)) \ ((w / (1 / u)) / x),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2270,a(flip),b,30707,a)].">
      <j1 rule="hyper" parents="64 2270 30707"/>
    </justification>
  </clause>

  <clause id="31413">
    <literal><![CDATA[
      (x * y) \ (x * (((x * y) \ x) \ 1)) = (x * y) * ((x / (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(30598(a,1),30798(a,2,2))].">
      <j1 rule="para" parents="30598 30798"/>
    </justification>
  </clause>

  <clause id="31414">
    <literal><![CDATA[
      (x * y) * ((x / (1 / y)) \ 1) = y \ (((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,30848,a(flip),b,31413,a),flip(a)].">
      <j1 rule="hyper" parents="64 30848 31413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31415">
    <literal><![CDATA[
      (x / (1 / y)) \ (x * y) = y \ (((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,2954,a(flip),b,31414,a)].">
      <j1 rule="hyper" parents="64 2954 31414"/>
    </justification>
  </clause>

  <clause id="31416">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ 1 = (x / (1 / y)) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30695,a,b,31415,a)].">
      <j1 rule="hyper" parents="373 30695 31415"/>
    </justification>
  </clause>

  <clause id="31417">
    <literal><![CDATA[
      (x * x) * (y \ (((z * y) \ z) \ 1)) = (z / ((x * x) / y)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(31415(a,1),1235(a,1,2))].">
      <j1 rule="para" parents="31415 1235"/>
    </justification>
  </clause>

  <clause id="31418">
    <literal><![CDATA[
      (x * y) \ (x / (1 / y)) = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(40,a,31178,a,b,31416,a)].">
      <j1 rule="hyper" parents="40 31178 31416"/>
    </justification>
  </clause>

  <clause id="31419">
    <literal><![CDATA[
      a(x,y,(((z \ (z / u)) * u) * w) * v5) = a(x,y,(a(u,u,z) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27546,a(flip),b,30817,a)].">
      <j1 rule="hyper" parents="64 27546 30817"/>
    </justification>
  </clause>

  <clause id="31420">
    <literal><![CDATA[
      a(x,y,z \ (((u \ (u / w)) * w) * v5)) = a(x,y,z \ (a(w,w,u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27517,a(flip),b,30818,a)].">
      <j1 rule="hyper" parents="64 27517 30818"/>
    </justification>
  </clause>

  <clause id="31421">
    <literal><![CDATA[
      (((1 / (x / y)) * x) * (x / y)) / y = (y / (x * K(y,y \ x))) \ 1
    ]]></literal>
    <justification jstring="[para(570(a,1),31005(a,1,1,1))].">
      <j1 rule="para" parents="570 31005"/>
    </justification>
  </clause>

  <clause id="31422">
    <literal><![CDATA[
      ((1 / (x / y)) * x) * (x / y) = y * ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(38,a,10634,a(flip),b,31421,a),flip(a)].">
      <j1 rule="hyper" parents="38 10634 31421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31423">
    <literal><![CDATA[
      x * T(L(x,x,x * y) \ 1,y * x) = ((y / (y * x)) * x) \ 1
    ]]></literal>
    <justification jstring="[para(24180(a,1),31304(a,1,2))].">
      <j1 rule="para" parents="24180 31304"/>
    </justification>
  </clause>

  <clause id="31424">
    <literal><![CDATA[
      x * ((y \ ((1 / x) \ y)) \ 1) = ((y / (y * x)) * x) \ 1
    ]]></literal>
    <justification jstring="[para(27229(a,1),31423(a,1,2))].">
      <j1 rule="para" parents="27229 31423"/>
    </justification>
  </clause>

  <clause id="31425">
    <literal><![CDATA[
      x * ((y \ ((1 / x) \ y)) \ 1) = (y / (y * x)) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,31131,a(flip),b,31424,a),flip(a)].">
      <j1 rule="hyper" parents="373 31131 31424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31426">
    <literal><![CDATA[
      ((x \ 1) * (x * (y / (y / z)))) \ y = y / ((x \ 1) * (x * z))
    ]]></literal>
    <justification jstring="[para(3642(a,1),31342(a,1,1))].">
      <j1 rule="para" parents="3642 31342"/>
    </justification>
  </clause>

  <clause id="31427">
    <literal><![CDATA[
      ((K(x,y) \ 1) * (K(x,y) * (z / (z / ((a(u,w,v5) \ 1) * v6))))) \ z = z / ((K(x,y) \ 1) * ((a(u,w,v5) \ K(x,y)) * v6))
    ]]></literal>
    <justification jstring="[para(24366(a,1),31426(a,2,2,2))].">
      <j1 rule="para" parents="24366 31426"/>
    </justification>
  </clause>

  <clause id="31428">
    <literal><![CDATA[
      T(x,(y * (z * u)) * (u \ ((w * z) \ v5))) = T(x,(R(w,z,u) / y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28289,a(flip),b,31346,a)].">
      <j1 rule="hyper" parents="64 28289 31346"/>
    </justification>
  </clause>

  <clause id="31429">
    <literal><![CDATA[
      1 / L(x,x * y,L(y,x,x)) = (1 / R(y,x,x)) * (y * (1 / x))
    ]]></literal>
    <justification jstring="[para(29520(a,1),31357(a,1,2))].">
      <j1 rule="para" parents="29520 31357"/>
    </justification>
  </clause>

  <clause id="31430">
    <literal><![CDATA[
      x \ (y * (y \ ((1 / y) \ (x / y)))) = ((y \ x) / ((y \ x) * y)) * y
    ]]></literal>
    <justification jstring="[para(30249(a,1),31403(a,1,2,2))].">
      <j1 rule="para" parents="30249 31403"/>
    </justification>
  </clause>

  <clause id="31431">
    <literal><![CDATA[
      ((x \ y) / ((x \ y) * x)) * x = y \ ((1 / x) \ (y / x))
    ]]></literal>
    <justification jstring="[para(10(a,1),31430(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 31430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31433">
    <literal><![CDATA[
      x \ ((1 / y) \ (x / y)) = ((x / y) / x) * y
    ]]></literal>
    <justification jstring="[para(10252(a,1),31431(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10252 31431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31434">
    <literal><![CDATA[
      x * (((x / y) / x) * y) = (1 / y) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(157,a,31433,a)].">
      <j1 rule="hyper" parents="157 31433"/>
    </justification>
  </clause>

  <clause id="31435">
    <literal><![CDATA[
      R(x \ (L(1 / x,y,z) \ 1),x,x) = ((1 / x) \ L(1 / x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(9393(a,1),31411(a,1,1))].">
      <j1 rule="para" parents="9393 31411"/>
    </justification>
  </clause>

  <clause id="31436">
    <literal><![CDATA[
      a(x,y,((a(z,u,u) \ 1) * w) * v5) = a(x,y,(a(u,u,z) * w) * v5)
    ]]></literal>
    <justification jstring="[para(30493(a,1),31419(a,1,3,1,1))].">
      <j1 rule="para" parents="30493 31419"/>
    </justification>
  </clause>

  <clause id="31437">
    <literal><![CDATA[
      a(x,y,z \ ((a(u,w,w) \ 1) * v5)) = a(x,y,z \ (a(w,w,u) * v5))
    ]]></literal>
    <justification jstring="[para(30493(a,1),31420(a,1,3,2,1))].">
      <j1 rule="para" parents="30493 31420"/>
    </justification>
  </clause>

  <clause id="31438">
    <literal><![CDATA[
      T(x,y * ((z * u) * (u \ ((w * z) \ v5)))) = T(x,(R(w,z,u) / y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,25009,a(flip),b,31428,a)].">
      <j1 rule="hyper" parents="64 25009 31428"/>
    </justification>
  </clause>

  <clause id="31439">
    <literal><![CDATA[
      R(x \ (L(1 / x,y,z) \ 1),x,x) = (x * L(x \ 1,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(1309(a,1),31435(a,2,1))].">
      <j1 rule="para" parents="1309 31435"/>
    </justification>
  </clause>

  <clause id="31440">
    <literal><![CDATA[
      R(x \ (L(1 / x,y,z) \ 1),x,x) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,9393,a(flip),b,31439,a),flip(a)].">
      <j1 rule="hyper" parents="373 9393 31439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31441">
    <literal><![CDATA[
      T(x,y * (z * (u * (u \ ((w * z) \ v5))))) = T(x,(R(w,z,u) / y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28454,a(flip),b,31438,a)].">
      <j1 rule="hyper" parents="64 28454 31438"/>
    </justification>
  </clause>

  <clause id="31442">
    <literal><![CDATA[
      T(x,(R(y,z,u) / w) \ v5) = T(x,w * (z * ((y * z) \ v5)))
    ]]></literal>
    <justification jstring="[para(10(a,1),31441(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 31441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31443">
    <literal><![CDATA[
      T(x,(R(y,z,u) / w) \ v5) = T(x,w * (y \ v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,28280,a(flip),b,31442,a),flip(a)].">
      <j1 rule="hyper" parents="373 28280 31442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31446">
    <literal><![CDATA[
      T(x,y * (R(z,u,w) \ v5)) = T(x,y * (z \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,24707,a(flip),b,31443,a)].">
      <j1 rule="hyper" parents="64 24707 31443"/>
    </justification>
  </clause>

  <clause id="31447">
    <literal><![CDATA[
      K((x * (y * y)) * K(z,u),T(x,w)) = K(x,K(z,u)) * K(y * y,x)
    ]]></literal>
    <justification jstring="[para(17235(a,1),22987(a,2,1))].">
      <j1 rule="para" parents="17235 22987"/>
    </justification>
  </clause>

  <clause id="31448">
    <literal><![CDATA[
      K((x * (y * y)) * K(z,u),T(x,w)) = K(x,y \ (y \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,17635,a(flip),b,31447,a),flip(a)].">
      <j1 rule="hyper" parents="373 17635 31447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31450">
    <literal><![CDATA[
      K(x * ((y * y) * K(z,u)),T(x,w)) = K(x,y \ (y \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(19513,a,31448,a)].">
      <j1 rule="hyper" parents="19513 31448"/>
    </justification>
  </clause>

  <clause id="31451">
    <literal><![CDATA[
      K(x * (y * (y * K(z,u))),T(x,w)) = K(x,y \ (y \ K(z,u)))
    ]]></literal>
    <justification jstring="[para(23053(a,1),31450(a,1,1,2))].">
      <j1 rule="para" parents="23053 31450"/>
    </justification>
  </clause>

  <clause id="31452">
    <literal><![CDATA[
      K(x * (y * T(y,z)),T(x,u)) = K(x,y \ (y \ K(y \ z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,28552,a(flip),b,31451,a)].">
      <j1 rule="hyper" parents="64 28552 31451"/>
    </justification>
  </clause>

  <clause id="31453">
    <literal><![CDATA[
      K(x,y \ (y \ K(y \ z,y))) = K(y * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26720,a(flip),b,31452,a),flip(a)].">
      <j1 rule="hyper" parents="64 26720 31452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31454">
    <literal><![CDATA[
      L(x \ R(x,y,z),x \ R(x,y,z),u) \ u = u * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(24810(a,1),23552(a,2,2))].">
      <j1 rule="para" parents="24810 23552"/>
    </justification>
  </clause>

  <clause id="31455">
    <literal><![CDATA[
      L(x \ R(x,y,z),x * R(x,y,z),u) \ u = u * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(11865(a,1),31454(a,1,1))].">
      <j1 rule="para" parents="11865 31454"/>
    </justification>
  </clause>

  <clause id="31456">
    <literal><![CDATA[
      L(x,y,y) \ (z * ((1 / y) \ L(x,y,y))) = R(T(z / (1 / y),x),1 / y,y * x)
    ]]></literal>
    <justification jstring="[para(561(a,1),23624(a,1,3)),flip(a)].">
      <j1 rule="para" parents="561 23624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31458">
    <literal><![CDATA[
      (((x \ y) * x) * z) \ ((x \ y) * u) = (y * z) \ ((y / x) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11087,a(flip),b,24165,a),flip(a)].">
      <j1 rule="hyper" parents="64 11087 24165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31459">
    <literal><![CDATA[
      (((x \ y) * x) * z) \ (x \ y) = (y * z) \ ((y / x) * 1)
    ]]></literal>
    <justification jstring="[hyper(341,a,31458,a)].">
      <j1 rule="hyper" parents="341 31458"/>
    </justification>
  </clause>

  <clause id="31460">
    <literal><![CDATA[
      (((x \ y) * x) * z) \ (x \ y) = (y * z) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,177,a(flip),b,31459,a),flip(a)].">
      <j1 rule="hyper" parents="373 177 31459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31461">
    <literal><![CDATA[
      (x * x) \ (R(x \ y,x,x) \ (x \ y)) = (y * x) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,875,a,b,31460,a)].">
      <j1 rule="hyper" parents="64 875 31460"/>
    </justification>
  </clause>

  <clause id="31462">
    <literal><![CDATA[
      ((x * y) \ (z \ (x * (y * z)))) * K(a(x,y,z) * K(z,x * y),(x * y) \ (z \ (x * (y * z)))) = 1 / (1 / ((x * y) \ (z \ (x * (y * z)))))
    ]]></literal>
    <justification jstring="[para(15232(a,1),24246(a,1,2,1))].">
      <j1 rule="para" parents="15232 24246"/>
    </justification>
  </clause>

  <clause id="31463">
    <literal><![CDATA[
      (x / (y \ x)) \ ((y \ x) / x) = ((y \ x) / x) / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(12(a,1),24627(a,1,1,2))].">
      <j1 rule="para" parents="12 24627"/>
    </justification>
  </clause>

  <clause id="31464">
    <literal><![CDATA[
      ((x \ y) / y) / ((x \ 1) \ 1) = x \ ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,207,a(flip),b,31463,a),flip(a)].">
      <j1 rule="hyper" parents="64 207 31463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31467">
    <literal><![CDATA[
      (((x * y) * z) / x) * K(((x * y) * z) \ x,y * z) = 1 / (1 / (((x * y) * z) / x))
    ]]></literal>
    <justification jstring="[para(9(a,1),24677(a,1,2,2,1))].">
      <j1 rule="para" parents="9 24677"/>
    </justification>
  </clause>

  <clause id="31468">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * ((T(y,x) \ 1) \ z)) = (y * ((T(y,x) \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(1175(a,1),24774(a,1,2))].">
      <j1 rule="para" parents="1175 24774"/>
    </justification>
  </clause>

  <clause id="31469">
    <literal><![CDATA[
      x * ((((x \ L(x,y,z)) \ 1) \ L(x,y,z)) \ u) = ((L(x,y,z) \ x) * (L(x,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[para(24800(a,1),11677(a,2,1))].">
      <j1 rule="para" parents="24800 11677"/>
    </justification>
  </clause>

  <clause id="31470">
    <literal><![CDATA[
      T(x / y,x) * ((y / x) * y) = y * K(y \ ((y / x) \ y),y * (x \ y))
    ]]></literal>
    <justification jstring="[para(23046(a,1),24991(a,2,2))].">
      <j1 rule="para" parents="23046 24991"/>
    </justification>
  </clause>

  <clause id="31471">
    <literal><![CDATA[
      K(x \ ((y \ z) * u),T(y * ((y \ z) * u),K(w,v5))) = K(((y \ z) * u) / x,T(z * u,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,28478,a(flip),b,25014,a),flip(a)].">
      <j1 rule="hyper" parents="373 28478 25014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31473">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u \ (x \ u),y * z),x,u) = a((x * u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(29603(a,1),25034(a,1,1))].">
      <j1 rule="para" parents="29603 25034"/>
    </justification>
  </clause>

  <clause id="31474">
    <literal><![CDATA[
      ((x \ 1) * (L(x,y,z) * u)) * x = ((x \ 1) * (x * u)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(23632(a,1),25140(a,1,1))].">
      <j1 rule="para" parents="23632 25140"/>
    </justification>
  </clause>

  <clause id="31475">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * L(x,z,u) = L(y * L(x,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24915,a(flip),b,31474,a),flip(a)].">
      <j1 rule="hyper" parents="64 24915 31474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31476">
    <literal><![CDATA[
      (x \ 1) * (x * (L(x,y,z) \ u)) = L(x,y,z) \ L(u,x,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,5544,a(flip),b,31475,a),flip(a)].">
      <j1 rule="hyper" parents="36 5544 31475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31477">
    <literal><![CDATA[
      (x \ 1) \ (L(x,y,z) \ L(u,x,x)) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(149,a,31476,a)].">
      <j1 rule="hyper" parents="149 31476"/>
    </justification>
  </clause>

  <clause id="31478">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ u),x,x) = x * (L(x,y,z) \ L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,31476,a(flip),b,1148,a),flip(a)].">
      <j1 rule="hyper" parents="145 31476 1148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31479">
    <literal><![CDATA[
      L(x,y,y) * a(L(y,z,u),y \ 1,y * (L(y,z,u) \ x)) = (L(y,z,u) * (y \ 1)) * ((y \ 1) \ (L(y,z,u) \ L(x,y,y)))
    ]]></literal>
    <justification jstring="[para(31477(a,1),960(a,1,2,3))].">
      <j1 rule="para" parents="31477 960"/>
    </justification>
  </clause>

  <clause id="31480">
    <literal><![CDATA[
      ((x * (R(x,y,z) * (x \ (u / x)))) * x) * x = T(x * (R(x,y,z) * u),x)
    ]]></literal>
    <justification jstring="[para(25153(a,1),25259(a,1,1,1,2))].">
      <j1 rule="para" parents="25153 25259"/>
    </justification>
  </clause>

  <clause id="31481">
    <literal><![CDATA[
      K(x \ ((y * z) / y),T(T(K(z,y) * x,z),y)) = K(x \ z,T(x,y))
    ]]></literal>
    <justification jstring="[para(7771(a,1),25265(a,1,2,1))].">
      <j1 rule="para" parents="7771 25265"/>
    </justification>
  </clause>

  <clause id="31482">
    <literal><![CDATA[
      K(x \ ((y * z) / y),T(K(z,y) * x,z * y)) = K(x \ z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,25272,a(flip),b,31481,a)].">
      <j1 rule="hyper" parents="64 25272 31481"/>
    </justification>
  </clause>

  <clause id="31483">
    <literal><![CDATA[
      K(x \ T(y,z),T(K(y,z) * x,y * z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16313,a(flip),b,31482,a)].">
      <j1 rule="hyper" parents="64 16313 31482"/>
    </justification>
  </clause>

  <clause id="31484">
    <literal><![CDATA[
      K(T(x,y) / z,T(K(x,y) * z,y)) = K(z \ x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,25278,a(flip),b,31483,a)].">
      <j1 rule="hyper" parents="64 25278 31483"/>
    </justification>
  </clause>

  <clause id="31485">
    <literal><![CDATA[
      K(x \ T(y,z),T(x * K(y,z),z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11227,a(flip),b,31484,a)].">
      <j1 rule="hyper" parents="64 11227 31484"/>
    </justification>
  </clause>

  <clause id="31486">
    <literal><![CDATA[
      (a(x,x,y) * a(x,x,y)) \ (z \ y) = z \ ((a(x,x,y) \ 1) * L(y,x,x))
    ]]></literal>
    <justification jstring="[para(13923(a,1),25320(a,2,2,1))].">
      <j1 rule="para" parents="13923 25320"/>
    </justification>
  </clause>

  <clause id="31487">
    <literal><![CDATA[
      R(x,y,z) \ (R(T(T(x,u),w),y,z) * v5) = (x \ T(T(x,u),w)) * v5
    ]]></literal>
    <justification jstring="[hyper(373,a,24900,a(flip),b,25433,a),flip(a)].">
      <j1 rule="hyper" parents="373 24900 25433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31488">
    <literal><![CDATA[
      R(x,y,z) \ R(T(T(x,u),w),y,z) = x \ T(T(x,u),w)
    ]]></literal>
    <justification jstring="[hyper(3740,a,31487,a)].">
      <j1 rule="hyper" parents="3740 31487"/>
    </justification>
  </clause>

  <clause id="31489">
    <literal><![CDATA[
      (((x * x) \ y) * R(y \ x,z,u)) * x = (1 / x) * (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(484(a,1),25504(a,1,1))].">
      <j1 rule="para" parents="484 25504"/>
    </justification>
  </clause>

  <clause id="31490">
    <literal><![CDATA[
      ((x / y) / x) / T(1 / y,K(x,y)) = (1 / y) \ ((x / y) / x)
    ]]></literal>
    <justification jstring="[para(22644(a,1),25543(a,1,2))].">
      <j1 rule="para" parents="22644 25543"/>
    </justification>
  </clause>

  <clause id="31491">
    <literal><![CDATA[
      ((x / y) / x) / (1 / y) = (1 / y) \ ((x / y) / x)
    ]]></literal>
    <justification jstring="[para(3343(a,1),31490(a,1,2))].">
      <j1 rule="para" parents="3343 31490"/>
    </justification>
  </clause>

  <clause id="31492">
    <literal><![CDATA[
      (1 / x) \ ((y / x) / y) = ((y / x) / y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,14920,a(flip),b,31491,a),flip(a)].">
      <j1 rule="hyper" parents="64 14920 31491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31494">
    <literal><![CDATA[
      ((x / (y \ 1)) / x) * (y \ 1) = y \ ((x / (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,207,a(flip),b,31492,a),flip(a)].">
      <j1 rule="hyper" parents="64 207 31492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31495">
    <literal><![CDATA[
      (((x / (1 / (1 / y))) / x) * (1 / (1 / y))) \ (y * z) = (y \ ((x / (1 / (1 / y))) / x)) \ ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(31492(a,1),3407(a,1,1))].">
      <j1 rule="para" parents="31492 3407"/>
    </justification>
  </clause>

  <clause id="31496">
    <literal><![CDATA[
      ((x / (y \ 1)) / x) / y = y \ ((x / (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,14921,a(flip),b,31494,a)].">
      <j1 rule="hyper" parents="64 14921 31494"/>
    </justification>
  </clause>

  <clause id="31497">
    <literal><![CDATA[
      T(x,K(y * T(z,y),u) * (w / u)) = T(x,w / T(u * K(y,u),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,25904,a(flip),b,25745,a)].">
      <j1 rule="hyper" parents="64 25904 25745"/>
    </justification>
  </clause>

  <clause id="31498">
    <literal><![CDATA[
      T(x,y / T(z * K(u,z),w)) = T(x,K(w * u,z) * (y / z))
    ]]></literal>
    <justification jstring="[para(115(a,1),31497(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="115 31497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31499">
    <literal><![CDATA[
      T(x,y / T(z * K(u,z),w)) = T(x,y / T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,17211,a(flip),b,31498,a),flip(a)].">
      <j1 rule="hyper" parents="373 17211 31498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31500">
    <literal><![CDATA[
      T(x,y / T(T(z,u),w)) = T(x,y / T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16315,a(flip),b,31499,a)].">
      <j1 rule="hyper" parents="64 16315 31499"/>
    </justification>
  </clause>

  <clause id="31501">
    <literal><![CDATA[
      T(x,y / T(z \ 1,u * w)) = T(x,y * T(T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,28005,a(flip),b,31500,a),flip(a)].">
      <j1 rule="hyper" parents="64 28005 31500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31502">
    <literal><![CDATA[
      T(x,y * T(T(z,u),w)) = T(x,y * T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,17717,a(flip),b,31501,a),flip(a)].">
      <j1 rule="hyper" parents="64 17717 31501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31503">
    <literal><![CDATA[
      T(x,(y \ 1) * T(z,u * w)) = T(x,y \ T(T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(14732,a,31502,a),flip(a)].">
      <j1 rule="hyper" parents="14732 31502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31504">
    <literal><![CDATA[
      T(x,y * T(z * (u / z),w)) = T(x,y * T(u,z * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17684,a,b,31502,a)].">
      <j1 rule="hyper" parents="64 17684 31502"/>
    </justification>
  </clause>

  <clause id="31505">
    <literal><![CDATA[
      K(x,T(y * (T(T(z,u),w) \ z),z * T(z,w * u))) = K(x,(z / T(T(z,u),w)) * y)
    ]]></literal>
    <justification jstring="[para(31502(a,1),17633(a,1,2))].">
      <j1 rule="para" parents="31502 17633"/>
    </justification>
  </clause>

  <clause id="31506">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),w)) = T(x,y \ T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(14732,a,31503,a),flip(a)].">
      <j1 rule="hyper" parents="14732 31503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31507">
    <literal><![CDATA[
      (x \ y) / (T(x,z \ T(u,w * v5)) \ y) = K(x,z \ T(T(u,v5),w))
    ]]></literal>
    <justification jstring="[para(31506(a,1),6136(a,1,2,1))].">
      <j1 rule="para" parents="31506 6136"/>
    </justification>
  </clause>

  <clause id="31508">
    <literal><![CDATA[
      T(x,(y / z) * T(z,u * w)) = T(x,z * (T(T(z,u),w) \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,19743,a(flip),b,31504,a),flip(a)].">
      <j1 rule="hyper" parents="64 19743 31504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31509">
    <literal><![CDATA[
      T(x,y * (T(T(y,z),u) \ w)) = T(x,w * K(y,z * u))
    ]]></literal>
    <justification jstring="[para(6840(a,1),31508(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6840 31508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31510">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),w)) = K(x,y \ T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,6136,a(flip),b,31507,a),flip(a)].">
      <j1 rule="hyper" parents="64 6136 31507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31511">
    <literal><![CDATA[
      K(x,(y \ z) \ T(u,w * y)) = K(x,z \ (T(u,w) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,24236,a(flip),b,31510,a),flip(a)].">
      <j1 rule="hyper" parents="64 24236 31510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31512">
    <literal><![CDATA[
      K(x,y \ (z * T(u,w * z))) = K(x,y \ (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,23043,a(flip),b,31511,a)].">
      <j1 rule="hyper" parents="64 23043 31511"/>
    </justification>
  </clause>

  <clause id="31513">
    <literal><![CDATA[
      K(x,y \ (T(z,u \ w) * (w \ u))) = K(x,y \ ((w \ u) * z))
    ]]></literal>
    <justification jstring="[para(9462(a,1),31512(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="9462 31512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31514">
    <literal><![CDATA[
      K(x,(y \ T(z,u \ w)) * (w \ u)) = K(x,y \ ((w \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,24234,a(flip),b,31513,a)].">
      <j1 rule="hyper" parents="64 24234 31513"/>
    </justification>
  </clause>

  <clause id="31515">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,25469,a(flip),b,31514,a)].">
      <j1 rule="hyper" parents="64 25469 31514"/>
    </justification>
  </clause>

  <clause id="31516">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ w)) = K(x,(y \ (u \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,24234,a(flip),b,31515,a),flip(a)].">
      <j1 rule="hyper" parents="373 24234 31515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31519">
    <literal><![CDATA[
      T(x \ y,x * ((x \ y) \ y)) / (y * x) = (x \ y) / T(y * x,x \ y)
    ]]></literal>
    <justification jstring="[para(371(a,1),25764(a,1,1,2))].">
      <j1 rule="para" parents="371 25764"/>
    </justification>
  </clause>

  <clause id="31520">
    <literal><![CDATA[
      x \ ((y \ (y \ K(y \ 1,z))) * u) = ((T(y \ 1,z) \ y) * x) \ u
    ]]></literal>
    <justification jstring="[para(22784(a,1),25797(a,1,2))].">
      <j1 rule="para" parents="22784 25797"/>
    </justification>
  </clause>

  <clause id="31521">
    <literal><![CDATA[
      ((T(x \ 1,y) \ x) * z) \ u = z \ ((x \ T(x \ 1,y)) * u)
    ]]></literal>
    <justification jstring="[para(5762(a,1),31520(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5762 31520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31522">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ x)) * (x \ K(w,v5)) = a(y,z,u) \ (x \ K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,24310,a(flip),b,25903,a),flip(a)].">
      <j1 rule="hyper" parents="373 24310 25903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31523">
    <literal><![CDATA[
      L(x,y,R(y,z,u)) * (R(y,z,u) \ y) = (1 / R(y,z,u)) * (y * x)
    ]]></literal>
    <justification jstring="[para(2835(a,1),25928(a,1,2))].">
      <j1 rule="para" parents="2835 25928"/>
    </justification>
  </clause>

  <clause id="31524">
    <literal><![CDATA[
      (1 / R(x,y,z)) * (x * u) = x * ((R(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25935,a(flip),b,31523,a),flip(a)].">
      <j1 rule="hyper" parents="64 25935 31523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31525">
    <literal><![CDATA[
      1 / L(x,x * y,L(y,x,x)) = y * ((R(y,x,x) \ 1) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,31429,a,b,31524,a)].">
      <j1 rule="hyper" parents="64 31429 31524"/>
    </justification>
  </clause>

  <clause id="31526">
    <literal><![CDATA[
      1 / L(x,x * y,L(y,x,x)) = y * ((y \ 1) / x)
    ]]></literal>
    <justification jstring="[para(30593(a,1),31525(a,2,2))].">
      <j1 rule="para" parents="30593 31525"/>
    </justification>
  </clause>

  <clause id="31527">
    <literal><![CDATA[
      (1 / ((x * y) * x)) * (x * y) = y * ((y \ 1) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,21693,a(flip),b,31526,a)].">
      <j1 rule="hyper" parents="64 21693 31526"/>
    </justification>
  </clause>

  <clause id="31528">
    <literal><![CDATA[
      L(x,x * y,L(y,x,x)) = L(x,x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(37,a,10275,a,b,31526,a),flip(a)].">
      <j1 rule="hyper" parents="37 10275 31526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31529">
    <literal><![CDATA[
      a(L(x,x * y,x * y),z,u) = a(L(x,x \ y,y),z,u)
    ]]></literal>
    <justification jstring="[para(31528(a,1),26884(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31528 26884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31530">
    <literal><![CDATA[
      ((x * ((x \ 1) / y)) / z) \ (((1 / ((y * x) * y)) * ((y * x) * z)) / z) = L(z,y * x,1 / ((y * x) * y))
    ]]></literal>
    <justification jstring="[para(31527(a,1),3209(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="31527 3209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31531">
    <literal><![CDATA[
      L(x * (T(y \ 1,z) * y),u,w) = L(x,u,w) * (T(y \ 1,z) * y)
    ]]></literal>
    <justification jstring="[para(17393(a,1),26081(a,1,1,2))].">
      <j1 rule="para" parents="17393 26081"/>
    </justification>
  </clause>

  <clause id="31532">
    <literal><![CDATA[
      R(x,y,(z * z) * (T(u * w,u) \ v5)) = R(x,y,(u * ((z * z) \ w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26211,a(flip),b,26239,a)].">
      <j1 rule="hyper" parents="64 26211 26239"/>
    </justification>
  </clause>

  <clause id="31533">
    <literal><![CDATA[
      R(x,y,((z \ u) * (u / z)) \ (u \ u)) = R(x,y,u \ ((1 / (z \ u)) * z))
    ]]></literal>
    <justification jstring="[para(28017(a,1),26313(a,1,3))].">
      <j1 rule="para" parents="28017 26313"/>
    </justification>
  </clause>

  <clause id="31534">
    <literal><![CDATA[
      R(x,K(y,z) * (((z * u) * w) \ v5),v6) = R(x,((T(z,y) * u) * w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(24525(a,1),26527(a,1,2))].">
      <j1 rule="para" parents="24525 26527"/>
    </justification>
  </clause>

  <clause id="31535">
    <literal><![CDATA[
      (x * R(y,z,u)) / (y \ R(y,z,u)) = R(x / (1 / y),y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,2975,a(flip),b,26621,a),flip(a)].">
      <j1 rule="hyper" parents="64 2975 26621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31536">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (u * R(x,y,z)) = R(u / (1 / x),x,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,23705,a(flip),b,31535,a)].">
      <j1 rule="hyper" parents="64 23705 31535"/>
    </justification>
  </clause>

  <clause id="31537">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (u * R(x,y,z)) = R(u / (1 / x),x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,26360,a(flip),b,31536,a),flip(a)].">
      <j1 rule="hyper" parents="373 26360 31536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31538">
    <literal><![CDATA[
      (x * L(y,z,u)) / (y \ L(y,z,u)) = R(x / (1 / y),y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,2975,a(flip),b,26622,a),flip(a)].">
      <j1 rule="hyper" parents="64 2975 26622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31539">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (u * L(x,y,z)) = R(u / (1 / x),x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,23740,a(flip),b,31538,a)].">
      <j1 rule="hyper" parents="64 23740 31538"/>
    </justification>
  </clause>

  <clause id="31540">
    <literal><![CDATA[
      L((x \ 1) \ T(y,L(x,z,u)),x,L(x,z,u)) = R(y / (1 / x),x,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,12016,a,b,31539,a)].">
      <j1 rule="hyper" parents="64 12016 31539"/>
    </justification>
  </clause>

  <clause id="31541">
    <literal><![CDATA[
      T((x \ 1) \ ((1 / x) \ y),K(1,x) * x) = (x \ 1) \ ((x \ 1) \ T(y,x))
    ]]></literal>
    <justification jstring="[para(2455(a,1),26735(a,1,1))].">
      <j1 rule="para" parents="2455 26735"/>
    </justification>
  </clause>

  <clause id="31542">
    <literal><![CDATA[
      a(L(x * x,y,z) \ u,w,v5) = a(a(z,y,x * x) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(31255(a,1),26906(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="31255 26906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31543">
    <literal><![CDATA[
      a(a(x,y,z * z) * u,w,v5) = a(u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,4185,a(flip),b,31542,a),flip(a)].">
      <j1 rule="hyper" parents="64 4185 31542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31545">
    <literal><![CDATA[
      x * ((a(x,x,y) * R(x,x,y)) \ z) = (a(x,x,y) * a(x,x,y)) \ z
    ]]></literal>
    <justification jstring="[para(30224(a,1),26958(a,1,2,1))].">
      <j1 rule="para" parents="30224 26958"/>
    </justification>
  </clause>

  <clause id="31546">
    <literal><![CDATA[
      (a(x,x,y) * a(x,x,y)) \ z = x * (R(R(x,x,y),x,y) \ z)
    ]]></literal>
    <justification jstring="[para(30770(a,1),31545(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30770 31545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31547">
    <literal><![CDATA[
      R((a(x,x,y) * a(x,x,y)) \ R(x,x,y),x,y) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,2054,a,b,31546,a(flip))].">
      <j1 rule="hyper" parents="36 2054 31546"/>
    </justification>
  </clause>

  <clause id="31548">
    <literal><![CDATA[
      R(R((a(x,x,y) * a(x,x,y)) \ x,x,y),x,y) = x
    ]]></literal>
    <justification jstring="[para(2051(a,2),31547(a,1,1))].">
      <j1 rule="para" parents="2051 31547"/>
    </justification>
  </clause>

  <clause id="31549">
    <literal><![CDATA[
      R(a(x,x,y) \ x,x,y) = x
    ]]></literal>
    <justification jstring="[para(30928(a,1),31548(a,1,1))].">
      <j1 rule="para" parents="30928 31548"/>
    </justification>
  </clause>

  <clause id="31550">
    <literal><![CDATA[
      R(a(x,x,y) \ x,x,y) * ((a(x,x,y) \ x) \ z) = (a(x,x,y) \ x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(31549(a,1),1898(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="31549 1898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31551">
    <literal><![CDATA[
      L((a(x,x,y) \ x) \ x,z,u) \ L(R(a(x,x,y) \ x,x,y),z,u) = L(a(x,x,y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(31549(a,1),4251(a,1,1,1,2))].">
      <j1 rule="para" parents="31549 4251"/>
    </justification>
  </clause>

  <clause id="31552">
    <literal><![CDATA[
      (x * (a(y,y,y \ x) \ y)) * a(a(y,y,y \ x) \ y,y,y \ x) = x * y
    ]]></literal>
    <justification jstring="[para(31549(a,1),16045(a,2,2))].">
      <j1 rule="para" parents="31549 16045"/>
    </justification>
  </clause>

  <clause id="31554">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * ((x \ 1) \ u)) = (x * (L(x,y,z) \ x)) * u
    ]]></literal>
    <justification jstring="[para(9372(a,1),26999(a,2,1))].">
      <j1 rule="para" parents="9372 26999"/>
    </justification>
  </clause>

  <clause id="31555">
    <literal><![CDATA[
      T((x \ L(x * y,z,u)) \ y,w) = (x \ L(x * y,z,u)) \ y
    ]]></literal>
    <justification jstring="[para(1389(a,1),27011(a,2,1))].">
      <j1 rule="para" parents="1389 27011"/>
    </justification>
  </clause>

  <clause id="31556">
    <literal><![CDATA[
      T(x,y * y) \ L(T(x,z),u,w) = x \ L(T(x,y \ (y \ z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,23442,a(flip),b,27034,a),flip(a)].">
      <j1 rule="hyper" parents="64 23442 27034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31557">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ (1 / x),z,u) = (y / (1 / x)) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,876,a(flip),b,27052,a),flip(a)].">
      <j1 rule="hyper" parents="373 876 27052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31558">
    <literal><![CDATA[
      (x / (1 / y)) \ R(x,z,u) = (x \ R(x,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,28021,a(flip),b,31557,a),flip(a)].">
      <j1 rule="hyper" parents="64 28021 31557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31559">
    <literal><![CDATA[
      R(x,y,z) / ((1 / u) \ x) = (x \ R(x,y,z)) / u
    ]]></literal>
    <justification jstring="[hyper(64,a,27050,a,b,31558,a)].">
      <j1 rule="hyper" parents="64 27050 31558"/>
    </justification>
  </clause>

  <clause id="31560">
    <literal><![CDATA[
      (x \ R(x,y,z)) / (u \ 1) = (x / u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),31558(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 31558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31561">
    <literal><![CDATA[
      ((x \ R(x,y,z)) / u) \ R(x,y,z) = (1 / u) \ x
    ]]></literal>
    <justification jstring="[hyper(215,a,31559,a)].">
      <j1 rule="hyper" parents="215 31559"/>
    </justification>
  </clause>

  <clause id="31562">
    <literal><![CDATA[
      (1 / x) \ (y \ R(y,z,u)) = (y / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28882,a(flip),b,31560,a)].">
      <j1 rule="hyper" parents="64 28882 31560"/>
    </justification>
  </clause>

  <clause id="31566">
    <literal><![CDATA[
      (x \ R(x,y,z)) / (u \ R(x,y,z)) = 1 / (u \ x)
    ]]></literal>
    <justification jstring="[hyper(225,a,207,a(flip),b,31562,a)].">
      <j1 rule="hyper" parents="225 207 31562"/>
    </justification>
  </clause>

  <clause id="31567">
    <literal><![CDATA[
      (1 / (x \ y)) * (x \ R(y,z,u)) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,207,a(flip),b,31562,a)].">
      <j1 rule="hyper" parents="145 207 31562"/>
    </justification>
  </clause>

  <clause id="31568">
    <literal><![CDATA[
      L(x,x,x) \ (y \ R(y,z,u)) = (y / (1 / x)) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,823,a,b,31562,a)].">
      <j1 rule="hyper" parents="64 823 31562"/>
    </justification>
  </clause>

  <clause id="31569">
    <literal><![CDATA[
      (x / (y \ 1)) \ R(x,z,u) = y \ (x \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,207,a(flip),b,31562,a),flip(a)].">
      <j1 rule="hyper" parents="64 207 31562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31570">
    <literal><![CDATA[
      (1 / (x \ y)) \ a(y,z,z) = x \ R(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,15987,a(flip),b,31567,a)].">
      <j1 rule="hyper" parents="139 15987 31567"/>
    </justification>
  </clause>

  <clause id="31571">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ u) \ R(u,w,v5) = a(x,y,z) \ (u \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(23737(a,1),31569(a,1,1))].">
      <j1 rule="para" parents="23737 31569"/>
    </justification>
  </clause>

  <clause id="31572">
    <literal><![CDATA[
      L(x,x,x) \ (y \ R(y,z,u)) = (y \ R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,31558,a(flip),b,31568,a),flip(a)].">
      <j1 rule="hyper" parents="373 31558 31568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31573">
    <literal><![CDATA[
      L((x / (x * y)) \ L(y \ z,y,y),u,w * w) = R(T(y,x),y,x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(569(a,2),27075(a,1,1,2))].">
      <j1 rule="para" parents="569 27075"/>
    </justification>
  </clause>

  <clause id="31574">
    <literal><![CDATA[
      ((x * y) / (x / y)) * (x * y) = (x * y) * ((x / y) \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,25774,a(flip),b,27189,a),flip(a)].">
      <j1 rule="hyper" parents="64 25774 27189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31575">
    <literal><![CDATA[
      T((x / T(x * y,y)) \ 1,y) = ((x / y) / T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,24576,a(flip),b,27205,a)].">
      <j1 rule="hyper" parents="64 24576 27205"/>
    </justification>
  </clause>

  <clause id="31577">
    <literal><![CDATA[
      T((x / T(x * y,y)) \ 1,y) = (x / T(x * y,y)) \ 1
    ]]></literal>
    <justification jstring="[para(27202(a,1),31575(a,2,1))].">
      <j1 rule="para" parents="27202 31575"/>
    </justification>
  </clause>

  <clause id="31578">
    <literal><![CDATA[
      a(x,y,(z * z) * (u \ T(w * v5,w))) = a(x,y,u \ (w * ((z * z) * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27668,a(flip),b,27437,a)].">
      <j1 rule="hyper" parents="64 27668 27437"/>
    </justification>
  </clause>

  <clause id="31579">
    <literal><![CDATA[
      a(x,y,(z * z) * (T(u * w,u) \ v5)) = a(x,y,(u * ((z * z) \ w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27541,a(flip),b,27449,a)].">
      <j1 rule="hyper" parents="64 27541 27449"/>
    </justification>
  </clause>

  <clause id="31580">
    <literal><![CDATA[
      a(x,y,(z \ ((z \ 1) \ (u * z))) \ w) = a(x,y,((z \ 1) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27405,a(flip),b,27560,a),flip(a)].">
      <j1 rule="hyper" parents="373 27405 27560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31582">
    <literal><![CDATA[
      a(x,y,z \ ((u / (u * w)) \ v5)) = a(x,y,z \ ((u \ (w \ u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27491,a(flip),b,27751,a)].">
      <j1 rule="hyper" parents="64 27491 27751"/>
    </justification>
  </clause>

  <clause id="31584">
    <literal><![CDATA[
      a(x,y,z \ (((u * w) \ u) \ v5)) = a(x,y,z \ ((u \ (w \ u)) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27511,a(flip),b,31582,a)].">
      <j1 rule="hyper" parents="64 27511 31582"/>
    </justification>
  </clause>

  <clause id="31585">
    <literal><![CDATA[
      (x / (y * x)) * ((1 / y) \ (z * (y \ 1))) = z * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(3032(a,1),27829(a,2,2))].">
      <j1 rule="para" parents="3032 27829"/>
    </justification>
  </clause>

  <clause id="31586">
    <literal><![CDATA[
      L((x \ 1) \ a(x,y,z),x,a(x,y,z)) = (x \ (a(x,y,z) \ 1)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,24631,a(flip),b,27847,a)].">
      <j1 rule="hyper" parents="64 24631 27847"/>
    </justification>
  </clause>

  <clause id="31587">
    <literal><![CDATA[
      x * (L(x,x \ y,y) \ T(x,x \ 1)) = T(x,x \ 1) * a(y,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,28750,a(flip),b,27956,a),flip(a)].">
      <j1 rule="hyper" parents="373 28750 27956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31588">
    <literal><![CDATA[
      (1 / x) * ((1 / L(x,y,z)) \ u) = (x \ 1) * ((L(x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(35,a,310,a,b,28006,a)].">
      <j1 rule="hyper" parents="35 310 28006"/>
    </justification>
  </clause>

  <clause id="31589">
    <literal><![CDATA[
      (x \ 1) * ((L(x,y,y) \ 1) \ z) = x * ((x * a(y,y,x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,28019,a(flip),b,31588,a),flip(a)].">
      <j1 rule="hyper" parents="64 28019 31588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31590">
    <literal><![CDATA[
      (x \ 1) * ((L(x,y,y) \ 1) \ z) = x * ((a(y,y,x) * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,24797,a,b,31589,a),flip(a)].">
      <j1 rule="hyper" parents="373 24797 31589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31591">
    <literal><![CDATA[
      K(x,y \ T(z * (u / w),w)) = K(x,w \ ((z \ T(y,w)) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,28036,a(flip),b,28030,a),flip(a)].">
      <j1 rule="hyper" parents="64 28036 28030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31592">
    <literal><![CDATA[
      K(x,y \ T(z * (u / w),w)) = K(x,(w \ (T(y,w) \ z)) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,31516,a(flip),b,31591,a),flip(a)].">
      <j1 rule="hyper" parents="373 31516 31591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31593">
    <literal><![CDATA[
      K(x,T(y \ (((z \ u) \ u) \ w),K(v5,v6))) = K(x,T(w / (T(z,u) * y),w))
    ]]></literal>
    <justification jstring="[hyper(373,a,23505,a(flip),b,28035,a),flip(a)].">
      <j1 rule="hyper" parents="373 23505 28035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31594">
    <literal><![CDATA[
      T(K(x * x,y) * (y \ (x \ (x \ y))),z) = T((x \ (x \ y)) / y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17063,a,b,28445,a)].">
      <j1 rule="hyper" parents="64 17063 28445"/>
    </justification>
  </clause>

  <clause id="31595">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) * (a(y,z,u) / y) = a(y,z,u) * (x * (1 / y))
    ]]></literal>
    <justification jstring="[para(25236(a,1),28829(a,1,2))].">
      <j1 rule="para" parents="25236 28829"/>
    </justification>
  </clause>

  <clause id="31596">
    <literal><![CDATA[
      L(x,y,a(y,y,z)) * R(1 / y,y,z) = a(y,y,z) * (x * (1 / y))
    ]]></literal>
    <justification jstring="[para(30081(a,2),31595(a,1,2))].">
      <j1 rule="para" parents="30081 31595"/>
    </justification>
  </clause>

  <clause id="31597">
    <literal><![CDATA[
      (R(x,y,y) * z) \ (a(x,y,y) * (x * z)) = a(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(16012(a,1),28842(a,1,2))].">
      <j1 rule="para" parents="16012 28842"/>
    </justification>
  </clause>

  <clause id="31598">
    <literal><![CDATA[
      (R(x,y,y) * (x \ z)) \ (z * a(x,y,y)) = a(x \ z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(23182(a,1),31597(a,1,2))].">
      <j1 rule="para" parents="23182 31597"/>
    </justification>
  </clause>

  <clause id="31599">
    <literal><![CDATA[
      (1 / x) * (a(y,x,x) \ y) = (y / x) * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(30575(a,1),28855(a,1,1))].">
      <j1 rule="para" parents="30575 28855"/>
    </justification>
  </clause>

  <clause id="31600">
    <literal><![CDATA[
      L(x * a(y,z,u),x,a(y,z,u)) = x * (x * (((a(y,z,u) \ 1) * x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(157,a,28867,a),flip(a)].">
      <j1 rule="hyper" parents="157 28867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31601">
    <literal><![CDATA[
      L(a(x,y,z) / u,u,a(x,y,z)) = 1 / ((a(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(36,a,836,a,b,28925,a(flip))].">
      <j1 rule="hyper" parents="36 836 28925"/>
    </justification>
  </clause>

  <clause id="31602">
    <literal><![CDATA[
      L(a(x,y,z) * u,L(u \ 1,u,a(x,y,z)),a(x,y,z)) = 1 / ((a(x,y,z) \ 1) * L(u \ 1,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(441(a,1),31601(a,1,1))].">
      <j1 rule="para" parents="441 31601"/>
    </justification>
  </clause>

  <clause id="31603">
    <literal><![CDATA[
      (x \ 1) * (y * ((x \ R(x,z,u)) / y)) = R(x \ K(y,y \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(5101(a,1),28930(a,2,1))].">
      <j1 rule="para" parents="5101 28930"/>
    </justification>
  </clause>

  <clause id="31604">
    <literal><![CDATA[
      K(x,R(T(y / z,u),z,y \ 1) * w) = K(x,y * ((z \ w) * K(z * y,u)))
    ]]></literal>
    <justification jstring="[para(1031(a,1),28932(a,1,2,1))].">
      <j1 rule="para" parents="1031 28932"/>
    </justification>
  </clause>

  <clause id="31605">
    <literal><![CDATA[
      (x \ (y / (y \ x))) * x = T(y / (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(37,a,28901,a,b,28947,a),flip(a)].">
      <j1 rule="hyper" parents="37 28901 28947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31606">
    <literal><![CDATA[
      T(x \ (y / (y \ x)),x) = x \ T(y / (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(493,a,xx,b,31605,a)].">
      <j1 rule="hyper" parents="493 31605"/>
    </justification>
  </clause>

  <clause id="31607">
    <literal><![CDATA[
      L(x,y,L(R(z,u,z) \ 1,z,u) * w) = L(x,y,((u / z) / u) * w)
    ]]></literal>
    <justification jstring="[para(26367(a,1),29078(a,2,3,1))].">
      <j1 rule="para" parents="26367 29078"/>
    </justification>
  </clause>

  <clause id="31608">
    <literal><![CDATA[
      L(x,y,L(R(z,u,z) \ 1,z,u) * w) = L(x,y,(u \ (z \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29244,a(flip),b,31607,a),flip(a)].">
      <j1 rule="hyper" parents="373 29244 31607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31609">
    <literal><![CDATA[
      L(x,y,(T(z * u,z) \ u) * w) = L(x,y,(u \ (z \ u)) * w)
    ]]></literal>
    <justification jstring="[para(14173(a,1),31608(a,1,3,1))].">
      <j1 rule="para" parents="14173 31608"/>
    </justification>
  </clause>

  <clause id="31610">
    <literal><![CDATA[
      L(x,y,((z * u) \ u) * w) = L(x,y,(u \ (z \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28995,a(flip),b,31609,a)].">
      <j1 rule="hyper" parents="64 28995 31609"/>
    </justification>
  </clause>

  <clause id="31611">
    <literal><![CDATA[
      L(x,y,z * ((u * (w \ 1)) \ u)) = L(x,y,(u \ (w \ u)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29374,a,b,31610,a)].">
      <j1 rule="hyper" parents="64 29374 31610"/>
    </justification>
  </clause>

  <clause id="31613">
    <literal><![CDATA[
      L(x,y,(z \ (u \ z)) * w) = L(x,y,w * L(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29237,a,b,31611,a),flip(a)].">
      <j1 rule="hyper" parents="64 29237 31611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31614">
    <literal><![CDATA[
      K(x / (y * T(y,z)),x) = K(x,y * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(358,a,29252,a)].">
      <j1 rule="hyper" parents="358 29252"/>
    </justification>
  </clause>

  <clause id="31615">
    <literal><![CDATA[
      K(x / (y * T(y,z)),x) = K(x,y * T(y,z)) * 1
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a,b,31614,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 31614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31616">
    <literal><![CDATA[
      K(x / (y * T(y,z)),x) = K(x,y * T(y,z)) * a(u,w * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(26598(a,2),31615(a,2,2))].">
      <j1 rule="para" parents="26598 31615"/>
    </justification>
  </clause>

  <clause id="31617">
    <literal><![CDATA[
      K(x / (y * T(y,z)),x) = K(x,y * T(y,z)) * a(u,(w * T(w,v5)) \ 1,v6)
    ]]></literal>
    <justification jstring="[para(11980(a,2),31616(a,2,2))].">
      <j1 rule="para" parents="11980 31616"/>
    </justification>
  </clause>

  <clause id="31618">
    <literal><![CDATA[
      L(((x / y) / x) * y,a(z,u,w),a(y,y,x)) = ((x / y) / x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,30112,a(flip),b,29253,a)].">
      <j1 rule="hyper" parents="64 30112 29253"/>
    </justification>
  </clause>

  <clause id="31619">
    <literal><![CDATA[
      L(x,y,(z \ (u * (1 / w))) * v5) = L(x,y,(z \ (w * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29097,a(flip),b,29260,a),flip(a)].">
      <j1 rule="hyper" parents="64 29097 29260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31621">
    <literal><![CDATA[
      L(x,y,(z \ (u * (w \ 1))) * v5) = L(x,y,(z \ (w * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29345,a(flip),b,31619,a)].">
      <j1 rule="hyper" parents="64 29345 31619"/>
    </justification>
  </clause>

  <clause id="31622">
    <literal><![CDATA[
      L(x,y,z * (u \ ((w \ 1) * v5))) = L(x,y,(u \ (w * v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29367,a(flip),b,31621,a)].">
      <j1 rule="hyper" parents="64 29367 31621"/>
    </justification>
  </clause>

  <clause id="31623">
    <literal><![CDATA[
      L(x,y,(z \ ((u \ 1) * w)) * v5) = L(x,y,(z \ (u * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(24201,a,31622,a)].">
      <j1 rule="hyper" parents="24201 31622"/>
    </justification>
  </clause>

  <clause id="31624">
    <literal><![CDATA[
      R(((x * y) \ x) / y,y,y) = ((x * y) \ x) / y
    ]]></literal>
    <justification jstring="[para(29118(a,1),29277(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29118 29277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31625">
    <literal><![CDATA[
      ((x * y) * y) * L(z,x,x * L(x,y,y)) = (((x * y) * y) / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(5608(a,1),29306(a,1,2))].">
      <j1 rule="para" parents="5608 29306"/>
    </justification>
  </clause>

  <clause id="31626">
    <literal><![CDATA[
      L(x,y,z \ ((u * a(w,w,u)) \ v5)) = L(x,y,z \ (L(u,w,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,29359,a(flip),b,29370,a),flip(a)].">
      <j1 rule="hyper" parents="64 29359 29370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31627">
    <literal><![CDATA[
      L(x,y,z * (u \ (((1 / w) \ 1) \ v5))) = L(x,y,z * (u \ ((w \ 1) \ v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29242,a(flip),b,29410,a)].">
      <j1 rule="hyper" parents="64 29242 29410"/>
    </justification>
  </clause>

  <clause id="31628">
    <literal><![CDATA[
      L(x,y \ (z / (u \ K(w,v5))),v6) = L(x,y \ ((u \ 1) \ z),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29556,a(flip),b,29594,a),flip(a)].">
      <j1 rule="hyper" parents="64 29556 29594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31630">
    <literal><![CDATA[
      L(x,y \ (z / (u \ K(w,v5))),v6) = L(x,y \ (u \ z),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,30873,a(flip),b,31628,a),flip(a)].">
      <j1 rule="hyper" parents="373 30873 31628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31631">
    <literal><![CDATA[
      L(x,y \ ((z \ K(u,w)) \ v5),v6) = L(x,y \ (z \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29552,a(flip),b,31630,a)].">
      <j1 rule="hyper" parents="64 29552 31630"/>
    </justification>
  </clause>

  <clause id="31632">
    <literal><![CDATA[
      L(x,y \ ((z \ (((1 / u) * z) * u)) \ w),v5) = L(x,y \ (a(u,u,z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(26403(a,1),31631(a,1,2,2,1))].">
      <j1 rule="para" parents="26403 31631"/>
    </justification>
  </clause>

  <clause id="31633">
    <literal><![CDATA[
      L(x,(((1 / y) * z) \ u) \ w,v5) = L(x,((y * z) \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29466,a(flip),b,29736,a),flip(a)].">
      <j1 rule="hyper" parents="64 29466 29736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31635">
    <literal><![CDATA[
      L(x,(L(y * z,y,y) \ u) \ w,v5) = L(x,(((z / (y * z)) * z) \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(30955(a,2),31633(a,1,2,1,1))].">
      <j1 rule="para" parents="30955 31633"/>
    </justification>
  </clause>

  <clause id="31636">
    <literal><![CDATA[
      (x \ y) / T(y * x,x \ y) = (y * x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(625(a,1),29744(a,1,1)),flip(a)].">
      <j1 rule="para" parents="625 29744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31637">
    <literal><![CDATA[
      L(x,L(T(y * y,y) * (z / y),u,w),v5) = L(x,L((y \ 1) \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(1439(a,1),29752(a,1,2,1))].">
      <j1 rule="para" parents="1439 29752"/>
    </justification>
  </clause>

  <clause id="31638">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) * (x * v5) = x * (v5 * L(x \ R(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,24383,a,b,29810,a)].">
      <j1 rule="hyper" parents="64 24383 29810"/>
    </justification>
  </clause>

  <clause id="31639">
    <literal><![CDATA[
      K(x,y \ z) * (a(y,u,w) \ y) = y * (a(y,u,w) \ K(x,z / y))
    ]]></literal>
    <justification jstring="[para(19253(a,1),29935(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19253 29935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31640">
    <literal><![CDATA[
      (R(1 / x,y,z) \ 1) * a(x,u,w) = x * (x * (R(x,y,z) \ a(x,u,w)))
    ]]></literal>
    <justification jstring="[para(30910(a,1),29943(a,2,2))].">
      <j1 rule="para" parents="30910 29943"/>
    </justification>
  </clause>

  <clause id="31641">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (T(x,u) * w) = T(x,u) * ((a(x,y,z) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28648,a(flip),b,30000,a),flip(a)].">
      <j1 rule="hyper" parents="64 28648 30000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31642">
    <literal><![CDATA[
      x * T((x \ 1) * (a(y,x,x) \ 1),z) = T(1 / x,z) * (a(y,x,x) \ x)
    ]]></literal>
    <justification jstring="[para(28756(a,2),30018(a,1,2))].">
      <j1 rule="para" parents="28756 30018"/>
    </justification>
  </clause>

  <clause id="31643">
    <literal><![CDATA[
      ((a(x,x,y) / x) \ 1) \ L(y,x \ a(x,x,y),x \ a(x,x,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(25195(a,1),30127(a,1,1))].">
      <j1 rule="para" parents="25195 30127"/>
    </justification>
  </clause>

  <clause id="31644">
    <literal><![CDATA[
      R(R(T(x \ 1,y),x,z),R(x,x,z),y) = y \ (((a(x,x,z) / x) \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(25195(a,1),30139(a,2,2,1))].">
      <j1 rule="para" parents="25195 30139"/>
    </justification>
  </clause>

  <clause id="31645">
    <literal><![CDATA[
      R(x,y * a(z,z,y),y) = R(x,y,y * a(z,z,y))
    ]]></literal>
    <justification jstring="[para(30229(a,1),30237(a,1,3))].">
      <j1 rule="para" parents="30229 30237"/>
    </justification>
  </clause>

  <clause id="31646">
    <literal><![CDATA[
      R(x,y,y * a(z,z,y)) = R(x,L(y,z,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26536,a(flip),b,31645,a),flip(a)].">
      <j1 rule="hyper" parents="64 26536 31645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31647">
    <literal><![CDATA[
      R(x,y,y * a(z,z,y)) = R(x,y,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,26646,a(flip),b,31646,a),flip(a)].">
      <j1 rule="hyper" parents="373 26646 31646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31648">
    <literal><![CDATA[
      L(x,(a(y,z,z) * (z \ R(y,z,z))) * u,w) = L(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(30282(a,1),30308(a,1,2,1,2))].">
      <j1 rule="para" parents="30282 30308"/>
    </justification>
  </clause>

  <clause id="31649">
    <literal><![CDATA[
      L(x,((y * z) * a(z,y,y)) * u,w) = L(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31386,a(flip),b,31648,a)].">
      <j1 rule="hyper" parents="64 31386 31648"/>
    </justification>
  </clause>

  <clause id="31650">
    <literal><![CDATA[
      L(x,(y * (z * a(z,y,y))) * u,w) = L(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(29988(a,1),31649(a,1,2,1))].">
      <j1 rule="para" parents="29988 31649"/>
    </justification>
  </clause>

  <clause id="31651">
    <literal><![CDATA[
      L(x,(y * R(z,y,y)) * u,w) = L(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(15984(a,1),31650(a,1,2,1,2))].">
      <j1 rule="para" parents="15984 31650"/>
    </justification>
  </clause>

  <clause id="31652">
    <literal><![CDATA[
      L(x,y \ ((z * u) * (z * (u * a(z,z,u)))),w) = L(x,y \ a(z,z,u),w)
    ]]></literal>
    <justification jstring="[para(29910(a,1),30319(a,1,2,2,2))].">
      <j1 rule="para" parents="29910 30319"/>
    </justification>
  </clause>

  <clause id="31653">
    <literal><![CDATA[
      a(x,y,z) * a(a(x,y,z),u,u \ x) = L(a(x,y,z),u,u \ x)
    ]]></literal>
    <justification jstring="[hyper(35,a,28776,a,b,30345,a),flip(a)].">
      <j1 rule="hyper" parents="35 28776 30345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31654">
    <literal><![CDATA[
      a(x,x,x \ (R(T(x,y),z,u) * w)) = a(x,x,x * (R(x \ 1,z,u) * w))
    ]]></literal>
    <justification jstring="[para(2769(a,1),30362(a,2,3))].">
      <j1 rule="para" parents="2769 30362"/>
    </justification>
  </clause>

  <clause id="31655">
    <literal><![CDATA[
      a(x,y,z) \ (x \ (u * ((u \ x) * a(x,y,z)))) = a(a(x,y,z),u \ x,u)
    ]]></literal>
    <justification jstring="[para(28742(a,1),30403(a,1,2,2))].">
      <j1 rule="para" parents="28742 30403"/>
    </justification>
  </clause>

  <clause id="31656">
    <literal><![CDATA[
      (L(x,x,y) * z) / L(x,a(y,x,x),z) = z * (T(L(x,x,y),z) / x)
    ]]></literal>
    <justification jstring="[para(11794(a,1),30498(a,1,2))].">
      <j1 rule="para" parents="11794 30498"/>
    </justification>
  </clause>

  <clause id="31657">
    <literal><![CDATA[
      (L(x,x,y) * z) / L(x,a(y,x,x),z) = z * (L(T(x,z),x,y) / x)
    ]]></literal>
    <justification jstring="[para(25(a,2),31656(a,2,2,1))].">
      <j1 rule="para" parents="25 31656"/>
    </justification>
  </clause>

  <clause id="31658">
    <literal><![CDATA[
      (L(x,x,y) * z) / L(x,a(y,x,x),z) = z * (x \ L(T(x,z),x,y))
    ]]></literal>
    <justification jstring="[para(5620(a,1),31657(a,2,2))].">
      <j1 rule="para" parents="5620 31657"/>
    </justification>
  </clause>

  <clause id="31659">
    <literal><![CDATA[
      (x * (y * L(z,z,y))) \ (x * (y * z)) = L(a(y,z,z),z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29779,a(flip),b,30541,a),flip(a)].">
      <j1 rule="hyper" parents="64 29779 30541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31660">
    <literal><![CDATA[
      (a(x * y,x,x) \ z) \ T(z,a(u,w,v5)) = y \ ((y * x) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(467,a,30557,a),flip(a)].">
      <j1 rule="hyper" parents="467 30557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31661">
    <literal><![CDATA[
      L(a(x * y,x,x),a(x,x,y),z) \ z = z * (L(x \ 1,x,y) * x)
    ]]></literal>
    <justification jstring="[para(30728(a,1),30561(a,1,1))].">
      <j1 rule="para" parents="30728 30561"/>
    </justification>
  </clause>

  <clause id="31662">
    <literal><![CDATA[
      L((x \ 1) \ 1,x \ 1,x * ((y * z) \ u)) * (x \ 1) = (x \ 1) \ L(x \ 1,x \ 1,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(23997(a,1),30690(a,1,1))].">
      <j1 rule="para" parents="23997 30690"/>
    </justification>
  </clause>

  <clause id="31663">
    <literal><![CDATA[
      L(x,y \ z,a(y \ z,y \ z,y)) = L(x,(z / y) * (y / z),y \ z)
    ]]></literal>
    <justification jstring="[para(30068(a,1),30915(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30068 30915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31664">
    <literal><![CDATA[
      L(x,y \ z,a(y \ z,y \ z,y)) = L(x,a(y,z \ y,z),y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31140,a(flip),b,31663,a),flip(a)].">
      <j1 rule="hyper" parents="373 31140 31663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31665">
    <literal><![CDATA[
      L(x,a(y,z \ y,z),y \ z) = L(x,y \ z,a(z,y \ z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29296,a(flip),b,31664,a),flip(a)].">
      <j1 rule="hyper" parents="64 29296 31664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31666">
    <literal><![CDATA[
      L(x,a(y,z \ y,z),z \ y) = L(x,z \ y,a(y,z \ y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,31145,a,b,31665,a)].">
      <j1 rule="hyper" parents="64 31145 31665"/>
    </justification>
  </clause>

  <clause id="31667">
    <literal><![CDATA[
      ((x * y) * y) * L(z,x * L(x,y,y),x) = x * ((x \ ((x * y) * y)) * z)
    ]]></literal>
    <justification jstring="[para(11786(a,1),31030(a,1,2))].">
      <j1 rule="para" parents="11786 31030"/>
    </justification>
  </clause>

  <clause id="31668">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,a(x,w,v5)) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(28860,a,31095,a)].">
      <j1 rule="hyper" parents="28860 31095"/>
    </justification>
  </clause>

  <clause id="31670">
    <literal><![CDATA[
      L(x,y,a(z,y,y)) * (a(z,y,y) \ y) = (a(z,y,y) \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,251,a(flip),b,31109,a),flip(a)].">
      <j1 rule="hyper" parents="373 251 31109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31671">
    <literal><![CDATA[
      L(x,y,a(z,y,y)) * L(y,y,z) = (a(z,y,y) \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(30459(a,1),31670(a,1,2))].">
      <j1 rule="para" parents="30459 31670"/>
    </justification>
  </clause>

  <clause id="31672">
    <literal><![CDATA[
      L(x \ K(y,z),x,x * u) * x = K(y,T(z,x)) * (x \ L(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(464,a,31130,a)].">
      <j1 rule="hyper" parents="464 31130"/>
    </justification>
  </clause>

  <clause id="31673">
    <literal><![CDATA[
      L(x \ K(y,z),x,x * y) = y \ (T(y,T(z,x)) / x)
    ]]></literal>
    <justification jstring="[hyper(36,a,26663,a(flip),b,31672,a),flip(a)].">
      <j1 rule="hyper" parents="36 26663 31672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31674">
    <literal><![CDATA[
      L(x * K(x * y,y),y,y) \ (x * (1 / y)) = x \ (T(x,T(y \ 1,y)) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16534,a,b,31673,a)].">
      <j1 rule="hyper" parents="64 16534 31673"/>
    </justification>
  </clause>

  <clause id="31675">
    <literal><![CDATA[
      (x \ L(L(x,y,y),y,y)) \ z = x * (L(L(x,y,y),y,y) \ z)
    ]]></literal>
    <justification jstring="[para(30736(a,1),31137(a,1,1))].">
      <j1 rule="para" parents="30736 31137"/>
    </justification>
  </clause>

  <clause id="31676">
    <literal><![CDATA[
      a(x,y,z \ R(u,w,v5)) = a(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1863(a,1),31320(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1863 31320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31677">
    <literal><![CDATA[
      a(x,y,z \ R(T(u,w),v5,v6)) = a(x,y,z \ L(u,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,27324,a(flip),b,31676,a),flip(a)].">
      <j1 rule="hyper" parents="373 27324 31676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31678">
    <literal><![CDATA[
      a(x,y,z \ L(z * u,w,v5)) = a(x,y,z * R(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(2124(a,1),31676(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2124 31676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31679">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u \ R(w,v5,v6)) \ L(w,v5,v6)) = a(x,y,T((R(w,v5,v6) / u) * z,z \ u))
    ]]></literal>
    <justification jstring="[para(15117(a,1),31676(a,1,3)),flip(a)].">
      <j1 rule="para" parents="15117 31676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31680">
    <literal><![CDATA[
      a(x,y,z \ L(z * u,w,v5)) = a(x,y,z * L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,31317,a(flip),b,31678,a),flip(a)].">
      <j1 rule="hyper" parents="373 31317 31678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31681">
    <literal><![CDATA[
      a(x,y,R(z \ 1,u,w) * T(v5,v6)) = a(x,y,v5 * ((z * z) \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27391,a(flip),b,31331,a),flip(a)].">
      <j1 rule="hyper" parents="373 27391 31331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31682">
    <literal><![CDATA[
      (((x \ y) / y) / (1 / x)) \ (x * x) = (x \ (y / (x * y))) \ 1
    ]]></literal>
    <justification jstring="[para(25702(a,1),31376(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25702 31376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31683">
    <literal><![CDATA[
      (((x \ y) / y) * x) \ (x * x) = (x \ (y / (x * y))) \ 1
    ]]></literal>
    <justification jstring="[para(3363(a,1),31682(a,1,1))].">
      <j1 rule="para" parents="3363 31682"/>
    </justification>
  </clause>

  <clause id="31684">
    <literal><![CDATA[
      (x \ (y / (x * y))) \ 1 = (x * y) / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31161,a(flip),b,31683,a),flip(a)].">
      <j1 rule="hyper" parents="64 31161 31683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31685">
    <literal><![CDATA[
      K(x,y \ 1) * (((x \ (y \ x)) / y) * z) = (y \ (x / (y * x))) * z
    ]]></literal>
    <justification jstring="[para(5962(a,1),31378(a,1,1))].">
      <j1 rule="para" parents="5962 31378"/>
    </justification>
  </clause>

  <clause id="31686">
    <literal><![CDATA[
      (x * ((T(x,y) \ 1) \ 1)) * z = x * ((T(x,y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,5811,a(flip),b,31468,a),flip(a)].">
      <j1 rule="hyper" parents="64 5811 31468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31688">
    <literal><![CDATA[
      (x * T((x \ 1) \ 1,y)) * z = x * ((T(x,y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3568(a,2),31686(a,1,1,2))].">
      <j1 rule="para" parents="3568 31686"/>
    </justification>
  </clause>

  <clause id="31689">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * ((T(T(y,x),z) \ 1) \ u)) = (y * T((T(y,x) \ 1) \ 1,z)) * u
    ]]></literal>
    <justification jstring="[para(31688(a,1),23389(a,1,2))].">
      <j1 rule="para" parents="31688 23389"/>
    </justification>
  </clause>

  <clause id="31690">
    <literal><![CDATA[
      T(x / y,x) * ((y / x) * y) = y * K(y \ x,y * (x \ y))
    ]]></literal>
    <justification jstring="[para(82(a,1),31470(a,2,2,1,2))].">
      <j1 rule="para" parents="82 31470"/>
    </justification>
  </clause>

  <clause id="31691">
    <literal><![CDATA[
      T(x / y,x) * ((y / x) * y) = (y \ x) * (y / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,18969,a(flip),b,31690,a),flip(a)].">
      <j1 rule="hyper" parents="373 18969 31690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31692">
    <literal><![CDATA[
      R(T(x / y,x) * (((y / x) * y) * T(x / y,x)),z,u) / T(T(x / y,x),(y \ x) * (y / (y \ x))) = R((y / x) * y,z,u) * T(x / y,x)
    ]]></literal>
    <justification jstring="[para(31691(a,1),28115(a,1,2,2))].">
      <j1 rule="para" parents="31691 28115"/>
    </justification>
  </clause>

  <clause id="31693">
    <literal><![CDATA[
      ((R(x,y,z) * (u / x)) * x) * x = T(x * (R(x,y,z) * u),x)
    ]]></literal>
    <justification jstring="[para(1902(a,1),31480(a,1,1,1))].">
      <j1 rule="para" parents="1902 31480"/>
    </justification>
  </clause>

  <clause id="31694">
    <literal><![CDATA[
      ((x * (y / x)) * R(x,z,u)) * x = T(x * (R(x,z,u) * y),x)
    ]]></literal>
    <justification jstring="[para(25050(a,1),31693(a,1,1))].">
      <j1 rule="para" parents="25050 31693"/>
    </justification>
  </clause>

  <clause id="31695">
    <literal><![CDATA[
      ((x * (y / x)) * x) * R(x,z,u) = T(x * (R(x,z,u) * y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2823,a(flip),b,31694,a)].">
      <j1 rule="hyper" parents="64 2823 31694"/>
    </justification>
  </clause>

  <clause id="31696">
    <literal><![CDATA[
      x * (y * R(T(x,x \ 1),z,u)) = T(x * (R(x,z,u) * y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27845,a(flip),b,31695,a)].">
      <j1 rule="hyper" parents="64 27845 31695"/>
    </justification>
  </clause>

  <clause id="31697">
    <literal><![CDATA[
      (R(x,y,z) * u) * K((R(x,y,z) * u) * x,x) = u * R(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,14656,a,b,31696,a)].">
      <j1 rule="hyper" parents="35 14656 31696"/>
    </justification>
  </clause>

  <clause id="31698">
    <literal><![CDATA[
      (a(x,x,y) * a(x,x,y)) \ (z \ y) = z \ (a(x,x,y) \ L(y,x,x))
    ]]></literal>
    <justification jstring="[para(5693(a,1),31486(a,2,2))].">
      <j1 rule="para" parents="5693 31486"/>
    </justification>
  </clause>

  <clause id="31699">
    <literal><![CDATA[
      (a(x,x,y) * a(x,x,y)) \ (z \ y) = z \ L(L(y,x,x),x,x)
    ]]></literal>
    <justification jstring="[para(30358(a,1),31698(a,2,2))].">
      <j1 rule="para" parents="30358 31698"/>
    </justification>
  </clause>

  <clause id="31700">
    <literal><![CDATA[
      (x * R(x \ ((y * y) \ y),z,u)) * y = (1 / y) * (x * R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(2786(a,1),31489(a,1,1))].">
      <j1 rule="para" parents="2786 31489"/>
    </justification>
  </clause>

  <clause id="31701">
    <literal><![CDATA[
      T(x \ y,x * x) / (y * x) = (x \ y) / T(y * x,x \ y)
    ]]></literal>
    <justification jstring="[para(8505(a,1),31519(a,1,1))].">
      <j1 rule="para" parents="8505 31519"/>
    </justification>
  </clause>

  <clause id="31702">
    <literal><![CDATA[
      T(x \ y,x * x) / (y * x) = (y * x) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,31636,a(flip),b,31701,a),flip(a)].">
      <j1 rule="hyper" parents="373 31636 31701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31703">
    <literal><![CDATA[
      T(((x \ y) / y) \ x,((x \ y) / y) * ((x \ y) / y)) = ((x \ y) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(38,a,23868,a,b,31702,a),flip(a)].">
      <j1 rule="hyper" parents="38 23868 31702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31704">
    <literal><![CDATA[
      (T(x \ y,x * x) / (x * y)) \ z = K(x,y) * (((y * x) \ (x \ y)) \ z)
    ]]></literal>
    <justification jstring="[para(31702(a,1),24515(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="31702 24515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31705">
    <literal><![CDATA[
      R(x,y,(z * ((u * u) \ w)) \ v5) = R(x,y,((z * w) \ v5) * (u * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26286,a(flip),b,31532,a),flip(a)].">
      <j1 rule="hyper" parents="64 26286 31532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31707">
    <literal><![CDATA[
      R(x,y,((z * (a(u,w,w) * R(u,w,w))) \ v5) * (a(u,w,w) * a(u,w,w))) = R(x,y,(z * L(u,a(u,w,w),a(u,w,w))) \ v5)
    ]]></literal>
    <justification jstring="[para(16014(a,1),31705(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="16014 31705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31708">
    <literal><![CDATA[
      R(x,y,((z \ u) * (u / z)) \ 1) = R(x,y,u \ ((1 / (z \ u)) * z))
    ]]></literal>
    <justification jstring="[para(68(a,1),31533(a,1,3,2))].">
      <j1 rule="para" parents="68 31533"/>
    </justification>
  </clause>

  <clause id="31709">
    <literal><![CDATA[
      R(x,y,((z \ u) * (z \ u)) \ 1) = R(x,y,u \ ((1 / (z \ u)) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26332,a,b,31708,a)].">
      <j1 rule="hyper" parents="64 26332 31708"/>
    </justification>
  </clause>

  <clause id="31711">
    <literal><![CDATA[
      R(x,y,(z \ u) \ ((z \ u) \ 1)) = R(x,y,u \ ((1 / (z \ u)) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26256,a(flip),b,31709,a)].">
      <j1 rule="hyper" parents="64 26256 31709"/>
    </justification>
  </clause>

  <clause id="31712">
    <literal><![CDATA[
      R(x,y,(z \ u) \ ((z \ u) \ 1)) = R(x,y,u \ (((z \ u) \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,26270,a(flip),b,31711,a),flip(a)].">
      <j1 rule="hyper" parents="373 26270 31711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31713">
    <literal><![CDATA[
      R(x,((T(y,z) * u) * w) \ v5,v6) = R(x,((y * u) * w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26404,a(flip),b,31534,a),flip(a)].">
      <j1 rule="hyper" parents="64 26404 31534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31715">
    <literal><![CDATA[
      T((x \ 1) \ ((1 / x) \ y),1 * x) = (x \ 1) \ ((x \ 1) \ T(y,x))
    ]]></literal>
    <justification jstring="[para(381(a,1),31541(a,1,2,1))].">
      <j1 rule="para" parents="381 31541"/>
    </justification>
  </clause>

  <clause id="31716">
    <literal><![CDATA[
      T((x \ 1) \ ((1 / x) \ y),x) = (x \ 1) \ ((x \ 1) \ T(y,x))
    ]]></literal>
    <justification jstring="[para(7(a,1),31715(a,1,2))].">
      <j1 rule="para" parents="7 31715"/>
    </justification>
  </clause>

  <clause id="31718">
    <literal><![CDATA[
      a(x,y,z \ (u * ((w * w) * v5))) = a(x,y,(z \ (u * v5)) * (w * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27573,a(flip),b,31578,a),flip(a)].">
      <j1 rule="hyper" parents="64 27573 31578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31720">
    <literal><![CDATA[
      a(x,y,(z \ (u * ((w * w) \ v5))) * (w * w)) = a(x,y,z \ (u * v5))
    ]]></literal>
    <justification jstring="[para(10(a,1),31718(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="10 31718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31721">
    <literal><![CDATA[
      a(x,y,((z * u) \ (z * (u * w))) * (v5 * v5)) = a(x,y,L(T(v5 * v5,u) * w,u,z))
    ]]></literal>
    <justification jstring="[para(6651(a,1),31718(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6651 31718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31722">
    <literal><![CDATA[
      a(x,y,(z * z) * (u \ (w * ((z * z) \ v5)))) = a(x,y,u \ (w * v5))
    ]]></literal>
    <justification jstring="[hyper(27453,a,31720,a)].">
      <j1 rule="hyper" parents="27453 31720"/>
    </justification>
  </clause>

  <clause id="31723">
    <literal><![CDATA[
      a(x,y,(z * ((u * u) \ w)) \ v5) = a(x,y,((z * w) \ v5) * (u * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27531,a(flip),b,31579,a),flip(a)].">
      <j1 rule="hyper" parents="64 27531 31579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31725">
    <literal><![CDATA[
      L(x,x \ y,y) \ x = a(y,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,15046,a,b,31587,a(flip))].">
      <j1 rule="hyper" parents="35 15046 31587"/>
    </justification>
  </clause>

  <clause id="31726">
    <literal><![CDATA[
      a(x,y \ x,y) \ y = L(y,y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,31725,a)].">
      <j1 rule="hyper" parents="40 23134 31725"/>
    </justification>
  </clause>

  <clause id="31728">
    <literal><![CDATA[
      L(x,x * y,L(y,x,x)) = a(y,x \ y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,31528,a,b,31726,a)].">
      <j1 rule="hyper" parents="373 31528 31726"/>
    </justification>
  </clause>

  <clause id="31729">
    <literal><![CDATA[
      a(L(x,y,y),y * x,y) = a(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,26857,a,b,31728,a(flip))].">
      <j1 rule="hyper" parents="40 26857 31728"/>
    </justification>
  </clause>

  <clause id="31730">
    <literal><![CDATA[
      K(x,T(y \ (((z \ u) \ u) \ w),K(v5,v6))) = K(x,(T(z,u) * y) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,7423,a(flip),b,31593,a),flip(a)].">
      <j1 rule="hyper" parents="373 7423 31593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31731">
    <literal><![CDATA[
      K(x,T(y \ (((z \ u) \ u) \ w),K(v5,v6))) = K(x,y \ (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,23002,a(flip),b,31730,a),flip(a)].">
      <j1 rule="hyper" parents="373 23002 31730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31732">
    <literal><![CDATA[
      K(x,y \ (((z \ u) \ u) \ w)) = K(x,y \ (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(17156,a,31731,a)].">
      <j1 rule="hyper" parents="17156 31731"/>
    </justification>
  </clause>

  <clause id="31733">
    <literal><![CDATA[
      K(x,y \ (z \ K(z \ u,z))) = K(x,y \ (T(z,u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,15208,a(flip),b,31732,a)].">
      <j1 rule="hyper" parents="64 15208 31732"/>
    </justification>
  </clause>

  <clause id="31734">
    <literal><![CDATA[
      K(x,y \ (z \ K(z \ u,z))) = K(x,y \ T(1 / z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,25423,a,b,31733,a),flip(a)].">
      <j1 rule="hyper" parents="373 25423 31733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31735">
    <literal><![CDATA[
      K(x,y \ T(1 / y,z)) = K(y * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,31453,a(flip),b,31734,a),flip(a)].">
      <j1 rule="hyper" parents="64 31453 31734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31736">
    <literal><![CDATA[
      K(x,y \ T(y \ 1,z)) = K(y * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,28109,a(flip),b,31735,a)].">
      <j1 rule="hyper" parents="64 28109 31735"/>
    </justification>
  </clause>

  <clause id="31737">
    <literal><![CDATA[
      K(x,y \ (y \ K(y,z))) = K(y * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,28278,a(flip),b,31736,a)].">
      <j1 rule="hyper" parents="64 28278 31736"/>
    </justification>
  </clause>

  <clause id="31738">
    <literal><![CDATA[
      T((x \ (x \ y)) / y,T(z,y)) = T((x \ (x \ y)) / y,z)
    ]]></literal>
    <justification jstring="[para(26689(a,1),31594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26689 31594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31739">
    <literal><![CDATA[
      ((x \ (x \ y)) / y) * K(z,x * x) = T((x \ (x \ y)) / y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,28471,a(flip),b,31738,a)].">
      <j1 rule="hyper" parents="64 28471 31738"/>
    </justification>
  </clause>

  <clause id="31740">
    <literal><![CDATA[
      ((x * y) * y) * L(z,x,a(y,y,x)) = (((x * y) * y) / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(9388(a,1),31625(a,1,2))].">
      <j1 rule="para" parents="9388 31625"/>
    </justification>
  </clause>

  <clause id="31741">
    <literal><![CDATA[
      L(x,y,z * (u \ ((w \ 1) \ v5))) = L(x,y,z * (u \ (w \ v5)))
    ]]></literal>
    <justification jstring="[para(82(a,1),31627(a,1,3,2,2,1)),flip(a)].">
      <j1 rule="para" parents="82 31627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31744">
    <literal><![CDATA[
      L(x,L((y * y) * (z / y),u,w),v5) = L(x,L((y \ 1) \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29472,a(flip),b,31637,a)].">
      <j1 rule="hyper" parents="64 29472 31637"/>
    </justification>
  </clause>

  <clause id="31746">
    <literal><![CDATA[
      (R(1 / x,y,z) \ 1) * a(x,u,w) = R(1 / x,y,z) \ a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,16063,a(flip),b,31640,a),flip(a)].">
      <j1 rule="hyper" parents="373 16063 31640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31747">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ L(y,x \ a(x,x,y),x \ a(x,x,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(30165(a,1),31643(a,1,1))].">
      <j1 rule="para" parents="30165 31643"/>
    </justification>
  </clause>

  <clause id="31748">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ L(y,x \ a(x,x,y),a(x,x,y) * x) = x \ y
    ]]></literal>
    <justification jstring="[para(24662(a,1),31747(a,1,2))].">
      <j1 rule="para" parents="24662 31747"/>
    </justification>
  </clause>

  <clause id="31749">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ L(y,x \ a(x,x,y),R(x,x,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(30053(a,1),31748(a,1,2,3))].">
      <j1 rule="para" parents="30053 31748"/>
    </justification>
  </clause>

  <clause id="31750">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ L(y,x \ a(x,x,y),L(x,x,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(29203(a,1),31749(a,1,2))].">
      <j1 rule="para" parents="29203 31749"/>
    </justification>
  </clause>

  <clause id="31751">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ L(y,x * a(x,x,y),L(x,x,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(16066(a,1),31750(a,1,2))].">
      <j1 rule="para" parents="16066 31750"/>
    </justification>
  </clause>

  <clause id="31752">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ L(y,R(x,x,y),L(x,x,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(30054(a,1),31751(a,1,2,2))].">
      <j1 rule="para" parents="30054 31751"/>
    </justification>
  </clause>

  <clause id="31753">
    <literal><![CDATA[
      L(x,R(y,y,x),L(y,y,x)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,30952,a,b,31752,a),flip(a)].">
      <j1 rule="hyper" parents="39 30952 31752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31754">
    <literal><![CDATA[
      L(x,L(y,y,x),L(y,y,x)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(30986,a,31753,a)].">
      <j1 rule="hyper" parents="30986 31753"/>
    </justification>
  </clause>

  <clause id="31755">
    <literal><![CDATA[
      (L(x,y,z) * L(u,L(x,x,u),L(x,x,u))) \ (L(x,y,z) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[para(31754(a,2),30888(a,1,1,2))].">
      <j1 rule="para" parents="31754 30888"/>
    </justification>
  </clause>

  <clause id="31756">
    <literal><![CDATA[
      L(x,y \ (y \ z),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(31754(a,1),31150(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31754 31150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31757">
    <literal><![CDATA[
      L(x,L(y * z,z * y,z),u) = L(x,L(y \ z,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30938,a,b,31756,a)].">
      <j1 rule="hyper" parents="64 30938 31756"/>
    </justification>
  </clause>

  <clause id="31758">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (x * (y * (x \ ((x \ 1) \ y)))) = L(y,L(y,x,x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30874,a,b,31756,a)].">
      <j1 rule="hyper" parents="64 30874 31756"/>
    </justification>
  </clause>

  <clause id="31759">
    <literal><![CDATA[
      L(x,L(y * z,y,y),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),31756(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 31756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31760">
    <literal><![CDATA[
      L(x,L(y * z,z,z),u) = L(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29541,a,b,31759,a)].">
      <j1 rule="hyper" parents="64 29541 31759"/>
    </justification>
  </clause>

  <clause id="31761">
    <literal><![CDATA[
      L(x,y * L(z,y,y),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29756,a(flip),b,31759,a)].">
      <j1 rule="hyper" parents="64 29756 31759"/>
    </justification>
  </clause>

  <clause id="31762">
    <literal><![CDATA[
      L(x,L(y * z,y * z,y),u) = L(x,L(z \ y,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29541,a,b,31757,a)].">
      <j1 rule="hyper" parents="64 29541 31757"/>
    </justification>
  </clause>

  <clause id="31763">
    <literal><![CDATA[
      L(x,L(y * z,z * y,y),u) = L(x,L(z \ y,y,y),u)
    ]]></literal>
    <justification jstring="[para(14181(a,2),31762(a,1,2))].">
      <j1 rule="para" parents="14181 31762"/>
    </justification>
  </clause>

  <clause id="31764">
    <literal><![CDATA[
      R(R(T(x \ 1,y),x,z),R(x,x,z),y) = y \ ((a(x,x,z) \ x) \ y)
    ]]></literal>
    <justification jstring="[para(30165(a,1),31644(a,2,2,1))].">
      <j1 rule="para" parents="30165 31644"/>
    </justification>
  </clause>

  <clause id="31765">
    <literal><![CDATA[
      x \ ((a(y,y,z) \ y) \ x) = x \ ((1 / R(y \ 1,y,z)) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,3045,a(flip),b,31764,a),flip(a)].">
      <j1 rule="hyper" parents="64 3045 31764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31766">
    <literal><![CDATA[
      x \ ((R(1 / y,y,z) \ 1) \ x) = x \ ((a(y,y,z) \ y) \ x)
    ]]></literal>
    <justification jstring="[para(11425(a,1),31765(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="11425 31765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31767">
    <literal><![CDATA[
      L(x,y \ ((z * u) * ((1 / z) \ u)),w) = L(x,y \ a(z,z,u),w)
    ]]></literal>
    <justification jstring="[para(30219(a,1),31652(a,1,2,2,2))].">
      <j1 rule="para" parents="30219 31652"/>
    </justification>
  </clause>

  <clause id="31768">
    <literal><![CDATA[
      L(x,y \ ((z \ u) * (z * u)),w) = L(x,y \ a(z,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30978,a(flip),b,31767,a)].">
      <j1 rule="hyper" parents="64 30978 31767"/>
    </justification>
  </clause>

  <clause id="31769">
    <literal><![CDATA[
      a(x,x,R(T(x,y),z,u) * (x \ w)) = a(x,x,x * (R(x \ 1,z,u) * w))
    ]]></literal>
    <justification jstring="[para(27136(a,1),31654(a,1,3))].">
      <j1 rule="para" parents="27136 31654"/>
    </justification>
  </clause>

  <clause id="31770">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u \ x,u) = a(a(x,y,z),u \ x,u)
    ]]></literal>
    <justification jstring="[para(101(a,1),31655(a,1,2))].">
      <j1 rule="para" parents="101 31655"/>
    </justification>
  </clause>

  <clause id="31771">
    <literal><![CDATA[
      ((x * y) * y) * L(z,a(y,y,x),x) = x * ((x \ ((x * y) * y)) * z)
    ]]></literal>
    <justification jstring="[para(11916(a,1),31667(a,1,2))].">
      <j1 rule="para" parents="11916 31667"/>
    </justification>
  </clause>

  <clause id="31772">
    <literal><![CDATA[
      a(x,y,z * ((u * u) \ L(u,w,v5))) = a(x,y,R(u \ 1,w,v5) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27309,a(flip),b,31681,a),flip(a)].">
      <j1 rule="hyper" parents="64 27309 31681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31773">
    <literal><![CDATA[
      a(x,y,z * ((u * u) \ L(u,w,v5))) = a(x,y,L(u \ 1,w,v5) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31314,a(flip),b,31772,a),flip(a)].">
      <j1 rule="hyper" parents="373 31314 31772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31774">
    <literal><![CDATA[
      (x * R(x \ (1 / y),z,u)) * y = (1 / y) * (x * R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(309(a,1),31700(a,1,1,2,1,2))].">
      <j1 rule="para" parents="309 31700"/>
    </justification>
  </clause>

  <clause id="31775">
    <literal><![CDATA[
      (1 / x) * (y * R(y \ x,z,u)) = y * (x * R(x \ (y \ 1),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,2839,a(flip),b,31774,a),flip(a)].">
      <j1 rule="hyper" parents="64 2839 31774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31776">
    <literal><![CDATA[
      (1 / x) * (y * R(y \ x,z,u)) = (y * x) \ R(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2740,a(flip),b,31775,a),flip(a)].">
      <j1 rule="hyper" parents="373 2740 31775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31777">
    <literal><![CDATA[
      T(((x \ y) / y) \ x,((x \ y) / y) * (x \ (y / y))) = ((x \ y) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,28284,a(flip),b,31703,a)].">
      <j1 rule="hyper" parents="64 28284 31703"/>
    </justification>
  </clause>

  <clause id="31778">
    <literal><![CDATA[
      a(L(x,x,y),L(x,x,y),y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29905,a(flip),b,31755,a)].">
      <j1 rule="hyper" parents="64 29905 31755"/>
    </justification>
  </clause>

  <clause id="31779">
    <literal><![CDATA[
      L(x,L(y,y,z),a(L(y,y,z),L(y,y,z),z)) = L(x,a(y,y,z),L(y,y,z))
    ]]></literal>
    <justification jstring="[para(31778(a,1),30415(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31778 30415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31780">
    <literal><![CDATA[
      a(x,x,x * (R(x \ 1,y,z) * u)) = a(x,x,(x \ u) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27529,a(flip),b,31769,a),flip(a)].">
      <j1 rule="hyper" parents="64 27529 31769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31781">
    <literal><![CDATA[
      T(((x \ y) / y) \ x,((x \ y) / y) * (x \ 1)) = ((x \ y) / y) \ x
    ]]></literal>
    <justification jstring="[para(76(a,1),31777(a,1,2,2,2))].">
      <j1 rule="para" parents="76 31777"/>
    </justification>
  </clause>

  <clause id="31782">
    <literal><![CDATA[
      ((((x \ y) / y) \ x) \ 1) \ 1 = ((x \ y) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,11453,a(flip),b,31781,a)].">
      <j1 rule="hyper" parents="64 11453 31781"/>
    </justification>
  </clause>

  <clause id="31784">
    <literal><![CDATA[
      L(x,a(y,y,z),L(y,y,z)) = L(x,L(y,y,z),a(y,y,z))
    ]]></literal>
    <justification jstring="[para(31778(a,1),31779(a,1,3)),flip(a)].">
      <j1 rule="para" parents="31778 31779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31785">
    <literal><![CDATA[
      T((a(x,y,z) \ u) / w,w) = (((a(x,y,z) \ u) / w) \ u) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,28644,a(flip),b,23921,a)].">
      <j1 rule="hyper" parents="64 28644 23921"/>
    </justification>
  </clause>

  <clause id="31786">
    <literal><![CDATA[
      (((a(x,y,z) \ u) / w) \ u) \ u = w \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(467,a,31785,a),flip(a)].">
      <j1 rule="hyper" parents="467 31785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31788">
    <literal><![CDATA[
      x / (y \ (a(z,u,w) \ x)) = ((a(z,u,w) \ x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,117,a(flip),b,31785,a(flip))].">
      <j1 rule="hyper" parents="225 117 31785"/>
    </justification>
  </clause>

  <clause id="31789">
    <literal><![CDATA[
      ((a(x,y,z) * u) * w) / T(u,w) = u \ ((u * a(x,y,z)) * w)
    ]]></literal>
    <justification jstring="[para(28631(a,1),23958(a,1,2))].">
      <j1 rule="para" parents="28631 23958"/>
    </justification>
  </clause>

  <clause id="31790">
    <literal><![CDATA[
      (x * (a(y,z,u) * w)) / w = w \ ((w * a(y,z,u)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,28739,a(flip),b,31789,a)].">
      <j1 rule="hyper" parents="64 28739 31789"/>
    </justification>
  </clause>

  <clause id="31792">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (a(y,z,u) * w) = (a(y,z,u) * x) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,344,a(flip),b,31790,a),flip(a)].">
      <j1 rule="hyper" parents="144 344 31790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31793">
    <literal><![CDATA[
      (x * a(y,z,u)) * (w / (a(y,z,u) * x)) = x * (w / x)
    ]]></literal>
    <justification jstring="[hyper(145,a,170,a(flip),b,31790,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 170 31790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31794">
    <literal><![CDATA[
      (x * a(y,z,u)) * (w / (x * a(y,z,u))) = x * (w / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24795,a(flip),b,31793,a)].">
      <j1 rule="hyper" parents="64 24795 31793"/>
    </justification>
  </clause>

  <clause id="31795">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (w / u)) = w / (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(139,a,31793,a(flip),b,23168,a)].">
      <j1 rule="hyper" parents="139 31793 23168"/>
    </justification>
  </clause>

  <clause id="31796">
    <literal><![CDATA[
      (x * y) / (a(z,u,w) * y) = (a(z,u,w) * y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),31795(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 31795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31798">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (a(x,y,z) * w)) = R(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23137,a(flip),b,31796,a),flip(a)].">
      <j1 rule="hyper" parents="64 23137 31796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31799">
    <literal><![CDATA[
      T((a(x,y,z) * u) \ (u * w),v5) = R(T(w / a(x,y,z),v5),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(31796(a,1),679(a,1,1))].">
      <j1 rule="para" parents="31796 679"/>
    </justification>
  </clause>

  <clause id="31801">
    <literal><![CDATA[
      L(K(x,a(y,z,u)) * w,a(y,z,u),x) = R(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10985,a(flip),b,31798,a)].">
      <j1 rule="hyper" parents="64 10985 31798"/>
    </justification>
  </clause>

  <clause id="31802">
    <literal><![CDATA[
      R(x,a(y,z,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(23104(a,1),31801(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23104 31801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31803">
    <literal><![CDATA[
      R(x,a(y,z,u),y) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,30415,a(flip),b,31802,a),flip(a)].">
      <j1 rule="hyper" parents="373 30415 31802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31804">
    <literal><![CDATA[
      R(T(a(x,y,z) \ u,w),a(x,y,z),w) = (a(x,y,z) * w) \ (u * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,28763,a(flip),b,31802,a),flip(a)].">
      <j1 rule="hyper" parents="373 28763 31802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31805">
    <literal><![CDATA[
      R(x,a(y,z,u),w \ 1) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,1631,a(flip),b,31802,a),flip(a)].">
      <j1 rule="hyper" parents="373 1631 31802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31806">
    <literal><![CDATA[
      R(x,a(y,z,u),w * w) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,594,a(flip),b,31802,a),flip(a)].">
      <j1 rule="hyper" parents="373 594 31802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31807">
    <literal><![CDATA[
      R(x,a(y,y,z),u) = L(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27287,a(flip),b,31802,a)].">
      <j1 rule="hyper" parents="64 27287 31802"/>
    </justification>
  </clause>

  <clause id="31808">
    <literal><![CDATA[
      x * L(x \ 1,a(y,z,u),w) = x \ R(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(145,a,31802,a(flip),b,1990,a)].">
      <j1 rule="hyper" parents="145 31802 1990"/>
    </justification>
  </clause>

  <clause id="31809">
    <literal><![CDATA[
      x \ L(x * y,a(z,u,w),v5) = x * R(x \ y,a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(139,a,31802,a(flip),b,2125,a)].">
      <j1 rule="hyper" parents="139 31802 2125"/>
    </justification>
  </clause>

  <clause id="31810">
    <literal><![CDATA[
      x \ (L(1 / x,a(y,z,u),w) \ 1) = R(x,a(y,z,u),w) \ x
    ]]></literal>
    <justification jstring="[para(31802(a,1),2467(a,1,2,1))].">
      <j1 rule="para" parents="31802 2467"/>
    </justification>
  </clause>

  <clause id="31811">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,u),w),x,a(y,z,u) * w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(31802(a,1),16031(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="31802 16031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31812">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,u),w),x,w * a(y,z,u)) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(31802(a,1),23986(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="31802 23986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31813">
    <literal><![CDATA[
      L(x \ (y \ x),a(x,y,y),z) \ (y * z) = ((x \ (y \ x)) \ y) * z
    ]]></literal>
    <justification jstring="[para(31802(a,1),30611(a,1,1))].">
      <j1 rule="para" parents="31802 30611"/>
    </justification>
  </clause>

  <clause id="31815">
    <literal><![CDATA[
      R(x,y * (z \ (y \ z)),u * u) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,30606,a,b,31806,a)].">
      <j1 rule="hyper" parents="64 30606 31806"/>
    </justification>
  </clause>

  <clause id="31816">
    <literal><![CDATA[
      (x * x) \ ((y * (z \ (y \ z))) \ (x * x)) = T((y * (z \ (y \ z))) \ 1,x * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26197,a(flip),b,31815,a)].">
      <j1 rule="hyper" parents="64 26197 31815"/>
    </justification>
  </clause>

  <clause id="31817">
    <literal><![CDATA[
      R(x,a(y,z,z),z) = L(x,z,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,27287,a,b,31803,a)].">
      <j1 rule="hyper" parents="64 27287 31803"/>
    </justification>
  </clause>

  <clause id="31818">
    <literal><![CDATA[
      L(x \ L(x,y,a(y,z,u)),x,y * a(y,z,u)) = a(x,a(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(31803(a,1),23986(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="31803 23986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31819">
    <literal><![CDATA[
      R(x,a(y * z,y,y),y \ z) = L(x,y \ z,a(y \ z,y,y))
    ]]></literal>
    <justification jstring="[para(30543(a,1),31803(a,1,2))].">
      <j1 rule="para" parents="30543 31803"/>
    </justification>
  </clause>

  <clause id="31820">
    <literal><![CDATA[
      L(x,a(y,z,z),z) = L(x,z,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,31803,a(flip),b,31807,a),flip(a)].">
      <j1 rule="hyper" parents="64 31803 31807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31821">
    <literal><![CDATA[
      L(x,a(y,z,z),u) = L(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31802,a(flip),b,31807,a),flip(a)].">
      <j1 rule="hyper" parents="64 31802 31807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31822">
    <literal><![CDATA[
      R(x,y,L(z,a(u,w,w),v5)) = R(x,y,L(z,a(w,w,u),v5))
    ]]></literal>
    <justification jstring="[para(31807(a,1),26360(a,1,3))].">
      <j1 rule="para" parents="31807 26360"/>
    </justification>
  </clause>

  <clause id="31823">
    <literal><![CDATA[
      L(x,a(y,z,z),u * w) = L(x,a(z,z,y),w * u)
    ]]></literal>
    <justification jstring="[hyper(24201,a,31821,a)].">
      <j1 rule="hyper" parents="24201 31821"/>
    </justification>
  </clause>

  <clause id="31824">
    <literal><![CDATA[
      L(x,a(y * z,z,z),u) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,30729,a,b,31821,a)].">
      <j1 rule="hyper" parents="373 30729 31821"/>
    </justification>
  </clause>

  <clause id="31825">
    <literal><![CDATA[
      L(x,a(y,z,z),y * z) = L(x,y * z,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,30750,a(flip),b,31821,a),flip(a)].">
      <j1 rule="hyper" parents="373 30750 31821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31826">
    <literal><![CDATA[
      L(x,a(y,y,z),z) = L(x,z,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29231,a(flip),b,31821,a),flip(a)].">
      <j1 rule="hyper" parents="64 29231 31821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31827">
    <literal><![CDATA[
      (x * a(y,z,z)) * L(u,a(z,z,y),x) = x * (a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,31821,a(flip),b,18,a(flip))].">
      <j1 rule="hyper" parents="145 31821 18"/>
    </justification>
  </clause>

  <clause id="31828">
    <literal><![CDATA[
      (x * ((a(y,y,x) \ 1) * z)) / L(T(x,z),y,y) = L(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,16385,a,b,31826,a)].">
      <j1 rule="hyper" parents="64 16385 31826"/>
    </justification>
  </clause>

  <clause id="31829">
    <literal><![CDATA[
      (L(x,y,y) \ 1) * L(z,x,a(y,y,x)) = (x \ 1) * (a(y,y,x) * z)
    ]]></literal>
    <justification jstring="[para(31826(a,1),9369(a,1,2))].">
      <j1 rule="para" parents="31826 9369"/>
    </justification>
  </clause>

  <clause id="31830">
    <literal><![CDATA[
      L(a(x * y,x,x),y,a(x,x,y)) \ y = y * (L(x \ 1,x,y) * x)
    ]]></literal>
    <justification jstring="[para(31826(a,1),31661(a,1,1))].">
      <j1 rule="para" parents="31826 31661"/>
    </justification>
  </clause>

  <clause id="31831">
    <literal><![CDATA[
      ((x * y) * y) * L(z,x,a(y,y,x)) = x * ((x \ ((x * y) * y)) * z)
    ]]></literal>
    <justification jstring="[para(31826(a,1),31771(a,1,2))].">
      <j1 rule="para" parents="31826 31771"/>
    </justification>
  </clause>

  <clause id="31832">
    <literal><![CDATA[
      x * L(x \ 1,a(y,z,u),w) = x \ L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(31802(a,1),31808(a,2,2))].">
      <j1 rule="para" parents="31802 31808"/>
    </justification>
  </clause>

  <clause id="31833">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),a(u,w,v5),v6) = L(x * L(x \ 1,a(u,w,v5),v6),y,z)
    ]]></literal>
    <justification jstring="[hyper(4274,a,31832,a),flip(a)].">
      <j1 rule="hyper" parents="4274 31832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31834">
    <literal><![CDATA[
      (x \ y) \ L(x \ y,a(z,u,w),v5) = x \ (y * L(y \ x,a(z,u,w),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,2469,a(flip),b,31832,a),flip(a)].">
      <j1 rule="hyper" parents="64 2469 31832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31836">
    <literal><![CDATA[
      x \ L(x * y,a(z,u,w),v5) = x * L(x \ y,a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(31802(a,1),31809(a,2,2))].">
      <j1 rule="para" parents="31802 31809"/>
    </justification>
  </clause>

  <clause id="31837">
    <literal><![CDATA[
      x \ (L(1 / x,a(y,z,u),w) \ 1) = L(x,a(y,z,u),w) \ x
    ]]></literal>
    <justification jstring="[para(31802(a,1),31810(a,2,1))].">
      <j1 rule="para" parents="31802 31810"/>
    </justification>
  </clause>

  <clause id="31838">
    <literal><![CDATA[
      L(x,y \ z,a(y \ z,y,y)) = R(x,a(z,y,y),y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30650,a(flip),b,31819,a),flip(a)].">
      <j1 rule="hyper" parents="64 30650 31819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31839">
    <literal><![CDATA[
      L(x,y \ z,a(y * z,y,y)) = R(x,a(z,y,y),y \ z)
    ]]></literal>
    <justification jstring="[para(30543(a,1),31838(a,1,3))].">
      <j1 rule="para" parents="30543 31838"/>
    </justification>
  </clause>

  <clause id="31840">
    <literal><![CDATA[
      R(x,a(y,z,z),z \ y) = L(x,z \ y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30331,a(flip),b,31839,a),flip(a)].">
      <j1 rule="hyper" parents="64 30331 31839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31841">
    <literal><![CDATA[
      L(x,a(y,z,z),z \ y) = L(x,z \ y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,31802,a(flip),b,31840,a)].">
      <j1 rule="hyper" parents="64 31802 31840"/>
    </justification>
  </clause>

  <clause id="31842">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,u),w),x,(w \ (v5 * v5)) * a(y,z,u)) = a(x,a(y,z,u),w \ (v5 * v5))
    ]]></literal>
    <justification jstring="[para(2183(a,1),31812(a,1,1,2))].">
      <j1 rule="para" parents="2183 31812"/>
    </justification>
  </clause>

  <clause id="31843">
    <literal><![CDATA[
      a(x,a(y,z,u),y) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,28841,a(flip),b,31818,a),flip(a)].">
      <j1 rule="hyper" parents="64 28841 31818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31844">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * (y * z) = y * ((a(x,x,y) \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(38,a,16386,a,b,31828,a)].">
      <j1 rule="hyper" parents="38 16386 31828"/>
    </justification>
  </clause>

  <clause id="31845">
    <literal><![CDATA[
      L(x,y,y) * L(z,x,a(x,y,y)) = x * ((a(y,y,x) \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29300,a,b,31844,a)].">
      <j1 rule="hyper" parents="64 29300 31844"/>
    </justification>
  </clause>

  <clause id="31846">
    <literal><![CDATA[
      (L(x,y,y) * z) / (x * ((a(y,y,x) \ 1) * z)) = a(a(y,y,x),x,z)
    ]]></literal>
    <justification jstring="[para(31844(a,1),16241(a,1,2))].">
      <j1 rule="para" parents="31844 16241"/>
    </justification>
  </clause>

  <clause id="31847">
    <literal><![CDATA[
      L(x,y,y) * (a(x,y,y) * (R(x,y,y) \ z)) = x * ((a(y,y,x) \ 1) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30980,a(flip),b,31845,a)].">
      <j1 rule="hyper" parents="64 30980 31845"/>
    </justification>
  </clause>

  <clause id="31848">
    <literal><![CDATA[
      L(L(x,y,a(z,z,y)),L(y,z,z),L(y,z,z)) = L(y,z,z) * ((y \ 1) * (a(z,z,y) * x))
    ]]></literal>
    <justification jstring="[hyper(145,a,31829,a(flip),b,1148,a),flip(a)].">
      <j1 rule="hyper" parents="145 31829 1148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31849">
    <literal><![CDATA[
      x * (L(y \ 1,y,x) * y) = a(y * x,y,y) \ x
    ]]></literal>
    <justification jstring="[para(30295(a,1),31830(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30295 31830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31851">
    <literal><![CDATA[
      (((x * y) * y) / x) * (x * z) = x * ((x \ ((x * y) * y)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31740,a(flip),b,31831,a)].">
      <j1 rule="hyper" parents="64 31740 31831"/>
    </justification>
  </clause>

  <clause id="31852">
    <literal><![CDATA[
      x * ((x \ ((x * y) * y)) * y) = ((x * y) * y) * y
    ]]></literal>
    <justification jstring="[para(29954(a,1),31831(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29954 31831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31853">
    <literal><![CDATA[
      (x * y) * ((x / y) \ (x * y)) = x * ((x \ ((x * y) * y)) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30808,a,b,31852,a)].">
      <j1 rule="hyper" parents="373 30808 31852"/>
    </justification>
  </clause>

  <clause id="31856">
    <literal><![CDATA[
      (x * y) \ ((x * (L(z,u,w) \ z)) * y) = L(L(z,u,w) \ z,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,28922,a(flip),b,24801,a),flip(a)].">
      <j1 rule="hyper" parents="373 28922 24801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31859">
    <literal><![CDATA[
      ((a(x,y,y) * z) / y) * L(y,y,x) = L(z,L(y,y,x) \ y,L(y,y,x))
    ]]></literal>
    <justification jstring="[para(30462(a,1),25123(a,1,1,1,1))].">
      <j1 rule="para" parents="30462 25123"/>
    </justification>
  </clause>

  <clause id="31860">
    <literal><![CDATA[
      (a(x,y,y) * (z / y)) * L(y,y,x) = L(z,L(y,y,x) \ y,L(y,y,x))
    ]]></literal>
    <justification jstring="[para(29984(a,1),31859(a,1,1))].">
      <j1 rule="para" parents="29984 31859"/>
    </justification>
  </clause>

  <clause id="31861">
    <literal><![CDATA[
      a(x,y,y) * ((z / y) * L(y,y,x)) = L(z,L(y,y,x) \ y,L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,29987,a(flip),b,31860,a)].">
      <j1 rule="hyper" parents="64 29987 31860"/>
    </justification>
  </clause>

  <clause id="31862">
    <literal><![CDATA[
      a(x,y,y) * ((z / y) * L(y,y,x)) = L(z,a(x,y,y),L(y,y,x))
    ]]></literal>
    <justification jstring="[para(30462(a,1),31861(a,2,2))].">
      <j1 rule="para" parents="30462 31861"/>
    </justification>
  </clause>

  <clause id="31863">
    <literal><![CDATA[
      L(x,a(y,z,z),L(z,z,y)) = L(x,L(z,z,y),a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,31038,a(flip),b,31862,a),flip(a)].">
      <j1 rule="hyper" parents="64 31038 31862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31864">
    <literal><![CDATA[
      x * L(y,a(z,x,x),L(x,x,z)) = a(z,x,x) * (L(x,x,z) * y)
    ]]></literal>
    <justification jstring="[para(31863(a,2),30468(a,1,2))].">
      <j1 rule="para" parents="31863 30468"/>
    </justification>
  </clause>

  <clause id="31865">
    <literal><![CDATA[
      x * L(y,a(x,x,z),L(x,x,z)) = a(z,x,x) * (L(x,x,z) * y)
    ]]></literal>
    <justification jstring="[para(31821(a,1),31864(a,1,2))].">
      <j1 rule="para" parents="31821 31864"/>
    </justification>
  </clause>

  <clause id="31866">
    <literal><![CDATA[
      ((x \ 1) \ y) * (z / ((x \ 1) \ y)) = (x * y) * (z / (x * y))
    ]]></literal>
    <justification jstring="[para(1137(a,1),25143(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1137 25143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31867">
    <literal><![CDATA[
      (x * y) * ((z * ((x \ 1) \ y)) / (x * y)) = ((x \ 1) \ y) * z
    ]]></literal>
    <justification jstring="[para(11(a,1),31866(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 31866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31868">
    <literal><![CDATA[
      (x * ((y \ 1) \ z)) / (y * z) = (y * z) \ (((y \ 1) \ z) * x)
    ]]></literal>
    <justification jstring="[hyper(149,a,31867,a),flip(a)].">
      <j1 rule="hyper" parents="149 31867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31869">
    <literal><![CDATA[
      (((x \ 1) \ y) * T(z,x * y)) / (x * y) = (x * y) \ (((x \ 1) \ y) * z)
    ]]></literal>
    <justification jstring="[para(14486(a,2),31868(a,1,1))].">
      <j1 rule="para" parents="14486 31868"/>
    </justification>
  </clause>

  <clause id="31870">
    <literal><![CDATA[
      (((x \ 1) \ y) * z) / T(x * y,z) = (x * y) \ (((x \ 1) \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6846,a(flip),b,31869,a)].">
      <j1 rule="hyper" parents="64 6846 31869"/>
    </justification>
  </clause>

  <clause id="31871">
    <literal><![CDATA[
      (x * L(x \ ((x \ 1) \ y),y,x)) * y = x * (y * ((((x \ 1) \ y) * y) / T(x * y,y)))
    ]]></literal>
    <justification jstring="[para(31870(a,2),2842(a,2,2,2))].">
      <j1 rule="para" parents="31870 2842"/>
    </justification>
  </clause>

  <clause id="31872">
    <literal><![CDATA[
      K(x,y \ 1) * (y / (L(y,z,u) \ 1)) = y / T(L(y,z,u) \ 1,x)
    ]]></literal>
    <justification jstring="[para(23047(a,1),25343(a,1,1))].">
      <j1 rule="para" parents="23047 25343"/>
    </justification>
  </clause>

  <clause id="31873">
    <literal><![CDATA[
      K(x,y \ 1) * ((1 / y) \ L(y,z,u)) = y / T(L(y,z,u) \ 1,x)
    ]]></literal>
    <justification jstring="[para(7709(a,1),31872(a,1,2))].">
      <j1 rule="para" parents="7709 31872"/>
    </justification>
  </clause>

  <clause id="31875">
    <literal><![CDATA[
      T(1 / x,T(y,x)) \ L(x,z,u) = x / T(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,7990,a(flip),b,31873,a)].">
      <j1 rule="hyper" parents="64 7990 31873"/>
    </justification>
  </clause>

  <clause id="31876">
    <literal><![CDATA[
      x / T(L(x,y,z) \ 1,u) = T(1 / x,u) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(7850(a,1),31875(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7850 31875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31877">
    <literal><![CDATA[
      T(1 / x,x) \ L(x,y,z) = (L(x,y,z) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,28896,a(flip),b,31876,a),flip(a)].">
      <j1 rule="hyper" parents="64 28896 31876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31878">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ x = (x \ 1) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(117(a,1),31877(a,1,1)),flip(a)].">
      <j1 rule="para" parents="117 31877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31879">
    <literal><![CDATA[
      a(x,y * K(z,u),w) = a(x,y,K(z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24455,a(flip),b,25405,a)].">
      <j1 rule="hyper" parents="64 24455 25405"/>
    </justification>
  </clause>

  <clause id="31880">
    <literal><![CDATA[
      a(x,y * K(z,u),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27311,a(flip),b,31879,a),flip(a)].">
      <j1 rule="hyper" parents="373 27311 31879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31882">
    <literal><![CDATA[
      a(x,y * K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w) = v5
    ]]></literal>
    <justification jstring="[para(31879(a,2),27587(a,1))].">
      <j1 rule="para" parents="31879 27587"/>
    </justification>
  </clause>

  <clause id="31888">
    <literal><![CDATA[
      a(x,y * z,u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(94(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="94 31880"/>
    </justification>
  </clause>

  <clause id="31889">
    <literal><![CDATA[
      a(x,(y \ z) * y,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(353(a,1),31880(a,1,2)),flip(a)].">
      <j1 rule="para" parents="353 31880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31890">
    <literal><![CDATA[
      a(x,y * (z / y),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(355(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="355 31880"/>
    </justification>
  </clause>

  <clause id="31891">
    <literal><![CDATA[
      a(x,y \ T(z,u),w) = a(x,y \ z,w)
    ]]></literal>
    <justification jstring="[para(2433(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="2433 31880"/>
    </justification>
  </clause>

  <clause id="31892">
    <literal><![CDATA[
      a(x,T(y,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(5748(a,1),31880(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5748 31880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31895">
    <literal><![CDATA[
      a(x,y / z,u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(5774(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="5774 31880"/>
    </justification>
  </clause>

  <clause id="31896">
    <literal><![CDATA[
      a(x,y * T(z,u),w) = a(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(6249(a,1),31880(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6249 31880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31897">
    <literal><![CDATA[
      a(x,y * (z / u),w) = a(x,y * (u \ z),w)
    ]]></literal>
    <justification jstring="[para(6471(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="6471 31880"/>
    </justification>
  </clause>

  <clause id="31898">
    <literal><![CDATA[
      a(x,K(y,z) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(6576(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="6576 31880"/>
    </justification>
  </clause>

  <clause id="31899">
    <literal><![CDATA[
      a(x,T(y,z) * u,w) = a(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(6570(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="6570 31880"/>
    </justification>
  </clause>

  <clause id="31900">
    <literal><![CDATA[
      a(x,(y * y) * (z / y),u) = a(x,(1 / y) \ z,u)
    ]]></literal>
    <justification jstring="[para(7211(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="7211 31880"/>
    </justification>
  </clause>

  <clause id="31901">
    <literal><![CDATA[
      a(x,y * (z * T(u,w)),v5) = a(x,y * (z * u),v5)
    ]]></literal>
    <justification jstring="[para(7368(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="7368 31880"/>
    </justification>
  </clause>

  <clause id="31902">
    <literal><![CDATA[
      a(x,y * (z * u),w) = a(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[para(7591(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="7591 31880"/>
    </justification>
  </clause>

  <clause id="31903">
    <literal><![CDATA[
      a(x,T(y,z) \ u,w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(7948(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="7948 31880"/>
    </justification>
  </clause>

  <clause id="31904">
    <literal><![CDATA[
      a(x,(y / z) * u,w) = a(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[para(8651(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="8651 31880"/>
    </justification>
  </clause>

  <clause id="31905">
    <literal><![CDATA[
      a(x,y * ((z \ u) * z),w) = a(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(10196(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="10196 31880"/>
    </justification>
  </clause>

  <clause id="31906">
    <literal><![CDATA[
      a(x,y * (z * K(u,w)),v5) = a(x,y * z,v5)
    ]]></literal>
    <justification jstring="[para(12078(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="12078 31880"/>
    </justification>
  </clause>

  <clause id="31907">
    <literal><![CDATA[
      a(x,y \ K(z,u),w) = a(x,y \ 1,w)
    ]]></literal>
    <justification jstring="[para(14444(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="14444 31880"/>
    </justification>
  </clause>

  <clause id="31908">
    <literal><![CDATA[
      a(x,y \ (z / u),w) = a(x,y \ (u \ z),w)
    ]]></literal>
    <justification jstring="[para(15028(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="15028 31880"/>
    </justification>
  </clause>

  <clause id="31909">
    <literal><![CDATA[
      a(x,y \ (z * u),w) = a(x,y \ (u * z),w)
    ]]></literal>
    <justification jstring="[para(14934(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="14934 31880"/>
    </justification>
  </clause>

  <clause id="31910">
    <literal><![CDATA[
      a(x,y \ (z * K(u,w)),v5) = a(x,y \ z,v5)
    ]]></literal>
    <justification jstring="[para(16164(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="16164 31880"/>
    </justification>
  </clause>

  <clause id="31912">
    <literal><![CDATA[
      a(x,L(T(y,z),u,w),v5) = a(x,L(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(23430(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="23430 31880"/>
    </justification>
  </clause>

  <clause id="31913">
    <literal><![CDATA[
      a(x,y * (K(z,u) * w),v5) = a(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(23252(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="23252 31880"/>
    </justification>
  </clause>

  <clause id="31914">
    <literal><![CDATA[
      a(x,y \ (K(z,u) * w),v5) = a(x,y \ w,v5)
    ]]></literal>
    <justification jstring="[para(23401(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="23401 31880"/>
    </justification>
  </clause>

  <clause id="31916">
    <literal><![CDATA[
      a(x,y \ (T(z,u) * w),v5) = a(x,y \ (z * w),v5)
    ]]></literal>
    <justification jstring="[para(24312(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="24312 31880"/>
    </justification>
  </clause>

  <clause id="31917">
    <literal><![CDATA[
      a(x,y \ (z \ (u / w)),v5) = a(x,y \ (z \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(24307(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="24307 31880"/>
    </justification>
  </clause>

  <clause id="31918">
    <literal><![CDATA[
      a(x,y \ (z * (u / w)),v5) = a(x,y \ (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(24314(a,1),31880(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24314 31880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31919">
    <literal><![CDATA[
      a(x,L(y * K(z,u),w,v5),v6) = a(x,L(y,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(26070(a,2),31880(a,1,2))].">
      <j1 rule="para" parents="26070 31880"/>
    </justification>
  </clause>

  <clause id="31920">
    <literal><![CDATA[
      a(x,L(y / z,u,w),v5) = a(x,L(z \ y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(26077(a,1),31880(a,1,2))].">
      <j1 rule="para" parents="26077 31880"/>
    </justification>
  </clause>

  <clause id="31922">
    <literal><![CDATA[
      T(a(x,y,z),u) = a(x,T(y,w),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,23127,a,b,31892,a)].">
      <j1 rule="hyper" parents="373 23127 31892"/>
    </justification>
  </clause>

  <clause id="31927">
    <literal><![CDATA[
      a(T(x,y),T(z,u),w) = a(x,z,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26779,a(flip),b,31892,a),flip(a)].">
      <j1 rule="hyper" parents="373 26779 31892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31931">
    <literal><![CDATA[
      a(x,R(y / z,u,w),v5) = a(x,R(z \ y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(280(a,1),31892(a,1,2)),flip(a)].">
      <j1 rule="para" parents="280 31892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31932">
    <literal><![CDATA[
      a(x,(y * z) * (y \ 1),u) = a(x,R(z,y,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(1042(a,1),31892(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1042 31892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31934">
    <literal><![CDATA[
      (R(x,T(y,x),z) * T(y,x)) * z = ((y * x) * z) * a(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(31892(a,1),14087(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31892 14087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31937">
    <literal><![CDATA[
      L(x,y,a(z * T(u,w),u,z)) = L(x,y,a(z,T(u,w),T(u,w)))
    ]]></literal>
    <justification jstring="[para(31892(a,1),29200(a,1,3))].">
      <j1 rule="para" parents="31892 29200"/>
    </justification>
  </clause>

  <clause id="31938">
    <literal><![CDATA[
      a(x,y * z,u * w) = a(x,z * y,w * u)
    ]]></literal>
    <justification jstring="[hyper(27453,a,31888,a)].">
      <j1 rule="hyper" parents="27453 31888"/>
    </justification>
  </clause>

  <clause id="31939">
    <literal><![CDATA[
      a(x,y * (z * z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(26848,a,31888,a),flip(a)].">
      <j1 rule="hyper" parents="26848 31888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31940">
    <literal><![CDATA[
      a(x * y,z * u,w) = a(y * x,u * z,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,31888,a)].">
      <j1 rule="hyper" parents="26847 31888"/>
    </justification>
  </clause>

  <clause id="31943">
    <literal><![CDATA[
      a(x,(y \ 1) * z,u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11984,a,b,31888,a)].">
      <j1 rule="hyper" parents="373 11984 31888"/>
    </justification>
  </clause>

  <clause id="31944">
    <literal><![CDATA[
      a(L(x,y,y),x * y,y) = a(x,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,31729,a(flip),b,31888,a),flip(a)].">
      <j1 rule="hyper" parents="373 31729 31888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31945">
    <literal><![CDATA[
      a(x,y * (z \ 1),u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11984,a(flip),b,31888,a),flip(a)].">
      <j1 rule="hyper" parents="373 11984 31888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31946">
    <literal><![CDATA[
      a(x,y * (((z * z) \ u) * w),v5) = a(x,(u * w) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,11973,a(flip),b,31888,a),flip(a)].">
      <j1 rule="hyper" parents="373 11973 31888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31947">
    <literal><![CDATA[
      a(x,y * ((z * z) \ u),w) = a(x,u * y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11969,a(flip),b,31888,a),flip(a)].">
      <j1 rule="hyper" parents="373 11969 31888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31948">
    <literal><![CDATA[
      a(x,y * (1 / z),u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11967,a(flip),b,31888,a),flip(a)].">
      <j1 rule="hyper" parents="373 11967 31888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31949">
    <literal><![CDATA[
      a(x,y * z,u) \ (a(x,z * y,u) * w) = w
    ]]></literal>
    <justification jstring="[hyper(143,a,31888,a,b,79,a),flip(a)].">
      <j1 rule="hyper" parents="143 31888 79"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31950">
    <literal><![CDATA[
      a(x,y * z,u) \ w = a(x,z * y,u) \ w
    ]]></literal>
    <justification jstring="[hyper(62,a,31888,a)].">
      <j1 rule="hyper" parents="62 31888"/>
    </justification>
  </clause>

  <clause id="31951">
    <literal><![CDATA[
      a(x,y * ((z * z) * u),w) = a(x,u * (y * (z * z)),w)
    ]]></literal>
    <justification jstring="[para(34(a,1),31888(a,1,2))].">
      <j1 rule="para" parents="34 31888"/>
    </justification>
  </clause>

  <clause id="31955">
    <literal><![CDATA[
      a(x,L((y \ z) * y,u,w),v5) = a(x,L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(5544(a,2),31889(a,1,2))].">
      <j1 rule="para" parents="5544 31889"/>
    </justification>
  </clause>

  <clause id="31956">
    <literal><![CDATA[
      a(x,L(y * z,u,w),v5) = a(x,L(z * y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(5545(a,1),31889(a,1,2))].">
      <j1 rule="para" parents="5545 31889"/>
    </justification>
  </clause>

  <clause id="31957">
    <literal><![CDATA[
      a(x,a(y,y,y \ z),u) = a(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(30155(a,1),31889(a,1,2))].">
      <j1 rule="para" parents="30155 31889"/>
    </justification>
  </clause>

  <clause id="31962">
    <literal><![CDATA[
      a(x,T(y / z,u),w) = a(x,z \ y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31892,a,b,31895,a)].">
      <j1 rule="hyper" parents="64 31892 31895"/>
    </justification>
  </clause>

  <clause id="31963">
    <literal><![CDATA[
      a(x,(y / z) \ 1,u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11980,a,b,31895,a)].">
      <j1 rule="hyper" parents="64 11980 31895"/>
    </justification>
  </clause>

  <clause id="31965">
    <literal><![CDATA[
      a(x / y,y \ x,x) \ y = ((x / y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(31895(a,1),30049(a,1,1))].">
      <j1 rule="para" parents="31895 30049"/>
    </justification>
  </clause>

  <clause id="31969">
    <literal><![CDATA[
      (x * (K(y,z) * (u * w))) \ ((x * (K(y,z) * u)) * w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24340,a,b,31898,a)].">
      <j1 rule="hyper" parents="64 24340 31898"/>
    </justification>
  </clause>

  <clause id="31970">
    <literal><![CDATA[
      a(x,((y \ z) \ z) * u,w) = a(x,y * u,w)
    ]]></literal>
    <justification jstring="[para(6025(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="6025 31898"/>
    </justification>
  </clause>

  <clause id="31971">
    <literal><![CDATA[
      a(x,((y \ z) \ z) \ u,w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(6073(a,1),31898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6073 31898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31972">
    <literal><![CDATA[
      a(x,(y / z) \ u,w) = a(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),31898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 31898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31973">
    <literal><![CDATA[
      a(x,y \ ((z * z) * u),w) = a(x,(z * z) * (y \ u),w)
    ]]></literal>
    <justification jstring="[para(6626(a,1),31898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6626 31898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31974">
    <literal><![CDATA[
      a(x,(K(y,z) * u) * w,v5) = a(x,u * w,v5)
    ]]></literal>
    <justification jstring="[para(7760(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="7760 31898"/>
    </justification>
  </clause>

  <clause id="31975">
    <literal><![CDATA[
      a(x,(y * z) \ u,w) = a(x,(z * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(10833(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="10833 31898"/>
    </justification>
  </clause>

  <clause id="31976">
    <literal><![CDATA[
      a(x,(y * z) * u,w) = a(x,(z * y) * u,w)
    ]]></literal>
    <justification jstring="[para(10834(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="10834 31898"/>
    </justification>
  </clause>

  <clause id="31977">
    <literal><![CDATA[
      a(x,(y \ T(z,u)) \ w,v5) = a(x,(y \ z) \ w,v5)
    ]]></literal>
    <justification jstring="[para(24519(a,1),31898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24519 31898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31978">
    <literal><![CDATA[
      a(x,(y * T(z,u)) * w,v5) = a(x,(y * z) * w,v5)
    ]]></literal>
    <justification jstring="[para(24355(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="24355 31898"/>
    </justification>
  </clause>

  <clause id="31979">
    <literal><![CDATA[
      a(x,L(T(y,z),u,w) \ v5,v6) = a(x,L(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(24557(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="24557 31898"/>
    </justification>
  </clause>

  <clause id="31980">
    <literal><![CDATA[
      a(x,L(T(y,z),u,w) * v5,v6) = a(x,L(y,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(24680(a,1),31898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24680 31898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31981">
    <literal><![CDATA[
      a(x,(T(y,z) \ u) \ w,v5) = a(x,(y \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(25410(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="25410 31898"/>
    </justification>
  </clause>

  <clause id="31982">
    <literal><![CDATA[
      a(x,((y / z) * u) * w,v5) = a(x,((z \ y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(24351(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="24351 31898"/>
    </justification>
  </clause>

  <clause id="31983">
    <literal><![CDATA[
      a(x,((y / z) \ u) * w,v5) = a(x,((z \ y) \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(24352(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="24352 31898"/>
    </justification>
  </clause>

  <clause id="31984">
    <literal><![CDATA[
      a(x,(y * (K(z,u) * w)) * v5,v6) = a(x,(y * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(24368(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="24368 31898"/>
    </justification>
  </clause>

  <clause id="31985">
    <literal><![CDATA[
      a(x,(y * (z / u)) \ w,v5) = a(x,(y * (u \ z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(24507(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="24507 31898"/>
    </justification>
  </clause>

  <clause id="31986">
    <literal><![CDATA[
      a(x,(y \ (z / u)) \ w,v5) = a(x,(y \ (u \ z)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(24522(a,1),31898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24522 31898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31987">
    <literal><![CDATA[
      a(x,(y * (K(z,u) * w)) \ v5,v6) = a(x,(y * w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(25411(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="25411 31898"/>
    </justification>
  </clause>

  <clause id="31988">
    <literal><![CDATA[
      a(x,(y \ (K(z,u) * w)) \ v5,v6) = a(x,(y \ w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(25412(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="25412 31898"/>
    </justification>
  </clause>

  <clause id="31990">
    <literal><![CDATA[
      a(x,L(K(y,z) * u,w,v5),v6) = a(x,L(u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(26085(a,2),31898(a,1,2))].">
      <j1 rule="para" parents="26085 31898"/>
    </justification>
  </clause>

  <clause id="31991">
    <literal><![CDATA[
      a(x,L(y * z,u,w) * v5,v6) = a(x,L(z * y,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(26140(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="26140 31898"/>
    </justification>
  </clause>

  <clause id="31992">
    <literal><![CDATA[
      a(x,L(y / z,u,w) * v5,v6) = a(x,L(z \ y,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(25447(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="25447 31898"/>
    </justification>
  </clause>

  <clause id="31993">
    <literal><![CDATA[
      a(x,R(y / z,u,w) \ v5,v6) = a(x,R(z \ y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(25674(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="25674 31898"/>
    </justification>
  </clause>

  <clause id="31994">
    <literal><![CDATA[
      a(x,L(y / z,u,w) \ v5,v6) = a(x,L(z \ y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(26119(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="26119 31898"/>
    </justification>
  </clause>

  <clause id="31995">
    <literal><![CDATA[
      a(x,L((y \ z) * y,u,w) \ v5,v6) = a(x,L(z,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(26138(a,1),31898(a,1,2))].">
      <j1 rule="para" parents="26138 31898"/>
    </justification>
  </clause>

  <clause id="31996">
    <literal><![CDATA[
      a(x,(y * z) \ ((z * u) * y),w) = a(x,L(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(27292(a,2),31898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="27292 31898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="31997">
    <literal><![CDATA[
      a(x,T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(31922(a,1),203(a,1)),flip(b)].">
      <j1 rule="para" parents="31922 203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32005">
    <literal><![CDATA[
      a(x,R(y * (z * z),u,w),v5) = a(x,R(y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(2102(a,2),31939(a,1,2))].">
      <j1 rule="para" parents="2102 31939"/>
    </justification>
  </clause>

  <clause id="32007">
    <literal><![CDATA[
      a(x,(y \ z) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(116(a,1),31997(a,1,2))].">
      <j1 rule="para" parents="116 31997"/>
    </justification>
  </clause>

  <clause id="32008">
    <literal><![CDATA[
      a(x,y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z * y,u) = w
    ]]></literal>
    <justification jstring="[para(13831(a,1),31997(a,1))].">
      <j1 rule="para" parents="13831 31997"/>
    </justification>
  </clause>

  <clause id="32013">
    <literal><![CDATA[
      a(x,y \ R(z / u,w,v5),v6) = a(x,y \ R(u \ z,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(280(a,1),31891(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="280 31891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32016">
    <literal><![CDATA[
      a(x,y * T(z,u),w) = a(x,z * y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31888,a,b,31896,a),flip(a)].">
      <j1 rule="hyper" parents="373 31888 31896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32017">
    <literal><![CDATA[
      a(x,((y * z) * z) * y,u) = a(x,a(y * z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25792,a(flip),b,31896,a),flip(a)].">
      <j1 rule="hyper" parents="64 25792 31896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32018">
    <literal><![CDATA[
      a(x,y * (z * (u * (z \ 1))),w) = a(x,y * L(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(1178(a,1),31896(a,1,2,2))].">
      <j1 rule="para" parents="1178 31896"/>
    </justification>
  </clause>

  <clause id="32019">
    <literal><![CDATA[
      a(x,y * (z \ ((u * u) * w)),v5) = a(x,y * ((u * u) * (w / z)),v5)
    ]]></literal>
    <justification jstring="[para(946(a,1),31896(a,1,2,2))].">
      <j1 rule="para" parents="946 31896"/>
    </justification>
  </clause>

  <clause id="32020">
    <literal><![CDATA[
      a(x,y * (z \ (u * (z * z))),w) = a(x,y * (u * L(z,z,u)),w)
    ]]></literal>
    <justification jstring="[para(2848(a,1),31896(a,1,2,2))].">
      <j1 rule="para" parents="2848 31896"/>
    </justification>
  </clause>

  <clause id="32021">
    <literal><![CDATA[
      a(x,(y * z) * (y \ 1),u) = a(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(5134(a,1),31896(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5134 31896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32024">
    <literal><![CDATA[
      a(x,T(((y * y) \ z) * u,w) * v5,v6) = a(x,(z * u) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,11973,a(flip),b,31899,a),flip(a)].">
      <j1 rule="hyper" parents="373 11973 31899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32025">
    <literal><![CDATA[
      a(x,y * ((z * z) * u),w) = a(x,y * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11974,a(flip),b,31899,a)].">
      <j1 rule="hyper" parents="64 11974 31899"/>
    </justification>
  </clause>

  <clause id="32026">
    <literal><![CDATA[
      a(x,(y / z) \ z,u) = a(x,(z / y) * z,u)
    ]]></literal>
    <justification jstring="[para(3818(a,1),31899(a,1,2))].">
      <j1 rule="para" parents="3818 31899"/>
    </justification>
  </clause>

  <clause id="32031">
    <literal><![CDATA[
      a(x,R(y,z,y) \ 1,L(R(y,z,y) \ 1,y,z)) = a(x,(y * z) \ z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,16723,a,b,31903,a)].">
      <j1 rule="hyper" parents="64 16723 31903"/>
    </justification>
  </clause>

  <clause id="32033">
    <literal><![CDATA[
      a(x,y \ K(z,u),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11980,a(flip),b,31907,a),flip(a)].">
      <j1 rule="hyper" parents="373 11980 31907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32034">
    <literal><![CDATA[
      a(x,y * (z \ 1),u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31888,a,b,31943,a)].">
      <j1 rule="hyper" parents="64 31888 31943"/>
    </justification>
  </clause>

  <clause id="32035">
    <literal><![CDATA[
      a(x,L(y,z,z) * y,u) = a(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(1847(a,1),31945(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1847 31945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32037">
    <literal><![CDATA[
      a(x,(y * z) \ ((y * u) * z),w) = a(x,R(u,y,z),w)
    ]]></literal>
    <justification jstring="[para(1039(a,2),31962(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1039 31962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32038">
    <literal><![CDATA[
      a(x,(y * z) \ z,u) = a(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[para(5144(a,1),31962(a,1,2))].">
      <j1 rule="para" parents="5144 31962"/>
    </justification>
  </clause>

  <clause id="32039">
    <literal><![CDATA[
      a(x,(y / z) * u,w) = a(x,u * (z \ y),w)
    ]]></literal>
    <justification jstring="[para(117(a,1),32016(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="117 32016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32040">
    <literal><![CDATA[
      a(x,y * L(y,z,z),u) = a(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(1847(a,1),32034(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1847 32034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32041">
    <literal><![CDATA[
      a(x,y \ T(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ z,w) = v5
    ]]></literal>
    <justification jstring="[para(2433(a,1),31882(a,1,2))].">
      <j1 rule="para" parents="2433 31882"/>
    </justification>
  </clause>

  <clause id="32042">
    <literal><![CDATA[
      a(x,y / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,u) = w
    ]]></literal>
    <justification jstring="[para(5774(a,1),31882(a,1,2))].">
      <j1 rule="para" parents="5774 31882"/>
    </justification>
  </clause>

  <clause id="32046">
    <literal><![CDATA[
      a(x,y \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(11980(a,1),32007(a,1))].">
      <j1 rule="para" parents="11980 32007"/>
    </justification>
  </clause>

  <clause id="32047">
    <literal><![CDATA[
      a(x,1 / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(5355(a,2),32046(a,1))].">
      <j1 rule="para" parents="5355 32046"/>
    </justification>
  </clause>

  <clause id="32048">
    <literal><![CDATA[
      a(x,y * R(z * K(u,z),u,w),v5) = a(x,y * ((u * w) \ ((u * z) * w)),v5)
    ]]></literal>
    <justification jstring="[para(5897(a,2),31897(a,1,2,2))].">
      <j1 rule="para" parents="5897 31897"/>
    </justification>
  </clause>

  <clause id="32049">
    <literal><![CDATA[
      a(x,(y * z) * u,w) = a(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[hyper(32008,a,31902,a)].">
      <j1 rule="hyper" parents="32008 31902"/>
    </justification>
  </clause>

  <clause id="32050">
    <literal><![CDATA[
      a(x,y * (((T(z,u * u) * w) / v5) * (u * u)),v6) = a(x,y * ((z * ((u * u) * w)) / v5),v6)
    ]]></literal>
    <justification jstring="[para(1523(a,1),31902(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1523 31902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32052">
    <literal><![CDATA[
      a(x,y,L(y,y \ z,y \ z)) = a(x,(y \ z) * z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16196,a,b,31904,a)].">
      <j1 rule="hyper" parents="64 16196 31904"/>
    </justification>
  </clause>

  <clause id="32053">
    <literal><![CDATA[
      a(x,(y \ (1 / z)) * u,w) = a(x,(z / y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11993,a(flip),b,31904,a),flip(a)].">
      <j1 rule="hyper" parents="64 11993 31904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32054">
    <literal><![CDATA[
      a(x,((y \ z) * y) * u,w) = a(x,u * z,w)
    ]]></literal>
    <justification jstring="[hyper(32008,a,31905,a)].">
      <j1 rule="hyper" parents="32008 31905"/>
    </justification>
  </clause>

  <clause id="32055">
    <literal><![CDATA[
      a(x,y * a(z,z,z * u),w) = a(x,y * a(z,z,u),w)
    ]]></literal>
    <justification jstring="[para(30156(a,1),31905(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="30156 31905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32056">
    <literal><![CDATA[
      a(x,y * a(z * u,u,u \ 1),w) = a(x,y * a(z,u,u),w)
    ]]></literal>
    <justification jstring="[para(30717(a,2),31905(a,1,2,2))].">
      <j1 rule="para" parents="30717 31905"/>
    </justification>
  </clause>

  <clause id="32057">
    <literal><![CDATA[
      a(x,y * (z * (u / w)),v5) = a(x,y * (z * (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(6471(a,1),31906(a,1,2,2))].">
      <j1 rule="para" parents="6471 31906"/>
    </justification>
  </clause>

  <clause id="32058">
    <literal><![CDATA[
      a(x,y * ((z / u) * w),v5) = a(x,y * ((u \ z) * w),v5)
    ]]></literal>
    <justification jstring="[para(8651(a,1),31906(a,1,2,2))].">
      <j1 rule="para" parents="8651 31906"/>
    </justification>
  </clause>

  <clause id="32059">
    <literal><![CDATA[
      a(x,y * (z \ (u / w)),v5) = a(x,y * (z \ (w \ u)),v5)
    ]]></literal>
    <justification jstring="[para(15028(a,1),31906(a,1,2,2))].">
      <j1 rule="para" parents="15028 31906"/>
    </justification>
  </clause>

  <clause id="32060">
    <literal><![CDATA[
      a(x,y * (z \ (u / (w / v5))),v6) = a(x,y * (z \ (u / (v5 \ w))),v6)
    ]]></literal>
    <justification jstring="[para(24313(a,1),31906(a,1,2,2))].">
      <j1 rule="para" parents="24313 31906"/>
    </justification>
  </clause>

  <clause id="32061">
    <literal><![CDATA[
      a(x,y * R(z * K(u,w),v5,v6),v7) = a(x,y * R(z,v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(25973(a,2),31906(a,1,2,2))].">
      <j1 rule="para" parents="25973 31906"/>
    </justification>
  </clause>

  <clause id="32062">
    <literal><![CDATA[
      a((x / y) \ z,z \ (y \ x),z) = (z / (x / y)) * ((x / y) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26894,a(flip),b,31908,a),flip(a)].">
      <j1 rule="hyper" parents="64 26894 31908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32063">
    <literal><![CDATA[
      a(x,(y * z) / u,w) = a(x,u \ (z * y),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31895,a,b,31909,a)].">
      <j1 rule="hyper" parents="373 31895 31909"/>
    </justification>
  </clause>

  <clause id="32067">
    <literal><![CDATA[
      a(x,y \ (z * (u * w)),v5) = a(x,y \ (z * (w * u)),v5)
    ]]></literal>
    <justification jstring="[para(7591(a,1),31910(a,1,2,2))].">
      <j1 rule="para" parents="7591 31910"/>
    </justification>
  </clause>

  <clause id="32070">
    <literal><![CDATA[
      a(x,y \ (z \ (T(u,w) * v5)),v6) = a(x,y \ (z \ (u * v5)),v6)
    ]]></literal>
    <justification jstring="[para(24312(a,1),31910(a,1,2,2))].">
      <j1 rule="para" parents="24312 31910"/>
    </justification>
  </clause>

  <clause id="32072">
    <literal><![CDATA[
      a(x,L(y / ((z * z) * u),w,v5),v6) = a(x,L((z * z) \ (y / u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(893(a,1),31912(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="893 31912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32073">
    <literal><![CDATA[
      a(x,y * (K(z,u) * w),v5) = a(x,w * y,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31888,a,b,31913,a),flip(a)].">
      <j1 rule="hyper" parents="373 31888 31913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32074">
    <literal><![CDATA[
      a(x,y * ((z / u) \ w),v5) = a(x,y * ((u \ z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(6270(a,1),31913(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6270 31913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32075">
    <literal><![CDATA[
      a(x,(y \ T(z,u)) * w,v5) = a(x,(y \ z) * w,v5)
    ]]></literal>
    <justification jstring="[para(24474(a,1),31913(a,1,2))].">
      <j1 rule="para" parents="24474 31913"/>
    </justification>
  </clause>

  <clause id="32076">
    <literal><![CDATA[
      a(x,y * ((T(z,u) \ w) \ v5),v6) = a(x,y * ((z \ w) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(25410(a,1),31913(a,1,2,2))].">
      <j1 rule="para" parents="25410 31913"/>
    </justification>
  </clause>

  <clause id="32077">
    <literal><![CDATA[
      a(x,(y \ (z / u)) * w,v5) = a(x,(y \ (u \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(24475(a,1),31913(a,1,2))].">
      <j1 rule="para" parents="24475 31913"/>
    </justification>
  </clause>

  <clause id="32078">
    <literal><![CDATA[
      a(x,(y * (z * T(u,w))) * v5,v6) = a(x,(y * (z * u)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(24746(a,1),31913(a,1,2))].">
      <j1 rule="para" parents="24746 31913"/>
    </justification>
  </clause>

  <clause id="32079">
    <literal><![CDATA[
      a(x,(y \ (K(z,u) * w)) * v5,v6) = a(x,(y \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(24778(a,1),31913(a,1,2))].">
      <j1 rule="para" parents="24778 31913"/>
    </justification>
  </clause>

  <clause id="32080">
    <literal><![CDATA[
      a(x,(y * (z \ K(u,w))) * v5,v6) = a(x,(y * (z \ 1)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(24883(a,1),31913(a,1,2))].">
      <j1 rule="para" parents="24883 31913"/>
    </justification>
  </clause>

  <clause id="32081">
    <literal><![CDATA[
      a(x,(y \ L(T(z,u),w,v5)) * v6,v7) = a(x,(y \ L(z,w,v5)) * v6,v7)
    ]]></literal>
    <justification jstring="[para(25329(a,1),31913(a,1,2))].">
      <j1 rule="para" parents="25329 31913"/>
    </justification>
  </clause>

  <clause id="32084">
    <literal><![CDATA[
      a(x,(T(y,z) * u) \ w,v5) = a(x,(y * u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(24191(a,1),31914(a,1,2))].">
      <j1 rule="para" parents="24191 31914"/>
    </justification>
  </clause>

  <clause id="32085">
    <literal><![CDATA[
      a(x,((y / z) * u) \ w,v5) = a(x,((z \ y) * u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(24400(a,1),31914(a,1,2))].">
      <j1 rule="para" parents="24400 31914"/>
    </justification>
  </clause>

  <clause id="32087">
    <literal><![CDATA[
      a(x,(((y \ z) \ z) \ u) \ w,v5) = a(x,(y \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(24419(a,2),31914(a,1,2))].">
      <j1 rule="para" parents="24419 31914"/>
    </justification>
  </clause>

  <clause id="32088">
    <literal><![CDATA[
      L(x,y,a(z,u * w,v5)) = L(x,y,a(z,w * u,v5))
    ]]></literal>
    <justification jstring="[para(31949(a,1),2183(a,1,3))].">
      <j1 rule="para" parents="31949 2183"/>
    </justification>
  </clause>

  <clause id="32089">
    <literal><![CDATA[
      a(a(x,y * z,u),w,v5) = a(a(x,z * y,u),w,v5)
    ]]></literal>
    <justification jstring="[para(31949(a,1),2666(a,1,1))].">
      <j1 rule="para" parents="31949 2666"/>
    </justification>
  </clause>

  <clause id="32090">
    <literal><![CDATA[
      a(x,y,(a(z,u * w,v5) \ v6) \ v6) = a(x,y,a(z,w * u,v5))
    ]]></literal>
    <justification jstring="[para(31950(a,1),27307(a,1,3,1))].">
      <j1 rule="para" parents="31950 27307"/>
    </justification>
  </clause>

  <clause id="32091">
    <literal><![CDATA[
      a(x,((y \ z) \ z) * u,w) = a(x,u * y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31888,a,b,31970,a),flip(a)].">
      <j1 rule="hyper" parents="373 31888 31970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32092">
    <literal><![CDATA[
      a(x,((((y * (1 / z)) * u) \ y) \ (y * (z * z))) \ w,v5) = a(x,((y * z) * u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(25861(a,1),31971(a,1,2,1,1))].">
      <j1 rule="para" parents="25861 31971"/>
    </justification>
  </clause>

  <clause id="32093">
    <literal><![CDATA[
      a(x \ (y / z),(z \ y) \ x,z \ y) = ((y / z) / x) * (x / (y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27381,a(flip),b,31972,a),flip(a)].">
      <j1 rule="hyper" parents="64 27381 31972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32094">
    <literal><![CDATA[
      a(x,((1 / y) \ z) \ u,w) = a(x,(z / y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11971,a(flip),b,31972,a),flip(a)].">
      <j1 rule="hyper" parents="64 11971 31972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32095">
    <literal><![CDATA[
      a(x,(((y / z) / u) / (y * y)) \ w,v5) = a(x,(((1 / y) / z) / u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(935(a,1),31972(a,2,2,1))].">
      <j1 rule="para" parents="935 31972"/>
    </justification>
  </clause>

  <clause id="32096">
    <literal><![CDATA[
      a(x,(((y * (z * z)) / u) / (z * z)) \ w,v5) = a(x,(T(y,z * z) / u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(934(a,1),31972(a,2,2,1))].">
      <j1 rule="para" parents="934 31972"/>
    </justification>
  </clause>

  <clause id="32097">
    <literal><![CDATA[
      a(x,((1 / y) \ ((1 / z) / y)) \ u,w) = a(x,(1 / R(z,y,y)) \ u,w)
    ]]></literal>
    <justification jstring="[para(30570(a,1),31972(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30570 31972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32098">
    <literal><![CDATA[
      a(x,(((y / z) \ u) * w) * v5,v6) = a(x,(((z \ y) \ u) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(24352(a,1),31974(a,1,2,1))].">
      <j1 rule="para" parents="24352 31974"/>
    </justification>
  </clause>

  <clause id="32099">
    <literal><![CDATA[
      a(x,(((y \ K(z,u)) \ w) * v5) * v6,v7) = a(x,(((y \ 1) \ w) * v5) * v6,v7)
    ]]></literal>
    <justification jstring="[para(24969(a,1),31974(a,1,2,1))].">
      <j1 rule="para" parents="24969 31974"/>
    </justification>
  </clause>

  <clause id="32100">
    <literal><![CDATA[
      a(x,L(T(y,z) * u,w,v5) * v6,v7) = a(x,L(y * u,w,v5) * v6,v7)
    ]]></literal>
    <justification jstring="[para(26086(a,1),31974(a,1,2,1))].">
      <j1 rule="para" parents="26086 31974"/>
    </justification>
  </clause>

  <clause id="32101">
    <literal><![CDATA[
      a(x,L(T(y,z) \ u,w,v5) * v6,v7) = a(x,L(y \ u,w,v5) * v6,v7)
    ]]></literal>
    <justification jstring="[para(26100(a,1),31974(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="26100 31974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32102">
    <literal><![CDATA[
      a(x,(y * z) * T(u,w),v5) = a(x,(z * y) * u,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31896,a,b,31976,a)].">
      <j1 rule="hyper" parents="373 31896 31976"/>
    </justification>
  </clause>

  <clause id="32103">
    <literal><![CDATA[
      a(x,((y \ 1) * z) * u,w) = a(x,(z * y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11998,a,b,31976,a)].">
      <j1 rule="hyper" parents="373 11998 31976"/>
    </justification>
  </clause>

  <clause id="32104">
    <literal><![CDATA[
      a(x,(y * ((1 / z) * u)) * w,v5) = a(x,((z * u) * y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,12002,a(flip),b,31976,a),flip(a)].">
      <j1 rule="hyper" parents="373 12002 31976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32105">
    <literal><![CDATA[
      a(x,(y * (z \ 1)) * u,w) = a(x,(z * y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11998,a(flip),b,31976,a),flip(a)].">
      <j1 rule="hyper" parents="373 11998 31976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32106">
    <literal><![CDATA[
      a(x,((y * z) * y) * u,w) = a(x,L(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11972,a(flip),b,31976,a),flip(a)].">
      <j1 rule="hyper" parents="373 11972 31976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32107">
    <literal><![CDATA[
      a(x,(((y * y) * z) * (u / y)) * w,v5) = a(x,((u / (1 / y)) * z) * w,v5)
    ]]></literal>
    <justification jstring="[para(819(a,1),31976(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="819 31976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32109">
    <literal><![CDATA[
      a(x,L((y \ 1) * (y * y),z,u) * w,v5) = a(x,L(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,12028,a,b,32025,a)].">
      <j1 rule="hyper" parents="64 12028 32025"/>
    </justification>
  </clause>

  <clause id="32110">
    <literal><![CDATA[
      a(x,y * (z * (z * u)),w) = a(x,y * L(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(100(a,1),32025(a,1,2,2))].">
      <j1 rule="para" parents="100 32025"/>
    </justification>
  </clause>

  <clause id="32111">
    <literal><![CDATA[
      a(x,y * ((a(z,u,w) \ 1) \ v5),v6) = a(x,y * (a(z,u,w) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(14002(a,1),32025(a,1,2,2))].">
      <j1 rule="para" parents="14002 32025"/>
    </justification>
  </clause>

  <clause id="32112">
    <literal><![CDATA[
      a(x,(y \ z) \ y,u) = a(x,(y / z) * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31972,a(flip),b,32026,a)].">
      <j1 rule="hyper" parents="64 31972 32026"/>
    </justification>
  </clause>

  <clause id="32113">
    <literal><![CDATA[
      a(x,(y * z) \ y,u) = a(x,y \ (z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31975,a,b,32038,a)].">
      <j1 rule="hyper" parents="64 31975 32038"/>
    </justification>
  </clause>

  <clause id="32114">
    <literal><![CDATA[
      a(x,(y * z) * (y \ 1),u) = a(x,L(z,y,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(1635(a,1),32039(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1635 32039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32115">
    <literal><![CDATA[
      (L(x,y,y) * z) / (x * ((a(y,y,x) \ 1) * z)) = a(x,a(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,16242,a,b,32040,a)].">
      <j1 rule="hyper" parents="64 16242 32040"/>
    </justification>
  </clause>

  <clause id="32116">
    <literal><![CDATA[
      a(x,(y * z) * z,u) = a(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11968,a(flip),b,32049,a),flip(a)].">
      <j1 rule="hyper" parents="373 11968 32049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32117">
    <literal><![CDATA[
      a(x,y * (z * (u \ 1)),w) = a(x,(u * z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11998,a(flip),b,32049,a),flip(a)].">
      <j1 rule="hyper" parents="64 11998 32049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32118">
    <literal><![CDATA[
      a(x,((y * z) \ u) * w,v5) = a(x,w * ((z * y) \ u),v5)
    ]]></literal>
    <justification jstring="[para(10833(a,1),32073(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10833 32073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32119">
    <literal><![CDATA[
      a(x,((y * z) * u) * w,v5) = a(x,w * ((z * y) * u),v5)
    ]]></literal>
    <justification jstring="[para(10834(a,1),32073(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10834 32073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32120">
    <literal><![CDATA[
      a(x,y * R(K(z,u) * w,v5,v6),v7) = a(x,R(w,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[para(25964(a,2),32073(a,1,2,2))].">
      <j1 rule="para" parents="25964 32073"/>
    </justification>
  </clause>

  <clause id="32121">
    <literal><![CDATA[
      a(x,y * L(K(z,u) * w,v5,v6),v7) = a(x,L(w,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[para(26085(a,2),32073(a,1,2,2))].">
      <j1 rule="para" parents="26085 32073"/>
    </justification>
  </clause>

  <clause id="32122">
    <literal><![CDATA[
      a(x,((y * z) \ ((z * u) * y)) * w,v5) = a(x,w * L(u,z,y),v5)
    ]]></literal>
    <justification jstring="[para(27292(a,2),32073(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="27292 32073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32124">
    <literal><![CDATA[
      a(x,(y \ z) \ y,u) = a(x,(z \ y) * y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,31904,a(flip),b,32112,a),flip(a)].">
      <j1 rule="hyper" parents="373 31904 32112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32125">
    <literal><![CDATA[
      a(x,L(y \ 1,y,z),u) = a(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13840,a,b,32113,a)].">
      <j1 rule="hyper" parents="64 13840 32113"/>
    </justification>
  </clause>

  <clause id="32126">
    <literal><![CDATA[
      a(x,x \ (y \ x),x * y) * x = R(x,(x * y) \ x,x * y)
    ]]></literal>
    <justification jstring="[para(32113(a,1),24669(a,1,1))].">
      <j1 rule="para" parents="32113 24669"/>
    </justification>
  </clause>

  <clause id="32127">
    <literal><![CDATA[
      a(x \ y,x \ y,y) \ x = ((y / x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(26785(a,1),31965(a,1,1))].">
      <j1 rule="para" parents="26785 31965"/>
    </justification>
  </clause>

  <clause id="32128">
    <literal><![CDATA[
      a(x,L((y * z) * (y \ 1),u,w),v5) = a(x,L(L(z,u,w),y,y),v5)
    ]]></literal>
    <justification jstring="[para(1836(a,2),32021(a,1,2))].">
      <j1 rule="para" parents="1836 32021"/>
    </justification>
  </clause>

  <clause id="32129">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ y = ((x / y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(30068(a,1),32127(a,1,1))].">
      <j1 rule="para" parents="30068 32127"/>
    </justification>
  </clause>

  <clause id="32130">
    <literal><![CDATA[
      x / (((y / x) \ 1) * y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(226,a,32129,a)].">
      <j1 rule="hyper" parents="226 32129"/>
    </justification>
  </clause>

  <clause id="32131">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ T(y,z) = ((x / T(y,z)) \ 1) * x
    ]]></literal>
    <justification jstring="[para(24948(a,1),32129(a,1,1))].">
      <j1 rule="para" parents="24948 32129"/>
    </justification>
  </clause>

  <clause id="32132">
    <literal><![CDATA[
      ((x / y) \ 1) \ (((x / y) * (y / x)) \ z) = (x / y) \ ((y / ((x / y) * x)) \ z)
    ]]></literal>
    <justification jstring="[para(32130(a,1),2317(a,1,2,1))].">
      <j1 rule="para" parents="32130 2317"/>
    </justification>
  </clause>

  <clause id="32133">
    <literal><![CDATA[
      a(x,(1 / y) \ z,u) = a(x,z / y,u)
    ]]></literal>
    <justification jstring="[hyper(26848,a,31900,a),flip(a)].">
      <j1 rule="hyper" parents="26848 31900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32135">
    <literal><![CDATA[
      a(x,(1 / y) \ z,u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,31895,a(flip),b,32133,a),flip(a)].">
      <j1 rule="hyper" parents="373 31895 32133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32136">
    <literal><![CDATA[
      a(x,y / (z \ 1),u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),32133(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 32133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32137">
    <literal><![CDATA[
      a(x,((y / (z * y)) \ 1) \ u,w) = a(x,u / ((z \ y) / y),w)
    ]]></literal>
    <justification jstring="[para(2032(a,1),32133(a,1,2,1))].">
      <j1 rule="para" parents="2032 32133"/>
    </justification>
  </clause>

  <clause id="32138">
    <literal><![CDATA[
      a(x,(y \ 1) \ z,u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31972,a(flip),b,32135,a)].">
      <j1 rule="hyper" parents="64 31972 32135"/>
    </justification>
  </clause>

  <clause id="32139">
    <literal><![CDATA[
      a(x,((y / (z * y)) \ 1) \ u,w) = a(x,((z \ y) / y) \ u,w)
    ]]></literal>
    <justification jstring="[para(2032(a,1),32135(a,1,2,1))].">
      <j1 rule="para" parents="2032 32135"/>
    </justification>
  </clause>

  <clause id="32140">
    <literal><![CDATA[
      a(x,T((y \ 1) \ z,u),w) = a(x,y \ z,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31892,a,b,32138,a)].">
      <j1 rule="hyper" parents="64 31892 32138"/>
    </justification>
  </clause>

  <clause id="32141">
    <literal><![CDATA[
      a(x,L(y * z,y,y),u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30368,a,b,32138,a)].">
      <j1 rule="hyper" parents="64 30368 32138"/>
    </justification>
  </clause>

  <clause id="32142">
    <literal><![CDATA[
      a(x,y \ (y \ z),u) = a(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30405,a(flip),b,32138,a),flip(a)].">
      <j1 rule="hyper" parents="64 30405 32138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32143">
    <literal><![CDATA[
      a(x,y \ (z \ (y \ z)),u) = a(x,y * (z \ (y \ z)),u)
    ]]></literal>
    <justification jstring="[para(26262(a,1),32138(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26262 32138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32144">
    <literal><![CDATA[
      a(x,a(y,y,z) \ y,u) = a(x,R(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(30056(a,1),32138(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30056 32138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32145">
    <literal><![CDATA[
      a(x,y * L(z,y,y),u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,13846,a(flip),b,32141,a)].">
      <j1 rule="hyper" parents="64 13846 32141"/>
    </justification>
  </clause>

  <clause id="32146">
    <literal><![CDATA[
      a(x,y * L((y \ 1) * z,u,w),v5) = a(x,y \ L(y \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(5632(a,1),32141(a,1,2))].">
      <j1 rule="para" parents="5632 32141"/>
    </justification>
  </clause>

  <clause id="32147">
    <literal><![CDATA[
      a(x,R(y \ (y \ z),u,w),v5) = a(x,L(R(z,u,w),y,y),v5)
    ]]></literal>
    <justification jstring="[para(2144(a,2),32142(a,1,2))].">
      <j1 rule="para" parents="2144 32142"/>
    </justification>
  </clause>

  <clause id="32148">
    <literal><![CDATA[
      (x \ y) * a(x \ y,L(y,x,x),x) = R(x \ y,L(y,x,x),x)
    ]]></literal>
    <justification jstring="[para(32142(a,1),30398(a,1,2))].">
      <j1 rule="para" parents="32142 30398"/>
    </justification>
  </clause>

  <clause id="32149">
    <literal><![CDATA[
      a(x,L(y,z,z) * z,u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(32008,a,32145,a)].">
      <j1 rule="hyper" parents="32008 32145"/>
    </justification>
  </clause>

  <clause id="32150">
    <literal><![CDATA[
      a(x,L(y,z * u,z * u) * (u * z),w) = a(x,(z * u) \ y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32049,a(flip),b,32145,a)].">
      <j1 rule="hyper" parents="64 32049 32145"/>
    </justification>
  </clause>

  <clause id="32151">
    <literal><![CDATA[
      a(x,R(y * (y * z),u,w) * y,v5) = a(x,y \ R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,12001,a,b,32149,a)].">
      <j1 rule="hyper" parents="64 12001 32149"/>
    </justification>
  </clause>

  <clause id="32152">
    <literal><![CDATA[
      a(x,L(y,z \ 1,z \ 1) * z,u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(1151(a,2),32149(a,1,2,1))].">
      <j1 rule="para" parents="1151 32149"/>
    </justification>
  </clause>

  <clause id="32153">
    <literal><![CDATA[
      a(x,y * (z * T(u,w)),v5) = a(x,y * (u * z),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31902,a,b,31901,a),flip(a)].">
      <j1 rule="hyper" parents="373 31902 31901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32157">
    <literal><![CDATA[
      a(x,L(y \ z,y,u),w) = a(x,(u * y) \ (u * z),w)
    ]]></literal>
    <justification jstring="[para(25216(a,2),31916(a,1,2))].">
      <j1 rule="para" parents="25216 31916"/>
    </justification>
  </clause>

  <clause id="32159">
    <literal><![CDATA[
      a(x,L(y \ T(z,u),w,v5),v6) = a(x,L(y \ z,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(2433(a,1),31919(a,1,2,1))].">
      <j1 rule="para" parents="2433 31919"/>
    </justification>
  </clause>

  <clause id="32160">
    <literal><![CDATA[
      a(x,L(y * (z / u),w,v5),v6) = a(x,L(y * (u \ z),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(6471(a,1),31919(a,1,2,1))].">
      <j1 rule="para" parents="6471 31919"/>
    </justification>
  </clause>

  <clause id="32161">
    <literal><![CDATA[
      a(x,L((y / z) * u,w,v5),v6) = a(x,L((z \ y) * u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(8651(a,1),31919(a,1,2,1))].">
      <j1 rule="para" parents="8651 31919"/>
    </justification>
  </clause>

  <clause id="32162">
    <literal><![CDATA[
      a(x,L(L(y * K(z,u),w,v5),v6,v7),v8) = a(x,L(L(y,w,v5),v6,v7),v8)
    ]]></literal>
    <justification jstring="[para(26070(a,2),31919(a,1,2,1))].">
      <j1 rule="para" parents="26070 31919"/>
    </justification>
  </clause>

  <clause id="32163">
    <literal><![CDATA[
      a(x,L((y \ ((y * z) * u)) * (y \ 1),w,v5),v6) = a(x,L(((y \ 1) * z) * u,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(1600(a,1),31955(a,1,2,1,1))].">
      <j1 rule="para" parents="1600 31955"/>
    </justification>
  </clause>

  <clause id="32164">
    <literal><![CDATA[
      a(x,L(y * z,z,z),u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32141,a(flip),b,31956,a),flip(a)].">
      <j1 rule="hyper" parents="373 32141 31956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32165">
    <literal><![CDATA[
      a(x,L((y * ((y \ 1) \ z)) * (u / y),w,v5),v6) = a(x,L((u / (y \ 1)) * z,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(1674(a,1),31956(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1674 31956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32166">
    <literal><![CDATA[
      a(x,(T(y,z) / u) \ w,v5) = a(x,(u \ y) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31972,a,b,31977,a)].">
      <j1 rule="hyper" parents="64 31972 31977"/>
    </justification>
  </clause>

  <clause id="32167">
    <literal><![CDATA[
      a(x,(y * (z / u)) * w,v5) = a(x,(y * (u \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(117(a,1),31978(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="117 31978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32168">
    <literal><![CDATA[
      a(x,(y * ((z * u) * (z \ 1))) * w,v5) = a(x,(y * R(u,z,z \ 1)) * w,v5)
    ]]></literal>
    <justification jstring="[para(1042(a,1),31978(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1042 31978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32169">
    <literal><![CDATA[
      a(x,(y * ((z \ u) / u)) * w,v5) = a(x,(y * ((z * u) \ u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(5144(a,1),31978(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5144 31978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32170">
    <literal><![CDATA[
      a(x,(T(y * z,u) \ (y * ((w * w) * (z * v5)))) \ v6,v7) = a(x,L(T(w * w,z) * v5,z,y) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(6651(a,1),31981(a,2,2,1))].">
      <j1 rule="para" parents="6651 31981"/>
    </justification>
  </clause>

  <clause id="32172">
    <literal><![CDATA[
      a(x,L(K(y,z) * (u * w),v5,v6),v7) = a(x,L(w * u,v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(373,a,31956,a,b,31990,a),flip(a)].">
      <j1 rule="hyper" parents="373 31956 31990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32174">
    <literal><![CDATA[
      a(x,L(y \ ((z * z) * u),w,v5),v6) = a(x,L((z * z) * (y \ u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(6626(a,1),31990(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6626 31990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32175">
    <literal><![CDATA[
      a(x,L((y * T(z,u)) \ w,v5,v6),v7) = a(x,L((y * z) \ w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(24506(a,1),31990(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="24506 31990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32176">
    <literal><![CDATA[
      a(x,L((y / (y * z)) * z,u,w),v5) = a(x,L(a(z,z,y),u,w),v5)
    ]]></literal>
    <justification jstring="[para(30285(a,1),31990(a,1,2,1))].">
      <j1 rule="para" parents="30285 31990"/>
    </justification>
  </clause>

  <clause id="32177">
    <literal><![CDATA[
      a(x,R(y / (1 / z),u,w),v5) = a(x,R(y / z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(809(a,1),32005(a,1,2,1))].">
      <j1 rule="para" parents="809 32005"/>
    </justification>
  </clause>

  <clause id="32179">
    <literal><![CDATA[
      a(x,((1 / y) \ z) \ u,w) = a(x,(y \ z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31972,a(flip),b,32094,a),flip(a)].">
      <j1 rule="hyper" parents="373 31972 32094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32180">
    <literal><![CDATA[
      a(x,(y * ((z * z) \ u)) * w,v5) = a(x,(u * y) * T(w,v6),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,11973,a(flip),b,32102,a),flip(a)].">
      <j1 rule="hyper" parents="64 11973 32102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32181">
    <literal><![CDATA[
      a(x,(y * a(z,z,y)) * u,w) = a(x,L(y,z,z) * u,w)
    ]]></literal>
    <justification jstring="[para(5669(a,1),32103(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5669 32103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32182">
    <literal><![CDATA[
      a(x,y * (z * (u \ a(w,v5,w))),v6) = a(x,(u * z) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,13847,a,b,32117,a)].">
      <j1 rule="hyper" parents="64 13847 32117"/>
    </justification>
  </clause>

  <clause id="32183">
    <literal><![CDATA[
      a(x,y * ((z * (u / w)) * w),v5) = a(x,y * (w * (z * (w \ u))),v5)
    ]]></literal>
    <justification jstring="[para(6855(a,1),32153(a,1,2,2))].">
      <j1 rule="para" parents="6855 32153"/>
    </justification>
  </clause>

  <clause id="32184">
    <literal><![CDATA[
      a(x,((y \ 1) \ z) \ u,w) = a(x,(y \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),32179(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 32179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32185">
    <literal><![CDATA[
      a(x,(y * z) \ ((y * u) * z),w) = a(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31975,a,b,31996,a)].">
      <j1 rule="hyper" parents="64 31975 31996"/>
    </justification>
  </clause>

  <clause id="32187">
    <literal><![CDATA[
      a(x,R(y,z,z),u) = a(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31996,a(flip),b,32037,a),flip(a)].">
      <j1 rule="hyper" parents="64 31996 32037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32188">
    <literal><![CDATA[
      a(x,y,(1 / (z / y)) * z) = a(x,(y \ z) * z,y)
    ]]></literal>
    <justification jstring="[para(10627(a,1),32052(a,1,3))].">
      <j1 rule="para" parents="10627 32052"/>
    </justification>
  </clause>

  <clause id="32189">
    <literal><![CDATA[
      a(x,y,((y \ z) \ 1) * z) = a(x,(y \ z) * z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27671,a(flip),b,32188,a)].">
      <j1 rule="hyper" parents="64 27671 32188"/>
    </justification>
  </clause>

  <clause id="32190">
    <literal><![CDATA[
      a(x,a(y * z,y,z),u) = a(x,L(z,y,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11970,a(flip),b,32106,a)].">
      <j1 rule="hyper" parents="64 11970 32106"/>
    </justification>
  </clause>

  <clause id="32191">
    <literal><![CDATA[
      a(x,((y * T((y \ z) / z,u)) * T(z / (y * z),u)) * w,v5) = a(x,L(y,T(z / (y * z),u),T(z / (y * z),u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(3013(a,1),32106(a,1,2,1,1))].">
      <j1 rule="para" parents="3013 32106"/>
    </justification>
  </clause>

  <clause id="32192">
    <literal><![CDATA[
      a(x,a(y * z,y,z),u) = a(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32035,a(flip),b,32190,a),flip(a)].">
      <j1 rule="hyper" parents="373 32035 32190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32193">
    <literal><![CDATA[
      a(x,a(y * z,z,y),u) = a(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(26787(a,1),32192(a,1,2))].">
      <j1 rule="para" parents="26787 32192"/>
    </justification>
  </clause>

  <clause id="32194">
    <literal><![CDATA[
      a(x,a(y \ z,y \ z,y),u) = a(x,a(z,y \ z,y),u)
    ]]></literal>
    <justification jstring="[para(26836(a,1),32192(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26836 32192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32195">
    <literal><![CDATA[
      a(x,y * ((z * u) * z),w) = a(x,y * L(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31902,a,b,32110,a)].">
      <j1 rule="hyper" parents="64 31902 32110"/>
    </justification>
  </clause>

  <clause id="32196">
    <literal><![CDATA[
      a(x,R(y,z,z \ 1),u) = a(x,L(y,z,z \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31932,a(flip),b,32114,a)].">
      <j1 rule="hyper" parents="64 31932 32114"/>
    </justification>
  </clause>

  <clause id="32197">
    <literal><![CDATA[
      a(x,R(y,z,u),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32037,a(flip),b,32185,a)].">
      <j1 rule="hyper" parents="64 32037 32185"/>
    </justification>
  </clause>

  <clause id="32198">
    <literal><![CDATA[
      a(x,a(y,y,z) \ y,u) = a(x,L(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32144,a,b,32197,a)].">
      <j1 rule="hyper" parents="64 32144 32197"/>
    </justification>
  </clause>

  <clause id="32199">
    <literal><![CDATA[
      a(R(x,y,z),x,u) = a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16191,a,b,32197,a)].">
      <j1 rule="hyper" parents="64 16191 32197"/>
    </justification>
  </clause>

  <clause id="32200">
    <literal><![CDATA[
      a(x,R(y \ 1,z,u),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11996,a,b,32197,a)].">
      <j1 rule="hyper" parents="64 11996 32197"/>
    </justification>
  </clause>

  <clause id="32201">
    <literal><![CDATA[
      a(x,R(L(y,z,u),w,v5),v6) = a(x,L(L(y,w,v5),z,u),v6)
    ]]></literal>
    <justification jstring="[para(30(a,1),32197(a,2,2))].">
      <j1 rule="para" parents="30 32197"/>
    </justification>
  </clause>

  <clause id="32202">
    <literal><![CDATA[
      a(x,L(x,x,y),x \ y) = (x \ 1) * R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26045,a(flip),b,32199,a),flip(a)].">
      <j1 rule="hyper" parents="64 26045 32199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32203">
    <literal><![CDATA[
      a(x,L(y \ 1,z,u),w) = a(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32197,a(flip),b,32200,a)].">
      <j1 rule="hyper" parents="64 32197 32200"/>
    </justification>
  </clause>

  <clause id="32204">
    <literal><![CDATA[
      (R(x \ 1,y,z) * u) * a(R(x \ 1,y,z),L(x,y,z),u) = (1 / R(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(145,a,32200,a(flip),b,30034,a)].">
      <j1 rule="hyper" parents="145 32200 30034"/>
    </justification>
  </clause>

  <clause id="32205">
    <literal><![CDATA[
      a(x,L(y,y,z),u) = a(x,z \ (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32125,a(flip),b,32203,a),flip(a)].">
      <j1 rule="hyper" parents="64 32125 32203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32206">
    <literal><![CDATA[
      a(x,L(y \ z,y \ z,y),u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[para(436(a,1),32203(a,1,2)),flip(a)].">
      <j1 rule="para" parents="436 32203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32207">
    <literal><![CDATA[
      a(x,y \ (z \ y),z) = a(x,z,L(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16192,a(flip),b,32205,a),flip(a)].">
      <j1 rule="hyper" parents="64 16192 32205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32208">
    <literal><![CDATA[
      a(x,y \ (z \ y),z) = a(x,z,L(z,z,z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,27599,a,b,32207,a),flip(a)].">
      <j1 rule="hyper" parents="373 27599 32207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32209">
    <literal><![CDATA[
      a(x,L(x,x,y),x \ y) = a(x,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30078,a(flip),b,32202,a),flip(a)].">
      <j1 rule="hyper" parents="373 30078 32202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32210">
    <literal><![CDATA[
      a(x,(y * ((z * z) \ y)) * (u / ((((z * z) \ y) * w) / v5)),v6) = a(x,u / (((1 / ((z * z) \ y)) * w) / v5),v6)
    ]]></literal>
    <justification jstring="[para(1241(a,1),31946(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1241 31946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32211">
    <literal><![CDATA[
      a(x,y * (z * (u * u)),w) = a(x,z * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32025,a(flip),b,31951,a),flip(a)].">
      <j1 rule="hyper" parents="64 32025 31951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32213">
    <literal><![CDATA[
      a(x,y \ ((z * z) * u),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11960,a(flip),b,31973,a),flip(a)].">
      <j1 rule="hyper" parents="373 11960 31973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32214">
    <literal><![CDATA[
      a(x,(y * y) * (((y * z) / u) \ w),v5) = a(x,(((1 / y) * z) / u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(1240(a,1),31973(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1240 31973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32216">
    <literal><![CDATA[
      a(x,y \ (z * (u * u)),w) = a(x,y \ z,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31909,a,b,32213,a)].">
      <j1 rule="hyper" parents="64 31909 32213"/>
    </justification>
  </clause>

  <clause id="32217">
    <literal><![CDATA[
      a(x,y \ (z * z),u) = a(x,y \ 1,u)
    ]]></literal>
    <justification jstring="[para(8(a,1),32213(a,1,2,2))].">
      <j1 rule="para" parents="8 32213"/>
    </justification>
  </clause>

  <clause id="32218">
    <literal><![CDATA[
      a(x,y \ ((z * z) \ u),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),32213(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 32213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32219">
    <literal><![CDATA[
      a(x,y \ (1 / z),u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(245(a,1),32213(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="245 32213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32220">
    <literal><![CDATA[
      a(x,y \ ((1 / z) * u),w) = a(x,y \ (z * u),w)
    ]]></literal>
    <justification jstring="[para(310(a,1),32213(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="310 32213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32221">
    <literal><![CDATA[
      a(x,y \ (z * (z * u)),w) = a(x,y \ L(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(100(a,1),32213(a,1,2,2))].">
      <j1 rule="para" parents="100 32213"/>
    </justification>
  </clause>

  <clause id="32222">
    <literal><![CDATA[
      a(x,((1 / y) * z) \ u,w) = a(x,(y * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(941(a,1),32213(a,1,2))].">
      <j1 rule="para" parents="941 32213"/>
    </justification>
  </clause>

  <clause id="32223">
    <literal><![CDATA[
      a(x,(T(y,z * z) * u) \ w,v5) = a(x,(y * ((z * z) * u)) \ w,v5)
    ]]></literal>
    <justification jstring="[para(1463(a,1),32213(a,1,2))].">
      <j1 rule="para" parents="1463 32213"/>
    </justification>
  </clause>

  <clause id="32224">
    <literal><![CDATA[
      a(x,y \ ((T(z,u * u) * w) / v5),v6) = a(x,y \ ((z * ((u * u) * w)) / v5),v6)
    ]]></literal>
    <justification jstring="[para(1523(a,1),32213(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1523 32213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32225">
    <literal><![CDATA[
      a(x,y \ ((z * T(u,z \ 1)) * z),w) = a(x,y \ R(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(3954(a,2),32213(a,1,2,2))].">
      <j1 rule="para" parents="3954 32213"/>
    </justification>
  </clause>

  <clause id="32226">
    <literal><![CDATA[
      a(x,y \ (1 / R(1 / z,u,w)),v5) = a(x,y \ (R(z,u,w) \ 1),v5)
    ]]></literal>
    <justification jstring="[para(11454(a,1),32213(a,1,2,2))].">
      <j1 rule="para" parents="11454 32213"/>
    </justification>
  </clause>

  <clause id="32227">
    <literal><![CDATA[
      a(x,y \ (z * z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11980,a(flip),b,32217,a),flip(a)].">
      <j1 rule="hyper" parents="373 11980 32217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32228">
    <literal><![CDATA[
      a(x,L(y \ z,y,z),u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32157,a,b,32227,a)].">
      <j1 rule="hyper" parents="64 32157 32227"/>
    </justification>
  </clause>

  <clause id="32229">
    <literal><![CDATA[
      a(x,(y \ z) \ (y \ (u * u)),(y * (y \ z)) \ (u * u)) = a(x,z,(y \ z) \ (y \ (u * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16405,a,b,32227,a)].">
      <j1 rule="hyper" parents="64 16405 32227"/>
    </justification>
  </clause>

  <clause id="32230">
    <literal><![CDATA[
      a(x,y \ (z \ 1),u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31908,a(flip),b,32219,a)].">
      <j1 rule="hyper" parents="64 31908 32219"/>
    </justification>
  </clause>

  <clause id="32231">
    <literal><![CDATA[
      a(x \ y,y * x,z) = a(y * x,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2785,a(flip),b,32228,a),flip(a)].">
      <j1 rule="hyper" parents="64 2785 32228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32232">
    <literal><![CDATA[
      a(x,y \ ((z * u) * u),w) = a(x,y \ R(z,u,u),w)
    ]]></literal>
    <justification jstring="[para(111(a,1),32216(a,1,2,2))].">
      <j1 rule="para" parents="111 32216"/>
    </justification>
  </clause>

  <clause id="32233">
    <literal><![CDATA[
      a(x,y \ T((z * z) \ u,w),v5) = a(x,y \ u,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31891,a,b,32218,a)].">
      <j1 rule="hyper" parents="64 31891 32218"/>
    </justification>
  </clause>

  <clause id="32234">
    <literal><![CDATA[
      a(x,y \ (z * ((z \ 1) \ u)),w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(582(a,1),32218(a,1,2,2))].">
      <j1 rule="para" parents="582 32218"/>
    </justification>
  </clause>

  <clause id="32235">
    <literal><![CDATA[
      a(x,(y * (y * z)) \ u,w) = a(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[para(881(a,1),32218(a,1,2))].">
      <j1 rule="para" parents="881 32218"/>
    </justification>
  </clause>

  <clause id="32236">
    <literal><![CDATA[
      a(x,R(y \ 1,z,u) \ w,v5) = a(x,R(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(2770(a,1),32218(a,1,2))].">
      <j1 rule="para" parents="2770 32218"/>
    </justification>
  </clause>

  <clause id="32238">
    <literal><![CDATA[
      a(x,y \ (z * (1 / u)),w) = a(x,y \ (u * z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31909,a,b,32220,a)].">
      <j1 rule="hyper" parents="64 31909 32220"/>
    </justification>
  </clause>

  <clause id="32239">
    <literal><![CDATA[
      a(x,((y \ 1) * z) \ u,w) = a(x,(y * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),32222(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 32222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32240">
    <literal><![CDATA[
      a(x,a(y \ z,y \ z,y),u) = a(x,((z / y) * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(10628(a,2),32222(a,1,2))].">
      <j1 rule="para" parents="10628 32222"/>
    </justification>
  </clause>

  <clause id="32241">
    <literal><![CDATA[
      a(x,y \ T((z * z) \ (u / w),v5),v6) = a(x,y \ (w \ u),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,31908,a(flip),b,32233,a),flip(a)].">
      <j1 rule="hyper" parents="373 31908 32233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32242">
    <literal><![CDATA[
      a(x,y \ ((1 / z) \ u),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(1138(a,1),32234(a,1,2,2))].">
      <j1 rule="para" parents="1138 32234"/>
    </justification>
  </clause>

  <clause id="32243">
    <literal><![CDATA[
      a(x,y \ (z * (u \ 1)),w) = a(x,y \ (u * z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31918,a(flip),b,32238,a)].">
      <j1 rule="hyper" parents="64 31918 32238"/>
    </justification>
  </clause>

  <clause id="32244">
    <literal><![CDATA[
      a(x,y \ ((z \ 1) \ u),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[para(79(a,1),32242(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="79 32242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32245">
    <literal><![CDATA[
      a(x,((y * z) * y) \ u,w) = a(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31975,a,b,32235,a)].">
      <j1 rule="hyper" parents="64 31975 32235"/>
    </justification>
  </clause>

  <clause id="32246">
    <literal><![CDATA[
      a(x,L(y \ 1,y * (z / (y * z)),y * (z / (y * z))) \ u,w) = a(x,((y * (z / (y * z))) * (z / (y * z))) \ u,w)
    ]]></literal>
    <justification jstring="[para(26315(a,1),32235(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="26315 32235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32247">
    <literal><![CDATA[
      a(x,(y * (z * y)) \ u,w) = a(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13851,a(flip),b,32245,a)].">
      <j1 rule="hyper" parents="64 13851 32245"/>
    </justification>
  </clause>

  <clause id="32248">
    <literal><![CDATA[
      a(x,((y * z) * z) \ u,w) = a(x,L(y,z,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31975,a,b,32247,a)].">
      <j1 rule="hyper" parents="64 31975 32247"/>
    </justification>
  </clause>

  <clause id="32249">
    <literal><![CDATA[
      a(x,R(y,z,z) \ u,w) = a(x,L(y,z,z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11983,a(flip),b,32248,a)].">
      <j1 rule="hyper" parents="64 11983 32248"/>
    </justification>
  </clause>

  <clause id="32250">
    <literal><![CDATA[
      a(x,L((1 / y) * (z * z),u,w) \ v5,v6) = a(x,L((z * z) / y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(829(a,1),31979(a,1,2,1,1))].">
      <j1 rule="para" parents="829 31979"/>
    </justification>
  </clause>

  <clause id="32251">
    <literal><![CDATA[
      a(x,L((y * z) * (y \ (1 / y)),u,w) * v5,v6) = a(x,L((y \ 1) * z,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(1602(a,1),31980(a,1,2,1,1))].">
      <j1 rule="para" parents="1602 31980"/>
    </justification>
  </clause>

  <clause id="32252">
    <literal><![CDATA[
      a(x,L(((1 / y) \ z) * K(u,y),w,v5) * v6,v7) = a(x,L((y * y) * (z / T(y,u)),w,v5) * v6,v7)
    ]]></literal>
    <justification jstring="[para(7295(a,1),31980(a,1,2,1,1))].">
      <j1 rule="para" parents="7295 31980"/>
    </justification>
  </clause>

  <clause id="32253">
    <literal><![CDATA[
      a(x,((y / z) * u) * w,v5) = a(x,(u * (z \ y)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31976,a,b,31982,a),flip(a)].">
      <j1 rule="hyper" parents="373 31976 31982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32254">
    <literal><![CDATA[
      a(x,(((1 / y) \ z) \ u) * w,v5) = a(x,((z / y) \ u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,11994,a(flip),b,31983,a),flip(a)].">
      <j1 rule="hyper" parents="64 11994 31983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32255">
    <literal><![CDATA[
      a(x,(y * (z * u)) * w,v5) = a(x,(y * (u * z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(5796(a,1),31984(a,1,2,1,2))].">
      <j1 rule="para" parents="5796 31984"/>
    </justification>
  </clause>

  <clause id="32256">
    <literal><![CDATA[
      a(x,(y * (T(z,u) * w)) * v5,v6) = a(x,(y * (z * w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(5755(a,1),31984(a,1,2,1,2))].">
      <j1 rule="para" parents="5755 31984"/>
    </justification>
  </clause>

  <clause id="32257">
    <literal><![CDATA[
      a(x,(y * ((z / u) * w)) * v5,v6) = a(x,(y * ((u \ z) * w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(5982(a,1),31984(a,1,2,1,2))].">
      <j1 rule="para" parents="5982 31984"/>
    </justification>
  </clause>

  <clause id="32258">
    <literal><![CDATA[
      a(x,((y / z) / u) \ w,v5) = a(x,(u \ (z \ y)) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31972,a,b,31986,a)].">
      <j1 rule="hyper" parents="64 31972 31986"/>
    </justification>
  </clause>

  <clause id="32259">
    <literal><![CDATA[
      a(x,(y * (z \ T(u,w))) \ v5,v6) = a(x,(y * (z \ u)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(6417(a,1),31987(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6417 31987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32260">
    <literal><![CDATA[
      a(x,(y * (((z \ u) * z) / w)) \ v5,v6) = a(x,(y * (u / w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(14888(a,1),31987(a,1,2,1,2))].">
      <j1 rule="para" parents="14888 31987"/>
    </justification>
  </clause>

  <clause id="32261">
    <literal><![CDATA[
      a(x,(y \ ((z / u) \ w)) \ v5,v6) = a(x,(y \ ((u \ z) \ w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(6270(a,1),31988(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 31988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32262">
    <literal><![CDATA[
      a(x,a(y,y,z * y) * u,w) = a(x,u * a(y,y,z),w)
    ]]></literal>
    <justification jstring="[para(27364(a,2),32055(a,1,2))].">
      <j1 rule="para" parents="27364 32055"/>
    </justification>
  </clause>

  <clause id="32263">
    <literal><![CDATA[
      a(x,(y * y) * ((z \ T(u,y * y)) * w),v5) = a(x,((u * (y * y)) / z) * w,v5)
    ]]></literal>
    <justification jstring="[para(1459(a,1),32058(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1459 32058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32264">
    <literal><![CDATA[
      a(x,y \ (z * (u * z)),w) = a(x,y \ L(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32221,a(flip),b,32067,a),flip(a)].">
      <j1 rule="hyper" parents="373 32221 32067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32265">
    <literal><![CDATA[
      a(x,y \ ((z * u) * u),w) = a(x,y \ L(z,u,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31909,a,b,32264,a)].">
      <j1 rule="hyper" parents="64 31909 32264"/>
    </justification>
  </clause>

  <clause id="32266">
    <literal><![CDATA[
      a(x,y \ R(z,u,u),w) = a(x,y \ L(z,u,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32232,a(flip),b,32265,a)].">
      <j1 rule="hyper" parents="64 32232 32265"/>
    </justification>
  </clause>

  <clause id="32267">
    <literal><![CDATA[
      a(x,(y \ (z \ 1)) * u,w) = a(x,(z / y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32053,a(flip),b,32077,a),flip(a)].">
      <j1 rule="hyper" parents="64 32053 32077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32268">
    <literal><![CDATA[
      a(x,(y \ (z \ 1)) * u,w) = a(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31904,a(flip),b,32267,a),flip(a)].">
      <j1 rule="hyper" parents="373 31904 32267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32269">
    <literal><![CDATA[
      a(x,y * (z \ (u \ 1)),w) = a(x,(z \ u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(32008,a,32268,a)].">
      <j1 rule="hyper" parents="32008 32268"/>
    </justification>
  </clause>

  <clause id="32270">
    <literal><![CDATA[
      a(x,(y \ 1) * (z \ (u \ 1)),w) = a(x,y * (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31945,a(flip),b,32269,a),flip(a)].">
      <j1 rule="hyper" parents="373 31945 32269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32271">
    <literal><![CDATA[
      a(x,(y \ (z * u)) * w,v5) = a(x,(y \ (u * z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(5796(a,1),32079(a,1,2,1,2))].">
      <j1 rule="para" parents="5796 32079"/>
    </justification>
  </clause>

  <clause id="32272">
    <literal><![CDATA[
      a(x,(y \ (T(z,u) * w)) * v5,v6) = a(x,(y \ (z * w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(5755(a,1),32079(a,1,2,1,2))].">
      <j1 rule="para" parents="5755 32079"/>
    </justification>
  </clause>

  <clause id="32273">
    <literal><![CDATA[
      a(x,(y \ ((z / u) \ w)) * v5,v6) = a(x,(y \ ((u \ z) \ w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(6270(a,1),32079(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 32079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32274">
    <literal><![CDATA[
      a(x,((y \ 1) \ (y \ z)) \ u,w) = a(x,(y \ ((y \ 1) \ z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(1612(a,1),32087(a,1,2,1))].">
      <j1 rule="para" parents="1612 32087"/>
    </justification>
  </clause>

  <clause id="32275">
    <literal><![CDATA[
      a(x,((y * z) * z) * u,w) = a(x,u * L(y,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32195,a(flip),b,32119,a),flip(a)].">
      <j1 rule="hyper" parents="373 32195 32119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32276">
    <literal><![CDATA[
      a(x,(y * (z * u)) * w,v5) = a(x,w * ((u * z) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31976,a,b,32119,a)].">
      <j1 rule="hyper" parents="64 31976 32119"/>
    </justification>
  </clause>

  <clause id="32277">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ T(y,y \ x) = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(301(a,1),32131(a,2,1,1))].">
      <j1 rule="para" parents="301 32131"/>
    </justification>
  </clause>

  <clause id="32278">
    <literal><![CDATA[
      a(x,R((1 / y) \ z,u,w),v5) = a(x,R(z / y,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31931,a(flip),b,32177,a)].">
      <j1 rule="hyper" parents="64 31931 32177"/>
    </justification>
  </clause>

  <clause id="32279">
    <literal><![CDATA[
      a(x,L(y * z,y,y) * u,w) = a(x,((y \ 1) \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(30227(a,1),32181(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30227 32181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32280">
    <literal><![CDATA[
      a(x,L(L(y,z,u),w,v5),v6) = a(x,L(L(y,w,v5),z,u),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32197,a(flip),b,32201,a)].">
      <j1 rule="hyper" parents="64 32197 32201"/>
    </justification>
  </clause>

  <clause id="32281">
    <literal><![CDATA[
      a(x,L(R(y,z,u),w,v5),v6) = a(x,L(L(y,z,u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(29(a,1),32201(a,1,2))].">
      <j1 rule="para" parents="29 32201"/>
    </justification>
  </clause>

  <clause id="32282">
    <literal><![CDATA[
      a(x,(y * (z * y)) * u,w) = a(x,L(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11972,a(flip),b,32255,a),flip(a)].">
      <j1 rule="hyper" parents="373 11972 32255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32283">
    <literal><![CDATA[
      ((x \ y) * (x / y)) \ x = ((x \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,14835,a(flip),b,32277,a)].">
      <j1 rule="hyper" parents="64 14835 32277"/>
    </justification>
  </clause>

  <clause id="32284">
    <literal><![CDATA[
      a(x,R((1 / y) \ z,u,w),v5) = a(x,R(y \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31931,a(flip),b,32278,a),flip(a)].">
      <j1 rule="hyper" parents="373 31931 32278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32285">
    <literal><![CDATA[
      a(x,R((y \ 1) \ z,u,w),v5) = a(x,R(y \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),32284(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="79 32284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32286">
    <literal><![CDATA[
      a(x,R((y \ 1) \ (y * z),u,w),v5) = a(x,R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),32285(a,2,2,1))].">
      <j1 rule="para" parents="9 32285"/>
    </justification>
  </clause>

  <clause id="32287">
    <literal><![CDATA[
      a(x,R(((y \ 1) \ y) * z,u,w),v5) = a(x,R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(1115(a,1),32286(a,1,2,1))].">
      <j1 rule="para" parents="1115 32286"/>
    </justification>
  </clause>

  <clause id="32288">
    <literal><![CDATA[
      a(x,L(((y \ 1) \ y) * z,u,w),v5) = a(x,R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32197,a(flip),b,32287,a)].">
      <j1 rule="hyper" parents="64 32197 32287"/>
    </justification>
  </clause>

  <clause id="32289">
    <literal><![CDATA[
      a(x,L(((y \ 1) \ y) * z,u,w),v5) = a(x,L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32197,a(flip),b,32288,a),flip(a)].">
      <j1 rule="hyper" parents="373 32197 32288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32290">
    <literal><![CDATA[
      a(x,L((y \ 1) \ z,u,w),v5) = a(x,L(y \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(1131(a,1),32289(a,1,2,1))].">
      <j1 rule="para" parents="1131 32289"/>
    </justification>
  </clause>

  <clause id="32291">
    <literal><![CDATA[
      a(x,L((1 / y) \ z,u,w),v5) = a(x,L(y \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(82(a,1),32290(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="82 32290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32292">
    <literal><![CDATA[
      a(x,L((1 / y) \ (y * z),u,w),v5) = a(x,L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),32291(a,2,2,1))].">
      <j1 rule="para" parents="9 32291"/>
    </justification>
  </clause>

  <clause id="32293">
    <literal><![CDATA[
      a(x,L(y * ((y \ 1) \ z),u,w),v5) = a(x,L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(1124(a,1),32292(a,1,2,1))].">
      <j1 rule="para" parents="1124 32292"/>
    </justification>
  </clause>

  <clause id="32294">
    <literal><![CDATA[
      a(x,L((y * y) \ z,u,w),v5) = a(x,L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(1187(a,1),32292(a,1,2,1))].">
      <j1 rule="para" parents="1187 32292"/>
    </justification>
  </clause>

  <clause id="32295">
    <literal><![CDATA[
      a(x,L((y * y) * z,u,w),v5) = a(x,L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),32294(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 32294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32296">
    <literal><![CDATA[
      a(x,L(y \ (y \ z),u,w),v5) = a(x,L(R(z,u,w),y,y),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32197,a(flip),b,32147,a)].">
      <j1 rule="hyper" parents="64 32197 32147"/>
    </justification>
  </clause>

  <clause id="32297">
    <literal><![CDATA[
      a(x,a(y \ z,y \ z,y),u) = a(x,((y \ z) * z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32085,a(flip),b,32240,a),flip(a)].">
      <j1 rule="hyper" parents="373 32085 32240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32298">
    <literal><![CDATA[
      a(x,L(y \ (y \ z),u,w),v5) = a(x,L(L(z,u,w),y,y),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32281,a(flip),b,32296,a),flip(a)].">
      <j1 rule="hyper" parents="373 32281 32296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32299">
    <literal><![CDATA[
      a(x,((y \ z) * z) \ y,u) = a(x,a(z,y \ z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32194,a(flip),b,32297,a),flip(a)].">
      <j1 rule="hyper" parents="64 32194 32297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32300">
    <literal><![CDATA[
      a(x,L(L(y * z,u,w),y,y),v5) = a(x,L(y \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),32298(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 32298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32301">
    <literal><![CDATA[
      L(x,y,a(z * T(u \ (u \ w),v5),L(w,u,u),z)) = L(x,y,a(z,T(u \ (u \ w),v5),T(u \ (u \ w),v5)))
    ]]></literal>
    <justification jstring="[para(32142(a,1),31937(a,1,3))].">
      <j1 rule="para" parents="32142 31937"/>
    </justification>
  </clause>

  <clause id="32302">
    <literal><![CDATA[
      a(x,R((1 / y) \ z,u,w) \ v5,v6) = a(x,R(z / y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,11977,a(flip),b,31993,a),flip(a)].">
      <j1 rule="hyper" parents="64 11977 31993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32303">
    <literal><![CDATA[
      a(x,L((K(y,z) * u) * y,w,v5) \ v6,v7) = a(x,L(T(y,z) * u,w,v5) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(6071(a,1),31995(a,1,2,1,1,1))].">
      <j1 rule="para" parents="6071 31995"/>
    </justification>
  </clause>

  <clause id="32305">
    <literal><![CDATA[
      a(x,y * (((z / u) \ w) \ v5),v6) = a(x,y * (((u \ z) \ w) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(117(a,1),32076(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="117 32076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32306">
    <literal><![CDATA[
      a(x,((y * T(z,u)) * w) * v5,v6) = a(x,(w * (y * z)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,31976,a,b,32078,a)].">
      <j1 rule="hyper" parents="64 31976 32078"/>
    </justification>
  </clause>

  <clause id="32307">
    <literal><![CDATA[
      a(x,(y * (z \ K(u,w))) * v5,v6) = a(x,(z * y) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32105,a(flip),b,32080,a),flip(a)].">
      <j1 rule="hyper" parents="373 32105 32080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32308">
    <literal><![CDATA[
      a(x,((K(y,z) / u) * w) * v5,v6) = a(x,(u * w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32253,a,b,32307,a)].">
      <j1 rule="hyper" parents="64 32253 32307"/>
    </justification>
  </clause>

  <clause id="32309">
    <literal><![CDATA[
      a(x,(y * (((z * u) \ w) \ 1)) * v5,v6) = a(x,(((u * z) \ w) * y) * v5,v6)
    ]]></literal>
    <justification jstring="[para(14458(a,1),32307(a,1,2,1,2))].">
      <j1 rule="para" parents="14458 32307"/>
    </justification>
  </clause>

  <clause id="32310">
    <literal><![CDATA[
      a(x,(((y / (z * y)) \ 1) * u) * w,v5) = a(x,((y \ (z \ y)) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(7031(a,1),32308(a,1,2,1,1))].">
      <j1 rule="para" parents="7031 32308"/>
    </justification>
  </clause>

  <clause id="32311">
    <literal><![CDATA[
      a(x,y,a(z,u * w,v5)) = a(x,y,a(z,w * u,v5))
    ]]></literal>
    <justification jstring="[hyper(27585,a,32090,a)].">
      <j1 rule="hyper" parents="27585 32090"/>
    </justification>
  </clause>

  <clause id="32313">
    <literal><![CDATA[
      a(x,x \ (y \ x),x * y) * x = R(x,x \ (y \ x),x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,26610,a(flip),b,32126,a),flip(a)].">
      <j1 rule="hyper" parents="373 26610 32126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32314">
    <literal><![CDATA[
      a(x,y / ((y \ z) / z),u) = a(x,y * ((y \ z) / z),u)
    ]]></literal>
    <justification jstring="[para(25353(a,1),32137(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25353 32137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32315">
    <literal><![CDATA[
      a(x,y / ((y \ z) / z),u) = a(x,y * (z \ (y \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,31897,a(flip),b,32314,a),flip(a)].">
      <j1 rule="hyper" parents="373 31897 32314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32316">
    <literal><![CDATA[
      a(x,(y / (z * y)) \ z,u) = a(x,z * (y \ (z \ y)),u)
    ]]></literal>
    <justification jstring="[para(23871(a,1),32315(a,1,2))].">
      <j1 rule="para" parents="23871 32315"/>
    </justification>
  </clause>

  <clause id="32317">
    <literal><![CDATA[
      a((x / (y * x)) \ y,y * (x \ (y \ x)),y) = (y / (x / (y * x))) * ((x / (y * x)) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30068,a(flip),b,32316,a),flip(a)].">
      <j1 rule="hyper" parents="64 30068 32316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32318">
    <literal><![CDATA[
      a(x,((y / (z * y)) \ 1) \ u,w) = a(x,(y \ (z \ y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31972,a(flip),b,32139,a),flip(a)].">
      <j1 rule="hyper" parents="373 31972 32139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32319">
    <literal><![CDATA[
      a(x,L((y \ z) * u,w,v5),v6) = a(x,L(u * (z / y),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,31956,a,b,32160,a)].">
      <j1 rule="hyper" parents="373 31956 32160"/>
    </justification>
  </clause>

  <clause id="32320">
    <literal><![CDATA[
      a(x,L((y / (z * (u \ 1))) * ((1 / u) / u),w,v5),v6) = a(x,L(y / (u * T(z,u \ 1)),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(1625(a,1),32160(a,2,2,1))].">
      <j1 rule="para" parents="1625 32160"/>
    </justification>
  </clause>

  <clause id="32321">
    <literal><![CDATA[
      a(x,L(y * (T(z,u) * w),v5,v6),v7) = a(x,L((z * w) * y,v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(23389(a,1),32172(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23389 32172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32322">
    <literal><![CDATA[
      a(x,(y * ((z * z) \ u)) * w,v5) = a(x,(y * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32102,a(flip),b,32180,a),flip(a)].">
      <j1 rule="hyper" parents="373 32102 32180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32323">
    <literal><![CDATA[
      a(x,y * (z * ((u * u) \ w)),v5) = a(x,(z * w) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(32008,a,32322,a)].">
      <j1 rule="hyper" parents="32008 32322"/>
    </justification>
  </clause>

  <clause id="32324">
    <literal><![CDATA[
      a(x,(y * ((z * z) * u)) * w,v5) = a(x,(y * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),32322(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 32322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32325">
    <literal><![CDATA[
      a(x,(y * (z * (u * u))) * w,v5) = a(x,(y * z) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32255,a,b,32324,a)].">
      <j1 rule="hyper" parents="64 32255 32324"/>
    </justification>
  </clause>

  <clause id="32326">
    <literal><![CDATA[
      a(x,(y * ((z * u) * u)) * w,v5) = a(x,(y * R(z,u,u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(111(a,1),32325(a,1,2,1,2))].">
      <j1 rule="para" parents="111 32325"/>
    </justification>
  </clause>

  <clause id="32327">
    <literal><![CDATA[
      a(x,y \ T(1 / z,u),w) = a(x,y \ (z \ (v5 * v5)),w)
    ]]></literal>
    <justification jstring="[para(548(a,1),32241(a,1,2,2,1))].">
      <j1 rule="para" parents="548 32241"/>
    </justification>
  </clause>

  <clause id="32328">
    <literal><![CDATA[
      a(x,y \ (z \ (u * u)),w) = a(x,y \ (1 / z),w)
    ]]></literal>
    <justification jstring="[hyper(32041,a,32327,a),flip(a)].">
      <j1 rule="hyper" parents="32041 32327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32329">
    <literal><![CDATA[
      a(x,y \ (z \ (u * u)),w) = a(x,y \ z,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32219,a(flip),b,32328,a),flip(a)].">
      <j1 rule="hyper" parents="373 32219 32328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32330">
    <literal><![CDATA[
      a(x,(((1 / y) \ z) \ u) * w,v5) = a(x,((y \ z) \ u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31983,a(flip),b,32254,a),flip(a)].">
      <j1 rule="hyper" parents="373 31983 32254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32331">
    <literal><![CDATA[
      a(x,((T(y,z) * u) / w) * v5,v6) = a(x,(w \ (y * u)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,31904,a,b,32272,a)].">
      <j1 rule="hyper" parents="64 31904 32272"/>
    </justification>
  </clause>

  <clause id="32332">
    <literal><![CDATA[
      a(x,(((y * z) * y) * u) * w,v5) = a(x,(u * ((z * y) * y)) * w,v5)
    ]]></literal>
    <justification jstring="[para(1296(a,1),32306(a,1,2,1,1))].">
      <j1 rule="para" parents="1296 32306"/>
    </justification>
  </clause>

  <clause id="32333">
    <literal><![CDATA[
      a(x,(y / (z * y)) \ u,w) = a(x,(y \ (z \ y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32138,a(flip),b,32318,a)].">
      <j1 rule="hyper" parents="64 32138 32318"/>
    </justification>
  </clause>

  <clause id="32334">
    <literal><![CDATA[
      a(x,((y * z) \ z) \ u,w) = a(x,(z \ (y \ z)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31972,a(flip),b,32333,a)].">
      <j1 rule="hyper" parents="64 31972 32333"/>
    </justification>
  </clause>

  <clause id="32335">
    <literal><![CDATA[
      a(x,(L(y * z,y,y) \ z) \ u,w) = a(x,(z \ ((1 / R(1 / y,y,z)) \ z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(30958(a,2),32334(a,1,2,1,1))].">
      <j1 rule="para" parents="30958 32334"/>
    </justification>
  </clause>

  <clause id="32336">
    <literal><![CDATA[
      a(x,((y \ 1) \ z) * u,w) = a(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[para(82(a,1),32330(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="82 32330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32337">
    <literal><![CDATA[
      a(x,L(y * z,y,y) * u,w) = a(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32279,a,b,32336,a)].">
      <j1 rule="hyper" parents="64 32279 32336"/>
    </justification>
  </clause>

  <clause id="32338">
    <literal><![CDATA[
      a(x,y * L(z * u,z,z),w) = a(x,(z \ u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(32008,a,32337,a)].">
      <j1 rule="hyper" parents="32008 32337"/>
    </justification>
  </clause>

  <clause id="32339">
    <literal><![CDATA[
      a(x,(y \ (y \ z)) * u,w) = a(x,L(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),32337(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 32337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32340">
    <literal><![CDATA[
      a(x,y * (z \ (z \ u)),w) = a(x,L(u,z,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(32008,a,32339,a)].">
      <j1 rule="hyper" parents="32008 32339"/>
    </justification>
  </clause>

  <clause id="32344">
    <literal><![CDATA[
      (x * (K(y,z) * (u * w))) \ (((x * K(y,z)) * u) * w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(23256(a,2),31969(a,1,2,1))].">
      <j1 rule="para" parents="23256 31969"/>
    </justification>
  </clause>

  <clause id="32345">
    <literal><![CDATA[
      a(x,((y * (z * z)) / z) * u,w) = a(x,u * (y * L(z,z,y)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32039,a,b,32020,a)].">
      <j1 rule="hyper" parents="64 32039 32020"/>
    </justification>
  </clause>

  <clause id="32346">
    <literal><![CDATA[
      a(((x \ y) / y) \ x,x \ (y \ (x \ y)),x) = (x / ((x \ y) / y)) * (x \ (y / (x * y)))
    ]]></literal>
    <justification jstring="[para(31373(a,1),32062(a,2,2))].">
      <j1 rule="para" parents="31373 32062"/>
    </justification>
  </clause>

  <clause id="32347">
    <literal><![CDATA[
      a(x,L(((y * z) \ y) * z,u,w),v5) = a(x,L(a(z,z,y),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32161,a(flip),b,32176,a)].">
      <j1 rule="hyper" parents="64 32161 32176"/>
    </justification>
  </clause>

  <clause id="32348">
    <literal><![CDATA[
      a(x,y \ (((z / u) / u) \ 1),w) = a(x,y \ R(z \ 1,u,u),w)
    ]]></literal>
    <justification jstring="[para(30607(a,1),32225(a,1,2,2))].">
      <j1 rule="para" parents="30607 32225"/>
    </justification>
  </clause>

  <clause id="32350">
    <literal><![CDATA[
      a(x * K(y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24456,a(flip),b,32344,a)].">
      <j1 rule="hyper" parents="64 24456 32344"/>
    </justification>
  </clause>

  <clause id="32352">
    <literal><![CDATA[
      a(K(x,y) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32350,a)].">
      <j1 rule="hyper" parents="26847 32350"/>
    </justification>
  </clause>

  <clause id="32358">
    <literal><![CDATA[
      a((x * (y / x)) * z,u,w) = a(y * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26840,a(flip),b,32350,a)].">
      <j1 rule="hyper" parents="64 26840 32350"/>
    </justification>
  </clause>

  <clause id="32359">
    <literal><![CDATA[
      a((T(x,y) * z) * u,w,v5) = a((x * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26803,a(flip),b,32350,a)].">
      <j1 rule="hyper" parents="64 26803 32350"/>
    </justification>
  </clause>

  <clause id="32360">
    <literal><![CDATA[
      a(x \ T(y,z),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[para(2433(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="2433 32350"/>
    </justification>
  </clause>

  <clause id="32361">
    <literal><![CDATA[
      a(x * T(y,z),u,w) = a(x * y,u,w)
    ]]></literal>
    <justification jstring="[para(6249(a,1),32350(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6249 32350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32362">
    <literal><![CDATA[
      a(x * (y / z),u,w) = a(x * (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6471(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="6471 32350"/>
    </justification>
  </clause>

  <clause id="32363">
    <literal><![CDATA[
      a(T(x,y) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(6570(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="6570 32350"/>
    </justification>
  </clause>

  <clause id="32364">
    <literal><![CDATA[
      a(x * (y * T(z,u)),w,v5) = a(x * (y * z),w,v5)
    ]]></literal>
    <justification jstring="[para(7368(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="7368 32350"/>
    </justification>
  </clause>

  <clause id="32365">
    <literal><![CDATA[
      a(x * (y * z),u,w) = a(x * (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(7591(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="7591 32350"/>
    </justification>
  </clause>

  <clause id="32366">
    <literal><![CDATA[
      a(T(x,y) \ z,u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(7948(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="7948 32350"/>
    </justification>
  </clause>

  <clause id="32367">
    <literal><![CDATA[
      a((x / y) * z,u,w) = a((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(8651(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="8651 32350"/>
    </justification>
  </clause>

  <clause id="32368">
    <literal><![CDATA[
      a(x * (y * K(z,u)),w,v5) = a(x * y,w,v5)
    ]]></literal>
    <justification jstring="[para(12078(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="12078 32350"/>
    </justification>
  </clause>

  <clause id="32369">
    <literal><![CDATA[
      a(x \ (y / z),u,w) = a(x \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(15028(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="15028 32350"/>
    </justification>
  </clause>

  <clause id="32370">
    <literal><![CDATA[
      a(x \ ((y \ z) \ z),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[para(15035(a,2),32350(a,1,1))].">
      <j1 rule="para" parents="15035 32350"/>
    </justification>
  </clause>

  <clause id="32371">
    <literal><![CDATA[
      a(x \ (y * z),u,w) = a(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(14934(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="14934 32350"/>
    </justification>
  </clause>

  <clause id="32372">
    <literal><![CDATA[
      a(x \ ((y \ z) * y),u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(15230(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="15230 32350"/>
    </justification>
  </clause>

  <clause id="32373">
    <literal><![CDATA[
      a(x \ (y * K(z,u)),w,v5) = a(x \ y,w,v5)
    ]]></literal>
    <justification jstring="[para(16164(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="16164 32350"/>
    </justification>
  </clause>

  <clause id="32374">
    <literal><![CDATA[
      a(x * (K(y,z) * u),w,v5) = a(x * u,w,v5)
    ]]></literal>
    <justification jstring="[para(23252(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="23252 32350"/>
    </justification>
  </clause>

  <clause id="32375">
    <literal><![CDATA[
      a(x \ (K(y,z) * u),w,v5) = a(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(23401(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="23401 32350"/>
    </justification>
  </clause>

  <clause id="32376">
    <literal><![CDATA[
      a(x \ (y * T(z,u)),w,v5) = a(x \ (y * z),w,v5)
    ]]></literal>
    <justification jstring="[para(24315(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="24315 32350"/>
    </justification>
  </clause>

  <clause id="32377">
    <literal><![CDATA[
      a(x \ (y \ (z / u)),w,v5) = a(x \ (y \ (u \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(24307(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="24307 32350"/>
    </justification>
  </clause>

  <clause id="32378">
    <literal><![CDATA[
      a(x \ (y \ (z * T(u,w))),v5,v6) = a(x \ (y \ (z * u)),v5,v6)
    ]]></literal>
    <justification jstring="[para(24893(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="24893 32350"/>
    </justification>
  </clause>

  <clause id="32379">
    <literal><![CDATA[
      a(x * (y * (z * K(u,w))),v5,v6) = a(x * (y * z),v5,v6)
    ]]></literal>
    <justification jstring="[para(25230(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="25230 32350"/>
    </justification>
  </clause>

  <clause id="32380">
    <literal><![CDATA[
      a(x * L(T(y,z),u,w),v5,v6) = a(x * L(y,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(25231(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="25231 32350"/>
    </justification>
  </clause>

  <clause id="32381">
    <literal><![CDATA[
      a(L(x * K(y,z),u,w),v5,v6) = a(L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(26070(a,2),32350(a,1,1))].">
      <j1 rule="para" parents="26070 32350"/>
    </justification>
  </clause>

  <clause id="32382">
    <literal><![CDATA[
      a(L(x \ K(y,z),u,w),v5,v6) = a(L(x \ 1,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(26080(a,1),32350(a,1,1))].">
      <j1 rule="para" parents="26080 32350"/>
    </justification>
  </clause>

  <clause id="32384">
    <literal><![CDATA[
      a(((x \ y) \ y) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(6025(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="6025 32352"/>
    </justification>
  </clause>

  <clause id="32385">
    <literal><![CDATA[
      a(((x \ y) \ y) \ z,u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(6073(a,1),32352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6073 32352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32386">
    <literal><![CDATA[
      a((x / y) \ z,u,w) = a((y \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(6270(a,1),32352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6270 32352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32387">
    <literal><![CDATA[
      a((x * y) \ z,u,w) = a((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(10833(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="10833 32352"/>
    </justification>
  </clause>

  <clause id="32388">
    <literal><![CDATA[
      a((x * y) * z,u,w) = a((y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(10834(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="10834 32352"/>
    </justification>
  </clause>

  <clause id="32389">
    <literal><![CDATA[
      a(((x \ y) * x) * z,u,w) = a(y * z,u,w)
    ]]></literal>
    <justification jstring="[para(10858(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="10858 32352"/>
    </justification>
  </clause>

  <clause id="32390">
    <literal><![CDATA[
      a((x * K(y,z)) \ u,w,v5) = a(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(23272(a,2),32352(a,1,1))].">
      <j1 rule="para" parents="23272 32352"/>
    </justification>
  </clause>

  <clause id="32391">
    <literal><![CDATA[
      a((T(x,y) \ z) * u,w,v5) = a((x \ z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(24347(a,1),32352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24347 32352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32392">
    <literal><![CDATA[
      a((x * T(y,z)) * u,w,v5) = a((x * y) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(24355(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="24355 32352"/>
    </justification>
  </clause>

  <clause id="32393">
    <literal><![CDATA[
      a(((x * y) * z) * u,w,v5) = a(((y * x) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(24358(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="24358 32352"/>
    </justification>
  </clause>

  <clause id="32394">
    <literal><![CDATA[
      a(L(T(x,y),z,u) \ w,v5,v6) = a(L(x,z,u) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(24557(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="24557 32352"/>
    </justification>
  </clause>

  <clause id="32395">
    <literal><![CDATA[
      a(L(T(x,y),z,u) * w,v5,v6) = a(L(x,z,u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(24680(a,1),32352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24680 32352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32396">
    <literal><![CDATA[
      a(((x / y) * z) * u,w,v5) = a(((y \ x) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(24351(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="24351 32352"/>
    </justification>
  </clause>

  <clause id="32397">
    <literal><![CDATA[
      a(((x / y) \ z) * u,w,v5) = a(((y \ x) \ z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(24352(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="24352 32352"/>
    </justification>
  </clause>

  <clause id="32398">
    <literal><![CDATA[
      a((x * (K(y,z) * u)) * w,v5,v6) = a((x * u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(24368(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="24368 32352"/>
    </justification>
  </clause>

  <clause id="32399">
    <literal><![CDATA[
      a((x * (y / z)) \ u,w,v5) = a((x * (z \ y)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(24507(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="24507 32352"/>
    </justification>
  </clause>

  <clause id="32400">
    <literal><![CDATA[
      a((x * (y \ K(z,u))) \ w,v5,v6) = a((x * (y \ 1)) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(24886(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="24886 32352"/>
    </justification>
  </clause>

  <clause id="32401">
    <literal><![CDATA[
      a(((x * T(y,z)) \ u) * w,v5,v6) = a(((x * y) \ u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(24968(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="24968 32352"/>
    </justification>
  </clause>

  <clause id="32402">
    <literal><![CDATA[
      a(((x \ T(y,z)) \ u) * w,v5,v6) = a(((x \ y) \ u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(24979(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="24979 32352"/>
    </justification>
  </clause>

  <clause id="32403">
    <literal><![CDATA[
      a((x \ (K(y,z) * u)) \ w,v5,v6) = a((x \ u) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(25412(a,1),32352(a,1,1))].">
      <j1 rule="para" parents="25412 32352"/>
    </justification>
  </clause>

  <clause id="32404">
    <literal><![CDATA[
      a(L(K(x,y) * z,u,w),v5,v6) = a(L(z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(26085(a,2),32352(a,1,1))].">
      <j1 rule="para" parents="26085 32352"/>
    </justification>
  </clause>

  <clause id="32405">
    <literal><![CDATA[
      a((x * y) \ ((y * z) * x),u,w) = a(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(27292(a,2),32352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27292 32352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32406">
    <literal><![CDATA[
      a(((x * y) \ ((y * z) * x)) * u,w,v5) = a(L(z,y,x) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(27293(a,1),32352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27293 32352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32408">
    <literal><![CDATA[
      a(((x / y) * z) \ y,u,w) = a(((y \ x) * z) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(14835(a,1),32360(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14835 32360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32409">
    <literal><![CDATA[
      a(x * T((y * y) * z,u),w,v5) = a(x * z,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,11957,a(flip),b,32361,a),flip(a)].">
      <j1 rule="hyper" parents="373 11957 32361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32410">
    <literal><![CDATA[
      a(x * (y \ (z * (y * y))),u,w) = a(x * (z * L(y,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(2848(a,1),32361(a,1,1,2))].">
      <j1 rule="para" parents="2848 32361"/>
    </justification>
  </clause>

  <clause id="32412">
    <literal><![CDATA[
      a(R(x,y,x) \ 1,L(R(x,y,x) \ 1,x,y),z) = a((x * y) \ y,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14235,a,b,32366,a)].">
      <j1 rule="hyper" parents="64 14235 32366"/>
    </justification>
  </clause>

  <clause id="32413">
    <literal><![CDATA[
      a(x * (y * (z / y)),u,w) = a(z * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32358,a)].">
      <j1 rule="hyper" parents="26847 32358"/>
    </justification>
  </clause>

  <clause id="32415">
    <literal><![CDATA[
      a(x * (y / (z * z)),u,w) = a(y * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26825,a(flip),b,32358,a)].">
      <j1 rule="hyper" parents="64 26825 32358"/>
    </justification>
  </clause>

  <clause id="32416">
    <literal><![CDATA[
      a((x / y) * z,u,w) = a(z * (y \ x),u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32362,a)].">
      <j1 rule="hyper" parents="26847 32362"/>
    </justification>
  </clause>

  <clause id="32417">
    <literal><![CDATA[
      a((x \ y) * z,u,w) = a(z * (y / x),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,32362,a)].">
      <j1 rule="hyper" parents="373 26787 32362"/>
    </justification>
  </clause>

  <clause id="32418">
    <literal><![CDATA[
      a(x * T(y / z,u),w,v5) = a(x * (z \ y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32361,a,b,32362,a)].">
      <j1 rule="hyper" parents="64 32361 32362"/>
    </justification>
  </clause>

  <clause id="32419">
    <literal><![CDATA[
      a(x / ((x \ y) / y),z,u) = a(x * (y \ (x \ y)),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26932,a,b,32362,a)].">
      <j1 rule="hyper" parents="64 26932 32362"/>
    </justification>
  </clause>

  <clause id="32420">
    <literal><![CDATA[
      a(L(x,x \ y,y),z,u) = a(((w * w) / y) * (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16205,a,b,32362,a)].">
      <j1 rule="hyper" parents="64 16205 32362"/>
    </justification>
  </clause>

  <clause id="32421">
    <literal><![CDATA[
      a(x * R(1 / y,y,z),u,w) = a(x * ((y * z) \ z),u,w)
    ]]></literal>
    <justification jstring="[para(244(a,2),32362(a,1,1,2))].">
      <j1 rule="para" parents="244 32362"/>
    </justification>
  </clause>

  <clause id="32422">
    <literal><![CDATA[
      a((x * y) * z,u,w) = a(z * (y * x),u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32365,a)].">
      <j1 rule="hyper" parents="26847 32365"/>
    </justification>
  </clause>

  <clause id="32423">
    <literal><![CDATA[
      a(x * T(y * z,u),w,v5) = a(x * (z * y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32361,a,b,32365,a)].">
      <j1 rule="hyper" parents="373 32361 32365"/>
    </justification>
  </clause>

  <clause id="32424">
    <literal><![CDATA[
      a(x * (y * z),(u * T(w,v5)) * v6,v7) = a(x * (z * y),(u * w) * v6,v7)
    ]]></literal>
    <justification jstring="[hyper(373,a,31978,a,b,32365,a)].">
      <j1 rule="hyper" parents="373 31978 32365"/>
    </justification>
  </clause>

  <clause id="32425">
    <literal><![CDATA[
      a(L(x,y * z,y * z) * (z * y),u,w) = a((y * z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,30779,a(flip),b,32365,a),flip(a)].">
      <j1 rule="hyper" parents="373 30779 32365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32426">
    <literal><![CDATA[
      a(x * (y * (z \ 1)),u,w) = a((z * y) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26830,a(flip),b,32365,a),flip(a)].">
      <j1 rule="hyper" parents="373 26830 32365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32427">
    <literal><![CDATA[
      a(x * (y * z),u,w) \ v5 = a(x * (z * y),u,w) \ v5
    ]]></literal>
    <justification jstring="[hyper(62,a,32365,a)].">
      <j1 rule="hyper" parents="62 32365"/>
    </justification>
  </clause>

  <clause id="32428">
    <literal><![CDATA[
      a(x * (y * R(z,z,y)),u,w) = a(x * ((1 / z) \ y),u,w)
    ]]></literal>
    <justification jstring="[para(1913(a,1),32365(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1913 32365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32429">
    <literal><![CDATA[
      a(x,y,a((z * u) * w,v5,v6)) = a(x,y,a(w * (u * z),v5,v6))
    ]]></literal>
    <justification jstring="[para(32365(a,1),26881(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32365 26881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32430">
    <literal><![CDATA[
      a(x,L(x,x \ y,x \ y),z) = a((x \ y) * y,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10637,a,b,32367,a)].">
      <j1 rule="hyper" parents="64 10637 32367"/>
    </justification>
  </clause>

  <clause id="32431">
    <literal><![CDATA[
      a(((x \ y) \ (y \ x)) * z,u,w) = a(((y \ x) * (x \ y)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30932,a(flip),b,32367,a),flip(a)].">
      <j1 rule="hyper" parents="64 30932 32367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32432">
    <literal><![CDATA[
      a(((x * y) \ y) * y,z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2701,a(flip),b,32367,a),flip(a)].">
      <j1 rule="hyper" parents="64 2701 32367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32433">
    <literal><![CDATA[
      a((x \ ((1 / y) * z)) * u,w,v5) = a(((y * z) / x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,2685,a(flip),b,32367,a),flip(a)].">
      <j1 rule="hyper" parents="64 2685 32367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32434">
    <literal><![CDATA[
      a((x \ (1 / y)) * z,u,w) = a((y / x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2681,a(flip),b,32367,a),flip(a)].">
      <j1 rule="hyper" parents="64 2681 32367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32435">
    <literal><![CDATA[
      a(((x * T(y,z)) \ ((y * z) * x)) * u,w,v5) = a(R(K(y,x) * z,y,x) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(26450(a,1),32367(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="26450 32367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32436">
    <literal><![CDATA[
      a(x * (y * K(z,u)),w,v5) = a(y * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,32368,a),flip(a)].">
      <j1 rule="hyper" parents="373 26787 32368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32437">
    <literal><![CDATA[
      a(x * (y \ T(z,u)),w,v5) = a(x * (y \ z),w,v5)
    ]]></literal>
    <justification jstring="[para(2433(a,1),32368(a,1,1,2))].">
      <j1 rule="para" parents="2433 32368"/>
    </justification>
  </clause>

  <clause id="32438">
    <literal><![CDATA[
      a(x * (y * (z / u)),w,v5) = a(x * (y * (u \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(6471(a,1),32368(a,1,1,2))].">
      <j1 rule="para" parents="6471 32368"/>
    </justification>
  </clause>

  <clause id="32439">
    <literal><![CDATA[
      a(x * (y * (z * T(u,w))),v5,v6) = a(x * (y * (z * u)),v5,v6)
    ]]></literal>
    <justification jstring="[para(7368(a,1),32368(a,1,1,2))].">
      <j1 rule="para" parents="7368 32368"/>
    </justification>
  </clause>

  <clause id="32440">
    <literal><![CDATA[
      a(x * ((y / z) * u),w,v5) = a(x * ((z \ y) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(8651(a,1),32368(a,1,1,2))].">
      <j1 rule="para" parents="8651 32368"/>
    </justification>
  </clause>

  <clause id="32441">
    <literal><![CDATA[
      a(x * (y \ (z / u)),w,v5) = a(x * (y \ (u \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(15028(a,1),32368(a,1,1,2))].">
      <j1 rule="para" parents="15028 32368"/>
    </justification>
  </clause>

  <clause id="32442">
    <literal><![CDATA[
      a(x * (y \ ((z \ u) \ u)),w,v5) = a(x * (y \ z),w,v5)
    ]]></literal>
    <justification jstring="[para(15035(a,2),32368(a,1,1,2))].">
      <j1 rule="para" parents="15035 32368"/>
    </justification>
  </clause>

  <clause id="32443">
    <literal><![CDATA[
      a(x * (y \ (K(z,u) * w)),v5,v6) = a(x * (y \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(23401(a,1),32368(a,1,1,2))].">
      <j1 rule="para" parents="23401 32368"/>
    </justification>
  </clause>

  <clause id="32444">
    <literal><![CDATA[
      a(x * (y \ (z * T(u,w))),v5,v6) = a(x * (y \ (z * u)),v5,v6)
    ]]></literal>
    <justification jstring="[para(24315(a,1),32368(a,1,1,2))].">
      <j1 rule="para" parents="24315 32368"/>
    </justification>
  </clause>

  <clause id="32445">
    <literal><![CDATA[
      a(x * K(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,u,w) = v5
    ]]></literal>
    <justification jstring="[para(32368(a,1),26858(a,1))].">
      <j1 rule="para" parents="32368 26858"/>
    </justification>
  </clause>

  <clause id="32446">
    <literal><![CDATA[
      a(K(x,y) * z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(6576(a,1),32445(a,1,1))].">
      <j1 rule="para" parents="6576 32445"/>
    </justification>
  </clause>

  <clause id="32447">
    <literal><![CDATA[
      a(x * T(y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * y,u,w) = v5
    ]]></literal>
    <justification jstring="[para(6852(a,1),32445(a,1,1))].">
      <j1 rule="para" parents="6852 32445"/>
    </justification>
  </clause>

  <clause id="32448">
    <literal><![CDATA[
      a(x * (y * z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x * (z * y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(7591(a,1),32445(a,1,1))].">
      <j1 rule="para" parents="7591 32445"/>
    </justification>
  </clause>

  <clause id="32449">
    <literal><![CDATA[
      a(x \ (y / z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x \ (z \ y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(15028(a,1),32445(a,1,1))].">
      <j1 rule="para" parents="15028 32445"/>
    </justification>
  </clause>

  <clause id="32450">
    <literal><![CDATA[
      a(x * (K(y,z) * u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x * u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(23252(a,1),32445(a,1,1))].">
      <j1 rule="para" parents="23252 32445"/>
    </justification>
  </clause>

  <clause id="32451">
    <literal><![CDATA[
      a((x * y) \ z,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((y * x) \ z,u,w) = v5
    ]]></literal>
    <justification jstring="[para(10833(a,1),32446(a,1,1))].">
      <j1 rule="para" parents="10833 32446"/>
    </justification>
  </clause>

  <clause id="32452">
    <literal><![CDATA[
      a((T(x,y) \ z) * u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a((x \ z) * u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(24348(a,1),32446(a,1,1))].">
      <j1 rule="para" parents="24348 32446"/>
    </justification>
  </clause>

  <clause id="32453">
    <literal><![CDATA[
      a(((x / y) * z) * u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(((y \ x) * z) * u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(24351(a,1),32446(a,1,1))].">
      <j1 rule="para" parents="24351 32446"/>
    </justification>
  </clause>

  <clause id="32454">
    <literal><![CDATA[
      a((x \ 1) \ (y / z),u,w) = a(x \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2675,a(flip),b,32369,a),flip(a)].">
      <j1 rule="hyper" parents="373 2675 32369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32455">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = a(y \ (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26058,a,b,32369,a)].">
      <j1 rule="hyper" parents="64 26058 32369"/>
    </justification>
  </clause>

  <clause id="32456">
    <literal><![CDATA[
      a(x \ (y \ (z * T(u,z \ 1))),w,v5) = a(x \ ((u * (1 / z)) / y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26910,a(flip),b,32369,a),flip(a)].">
      <j1 rule="hyper" parents="64 26910 32369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32457">
    <literal><![CDATA[
      a(x \ (y \ (1 / z)),u,w) = a(x \ (z / y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26904,a(flip),b,32369,a),flip(a)].">
      <j1 rule="hyper" parents="64 26904 32369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32458">
    <literal><![CDATA[
      a(x \ (y \ z),x,y) \ z = ((z / y) / x) * (x * y)
    ]]></literal>
    <justification jstring="[para(32369(a,1),26879(a,1,1))].">
      <j1 rule="para" parents="32369 26879"/>
    </justification>
  </clause>

  <clause id="32459">
    <literal><![CDATA[
      a(x,y,a(z \ (x \ z),u,w)) = 1
    ]]></literal>
    <justification jstring="[para(32369(a,1),30892(a,1,3))].">
      <j1 rule="para" parents="32369 30892"/>
    </justification>
  </clause>

  <clause id="32460">
    <literal><![CDATA[
      L(a(x \ (y \ x),z,u),w,y) = a(x \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(53,a,32459,a)].">
      <j1 rule="hyper" parents="53 32459"/>
    </justification>
  </clause>

  <clause id="32461">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = a(y \ ((x \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26925,a,b,32455,a),flip(a)].">
      <j1 rule="hyper" parents="373 26925 32455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32462">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = a((y \ (x \ y)) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2653,a,b,32455,a),flip(a)].">
      <j1 rule="hyper" parents="373 2653 32455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32463">
    <literal><![CDATA[
      a(L(x,x,y * z),z,y) = x \ R(x,z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,28073,a(flip),b,32455,a),flip(a)].">
      <j1 rule="hyper" parents="373 28073 32455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32464">
    <literal><![CDATA[
      x * a(L(y,y,z),u,w) = x * a(z \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,32455,a,b,9,a)].">
      <j1 rule="hyper" parents="145 32455 9"/>
    </justification>
  </clause>

  <clause id="32465">
    <literal><![CDATA[
      a(x \ (y \ x),z,a(y,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,30889,a(flip),b,32455,a),flip(a)].">
      <j1 rule="hyper" parents="64 30889 32455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32466">
    <literal><![CDATA[
      L(a(x,y,z),u,w \ (x \ w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,32465,a)].">
      <j1 rule="hyper" parents="53 32465"/>
    </justification>
  </clause>

  <clause id="32467">
    <literal><![CDATA[
      a(L(x,x,y * z),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(23253(a,1),32463(a,1,1))].">
      <j1 rule="para" parents="23253 32463"/>
    </justification>
  </clause>

  <clause id="32468">
    <literal><![CDATA[
      a(x * y,z,z) \ R(a(x * y,z,z),y,x) = a(a(x * y,z,z),y,x)
    ]]></literal>
    <justification jstring="[para(29327(a,1),32463(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29327 32463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32470">
    <literal><![CDATA[
      L(x,y,x \ R(x,z,u)) = x
    ]]></literal>
    <justification jstring="[para(32463(a,1),29969(a,1,3))].">
      <j1 rule="para" parents="32463 29969"/>
    </justification>
  </clause>

  <clause id="32471">
    <literal><![CDATA[
      a(x,y,z) \ R(a(x,y,z),x \ u,u) = a(a(x,y,z),x \ u,u)
    ]]></literal>
    <justification jstring="[para(30887(a,1),32463(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30887 32463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32472">
    <literal><![CDATA[
      L(x,y,x * R(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,2212,a(flip),b,32470,a)].">
      <j1 rule="hyper" parents="64 2212 32470"/>
    </justification>
  </clause>

  <clause id="32473">
    <literal><![CDATA[
      L(x \ 1,y,x \ R(x,z,u)) = x \ 1
    ]]></literal>
    <justification jstring="[para(2009(a,1),32470(a,1,3))].">
      <j1 rule="para" parents="2009 32470"/>
    </justification>
  </clause>

  <clause id="32474">
    <literal><![CDATA[
      L(x,y,R(x,z,u) \ x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,24701,a,b,32472,a)].">
      <j1 rule="hyper" parents="64 24701 32472"/>
    </justification>
  </clause>

  <clause id="32475">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (u * T(x,(R(x,y,z) \ x) * u)) = x * ((R(x,y,z) \ x) * u)
    ]]></literal>
    <justification jstring="[para(32474(a,1),793(a,2,1))].">
      <j1 rule="para" parents="32474 793"/>
    </justification>
  </clause>

  <clause id="32476">
    <literal><![CDATA[
      L(L(x \ 1,y,z),u,x \ R(x,w,v5)) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(32473(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32473 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32477">
    <literal><![CDATA[
      (x * a(y,z,u)) * (w \ (y \ w)) = a(y,z,u) * (x * (w \ (y \ w)))
    ]]></literal>
    <justification jstring="[hyper(144,a,32466,a(flip),b,28786,a),flip(a)].">
      <j1 rule="hyper" parents="144 32466 28786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32478">
    <literal><![CDATA[
      a((x \ (y * z)) \ (z * y),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(26846,a,32371,a),flip(a)].">
      <j1 rule="hyper" parents="26846 32371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32479">
    <literal><![CDATA[
      a(x \ (y * (z * z)),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26898,a(flip),b,32371,a),flip(a)].">
      <j1 rule="hyper" parents="373 26898 32371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32480">
    <literal><![CDATA[
      a(L(x \ y,x,z),u,w) = a((z * x) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(102(a,2),32371(a,1,1))].">
      <j1 rule="para" parents="102 32371"/>
    </justification>
  </clause>

  <clause id="32481">
    <literal><![CDATA[
      a(x \ K(y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2666,a(flip),b,32373,a),flip(a)].">
      <j1 rule="hyper" parents="64 2666 32373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32482">
    <literal><![CDATA[
      a(x \ (y * (z * u)),w,v5) = a(x \ (y * (u * z)),w,v5)
    ]]></literal>
    <justification jstring="[para(7591(a,1),32373(a,1,1,2))].">
      <j1 rule="para" parents="7591 32373"/>
    </justification>
  </clause>

  <clause id="32483">
    <literal><![CDATA[
      a(x \ ((y / z) * u),w,v5) = a(x \ ((z \ y) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(8651(a,1),32373(a,1,1,2))].">
      <j1 rule="para" parents="8651 32373"/>
    </justification>
  </clause>

  <clause id="32484">
    <literal><![CDATA[
      a(x \ (y * (K(z,u) * w)),v5,v6) = a(x \ (y * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(23252(a,1),32373(a,1,1,2))].">
      <j1 rule="para" parents="23252 32373"/>
    </justification>
  </clause>

  <clause id="32485">
    <literal><![CDATA[
      a(x \ (y \ (T(z,u) * w)),v5,v6) = a(x \ (y \ (z * w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(24312(a,1),32373(a,1,1,2))].">
      <j1 rule="para" parents="24312 32373"/>
    </justification>
  </clause>

  <clause id="32486">
    <literal><![CDATA[
      a(x \ (y \ (z * (u / w))),v5,v6) = a(x \ (y \ (z * (w \ u))),v5,v6)
    ]]></literal>
    <justification jstring="[para(24314(a,1),32373(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="24314 32373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32487">
    <literal><![CDATA[
      a(x \ (y \ (z * (u \ K(w,v5)))),v6,v7) = a(x \ (y \ (z * (u \ 1))),v6,v7)
    ]]></literal>
    <justification jstring="[para(24885(a,1),32373(a,1,1,2))].">
      <j1 rule="para" parents="24885 32373"/>
    </justification>
  </clause>

  <clause id="32488">
    <literal><![CDATA[
      a((x \ (y \ x)) * y,z,u) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[para(30565(a,1),32481(a,1,1))].">
      <j1 rule="para" parents="30565 32481"/>
    </justification>
  </clause>

  <clause id="32489">
    <literal><![CDATA[
      a(x * ((y / z) \ u),w,v5) = a(x * ((z \ y) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(6270(a,1),32374(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 32374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32490">
    <literal><![CDATA[
      a(x * ((y * z) \ u),w,v5) = a(x * ((z * y) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(10833(a,1),32374(a,1,1,2))].">
      <j1 rule="para" parents="10833 32374"/>
    </justification>
  </clause>

  <clause id="32491">
    <literal><![CDATA[
      a((x \ T(y,z)) * u,w,v5) = a((x \ y) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(24474(a,1),32374(a,1,1))].">
      <j1 rule="para" parents="24474 32374"/>
    </justification>
  </clause>

  <clause id="32492">
    <literal><![CDATA[
      a((x \ (y / z)) * u,w,v5) = a((x \ (z \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(24475(a,1),32374(a,1,1))].">
      <j1 rule="para" parents="24475 32374"/>
    </justification>
  </clause>

  <clause id="32493">
    <literal><![CDATA[
      a((x * (y * T(z,u))) * w,v5,v6) = a((x * (y * z)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(24746(a,1),32374(a,1,1))].">
      <j1 rule="para" parents="24746 32374"/>
    </justification>
  </clause>

  <clause id="32494">
    <literal><![CDATA[
      a((x \ (K(y,z) * u)) * w,v5,v6) = a((x \ u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(24778(a,1),32374(a,1,1))].">
      <j1 rule="para" parents="24778 32374"/>
    </justification>
  </clause>

  <clause id="32495">
    <literal><![CDATA[
      a(x \ ((y / z) \ u),w,v5) = a(x \ ((z \ y) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(6270(a,1),32375(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 32375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32496">
    <literal><![CDATA[
      a((T(x,y) * z) \ u,w,v5) = a((x * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(24191(a,1),32375(a,1,1))].">
      <j1 rule="para" parents="24191 32375"/>
    </justification>
  </clause>

  <clause id="32497">
    <literal><![CDATA[
      a(((x / y) * z) \ u,w,v5) = a(((y \ x) * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(24400(a,1),32375(a,1,1))].">
      <j1 rule="para" parents="24400 32375"/>
    </justification>
  </clause>

  <clause id="32498">
    <literal><![CDATA[
      a(((x / y) \ z) \ u,w,v5) = a(((y \ x) \ z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(24402(a,1),32375(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24402 32375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32499">
    <literal><![CDATA[
      a(x * ((y \ z) \ z),u,w) = a(y * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32384,a)].">
      <j1 rule="hyper" parents="26847 32384"/>
    </justification>
  </clause>

  <clause id="32500">
    <literal><![CDATA[
      a(((x \ y) \ y) * z,u,w) = a(z * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,32384,a),flip(a)].">
      <j1 rule="hyper" parents="373 26787 32384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32501">
    <literal><![CDATA[
      a((T(x \ 1,y * (x \ z)) \ (x * (((x \ 1) * y) * z))) \ u,w,v5) = a(((x * y) * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(28045(a,1),32385(a,1,1,1,1))].">
      <j1 rule="para" parents="28045 32385"/>
    </justification>
  </clause>

  <clause id="32502">
    <literal><![CDATA[
      a((1 / (x / (y * y))) \ z,u,w) = a(x \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26924,a(flip),b,32386,a),flip(a)].">
      <j1 rule="hyper" parents="373 26924 32386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32503">
    <literal><![CDATA[
      a((x \ y) \ x,z,u) = a((x / y) * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2702,a(flip),b,32386,a),flip(a)].">
      <j1 rule="hyper" parents="64 2702 32386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32504">
    <literal><![CDATA[
      a((x * y) \ (z * u),w,v5) = a((y * x) \ (u * z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32371,a,b,32387,a)].">
      <j1 rule="hyper" parents="373 32371 32387"/>
    </justification>
  </clause>

  <clause id="32505">
    <literal><![CDATA[
      a((x * (y \ 1)) \ z,u,w) = a((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26918,a(flip),b,32387,a),flip(a)].">
      <j1 rule="hyper" parents="373 26918 32387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32506">
    <literal><![CDATA[
      a((x * y) \ x,z,u) = a(x \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,13122,a(flip),b,32387,a),flip(a)].">
      <j1 rule="hyper" parents="373 13122 32387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32507">
    <literal><![CDATA[
      a((((x \ y) * y) * x) * z,u,w) = a(z * a(x,x \ y,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26876,a(flip),b,32388,a),flip(a)].">
      <j1 rule="hyper" parents="373 26876 32388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32508">
    <literal><![CDATA[
      a((x * R(y \ 1,z,u)) * w,v5,v6) = a((R(y,z,u) * x) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,3387,a(flip),b,32388,a),flip(a)].">
      <j1 rule="hyper" parents="373 3387 32388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32509">
    <literal><![CDATA[
      a((x * (y \ 1)) * z,u,w) = a((y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2690,a(flip),b,32388,a),flip(a)].">
      <j1 rule="hyper" parents="373 2690 32388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32510">
    <literal><![CDATA[
      a(((x * y) * x) * z,u,w) = a(L(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2657,a(flip),b,32388,a),flip(a)].">
      <j1 rule="hyper" parents="373 2657 32388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32511">
    <literal><![CDATA[
      a((x * y) * a(y,z,u),w,v5) = a(y * (x * a(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(29910(a,1),32388(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29910 32388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32512">
    <literal><![CDATA[
      a(x * ((y \ z) * y),u,w) = a(z * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32389,a)].">
      <j1 rule="hyper" parents="26847 32389"/>
    </justification>
  </clause>

  <clause id="32513">
    <literal><![CDATA[
      a(a(x,x,x \ y) * z,u,w) = a(a(x,x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(30155(a,1),32389(a,1,1,1))].">
      <j1 rule="para" parents="30155 32389"/>
    </justification>
  </clause>

  <clause id="32514">
    <literal><![CDATA[
      a((x * (y * z)) \ u,w,v5) = a((x * (z * y)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(7591(a,1),32390(a,1,1,1))].">
      <j1 rule="para" parents="7591 32390"/>
    </justification>
  </clause>

  <clause id="32515">
    <literal><![CDATA[
      a((x \ (y * z)) \ u,w,v5) = a((x \ (z * y)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(14934(a,1),32390(a,1,1,1))].">
      <j1 rule="para" parents="14934 32390"/>
    </justification>
  </clause>

  <clause id="32516">
    <literal><![CDATA[
      a(((x * y) * y) * z,u,w) = a(z * R(x,y,y),u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),32415(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="20 32415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32517">
    <literal><![CDATA[
      a((x / y) * z,(u / w) * v5,v6) = a(z * (y \ x),v5 * (w \ u),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32039,a(flip),b,32416,a),flip(a)].">
      <j1 rule="hyper" parents="373 32039 32416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32518">
    <literal><![CDATA[
      a((x \ (y \ x)) * y,z,u) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(30070(a,1),32417(a,2,1))].">
      <j1 rule="para" parents="30070 32417"/>
    </justification>
  </clause>

  <clause id="32519">
    <literal><![CDATA[
      a((x * y) * R(R(z,y,x),u,w),v5,v6) = a((R(z,u,w) * y) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(506(a,1),32422(a,2,1))].">
      <j1 rule="para" parents="506 32422"/>
    </justification>
  </clause>

  <clause id="32520">
    <literal><![CDATA[
      a((x * y) * L(R(z,y,x),u,w),v5,v6) = a((L(z,u,w) * y) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(510(a,1),32422(a,2,1))].">
      <j1 rule="para" parents="510 32422"/>
    </justification>
  </clause>

  <clause id="32521">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,v6)) = a(x,y,a(z * (w * u),v5,v6))
    ]]></literal>
    <justification jstring="[para(32422(a,1),26881(a,1,3))].">
      <j1 rule="para" parents="32422 26881"/>
    </justification>
  </clause>

  <clause id="32522">
    <literal><![CDATA[
      a((x * (y \ z)) * u,w,v5) = a(u * (x * (z / y)),w,v5)
    ]]></literal>
    <justification jstring="[para(6471(a,1),32436(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6471 32436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32523">
    <literal><![CDATA[
      a(x * (T(y,z) * u),w,v5) = a((y * u) * x,w,v5)
    ]]></literal>
    <justification jstring="[para(6570(a,1),32436(a,1,1,2))].">
      <j1 rule="para" parents="6570 32436"/>
    </justification>
  </clause>

  <clause id="32524">
    <literal><![CDATA[
      a(x * (T(y,z) \ u),w,v5) = a((y \ u) * x,w,v5)
    ]]></literal>
    <justification jstring="[para(7948(a,1),32436(a,1,1,2))].">
      <j1 rule="para" parents="7948 32436"/>
    </justification>
  </clause>

  <clause id="32525">
    <literal><![CDATA[
      a(x * (y * (z * K(u,w))),v5,v6) = a((y * z) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(12078(a,1),32436(a,1,1,2))].">
      <j1 rule="para" parents="12078 32436"/>
    </justification>
  </clause>

  <clause id="32526">
    <literal><![CDATA[
      a((x \ (y * z)) * u,w,v5) = a(u * (x \ (z * y)),w,v5)
    ]]></literal>
    <justification jstring="[para(14934(a,1),32436(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14934 32436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32527">
    <literal><![CDATA[
      a(x * (y * (K(z,u) * w)),v5,v6) = a((y * w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(23252(a,1),32436(a,1,1,2))].">
      <j1 rule="para" parents="23252 32436"/>
    </justification>
  </clause>

  <clause id="32528">
    <literal><![CDATA[
      a(x * (y \ (K(z,u) * w)),v5,v6) = a((y \ w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(23401(a,1),32436(a,1,1,2))].">
      <j1 rule="para" parents="23401 32436"/>
    </justification>
  </clause>

  <clause id="32529">
    <literal><![CDATA[
      a((x \ (y \ T(z,u))) * w,v5,v6) = a(w * (x \ (y \ z)),v5,v6)
    ]]></literal>
    <justification jstring="[para(24309(a,1),32436(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="24309 32436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32530">
    <literal><![CDATA[
      a((x \ L(T(y,z),u,w)) * v5,v6,v7) = a(v5 * (x \ L(y,u,w)),v6,v7)
    ]]></literal>
    <justification jstring="[para(25328(a,1),32436(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="25328 32436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32531">
    <literal><![CDATA[
      a((L(1 / x,y,z) \ u) * w,v5,v6) = a(w * (L(x \ 1,y,z) \ u),v5,v6)
    ]]></literal>
    <justification jstring="[para(27083(a,1),32436(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="27083 32436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32532">
    <literal><![CDATA[
      a(x * L(y,y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26799,a(flip),b,32479,a)].">
      <j1 rule="hyper" parents="64 26799 32479"/>
    </justification>
  </clause>

  <clause id="32533">
    <literal><![CDATA[
      a(L(x,x,y) * y,z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32532,a)].">
      <j1 rule="hyper" parents="26847 32532"/>
    </justification>
  </clause>

  <clause id="32535">
    <literal><![CDATA[
      a((x \ a(y,x,x)) * y,z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30500,a,b,32533,a)].">
      <j1 rule="hyper" parents="64 30500 32533"/>
    </justification>
  </clause>

  <clause id="32536">
    <literal><![CDATA[
      a(L(x,x,L(y,z,z)) * (z \ (z \ y)),u,w) = a(x \ (z \ (z \ y)),u,w)
    ]]></literal>
    <justification jstring="[para(30390(a,1),32533(a,1,1,1))].">
      <j1 rule="para" parents="30390 32533"/>
    </justification>
  </clause>

  <clause id="32537">
    <literal><![CDATA[
      a(x \ y,y,y) = a(y * x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31290,a(flip),b,32500,a)].">
      <j1 rule="hyper" parents="64 31290 32500"/>
    </justification>
  </clause>

  <clause id="32538">
    <literal><![CDATA[
      a(x * (y \ 1),x,x) = a(y \ x,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,26850,a,b,32537,a)].">
      <j1 rule="hyper" parents="373 26850 32537"/>
    </justification>
  </clause>

  <clause id="32539">
    <literal><![CDATA[
      a((x \ y) \ x,z,u) = a((y \ x) * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32367,a(flip),b,32503,a),flip(a)].">
      <j1 rule="hyper" parents="373 32367 32503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32540">
    <literal><![CDATA[
      a(L(x,x,y \ 1),z,u) = a(y \ ((x \ 1) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(1631(a,2),32461(a,1,1))].">
      <j1 rule="para" parents="1631 32461"/>
    </justification>
  </clause>

  <clause id="32541">
    <literal><![CDATA[
      a(L(T(x * K(y,x),z),T(x * K(y,x),z),y * x),u,w) = a(((y * x) \ (y * K(z,x))) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(8660(a,1),32462(a,2,1,1,2))].">
      <j1 rule="para" parents="8660 32462"/>
    </justification>
  </clause>

  <clause id="32542">
    <literal><![CDATA[
      a(x * (y \ (x \ y)),z,u) = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32488,a)].">
      <j1 rule="hyper" parents="26847 32488"/>
    </justification>
  </clause>

  <clause id="32543">
    <literal><![CDATA[
      a(a(x,y,y),z,u) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32488,a(flip),b,32518,a)].">
      <j1 rule="hyper" parents="64 32488 32518"/>
    </justification>
  </clause>

  <clause id="32544">
    <literal><![CDATA[
      a(x * L(x,y,y),z,u) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,9391,a,b,32543,a)].">
      <j1 rule="hyper" parents="373 9391 32543"/>
    </justification>
  </clause>

  <clause id="32545">
    <literal><![CDATA[
      a(a(x,x,y),z,u) * w = w * a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,32543,a,b,23174,a),flip(a)].">
      <j1 rule="hyper" parents="145 32543 23174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32546">
    <literal><![CDATA[
      x \ a(a(y,z,z),u,w) = x \ a(a(z,z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,32543,a,b,10,a)].">
      <j1 rule="hyper" parents="139 32543 10"/>
    </justification>
  </clause>

  <clause id="32547">
    <literal><![CDATA[
      a(a(x,x,y \ 1),z,u) = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(2653(a,1),32543(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2653 32543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32548">
    <literal><![CDATA[
      (a(x,x,y) * z) * a(a(y,x,x),u,w) = a(x,x,y) * (z * a(a(x,x,y),u,w))
    ]]></literal>
    <justification jstring="[para(32543(a,2),29910(a,1,2))].">
      <j1 rule="para" parents="32543 29910"/>
    </justification>
  </clause>

  <clause id="32549">
    <literal><![CDATA[
      a(x \ L(x,y,y),z,u) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5609,a,b,32544,a)].">
      <j1 rule="hyper" parents="64 5609 32544"/>
    </justification>
  </clause>

  <clause id="32550">
    <literal><![CDATA[
      a((x \ (y \ x)) \ y,z,u) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25910,a,b,32542,a)].">
      <j1 rule="hyper" parents="64 25910 32542"/>
    </justification>
  </clause>

  <clause id="32552">
    <literal><![CDATA[
      a((T(x,y) * z) * u,w,v5) = a(u * (z * x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32422,a(flip),b,32359,a),flip(a)].">
      <j1 rule="hyper" parents="373 32422 32359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32553">
    <literal><![CDATA[
      a((x * ((y * y) * z)) * u,w,v5) = a((x * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,2660,a(flip),b,32359,a)].">
      <j1 rule="hyper" parents="64 2660 32359"/>
    </justification>
  </clause>

  <clause id="32554">
    <literal><![CDATA[
      a(x * (T(y,z) * u),w,v5) = a(x * (u * y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32365,a,b,32364,a)].">
      <j1 rule="hyper" parents="64 32365 32364"/>
    </justification>
  </clause>

  <clause id="32555">
    <literal><![CDATA[
      a(x \ (y * T(z,u)),w,v5) = a(x \ (z * y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32371,a,b,32376,a),flip(a)].">
      <j1 rule="hyper" parents="373 32371 32376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32556">
    <literal><![CDATA[
      a(L(x * (y / z),u,w),v5,v6) = a(L(x * (z \ y),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(6471(a,1),32381(a,1,1,1))].">
      <j1 rule="para" parents="6471 32381"/>
    </justification>
  </clause>

  <clause id="32557">
    <literal><![CDATA[
      a(L((x / y) * z,u,w),v5,v6) = a(L((y \ x) * z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(8651(a,1),32381(a,1,1,1))].">
      <j1 rule="para" parents="8651 32381"/>
    </justification>
  </clause>

  <clause id="32558">
    <literal><![CDATA[
      a(L(x \ (y / z),u,w),v5,v6) = a(L(x \ (z \ y),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(15028(a,1),32381(a,1,1,1))].">
      <j1 rule="para" parents="15028 32381"/>
    </justification>
  </clause>

  <clause id="32559">
    <literal><![CDATA[
      a(L(x \ (y * (z / y)),u,w),v5,v6) = a(L(x \ z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(16688(a,1),32381(a,1,1,1))].">
      <j1 rule="para" parents="16688 32381"/>
    </justification>
  </clause>

  <clause id="32560">
    <literal><![CDATA[
      a((x * (y / z)) * u,w,v5) = a((x * (z \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(117(a,1),32392(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="117 32392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32561">
    <literal><![CDATA[
      a(L(K(x,y) * (z * ((u * w) \ u)),v5,v6),v7,v8) = a(L(z * L(w \ 1,w,u),v5,v6),v7,v8)
    ]]></literal>
    <justification jstring="[para(999(a,1),32404(a,1,1,1))].">
      <j1 rule="para" parents="999 32404"/>
    </justification>
  </clause>

  <clause id="32562">
    <literal><![CDATA[
      a(L((x * T(y,z)) \ u,w,v5),v6,v7) = a(L((x * y) \ u,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(24506(a,1),32404(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="24506 32404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32563">
    <literal><![CDATA[
      a(L((x / (x * y)) * y,z,u),w,v5) = a(L(a(y,y,x),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(30285(a,1),32404(a,1,1,1))].">
      <j1 rule="para" parents="30285 32404"/>
    </justification>
  </clause>

  <clause id="32564">
    <literal><![CDATA[
      a(x * (y \ ((z * z) * u)),w,v5) = a(x * (u / y),w,v5)
    ]]></literal>
    <justification jstring="[para(946(a,1),32409(a,1,1,2))].">
      <j1 rule="para" parents="946 32409"/>
    </justification>
  </clause>

  <clause id="32565">
    <literal><![CDATA[
      a(x * ((y * z) \ z),u,w) = a(x * (z \ (y \ z)),u,w)
    ]]></literal>
    <justification jstring="[para(5144(a,1),32418(a,1,1,2))].">
      <j1 rule="para" parents="5144 32418"/>
    </justification>
  </clause>

  <clause id="32566">
    <literal><![CDATA[
      a(x * (y \ (z * (y * y))),u,w) = a(x * (L(y,y,z) * z),u,w)
    ]]></literal>
    <justification jstring="[para(2848(a,1),32423(a,1,1,2))].">
      <j1 rule="para" parents="2848 32423"/>
    </justification>
  </clause>

  <clause id="32567">
    <literal><![CDATA[
      a(x * R(y * z,y,y),u,w) = a(x * (y * L(z,y,y)),u,w)
    ]]></literal>
    <justification jstring="[para(3884(a,1),32423(a,1,1,2))].">
      <j1 rule="para" parents="3884 32423"/>
    </justification>
  </clause>

  <clause id="32568">
    <literal><![CDATA[
      a((((x * (1 / y)) \ x) * y) * z,u,w) = a(z * a(x,y,y),u,w)
    ]]></literal>
    <justification jstring="[para(30473(a,1),32426(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="30473 32426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32569">
    <literal><![CDATA[
      a(x * (T(y,z) / u),w,v5) = a(x * (u \ y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32362,a,b,32437,a)].">
      <j1 rule="hyper" parents="64 32362 32437"/>
    </justification>
  </clause>

  <clause id="32570">
    <literal><![CDATA[
      a(x * (y \ ((z \ u) / u)),w,v5) = a(x * (y \ ((z * u) \ u)),w,v5)
    ]]></literal>
    <justification jstring="[para(5144(a,1),32437(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5144 32437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32571">
    <literal><![CDATA[
      a((x * ((y * y) * z)) \ u,w,v5) = a((x * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26908,a(flip),b,32496,a)].">
      <j1 rule="hyper" parents="64 26908 32496"/>
    </justification>
  </clause>

  <clause id="32573">
    <literal><![CDATA[
      a((x * (y \ 1)) * z,u,w) = a((x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32388,a,b,32509,a),flip(a)].">
      <j1 rule="hyper" parents="373 32388 32509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32574">
    <literal><![CDATA[
      a(L(x,y,z) * (y * z),u,w) = a((y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26839,a,b,32523,a)].">
      <j1 rule="hyper" parents="64 26839 32523"/>
    </justification>
  </clause>

  <clause id="32575">
    <literal><![CDATA[
      a(x * (((y \ z) \ z) * u),w,v5) = a((y * u) * x,w,v5)
    ]]></literal>
    <justification jstring="[para(116(a,1),32523(a,1,1,2,1))].">
      <j1 rule="para" parents="116 32523"/>
    </justification>
  </clause>

  <clause id="32577">
    <literal><![CDATA[
      a(x * (((y * z) * u) * z),w,v5) = a(x * (z * ((z * y) * u)),w,v5)
    ]]></literal>
    <justification jstring="[para(10855(a,1),32554(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10855 32554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32578">
    <literal><![CDATA[
      a(L(R(x,y,x),y,z),u,w) = a((z * y) \ ((x * y) * z),u,w)
    ]]></literal>
    <justification jstring="[para(4748(a,1),32555(a,1,1))].">
      <j1 rule="para" parents="4748 32555"/>
    </justification>
  </clause>

  <clause id="32579">
    <literal><![CDATA[
      a((x * y) \ ((x * z) * y),u,w) = a(L(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32387,a,b,32405,a)].">
      <j1 rule="hyper" parents="64 32387 32405"/>
    </justification>
  </clause>

  <clause id="32580">
    <literal><![CDATA[
      a(x,(1 / (y / x)) * y,z) = a((x \ y) * y,x,z)
    ]]></literal>
    <justification jstring="[para(10627(a,1),32430(a,1,2))].">
      <j1 rule="para" parents="10627 32430"/>
    </justification>
  </clause>

  <clause id="32581">
    <literal><![CDATA[
      a((x \ y) * y,x,z) = a(x,(y / x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11967,a(flip),b,32580,a),flip(a)].">
      <j1 rule="hyper" parents="64 11967 32580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32582">
    <literal><![CDATA[
      a((x \ y) * y,x,z) = a(x,(x \ y) * y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31904,a(flip),b,32581,a),flip(a)].">
      <j1 rule="hyper" parents="373 31904 32581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32583">
    <literal><![CDATA[
      a((x \ T(y,z)) * u,w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a((x \ y) * u,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(24474(a,1),32450(a,1,1))].">
      <j1 rule="para" parents="24474 32450"/>
    </justification>
  </clause>

  <clause id="32584">
    <literal><![CDATA[
      x \ (y * a(z \ (x \ z),u,w)) = (x \ y) * a(z \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[para(32460(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="32460 598"/>
    </justification>
  </clause>

  <clause id="32585">
    <literal><![CDATA[
      a(L(x \ y,x,z),u,w) = a((x * z) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32387,a,b,32480,a),flip(a)].">
      <j1 rule="hyper" parents="373 32387 32480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32586">
    <literal><![CDATA[
      a(L(x \ y,x,z),u,w) = a((z * x) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32371,a,b,32480,a),flip(a)].">
      <j1 rule="hyper" parents="373 32371 32480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32587">
    <literal><![CDATA[
      a(L(x,x,y \ 1),z,u) = a(L(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32461,a,b,32540,a),flip(a)].">
      <j1 rule="hyper" parents="373 32461 32540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32588">
    <literal><![CDATA[
      a(L(x,x \ 1,y \ 1),z,u) = a(L(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11794(a,2),32587(a,1,1))].">
      <j1 rule="para" parents="11794 32587"/>
    </justification>
  </clause>

  <clause id="32590">
    <literal><![CDATA[
      a(R(x,y,z),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26895,a(flip),b,32579,a)].">
      <j1 rule="hyper" parents="64 26895 32579"/>
    </justification>
  </clause>

  <clause id="32591">
    <literal><![CDATA[
      a(R(L(x,y,z),u,w),v5,v6) = a(L(L(x,u,w),y,z),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,27170,a,b,32590,a),flip(a)].">
      <j1 rule="hyper" parents="373 27170 32590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32592">
    <literal><![CDATA[
      a(a(x,x,y) \ x,z,u) = a(L(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30135,a,b,32590,a)].">
      <j1 rule="hyper" parents="64 30135 32590"/>
    </justification>
  </clause>

  <clause id="32593">
    <literal><![CDATA[
      a(L(x \ a(x,y,y),z,u),w,v5) = a(L(R(x,z,u),y,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26928,a(flip),b,32590,a),flip(a)].">
      <j1 rule="hyper" parents="64 26928 32590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32594">
    <literal><![CDATA[
      a(L((x \ 1) * y,z,u),w,v5) = a(R(y * x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26887,a(flip),b,32590,a),flip(a)].">
      <j1 rule="hyper" parents="64 26887 32590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32595">
    <literal><![CDATA[
      a(L(x,y,z),u,u) = R(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26873,a(flip),b,32590,a),flip(a)].">
      <j1 rule="hyper" parents="64 26873 32590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32596">
    <literal><![CDATA[
      a(L(x,y,(x * y) \ z),u,w) = a((y * ((x * y) \ z)) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26805,a(flip),b,32590,a),flip(a)].">
      <j1 rule="hyper" parents="64 26805 32590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32597">
    <literal><![CDATA[
      a(L(x * (y \ (a(z,u,z) / y)),w,v5),v6,v7) = a(R(x,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,13611,a(flip),b,32590,a),flip(a)].">
      <j1 rule="hyper" parents="64 13611 32590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32598">
    <literal><![CDATA[
      a(L((x \ 1) \ y,z,u),w,v5) = a(R(x \ y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,2699,a(flip),b,32590,a),flip(a)].">
      <j1 rule="hyper" parents="64 2699 32590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32599">
    <literal><![CDATA[
      a(L(x \ 1,y,z),u,w) = a(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2697,a(flip),b,32590,a),flip(a)].">
      <j1 rule="hyper" parents="64 2697 32590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32600">
    <literal><![CDATA[
      a(L(((x * x) \ y) * z,u,w),v5,v6) = a(R(y * z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,2687,a(flip),b,32590,a),flip(a)].">
      <j1 rule="hyper" parents="64 2687 32590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32601">
    <literal><![CDATA[
      ((x * y) * z) * a(L(x,y,z),y,z) = (R(x,y,z) * y) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,32590,a(flip),b,658,a)].">
      <j1 rule="hyper" parents="145 32590 658"/>
    </justification>
  </clause>

  <clause id="32603">
    <literal><![CDATA[
      L(x * a(L(y \ z,u,w),x,x),x,R(z / y,u,w)) = x
    ]]></literal>
    <justification jstring="[para(32590(a,1),25351(a,1,1,2))].">
      <j1 rule="para" parents="32590 25351"/>
    </justification>
  </clause>

  <clause id="32604">
    <literal><![CDATA[
      (R(x,y,z) \ a(L(x,y,z),R(x,y,z),u)) * u = R(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(32590(a,1),30104(a,1,1,2))].">
      <j1 rule="para" parents="32590 30104"/>
    </justification>
  </clause>

  <clause id="32605">
    <literal><![CDATA[
      (a(L(x,y,z),R(x,y,z),u) / R(x,y,z)) \ u = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(32590(a,1),30118(a,1,1,1))].">
      <j1 rule="para" parents="32590 30118"/>
    </justification>
  </clause>

  <clause id="32606">
    <literal><![CDATA[
      R(x,y,z) * (a(L(x,y,z),u,w) * (u * w)) = (R(x,y,z) * u) * w
    ]]></literal>
    <justification jstring="[para(32590(a,1),30023(a,1,2,1))].">
      <j1 rule="para" parents="32590 30023"/>
    </justification>
  </clause>

  <clause id="32607">
    <literal><![CDATA[
      a(L(x,y,z),u,u) = L(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,28787,a(flip),b,32595,a),flip(a)].">
      <j1 rule="hyper" parents="373 28787 32595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32608">
    <literal><![CDATA[
      (x * y) * a(L(z,y,x),u,u) = x * (y * a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,32595,a,b,28789,a)].">
      <j1 rule="hyper" parents="145 32595 28789"/>
    </justification>
  </clause>

  <clause id="32609">
    <literal><![CDATA[
      a(L(x,y,z),u,u) * (y * z) = (a(x,u,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,32595,a,b,20,a(flip))].">
      <j1 rule="hyper" parents="144 32595 20"/>
    </justification>
  </clause>

  <clause id="32610">
    <literal><![CDATA[
      a(L(x * (y \ 1),z,u),x,x) = R(a(y \ x,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(32538(a,1),32595(a,2,1))].">
      <j1 rule="para" parents="32538 32595"/>
    </justification>
  </clause>

  <clause id="32611">
    <literal><![CDATA[
      (x * (y * L(z,z,y))) \ (x * (y * z)) = a(L(y,z \ y,x),z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31659,a,b,32607,a)].">
      <j1 rule="hyper" parents="373 31659 32607"/>
    </justification>
  </clause>

  <clause id="32612">
    <literal><![CDATA[
      x \ (R(y,z,z) * (y \ x)) = a(L(y,y,x),z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29391,a,b,32607,a)].">
      <j1 rule="hyper" parents="373 29391 32607"/>
    </justification>
  </clause>

  <clause id="32613">
    <literal><![CDATA[
      a(L(x,y,z),z,z) = a(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,30279,a(flip),b,32607,a),flip(a)].">
      <j1 rule="hyper" parents="373 30279 32607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32614">
    <literal><![CDATA[
      a(L(x,y,z),u,u) * (z * y) = z * (y * a(x,u,u))
    ]]></literal>
    <justification jstring="[hyper(144,a,32607,a,b,23157,a)].">
      <j1 rule="hyper" parents="144 32607 23157"/>
    </justification>
  </clause>

  <clause id="32615">
    <literal><![CDATA[
      a(L(x,y,y),z,z) \ a(x,z,z) = a(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[para(32607(a,2),1243(a,1,1))].">
      <j1 rule="para" parents="32607 1243"/>
    </justification>
  </clause>

  <clause id="32616">
    <literal><![CDATA[
      L((x \ a(y,z,z)) * x,u,w) = (x \ a(L(y,u,w),z,z)) * x
    ]]></literal>
    <justification jstring="[para(32607(a,2),5544(a,2,1,2))].">
      <j1 rule="para" parents="32607 5544"/>
    </justification>
  </clause>

  <clause id="32617">
    <literal><![CDATA[
      (T(x,y) * z) * a(L(u,z,x),w,w) = T(x,y) * (z * a(u,w,w))
    ]]></literal>
    <justification jstring="[para(32607(a,2),23841(a,1,2))].">
      <j1 rule="para" parents="32607 23841"/>
    </justification>
  </clause>

  <clause id="32618">
    <literal><![CDATA[
      a(L(x,x,L(x,y,y) \ z),y,y) \ z = x * (R(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[para(32607(a,2),29270(a,1,1))].">
      <j1 rule="para" parents="32607 29270"/>
    </justification>
  </clause>

  <clause id="32619">
    <literal><![CDATA[
      L(a(L(x,y,z),u,u),w,u * x) = L(a(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[para(32607(a,2),30715(a,1,1))].">
      <j1 rule="para" parents="32607 30715"/>
    </justification>
  </clause>

  <clause id="32620">
    <literal><![CDATA[
      a(L(x,y \ x,z),y,y) \ (z * (x * (1 / y))) = z * (x / y)
    ]]></literal>
    <justification jstring="[para(32607(a,2),30930(a,1,1))].">
      <j1 rule="para" parents="32607 30930"/>
    </justification>
  </clause>

  <clause id="32623">
    <literal><![CDATA[
      L(x,y,z) * a(x,z,z) = L(R(x,z,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,32613,a(flip),b,15989,a)].">
      <j1 rule="hyper" parents="145 32613 15989"/>
    </justification>
  </clause>

  <clause id="32624">
    <literal><![CDATA[
      a((x * y) \ z,x,x) = a(y \ (x \ z),x,x)
    ]]></literal>
    <justification jstring="[para(346(a,1),32613(a,1,1))].">
      <j1 rule="para" parents="346 32613"/>
    </justification>
  </clause>

  <clause id="32625">
    <literal><![CDATA[
      a((x \ y) \ z,x,x) = a(y \ (x * z),x,x)
    ]]></literal>
    <justification jstring="[para(630(a,1),32613(a,1,1)),flip(a)].">
      <j1 rule="para" parents="630 32613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32626">
    <literal><![CDATA[
      L(x * a(y,x,x),x,L(y,z,x)) = x
    ]]></literal>
    <justification jstring="[para(32613(a,1),9445(a,1,1,2))].">
      <j1 rule="para" parents="32613 9445"/>
    </justification>
  </clause>

  <clause id="32627">
    <literal><![CDATA[
      L(x,x,L(y,z,x)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[para(32626(a,1),9446(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32626 9446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32630">
    <literal><![CDATA[
      L(L(x \ 1,x \ 1,L(y,z,x \ 1)),a(u,w,v5),x) = L(x \ 1,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13942,a,b,32627,a)].">
      <j1 rule="hyper" parents="64 13942 32627"/>
    </justification>
  </clause>

  <clause id="32631">
    <literal><![CDATA[
      L(x,x,(x * y) \ z) = L(x,x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(346(a,1),32627(a,1,3))].">
      <j1 rule="para" parents="346 32627"/>
    </justification>
  </clause>

  <clause id="32633">
    <literal><![CDATA[
      L(x * K(y,z),x,L(u,w,x)) = L(x,x,u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(32627(a,1),26070(a,2,1))].">
      <j1 rule="para" parents="32627 26070"/>
    </justification>
  </clause>

  <clause id="32634">
    <literal><![CDATA[
      a(L(x \ 1,y,z),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32590,a(flip),b,32599,a),flip(a)].">
      <j1 rule="hyper" parents="373 32590 32599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32635">
    <literal><![CDATA[
      L(x,x,(y * x) \ z) = L(x,x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,28988,a,b,32631,a)].">
      <j1 rule="hyper" parents="64 28988 32631"/>
    </justification>
  </clause>

  <clause id="32636">
    <literal><![CDATA[
      a(L(x \ 1,y,z),u,w) = a(L(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2653,a,b,32634,a),flip(a)].">
      <j1 rule="hyper" parents="373 2653 32634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32637">
    <literal><![CDATA[
      a(L(1 / x,y,z),u,w) = a(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26794,a,b,32634,a)].">
      <j1 rule="hyper" parents="64 26794 32634"/>
    </justification>
  </clause>

  <clause id="32638">
    <literal><![CDATA[
      a(L(x \ (x / y),y,x),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(30519(a,1),32634(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30519 32634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32639">
    <literal><![CDATA[
      a(L(x \ 1,y \ 1,z \ 1),u,w) = a(L(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(11807(a,1),32636(a,2,1,1))].">
      <j1 rule="para" parents="11807 32636"/>
    </justification>
  </clause>

  <clause id="32640">
    <literal><![CDATA[
      a(L(x,y,a(z,u,w)),z,z) = a(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,31100,a,b,32608,a),flip(a)].">
      <j1 rule="hyper" parents="35 31100 32608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32642">
    <literal><![CDATA[
      (x * (y \ z)) * a(L(z,y \ z,x),y,y) = x * (y \ R(z,y,y))
    ]]></literal>
    <justification jstring="[para(30282(a,1),32608(a,2,2))].">
      <j1 rule="para" parents="30282 32608"/>
    </justification>
  </clause>

  <clause id="32643">
    <literal><![CDATA[
      a(L(x,y,a(z,u,u)),u,u) = a(x,u,u)
    ]]></literal>
    <justification jstring="[para(29287(a,2),32640(a,1,1))].">
      <j1 rule="para" parents="29287 32640"/>
    </justification>
  </clause>

  <clause id="32644">
    <literal><![CDATA[
      a(x,y,y) * L(x,z,a(u,y,y)) = R(L(x,z,a(u,y,y)),y,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,32643,a(flip),b,15990,a)].">
      <j1 rule="hyper" parents="144 32643 15990"/>
    </justification>
  </clause>

  <clause id="32645">
    <literal><![CDATA[
      a(L(x,y,L(z,u,w)),z,z) = a(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,29987,a(flip),b,32609,a),flip(a)].">
      <j1 rule="hyper" parents="36 29987 32609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32646">
    <literal><![CDATA[
      a(L(x,y,z \ u),z * u,z * u) = a(x,z * u,z * u)
    ]]></literal>
    <justification jstring="[para(30387(a,1),32645(a,1,1))].">
      <j1 rule="para" parents="30387 32645"/>
    </justification>
  </clause>

  <clause id="32647">
    <literal><![CDATA[
      a(L(x,y,y),z,z) \ R(x,z,z) = x * a(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[para(32615(a,1),30943(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32615 30943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32648">
    <literal><![CDATA[
      L(a(x,y,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(L(x,z,u),y,y) = w
    ]]></literal>
    <justification jstring="[para(32619(a,1),616(a,1))].">
      <j1 rule="para" parents="32619 616"/>
    </justification>
  </clause>

  <clause id="32649">
    <literal><![CDATA[
      L(x * K(y,z),x,L(u,w,x)) = L(x * K(y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26070,a,b,32633,a),flip(a)].">
      <j1 rule="hyper" parents="373 26070 32633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32650">
    <literal><![CDATA[
      a(x \ (y \ (z \ 1)),u,w) = a(x \ (z / y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32457,a(flip),b,32377,a),flip(a)].">
      <j1 rule="hyper" parents="64 32457 32377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32651">
    <literal><![CDATA[
      a(x \ (y \ (z \ 1)),u,w) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32369,a(flip),b,32650,a),flip(a)].">
      <j1 rule="hyper" parents="373 32369 32650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32652">
    <literal><![CDATA[
      a(x * ((y * K(z,u)) * w),v5,v6) = a(x * (w * y),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(32448,a,32379,a)].">
      <j1 rule="hyper" parents="32448 32379"/>
    </justification>
  </clause>

  <clause id="32653">
    <literal><![CDATA[
      a(x * (y * (z \ (u / w))),v5,v6) = a(x * (y * (z \ (w \ u))),v5,v6)
    ]]></literal>
    <justification jstring="[para(15028(a,1),32379(a,1,1,2,2))].">
      <j1 rule="para" parents="15028 32379"/>
    </justification>
  </clause>

  <clause id="32654">
    <literal><![CDATA[
      a(L(x \ K(y,z),u,w),v5,v6) = a(L(x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32634,a(flip),b,32382,a),flip(a)].">
      <j1 rule="hyper" parents="373 32634 32382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32655">
    <literal><![CDATA[
      a(((x * y) * z) * u,w,v5) = a(u * ((y * x) * z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32393,a),flip(a)].">
      <j1 rule="hyper" parents="26847 32393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32656">
    <literal><![CDATA[
      a(((x * y) * z) * u,w,v5) = a((z * (y * x)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32388,a,b,32393,a),flip(a)].">
      <j1 rule="hyper" parents="373 32388 32393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32657">
    <literal><![CDATA[
      a(((x * y) * z) * u,w,v5) = a(u * (z * (y * x)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32422,a(flip),b,32393,a),flip(a)].">
      <j1 rule="hyper" parents="373 32422 32393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32658">
    <literal><![CDATA[
      a(((x * (y \ 1)) * z) * u,w,v5) = a(((y * x) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,2706,a(flip),b,32393,a),flip(a)].">
      <j1 rule="hyper" parents="373 2706 32393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32659">
    <literal><![CDATA[
      a((((x * y) * x) * z) * u,w,v5) = a((L(y,x,x) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,2659,a(flip),b,32393,a),flip(a)].">
      <j1 rule="hyper" parents="373 2659 32393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32660">
    <literal><![CDATA[
      a((x * (y * x)) * z,u,w) = a(L(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2682,a(flip),b,32395,a)].">
      <j1 rule="hyper" parents="64 2682 32395"/>
    </justification>
  </clause>

  <clause id="32662">
    <literal><![CDATA[
      a(((1 / (x / y)) * z) * u,w,v5) = a(((y \ x) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,2679,a,b,32396,a)].">
      <j1 rule="hyper" parents="64 2679 32396"/>
    </justification>
  </clause>

  <clause id="32663">
    <literal><![CDATA[
      a((x / L(y,x,y)) * z,u,w) = a((((x * y) \ x) * x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(5151(a,2),32396(a,1,1,1))].">
      <j1 rule="para" parents="5151 32396"/>
    </justification>
  </clause>

  <clause id="32664">
    <literal><![CDATA[
      a(a(x,x,x \ y) * z,u,w) = a(((y \ (x \ y)) * x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(30080(a,2),32396(a,1,1,1))].">
      <j1 rule="para" parents="30080 32396"/>
    </justification>
  </clause>

  <clause id="32665">
    <literal><![CDATA[
      a((((1 / x) \ y) \ z) * u,w,v5) = a(((y / x) \ z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,2684,a(flip),b,32397,a),flip(a)].">
      <j1 rule="hyper" parents="64 2684 32397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32666">
    <literal><![CDATA[
      a((x * (y * z)) * u,w,v5) = a((x * (z * y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(5796(a,1),32398(a,1,1,1,2))].">
      <j1 rule="para" parents="5796 32398"/>
    </justification>
  </clause>

  <clause id="32667">
    <literal><![CDATA[
      a(((x \ (y / z)) * u) * w,v5,v6) = a(((x \ (z \ y)) * u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(24475(a,1),32398(a,1,1,1))].">
      <j1 rule="para" parents="24475 32398"/>
    </justification>
  </clause>

  <clause id="32668">
    <literal><![CDATA[
      a((x \ (K(y,z) * u)) \ w,v5,v6) = a((u / x) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32386,a,b,32403,a),flip(a)].">
      <j1 rule="hyper" parents="373 32386 32403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32669">
    <literal><![CDATA[
      a(a(x \ y,x \ y,x),z,u) = a(((x \ y) * y) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26919,a,b,32408,a)].">
      <j1 rule="hyper" parents="64 26919 32408"/>
    </justification>
  </clause>

  <clause id="32670">
    <literal><![CDATA[
      a((x / (y * x)) \ y,z,u) = a(y * (x \ (y \ x)),z,u)
    ]]></literal>
    <justification jstring="[para(23871(a,1),32419(a,1,1))].">
      <j1 rule="para" parents="23871 32419"/>
    </justification>
  </clause>

  <clause id="32671">
    <literal><![CDATA[
      a(x * (((y * (z * z)) / u) * w),v5,v6) = a(x * ((u \ T(y,z * z)) * w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,11987,a(flip),b,32440,a)].">
      <j1 rule="hyper" parents="64 11987 32440"/>
    </justification>
  </clause>

  <clause id="32672">
    <literal><![CDATA[
      a(x * ((y \ (z * z)) * u),w,v5) = a(x * ((1 / y) * u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,11986,a(flip),b,32440,a),flip(a)].">
      <j1 rule="hyper" parents="64 11986 32440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32673">
    <literal><![CDATA[
      a(x * (y \ K(z,u)),w,v5) = a(y * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26875,a(flip),b,32443,a),flip(a)].">
      <j1 rule="hyper" parents="64 26875 32443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32674">
    <literal><![CDATA[
      a(x * (y \ ((z / u) * w)),v5,v6) = a(x * (y \ ((u \ z) * w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(5982(a,1),32443(a,1,1,2,2))].">
      <j1 rule="para" parents="5982 32443"/>
    </justification>
  </clause>

  <clause id="32675">
    <literal><![CDATA[
      a(x * (y \ ((z / u) \ w)),v5,v6) = a(x * (y \ ((u \ z) \ w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(6270(a,1),32443(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6270 32443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32676">
    <literal><![CDATA[
      a(x * (y \ ((z * u) \ w)),v5,v6) = a(x * (y \ ((u * z) \ w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(10833(a,1),32443(a,1,1,2,2))].">
      <j1 rule="para" parents="10833 32443"/>
    </justification>
  </clause>

  <clause id="32677">
    <literal><![CDATA[
      a(x * (((y / z) \ u) \ w),v5,v6) = a(x * (((z \ y) \ u) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(24402(a,1),32443(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="24402 32443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32678">
    <literal><![CDATA[
      a((x \ K(y,z)) * u,w,v5) = a(x * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32673,a)].">
      <j1 rule="hyper" parents="26847 32673"/>
    </justification>
  </clause>

  <clause id="32679">
    <literal><![CDATA[
      a(L(x,x,y) \ y,z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(14983(a,1),32673(a,1,1))].">
      <j1 rule="para" parents="14983 32673"/>
    </justification>
  </clause>

  <clause id="32680">
    <literal><![CDATA[
      a(((x \ (y \ x)) * y) * z,u,w) = a(a(x,y,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(30565(a,1),32678(a,1,1,1))].">
      <j1 rule="para" parents="30565 32678"/>
    </justification>
  </clause>

  <clause id="32681">
    <literal><![CDATA[
      a(x \ (y * (z * y)),u,w) = a(x \ L(z,y,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26902,a(flip),b,32482,a),flip(a)].">
      <j1 rule="hyper" parents="373 26902 32482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32682">
    <literal><![CDATA[
      a(L(x \ (y * z),x,z),u,w) = a((z * x) \ L(y,z,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32586,a,b,32681,a)].">
      <j1 rule="hyper" parents="64 32586 32681"/>
    </justification>
  </clause>

  <clause id="32683">
    <literal><![CDATA[
      a(x \ ((y * z) * z),u,w) = a(x \ L(y,z,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32371,a,b,32681,a)].">
      <j1 rule="hyper" parents="64 32371 32681"/>
    </justification>
  </clause>

  <clause id="32684">
    <literal><![CDATA[
      a(x \ ((y \ (1 / z)) * u),w,v5) = a(x \ ((z / y) * u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26929,a(flip),b,32483,a),flip(a)].">
      <j1 rule="hyper" parents="64 26929 32483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32685">
    <literal><![CDATA[
      a(x \ ((y \ T(z,u)) * w),v5,v6) = a(x \ ((y \ z) * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(24474(a,1),32484(a,1,1,2))].">
      <j1 rule="para" parents="24474 32484"/>
    </justification>
  </clause>

  <clause id="32686">
    <literal><![CDATA[
      a(((x * y) \ z) * u,w,v5) = a(u * ((y * x) \ z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32490,a)].">
      <j1 rule="hyper" parents="26847 32490"/>
    </justification>
  </clause>

  <clause id="32687">
    <literal><![CDATA[
      a((x \ (y \ 1)) * z,u,w) = a((y / x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32434,a(flip),b,32492,a),flip(a)].">
      <j1 rule="hyper" parents="64 32434 32492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32688">
    <literal><![CDATA[
      a((x \ (y \ 1)) * z,u,w) = a((x \ y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32367,a(flip),b,32687,a),flip(a)].">
      <j1 rule="hyper" parents="373 32367 32687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32689">
    <literal><![CDATA[
      a(x * (y \ (z \ 1)),u,w) = a((y \ z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32688,a)].">
      <j1 rule="hyper" parents="26847 32688"/>
    </justification>
  </clause>

  <clause id="32690">
    <literal><![CDATA[
      a((x \ (T(y,z) \ u)) * w,v5,v6) = a((x \ (y \ u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(6075(a,1),32494(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6075 32494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32691">
    <literal><![CDATA[
      a((x \ ((y / z) \ u)) * w,v5,v6) = a((x \ ((z \ y) \ u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(6270(a,1),32494(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6270 32494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32692">
    <literal><![CDATA[
      a(a(x,x,x \ y) * z,u,w) = a(z * a(x,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,32513,a),flip(a)].">
      <j1 rule="hyper" parents="373 26787 32513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32693">
    <literal><![CDATA[
      a((x * (y * x)) \ z,u,w) = a(L(y,x,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26914,a(flip),b,32514,a),flip(a)].">
      <j1 rule="hyper" parents="373 26914 32514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32694">
    <literal><![CDATA[
      a(((x * y) * y) \ z,u,w) = a(L(x,y,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(32451,a,32693,a)].">
      <j1 rule="hyper" parents="32451 32693"/>
    </justification>
  </clause>

  <clause id="32695">
    <literal><![CDATA[
      a(L((x * y) \ z,x * y,y),u,w) = a(L(x,y,y) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32586,a,b,32693,a)].">
      <j1 rule="hyper" parents="64 32586 32693"/>
    </justification>
  </clause>

  <clause id="32696">
    <literal><![CDATA[
      a(((x * y) \ ((z * y) * x)) \ u,w,v5) = a(L(T(z,y),y,x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(262(a,1),32515(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="262 32515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32697">
    <literal><![CDATA[
      a((x * (y \ (z / u))) * w,v5,v6) = a(w * (x * (y \ (u \ z))),v5,v6)
    ]]></literal>
    <justification jstring="[para(15045(a,1),32525(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15045 32525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32698">
    <literal><![CDATA[
      a(((x * y) \ ((y * z) * x)) * u,w,v5) = a(u * L(z,y,x),w,v5)
    ]]></literal>
    <justification jstring="[para(18(a,2),32526(a,2,1,2))].">
      <j1 rule="para" parents="18 32526"/>
    </justification>
  </clause>

  <clause id="32699">
    <literal><![CDATA[
      a(x * (y \ (T(z,u) \ w)),v5,v6) = a((y \ (z \ w)) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(6157(a,1),32528(a,1,1,2,2))].">
      <j1 rule="para" parents="6157 32528"/>
    </justification>
  </clause>

  <clause id="32700">
    <literal><![CDATA[
      a(x * ((T(y,z) * u) \ w),v5,v6) = a(((y * u) \ w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[para(24191(a,1),32528(a,1,1,2))].">
      <j1 rule="para" parents="24191 32528"/>
    </justification>
  </clause>

  <clause id="32701">
    <literal><![CDATA[
      a(x * (y * ((z * z) * u)),w,v5) = a((y * u) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32553,a)].">
      <j1 rule="hyper" parents="26847 32553"/>
    </justification>
  </clause>

  <clause id="32703">
    <literal><![CDATA[
      a((x * ((y * y) \ z)) * u,w,v5) = a((x * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),32553(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 32553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32704">
    <literal><![CDATA[
      a((x * ((y * T(z,y \ 1)) * y)) * u,w,v5) = a((x * R(z,y,y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(3954(a,2),32553(a,1,1,1,2))].">
      <j1 rule="para" parents="3954 32553"/>
    </justification>
  </clause>

  <clause id="32705">
    <literal><![CDATA[
      a(x * (y \ ((z * z) * u)),w,v5) = a(x * (y \ u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32362,a(flip),b,32564,a),flip(a)].">
      <j1 rule="hyper" parents="373 32362 32564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32706">
    <literal><![CDATA[
      a(x * (T(y,z * z) / u),w,v5) = a(x * (u \ (y * (z * z))),w,v5)
    ]]></literal>
    <justification jstring="[para(115(a,1),32564(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="115 32564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32707">
    <literal><![CDATA[
      a(x * (y \ (((z * z) / u) * w)),v5,v6) = a(x * (((1 / u) * w) / y),v5,v6)
    ]]></literal>
    <justification jstring="[para(556(a,1),32564(a,1,1,2,2))].">
      <j1 rule="para" parents="556 32564"/>
    </justification>
  </clause>

  <clause id="32708">
    <literal><![CDATA[
      a(x * ((y * z) \ y),u,w) = a(x * (y \ (z \ y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32490,a,b,32565,a)].">
      <j1 rule="hyper" parents="64 32490 32565"/>
    </justification>
  </clause>

  <clause id="32710">
    <literal><![CDATA[
      a((x * y) \ (z \ ((z * x) * ((u * u) * y))),w,v5) = a(a(z,x,(u * u) * y),w,v5)
    ]]></literal>
    <justification jstring="[para(30027(a,2),32571(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30027 32571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32711">
    <literal><![CDATA[
      a(L(R(x,y,z),u,w),v5,v6) = a(L(L(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(29(a,1),32591(a,1,1))].">
      <j1 rule="para" parents="29 32591"/>
    </justification>
  </clause>

  <clause id="32712">
    <literal><![CDATA[
      a(L((x \ 1) * y,z,u),w,v5) = a(L(y * x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32590,a(flip),b,32594,a),flip(a)].">
      <j1 rule="hyper" parents="373 32590 32594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32713">
    <literal><![CDATA[
      a(L((x \ 1) \ y,z,u),w,v5) = a(L(x \ y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32590,a(flip),b,32598,a),flip(a)].">
      <j1 rule="hyper" parents="373 32590 32598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32714">
    <literal><![CDATA[
      L(x * a(L(y,z,u),x,x),x,R(1 / y,z,u)) = x
    ]]></literal>
    <justification jstring="[para(32634(a,1),32603(a,1,1,2))].">
      <j1 rule="para" parents="32634 32603"/>
    </justification>
  </clause>

  <clause id="32715">
    <literal><![CDATA[
      L(L(x,y,z) * a(x,x,x),L(x,y,z),R(1 / x,u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(16457(a,1),32714(a,1,1,2))].">
      <j1 rule="para" parents="16457 32714"/>
    </justification>
  </clause>

  <clause id="32716">
    <literal><![CDATA[
      a(L(x * (y \ 1),z,u),x,x) = a(L(y \ x,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,32595,a,b,32610,a),flip(a)].">
      <j1 rule="hyper" parents="373 32595 32610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32717">
    <literal><![CDATA[
      a(x * ((y \ T(z,u)) * w),v5,v6) = a(x * (w * (y \ z)),v5,v6)
    ]]></literal>
    <justification jstring="[para(2433(a,1),32652(a,1,1,2,1))].">
      <j1 rule="para" parents="2433 32652"/>
    </justification>
  </clause>

  <clause id="32718">
    <literal><![CDATA[
      a(x * ((y * T(z,u)) * w),v5,v6) = a(x * (w * (y * z)),v5,v6)
    ]]></literal>
    <justification jstring="[para(6852(a,1),32652(a,1,1,2,1))].">
      <j1 rule="para" parents="6852 32652"/>
    </justification>
  </clause>

  <clause id="32719">
    <literal><![CDATA[
      a(((x * y) * y) * z,u,w) = a(z * L(x,y,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26824,a(flip),b,32656,a),flip(a)].">
      <j1 rule="hyper" parents="373 26824 32656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32720">
    <literal><![CDATA[
      a(x * ((y * z) * z),u,w) = a(x * L(y,z,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32719,a)].">
      <j1 rule="hyper" parents="26847 32719"/>
    </justification>
  </clause>

  <clause id="32721">
    <literal><![CDATA[
      a(x * R(y,z,z),u,w) = a(x * L(y,z,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32516,a(flip),b,32719,a)].">
      <j1 rule="hyper" parents="64 32516 32719"/>
    </justification>
  </clause>

  <clause id="32722">
    <literal><![CDATA[
      a(x * (y * (z * (u \ 1))),w,v5) = a(((u * z) * y) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,2706,a(flip),b,32657,a),flip(a)].">
      <j1 rule="hyper" parents="64 2706 32657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32723">
    <literal><![CDATA[
      a((x / (y * z)) \ u,w,v5) = a(((z * y) \ x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(10850(a,1),32668(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10850 32668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32724">
    <literal><![CDATA[
      a(((x * y) \ x) * z,u,w) = a(z * (x \ (y \ x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32565,a(flip),b,32686,a),flip(a)].">
      <j1 rule="hyper" parents="373 32565 32686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32725">
    <literal><![CDATA[
      a(x * a(y,y,y \ z),u,w) = a(x * a(y,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32692,a)].">
      <j1 rule="hyper" parents="26847 32692"/>
    </justification>
  </clause>

  <clause id="32726">
    <literal><![CDATA[
      a(L(R(x,x,y * x),z,u),w,v5) = a(L(L(x,x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26866,a,b,32711,a)].">
      <j1 rule="hyper" parents="64 26866 32711"/>
    </justification>
  </clause>

  <clause id="32727">
    <literal><![CDATA[
      a(L(L(x \ 1,x,y),y,y),z,u) = a(y * (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26870,a(flip),b,32711,a),flip(a)].">
      <j1 rule="hyper" parents="64 26870 32711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32728">
    <literal><![CDATA[
      a(L(L(x * y,x,x),z,u),w,v5) = a(L(L(y,x,x) * x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26865,a(flip),b,32711,a),flip(a)].">
      <j1 rule="hyper" parents="64 26865 32711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32729">
    <literal><![CDATA[
      a(L(L(x,y,z),u,w),x,v5) = a(x,L(R(x,y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,3515,a(flip),b,32711,a),flip(a)].">
      <j1 rule="hyper" parents="64 3515 32711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32730">
    <literal><![CDATA[
      a(L(L(x \ 1,y,y),z,u),w,v5) = a(L(x \ a(x,y,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(16002(a,1),32711(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="16002 32711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32731">
    <literal><![CDATA[
      a(x \ (x \ L(x * y,z,u)),w,v5) = a(L(x \ y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27918,a,b,32713,a)].">
      <j1 rule="hyper" parents="64 27918 32713"/>
    </justification>
  </clause>

  <clause id="32732">
    <literal><![CDATA[
      a(((x * y) \ ((z * y) * x)) \ u,w,v5) = a(R(z,y,x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(20(a,2),32723(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="20 32723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32733">
    <literal><![CDATA[
      a(((x * y) \ x) * z,u,w) = a((x \ (y \ x)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,32724,a),flip(a)].">
      <j1 rule="hyper" parents="373 26787 32724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32734">
    <literal><![CDATA[
      a(L(L(x,y,z),u,w),x,v5) = a(x,L(L(x,y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32281,a(flip),b,32729,a),flip(a)].">
      <j1 rule="hyper" parents="373 32281 32729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32735">
    <literal><![CDATA[
      a(L(x,x \ y,y),z,u) = a((x \ y) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26822,a(flip),b,32420,a),flip(a)].">
      <j1 rule="hyper" parents="373 26822 32420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32736">
    <literal><![CDATA[
      a(L(x,x * y,x * y),z,u) = a((x \ y) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31529,a,b,32735,a)].">
      <j1 rule="hyper" parents="64 31529 32735"/>
    </justification>
  </clause>

  <clause id="32737">
    <literal><![CDATA[
      a(R(x,x,y) * z,u,w) = a(z * ((x * y) \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26829,a(flip),b,32421,a)].">
      <j1 rule="hyper" parents="64 26829 32421"/>
    </justification>
  </clause>

  <clause id="32738">
    <literal><![CDATA[
      a((x * (y \ K(z,u))) \ w,v5,v6) = a((y * x) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32505,a(flip),b,32400,a),flip(a)].">
      <j1 rule="hyper" parents="373 32505 32400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32739">
    <literal><![CDATA[
      a((x * y) \ ((z / y) \ (z * (x \ K(u,w)))),v5,v6) = a(a(y \ z,y,x \ K(u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(30032(a,1),32738(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30032 32738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32740">
    <literal><![CDATA[
      a((x \ ((1 / y) * z)) * u,w,v5) = a((x \ (y * z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32367,a(flip),b,32433,a),flip(a)].">
      <j1 rule="hyper" parents="373 32367 32433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32741">
    <literal><![CDATA[
      a((x * (y * T(z,u))) * w,v5,v6) = a((x * (z * y)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32666,a,b,32493,a),flip(a)].">
      <j1 rule="hyper" parents="373 32666 32493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32742">
    <literal><![CDATA[
      a(L((x / y) * z,u,w),v5,v6) = a(L(z * (y \ x),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26845,a,b,32556,a)].">
      <j1 rule="hyper" parents="64 26845 32556"/>
    </justification>
  </clause>

  <clause id="32743">
    <literal><![CDATA[
      a(L(x \ (y \ x),y,x),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32638,a(flip),b,32558,a),flip(a)].">
      <j1 rule="hyper" parents="64 32638 32558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32744">
    <literal><![CDATA[
      a(a(x,y,z),u,w \ (x \ w)) = 1
    ]]></literal>
    <justification jstring="[para(32743(a,1),29990(a,1,1))].">
      <j1 rule="para" parents="32743 29990"/>
    </justification>
  </clause>

  <clause id="32745">
    <literal><![CDATA[
      L((x \ y) / y,z,a(x,u,w)) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(32743(a,1),29992(a,1,3))].">
      <j1 rule="para" parents="32743 29992"/>
    </justification>
  </clause>

  <clause id="32746">
    <literal><![CDATA[
      (x \ (y \ x)) / (a(y,z,u) * (x \ (y \ x))) = 1 / a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(142,a,32744,a(flip),b,30057,a),flip(a)].">
      <j1 rule="hyper" parents="142 32744 30057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32747">
    <literal><![CDATA[
      ((x \ y) * a(x,z,u)) / (a(x,z,u) * y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,28835,a(flip),b,32745,a)].">
      <j1 rule="hyper" parents="64 28835 32745"/>
    </justification>
  </clause>

  <clause id="32748">
    <literal><![CDATA[
      a(x,x,a(x,y,z) * u) = x * ((x \ u) / u)
    ]]></literal>
    <justification jstring="[para(32747(a,1),30270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32747 30270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32749">
    <literal><![CDATA[
      a(x,x,a(x,y,z) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,30070,a(flip),b,32748,a),flip(a)].">
      <j1 rule="hyper" parents="373 30070 32748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32751">
    <literal><![CDATA[
      a(x,x,y * a(x,z,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(27453,a,32749,a)].">
      <j1 rule="hyper" parents="27453 32749"/>
    </justification>
  </clause>

  <clause id="32752">
    <literal><![CDATA[
      a(x,x,a(x,y,z) \ u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),32749(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 32749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32753">
    <literal><![CDATA[
      a(x,x,(x * y) * z) = a(x,x,x * (y * z))
    ]]></literal>
    <justification jstring="[para(15463(a,1),32749(a,1,3))].">
      <j1 rule="para" parents="15463 32749"/>
    </justification>
  </clause>

  <clause id="32754">
    <literal><![CDATA[
      a(x,x,L(y,y,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(30461(a,1),32749(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30461 32749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32755">
    <literal><![CDATA[
      a(x,x,L(y,y,x)) = x \ R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30058,a,b,32754,a),flip(a)].">
      <j1 rule="hyper" parents="373 30058 32754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32756">
    <literal><![CDATA[
      a(x,x,L(y \ 1,y,x)) = a(x,x,y \ 1)
    ]]></literal>
    <justification jstring="[para(11794(a,1),32754(a,1,3))].">
      <j1 rule="para" parents="11794 32754"/>
    </justification>
  </clause>

  <clause id="32757">
    <literal><![CDATA[
      a(x,x,y * a(x,z,u)) = x \ R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30058,a,b,32751,a),flip(a)].">
      <j1 rule="hyper" parents="373 30058 32751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32758">
    <literal><![CDATA[
      a(x,x,x * ((x \ y) * z)) = a(x,x,y * z)
    ]]></literal>
    <justification jstring="[para(15481(a,1),32752(a,1,3))].">
      <j1 rule="para" parents="15481 32752"/>
    </justification>
  </clause>

  <clause id="32759">
    <literal><![CDATA[
      a(x,x,x * (a(x,y,z) \ u)) = a(x,x,x * u)
    ]]></literal>
    <justification jstring="[para(29923(a,1),32752(a,1,3))].">
      <j1 rule="para" parents="29923 32752"/>
    </justification>
  </clause>

  <clause id="32760">
    <literal><![CDATA[
      R(x,x,L(y,y,x)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,30058,a,b,32755,a(flip))].">
      <j1 rule="hyper" parents="39 30058 32755"/>
    </justification>
  </clause>

  <clause id="32761">
    <literal><![CDATA[
      R(x,x,x \ ((y \ 1) \ x)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27178,a(flip),b,32760,a)].">
      <j1 rule="hyper" parents="64 27178 32760"/>
    </justification>
  </clause>

  <clause id="32762">
    <literal><![CDATA[
      R(x,x,x \ (y \ x)) = R(x,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,26277,a(flip),b,32761,a)].">
      <j1 rule="hyper" parents="64 26277 32761"/>
    </justification>
  </clause>

  <clause id="32763">
    <literal><![CDATA[
      R(R(x,y,z),x,x \ (u \ x)) = R(R(x,x,u \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(32762(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32762 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32764">
    <literal><![CDATA[
      a(x,x,x \ (y \ x)) = a(x,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27580,a(flip),b,32756,a)].">
      <j1 rule="hyper" parents="64 27580 32756"/>
    </justification>
  </clause>

  <clause id="32765">
    <literal><![CDATA[
      a(a(x,x,y \ 1),z,u) = a(a(x,x,y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(32764(a,1),30184(a,1,1))].">
      <j1 rule="para" parents="32764 30184"/>
    </justification>
  </clause>

  <clause id="32766">
    <literal><![CDATA[
      R(x,x,y * a(x,z,u)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,30058,a,b,32757,a(flip))].">
      <j1 rule="hyper" parents="39 30058 32757"/>
    </justification>
  </clause>

  <clause id="32767">
    <literal><![CDATA[
      R(x,x,a(x,y,z) * u) = R(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26164,a,b,32766,a)].">
      <j1 rule="hyper" parents="64 26164 32766"/>
    </justification>
  </clause>

  <clause id="32768">
    <literal><![CDATA[
      R(x,x,(x * y) * z) = R(x,x,x * (y * z))
    ]]></literal>
    <justification jstring="[para(88(a,1),32766(a,1,3))].">
      <j1 rule="para" parents="88 32766"/>
    </justification>
  </clause>

  <clause id="32769">
    <literal><![CDATA[
      R(x,x,x \ (y * z)) = R(x,x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(30036(a,1),32766(a,1,3))].">
      <j1 rule="para" parents="30036 32766"/>
    </justification>
  </clause>

  <clause id="32770">
    <literal><![CDATA[
      a(x,x,x * ((((x / y) / x) * y) * z)) = a(x,x,((1 / y) \ (x / y)) * z)
    ]]></literal>
    <justification jstring="[para(31434(a,1),32753(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="31434 32753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32771">
    <literal><![CDATA[
      a(x,x,x * (y * (x \ z))) = a(x,x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27315,a,b,32758,a)].">
      <j1 rule="hyper" parents="64 27315 32758"/>
    </justification>
  </clause>

  <clause id="32773">
    <literal><![CDATA[
      R(x,x,x * ((x \ y) * z)) = R(x,x,y * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),32768(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 32768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32774">
    <literal><![CDATA[
      R(1 / (1 / x),x,y * z) = R(x,x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26196,a,b,32769,a)].">
      <j1 rule="hyper" parents="64 26196 32769"/>
    </justification>
  </clause>

  <clause id="32775">
    <literal><![CDATA[
      a(x,x,y * (x \ z)) = a(x,x,z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32758,a(flip),b,32771,a)].">
      <j1 rule="hyper" parents="64 32758 32771"/>
    </justification>
  </clause>

  <clause id="32776">
    <literal><![CDATA[
      a(x,x,(x \ y) * z) = a(x,x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(27453,a,32775,a)].">
      <j1 rule="hyper" parents="27453 32775"/>
    </justification>
  </clause>

  <clause id="32777">
    <literal><![CDATA[
      (a(x,x,y * (x \ z)) \ x) \ 1 = R(x \ 1,x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(32776(a,1),30163(a,1,1,1))].">
      <j1 rule="para" parents="32776 30163"/>
    </justification>
  </clause>

  <clause id="32778">
    <literal><![CDATA[
      a(a(x,x,y \ x),z,u) = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32547,a(flip),b,32765,a),flip(a)].">
      <j1 rule="hyper" parents="64 32547 32765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32779">
    <literal><![CDATA[
      a(a(x \ y,y,y),z,u) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(27307(a,1),32778(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27307 32778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32780">
    <literal><![CDATA[
      x \ R(R(x,x,y \ 1),y,y) = ((1 / y) / (x / y)) * x
    ]]></literal>
    <justification jstring="[para(32763(a,1),31146(a,1,2))].">
      <j1 rule="para" parents="32763 31146"/>
    </justification>
  </clause>

  <clause id="32781">
    <literal><![CDATA[
      a(L((x * (y \ 1)) \ z,y,y),u,w) = a(L(y * (z / x),y,x),u,w)
    ]]></literal>
    <justification jstring="[para(11809(a,1),32559(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11809 32559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32782">
    <literal><![CDATA[
      a(x * L(y * z,y,y),u,w) = a(x * (y * L(z,y,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32721,a(flip),b,32567,a)].">
      <j1 rule="hyper" parents="64 32721 32567"/>
    </justification>
  </clause>

  <clause id="32783">
    <literal><![CDATA[
      a((x * y) \ ((z * y) * x),u,w) = a(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13112,a(flip),b,32578,a),flip(a)].">
      <j1 rule="hyper" parents="64 13112 32578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32785">
    <literal><![CDATA[
      a((x * y) \ (y * (z * x)),u,w) = a(L(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32504,a,b,32783,a)].">
      <j1 rule="hyper" parents="64 32504 32783"/>
    </justification>
  </clause>

  <clause id="32786">
    <literal><![CDATA[
      a(L(R(x,x,y),(x \ 1) * y,z),u,w) = a((z * ((x \ 1) * y)) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(1996(a,1),32783(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1996 32783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32787">
    <literal><![CDATA[
      a(L(x \ a(x,y,y),z,u),w,v5) = a(L(L(x,z,u),y,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32711,a(flip),b,32593,a),flip(a)].">
      <j1 rule="hyper" parents="373 32711 32593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32788">
    <literal><![CDATA[
      a(L(((x * x) \ y) * z,u,w),v5,v6) = a(L(y * z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32590,a(flip),b,32600,a),flip(a)].">
      <j1 rule="hyper" parents="373 32590 32600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32789">
    <literal><![CDATA[
      a(L(x,y \ 1,z \ 1),u,w) = a(L(x \ 1,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26796,a(flip),b,32639,a)].">
      <j1 rule="hyper" parents="64 26796 32639"/>
    </justification>
  </clause>

  <clause id="32790">
    <literal><![CDATA[
      a(x,y,y) * L(x,z,a(u,y,y)) = L(R(x,y,y),z,a(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,29,a(flip),b,32644,a),flip(a)].">
      <j1 rule="hyper" parents="373 29 32644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32791">
    <literal><![CDATA[
      a(((x * (y \ 1)) * z) * u,w,v5) = a(((y * x) * (z \ 1)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32573,a,b,32658,a),flip(a)].">
      <j1 rule="hyper" parents="373 32573 32658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32792">
    <literal><![CDATA[
      a(((x * (y \ 1)) * z) * u,w,v5) = a(((x * y) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32393,a,b,32658,a),flip(a)].">
      <j1 rule="hyper" parents="373 32393 32658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32793">
    <literal><![CDATA[
      a((((1 / x) \ y) \ z) * u,w,v5) = a(((x \ y) \ z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32397,a(flip),b,32665,a),flip(a)].">
      <j1 rule="hyper" parents="373 32397 32665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32794">
    <literal><![CDATA[
      a(x * ((y \ (z * z)) * u),w,v5) = a(x * ((y \ 1) * u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32440,a(flip),b,32672,a),flip(a)].">
      <j1 rule="hyper" parents="373 32440 32672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32795">
    <literal><![CDATA[
      a(x \ ((y \ (1 / z)) * u),w,v5) = a(x \ ((y \ z) * u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32483,a(flip),b,32684,a),flip(a)].">
      <j1 rule="hyper" parents="373 32483 32684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32796">
    <literal><![CDATA[
      a((T(x * y,z) \ u) * w,v5,v6) = a(w * ((T(x,v7) * y) \ u),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32391,a,b,32700,a)].">
      <j1 rule="hyper" parents="373 32391 32700"/>
    </justification>
  </clause>

  <clause id="32797">
    <literal><![CDATA[
      a(x * (y * ((z \ y) * ((y \ z) \ 1))),u,w) = a((z / (1 / (z \ y))) * x,u,w)
    ]]></literal>
    <justification jstring="[para(30637(a,1),32722(a,2,1,1))].">
      <j1 rule="para" parents="30637 32722"/>
    </justification>
  </clause>

  <clause id="32798">
    <literal><![CDATA[
      a(L(L(x,x,y * x),z,u),w,v5) = a(L(L(x,x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32711,a(flip),b,32726,a)].">
      <j1 rule="hyper" parents="64 32711 32726"/>
    </justification>
  </clause>

  <clause id="32799">
    <literal><![CDATA[
      a(L(L(x * y,z,u),x,x),w,v5) = a(L(x \ y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,30384,a(flip),b,32731,a)].">
      <j1 rule="hyper" parents="64 30384 32731"/>
    </justification>
  </clause>

  <clause id="32800">
    <literal><![CDATA[
      a(L(L(x * y,x,x),z,u),w,v5) = a(L(x \ y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27170,a,b,32799,a)].">
      <j1 rule="hyper" parents="64 27170 32799"/>
    </justification>
  </clause>

  <clause id="32801">
    <literal><![CDATA[
      a(x * (((1 / y) * z) / u),w,v5) = a((u \ (y * z)) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32417,a(flip),b,32740,a)].">
      <j1 rule="hyper" parents="64 32417 32740"/>
    </justification>
  </clause>

  <clause id="32802">
    <literal><![CDATA[
      a((x \ (y * (y * z))) * u,w,v5) = a((x \ L(z,y,y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(559(a,1),32740(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="559 32740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32803">
    <literal><![CDATA[
      (x \ (y \ x)) / (a(y,z,u) * (x \ (y \ x))) = a(y,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,23133,a(flip),b,32746,a),flip(a)].">
      <j1 rule="hyper" parents="373 23133 32746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32804">
    <literal><![CDATA[
      R(x \ 1,x,(x \ y) * z) = R(x \ 1,x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30163,a(flip),b,32777,a),flip(a)].">
      <j1 rule="hyper" parents="64 30163 32777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32805">
    <literal><![CDATA[
      R(T(x \ 1,y),x,(x \ z) * u) = T(R(x \ 1,x,z * (x \ u)),y)
    ]]></literal>
    <justification jstring="[para(32804(a,1),27(a,2,1))].">
      <j1 rule="para" parents="32804 27"/>
    </justification>
  </clause>

  <clause id="32806">
    <literal><![CDATA[
      a(L(x * (y * y),z,u),w,v5) = a(L(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26844,a(flip),b,32788,a),flip(a)].">
      <j1 rule="hyper" parents="64 26844 32788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32807">
    <literal><![CDATA[
      a(L(x * (x * y),z,u),w,v5) = a(L(L(y,x,x),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(572(a,1),32788(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="572 32788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32808">
    <literal><![CDATA[
      a((((x \ 1) \ y) \ z) * u,w,v5) = a(((x \ y) \ z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),32793(a,1,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 32793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32809">
    <literal><![CDATA[
      a(((x \ 1) \ y) * z,u,w) = a((x \ y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(82(a,1),32793(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 32793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32810">
    <literal><![CDATA[
      a(x * ((y \ 1) \ z),u,w) = a((y \ z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32809,a)].">
      <j1 rule="hyper" parents="26847 32809"/>
    </justification>
  </clause>

  <clause id="32811">
    <literal><![CDATA[
      a((x \ (x \ y)) * z,u,w) = a(L(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30778,a(flip),b,32809,a),flip(a)].">
      <j1 rule="hyper" parents="64 30778 32809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32812">
    <literal><![CDATA[
      a(x * ((1 / y) \ z),u,w) = a((y \ z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32489,a,b,32810,a)].">
      <j1 rule="hyper" parents="64 32489 32810"/>
    </justification>
  </clause>

  <clause id="32813">
    <literal><![CDATA[
      a(((1 / x) \ y) * z,u,w) = a(z * (x \ y),u,w)
    ]]></literal>
    <justification jstring="[para(82(a,1),32810(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 32810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32814">
    <literal><![CDATA[
      a(x * (y * R(z,z,y)),u,w) = a((z \ y) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32428,a,b,32812,a)].">
      <j1 rule="hyper" parents="64 32428 32812"/>
    </justification>
  </clause>

  <clause id="32815">
    <literal><![CDATA[
      a(L(R(x,x,y),y,y),z,u) = a((x \ y) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26869,a,b,32812,a)].">
      <j1 rule="hyper" parents="64 26869 32812"/>
    </justification>
  </clause>

  <clause id="32816">
    <literal><![CDATA[
      a(L(L(x,x,y),y,y),z,u) = a((x \ y) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32711,a(flip),b,32815,a)].">
      <j1 rule="hyper" parents="64 32711 32815"/>
    </justification>
  </clause>

  <clause id="32817">
    <literal><![CDATA[
      a(x * (y \ (y \ z)),u,w) = a(L(z,y,y) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32811,a)].">
      <j1 rule="hyper" parents="26847 32811"/>
    </justification>
  </clause>

  <clause id="32818">
    <literal><![CDATA[
      a(L(x * y,x,x) * z,u,w) = a((x \ y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),32811(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 32811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32819">
    <literal><![CDATA[
      a((x \ y) * (y * x),z,u) = a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30967,a(flip),b,32814,a),flip(a)].">
      <j1 rule="hyper" parents="64 30967 32814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32820">
    <literal><![CDATA[
      a(a(x,y,y \ x),z,u) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26833,a(flip),b,32819,a)].">
      <j1 rule="hyper" parents="64 26833 32819"/>
    </justification>
  </clause>

  <clause id="32821">
    <literal><![CDATA[
      a(a(x \ y,x \ y,x),z,u) = a(a(y,x \ y,(x \ y) \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,30309,a(flip),b,32820,a)].">
      <j1 rule="hyper" parents="373 30309 32820"/>
    </justification>
  </clause>

  <clause id="32822">
    <literal><![CDATA[
      a(x * L(y * z,y,y),u,w) = a((y \ z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32818,a)].">
      <j1 rule="hyper" parents="26847 32818"/>
    </justification>
  </clause>

  <clause id="32823">
    <literal><![CDATA[
      a(x * (y * L(z,y,y)),u,w) = a((y \ z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32782,a(flip),b,32822,a)].">
      <j1 rule="hyper" parents="64 32782 32822"/>
    </justification>
  </clause>

  <clause id="32824">
    <literal><![CDATA[
      a((L(x,y,y) * y) * z,u,w) = a((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32422,a,b,32823,a)].">
      <j1 rule="hyper" parents="64 32422 32823"/>
    </justification>
  </clause>

  <clause id="32825">
    <literal><![CDATA[
      a(x * ((y \ (z * z)) * u),w,v5) = a((y * u) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26830,a(flip),b,32794,a),flip(a)].">
      <j1 rule="hyper" parents="373 26830 32794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32826">
    <literal><![CDATA[
      a(x * (y * (z \ (u * u))),w,v5) = a((z * y) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(32448,a,32825,a)].">
      <j1 rule="hyper" parents="32448 32825"/>
    </justification>
  </clause>

  <clause id="32827">
    <literal><![CDATA[
      a(x \ ((y \ (z \ 1)) * u),w,v5) = a(x \ ((y \ z) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),32795(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 32795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32828">
    <literal><![CDATA[
      a(L(L(x,x,x * y),z,u),w,v5) = a(L(L(x,x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(23253(a,1),32798(a,1,1,1))].">
      <j1 rule="para" parents="23253 32798"/>
    </justification>
  </clause>

  <clause id="32829">
    <literal><![CDATA[
      (x \ (y \ x)) \ (a(y,z,u) \ (x \ (y \ x))) = a(y,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,25103,a(flip),b,32803,a)].">
      <j1 rule="hyper" parents="64 25103 32803"/>
    </justification>
  </clause>

  <clause id="32830">
    <literal><![CDATA[
      a(x * (((y \ 1) \ z) \ u),w,v5) = a(((y \ z) \ u) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32808,a)].">
      <j1 rule="hyper" parents="26847 32808"/>
    </justification>
  </clause>

  <clause id="32831">
    <literal><![CDATA[
      (x \ (y \ x)) \ T(y \ 1,x) = a(y,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(30168(a,1),32829(a,1,2))].">
      <j1 rule="para" parents="30168 32829"/>
    </justification>
  </clause>

  <clause id="32832">
    <literal><![CDATA[
      ((x \ y) / y) \ (x \ 1) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,14858,a(flip),b,32831,a)].">
      <j1 rule="hyper" parents="64 14858 32831"/>
    </justification>
  </clause>

  <clause id="32833">
    <literal><![CDATA[
      ((x \ T(y,x)) / y) \ (T(x,y) \ 1) = a(T(x,y),T(x,y),y) \ 1
    ]]></literal>
    <justification jstring="[para(4632(a,1),32832(a,1,1,1))].">
      <j1 rule="para" parents="4632 32832"/>
    </justification>
  </clause>

  <clause id="32834">
    <literal><![CDATA[
      L(x,y,(((z \ u) / u) \ z) \ w) = L(x,y,(a(z,z,u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(32832(a,1),29355(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="32832 29355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32835">
    <literal><![CDATA[
      a(x,y \ R(z \ 1,u,u),w) = a(x,y \ ((z / u) / u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32230,a(flip),b,32348,a),flip(a)].">
      <j1 rule="hyper" parents="64 32230 32348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32836">
    <literal><![CDATA[
      a(x,y \ R(z \ 1,u,u),w) = a(x,y \ (u \ (z / u)),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31908,a(flip),b,32835,a),flip(a)].">
      <j1 rule="hyper" parents="373 31908 32835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32837">
    <literal><![CDATA[
      a(x,y \ R(z \ 1,u,u),w) = a(x,y \ (u \ (u \ z)),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31917,a(flip),b,32836,a),flip(a)].">
      <j1 rule="hyper" parents="373 31917 32836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32838">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),x \ u,u) = a(a(x,y,z),x \ u,u)
    ]]></literal>
    <justification jstring="[para(28787(a,1),32471(a,1,2))].">
      <j1 rule="para" parents="28787 32471"/>
    </justification>
  </clause>

  <clause id="32839">
    <literal><![CDATA[
      a(L(x * ((y * x) \ y),z,u),w,v5) = a(L(a(x,x,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32742,a(flip),b,32563,a)].">
      <j1 rule="hyper" parents="64 32742 32563"/>
    </justification>
  </clause>

  <clause id="32840">
    <literal><![CDATA[
      a((x * ((y * (1 / x)) \ y)) * z,u,w) = a(z * a(y,x,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32388,a,b,32568,a)].">
      <j1 rule="hyper" parents="64 32388 32568"/>
    </justification>
  </clause>

  <clause id="32841">
    <literal><![CDATA[
      a(L(x * (y \ (a(z,u,z) / y)),w,v5),v6,v7) = a(L(x,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(373,a,32590,a(flip),b,32597,a),flip(a)].">
      <j1 rule="hyper" parents="373 32590 32597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32842">
    <literal><![CDATA[
      (a(L(x,y,z),L(x,y,z),u) / R(x,y,z)) \ u = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(32197(a,1),32605(a,1,1,1))].">
      <j1 rule="para" parents="32197 32605"/>
    </justification>
  </clause>

  <clause id="32843">
    <literal><![CDATA[
      a(a(x * y,x,y) * z,u,w) = a((L(y,x,x) * y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2678,a(flip),b,32659,a)].">
      <j1 rule="hyper" parents="64 2678 32659"/>
    </justification>
  </clause>

  <clause id="32844">
    <literal><![CDATA[
      a(a(x * y,x,y) * z,u,w) = a((y * L(y,x,x)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32388,a,b,32843,a),flip(a)].">
      <j1 rule="hyper" parents="373 32388 32843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32845">
    <literal><![CDATA[
      a(a(x * y,x,y) * z,u,w) = a(a(x,x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,5686,a(flip),b,32844,a),flip(a)].">
      <j1 rule="hyper" parents="373 5686 32844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32846">
    <literal><![CDATA[
      a(x * a(y * z,y,z),u,w) = a(a(y,y,z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32845,a)].">
      <j1 rule="hyper" parents="26847 32845"/>
    </justification>
  </clause>

  <clause id="32847">
    <literal><![CDATA[
      a((L(x,y,x) \ y) * z,u,w) = a((((y * x) \ y) * y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32367,a(flip),b,32663,a)].">
      <j1 rule="hyper" parents="64 32367 32663"/>
    </justification>
  </clause>

  <clause id="32848">
    <literal><![CDATA[
      a(a(x,x,x \ y) * z,u,w) = a(a(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32680,a(flip),b,32664,a),flip(a)].">
      <j1 rule="hyper" parents="373 32680 32664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32849">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,w) = a(z * a(y,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32692,a(flip),b,32848,a),flip(a)].">
      <j1 rule="hyper" parents="64 32692 32848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32850">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,w) = a(a(y,y,x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32513,a(flip),b,32848,a),flip(a)].">
      <j1 rule="hyper" parents="64 32513 32848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32851">
    <literal><![CDATA[
      a(x * a(y,z,z),u,w) = a(x * a(z,z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32849,a)].">
      <j1 rule="hyper" parents="26847 32849"/>
    </justification>
  </clause>

  <clause id="32852">
    <literal><![CDATA[
      a(a(x,x,y) * z,u,w) = a(z * a(y,x,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32850,a),flip(a)].">
      <j1 rule="hyper" parents="26847 32850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32853">
    <literal><![CDATA[
      a(x * a(y * z,y,z),u,w) = a(a(z,y,y) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32846,a,b,32850,a)].">
      <j1 rule="hyper" parents="373 32846 32850"/>
    </justification>
  </clause>

  <clause id="32854">
    <literal><![CDATA[
      a(a(x,x,y) * (z * u),w,v5) = a((u * z) * a(y,x,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32422,a,b,32850,a),flip(a)].">
      <j1 rule="hyper" parents="64 32422 32850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32855">
    <literal><![CDATA[
      a(a(x,y,y) * (y * x),z,u) = a(R(y * x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(16046(a,1),32853(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16046 32853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32856">
    <literal><![CDATA[
      a(a(x,x \ y,x \ y) * z,u,w) = a(z * a(y,x \ y,x),u,w)
    ]]></literal>
    <justification jstring="[para(26836(a,1),32853(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="26836 32853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32857">
    <literal><![CDATA[
      a(a(x,y,y) * (y * x),z,u) = a(L(y * x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32590,a(flip),b,32855,a),flip(a)].">
      <j1 rule="hyper" parents="373 32590 32855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32858">
    <literal><![CDATA[
      a(L(x * y,x,y),z,u) = a(x * R(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(29982(a,1),32857(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29982 32857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32859">
    <literal><![CDATA[
      a(L(x * y,x,y),z,u) = a(x * L(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32721,a(flip),b,32858,a),flip(a)].">
      <j1 rule="hyper" parents="373 32721 32858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32860">
    <literal><![CDATA[
      a(L(x * y,x,y),z,u) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,30780,a(flip),b,32859,a),flip(a)].">
      <j1 rule="hyper" parents="373 30780 32859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32861">
    <literal><![CDATA[
      a(L(x * y,y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26845,a,b,32860,a)].">
      <j1 rule="hyper" parents="64 26845 32860"/>
    </justification>
  </clause>

  <clause id="32862">
    <literal><![CDATA[
      a((x \ L(T(y * z,z),(y / z) / y,(y / z) / y)) * u,w,v5) = a((x \ (((y / z) / y) * T(y,z))) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(26377(a,1),32802(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="26377 32802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32863">
    <literal><![CDATA[
      ((x \ T(y,x)) / y) \ (T(x,y) \ 1) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(31927(a,1),32833(a,2,1))].">
      <j1 rule="para" parents="31927 32833"/>
    </justification>
  </clause>

  <clause id="32864">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) \ 1) * (((T(z,u) \ 1) * (T(z,u) \ 1)) \ w)) = a(x,y,(((z \ T(u,z)) / u) \ ((T(z,u) \ 1) \ 1)) * w)
    ]]></literal>
    <justification jstring="[para(32863(a,1),27971(a,1,3,1))].">
      <j1 rule="para" parents="32863 27971"/>
    </justification>
  </clause>

  <clause id="32866">
    <literal><![CDATA[
      L(x,y,((z \ (u \ z)) \ u) \ w) = L(x,y,(a(u,u,z) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29111,a(flip),b,32834,a)].">
      <j1 rule="hyper" parents="64 29111 32834"/>
    </justification>
  </clause>

  <clause id="32867">
    <literal><![CDATA[
      a((x * ((y * (1 / x)) \ y)) * z,u,w) = a(z * a(x,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32851,a(flip),b,32840,a),flip(a)].">
      <j1 rule="hyper" parents="373 32851 32840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32868">
    <literal><![CDATA[
      a(L(x / (y * T(z,y \ 1)),u,w),v5,v6) = a(L(x / (z * (y \ 1)),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,14249,a(flip),b,32841,a)].">
      <j1 rule="hyper" parents="64 14249 32841"/>
    </justification>
  </clause>

  <clause id="32869">
    <literal><![CDATA[
      a((((x * y) \ x) * x) * z,u,w) = a((y \ x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13109,a(flip),b,32847,a),flip(a)].">
      <j1 rule="hyper" parents="64 13109 32847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32871">
    <literal><![CDATA[
      a(((x \ y) \ x) * z,u,w) = a(((y \ x) * x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),32869(a,1,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 32869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32872">
    <literal><![CDATA[
      a(x * (y * ((z * (1 / y)) \ z)),u,w) = a(x * a(y,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32867,a)].">
      <j1 rule="hyper" parents="26847 32867"/>
    </justification>
  </clause>

  <clause id="32873">
    <literal><![CDATA[
      a(x,y * ((z * z) * (u / (z * w))),v5) = a(x,y * (((1 / z) * w) \ u),v5)
    ]]></literal>
    <justification jstring="[para(941(a,1),32019(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="941 32019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32874">
    <literal><![CDATA[
      a(x,y * (z \ (u / (w / v5))),v6) = a(x,y * (z \ ((v5 \ w) \ u)),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32059,a(flip),b,32060,a),flip(a)].">
      <j1 rule="hyper" parents="373 32059 32060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32875">
    <literal><![CDATA[
      a(x,L(T(y,z) * u,w,v5) * v6,v7) = a(x,L(u * y,w,v5) * v6,v7)
    ]]></literal>
    <justification jstring="[hyper(373,a,31991,a,b,32100,a),flip(a)].">
      <j1 rule="hyper" parents="373 31991 32100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32876">
    <literal><![CDATA[
      a(x,L(y / T(z,u),w,v5) * v6,v7) = a(x,L(z \ y,w,v5) * v6,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,31992,a,b,32101,a)].">
      <j1 rule="hyper" parents="64 31992 32101"/>
    </justification>
  </clause>

  <clause id="32878">
    <literal><![CDATA[
      a(a(x,x,y),y,z) = a(y,a(x,x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31846,a(flip),b,32115,a)].">
      <j1 rule="hyper" parents="64 31846 32115"/>
    </justification>
  </clause>

  <clause id="32879">
    <literal><![CDATA[
      a(x,L((y \ 1) * z,u,w) * y,v5) = a(x,y \ L(y \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(32008,a,32146,a)].">
      <j1 rule="hyper" parents="32008 32146"/>
    </justification>
  </clause>

  <clause id="32880">
    <literal><![CDATA[
      a(x,(y * ((z * u) \ u)) * w,v5) = a(x,(y * (u \ (z \ u))) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32167,a(flip),b,32169,a),flip(a)].">
      <j1 rule="hyper" parents="64 32167 32169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32881">
    <literal><![CDATA[
      a(x,L(y / (z * T(u,w)),v5,v6),v7) = a(x,L((z * u) \ y,v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,31920,a,b,32175,a)].">
      <j1 rule="hyper" parents="64 31920 32175"/>
    </justification>
  </clause>

  <clause id="32882">
    <literal><![CDATA[
      a(x,y * ((z * (1 / u)) * u),w) = a(x,y * L(z,u,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32018,a(flip),b,32183,a),flip(a)].">
      <j1 rule="hyper" parents="373 32018 32183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32883">
    <literal><![CDATA[
      a(x,y * R(z,u,u),w) = a(x,y * L(z,u,u),w)
    ]]></literal>
    <justification jstring="[para(1405(a,1),32882(a,1,2,2))].">
      <j1 rule="para" parents="1405 32882"/>
    </justification>
  </clause>

  <clause id="32884">
    <literal><![CDATA[
      a(x,((y * z) * z) * u,w) = a(x,u * R(y,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32275,a,b,32883,a)].">
      <j1 rule="hyper" parents="373 32275 32883"/>
    </justification>
  </clause>

  <clause id="32885">
    <literal><![CDATA[
      a(x,a(y * z,z,y),u) = a(x,y * R(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32017,a(flip),b,32884,a)].">
      <j1 rule="hyper" parents="64 32017 32884"/>
    </justification>
  </clause>

  <clause id="32886">
    <literal><![CDATA[
      a(x,a(y * z,z,y),u) = a(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,16008,a(flip),b,32885,a),flip(a)].">
      <j1 rule="hyper" parents="373 16008 32885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32887">
    <literal><![CDATA[
      a(x,a(y,z,z),u) = a(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32193,a(flip),b,32886,a),flip(a)].">
      <j1 rule="hyper" parents="64 32193 32886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32888">
    <literal><![CDATA[
      a(x * y,a(z,u,u),w) = a(y * x,a(u,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32887,a)].">
      <j1 rule="hyper" parents="26847 32887"/>
    </justification>
  </clause>

  <clause id="32889">
    <literal><![CDATA[
      a(x,a(y \ z,y,y),u) = a(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,31957,a(flip),b,32887,a),flip(a)].">
      <j1 rule="hyper" parents="373 31957 32887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32890">
    <literal><![CDATA[
      a(x,a(y,y,z),u) * w = w * a(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(145,a,32887,a,b,23174,a),flip(a)].">
      <j1 rule="hyper" parents="145 32887 23174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32891">
    <literal><![CDATA[
      (x * (a(x,y,y) * z)) \ (R(x,y,y) * z) = a(x,a(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,15992,a,b,32887,a)].">
      <j1 rule="hyper" parents="64 15992 32887"/>
    </justification>
  </clause>

  <clause id="32892">
    <literal><![CDATA[
      a(x,a(y,y,z),z) = a(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,31843,a(flip),b,32887,a),flip(a)].">
      <j1 rule="hyper" parents="64 31843 32887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32893">
    <literal><![CDATA[
      a(x,a(y,y,x),x \ z) = a(x,a(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31119,a(flip),b,32887,a),flip(a)].">
      <j1 rule="hyper" parents="64 31119 32887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32894">
    <literal><![CDATA[
      a(x,a(y,y,y * z),u) = a(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),32889(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 32889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32895">
    <literal><![CDATA[
      a(x,a(y * z,y,y),u) = a(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[para(30543(a,1),32889(a,1,2))].">
      <j1 rule="para" parents="30543 32889"/>
    </justification>
  </clause>

  <clause id="32896">
    <literal><![CDATA[
      a(x,a(y * z,z,z),u) = a(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[para(30545(a,1),32889(a,1,2))].">
      <j1 rule="para" parents="30545 32889"/>
    </justification>
  </clause>

  <clause id="32897">
    <literal><![CDATA[
      a(x,a(y,y,x),z) = a(x,a(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,15992,a(flip),b,32891,a),flip(a)].">
      <j1 rule="hyper" parents="64 15992 32891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32898">
    <literal><![CDATA[
      a(x,(y * ((z * z) * u)) \ w,v5) = a(x,(y * u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32084,a(flip),b,32223,a),flip(a)].">
      <j1 rule="hyper" parents="64 32084 32223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32900">
    <literal><![CDATA[
      a(x,(y * z) \ (u \ ((u * y) * ((w * w) * z))),v5) = a(x,a(u,y,(w * w) * z),v5)
    ]]></literal>
    <justification jstring="[para(30027(a,2),32898(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30027 32898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32901">
    <literal><![CDATA[
      a(x,y \ R(1 / z,u,w),v5) = a(x,y \ (R(z,u,w) \ 1),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32219,a(flip),b,32226,a)].">
      <j1 rule="hyper" parents="64 32219 32226"/>
    </justification>
  </clause>

  <clause id="32902">
    <literal><![CDATA[
      a(x,y \ R(1 / z,u,w),v5) = a(x,y \ R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32230,a(flip),b,32901,a),flip(a)].">
      <j1 rule="hyper" parents="373 32230 32901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32903">
    <literal><![CDATA[
      a(x,y \ R(z \ 1,u,w),v5) = a(x,y \ R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32013,a(flip),b,32902,a)].">
      <j1 rule="hyper" parents="64 32013 32902"/>
    </justification>
  </clause>

  <clause id="32904">
    <literal><![CDATA[
      a(x,y \ (z \ (z \ u)),w) = a(x,y \ R(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32837,a(flip),b,32903,a)].">
      <j1 rule="hyper" parents="64 32837 32903"/>
    </justification>
  </clause>

  <clause id="32905">
    <literal><![CDATA[
      a(x,y \ (z \ (z \ u)),w) = a(x,y \ L(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32266,a(flip),b,32904,a),flip(a)].">
      <j1 rule="hyper" parents="373 32266 32904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32906">
    <literal><![CDATA[
      a(((x \ y) / x) \ z,z \ L(y,x,x),z) = (z / ((x \ y) / x)) * (((x \ y) / x) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32062,a(flip),b,32905,a),flip(a)].">
      <j1 rule="hyper" parents="64 32062 32905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32908">
    <literal><![CDATA[
      a(x,(y * ((z \ 1) * u)) * w,v5) = a(x,((z * u) * y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32104,a(flip),b,32257,a),flip(a)].">
      <j1 rule="hyper" parents="64 32104 32257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32909">
    <literal><![CDATA[
      a(x,(y * (z * (u \ 1))) * w,v5) = a(x,((u * z) * y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32255,a,b,32908,a)].">
      <j1 rule="hyper" parents="64 32255 32908"/>
    </justification>
  </clause>

  <clause id="32910">
    <literal><![CDATA[
      a(x,y * T(z * (u * (w \ 1)),v5),v6) = a(x,((w * u) * z) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32016,a,b,32909,a)].">
      <j1 rule="hyper" parents="64 32016 32909"/>
    </justification>
  </clause>

  <clause id="32911">
    <literal><![CDATA[
      a(x,(y * (z \ ((u \ w) * u))) \ v5,v6) = a(x,(y * (w / z)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,31985,a(flip),b,32260,a)].">
      <j1 rule="hyper" parents="64 31985 32260"/>
    </justification>
  </clause>

  <clause id="32912">
    <literal><![CDATA[
      a(x,R((1 / y) \ z,u,w) \ v5,v6) = a(x,R(y \ z,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,31993,a(flip),b,32302,a),flip(a)].">
      <j1 rule="hyper" parents="373 31993 32302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32913">
    <literal><![CDATA[
      a(x,y * ((((1 / z) \ 1) \ u) \ w),v5) = a(x,y * (((u / (z * u)) * u) \ w),v5)
    ]]></literal>
    <justification jstring="[para(2014(a,1),32305(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2014 32305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32914">
    <literal><![CDATA[
      a(x,(y * ((y * z) * z)) * u,w) = a(x,a(z * y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,11990,a(flip),b,32332,a),flip(a)].">
      <j1 rule="hyper" parents="64 11990 32332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32915">
    <literal><![CDATA[
      a(x,a(y * z,y,z) * u,w) = a(x,(z * R(z,y,y)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32326,a(flip),b,32914,a),flip(a)].">
      <j1 rule="hyper" parents="64 32326 32914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32916">
    <literal><![CDATA[
      a(x,a(y * z,y,z) * u,w) = a(x,a(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,16009,a(flip),b,32915,a),flip(a)].">
      <j1 rule="hyper" parents="373 16009 32915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32917">
    <literal><![CDATA[
      a(x,a(y,z,z) * (z * y),u) = a(x,R(z * y,z,y),u)
    ]]></literal>
    <justification jstring="[para(16047(a,1),32916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16047 32916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32918">
    <literal><![CDATA[
      a(x,R(y * z,y,z),u) = a(x,y * R(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(29982(a,1),32917(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29982 32917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32919">
    <literal><![CDATA[
      a(x,R(y * z,y,z),u) = a(x,y * L(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32883,a(flip),b,32918,a),flip(a)].">
      <j1 rule="hyper" parents="373 32883 32918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32920">
    <literal><![CDATA[
      a(x,R(y * z,y,z),u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32145,a(flip),b,32919,a),flip(a)].">
      <j1 rule="hyper" parents="373 32145 32919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32921">
    <literal><![CDATA[
      a(x,L(y * z,y,z),u) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32197,a(flip),b,32920,a)].">
      <j1 rule="hyper" parents="64 32197 32920"/>
    </justification>
  </clause>

  <clause id="32922">
    <literal><![CDATA[
      a(x,L(y * z,z,y),u) = a(x,z \ y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31956,a,b,32921,a)].">
      <j1 rule="hyper" parents="64 31956 32921"/>
    </justification>
  </clause>

  <clause id="32923">
    <literal><![CDATA[
      a(x,L(y,z \ y,z),u) = a(x,(z \ y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31955,a(flip),b,32921,a)].">
      <j1 rule="hyper" parents="64 31955 32921"/>
    </justification>
  </clause>

  <clause id="32924">
    <literal><![CDATA[
      a(x,L(y,z \ y,z),u) = a(x,(y \ z) * z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32124,a(flip),b,32923,a),flip(a)].">
      <j1 rule="hyper" parents="373 32124 32923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32925">
    <literal><![CDATA[
      ((x \ (y \ x)) * a(y,z,u)) \ (w \ (a(y,z,u) * (w * (x \ (y \ x))))) = a(w,a(y,z,u),x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(32477(a,1),30025(a,1,2,2))].">
      <j1 rule="para" parents="32477 30025"/>
    </justification>
  </clause>

  <clause id="32926">
    <literal><![CDATA[
      a(L(x / (y * T(z,u)),w,v5),v6,v7) = a(L((y * z) \ x,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,26794,a,b,32562,a)].">
      <j1 rule="hyper" parents="64 26794 32562"/>
    </justification>
  </clause>

  <clause id="32927">
    <literal><![CDATA[
      a(x * (y \ ((z * u) \ u)),w,v5) = a(x * (y \ (u \ (z \ u))),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32441,a(flip),b,32570,a),flip(a)].">
      <j1 rule="hyper" parents="64 32441 32570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32928">
    <literal><![CDATA[
      a(x,y,y) \ (x * a(z \ (a(x,y,y) \ z),u,w)) = ((x / y) / (1 / y)) * a(z \ (a(x,y,y) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,30574,a(flip),b,32584,a),flip(a)].">
      <j1 rule="hyper" parents="373 30574 32584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32929">
    <literal><![CDATA[
      R(x,y,z) * ((L(L(x,y,z),L(x,y,z) \ u,L(x,y,z)) \ u) * L(x,y,z)) = (R(x,y,z) * (L(x,y,z) \ u)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(12912(a,1),32606(a,1,2))].">
      <j1 rule="para" parents="12912 32606"/>
    </justification>
  </clause>

  <clause id="32930">
    <literal><![CDATA[
      (R(x,y,z) * (L(x,y,z) \ 1)) * u = R(x,y,z) * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(30051(a,1),32606(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30051 32606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32931">
    <literal><![CDATA[
      a((x \ ((x \ 1) \ y)) * z,u,w) = a(L(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30248,a(flip),b,32691,a),flip(a)].">
      <j1 rule="hyper" parents="64 30248 32691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32932">
    <literal><![CDATA[
      a(x * (y \ ((y \ 1) \ z)),u,w) = a(L(z,y,y) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,32931,a)].">
      <j1 rule="hyper" parents="26847 32931"/>
    </justification>
  </clause>

  <clause id="32933">
    <literal><![CDATA[
      a((x * (y \ (z / u))) * w,v5,v6) = a((x * (y \ (u \ z))) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,32697,a),flip(a)].">
      <j1 rule="hyper" parents="373 26787 32697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32934">
    <literal><![CDATA[
      a(x * (y \ (z * (u * u))),w,v5) = a(x * (y \ z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32569,a(flip),b,32706,a),flip(a)].">
      <j1 rule="hyper" parents="64 32569 32706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32936">
    <literal><![CDATA[
      a(x * (L(y,y,z) * z),u,w) = a(x * (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32566,a(flip),b,32934,a)].">
      <j1 rule="hyper" parents="64 32566 32934"/>
    </justification>
  </clause>

  <clause id="32937">
    <literal><![CDATA[
      a(x * (y * L(z,z,y)),u,w) = a(x * (z \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32410,a(flip),b,32934,a)].">
      <j1 rule="hyper" parents="64 32410 32934"/>
    </justification>
  </clause>

  <clause id="32938">
    <literal><![CDATA[
      a(x * (y \ ((z * u) * u)),w,v5) = a(x * (y \ R(z,u,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(111(a,1),32934(a,1,1,2,2))].">
      <j1 rule="para" parents="111 32934"/>
    </justification>
  </clause>

  <clause id="32941">
    <literal><![CDATA[
      L(L(R(x,x,x),y,z),L(x,y,z),R(1 / x,u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(13191(a,1),32715(a,1,1))].">
      <j1 rule="para" parents="13191 32715"/>
    </justification>
  </clause>

  <clause id="32942">
    <literal><![CDATA[
      L(L(R(x,x,x),y,z),L(x,y,z),L(1 / x,u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29221,a(flip),b,32941,a)].">
      <j1 rule="hyper" parents="64 29221 32941"/>
    </justification>
  </clause>

  <clause id="32943">
    <literal><![CDATA[
      a(L(L(x,y,y) * y,z,u),w,v5) = a(L(y \ x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32800,a(flip),b,32728,a),flip(a)].">
      <j1 rule="hyper" parents="64 32800 32728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32944">
    <literal><![CDATA[
      a(L(x * L(y,x,x),z,u),w,v5) = a(L(x \ y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26845,a,b,32943,a)].">
      <j1 rule="hyper" parents="64 26845 32943"/>
    </justification>
  </clause>

  <clause id="32945">
    <literal><![CDATA[
      a(L(L(x \ 1,y,y),z,u),w,v5) = a(L(L(x,z,u),y,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32787,a(flip),b,32730,a),flip(a)].">
      <j1 rule="hyper" parents="373 32787 32730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32946">
    <literal><![CDATA[
      a(L(L(x \ 1,y,z),u,u),w,v5) = a(L(L(x,u,u),y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26864,a(flip),b,32945,a),flip(a)].">
      <j1 rule="hyper" parents="64 26864 32945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32947">
    <literal><![CDATA[
      a(L(L(x,y,y),x,y),z,u) = a(y * (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32727,a(flip),b,32946,a),flip(a)].">
      <j1 rule="hyper" parents="64 32727 32946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32948">
    <literal><![CDATA[
      a(L((x * (y \ 1)) \ z,y,y),u,w) = a(L(y * (x \ z),y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32556,a(flip),b,32781,a),flip(a)].">
      <j1 rule="hyper" parents="373 32556 32781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32949">
    <literal><![CDATA[
      a(x * ((T(y,z) * u) \ w),v5,v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(((y * u) \ w) * x,v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(32796(a,1),32452(a,1))].">
      <j1 rule="para" parents="32796 32452"/>
    </justification>
  </clause>

  <clause id="32950">
    <literal><![CDATA[
      R(T(x \ 1,y),x,(x \ z) * u) = R(T(x \ 1,y),x,z * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27,a,b,32805,a),flip(a)].">
      <j1 rule="hyper" parents="373 27 32805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32951">
    <literal><![CDATA[
      a(a(x \ y,x \ y,x),z,u) = a(a(y,x \ y,x),z,u)
    ]]></literal>
    <justification jstring="[para(27307(a,1),32821(a,2,1))].">
      <j1 rule="para" parents="27307 32821"/>
    </justification>
  </clause>

  <clause id="32952">
    <literal><![CDATA[
      a(((x \ y) * y) \ x,z,u) = a(a(y,x \ y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32669,a(flip),b,32951,a)].">
      <j1 rule="hyper" parents="64 32669 32951"/>
    </justification>
  </clause>

  <clause id="32954">
    <literal><![CDATA[
      a(x,y * (z \ ((u / w) \ v5)),v6) = a(x,y * (z \ ((w \ u) \ v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32059,a(flip),b,32874,a)].">
      <j1 rule="hyper" parents="64 32059 32874"/>
    </justification>
  </clause>

  <clause id="32955">
    <literal><![CDATA[
      a(x,y * (K(z,u) * (w * (v5 * (v6 \ K(u,z))))),v7) = a(x,((v6 * v5) * w) * y,v7)
    ]]></literal>
    <justification jstring="[para(25385(a,2),32910(a,1,2,2))].">
      <j1 rule="para" parents="25385 32910"/>
    </justification>
  </clause>

  <clause id="32956">
    <literal><![CDATA[
      a(x,(y * (z \ ((u \ w) * u))) \ v5,v6) = a(x,(y * (z \ w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,31985,a(flip),b,32911,a),flip(a)].">
      <j1 rule="hyper" parents="373 31985 32911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32957">
    <literal><![CDATA[
      a(x * (y \ ((z * u) \ z)),w,v5) = a(x * (y \ (z \ (u \ z))),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32676,a,b,32927,a)].">
      <j1 rule="hyper" parents="64 32676 32927"/>
    </justification>
  </clause>

  <clause id="32958">
    <literal><![CDATA[
      (L(x,y,z) \ R(x,y,z)) * u = R(x,y,z) * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(1879(a,1),32930(a,1,1))].">
      <j1 rule="para" parents="1879 32930"/>
    </justification>
  </clause>

  <clause id="32959">
    <literal><![CDATA[
      ((x * y) * z) * a(R(y,x,z),x,z) = (R(y,x,z) * T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(14081(a,1),31934(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14081 31934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32961">
    <literal><![CDATA[
      ((x * y) * z) * a(R(y,x,z),x,z) = (x * R(y,x,z)) * z
    ]]></literal>
    <justification jstring="[para(23681(a,1),32959(a,2,1))].">
      <j1 rule="para" parents="23681 32959"/>
    </justification>
  </clause>

  <clause id="32963">
    <literal><![CDATA[
      ((x * y) * z) * a(L(y,x,z),x,z) = (x * R(y,x,z)) * z
    ]]></literal>
    <justification jstring="[para(32590(a,1),32961(a,1,2))].">
      <j1 rule="para" parents="32590 32961"/>
    </justification>
  </clause>

  <clause id="32964">
    <literal><![CDATA[
      a(x \ (y \ z),(y \ z) \ x,y \ z) = ((z / y) / x) * (x / (z / y))
    ]]></literal>
    <justification jstring="[hyper(32449,a,32093,a)].">
      <j1 rule="hyper" parents="32449 32093"/>
    </justification>
  </clause>

  <clause id="32965">
    <literal><![CDATA[
      a(x,((1 / y) \ ((1 / z) / y)) \ u,w) = a(x,R(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32135,a(flip),b,32097,a),flip(a)].">
      <j1 rule="hyper" parents="373 32135 32097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32966">
    <literal><![CDATA[
      a(x,((1 / y) \ ((1 / z) / y)) \ u,w) = a(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32249,a(flip),b,32965,a),flip(a)].">
      <j1 rule="hyper" parents="373 32249 32965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32967">
    <literal><![CDATA[
      a(x,(y \ ((1 / z) / y)) \ u,w) = a(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32179,a(flip),b,32966,a)].">
      <j1 rule="hyper" parents="64 32179 32966"/>
    </justification>
  </clause>

  <clause id="32968">
    <literal><![CDATA[
      a(x,(y \ (y \ (1 / z))) \ u,w) = a(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31986,a(flip),b,32967,a)].">
      <j1 rule="hyper" parents="64 31986 32967"/>
    </justification>
  </clause>

  <clause id="32970">
    <literal><![CDATA[
      a(R(x,y,x) \ 1,T(x * y,x) \ y,z) = a((x * y) \ y,x,z)
    ]]></literal>
    <justification jstring="[para(14173(a,1),32412(a,1,2))].">
      <j1 rule="para" parents="14173 32412"/>
    </justification>
  </clause>

  <clause id="32971">
    <literal><![CDATA[
      a(R(x,y,x) \ 1,(x * y) \ y,z) = a((x * y) \ y,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31903,a(flip),b,32970,a)].">
      <j1 rule="hyper" parents="64 31903 32970"/>
    </justification>
  </clause>

  <clause id="32973">
    <literal><![CDATA[
      a(R(x,y,x),(x * y) \ y,z) = a((x * y) \ y,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2653,a(flip),b,32971,a)].">
      <j1 rule="hyper" parents="64 2653 32971"/>
    </justification>
  </clause>

  <clause id="32974">
    <literal><![CDATA[
      a((x * y) \ y,x,z) = a(x,(x * y) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13103,a(flip),b,32973,a),flip(a)].">
      <j1 rule="hyper" parents="64 13103 32973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32976">
    <literal><![CDATA[
      a(x \ (y \ x),y,z) = a(y,(y * x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13122,a(flip),b,32974,a)].">
      <j1 rule="hyper" parents="64 13122 32974"/>
    </justification>
  </clause>

  <clause id="32977">
    <literal><![CDATA[
      a(x \ (y \ x),y,z) = a(y,x \ (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32038,a(flip),b,32976,a),flip(a)].">
      <j1 rule="hyper" parents="373 32038 32976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32978">
    <literal><![CDATA[
      a(x \ (y / x),(x \ y) \ ((x \ (y / x)) \ (x \ y)),z) = a((x \ y) \ R(x,y,x),x \ (y / x),z)
    ]]></literal>
    <justification jstring="[para(26513(a,1),32977(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="26513 32977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32979">
    <literal><![CDATA[
      a(x * y,z,z) \ a(L(x * y,y,x),z,z) = a(a(x * y,z,z),y,x)
    ]]></literal>
    <justification jstring="[para(32595(a,2),32468(a,1,2))].">
      <j1 rule="para" parents="32595 32468"/>
    </justification>
  </clause>

  <clause id="32980">
    <literal><![CDATA[
      a(((x * y) \ ((z * y) * x)) \ u,w,v5) = a(L(z,y,x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32394,a(flip),b,32696,a),flip(a)].">
      <j1 rule="hyper" parents="373 32394 32696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32982">
    <literal><![CDATA[
      a(R(x,y,z) \ u,w,v5) = a(L(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32732,a(flip),b,32980,a)].">
      <j1 rule="hyper" parents="64 32732 32980"/>
    </justification>
  </clause>

  <clause id="32983">
    <literal><![CDATA[
      a(L(x \ 1,y,z) \ u,w,v5) = a(R(x,y,z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26915,a(flip),b,32982,a),flip(a)].">
      <j1 rule="hyper" parents="64 26915 32982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32984">
    <literal><![CDATA[
      a(L(x,y,z) \ u,w,w) \ w = L(w,w,R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(32982(a,1),30459(a,1,1))].">
      <j1 rule="para" parents="32982 30459"/>
    </justification>
  </clause>

  <clause id="32985">
    <literal><![CDATA[
      a(x * L(y \ 1,z,u),x,x) = a(R(y,z,u) \ x,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32537,a(flip),b,32983,a)].">
      <j1 rule="hyper" parents="64 32537 32983"/>
    </justification>
  </clause>

  <clause id="32986">
    <literal><![CDATA[
      L(x,x,R(y,z,u) \ w) = L(x,x,L(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30459,a(flip),b,32984,a),flip(a)].">
      <j1 rule="hyper" parents="64 30459 32984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32987">
    <literal><![CDATA[
      L(x,(R(y,z,u) \ w) * L(v5,v5,L(y,z,u) \ w),v6) = L(x,v5 \ (R(y,z,u) \ w),v6)
    ]]></literal>
    <justification jstring="[para(32986(a,1),29779(a,1,2,2))].">
      <j1 rule="para" parents="32986 29779"/>
    </justification>
  </clause>

  <clause id="32988">
    <literal><![CDATA[
      ((x / y) / z) * (z / (x / y)) = ((y \ x) / z) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,26894,a(flip),b,32964,a),flip(a)].">
      <j1 rule="hyper" parents="64 26894 32964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32989">
    <literal><![CDATA[
      a(x * y,z,z) \ a(y \ x,z,z) = a(a(x * y,z,z),y,x)
    ]]></literal>
    <justification jstring="[para(32861(a,1),32979(a,1,2))].">
      <j1 rule="para" parents="32861 32979"/>
    </justification>
  </clause>

  <clause id="32990">
    <literal><![CDATA[
      a(x,L(y / ((z * z) * u),w,v5),v6) = a(x,L(y / u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32294,a(flip),b,32072,a),flip(a)].">
      <j1 rule="hyper" parents="373 32294 32072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32992">
    <literal><![CDATA[
      a(x,L(y / ((z * z) * u),w,v5),v6) = a(x,L(u \ y,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,31920,a(flip),b,32990,a),flip(a)].">
      <j1 rule="hyper" parents="373 31920 32990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32993">
    <literal><![CDATA[
      a(x,(y * y) * (((y / z) / u) \ w),v5) = a(x,(((1 / y) / z) / u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(890(a,1),32095(a,1,2))].">
      <j1 rule="para" parents="890 32095"/>
    </justification>
  </clause>

  <clause id="32994">
    <literal><![CDATA[
      a(x,(((y * y) * z) * (u / y)) * w,v5) = a(x,(((1 / y) \ u) * z) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31982,a(flip),b,32107,a),flip(a)].">
      <j1 rule="hyper" parents="373 31982 32107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32995">
    <literal><![CDATA[
      a(x,L(y \ ((z * z) * u),w,v5),v6) = a(x,L(y \ u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32295,a(flip),b,32174,a),flip(a)].">
      <j1 rule="hyper" parents="373 32295 32174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32997">
    <literal><![CDATA[
      a(x,L(y \ ((1 / z) * u),w,v5),v6) = a(x,L(y \ (z * u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(310(a,1),32995(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="310 32995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32998">
    <literal><![CDATA[
      a(x,L(y \ ((z \ 1) * u),w,v5),v6) = a(x,L(y \ (z * u),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(79(a,1),32997(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="79 32997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="32999">
    <literal><![CDATA[
      a(x,(y * y) * ((z \ (y * u)) \ w),v5) = a(x,(((1 / y) * u) / z) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32074,a(flip),b,32214,a)].">
      <j1 rule="hyper" parents="64 32074 32214"/>
    </justification>
  </clause>

  <clause id="33000">
    <literal><![CDATA[
      a(x,((y / (z * y)) * u) * w,v5) = a(x,((y \ (z \ y)) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,11998,a(flip),b,32310,a)].">
      <j1 rule="hyper" parents="64 11998 32310"/>
    </justification>
  </clause>

  <clause id="33001">
    <literal><![CDATA[
      a(x,(((y * z) \ z) * u) * w,v5) = a(x,((z \ (y \ z)) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31982,a(flip),b,33000,a)].">
      <j1 rule="hyper" parents="64 31982 33000"/>
    </justification>
  </clause>

  <clause id="33002">
    <literal><![CDATA[
      a(x,(y * (((z * u) \ z) \ 1)) * w,v5) = a(x,((z \ (u \ z)) * y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32309,a,b,33001,a)].">
      <j1 rule="hyper" parents="64 32309 33001"/>
    </justification>
  </clause>

  <clause id="33003">
    <literal><![CDATA[
      a(x \ ((y * (1 / z)) / u),w,v5) = a(x \ (u \ (z * y)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32378,a(flip),b,32456,a),flip(a)].">
      <j1 rule="hyper" parents="64 32378 32456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33004">
    <literal><![CDATA[
      a(x \ (y \ (z * (1 / u))),w,v5) = a(x \ (y \ (u * z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(32449,a,33003,a)].">
      <j1 rule="hyper" parents="32449 33003"/>
    </justification>
  </clause>

  <clause id="33006">
    <literal><![CDATA[
      a(x \ (y \ (z * (u \ 1))),w,v5) = a(x \ (y \ (u * z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32486,a(flip),b,33004,a)].">
      <j1 rule="hyper" parents="64 32486 33004"/>
    </justification>
  </clause>

  <clause id="33007">
    <literal><![CDATA[
      a(x \ (y \ (z * (u \ K(w,v5)))),v6,v7) = a(x \ (y \ (u * z)),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(373,a,33006,a(flip),b,32487,a),flip(a)].">
      <j1 rule="hyper" parents="373 33006 32487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33008">
    <literal><![CDATA[
      a(L(x,y,y) * L(z,z,L(x,y,y)),u,w) = a(z \ (y \ (y \ x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32817,a(flip),b,32536,a)].">
      <j1 rule="hyper" parents="64 32817 32536"/>
    </justification>
  </clause>

  <clause id="33009">
    <literal><![CDATA[
      a(x \ (y \ (y \ z)),u,w) = a(x \ L(z,y,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32532,a(flip),b,33008,a),flip(a)].">
      <j1 rule="hyper" parents="64 32532 33008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33010">
    <literal><![CDATA[
      a(x \ L(y * z,y,y),u,w) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),33009(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 33009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33011">
    <literal><![CDATA[
      a(x * (y \ (((z * z) / u) * w)),v5,v6) = a((y \ (u * w)) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32801,a(flip),b,32707,a),flip(a)].">
      <j1 rule="hyper" parents="373 32801 32707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33012">
    <literal><![CDATA[
      a((x \ (((y * y) / z) * u)) * w,v5,v6) = a((x \ (z * u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26847,a,33011,a)].">
      <j1 rule="hyper" parents="26847 33011"/>
    </justification>
  </clause>

  <clause id="33013">
    <literal><![CDATA[
      a((x \ ((y * y) * z)) * u,w,v5) = a((x \ z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(192(a,1),33012(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="192 33012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33014">
    <literal><![CDATA[
      a((R(1 / x,y,z) \ u) * w,v5,v6) = a((R(x,y,z) \ u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(2118(a,1),33013(a,1,1,1))].">
      <j1 rule="para" parents="2118 33013"/>
    </justification>
  </clause>

  <clause id="33015">
    <literal><![CDATA[
      a((x / R(1 / y,z,u)) * w,v5,v6) = a((R(y,z,u) \ x) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32367,a,b,33014,a)].">
      <j1 rule="hyper" parents="64 32367 33014"/>
    </justification>
  </clause>

  <clause id="33016">
    <literal><![CDATA[
      a(x,x,x * ((((x / y) / x) * y) * z)) = a(x,x,((1 / y) \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27470,a(flip),b,32770,a),flip(a)].">
      <j1 rule="hyper" parents="373 27470 32770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33017">
    <literal><![CDATA[
      a(x,y * ((z * z) * ((z * u) \ w)),v5) = a(x,y * (((1 / z) * u) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32057,a(flip),b,32873,a)].">
      <j1 rule="hyper" parents="64 32057 32873"/>
    </justification>
  </clause>

  <clause id="33018">
    <literal><![CDATA[
      a(x,(y * y) * ((z \ (y / u)) \ w),v5) = a(x,(((1 / y) / u) / z) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32074,a(flip),b,32993,a)].">
      <j1 rule="hyper" parents="64 32074 32993"/>
    </justification>
  </clause>

  <clause id="33019">
    <literal><![CDATA[
      a(x,((y * y) * (z * (u / y))) * w,v5) = a(x,(((1 / y) \ u) * z) * w,v5)
    ]]></literal>
    <justification jstring="[para(33(a,1),32994(a,1,2,1))].">
      <j1 rule="para" parents="33 32994"/>
    </justification>
  </clause>

  <clause id="33020">
    <literal><![CDATA[
      a(x,(((1 / y) * z) / u) \ w,v5) = a(x,(u \ (y * z)) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(26848,a,32999,a),flip(a)].">
      <j1 rule="hyper" parents="26848 32999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33022">
    <literal><![CDATA[
      a(x,(((y * z) \ y) * u) * w,v5) = a(x,((y \ (z \ y)) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32105,a(flip),b,33002,a)].">
      <j1 rule="hyper" parents="64 32105 33002"/>
    </justification>
  </clause>

  <clause id="33023">
    <literal><![CDATA[
      a(x,x,x * ((((x / y) / x) * y) * z)) = a(x,x,((y \ 1) \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27412,a(flip),b,33016,a),flip(a)].">
      <j1 rule="hyper" parents="373 27412 33016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33024">
    <literal><![CDATA[
      a(x,y * (((1 / z) * u) \ w),v5) = a(x,y * ((z * u) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32025,a(flip),b,33017,a),flip(a)].">
      <j1 rule="hyper" parents="64 32025 33017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33026">
    <literal><![CDATA[
      a(x,y * (L(z * u,z,z) \ w),v5) = a(x,y * (((u / (z * u)) * u) \ w),v5)
    ]]></literal>
    <justification jstring="[para(30955(a,2),33024(a,1,2,2,1))].">
      <j1 rule="para" parents="30955 33024"/>
    </justification>
  </clause>

  <clause id="33027">
    <literal><![CDATA[
      a(x,(((1 / y) / z) / u) \ w,v5) = a(x,(u \ (y / z)) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(26848,a,33018,a),flip(a)].">
      <j1 rule="hyper" parents="26848 33018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33029">
    <literal><![CDATA[
      a(x,(y \ (z \ (1 / u))) \ w,v5) = a(x,(y \ (u / z)) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32258,a(flip),b,33027,a)].">
      <j1 rule="hyper" parents="64 32258 33027"/>
    </justification>
  </clause>

  <clause id="33030">
    <literal><![CDATA[
      a(x,(y \ (z \ (1 / u))) \ w,v5) = a(x,(y \ (z \ u)) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31986,a(flip),b,33029,a),flip(a)].">
      <j1 rule="hyper" parents="373 31986 33029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33031">
    <literal><![CDATA[
      a(x,(y \ (y \ z)) \ u,w) = a(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32968,a(flip),b,33030,a),flip(a)].">
      <j1 rule="hyper" parents="64 32968 33030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33032">
    <literal><![CDATA[
      a(x,((y \ 1) \ (y \ z)) \ u,w) = a(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32184,a,b,33031,a)].">
      <j1 rule="hyper" parents="64 32184 33031"/>
    </justification>
  </clause>

  <clause id="33033">
    <literal><![CDATA[
      a(x,(y \ ((y \ 1) \ z)) \ u,w) = a(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32274,a(flip),b,33032,a)].">
      <j1 rule="hyper" parents="64 32274 33032"/>
    </justification>
  </clause>

  <clause id="33034">
    <literal><![CDATA[
      a(x,(y * y) * ((z * (u / y)) * w),v5) = a(x,(((1 / y) \ u) * z) * w,v5)
    ]]></literal>
    <justification jstring="[para(33(a,1),33019(a,1,2))].">
      <j1 rule="para" parents="33 33019"/>
    </justification>
  </clause>

  <clause id="33035">
    <literal><![CDATA[
      a(x,x,x * ((((x / y) / x) * y) * z)) = a(x,x,(y \ ((1 / y) \ x)) * z)
    ]]></literal>
    <justification jstring="[para(1166(a,1),33023(a,2,3,1))].">
      <j1 rule="para" parents="1166 33023"/>
    </justification>
  </clause>

  <clause id="33036">
    <literal><![CDATA[
      a(x,(((1 / y) \ z) * u) * w,v5) = a(x,(u * (z / y)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(26848,a,33034,a),flip(a)].">
      <j1 rule="hyper" parents="26848 33034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33038">
    <literal><![CDATA[
      a(x,(((1 / y) \ z) * u) * w,v5) = a(x,(u * (y \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32167,a(flip),b,33036,a),flip(a)].">
      <j1 rule="hyper" parents="373 32167 33036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33040">
    <literal><![CDATA[
      a(x,(((y \ 1) \ z) * u) * w,v5) = a(x,(u * (y \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32098,a(flip),b,33038,a)].">
      <j1 rule="hyper" parents="64 32098 33038"/>
    </justification>
  </clause>

  <clause id="33041">
    <literal><![CDATA[
      a(x,(((y \ K(z,u)) \ w) * v5) * v6,v7) = a(x,(v5 * (y \ w)) * v6,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,32099,a,b,33040,a)].">
      <j1 rule="hyper" parents="64 32099 33040"/>
    </justification>
  </clause>

  <clause id="33042">
    <literal><![CDATA[
      a(x,y * (z * ((u \ K(w,v5)) \ v6)),v7) = a(x,(z * (u \ v6)) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,32049,a(flip),b,33041,a)].">
      <j1 rule="hyper" parents="64 32049 33041"/>
    </justification>
  </clause>

  <clause id="33043">
    <literal><![CDATA[
      a(x,x,x * ((((x / y) / x) * y) * z)) = a(x,x,(y \ ((y \ 1) \ x)) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27684,a(flip),b,33035,a),flip(a)].">
      <j1 rule="hyper" parents="373 27684 33035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33044">
    <literal><![CDATA[
      a(x,x,x * (((x \ (x / y)) * y) * z)) = a(x,x,(y \ ((y \ 1) \ x)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27509,a(flip),b,33043,a)].">
      <j1 rule="hyper" parents="64 27509 33043"/>
    </justification>
  </clause>

  <clause id="33045">
    <literal><![CDATA[
      a(x,x,x * ((a(x,y,y) \ 1) * z)) = a(x,x,(y \ ((y \ 1) \ x)) * z)
    ]]></literal>
    <justification jstring="[para(30493(a,1),33044(a,1,3,2,1))].">
      <j1 rule="para" parents="30493 33044"/>
    </justification>
  </clause>

  <clause id="33046">
    <literal><![CDATA[
      a(x,y,z) * (u * K(u / w,w)) = (w \ (u * a(x,y,z))) * w
    ]]></literal>
    <justification jstring="[para(28681(a,1),25717(a,1,2,2))].">
      <j1 rule="para" parents="28681 25717"/>
    </justification>
  </clause>

  <clause id="33047">
    <literal><![CDATA[
      (x \ (y * a(z,u,w))) * x = a(z,u,w) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(6122(a,1),33046(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6122 33046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33049">
    <literal><![CDATA[
      (x \ (a(y,z,u) * w)) * x = a(y,z,u) * ((x \ w) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24761,a,b,33047,a)].">
      <j1 rule="hyper" parents="64 24761 33047"/>
    </justification>
  </clause>

  <clause id="33050">
    <literal><![CDATA[
      L(R(x,y,z),x,u) * (L(x,x,u) \ u) = u * ((1 / x) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,11796,a(flip),b,25729,a),flip(a)].">
      <j1 rule="hyper" parents="373 11796 25729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33051">
    <literal><![CDATA[
      L(R(x,y,z),x,u) * (L(x,x,u) \ u) = u * (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(2067(a,1),33050(a,2,2))].">
      <j1 rule="para" parents="2067 33050"/>
    </justification>
  </clause>

  <clause id="33052">
    <literal><![CDATA[
      x / (a(y,z,u) * K(w,w \ x)) = (w \ (a(y,z,u) \ x)) * w
    ]]></literal>
    <justification jstring="[para(28686(a,1),25802(a,1,2,2))].">
      <j1 rule="para" parents="28686 25802"/>
    </justification>
  </clause>

  <clause id="33053">
    <literal><![CDATA[
      a(x,y,z) \ ((u \ w) * u) = (u \ (a(x,y,z) \ w)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,23908,a(flip),b,33052,a)].">
      <j1 rule="hyper" parents="64 23908 33052"/>
    </justification>
  </clause>

  <clause id="33055">
    <literal><![CDATA[
      a(x,y,z) \ ((1 / x) \ u) = (1 / x) \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(36,a,30002,a(flip),b,33053,a(flip))].">
      <j1 rule="hyper" parents="36 30002 33053"/>
    </justification>
  </clause>

  <clause id="33056">
    <literal><![CDATA[
      a(x,x,y) \ (y \ z) = y \ (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(36,a,29322,a(flip),b,33053,a(flip))].">
      <j1 rule="hyper" parents="36 29322 33053"/>
    </justification>
  </clause>

  <clause id="33058">
    <literal><![CDATA[
      T(a(x,y,z) * a(x,y,z),u * w) = L(a(x,y,z) * a(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[para(25318(a,1),25835(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25318 25835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33059">
    <literal><![CDATA[
      L(a(x,y,z) * a(x,y,z),u,w) = a(x,y,z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,28748,a(flip),b,33058,a),flip(a)].">
      <j1 rule="hyper" parents="64 28748 33058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33062">
    <literal><![CDATA[
      R(x,y,L(a(z,u,w) * a(z,u,w),y,x)) = (x * (y * (a(z,u,w) * a(z,u,w)))) / (y * (a(z,u,w) * a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(33059(a,1),604(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="33059 604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33063">
    <literal><![CDATA[
      L(L(a(x,y,z),a(x,y,z),u),u * a(x,y,z),u) = L(a(x,y,z),u,u) \ (a(x,y,z) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(33059(a,1),2290(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33059 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33064">
    <literal><![CDATA[
      L(L(x,x,y),L(x,x,y),y) = (L(x,x,y) * L(x,x,y)) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(739,a,26060,a),flip(a)].">
      <j1 rule="hyper" parents="739 26060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33066">
    <literal><![CDATA[
      L(L(x,x,y),L(x,x,y),y) = (L(x,x,y) * L(x,x,y)) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,497,a(flip),b,33064,a),flip(a)].">
      <j1 rule="hyper" parents="373 497 33064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33067">
    <literal><![CDATA[
      L(L(x,x,y),L(x,x,y),y) = L(x,x,y) * (x \ L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,24378,a(flip),b,33066,a),flip(a)].">
      <j1 rule="hyper" parents="373 24378 33066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33068">
    <literal><![CDATA[
      L(L(x,x,y),L(x,x,y),y) = a(y,x,x) \ L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30559,a(flip),b,33067,a),flip(a)].">
      <j1 rule="hyper" parents="373 30559 33067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33069">
    <literal><![CDATA[
      a(x,L(y,y,x),L(y,y,x)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,30459,a,b,33068,a(flip))].">
      <j1 rule="hyper" parents="40 30459 33068"/>
    </justification>
  </clause>

  <clause id="33070">
    <literal><![CDATA[
      R(x \ (a(y,z,u) \ x),x,(a(y,z,u) \ (x \ 1)) \ w) \ w = (x \ 1) * ((((x \ 1) \ (a(y,z,u) \ (x \ 1))) * (x \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(25895(a,1),26295(a,1,1,1))].">
      <j1 rule="para" parents="25895 26295"/>
    </justification>
  </clause>

  <clause id="33071">
    <literal><![CDATA[
      L(T(x * y,x) \ 1,T(x * y,x),y \ (x \ y)) = y \ ((y / x) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29052,a(flip),b,26371,a)].">
      <j1 rule="hyper" parents="64 29052 26371"/>
    </justification>
  </clause>

  <clause id="33072">
    <literal><![CDATA[
      L(T(x * y,x) \ 1,x * y,y \ (x \ y)) = y \ ((y / x) / y)
    ]]></literal>
    <justification jstring="[hyper(29565,a,33071,a)].">
      <j1 rule="hyper" parents="29565 33071"/>
    </justification>
  </clause>

  <clause id="33075">
    <literal><![CDATA[
      a(L(T(x * y,x) \ 1,x * y,y \ (x \ y)),L(T(x * y,x) \ 1,x * y,y \ (x \ y)),z) = L((T(x * y,x) \ 1) \ R(T(x * y,x) \ 1,y \ ((y / x) / y),z),x * y,y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(33072(a,1),30077(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="33072 30077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33076">
    <literal><![CDATA[
      R(T(x \ 1,y) * (x * x),x,y) = (1 * y) / (y * (x / (x * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,2967,a(flip),b,26484,a)].">
      <j1 rule="hyper" parents="64 2967 26484"/>
    </justification>
  </clause>

  <clause id="33077">
    <literal><![CDATA[
      R(T(x \ 1,y) * (x * x),x,y) = y / (y * (x / (x * x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,172,a(flip),b,33076,a),flip(a)].">
      <j1 rule="hyper" parents="373 172 33076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33079">
    <literal><![CDATA[
      x / (x * (y / (y * y))) = (x \ (y \ x)) * (y * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2999,a(flip),b,33077,a),flip(a)].">
      <j1 rule="hyper" parents="64 2999 33077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33080">
    <literal><![CDATA[
      ((x \ (y \ x)) * (y * y)) \ 1 = 1 / (x / (x * (1 / y)))
    ]]></literal>
    <justification jstring="[para(33079(a,1),3745(a,1,1))].">
      <j1 rule="para" parents="33079 3745"/>
    </justification>
  </clause>

  <clause id="33081">
    <literal><![CDATA[
      (x * x) \ ((y \ (x \ y)) \ 1) = 1 / (y / (y * (1 / x)))
    ]]></literal>
    <justification jstring="[hyper(712,a,33080,a)].">
      <j1 rule="hyper" parents="712 33080"/>
    </justification>
  </clause>

  <clause id="33082">
    <literal><![CDATA[
      ((x / y) / x) / R(y,y * (x * (x / y)),y) = y \ (1 / (1 / ((x / y) / x)))
    ]]></literal>
    <justification jstring="[para(28876(a,1),26554(a,1,2))].">
      <j1 rule="para" parents="28876 26554"/>
    </justification>
  </clause>

  <clause id="33083">
    <literal><![CDATA[
      L(R(x,y,y) * (T(y \ 1,z) * y),u,w) = (L(x,u,w) * T(y \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,31531,a,b,26734,a)].">
      <j1 rule="hyper" parents="64 31531 26734"/>
    </justification>
  </clause>

  <clause id="33084">
    <literal><![CDATA[
      a(L(L(x,y,y * x) \ 1,z,u),w,v5) = a(L(((y * x) \ 1) * y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32557,a(flip),b,26885,a),flip(a)].">
      <j1 rule="hyper" parents="373 32557 26885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33085">
    <literal><![CDATA[
      (x * y) * L(L(T(y,y * x),z,u),w,v5) = y * (x * L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(1767(a,1),27087(a,1,2))].">
      <j1 rule="para" parents="1767 27087"/>
    </justification>
  </clause>

  <clause id="33086">
    <literal><![CDATA[
      (x * y) * L(L(T(y,x * y),z,u),w,v5) = y * (x * L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(4683(a,2),33085(a,1,2,1,1))].">
      <j1 rule="para" parents="4683 33085"/>
    </justification>
  </clause>

  <clause id="33087">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (v5 * x) = x * (v5 * L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,834,a(flip),b,33086,a)].">
      <j1 rule="hyper" parents="64 834 33086"/>
    </justification>
  </clause>

  <clause id="33088">
    <literal><![CDATA[
      (x * (y * L(L(x,z,u),w,v5))) / T(L(L(x,z,u),w,v5) * y,x) = L(x,y,L(L(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(142,a,33087,a(flip),b,14660,a)].">
      <j1 rule="hyper" parents="142 33087 14660"/>
    </justification>
  </clause>

  <clause id="33089">
    <literal><![CDATA[
      a(L(x,y,z),L(x,u,w),L(x,u,w) \ L(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,68,a(flip),b,27118,a),flip(a)].">
      <j1 rule="hyper" parents="373 68 27118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33091">
    <literal><![CDATA[
      a(x,y,L(z * ((u * u) * w),u,u)) = a(x,y,((z * w) * u) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27700,a(flip),b,27653,a),flip(a)].">
      <j1 rule="hyper" parents="64 27700 27653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33093">
    <literal><![CDATA[
      a(x,y,L(z * ((u * u) * w),u,u)) = a(x,y,u * (u * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27462,a(flip),b,33091,a),flip(a)].">
      <j1 rule="hyper" parents="373 27462 33091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33094">
    <literal><![CDATA[
      a(x,y,L((z \ T(u,w)) / u,v5,v6)) = a(x,y,L((u * z) \ T(u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(25990(a,1),27720(a,1,3,1))].">
      <j1 rule="para" parents="25990 27720"/>
    </justification>
  </clause>

  <clause id="33095">
    <literal><![CDATA[
      a(x,y,L((z * u) \ T(z,w),v5,v6)) = a(x,y,L(z \ (u \ T(z,w)),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,27344,a(flip),b,33094,a),flip(a)].">
      <j1 rule="hyper" parents="64 27344 33094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33096">
    <literal><![CDATA[
      a(x,y,L(z \ (u \ T(z,w)),v5,v6)) = a(x,y,L((z * u) \ z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,27603,a(flip),b,33095,a),flip(a)].">
      <j1 rule="hyper" parents="64 27603 33095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33098">
    <literal><![CDATA[
      a(x,y,L((z * u) \ z,w,v5)) = a(x,y,L(z \ (u \ z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27610,a(flip),b,33096,a),flip(a)].">
      <j1 rule="hyper" parents="64 27610 33096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33099">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u) * R(y,y,T(x,z)) = (1 / y) \ T(T(x,z),u)
    ]]></literal>
    <justification jstring="[para(23198(a,1),27817(a,1,2))].">
      <j1 rule="para" parents="23198 27817"/>
    </justification>
  </clause>

  <clause id="33101">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u) * R(y,y,x) = (1 / y) \ T(T(x,z),u)
    ]]></literal>
    <justification jstring="[para(23198(a,1),33099(a,1,2))].">
      <j1 rule="para" parents="23198 33099"/>
    </justification>
  </clause>

  <clause id="33103">
    <literal><![CDATA[
      R(x,x,y) * T(T(y,z),u) = (1 / x) \ T(T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,24608,a(flip),b,33101,a)].">
      <j1 rule="hyper" parents="64 24608 33101"/>
    </justification>
  </clause>

  <clause id="33104">
    <literal><![CDATA[
      (x \ y) \ ((1 / (1 / (y \ x))) * z) = (y \ (x * 1)) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(4305(a,1),28027(a,1,2,1))].">
      <j1 rule="para" parents="4305 28027"/>
    </justification>
  </clause>

  <clause id="33105">
    <literal><![CDATA[
      (x \ y) \ ((1 / (1 / (y \ x))) * z) = (y \ x) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(8(a,1),33104(a,2,1,2))].">
      <j1 rule="para" parents="8 33104"/>
    </justification>
  </clause>

  <clause id="33106">
    <literal><![CDATA[
      K(1 / (1 / (x \ y)),(1 / (1 / (x \ y))) \ 1) * ((x \ y) * ((y \ x) \ z)) = (y \ x) \ (T(1 / (1 / (x \ y)),(1 / (1 / (x \ y))) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(33105(a,1),5231(a,1,2))].">
      <j1 rule="para" parents="33105 5231"/>
    </justification>
  </clause>

  <clause id="33107">
    <literal><![CDATA[
      a(x / (1 / y),z,x / (1 / y)) = a(x * y,z,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10892,a(flip),b,28600,a),flip(a)].">
      <j1 rule="hyper" parents="64 10892 28600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33108">
    <literal><![CDATA[
      a(x / (1 / y),z,(1 / y) \ x) = a(x * y,z,x * y)
    ]]></literal>
    <justification jstring="[hyper(27586,a,33107,a)].">
      <j1 rule="hyper" parents="27586 33107"/>
    </justification>
  </clause>

  <clause id="33109">
    <literal><![CDATA[
      a(x / (1 / y),z,(y \ 1) \ x) = a(x * y,z,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27389,a(flip),b,33108,a)].">
      <j1 rule="hyper" parents="64 27389 33108"/>
    </justification>
  </clause>

  <clause id="33110">
    <literal><![CDATA[
      a((1 / x) \ y,z,(x \ 1) \ y) = a(y * x,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(26880,a,33109,a)].">
      <j1 rule="hyper" parents="26880 33109"/>
    </justification>
  </clause>

  <clause id="33111">
    <literal><![CDATA[
      a(x \ y,z,(x \ 1) \ y) = a(y * x,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2671,a(flip),b,33110,a)].">
      <j1 rule="hyper" parents="64 2671 33110"/>
    </justification>
  </clause>

  <clause id="33112">
    <literal><![CDATA[
      L(a(x * y,z,x * y) \ ((y \ 1) \ x),y,y) = L(y * x,z,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(33111(a,1),11618(a,1,1,1))].">
      <j1 rule="para" parents="33111 11618"/>
    </justification>
  </clause>

  <clause id="33113">
    <literal><![CDATA[
      T(T(x * K(y,x),z),x * y) = L(T(x,z),y * a(u,w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,28642,a(flip),b,28683,a)].">
      <j1 rule="hyper" parents="64 28642 28683"/>
    </justification>
  </clause>

  <clause id="33115">
    <literal><![CDATA[
      L(T(x,y),z * a(u,w,v5),x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6661,a(flip),b,33113,a),flip(a)].">
      <j1 rule="hyper" parents="64 6661 33113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33116">
    <literal><![CDATA[
      ((x * y) * a(z,u,w)) \ (y * (T(x,y) * a(z,u,w))) = a(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[para(10989(a,1),28796(a,1,2))].">
      <j1 rule="para" parents="10989 28796"/>
    </justification>
  </clause>

  <clause id="33117">
    <literal><![CDATA[
      ((x * y) * a(z,u,w)) \ (y * T(x * a(z,u,w),y)) = a(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[para(28750(a,2),33116(a,1,2,2))].">
      <j1 rule="para" parents="28750 33116"/>
    </justification>
  </clause>

  <clause id="33118">
    <literal><![CDATA[
      ((x * y) * a(z,u,w)) \ ((x * a(z,u,w)) * y) = a(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,33117,a)].">
      <j1 rule="hyper" parents="64 249 33117"/>
    </justification>
  </clause>

  <clause id="33119">
    <literal><![CDATA[
      (((x * (y * y)) * z) * a(u,w,v5)) \ (((x * (y * y)) * a(u,w,v5)) * z) = a(a(u,w,v5),x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31939,a(flip),b,33118,a),flip(a)].">
      <j1 rule="hyper" parents="373 31939 33118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33120">
    <literal><![CDATA[
      L(x,y,((z * u) * w) \ (u * (w * z))) = L(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,28973,a(flip),b,29103,a),flip(a)].">
      <j1 rule="hyper" parents="373 28973 29103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33122">
    <literal><![CDATA[
      L(x,y,z \ ((u * w) \ ((v5 * w) * u))) = L(x,y,z \ R(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,29033,a(flip),b,29129,a),flip(a)].">
      <j1 rule="hyper" parents="373 29033 29129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33124">
    <literal><![CDATA[
      L(x,y,z \ R(u,w,v5)) = L(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,31359,a(flip),b,33122,a),flip(a)].">
      <j1 rule="hyper" parents="64 31359 33122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33125">
    <literal><![CDATA[
      L(L(x \ 1,y,z),u,x \ L(x,w,v5)) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32476,a(flip),b,33124,a),flip(a)].">
      <j1 rule="hyper" parents="64 32476 33124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33127">
    <literal><![CDATA[
      L(x,y,x \ L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,32470,a(flip),b,33124,a),flip(a)].">
      <j1 rule="hyper" parents="64 32470 33124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33128">
    <literal><![CDATA[
      L(x,y,R(1 / z,z,R(u,w,v5)) \ L(u,w,v5)) = L(x,y,z * R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(452(a,1),33124(a,1,3)),flip(a)].">
      <j1 rule="para" parents="452 33124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33129">
    <literal><![CDATA[
      L(x,y,x * L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,5608,a(flip),b,33127,a)].">
      <j1 rule="hyper" parents="64 5608 33127"/>
    </justification>
  </clause>

  <clause id="33130">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) * x = (x \ L(x,y,z)) * (u * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,33127,a(flip),b,5318,a(flip))].">
      <j1 rule="hyper" parents="145 33127 5318"/>
    </justification>
  </clause>

  <clause id="33131">
    <literal><![CDATA[
      x * R(T(y,(y \ L(y,z,u)) * x),y \ L(y,z,u),x) = (y \ L(y,z,u)) \ ((y * (y \ L(y,z,u))) * x)
    ]]></literal>
    <justification jstring="[para(33127(a,1),1821(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="33127 1821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33132">
    <literal><![CDATA[
      L(x,y,L(x,z,u) \ x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,9385,a,b,33129,a)].">
      <j1 rule="hyper" parents="64 9385 33129"/>
    </justification>
  </clause>

  <clause id="33133">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) / x = (L(x,y,z) \ x) * (u / x)
    ]]></literal>
    <justification jstring="[hyper(225,a,33132,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 33132 10262"/>
    </justification>
  </clause>

  <clause id="33134">
    <literal><![CDATA[
      ((L(x,y,z) \ x) \ 1) * L(x,u,w) = (L(x,y,z) \ x) \ L(x,u,w)
    ]]></literal>
    <justification jstring="[para(33132(a,1),1149(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="33132 1149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33135">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * u) * L(x,w,v5) = (L(x,y,z) \ x) * (u * L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(33132(a,1),513(a,1,2,1))].">
      <j1 rule="para" parents="33132 513"/>
    </justification>
  </clause>

  <clause id="33136">
    <literal><![CDATA[
      L(x \ 1,y,x * L(x,z,u)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(42,a,5608,a,b,33125,a),flip(a)].">
      <j1 rule="hyper" parents="42 5608 33125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33137">
    <literal><![CDATA[
      L(R(x \ 1,y,z),u,x * L(x,w,v5)) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(33136(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33136 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33138">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * y = (y \ L(y,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,23746,a(flip),b,33130,a)].">
      <j1 rule="hyper" parents="64 23746 33130"/>
    </justification>
  </clause>

  <clause id="33139">
    <literal><![CDATA[
      (x * (L(y,z,u) \ y)) / y = (L(y,z,u) \ y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,23590,a(flip),b,33133,a)].">
      <j1 rule="hyper" parents="64 23590 33133"/>
    </justification>
  </clause>

  <clause id="33140">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * (u / x)) * L(x,y,z) = L(u,L(x,y,z) \ x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(33133(a,1),25123(a,1,1))].">
      <j1 rule="para" parents="33133 25123"/>
    </justification>
  </clause>

  <clause id="33141">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) \ ((u * ((x \ L(x,y,z)) * x)) * x) = L(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(33138(a,1),3203(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33138 3203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33142">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) / L(x,y,z) = R(u,x \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(33138(a,1),5575(a,1,1))].">
      <j1 rule="para" parents="33138 5575"/>
    </justification>
  </clause>

  <clause id="33143">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((y \ L(y,z,u)) * (x * y)) = a(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(33138(a,1),5577(a,1,2))].">
      <j1 rule="para" parents="33138 5577"/>
    </justification>
  </clause>

  <clause id="33144">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) / T(u,(x \ L(x,y,z)) * x) = u \ ((u * (x \ L(x,y,z))) * x)
    ]]></literal>
    <justification jstring="[para(33138(a,1),15270(a,1,1))].">
      <j1 rule="para" parents="33138 15270"/>
    </justification>
  </clause>

  <clause id="33145">
    <literal><![CDATA[
      (L(x,y,z) \ x) * ((u * L(x,y,z)) / x) = R(u,L(x,y,z),L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,110,a(flip),b,33139,a),flip(a)].">
      <j1 rule="hyper" parents="64 110 33139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33146">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(x,u,w) = (x \ L(x,y,z)) * L(x,u,w)
    ]]></literal>
    <justification jstring="[para(5658(a,1),33134(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5658 33134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33147">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(x,u,w) = L(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,26936,a(flip),b,33146,a),flip(a)].">
      <j1 rule="hyper" parents="373 26936 33146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33148">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x,u,w))) \ L(x,u,w) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(33147(a,1),23580(a,1,1))].">
      <j1 rule="para" parents="33147 23580"/>
    </justification>
  </clause>

  <clause id="33149">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),y) = R(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,24820,a(flip),b,33142,a),flip(a)].">
      <j1 rule="hyper" parents="64 24820 33142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33150">
    <literal><![CDATA[
      R(x,y,y \ L(y,z,u)) = L(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27837,a(flip),b,33149,a),flip(a)].">
      <j1 rule="hyper" parents="64 27837 33149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33151">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),y) = L(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27863,a(flip),b,33150,a),flip(a)].">
      <j1 rule="hyper" parents="64 27863 33150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33152">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),y) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,5608,a(flip),b,33151,a),flip(a)].">
      <j1 rule="hyper" parents="373 5608 33151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33153">
    <literal><![CDATA[
      L(x,y,z) \ (x * (u * (x \ L(x,y,z)))) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,23744,a,b,33151,a)].">
      <j1 rule="hyper" parents="64 23744 33151"/>
    </justification>
  </clause>

  <clause id="33154">
    <literal><![CDATA[
      L(x,y,z) \ (x * (u * (x \ L(x,y,z)))) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,23744,a,b,33152,a)].">
      <j1 rule="hyper" parents="64 23744 33152"/>
    </justification>
  </clause>

  <clause id="33155">
    <literal><![CDATA[
      L(x,y * L(y,z,u),y) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11786,a(flip),b,33152,a)].">
      <j1 rule="hyper" parents="64 11786 33152"/>
    </justification>
  </clause>

  <clause id="33156">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ 1,u,u * L(u,w,v5)) = L(x * L(x \ 1,u * L(u,w,v5),u),y,z)
    ]]></literal>
    <justification jstring="[para(33155(a,1),4273(a,1,2))].">
      <j1 rule="para" parents="33155 4273"/>
    </justification>
  </clause>

  <clause id="33157">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * u) = x * (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(39,a,5578,a,b,33153,a)].">
      <j1 rule="hyper" parents="39 5578 33153"/>
    </justification>
  </clause>

  <clause id="33158">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,23745,a,b,33157,a)].">
      <j1 rule="hyper" parents="36 23745 33157"/>
    </justification>
  </clause>

  <clause id="33159">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * u) = x * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(23742(a,2),33157(a,2,2))].">
      <j1 rule="para" parents="23742 33157"/>
    </justification>
  </clause>

  <clause id="33160">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,x * R(x,u,w)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11914,a(flip),b,33158,a)].">
      <j1 rule="hyper" parents="64 11914 33158"/>
    </justification>
  </clause>

  <clause id="33161">
    <literal><![CDATA[
      x * ((x \ y) * (x \ L(x,z,u))) = y * (x \ L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,33158,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 33158 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33162">
    <literal><![CDATA[
      L(L(x \ L(x,y,z),u,w),v5,x) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(33158(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33158 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33163">
    <literal><![CDATA[
      x * R(T(y \ L(y,z,u),y * x),y,x) = y \ (((y \ L(y,z,u)) * y) * x)
    ]]></literal>
    <justification jstring="[para(33158(a,1),1821(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="33158 1821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33164">
    <literal><![CDATA[
      x \ (y * ((1 / x) \ (x \ L(x,z,u)))) = T(y,x) * L(x \ L(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(33158(a,1),11091(a,1,2,2,2))].">
      <j1 rule="para" parents="33158 11091"/>
    </justification>
  </clause>

  <clause id="33165">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (x * ((x \ L(x,y,z)) * u)) = (1 / x) * u
    ]]></literal>
    <justification jstring="[hyper(139,a,33159,a(flip),b,27802,a)].">
      <j1 rule="hyper" parents="139 33159 27802"/>
    </justification>
  </clause>

  <clause id="33166">
    <literal><![CDATA[
      (L(x,y,z) * u) / (x * ((x \ L(x,y,z)) * u)) = a(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(33159(a,1),15476(a,1,2))].">
      <j1 rule="para" parents="33159 15476"/>
    </justification>
  </clause>

  <clause id="33167">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(x,u,w) = R(x,y,z) * (x \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,33160,a(flip),b,2755,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 33160 2755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33168">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (x \ L(x,y,z))) \ (x \ u) = (L(x,y,z) * (x \ L(x,y,z))) \ u
    ]]></literal>
    <justification jstring="[para(33161(a,1),486(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33161 486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33169">
    <literal><![CDATA[
      L(L(a(x,y,y) \ 1,z,u),w,y) = L(y \ L(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(30465(a,2),33162(a,1,1,1))].">
      <j1 rule="para" parents="30465 33162"/>
    </justification>
  </clause>

  <clause id="33170">
    <literal><![CDATA[
      L(a(x,y,y) \ 1,z,u) = L(y \ L(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(23283,a,33169,a),flip(a)].">
      <j1 rule="hyper" parents="23283 33169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33171">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (x * ((1 / (L(x,y,z) / x)) * (L(x,y,z) * u))) = (1 / x) * ((((x \ L(x,y,z)) \ 1) * x) * u)
    ]]></literal>
    <justification jstring="[para(27016(a,1),33165(a,1,2,2))].">
      <j1 rule="para" parents="27016 33165"/>
    </justification>
  </clause>

  <clause id="33172">
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) * L(y,z,u) = (x * (y \ L(y,z,u))) * y
    ]]></literal>
    <justification jstring="[hyper(144,a,33154,a(flip),b,25109,a)].">
      <j1 rule="hyper" parents="144 33154 25109"/>
    </justification>
  </clause>

  <clause id="33173">
    <literal><![CDATA[
      L(x,y * L(y,z,u),y) * L(y,z,u) = (x * (y \ L(y,z,u))) * y
    ]]></literal>
    <justification jstring="[para(33155(a,2),33172(a,1,1))].">
      <j1 rule="para" parents="33155 33172"/>
    </justification>
  </clause>

  <clause id="33174">
    <literal><![CDATA[
      L(x,y,R(1 / z,z,L(u,w,v5)) \ L(u,w,v5)) = L(x,y,z * R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(26360(a,1),33128(a,1,3,1))].">
      <j1 rule="para" parents="26360 33128"/>
    </justification>
  </clause>

  <clause id="33175">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,L(x,w,v5)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(36,a,28920,a,b,33135,a(flip))].">
      <j1 rule="hyper" parents="36 28920 33135"/>
    </justification>
  </clause>

  <clause id="33176">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(24745,a,33175,a)].">
      <j1 rule="hyper" parents="24745 33175"/>
    </justification>
  </clause>

  <clause id="33178">
    <literal><![CDATA[
      L(x,y,z) * (u * ((L(x,y,z) * u) \ (u * x))) = u * (L(x,y,z) * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(33175(a,1),11096(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="33175 11096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33179">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * (L(x,u,w) \ x)) = (L(x,y,z) \ x) * (L(x,u,w) \ x)
    ]]></literal>
    <justification jstring="[para(33175(a,1),11934(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33175 11934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33181">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),v5,x) = L(L(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(33176(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33176 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33182">
    <literal><![CDATA[
      a(x,y,L(L(x,z,u) \ x,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,33181,a)].">
      <j1 rule="hyper" parents="54 33181"/>
    </justification>
  </clause>

  <clause id="33183">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(L(x,u,w) \ x,v5,v6) = L(x,y,z) * (x \ L(L(x,u,w) \ x,v5,v6))
    ]]></literal>
    <justification jstring="[para(33181(a,1),2338(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="33181 2338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33184">
    <literal><![CDATA[
      a(x,y,a(z,u,x)) = 1
    ]]></literal>
    <justification jstring="[para(2869(a,2),33182(a,1,3))].">
      <j1 rule="para" parents="2869 33182"/>
    </justification>
  </clause>

  <clause id="33185">
    <literal><![CDATA[
      (x * y) * a(z,u,x) = x * (y * a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(1432,a,33184,a)].">
      <j1 rule="hyper" parents="1432 33184"/>
    </justification>
  </clause>

  <clause id="33186">
    <literal><![CDATA[
      L(a(x,y,z),u,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,33184,a)].">
      <j1 rule="hyper" parents="53 33184"/>
    </justification>
  </clause>

  <clause id="33187">
    <literal><![CDATA[
      a(x,y,z \ R(z,u,x)) = 1
    ]]></literal>
    <justification jstring="[para(28073(a,1),33184(a,1,3))].">
      <j1 rule="para" parents="28073 33184"/>
    </justification>
  </clause>

  <clause id="33188">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,31676,a(flip),b,33187,a)].">
      <j1 rule="hyper" parents="64 31676 33187"/>
    </justification>
  </clause>

  <clause id="33189">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,33187,a)].">
      <j1 rule="hyper" parents="53 33187"/>
    </justification>
  </clause>

  <clause id="33190">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,33188,a)].">
      <j1 rule="hyper" parents="53 33188"/>
    </justification>
  </clause>

  <clause id="33191">
    <literal><![CDATA[
      L(a(x,y,z),u,1 / z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2277,a,33186,a)].">
      <j1 rule="hyper" parents="2277 33186"/>
    </justification>
  </clause>

  <clause id="33192">
    <literal><![CDATA[
      L(a(x,y,z \ 1),u,z) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(2275,a,33186,a)].">
      <j1 rule="hyper" parents="2275 33186"/>
    </justification>
  </clause>

  <clause id="33193">
    <literal><![CDATA[
      L(a(x,y,z),u,z) = (a(x,y,z) / w) * w
    ]]></literal>
    <justification jstring="[hyper(373,a,12,a,b,33186,a),flip(a)].">
      <j1 rule="hyper" parents="373 12 33186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33194">
    <literal><![CDATA[
      L(a(x,a(y,z,u),y),w,y) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,31843,a(flip),b,33186,a),flip(a)].">
      <j1 rule="hyper" parents="373 31843 33186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33195">
    <literal><![CDATA[
      R(a(x,y,z),u,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,28787,a,b,33186,a)].">
      <j1 rule="hyper" parents="64 28787 33186"/>
    </justification>
  </clause>

  <clause id="33196">
    <literal><![CDATA[
      (x * a(y,z,u)) * u = (x * u) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,33186,a(flip),b,28783,a),flip(a)].">
      <j1 rule="hyper" parents="145 33186 28783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33197">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,x)) = y * a(z,u,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,33186,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 33186 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33198">
    <literal><![CDATA[
      (T(x,y) * z) * a(u,w,x) = T(x,y) * (z * a(u,w,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,33186,a(flip),b,24625,a(flip))].">
      <j1 rule="hyper" parents="145 33186 24625"/>
    </justification>
  </clause>

  <clause id="33200">
    <literal><![CDATA[
      a(x,y,z) * (z * u) = z * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(144,a,33186,a(flip),b,23157,a)].">
      <j1 rule="hyper" parents="144 33186 23157"/>
    </justification>
  </clause>

  <clause id="33201">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),v5,z) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(33186(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33186 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33202">
    <literal><![CDATA[
      x \ (y * a(z,u,x)) = (x \ y) * a(z,u,x)
    ]]></literal>
    <justification jstring="[para(33186(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="33186 598"/>
    </justification>
  </clause>

  <clause id="33204">
    <literal><![CDATA[
      ((x \ 1) * y) * a(z,u,x) = (x \ 1) * (y * a(z,u,x))
    ]]></literal>
    <justification jstring="[para(33186(a,1),1630(a,1,2))].">
      <j1 rule="para" parents="33186 1630"/>
    </justification>
  </clause>

  <clause id="33206">
    <literal><![CDATA[
      a(x,y,z) \ (z * u) = z * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(33186(a,1),27804(a,1,1))].">
      <j1 rule="para" parents="33186 27804"/>
    </justification>
  </clause>

  <clause id="33207">
    <literal><![CDATA[
      (a(x,y,z) * u) * z = (u * z) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(33186(a,1),28775(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33186 28775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33208">
    <literal><![CDATA[
      (a(x,y,z) * u) * z = a(x,y,z) * (u * z)
    ]]></literal>
    <justification jstring="[para(33186(a,1),28784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33186 28784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33209">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ z = a(x,y,z) * z
    ]]></literal>
    <justification jstring="[para(33186(a,1),28795(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33186 28795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33210">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ z = z * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(33186(a,1),28814(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33186 28814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33211">
    <literal><![CDATA[
      x * (y * L(a(z,u,x),x,y)) = (x * a(z,u,x)) * y
    ]]></literal>
    <justification jstring="[para(33186(a,1),28785(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="33186 28785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33212">
    <literal><![CDATA[
      (x \ 1) * (y * a(x,z,y)) = (x \ a(x,z,y)) * y
    ]]></literal>
    <justification jstring="[para(33186(a,1),31391(a,1,2,2))].">
      <j1 rule="para" parents="33186 31391"/>
    </justification>
  </clause>

  <clause id="33213">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * z = a(x,y,z) \ z
    ]]></literal>
    <justification jstring="[para(33195(a,1),475(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33195 475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33214">
    <literal><![CDATA[
      a(x,y,z) \ (u * z) = (a(x,y,z) \ u) * z
    ]]></literal>
    <justification jstring="[para(33195(a,1),649(a,1,1))].">
      <j1 rule="para" parents="33195 649"/>
    </justification>
  </clause>

  <clause id="33215">
    <literal><![CDATA[
      (1 / x) \ (y * a(z,u,x)) = ((1 / x) \ y) * a(z,u,x)
    ]]></literal>
    <justification jstring="[para(33191(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="33191 598"/>
    </justification>
  </clause>

  <clause id="33216">
    <literal><![CDATA[
      R(a(x,y,z),z,(z \ 1) * u) * L(u,z,z) = ((a(x,y,z) \ 1) \ z) * ((z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(33209(a,2),1153(a,2,1))].">
      <j1 rule="para" parents="33209 1153"/>
    </justification>
  </clause>

  <clause id="33222">
    <literal><![CDATA[
      L(x,y,z) * (x \ R(x,u,z)) = L(R(x,u,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,33189,a(flip),b,4243,a)].">
      <j1 rule="hyper" parents="145 33189 4243"/>
    </justification>
  </clause>

  <clause id="33223">
    <literal><![CDATA[
      (x \ R(x,y,z)) * L(x,u,z) = L(R(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[para(33189(a,1),4250(a,1,1))].">
      <j1 rule="para" parents="33189 4250"/>
    </justification>
  </clause>

  <clause id="33224">
    <literal><![CDATA[
      a(L(x,y,z),z,z \ 1) = a(x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,4248,a,b,33192,a)].">
      <j1 rule="hyper" parents="64 4248 33192"/>
    </justification>
  </clause>

  <clause id="33225">
    <literal><![CDATA[
      (x * a(y,z,u \ 1)) * u = a(y,z,u \ 1) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,33192,a(flip),b,28786,a),flip(a)].">
      <j1 rule="hyper" parents="144 33192 28786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33226">
    <literal><![CDATA[
      (a(x,y,z \ 1) * u) * z = a(x,y,z \ 1) * (u * z)
    ]]></literal>
    <justification jstring="[para(33192(a,1),28784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33192 28784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33227">
    <literal><![CDATA[
      L(a(x,y,z),u,z) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(33193(a,2),285(a,1)),flip(b)].">
      <j1 rule="para" parents="33193 285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33228">
    <literal><![CDATA[
      a((x * y) * y,y,y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,26867,a,b,33224,a)].">
      <j1 rule="hyper" parents="64 26867 33224"/>
    </justification>
  </clause>

  <clause id="33229">
    <literal><![CDATA[
      ((x / (y \ 1)) / y) \ x = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,30407,a(flip),b,33224,a)].">
      <j1 rule="hyper" parents="64 30407 33224"/>
    </justification>
  </clause>

  <clause id="33230">
    <literal><![CDATA[
      a(x \ y,x,x \ 1) = a(y * x,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,30383,a(flip),b,33224,a)].">
      <j1 rule="hyper" parents="64 30383 33224"/>
    </justification>
  </clause>

  <clause id="33231">
    <literal><![CDATA[
      a((x * y) \ z,x,x \ 1) = a(y \ (x \ z),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(346(a,1),33224(a,1,1))].">
      <j1 rule="para" parents="346 33224"/>
    </justification>
  </clause>

  <clause id="33233">
    <literal><![CDATA[
      a(x,y,y \ 1) \ x = (x / (y \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,33229,a)].">
      <j1 rule="hyper" parents="40 23134 33229"/>
    </justification>
  </clause>

  <clause id="33234">
    <literal><![CDATA[
      x / ((x / (y \ 1)) / y) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(226,a,33233,a)].">
      <j1 rule="hyper" parents="226 33233"/>
    </justification>
  </clause>

  <clause id="33235">
    <literal><![CDATA[
      1 / ((x / (y \ 1)) / y) = R(1 / x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(225,a,33233,a(flip),b,25544,a)].">
      <j1 rule="hyper" parents="225 33233 25544"/>
    </justification>
  </clause>

  <clause id="33236">
    <literal><![CDATA[
      L(x,y,a(z,u,x)) = x
    ]]></literal>
    <justification jstring="[hyper(28860,a,33185,a)].">
      <j1 rule="hyper" parents="28860 33185"/>
    </justification>
  </clause>

  <clause id="33237">
    <literal><![CDATA[
      R(x,y,a(z,u,x)) = x
    ]]></literal>
    <justification jstring="[hyper(664,a,33185,a)].">
      <j1 rule="hyper" parents="664 33185"/>
    </justification>
  </clause>

  <clause id="33239">
    <literal><![CDATA[
      x \ ((x * a(y,z,u)) * w) = w * (a(y,z,u) * a(x,a(y,z,u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,30022,a,b,33185,a)].">
      <j1 rule="hyper" parents="64 30022 33185"/>
    </justification>
  </clause>

  <clause id="33240">
    <literal><![CDATA[
      x \ ((x * y) * T(z,y)) = z * (y * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29952,a,b,33185,a)].">
      <j1 rule="hyper" parents="64 29952 33185"/>
    </justification>
  </clause>

  <clause id="33241">
    <literal><![CDATA[
      x * (y * (z * a(x,z,y))) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,33185,a(flip),b,29952,a)].">
      <j1 rule="hyper" parents="145 33185 29952"/>
    </justification>
  </clause>

  <clause id="33242">
    <literal><![CDATA[
      x \ (y \ ((y * a(z,u,w)) * x)) = a(z,u,w) * a(y,a(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(139,a,30022,a,b,33185,a(flip))].">
      <j1 rule="hyper" parents="139 30022 33185"/>
    </justification>
  </clause>

  <clause id="33243">
    <literal><![CDATA[
      x \ (a(y,z,x) * u) = (x \ u) * a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,23906,a(flip),b,33185,a(flip))].">
      <j1 rule="hyper" parents="139 23906 33185"/>
    </justification>
  </clause>

  <clause id="33244">
    <literal><![CDATA[
      R(R(1 / x,x,y),x * y,a(z,u,x)) = (y * a(z,u,x)) / (x * (y * a(z,u,x)))
    ]]></literal>
    <justification jstring="[para(33185(a,1),685(a,2,2))].">
      <j1 rule="para" parents="33185 685"/>
    </justification>
  </clause>

  <clause id="33245">
    <literal><![CDATA[
      (x * (y * a(z,u,x))) \ ((x * a(z,u,x)) * y) = a(a(z,u,x),x,y)
    ]]></literal>
    <justification jstring="[para(33185(a,1),33118(a,1,1))].">
      <j1 rule="para" parents="33185 33118"/>
    </justification>
  </clause>

  <clause id="33248">
    <literal><![CDATA[
      (a(x,y,z) * u) / z = a(x,y,z) * (u / z)
    ]]></literal>
    <justification jstring="[hyper(225,a,33236,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 33236 10262"/>
    </justification>
  </clause>

  <clause id="33249">
    <literal><![CDATA[
      a(x,y,z) * (z * u) = z * (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,33236,a(flip),b,28734,a),flip(a)].">
      <j1 rule="hyper" parents="144 33236 28734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33250">
    <literal><![CDATA[
      L(x,y,a(z,u,L(x,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,30,a,b,33236,a(flip))].">
      <j1 rule="hyper" parents="42 30 33236"/>
    </justification>
  </clause>

  <clause id="33251">
    <literal><![CDATA[
      L(R(x,y,z),u,a(w,v5,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(33236(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33236 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33252">
    <literal><![CDATA[
      L(L(x,y,z),u,a(w,v5,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(33236(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33236 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33254">
    <literal><![CDATA[
      (a(x,y,z) * u) * L(z,w,v5) = a(x,y,z) * (u * L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(33236(a,1),513(a,1,2,1))].">
      <j1 rule="para" parents="33236 513"/>
    </justification>
  </clause>

  <clause id="33255">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,a(w,v5,x)) = x \ L(R(x,y,z),u,a(w,v5,x))
    ]]></literal>
    <justification jstring="[para(33236(a,1),4243(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33236 4243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33256">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * (v5 * w)) = a(x,y,w * (a(z,u,w) * v5))
    ]]></literal>
    <justification jstring="[para(33236(a,1),27300(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="33236 27300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33257">
    <literal><![CDATA[
      L(x,y,z \ R(z,u,x)) = x
    ]]></literal>
    <justification jstring="[para(28073(a,1),33236(a,1,3))].">
      <j1 rule="para" parents="28073 33236"/>
    </justification>
  </clause>

  <clause id="33259">
    <literal><![CDATA[
      (R(x,y,z) * u) * a(w,v5,x) = R(x,y,z) * (u * a(w,v5,x))
    ]]></literal>
    <justification jstring="[para(33237(a,1),506(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="33237 506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33260">
    <literal><![CDATA[
      (L(x,y,z) * u) * a(w,v5,x) = L(x,y,z) * (u * a(w,v5,x))
    ]]></literal>
    <justification jstring="[para(33237(a,1),510(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="33237 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33261">
    <literal><![CDATA[
      L(x,y,z \ L(z,u,x)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,33124,a(flip),b,33257,a)].">
      <j1 rule="hyper" parents="64 33124 33257"/>
    </justification>
  </clause>

  <clause id="33262">
    <literal><![CDATA[
      L(x,y,z * L(z,u,x)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,5608,a(flip),b,33261,a)].">
      <j1 rule="hyper" parents="64 5608 33261"/>
    </justification>
  </clause>

  <clause id="33263">
    <literal><![CDATA[
      L(x,y,L(z,u,x) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,9385,a,b,33262,a)].">
      <j1 rule="hyper" parents="64 9385 33262"/>
    </justification>
  </clause>

  <clause id="33264">
    <literal><![CDATA[
      R(L(x,y,z) \ x,u,L(z,u,L(x,y,z) \ x)) = (z * u) \ ((z * u) * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(33263(a,1),25191(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="33263 25191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33265">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * ((a(x,y,L(z,u,w)) \ v5) * z) = v5 * z
    ]]></literal>
    <justification jstring="[hyper(145,a,33250,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 33250 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33266">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * (z * v5) = z * (a(x,y,L(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(144,a,33250,a(flip),b,28734,a),flip(a)].">
      <j1 rule="hyper" parents="144 33250 28734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33267">
    <literal><![CDATA[
      L(R(x,y,z),u,a(w,v5,L(x,v6,v7))) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(33250(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33250 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33268">
    <literal><![CDATA[
      L(L(x,y,z),u,a(w,v5,L(x,v6,v7))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(33250(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33250 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33269">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,a(w,v5,L(x,v6,v7))) = x \ L(R(x,y,z),u,a(w,v5,L(x,v6,v7)))
    ]]></literal>
    <justification jstring="[para(33250(a,1),4243(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33250 4243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33270">
    <literal><![CDATA[
      x \ (y \ ((y * x) * L(x,z,u))) = L(x,z,u) * a(y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(33250(a,1),30024(a,1,1))].">
      <j1 rule="para" parents="33250 30024"/>
    </justification>
  </clause>

  <clause id="33271">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u,L(R(z,w,v5),u,a(x,y,z))) = ((a(x,y,z) \ 1) * (u * R(z,w,v5))) / (u * R(z,w,v5))
    ]]></literal>
    <justification jstring="[para(33251(a,1),1634(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="33251 1634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33272">
    <literal><![CDATA[
      a(a(x,y,z),u,L(z,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,33252,a)].">
      <j1 rule="hyper" parents="54 33252"/>
    </justification>
  </clause>

  <clause id="33274">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(z,w,v5)) = (a(x,y,z) \ u) * L(z,w,v5)
    ]]></literal>
    <justification jstring="[para(33252(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="33252 598"/>
    </justification>
  </clause>

  <clause id="33275">
    <literal><![CDATA[
      (x \ ((x * y) * z)) / z = y * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(142,a,29944,a,b,33196,a)].">
      <j1 rule="hyper" parents="142 29944 33196"/>
    </justification>
  </clause>

  <clause id="33276">
    <literal><![CDATA[
      (x \ y) / ((x * z) \ y) = z * a(x,z,(x * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(142,a,29961,a(flip),b,33196,a)].">
      <j1 rule="hyper" parents="142 29961 33196"/>
    </justification>
  </clause>

  <clause id="33277">
    <literal><![CDATA[
      (x * a(y,x,L(z,x,y))) \ (x * z) = L(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,30029,a(flip),b,33196,a)].">
      <j1 rule="hyper" parents="139 30029 33196"/>
    </justification>
  </clause>

  <clause id="33278">
    <literal><![CDATA[
      (x * y) * a(L(y,x,z),x,z) = x * R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,32963,a(flip),b,33196,a),flip(a)].">
      <j1 rule="hyper" parents="36 32963 33196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33279">
    <literal><![CDATA[
      (x \ ((x * y) * z)) / z = a(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a,b,33275,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 33275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33280">
    <literal><![CDATA[
      a(x,y,z) = y \ ((x \ ((x * y) * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(139,a,33275,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="139 33275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33281">
    <literal><![CDATA[
      (x / ((y \ ((y * z) * u)) / u)) * (z * a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,33275,a(flip),b,82,a)].">
      <j1 rule="hyper" parents="145 33275 82"/>
    </justification>
  </clause>

  <clause id="33282">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),y) = ((x \ ((x * y) * z)) / z) \ y
    ]]></literal>
    <justification jstring="[para(33275(a,2),241(a,2,1))].">
      <j1 rule="para" parents="33275 241"/>
    </justification>
  </clause>

  <clause id="33283">
    <literal><![CDATA[
      ((x * y) \ ((x * y) * R(z,x,y))) / a(z,x,y) = z * a(x * y,z,a(z,x,y))
    ]]></literal>
    <justification jstring="[para(15980(a,1),33275(a,1,1,2))].">
      <j1 rule="para" parents="15980 33275"/>
    </justification>
  </clause>

  <clause id="33284">
    <literal><![CDATA[
      (x \ (R(x,y,y) * z)) / z = a(x,y,y) * a(x,a(x,y,y),z)
    ]]></literal>
    <justification jstring="[para(15984(a,1),33275(a,1,1,2,1))].">
      <j1 rule="para" parents="15984 33275"/>
    </justification>
  </clause>

  <clause id="33285">
    <literal><![CDATA[
      L((x \ ((x * y) * z)) / z,u,w) = L(a(x,y,z) * y,u,w)
    ]]></literal>
    <justification jstring="[para(33275(a,2),23910(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33275 23910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33286">
    <literal><![CDATA[
      a(x \ (y \ ((y * z) * x)),u,w) = a(z * a(y,z,x),u,w)
    ]]></literal>
    <justification jstring="[para(33275(a,1),26785(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33275 26785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33287">
    <literal><![CDATA[
      ((x \ ((x * y) * z)) / z) \ ((y * u) * a(x,y,z)) = L(u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(33275(a,2),26739(a,1,1))].">
      <j1 rule="para" parents="33275 26739"/>
    </justification>
  </clause>

  <clause id="33288">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * w) * z))) = a(x,y,w * a(u,w,z))
    ]]></literal>
    <justification jstring="[para(33275(a,1),27308(a,1,3)),flip(a)].">
      <j1 rule="para" parents="33275 27308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33289">
    <literal><![CDATA[
      T(x / ((y \ ((y * z) * u)) / u),z) = (a(y,z,u) * z) \ x
    ]]></literal>
    <justification jstring="[para(33275(a,2),28735(a,1,1,2))].">
      <j1 rule="para" parents="33275 28735"/>
    </justification>
  </clause>

  <clause id="33290">
    <literal><![CDATA[
      L(x,L(a(y,z,u),a(y,z,u),z),w) = L(x,((y \ ((y * z) * u)) / u) \ z,w)
    ]]></literal>
    <justification jstring="[para(33275(a,2),29723(a,2,2,1))].">
      <j1 rule="para" parents="33275 29723"/>
    </justification>
  </clause>

  <clause id="33291">
    <literal><![CDATA[
      a(x,y,z) \ (u \ ((u * w) * a(x,y,z))) = a(u,w,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(23179,a,33279,a)].">
      <j1 rule="hyper" parents="23179 33279"/>
    </justification>
  </clause>

  <clause id="33292">
    <literal><![CDATA[
      ((x \ ((x * y) * z)) / z) * L(y \ 1,y,a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,33279,a,b,441,a)].">
      <j1 rule="hyper" parents="144 33279 441"/>
    </justification>
  </clause>

  <clause id="33293">
    <literal><![CDATA[
      L(x,(y \ ((y * z) * u)) / u,w) = L(x,z * a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(33279(a,2),23193(a,1,2))].">
      <j1 rule="para" parents="33279 23193"/>
    </justification>
  </clause>

  <clause id="33294">
    <literal><![CDATA[
      a(x,y \ (z \ ((z * u) * y)),w) = a(x,a(z,u,y) * u,w)
    ]]></literal>
    <justification jstring="[para(33279(a,1),31895(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33279 31895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33296">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (((x * L(x \ 1,y,z)) * (x \ u)) / u) = a(x,L(x \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(3101(a,1),33280(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3101 33280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33297">
    <literal><![CDATA[
      (x \ L(y,x \ a(z,u,x),x)) * a(z,u,x) = (x \ a(z,u,x)) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,23187,a(flip),b,33197,a),flip(a)].">
      <j1 rule="hyper" parents="35 23187 33197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33298">
    <literal><![CDATA[
      (x * a(y,z,u)) / u = a(y,z,u) * (x / u)
    ]]></literal>
    <justification jstring="[hyper(142,a,33197,a(flip),b,28742,a)].">
      <j1 rule="hyper" parents="142 33197 28742"/>
    </justification>
  </clause>

  <clause id="33299">
    <literal><![CDATA[
      a(x,y,z) * u != z * (w * a(x,y,z))
    ]]></literal>
    <literal><![CDATA[
      z * w = u
    ]]></literal>
    <justification jstring="[para(33200(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="33200 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33300">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * a(y,y,x))) = L(z,y,x) * a(y,y,x)
    ]]></literal>
    <justification jstring="[para(33200(a,1),30738(a,1,2))].">
      <j1 rule="para" parents="33200 30738"/>
    </justification>
  </clause>

  <clause id="33301">
    <literal><![CDATA[
      (x * a(y,z,x)) \ (x * (u * a(y,z,x))) = L(u,T(x,a(y,z,x)),a(y,z,x))
    ]]></literal>
    <justification jstring="[para(33200(a,1),23186(a,1,2))].">
      <j1 rule="para" parents="33200 23186"/>
    </justification>
  </clause>

  <clause id="33303">
    <literal><![CDATA[
      x * (a(y,z,x) \ (y * z)) = L(x,z,y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,15715,a(flip),b,33206,a),flip(a)].">
      <j1 rule="hyper" parents="64 15715 33206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33304">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * z) \ (u * z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(783,a,33207,a)].">
      <j1 rule="hyper" parents="783 33207"/>
    </justification>
  </clause>

  <clause id="33305">
    <literal><![CDATA[
      (a(x,y,L(z,y,x)) * y) \ (y * z) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,30029,a(flip),b,33207,a)].">
      <j1 rule="hyper" parents="139 30029 33207"/>
    </justification>
  </clause>

  <clause id="33306">
    <literal><![CDATA[
      a(L(x,y,z),y,z) * (y * x) = y * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,32963,a(flip),b,33207,a),flip(a)].">
      <j1 rule="hyper" parents="36 32963 33207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33307">
    <literal><![CDATA[
      a(L(x,y,z),y,z) * (x * y) = R(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(36,a,32601,a(flip),b,33207,a),flip(a)].">
      <j1 rule="hyper" parents="36 32601 33207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33308">
    <literal><![CDATA[
      x \ (a(y,z,x) * u) = a(y,z,x) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(36,a,33049,a,b,33208,a)].">
      <j1 rule="hyper" parents="36 33049 33208"/>
    </justification>
  </clause>

  <clause id="33309">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (u * z) = ((a(x,y,z) \ 1) \ u) * z
    ]]></literal>
    <justification jstring="[hyper(35,a,1589,a(flip),b,33208,a(flip))].">
      <j1 rule="hyper" parents="35 1589 33208"/>
    </justification>
  </clause>

  <clause id="33310">
    <literal><![CDATA[
      a(x,y,z) * ((x \ 1) * z) = (x \ a(x,y,z)) * z
    ]]></literal>
    <justification jstring="[para(23929(a,1),33208(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23929 33208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33311">
    <literal><![CDATA[
      (x * (a(y,z,u) * u)) \ (a(y,z,u) * (x * u)) = a(x,a(y,z,u),u)
    ]]></literal>
    <justification jstring="[para(33208(a,1),23940(a,1,2))].">
      <j1 rule="para" parents="33208 23940"/>
    </justification>
  </clause>

  <clause id="33312">
    <literal><![CDATA[
      (a(x,y,z) \ x) * z = x * (a(x,y,z) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29923,a(flip),b,33214,a),flip(a)].">
      <j1 rule="hyper" parents="64 29923 33214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33313">
    <literal><![CDATA[
      (a(x,y,z) \ (x * y)) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,15467,a(flip),b,33214,a),flip(a)].">
      <j1 rule="hyper" parents="64 15467 33214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33314">
    <literal><![CDATA[
      a(x,x \ y,z) \ y = (x * ((x \ y) * z)) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,15481,a(flip),b,33214,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="142 15481 33214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33315">
    <literal><![CDATA[
      a(x,y,z) \ (x * y) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,15467,a(flip),b,33214,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="142 15467 33214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33316">
    <literal><![CDATA[
      a(x,y,z) \ (z \ u) = z \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(36,a,33053,a(flip),b,33214,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 33053 33214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33317">
    <literal><![CDATA[
      (x * (a(x,y,z) \ y)) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[para(29923(a,1),33313(a,1,1))].">
      <j1 rule="para" parents="29923 33313"/>
    </justification>
  </clause>

  <clause id="33318">
    <literal><![CDATA[
      a(x,y,z) = (x * y) / ((x * (y * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(226,a,33315,a),flip(a)].">
      <j1 rule="hyper" parents="226 33315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33319">
    <literal><![CDATA[
      (x * (y * z)) / z = (x * y) / a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23133,a,b,33315,a),flip(a)].">
      <j1 rule="hyper" parents="64 23133 33315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33320">
    <literal><![CDATA[
      (x * (y * z)) / z = x * (a(x,y,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29923,a(flip),b,33315,a),flip(a)].">
      <j1 rule="hyper" parents="64 29923 33315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33321">
    <literal><![CDATA[
      a(x,y,z) = ((x * (y * z)) / z) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(40,a,31211,a,b,33315,a),flip(a)].">
      <j1 rule="hyper" parents="40 31211 33315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33322">
    <literal><![CDATA[
      a(x,y,z) \ y = x \ ((x * (y * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(139,a,33315,a(flip),b,29923,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 33315 29923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33323">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ y,x,a(z,u,w)) = (a(z,u,w) * x) \ (x * (y * a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(33317(a,1),23171(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33317 23171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33324">
    <literal><![CDATA[
      K(x,(a(y,z,x) \ z) * y) * ((x * y) \ (y * (z * x))) = L(a(y,z,x) \ z,y,x)
    ]]></literal>
    <justification jstring="[para(33317(a,1),27292(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="33317 27292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33325">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w) \ u,z,w)) = L(x,y,(w * z) \ (z * (u * w)))
    ]]></literal>
    <justification jstring="[para(33317(a,1),29008(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="33317 29008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33326">
    <literal><![CDATA[
      L(x,y * (z * (a(z,u,y \ 1) \ u)),w) = L(x,z * (u * (y \ 1)),w)
    ]]></literal>
    <justification jstring="[para(33317(a,1),29520(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33317 29520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33327">
    <literal><![CDATA[
      ((a(x,y,z) \ y) * z) \ (x \ (x * (y * z))) = a(x,a(x,y,z) \ y,z)
    ]]></literal>
    <justification jstring="[para(33317(a,1),30027(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="33317 30027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33328">
    <literal><![CDATA[
      a(L(a(x,y,z) \ y,x,z),u,w) = a((z * x) \ (x * (y * z)),u,w)
    ]]></literal>
    <justification jstring="[para(33317(a,1),32405(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="33317 32405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33329">
    <literal><![CDATA[
      (x * y) / ((x * z) / (y \ z)) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(10(a,1),33318(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 33318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33330">
    <literal><![CDATA[
      (x * R(y,z,u)) / ((x * (y * R(y,z,u))) / y) = a(x,R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(274(a,1),33318(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="274 33318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33331">
    <literal><![CDATA[
      (x * y) / ((x * L(z,y,y)) / ((y \ 1) * z)) = a(x,y,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(1139(a,1),33318(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1139 33318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33332">
    <literal><![CDATA[
      (((x / y) * (y * z)) / z) \ x = a(x / y,y,z)
    ]]></literal>
    <justification jstring="[para(33319(a,2),387(a,1,1))].">
      <j1 rule="para" parents="33319 387"/>
    </justification>
  </clause>

  <clause id="33333">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ y = x \ (a(z,u,w) \ (x * (y * a(z,u,w))))
    ]]></literal>
    <justification jstring="[hyper(139,a,23133,a(flip),b,33320,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 23133 33320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33334">
    <literal><![CDATA[
      ((x * y) / (z \ y)) \ (x * z) = a(x,z,z \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),33321(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 33321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33335">
    <literal><![CDATA[
      ((x * R(y,z,z)) / y) \ (x * a(y,z,z)) = a(x,a(y,z,z),y)
    ]]></literal>
    <justification jstring="[para(15998(a,1),33321(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15998 33321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33336">
    <literal><![CDATA[
      ((x / y) \ (x * a(z,u,w))) \ (a(z,u,w) * y) = a(a(z,u,w),y,y \ x)
    ]]></literal>
    <justification jstring="[para(28816(a,1),33321(a,2,1)),flip(a)].">
      <j1 rule="para" parents="28816 33321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33337">
    <literal><![CDATA[
      (((x * y) * z) / (y * z)) \ (x * a(x,y,z)) = a(x,a(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[para(30023(a,1),33321(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="30023 33321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33338">
    <literal><![CDATA[
      a(x,y,z) = y / (x \ ((x * (y * z)) / z))
    ]]></literal>
    <justification jstring="[hyper(226,a,33322,a),flip(a)].">
      <j1 rule="hyper" parents="226 33322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33339">
    <literal><![CDATA[
      a(x * y,z,u) \ z = (y * x) \ (((y * x) * (z * u)) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26835,a,b,33322,a)].">
      <j1 rule="hyper" parents="64 26835 33322"/>
    </justification>
  </clause>

  <clause id="33340">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),y) = y \ (x \ ((x * (y * z)) / z))
    ]]></literal>
    <justification jstring="[hyper(139,a,33322,a(flip),b,25198,a),flip(a)].">
      <j1 rule="hyper" parents="139 33322 25198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33341">
    <literal><![CDATA[
      a(x,y,y \ 1) \ y = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(72(a,1),33322(a,2,2,1))].">
      <j1 rule="para" parents="72 33322"/>
    </justification>
  </clause>

  <clause id="33342">
    <literal><![CDATA[
      R(x,y,z) \ (((x * y) * z) / z) = a(R(x,y,z),y,z) \ y
    ]]></literal>
    <justification jstring="[para(111(a,1),33322(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="111 33322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33344">
    <literal><![CDATA[
      L(x,x,a(x,y,z) \ y) = L(x,x,x * ((x * (y * z)) / z))
    ]]></literal>
    <justification jstring="[para(33322(a,2),25574(a,1,3))].">
      <j1 rule="para" parents="33322 25574"/>
    </justification>
  </clause>

  <clause id="33345">
    <literal><![CDATA[
      a(x,y,a(z,u,w) \ u) = a(x,y,z \ (w \ (z * (u * w))))
    ]]></literal>
    <justification jstring="[para(33322(a,2),27322(a,1,3))].">
      <j1 rule="para" parents="33322 27322"/>
    </justification>
  </clause>

  <clause id="33346">
    <literal><![CDATA[
      a(L(a(x,y,z),a(x,y,z),y),u,w) = a(y \ (x \ ((x * (y * z)) / z)),u,w)
    ]]></literal>
    <justification jstring="[para(33322(a,1),26062(a,2,1,2))].">
      <j1 rule="para" parents="33322 26062"/>
    </justification>
  </clause>

  <clause id="33348">
    <literal><![CDATA[
      a(a(x,y,z) \ y,u,w) = a(x \ (z \ (x * (y * z))),u,w)
    ]]></literal>
    <justification jstring="[para(33322(a,2),32369(a,1,1))].">
      <j1 rule="para" parents="33322 32369"/>
    </justification>
  </clause>

  <clause id="33349">
    <literal><![CDATA[
      R(x,y,y \ 1) \ (x * y) = a(x,y,y \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,30693,a,b,33341,a)].">
      <j1 rule="hyper" parents="373 30693 33341"/>
    </justification>
  </clause>

  <clause id="33350">
    <literal><![CDATA[
      (x \ (y * ((x \ y) \ 1))) \ (x \ y) = x \ (x / ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(980(a,1),33341(a,1,1))].">
      <j1 rule="para" parents="980 33341"/>
    </justification>
  </clause>

  <clause id="33351">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) \ y = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(33341(a,1),23134(a,1,1))].">
      <j1 rule="para" parents="33341 23134"/>
    </justification>
  </clause>

  <clause id="33352">
    <literal><![CDATA[
      x \ (L(1 / x,x,y) \ 1) = a(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,30656,a(flip),b,33351,a)].">
      <j1 rule="hyper" parents="64 30656 33351"/>
    </justification>
  </clause>

  <clause id="33353">
    <literal><![CDATA[
      (x \ a(y * x,x,x)) * x = a(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,30717,a(flip),b,33228,a)].">
      <j1 rule="hyper" parents="64 30717 33228"/>
    </justification>
  </clause>

  <clause id="33354">
    <literal><![CDATA[
      ((x \ 1) \ y) * a(y * x,x,x \ 1) = (1 / x) \ R(y,x,x)
    ]]></literal>
    <justification jstring="[para(33230(a,1),5303(a,1,2))].">
      <j1 rule="para" parents="33230 5303"/>
    </justification>
  </clause>

  <clause id="33357">
    <literal><![CDATA[
      ((a(x,y,z) * u) \ (a(x,y,z) * (u / z))) \ (1 / z) = a(a(x,y,z) * u,z,z)
    ]]></literal>
    <justification jstring="[para(33248(a,1),30472(a,1,1,2))].">
      <j1 rule="para" parents="33248 30472"/>
    </justification>
  </clause>

  <clause id="33359">
    <literal><![CDATA[
      L(1 / x,x,y) \ 1 = a(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(39,a,23174,a,b,33352,a),flip(a)].">
      <j1 rule="hyper" parents="39 23174 33352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33360">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * a(y,x,x \ 1) = 1
    ]]></literal>
    <justification jstring="[para(33352(a,1),9399(a,1,2))].">
      <j1 rule="para" parents="33352 9399"/>
    </justification>
  </clause>

  <clause id="33361">
    <literal><![CDATA[
      a(x,y,y \ 1) \ 1 = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(23920,a,33360,a)].">
      <j1 rule="hyper" parents="23920 33360"/>
    </justification>
  </clause>

  <clause id="33362">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ 1 = a(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(149,a,33360,a)].">
      <j1 rule="hyper" parents="149 33360"/>
    </justification>
  </clause>

  <clause id="33363">
    <literal><![CDATA[
      (a(x,y,y \ 1) \ 1) * z = (y * ((x * y) \ x)) * z
    ]]></literal>
    <justification jstring="[hyper(144,a,33361,a,b,11,a)].">
      <j1 rule="hyper" parents="144 33361 11"/>
    </justification>
  </clause>

  <clause id="33364">
    <literal><![CDATA[
      x \ (a(y,x,x \ 1) \ 1) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,33361,a,b,439,a)].">
      <j1 rule="hyper" parents="139 33361 439"/>
    </justification>
  </clause>

  <clause id="33365">
    <literal><![CDATA[
      x * (y * ((x * y) \ x)) = a(x,y,y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,33361,a(flip),b,29932,a)].">
      <j1 rule="hyper" parents="145 33361 29932"/>
    </justification>
  </clause>

  <clause id="33366">
    <literal><![CDATA[
      a((a(x,(y * y) \ z,((y * y) \ z) \ 1) \ 1) * u,w,v5) = a((z * ((x * ((y * y) \ z)) \ x)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(33361(a,2),2658(a,1,1,1))].">
      <j1 rule="para" parents="33361 2658"/>
    </justification>
  </clause>

  <clause id="33367">
    <literal><![CDATA[
      K(x,y) * (z * ((u * z) \ u)) = a(u,z,z \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(33361(a,1),19253(a,1,2))].">
      <j1 rule="para" parents="33361 19253"/>
    </justification>
  </clause>

  <clause id="33368">
    <literal><![CDATA[
      a(x * (y * ((z * y) \ z)),u,w) = a(x * a(z,y,y \ 1),u,w)
    ]]></literal>
    <justification jstring="[para(33361(a,1),26850(a,1,1,2))].">
      <j1 rule="para" parents="33361 26850"/>
    </justification>
  </clause>

  <clause id="33369">
    <literal><![CDATA[
      a(x,y,L(a(z,u,u \ 1) \ 1,w,v5)) = a(x,y,L(((z * u) \ z) * u,w,v5))
    ]]></literal>
    <justification jstring="[para(33361(a,2),27377(a,1,3,1))].">
      <j1 rule="para" parents="33361 27377"/>
    </justification>
  </clause>

  <clause id="33370">
    <literal><![CDATA[
      x * L(((y * x) \ y) \ 1,(y * x) \ y,a(y,x,x \ 1) \ 1) = x / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(33361(a,2),30670(a,1,2,3))].">
      <j1 rule="para" parents="33361 30670"/>
    </justification>
  </clause>

  <clause id="33371">
    <literal><![CDATA[
      a(x,L(a(y,z,z \ 1) \ 1,u,w),v5) = a(x,L(((y * z) \ y) * z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(33361(a,2),31956(a,1,2,1))].">
      <j1 rule="para" parents="33361 31956"/>
    </justification>
  </clause>

  <clause id="33372">
    <literal><![CDATA[
      ((x * y) \ x) \ (y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27962,a(flip),b,33362,a)].">
      <j1 rule="hyper" parents="64 27962 33362"/>
    </justification>
  </clause>

  <clause id="33373">
    <literal><![CDATA[
      ((x * y) \ x) * a(x,y,y \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(145,a,33362,a(flip),b,27962,a(flip))].">
      <j1 rule="hyper" parents="145 33362 27962"/>
    </justification>
  </clause>

  <clause id="33374">
    <literal><![CDATA[
      (x \ 1) \ a(y,x,x \ 1) = L(x \ 1,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(33372(a,1),1857(a,1,2))].">
      <j1 rule="para" parents="33372 1857"/>
    </justification>
  </clause>

  <clause id="33375">
    <literal><![CDATA[
      a(x,y,y \ 1) \ (y \ 1) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(33372(a,1),5586(a,1,1))].">
      <j1 rule="para" parents="33372 5586"/>
    </justification>
  </clause>

  <clause id="33376">
    <literal><![CDATA[
      (x \ a(x * y,x,x)) * x = a(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(26016(a,1),33353(a,1,1,2))].">
      <j1 rule="para" parents="26016 33353"/>
    </justification>
  </clause>

  <clause id="33377">
    <literal><![CDATA[
      R(x,y,a(z,u,u \ 1) * w) = R(x,y,w * a(z * u,u,u))
    ]]></literal>
    <justification jstring="[para(33353(a,1),26249(a,1,3,1))].">
      <j1 rule="para" parents="33353 26249"/>
    </justification>
  </clause>

  <clause id="33378">
    <literal><![CDATA[
      L(1 / x,x,y * x) \ 1 = a(y,x,x) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,30743,a(flip),b,33359,a),flip(a)].">
      <j1 rule="hyper" parents="373 30743 33359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33379">
    <literal><![CDATA[
      1 / ((x * y) \ x) = a(x,y,y \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,4307,a(flip),b,33359,a)].">
      <j1 rule="hyper" parents="64 4307 33359"/>
    </justification>
  </clause>

  <clause id="33380">
    <literal><![CDATA[
      1 / ((x * y) \ x) = y * a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a(flip),b,33379,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 33379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33381">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) \ ((1 / (1 / a(x,y,y \ 1))) * z) = (y * ((a(x,y,y \ 1) \ 1) \ 1)) \ (a(x,y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(33380(a,2),3918(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33380 3918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33382">
    <literal><![CDATA[
      L(a(x,y,y \ 1),z,u) \ K(y \ a(y * x,y,y),y) = L(y * (y \ a(y * x,y,y)),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(33376(a,1),26149(a,1,1,1))].">
      <j1 rule="para" parents="33376 26149"/>
    </justification>
  </clause>

  <clause id="33383">
    <literal><![CDATA[
      a(x,y,a(z,u,u \ 1) * w) = a(x,y,w * a(u * z,u,u))
    ]]></literal>
    <justification jstring="[para(33376(a,1),27476(a,1,3,1))].">
      <j1 rule="para" parents="33376 27476"/>
    </justification>
  </clause>

  <clause id="33384">
    <literal><![CDATA[
      a(a(x * y,x,x) * z,u,w) = a(z * a(y,x,x \ 1),u,w)
    ]]></literal>
    <justification jstring="[para(33376(a,1),32512(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="33376 32512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33385">
    <literal><![CDATA[
      L(a(x,y,a(y,z,u)),w,y) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(31843(a,1),33194(a,1,1))].">
      <j1 rule="para" parents="31843 33194"/>
    </justification>
  </clause>

  <clause id="33386">
    <literal><![CDATA[
      R(1 / x,y,y \ 1) \ L(z,(x / (y \ 1)) / y,(x / (y \ 1)) / y) = ((x / (y \ 1)) / y) * z
    ]]></literal>
    <justification jstring="[para(33235(a,1),561(a,1,1))].">
      <j1 rule="para" parents="33235 561"/>
    </justification>
  </clause>

  <clause id="33387">
    <literal><![CDATA[
      a(x,y,z) * (z * a(y,z,a(x,y,z))) = y \ (x \ ((x * y) * z))
    ]]></literal>
    <justification jstring="[para(30038(a,2),33240(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30038 33240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33388">
    <literal><![CDATA[
      L(x * a(y / z,x,z),z,y / z) = y \ (((y / z) * x) * T(z,x))
    ]]></literal>
    <justification jstring="[hyper(139,a,33241,a(flip),b,592,a),flip(a)].">
      <j1 rule="hyper" parents="139 33241 592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33389">
    <literal><![CDATA[
      (x * y) \ ((x * z) * T(y,z)) = L(z * a(x,z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,33241,a(flip),b,100,a)].">
      <j1 rule="hyper" parents="139 33241 100"/>
    </justification>
  </clause>

  <clause id="33390">
    <literal><![CDATA[
      a(x,y,R(T(z,u),w,v5) * (v6 * (v7 * a(R(T(z,u),w,v5),v7,v6)))) = a(x,y,(R(z,w,v5) * v7) * T(v6,v7))
    ]]></literal>
    <justification jstring="[para(33241(a,2),27428(a,1,3))].">
      <j1 rule="para" parents="33241 27428"/>
    </justification>
  </clause>

  <clause id="33391">
    <literal><![CDATA[
      (L(x,y,z) * a(x,L(x,y,z),L(u,L(x,y,z),x))) \ (L(x,y,z) * u) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,2482,a(flip),b,33277,a),flip(a)].">
      <j1 rule="hyper" parents="373 2482 33277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33392">
    <literal><![CDATA[
      x * a(y,x,L(z,x,y)) = z * (L(z,x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(40,a,24847,a,b,33277,a),flip(a)].">
      <j1 rule="hyper" parents="40 24847 33277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33393">
    <literal><![CDATA[
      a(L(x,y,z),y,z) = (y * x) \ (y * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(149,a,33278,a),flip(a)].">
      <j1 rule="hyper" parents="149 33278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33394">
    <literal><![CDATA[
      L(((1 / (x * y)) \ a(L(y,x,z),x,z)) / (x * y),x * y,x * y) = (x * R(y,x,z)) / (x * y)
    ]]></literal>
    <justification jstring="[para(33278(a,1),1211(a,2,1))].">
      <j1 rule="para" parents="33278 1211"/>
    </justification>
  </clause>

  <clause id="33395">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) * y = z * (L(z,y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(40,a,24847,a,b,33305,a),flip(a)].">
      <j1 rule="hyper" parents="40 24847 33305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33396">
    <literal><![CDATA[
      x * (a(L(x,y,z),y,z) * y) = R(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,29991,a(flip),b,33307,a)].">
      <j1 rule="hyper" parents="64 29991 33307"/>
    </justification>
  </clause>

  <clause id="33397">
    <literal><![CDATA[
      L(x,y,z) \ ((x * ((x \ L(x,y,z)) * u)) / u) = a(x,x \ L(x,y,z),u) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,33314,a(flip),b,30013,a)].">
      <j1 rule="hyper" parents="139 33314 30013"/>
    </justification>
  </clause>

  <clause id="33398">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) \ L(x,y,z) = (x * ((x \ L(x,y,z)) * u)) / u
    ]]></literal>
    <justification jstring="[para(11978(a,1),33314(a,1,1))].">
      <j1 rule="para" parents="11978 33314"/>
    </justification>
  </clause>

  <clause id="33399">
    <literal><![CDATA[
      (((x / y) * (y * z)) / z) \ x = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,26785,a(flip),b,33332,a),flip(a)].">
      <j1 rule="hyper" parents="373 26785 33332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33400">
    <literal><![CDATA[
      x * (y * L(y \ 1,y,x)) = a(x,y,y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,999,a,b,33365,a)].">
      <j1 rule="hyper" parents="64 999 33365"/>
    </justification>
  </clause>

  <clause id="33401">
    <literal><![CDATA[
      R(x,y,y \ 1) \ x = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(35,a,25511,a,b,33365,a)].">
      <j1 rule="hyper" parents="35 25511 33365"/>
    </justification>
  </clause>

  <clause id="33402">
    <literal><![CDATA[
      R(x,y,(y * x) \ x) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(40,a,26294,a,b,33401,a)].">
      <j1 rule="hyper" parents="40 26294 33401"/>
    </justification>
  </clause>

  <clause id="33403">
    <literal><![CDATA[
      R(x / y,y,y \ 1) \ (x * ((y * (x / y)) \ (x / y))) = y * ((y * (x / y)) \ (x / y))
    ]]></literal>
    <justification jstring="[para(33402(a,1),650(a,1,1))].">
      <j1 rule="para" parents="33402 650"/>
    </justification>
  </clause>

  <clause id="33404">
    <literal><![CDATA[
      (x * y) * a(z,x,a(x,u,w)) = x * (y * a(z,x,a(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(145,a,33385,a(flip),b,5318,a(flip))].">
      <j1 rule="hyper" parents="145 33385 5318"/>
    </justification>
  </clause>

  <clause id="33405">
    <literal><![CDATA[
      x \ (y * a(z,y,L(x,y,z))) = L(x,y,z) \ y
    ]]></literal>
    <justification jstring="[hyper(720,a,33392,a)].">
      <j1 rule="hyper" parents="720 33392"/>
    </justification>
  </clause>

  <clause id="33406">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) = y \ (z * (L(z,y,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(149,a,33392,a),flip(a)].">
      <j1 rule="hyper" parents="149 33392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33407">
    <literal><![CDATA[
      a(x,y,L(y \ z,y,x)) = y \ (L(z / y,y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,25820,a(flip),b,33392,a),flip(a)].">
      <j1 rule="hyper" parents="139 25820 33392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33408">
    <literal><![CDATA[
      R(x,(L(y,z,u) \ z) * y,w) = R(x,z * a(u,z,L(y,z,u)),w)
    ]]></literal>
    <justification jstring="[para(33392(a,2),26409(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33392 26409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33409">
    <literal><![CDATA[
      a(x,(L(y,z,u) \ z) * y,w) = a(x,z * a(u,z,L(y,z,u)),w)
    ]]></literal>
    <justification jstring="[para(33392(a,2),31888(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33392 31888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33410">
    <literal><![CDATA[
      L(a(x,y,z) \ R(a(x,y,z),x,u),x,a(x,y,z)) = a(L(a(x,y,z),x,u),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,30327,a,b,33393,a)].">
      <j1 rule="hyper" parents="373 30327 33393"/>
    </justification>
  </clause>

  <clause id="33411">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,y) = a(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,102,a,b,33393,a)].">
      <j1 rule="hyper" parents="373 102 33393"/>
    </justification>
  </clause>

  <clause id="33412">
    <literal><![CDATA[
      L(a(x,y,y) \ R(a(x,y,y),z,u),a(y,y,x * y),z) = a(L(a(x,y,y),z,u),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30724,a,b,33411,a)].">
      <j1 rule="hyper" parents="64 30724 33411"/>
    </justification>
  </clause>

  <clause id="33413">
    <literal><![CDATA[
      L(L(L(x,y,z),u,w) \ R(L(L(x,y,z),u,w),x,v5),x,L(L(x,y,z),u,w)) = a(L(L(L(x,y,z),u,w),x,v5),x,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29874,a(flip),b,33411,a)].">
      <j1 rule="hyper" parents="64 29874 33411"/>
    </justification>
  </clause>

  <clause id="33414">
    <literal><![CDATA[
      L(a(L(x,y,z),y,z),y * x,y) = L(x,y,y) \ L(x * (x \ R(x,y,z)),y,y)
    ]]></literal>
    <justification jstring="[para(33411(a,1),2290(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33411 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33415">
    <literal><![CDATA[
      L(a(L(x,y,z),y,z),x * y,x * y) = (1 / (y * x)) * (y * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(33411(a,1),29664(a,1,1))].">
      <j1 rule="para" parents="33411 29664"/>
    </justification>
  </clause>

  <clause id="33416">
    <literal><![CDATA[
      ((x * y) * z) * L(x \ R(x,y,z),x,y) = (R(x,y,z) * y) * z
    ]]></literal>
    <justification jstring="[para(33411(a,2),32601(a,1,2))].">
      <j1 rule="para" parents="33411 32601"/>
    </justification>
  </clause>

  <clause id="33417">
    <literal><![CDATA[
      ((x * y) * z) * L(y \ R(y,x,z),y,x) = (x * R(y,x,z)) * z
    ]]></literal>
    <justification jstring="[para(33411(a,2),32963(a,1,2))].">
      <j1 rule="para" parents="33411 32963"/>
    </justification>
  </clause>

  <clause id="33418">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),x,y),u,z) = a(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(33411(a,2),33186(a,1,1))].">
      <j1 rule="para" parents="33411 33186"/>
    </justification>
  </clause>

  <clause id="33419">
    <literal><![CDATA[
      L(x,y,z * a(u,z,L(w,z,u))) = L(x,y,w * (L(w,z,u) \ z))
    ]]></literal>
    <justification jstring="[para(33395(a,1),23253(a,1,3)),flip(a)].">
      <j1 rule="para" parents="33395 23253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33420">
    <literal><![CDATA[
      x * (y * a(L(x,y,z),y,z)) = R(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(23185,a,33396,a)].">
      <j1 rule="hyper" parents="23185 33396"/>
    </justification>
  </clause>

  <clause id="33421">
    <literal><![CDATA[
      a(L(x,y,z),y,z) * y = (y / x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,25045,a,b,33396,a),flip(a)].">
      <j1 rule="hyper" parents="35 25045 33396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33422">
    <literal><![CDATA[
      R(x,y,z) * (x \ y) = a(L(x,y,z),y,z) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,1902,a,b,33396,a)].">
      <j1 rule="hyper" parents="35 1902 33396"/>
    </justification>
  </clause>

  <clause id="33423">
    <literal><![CDATA[
      a(x \ y,x,z) \ y = ((y / x) * (x * z)) / z
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,33399,a)].">
      <j1 rule="hyper" parents="40 23134 33399"/>
    </justification>
  </clause>

  <clause id="33424">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,u,z))) = L(x,y,u \ ((L(w,u,z) \ u) * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(33406(a,2),29131(a,2,3)),flip(a)].">
      <j1 rule="para" parents="33406 29131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33425">
    <literal><![CDATA[
      a(L(x,y,z),y,z) = y \ ((y / x) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,25844,a,b,33421,a),flip(a)].">
      <j1 rule="hyper" parents="36 25844 33421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33426">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),u,w) * u) = a(x,y,(u / z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(33421(a,2),31317(a,1,3))].">
      <j1 rule="para" parents="33421 31317"/>
    </justification>
  </clause>

  <clause id="33427">
    <literal><![CDATA[
      L(x,y,a(L(z,u,w),u,w)) = L(x,y,u \ (R(z,u,w) * (z \ u)))
    ]]></literal>
    <justification jstring="[para(33422(a,2),23842(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="33422 23842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33428">
    <literal><![CDATA[
      a((x \ 1) \ y,x \ 1,a(z,u,x)) \ y = ((y / (x \ 1)) * (x \ a(z,u,x))) / a(z,u,x)
    ]]></literal>
    <justification jstring="[para(9433(a,1),33423(a,2,1,2))].">
      <j1 rule="para" parents="9433 33423"/>
    </justification>
  </clause>

  <clause id="33429">
    <literal><![CDATA[
      a(L(x \ y,y,z),y,z) = y \ (x * R(x \ y,y,z))
    ]]></literal>
    <justification jstring="[para(79(a,1),33425(a,2,2,1))].">
      <j1 rule="para" parents="79 33425"/>
    </justification>
  </clause>

  <clause id="33430">
    <literal><![CDATA[
      L(x,y,z) * ((x \ 1) * (x \ R(x,u,z))) = (1 / x) * L(R(x,u,z),y,z)
    ]]></literal>
    <justification jstring="[para(33222(a,1),27183(a,2,2))].">
      <j1 rule="para" parents="33222 27183"/>
    </justification>
  </clause>

  <clause id="33431">
    <literal><![CDATA[
      R(x,y,z) * (x \ L(x,u,z)) = L(R(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33167,a(flip),b,33223,a)].">
      <j1 rule="hyper" parents="64 33167 33223"/>
    </justification>
  </clause>

  <clause id="33432">
    <literal><![CDATA[
      x * (y * (a(y,z,x) \ z)) = L(x,z,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(29923(a,1),33303(a,1,2))].">
      <j1 rule="para" parents="29923 33303"/>
    </justification>
  </clause>

  <clause id="33433">
    <literal><![CDATA[
      L((x \ 1) \ 1,x,x * y) = a(y,x,x \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,15188,a,b,33349,a)].">
      <j1 rule="hyper" parents="64 15188 33349"/>
    </justification>
  </clause>

  <clause id="33434">
    <literal><![CDATA[
      L(R(x,x,x),x,y * x) = a(y,x,x \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,11933,a,b,33349,a)].">
      <j1 rule="hyper" parents="64 11933 33349"/>
    </justification>
  </clause>

  <clause id="33435">
    <literal><![CDATA[
      a(x,y,(a(z,u,u \ 1) / (u \ 1)) * w) = a(x,y,(L(u \ 1,u,z) \ 1) * w)
    ]]></literal>
    <justification jstring="[para(33374(a,1),27317(a,2,3,1))].">
      <j1 rule="para" parents="33374 27317"/>
    </justification>
  </clause>

  <clause id="33436">
    <literal><![CDATA[
      L(1 / x,x,x * y) \ 1 = a(y,x,x) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24003,a,b,33378,a)].">
      <j1 rule="hyper" parents="64 24003 33378"/>
    </justification>
  </clause>

  <clause id="33437">
    <literal><![CDATA[
      x * (y * L(y \ 1,y,x)) = (x / (y \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,33233,a(flip),b,33400,a),flip(a)].">
      <j1 rule="hyper" parents="373 33233 33400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33438">
    <literal><![CDATA[
      (x \ y) * (x * (y \ (y / x))) = ((x \ y) / (x \ 1)) / x
    ]]></literal>
    <justification jstring="[para(10975(a,1),33437(a,1,2,2))].">
      <j1 rule="para" parents="10975 33437"/>
    </justification>
  </clause>

  <clause id="33439">
    <literal><![CDATA[
      (x \ (x / y)) \ K(y,y * y) = a(x,y,y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30747,a,b,33436,a)].">
      <j1 rule="hyper" parents="64 30747 33436"/>
    </justification>
  </clause>

  <clause id="33441">
    <literal><![CDATA[
      x * (y * a(L(z,x,y),x,x)) = (x * a(z,x,x)) * y
    ]]></literal>
    <justification jstring="[para(32607(a,2),33211(a,1,2,2))].">
      <j1 rule="para" parents="32607 33211"/>
    </justification>
  </clause>

  <clause id="33442">
    <literal><![CDATA[
      L(T(1 / ((x \ ((x * y) * z)) / z),y * a(x,y,z)) \ u,(x \ ((x * y) * z)) / z,y * a(x,y,z)) = 1 \ ((y * a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(33281(a,1),11793(a,2,1))].">
      <j1 rule="para" parents="33281 11793"/>
    </justification>
  </clause>

  <clause id="33443">
    <literal><![CDATA[
      (x * L(x \ y,x,z)) \ y = x \ (L(y / x,x,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30348,a(flip),b,33407,a)].">
      <j1 rule="hyper" parents="64 30348 33407"/>
    </justification>
  </clause>

  <clause id="33444">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * R(z,y,x))) = a(L(z,y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,647,a(flip),b,33418,a)].">
      <j1 rule="hyper" parents="64 647 33418"/>
    </justification>
  </clause>

  <clause id="33445">
    <literal><![CDATA[
      a(L(L(x,y,z) \ x,x,u),x,u) = x \ (L(x,y,z) * L(L(x,y,z) \ x,x,u))
    ]]></literal>
    <justification jstring="[para(28919(a,1),33429(a,2,2,2))].">
      <j1 rule="para" parents="28919 33429"/>
    </justification>
  </clause>

  <clause id="33446">
    <literal><![CDATA[
      x \ (T(y,z) * (u * a(x,w,y))) = (x \ (T(y,z) * u)) * a(x,w,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,33198,a(flip),b,29909,a)].">
      <j1 rule="hyper" parents="139 33198 29909"/>
    </justification>
  </clause>

  <clause id="33447">
    <literal><![CDATA[
      L(x \ 1,y,a(z,u,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(28860,a,33204,a)].">
      <j1 rule="hyper" parents="28860 33204"/>
    </justification>
  </clause>

  <clause id="33448">
    <literal><![CDATA[
      (x \ 1) * ((R(x,x,x) * y) * a(z,u,x)) = L(y,x,x) * a(z,u,x)
    ]]></literal>
    <justification jstring="[para(1665(a,1),33204(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1665 33204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33451">
    <literal><![CDATA[
      L((x \ 1) * L((x \ 1) \ 1,y,z),u,a(w,v5,x)) = (x \ 1) * L(L(x \ 1,u,a(w,v5,x)) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(33447(a,1),4273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33447 4273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33452">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (a(x,y,z) * (u / z)) = L(z \ 1,z,z * u)
    ]]></literal>
    <justification jstring="[para(33447(a,1),30748(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33447 30748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33453">
    <literal><![CDATA[
      (1 / x) \ (a(y,z,x) * u) = ((1 / x) \ u) * a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,23180,a,b,33215,a)].">
      <j1 rule="hyper" parents="64 23180 33215"/>
    </justification>
  </clause>

  <clause id="33454">
    <literal><![CDATA[
      L(x,y,a(z,u,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(14211,a,33226,a)].">
      <j1 rule="hyper" parents="14211 33226"/>
    </justification>
  </clause>

  <clause id="33455">
    <literal><![CDATA[
      a(x,y,z \ 1) * (z * u) = z * (a(x,y,z \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,33454,a(flip),b,28734,a),flip(a)].">
      <j1 rule="hyper" parents="144 33454 28734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33456">
    <literal><![CDATA[
      L(1 / x,y,a(z,u,x)) = 1 / x
    ]]></literal>
    <justification jstring="[para(82(a,1),33454(a,1,3,3))].">
      <j1 rule="para" parents="82 33454"/>
    </justification>
  </clause>

  <clause id="33457">
    <literal><![CDATA[
      L(R(1 / x,y,z),u,a(w,v5,x)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(33456(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33456 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33458">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ u) * T(1 / z,u) = (a(x,y,z) \ 1) \ ((1 / z) * u)
    ]]></literal>
    <justification jstring="[para(33456(a,1),1614(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="33456 1614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33459">
    <literal><![CDATA[
      x * T((a(y,z,x) \ 1) \ u,x) = (a(y,z,x) \ 1) \ (u * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,115,a,b,33309,a)].">
      <j1 rule="hyper" parents="373 115 33309"/>
    </justification>
  </clause>

  <clause id="33460">
    <literal><![CDATA[
      L(x * a(y,x,z * K(x,z)),z * K(x,z),y) = (y * (z * K(x,z))) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(5785(a,1),33389(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5785 33389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33461">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,w),w,a(y,z,u)) = (a(y,z,u) * w) \ (w * (a(y,z,u) * x))
    ]]></literal>
    <justification jstring="[para(28646(a,1),33389(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28646 33389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33462">
    <literal><![CDATA[
      x \ (L(y / x,x,y \ z) \ y) = y / (x * (((z / y) * x) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,25666,a(flip),b,33443,a),flip(a)].">
      <j1 rule="hyper" parents="64 25666 33443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33463">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * a(w,L(z,u,w),u)) = a(x,y,(w * u) \ ((w * z) * u))
    ]]></literal>
    <justification jstring="[para(2847(a,1),33288(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2847 33288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33464">
    <literal><![CDATA[
      a(x,y,z \ (u \ (T(T(w,v5) * u,w) * z))) = a(x,y,R(T(w,T(v5,u)),u,w) * a(u,R(T(w,T(v5,u)),u,w),z))
    ]]></literal>
    <justification jstring="[para(25588(a,1),33288(a,1,3,2,2,1))].">
      <j1 rule="para" parents="25588 33288"/>
    </justification>
  </clause>

  <clause id="33465">
    <literal><![CDATA[
      R(x,y,z) \ (((x * y) * z) / z) = a(L(x,y,z),y,z) \ y
    ]]></literal>
    <justification jstring="[para(32590(a,1),33342(a,2,1))].">
      <j1 rule="para" parents="32590 33342"/>
    </justification>
  </clause>

  <clause id="33466">
    <literal><![CDATA[
      L(x,x,a(x,y,z) \ y) = L(x,x,x * (z \ (x * (y * z))))
    ]]></literal>
    <justification jstring="[hyper(373,a,29018,a(flip),b,33344,a),flip(a)].">
      <j1 rule="hyper" parents="373 29018 33344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33467">
    <literal><![CDATA[
      (x * (y / z)) \ (x * (y * R(L(z \ 1,z,z * y),y,x))) = a(L(L(z \ 1,z,z * y),y,x),y,x)
    ]]></literal>
    <justification jstring="[para(30665(a,1),33444(a,1,1,2))].">
      <j1 rule="para" parents="30665 33444"/>
    </justification>
  </clause>

  <clause id="33468">
    <literal><![CDATA[
      R(x,y,z) \ (x * y) = a(L(x,y,z),y,z) \ y
    ]]></literal>
    <justification jstring="[para(11(a,1),33465(a,1,2))].">
      <j1 rule="para" parents="11 33465"/>
    </justification>
  </clause>

  <clause id="33469">
    <literal><![CDATA[
      a(L(x,y,z),y,z) \ y = x * (R(x,y,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1907,a(flip),b,33468,a),flip(a)].">
      <j1 rule="hyper" parents="64 1907 33468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33471">
    <literal><![CDATA[
      R(x,y,z / a(L(u,z,w),z,w)) = R(x,y,u * (R(u,z,w) \ z))
    ]]></literal>
    <justification jstring="[para(33469(a,1),23813(a,2,3))].">
      <j1 rule="para" parents="33469 23813"/>
    </justification>
  </clause>

  <clause id="33472">
    <literal><![CDATA[
      R(x,a(L(y,z,u),z,u) \ z,w) = R(x,(R(y,z,u) \ z) * y,w)
    ]]></literal>
    <justification jstring="[para(33469(a,2),26409(a,1,2))].">
      <j1 rule="para" parents="33469 26409"/>
    </justification>
  </clause>

  <clause id="33473">
    <literal><![CDATA[
      L(x,(y * a(L(z,y,u),y,u)) \ a(a(L(z,y,u),y,u),a(L(z,y,u),y,u),y),w) = L(x,z * (R(z,y,u) \ y),w)
    ]]></literal>
    <justification jstring="[para(33469(a,1),30945(a,2,2))].">
      <j1 rule="para" parents="33469 30945"/>
    </justification>
  </clause>

  <clause id="33474">
    <literal><![CDATA[
      a(x,a(L(y,z,u),z,u) \ z,w) = a(x,(R(y,z,u) \ z) * y,w)
    ]]></literal>
    <justification jstring="[para(33469(a,2),31888(a,1,2))].">
      <j1 rule="para" parents="33469 31888"/>
    </justification>
  </clause>

  <clause id="33475">
    <literal><![CDATA[
      R(a(x,y,z),u,L(z,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(664,a,33254,a)].">
      <j1 rule="hyper" parents="664 33254"/>
    </justification>
  </clause>

  <clause id="33476">
    <literal><![CDATA[
      L(a(x,y,z),u,L(z,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,28784,a,b,33254,a(flip))].">
      <j1 rule="hyper" parents="36 28784 33254"/>
    </justification>
  </clause>

  <clause id="33477">
    <literal><![CDATA[
      x \ R(x,y \ L(y,z,u),y) = a(x,y \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(43,a,25612,a,b,33475,a)].">
      <j1 rule="hyper" parents="43 25612 33475"/>
    </justification>
  </clause>

  <clause id="33478">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ u) * a(w,v5,x)) = u * a(w,v5,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,33476,a(flip),b,101,a),flip(a)].">
      <j1 rule="hyper" parents="145 33476 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33479">
    <literal><![CDATA[
      L(a(x,y,z),u,(1 / (w / z)) * w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(570(a,1),33476(a,1,3))].">
      <j1 rule="para" parents="570 33476"/>
    </justification>
  </clause>

  <clause id="33480">
    <literal><![CDATA[
      L(a(x,y,z),u,(w / z) * w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2186,a(flip),b,33479,a)].">
      <j1 rule="hyper" parents="64 2186 33479"/>
    </justification>
  </clause>

  <clause id="33481">
    <literal><![CDATA[
      L(a(x,y,z),u,(z \ w) * w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29066,a,33480,a)].">
      <j1 rule="hyper" parents="29066 33480"/>
    </justification>
  </clause>

  <clause id="33482">
    <literal><![CDATA[
      L(x,y,z) * ((z * y) * a(z,y,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16109,a(flip),b,33260,a),flip(a)].">
      <j1 rule="hyper" parents="64 16109 33260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33483">
    <literal><![CDATA[
      x * (L(x,y,z) \ (z * y)) = (z * y) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,2328,a,b,33482,a)].">
      <j1 rule="hyper" parents="35 2328 33482"/>
    </justification>
  </clause>

  <clause id="33484">
    <literal><![CDATA[
      a(x,y,z) = (x * y) \ (z * (L(z,y,x) \ (x * y)))
    ]]></literal>
    <justification jstring="[hyper(720,a,33483,a),flip(a)].">
      <j1 rule="hyper" parents="720 33483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33485">
    <literal><![CDATA[
      x * (L(x,y,z) \ (z * y)) = z * (y * a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,29910,a(flip),b,33483,a),flip(a)].">
      <j1 rule="hyper" parents="373 29910 33483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33486">
    <literal><![CDATA[
      (a(x,y,L(z,y,x)) \ y) * z = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,30195,a,b,33265,a),flip(a)].">
      <j1 rule="hyper" parents="35 30195 33265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33487">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) \ y = (y / z) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,3194,a,b,33486,a),flip(a)].">
      <j1 rule="hyper" parents="36 3194 33486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33488">
    <literal><![CDATA[
      x * (a(y,z,L(x,z,y)) \ z) = L(x,z,y) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,33487,a,b,24852,a)].">
      <j1 rule="hyper" parents="145 33487 24852"/>
    </justification>
  </clause>

  <clause id="33489">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ (z * v5) = z * (a(x,y,L(z,u,w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,33266,a)].">
      <j1 rule="hyper" parents="139 168 33266"/>
    </justification>
  </clause>

  <clause id="33490">
    <literal><![CDATA[
      x \ (y * a(z,u,L(x,w,v5))) = a(z,u,L(x,w,v5)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,23182,a(flip),b,33266,a(flip))].">
      <j1 rule="hyper" parents="139 23182 33266"/>
    </justification>
  </clause>

  <clause id="33491">
    <literal><![CDATA[
      L(x,y,z) * T(a(u,w,x) \ v5,x) = a(u,w,x) \ (v5 * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,23149,a,b,33274,a)].">
      <j1 rule="hyper" parents="373 23149 33274"/>
    </justification>
  </clause>

  <clause id="33492">
    <literal><![CDATA[
      (R(x,y,y) * (x \ z)) / z = a(x,y,y) * a(x,a(x,y,y),z)
    ]]></literal>
    <justification jstring="[para(1898(a,1),33284(a,1,1))].">
      <j1 rule="para" parents="1898 33284"/>
    </justification>
  </clause>

  <clause id="33493">
    <literal><![CDATA[
      (R(x,y,y) * (x \ z)) \ (z * a(x,y,y)) = a(z,a(x,y,y),x)
    ]]></literal>
    <justification jstring="[para(25042(a,1),33335(a,1,1))].">
      <j1 rule="para" parents="25042 33335"/>
    </justification>
  </clause>

  <clause id="33494">
    <literal><![CDATA[
      (x \ (y * ((x \ y) \ 1))) \ (x \ y) = (y * ((x \ y) \ 1)) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,30623,a,b,33350,a),flip(a)].">
      <j1 rule="hyper" parents="373 30623 33350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33495">
    <literal><![CDATA[
      x * ((a(y,z,x) \ 1) \ T(u,x)) = (a(y,z,x) \ 1) \ (u * x)
    ]]></literal>
    <justification jstring="[para(28762(a,1),33459(a,1,2))].">
      <j1 rule="para" parents="28762 33459"/>
    </justification>
  </clause>

  <clause id="33496">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) * (z \ y) = L(z,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,33405,a(flip),b,33490,a),flip(a)].">
      <j1 rule="hyper" parents="64 33405 33490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33497">
    <literal><![CDATA[
      (x \ y) * a(z,y,L(x,y,z)) = L(x,y,z) \ y
    ]]></literal>
    <justification jstring="[hyper(23177,a,33496,a)].">
      <j1 rule="hyper" parents="23177 33496"/>
    </justification>
  </clause>

  <clause id="33498">
    <literal><![CDATA[
      a(x,y,L(z \ y,y,x)) = T(z,z \ y) \ (L(z \ y,y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,422,a,b,33497,a),flip(a)].">
      <j1 rule="hyper" parents="35 422 33497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33499">
    <literal><![CDATA[
      x \ (R(y,z,z) * (y \ x)) = a(y,z,z) * a(y,a(y,z,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25457,a(flip),b,33492,a)].">
      <j1 rule="hyper" parents="64 25457 33492"/>
    </justification>
  </clause>

  <clause id="33500">
    <literal><![CDATA[
      a(x \ y,x,a(x,z,z)) = a(y,a(x,z,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,31598,a(flip),b,33493,a)].">
      <j1 rule="hyper" parents="64 31598 33493"/>
    </justification>
  </clause>

  <clause id="33501">
    <literal><![CDATA[
      a(x \ y,x,a(x,z,z)) = a(y,x,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,31843,a(flip),b,33500,a),flip(a)].">
      <j1 rule="hyper" parents="373 31843 33500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33502">
    <literal><![CDATA[
      x * (T(y,x) / (a(z,u,x) \ 1)) = (a(z,u,x) \ 1) \ (y * x)
    ]]></literal>
    <justification jstring="[para(23737(a,2),33495(a,1,2))].">
      <j1 rule="para" parents="23737 33495"/>
    </justification>
  </clause>

  <clause id="33503">
    <literal><![CDATA[
      a(x,a(x,y,y),z) * R(x,y,y) = x * (z \ (R(x,y,y) * (x \ z)))
    ]]></literal>
    <justification jstring="[para(33499(a,2),30223(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33499 30223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33504">
    <literal><![CDATA[
      x * (T(y,x) / (a(z,u,x) \ 1)) = (y * x) / (a(z,u,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,23737,a,b,33502,a),flip(a)].">
      <j1 rule="hyper" parents="373 23737 33502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33505">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(37,a,29785,a,b,33504,a(flip))].">
      <j1 rule="hyper" parents="37 29785 33504"/>
    </justification>
  </clause>

  <clause id="33506">
    <literal><![CDATA[
      x * ((x \ y) / (a(z,u,x) \ 1)) = y / (a(z,u,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(225,a,33505,a(flip),b,10261,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 33505 10261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33507">
    <literal><![CDATA[
      (x \ 1) * (a(y,z,x) \ 1) = x \ (a(y,z,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(139,a,33505,a(flip),b,1139,a),flip(a)].">
      <j1 rule="hyper" parents="139 33505 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33508">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (z \ 1) = z \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,23736,a,b,33507,a)].">
      <j1 rule="hyper" parents="64 23736 33507"/>
    </justification>
  </clause>

  <clause id="33509">
    <literal><![CDATA[
      L(L((x \ 1) \ y,x \ 1,a(z,u,x) \ 1),x \ (a(z,u,x) \ 1),(x \ 1) * (a(z,u,x) \ 1)) = (1 / ((a(z,u,x) \ 1) * (x \ 1))) * ((a(z,u,x) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(33507(a,1),29664(a,1,2))].">
      <j1 rule="para" parents="33507 29664"/>
    </justification>
  </clause>

  <clause id="33510">
    <literal><![CDATA[
      T(1 / x,y) * (a(z,x,x) \ x) = x * T(x \ (a(z,x,x) \ 1),y)
    ]]></literal>
    <justification jstring="[para(33507(a,1),31642(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="33507 31642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33511">
    <literal><![CDATA[
      x * ((x \ y) / (a(z,u,x) \ 1)) = (a(z,u,x) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,23737,a(flip),b,33506,a),flip(a)].">
      <j1 rule="hyper" parents="373 23737 33506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33512">
    <literal><![CDATA[
      x * ((a(y,z,x) \ 1) \ (x \ u)) = (a(y,z,x) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(23737(a,1),33511(a,1,2))].">
      <j1 rule="para" parents="23737 33511"/>
    </justification>
  </clause>

  <clause id="33513">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ (z * u) = z * ((a(x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),33512(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 33512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33515">
    <literal><![CDATA[
      x * ((a(y,z,x) \ 1) * (x \ u)) = (a(y,z,x) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(733,a,33513,a),flip(a)].">
      <j1 rule="hyper" parents="733 33513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33516">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(y,y,x)))) = L(z,y,x) * a(y,y,x)
    ]]></literal>
    <justification jstring="[para(29910(a,1),33300(a,1,2,2))].">
      <j1 rule="para" parents="29910 33300"/>
    </justification>
  </clause>

  <clause id="33517">
    <literal><![CDATA[
      ((x \ ((x * y) * z)) / z) \ y = y \ (x \ ((x * (y * z)) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33282,a(flip),b,33340,a)].">
      <j1 rule="hyper" parents="64 33282 33340"/>
    </justification>
  </clause>

  <clause id="33518">
    <literal><![CDATA[
      x * (a(y,x,a(z,y,x)) * a(z,y,x)) = y \ (z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,33200,a(flip),b,33387,a)].">
      <j1 rule="hyper" parents="64 33200 33387"/>
    </justification>
  </clause>

  <clause id="33519">
    <literal><![CDATA[
      R(x,y,a(L(z,u,w),u,w) \ u) = R(x,y,z * (R(z,u,w) \ u))
    ]]></literal>
    <justification jstring="[hyper(25233,a,33471,a)].">
      <j1 rule="hyper" parents="25233 33471"/>
    </justification>
  </clause>

  <clause id="33520">
    <literal><![CDATA[
      a(x,y,L(z \ y,y,x)) = z \ (L(y / z,y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,27084,a(flip),b,33498,a),flip(a)].">
      <j1 rule="hyper" parents="373 27084 33498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33521">
    <literal><![CDATA[
      x \ ((x * (a(y,z,u) * w)) / w) = a(y,z,u) * a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(139,a,31790,a,b,33239,a(flip))].">
      <j1 rule="hyper" parents="139 31790 33239"/>
    </justification>
  </clause>

  <clause id="33522">
    <literal><![CDATA[
      a(a(x,y,z),z,u) = a(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23939,a(flip),b,33245,a),flip(a)].">
      <j1 rule="hyper" parents="64 23939 33245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33523">
    <literal><![CDATA[
      a(x,a(L(y,y,z * x),z,x),u) = a(y \ R(y,z,x),x,u)
    ]]></literal>
    <justification jstring="[para(32467(a,1),33522(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32467 33522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33524">
    <literal><![CDATA[
      a(x,y,z) \ ((a(x,y,z) * (z * u)) / u) = a(z,a(x,y,z),u) \ z
    ]]></literal>
    <justification jstring="[para(33522(a,1),33322(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33522 33322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33525">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,a(w,v5,x)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(33251(a,1),33255(a,2,2))].">
      <j1 rule="para" parents="33251 33255"/>
    </justification>
  </clause>

  <clause id="33527">
    <literal><![CDATA[
      L(x,y,z) * a(u,x,L(x,y,z)) = L(x * a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9447,a(flip),b,33270,a),flip(a)].">
      <j1 rule="hyper" parents="64 9447 33270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33528">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * L(z * a(u,z,z),y,x)) = L(a(u,z,L(z,y,x)),L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(33527(a,1),601(a,1,2,2))].">
      <j1 rule="para" parents="33527 601"/>
    </justification>
  </clause>

  <clause id="33530">
    <literal><![CDATA[
      (x \ L(y,x * a(z,u,x),x)) * a(z,u,x) = (x \ a(z,u,x)) * y
    ]]></literal>
    <justification jstring="[para(11879(a,1),33297(a,1,1,2))].">
      <j1 rule="para" parents="11879 33297"/>
    </justification>
  </clause>

  <clause id="33531">
    <literal><![CDATA[
      a(x,a(y,z,u),u) = a(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,25791,a(flip),b,33311,a),flip(a)].">
      <j1 rule="hyper" parents="64 25791 33311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33532">
    <literal><![CDATA[
      L(x,y,a(z,x,a(u,w,x))) = x
    ]]></literal>
    <justification jstring="[para(33531(a,1),33236(a,1,3))].">
      <j1 rule="para" parents="33531 33236"/>
    </justification>
  </clause>

  <clause id="33533">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * (y * w) = y * (a(x,y,a(z,u,y)) * w)
    ]]></literal>
    <justification jstring="[hyper(144,a,33532,a(flip),b,28734,a),flip(a)].">
      <j1 rule="hyper" parents="144 33532 28734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33534">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w) \ u,z,w)) = L(x,y,L(u,w,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,29207,a(flip),b,33325,a),flip(a)].">
      <j1 rule="hyper" parents="373 29207 33325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33535">
    <literal><![CDATA[
      a(L(a(x,y,z) \ y,x,z),u,w) = a(L(y,z,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32785,a(flip),b,33328,a),flip(a)].">
      <j1 rule="hyper" parents="373 32785 33328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33536">
    <literal><![CDATA[
      (x * R(y,z,u)) / ((x * (y * R(y,z,u))) / y) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27647,a(flip),b,33330,a),flip(a)].">
      <j1 rule="hyper" parents="373 27647 33330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33537">
    <literal><![CDATA[
      L(x * a(y \ z,x,y),y,z / y) = z \ (((z / y) * x) * T(y,x))
    ]]></literal>
    <justification jstring="[para(26785(a,1),33388(a,1,1,2))].">
      <j1 rule="para" parents="26785 33388"/>
    </justification>
  </clause>

  <clause id="33538">
    <literal><![CDATA[
      (x \ 1) * (R(x,x,x) * (y * a(z,u,x))) = L(y,x,x) * a(z,u,x)
    ]]></literal>
    <justification jstring="[para(33259(a,1),33448(a,1,2))].">
      <j1 rule="para" parents="33259 33448"/>
    </justification>
  </clause>

  <clause id="33539">
    <literal><![CDATA[
      a(x,a(x,y,y),z) * R(x,y,y) = x * a(L(x,x,z),y,y)
    ]]></literal>
    <justification jstring="[para(32612(a,1),33503(a,2,2))].">
      <j1 rule="para" parents="32612 33503"/>
    </justification>
  </clause>

  <clause id="33540">
    <literal><![CDATA[
      T(1 / x,y) * (a(z,x,x) \ x) = a(z,x,x) \ K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,28719,a(flip),b,33510,a),flip(a)].">
      <j1 rule="hyper" parents="373 28719 33510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33541">
    <literal><![CDATA[
      a(x,y,y) \ K(y \ 1,z) = T(1 / y,z) * L(y,y,x)
    ]]></literal>
    <justification jstring="[para(30459(a,1),33540(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30459 33540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33542">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ a(y,z,u) = a(y,z,u) * a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33322,a,b,33521,a)].">
      <j1 rule="hyper" parents="64 33322 33521"/>
    </justification>
  </clause>

  <clause id="33543">
    <literal><![CDATA[
      L(x * a(y,z,u),u,u) = L(x,u,u) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1665,a(flip),b,33538,a)].">
      <j1 rule="hyper" parents="64 1665 33538"/>
    </justification>
  </clause>

  <clause id="33544">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ a(y,z,u) = a(w,a(y,z,u),x) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a,b,33542,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 33542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33545">
    <literal><![CDATA[
      a(x,a(x,y,z),u) \ 1 = a(u,a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(35,a,31093,a,b,33542,a(flip))].">
      <j1 rule="hyper" parents="35 31093 33542"/>
    </justification>
  </clause>

  <clause id="33546">
    <literal><![CDATA[
      a(x,a(x,y,z),u) \ 1 = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,31843,a(flip),b,33545,a),flip(a)].">
      <j1 rule="hyper" parents="373 31843 33545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33548">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) \ 1 = a(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,33546,a)].">
      <j1 rule="hyper" parents="40 23134 33546"/>
    </justification>
  </clause>

  <clause id="33549">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) \ y = a(y,a(y,z,u),x) * y
    ]]></literal>
    <justification jstring="[para(33546(a,1),29925(a,1,1))].">
      <j1 rule="para" parents="33546 29925"/>
    </justification>
  </clause>

  <clause id="33550">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) \ y = y * a(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(33546(a,1),29926(a,1,1))].">
      <j1 rule="para" parents="33546 29926"/>
    </justification>
  </clause>

  <clause id="33551">
    <literal><![CDATA[
      a(x,y \ z,a(y \ z,y,y)) = a(y \ z,a(y,y,z),x) \ 1
    ]]></literal>
    <justification jstring="[para(32889(a,1),33546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32889 33546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33552">
    <literal><![CDATA[
      a(x,y * z,a(y * z,y,y)) = a(y * z,a(y,y,z),x) \ 1
    ]]></literal>
    <justification jstring="[para(32895(a,1),33546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32895 33546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33553">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) \ x = a(y,a(y,z,u),x) * x
    ]]></literal>
    <justification jstring="[para(33546(a,1),33209(a,1,1))].">
      <j1 rule="para" parents="33546 33209"/>
    </justification>
  </clause>

  <clause id="33554">
    <literal><![CDATA[
      a(x,a(x,y,z),u) \ u = a(u,x,a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(33546(a,1),33213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33546 33213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33555">
    <literal><![CDATA[
      a(x,a(x,y,z),u) \ a(x,y,z) = a(u,x,a(x,y,z)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(33548(a,1),33209(a,1,1))].">
      <j1 rule="para" parents="33548 33209"/>
    </justification>
  </clause>

  <clause id="33558">
    <literal><![CDATA[
      a(x,y \ z,a(y * z,y,y)) = a(y \ z,a(y,y,z),x) \ 1
    ]]></literal>
    <justification jstring="[para(30543(a,1),33551(a,1,3))].">
      <j1 rule="para" parents="30543 33551"/>
    </justification>
  </clause>

  <clause id="33559">
    <literal><![CDATA[
      (a(x,a(y,z,u),w) * a(y,z,u)) \ T(a(y,z,u),a(v5,v6,v7)) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(33544(a,1),23924(a,1,1))].">
      <j1 rule="para" parents="33544 23924"/>
    </justification>
  </clause>

  <clause id="33560">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) / z) \ a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,(y * u) * a(x,y,z))) * ((x \ ((x * y) * z)) / z) = a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(33287(a,1),30155(a,2,3))].">
      <j1 rule="para" parents="33287 30155"/>
    </justification>
  </clause>

  <clause id="33561">
    <literal><![CDATA[
      L(x,y * (z * (a(z,u,y \ 1) \ u)),w) = L(x,(y * u) * z,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29713,a(flip),b,33326,a),flip(a)].">
      <j1 rule="hyper" parents="373 29713 33326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33562">
    <literal><![CDATA[
      a(x,a(x,y,z) \ y,z) = ((a(x,y,z) \ y) * z) \ (y * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),33327(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 33327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33563">
    <literal><![CDATA[
      a(x,a(x,y,z) \ y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,33304,a(flip),b,33562,a),flip(a)].">
      <j1 rule="hyper" parents="373 33304 33562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33566">
    <literal><![CDATA[
      R(x,y,z) \ (x * a(x,y,z)) = a(x,a(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[para(20(a,2),33337(a,1,1))].">
      <j1 rule="para" parents="20 33337"/>
    </justification>
  </clause>

  <clause id="33567">
    <literal><![CDATA[
      x * (R(x,y,z) \ a(x,y,z)) = a(x,a(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1907,a(flip),b,33566,a)].">
      <j1 rule="hyper" parents="64 1907 33566"/>
    </justification>
  </clause>

  <clause id="33568">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),y) = a(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,24822,a(flip),b,33143,a),flip(a)].">
      <j1 rule="hyper" parents="64 24822 33143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33569">
    <literal><![CDATA[
      x \ R(x,y \ L(y,z,u),y) = a(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,33477,a,b,33568,a)].">
      <j1 rule="hyper" parents="64 33477 33568"/>
    </justification>
  </clause>

  <clause id="33570">
    <literal><![CDATA[
      a(x,y * L(y,z,u),y) = a(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11978,a(flip),b,33568,a)].">
      <j1 rule="hyper" parents="64 11978 33568"/>
    </justification>
  </clause>

  <clause id="33571">
    <literal><![CDATA[
      a(x \ L(x,y,z),x,u) = a(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15468,a(flip),b,33166,a),flip(a)].">
      <j1 rule="hyper" parents="64 15468 33166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33572">
    <literal><![CDATA[
      a(x \ L(x,y,z),x,u) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11978,a(flip),b,33571,a),flip(a)].">
      <j1 rule="hyper" parents="373 11978 33571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33573">
    <literal><![CDATA[
      a(x * L(x,y,z),x,u) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5609,a(flip),b,33572,a)].">
      <j1 rule="hyper" parents="64 5609 33572"/>
    </justification>
  </clause>

  <clause id="33574">
    <literal><![CDATA[
      L(x,y,z * R(u,w,v5)) = L(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(452(a,1),33174(a,1,3)),flip(a)].">
      <j1 rule="para" parents="452 33174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33575">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * v5) = L(x,y,v5 * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,33574,a)].">
      <j1 rule="hyper" parents="373 23253 33574"/>
    </justification>
  </clause>

  <clause id="33576">
    <literal><![CDATA[
      L(x,y,T(z * L(u,w,v5),v6)) = L(x,y,z * R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,23215,a,b,33574,a)].">
      <j1 rule="hyper" parents="373 23215 33574"/>
    </justification>
  </clause>

  <clause id="33577">
    <literal><![CDATA[
      L(x,y * R(y,z,u),y) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11914,a,b,33574,a)].">
      <j1 rule="hyper" parents="64 11914 33574"/>
    </justification>
  </clause>

  <clause id="33578">
    <literal><![CDATA[
      L(x,y,(z * u) * L(R(w,u,z),v5,v6)) = L(x,y,(R(w,v5,v6) * u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29155,a(flip),b,33574,a),flip(a)].">
      <j1 rule="hyper" parents="64 29155 33574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33579">
    <literal><![CDATA[
      L(R(x,y,z) \ x,u,x * L(x,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,25946,a(flip),b,33574,a),flip(a)].">
      <j1 rule="hyper" parents="64 25946 33574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33580">
    <literal><![CDATA[
      L(x \ y,x,x * L(x,z,u)) = R(x,z,u) \ ((x \ R(x,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2755,a(flip),b,33574,a),flip(a)].">
      <j1 rule="hyper" parents="64 2755 33574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33581">
    <literal><![CDATA[
      a(x,y,(z * R(u,w,v5)) * L(v6 \ 1,v6,z * L(u,w,v5))) = a(x,y,v6 \ (z * R(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(33574(a,1),27737(a,1,3,2))].">
      <j1 rule="para" parents="33574 27737"/>
    </justification>
  </clause>

  <clause id="33582">
    <literal><![CDATA[
      L(x,y,(z * R(u,w,v5)) * L(v6,v6,z * L(u,w,v5))) = L(x,y,v6 \ (z * R(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(33574(a,1),29158(a,1,3,2))].">
      <j1 rule="para" parents="33574 29158"/>
    </justification>
  </clause>

  <clause id="33583">
    <literal><![CDATA[
      L(x,x,y * L(z,u,w)) \ x = a(y * R(z,u,w),x,x)
    ]]></literal>
    <justification jstring="[para(33574(a,1),30462(a,1,1))].">
      <j1 rule="para" parents="33574 30462"/>
    </justification>
  </clause>

  <clause id="33584">
    <literal><![CDATA[
      L(x,y,R(z,u,w) * v5) = L(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,33575,a)].">
      <j1 rule="hyper" parents="373 23253 33575"/>
    </justification>
  </clause>

  <clause id="33585">
    <literal><![CDATA[
      L(x,y,L((z * z) \ u,w,v5) * v6) = L(x,y,v6 * R(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,25182,a(flip),b,33575,a),flip(a)].">
      <j1 rule="hyper" parents="373 25182 33575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33586">
    <literal><![CDATA[
      L(x,y,z * R(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z * L(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(33575(a,1),24201(a,1))].">
      <j1 rule="para" parents="33575 24201"/>
    </justification>
  </clause>

  <clause id="33587">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) * v5) * L(v6 \ 1,v6,L(z,u,w) * v5)) = a(x,y,v6 \ (R(z,u,w) * v5))
    ]]></literal>
    <justification jstring="[para(33584(a,1),27737(a,1,3,2))].">
      <j1 rule="para" parents="33584 27737"/>
    </justification>
  </clause>

  <clause id="33588">
    <literal><![CDATA[
      a(L(x,x,L(y,z,u) * w) * (R(y,z,u) * w),v5,v6) = a(x \ (R(y,z,u) * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(33584(a,1),32533(a,1,1,1))].">
      <j1 rule="para" parents="33584 32533"/>
    </justification>
  </clause>

  <clause id="33589">
    <literal><![CDATA[
      L(x,y,z * R(z \ u,z,w)) = L(x,y,z * ((w * z) \ (u * w)))
    ]]></literal>
    <justification jstring="[para(11290(a,1),33576(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11290 33576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33590">
    <literal><![CDATA[
      a(L(R(x,y,z) \ x,u,x * L(x,y,z)),R(x,y,z),w) = (((x / R(x,y,z)) * (R(x,y,z) * w)) / w) \ x
    ]]></literal>
    <justification jstring="[para(33579(a,2),33399(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33579 33399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33591">
    <literal><![CDATA[
      a(x * R(y,z,u),w,w) = a(x * L(y,z,u),w,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30462,a(flip),b,33583,a),flip(a)].">
      <j1 rule="hyper" parents="64 30462 33583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33592">
    <literal><![CDATA[
      a((x \ a(y * L(z,u,w),x,x)) * (y * R(z,u,w)),v5,v6) = a(x \ (y * R(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(33591(a,1),32535(a,1,1,1,2))].">
      <j1 rule="para" parents="33591 32535"/>
    </justification>
  </clause>

  <clause id="33593">
    <literal><![CDATA[
      a(L(x * R(y,z,u),w,v5),v6,v6) = L(a(x * L(y,z,u),v6,v6),w,v5)
    ]]></literal>
    <justification jstring="[para(33591(a,1),32607(a,2,1))].">
      <j1 rule="para" parents="33591 32607"/>
    </justification>
  </clause>

  <clause id="33594">
    <literal><![CDATA[
      L(x,y,L((z * z) \ u,w,v5) * v6) = L(x,y,v6 * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,33574,a(flip),b,33585,a),flip(a)].">
      <j1 rule="hyper" parents="373 33574 33585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33595">
    <literal><![CDATA[
      L(x,y,z * L((u * u) / w,v5,v6)) = L(x,y,L(1 / w,v5,v6) * z)
    ]]></literal>
    <justification jstring="[para(548(a,1),33594(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="548 33594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33596">
    <literal><![CDATA[
      a(x,y,L(z \ (z \ R(z,u,w)),z,z * L(z,u,w)) \ v5) = a(x,y,((z \ R(z,u,w)) * (z \ R(z,u,w))) \ ((R(z,u,w) \ 1) \ v5))
    ]]></literal>
    <justification jstring="[para(33580(a,2),27770(a,2,3,1)),flip(a)].">
      <j1 rule="para" parents="33580 27770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33597">
    <literal><![CDATA[
      a(L(x * R(y,z,u),w,v5),v6,v6) = a(L(x * L(y,z,u),w,v5),v6,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32607,a,b,33593,a),flip(a)].">
      <j1 rule="hyper" parents="373 32607 33593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33598">
    <literal><![CDATA[
      L(x,y,z * L((u * u) / w,v5,v6)) = L(x,y,L(w \ 1,v5,v6) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29007,a(flip),b,33595,a),flip(a)].">
      <j1 rule="hyper" parents="373 29007 33595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33599">
    <literal><![CDATA[
      a(L(x * L(y,z,u),w,v5),v6,v6) \ v6 = L(v6,v6,L(x * R(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(33597(a,1),30459(a,1,1))].">
      <j1 rule="para" parents="33597 30459"/>
    </justification>
  </clause>

  <clause id="33600">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w) * v5) = L(x,y,v5 * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(11(a,1),33598(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="11 33598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33601">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w) * v5) = L(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,33600,a),flip(a)].">
      <j1 rule="hyper" parents="373 23253 33600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33602">
    <literal><![CDATA[
      L(x,y,z * L(u \ 1,w,v5)) = L(x,y,L(u,w,v5) * z)
    ]]></literal>
    <justification jstring="[hyper(24201,a,33601,a)].">
      <j1 rule="hyper" parents="24201 33601"/>
    </justification>
  </clause>

  <clause id="33603">
    <literal><![CDATA[
      L(x,y,z \ L(1 / z,u,w)) = L(x,y,L(z,u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2233,a,b,33602,a)].">
      <j1 rule="hyper" parents="64 2233 33602"/>
    </justification>
  </clause>

  <clause id="33604">
    <literal><![CDATA[
      L(x,y,z \ (u * L(u \ z,w,v5))) = L(x,y,L(z \ u,w,v5) * (z \ u))
    ]]></literal>
    <justification jstring="[para(2469(a,1),33602(a,1,3))].">
      <j1 rule="para" parents="2469 33602"/>
    </justification>
  </clause>

  <clause id="33605">
    <literal><![CDATA[
      L(x,y,z \ L(1 / z,u,w)) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,33603,a),flip(a)].">
      <j1 rule="hyper" parents="373 23253 33603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33606">
    <literal><![CDATA[
      L(x,y,(R(z,u,w) * v5) * v6) = L(x,y,(L(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29156,a(flip),b,33578,a),flip(a)].">
      <j1 rule="hyper" parents="64 29156 33578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33607">
    <literal><![CDATA[
      L(x,y,(R(z,u,w) * v5) * v6) = L(x,y,(v5 * L(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,28989,a,b,33606,a),flip(a)].">
      <j1 rule="hyper" parents="373 28989 33606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33608">
    <literal><![CDATA[
      L(x,y,(R(z,u,w) * (v5 \ 1)) * v6) = L(x,y,v6 * (v5 * L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,29153,a(flip),b,33606,a),flip(a)].">
      <j1 rule="hyper" parents="373 29153 33606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33609">
    <literal><![CDATA[
      L(x,y,(L(z,u,w) * (z \ R(z,u,w))) * v5) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,2250,a(flip),b,33606,a),flip(a)].">
      <j1 rule="hyper" parents="64 2250 33606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33610">
    <literal><![CDATA[
      L(x,y,(z * R(u,w,v5)) * v6) = L(x,y,(z * L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,28989,a,b,33607,a)].">
      <j1 rule="hyper" parents="64 28989 33607"/>
    </justification>
  </clause>

  <clause id="33611">
    <literal><![CDATA[
      L(x,y,z * (L(u,w,v5) * (u \ R(u,w,v5)))) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(24201,a,33609,a)].">
      <j1 rule="hyper" parents="24201 33609"/>
    </justification>
  </clause>

  <clause id="33612">
    <literal><![CDATA[
      L(x,y,((z \ 1) * R(u,w,v5)) * v6) = L(x,y,(z * L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,2271,a(flip),b,33610,a),flip(a)].">
      <j1 rule="hyper" parents="373 2271 33610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33613">
    <literal><![CDATA[
      L(x,y,z * L(R(u,w,v5),w,v5)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(33222(a,1),33611(a,1,3,2))].">
      <j1 rule="para" parents="33222 33611"/>
    </justification>
  </clause>

  <clause id="33614">
    <literal><![CDATA[
      L(x,y,(L(z,u,w) * u) * w) = L(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29156,a(flip),b,33613,a)].">
      <j1 rule="hyper" parents="64 29156 33613"/>
    </justification>
  </clause>

  <clause id="33615">
    <literal><![CDATA[
      L(x,y,z * (u * R(w,v5,v6))) = L(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29153,a(flip),b,33608,a)].">
      <j1 rule="hyper" parents="64 29153 33608"/>
    </justification>
  </clause>

  <clause id="33616">
    <literal><![CDATA[
      L(x,y,(z * L(z \ ((1 / z) \ u),w,v5)) * v6) = L(x,y,(z \ R(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[para(1789(a,1),33612(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1789 33612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33617">
    <literal><![CDATA[
      L(x,y,z) * R((x \ 1) * (x \ x),u,z) = (1 / x) * L(R(x,u,z),y,z)
    ]]></literal>
    <justification jstring="[para(2166(a,2),33430(a,1,2))].">
      <j1 rule="para" parents="2166 33430"/>
    </justification>
  </clause>

  <clause id="33618">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ ((1 / z) * u) = (1 / z) * ((a(x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28648,a(flip),b,33458,a),flip(a)].">
      <j1 rule="hyper" parents="64 28648 33458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33619">
    <literal><![CDATA[
      (1 / x) * ((a(y,y,x) \ 1) \ (L(x,y,y) * z)) = L(z,x,L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,7750,a(flip),b,33618,a),flip(a)].">
      <j1 rule="hyper" parents="64 7750 33618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33620">
    <literal><![CDATA[
      L(x,x,L(y * R(z,u,w),v5,v6)) = L(x,x,L(y * L(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,30459,a(flip),b,33599,a),flip(a)].">
      <j1 rule="hyper" parents="64 30459 33599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33621">
    <literal><![CDATA[
      L(x,y,z \ (u * L(u \ z,w,v5))) = L(x,y,(z \ u) * L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,33604,a),flip(a)].">
      <j1 rule="hyper" parents="373 23253 33604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33622">
    <literal><![CDATA[
      L(x,y,z) * R(x \ 1,u,z) = (1 / x) * L(R(x,u,z),y,z)
    ]]></literal>
    <justification jstring="[para(191(a,1),33617(a,1,2,1))].">
      <j1 rule="para" parents="191 33617"/>
    </justification>
  </clause>

  <clause id="33623">
    <literal><![CDATA[
      L(x,y,z) * R(x \ 1,u,z) = x \ L(R(x,u,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,26946,a(flip),b,33622,a),flip(a)].">
      <j1 rule="hyper" parents="373 26946 33622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33625">
    <literal><![CDATA[
      L(x,y,((z * u) * w) \ (z * (w * u))) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,28973,a(flip),b,29267,a),flip(a)].">
      <j1 rule="hyper" parents="373 28973 29267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33628">
    <literal><![CDATA[
      L(x,y,(L(z,u,w) * (u * w)) * v5) = L(x,y,((w \ 1) * (u * z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29234,a(flip),b,29343,a),flip(a)].">
      <j1 rule="hyper" parents="373 29234 29343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33630">
    <literal><![CDATA[
      L(x,y,(L(z,u,w) * (u * w)) * v5) = L(x,y,(w * (u * z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,2271,a(flip),b,33628,a),flip(a)].">
      <j1 rule="hyper" parents="373 2271 33628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33631">
    <literal><![CDATA[
      L(x,y,((z * u) * R(w,z,u)) \ v5) = L(x,y,((w * (z \ 1)) * u) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27009,a(flip),b,29378,a)].">
      <j1 rule="hyper" parents="64 27009 29378"/>
    </justification>
  </clause>

  <clause id="33632">
    <literal><![CDATA[
      L(x,y,((z * (u \ 1)) * w) \ v5) = L(x,y,((z * u) * w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29102,a(flip),b,33631,a),flip(a)].">
      <j1 rule="hyper" parents="64 29102 33631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33633">
    <literal><![CDATA[
      L(x,y,(z * (u * (w \ 1))) \ v5) = L(x,y,((u * w) * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28988,a,b,33632,a)].">
      <j1 rule="hyper" parents="64 28988 33632"/>
    </justification>
  </clause>

  <clause id="33634">
    <literal><![CDATA[
      L(x,y,((z * u) * w) \ (u * (w * z))) = L(x,y,a(w,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,29187,a(flip),b,33633,a),flip(a)].">
      <j1 rule="hyper" parents="64 29187 33633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33635">
    <literal><![CDATA[
      L(x,y,a(z,u,u \ 1)) = L(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,33625,a(flip),b,33634,a),flip(a)].">
      <j1 rule="hyper" parents="64 33625 33634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33636">
    <literal><![CDATA[
      L(x,y,a(z,u,w \ 1)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,33120,a(flip),b,33634,a),flip(a)].">
      <j1 rule="hyper" parents="64 33120 33634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33638">
    <literal><![CDATA[
      L(x,y,a(z * (u * w),v5,v6 \ 1)) = L(x,y,a(z * (w * u),v5,v6))
    ]]></literal>
    <justification jstring="[para(32365(a,1),33636(a,1,3))].">
      <j1 rule="para" parents="32365 33636"/>
    </justification>
  </clause>

  <clause id="33639">
    <literal><![CDATA[
      L(x,y,a(z * (u * w),v5,v6)) = L(x,y,a(z * (w * u),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,33636,a(flip),b,33638,a)].">
      <j1 rule="hyper" parents="64 33636 33638"/>
    </justification>
  </clause>

  <clause id="33640">
    <literal><![CDATA[
      L(x,y,(((z \ u) * u) * z) * w) = L(x,y,w * a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[para(27307(a,1),29383(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="27307 29383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33642">
    <literal><![CDATA[
      a(x,y,y) \ a(L(x,z * u,z * u),y,y) = a(a(x,y,y),u * z,u * z)
    ]]></literal>
    <justification jstring="[para(32607(a,2),29665(a,1,2))].">
      <j1 rule="para" parents="32607 29665"/>
    </justification>
  </clause>

  <clause id="33643">
    <literal><![CDATA[
      L(x,(y \ z) * L(u,u,y \ z),w) = L(x,u \ (L(y,y,z) * z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31063,a(flip),b,29781,a)].">
      <j1 rule="hyper" parents="64 31063 29781"/>
    </justification>
  </clause>

  <clause id="33644">
    <literal><![CDATA[
      L(x,y \ (L(z,z,u) * u),w) = L(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29779,a(flip),b,33643,a),flip(a)].">
      <j1 rule="hyper" parents="64 29779 33643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33645">
    <literal><![CDATA[
      R(a(x,x,y),x * y,z) \ ((x \ y) * z) = (a(x,x,y) \ (x \ y)) * z
    ]]></literal>
    <justification jstring="[para(3018(a,1),30052(a,1,1))].">
      <j1 rule="para" parents="3018 30052"/>
    </justification>
  </clause>

  <clause id="33646">
    <literal><![CDATA[
      L(a(x,x,y),x * y,z) \ ((x \ y) * z) = (a(x,x,y) \ (x \ y)) * z
    ]]></literal>
    <justification jstring="[para(28787(a,1),33645(a,1,1))].">
      <j1 rule="para" parents="28787 33645"/>
    </justification>
  </clause>

  <clause id="33647">
    <literal><![CDATA[
      L(a(x,x,y),x * y,z) \ ((x \ y) * z) = ((x \ 1) * y) * z
    ]]></literal>
    <justification jstring="[para(30044(a,1),33646(a,2,1))].">
      <j1 rule="para" parents="30044 33646"/>
    </justification>
  </clause>

  <clause id="33648">
    <literal><![CDATA[
      ((x \ a(x,x,y)) * (x \ a(x,x,y))) \ (x \ y) = ((a(x,x,y) / x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(25195(a,1),30128(a,2,1))].">
      <j1 rule="para" parents="25195 30128"/>
    </justification>
  </clause>

  <clause id="33649">
    <literal><![CDATA[
      L(x,(a(y,y,z * y) * u) * w,v5) = L(x,w * (a(y,y,z) * u),v5)
    ]]></literal>
    <justification jstring="[para(30057(a,1),30150(a,2,2,2,1))].">
      <j1 rule="para" parents="30057 30150"/>
    </justification>
  </clause>

  <clause id="33650">
    <literal><![CDATA[
      (a(R(x,y,y),L(x,y,y),y) \ 1) * (x \ L(y,y,x)) = (R(x,y,y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(32187(a,1),30428(a,1,1,1))].">
      <j1 rule="para" parents="32187 30428"/>
    </justification>
  </clause>

  <clause id="33651">
    <literal><![CDATA[
      1 / ((x * (1 / y)) \ (x / y)) = ((x * (1 / y)) \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(13983(a,1),30538(a,1,2))].">
      <j1 rule="para" parents="13983 30538"/>
    </justification>
  </clause>

  <clause id="33654">
    <literal><![CDATA[
      (x / (x * y)) * L(z,a(y,y,x),y) = y * ((y \ (x / (x * y))) * z)
    ]]></literal>
    <justification jstring="[para(30377(a,1),30869(a,1,2))].">
      <j1 rule="para" parents="30377 30869"/>
    </justification>
  </clause>

  <clause id="33655">
    <literal><![CDATA[
      L((x \ (y / (y * x))) \ z,a(x,x,y),x) = (y / (y * x)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,33654,a),flip(a)].">
      <j1 rule="hyper" parents="139 168 33654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33656">
    <literal><![CDATA[
      (x / (x * y)) * L(z,y,a(y,y,x)) = y * ((y \ (x / (x * y))) * z)
    ]]></literal>
    <justification jstring="[para(30415(a,1),33654(a,1,2))].">
      <j1 rule="para" parents="30415 33654"/>
    </justification>
  </clause>

  <clause id="33657">
    <literal><![CDATA[
      L((x \ (y / (y * x))) \ z,x,a(x,x,y)) = (y / (y * x)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30415,a(flip),b,33655,a)].">
      <j1 rule="hyper" parents="64 30415 33655"/>
    </justification>
  </clause>

  <clause id="33658">
    <literal><![CDATA[
      L(x,L(K(y,z) * (u \ w),u,u) * v5,v6) = L(x,K(y,z) * ((u * w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(23073(a,1),30878(a,2,2))].">
      <j1 rule="para" parents="23073 30878"/>
    </justification>
  </clause>

  <clause id="33659">
    <literal><![CDATA[
      a(a(x,x \ y,x \ y) * y,z,u) = a(((y * (x \ y)) \ y) * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26831,a(flip),b,31015,a),flip(a)].">
      <j1 rule="hyper" parents="373 26831 31015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33660">
    <literal><![CDATA[
      a(a(x,x \ y,x \ y) * y,z,u) = a((y \ ((x \ y) \ y)) * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32733,a(flip),b,33659,a),flip(a)].">
      <j1 rule="hyper" parents="373 32733 33659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33661">
    <literal><![CDATA[
      a(a(x,x \ y,x \ y) * y,z,u) = a((y \ x) * ((x \ y) \ y),z,u)
    ]]></literal>
    <justification jstring="[para(15094(a,1),33660(a,2,1))].">
      <j1 rule="para" parents="15094 33660"/>
    </justification>
  </clause>

  <clause id="33662">
    <literal><![CDATA[
      a(a(x,x \ y,x \ y) * y,z,u) = a(x * (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32499,a(flip),b,33661,a),flip(a)].">
      <j1 rule="hyper" parents="373 32499 33661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33664">
    <literal><![CDATA[
      a(x * a(x,y \ x,y),z,u) = a(y * (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32856,a(flip),b,33662,a)].">
      <j1 rule="hyper" parents="64 32856 33662"/>
    </justification>
  </clause>

  <clause id="33665">
    <literal><![CDATA[
      a(R(x,y \ x,y),z,u) = a(y * (x \ y),z,u)
    ]]></literal>
    <justification jstring="[para(24668(a,1),33664(a,1,1))].">
      <j1 rule="para" parents="24668 33664"/>
    </justification>
  </clause>

  <clause id="33666">
    <literal><![CDATA[
      a(L(x,y \ x,y),z,u) = a(y * (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32590,a(flip),b,33665,a)].">
      <j1 rule="hyper" parents="64 32590 33665"/>
    </justification>
  </clause>

  <clause id="33668">
    <literal><![CDATA[
      R(T(x / y,T(y,x)),x,T(x / y,x \ y)) = T(T(x / y,x \ y),x)
    ]]></literal>
    <justification jstring="[para(22(a,2),31180(a,1,1,2))].">
      <j1 rule="para" parents="22 31180"/>
    </justification>
  </clause>

  <clause id="33670">
    <literal><![CDATA[
      R(x \ y,y,T(y / x,y \ x)) = T(T(y / x,y \ x),y)
    ]]></literal>
    <justification jstring="[para(4470(a,1),33668(a,1,1))].">
      <j1 rule="para" parents="4470 33668"/>
    </justification>
  </clause>

  <clause id="33672">
    <literal><![CDATA[
      T(T(x / y,x \ y),x) = R(y \ x,x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24131,a(flip),b,33670,a),flip(a)].">
      <j1 rule="hyper" parents="64 24131 33670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33673">
    <literal><![CDATA[
      T(T(x / y,x),x \ y) = R(y \ x,x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(481,a,33672,a)].">
      <j1 rule="hyper" parents="481 33672"/>
    </justification>
  </clause>

  <clause id="33674">
    <literal><![CDATA[
      R(x \ y,y,x \ y) = y \ ((x / y) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3821,a(flip),b,33673,a),flip(a)].">
      <j1 rule="hyper" parents="64 3821 33673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33675">
    <literal><![CDATA[
      T((x \ (x \ y)) \ y,x \ (x \ 1)) = y \ (((x \ (x \ y)) / y) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16736,a(flip),b,33674,a)].">
      <j1 rule="hyper" parents="64 16736 33674"/>
    </justification>
  </clause>

  <clause id="33676">
    <literal><![CDATA[
      x \ (((y * y) / x) \ x) = (x \ (y * y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,2988,a(flip),b,33674,a),flip(a)].">
      <j1 rule="hyper" parents="64 2988 33674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33677">
    <literal><![CDATA[
      T((x \ y) * y,x \ y) = (x / y) \ y
    ]]></literal>
    <justification jstring="[hyper(39,a,4736,a,b,33674,a(flip))].">
      <j1 rule="hyper" parents="39 4736 33674"/>
    </justification>
  </clause>

  <clause id="33678">
    <literal><![CDATA[
      (x \ ((y / x) \ x)) * y = y * (((y \ x) \ y) \ y)
    ]]></literal>
    <justification jstring="[para(33674(a,1),26732(a,1,1))].">
      <j1 rule="para" parents="33674 26732"/>
    </justification>
  </clause>

  <clause id="33679">
    <literal><![CDATA[
      T(((x \ y) \ z) * z,(y \ x) * z) = ((x \ y) / z) \ z
    ]]></literal>
    <justification jstring="[hyper(22661,a,33677,a)].">
      <j1 rule="hyper" parents="22661 33677"/>
    </justification>
  </clause>

  <clause id="33680">
    <literal><![CDATA[
      R(x,y,z \ ((u / w) \ w)) = R(x,y,z \ ((u \ w) * w))
    ]]></literal>
    <justification jstring="[para(33677(a,1),26168(a,1,3,2))].">
      <j1 rule="para" parents="33677 26168"/>
    </justification>
  </clause>

  <clause id="33681">
    <literal><![CDATA[
      R(x,L((y / z) \ z,u,w),v5) = R(x,L((y \ z) * z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(33677(a,1),26430(a,1,2,1))].">
      <j1 rule="para" parents="33677 26430"/>
    </justification>
  </clause>

  <clause id="33682">
    <literal><![CDATA[
      a(x,y,z \ ((u / w) \ w)) = a(x,y,z \ ((u \ w) * w))
    ]]></literal>
    <justification jstring="[para(33677(a,1),27301(a,1,3,2))].">
      <j1 rule="para" parents="33677 27301"/>
    </justification>
  </clause>

  <clause id="33683">
    <literal><![CDATA[
      a(x,y,(z \ ((u / w) \ w)) * v5) = a(x,y,(z \ ((u \ w) * w)) * v5)
    ]]></literal>
    <justification jstring="[para(33677(a,1),27468(a,1,3,1,2))].">
      <j1 rule="para" parents="33677 27468"/>
    </justification>
  </clause>

  <clause id="33684">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w / v5) \ v5))) = a(x,y,z * (u \ ((w \ v5) * v5)))
    ]]></literal>
    <justification jstring="[para(33677(a,1),27477(a,1,3,2,2))].">
      <j1 rule="para" parents="33677 27477"/>
    </justification>
  </clause>

  <clause id="33685">
    <literal><![CDATA[
      L(x,y,z \ ((u / w) \ w)) = L(x,y,z \ ((u \ w) * w))
    ]]></literal>
    <justification jstring="[para(33677(a,1),28984(a,1,3,2))].">
      <j1 rule="para" parents="33677 28984"/>
    </justification>
  </clause>

  <clause id="33686">
    <literal><![CDATA[
      L(x,y,(z \ ((u / w) \ w)) * v5) = L(x,y,(z \ ((u \ w) * w)) * v5)
    ]]></literal>
    <justification jstring="[para(33677(a,1),29085(a,1,3,1,2))].">
      <j1 rule="para" parents="33677 29085"/>
    </justification>
  </clause>

  <clause id="33687">
    <literal><![CDATA[
      L(x,y \ ((z / u) \ u),w) = L(x,y \ ((z \ u) * u),w)
    ]]></literal>
    <justification jstring="[para(33677(a,1),29450(a,1,2,2))].">
      <j1 rule="para" parents="33677 29450"/>
    </justification>
  </clause>

  <clause id="33688">
    <literal><![CDATA[
      T(((a(x,y,y) \ x) \ L(y,y,x)) * L(y,y,x),(a(x,y,y) \ x) \ L(y,y,x)) = (x / y) \ L(y,y,x)
    ]]></literal>
    <justification jstring="[para(30576(a,1),33677(a,2,1))].">
      <j1 rule="para" parents="30576 33677"/>
    </justification>
  </clause>

  <clause id="33689">
    <literal><![CDATA[
      T((x \ ((x * y) * y)) * x,((x / y) / y) \ x) = (((x / y) / y) / x) \ x
    ]]></literal>
    <justification jstring="[para(30801(a,1),33677(a,1,1,1))].">
      <j1 rule="para" parents="30801 33677"/>
    </justification>
  </clause>

  <clause id="33690">
    <literal><![CDATA[
      a(x,y \ ((z / u) \ u),w) = a(x,y \ ((z \ u) * u),w)
    ]]></literal>
    <justification jstring="[para(33677(a,1),31891(a,1,2,2))].">
      <j1 rule="para" parents="33677 31891"/>
    </justification>
  </clause>

  <clause id="33691">
    <literal><![CDATA[
      a(x,((y / z) \ z) \ u,w) = a(x,((y \ z) * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(33677(a,1),31903(a,1,2,1))].">
      <j1 rule="para" parents="33677 31903"/>
    </justification>
  </clause>

  <clause id="33692">
    <literal><![CDATA[
      a(x \ ((y / z) \ z),u,w) = a(x \ ((y \ z) * z),u,w)
    ]]></literal>
    <justification jstring="[para(33677(a,1),32360(a,1,1,2))].">
      <j1 rule="para" parents="33677 32360"/>
    </justification>
  </clause>

  <clause id="33693">
    <literal><![CDATA[
      a(((x / y) \ y) \ z,u,w) = a(((x \ y) * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(33677(a,1),32366(a,1,1,1))].">
      <j1 rule="para" parents="33677 32366"/>
    </justification>
  </clause>

  <clause id="33694">
    <literal><![CDATA[
      a((x \ ((y / z) \ z)) * u,w,v5) = a((x \ ((y \ z) * z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(33677(a,1),32491(a,1,1,1,2))].">
      <j1 rule="para" parents="33677 32491"/>
    </justification>
  </clause>

  <clause id="33695">
    <literal><![CDATA[
      ((x / y) \ y) \ y = x \ ((y / x) \ x)
    ]]></literal>
    <justification jstring="[hyper(36,a,8703,a,b,33678,a)].">
      <j1 rule="hyper" parents="36 8703 33678"/>
    </justification>
  </clause>

  <clause id="33696">
    <literal><![CDATA[
      T(((x \ L(y,z,u)) \ w) * w,(y \ x) * w) = ((x \ L(y,z,u)) / w) \ w
    ]]></literal>
    <justification jstring="[hyper(64,a,28448,a(flip),b,33679,a)].">
      <j1 rule="hyper" parents="64 28448 33679"/>
    </justification>
  </clause>

  <clause id="33697">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) \ u)) = R(x,y,z \ ((w \ u) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26278,a(flip),b,33680,a)].">
      <j1 rule="hyper" parents="64 26278 33680"/>
    </justification>
  </clause>

  <clause id="33698">
    <literal><![CDATA[
      L(x,y,z \ ((u \ w) \ u)) = L(x,y,z \ ((w \ u) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29110,a(flip),b,33685,a)].">
      <j1 rule="hyper" parents="64 29110 33685"/>
    </justification>
  </clause>

  <clause id="33699">
    <literal><![CDATA[
      L(x,y \ (z / (u / z)),w) = L(x,y \ ((u \ z) * z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29552,a,b,33687,a)].">
      <j1 rule="hyper" parents="64 29552 33687"/>
    </justification>
  </clause>

  <clause id="33700">
    <literal><![CDATA[
      L(x,y \ ((z \ u) \ z),w) = L(x,y \ ((u \ z) * z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29656,a(flip),b,33687,a)].">
      <j1 rule="hyper" parents="64 29656 33687"/>
    </justification>
  </clause>

  <clause id="33701">
    <literal><![CDATA[
      a(x,(y / (z / y)) \ u,w) = a(x,((z \ y) * y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31972,a,b,33691,a)].">
      <j1 rule="hyper" parents="64 31972 33691"/>
    </justification>
  </clause>

  <clause id="33702">
    <literal><![CDATA[
      a(x \ ((y \ z) \ y),u,w) = a(x \ ((z \ y) * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32495,a(flip),b,33692,a)].">
      <j1 rule="hyper" parents="64 32495 33692"/>
    </justification>
  </clause>

  <clause id="33703">
    <literal><![CDATA[
      a((x / (y / x)) \ z,u,w) = a(((y \ x) * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32386,a,b,33693,a)].">
      <j1 rule="hyper" parents="64 32386 33693"/>
    </justification>
  </clause>

  <clause id="33704">
    <literal><![CDATA[
      a((((x * y) \ y) * y) \ z,u,w) = a((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(11(a,1),33693(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11 33693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33705">
    <literal><![CDATA[
      R(x,y,((1 / (z \ u)) \ z) \ ((u \ z) * z)) = R(x,y,((z \ u) * z) \ (((z \ u) \ 1) * z))
    ]]></literal>
    <justification jstring="[para(28617(a,1),33697(a,1,3)),flip(a)].">
      <j1 rule="para" parents="28617 33697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33706">
    <literal><![CDATA[
      (x / (x \ y)) * L(z,u,u \ ((y \ x) * x)) = ((x / (x \ y)) / u) * (u * z)
    ]]></literal>
    <justification jstring="[para(33698(a,1),29128(a,1,2))].">
      <j1 rule="para" parents="33698 29128"/>
    </justification>
  </clause>

  <clause id="33707">
    <literal><![CDATA[
      (x / (x \ y)) * L(z,u \ ((y \ x) * x),u) = u * ((u \ (x / (x \ y))) * z)
    ]]></literal>
    <justification jstring="[para(33700(a,1),29681(a,1,2))].">
      <j1 rule="para" parents="33700 29681"/>
    </justification>
  </clause>

  <clause id="33708">
    <literal><![CDATA[
      a(((x / (y * x)) * x) \ z,u,w) = a((y \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32497,a,b,33704,a)].">
      <j1 rule="hyper" parents="64 32497 33704"/>
    </justification>
  </clause>

  <clause id="33709">
    <literal><![CDATA[
      a(L(x * y,x,x) \ z,u,w) = a((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30960,a,b,33708,a)].">
      <j1 rule="hyper" parents="64 30960 33708"/>
    </justification>
  </clause>

  <clause id="33710">
    <literal><![CDATA[
      a((x * L(y,x,x)) \ z,u,w) = a((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26931,a(flip),b,33709,a)].">
      <j1 rule="hyper" parents="64 26931 33709"/>
    </justification>
  </clause>

  <clause id="33711">
    <literal><![CDATA[
      a((x \ (x \ y)) \ z,u,w) = a(L(y,x,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),33709(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 33709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33712">
    <literal><![CDATA[
      a((L(x,y,y) * y) \ z,u,w) = a((y \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(32451,a,33710,a)].">
      <j1 rule="hyper" parents="32451 33710"/>
    </justification>
  </clause>

  <clause id="33713">
    <literal><![CDATA[
      R(x,L((y \ z) \ y,u,w),v5) = R(x,L((z \ y) * y,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26587,a(flip),b,33681,a)].">
      <j1 rule="hyper" parents="64 26587 33681"/>
    </justification>
  </clause>

  <clause id="33714">
    <literal><![CDATA[
      a(x,y,(z \ (u / (u \ w))) * v5) = a(x,y,(z \ ((w \ u) * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27983,a,b,33683,a)].">
      <j1 rule="hyper" parents="64 27983 33683"/>
    </justification>
  </clause>

  <clause id="33715">
    <literal><![CDATA[
      a(x,y,(z \ (u / (w / u))) * v5) = a(x,y,(z \ ((w \ u) * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27470,a,b,33683,a)].">
      <j1 rule="hyper" parents="64 27470 33683"/>
    </justification>
  </clause>

  <clause id="33716">
    <literal><![CDATA[
      L(x,y,(z \ (u / (w / u))) * v5) = L(x,y,(z \ ((w \ u) * u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29095,a,b,33686,a)].">
      <j1 rule="hyper" parents="64 29095 33686"/>
    </justification>
  </clause>

  <clause id="33717">
    <literal><![CDATA[
      a((x \ (y / (z / y))) * u,w,v5) = a((x \ ((z \ y) * y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32492,a,b,33694,a)].">
      <j1 rule="hyper" parents="64 32492 33694"/>
    </justification>
  </clause>

  <clause id="33718">
    <literal><![CDATA[
      a((x \ ((y \ z) \ y)) * u,w,v5) = a((x \ ((z \ y) * y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32691,a(flip),b,33694,a)].">
      <j1 rule="hyper" parents="64 32691 33694"/>
    </justification>
  </clause>

  <clause id="33719">
    <literal><![CDATA[
      T(T((x * y) * y,x),((x / y) / y) \ x) = (((x / y) / y) / x) \ x
    ]]></literal>
    <justification jstring="[para(27902(a,1),33689(a,1,1))].">
      <j1 rule="para" parents="27902 33689"/>
    </justification>
  </clause>

  <clause id="33720">
    <literal><![CDATA[
      T(T((x * y) * y,x),x \ ((x * y) * y)) = (((x / y) / y) / x) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,21315,a(flip),b,33719,a)].">
      <j1 rule="hyper" parents="64 21315 33719"/>
    </justification>
  </clause>

  <clause id="33721">
    <literal><![CDATA[
      T(T((x * y) * y,x),(x \ (x * y)) * y) = (((x / y) / y) / x) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,24579,a(flip),b,33720,a)].">
      <j1 rule="hyper" parents="64 24579 33720"/>
    </justification>
  </clause>

  <clause id="33722">
    <literal><![CDATA[
      T(T((x * y) * y,x),y * y) = (((x / y) / y) / x) \ x
    ]]></literal>
    <justification jstring="[para(9(a,1),33721(a,1,2,1))].">
      <j1 rule="para" parents="9 33721"/>
    </justification>
  </clause>

  <clause id="33723">
    <literal><![CDATA[
      T((x * y) * y,y * (y * x)) = (((x / y) / y) / x) \ x
    ]]></literal>
    <justification jstring="[hyper(15895,a,33722,a)].">
      <j1 rule="hyper" parents="15895 33722"/>
    </justification>
  </clause>

  <clause id="33724">
    <literal><![CDATA[
      (((x / y) / y) / x) \ x = (x * y) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,26768,a(flip),b,33723,a),flip(a)].">
      <j1 rule="hyper" parents="64 26768 33723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33725">
    <literal><![CDATA[
      T(((x \ L(x * y,z,u)) \ y) * y,((x * y) \ x) * y) = (y \ (x \ L(x * y,z,u))) \ y
    ]]></literal>
    <justification jstring="[para(24573(a,1),33696(a,2,1))].">
      <j1 rule="para" parents="24573 33696"/>
    </justification>
  </clause>

  <clause id="33726">
    <literal><![CDATA[
      a(x,y,((z * u) \ z) * (((z * u) \ z) * u)) = a(x,y,L(z \ (u \ z),u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,33098,a(flip),b,31303,a),flip(a)].">
      <j1 rule="hyper" parents="373 33098 31303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33727">
    <literal><![CDATA[
      L((x \ 1) \ T(y,x),x,L(x,z,u)) = R(y / (1 / x),x,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(23153(a,1),31540(a,1,1,2))].">
      <j1 rule="para" parents="23153 31540"/>
    </justification>
  </clause>

  <clause id="33729">
    <literal><![CDATA[
      (x * (a(y,y,y \ x) \ y)) * a(L(y,y,y \ x),y,y \ x) = x * y
    ]]></literal>
    <justification jstring="[para(32592(a,1),31552(a,1,2))].">
      <j1 rule="para" parents="32592 31552"/>
    </justification>
  </clause>

  <clause id="33730">
    <literal><![CDATA[
      (x * (a(y,y,y \ x) \ y)) * a(L(y,y,y * x),y,y \ x) = x * y
    ]]></literal>
    <justification jstring="[para(25574(a,1),33729(a,1,2,1))].">
      <j1 rule="para" parents="25574 33729"/>
    </justification>
  </clause>

  <clause id="33731">
    <literal><![CDATA[
      (x * x) * (y / (y * x)) = R(T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,24001,a(flip),b,31573,a(flip))].">
      <j1 rule="hyper" parents="40 24001 31573"/>
    </justification>
  </clause>

  <clause id="33732">
    <literal><![CDATA[
      ((x \ a(x,x,y)) * (x \ a(x,x,y))) * (y / (y * (x \ a(x,x,y)))) = R(y \ (x \ y),x \ a(x,x,y),y)
    ]]></literal>
    <justification jstring="[para(30124(a,1),33731(a,2,1))].">
      <j1 rule="para" parents="30124 33731"/>
    </justification>
  </clause>

  <clause id="33733">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(z * y,w))) = K(x,T(y / z,w) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28103,a(flip),b,31604,a),flip(a)].">
      <j1 rule="hyper" parents="64 28103 31604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33735">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),u) \ w) = K(x,T(z / y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28881,a(flip),b,33733,a)].">
      <j1 rule="hyper" parents="64 28881 33733"/>
    </justification>
  </clause>

  <clause id="33736">
    <literal><![CDATA[
      K(x,(y \ 1) * ((z \ u) * K(y \ z,y))) = K(x,T((y \ 1) / z,y) * u)
    ]]></literal>
    <justification jstring="[para(7522(a,1),33733(a,1,2,2,2))].">
      <j1 rule="para" parents="7522 33733"/>
    </justification>
  </clause>

  <clause id="33737">
    <literal><![CDATA[
      K(x,y * (K(y * z,u) * (z \ w))) = K(x,T(y / z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28085,a,b,33735,a)].">
      <j1 rule="hyper" parents="64 28085 33735"/>
    </justification>
  </clause>

  <clause id="33738">
    <literal><![CDATA[
      K(x,T(y / z,u) \ w) = K(x,T(z / y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28149,a(flip),b,33735,a)].">
      <j1 rule="hyper" parents="64 28149 33735"/>
    </justification>
  </clause>

  <clause id="33739">
    <literal><![CDATA[
      K(x,T(y \ z,u * (w * z)) * v5) = K(x,T(z / y,u * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28966,a,b,33738,a)].">
      <j1 rule="hyper" parents="64 28966 33738"/>
    </justification>
  </clause>

  <clause id="33740">
    <literal><![CDATA[
      K(x,T(y / z,y * u) * w) = K(x,T(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,21579,a(flip),b,33739,a),flip(a)].">
      <j1 rule="hyper" parents="64 21579 33739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33741">
    <literal><![CDATA[
      K(x,T(y \ (L(z,u,w) \ v5),K(z,z \ v5)) * v6) = K(x,T((L(z,u,w) \ v5) / y,v5 / L(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(25183(a,1),33740(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="25183 33740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33742">
    <literal><![CDATA[
      K(x,(y \ 1) * T(z / (y * (u / y)),u)) = K(x,T((y \ 1) / u,y) * z)
    ]]></literal>
    <justification jstring="[para(24939(a,2),33736(a,1,2,2))].">
      <j1 rule="para" parents="24939 33736"/>
    </justification>
  </clause>

  <clause id="33743">
    <literal><![CDATA[
      K(x,T((y \ 1) / z,y) * u) = K(x,(y \ 1) * (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27876,a(flip),b,33742,a),flip(a)].">
      <j1 rule="hyper" parents="64 27876 33742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33744">
    <literal><![CDATA[
      K(x,T((y \ 1) / z,y) * (u * w)) = K(x,(y \ 1) * ((T(z,y) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,30371,a(flip),b,33743,a),flip(a)].">
      <j1 rule="hyper" parents="373 30371 33743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33745">
    <literal><![CDATA[
      K(x,T((y \ 1) / z,y) * (u * w)) = K(x,y \ ((T(z,y) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,14466,a(flip),b,33744,a),flip(a)].">
      <j1 rule="hyper" parents="373 14466 33744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33746">
    <literal><![CDATA[
      K(x,T((y \ 1) / z,y) * (u * w)) = K(x,(y \ (T(z,y) \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,24234,a(flip),b,33745,a),flip(a)].">
      <j1 rule="hyper" parents="373 24234 33745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33747">
    <literal><![CDATA[
      L(x * K(x * y,y),y,y) \ (x * (1 / y)) = x \ (T(x,1 / y) / y)
    ]]></literal>
    <justification jstring="[para(8241(a,1),31674(a,2,2,1))].">
      <j1 rule="para" parents="8241 31674"/>
    </justification>
  </clause>

  <clause id="33748">
    <literal><![CDATA[
      L(x * K(x * y,y),y,y) \ (x * (1 / y)) = (x / y) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,4411,a(flip),b,33747,a),flip(a)].">
      <j1 rule="hyper" parents="373 4411 33747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33749">
    <literal><![CDATA[
      (((1 / x) * y) * x) \ (y * (1 / x)) = (y / x) / y
    ]]></literal>
    <justification jstring="[para(15142(a,1),33748(a,1,1))].">
      <j1 rule="para" parents="15142 33748"/>
    </justification>
  </clause>

  <clause id="33750">
    <literal><![CDATA[
      (R(((1 / x) * y) / x,x,x) \ (y * (1 / x))) \ (x * z) = ((y / x) / y) \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(33749(a,1),1973(a,2,1))].">
      <j1 rule="para" parents="33749 1973"/>
    </justification>
  </clause>

  <clause id="33751">
    <literal><![CDATA[
      L(x * R(T(y,y \ 1),z,u),y,y) = ((1 / y) * (R(y,z,u) * x)) * y
    ]]></literal>
    <justification jstring="[para(31697(a,1),15142(a,1,1))].">
      <j1 rule="para" parents="31697 15142"/>
    </justification>
  </clause>

  <clause id="33752">
    <literal><![CDATA[
      ((1 / x) * (R(x,y,z) * u)) * x = L(u,x,x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,12282,a(flip),b,33751,a),flip(a)].">
      <j1 rule="hyper" parents="64 12282 33751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33753">
    <literal><![CDATA[
      T(L(x,y,y) * R(y,z,u),y \ 1) = R(R(y,z,u) * x,y,y)
    ]]></literal>
    <justification jstring="[para(33752(a,1),3883(a,1,1))].">
      <j1 rule="para" parents="33752 3883"/>
    </justification>
  </clause>

  <clause id="33754">
    <literal><![CDATA[
      L(R(x,y,z) \ T(R(x,y,z) * u,x \ 1),x,x) = R(R(x,y,z) * u,x,x) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(33753(a,1),26158(a,2,1))].">
      <j1 rule="para" parents="33753 26158"/>
    </justification>
  </clause>

  <clause id="33756">
    <literal><![CDATA[
      a(x,R(y,z,y) \ 1,T(y * z,y) \ z) = a(x,(y * z) \ z,y \ 1)
    ]]></literal>
    <justification jstring="[para(14173(a,1),32031(a,1,3))].">
      <j1 rule="para" parents="14173 32031"/>
    </justification>
  </clause>

  <clause id="33757">
    <literal><![CDATA[
      a(x,R(y,z,y) \ 1,(y * z) \ z) = a(x,(y * z) \ z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(27588,a,33756,a)].">
      <j1 rule="hyper" parents="27588 33756"/>
    </justification>
  </clause>

  <clause id="33758">
    <literal><![CDATA[
      a(x,R(y,z,y),(y * z) \ z) = a(x,(y * z) \ z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(32046,a,33757,a)].">
      <j1 rule="hyper" parents="32046 33757"/>
    </justification>
  </clause>

  <clause id="33760">
    <literal><![CDATA[
      a(x,(y * z) \ z,y \ 1) = a(x,y,(y * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13829,a(flip),b,33758,a),flip(a)].">
      <j1 rule="hyper" parents="64 13829 33758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33762">
    <literal><![CDATA[
      a(x,y \ (z \ y),z \ 1) = a(x,z,(z * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32038,a(flip),b,33760,a)].">
      <j1 rule="hyper" parents="64 32038 33760"/>
    </justification>
  </clause>

  <clause id="33763">
    <literal><![CDATA[
      a(x,y \ (z \ y),z \ 1) = a(x,z,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,27457,a(flip),b,33762,a),flip(a)].">
      <j1 rule="hyper" parents="373 27457 33762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33764">
    <literal><![CDATA[
      a(x,y * ((z * u) \ ((z * w) * u)),v5) = a(x,y * R(w,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32061,a(flip),b,32048,a),flip(a)].">
      <j1 rule="hyper" parents="64 32061 32048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33766">
    <literal><![CDATA[
      a(x,((y * z) \ ((z * u) * y)) * w,v5) = a(x,w * R(u,z,y),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32118,a,b,33764,a)].">
      <j1 rule="hyper" parents="64 32118 33764"/>
    </justification>
  </clause>

  <clause id="33767">
    <literal><![CDATA[
      a(x,y * R(z,u,w),v5) = a(x,y * L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32122,a(flip),b,33766,a),flip(a)].">
      <j1 rule="hyper" parents="64 32122 33766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33768">
    <literal><![CDATA[
      a(x,y * L(K(z,u) * w,v5,v6),v7) = a(x,R(w,v5,v6) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,32120,a(flip),b,33767,a),flip(a)].">
      <j1 rule="hyper" parents="64 32120 33767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33769">
    <literal><![CDATA[
      a(x,y * L(z,u,w),x) = a(x,y * z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,31344,a(flip),b,33767,a),flip(a)].">
      <j1 rule="hyper" parents="64 31344 33767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33770">
    <literal><![CDATA[
      L(x,L(y,z,u) \ w,x) = a(x,w * T(y,v5),x) \ x
    ]]></literal>
    <justification jstring="[para(33769(a,1),30876(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33769 30876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33771">
    <literal><![CDATA[
      L(x,L(y,z,u) \ w,x) = a(x,w * y,x) \ x
    ]]></literal>
    <justification jstring="[para(114(a,1),33770(a,2,1,2,2))].">
      <j1 rule="para" parents="114 33770"/>
    </justification>
  </clause>

  <clause id="33773">
    <literal><![CDATA[
      L(x,L(y,z,u) \ w,x) = L(x,w * y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10905,a(flip),b,33771,a),flip(a)].">
      <j1 rule="hyper" parents="373 10905 33771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33774">
    <literal><![CDATA[
      a(x,R(y,z,u) * w,v5) = a(x,L(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32121,a(flip),b,33768,a),flip(a)].">
      <j1 rule="hyper" parents="64 32121 33768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33775">
    <literal><![CDATA[
      a(x,L(y * (y * z),u,w) * y,v5) = a(x,y \ R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32151,a(flip),b,33774,a),flip(a)].">
      <j1 rule="hyper" parents="64 32151 33774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33776">
    <literal><![CDATA[
      a(x,(y * R(z,u,u \ 1)) * w,v5) = a(x,((u * (u * z)) * y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32909,a(flip),b,32168,a),flip(a)].">
      <j1 rule="hyper" parents="64 32909 32168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33777">
    <literal><![CDATA[
      a(x,(y * R(z,u,u \ 1)) * w,v5) = a(x,(L(z,u,u) * y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,11975,a(flip),b,33776,a),flip(a)].">
      <j1 rule="hyper" parents="373 11975 33776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33778">
    <literal><![CDATA[
      a(x,a(y,z,z \ 1) * u,w) = a(x,(L(y,z,z) * y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,12003,a(flip),b,33777,a)].">
      <j1 rule="hyper" parents="64 12003 33777"/>
    </justification>
  </clause>

  <clause id="33779">
    <literal><![CDATA[
      a(x,a(y,z,z \ 1) * u,w) = a(x,(y * L(y,z,z)) * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31976,a,b,33778,a),flip(a)].">
      <j1 rule="hyper" parents="373 31976 33778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33780">
    <literal><![CDATA[
      L(L(x \ 1,x \ 1,L(y,z,x)),a(u,w,v5),x) = L(x \ 1,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1631(a,1),32630(a,1,1,3))].">
      <j1 rule="para" parents="1631 32630"/>
    </justification>
  </clause>

  <clause id="33781">
    <literal><![CDATA[
      L(L(x \ 1,x,L(y,z,x)),a(u,w,v5),x) = L(x \ 1,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(11794(a,1),33780(a,1,1))].">
      <j1 rule="para" parents="11794 33780"/>
    </justification>
  </clause>

  <clause id="33782">
    <literal><![CDATA[
      L(x \ 1,x,L(y,z,x)) = L(x \ 1,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31266,a(flip),b,33781,a)].">
      <j1 rule="hyper" parents="64 31266 33781"/>
    </justification>
  </clause>

  <clause id="33783">
    <literal><![CDATA[
      L(x \ 1,x,L(y,z,x)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11794,a(flip),b,33782,a),flip(a)].">
      <j1 rule="hyper" parents="373 11794 33782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33784">
    <literal><![CDATA[
      L(x \ 1,x,(x * y) \ z) = L(x \ 1,x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(346(a,1),33783(a,1,3))].">
      <j1 rule="para" parents="346 33783"/>
    </justification>
  </clause>

  <clause id="33785">
    <literal><![CDATA[
      L(x \ 1,x,(y * x) \ z) = L(x \ 1,x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,28988,a,b,33784,a)].">
      <j1 rule="hyper" parents="64 28988 33784"/>
    </justification>
  </clause>

  <clause id="33786">
    <literal><![CDATA[
      x \ (L(x \ 1,x,y \ (x \ z)) \ 1) = a(x * ((x * y) \ z),x,x)
    ]]></literal>
    <justification jstring="[para(33784(a,1),30534(a,1,2,1))].">
      <j1 rule="para" parents="33784 30534"/>
    </justification>
  </clause>

  <clause id="33787">
    <literal><![CDATA[
      (((x * y) \ z) * y) \ ((x * y) \ z) = L(y \ 1,y,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(642,a,33785,a)].">
      <j1 rule="hyper" parents="642 33785"/>
    </justification>
  </clause>

  <clause id="33788">
    <literal><![CDATA[
      a(x * ((x * y) \ z),x,x) = a(x * (y \ (x \ z)),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30534,a(flip),b,33786,a),flip(a)].">
      <j1 rule="hyper" parents="64 30534 33786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33789">
    <literal><![CDATA[
      a((x * (((y / z) / z) \ 1)) * u,w,v5) = a((x * R(y \ 1,z,z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(30607(a,1),32704(a,1,1,1,2))].">
      <j1 rule="para" parents="30607 32704"/>
    </justification>
  </clause>

  <clause id="33790">
    <literal><![CDATA[
      x \ (1 / (1 / ((y / x) / y))) = ((y / x) / y) / x
    ]]></literal>
    <justification jstring="[para(26715(a,1),33082(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26715 33082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33791">
    <literal><![CDATA[
      L((x * T(y \ 1,z)) * y,u,w) = (L(x,u,w) * T(y \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(26581(a,1),33083(a,1,1))].">
      <j1 rule="para" parents="26581 33083"/>
    </justification>
  </clause>

  <clause id="33792">
    <literal><![CDATA[
      a(L(L(x,y,y * x) \ 1,z,u),w,v5) = a(L(y * (y * x),z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32712,a(flip),b,33084,a),flip(a)].">
      <j1 rule="hyper" parents="373 32712 33084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33793">
    <literal><![CDATA[
      a(L(L(x,y,y * x) \ 1,z,u),w,v5) = a(L(L(x,y,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32807,a(flip),b,33792,a),flip(a)].">
      <j1 rule="hyper" parents="373 32807 33792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33794">
    <literal><![CDATA[
      a(L(L(x,y,y * x),z,u),w,v5) = a(L(L(x,y,y),z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32634,a(flip),b,33793,a)].">
      <j1 rule="hyper" parents="64 32634 33793"/>
    </justification>
  </clause>

  <clause id="33795">
    <literal><![CDATA[
      a(L(L(x,y,z),u,u * x),w,v5) = a(L(L(x,u,u),y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27170,a,b,33794,a)].">
      <j1 rule="hyper" parents="64 27170 33794"/>
    </justification>
  </clause>

  <clause id="33796">
    <literal><![CDATA[
      L((x \ a(y * x,z,y * x)) \ y,x,x) = L(x * y,z,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(13284(a,1),33112(a,1,1))].">
      <j1 rule="para" parents="13284 33112"/>
    </justification>
  </clause>

  <clause id="33797">
    <literal><![CDATA[
      x * (a(y * x,z,y * x) \ y) = L(x * y,z,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13510,a(flip),b,33796,a)].">
      <j1 rule="hyper" parents="64 13510 33796"/>
    </justification>
  </clause>

  <clause id="33798">
    <literal><![CDATA[
      L(x * y,z,(x \ 1) \ y) = L(x * y,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27086,a(flip),b,33797,a),flip(a)].">
      <j1 rule="hyper" parents="64 27086 33797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33799">
    <literal><![CDATA[
      L(x * y,z,x \ y) = L(x * y,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2234,a(flip),b,33798,a)].">
      <j1 rule="hyper" parents="64 2234 33798"/>
    </justification>
  </clause>

  <clause id="33800">
    <literal><![CDATA[
      (L(x,y,z) \ x) * ((u / x) * L(x,y,z)) = L(u,L(x,y,z) \ x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33135,a(flip),b,33140,a)].">
      <j1 rule="hyper" parents="64 33135 33140"/>
    </justification>
  </clause>

  <clause id="33801">
    <literal><![CDATA[
      (L(x,y,z) \ x) * ((u / x) * L(x,y,z)) = R(u,L(x,y,z),L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(3196(a,1),33145(a,1,2))].">
      <j1 rule="para" parents="3196 33145"/>
    </justification>
  </clause>

  <clause id="33802">
    <literal><![CDATA[
      x * R(T(y \ L(y,z,u),y * x),y,x) = y \ (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(5550(a,1),33163(a,2,2,1))].">
      <j1 rule="para" parents="5550 33163"/>
    </justification>
  </clause>

  <clause id="33803">
    <literal><![CDATA[
      x * R(T(y \ L(y,z,u),y * x),y,x) = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,24852,a(flip),b,33802,a),flip(a)].">
      <j1 rule="hyper" parents="373 24852 33802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33804">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),y,x) = (x / y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(26994(a,1),33803(a,1,2))].">
      <j1 rule="para" parents="26994 33803"/>
    </justification>
  </clause>

  <clause id="33805">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),y,x) = L(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,23898,a,b,33804,a),flip(a)].">
      <j1 rule="hyper" parents="373 23898 33804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33806">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) = u \ ((u / x) * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(149,a,33804,a),flip(a)].">
      <j1 rule="hyper" parents="149 33804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33807">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) = u \ (L(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(139,a,23898,a,b,33804,a),flip(a)].">
      <j1 rule="hyper" parents="139 23898 33804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33808">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,L(x,y,z) \ u) = (L(x,y,z) \ u) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,24853,a(flip),b,33804,a),flip(a)].">
      <j1 rule="hyper" parents="139 24853 33804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33809">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,z * y) = (z * y) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(139,a,3205,a(flip),b,33804,a),flip(a)].">
      <j1 rule="hyper" parents="139 3205 33804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33810">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,y,z) * z = L(y,x,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26747,a,b,33805,a)].">
      <j1 rule="hyper" parents="64 26747 33805"/>
    </justification>
  </clause>

  <clause id="33811">
    <literal><![CDATA[
      (x * y) \ (x * L(y,z,u)) = x \ (L(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(139,a,33805,a(flip),b,632,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 33805 632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33812">
    <literal><![CDATA[
      L(x,y,z) * (x \ z) = z * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(33190(a,1),33805(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33190 33805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33813">
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) * (x \ y) = y * (x \ L(x,y * L(y,z,u),y))
    ]]></literal>
    <justification jstring="[para(33155(a,1),33812(a,1,1))].">
      <j1 rule="para" parents="33155 33812"/>
    </justification>
  </clause>

  <clause id="33814">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,x * u) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11086,a(flip),b,33806,a),flip(a)].">
      <j1 rule="hyper" parents="373 11086 33806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33815">
    <literal><![CDATA[
      (x * y) \ (L(x,z,u) * y) = y \ (L(x,z,u) * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,24918,a(flip),b,33807,a)].">
      <j1 rule="hyper" parents="64 24918 33807"/>
    </justification>
  </clause>

  <clause id="33816">
    <literal><![CDATA[
      L(x \ (L(y,z,u) * (y \ x)),w,y) = L(y \ L(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(33807(a,1),33162(a,1,1))].">
      <j1 rule="para" parents="33807 33162"/>
    </justification>
  </clause>

  <clause id="33817">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u * x) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(24201,a,33814,a)].">
      <j1 rule="hyper" parents="24201 33814"/>
    </justification>
  </clause>

  <clause id="33818">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (y * z)) = (x * y) \ ((x * (y * z)) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,646,a(flip),b,33809,a)].">
      <j1 rule="hyper" parents="64 646 33809"/>
    </justification>
  </clause>

  <clause id="33819">
    <literal><![CDATA[
      L(x,L(y * L(y,z,u),y,u * z),w) = L(x,(u * z) \ ((u * (z * y)) / y),w)
    ]]></literal>
    <justification jstring="[para(33809(a,1),29878(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33809 29878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33820">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) \ x = (L(y,z,u) \ x) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,15002,a(flip),b,33808,a)].">
      <j1 rule="hyper" parents="64 15002 33808"/>
    </justification>
  </clause>

  <clause id="33821">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) \ u = (L(x,y,z) \ u) \ (x \ u)
    ]]></literal>
    <justification jstring="[para(23887(a,1),33820(a,1,1))].">
      <j1 rule="para" parents="23887 33820"/>
    </justification>
  </clause>

  <clause id="33822">
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) * (x \ y) = y * (x \ L(x,y,y * L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(33155(a,1),33813(a,2,2,2))].">
      <j1 rule="para" parents="33155 33813"/>
    </justification>
  </clause>

  <clause id="33823">
    <literal><![CDATA[
      T(x,y) * L(y \ L(y,z,u),y,x) = y \ (x * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5591(a,1),33164(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5591 33164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33825">
    <literal><![CDATA[
      (x * y) \ (y * L(x,z,u)) = y \ (x \ (y * L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(139,a,33823,a(flip),b,10962,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 33823 10962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33826">
    <literal><![CDATA[
      (L(x \ L(x,y,z),x,u) \ T(u,x)) / T(T(u,x),L(x \ L(x,y,z),x,u)) = T(T(u,x) / (x \ (u * L(x,y,z))),L(x \ L(x,y,z),x,u))
    ]]></literal>
    <justification jstring="[para(33823(a,1),25992(a,2,1,2))].">
      <j1 rule="para" parents="33823 25992"/>
    </justification>
  </clause>

  <clause id="33827">
    <literal><![CDATA[
      (T(L(x,y,z),x) * L(x \ L(x,y,z),x,L(x,y,z))) \ 1 = x \ (((L(x,y,z) * L(x,y,z)) / x) \ x)
    ]]></literal>
    <justification jstring="[para(33823(a,2),33676(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33823 33676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33828">
    <literal><![CDATA[
      (x * y) \ (z \ ((x * y) * L(z,y,x))) = (z * (x * y)) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(100(a,1),33825(a,1,2)),flip(a)].">
      <j1 rule="para" parents="100 33825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33829">
    <literal><![CDATA[
      (x * (y * z)) \ (y * (z * x)) = (y * z) \ (x \ (y * (z * x)))
    ]]></literal>
    <justification jstring="[para(100(a,1),33828(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="100 33828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33830">
    <literal><![CDATA[
      L(T(x,a(y,z,u)),a(y,z,u),u) = L(x,T(u,a(y,z,u)),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(1021,a,33301,a)].">
      <j1 rule="hyper" parents="1021 33301"/>
    </justification>
  </clause>

  <clause id="33831">
    <literal><![CDATA[
      L(x,T(y,a(z,u,y)),a(z,u,y)) = L(x,a(z,u,y),y)
    ]]></literal>
    <justification jstring="[hyper(23184,a,33830,a),flip(a)].">
      <j1 rule="hyper" parents="23184 33830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33832">
    <literal><![CDATA[
      L(x,a(y,z,u),u) = L(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(29565,a,33831,a),flip(a)].">
      <j1 rule="hyper" parents="29565 33831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33835">
    <literal><![CDATA[
      L(x,y,a(L(z,z,u * y),u,y)) = L(x,z \ R(z,u,y),y)
    ]]></literal>
    <justification jstring="[para(32467(a,1),33832(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32467 33832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33836">
    <literal><![CDATA[
      a(x,y,L(a(z,u,u \ 1) \ 1,w,v5)) = a(x,y,L(a(u,u,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,30998,a(flip),b,33369,a),flip(a)].">
      <j1 rule="hyper" parents="373 30998 33369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33837">
    <literal><![CDATA[
      a(x,L(((y * z) \ y) * z,u,w),v5) = a(x,L(a(y,z,z \ 1),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32203,a(flip),b,33371,a),flip(a)].">
      <j1 rule="hyper" parents="64 32203 33371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33838">
    <literal><![CDATA[
      a(x,L(((y * z) \ y) * z,u,w),v5) = a(x,a(L(y,u,w),z,z \ 1),v5)
    ]]></literal>
    <justification jstring="[para(4248(a,2),33837(a,2,2))].">
      <j1 rule="para" parents="4248 33837"/>
    </justification>
  </clause>

  <clause id="33839">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * a(w,L(z,u,w),u)) = a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27639,a(flip),b,33463,a),flip(a)].">
      <j1 rule="hyper" parents="373 27639 33463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33840">
    <literal><![CDATA[
      ((x \ a(x,x,y)) * (x \ a(x,x,y))) \ (x \ y) = (a(x,x,y) \ x) * y
    ]]></literal>
    <justification jstring="[para(30165(a,1),33648(a,2,1))].">
      <j1 rule="para" parents="30165 33648"/>
    </justification>
  </clause>

  <clause id="33841">
    <literal><![CDATA[
      (a(x,x,y) / (1 / (x \ a(x,x,y)))) \ y = (a(x,x,y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,1089,a(flip),b,33840,a)].">
      <j1 rule="hyper" parents="64 1089 33840"/>
    </justification>
  </clause>

  <clause id="33842">
    <literal><![CDATA[
      (a(x,x,y) / ((a(x,x,y) / x) \ 1)) \ y = (a(x,x,y) \ x) * y
    ]]></literal>
    <justification jstring="[para(25195(a,1),33841(a,1,1,2))].">
      <j1 rule="para" parents="25195 33841"/>
    </justification>
  </clause>

  <clause id="33843">
    <literal><![CDATA[
      (a(x,x,y) / (a(x,x,y) \ x)) \ y = (a(x,x,y) \ x) * y
    ]]></literal>
    <justification jstring="[para(30165(a,1),33842(a,1,1,2))].">
      <j1 rule="para" parents="30165 33842"/>
    </justification>
  </clause>

  <clause id="33844">
    <literal><![CDATA[
      (a(x,x,y) * (a(x,x,y) / x)) \ y = (a(x,x,y) \ x) * y
    ]]></literal>
    <justification jstring="[para(27166(a,1),33843(a,1,1))].">
      <j1 rule="para" parents="27166 33843"/>
    </justification>
  </clause>

  <clause id="33845">
    <literal><![CDATA[
      a(x,x,y) * (a(x,x,y) / x) = y / (x * L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(225,a,30433,a(flip),b,33844,a),flip(a)].">
      <j1 rule="hyper" parents="225 30433 33844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33846">
    <literal><![CDATA[
      (1 / (x / (y * x))) \ a(y,y,x) = x / (y * L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30995,a,b,33845,a)].">
      <j1 rule="hyper" parents="64 30995 33845"/>
    </justification>
  </clause>

  <clause id="33847">
    <literal><![CDATA[
      (a(L(x,y,y),L(x,y,y),y) \ 1) * (x \ L(y,y,x)) = (R(x,y,y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(26871(a,1),33650(a,1,1,1))].">
      <j1 rule="para" parents="26871 33650"/>
    </justification>
  </clause>

  <clause id="33848">
    <literal><![CDATA[
      L(x,L(K(y,z) * (u \ w),u,u) * v5,v6) = L(x,(u * w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29429,a(flip),b,33658,a),flip(a)].">
      <j1 rule="hyper" parents="373 29429 33658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33850">
    <literal><![CDATA[
      L(x,((K(y,z) / u) * w) * v5,v6) = L(x,(u * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(26111(a,1),33848(a,1,2,1))].">
      <j1 rule="para" parents="26111 33848"/>
    </justification>
  </clause>

  <clause id="33851">
    <literal><![CDATA[
      L(x,(y * (z \ K(u,w))) * v5,v6) = L(x,(z * y) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29770,a(flip),b,33850,a)].">
      <j1 rule="hyper" parents="64 29770 33850"/>
    </justification>
  </clause>

  <clause id="33852">
    <literal><![CDATA[
      a(x,y,((z * u) \ z) * a(u,u,z)) = a(x,y,L(z \ (u \ z),u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30781,a(flip),b,33726,a)].">
      <j1 rule="hyper" parents="64 30781 33726"/>
    </justification>
  </clause>

  <clause id="33853">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * a(u,u,z)) = a(x,y,L(z \ (u \ z),u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27721,a(flip),b,33852,a)].">
      <j1 rule="hyper" parents="64 27721 33852"/>
    </justification>
  </clause>

  <clause id="33854">
    <literal><![CDATA[
      a((x * R(y \ 1,z,z)) * u,w,v5) = a((((y / z) / z) * x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32509,a(flip),b,33789,a),flip(a)].">
      <j1 rule="hyper" parents="64 32509 33789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33855">
    <literal><![CDATA[
      a((x * R(y \ 1,z,z)) * u,w,v5) = a(((z \ (y / z)) * x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32396,a(flip),b,33854,a),flip(a)].">
      <j1 rule="hyper" parents="373 32396 33854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33856">
    <literal><![CDATA[
      a((x * R(y \ 1,z,z)) * u,w,v5) = a(((z \ (z \ y)) * x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32667,a(flip),b,33855,a),flip(a)].">
      <j1 rule="hyper" parents="373 32667 33855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33857">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y,z,u) \ y) = L(x,L(y,z,u) \ y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,33800,a(flip),b,33801,a),flip(a)].">
      <j1 rule="hyper" parents="64 33800 33801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33858">
    <literal><![CDATA[
      (((x \ L(x,y,z)) * u) * w) / ((x \ L(x,y,z)) * w) = R(u,x * L(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,5612,a(flip),b,23743,a),flip(a)].">
      <j1 rule="hyper" parents="373 5612 23743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33859">
    <literal><![CDATA[
      (x * y) / (x * (y * a(z,u,w))) = (x * (y * a(z,u,w))) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,23769,a),flip(a)].">
      <j1 rule="hyper" parents="64 102 23769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33860">
    <literal><![CDATA[
      (x * (y * a(z,z,y))) \ (x * y) = (x * y) / (x * (z \ ((1 / z) \ y)))
    ]]></literal>
    <justification jstring="[para(30220(a,2),33859(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="30220 33859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33861">
    <literal><![CDATA[
      ((x * x) \ y) \ T(y * ((x * x) \ 1),K(z,u)) = K(y,(x * x) \ K(z,u))
    ]]></literal>
    <justification jstring="[para(24879(a,1),24394(a,1,2))].">
      <j1 rule="para" parents="24879 24394"/>
    </justification>
  </clause>

  <clause id="33862">
    <literal><![CDATA[
      ((x * x) \ y) \ T(y / (x * x),K(z,u)) = K(y,(x * x) \ K(z,u))
    ]]></literal>
    <justification jstring="[para(557(a,1),33861(a,1,2,1))].">
      <j1 rule="para" parents="557 33861"/>
    </justification>
  </clause>

  <clause id="33863">
    <literal><![CDATA[
      K(K(x,y) * (z * z),(z * z) \ u) = K(u,(z * z) \ K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,27108,a(flip),b,33862,a)].">
      <j1 rule="hyper" parents="64 27108 33862"/>
    </justification>
  </clause>

  <clause id="33864">
    <literal><![CDATA[
      K(K(x,y) * (z * z),z \ (z \ u)) = K(u,(z * z) \ K(x,y))
    ]]></literal>
    <justification jstring="[hyper(25260,a,33863,a)].">
      <j1 rule="hyper" parents="25260 33863"/>
    </justification>
  </clause>

  <clause id="33865">
    <literal><![CDATA[
      K(K(x,y) * (z * z),z \ (z \ u)) = K(u,z \ (z \ K(x,y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,23002,a(flip),b,33864,a),flip(a)].">
      <j1 rule="hyper" parents="373 23002 33864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33866">
    <literal><![CDATA[
      K(x * T(x,y),x \ (x \ z)) = K(z,x \ (x \ K(x,y)))
    ]]></literal>
    <justification jstring="[hyper(17265,a,33865,a)].">
      <j1 rule="hyper" parents="17265 33865"/>
    </justification>
  </clause>

  <clause id="33867">
    <literal><![CDATA[
      K(x * T(x,y),x \ (x \ z)) = K(x * T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31737,a(flip),b,33866,a),flip(a)].">
      <j1 rule="hyper" parents="373 31737 33866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33868">
    <literal><![CDATA[
      K(x * T(x,y),x \ z) = K(x * T(x,y),x * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),33867(a,1,2,2))].">
      <j1 rule="para" parents="9 33867"/>
    </justification>
  </clause>

  <clause id="33869">
    <literal><![CDATA[
      (x \ y) * K(x * T(x,y),x * y) = (x \ y) * K(y * x,x \ y)
    ]]></literal>
    <justification jstring="[para(33868(a,1),17479(a,1,2))].">
      <j1 rule="para" parents="33868 17479"/>
    </justification>
  </clause>

  <clause id="33870">
    <literal><![CDATA[
      (x \ y) * K(y * x,x \ y) = (x \ y) * K(x * x,y * x)
    ]]></literal>
    <justification jstring="[para(17615(a,1),33869(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17615 33869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33871">
    <literal><![CDATA[
      (x \ y) * K(y * x,x \ y) = T(y / x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,22825,a(flip),b,33870,a),flip(a)].">
      <j1 rule="hyper" parents="373 22825 33870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33872">
    <literal><![CDATA[
      T(x * y,y * y) \ (y \ x) = (x * y) \ T(x / y,y \ 1)
    ]]></literal>
    <justification jstring="[para(33871(a,1),16556(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33871 16556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33873">
    <literal><![CDATA[
      (x * y) \ T(x / y,y \ 1) = y \ (x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,31164,a(flip),b,33872,a),flip(a)].">
      <j1 rule="hyper" parents="64 31164 33872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33874">
    <literal><![CDATA[
      (1 / x) * (((L(x,y,z) \ x) * x) * u) = x * ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(9363(a,1),24802(a,2,2,1))].">
      <j1 rule="para" parents="9363 24802"/>
    </justification>
  </clause>

  <clause id="33875">
    <literal><![CDATA[
      T(R(x \ 1,x,y),R(x \ 1,x,y) * y) = T(y / x,x * x) / y
    ]]></literal>
    <justification jstring="[para(7579(a,1),24808(a,2,1))].">
      <j1 rule="para" parents="7579 24808"/>
    </justification>
  </clause>

  <clause id="33877">
    <literal><![CDATA[
      T(R(x \ 1,x,y),x \ y) = T(y / x,x * x) / y
    ]]></literal>
    <justification jstring="[para(2998(a,1),33875(a,1,2))].">
      <j1 rule="para" parents="2998 33875"/>
    </justification>
  </clause>

  <clause id="33878">
    <literal><![CDATA[
      T(x / y,y * y) / x = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,5143,a(flip),b,33877,a),flip(a)].">
      <j1 rule="hyper" parents="64 5143 33877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33879">
    <literal><![CDATA[
      L(x,y,(z * (u \ T(u / w,w * w))) \ v5) = L(x,y,(z * ((w * u) \ u)) \ v5)
    ]]></literal>
    <justification jstring="[para(33878(a,1),29003(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="33878 29003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33880">
    <literal><![CDATA[
      L(x,y,L(R(z,z,u),u / z,u / z)) = L(x,y,(z \ u) * (z \ ((1 / z) \ u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,28980,a(flip),b,25049,a),flip(a)].">
      <j1 rule="hyper" parents="373 28980 25049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33881">
    <literal><![CDATA[
      ((a(x,y,z) * a(x,y,z)) \ u) * (a(x,y,z) * w) = u * ((a(x,y,z) \ 1) * w)
    ]]></literal>
    <justification jstring="[para(13923(a,1),25319(a,2,2,1))].">
      <j1 rule="para" parents="13923 25319"/>
    </justification>
  </clause>

  <clause id="33882">
    <literal><![CDATA[
      (x * (y / x)) \ (R(x,z,u) * (y / x)) = y \ (R(x,z,u) * (x \ y))
    ]]></literal>
    <justification jstring="[para(4681(a,1),25483(a,1,2))].">
      <j1 rule="para" parents="4681 25483"/>
    </justification>
  </clause>

  <clause id="33883">
    <literal><![CDATA[
      T(x,y) \ (R(y,z,u) * (y \ T(x,y))) = x \ (R(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,27235,a(flip),b,33882,a)].">
      <j1 rule="hyper" parents="64 27235 33882"/>
    </justification>
  </clause>

  <clause id="33884">
    <literal><![CDATA[
      T(x,y) \ T(R(y,z,u) * (y \ x),y) = x \ (R(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(28613(a,2),33883(a,1,2))].">
      <j1 rule="para" parents="28613 33883"/>
    </justification>
  </clause>

  <clause id="33885">
    <literal><![CDATA[
      T(x,y) \ (y \ (x * R(y,z,u))) = x \ (R(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(25152(a,1),33884(a,1,2))].">
      <j1 rule="para" parents="25152 33884"/>
    </justification>
  </clause>

  <clause id="33886">
    <literal><![CDATA[
      T(x,L(x,y,y)) \ (L(x,y,y) \ (x * R(L(x,y,y),z,u))) = x \ (R(L(x,y,y),z,u) * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(1243(a,1),33885(a,2,2,2))].">
      <j1 rule="para" parents="1243 33885"/>
    </justification>
  </clause>

  <clause id="33887">
    <literal><![CDATA[
      L(x,L(L(y,y,z),y \ z,y \ z),u) = L(x,(y \ z) * ((1 / y) \ (y \ z)),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29547,a(flip),b,25580,a),flip(a)].">
      <j1 rule="hyper" parents="373 29547 25580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33888">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),y) * L(y,z,u) = y * (K(x,y) * ((y \ L(y,z,u)) * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,4534,a(flip),b,25592,a),flip(a)].">
      <j1 rule="hyper" parents="373 4534 25592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33889">
    <literal><![CDATA[
      (((1 / x) \ y) \ z) * T(u,y \ (x \ z)) = u * ((R(x,x,y) * y) \ z)
    ]]></literal>
    <justification jstring="[para(28530(a,1),25703(a,1,2))].">
      <j1 rule="para" parents="28530 25703"/>
    </justification>
  </clause>

  <clause id="33890">
    <literal><![CDATA[
      (((1 / x) \ y) \ z) * T(u,y \ (x \ z)) = u * (((1 / x) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(1913(a,1),33889(a,2,2,1))].">
      <j1 rule="para" parents="1913 33889"/>
    </justification>
  </clause>

  <clause id="33892">
    <literal><![CDATA[
      (L(x,y,z) * (u / x)) \ (x * (u / x)) = (L(x,y,z) * (x \ u)) \ u
    ]]></literal>
    <justification jstring="[para(4680(a,1),25731(a,1,1))].">
      <j1 rule="para" parents="4680 25731"/>
    </justification>
  </clause>

  <clause id="33893">
    <literal><![CDATA[
      T(x,(y * z) * T(K(z \ u,z) * w,v5)) = T(x,y * (T(z,u) * T(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27028,a(flip),b,25736,a),flip(a)].">
      <j1 rule="hyper" parents="64 27028 25736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33894">
    <literal><![CDATA[
      T(x,T((y * y) * (K(y \ z,y) * u),w)) = T(x,y * (T(y,z) * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22998,a,b,33893,a)].">
      <j1 rule="hyper" parents="64 22998 33893"/>
    </justification>
  </clause>

  <clause id="33895">
    <literal><![CDATA[
      T(x,T(K(y,z) * ((y * y) * u),w)) = T(x,y * (T(y,z) * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22833,a(flip),b,33894,a)].">
      <j1 rule="hyper" parents="64 22833 33894"/>
    </justification>
  </clause>

  <clause id="33896">
    <literal><![CDATA[
      T(x,T((y * T(y,z)) * u,w)) = T(x,y * (T(y,z) * T(u,w)))
    ]]></literal>
    <justification jstring="[para(24788(a,1),33895(a,1,2,1))].">
      <j1 rule="para" parents="24788 33895"/>
    </justification>
  </clause>

  <clause id="33897">
    <literal><![CDATA[
      T(x,T((y * T(y,z)) * z,u)) = T(x,y * (T(z,u) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,18230,a(flip),b,33896,a),flip(a)].">
      <j1 rule="hyper" parents="373 18230 33896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33898">
    <literal><![CDATA[
      T(x,T(y * (T(y,z) * z),u)) = T(x,y * (T(z,u) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,28752,a(flip),b,33897,a)].">
      <j1 rule="hyper" parents="64 28752 33897"/>
    </justification>
  </clause>

  <clause id="33899">
    <literal><![CDATA[
      (x \ 1) * (K(y * x,x \ 1) * (y * R(x,z,u))) = (y * x) * R(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(4556,a,25751,a)].">
      <j1 rule="hyper" parents="4556 25751"/>
    </justification>
  </clause>

  <clause id="33900">
    <literal><![CDATA[
      (x * T((T(x,y) \ 1) \ 1,z)) \ 1 = (T(x,y) \ 1) * (T(x,T(z,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(14457(a,1),25865(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14457 25865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33901">
    <literal><![CDATA[
      T(x,y) \ (1 / T(x,T(z,y))) = (x * T((T(x,y) \ 1) \ 1,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,24742,a(flip),b,33900,a)].">
      <j1 rule="hyper" parents="373 24742 33900"/>
    </justification>
  </clause>

  <clause id="33902">
    <literal><![CDATA[
      (x * T((T(x,y) \ 1) \ 1,z)) \ 1 = x \ (1 / T(T(x,z),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,14816,a(flip),b,33901,a),flip(a)].">
      <j1 rule="hyper" parents="64 14816 33901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33903">
    <literal><![CDATA[
      (x * T(T((x \ 1) \ 1,y),z)) \ 1 = x \ (1 / T(T(x,z),y))
    ]]></literal>
    <justification jstring="[para(3568(a,2),33902(a,1,1,2,1))].">
      <j1 rule="para" parents="3568 33902"/>
    </justification>
  </clause>

  <clause id="33904">
    <literal><![CDATA[
      ((1 / x) \ T(T(x,y),z)) \ 1 = x \ (1 / T(T(x,z),y))
    ]]></literal>
    <justification jstring="[para(15193(a,1),33903(a,1,1))].">
      <j1 rule="para" parents="15193 33903"/>
    </justification>
  </clause>

  <clause id="33905">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) * T(y,w) = (x * y) * (y \ R(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[para(2299(a,1),26029(a,1,1))].">
      <j1 rule="para" parents="2299 26029"/>
    </justification>
  </clause>

  <clause id="33906">
    <literal><![CDATA[
      L(K(x \ K(y,z),x) * (u * K(y,z)),w,v5) = L(u,w,v5) * ((x \ K(y,z)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26085,a,b,26082,a)].">
      <j1 rule="hyper" parents="64 26085 26082"/>
    </justification>
  </clause>

  <clause id="33907">
    <literal><![CDATA[
      ((1 / x) * L(x,x,x * y)) \ ((x * x) * z) = (x \ L(1 / x,x,y)) \ z
    ]]></literal>
    <justification jstring="[para(1391(a,1),26681(a,2,1))].">
      <j1 rule="para" parents="1391 26681"/>
    </justification>
  </clause>

  <clause id="33908">
    <literal><![CDATA[
      (x \ L(x,x,x * y)) \ ((x * x) * z) = (x \ L(1 / x,x,y)) \ z
    ]]></literal>
    <justification jstring="[para(5590(a,1),33907(a,1,1))].">
      <j1 rule="para" parents="5590 33907"/>
    </justification>
  </clause>

  <clause id="33909">
    <literal><![CDATA[
      (x * x) * ((x \ L(x,x,x * y)) \ z) = (x \ L(1 / x,x,y)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,23751,a(flip),b,33908,a)].">
      <j1 rule="hyper" parents="64 23751 33908"/>
    </justification>
  </clause>

  <clause id="33910">
    <literal><![CDATA[
      R(x,((y * ((z * z) * u)) * w) \ v5,v6) = R(x,((y * u) * w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,31713,a(flip),b,26729,a),flip(a)].">
      <j1 rule="hyper" parents="64 31713 26729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33912">
    <literal><![CDATA[
      R(x,(y * (z * ((u * u) * w))) \ v5,v6) = R(x,((z * w) * y) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26425,a,b,33910,a)].">
      <j1 rule="hyper" parents="64 26425 33910"/>
    </justification>
  </clause>

  <clause id="33913">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ ((u / x) * L(x,y,z)) = a(x \ L(x,y,z),x,x \ u)
    ]]></literal>
    <justification jstring="[para(5572(a,1),26890(a,1,1,1))].">
      <j1 rule="para" parents="5572 26890"/>
    </justification>
  </clause>

  <clause id="33914">
    <literal><![CDATA[
      a(x \ ((y * ((z * z) * u)) / w),v5,v6) = a(x \ (w \ (T(y,z * z) * u)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(32449,a,26909,a),flip(a)].">
      <j1 rule="hyper" parents="32449 26909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33915">
    <literal><![CDATA[
      (x / y) * ((1 / (x / y)) * z) = (y \ x) * ((1 / (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(4339(a,1),27012(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4339 27012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33916">
    <literal><![CDATA[
      ((x * y) \ T(x / y,y \ 1)) * ((1 / (y \ (x / (x * y)))) * z) = ((x / (x * y)) / y) * ((1 / ((x / (x * y)) / y)) * z)
    ]]></literal>
    <justification jstring="[para(33873(a,2),33915(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33873 33915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33917">
    <literal><![CDATA[
      (1 / x) \ ((1 / L(x,y,z)) * u) = (x \ 1) \ ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(9363(a,1),27015(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9363 27015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33918">
    <literal><![CDATA[
      (x \ (a(y,z,u) * L(R(x,w,v5),y,y))) * x = L(R(x,w,v5) * a(y,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30821,a,b,27021,a),flip(a)].">
      <j1 rule="hyper" parents="373 30821 27021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33919">
    <literal><![CDATA[
      L((x \ ((x * y) * a(z,u,w))) / a(z,u,w),a(z,u,w),x) = L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(23133(a,2),27110(a,1,1))].">
      <j1 rule="para" parents="23133 27110"/>
    </justification>
  </clause>

  <clause id="33920">
    <literal><![CDATA[
      L(x,a(y,z,u * w),v5) = L(x,a(y,z,w * u),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,24645,a(flip),b,27375,a)].">
      <j1 rule="hyper" parents="64 24645 27375"/>
    </justification>
  </clause>

  <clause id="33921">
    <literal><![CDATA[
      L(x,a(y,z,(u \ (u / w)) \ 1),v5) = L(x,a(y,z,w * a(u,w,w)),v5)
    ]]></literal>
    <justification jstring="[para(30515(a,2),33920(a,1,2,3))].">
      <j1 rule="para" parents="30515 33920"/>
    </justification>
  </clause>

  <clause id="33922">
    <literal><![CDATA[
      L(x,a(y,z,(u \ (w \ u)) \ 1),v5) = L(x,a(y,z,w * a(u,w,w)),v5)
    ]]></literal>
    <justification jstring="[para(27419(a,1),33921(a,1,2))].">
      <j1 rule="para" parents="27419 33921"/>
    </justification>
  </clause>

  <clause id="33923">
    <literal><![CDATA[
      a(x,y,((z * (u * u)) / w) * v5) = a(x,y,(w \ z) * ((u * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27617,a(flip),b,27691,a),flip(a)].">
      <j1 rule="hyper" parents="64 27617 27691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33925">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),u,u)) = a(x,y,(z \ u) * ((z * z) * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27594,a,b,33923,a)].">
      <j1 rule="hyper" parents="64 27594 33923"/>
    </justification>
  </clause>

  <clause id="33926">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),u,u)) = a(x,y,(z \ u) * (u \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27501,a(flip),b,33925,a),flip(a)].">
      <j1 rule="hyper" parents="373 27501 33925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33927">
    <literal><![CDATA[
      (x / (x / y)) \ (x * a(z,u,w)) = y \ (a(z,u,w) * (y * (x / y)))
    ]]></literal>
    <justification jstring="[para(82(a,1),27808(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="82 27808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33928">
    <literal><![CDATA[
      x \ (a(y,z,u) * (x * (w / x))) = (a(y,z,u) * w) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,28818,a(flip),b,33927,a),flip(a)].">
      <j1 rule="hyper" parents="64 28818 33927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33930">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) / w = w \ (a(x,y,z) * (w * u))
    ]]></literal>
    <justification jstring="[para(11(a,1),33928(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11 33928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33931">
    <literal><![CDATA[
      (a(x,y,z) * (u * w)) / w = w \ ((w * u) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,23180,a(flip),b,33930,a),flip(a)].">
      <j1 rule="hyper" parents="373 23180 33930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33932">
    <literal><![CDATA[
      a(x,y,z) \ (u \ ((u * z) * a(x,y,z))) = a(z,a(x,y,z),u) \ z
    ]]></literal>
    <justification jstring="[para(33931(a,1),33524(a,1,2))].">
      <j1 rule="para" parents="33931 33524"/>
    </justification>
  </clause>

  <clause id="33933">
    <literal><![CDATA[
      a(x,a(y,z,x),u) \ x = a(u,x,a(y,z,x)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,33291,a(flip),b,33932,a),flip(a)].">
      <j1 rule="hyper" parents="64 33291 33932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33934">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * (w / u)) = ((w / (w / u)) * a(x,y,z)) \ w
    ]]></literal>
    <justification jstring="[para(82(a,1),27809(a,1,2,1))].">
      <j1 rule="para" parents="82 27809"/>
    </justification>
  </clause>

  <clause id="33935">
    <literal><![CDATA[
      ((x / (x / y)) * a(z,u,w)) \ x = x / (a(z,u,w) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31795,a(flip),b,33934,a),flip(a)].">
      <j1 rule="hyper" parents="64 31795 33934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33937">
    <literal><![CDATA[
      x / (a(y,z,u) * (w \ x)) = ((x / w) * a(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(79(a,1),33935(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 33935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33938">
    <literal><![CDATA[
      x / (a(y,z,u) * (w \ x)) = (a(y,z,u) * (x / w)) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,23560,a,b,33937,a),flip(a)].">
      <j1 rule="hyper" parents="373 23560 33937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33939">
    <literal><![CDATA[
      (a(x,y,z) * (u / (u / w))) \ u = u / (w * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,24796,a(flip),b,33938,a),flip(a)].">
      <j1 rule="hyper" parents="64 24796 33938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33940">
    <literal><![CDATA[
      x / (x / (y * a(z,u,w))) = a(z,u,w) * (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(225,a,24796,a(flip),b,33938,a(flip))].">
      <j1 rule="hyper" parents="225 24796 33938"/>
    </justification>
  </clause>

  <clause id="33941">
    <literal><![CDATA[
      a(x,y,z) * (u / (u / (a(x,y,z) \ w))) = u / (u / w)
    ]]></literal>
    <justification jstring="[para(23135(a,1),33940(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23135 33940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33942">
    <literal><![CDATA[
      ((x / (y * x)) / y) \ K(y * (x / (y * x)),y * y) = 1 / ((x / (y * x)) / y)
    ]]></literal>
    <justification jstring="[para(14711(a,1),27821(a,1,2))].">
      <j1 rule="para" parents="14711 27821"/>
    </justification>
  </clause>

  <clause id="33943">
    <literal><![CDATA[
      (x * T(y / z,T(z,z))) * T(y / z,u) = (x * T(y / z,u)) * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,24951,a(flip),b,27828,a),flip(a)].">
      <j1 rule="hyper" parents="373 24951 27828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33944">
    <literal><![CDATA[
      (x * T(y / z,z)) * T(y / z,u) = (x * T(y / z,u)) * (z \ y)
    ]]></literal>
    <justification jstring="[para(114(a,1),33943(a,1,1,2,2))].">
      <j1 rule="para" parents="114 33943"/>
    </justification>
  </clause>

  <clause id="33945">
    <literal><![CDATA[
      (x * T(y / z,u)) * (z \ y) = (x * (z \ y)) * T(y / z,u)
    ]]></literal>
    <justification jstring="[para(117(a,1),33944(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="117 33944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33946">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (R(x \ 1,y,z) * R(x,u,w)) = R(x,y,z) * (x \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,2763,a(flip),b,27874,a)].">
      <j1 rule="hyper" parents="64 2763 27874"/>
    </justification>
  </clause>

  <clause id="33947">
    <literal><![CDATA[
      x / T((1 / y) * x,T(y,x * z)) = ((1 / y) * x) \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16484,a(flip),b,27945,a),flip(a)].">
      <j1 rule="hyper" parents="64 16484 27945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33948">
    <literal><![CDATA[
      x / T((1 / y) * x,T(y,z)) = ((1 / y) * x) \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(25293(a,1),33947(a,1,2))].">
      <j1 rule="para" parents="25293 33947"/>
    </justification>
  </clause>

  <clause id="33949">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) * (L(T(z,v5),u,w) \ v6)) = a(x,y,(z * z) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,31773,a(flip),b,27973,a)].">
      <j1 rule="hyper" parents="64 31773 27973"/>
    </justification>
  </clause>

  <clause id="33950">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) * (L(z,u,w) \ v5)) = a(x,y,(z * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27506,a(flip),b,33949,a)].">
      <j1 rule="hyper" parents="64 27506 33949"/>
    </justification>
  </clause>

  <clause id="33951">
    <literal><![CDATA[
      a(x,y,(z * z) \ (R(u / L(z,w,v5),L(z,w,v5),L(z,w,v5)) \ v6)) = a(x,y,L(z \ 1,w,v5) * ((1 / L(z,w,v5)) \ ((u * L(z,w,v5)) \ v6)))
    ]]></literal>
    <justification jstring="[para(1373(a,1),33950(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="1373 33950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33952">
    <literal><![CDATA[
      a(x,y,(1 / z) * R((u * u) * w,v5,v5)) = a(x,y,(z \ (u * u)) * L(w,v5,v5))
    ]]></literal>
    <justification jstring="[para(1981(a,2),27988(a,1,3,2))].">
      <j1 rule="para" parents="1981 27988"/>
    </justification>
  </clause>

  <clause id="33953">
    <literal><![CDATA[
      K(x,(y * T(T(y,z) \ 1,u)) * w) = K(x,K(y \ 1,u) * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,17935,a(flip),b,28001,a),flip(a)].">
      <j1 rule="hyper" parents="64 17935 28001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33955">
    <literal><![CDATA[
      K(x,(y * T(T(y,z) \ 1,u)) * w) = K(x,K(y,u) * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,16821,a(flip),b,33953,a),flip(a)].">
      <j1 rule="hyper" parents="373 16821 33953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33956">
    <literal><![CDATA[
      K(x,(y * T(T(y,z) \ 1,u)) * w) = K(x,K(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,28965,a(flip),b,33955,a),flip(a)].">
      <j1 rule="hyper" parents="373 28965 33955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33957">
    <literal><![CDATA[
      K(x,T(T(T(y,z) \ 1,u) * (w * y),y)) = K(x,K(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28101,a,b,33956,a)].">
      <j1 rule="hyper" parents="64 28101 33956"/>
    </justification>
  </clause>

  <clause id="33958">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u) \ (w * y),y)) = K(x,K(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,16876,a(flip),b,33957,a)].">
      <j1 rule="hyper" parents="64 16876 33957"/>
    </justification>
  </clause>

  <clause id="33959">
    <literal><![CDATA[
      K(x,(T(T(y,z),u) / y) \ w) = K(x,K(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,25266,a(flip),b,33958,a)].">
      <j1 rule="hyper" parents="64 25266 33958"/>
    </justification>
  </clause>

  <clause id="33960">
    <literal><![CDATA[
      K(x,y * (T(T(y,z),u) \ w)) = K(x,K(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24703,a(flip),b,33959,a)].">
      <j1 rule="hyper" parents="64 24703 33959"/>
    </justification>
  </clause>

  <clause id="33961">
    <literal><![CDATA[
      R(x,y,((z \ (u / w)) * (v5 \ (v6 / v7))) * (K(v8,v9) \ v10)) = R(x,y,((v5 \ (v7 \ v6)) * (z \ (w \ u))) * v10)
    ]]></literal>
    <justification jstring="[hyper(373,a,27192,a(flip),b,28037,a),flip(a)].">
      <j1 rule="hyper" parents="373 27192 28037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33962">
    <literal><![CDATA[
      K(x,T(R(y,z,u) \ w,v5) * v6) = K(x,(y \ w) * (v6 * K(y * w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,28251,a(flip),b,28189,a),flip(a)].">
      <j1 rule="hyper" parents="64 28251 28189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33964">
    <literal><![CDATA[
      K(x,T(R(y,z,u) \ w,v5) * v6) = K(x,T(y \ w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,21564,a(flip),b,33962,a),flip(a)].">
      <j1 rule="hyper" parents="373 21564 33962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33965">
    <literal><![CDATA[
      K(x,T((y / z) \ u,w) * v5) = K(x,T(z * (y \ u),w) * v5)
    ]]></literal>
    <justification jstring="[para(684(a,1),33964(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="684 33964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33966">
    <literal><![CDATA[
      K(x,T(L(y,z,u) \ w,v5) * v6) = K(x,(y \ w) * (v6 * K(y * w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,28898,a(flip),b,28413,a),flip(a)].">
      <j1 rule="hyper" parents="64 28898 28413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33968">
    <literal><![CDATA[
      K(x,T(L(y,z,u) \ w,v5) * v6) = K(x,T(y \ w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,21564,a(flip),b,33966,a),flip(a)].">
      <j1 rule="hyper" parents="373 21564 33966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33969">
    <literal><![CDATA[
      K(x,K(y / z,u) * (L(z,w,v5) * (y \ v6))) = K(x,T(y / L(z,w,v5),u) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,28281,a(flip),b,28428,a)].">
      <j1 rule="hyper" parents="64 28281 28428"/>
    </justification>
  </clause>

  <clause id="33970">
    <literal><![CDATA[
      ((x \ (x \ y)) \ y) \ K(x * x,((x \ y) \ x) * y) = 1 / ((x \ (x \ y)) \ y)
    ]]></literal>
    <justification jstring="[para(22656(a,1),28443(a,1,2))].">
      <j1 rule="para" parents="22656 28443"/>
    </justification>
  </clause>

  <clause id="33971">
    <literal><![CDATA[
      ((x \ y) / y) \ K((y / (x * y)) \ x,z) = x \ T((y / (x * y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(25776(a,1),28521(a,2,2,1))].">
      <j1 rule="para" parents="25776 28521"/>
    </justification>
  </clause>

  <clause id="33972">
    <literal><![CDATA[
      ((x \ y) / y) \ K((x * y) * (y \ x),z) = x \ T((y / (x * y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(28198(a,1),33971(a,1,2))].">
      <j1 rule="para" parents="28198 33971"/>
    </justification>
  </clause>

  <clause id="33973">
    <literal><![CDATA[
      ((x \ y) / y) \ K(x * x,z) = x \ T((y / (x * y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(28168(a,1),33972(a,1,2))].">
      <j1 rule="para" parents="28168 33972"/>
    </justification>
  </clause>

  <clause id="33975">
    <literal><![CDATA[
      (a(x,x,x) / x) \ R(R(x,y,z),u,w) = R(R(x,y,z),u,w) / (1 / x)
    ]]></literal>
    <justification jstring="[para(7729(a,1),28595(a,1,1,1))].">
      <j1 rule="para" parents="7729 28595"/>
    </justification>
  </clause>

  <clause id="33976">
    <literal><![CDATA[
      (x / (x * x)) \ R(R(x,y,z),u,w) = R(R(x,y,z),u,w) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1854(a,1),33975(a,1,1))].">
      <j1 rule="para" parents="1854 33975"/>
    </justification>
  </clause>

  <clause id="33977">
    <literal><![CDATA[
      x * T((y \ z) * K(y,(y \ z) * z),x) = (y \ z) * (x * K(y,(y \ z) * z))
    ]]></literal>
    <justification jstring="[para(11119(a,1),28615(a,1,2,1))].">
      <j1 rule="para" parents="11119 28615"/>
    </justification>
  </clause>

  <clause id="33978">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (1 / a(x,y,z)) = a(x,y,z) * R(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(13923(a,1),28793(a,2,2,1))].">
      <j1 rule="para" parents="13923 28793"/>
    </justification>
  </clause>

  <clause id="33979">
    <literal><![CDATA[
      K((x * y) * (z / R(x,u,w)),T(v5,z)) = K(z * y,T(v5,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,28732,a(flip),b,28889,a),flip(a)].">
      <j1 rule="hyper" parents="373 28732 28889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33980">
    <literal><![CDATA[
      K((x * (y / x)) * (z / R(x,u,w)),T(v5,z)) = K((R(x,u,w) \ z) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,28245,a(flip),b,28890,a),flip(a)].">
      <j1 rule="hyper" parents="373 28245 28890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33981">
    <literal><![CDATA[
      K((R(x,y,z) \ u) * w,v5) = K(u * (w / x),T(v5,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,33979,a(flip),b,33980,a),flip(a)].">
      <j1 rule="hyper" parents="64 33979 33980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33983">
    <literal><![CDATA[
      K((R(x,y,z) \ u) * w,v5) = K((x \ u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,28244,a(flip),b,33981,a),flip(a)].">
      <j1 rule="hyper" parents="373 28244 33981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33984">
    <literal><![CDATA[
      K(x,T(y / (y / (z \ u)),w) \ v5) = K(x,T(u / z,y * (z * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28960,a(flip),b,28962,a),flip(a)].">
      <j1 rule="hyper" parents="64 28960 28962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33985">
    <literal><![CDATA[
      K(x,T(y / z,u * (z * w)) \ v5) = K(x,T(z \ y,u * w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28960,a(flip),b,33984,a),flip(a)].">
      <j1 rule="hyper" parents="64 28960 33984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33986">
    <literal><![CDATA[
      K(x,T(y / z,u * (y * w)) * v5) = K(x,T(y \ z,u * w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,33738,a(flip),b,33985,a)].">
      <j1 rule="hyper" parents="64 33738 33985"/>
    </justification>
  </clause>

  <clause id="33987">
    <literal><![CDATA[
      K(x,T(y / z,u * (y * w)) * v5) = K(x,T(z \ y,u * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,28621,a(flip),b,33986,a),flip(a)].">
      <j1 rule="hyper" parents="373 28621 33986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33988">
    <literal><![CDATA[
      K((x * T(x,y)) \ z,x * T(x,y)) = K(z,x * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(359,a,29183,a),flip(a)].">
      <j1 rule="hyper" parents="359 29183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33989">
    <literal><![CDATA[
      K(T(x,y) \ (x \ z),x * T(x,y)) = K(z,x * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,23046,a(flip),b,33988,a)].">
      <j1 rule="hyper" parents="64 23046 33988"/>
    </justification>
  </clause>

  <clause id="33990">
    <literal><![CDATA[
      L(x,y,a(T(z,u),u * z,u * z)) = L(x,y,a(z * (z * u),u * z,z))
    ]]></literal>
    <justification jstring="[para(27304(a,1),29202(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27304 29202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33991">
    <literal><![CDATA[
      L(x,y,a(T(z,u),u * z,u * z)) = L(x,y,a(L(u,z,z),u * z,z))
    ]]></literal>
    <justification jstring="[para(2640(a,1),33990(a,2,3))].">
      <j1 rule="para" parents="2640 33990"/>
    </justification>
  </clause>

  <clause id="33993">
    <literal><![CDATA[
      L(x,y,a(T(z,u),u * z,u * z)) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[para(31944(a,1),33991(a,2,3))].">
      <j1 rule="para" parents="31944 33991"/>
    </justification>
  </clause>

  <clause id="33994">
    <literal><![CDATA[
      L(x,y,a(z,u * z,u * z)) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[para(26779(a,1),33993(a,1,3))].">
      <j1 rule="para" parents="26779 33993"/>
    </justification>
  </clause>

  <clause id="33996">
    <literal><![CDATA[
      L(x,y,a(z,z * u,z * u)) = L(x,y,a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[para(31938(a,1),33994(a,1,3))].">
      <j1 rule="para" parents="31938 33994"/>
    </justification>
  </clause>

  <clause id="33997">
    <literal><![CDATA[
      T(K(x,y) * (z \ 1),u * (z \ K(x,y))) = T(K(x,y) / z,K(x,y) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,22929,a(flip),b,29380,a),flip(a)].">
      <j1 rule="hyper" parents="373 22929 29380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="33999">
    <literal><![CDATA[
      L(x,y,L(z / (u * T(w,u \ 1)),v5,v6)) = L(x,y,L((w * (u \ 1)) \ z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,23846,a(flip),b,29397,a),flip(a)].">
      <j1 rule="hyper" parents="373 23846 29397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34000">
    <literal><![CDATA[
      L(x,y,z * (((u / (w * u)) * u) \ v5)) = L(x,y,z * ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(82(a,1),29422(a,1,3,2,1,1)),flip(a)].">
      <j1 rule="para" parents="82 29422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34002">
    <literal><![CDATA[
      L(x,(y \ ((z * T(z,u)) * w)) * v5,v6) = L(x,((w / y) * (z * T(z,u))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(25871(a,1),29621(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="25871 29621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34003">
    <literal><![CDATA[
      ((x * x) \ y) * L(T(x * x,y),z,u) = L(x * x,u,z) * ((x * x) \ y)
    ]]></literal>
    <justification jstring="[para(850(a,1),29814(a,1,2,1))].">
      <j1 rule="para" parents="850 29814"/>
    </justification>
  </clause>

  <clause id="34004">
    <literal><![CDATA[
      ((x * x) \ L(x * x,y,z)) * u = L(x * x,z,y) * ((x * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1266,a(flip),b,34003,a)].">
      <j1 rule="hyper" parents="64 1266 34003"/>
    </justification>
  </clause>

  <clause id="34005">
    <literal><![CDATA[
      L(x * x,y,z) * ((x * x) \ u) = (a(y,z,x * x) \ 1) * u
    ]]></literal>
    <justification jstring="[para(31257(a,1),34004(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31257 34004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34006">
    <literal><![CDATA[
      L(x * x,y,z) * ((x * x) \ u) = a(y,z,x * x) \ u
    ]]></literal>
    <justification jstring="[hyper(373,a,31264,a(flip),b,34005,a),flip(a)].">
      <j1 rule="hyper" parents="373 31264 34005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34007">
    <literal><![CDATA[
      x * (a(y,z,u * u) \ 1) = a(z,y,u * u) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,31260,a(flip),b,34006,a)].">
      <j1 rule="hyper" parents="64 31260 34006"/>
    </justification>
  </clause>

  <clause id="34008">
    <literal><![CDATA[
      L(x,(y * (T(z * u,u) \ z)) \ w,v5) = L(x,(y * (T(z,u) \ (z / u))) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29469,a(flip),b,29821,a)].">
      <j1 rule="hyper" parents="64 29469 29821"/>
    </justification>
  </clause>

  <clause id="34009">
    <literal><![CDATA[
      L(x,(y \ (z * ((u * u) * w))) * v5,v6) = L(x,(y \ (z * w)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29837,a(flip),b,29833,a),flip(a)].">
      <j1 rule="hyper" parents="64 29837 29833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34011">
    <literal><![CDATA[
      R(x,x,a(x,y,y) * y) = (a(x \ 1,y,y) * y) / (R(x \ 1,y,y) * y)
    ]]></literal>
    <justification jstring="[para(2653(a,1),30008(a,1,3,1))].">
      <j1 rule="para" parents="2653 30008"/>
    </justification>
  </clause>

  <clause id="34012">
    <literal><![CDATA[
      R(x,x,a(x,y,y) * y) = (a(x,y,y) * y) / (R(x \ 1,y,y) * y)
    ]]></literal>
    <justification jstring="[para(2653(a,1),34011(a,2,1,1))].">
      <j1 rule="para" parents="2653 34011"/>
    </justification>
  </clause>

  <clause id="34013">
    <literal><![CDATA[
      R(x,x,a(x,y,y) * y) = R(x,L(x,y,y),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,26692,a(flip),b,34012,a),flip(a)].">
      <j1 rule="hyper" parents="373 26692 34012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34014">
    <literal><![CDATA[
      R(x,L(x,y,y),y) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32767,a(flip),b,34013,a),flip(a)].">
      <j1 rule="hyper" parents="64 32767 34013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34016">
    <literal><![CDATA[
      R(x \ y,(1 / x) * y,x) = R(x \ y,x \ y,x)
    ]]></literal>
    <justification jstring="[para(569(a,1),34014(a,1,2))].">
      <j1 rule="para" parents="569 34014"/>
    </justification>
  </clause>

  <clause id="34017">
    <literal><![CDATA[
      R(x \ y,x \ y,x) = R(x \ y,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2969,a(flip),b,34016,a),flip(a)].">
      <j1 rule="hyper" parents="64 2969 34016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34018">
    <literal><![CDATA[
      L(x,x,a(x,y,z) * u) = (x * x) * L(x \ 1,x,x * u)
    ]]></literal>
    <justification jstring="[para(30751(a,1),30277(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30751 30277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34019">
    <literal><![CDATA[
      L(x,x,a(x,y,z) * u) = x * (L(x \ 1,x,x * u) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1830,a(flip),b,34018,a),flip(a)].">
      <j1 rule="hyper" parents="373 1830 34018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34021">
    <literal><![CDATA[
      L(x,x,a(x,y,z) * u) = x * (x \ L(x,x,u))
    ]]></literal>
    <justification jstring="[para(30679(a,1),34019(a,2,2))].">
      <j1 rule="para" parents="30679 34019"/>
    </justification>
  </clause>

  <clause id="34022">
    <literal><![CDATA[
      L(x,x,a(x,y,z) * u) = L(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,10,a(flip),b,34021,a),flip(a)].">
      <j1 rule="hyper" parents="373 10 34021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34023">
    <literal><![CDATA[
      L(x,x,a(x,y,z) * u) = a(u,x,x) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,30459,a,b,34022,a),flip(a)].">
      <j1 rule="hyper" parents="373 30459 34022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34025">
    <literal><![CDATA[
      L(x,x,a(x,y,z) \ u) = L(x,x,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),34022(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 34022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34026">
    <literal><![CDATA[
      x * (L(x,x,y) \ (a(x,z,u) * y)) = R(a(x,z,u) * y,x,x)
    ]]></literal>
    <justification jstring="[para(34022(a,1),11857(a,1,2,1))].">
      <j1 rule="para" parents="34022 11857"/>
    </justification>
  </clause>

  <clause id="34027">
    <literal><![CDATA[
      L(x,x,(x * y) * z) = L(x,x,x * (y * z))
    ]]></literal>
    <justification jstring="[para(15463(a,1),34022(a,1,3))].">
      <j1 rule="para" parents="15463 34022"/>
    </justification>
  </clause>

  <clause id="34028">
    <literal><![CDATA[
      L(x,x,x \ (y * z)) = L(x,x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(30197(a,1),34022(a,1,3))].">
      <j1 rule="para" parents="30197 34022"/>
    </justification>
  </clause>

  <clause id="34029">
    <literal><![CDATA[
      (a(x,y,z) \ u) / L(x,x,u) = (a(x,y,z) \ u) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(225,a,34025,a(flip),b,11792,a(flip))].">
      <j1 rule="hyper" parents="225 34025 11792"/>
    </justification>
  </clause>

  <clause id="34030">
    <literal><![CDATA[
      L(x,x,x * ((x \ y) * z)) = L(x,x,y * z)
    ]]></literal>
    <justification jstring="[para(15481(a,1),34025(a,1,3))].">
      <j1 rule="para" parents="15481 34025"/>
    </justification>
  </clause>

  <clause id="34031">
    <literal><![CDATA[
      a(a(x,y,z) * u,x,x) = a(u,x,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,30459,a,b,34023,a(flip))].">
      <j1 rule="hyper" parents="40 30459 34023"/>
    </justification>
  </clause>

  <clause id="34032">
    <literal><![CDATA[
      a(x * a(y,z,u),y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(26847,a,34031,a)].">
      <j1 rule="hyper" parents="26847 34031"/>
    </justification>
  </clause>

  <clause id="34033">
    <literal><![CDATA[
      ((x * a(y,z,u)) * y) / (((x * a(y,z,u)) * (y * y)) / y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,33318,a(flip),b,34032,a)].">
      <j1 rule="hyper" parents="64 33318 34032"/>
    </justification>
  </clause>

  <clause id="34034">
    <literal><![CDATA[
      L(x,x,(y * z) * x) = L(x,x,(x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,34027,a)].">
      <j1 rule="hyper" parents="373 23253 34027"/>
    </justification>
  </clause>

  <clause id="34035">
    <literal><![CDATA[
      L(x,x,(y * x) * z) = L(x,x,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,28989,a,b,34027,a)].">
      <j1 rule="hyper" parents="64 28989 34027"/>
    </justification>
  </clause>

  <clause id="34036">
    <literal><![CDATA[
      L(x,x,(x \ y) * z) = L(x,x,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,25574,a(flip),b,34028,a),flip(a)].">
      <j1 rule="hyper" parents="64 25574 34028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34037">
    <literal><![CDATA[
      L(x,x,x * L(K(y,x \ z) * u,x \ z,x \ z)) = L(x,x,z * ((T(x \ z,y) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(12412(a,2),34030(a,1,3,2))].">
      <j1 rule="para" parents="12412 34030"/>
    </justification>
  </clause>

  <clause id="34038">
    <literal><![CDATA[
      L(x,x,(y * z) * x) = L(x,x,z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,29105,a(flip),b,34034,a),flip(a)].">
      <j1 rule="hyper" parents="373 29105 34034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34039">
    <literal><![CDATA[
      L(x,x,x * ((x * y) * z)) = L(x,x,y * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),34036(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="9 34036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34040">
    <literal><![CDATA[
      L(x,x,y * (z * x)) = L(x,x,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29105,a(flip),b,34038,a),flip(a)].">
      <j1 rule="hyper" parents="64 29105 34038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34041">
    <literal><![CDATA[
      L(x,x,x * ((y * x) * z)) = L(x,x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29092,a,b,34039,a)].">
      <j1 rule="hyper" parents="64 29092 34039"/>
    </justification>
  </clause>

  <clause id="34042">
    <literal><![CDATA[
      L(x,x,x * ((y * x) * z)) = L(x,x,x * (y * (z * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,34035,a(flip),b,34040,a),flip(a)].">
      <j1 rule="hyper" parents="64 34035 34040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34043">
    <literal><![CDATA[
      ((x * y) * z) * L(y,y,x * z) = ((x * y) * z) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(145,a,34041,a(flip),b,25566,a(flip))].">
      <j1 rule="hyper" parents="145 34041 25566"/>
    </justification>
  </clause>

  <clause id="34044">
    <literal><![CDATA[
      L(x,x,x * (y * (z * x))) = L(x,x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34041,a(flip),b,34042,a),flip(a)].">
      <j1 rule="hyper" parents="64 34041 34042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34045">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * (y * z)) / (1 / z)) = L(z,z,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,25566,a(flip),b,34044,a)].">
      <j1 rule="hyper" parents="64 25566 34044"/>
    </justification>
  </clause>

  <clause id="34046">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * (y * z)) / (1 / z)) = L(z,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,34045,a),flip(a)].">
      <j1 rule="hyper" parents="373 23253 34045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34047">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ ((x * (y * a(z,u,w))) / (a(z,u,w) \ 1)) = L(a(z,u,w),a(z,u,w),x * y)
    ]]></literal>
    <justification jstring="[para(13923(a,1),34045(a,1,2,2))].">
      <j1 rule="para" parents="13923 34045"/>
    </justification>
  </clause>

  <clause id="34048">
    <literal><![CDATA[
      x * L(x \ 1,x,y * (z * x)) = L(x,x,y * z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(34045(a,1),30644(a,1,1)),flip(a)].">
      <j1 rule="para" parents="34045 30644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34049">
    <literal><![CDATA[
      x * L(x \ 1,x,y * (z * x)) = L(x,x,z * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(34046(a,1),30644(a,1,1)),flip(a)].">
      <j1 rule="para" parents="34046 30644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34050">
    <literal><![CDATA[
      x * ((L(x,x,y) \ y) * a(x,z,u)) = R(a(x,z,u) * y,x,x)
    ]]></literal>
    <justification jstring="[para(30903(a,1),34026(a,1,2))].">
      <j1 rule="para" parents="30903 34026"/>
    </justification>
  </clause>

  <clause id="34051">
    <literal><![CDATA[
      x * L(x \ 1,x,y * (x * z)) = L(x,x,z * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(29020(a,1),34049(a,1,2))].">
      <j1 rule="para" parents="29020 34049"/>
    </justification>
  </clause>

  <clause id="34052">
    <literal><![CDATA[
      R(a(x,y,z) * u,x,x) = a(x,y,z) * R(u,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30222,a(flip),b,34050,a),flip(a)].">
      <j1 rule="hyper" parents="64 30222 34050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34053">
    <literal><![CDATA[
      x \ R(a(y,z,u) * (a(y,z,u) \ x),y,y) = a((x \ a(y,z,u)) \ 1,y,y)
    ]]></literal>
    <justification jstring="[para(34052(a,2),16027(a,1,2))].">
      <j1 rule="para" parents="34052 16027"/>
    </justification>
  </clause>

  <clause id="34054">
    <literal><![CDATA[
      x \ (y * R(a(z,u,w) * (a(z,u,w) \ (y \ x)),z,z)) = a(x \ (y * a(z,u,w)),z,z)
    ]]></literal>
    <justification jstring="[para(34052(a,2),16030(a,1,2,2))].">
      <j1 rule="para" parents="34052 16030"/>
    </justification>
  </clause>

  <clause id="34055">
    <literal><![CDATA[
      L(x \ 1,x,y * (z * x)) = L(x \ 1,x,z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(35,a,34048,a,b,34051,a)].">
      <j1 rule="hyper" parents="35 34048 34051"/>
    </justification>
  </clause>

  <clause id="34056">
    <literal><![CDATA[
      L((1 / x) \ 1,1 / x,y * L(L(x,z,z) \ z,x,x)) = L((1 / x) \ 1,1 / x,R(z,z,x) * (y * (1 / x)))
    ]]></literal>
    <justification jstring="[para(25118(a,2),34055(a,2,3,2)),flip(a)].">
      <j1 rule="para" parents="25118 34055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34057">
    <literal><![CDATA[
      (a(x,y,z) * (u * x)) / (((u * a(x,y,z)) * (x * x)) / x) = a(u,x,x)
    ]]></literal>
    <justification jstring="[para(29911(a,1),34033(a,1,1))].">
      <j1 rule="para" parents="29911 34033"/>
    </justification>
  </clause>

  <clause id="34058">
    <literal><![CDATA[
      (a(x,y,z) * (u * x)) / ((u * ((x * x) * a(x,y,z))) / x) = a(u,x,x)
    ]]></literal>
    <justification jstring="[para(28825(a,1),34057(a,1,2,1))].">
      <j1 rule="para" parents="28825 34057"/>
    </justification>
  </clause>

  <clause id="34059">
    <literal><![CDATA[
      (a(x,y,z) * (u * x)) / ((u * (x * (x * a(x,y,z)))) / x) = a(u,x,x)
    ]]></literal>
    <justification jstring="[para(16058(a,1),34058(a,1,2,1,2))].">
      <j1 rule="para" parents="16058 34058"/>
    </justification>
  </clause>

  <clause id="34060">
    <literal><![CDATA[
      (a(x,x,y) * (z * x)) / ((z * (x * R(x,x,y))) / x) = a(z,x,x)
    ]]></literal>
    <justification jstring="[para(30054(a,1),34059(a,1,2,1,2,2))].">
      <j1 rule="para" parents="30054 34059"/>
    </justification>
  </clause>

  <clause id="34061">
    <literal><![CDATA[
      a((x \ a(y,z,u)) \ 1,y,y) = x \ R(x,y,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),34053(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 34053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34062">
    <literal><![CDATA[
      a((x \ a(y,z,u)) \ 1,y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,15987,a(flip),b,34061,a),flip(a)].">
      <j1 rule="hyper" parents="373 15987 34061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34063">
    <literal><![CDATA[
      a(x \ a(y,z,u),y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2653,a(flip),b,34062,a)].">
      <j1 rule="hyper" parents="64 2653 34062"/>
    </justification>
  </clause>

  <clause id="34064">
    <literal><![CDATA[
      R(x,y,(z \ (R(u,w,u) \ z)) \ 1) = R(x,y,u * a(z,R(u,w,u),R(u,w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,26222,a(flip),b,30520,a)].">
      <j1 rule="hyper" parents="64 26222 30520"/>
    </justification>
  </clause>

  <clause id="34065">
    <literal><![CDATA[
      (x \ (x / y)) * L(z,y,a(y,y,x)) = y * ((y \ (1 / ((x \ (x / y)) \ 1))) * z)
    ]]></literal>
    <justification jstring="[para(31820(a,1),30535(a,1,2))].">
      <j1 rule="para" parents="31820 30535"/>
    </justification>
  </clause>

  <clause id="34066">
    <literal><![CDATA[
      (a(x,y,y) \ x) \ (x * z) = x * ((a(x,y,y) \ x) \ z)
    ]]></literal>
    <justification jstring="[para(30651(a,1),30653(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30651 30653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34067">
    <literal><![CDATA[
      L((a(x,y,y) \ 1) \ z,x,a(y,y,x)) = x * ((a(x,y,y) \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29233,a,b,34066,a)].">
      <j1 rule="hyper" parents="64 29233 34066"/>
    </justification>
  </clause>

  <clause id="34068">
    <literal><![CDATA[
      T(x,y) \ ((T(x,y) * (z \ x)) * (z \ x)) = (K(x,y) * (z / (z \ x))) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(23224(a,1),30805(a,2,1))].">
      <j1 rule="para" parents="23224 30805"/>
    </justification>
  </clause>

  <clause id="34069">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),u) = L(a(x,L(x,y,z),u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30313,a(flip),b,30912,a)].">
      <j1 rule="hyper" parents="64 30313 30912"/>
    </justification>
  </clause>

  <clause id="34071">
    <literal><![CDATA[
      L(x,(((y / (z * y)) * y) \ u) \ w,v5) = L(x,((z \ y) \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(82(a,1),31059(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 31059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34072">
    <literal><![CDATA[
      L(x,(L(y * z,y,y) \ u) \ w,v5) = L(x,((y \ z) \ u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31635,a,b,34071,a)].">
      <j1 rule="hyper" parents="64 31635 34071"/>
    </justification>
  </clause>

  <clause id="34074">
    <literal><![CDATA[
      L(x * y,y \ ((z * (y / z)) \ (x \ y)),y) = L(x * y,x * y,z * (y / z))
    ]]></literal>
    <justification jstring="[para(24935(a,1),31128(a,1,2))].">
      <j1 rule="para" parents="24935 31128"/>
    </justification>
  </clause>

  <clause id="34075">
    <literal><![CDATA[
      a(x,x,y) * (z * a(y,a(x,x,y),y \ z)) = ((x / y) \ R(x,x,y)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(32878(a,1),31298(a,1,2,2))].">
      <j1 rule="para" parents="32878 31298"/>
    </justification>
  </clause>

  <clause id="34076">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ (x * z) = x * ((a(x,x,y) \ x) \ z)
    ]]></literal>
    <justification jstring="[para(31549(a,1),31550(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31549 31550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34077">
    <literal><![CDATA[
      L((R(x,x,y) \ x) \ z,x,a(x,x,y)) = x * ((a(x,x,y) \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31156,a,b,34076,a)].">
      <j1 rule="hyper" parents="64 31156 34076"/>
    </justification>
  </clause>

  <clause id="34078">
    <literal><![CDATA[
      (x * ((a(x,x,y) \ x) \ z)) \ (z * x) = a(x,x,y) \ x
    ]]></literal>
    <justification jstring="[para(34076(a,1),28858(a,1,1))].">
      <j1 rule="para" parents="34076 28858"/>
    </justification>
  </clause>

  <clause id="34079">
    <literal><![CDATA[
      T((x * (y \ (x \ y))) \ 1,z * z) = T(x * (y \ (x \ y)),z * z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,1457,a(flip),b,31816,a),flip(a)].">
      <j1 rule="hyper" parents="64 1457 31816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34080">
    <literal><![CDATA[
      T((x * (y \ (x \ y))) \ 1,z * z) = (x * (y \ (x \ y))) \ 1
    ]]></literal>
    <justification jstring="[para(28886(a,1),34079(a,2,1))].">
      <j1 rule="para" parents="28886 34079"/>
    </justification>
  </clause>

  <clause id="34082">
    <literal><![CDATA[
      T(x \ (y * (x * (y \ 1))),z * z) = (y * (x \ (y \ x))) \ 1
    ]]></literal>
    <justification jstring="[para(30759(a,1),34080(a,1,1))].">
      <j1 rule="para" parents="30759 34080"/>
    </justification>
  </clause>

  <clause id="34083">
    <literal><![CDATA[
      T(x \ (y * (x * (y \ 1))),z * z) = x \ (y * (x * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,30759,a(flip),b,34082,a),flip(a)].">
      <j1 rule="hyper" parents="373 30759 34082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34084">
    <literal><![CDATA[
      x * ((a(y,y,x) \ 1) * (x \ (a(x,y,y) \ z))) = L(x,y,y) * (R(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[para(30979(a,1),31847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30979 31847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34085">
    <literal><![CDATA[
      a(x,(y * y) * (((z * (y * y)) / u) \ w),v5) = a(x,(T(z,y * y) / u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(890(a,1),32096(a,1,2))].">
      <j1 rule="para" parents="890 32096"/>
    </justification>
  </clause>

  <clause id="34086">
    <literal><![CDATA[
      a(x,y \ ((z * ((u * u) * w)) / v5),v6) = a(x,y \ (v5 \ (T(z,u * u) * w)),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,31908,a(flip),b,32224,a),flip(a)].">
      <j1 rule="hyper" parents="64 31908 32224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34087">
    <literal><![CDATA[
      a(x,((y * (z * z)) / u) * w,v5) = a(x,(u \ T(y,z * z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(26848,a,32263,a),flip(a)].">
      <j1 rule="hyper" parents="26848 32263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34089">
    <literal><![CDATA[
      a(x,((y * (z * z)) / u) * w,v5) = a(x,(u \ y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32075,a(flip),b,34087,a),flip(a)].">
      <j1 rule="hyper" parents="373 32075 34087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34091">
    <literal><![CDATA[
      a(x,y * (z * L(u,u,z)),w) = a(x,(u \ z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32345,a(flip),b,34089,a)].">
      <j1 rule="hyper" parents="64 32345 34089"/>
    </justification>
  </clause>

  <clause id="34092">
    <literal><![CDATA[
      a(x,(y \ (z * (u * u))) * w,v5) = a(x,(y \ z) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31904,a(flip),b,34089,a)].">
      <j1 rule="hyper" parents="64 31904 34089"/>
    </justification>
  </clause>

  <clause id="34094">
    <literal><![CDATA[
      a(x,L(L(y,y,z),z,z),u) = a(x,(y \ z) * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11968,a(flip),b,34091,a)].">
      <j1 rule="hyper" parents="64 11968 34091"/>
    </justification>
  </clause>

  <clause id="34095">
    <literal><![CDATA[
      a(x,L(L(y,z,z),y,z),u) = a(x,(y \ z) * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32280,a,b,34094,a)].">
      <j1 rule="hyper" parents="64 32280 34094"/>
    </justification>
  </clause>

  <clause id="34096">
    <literal><![CDATA[
      a(x,(y \ ((z * z) * u)) * w,v5) = a(x,(y \ u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32271,a,b,34092,a)].">
      <j1 rule="hyper" parents="64 32271 34092"/>
    </justification>
  </clause>

  <clause id="34097">
    <literal><![CDATA[
      a(x,(y \ (z / (1 / u))) * w,v5) = a(x,(y \ (z / u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(809(a,1),34092(a,1,2,1,2))].">
      <j1 rule="para" parents="809 34092"/>
    </justification>
  </clause>

  <clause id="34098">
    <literal><![CDATA[
      a(x,(L(y,z,u) \ y) * w,v5) = a(x,(y * L(y,z,u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(2324(a,1),34092(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2324 34092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34099">
    <literal><![CDATA[
      a(x,(y \ ((z * z) \ u)) * w,v5) = a(x,(y \ u) * w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),34096(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="10 34096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34100">
    <literal><![CDATA[
      a(x,(y \ (((z * z) \ u) * w)) * v5,v6) = a(x,(y \ (u * w)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(126(a,1),34096(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="126 34096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34101">
    <literal><![CDATA[
      a(x,(R(1 / y,z,u) \ w) * v5,v6) = a(x,(R(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(2118(a,1),34096(a,1,2,1))].">
      <j1 rule="para" parents="2118 34096"/>
    </justification>
  </clause>

  <clause id="34102">
    <literal><![CDATA[
      a(x,y * (z \ ((u * u) \ w)),v5) = a(x,(z \ w) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(32008,a,34099,a)].">
      <j1 rule="hyper" parents="32008 34099"/>
    </justification>
  </clause>

  <clause id="34103">
    <literal><![CDATA[
      a(x,(R(y \ 1,z,u) \ w) * v5,v6) = a(x,(R(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(2770(a,1),34099(a,1,2,1))].">
      <j1 rule="para" parents="2770 34099"/>
    </justification>
  </clause>

  <clause id="34104">
    <literal><![CDATA[
      a(x,y * ((z * u) \ ((w * w) \ (z * ((v5 * v5) * (u * v6))))),v7) = a(x,L(T(v5 * v5,u) * v6,u,z) * y,v7)
    ]]></literal>
    <justification jstring="[para(6651(a,1),34102(a,2,2,1))].">
      <j1 rule="para" parents="6651 34102"/>
    </justification>
  </clause>

  <clause id="34105">
    <literal><![CDATA[
      a(x,(y \ ((1 / z) \ u)) * w,v5) = a(x,(y \ (u / z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32077,a(flip),b,34097,a)].">
      <j1 rule="hyper" parents="64 32077 34097"/>
    </justification>
  </clause>

  <clause id="34106">
    <literal><![CDATA[
      a(x,(y * L(y,z,z)) * u,w) = a(x,a(z,z,y) * u,w)
    ]]></literal>
    <justification jstring="[para(1243(a,1),34098(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1243 34098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34107">
    <literal><![CDATA[
      a(x,a(y,z,z \ 1) * u,w) = a(x,a(z,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33779,a,b,34106,a)].">
      <j1 rule="hyper" parents="64 33779 34106"/>
    </justification>
  </clause>

  <clause id="34108">
    <literal><![CDATA[
      a(x,y * a(z,u,u \ 1),w) = a(x,a(u,u,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(32008,a,34107,a)].">
      <j1 rule="hyper" parents="32008 34107"/>
    </justification>
  </clause>

  <clause id="34109">
    <literal><![CDATA[
      a(x,a(y,y,z * y) * u,w) = a(x,u * a(z,y,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32056,a(flip),b,34108,a),flip(a)].">
      <j1 rule="hyper" parents="64 32056 34108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34110">
    <literal><![CDATA[
      a(x,y * a(z,u,u),w) = a(x,y * a(u,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32262,a(flip),b,34109,a),flip(a)].">
      <j1 rule="hyper" parents="64 32262 34109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34111">
    <literal><![CDATA[
      a(x,a(y,y,z) * u,w) = a(x,u * a(z,y,y),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31888,a,b,34110,a)].">
      <j1 rule="hyper" parents="373 31888 34110"/>
    </justification>
  </clause>

  <clause id="34112">
    <literal><![CDATA[
      a(x,a(y,z,z) * u,w) = a(x,a(z,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31888,a,b,34111,a)].">
      <j1 rule="hyper" parents="373 31888 34111"/>
    </justification>
  </clause>

  <clause id="34113">
    <literal><![CDATA[
      a(x,(y \ ((z \ 1) \ u)) * w,v5) = a(x,(y \ (u / z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32273,a(flip),b,34105,a)].">
      <j1 rule="hyper" parents="64 32273 34105"/>
    </justification>
  </clause>

  <clause id="34114">
    <literal><![CDATA[
      a(x,(y \ ((z \ 1) \ u)) * w,v5) = a(x,(y \ (z \ u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32077,a(flip),b,34113,a),flip(a)].">
      <j1 rule="hyper" parents="373 32077 34113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34115">
    <literal><![CDATA[
      a(x,y * (z \ ((u \ 1) \ w)),v5) = a(x,(z \ (u \ w)) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(32008,a,34114,a)].">
      <j1 rule="hyper" parents="32008 34114"/>
    </justification>
  </clause>

  <clause id="34116">
    <literal><![CDATA[
      a(x,R(y \ 1,z,u) \ (L(w,R(y \ 1,z,u) \ v5,R(y \ 1,z,u)) * v5),v6) = a(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(1010(a,2),34103(a,1,2))].">
      <j1 rule="para" parents="1010 34103"/>
    </justification>
  </clause>

  <clause id="34117">
    <literal><![CDATA[
      a(x,(R(y \ 1,z,u) \ R(T(w,R(y,z,u) * R(y,z,u)),R(y,z,u),R(y,z,u))) * v5,v6) = a(x,T(((R(y,z,u) * R(y,z,u)) \ w) * R(y,z,u),R(y,z,u)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(1400(a,1),34103(a,2,2,1))].">
      <j1 rule="para" parents="1400 34103"/>
    </justification>
  </clause>

  <clause id="34118">
    <literal><![CDATA[
      a(x,L(K(y,z) * (u * y),w,v5) \ v6,v7) = a(x,L(T(y,z) * u,w,v5) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(7764(a,1),32303(a,1,2,1,1))].">
      <j1 rule="para" parents="7764 32303"/>
    </justification>
  </clause>

  <clause id="34119">
    <literal><![CDATA[
      a(x * (((y * (z * z)) / u) * w),v5,v6) = a(x * (w * (u \ y)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32717,a(flip),b,32671,a),flip(a)].">
      <j1 rule="hyper" parents="373 32717 32671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34120">
    <literal><![CDATA[
      a(x * (y * ((z * (u * u)) / w)),v5,v6) = a(x * (y * (w \ z)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(32448,a,34119,a)].">
      <j1 rule="hyper" parents="32448 34119"/>
    </justification>
  </clause>

  <clause id="34122">
    <literal><![CDATA[
      a((x * (y \ (z * (u * u)))) * w,v5,v6) = a(w * (x * (y \ z)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32522,a,b,34120,a)].">
      <j1 rule="hyper" parents="64 32522 34120"/>
    </justification>
  </clause>

  <clause id="34124">
    <literal><![CDATA[
      a(L(x / (y * T(z,y \ 1)),u,w),v5,v6) = a(L((z * (y \ 1)) \ x,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,26794,a(flip),b,32868,a),flip(a)].">
      <j1 rule="hyper" parents="373 26794 32868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34125">
    <literal><![CDATA[
      a(x,y * (((z / (u * z)) * z) \ w),v5) = a(x,y * ((u \ z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(82(a,1),32913(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="82 32913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34126">
    <literal><![CDATA[
      a(x,y * (L(z * u,z,z) \ w),v5) = a(x,y * ((z \ u) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,33026,a,b,34125,a)].">
      <j1 rule="hyper" parents="64 33026 34125"/>
    </justification>
  </clause>

  <clause id="34128">
    <literal><![CDATA[
      a(x,(L(y * z,y,y) \ u) * w,v5) = a(x,w * ((y \ z) \ u),v5)
    ]]></literal>
    <justification jstring="[hyper(32008,a,34126,a)].">
      <j1 rule="hyper" parents="32008 34126"/>
    </justification>
  </clause>

  <clause id="34129">
    <literal><![CDATA[
      a(x,y * (z * (u * (w \ K(v5,v6)))),v7) = a(x,((w * u) * z) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,31913,a(flip),b,32955,a)].">
      <j1 rule="hyper" parents="64 31913 32955"/>
    </justification>
  </clause>

  <clause id="34131">
    <literal><![CDATA[
      a(x,y * ((z * (u \ K(w,v5))) * v6),v7) = a(x,((u * z) * v6) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,31902,a,b,34129,a)].">
      <j1 rule="hyper" parents="64 31902 34129"/>
    </justification>
  </clause>

  <clause id="34132">
    <literal><![CDATA[
      a(x,((y * z) * L(u,y,z)) * w,v5) = a(x,w * (z * ((y \ K(v6,v7)) * u)),v5)
    ]]></literal>
    <justification jstring="[para(29662(a,1),34131(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="29662 34131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34133">
    <literal><![CDATA[
      a(x,(y * (T(z,y) * u)) * w,v5) = a(x,w * (y * ((z \ K(v6,v7)) * u)),v5)
    ]]></literal>
    <justification jstring="[para(10989(a,1),34132(a,1,2,1))].">
      <j1 rule="para" parents="10989 34132"/>
    </justification>
  </clause>

  <clause id="34134">
    <literal><![CDATA[
      a(x,y * (z * ((u \ K(w,v5)) * v6)),v7) = a(x,(z * (u * v6)) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,32256,a(flip),b,34133,a),flip(a)].">
      <j1 rule="hyper" parents="64 32256 34133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34136">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) \ x) = x * (L(x,y,z) \ (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(5595(a,1),33179(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5595 33179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34137">
    <literal><![CDATA[
      x * a(y * z,x,a(x,y,z)) = R(x,y,z) / a(x,y,z)
    ]]></literal>
    <justification jstring="[para(9(a,1),33283(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 33283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34138">
    <literal><![CDATA[
      x * a(y * z,x,a(x,y,z)) = a(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,23133,a(flip),b,34137,a),flip(a)].">
      <j1 rule="hyper" parents="373 23133 34137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34139">
    <literal><![CDATA[
      x \ (a(x,y,z) \ R(x,y,z)) = a(y * z,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,23133,a(flip),b,34137,a)].">
      <j1 rule="hyper" parents="139 23133 34137"/>
    </justification>
  </clause>

  <clause id="34141">
    <literal><![CDATA[
      a(x,y,z) \ (x \ R(x,y,z)) = a(y * z,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,30269,a,b,34138,a)].">
      <j1 rule="hyper" parents="35 30269 34138"/>
    </justification>
  </clause>

  <clause id="34142">
    <literal><![CDATA[
      a(x,y,z) * a(y * z,x,a(x,y,z)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,34139,a(flip),b,30271,a)].">
      <j1 rule="hyper" parents="145 34139 30271"/>
    </justification>
  </clause>

  <clause id="34143">
    <literal><![CDATA[
      a(x * y,z,a(z,x,y)) * a(z,x,y) = z \ R(z,x,y)
    ]]></literal>
    <justification jstring="[para(34139(a,1),29942(a,1,1))].">
      <j1 rule="para" parents="34139 29942"/>
    </justification>
  </clause>

  <clause id="34144">
    <literal><![CDATA[
      a(R(x,y,z),u,w) * a(u * w,R(x,y,z),a(R(x,y,z),u,w)) = R(x,y,z) \ R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(31(a,1),34142(a,2,2))].">
      <j1 rule="para" parents="31 34142"/>
    </justification>
  </clause>

  <clause id="34145">
    <literal><![CDATA[
      a(x,a(x,y,z),y * z) \ a(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33555,a,b,34143,a)].">
      <j1 rule="hyper" parents="64 33555 34143"/>
    </justification>
  </clause>

  <clause id="34146">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ a(x,y,z) = a(x,a(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(40,a,23706,a,b,34145,a)].">
      <j1 rule="hyper" parents="40 23706 34145"/>
    </justification>
  </clause>

  <clause id="34147">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ a(x,y,z) = x * (R(x,y,z) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,33567,a,b,34146,a),flip(a)].">
      <j1 rule="hyper" parents="373 33567 34146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34148">
    <literal><![CDATA[
      a(a(x,y,z) * u,z,z) = L(z \ 1,z,z * u) \ (1 / z)
    ]]></literal>
    <justification jstring="[para(33452(a,1),33357(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33452 33357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34150">
    <literal><![CDATA[
      L(a(x,y,z) \ L(a(x,y,z),x,u),x,a(x,y,z)) = a(L(a(x,y,z),x,u),x,u)
    ]]></literal>
    <justification jstring="[para(28787(a,1),33410(a,1,1,2))].">
      <j1 rule="para" parents="28787 33410"/>
    </justification>
  </clause>

  <clause id="34151">
    <literal><![CDATA[
      L(a(L(x,y,z),y,z),y * x,y) = L(x,y,y) \ L(R(x,y,z),y,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),33414(a,2,2,1))].">
      <j1 rule="para" parents="10 33414"/>
    </justification>
  </clause>

  <clause id="34152">
    <literal><![CDATA[
      L(a(L(x,y,z),y,z),y * x,y) = L(x \ R(x,y,z),y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,4243,a(flip),b,34151,a),flip(a)].">
      <j1 rule="hyper" parents="373 4243 34151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34154">
    <literal><![CDATA[
      a(x,y,(L(z \ 1,z,u) \ 1) * w) = a(x,y,(a(u,z,z \ 1) * z) * w)
    ]]></literal>
    <justification jstring="[para(25756(a,1),33435(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="25756 33435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34155">
    <literal><![CDATA[
      a(L(L(x,y,z) \ x,x,u),x,u) = L(x,y,z) * (x \ L(L(x,y,z) \ x,x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,2325,a(flip),b,33445,a),flip(a)].">
      <j1 rule="hyper" parents="373 2325 33445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34156">
    <literal><![CDATA[
      L(x,y,((1 / z) \ L(u,w,v5)) * v6) = L(x,y,(z \ R(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[para(1779(a,1),33616(a,1,3,1))].">
      <j1 rule="para" parents="1779 33616"/>
    </justification>
  </clause>

  <clause id="34157">
    <literal><![CDATA[
      L(x,y,(z \ R(u,w,v5)) * v6) = L(x,y,(z \ L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,2270,a(flip),b,34156,a),flip(a)].">
      <j1 rule="hyper" parents="64 2270 34156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34158">
    <literal><![CDATA[
      L(x,y,(z \ L(T(u,w),v5,v6)) * v7) = L(x,y,v7 * (z \ R(u,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29188,a(flip),b,34157,a),flip(a)].">
      <j1 rule="hyper" parents="64 29188 34157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34159">
    <literal><![CDATA[
      L(x,y,z * (u \ R(w,v5,v6))) = L(x,y,z * (u \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29150,a(flip),b,34158,a),flip(a)].">
      <j1 rule="hyper" parents="64 29150 34158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34160">
    <literal><![CDATA[
      L(x,y,R(z,u,w) * (z \ L(z,u,w))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2200,a(flip),b,34159,a),flip(a)].">
      <j1 rule="hyper" parents="64 2200 34159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34161">
    <literal><![CDATA[
      L(x,y,L(R(z,u,w),u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(33431(a,1),34160(a,1,3))].">
      <j1 rule="para" parents="33431 34160"/>
    </justification>
  </clause>

  <clause id="34162">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w),u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29264,a(flip),b,34161,a)].">
      <j1 rule="hyper" parents="64 29264 34161"/>
    </justification>
  </clause>

  <clause id="34163">
    <literal><![CDATA[
      L(x,y,L(T((z * (u \ 1)) \ w,v5),u,z)) = L(x,y,T((u \ 1) \ (z \ w),v5))
    ]]></literal>
    <justification jstring="[para(11810(a,1),34162(a,1,3,1))].">
      <j1 rule="para" parents="11810 34162"/>
    </justification>
  </clause>

  <clause id="34164">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),v5,z)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(34162(a,1),27645(a,1,3))].">
      <j1 rule="para" parents="34162 27645"/>
    </justification>
  </clause>

  <clause id="34165">
    <literal><![CDATA[
      L(x,y,T((z \ 1) \ (u \ w),v5)) = L(x,y,L((u * (z \ 1)) \ w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,23843,a(flip),b,34163,a),flip(a)].">
      <j1 rule="hyper" parents="64 23843 34163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34167">
    <literal><![CDATA[
      L(x,L(y * L(y,z,u),y,u * z),w) = L(x,(u * z) \ (y \ (u * (z * y))),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29552,a(flip),b,33819,a),flip(a)].">
      <j1 rule="hyper" parents="373 29552 33819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34168">
    <literal><![CDATA[
      L(x,y,(z * ((u * w) \ w)) \ v5) = L(x,y,(z * (w \ (w / u))) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29363,a(flip),b,33879,a),flip(a)].">
      <j1 rule="hyper" parents="64 29363 33879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34170">
    <literal><![CDATA[
      L(x,y,(z * ((u * w) \ w)) \ v5) = L(x,y,(z * (w \ (u \ w))) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29009,a(flip),b,34168,a),flip(a)].">
      <j1 rule="hyper" parents="373 29009 34168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34171">
    <literal><![CDATA[
      L(x,y,L(R(z,z,u),u / z,u / z)) = L(x,y,(z \ u) * (z \ ((z \ 1) \ u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,29242,a(flip),b,33880,a),flip(a)].">
      <j1 rule="hyper" parents="373 29242 33880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34172">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * (u * ((a(x,y,z) \ 1) * w)) = u * (a(x,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(145,a,33881,a(flip),b,484,a)].">
      <j1 rule="hyper" parents="145 33881 484"/>
    </justification>
  </clause>

  <clause id="34173">
    <literal><![CDATA[
      L(x,L(L(y,y,z),y \ z,y \ z),u) = L(x,(y \ (y \ z)) * (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29862,a(flip),b,33887,a),flip(a)].">
      <j1 rule="hyper" parents="373 29862 33887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34174">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),y) * L(y,z,u) = y * ((T(y,x) \ L(y,z,u)) * x)
    ]]></literal>
    <justification jstring="[para(24348(a,1),33888(a,2,2))].">
      <j1 rule="para" parents="24348 33888"/>
    </justification>
  </clause>

  <clause id="34175">
    <literal><![CDATA[
      L(x,y * L(y,z,u),y) * L(y,z,u) = y * ((T(y,x) \ L(y,z,u)) * x)
    ]]></literal>
    <justification jstring="[para(11786(a,1),34174(a,1,1))].">
      <j1 rule="para" parents="11786 34174"/>
    </justification>
  </clause>

  <clause id="34176">
    <literal><![CDATA[
      x * ((T(x,y) \ L(x,z,u)) * y) = (y * (x \ L(x,z,u))) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,33173,a(flip),b,34175,a),flip(a)].">
      <j1 rule="hyper" parents="64 33173 34175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34177">
    <literal><![CDATA[
      x * ((T(x,y) \ L(x,z,u)) * y) = (x \ L(x,z,u)) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,33138,a(flip),b,34176,a),flip(a)].">
      <j1 rule="hyper" parents="373 33138 34176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34178">
    <literal><![CDATA[
      (x \ 1) * (y * (K(x * y,x \ 1) * R(x,z,u))) = (y * x) * R(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(22763(a,1),33899(a,1,2))].">
      <j1 rule="para" parents="22763 33899"/>
    </justification>
  </clause>

  <clause id="34179">
    <literal><![CDATA[
      L(x * ((y \ K(z,u)) * y),w,v5) = L(x,w,v5) * ((y \ K(z,u)) * y)
    ]]></literal>
    <justification jstring="[para(17172(a,1),33906(a,1,1))].">
      <j1 rule="para" parents="17172 33906"/>
    </justification>
  </clause>

  <clause id="34180">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ ((u / x) * L(x,y,z)) = a(x * L(x,y,z),x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5609,a(flip),b,33913,a),flip(a)].">
      <j1 rule="hyper" parents="373 5609 33913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34181">
    <literal><![CDATA[
      a(x \ ((y * ((z * z) * u)) / w),v5,v6) = a(x \ (w \ (y * u)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32485,a(flip),b,33914,a),flip(a)].">
      <j1 rule="hyper" parents="373 32485 33914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34182">
    <literal><![CDATA[
      a(x \ (y \ (z * ((u * u) * w))),v5,v6) = a(x \ (y \ (z * w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(32449,a,34181,a)].">
      <j1 rule="hyper" parents="32449 34181"/>
    </justification>
  </clause>

  <clause id="34184">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),a(z,u,w),y) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(33275(a,1),33919(a,1,1))].">
      <j1 rule="para" parents="33275 33919"/>
    </justification>
  </clause>

  <clause id="34185">
    <literal><![CDATA[
      1 / ((x / (y * x)) / y) = ((x / (y * x)) / y) \ 1
    ]]></literal>
    <justification jstring="[para(23875(a,1),33942(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23875 33942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34187">
    <literal><![CDATA[
      x * (R(1 / x,y,z) * R(x,u,w)) = R(x,y,z) * (x \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27060,a(flip),b,33946,a)].">
      <j1 rule="hyper" parents="64 27060 33946"/>
    </justification>
  </clause>

  <clause id="34188">
    <literal><![CDATA[
      R(1 / x,y,z) * R(x,u,w) = R(x,y,z) * R(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,2010,a,b,34187,a),flip(a)].">
      <j1 rule="hyper" parents="35 2010 34187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34189">
    <literal><![CDATA[
      a(x,y,(1 / z) * L((u * u) * w,v5,v5)) = a(x,y,(z \ (u * u)) * L(w,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,31317,a(flip),b,33952,a)].">
      <j1 rule="hyper" parents="64 31317 33952"/>
    </justification>
  </clause>

  <clause id="34190">
    <literal><![CDATA[
      K(x,T(y / L(z,u,w),v5) \ v6) = K(x,K(y / z,v5) * (z * (y \ v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,28611,a(flip),b,33969,a),flip(a)].">
      <j1 rule="hyper" parents="64 28611 33969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34192">
    <literal><![CDATA[
      K(x,T(y / L(z,u,w),v5) \ v6) = K(x,z * (K(z \ y,v5) * (y \ v6)))
    ]]></literal>
    <justification jstring="[para(22759(a,1),34190(a,2,2))].">
      <j1 rule="para" parents="22759 34190"/>
    </justification>
  </clause>

  <clause id="34193">
    <literal><![CDATA[
      K(x,T(y / L(z,u,w),v5) \ v6) = K(x,z * (K(z * y,v5) * (y \ v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,21570,a(flip),b,34192,a),flip(a)].">
      <j1 rule="hyper" parents="373 21570 34192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34194">
    <literal><![CDATA[
      K(x,T(y / L(z,u,w),v5) \ v6) = K(x,T(z / y,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,33737,a(flip),b,34193,a),flip(a)].">
      <j1 rule="hyper" parents="373 33737 34193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34195">
    <literal><![CDATA[
      K(x,T((y \ 1) / z,u) * w) = K(x,T(z * y,u) \ w)
    ]]></literal>
    <justification jstring="[para(441(a,1),34194(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="441 34194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34196">
    <literal><![CDATA[
      K(x,T(y * z,z) \ (u * w)) = K(x,(z \ (T(y,z) \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33746,a(flip),b,34195,a),flip(a)].">
      <j1 rule="hyper" parents="64 33746 34195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34197">
    <literal><![CDATA[
      K(x,(T(y * z,z) \ u) * w) = K(x,(z \ (T(y,z) \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24234,a(flip),b,34196,a)].">
      <j1 rule="hyper" parents="64 24234 34196"/>
    </justification>
  </clause>

  <clause id="34198">
    <literal><![CDATA[
      K(x,((L(y,z,y) * z) \ u) * w) = K(x,(y \ (T(z,y) \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,20023,a,b,34197,a)].">
      <j1 rule="hyper" parents="64 20023 34197"/>
    </justification>
  </clause>

  <clause id="34199">
    <literal><![CDATA[
      K(x,(y \ (L(z,y,z) \ u)) * w) = K(x,(z \ (T(y,z) \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28348,a(flip),b,34198,a)].">
      <j1 rule="hyper" parents="64 28348 34198"/>
    </justification>
  </clause>

  <clause id="34200">
    <literal><![CDATA[
      ((x \ (x \ y)) \ y) \ K(x * x,x * (x * (y \ y))) = 1 / ((x \ (x \ y)) \ y)
    ]]></literal>
    <justification jstring="[para(28553(a,1),33970(a,1,2))].">
      <j1 rule="para" parents="28553 33970"/>
    </justification>
  </clause>

  <clause id="34201">
    <literal><![CDATA[
      x * T((y \ z) * K(y,z * (y \ z)),x) = (y \ z) * (x * K(y,(y \ z) * z))
    ]]></literal>
    <justification jstring="[para(14018(a,1),33977(a,1,2,1,2))].">
      <j1 rule="para" parents="14018 33977"/>
    </justification>
  </clause>

  <clause id="34202">
    <literal><![CDATA[
      T(K(x,y) * (z \ 1),u * (z \ K(x,y))) = T((1 / z) * K(x,y),u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,22940,a(flip),b,33997,a),flip(a)].">
      <j1 rule="hyper" parents="373 22940 33997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34203">
    <literal><![CDATA[
      T((1 / x) * K(y,z),u * x) = T((x \ 1) * K(y,z),u / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,22973,a(flip),b,34202,a),flip(a)].">
      <j1 rule="hyper" parents="64 22973 34202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34204">
    <literal><![CDATA[
      T((1 / x) * K(y,z),u * x) = T(x \ K(y,z),u / x)
    ]]></literal>
    <justification jstring="[para(14444(a,1),34203(a,2,1))].">
      <j1 rule="para" parents="14444 34203"/>
    </justification>
  </clause>

  <clause id="34205">
    <literal><![CDATA[
      T((1 / x) * K(y,z),u * x) = T(x \ K(y,z),x \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,17321,a(flip),b,34204,a),flip(a)].">
      <j1 rule="hyper" parents="373 17321 34204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34206">
    <literal><![CDATA[
      T(K(x,y) / x,z * x) = T(x \ K(x,y),x \ z)
    ]]></literal>
    <justification jstring="[para(6862(a,1),34205(a,1,1))].">
      <j1 rule="para" parents="6862 34205"/>
    </justification>
  </clause>

  <clause id="34207">
    <literal><![CDATA[
      T(K(x,y) / x,x * z) = T(x \ K(x,y),x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,17204,a(flip),b,34206,a)].">
      <j1 rule="hyper" parents="64 17204 34206"/>
    </justification>
  </clause>

  <clause id="34208">
    <literal><![CDATA[
      T(x \ K(x,y),x \ y) = (y * x) \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10615,a(flip),b,34206,a),flip(a)].">
      <j1 rule="hyper" parents="64 10615 34206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34209">
    <literal><![CDATA[
      T(K(x,y) / x,(K(x,y) / x) \ y) = T(x \ K(x,y),x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16234,a,b,34207,a)].">
      <j1 rule="hyper" parents="64 16234 34207"/>
    </justification>
  </clause>

  <clause id="34210">
    <literal><![CDATA[
      T(K(x,y) / x,(K(x,y) / x) \ y) = (y * x) \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,34208,a(flip),b,34209,a),flip(a)].">
      <j1 rule="hyper" parents="373 34208 34209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34211">
    <literal><![CDATA[
      ((K(x,y) / x) \ y) \ y = (y * x) \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(478,a,34210,a)].">
      <j1 rule="hyper" parents="478 34210"/>
    </justification>
  </clause>

  <clause id="34212">
    <literal><![CDATA[
      (x * R(y,y,x)) \ x = (x * y) \ L(x,y,y)
    ]]></literal>
    <justification jstring="[para(24612(a,1),34211(a,1,1))].">
      <j1 rule="para" parents="24612 34211"/>
    </justification>
  </clause>

  <clause id="34213">
    <literal><![CDATA[
      (a(x,y,y) * R(z,z,a(x,y,y))) \ a(x,y,y) = (a(x,y,y) * z) \ a(L(x,z,z),y,y)
    ]]></literal>
    <justification jstring="[para(32607(a,2),34212(a,2,2))].">
      <j1 rule="para" parents="32607 34212"/>
    </justification>
  </clause>

  <clause id="34214">
    <literal><![CDATA[
      L(x,y,L((z * (u \ 1)) \ w,v5,v6)) = L(x,y,L((u * z) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,29415,a(flip),b,33999,a),flip(a)].">
      <j1 rule="hyper" parents="64 29415 33999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34216">
    <literal><![CDATA[
      L(x,y,T((z \ 1) \ (u \ w),v5)) = L(x,y,L((z * u) \ w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,34165,a,b,34214,a)].">
      <j1 rule="hyper" parents="64 34165 34214"/>
    </justification>
  </clause>

  <clause id="34217">
    <literal><![CDATA[
      L(x,y,L((z * z) \ u,w,v5)) = L(x,y,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(185(a,1),34214(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="185 34214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34218">
    <literal><![CDATA[
      L(x,x,L(x \ y,z,u)) = L(x,x,L(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29197,a(flip),b,34217,a)].">
      <j1 rule="hyper" parents="64 29197 34217"/>
    </justification>
  </clause>

  <clause id="34219">
    <literal><![CDATA[
      L(x,y,L((z * z) * u,w,v5)) = L(x,y,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(9(a,1),34217(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="9 34217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34220">
    <literal><![CDATA[
      L(x,y,L(z * (z * u),w,v5)) = L(x,y,L(L(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[para(18(a,2),34217(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="18 34217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34221">
    <literal><![CDATA[
      L(x,y,L(1 / z,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(309(a,1),34217(a,1,3,1))].">
      <j1 rule="para" parents="309 34217"/>
    </justification>
  </clause>

  <clause id="34222">
    <literal><![CDATA[
      L(x,y,L(z * ((z \ 1) \ u),w,v5)) = L(x,y,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(582(a,1),34217(a,1,3,1))].">
      <j1 rule="para" parents="582 34217"/>
    </justification>
  </clause>

  <clause id="34223">
    <literal><![CDATA[
      L(L(R(x,x,x),y,z),L(x,y,z),L(x,u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32942,a(flip),b,34221,a),flip(a)].">
      <j1 rule="hyper" parents="64 32942 34221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34224">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,23846,a(flip),b,34221,a)].">
      <j1 rule="hyper" parents="64 23846 34221"/>
    </justification>
  </clause>

  <clause id="34225">
    <literal><![CDATA[
      L(x,y \ 1,L(z,u,w)) = L(x,y,L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(11853,a,34224,a),flip(a)].">
      <j1 rule="hyper" parents="11853 34224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34226">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w) \ 1) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(2274,a,34224,a)].">
      <j1 rule="hyper" parents="2274 34224"/>
    </justification>
  </clause>

  <clause id="34227">
    <literal><![CDATA[
      L(x,y,L(z \ K(u,w),v5,v6)) = L(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,29036,a,b,34224,a)].">
      <j1 rule="hyper" parents="64 29036 34224"/>
    </justification>
  </clause>

  <clause id="34229">
    <literal><![CDATA[
      L(x,y,L(z * (u * u),w,v5)) = L(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,24167,a,b,34219,a)].">
      <j1 rule="hyper" parents="64 24167 34219"/>
    </justification>
  </clause>

  <clause id="34230">
    <literal><![CDATA[
      L(x,y,L(z \ 1,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,L(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(34225(a,1),11853(a,1))].">
      <j1 rule="para" parents="34225 11853"/>
    </justification>
  </clause>

  <clause id="34231">
    <literal><![CDATA[
      L(x,y,L(z \ u,z \ u,z)) = L(x,y,(u \ z) \ 1)
    ]]></literal>
    <justification jstring="[para(436(a,1),34226(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="436 34226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34232">
    <literal><![CDATA[
      L(x,y,L(z \ R(z,u,w),v5,v6)) = L(x,y,L(z * R(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(2796(a,1),34229(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2796 34229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34233">
    <literal><![CDATA[
      L(x,y,L((z \ 1) * u,w,v5)) = L(x,y,L(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(9(a,1),34222(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="9 34222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34234">
    <literal><![CDATA[
      L(x,y,L((z * u) \ w,z,u)) = L(x,y,(z \ 1) \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(23856,a,34216,a),flip(a)].">
      <j1 rule="hyper" parents="23856 34216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34235">
    <literal><![CDATA[
      L(x,y,L((z * u) \ w,z,u)) = L(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,2234,a(flip),b,34234,a),flip(a)].">
      <j1 rule="hyper" parents="373 2234 34234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34236">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) * (R(L(x \ R(x,y,z),u,w),v5,v5) \ v5) = L(v5,v5,L(x * R(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,16074,a,b,34232,a)].">
      <j1 rule="hyper" parents="64 16074 34232"/>
    </justification>
  </clause>

  <clause id="34237">
    <literal><![CDATA[
      L(x,(y \ ((z * T(z,u)) * w)) * v5,v6) = L(x,(w / y) * ((z * T(z,u)) * v5),v6)
    ]]></literal>
    <justification jstring="[para(26518(a,1),34002(a,2,2))].">
      <j1 rule="para" parents="26518 34002"/>
    </justification>
  </clause>

  <clause id="34238">
    <literal><![CDATA[
      L(x,(y * (T(z,u) \ (z / u))) \ w,v5) = L(x,(((z * u) \ z) * y) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29870,a(flip),b,34008,a),flip(a)].">
      <j1 rule="hyper" parents="64 29870 34008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34240">
    <literal><![CDATA[
      L(x,(y * (T(z,u) \ (u \ z))) \ w,v5) = L(x,(((z * u) \ z) * y) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29477,a(flip),b,34238,a)].">
      <j1 rule="hyper" parents="64 29477 34238"/>
    </justification>
  </clause>

  <clause id="34241">
    <literal><![CDATA[
      L(x,(((y * z) \ y) * u) \ w,v5) = L(x,((y \ (z \ y)) * u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29870,a(flip),b,34240,a),flip(a)].">
      <j1 rule="hyper" parents="64 29870 34240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34243">
    <literal><![CDATA[
      R(x,y,(z \ (R(u,w,u) \ z)) \ 1) = R(x,y,u * a(z,R(u,w,u),u))
    ]]></literal>
    <justification jstring="[para(13864(a,1),34064(a,2,3,2))].">
      <j1 rule="para" parents="13864 34064"/>
    </justification>
  </clause>

  <clause id="34244">
    <literal><![CDATA[
      R(x,y,(z \ (R(u,w,u) \ z)) \ 1) = R(x,y,u * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(13829(a,1),34243(a,2,3,2))].">
      <j1 rule="para" parents="13829 34243"/>
    </justification>
  </clause>

  <clause id="34247">
    <literal><![CDATA[
      (x \ (x / y)) * L(z,y,a(y,y,x)) = y * ((y \ (x \ (x / y))) * z)
    ]]></literal>
    <justification jstring="[para(79(a,1),34065(a,2,2,1,2))].">
      <j1 rule="para" parents="79 34065"/>
    </justification>
  </clause>

  <clause id="34249">
    <literal><![CDATA[
      T(x,y) \ ((T(x,y) * (z \ x)) * (z \ x)) = (z / (z \ x)) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,14824,a(flip),b,34068,a),flip(a)].">
      <j1 rule="hyper" parents="373 14824 34068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34251">
    <literal><![CDATA[
      T(x,y) \ ((x * (z \ x)) * (z \ T(x,y))) = (z / (z \ x)) \ x
    ]]></literal>
    <justification jstring="[para(25094(a,1),34249(a,1,2))].">
      <j1 rule="para" parents="25094 34249"/>
    </justification>
  </clause>

  <clause id="34252">
    <literal><![CDATA[
      L(x * y,y \ ((z * (z \ y)) \ (x \ y)),y) = L(x * y,x * y,z * (y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29660,a(flip),b,34074,a)].">
      <j1 rule="hyper" parents="64 29660 34074"/>
    </justification>
  </clause>

  <clause id="34253">
    <literal><![CDATA[
      a(x,x,y) * (z * a(y,a(y,x,x),z)) = ((x / y) \ R(x,x,y)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(32893(a,1),34075(a,1,2,2))].">
      <j1 rule="para" parents="32893 34075"/>
    </justification>
  </clause>

  <clause id="34254">
    <literal><![CDATA[
      a(x,x,y) * (z * a(y,a(y,x,x),z)) = (a(x,x,y) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(31297(a,1),34253(a,2,1))].">
      <j1 rule="para" parents="31297 34253"/>
    </justification>
  </clause>

  <clause id="34255">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * (a(y,x,x) \ z) = L(y,x,x) * (R(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33515,a(flip),b,34084,a)].">
      <j1 rule="hyper" parents="64 33515 34084"/>
    </justification>
  </clause>

  <clause id="34256">
    <literal><![CDATA[
      a((L(x,y,y) * (R(x,y,y) \ z)) * u,w,v5) = a(u * (a(y,y,x) * (a(x,y,y) \ z)),w,v5)
    ]]></literal>
    <justification jstring="[para(34255(a,1),26821(a,1,1,1))].">
      <j1 rule="para" parents="34255 26821"/>
    </justification>
  </clause>

  <clause id="34257">
    <literal><![CDATA[
      a(x,(y * y) * ((z \ (u * (y * y))) \ w),v5) = a(x,(T(u,y * y) / z) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32074,a(flip),b,34085,a)].">
      <j1 rule="hyper" parents="64 32074 34085"/>
    </justification>
  </clause>

  <clause id="34258">
    <literal><![CDATA[
      a(x,y \ ((z * ((u * u) * w)) / v5),v6) = a(x,y \ (v5 \ (z * w)),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32070,a(flip),b,34086,a),flip(a)].">
      <j1 rule="hyper" parents="373 32070 34086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34260">
    <literal><![CDATA[
      a(x,y \ (z \ (u * ((w * w) * v5))),v6) = a(x,y \ (z \ (u * v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,31908,a(flip),b,34258,a)].">
      <j1 rule="hyper" parents="64 31908 34258"/>
    </justification>
  </clause>

  <clause id="34261">
    <literal><![CDATA[
      a(x,L(y * z,u,w) \ (K(v5,z) * v6),v7) = a(x,L(T(z,v5) * y,u,w) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(26104(a,1),34118(a,1,2))].">
      <j1 rule="para" parents="26104 34118"/>
    </justification>
  </clause>

  <clause id="34262">
    <literal><![CDATA[
      a(L((x * (y \ 1)) \ z,u,w),v5,v6) = a(L((y * x) \ z,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32926,a(flip),b,34124,a),flip(a)].">
      <j1 rule="hyper" parents="64 32926 34124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34264">
    <literal><![CDATA[
      a(L((x * y) \ z,x,x),u,w) = a(L(x * (y \ z),x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32948,a(flip),b,34262,a),flip(a)].">
      <j1 rule="hyper" parents="64 32948 34262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34265">
    <literal><![CDATA[
      a(L(a(x,y,z),x,u),x,u) = a(x,y,z) \ L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,33158,a(flip),b,34150,a),flip(a)].">
      <j1 rule="hyper" parents="64 33158 34150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34267">
    <literal><![CDATA[
      L(x,L(y * L(y,z,u),y,u * z),w) = L(x,(z * u) \ (y \ (u * (z * y))),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29454,a,b,34167,a),flip(a)].">
      <j1 rule="hyper" parents="373 29454 34167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34268">
    <literal><![CDATA[
      L(x,y,L(R(z,z,u),u / z,u / z)) = L(x,y,(z \ u) * (z \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,31741,a(flip),b,34171,a),flip(a)].">
      <j1 rule="hyper" parents="373 31741 34171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34269">
    <literal><![CDATA[
      (a(x,x,y) * a(x,x,y)) * (z * L(y,x,x)) = z * (a(x,x,y) * y)
    ]]></literal>
    <justification jstring="[para(5669(a,1),34172(a,1,2,2))].">
      <j1 rule="para" parents="5669 34172"/>
    </justification>
  </clause>

  <clause id="34270">
    <literal><![CDATA[
      x * (L(L(x,y,y),y,y) \ (z * L(x,y,y))) = z * (a(y,y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30365,a(flip),b,34269,a)].">
      <j1 rule="hyper" parents="64 30365 34269"/>
    </justification>
  </clause>

  <clause id="34271">
    <literal><![CDATA[
      L(x,y,(z * (a(u,u,w) * w)) * v5) = L(x,y,(z * L(w,u,u)) * v5)
    ]]></literal>
    <justification jstring="[para(34269(a,1),2202(a,1,3,1))].">
      <j1 rule="para" parents="34269 2202"/>
    </justification>
  </clause>

  <clause id="34272">
    <literal><![CDATA[
      L(x,y * (a(z,z,u) * u),w) = L(x,y * L(u,z,z),w)
    ]]></literal>
    <justification jstring="[para(34269(a,1),11772(a,1,2))].">
      <j1 rule="para" parents="34269 11772"/>
    </justification>
  </clause>

  <clause id="34273">
    <literal><![CDATA[
      L(x,y,((z \ 1) * L(u,z,z)) * w) = L(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[para(30238(a,1),34271(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30238 34271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34274">
    <literal><![CDATA[
      L(x,y,(z * L(u,z,z)) * w) = L(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2271,a(flip),b,34273,a)].">
      <j1 rule="hyper" parents="64 2271 34273"/>
    </justification>
  </clause>

  <clause id="34275">
    <literal><![CDATA[
      L(x,y,L(z * u,z,z) * w) = L(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13560,a,b,34274,a)].">
      <j1 rule="hyper" parents="64 13560 34274"/>
    </justification>
  </clause>

  <clause id="34276">
    <literal><![CDATA[
      L(x,y,(z \ (z \ u)) * w) = L(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),34275(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="10 34275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34277">
    <literal><![CDATA[
      L(x,y,z * (u \ (u \ w))) = L(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(24201,a,34276,a)].">
      <j1 rule="hyper" parents="24201 34276"/>
    </justification>
  </clause>

  <clause id="34278">
    <literal><![CDATA[
      L(x,y,L(R(z,z,u),u / z,u / z)) = L(x,y,L(u,z,z) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,34268,a,b,34277,a)].">
      <j1 rule="hyper" parents="64 34268 34277"/>
    </justification>
  </clause>

  <clause id="34279">
    <literal><![CDATA[
      L(x,y,L(R(z,z,u),u / z,u / z)) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,26047,a(flip),b,34278,a),flip(a)].">
      <j1 rule="hyper" parents="373 26047 34278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34280">
    <literal><![CDATA[
      L(x,y,R((1 / (z / u)) * z,u,z)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(1017(a,1),34279(a,1,3))].">
      <j1 rule="para" parents="1017 34279"/>
    </justification>
  </clause>

  <clause id="34281">
    <literal><![CDATA[
      L(x,y,L((1 / (z / u)) * z,u,z)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29203,a(flip),b,34280,a)].">
      <j1 rule="hyper" parents="64 29203 34280"/>
    </justification>
  </clause>

  <clause id="34282">
    <literal><![CDATA[
      L(x,y,L(((z / u) \ 1) * z,u,z)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29174,a(flip),b,34281,a)].">
      <j1 rule="hyper" parents="64 29174 34281"/>
    </justification>
  </clause>

  <clause id="34283">
    <literal><![CDATA[
      L(x,y,L((z / u) * z,u,z)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,34233,a(flip),b,34282,a)].">
      <j1 rule="hyper" parents="64 34233 34282"/>
    </justification>
  </clause>

  <clause id="34284">
    <literal><![CDATA[
      L(x,y,L(z * (u \ z),u,z)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29348,a(flip),b,34283,a)].">
      <j1 rule="hyper" parents="64 29348 34283"/>
    </justification>
  </clause>

  <clause id="34285">
    <literal><![CDATA[
      L(x,y,R(z * (u \ z),u,z)) = L(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29203,a,b,34284,a)].">
      <j1 rule="hyper" parents="64 29203 34284"/>
    </justification>
  </clause>

  <clause id="34286">
    <literal><![CDATA[
      (x \ 1) * (y * R(K(x * y,x \ 1) * x,z,u)) = (y * x) * R(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(25964(a,2),34178(a,1,2,2))].">
      <j1 rule="para" parents="25964 34178"/>
    </justification>
  </clause>

  <clause id="34287">
    <literal><![CDATA[
      a(x \ 1,x \ L(x,y,z),u) = a(x * L(x,y,z),x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30441,a(flip),b,34180,a)].">
      <j1 rule="hyper" parents="64 30441 34180"/>
    </justification>
  </clause>

  <clause id="34288">
    <literal><![CDATA[
      a(x \ 1,x * L(x,y,z),u) = a(x * L(x,y,z),x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11978,a(flip),b,34287,a)].">
      <j1 rule="hyper" parents="64 11978 34287"/>
    </justification>
  </clause>

  <clause id="34289">
    <literal><![CDATA[
      a(x * L(x,y,z),x,x \ u) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2653,a(flip),b,34288,a),flip(a)].">
      <j1 rule="hyper" parents="64 2653 34288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34290">
    <literal><![CDATA[
      a(x,x * L(x,y,z),x \ u) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,33573,a(flip),b,34289,a)].">
      <j1 rule="hyper" parents="64 33573 34289"/>
    </justification>
  </clause>

  <clause id="34291">
    <literal><![CDATA[
      a(x,y,L((z \ 1) * ((u * u) * w),z,z)) = a(x,y,(z \ (u * u)) * L(w,z,z))
    ]]></literal>
    <justification jstring="[para(1152(a,2),34189(a,1,3))].">
      <j1 rule="para" parents="1152 34189"/>
    </justification>
  </clause>

  <clause id="34292">
    <literal><![CDATA[
      ((x \ (x \ y)) \ y) \ K(x * x,x * x) = 1 / ((x \ (x \ y)) \ y)
    ]]></literal>
    <justification jstring="[para(191(a,1),34200(a,1,2,2,2))].">
      <j1 rule="para" parents="191 34200"/>
    </justification>
  </clause>

  <clause id="34293">
    <literal><![CDATA[
      1 / ((x \ (x \ y)) \ y) = ((x \ (x \ y)) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(188(a,1),34292(a,1,2)),flip(a)].">
      <j1 rule="para" parents="188 34292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34295">
    <literal><![CDATA[
      (x \ y) * (z * K(x,(x \ y) * y)) = z * T(y / T(x,y \ x),z)
    ]]></literal>
    <justification jstring="[para(28627(a,1),34201(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="28627 34201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34296">
    <literal><![CDATA[
      (x \ y) * (z * K(x,(x \ y) * y)) = (y / T(x,y \ x)) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,115,a(flip),b,34295,a),flip(a)].">
      <j1 rule="hyper" parents="373 115 34295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34297">
    <literal><![CDATA[
      (x \ y) * (z * K(x,y * (x \ y))) = (y / T(x,y \ x)) * z
    ]]></literal>
    <justification jstring="[para(14018(a,1),34296(a,1,2,2))].">
      <j1 rule="para" parents="14018 34296"/>
    </justification>
  </clause>

  <clause id="34298">
    <literal><![CDATA[
      T((x / T(y,x \ y)) * x,y) = T((y \ x) * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(34297(a,1),16664(a,1,1))].">
      <j1 rule="para" parents="34297 16664"/>
    </justification>
  </clause>

  <clause id="34299">
    <literal><![CDATA[
      T((x \ y) * y,K(y,x)) = T(y / (x / y),x)
    ]]></literal>
    <justification jstring="[para(27197(a,1),34298(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27197 34298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34300">
    <literal><![CDATA[
      T((x \ y) * y,K(x,y)) = T(y / (x / y),x)
    ]]></literal>
    <justification jstring="[hyper(8184,a,34299,a)].">
      <j1 rule="hyper" parents="8184 34299"/>
    </justification>
  </clause>

  <clause id="34301">
    <literal><![CDATA[
      T(x / (y / x),y) = (y \ x) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,17644,a(flip),b,34300,a),flip(a)].">
      <j1 rule="hyper" parents="64 17644 34300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34303">
    <literal><![CDATA[
      R(1 / (x \ T(y,z)),x \ T(y,z),y) \ T(y,z) = T(T(y,z) / (x / T(y,z)),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,15091,a,b,34301,a)].">
      <j1 rule="hyper" parents="373 15091 34301"/>
    </justification>
  </clause>

  <clause id="34304">
    <literal><![CDATA[
      (x * ((x \ y) * y)) / x = y / (x / y)
    ]]></literal>
    <justification jstring="[hyper(313,a,34301,a)].">
      <j1 rule="hyper" parents="313 34301"/>
    </justification>
  </clause>

  <clause id="34305">
    <literal><![CDATA[
      (x / (y / x)) * y = y * ((y \ x) * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,34301,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 34301 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34306">
    <literal><![CDATA[
      (x \ (y \ x)) * (y \ x) = T((y \ x) / y,x)
    ]]></literal>
    <justification jstring="[para(79(a,1),34301(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 34301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34307">
    <literal><![CDATA[
      R((x \ y) * y,(y / (x / y)) * x,y / (x / y)) = T(y / (x / y),(y / (x / y)) \ x)
    ]]></literal>
    <justification jstring="[para(34301(a,1),13752(a,1,1))].">
      <j1 rule="para" parents="34301 13752"/>
    </justification>
  </clause>

  <clause id="34308">
    <literal><![CDATA[
      ((x \ y) * y) / R(x,(y / (x / y)) * x,x) = x \ (y / (x / y))
    ]]></literal>
    <justification jstring="[para(34301(a,1),13766(a,1,1))].">
      <j1 rule="para" parents="34301 13766"/>
    </justification>
  </clause>

  <clause id="34309">
    <literal><![CDATA[
      T(x / (R(y,x,x) / x),R(y,x,x)) = (y \ L(x,x,y)) * x
    ]]></literal>
    <justification jstring="[para(16075(a,1),34301(a,2,1))].">
      <j1 rule="para" parents="16075 34301"/>
    </justification>
  </clause>

  <clause id="34310">
    <literal><![CDATA[
      ((x \ y) * y) \ R(T(y / (x / y),x),z,u) = (y / (x / y)) \ R(y / (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(34301(a,1),24594(a,1,1))].">
      <j1 rule="para" parents="34301 24594"/>
    </justification>
  </clause>

  <clause id="34311">
    <literal><![CDATA[
      T(x / ((1 / x) * a(y,z,u)),L(a(y,z,u),x,x)) = (L(a(y,z,u),x,x) \ x) * x
    ]]></literal>
    <justification jstring="[para(24637(a,1),34301(a,1,1,2))].">
      <j1 rule="para" parents="24637 34301"/>
    </justification>
  </clause>

  <clause id="34312">
    <literal><![CDATA[
      (x \ (((y \ x) * y) * ((((y \ x) * y) \ z) * z))) * K(y,y \ x) = T(z / (((y \ x) * y) / z),x)
    ]]></literal>
    <justification jstring="[para(34304(a,1),24300(a,1,1)),flip(a)].">
      <j1 rule="para" parents="34304 24300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34313">
    <literal><![CDATA[
      (x * y) * (((x * y) \ x) * x) = (x / y) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10593,a(flip),b,34305,a),flip(a)].">
      <j1 rule="hyper" parents="64 10593 34305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34314">
    <literal><![CDATA[
      T(x \ (y \ x),K(z,u)) * (T(y,K(z,u)) \ x) = T((T(y,K(z,u)) \ x) / T(y,K(z,u)),x)
    ]]></literal>
    <justification jstring="[para(17705(a,2),34306(a,1,1))].">
      <j1 rule="para" parents="17705 34306"/>
    </justification>
  </clause>

  <clause id="34315">
    <literal><![CDATA[
      L(x,y,(L(z,z \ (u \ z),z \ (u \ z)) * w) * v5) = L(x,y,(T((u \ z) / u,z) * w) * v5)
    ]]></literal>
    <justification jstring="[para(34306(a,1),29413(a,2,3,1,1))].">
      <j1 rule="para" parents="34306 29413"/>
    </justification>
  </clause>

  <clause id="34316">
    <literal><![CDATA[
      (x * y) * (L(y \ 1,y,x) * x) = (x / y) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1000,a,b,34313,a)].">
      <j1 rule="hyper" parents="64 1000 34313"/>
    </justification>
  </clause>

  <clause id="34317">
    <literal><![CDATA[
      L(x,x \ (y \ x),x * y) = ((x / y) * (y * x)) / x
    ]]></literal>
    <justification jstring="[para(34316(a,1),29721(a,1,1)),flip(a)].">
      <j1 rule="para" parents="34316 29721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34318">
    <literal><![CDATA[
      L(x,x \ (y \ x),x * y) = L(x,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,11074,a(flip),b,34317,a),flip(a)].">
      <j1 rule="hyper" parents="373 11074 34317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34319">
    <literal><![CDATA[
      L(x,x \ (y \ x),y * x) = L(x,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(24201,a,34318,a)].">
      <j1 rule="hyper" parents="24201 34318"/>
    </justification>
  </clause>

  <clause id="34320">
    <literal><![CDATA[
      (x * y) * (((x * y) \ y) * y) = y / (1 / L(y,x,x \ y))
    ]]></literal>
    <justification jstring="[para(34319(a,1),30990(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="34319 30990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34321">
    <literal><![CDATA[
      T(x / (y * (1 / x)),R(y,x,x)) = (y \ L(x,x,y)) * x
    ]]></literal>
    <justification jstring="[para(1408(a,1),34309(a,1,1,2))].">
      <j1 rule="para" parents="1408 34309"/>
    </justification>
  </clause>

  <clause id="34322">
    <literal><![CDATA[
      T(x / (y * (1 / x)),y) = (y \ L(x,x,y)) * x
    ]]></literal>
    <justification jstring="[hyper(23890,a,34321,a)].">
      <j1 rule="hyper" parents="23890 34321"/>
    </justification>
  </clause>

  <clause id="34324">
    <literal><![CDATA[
      (x \ L(y,y,x)) * y = (x \ y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31278,a(flip),b,34322,a),flip(a)].">
      <j1 rule="hyper" parents="64 31278 34322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34325">
    <literal><![CDATA[
      ((x \ 1) \ L(y,y,x)) * y = ((x \ 1) \ y) / (1 / y)
    ]]></literal>
    <justification jstring="[para(1631(a,1),34324(a,1,1,2))].">
      <j1 rule="para" parents="1631 34324"/>
    </justification>
  </clause>

  <clause id="34326">
    <literal><![CDATA[
      ((x \ y) * y) / R(x,x * ((x \ y) * y),x) = x \ (y / (x / y))
    ]]></literal>
    <justification jstring="[para(34305(a,1),34308(a,1,2,2))].">
      <j1 rule="para" parents="34305 34308"/>
    </justification>
  </clause>

  <clause id="34327">
    <literal><![CDATA[
      ((x \ y) * y) / R(x,a(x,x \ y,y),x) = x \ (y / (x / y))
    ]]></literal>
    <justification jstring="[para(26593(a,1),34326(a,1,2))].">
      <j1 rule="para" parents="26593 34326"/>
    </justification>
  </clause>

  <clause id="34328">
    <literal><![CDATA[
      ((x \ y) * y) / x = x \ (y / (x / y))
    ]]></literal>
    <justification jstring="[para(13920(a,1),34327(a,1,2))].">
      <j1 rule="para" parents="13920 34327"/>
    </justification>
  </clause>

  <clause id="34329">
    <literal><![CDATA[
      ((x \ y) * y) * (x \ 1) = x \ (y / (x / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30710,a,b,34328,a)].">
      <j1 rule="hyper" parents="64 30710 34328"/>
    </justification>
  </clause>

  <clause id="34330">
    <literal><![CDATA[
      (x \ (y / (x / y))) * (z * (x / z)) = ((x \ y) * y) * K(z,z \ x)
    ]]></literal>
    <justification jstring="[para(34328(a,1),10245(a,1,1))].">
      <j1 rule="para" parents="34328 10245"/>
    </justification>
  </clause>

  <clause id="34331">
    <literal><![CDATA[
      K(x,T(y,z * ((z \ u) * u))) / (z \ (u / (z / u))) = (1 / (((z \ u) * u) / z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(34328(a,1),17395(a,1,2))].">
      <j1 rule="para" parents="34328 17395"/>
    </justification>
  </clause>

  <clause id="34332">
    <literal><![CDATA[
      a(x,y,(((z \ u) * u) * (z \ 1)) * w) = a(x,y,((u / (z / u)) / z) * w)
    ]]></literal>
    <justification jstring="[para(34329(a,2),27317(a,2,3,1)),flip(a)].">
      <j1 rule="para" parents="34329 27317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34333">
    <literal><![CDATA[
      L(x,y,((z * ((u \ z) \ 1)) * u) * w) = L(x,y,(u \ (z / (u / z))) * w)
    ]]></literal>
    <justification jstring="[para(34329(a,1),29360(a,2,3,1))].">
      <j1 rule="para" parents="34329 29360"/>
    </justification>
  </clause>

  <clause id="34334">
    <literal><![CDATA[
      L(x,(y * ((z \ y) \ 1)) * z,u) = L(x,z \ (y / (z / y)),u)
    ]]></literal>
    <justification jstring="[para(34329(a,1),29761(a,2,2))].">
      <j1 rule="para" parents="34329 29761"/>
    </justification>
  </clause>

  <clause id="34335">
    <literal><![CDATA[
      a(((x * ((y \ x) \ 1)) * y) * z,u,w) = a((y \ (x / (y / x))) * z,u,w)
    ]]></literal>
    <justification jstring="[para(34329(a,1),32791(a,2,1,1))].">
      <j1 rule="para" parents="34329 32791"/>
    </justification>
  </clause>

  <clause id="34336">
    <literal><![CDATA[
      L(x,(y * ((z \ y) \ 1)) * z,u) = L(x,z \ ((z \ y) * y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,33699,a(flip),b,34334,a),flip(a)].">
      <j1 rule="hyper" parents="373 33699 34334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34337">
    <literal><![CDATA[
      L(x,y \ ((y \ z) * z),u) = L(x,((y \ z) * z) * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29643,a(flip),b,34336,a),flip(a)].">
      <j1 rule="hyper" parents="64 29643 34336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34338">
    <literal><![CDATA[
      L(x,y \ ((y \ z) * z),u) = L(x,a(z,y \ z,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29861,a(flip),b,34337,a),flip(a)].">
      <j1 rule="hyper" parents="373 29861 34337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34339">
    <literal><![CDATA[
      L(x,y,((z * ((u \ z) \ 1)) * u) * w) = L(x,y,(u \ ((u \ z) * z)) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,33716,a(flip),b,34333,a),flip(a)].">
      <j1 rule="hyper" parents="373 33716 34333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34340">
    <literal><![CDATA[
      a(((x * ((y \ x) \ 1)) * y) * z,u,w) = a((y \ ((y / x) \ x)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32492,a(flip),b,34335,a),flip(a)].">
      <j1 rule="hyper" parents="373 32492 34335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34341">
    <literal><![CDATA[
      L(x,y,(z \ ((z \ u) * u)) * w) = L(x,y,(((z \ u) * u) * z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29255,a(flip),b,34339,a),flip(a)].">
      <j1 rule="hyper" parents="64 29255 34339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34342">
    <literal><![CDATA[
      L(x,y,(z \ ((z \ u) * u)) * w) = L(x,y,w * a(u,z \ u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,33640,a(flip),b,34341,a),flip(a)].">
      <j1 rule="hyper" parents="373 33640 34341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34343">
    <literal><![CDATA[
      a(((x * ((y \ x) \ 1)) * y) * z,u,w) = a((y \ ((x \ y) \ x)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32691,a(flip),b,34340,a),flip(a)].">
      <j1 rule="hyper" parents="373 32691 34340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34344">
    <literal><![CDATA[
      L(x,(y \ ((z * T(z,u)) * w)) * v5,v6) = L(x,v5 * (w / y),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,31042,a(flip),b,34237,a),flip(a)].">
      <j1 rule="hyper" parents="373 31042 34237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34346">
    <literal><![CDATA[
      L(x,(y \ ((z * T(z,u)) * w)) * v5,v6) = L(x,v5 * (y \ w),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29547,a(flip),b,34344,a),flip(a)].">
      <j1 rule="hyper" parents="373 29547 34344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34347">
    <literal><![CDATA[
      L(x * y,y \ (y \ (x \ y)),y) = L(x * y,x * y,z * (y / z))
    ]]></literal>
    <justification jstring="[para(10(a,1),34252(a,1,2,2,1))].">
      <j1 rule="para" parents="10 34252"/>
    </justification>
  </clause>

  <clause id="34348">
    <literal><![CDATA[
      L(x * y,L(x \ y,y,y),y) = L(x * y,x * y,z * (y / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,31756,a(flip),b,34347,a)].">
      <j1 rule="hyper" parents="64 31756 34347"/>
    </justification>
  </clause>

  <clause id="34350">
    <literal><![CDATA[
      L(x * y,L(x \ y,y,y),y) = L(x * y,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,24004,a(flip),b,34348,a),flip(a)].">
      <j1 rule="hyper" parents="373 24004 34348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34351">
    <literal><![CDATA[
      a(x,(T(y,z * z) / u) \ w,v5) = a(x,(u \ (y * (z * z))) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(26848,a,34257,a),flip(a)].">
      <j1 rule="hyper" parents="26848 34257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34353">
    <literal><![CDATA[
      a(x,(y \ (z * (u * u))) \ w,v5) = a(x,(y \ z) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32166,a(flip),b,34351,a),flip(a)].">
      <j1 rule="hyper" parents="64 32166 34351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34355">
    <literal><![CDATA[
      a(x,L(T(y,z) * u,w,v5) \ v6,v7) = a(x,L(u * y,w,v5) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,31914,a(flip),b,34261,a),flip(a)].">
      <j1 rule="hyper" parents="64 31914 34261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34357">
    <literal><![CDATA[
      (x \ 1) * (y * R(x * K(x * y,x \ 1),z,u)) = (y * x) * R(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(3348(a,1),34286(a,1,2,2,1))].">
      <j1 rule="para" parents="3348 34286"/>
    </justification>
  </clause>

  <clause id="34358">
    <literal><![CDATA[
      (x \ 1) * T(y * R(x,z,u),T(x \ 1,x)) = (y * x) * R(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(28629(a,1),34357(a,1,2))].">
      <j1 rule="para" parents="28629 34357"/>
    </justification>
  </clause>

  <clause id="34359">
    <literal><![CDATA[
      (x \ 1) * T(y * R(x,z,u),x \ 1) = (y * x) * R(x \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(3877(a,1),34358(a,1,2))].">
      <j1 rule="para" parents="3877 34358"/>
    </justification>
  </clause>

  <clause id="34360">
    <literal><![CDATA[
      (x * R(y,z,u)) * (y \ 1) = (x * y) * R(y \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(328,a,34359,a)].">
      <j1 rule="hyper" parents="328 34359"/>
    </justification>
  </clause>

  <clause id="34361">
    <literal><![CDATA[
      T(x,y) * K(y \ T(x,y),y \ 1) = (x * y) * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24615,a,b,34360,a)].">
      <j1 rule="hyper" parents="64 24615 34360"/>
    </justification>
  </clause>

  <clause id="34362">
    <literal><![CDATA[
      T(x,y) * K(x / y,y \ 1) = (x * y) * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(13587(a,1),34361(a,1,2))].">
      <j1 rule="para" parents="13587 34361"/>
    </justification>
  </clause>

  <clause id="34363">
    <literal><![CDATA[
      T(x * K(y \ x,y \ 1),y) = (x * y) * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25085,a,b,34362,a)].">
      <j1 rule="hyper" parents="64 25085 34362"/>
    </justification>
  </clause>

  <clause id="34364">
    <literal><![CDATA[
      L(L((a(x,y,z) \ 1) \ u,w,v5),a(x,y,z),a(x,y,z)) != L(v6,w,v5)
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(23943(a,2),51(a,1))].">
      <j1 rule="para" parents="23943 51"/>
    </justification>
  </clause>

  <clause id="34365">
    <literal><![CDATA[
      x / ((x / (a(y,z,u) * w)) * w) = ((x / (w * a(y,z,u))) * w) \ x
    ]]></literal>
    <justification jstring="[para(23105(a,1),23957(a,1,2))].">
      <j1 rule="para" parents="23105 23957"/>
    </justification>
  </clause>

  <clause id="34367">
    <literal><![CDATA[
      x / (y * ((a(z,u,w) * y) \ x)) = ((x / (y * a(z,u,w))) * y) \ x
    ]]></literal>
    <justification jstring="[para(28668(a,1),34365(a,1,2))].">
      <j1 rule="para" parents="28668 34365"/>
    </justification>
  </clause>

  <clause id="34368">
    <literal><![CDATA[
      x / (y * ((a(z,u,w) * y) \ x)) = (y * ((a(z,u,w) * y) \ x)) \ x
    ]]></literal>
    <justification jstring="[para(28774(a,1),34367(a,2,1))].">
      <j1 rule="para" parents="28774 34367"/>
    </justification>
  </clause>

  <clause id="34369">
    <literal><![CDATA[
      ((x / a(y,z,u)) * ((a(y,z,u) * (x / a(y,z,u))) \ (x * w))) \ (x * w) = (x * w) / ((x / a(y,z,u)) * (K(a(y,z,u) \ x,a(y,z,u)) * w))
    ]]></literal>
    <justification jstring="[para(11848(a,1),34368(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11848 34368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34370">
    <literal><![CDATA[
      L(T((x \ 1) \ K(y,x),z),x,x \ y) = ((y / x) * ((1 / x) \ T(x,z))) / y
    ]]></literal>
    <justification jstring="[para(14444(a,1),25088(a,1,1,1))].">
      <j1 rule="para" parents="14444 25088"/>
    </justification>
  </clause>

  <clause id="34371">
    <literal><![CDATA[
      L(x,(L(y,z,y * z) * u) * w,v5) = L(x,(((T(y,z) * z) * z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29457,a(flip),b,25095,a),flip(a)].">
      <j1 rule="hyper" parents="64 29457 25095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34373">
    <literal><![CDATA[
      L(x,(L(y,z,y * z) * u) * w,v5) = L(x,(u * R(T(y,z),z,z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31154,a(flip),b,34371,a),flip(a)].">
      <j1 rule="hyper" parents="373 31154 34371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34374">
    <literal><![CDATA[
      L(x,(L(y,z,y * z) * u) * w,v5) = L(x,(R(y,z,z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29769,a(flip),b,34373,a),flip(a)].">
      <j1 rule="hyper" parents="373 29769 34373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34376">
    <literal><![CDATA[
      L(x,(R(y,z,z) * u) * w,v5) = L(x,(L(y,z,z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31031,a(flip),b,34374,a),flip(a)].">
      <j1 rule="hyper" parents="64 31031 34374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34377">
    <literal><![CDATA[
      L(x,(L(y,z,z) * (u \ 1)) * w,v5) = L(x,(u * R(y,z,z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29643,a(flip),b,34376,a),flip(a)].">
      <j1 rule="hyper" parents="64 29643 34376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34378">
    <literal><![CDATA[
      L(x,(y * R(z,u,u)) * w,v5) = L(x,(y * L(z,u,u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29643,a(flip),b,34377,a),flip(a)].">
      <j1 rule="hyper" parents="64 29643 34377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34379">
    <literal><![CDATA[
      L(x,(y * L(z,y,y)) * u,w) = L(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31651,a(flip),b,34378,a),flip(a)].">
      <j1 rule="hyper" parents="64 31651 34378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34381">
    <literal><![CDATA[
      L(x,L(y * z,y,y) * u,w) = L(x,(y \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29853,a,b,34379,a)].">
      <j1 rule="hyper" parents="64 29853 34379"/>
    </justification>
  </clause>

  <clause id="34382">
    <literal><![CDATA[
      L(x,y * L(z * u,z,z),w) = L(x,(z \ u) * y,w)
    ]]></literal>
    <justification jstring="[hyper(29572,a,34381,a)].">
      <j1 rule="hyper" parents="29572 34381"/>
    </justification>
  </clause>

  <clause id="34383">
    <literal><![CDATA[
      L(x,L(y * z,z,z) * u,w) = L(x,(z \ y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29474,a,b,34381,a)].">
      <j1 rule="hyper" parents="64 29474 34381"/>
    </justification>
  </clause>

  <clause id="34384">
    <literal><![CDATA[
      L(x,(y \ (y \ z)) * u,w) = L(x,L(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),34381(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="10 34381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34386">
    <literal><![CDATA[
      L(x,L(L(y,y,z),y \ z,y \ z),u) = L(x,L(z,y,y) * (y \ z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34173,a,b,34384,a)].">
      <j1 rule="hyper" parents="64 34173 34384"/>
    </justification>
  </clause>

  <clause id="34389">
    <literal><![CDATA[
      L(x,L(L(y,y,z),y \ z,y \ z),u) = L(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29890,a(flip),b,34386,a),flip(a)].">
      <j1 rule="hyper" parents="373 29890 34386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34390">
    <literal><![CDATA[
      L(x,L((1 / (y / z)) * y,z,y),u) = L(x,L(z,y,y),u)
    ]]></literal>
    <justification jstring="[para(10629(a,1),34389(a,1,2))].">
      <j1 rule="para" parents="10629 34389"/>
    </justification>
  </clause>

  <clause id="34391">
    <literal><![CDATA[
      L(x,L((y \ z) * z,y,z),u) = L(x,L(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30865,a(flip),b,34390,a)].">
      <j1 rule="hyper" parents="64 30865 34390"/>
    </justification>
  </clause>

  <clause id="34393">
    <literal><![CDATA[
      ((x \ y) * (1 / (y \ x))) * L(z,y \ x,x \ y) = (1 / (y \ x)) * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(6430(a,1),25373(a,1,1))].">
      <j1 rule="para" parents="6430 25373"/>
    </justification>
  </clause>

  <clause id="34394">
    <literal><![CDATA[
      K(x \ T(x \ 1,y),z) * a(z,(x * T(x,y)) \ 1,z) = K(z / (x * T(x,y)),z)
    ]]></literal>
    <justification jstring="[para(28271(a,2),25377(a,1,1))].">
      <j1 rule="para" parents="28271 25377"/>
    </justification>
  </clause>

  <clause id="34395">
    <literal><![CDATA[
      T(x \ (y * L(x,z,u)),K(w,x * (x * y))) = T(x,y) \ (L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(28611(a,1),25470(a,1,2))].">
      <j1 rule="para" parents="28611 25470"/>
    </justification>
  </clause>

  <clause id="34396">
    <literal><![CDATA[
      T(x \ (y * L(x,z,u)),K(w,y)) = T(x,y) \ (L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,17561,a(flip),b,34395,a)].">
      <j1 rule="hyper" parents="64 17561 34395"/>
    </justification>
  </clause>

  <clause id="34398">
    <literal><![CDATA[
      T(x \ (y * L(x,z,u)),K(y,w)) = T(x,y) \ (L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(8728,a,34396,a)].">
      <j1 rule="hyper" parents="8728 34396"/>
    </justification>
  </clause>

  <clause id="34400">
    <literal><![CDATA[
      T(x \ (y * L(x,z,u)),K(y,w)) = x \ (y * L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,24777,a(flip),b,34398,a),flip(a)].">
      <j1 rule="hyper" parents="373 24777 34398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34401">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),w) * T(x \ (y * L(x,z,u)),K(y,v5)) = T(x \ (y * L(x,z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(145,a,34400,a,b,5814,a)].">
      <j1 rule="hyper" parents="145 34400 5814"/>
    </justification>
  </clause>

  <clause id="34402">
    <literal><![CDATA[
      (x / L(y,z,u)) \ T(L(y,z,u) \ x,w) = K(y \ x,y) * K(y \ x,w)
    ]]></literal>
    <justification jstring="[para(28404(a,1),25521(a,2,2))].">
      <j1 rule="para" parents="28404 25521"/>
    </justification>
  </clause>

  <clause id="34403">
    <literal><![CDATA[
      (x / L(y,z,u)) \ T(L(y,z,u) \ x,w) = (x / y) \ T(y \ x,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,6614,a(flip),b,34402,a),flip(a)].">
      <j1 rule="hyper" parents="373 6614 34402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34405">
    <literal><![CDATA[
      ((L(x,y,z) \ u) * w) / (u / L(x,y,z)) = w * ((u / x) \ T(x \ u,w))
    ]]></literal>
    <justification jstring="[para(34403(a,1),20944(a,1,2)),flip(a)].">
      <j1 rule="para" parents="34403 20944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34406">
    <literal><![CDATA[
      ((L(x,y,z) \ u) * w) / (u / L(x,y,z)) = ((x \ u) * w) / (u / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,20944,a(flip),b,34405,a),flip(a)].">
      <j1 rule="hyper" parents="373 20944 34405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34407">
    <literal><![CDATA[
      ((x \ y) * ((L(x,z,u) \ y) \ w)) / (y / x) = w / (y / L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(393,a,34406,a),flip(a)].">
      <j1 rule="hyper" parents="393 34406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34409">
    <literal><![CDATA[
      R(x / (y * K(z,K(u,w))),y,T(u,K(z,w))) = (x * u) / (y * (K(z,K(u,w)) * u))
    ]]></literal>
    <justification jstring="[para(8108(a,1),25955(a,1,1,2,2))].">
      <j1 rule="para" parents="8108 25955"/>
    </justification>
  </clause>

  <clause id="34410">
    <literal><![CDATA[
      (x * ((y \ K(z,u)) * y)) \ w = (y * (K(u,z) / y)) * (x \ w)
    ]]></literal>
    <justification jstring="[para(23270(a,1),26495(a,1,1))].">
      <j1 rule="para" parents="23270 26495"/>
    </justification>
  </clause>

  <clause id="34413">
    <literal><![CDATA[
      R(x,y,((z * T(u,w)) \ ((u * w) * z)) * v5) = R(x,y,R(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26226,a(flip),b,26614,a),flip(a)].">
      <j1 rule="hyper" parents="373 26226 26614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34415">
    <literal><![CDATA[
      R(x,y,((z * u) \ ((u * w) * z)) * v5) = R(x,y,R(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26224,a(flip),b,34413,a)].">
      <j1 rule="hyper" parents="64 26224 34413"/>
    </justification>
  </clause>

  <clause id="34417">
    <literal><![CDATA[
      R(x,y,R(z,u,w) * v5) = R(x,y,L(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27785,a(flip),b,34415,a),flip(a)].">
      <j1 rule="hyper" parents="64 27785 34415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34418">
    <literal><![CDATA[
      R(x,y,R(z,u,w) * v5) = R(x,y,v5 * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,26164,a,b,34417,a),flip(a)].">
      <j1 rule="hyper" parents="373 26164 34417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34419">
    <literal><![CDATA[
      R(x,y,z * R(u,w,v5)) = R(x,y,z * L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,26164,a,b,34418,a)].">
      <j1 rule="hyper" parents="64 26164 34418"/>
    </justification>
  </clause>

  <clause id="34420">
    <literal><![CDATA[
      R(x,y,z \ ((u * T(w,v5)) \ ((w * v5) * u))) = R(x,y,z \ R(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,26282,a(flip),b,26615,a),flip(a)].">
      <j1 rule="hyper" parents="373 26282 26615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34422">
    <literal><![CDATA[
      R(x,y,z \ ((u * w) \ ((w * v5) * u))) = R(x,y,z \ R(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26279,a(flip),b,34420,a)].">
      <j1 rule="hyper" parents="64 26279 34420"/>
    </justification>
  </clause>

  <clause id="34424">
    <literal><![CDATA[
      R(x,y,z \ R(u,w,v5)) = R(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,26348,a(flip),b,34422,a),flip(a)].">
      <j1 rule="hyper" parents="64 26348 34422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34425">
    <literal><![CDATA[
      R(x,y,((z * T(u,w)) \ ((u * w) * z)) \ v5) = R(x,y,R(w,u,z) \ (K(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(25976(a,1),26616(a,2,3))].">
      <j1 rule="para" parents="25976 26616"/>
    </justification>
  </clause>

  <clause id="34426">
    <literal><![CDATA[
      R(x,((y * T(z,u)) \ ((z * u) * y)) * w,v5) = R(x,R(u,z,y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26439,a(flip),b,26617,a),flip(a)].">
      <j1 rule="hyper" parents="373 26439 26617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34428">
    <literal><![CDATA[
      R(x,((y * z) \ ((z * u) * y)) * w,v5) = R(x,R(u,z,y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26437,a(flip),b,34426,a)].">
      <j1 rule="hyper" parents="64 26437 34426"/>
    </justification>
  </clause>

  <clause id="34430">
    <literal><![CDATA[
      ((x / y) \ 1) * ((y / x) * z) = (y / x) * (((x / y) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(26623(a,1),26624(a,1,2,1))].">
      <j1 rule="para" parents="26623 26624"/>
    </justification>
  </clause>

  <clause id="34431">
    <literal><![CDATA[
      R(x,(y \ z) \ u,z \ (y * u)) = R(x,z \ (y * u),(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(630(a,1),26648(a,1,3))].">
      <j1 rule="para" parents="630 26648"/>
    </justification>
  </clause>

  <clause id="34432">
    <literal><![CDATA[
      R(x,(y \ z) \ (T(T(y,u),u) \ w),y * (T(T(y,u),u) \ (z \ w))) = R(x,z \ (y * (T(T(y,u),u) \ w)),(y \ z) \ (T(T(y,u),u) \ w))
    ]]></literal>
    <justification jstring="[para(22835(a,1),34431(a,1,3))].">
      <j1 rule="para" parents="22835 34431"/>
    </justification>
  </clause>

  <clause id="34433">
    <literal><![CDATA[
      L(x,x,T(x,y) * ((x * y) \ z)) = (L(x \ 1,x,y \ (x \ z)) * x) * x
    ]]></literal>
    <justification jstring="[para(33787(a,1),26671(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="33787 26671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34434">
    <literal><![CDATA[
      L(x,x,T(x,y) * ((x * y) \ z)) = x * (L(x \ 1,x,y \ (x \ z)) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,4931,a(flip),b,34433,a),flip(a)].">
      <j1 rule="hyper" parents="373 4931 34433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34435">
    <literal><![CDATA[
      L(x,x,T(x,y) * ((x * y) \ z)) = L(x,x,x * (y \ (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,26664,a(flip),b,34434,a),flip(a)].">
      <j1 rule="hyper" parents="373 26664 34434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34436">
    <literal><![CDATA[
      L(x,x,x * ((y * x) \ z)) = L(x,x,x * (y \ (x \ z)))
    ]]></literal>
    <justification jstring="[para(10844(a,1),34435(a,1,3))].">
      <j1 rule="para" parents="10844 34435"/>
    </justification>
  </clause>

  <clause id="34437">
    <literal><![CDATA[
      L(x,x,x * R(x \ y,x,z)) = L(x,x,x * (z \ (x \ (y * z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,33589,a,b,34436,a)].">
      <j1 rule="hyper" parents="64 33589 34436"/>
    </justification>
  </clause>

  <clause id="34438">
    <literal><![CDATA[
      L(x,x,x * L(x \ y,x,z)) = L(x,x,x * (z \ (x \ (y * z))))
    ]]></literal>
    <justification jstring="[hyper(33586,a,34437,a)].">
      <j1 rule="hyper" parents="33586 34437"/>
    </justification>
  </clause>

  <clause id="34439">
    <literal><![CDATA[
      K(x,y) * T((y * R(x,z,u)) / (y * x),w) = (R(x,z,u) * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(23385(a,1),26759(a,1,1))].">
      <j1 rule="para" parents="23385 26759"/>
    </justification>
  </clause>

  <clause id="34441">
    <literal><![CDATA[
      ((R(x,y,y \ 1) / (y * x)) * y) * x = a(T(y,x),y,x) * R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2653(a,1),26892(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2653 26892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34442">
    <literal><![CDATA[
      ((R(x,y,y \ 1) / (y * x)) * y) * x = a(y,y,x) * R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(26779(a,1),34441(a,2,1))].">
      <j1 rule="para" parents="26779 34441"/>
    </justification>
  </clause>

  <clause id="34443">
    <literal><![CDATA[
      a(x,x,y) * R(y,x,x \ 1) = ((T(y,x) / (y / (x \ 1))) * x) * y
    ]]></literal>
    <justification jstring="[para(22843(a,1),34442(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="22843 34442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34445">
    <literal><![CDATA[
      a(x,x,y) * R(y,x,x \ 1) = (K(y,x) * K(x \ y,x \ 1)) * y
    ]]></literal>
    <justification jstring="[para(24910(a,1),34443(a,2,1))].">
      <j1 rule="para" parents="24910 34443"/>
    </justification>
  </clause>

  <clause id="34446">
    <literal><![CDATA[
      K(x,y) * (K(y \ x,y \ 1) * x) = a(y,y,x) * R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,23256,a(flip),b,34445,a)].">
      <j1 rule="hyper" parents="373 23256 34445"/>
    </justification>
  </clause>

  <clause id="34447">
    <literal><![CDATA[
      K(x,y) * (x * K(x / y,y \ 1)) = a(y,y,x) * R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(8196(a,1),34446(a,1,2))].">
      <j1 rule="para" parents="8196 34446"/>
    </justification>
  </clause>

  <clause id="34448">
    <literal><![CDATA[
      K(x,y) * (x * K(y \ x,1 / y)) = a(y,y,x) * R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(7981(a,1),34447(a,1,2,2))].">
      <j1 rule="para" parents="7981 34447"/>
    </justification>
  </clause>

  <clause id="34449">
    <literal><![CDATA[
      K(x,y) * (x * K(y \ x,y \ 1)) = a(y,y,x) * R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(6041(a,1),34448(a,1,2,2))].">
      <j1 rule="para" parents="6041 34448"/>
    </justification>
  </clause>

  <clause id="34450">
    <literal><![CDATA[
      T(x,y) * K(y \ x,y \ 1) = a(y,y,x) * R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5985,a,34449,a)].">
      <j1 rule="hyper" parents="5985 34449"/>
    </justification>
  </clause>

  <clause id="34451">
    <literal><![CDATA[
      T(x * K(y \ x,y \ 1),y) = a(y,y,x) * R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,24750,a,b,34450,a)].">
      <j1 rule="hyper" parents="64 24750 34450"/>
    </justification>
  </clause>

  <clause id="34452">
    <literal><![CDATA[
      (L(x,y,z) \ u) \ (w * (u / L(x,y,z))) = K(x,x \ u) * T(w,u / x)
    ]]></literal>
    <justification jstring="[para(28333(a,1),26978(a,2,2))].">
      <j1 rule="para" parents="28333 26978"/>
    </justification>
  </clause>

  <clause id="34453">
    <literal><![CDATA[
      (L(x,y,z) \ u) * ((x \ u) \ (w * (u / x))) = w * (u / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,6590,a(flip),b,34452,a)].">
      <j1 rule="hyper" parents="145 6590 34452"/>
    </justification>
  </clause>

  <clause id="34455">
    <literal><![CDATA[
      R(x,L(K(y * z,u) * z,y,u) * w,v5) = R(x,R(z,y,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,34428,a(flip),b,27100,a),flip(a)].">
      <j1 rule="hyper" parents="373 34428 27100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34456">
    <literal><![CDATA[
      R(x,L(y * K(y * z,u),z,u) * w,v5) = R(x,R(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(11186(a,1),34455(a,1,2,1,1))].">
      <j1 rule="para" parents="11186 34455"/>
    </justification>
  </clause>

  <clause id="34457">
    <literal><![CDATA[
      R(x,L(y,z,u) * (K(y * z,u) * w),v5) = R(x,R(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(26075(a,1),34456(a,1,2))].">
      <j1 rule="para" parents="26075 34456"/>
    </justification>
  </clause>

  <clause id="34458">
    <literal><![CDATA[
      R(x,R(y,z,u) * w,v5) = R(x,L(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26424,a(flip),b,34457,a),flip(a)].">
      <j1 rule="hyper" parents="64 26424 34457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34460">
    <literal><![CDATA[
      R(x,L(y,z,u) * w,v5) = R(x,w * R(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26409,a,b,34458,a),flip(a)].">
      <j1 rule="hyper" parents="64 26409 34458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34461">
    <literal><![CDATA[
      R(x,L(y,z,u) * L(w,w,L(y,z,u)),v5) = R(x,w \ R(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29222,a(flip),b,34458,a),flip(a)].">
      <j1 rule="hyper" parents="64 29222 34458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34464">
    <literal><![CDATA[
      R(x,y / R(T(R(z,u,w),y),R(z,u,w),R(z,u,w)),v5) = R(x,L(z,u,w) * (R(z,u,w) \ (y / R(z,u,w))),v5)
    ]]></literal>
    <justification jstring="[para(8877(a,2),34460(a,2,2)),flip(a)].">
      <j1 rule="para" parents="8877 34460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34465">
    <literal><![CDATA[
      R(x,y \ R(z,u,w),v5) = R(x,y \ L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26705,a(flip),b,34461,a),flip(a)].">
      <j1 rule="hyper" parents="64 26705 34461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34466">
    <literal><![CDATA[
      a(x,y,(z \ ((u * (z \ 1)) \ w)) * (z \ 1)) = a(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31307,a(flip),b,27372,a),flip(a)].">
      <j1 rule="hyper" parents="373 31307 27372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34467">
    <literal><![CDATA[
      a(x,y,(z * z) \ ((u * (z \ 1)) \ w)) = a(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27566,a(flip),b,34466,a)].">
      <j1 rule="hyper" parents="64 27566 34466"/>
    </justification>
  </clause>

  <clause id="34468">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) \ ((u * u) \ w)) = a(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27445,a(flip),b,34467,a)].">
      <j1 rule="hyper" parents="64 27445 34467"/>
    </justification>
  </clause>

  <clause id="34469">
    <literal><![CDATA[
      a(x,y,R(z,u,u) \ (((u \ 1) * (u \ 1)) \ w)) = a(x,y,((u \ 1) * (z * (u \ 1))) \ w)
    ]]></literal>
    <justification jstring="[para(3757(a,1),34468(a,1,3,1))].">
      <j1 rule="para" parents="3757 34468"/>
    </justification>
  </clause>

  <clause id="34470">
    <literal><![CDATA[
      a(x,y * R(z,u,u \ a(w,v5,w)),v6) = a(x,(u * (z * u)) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32182,a(flip),b,27799,a),flip(a)].">
      <j1 rule="hyper" parents="64 32182 27799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34472">
    <literal><![CDATA[
      a(x,y * R(z,u,u \ a(w,v5,w)),v6) = a(x,L(z,u,u) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32282,a(flip),b,34470,a),flip(a)].">
      <j1 rule="hyper" parents="373 32282 34470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34473">
    <literal><![CDATA[
      a(x,y * R(z,u,u \ 1),w) = a(x,L(z,u,u) * y,w)
    ]]></literal>
    <justification jstring="[para(427(a,1),34472(a,1,2,2,3,2))].">
      <j1 rule="para" parents="427 34472"/>
    </justification>
  </clause>

  <clause id="34474">
    <literal><![CDATA[
      a(x,a(y,z,z \ 1),u) = a(x,L(y,z,z) * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11997,a(flip),b,34473,a)].">
      <j1 rule="hyper" parents="64 11997 34473"/>
    </justification>
  </clause>

  <clause id="34475">
    <literal><![CDATA[
      a(x,a(y,z,z \ 1),u) = a(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32035,a(flip),b,34474,a),flip(a)].">
      <j1 rule="hyper" parents="373 32035 34474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34476">
    <literal><![CDATA[
      a(x,a(y,z,z \ 1),u) = a(x,a(z,z,z \ y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,31957,a,b,34475,a),flip(a)].">
      <j1 rule="hyper" parents="373 31957 34475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34477">
    <literal><![CDATA[
      a(x,L(((y * z) \ y) * z,u,w),v5) = a(x,a(z,z,L(y,u,w)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,33838,a,b,34475,a)].">
      <j1 rule="hyper" parents="64 33838 34475"/>
    </justification>
  </clause>

  <clause id="34478">
    <literal><![CDATA[
      a(x,a(y \ z,y,y \ 1),u) = a(x,a(z,y,y \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,34475,a,b,34476,a)].">
      <j1 rule="hyper" parents="373 34475 34476"/>
    </justification>
  </clause>

  <clause id="34479">
    <literal><![CDATA[
      a(x,a(y,y,L(z,u,w)),v5) = a(x,L(a(y,y,z),u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32347,a(flip),b,34477,a),flip(a)].">
      <j1 rule="hyper" parents="64 32347 34477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34480">
    <literal><![CDATA[
      R(x,a(y,z,(u * u) * w),v5) = R(x,((z * w) * y) \ ((y * z) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,33912,a(flip),b,27908,a),flip(a)].">
      <j1 rule="hyper" parents="64 33912 27908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34482">
    <literal><![CDATA[
      R(x,a(y,z,(u * u) * w),v5) = R(x,a(y,z,w) * K(y,z * w),v5)
    ]]></literal>
    <justification jstring="[para(23926(a,1),34480(a,2,2))].">
      <j1 rule="para" parents="23926 34480"/>
    </justification>
  </clause>

  <clause id="34483">
    <literal><![CDATA[
      R(x,a(y,z,(u * u) * w),v5) = R(x,a(y,z,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26421,a(flip),b,34482,a),flip(a)].">
      <j1 rule="hyper" parents="373 26421 34482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34485">
    <literal><![CDATA[
      L(x,a(y,z,(u * u) * w),v5) = R(x,a(y,z,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31802,a(flip),b,34483,a)].">
      <j1 rule="hyper" parents="64 31802 34483"/>
    </justification>
  </clause>

  <clause id="34486">
    <literal><![CDATA[
      L(x,a(y,z,(u * u) * w),v5) = L(x,a(y,z,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31802,a(flip),b,34485,a),flip(a)].">
      <j1 rule="hyper" parents="373 31802 34485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34487">
    <literal><![CDATA[
      L(x,a(y,z,u * (w * w)),v5) = L(x,a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,33920,a,b,34486,a)].">
      <j1 rule="hyper" parents="64 33920 34486"/>
    </justification>
  </clause>

  <clause id="34488">
    <literal><![CDATA[
      L(x,a(y * z,u,(w * w) * v5),v6) = L(x,a(z * y,u,v5),v6)
    ]]></literal>
    <justification jstring="[para(26787(a,1),34486(a,1,2))].">
      <j1 rule="para" parents="26787 34486"/>
    </justification>
  </clause>

  <clause id="34489">
    <literal><![CDATA[
      L(x,a(y,z,(u \ 1) \ w),v5) = L(x,a(y,z,u \ w),v5)
    ]]></literal>
    <justification jstring="[para(27635(a,1),34486(a,1,2))].">
      <j1 rule="para" parents="27635 34486"/>
    </justification>
  </clause>

  <clause id="34490">
    <literal><![CDATA[
      L(x,a(y,z,(u * (w \ 1)) * v5),v6) = L(x,a(y,z,v5 * (w * u)),v6)
    ]]></literal>
    <justification jstring="[para(31311(a,1),34486(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31311 34486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34491">
    <literal><![CDATA[
      L(x,a(y,z,u \ 1),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(5340(a,1),34489(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5340 34489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34492">
    <literal><![CDATA[
      L(x,a(y,z,u \ (w \ u)),v5) = L(x,a(y,z,w * a(u,w,w)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,33922,a(flip),b,34491,a),flip(a)].">
      <j1 rule="hyper" parents="64 33922 34491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34493">
    <literal><![CDATA[
      L(x,a(y * z,u,w),v5) = L(x,a(z * y,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34486,a(flip),b,34488,a)].">
      <j1 rule="hyper" parents="64 34486 34488"/>
    </justification>
  </clause>

  <clause id="34494">
    <literal><![CDATA[
      L(x \ R(x,y,z),x \ u,x \ u) = (u * (x \ u)) \ R(u * (x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31776,a(flip),b,28063,a),flip(a)].">
      <j1 rule="hyper" parents="373 31776 28063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34495">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),u,a(w,v5,v6)) = L(x \ L(x,u,a(w,v5,v6)),y,z)
    ]]></literal>
    <justification jstring="[para(28848(a,1),28849(a,2,1))].">
      <j1 rule="para" parents="28848 28849"/>
    </justification>
  </clause>

  <clause id="34496">
    <literal><![CDATA[
      x / L(y,y \ (z \ u),(z \ u) \ x) = ((u / z) \ x) * ((((u / z) \ x) \ x) / y)
    ]]></literal>
    <justification jstring="[para(29552(a,1),29083(a,1,2))].">
      <j1 rule="para" parents="29552 29083"/>
    </justification>
  </clause>

  <clause id="34497">
    <literal><![CDATA[
      K(x,x * x) \ ((x * T(T(x,y),z)) * u) = (((1 / x) \ T(T(x,y),z)) \ 1) \ u
    ]]></literal>
    <justification jstring="[para(33103(a,1),29342(a,2,1,1))].">
      <j1 rule="para" parents="33103 29342"/>
    </justification>
  </clause>

  <clause id="34498">
    <literal><![CDATA[
      K(x,x * x) \ ((x * T(T(x,y),z)) * u) = (x \ (1 / T(T(x,z),y))) \ u
    ]]></literal>
    <justification jstring="[para(33904(a,1),34497(a,2,1))].">
      <j1 rule="para" parents="33904 34497"/>
    </justification>
  </clause>

  <clause id="34499">
    <literal><![CDATA[
      K(x,x * x) \ ((x * T(T(x,y),z)) * u) = (1 / x) \ (T(T(x,z),y) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,27234,a(flip),b,34498,a),flip(a)].">
      <j1 rule="hyper" parents="373 27234 34498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34500">
    <literal><![CDATA[
      K(x * x,x) * ((x * T(T(x,y),z)) * u) = (1 / x) \ (T(T(x,z),y) * u)
    ]]></literal>
    <justification jstring="[hyper(6198,a,34499,a)].">
      <j1 rule="hyper" parents="6198 34499"/>
    </justification>
  </clause>

  <clause id="34501">
    <literal><![CDATA[
      a(x,x,x) * ((x * T(T(x,y),z)) * u) = (1 / x) \ (T(T(x,z),y) * u)
    ]]></literal>
    <justification jstring="[para(98(a,1),34500(a,1,1))].">
      <j1 rule="para" parents="98 34500"/>
    </justification>
  </clause>

  <clause id="34502">
    <literal><![CDATA[
      (R(x,x,x) * T(T(x,y),z)) * u = (1 / x) \ (T(T(x,z),y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12909,a(flip),b,34501,a)].">
      <j1 rule="hyper" parents="64 12909 34501"/>
    </justification>
  </clause>

  <clause id="34503">
    <literal><![CDATA[
      (1 / x) \ (T(T(x,y),z) * u) = ((1 / x) \ T(T(x,z),y)) * u
    ]]></literal>
    <justification jstring="[para(33103(a,1),34502(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33103 34502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34504">
    <literal><![CDATA[
      L(x,y,(((1 / (z / u)) * z) \ u) * w) = L(x,y,w * a(z,u \ z,u))
    ]]></literal>
    <justification jstring="[para(26836(a,1),29387(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="26836 29387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34505">
    <literal><![CDATA[
      L(x,y,(((z / u) * z) \ u) * w) = L(x,y,w * a(z,u \ z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29259,a(flip),b,34504,a)].">
      <j1 rule="hyper" parents="64 29259 34504"/>
    </justification>
  </clause>

  <clause id="34507">
    <literal><![CDATA[
      L(x,y,z * a(u \ w,u \ w,u)) = L(x,y,z * a(w,u \ w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29371,a,b,34505,a)].">
      <j1 rule="hyper" parents="64 29371 34505"/>
    </justification>
  </clause>

  <clause id="34508">
    <literal><![CDATA[
      L(x,y,z * ((u / w) * (w / u))) = L(x,y,z * a(w,u \ w,u))
    ]]></literal>
    <justification jstring="[para(30069(a,1),34507(a,1,3,2))].">
      <j1 rule="para" parents="30069 34507"/>
    </justification>
  </clause>

  <clause id="34509">
    <literal><![CDATA[
      L(x,y,z * ((u / w) * (u \ w))) = L(x,y,z * a(w,u \ w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29122,a(flip),b,34508,a)].">
      <j1 rule="hyper" parents="64 29122 34508"/>
    </justification>
  </clause>

  <clause id="34510">
    <literal><![CDATA[
      L(x,y,z * ((u \ w) * (w \ u))) = L(x,y,z * a(u,w \ u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,29089,a(flip),b,34509,a)].">
      <j1 rule="hyper" parents="64 29089 34509"/>
    </justification>
  </clause>

  <clause id="34511">
    <literal><![CDATA[
      L(x,y,R(z,z \ u,u \ z)) = L(x,y,z * a(z,u \ z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,2247,a(flip),b,34510,a)].">
      <j1 rule="hyper" parents="64 2247 34510"/>
    </justification>
  </clause>

  <clause id="34512">
    <literal><![CDATA[
      L(x,y,R(z,z \ u,u \ z)) = L(x,y,R(z,u \ z,u))
    ]]></literal>
    <justification jstring="[para(24668(a,1),34511(a,2,3))].">
      <j1 rule="para" parents="24668 34511"/>
    </justification>
  </clause>

  <clause id="34513">
    <literal><![CDATA[
      L(x,y,R(z,u \ z,u)) = L(x,y,u * ((z \ u) \ 1))
    ]]></literal>
    <justification jstring="[para(30789(a,1),34512(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30789 34512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34514">
    <literal><![CDATA[
      L(x,y,R(z,u \ z,u)) = L(x,y,(z \ u) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23997,a(flip),b,34513,a),flip(a)].">
      <j1 rule="hyper" parents="373 23997 34513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34515">
    <literal><![CDATA[
      L(x,y,L(z,u \ z,u)) = L(x,y,(z \ u) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29203,a(flip),b,34514,a)].">
      <j1 rule="hyper" parents="64 29203 34514"/>
    </justification>
  </clause>

  <clause id="34516">
    <literal><![CDATA[
      L(x,R(((1 / y) * z) * y,u,w) * y,v5) = L(x,L(y * R(z,u,w),y,y),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29873,a(flip),b,29650,a),flip(a)].">
      <j1 rule="hyper" parents="373 29873 29650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34517">
    <literal><![CDATA[
      L(x,R(((1 / y) * z) * y,u,w) * y,v5) = L(x,y \ R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31759,a(flip),b,34516,a),flip(a)].">
      <j1 rule="hyper" parents="373 31759 34516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34518">
    <literal><![CDATA[
      L(x,L(((1 / y) * z) * y,u,w) * y,v5) = L(x,L(y * L(z,u,w),y,y),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29873,a(flip),b,29651,a),flip(a)].">
      <j1 rule="hyper" parents="373 29873 29651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34519">
    <literal><![CDATA[
      L(x,L(((1 / y) * z) * y,u,w) * y,v5) = L(x,y \ L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31759,a(flip),b,34518,a),flip(a)].">
      <j1 rule="hyper" parents="373 31759 34518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34520">
    <literal><![CDATA[
      L(L(x \ 1,y,z) \ u,L(x,y,z),L(x,y,z)) = (1 / L(x \ 1,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(34230,a,29881,a)].">
      <j1 rule="hyper" parents="34230 29881"/>
    </justification>
  </clause>

  <clause id="34521">
    <literal><![CDATA[
      L(L(x \ 1,y,z) \ u,L(x,y,z),L(x,y,z)) = (L(1 / x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(10467(a,1),34520(a,2,1))].">
      <j1 rule="para" parents="10467 34520"/>
    </justification>
  </clause>

  <clause id="34522">
    <literal><![CDATA[
      (a(x,x,L(R(x,y,z),u,w)) / x) \ R(R(x,y,z),u,w) = R(R(x,y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(27644(a,1),30133(a,1,1,1))].">
      <j1 rule="para" parents="27644 30133"/>
    </justification>
  </clause>

  <clause id="34523">
    <literal><![CDATA[
      L(a(x,x,y),z,u) \ K(y / (x * y),x) = L(a(x,x,x * y),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(30057(a,1),30151(a,1,1,1))].">
      <j1 rule="para" parents="30057 30151"/>
    </justification>
  </clause>

  <clause id="34524">
    <literal><![CDATA[
      L(a(x,x,y),z,u) \ K(x \ 1,x) = L(a(x,x,x * y),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(3393(a,1),34523(a,1,2))].">
      <j1 rule="para" parents="3393 34523"/>
    </justification>
  </clause>

  <clause id="34526">
    <literal><![CDATA[
      (a(x,x,L(y,y,x)) \ 1) * (x \ L(y,y,x \ 1)) = ((x \ 1) * (y * y)) / y
    ]]></literal>
    <justification jstring="[para(1631(a,1),30426(a,1,1,1,3))].">
      <j1 rule="para" parents="1631 30426"/>
    </justification>
  </clause>

  <clause id="34527">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * (x \ L(y,y,x \ 1)) = ((x \ 1) * (y * y)) / y
    ]]></literal>
    <justification jstring="[para(32754(a,1),34526(a,1,1,1))].">
      <j1 rule="para" parents="32754 34526"/>
    </justification>
  </clause>

  <clause id="34528">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * (x \ L(y,y,x)) = ((x \ 1) * (y * y)) / y
    ]]></literal>
    <justification jstring="[para(1631(a,1),34527(a,1,2,2))].">
      <j1 rule="para" parents="1631 34527"/>
    </justification>
  </clause>

  <clause id="34529">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * (x \ L(y,y,x)) = (R(x,y,y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,30596,a(flip),b,34528,a),flip(a)].">
      <j1 rule="hyper" parents="373 30596 34528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34530">
    <literal><![CDATA[
      a(L(x,y,y),L(x,y,y),y) \ 1 = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,33847,a,b,34529,a)].">
      <j1 rule="hyper" parents="36 33847 34529"/>
    </justification>
  </clause>

  <clause id="34531">
    <literal><![CDATA[
      a(L(x,y,y),L(x,y,y),y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,34530,a),flip(a)].">
      <j1 rule="hyper" parents="325 34530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34532">
    <literal><![CDATA[
      a(L(x,y,y),L(x,y,y),y) = L(y,x,x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,1243,a,b,34531,a),flip(a)].">
      <j1 rule="hyper" parents="373 1243 34531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34534">
    <literal><![CDATA[
      a(L(x \ T(y,x),x,x),(x * x) \ (y * x),x) = a(x \ T(y,x),x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(521(a,1),34531(a,1,2))].">
      <j1 rule="para" parents="521 34531"/>
    </justification>
  </clause>

  <clause id="34535">
    <literal><![CDATA[
      L(x,L(y,x,x),L(y,x,x)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,1243,a,b,34532,a(flip))].">
      <j1 rule="hyper" parents="40 1243 34532"/>
    </justification>
  </clause>

  <clause id="34536">
    <literal><![CDATA[
      L(x,L(y * x,x,x),x \ y) = L(x,y * x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30388,a(flip),b,34535,a)].">
      <j1 rule="hyper" parents="64 30388 34535"/>
    </justification>
  </clause>

  <clause id="34537">
    <literal><![CDATA[
      L(x,y,R(z * (u \ z),u,z)) = L(x,y,L(u,L(z,u,u),L(z,u,u)))
    ]]></literal>
    <justification jstring="[para(34535(a,2),34285(a,2,3))].">
      <j1 rule="para" parents="34535 34285"/>
    </justification>
  </clause>

  <clause id="34538">
    <literal><![CDATA[
      L(x,x \ y,x \ y) = L(x,y * x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,31760,a(flip),b,34536,a)].">
      <j1 rule="hyper" parents="64 31760 34536"/>
    </justification>
  </clause>

  <clause id="34539">
    <literal><![CDATA[
      L(x,y * x,y * x) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,10627,a(flip),b,34538,a),flip(a)].">
      <j1 rule="hyper" parents="64 10627 34538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34540">
    <literal><![CDATA[
      L(x,x * y,x * y) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,29507,a,b,34539,a)].">
      <j1 rule="hyper" parents="64 29507 34539"/>
    </justification>
  </clause>

  <clause id="34541">
    <literal><![CDATA[
      L(x,y,L(z,L(u,z,z),L(u,z,z))) = L(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,34285,a(flip),b,34537,a),flip(a)].">
      <j1 rule="hyper" parents="64 34285 34537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34542">
    <literal><![CDATA[
      T((1 / x) / (y / x),(1 / x) \ (y / x)) = T((1 / x) / (y / x),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,28638,a(flip),b,30577,a),flip(a)].">
      <j1 rule="hyper" parents="64 28638 30577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34544">
    <literal><![CDATA[
      T((1 / x) / (y / x),x * (y / x)) = T((1 / x) / (y / x),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14478,a(flip),b,34542,a)].">
      <j1 rule="hyper" parents="64 14478 34542"/>
    </justification>
  </clause>

  <clause id="34545">
    <literal><![CDATA[
      T((1 / x) / (y / x),T(y,x)) = T((1 / x) / (y / x),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11107,a(flip),b,34544,a)].">
      <j1 rule="hyper" parents="64 11107 34544"/>
    </justification>
  </clause>

  <clause id="34546">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (z * ((a(w,v5,w) / z) \ v6))) = a(x,y,(z * R(z,z,u)) * v6)
    ]]></literal>
    <justification jstring="[para(12932(a,1),30733(a,1,3,2))].">
      <j1 rule="para" parents="12932 30733"/>
    </justification>
  </clause>

  <clause id="34547">
    <literal><![CDATA[
      L(L(x,a(y,z,u),y),y * a(y,z,u),y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),30825(a,2,1))].">
      <j1 rule="para" parents="9 30825"/>
    </justification>
  </clause>

  <clause id="34548">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),y * a(y,z,u),y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(30415(a,1),34547(a,1,1))].">
      <j1 rule="para" parents="30415 34547"/>
    </justification>
  </clause>

  <clause id="34549">
    <literal><![CDATA[
      L(L(x,y,a(y,y,z)),R(y,y,z),y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(30054(a,1),34548(a,1,2))].">
      <j1 rule="para" parents="30054 34548"/>
    </justification>
  </clause>

  <clause id="34550">
    <literal><![CDATA[
      L(L(x,y,a(y,y,z)),y,L(y,y,z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29211,a(flip),b,34549,a)].">
      <j1 rule="hyper" parents="64 29211 34549"/>
    </justification>
  </clause>

  <clause id="34551">
    <literal><![CDATA[
      L(T(x \ (x / y),y * y),y,y) = ((((x * y) \ z) \ z) * y) \ T(x * y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(7291(a,2),31135(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7291 31135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34552">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) \ 1) * v5) = a(x,y,(L(z,u,w) \ 1) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,13877,a(flip),b,31338,a),flip(a)].">
      <j1 rule="hyper" parents="64 13877 31338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34553">
    <literal><![CDATA[
      L(x,y,y) \ (z * ((1 / y) \ L(x,y,y))) = R(T(z / (1 / y),x),y,y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2968,a(flip),b,31456,a),flip(a)].">
      <j1 rule="hyper" parents="373 2968 31456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34554">
    <literal><![CDATA[
      R(T(x / (1 / y),z),y,y * z) = L(z,y,y) \ (x * (y * z))
    ]]></literal>
    <justification jstring="[para(561(a,1),34553(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="561 34553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34555">
    <literal><![CDATA[
      R(T(x / (1 / y),a(z,u,y)),y,y * a(z,u,y)) = a(z,u,y) \ (x * (y * a(z,u,y)))
    ]]></literal>
    <justification jstring="[para(9435(a,1),34554(a,2,1))].">
      <j1 rule="para" parents="9435 34554"/>
    </justification>
  </clause>

  <clause id="34556">
    <literal><![CDATA[
      a(x,y,L(T(z * z,u) * w,u,v5)) = a(x,y,L(w,u,v5) * (z * z))
    ]]></literal>
    <justification jstring="[para(18(a,2),31721(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="18 31721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34557">
    <literal><![CDATA[
      a(x,y,L((z * z) * u,w,v5)) = a(x,y,L(u,w,v5) * (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27426,a(flip),b,34556,a)].">
      <j1 rule="hyper" parents="64 27426 34556"/>
    </justification>
  </clause>

  <clause id="34558">
    <literal><![CDATA[
      a(x,y,L((z * z) * L(u,z,z),w,v5)) = a(x,y,z * (z * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27371,a(flip),b,34557,a),flip(a)].">
      <j1 rule="hyper" parents="373 27371 34557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34560">
    <literal><![CDATA[
      a(x,y,L(z * (z * u),w,v5)) = a(x,y,z * (z * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(100(a,1),34558(a,1,3,1))].">
      <j1 rule="para" parents="100 34558"/>
    </justification>
  </clause>

  <clause id="34561">
    <literal><![CDATA[
      a(x,y,L(z * (z * u),w,v5)) = a(x,y,z * (L(u,w,v5) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27315,a,b,34560,a),flip(a)].">
      <j1 rule="hyper" parents="373 27315 34560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34562">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),a(u,w,v5),v6) = L(x \ L(x,a(u,w,v5),v6),y,z)
    ]]></literal>
    <justification jstring="[para(31832(a,1),31833(a,2,1))].">
      <j1 rule="para" parents="31832 31833"/>
    </justification>
  </clause>

  <clause id="34563">
    <literal><![CDATA[
      a(((x * T(y,z)) \ ((y * z) * x)) * u,w,v5) = a(K(y,x) * (R(z,y,x) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(25968(a,1),32435(a,2,1))].">
      <j1 rule="para" parents="25968 32435"/>
    </justification>
  </clause>

  <clause id="34564">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x * u) = x * ((R(x,y,z) \ x) * u)
    ]]></literal>
    <justification jstring="[para(28224(a,1),32475(a,1,2))].">
      <j1 rule="para" parents="28224 32475"/>
    </justification>
  </clause>

  <clause id="34565">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ (x * u) = x * ((R(x,y,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,34564,a)].">
      <j1 rule="hyper" parents="139 168 34564"/>
    </justification>
  </clause>

  <clause id="34567">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ (x * u) = x * (u / (R(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(25925(a,2),34565(a,2,2))].">
      <j1 rule="para" parents="25925 34565"/>
    </justification>
  </clause>

  <clause id="34568">
    <literal><![CDATA[
      (x * y) / (R(x,z,u) \ x) = x * (y / (R(x,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,25925,a,b,34567,a)].">
      <j1 rule="hyper" parents="64 25925 34567"/>
    </justification>
  </clause>

  <clause id="34569">
    <literal><![CDATA[
      x * (T(y,x) / (R(x,z,u) \ x)) = (y * x) / (R(x,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,250,a(flip),b,34568,a),flip(a)].">
      <j1 rule="hyper" parents="64 250 34568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34570">
    <literal><![CDATA[
      L(R(x,y,z) \ x,u,x) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(37,a,29785,a,b,34569,a(flip))].">
      <j1 rule="hyper" parents="37 29785 34569"/>
    </justification>
  </clause>

  <clause id="34571">
    <literal><![CDATA[
      L(R(x,y,z) \ x,x,L(x,u,w)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,29882,a(flip),b,34570,a)].">
      <j1 rule="hyper" parents="64 29882 34570"/>
    </justification>
  </clause>

  <clause id="34572">
    <literal><![CDATA[
      x * ((R(x,y,z) \ 1) * (R(x,u,w) \ x)) = (R(x,y,z) \ x) * (R(x,u,w) \ x)
    ]]></literal>
    <justification jstring="[para(34571(a,1),29220(a,1,2)),flip(a)].">
      <j1 rule="para" parents="34571 29220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34573">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (R(x,y,z) \ x) = x * (R(x,y,z) \ (R(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(2837(a,1),34572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2837 34572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34574">
    <literal><![CDATA[
      a(a(x,y,(z * z) * u),w,v5) = a((y * u) \ (x \ ((x * y) * u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34182,a(flip),b,32710,a),flip(a)].">
      <j1 rule="hyper" parents="64 34182 32710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34576">
    <literal><![CDATA[
      a(a(x,y,(z * z) * u),w,v5) = a(a(x,y,u),w,v5)
    ]]></literal>
    <justification jstring="[para(30027(a,2),34574(a,2,1))].">
      <j1 rule="para" parents="30027 34574"/>
    </justification>
  </clause>

  <clause id="34577">
    <literal><![CDATA[
      a(a(x,y,(z * z) \ u),w,v5) = a(a(x,y,u),w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),34576(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="10 34576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34578">
    <literal><![CDATA[
      a(a(x,y,z * ((z * z) \ u)),w,v5) = a(a(x,y,z * u),w,v5)
    ]]></literal>
    <justification jstring="[para(1761(a,1),34576(a,1,1,3))].">
      <j1 rule="para" parents="1761 34576"/>
    </justification>
  </clause>

  <clause id="34579">
    <literal><![CDATA[
      a(a(x,y,z * (u * u)),w,v5) = a(a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(27298(a,1),34576(a,1,1))].">
      <j1 rule="para" parents="27298 34576"/>
    </justification>
  </clause>

  <clause id="34580">
    <literal><![CDATA[
      a(a(x,y,z * T(u * u,w)),v5,v6) = a(a(x,y,z),v5,v6)
    ]]></literal>
    <justification jstring="[para(27438(a,2),34576(a,1,1))].">
      <j1 rule="para" parents="27438 34576"/>
    </justification>
  </clause>

  <clause id="34581">
    <literal><![CDATA[
      a(a(x,y,(z \ 1) * u),w,v5) = a(a(x,y,z * u),w,v5)
    ]]></literal>
    <justification jstring="[para(27667(a,1),34578(a,1,1))].">
      <j1 rule="para" parents="27667 34578"/>
    </justification>
  </clause>

  <clause id="34582">
    <literal><![CDATA[
      a(a(x,y,z * T(u * u,w)),v5,v6) = a(a(x,y,z \ 1),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,34580,a(flip),b,34581,a),flip(a)].">
      <j1 rule="hyper" parents="64 34580 34581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34583">
    <literal><![CDATA[
      a(a(x,y,z * (u \ 1)),w,v5) = a(a(x,y,u * z),w,v5)
    ]]></literal>
    <justification jstring="[para(27298(a,1),34581(a,1,1))].">
      <j1 rule="para" parents="27298 34581"/>
    </justification>
  </clause>

  <clause id="34584">
    <literal><![CDATA[
      a(a(x,y,z \ 1),u,w) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,34580,a(flip),b,34582,a),flip(a)].">
      <j1 rule="hyper" parents="64 34580 34582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34585">
    <literal><![CDATA[
      a(a(x,y,(z * z) \ u),w,v5) = a(a(x,y,u \ (z * z)),w,v5)
    ]]></literal>
    <justification jstring="[para(550(a,1),34584(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="550 34584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34586">
    <literal><![CDATA[
      a(a(x,y,z \ (u * u)),w,v5) = a(a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34577,a(flip),b,34585,a),flip(a)].">
      <j1 rule="hyper" parents="64 34577 34585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34588">
    <literal><![CDATA[
      a(x,a(y,z,(u * u) * w),v5) = a(x,(z * w) \ (y \ ((y * z) * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34260,a(flip),b,32900,a),flip(a)].">
      <j1 rule="hyper" parents="64 34260 32900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34590">
    <literal><![CDATA[
      a(x,a(y,z,(u * u) * w),v5) = a(x,a(y,z,w),v5)
    ]]></literal>
    <justification jstring="[para(30027(a,2),34588(a,2,2))].">
      <j1 rule="para" parents="30027 34588"/>
    </justification>
  </clause>

  <clause id="34591">
    <literal><![CDATA[
      a(x,a(y,z,(u \ 1) \ w),v5) = a(x,a(y,z,u \ w),v5)
    ]]></literal>
    <justification jstring="[para(27635(a,1),34590(a,1,2))].">
      <j1 rule="para" parents="27635 34590"/>
    </justification>
  </clause>

  <clause id="34592">
    <literal><![CDATA[
      a(x,a(y,z,u \ 1),w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(5340(a,1),34591(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5340 34591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34593">
    <literal><![CDATA[
      L(R(1 / x,x,y),x * y,a(z,u,x)) = (y * a(z,u,x)) / (x * (y * a(z,u,x)))
    ]]></literal>
    <justification jstring="[hyper(28845,a,33244,a)].">
      <j1 rule="hyper" parents="28845 33244"/>
    </justification>
  </clause>

  <clause id="34594">
    <literal><![CDATA[
      K(x,y * z) * ((x * z) \ (z * (y * x))) = L(a(z,y,x) \ y,z,x)
    ]]></literal>
    <justification jstring="[para(28689(a,1),33324(a,1,1))].">
      <j1 rule="para" parents="28689 33324"/>
    </justification>
  </clause>

  <clause id="34596">
    <literal><![CDATA[
      R(1 / (x \ T(y,z)),x \ T(y,z),y) \ T(y,z) = T(y / (x / T(T(y,z),z)),x)
    ]]></literal>
    <justification jstring="[para(15057(a,1),34303(a,2,1))].">
      <j1 rule="para" parents="15057 34303"/>
    </justification>
  </clause>

  <clause id="34597">
    <literal><![CDATA[
      (L(a(x,y,z),u,u) \ u) * u = u / ((1 / u) * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,23605,a(flip),b,34311,a),flip(a)].">
      <j1 rule="hyper" parents="64 23605 34311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34599">
    <literal><![CDATA[
      x \ (x / ((1 / x) * a(y,z,u))) = L(a(y,z,u),x,x) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,34597,a(flip),b,28556,a(flip))].">
      <j1 rule="hyper" parents="139 34597 28556"/>
    </justification>
  </clause>

  <clause id="34600">
    <literal><![CDATA[
      (1 / x) \ (x \ (a(y,z,u) \ x)) = L(a(y,z,u),x,x) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,27836,a,b,34599,a)].">
      <j1 rule="hyper" parents="64 27836 34599"/>
    </justification>
  </clause>

  <clause id="34601">
    <literal><![CDATA[
      (1 / (x \ y)) * ((y \ x) * z) = (y \ x) * ((1 / (x \ y)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11796,a(flip),b,34393,a),flip(a)].">
      <j1 rule="hyper" parents="64 11796 34393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34602">
    <literal><![CDATA[
      K(x \ T(x \ 1,y),z) = K(z,x * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,31617,a(flip),b,34394,a),flip(a)].">
      <j1 rule="hyper" parents="36 31617 34394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34605">
    <literal><![CDATA[
      R((x / y) * K(z,K(u,w)),y,T(u,K(z,w))) = (x * u) / (y * (K(z,K(u,w)) * u))
    ]]></literal>
    <justification jstring="[para(20347(a,1),34409(a,1,1))].">
      <j1 rule="para" parents="20347 34409"/>
    </justification>
  </clause>

  <clause id="34606">
    <literal><![CDATA[
      R(x,y,((z * T(u,w)) \ ((u * w) * z)) \ v5) = R(x,y,R(w,u,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26189,a(flip),b,34425,a),flip(a)].">
      <j1 rule="hyper" parents="373 26189 34425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34608">
    <literal><![CDATA[
      R(x,y,((z * u) \ ((u * w) * z)) \ v5) = R(x,y,R(w,u,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26281,a(flip),b,34606,a)].">
      <j1 rule="hyper" parents="64 26281 34606"/>
    </justification>
  </clause>

  <clause id="34610">
    <literal><![CDATA[
      ((x / y) \ z) * ((((x / y) \ z) \ z) / u) = (z / (y \ x)) * ((y \ x) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,15122,a(flip),b,34496,a),flip(a)].">
      <j1 rule="hyper" parents="64 15122 34496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34611">
    <literal><![CDATA[
      (x / (y / z)) * ((y / z) / u) = (x / (z \ y)) * ((z \ y) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14901,a(flip),b,34610,a)].">
      <j1 rule="hyper" parents="64 14901 34610"/>
    </justification>
  </clause>

  <clause id="34612">
    <literal><![CDATA[
      (a(x,x,L(L(x,y,z),u,w)) / x) \ R(R(x,y,z),u,w) = R(R(x,y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(27703(a,1),34522(a,1,1,1))].">
      <j1 rule="para" parents="27703 34522"/>
    </justification>
  </clause>

  <clause id="34613">
    <literal><![CDATA[
      a((1 / x) * T(y,x),(x * x) \ (y * x),x) = a(x \ T(y,x),x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(569(a,1),34534(a,1,1))].">
      <j1 rule="para" parents="569 34534"/>
    </justification>
  </clause>

  <clause id="34614">
    <literal><![CDATA[
      a(x \ T(y,x),x \ T(y,x),x) = a((1 / x) * T(y,x),y * x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11965,a(flip),b,34613,a),flip(a)].">
      <j1 rule="hyper" parents="64 11965 34613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34616">
    <literal><![CDATA[
      a(x \ T(y,x),x \ T(y,x),x) = a((1 / x) * y,y * x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,32361,a(flip),b,34614,a),flip(a)].">
      <j1 rule="hyper" parents="373 32361 34614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34618">
    <literal><![CDATA[
      a(x \ T(y,x),x \ T(y,x),x) = a(x * y,y * x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2642,a(flip),b,34616,a),flip(a)].">
      <j1 rule="hyper" parents="373 2642 34616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34619">
    <literal><![CDATA[
      a(x \ T(y,x),x \ y,x) = a(x * y,y * x,x)
    ]]></literal>
    <justification jstring="[hyper(32041,a,34618,a)].">
      <j1 rule="hyper" parents="32041 34618"/>
    </justification>
  </clause>

  <clause id="34621">
    <literal><![CDATA[
      a(x \ y,x \ y,x) = a(x * y,y * x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32360,a(flip),b,34619,a)].">
      <j1 rule="hyper" parents="64 32360 34619"/>
    </justification>
  </clause>

  <clause id="34623">
    <literal><![CDATA[
      a(x * y,y * x,x) = (x / y) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30069,a(flip),b,34621,a),flip(a)].">
      <j1 rule="hyper" parents="64 30069 34621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34624">
    <literal><![CDATA[
      a(x * y,x * y,x) = (x / y) * (y / x)
    ]]></literal>
    <justification jstring="[hyper(32008,a,34623,a)].">
      <j1 rule="hyper" parents="32008 34623"/>
    </justification>
  </clause>

  <clause id="34625">
    <literal><![CDATA[
      a(x * y,x * y,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(26847,a,34623,a)].">
      <j1 rule="hyper" parents="26847 34623"/>
    </justification>
  </clause>

  <clause id="34626">
    <literal><![CDATA[
      (x * y) \ ((1 / (x * y)) \ x) = ((x / y) * (y / x)) * x
    ]]></literal>
    <justification jstring="[para(34624(a,1),30228(a,2,1))].">
      <j1 rule="para" parents="34624 30228"/>
    </justification>
  </clause>

  <clause id="34627">
    <literal><![CDATA[
      (x * y) \ ((1 / (x * y)) \ x) = ((x / y) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,30381,a(flip),b,34626,a),flip(a)].">
      <j1 rule="hyper" parents="373 30381 34626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34628">
    <literal><![CDATA[
      a(x,y,z * (a(z,z,u) * ((a(w,v5,w) / z) \ v6))) = a(x,y,(z * R(z,z,u)) * v6)
    ]]></literal>
    <justification jstring="[para(29956(a,1),34546(a,1,3))].">
      <j1 rule="para" parents="29956 34546"/>
    </justification>
  </clause>

  <clause id="34629">
    <literal><![CDATA[
      a(((x * T(y,z)) \ ((y * z) * x)) * u,w,v5) = a(R(z,y,x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32352,a(flip),b,34563,a),flip(a)].">
      <j1 rule="hyper" parents="373 32352 34563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34631">
    <literal><![CDATA[
      a(((x * y) \ ((y * z) * x)) * u,w,v5) = a(R(z,y,x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32401,a(flip),b,34629,a)].">
      <j1 rule="hyper" parents="64 32401 34629"/>
    </justification>
  </clause>

  <clause id="34633">
    <literal><![CDATA[
      a(R(x,y,z) * u,w,v5) = a(u * L(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32698,a(flip),b,34631,a),flip(a)].">
      <j1 rule="hyper" parents="64 32698 34631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34634">
    <literal><![CDATA[
      a(R(x,y,z) * u,w,v5) = a(L(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32406,a(flip),b,34631,a),flip(a)].">
      <j1 rule="hyper" parents="64 32406 34631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34635">
    <literal><![CDATA[
      a(x * R(y,z,u),w,v5) = a(x * L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26847,a,34633,a)].">
      <j1 rule="hyper" parents="26847 34633"/>
    </justification>
  </clause>

  <clause id="34636">
    <literal><![CDATA[
      a(L(x,y,z) * u,w,v5) = a(u * R(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26847,a,34634,a),flip(a)].">
      <j1 rule="hyper" parents="26847 34634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34637">
    <literal><![CDATA[
      a(x * R((y \ 1) * z,u,w),v5,v6) = a(L(y * z,u,w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26828,a,b,34634,a)].">
      <j1 rule="hyper" parents="64 26828 34634"/>
    </justification>
  </clause>

  <clause id="34638">
    <literal><![CDATA[
      a(L(x * (x * y),z,u) * x,w,v5) = a(x \ R(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31305,a(flip),b,34634,a),flip(a)].">
      <j1 rule="hyper" parents="64 31305 34634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34639">
    <literal><![CDATA[
      a(L(x \ 1,y,z) * u,w,v5) = a(R(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,2705,a(flip),b,34634,a),flip(a)].">
      <j1 rule="hyper" parents="64 2705 34634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34640">
    <literal><![CDATA[
      a((x * y) * L(R(z,y,x),u,w),v5,v6) = a((R(z,u,w) * y) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32519,a(flip),b,34635,a),flip(a)].">
      <j1 rule="hyper" parents="64 32519 34635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34641">
    <literal><![CDATA[
      a(x * R(L(y,z,u),w,v5),v6,v7) = a(x * L(L(y,w,v5),z,u),v6,v7)
    ]]></literal>
    <justification jstring="[para(30(a,1),34635(a,2,1,2))].">
      <j1 rule="para" parents="30 34635"/>
    </justification>
  </clause>

  <clause id="34642">
    <literal><![CDATA[
      a((x * y) * R(L(z,y,x),u,w),v5,v6) = a(x * (y * L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(513(a,1),34635(a,2,1))].">
      <j1 rule="para" parents="513 34635"/>
    </justification>
  </clause>

  <clause id="34643">
    <literal><![CDATA[
      a(L(x \ 1,y,z) * u,w,v5) = a(L(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,34634,a(flip),b,34639,a),flip(a)].">
      <j1 rule="hyper" parents="373 34634 34639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34644">
    <literal><![CDATA[
      a(L((x \ 1) * y,z,u) * w,v5,v6) = a(L(x * y,z,u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,34636,a,b,34637,a)].">
      <j1 rule="hyper" parents="64 34636 34637"/>
    </justification>
  </clause>

  <clause id="34645">
    <literal><![CDATA[
      a(x * L((y \ 1) * z,u,w),v5,v6) = a(L(y * z,u,w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,34635,a(flip),b,34637,a)].">
      <j1 rule="hyper" parents="64 34635 34637"/>
    </justification>
  </clause>

  <clause id="34646">
    <literal><![CDATA[
      a(x * L(R(y,z,u),w,v5),v6,v7) = a(x * L(L(y,z,u),w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(29(a,1),34641(a,1,1,2))].">
      <j1 rule="para" parents="29 34641"/>
    </justification>
  </clause>

  <clause id="34647">
    <literal><![CDATA[
      a(x \ L(x \ y,z,u),w,v5) = a(L(x * y,z,u) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,30385,a(flip),b,34645,a)].">
      <j1 rule="hyper" parents="64 30385 34645"/>
    </justification>
  </clause>

  <clause id="34648">
    <literal><![CDATA[
      a(L(x * (x * y),z,u) * x,w,v5) = a(x \ L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),34647(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 34647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34649">
    <literal><![CDATA[
      a(x \ R(y,z,u),w,v5) = a(x \ L(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34638,a(flip),b,34648,a)].">
      <j1 rule="hyper" parents="64 34638 34648"/>
    </justification>
  </clause>

  <clause id="34650">
    <literal><![CDATA[
      a(x,a(L(y,y,z * x),z,x),u) = a(y \ L(y,z,x),x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,33523,a,b,34649,a)].">
      <j1 rule="hyper" parents="64 33523 34649"/>
    </justification>
  </clause>

  <clause id="34651">
    <literal><![CDATA[
      a(x,a(L(y,y,z * x),z,x),u) = a(y * L(y,z,x),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,5609,a(flip),b,34650,a),flip(a)].">
      <j1 rule="hyper" parents="373 5609 34650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34652">
    <literal><![CDATA[
      a(x * L(x,y,z),z,u) = a(z,x \ R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(32467(a,1),34651(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32467 34651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34653">
    <literal><![CDATA[
      a((R(x,y,z) * u) * w,v5,v6) = a((L(x,y,z) * u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32520,a(flip),b,34640,a),flip(a)].">
      <j1 rule="hyper" parents="64 32520 34640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34654">
    <literal><![CDATA[
      a((L(x,y,z) * u) * w,v5,v6) = a(w * (R(x,y,z) * u),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26847,a,34653,a),flip(a)].">
      <j1 rule="hyper" parents="26847 34653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34655">
    <literal><![CDATA[
      a((x * R(y \ 1,z,u)) * w,v5,v6) = a((L(y,z,u) * x) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32508,a,b,34653,a)].">
      <j1 rule="hyper" parents="64 32508 34653"/>
    </justification>
  </clause>

  <clause id="34656">
    <literal><![CDATA[
      a((L(x,y,z) * u) * w,v5,v6) = a((u * R(x,y,z)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32388,a,b,34653,a),flip(a)].">
      <j1 rule="hyper" parents="64 32388 34653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34657">
    <literal><![CDATA[
      a((L(x,y,z) * (x \ R(x,y,z))) * u,w,v5) = a(x * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,2689,a(flip),b,34653,a),flip(a)].">
      <j1 rule="hyper" parents="64 2689 34653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34658">
    <literal><![CDATA[
      a((L(x,y,z) * (R(x,y,z) \ u)) * w,v5,v6) = a(u * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(10(a,1),34653(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 34653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34659">
    <literal><![CDATA[
      a(x * (R(y,z,u) * w),v5,v6) = a(x * (L(y,z,u) * w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26847,a,34654,a),flip(a)].">
      <j1 rule="hyper" parents="26847 34654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34660">
    <literal><![CDATA[
      a((L(x,y,z) * u) * T((u * R(x,y,z)) \ ((1 / (u * R(x,y,z))) \ w),v5),v6,v7) = a((1 / (u * R(x,y,z))) \ T(w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(1469(a,1),34656(a,2,1))].">
      <j1 rule="para" parents="1469 34656"/>
    </justification>
  </clause>

  <clause id="34661">
    <literal><![CDATA[
      a((x / R(T(R(y,z,u),x),R(y,z,u),R(y,z,u))) * w,v5,v6) = a((L(y,z,u) * (R(y,z,u) \ (x / R(y,z,u)))) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(8877(a,2),34656(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="8877 34656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34662">
    <literal><![CDATA[
      a((L(x,y,z) * R(u,u,L(x,y,z))) * w,v5,v6) = a(((1 / u) \ R(x,y,z)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(26362(a,1),34656(a,2,1,1))].">
      <j1 rule="para" parents="26362 34656"/>
    </justification>
  </clause>

  <clause id="34663">
    <literal><![CDATA[
      a(x * (L(y,z,u) * (y \ R(y,z,u))),w,v5) = a(y * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26847,a,34657,a)].">
      <j1 rule="hyper" parents="26847 34657"/>
    </justification>
  </clause>

  <clause id="34664">
    <literal><![CDATA[
      a(x * L(R(y,z,u),z,u),w,v5) = a(y * x,w,v5)
    ]]></literal>
    <justification jstring="[para(33222(a,1),34663(a,1,1,2))].">
      <j1 rule="para" parents="33222 34663"/>
    </justification>
  </clause>

  <clause id="34665">
    <literal><![CDATA[
      a(x * L(L(y,z,u),z,u),w,v5) = a(y * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34646,a(flip),b,34664,a)].">
      <j1 rule="hyper" parents="64 34646 34664"/>
    </justification>
  </clause>

  <clause id="34666">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z) * u,w,v5) = a(x * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26847,a,34665,a)].">
      <j1 rule="hyper" parents="26847 34665"/>
    </justification>
  </clause>

  <clause id="34667">
    <literal><![CDATA[
      a(((x \ (x \ y)) * z) * u,w,v5) = a((L(y,x,x) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,33856,a(flip),b,34655,a)].">
      <j1 rule="hyper" parents="64 33856 34655"/>
    </justification>
  </clause>

  <clause id="34668">
    <literal><![CDATA[
      a((x * (y \ (y \ z))) * u,w,v5) = a((L(z,y,y) * x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32388,a,b,34667,a)].">
      <j1 rule="hyper" parents="64 32388 34667"/>
    </justification>
  </clause>

  <clause id="34669">
    <literal><![CDATA[
      a((x * (y \ (z / y))) * u,w,v5) = a((L(z,y,y) * x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32933,a,b,34668,a)].">
      <j1 rule="hyper" parents="64 32933 34668"/>
    </justification>
  </clause>

  <clause id="34670">
    <literal><![CDATA[
      a(x * (y * R(z,u,w)),v5,v6) = a(x * (y * L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(514(a,1),34642(a,1,1))].">
      <j1 rule="para" parents="514 34642"/>
    </justification>
  </clause>

  <clause id="34671">
    <literal><![CDATA[
      (x * a(y,z,u)) / (u * (x * a(y,z,u))) = R(1 / u,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33457,a(flip),b,34593,a),flip(a)].">
      <j1 rule="hyper" parents="64 33457 34593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34673">
    <literal><![CDATA[
      (x \ (y * a(z,u,x))) / (y * a(z,u,x)) = (R(1 / x,x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(34671(a,1),2033(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="34671 2033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34674">
    <literal><![CDATA[
      (x \ (y * a(z,u,x))) / (y * a(z,u,x)) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11418,a(flip),b,34673,a),flip(a)].">
      <j1 rule="hyper" parents="373 11418 34673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34675">
    <literal><![CDATA[
      a(x,x,y * a(z,u,x)) = x * R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,34674,a(flip),b,30085,a),flip(a)].">
      <j1 rule="hyper" parents="145 34674 30085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34676">
    <literal><![CDATA[
      a(x,x,y * a(z,u,x)) = x \ R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1987,a(flip),b,34675,a),flip(a)].">
      <j1 rule="hyper" parents="373 1987 34675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34677">
    <literal><![CDATA[
      R(x,x,y * a(z,u,x)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,30058,a,b,34676,a(flip))].">
      <j1 rule="hyper" parents="39 30058 34676"/>
    </justification>
  </clause>

  <clause id="34678">
    <literal><![CDATA[
      R(x,x,(y * z) * x) = R(x,x,y * (z * x))
    ]]></literal>
    <justification jstring="[para(88(a,1),34677(a,1,3))].">
      <j1 rule="para" parents="88 34677"/>
    </justification>
  </clause>

  <clause id="34679">
    <literal><![CDATA[
      R(x,x,y * (z * x)) = R(x,x,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26164,a,b,34678,a),flip(a)].">
      <j1 rule="hyper" parents="64 26164 34678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34680">
    <literal><![CDATA[
      R(x,x,x * (y * (x \ z))) = R(x,x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26181,a(flip),b,34679,a),flip(a)].">
      <j1 rule="hyper" parents="64 26181 34679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34681">
    <literal><![CDATA[
      R(x,x,(x \ y) * z) = R(x,x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,32773,a(flip),b,34680,a),flip(a)].">
      <j1 rule="hyper" parents="64 32773 34680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34682">
    <literal><![CDATA[
      R(1 / (1 / x),x,y * z) = R(x,x,z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32774,a,b,34681,a)].">
      <j1 rule="hyper" parents="64 32774 34681"/>
    </justification>
  </clause>

  <clause id="34683">
    <literal><![CDATA[
      R(x,x,x \ (y * z)) = R(x,x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,32769,a,b,34681,a)].">
      <j1 rule="hyper" parents="64 32769 34681"/>
    </justification>
  </clause>

  <clause id="34684">
    <literal><![CDATA[
      R(1 / (x \ T(y,z)),x \ y,y) \ T(y,z) = T(y / (x / T(T(y,z),z)),x)
    ]]></literal>
    <justification jstring="[para(26422(a,1),34596(a,1,1))].">
      <j1 rule="para" parents="26422 34596"/>
    </justification>
  </clause>

  <clause id="34686">
    <literal><![CDATA[
      T(x / (y / T(T(x,z),z)),y) = ((1 * x) / ((y \ x) * T(x,z))) \ T(x,z)
    ]]></literal>
    <justification jstring="[para(25956(a,1),34684(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25956 34684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34687">
    <literal><![CDATA[
      T(x / (y / T(T(x,z),z)),y) = (x / ((y \ x) * T(x,z))) \ T(x,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),34686(a,2,1,1))].">
      <j1 rule="para" parents="7 34686"/>
    </justification>
  </clause>

  <clause id="34688">
    <literal><![CDATA[
      T(x / (y / T(T(x,z),z)),y) = (y \ x) * (T(x,z) * K(x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,24293,a(flip),b,34687,a),flip(a)].">
      <j1 rule="hyper" parents="373 24293 34687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34689">
    <literal><![CDATA[
      T(x / (y / T(T(x,z),z)),y) = (y \ x) * T(T(x,z),z)
    ]]></literal>
    <justification jstring="[para(6113(a,1),34688(a,2,2))].">
      <j1 rule="para" parents="6113 34688"/>
    </justification>
  </clause>

  <clause id="34690">
    <literal><![CDATA[
      ((x * y) \ x) * T(T(x,y),y) = T(x / T(y,x),x * y)
    ]]></literal>
    <justification jstring="[para(4795(a,1),34689(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4795 34689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34691">
    <literal><![CDATA[
      T(x / T(y,x),x * y) = ((y * x) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,25499,a(flip),b,34690,a),flip(a)].">
      <j1 rule="hyper" parents="64 25499 34690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34693">
    <literal><![CDATA[
      R((x / y) * K(z,K(u,w)),y,u) = (x * u) / (y * (K(z,K(u,w)) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,23198,a(flip),b,34605,a)].">
      <j1 rule="hyper" parents="64 23198 34605"/>
    </justification>
  </clause>

  <clause id="34694">
    <literal><![CDATA[
      R((x / y) * K(z,K(u,w)),y,u) = (x * u) / (y * T(u,K(z,w)))
    ]]></literal>
    <justification jstring="[para(8115(a,1),34693(a,2,2,2))].">
      <j1 rule="para" parents="8115 34693"/>
    </justification>
  </clause>

  <clause id="34695">
    <literal><![CDATA[
      R((((x * y) \ x) / T(y,K(z,u))) * K(z,K(y,u)),T(y,K(z,u)),y) = ((T(y,K(z,u)) * T(y,K(z,u))) \ ((x * y) \ x)) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,9476,a(flip),b,34694,a),flip(a)].">
      <j1 rule="hyper" parents="373 9476 34694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34696">
    <literal><![CDATA[
      (x \ y) / ((x * a(z,u,w)) \ y) = ((x * a(z,u,w)) \ y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(346(a,1),23915(a,1,1)),flip(a)].">
      <j1 rule="para" parents="346 23915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34697">
    <literal><![CDATA[
      (((a(x,y,z) \ u) * a(x,y,z)) \ w) \ ((a(x,y,z) \ u) \ w) = ((a(x,y,z) \ u) \ w) / (u \ w)
    ]]></literal>
    <justification jstring="[para(23135(a,1),34696(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23135 34696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34698">
    <literal><![CDATA[
      (K(x,y) * (z * u)) * T(u \ K(u,z),K(x,y)) = (K(x,T(y,u)) * (u * z)) * (u \ 1)
    ]]></literal>
    <justification jstring="[para(22969(a,2),24369(a,1,2))].">
      <j1 rule="para" parents="22969 24369"/>
    </justification>
  </clause>

  <clause id="34699">
    <literal><![CDATA[
      ((1 / (1 / (x \ y))) \ y) / (1 / (x \ y)) = x / (1 / T(y / x,T(y \ x,x)))
    ]]></literal>
    <justification jstring="[para(7987(a,1),24414(a,2,2))].">
      <j1 rule="para" parents="7987 24414"/>
    </justification>
  </clause>

  <clause id="34700">
    <literal><![CDATA[
      ((1 / (1 / (x \ y))) \ y) / (1 / (x \ y)) = x / (1 / T(y / x,x / y))
    ]]></literal>
    <justification jstring="[para(8271(a,1),34699(a,2,2,2))].">
      <j1 rule="para" parents="8271 34699"/>
    </justification>
  </clause>

  <clause id="34701">
    <literal><![CDATA[
      ((1 / (1 / (x \ y))) \ y) / (1 / (x \ y)) = x / ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(3040(a,1),34700(a,2,2))].">
      <j1 rule="para" parents="3040 34700"/>
    </justification>
  </clause>

  <clause id="34702">
    <literal><![CDATA[
      ((x \ y) \ y) / ((x \ y) \ 1) = x / ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3691,a(flip),b,34701,a)].">
      <j1 rule="hyper" parents="64 3691 34701"/>
    </justification>
  </clause>

  <clause id="34703">
    <literal><![CDATA[
      R((x / ((y / x) \ 1)) \ 1,((x \ y) \ 1) \ ((x \ y) \ y),(x \ y) \ y) = ((x \ y) \ 1) / ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(34702(a,1),26623(a,1,1,1))].">
      <j1 rule="para" parents="34702 26623"/>
    </justification>
  </clause>

  <clause id="34704">
    <literal><![CDATA[
      ((T(x,y * T(z,u * T(w,v5))) * v6) * v7) / ((x * v6) * v7) = K(x,y * T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(31502(a,1),24806(a,1,1,1,1))].">
      <j1 rule="para" parents="31502 24806"/>
    </justification>
  </clause>

  <clause id="34705">
    <literal><![CDATA[
      L(x,y,L((z * z) * (u / T(z,w)),v5,v6)) = L(x,y,L((1 / z) \ u,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,29034,a(flip),b,24837,a),flip(a)].">
      <j1 rule="hyper" parents="64 29034 24837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34707">
    <literal><![CDATA[
      L(x,y,L((z * z) * (u / T(z,w)),v5,v6)) = L(x,y,L((z \ 1) \ u,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,29175,a(flip),b,34705,a),flip(a)].">
      <j1 rule="hyper" parents="373 29175 34705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34708">
    <literal><![CDATA[
      L(x,y,L((z * z) * (T(z,u) \ w),v5,v6)) = L(x,y,L((z \ 1) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,29179,a(flip),b,34707,a)].">
      <j1 rule="hyper" parents="64 29179 34707"/>
    </justification>
  </clause>

  <clause id="34709">
    <literal><![CDATA[
      L(x,y,L(T(z,u) \ w,v5,v6)) = L(x,y,L((z \ 1) \ w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,34219,a(flip),b,34708,a)].">
      <j1 rule="hyper" parents="64 34219 34708"/>
    </justification>
  </clause>

  <clause id="34711">
    <literal><![CDATA[
      L(x,y,L((z \ 1) \ u,w,v5)) = L(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,29006,a(flip),b,34709,a),flip(a)].">
      <j1 rule="hyper" parents="64 29006 34709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34712">
    <literal><![CDATA[
      L(x,y,L(L(z * u,w,v5),z,z)) = L(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,30367,a,b,34711,a)].">
      <j1 rule="hyper" parents="64 30367 34711"/>
    </justification>
  </clause>

  <clause id="34713">
    <literal><![CDATA[
      L(x,y,L(z \ (z \ u),w,v5)) = L(x,y,L(L(u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),34712(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="10 34712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34714">
    <literal><![CDATA[
      (x \ ((y / (z * u)) \ 1)) \ K(x \ ((y / (z * u)) \ 1),y * (u \ (z \ x))) = 1 / (x \ ((y / (z * u)) \ 1))
    ]]></literal>
    <justification jstring="[para(28282(a,1),24992(a,1,2))].">
      <j1 rule="para" parents="28282 24992"/>
    </justification>
  </clause>

  <clause id="34715">
    <literal><![CDATA[
      (x * R((y * y) * (T(x,y * y) \ 1),z,u)) / w = (y * y) * ((x \ R(x,z,u)) / w)
    ]]></literal>
    <justification jstring="[para(1981(a,2),25033(a,1,1,2))].">
      <j1 rule="para" parents="1981 25033"/>
    </justification>
  </clause>

  <clause id="34717">
    <literal><![CDATA[
      L(x,y \ z,y \ z) * R((z / y) \ 1,(z / y) \ 1,x) = x * ((z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(29526(a,1),25121(a,1,1))].">
      <j1 rule="para" parents="29526 25121"/>
    </justification>
  </clause>

  <clause id="34718">
    <literal><![CDATA[
      L(x,y \ z,y \ z) * R((z / y) \ 1,z / y,x) = x * ((z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(2975(a,1),34717(a,1,2))].">
      <j1 rule="para" parents="2975 34717"/>
    </justification>
  </clause>

  <clause id="34719">
    <literal><![CDATA[
      L(x,y \ z,y \ z) * R((z / y) \ 1,y \ z,x) = x * ((z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(26410(a,1),34718(a,1,2))].">
      <j1 rule="para" parents="26410 34718"/>
    </justification>
  </clause>

  <clause id="34720">
    <literal><![CDATA[
      L(x,y \ x,y \ x) * (y / x) = x * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(26623(a,1),34719(a,1,2))].">
      <j1 rule="para" parents="26623 34719"/>
    </justification>
  </clause>

  <clause id="34721">
    <literal><![CDATA[
      L(x,y \ x,y \ x) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(36,a,31422,a,b,34720,a),flip(a)].">
      <j1 rule="hyper" parents="36 31422 34720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34722">
    <literal><![CDATA[
      (((x / y) \ 1) * x) * (y \ x) = (1 / (y / x)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,27240,a,b,34721,a)].">
      <j1 rule="hyper" parents="64 27240 34721"/>
    </justification>
  </clause>

  <clause id="34723">
    <literal><![CDATA[
      (x \ y) \ ((1 / (x / y)) * x) = ((x \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(139,a,34721,a(flip),b,1139,a)].">
      <j1 rule="hyper" parents="139 34721 1139"/>
    </justification>
  </clause>

  <clause id="34724">
    <literal><![CDATA[
      L(x * (x \ y),x \ y,x \ y) = (1 / (x / y)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,25809,a,b,34722,a)].">
      <j1 rule="hyper" parents="64 25809 34722"/>
    </justification>
  </clause>

  <clause id="34725">
    <literal><![CDATA[
      (((x \ y) \ 1) * y) * (x \ y) = x * (1 / (x / y))
    ]]></literal>
    <justification jstring="[para(34723(a,1),18945(a,1,1))].">
      <j1 rule="para" parents="34723 18945"/>
    </justification>
  </clause>

  <clause id="34726">
    <literal><![CDATA[
      (((x \ y) \ 1) * y) \ (x * (1 / (x / y))) = x \ y
    ]]></literal>
    <justification jstring="[hyper(149,a,34725,a)].">
      <j1 rule="hyper" parents="149 34725"/>
    </justification>
  </clause>

  <clause id="34727">
    <literal><![CDATA[
      ((((x * (y * z)) \ (z * (x * y))) \ 1) * (z * (x * y))) \ ((x * (y * z)) * (1 / ((x * (y * z)) / (z * (x * y))))) = a(x,y,z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,15232,a(flip),b,34726,a),flip(a)].">
      <j1 rule="hyper" parents="373 15232 34726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34728">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) / (u / (z / (z * u))) = (1 / (u / (z / (z * u)))) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5731(a,2),25145(a,1,1,2,2))].">
      <j1 rule="para" parents="5731 25145"/>
    </justification>
  </clause>

  <clause id="34729">
    <literal><![CDATA[
      (1 / (x / (y / (y * x)))) * K(z,u) = K(z,u) / (x / (y / (y * x)))
    ]]></literal>
    <justification jstring="[para(17134(a,1),34728(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17134 34728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34730">
    <literal><![CDATA[
      T(x / (y / (y * x)),K(z,u)) = x / (y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(37,a,25415,a,b,34729,a(flip))].">
      <j1 rule="hyper" parents="37 25415 34729"/>
    </justification>
  </clause>

  <clause id="34732">
    <literal><![CDATA[
      K(x,y) * ((z / (u / (u * z))) \ 1) = (z / (u / (u * z))) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(34730(a,1),18383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="34730 18383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34733">
    <literal><![CDATA[
      T(x * (((x \ y) / y) * (y / (x * y))),K(x,z)) = (x * (y / (x * y))) * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(31371(a,1),25358(a,1,1))].">
      <j1 rule="para" parents="31371 25358"/>
    </justification>
  </clause>

  <clause id="34734">
    <literal><![CDATA[
      ((x \ 1) * R(y,x,x)) \ (y * (x \ 1)) = K(x,x \ y) * a(x,x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(10148(a,1),25428(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10148 25428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34735">
    <literal><![CDATA[
      ((x \ 1) * R(y,x,x)) \ (y * (x \ 1)) = K(x,x \ y) * a(x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(30356(a,1),34734(a,2,2))].">
      <j1 rule="para" parents="30356 34734"/>
    </justification>
  </clause>

  <clause id="34736">
    <literal><![CDATA[
      ((x \ 1) * R(y,x,x)) \ (y * (x \ 1)) = ((x \ y) / ((x \ y) * x)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,30285,a(flip),b,34735,a),flip(a)].">
      <j1 rule="hyper" parents="373 30285 34735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34737">
    <literal><![CDATA[
      ((x \ 1) * R(y,x,x)) \ (y * (x \ 1)) = ((y / x) / y) * x
    ]]></literal>
    <justification jstring="[para(10252(a,1),34736(a,2,1))].">
      <j1 rule="para" parents="10252 34736"/>
    </justification>
  </clause>

  <clause id="34738">
    <literal><![CDATA[
      T(x,y) * (a(x,z,z) * (R(T(x,y),z,z) \ u)) = L(u,x,a(z,z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,30981,a(flip),b,25429,a),flip(a)].">
      <j1 rule="hyper" parents="373 30981 25429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34739">
    <literal><![CDATA[
      K(x,(y / (z / (u * K(w \ y,w)))) \ w) = K(x,z / (T(w \ y,w) * u))
    ]]></literal>
    <justification jstring="[hyper(18009,a,25460,a),flip(a)].">
      <j1 rule="hyper" parents="18009 25460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34741">
    <literal><![CDATA[
      K(x,(y / (z / (u * K(w \ y,w)))) \ w) = K(x,z / ((y / w) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,25749,a(flip),b,34739,a),flip(a)].">
      <j1 rule="hyper" parents="373 25749 34739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34742">
    <literal><![CDATA[
      K(x,(y / (z * K(u \ w,u))) * (w \ u)) = K(x,y / ((w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,24703,a(flip),b,34741,a)].">
      <j1 rule="hyper" parents="64 24703 34741"/>
    </justification>
  </clause>

  <clause id="34743">
    <literal><![CDATA[
      K(x,y * ((z * K(u \ w,u)) \ (w \ u))) = K(x,y / ((w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,24984,a(flip),b,34742,a)].">
      <j1 rule="hyper" parents="64 24984 34742"/>
    </justification>
  </clause>

  <clause id="34744">
    <literal><![CDATA[
      K(x,y * (K(z,z \ u) * (w \ (u \ z)))) = K(x,y / ((u / z) * w))
    ]]></literal>
    <justification jstring="[para(23272(a,1),34743(a,1,2,2))].">
      <j1 rule="para" parents="23272 34743"/>
    </justification>
  </clause>

  <clause id="34745">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) * K(w,u))) = K(x,y / ((u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,18109,a(flip),b,34744,a)].">
      <j1 rule="hyper" parents="64 18109 34744"/>
    </justification>
  </clause>

  <clause id="34746">
    <literal><![CDATA[
      K(x,y * (z \ (u \ T(w,u)))) = K(x,y / ((u / w) * z))
    ]]></literal>
    <justification jstring="[para(16684(a,1),34745(a,1,2,2))].">
      <j1 rule="para" parents="16684 34745"/>
    </justification>
  </clause>

  <clause id="34747">
    <literal><![CDATA[
      K(x,y / ((z / u) * w)) = K(x,y * (w \ (u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,16686,a(flip),b,34746,a),flip(a)].">
      <j1 rule="hyper" parents="64 16686 34746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34748">
    <literal><![CDATA[
      K(x,y / (z * L(u \ w,u,w \ y))) = K(x,y * (w \ (u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27273,a,b,34747,a)].">
      <j1 rule="hyper" parents="64 27273 34747"/>
    </justification>
  </clause>

  <clause id="34749">
    <literal><![CDATA[
      K(x,y / (z * (u \ w))) = K(x,y * (w \ (u / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,28536,a(flip),b,34748,a)].">
      <j1 rule="hyper" parents="64 28536 34748"/>
    </justification>
  </clause>

  <clause id="34751">
    <literal><![CDATA[
      K(x,y * ((z \ u) / w)) = K(x,y * (z \ (u / w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,22684,a(flip),b,34749,a)].">
      <j1 rule="hyper" parents="64 22684 34749"/>
    </justification>
  </clause>

  <clause id="34752">
    <literal><![CDATA[
      x * (((y \ z) / u) \ K(((y \ z) / u) \ x,w * (y \ (z / u)))) = T(x * (((y \ z) / u) \ 1),((y \ z) / u) * w)
    ]]></literal>
    <justification jstring="[para(34751(a,1),25138(a,1,2,2))].">
      <j1 rule="para" parents="34751 25138"/>
    </justification>
  </clause>

  <clause id="34753">
    <literal><![CDATA[
      T(x,x \ y) \ ((x \ y) \ K(x,T(y \ 1,y))) = ((x \ y) \ 1) / ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(7871(a,1),25763(a,1,2,2))].">
      <j1 rule="para" parents="7871 25763"/>
    </justification>
  </clause>

  <clause id="34754">
    <literal><![CDATA[
      T(x,x \ y) \ ((x \ y) \ K(x,y \ 1)) = ((x \ y) \ 1) / ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(6053(a,1),34753(a,1,2,2))].">
      <j1 rule="para" parents="6053 34753"/>
    </justification>
  </clause>

  <clause id="34755">
    <literal><![CDATA[
      x \ ((y / x) \ K(x,y \ 1)) = ((x \ y) \ 1) / ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,5045,a(flip),b,34754,a)].">
      <j1 rule="hyper" parents="64 5045 34754"/>
    </justification>
  </clause>

  <clause id="34756">
    <literal><![CDATA[
      (x * (y * (x * R(y,z,u)))) \ ((x * y) * (x * R(y,z,u))) = a(x,R(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(24605(a,1),25815(a,1,1,2))].">
      <j1 rule="para" parents="24605 25815"/>
    </justification>
  </clause>

  <clause id="34757">
    <literal><![CDATA[
      L(R(x,y,R(T(x,z),u,w)),y,R(x,u,w)) = (x * (R(x,u,w) * y)) / (R(x,u,w) * y)
    ]]></literal>
    <justification jstring="[para(1897(a,1),25952(a,2,1))].">
      <j1 rule="para" parents="1897 25952"/>
    </justification>
  </clause>

  <clause id="34758">
    <literal><![CDATA[
      T(x,y * y) / (y * (y * x)) = (y * (y * x)) \ x
    ]]></literal>
    <justification jstring="[para(25366(a,1),26619(a,1,2))].">
      <j1 rule="para" parents="25366 26619"/>
    </justification>
  </clause>

  <clause id="34759">
    <literal><![CDATA[
      T(x \ y,x * x) / (x * y) = (x * (x * (x \ y))) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),34758(a,1,2,2))].">
      <j1 rule="para" parents="10 34758"/>
    </justification>
  </clause>

  <clause id="34761">
    <literal><![CDATA[
      T(x \ y,x * x) / (x * y) = (x * y) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),34759(a,2,1,2))].">
      <j1 rule="para" parents="10 34759"/>
    </justification>
  </clause>

  <clause id="34763">
    <literal><![CDATA[
      T(x,y * y) / (y * (x * y)) = (y * (x * y)) \ x
    ]]></literal>
    <justification jstring="[para(13920(a,1),26634(a,1,2))].">
      <j1 rule="para" parents="13920 26634"/>
    </justification>
  </clause>

  <clause id="34764">
    <literal><![CDATA[
      K(x * x,y) * ((x * (y * x)) \ y) = y / (x * (y * x))
    ]]></literal>
    <justification jstring="[hyper(145,a,34763,a(flip),b,14841,a)].">
      <j1 rule="hyper" parents="145 34763 14841"/>
    </justification>
  </clause>

  <clause id="34766">
    <literal><![CDATA[
      a(L((R(x,y,z) \ 1) * (x * x),u,w),v5,v6) = a(L(R(1 / x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32637,a(flip),b,26888,a),flip(a)].">
      <j1 rule="hyper" parents="373 32637 26888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34767">
    <literal><![CDATA[
      a(L((R(x,y,z) \ 1) * (x * x),u,w),v5,v6) = a(L(L(1 / x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32711,a(flip),b,34766,a),flip(a)].">
      <j1 rule="hyper" parents="373 32711 34766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34768">
    <literal><![CDATA[
      a(L((R(x,y,z) \ 1) * (x * x),u,w),v5,v6) = a(L(L(x \ 1,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,26863,a(flip),b,34767,a),flip(a)].">
      <j1 rule="hyper" parents="373 26863 34767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34769">
    <literal><![CDATA[
      a(L(L(x \ 1,y,z),u,w),v5,v6) = a(L(R(x,y,z) \ 1,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32806,a(flip),b,34768,a),flip(a)].">
      <j1 rule="hyper" parents="64 32806 34768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34771">
    <literal><![CDATA[
      a(L(L(x \ 1,y,z),u,w),v5,v6) = a(L(R(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32634,a(flip),b,34769,a),flip(a)].">
      <j1 rule="hyper" parents="373 32634 34769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34772">
    <literal><![CDATA[
      a(L(L(x \ 1,y,z),u,w),v5,v6) = a(L(L(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32711,a(flip),b,34771,a),flip(a)].">
      <j1 rule="hyper" parents="373 32711 34771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34774">
    <literal><![CDATA[
      a(L(L(x,x,y),y * x,z),u,w) = a((z * (y * x)) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27171,a(flip),b,34772,a),flip(a)].">
      <j1 rule="hyper" parents="64 27171 34772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34775">
    <literal><![CDATA[
      (1 / x) \ T(y * (x * R(x \ (y \ 1),z,z)),x) = T(a((1 / x) \ y,z,z) * x,x)
    ]]></literal>
    <justification jstring="[para(2839(a,1),26939(a,1,2,1))].">
      <j1 rule="para" parents="2839 26939"/>
    </justification>
  </clause>

  <clause id="34776">
    <literal><![CDATA[
      T(x,y) \ (((z * z) \ (T(x,z \ (z \ y)) * u)) * w) = (z * z) \ (x \ ((x * u) * w))
    ]]></literal>
    <justification jstring="[para(484(a,1),26942(a,1,2))].">
      <j1 rule="para" parents="484 26942"/>
    </justification>
  </clause>

  <clause id="34777">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * R((x \ 1) \ 1,u,w) = (1 / L(x,y,z)) * R(x,u,w)
    ]]></literal>
    <justification jstring="[para(5399(a,1),26965(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5399 26965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34778">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * R((x \ 1) \ 1,u,w) = L(x,y,z) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26758,a(flip),b,34777,a),flip(a)].">
      <j1 rule="hyper" parents="373 26758 34777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34779">
    <literal><![CDATA[
      K(x,y) * T(K(y,x) * K(z,u * T(u,w)),u * T(u,w)) = K(z,u * T(u,w))
    ]]></literal>
    <justification jstring="[para(5918(a,1),26967(a,1,2))].">
      <j1 rule="para" parents="5918 26967"/>
    </justification>
  </clause>

  <clause id="34780">
    <literal><![CDATA[
      K(x * K(y,z),u * T(u,w)) = K(x,u * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,22989,a(flip),b,34779,a)].">
      <j1 rule="hyper" parents="64 22989 34779"/>
    </justification>
  </clause>

  <clause id="34781">
    <literal><![CDATA[
      K(T(x,y) \ z,u * T(u,w)) = K(x \ z,u * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,17364,a(flip),b,34780,a)].">
      <j1 rule="hyper" parents="64 17364 34780"/>
    </justification>
  </clause>

  <clause id="34782">
    <literal><![CDATA[
      K(x * (y / z),u * T(u,w)) = K(x * (z \ y),u * T(u,w))
    ]]></literal>
    <justification jstring="[para(6471(a,1),34780(a,1,1))].">
      <j1 rule="para" parents="6471 34780"/>
    </justification>
  </clause>

  <clause id="34783">
    <literal><![CDATA[
      K(x \ (x \ y),x * T(x,z)) = K(y,x * T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33989,a(flip),b,34781,a),flip(a)].">
      <j1 rule="hyper" parents="64 33989 34781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34785">
    <literal><![CDATA[
      K(x \ y,x * T(x,z)) = K(x * y,x * T(x,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),34783(a,1,1,2))].">
      <j1 rule="para" parents="9 34783"/>
    </justification>
  </clause>

  <clause id="34786">
    <literal><![CDATA[
      ((x * x) \ (y / x)) / T((x * x) \ y,x) = ((x * x) \ y) / T((1 / x) * T(y,x),x)
    ]]></literal>
    <justification jstring="[para(933(a,1),27204(a,2,1)),flip(a)].">
      <j1 rule="para" parents="933 27204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34787">
    <literal><![CDATA[
      (((x * y) * y) \ z) * K(u,K(w,x * z)) = T(((x * y) * y) \ z,K(u,w))
    ]]></literal>
    <justification jstring="[para(25503(a,1),27831(a,1,2))].">
      <j1 rule="para" parents="25503 27831"/>
    </justification>
  </clause>

  <clause id="34788">
    <literal><![CDATA[
      T(((x * y) * y) \ x,K(z,u)) = (((x * y) * y) \ x) * 1
    ]]></literal>
    <justification jstring="[para(17038(a,1),34787(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17038 34787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34789">
    <literal><![CDATA[
      T(((x * y) * y) \ x,K(z,u)) = ((x * y) * y) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a(flip),b,34788,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 34788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34790">
    <literal><![CDATA[
      L((x \ y) / (T(x,z) \ 1),u,w) = (x \ L(y,u,w)) / (T(x,z) \ 1)
    ]]></literal>
    <justification jstring="[para(6075(a,1),27891(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6075 27891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34792">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (x \ L(x,y,z))) \ (x \ 1) = L(x,y,z) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(5659(a,1),28446(a,2,2))].">
      <j1 rule="para" parents="5659 28446"/>
    </justification>
  </clause>

  <clause id="34794">
    <literal><![CDATA[
      K(x \ ((y * z) * z),x / (z * z)) / (((x / z) / z) \ y) = 1 / (y / ((x / z) / z))
    ]]></literal>
    <justification jstring="[para(23387(a,1),28514(a,1,1))].">
      <j1 rule="para" parents="23387 28514"/>
    </justification>
  </clause>

  <clause id="34795">
    <literal><![CDATA[
      x * (a(y,z,x) \ ((u / x) * (x * a(y,z,x)))) = L((x \ 1) \ u,x \ a(y,z,x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33206,a(flip),b,28917,a)].">
      <j1 rule="hyper" parents="64 33206 28917"/>
    </justification>
  </clause>

  <clause id="34796">
    <literal><![CDATA[
      L((x \ R(y,x,x)) \ z,x * y,x) = R(y,x,x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(1409(a,1),29597(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1409 29597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34797">
    <literal><![CDATA[
      L(x,y * ((z * z) \ (u / (w * (1 / z)))),v5) = L(x,y * ((z * T(w,z \ 1)) \ u),v5)
    ]]></literal>
    <justification jstring="[para(933(a,1),29674(a,1,2,2))].">
      <j1 rule="para" parents="933 29674"/>
    </justification>
  </clause>

  <clause id="34798">
    <literal><![CDATA[
      L(x,L((y \ (z * u)) \ ((z \ 1) * u),w,v5),v6) = L(x,L(z * (z \ y),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29855,a(flip),b,29753,a),flip(a)].">
      <j1 rule="hyper" parents="373 29855 29753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34799">
    <literal><![CDATA[
      L(x,L((y \ (z * u)) \ ((z \ 1) * u),w,v5),v6) = L(x,L(y,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(10(a,1),34798(a,2,2,1))].">
      <j1 rule="para" parents="10 34798"/>
    </justification>
  </clause>

  <clause id="34800">
    <literal><![CDATA[
      L(x,L(y \ ((z \ 1) * u),w,v5),v6) = L(x,L(y \ (z * u),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29749,a(flip),b,34799,a)].">
      <j1 rule="hyper" parents="64 29749 34799"/>
    </justification>
  </clause>

  <clause id="34802">
    <literal><![CDATA[
      (x * x) \ ((a(y,z,u) * w) \ (w * (a(y,z,u) * v5))) = L((x * x) \ v5,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28828,a(flip),b,29892,a)].">
      <j1 rule="hyper" parents="64 28828 29892"/>
    </justification>
  </clause>

  <clause id="34803">
    <literal><![CDATA[
      x * (L(x \ 1,y,z) * ((x \ K(u,w)) * x)) = (1 / (K(w,u) / x)) * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23065,a(flip),b,29899,a)].">
      <j1 rule="hyper" parents="64 23065 29899"/>
    </justification>
  </clause>

  <clause id="34804">
    <literal><![CDATA[
      a(x,x,((y / x) * x) * R(x,z,u)) = x * (((y / x) * R(x,z,u)) / (R(x,z,u) * y))
    ]]></literal>
    <justification jstring="[para(2823(a,1),30149(a,1,3))].">
      <j1 rule="para" parents="2823 30149"/>
    </justification>
  </clause>

  <clause id="34805">
    <literal><![CDATA[
      (x \ a(x,x,y)) * (a(x,x,y) * K(x \ 1,y)) = (y \ (x \ y)) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(28673(a,1),30170(a,1,2,2))].">
      <j1 rule="para" parents="28673 30170"/>
    </justification>
  </clause>

  <clause id="34807">
    <literal><![CDATA[
      (x \ a(x,x,y)) * (x * R(T(x \ 1,y),x,y)) = (y \ (x \ y)) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(30172(a,1),34805(a,1,2))].">
      <j1 rule="para" parents="30172 34805"/>
    </justification>
  </clause>

  <clause id="34808">
    <literal><![CDATA[
      (x \ a(x,x,y)) * (x * (y \ (x \ y))) = (y \ (x \ y)) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(2985(a,1),34807(a,1,2,2))].">
      <j1 rule="para" parents="2985 34807"/>
    </justification>
  </clause>

  <clause id="34809">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) * z) / L(x,R(x,x,y),z) = z * (T(a(x,x,y) \ 1,z) / x)
    ]]></literal>
    <justification jstring="[para(11794(a,1),30177(a,1,2))].">
      <j1 rule="para" parents="11794 30177"/>
    </justification>
  </clause>

  <clause id="34810">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) * z) / L(x,R(x,x,y),z) = z * ((a(x,x,y) \ 1) / x)
    ]]></literal>
    <justification jstring="[para(23735(a,1),34809(a,2,2,1))].">
      <j1 rule="para" parents="23735 34809"/>
    </justification>
  </clause>

  <clause id="34812">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) * z) / L(x,R(x,x,y),z) = z * (1 / R(x,x,y))
    ]]></literal>
    <justification jstring="[para(30143(a,1),34810(a,2,2))].">
      <j1 rule="para" parents="30143 34810"/>
    </justification>
  </clause>

  <clause id="34813">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) * z) / L(x,L(x,x,y),z) = z * (1 / R(x,x,y))
    ]]></literal>
    <justification jstring="[para(29794(a,1),34812(a,1,2))].">
      <j1 rule="para" parents="29794 34812"/>
    </justification>
  </clause>

  <clause id="34814">
    <literal><![CDATA[
      T((x \ L(x,y,z)) * u,w) * a(x,x \ L(x,y,z),u) = x \ (L(x,y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,28750,a(flip),b,30370,a)].">
      <j1 rule="hyper" parents="64 28750 30370"/>
    </justification>
  </clause>

  <clause id="34815">
    <literal><![CDATA[
      a(x,a(x,y,z),u) * (a(x,y,z) * (u * x)) = u * (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28743(a,1),30418(a,1,2))].">
      <j1 rule="para" parents="28743 30418"/>
    </justification>
  </clause>

  <clause id="34816">
    <literal><![CDATA[
      a(x,y,L((R(z,z,u) \ 1) * u,w,v5)) = a(x,y,L((z \ 1) * L(u,z,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27426,a(flip),b,30456,a)].">
      <j1 rule="hyper" parents="64 27426 30456"/>
    </justification>
  </clause>

  <clause id="34817">
    <literal><![CDATA[
      x * ((x \ 1) \ (a(y,x \ 1,x \ 1) * z)) = (x * (L(x \ 1,x,y) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(11794(a,1),30499(a,2,1,2,1))].">
      <j1 rule="para" parents="11794 30499"/>
    </justification>
  </clause>

  <clause id="34818">
    <literal><![CDATA[
      x * ((x \ 1) \ (a(y,x \ 1,x \ 1) * z)) = (L(1 / x,x,y) \ x) * z
    ]]></literal>
    <justification jstring="[para(28026(a,1),34817(a,2,1))].">
      <j1 rule="para" parents="28026 34817"/>
    </justification>
  </clause>

  <clause id="34819">
    <literal><![CDATA[
      x * ((x \ 1) \ (a(y,x,x \ 1) * z)) = (L(1 / x,x,y) \ x) * z
    ]]></literal>
    <justification jstring="[para(11980(a,1),34818(a,1,2,2,1))].">
      <j1 rule="para" parents="11980 34818"/>
    </justification>
  </clause>

  <clause id="34820">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * a(z,x,x \ 1)) = (L(1 / x,x,z) \ x) * y
    ]]></literal>
    <justification jstring="[para(33243(a,1),34819(a,1,2))].">
      <j1 rule="para" parents="33243 34819"/>
    </justification>
  </clause>

  <clause id="34821">
    <literal><![CDATA[
      L(x,x,y) \ ((a(y,x,x) \ (x * x)) * z) = L((1 / x) \ z,x,R(y,x,x) \ y)
    ]]></literal>
    <justification jstring="[para(25545(a,1),30509(a,1,2))].">
      <j1 rule="para" parents="25545 30509"/>
    </justification>
  </clause>

  <clause id="34822">
    <literal><![CDATA[
      L(x,x,y) \ ((x * (a(y,x,x) \ x)) * z) = L((1 / x) \ z,x,R(y,x,x) \ y)
    ]]></literal>
    <justification jstring="[para(30281(a,1),34821(a,1,2,1))].">
      <j1 rule="para" parents="30281 34821"/>
    </justification>
  </clause>

  <clause id="34823">
    <literal><![CDATA[
      L((1 / x) \ y,x,R(z,x,x) \ z) = L(x,x,z) \ ((x * L(x,x,z)) * y)
    ]]></literal>
    <justification jstring="[para(30459(a,1),34822(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="30459 34822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34824">
    <literal><![CDATA[
      L(x,x,y) \ ((x * L(x,x,y)) * z) = L((1 / x) \ z,x,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29269,a(flip),b,34823,a),flip(a)].">
      <j1 rule="hyper" parents="64 29269 34823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34825">
    <literal><![CDATA[
      (L(x,x,y) \ 1) * (L(x,x,y) \ ((x * L(x,x,y)) * z)) = a(y * x,x,x \ 1) * z
    ]]></literal>
    <justification jstring="[para(275(a,1),30723(a,1,2,2,1))].">
      <j1 rule="para" parents="275 30723"/>
    </justification>
  </clause>

  <clause id="34826">
    <literal><![CDATA[
      (x \ (y * ((x \ y) \ 1))) * (((x \ y) \ 1) \ 1) = (y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,30796,a(flip),b,30795,a),flip(a)].">
      <j1 rule="hyper" parents="373 30796 30795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34827">
    <literal><![CDATA[
      L(x,L(y \ z,y,z \ R(u,w,w)) \ L(u,w,w),v5) = L(x,(z \ R(u,w,w)) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29443,a(flip),b,31028,a),flip(a)].">
      <j1 rule="hyper" parents="373 29443 31028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34828">
    <literal><![CDATA[
      (((x * y) * z) / x) * K(z \ ((x * y) \ x),y * z) = 1 / (1 / (((x * y) * z) / x))
    ]]></literal>
    <justification jstring="[para(23046(a,1),31467(a,1,2))].">
      <j1 rule="para" parents="23046 31467"/>
    </justification>
  </clause>

  <clause id="34829">
    <literal><![CDATA[
      K(x,T(y * (T(T(z,u),w) \ z),z * z)) = K(x,(z / T(T(z,u),w)) * y)
    ]]></literal>
    <justification jstring="[hyper(18271,a,31505,a)].">
      <j1 rule="hyper" parents="18271 31505"/>
    </justification>
  </clause>

  <clause id="34831">
    <literal><![CDATA[
      K(x,(y / T(T(y,z),u)) * w) = K(x,w * (T(T(y,z),u) \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,17031,a(flip),b,34829,a),flip(a)].">
      <j1 rule="hyper" parents="64 17031 34829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34833">
    <literal><![CDATA[
      K(x,y * (T(T(z,u),w) \ z)) = K(x,z * (T(T(z,u),w) \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,24984,a(flip),b,34831,a),flip(a)].">
      <j1 rule="hyper" parents="64 24984 34831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34834">
    <literal><![CDATA[
      K(x,y * (T(T(z,u),w) \ z)) = K(x,K(z,w * u) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,33960,a(flip),b,34833,a),flip(a)].">
      <j1 rule="hyper" parents="373 33960 34833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34835">
    <literal><![CDATA[
      T(x,(T(T(y,z),u) \ y) * (w * K(v5,K(y,u * z) * w))) = T(x,T((T(T(y,z),u) \ y) * w,v5))
    ]]></literal>
    <justification jstring="[para(34834(a,1),18167(a,1,2,2,2))].">
      <j1 rule="para" parents="34834 18167"/>
    </justification>
  </clause>

  <clause id="34836">
    <literal><![CDATA[
      (x * T((T(x,y) \ 1) \ 1,z)) * u = x * ((T(T(x,y),z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5811,a(flip),b,31689,a),flip(a)].">
      <j1 rule="hyper" parents="64 5811 31689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34838">
    <literal><![CDATA[
      (x * T(T((x \ 1) \ 1,y),z)) * u = x * ((T(T(x,y),z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(3568(a,2),34836(a,1,1,2,1))].">
      <j1 rule="para" parents="3568 34836"/>
    </justification>
  </clause>

  <clause id="34839">
    <literal><![CDATA[
      ((1 / x) \ T(T(x,y),z)) * u = x * ((T(T(x,y),z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(15193(a,1),34838(a,1,1))].">
      <j1 rule="para" parents="15193 34838"/>
    </justification>
  </clause>

  <clause id="34840">
    <literal><![CDATA[
      (1 / x) \ (T(T(x,y),z) * u) = x * ((T(T(x,z),y) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34503,a,b,34839,a)].">
      <j1 rule="hyper" parents="64 34503 34839"/>
    </justification>
  </clause>

  <clause id="34841">
    <literal><![CDATA[
      (x \ (1 / T(T(x,y),z))) \ u = x * ((T(T(x,z),y) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27234,a,b,34840,a)].">
      <j1 rule="hyper" parents="64 27234 34840"/>
    </justification>
  </clause>

  <clause id="34842">
    <literal><![CDATA[
      a(x,((((y * (1 / z)) * u) \ y) \ y) \ w,v5) = a(x,((y * z) * u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34353,a(flip),b,32092,a)].">
      <j1 rule="hyper" parents="64 34353 32092"/>
    </justification>
  </clause>

  <clause id="34844">
    <literal><![CDATA[
      a(x,((y * (1 / z)) * u) \ w,v5) = a(x,((y * z) * u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31971,a(flip),b,34842,a)].">
      <j1 rule="hyper" parents="64 31971 34842"/>
    </justification>
  </clause>

  <clause id="34846">
    <literal><![CDATA[
      a(x,L((y * ((y \ 1) \ z)) * (u / y),w,v5),v6) = a(x,L(((y \ 1) \ u) * z,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32161,a(flip),b,32165,a),flip(a)].">
      <j1 rule="hyper" parents="373 32161 32165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34847">
    <literal><![CDATA[
      a(((x \ y) / x) \ y,y * L(y,x,x),y) = (y / ((x \ y) / x)) * (((x \ y) / x) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11978,a(flip),b,32906,a)].">
      <j1 rule="hyper" parents="64 11978 32906"/>
    </justification>
  </clause>

  <clause id="34848">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x,y,z))) \ 1 = L(x,y,z) \ (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,34792,a(flip),b,33168,a),flip(a)].">
      <j1 rule="hyper" parents="64 34792 33168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34849">
    <literal><![CDATA[
      L(x,y,z) * (u * ((L(x,y,z) * u) \ (u * x))) = u * x
    ]]></literal>
    <justification jstring="[hyper(373,a,168,a(flip),b,33178,a),flip(a)].">
      <j1 rule="hyper" parents="373 168 33178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34851">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (u * x) = u \ (L(x,y,z) \ (u * x))
    ]]></literal>
    <justification jstring="[para(34849(a,1),69(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="34849 69"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34852">
    <literal><![CDATA[
      K(x,y) * (x \ (y * (L(y,z,u) \ x))) = (L(y,z,u) * x) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,28913,a,b,34851,a)].">
      <j1 rule="hyper" parents="373 28913 34851"/>
    </justification>
  </clause>

  <clause id="34853">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (x * u) = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(35,a,26974,a,b,34852,a)].">
      <j1 rule="hyper" parents="35 26974 34852"/>
    </justification>
  </clause>

  <clause id="34854">
    <literal><![CDATA[
      x * ((L(y,z,u) * x) \ (y * x)) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,34853,a,b,xx)].">
      <j1 rule="hyper" parents="145 34853"/>
    </justification>
  </clause>

  <clause id="34855">
    <literal><![CDATA[
      L(L(x,y,z) \ x,L(x,y,z),u) = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,25710,a,b,34853,a)].">
      <j1 rule="hyper" parents="64 25710 34853"/>
    </justification>
  </clause>

  <clause id="34856">
    <literal><![CDATA[
      (x / y) \ (y * (L(y,z,u) \ (x / y))) = (L(y,z,u) * (y \ x)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,33892,a(flip),b,34853,a),flip(a)].">
      <j1 rule="hyper" parents="64 33892 34853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34857">
    <literal><![CDATA[
      x \ ((x \ y) * (L(x \ y,z,u) \ x)) = (x * L(x \ y,z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,25711,a(flip),b,34853,a),flip(a)].">
      <j1 rule="hyper" parents="64 25711 34853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34858">
    <literal><![CDATA[
      x * (L(x,y,z) \ (y * z)) = (y * z) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,23922,a,b,34853,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 23922 34853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34859">
    <literal><![CDATA[
      L(x,y,z) \ (x * (y * z)) = (y * z) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2329,a,b,34858,a)].">
      <j1 rule="hyper" parents="64 2329 34858"/>
    </justification>
  </clause>

  <clause id="34860">
    <literal><![CDATA[
      (x * y) * a(y,x,z) != u
    ]]></literal>
    <literal><![CDATA[
      z * (L(z,x,y) \ (x * y)) = u
    ]]></literal>
    <justification jstring="[para(34859(a,1),2342(a,1))].">
      <j1 rule="para" parents="34859 2342"/>
    </justification>
  </clause>

  <clause id="34861">
    <literal><![CDATA[
      x * (L(x,y,z) \ u) != u * w
    ]]></literal>
    <literal><![CDATA[
      (L(x,y,z) * u) \ (x * u) = w
    ]]></literal>
    <justification jstring="[para(34854(a,1),44(a,1))].">
      <j1 rule="para" parents="34854 44"/>
    </justification>
  </clause>

  <clause id="34862">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) \ u = (u / x) \ (u / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(24919(a,1),34856(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24919 34856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34863">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) \ u = (x \ u) \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26982,a(flip),b,34862,a),flip(a)].">
      <j1 rule="hyper" parents="373 26982 34862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34864">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ x = (y \ x) \ (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(23898(a,1),34863(a,1,1))].">
      <j1 rule="para" parents="23898 34863"/>
    </justification>
  </clause>

  <clause id="34865">
    <literal><![CDATA[
      x / ((x / y) * L(y,z,u)) = (y \ x) \ (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,23587,a,b,34864,a)].">
      <j1 rule="hyper" parents="64 23587 34864"/>
    </justification>
  </clause>

  <clause id="34866">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) \ y = x \ (L(y / x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(25820(a,1),34857(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25820 34857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34867">
    <literal><![CDATA[
      L(a(x,y,z),z,(z \ 1) * u) * L(u,z,z) = ((a(x,y,z) \ 1) \ z) * ((z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(28787(a,1),33216(a,1,1))].">
      <j1 rule="para" parents="28787 33216"/>
    </justification>
  </clause>

  <clause id="34868">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,a(w,v5,L(x,v6,v7))) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(33267(a,1),33269(a,2,2))].">
      <j1 rule="para" parents="33267 33269"/>
    </justification>
  </clause>

  <clause id="34870">
    <literal><![CDATA[
      L(x \ 1,y,z) \ L((1 * (x \ u)) / u,y,z) = a(x,L(x \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(2812(a,1),33296(a,1,2))].">
      <j1 rule="para" parents="2812 33296"/>
    </justification>
  </clause>

  <clause id="34871">
    <literal><![CDATA[
      L(x \ 1,y,z) \ L((x \ u) / u,y,z) = a(x,L(x \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(7(a,1),34870(a,1,2,1,1))].">
      <j1 rule="para" parents="7 34870"/>
    </justification>
  </clause>

  <clause id="34872">
    <literal><![CDATA[
      L(x \ 1,y,z) \ L((x \ u) / u,y,z) = a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32203,a(flip),b,34871,a),flip(a)].">
      <j1 rule="hyper" parents="373 32203 34871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34873">
    <literal><![CDATA[
      L((x \ 1) \ R(x \ 1,x,y),z,u) = a(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,4247,a,b,34872,a)].">
      <j1 rule="hyper" parents="64 4247 34872"/>
    </justification>
  </clause>

  <clause id="34874">
    <literal><![CDATA[
      L(x \ R(x,x,y),z,u) = a(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(2009(a,1),34873(a,1,1))].">
      <j1 rule="para" parents="2009 34873"/>
    </justification>
  </clause>

  <clause id="34875">
    <literal><![CDATA[
      L(x * (y / (x * y)),z,u) = a(x,L(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(3015(a,1),34874(a,1,1))].">
      <j1 rule="para" parents="3015 34874"/>
    </justification>
  </clause>

  <clause id="34876">
    <literal><![CDATA[
      a(x,L(x,y,z),u) * L(x,y,z) = L(R(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(34874(a,1),4250(a,1,1))].">
      <j1 rule="para" parents="34874 4250"/>
    </justification>
  </clause>

  <clause id="34877">
    <literal><![CDATA[
      a(x,L(x,y,z),u) = L(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(30058(a,1),34874(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30058 34874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34878">
    <literal><![CDATA[
      (x * y) * a(z,L(z,y,x),u) = x * (y * a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,34877,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="145 34877 18"/>
    </justification>
  </clause>

  <clause id="34879">
    <literal><![CDATA[
      L(a(x,x,y),x,z) = a(x,z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32205,a(flip),b,34877,a),flip(a)].">
      <j1 rule="hyper" parents="64 32205 34877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34880">
    <literal><![CDATA[
      L(a(x,L(x,y,z),u),w,x * u) = L(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(34877(a,2),30315(a,1,1))].">
      <j1 rule="para" parents="34877 30315"/>
    </justification>
  </clause>

  <clause id="34881">
    <literal><![CDATA[
      (x * y) * (z * a(x,L(x,x * y,z),y)) = ((1 / x) \ y) * z
    ]]></literal>
    <justification jstring="[para(34877(a,2),31405(a,1,2,2))].">
      <j1 rule="para" parents="34877 31405"/>
    </justification>
  </clause>

  <clause id="34883">
    <literal><![CDATA[
      a(x,L(x,x * y,z),y) \ ((x \ y) * z) = ((x \ 1) * y) * z
    ]]></literal>
    <justification jstring="[para(34877(a,2),33647(a,1,1))].">
      <j1 rule="para" parents="34877 33647"/>
    </justification>
  </clause>

  <clause id="34884">
    <literal><![CDATA[
      a(x,y,L(a(z,u,u \ 1) \ 1,w,v5)) = a(x,y,a(u,L(u,w,v5),z))
    ]]></literal>
    <justification jstring="[para(34877(a,2),33836(a,2,3))].">
      <j1 rule="para" parents="34877 33836"/>
    </justification>
  </clause>

  <clause id="34885">
    <literal><![CDATA[
      a(x,a(y,L(y,z,u),w),v5) = a(x,a(y,y,L(w,z,u)),v5)
    ]]></literal>
    <justification jstring="[para(34877(a,2),34479(a,2,2)),flip(a)].">
      <j1 rule="para" parents="34877 34479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34886">
    <literal><![CDATA[
      a(x,L(x,y,z),u) \ a((z * y) \ (a(x,x,u) \ (z * y)),y,z) = a(x,x,u) \ 1
    ]]></literal>
    <justification jstring="[para(34877(a,2),28799(a,1,1))].">
      <j1 rule="para" parents="34877 28799"/>
    </justification>
  </clause>

  <clause id="34887">
    <literal><![CDATA[
      a(x,L(x,y,z),u) \ K(x \ 1,x) = L(a(x,x,x * u),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(34877(a,2),34524(a,1,1))].">
      <j1 rule="para" parents="34877 34524"/>
    </justification>
  </clause>

  <clause id="34888">
    <literal><![CDATA[
      L(a(x,x,y),x,z) = a(z \ (x \ z),x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,32977,a,b,34879,a),flip(a)].">
      <j1 rule="hyper" parents="373 32977 34879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34889">
    <literal><![CDATA[
      L(x * (y / (x * y)),z,u) = a(x,L(x,z,u),x * T(y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27309,a,b,34875,a),flip(a)].">
      <j1 rule="hyper" parents="373 27309 34875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34890">
    <literal><![CDATA[
      x \ ((x * L(x,y,z)) * u) = L(R(x,x,u),y,z) * u
    ]]></literal>
    <justification jstring="[hyper(144,a,34876,a(flip),b,33279,a),flip(a)].">
      <j1 rule="hyper" parents="144 34876 33279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34891">
    <literal><![CDATA[
      a(x * (y * a(z,z,u)),z,z) = a(x * y,z,z)
    ]]></literal>
    <justification jstring="[para(34878(a,1),34032(a,1,1))].">
      <j1 rule="para" parents="34878 34032"/>
    </justification>
  </clause>

  <clause id="34892">
    <literal><![CDATA[
      a(x * L(y,z,z),z,z) = a(x * y,z,z)
    ]]></literal>
    <justification jstring="[para(1245(a,1),34891(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1245 34891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34893">
    <literal><![CDATA[
      a(x * (((y * y) \ z) * y),y,y) = a(x * (y \ T(z,y)),y,y)
    ]]></literal>
    <justification jstring="[para(1014(a,1),34892(a,1,1,2))].">
      <j1 rule="para" parents="1014 34892"/>
    </justification>
  </clause>

  <clause id="34894">
    <literal><![CDATA[
      L(a(x,L(x,y,z),u),w,x * u) = a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,34877,a,b,34880,a),flip(a)].">
      <j1 rule="hyper" parents="373 34877 34880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34895">
    <literal><![CDATA[
      a(x,L(x,x * y,z),y) \ a(a(x,L(x,x * y,z),y),a(x,L(x,x * y,z),y),(x \ y) * z) = (((x \ 1) * y) * z) / ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(142,a,34883,a(flip),b,30104,a),flip(a)].">
      <j1 rule="hyper" parents="142 34883 30104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34896">
    <literal><![CDATA[
      a(x * (y \ T(z,y)),y,y) = a(x * (z * y),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11959,a(flip),b,34893,a),flip(a)].">
      <j1 rule="hyper" parents="64 11959 34893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34898">
    <literal><![CDATA[
      a(x * (y \ z),y,y) = a(x * (z * y),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32437,a(flip),b,34896,a)].">
      <j1 rule="hyper" parents="64 32437 34896"/>
    </justification>
  </clause>

  <clause id="34900">
    <literal><![CDATA[
      a(x * (((y * y) * ((z * u) * w)) * R(u,z,w)),R(u,z,w),R(u,z,w)) = a(x * (T((y * y) * z,u) * w),R(u,z,w),R(u,z,w))
    ]]></literal>
    <justification jstring="[para(14113(a,1),34898(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14113 34898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34901">
    <literal><![CDATA[
      (x \ (a(x,L(x,y,z),u) \ 1)) * x = L(a(x,x,x * u),y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,28830,a(flip),b,34887,a)].">
      <j1 rule="hyper" parents="64 28830 34887"/>
    </justification>
  </clause>

  <clause id="34902">
    <literal><![CDATA[
      (x \ (a(x,L(x,y,z),u) \ 1)) * x = a(x,L(x,y,z),x * u) \ 1
    ]]></literal>
    <justification jstring="[para(34877(a,2),34901(a,2,1))].">
      <j1 rule="para" parents="34877 34901"/>
    </justification>
  </clause>

  <clause id="34903">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ y,x,a(z,u,w)) = L(y,a(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,24645,a(flip),b,33323,a),flip(a)].">
      <j1 rule="hyper" parents="373 24645 33323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34904">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) \ y = L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(42,a,29972,a,b,34903,a),flip(a)].">
      <j1 rule="hyper" parents="42 29972 34903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34905">
    <literal><![CDATA[
      x * a(x,a(x,y,z),u) = L(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,33550,a(flip),b,34904,a)].">
      <j1 rule="hyper" parents="64 33550 34904"/>
    </justification>
  </clause>

  <clause id="34906">
    <literal><![CDATA[
      a(x,a(x,y,z),u) * x = L(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,33549,a(flip),b,34904,a)].">
      <j1 rule="hyper" parents="64 33549 34904"/>
    </justification>
  </clause>

  <clause id="34907">
    <literal><![CDATA[
      x \ (a(y,z,u) \ (x * (y * a(y,z,u)))) = L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33333,a(flip),b,34904,a)].">
      <j1 rule="hyper" parents="64 33333 34904"/>
    </justification>
  </clause>

  <clause id="34908">
    <literal><![CDATA[
      L(x,a(x,y,z),u) \ x = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(40,a,5559,a,b,34904,a)].">
      <j1 rule="hyper" parents="40 5559 34904"/>
    </justification>
  </clause>

  <clause id="34909">
    <literal><![CDATA[
      L(x,a(x,y,z),u) / x = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(142,a,34904,a(flip),b,33549,a(flip))].">
      <j1 rule="hyper" parents="142 34904 33549"/>
    </justification>
  </clause>

  <clause id="34910">
    <literal><![CDATA[
      x \ L(x,a(x,y,z),u) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(139,a,34904,a(flip),b,33550,a(flip))].">
      <j1 rule="hyper" parents="139 34904 33550"/>
    </justification>
  </clause>

  <clause id="34911">
    <literal><![CDATA[
      (x * y) \ L(x * y,a(y,y,x),z) = a(x * y,a(x * y,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(139,a,30729,a(flip),b,34905,a)].">
      <j1 rule="hyper" parents="139 30729 34905"/>
    </justification>
  </clause>

  <clause id="34912">
    <literal><![CDATA[
      (x * y) \ (x * L(y,a(y,z,u),w)) = L(a(y,a(y,z,u),w),y,x)
    ]]></literal>
    <justification jstring="[para(34905(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="34905 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34913">
    <literal><![CDATA[
      L(1 / x,a(x,y,z),u) \ 1 = x * a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,34908,a(flip),b,31837,a),flip(a)].">
      <j1 rule="hyper" parents="145 34908 31837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34914">
    <literal><![CDATA[
      L(x * y,a(x * y,y,y),z) \ (x * y) = a(z,x * y,y \ (((x * y) \ x) \ 1))
    ]]></literal>
    <justification jstring="[para(30532(a,1),34908(a,2,3))].">
      <j1 rule="para" parents="30532 34908"/>
    </justification>
  </clause>

  <clause id="34915">
    <literal><![CDATA[
      (x * y) \ L(x * y,a(y,y,x),z) = a(x * y,a(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32896,a(flip),b,34911,a),flip(a)].">
      <j1 rule="hyper" parents="373 32896 34911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34916">
    <literal><![CDATA[
      a(x,y * z,z \ (((y * z) \ y) \ 1)) = L(y * z,a(y,z,z),x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(31824(a,1),34914(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31824 34914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34917">
    <literal><![CDATA[
      a(x,y * z,z \ ((y \ (z \ y)) \ 1)) = L(y * z,a(y,z,z),x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31584,a(flip),b,34916,a)].">
      <j1 rule="hyper" parents="64 31584 34916"/>
    </justification>
  </clause>

  <clause id="34918">
    <literal><![CDATA[
      x * L(((y * x) \ y) \ 1,(y * x) \ y,a(y,x,x \ 1)) = x / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(1223(a,1),33370(a,1,2))].">
      <j1 rule="para" parents="1223 33370"/>
    </justification>
  </clause>

  <clause id="34919">
    <literal><![CDATA[
      x * L(((y * x) \ y) \ 1,(y * x) \ y,a(y,x,x)) = x / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(33635(a,1),34918(a,1,2))].">
      <j1 rule="para" parents="33635 34918"/>
    </justification>
  </clause>

  <clause id="34920">
    <literal><![CDATA[
      x * L(((y * x) \ y) \ 1,y \ (x \ y),a(y,x,x)) = x / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(29687(a,1),34919(a,1,2))].">
      <j1 rule="para" parents="29687 34919"/>
    </justification>
  </clause>

  <clause id="34921">
    <literal><![CDATA[
      L(a(x,y,y) \ a(L(x,z,u),y,y),a(y,y,x * y),z) = a(L(a(x,y,y),z,u),z,u)
    ]]></literal>
    <justification jstring="[para(32595(a,2),33412(a,1,1,2))].">
      <j1 rule="para" parents="32595 33412"/>
    </justification>
  </clause>

  <clause id="34922">
    <literal><![CDATA[
      L(x * a(y,x,z * K(x,z)),z * K(x,z),y) = K(z,x) * ((y * z) \ ((y * x) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,24525,a(flip),b,33460,a),flip(a)].">
      <j1 rule="hyper" parents="373 24525 33460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34923">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,w),w,a(y,z,u)) = L(K(w,a(y,z,u)) * x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,10985,a(flip),b,33461,a),flip(a)].">
      <j1 rule="hyper" parents="373 10985 33461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34924">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,w),w,a(y,z,u)) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(23104(a,1),34923(a,2,1))].">
      <j1 rule="para" parents="23104 34923"/>
    </justification>
  </clause>

  <clause id="34925">
    <literal><![CDATA[
      L(a(a(x,y,z),u,w) * u,w,a(x,y,z)) = L(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(24736,a,34924,a)].">
      <j1 rule="hyper" parents="24736 34924"/>
    </justification>
  </clause>

  <clause id="34927">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ y = a(a(z,u,w),y,x) * y
    ]]></literal>
    <justification jstring="[hyper(42,a,34903,a,b,34925,a)].">
      <j1 rule="hyper" parents="42 34903 34925"/>
    </justification>
  </clause>

  <clause id="34928">
    <literal><![CDATA[
      a(a(x,y,z),z,u) * z = L(z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(42,a,33252,a,b,34925,a),flip(a)].">
      <j1 rule="hyper" parents="42 33252 34925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34929">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * x = L(x,a(y,z,x),u)
    ]]></literal>
    <justification jstring="[para(33522(a,1),34928(a,1,1))].">
      <j1 rule="para" parents="33522 34928"/>
    </justification>
  </clause>

  <clause id="34930">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * L(y,a(z,u,y),x) = y
    ]]></literal>
    <justification jstring="[hyper(145,a,34928,a(flip),b,34927,a)].">
      <j1 rule="hyper" parents="145 34928 34927"/>
    </justification>
  </clause>

  <clause id="34931">
    <literal><![CDATA[
      L(x,a(y,z,x),u) \ x = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,5548,a,b,34930,a)].">
      <j1 rule="hyper" parents="36 5548 34930"/>
    </justification>
  </clause>

  <clause id="34932">
    <literal><![CDATA[
      L(x,y,(z * L(u,w,v5)) * L(v6,v6,z * L(u,w,v5))) = L(x,y,v6 \ (z * R(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,33610,a(flip),b,33582,a)].">
      <j1 rule="hyper" parents="64 33610 33582"/>
    </justification>
  </clause>

  <clause id="34933">
    <literal><![CDATA[
      a(L(x,x,L(y,z,u) * w) * (L(y,z,u) * w),v5,v6) = a(x \ (R(y,z,u) * w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,34659,a(flip),b,33588,a)].">
      <j1 rule="hyper" parents="64 34659 33588"/>
    </justification>
  </clause>

  <clause id="34934">
    <literal><![CDATA[
      (x / (y / x)) \ R(x / (y / x),z,u) = ((y \ x) * x) \ R((y \ x) * x,z,u)
    ]]></literal>
    <justification jstring="[para(34301(a,1),34310(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="34301 34310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34935">
    <literal><![CDATA[
      ((x \ y) * y) \ R((x \ y) * y,z,u) = (x / y) \ (y * R(y \ (x / y),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26012,a(flip),b,34934,a),flip(a)].">
      <j1 rule="hyper" parents="64 26012 34934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34936">
    <literal><![CDATA[
      ((x \ y) * y) \ R((x \ y) * y,z,u) = (x / y) \ (R(x,z,u) / y)
    ]]></literal>
    <justification jstring="[para(2115(a,1),34935(a,2,2))].">
      <j1 rule="para" parents="2115 34935"/>
    </justification>
  </clause>

  <clause id="34937">
    <literal><![CDATA[
      ((x \ y) * y) \ R((x \ y) * y,z,u) = (y \ x) \ (y \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27064,a(flip),b,34936,a),flip(a)].">
      <j1 rule="hyper" parents="373 27064 34936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34938">
    <literal><![CDATA[
      (x * (y \ x)) \ R(x * (y \ x),z,u) = (x \ y) \ (x \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26003,a,b,34937,a)].">
      <j1 rule="hyper" parents="64 26003 34937"/>
    </justification>
  </clause>

  <clause id="34939">
    <literal><![CDATA[
      L(x \ R(x,y,z),x \ u,x \ u) = (u \ x) \ (u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,34494,a,b,34938,a)].">
      <j1 rule="hyper" parents="64 34494 34938"/>
    </justification>
  </clause>

  <clause id="34940">
    <literal><![CDATA[
      L(x \ R(x,y,z),x \ u,u) = (u \ x) \ (u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,28067,a,b,34938,a)].">
      <j1 rule="hyper" parents="64 28067 34938"/>
    </justification>
  </clause>

  <clause id="34941">
    <literal><![CDATA[
      (a(x,y,z) \ z) \ (a(x,y,z) \ R(z,u,w)) = z \ R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33525,a(flip),b,34940,a),flip(a)].">
      <j1 rule="hyper" parents="64 33525 34940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34942">
    <literal><![CDATA[
      L((x \ y) \ (x \ R(y,z,u)),y,z * u) = L(a(y,z,u),y \ x,x)
    ]]></literal>
    <justification jstring="[para(34940(a,1),16033(a,1,1))].">
      <j1 rule="para" parents="34940 16033"/>
    </justification>
  </clause>

  <clause id="34943">
    <literal><![CDATA[
      a(((1 / x) \ L(T(y,x),z,u)) * w,v5,v6) = a(((1 / x) \ R(y,z,u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(24613(a,1),34662(a,1,1,1))].">
      <j1 rule="para" parents="24613 34662"/>
    </justification>
  </clause>

  <clause id="34944">
    <literal><![CDATA[
      a(((1 / x) \ R(y,z,u)) * w,v5,v6) = a(w * ((1 / x) \ L(y,z,u)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32530,a(flip),b,34943,a),flip(a)].">
      <j1 rule="hyper" parents="64 32530 34943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34946">
    <literal><![CDATA[
      a(((1 / x) \ R(y,z,u)) * w,v5,v6) = a((x \ L(y,z,u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32812,a(flip),b,34944,a),flip(a)].">
      <j1 rule="hyper" parents="373 32812 34944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34947">
    <literal><![CDATA[
      a((x \ L(y,z,u)) * w,v5,v6) = a(w * (x \ R(y,z,u)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32813,a(flip),b,34946,a),flip(a)].">
      <j1 rule="hyper" parents="64 32813 34946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34948">
    <literal><![CDATA[
      a(x * (y \ R(z,u,w)),v5,v6) = a(x * (y \ L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26847,a,34947,a),flip(a)].">
      <j1 rule="hyper" parents="26847 34947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34949">
    <literal><![CDATA[
      a((x \ R(y,z,u)) * w,v5,v6) = a((x \ L(y,z,u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,34947,a)].">
      <j1 rule="hyper" parents="373 26787 34947"/>
    </justification>
  </clause>

  <clause id="34951">
    <literal><![CDATA[
      a(x * (y \ ((z * u) * u)),w,v5) = a(x * (y \ L(z,u,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32938,a,b,34948,a)].">
      <j1 rule="hyper" parents="64 32938 34948"/>
    </justification>
  </clause>

  <clause id="34952">
    <literal><![CDATA[
      a(R(x,y,z) * (x \ L(x,y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2670,a(flip),b,34948,a),flip(a)].">
      <j1 rule="hyper" parents="64 2670 34948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34953">
    <literal><![CDATA[
      a(L(R(x,y,z),y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(33431(a,1),34952(a,1,1))].">
      <j1 rule="para" parents="33431 34952"/>
    </justification>
  </clause>

  <clause id="34954">
    <literal><![CDATA[
      a(L(L(x,y,z),y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32711,a(flip),b,34953,a)].">
      <j1 rule="hyper" parents="64 32711 34953"/>
    </justification>
  </clause>

  <clause id="34955">
    <literal><![CDATA[
      a(x,y,z) = L(L(x,y,z) \ R(L(x,y,z),y,z),L(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,33411,a,b,34954,a),flip(a)].">
      <j1 rule="hyper" parents="64 33411 34954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34956">
    <literal><![CDATA[
      L(L(L(x,y,z) \ R(L(x,y,z),u,w),y,z),L(L(x,y,z),y,z),w * u) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,23991,a,b,34954,a)].">
      <j1 rule="hyper" parents="64 23991 34954"/>
    </justification>
  </clause>

  <clause id="34957">
    <literal><![CDATA[
      a(L(x \ y,z,z \ x),u,w) = a(z \ ((x / z) \ y),u,w)
    ]]></literal>
    <justification jstring="[para(11079(a,1),34954(a,1,1))].">
      <j1 rule="para" parents="11079 34954"/>
    </justification>
  </clause>

  <clause id="34958">
    <literal><![CDATA[
      a(L(T((x * (y \ 1)) \ z,u),y,x),w,v5) = a(T((y \ 1) \ (x \ z),u),w,v5)
    ]]></literal>
    <justification jstring="[para(11810(a,1),34954(a,1,1,1))].">
      <j1 rule="para" parents="11810 34954"/>
    </justification>
  </clause>

  <clause id="34959">
    <literal><![CDATA[
      x * (y * a(L(z,y,x),u,u)) = (x * y) * a(z,u,u)
    ]]></literal>
    <justification jstring="[para(34954(a,1),32608(a,1,2)),flip(a)].">
      <j1 rule="para" parents="34954 32608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34960">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,u)) = y * a(L(z,y,x),u,u)
    ]]></literal>
    <justification jstring="[hyper(149,a,34959,a)].">
      <j1 rule="hyper" parents="149 34959"/>
    </justification>
  </clause>

  <clause id="34962">
    <literal><![CDATA[
      x \ ((x * y) * a(y,z,z)) = a(y,a(y,z,z),x) * R(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,33539,a,b,34960,a),flip(a)].">
      <j1 rule="hyper" parents="373 33539 34960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34963">
    <literal><![CDATA[
      a(L(x \ y,z,z \ x),u,w) = a(z \ ((z \ x) \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32495,a(flip),b,34957,a),flip(a)].">
      <j1 rule="hyper" parents="373 32495 34957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34964">
    <literal><![CDATA[
      a((x \ L(y,z,u)) * ((w * v5) * a(x \ R(y,z,u),w,v5)),v6,v7) = a(((x \ R(y,z,u)) * w) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(29951(a,1),34949(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29951 34949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34965">
    <literal><![CDATA[
      x \ ((x * y) * a(y,z,z)) = a(y,a(y,z,z),x) * (y * a(y,z,z))
    ]]></literal>
    <justification jstring="[para(15984(a,2),34962(a,2,2))].">
      <j1 rule="para" parents="15984 34962"/>
    </justification>
  </clause>

  <clause id="34966">
    <literal><![CDATA[
      a(x,a(x,y,y),z) = a(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,30021,a(flip),b,34965,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 30021 34965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34967">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * u = u * a(y,a(y,z,z),x)
    ]]></literal>
    <justification jstring="[hyper(145,a,34966,a,b,23174,a),flip(a)].">
      <j1 rule="hyper" parents="145 34966 23174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34968">
    <literal><![CDATA[
      a(x,a(y,y,x),z) = a(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32897,a,b,34966,a)].">
      <j1 rule="hyper" parents="64 32897 34966"/>
    </justification>
  </clause>

  <clause id="34969">
    <literal><![CDATA[
      a(x,y * z,a(y * z,z,z)) = a(y * z,a(z,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32896,a(flip),b,34966,a),flip(a)].">
      <j1 rule="hyper" parents="64 32896 34966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34970">
    <literal><![CDATA[
      a(x,y \ z,a(y \ z,y,y)) = a(y \ z,a(y,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32889,a(flip),b,34966,a),flip(a)].">
      <j1 rule="hyper" parents="64 32889 34966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34971">
    <literal><![CDATA[
      a(x,y * z,a(y * z,y,y)) = a(y * z,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32894,a(flip),b,34968,a),flip(a)].">
      <j1 rule="hyper" parents="64 32894 34968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34972">
    <literal><![CDATA[
      a(x,y \ z,a(y * z,y,y)) = a(y \ z,a(y,y,z),x)
    ]]></literal>
    <justification jstring="[para(30543(a,1),34970(a,1,3))].">
      <j1 rule="para" parents="30543 34970"/>
    </justification>
  </clause>

  <clause id="34973">
    <literal><![CDATA[
      a(T((x \ 1) \ (y \ z),u),w,v5) = a(L((y * (x \ 1)) \ z,x,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26792,a(flip),b,34958,a),flip(a)].">
      <j1 rule="hyper" parents="64 26792 34958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34975">
    <literal><![CDATA[
      a(T((x \ 1) \ (y \ z),u),w,v5) = a(L((x * y) \ z,x,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,34262,a(flip),b,34973,a),flip(a)].">
      <j1 rule="hyper" parents="373 34262 34973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34976">
    <literal><![CDATA[
      a(L((x * y) \ z,x,y),u,w) = a((x \ 1) \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(26780,a,34975,a),flip(a)].">
      <j1 rule="hyper" parents="26780 34975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34977">
    <literal><![CDATA[
      a(L((x * y) \ z,x,y),u,w) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2675,a(flip),b,34976,a),flip(a)].">
      <j1 rule="hyper" parents="373 2675 34976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34978">
    <literal><![CDATA[
      a(L(x \ y,x / z,z),u,w) = a((x / z) \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(12(a,1),34977(a,1,1,1,1))].">
      <j1 rule="para" parents="12 34977"/>
    </justification>
  </clause>

  <clause id="34979">
    <literal><![CDATA[
      a(L(L(T(x,y),y,z),z,y),u,w) = a(z \ (y \ (z * (x * y))),u,w)
    ]]></literal>
    <justification jstring="[para(262(a,1),34977(a,1,1,1))].">
      <j1 rule="para" parents="262 34977"/>
    </justification>
  </clause>

  <clause id="34980">
    <literal><![CDATA[
      a(L(x \ y,z \ x,z),u,w) = a((x / z) \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(10996(a,1),34978(a,1,1))].">
      <j1 rule="para" parents="10996 34978"/>
    </justification>
  </clause>

  <clause id="34981">
    <literal><![CDATA[
      a(x \ (y \ (x * (z * y))),u,w) = a(L(L(z,y,x),x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26862,a(flip),b,34979,a),flip(a)].">
      <j1 rule="hyper" parents="64 26862 34979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34985">
    <literal><![CDATA[
      K(x,y) * ((z * u) * T(u \ K(u,z),K(x,y))) = (K(x,T(y,u)) * (u * z)) * (u \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,23073,a(flip),b,34698,a)].">
      <j1 rule="hyper" parents="64 23073 34698"/>
    </justification>
  </clause>

  <clause id="34986">
    <literal><![CDATA[
      ((T(x,y * T(z,u * w)) * v5) * v6) / ((x * v5) * v6) = K(x,y * T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(114(a,1),34704(a,1,1,1,1,2,2,2,2))].">
      <j1 rule="para" parents="114 34704"/>
    </justification>
  </clause>

  <clause id="34987">
    <literal><![CDATA[
      K(x,y * T(T(z,u),w)) = K(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,23656,a(flip),b,34986,a),flip(a)].">
      <j1 rule="hyper" parents="64 23656 34986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34988">
    <literal><![CDATA[
      K(x,y * T(T(z,z * u),w * v5)) = K(x,y * T(z,w * (u * v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,26941,a(flip),b,34987,a),flip(a)].">
      <j1 rule="hyper" parents="373 26941 34987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34989">
    <literal><![CDATA[
      K(x,y * T(T(z,u),w * v5)) = K(x,y * T(z,v5 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,25023,a(flip),b,34987,a),flip(a)].">
      <j1 rule="hyper" parents="373 25023 34987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34990">
    <literal><![CDATA[
      K(x,y * T(T((T(z,u) \ w) \ w,v5),z)) = K(x,y * T(T(z,u),(z \ w) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,18660,a,b,34987,a)].">
      <j1 rule="hyper" parents="64 18660 34987"/>
    </justification>
  </clause>

  <clause id="34991">
    <literal><![CDATA[
      K(x,y * T(z,u * ((z \ w) * v5))) = K(x,y * T(T(z,v5 * u),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13437,a(flip),b,34989,a),flip(a)].">
      <j1 rule="hyper" parents="64 13437 34989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34992">
    <literal><![CDATA[
      K(x,y * T(T(T(z,z * u),w),v5)) = K(x,y * T(z,w * (u * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,34987,a,b,34988,a)].">
      <j1 rule="hyper" parents="64 34987 34988"/>
    </justification>
  </clause>

  <clause id="34993">
    <literal><![CDATA[
      K(x,y * T(z,u * ((z \ w) * v5))) = K(x,y * T(z,(v5 * u) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,34987,a(flip),b,34991,a),flip(a)].">
      <j1 rule="hyper" parents="373 34987 34991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34994">
    <literal><![CDATA[
      K(x,y * T(T((T(z,u) \ w) \ w,v5),z)) = K(x,y * T(z,u * ((z \ w) * v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,34987,a(flip),b,34990,a),flip(a)].">
      <j1 rule="hyper" parents="373 34987 34990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34995">
    <literal><![CDATA[
      K(x,y * T(T((T(z,u) \ w) \ w,v5),z)) = K(x,y * T(z,(v5 * u) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,34993,a(flip),b,34994,a),flip(a)].">
      <j1 rule="hyper" parents="373 34993 34994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="34996">
    <literal><![CDATA[
      K(x,y * T((T(z,u) \ w) \ w,v5 * z)) = K(x,y * T(z,(v5 * u) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,34987,a(flip),b,34995,a)].">
      <j1 rule="hyper" parents="64 34987 34995"/>
    </justification>
  </clause>

  <clause id="34997">
    <literal><![CDATA[
      K(x,y * T(T(T(z,u),w * z),v5)) = K(x,y * T(z,(w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,13436,a(flip),b,34996,a)].">
      <j1 rule="hyper" parents="64 13436 34996"/>
    </justification>
  </clause>

  <clause id="34998">
    <literal><![CDATA[
      K(x,y * T(T(T(z,z * u),w),v5)) = K(x,y * T(z,(u * T(v5,v6)) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,18207,a(flip),b,34997,a)].">
      <j1 rule="hyper" parents="64 18207 34997"/>
    </justification>
  </clause>

  <clause id="34999">
    <literal><![CDATA[
      K(x,y * T(z,(u * T(w,v5)) * v6)) = K(x,y * T(z,v6 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,34992,a(flip),b,34998,a),flip(a)].">
      <j1 rule="hyper" parents="64 34992 34998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35000">
    <literal><![CDATA[
      K(x,y * T(z,u * (w * T(v5,v6)))) = K(x,y * T(z,w * (u * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,25024,a(flip),b,34999,a)].">
      <j1 rule="hyper" parents="64 25024 34999"/>
    </justification>
  </clause>

  <clause id="35001">
    <literal><![CDATA[
      K(x,y * T(z,u * (w \ v5))) = K(x,y * T(z,u * (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,28942,a(flip),b,35000,a)].">
      <j1 rule="hyper" parents="64 28942 35000"/>
    </justification>
  </clause>

  <clause id="35002">
    <literal><![CDATA[
      K(x,T(y,T((z \ u) * w,v5)) * v6) = K(x,T(v6,y) * T(y,w * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18145,a,b,35001,a)].">
      <j1 rule="hyper" parents="64 18145 35001"/>
    </justification>
  </clause>

  <clause id="35003">
    <literal><![CDATA[
      K(x,T(y,T((z \ u) * w,v5)) * v6) = K(x,T(y,w * (u * z)) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,18035,a(flip),b,35002,a),flip(a)].">
      <j1 rule="hyper" parents="373 18035 35002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35004">
    <literal><![CDATA[
      K(x,T(y,z * (u \ w)) * v5) = K(x,T(y,z * (w * u)) * v5)
    ]]></literal>
    <justification jstring="[para(11103(a,1),35003(a,1,2,1))].">
      <j1 rule="para" parents="11103 35003"/>
    </justification>
  </clause>

  <clause id="35005">
    <literal><![CDATA[
      (x * R(x \ ((y * y) * 1),z,u)) / w = (y * y) * ((x \ R(x,z,u)) / w)
    ]]></literal>
    <justification jstring="[para(1460(a,1),34715(a,1,1,2,1))].">
      <j1 rule="para" parents="1460 34715"/>
    </justification>
  </clause>

  <clause id="35006">
    <literal><![CDATA[
      (x * R(x \ (y * y),z,u)) / w = (y * y) * ((x \ R(x,z,u)) / w)
    ]]></literal>
    <justification jstring="[para(8(a,1),35005(a,1,1,2,1,2))].">
      <j1 rule="para" parents="8 35005"/>
    </justification>
  </clause>

  <clause id="35007">
    <literal><![CDATA[
      (x * x) * ((y \ R(y,z,u)) / (((y * R(y \ (x * x),z,u)) / (w \ 1)) / w)) = a(y * R(y \ (x * x),z,u),w,w \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,33234,a(flip),b,35006,a),flip(a)].">
      <j1 rule="hyper" parents="64 33234 35006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35008">
    <literal><![CDATA[
      T(x * ((y / (x * y)) * ((x \ y) / y)),K(x,z)) = (x * (y / (x * y))) * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(4849(a,1),34733(a,1,1,2))].">
      <j1 rule="para" parents="4849 34733"/>
    </justification>
  </clause>

  <clause id="35009">
    <literal><![CDATA[
      a(x,R(y,z,u),x * y) = a(x,y,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(959,a,34756,a),flip(a)].">
      <j1 rule="hyper" parents="959 34756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35010">
    <literal><![CDATA[
      a(x,L(y,z,u),x * y) = a(x,y,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,32197,a(flip),b,35009,a)].">
      <j1 rule="hyper" parents="64 32197 35009"/>
    </justification>
  </clause>

  <clause id="35011">
    <literal><![CDATA[
      L(R(x,y,R(T(x,z),u,w)),y,R(x,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,11,a(flip),b,34757,a),flip(a)].">
      <j1 rule="hyper" parents="373 11 34757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35013">
    <literal><![CDATA[
      L(R(x,y,R(x,z,u)),y,R(x,z,u)) = x
    ]]></literal>
    <justification jstring="[para(114(a,1),35011(a,1,1,3,1))].">
      <j1 rule="para" parents="114 35011"/>
    </justification>
  </clause>

  <clause id="35014">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,z,u)) = x
    ]]></literal>
    <justification jstring="[para(11593(a,1),35013(a,1,1))].">
      <j1 rule="para" parents="11593 35013"/>
    </justification>
  </clause>

  <clause id="35015">
    <literal><![CDATA[
      L(x,y,R(x,z,u)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(35014(a,1),4739(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35014 4739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35017">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29221,a(flip),b,35015,a)].">
      <j1 rule="hyper" parents="64 29221 35015"/>
    </justification>
  </clause>

  <clause id="35018">
    <literal><![CDATA[
      L(x,y,(x * z) \ z) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24855,a(flip),b,35015,a)].">
      <j1 rule="hyper" parents="64 24855 35015"/>
    </justification>
  </clause>

  <clause id="35019">
    <literal><![CDATA[
      L(x,x,L(x,y,z)) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,818,a(flip),b,35017,a),flip(a)].">
      <j1 rule="hyper" parents="373 818 35017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35020">
    <literal><![CDATA[
      L(x \ y,z,y \ x) = L(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26065,a(flip),b,35017,a)].">
      <j1 rule="hyper" parents="64 26065 35017"/>
    </justification>
  </clause>

  <clause id="35021">
    <literal><![CDATA[
      L(x \ y,z,x \ y) = L(x \ y,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2198,a(flip),b,35017,a),flip(a)].">
      <j1 rule="hyper" parents="64 2198 35017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35022">
    <literal><![CDATA[
      L(R(x,y,z),u,L(x,w,v5)) = R(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(35017(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35017 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35023">
    <literal><![CDATA[
      L(L(x,y,z),u,L(x,w,v5)) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(35017(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35017 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35024">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),L(x,u,w)) = L(L(x,L(x,y,z),x),u,w) \ L(x,u,w)
    ]]></literal>
    <justification jstring="[para(35017(a,1),1246(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="35017 1246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35025">
    <literal><![CDATA[
      L(x,y,z \ (x \ z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13011,a(flip),b,35018,a)].">
      <j1 rule="hyper" parents="64 13011 35018"/>
    </justification>
  </clause>

  <clause id="35026">
    <literal><![CDATA[
      L(L(x,y,z),x,L(x,u,w)) = L(1 / (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(35019(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35019 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35027">
    <literal><![CDATA[
      L(x,y \ (x \ y),z \ (x \ z)) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,11396,a(flip),b,35025,a),flip(a)].">
      <j1 rule="hyper" parents="373 11396 35025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35028">
    <literal><![CDATA[
      L(a(x,y,z),u,(T(z,w) * (x * y)) \ (L(T(z,w),y,x) * (x * y))) = L(a(x,y,z),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(27356(a,1),35025(a,1,3,2))].">
      <j1 rule="para" parents="27356 35025"/>
    </justification>
  </clause>

  <clause id="35029">
    <literal><![CDATA[
      L(x \ (y \ x),z,x \ (y \ x)) = L(x \ (y \ x),z,y)
    ]]></literal>
    <justification jstring="[hyper(24200,a,35020,a),flip(a)].">
      <j1 rule="hyper" parents="24200 35020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35030">
    <literal><![CDATA[
      L(x \ y,z,y \ x) = L(x \ y,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,35020,a,b,35021,a)].">
      <j1 rule="hyper" parents="64 35020 35021"/>
    </justification>
  </clause>

  <clause id="35031">
    <literal><![CDATA[
      L(x \ y,y * x,y * x) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,13724,a(flip),b,35021,a),flip(a)].">
      <j1 rule="hyper" parents="64 13724 35021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35032">
    <literal><![CDATA[
      a(x \ L(y \ z,u,z * y),w,v5) = a(x \ (y \ z),w,v5)
    ]]></literal>
    <justification jstring="[para(35021(a,1),13234(a,1,1,2))].">
      <j1 rule="para" parents="35021 13234"/>
    </justification>
  </clause>

  <clause id="35033">
    <literal><![CDATA[
      L(R(x,y,z),u,L(x,w,v5)) = L(R(x,y,z),u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,29,a(flip),b,35022,a),flip(a)].">
      <j1 rule="hyper" parents="373 29 35022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35034">
    <literal><![CDATA[
      L(L(x,y,z),u,L(x,w,v5)) = L(L(x,y,z),u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,30,a,b,35023,a),flip(a)].">
      <j1 rule="hyper" parents="373 30 35023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35035">
    <literal><![CDATA[
      R(x,y,z * L(L(u,w,u),v5,v6)) = R(x,y,z * L(u,v5,v6))
    ]]></literal>
    <justification jstring="[para(35023(a,1),13898(a,1,3,2))].">
      <j1 rule="para" parents="35023 13898"/>
    </justification>
  </clause>

  <clause id="35036">
    <literal><![CDATA[
      L(R(x,y,z),u,R(x,w,v5)) = L(R(x,y,z),u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29203,a,b,35033,a)].">
      <j1 rule="hyper" parents="64 29203 35033"/>
    </justification>
  </clause>

  <clause id="35037">
    <literal><![CDATA[
      L(x,L(L(y,z,u),w,y),v5) = L(x,L(y,z,u),v5)
    ]]></literal>
    <justification jstring="[para(35034(a,1),14160(a,1,2))].">
      <j1 rule="para" parents="35034 14160"/>
    </justification>
  </clause>

  <clause id="35038">
    <literal><![CDATA[
      ((x * (y * R(x,z,u))) / x) / y = L(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25099,a(flip),b,35036,a)].">
      <j1 rule="hyper" parents="64 25099 35036"/>
    </justification>
  </clause>

  <clause id="35039">
    <literal><![CDATA[
      (R(x,y,z) \ u) * a(x,w,x) = L(R(x,y,z),w,x) \ u
    ]]></literal>
    <justification jstring="[para(35036(a,1),12910(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35036 12910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35040">
    <literal><![CDATA[
      1 / L(1 / (1 / x),y,z) = x / (x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(35026(a,1),11402(a,1,2))].">
      <j1 rule="para" parents="35026 11402"/>
    </justification>
  </clause>

  <clause id="35041">
    <literal><![CDATA[
      (x \ 1) / ((x \ 1) * L(x \ 1,y,z)) = 1 / L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(79(a,1),35040(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 35040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35044">
    <literal><![CDATA[
      (((x * (x * R(x,y,z))) / x) / x) \ ((x \ 1) * u) = (x * (x * R(x,y,z))) \ ((1 / (1 / x)) * u)
    ]]></literal>
    <justification jstring="[para(35038(a,2),2474(a,2,1)),flip(a)].">
      <j1 rule="para" parents="35038 2474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35045">
    <literal><![CDATA[
      L(x,y,L(z \ (u \ z),w,u)) = L(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[para(35029(a,1),12978(a,1,3))].">
      <j1 rule="para" parents="35029 12978"/>
    </justification>
  </clause>

  <clause id="35046">
    <literal><![CDATA[
      a(x,y,L(z \ (u \ z),w,u)) = a(x,y,z \ (u \ z))
    ]]></literal>
    <justification jstring="[para(35029(a,1),13865(a,1,3))].">
      <j1 rule="para" parents="35029 13865"/>
    </justification>
  </clause>

  <clause id="35047">
    <literal><![CDATA[
      L(x,L(y \ (z \ y),u,z),w) = L(x,y \ (z \ y),w)
    ]]></literal>
    <justification jstring="[para(35029(a,1),14160(a,1,2))].">
      <j1 rule="para" parents="35029 14160"/>
    </justification>
  </clause>

  <clause id="35048">
    <literal><![CDATA[
      L(x,y,L(z,z,u)) = L(x,y,u \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29208,a(flip),b,35045,a)].">
      <j1 rule="hyper" parents="64 29208 35045"/>
    </justification>
  </clause>

  <clause id="35050">
    <literal><![CDATA[
      L(x,L(y,y,z),L(u,u,w)) = L(x,z \ (y \ z),w \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,29726,a(flip),b,35048,a),flip(a)].">
      <j1 rule="hyper" parents="373 29726 35048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35051">
    <literal><![CDATA[
      L(x,y,L(z * u,z * u,z)) = L(x,y,L(u,z,z) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29151,a(flip),b,35048,a),flip(a)].">
      <j1 rule="hyper" parents="373 29151 35048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35052">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) / y) * z) = L(y \ z,y,L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,11070,a(flip),b,35048,a)].">
      <j1 rule="hyper" parents="373 11070 35048"/>
    </justification>
  </clause>

  <clause id="35053">
    <literal><![CDATA[
      L(x,y,L(z * u,z * u,R(z,u,u \ 1))) = L(x,y,R(z,u,u \ 1) \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(482(a,1),35048(a,2,3,2))].">
      <j1 rule="para" parents="482 35048"/>
    </justification>
  </clause>

  <clause id="35054">
    <literal><![CDATA[
      (x / (x * y)) * ((x * y) * z) = x * L(z,x * y,L(y,y,x))
    ]]></literal>
    <justification jstring="[para(35048(a,2),29152(a,1,2)),flip(a)].">
      <j1 rule="para" parents="35048 29152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35055">
    <literal><![CDATA[
      L(x,L(y \ (z \ y),u,z),w) = L(x,L(z,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29726,a,b,35047,a),flip(a)].">
      <j1 rule="hyper" parents="373 29726 35047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35056">
    <literal><![CDATA[
      a(x,y,x) \ (L(R(x,z,u),y,x) \ w) = R(x,z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(23920,a,35039,a)].">
      <j1 rule="hyper" parents="23920 35039"/>
    </justification>
  </clause>

  <clause id="35057">
    <literal><![CDATA[
      L(R(x,y,z),u,x) \ (a(x,u,x) \ w) = R(x,y,z) \ w
    ]]></literal>
    <justification jstring="[hyper(13268,a,35039,a),flip(a)].">
      <j1 rule="hyper" parents="13268 35039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35059">
    <literal><![CDATA[
      L(x \ y,x,L(y,y,x)) = ((1 / y) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,30413,a(flip),b,35052,a),flip(a)].">
      <j1 rule="hyper" parents="64 30413 35052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35060">
    <literal><![CDATA[
      a(x,x,y) / (((1 / x) * y) \ 1) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(35059(a,1),31036(a,1,2))].">
      <j1 rule="para" parents="35059 31036"/>
    </justification>
  </clause>

  <clause id="35061">
    <literal><![CDATA[
      (1 / ((1 / x) * y)) \ a(x,x,y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,24641,a(flip),b,35060,a)].">
      <j1 rule="hyper" parents="64 24641 35060"/>
    </justification>
  </clause>

  <clause id="35062">
    <literal><![CDATA[
      a(x,x,x) \ L(L(y,R(x,z,u),x),x * R(x,z,u),x) = R(x,z,u) \ L(R(x,z,u) * y,x,x)
    ]]></literal>
    <justification jstring="[para(2290(a,1),35056(a,1,2))].">
      <j1 rule="para" parents="2290 35056"/>
    </justification>
  </clause>

  <clause id="35063">
    <literal><![CDATA[
      L(R(x,y,z),x,x) \ ((x \ 1) * (x * u)) = R(x,y,z) \ L(u,x,x)
    ]]></literal>
    <justification jstring="[para(3693(a,1),35057(a,1,2))].">
      <j1 rule="para" parents="3693 35057"/>
    </justification>
  </clause>

  <clause id="35064">
    <literal><![CDATA[
      (x \ 1) / (x \ L(1 / x,y,z)) = 1 / L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1391(a,1),35041(a,1,2))].">
      <j1 rule="para" parents="1391 35041"/>
    </justification>
  </clause>

  <clause id="35065">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),L(x,u,w)) = L(L(x,x,x),u,w) \ L(x,u,w)
    ]]></literal>
    <justification jstring="[para(13718(a,1),35024(a,2,1,1))].">
      <j1 rule="para" parents="13718 35024"/>
    </justification>
  </clause>

  <clause id="35066">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),L(x,u,w)) = L(x,u,w) \ L(R(x,x,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,13636,a(flip),b,35065,a),flip(a)].">
      <j1 rule="hyper" parents="373 13636 35065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35068">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),L(x,u,w)) = L(x,u,w) * (1 / L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,28910,a(flip),b,35066,a),flip(a)].">
      <j1 rule="hyper" parents="373 28910 35066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35069">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),L(x,u,w)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,5398,a(flip),b,35068,a),flip(a)].">
      <j1 rule="hyper" parents="373 5398 35068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35071">
    <literal><![CDATA[
      a(L(x,y,z),R(x,y,z),L(x,u,w)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,32197,a,b,35069,a)].">
      <j1 rule="hyper" parents="64 32197 35069"/>
    </justification>
  </clause>

  <clause id="35072">
    <literal><![CDATA[
      (R(x,y,z) \ K(x,x \ 1)) * L(x,u,w) = R(x,y,z) \ L(x,u,w)
    ]]></literal>
    <justification jstring="[para(35071(a,1),32604(a,1,1,2))].">
      <j1 rule="para" parents="35071 32604"/>
    </justification>
  </clause>

  <clause id="35073">
    <literal><![CDATA[
      (1 / R(x,y,z)) * L(x,u,w) = R(x,y,z) \ L(x,u,w)
    ]]></literal>
    <justification jstring="[para(3760(a,1),35072(a,1,1))].">
      <j1 rule="para" parents="3760 35072"/>
    </justification>
  </clause>

  <clause id="35074">
    <literal><![CDATA[
      L(1 / L(x,y,z),1 / R(x,u,w),R(x,u,w) \ L(x,y,z)) \ 1 = (1 / ((1 / R(x,u,w)) * (L(x,y,z) \ 1))) * (1 / R(x,u,w))
    ]]></literal>
    <justification jstring="[para(35073(a,1),24009(a,1,1,3))].">
      <j1 rule="para" parents="35073 24009"/>
    </justification>
  </clause>

  <clause id="35075">
    <literal><![CDATA[
      (L(x,y,z) \ (R(x,u,w) * ((L(x,y,z) \ R(x,u,w)) \ 1))) * (((L(x,y,z) \ R(x,u,w)) \ 1) \ 1) = ((1 / R(x,u,w)) * L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(35073(a,2),34826(a,2,1))].">
      <j1 rule="para" parents="35073 34826"/>
    </justification>
  </clause>

  <clause id="35076">
    <literal><![CDATA[
      L(x,y,L(z * u,z * u,L(z,u,u))) = L(x,y,R(z,u,u \ 1) \ (u \ 1))
    ]]></literal>
    <justification jstring="[para(25241(a,1),35053(a,1,3))].">
      <j1 rule="para" parents="25241 35053"/>
    </justification>
  </clause>

  <clause id="35077">
    <literal><![CDATA[
      L(x,y,R(z,u,u \ 1) \ (u \ 1)) = L(x,y,u \ (u / (1 / (z * u))))
    ]]></literal>
    <justification jstring="[para(25575(a,1),35076(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25575 35076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35078">
    <literal><![CDATA[
      L(x,y,R(z,u,u \ 1) \ (u \ 1)) = L(x,y,u \ (((z * u) \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,29236,a(flip),b,35077,a),flip(a)].">
      <j1 rule="hyper" parents="373 29236 35077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35079">
    <literal><![CDATA[
      L(x,y,R(z,u,u \ 1) \ (u \ 1)) = L(x,y,u \ ((z * u) \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,29358,a(flip),b,35078,a),flip(a)].">
      <j1 rule="hyper" parents="373 29358 35078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35080">
    <literal><![CDATA[
      L(x,y,R(z,u,u \ 1) \ (u \ 1)) = L(x,y,u \ (u \ (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,29347,a(flip),b,35079,a),flip(a)].">
      <j1 rule="hyper" parents="373 29347 35079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35081">
    <literal><![CDATA[
      L(x,y,R(z,u,u \ 1) \ (u \ 1)) = L(x,y,L(z \ u,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,30390,a(flip),b,35080,a),flip(a)].">
      <j1 rule="hyper" parents="373 30390 35080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35082">
    <literal><![CDATA[
      L(x,y,R(z,u,u \ 1) \ u) = L(x,y,L(z \ u,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,25696,a(flip),b,35081,a)].">
      <j1 rule="hyper" parents="64 25696 35081"/>
    </justification>
  </clause>

  <clause id="35083">
    <literal><![CDATA[
      L(x,y,L(z \ u,u,u)) = L(x,y,L(z,u,u) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29377,a(flip),b,35082,a),flip(a)].">
      <j1 rule="hyper" parents="64 29377 35082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35084">
    <literal><![CDATA[
      L(x,y,L(z * u,z * u,z)) = L(x,y,L(u \ z,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,35051,a,b,35083,a)].">
      <j1 rule="hyper" parents="373 35051 35083"/>
    </justification>
  </clause>

  <clause id="35085">
    <literal><![CDATA[
      (1 / x) \ T((y * x) \ R(y * x,z,z),x) = T(a((1 / x) \ y,z,z) * x,x)
    ]]></literal>
    <justification jstring="[para(2740(a,1),34775(a,1,2,1))].">
      <j1 rule="para" parents="2740 34775"/>
    </justification>
  </clause>

  <clause id="35086">
    <literal><![CDATA[
      T(a((1 / x) \ y,z,z) * x,x) = (1 / x) \ a(y * x,z,z)
    ]]></literal>
    <justification jstring="[para(16010(a,1),35085(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16010 35085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35087">
    <literal><![CDATA[
      T(a(x \ y,z,z) * x,x) = (1 / x) \ a(y * x,z,z)
    ]]></literal>
    <justification jstring="[para(2671(a,1),35086(a,1,1,1))].">
      <j1 rule="para" parents="2671 35086"/>
    </justification>
  </clause>

  <clause id="35089">
    <literal><![CDATA[
      (1 / x) \ a(y * x,z,z) = a(x \ y,z,z) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,23701,a(flip),b,35087,a),flip(a)].">
      <j1 rule="hyper" parents="64 23701 35087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35090">
    <literal><![CDATA[
      T(x,y) \ ((((z * z) \ T(x,z \ (z \ y))) * u) * w) = (z * z) \ (x \ ((x * u) * w))
    ]]></literal>
    <justification jstring="[para(484(a,1),34776(a,1,2,1))].">
      <j1 rule="para" parents="484 34776"/>
    </justification>
  </clause>

  <clause id="35091">
    <literal><![CDATA[
      (x * x) \ ((y / x) / T((x * x) \ y,x)) = ((x * x) \ y) / T((1 / x) * T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,933,a(flip),b,34786,a)].">
      <j1 rule="hyper" parents="64 933 34786"/>
    </justification>
  </clause>

  <clause id="35092">
    <literal><![CDATA[
      K(x \ ((y * z) * z),z \ (z \ x)) / (((x / z) / z) \ y) = 1 / (y / ((x / z) / z))
    ]]></literal>
    <justification jstring="[para(25466(a,1),34794(a,1,1))].">
      <j1 rule="para" parents="25466 34794"/>
    </justification>
  </clause>

  <clause id="35093">
    <literal><![CDATA[
      L(x,y * ((z * T(u,z \ 1)) \ w),v5) = L(x,y * (w / (u * (1 / z))),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29669,a(flip),b,34797,a),flip(a)].">
      <j1 rule="hyper" parents="64 29669 34797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35095">
    <literal><![CDATA[
      L(x,y * ((z * T(u,z \ 1)) \ w),v5) = L(x,y * ((u * (1 / z)) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29547,a(flip),b,35093,a),flip(a)].">
      <j1 rule="hyper" parents="373 29547 35093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35096">
    <literal><![CDATA[
      L(x,y * ((z * (1 / u)) \ w),v5) = L(x,y * ((u * z) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29630,a(flip),b,35095,a),flip(a)].">
      <j1 rule="hyper" parents="64 29630 35095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35098">
    <literal><![CDATA[
      (x * x) \ L(K(y,a(z,u,w)) * v5,a(z,u,w),y) = L((x * x) \ v5,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(10985(a,1),34802(a,1,2))].">
      <j1 rule="para" parents="10985 34802"/>
    </justification>
  </clause>

  <clause id="35099">
    <literal><![CDATA[
      L((x * x) \ y,a(z,u,w),v5) = (x * x) \ L(y,a(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(23104(a,1),35098(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23104 35098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35100">
    <literal><![CDATA[
      x * L((x \ 1) * ((x \ K(y,z)) * x),u,w) = (1 / (K(z,y) / x)) * L(x \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(34179(a,2),34803(a,1,2))].">
      <j1 rule="para" parents="34179 34803"/>
    </justification>
  </clause>

  <clause id="35101">
    <literal><![CDATA[
      x * (((y / x) * R(x,z,u)) / (R(x,z,u) * y)) = a(x,x,y * R(x,z,u))
    ]]></literal>
    <justification jstring="[para(12(a,1),34804(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="12 34804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35103">
    <literal><![CDATA[
      T((x \ L(x,y,z)) * u,w) = (x \ L(x,y,z)) * T(u,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,30369,a,b,34814,a),flip(a)].">
      <j1 rule="hyper" parents="36 30369 34814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35104">
    <literal><![CDATA[
      T((x \ L(x,y,z)) * u,w) = T(u,w) * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,23742,a(flip),b,35103,a),flip(a)].">
      <j1 rule="hyper" parents="373 23742 35103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35105">
    <literal><![CDATA[
      T(L(x \ L(x,y,z),u,w) \ v5,v6) = L(x \ L(x,y,z),u,w) \ T(v5,v6)
    ]]></literal>
    <justification jstring="[hyper(35,a,28559,a(flip),b,35103,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 28559 35103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35106">
    <literal><![CDATA[
      (x * y) / T((z \ L(z,u,w)) * x,y) = (y * x) / ((z \ L(z,u,w)) * x)
    ]]></literal>
    <justification jstring="[para(35103(a,2),15235(a,1,2))].">
      <j1 rule="para" parents="35103 15235"/>
    </justification>
  </clause>

  <clause id="35107">
    <literal><![CDATA[
      x * (T(y,x) * (z \ L(z,u,w))) = ((z \ L(z,u,w)) * y) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,35104,a(flip),b,22,a(flip))].">
      <j1 rule="hyper" parents="145 35104 22"/>
    </justification>
  </clause>

  <clause id="35108">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * (u * w) = ((x \ L(x,y,z)) * u) * w
    ]]></literal>
    <justification jstring="[hyper(64,a,26746,a,b,35107,a)].">
      <j1 rule="hyper" parents="64 26746 35107"/>
    </justification>
  </clause>

  <clause id="35109">
    <literal><![CDATA[
      R(x \ L(x,y,z),u,w) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,111,a,b,35108,a)].">
      <j1 rule="hyper" parents="36 111 35108"/>
    </justification>
  </clause>

  <clause id="35110">
    <literal><![CDATA[
      (x * y) / ((z \ L(z,u,w)) * y) = ((z \ L(z,u,w)) * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,28451,a(flip),b,35106,a),flip(a)].">
      <j1 rule="hyper" parents="64 28451 35106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35111">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) \ (u * ((x \ L(x,y,z)) * w)) = R(w,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,33858,a(flip),b,35110,a),flip(a)].">
      <j1 rule="hyper" parents="64 33858 35110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35112">
    <literal><![CDATA[
      L(K(x,y \ L(y,z,u)) * w,y \ L(y,z,u),x) = R(w,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10985,a(flip),b,35111,a)].">
      <j1 rule="hyper" parents="64 10985 35111"/>
    </justification>
  </clause>

  <clause id="35113">
    <literal><![CDATA[
      R(x,y * L(y,z,u),w) = L(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(23694(a,1),35112(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23694 35112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35114">
    <literal><![CDATA[
      R(x,y * L(y,z,u),w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11786,a(flip),b,35113,a),flip(a)].">
      <j1 rule="hyper" parents="373 11786 35113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35115">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),w) = L(x,y \ L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,5612,a,b,35113,a)].">
      <j1 rule="hyper" parents="64 5612 35113"/>
    </justification>
  </clause>

  <clause id="35116">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26595,a,b,35114,a)].">
      <j1 rule="hyper" parents="64 26595 35114"/>
    </justification>
  </clause>

  <clause id="35117">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,5612,a,b,35114,a)].">
      <j1 rule="hyper" parents="64 5612 35114"/>
    </justification>
  </clause>

  <clause id="35118">
    <literal><![CDATA[
      x \ L(x,y * L(y,z,u),y) = a(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(35117(a,1),33569(a,1,2))].">
      <j1 rule="para" parents="35117 33569"/>
    </justification>
  </clause>

  <clause id="35119">
    <literal><![CDATA[
      x \ L(x,y,y * L(y,z,u)) = a(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(33155(a,1),35118(a,1,2))].">
      <j1 rule="para" parents="33155 35118"/>
    </justification>
  </clause>

  <clause id="35120">
    <literal><![CDATA[
      (L(x,x,y) \ 1) * L((1 / x) \ z,x,a(x,x,y)) = a(y * x,x,x \ 1) * z
    ]]></literal>
    <justification jstring="[para(34824(a,1),34825(a,1,2))].">
      <j1 rule="para" parents="34824 34825"/>
    </justification>
  </clause>

  <clause id="35121">
    <literal><![CDATA[
      L(x,L(y \ z,y,z \ L(u,w,w)) \ L(u,w,w),v5) = L(x,(z \ R(u,w,w)) * y,v5)
    ]]></literal>
    <justification jstring="[para(29283(a,1),34827(a,1,2,1))].">
      <j1 rule="para" parents="29283 34827"/>
    </justification>
  </clause>

  <clause id="35122">
    <literal><![CDATA[
      (((x * y) * y) / x) * K(y * ((x * y) \ x),y * y) = 1 / (1 / (((x * y) * y) / x))
    ]]></literal>
    <justification jstring="[para(14711(a,1),34828(a,1,2))].">
      <j1 rule="para" parents="14711 34828"/>
    </justification>
  </clause>

  <clause id="35123">
    <literal><![CDATA[
      a(x,L(y * ((y \ 1) \ (z * (u / y))),w,v5),v6) = a(x,L(((y \ 1) \ u) * z,w,v5),v6)
    ]]></literal>
    <justification jstring="[para(1589(a,1),34846(a,1,2,1))].">
      <j1 rule="para" parents="1589 34846"/>
    </justification>
  </clause>

  <clause id="35124">
    <literal><![CDATA[
      (x / ((y \ x) / y)) * (((y \ x) / y) / x) = a(((y \ x) / y) \ x,a(y,y,x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32040,a(flip),b,34847,a),flip(a)].">
      <j1 rule="hyper" parents="64 32040 34847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35125">
    <literal><![CDATA[
      (x / ((y \ x) / y)) * (((y \ x) / y) / x) = a(((y \ x) / y) \ x,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,32892,a(flip),b,35124,a),flip(a)].">
      <j1 rule="hyper" parents="373 32892 35124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35126">
    <literal><![CDATA[
      (x / ((y \ x) / y)) * (((y \ x) / y) / x) = a((y \ (y \ x)) \ x,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,32386,a(flip),b,35125,a),flip(a)].">
      <j1 rule="hyper" parents="373 32386 35125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35127">
    <literal><![CDATA[
      L(a(x,y,z),z,z * u) * L(u,z,z) = ((a(x,y,z) \ 1) \ z) * ((z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(2211(a,1),34867(a,1,1))].">
      <j1 rule="para" parents="2211 34867"/>
    </justification>
  </clause>

  <clause id="35128">
    <literal><![CDATA[
      L(x * a(y,x,z),z * K(x,z),y) = K(z,x) * ((y * z) \ ((y * x) * z))
    ]]></literal>
    <justification jstring="[para(27296(a,1),34922(a,1,1,2))].">
      <j1 rule="para" parents="27296 34922"/>
    </justification>
  </clause>

  <clause id="35129">
    <literal><![CDATA[
      K(x,y) * ((z * x) \ ((z * y) * x)) = L(y * a(z,y,x),x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29449,a(flip),b,35128,a),flip(a)].">
      <j1 rule="hyper" parents="64 29449 35128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35132">
    <literal><![CDATA[
      L(L(x,y,z) * a(u,L(x,y,z),w),w,u) = K(w,x) * ((u * w) \ ((u * L(x,y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,23383,a(flip),b,35129,a),flip(a)].">
      <j1 rule="hyper" parents="64 23383 35129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35133">
    <literal><![CDATA[
      L(x,y,z \ (u * R(w,v5,v6))) = L(x,y,z \ (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29158,a(flip),b,34932,a),flip(a)].">
      <j1 rule="hyper" parents="64 29158 34932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35134">
    <literal><![CDATA[
      L(x,y,z \ (u * ((w * v5) * v5))) = L(x,y,z \ (u * L(w,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,31358,a,b,35133,a)].">
      <j1 rule="hyper" parents="64 31358 35133"/>
    </justification>
  </clause>

  <clause id="35135">
    <literal><![CDATA[
      a(x \ (R(y,z,u) * w),v5,v6) = a(x \ (L(y,z,u) * w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32533,a(flip),b,34933,a),flip(a)].">
      <j1 rule="hyper" parents="64 32533 34933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35136">
    <literal><![CDATA[
      L(L(L(x \ R(x,y,z),u,w),u,w),L(L(x,u,w),u,w),z * y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(4246(a,1),34956(a,1,1,1))].">
      <j1 rule="para" parents="4246 34956"/>
    </justification>
  </clause>

  <clause id="35137">
    <literal><![CDATA[
      L(L(x \ R(x,x,y),z,u),z,u) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,30314,a,b,35136,a),flip(a)].">
      <j1 rule="hyper" parents="42 30314 35136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35138">
    <literal><![CDATA[
      L(a(x,L(x,y,z),u),y,z) = a(x,x,u)
    ]]></literal>
    <justification jstring="[para(34874(a,1),35137(a,1,1))].">
      <j1 rule="para" parents="34874 35137"/>
    </justification>
  </clause>

  <clause id="35139">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34069,a,b,35138,a)].">
      <j1 rule="hyper" parents="64 34069 35138"/>
    </justification>
  </clause>

  <clause id="35140">
    <literal><![CDATA[
      L(a(x * y,y \ x,z),y,y) = a(x * y,x * y,z)
    ]]></literal>
    <justification jstring="[para(32164(a,1),35138(a,1,1))].">
      <j1 rule="para" parents="32164 35138"/>
    </justification>
  </clause>

  <clause id="35143">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),u) = L(u,x,x) \ u
    ]]></literal>
    <justification jstring="[hyper(373,a,1243,a,b,35139,a),flip(a)].">
      <j1 rule="hyper" parents="373 1243 35139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35144">
    <literal><![CDATA[
      a(R(x,y,z),L(x,y,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32590,a,b,35139,a)].">
      <j1 rule="hyper" parents="64 32590 35139"/>
    </justification>
  </clause>

  <clause id="35146">
    <literal><![CDATA[
      a((x * y) \ z,L(y \ (x \ z),y,x),u) = a(y \ (x \ z),y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[para(346(a,1),35139(a,1,1))].">
      <j1 rule="para" parents="346 35139"/>
    </justification>
  </clause>

  <clause id="35148">
    <literal><![CDATA[
      a(x \ (y * z),L((y \ x) \ z,y \ x,y),u) = a((y \ x) \ z,(y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[para(630(a,1),35139(a,1,1))].">
      <j1 rule="para" parents="630 35139"/>
    </justification>
  </clause>

  <clause id="35149">
    <literal><![CDATA[
      a((x * y) \ (y * z),L(T(x,y) \ z,x,y),u) = a(T(x,y) \ z,T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(10979(a,1),35139(a,1,1))].">
      <j1 rule="para" parents="10979 35139"/>
    </justification>
  </clause>

  <clause id="35150">
    <literal><![CDATA[
      L(x,y,a(z,L(u,w,v5),L(u,w,v5))) = L(x,y,a(u,u,z \ 1))
    ]]></literal>
    <justification jstring="[para(35139(a,1),29298(a,1,3)),flip(a)].">
      <j1 rule="para" parents="35139 29298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35151">
    <literal><![CDATA[
      L(x,y,z) * (a(x,x,u) * u) = (1 / L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(35139(a,1),30225(a,1,2,1))].">
      <j1 rule="para" parents="35139 30225"/>
    </justification>
  </clause>

  <clause id="35154">
    <literal><![CDATA[
      (a(x,x,y) / R(x,z,u)) \ y = R(x,z,u) * y
    ]]></literal>
    <justification jstring="[para(35139(a,1),32842(a,1,1,1))].">
      <j1 rule="para" parents="35139 32842"/>
    </justification>
  </clause>

  <clause id="35156">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32197,a,b,35144,a)].">
      <j1 rule="hyper" parents="64 32197 35144"/>
    </justification>
  </clause>

  <clause id="35159">
    <literal><![CDATA[
      R(x,y,z) * (u * a(x,x,u)) = (1 / R(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(35156(a,1),30219(a,1,2,2))].">
      <j1 rule="para" parents="35156 30219"/>
    </justification>
  </clause>

  <clause id="35161">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,z,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,1243,a,b,35143,a(flip))].">
      <j1 rule="hyper" parents="40 1243 35143"/>
    </justification>
  </clause>

  <clause id="35162">
    <literal><![CDATA[
      L((L(x,y,z) \ 1) \ u,x,x) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(40,a,1244,a(flip),b,35143,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 1244 35143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35163">
    <literal><![CDATA[
      L(L(x,y,z) \ u,x,x) = (1 / L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(742,a,35161,a),flip(a)].">
      <j1 rule="hyper" parents="742 35161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35165">
    <literal><![CDATA[
      L(x,L(y,z * u,w),L(y,u * z,w)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29740,a,b,35161,a)].">
      <j1 rule="hyper" parents="64 29740 35161"/>
    </justification>
  </clause>

  <clause id="35166">
    <literal><![CDATA[
      L(x,y \ (z \ y),y \ (z \ y)) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35050,a(flip),b,35161,a)].">
      <j1 rule="hyper" parents="64 35050 35161"/>
    </justification>
  </clause>

  <clause id="35167">
    <literal><![CDATA[
      L(L(x \ 1,y,z) \ u,x,x) = (L(1 / x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,34521,a(flip),b,35161,a),flip(a)].">
      <j1 rule="hyper" parents="64 34521 35161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35169">
    <literal><![CDATA[
      L(R(x,y,z) \ u,x,x) = (1 / R(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,29797,a(flip),b,35161,a),flip(a)].">
      <j1 rule="hyper" parents="64 29797 35161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35170">
    <literal><![CDATA[
      L(x,y \ z,L(z \ y,z \ y,y)) = L(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26066,a(flip),b,35161,a)].">
      <j1 rule="hyper" parents="64 26066 35161"/>
    </justification>
  </clause>

  <clause id="35171">
    <literal><![CDATA[
      L(x,y,z) \ L(u,x,x) = (L(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(139,a,35161,a(flip),b,1139,a)].">
      <j1 rule="hyper" parents="139 35161 1139"/>
    </justification>
  </clause>

  <clause id="35172">
    <literal><![CDATA[
      L(x,(y * z) \ u,L(z \ (y \ u),z,y)) = L(x,z \ (y \ u),z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(346(a,1),35161(a,1,2))].">
      <j1 rule="para" parents="346 35161"/>
    </justification>
  </clause>

  <clause id="35173">
    <literal><![CDATA[
      L(x,y \ (z * u),L((z \ y) \ u,z \ y,z)) = L(x,(z \ y) \ u,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(630(a,1),35161(a,1,2))].">
      <j1 rule="para" parents="630 35161"/>
    </justification>
  </clause>

  <clause id="35174">
    <literal><![CDATA[
      L(x,y,L(z * L(u,w,v5),u,u)) = L(x,y,L(u,w,v5) \ z)
    ]]></literal>
    <justification jstring="[para(35161(a,1),30388(a,1,3))].">
      <j1 rule="para" parents="35161 30388"/>
    </justification>
  </clause>

  <clause id="35176">
    <literal><![CDATA[
      R(x,y,z) \ L(u,x,x) = (R(x,y,z) \ 1) * u
    ]]></literal>
    <justification jstring="[para(35161(a,1),29803(a,1,2))].">
      <j1 rule="para" parents="35161 29803"/>
    </justification>
  </clause>

  <clause id="35178">
    <literal><![CDATA[
      a(x,L(L(y,z,u) * w,y,y),v5) = a(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(35161(a,1),32141(a,1,2))].">
      <j1 rule="para" parents="35161 32141"/>
    </justification>
  </clause>

  <clause id="35180">
    <literal><![CDATA[
      (x \ (y \ x)) \ L(z,y,y) = ((x \ (y \ x)) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,35166,a(flip),b,1139,a)].">
      <j1 rule="hyper" parents="139 35166 1139"/>
    </justification>
  </clause>

  <clause id="35181">
    <literal><![CDATA[
      ((x \ (y \ x)) \ 1) \ L(z,y,y) = (((x \ (y \ x)) \ 1) \ 1) * z
    ]]></literal>
    <justification jstring="[para(35166(a,1),1163(a,1,2))].">
      <j1 rule="para" parents="35166 1163"/>
    </justification>
  </clause>

  <clause id="35182">
    <literal><![CDATA[
      (a(x \ 1,x \ 1,L(y,z,u)) / R(x \ 1,x,y)) \ L(y,z,u) = L(y,z,u) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,24381,a(flip),b,35154,a),flip(a)].">
      <j1 rule="hyper" parents="373 24381 35154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35184">
    <literal><![CDATA[
      (1 / x) * (x * ((L(x,y,z) \ 1) \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(923,a,35162,a)].">
      <j1 rule="hyper" parents="923 35162"/>
    </justification>
  </clause>

  <clause id="35185">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w) \ v5,a(x,y,z),a(x,y,z)) = (L(a(x,y,z),u,w) \ 1) * v5
    ]]></literal>
    <justification jstring="[para(23785(a,1),35163(a,2,1))].">
      <j1 rule="para" parents="23785 35163"/>
    </justification>
  </clause>

  <clause id="35187">
    <literal><![CDATA[
      (x \ 1) \ ((L(x,y,z) \ 1) * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,35171,a(flip),b,31476,a)].">
      <j1 rule="hyper" parents="139 35171 31476"/>
    </justification>
  </clause>

  <clause id="35188">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ u),x,x) = x * ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(35171(a,1),31478(a,2,2))].">
      <j1 rule="para" parents="35171 31478"/>
    </justification>
  </clause>

  <clause id="35191">
    <literal><![CDATA[
      L(x,L(y * z,z * y,y),L(z \ y,y,y)) = L(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35084,a(flip),b,35165,a)].">
      <j1 rule="hyper" parents="64 35084 35165"/>
    </justification>
  </clause>

  <clause id="35192">
    <literal><![CDATA[
      L(a(((x * (y * z)) / z) * x,a(x,y,z) \ y,u),x,x) = a(((x * (y * z)) / z) * x,((x * (y * z)) / z) * x,u)
    ]]></literal>
    <justification jstring="[para(33322(a,2),35140(a,1,1,2))].">
      <j1 rule="para" parents="33322 35140"/>
    </justification>
  </clause>

  <clause id="35193">
    <literal><![CDATA[
      (1 / x) * ((1 / L(x,y,z)) \ u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(35151(a,1),30252(a,1,2))].">
      <j1 rule="para" parents="35151 30252"/>
    </justification>
  </clause>

  <clause id="35194">
    <literal><![CDATA[
      R(x,y,z) * (x \ ((1 / x) \ u)) = (1 / R(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,30231,a,b,35159,a)].">
      <j1 rule="hyper" parents="64 30231 35159"/>
    </justification>
  </clause>

  <clause id="35195">
    <literal><![CDATA[
      a(x,y,(((z \ (u \ z)) \ 1) * w) * ((z \ (u \ z)) * (z \ (u \ z)))) = a(x,y,((z \ (u \ z)) \ 1) \ L(w,u,u))
    ]]></literal>
    <justification jstring="[para(35180(a,1),27637(a,1,3,1))].">
      <j1 rule="para" parents="35180 27637"/>
    </justification>
  </clause>

  <clause id="35196">
    <literal><![CDATA[
      a(x,y,(z \ u) \ L(w,u \ z,u \ z)) = a(x,y,((z \ ((u \ z) \ z)) \ 1) * w)
    ]]></literal>
    <justification jstring="[para(35180(a,1),27420(a,1,3)),flip(a)].">
      <j1 rule="para" parents="35180 27420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35197">
    <literal><![CDATA[
      L(x,y,z) * ((x \ 1) \ u) = x * ((L(x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(35,a,27182,a,b,35184,a)].">
      <j1 rule="hyper" parents="35 27182 35184"/>
    </justification>
  </clause>

  <clause id="35198">
    <literal><![CDATA[
      a(x \ ((L(x,y,z) \ 1) * u),w,v5) = a(x * (L(x,y,z) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(35187(a,1),2675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35187 2675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35199">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * (x \ 1) = u * (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(35187(a,1),28936(a,1,1))].">
      <j1 rule="para" parents="35187 28936"/>
    </justification>
  </clause>

  <clause id="35200">
    <literal><![CDATA[
      (x \ 1) * ((L(x,y,z) \ 1) \ u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31588,a(flip),b,35193,a)].">
      <j1 rule="hyper" parents="64 31588 35193"/>
    </justification>
  </clause>

  <clause id="35201">
    <literal><![CDATA[
      L(x,y,z) * (x \ ((x \ 1) \ u)) = (L(x,y,z) \ 1) \ u
    ]]></literal>
    <justification jstring="[hyper(2340,a,35197,a)].">
      <j1 rule="hyper" parents="2340 35197"/>
    </justification>
  </clause>

  <clause id="35202">
    <literal><![CDATA[
      (L(x,y,z) \ u) * (x \ 1) = (x \ u) * (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(2330(a,1),35199(a,1,1))].">
      <j1 rule="para" parents="2330 35199"/>
    </justification>
  </clause>

  <clause id="35203">
    <literal><![CDATA[
      x * ((a(y,y,x) * x) \ z) = L(x,y,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31590,a(flip),b,35200,a)].">
      <j1 rule="hyper" parents="64 31590 35200"/>
    </justification>
  </clause>

  <clause id="35204">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) / (1 / x) = u / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(35200(a,1),34407(a,1,1))].">
      <j1 rule="para" parents="35200 34407"/>
    </justification>
  </clause>

  <clause id="35205">
    <literal><![CDATA[
      x * ((a(y,y,x) * x) \ z) = (z / x) * L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,23898,a(flip),b,35203,a),flip(a)].">
      <j1 rule="hyper" parents="373 23898 35203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35206">
    <literal><![CDATA[
      x * ((x * a(y,y,x)) \ z) = (z / x) * L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,24797,a(flip),b,35205,a)].">
      <j1 rule="hyper" parents="64 24797 35205"/>
    </justification>
  </clause>

  <clause id="35207">
    <literal><![CDATA[
      L(x,y,L((z / u) * L(u,w,w),u,u)) = L(x,y,u \ ((u * a(w,w,u)) \ z))
    ]]></literal>
    <justification jstring="[para(35206(a,1),30387(a,1,3,1))].">
      <j1 rule="para" parents="35206 30387"/>
    </justification>
  </clause>

  <clause id="35208">
    <literal><![CDATA[
      L(x,y,z) \ ((L(x,y,z) \ 1) \ u) = x \ ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(149,a,35201,a)].">
      <j1 rule="hyper" parents="149 35201"/>
    </justification>
  </clause>

  <clause id="35209">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,u,z))) = L(x,y,u \ ((w \ u) * (L(w,u,z) \ 1)))
    ]]></literal>
    <justification jstring="[para(35202(a,1),33424(a,2,3,2))].">
      <j1 rule="para" parents="35202 33424"/>
    </justification>
  </clause>

  <clause id="35211">
    <literal><![CDATA[
      L(L(x \ 1,x,y) \ z,x,x) = (a(y,x,x \ 1) * x) * z
    ]]></literal>
    <justification jstring="[para(33359(a,1),35167(a,2,1))].">
      <j1 rule="para" parents="33359 35167"/>
    </justification>
  </clause>

  <clause id="35212">
    <literal><![CDATA[
      L(x,y \ z,y \ z) = L(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26065,a(flip),b,35170,a)].">
      <j1 rule="hyper" parents="64 26065 35170"/>
    </justification>
  </clause>

  <clause id="35213">
    <literal><![CDATA[
      L((x \ y) \ z,y \ x,y \ x) = (1 / (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(742,a,35212,a),flip(a)].">
      <j1 rule="hyper" parents="742 35212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35214">
    <literal><![CDATA[
      (x \ y) \ L(z,y \ x,y \ x) = ((x \ y) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,35212,a,b,1139,a)].">
      <j1 rule="hyper" parents="139 35212 1139"/>
    </justification>
  </clause>

  <clause id="35215">
    <literal><![CDATA[
      L(x,y,a(z,L(u,w,v5),L(u,w,v5))) = L(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,29298,a(flip),b,35150,a),flip(a)].">
      <j1 rule="hyper" parents="373 29298 35150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35216">
    <literal><![CDATA[
      L(x,y,a(z / u,L(u,w,v5),L(u,w,v5))) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,30333,a(flip),b,35215,a),flip(a)].">
      <j1 rule="hyper" parents="373 30333 35215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35217">
    <literal><![CDATA[
      ((x \ (y \ x)) \ 1) \ L(z,y,y) = (x \ (((y \ 1) \ 1) \ x)) * z
    ]]></literal>
    <justification jstring="[para(3673(a,1),35181(a,2,1))].">
      <j1 rule="para" parents="3673 35181"/>
    </justification>
  </clause>

  <clause id="35218">
    <literal><![CDATA[
      L(x,L(y \ z,z,z),L(y \ z,z,z)) = L(x,z * y,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31763,a(flip),b,35191,a)].">
      <j1 rule="hyper" parents="64 31763 35191"/>
    </justification>
  </clause>

  <clause id="35219">
    <literal><![CDATA[
      L(x,y \ z,y \ z) = L(x,z * y,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35161,a(flip),b,35218,a)].">
      <j1 rule="hyper" parents="64 35161 35218"/>
    </justification>
  </clause>

  <clause id="35220">
    <literal><![CDATA[
      L((x \ y) \ z,y * x,y * x) = (1 / (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(742,a,35219,a),flip(a)].">
      <j1 rule="hyper" parents="742 35219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35221">
    <literal><![CDATA[
      L(x,y * (1 / z),y * (z \ 1)) = L(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,29613,a,b,35219,a)].">
      <j1 rule="hyper" parents="373 29613 35219"/>
    </justification>
  </clause>

  <clause id="35222">
    <literal><![CDATA[
      L(x,y \ z,y \ z) = L(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29507,a,b,35219,a),flip(a)].">
      <j1 rule="hyper" parents="373 29507 35219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35224">
    <literal><![CDATA[
      L((x \ y) \ z,x * y,x * y) = (1 / (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,35213,a(flip),b,35219,a),flip(a)].">
      <j1 rule="hyper" parents="64 35213 35219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35225">
    <literal><![CDATA[
      L(x \ R(x,y,z),u * x,u * x) = (u \ x) \ (u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,34939,a(flip),b,35219,a),flip(a)].">
      <j1 rule="hyper" parents="64 34939 35219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35226">
    <literal><![CDATA[
      (x \ y) \ L(z,y * x,y * x) = ((x \ y) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,35219,a(flip),b,1139,a)].">
      <j1 rule="hyper" parents="139 35219 1139"/>
    </justification>
  </clause>

  <clause id="35227">
    <literal><![CDATA[
      a(x * L(x,y * z,y * z),u,w) = a(a(x,y \ z,y \ z),u,w)
    ]]></literal>
    <justification jstring="[para(35222(a,1),32544(a,1,1,2))].">
      <j1 rule="para" parents="35222 32544"/>
    </justification>
  </clause>

  <clause id="35228">
    <literal><![CDATA[
      L((x \ y) \ z,x * y,y * x) = (1 / (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(29572,a,35220,a)].">
      <j1 rule="hyper" parents="29572 35220"/>
    </justification>
  </clause>

  <clause id="35229">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ u,x * R(x,y,z),x * R(x,y,z)) = ((x \ R(x,y,z)) \ 1) * u
    ]]></literal>
    <justification jstring="[para(23705(a,1),35224(a,2,1))].">
      <j1 rule="para" parents="23705 35224"/>
    </justification>
  </clause>

  <clause id="35230">
    <literal><![CDATA[
      L((x \ y) \ ((x \ y) / z),x * y,y * x) = (x \ y) * (((x \ y) \ 1) / z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1217,a(flip),b,35228,a),flip(a)].">
      <j1 rule="hyper" parents="373 1217 35228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35231">
    <literal><![CDATA[
      L(L((x \ 1) \ y,x,a(z,u,x)),x * a(z,u,x),a(z,u,x) * x) = (1 / (x \ a(z,u,x))) * (y * a(z,u,x))
    ]]></literal>
    <justification jstring="[para(27820(a,1),35228(a,1,1))].">
      <j1 rule="para" parents="27820 35228"/>
    </justification>
  </clause>

  <clause id="35232">
    <literal><![CDATA[
      L(x,y * (1 / z),y * (1 / z)) = L(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29018,a,b,35221,a)].">
      <j1 rule="hyper" parents="64 29018 35221"/>
    </justification>
  </clause>

  <clause id="35233">
    <literal><![CDATA[
      L(((1 / x) \ y) \ z,x \ y,x \ y) = (1 / ((1 / x) \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,35220,a(flip),b,35232,a),flip(a)].">
      <j1 rule="hyper" parents="64 35220 35232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35234">
    <literal><![CDATA[
      L(((1 / (1 / x)) \ ((y / x) / y)) \ z,((y / x) / y) * x,(1 / x) \ ((y / x) / y)) = (1 / ((1 / (1 / x)) \ ((y / x) / y))) * z
    ]]></literal>
    <justification jstring="[para(31492(a,1),35233(a,1,2))].">
      <j1 rule="para" parents="31492 35233"/>
    </justification>
  </clause>

  <clause id="35235">
    <literal><![CDATA[
      a(x \ (L(x,y,z) * u),w,v5) = a(x * (L(x,y,z) \ u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26916,a(flip),b,35198,a)].">
      <j1 rule="hyper" parents="64 26916 35198"/>
    </justification>
  </clause>

  <clause id="35236">
    <literal><![CDATA[
      a(L(x,y,z) * (x \ u),w,v5) = a(x * (L(x,y,z) \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(2325(a,1),35235(a,1,1))].">
      <j1 rule="para" parents="2325 35235"/>
    </justification>
  </clause>

  <clause id="35237">
    <literal><![CDATA[
      a((x \ y) * L(x,z,u),w,v5) = a(x * (L(x,z,u) \ y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(26847,a,35236,a)].">
      <j1 rule="hyper" parents="26847 35236"/>
    </justification>
  </clause>

  <clause id="35238">
    <literal><![CDATA[
      a(a(x,y \ z,y \ z),u,w) = a(a(x,y * z,y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32544,a(flip),b,35227,a),flip(a)].">
      <j1 rule="hyper" parents="64 32544 35227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35239">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,u,z))) = L(x,y,u \ (L(w,u,z) * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,29131,a(flip),b,35209,a),flip(a)].">
      <j1 rule="hyper" parents="373 29131 35209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35240">
    <literal><![CDATA[
      a((x * y) \ z,(x * y) \ z,u) = a(y \ (x \ z),y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[para(346(a,1),35146(a,1,2))].">
      <j1 rule="para" parents="346 35146"/>
    </justification>
  </clause>

  <clause id="35241">
    <literal><![CDATA[
      L(x,(y * z) \ u,(y * z) \ u) = L(x,z \ (y \ u),z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(346(a,1),35172(a,1,3))].">
      <j1 rule="para" parents="346 35172"/>
    </justification>
  </clause>

  <clause id="35242">
    <literal><![CDATA[
      L(x,y \ (z \ u),y \ (z \ u)) = L(x,u * (z * y),u * (z * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,35219,a(flip),b,35241,a),flip(a)].">
      <j1 rule="hyper" parents="64 35219 35241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35243">
    <literal><![CDATA[
      L(x,y \ (z \ 1),y \ (z \ 1)) = L(x,z * y,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11807,a(flip),b,35241,a),flip(a)].">
      <j1 rule="hyper" parents="64 11807 35241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35244">
    <literal><![CDATA[
      L(x \ 1,x * y,x * y) = (1 / (y / (x \ 1))) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,34721,a(flip),b,35243,a),flip(a)].">
      <j1 rule="hyper" parents="64 34721 35243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35245">
    <literal><![CDATA[
      L(x,(y \ z) * u,(y \ z) * u) = L(x,z * (y * u),z * (y * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,35219,a(flip),b,35242,a)].">
      <j1 rule="hyper" parents="64 35219 35242"/>
    </justification>
  </clause>

  <clause id="35246">
    <literal><![CDATA[
      L(x,(y \ z) * u,u * (y \ z)) = L(x,z * (y * u),z * (y * u))
    ]]></literal>
    <justification jstring="[hyper(24201,a,35245,a)].">
      <j1 rule="hyper" parents="24201 35245"/>
    </justification>
  </clause>

  <clause id="35247">
    <literal><![CDATA[
      L(x,y,z \ ((z * a(u,u,z)) \ w)) = L(x,y,(1 / z) * (L(z,u,u) * w))
    ]]></literal>
    <justification jstring="[para(25125(a,1),35207(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25125 35207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35248">
    <literal><![CDATA[
      L(x,y,z \ ((z * a(u,u,z)) \ w)) = L(x,y,z * (L(z,u,u) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,2186,a(flip),b,35247,a),flip(a)].">
      <j1 rule="hyper" parents="373 2186 35247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35249">
    <literal><![CDATA[
      L(x,y,z \ (L(z,u,u) \ w)) = L(x,y,z * (L(z,u,u) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,31626,a(flip),b,35248,a)].">
      <j1 rule="hyper" parents="64 31626 35248"/>
    </justification>
  </clause>

  <clause id="35250">
    <literal><![CDATA[
      a((x \ y) \ z,(x \ y) \ z,u) = a(y \ (x * z),y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(630(a,1),35148(a,1,2)),flip(a)].">
      <j1 rule="para" parents="630 35148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35251">
    <literal><![CDATA[
      a((x * y) \ (y * z),(x * y) \ (y * z),u) = a(T(x,y) \ z,T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(10979(a,1),35149(a,1,2))].">
      <j1 rule="para" parents="10979 35149"/>
    </justification>
  </clause>

  <clause id="35252">
    <literal><![CDATA[
      L(x,(y \ z) \ u,(y \ z) \ u) = L(x,z \ (y * u),z \ (y * u))
    ]]></literal>
    <justification jstring="[para(630(a,1),35173(a,1,3)),flip(a)].">
      <j1 rule="para" parents="630 35173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35253">
    <literal><![CDATA[
      L(x,(y \ z) \ u,(y \ z) \ u) = L(x,(y * u) * z,(y * u) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,35219,a(flip),b,35252,a),flip(a)].">
      <j1 rule="hyper" parents="373 35219 35252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35254">
    <literal><![CDATA[
      L(x,(y * z) * u,(y * z) * u) = L(x,z * (y \ u),z * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,35219,a(flip),b,35253,a),flip(a)].">
      <j1 rule="hyper" parents="64 35219 35253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35255">
    <literal><![CDATA[
      L(x,(y * z) * u,(z * y) * u) = L(x,z * (y \ u),z * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,28989,a,b,35254,a)].">
      <j1 rule="hyper" parents="64 28989 35254"/>
    </justification>
  </clause>

  <clause id="35256">
    <literal><![CDATA[
      L(x,y * (z \ x),y * (z \ x)) = (1 / ((z * y) / x)) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,34539,a(flip),b,35254,a),flip(a)].">
      <j1 rule="hyper" parents="64 34539 35254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35257">
    <literal><![CDATA[
      L(x,(y * z) * u,u * (y * z)) = L(x,y * (z \ u),y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29639,a(flip),b,35254,a)].">
      <j1 rule="hyper" parents="64 29639 35254"/>
    </justification>
  </clause>

  <clause id="35258">
    <literal><![CDATA[
      L(x,(y * z) * u,(y * z) * u) = L(x,y * (z \ u),y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29455,a,b,35255,a)].">
      <j1 rule="hyper" parents="64 29455 35255"/>
    </justification>
  </clause>

  <clause id="35259">
    <literal><![CDATA[
      L(x,y * (z \ u),y * (z \ u)) = L(x,z * (y \ u),z * (y \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,35254,a(flip),b,35258,a)].">
      <j1 rule="hyper" parents="64 35254 35258"/>
    </justification>
  </clause>

  <clause id="35260">
    <literal><![CDATA[
      L(x,y * (x \ z),y * (x \ z)) = (1 / ((y \ z) / x)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,34540,a(flip),b,35259,a),flip(a)].">
      <j1 rule="hyper" parents="373 34540 35259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35261">
    <literal><![CDATA[
      L(x,y * (x \ z),(x \ z) * y) = (1 / ((y \ z) / x)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(24201,a,35260,a)].">
      <j1 rule="hyper" parents="24201 35260"/>
    </justification>
  </clause>

  <clause id="35262">
    <literal><![CDATA[
      L(x,(x \ y) * z,(x \ y) * z) = (1 / ((z \ y) / x)) * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29507,a,b,35260,a)].">
      <j1 rule="hyper" parents="64 29507 35260"/>
    </justification>
  </clause>

  <clause id="35263">
    <literal><![CDATA[
      L(x,y * (x \ (y \ T(y * z,u))),y * (x \ (y \ T(y * z,u)))) = (1 / (((y \ (y \ 1)) * T((y \ 1) \ z,u)) / x)) * (y \ (y \ T(y * z,u)))
    ]]></literal>
    <justification jstring="[para(1559(a,2),35260(a,2,1,2,1))].">
      <j1 rule="para" parents="1559 35260"/>
    </justification>
  </clause>

  <clause id="35264">
    <literal><![CDATA[
      L(x,y * (x \ ((1 / y) \ z)),y * (x \ ((1 / y) \ z))) = (1 / ((a(y,y,z) * z) / x)) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(30228(a,1),35260(a,2,1,2,1))].">
      <j1 rule="para" parents="30228 35260"/>
    </justification>
  </clause>

  <clause id="35265">
    <literal><![CDATA[
      L(x,y * (x * z),y * (x * z)) = (1 / ((z \ y) / x)) * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35245,a(flip),b,35262,a)].">
      <j1 rule="hyper" parents="64 35245 35262"/>
    </justification>
  </clause>

  <clause id="35266">
    <literal><![CDATA[
      T((x * y) * (K(z,u) * (y \ K(y,x))),K(z,u)) = (K(z,T(u,y)) * (y * x)) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,25383,a,b,34985,a)].">
      <j1 rule="hyper" parents="64 25383 34985"/>
    </justification>
  </clause>

  <clause id="35267">
    <literal><![CDATA[
      T(x,y) \ (((T(x,y) / (z * z)) * u) * w) = (z * z) \ (x \ ((x * u) * w))
    ]]></literal>
    <justification jstring="[para(18767(a,1),35090(a,1,2,1,1))].">
      <j1 rule="para" parents="18767 35090"/>
    </justification>
  </clause>

  <clause id="35268">
    <literal><![CDATA[
      T(x,y) \ ((T(x,y) * (1 / z)) * u) = (z * z) \ (x \ ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(811(a,1),35267(a,1,2,1))].">
      <j1 rule="para" parents="811 35267"/>
    </justification>
  </clause>

  <clause id="35269">
    <literal><![CDATA[
      (x * x) \ (y \ ((y * x) * z)) = y \ ((y * (1 / x)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,24773,a(flip),b,35268,a),flip(a)].">
      <j1 rule="hyper" parents="64 24773 35268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35270">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) * (a(x,x,y) \ 1)) \ (y \ (L(y,x,x) * z)) = y \ ((y * (1 / (a(x,x,y) \ 1))) * z)
    ]]></literal>
    <justification jstring="[para(5668(a,1),35269(a,1,2,2,1))].">
      <j1 rule="para" parents="5668 35269"/>
    </justification>
  </clause>

  <clause id="35271">
    <literal><![CDATA[
      ((x \ y) * (x \ y)) \ ((x \ y) \ (L(x \ y,x \ y,y) * z)) = (x \ y) \ (((x \ y) * (1 / (x \ y))) * ((y \ x) * z))
    ]]></literal>
    <justification jstring="[para(26064(a,1),35269(a,1,2,2))].">
      <j1 rule="para" parents="26064 35269"/>
    </justification>
  </clause>

  <clause id="35272">
    <literal><![CDATA[
      ((x * x) \ y) / T((1 / x) * T(y,x),x) = (x * x) \ (y \ ((x * x) * (y / x)))
    ]]></literal>
    <justification jstring="[para(17845(a,1),35091(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17845 35091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35273">
    <literal><![CDATA[
      ((x * x) \ y) / T((1 / x) * T(y,x),x) = T(y,x * x) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1458,a(flip),b,35272,a),flip(a)].">
      <j1 rule="hyper" parents="373 1458 35272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35274">
    <literal><![CDATA[
      ((x * x) \ y) / T((1 / x) * T(y,x),x) = y / T(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,27207,a(flip),b,35273,a),flip(a)].">
      <j1 rule="hyper" parents="373 27207 35273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35275">
    <literal><![CDATA[
      (x * x) \ (y / T((1 / x) * T(y,x),x)) = y / T(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,933,a(flip),b,35274,a)].">
      <j1 rule="hyper" parents="64 933 35274"/>
    </justification>
  </clause>

  <clause id="35276">
    <literal><![CDATA[
      K(x * x,x \ (x \ y)) / (((y / x) / x) \ y) = 1 / (y / ((y / x) / x))
    ]]></literal>
    <justification jstring="[para(28196(a,1),35092(a,1,1))].">
      <j1 rule="para" parents="28196 35092"/>
    </justification>
  </clause>

  <clause id="35277">
    <literal><![CDATA[
      K(x * x,(x \ y) * x) / (((y / x) / x) \ y) = 1 / (y / ((y / x) / x))
    ]]></literal>
    <justification jstring="[para(22812(a,1),35276(a,1,1))].">
      <j1 rule="para" parents="22812 35276"/>
    </justification>
  </clause>

  <clause id="35278">
    <literal><![CDATA[
      K(x * x,T(y,x)) / (((y / x) / x) \ y) = 1 / (y / ((y / x) / x))
    ]]></literal>
    <justification jstring="[para(11123(a,1),35277(a,1,1))].">
      <j1 rule="para" parents="11123 35277"/>
    </justification>
  </clause>

  <clause id="35279">
    <literal><![CDATA[
      K(x * x,y) / (((y / x) / x) \ y) = 1 / (y / ((y / x) / x))
    ]]></literal>
    <justification jstring="[para(11177(a,1),35278(a,1,1))].">
      <j1 rule="para" parents="11177 35278"/>
    </justification>
  </clause>

  <clause id="35281">
    <literal><![CDATA[
      K(x * x,y) / (y \ ((y * x) * x)) = 1 / (y / ((y / x) / x))
    ]]></literal>
    <justification jstring="[para(30801(a,1),35279(a,1,2))].">
      <j1 rule="para" parents="30801 35279"/>
    </justification>
  </clause>

  <clause id="35282">
    <literal><![CDATA[
      ((x * y) * y) / x = x / ((x / y) / y)
    ]]></literal>
    <justification jstring="[hyper(37,a,15160,a(flip),b,35281,a(flip))].">
      <j1 rule="hyper" parents="37 15160 35281"/>
    </justification>
  </clause>

  <clause id="35283">
    <literal><![CDATA[
      (((x * y) * y) / x) \ z = (x / ((x / y) / y)) \ z
    ]]></literal>
    <justification jstring="[hyper(62,a,35282,a)].">
      <j1 rule="hyper" parents="62 35282"/>
    </justification>
  </clause>

  <clause id="35284">
    <literal><![CDATA[
      ((x * x) \ y) / ((((x * x) \ y) / x) / x) = R(T(y,x * x),x,x) / ((x * x) \ y)
    ]]></literal>
    <justification jstring="[para(1397(a,1),35282(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1397 35282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35285">
    <literal><![CDATA[
      K(x,y) * (y / ((y / x) / x)) = ((x * y) * x) / y
    ]]></literal>
    <justification jstring="[para(35282(a,1),24430(a,1,2))].">
      <j1 rule="para" parents="35282 24430"/>
    </justification>
  </clause>

  <clause id="35286">
    <literal><![CDATA[
      (x / ((x / y) / y)) * (x * z) = x * ((x \ ((x * y) * y)) * z)
    ]]></literal>
    <justification jstring="[para(35282(a,1),31851(a,1,1))].">
      <j1 rule="para" parents="35282 31851"/>
    </justification>
  </clause>

  <clause id="35287">
    <literal><![CDATA[
      (x / ((x / y) / y)) * (x * y) = (x * y) * ((x / y) \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,31853,a,b,35286,a),flip(a)].">
      <j1 rule="hyper" parents="373 31853 35286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35288">
    <literal><![CDATA[
      (x * y) / (x / y) = x / ((x / y) / y)
    ]]></literal>
    <justification jstring="[hyper(36,a,31574,a,b,35287,a)].">
      <j1 rule="hyper" parents="36 31574 35287"/>
    </justification>
  </clause>

  <clause id="35289">
    <literal><![CDATA[
      T(x / ((x / y) / y),y * y) = (x * y) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,25074,a,b,35288,a)].">
      <j1 rule="hyper" parents="373 25074 35288"/>
    </justification>
  </clause>

  <clause id="35290">
    <literal><![CDATA[
      K(x,y) * (y / ((y / x) / x)) = (x * y) / (y / x)
    ]]></literal>
    <justification jstring="[para(35288(a,1),14887(a,1,2))].">
      <j1 rule="para" parents="35288 14887"/>
    </justification>
  </clause>

  <clause id="35291">
    <literal><![CDATA[
      L(x,y,(z / ((z / u) / u)) \ w) = L(x,y,((z / u) \ (z * u)) \ w)
    ]]></literal>
    <justification jstring="[para(35288(a,1),28982(a,1,3,1))].">
      <j1 rule="para" parents="35288 28982"/>
    </justification>
  </clause>

  <clause id="35292">
    <literal><![CDATA[
      ((x * x) \ (y / ((y / x) / x))) * (x * x) = (y * x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,798,a,b,35289,a)].">
      <j1 rule="hyper" parents="64 798 35289"/>
    </justification>
  </clause>

  <clause id="35293">
    <literal><![CDATA[
      ((x * y) * x) / y = (x * y) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,35285,a(flip),b,35290,a)].">
      <j1 rule="hyper" parents="64 35285 35290"/>
    </justification>
  </clause>

  <clause id="35294">
    <literal><![CDATA[
      (((x * x) \ y) / ((y / x) / x)) * (x * x) = (y * x) / (y / x)
    ]]></literal>
    <justification jstring="[para(933(a,2),35292(a,1,1))].">
      <j1 rule="para" parents="933 35292"/>
    </justification>
  </clause>

  <clause id="35295">
    <literal><![CDATA[
      ((x * x) \ y) / ((x * x) \ ((y / x) / x)) = (y * x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,900,a,b,35294,a)].">
      <j1 rule="hyper" parents="64 900 35294"/>
    </justification>
  </clause>

  <clause id="35296">
    <literal><![CDATA[
      ((x * x) \ y) / (((x * x) \ (y / x)) / x) = (y * x) / (y / x)
    ]]></literal>
    <justification jstring="[para(933(a,2),35295(a,1,2))].">
      <j1 rule="para" parents="933 35295"/>
    </justification>
  </clause>

  <clause id="35297">
    <literal><![CDATA[
      ((x * x) \ y) / ((((x * x) \ y) / x) / x) = (y * x) / (y / x)
    ]]></literal>
    <justification jstring="[para(933(a,2),35296(a,1,2,1))].">
      <j1 rule="para" parents="933 35296"/>
    </justification>
  </clause>

  <clause id="35298">
    <literal><![CDATA[
      L(x,y,(((z / u) / u) \ z) \ w) = L(x,y,((z / u) \ (z * u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28982,a(flip),b,35291,a)].">
      <j1 rule="hyper" parents="64 28982 35291"/>
    </justification>
  </clause>

  <clause id="35299">
    <literal><![CDATA[
      L(x,y,((z / u) \ (z * u)) \ w) = L(x,y,(z \ ((z * u) * u)) \ w)
    ]]></literal>
    <justification jstring="[para(30801(a,1),35298(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30801 35298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35300">
    <literal><![CDATA[
      L(x,y,((z / u) \ (z * u)) \ w) = L(x,y,a(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,25694,a(flip),b,35299,a),flip(a)].">
      <j1 rule="hyper" parents="373 25694 35299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35301">
    <literal><![CDATA[
      L(x,y,((z \ u) \ (u * z)) \ w) = L(x,y,a(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29111,a(flip),b,35300,a)].">
      <j1 rule="hyper" parents="64 29111 35300"/>
    </justification>
  </clause>

  <clause id="35302">
    <literal><![CDATA[
      L(x,y,((z \ u) \ (z * u)) \ w) = L(x,y,a(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29235,a,b,35301,a)].">
      <j1 rule="hyper" parents="64 29235 35301"/>
    </justification>
  </clause>

  <clause id="35303">
    <literal><![CDATA[
      ((x * x) \ y) / ((((x * x) \ y) / x) / x) = (R(T(y,x * x),x,x) / y) * (x * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,900,a(flip),b,35284,a),flip(a)].">
      <j1 rule="hyper" parents="373 900 35284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35304">
    <literal><![CDATA[
      ((x * x) \ y) / ((((x * x) \ y) / x) / x) = (y \ R(T(y,x * x),x,x)) * (x * x)
    ]]></literal>
    <justification jstring="[para(4050(a,1),35303(a,2,1))].">
      <j1 rule="para" parents="4050 35303"/>
    </justification>
  </clause>

  <clause id="35305">
    <literal><![CDATA[
      ((x * x) \ y) / ((((x * x) \ y) / x) / x) = (K(y,x * x) * a(y,x,x)) * (x * x)
    ]]></literal>
    <justification jstring="[para(25348(a,1),35304(a,2,1))].">
      <j1 rule="para" parents="25348 35304"/>
    </justification>
  </clause>

  <clause id="35306">
    <literal><![CDATA[
      ((x * x) \ y) / ((((x * x) \ y) / x) / x) = a(y,x,x) * (K(y,x * x) * (x * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,24477,a(flip),b,35305,a),flip(a)].">
      <j1 rule="hyper" parents="373 24477 35305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35307">
    <literal><![CDATA[
      ((x * x) \ y) / ((((x * x) \ y) / x) / x) = a(y,x,x) * (x * (x * K(y,x * x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,22768,a(flip),b,35306,a),flip(a)].">
      <j1 rule="hyper" parents="373 22768 35306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35308">
    <literal><![CDATA[
      ((x * x) \ y) / ((((x * x) \ y) / x) / x) = x * (a(y,x,x) * (x * K(y,x * x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,33249,a(flip),b,35307,a),flip(a)].">
      <j1 rule="hyper" parents="373 33249 35307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35309">
    <literal><![CDATA[
      ((x * x) \ y) / ((((x * x) \ y) / x) / x) = x * ((T(y,x * x) \ (y / x)) \ 1)
    ]]></literal>
    <justification jstring="[para(31010(a,1),35308(a,2,2))].">
      <j1 rule="para" parents="31010 35308"/>
    </justification>
  </clause>

  <clause id="35310">
    <literal><![CDATA[
      ((x * x) \ y) / ((((x * x) \ y) / x) / x) = x * ((y / T(y * x,x)) \ 1)
    ]]></literal>
    <justification jstring="[para(27207(a,1),35309(a,2,2,1))].">
      <j1 rule="para" parents="27207 35309"/>
    </justification>
  </clause>

  <clause id="35311">
    <literal><![CDATA[
      x * ((y / T(y * x,x)) \ 1) = (y * x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,35297,a(flip),b,35310,a),flip(a)].">
      <j1 rule="hyper" parents="64 35297 35310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35312">
    <literal><![CDATA[
      x * ((y / T(y * x,x)) \ 1) = y / ((y / x) / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,35288,a(flip),b,35311,a),flip(a)].">
      <j1 rule="hyper" parents="373 35288 35311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35313">
    <literal><![CDATA[
      (1 / (K(x,y) / z)) * L(z \ 1,u,w) = z * L(T((z \ 1) * K(y,x),z),u,w)
    ]]></literal>
    <justification jstring="[para(3425(a,1),35100(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3425 35100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35314">
    <literal><![CDATA[
      (1 / (K(x,y) / z)) * L(z \ 1,u,w) = z * L(T(z \ K(y,x),z),u,w)
    ]]></literal>
    <justification jstring="[para(14444(a,1),35313(a,2,2,1,1))].">
      <j1 rule="para" parents="14444 35313"/>
    </justification>
  </clause>

  <clause id="35315">
    <literal><![CDATA[
      (1 / (K(x,y) / z)) * L(z \ 1,u,w) = L(z \ K(y,x),u,w) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,266,a(flip),b,35314,a),flip(a)].">
      <j1 rule="hyper" parents="373 266 35314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35316">
    <literal><![CDATA[
      R(x,x,(1 / (K(y,z) / (x \ u))) * L((x \ u) \ 1,w,v5)) = R(1 / (1 / x),x,u * L((x \ u) \ K(z,y),w,v5))
    ]]></literal>
    <justification jstring="[para(35315(a,2),34682(a,2,3)),flip(a)].">
      <j1 rule="para" parents="35315 34682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35317">
    <literal><![CDATA[
      L(x,T((L(y,z,z) / u) * w,w \ u),v5) = L(x,(u \ R(y,z,z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(15117(a,1),35121(a,1,2))].">
      <j1 rule="para" parents="15117 35121"/>
    </justification>
  </clause>

  <clause id="35318">
    <literal><![CDATA[
      L(x,(L(y,z,z) / u) * w,v5) = L(x,(u \ R(y,z,z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(29565,a,35317,a)].">
      <j1 rule="hyper" parents="29565 35317"/>
    </justification>
  </clause>

  <clause id="35320">
    <literal><![CDATA[
      L(x,(y \ R(z,u,u)) * w,v5) = L(x,(y \ L(z,u,u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29443,a(flip),b,35318,a),flip(a)].">
      <j1 rule="hyper" parents="64 29443 35318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35321">
    <literal><![CDATA[
      1 / (1 / (((x * y) * y) / x)) = (((x * y) * y) / x) * 1
    ]]></literal>
    <justification jstring="[para(9475(a,1),35122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9475 35122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35322">
    <literal><![CDATA[
      1 / (1 / (((x * y) * y) / x)) = ((x * y) * y) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a(flip),b,35321,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 35321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35324">
    <literal><![CDATA[
      1 / (1 / (x / ((x / y) / y))) = ((x * y) * y) / x
    ]]></literal>
    <justification jstring="[para(35282(a,1),35322(a,1,2,2))].">
      <j1 rule="para" parents="35282 35322"/>
    </justification>
  </clause>

  <clause id="35325">
    <literal><![CDATA[
      1 / (1 / (x / ((x / y) / y))) = x / ((x / y) / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,35282,a(flip),b,35324,a),flip(a)].">
      <j1 rule="hyper" parents="373 35282 35324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35326">
    <literal><![CDATA[
      1 / (x / ((x / y) / y)) = (x / ((x / y) / y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(215,a,35325,a),flip(a)].">
      <j1 rule="hyper" parents="215 35325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35327">
    <literal><![CDATA[
      a(x,L(((y \ 1) \ z) * u,w,v5),v6) = a(x,L(u * (z / y),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32293,a(flip),b,35123,a),flip(a)].">
      <j1 rule="hyper" parents="64 32293 35123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35329">
    <literal><![CDATA[
      a(x,L(((y \ 1) \ z) * u,w,v5),v6) = a(x,L(u * (y \ z),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32160,a(flip),b,35327,a),flip(a)].">
      <j1 rule="hyper" parents="373 32160 35327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35330">
    <literal><![CDATA[
      a(x,L(y * ((z \ 1) \ u),w,v5),v6) = a(x,L(y * (z \ u),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,31956,a,b,35329,a)].">
      <j1 rule="hyper" parents="64 31956 35329"/>
    </justification>
  </clause>

  <clause id="35331">
    <literal><![CDATA[
      a(x,L(y * (z / (u \ 1)),w,v5),v6) = a(x,L(y * (u \ z),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32319,a(flip),b,35329,a)].">
      <j1 rule="hyper" parents="64 32319 35329"/>
    </justification>
  </clause>

  <clause id="35332">
    <literal><![CDATA[
      a(x,L(y * (z \ 1),u,w),v5) = a(x,L(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),35331(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="79 35331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35333">
    <literal><![CDATA[
      a(x,L((y \ ((y * z) * u)) * y,w,v5),v6) = a(x,L(((y \ 1) * z) * u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32163,a(flip),b,35332,a),flip(a)].">
      <j1 rule="hyper" parents="64 32163 35332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35334">
    <literal><![CDATA[
      a(x,L((y * z) * y,u,w),v5) = a(x,L(L(z,u,w),y,y),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32128,a(flip),b,35332,a),flip(a)].">
      <j1 rule="hyper" parents="64 32128 35332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35335">
    <literal><![CDATA[
      a(x,L(((y \ 1) * z) * u,w,v5),v6) = a(x,L((y * z) * u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,31955,a(flip),b,35333,a),flip(a)].">
      <j1 rule="hyper" parents="64 31955 35333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35337">
    <literal><![CDATA[
      T((x * y) * (K(z,u) * (x \ 1)),K(z,u)) = (K(z,T(u,x)) * (x * y)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(27873(a,1),35266(a,1,1))].">
      <j1 rule="para" parents="27873 35266"/>
    </justification>
  </clause>

  <clause id="35338">
    <literal><![CDATA[
      T(x * y,K(z,u)) * (x \ K(z,u)) = (K(z,T(u,x)) * (x * y)) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,22977,a(flip),b,35337,a)].">
      <j1 rule="hyper" parents="64 22977 35337"/>
    </justification>
  </clause>

  <clause id="35339">
    <literal><![CDATA[
      T(x * y,K(z,u)) * (x \ K(z,u)) = (x * (K(z,u) * y)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(22760(a,1),35338(a,2,1))].">
      <j1 rule="para" parents="22760 35338"/>
    </justification>
  </clause>

  <clause id="35340">
    <literal><![CDATA[
      (x * K(y \ z,y)) \ (u / (z / y)) = T(x \ (u / (y \ z)),K(y,z))
    ]]></literal>
    <justification jstring="[hyper(23316,a,22961,a),flip(a)].">
      <j1 rule="hyper" parents="23316 22961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35342">
    <literal><![CDATA[
      K(x,x \ y) * (z \ (u / (y / x))) = T(z \ (u / (x \ y)),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,23272,a(flip),b,35340,a)].">
      <j1 rule="hyper" parents="64 23272 35340"/>
    </justification>
  </clause>

  <clause id="35343">
    <literal><![CDATA[
      K(x,T((y \ z) \ T(u,y \ z),w) * v5) = K(x,T((u / z) * y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,33968,a(flip),b,23640,a)].">
      <j1 rule="hyper" parents="64 33968 23640"/>
    </justification>
  </clause>

  <clause id="35346">
    <literal><![CDATA[
      K(x,T(y / (z \ u),w) * v5) = K(x,T((y / u) * z,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,18571,a(flip),b,35343,a)].">
      <j1 rule="hyper" parents="64 18571 35343"/>
    </justification>
  </clause>

  <clause id="35347">
    <literal><![CDATA[
      T(L(x,1 / y,L(y,z,u)) * (1 / y),L(y,z,u)) = (y \ 1) * R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(2968(a,1),23754(a,2,2))].">
      <j1 rule="para" parents="2968 23754"/>
    </justification>
  </clause>

  <clause id="35348">
    <literal><![CDATA[
      T(L(x,y,L(y,z,u)) * (1 / y),L(y,z,u)) = (y \ 1) * R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11776(a,1),35347(a,1,1,1))].">
      <j1 rule="para" parents="11776 35347"/>
    </justification>
  </clause>

  <clause id="35349">
    <literal><![CDATA[
      (L(x,y,L(y,z,u)) * (1 / y)) * y = y * ((y \ 1) * R(x,y,L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(145,a,35348,a(flip),b,23167,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 35348 23167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35350">
    <literal><![CDATA[
      (L(x,y,L(y,z,u)) * (1 / y)) * y = L(R(x,y,L(y,z,u)),y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1139,a(flip),b,35349,a),flip(a)].">
      <j1 rule="hyper" parents="373 1139 35349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35352">
    <literal><![CDATA[
      R(L(x,y,L(y,z,u)),y,y) = L(R(x,y,L(y,z,u)),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1405,a(flip),b,35350,a)].">
      <j1 rule="hyper" parents="64 1405 35350"/>
    </justification>
  </clause>

  <clause id="35353">
    <literal><![CDATA[
      L(R(x,y,L(y,z,u)),y,y) = L(R(x,y,y),y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(25244,a,35352,a),flip(a)].">
      <j1 rule="hyper" parents="25244 35352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35355">
    <literal><![CDATA[
      ((x \ y) / x) * K(x * ((x \ y) / x),x) = x \ (L(x,y,x) \ y)
    ]]></literal>
    <justification jstring="[para(82(a,1),24937(a,1,2,2))].">
      <j1 rule="para" parents="82 24937"/>
    </justification>
  </clause>

  <clause id="35356">
    <literal><![CDATA[
      ((x \ y) / x) * K(x \ y,x) = x \ (L(x,y,x) \ y)
    ]]></literal>
    <justification jstring="[para(8519(a,1),35355(a,1,2))].">
      <j1 rule="para" parents="8519 35355"/>
    </justification>
  </clause>

  <clause id="35357">
    <literal><![CDATA[
      x \ (L(x,y,x) \ y) = T(x \ y,x) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,6315,a(flip),b,35356,a),flip(a)].">
      <j1 rule="hyper" parents="64 6315 35356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35358">
    <literal><![CDATA[
      L(x,x \ T(x \ y,x),x \ (x \ y)) = (1 / (x \ (L(x,y,x) \ y))) * T(x \ y,x)
    ]]></literal>
    <justification jstring="[para(35357(a,2),29062(a,2,1,2))].">
      <j1 rule="para" parents="35357 29062"/>
    </justification>
  </clause>

  <clause id="35359">
    <literal><![CDATA[
      L(x,x \ T(x \ y,x),L(y,x,x)) = (1 / (x \ (L(x,y,x) \ y))) * T(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30390,a(flip),b,35358,a)].">
      <j1 rule="hyper" parents="64 30390 35358"/>
    </justification>
  </clause>

  <clause id="35360">
    <literal><![CDATA[
      (1 / (x \ (L(x,y,x) \ y))) * T(x \ y,x) = L(x,x \ (x \ y),L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,29450,a(flip),b,35359,a),flip(a)].">
      <j1 rule="hyper" parents="64 29450 35359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35362">
    <literal><![CDATA[
      (1 / (x \ (L(x,y,x) \ y))) * T(x \ y,x) = L(x,L(y,x,x),L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,31756,a(flip),b,35360,a),flip(a)].">
      <j1 rule="hyper" parents="373 31756 35360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35363">
    <literal><![CDATA[
      (1 / (T(x \ y,x) / x)) * T(x \ y,x) = L(x,L(y,x,x),L(y,x,x))
    ]]></literal>
    <justification jstring="[para(35357(a,1),35362(a,1,1,2))].">
      <j1 rule="para" parents="35357 35362"/>
    </justification>
  </clause>

  <clause id="35364">
    <literal><![CDATA[
      L(x,L(y,x,x),L(y,x,x)) = (1 / ((x \ y) / x)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,24964,a(flip),b,35363,a),flip(a)].">
      <j1 rule="hyper" parents="64 24964 35363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35366">
    <literal><![CDATA[
      (1 / ((x \ y) / x)) * (x \ y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35161,a(flip),b,35364,a),flip(a)].">
      <j1 rule="hyper" parents="64 35161 35364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35368">
    <literal><![CDATA[
      (L(x,y,y) / z) \ (((1 / ((x \ y) / x)) * ((x \ y) * z)) / z) = L(z,x \ y,1 / ((x \ y) / x))
    ]]></literal>
    <justification jstring="[para(35366(a,1),3209(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="35366 3209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35369">
    <literal><![CDATA[
      L(((x \ 1) * y) \ z,x * y,x * y) = K(u,w) \ ((K(u,w) / ((x \ 1) * y)) * z)
    ]]></literal>
    <justification jstring="[hyper(29615,a,25261,a)].">
      <j1 rule="hyper" parents="29615 25261"/>
    </justification>
  </clause>

  <clause id="35370">
    <literal><![CDATA[
      L(((x \ 1) * y) \ z,x * y,x * y) = K(x,x * x) \ ((1 / ((1 / x) * y)) * z)
    ]]></literal>
    <justification jstring="[para(14941(a,1),35369(a,2,2,1))].">
      <j1 rule="para" parents="14941 35369"/>
    </justification>
  </clause>

  <clause id="35371">
    <literal><![CDATA[
      L(((x \ 1) * y) \ z,x * y,x * y) = K(x * x,x) * ((1 / ((1 / x) * y)) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,6156,a(flip),b,35370,a),flip(a)].">
      <j1 rule="hyper" parents="373 6156 35370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35372">
    <literal><![CDATA[
      L(((x \ 1) * y) \ z,x * y,x * y) = a(x,x,x) * ((1 / ((1 / x) * y)) * z)
    ]]></literal>
    <justification jstring="[para(98(a,1),35371(a,2,1))].">
      <j1 rule="para" parents="98 35371"/>
    </justification>
  </clause>

  <clause id="35373">
    <literal><![CDATA[
      L(((x \ 1) * y) \ z,x * y,x * y) = (a(x,x,x) / ((1 / x) * y)) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,12913,a(flip),b,35372,a),flip(a)].">
      <j1 rule="hyper" parents="373 12913 35372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35374">
    <literal><![CDATA[
      L(((x \ 1) * y) \ z,x * y,x * y) = (1 / ((x \ 1) * y)) * z
    ]]></literal>
    <justification jstring="[para(15146(a,1),35373(a,2,1))].">
      <j1 rule="para" parents="15146 35373"/>
    </justification>
  </clause>

  <clause id="35375">
    <literal><![CDATA[
      L((((x / y) / x) * y) \ z,y * (((y \ 1) * x) \ x),y * (((y \ 1) * x) \ x)) = (1 / ((y \ 1) * (((y \ 1) * x) \ x))) * z
    ]]></literal>
    <justification jstring="[para(26380(a,1),35374(a,1,1,1))].">
      <j1 rule="para" parents="26380 35374"/>
    </justification>
  </clause>

  <clause id="35376">
    <literal><![CDATA[
      K(x,T(y,z)) * ((z \ 1) * ((x * z) \ x)) = ((z \ 1) * K(x,y)) * L(z \ 1,z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27812,a(flip),b,25446,a)].">
      <j1 rule="hyper" parents="64 27812 25446"/>
    </justification>
  </clause>

  <clause id="35377">
    <literal><![CDATA[
      K(x,T(y,z)) * (((x * z) \ x) / z) = ((z \ 1) * K(x,y)) * L(z \ 1,z,x)
    ]]></literal>
    <justification jstring="[para(30687(a,1),35376(a,1,2))].">
      <j1 rule="para" parents="30687 35376"/>
    </justification>
  </clause>

  <clause id="35378">
    <literal><![CDATA[
      ((x * y) \ (K(x,z) * x)) / y = ((y \ 1) * K(x,z)) * L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25733,a(flip),b,35377,a)].">
      <j1 rule="hyper" parents="64 25733 35377"/>
    </justification>
  </clause>

  <clause id="35379">
    <literal><![CDATA[
      ((x \ 1) * K(y,z)) * L(x \ 1,x,y) = ((y * x) \ T(y,z)) / x
    ]]></literal>
    <justification jstring="[para(5756(a,2),35378(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5756 35378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35380">
    <literal><![CDATA[
      (x \ K(y,z)) * L(x \ 1,x,y) = ((y * x) \ T(y,z)) / x
    ]]></literal>
    <justification jstring="[para(14444(a,1),35379(a,1,1))].">
      <j1 rule="para" parents="14444 35379"/>
    </justification>
  </clause>

  <clause id="35381">
    <literal><![CDATA[
      x \ L(K(y,z) / x,x,y) = ((y * x) \ T(y,z)) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,27892,a(flip),b,35380,a)].">
      <j1 rule="hyper" parents="64 27892 35380"/>
    </justification>
  </clause>

  <clause id="35382">
    <literal><![CDATA[
      a(x,y,x) * (L(R(x,y,x),z,x * z) \ x) = a(z * R(x,y,x),z,R(x,y,x))
    ]]></literal>
    <justification jstring="[para(23988(a,1),25597(a,1,2,1))].">
      <j1 rule="para" parents="23988 25597"/>
    </justification>
  </clause>

  <clause id="35383">
    <literal><![CDATA[
      a(x,y,x) * (L(x,z,x * z) \ L(x,y,x)) = a(z * R(x,y,x),z,R(x,y,x))
    ]]></literal>
    <justification jstring="[para(13574(a,1),35382(a,1,2))].">
      <j1 rule="para" parents="13574 35382"/>
    </justification>
  </clause>

  <clause id="35385">
    <literal><![CDATA[
      a(x * R(y,z,y),x,R(y,z,y)) = L(y,x,y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,13232,a(flip),b,35383,a),flip(a)].">
      <j1 rule="hyper" parents="64 13232 35383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35387">
    <literal><![CDATA[
      a(x * R(y,z,y),x,y) = L(y,x,y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,13864,a(flip),b,35385,a)].">
      <j1 rule="hyper" parents="64 13864 35385"/>
    </justification>
  </clause>

  <clause id="35389">
    <literal><![CDATA[
      L(x,y,x * y) \ x = a(x * y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26826,a(flip),b,35387,a),flip(a)].">
      <j1 rule="hyper" parents="64 26826 35387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35390">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ u,R(x,y,z) \ x,R(x,y,z) \ x) = u * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(24813(a,1),25933(a,1,1,1))].">
      <j1 rule="para" parents="24813 25933"/>
    </justification>
  </clause>

  <clause id="35391">
    <literal><![CDATA[
      L(a(x,y,y) \ z,R(x,y,y) \ x,R(x,y,y) \ x) = z * (R(x,y,y) \ x)
    ]]></literal>
    <justification jstring="[para(15987(a,1),35390(a,1,1,1))].">
      <j1 rule="para" parents="15987 35390"/>
    </justification>
  </clause>

  <clause id="35392">
    <literal><![CDATA[
      L(a(x,y,y) \ z,R(x,y,y) \ x,a(y,y,x)) = z * (R(x,y,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29269,a(flip),b,35391,a)].">
      <j1 rule="hyper" parents="64 29269 35391"/>
    </justification>
  </clause>

  <clause id="35393">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(x,y,y),a(y,y,x)) = z * (R(x,y,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,16024,a(flip),b,35392,a)].">
      <j1 rule="hyper" parents="64 16024 35392"/>
    </justification>
  </clause>

  <clause id="35394">
    <literal><![CDATA[
      L(L(T(K(x \ 1,y) * z,T(x \ 1,y)),u,w),x,x) = x * (L(z,u,w) * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(25479(a,2),26101(a,1,1,1))].">
      <j1 rule="para" parents="25479 26101"/>
    </justification>
  </clause>

  <clause id="35395">
    <literal><![CDATA[
      x \ (y * (z \ T(T(z,u),w))) = (x \ y) * (z \ T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(23319(a,1),26235(a,1,1))].">
      <j1 rule="para" parents="23319 26235"/>
    </justification>
  </clause>

  <clause id="35397">
    <literal><![CDATA[
      (x \ 1) \ (x * (R(x,y,z) \ T(T(R(x,y,z),u),w))) = R(x \ 1,y,z) \ T(T(R(x,y,z),w),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2759,a(flip),b,35395,a),flip(a)].">
      <j1 rule="hyper" parents="373 2759 35395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35398">
    <literal><![CDATA[
      L(x \ R(x,y,z * (u * w)),x,y * ((u * w) * z)) = a(x,y,(u * T(w,v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29094,a(flip),b,26330,a)].">
      <j1 rule="hyper" parents="64 29094 26330"/>
    </justification>
  </clause>

  <clause id="35400">
    <literal><![CDATA[
      L(x \ R(x,y,z * (u * u)),x,y * z) = a(x,y,(u * T(u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,24856,a(flip),b,35398,a)].">
      <j1 rule="hyper" parents="64 24856 35398"/>
    </justification>
  </clause>

  <clause id="35401">
    <literal><![CDATA[
      L(x \ R(x,y,z * (u * u)),x,y * z) = a(x,y,z * (u * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27533,a(flip),b,35400,a),flip(a)].">
      <j1 rule="hyper" parents="373 27533 35400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35402">
    <literal><![CDATA[
      a(((x * y) * z) \ (R(z,x,y * (u * u)) * (x * y)),w,v5) = a(a(z,x,y * (u * u)),w,v5)
    ]]></literal>
    <justification jstring="[para(35401(a,1),32480(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35401 32480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35403">
    <literal><![CDATA[
      R(x,y * z,y * z) * ((z * y) * T(y * z,u)) = (x * T(y * z,u)) * (z * y)
    ]]></literal>
    <justification jstring="[para(23810(a,1),26335(a,1,1))].">
      <j1 rule="para" parents="23810 26335"/>
    </justification>
  </clause>

  <clause id="35404">
    <literal><![CDATA[
      (x * T(y * z,u)) * (z * y) = (x * (z * y)) * T(y * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26476,a(flip),b,35403,a),flip(a)].">
      <j1 rule="hyper" parents="64 26476 35403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35406">
    <literal><![CDATA[
      L((x \ (y \ x)) \ z,L(y,y,x),y) = (L(x \ (y \ x),y,y) * y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35055,a(flip),b,26346,a)].">
      <j1 rule="hyper" parents="64 35055 26346"/>
    </justification>
  </clause>

  <clause id="35408">
    <literal><![CDATA[
      L((x \ (y \ x)) \ z,y,L(y,y,x)) = (L(x \ (y \ x),y,y) * y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2482,a(flip),b,35406,a)].">
      <j1 rule="hyper" parents="64 2482 35406"/>
    </justification>
  </clause>

  <clause id="35409">
    <literal><![CDATA[
      L((x \ (y \ x)) \ z,y,L(y,y,x)) = (y * (x \ (y \ x))) \ (y * z)
    ]]></literal>
    <justification jstring="[para(26345(a,1),35408(a,2,1))].">
      <j1 rule="para" parents="26345 35408"/>
    </justification>
  </clause>

  <clause id="35410">
    <literal><![CDATA[
      R(x,y,(T(z * u,w) \ ((u * w) * z)) \ v5) = R(x,y,K(z,w * u) * (L(w,u,z) \ v5))
    ]]></literal>
    <justification jstring="[para(26084(a,1),26402(a,2,3))].">
      <j1 rule="para" parents="26084 26402"/>
    </justification>
  </clause>

  <clause id="35411">
    <literal><![CDATA[
      (x \ 1) / (y \ (x \ y)) = (y \ (x \ y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(26632(a,1),26537(a,1,2))].">
      <j1 rule="para" parents="26632 26537"/>
    </justification>
  </clause>

  <clause id="35412">
    <literal><![CDATA[
      (1 / x) / (y \ ((1 / (1 / x)) \ y)) = (y \ (x \ y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,15111,a,b,35411,a)].">
      <j1 rule="hyper" parents="64 15111 35411"/>
    </justification>
  </clause>

  <clause id="35414">
    <literal><![CDATA[
      R(x,1 / (y \ z),L(1 / (y \ z),y \ z,y)) = R(x,1 / (1 / (z \ y)),(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,23813,a(flip),b,26649,a),flip(a)].">
      <j1 rule="hyper" parents="373 23813 26649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35415">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((z * u) * w)) = a(x,y,(z * u) * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27572,a(flip),b,27638,a)].">
      <j1 rule="hyper" parents="64 27572 27638"/>
    </justification>
  </clause>

  <clause id="35417">
    <literal><![CDATA[
      ((x \ R(x,x,y)) \ z) * K(y,y \ (x \ y)) = z / T(x * (y \ (x \ y)),K(x \ y,y))
    ]]></literal>
    <justification jstring="[para(23705(a,1),28000(a,1,1))].">
      <j1 rule="para" parents="23705 28000"/>
    </justification>
  </clause>

  <clause id="35418">
    <literal><![CDATA[
      L(x,y,L(a(z,u,u \ 1) \ K(w,v5),v6,v7)) = L(x,y,L(u * L(u \ 1,u,z),v6,v7))
    ]]></literal>
    <justification jstring="[para(33367(a,1),29173(a,1,3,1))].">
      <j1 rule="para" parents="33367 29173"/>
    </justification>
  </clause>

  <clause id="35419">
    <literal><![CDATA[
      L(x,y,L(z * L(z \ 1,z,u),w,v5)) = L(x,y,L(a(u,z,z \ 1),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,34227,a(flip),b,35418,a),flip(a)].">
      <j1 rule="hyper" parents="64 34227 35418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35420">
    <literal><![CDATA[
      L(x,y,L(z * L(z \ 1,z,u),w,v5)) = L(x,y,a(L(u,w,v5),z,z \ 1))
    ]]></literal>
    <justification jstring="[para(4248(a,2),35419(a,2,3))].">
      <j1 rule="para" parents="4248 35419"/>
    </justification>
  </clause>

  <clause id="35421">
    <literal><![CDATA[
      L(x,y,L(z * L(z \ 1,z,u),w,v5)) = L(x,y,a(L(u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,33636,a(flip),b,35420,a),flip(a)].">
      <j1 rule="hyper" parents="373 33636 35420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35422">
    <literal><![CDATA[
      L(x,y,L(z * ((u * z) \ u),w,v5)) = L(x,y,a(L(u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[para(241(a,1),35421(a,1,3,1,2))].">
      <j1 rule="para" parents="241 35421"/>
    </justification>
  </clause>

  <clause id="35423">
    <literal><![CDATA[
      L(x,y,a(L(z,u,w),v5,v5)) = L(x,y,L(a(v5,v5,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,30999,a(flip),b,35422,a),flip(a)].">
      <j1 rule="hyper" parents="64 30999 35422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35424">
    <literal><![CDATA[
      L(x,y,a(L(z,u,w),v5,v5)) = L(x,y,a(v5,L(v5,u,w),z))
    ]]></literal>
    <justification jstring="[para(34877(a,2),35423(a,2,3))].">
      <j1 rule="para" parents="34877 35423"/>
    </justification>
  </clause>

  <clause id="35425">
    <literal><![CDATA[
      L(x,(1 / x) * y,L(y,x,x)) = ((1 / (((1 / x) * y) * x)) * ((1 / x) * y)) \ 1
    ]]></literal>
    <justification jstring="[para(1139(a,1),29239(a,1,3))].">
      <j1 rule="para" parents="1139 29239"/>
    </justification>
  </clause>

  <clause id="35426">
    <literal><![CDATA[
      L(x,x * y,L(y,x,x)) = ((1 / (((1 / x) * y) * x)) * ((1 / x) * y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,11777,a(flip),b,35425,a)].">
      <j1 rule="hyper" parents="64 11777 35425"/>
    </justification>
  </clause>

  <clause id="35427">
    <literal><![CDATA[
      ((1 / (((1 / x) * y) * x)) * ((1 / x) * y)) \ 1 = L(x,x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31528,a(flip),b,35426,a),flip(a)].">
      <j1 rule="hyper" parents="64 31528 35426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35428">
    <literal><![CDATA[
      ((1 / (((1 / x) * (y * x)) * x)) * ((1 / x) * (y * x))) \ 1 = L(x,x * (y * x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30388,a(flip),b,35426,a),flip(a)].">
      <j1 rule="hyper" parents="64 30388 35426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35429">
    <literal><![CDATA[
      (R(x,y,y) * y) \ (a(x,y,y) * (x * (y * z))) = L(L(z,y,x),x * y,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(29967(a,1),29310(a,1,1))].">
      <j1 rule="para" parents="29967 29310"/>
    </justification>
  </clause>

  <clause id="35430">
    <literal><![CDATA[
      (R(x,y,y) * y) \ (x * (a(x,y,y) * (y * z))) = L(L(z,y,x),x * y,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(29307(a,1),35429(a,1,2))].">
      <j1 rule="para" parents="29307 35429"/>
    </justification>
  </clause>

  <clause id="35431">
    <literal><![CDATA[
      (R(x,y,y) * y) \ (x * (y * (z * a(x,y,y)))) = L(L(z,y,x),x * y,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(33200(a,1),35430(a,1,2,2))].">
      <j1 rule="para" parents="33200 35430"/>
    </justification>
  </clause>

  <clause id="35432">
    <literal><![CDATA[
      L(x,L(T(y * y,z) * u,z,w),v5) = L(x,T(w * z,v6) \ (w * (z * u)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29875,a(flip),b,29583,a),flip(a)].">
      <j1 rule="hyper" parents="64 29875 29583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35434">
    <literal><![CDATA[
      L(x,L(T(y * y,z) * u,z,w),v5) = L(x,L(K(v6,w * z) * u,z,w),v5)
    ]]></literal>
    <justification jstring="[para(26090(a,1),35432(a,2,2))].">
      <j1 rule="para" parents="26090 35432"/>
    </justification>
  </clause>

  <clause id="35435">
    <literal><![CDATA[
      L(x,L(T(y * y,z) * u,z,w),v5) = L(x,L(u,z,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29471,a(flip),b,35434,a),flip(a)].">
      <j1 rule="hyper" parents="373 29471 35434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35437">
    <literal><![CDATA[
      L(x,L((y * y) * z,u,w),v5) = L(x,L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29472,a(flip),b,35435,a)].">
      <j1 rule="hyper" parents="64 29472 35435"/>
    </justification>
  </clause>

  <clause id="35439">
    <literal><![CDATA[
      L(x,L((y \ 1) \ z,u,w),v5) = L(x,L(z / y,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31744,a(flip),b,35437,a)].">
      <j1 rule="hyper" parents="64 31744 35437"/>
    </justification>
  </clause>

  <clause id="35441">
    <literal><![CDATA[
      L(x,L((y \ 1) \ z,u,w),v5) = L(x,L(y \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29495,a(flip),b,35439,a),flip(a)].">
      <j1 rule="hyper" parents="373 29495 35439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35442">
    <literal><![CDATA[
      L(x,L((1 / y) \ z,u,w),v5) = L(x,L(y \ z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29750,a,b,35441,a)].">
      <j1 rule="hyper" parents="64 29750 35441"/>
    </justification>
  </clause>

  <clause id="35443">
    <literal><![CDATA[
      L(x,y \ ((z * T(u,w)) * L(v5,z,u)),v6) = L(x,y \ (u * (T(z,T(u,w)) * v5)),v6)
    ]]></literal>
    <justification jstring="[para(23215(a,1),29754(a,1,2,2,2))].">
      <j1 rule="para" parents="23215 29754"/>
    </justification>
  </clause>

  <clause id="35444">
    <literal><![CDATA[
      L(x,y \ (L(z,u,w) * (u * w)),v5) = L(x,y \ (w * (T(u,T(w,v6)) * z)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29847,a(flip),b,35443,a)].">
      <j1 rule="hyper" parents="64 29847 35443"/>
    </justification>
  </clause>

  <clause id="35446">
    <literal><![CDATA[
      L(x,y \ (L(z,u,w) * (u * w)),v5) = L(x,y \ ((u * z) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29846,a(flip),b,35444,a),flip(a)].">
      <j1 rule="hyper" parents="373 29846 35444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35449">
    <literal><![CDATA[
      L(x,(y * (z * u)) \ (L(y,z,u) * (z * u)),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29842,a(flip),b,35446,a),flip(a)].">
      <j1 rule="hyper" parents="373 29842 35446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35450">
    <literal><![CDATA[
      L(x,L(y * L(y,z,u),y,z * u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31078,a,b,35449,a)].">
      <j1 rule="hyper" parents="64 31078 35449"/>
    </justification>
  </clause>

  <clause id="35451">
    <literal><![CDATA[
      L(x,L(y * L(y,z,u),y,u * z),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(23253(a,1),35450(a,1,2))].">
      <j1 rule="para" parents="23253 35450"/>
    </justification>
  </clause>

  <clause id="35452">
    <literal><![CDATA[
      L(x,(y * z) \ (u \ (z * (y * u))),w) = L(x,a(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,34267,a(flip),b,35451,a)].">
      <j1 rule="hyper" parents="64 34267 35451"/>
    </justification>
  </clause>

  <clause id="35453">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * (z * u)) / u),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33819,a(flip),b,35451,a)].">
      <j1 rule="hyper" parents="64 33819 35451"/>
    </justification>
  </clause>

  <clause id="35454">
    <literal><![CDATA[
      L(x,((y \ z) * u) \ (y \ (u * z)),w) = L(x,a(y,y \ z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29685,a(flip),b,35452,a)].">
      <j1 rule="hyper" parents="64 29685 35452"/>
    </justification>
  </clause>

  <clause id="35455">
    <literal><![CDATA[
      L(x,a(y,z,u * (w * w)),v5) = L(x,(u * z) \ ((u * (z * y)) / y),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,34487,a,b,35453,a)].">
      <j1 rule="hyper" parents="373 34487 35453"/>
    </justification>
  </clause>

  <clause id="35456">
    <literal><![CDATA[
      (x * ((1 / x) * (L(x,y,z) * u))) \ (L(x,y,z) * u) = a(x,x,(u / x) * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(25125(a,1),29931(a,1,1,2))].">
      <j1 rule="para" parents="25125 29931"/>
    </justification>
  </clause>

  <clause id="35457">
    <literal><![CDATA[
      (L(x,y,z) * L(u,x,x)) \ (L(x,y,z) * u) = a(x,x,(u / x) * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(27185(a,1),35456(a,1,1))].">
      <j1 rule="para" parents="27185 35456"/>
    </justification>
  </clause>

  <clause id="35458">
    <literal><![CDATA[
      a(x,x,(y / x) * L(x,z,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30888,a(flip),b,35457,a),flip(a)].">
      <j1 rule="hyper" parents="64 30888 35457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35460">
    <literal><![CDATA[
      a(x,x,(x \ y) * L(x,z,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27317,a(flip),b,35458,a)].">
      <j1 rule="hyper" parents="64 27317 35458"/>
    </justification>
  </clause>

  <clause id="35461">
    <literal><![CDATA[
      a(x,x,y * L(x,z,u)) = a(x,x,y * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),35458(a,1,3,1))].">
      <j1 rule="para" parents="11 35458"/>
    </justification>
  </clause>

  <clause id="35462">
    <literal><![CDATA[
      a(x,x,L(x,y,z) * u) = a(x,x,x * u)
    ]]></literal>
    <justification jstring="[para(24379(a,1),35458(a,1,3))].">
      <j1 rule="para" parents="24379 35458"/>
    </justification>
  </clause>

  <clause id="35463">
    <literal><![CDATA[
      a(x,x,(x \ y) * R(x,z,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31317,a,b,35460,a)].">
      <j1 rule="hyper" parents="64 31317 35460"/>
    </justification>
  </clause>

  <clause id="35464">
    <literal><![CDATA[
      a(x,x,L(x,y,z) * u) = a(x,x,u * x)
    ]]></literal>
    <justification jstring="[hyper(27453,a,35461,a)].">
      <j1 rule="hyper" parents="27453 35461"/>
    </justification>
  </clause>

  <clause id="35465">
    <literal><![CDATA[
      a(x,x,x * (L(x,y,z) \ u)) = a(x,x,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),35462(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 35462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35466">
    <literal><![CDATA[
      a(x,x,x * (R(x \ 1,y,z) * u)) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31780,a,b,35463,a)].">
      <j1 rule="hyper" parents="64 31780 35463"/>
    </justification>
  </clause>

  <clause id="35467">
    <literal><![CDATA[
      a(x,x,y * R(x,z,u)) = a(x,x,x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),35463(a,1,3,1))].">
      <j1 rule="para" parents="9 35463"/>
    </justification>
  </clause>

  <clause id="35468">
    <literal><![CDATA[
      a(x,x,L(x,y,z) * u) = x \ R(x,x,u * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,30058,a,b,35464,a),flip(a)].">
      <j1 rule="hyper" parents="373 30058 35464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35469">
    <literal><![CDATA[
      (L(x,y,z) \ u) / (x * (L(x,y,z) \ u)) = x \ a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,35465,a(flip),b,30079,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 35465 30079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35470">
    <literal><![CDATA[
      a(x,x,y * R(x,z,u)) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30137,a,b,35467,a),flip(a)].">
      <j1 rule="hyper" parents="373 30137 35467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35472">
    <literal><![CDATA[
      x \ ((x \ 1) \ (R(x \ 1,y,z) * u)) = (R(x \ 1,y,z) * u) * a(x,x,u)
    ]]></literal>
    <justification jstring="[para(35466(a,1),30254(a,1,2)),flip(a)].">
      <j1 rule="para" parents="35466 30254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35473">
    <literal><![CDATA[
      R(x,x,L(x,y,z) * u) = R(x,x,u * x)
    ]]></literal>
    <justification jstring="[hyper(39,a,30058,a,b,35468,a(flip))].">
      <j1 rule="hyper" parents="39 30058 35468"/>
    </justification>
  </clause>

  <clause id="35474">
    <literal><![CDATA[
      R(x,x,(y / L(x,z,u)) * x) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26166,a(flip),b,35473,a),flip(a)].">
      <j1 rule="hyper" parents="64 26166 35473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35475">
    <literal><![CDATA[
      R(x,x,x * (L(x,y,z) \ u)) = R(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26241,a(flip),b,35474,a)].">
      <j1 rule="hyper" parents="64 26241 35474"/>
    </justification>
  </clause>

  <clause id="35476">
    <literal><![CDATA[
      a(L(x,x,x * (L(x,y,z) \ u)),w,v5) = a(R(x,x,u),w,v5)
    ]]></literal>
    <justification jstring="[para(35475(a,1),32590(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35475 32590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35477">
    <literal><![CDATA[
      ((x / y) * R(y,z,u)) / (R(y,z,u) * x) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,35101,a,b,35470,a(flip))].">
      <j1 rule="hyper" parents="35 35101 35470"/>
    </justification>
  </clause>

  <clause id="35478">
    <literal><![CDATA[
      a(x,L(x,y,z),x * T(L(x,u,w) \ v5,v6)) = L(x * (x \ a(x,x,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(35469(a,1),34889(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="35469 34889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35479">
    <literal><![CDATA[
      a(L(x,x,x * (L(x,y,z) \ u)),w,v5) = a(L(x,x,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32590,a(flip),b,35476,a),flip(a)].">
      <j1 rule="hyper" parents="373 32590 35476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35480">
    <literal><![CDATA[
      R(1 / x,x,(x \ y) * R(x,z,u)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27244,a,b,35477,a)].">
      <j1 rule="hyper" parents="64 27244 35477"/>
    </justification>
  </clause>

  <clause id="35483">
    <literal><![CDATA[
      R(1 / x,x,(y / x) * R(x,z,u)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26180,a,b,35480,a)].">
      <j1 rule="hyper" parents="64 26180 35480"/>
    </justification>
  </clause>

  <clause id="35484">
    <literal><![CDATA[
      R(T(x \ 1,y),x,(z / x) * R(x,u,w)) = T(T(R(1 / x,x,z),y),x)
    ]]></literal>
    <justification jstring="[para(35483(a,1),1263(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="35483 1263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35485">
    <literal><![CDATA[
      R(T(x \ 1,y),x,(z / x) * R(x,u,w)) = R(T(x \ 1,y),x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1263,a(flip),b,35484,a),flip(a)].">
      <j1 rule="hyper" parents="373 1263 35484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35486">
    <literal><![CDATA[
      R(T(x \ 1,y),x,(x \ z) * R(x,u,w)) = R(T(x \ 1,y),x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26180,a(flip),b,35485,a)].">
      <j1 rule="hyper" parents="64 26180 35485"/>
    </justification>
  </clause>

  <clause id="35487">
    <literal><![CDATA[
      R(T(x \ 1,y),x,z * (x \ R(x,u,w))) = R(T(x \ 1,y),x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32950,a(flip),b,35486,a)].">
      <j1 rule="hyper" parents="64 32950 35486"/>
    </justification>
  </clause>

  <clause id="35488">
    <literal><![CDATA[
      x \ (R(x \ 1,y,z) * ((x \ 1) \ u)) = (R(x \ 1,y,z) * u) * a(x,x,u)
    ]]></literal>
    <justification jstring="[para(1898(a,1),35472(a,1,2))].">
      <j1 rule="para" parents="1898 35472"/>
    </justification>
  </clause>

  <clause id="35489">
    <literal><![CDATA[
      a(x,L(x,y,z),x * T(L(x,u,w) \ v5,v6)) = L(a(x,x,v5),y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),35478(a,2,1))].">
      <j1 rule="para" parents="10 35478"/>
    </justification>
  </clause>

  <clause id="35490">
    <literal><![CDATA[
      a(x,L(x,y,z),x * T(L(x,u,w) \ v5,v6)) = a(x,L(x,y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,34877,a,b,35489,a),flip(a)].">
      <j1 rule="hyper" parents="373 34877 35489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35492">
    <literal><![CDATA[
      a(x,L(x,y,z),x * (L(x,u,w) \ v5)) = a(x,L(x,y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27309,a(flip),b,35490,a)].">
      <j1 rule="hyper" parents="64 27309 35490"/>
    </justification>
  </clause>

  <clause id="35493">
    <literal><![CDATA[
      (R(x \ 1,y,z) * u) * a(x,x,u) = x \ (R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[para(2760(a,1),35488(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2760 35488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35494">
    <literal><![CDATA[
      (R(x \ 1,y,z) * u) * a(x,x,u) = R(x,y,z) * (x \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,1898,a(flip),b,35493,a),flip(a)].">
      <j1 rule="hyper" parents="373 1898 35493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35495">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * T(x \ 1,a(x,y,z) \ u)) = (x \ 1) * ((1 / a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(13923(a,1),30003(a,1,1))].">
      <j1 rule="para" parents="13923 30003"/>
    </justification>
  </clause>

  <clause id="35496">
    <literal><![CDATA[
      L(x \ R(x,R(y,y,z),z \ (y \ z)),x,1) = a(x,a(y,y,z) \ y,(y \ z) / z)
    ]]></literal>
    <justification jstring="[para(30136(a,1),30171(a,1,1,2))].">
      <j1 rule="para" parents="30136 30171"/>
    </justification>
  </clause>

  <clause id="35497">
    <literal><![CDATA[
      a(x,a(y,y,z) \ y,(y \ z) / z) = x \ R(x,R(y,y,z),z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(624,a,35496,a),flip(a)].">
      <j1 rule="hyper" parents="624 35496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35498">
    <literal><![CDATA[
      a(x,a(y,y,z) \ y,z \ (y \ z)) = x \ R(x,R(y,y,z),z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(27586,a,35497,a)].">
      <j1 rule="hyper" parents="27586 35497"/>
    </justification>
  </clause>

  <clause id="35500">
    <literal><![CDATA[
      x * a(x,L(y,y,z),z \ (y \ z)) = R(x,R(y,y,z),z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(145,a,32198,a(flip),b,35498,a(flip))].">
      <j1 rule="hyper" parents="145 32198 35498"/>
    </justification>
  </clause>

  <clause id="35501">
    <literal><![CDATA[
      x * a(x,L(y,y,z),z \ (y \ z)) = R(x,L(y,y,z),z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,26636,a(flip),b,35500,a),flip(a)].">
      <j1 rule="hyper" parents="373 26636 35500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35502">
    <literal><![CDATA[
      a(x,y,z) * (x \ (L(a(x,y,z),x,L(u,x,a(x,y,z))) \ (x * u))) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28787(a,1),30325(a,1,2,2,1))].">
      <j1 rule="para" parents="28787 30325"/>
    </justification>
  </clause>

  <clause id="35503">
    <literal><![CDATA[
      ((x * y) \ x) * L(z,a(y,y,x),y) = y * ((y \ (1 / (((x * y) \ x) \ 1))) * z)
    ]]></literal>
    <justification jstring="[para(30377(a,1),30870(a,1,2))].">
      <j1 rule="para" parents="30377 30870"/>
    </justification>
  </clause>

  <clause id="35504">
    <literal><![CDATA[
      ((x * y) \ x) * L(z,y,a(y,y,x)) = y * ((y \ (1 / (((x * y) \ x) \ 1))) * z)
    ]]></literal>
    <justification jstring="[para(30415(a,1),35503(a,1,2))].">
      <j1 rule="para" parents="30415 35503"/>
    </justification>
  </clause>

  <clause id="35505">
    <literal><![CDATA[
      ((x * y) \ x) * L(z,y,a(y,y,x)) = y * ((y \ ((x * y) \ x)) * z)
    ]]></literal>
    <justification jstring="[para(79(a,1),35504(a,2,2,1,2))].">
      <j1 rule="para" parents="79 35504"/>
    </justification>
  </clause>

  <clause id="35507">
    <literal><![CDATA[
      a(1 / x,L(y,x,x),(1 / x) \ L(y,x,x)) = x \ R(x,L(y,x,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1985,a(flip),b,30897,a),flip(a)].">
      <j1 rule="hyper" parents="373 1985 30897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35508">
    <literal><![CDATA[
      a(1 / x,L(y,x,x),x * y) = x \ R(x,L(y,x,x),x * y)
    ]]></literal>
    <justification jstring="[para(561(a,1),35507(a,1,3))].">
      <j1 rule="para" parents="561 35507"/>
    </justification>
  </clause>

  <clause id="35509">
    <literal><![CDATA[
      x \ R(x,L(y,x,x),x * y) = a(x,L(y,x,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2641,a(flip),b,35508,a),flip(a)].">
      <j1 rule="hyper" parents="64 2641 35508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35510">
    <literal><![CDATA[
      a(x,L(y,x,x),x * y) * x = R(x,L(y,x,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(39,a,23174,a,b,35509,a)].">
      <j1 rule="hyper" parents="39 23174 35509"/>
    </justification>
  </clause>

  <clause id="35511">
    <literal><![CDATA[
      R(x,a(y,z,u),R(y,w,v5)) = L(x,R(y,w,v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,28734,a(flip),b,30906,a),flip(a)].">
      <j1 rule="hyper" parents="64 28734 30906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35512">
    <literal><![CDATA[
      R(x,a(y,z,u),R(y,w,v5)) = L(x,L(y,w,v5),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,29794,a(flip),b,35511,a),flip(a)].">
      <j1 rule="hyper" parents="373 29794 35511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35513">
    <literal><![CDATA[
      L(x,L(y,z,u),a(y,w,v5)) = L(x,a(y,w,v5),R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,31802,a(flip),b,35512,a),flip(a)].">
      <j1 rule="hyper" parents="64 31802 35512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35514">
    <literal><![CDATA[
      L(x,L(y,z,u),a(y,w,v5)) = L(x,a(y,w,v5),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,29203,a(flip),b,35513,a),flip(a)].">
      <j1 rule="hyper" parents="373 29203 35513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35517">
    <literal><![CDATA[
      L(x,y,(L(z * u,z,z) \ w) * v5) = L(x,y,v5 * (((u / (z * u)) * u) \ w))
    ]]></literal>
    <justification jstring="[para(82(a,1),30961(a,2,3,2,1,1))].">
      <j1 rule="para" parents="82 30961"/>
    </justification>
  </clause>

  <clause id="35518">
    <literal><![CDATA[
      L(x,y,(L(z * u,z,z) \ w) * v5) = L(x,y,v5 * ((z \ u) \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,34000,a(flip),b,35517,a),flip(a)].">
      <j1 rule="hyper" parents="373 34000 35517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35520">
    <literal><![CDATA[
      L(x,y,z * (L(u * w,w,w) \ v5)) = L(x,y,z * ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,29149,a(flip),b,35518,a)].">
      <j1 rule="hyper" parents="64 29149 35518"/>
    </justification>
  </clause>

  <clause id="35521">
    <literal><![CDATA[
      a(x,y,((z \ (u \ w)) * v5) * R(v6,z \ (u \ w),v5)) = a(x,y,(v6 * ((w / u) / z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27974,a(flip),b,31306,a)].">
      <j1 rule="hyper" parents="64 27974 31306"/>
    </justification>
  </clause>

  <clause id="35522">
    <literal><![CDATA[
      ((x / (y \ z)) * (y \ 1)) * L(u,y,(y \ z) \ x) = (x / ((1 / y) \ z)) * (y * u)
    ]]></literal>
    <justification jstring="[para(29184(a,1),31402(a,1,2))].">
      <j1 rule="para" parents="29184 31402"/>
    </justification>
  </clause>

  <clause id="35523">
    <literal><![CDATA[
      (x / ((1 / y) \ z)) * (y * u) = (x / (y \ z)) * ((y \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23981,a(flip),b,35522,a),flip(a)].">
      <j1 rule="hyper" parents="64 23981 35522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35524">
    <literal><![CDATA[
      L(L(x,y,a(z,z,y)),L(y,z,z),L(y,z,z)) = (1 / y) * (L(y,z,z) * (a(z,z,y) * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,27183,a(flip),b,31848,a),flip(a)].">
      <j1 rule="hyper" parents="373 27183 31848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35525">
    <literal><![CDATA[
      x * (y * ((((x \ 1) \ y) * y) / T(x * y,y))) = ((x \ 1) \ L(y,y,x)) * y
    ]]></literal>
    <justification jstring="[para(5631(a,1),31871(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5631 31871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35526">
    <literal><![CDATA[
      x * (y * ((((x \ 1) \ y) * y) / T(x * y,y))) = ((x \ 1) \ y) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,34325,a(flip),b,35525,a),flip(a)].">
      <j1 rule="hyper" parents="373 34325 35525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35527">
    <literal><![CDATA[
      x * (y * ((x * y) \ (((x \ 1) \ y) * y))) = ((x \ 1) \ y) / (1 / y)
    ]]></literal>
    <justification jstring="[para(31870(a,1),35526(a,1,2,2))].">
      <j1 rule="para" parents="31870 35526"/>
    </justification>
  </clause>

  <clause id="35528">
    <literal><![CDATA[
      x * (y * (x \ ((x \ 1) \ y))) = ((x \ 1) \ y) / (1 / y)
    ]]></literal>
    <justification jstring="[para(31219(a,1),35527(a,1,2,2))].">
      <j1 rule="para" parents="31219 35527"/>
    </justification>
  </clause>

  <clause id="35529">
    <literal><![CDATA[
      L(x,L(x,y,y),y) = ((y \ 1) \ x) \ (((y \ 1) \ x) / (1 / x))
    ]]></literal>
    <justification jstring="[para(35528(a,1),31758(a,1,2)),flip(a)].">
      <j1 rule="para" parents="35528 31758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35530">
    <literal><![CDATA[
      L(x,L(x,y,y),y) = L(x,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,31281,a(flip),b,35529,a),flip(a)].">
      <j1 rule="hyper" parents="373 31281 35529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35531">
    <literal><![CDATA[
      L(x,L(x,y,y),y) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1631,a(flip),b,35530,a),flip(a)].">
      <j1 rule="hyper" parents="373 1631 35530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35532">
    <literal><![CDATA[
      L(x \ y,x \ y,x) = L(x \ y,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(29742,a,35531,a),flip(a)].">
      <j1 rule="hyper" parents="29742 35531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35533">
    <literal><![CDATA[
      L(R(x,y,z),L(x,u,u),u) = R(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(35531(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35531 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35534">
    <literal><![CDATA[
      L(L(x,y,z),L(x,u,u),u) = L(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(35531(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35531 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35535">
    <literal><![CDATA[
      L(L((x \ 1) \ y,(x \ 1) \ y,z),x,x) = L(x * y,L((x \ 1) \ y,z,z),z)
    ]]></literal>
    <justification jstring="[para(35531(a,1),1143(a,1,1))].">
      <j1 rule="para" parents="35531 1143"/>
    </justification>
  </clause>

  <clause id="35536">
    <literal><![CDATA[
      L(x,x,y) \ L(R(x,z,u),L(x,y,y),y) = L(x \ R(x,z,u),L(x,y,y),y)
    ]]></literal>
    <justification jstring="[para(35531(a,1),4243(a,1,1))].">
      <j1 rule="para" parents="35531 4243"/>
    </justification>
  </clause>

  <clause id="35537">
    <literal><![CDATA[
      L(x \ y,y \ x,x) = L(x \ y,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30632,a,b,35532,a)].">
      <j1 rule="hyper" parents="64 30632 35532"/>
    </justification>
  </clause>

  <clause id="35538">
    <literal><![CDATA[
      x \ (y * L(y \ x,y * x,y)) = R(y,x \ y,y \ x) \ y
    ]]></literal>
    <justification jstring="[para(35537(a,1),26398(a,1,2,2))].">
      <j1 rule="para" parents="35537 26398"/>
    </justification>
  </clause>

  <clause id="35539">
    <literal><![CDATA[
      L(R(x,y,z),L(x,u,u),u) = L(R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29,a(flip),b,35533,a),flip(a)].">
      <j1 rule="hyper" parents="373 29 35533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35540">
    <literal><![CDATA[
      (R(x,y \ x,x \ y) \ x) * ((y \ x) \ 1) = L((y \ x) \ 1,x * y,x)
    ]]></literal>
    <justification jstring="[para(35538(a,1),2556(a,1,1))].">
      <j1 rule="para" parents="35538 2556"/>
    </justification>
  </clause>

  <clause id="35541">
    <literal><![CDATA[
      L(x \ R(x,y,z),L(x,u,u),u) = L(x,x,u) \ L(R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(35539(a,1),35536(a,1,2)),flip(a)].">
      <j1 rule="para" parents="35539 35536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35542">
    <literal><![CDATA[
      L(x \ R(x,y,z),L(x,u,u),u) = L(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,4243,a(flip),b,35541,a),flip(a)].">
      <j1 rule="hyper" parents="373 4243 35541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35543">
    <literal><![CDATA[
      L(L((x \ 1) \ y,x \ y,z),x,x) = L(x * y,L((x \ 1) \ y,z,z),z)
    ]]></literal>
    <justification jstring="[para(29704(a,1),35535(a,1,1))].">
      <j1 rule="para" parents="29704 35535"/>
    </justification>
  </clause>

  <clause id="35544">
    <literal><![CDATA[
      L(x * y,L((x \ 1) \ y,z,z),z) = L(x * y,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1143,a(flip),b,35543,a),flip(a)].">
      <j1 rule="hyper" parents="64 1143 35543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35545">
    <literal><![CDATA[
      L(x * y,L(x \ y,z,z),z) = L(x * y,x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35441,a(flip),b,35544,a)].">
      <j1 rule="hyper" parents="64 35441 35544"/>
    </justification>
  </clause>

  <clause id="35546">
    <literal><![CDATA[
      L(x * y,x \ y,y) = L(x * y,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,34350,a(flip),b,35545,a),flip(a)].">
      <j1 rule="hyper" parents="64 34350 35545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35547">
    <literal><![CDATA[
      L((x \ y) * y,(x \ y) * y,y) = L((x \ y) * y,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29440,a(flip),b,35546,a),flip(a)].">
      <j1 rule="hyper" parents="64 29440 35546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35548">
    <literal><![CDATA[
      ((x \ y) * (y * L(x * y,x * y,y))) \ ((x \ y) * (y * (x * y))) = a(y,x \ y,L(x * y,y,x \ y))
    ]]></literal>
    <justification jstring="[para(35546(a,1),27623(a,1,1,2,2))].">
      <j1 rule="para" parents="35546 27623"/>
    </justification>
  </clause>

  <clause id="35549">
    <literal><![CDATA[
      (R(x \ 1,y,z) * u) * a(L(x \ 1,y,z),L(x,y,z),u) = (1 / R(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(32590(a,1),32204(a,1,2))].">
      <j1 rule="para" parents="32590 32204"/>
    </justification>
  </clause>

  <clause id="35550">
    <literal><![CDATA[
      a(x * (y \ (x \ y)),x * (y \ (x \ y)),x) = (x / (y / (x * y))) * ((y / (x * y)) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32670,a(flip),b,32317,a)].">
      <j1 rule="hyper" parents="64 32670 32317"/>
    </justification>
  </clause>

  <clause id="35551">
    <literal><![CDATA[
      a(((x \ y) / y) \ x,x * (y \ (x \ y)),x) = (x / ((x \ y) / y)) * (x \ (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,32143,a(flip),b,32346,a)].">
      <j1 rule="hyper" parents="64 32143 32346"/>
    </justification>
  </clause>

  <clause id="35552">
    <literal><![CDATA[
      a(L(a(x,y,y \ 1) \ K(z,u),w,v5),v6,v7) = a(L(y * L(y \ 1,y,x),w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(33367(a,1),32561(a,1,1,1))].">
      <j1 rule="para" parents="33367 32561"/>
    </justification>
  </clause>

  <clause id="35553">
    <literal><![CDATA[
      a(L(x * L(x \ 1,x,y),z,u),w,v5) = a(L(a(y,x,x \ 1),z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32654,a(flip),b,35552,a),flip(a)].">
      <j1 rule="hyper" parents="64 32654 35552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35554">
    <literal><![CDATA[
      a(L(x * L(x \ 1,x,y),z,u),w,v5) = a(a(L(y,z,u),x,x \ 1),w,v5)
    ]]></literal>
    <justification jstring="[para(4248(a,2),35553(a,2,1))].">
      <j1 rule="para" parents="4248 35553"/>
    </justification>
  </clause>

  <clause id="35555">
    <literal><![CDATA[
      a(L(x * L(x \ 1,x,y),z,u),w,v5) = a(a(L(y,z,u),x,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,34584,a(flip),b,35554,a),flip(a)].">
      <j1 rule="hyper" parents="373 34584 35554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35556">
    <literal><![CDATA[
      a(L(x * ((y * x) \ y),z,u),w,v5) = a(a(L(y,z,u),x,x),w,v5)
    ]]></literal>
    <justification jstring="[para(241(a,1),35555(a,1,1,1,2))].">
      <j1 rule="para" parents="241 35555"/>
    </justification>
  </clause>

  <clause id="35557">
    <literal><![CDATA[
      a(a(L(x,y,z),u,u),w,v5) = a(L(a(u,u,x),y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32839,a(flip),b,35556,a),flip(a)].">
      <j1 rule="hyper" parents="64 32839 35556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35558">
    <literal><![CDATA[
      a(a(L(x,y,z),u,u),w,v5) = a(a(u,L(u,y,z),x),w,v5)
    ]]></literal>
    <justification jstring="[para(34877(a,2),35557(a,2,1))].">
      <j1 rule="para" parents="34877 35557"/>
    </justification>
  </clause>

  <clause id="35559">
    <literal><![CDATA[
      a((x * y) \ ((z / y) \ (z * (x \ K(u,w)))),v5,v6) = a(a(y \ z,y,x \ 1),v5,v6)
    ]]></literal>
    <justification jstring="[para(27321(a,1),32739(a,2,1))].">
      <j1 rule="para" parents="27321 32739"/>
    </justification>
  </clause>

  <clause id="35560">
    <literal><![CDATA[
      a((x * y) \ ((z / y) \ (z * (x \ K(u,w)))),v5,v6) = a(a(y \ z,y,x),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,34584,a(flip),b,35559,a),flip(a)].">
      <j1 rule="hyper" parents="373 34584 35559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35562">
    <literal><![CDATA[
      a((x * y) \ ((z / y) \ (x * z)),u,w) = a(a(y \ z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33007,a(flip),b,35560,a)].">
      <j1 rule="hyper" parents="64 33007 35560"/>
    </justification>
  </clause>

  <clause id="35563">
    <literal><![CDATA[
      a((x * y) \ ((y \ z) \ (x * z)),u,w) = a(a(y \ z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32495,a(flip),b,35562,a)].">
      <j1 rule="hyper" parents="64 32495 35562"/>
    </justification>
  </clause>

  <clause id="35564">
    <literal><![CDATA[
      R(L(x,y,z) \ x,u,L(z,u,L(x,y,z) \ x)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,9,a(flip),b,33264,a),flip(a)].">
      <j1 rule="hyper" parents="373 9 33264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35566">
    <literal><![CDATA[
      R(L(x,y,z) \ x,u,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(33263(a,1),35564(a,1,3))].">
      <j1 rule="para" parents="33263 35564"/>
    </justification>
  </clause>

  <clause id="35567">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,28919,a(flip),b,35566,a)].">
      <j1 rule="hyper" parents="64 28919 35566"/>
    </justification>
  </clause>

  <clause id="35568">
    <literal><![CDATA[
      x \ (y * (L(y,z,x) \ x)) = L(y,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,34855,a(flip),b,35567,a)].">
      <j1 rule="hyper" parents="64 34855 35567"/>
    </justification>
  </clause>

  <clause id="35569">
    <literal><![CDATA[
      x * (1 / (L(y,z,x) \ y)) = x / (L(y,z,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(225,a,35567,a(flip),b,11792,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="225 35567 11792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35570">
    <literal><![CDATA[
      x * (L(y,z,x) \ y) = y * (L(y,z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,35567,a(flip),b,34855,a(flip))].">
      <j1 rule="hyper" parents="145 35567 34855"/>
    </justification>
  </clause>

  <clause id="35571">
    <literal><![CDATA[
      L(1 / (L(x,y,z) \ x),z \ (x * (L(x,y,z) \ z)),z) = 1 / (1 / ((x * (L(x,y,z) \ z)) \ z))
    ]]></literal>
    <justification jstring="[para(35568(a,1),4305(a,1,1,2))].">
      <j1 rule="para" parents="35568 4305"/>
    </justification>
  </clause>

  <clause id="35572">
    <literal><![CDATA[
      L(x \ y,z,x) \ (x \ y) = x \ (L(y / x,z,x) \ y)
    ]]></literal>
    <justification jstring="[para(25820(a,1),35568(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25820 35568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35573">
    <literal><![CDATA[
      (x * (L(y,z,x) \ y)) \ (x * y) = L(y,z,x)
    ]]></literal>
    <justification jstring="[para(35570(a,2),24847(a,1,1))].">
      <j1 rule="para" parents="35570 24847"/>
    </justification>
  </clause>

  <clause id="35574">
    <literal><![CDATA[
      (x * a(x,y,a(y,z,u))) \ (x * y) = L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(34908(a,1),35573(a,1,1,2))].">
      <j1 rule="para" parents="34908 35573"/>
    </justification>
  </clause>

  <clause id="35575">
    <literal><![CDATA[
      x * (1 / (L(y,z,x) \ y)) = (L(y,z,x) \ y) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,23579,a(flip),b,35569,a),flip(a)].">
      <j1 rule="hyper" parents="373 23579 35569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35576">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ z = z * (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(9375(a,1),35575(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9375 35575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35577">
    <literal><![CDATA[
      (L(x,a(y,z,z),u) \ x) \ u = u * (x \ L(x,a(z,z,y),u))
    ]]></literal>
    <justification jstring="[para(31821(a,1),35576(a,2,2,2))].">
      <j1 rule="para" parents="31821 35576"/>
    </justification>
  </clause>

  <clause id="35578">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * ((y * (x / y)) \ (x / y))) = y * ((y * (x / y)) \ (x / y))
    ]]></literal>
    <justification jstring="[para(675(a,1),33403(a,1,1))].">
      <j1 rule="para" parents="675 33403"/>
    </justification>
  </clause>

  <clause id="35579">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * (x \ (y \ x))) = y * ((y * (x / y)) \ (x / y))
    ]]></literal>
    <justification jstring="[para(24925(a,1),35578(a,1,2,2))].">
      <j1 rule="para" parents="24925 35578"/>
    </justification>
  </clause>

  <clause id="35580">
    <literal><![CDATA[
      x * ((x * (y / x)) \ (y / x)) = (y * (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),35579(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 35579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35582">
    <literal><![CDATA[
      (x * (y \ 1)) \ (y \ x) = y * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[para(24925(a,1),35580(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24925 35580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35583">
    <literal><![CDATA[
      L(x * K(y,1 / x),x,x * ((1 / x) * y)) \ (x * z) = ((y / x) / y) \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(27881(a,2),33750(a,1,1))].">
      <j1 rule="para" parents="27881 33750"/>
    </justification>
  </clause>

  <clause id="35584">
    <literal><![CDATA[
      a(x \ (y * a(z,u,w)),z,z) = x \ (y * R(y \ x,z,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),34054(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="10 34054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35585">
    <literal><![CDATA[
      a(x \ (y * a(z,u,w)),z,z) = a(x \ y,z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,15997,a(flip),b,35584,a),flip(a)].">
      <j1 rule="hyper" parents="373 15997 35584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35587">
    <literal><![CDATA[
      a(L(x \ y,x,a(z,u,w)),z,z) = a((x * a(z,u,w)) \ y,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32585,a,b,35585,a)].">
      <j1 rule="hyper" parents="64 32585 35585"/>
    </justification>
  </clause>

  <clause id="35588">
    <literal><![CDATA[
      a(x \ L(y,z,z),z,z) = a(x \ y,z,z)
    ]]></literal>
    <justification jstring="[para(1245(a,1),35585(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1245 35585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35589">
    <literal><![CDATA[
      a(x \ (y * (z * y)),y,y) = a(x \ z,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32681,a,b,35588,a)].">
      <j1 rule="hyper" parents="64 32681 35588"/>
    </justification>
  </clause>

  <clause id="35590">
    <literal><![CDATA[
      a(x \ (y \ z),y,y) = a(x \ (y * z),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,33010,a(flip),b,35588,a)].">
      <j1 rule="hyper" parents="64 33010 35588"/>
    </justification>
  </clause>

  <clause id="35591">
    <literal><![CDATA[
      L(x,x,y \ L(z,x,x)) = a(y \ z,x,x) \ x
    ]]></literal>
    <justification jstring="[para(35588(a,1),30459(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35588 30459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35592">
    <literal><![CDATA[
      a((x * y) \ z,x,x) = a(y \ (x * z),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32624,a,b,35590,a)].">
      <j1 rule="hyper" parents="64 32624 35590"/>
    </justification>
  </clause>

  <clause id="35593">
    <literal><![CDATA[
      L(x,x,y \ L(z,x,x)) = L(x,x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,30459,a(flip),b,35591,a),flip(a)].">
      <j1 rule="hyper" parents="373 30459 35591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35594">
    <literal><![CDATA[
      L(x,x,y \ ((1 / x) * z)) = L(x,x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(569(a,1),35593(a,1,3,2))].">
      <j1 rule="para" parents="569 35593"/>
    </justification>
  </clause>

  <clause id="35595">
    <literal><![CDATA[
      L(x,x,y \ (x \ z)) = L(x,x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,25687,a(flip),b,35594,a),flip(a)].">
      <j1 rule="hyper" parents="64 25687 35594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35596">
    <literal><![CDATA[
      L(x,x,(y * x) \ z) = L(x,x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,32635,a,b,35595,a)].">
      <j1 rule="hyper" parents="64 32635 35595"/>
    </justification>
  </clause>

  <clause id="35597">
    <literal><![CDATA[
      a((x * a(y,z,u)) \ w,y,y) = a(x \ w,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32640,a(flip),b,35587,a),flip(a)].">
      <j1 rule="hyper" parents="64 32640 35587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35598">
    <literal><![CDATA[
      a((a(x,y,z) * u) \ w,x,x) = a(u \ w,x,x)
    ]]></literal>
    <justification jstring="[hyper(32451,a,35597,a)].">
      <j1 rule="hyper" parents="32451 35597"/>
    </justification>
  </clause>

  <clause id="35600">
    <literal><![CDATA[
      (a(x,y,y) * z) \ a(L(x,z,z),y,y) = ((1 / z) \ a(x,y,y)) \ a(x,y,y)
    ]]></literal>
    <justification jstring="[para(23188(a,1),34213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23188 34213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35601">
    <literal><![CDATA[
      (a(x,y,y) * z) \ a(L(x,z,z),y,y) = ((1 / z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,25160,a(flip),b,35600,a),flip(a)].">
      <j1 rule="hyper" parents="373 25160 35600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35603">
    <literal><![CDATA[
      (a(x,y,y) * z) \ a(L(x,z,z),y,y) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,219,a(flip),b,35601,a),flip(a)].">
      <j1 rule="hyper" parents="373 219 35601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35605">
    <literal><![CDATA[
      a(x,y,(a(z,u,u) * a(z,u,u)) * (w \ (v5 * (a(z,u,u) \ 1)))) = a(x,y,w \ (v5 * a(L(z,a(z,u,u),a(z,u,u)),u,u)))
    ]]></literal>
    <justification jstring="[para(35603(a,1),31722(a,1,3,2,2,2))].">
      <j1 rule="para" parents="35603 31722"/>
    </justification>
  </clause>

  <clause id="35606">
    <literal><![CDATA[
      R((x \ y) * y,x * ((x \ y) * y),y / (x / y)) = T(y / (x / y),(y / (x / y)) \ x)
    ]]></literal>
    <justification jstring="[para(34305(a,1),34307(a,1,2))].">
      <j1 rule="para" parents="34305 34307"/>
    </justification>
  </clause>

  <clause id="35607">
    <literal><![CDATA[
      a(x,y,R(z,u,u) \ (u * ((u \ 1) \ w))) = a(x,y,((u \ 1) * (z * (u \ 1))) \ w)
    ]]></literal>
    <justification jstring="[para(582(a,1),34469(a,1,3,2))].">
      <j1 rule="para" parents="582 34469"/>
    </justification>
  </clause>

  <clause id="35608">
    <literal><![CDATA[
      a(x,y,((z \ 1) * (u * (z \ 1))) \ w) = a(x,y,(R(u,z,z) \ w) * (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27782,a(flip),b,35607,a),flip(a)].">
      <j1 rule="hyper" parents="64 27782 35607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35609">
    <literal><![CDATA[
      a(x,y,((z \ 1) * ((z \ 1) * u)) \ w) = a(x,y,(R(u,z,z) \ w) * (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27557,a,b,35608,a)].">
      <j1 rule="hyper" parents="64 27557 35608"/>
    </justification>
  </clause>

  <clause id="35610">
    <literal><![CDATA[
      L(T((x / y) / x,y * (y * x)),y,y) = ((((x * y) \ z) \ z) * y) \ T(x * y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(15744(a,2),34551(a,1,1))].">
      <j1 rule="para" parents="15744 34551"/>
    </justification>
  </clause>

  <clause id="35611">
    <literal><![CDATA[
      R(x / (1 / y),y,y * a(z,u,y)) = a(z,u,y) \ (x * (y * a(z,u,y)))
    ]]></literal>
    <justification jstring="[para(23105(a,1),34555(a,1,1))].">
      <j1 rule="para" parents="23105 34555"/>
    </justification>
  </clause>

  <clause id="35612">
    <literal><![CDATA[
      a(x,x,y) \ (z * (y * a(x,x,y))) = R(z / (1 / y),y,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,31647,a(flip),b,35611,a),flip(a)].">
      <j1 rule="hyper" parents="64 31647 35611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35614">
    <literal><![CDATA[
      L(L(x,y,z) * a(u,L(x,y,z),w),w,u) = K(w,x) * L((u * w) \ ((u * x) * w),y,z)
    ]]></literal>
    <justification jstring="[para(3182(a,2),35132(a,2,2))].">
      <j1 rule="para" parents="3182 35132"/>
    </justification>
  </clause>

  <clause id="35615">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ u,x * R(x,y,z),x * L(x,y,z)) = ((x \ R(x,y,z)) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(33586,a,35229,a)].">
      <j1 rule="hyper" parents="33586 35229"/>
    </justification>
  </clause>

  <clause id="35616">
    <literal><![CDATA[
      L(L(T(x * K(y \ 1,z),y \ 1),u,w),y,y) = y * (L(x,u,w) * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(7852(a,1),35394(a,1,1,1))].">
      <j1 rule="para" parents="7852 35394"/>
    </justification>
  </clause>

  <clause id="35617">
    <literal><![CDATA[
      L(x * ((y * K(x \ 1,z)) * (x \ 1)),u,w) = x * (L(y,u,w) * T(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1180,a(flip),b,35616,a)].">
      <j1 rule="hyper" parents="64 1180 35616"/>
    </justification>
  </clause>

  <clause id="35618">
    <literal><![CDATA[
      L(x * (y * T(x \ 1,z)),u,w) = x * (L(y,u,w) * T(x \ 1,z))
    ]]></literal>
    <justification jstring="[para(6850(a,1),35617(a,1,1,2))].">
      <j1 rule="para" parents="6850 35617"/>
    </justification>
  </clause>

  <clause id="35619">
    <literal><![CDATA[
      R(x,y,(T(z * u,w) \ ((u * w) * z)) \ v5) = R(x,y,L(w,u,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26172,a(flip),b,35410,a),flip(a)].">
      <j1 rule="hyper" parents="373 26172 35410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35621">
    <literal><![CDATA[
      R(x,y,((z * u) \ ((u * w) * z)) \ v5) = R(x,y,L(w,u,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26219,a(flip),b,35619,a)].">
      <j1 rule="hyper" parents="64 26219 35619"/>
    </justification>
  </clause>

  <clause id="35623">
    <literal><![CDATA[
      R(x,y,R(z,u,w) \ v5) = R(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34608,a(flip),b,35621,a)].">
      <j1 rule="hyper" parents="64 34608 35621"/>
    </justification>
  </clause>

  <clause id="35624">
    <literal><![CDATA[
      R(x,y,L(z,u,w) \ (v5 * z)) = R(x,y,z * (R(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,25192,a(flip),b,35623,a),flip(a)].">
      <j1 rule="hyper" parents="64 25192 35623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35625">
    <literal><![CDATA[
      R(x,R(y,z,u),L(y,z,u) \ w) * (x \ w) = x \ ((x * R(y,z,u)) * (R(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(35623(a,1),1932(a,1,1))].">
      <j1 rule="para" parents="35623 1932"/>
    </justification>
  </clause>

  <clause id="35626">
    <literal><![CDATA[
      R(x,y,z * (R(z,u,w) \ v5)) = R(x,y,z * (L(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,25112,a(flip),b,35624,a),flip(a)].">
      <j1 rule="hyper" parents="64 25112 35624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35627">
    <literal><![CDATA[
      R(x,y,a(L(z,u,w),u,w) \ u) = R(x,y,z * (L(z,u,w) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,33519,a,b,35626,a)].">
      <j1 rule="hyper" parents="64 33519 35626"/>
    </justification>
  </clause>

  <clause id="35628">
    <literal><![CDATA[
      R(x,1 / (y \ z),L(1 / (y \ z),y \ z,y)) = R(x,z \ y,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,26411,a(flip),b,35414,a),flip(a)].">
      <j1 rule="hyper" parents="373 26411 35414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35630">
    <literal><![CDATA[
      R(x,1 / (y \ z),1 / (1 / (z \ y))) = R(x,z \ y,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[para(4305(a,1),35628(a,1,3))].">
      <j1 rule="para" parents="4305 35628"/>
    </justification>
  </clause>

  <clause id="35631">
    <literal><![CDATA[
      R(x,1 / (y \ z),z \ y) = R(x,z \ y,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,23814,a(flip),b,35630,a)].">
      <j1 rule="hyper" parents="64 23814 35630"/>
    </justification>
  </clause>

  <clause id="35633">
    <literal><![CDATA[
      R(x,y \ z,(z \ y) \ 1) = R(x,z \ y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2968,a(flip),b,35631,a),flip(a)].">
      <j1 rule="hyper" parents="64 2968 35631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35634">
    <literal><![CDATA[
      x / T(y * (z \ (y \ z)),K(y \ z,z)) = ((y \ R(y,y,z)) \ x) * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(5962(a,1),35417(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5962 35417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35635">
    <literal><![CDATA[
      ((x \ R(x,x,y)) \ z) * K(y,x \ 1) = z / (x * (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(28887(a,1),35634(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28887 35634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35637">
    <literal><![CDATA[
      (a(x,x,y) \ z) * K(y,x \ 1) = z / (x * (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(30058(a,1),35635(a,1,1,1))].">
      <j1 rule="para" parents="30058 35635"/>
    </justification>
  </clause>

  <clause id="35638">
    <literal><![CDATA[
      ((1 / (((1 / x) * (y * x)) * x)) * ((1 / x) * (y * x))) \ 1 = L(x,L(y,x,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,29648,a(flip),b,35428,a),flip(a)].">
      <j1 rule="hyper" parents="373 29648 35428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35639">
    <literal><![CDATA[
      L(x,x \ (y * x),y * x) = L(x,L(y,x,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35427,a(flip),b,35638,a)].">
      <j1 rule="hyper" parents="64 35427 35638"/>
    </justification>
  </clause>

  <clause id="35640">
    <literal><![CDATA[
      L(x,L(y,x,x),x \ y) = L(x,y,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29493,a(flip),b,35639,a),flip(a)].">
      <j1 rule="hyper" parents="64 29493 35639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35642">
    <literal><![CDATA[
      L(x,x \ (x \ y),x \ y) = L(x,y,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,31756,a,b,35640,a)].">
      <j1 rule="hyper" parents="64 31756 35640"/>
    </justification>
  </clause>

  <clause id="35643">
    <literal><![CDATA[
      L(x,((x \ y) \ y) \ (y / x),x \ y) = L(x,y,y * x)
    ]]></literal>
    <justification jstring="[para(4511(a,2),35642(a,1,2))].">
      <j1 rule="para" parents="4511 35642"/>
    </justification>
  </clause>

  <clause id="35644">
    <literal><![CDATA[
      L(x,((x \ y) \ y) \ (y / x),x \ y) = a(y * x,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,25598,a,b,35643,a),flip(a)].">
      <j1 rule="hyper" parents="373 25598 35643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35645">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * (u * T(x \ 1,u)) = (x \ 1) * ((1 / a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(28638(a,1),35495(a,1,2,2))].">
      <j1 rule="para" parents="28638 35495"/>
    </justification>
  </clause>

  <clause id="35646">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * ((x \ 1) * u) = (x \ 1) * ((1 / a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(737,a,35645,a)].">
      <j1 rule="hyper" parents="737 35645"/>
    </justification>
  </clause>

  <clause id="35648">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * ((x \ 1) * u) = (x \ 1) * ((a(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(13923(a,1),35646(a,2,2,1))].">
      <j1 rule="para" parents="13923 35646"/>
    </justification>
  </clause>

  <clause id="35649">
    <literal><![CDATA[
      a(x,y,(z * ((u / w) / v5)) * v6) = a(x,y,(z * (v5 \ (w \ u))) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,27326,a(flip),b,35521,a),flip(a)].">
      <j1 rule="hyper" parents="64 27326 35521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35650">
    <literal><![CDATA[
      a(x,y,(z * (u \ (w / v5))) * v6) = a(x,y,(z * (u \ (v5 \ w))) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,27469,a(flip),b,35649,a)].">
      <j1 rule="hyper" parents="64 27469 35649"/>
    </justification>
  </clause>

  <clause id="35651">
    <literal><![CDATA[
      a(x,y,(z * (u \ (z \ u))) * w) = a(x,y,(a(u,z,z) \ 1) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30524,a(flip),b,35650,a),flip(a)].">
      <j1 rule="hyper" parents="64 30524 35650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35652">
    <literal><![CDATA[
      a(x,y,(a(z,u,u) \ 1) * w) = a(x,y,a(u,u,z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30110,a(flip),b,35651,a),flip(a)].">
      <j1 rule="hyper" parents="64 30110 35651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35653">
    <literal><![CDATA[
      L(L(x,y,a(z,z,y)),L(y,z,z),L(y,z,z)) = (1 / y) * (a(z,z,y) * (L(y,z,z) * x))
    ]]></literal>
    <justification jstring="[para(29401(a,2),35524(a,2,2))].">
      <j1 rule="para" parents="29401 35524"/>
    </justification>
  </clause>

  <clause id="35654">
    <literal><![CDATA[
      (R(x \ 1,y,z) * u) * a(L(x,y,z),L(x,y,z),u) = (1 / R(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(32634(a,1),35549(a,1,2))].">
      <j1 rule="para" parents="32634 35549"/>
    </justification>
  </clause>

  <clause id="35655">
    <literal><![CDATA[
      (R(x \ 1,y,z) * u) * a(x,x,u) = (1 / R(x \ 1,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(35139(a,1),35654(a,1,2))].">
      <j1 rule="para" parents="35139 35654"/>
    </justification>
  </clause>

  <clause id="35656">
    <literal><![CDATA[
      (1 / R(x \ 1,y,z)) \ u = R(x,y,z) * (x \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,35494,a(flip),b,35655,a),flip(a)].">
      <j1 rule="hyper" parents="64 35494 35655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35658">
    <literal><![CDATA[
      (x * (R(x,y,z) \ x)) \ u = R(x,y,z) * (x \ (x \ u))
    ]]></literal>
    <justification jstring="[para(11435(a,1),35656(a,1,1))].">
      <j1 rule="para" parents="11435 35656"/>
    </justification>
  </clause>

  <clause id="35659">
    <literal><![CDATA[
      R(x,y,y) * (x \ (x \ z)) = (a(x,y,y) \ x) \ z
    ]]></literal>
    <justification jstring="[para(25172(a,1),35658(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25172 35658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35660">
    <literal><![CDATA[
      x * ((a(x,y,y) \ x) \ z) = R(x,y,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,35659,a(flip),b,1898,a)].">
      <j1 rule="hyper" parents="145 35659 1898"/>
    </justification>
  </clause>

  <clause id="35661">
    <literal><![CDATA[
      (x / (y / (x * y))) * ((y / (x * y)) / x) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,30375,a(flip),b,35550,a),flip(a)].">
      <j1 rule="hyper" parents="64 30375 35550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35662">
    <literal><![CDATA[
      1 / ((x / (y * x)) / y) = y / (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(142,a,30375,a(flip),b,35550,a(flip))].">
      <j1 rule="hyper" parents="142 30375 35550"/>
    </justification>
  </clause>

  <clause id="35664">
    <literal><![CDATA[
      (x / ((x * y) \ y)) * (((x * y) \ y) / x) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,34611,a(flip),b,35661,a)].">
      <j1 rule="hyper" parents="64 34611 35661"/>
    </justification>
  </clause>

  <clause id="35665">
    <literal><![CDATA[
      ((x / (y * x)) / y) * (y / (x / (y * x))) = 1
    ]]></literal>
    <justification jstring="[hyper(145,a,35662,a(flip),b,34185,a(flip))].">
      <j1 rule="hyper" parents="145 35662 34185"/>
    </justification>
  </clause>

  <clause id="35666">
    <literal><![CDATA[
      (((x * y) \ y) / x) * (x / ((x * y) \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,32988,a(flip),b,35665,a)].">
      <j1 rule="hyper" parents="64 32988 35665"/>
    </justification>
  </clause>

  <clause id="35667">
    <literal><![CDATA[
      a((x \ (y \ x)) \ y,y * (x \ (y \ x)),y) = (y / ((y \ x) / x)) * (y \ (x / (y * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,32386,a(flip),b,35551,a)].">
      <j1 rule="hyper" parents="64 32386 35551"/>
    </justification>
  </clause>

  <clause id="35668">
    <literal><![CDATA[
      L(x * K(y,x \ 1),x,x * ((1 / x) * y)) \ (x * z) = ((y / x) / y) \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(6041(a,1),35583(a,1,1,1,2))].">
      <j1 rule="para" parents="6041 35583"/>
    </justification>
  </clause>

  <clause id="35669">
    <literal><![CDATA[
      R((x \ y) * y,x * ((x \ y) * y),(x / y) \ y) = T(y / (x / y),(y / (x / y)) \ x)
    ]]></literal>
    <justification jstring="[hyper(25233,a,35606,a)].">
      <j1 rule="hyper" parents="25233 35606"/>
    </justification>
  </clause>

  <clause id="35670">
    <literal><![CDATA[
      L(L(x,y,z) * a(u,L(x,y,z),w),w,u) = L(K(w,x) * ((u * w) \ ((u * x) * w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,26085,a,b,35614,a),flip(a)].">
      <j1 rule="hyper" parents="373 26085 35614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35671">
    <literal><![CDATA[
      a(x * (y \ (x \ y)),(y \ (x \ y)) \ x,x) = (x / ((x \ y) / y)) * (x \ (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,32231,a(flip),b,35667,a)].">
      <j1 rule="hyper" parents="64 32231 35667"/>
    </justification>
  </clause>

  <clause id="35672">
    <literal><![CDATA[
      L(x * K(y,x \ 1),x,x * ((x \ 1) * y)) \ (x * z) = ((y / x) / y) \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(29089(a,1),35668(a,1,1))].">
      <j1 rule="para" parents="29089 35668"/>
    </justification>
  </clause>

  <clause id="35673">
    <literal><![CDATA[
      R((x \ y) * y,x * ((x \ y) * y),(y \ x) \ y) = T(y / (x / y),(y / (x / y)) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26209,a(flip),b,35669,a)].">
      <j1 rule="hyper" parents="64 26209 35669"/>
    </justification>
  </clause>

  <clause id="35674">
    <literal><![CDATA[
      L(L(x,y,z) * a(u,L(x,y,z),w),w,u) = L(L(x * a(u,x,w),w,u),y,z)
    ]]></literal>
    <justification jstring="[para(35129(a,1),35670(a,2,1))].">
      <j1 rule="para" parents="35129 35670"/>
    </justification>
  </clause>

  <clause id="35675">
    <literal><![CDATA[
      L(x,y,z) * a(u,L(x,y,z),w) = L(x * a(u,x,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(42,a,30,a,b,35674,a),flip(a)].">
      <j1 rule="hyper" parents="42 30 35674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35676">
    <literal><![CDATA[
      a(x,L(y,z,z),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,33543,a(flip),b,35675,a),flip(a)].">
      <j1 rule="hyper" parents="35 33543 35675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35677">
    <literal><![CDATA[
      a(x,L(y,x,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,30820,a(flip),b,35675,a),flip(a)].">
      <j1 rule="hyper" parents="35 30820 35675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35679">
    <literal><![CDATA[
      L(x * a(y,x,z),x,x) = L(x,x,x) * a(y,x,z)
    ]]></literal>
    <justification jstring="[para(13827(a,1),35675(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13827 35675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35680">
    <literal><![CDATA[
      L(x * a(y,x,z),u,x) = L(x,u,x) * a(y,x,z)
    ]]></literal>
    <justification jstring="[para(13828(a,1),35675(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13828 35675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35681">
    <literal><![CDATA[
      a(x,y,L(z * a(u,z,w),w,u)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(35675(a,1),33839(a,1,3))].">
      <j1 rule="para" parents="35675 33839"/>
    </justification>
  </clause>

  <clause id="35682">
    <literal><![CDATA[
      a(x,L(y,y,z),z) = a(x,(y \ z) * z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34094,a(flip),b,35676,a),flip(a)].">
      <j1 rule="hyper" parents="64 34094 35676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35683">
    <literal><![CDATA[
      a(x,y \ z,y) = a(x,z * y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32164,a(flip),b,35676,a)].">
      <j1 rule="hyper" parents="64 32164 35676"/>
    </justification>
  </clause>

  <clause id="35684">
    <literal><![CDATA[
      a(x,y \ z,y) = a(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32141,a(flip),b,35676,a)].">
      <j1 rule="hyper" parents="64 32141 35676"/>
    </justification>
  </clause>

  <clause id="35685">
    <literal><![CDATA[
      a(x,L(y,x,x),L(y,y,x)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30471,a(flip),b,35677,a),flip(a)].">
      <j1 rule="hyper" parents="373 30471 35677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35686">
    <literal><![CDATA[
      a(x,L(x,y,z) \ u,w) = a(x,L(x,y,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,35178,a(flip),b,35677,a)].">
      <j1 rule="hyper" parents="64 35178 35677"/>
    </justification>
  </clause>

  <clause id="35687">
    <literal><![CDATA[
      a(x,x \ y,z) = a(x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32164,a(flip),b,35677,a)].">
      <j1 rule="hyper" parents="64 32164 35677"/>
    </justification>
  </clause>

  <clause id="35688">
    <literal><![CDATA[
      a(x,x \ y,z) = a(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32141,a(flip),b,35677,a)].">
      <j1 rule="hyper" parents="64 32141 35677"/>
    </justification>
  </clause>

  <clause id="35689">
    <literal><![CDATA[
      a(x,x * y,y) * x = R(x,y \ x,y)
    ]]></literal>
    <justification jstring="[para(35683(a,1),24669(a,1,1))].">
      <j1 rule="para" parents="35683 24669"/>
    </justification>
  </clause>

  <clause id="35690">
    <literal><![CDATA[
      L(x,y,a(z,z \ u,z \ u)) = L(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[para(35683(a,1),29201(a,2,3))].">
      <j1 rule="para" parents="35683 29201"/>
    </justification>
  </clause>

  <clause id="35691">
    <literal><![CDATA[
      L(x,y,z \ ((z \ u) * u)) = L(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[para(35683(a,1),29263(a,2,3))].">
      <j1 rule="para" parents="35683 29263"/>
    </justification>
  </clause>

  <clause id="35692">
    <literal><![CDATA[
      L(x,y,((z \ u) * u) * z) = L(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[para(35683(a,1),29274(a,2,3))].">
      <j1 rule="para" parents="35683 29274"/>
    </justification>
  </clause>

  <clause id="35693">
    <literal><![CDATA[
      L(x,y,(z \ u) * (u \ z)) = L(x,y,a(z,z * u,u))
    ]]></literal>
    <justification jstring="[para(35683(a,1),30453(a,2,3))].">
      <j1 rule="para" parents="35683 30453"/>
    </justification>
  </clause>

  <clause id="35694">
    <literal><![CDATA[
      L(x,(y \ z) * (z \ y),u) = L(x,a(y,y * z,z),u)
    ]]></literal>
    <justification jstring="[para(35683(a,1),31143(a,2,2))].">
      <j1 rule="para" parents="35683 31143"/>
    </justification>
  </clause>

  <clause id="35695">
    <literal><![CDATA[
      R(x,y,z \ (u * ((z \ u) \ 1))) = L(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[para(35683(a,1),31349(a,2,3))].">
      <j1 rule="para" parents="35683 31349"/>
    </justification>
  </clause>

  <clause id="35696">
    <literal><![CDATA[
      L(x,a(y,y * z,z),z \ y) = L(x,z \ y,a(y,z \ y,z))
    ]]></literal>
    <justification jstring="[para(35683(a,1),31666(a,1,2))].">
      <j1 rule="para" parents="35683 31666"/>
    </justification>
  </clause>

  <clause id="35697">
    <literal><![CDATA[
      a(x,x * y,y) \ y = L(y,y \ x,x)
    ]]></literal>
    <justification jstring="[para(35683(a,1),31726(a,1,1))].">
      <j1 rule="para" parents="35683 31726"/>
    </justification>
  </clause>

  <clause id="35698">
    <literal><![CDATA[
      L(x,y,a(z,u * z,u * z)) = L(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[para(35683(a,1),33994(a,2,3))].">
      <j1 rule="para" parents="35683 33994"/>
    </justification>
  </clause>

  <clause id="35699">
    <literal><![CDATA[
      L(x,y,a(z,z * u,z * u)) = L(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[para(35683(a,1),33996(a,2,3))].">
      <j1 rule="para" parents="35683 33996"/>
    </justification>
  </clause>

  <clause id="35700">
    <literal><![CDATA[
      L(x,y \ ((y \ z) * z),u) = L(x,a(z,z * y,y),u)
    ]]></literal>
    <justification jstring="[para(35683(a,1),34338(a,2,2))].">
      <j1 rule="para" parents="35683 34338"/>
    </justification>
  </clause>

  <clause id="35701">
    <literal><![CDATA[
      L(x,y,(z \ ((z \ u) * u)) * w) = L(x,y,w * a(u,u * z,z))
    ]]></literal>
    <justification jstring="[para(35683(a,1),34342(a,2,3,2))].">
      <j1 rule="para" parents="35683 34342"/>
    </justification>
  </clause>

  <clause id="35702">
    <literal><![CDATA[
      (x * y) \ ((x * (y / z)) * z) = a(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,25644,a,b,35684,a)].">
      <j1 rule="hyper" parents="64 25644 35684"/>
    </justification>
  </clause>

  <clause id="35704">
    <literal><![CDATA[
      a(x,y * x,y) \ y = L(y,y \ x,x)
    ]]></literal>
    <justification jstring="[para(35684(a,1),31726(a,1,1))].">
      <j1 rule="para" parents="35684 31726"/>
    </justification>
  </clause>

  <clause id="35705">
    <literal><![CDATA[
      a(x,y,a(z,u \ w,u)) = a(x,y,a(z,w * u,u))
    ]]></literal>
    <justification jstring="[para(35684(a,2),32311(a,1,3))].">
      <j1 rule="para" parents="35684 32311"/>
    </justification>
  </clause>

  <clause id="35706">
    <literal><![CDATA[
      a(x,y * x,y \ z) \ z = x * ((x \ y) * (y \ z))
    ]]></literal>
    <justification jstring="[para(35687(a,1),15499(a,1,1))].">
      <j1 rule="para" parents="35687 15499"/>
    </justification>
  </clause>

  <clause id="35707">
    <literal><![CDATA[
      a(x,y * x,z) \ y = (x * ((x \ y) * z)) / z
    ]]></literal>
    <justification jstring="[para(35687(a,1),33314(a,1,1))].">
      <j1 rule="para" parents="35687 33314"/>
    </justification>
  </clause>

  <clause id="35708">
    <literal><![CDATA[
      L(x,((y \ z) * u) \ (y \ (u * z)),w) = L(x,a(y,z * y,u),w)
    ]]></literal>
    <justification jstring="[para(35687(a,1),35454(a,2,2))].">
      <j1 rule="para" parents="35687 35454"/>
    </justification>
  </clause>

  <clause id="35709">
    <literal><![CDATA[
      a(x \ y,(x \ y) * y,z) = a(x \ y,x,z)
    ]]></literal>
    <justification jstring="[hyper(32007,a,35688,a),flip(a)].">
      <j1 rule="hyper" parents="32007 35688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35710">
    <literal><![CDATA[
      ((x \ y) * z) * a(x,x * y,z) = x \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,35688,a(flip),b,30202,a)].">
      <j1 rule="hyper" parents="145 35688 30202"/>
    </justification>
  </clause>

  <clause id="35711">
    <literal><![CDATA[
      a(x,x * y,z) \ (y * z) = x * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(35688(a,1),15481(a,1,1))].">
      <j1 rule="para" parents="35688 15481"/>
    </justification>
  </clause>

  <clause id="35712">
    <literal><![CDATA[
      L(x,y,a(z,u \ z,u)) = L(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[para(35688(a,1),29276(a,2,3))].">
      <j1 rule="para" parents="35688 29276"/>
    </justification>
  </clause>

  <clause id="35713">
    <literal><![CDATA[
      a(x,x * y,y) * x = R(x,x \ y,y)
    ]]></literal>
    <justification jstring="[para(35688(a,1),30895(a,1,1))].">
      <j1 rule="para" parents="35688 30895"/>
    </justification>
  </clause>

  <clause id="35714">
    <literal><![CDATA[
      a((((x \ y) * y) * x) * z,u,w) = a(z * a(x,x * y,y),u,w)
    ]]></literal>
    <justification jstring="[para(35688(a,1),32507(a,2,1,2))].">
      <j1 rule="para" parents="35688 32507"/>
    </justification>
  </clause>

  <clause id="35716">
    <literal><![CDATA[
      a(x,(x * x) \ y,L(x \ (x \ y),x \ (x \ y),x)) = a(x,x \ (x \ y),x \ (x \ y))
    ]]></literal>
    <justification jstring="[para(346(a,1),35685(a,1,2))].">
      <j1 rule="para" parents="346 35685"/>
    </justification>
  </clause>

  <clause id="35717">
    <literal><![CDATA[
      R(x,y \ x,y) = R(x,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30902,a(flip),b,35689,a),flip(a)].">
      <j1 rule="hyper" parents="64 30902 35689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35718">
    <literal><![CDATA[
      R(x \ y,(x \ y) * x,x) = R(x \ y,L(y,x,x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30397,a(flip),b,35717,a),flip(a)].">
      <j1 rule="hyper" parents="64 30397 35717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35719">
    <literal><![CDATA[
      R(x * y,(x * y) * y,y) = R(x * y,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(22(a,2),35717(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22 35717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35720">
    <literal><![CDATA[
      R(x,(x * ((x \ y) * x)) \ x,x * ((x \ y) * x)) = R(x,(x * y) * L(x,x,x),x * ((x \ y) * x))
    ]]></literal>
    <justification jstring="[para(25673(a,1),35717(a,2,2))].">
      <j1 rule="para" parents="25673 35717"/>
    </justification>
  </clause>

  <clause id="35721">
    <literal><![CDATA[
      L(x,y,R(z,z * u,u)) = L(x,y,L(z,u \ z,u))
    ]]></literal>
    <justification jstring="[para(35717(a,1),29203(a,1,3))].">
      <j1 rule="para" parents="35717 29203"/>
    </justification>
  </clause>

  <clause id="35722">
    <literal><![CDATA[
      a(x,R(y,y * z,z),u) = a(x,L(y,z \ y,z),u)
    ]]></literal>
    <justification jstring="[para(35717(a,1),32197(a,1,2))].">
      <j1 rule="para" parents="35717 32197"/>
    </justification>
  </clause>

  <clause id="35723">
    <literal><![CDATA[
      a(R(x,x * y,y),z,u) = a(L(x,y \ x,y),z,u)
    ]]></literal>
    <justification jstring="[para(35717(a,1),32590(a,1,1))].">
      <j1 rule="para" parents="35717 32590"/>
    </justification>
  </clause>

  <clause id="35724">
    <literal><![CDATA[
      a(x \ 1,R(y,x,x \ 1),y * x) \ (y * x) = L(y * x,(y * x) \ (x \ 1),x \ 1)
    ]]></literal>
    <justification jstring="[para(297(a,1),35704(a,1,1,2))].">
      <j1 rule="para" parents="297 35704"/>
    </justification>
  </clause>

  <clause id="35725">
    <literal><![CDATA[
      L(L(x,x \ y,y),a(y,x * y,x),y * ((x * y) * x)) = ((y * (x * y)) * x) \ ((y * ((x * y) * x)) * x)
    ]]></literal>
    <justification jstring="[para(35704(a,1),961(a,1,1))].">
      <j1 rule="para" parents="35704 961"/>
    </justification>
  </clause>

  <clause id="35726">
    <literal><![CDATA[
      L(x,((x \ y) \ y) \ (y / x),x \ y) = a(x \ y,x * (x \ y),x) \ x
    ]]></literal>
    <justification jstring="[para(4511(a,2),35704(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4511 35704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35727">
    <literal><![CDATA[
      R(x,x \ y,y) = R(x,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30902,a(flip),b,35713,a),flip(a)].">
      <j1 rule="hyper" parents="64 30902 35713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35728">
    <literal><![CDATA[
      R(x,x * (x * y),x * y) = R(x,y,x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),35727(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 35727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35729">
    <literal><![CDATA[
      1 / R(x,x * y,y) = ((1 / (1 / x)) \ (1 / y)) * y
    ]]></literal>
    <justification jstring="[para(35727(a,1),31224(a,1,2))].">
      <j1 rule="para" parents="35727 31224"/>
    </justification>
  </clause>

  <clause id="35730">
    <literal><![CDATA[
      R(x,L(y,x,x),x * y) = R(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2970,a(flip),b,35728,a)].">
      <j1 rule="hyper" parents="64 2970 35728"/>
    </justification>
  </clause>

  <clause id="35731">
    <literal><![CDATA[
      a(x,x * y,z) \ (y \ 1) = (x * ((x \ (y \ 1)) * z)) / z
    ]]></literal>
    <justification jstring="[para(31943(a,1),35707(a,1,1))].">
      <j1 rule="para" parents="31943 35707"/>
    </justification>
  </clause>

  <clause id="35732">
    <literal><![CDATA[
      x * (a(y,y * x,x) \ x) = y * ((y \ x) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33206,a(flip),b,35711,a)].">
      <j1 rule="hyper" parents="64 33206 35711"/>
    </justification>
  </clause>

  <clause id="35733">
    <literal><![CDATA[
      (1 / x) \ a(y,x,z) = x * a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(42,a,1256,a,b,35679,a)].">
      <j1 rule="hyper" parents="42 1256 35679"/>
    </justification>
  </clause>

  <clause id="35734">
    <literal><![CDATA[
      L(a(x,y,z),y,y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,1257,a,b,35679,a(flip))].">
      <j1 rule="hyper" parents="35 1257 35679"/>
    </justification>
  </clause>

  <clause id="35735">
    <literal><![CDATA[
      a(x,x,a(y,x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,35734,a,b,5563,a),flip(a)].">
      <j1 rule="hyper" parents="140 35734 5563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35736">
    <literal><![CDATA[
      a(x,y,z) * (y \ 1) = y \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,35734,a(flip),b,23782,a),flip(a)].">
      <j1 rule="hyper" parents="139 35734 23782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35737">
    <literal><![CDATA[
      (1 / x) \ a(y,x,z) = a(y,x,z) * x
    ]]></literal>
    <justification jstring="[hyper(139,a,35734,a(flip),b,23778,a)].">
      <j1 rule="hyper" parents="139 35734 23778"/>
    </justification>
  </clause>

  <clause id="35738">
    <literal><![CDATA[
      R(x,x,x) * a(y,x,z) = (x \ 1) \ a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,35734,a(flip),b,1665,a),flip(a)].">
      <j1 rule="hyper" parents="139 35734 1665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35739">
    <literal><![CDATA[
      (x \ 1) * a(y,x,z) = x \ a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,35734,a(flip),b,1139,a),flip(a)].">
      <j1 rule="hyper" parents="139 35734 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35741">
    <literal><![CDATA[
      ((x \ 1) \ 1) * a(y,x,z) = (x \ 1) \ a(y,x,z)
    ]]></literal>
    <justification jstring="[para(35734(a,1),1163(a,1,2)),flip(a)].">
      <j1 rule="para" parents="35734 1163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35742">
    <literal><![CDATA[
      (x * (x * a(y,x,z))) / u = (x * x) * (a(y,x,z) / u)
    ]]></literal>
    <justification jstring="[para(35734(a,1),947(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="35734 947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35743">
    <literal><![CDATA[
      (1 / x) * a(y,x,z) = a(y,x,z) / x
    ]]></literal>
    <justification jstring="[para(35734(a,1),24637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35734 24637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35744">
    <literal><![CDATA[
      L(x,y,z \ a(u,z,w)) = L(x,y,z * a(u,z,w))
    ]]></literal>
    <justification jstring="[para(35734(a,1),30389(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="35734 30389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35745">
    <literal><![CDATA[
      R(x,y \ a(z,y,u),w) = R(x,a(z,y,u) * y,w)
    ]]></literal>
    <justification jstring="[para(35734(a,1),30396(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="35734 30396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35746">
    <literal><![CDATA[
      a(x \ a(y,x,z),u,w) = a(x * a(y,x,z),u,w)
    ]]></literal>
    <justification jstring="[para(35734(a,1),30780(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="35734 30780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35747">
    <literal><![CDATA[
      L(x,y \ a(z,y,u),w) = L(x,y * a(z,y,u),w)
    ]]></literal>
    <justification jstring="[para(35734(a,1),31761(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="35734 31761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35748">
    <literal><![CDATA[
      a(x,y \ a(z,y,u),w) = a(x,y * a(z,y,u),w)
    ]]></literal>
    <justification jstring="[para(35734(a,1),32145(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="35734 32145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35749">
    <literal><![CDATA[
      a(x,y \ a(z,y,u),w) = a(x,a(z,y,u) * y,w)
    ]]></literal>
    <justification jstring="[para(35734(a,1),32149(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="35734 32149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35750">
    <literal><![CDATA[
      a(L(x \ a(y,x,z),u,w),v5,v6) = a(L(x * a(y,x,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(35734(a,1),32944(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="35734 32944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35751">
    <literal><![CDATA[
      a(x,x,y \ R(y,x,z)) = 1
    ]]></literal>
    <justification jstring="[para(28073(a,1),35735(a,1,3))].">
      <j1 rule="para" parents="28073 35735"/>
    </justification>
  </clause>

  <clause id="35752">
    <literal><![CDATA[
      a(a(x,y,z) \ y,a(x,y,z) \ y,a(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[para(33563(a,1),35735(a,1,3))].">
      <j1 rule="para" parents="33563 35735"/>
    </justification>
  </clause>

  <clause id="35753">
    <literal><![CDATA[
      L(x \ R(x,y,z),y,y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,35751,a)].">
      <j1 rule="hyper" parents="53 35751"/>
    </justification>
  </clause>

  <clause id="35754">
    <literal><![CDATA[
      L(x,x,a(y,x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,27126,a,b,35733,a(flip))].">
      <j1 rule="hyper" parents="36 27126 35733"/>
    </justification>
  </clause>

  <clause id="35755">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ a(u,z,w)) = R(x,y,z * a(u,z,w))
    ]]></literal>
    <justification jstring="[para(35733(a,1),13905(a,1,3)),flip(a)].">
      <j1 rule="para" parents="35733 13905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35756">
    <literal><![CDATA[
      L(x,y \ (z \ a(u,z,w)),v5) = L(x,y \ (z * a(u,z,w)),v5)
    ]]></literal>
    <justification jstring="[para(35733(a,1),30872(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="35733 30872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35757">
    <literal><![CDATA[
      L(R(x,y,z),x,a(u,x,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(35754(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35754 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35758">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,a(u,x,w)) = x \ L(R(x,y,z),x,a(u,x,w))
    ]]></literal>
    <justification jstring="[para(35754(a,1),4243(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35754 4243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35759">
    <literal><![CDATA[
      a(a(x,y,z) * (y \ 1),a(x,y,z),y \ 1) = y \ ((1 / (y \ a(x,y,z))) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(35736(a,1),27148(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="35736 27148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35760">
    <literal><![CDATA[
      (x \ a(y,x,z)) * ((x \ 1) \ u) = (u / x) * (x * a(y,x,z))
    ]]></literal>
    <justification jstring="[para(35736(a,1),28806(a,1,1))].">
      <j1 rule="para" parents="35736 28806"/>
    </justification>
  </clause>

  <clause id="35761">
    <literal><![CDATA[
      a((x \ a(y,x,z)) * u,w,v5) = a((x * a(y,x,z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(35736(a,1),32509(a,1,1,1))].">
      <j1 rule="para" parents="35736 32509"/>
    </justification>
  </clause>

  <clause id="35762">
    <literal><![CDATA[
      a(x,y,z) * ((y \ 1) * z) = (y \ a(x,y,z)) * z
    ]]></literal>
    <justification jstring="[para(35736(a,1),33208(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35736 33208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35763">
    <literal><![CDATA[
      (x \ a(y,x,z)) \ ((x \ 1) * u) = (a(y,x,z) * x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(35737(a,1),1692(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35737 1692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35764">
    <literal><![CDATA[
      a(x \ (y \ a(z,y,u)),w,v5) = a(x \ (a(z,y,u) * y),w,v5)
    ]]></literal>
    <justification jstring="[para(35737(a,1),26921(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="35737 26921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35765">
    <literal><![CDATA[
      L(x \ 1,x,a(y,x,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,27124,a,b,35739,a)].">
      <j1 rule="hyper" parents="36 27124 35739"/>
    </justification>
  </clause>

  <clause id="35766">
    <literal><![CDATA[
      ((a(x,y,z) / y) \ 1) * (y \ 1) = ((a(x,y,z) / y) \ 1) / y
    ]]></literal>
    <justification jstring="[para(35765(a,1),30624(a,1,2))].">
      <j1 rule="para" parents="35765 30624"/>
    </justification>
  </clause>

  <clause id="35767">
    <literal><![CDATA[
      a(x,y,z) = ((x \ ((x * y) * z)) / z) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(35765(a,1),33292(a,1,2)),flip(a)].">
      <j1 rule="para" parents="35765 33292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35768">
    <literal><![CDATA[
      (x \ 1) * (x \ a(y,x,z)) = x \ (a(y,x,z) / x)
    ]]></literal>
    <justification jstring="[hyper(139,a,35743,a(flip),b,1127,a),flip(a)].">
      <j1 rule="hyper" parents="139 35743 1127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35769">
    <literal><![CDATA[
      L(a(L(x,y,z),y,z),y * x,y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34152,a,b,35753,a)].">
      <j1 rule="hyper" parents="64 34152 35753"/>
    </justification>
  </clause>

  <clause id="35770">
    <literal><![CDATA[
      L(x \ R(x,y,z),L(x,y,y),y * z) = a(L(x,y,y),y,z)
    ]]></literal>
    <justification jstring="[para(35753(a,1),16038(a,1,1))].">
      <j1 rule="para" parents="35753 16038"/>
    </justification>
  </clause>

  <clause id="35771">
    <literal><![CDATA[
      (R(x,x,x) * (R(x,x,x) * (L(R(x,x,x),y,z) \ a(u,x,w)))) / R(x,x,x) = ((x \ 1) \ a(u,x,w)) / L(R(x,x,x),y,z)
    ]]></literal>
    <justification jstring="[para(35738(a,1),24916(a,2,1))].">
      <j1 rule="para" parents="35738 24916"/>
    </justification>
  </clause>

  <clause id="35773">
    <literal><![CDATA[
      (x * (y * x)) \ ((x * y) * L(x * a(z,x,u),y,x)) = L(a(z,x,u),L(x,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(35680(a,2),601(a,1,2,2))].">
      <j1 rule="para" parents="35680 601"/>
    </justification>
  </clause>

  <clause id="35774">
    <literal><![CDATA[
      L(x * a(y,x,z),a(u,w,v5),x) = x * a(y,x,z)
    ]]></literal>
    <justification jstring="[para(13919(a,1),35680(a,2,1))].">
      <j1 rule="para" parents="13919 35680"/>
    </justification>
  </clause>

  <clause id="35775">
    <literal><![CDATA[
      L(x,y,a(z,z * u,u)) = L(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[para(35683(a,1),35712(a,1,3))].">
      <j1 rule="para" parents="35683 35712"/>
    </justification>
  </clause>

  <clause id="35776">
    <literal><![CDATA[
      R(x * y,(x * y) * y,y) = R(x * y,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,26406,a(flip),b,35719,a),flip(a)].">
      <j1 rule="hyper" parents="373 26406 35719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35778">
    <literal><![CDATA[
      L(x,y,L(z,u \ z,u)) = L(x,y,L(z,z * u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29203,a(flip),b,35721,a),flip(a)].">
      <j1 rule="hyper" parents="64 29203 35721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35779">
    <literal><![CDATA[
      a(x,L(y,z \ y,z),u) = a(x,L(y,y * z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32197,a(flip),b,35722,a),flip(a)].">
      <j1 rule="hyper" parents="64 32197 35722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35780">
    <literal><![CDATA[
      a(L(x,y \ x,y),z,u) = a(L(x,x * y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32590,a(flip),b,35723,a),flip(a)].">
      <j1 rule="hyper" parents="64 32590 35723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35781">
    <literal><![CDATA[
      a(x,y,z) * ((y \ 1) \ 1) = (y \ 1) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(23777,a,35741,a)].">
      <j1 rule="hyper" parents="23777 35741"/>
    </justification>
  </clause>

  <clause id="35782">
    <literal><![CDATA[
      (((x \ 1) \ 1) * y) \ (((x \ 1) \ a(z,x,u)) * (a(z,x,u) \ y)) = a((x \ 1) \ 1,a(z,x,u),a(z,x,u) \ y)
    ]]></literal>
    <justification jstring="[para(35741(a,1),89(a,1,2,1))].">
      <j1 rule="para" parents="35741 89"/>
    </justification>
  </clause>

  <clause id="35783">
    <literal><![CDATA[
      R(x / (a(y,z,u) / (a(y,z,u) / (z \ 1))),z \ 1,((z \ 1) \ 1) * a(y,z,u)) = (x * (a(y,z,u) / (z \ 1))) / a(y,z,u)
    ]]></literal>
    <justification jstring="[para(35741(a,2),7114(a,1,3))].">
      <j1 rule="para" parents="35741 7114"/>
    </justification>
  </clause>

  <clause id="35784">
    <literal><![CDATA[
      L(L(((x \ 1) \ 1) \ y,(x \ 1) \ 1,a(z,x,u)),(x \ 1) \ a(z,x,u),((x \ 1) \ 1) * a(z,x,u)) = (1 / (a(z,x,u) * ((x \ 1) \ 1))) * (a(z,x,u) * y)
    ]]></literal>
    <justification jstring="[para(35741(a,1),29664(a,1,2))].">
      <j1 rule="para" parents="35741 29664"/>
    </justification>
  </clause>

  <clause id="35785">
    <literal><![CDATA[
      (a(x,y,z) / y) * (y / a(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,30069,a(flip),b,35752,a)].">
      <j1 rule="hyper" parents="64 30069 35752"/>
    </justification>
  </clause>

  <clause id="35786">
    <literal><![CDATA[
      (a(x,y,z) / y) * (a(x,y,z) \ y) = 1
    ]]></literal>
    <justification jstring="[para(23133(a,1),35785(a,1,2))].">
      <j1 rule="para" parents="23133 35785"/>
    </justification>
  </clause>

  <clause id="35787">
    <literal><![CDATA[
      1 / (a(x,y,z) \ y) = a(x,y,z) / y
    ]]></literal>
    <justification jstring="[hyper(154,a,35786,a)].">
      <j1 rule="hyper" parents="154 35786"/>
    </justification>
  </clause>

  <clause id="35788">
    <literal><![CDATA[
      (a(x,y,z) / y) \ 1 = a(x,y,z) \ y
    ]]></literal>
    <justification jstring="[hyper(149,a,35786,a)].">
      <j1 rule="hyper" parents="149 35786"/>
    </justification>
  </clause>

  <clause id="35789">
    <literal><![CDATA[
      1 / (x \ a(y,x,z)) = a(y,x,z) \ x
    ]]></literal>
    <justification jstring="[hyper(142,a,35786,a(flip),b,28765,a)].">
      <j1 rule="hyper" parents="142 35786 28765"/>
    </justification>
  </clause>

  <clause id="35790">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ 1 = y \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,35786,a(flip),b,28765,a)].">
      <j1 rule="hyper" parents="139 35786 28765"/>
    </justification>
  </clause>

  <clause id="35791">
    <literal><![CDATA[
      a(x \ L(a(y,z,u) \ z,a(y,z,u) / z,a(y,z,u) / z),w,v5) = a(x \ ((a(y,z,u) / z) * 1),w,v5)
    ]]></literal>
    <justification jstring="[para(35786(a,1),26902(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="35786 26902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35792">
    <literal><![CDATA[
      L(x,y \ L(a(z,u,w) \ u,a(z,u,w) / u,a(z,u,w) / u),v5) = L(x,y \ ((a(z,u,w) / u) * 1),v5)
    ]]></literal>
    <justification jstring="[para(35786(a,1),29695(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="35786 29695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35794">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ u) = L(x,y,u \ a(z,u,w))
    ]]></literal>
    <justification jstring="[para(35788(a,1),23969(a,1,3))].">
      <j1 rule="para" parents="35788 23969"/>
    </justification>
  </clause>

  <clause id="35795">
    <literal><![CDATA[
      R(x,y,(z \ a(u,z,w)) \ 1) = R(x,y,a(u,z,w) \ z)
    ]]></literal>
    <justification jstring="[para(35788(a,1),26209(a,1,3)),flip(a)].">
      <j1 rule="para" parents="35788 26209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35796">
    <literal><![CDATA[
      L(x,L(a(y,z,u),a(y,z,u),z),w) = L(x,z \ ((a(y,z,u) / z) \ 1),w)
    ]]></literal>
    <justification jstring="[para(35788(a,2),29726(a,2,2,2))].">
      <j1 rule="para" parents="35788 29726"/>
    </justification>
  </clause>

  <clause id="35797">
    <literal><![CDATA[
      a(x,a(y,z,u) \ z,w) = a(x,z \ a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(35788(a,1),31963(a,1,2))].">
      <j1 rule="para" parents="35788 31963"/>
    </justification>
  </clause>

  <clause id="35800">
    <literal><![CDATA[
      R(x,a(y,z,u) \ z,w) = R(x,z \ a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(35789(a,1),2968(a,1,2))].">
      <j1 rule="para" parents="35789 2968"/>
    </justification>
  </clause>

  <clause id="35801">
    <literal><![CDATA[
      a(L(a(x,y,z) \ y,u,w),v5,v6) = a(L(y \ a(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(35789(a,1),32637(a,1,1,1))].">
      <j1 rule="para" parents="35789 32637"/>
    </justification>
  </clause>

  <clause id="35802">
    <literal><![CDATA[
      (a(x,y,z) \ (a(x,y,z) \ 1)) * (y \ a(x,y,z)) = T(y / (a(x,y,z) \ 1),a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(35790(a,1),15014(a,1,2))].">
      <j1 rule="para" parents="35790 15014"/>
    </justification>
  </clause>

  <clause id="35803">
    <literal><![CDATA[
      a(x,y,z) \ ((y \ 1) \ 1) = (y \ a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(35790(a,1),28820(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35790 28820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35804">
    <literal><![CDATA[
      x \ ((x * (y \ 1)) * z) = (y \ a(x,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,30199,a,b,35762,a)].">
      <j1 rule="hyper" parents="64 30199 35762"/>
    </justification>
  </clause>

  <clause id="35805">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,a(x,y,z),z) * z) = u \ ((u * (a(x,y,z) \ 1)) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,33214,a,b,35804,a)].">
      <j1 rule="hyper" parents="373 33214 35804"/>
    </justification>
  </clause>

  <clause id="35806">
    <literal><![CDATA[
      a(a(x,y,z) \ y,u,w) = a(y * a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(35774(a,1),32861(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35774 32861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35807">
    <literal><![CDATA[
      L(x,y,L(z,z * u,u)) = L(x,y,(z \ u) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34515,a(flip),b,35778,a),flip(a)].">
      <j1 rule="hyper" parents="64 34515 35778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35808">
    <literal><![CDATA[
      L(x,y,L(z,u * z,u)) = L(x,y,(z \ u) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29740,a,b,35807,a)].">
      <j1 rule="hyper" parents="64 29740 35807"/>
    </justification>
  </clause>

  <clause id="35809">
    <literal><![CDATA[
      a(x,L(y,y * z,z),u) = a(x,(y \ z) * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32924,a(flip),b,35779,a),flip(a)].">
      <j1 rule="hyper" parents="64 32924 35779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35810">
    <literal><![CDATA[
      a(x,L(y,z * y,z),u) = a(x,(y \ z) * z,u)
    ]]></literal>
    <justification jstring="[para(14181(a,1),35809(a,1,2))].">
      <j1 rule="para" parents="14181 35809"/>
    </justification>
  </clause>

  <clause id="35811">
    <literal><![CDATA[
      a(L(x,x * y,y),z,u) = a(y * (x \ y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,33666,a(flip),b,35780,a),flip(a)].">
      <j1 rule="hyper" parents="64 33666 35780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35812">
    <literal><![CDATA[
      a(x * (y \ x),x,x \ y) = (x * L(x \ y,x,y)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,30408,a(flip),b,35811,a),flip(a)].">
      <j1 rule="hyper" parents="64 30408 35811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35813">
    <literal><![CDATA[
      a(L(x,y * x,y),z,u) = a(y * (x \ y),z,u)
    ]]></literal>
    <justification jstring="[para(14181(a,1),35811(a,1,1))].">
      <j1 rule="para" parents="14181 35811"/>
    </justification>
  </clause>

  <clause id="35814">
    <literal><![CDATA[
      a(L(x,y * x,y),z,u) = a((x \ y) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,35813,a),flip(a)].">
      <j1 rule="hyper" parents="373 26787 35813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35815">
    <literal><![CDATA[
      (x \ 1) * L(y,a(z,x,u),x \ a(z,x,u)) = ((x \ 1) / a(z,x,u)) * (a(z,x,u) * y)
    ]]></literal>
    <justification jstring="[para(35794(a,1),11084(a,1,2))].">
      <j1 rule="para" parents="35794 11084"/>
    </justification>
  </clause>

  <clause id="35816">
    <literal><![CDATA[
      a(x,a(y,z,u) \ z,w) = a(x,a(y,z,u) * z,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,35749,a(flip),b,35797,a),flip(a)].">
      <j1 rule="hyper" parents="373 35749 35797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35817">
    <literal><![CDATA[
      R(x,a(y,z,u) \ z,w) = R(x,a(y,z,u) * z,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,35745,a(flip),b,35800,a),flip(a)].">
      <j1 rule="hyper" parents="373 35745 35800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35818">
    <literal><![CDATA[
      a(x \ (y \ (x * (z * y))),u,w) = a(z * a(x,z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33348,a(flip),b,35806,a)].">
      <j1 rule="hyper" parents="64 33348 35806"/>
    </justification>
  </clause>

  <clause id="35819">
    <literal><![CDATA[
      a(x,a(x,y,z) * y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33563,a(flip),b,35816,a),flip(a)].">
      <j1 rule="hyper" parents="64 33563 35816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35820">
    <literal><![CDATA[
      R(x,a(L(y,z,u),z,u) * z,w) = R(x,(R(y,z,u) \ z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33472,a(flip),b,35817,a),flip(a)].">
      <j1 rule="hyper" parents="64 33472 35817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35821">
    <literal><![CDATA[
      (x / (x \ y)) * L(z,y,a(x,x * y,y)) = ((x / (x \ y)) / y) * (y * z)
    ]]></literal>
    <justification jstring="[para(35691(a,1),33706(a,1,2))].">
      <j1 rule="para" parents="35691 33706"/>
    </justification>
  </clause>

  <clause id="35822">
    <literal><![CDATA[
      (x / (x \ y)) * L(z,a(x,x * y,y),y) = y * ((y \ (x / (x \ y))) * z)
    ]]></literal>
    <justification jstring="[para(35700(a,1),33707(a,1,2))].">
      <j1 rule="para" parents="35700 33707"/>
    </justification>
  </clause>

  <clause id="35823">
    <literal><![CDATA[
      a(x,y \ x,y \ x) = a(x,y * x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(40,a,30547,a,b,35706,a)].">
      <j1 rule="hyper" parents="40 30547 35706"/>
    </justification>
  </clause>

  <clause id="35824">
    <literal><![CDATA[
      R(x \ y,L(y,x,x),x) = R(x \ y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26415,a(flip),b,35718,a),flip(a)].">
      <j1 rule="hyper" parents="64 26415 35718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35826">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,z * u,u)),x,(u \ (z * ((u \ z) \ 1))) * y) = a(x,y,u \ (z * ((u \ z) \ 1)))
    ]]></literal>
    <justification jstring="[para(35695(a,1),23986(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="35695 23986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35827">
    <literal><![CDATA[
      ((x \ y) * (((x \ y) \ (x \ 1)) * z)) / z = a(x \ y,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(31889(a,1),35731(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31889 35731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35828">
    <literal><![CDATA[
      a(L(L(x,y,z),z,y),u,w) = a(x * a(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,34981,a(flip),b,35818,a)].">
      <j1 rule="hyper" parents="64 34981 35818"/>
    </justification>
  </clause>

  <clause id="35829">
    <literal><![CDATA[
      a(L(L(x,y,z),z,y),u,w) = a(x * a(y,x,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27170,a,b,35828,a)].">
      <j1 rule="hyper" parents="64 27170 35828"/>
    </justification>
  </clause>

  <clause id="35830">
    <literal><![CDATA[
      a(x \ (y \ ((y * z) * x)),u,w) = a(L(L(z,y,x),x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,33286,a,b,35829,a)].">
      <j1 rule="hyper" parents="373 33286 35829"/>
    </justification>
  </clause>

  <clause id="35831">
    <literal><![CDATA[
      L(x,a(y,y * z,z),z \ y) = L(x,z \ y,a(y,y * z,z))
    ]]></literal>
    <justification jstring="[para(35683(a,1),35696(a,2,3))].">
      <j1 rule="para" parents="35683 35696"/>
    </justification>
  </clause>

  <clause id="35832">
    <literal><![CDATA[
      ((a(x,y,z) / y) \ 1) / y = (a(x,y,z) \ y) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(35788(a,1),35766(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35788 35766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35833">
    <literal><![CDATA[
      ((a(x,y,z) / y) \ 1) / y = y * (a(x,y,z) \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,28807,a(flip),b,35832,a),flip(a)].">
      <j1 rule="hyper" parents="373 28807 35832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35834">
    <literal><![CDATA[
      (a(x,y,z) * y) \ 1 = a(x,y,z) \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,30745,a(flip),b,35833,a(flip))].">
      <j1 rule="hyper" parents="35 30745 35833"/>
    </justification>
  </clause>

  <clause id="35835">
    <literal><![CDATA[
      a(x \ (T(y,z) \ ((T(y,z) * u) * x)),w,v5) = a(L(L(u,y,x),x,y),w,v5)
    ]]></literal>
    <justification jstring="[para(24773(a,2),35830(a,1,1,2))].">
      <j1 rule="para" parents="24773 35830"/>
    </justification>
  </clause>

  <clause id="35836">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,a(u,x,w)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(35757(a,1),35758(a,2,2))].">
      <j1 rule="para" parents="35757 35758"/>
    </justification>
  </clause>

  <clause id="35838">
    <literal><![CDATA[
      a(L(a(x,y,z) \ y,u,w),v5,v6) = a(L(y * a(x,y,z),u,w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,35750,a(flip),b,35801,a),flip(a)].">
      <j1 rule="hyper" parents="373 35750 35801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35839">
    <literal><![CDATA[
      a(L(x * a(y,x,z),y,z),u,w) = a(L(x,z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33535,a(flip),b,35838,a),flip(a)].">
      <j1 rule="hyper" parents="64 33535 35838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35840">
    <literal><![CDATA[
      ((x \ a(y,x,z)) * (((x \ a(y,x,z)) \ (x \ 1)) * u)) / u = a(x * a(y,x,z),a(y,x,z),u) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(35746(a,1),35827(a,2,1))].">
      <j1 rule="para" parents="35746 35827"/>
    </justification>
  </clause>

  <clause id="35841">
    <literal><![CDATA[
      L(x,((x \ y) \ y) \ (y / x),x \ y) = a(x \ y,y,x) \ x
    ]]></literal>
    <justification jstring="[para(10(a,1),35726(a,2,1,2))].">
      <j1 rule="para" parents="10 35726"/>
    </justification>
  </clause>

  <clause id="35842">
    <literal><![CDATA[
      a(x \ y,y,x) = a(y * x,y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,35644,a(flip),b,35841,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 35644 35841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35843">
    <literal><![CDATA[
      a(x \ y,L(y,x,x),x) = a(y * x,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,35676,a,b,35842,a)].">
      <j1 rule="hyper" parents="64 35676 35842"/>
    </justification>
  </clause>

  <clause id="35844">
    <literal><![CDATA[
      a((x \ y) * y,y,y \ x) = a(y * (y \ x),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32539,a(flip),b,35842,a)].">
      <j1 rule="hyper" parents="64 32539 35842"/>
    </justification>
  </clause>

  <clause id="35845">
    <literal><![CDATA[
      R(x \ y,L(y,x,x),x) = (x \ y) * a(y * x,y,x)
    ]]></literal>
    <justification jstring="[para(35843(a,1),32148(a,1,2)),flip(a)].">
      <j1 rule="para" parents="35843 32148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35846">
    <literal><![CDATA[
      (x \ y) * a(y * x,y,x) = R(x \ y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,35824,a(flip),b,35845,a),flip(a)].">
      <j1 rule="hyper" parents="64 35824 35845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35847">
    <literal><![CDATA[
      a((x \ y) * y,y,y \ x) = a(x,y,y \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),35844(a,2,1))].">
      <j1 rule="para" parents="10 35844"/>
    </justification>
  </clause>

  <clause id="35848">
    <literal><![CDATA[
      a(x * (y \ x),x,x \ y) = a(y,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(26847,a,35847,a)].">
      <j1 rule="hyper" parents="26847 35847"/>
    </justification>
  </clause>

  <clause id="35849">
    <literal><![CDATA[
      (x * L(x \ y,x,y)) \ y = a(y,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35812,a(flip),b,35848,a)].">
      <j1 rule="hyper" parents="64 35812 35848"/>
    </justification>
  </clause>

  <clause id="35850">
    <literal><![CDATA[
      T(x * L(x \ y,x,y),y) = a(y,x,x \ y) \ y
    ]]></literal>
    <justification jstring="[para(35849(a,1),19229(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35849 19229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35851">
    <literal><![CDATA[
      x * ((y * x) \ (y * y)) = a(y,x,x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,11290,a(flip),b,35850,a)].">
      <j1 rule="hyper" parents="64 11290 35850"/>
    </justification>
  </clause>

  <clause id="35852">
    <literal><![CDATA[
      (x / (x \ y)) * L(z,y,a(x,x * y,y)) = y * ((y \ (x / (x \ y))) * z)
    ]]></literal>
    <justification jstring="[para(33832(a,1),35822(a,1,2))].">
      <j1 rule="para" parents="33832 35822"/>
    </justification>
  </clause>

  <clause id="35853">
    <literal><![CDATA[
      ((x / (x \ y)) / y) \ (y * ((y \ (x / (x \ y))) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(139,a,35852,a(flip),b,35821,a(flip))].">
      <j1 rule="hyper" parents="139 35852 35821"/>
    </justification>
  </clause>

  <clause id="35854">
    <literal><![CDATA[
      (x \ (y / (y \ x))) \ (x * (T(x \ (y / (y \ x)),x) * z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(64,a,6594,a,b,35853,a)].">
      <j1 rule="hyper" parents="64 6594 35853"/>
    </justification>
  </clause>

  <clause id="35855">
    <literal><![CDATA[
      (x \ (y / (y \ x))) \ (x * ((x \ T(y / (y \ x),x)) * z)) = x * z
    ]]></literal>
    <justification jstring="[para(31606(a,1),35854(a,1,2,2,1))].">
      <j1 rule="para" parents="31606 35854"/>
    </justification>
  </clause>

  <clause id="35856">
    <literal><![CDATA[
      (x / ((x \ y) / y)) * (x \ (y / (x * y))) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,30375,a(flip),b,35671,a),flip(a)].">
      <j1 rule="hyper" parents="64 30375 35671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35858">
    <literal><![CDATA[
      ((x / (y * x)) \ y) * (y \ (x / (y * x))) = 1
    ]]></literal>
    <justification jstring="[para(23871(a,1),35856(a,1,1))].">
      <j1 rule="para" parents="23871 35856"/>
    </justification>
  </clause>

  <clause id="35859">
    <literal><![CDATA[
      1 / (x \ (y / (x * y))) = (y / (x * y)) \ x
    ]]></literal>
    <justification jstring="[hyper(154,a,35858,a)].">
      <j1 rule="hyper" parents="154 35858"/>
    </justification>
  </clause>

  <clause id="35860">
    <literal><![CDATA[
      (x \ (y / (x * y))) \ 1 = (y / (x * y)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,27020,a(flip),b,35859,a)].">
      <j1 rule="hyper" parents="64 27020 35859"/>
    </justification>
  </clause>

  <clause id="35861">
    <literal><![CDATA[
      (x * y) / (x \ y) = (y / (x * y)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,31684,a(flip),b,35860,a)].">
      <j1 rule="hyper" parents="64 31684 35860"/>
    </justification>
  </clause>

  <clause id="35862">
    <literal><![CDATA[
      ((x \ y) / (x * (x \ y))) \ x = y / (x \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(393,a,35861,a),flip(a)].">
      <j1 rule="hyper" parents="393 35861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35863">
    <literal><![CDATA[
      K(x,y) * ((x / (y * x)) \ y) = (x * y) / (y \ x)
    ]]></literal>
    <justification jstring="[para(35861(a,1),14887(a,1,2))].">
      <j1 rule="para" parents="35861 14887"/>
    </justification>
  </clause>

  <clause id="35864">
    <literal><![CDATA[
      L(x,y,((z / (u * z)) \ u) \ w) = L(x,y,((u \ z) \ (u * z)) \ w)
    ]]></literal>
    <justification jstring="[para(35861(a,1),28982(a,1,3,1))].">
      <j1 rule="para" parents="35861 28982"/>
    </justification>
  </clause>

  <clause id="35865">
    <literal><![CDATA[
      x / (y \ (y \ x)) = ((y \ x) / x) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),35862(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10 35862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35866">
    <literal><![CDATA[
      (((((x \ y) / y) \ x) \ 1) \ 1) * y = ((x \ (x \ y)) / y) \ y
    ]]></literal>
    <justification jstring="[para(35865(a,1),2040(a,1,1,1,1))].">
      <j1 rule="para" parents="35865 2040"/>
    </justification>
  </clause>

  <clause id="35867">
    <literal><![CDATA[
      T(((x \ y) / y) \ x,y * ((x \ (x \ y)) \ y)) = 1 / (1 / ((x \ (x \ y)) \ y))
    ]]></literal>
    <justification jstring="[para(35865(a,1),8329(a,1,1))].">
      <j1 rule="para" parents="35865 8329"/>
    </justification>
  </clause>

  <clause id="35868">
    <literal><![CDATA[
      K(x,T(y,z \ (z \ y))) * (((z \ y) / y) \ z) = (y / (z \ (z \ y))) * K(x,y)
    ]]></literal>
    <justification jstring="[para(35865(a,1),11160(a,1,2))].">
      <j1 rule="para" parents="35865 11160"/>
    </justification>
  </clause>

  <clause id="35869">
    <literal><![CDATA[
      a((x \ (x \ y)) \ y,z,u) = a(((x \ y) / y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(35865(a,1),26785(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35865 26785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35870">
    <literal><![CDATA[
      a(x,y,((z \ (z \ u)) \ u) * w) = a(x,y,(((z \ u) / u) \ z) * w)
    ]]></literal>
    <justification jstring="[para(35865(a,1),27317(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="35865 27317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35871">
    <literal><![CDATA[
      (x * y) / (y \ x) = (x / (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,24515,a(flip),b,35863,a),flip(a)].">
      <j1 rule="hyper" parents="64 24515 35863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35872">
    <literal><![CDATA[
      ((x * y) / ((x * y) * x)) \ x = ((x * y) * x) / y
    ]]></literal>
    <justification jstring="[para(9(a,1),35871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 35871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35873">
    <literal><![CDATA[
      ((x * y) / ((x * y) * x)) \ x = (x * y) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,35293,a(flip),b,35872,a),flip(a)].">
      <j1 rule="hyper" parents="373 35293 35872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35874">
    <literal><![CDATA[
      ((x * y) / ((x * y) * y)) \ y = (y * x) / (x / y)
    ]]></literal>
    <justification jstring="[para(15240(a,2),35873(a,1,1))].">
      <j1 rule="para" parents="15240 35873"/>
    </justification>
  </clause>

  <clause id="35875">
    <literal><![CDATA[
      (((x \ y) * x) / (((x \ y) * x) * x)) \ x = y / ((x \ y) / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,171,a(flip),b,35874,a),flip(a)].">
      <j1 rule="hyper" parents="373 171 35874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35876">
    <literal><![CDATA[
      a((x \ (y \ x)) \ y,z,u) = a((y \ (y \ x)) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32386,a(flip),b,35869,a)].">
      <j1 rule="hyper" parents="373 32386 35869"/>
    </justification>
  </clause>

  <clause id="35877">
    <literal><![CDATA[
      a((x \ (x \ y)) \ y,z,u) = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32550,a(flip),b,35876,a),flip(a)].">
      <j1 rule="hyper" parents="64 32550 35876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35878">
    <literal><![CDATA[
      (x / ((y \ x) / y)) * (((y \ x) / y) / x) = a(a(x,y,y),x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,35126,a,b,35877,a)].">
      <j1 rule="hyper" parents="64 35126 35877"/>
    </justification>
  </clause>

  <clause id="35879">
    <literal><![CDATA[
      ((x \ (x \ y)) / y) \ y = (((x \ y) / y) \ x) * y
    ]]></literal>
    <justification jstring="[para(31782(a,1),35866(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31782 35866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35880">
    <literal><![CDATA[
      L(x,y,(((z * u) \ u) \ z) \ w) = L(x,y,((z \ u) \ (z * u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29111,a(flip),b,35864,a)].">
      <j1 rule="hyper" parents="64 29111 35864"/>
    </justification>
  </clause>

  <clause id="35881">
    <literal><![CDATA[
      a(x,y,((z \ (u \ z)) \ u) * w) = a(x,y,((u \ (u \ z)) \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27412,a(flip),b,35870,a)].">
      <j1 rule="hyper" parents="373 27412 35870"/>
    </justification>
  </clause>

  <clause id="35882">
    <literal><![CDATA[
      L(x,y,((z \ (u \ z)) \ u) \ w) = L(x,y,((u \ z) \ (u * z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29414,a(flip),b,35880,a)].">
      <j1 rule="hyper" parents="64 29414 35880"/>
    </justification>
  </clause>

  <clause id="35883">
    <literal><![CDATA[
      L(x,y,((z \ (u \ z)) \ u) \ w) = L(x,y,a(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,35302,a(flip),b,35882,a),flip(a)].">
      <j1 rule="hyper" parents="373 35302 35882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35884">
    <literal><![CDATA[
      L(x,y,(a(z,z,u) \ 1) \ w) = L(x,y,a(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32866,a(flip),b,35883,a)].">
      <j1 rule="hyper" parents="64 32866 35883"/>
    </justification>
  </clause>

  <clause id="35885">
    <literal><![CDATA[
      L(x,y,a(z,u,u) \ w) = L(x,y,a(u,u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,2234,a(flip),b,35884,a),flip(a)].">
      <j1 rule="hyper" parents="64 2234 35884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35887">
    <literal><![CDATA[
      (x / ((y \ x) / y)) * (((y \ x) / y) / x) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,31089,a(flip),b,35878,a),flip(a)].">
      <j1 rule="hyper" parents="373 31089 35878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35889">
    <literal><![CDATA[
      T(((x \ y) / y) \ x,y * (((x \ y) \ x) * y)) = 1 / (1 / ((x \ (x \ y)) \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,28459,a(flip),b,35867,a)].">
      <j1 rule="hyper" parents="64 28459 35867"/>
    </justification>
  </clause>

  <clause id="35890">
    <literal><![CDATA[
      K(x,T(y,y)) * (((z \ y) / y) \ z) = (y / (z \ (z \ y))) * K(x,y)
    ]]></literal>
    <justification jstring="[para(17030(a,1),35868(a,1,1))].">
      <j1 rule="para" parents="17030 35868"/>
    </justification>
  </clause>

  <clause id="35891">
    <literal><![CDATA[
      K(x,y) * (((z \ y) / y) \ z) = (y / (z \ (z \ y))) * K(x,y)
    ]]></literal>
    <justification jstring="[para(114(a,1),35890(a,1,1,2))].">
      <j1 rule="para" parents="114 35890"/>
    </justification>
  </clause>

  <clause id="35893">
    <literal><![CDATA[
      (x / (y \ (y \ x))) * K(z,x) = ((y \ T(x,z)) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,24521,a(flip),b,35891,a),flip(a)].">
      <j1 rule="hyper" parents="64 24521 35891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35894">
    <literal><![CDATA[
      (((x \ y) / y) \ x) * K(z,y) = ((x \ T(y,z)) / y) \ x
    ]]></literal>
    <justification jstring="[para(35865(a,1),35893(a,1,1))].">
      <j1 rule="para" parents="35865 35893"/>
    </justification>
  </clause>

  <clause id="35895">
    <literal><![CDATA[
      T(((x \ y) / y) \ x,x * (x * y)) = 1 / (1 / ((x \ (x \ y)) \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,28295,a(flip),b,35889,a)].">
      <j1 rule="hyper" parents="64 28295 35889"/>
    </justification>
  </clause>

  <clause id="35897">
    <literal><![CDATA[
      T(((x \ y) / y) \ x,y) = 1 / (1 / ((x \ (x \ y)) \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,27142,a(flip),b,35895,a)].">
      <j1 rule="hyper" parents="64 27142 35895"/>
    </justification>
  </clause>

  <clause id="35898">
    <literal><![CDATA[
      T(((x \ y) / y) \ x,y) = 1 / (((x \ (x \ y)) \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(34293(a,1),35897(a,2,2))].">
      <j1 rule="para" parents="34293 35897"/>
    </justification>
  </clause>

  <clause id="35899">
    <literal><![CDATA[
      T(((x \ y) / y) \ x,y) = (x \ (x \ y)) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,79,a(flip),b,35898,a),flip(a)].">
      <j1 rule="hyper" parents="373 79 35898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35901">
    <literal><![CDATA[
      (((x \ y) / y) \ x) * y = y * ((x \ (x \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(145,a,35899,a(flip),b,22,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 35899 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35902">
    <literal><![CDATA[
      ((x \ (x \ y)) / y) \ y = y * ((x \ (x \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35879,a,b,35901,a)].">
      <j1 rule="hyper" parents="64 35879 35901"/>
    </justification>
  </clause>

  <clause id="35903">
    <literal><![CDATA[
      T((x \ (x \ y)) \ y,x \ (x \ 1)) = y \ (y * ((x \ (x \ y)) \ y))
    ]]></literal>
    <justification jstring="[para(35902(a,1),33675(a,2,2))].">
      <j1 rule="para" parents="35902 33675"/>
    </justification>
  </clause>

  <clause id="35904">
    <literal><![CDATA[
      T((x \ (x \ y)) \ y,x \ (x \ 1)) = (x \ (x \ y)) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,9,a(flip),b,35903,a),flip(a)].">
      <j1 rule="hyper" parents="373 9 35903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35906">
    <literal><![CDATA[
      L(x * K(y,x \ 1),x,L(y,x,x)) \ (x * z) = ((y / x) / y) \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(1139(a,1),35672(a,1,1,3))].">
      <j1 rule="para" parents="1139 35672"/>
    </justification>
  </clause>

  <clause id="35907">
    <literal><![CDATA[
      L(x * K(y,x \ 1),x,y) \ (x * z) = ((y / x) / y) \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(32649(a,1),35906(a,1,1))].">
      <j1 rule="para" parents="32649 35906"/>
    </justification>
  </clause>

  <clause id="35908">
    <literal><![CDATA[
      (((1 / x) * y) \ y) \ (x * z) = ((y / x) / y) \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(27277(a,1),35907(a,1,1))].">
      <j1 rule="para" parents="27277 35907"/>
    </justification>
  </clause>

  <clause id="35910">
    <literal><![CDATA[
      R((x \ y) * y,x * ((x \ y) * y),(x \ y) * y) = T(y / (x / y),(y / (x / y)) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26314,a(flip),b,35673,a)].">
      <j1 rule="hyper" parents="64 26314 35673"/>
    </justification>
  </clause>

  <clause id="35911">
    <literal><![CDATA[
      a(x \ 1,L(y,x,x \ 1),y * x) \ (y * x) = L(y * x,(y * x) \ (x \ 1),x \ 1)
    ]]></literal>
    <justification jstring="[para(32196(a,1),35724(a,1,1))].">
      <j1 rule="para" parents="32196 35724"/>
    </justification>
  </clause>

  <clause id="35912">
    <literal><![CDATA[
      a(a(x,y,z) * (y \ 1),a(x,y,z),y \ 1) = y \ ((a(x,y,z) \ y) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(35789(a,1),35759(a,2,2,1))].">
      <j1 rule="para" parents="35789 35759"/>
    </justification>
  </clause>

  <clause id="35913">
    <literal><![CDATA[
      a(a(x,y,z) * (y \ 1),a(x,y,z),y \ 1) = y \ y
    ]]></literal>
    <justification jstring="[para(23135(a,1),35912(a,2,2))].">
      <j1 rule="para" parents="23135 35912"/>
    </justification>
  </clause>

  <clause id="35914">
    <literal><![CDATA[
      a(a(x,y,z) * (y \ 1),a(x,y,z),y \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,68,a(flip),b,35913,a),flip(a)].">
      <j1 rule="hyper" parents="373 68 35913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35916">
    <literal><![CDATA[
      a(x \ a(y,x,z),a(y,x,z),x \ 1) = 1
    ]]></literal>
    <justification jstring="[para(35736(a,1),35914(a,1,1))].">
      <j1 rule="para" parents="35736 35914"/>
    </justification>
  </clause>

  <clause id="35917">
    <literal><![CDATA[
      L(x \ 1,a(y,x,z),x \ a(y,x,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(53,a,35916,a)].">
      <j1 rule="hyper" parents="53 35916"/>
    </justification>
  </clause>

  <clause id="35918">
    <literal><![CDATA[
      (x * (y * x)) \ (x * (y * (x * a(z,x,u)))) = L(a(z,x,u),L(x,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(100(a,1),35773(a,1,2))].">
      <j1 rule="para" parents="100 35773"/>
    </justification>
  </clause>

  <clause id="35919">
    <literal><![CDATA[
      L(L(a(x,y,z),y,u),u * y,y) = L(a(x,y,z),L(y,u,y),y * u)
    ]]></literal>
    <justification jstring="[hyper(1081,a,35918,a)].">
      <j1 rule="hyper" parents="1081 35918"/>
    </justification>
  </clause>

  <clause id="35920">
    <literal><![CDATA[
      ((x \ 1) / a(y,x,z)) * (a(y,x,z) * (x \ 1)) = (x \ 1) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(35917(a,1),35815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="35917 35815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35921">
    <literal><![CDATA[
      ((x \ 1) / a(y,x,z)) * (a(y,x,z) * (x \ 1)) = x \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1090,a(flip),b,35920,a),flip(a)].">
      <j1 rule="hyper" parents="373 1090 35920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35922">
    <literal><![CDATA[
      (a(x,y,z) \ (y \ 1)) * (a(x,y,z) * (y \ 1)) = y \ (1 / y)
    ]]></literal>
    <justification jstring="[para(23133(a,1),35921(a,1,1))].">
      <j1 rule="para" parents="23133 35921"/>
    </justification>
  </clause>

  <clause id="35923">
    <literal><![CDATA[
      L(x,y \ a(a(z,u,w),a(z,u,w),u \ 1),v5) = L(x,y \ (u \ (1 / u)),v5)
    ]]></literal>
    <justification jstring="[para(35922(a,1),31768(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="35922 31768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35924">
    <literal><![CDATA[
      L(x,y \ a(a(z,u,w),a(z,u,w),u \ 1),v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,11873,a(flip),b,35923,a),flip(a)].">
      <j1 rule="hyper" parents="373 11873 35923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35926">
    <literal><![CDATA[
      R((x \ y) * y,a(x,x \ y,y),(x \ y) * y) = T(y / (x / y),(y / (x / y)) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26593,a(flip),b,35910,a)].">
      <j1 rule="hyper" parents="64 26593 35910"/>
    </justification>
  </clause>

  <clause id="35927">
    <literal><![CDATA[
      T(x / (y / x),(x / (y / x)) \ y) = (y \ x) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,13920,a(flip),b,35926,a),flip(a)].">
      <j1 rule="hyper" parents="64 13920 35926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35928">
    <literal><![CDATA[
      ((x / (y / x)) \ y) \ y = (y \ x) * x
    ]]></literal>
    <justification jstring="[hyper(478,a,35927,a)].">
      <j1 rule="hyper" parents="478 35927"/>
    </justification>
  </clause>

  <clause id="35930">
    <literal><![CDATA[
      x / ((x \ y) * y) = (y / (x / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,35927,a(flip),b,116,a(flip))].">
      <j1 rule="hyper" parents="225 35927 116"/>
    </justification>
  </clause>

  <clause id="35931">
    <literal><![CDATA[
      ((x / (y / x)) \ y) \ a((x / (y / x)) \ y,(x / (y / x)) \ y,y) = ((y \ x) * x) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,35928,a(flip),b,30104,a),flip(a)].">
      <j1 rule="hyper" parents="142 35928 30104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35932">
    <literal><![CDATA[
      a(x \ 1,L(y,x,x),y * x) \ (y * x) = L(y * x,(y * x) \ (x \ 1),x \ 1)
    ]]></literal>
    <justification jstring="[para(1631(a,1),35911(a,1,1,2))].">
      <j1 rule="para" parents="1631 35911"/>
    </justification>
  </clause>

  <clause id="35933">
    <literal><![CDATA[
      L(x * y,(x * y) \ (y \ 1),y \ 1) = a(y,L(x,y,y),x * y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(2653(a,1),35932(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2653 35932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35934">
    <literal><![CDATA[
      L(x * y,(x * y) \ (y \ 1),y \ 1) = (a(y,L(x,y,y),x * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,29973,a(flip),b,35933,a),flip(a)].">
      <j1 rule="hyper" parents="373 29973 35933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35935">
    <literal><![CDATA[
      (a(x,L(y,x,x),y * x) \ y) * x = L(y * x,x \ (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29766,a(flip),b,35934,a),flip(a)].">
      <j1 rule="hyper" parents="64 29766 35934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35936">
    <literal><![CDATA[
      ((x / (y / x)) \ y) \ a((x / (y / x)) \ y,((y \ x) * x) \ y,y) = ((y \ x) * x) / y
    ]]></literal>
    <justification jstring="[para(33701(a,1),35931(a,1,2))].">
      <j1 rule="para" parents="33701 35931"/>
    </justification>
  </clause>

  <clause id="35937">
    <literal><![CDATA[
      ((x / (y / x)) \ y) \ a((x / (y / x)) \ y,a(x,y \ x,y),y) = ((y \ x) * x) / y
    ]]></literal>
    <justification jstring="[para(32299(a,1),35936(a,1,2))].">
      <j1 rule="para" parents="32299 35936"/>
    </justification>
  </clause>

  <clause id="35938">
    <literal><![CDATA[
      ((x / (y / x)) \ y) \ a(((y \ x) * x) \ y,a(x,y \ x,y),y) = ((y \ x) * x) / y
    ]]></literal>
    <justification jstring="[para(33703(a,1),35937(a,1,2))].">
      <j1 rule="para" parents="33703 35937"/>
    </justification>
  </clause>

  <clause id="35939">
    <literal><![CDATA[
      ((x / (y / x)) \ y) \ a(a(x,y \ x,y),a(x,y \ x,y),y) = ((y \ x) * x) / y
    ]]></literal>
    <justification jstring="[para(32952(a,1),35938(a,1,2))].">
      <j1 rule="para" parents="32952 35938"/>
    </justification>
  </clause>

  <clause id="35940">
    <literal><![CDATA[
      ((x / (y / x)) \ y) \ 1 = ((y \ x) * x) / y
    ]]></literal>
    <justification jstring="[para(29325(a,1),35939(a,1,2))].">
      <j1 rule="para" parents="29325 35939"/>
    </justification>
  </clause>

  <clause id="35941">
    <literal><![CDATA[
      ((x / (y / x)) \ y) \ 1 = y \ (x / (y / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,34328,a(flip),b,35940,a),flip(a)].">
      <j1 rule="hyper" parents="373 34328 35940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35942">
    <literal><![CDATA[
      1 / (x \ (y / (x / y))) = (y / (x / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,34328,a(flip),b,35940,a)].">
      <j1 rule="hyper" parents="225 34328 35940"/>
    </justification>
  </clause>

  <clause id="35944">
    <literal><![CDATA[
      (((x \ y) * x) * (z / y)) * ((z / y) \ u) = z * ((y \ z) \ (K(x \ y,x) * u))
    ]]></literal>
    <justification jstring="[para(22797(a,1),24453(a,1,2)),flip(a)].">
      <j1 rule="para" parents="22797 24453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35945">
    <literal><![CDATA[
      (((x \ y) * x) * (z / y)) * ((z / y) \ u) = z * ((((x \ y) * x) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(24405(a,1),35944(a,2,2))].">
      <j1 rule="para" parents="24405 35944"/>
    </justification>
  </clause>

  <clause id="35946">
    <literal><![CDATA[
      (((x \ y) * x) * (y \ z)) * ((y \ z) \ u) = z * ((((x \ y) * x) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27257,a(flip),b,35945,a)].">
      <j1 rule="hyper" parents="64 27257 35945"/>
    </justification>
  </clause>

  <clause id="35947">
    <literal><![CDATA[
      (K(x \ y,x) * z) * ((y \ z) \ u) = z * ((((x \ y) * x) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(10873(a,1),35946(a,1,1))].">
      <j1 rule="para" parents="10873 35946"/>
    </justification>
  </clause>

  <clause id="35948">
    <literal><![CDATA[
      T(x,y \ 1) * (y \ K(y \ x,z)) = T(T(x,y \ 1) * (y \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(41,a,17320,a,b,24880,a)].">
      <j1 rule="hyper" parents="41 17320 24880"/>
    </justification>
  </clause>

  <clause id="35949">
    <literal><![CDATA[
      T(x,y \ z) * ((z \ y) \ K((z \ y) \ x,u)) = T(T(x,(z \ y) \ 1) * ((z \ y) \ 1),u)
    ]]></literal>
    <justification jstring="[para(6704(a,1),35948(a,1,1))].">
      <j1 rule="para" parents="6704 35948"/>
    </justification>
  </clause>

  <clause id="35950">
    <literal><![CDATA[
      R(x \ (x \ y),z,u) * ((x \ (x \ y)) \ (y / x)) = R(x * (x \ y),z,u) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,27059,a(flip),b,25047,a),flip(a)].">
      <j1 rule="hyper" parents="373 27059 25047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35951">
    <literal><![CDATA[
      R(x \ (x \ y),z,u) * ((x \ (x \ y)) \ (y / x)) = R(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(10(a,1),35950(a,2,1,1))].">
      <j1 rule="para" parents="10 35950"/>
    </justification>
  </clause>

  <clause id="35952">
    <literal><![CDATA[
      L((x \ 1) \ y,1 / x,x * a(z,u,x)) = a(z,u,x) \ (((1 / x) \ a(z,u,x)) * y)
    ]]></literal>
    <justification jstring="[para(9440(a,1),25240(a,1,3))].">
      <j1 rule="para" parents="9440 25240"/>
    </justification>
  </clause>

  <clause id="35954">
    <literal><![CDATA[
      a(x,x,y) \ (((1 / y) \ a(x,x,y)) * z) = L((y \ 1) \ z,1 / y,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,24660,a(flip),b,35952,a),flip(a)].">
      <j1 rule="hyper" parents="64 24660 35952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35955">
    <literal><![CDATA[
      a(x,x,y) \ (((1 / y) \ a(x,x,y)) * z) = L((y \ 1) \ z,y,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,11776,a(flip),b,35954,a),flip(a)].">
      <j1 rule="hyper" parents="373 11776 35954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35956">
    <literal><![CDATA[
      a(x,x,y) \ ((y * a(x,x,y)) * z) = L((y \ 1) \ z,y,L(y,x,x))
    ]]></literal>
    <justification jstring="[para(9440(a,1),35955(a,1,2,1))].">
      <j1 rule="para" parents="9440 35955"/>
    </justification>
  </clause>

  <clause id="35957">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),R(x,y,z) \ L(x,y,z)) \ (((R(x,y,z) \ L(x,y,z)) * a(L(x,y,z),L(x,y,z),R(x,y,z) \ L(x,y,z))) * u) = L(((R(x,y,z) \ L(x,y,z)) \ 1) \ u,R(x,y,z) \ L(x,y,z),((1 / L(x,y,z)) * R(x,y,z)) \ 1)
    ]]></literal>
    <justification jstring="[para(29800(a,1),35956(a,2,3))].">
      <j1 rule="para" parents="29800 35956"/>
    </justification>
  </clause>

  <clause id="35958">
    <literal><![CDATA[
      x / ((y * (z / (y * z))) * x) = (x * (y * (z / (y * z)))) \ x
    ]]></literal>
    <justification jstring="[para(25924(a,1),25357(a,1,2))].">
      <j1 rule="para" parents="25924 25357"/>
    </justification>
  </clause>

  <clause id="35959">
    <literal><![CDATA[
      (x * (y * (z / (y * z)))) \ x = x \ ((y * (z / (y * z))) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27041,a(flip),b,35958,a),flip(a)].">
      <j1 rule="hyper" parents="64 27041 35958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35961">
    <literal><![CDATA[
      (x / (y * x)) \ ((y * (x / (y * x))) \ (x / (y * x))) = y \ (y / (y * (x / (y * x))))
    ]]></literal>
    <justification jstring="[hyper(64,a,31188,a(flip),b,35959,a),flip(a)].">
      <j1 rule="hyper" parents="64 31188 35959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35962">
    <literal><![CDATA[
      x \ (x / (x * (y / (x * y)))) = (y / (x * y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(26307(a,1),35961(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26307 35961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35963">
    <literal><![CDATA[
      x \ ((x * (y / (x * y))) \ x) = (y / (x * y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(23872(a,1),35962(a,1,2))].">
      <j1 rule="para" parents="23872 35962"/>
    </justification>
  </clause>

  <clause id="35965">
    <literal><![CDATA[
      (x / (y * x)) \ (y \ 1) = y \ (1 / (x / (y * x)))
    ]]></literal>
    <justification jstring="[para(3368(a,1),35963(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3368 35963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35966">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (x * y) = x \ (1 / (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,30977,a,b,35965,a)].">
      <j1 rule="hyper" parents="64 30977 35965"/>
    </justification>
  </clause>

  <clause id="35967">
    <literal><![CDATA[
      (x * (y / (x * y))) \ 1 = x \ (1 / (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,30334,a,b,35966,a)].">
      <j1 rule="hyper" parents="64 30334 35966"/>
    </justification>
  </clause>

  <clause id="35968">
    <literal><![CDATA[
      (x \ (1 / (y / (x * y)))) * z = z * (((x \ 1) \ y) \ (x * y))
    ]]></literal>
    <justification jstring="[para(35966(a,1),22548(a,1,1))].">
      <j1 rule="para" parents="35966 22548"/>
    </justification>
  </clause>

  <clause id="35969">
    <literal><![CDATA[
      (x * y) \ (y \ (1 / (x / (y * x)))) = ((y \ 1) \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(35966(a,1),24981(a,1,2))].">
      <j1 rule="para" parents="35966 24981"/>
    </justification>
  </clause>

  <clause id="35970">
    <literal><![CDATA[
      1 / (x * (y / (x * y))) = x \ (1 / (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,23872,a,b,35967,a)].">
      <j1 rule="hyper" parents="64 23872 35967"/>
    </justification>
  </clause>

  <clause id="35971">
    <literal><![CDATA[
      (x \ (1 / (y / (x * y)))) * z = z * (x \ (1 / (y / (x * y))))
    ]]></literal>
    <justification jstring="[para(35966(a,1),35968(a,2,2))].">
      <j1 rule="para" parents="35966 35968"/>
    </justification>
  </clause>

  <clause id="35972">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) * (a(x,y \ x,y \ x) * (y \ x)) = R(x \ 1,y \ x,y \ x)
    ]]></literal>
    <justification jstring="[para(2653(a,1),27056(a,1,2,1))].">
      <j1 rule="para" parents="2653 27056"/>
    </justification>
  </clause>

  <clause id="35973">
    <literal><![CDATA[
      ((x \ 1) * (x \ y)) * ((x \ y) \ 1) = R(x \ 1,y \ x,y \ x)
    ]]></literal>
    <justification jstring="[para(30528(a,1),35972(a,1,2))].">
      <j1 rule="para" parents="30528 35972"/>
    </justification>
  </clause>

  <clause id="35974">
    <literal><![CDATA[
      R(x \ 1,x \ y,(x \ y) \ 1) = R(x \ 1,y \ x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(669,a,35973,a)].">
      <j1 rule="hyper" parents="669 35973"/>
    </justification>
  </clause>

  <clause id="35975">
    <literal><![CDATA[
      R(x \ 1,y \ x,y \ x) = R(x \ 1,x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30828,a(flip),b,35974,a),flip(a)].">
      <j1 rule="hyper" parents="64 30828 35974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35976">
    <literal><![CDATA[
      R(x \ 1,x \ y,y \ x) = (y / (1 / (y \ x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,30599,a(flip),b,35975,a),flip(a)].">
      <j1 rule="hyper" parents="64 30599 35975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35977">
    <literal><![CDATA[
      a(x,y,(R(T(z,u),w,v5) \ 1) \ L(z,w,v5)) = a(x,y,K(z,u) * (R(z,w,v5) * R(z,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,31676,a(flip),b,27636,a)].">
      <j1 rule="hyper" parents="64 31676 27636"/>
    </justification>
  </clause>

  <clause id="35978">
    <literal><![CDATA[
      ((x / (x * y)) / z) \ K(z \ (x / (x * y)),T(y,x) * z) = 1 / ((x / (x * y)) / z)
    ]]></literal>
    <justification jstring="[para(28533(a,1),27822(a,1,2))].">
      <j1 rule="para" parents="28533 27822"/>
    </justification>
  </clause>

  <clause id="35979">
    <literal><![CDATA[
      ((x / (x * y)) / y) \ K(y \ (x / (x * y)),y * T(y,x)) = 1 / ((x / (x * y)) / y)
    ]]></literal>
    <justification jstring="[para(273(a,1),35978(a,1,2,2))].">
      <j1 rule="para" parents="273 35978"/>
    </justification>
  </clause>

  <clause id="35980">
    <literal><![CDATA[
      ((x / (x * y)) / y) \ K(y * (x / (x * y)),y * T(y,x)) = 1 / ((x / (x * y)) / y)
    ]]></literal>
    <justification jstring="[para(34785(a,1),35979(a,1,2))].">
      <j1 rule="para" parents="34785 35979"/>
    </justification>
  </clause>

  <clause id="35981">
    <literal><![CDATA[
      ((x / (x * y)) / y) \ K(y * ((x * y) \ x),y * T(y,x)) = 1 / ((x / (x * y)) / y)
    ]]></literal>
    <justification jstring="[para(34782(a,1),35980(a,1,2))].">
      <j1 rule="para" parents="34782 35980"/>
    </justification>
  </clause>

  <clause id="35982">
    <literal><![CDATA[
      1 / ((x / (x * y)) / y) = ((x / (x * y)) / y) \ 1
    ]]></literal>
    <justification jstring="[para(9475(a,1),35981(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9475 35981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35983">
    <literal><![CDATA[
      x * ((((y / (y * z)) / z) \ 1) \ 1) = x * ((y / (y * z)) / z)
    ]]></literal>
    <justification jstring="[para(35982(a,1),220(a,1,2,1))].">
      <j1 rule="para" parents="35982 220"/>
    </justification>
  </clause>

  <clause id="35985">
    <literal><![CDATA[
      (K((x \ y) * K(x \ 1,y),T(x,y)) / (y \ (x \ y))) \ y = y / (1 / (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(7422(a,1),27880(a,1,1,1))].">
      <j1 rule="para" parents="7422 27880"/>
    </justification>
  </clause>

  <clause id="35986">
    <literal><![CDATA[
      (K((x \ y) * K(x,y),T(x,y)) / (y \ (x \ y))) \ y = y / (1 / (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(16864(a,1),35985(a,1,1,1))].">
      <j1 rule="para" parents="16864 35985"/>
    </justification>
  </clause>

  <clause id="35987">
    <literal><![CDATA[
      (K(x * (y \ K(y,x)),y) / (x \ (y \ x))) \ x = x / (1 / (x \ (y \ x)))
    ]]></literal>
    <justification jstring="[para(20787(a,1),35986(a,1,1,1))].">
      <j1 rule="para" parents="20787 35986"/>
    </justification>
  </clause>

  <clause id="35988">
    <literal><![CDATA[
      (K(x / T(y,x),y) / (x \ (y \ x))) \ x = x / (1 / (x \ (y \ x)))
    ]]></literal>
    <justification jstring="[para(19792(a,1),35987(a,1,1,1))].">
      <j1 rule="para" parents="19792 35987"/>
    </justification>
  </clause>

  <clause id="35989">
    <literal><![CDATA[
      (K(x \ y,x) / (y \ (x \ y))) \ y = y / (1 / (y \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(13400(a,1),35988(a,1,1,1))].">
      <j1 rule="para" parents="13400 35988"/>
    </justification>
  </clause>

  <clause id="35990">
    <literal><![CDATA[
      x / (1 / (x \ (y \ x))) = (1 / (x \ (x / y))) \ x
    ]]></literal>
    <justification jstring="[para(15105(a,1),35989(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15105 35989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="35991">
    <literal><![CDATA[
      R(T(x / (y * x),z),y,y \ z) = (z \ (R(y,y,x) * (y \ z))) * (z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(845(a,1),28069(a,2,1,2))].">
      <j1 rule="para" parents="845 28069"/>
    </justification>
  </clause>

  <clause id="35992">
    <literal><![CDATA[
      ((x \ (x \ y)) / y) \ K(x * x,(x \ y) * x) = T((x \ (x \ y)) / y,x \ (x \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(22812(a,1),28444(a,1,2))].">
      <j1 rule="para" parents="22812 28444"/>
    </justification>
  </clause>

  <clause id="35993">
    <literal><![CDATA[
      ((x \ ((y / z) / z)) \ 1) \ K(y \ ((x * z) * z),x \ (y / (z * z))) = x \ ((y / z) / z)
    ]]></literal>
    <justification jstring="[para(28108(a,1),28513(a,1,2))].">
      <j1 rule="para" parents="28108 28513"/>
    </justification>
  </clause>

  <clause id="35994">
    <literal><![CDATA[
      (1 / (L(x,y,z) \ R(x,u,w))) * R(x,u,w) = R(x,u,w) * (1 / (R(x,u,w) / L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(5589(a,1),28900(a,1,1,2))].">
      <j1 rule="para" parents="5589 28900"/>
    </justification>
  </clause>

  <clause id="35995">
    <literal><![CDATA[
      L(x,y * (K(z,u) * (w * (u * (z * K(v5,v6))))),v7) = L(x,y * T(w * (z * u),K(z,u)),v7)
    ]]></literal>
    <justification jstring="[para(25230(a,1),29679(a,1,2,2,2))].">
      <j1 rule="para" parents="25230 29679"/>
    </justification>
  </clause>

  <clause id="35996">
    <literal><![CDATA[
      L((x * (y / (x * y))) \ z,a(x,x,x * y),a(x,x,y)) = (1 / (x * (y / (x * y)))) * z
    ]]></literal>
    <justification jstring="[para(30079(a,2),30100(a,1,2))].">
      <j1 rule="para" parents="30079 30100"/>
    </justification>
  </clause>

  <clause id="35997">
    <literal><![CDATA[
      L((x * (y / (x * y))) \ z,a(y,x,x),a(x,x,y)) = (1 / (x * (y / (x * y)))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,30725,a(flip),b,35996,a)].">
      <j1 rule="hyper" parents="64 30725 35996"/>
    </justification>
  </clause>

  <clause id="35998">
    <literal><![CDATA[
      L((x * (y / (x * y))) \ z,a(y,x,x),a(x,x,y)) = (x \ (1 / (y / (x * y)))) * z
    ]]></literal>
    <justification jstring="[para(35970(a,1),35997(a,2,1))].">
      <j1 rule="para" parents="35970 35997"/>
    </justification>
  </clause>

  <clause id="35999">
    <literal><![CDATA[
      T(x,x \ y) * (x \ R(x \ y,x * y,x)) = x * ((x \ (y / x)) * a(x \ y,x \ y,x))
    ]]></literal>
    <justification jstring="[para(34017(a,1),30174(a,1,2,2))].">
      <j1 rule="para" parents="34017 30174"/>
    </justification>
  </clause>

  <clause id="36000">
    <literal><![CDATA[
      a(x,x,R(y,1 / x,1 / x)) * R(y,1 / x,1 / x) = x \ (L(1 / x,x,y) \ y)
    ]]></literal>
    <justification jstring="[para(11776(a,1),30245(a,2,2,1))].">
      <j1 rule="para" parents="11776 30245"/>
    </justification>
  </clause>

  <clause id="36001">
    <literal><![CDATA[
      a(x,x,R(y,1 / x,x \ 1)) * R(y,1 / x,1 / x) = x \ (L(1 / x,x,y) \ y)
    ]]></literal>
    <justification jstring="[para(5107(a,1),36000(a,1,1,3))].">
      <j1 rule="para" parents="5107 36000"/>
    </justification>
  </clause>

  <clause id="36002">
    <literal><![CDATA[
      a(x,x,R(y,x,x \ 1)) * R(y,1 / x,1 / x) = x \ (L(1 / x,x,y) \ y)
    ]]></literal>
    <justification jstring="[para(2968(a,1),36001(a,1,1,3))].">
      <j1 rule="para" parents="2968 36001"/>
    </justification>
  </clause>

  <clause id="36003">
    <literal><![CDATA[
      a(x,x,L(y,x,x)) * R(y,1 / x,1 / x) = x \ (L(1 / x,x,y) \ y)
    ]]></literal>
    <justification jstring="[para(27596(a,1),36002(a,1,1))].">
      <j1 rule="para" parents="27596 36002"/>
    </justification>
  </clause>

  <clause id="36004">
    <literal><![CDATA[
      a(x,x,y) * R(y,1 / x,1 / x) = x \ (L(1 / x,x,y) \ y)
    ]]></literal>
    <justification jstring="[para(30352(a,1),36003(a,1,1))].">
      <j1 rule="para" parents="30352 36003"/>
    </justification>
  </clause>

  <clause id="36005">
    <literal><![CDATA[
      a(x,x,y) * R(y,1 / x,x \ 1) = x \ (L(1 / x,x,y) \ y)
    ]]></literal>
    <justification jstring="[para(5107(a,1),36004(a,1,2))].">
      <j1 rule="para" parents="5107 36004"/>
    </justification>
  </clause>

  <clause id="36006">
    <literal><![CDATA[
      a(x,x,y) * R(y,x,x \ 1) = x \ (L(1 / x,x,y) \ y)
    ]]></literal>
    <justification jstring="[para(2968(a,1),36005(a,1,2))].">
      <j1 rule="para" parents="2968 36005"/>
    </justification>
  </clause>

  <clause id="36007">
    <literal><![CDATA[
      T(x * K(y \ x,y \ 1),y) = y \ (L(1 / y,y,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,34451,a,b,36006,a)].">
      <j1 rule="hyper" parents="64 34451 36006"/>
    </justification>
  </clause>

  <clause id="36008">
    <literal><![CDATA[
      x \ (L(1 / x,x,y) \ y) = (y * x) * R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,34363,a(flip),b,36007,a),flip(a)].">
      <j1 rule="hyper" parents="64 34363 36007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36009">
    <literal><![CDATA[
      a(x,y,(z \ (L(1 / z,z,z \ u) \ (z \ u))) * w) = a(x,y,(u * R(z \ 1,z,z \ u)) * w)
    ]]></literal>
    <justification jstring="[para(36008(a,2),27414(a,1,3,1))].">
      <j1 rule="para" parents="36008 27414"/>
    </justification>
  </clause>

  <clause id="36010">
    <literal><![CDATA[
      (x * (y \ (x \ y))) * (z * T(x,x * ((y \ (x \ y)) * z))) = x * ((x * (y \ (x \ y))) * z)
    ]]></literal>
    <justification jstring="[para(25009(a,1),30376(a,1,2,2))].">
      <j1 rule="para" parents="25009 30376"/>
    </justification>
  </clause>

  <clause id="36011">
    <literal><![CDATA[
      L(a(x,y,y) \ 1,(x / y) \ (x * (1 / y)),x / y) = 1 / (1 / ((x * (1 / y)) \ (x / y)))
    ]]></literal>
    <justification jstring="[para(13923(a,1),30539(a,1,1))].">
      <j1 rule="para" parents="13923 30539"/>
    </justification>
  </clause>

  <clause id="36012">
    <literal><![CDATA[
      x * ((x \ y) * (y \ (K(z,u) * (K(u,z) * x)))) = (K(z,u) * y) / (1 / ((K(z,u) * y) \ x))
    ]]></literal>
    <justification jstring="[para(25778(a,1),30638(a,1,2))].">
      <j1 rule="para" parents="25778 30638"/>
    </justification>
  </clause>

  <clause id="36013">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ a(u,u,a(x,y,z)) = R(a(x,y,z) \ 1,u,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,23734,a(flip),b,31213,a)].">
      <j1 rule="hyper" parents="64 23734 31213"/>
    </justification>
  </clause>

  <clause id="36014">
    <literal><![CDATA[
      (x * y) / T((1 / y) \ x,x * y) = ((1 / y) \ x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(13927(a,1),31388(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13927 31388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36015">
    <literal><![CDATA[
      (x * y) / ((1 / y) \ x) = ((1 / y) \ x) \ (x * y)
    ]]></literal>
    <justification jstring="[para(6339(a,1),36014(a,1,2))].">
      <j1 rule="para" parents="6339 36014"/>
    </justification>
  </clause>

  <clause id="36017">
    <literal><![CDATA[
      K(x \ ((y \ z) * u),T(y * ((y \ z) * u),K(w,v5))) = K((y \ z) * (u / x),T(z * u,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,28232,a(flip),b,31471,a),flip(a)].">
      <j1 rule="hyper" parents="373 28232 31471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36018">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,u),w),x,a(y,z,u) * w) = a(x,a(y,z,u),w \ (v5 * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,29077,a(flip),b,31842,a)].">
      <j1 rule="hyper" parents="64 29077 31842"/>
    </justification>
  </clause>

  <clause id="36020">
    <literal><![CDATA[
      a(x,a(y,z,u),w \ (v5 * v5)) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31811,a(flip),b,36018,a),flip(a)].">
      <j1 rule="hyper" parents="64 31811 36018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36021">
    <literal><![CDATA[
      a(x,a(y,z,u),((w \ 1) * v5) \ 1) = a(x,a(y,z,u),w * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27655,a,b,36020,a)].">
      <j1 rule="hyper" parents="64 27655 36020"/>
    </justification>
  </clause>

  <clause id="36022">
    <literal><![CDATA[
      a(x,a(y,z,u),w \ 1) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(7(a,1),36020(a,1,3,2))].">
      <j1 rule="para" parents="7 36020"/>
    </justification>
  </clause>

  <clause id="36023">
    <literal><![CDATA[
      a(x,a(y,z,u),(w * v5) \ 1) = a(x,a(y,z,u),v5 * w)
    ]]></literal>
    <justification jstring="[hyper(27591,a,36022,a)].">
      <j1 rule="hyper" parents="27591 36022"/>
    </justification>
  </clause>

  <clause id="36024">
    <literal><![CDATA[
      a(x,a(y,z,u),((w * v5) \ 1) * (v6 * v6)) = a(x,a(y,z,u),w * ((v6 * v6) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,31723,a(flip),b,36022,a)].">
      <j1 rule="hyper" parents="64 31723 36022"/>
    </justification>
  </clause>

  <clause id="36025">
    <literal><![CDATA[
      L(x,y \ a(a(z,u,w),a(z,u,w),u),v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(36022(a,1),35924(a,1,2,2))].">
      <j1 rule="para" parents="36022 35924"/>
    </justification>
  </clause>

  <clause id="36026">
    <literal><![CDATA[
      a(x,a(y,z,u),w * (v5 \ 1)) = a(x,a(y,z,u),v5 * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,36023,a(flip),b,36021,a)].">
      <j1 rule="hyper" parents="64 36023 36021"/>
    </justification>
  </clause>

  <clause id="36027">
    <literal><![CDATA[
      a(x,a(y,z,u),(w \ 1) * v5) = a(x,a(y,z,u),w * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,36022,a(flip),b,36021,a)].">
      <j1 rule="hyper" parents="64 36022 36021"/>
    </justification>
  </clause>

  <clause id="36028">
    <literal><![CDATA[
      a(x,a(y,z,u),w * (w * v5)) = a(x,a(y,z,u),L(v5,w,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27363,a(flip),b,36026,a),flip(a)].">
      <j1 rule="hyper" parents="64 27363 36026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36029">
    <literal><![CDATA[
      a(x,a(y,z,u),(w \ 1) * v5) = a(x,a(y,z,u),v5 * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,36027,a),flip(a)].">
      <j1 rule="hyper" parents="373 27298 36027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36030">
    <literal><![CDATA[
      a(x,a(y,z,u),(w * v5) \ (v6 * v6)) = a(x,a(y,z,u),w * ((v6 * v6) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27613,a(flip),b,36024,a)].">
      <j1 rule="hyper" parents="64 27613 36024"/>
    </justification>
  </clause>

  <clause id="36031">
    <literal><![CDATA[
      a(x,a(y,z,u),w * ((v5 * v5) \ v6)) = a(x,a(y,z,u),w * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,36020,a(flip),b,36030,a),flip(a)].">
      <j1 rule="hyper" parents="64 36020 36030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36033">
    <literal><![CDATA[
      a(x,a(y,z,u),(w * w) * v5) = a(x,a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),36031(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 36031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36034">
    <literal><![CDATA[
      a(x,a(y,z,u),(w \ 1) \ v5) = a(x,a(y,z,u),w \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27635,a(flip),b,36033,a)].">
      <j1 rule="hyper" parents="64 27635 36033"/>
    </justification>
  </clause>

  <clause id="36035">
    <literal><![CDATA[
      a(x,y * (((T(z,u * u) * w) / v5) * (u * u)),v6) = a(x,y * (v5 \ (z * ((u * u) * w))),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,31897,a(flip),b,32050,a),flip(a)].">
      <j1 rule="hyper" parents="373 31897 32050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36036">
    <literal><![CDATA[
      a(x,(y \ z) \ (y \ (u * u)),z \ (u * u)) = a(x,z,(y \ z) \ (y \ (u * u)))
    ]]></literal>
    <justification jstring="[para(10(a,1),32229(a,1,3,1))].">
      <j1 rule="para" parents="10 32229"/>
    </justification>
  </clause>

  <clause id="36037">
    <literal><![CDATA[
      a(x,(y \ z) \ y,z \ (u * u)) = a(x,z,(y \ z) \ (y \ (u * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,32329,a(flip),b,36036,a)].">
      <j1 rule="hyper" parents="64 32329 36036"/>
    </justification>
  </clause>

  <clause id="36040">
    <literal><![CDATA[
      a(x,(y \ z) * z,y \ (u * u)) = a(x,y,(z \ y) \ (z \ (u * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,32124,a(flip),b,36037,a)].">
      <j1 rule="hyper" parents="64 32124 36037"/>
    </justification>
  </clause>

  <clause id="36041">
    <literal><![CDATA[
      ((x * ((y * y) * z)) * a(u,w,v5)) \ (((x * (y * y)) * a(u,w,v5)) * z) = a(a(u,w,v5),x,z)
    ]]></literal>
    <justification jstring="[para(34(a,1),33119(a,1,1,1))].">
      <j1 rule="para" parents="34 33119"/>
    </justification>
  </clause>

  <clause id="36042">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) \ ((u * L(x,y,z)) * x) = L(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5550(a,1),33141(a,1,2,1,2))].">
      <j1 rule="para" parents="5550 33141"/>
    </justification>
  </clause>

  <clause id="36043">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) \ ((u * x) * L(x,y,z)) = L(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(3184(a,1),36042(a,1,2))].">
      <j1 rule="para" parents="3184 36042"/>
    </justification>
  </clause>

  <clause id="36044">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u * x) = L(x,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27824,a(flip),b,36043,a)].">
      <j1 rule="hyper" parents="64 27824 36043"/>
    </justification>
  </clause>

  <clause id="36045">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u * x) = L(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11786,a(flip),b,36044,a),flip(a)].">
      <j1 rule="hyper" parents="373 11786 36044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36046">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u * x) \ x = (x \ L(x,x * L(x,y,z),u)) \ 1
    ]]></literal>
    <justification jstring="[para(36045(a,1),9374(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="36045 9374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36047">
    <literal><![CDATA[
      (L(x,y,z) * a(x,L(x,y,z),L(u,x,L(x,y,z)))) \ (L(x,y,z) * u) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(2482(a,1),33391(a,1,1,2,3))].">
      <j1 rule="para" parents="2482 33391"/>
    </justification>
  </clause>

  <clause id="36048">
    <literal><![CDATA[
      a((x \ 1) \ y,x,a(z,u,x)) \ y = ((y / (x \ 1)) * (x \ a(z,u,x))) / a(z,u,x)
    ]]></literal>
    <justification jstring="[para(11980(a,1),33428(a,1,1))].">
      <j1 rule="para" parents="11980 33428"/>
    </justification>
  </clause>

  <clause id="36049">
    <literal><![CDATA[
      a(x \ y,x,a(z,u,x)) \ y = ((y / (x \ 1)) * (x \ a(z,u,x))) / a(z,u,x)
    ]]></literal>
    <justification jstring="[para(2675(a,1),36048(a,1,1))].">
      <j1 rule="para" parents="2675 36048"/>
    </justification>
  </clause>

  <clause id="36050">
    <literal><![CDATA[
      a((x \ a(y * L(z,u,w),x,x)) * (y * L(z,u,w)),v5,v6) = a(x \ (y * R(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,34670,a(flip),b,33592,a)].">
      <j1 rule="hyper" parents="64 34670 33592"/>
    </justification>
  </clause>

  <clause id="36051">
    <literal><![CDATA[
      R(x,y,((1 / (z \ u)) \ z) \ ((u \ z) * z)) = R(x,y,u \ (((z \ u) \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,26214,a(flip),b,33705,a),flip(a)].">
      <j1 rule="hyper" parents="373 26214 33705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36053">
    <literal><![CDATA[
      R(x,y,(((z \ u) \ 1) \ z) \ ((u \ z) * z)) = R(x,y,u \ (((z \ u) \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26280,a(flip),b,36051,a)].">
      <j1 rule="hyper" parents="64 26280 36051"/>
    </justification>
  </clause>

  <clause id="36054">
    <literal><![CDATA[
      (x \ (y \ L(y * x,z,u))) \ x = ((y \ L(y * x,z,u)) \ x) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,9465,a(flip),b,33725,a),flip(a)].">
      <j1 rule="hyper" parents="64 9465 33725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36056">
    <literal><![CDATA[
      L(x \ T(x * y,x \ 1),x,x) = R(R(x,z,u) * y,x,x) / R(x,z,u)
    ]]></literal>
    <justification jstring="[para(28599(a,1),33754(a,1,1))].">
      <j1 rule="para" parents="28599 33754"/>
    </justification>
  </clause>

  <clause id="36057">
    <literal><![CDATA[
      R(R(x,y,z) * u,x,x) / R(x,y,z) = (1 / x) * T(x * u,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(742,a,36056,a),flip(a)].">
      <j1 rule="hyper" parents="742 36056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36059">
    <literal><![CDATA[
      R(R(x,y,z) * u,x,x) / R(x,y,z) = (x * u) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,3873,a(flip),b,36057,a),flip(a)].">
      <j1 rule="hyper" parents="373 3873 36057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36060">
    <literal><![CDATA[
      (x * (R(x,y,z) \ u)) * (1 / x) = R(u,x,x) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),36059(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 36059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36061">
    <literal><![CDATA[
      a(x * (a(y,y,z) * (a(z,y,y) \ u)),w,v5) = a(u * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34658,a(flip),b,34256,a),flip(a)].">
      <j1 rule="hyper" parents="64 34658 34256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36063">
    <literal><![CDATA[
      a((x * a(y,z,z)) * u,w,v5) = a(u * (a(z,z,y) * x),w,v5)
    ]]></literal>
    <justification jstring="[para(23138(a,1),36061(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="23138 36061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36064">
    <literal><![CDATA[
      a((a(x,x,y) * z) * u,w,v5) = a((z * a(y,x,x)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,36063,a)].">
      <j1 rule="hyper" parents="373 26787 36063"/>
    </justification>
  </clause>

  <clause id="36065">
    <literal><![CDATA[
      T(x \ (y \ x),K(z,u)) * (T(y,K(z,u)) \ x) = T((y \ x) / y,x)
    ]]></literal>
    <justification jstring="[para(17480(a,1),34314(a,2,1))].">
      <j1 rule="para" parents="17480 34314"/>
    </justification>
  </clause>

  <clause id="36067">
    <literal><![CDATA[
      K(x,T(y,z * z)) / (u \ (z / (u / z))) = (1 / (((u \ z) * z) / u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(25012(a,1),34331(a,1,1,2))].">
      <j1 rule="para" parents="25012 34331"/>
    </justification>
  </clause>

  <clause id="36068">
    <literal><![CDATA[
      (1 / (((x \ y) * y) / x)) * K(z,u) = K(z,u) / (x \ (y / (x / y)))
    ]]></literal>
    <justification jstring="[para(17031(a,1),36067(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17031 36067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36071">
    <literal><![CDATA[
      (1 / (x \ (y / (x / y)))) * K(z,u) = K(z,u) / (x \ (y / (x / y)))
    ]]></literal>
    <justification jstring="[para(34328(a,1),36068(a,1,1,2))].">
      <j1 rule="para" parents="34328 36068"/>
    </justification>
  </clause>

  <clause id="36072">
    <literal><![CDATA[
      K(x,y) / (z \ (u / (z / u))) = ((u / (z / u)) \ z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(35942(a,1),36071(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35942 36071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36073">
    <literal><![CDATA[
      T(T(x,(y \ R(y,z,u)) \ 1) * ((y \ R(y,z,u)) \ 1),w) = x * ((y \ R(y,z,u)) \ K((y \ R(y,z,u)) \ x,w))
    ]]></literal>
    <justification jstring="[para(25923(a,1),35949(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25923 35949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36074">
    <literal><![CDATA[
      T((x \ (x \ y)) / y,x \ (x \ y)) \ 1 = ((x \ (x \ y)) / y) \ K(x * x,T(y,x))
    ]]></literal>
    <justification jstring="[para(11123(a,1),35992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11123 35992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36075">
    <literal><![CDATA[
      T((x \ (x \ y)) / y,x \ (x \ y)) \ 1 = ((x \ (x \ y)) / y) \ K(x * x,y)
    ]]></literal>
    <justification jstring="[para(11177(a,1),36074(a,2,2))].">
      <j1 rule="para" parents="11177 36074"/>
    </justification>
  </clause>

  <clause id="36077">
    <literal><![CDATA[
      ((x \ ((x / y) / y)) \ 1) \ K(x \ ((x * y) * y),(y * y) \ 1) = x \ ((x / y) / y)
    ]]></literal>
    <justification jstring="[para(6709(a,1),35993(a,1,2))].">
      <j1 rule="para" parents="6709 35993"/>
    </justification>
  </clause>

  <clause id="36078">
    <literal><![CDATA[
      ((x \ ((x / y) / y)) \ 1) \ K(x \ ((x * y) * y),y \ (y \ 1)) = x \ ((x / y) / y)
    ]]></literal>
    <justification jstring="[para(14419(a,1),36077(a,1,2))].">
      <j1 rule="para" parents="14419 36077"/>
    </justification>
  </clause>

  <clause id="36079">
    <literal><![CDATA[
      ((x \ ((x / y) / y)) \ 1) \ K(y * y,x \ ((x * y) * y)) = x \ ((x / y) / y)
    ]]></literal>
    <justification jstring="[para(15871(a,1),36078(a,1,2))].">
      <j1 rule="para" parents="15871 36078"/>
    </justification>
  </clause>

  <clause id="36080">
    <literal><![CDATA[
      ((x \ ((x / y) / y)) \ 1) \ K(y * y,(x \ (x * y)) * y) = x \ ((x / y) / y)
    ]]></literal>
    <justification jstring="[para(24234(a,1),36079(a,1,2))].">
      <j1 rule="para" parents="24234 36079"/>
    </justification>
  </clause>

  <clause id="36081">
    <literal><![CDATA[
      ((x \ ((x / y) / y)) \ 1) \ K(y * y,y * y) = x \ ((x / y) / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),36080(a,1,2,2,1))].">
      <j1 rule="para" parents="9 36080"/>
    </justification>
  </clause>

  <clause id="36082">
    <literal><![CDATA[
      ((x \ ((x / y) / y)) \ 1) \ 1 = x \ ((x / y) / y)
    ]]></literal>
    <justification jstring="[para(188(a,1),36081(a,1,2))].">
      <j1 rule="para" parents="188 36081"/>
    </justification>
  </clause>

  <clause id="36083">
    <literal><![CDATA[
      T(x \ ((x / y) / y),y * y) = x \ ((x / y) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,25773,a,b,36082,a)].">
      <j1 rule="hyper" parents="64 25773 36082"/>
    </justification>
  </clause>

  <clause id="36085">
    <literal><![CDATA[
      ((x \ ((x / y) / y)) \ z) / z = z / ((x \ ((x / y) / y)) * z)
    ]]></literal>
    <justification jstring="[para(36082(a,1),2013(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="36082 2013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36086">
    <literal><![CDATA[
      ((((x / y) / y) / x) \ x) \ x = x \ ((x / y) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,28909,a(flip),b,36083,a)].">
      <j1 rule="hyper" parents="64 28909 36083"/>
    </justification>
  </clause>

  <clause id="36087">
    <literal><![CDATA[
      ((x * y) * y) \ x = x \ ((x / y) / y)
    ]]></literal>
    <justification jstring="[para(33724(a,1),36086(a,1,1))].">
      <j1 rule="para" parents="33724 36086"/>
    </justification>
  </clause>

  <clause id="36088">
    <literal><![CDATA[
      T(x \ ((x / y) / y),K(x * y,y)) \ z = K(x * y,y) * (((y * (x * y)) \ x) \ z)
    ]]></literal>
    <justification jstring="[para(36087(a,1),25419(a,1,1,1))].">
      <j1 rule="para" parents="36087 25419"/>
    </justification>
  </clause>

  <clause id="36089">
    <literal><![CDATA[
      (K((x \ ((x * y) * y)) * z,x \ ((x / y) / y)) / (x \ ((x * y) * y))) \ z = z / (1 / (x \ ((x * y) * y)))
    ]]></literal>
    <justification jstring="[para(36087(a,1),27878(a,1,1,1,2))].">
      <j1 rule="para" parents="36087 27878"/>
    </justification>
  </clause>

  <clause id="36090">
    <literal><![CDATA[
      T(x \ ((x / y) / y),K(z,u)) = ((x * y) * y) \ x
    ]]></literal>
    <justification jstring="[para(36087(a,1),34789(a,1,1))].">
      <j1 rule="para" parents="36087 34789"/>
    </justification>
  </clause>

  <clause id="36091">
    <literal><![CDATA[
      T(x \ ((x / y) / y),K(z,u)) = x \ ((x / y) / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,36087,a(flip),b,36090,a),flip(a)].">
      <j1 rule="hyper" parents="373 36087 36090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36092">
    <literal><![CDATA[
      K(x * y,y) * (((y * (x * y)) \ x) \ z) = (x \ ((x / y) / y)) \ z
    ]]></literal>
    <justification jstring="[para(36091(a,1),36088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="36091 36088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36094">
    <literal><![CDATA[
      L(x,y * T(z * (u * w),K(u,w)),v5) = L(x,y * (z * (w * (u * K(v6,v7)))),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29453,a(flip),b,35995,a),flip(a)].">
      <j1 rule="hyper" parents="64 29453 35995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36096">
    <literal><![CDATA[
      L(x,y * (z * (u * (w * K(v5,v6)))),v7) = L(x,y * (z * (w * u)),v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,29447,a(flip),b,36094,a),flip(a)].">
      <j1 rule="hyper" parents="64 29447 36094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36098">
    <literal><![CDATA[
      x * ((x \ (y / x)) * a(x \ y,x \ y,x)) = K(x,x \ y) * R(x \ y,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(6030,a,35999,a),flip(a)].">
      <j1 rule="hyper" parents="6030 35999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36099">
    <literal><![CDATA[
      x * ((x \ (y / x)) * a(x \ y,x \ y,x)) = R(y / x,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25975,a(flip),b,36098,a),flip(a)].">
      <j1 rule="hyper" parents="373 25975 36098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36100">
    <literal><![CDATA[
      x * ((x \ (y / x)) * ((x / y) * (y / x))) = R(y / x,x * y,x)
    ]]></literal>
    <justification jstring="[para(30069(a,1),36099(a,1,2,2))].">
      <j1 rule="para" parents="30069 36099"/>
    </justification>
  </clause>

  <clause id="36101">
    <literal><![CDATA[
      x * (x \ R(y / x,x \ y,x)) = R(y / x,x * y,x)
    ]]></literal>
    <justification jstring="[para(31159(a,1),36100(a,1,2))].">
      <j1 rule="para" parents="31159 36100"/>
    </justification>
  </clause>

  <clause id="36102">
    <literal><![CDATA[
      R(x / y,y \ x,y) = R(x / y,y * x,y)
    ]]></literal>
    <justification jstring="[hyper(292,a,36101,a),flip(a)].">
      <j1 rule="hyper" parents="292 36101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36104">
    <literal><![CDATA[
      R(x / y,y * x,y) = y / (((x / y) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10217,a(flip),b,36102,a),flip(a)].">
      <j1 rule="hyper" parents="64 10217 36102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36105">
    <literal><![CDATA[
      R(x / y,x * y,y) = y / (((x / y) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26409,a,b,36104,a)].">
      <j1 rule="hyper" parents="64 26409 36104"/>
    </justification>
  </clause>

  <clause id="36106">
    <literal><![CDATA[
      a(x,y,R(z / u,z * u,u) \ w) = a(x,y,((((z / u) \ 1) * u) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(36105(a,2),27389(a,1,3,1))].">
      <j1 rule="para" parents="36105 27389"/>
    </justification>
  </clause>

  <clause id="36107">
    <literal><![CDATA[
      a(x,y,L(z / u,z * u,u) \ w) = a(x,y,((((z / u) \ 1) * u) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31334,a(flip),b,36106,a)].">
      <j1 rule="hyper" parents="64 31334 36106"/>
    </justification>
  </clause>

  <clause id="36108">
    <literal><![CDATA[
      a(x,y,L(z \ u,u * z,z) \ w) = a(x,y,((((u / z) \ 1) * z) \ z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27431,a(flip),b,36107,a)].">
      <j1 rule="hyper" parents="64 27431 36107"/>
    </justification>
  </clause>

  <clause id="36109">
    <literal><![CDATA[
      a(x,y,L(z \ u,u * z,z) \ w) = a(x,y,(z \ (((u / z) \ 1) \ z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27680,a(flip),b,36108,a),flip(a)].">
      <j1 rule="hyper" parents="373 27680 36108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36110">
    <literal><![CDATA[
      (x * (y \ (x \ y))) * (z * T(x,(T(y,x) \ y) * z)) = x * ((x * (y \ (x \ y))) * z)
    ]]></literal>
    <justification jstring="[para(28561(a,1),36010(a,1,2,2))].">
      <j1 rule="para" parents="28561 36010"/>
    </justification>
  </clause>

  <clause id="36111">
    <literal><![CDATA[
      (x * (y \ (x \ y))) * (z * T(x,K(x,y) * z)) = x * ((x * (y \ (x \ y))) * z)
    ]]></literal>
    <justification jstring="[para(5731(a,2),36110(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5731 36110"/>
    </justification>
  </clause>

  <clause id="36112">
    <literal><![CDATA[
      (x * (y \ (x \ y))) * (z * T(x,z)) = x * ((x * (y \ (x \ y))) * z)
    ]]></literal>
    <justification jstring="[para(8482(a,1),36111(a,1,2,2))].">
      <j1 rule="para" parents="8482 36111"/>
    </justification>
  </clause>

  <clause id="36113">
    <literal><![CDATA[
      (x * (y \ (x \ y))) * (x * z) = x * ((x * (y \ (x \ y))) * z)
    ]]></literal>
    <justification jstring="[hyper(737,a,36112,a)].">
      <j1 rule="hyper" parents="737 36112"/>
    </justification>
  </clause>

  <clause id="36115">
    <literal><![CDATA[
      (x * (y \ (x \ y))) \ (x * z) = x * ((x * (y \ (x \ y))) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,36113,a)].">
      <j1 rule="hyper" parents="139 168 36113"/>
    </justification>
  </clause>

  <clause id="36116">
    <literal><![CDATA[
      x * ((x * (y \ (x \ y))) \ 1) = (x * (y \ (x \ y))) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,72,a(flip),b,36113,a),flip(a)].">
      <j1 rule="hyper" parents="139 72 36113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36117">
    <literal><![CDATA[
      x * ((x * (y \ (x \ y))) \ 1) = 1 / (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,15119,a(flip),b,36116,a),flip(a)].">
      <j1 rule="hyper" parents="373 15119 36116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36118">
    <literal><![CDATA[
      x * (y \ (x * (y * (x \ 1)))) = 1 / (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(30759(a,1),36117(a,1,2))].">
      <j1 rule="para" parents="30759 36117"/>
    </justification>
  </clause>

  <clause id="36119">
    <literal><![CDATA[
      L((x \ (y \ x)) \ z,y,L(y,y,x)) = y * ((y * (x \ (y \ x))) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35409,a,b,36115,a)].">
      <j1 rule="hyper" parents="64 35409 36115"/>
    </justification>
  </clause>

  <clause id="36120">
    <literal><![CDATA[
      L(a(x,y,y) \ 1,a(x,y,y),x / y) = 1 / (1 / ((x * (1 / y)) \ (x / y)))
    ]]></literal>
    <justification jstring="[para(30536(a,1),36011(a,1,2))].">
      <j1 rule="para" parents="30536 36011"/>
    </justification>
  </clause>

  <clause id="36121">
    <literal><![CDATA[
      L(a(x,y,y) \ 1,a(x,y,y),y \ x) = 1 / (1 / ((x * (1 / y)) \ (x / y)))
    ]]></literal>
    <justification jstring="[hyper(23857,a,36120,a)].">
      <j1 rule="hyper" parents="23857 36120"/>
    </justification>
  </clause>

  <clause id="36122">
    <literal><![CDATA[
      (K(x,y) * z) / (1 / ((K(x,y) * z) \ u)) = u * ((u \ z) * (z \ u))
    ]]></literal>
    <justification jstring="[para(6161(a,1),36012(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6161 36012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36123">
    <literal><![CDATA[
      (K(x,y) * z) / (1 / ((K(x,y) * z) \ (u \ z))) = (u \ z) * (u * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[para(25484(a,1),36122(a,2,2))].">
      <j1 rule="para" parents="25484 36122"/>
    </justification>
  </clause>

  <clause id="36124">
    <literal><![CDATA[
      K(x \ ((y \ z) * u),T(y * ((y \ z) * u),K(w,v5))) = K(z * (u / (y * x)),z * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,28270,a(flip),b,36017,a),flip(a)].">
      <j1 rule="hyper" parents="373 28270 36017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36125">
    <literal><![CDATA[
      K(x \ ((y \ z) * u),T(y * ((y \ z) * u),K(w,v5))) = K(z * ((y * x) \ u),u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,28567,a(flip),b,36124,a),flip(a)].">
      <j1 rule="hyper" parents="373 28567 36124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36126">
    <literal><![CDATA[
      K(x \ ((y \ z) * u),T(y * ((y \ z) * u),K(w,v5))) = K(z * (x \ (y \ u)),u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,28283,a(flip),b,36125,a),flip(a)].">
      <j1 rule="hyper" parents="373 28283 36125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36127">
    <literal><![CDATA[
      K(x \ ((y \ z) * u),y * ((y \ z) * u)) = K(z * (x \ (y \ u)),u * z)
    ]]></literal>
    <justification jstring="[hyper(17156,a,36126,a)].">
      <j1 rule="hyper" parents="17156 36126"/>
    </justification>
  </clause>

  <clause id="36128">
    <literal><![CDATA[
      K(x \ ((y \ z) * u),z * u) = K(z * (x \ (y \ u)),u * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,25015,a(flip),b,36127,a)].">
      <j1 rule="hyper" parents="64 25015 36127"/>
    </justification>
  </clause>

  <clause id="36130">
    <literal><![CDATA[
      K(x * (y \ ((z * u) \ u)),u * x) = K(y \ (x / z),x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28597,a(flip),b,36128,a),flip(a)].">
      <j1 rule="hyper" parents="64 28597 36128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36131">
    <literal><![CDATA[
      K(x * (y \ (1 / z)),z * x) = K(y \ (x / z),x * z)
    ]]></literal>
    <justification jstring="[para(309(a,1),36130(a,1,1,2,2))].">
      <j1 rule="para" parents="309 36130"/>
    </justification>
  </clause>

  <clause id="36132">
    <literal><![CDATA[
      K(x / (y * z),y * x) = K(z \ (x / y),x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,28863,a(flip),b,36131,a)].">
      <j1 rule="hyper" parents="64 28863 36131"/>
    </justification>
  </clause>

  <clause id="36133">
    <literal><![CDATA[
      K((x * y) \ z,z * x) = K(y \ (z / x),z * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11116,a(flip),b,36132,a)].">
      <j1 rule="hyper" parents="64 11116 36132"/>
    </justification>
  </clause>

  <clause id="36134">
    <literal><![CDATA[
      K(x \ (y / z),y * z) = K(x \ (z \ y),y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23046,a(flip),b,36133,a),flip(a)].">
      <j1 rule="hyper" parents="64 23046 36133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36135">
    <literal><![CDATA[
      a(x,((T(y,z * z) * u) / w) * v5,v6) = a(x,v5 * (w \ (y * ((z * z) * u))),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32211,a(flip),b,36035,a)].">
      <j1 rule="hyper" parents="64 32211 36035"/>
    </justification>
  </clause>

  <clause id="36137">
    <literal><![CDATA[
      a(x,y * (z \ (u * ((w * w) * v5))),v6) = a(x,(z \ (u * v5)) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32331,a(flip),b,36135,a),flip(a)].">
      <j1 rule="hyper" parents="64 32331 36135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36139">
    <literal><![CDATA[
      ((x * ((y * y) * z)) * a(u,w,v5)) \ ((x * ((y * y) * a(u,w,v5))) * z) = a(a(u,w,v5),x,z)
    ]]></literal>
    <justification jstring="[para(34(a,1),36041(a,1,2,1))].">
      <j1 rule="para" parents="34 36041"/>
    </justification>
  </clause>

  <clause id="36140">
    <literal><![CDATA[
      a(x \ (y * R(z,u,w)),v5,v6) = a(x \ (y * L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32535,a(flip),b,36050,a),flip(a)].">
      <j1 rule="hyper" parents="64 32535 36050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36141">
    <literal><![CDATA[
      ((x * ((y * y) * z)) * a(u,w,v5)) \ ((x * a(u,w,v5)) * ((y * y) * z)) = a(a(u,w,v5),x,z)
    ]]></literal>
    <justification jstring="[para(28826(a,1),36139(a,1,2))].">
      <j1 rule="para" parents="28826 36139"/>
    </justification>
  </clause>

  <clause id="36142">
    <literal><![CDATA[
      a(a(x,y,z),u,(w * w) * v5) = a(a(x,y,z),u,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,33118,a(flip),b,36141,a)].">
      <j1 rule="hyper" parents="64 33118 36141"/>
    </justification>
  </clause>

  <clause id="36143">
    <literal><![CDATA[
      a(a(x,y,z),u,(w \ 1) \ v5) = a(a(x,y,z),u,w \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27635,a(flip),b,36142,a)].">
      <j1 rule="hyper" parents="64 27635 36142"/>
    </justification>
  </clause>

  <clause id="36144">
    <literal><![CDATA[
      a(a(x,y,z),u,w \ 1) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(27585,a,36143,a),flip(a)].">
      <j1 rule="hyper" parents="27585 36143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36145">
    <literal><![CDATA[
      L(x \ ((y \ z) * R((y \ z) \ u,w,v5)),x,y \ z) = ((z / y) * x) \ R((z / y) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(27047(a,1),23975(a,1,1,2))].">
      <j1 rule="para" parents="27047 23975"/>
    </justification>
  </clause>

  <clause id="36146">
    <literal><![CDATA[
      (1 / (x / y)) * (((1 / (x / y)) \ (y / x)) * z) = (y / x) * L(z,(y / x) * (y \ x),y \ x)
    ]]></literal>
    <justification jstring="[para(29547(a,1),23980(a,2,2))].">
      <j1 rule="para" parents="29547 23980"/>
    </justification>
  </clause>

  <clause id="36147">
    <literal><![CDATA[
      K(x,R(T(y / (z \ u),(y * z) * (T(u,z) \ w)),z \ u,z) * v5) = K(x,T((y * z) / ((z \ u) * z),w) * v5)
    ]]></literal>
    <justification jstring="[para(19636(a,1),25001(a,1,2,1,1))].">
      <j1 rule="para" parents="19636 25001"/>
    </justification>
  </clause>

  <clause id="36148">
    <literal><![CDATA[
      L(R(T(x,y) * K(z,T(x,y)),x,x),x,x \ z) = ((z / x) * T(x * T(x,y),x)) / z
    ]]></literal>
    <justification jstring="[para(6388(a,1),25032(a,1,1))].">
      <j1 rule="para" parents="6388 25032"/>
    </justification>
  </clause>

  <clause id="36149">
    <literal><![CDATA[
      L(R(T(x * K(y,x),z),x,x),x,x \ y) = ((y / x) * T(x * T(x,z),x)) / y
    ]]></literal>
    <justification jstring="[para(6237(a,1),36148(a,1,1,1))].">
      <j1 rule="para" parents="6237 36148"/>
    </justification>
  </clause>

  <clause id="36150">
    <literal><![CDATA[
      L(T((x \ 1) \ K(y,x),z),x,x \ y) = ((y / x) * T(x * T(x,z),x)) / y
    ]]></literal>
    <justification jstring="[para(14757(a,1),36149(a,1,1))].">
      <j1 rule="para" parents="14757 36149"/>
    </justification>
  </clause>

  <clause id="36151">
    <literal><![CDATA[
      L(T((x \ 1) \ K(y,x),z),x,x \ y) = (y / (T(x,z) \ 1)) / y
    ]]></literal>
    <justification jstring="[para(25814(a,1),36150(a,2,1))].">
      <j1 rule="para" parents="25814 36150"/>
    </justification>
  </clause>

  <clause id="36152">
    <literal><![CDATA[
      ((x / y) * ((1 / y) \ T(y,z))) / x = (x / (T(y,z) \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,34370,a(flip),b,36151,a)].">
      <j1 rule="hyper" parents="64 34370 36151"/>
    </justification>
  </clause>

  <clause id="36153">
    <literal><![CDATA[
      (x / (T(y,z) \ 1)) / x = T((x / (y \ 1)) / x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10057,a(flip),b,36152,a),flip(a)].">
      <j1 rule="hyper" parents="64 10057 36152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36154">
    <literal><![CDATA[
      T(((x / (y \ 1)) * ((y \ 1) * y)) / x,y \ z) = T((x / (y \ 1)) / x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10136,a,b,36153,a)].">
      <j1 rule="hyper" parents="64 10136 36153"/>
    </justification>
  </clause>

  <clause id="36155">
    <literal><![CDATA[
      T(((x / (y \ 1)) * K(y \ 1,y)) / x,y \ z) = T((x / (y \ 1)) / x,y * z)
    ]]></literal>
    <justification jstring="[para(294(a,2),36154(a,1,1,1,2))].">
      <j1 rule="para" parents="294 36154"/>
    </justification>
  </clause>

  <clause id="36156">
    <literal><![CDATA[
      T((x / (1 / y)) / x,y \ z) = T((x / (y \ 1)) / x,y * z)
    ]]></literal>
    <justification jstring="[para(3714(a,1),36155(a,1,1,1))].">
      <j1 rule="para" parents="3714 36155"/>
    </justification>
  </clause>

  <clause id="36157">
    <literal><![CDATA[
      T((x / L(y,z,u)) * a(y,L(y,z,u) \ x,y),y) = x / L(T(y,(x / L(y,z,u)) * y),z,u)
    ]]></literal>
    <justification jstring="[para(13169(a,1),25450(a,1,1,2))].">
      <j1 rule="para" parents="13169 25450"/>
    </justification>
  </clause>

  <clause id="36158">
    <literal><![CDATA[
      (1 / x) / L(y \ (x \ y),y \ (x \ y),x \ 1) = (x \ 1) * ((y \ (x \ y)) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),25585(a,1,1,1))].">
      <j1 rule="para" parents="10 25585"/>
    </justification>
  </clause>

  <clause id="36160">
    <literal><![CDATA[
      (1 / x) / L(y \ (x \ y),y \ (x \ y),x) = (x \ 1) * ((y \ (x \ y)) \ 1)
    ]]></literal>
    <justification jstring="[para(1631(a,1),36158(a,1,2))].">
      <j1 rule="para" parents="1631 36158"/>
    </justification>
  </clause>

  <clause id="36161">
    <literal><![CDATA[
      (1 / x) / L(y \ (x \ y),x,y \ (x \ y)) = (x \ 1) * ((y \ (x \ y)) \ 1)
    ]]></literal>
    <justification jstring="[para(31369(a,1),36160(a,1,2))].">
      <j1 rule="para" parents="31369 36160"/>
    </justification>
  </clause>

  <clause id="36162">
    <literal><![CDATA[
      (1 / x) / (y \ ((1 / (1 / x)) \ y)) = (x \ 1) * ((y \ (x \ y)) \ 1)
    ]]></literal>
    <justification jstring="[para(13777(a,1),36161(a,1,2))].">
      <j1 rule="para" parents="13777 36161"/>
    </justification>
  </clause>

  <clause id="36163">
    <literal><![CDATA[
      (x \ 1) * ((y \ (x \ y)) \ 1) = (y \ (x \ y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,35412,a(flip),b,36162,a),flip(a)].">
      <j1 rule="hyper" parents="64 35412 36162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36164">
    <literal><![CDATA[
      x * R(y,L(T(x,y),z,u),L(T(x,y),z,u) \ x) = (L(x,z,u) \ x) * (L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,520,a(flip),b,25819,a),flip(a)].">
      <j1 rule="hyper" parents="373 520 25819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36165">
    <literal><![CDATA[
      x * R(y,L(T(x,y),z,u),L(x,z,u) \ x) = (L(x,z,u) \ x) * (L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(26218(a,1),36164(a,1,2))].">
      <j1 rule="para" parents="26218 36164"/>
    </justification>
  </clause>

  <clause id="36167">
    <literal><![CDATA[
      x * R(y,L(x,z,u),L(x,z,u) \ x) = (L(x,z,u) \ x) * (L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(26430(a,1),36165(a,1,2))].">
      <j1 rule="para" parents="26430 36165"/>
    </justification>
  </clause>

  <clause id="36169">
    <literal><![CDATA[
      x * L(y,L(x,z,u) \ x,L(x,z,u)) = (L(x,z,u) \ x) * (L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[para(33857(a,1),36167(a,1,2))].">
      <j1 rule="para" parents="33857 36167"/>
    </justification>
  </clause>

  <clause id="36170">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) * u) = L(x,y,z) * ((L(x,y,z) \ x) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,515,a(flip),b,36169,a),flip(a)].">
      <j1 rule="hyper" parents="64 515 36169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36171">
    <literal><![CDATA[
      ((R(x,y,z) \ x) * (u * w)) / T(u,w * (x \ x)) = u \ ((u * w) * (R(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(31446(a,1),25937(a,1,2))].">
      <j1 rule="para" parents="31446 25937"/>
    </justification>
  </clause>

  <clause id="36172">
    <literal><![CDATA[
      ((R(x,y,z) \ x) * (u * w)) / T(u,w) = u \ ((u * w) * (R(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(191(a,1),36171(a,1,2,2))].">
      <j1 rule="para" parents="191 36171"/>
    </justification>
  </clause>

  <clause id="36174">
    <literal><![CDATA[
      ((R(x,y,z) \ x) * (u * w)) / w = w \ ((w * u) * (R(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,10195,a(flip),b,36172,a)].">
      <j1 rule="hyper" parents="64 10195 36172"/>
    </justification>
  </clause>

  <clause id="36175">
    <literal><![CDATA[
      R(x,y,(L(T(z,z \ 1),z,u) \ w) * (u \ (u / z))) = R(x,y,(z * z) \ w)
    ]]></literal>
    <justification jstring="[para(3811(a,1),27095(a,1,3,2))].">
      <j1 rule="para" parents="3811 27095"/>
    </justification>
  </clause>

  <clause id="36176">
    <literal><![CDATA[
      R(x,y,(L(T(z,z \ 1),z,u) \ w) * (u \ (z \ u))) = R(x,y,(z * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26254,a(flip),b,36175,a)].">
      <j1 rule="hyper" parents="64 26254 36175"/>
    </justification>
  </clause>

  <clause id="36177">
    <literal><![CDATA[
      R(x,y,(L(z,z,u) \ w) * (u \ (z \ u))) = R(x,y,(z * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26322,a(flip),b,36176,a)].">
      <j1 rule="hyper" parents="64 26322 36176"/>
    </justification>
  </clause>

  <clause id="36179">
    <literal><![CDATA[
      (L(x,y,z) \ ((x * x) * u)) / T(x,(x \ 1) \ (x \ u)) = (x \ 1) \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(28539(a,1),27180(a,1,2))].">
      <j1 rule="para" parents="28539 27180"/>
    </justification>
  </clause>

  <clause id="36180">
    <literal><![CDATA[
      (L(x,y,z) \ ((x * x) * u)) / T(x,x \ ((1 / x) \ u)) = (x \ 1) \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(1166(a,1),36179(a,1,2,2))].">
      <j1 rule="para" parents="1166 36179"/>
    </justification>
  </clause>

  <clause id="36182">
    <literal><![CDATA[
      (L(x,y,z) \ ((x * x) * u)) / T(x,u) = (x \ 1) \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(14481(a,1),36180(a,1,2))].">
      <j1 rule="para" parents="14481 36180"/>
    </justification>
  </clause>

  <clause id="36183">
    <literal><![CDATA[
      (x \ ((x * x) * y)) / L(T(x,y),z,u) = (x \ 1) \ (L(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,25806,a(flip),b,36182,a)].">
      <j1 rule="hyper" parents="64 25806 36182"/>
    </justification>
  </clause>

  <clause id="36185">
    <literal><![CDATA[
      ((1 / x) \ y) / L(T(x,y),z,u) = (x \ 1) \ (L(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(539(a,1),36183(a,1,1))].">
      <j1 rule="para" parents="539 36183"/>
    </justification>
  </clause>

  <clause id="36186">
    <literal><![CDATA[
      L(x,y,z) \ ((1 / x) \ u) = (x \ 1) \ (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14578,a(flip),b,36185,a)].">
      <j1 rule="hyper" parents="64 14578 36185"/>
    </justification>
  </clause>

  <clause id="36187">
    <literal><![CDATA[
      L(x,y,y) \ ((1 / x) \ ((y * y) \ z)) = (x \ 1) \ ((y * (y * x)) \ z)
    ]]></literal>
    <justification jstring="[para(881(a,1),36186(a,2,2))].">
      <j1 rule="para" parents="881 36186"/>
    </justification>
  </clause>

  <clause id="36188">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) \ (L(x,z,u) \ y)) = ((1 / x) \ y) / L(x,z,u)
    ]]></literal>
    <justification jstring="[para(36186(a,1),26984(a,1,2))].">
      <j1 rule="para" parents="36186 26984"/>
    </justification>
  </clause>

  <clause id="36189">
    <literal><![CDATA[
      L(x,y,y) \ (((y * y) / x) \ z) = (x \ 1) \ ((y * (y * x)) \ z)
    ]]></literal>
    <justification jstring="[para(879(a,1),36187(a,1,2))].">
      <j1 rule="para" parents="879 36187"/>
    </justification>
  </clause>

  <clause id="36190">
    <literal><![CDATA[
      L((x \ 1) \ ((y * (y * x)) \ z),L(x,y,y),x) = ((y * (y * x)) / x) \ z
    ]]></literal>
    <justification jstring="[para(36189(a,1),3211(a,1,1))].">
      <j1 rule="para" parents="36189 3211"/>
    </justification>
  </clause>

  <clause id="36191">
    <literal><![CDATA[
      L((x \ 1) \ ((y * (y * x)) \ z),x,L(x,y,y)) = ((y * (y * x)) / x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,2482,a(flip),b,36190,a)].">
      <j1 rule="hyper" parents="64 2482 36190"/>
    </justification>
  </clause>

  <clause id="36192">
    <literal><![CDATA[
      a(x,y,L(z \ ((u * u) / w),z,w)) = a(x,y,(((1 / w) \ ((u * u) \ 1)) * z) \ 1)
    ]]></literal>
    <justification jstring="[para(2197(a,1),27657(a,1,3))].">
      <j1 rule="para" parents="2197 27657"/>
    </justification>
  </clause>

  <clause id="36193">
    <literal><![CDATA[
      a(x,y,L(z \ (u \ (w * w)),z,u)) = a(x,y,(((1 / u) \ ((w * w) \ 1)) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27609,a(flip),b,36192,a)].">
      <j1 rule="hyper" parents="64 27609 36192"/>
    </justification>
  </clause>

  <clause id="36195">
    <literal><![CDATA[
      a(x,y,(((1 / z) \ ((u * u) \ 1)) * w) \ 1) = a(x,y,(z * w) \ (u * u))
    ]]></literal>
    <justification jstring="[para(346(a,1),36193(a,1,3)),flip(a)].">
      <j1 rule="para" parents="346 36193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36196">
    <literal><![CDATA[
      a(x,y,((((z * z) / u) \ 1) * w) \ 1) = a(x,y,(u * w) \ (z * z))
    ]]></literal>
    <justification jstring="[para(879(a,1),36195(a,1,3,1,1))].">
      <j1 rule="para" parents="879 36195"/>
    </justification>
  </clause>

  <clause id="36197">
    <literal><![CDATA[
      a(x,y,(((z \ (u * u)) \ 1) * w) \ 1) = a(x,y,(z * w) \ (u * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27561,a(flip),b,36196,a)].">
      <j1 rule="hyper" parents="64 27561 36196"/>
    </justification>
  </clause>

  <clause id="36198">
    <literal><![CDATA[
      a(x,y,R(z / u,u,z \ (w \ (v5 \ w))) \ (w \ (v5 \ w))) = a(x,y,u * (z \ ((v5 * w) \ w)))
    ]]></literal>
    <justification jstring="[para(26358(a,1),27712(a,1,3,1))].">
      <j1 rule="para" parents="26358 27712"/>
    </justification>
  </clause>

  <clause id="36199">
    <literal><![CDATA[
      (R(x,y,y) * y) \ (x * ((y * a(x,y,y)) * z)) = L(z,a(x,y,y) * y,x)
    ]]></literal>
    <justification jstring="[para(23104(a,1),30010(a,2,1))].">
      <j1 rule="para" parents="23104 30010"/>
    </justification>
  </clause>

  <clause id="36200">
    <literal><![CDATA[
      (R(x,y,y) * y) \ (x * ((y * a(x,y,y)) * z)) = L(z,L(y,y,x),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,30503,a(flip),b,36199,a),flip(a)].">
      <j1 rule="hyper" parents="373 30503 36199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36201">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * (R(x,x,y) * (a(x,x,y) \ z)) = ((a(x,x,y) \ 1) * T(x,a(x,x,y))) * z
    ]]></literal>
    <justification jstring="[para(30885(a,1),30074(a,1,2))].">
      <j1 rule="para" parents="30885 30074"/>
    </justification>
  </clause>

  <clause id="36202">
    <literal><![CDATA[
      L(x,y,L(K(z,u) * ((L(w,v5,v6) * v7) * w),w,w)) = L(x,y,L(w,v5,v6) * (K(z,u) * (w \ v7)))
    ]]></literal>
    <justification jstring="[para(23073(a,1),30391(a,1,3,1))].">
      <j1 rule="para" parents="23073 30391"/>
    </justification>
  </clause>

  <clause id="36203">
    <literal><![CDATA[
      a(a((x * y) \ 1,y,y) * z,u,w) = a((((x * y) \ 1) \ ((x / y) \ 1)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(32583,a,30643,a),flip(a)].">
      <j1 rule="hyper" parents="32583 30643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36205">
    <literal><![CDATA[
      a(a((x * y) \ 1,y,y) * z,u,w) = a((((x * y) \ 1) \ (x / y)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32688,a(flip),b,36203,a),flip(a)].">
      <j1 rule="hyper" parents="373 32688 36203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36206">
    <literal><![CDATA[
      a(a((x * y) \ 1,y,y) * z,u,w) = a((((x * y) \ 1) \ (y \ x)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32492,a(flip),b,36205,a),flip(a)].">
      <j1 rule="hyper" parents="373 32492 36205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36207">
    <literal><![CDATA[
      a(a((x * y) \ 1,y,y) * z,u,w) = a(((x * y) \ (y \ x)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32809,a(flip),b,36206,a),flip(a)].">
      <j1 rule="hyper" parents="373 32809 36206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36208">
    <literal><![CDATA[
      a(a(x * y,y,y) * z,u,w) = a(((x * y) \ (y \ x)) * z,u,w)
    ]]></literal>
    <justification jstring="[para(2653(a,1),36207(a,1,1,1))].">
      <j1 rule="para" parents="2653 36207"/>
    </justification>
  </clause>

  <clause id="36209">
    <literal><![CDATA[
      ((x \ y) \ 1) * (z * (y \ x)) = (y \ x) * (z * ((x \ y) \ 1))
    ]]></literal>
    <justification jstring="[para(30675(a,1),30692(a,1,2,2))].">
      <j1 rule="para" parents="30675 30692"/>
    </justification>
  </clause>

  <clause id="36210">
    <literal><![CDATA[
      a(x,R(y,z,u),a(y,w,v5)) = a(x,a(y,w,v5),R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,25791,a(flip),b,30907,a)].">
      <j1 rule="hyper" parents="64 25791 30907"/>
    </justification>
  </clause>

  <clause id="36211">
    <literal><![CDATA[
      a(x,L(y,z,u),a(y,w,v5)) = a(x,a(y,w,v5),R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,32197,a(flip),b,36210,a)].">
      <j1 rule="hyper" parents="64 32197 36210"/>
    </justification>
  </clause>

  <clause id="36212">
    <literal><![CDATA[
      a(x,L(y,z,u),a(y,w,v5)) = a(x,a(y,w,v5),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27644,a(flip),b,36211,a),flip(a)].">
      <j1 rule="hyper" parents="373 27644 36211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36213">
    <literal><![CDATA[
      L(x,((T(y,z) * u) \ ((T(y,z) * z) * u)) * w,v5) = L(x,L(z,y,u) * (K(z * y,u) * w),v5)
    ]]></literal>
    <justification jstring="[para(26075(a,1),30983(a,2,2))].">
      <j1 rule="para" parents="26075 30983"/>
    </justification>
  </clause>

  <clause id="36214">
    <literal><![CDATA[
      L(x,((y * a(z,z,y)) * u) * w,v5) = L(x,(L(y,z,z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(5694(a,1),31032(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5694 31032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36216">
    <literal><![CDATA[
      L(x,(L(y * z,y,y) * u) * w,v5) = L(x,(((y \ 1) \ z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(30227(a,1),36214(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="30227 36214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36218">
    <literal><![CDATA[
      L(((x / y) / x) * y,y * ((x / y) / x),a(y,y,x)) = 1 / (1 / (((x / y) / x) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30112,a(flip),b,31383,a)].">
      <j1 rule="hyper" parents="64 30112 31383"/>
    </justification>
  </clause>

  <clause id="36219">
    <literal><![CDATA[
      L(((x / y) / x) * y,y * (x \ (x / y)),a(y,y,x)) = 1 / (1 / (((x / y) / x) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29547,a(flip),b,36218,a)].">
      <j1 rule="hyper" parents="64 29547 36218"/>
    </justification>
  </clause>

  <clause id="36220">
    <literal><![CDATA[
      L(((x / y) / x) * y,y * (x \ (y \ x)),a(y,y,x)) = 1 / (1 / (((x / y) / x) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29676,a(flip),b,36219,a)].">
      <j1 rule="hyper" parents="64 29676 36219"/>
    </justification>
  </clause>

  <clause id="36221">
    <literal><![CDATA[
      L(((x / y) / x) * y,a(y,y,x),a(y,y,x)) = 1 / (1 / (((x / y) / x) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30115,a(flip),b,36220,a)].">
      <j1 rule="hyper" parents="64 30115 36220"/>
    </justification>
  </clause>

  <clause id="36222">
    <literal><![CDATA[
      1 / (1 / (((x / y) / x) * y)) = ((x / y) / x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,31618,a(flip),b,36221,a),flip(a)].">
      <j1 rule="hyper" parents="64 31618 36221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36224">
    <literal><![CDATA[
      1 / (((x / y) / x) * y) = x \ (((1 / y) * x) * y)
    ]]></literal>
    <justification jstring="[hyper(37,a,30741,a,b,36222,a),flip(a)].">
      <j1 rule="hyper" parents="37 30741 36222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36225">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ (((1 / x) * (x * (y \ R(y,z,u)))) * x) = 1 / (((y \ R(y,z,u)) / (x * (y \ R(y,z,u)))) * x)
    ]]></literal>
    <justification jstring="[para(23715(a,1),36224(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="23715 36224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36226">
    <literal><![CDATA[
      L(a(x,x,y),z,u) \ L(R(a(x,x,y) \ x,x,y),z,u) = L(a(x,x,y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(23134(a,1),31551(a,1,1,1))].">
      <j1 rule="para" parents="23134 31551"/>
    </justification>
  </clause>

  <clause id="36228">
    <literal><![CDATA[
      a(x,L(x,y,z),u) \ L(R(a(x,x,u) \ x,x,u),y,z) = L(a(x,x,u) \ x,y,z)
    ]]></literal>
    <justification jstring="[para(34877(a,2),36226(a,1,1))].">
      <j1 rule="para" parents="34877 36226"/>
    </justification>
  </clause>

  <clause id="36229">
    <literal><![CDATA[
      a(x,L(x,y,z),u) \ L(x,y,z) = L(a(x,x,u) \ x,y,z)
    ]]></literal>
    <justification jstring="[para(31549(a,1),36228(a,1,2,1))].">
      <j1 rule="para" parents="31549 36228"/>
    </justification>
  </clause>

  <clause id="36230">
    <literal><![CDATA[
      x * (K(y,L(L(x,z,u),w,v5)) * K(x,L(L(x,z,u),w,v5) * y)) = L(x,y,L(L(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,20719,a(flip),b,33088,a)].">
      <j1 rule="hyper" parents="64 20719 33088"/>
    </justification>
  </clause>

  <clause id="36231">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) / T(u,x) = u \ ((u * (x \ L(x,y,z))) * x)
    ]]></literal>
    <justification jstring="[para(28372(a,1),33144(a,1,2))].">
      <j1 rule="para" parents="28372 33144"/>
    </justification>
  </clause>

  <clause id="36232">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (x * u)) / u = u \ ((u * (x \ L(x,y,z))) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10195,a(flip),b,36231,a)].">
      <j1 rule="hyper" parents="64 10195 36231"/>
    </justification>
  </clause>

  <clause id="36234">
    <literal><![CDATA[
      (x * ((x \ L(x,y,z)) * u)) / u = u \ ((u * (x \ L(x,y,z))) * x)
    ]]></literal>
    <justification jstring="[para(33159(a,1),36232(a,1,1))].">
      <j1 rule="para" parents="33159 36232"/>
    </justification>
  </clause>

  <clause id="36235">
    <literal><![CDATA[
      (x * ((x \ L(x,y,z)) * u)) / u = u \ ((x \ L(x,y,z)) * (u * x))
    ]]></literal>
    <justification jstring="[para(33138(a,1),36234(a,2,2))].">
      <j1 rule="para" parents="33138 36234"/>
    </justification>
  </clause>

  <clause id="36236">
    <literal><![CDATA[
      L(x,y,z) \ (u \ ((x \ L(x,y,z)) * (u * x))) = a(x,x \ L(x,y,z),u) \ 1
    ]]></literal>
    <justification jstring="[para(36235(a,1),33397(a,1,2))].">
      <j1 rule="para" parents="36235 33397"/>
    </justification>
  </clause>

  <clause id="36237">
    <literal><![CDATA[
      L(x,y,(L(z,z \ (u \ z),z \ (u \ z)) * w) * v5) = L(x,y,(((u \ z) / u) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,28992,a(flip),b,34315,a),flip(a)].">
      <j1 rule="hyper" parents="373 28992 34315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36239">
    <literal><![CDATA[
      L(x,y,(L(z,z \ (u \ z),z \ (u \ z)) * w) * v5) = L(x,y,((u \ (u \ z)) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29001,a(flip),b,36237,a),flip(a)].">
      <j1 rule="hyper" parents="373 29001 36237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36240">
    <literal><![CDATA[
      L(x,y,((z \ (z \ u)) * w) * v5) = L(x,y,(L(u,z,z) * w) * v5)
    ]]></literal>
    <justification jstring="[para(35166(a,1),36239(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="35166 36239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36241">
    <literal><![CDATA[
      L(x,y,(L(z * u,z,z) * w) * v5) = L(x,y,((z \ u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),36240(a,1,3,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 36240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36243">
    <literal><![CDATA[
      L(x,y,z * (L(u * w,u,u) * v5)) = L(x,y,((u \ w) * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(24201,a,36241,a)].">
      <j1 rule="hyper" parents="24201 36241"/>
    </justification>
  </clause>

  <clause id="36244">
    <literal><![CDATA[
      K((x \ y) * L(x,z,u),w) * T(x \ (y * L(x,z,u)),K(y,v5)) = T(x \ (y * L(x,z,u)),w)
    ]]></literal>
    <justification jstring="[para(28197(a,1),34401(a,1,1))].">
      <j1 rule="para" parents="28197 34401"/>
    </justification>
  </clause>

  <clause id="36245">
    <literal><![CDATA[
      (a(x,x,L(y,z,u)) / R(x \ 1,x,y)) \ L(y,z,u) = L(y,z,u) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(5599(a,1),35182(a,1,1,1))].">
      <j1 rule="para" parents="5599 35182"/>
    </justification>
  </clause>

  <clause id="36246">
    <literal><![CDATA[
      (R(1 / x,x,y) \ a(x,x,L(y,z,u))) \ L(y,z,u) = L(y,z,u) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(25161(a,1),36245(a,1,1))].">
      <j1 rule="para" parents="25161 36245"/>
    </justification>
  </clause>

  <clause id="36247">
    <literal><![CDATA[
      T(L((x / y) / x,y,y),y * (y * x)) = ((((x * y) \ z) \ z) * y) \ T(x * y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(794,a,35610,a)].">
      <j1 rule="hyper" parents="794 35610"/>
    </justification>
  </clause>

  <clause id="36248">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ (y \ a(x,y,z)) = T(y / (a(x,y,z) \ 1),a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,14003,a(flip),b,35802,a)].">
      <j1 rule="hyper" parents="64 14003 35802"/>
    </justification>
  </clause>

  <clause id="36249">
    <literal><![CDATA[
      T(x / (a(y,x,z) \ 1),a(y,x,z)) \ 1 = x \ (a(y,x,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27846,a(flip),b,36248,a),flip(a)].">
      <j1 rule="hyper" parents="64 27846 36248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36250">
    <literal><![CDATA[
      T((a(x,y,z) \ 1) \ y,a(x,y,z)) \ 1 = y \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(23737(a,1),36249(a,1,1,1))].">
      <j1 rule="para" parents="23737 36249"/>
    </justification>
  </clause>

  <clause id="36251">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ y) \ 1 = y \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(23105(a,1),36250(a,1,1))].">
      <j1 rule="para" parents="23105 36250"/>
    </justification>
  </clause>

  <clause id="36252">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) / y) \ 1 = (a(x,y,z) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(40,a,31786,a,b,36251,a)].">
      <j1 rule="hyper" parents="40 31786 36251"/>
    </justification>
  </clause>

  <clause id="36254">
    <literal><![CDATA[
      ((x / y) * z) \ R((x / y) * u,w,v5) = ((y \ x) * z) \ R((y \ x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,2134,a(flip),b,36145,a),flip(a)].">
      <j1 rule="hyper" parents="64 2134 36145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36255">
    <literal><![CDATA[
      (1 / (x / y)) * (((1 / (x / y)) \ (y / x)) * z) = (y / x) * L(z,(x \ y) * (y \ x),y \ x)
    ]]></literal>
    <justification jstring="[para(29443(a,1),36146(a,2,2))].">
      <j1 rule="para" parents="29443 36146"/>
    </justification>
  </clause>

  <clause id="36256">
    <literal><![CDATA[
      T((x / L(y,z,u)) * a(y,x * L(y,z,u),y),y) = x / L(T(y,(x / L(y,z,u)) * y),z,u)
    ]]></literal>
    <justification jstring="[para(13566(a,1),36157(a,1,1,2))].">
      <j1 rule="para" parents="13566 36157"/>
    </justification>
  </clause>

  <clause id="36257">
    <literal><![CDATA[
      a(x,y,z * (u \ ((w * v5) \ v5))) = a(x,y,z * (u \ (v5 \ (w \ v5))))
    ]]></literal>
    <justification jstring="[para(684(a,1),36198(a,1,3)),flip(a)].">
      <j1 rule="para" parents="684 36198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36258">
    <literal><![CDATA[
      L(x,y,L(K(z,u) * ((w * v5) * L(w,v6,v7)),w,w)) = L(x,y,L(w,v6,v7) * (K(z,u) * (w \ v5)))
    ]]></literal>
    <justification jstring="[para(24913(a,1),36202(a,1,3,1,2))].">
      <j1 rule="para" parents="24913 36202"/>
    </justification>
  </clause>

  <clause id="36259">
    <literal><![CDATA[
      L(x,((T(y,z) * u) \ ((T(y,z) * z) * u)) * w,v5) = L(x,L(z,y,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29453,a(flip),b,36213,a),flip(a)].">
      <j1 rule="hyper" parents="373 29453 36213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36261">
    <literal><![CDATA[
      L(x,((y * z) \ ((y * u) * z)) * w,v5) = L(x,L(u,y,z) * w,v5)
    ]]></literal>
    <justification jstring="[para(24860(a,1),36259(a,1,2,1))].">
      <j1 rule="para" parents="24860 36259"/>
    </justification>
  </clause>

  <clause id="36262">
    <literal><![CDATA[
      L(x,R(y,z,u) * w,v5) = L(x,L(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29757,a(flip),b,36261,a)].">
      <j1 rule="hyper" parents="64 29757 36261"/>
    </justification>
  </clause>

  <clause id="36264">
    <literal><![CDATA[
      L(x,R(y,z,u) * w,v5) = L(x,w * L(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29436,a,b,36262,a),flip(a)].">
      <j1 rule="hyper" parents="373 29436 36262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36265">
    <literal><![CDATA[
      L(x,L(((1 / y) * z) * y,u,w) * y,v5) = L(x,y \ R(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34517,a(flip),b,36262,a),flip(a)].">
      <j1 rule="hyper" parents="64 34517 36262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36266">
    <literal><![CDATA[
      L(x,y * R(z,u,w),v5) = L(x,y * L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(29572,a,36264,a)].">
      <j1 rule="hyper" parents="29572 36264"/>
    </justification>
  </clause>

  <clause id="36267">
    <literal><![CDATA[
      L(x,R(y,z,u) \ y,w) = L(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29610,a,b,36266,a)].">
      <j1 rule="hyper" parents="64 29610 36266"/>
    </justification>
  </clause>

  <clause id="36268">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ u,x * L(x,y,z),x * L(x,y,z)) = ((x \ R(x,y,z)) \ 1) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,35615,a(flip),b,36266,a),flip(a)].">
      <j1 rule="hyper" parents="64 35615 36266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36269">
    <literal><![CDATA[
      L(x,(y * z) * R(L(u,z,y),w,v5),v6) = L(x,y * (z * L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(513(a,1),36266(a,2,2))].">
      <j1 rule="para" parents="513 36266"/>
    </justification>
  </clause>

  <clause id="36270">
    <literal><![CDATA[
      L(x \ R(x,y,z),x * L(x,y,z),u) \ u = u * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(36266(a,1),31455(a,1,1))].">
      <j1 rule="para" parents="36266 31455"/>
    </justification>
  </clause>

  <clause id="36271">
    <literal><![CDATA[
      L(x,y \ R(z,u,w),v5) = L(x,y \ L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34519,a(flip),b,36265,a),flip(a)].">
      <j1 rule="hyper" parents="64 34519 36265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36272">
    <literal><![CDATA[
      L(x,y,a(L(z,z,u * y),u,y)) = L(x,z \ L(z,u,y),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,33835,a,b,36271,a)].">
      <j1 rule="hyper" parents="64 33835 36271"/>
    </justification>
  </clause>

  <clause id="36274">
    <literal><![CDATA[
      L(x,y,a(L(z,z,u * y),u,y)) = L(x,z * L(z,u,y),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11786,a(flip),b,36272,a),flip(a)].">
      <j1 rule="hyper" parents="373 11786 36272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36275">
    <literal><![CDATA[
      L(x,y * L(y,z,u),u) = L(x,u,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(32467(a,1),36274(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32467 36274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36276">
    <literal><![CDATA[
      L(x,y * L(y,z,u),u) = L(x,u,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,33124,a(flip),b,36275,a),flip(a)].">
      <j1 rule="hyper" parents="373 33124 36275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36277">
    <literal><![CDATA[
      L(x,y * L(y,z,u),u) = L(x,u,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,5608,a(flip),b,36276,a),flip(a)].">
      <j1 rule="hyper" parents="373 5608 36276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36278">
    <literal><![CDATA[
      L(x,y * (z * R(u,w,v5)),v6) = L(x,y * (z * L(u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(514(a,1),36269(a,1,2))].">
      <j1 rule="para" parents="514 36269"/>
    </justification>
  </clause>

  <clause id="36279">
    <literal><![CDATA[
      L(x,(y * L(z,u,w)) * v5,v6) = L(x,v5 * (y * R(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29436,a,b,36278,a)].">
      <j1 rule="hyper" parents="373 29436 36278"/>
    </justification>
  </clause>

  <clause id="36280">
    <literal><![CDATA[
      L(x,(y * R(z,u,w)) * v5,v6) = L(x,(y * L(z,u,w)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29436,a,b,36279,a)].">
      <j1 rule="hyper" parents="373 29436 36279"/>
    </justification>
  </clause>

  <clause id="36282">
    <literal><![CDATA[
      L(x,(L(y,z,u) * w) * v5,v6) = L(x,(w * R(y,z,u)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29455,a,b,36280,a)].">
      <j1 rule="hyper" parents="373 29455 36280"/>
    </justification>
  </clause>

  <clause id="36283">
    <literal><![CDATA[
      L(x,(R(y,z,u) * T(w,v5)) * ((v6 \ T(w,v5)) \ v7),v8) = L(x,(w * L(y,z,u)) * ((v6 \ w) \ v7),v8)
    ]]></literal>
    <justification jstring="[hyper(64,a,29647,a,b,36280,a)].">
      <j1 rule="hyper" parents="64 29647 36280"/>
    </justification>
  </clause>

  <clause id="36284">
    <literal><![CDATA[
      L(x,(R(y,z,u) * w) * v5,v6) = L(x,(L(y,z,u) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29455,a,b,36282,a)].">
      <j1 rule="hyper" parents="373 29455 36282"/>
    </justification>
  </clause>

  <clause id="36285">
    <literal><![CDATA[
      L(x,(L(1 / y,z,u) * w) * v5,v6) = L(x,(R(y,z,u) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29644,a(flip),b,36282,a),flip(a)].">
      <j1 rule="hyper" parents="373 29644 36282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36286">
    <literal><![CDATA[
      L(x,(L(y,z,u) * (y \ R(y,z,u))) * w,v5) = L(x,y * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29776,a(flip),b,36284,a),flip(a)].">
      <j1 rule="hyper" parents="64 29776 36284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36287">
    <literal><![CDATA[
      L(x,L(R(y,z,u),z,u) * w,v5) = L(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(33222(a,1),36286(a,1,2,1))].">
      <j1 rule="para" parents="33222 36286"/>
    </justification>
  </clause>

  <clause id="36288">
    <literal><![CDATA[
      L(x,y * (L(R(y,z,u),z,u) \ w),v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),36287(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 36287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36289">
    <literal><![CDATA[
      L(x,L(R(y,z,u),z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(191(a,1),36288(a,1,2)),flip(a)].">
      <j1 rule="para" parents="191 36288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36290">
    <literal><![CDATA[
      L(x,L(L(y,z,u),z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29856,a(flip),b,36289,a)].">
      <j1 rule="hyper" parents="64 29856 36289"/>
    </justification>
  </clause>

  <clause id="36291">
    <literal><![CDATA[
      L(L(L(x \ R(x,y,z),u,w),u,w),x,z * y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35136,a(flip),b,36290,a),flip(a)].">
      <j1 rule="hyper" parents="64 35136 36290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36292">
    <literal><![CDATA[
      L(x,L(T((y * (z \ 1)) \ u,w),z,y),v5) = L(x,T((z \ 1) \ (y \ u),w),v5)
    ]]></literal>
    <justification jstring="[para(11810(a,1),36290(a,1,2,1))].">
      <j1 rule="para" parents="11810 36290"/>
    </justification>
  </clause>

  <clause id="36294">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),u,w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,24741,a(flip),b,36291,a)].">
      <j1 rule="hyper" parents="64 24741 36291"/>
    </justification>
  </clause>

  <clause id="36295">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),u,w) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(42,a,23986,a(flip),b,36291,a),flip(a)].">
      <j1 rule="hyper" parents="42 23986 36291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36296">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * a(y,z,u) = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(42,a,30233,a,b,36294,a)].">
      <j1 rule="hyper" parents="42 30233 36294"/>
    </justification>
  </clause>

  <clause id="36297">
    <literal><![CDATA[
      x \ (y \ ((y * x) * a(z,u,w))) = L(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,596,a,b,36294,a)].">
      <j1 rule="hyper" parents="42 596 36294"/>
    </justification>
  </clause>

  <clause id="36298">
    <literal><![CDATA[
      L(a(x,y,z),x,y * z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(42,a,16031,a(flip),b,36294,a),flip(a)].">
      <j1 rule="hyper" parents="42 16031 36294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36299">
    <literal><![CDATA[
      x * (T(y,x) * L(a(z,u,w),y,x)) = (y * x) * a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,36294,a(flip),b,10980,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 36294 10980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36300">
    <literal><![CDATA[
      x * (y * L(a(z,u,w),y,x)) = (x * y) * a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,36294,a(flip),b,18,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 36294 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36301">
    <literal><![CDATA[
      (x \ 1) * L(a(y,z,u),x,x) = x \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,36294,a(flip),b,1139,a),flip(a)].">
      <j1 rule="hyper" parents="139 36294 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36302">
    <literal><![CDATA[
      x * L(a(y,z,u),x,x) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,36294,a(flip),b,559,a),flip(a)].">
      <j1 rule="hyper" parents="139 36294 559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36303">
    <literal><![CDATA[
      L(x,y,z) != a(u,w,v5)
    ]]></literal>
    <literal><![CDATA[
      L(a(u,w,v5),y,z) = x
    ]]></literal>
    <justification jstring="[para(36294(a,1),51(a,1)),flip(a)].">
      <j1 rule="para" parents="36294 51"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36304">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,w)) = y * L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(36294(a,1),344(a,1,2,2))].">
      <j1 rule="para" parents="36294 344"/>
    </justification>
  </clause>

  <clause id="36305">
    <literal><![CDATA[
      x * (L(a(y,z,u),w,x) * w) = (x * w) * T(a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(36294(a,1),988(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="36294 988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36306">
    <literal><![CDATA[
      L(L(a(x,y,z),u,u) / (u \ 1),u,u) = a(x,y,z) / (1 / u)
    ]]></literal>
    <justification jstring="[para(36294(a,1),11268(a,2,1))].">
      <j1 rule="para" parents="36294 11268"/>
    </justification>
  </clause>

  <clause id="36307">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ L(a(y,z,u),a(y,z,u),x)),a(y,z,u)) = L(a(y,z,u),a(y,z,u),x) \ (x * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(36294(a,1),12031(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="36294 12031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36308">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),x,z * y) = L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(36298(a,1),23982(a,1,1)),flip(a)].">
      <j1 rule="para" parents="36298 23982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36310">
    <literal><![CDATA[
      x \ ((1 / x) \ a(y,z,u)) = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,1165,a,b,36301,a)].">
      <j1 rule="hyper" parents="35 1165 36301"/>
    </justification>
  </clause>

  <clause id="36311">
    <literal><![CDATA[
      L(a(x,y,z),u,u) * u = (1 / u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23557,a,b,36302,a)].">
      <j1 rule="hyper" parents="64 23557 36302"/>
    </justification>
  </clause>

  <clause id="36312">
    <literal><![CDATA[
      ((1 / x) \ a(y,z,u)) / x = L(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(142,a,36302,a(flip),b,23557,a)].">
      <j1 rule="hyper" parents="142 36302 23557"/>
    </justification>
  </clause>

  <clause id="36313">
    <literal><![CDATA[
      x * a(L(y,x,x),z,z \ 1) = (1 / x) \ a(y,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(4248(a,2),36302(a,1,2))].">
      <j1 rule="para" parents="4248 36302"/>
    </justification>
  </clause>

  <clause id="36314">
    <literal><![CDATA[
      L(a(x,y,z),u,u) * u = a(x,y,z) * L(u,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27122,a,b,36311,a),flip(a)].">
      <j1 rule="hyper" parents="373 27122 36311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36315">
    <literal><![CDATA[
      L((x * y) \ R(x * y,z,u),y,x) = y \ (x * R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(42,a,2134,a,b,36295,a),flip(a)].">
      <j1 rule="hyper" parents="42 2134 36295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36316">
    <literal><![CDATA[
      x * L(y \ R(y,z,u),x,x) = (1 / x) \ (y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,36295,a(flip),b,559,a),flip(a)].">
      <j1 rule="hyper" parents="139 36295 559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36317">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (y * a(z,u,w)) = y * L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,30023,a,b,36300,a)].">
      <j1 rule="hyper" parents="35 30023 36300"/>
    </justification>
  </clause>

  <clause id="36318">
    <literal><![CDATA[
      x * (L(a(y,z,u),w,x) * w) = (x * w) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(23557(a,2),36300(a,1,2))].">
      <j1 rule="para" parents="23557 36300"/>
    </justification>
  </clause>

  <clause id="36319">
    <literal><![CDATA[
      x \ (a(y,z,u) * (x * w)) = L(a(y,z,u),w,x) * w
    ]]></literal>
    <justification jstring="[hyper(139,a,23136,a,b,36318,a)].">
      <j1 rule="hyper" parents="139 23136 36318"/>
    </justification>
  </clause>

  <clause id="36321">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * u) * w = a(x,y,z) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(144,a,36319,a(flip),b,33930,a)].">
      <j1 rule="hyper" parents="144 36319 33930"/>
    </justification>
  </clause>

  <clause id="36322">
    <literal><![CDATA[
      x * (R(a(y,z,u),w,x) * w) = (x * w) * T(a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(28787(a,2),36305(a,1,2,1))].">
      <j1 rule="para" parents="28787 36305"/>
    </justification>
  </clause>

  <clause id="36323">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) \ x = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,30435,a,b,36314,a(flip))].">
      <j1 rule="hyper" parents="35 30435 36314"/>
    </justification>
  </clause>

  <clause id="36324">
    <literal><![CDATA[
      a(a(x,y,z),u,u) * u = L(u,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,34927,a(flip),b,36323,a)].">
      <j1 rule="hyper" parents="64 34927 36323"/>
    </justification>
  </clause>

  <clause id="36325">
    <literal><![CDATA[
      x * a(a(y,z,u),x,x) = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29937,a(flip),b,36323,a)].">
      <j1 rule="hyper" parents="64 29937 36323"/>
    </justification>
  </clause>

  <clause id="36326">
    <literal><![CDATA[
      a(a(x,y,z),u,u) = a(u,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(40,a,30459,a,b,36323,a)].">
      <j1 rule="hyper" parents="40 30459 36323"/>
    </justification>
  </clause>

  <clause id="36327">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ x = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(40,a,5559,a,b,36323,a)].">
      <j1 rule="hyper" parents="40 5559 36323"/>
    </justification>
  </clause>

  <clause id="36328">
    <literal><![CDATA[
      x \ L(x,x,a(y,z,u)) = a(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,36323,a(flip),b,29937,a(flip))].">
      <j1 rule="hyper" parents="139 36323 29937"/>
    </justification>
  </clause>

  <clause id="36330">
    <literal><![CDATA[
      a(a(a(x,y,y) * z,u,w),v5,v5) = a(v5,v5,a(z * a(y,y,x),u,w))
    ]]></literal>
    <justification jstring="[para(32849(a,1),36326(a,2,3))].">
      <j1 rule="para" parents="32849 36326"/>
    </justification>
  </clause>

  <clause id="36331">
    <literal><![CDATA[
      a(a(x * a(y,z,z),u,w),v5,v5) = a(v5,v5,a(x * a(z,z,y),u,w))
    ]]></literal>
    <justification jstring="[para(32851(a,1),36326(a,2,3))].">
      <j1 rule="para" parents="32851 36326"/>
    </justification>
  </clause>

  <clause id="36332">
    <literal><![CDATA[
      L(1 / x,x,a(y,z,u)) \ 1 = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,30531,a,b,36324,a)].">
      <j1 rule="hyper" parents="64 30531 36324"/>
    </justification>
  </clause>

  <clause id="36333">
    <literal><![CDATA[
      L(1 / x,x,a(y,z,u)) = 1 / L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(225,a,36324,a(flip),b,30531,a),flip(a)].">
      <j1 rule="hyper" parents="225 36324 30531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36334">
    <literal><![CDATA[
      L(x \ 1,x,a(y,z,u)) = x \ a(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,36328,a(flip),b,28848,a),flip(a)].">
      <j1 rule="hyper" parents="139 36328 28848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36335">
    <literal><![CDATA[
      L(1 / x,x,a(y,z,u)) = 1 / R(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(225,a,28832,a,b,36332,a),flip(a)].">
      <j1 rule="hyper" parents="225 28832 36332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36336">
    <literal><![CDATA[
      L(1 / x,x,a(y,z,u)) = a(a(y,z,u),x,x) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,30474,a,b,36333,a),flip(a)].">
      <j1 rule="hyper" parents="373 30474 36333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36337">
    <literal><![CDATA[
      a(x,y,z) \ (u \ a(x,y,z)) = u \ a(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27121,a(flip),b,36334,a)].">
      <j1 rule="hyper" parents="64 27121 36334"/>
    </justification>
  </clause>

  <clause id="36338">
    <literal><![CDATA[
      x * L(y \ R(y,z,u),x,x) = (y / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,31562,a(flip),b,36316,a),flip(a)].">
      <j1 rule="hyper" parents="373 31562 36316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36339">
    <literal><![CDATA[
      x \ ((x \ y) * R((x \ y) \ x,z,u)) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,27049,a,b,36338,a)].">
      <j1 rule="hyper" parents="139 27049 36338"/>
    </justification>
  </clause>

  <clause id="36340">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,u) * u = (x / u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,24383,a,b,36338,a)].">
      <j1 rule="hyper" parents="64 24383 36338"/>
    </justification>
  </clause>

  <clause id="36341">
    <literal><![CDATA[
      ((x / y) \ R(x,z,u)) / y = L(x \ R(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(142,a,36338,a(flip),b,24383,a)].">
      <j1 rule="hyper" parents="142 36338 24383"/>
    </justification>
  </clause>

  <clause id="36342">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(z,u,w) * y) = R(a(z,u,w),y,x) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,30272,a,b,36322,a)].">
      <j1 rule="hyper" parents="35 30272 36322"/>
    </justification>
  </clause>

  <clause id="36343">
    <literal><![CDATA[
      L((1 / x) \ L(a(y,z,u),x,x),x,x) = a(y,z,u) / (1 / x)
    ]]></literal>
    <justification jstring="[para(28614(a,1),36306(a,1,1))].">
      <j1 rule="para" parents="28614 36306"/>
    </justification>
  </clause>

  <clause id="36344">
    <literal><![CDATA[
      L(x * a(y,z,u),x,x) = a(y,z,u) / (1 / x)
    ]]></literal>
    <justification jstring="[para(561(a,1),36343(a,1,1))].">
      <j1 rule="para" parents="561 36343"/>
    </justification>
  </clause>

  <clause id="36345">
    <literal><![CDATA[
      L((x \ ((x * y) * z)) / z,y,y) = a(x,y,z) / (1 / y)
    ]]></literal>
    <justification jstring="[para(33275(a,2),36344(a,1,1))].">
      <j1 rule="para" parents="33275 36344"/>
    </justification>
  </clause>

  <clause id="36346">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * a(z,u,y) = L(a(z,u,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,33533,a(flip),b,36317,a(flip))].">
      <j1 rule="hyper" parents="35 33533 36317"/>
    </justification>
  </clause>

  <clause id="36347">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),z,u) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(23920,a,36346,a)].">
      <j1 rule="hyper" parents="23920 36346"/>
    </justification>
  </clause>

  <clause id="36348">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ (a(z,u,y) \ 1) = L(a(z,u,y),y,x) \ 1
    ]]></literal>
    <justification jstring="[para(36347(a,1),7708(a,1,1))].">
      <j1 rule="para" parents="36347 7708"/>
    </justification>
  </clause>

  <clause id="36349">
    <literal><![CDATA[
      (1 / x) \ ((x \ y) * R((x \ y) \ (1 / x),z,u)) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27890,a,b,36339,a)].">
      <j1 rule="hyper" parents="64 27890 36339"/>
    </justification>
  </clause>

  <clause id="36350">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),u,w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,33307,a,b,36342,a)].">
      <j1 rule="hyper" parents="36 33307 36342"/>
    </justification>
  </clause>

  <clause id="36351">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,z,a(x,y,z)) \ 1) = L(a(x,y,z),z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,33316,a(flip),b,36348,a)].">
      <j1 rule="hyper" parents="64 33316 36348"/>
    </justification>
  </clause>

  <clause id="36352">
    <literal><![CDATA[
      L(x,(L(1 / y,z,u) * w) * v5,v6) = L(x,(L(y,z,u) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,36284,a(flip),b,36285,a),flip(a)].">
      <j1 rule="hyper" parents="373 36284 36285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36353">
    <literal><![CDATA[
      L(x,T((y \ 1) \ (z \ u),w),v5) = L(x,L((z * (y \ 1)) \ u,y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(29570,a,36292,a),flip(a)].">
      <j1 rule="hyper" parents="29570 36292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36355">
    <literal><![CDATA[
      (1 / x) \ ((y \ R(y,z,u)) / x) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(28021(a,1),36349(a,1,2))].">
      <j1 rule="para" parents="28021 36349"/>
    </justification>
  </clause>

  <clause id="36356">
    <literal><![CDATA[
      ((x \ R(x,y,z)) / u) / (1 / u) = L(x \ R(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23725,a,b,36355,a)].">
      <j1 rule="hyper" parents="64 23725 36355"/>
    </justification>
  </clause>

  <clause id="36357">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ u,x * L(x,y,z),x * L(x,y,z)) = (R(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,5384,a(flip),b,36268,a),flip(a)].">
      <j1 rule="hyper" parents="373 5384 36268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36358">
    <literal><![CDATA[
      x * (K(y,x) * K(x,L(L(x,z,u),w,v5) * y)) = L(x,y,L(L(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(23380(a,1),36230(a,1,2,1))].">
      <j1 rule="para" parents="23380 36230"/>
    </justification>
  </clause>

  <clause id="36360">
    <literal><![CDATA[
      L(x,y,L(L(x,z,u),w,v5)) = x * (K(y,x) * K(x,L(x,z,u) * y))
    ]]></literal>
    <justification jstring="[para(28329(a,1),36358(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28329 36358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36361">
    <literal><![CDATA[
      L(x,y,L(L(x,z,u),w,v5)) = x * (K(y,x) * K(x,x * y))
    ]]></literal>
    <justification jstring="[para(11583(a,1),36360(a,2,2,2))].">
      <j1 rule="para" parents="11583 36360"/>
    </justification>
  </clause>

  <clause id="36363">
    <literal><![CDATA[
      L(x,y,L(L(x,z,u),w,v5)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,6505,a(flip),b,36361,a),flip(a)].">
      <j1 rule="hyper" parents="373 6505 36361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36365">
    <literal><![CDATA[
      K((x \ y) * x,z) * T(x \ (y * L(x,u,w)),K(y,v5)) = T(x \ (y * L(x,u,w)),z)
    ]]></literal>
    <justification jstring="[para(28406(a,1),36244(a,1,1))].">
      <j1 rule="para" parents="28406 36244"/>
    </justification>
  </clause>

  <clause id="36366">
    <literal><![CDATA[
      K(x,T(y,z)) * T(z \ (x * L(z,u,w)),K(x,v5)) = T(z \ (x * L(z,u,w)),y)
    ]]></literal>
    <justification jstring="[para(11175(a,1),36365(a,1,1))].">
      <j1 rule="para" parents="11175 36365"/>
    </justification>
  </clause>

  <clause id="36368">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ (x * L(z,u,w))) = T(z \ (x * L(z,u,w)),y)
    ]]></literal>
    <justification jstring="[para(3347(a,1),36366(a,1,2))].">
      <j1 rule="para" parents="3347 36366"/>
    </justification>
  </clause>

  <clause id="36369">
    <literal><![CDATA[
      x \ (K(y,z) * (y * L(x,u,w))) = T(x \ (y * L(x,u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,22758,a(flip),b,36368,a)].">
      <j1 rule="hyper" parents="64 22758 36368"/>
    </justification>
  </clause>

  <clause id="36370">
    <literal><![CDATA[
      T(x \ (y * L(x,z,u)),w) = x \ (T(y,w) * L(x,z,u))
    ]]></literal>
    <justification jstring="[para(5755(a,1),36369(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5755 36369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36371">
    <literal><![CDATA[
      T(x * L(a(y,z,u),w,v5),v6) = T(x,v6) * L(a(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(39,a,28757,a(flip),b,36370,a(flip))].">
      <j1 rule="hyper" parents="39 28757 36370"/>
    </justification>
  </clause>

  <clause id="36373">
    <literal><![CDATA[
      T(x * L(a(y,z,u),w,v5),v6) = L(a(y,z,u),w,v5) * T(x,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,23557,a,b,36371,a),flip(a)].">
      <j1 rule="hyper" parents="373 23557 36371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36374">
    <literal><![CDATA[
      x * T(y * L(a(x,z,u),w,v5),x) = (y * x) * L(a(x,z,u),w,v5)
    ]]></literal>
    <justification jstring="[para(36371(a,2),29918(a,1,2))].">
      <j1 rule="para" parents="36371 29918"/>
    </justification>
  </clause>

  <clause id="36375">
    <literal><![CDATA[
      x * T(y * L(a(z,u,w),y,x),x) = (y * x) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(36371(a,2),36299(a,1,2))].">
      <j1 rule="para" parents="36371 36299"/>
    </justification>
  </clause>

  <clause id="36376">
    <literal><![CDATA[
      (x * L(a(y,z,u),x,w)) * w = (x * w) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(328,a,36375,a)].">
      <j1 rule="hyper" parents="328 36375"/>
    </justification>
  </clause>

  <clause id="36377">
    <literal><![CDATA[
      (x * L(a(y,z,u),w,v5)) * y = (x * y) * L(a(y,z,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(328,a,36374,a)].">
      <j1 rule="hyper" parents="328 36374"/>
    </justification>
  </clause>

  <clause id="36378">
    <literal><![CDATA[
      (x * L(a(x,y,z),u,w)) \ (v5 \ ((v5 * x) * L(a(x,y,z),u,w))) = a(v5,L(a(x,y,z),u,w),x)
    ]]></literal>
    <justification jstring="[para(36377(a,1),30200(a,1,2,2))].">
      <j1 rule="para" parents="36377 30200"/>
    </justification>
  </clause>

  <clause id="36379">
    <literal><![CDATA[
      (1 / (x / y)) * (((1 / (x / y)) \ (y / x)) * z) = (y / x) * L(z,a(x,x * y,y),y \ x)
    ]]></literal>
    <justification jstring="[para(35694(a,1),36255(a,2,2))].">
      <j1 rule="para" parents="35694 36255"/>
    </justification>
  </clause>

  <clause id="36380">
    <literal><![CDATA[
      (1 / (x / y)) * (((1 / (x / y)) \ (y / x)) * z) = (y / x) * L(z,y \ x,a(x,x * y,y))
    ]]></literal>
    <justification jstring="[para(35831(a,1),36379(a,2,2))].">
      <j1 rule="para" parents="35831 36379"/>
    </justification>
  </clause>

  <clause id="36381">
    <literal><![CDATA[
      (1 / (x / y)) * (((y / x) * (x / y)) * z) = (y / x) * L(z,y \ x,a(x,x * y,y))
    ]]></literal>
    <justification jstring="[para(2719(a,1),36380(a,1,2,1))].">
      <j1 rule="para" parents="2719 36380"/>
    </justification>
  </clause>

  <clause id="36382">
    <literal><![CDATA[
      T((x / L(y,z,u)) * a(y,x * y,y),y) = x / L(T(y,(x / L(y,z,u)) * y),z,u)
    ]]></literal>
    <justification jstring="[para(33769(a,1),36256(a,1,1,2))].">
      <j1 rule="para" parents="33769 36256"/>
    </justification>
  </clause>

  <clause id="36383">
    <literal><![CDATA[
      T(x / L(L(y,x * y,y),z,u),y) = x / L(T(y,(x / L(y,z,u)) * y),z,u)
    ]]></literal>
    <justification jstring="[para(13631(a,1),36382(a,1,1))].">
      <j1 rule="para" parents="13631 36382"/>
    </justification>
  </clause>

  <clause id="36385">
    <literal><![CDATA[
      x / L(T(y,(x / L(y,z,u)) * y),z,u) = L(L(y,x * y,y),z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,24386,a(flip),b,36383,a),flip(a)].">
      <j1 rule="hyper" parents="64 24386 36383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36386">
    <literal><![CDATA[
      x / L(T(y,y * (L(y,z,u) \ x)),z,u) = L(L(y,x * y,y),z,u) \ x
    ]]></literal>
    <justification jstring="[para(23887(a,1),36385(a,1,2,1,2))].">
      <j1 rule="para" parents="23887 36385"/>
    </justification>
  </clause>

  <clause id="36387">
    <literal><![CDATA[
      L(L(x,y * x,x),z,u) \ y = y / L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11575(a,1),36386(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11575 36386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36389">
    <literal><![CDATA[
      L(x,y,L((z * u) * L(z,w,v5),z,z)) = L(x,y,L(z,w,v5) * (K(v6,v7) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29005,a(flip),b,36258,a)].">
      <j1 rule="hyper" parents="64 29005 36258"/>
    </justification>
  </clause>

  <clause id="36391">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * (K(v5,v6) * (z \ v7))) = L(x,y,L(z,u,w) \ (z * v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,35174,a(flip),b,36389,a),flip(a)].">
      <j1 rule="hyper" parents="64 35174 36389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36392">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * (K(v5,v6) * (z \ v7))) = L(x,y,z * (L(z,u,w) \ v7))
    ]]></literal>
    <justification jstring="[para(2329(a,1),36391(a,2,3))].">
      <j1 rule="para" parents="2329 36391"/>
    </justification>
  </clause>

  <clause id="36393">
    <literal><![CDATA[
      L(x,y,(z \ u) * L(z,w,v5)) = L(x,y,z * (L(z,w,v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29084,a(flip),b,36392,a)].">
      <j1 rule="hyper" parents="64 29084 36392"/>
    </justification>
  </clause>

  <clause id="36394">
    <literal><![CDATA[
      a(x,L(a(y,z,u),w,v5),y) = a(x,y,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,30027,a,b,36378,a),flip(a)].">
      <j1 rule="hyper" parents="64 30027 36378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36395">
    <literal><![CDATA[
      (x \ ((x * y) * z)) * T(u,y * z) = u * (T(x \ ((y * x) * z),K(x,y)) * K(x,y))
    ]]></literal>
    <justification jstring="[para(9(a,1),24695(a,1,2,2,1))].">
      <j1 rule="para" parents="9 24695"/>
    </justification>
  </clause>

  <clause id="36396">
    <literal><![CDATA[
      (x \ ((x * y) * z)) * T(u,y * z) = u * T((x \ ((y * x) * z)) * K(x,y),K(x,y))
    ]]></literal>
    <justification jstring="[para(10018(a,2),36395(a,2,2))].">
      <j1 rule="para" parents="10018 36395"/>
    </justification>
  </clause>

  <clause id="36397">
    <literal><![CDATA[
      (x \ ((x * y) * z)) * T(u,y * z) = u * T(T(x \ ((x * y) * z),K(x,y)),K(x,y))
    ]]></literal>
    <justification jstring="[para(10969(a,2),36396(a,2,2,1))].">
      <j1 rule="para" parents="10969 36396"/>
    </justification>
  </clause>

  <clause id="36398">
    <literal><![CDATA[
      (x \ ((x * y) * z)) * T(u,y * z) = u * (x \ ((x * y) * z))
    ]]></literal>
    <justification jstring="[para(8157(a,1),36397(a,2,2))].">
      <j1 rule="para" parents="8157 36397"/>
    </justification>
  </clause>

  <clause id="36401">
    <literal><![CDATA[
      T(x * ((x \ 1) * (x * (y \ L(y,z,u)))),x \ (x \ 1)) = x * (x * ((x \ 1) * (y \ L(y,z,u))))
    ]]></literal>
    <justification jstring="[para(25362(a,1),25363(a,1,1,2))].">
      <j1 rule="para" parents="25362 25363"/>
    </justification>
  </clause>

  <clause id="36402">
    <literal><![CDATA[
      T((x * y) / ((x * y) * y),y * (y * x)) = ((((x * y) \ z) \ z) * y) \ T(x * y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(14661(a,1),25868(a,2,2))].">
      <j1 rule="para" parents="14661 25868"/>
    </justification>
  </clause>

  <clause id="36403">
    <literal><![CDATA[
      (x * T(y,z)) / L(T(y,z),u,L(u \ x,u,y)) = ((x * T(y,z)) / (u * T(y,z))) * u
    ]]></literal>
    <justification jstring="[para(29176(a,1),25907(a,1,2))].">
      <j1 rule="para" parents="29176 25907"/>
    </justification>
  </clause>

  <clause id="36404">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,L(z \ u,z,x)) \ u) = ((u * T(x,y)) / (z * T(x,y))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,24843,a(flip),b,36403,a)].">
      <j1 rule="hyper" parents="64 24843 36403"/>
    </justification>
  </clause>

  <clause id="36406">
    <literal><![CDATA[
      ((x * T(y,z)) / (u * T(y,z))) * u = y * (L(y,u,L(u \ x,u,y)) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25425,a(flip),b,36404,a),flip(a)].">
      <j1 rule="hyper" parents="64 25425 36404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36408">
    <literal><![CDATA[
      x * (L(x,y,L(y \ z,y,x)) \ z) = ((z * x) / (y * x)) * y
    ]]></literal>
    <justification jstring="[para(24873(a,1),36406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="24873 36406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36409">
    <literal><![CDATA[
      x * (L(x,y,L(y \ (y \ z),y,x)) \ (y \ z)) = y \ R(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2145,a(flip),b,36408,a),flip(a)].">
      <j1 rule="hyper" parents="373 2145 36408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36410">
    <literal><![CDATA[
      x * (L(x,y,L(L(z,y,x),y,y)) \ (y \ z)) = y \ R(z,y,x)
    ]]></literal>
    <justification jstring="[para(34713(a,1),36409(a,1,2,1))].">
      <j1 rule="para" parents="34713 36409"/>
    </justification>
  </clause>

  <clause id="36411">
    <literal><![CDATA[
      T((x * y) / T((x * y) * (1 / x),K(y,z)),1 / x) = (x * ((x \ 1) \ y)) / T(x * y,1 / x)
    ]]></literal>
    <justification jstring="[para(1124(a,1),25994(a,2,1))].">
      <j1 rule="para" parents="1124 25994"/>
    </justification>
  </clause>

  <clause id="36412">
    <literal><![CDATA[
      (L(x,y,y) / z) \ (K(u,y) * (((1 / y) * ((T(y,u) * x) * z)) / z)) = L(z,T(y,u) * x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,23199,a(flip),b,26142,a)].">
      <j1 rule="hyper" parents="64 23199 26142"/>
    </justification>
  </clause>

  <clause id="36413">
    <literal><![CDATA[
      L((((x / y) / x) * y) \ z,y * (x \ ((y \ 1) \ x)),y) = L(((y \ 1) * x) \ x,y,y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29764,a(flip),b,26381,a)].">
      <j1 rule="hyper" parents="64 29764 26381"/>
    </justification>
  </clause>

  <clause id="36414">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,(u * (x \ R(x,y,z))) \ w) \ w = u * ((T(x \ R(x,y,z),v5) * u) \ w)
    ]]></literal>
    <justification jstring="[para(28821(a,1),26399(a,1,1))].">
      <j1 rule="para" parents="28821 26399"/>
    </justification>
  </clause>

  <clause id="36415">
    <literal><![CDATA[
      (x * y) / ((y / (z * z)) * ((x * (y / (z * z))) \ (x * y))) = R(x,y,L(z * z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,2967,a(flip),b,26482,a),flip(a)].">
      <j1 rule="hyper" parents="373 2967 26482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36417">
    <literal><![CDATA[
      (x * y) / ((y / (z * z)) * L(z * z,y,x)) = R(x,y,L(z * z,y,x))
    ]]></literal>
    <justification jstring="[para(11834(a,1),36415(a,1,2,2))].">
      <j1 rule="para" parents="11834 36415"/>
    </justification>
  </clause>

  <clause id="36418">
    <literal><![CDATA[
      (x * y) / (y * ((z * z) \ L(z * z,y,x))) = R(x,y,L(z * z,y,x))
    ]]></literal>
    <justification jstring="[para(897(a,1),36417(a,1,2))].">
      <j1 rule="para" parents="897 36417"/>
    </justification>
  </clause>

  <clause id="36419">
    <literal><![CDATA[
      (x * y) / (y * (a(x,y,z * z) \ 1)) = R(x,y,L(z * z,y,x))
    ]]></literal>
    <justification jstring="[para(31257(a,1),36418(a,1,2,2))].">
      <j1 rule="para" parents="31257 36418"/>
    </justification>
  </clause>

  <clause id="36420">
    <literal><![CDATA[
      (x * y) / (a(y,x,z * z) \ y) = R(x,y,L(z * z,y,x))
    ]]></literal>
    <justification jstring="[para(34007(a,1),36419(a,1,2))].">
      <j1 rule="para" parents="34007 36419"/>
    </justification>
  </clause>

  <clause id="36421">
    <literal><![CDATA[
      (x * y) / (a(y,x,z * z) \ y) = R(x,y,z * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,26361,a(flip),b,36420,a),flip(a)].">
      <j1 rule="hyper" parents="373 26361 36420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36423">
    <literal><![CDATA[
      x * a(y,x,z * z) = R(x,y,z * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31268,a(flip),b,36421,a)].">
      <j1 rule="hyper" parents="64 31268 36421"/>
    </justification>
  </clause>

  <clause id="36425">
    <literal><![CDATA[
      R(x,y,L(L(z,u,z),w,v5) * L(L(z,u,z),w,v5)) = x * a(y,x,L(z,w,v5) * L(L(z,u,z),w,v5))
    ]]></literal>
    <justification jstring="[para(27361(a,1),36423(a,1,2)),flip(a)].">
      <j1 rule="para" parents="27361 36423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36426">
    <literal><![CDATA[
      x / (x / ((1 / a(y,z,u)) * w)) = (x / (x / w)) * (a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(33941(a,1),27214(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33941 27214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36427">
    <literal><![CDATA[
      x / (x / ((a(y,z,u) \ 1) * w)) = (x / (x / w)) * (a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(13923(a,1),36426(a,1,2,2,1))].">
      <j1 rule="para" parents="13923 36426"/>
    </justification>
  </clause>

  <clause id="36429">
    <literal><![CDATA[
      R(x,y,(K(z,z \ u) * (w / (v5 / (z \ u)))) \ v6) = R(x,y,(T(v5 / (u / z),K(z,u)) \ w) \ v6)
    ]]></literal>
    <justification jstring="[para(23224(a,1),27813(a,1,3,1))].">
      <j1 rule="para" parents="23224 27813"/>
    </justification>
  </clause>

  <clause id="36430">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) * a(y \ (x \ y),z,(z \ 1) \ y)) = x \ R(x,z,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),28061(a,1,2,1))].">
      <j1 rule="para" parents="10 28061"/>
    </justification>
  </clause>

  <clause id="36431">
    <literal><![CDATA[
      a(x \ (y \ x),z,(z \ 1) \ x) = y \ R(y,z,(z \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(396,a,36430,a)].">
      <j1 rule="hyper" parents="396 36430"/>
    </justification>
  </clause>

  <clause id="36434">
    <literal><![CDATA[
      T(((x \ (y \ (y \ x))) \ 1) * K(x,y * y),z) = ((y \ (y \ x)) / x) \ K((y \ (y \ x)) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,17826,a,b,28470,a)].">
      <j1 rule="hyper" parents="373 17826 28470"/>
    </justification>
  </clause>

  <clause id="36435">
    <literal><![CDATA[
      (x \ ((y \ (x \ y)) \ 1)) \ K(y,K(K(x,x \ y) * 1,x)) = 1 / (x \ ((y \ (x \ y)) \ 1))
    ]]></literal>
    <justification jstring="[para(5745(a,1),28485(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5745 28485"/>
    </justification>
  </clause>

  <clause id="36436">
    <literal><![CDATA[
      (x \ ((y \ (x \ y)) \ 1)) \ K(y,K(K(x,x \ y),x)) = 1 / (x \ ((y \ (x \ y)) \ 1))
    ]]></literal>
    <justification jstring="[para(8(a,1),36435(a,1,2,2,1))].">
      <j1 rule="para" parents="8 36435"/>
    </justification>
  </clause>

  <clause id="36437">
    <literal><![CDATA[
      1 / (x \ ((y \ (x \ y)) \ 1)) = (x \ ((y \ (x \ y)) \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(17143(a,1),36436(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17143 36436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36439">
    <literal><![CDATA[
      T(T((x \ y) * z,u) / (x \ y),x \ y) = ((y \ x) \ 1) \ T(((y \ x) \ 1) * z,u)
    ]]></literal>
    <justification jstring="[para(22792(a,1),28512(a,1,1))].">
      <j1 rule="para" parents="22792 28512"/>
    </justification>
  </clause>

  <clause id="36440">
    <literal><![CDATA[
      ((x \ y) \ 1) \ T(((x \ y) \ 1) * z,u) = (y \ x) \ T((y \ x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(467,a,36439,a),flip(a)].">
      <j1 rule="hyper" parents="467 36439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36441">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * z,u) = (y \ x) * T((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,5441,a(flip),b,36440,a),flip(a)].">
      <j1 rule="hyper" parents="64 5441 36440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36442">
    <literal><![CDATA[
      (x \ y) * ((y \ x) * T((y \ x) \ z,u)) = 1 * T(1 \ ((x \ y) * z),u)
    ]]></literal>
    <justification jstring="[para(36441(a,1),2398(a,2,2)),flip(a)].">
      <j1 rule="para" parents="36441 2398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36443">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ x)) * (a(y,z,u) * T(((a(y,z,u) \ x) \ x) \ w,v5)) = 1 * T(1 \ ((x \ (a(y,z,u) \ x)) * w),v5)
    ]]></literal>
    <justification jstring="[para(23134(a,1),36442(a,1,2,1))].">
      <j1 rule="para" parents="23134 36442"/>
    </justification>
  </clause>

  <clause id="36444">
    <literal><![CDATA[
      K(x,T((K(y,y \ z) / u) * (y \ z),w) * v5) = K(x,T((z / y) * (1 / u),w * (z * y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,35004,a(flip),b,28953,a),flip(a)].">
      <j1 rule="hyper" parents="373 35004 28953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36445">
    <literal><![CDATA[
      L(x,y,(z \ (R(1 / u,w,v5) * v6)) * (v7 * v7)) = L(x,y,(R(u,w,v5) * v6) * L(z,z,R(1 / u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,11774,a,b,29162,a)].">
      <j1 rule="hyper" parents="373 11774 29162"/>
    </justification>
  </clause>

  <clause id="36446">
    <literal><![CDATA[
      L(x,y,(R(z,u,w) * v5) * L(v6,v6,R(z,u,w) * v5)) = L(x,y,v6 \ (R(1 / z,u,w) * v5))
    ]]></literal>
    <justification jstring="[para(2477(a,1),29162(a,1,3,2))].">
      <j1 rule="para" parents="2477 29162"/>
    </justification>
  </clause>

  <clause id="36447">
    <literal><![CDATA[
      L(x,y,z \ (R(1 / u,w,v5) * v6)) = L(x,y,z \ (R(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,29158,a(flip),b,36446,a),flip(a)].">
      <j1 rule="hyper" parents="64 29158 36446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36448">
    <literal><![CDATA[
      L(x,y \ a(y,y,x),a(y,y,x) * y) \ (y \ x) = R(T(y \ a(y,y,x),x),y \ a(y,y,x),x)
    ]]></literal>
    <justification jstring="[para(24662(a,1),30130(a,1,1))].">
      <j1 rule="para" parents="24662 30130"/>
    </justification>
  </clause>

  <clause id="36449">
    <literal><![CDATA[
      (x * x) * (y * (L(x \ 1,x \ 1,z) \ (1 / x))) = x * ((x \ 1) \ (y * a(z,x,x \ 1)))
    ]]></literal>
    <justification jstring="[para(11980(a,1),30488(a,2,2,2,2))].">
      <j1 rule="para" parents="11980 30488"/>
    </justification>
  </clause>

  <clause id="36450">
    <literal><![CDATA[
      (x * x) * (y * (L(x \ 1,x \ 1,z) \ (1 / x))) = x * (((x \ 1) \ y) * a(z,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(33202(a,1),36449(a,2,2))].">
      <j1 rule="para" parents="33202 36449"/>
    </justification>
  </clause>

  <clause id="36451">
    <literal><![CDATA[
      (x * x) * (y * (L(x \ 1,x \ 1,z) \ (1 / x))) = (L(1 / x,x,z) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,34820,a(flip),b,36450,a),flip(a)].">
      <j1 rule="hyper" parents="373 34820 36450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36452">
    <literal><![CDATA[
      (x * x) * (y * (L(x \ 1,x,z) \ (1 / x))) = (L(1 / x,x,z) \ x) * y
    ]]></literal>
    <justification jstring="[para(11794(a,1),36451(a,1,2,2,1))].">
      <j1 rule="para" parents="11794 36451"/>
    </justification>
  </clause>

  <clause id="36453">
    <literal><![CDATA[
      (x * x) * (y * a(x * z,x,x)) = (L(1 / x,x,z) \ x) * y
    ]]></literal>
    <justification jstring="[para(30513(a,1),36452(a,1,2,2))].">
      <j1 rule="para" parents="30513 36452"/>
    </justification>
  </clause>

  <clause id="36454">
    <literal><![CDATA[
      ((L(x,x,y) \ 1) / a(y,x,x)) * (a(y,x,x) * z) = (L(x,x,y) \ 1) * L(z,a(y,x,x),x)
    ]]></literal>
    <justification jstring="[para(1631(a,1),30542(a,2,2))].">
      <j1 rule="para" parents="1631 30542"/>
    </justification>
  </clause>

  <clause id="36455">
    <literal><![CDATA[
      ((L(x,x,y) \ 1) / a(y,x,x)) * (a(y,x,x) * z) = (L(x,x,y) \ 1) * L(z,x,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(31820(a,1),36454(a,2,2))].">
      <j1 rule="para" parents="31820 36454"/>
    </justification>
  </clause>

  <clause id="36456">
    <literal><![CDATA[
      (a(x,y,y) \ (L(y,y,x) \ 1)) * (a(x,y,y) * z) = (L(y,y,x) \ 1) * L(z,y,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(23133(a,1),36455(a,1,1))].">
      <j1 rule="para" parents="23133 36455"/>
    </justification>
  </clause>

  <clause id="36457">
    <literal><![CDATA[
      (L(x,x,y) \ 1) * L(z,x,a(x,x,y)) = (x \ 1) * (a(y,x,x) * z)
    ]]></literal>
    <justification jstring="[para(30479(a,1),36456(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30479 36456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36458">
    <literal><![CDATA[
      (x \ 1) * (a(y,x,x) * ((1 / x) \ z)) = a(y * x,x,x \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,35120,a(flip),b,36457,a),flip(a)].">
      <j1 rule="hyper" parents="64 35120 36457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36460">
    <literal><![CDATA[
      (x \ 1) * (x \ ((x \ L(1 / x,x,x * y)) \ z)) = T(L(x,x,y) * (1 / x),x * x) \ z
    ]]></literal>
    <justification jstring="[para(1391(a,1),30660(a,1,2,2,1))].">
      <j1 rule="para" parents="1391 30660"/>
    </justification>
  </clause>

  <clause id="36461">
    <literal><![CDATA[
      a(x,y,(a(z,z,z \ u) \ w) \ v5) = a(x,y,((((u / z) / u) * z) \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(34737(a,1),30923(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="34737 30923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36462">
    <literal><![CDATA[
      a(x,y,(a(z,z,z \ u) \ w) \ v5) = a(x,y,(((u \ (u / z)) * z) \ w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,27676,a(flip),b,36461,a),flip(a)].">
      <j1 rule="hyper" parents="373 27676 36461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36463">
    <literal><![CDATA[
      a(x,y,(a(z,z,z \ u) \ w) \ v5) = a(x,y,((a(u,z,z) \ 1) \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(30493(a,1),36462(a,2,3,1,1))].">
      <j1 rule="para" parents="30493 36462"/>
    </justification>
  </clause>

  <clause id="36464">
    <literal><![CDATA[
      a(x,y,(z * (K(u,w) / z)) * (a(w,w,v5 * w) \ v6)) = a(x,y,(w * R(K(w,u) / w,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(34410(a,1),31237(a,1,3))].">
      <j1 rule="para" parents="34410 31237"/>
    </justification>
  </clause>

  <clause id="36465">
    <literal><![CDATA[
      a(x * (y * L(y \ ((z * z) \ y),u,w)),v5,v6) = a(x * (a(w,u,z * z) * y),v5,v6)
    ]]></literal>
    <justification jstring="[para(31256(a,1),31253(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="31256 31253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36466">
    <literal><![CDATA[
      a(x * (L(y * y,z,u) \ w),v5,v6) = a(x * (a(u,z,y * y) * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(31252(a,1),36465(a,1,1,2))].">
      <j1 rule="para" parents="31252 36465"/>
    </justification>
  </clause>

  <clause id="36467">
    <literal><![CDATA[
      a(x * (a(y,z,u * u) * w),v5,v6) = a(w * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26827,a(flip),b,36466,a),flip(a)].">
      <j1 rule="hyper" parents="64 26827 36466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36469">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u \ R(w,v5,v6)) \ L(w,v5,v6)) = a(x,y,(R(w,v5,v6) / u) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27304,a(flip),b,31679,a),flip(a)].">
      <j1 rule="hyper" parents="373 27304 31679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36471">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u \ R(w,v5,v6)) \ L(w,v5,v6)) = a(x,y,(u \ R(w,v5,v6)) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27317,a(flip),b,36469,a),flip(a)].">
      <j1 rule="hyper" parents="373 27317 36469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36472">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u \ L(w,v5,v6)) \ L(w,v5,v6)) = a(x,y,(u \ R(w,v5,v6)) * z)
    ]]></literal>
    <justification jstring="[para(33124(a,1),36471(a,1,3,1))].">
      <j1 rule="para" parents="33124 36471"/>
    </justification>
  </clause>

  <clause id="36473">
    <literal><![CDATA[
      a(x,y,T((L(z,u,w) / v5) * v6,v6 \ v5)) = a(x,y,(v5 \ R(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(15117(a,1),36472(a,1,3))].">
      <j1 rule="para" parents="15117 36472"/>
    </justification>
  </clause>

  <clause id="36474">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) / v5) * v6) = a(x,y,(v5 \ R(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(27584,a,36473,a)].">
      <j1 rule="hyper" parents="27584 36473"/>
    </justification>
  </clause>

  <clause id="36476">
    <literal><![CDATA[
      a(x,y,(z \ R(u,w,v5)) * v6) = a(x,y,(z \ L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,27317,a(flip),b,36474,a),flip(a)].">
      <j1 rule="hyper" parents="64 27317 36474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36477">
    <literal><![CDATA[
      a(x,L((1 / y) \ z,u,w) * (K(v5,y) * v6),v7) = a(x,L((y * y) * (z / T(y,v5)),u,w) * v6,v7)
    ]]></literal>
    <justification jstring="[para(26075(a,1),32252(a,1,2))].">
      <j1 rule="para" parents="26075 32252"/>
    </justification>
  </clause>

  <clause id="36478">
    <literal><![CDATA[
      a(x,L((y / (z * (u \ 1))) * ((u * u) \ 1),w,v5),v6) = a(x,L(y / (u * T(z,u \ 1)),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(553(a,1),32320(a,1,2,1,2))].">
      <j1 rule="para" parents="553 32320"/>
    </justification>
  </clause>

  <clause id="36479">
    <literal><![CDATA[
      a(((T(x \ 1,y * (x \ z)) \ x) * (((x \ 1) * y) * z)) \ u,w,v5) = a(((x * y) * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(25961(a,1),32501(a,1,1,1))].">
      <j1 rule="para" parents="25961 32501"/>
    </justification>
  </clause>

  <clause id="36480">
    <literal><![CDATA[
      R(1 / x,y,y \ 1) \ L(z,(x / (y \ 1)) / y,y \ (x / (y \ 1))) = ((x / (y \ 1)) / y) * z
    ]]></literal>
    <justification jstring="[para(23216(a,1),33386(a,1,2))].">
      <j1 rule="para" parents="23216 33386"/>
    </justification>
  </clause>

  <clause id="36481">
    <literal><![CDATA[
      L(L(a(L(x,y,z),y,z),y * x,y * x),y * x,y * x) = (y * R(x,y,z)) / (y * x)
    ]]></literal>
    <justification jstring="[para(36312(a,1),33394(a,1,1))].">
      <j1 rule="para" parents="36312 33394"/>
    </justification>
  </clause>

  <clause id="36482">
    <literal><![CDATA[
      L(a(x,y,L(y,z,u)),L(y,z,u),u * z) = (u * (z * y)) \ (u * (z * (y * a(x,y,y))))
    ]]></literal>
    <justification jstring="[para(100(a,1),33528(a,1,2)),flip(a)].">
      <j1 rule="para" parents="100 33528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36483">
    <literal><![CDATA[
      L(L(a(x,y,y),y,z),z * y,u) = L(a(x,y,L(y,z,u)),L(y,z,u),u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,602,a(flip),b,36482,a)].">
      <j1 rule="hyper" parents="373 602 36482"/>
    </justification>
  </clause>

  <clause id="36484">
    <literal><![CDATA[
      (x \ (x * ((x \ y) * y))) * K(z,z \ x) = T(y / (((z \ x) * z) / y),x)
    ]]></literal>
    <justification jstring="[para(25728(a,1),34312(a,1,1,2))].">
      <j1 rule="para" parents="25728 34312"/>
    </justification>
  </clause>

  <clause id="36485">
    <literal><![CDATA[
      T(x / (((y \ z) * y) / x),z) = ((z \ x) * x) * K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),36484(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 36484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36487">
    <literal><![CDATA[
      (x \ (y / (x / y))) * (z * (x / z)) = T(y / (((z \ x) * z) / y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,34330,a,b,36485,a)].">
      <j1 rule="hyper" parents="373 34330 36485"/>
    </justification>
  </clause>

  <clause id="36489">
    <literal><![CDATA[
      ((a(x,y,z) \ u) \ w) / (u \ w) = (u \ w) \ ((a(x,y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(23135(a,1),34697(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="23135 34697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36490">
    <literal><![CDATA[
      T(x,y * (T(T(y,z),u) \ (w * K(v5,K(y,u * z) * w)))) = T(x,T((T(T(y,z),u) \ y) * w,v5))
    ]]></literal>
    <justification jstring="[para(20810(a,1),34835(a,1,2))].">
      <j1 rule="para" parents="20810 34835"/>
    </justification>
  </clause>

  <clause id="36491">
    <literal><![CDATA[
      L(a(x,y,z),u,((x * y) * T(z,w)) \ (x * (y * T(z,w)))) = L(a(x,y,z),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(25591(a,1),35028(a,1,3))].">
      <j1 rule="para" parents="25591 35028"/>
    </justification>
  </clause>

  <clause id="36492">
    <literal><![CDATA[
      (((x * (x * R(x,y,z))) / x) / x) \ ((x \ 1) * u) = R(x * (x * x),y,z) \ ((1 / (1 / x)) * u)
    ]]></literal>
    <justification jstring="[para(2137(a,2),35044(a,2,1))].">
      <j1 rule="para" parents="2137 35044"/>
    </justification>
  </clause>

  <clause id="36493">
    <literal><![CDATA[
      a(x,x,x) \ L(L(y,x,L(x,z,u)),x * R(x,z,u),x) = R(x,z,u) \ L(R(x,z,u) * y,x,x)
    ]]></literal>
    <justification jstring="[para(29211(a,1),35062(a,1,2,1))].">
      <j1 rule="para" parents="29211 35062"/>
    </justification>
  </clause>

  <clause id="36494">
    <literal><![CDATA[
      (x \ 1) \ (x * (R(x,y,z) \ T(R(T(x,u),y,z),w))) = R(x \ 1,y,z) \ T(T(R(x,y,z),w),u)
    ]]></literal>
    <justification jstring="[para(27(a,2),35397(a,1,2,2,2,1))].">
      <j1 rule="para" parents="27 35397"/>
    </justification>
  </clause>

  <clause id="36495">
    <literal><![CDATA[
      L(x \ L(x,y,z),z \ (x * (L(x,y,z) \ z)),z) = 1 / (1 / ((x * (L(x,y,z) \ z)) \ z))
    ]]></literal>
    <justification jstring="[para(9375(a,1),35571(a,1,1))].">
      <j1 rule="para" parents="9375 35571"/>
    </justification>
  </clause>

  <clause id="36496">
    <literal><![CDATA[
      1 / (1 / ((x * (L(x,y,z) \ z)) \ z)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33190,a(flip),b,36495,a),flip(a)].">
      <j1 rule="hyper" parents="64 33190 36495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36498">
    <literal><![CDATA[
      1 / (1 / ((L(x,y,z) \ z) \ (x \ z))) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(33821(a,1),36496(a,1,2,2))].">
      <j1 rule="para" parents="33821 36496"/>
    </justification>
  </clause>

  <clause id="36499">
    <literal><![CDATA[
      1 / (((L(x,y,z) \ z) \ (x \ z)) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(28587(a,1),36498(a,1,2))].">
      <j1 rule="para" parents="28587 36498"/>
    </justification>
  </clause>

  <clause id="36500">
    <literal><![CDATA[
      (L(x,y,z) \ z) \ (x \ z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(330,a,36499,a),flip(a)].">
      <j1 rule="hyper" parents="330 36499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36502">
    <literal><![CDATA[
      a(x,(L(y,z,u) \ u) \ (y \ u),y) = L(y,z,u) \ (x \ ((x * (L(y,z,u) / y)) * y))
    ]]></literal>
    <justification jstring="[para(36500(a,2),30344(a,2,2)),flip(a)].">
      <j1 rule="para" parents="36500 30344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36503">
    <literal><![CDATA[
      a(x,(L(y,z,u) \ u) \ (y \ u),y) = L(y,z,u) \ (x \ ((x * (y \ L(y,z,u))) * y))
    ]]></literal>
    <justification jstring="[para(5572(a,1),36502(a,2,2,2,1,2))].">
      <j1 rule="para" parents="5572 36502"/>
    </justification>
  </clause>

  <clause id="36504">
    <literal><![CDATA[
      a(x,(L(y,z,u) \ u) \ (y \ u),y) = L(y,z,u) \ (x \ ((y \ L(y,z,u)) * (x * y)))
    ]]></literal>
    <justification jstring="[para(33138(a,1),36503(a,2,2,2))].">
      <j1 rule="para" parents="33138 36503"/>
    </justification>
  </clause>

  <clause id="36505">
    <literal><![CDATA[
      L(x,y,z) \ (u \ ((x \ L(x,y,z)) * (u * x))) = a(u,x \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(36500(a,1),36504(a,1,2)),flip(a)].">
      <j1 rule="para" parents="36500 36504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36506">
    <literal><![CDATA[
      L(x,y,z) \ (u \ ((x \ L(x,y,z)) * (u * x))) = a(u,x * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,35684,a(flip),b,36505,a),flip(a)].">
      <j1 rule="hyper" parents="373 35684 36505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36507">
    <literal><![CDATA[
      a(x,y,(z \ ((z \ u) * (1 / T(1 / z,u)))) * w) = a(x,y,(u * R(z \ 1,z,z \ u)) * w)
    ]]></literal>
    <justification jstring="[para(16395(a,1),36009(a,1,3,1,2))].">
      <j1 rule="para" parents="16395 36009"/>
    </justification>
  </clause>

  <clause id="36508">
    <literal><![CDATA[
      a(x,y,(z \ ((z \ u) * (T(1 / z,u) \ 1))) * w) = a(x,y,(u * R(z \ 1,z,z \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27475,a(flip),b,36507,a)].">
      <j1 rule="hyper" parents="64 27475 36507"/>
    </justification>
  </clause>

  <clause id="36509">
    <literal><![CDATA[
      a(x,y,T((z \ u) * K(u,1 / z),z) * w) = a(x,y,(u * R(z \ 1,z,z \ u)) * w)
    ]]></literal>
    <justification jstring="[para(24768(a,1),36508(a,1,3,1))].">
      <j1 rule="para" parents="24768 36508"/>
    </justification>
  </clause>

  <clause id="36510">
    <literal><![CDATA[
      a(x,y,T((z \ u) * K(u,z \ 1),z) * w) = a(x,y,(u * R(z \ 1,z,z \ u)) * w)
    ]]></literal>
    <justification jstring="[para(6041(a,1),36509(a,1,3,1,1,2))].">
      <j1 rule="para" parents="6041 36509"/>
    </justification>
  </clause>

  <clause id="36511">
    <literal><![CDATA[
      a(x,y,(z * R(u \ 1,u,u \ z)) * w) = a(x,y,T(u \ T(z,u \ 1),u) * w)
    ]]></literal>
    <justification jstring="[para(15021(a,1),36510(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="15021 36510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36512">
    <literal><![CDATA[
      a(x,y,(z * R(u \ 1,u,u \ z)) * w) = a(x,y,(u \ T(z,u \ 1)) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27312,a(flip),b,36511,a),flip(a)].">
      <j1 rule="hyper" parents="373 27312 36511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36514">
    <literal><![CDATA[
      a(x,y,(z * R(u \ 1,u,u \ z)) * w) = a(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27468,a(flip),b,36512,a),flip(a)].">
      <j1 rule="hyper" parents="373 27468 36512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36516">
    <literal><![CDATA[
      L(x,(y * R(T(y,z),u,w)) * ((v5 \ T(y,z)) \ v6),v7) = L(x,(y * L(y,u,w)) * ((v5 \ y) \ v6),v7)
    ]]></literal>
    <justification jstring="[para(25030(a,1),36283(a,1,2,1))].">
      <j1 rule="para" parents="25030 36283"/>
    </justification>
  </clause>

  <clause id="36517">
    <literal><![CDATA[
      T(L(x * (y \ L(y,z,u)),x,x),x \ (x \ 1)) = x * (x * ((x \ 1) * (y \ L(y,z,u))))
    ]]></literal>
    <justification jstring="[para(1139(a,1),36401(a,1,1))].">
      <j1 rule="para" parents="1139 36401"/>
    </justification>
  </clause>

  <clause id="36518">
    <literal><![CDATA[
      (x * y) / ((x * y) * y) = L((x / y) / x,y,y)
    ]]></literal>
    <justification jstring="[hyper(41,a,36247,a,b,36402,a),flip(a)].">
      <j1 rule="hyper" parents="41 36247 36402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36519">
    <literal><![CDATA[
      L(((x \ y) / x) / (x \ y),x,x) \ x = y / ((x \ y) / x)
    ]]></literal>
    <justification jstring="[para(36518(a,1),35875(a,1,1))].">
      <j1 rule="para" parents="36518 35875"/>
    </justification>
  </clause>

  <clause id="36520">
    <literal><![CDATA[
      L(T(x / (x * y),y),y,y) \ y = x / ((y \ x) / y)
    ]]></literal>
    <justification jstring="[para(26376(a,1),36519(a,1,1,1))].">
      <j1 rule="para" parents="26376 36519"/>
    </justification>
  </clause>

  <clause id="36521">
    <literal><![CDATA[
      x / ((y \ x) / y) = (x / (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(14269(a,1),36520(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14269 36520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36522">
    <literal><![CDATA[
      ((x / (x * y)) \ y) * (((y \ x) / y) / x) = 1
    ]]></literal>
    <justification jstring="[para(36521(a,1),35887(a,1,1))].">
      <j1 rule="para" parents="36521 35887"/>
    </justification>
  </clause>

  <clause id="36523">
    <literal><![CDATA[
      T((x * y) / T((x * y) * (1 / x),K(y,z)),1 / x) = (x * ((x \ 1) \ y)) / T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(3870(a,1),36411(a,2,2))].">
      <j1 rule="para" parents="3870 36411"/>
    </justification>
  </clause>

  <clause id="36524">
    <literal><![CDATA[
      (L(x,y,y) / z) \ (((K(u,y) / y) * ((T(y,u) * x) * z)) / z) = L(z,T(y,u) * x,1 / y)
    ]]></literal>
    <justification jstring="[para(24908(a,1),36412(a,1,2))].">
      <j1 rule="para" parents="24908 36412"/>
    </justification>
  </clause>

  <clause id="36525">
    <literal><![CDATA[
      L(x,T(y,z) * u,1 / y) = (L(u,y,y) / x) \ ((y * (((y \ 1) * u) * x)) / x)
    ]]></literal>
    <justification jstring="[para(27026(a,1),36524(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="27026 36524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36526">
    <literal><![CDATA[
      L(x,T(y,z) * u,y) = (L(u,y,y) / x) \ ((y * (((y \ 1) * u) * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(2273,a,36525,a)].">
      <j1 rule="hyper" parents="2273 36525"/>
    </justification>
  </clause>

  <clause id="36528">
    <literal><![CDATA[
      (L(x,y,y) / z) \ ((y * (((y \ 1) * x) * z)) / z) = L(z,y * x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29438,a(flip),b,36526,a),flip(a)].">
      <j1 rule="hyper" parents="64 29438 36526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36529">
    <literal><![CDATA[
      L((((x / y) / x) * y) \ z,(x \ (y \ x)) * y,y) = L(((y \ 1) * x) \ x,y,y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31147,a(flip),b,36413,a)].">
      <j1 rule="hyper" parents="64 31147 36413"/>
    </justification>
  </clause>

  <clause id="36530">
    <literal><![CDATA[
      L((((x / y) / x) * y) \ z,y,a(y,y,x)) = L(((y \ 1) * x) \ x,y,y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30416,a(flip),b,36529,a)].">
      <j1 rule="hyper" parents="64 30416 36529"/>
    </justification>
  </clause>

  <clause id="36531">
    <literal><![CDATA[
      T((x / (y * (z \ R(z,u,w)))) * y,z \ R(z,u,w)) = y * ((T(z \ R(z,u,w),v5) * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24388,a(flip),b,36414,a)].">
      <j1 rule="hyper" parents="64 24388 36414"/>
    </justification>
  </clause>

  <clause id="36532">
    <literal><![CDATA[
      (x / (y * (z \ R(z,u,w)))) * y = y * (((z \ R(z,u,w)) * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(41,a,27954,a(flip),b,36531,a),flip(a)].">
      <j1 rule="hyper" parents="41 27954 36531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36533">
    <literal><![CDATA[
      x * (((y \ R(y,z,u)) * x) \ (y \ R(y,z,u))) = a(x,x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,30057,a(flip),b,36532,a),flip(a)].">
      <j1 rule="hyper" parents="64 30057 36532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36534">
    <literal><![CDATA[
      a(x \ R(x,y,z),u,u \ 1) \ 1 = a(u,u,x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33361,a,b,36533,a)].">
      <j1 rule="hyper" parents="64 33361 36533"/>
    </justification>
  </clause>

  <clause id="36535">
    <literal><![CDATA[
      a(x * R(x,y,z),u,u \ 1) \ 1 = a(u,u,x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(2664(a,1),36534(a,1,1))].">
      <j1 rule="para" parents="2664 36534"/>
    </justification>
  </clause>

  <clause id="36536">
    <literal><![CDATA[
      R(x,y,(z / (u / (w \ v5))) \ (K(w \ v5,w) * v6)) = R(x,y,(T(u / (v5 / w),K(w,v5)) \ z) \ v6)
    ]]></literal>
    <justification jstring="[para(23199(a,1),36429(a,1,3))].">
      <j1 rule="para" parents="23199 36429"/>
    </justification>
  </clause>

  <clause id="36537">
    <literal><![CDATA[
      ((x \ (x \ y)) / y) \ K((x \ (x \ y)) \ y,z) = T((y \ (x \ (x \ y))) \ K(y,x * x),z)
    ]]></literal>
    <justification jstring="[para(14444(a,1),36434(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14444 36434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36538">
    <literal><![CDATA[
      ((x \ (x \ y)) / y) \ K((x \ (x \ y)) \ y,z) = T(((x \ (x \ y)) / y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(26725(a,1),36537(a,2,1))].">
      <j1 rule="para" parents="26725 36537"/>
    </justification>
  </clause>

  <clause id="36539">
    <literal><![CDATA[
      ((x \ (x \ y)) / y) \ K(((x \ y) \ x) * y,z) = T(((x \ (x \ y)) / y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(28209(a,1),36538(a,1,2))].">
      <j1 rule="para" parents="28209 36538"/>
    </justification>
  </clause>

  <clause id="36540">
    <literal><![CDATA[
      ((x \ (x \ y)) / y) \ K((y \ x) * (x * y),z) = T(((x \ (x \ y)) / y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(28220(a,1),36539(a,1,2))].">
      <j1 rule="para" parents="28220 36539"/>
    </justification>
  </clause>

  <clause id="36541">
    <literal><![CDATA[
      ((x \ (x \ y)) / y) \ K(x * (x * (y \ y)),z) = T(((x \ (x \ y)) / y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(28907(a,1),36540(a,1,2))].">
      <j1 rule="para" parents="28907 36540"/>
    </justification>
  </clause>

  <clause id="36542">
    <literal><![CDATA[
      ((x \ (x \ y)) / y) \ K(x * x,z) = T(((x \ (x \ y)) / y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(191(a,1),36541(a,1,2,1,2))].">
      <j1 rule="para" parents="191 36541"/>
    </justification>
  </clause>

  <clause id="36543">
    <literal><![CDATA[
      T((x \ (x \ y)) / y,x \ (x \ y)) \ 1 = T(((x \ (x \ y)) / y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,36075,a,b,36542,a)].">
      <j1 rule="hyper" parents="64 36075 36542"/>
    </justification>
  </clause>

  <clause id="36544">
    <literal><![CDATA[
      K(x,T((K(y,y \ z) / u) * (y \ z),w) * v5) = K(x,T((z / y) / u,w * (z * y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,28934,a(flip),b,36444,a),flip(a)].">
      <j1 rule="hyper" parents="373 28934 36444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36545">
    <literal><![CDATA[
      K(x,T((K(y,y \ z) / u) * (y \ z),w) * v5) = K(x,T(z / (u * y),w * (z * y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,28129,a(flip),b,36544,a),flip(a)].">
      <j1 rule="hyper" parents="373 28129 36544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36546">
    <literal><![CDATA[
      K(x,T((K(y,y \ z) / u) * (y \ z),w) * v5) = K(x,T((u * y) \ z,w * y) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,33987,a(flip),b,36545,a),flip(a)].">
      <j1 rule="hyper" parents="373 33987 36545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36547">
    <literal><![CDATA[
      K(x,T((K(y,y \ z) / u) * (y \ z),w) * v5) = K(x,T(y \ (u \ z),w * y) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,28350,a(flip),b,36546,a),flip(a)].">
      <j1 rule="hyper" parents="373 28350 36546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36548">
    <literal><![CDATA[
      K(x,T((K(y,y \ z) / u) * (y \ z),w) * v5) = K(x,T((u \ z) / y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,28958,a(flip),b,36547,a),flip(a)].">
      <j1 rule="hyper" parents="373 28958 36547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36549">
    <literal><![CDATA[
      R(T(x \ a(x,x,y),y),x \ a(x,x,y),y) = L(y,x \ a(x,x,y),R(x,x,y)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(30053(a,1),36448(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="30053 36448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36550">
    <literal><![CDATA[
      R(T(x \ a(x,x,y),y),x \ a(x,x,y),y) = L(y,x \ a(x,x,y),L(x,x,y)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(29203(a,1),36549(a,2,1))].">
      <j1 rule="para" parents="29203 36549"/>
    </justification>
  </clause>

  <clause id="36551">
    <literal><![CDATA[
      R(T(x \ a(x,x,y),y),x \ a(x,x,y),y) = L(y,x * a(x,x,y),L(x,x,y)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(16066(a,1),36550(a,2,1))].">
      <j1 rule="para" parents="16066 36550"/>
    </justification>
  </clause>

  <clause id="36552">
    <literal><![CDATA[
      R(T(x \ a(x,x,y),y),x \ a(x,x,y),y) = L(y,R(x,x,y),L(x,x,y)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(30054(a,1),36551(a,2,1,2))].">
      <j1 rule="para" parents="30054 36551"/>
    </justification>
  </clause>

  <clause id="36553">
    <literal><![CDATA[
      R(T(x \ a(x,x,y),y),x \ a(x,x,y),y) = L(y,x,x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(31753(a,1),36552(a,2,1))].">
      <j1 rule="para" parents="31753 36552"/>
    </justification>
  </clause>

  <clause id="36554">
    <literal><![CDATA[
      R(x \ (y \ x),y \ a(y,y,x),x) = L(x,y,y) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(30124(a,1),36553(a,1,1))].">
      <j1 rule="para" parents="30124 36553"/>
    </justification>
  </clause>

  <clause id="36555">
    <literal><![CDATA[
      a(x,L((y * y) * (z / T(y,u)),w,v5) * v6,v7) = a(x,L((1 / y) \ z,w,v5) * v6,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,31913,a(flip),b,36477,a),flip(a)].">
      <j1 rule="hyper" parents="64 31913 36477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36557">
    <literal><![CDATA[
      a(x,L((y / (z * (u \ 1))) / (u * u),w,v5),v6) = a(x,L(y / (u * T(z,u \ 1)),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(557(a,1),36478(a,1,2,1))].">
      <j1 rule="para" parents="557 36478"/>
    </justification>
  </clause>

  <clause id="36558">
    <literal><![CDATA[
      a(x,L(y / ((z * z) * (u * (z \ 1))),w,v5),v6) = a(x,L(y / (z * T(u,z \ 1)),w,v5),v6)
    ]]></literal>
    <justification jstring="[para(496(a,1),36557(a,1,2,1))].">
      <j1 rule="para" parents="496 36557"/>
    </justification>
  </clause>

  <clause id="36559">
    <literal><![CDATA[
      a(x,L(y / (z * T(u,z \ 1)),w,v5),v6) = a(x,L((u * (z \ 1)) \ y,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32992,a(flip),b,36558,a),flip(a)].">
      <j1 rule="hyper" parents="64 32992 36558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36561">
    <literal><![CDATA[
      a(x,L((y * (z \ 1)) \ u,w,v5),v6) = a(x,L((z * y) \ u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32881,a(flip),b,36559,a),flip(a)].">
      <j1 rule="hyper" parents="64 32881 36559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36563">
    <literal><![CDATA[
      a((((x \ 1) * y) * z) \ ((x \ T(x \ 1,y * (x \ z))) * u),w,v5) = a(((x * y) * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(31521(a,1),36479(a,1,1))].">
      <j1 rule="para" parents="31521 36479"/>
    </justification>
  </clause>

  <clause id="36564">
    <literal><![CDATA[
      R(1 / x,y,y \ 1) \ L(z,(x / (y \ 1)) / y,y \ ((y \ 1) \ x)) = ((x / (y \ 1)) / y) * z
    ]]></literal>
    <justification jstring="[para(29023(a,1),36480(a,1,2))].">
      <j1 rule="para" parents="29023 36480"/>
    </justification>
  </clause>

  <clause id="36565">
    <literal><![CDATA[
      T(x,y * ((T(T(y,z),u) \ w) * K(v5,K(y,u * z) * w))) = T(x,T((T(T(y,z),u) \ y) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,28285,a(flip),b,36490,a)].">
      <j1 rule="hyper" parents="64 28285 36490"/>
    </justification>
  </clause>

  <clause id="36566">
    <literal><![CDATA[
      (((x * (x * R(x,y,z))) / x) / x) \ ((x \ 1) * u) = (x * x) \ (R(x,y,z) \ ((1 / (1 / x)) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,2105,a(flip),b,36492,a),flip(a)].">
      <j1 rule="hyper" parents="373 2105 36492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36567">
    <literal><![CDATA[
      a(x,x,x) \ L(L(y,x,L(x,z,u)),x,x * L(x,z,u)) = R(x,z,u) \ L(R(x,z,u) * y,x,x)
    ]]></literal>
    <justification jstring="[para(33577(a,1),36493(a,1,2))].">
      <j1 rule="para" parents="33577 36493"/>
    </justification>
  </clause>

  <clause id="36568">
    <literal><![CDATA[
      (x \ 1) \ (x * (R(x,y,z) \ R(T(T(x,u),w),y,z))) = R(x \ 1,y,z) \ T(T(R(x,y,z),w),u)
    ]]></literal>
    <justification jstring="[para(27(a,2),36494(a,1,2,2,2))].">
      <j1 rule="para" parents="27 36494"/>
    </justification>
  </clause>

  <clause id="36569">
    <literal><![CDATA[
      L(x,T(y * R(y,z,u),y) * ((w \ T(y,y \ 1)) \ v5),v6) = L(x,(y * L(y,z,u)) * ((w \ y) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(25679(a,1),36516(a,1,2,1))].">
      <j1 rule="para" parents="25679 36516"/>
    </justification>
  </clause>

  <clause id="36570">
    <literal><![CDATA[
      T((x * y) / T((x * y) * (1 / x),K(y,z)),1 / x) = x * ((x \ 1) \ (y / T(x * y,x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,29420,a(flip),b,36523,a),flip(a)].">
      <j1 rule="hyper" parents="373 29420 36523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36571">
    <literal><![CDATA[
      R(x,y,(T(z / (u / w),K(w,u)) \ v5) \ v6) = R(x,y,(v5 / (z / (w \ u))) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26189,a(flip),b,36536,a),flip(a)].">
      <j1 rule="hyper" parents="64 26189 36536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36573">
    <literal><![CDATA[
      R(x,y,(T(z / (u / w),K(w,u)) \ v5) \ v6) = R(x,y,((z / (w \ u)) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,26209,a(flip),b,36571,a),flip(a)].">
      <j1 rule="hyper" parents="373 26209 36571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36574">
    <literal><![CDATA[
      R(x,y,(T(z / (u / w),K(w,u)) \ v5) \ v6) = R(x,y,(((w \ u) \ z) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,26280,a(flip),b,36573,a),flip(a)].">
      <j1 rule="hyper" parents="373 26280 36573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36575">
    <literal><![CDATA[
      R(x,y,((z / (u / w)) \ v5) \ v6) = R(x,y,(((w \ u) \ z) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26219,a(flip),b,36574,a)].">
      <j1 rule="hyper" parents="64 26219 36574"/>
    </justification>
  </clause>

  <clause id="36577">
    <literal><![CDATA[
      R(x,y,(((z / u) \ w) \ v5) \ v6) = R(x,y,(((u \ z) \ w) \ v5) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26280,a(flip),b,36575,a)].">
      <j1 rule="hyper" parents="64 26280 36575"/>
    </justification>
  </clause>

  <clause id="36578">
    <literal><![CDATA[
      a((((x \ 1) * y) * z) \ ((x \ (x \ 1)) * u),w,v5) = a(((x * y) * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32685,a(flip),b,36563,a)].">
      <j1 rule="hyper" parents="64 32685 36563"/>
    </justification>
  </clause>

  <clause id="36580">
    <literal><![CDATA[
      a((((x \ 1) * y) * z) \ ((x \ x) * u),w,v5) = a(((x * y) * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32827,a(flip),b,36578,a)].">
      <j1 rule="hyper" parents="64 32827 36578"/>
    </justification>
  </clause>

  <clause id="36581">
    <literal><![CDATA[
      a((((x \ 1) * y) * z) \ u,w,v5) = a(((x * y) * z) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(190(a,1),36580(a,1,1,2))].">
      <j1 rule="para" parents="190 36580"/>
    </justification>
  </clause>

  <clause id="36582">
    <literal><![CDATA[
      a((x * ((y \ 1) * z)) \ u,w,v5) = a(((y * z) * x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(32451,a,36581,a)].">
      <j1 rule="hyper" parents="32451 36581"/>
    </justification>
  </clause>

  <clause id="36583">
    <literal><![CDATA[
      a(L(R(x,x,y),(x \ 1) * y,z),u,w) = a(((x * y) * z) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32786,a,b,36582,a)].">
      <j1 rule="hyper" parents="64 32786 36582"/>
    </justification>
  </clause>

  <clause id="36584">
    <literal><![CDATA[
      a(L(R(x,x,y),x * y,z),u,w) = a(((x * y) * z) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(11864(a,1),36583(a,1,1))].">
      <j1 rule="para" parents="11864 36583"/>
    </justification>
  </clause>

  <clause id="36585">
    <literal><![CDATA[
      a(L(L(x,x,y),x * y,z),u,w) = a(((x * y) * z) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32711,a(flip),b,36584,a)].">
      <j1 rule="hyper" parents="64 32711 36584"/>
    </justification>
  </clause>

  <clause id="36586">
    <literal><![CDATA[
      a(L(L(x,x,y),x * y,z),u,w) = a((z * (x * y)) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32504,a,b,36585,a),flip(a)].">
      <j1 rule="hyper" parents="373 32504 36585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36587">
    <literal><![CDATA[
      R(1 / x,y,y \ 1) \ L(z,(x / (y \ 1)) / y,L(x,y,y)) = ((x / (y \ 1)) / y) * z
    ]]></literal>
    <justification jstring="[para(30393(a,1),36564(a,1,2))].">
      <j1 rule="para" parents="30393 36564"/>
    </justification>
  </clause>

  <clause id="36588">
    <literal><![CDATA[
      R(1 / x,y,y \ 1) \ L(z,y \ (x / (y \ 1)),L(x,y,y)) = ((x / (y \ 1)) / y) * z
    ]]></literal>
    <justification jstring="[para(29437(a,1),36587(a,1,2))].">
      <j1 rule="para" parents="29437 36587"/>
    </justification>
  </clause>

  <clause id="36589">
    <literal><![CDATA[
      R(1 / x,y,y \ 1) \ L(z,y \ ((y \ 1) \ x),L(x,y,y)) = ((x / (y \ 1)) / y) * z
    ]]></literal>
    <justification jstring="[para(29552(a,1),36588(a,1,2))].">
      <j1 rule="para" parents="29552 36588"/>
    </justification>
  </clause>

  <clause id="36590">
    <literal><![CDATA[
      R(1 / x,y,y \ 1) \ L(z,y \ (y \ x),L(x,y,y)) = ((x / (y \ 1)) / y) * z
    ]]></literal>
    <justification jstring="[para(30873(a,1),36589(a,1,2))].">
      <j1 rule="para" parents="30873 36589"/>
    </justification>
  </clause>

  <clause id="36591">
    <literal><![CDATA[
      R(1 / x,y,y \ 1) \ L(z,L(x,y,y),L(x,y,y)) = ((x / (y \ 1)) / y) * z
    ]]></literal>
    <justification jstring="[para(31756(a,1),36590(a,1,2))].">
      <j1 rule="para" parents="31756 36590"/>
    </justification>
  </clause>

  <clause id="36592">
    <literal><![CDATA[
      R(1 / x,y,y \ 1) \ L(z,x,x) = ((x / (y \ 1)) / y) * z
    ]]></literal>
    <justification jstring="[para(35161(a,1),36591(a,1,2))].">
      <j1 rule="para" parents="35161 36591"/>
    </justification>
  </clause>

  <clause id="36593">
    <literal><![CDATA[
      x * (x * (R(x,y,y \ 1) \ z)) = ((x / (y \ 1)) / y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,2636,a(flip),b,36592,a)].">
      <j1 rule="hyper" parents="64 2636 36592"/>
    </justification>
  </clause>

  <clause id="36595">
    <literal><![CDATA[
      x * (x * (R(x,y \ 1,(y \ 1) \ 1) \ ((y * y) \ z))) = ((x / ((y \ 1) \ 1)) / (1 / (1 / y))) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,2022,a(flip),b,36593,a),flip(a)].">
      <j1 rule="hyper" parents="373 2022 36593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36596">
    <literal><![CDATA[
      T(x,y * ((T(T(y,z),u) \ w) * K(w,v5))) = T(x,T((T(T(y,z),u) \ y) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,19632,a(flip),b,36565,a)].">
      <j1 rule="hyper" parents="64 19632 36565"/>
    </justification>
  </clause>

  <clause id="36598">
    <literal><![CDATA[
      T(x,T((T(T(y,z),u) \ y) * w,v5)) = T(x,y * (T(T(y,z),u) \ T(w,v5)))
    ]]></literal>
    <justification jstring="[para(15021(a,1),36596(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15021 36596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36599">
    <literal><![CDATA[
      T(x,T((T(T(y,z),u) \ y) * w,v5)) = T(x,T(w,v5) * K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,31509,a(flip),b,36598,a),flip(a)].">
      <j1 rule="hyper" parents="373 31509 36598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36600">
    <literal><![CDATA[
      T(x,T((T(T(y,z),u) \ y) * w,v5)) = T(x,T(K(y,z * u) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,18049,a,b,36599,a),flip(a)].">
      <j1 rule="hyper" parents="373 18049 36599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36601">
    <literal><![CDATA[
      T(x,T(K(y,z * u) * (w * v5),v5)) = T(x,v5 * (y * (T(T(y,z),u) \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,28780,a(flip),b,36600,a),flip(a)].">
      <j1 rule="hyper" parents="64 28780 36600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36602">
    <literal><![CDATA[
      T(x,y * (z * (T(T(z,u),w) \ v5))) = T(x,y * (v5 * K(z,u * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,28778,a(flip),b,36601,a),flip(a)].">
      <j1 rule="hyper" parents="64 28778 36601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36603">
    <literal><![CDATA[
      T(x,y * T(T(T(z,u),w) \ v5,z)) = T(x,y * ((v5 / z) * K(z,u * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27999,a(flip),b,36602,a)].">
      <j1 rule="hyper" parents="64 27999 36602"/>
    </justification>
  </clause>

  <clause id="36604">
    <literal><![CDATA[
      T(x,y * T(T(T(z,u),w) \ v5,z)) = T(x,y * (v5 / T(z,u * w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,24782,a(flip),b,36603,a),flip(a)].">
      <j1 rule="hyper" parents="373 24782 36603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36605">
    <literal><![CDATA[
      T(x,y * (z / T(T(u,w),v5))) = T(x,y * (z / T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,18556,a(flip),b,36604,a)].">
      <j1 rule="hyper" parents="64 18556 36604"/>
    </justification>
  </clause>

  <clause id="36606">
    <literal><![CDATA[
      T(x,y * ((z * u) / T(w,u * v5))) = T(x,y * (z * (T(w,v5) \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,28279,a(flip),b,36605,a),flip(a)].">
      <j1 rule="hyper" parents="64 28279 36605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36607">
    <literal><![CDATA[
      (((x * (x * R(x,y,z))) / x) / x) \ ((x \ 1) * u) = (x \ 1) * (x \ (R(x,y,z) \ (x * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,18905,a(flip),b,36566,a),flip(a)].">
      <j1 rule="hyper" parents="373 18905 36566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36608">
    <literal><![CDATA[
      (((x * (x * R(x,y,z))) / x) / x) \ ((x \ 1) * u) = (x \ 1) * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(1929(a,1),36607(a,2,2))].">
      <j1 rule="para" parents="1929 36607"/>
    </justification>
  </clause>

  <clause id="36609">
    <literal><![CDATA[
      L(R(x,y,z),x,x) \ ((x \ 1) * u) = (x \ 1) * (R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(35038(a,1),36608(a,1,1))].">
      <j1 rule="para" parents="35038 36608"/>
    </justification>
  </clause>

  <clause id="36610">
    <literal><![CDATA[
      (x \ 1) * (R(x,y,z) \ (x * u)) = R(x,y,z) \ L(u,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,35063,a(flip),b,36609,a),flip(a)].">
      <j1 rule="hyper" parents="64 35063 36609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36611">
    <literal><![CDATA[
      R(x,y,z) \ L(R(x,y,z) * u,x,x) = (x \ 1) * (x * u)
    ]]></literal>
    <justification jstring="[para(1905(a,1),36610(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1905 36610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36612">
    <literal><![CDATA[
      R(x,y,z) \ L(R(x,y,z) * u,x,x) = a(x,x,x) \ L(u,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,3693,a,b,36611,a),flip(a)].">
      <j1 rule="hyper" parents="373 3693 36611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36613">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * (R(x,y,z) * u) = (x \ 1) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,35176,a(flip),b,36611,a)].">
      <j1 rule="hyper" parents="64 35176 36611"/>
    </justification>
  </clause>

  <clause id="36614">
    <literal><![CDATA[
      R(x,y,z) \ ((R(x,y,z) \ 1) \ u) = (u \ ((x \ 1) * (x * u))) \ u
    ]]></literal>
    <justification jstring="[para(36613(a,1),30445(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="36613 30445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36615">
    <literal><![CDATA[
      R(x,y,z) \ ((R(x,y,z) \ 1) \ u) = x \ ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,30445,a(flip),b,36614,a),flip(a)].">
      <j1 rule="hyper" parents="373 30445 36614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36616">
    <literal><![CDATA[
      R(x,y,z) \ ((R(x,y,z) \ 1) \ u) = L(x,w,v5) \ ((L(x,w,v5) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,35208,a,b,36615,a),flip(a)].">
      <j1 rule="hyper" parents="373 35208 36615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36617">
    <literal><![CDATA[
      R(x,y,(L(z,u,w) \ ((L(z,u,w) \ 1) \ v5)) * R(z,v6,v7)) = R(x,y,(R(z,v6,v7) \ 1) \ v5)
    ]]></literal>
    <justification jstring="[para(36616(a,1),26165(a,1,3,1))].">
      <j1 rule="para" parents="36616 26165"/>
    </justification>
  </clause>

  <clause id="36618">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ ((L(z,u,w) \ 1) \ v5)) * R(z,v6,v7)) = a(x,y,(R(z,v6,v7) \ 1) \ v5)
    ]]></literal>
    <justification jstring="[para(36616(a,1),27299(a,1,3,1))].">
      <j1 rule="para" parents="36616 27299"/>
    </justification>
  </clause>

  <clause id="36619">
    <literal><![CDATA[
      R(x,y,(L(z,u,w) \ ((L(z,u,w) \ 1) \ v5)) * L(z,v6,v7)) = R(x,y,(R(z,v6,v7) \ 1) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34419,a(flip),b,36617,a)].">
      <j1 rule="hyper" parents="64 34419 36617"/>
    </justification>
  </clause>

  <clause id="36620">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ ((L(z,u,w) \ 1) \ v5)) * L(z,v6,v7)) = a(x,y,(R(z,v6,v7) \ 1) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31317,a(flip),b,36618,a)].">
      <j1 rule="hyper" parents="64 31317 36618"/>
    </justification>
  </clause>

  <clause id="36621">
    <literal><![CDATA[
      R(x,y,(R(z,u,w) \ 1) \ v5) = R(x,y,(L(z,u,w) \ 1) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26165,a(flip),b,36619,a),flip(a)].">
      <j1 rule="hyper" parents="64 26165 36619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36622">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) \ 1) \ v5) = a(x,y,(L(z,u,w) \ 1) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27299,a(flip),b,36620,a),flip(a)].">
      <j1 rule="hyper" parents="64 27299 36620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36623">
    <literal><![CDATA[
      L(L(x,y,L(y,z,u)),y,y * L(y,z,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,36612,a(flip),b,36567,a),flip(a)].">
      <j1 rule="hyper" parents="39 36612 36567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36624">
    <literal><![CDATA[
      L(L(x,y,z \ (y \ z)),y,y * L(y,y,z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(35048(a,1),36623(a,1,1))].">
      <j1 rule="para" parents="35048 36623"/>
    </justification>
  </clause>

  <clause id="36626">
    <literal><![CDATA[
      L(L(x,y,z \ (y \ z)),y,a(y,y,z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30562,a(flip),b,36624,a)].">
      <j1 rule="hyper" parents="64 30562 36624"/>
    </justification>
  </clause>

  <clause id="36627">
    <literal><![CDATA[
      R(x \ 1,y,z) \ T(T(R(x,y,z),u),w) = (x \ 1) \ (x * (x \ T(T(x,w),u)))
    ]]></literal>
    <justification jstring="[para(31488(a,1),36568(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="31488 36568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36628">
    <literal><![CDATA[
      R(x \ 1,y,z) \ T(T(R(x,y,z),u),w) = (x \ 1) \ T(T(x,w),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),36627(a,2,2))].">
      <j1 rule="para" parents="10 36627"/>
    </justification>
  </clause>

  <clause id="36631">
    <literal><![CDATA[
      R(x \ 1,y,z) \ T(R(T(x,u),y,z),w) = (x \ 1) \ T(T(x,w),u)
    ]]></literal>
    <justification jstring="[para(27(a,2),36628(a,1,2,1))].">
      <j1 rule="para" parents="27 36628"/>
    </justification>
  </clause>

  <clause id="36632">
    <literal><![CDATA[
      R(x \ 1,y,z) \ R(T(T(x,u),w),y,z) = (x \ 1) \ T(T(x,w),u)
    ]]></literal>
    <justification jstring="[para(27(a,2),36631(a,1,2))].">
      <j1 rule="para" parents="27 36631"/>
    </justification>
  </clause>

  <clause id="36633">
    <literal><![CDATA[
      a(x,y,R(T(z \ 1,u),w,v5) \ R(T(T(z,v6),v7),w,v5)) = a(x,y,(z \ 1) \ T(T(z,v7),v6))
    ]]></literal>
    <justification jstring="[para(36632(a,1),27408(a,2,3))].">
      <j1 rule="para" parents="36632 27408"/>
    </justification>
  </clause>

  <clause id="36634">
    <literal><![CDATA[
      a(x,y,R(T(z \ 1,u),w,v5) \ L(T(z,v6),w,v5)) = a(x,y,(z \ 1) \ T(T(z,v7),v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,31677,a(flip),b,36633,a)].">
      <j1 rule="hyper" parents="64 31677 36633"/>
    </justification>
  </clause>

  <clause id="36636">
    <literal><![CDATA[
      a(x,y,R(T(z \ 1,u),w,v5) \ L(z,w,v5)) = a(x,y,(z \ 1) \ T(T(z,v6),v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,27324,a(flip),b,36634,a)].">
      <j1 rule="hyper" parents="64 27324 36634"/>
    </justification>
  </clause>

  <clause id="36638">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) \ L(z,u,w)) = a(x,y,(z \ 1) \ T(T(z,v5),v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,31335,a(flip),b,36636,a)].">
      <j1 rule="hyper" parents="64 31335 36636"/>
    </justification>
  </clause>

  <clause id="36639">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) \ L(z,u,w)) = a(x,y,(z \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(374(a,1),36638(a,2,3,2))].">
      <j1 rule="para" parents="374 36638"/>
    </justification>
  </clause>

  <clause id="36640">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) \ L(z,u,w)) = a(x,y,z * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27525,a(flip),b,36639,a),flip(a)].">
      <j1 rule="hyper" parents="373 27525 36639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36641">
    <literal><![CDATA[
      T((x * y) / T((x * y) * (1 / x),K(y,z)),1 / x) = x * ((x \ 1) \ ((x * y) \ y))
    ]]></literal>
    <justification jstring="[para(4591(a,1),36570(a,2,2,2))].">
      <j1 rule="para" parents="4591 36570"/>
    </justification>
  </clause>

  <clause id="36642">
    <literal><![CDATA[
      T((x * y) / T((x * y) * (1 / x),K(y,z)),1 / x) = x * (x * ((x * y) \ y))
    ]]></literal>
    <justification jstring="[para(26264(a,1),36641(a,2,2))].">
      <j1 rule="para" parents="26264 36641"/>
    </justification>
  </clause>

  <clause id="36643">
    <literal><![CDATA[
      T((x * y) / ((x * y) * (1 / x)),1 / x) = x * (x * ((x * y) \ y))
    ]]></literal>
    <justification jstring="[para(3347(a,1),36642(a,1,1,2))].">
      <j1 rule="para" parents="3347 36642"/>
    </justification>
  </clause>

  <clause id="36644">
    <literal><![CDATA[
      T((x / (1 / y)) / x,1 / y) = y * (y * ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(25581(a,1),36643(a,1,1))].">
      <j1 rule="para" parents="25581 36643"/>
    </justification>
  </clause>

  <clause id="36645">
    <literal><![CDATA[
      T((x / (1 / y)) / x,y \ 1) = y * (y * ((y * x) \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,3870,a(flip),b,36644,a)].">
      <j1 rule="hyper" parents="64 3870 36644"/>
    </justification>
  </clause>

  <clause id="36646">
    <literal><![CDATA[
      T((x / (y \ 1)) / x,y * 1) = y * (y * ((y * x) \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,36156,a(flip),b,36645,a)].">
      <j1 rule="hyper" parents="64 36156 36645"/>
    </justification>
  </clause>

  <clause id="36647">
    <literal><![CDATA[
      T((x / (y \ 1)) / x,y) = y * (y * ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(8(a,1),36646(a,1,2))].">
      <j1 rule="para" parents="8 36646"/>
    </justification>
  </clause>

  <clause id="36648">
    <literal><![CDATA[
      x \ ((y / (x \ 1)) / y) = x * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(139,a,6810,a(flip),b,36647,a(flip))].">
      <j1 rule="hyper" parents="139 6810 36647"/>
    </justification>
  </clause>

  <clause id="36649">
    <literal><![CDATA[
      ((x / (y \ 1)) / x) / y = y * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,31496,a,b,36648,a)].">
      <j1 rule="hyper" parents="64 31496 36648"/>
    </justification>
  </clause>

  <clause id="36650">
    <literal><![CDATA[
      L((x \ R((x * y) \ y,x,x)) \ z,((y / (x \ 1)) / y) / x,x) = R((x * y) \ y,x,x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(36649(a,2),34796(a,1,2))].">
      <j1 rule="para" parents="36649 34796"/>
    </justification>
  </clause>

  <clause id="36651">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) * R(y \ 1,y \ 1,x * ((1 / y) \ y)) = y \ ((y \ 1) \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,207,a(flip),b,24614,a),flip(a)].">
      <j1 rule="hyper" parents="373 207 24614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36653">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) * R(y \ 1,y \ 1,(y * y) * x) = y \ ((y \ 1) \ (x * y))
    ]]></literal>
    <justification jstring="[para(26242(a,1),36651(a,1,2))].">
      <j1 rule="para" parents="26242 36651"/>
    </justification>
  </clause>

  <clause id="36654">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) * R(y \ 1,y,(y * y) * x) = y \ ((y \ 1) \ (x * y))
    ]]></literal>
    <justification jstring="[para(2975(a,1),36653(a,1,2))].">
      <j1 rule="para" parents="2975 36653"/>
    </justification>
  </clause>

  <clause id="36655">
    <literal><![CDATA[
      (x * ((1 / y) \ y)) * R(y / (y * y),y,x) = y \ ((y \ 1) \ (x * y))
    ]]></literal>
    <justification jstring="[para(3050(a,1),36654(a,1,2))].">
      <j1 rule="para" parents="3050 36654"/>
    </justification>
  </clause>

  <clause id="36656">
    <literal><![CDATA[
      x * (y * ((y \ 1) \ R(y / (y * y),y,x))) = y \ ((y \ 1) \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,1611,a(flip),b,36655,a)].">
      <j1 rule="hyper" parents="64 1611 36655"/>
    </justification>
  </clause>

  <clause id="36657">
    <literal><![CDATA[
      x * R(y * ((y \ 1) \ (y / (y * y))),y,x) = y \ ((y \ 1) \ (x * y))
    ]]></literal>
    <justification jstring="[para(2146(a,2),36656(a,1,2))].">
      <j1 rule="para" parents="2146 36656"/>
    </justification>
  </clause>

  <clause id="36658">
    <literal><![CDATA[
      x * R(y * (y * (y / (y * y))),y,x) = y \ ((y \ 1) \ (x * y))
    ]]></literal>
    <justification jstring="[para(15114(a,1),36657(a,1,2,1,2))].">
      <j1 rule="para" parents="15114 36657"/>
    </justification>
  </clause>

  <clause id="36659">
    <literal><![CDATA[
      x * R(R(y,y,y * y),y,x) = y \ ((y \ 1) \ (x * y))
    ]]></literal>
    <justification jstring="[para(26283(a,1),36658(a,1,2,1))].">
      <j1 rule="para" parents="26283 36658"/>
    </justification>
  </clause>

  <clause id="36660">
    <literal><![CDATA[
      x * R(y,y,(y * y) * x) = y \ ((y \ 1) \ (x * y))
    ]]></literal>
    <justification jstring="[para(26512(a,1),36659(a,1,2))].">
      <j1 rule="para" parents="26512 36659"/>
    </justification>
  </clause>

  <clause id="36661">
    <literal><![CDATA[
      x * R(y,y,y * (y * x)) = y \ ((y \ 1) \ (x * y))
    ]]></literal>
    <justification jstring="[para(26352(a,1),36660(a,1,2))].">
      <j1 rule="para" parents="26352 36660"/>
    </justification>
  </clause>

  <clause id="36662">
    <literal><![CDATA[
      a(x,y,L(R(z,z,z * (z * u)) * u,w,v5)) = a(x,y,L(z \ ((z \ 1) \ (u * z)),w,v5))
    ]]></literal>
    <justification jstring="[para(36661(a,1),27377(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="36661 27377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36663">
    <literal><![CDATA[
      R(T(x,y),z,u) * (w / R(x,z,u)) = (x * (w / x)) * T(K(x,y),T(w,R(x,z,u)))
    ]]></literal>
    <justification jstring="[para(25185(a,1),25344(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25185 25344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36664">
    <literal><![CDATA[
      R(T(x,y),z,u) * (w / R(x,z,u)) = (x * (w / x)) * K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(17098(a,1),36663(a,2,2))].">
      <j1 rule="para" parents="17098 36663"/>
    </justification>
  </clause>

  <clause id="36666">
    <literal><![CDATA[
      R(T(x,y),z,u) * (w / R(x,z,u)) = x * ((w / x) * K(x,T(y,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,23053,a(flip),b,36664,a),flip(a)].">
      <j1 rule="hyper" parents="373 23053 36664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36668">
    <literal><![CDATA[
      R(T(x,y),z,u) * (w / R(x,z,u)) = x * (K(x,y) * (w / x))
    ]]></literal>
    <justification jstring="[para(8034(a,1),36666(a,2,2))].">
      <j1 rule="para" parents="8034 36666"/>
    </justification>
  </clause>

  <clause id="36669">
    <literal><![CDATA[
      R(T(x,y),z,u) * (w / R(x,z,u)) = T(x,y) * (w / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5776,a(flip),b,36668,a),flip(a)].">
      <j1 rule="hyper" parents="373 5776 36668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36670">
    <literal><![CDATA[
      R(x,y,z) * (u / R(x \ 1,y,z)) = ((x \ 1) \ x) * (T(x \ 1,x) * (u / (x \ 1)))
    ]]></literal>
    <justification jstring="[para(36669(a,1),2476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="36669 2476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36671">
    <literal><![CDATA[
      R(x,y,z) * (u / R(x \ 1,y,z)) = ((x \ 1) \ x) * ((x \ 1) * (u / (1 / x)))
    ]]></literal>
    <justification jstring="[para(6089(a,1),36670(a,2,2))].">
      <j1 rule="para" parents="6089 36670"/>
    </justification>
  </clause>

  <clause id="36672">
    <literal><![CDATA[
      R(x,y,z) * (u / R(x \ 1,y,z)) = ((x \ 1) \ 1) * (u / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,1480,a(flip),b,36671,a),flip(a)].">
      <j1 rule="hyper" parents="373 1480 36671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36673">
    <literal><![CDATA[
      R(x,y,z) * (u / R(x \ 1,y,z)) = x * (u / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,3720,a(flip),b,36672,a),flip(a)].">
      <j1 rule="hyper" parents="373 3720 36672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36674">
    <literal><![CDATA[
      L((((x * x) / y) \ z) \ u,((x * x) / y) \ z,y) = z \ (T((x * x) / y,K(y,w)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2197,a(flip),b,25614,a)].">
      <j1 rule="hyper" parents="64 2197 25614"/>
    </justification>
  </clause>

  <clause id="36676">
    <literal><![CDATA[
      L((((x * x) / y) \ z) \ u,(y \ (x * x)) \ z,y) = z \ (T((x * x) / y,K(y,w)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29445,a(flip),b,36674,a)].">
      <j1 rule="hyper" parents="64 29445 36674"/>
    </justification>
  </clause>

  <clause id="36677">
    <literal><![CDATA[
      L((((x * x) / y) \ z) \ u,y \ z,y) = z \ (T((x * x) / y,K(y,w)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29850,a(flip),b,36676,a)].">
      <j1 rule="hyper" parents="64 29850 36676"/>
    </justification>
  </clause>

  <clause id="36679">
    <literal><![CDATA[
      L((((x * x) / y) \ z) \ u,y \ z,y) = z \ (((x * x) / y) * u)
    ]]></literal>
    <justification jstring="[para(3347(a,1),36677(a,2,2,1))].">
      <j1 rule="para" parents="3347 36677"/>
    </justification>
  </clause>

  <clause id="36680">
    <literal><![CDATA[
      L(x * y,L(y \ 1,y,x),x * K(y \ 1,x * y)) = a(x,L(y \ 1,y,x),x * y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(5995(a,1),26852(a,1,3))].">
      <j1 rule="para" parents="5995 26852"/>
    </justification>
  </clause>

  <clause id="36681">
    <literal><![CDATA[
      a(x,L(y \ 1,y,x),x * y) \ (x * y) = L(x * y,L(y \ 1,y,x),x)
    ]]></literal>
    <justification jstring="[hyper(29067,a,36680,a),flip(a)].">
      <j1 rule="hyper" parents="29067 36680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36683">
    <literal><![CDATA[
      a(x,L(y \ 1,y,x),x * y) \ (x * y) = L(x * y,L(y,y,x),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,29880,a(flip),b,36681,a),flip(a)].">
      <j1 rule="hyper" parents="373 29880 36681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36684">
    <literal><![CDATA[
      a(x,L(y,y,x),x * y) \ (x * y) = L(x * y,L(y,y,x),x)
    ]]></literal>
    <justification jstring="[para(32203(a,1),36683(a,1,1))].">
      <j1 rule="para" parents="32203 36683"/>
    </justification>
  </clause>

  <clause id="36685">
    <literal><![CDATA[
      x * (a(x,L(y,y,x),x * y) \ y) = L(x * y,L(y,y,x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29923,a(flip),b,36684,a)].">
      <j1 rule="hyper" parents="64 29923 36684"/>
    </justification>
  </clause>

  <clause id="36686">
    <literal><![CDATA[
      x * (a(x,y,x * R(y,y,x)) \ y) = L(x * y,L(y,y,x),x)
    ]]></literal>
    <justification jstring="[para(35010(a,1),36685(a,1,2,1))].">
      <j1 rule="para" parents="35010 36685"/>
    </justification>
  </clause>

  <clause id="36687">
    <literal><![CDATA[
      x * (a(x,y,x * L(y,y,x)) \ y) = L(x * y,L(y,y,x),x)
    ]]></literal>
    <justification jstring="[para(31317(a,1),36686(a,1,2,1))].">
      <j1 rule="para" parents="31317 36686"/>
    </justification>
  </clause>

  <clause id="36688">
    <literal><![CDATA[
      x * (a(x,y,(y \ 1) \ x) \ y) = L(x * y,L(y,y,x),x)
    ]]></literal>
    <justification jstring="[para(27709(a,1),36687(a,1,2,1))].">
      <j1 rule="para" parents="27709 36687"/>
    </justification>
  </clause>

  <clause id="36689">
    <literal><![CDATA[
      a(x,y,L((((z * z) / u) \ w) \ 1,(u \ (z * z)) \ w,u) * u) = a(x,y,(u \ w) \ (u \ (z * z)))
    ]]></literal>
    <justification jstring="[para(29445(a,1),27739(a,1,3,1))].">
      <j1 rule="para" parents="29445 27739"/>
    </justification>
  </clause>

  <clause id="36690">
    <literal><![CDATA[
      ((x * L(y,z,u)) * (L(y,z,u) \ T(y,w))) / T(y,w) = R(x,L(T(y,w),z,u),L(T(y,w),z,u) \ y)
    ]]></literal>
    <justification jstring="[para(26966(a,1),27854(a,1,1))].">
      <j1 rule="para" parents="26966 27854"/>
    </justification>
  </clause>

  <clause id="36691">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z) \ u,w) \ w = w * ((a(x,y,z) \ u) \ K(w * u,u))
    ]]></literal>
    <justification jstring="[para(28721(a,1),28699(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28721 28699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36693">
    <literal><![CDATA[
      x * (((x * a(y,z,u)) \ w) * K(a(y,z,u) \ w,v5)) = T(x * ((x * a(y,z,u)) \ w),v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),28893(a,1,2,2,1))].">
      <j1 rule="para" parents="10 28893"/>
    </justification>
  </clause>

  <clause id="36694">
    <literal><![CDATA[
      x * (((x * a(y,z,u)) \ w) * K(w,v5)) = T(x * ((x * a(y,z,u)) \ w),v5)
    ]]></literal>
    <justification jstring="[para(28676(a,1),36693(a,1,2,2))].">
      <j1 rule="para" parents="28676 36693"/>
    </justification>
  </clause>

  <clause id="36695">
    <literal><![CDATA[
      T(x * ((x * a(y,z,u)) \ w),v5) = x * ((x * a(y,z,u)) \ T(w,v5))
    ]]></literal>
    <justification jstring="[para(15021(a,1),36694(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15021 36694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36697">
    <literal><![CDATA[
      (x * y) \ (y * T(a(z,u,w) * ((a(z,u,w) * a(z,u,w)) \ x),y)) = L(T(a(z,u,w) \ 1,T(x,y)),x,y)
    ]]></literal>
    <justification jstring="[para(36695(a,2),14103(a,1,2,2))].">
      <j1 rule="para" parents="36695 14103"/>
    </justification>
  </clause>

  <clause id="36698">
    <literal><![CDATA[
      L(x,L(T(y * y,z) * u,z,w) * v5,v6) = L(x,(T(w * z,v7) \ (w * (z * u))) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,34009,a(flip),b,29747,a),flip(a)].">
      <j1 rule="hyper" parents="64 34009 29747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36700">
    <literal><![CDATA[
      L(x,L(T(y * y,z) * u,z,w) * v5,v6) = L(x,L(K(v7,w * z) * u,z,w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(26090(a,1),36698(a,2,2,1))].">
      <j1 rule="para" parents="26090 36698"/>
    </justification>
  </clause>

  <clause id="36701">
    <literal><![CDATA[
      L(x,L(T(y * y,z) * u,z,w) * v5,v6) = L(x,L(u,z,w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(23126(a,1),36700(a,2,2,1,1))].">
      <j1 rule="para" parents="23126 36700"/>
    </justification>
  </clause>

  <clause id="36702">
    <literal><![CDATA[
      L(x,L(y * (z * z),u,w) * v5,v6) = L(x,L(y,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,31136,a(flip),b,36701,a)].">
      <j1 rule="hyper" parents="64 31136 36701"/>
    </justification>
  </clause>

  <clause id="36704">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u) * w,v5) = L(x,L(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29737,a(flip),b,36702,a),flip(a)].">
      <j1 rule="hyper" parents="64 29737 36702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36706">
    <literal><![CDATA[
      L(x,L(1 / y,z,u) * w,v5) = L(x,L(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29475,a,b,36704,a)].">
      <j1 rule="hyper" parents="64 29475 36704"/>
    </justification>
  </clause>

  <clause id="36707">
    <literal><![CDATA[
      R(a(x,x,y) \ 1,z,L(x \ y,z,a(x,x,y))) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,11,a(flip),b,30304,a),flip(a)].">
      <j1 rule="hyper" parents="373 11 30304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36709">
    <literal><![CDATA[
      R(a(x,x,y) \ 1,z,x \ y) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(30298(a,1),36707(a,1,3))].">
      <j1 rule="para" parents="30298 36707"/>
    </justification>
  </clause>

  <clause id="36711">
    <literal><![CDATA[
      a(x,x,y) * ((a(x,x,y) \ ((1 / x) \ 1)) * z) = x * L(z,1 / R(x,x,y),a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(782,a,30330,a),flip(a)].">
      <j1 rule="hyper" parents="782 30330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36713">
    <literal><![CDATA[
      a(x,x,y) * ((a(x,x,y) \ ((1 / x) \ 1)) * z) = x * L(z,R(x,x,y),a(x,x,y))
    ]]></literal>
    <justification jstring="[para(11776(a,1),36711(a,2,2))].">
      <j1 rule="para" parents="11776 36711"/>
    </justification>
  </clause>

  <clause id="36714">
    <literal><![CDATA[
      a(x,x,y) * ((a(x,x,y) \ ((1 / x) \ 1)) * z) = x * L(z,L(x,x,y),a(x,x,y))
    ]]></literal>
    <justification jstring="[para(29794(a,1),36713(a,2,2))].">
      <j1 rule="para" parents="29794 36713"/>
    </justification>
  </clause>

  <clause id="36715">
    <literal><![CDATA[
      a(x,x,y) * ((a(x,x,y) \ ((1 / x) \ 1)) * z) = x * L(z,a(x,x,y),L(x,x,y))
    ]]></literal>
    <justification jstring="[para(31784(a,2),36714(a,2,2))].">
      <j1 rule="para" parents="31784 36714"/>
    </justification>
  </clause>

  <clause id="36716">
    <literal><![CDATA[
      a(x,x,y) * ((a(x,x,y) \ ((1 / x) \ 1)) * z) = a(y,x,x) * (L(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31865,a(flip),b,36715,a),flip(a)].">
      <j1 rule="hyper" parents="373 31865 36715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36717">
    <literal><![CDATA[
      a(x,x,y) * ((a(x,x,y) \ x) * z) = a(y,x,x) * (L(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(82(a,1),36716(a,1,2,1,2))].">
      <j1 rule="para" parents="82 36716"/>
    </justification>
  </clause>

  <clause id="36718">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * (R(x,x,y) * z) = a(y,x,x) * (L(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30134,a(flip),b,36717,a)].">
      <j1 rule="hyper" parents="64 30134 36717"/>
    </justification>
  </clause>

  <clause id="36719">
    <literal><![CDATA[
      a(x,y,y) * (L(y,y,x) * (a(y,y,x) \ z)) = ((a(y,y,x) \ 1) * T(y,a(y,y,x))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,36201,a(flip),b,36718,a),flip(a)].">
      <j1 rule="hyper" parents="64 36201 36718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36720">
    <literal><![CDATA[
      a(x,y,y) * (L(y,y,x) * (a(y,y,x) \ z)) = ((a(y,y,x) \ 1) * y) * z
    ]]></literal>
    <justification jstring="[para(13967(a,1),36719(a,2,1,2))].">
      <j1 rule="para" parents="13967 36719"/>
    </justification>
  </clause>

  <clause id="36721">
    <literal><![CDATA[
      a(x,y,y) * (L(y,y,x) * (a(y,y,x) \ z)) = (a(y,y,x) \ y) * z
    ]]></literal>
    <justification jstring="[para(29933(a,1),36720(a,2,1))].">
      <j1 rule="para" parents="29933 36720"/>
    </justification>
  </clause>

  <clause id="36722">
    <literal><![CDATA[
      a(x,y,y) * (a(y,y,x) \ (z * L(y,y,x))) = (a(y,y,x) \ y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(30941(a,1),36721(a,1,2))].">
      <j1 rule="para" parents="30941 36721"/>
    </justification>
  </clause>

  <clause id="36723">
    <literal><![CDATA[
      a(x,y,y) * (a(y,y,x) \ (z * L(y,y,x))) = z * (a(y,y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,28651,a(flip),b,36722,a),flip(a)].">
      <j1 rule="hyper" parents="373 28651 36722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36724">
    <literal><![CDATA[
      a(x,x,y) * (z * (a(x,x,y) \ x)) = a(y,x,x) * (z * L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,36723,a(flip),b,29303,a)].">
      <j1 rule="hyper" parents="145 36723 29303"/>
    </justification>
  </clause>

  <clause id="36725">
    <literal><![CDATA[
      a(x,y,y) * ((a(y,y,x) \ z) * L(y,y,x)) = z * (a(y,y,x) \ y)
    ]]></literal>
    <justification jstring="[para(30014(a,1),36723(a,1,2))].">
      <j1 rule="para" parents="30014 36723"/>
    </justification>
  </clause>

  <clause id="36726">
    <literal><![CDATA[
      R(a(x,y,y) \ 1,z,L(x / y,z,a(x,y,y))) = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,11,a(flip),b,30339,a),flip(a)].">
      <j1 rule="hyper" parents="373 11 30339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36728">
    <literal><![CDATA[
      R(a(x,y,y) \ 1,z,x / y) = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[para(30338(a,1),36726(a,1,3))].">
      <j1 rule="para" parents="30338 36726"/>
    </justification>
  </clause>

  <clause id="36729">
    <literal><![CDATA[
      R(a(x,y,y) \ 1,z,y \ x) = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(25233,a,36728,a)].">
      <j1 rule="hyper" parents="25233 36728"/>
    </justification>
  </clause>

  <clause id="36731">
    <literal><![CDATA[
      (x * (((y * z) * z) \ u)) * a(x \ L(y,z,z),x,(z * (z * y)) \ u) = (((y * z) * z) / x) \ u
    ]]></literal>
    <justification jstring="[para(32683(a,1),30449(a,1,2))].">
      <j1 rule="para" parents="32683 30449"/>
    </justification>
  </clause>

  <clause id="36732">
    <literal><![CDATA[
      (x * (((x * y) * y) \ z)) * a(a(x,y,y),x,(y * (y * x)) \ z) = (((x * y) * y) / x) \ z
    ]]></literal>
    <justification jstring="[para(32549(a,1),36731(a,1,2))].">
      <j1 rule="para" parents="32549 36731"/>
    </justification>
  </clause>

  <clause id="36733">
    <literal><![CDATA[
      (x * (((x * y) * y) \ z)) * a(x,a(x,y,y),(y * (y * x)) \ z) = (((x * y) * y) / x) \ z
    ]]></literal>
    <justification jstring="[para(29365(a,1),36732(a,1,2))].">
      <j1 rule="para" parents="29365 36732"/>
    </justification>
  </clause>

  <clause id="36734">
    <literal><![CDATA[
      L(x,y,(z \ u) \ (K(w,v5) * ((z * u) \ v6))) = L(x,y,(z * u) \ (L(z * u,z,z) \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,28993,a(flip),b,31020,a),flip(a)].">
      <j1 rule="hyper" parents="64 28993 31020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36736">
    <literal><![CDATA[
      L(x,y,(z \ u) \ (K(w,v5) * ((z * u) \ v6))) = L(x,y,(z * u) * (L(z * u,z,z) * v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,35249,a(flip),b,36734,a),flip(a)].">
      <j1 rule="hyper" parents="373 35249 36734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36737">
    <literal><![CDATA[
      L(x,y,(z \ u) \ (K(w,v5) * ((z * u) \ v6))) = L(x,y,((z \ u) * v6) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,36243,a(flip),b,36736,a),flip(a)].">
      <j1 rule="hyper" parents="373 36243 36736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36738">
    <literal><![CDATA[
      L(x,y,(z \ u) \ ((z * u) \ w)) = L(x,y,((z \ u) * w) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,28993,a(flip),b,36737,a)].">
      <j1 rule="hyper" parents="64 28993 36737"/>
    </justification>
  </clause>

  <clause id="36739">
    <literal><![CDATA[
      a(L(T(x * K(y,x),z),x * K(y,x),y * x),u,w) = a(((y * x) \ (y * K(z,x))) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(29434(a,1),32541(a,1,1))].">
      <j1 rule="para" parents="29434 32541"/>
    </justification>
  </clause>

  <clause id="36741">
    <literal><![CDATA[
      a(L(T(x * K(y,x),z),x,y * x),u,w) = a(((y * x) \ (y * K(z,x))) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(29435(a,1),36739(a,1,1))].">
      <j1 rule="para" parents="29435 36739"/>
    </justification>
  </clause>

  <clause id="36742">
    <literal><![CDATA[
      a(L(x * K(y,x),x,y * x),z,u) = a(((y * x) \ (y * K(w,x))) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26792,a(flip),b,36741,a)].">
      <j1 rule="hyper" parents="64 26792 36741"/>
    </justification>
  </clause>

  <clause id="36746">
    <literal><![CDATA[
      a(L(x,x,y * x),z,u) = a(((y * x) \ (y * K(w,x))) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32381,a(flip),b,36742,a)].">
      <j1 rule="hyper" parents="64 32381 36742"/>
    </justification>
  </clause>

  <clause id="36748">
    <literal><![CDATA[
      a(L(x,x,y * x),z,u) = a(L(T(x,w) \ 1,x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(5941(a,1),36746(a,2,1,1))].">
      <j1 rule="para" parents="5941 36746"/>
    </justification>
  </clause>

  <clause id="36749">
    <literal><![CDATA[
      a(L(x,x,y * x),z,u) = a(L(x \ 1,x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(114(a,1),36748(a,2,1,1,1,1))].">
      <j1 rule="para" parents="114 36748"/>
    </justification>
  </clause>

  <clause id="36750">
    <literal><![CDATA[
      a(L(x,x \ 1,y \ 1),z,u) = a(L(x,x,y * x),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32789,a,b,36749,a)].">
      <j1 rule="hyper" parents="373 32789 36749"/>
    </justification>
  </clause>

  <clause id="36751">
    <literal><![CDATA[
      a(L(x,x,y * x),z,u) = a(L(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32588,a(flip),b,36750,a),flip(a)].">
      <j1 rule="hyper" parents="64 32588 36750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36752">
    <literal><![CDATA[
      a(L(x,x,x * y),z,u) = a(L(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(23253(a,1),36751(a,1,1))].">
      <j1 rule="para" parents="23253 36751"/>
    </justification>
  </clause>

  <clause id="36753">
    <literal><![CDATA[
      a(L(x,x,L(x,y,z) \ u),w,v5) = a(L(x,x,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,35479,a(flip),b,36752,a),flip(a)].">
      <j1 rule="hyper" parents="64 35479 36752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36754">
    <literal><![CDATA[
      (x * (a(y,y,y \ x) \ y)) * a(L(y,y,x),y,y \ x) = x * y
    ]]></literal>
    <justification jstring="[para(36752(a,1),33730(a,1,2))].">
      <j1 rule="para" parents="36752 33730"/>
    </justification>
  </clause>

  <clause id="36755">
    <literal><![CDATA[
      a(L(x,x,y),z,z) \ y = x * (R(x,z,z) \ y)
    ]]></literal>
    <justification jstring="[para(36753(a,1),32618(a,1,1))].">
      <j1 rule="para" parents="36753 32618"/>
    </justification>
  </clause>

  <clause id="36757">
    <literal><![CDATA[
      (x * (a(y,y,y \ x) \ y)) * a(y,L(y,y,x),y \ x) = x * y
    ]]></literal>
    <justification jstring="[para(2784(a,1),36754(a,1,2))].">
      <j1 rule="para" parents="2784 36754"/>
    </justification>
  </clause>

  <clause id="36758">
    <literal><![CDATA[
      (x * (a(y,y,y \ x) \ y)) * a(y,y,y \ x) = x * y
    ]]></literal>
    <justification jstring="[para(32209(a,1),36757(a,1,2))].">
      <j1 rule="para" parents="32209 36757"/>
    </justification>
  </clause>

  <clause id="36759">
    <literal><![CDATA[
      a(x,x,x \ y) * (y * (a(x,x,x \ y) \ x)) = y * x
    ]]></literal>
    <justification jstring="[hyper(23777,a,36758,a)].">
      <j1 rule="hyper" parents="23777 36758"/>
    </justification>
  </clause>

  <clause id="36760">
    <literal><![CDATA[
      a(x \ y,x,x) * (y * L(x,x,x \ y)) = y * x
    ]]></literal>
    <justification jstring="[hyper(64,a,36724,a(flip),b,36759,a)].">
      <j1 rule="hyper" parents="64 36724 36759"/>
    </justification>
  </clause>

  <clause id="36761">
    <literal><![CDATA[
      a(x * y,x,x) * (y * L(x,x,x \ y)) = y * x
    ]]></literal>
    <justification jstring="[para(30543(a,1),36760(a,1,1))].">
      <j1 rule="para" parents="30543 36760"/>
    </justification>
  </clause>

  <clause id="36762">
    <literal><![CDATA[
      a(x * y,x,x) * (y * L(x,x,x * y)) = y * x
    ]]></literal>
    <justification jstring="[para(25574(a,1),36761(a,1,2,2))].">
      <j1 rule="para" parents="25574 36761"/>
    </justification>
  </clause>

  <clause id="36763">
    <literal><![CDATA[
      a(x * y,x,x) * (y / (1 / x)) = y * x
    ]]></literal>
    <justification jstring="[para(25565(a,1),36762(a,1,2))].">
      <j1 rule="para" parents="25565 36762"/>
    </justification>
  </clause>

  <clause id="36764">
    <literal><![CDATA[
      a(x * y,x,x) * K(1 / x,(1 / x) \ y) = (y * x) / ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(142,a,36763,a(flip),b,6064,a),flip(a)].">
      <j1 rule="hyper" parents="142 36763 6064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36765">
    <literal><![CDATA[
      a(x * y,x,x) * K(1 / x,(1 / x) \ y) = ((1 / x) \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,36015,a(flip),b,36764,a),flip(a)].">
      <j1 rule="hyper" parents="373 36015 36764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36766">
    <literal><![CDATA[
      a(x * y,x,x) * K(x \ 1,y * x) = ((1 / x) \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(10292(a,1),36765(a,1,2))].">
      <j1 rule="para" parents="10292 36765"/>
    </justification>
  </clause>

  <clause id="36767">
    <literal><![CDATA[
      x * T(L(x,x,x * y) \ 1,y * x) = ((1 / x) \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30486,a(flip),b,36766,a)].">
      <j1 rule="hyper" parents="64 30486 36766"/>
    </justification>
  </clause>

  <clause id="36768">
    <literal><![CDATA[
      x * ((y \ ((1 / x) \ y)) \ 1) = ((1 / x) \ y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(27229(a,1),36767(a,1,2))].">
      <j1 rule="para" parents="27229 36767"/>
    </justification>
  </clause>

  <clause id="36769">
    <literal><![CDATA[
      a(x \ (y / x),(x \ y) \ ((x \ (y / x)) \ (x \ y)),z) = a((x \ y) \ R(x,y,x),x \ (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31908,a(flip),b,32978,a),flip(a)].">
      <j1 rule="hyper" parents="373 31908 32978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36770">
    <literal><![CDATA[
      L(L(a(x,y,z),a(x,y,z),u),u * a(x,y,z),u) = a(u,u,a(x,y,z)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27007,a(flip),b,33063,a),flip(a)].">
      <j1 rule="hyper" parents="373 27007 33063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36771">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * a(y,z,u) = L(1 / a(y,z,u),x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,30855,a(flip),b,36770,a),flip(a)].">
      <j1 rule="hyper" parents="64 30855 36770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36772">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * a(y,z,u) = L(a(y,z,u) \ 1,x,x) \ 1
    ]]></literal>
    <justification jstring="[para(13923(a,1),36771(a,2,1,1))].">
      <j1 rule="para" parents="13923 36771"/>
    </justification>
  </clause>

  <clause id="36773">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,u) \ 1 = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,36296,a(flip),b,36772,a),flip(a)].">
      <j1 rule="hyper" parents="64 36296 36772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36774">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,u) = L(a(x,y,z),u,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(40,a,23792,a,b,36773,a),flip(a)].">
      <j1 rule="hyper" parents="40 23792 36773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36775">
    <literal><![CDATA[
      a(L(x,y,z),u,u \ 1) \ K(u \ a(u * x,u,u),u) = L(u * (u \ a(u * x,u,u)),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(4248(a,2),33382(a,1,1))].">
      <j1 rule="para" parents="4248 33382"/>
    </justification>
  </clause>

  <clause id="36776">
    <literal><![CDATA[
      (x * (y / z)) \ (x * ((y / z) * (z \ R(z,y,x)))) = a(L(L(z \ 1,z,z * y),y,x),y,x)
    ]]></literal>
    <justification jstring="[para(30676(a,1),33467(a,1,2,2))].">
      <j1 rule="para" parents="30676 33467"/>
    </justification>
  </clause>

  <clause id="36777">
    <literal><![CDATA[
      a(L(L(x \ 1,x,x * y),y,z),y,z) = L(x \ R(x,y,z),y / x,z)
    ]]></literal>
    <justification jstring="[hyper(608,a,36776,a),flip(a)].">
      <j1 rule="hyper" parents="608 36776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36778">
    <literal><![CDATA[
      a(L(L(x \ 1,x,x * y),y,z),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,33189,a(flip),b,36777,a),flip(a)].">
      <j1 rule="hyper" parents="373 33189 36777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36780">
    <literal><![CDATA[
      a(L(L(x,x,x * y),y,z),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34772,a(flip),b,36778,a)].">
      <j1 rule="hyper" parents="64 34772 36778"/>
    </justification>
  </clause>

  <clause id="36781">
    <literal><![CDATA[
      a(L(L(x,x,y),y,z),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32828,a(flip),b,36780,a)].">
      <j1 rule="hyper" parents="64 32828 36780"/>
    </justification>
  </clause>

  <clause id="36782">
    <literal><![CDATA[
      a(L(x \ R(x,y,z),a(x,y,z),x),x,z * y) = a(x,y,z) \ R(a(x,y,z),x,z * y)
    ]]></literal>
    <justification jstring="[para(36308(a,1),36781(a,1,1))].">
      <j1 rule="para" parents="36308 36781"/>
    </justification>
  </clause>

  <clause id="36783">
    <literal><![CDATA[
      a(x,y,z) \ R(a(x,y,z),x,z * y) = a(x \ R(x,y,z),x,z * y)
    ]]></literal>
    <justification jstring="[para(29806(a,1),36782(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29806 36782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36784">
    <literal><![CDATA[
      a(x,y,z) \ R(a(x,y,z),x,z * y) = a(x \ L(x,y,z),x,z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,34649,a(flip),b,36783,a),flip(a)].">
      <j1 rule="hyper" parents="373 34649 36783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36786">
    <literal><![CDATA[
      a(x,y,z) \ R(a(x,y,z),x,z * y) = a(x,x * L(x,y,z),z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,33572,a(flip),b,36784,a),flip(a)].">
      <j1 rule="hyper" parents="373 33572 36784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36787">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),x,z * y) = a(x,x * L(x,y,z),z * y)
    ]]></literal>
    <justification jstring="[para(28787(a,1),36786(a,1,2))].">
      <j1 rule="para" parents="28787 36786"/>
    </justification>
  </clause>

  <clause id="36788">
    <literal><![CDATA[
      x \ (L(x,y,y) \ (x * R(L(x,y,y),z,u))) = x \ (R(L(x,y,y),z,u) * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(198(a,1),33886(a,1,1))].">
      <j1 rule="para" parents="198 33886"/>
    </justification>
  </clause>

  <clause id="36789">
    <literal><![CDATA[
      x \ (L(x,y,y) \ (x * L(R(x,z,u),y,y))) = x \ (R(L(x,y,y),z,u) * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(29(a,1),36788(a,1,2,2,2))].">
      <j1 rule="para" parents="29 36788"/>
    </justification>
  </clause>

  <clause id="36790">
    <literal><![CDATA[
      x \ (x * (L(x,y,y) \ L(R(x,z,u),y,y))) = x \ (R(L(x,y,y),z,u) * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(2329(a,1),36789(a,1,2))].">
      <j1 rule="para" parents="2329 36789"/>
    </justification>
  </clause>

  <clause id="36791">
    <literal><![CDATA[
      x \ (R(L(x,y,y),z,u) * a(y,y,x)) = x \ (x * L(x \ R(x,z,u),y,y))
    ]]></literal>
    <justification jstring="[para(4243(a,1),36790(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4243 36790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36792">
    <literal><![CDATA[
      x \ (R(L(x,y,y),z,u) * a(y,y,x)) = L(x \ R(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,9,a(flip),b,36791,a),flip(a)].">
      <j1 rule="hyper" parents="373 9 36791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36794">
    <literal><![CDATA[
      x \ (a(y,y,x) * R(L(x,y,y),z,u)) = L(x \ R(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,23180,a,b,36792,a)].">
      <j1 rule="hyper" parents="64 23180 36792"/>
    </justification>
  </clause>

  <clause id="36795">
    <literal><![CDATA[
      x \ (a(y,y,x) * L(R(x,z,u),y,y)) = L(x \ R(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[para(29(a,1),36794(a,1,2,2))].">
      <j1 rule="para" parents="29 36794"/>
    </justification>
  </clause>

  <clause id="36796">
    <literal><![CDATA[
      L(R(x,y,z) * a(u,u,x),u,u) = L(x \ R(x,y,z),u,u) * x
    ]]></literal>
    <justification jstring="[para(36795(a,1),33918(a,1,1)),flip(a)].">
      <j1 rule="para" parents="36795 33918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36797">
    <literal><![CDATA[
      ((x \ R(x,y,z)) * x) \ L(R(x,y,z) * a(u,u,x),u,u) = x \ (L(x \ R(x,y,z),u,u) * ((x \ R(x,y,z)) \ x))
    ]]></literal>
    <justification jstring="[para(36796(a,2),33815(a,1,2))].">
      <j1 rule="para" parents="36796 33815"/>
    </justification>
  </clause>

  <clause id="36798">
    <literal><![CDATA[
      a(L(x,y,z),u,w) * a(u * w,R(x,y,z),a(R(x,y,z),u,w)) = R(x,y,z) \ R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(32590(a,1),34144(a,1,1))].">
      <j1 rule="para" parents="32590 34144"/>
    </justification>
  </clause>

  <clause id="36799">
    <literal><![CDATA[
      R(x,(x * y) * L(x,x,x),x * ((x \ y) * x)) = R(x,(x * ((x \ y) * x)) \ x,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26181,a(flip),b,35720,a),flip(a)].">
      <j1 rule="hyper" parents="64 26181 35720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36801">
    <literal><![CDATA[
      R(x,(x * y) * L(x,x,x),x * ((x \ y) * x)) = R(x,x \ (((x \ y) * x) \ x),x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,26610,a(flip),b,36799,a),flip(a)].">
      <j1 rule="hyper" parents="373 26610 36799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36802">
    <literal><![CDATA[
      R(x,(x * y) * L(x,x,x),x * ((x \ y) * x)) = R(x,x \ (x \ ((x \ y) \ x)),x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,26602,a(flip),b,36801,a),flip(a)].">
      <j1 rule="hyper" parents="373 26602 36801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36803">
    <literal><![CDATA[
      R(x,(x * y) * L(x,x,x),x * ((x \ y) * x)) = R(x,L((x \ y) \ x,x,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30397,a(flip),b,36802,a),flip(a)].">
      <j1 rule="hyper" parents="373 30397 36802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36804">
    <literal><![CDATA[
      R(x,(x * y) * L(x,x,x),x * ((x \ y) * x)) = R(x,L((y \ x) * x,x,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,33713,a(flip),b,36803,a),flip(a)].">
      <j1 rule="hyper" parents="373 33713 36803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36805">
    <literal><![CDATA[
      R(x,(x * y) * L(x,x,x),x * ((x \ y) * x)) = R(x,x \ (y \ x),x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30395,a(flip),b,36804,a),flip(a)].">
      <j1 rule="hyper" parents="373 30395 36804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36806">
    <literal><![CDATA[
      R(x,(x * y) * L(x,x,x),x * y) = R(x,x \ (y \ x),x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26181,a(flip),b,36805,a)].">
      <j1 rule="hyper" parents="64 26181 36805"/>
    </justification>
  </clause>

  <clause id="36808">
    <literal><![CDATA[
      R(x,x \ (y \ x),x * y) = R(x,(x * y) * x,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,14260,a(flip),b,36806,a),flip(a)].">
      <j1 rule="hyper" parents="64 14260 36806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36810">
    <literal><![CDATA[
      R(x,x \ (y \ x),x * y) = R(x,L(y,x,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,26474,a(flip),b,36808,a),flip(a)].">
      <j1 rule="hyper" parents="373 26474 36808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36811">
    <literal><![CDATA[
      a(x,x \ (y \ x),x * y) * x = R(x,L(y,x,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32313,a,b,36810,a)].">
      <j1 rule="hyper" parents="64 32313 36810"/>
    </justification>
  </clause>

  <clause id="36812">
    <literal><![CDATA[
      a(x,x \ (y \ x),x * y) = a(x,L(y,x,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(36,a,35510,a,b,36811,a),flip(a)].">
      <j1 rule="hyper" parents="36 35510 36811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36813">
    <literal><![CDATA[
      a(x,L(y,y,x),x * y) = a(x,L(y,x,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32205,a,b,36812,a)].">
      <j1 rule="hyper" parents="64 32205 36812"/>
    </justification>
  </clause>

  <clause id="36814">
    <literal><![CDATA[
      a(x,L(y,x,x),x * y) = a(x,y,x * R(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,35010,a(flip),b,36813,a),flip(a)].">
      <j1 rule="hyper" parents="64 35010 36813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36815">
    <literal><![CDATA[
      a(x,L(y,x,x),x * y) = a(x,y,x * L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,31317,a(flip),b,36814,a),flip(a)].">
      <j1 rule="hyper" parents="373 31317 36814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36816">
    <literal><![CDATA[
      a(x,L(y,x,x),x * y) = a(x,y,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,27709,a(flip),b,36815,a),flip(a)].">
      <j1 rule="hyper" parents="373 27709 36815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36817">
    <literal><![CDATA[
      a(x,y,(y \ 1) \ x) = a(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35677,a(flip),b,36816,a),flip(a)].">
      <j1 rule="hyper" parents="64 35677 36816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36818">
    <literal><![CDATA[
      R(x,L(y,x,x),x * y) = a(x,y,(y \ 1) \ x) * x
    ]]></literal>
    <justification jstring="[para(36816(a,1),35510(a,1,1)),flip(a)].">
      <j1 rule="para" parents="36816 35510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36819">
    <literal><![CDATA[
      x \ R(x,y,(y \ 1) \ x) = a(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16057,a,b,36817,a)].">
      <j1 rule="hyper" parents="64 16057 36817"/>
    </justification>
  </clause>

  <clause id="36820">
    <literal><![CDATA[
      x * (a(x,y,x * y) \ y) = L(x * y,L(y,y,x),x)
    ]]></literal>
    <justification jstring="[para(36817(a,1),36688(a,1,2,1))].">
      <j1 rule="para" parents="36817 36688"/>
    </justification>
  </clause>

  <clause id="36821">
    <literal><![CDATA[
      R(x,L(y,x,x),x * y) = R(x,y,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,16067,a(flip),b,36818,a),flip(a)].">
      <j1 rule="hyper" parents="373 16067 36818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36822">
    <literal><![CDATA[
      R(x,y,(y \ 1) \ x) = R(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35730,a(flip),b,36821,a),flip(a)].">
      <j1 rule="hyper" parents="64 35730 36821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36823">
    <literal><![CDATA[
      x \ R(x,y,x * y) = a(x,y,x * y)
    ]]></literal>
    <justification jstring="[para(36822(a,1),36819(a,1,2))].">
      <j1 rule="para" parents="36822 36819"/>
    </justification>
  </clause>

  <clause id="36824">
    <literal><![CDATA[
      a(x \ y,x,(x \ y) * x) = (x \ y) \ R(x \ y,x,y)
    ]]></literal>
    <justification jstring="[para(26165(a,1),36823(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26165 36823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36825">
    <literal><![CDATA[
      L(x * y,L(y,y,x),x) = L(x * y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29940,a(flip),b,36820,a),flip(a)].">
      <j1 rule="hyper" parents="64 29940 36820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36826">
    <literal><![CDATA[
      a(x \ y,x,(x \ y) * x) = x \ (y * R(y \ x,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,2744,a(flip),b,36824,a),flip(a)].">
      <j1 rule="hyper" parents="373 2744 36824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36827">
    <literal><![CDATA[
      a(x \ (y \ 1),x,(x \ (y \ 1)) * x) = x \ (y * R(y \ x,x,y \ 1))
    ]]></literal>
    <justification jstring="[para(2112(a,1),36826(a,2,2))].">
      <j1 rule="para" parents="2112 36826"/>
    </justification>
  </clause>

  <clause id="36828">
    <literal><![CDATA[
      x \ (y * R(y \ x,x,y \ 1)) = a(x \ (y \ 1),x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27299,a(flip),b,36827,a),flip(a)].">
      <j1 rule="hyper" parents="64 27299 36827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36830">
    <literal><![CDATA[
      R(x,y,L(L(z,u,z),w,v5) * L(L(z,u,z),w,v5)) = x * a(y,x,L(z,w,v5) * L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(13882(a,1),36425(a,2,2))].">
      <j1 rule="para" parents="13882 36425"/>
    </justification>
  </clause>

  <clause id="36832">
    <literal><![CDATA[
      x * (x * (R(x,y \ 1,y) \ ((y * y) \ z))) = ((x / ((y \ 1) \ 1)) / (1 / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(3756(a,1),36595(a,1,2,2,1))].">
      <j1 rule="para" parents="3756 36595"/>
    </justification>
  </clause>

  <clause id="36833">
    <literal><![CDATA[
      ((x / ((y \ 1) \ 1)) / (1 / (1 / y))) * z = x * (x * (R(x,y,y) \ ((y * y) \ z)))
    ]]></literal>
    <justification jstring="[para(2975(a,1),36832(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2975 36832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36835">
    <literal><![CDATA[
      ((x / ((y \ 1) \ 1)) / (1 / (1 / y))) * z = x * (((x * y) * y) \ (x * z))
    ]]></literal>
    <justification jstring="[para(16079(a,1),36833(a,2,2))].">
      <j1 rule="para" parents="16079 36833"/>
    </justification>
  </clause>

  <clause id="36836">
    <literal><![CDATA[
      x * (((x * y) * y) \ (x * z)) = ((x / y) / y) * z
    ]]></literal>
    <justification jstring="[para(6634(a,1),36835(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6634 36835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36837">
    <literal><![CDATA[
      ((x * y) * y) \ (x * x) = T((x / y) / y,x)
    ]]></literal>
    <justification jstring="[hyper(270,a,36836,a),flip(a)].">
      <j1 rule="hyper" parents="270 36836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36839">
    <literal><![CDATA[
      L((x \ L(K(y,x) / x,x,y)) \ z,((y / (x \ 1)) / y) / x,x) = R((x * y) \ y,x,x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(25886(a,1),36650(a,1,1,1,2))].">
      <j1 rule="para" parents="25886 36650"/>
    </justification>
  </clause>

  <clause id="36840">
    <literal><![CDATA[
      a(x,y,L((((z * z) / u) \ w) \ 1,u \ w,u) * u) = a(x,y,(u \ w) \ (u \ (z * z)))
    ]]></literal>
    <justification jstring="[para(29850(a,1),36689(a,1,3,1))].">
      <j1 rule="para" parents="29850 36689"/>
    </justification>
  </clause>

  <clause id="36842">
    <literal><![CDATA[
      a(x,y,(z \ (((u * u) / w) * 1)) * w) = a(x,y,(w \ z) \ (w \ (u * u)))
    ]]></literal>
    <justification jstring="[para(36679(a,1),36840(a,1,3,1))].">
      <j1 rule="para" parents="36679 36840"/>
    </justification>
  </clause>

  <clause id="36843">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (z \ (w * w))) = a(x,y,(u \ ((w * w) / z)) * z)
    ]]></literal>
    <justification jstring="[para(8(a,1),36842(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="8 36842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36844">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (z \ (w * w))) = a(x,y,(u \ (z \ (w * w))) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27470,a(flip),b,36843,a),flip(a)].">
      <j1 rule="hyper" parents="373 27470 36843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36845">
    <literal><![CDATA[
      a(x,(y \ z) * z,y \ (u * u)) = a(x,y,(y \ (z \ (u * u))) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,36040,a,b,36844,a)].">
      <j1 rule="hyper" parents="64 36040 36844"/>
    </justification>
  </clause>

  <clause id="36846">
    <literal><![CDATA[
      R(x,L(T(y,z),u,w),L(T(y,z),u,w) \ y) = ((x * L(y,u,w)) * (L(y,u,w) \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,24870,a(flip),b,36690,a),flip(a)].">
      <j1 rule="hyper" parents="64 24870 36690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36848">
    <literal><![CDATA[
      R(x,L(T(y,z),u,w),L(T(y,z),u,w) \ y) = (L(y,u,w) \ y) * ((x * L(y,u,w)) / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,33139,a(flip),b,36846,a),flip(a)].">
      <j1 rule="hyper" parents="373 33139 36846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36849">
    <literal><![CDATA[
      R(x,L(T(y,z),u,w),L(T(y,z),u,w) \ y) = (L(y,u,w) \ y) * (L(y,u,w) * (y \ x))
    ]]></literal>
    <justification jstring="[para(24378(a,1),36848(a,2,2))].">
      <j1 rule="para" parents="24378 36848"/>
    </justification>
  </clause>

  <clause id="36850">
    <literal><![CDATA[
      R(x,L(T(y,z),u,w),L(T(y,z),u,w) \ y) = L(y,u,w) * ((L(y,u,w) \ y) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,36170,a(flip),b,36849,a),flip(a)].">
      <j1 rule="hyper" parents="373 36170 36849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36851">
    <literal><![CDATA[
      R(x,L(T(y,z),u,w),L(y,u,w) \ y) = L(y,u,w) * ((L(y,u,w) \ y) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,26218,a(flip),b,36850,a)].">
      <j1 rule="hyper" parents="64 26218 36850"/>
    </justification>
  </clause>

  <clause id="36853">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ x) * (x \ u)) = R(u,L(x,y,z),L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26430,a(flip),b,36851,a),flip(a)].">
      <j1 rule="hyper" parents="64 26430 36851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36854">
    <literal><![CDATA[
      a(x \ (y / x),(x \ y) \ ((x \ (y / x)) \ (x \ y)),z) = a((x \ y) \ R(x,y,x),L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32142,a(flip),b,36769,a),flip(a)].">
      <j1 rule="hyper" parents="373 32142 36769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36855">
    <literal><![CDATA[
      a(x \ (y / x),(x \ y) \ ((x \ (y / x)) \ (x \ y)),z) = a((x \ y) \ x,L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,13231,a(flip),b,36854,a),flip(a)].">
      <j1 rule="hyper" parents="373 13231 36854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36857">
    <literal><![CDATA[
      a(x \ (y / x),(x \ y) \ ((x \ (y / x)) \ (x \ y)),z) = a((y \ x) * x,L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32539,a(flip),b,36855,a),flip(a)].">
      <j1 rule="hyper" parents="373 32539 36855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36858">
    <literal><![CDATA[
      a(x \ (y / x),(x \ y) \ R(x,y,x),z) = a((y \ x) * x,L(y,x,x),z)
    ]]></literal>
    <justification jstring="[para(26513(a,1),36857(a,1,2,2))].">
      <j1 rule="para" parents="26513 36857"/>
    </justification>
  </clause>

  <clause id="36859">
    <literal><![CDATA[
      a(x \ (y / x),(x \ y) \ x,z) = a((y \ x) * x,L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13833,a(flip),b,36858,a)].">
      <j1 rule="hyper" parents="64 13833 36858"/>
    </justification>
  </clause>

  <clause id="36861">
    <literal><![CDATA[
      a(x \ (y / x),(y \ x) * x,z) = a((y \ x) * x,L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32124,a(flip),b,36859,a)].">
      <j1 rule="hyper" parents="64 32124 36859"/>
    </justification>
  </clause>

  <clause id="36862">
    <literal><![CDATA[
      a(x \ (x \ y),(y \ x) * x,z) = a((y \ x) * x,L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(32449,a,36861,a)].">
      <j1 rule="hyper" parents="32449 36861"/>
    </justification>
  </clause>

  <clause id="36863">
    <literal><![CDATA[
      a((x \ y) * y,L(x,y,y),z) = a(L(x,y,y),(x \ y) * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30384,a(flip),b,36862,a),flip(a)].">
      <j1 rule="hyper" parents="64 30384 36862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36864">
    <literal><![CDATA[
      L(x * (x \ a(x * y,x,x)),z,u) \ 1 = a(L(y,z,u),x,x \ 1) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(28680(a,1),36775(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28680 36775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36865">
    <literal><![CDATA[
      L(x * (x \ a(x * y,x,x)),z,u) \ 1 = (x \ (a(L(y,z,u),x,x \ 1) \ 1)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,28830,a(flip),b,36864,a),flip(a)].">
      <j1 rule="hyper" parents="373 28830 36864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36867">
    <literal><![CDATA[
      L(x * (x \ a(x * y,x,x)),z,u) \ 1 = L(x \ 1,x,L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(33364(a,1),36865(a,2,1))].">
      <j1 rule="para" parents="33364 36865"/>
    </justification>
  </clause>

  <clause id="36868">
    <literal><![CDATA[
      L(a(x * y,x,x),z,u) \ 1 = L(x \ 1,x,L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),36867(a,1,1,1))].">
      <j1 rule="para" parents="10 36867"/>
    </justification>
  </clause>

  <clause id="36870">
    <literal><![CDATA[
      a(L(x * y,z,u),x,x) \ 1 = L(x \ 1,x,L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(32607(a,2),36868(a,1,1))].">
      <j1 rule="para" parents="32607 36868"/>
    </justification>
  </clause>

  <clause id="36871">
    <literal><![CDATA[
      a(L(x * y,z,u),x,x) = a(L(y,z,u) * x,x,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,30560,a,b,36870,a),flip(a)].">
      <j1 rule="hyper" parents="40 30560 36870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36872">
    <literal><![CDATA[
      a(L(x * y,z,u),x,x) = a(x * L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,30502,a,b,36870,a),flip(a)].">
      <j1 rule="hyper" parents="40 30502 36870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36873">
    <literal><![CDATA[
      a(L(x * ((y \ z) \ 1),y \ z,y),x,x) = a((z \ y) * x,x,x)
    ]]></literal>
    <justification jstring="[para(436(a,1),36871(a,2,1,1))].">
      <j1 rule="para" parents="436 36871"/>
    </justification>
  </clause>

  <clause id="36874">
    <literal><![CDATA[
      a(L((x \ y) \ z,x \ y,x),z,z) = a((y \ x) * z,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32716,a(flip),b,36873,a)].">
      <j1 rule="hyper" parents="64 32716 36873"/>
    </justification>
  </clause>

  <clause id="36875">
    <literal><![CDATA[
      a(x \ (y * z),z,z) = a((x \ y) * z,z,z)
    ]]></literal>
    <justification jstring="[para(630(a,1),36874(a,1,1))].">
      <j1 rule="para" parents="630 36874"/>
    </justification>
  </clause>

  <clause id="36876">
    <literal><![CDATA[
      a((x \ (y \ z)) * y,y,y) = a(x \ z,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32372,a(flip),b,36875,a),flip(a)].">
      <j1 rule="hyper" parents="64 32372 36875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36877">
    <literal><![CDATA[
      a(x * (y \ (x \ z)),x,x) = a(y \ z,x,x)
    ]]></literal>
    <justification jstring="[hyper(26847,a,36876,a)].">
      <j1 rule="hyper" parents="26847 36876"/>
    </justification>
  </clause>

  <clause id="36878">
    <literal><![CDATA[
      a(x * ((x * y) \ z),x,x) = a(y \ z,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33788,a,b,36877,a)].">
      <j1 rule="hyper" parents="64 33788 36877"/>
    </justification>
  </clause>

  <clause id="36879">
    <literal><![CDATA[
      a(x \ (y * z),y,y) = a(y * (x \ z),y,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),36877(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 36877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36880">
    <literal><![CDATA[
      a((x * y) \ z,x,x) = a(x * (y \ z),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,35592,a,b,36879,a)].">
      <j1 rule="hyper" parents="64 35592 36879"/>
    </justification>
  </clause>

  <clause id="36881">
    <literal><![CDATA[
      a(x * (y \ (z * x)),x,x) = a(y \ z,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,35589,a(flip),b,36879,a),flip(a)].">
      <j1 rule="hyper" parents="64 35589 36879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36882">
    <literal><![CDATA[
      a((x * a(y,z,x)) * (u \ ((y \ a(y,z,x)) * x)),x * a(y,z,x),x * a(y,z,x)) = a(u \ (y \ 1),x * a(y,z,x),x * a(y,z,x))
    ]]></literal>
    <justification jstring="[para(33212(a,1),36881(a,1,1,2,2))].">
      <j1 rule="para" parents="33212 36881"/>
    </justification>
  </clause>

  <clause id="36883">
    <literal><![CDATA[
      a(L(x,y,z),u,w) * a(u * w,R(x,y,z),a(L(x,y,z),u,w)) = R(x,y,z) \ R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(32590(a,1),36798(a,1,2,3))].">
      <j1 rule="para" parents="32590 36798"/>
    </justification>
  </clause>

  <clause id="36884">
    <literal><![CDATA[
      L((((x * y) \ T(x,y)) / y) \ z,((x / (y \ 1)) / x) / y,y) = R((y * x) \ x,y,y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(35381(a,1),36839(a,1,1,1))].">
      <j1 rule="para" parents="35381 36839"/>
    </justification>
  </clause>

  <clause id="36885">
    <literal><![CDATA[
      L((((x * y) \ y) / x) \ z,((y / (x \ 1)) / y) / x,x) = R((x * y) \ y,x,x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(6981(a,1),36884(a,1,1,1,1))].">
      <j1 rule="para" parents="6981 36884"/>
    </justification>
  </clause>

  <clause id="36886">
    <literal><![CDATA[
      a(L(x,y,z),u,w) * a(u * w,L(x,y,z),a(L(x,y,z),u,w)) = R(x,y,z) \ R(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(32197(a,1),36883(a,1,2))].">
      <j1 rule="para" parents="32197 36883"/>
    </justification>
  </clause>

  <clause id="36887">
    <literal><![CDATA[
      R(x,y,z) \ R(R(x,u,w),y,z) = L(x,y,z) \ R(L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,34142,a(flip),b,36886,a),flip(a)].">
      <j1 rule="hyper" parents="64 34142 36886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36888">
    <literal><![CDATA[
      R(x,y,z) \ R(R(x,u,w),y,z) = L(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,4246,a(flip),b,36887,a),flip(a)].">
      <j1 rule="hyper" parents="373 4246 36887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36889">
    <literal><![CDATA[
      R(x,y,z) \ R(R(x,y,z),u,w) = L(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(31(a,1),36888(a,1,2))].">
      <j1 rule="para" parents="31 36888"/>
    </justification>
  </clause>

  <clause id="36890">
    <literal><![CDATA[
      R(x,y,z) \ R(R(x,y,z),u,w) = R(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,28821,a,b,36889,a),flip(a)].">
      <j1 rule="hyper" parents="373 28821 36889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36891">
    <literal><![CDATA[
      R(R(x,y,z),u,w) \ R(x,y,z) = L(x \ R(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(36889(a,1),5382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="36889 5382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36892">
    <literal><![CDATA[
      L(L(L(x \ R(x,y,z),u,w),v5,v6),L(R(x,u,w),v5,v6),y * z) = a(L(R(x,u,w),v5,v6),y,z)
    ]]></literal>
    <justification jstring="[para(36889(a,1),16038(a,1,1,1))].">
      <j1 rule="para" parents="36889 16038"/>
    </justification>
  </clause>

  <clause id="36893">
    <literal><![CDATA[
      R(R(x,y,z),u,w) \ R(x,u,w) = L(x \ R(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,173,a,b,36891,a)].">
      <j1 rule="hyper" parents="64 173 36891"/>
    </justification>
  </clause>

  <clause id="36894">
    <literal><![CDATA[
      L((x / y) \ R(x / y,y,y),z,u) \ 1 = a(R((x / y) * K(y,y),z,u),y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,16773,a(flip),b,36893,a),flip(a)].">
      <j1 rule="hyper" parents="64 16773 36893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36895">
    <literal><![CDATA[
      a(R((x / y) * K(y,y),z,u),y,y) \ 1 = L(a(x / y,y,y),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(15987(a,1),36894(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="15987 36894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36896">
    <literal><![CDATA[
      a(R((x / y) * K(y,y),z,u),y,y) \ 1 = L(a(y \ x,y,y),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(26785(a,1),36895(a,2,1,1))].">
      <j1 rule="para" parents="26785 36895"/>
    </justification>
  </clause>

  <clause id="36897">
    <literal><![CDATA[
      a(R((x / y) * K(y,y),z,u),y,y) \ 1 = L(a(y * x,y,y),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(30543(a,1),36896(a,2,1,1))].">
      <j1 rule="para" parents="30543 36896"/>
    </justification>
  </clause>

  <clause id="36898">
    <literal><![CDATA[
      a(R((x / y) * K(y,y),z,u),y,y) \ 1 = L(y \ 1,y,L(x,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,36868,a(flip),b,36897,a),flip(a)].">
      <j1 rule="hyper" parents="373 36868 36897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36899">
    <literal><![CDATA[
      L(x,x,R((y / x) * K(x,x),z,u)) = x * (L(x \ 1,x,L(y,z,u)) * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,36898,a(flip),b,30465,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 36898 30465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36900">
    <literal><![CDATA[
      L(x,x,R((y / x) * K(x,x),z,u)) = L(x,x,x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,26664,a(flip),b,36899,a),flip(a)].">
      <j1 rule="hyper" parents="373 26664 36899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36901">
    <literal><![CDATA[
      L(x,x,R(y / x,z,u)) = L(x,x,x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29032,a(flip),b,36900,a)].">
      <j1 rule="hyper" parents="64 29032 36900"/>
    </justification>
  </clause>

  <clause id="36903">
    <literal><![CDATA[
      L(x,x,L(y / x,z,u)) = L(x,x,x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29203,a(flip),b,36901,a)].">
      <j1 rule="hyper" parents="64 29203 36901"/>
    </justification>
  </clause>

  <clause id="36904">
    <literal><![CDATA[
      L(x,x,L(x \ y,z,u)) = L(x,x,x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,23846,a(flip),b,36903,a)].">
      <j1 rule="hyper" parents="64 23846 36903"/>
    </justification>
  </clause>

  <clause id="36905">
    <literal><![CDATA[
      L(x,x,L(x * y,z,u)) = L(x,x,x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,34218,a(flip),b,36904,a)].">
      <j1 rule="hyper" parents="64 34218 36904"/>
    </justification>
  </clause>

  <clause id="36906">
    <literal><![CDATA[
      L(x,x,L(x * (K(y,x \ z) * u),x \ z,x \ z)) = L(x,x,z * ((T(x \ z,y) \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,34037,a(flip),b,36905,a),flip(a)].">
      <j1 rule="hyper" parents="373 34037 36905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36907">
    <literal><![CDATA[
      L(x,x,x * L(x \ y,z,u)) = L(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),36905(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 36905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36908">
    <literal><![CDATA[
      L(x,x,x * (y \ (x \ (z * y)))) = L(x,x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,34438,a(flip),b,36907,a)].">
      <j1 rule="hyper" parents="64 34438 36907"/>
    </justification>
  </clause>

  <clause id="36909">
    <literal><![CDATA[
      L(L(L(a(x,x,y),z,u),w,v5),L(R(x,z,u),w,v5),x * y) = a(L(R(x,z,u),w,v5),x,y)
    ]]></literal>
    <justification jstring="[para(30058(a,1),36892(a,1,1,1,1))].">
      <j1 rule="para" parents="30058 36892"/>
    </justification>
  </clause>

  <clause id="36910">
    <literal><![CDATA[
      L(x,x,L(x * y,x \ z,x \ z)) = L(x,x,z * ((T(x \ z,u) \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29177,a(flip),b,36906,a)].">
      <j1 rule="hyper" parents="64 29177 36906"/>
    </justification>
  </clause>

  <clause id="36911">
    <literal><![CDATA[
      L(x,x,L(x * y,x \ z,x \ z)) = L(x,x,(T(x \ z,u) * y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,23995,a(flip),b,36910,a),flip(a)].">
      <j1 rule="hyper" parents="373 23995 36910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36913">
    <literal><![CDATA[
      L(x,x,L(x * y,x \ z,x \ z)) = L(x,x,((x \ z) * y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,28992,a(flip),b,36911,a),flip(a)].">
      <j1 rule="hyper" parents="373 28992 36911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36914">
    <literal><![CDATA[
      T(K(x,y) * (z * x),u) \ (T(K(x,y) * (z * x),u) / w) = (z * T(x,y)) \ ((z * T(x,y)) / w)
    ]]></literal>
    <justification jstring="[para(22939(a,1),22994(a,1,2,1))].">
      <j1 rule="para" parents="22939 22994"/>
    </justification>
  </clause>

  <clause id="36915">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ ((K(x,y) * (z * x)) / u) = (z * T(x,y)) \ ((z * T(x,y)) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,14846,a(flip),b,36914,a)].">
      <j1 rule="hyper" parents="64 14846 36914"/>
    </justification>
  </clause>

  <clause id="36916">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * T(y,z)) / u) = (x * y) \ ((x * y) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,19780,a(flip),b,36915,a),flip(a)].">
      <j1 rule="hyper" parents="64 19780 36915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36918">
    <literal><![CDATA[
      (x * (1 / y)) \ ((x * (1 / y)) / z) = (y * x) \ ((y * x) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4269,a(flip),b,36916,a)].">
      <j1 rule="hyper" parents="64 4269 36916"/>
    </justification>
  </clause>

  <clause id="36920">
    <literal><![CDATA[
      (K(x,y) * K(x,y)) \ ((z \ K(y,x)) \ (y * (T(T(y,x),x) \ u))) = T(K(y,x) * (z \ 1),K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(9814(a,1),22995(a,1,2,2))].">
      <j1 rule="para" parents="9814 22995"/>
    </justification>
  </clause>

  <clause id="36921">
    <literal><![CDATA[
      R(L(x,y,z),u,w) * (T(x,x \ v5) / L((x \ v5) \ v5,y,z)) = L(x,y,z) \ (L(R(x,u,w),y,z) * x)
    ]]></literal>
    <justification jstring="[para(29(a,1),25818(a,2,2,1))].">
      <j1 rule="para" parents="29 25818"/>
    </justification>
  </clause>

  <clause id="36922">
    <literal><![CDATA[
      T(x * (T(T(y,z),u) * T(z,y)),K(y,z * K(y,u))) = K(y,z) * (x * ((z * K(y,u)) * y))
    ]]></literal>
    <justification jstring="[para(8550(a,1),25888(a,2,1))].">
      <j1 rule="para" parents="8550 25888"/>
    </justification>
  </clause>

  <clause id="36923">
    <literal><![CDATA[
      T(x * (T(T(y,z),u) * T(z,y)),K(y,z * K(y,u))) = K(y,z) * (x * (z * T(y,u)))
    ]]></literal>
    <justification jstring="[para(6850(a,1),36922(a,2,2,2))].">
      <j1 rule="para" parents="6850 36922"/>
    </justification>
  </clause>

  <clause id="36925">
    <literal><![CDATA[
      T(x * (y * (z * K(y,u))),K(y,z * K(y,u))) = K(y,z) * (x * (z * T(y,u)))
    ]]></literal>
    <justification jstring="[para(25887(a,1),36923(a,1,1,2))].">
      <j1 rule="para" parents="25887 36923"/>
    </justification>
  </clause>

  <clause id="36926">
    <literal><![CDATA[
      L(x,y,z \ (K(u,w) * (v5 * (w * T(u,v6))))) = L(x,y,z \ (v5 * (u * (w * K(u,v6)))))
    ]]></literal>
    <justification jstring="[para(36925(a,1),28984(a,1,3,2))].">
      <j1 rule="para" parents="36925 28984"/>
    </justification>
  </clause>

  <clause id="36927">
    <literal><![CDATA[
      L(x,y,z \ (u * (w * (v5 * K(w,v6))))) = L(x,y,z \ (u * (v5 * T(w,v6))))
    ]]></literal>
    <justification jstring="[hyper(64,a,28993,a(flip),b,36926,a),flip(a)].">
      <j1 rule="hyper" parents="64 28993 36926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36929">
    <literal><![CDATA[
      L(x,y,(z \ (u * (w * v5))) * K(w,v6)) = L(x,y,z \ (u * (v5 * T(w,v6))))
    ]]></literal>
    <justification jstring="[para(25392(a,1),36927(a,1,3))].">
      <j1 rule="para" parents="25392 36927"/>
    </justification>
  </clause>

  <clause id="36930">
    <literal><![CDATA[
      L(x,y,z \ (u * (w * T(v5,v6)))) = L(x,y,z \ (u * (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(29067,a,36929,a),flip(a)].">
      <j1 rule="hyper" parents="29067 36929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36932">
    <literal><![CDATA[
      L(a(x,y,z),u,((x * y) * T(z,w)) \ (x * (z * y))) = L(a(x,y,z),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,36491,a(flip),b,36930,a),flip(a)].">
      <j1 rule="hyper" parents="64 36491 36930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36934">
    <literal><![CDATA[
      L(a(x,y,z),u,((x * y) * z) \ (x * (z * y))) = L(a(x,y,z),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,28996,a(flip),b,36932,a)].">
      <j1 rule="hyper" parents="64 28996 36932"/>
    </justification>
  </clause>

  <clause id="36935">
    <literal><![CDATA[
      L(a(x,y,z),u,((x * y) * z) \ (x * (z * y))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31083,a(flip),b,36934,a),flip(a)].">
      <j1 rule="hyper" parents="373 31083 36934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36937">
    <literal><![CDATA[
      L(a(x,y,z),u,a(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33625,a(flip),b,36935,a)].">
      <j1 rule="hyper" parents="64 33625 36935"/>
    </justification>
  </clause>

  <clause id="36938">
    <literal><![CDATA[
      a(x,y,z) \ (a(z,y,x) * u) = a(z,y,x) * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(36937(a,1),27804(a,1,1))].">
      <j1 rule="para" parents="36937 27804"/>
    </justification>
  </clause>

  <clause id="36939">
    <literal><![CDATA[
      a(x \ (((y * y) / L(z * z,u,w)) * v5),v6,v7) = a(x \ (v5 * L(v5 \ ((z * z) \ v5),u,w)),v6,v7)
    ]]></literal>
    <justification jstring="[para(31251(a,1),26930(a,1,1,2,1))].">
      <j1 rule="para" parents="31251 26930"/>
    </justification>
  </clause>

  <clause id="36940">
    <literal><![CDATA[
      a(x \ (y * L(y \ ((z * z) \ y),u,w)),v5,v6) = a(x \ (a(w,u,z * z) * y),v5,v6)
    ]]></literal>
    <justification jstring="[para(31256(a,1),36939(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="31256 36939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36941">
    <literal><![CDATA[
      a(x \ (y * L(y \ ((z * z) \ y),u,w)),v5,v6) = a(a(w,u,z * z) * (x \ y),v5,v6)
    ]]></literal>
    <justification jstring="[para(31271(a,1),36940(a,2,1))].">
      <j1 rule="para" parents="31271 36940"/>
    </justification>
  </clause>

  <clause id="36942">
    <literal><![CDATA[
      a(x \ (y * L(y \ ((z * z) \ y),u,w)),v5,v6) = a(x \ y,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,31543,a(flip),b,36941,a),flip(a)].">
      <j1 rule="hyper" parents="373 31543 36941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36944">
    <literal><![CDATA[
      a(x \ (L(y * y,z,u) \ w),v5,v6) = a(x \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(31252(a,1),36942(a,1,1,2))].">
      <j1 rule="para" parents="31252 36942"/>
    </justification>
  </clause>

  <clause id="36945">
    <literal><![CDATA[
      (K(x \ y,x) * z) * (a(y,z \ y,z \ y) * (z \ y)) = R((x \ y) * x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[para(26836(a,1),27057(a,1,2,1))].">
      <j1 rule="para" parents="26836 27057"/>
    </justification>
  </clause>

  <clause id="36947">
    <literal><![CDATA[
      R((x \ y) * x,z \ y,z \ y) = (K(x \ y,x) * z) * ((y \ z) \ 1)
    ]]></literal>
    <justification jstring="[para(30528(a,1),36945(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30528 36945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36948">
    <literal><![CDATA[
      R((x \ y) * x,z \ y,z \ y) = z * ((((x \ y) * x) \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,35947,a(flip),b,36947,a),flip(a)].">
      <j1 rule="hyper" parents="373 35947 36947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36949">
    <literal><![CDATA[
      a(x,y,z) / (a(x,y,z) * T(a(x,y,z) \ (u \ a(x,y,z)),w)) = 1 / (1 / (T(u \ 1,w) \ 1))
    ]]></literal>
    <justification jstring="[para(25060(a,1),27130(a,1,2,2,1))].">
      <j1 rule="para" parents="25060 27130"/>
    </justification>
  </clause>

  <clause id="36950">
    <literal><![CDATA[
      a(x,y,z) / T((a(x,y,z) \ (u \ a(x,y,z))) * a(x,y,z),w) = 1 / (1 / (T(u \ 1,w) \ 1))
    ]]></literal>
    <justification jstring="[para(28753(a,2),36949(a,1,2))].">
      <j1 rule="para" parents="28753 36949"/>
    </justification>
  </clause>

  <clause id="36951">
    <literal><![CDATA[
      a(x,y,z) / T(u \ a(x,y,z),w) = 1 / (1 / (T(u \ 1,w) \ 1))
    ]]></literal>
    <justification jstring="[para(23135(a,1),36950(a,1,2,1))].">
      <j1 rule="para" parents="23135 36950"/>
    </justification>
  </clause>

  <clause id="36952">
    <literal><![CDATA[
      T(a(x,y,z) / u,w) \ a(x,y,z) = 1 / (1 / (T(u \ 1,w) \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,8071,a(flip),b,36951,a)].">
      <j1 rule="hyper" parents="64 8071 36951"/>
    </justification>
  </clause>

  <clause id="36954">
    <literal><![CDATA[
      T(a(x,y,z) / u,w) \ a(x,y,z) = 1 / T(u \ 1,w)
    ]]></literal>
    <justification jstring="[para(79(a,1),36952(a,2,2))].">
      <j1 rule="para" parents="79 36952"/>
    </justification>
  </clause>

  <clause id="36955">
    <literal><![CDATA[
      T(a(x,y,z) / u,w) \ a(x,y,z) = T(1 / u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,8071,a(flip),b,36954,a),flip(a)].">
      <j1 rule="hyper" parents="373 8071 36954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36957">
    <literal><![CDATA[
      a(x,y,z) / T(z * a(x,y,z),u) = T(1 / (1 / z),u) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,9444,a(flip),b,36955,a)].">
      <j1 rule="hyper" parents="64 9444 36955"/>
    </justification>
  </clause>

  <clause id="36959">
    <literal><![CDATA[
      a(x,y,z) / T(z * a(x,y,z),u) = 1 / T(z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,8331,a(flip),b,36957,a),flip(a)].">
      <j1 rule="hyper" parents="373 8331 36957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36960">
    <literal><![CDATA[
      T(K(x * (y \ (y / z)),z) / (y \ (y / z)),z \ 1) = K(z * x,z) / (y \ (y / z))
    ]]></literal>
    <justification jstring="[para(6710(a,1),28223(a,1,1,1))].">
      <j1 rule="para" parents="6710 28223"/>
    </justification>
  </clause>

  <clause id="36963">
    <literal><![CDATA[
      T(K(x / y,y) / (z \ (z / y)),y \ 1) = K(y * x,y) / (z \ (z / y))
    ]]></literal>
    <justification jstring="[para(28506(a,1),36960(a,1,1,1))].">
      <j1 rule="para" parents="28506 36960"/>
    </justification>
  </clause>

  <clause id="36964">
    <literal><![CDATA[
      T(K(x \ y,x) / (z \ (z / x)),x \ 1) = K(x * y,x) / (z \ (z / x))
    ]]></literal>
    <justification jstring="[para(6116(a,1),36963(a,1,1,1))].">
      <j1 rule="para" parents="6116 36963"/>
    </justification>
  </clause>

  <clause id="36966">
    <literal><![CDATA[
      K(x * y,x) / (z \ (z / x)) = (z \ (z / x)) \ K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,6754,a(flip),b,36964,a),flip(a)].">
      <j1 rule="hyper" parents="64 6754 36964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36967">
    <literal><![CDATA[
      L(x,L(T(y * (z \ 1),u) \ (z * (z \ w)),v5,v6),v7) = L(x,L((z * T(y,z \ 1)) \ w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,34800,a(flip),b,29823,a)].">
      <j1 rule="hyper" parents="64 34800 29823"/>
    </justification>
  </clause>

  <clause id="36968">
    <literal><![CDATA[
      L(x,L(T(y * (z \ 1),u) \ w,v5,v6),v7) = L(x,L((z * T(y,z \ 1)) \ w,v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(10(a,1),36967(a,1,2,1,2))].">
      <j1 rule="para" parents="10 36967"/>
    </justification>
  </clause>

  <clause id="36969">
    <literal><![CDATA[
      L(x,L((y * T(z,y \ 1)) \ u,w,v5),v6) = L(x,L((z * (y \ 1)) \ u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29473,a(flip),b,36968,a),flip(a)].">
      <j1 rule="hyper" parents="64 29473 36968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36970">
    <literal><![CDATA[
      L(x,L((y * (z \ 1)) \ u,w,v5),v6) = L(x,L((z * y) \ u,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29751,a(flip),b,36969,a),flip(a)].">
      <j1 rule="hyper" parents="64 29751 36969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36972">
    <literal><![CDATA[
      L(x,T((y \ 1) \ (z \ u),w),v5) = L(x,L((y * z) \ u,y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,36353,a,b,36970,a)].">
      <j1 rule="hyper" parents="64 36353 36970"/>
    </justification>
  </clause>

  <clause id="36973">
    <literal><![CDATA[
      L(x,L((y * z) \ u,y,z),w) = L(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29709,a(flip),b,36972,a),flip(a)].">
      <j1 rule="hyper" parents="64 29709 36972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36974">
    <literal><![CDATA[
      R(R(x,y,z),y * z,L(a(x,x,y),z,x * y)) = ((x * y) * (z * a(x,x,y))) / (y * (z * a(x,x,y)))
    ]]></literal>
    <justification jstring="[para(29324(a,1),30317(a,2,2))].">
      <j1 rule="para" parents="29324 30317"/>
    </justification>
  </clause>

  <clause id="36975">
    <literal><![CDATA[
      ((x * K(x \ y,x)) / (x \ y)) \ ((x \ y) * x) = ((x \ y) * x) \ ((y * T(x \ y,x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(5721(a,1),30804(a,1,1,1))].">
      <j1 rule="para" parents="5721 30804"/>
    </justification>
  </clause>

  <clause id="36976">
    <literal><![CDATA[
      ((x \ y) * x) \ ((y * T(x \ y,x)) * (x \ y)) = (x / (y / x)) \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(6895(a,1),36975(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6895 36975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36977">
    <literal><![CDATA[
      ((x \ y) * x) \ ((y * (x \ y)) * T(x \ y,x)) = (x / (y / x)) \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(2515(a,1),36976(a,1,2))].">
      <j1 rule="para" parents="2515 36976"/>
    </justification>
  </clause>

  <clause id="36978">
    <literal><![CDATA[
      a(x,y,z) \ ((T(x,u) \ L(T(x,u),w,v5)) \ a(x,y,z)) = (x \ a(x,y,z)) \ (L(x,w,v5) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,34863,a(flip),b,30880,a),flip(a)].">
      <j1 rule="hyper" parents="373 34863 30880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36979">
    <literal><![CDATA[
      ((x * x) \ T(x / y,z)) \ ((x * x) \ (T(x / y,z) / u)) = ((1 / x) / y) \ (((x * x) \ (x / y)) / u)
    ]]></literal>
    <justification jstring="[para(933(a,1),31013(a,1,2))].">
      <j1 rule="para" parents="933 31013"/>
    </justification>
  </clause>

  <clause id="36980">
    <literal><![CDATA[
      L(x,y \ ((((z * z) \ u) * u) * ((R(u,w,v5) \ 1) * v6)),v7) = L(x,y \ ((1 / R(1 / u,w,v5)) * v6),v7)
    ]]></literal>
    <justification jstring="[para(2557(a,1),31050(a,1,2,2))].">
      <j1 rule="para" parents="2557 31050"/>
    </justification>
  </clause>

  <clause id="36981">
    <literal><![CDATA[
      x \ ((x * (((x \ 1) \ 1) \ (T(x \ 1,y) \ z))) * u) = (x \ 1) \ (((K(x \ 1,y) * x) \ z) * u)
    ]]></literal>
    <justification jstring="[para(14384(a,1),31216(a,2,2,1,1))].">
      <j1 rule="para" parents="14384 31216"/>
    </justification>
  </clause>

  <clause id="36982">
    <literal><![CDATA[
      x \ ((x * (((x \ 1) \ 1) \ (T(x \ 1,y) \ z))) * u) = (x \ 1) \ (((x * K(x \ 1,y)) \ z) * u)
    ]]></literal>
    <justification jstring="[para(6013(a,1),36981(a,2,2,1,1))].">
      <j1 rule="para" parents="6013 36981"/>
    </justification>
  </clause>

  <clause id="36983">
    <literal><![CDATA[
      x \ ((x * (((x \ 1) \ 1) \ (T(x \ 1,y) \ z))) * u) = (x \ 1) \ ((K(y,x \ 1) * (x \ z)) * u)
    ]]></literal>
    <justification jstring="[para(23272(a,1),36982(a,2,2,1))].">
      <j1 rule="para" parents="23272 36982"/>
    </justification>
  </clause>

  <clause id="36984">
    <literal><![CDATA[
      x \ ((x * (((x \ 1) \ 1) \ (T(x \ 1,y) \ z))) * u) = (x \ 1) \ (K(y,x \ 1) * ((x \ z) * u))
    ]]></literal>
    <justification jstring="[para(23073(a,1),36983(a,2,2))].">
      <j1 rule="para" parents="23073 36983"/>
    </justification>
  </clause>

  <clause id="36985">
    <literal><![CDATA[
      x \ ((x * (((x \ 1) \ 1) \ (T(x \ 1,y) \ z))) * u) = T(x \ 1,y) \ ((x \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,6137,a(flip),b,36984,a),flip(a)].">
      <j1 rule="hyper" parents="373 6137 36984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36986">
    <literal><![CDATA[
      x \ ((x * (x \ (T(1 / x,y) \ z))) * u) = T(x \ 1,y) \ ((x \ z) * u)
    ]]></literal>
    <justification jstring="[para(4135(a,1),36985(a,1,2,1,2))].">
      <j1 rule="para" parents="4135 36985"/>
    </justification>
  </clause>

  <clause id="36987">
    <literal><![CDATA[
      T(x \ 1,y) \ ((x \ z) * u) = x \ ((T(1 / x,y) \ z) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),36986(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 36986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36989">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((T(1 / ((x \ y) * (y \ x)),z) \ (x \ y)) * u) = T(((x \ y) * (y \ x)) \ 1,z) \ ((1 / (y \ x)) * u)
    ]]></literal>
    <justification jstring="[para(2572(a,1),36987(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2572 36987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36990">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((T(1 / ((x \ y) * (y \ x)),z) \ (y \ x)) * u) = T(((x \ y) * (y \ x)) \ 1,z) \ (((x \ y) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(2617(a,1),36987(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2617 36987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36991">
    <literal><![CDATA[
      ((1 / (1 / ((x / y) / x))) * (1 / (1 / y))) \ (y * z) = (y \ ((x / (1 / (1 / y))) / x)) \ ((1 / y) * z)
    ]]></literal>
    <justification jstring="[para(3946(a,1),31495(a,1,1,1))].">
      <j1 rule="para" parents="3946 31495"/>
    </justification>
  </clause>

  <clause id="36992">
    <literal><![CDATA[
      a(x,a(y,z,u),w \ (y \ w)) = a(x,w \ (y \ w),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,30031,a(flip),b,32925,a),flip(a)].">
      <j1 rule="hyper" parents="64 30031 32925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36993">
    <literal><![CDATA[
      a(x,y,R(T(z,u),w,v5) * (v6 * (v7 * a(L(T(z,u),w,v5),v7,v6)))) = a(x,y,(R(z,w,v5) * v7) * T(v6,v7))
    ]]></literal>
    <justification jstring="[para(32590(a,1),33390(a,1,3,2,2,2))].">
      <j1 rule="para" parents="32590 33390"/>
    </justification>
  </clause>

  <clause id="36994">
    <literal><![CDATA[
      L((x \ 1) * L((x \ 1) \ 1,y,z),u,a(w,v5,x)) = (x \ 1) * L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(33447(a,1),33451(a,2,2,1,1))].">
      <j1 rule="para" parents="33447 33451"/>
    </justification>
  </clause>

  <clause id="36995">
    <literal><![CDATA[
      L((x \ 1) * L((x \ 1) \ 1,y,z),u,a(w,v5,x)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1804,a(flip),b,36994,a),flip(a)].">
      <j1 rule="hyper" parents="373 1804 36994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="36997">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,a(w,v5,x)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1804(a,1),36995(a,1,1))].">
      <j1 rule="para" parents="1804 36995"/>
    </justification>
  </clause>

  <clause id="36998">
    <literal><![CDATA[
      T((x \ y) * L(y,y,x),(a(x,y,y) \ x) \ L(y,y,x)) = (x / y) \ L(y,y,x)
    ]]></literal>
    <justification jstring="[para(30704(a,1),33688(a,1,1,1))].">
      <j1 rule="para" parents="30704 33688"/>
    </justification>
  </clause>

  <clause id="36999">
    <literal><![CDATA[
      T((x \ y) / (1 / y),(a(x,y,y) \ x) \ L(y,y,x)) = (x / y) \ L(y,y,x)
    ]]></literal>
    <justification jstring="[para(31282(a,1),36998(a,1,1))].">
      <j1 rule="para" parents="31282 36998"/>
    </justification>
  </clause>

  <clause id="37000">
    <literal><![CDATA[
      T((x \ y) / (1 / y),x \ y) = (x / y) \ L(y,y,x)
    ]]></literal>
    <justification jstring="[para(30704(a,1),36999(a,1,2))].">
      <j1 rule="para" parents="30704 36999"/>
    </justification>
  </clause>

  <clause id="37001">
    <literal><![CDATA[
      (x / y) \ L(y,y,x) = (x * (1 / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,7032,a(flip),b,37000,a),flip(a)].">
      <j1 rule="hyper" parents="64 7032 37000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37002">
    <literal><![CDATA[
      (T(L(x,y,z),x) * L(x \ L(x,y,z),x,L(x,y,z))) \ 1 = x \ ((L(x,y,z) * (x \ L(x,y,z))) \ x)
    ]]></literal>
    <justification jstring="[para(12220(a,1),33827(a,2,2,1))].">
      <j1 rule="para" parents="12220 33827"/>
    </justification>
  </clause>

  <clause id="37003">
    <literal><![CDATA[
      R(x,y,((z \ (u / w)) * (v5 \ (v6 / v7))) * (K(v8,v9) * v10)) = R(x,y,((v5 \ (v7 \ v6)) * (z \ (w \ u))) * v10)
    ]]></literal>
    <justification jstring="[para(6156(a,1),33961(a,1,3,2))].">
      <j1 rule="para" parents="6156 33961"/>
    </justification>
  </clause>

  <clause id="37004">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) \ ((a(z,u,w) \ 1) \ (x * (y * a(z,u,w)))) = L(a(z,u,w),a(z,u,w),x * y)
    ]]></literal>
    <justification jstring="[para(23737(a,1),34047(a,1,2))].">
      <j1 rule="para" parents="23737 34047"/>
    </justification>
  </clause>

  <clause id="37005">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) * (L(R(x \ R(x,y,z),v5,v5),u,w) \ v5) = L(v5,v5,L(x * R(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(29(a,1),34236(a,1,2,1))].">
      <j1 rule="para" parents="29 34236"/>
    </justification>
  </clause>

  <clause id="37006">
    <literal><![CDATA[
      a((x \ L(y,z,u)) * ((w * v5) * a(x \ L(y,z,u),w,v5)),v6,v7) = a(((x \ R(y,z,u)) * w) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(34649(a,1),34964(a,1,1,2,2))].">
      <j1 rule="para" parents="34649 34964"/>
    </justification>
  </clause>

  <clause id="37007">
    <literal><![CDATA[
      (a(x,x,y) \ (a(x,x,y) \ 1)) \ (y \ (L(y,x,x) * z)) = y \ ((y * (1 / (a(x,x,y) \ 1))) * z)
    ]]></literal>
    <justification jstring="[para(13928(a,1),35270(a,1,1))].">
      <j1 rule="para" parents="13928 35270"/>
    </justification>
  </clause>

  <clause id="37008">
    <literal><![CDATA[
      (x \ L(L(x,y,y),y,y)) \ (x \ (L(x,y,y) * z)) = x \ ((x * (1 / (a(y,y,x) \ 1))) * z)
    ]]></literal>
    <justification jstring="[para(30366(a,1),37007(a,1,1))].">
      <j1 rule="para" parents="30366 37007"/>
    </justification>
  </clause>

  <clause id="37009">
    <literal><![CDATA[
      (x \ L(L(x,y,y),y,y)) \ ((z / x) * L(x,y,y)) = x \ ((x * (1 / (a(y,y,x) \ 1))) * z)
    ]]></literal>
    <justification jstring="[para(24852(a,1),37008(a,1,2))].">
      <j1 rule="para" parents="24852 37008"/>
    </justification>
  </clause>

  <clause id="37010">
    <literal><![CDATA[
      x * (L(L(x,y,y),y,y) \ ((z / x) * L(x,y,y))) = x \ ((x * (1 / (a(y,y,x) \ 1))) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31675,a(flip),b,37009,a)].">
      <j1 rule="hyper" parents="64 31675 37009"/>
    </justification>
  </clause>

  <clause id="37011">
    <literal><![CDATA[
      x \ ((x * (1 / (a(y,y,x) \ 1))) * z) = (z / x) * (a(y,y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,34270,a(flip),b,37010,a),flip(a)].">
      <j1 rule="hyper" parents="64 34270 37010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37012">
    <literal><![CDATA[
      x \ ((x * a(y,y,x)) * z) = (z / x) * (a(y,y,x) * x)
    ]]></literal>
    <justification jstring="[para(79(a,1),37011(a,1,2,1,2))].">
      <j1 rule="para" parents="79 37011"/>
    </justification>
  </clause>

  <clause id="37013">
    <literal><![CDATA[
      x \ ((a(y,y,x) * x) * z) = (z / x) * (a(y,y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24755,a,b,37012,a)].">
      <j1 rule="hyper" parents="64 24755 37012"/>
    </justification>
  </clause>

  <clause id="37014">
    <literal><![CDATA[
      (x \ 1) \ ((L(x,y,y) \ 1) * z) = (z / x) * (a(y,y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9370,a,b,37012,a)].">
      <j1 rule="hyper" parents="64 9370 37012"/>
    </justification>
  </clause>

  <clause id="37016">
    <literal><![CDATA[
      (x / y) * (a(z,z,y) * y) = x * L(a(z,z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29394,a(flip),b,37013,a),flip(a)].">
      <j1 rule="hyper" parents="64 29394 37013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37017">
    <literal><![CDATA[
      (x / y) * (a(z,z,y) * y) = x * a(z,L(z,y,x),y)
    ]]></literal>
    <justification jstring="[para(34877(a,2),37016(a,2,2))].">
      <j1 rule="para" parents="34877 37016"/>
    </justification>
  </clause>

  <clause id="37018">
    <literal><![CDATA[
      (x / y) * (a(z,z,y) * y) = y * (L(y,z,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,35187,a(flip),b,37014,a),flip(a)].">
      <j1 rule="hyper" parents="64 35187 37014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37019">
    <literal><![CDATA[
      x * a(y,L(y,z,x),z) = z * (L(z,y,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,37017,a(flip),b,37018,a)].">
      <j1 rule="hyper" parents="64 37017 37018"/>
    </justification>
  </clause>

  <clause id="37020">
    <literal><![CDATA[
      (x * a(y,y,x)) * (x \ z) = x * (L(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,28805,a(flip),b,37018,a)].">
      <j1 rule="hyper" parents="64 28805 37018"/>
    </justification>
  </clause>

  <clause id="37021">
    <literal><![CDATA[
      (a(x,x,y) * y) * (y \ z) = y * (L(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,28738,a(flip),b,37018,a)].">
      <j1 rule="hyper" parents="64 28738 37018"/>
    </justification>
  </clause>

  <clause id="37022">
    <literal><![CDATA[
      x \ (y * (L(y,z,z) \ x)) = a(z,L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(139,a,37018,a(flip),b,37017,a(flip))].">
      <j1 rule="hyper" parents="139 37018 37017"/>
    </justification>
  </clause>

  <clause id="37023">
    <literal><![CDATA[
      (x \ y) * a(z,L(z,x,y),x) = L(x,z,z) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,33197,a,b,37019,a(flip))].">
      <j1 rule="hyper" parents="35 33197 37019"/>
    </justification>
  </clause>

  <clause id="37024">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * (y \ z) = y * (L(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[para(30220(a,2),37020(a,1,1))].">
      <j1 rule="para" parents="30220 37020"/>
    </justification>
  </clause>

  <clause id="37025">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,z * u,u)),x,(u \ ((u \ z) * z)) * y) = a(x,y,u \ (z * ((u \ z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,31621,a(flip),b,35826,a)].">
      <j1 rule="hyper" parents="64 31621 35826"/>
    </justification>
  </clause>

  <clause id="37026">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,z * u,u)),x,y * a(z,z * u,u)) = a(x,y,u \ (z * ((u \ z) \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,35701,a(flip),b,37025,a)].">
      <j1 rule="hyper" parents="64 35701 37025"/>
    </justification>
  </clause>

  <clause id="37027">
    <literal><![CDATA[
      a(x,y,z \ (u * ((z \ u) \ 1))) = a(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,28841,a(flip),b,37026,a),flip(a)].">
      <j1 rule="hyper" parents="64 28841 37026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37028">
    <literal><![CDATA[
      a(x,y,z \ (((z \ u) \ 1) * u)) = a(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[hyper(27589,a,37027,a)].">
      <j1 rule="hyper" parents="27589 37027"/>
    </justification>
  </clause>

  <clause id="37029">
    <literal><![CDATA[
      a(x,y,a(z,u \ z,u \ z)) = a(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[para(30786(a,2),37027(a,1,3))].">
      <j1 rule="para" parents="30786 37027"/>
    </justification>
  </clause>

  <clause id="37030">
    <literal><![CDATA[
      L(x,T(y * R(y,z,u),y) * ((y * (1 / R(y,w,v5))) \ v6),v7) = L(x,(y * L(y,z,u)) * ((R(y,w,v5) \ y) \ v6),v7)
    ]]></literal>
    <justification jstring="[para(28549(a,1),36569(a,1,2,2,1))].">
      <j1 rule="para" parents="28549 36569"/>
    </justification>
  </clause>

  <clause id="37031">
    <literal><![CDATA[
      (K(x,y) * K(x,y)) \ (y * (T(T(y,x),x) \ ((z \ K(y,x)) \ u))) = T(K(y,x) * (z \ 1),K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(22835(a,1),36920(a,1,2))].">
      <j1 rule="para" parents="22835 36920"/>
    </justification>
  </clause>

  <clause id="37032">
    <literal><![CDATA[
      R(L(x,y,z),u,w) * (T(x,x \ v5) / L((x \ v5) \ v5,y,z)) = L(x,y,z) \ (x * L(R(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[para(840(a,1),36921(a,2,2))].">
      <j1 rule="para" parents="840 36921"/>
    </justification>
  </clause>

  <clause id="37033">
    <literal><![CDATA[
      R(R(x,y,z),y * z,L(a(x,x,y),z,x * y)) = R(x,y,z * a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,20,a,b,36974,a),flip(a)].">
      <j1 rule="hyper" parents="373 20 36974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37034">
    <literal><![CDATA[
      R(R(x,y,z),y * z,a(x,x,y)) = R(x,y,z * a(x,x,y))
    ]]></literal>
    <justification jstring="[para(30313(a,1),37033(a,1,3))].">
      <j1 rule="para" parents="30313 37033"/>
    </justification>
  </clause>

  <clause id="37035">
    <literal><![CDATA[
      R(x,y,z * a(x,x,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29957,a(flip),b,37034,a),flip(a)].">
      <j1 rule="hyper" parents="64 29957 37034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37038">
    <literal><![CDATA[
      T(x / y,z) \ ((x * x) * ((x * x) \ (T(x / y,z) / u))) = ((1 / x) / y) \ (((x * x) \ (x / y)) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,804,a(flip),b,36979,a)].">
      <j1 rule="hyper" parents="64 804 36979"/>
    </justification>
  </clause>

  <clause id="37039">
    <literal><![CDATA[
      L(x,y \ ((R(z,u,w) * v5) * (((v6 * v6) \ z) * z)),v7) = L(x,y \ ((1 / R(1 / z,u,w)) * v5),v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,31074,a(flip),b,36980,a)].">
      <j1 rule="hyper" parents="64 31074 36980"/>
    </justification>
  </clause>

  <clause id="37040">
    <literal><![CDATA[
      L(x,y \ ((1 / R(1 / z,u,w)) * v5),v6) = L(x,y \ ((R(z,u,w) * v5) * (z * z)),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29876,a(flip),b,37039,a),flip(a)].">
      <j1 rule="hyper" parents="64 29876 37039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37041">
    <literal><![CDATA[
      L(x,y \ ((1 / R(1 / z,u,w)) * v5),v6) = L(x,y \ (R(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29690,a(flip),b,37040,a),flip(a)].">
      <j1 rule="hyper" parents="373 29690 37040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37043">
    <literal><![CDATA[
      L(x,y \ (R(1 / z,z,z * u) * w),v5) = L(x,y \ (R(z,z,u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29773,a,b,37041,a)].">
      <j1 rule="hyper" parents="64 29773 37041"/>
    </justification>
  </clause>

  <clause id="37044">
    <literal><![CDATA[
      L(x,y \ (R(1 / z,u,w) * v5),v6) = L(x,y \ (R(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29693,a(flip),b,37041,a)].">
      <j1 rule="hyper" parents="64 29693 37041"/>
    </justification>
  </clause>

  <clause id="37045">
    <literal><![CDATA[
      (x \ ((y / (1 / (1 / x))) / y)) \ ((1 / x) * z) = (((y / x) / y) * x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(9306(a,1),36991(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9306 36991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37046">
    <literal><![CDATA[
      a(x,y,R(T(z,u),w,v5) * (v6 * (v7 * a(L(z,w,v5),v7,v6)))) = a(x,y,(R(z,w,v5) * v7) * T(v6,v7))
    ]]></literal>
    <justification jstring="[para(26792(a,1),36993(a,1,3,2,2,2))].">
      <j1 rule="para" parents="26792 36993"/>
    </justification>
  </clause>

  <clause id="37047">
    <literal><![CDATA[
      a(x,y,L(T(z,u),w,v5) * (v6 * (v7 * a(L(z,w,v5),v7,v6)))) = a(x,y,(R(z,w,v5) * v7) * T(v6,v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,31314,a(flip),b,37046,a)].">
      <j1 rule="hyper" parents="64 31314 37046"/>
    </justification>
  </clause>

  <clause id="37049">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * (v5 * (v6 * a(L(z,u,w),v6,v5)))) = a(x,y,(R(z,u,w) * v6) * T(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,27409,a(flip),b,37047,a)].">
      <j1 rule="hyper" parents="64 27409 37047"/>
    </justification>
  </clause>

  <clause id="37050">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) * v5) * T(v6,v5)) = a(x,y,(L(z,u,w) * v5) * T(v6,v5))
    ]]></literal>
    <justification jstring="[para(33241(a,1),37049(a,1,3)),flip(a)].">
      <j1 rule="para" parents="33241 37049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37051">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) * v5) * T(v6,v5)) = a(x,y,(L(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,27309,a(flip),b,37050,a),flip(a)].">
      <j1 rule="hyper" parents="373 27309 37050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37053">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * v5) * v6) = a(x,y,v6 * (v5 * R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27463,a(flip),b,37051,a),flip(a)].">
      <j1 rule="hyper" parents="64 27463 37051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37054">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) * v5) * v6) = a(x,y,(L(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,27309,a(flip),b,37051,a)].">
      <j1 rule="hyper" parents="64 27309 37051"/>
    </justification>
  </clause>

  <clause id="37056">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * v5) * v6) = a(x,y,(v5 * R(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,37053,a),flip(a)].">
      <j1 rule="hyper" parents="373 27298 37053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37057">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * v5) * L(v6 \ 1,v6,L(z,u,w) * v5)) = a(x,y,v6 \ (R(z,u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,33587,a(flip),b,37054,a),flip(a)].">
      <j1 rule="hyper" parents="64 33587 37054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37058">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * (K(v5,v6) * v7)) * v8) = a(x,y,v8 * (R(z,u,w) * v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,27535,a(flip),b,37054,a),flip(a)].">
      <j1 rule="hyper" parents="64 27535 37054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37059">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * v5) * L(v6 \ 1,v6,v5 * L(z,u,w))) = a(x,y,v6 \ (v5 * R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,33581,a(flip),b,37056,a),flip(a)].">
      <j1 rule="hyper" parents="373 33581 37056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37060">
    <literal><![CDATA[
      a(x,y,(z * R(u,w,v5)) * v6) = a(x,y,(z * L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,27395,a,b,37056,a),flip(a)].">
      <j1 rule="hyper" parents="64 27395 37056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37061">
    <literal><![CDATA[
      a(x,y,z * (R(u,w,v5) * v6)) = a(x,y,z * (L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,27535,a(flip),b,37058,a),flip(a)].">
      <j1 rule="hyper" parents="64 27535 37058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37062">
    <literal><![CDATA[
      a(x,y,z \ (R(u,w,v5) * v6)) = a(x,y,z \ (L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,27737,a(flip),b,37057,a),flip(a)].">
      <j1 rule="hyper" parents="64 27737 37057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37063">
    <literal><![CDATA[
      a(x,y,z \ (u * R(w,v5,v6))) = a(x,y,z \ (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27738,a(flip),b,37059,a),flip(a)].">
      <j1 rule="hyper" parents="64 27738 37059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37064">
    <literal><![CDATA[
      R(x,y,(z \ (u / w)) * ((K(v5,v6) / (z \ (u / w))) \ v7)) = R(x,y,((z \ (w \ u)) * (z \ (w \ u))) * v7)
    ]]></literal>
    <justification jstring="[para(24930(a,1),37003(a,1,3))].">
      <j1 rule="para" parents="24930 37003"/>
    </justification>
  </clause>

  <clause id="37065">
    <literal><![CDATA[
      R(T(a(x,y,z),u),a(x,y,z),w * v5) = (w * (v5 * a(x,y,z))) \ ((a(x,y,z) \ 1) \ (w * (v5 * a(x,y,z))))
    ]]></literal>
    <justification jstring="[hyper(373,a,28798,a,b,37004,a)].">
      <j1 rule="hyper" parents="373 28798 37004"/>
    </justification>
  </clause>

  <clause id="37066">
    <literal><![CDATA[
      (x * (y * a(z,u,x))) \ (x * ((a(z,u,x) \ 1) \ (y * a(z,u,x)))) = L(a(z,u,x),a(z,u,x),x * y)
    ]]></literal>
    <justification jstring="[para(33513(a,1),37004(a,1,2))].">
      <j1 rule="para" parents="33513 37004"/>
    </justification>
  </clause>

  <clause id="37067">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) * (L(L(x \ R(x,y,z),v5,v5),u,w) \ v5) = L(v5,v5,L(x * R(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(28821(a,1),37005(a,1,2,1,1))].">
      <j1 rule="para" parents="28821 37005"/>
    </justification>
  </clause>

  <clause id="37068">
    <literal><![CDATA[
      a(((x \ R(y,z,u)) * w) * v5,v6,v7) = a(((x \ L(y,z,u)) * w) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(29951(a,1),37006(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29951 37006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37069">
    <literal><![CDATA[
      a(((x \ L(y,z,u)) * w) * v5,v6,v7) = a((w * (x \ R(y,z,u))) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,32388,a,b,37068,a),flip(a)].">
      <j1 rule="hyper" parents="64 32388 37068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37070">
    <literal><![CDATA[
      a(((x * L(x,y,z)) * u) * w,v5,v6) = a((u * (x \ R(x,y,z))) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,5611,a(flip),b,37069,a)].">
      <j1 rule="hyper" parents="64 5611 37069"/>
    </justification>
  </clause>

  <clause id="37071">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ ((K(y,x) * K(y,x)) \ ((z \ K(x,y)) \ u))) = T(K(x,y) * (z \ 1),K(y,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,22835,a(flip),b,37031,a)].">
      <j1 rule="hyper" parents="64 22835 37031"/>
    </justification>
  </clause>

  <clause id="37072">
    <literal><![CDATA[
      R(L(x,y,z),u,w) * (T(x,x \ v5) / L((x \ v5) \ v5,y,z)) = x * (L(x,y,z) \ L(R(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,2329,a(flip),b,37032,a),flip(a)].">
      <j1 rule="hyper" parents="373 2329 37032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37073">
    <literal><![CDATA[
      T(x / y,z) \ (T(x / y,z) / u) = ((1 / x) / y) \ (((x * x) \ (x / y)) / u)
    ]]></literal>
    <justification jstring="[para(10(a,1),37038(a,1,2))].">
      <j1 rule="para" parents="10 37038"/>
    </justification>
  </clause>

  <clause id="37074">
    <literal><![CDATA[
      ((1 / x) / y) \ (((x * x) \ (x / y)) / z) = (x / y) \ ((x / y) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14846,a(flip),b,37073,a),flip(a)].">
      <j1 rule="hyper" parents="64 14846 37073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37076">
    <literal><![CDATA[
      ((1 / x) / y) \ (((x * x) \ (x / y)) / z) = (y \ x) \ ((y \ x) / z)
    ]]></literal>
    <justification jstring="[hyper(373,a,14813,a(flip),b,37074,a),flip(a)].">
      <j1 rule="hyper" parents="373 14813 37074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37077">
    <literal><![CDATA[
      ((1 / x) / y) \ (((1 / x) / y) / z) = (y \ x) \ ((y \ x) / z)
    ]]></literal>
    <justification jstring="[para(887(a,1),37076(a,1,2,1))].">
      <j1 rule="para" parents="887 37076"/>
    </justification>
  </clause>

  <clause id="37078">
    <literal><![CDATA[
      (x \ (1 / y)) \ ((x \ (1 / y)) / z) = (x \ y) \ ((x \ y) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14813,a(flip),b,37077,a)].">
      <j1 rule="hyper" parents="64 14813 37077"/>
    </justification>
  </clause>

  <clause id="37079">
    <literal><![CDATA[
      ((x * y) \ (1 / (y * (x / (y * x))))) \ (((x * y) \ (1 / (y * (x / (y * x))))) / z) = (L(x * y,y,y) \ 1) \ (((x * y) \ (y * (x / (y * x)))) / z)
    ]]></literal>
    <justification jstring="[para(30148(a,1),37078(a,2,1))].">
      <j1 rule="para" parents="30148 37078"/>
    </justification>
  </clause>

  <clause id="37080">
    <literal><![CDATA[
      R(x,y,(z \ (z / u)) * ((1 / L(1 / u,u,u * z)) \ w)) = R(x,y,((z \ (u \ z)) * (z \ (u \ z))) * w)
    ]]></literal>
    <justification jstring="[para(30678(a,1),37064(a,1,3,2,1))].">
      <j1 rule="para" parents="30678 37064"/>
    </justification>
  </clause>

  <clause id="37081">
    <literal><![CDATA[
      (x * (y * a(z,u,x))) \ (x * (y * (a(z,u,x) * a(z,u,x)))) = L(a(z,u,x),a(z,u,x),x * y)
    ]]></literal>
    <justification jstring="[para(27920(a,1),37066(a,1,2,2))].">
      <j1 rule="para" parents="27920 37066"/>
    </justification>
  </clause>

  <clause id="37082">
    <literal><![CDATA[
      L(L(a(x,y,z),a(x,y,z),u),u * a(x,y,z),z) = L(a(x,y,z),a(x,y,z),z * u)
    ]]></literal>
    <justification jstring="[hyper(1081,a,37081,a)].">
      <j1 rule="hyper" parents="1081 37081"/>
    </justification>
  </clause>

  <clause id="37083">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),z * u) = L(a(x,y,z),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,33201,a(flip),b,37082,a),flip(a)].">
      <j1 rule="hyper" parents="64 33201 37082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37085">
    <literal><![CDATA[
      R(x,x,L(y \ R(y,z,u),w,v5)) = L(x,x,L(y * R(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,25119,a(flip),b,37067,a)].">
      <j1 rule="hyper" parents="64 25119 37067"/>
    </justification>
  </clause>

  <clause id="37086">
    <literal><![CDATA[
      R(x,x,L(y \ R(y,z,u),w,v5)) = L(x,x,L(y * L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,33620,a(flip),b,37085,a),flip(a)].">
      <j1 rule="hyper" parents="373 33620 37085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37087">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ (K(x,y) * (K(x,y) * ((z \ K(x,y)) \ u)))) = T(K(x,y) * (z \ 1),K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(20680(a,1),37071(a,1,2,2))].">
      <j1 rule="para" parents="20680 37071"/>
    </justification>
  </clause>

  <clause id="37088">
    <literal><![CDATA[
      R(L(x,y,z),u,w) * (T(x,x \ v5) / L((x \ v5) \ v5,y,z)) = x * L(x \ R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(4243(a,1),37072(a,2,2))].">
      <j1 rule="para" parents="4243 37072"/>
    </justification>
  </clause>

  <clause id="37089">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (T(x,x \ v5) / L((x \ v5) \ v5,u,w)) = x * L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29(a,1),37088(a,1,1))].">
      <j1 rule="para" parents="29 37088"/>
    </justification>
  </clause>

  <clause id="37090">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (L(x,u,w) \ x) = x * L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(25068(a,1),37089(a,1,2))].">
      <j1 rule="para" parents="25068 37089"/>
    </justification>
  </clause>

  <clause id="37091">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ (K(x,y) * ((z \ 1) \ u))) = T(K(x,y) * (z \ 1),K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(24517(a,1),37087(a,1,2,2,2))].">
      <j1 rule="para" parents="24517 37087"/>
    </justification>
  </clause>

  <clause id="37092">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ ((z \ K(y,x)) \ u)) = T(K(x,y) * (z \ 1),K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(24516(a,1),37091(a,1,2,2))].">
      <j1 rule="para" parents="24516 37091"/>
    </justification>
  </clause>

  <clause id="37094">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ ((z \ K(y,x)) \ u)) = ((z \ 1) * K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(8163(a,1),37092(a,2,1))].">
      <j1 rule="para" parents="8163 37092"/>
    </justification>
  </clause>

  <clause id="37095">
    <literal><![CDATA[
      x * (T(T(x,y),y) \ ((z \ K(y,x)) \ u)) = (z \ K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(14444(a,1),37094(a,2,1))].">
      <j1 rule="para" parents="14444 37094"/>
    </justification>
  </clause>

  <clause id="37096">
    <literal><![CDATA[
      (x * K(y * z,x)) * (T(x * K(y \ z,x),y * y) \ ((u \ K(y * y,x * K(y * z,x))) \ w)) = (u \ K(x * K(y * z,x),y * y)) \ w
    ]]></literal>
    <justification jstring="[para(27145(a,1),37095(a,1,2,1,1))].">
      <j1 rule="para" parents="27145 37095"/>
    </justification>
  </clause>

  <clause id="37097">
    <literal><![CDATA[
      T(x * ((y \ K(z,u)) * K(K(z,u) * (y * y),y)),y) = L(y,y,x) \ (x * (y * (y \ K(z,u))))
    ]]></literal>
    <justification jstring="[para(29653(a,1),22993(a,2,1))].">
      <j1 rule="para" parents="29653 22993"/>
    </justification>
  </clause>

  <clause id="37098">
    <literal><![CDATA[
      T(x * ((y \ K(z,u)) * K(K(z,u) * (y * y),y)),y) = L(y,y,x) \ (x * K(z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),37097(a,2,2,2))].">
      <j1 rule="para" parents="10 37097"/>
    </justification>
  </clause>

  <clause id="37100">
    <literal><![CDATA[
      T(x * ((y \ K(z,u)) * K(K(z,u) * (y * y),y)),y) = (L(y,y,x) \ x) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23058,a(flip),b,37098,a),flip(a)].">
      <j1 rule="hyper" parents="373 23058 37098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37102">
    <literal><![CDATA[
      T(x * ((y \ K(z,u)) * K(y,y \ K(z,u))),y) = (L(y,y,x) \ x) * K(z,u)
    ]]></literal>
    <justification jstring="[para(22992(a,1),37100(a,1,1,2,2))].">
      <j1 rule="para" parents="22992 37100"/>
    </justification>
  </clause>

  <clause id="37103">
    <literal><![CDATA[
      (L(x,x,y) \ y) * K(z,u) = T(y * (K(z,u) / x),x)
    ]]></literal>
    <justification jstring="[para(5774(a,1),37102(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5774 37102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37104">
    <literal><![CDATA[
      K(x,(x * x) \ x) * (x \ ((((x * x) \ L(x,y,z)) * x) * u)) = x \ ((L(x,y,z) * (1 / x)) * u)
    ]]></literal>
    <justification jstring="[para(14737(a,1),25540(a,1,1))].">
      <j1 rule="para" parents="14737 25540"/>
    </justification>
  </clause>

  <clause id="37105">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ ((((x * x) \ L(x,y,z)) * x) * u)) = x \ ((L(x,y,z) * (1 / x)) * u)
    ]]></literal>
    <justification jstring="[para(4329(a,1),37104(a,1,1))].">
      <j1 rule="para" parents="4329 37104"/>
    </justification>
  </clause>

  <clause id="37107">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ ((((x * x) \ x) * L(x,y,z)) * u)) = x \ ((L(x,y,z) * (1 / x)) * u)
    ]]></literal>
    <justification jstring="[para(1267(a,1),37105(a,1,2,2,1))].">
      <j1 rule="para" parents="1267 37105"/>
    </justification>
  </clause>

  <clause id="37109">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ (((1 / x) * L(x,y,z)) * u)) = x \ ((L(x,y,z) * (1 / x)) * u)
    ]]></literal>
    <justification jstring="[para(309(a,1),37107(a,1,2,2,1,1))].">
      <j1 rule="para" parents="309 37107"/>
    </justification>
  </clause>

  <clause id="37110">
    <literal><![CDATA[
      (1 / (1 / x)) \ (((1 / x) * L(x,y,z)) * u) = x \ ((L(x,y,z) * (1 / x)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,6413,a,b,37109,a)].">
      <j1 rule="hyper" parents="64 6413 37109"/>
    </justification>
  </clause>

  <clause id="37111">
    <literal><![CDATA[
      (K(x,a(x,y,z) \ (x \ 1)) / (x * a(x,y,z))) * (x * x) = (x * (1 / (x * a(x,y,z)))) * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(7148(a,1),25579(a,1,1,1))].">
      <j1 rule="para" parents="7148 25579"/>
    </justification>
  </clause>

  <clause id="37112">
    <literal><![CDATA[
      R(x,y \ (z \ u),z) * ((y \ (((u / z) \ u) \ u)) * ((u / z) \ u)) = (x * (y \ (u / z))) * (u / (u / z))
    ]]></literal>
    <justification jstring="[para(26506(a,1),25915(a,1,1))].">
      <j1 rule="para" parents="26506 25915"/>
    </justification>
  </clause>

  <clause id="37113">
    <literal><![CDATA[
      (((((x \ y) * x) * L(x,z,u)) \ ((x \ y) * L(x,z,u))) * x) * x = L(x,x,y * L(L(x,y * x,x),z,u))
    ]]></literal>
    <justification jstring="[para(3184(a,1),26672(a,1,1,1,1))].">
      <j1 rule="para" parents="3184 26672"/>
    </justification>
  </clause>

  <clause id="37114">
    <literal><![CDATA[
      (a((x * (y / (y / z))) \ u,x,z) * u) / z = ((u / (x * (y / (y / z)))) * x) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[para(27306(a,1),26891(a,1,1,1))].">
      <j1 rule="para" parents="27306 26891"/>
    </justification>
  </clause>

  <clause id="37116">
    <literal><![CDATA[
      (a((x * ((y / z) \ y)) \ u,x,z) * u) / z = ((u / (x * (y / (y / z)))) * x) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[para(32399(a,1),37114(a,1,1,1))].">
      <j1 rule="para" parents="32399 37114"/>
    </justification>
  </clause>

  <clause id="37117">
    <literal><![CDATA[
      (a((x * y) \ z,x,y) * z) / y = ((z / (x * (u / (u / y)))) * x) * K(y \ u,y)
    ]]></literal>
    <justification jstring="[para(82(a,1),37116(a,1,1,1,1,1,2))].">
      <j1 rule="para" parents="82 37116"/>
    </justification>
  </clause>

  <clause id="37119">
    <literal><![CDATA[
      ((x / (y * (z / (z / u)))) * y) * K(u \ z,u) = (((x / (y * u)) * y) * u) / u
    ]]></literal>
    <justification jstring="[para(26812(a,1),37117(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26812 37117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37120">
    <literal><![CDATA[
      ((x / (y * (z / (z / u)))) * y) * K(u \ z,u) = (x / (y * u)) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,11,a(flip),b,37119,a),flip(a)].">
      <j1 rule="hyper" parents="373 11 37119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37121">
    <literal><![CDATA[
      (x / (y * (z / (z / u)))) * (y * K(u \ z,u)) = (x / (y * u)) * y
    ]]></literal>
    <justification jstring="[hyper(23059,a,37120,a)].">
      <j1 rule="hyper" parents="23059 37120"/>
    </justification>
  </clause>

  <clause id="37123">
    <literal><![CDATA[
      a(x \ ((y \ 1) * L((y \ 1) * (y * z),u,w)),v5,v6) = a(x \ L(y * R(z,u,w),y \ 1,y \ 1),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,36140,a(flip),b,26926,a)].">
      <j1 rule="hyper" parents="64 36140 26926"/>
    </justification>
  </clause>

  <clause id="37124">
    <literal><![CDATA[
      a(x,y,L(z,(u * u) / w,(u * u) / w) \ (u * u)) = a(x,y,((w \ 1) * (w * ((u * u) \ z))) \ 1)
    ]]></literal>
    <justification jstring="[para(7037(a,1),27727(a,2,3,1))].">
      <j1 rule="para" parents="7037 27727"/>
    </justification>
  </clause>

  <clause id="37125">
    <literal><![CDATA[
      a(x,y,L(z,(u * u) / w,(u * u) / w) \ (u * u)) = a(x,y,L((u * u) \ z,w,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,27556,a(flip),b,37124,a),flip(a)].">
      <j1 rule="hyper" parents="373 27556 37124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37126">
    <literal><![CDATA[
      L((x \ (x / y)) \ z,x \ (y \ x),x \ (y \ x)) = (1 / (T(1,y \ 1) / (T(x \ (x / y),1) \ 1))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,29552,a(flip),b,29127,a)].">
      <j1 rule="hyper" parents="64 29552 29127"/>
    </justification>
  </clause>

  <clause id="37127">
    <literal><![CDATA[
      L(x,(R(T(y,z),u,w) \ 1) * (a(R(T(y,z),u,w),L(T(y,z),u,w),v5) * v5),v6) = L(x,R(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(32197(a,1),30253(a,1,2,2,1))].">
      <j1 rule="para" parents="32197 30253"/>
    </justification>
  </clause>

  <clause id="37128">
    <literal><![CDATA[
      ((x / (x * y)) * y) \ K((x / (x * y)) * y,a(y,y,x) \ (K(y,x) \ 1)) = 1 / (K(y,x) * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(30285(a,1),30287(a,1,2,1))].">
      <j1 rule="para" parents="30285 30287"/>
    </justification>
  </clause>

  <clause id="37129">
    <literal><![CDATA[
      ((x / (x * y)) * y) \ K((x / (x * y)) * y,a(y,y,x) \ K(x,y)) = 1 / (K(y,x) * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(6092(a,1),37128(a,1,2,2,2))].">
      <j1 rule="para" parents="6092 37128"/>
    </justification>
  </clause>

  <clause id="37130">
    <literal><![CDATA[
      ((x / (x * y)) * y) \ K((x / (x * y)) * y,K(x,y)) = 1 / (K(y,x) * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(28352(a,1),37129(a,1,2))].">
      <j1 rule="para" parents="28352 37129"/>
    </justification>
  </clause>

  <clause id="37131">
    <literal><![CDATA[
      ((x / (x * y)) * y) \ K(x,K((x / (x * y)) * y,y)) = 1 / (K(y,x) * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(8108(a,1),37130(a,1,2))].">
      <j1 rule="para" parents="8108 37130"/>
    </justification>
  </clause>

  <clause id="37134">
    <literal><![CDATA[
      ((x / (x * y)) * y) \ K(x,K(y * (x / (x * y)),y)) = 1 / (K(y,x) * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(8516(a,1),37131(a,1,2,2))].">
      <j1 rule="para" parents="8516 37131"/>
    </justification>
  </clause>

  <clause id="37135">
    <literal><![CDATA[
      ((x / (x * y)) * y) \ K(x,K(y / T(y,x),y)) = 1 / (K(y,x) * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(28233(a,1),37134(a,1,2,2))].">
      <j1 rule="para" parents="28233 37134"/>
    </justification>
  </clause>

  <clause id="37136">
    <literal><![CDATA[
      ((x / (x * y)) * y) \ K(x,K(K(x,y),y)) = 1 / (K(y,x) * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(5787(a,2),37135(a,1,2,2,1))].">
      <j1 rule="para" parents="5787 37135"/>
    </justification>
  </clause>

  <clause id="37137">
    <literal><![CDATA[
      1 / (K(x,y) * a(x,x,y)) = ((y / (y * x)) * x) \ 1
    ]]></literal>
    <justification jstring="[para(8038(a,1),37136(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8038 37136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37138">
    <literal><![CDATA[
      1 / (K(x,y) * a(x,x,y)) = (y / (y * x)) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,31131,a(flip),b,37137,a),flip(a)].">
      <j1 rule="hyper" parents="373 31131 37137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37141">
    <literal><![CDATA[
      1 / (1 / (x \ ((y / (y * x)) \ 1))) = (y / (y * x)) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30933,a,b,37138,a)].">
      <j1 rule="hyper" parents="64 30933 37138"/>
    </justification>
  </clause>

  <clause id="37142">
    <literal><![CDATA[
      a(x,y \ 1,L(y \ ((1 / y) \ z),y,x)) * (y \ L(z,y \ 1,x)) = (y \ 1) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(11794(a,1),30378(a,1,1,3))].">
      <j1 rule="para" parents="11794 30378"/>
    </justification>
  </clause>

  <clause id="37143">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,z,u * z) \ u,L(z \ 1,z,z * (u \ 1)),u)) = a(x,y,((u \ 1) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(23997(a,1),30684(a,1,3,1,1))].">
      <j1 rule="para" parents="23997 30684"/>
    </justification>
  </clause>

  <clause id="37144">
    <literal><![CDATA[
      L(L(x * ((y * x) \ y),z,x),u,w) * v5 = K(x,x \ 1) * (L(L(x \ 1,x,y) * x,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,23383,a(flip),b,31330,a),flip(a)].">
      <j1 rule="hyper" parents="373 23383 31330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37146">
    <literal><![CDATA[
      L(x,y,a(z * (u \ (u \ w)),L(w,u,u),z)) = L(x,y,a(z,T(u \ (u \ w),v5),T(u \ (u \ w),v5)))
    ]]></literal>
    <justification jstring="[para(32361(a,1),32301(a,1,3))].">
      <j1 rule="para" parents="32361 32301"/>
    </justification>
  </clause>

  <clause id="37147">
    <literal><![CDATA[
      L(x,y,a(z,T(z \ (z \ u),w),T(z \ (z \ u),w))) = L(x,y,a(z \ u,L(u,z,z),z))
    ]]></literal>
    <justification jstring="[para(10(a,1),37146(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 37146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37149">
    <literal><![CDATA[
      L(x,y,a(z,T(z \ (z \ u),w),T(z \ (z \ u),w))) = L(x,y,a(u * z,u,z))
    ]]></literal>
    <justification jstring="[para(35843(a,1),37147(a,2,3))].">
      <j1 rule="para" parents="35843 37147"/>
    </justification>
  </clause>

  <clause id="37150">
    <literal><![CDATA[
      L(x,y,a(z,T(z \ (z \ u),w),T(z \ (z \ u),w))) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,29304,a(flip),b,37149,a),flip(a)].">
      <j1 rule="hyper" parents="373 29304 37149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37151">
    <literal><![CDATA[
      L(x,y,a(z,z \ (z \ u),z \ (z \ u))) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(7107(a,1),37150(a,1,3))].">
      <j1 rule="para" parents="7107 37150"/>
    </justification>
  </clause>

  <clause id="37152">
    <literal><![CDATA[
      x * R(T(y,(y \ L(y,z,u)) * x),y \ L(y,z,u),x) = (y \ L(y,z,u)) \ (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(10(a,1),33131(a,2,2,1))].">
      <j1 rule="para" parents="10 33131"/>
    </justification>
  </clause>

  <clause id="37153">
    <literal><![CDATA[
      x * R(T(y,(y \ L(y,z,u)) * x),y \ L(y,z,u),x) = L((y \ 1) \ x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,11898,a(flip),b,37152,a),flip(a)].">
      <j1 rule="hyper" parents="373 11898 37152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37155">
    <literal><![CDATA[
      x * R(T(y,x),y \ L(y,z,u),x) = L((y \ 1) \ x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(28372(a,1),37153(a,1,2,1))].">
      <j1 rule="para" parents="28372 37153"/>
    </justification>
  </clause>

  <clause id="37157">
    <literal><![CDATA[
      a((a(x,(y * y) \ z,z \ (y * y)) \ 1) * u,w,v5) = a((z * ((x * ((y * y) \ z)) \ x)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(550(a,1),33366(a,1,1,1,1,3))].">
      <j1 rule="para" parents="550 33366"/>
    </justification>
  </clause>

  <clause id="37158">
    <literal><![CDATA[
      a((x * ((y * ((z * z) \ x)) \ y)) * u,w,v5) = a((a(y,x,x \ (z * z)) \ 1) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(11965(a,1),37157(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11965 37157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37159">
    <literal><![CDATA[
      a((x * ((y * ((z * z) \ x)) \ y)) * u,w,v5) = a(a(y,x,x \ (z * z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,2662,a(flip),b,37158,a),flip(a)].">
      <j1 rule="hyper" parents="373 2662 37158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37161">
    <literal><![CDATA[
      a((x * ((y * x) \ (y * (z * z)))) * u,w,v5) = a(a(y,x,x \ (z * z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(15290(a,1),37159(a,1,1,1,2))].">
      <j1 rule="para" parents="15290 37159"/>
    </justification>
  </clause>

  <clause id="37162">
    <literal><![CDATA[
      a(a(x,y,y \ (z * z)) * u,w,v5) = a(u * (y * ((x * y) \ x)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34122,a(flip),b,37161,a),flip(a)].">
      <j1 rule="hyper" parents="64 34122 37161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37164">
    <literal><![CDATA[
      a(x * (y * ((z * y) \ z)),u,w) = a(a(z,y,y) * x,u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),37162(a,1,1,1,3)),flip(a)].">
      <j1 rule="para" parents="9 37162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37165">
    <literal><![CDATA[
      a(a(x,y,y \ (z * z)) * u,w,v5) = a(a(x,y,y) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,37162,a,b,37164,a)].">
      <j1 rule="hyper" parents="64 37162 37164"/>
    </justification>
  </clause>

  <clause id="37166">
    <literal><![CDATA[
      a(x * a(y,z,z \ 1),u,w) = a(a(y,z,z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33368,a(flip),b,37164,a)].">
      <j1 rule="hyper" parents="64 33368 37164"/>
    </justification>
  </clause>

  <clause id="37167">
    <literal><![CDATA[
      a(a(x * y,x,x) * z,u,w) = a(a(y,x,x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33384,a,b,37166,a)].">
      <j1 rule="hyper" parents="64 33384 37166"/>
    </justification>
  </clause>

  <clause id="37168">
    <literal><![CDATA[
      a(a(x * y,y,y) * z,u,w) = a(a(x,y,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(26016(a,1),37167(a,1,1,1))].">
      <j1 rule="para" parents="26016 37167"/>
    </justification>
  </clause>

  <clause id="37169">
    <literal><![CDATA[
      a(((x * y) \ (y \ x)) * z,u,w) = a(a(x,y,y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,36208,a(flip),b,37168,a)].">
      <j1 rule="hyper" parents="64 36208 37168"/>
    </justification>
  </clause>

  <clause id="37170">
    <literal><![CDATA[
      a(x * ((y * z) \ (z \ y)),u,w) = a(a(y,z,z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,37169,a)].">
      <j1 rule="hyper" parents="26847 37169"/>
    </justification>
  </clause>

  <clause id="37171">
    <literal><![CDATA[
      a(x * a(y,z,z \ (u * u)),w,v5) = a(a(y,z,z) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(26847,a,37165,a)].">
      <j1 rule="hyper" parents="26847 37165"/>
    </justification>
  </clause>

  <clause id="37172">
    <literal><![CDATA[
      a(L(R(x,y,z) \ x,u,x * L(x,y,z)),R(x,y,z),w) = (((R(x,y,z) \ x) * (R(x,y,z) * w)) / w) \ x
    ]]></literal>
    <justification jstring="[para(2156(a,1),33590(a,2,1,1,1))].">
      <j1 rule="para" parents="2156 33590"/>
    </justification>
  </clause>

  <clause id="37173">
    <literal><![CDATA[
      ((x \ a(x,x,y)) * (x \ a(x,x,y))) * (y / (x \ T(y,x \ 1))) = R(y \ (x \ y),x \ a(x,x,y),y)
    ]]></literal>
    <justification jstring="[para(30121(a,1),33732(a,1,2,2))].">
      <j1 rule="para" parents="30121 33732"/>
    </justification>
  </clause>

  <clause id="37174">
    <literal><![CDATA[
      R(x \ (y \ x),y \ a(y,y,x),x) = ((y \ a(y,y,x)) * (y \ a(y,y,x))) * (K(y \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(14856(a,1),37173(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14856 37173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37175">
    <literal><![CDATA[
      R(x \ (y \ x),y \ a(y,y,x),x) = (y \ a(y,y,x)) * ((K(x,y \ 1) / (y \ a(y,y,x))) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,24930,a(flip),b,37174,a),flip(a)].">
      <j1 rule="hyper" parents="373 24930 37174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37176">
    <literal><![CDATA[
      R(x \ (y \ x),y \ a(y,y,x),x) = (y \ a(y,y,x)) * ((K(x,y \ 1) * (a(y,y,x) \ y)) \ y)
    ]]></literal>
    <justification jstring="[para(30193(a,1),37175(a,2,2,1))].">
      <j1 rule="para" parents="30193 37175"/>
    </justification>
  </clause>

  <clause id="37177">
    <literal><![CDATA[
      R(x \ (y \ x),y \ a(y,y,x),x) = (y \ a(y,y,x)) * ((y * (a(y,y,x) \ K(x,1 / y))) \ y)
    ]]></literal>
    <justification jstring="[para(31639(a,1),37176(a,2,2,1))].">
      <j1 rule="para" parents="31639 37176"/>
    </justification>
  </clause>

  <clause id="37178">
    <literal><![CDATA[
      R(x \ (y \ x),y \ a(y,y,x),x) = (y \ a(y,y,x)) * ((y * (a(y,y,x) \ K(x,y \ 1))) \ y)
    ]]></literal>
    <justification jstring="[para(6041(a,1),37177(a,2,2,1,2,2))].">
      <j1 rule="para" parents="6041 37177"/>
    </justification>
  </clause>

  <clause id="37179">
    <literal><![CDATA[
      R(x \ (y \ x),y \ a(y,y,x),x) = (y \ a(y,y,x)) * ((y * (x \ L(T(x,y \ 1),y,y))) \ y)
    ]]></literal>
    <justification jstring="[para(25528(a,1),37178(a,2,2,1,2))].">
      <j1 rule="para" parents="25528 37178"/>
    </justification>
  </clause>

  <clause id="37180">
    <literal><![CDATA[
      R(x \ (y \ x),y \ a(y,y,x),x) = (y \ a(y,y,x)) * ((y * (x \ (y * (x * (y \ 1))))) \ y)
    ]]></literal>
    <justification jstring="[para(1140(a,1),37179(a,2,2,1,2,2))].">
      <j1 rule="para" parents="1140 37179"/>
    </justification>
  </clause>

  <clause id="37181">
    <literal><![CDATA[
      R(x \ (y \ x),y \ a(y,y,x),x) = (y \ a(y,y,x)) * ((1 / (x \ (y \ x))) \ y)
    ]]></literal>
    <justification jstring="[para(36118(a,1),37180(a,2,2,1))].">
      <j1 rule="para" parents="36118 37180"/>
    </justification>
  </clause>

  <clause id="37182">
    <literal><![CDATA[
      R(x \ (y \ x),y \ a(y,y,x),x) = (y \ a(y,y,x)) * (y * (x \ (y \ x)))
    ]]></literal>
    <justification jstring="[para(25909(a,1),37181(a,2,2))].">
      <j1 rule="para" parents="25909 37181"/>
    </justification>
  </clause>

  <clause id="37183">
    <literal><![CDATA[
      R(x \ (y \ x),y \ a(y,y,x),x) = (x \ (y \ x)) * a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,34808,a(flip),b,37182,a),flip(a)].">
      <j1 rule="hyper" parents="373 34808 37182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37184">
    <literal><![CDATA[
      (x \ (y \ x)) * a(y,y,x) = L(x,y,y) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,36554,a(flip),b,37183,a),flip(a)].">
      <j1 rule="hyper" parents="64 36554 37183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37185">
    <literal><![CDATA[
      a(x,y,L(z \ (u \ z),u,z)) = a(x,y,L(z,u,u) \ (u \ z))
    ]]></literal>
    <justification jstring="[para(37184(a,1),33853(a,1,3)),flip(a)].">
      <j1 rule="para" parents="37184 33853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37186">
    <literal><![CDATA[
      K(x,T(y \ (L(z,u,w) \ v5),K(z,z \ v5)) * v6) = K(x,T((L(z,u,w) \ v5) / y,v5 / z) * v6)
    ]]></literal>
    <justification jstring="[para(28333(a,1),33741(a,2,2,1))].">
      <j1 rule="para" parents="28333 33741"/>
    </justification>
  </clause>

  <clause id="37187">
    <literal><![CDATA[
      K(x,T(y \ (L(z,u,w) \ v5),K(z,z \ v5)) * v6) = K(x,T((L(z,u,w) \ v5) / y,v5 * z) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,21577,a(flip),b,37186,a),flip(a)].">
      <j1 rule="hyper" parents="373 21577 37186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37189">
    <literal><![CDATA[
      a(x,y * ((z * u) \ (((w * w) \ z) * ((v5 * v5) * (u * v6)))),v7) = a(x,L(T(v5 * v5,u) * v6,u,z) * y,v7)
    ]]></literal>
    <justification jstring="[para(484(a,1),34104(a,1,2,2,2))].">
      <j1 rule="para" parents="484 34104"/>
    </justification>
  </clause>

  <clause id="37190">
    <literal><![CDATA[
      R((x / ((y / x) \ 1)) \ 1,((y / x) \ 1) \ x,(x \ y) \ y) = ((x \ y) \ 1) / ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(15009(a,1),34703(a,1,2))].">
      <j1 rule="para" parents="15009 34703"/>
    </justification>
  </clause>

  <clause id="37191">
    <literal><![CDATA[
      R((x / ((y / x) \ 1)) \ 1,((y / x) \ 1) \ x,x) = ((x \ y) \ 1) / ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,23313,a(flip),b,37190,a)].">
      <j1 rule="hyper" parents="64 23313 37190"/>
    </justification>
  </clause>

  <clause id="37193">
    <literal><![CDATA[
      ((x \ y) \ 1) / ((x \ y) \ y) = ((y / x) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,26623,a(flip),b,37191,a),flip(a)].">
      <j1 rule="hyper" parents="64 26623 37191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37194">
    <literal><![CDATA[
      x \ ((y / x) \ K(x,y \ 1)) = ((y / x) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,34755,a,b,37193,a)].">
      <j1 rule="hyper" parents="64 34755 37193"/>
    </justification>
  </clause>

  <clause id="37195">
    <literal><![CDATA[
      a(L(x,(y * x) \ x,y \ x),y * x,y * x) = a(x,y \ x,L(y * x,x,y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,32611,a(flip),b,35548,a)].">
      <j1 rule="hyper" parents="64 32611 35548"/>
    </justification>
  </clause>

  <clause id="37196">
    <literal><![CDATA[
      a(x,y \ x,L(y * x,x,y \ x)) = a(x,y * x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32646,a(flip),b,37195,a),flip(a)].">
      <j1 rule="hyper" parents="64 32646 37195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37198">
    <literal><![CDATA[
      a(x,y \ x,L(y * x,x,x * y)) = a(x,y * x,y * x)
    ]]></literal>
    <justification jstring="[para(33799(a,1),37196(a,1,3))].">
      <j1 rule="para" parents="33799 37196"/>
    </justification>
  </clause>

  <clause id="37199">
    <literal><![CDATA[
      a(x,y \ x,y * x) = a(x,y * x,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24008,a(flip),b,37198,a)].">
      <j1 rule="hyper" parents="64 24008 37198"/>
    </justification>
  </clause>

  <clause id="37200">
    <literal><![CDATA[
      a(x,(y \ x) * x,(y \ x) * x) = a(x,y,(y \ x) * x)
    ]]></literal>
    <justification jstring="[hyper(32007,a,37199,a),flip(a)].">
      <j1 rule="hyper" parents="32007 37199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37202">
    <literal><![CDATA[
      L(L(x,x \ y,y),a(y,x * y,x),L(y,x,x) * y) = ((y * (x * y)) * x) \ ((y * ((x * y) * x)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29154,a(flip),b,35725,a)].">
      <j1 rule="hyper" parents="64 29154 35725"/>
    </justification>
  </clause>

  <clause id="37203">
    <literal><![CDATA[
      L(L(x,x \ y,y),a(y,x * y,x),a(x,x,y)) = ((y * (x * y)) * x) \ ((y * ((x * y) * x)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,9390,a(flip),b,37202,a)].">
      <j1 rule="hyper" parents="64 9390 37202"/>
    </justification>
  </clause>

  <clause id="37204">
    <literal><![CDATA[
      ((x * (y * x)) * y) \ ((x * ((y * x) * y)) * y) = L(y,y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29972,a(flip),b,37203,a),flip(a)].">
      <j1 rule="hyper" parents="64 29972 37203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37206">
    <literal><![CDATA[
      L(x,x \ y,y) = L(x,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3203,a,b,37204,a),flip(a)].">
      <j1 rule="hyper" parents="64 3203 37204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37207">
    <literal><![CDATA[
      a(x,x * y,y) \ y = L(y,y * x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,35697,a,b,37206,a)].">
      <j1 rule="hyper" parents="64 35697 37206"/>
    </justification>
  </clause>

  <clause id="37208">
    <literal><![CDATA[
      L(x \ 1,(x \ 1) * y,y) = L(x \ 1,x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29704,a(flip),b,37206,a),flip(a)].">
      <j1 rule="hyper" parents="64 29704 37206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37209">
    <literal><![CDATA[
      L(x * y,y \ (x \ y),y) = L(x * y,(x * y) * y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29603,a(flip),b,37206,a)].">
      <j1 rule="hyper" parents="64 29603 37206"/>
    </justification>
  </clause>

  <clause id="37210">
    <literal><![CDATA[
      1 / L(x,x * y,y) = y * ((y \ 1) / x)
    ]]></literal>
    <justification jstring="[para(37206(a,1),10275(a,1,2))].">
      <j1 rule="para" parents="37206 10275"/>
    </justification>
  </clause>

  <clause id="37211">
    <literal><![CDATA[
      x * L(x,x * y,y) = y * ((y \ x) * x)
    ]]></literal>
    <justification jstring="[para(37207(a,1),35732(a,1,2))].">
      <j1 rule="para" parents="37207 35732"/>
    </justification>
  </clause>

  <clause id="37212">
    <literal><![CDATA[
      x / (y * ((y \ 1) / x)) = x * L(x,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(225,a,37210,a(flip),b,27917,a)].">
      <j1 rule="hyper" parents="225 37210 27917"/>
    </justification>
  </clause>

  <clause id="37213">
    <literal><![CDATA[
      L(x,y \ x,y) = L(x,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,515,a,b,37211,a)].">
      <j1 rule="hyper" parents="35 515 37211"/>
    </justification>
  </clause>

  <clause id="37214">
    <literal><![CDATA[
      R(L(x,x * y,y),z,u) = L(R(x,z,u),y \ x,y)
    ]]></literal>
    <justification jstring="[para(37213(a,1),29(a,1,1))].">
      <j1 rule="para" parents="37213 29"/>
    </justification>
  </clause>

  <clause id="37215">
    <literal><![CDATA[
      L(x,x * y,y) \ L(R(x,z,u),y \ x,y) = L(x \ R(x,z,u),y \ x,y)
    ]]></literal>
    <justification jstring="[para(37213(a,1),4243(a,1,1))].">
      <j1 rule="para" parents="37213 4243"/>
    </justification>
  </clause>

  <clause id="37216">
    <literal><![CDATA[
      x / (y * ((y \ 1) / x)) = y * ((y \ x) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,37211,a(flip),b,37212,a),flip(a)].">
      <j1 rule="hyper" parents="373 37211 37212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37217">
    <literal><![CDATA[
      (x * y) * (((x * y) \ y) * y) = y / ((1 / (x * y)) * x)
    ]]></literal>
    <justification jstring="[para(1221(a,1),37216(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1221 37216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37218">
    <literal><![CDATA[
      L(x \ 1,x \ y,y) = L(x \ 1,x * y,y)
    ]]></literal>
    <justification jstring="[hyper(29615,a,37208,a),flip(a)].">
      <j1 rule="hyper" parents="29615 37208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37219">
    <literal><![CDATA[
      L(R(x,y,z),u \ x,u) = L(R(x,y,z),x * u,u)
    ]]></literal>
    <justification jstring="[hyper(25244,a,37214,a),flip(a)].">
      <j1 rule="hyper" parents="25244 37214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37220">
    <literal><![CDATA[
      L(x * y,y \ (x \ y),y) = L(x * y,L(x,y,y),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,29641,a(flip),b,37209,a),flip(a)].">
      <j1 rule="hyper" parents="373 29641 37209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37221">
    <literal><![CDATA[
      (a(x,L(y,x,x),y * x) \ y) * x = L(y * x,L(y,x,x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,35935,a,b,37220,a)].">
      <j1 rule="hyper" parents="64 35935 37220"/>
    </justification>
  </clause>

  <clause id="37222">
    <literal><![CDATA[
      L(x * y,L(x,y,y),y) = L(x * y,L(x,x,y),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29726,a,b,37220,a),flip(a)].">
      <j1 rule="hyper" parents="64 29726 37220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37223">
    <literal><![CDATA[
      1 / L(x,y,y \ x) = (1 / (y * x)) * y
    ]]></literal>
    <justification jstring="[hyper(37,a,34320,a(flip),b,37217,a(flip))].">
      <j1 rule="hyper" parents="37 34320 37217"/>
    </justification>
  </clause>

  <clause id="37224">
    <literal><![CDATA[
      L(x,y,y \ x) = L(x,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(37,a,21690,a,b,37223,a),flip(a)].">
      <j1 rule="hyper" parents="37 21690 37223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37225">
    <literal><![CDATA[
      L(x,y,x * y) \ x = a(y \ x,y,x)
    ]]></literal>
    <justification jstring="[para(37224(a,1),27268(a,1,1))].">
      <j1 rule="para" parents="37224 27268"/>
    </justification>
  </clause>

  <clause id="37226">
    <literal><![CDATA[
      a(x \ y,x,y) = a(y * x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35389,a(flip),b,37225,a),flip(a)].">
      <j1 rule="hyper" parents="64 35389 37225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37227">
    <literal><![CDATA[
      x \ (y * R(y \ x,x,y \ 1)) = a((y \ 1) * x,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,36828,a,b,37226,a)].">
      <j1 rule="hyper" parents="64 36828 37226"/>
    </justification>
  </clause>

  <clause id="37228">
    <literal><![CDATA[
      L(x * y,L(x,y,y),y) = (a(y,x,x * y) \ x) * y
    ]]></literal>
    <justification jstring="[para(35677(a,1),37221(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="35677 37221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37229">
    <literal><![CDATA[
      L(x * y,L(x,y,y),y) = L(x * y,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30278,a(flip),b,37228,a),flip(a)].">
      <j1 rule="hyper" parents="373 30278 37228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37230">
    <literal><![CDATA[
      L(x * y,L(x,x,y),y) = L(x * y,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,37222,a(flip),b,37229,a)].">
      <j1 rule="hyper" parents="64 37222 37229"/>
    </justification>
  </clause>

  <clause id="37231">
    <literal><![CDATA[
      x \ (y * R(y \ x,x,y \ 1)) = a(y * x,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,2662,a(flip),b,37227,a),flip(a)].">
      <j1 rule="hyper" parents="373 2662 37227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37232">
    <literal><![CDATA[
      a(x * y,y,x \ 1) * (y * (x \ 1)) = (x / y) \ 1
    ]]></literal>
    <justification jstring="[para(37231(a,1),26024(a,1,1))].">
      <j1 rule="para" parents="37231 26024"/>
    </justification>
  </clause>

  <clause id="37233">
    <literal><![CDATA[
      R(x * (y \ 1),x,y \ 1) = (y / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,26851,a(flip),b,37232,a)].">
      <j1 rule="hyper" parents="64 26851 37232"/>
    </justification>
  </clause>

  <clause id="37234">
    <literal><![CDATA[
      R((a(x,y,z) \ 1) * u,u,a(x,y,z) \ 1) = (a(x,y,z) / u) \ 1
    ]]></literal>
    <justification jstring="[para(23736(a,2),37233(a,1,1))].">
      <j1 rule="para" parents="23736 37233"/>
    </justification>
  </clause>

  <clause id="37235">
    <literal><![CDATA[
      L(x,x * y,y) \ L(R(x,z,u),x * y,y) = L(x \ R(x,z,u),y \ x,y)
    ]]></literal>
    <justification jstring="[para(37219(a,1),37215(a,1,2))].">
      <j1 rule="para" parents="37219 37215"/>
    </justification>
  </clause>

  <clause id="37236">
    <literal><![CDATA[
      L(x \ R(x,y,z),u \ x,u) = L(x \ R(x,y,z),x * u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,4243,a(flip),b,37235,a),flip(a)].">
      <j1 rule="hyper" parents="64 4243 37235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37237">
    <literal><![CDATA[
      a(x \ L(a(y,z,u) \ z,a(y,z,u) / z,a(y,z,u) / z),w,v5) = a(x \ (a(y,z,u) / z),w,v5)
    ]]></literal>
    <justification jstring="[para(8(a,1),35791(a,2,1,2))].">
      <j1 rule="para" parents="8 35791"/>
    </justification>
  </clause>

  <clause id="37238">
    <literal><![CDATA[
      a(x \ L(a(y,z,u) \ z,a(y,z,u) / z,a(y,z,u) / z),w,v5) = a(x \ (z \ a(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32369,a(flip),b,37237,a),flip(a)].">
      <j1 rule="hyper" parents="373 32369 37237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37239">
    <literal><![CDATA[
      a(x \ L(a(y,z,u) \ z,a(y,z,u) / z,a(y,z,u) / z),w,v5) = a(x \ (a(y,z,u) * z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,35764,a(flip),b,37238,a),flip(a)].">
      <j1 rule="hyper" parents="373 35764 37238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37240">
    <literal><![CDATA[
      a(x \ L(a(y,z,u) \ z,a(y,z,u) / z,z \ a(y,z,u)),w,v5) = a(x \ (a(y,z,u) * z),w,v5)
    ]]></literal>
    <justification jstring="[para(23216(a,1),37239(a,1,1,2))].">
      <j1 rule="para" parents="23216 37239"/>
    </justification>
  </clause>

  <clause id="37241">
    <literal><![CDATA[
      a(x \ L(a(y,z,u) \ z,a(y,z,u) / z,z * a(y,z,u)),w,v5) = a(x \ (a(y,z,u) * z),w,v5)
    ]]></literal>
    <justification jstring="[para(35030(a,1),37240(a,1,1,2))].">
      <j1 rule="para" parents="35030 37240"/>
    </justification>
  </clause>

  <clause id="37242">
    <literal><![CDATA[
      a(x \ (a(y,z,u) \ z),w,v5) = a(x \ (a(y,z,u) * z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,35032,a(flip),b,37241,a)].">
      <j1 rule="hyper" parents="64 35032 37241"/>
    </justification>
  </clause>

  <clause id="37244">
    <literal><![CDATA[
      a(L(a(x,y,z),a(x,y,z),y),u,w) = a(y \ (a(x,y,z) * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32455,a,b,37242,a)].">
      <j1 rule="hyper" parents="64 32455 37242"/>
    </justification>
  </clause>

  <clause id="37245">
    <literal><![CDATA[
      a(L(a(x,y,z),a(x,y,z),y),u,w) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26791,a(flip),b,37244,a),flip(a)].">
      <j1 rule="hyper" parents="373 26791 37244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37247">
    <literal><![CDATA[
      a(x \ (y \ ((y * (x * z)) / z)),u,w) = a(a(y,x,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33346,a(flip),b,37245,a)].">
      <j1 rule="hyper" parents="64 33346 37245"/>
    </justification>
  </clause>

  <clause id="37248">
    <literal><![CDATA[
      a(x \ (y \ (z \ (y * (x * z)))),u,w) = a(a(y,x,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32377,a(flip),b,37247,a)].">
      <j1 rule="hyper" parents="64 32377 37247"/>
    </justification>
  </clause>

  <clause id="37249">
    <literal><![CDATA[
      L(x,y \ L(a(z,u,w) \ u,a(z,u,w) / u,a(z,u,w) / u),v5) = L(x,y \ (a(z,u,w) / u),v5)
    ]]></literal>
    <justification jstring="[para(8(a,1),35792(a,2,2,2))].">
      <j1 rule="para" parents="8 35792"/>
    </justification>
  </clause>

  <clause id="37250">
    <literal><![CDATA[
      L(x,y \ L(a(z,u,w) \ u,a(z,u,w) / u,a(z,u,w) / u),v5) = L(x,y \ (u \ a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29552,a(flip),b,37249,a),flip(a)].">
      <j1 rule="hyper" parents="373 29552 37249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37251">
    <literal><![CDATA[
      L(x,y \ L(a(z,u,w) \ u,a(z,u,w) / u,a(z,u,w) / u),v5) = L(x,y \ (u * a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,35756,a(flip),b,37250,a),flip(a)].">
      <j1 rule="hyper" parents="373 35756 37250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37252">
    <literal><![CDATA[
      L(x,y \ L(a(z,u,w) \ u,a(z,u,w) / u,u \ a(z,u,w)),v5) = L(x,y \ (u * a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(23216(a,1),37251(a,1,2,2))].">
      <j1 rule="para" parents="23216 37251"/>
    </justification>
  </clause>

  <clause id="37253">
    <literal><![CDATA[
      L(x,y \ L(a(z,u,w) \ u,a(z,u,w) / u,u * a(z,u,w)),v5) = L(x,y \ (u * a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(35030(a,1),37252(a,1,2,2))].">
      <j1 rule="para" parents="35030 37252"/>
    </justification>
  </clause>

  <clause id="37254">
    <literal><![CDATA[
      L(x,y \ L(a(z,u,w) \ u,u \ a(z,u,w),u * a(z,u,w)),v5) = L(x,y \ (u * a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(29437(a,1),37253(a,1,2,2))].">
      <j1 rule="para" parents="29437 37253"/>
    </justification>
  </clause>

  <clause id="37255">
    <literal><![CDATA[
      L(x,y \ L(a(z,u,w) \ u,u * a(z,u,w),u * a(z,u,w)),v5) = L(x,y \ (u * a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(35747(a,1),37254(a,1,2,2))].">
      <j1 rule="para" parents="35747 37254"/>
    </justification>
  </clause>

  <clause id="37256">
    <literal><![CDATA[
      L(x,y \ (1 / (1 / (a(z,u,w) \ u))),v5) = L(x,y \ (u * a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(35031(a,1),37255(a,1,2,2))].">
      <j1 rule="para" parents="35031 37255"/>
    </justification>
  </clause>

  <clause id="37257">
    <literal><![CDATA[
      L(x,y \ (1 / (a(z,u,w) / u)),v5) = L(x,y \ (u * a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(35787(a,1),37256(a,1,2,2,2))].">
      <j1 rule="para" parents="35787 37256"/>
    </justification>
  </clause>

  <clause id="37258">
    <literal><![CDATA[
      L(x,y \ ((a(z,u,w) / u) \ 1),v5) = L(x,y \ (u * a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29552,a(flip),b,37257,a)].">
      <j1 rule="hyper" parents="64 29552 37257"/>
    </justification>
  </clause>

  <clause id="37259">
    <literal><![CDATA[
      L(x,L(a(y,z,u),a(y,z,u),z),w) = L(x,z \ (z * a(y,z,u)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,35796,a,b,37258,a)].">
      <j1 rule="hyper" parents="64 35796 37258"/>
    </justification>
  </clause>

  <clause id="37260">
    <literal><![CDATA[
      L(x,L(a(y,z,u),a(y,z,u),z),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11871,a(flip),b,37259,a),flip(a)].">
      <j1 rule="hyper" parents="373 11871 37259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37262">
    <literal><![CDATA[
      L(x,((y \ ((y * z) * u)) / u) \ z,w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33290,a(flip),b,37260,a)].">
      <j1 rule="hyper" parents="64 33290 37260"/>
    </justification>
  </clause>

  <clause id="37263">
    <literal><![CDATA[
      L(x,y \ (z \ ((z * (y * u)) / u)),w) = L(x,a(z,y,u),w)
    ]]></literal>
    <justification jstring="[para(33517(a,1),37262(a,1,2))].">
      <j1 rule="para" parents="33517 37262"/>
    </justification>
  </clause>

  <clause id="37264">
    <literal><![CDATA[
      L(x,y \ (z \ (u \ (z * (y * u)))),w) = L(x,a(z,y,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29559,a(flip),b,37263,a)].">
      <j1 rule="hyper" parents="64 29559 37263"/>
    </justification>
  </clause>

  <clause id="37265">
    <literal><![CDATA[
      (x * y) \ (y * T((a(z,u,w) \ 1) * x,y)) = L(T(a(z,u,w) \ 1,T(x,y)),x,y)
    ]]></literal>
    <justification jstring="[para(14052(a,1),36697(a,1,2,2,1))].">
      <j1 rule="para" parents="14052 36697"/>
    </justification>
  </clause>

  <clause id="37266">
    <literal><![CDATA[
      (x * y) \ (((a(z,u,w) \ 1) * x) * y) = L(T(a(z,u,w) \ 1,T(x,y)),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,37265,a)].">
      <j1 rule="hyper" parents="64 249 37265"/>
    </justification>
  </clause>

  <clause id="37267">
    <literal><![CDATA[
      R(T(a(x,y,z) \ 1,u * w),u,w) = L(T(a(x,y,z) \ 1,T(u,w)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,796,a(flip),b,37266,a)].">
      <j1 rule="hyper" parents="64 796 37266"/>
    </justification>
  </clause>

  <clause id="37268">
    <literal><![CDATA[
      R(T(a(x,y,z) \ 1,u * w),u,w) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(23735(a,1),37267(a,2,1))].">
      <j1 rule="para" parents="23735 37267"/>
    </justification>
  </clause>

  <clause id="37269">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u,w) = L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(23735(a,1),37268(a,1,1))].">
      <j1 rule="para" parents="23735 37268"/>
    </justification>
  </clause>

  <clause id="37271">
    <literal><![CDATA[
      L(a(x,y,y) \ 1,z,y \ x) = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,36729,a(flip),b,37269,a),flip(a)].">
      <j1 rule="hyper" parents="64 36729 37269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37272">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,x \ y) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,36709,a(flip),b,37269,a),flip(a)].">
      <j1 rule="hyper" parents="64 36709 37269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37273">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,x \ y,z) = (((x \ 1) * y) * z) / ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30427,a(flip),b,37269,a),flip(a)].">
      <j1 rule="hyper" parents="64 30427 37269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37274">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,u) \ ((a(x,y,z) \ 1) * u) = L(u,u,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(37269(a,1),16070(a,1,1))].">
      <j1 rule="para" parents="37269 16070"/>
    </justification>
  </clause>

  <clause id="37276">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),u,w) \ a(x,y,z)) = 1 / L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(37269(a,1),28794(a,2,2))].">
      <j1 rule="para" parents="37269 28794"/>
    </justification>
  </clause>

  <clause id="37277">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (1 / a(x,y,z)) = a(x,y,z) * L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(37269(a,1),33978(a,2,2))].">
      <j1 rule="para" parents="37269 33978"/>
    </justification>
  </clause>

  <clause id="37278">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ a(u,u,a(x,y,z)) = L(a(x,y,z) \ 1,u,u) \ 1
    ]]></literal>
    <justification jstring="[para(37269(a,1),36013(a,2,1))].">
      <j1 rule="para" parents="37269 36013"/>
    </justification>
  </clause>

  <clause id="37279">
    <literal><![CDATA[
      1 / (1 / ((x * (1 / y)) \ (x / y))) = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,36121,a(flip),b,37271,a)].">
      <j1 rule="hyper" parents="64 36121 37271"/>
    </justification>
  </clause>

  <clause id="37280">
    <literal><![CDATA[
      x * R(T(a(y,y,z) \ 1,(y \ z) * x),y \ z,x) = (y \ z) \ (((a(y,y,z) \ 1) * (y \ z)) * x)
    ]]></literal>
    <justification jstring="[para(37272(a,1),1821(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="37272 1821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37282">
    <literal><![CDATA[
      1 / (((x * (1 / y)) \ (x / y)) \ 1) = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[para(33651(a,1),37279(a,1,2))].">
      <j1 rule="para" parents="33651 37279"/>
    </justification>
  </clause>

  <clause id="37283">
    <literal><![CDATA[
      (x * (1 / y)) \ (x / y) = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(330,a,37282,a),flip(a)].">
      <j1 rule="hyper" parents="330 37282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37285">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ y) * (((1 / x) \ y) / x) = y * (a((1 / x) \ y,x,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,37283,a(flip),b,10871,a),flip(a)].">
      <j1 rule="hyper" parents="145 37283 10871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37286">
    <literal><![CDATA[
      a(x,x,a(y,z,u) \ 1) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(39,a,27037,a,b,37278,a)].">
      <j1 rule="hyper" parents="39 27037 37278"/>
    </justification>
  </clause>

  <clause id="37287">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * a(u,u,a(x,y,z)) = u \ ((1 / u) \ (a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(145,a,37286,a(flip),b,30230,a)].">
      <j1 rule="hyper" parents="145 37286 30230"/>
    </justification>
  </clause>

  <clause id="37288">
    <literal><![CDATA[
      x \ ((1 / x) \ (a(y,z,u) \ 1)) = L(a(y,z,u),x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,9367,a(flip),b,37287,a),flip(a)].">
      <j1 rule="hyper" parents="64 9367 37287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37289">
    <literal><![CDATA[
      (x \ 1) * (L(a(y,z,u),x,x) \ 1) = x \ (a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,37288,a(flip),b,1166,a)].">
      <j1 rule="hyper" parents="145 37288 1166"/>
    </justification>
  </clause>

  <clause id="37290">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ 1)) / (x \ 1) = L(a(y,z,u),x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(142,a,37289,a(flip),b,25714,a)].">
      <j1 rule="hyper" parents="142 37289 25714"/>
    </justification>
  </clause>

  <clause id="37291">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ 1)) / (x \ 1) = L(a(y,z,u) \ 1,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,36774,a,b,37290,a),flip(a)].">
      <j1 rule="hyper" parents="373 36774 37290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37292">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) / u) / (1 / u) = L(a(x,y,z) \ 1,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25680,a,b,37291,a)].">
      <j1 rule="hyper" parents="64 25680 37291"/>
    </justification>
  </clause>

  <clause id="37293">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) / (a(x,y,z) * u)) / (1 / (a(x,y,z) * u)) = (1 / (u / (a(x,y,z) \ 1))) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,35244,a(flip),b,37292,a),flip(a)].">
      <j1 rule="hyper" parents="373 35244 37292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37294">
    <literal><![CDATA[
      R(x,x,a(y,z,u) \ 1) = L(x,x,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,25116,a(flip),b,37274,a)].">
      <j1 rule="hyper" parents="64 25116 37274"/>
    </justification>
  </clause>

  <clause id="37295">
    <literal><![CDATA[
      R(x,x,a(y,z,u) \ 1) = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,1631,a(flip),b,37294,a),flip(a)].">
      <j1 rule="hyper" parents="373 1631 37294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37296">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * L(u,u,a(x,y,z)) = (1 / u) \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(37295(a,1),23766(a,1,2))].">
      <j1 rule="para" parents="37295 23766"/>
    </justification>
  </clause>

  <clause id="37297">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),u,w) \ a(x,y,z)) = L(a(x,y,z) \ 1,u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,24385,a(flip),b,37276,a),flip(a)].">
      <j1 rule="hyper" parents="373 24385 37276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37298">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (a(x,y,z) \ 1) = a(x,y,z) * L(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(13923(a,1),37277(a,1,2))].">
      <j1 rule="para" parents="13923 37277"/>
    </justification>
  </clause>

  <clause id="37299">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ 1,u,w) = a(x,y,z) \ L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,1807,a(flip),b,37298,a),flip(a)].">
      <j1 rule="hyper" parents="64 1807 37298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37300">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ y) * (((1 / x) \ y) / x) = y * (a((x \ 1) \ y,x,x) \ 1)
    ]]></literal>
    <justification jstring="[para(32386(a,1),37285(a,2,2,1))].">
      <j1 rule="para" parents="32386 37285"/>
    </justification>
  </clause>

  <clause id="37301">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ y) * (((1 / x) \ y) / x) = y * (a(1 \ (x * y),x,x) \ 1)
    ]]></literal>
    <justification jstring="[para(32625(a,1),37300(a,2,2,1))].">
      <j1 rule="para" parents="32625 37300"/>
    </justification>
  </clause>

  <clause id="37302">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ y) * (((1 / x) \ y) / x) = y * (a(x * y,x,x) \ 1)
    ]]></literal>
    <justification jstring="[para(66(a,1),37301(a,2,2,1,1))].">
      <j1 rule="para" parents="66 37301"/>
    </justification>
  </clause>

  <clause id="37303">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ y) * (((1 / x) \ y) / x) = y * (L(x \ 1,x,y) * x)
    ]]></literal>
    <justification jstring="[para(30502(a,1),37302(a,2,2))].">
      <j1 rule="para" parents="30502 37302"/>
    </justification>
  </clause>

  <clause id="37304">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ y) * (((1 / x) \ y) / x) = a(x * y,x,x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,31849,a(flip),b,37303,a),flip(a)].">
      <j1 rule="hyper" parents="373 31849 37303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37305">
    <literal><![CDATA[
      a(x * y,x,x) \ y = (y / (1 / x)) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,14696,a(flip),b,37304,a),flip(a)].">
      <j1 rule="hyper" parents="64 14696 37304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37306">
    <literal><![CDATA[
      a(x,y,a(z * u,z,z) * w) = a(x,y,w * (((u / (1 / z)) / z) \ u))
    ]]></literal>
    <justification jstring="[para(37305(a,1),27459(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="37305 27459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37307">
    <literal><![CDATA[
      ((x / (1 / y)) / y) \ T(x,a(z,u,w)) = x \ ((x * y) * (1 / y))
    ]]></literal>
    <justification jstring="[para(37305(a,1),31660(a,1,1))].">
      <j1 rule="para" parents="37305 31660"/>
    </justification>
  </clause>

  <clause id="37308">
    <literal><![CDATA[
      ((x / (1 / y)) / y) \ x = x \ ((x * y) * (1 / y))
    ]]></literal>
    <justification jstring="[para(9188(a,1),37307(a,1,2))].">
      <j1 rule="para" parents="9188 37307"/>
    </justification>
  </clause>

  <clause id="37309">
    <literal><![CDATA[
      a(x,y,a(z * u,z,z) * w) = a(x,y,w * (u \ ((u * z) * (1 / z))))
    ]]></literal>
    <justification jstring="[para(37308(a,1),37306(a,2,3,2))].">
      <j1 rule="para" parents="37308 37306"/>
    </justification>
  </clause>

  <clause id="37310">
    <literal><![CDATA[
      a(x,y,a(z * u,z,z) * w) = a(x,y,w * (u \ ((u * z) * (z \ 1))))
    ]]></literal>
    <justification jstring="[hyper(373,a,27485,a(flip),b,37309,a),flip(a)].">
      <j1 rule="hyper" parents="373 27485 37309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37311">
    <literal><![CDATA[
      a(x,y,a(z * u,z,z) * w) = a(x,y,w * a(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(240(a,1),37310(a,2,3,2))].">
      <j1 rule="para" parents="240 37310"/>
    </justification>
  </clause>

  <clause id="37312">
    <literal><![CDATA[
      a(x,y,a(z * u,u,u) * w) = a(x,y,w * a(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(26016(a,1),37311(a,1,3,1))].">
      <j1 rule="para" parents="26016 37311"/>
    </justification>
  </clause>

  <clause id="37313">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) / (a(x,y,z) * u)) / (1 / (a(x,y,z) * u)) = (1 / ((a(x,y,z) \ 1) \ u)) * u
    ]]></literal>
    <justification jstring="[para(23737(a,1),37293(a,2,1,2))].">
      <j1 rule="para" parents="23737 37293"/>
    </justification>
  </clause>

  <clause id="37314">
    <literal><![CDATA[
      R(a(x,y,z),a(x,y,z) * u,a(x,y,z) * u) \ 1 = (1 / ((a(x,y,z) \ 1) \ u)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,30588,a(flip),b,37313,a)].">
      <j1 rule="hyper" parents="64 30588 37313"/>
    </justification>
  </clause>

  <clause id="37315">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) * u,a(x,y,z) * u) \ 1 = (1 / ((a(x,y,z) \ 1) \ u)) * u
    ]]></literal>
    <justification jstring="[para(28787(a,1),37314(a,1,1))].">
      <j1 rule="para" parents="28787 37314"/>
    </justification>
  </clause>

  <clause id="37316">
    <literal><![CDATA[
      ((1 / (x / a(y,z,u))) * x) \ 1 = (1 / ((a(y,z,u) \ 1) \ x)) * x
    ]]></literal>
    <justification jstring="[para(34540(a,1),37315(a,1,1))].">
      <j1 rule="para" parents="34540 37315"/>
    </justification>
  </clause>

  <clause id="37317">
    <literal><![CDATA[
      (x * ((a(y,z,u) \ x) \ 1)) \ 1 = (1 / ((a(y,z,u) \ 1) \ x)) * x
    ]]></literal>
    <justification jstring="[para(28803(a,1),37316(a,1,1))].">
      <j1 rule="para" parents="28803 37316"/>
    </justification>
  </clause>

  <clause id="37318">
    <literal><![CDATA[
      (x * ((a(y,z,u) \ x) \ 1)) \ 1 = x * (((a(y,z,u) \ 1) \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,28669,a(flip),b,37317,a),flip(a)].">
      <j1 rule="hyper" parents="373 28669 37317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37319">
    <literal><![CDATA[
      x * R(T(a(y,y,z) \ 1,(y \ z) * x),y \ z,x) = (y \ z) \ (((y \ 1) * z) * x)
    ]]></literal>
    <justification jstring="[para(30425(a,1),37280(a,2,2,1))].">
      <j1 rule="para" parents="30425 37280"/>
    </justification>
  </clause>

  <clause id="37320">
    <literal><![CDATA[
      x * L(a(y,y,z) \ 1,y \ z,x) = (y \ z) \ (((y \ 1) * z) * x)
    ]]></literal>
    <justification jstring="[para(37268(a,1),37319(a,1,2))].">
      <j1 rule="para" parents="37268 37319"/>
    </justification>
  </clause>

  <clause id="37321">
    <literal><![CDATA[
      R(x,y,(z \ (z / u)) * ((L(1 / u,u,u * z) \ 1) \ w)) = R(x,y,((z \ (u \ z)) * (z \ (u \ z))) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26275,a(flip),b,37080,a)].">
      <j1 rule="hyper" parents="64 26275 37080"/>
    </justification>
  </clause>

  <clause id="37322">
    <literal><![CDATA[
      (K(x,x \ 1) / (x * a(x,y,z))) * (x * x) = (x * (1 / (x * a(x,y,z)))) * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(28686(a,1),37111(a,1,1,1))].">
      <j1 rule="para" parents="28686 37111"/>
    </justification>
  </clause>

  <clause id="37323">
    <literal><![CDATA[
      (1 / (L(x,x,x) * a(x,y,z))) * (x * x) = (x * (1 / (x * a(x,y,z)))) * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(25473(a,1),37322(a,1,1))].">
      <j1 rule="para" parents="25473 37322"/>
    </justification>
  </clause>

  <clause id="37325">
    <literal><![CDATA[
      (x * (1 / (x * a(x,y,z)))) * (1 / (1 / x)) = (1 / (a(x,y,z) / (1 / x))) * (x * x)
    ]]></literal>
    <justification jstring="[para(30823(a,1),37323(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="30823 37323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37326">
    <literal><![CDATA[
      (x * (1 / (x * a(x,y,z)))) * (1 / (1 / x)) = 1 / T(a(x,y,z) / x,x * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1186,a(flip),b,37325,a),flip(a)].">
      <j1 rule="hyper" parents="373 1186 37325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37327">
    <literal><![CDATA[
      R(x,y \ (z \ u),z) * ((y \ (z \ u)) * ((u / z) \ u)) = (x * (y \ (u / z))) * (u / (u / z))
    ]]></literal>
    <justification jstring="[para(82(a,1),37112(a,1,2,1,2,1))].">
      <j1 rule="para" parents="82 37112"/>
    </justification>
  </clause>

  <clause id="37328">
    <literal><![CDATA[
      R(x,y \ (z \ u),z) * ((y \ (z \ u)) * z) = (x * (y \ (u / z))) * (u / (u / z))
    ]]></literal>
    <justification jstring="[para(82(a,1),37327(a,1,2,2))].">
      <j1 rule="para" parents="82 37327"/>
    </justification>
  </clause>

  <clause id="37330">
    <literal><![CDATA[
      (x * (y \ (z / u))) * (z / (z / u)) = (x * (y \ (u \ z))) * u
    ]]></literal>
    <justification jstring="[hyper(327,a,37328,a),flip(a)].">
      <j1 rule="hyper" parents="327 37328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37332">
    <literal><![CDATA[
      (((x * L(y,z,u)) \ ((x / y) * L(y,z,u))) * y) * y = L(y,y,x * L(L(y,x * y,y),z,u))
    ]]></literal>
    <justification jstring="[para(31458(a,1),37113(a,1,1,1))].">
      <j1 rule="para" parents="31458 37113"/>
    </justification>
  </clause>

  <clause id="37333">
    <literal><![CDATA[
      a(x \ L(y * R(z,u,w),y \ 1,y \ 1),v5,v6) = a(x \ (y * L((y \ 1) * (y * z),u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26916,a(flip),b,37123,a),flip(a)].">
      <j1 rule="hyper" parents="64 26916 37123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37334">
    <literal><![CDATA[
      a(x \ L(y * R(z,u,w),y \ 1,y \ 1),v5,v6) = a(x \ L(y * L(z,u,w),y,y),v5,v6)
    ]]></literal>
    <justification jstring="[para(5644(a,1),37333(a,2,1,2))].">
      <j1 rule="para" parents="5644 37333"/>
    </justification>
  </clause>

  <clause id="37335">
    <literal><![CDATA[
      a(x \ L(y * R(z,u,w),y \ 1,y \ 1),v5,v6) = a(x \ (y \ L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,33010,a(flip),b,37334,a),flip(a)].">
      <j1 rule="hyper" parents="373 33010 37334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37336">
    <literal><![CDATA[
      a(x \ L(y * R(z,u,w),y,y),v5,v6) = a(x \ (y \ L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(1151(a,1),37335(a,1,1,2))].">
      <j1 rule="para" parents="1151 37335"/>
    </justification>
  </clause>

  <clause id="37337">
    <literal><![CDATA[
      a(x \ (y \ R(z,u,w)),v5,v6) = a(x \ (y \ L(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,33010,a(flip),b,37336,a)].">
      <j1 rule="hyper" parents="64 33010 37336"/>
    </justification>
  </clause>

  <clause id="37338">
    <literal><![CDATA[
      L((x \ (x / y)) \ z,y,y) = (1 / (T(1,y \ 1) / (T(x \ (x / y),1) \ 1))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,35166,a(flip),b,37126,a)].">
      <j1 rule="hyper" parents="64 35166 37126"/>
    </justification>
  </clause>

  <clause id="37340">
    <literal><![CDATA[
      L((x \ (x / y)) \ z,y,y) = (1 / (1 / ((x \ (x / y)) \ 1))) * z
    ]]></literal>
    <justification jstring="[para(7205(a,1),37338(a,2,1,2))].">
      <j1 rule="para" parents="7205 37338"/>
    </justification>
  </clause>

  <clause id="37341">
    <literal><![CDATA[
      L((x \ (x / y)) \ z,y,y) = (1 / (x \ (x / y))) * z
    ]]></literal>
    <justification jstring="[para(79(a,1),37340(a,2,1,2))].">
      <j1 rule="para" parents="79 37340"/>
    </justification>
  </clause>

  <clause id="37343">
    <literal><![CDATA[
      L((x \ a(y,x,z)) \ u,y \ ((y * (x * z)) / z),y \ ((y * (x * z)) / z)) = (1 / (x \ (x / (y \ ((y * (x * z)) / z))))) * u
    ]]></literal>
    <justification jstring="[para(33338(a,2),37341(a,1,1,1,2))].">
      <j1 rule="para" parents="33338 37341"/>
    </justification>
  </clause>

  <clause id="37344">
    <literal><![CDATA[
      L(x,(R(T(y,z),u,w) \ 1) * (a(R(T(y,z),u,w),L(y,u,w),v5) * v5),v6) = L(x,R(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(31912(a,1),37127(a,1,2,2,1))].">
      <j1 rule="para" parents="31912 37127"/>
    </justification>
  </clause>

  <clause id="37346">
    <literal><![CDATA[
      L(x,(R(T(y,z),u,w) \ 1) * (a(L(T(y,z),u,w),L(y,u,w),v5) * v5),v6) = L(x,R(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(32590(a,1),37344(a,1,2,2,1))].">
      <j1 rule="para" parents="32590 37344"/>
    </justification>
  </clause>

  <clause id="37347">
    <literal><![CDATA[
      L(x,(R(T(y,z),u,w) \ 1) * (a(L(y,u,w),L(y,u,w),v5) * v5),v6) = L(x,R(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(26792(a,1),37346(a,1,2,2,1))].">
      <j1 rule="para" parents="26792 37346"/>
    </justification>
  </clause>

  <clause id="37348">
    <literal><![CDATA[
      L(x,(R(T(y,z),u,w) \ 1) * L(v5,L(y,u,w),L(y,u,w)),v6) = L(x,R(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,34272,a(flip),b,37347,a)].">
      <j1 rule="hyper" parents="64 34272 37347"/>
    </justification>
  </clause>

  <clause id="37350">
    <literal><![CDATA[
      L(x,R(T(y,z),u,w) * L(v5,L(y,u,w),L(y,u,w)),v6) = L(x,R(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(29615,a,37348,a)].">
      <j1 rule="hyper" parents="29615 37348"/>
    </justification>
  </clause>

  <clause id="37351">
    <literal><![CDATA[
      L(x,L(T(y,z),u,w) * L(v5,L(y,u,w),L(y,u,w)),v6) = L(x,R(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,36262,a(flip),b,37350,a)].">
      <j1 rule="hyper" parents="64 36262 37350"/>
    </justification>
  </clause>

  <clause id="37352">
    <literal><![CDATA[
      L(x,L(y,z,u) * L(w,L(y,z,u),L(y,z,u)),v5) = L(x,R(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29465,a(flip),b,37351,a)].">
      <j1 rule="hyper" parents="64 29465 37351"/>
    </justification>
  </clause>

  <clause id="37353">
    <literal><![CDATA[
      L(x,R(y,z,u) \ w,v5) = L(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31761,a(flip),b,37352,a),flip(a)].">
      <j1 rule="hyper" parents="64 31761 37352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37354">
    <literal><![CDATA[
      L(x,R(T(y,z),u,w) \ v5,v6) = L(x,L(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29463,a(flip),b,37353,a),flip(a)].">
      <j1 rule="hyper" parents="373 29463 37353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37355">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u) \ w,v5) = L(x,R(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29735,a(flip),b,37353,a),flip(a)].">
      <j1 rule="hyper" parents="64 29735 37353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37356">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u) \ w,v5) = L(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,37353,a(flip),b,37355,a),flip(a)].">
      <j1 rule="hyper" parents="373 37353 37355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37357">
    <literal><![CDATA[
      a(L(R(x,y,z) \ x,u,x * L(x,y,z)),R(x,y,z),w) = (w \ ((w * R(x,y,z)) * (R(x,y,z) \ x))) \ x
    ]]></literal>
    <justification jstring="[para(36174(a,1),37172(a,2,1))].">
      <j1 rule="para" parents="36174 37172"/>
    </justification>
  </clause>

  <clause id="37358">
    <literal><![CDATA[
      a(x,L(T(y * y,z) * u,z,w) * v5,v6) = a(x,((w * z) \ (((v7 * v7) \ w) * (z * u))) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,36137,a(flip),b,37189,a),flip(a)].">
      <j1 rule="hyper" parents="64 36137 37189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37360">
    <literal><![CDATA[
      a(x,L(T(y * y,z) * u,z,w) * v5,v6) = a(x,((w * z) \ (w * (z * u))) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,34100,a(flip),b,37358,a),flip(a)].">
      <j1 rule="hyper" parents="373 34100 37358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37361">
    <literal><![CDATA[
      a(x,L(T(y * y,z) * u,z,w) * v5,v6) = a(x,L(u,z,w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(18(a,2),37360(a,2,2,1))].">
      <j1 rule="para" parents="18 37360"/>
    </justification>
  </clause>

  <clause id="37362">
    <literal><![CDATA[
      a(x,L(y * (z * z),u,w) * v5,v6) = a(x,L(y,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32875,a(flip),b,37361,a)].">
      <j1 rule="hyper" parents="64 32875 37361"/>
    </justification>
  </clause>

  <clause id="37363">
    <literal><![CDATA[
      a(x,L((y * y) * z,u,w) * v5,v6) = a(x,L(z,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32100,a(flip),b,37361,a)].">
      <j1 rule="hyper" parents="64 32100 37361"/>
    </justification>
  </clause>

  <clause id="37365">
    <literal><![CDATA[
      a(x,L(y \ 1,z,u) * w,v5) = a(x,L(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32109,a(flip),b,37362,a),flip(a)].">
      <j1 rule="hyper" parents="64 32109 37362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37366">
    <literal><![CDATA[
      a(x,L(y * (z \ (1 / z)),u,w) * v5,v6) = a(x,L(y,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(1090(a,1),37362(a,1,2,1,1,2))].">
      <j1 rule="para" parents="1090 37362"/>
    </justification>
  </clause>

  <clause id="37367">
    <literal><![CDATA[
      a(x,y * L(z \ 1,u,w),v5) = a(x,L(z,u,w) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(32008,a,37365,a)].">
      <j1 rule="hyper" parents="32008 37365"/>
    </justification>
  </clause>

  <clause id="37369">
    <literal><![CDATA[
      a(x,L((1 / y) \ z,u,w) * v5,v6) = a(x,L(z / T(y,v7),u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,36555,a(flip),b,37363,a)].">
      <j1 rule="hyper" parents="64 36555 37363"/>
    </justification>
  </clause>

  <clause id="37370">
    <literal><![CDATA[
      a(x,L((y \ 1) * z,u,w) * v5,v6) = a(x,L(y * z,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32251,a(flip),b,37366,a)].">
      <j1 rule="hyper" parents="64 32251 37366"/>
    </justification>
  </clause>

  <clause id="37372">
    <literal><![CDATA[
      a(x,y \ L(y \ z,u,w),v5) = a(x,L(y * z,u,w) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32879,a(flip),b,37370,a)].">
      <j1 rule="hyper" parents="64 32879 37370"/>
    </justification>
  </clause>

  <clause id="37373">
    <literal><![CDATA[
      a(x,L(y * (y * z),u,w) * y,v5) = a(x,y \ L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),37372(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9 37372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37374">
    <literal><![CDATA[
      a(x,y \ R(z,u,w),v5) = a(x,y \ L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,33775,a(flip),b,37373,a)].">
      <j1 rule="hyper" parents="64 33775 37373"/>
    </justification>
  </clause>

  <clause id="37375">
    <literal><![CDATA[
      a(x * L(x,y,z),z,u) = a(z,x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34652,a,b,37374,a)].">
      <j1 rule="hyper" parents="64 34652 37374"/>
    </justification>
  </clause>

  <clause id="37376">
    <literal><![CDATA[
      a(x,L(y \ z,y,z \ R(u,w,v5)) \ L(u,w,v5),v6) = a(x,T((R(u,w,v5) / z) * y,y \ z),v6)
    ]]></literal>
    <justification jstring="[para(15117(a,1),37374(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15117 37374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37378">
    <literal><![CDATA[
      (a(x,y \ L(z,u,w),v5) \ v5) \ (a(x,y \ R(z,u,w),v5) \ R(v5,v6,v7)) = v5 \ R(v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(37374(a,1),34941(a,1,1,1))].">
      <j1 rule="para" parents="37374 34941"/>
    </justification>
  </clause>

  <clause id="37379">
    <literal><![CDATA[
      a(x * L(x,y,z),z,u) = a(z,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11978,a(flip),b,37375,a),flip(a)].">
      <j1 rule="hyper" parents="373 11978 37375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37381">
    <literal><![CDATA[
      a(x,L((1 / y) \ z,u,w) * v5,v6) = a(x,L(y \ z,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32876,a(flip),b,37369,a),flip(a)].">
      <j1 rule="hyper" parents="373 32876 37369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37382">
    <literal><![CDATA[
      (a(x,y * L(y,z,u),w) \ w) \ (a(x,y \ R(y,z,u),w) \ R(w,v5,v6)) = w \ R(w,v5,v6)
    ]]></literal>
    <justification jstring="[para(11978(a,1),37378(a,1,1,1))].">
      <j1 rule="para" parents="11978 37378"/>
    </justification>
  </clause>

  <clause id="37383">
    <literal><![CDATA[
      a(x,L(y \ z,y,z \ R(u,w,v5)) \ L(u,w,v5),v6) = a(x,(R(u,w,v5) / z) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,31892,a(flip),b,37376,a),flip(a)].">
      <j1 rule="hyper" parents="373 31892 37376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37385">
    <literal><![CDATA[
      a(x,L(y \ z,y,z \ R(u,w,v5)) \ L(u,w,v5),v6) = a(x,(z \ R(u,w,v5)) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,31904,a(flip),b,37383,a),flip(a)].">
      <j1 rule="hyper" parents="373 31904 37383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37386">
    <literal><![CDATA[
      a(x,L(y \ z,y,z \ L(u,w,v5)) \ L(u,w,v5),v6) = a(x,(z \ R(u,w,v5)) * y,v6)
    ]]></literal>
    <justification jstring="[para(33124(a,1),37385(a,1,2,1))].">
      <j1 rule="para" parents="33124 37385"/>
    </justification>
  </clause>

  <clause id="37387">
    <literal><![CDATA[
      a(x,T((L(y,z,u) / w) * v5,v5 \ w),v6) = a(x,(w \ R(y,z,u)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(15117(a,1),37386(a,1,2))].">
      <j1 rule="para" parents="15117 37386"/>
    </justification>
  </clause>

  <clause id="37388">
    <literal><![CDATA[
      a(x,(L(y,z,u) / w) * v5,v6) = a(x,(w \ R(y,z,u)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(31997,a,37387,a)].">
      <j1 rule="hyper" parents="31997 37387"/>
    </justification>
  </clause>

  <clause id="37390">
    <literal><![CDATA[
      a(x,(y \ R(z,u,w)) * v5,v6) = a(x,(y \ L(z,u,w)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,31904,a(flip),b,37388,a),flip(a)].">
      <j1 rule="hyper" parents="64 31904 37388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37391">
    <literal><![CDATA[
      R(x,y,(z \ (z / u)) * ((a(z,u,u) / (1 / u)) \ w)) = R(x,y,((z \ (u \ z)) * (z \ (u \ z))) * w)
    ]]></literal>
    <justification jstring="[para(33436(a,1),37321(a,1,3,2,1))].">
      <j1 rule="para" parents="33436 37321"/>
    </justification>
  </clause>

  <clause id="37392">
    <literal><![CDATA[
      R(x,y,(z \ (z / u)) * (((1 / u) \ a(z,u,u)) \ w)) = R(x,y,((z \ (u \ z)) * (z \ (u \ z))) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26275,a(flip),b,37391,a)].">
      <j1 rule="hyper" parents="64 26275 37391"/>
    </justification>
  </clause>

  <clause id="37393">
    <literal><![CDATA[
      R(x,y,(z \ (z / u)) * ((a(z,u,u) * u) \ w)) = R(x,y,((z \ (u \ z)) * (z \ (u \ z))) * w)
    ]]></literal>
    <justification jstring="[para(35737(a,1),37392(a,1,3,2,1))].">
      <j1 rule="para" parents="35737 37392"/>
    </justification>
  </clause>

  <clause id="37395">
    <literal><![CDATA[
      R(a(x,y,z),1 / z,z * u) * L(u,1 / z,1 / z) = (a(x,y,z) / z) * (((1 / z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(82(a,1),25757(a,1,1,3,1))].">
      <j1 rule="para" parents="82 25757"/>
    </justification>
  </clause>

  <clause id="37397">
    <literal><![CDATA[
      R(a(x,y,z),z,z * u) * L(u,1 / z,1 / z) = (a(x,y,z) / z) * (((1 / z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(2968(a,1),37395(a,1,1))].">
      <j1 rule="para" parents="2968 37395"/>
    </justification>
  </clause>

  <clause id="37398">
    <literal><![CDATA[
      L(a(x,y,z),z,z * u) * L(u,1 / z,1 / z) = (a(x,y,z) / z) * (((1 / z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(28787(a,1),37397(a,1,1))].">
      <j1 rule="para" parents="28787 37397"/>
    </justification>
  </clause>

  <clause id="37399">
    <literal><![CDATA[
      L(a(x,y,z),z,z * u) * L(u,z,z) = (a(x,y,z) / z) * (((1 / z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(1158(a,1),37398(a,1,2))].">
      <j1 rule="para" parents="1158 37398"/>
    </justification>
  </clause>

  <clause id="37400">
    <literal><![CDATA[
      L(a(x,y,z),z,z * u) * L(u,z,z) = (a(x,y,z) / z) * (z * u)
    ]]></literal>
    <justification jstring="[para(82(a,1),37399(a,2,2,1))].">
      <j1 rule="para" parents="82 37399"/>
    </justification>
  </clause>

  <clause id="37401">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) \ z) * ((z \ 1) * u) = (a(x,y,z) / z) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,35127,a(flip),b,37400,a)].">
      <j1 rule="hyper" parents="64 35127 37400"/>
    </justification>
  </clause>

  <clause id="37403">
    <literal><![CDATA[
      (a(x,y,z) * z) * ((z \ 1) * u) = (a(x,y,z) / z) * (z * u)
    ]]></literal>
    <justification jstring="[para(33209(a,1),37401(a,1,1))].">
      <j1 rule="para" parents="33209 37401"/>
    </justification>
  </clause>

  <clause id="37404">
    <literal><![CDATA[
      a(x,y,z) * ((z * ((z \ 1) * u)) * a(a(x,y,z),z,u * (z \ 1))) = (a(x,y,z) / z) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29947,a,b,37403,a)].">
      <j1 rule="hyper" parents="64 29947 37403"/>
    </justification>
  </clause>

  <clause id="37405">
    <literal><![CDATA[
      a(x,y,z) * (L(u,z,z) * a(a(x,y,z),z,u * (z \ 1))) = (a(x,y,z) / z) * (z * u)
    ]]></literal>
    <justification jstring="[para(1139(a,1),37404(a,1,2,1))].">
      <j1 rule="para" parents="1139 37404"/>
    </justification>
  </clause>

  <clause id="37406">
    <literal><![CDATA[
      a(x,y,z) * (L(u,z,z) * a(z,a(x,y,z),u * (z \ 1))) = (a(x,y,z) / z) * (z * u)
    ]]></literal>
    <justification jstring="[para(33522(a,1),37405(a,1,2,2))].">
      <j1 rule="para" parents="33522 37405"/>
    </justification>
  </clause>

  <clause id="37407">
    <literal><![CDATA[
      a(x,y,z) * (L(u,z,z) * a(z,a(x,y,z),z * u)) = (a(x,y,z) / z) * (z * u)
    ]]></literal>
    <justification jstring="[para(36026(a,1),37406(a,1,2,2))].">
      <j1 rule="para" parents="36026 37406"/>
    </justification>
  </clause>

  <clause id="37408">
    <literal><![CDATA[
      R(x,y,z * (R(T(u * K((w \ v5) \ v5,u),v6),v7,v8) * w)) = R(x,y,z * (((w \ v5) \ v5) * R(u,v7,v8)))
    ]]></literal>
    <justification jstring="[hyper(373,a,26320,a(flip),b,26341,a),flip(a)].">
      <j1 rule="hyper" parents="373 26320 26341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37410">
    <literal><![CDATA[
      R(x,y,z * (R(T(u * K((w \ v5) \ v5,u),v6),v7,v8) * w)) = R(x,y,(w * R(u,v7,v8)) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,26308,a(flip),b,37408,a),flip(a)].">
      <j1 rule="hyper" parents="373 26308 37408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37412">
    <literal><![CDATA[
      R(x,y,z * (R(T(u * K(w,T(u,v5)),v6),v7,v8) * w)) = R(x,y,(w * R(u,v7,v8)) * z)
    ]]></literal>
    <justification jstring="[para(7871(a,1),37410(a,1,3,2,1,1,1,2))].">
      <j1 rule="para" parents="7871 37410"/>
    </justification>
  </clause>

  <clause id="37413">
    <literal><![CDATA[
      T(x,y * y) \ ((y \ 1) * (x * (((y \ 1) \ y) * (y \ 1)))) = (y * ((y \ 1) * T(x,y))) / T(x,y * y)
    ]]></literal>
    <justification jstring="[para(7574(a,1),26603(a,2,1,2))].">
      <j1 rule="para" parents="7574 26603"/>
    </justification>
  </clause>

  <clause id="37414">
    <literal><![CDATA[
      T(x,y * y) \ ((y \ 1) * (x * (((y \ 1) \ y) * (y \ 1)))) = L(T(x,y),y,y) / T(x,y * y)
    ]]></literal>
    <justification jstring="[para(1139(a,1),37413(a,2,1))].">
      <j1 rule="para" parents="1139 37413"/>
    </justification>
  </clause>

  <clause id="37415">
    <literal><![CDATA[
      T(x,y * y) \ ((y \ 1) * (x * (((y \ 1) \ y) * (y \ 1)))) = T(x,y * y) \ L(T(x,y),y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8414,a(flip),b,37414,a),flip(a)].">
      <j1 rule="hyper" parents="373 8414 37414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37416">
    <literal><![CDATA[
      T(x,y * y) \ ((y \ 1) * (x * (((y \ 1) \ y) * (y \ 1)))) = x \ L(T(x,y \ (y \ y)),y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,31556,a(flip),b,37415,a),flip(a)].">
      <j1 rule="hyper" parents="373 31556 37415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37417">
    <literal><![CDATA[
      T(x,y * y) \ ((y \ 1) * (x * (((y \ 1) \ y) * (y \ 1)))) = x \ L(T(x,y \ 1),y,y)
    ]]></literal>
    <justification jstring="[para(68(a,1),37416(a,2,2,1,2,2))].">
      <j1 rule="para" parents="68 37416"/>
    </justification>
  </clause>

  <clause id="37419">
    <literal><![CDATA[
      T(x,y * y) \ ((y \ 1) * (x * (((y \ 1) \ y) * (y \ 1)))) = x \ (y * (x * (y \ 1)))
    ]]></literal>
    <justification jstring="[para(1140(a,1),37417(a,2,2))].">
      <j1 rule="para" parents="1140 37417"/>
    </justification>
  </clause>

  <clause id="37420">
    <literal><![CDATA[
      T(x,y * y) \ ((y \ 1) * (x * ((y \ 1) \ 1))) = x \ (y * (x * (y \ 1)))
    ]]></literal>
    <justification jstring="[para(1131(a,1),37419(a,1,2,2,2))].">
      <j1 rule="para" parents="1131 37419"/>
    </justification>
  </clause>

  <clause id="37421">
    <literal><![CDATA[
      T(x,y * y) \ ((1 / y) * (x * y)) = x \ (y * (x * (y \ 1)))
    ]]></literal>
    <justification jstring="[para(3911(a,1),37420(a,1,2))].">
      <j1 rule="para" parents="3911 37420"/>
    </justification>
  </clause>

  <clause id="37422">
    <literal><![CDATA[
      (x * x) \ (y \ (x * (y * x))) = y \ (x * (y * (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,1528,a(flip),b,37421,a)].">
      <j1 rule="hyper" parents="64 1528 37421"/>
    </justification>
  </clause>

  <clause id="37423">
    <literal><![CDATA[
      (x \ (y * (x * y))) \ ((y * y) * z) = (x \ (y * (x * (y \ 1)))) \ z
    ]]></literal>
    <justification jstring="[para(37422(a,1),804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37422 804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37424">
    <literal><![CDATA[
      T(x \ (y * (x * (y \ 1))),z * z) \ u = (x \ (y * (x * y))) \ ((y * y) * u)
    ]]></literal>
    <justification jstring="[para(34083(a,2),37423(a,2,1)),flip(a)].">
      <j1 rule="para" parents="34083 37423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37425">
    <literal><![CDATA[
      T((x * x) \ (y \ (x * (y * x))),z * z) \ u = (y \ (x * (y * x))) \ ((x * x) * u)
    ]]></literal>
    <justification jstring="[para(37422(a,2),37424(a,1,1,1))].">
      <j1 rule="para" parents="37422 37424"/>
    </justification>
  </clause>

  <clause id="37426">
    <literal><![CDATA[
      T(x \ (y * (x * y)),y * y) = x \ (y * (x * y))
    ]]></literal>
    <justification jstring="[hyper(40,a,1461,a(flip),b,37425,a(flip))].">
      <j1 rule="hyper" parents="40 1461 37425"/>
    </justification>
  </clause>

  <clause id="37427">
    <literal><![CDATA[
      ((x * x) \ (y \ (x * (y * x)))) * ((x * x) * z) = (y \ (x * (y * x))) * z
    ]]></literal>
    <justification jstring="[para(37426(a,1),930(a,2,1))].">
      <j1 rule="para" parents="37426 930"/>
    </justification>
  </clause>

  <clause id="37429">
    <literal><![CDATA[
      (x \ (y * (x * (y \ 1)))) * ((y * y) * z) = (x \ (y * (x * y))) * z
    ]]></literal>
    <justification jstring="[para(37422(a,1),37427(a,1,1))].">
      <j1 rule="para" parents="37422 37427"/>
    </justification>
  </clause>

  <clause id="37430">
    <literal><![CDATA[
      (x * x) * ((y \ (x * (y * x))) \ z) = (y \ (x * (y * (x \ 1)))) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,37429,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 37429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37431">
    <literal><![CDATA[
      x * ((R(x,y,z) / x) \ (x \ ((x * (R(x,y,z) / x)) * u))) = (x \ R(x,y,z)) \ (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(10(a,1),27025(a,2,2))].">
      <j1 rule="para" parents="10 27025"/>
    </justification>
  </clause>

  <clause id="37432">
    <literal><![CDATA[
      x * ((R(x,y,z) / x) \ (x \ ((x * (R(x,y,z) / x)) * u))) = L((x \ 1) \ u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,29209,a(flip),b,37431,a),flip(a)].">
      <j1 rule="hyper" parents="373 29209 37431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37434">
    <literal><![CDATA[
      x * ((x \ R(x,y,z)) \ (x \ (R(x,y,z) * u))) = L((x \ 1) \ u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(25796(a,1),37432(a,1,2))].">
      <j1 rule="para" parents="25796 37432"/>
    </justification>
  </clause>

  <clause id="37435">
    <literal><![CDATA[
      x * ((x \ R(x,y,z)) \ (R(x,y,z) * (x \ u))) = L((x \ 1) \ u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1898(a,1),37434(a,1,2,2))].">
      <j1 rule="para" parents="1898 37434"/>
    </justification>
  </clause>

  <clause id="37436">
    <literal><![CDATA[
      x * L((x \ 1) \ (x \ y),x,L(x,z,u)) = L((x \ 1) \ y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(29209(a,1),37435(a,1,2))].">
      <j1 rule="para" parents="29209 37435"/>
    </justification>
  </clause>

  <clause id="37437">
    <literal><![CDATA[
      L((x \ 1) \ y,x,L(x,z,u)) = (1 / x) \ L(y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,1841,a(flip),b,37436,a),flip(a)].">
      <j1 rule="hyper" parents="64 1841 37436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37438">
    <literal><![CDATA[
      (((x \ (x \ y)) \ y) \ z) * K(x * (y / (x \ y)),(x \ y) / x) = T((y / (x \ (x \ y))) \ z,K(y,x * x))
    ]]></literal>
    <justification jstring="[para(28243(a,1),28222(a,1,2))].">
      <j1 rule="para" parents="28243 28222"/>
    </justification>
  </clause>

  <clause id="37439">
    <literal><![CDATA[
      L(T(x \ a(y,z,u),(a(y,z,u) \ x) * w),x \ a(y,z,u),x \ a(y,z,u)) = T(x \ a(y,z,u),x \ w)
    ]]></literal>
    <justification jstring="[para(22657(a,1),28713(a,1,1))].">
      <j1 rule="para" parents="22657 28713"/>
    </justification>
  </clause>

  <clause id="37440">
    <literal><![CDATA[
      (R(T(x,y),z,z) / x) * (x * (T(R(x,z,z),y) \ (u * a(x,z,z)))) = (R(x,z,z) / x) * L(u,x,a(z,z,x))
    ]]></literal>
    <justification jstring="[para(27(a,2),29281(a,1,1,1))].">
      <j1 rule="para" parents="27 29281"/>
    </justification>
  </clause>

  <clause id="37441">
    <literal><![CDATA[
      (x * L(L(R(R(y,x,y),z,u),w,v5),x,y)) \ (x * L(R(R(y,x,y),z,u),w,v5)) = a(y,x,L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,27703,a(flip),b,30354,a),flip(a)].">
      <j1 rule="hyper" parents="373 27703 30354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37442">
    <literal><![CDATA[
      x \ ((y \ R(y,z,u)) \ (R(y,z,u) * (K(y \ x,y) * (x / y)))) = a(y \ R(y,z,u),(x / y) \ x,x / y)
    ]]></literal>
    <justification jstring="[para(25983(a,1),30404(a,1,2,2))].">
      <j1 rule="para" parents="25983 30404"/>
    </justification>
  </clause>

  <clause id="37443">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) * R(y,y,a(y * x,y,y)) = (y * y) * (T(y,y) \ (((x * y) \ x) \ 1))
    ]]></literal>
    <justification jstring="[para(6730(a,1),30551(a,2,2,1))].">
      <j1 rule="para" parents="6730 30551"/>
    </justification>
  </clause>

  <clause id="37444">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) * R(y,y,a(y * x,y,y)) = (y * y) * (y \ (((x * y) \ x) \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,10840,a(flip),b,37443,a),flip(a)].">
      <j1 rule="hyper" parents="373 10840 37443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37446">
    <literal><![CDATA[
      (x * x) * (x \ (((y * x) \ y) \ 1)) = (((y * x) \ y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(9434(a,1),37444(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9434 37444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37447">
    <literal><![CDATA[
      R((1 / x) / (y \ a(y,y,L(x,z,u))),L(y,y,R(x,z,u)),R(x,z,u)) = (x \ R(x,z,u)) / (y \ R(x,z,u))
    ]]></literal>
    <justification jstring="[para(27644(a,1),30771(a,1,1,2,2))].">
      <j1 rule="para" parents="27644 30771"/>
    </justification>
  </clause>

  <clause id="37448">
    <literal><![CDATA[
      L(x,(y \ (R(1 / z,u,w) * v5)) * (z * z),v6) = L(x,(R(z,u,w) * v5) * L(y,y,L(1 / z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(33584(a,1),31069(a,2,2,2))].">
      <j1 rule="para" parents="33584 31069"/>
    </justification>
  </clause>

  <clause id="37449">
    <literal><![CDATA[
      L(a(x,x,y),(x \ 1) * y,((x \ 1) * y) \ z) * z = (z / ((x \ y) / T(a(x,x,y),z))) * (x \ y)
    ]]></literal>
    <justification jstring="[para(30044(a,1),31356(a,1,1,3,1))].">
      <j1 rule="para" parents="30044 31356"/>
    </justification>
  </clause>

  <clause id="37450">
    <literal><![CDATA[
      L(a(x,x,y),(x \ 1) * y,(x * y) \ z) * z = (z / ((x \ y) / T(a(x,x,y),z))) * (x \ y)
    ]]></literal>
    <justification jstring="[para(25699(a,1),37449(a,1,1))].">
      <j1 rule="para" parents="25699 37449"/>
    </justification>
  </clause>

  <clause id="37451">
    <literal><![CDATA[
      (x / ((y \ z) / T(a(y,y,z),x))) * (y \ z) = L(a(y,y,z),y * z,(y * z) \ x) * x
    ]]></literal>
    <justification jstring="[para(11864(a,1),37450(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11864 37450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37452">
    <literal><![CDATA[
      (x / ((y \ z) / T(a(y,y,z),x))) * (y \ z) = (x / (y * z)) * ((y * z) * a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,23576,a(flip),b,37451,a),flip(a)].">
      <j1 rule="hyper" parents="373 23576 37451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37453">
    <literal><![CDATA[
      (x / ((y \ z) / T(a(y,y,z),x))) * (y \ z) = (x / (y * z)) * (y * (z * a(y,y,z)))
    ]]></literal>
    <justification jstring="[para(29910(a,1),37452(a,2,2))].">
      <j1 rule="para" parents="29910 37452"/>
    </justification>
  </clause>

  <clause id="37454">
    <literal><![CDATA[
      (x / ((y \ z) / T(a(y,y,z),x))) * (y \ z) = (x / (y * z)) * ((1 / y) \ z)
    ]]></literal>
    <justification jstring="[para(30219(a,1),37453(a,2,2))].">
      <j1 rule="para" parents="30219 37453"/>
    </justification>
  </clause>

  <clause id="37455">
    <literal><![CDATA[
      (x / (a(y,y,z) \ (y \ z))) * (y \ z) = (x / (y * z)) * ((1 / y) \ z)
    ]]></literal>
    <justification jstring="[para(23918(a,1),37454(a,1,1,2))].">
      <j1 rule="para" parents="23918 37454"/>
    </justification>
  </clause>

  <clause id="37457">
    <literal><![CDATA[
      (x / ((y \ 1) * z)) * (y \ z) = (x / (y * z)) * ((1 / y) \ z)
    ]]></literal>
    <justification jstring="[para(30044(a,1),37455(a,1,1,2))].">
      <j1 rule="para" parents="30044 37455"/>
    </justification>
  </clause>

  <clause id="37458">
    <literal><![CDATA[
      (x / (y * z)) * ((1 / y) \ z) = (y \ z) * (((y \ 1) * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,14958,a(flip),b,37457,a),flip(a)].">
      <j1 rule="hyper" parents="64 14958 37457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37459">
    <literal><![CDATA[
      ((x \ 1) * y) \ (x * y) = (x \ y) \ ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(459,a,37458,a),flip(a)].">
      <j1 rule="hyper" parents="459 37458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37460">
    <literal><![CDATA[
      ((1 / x) \ y) * ((x * y) \ z) = (x \ y) * (((x \ 1) * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14956,a,b,37458,a)].">
      <j1 rule="hyper" parents="64 14956 37458"/>
    </justification>
  </clause>

  <clause id="37461">
    <literal><![CDATA[
      ((1 / x) \ y) \ (x \ ((1 / x) \ y)) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,11452,a(flip),b,37460,a)].">
      <j1 rule="hyper" parents="139 11452 37460"/>
    </justification>
  </clause>

  <clause id="37462">
    <literal><![CDATA[
      x * (((y \ 1) * z) \ ((((1 / y) \ 1) \ z) * u)) = x * (((1 / y) \ z) * ((((1 / y) \ 1) * z) \ u))
    ]]></literal>
    <justification jstring="[para(37460(a,1),27865(a,2,2))].">
      <j1 rule="para" parents="37460 27865"/>
    </justification>
  </clause>

  <clause id="37463">
    <literal><![CDATA[
      ((x * y) \ y) * ((1 / x) \ y) = (x \ ((1 / x) \ y)) * K(x \ 1,(1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(37461(a,1),6328(a,1,1))].">
      <j1 rule="para" parents="37461 6328"/>
    </justification>
  </clause>

  <clause id="37464">
    <literal><![CDATA[
      (a(x,x,y) * y) * K(x \ 1,(1 / x) \ y) = ((x * y) \ y) * ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(30228(a,1),37463(a,2,1)),flip(a)].">
      <j1 rule="para" parents="30228 37463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37465">
    <literal><![CDATA[
      (a(x,x,y) * y) * K(x \ 1,x * y) = ((x * y) \ y) * ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[para(14469(a,1),37464(a,1,2))].">
      <j1 rule="para" parents="14469 37464"/>
    </justification>
  </clause>

  <clause id="37466">
    <literal><![CDATA[
      a(x,x,y) * (y * K(x \ 1,x * y)) = ((x * y) \ y) * ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(23059,a,37465,a)].">
      <j1 rule="hyper" parents="23059 37465"/>
    </justification>
  </clause>

  <clause id="37467">
    <literal><![CDATA[
      x * (a(y,y,x) * K(y \ 1,y * x)) = ((y * x) \ x) * ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33249,a(flip),b,37466,a)].">
      <j1 rule="hyper" parents="64 33249 37466"/>
    </justification>
  </clause>

  <clause id="37468">
    <literal><![CDATA[
      x * (y * R(T(y \ 1,y * x),y,x)) = ((y * x) \ x) * ((1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(30172(a,1),37467(a,1,2))].">
      <j1 rule="para" parents="30172 37467"/>
    </justification>
  </clause>

  <clause id="37469">
    <literal><![CDATA[
      ((x * y) \ y) * ((1 / x) \ y) = y * (x * T((x * y) \ y,x))
    ]]></literal>
    <justification jstring="[para(1364(a,1),37468(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1364 37468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37470">
    <literal><![CDATA[
      ((x * y) \ y) * ((1 / x) \ y) = y * (((x * y) \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,251,a(flip),b,37469,a),flip(a)].">
      <j1 rule="hyper" parents="373 251 37469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37471">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * K(x \ 1,(1 / x) \ y) = y * (((x * y) \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,37463,a(flip),b,37470,a)].">
      <j1 rule="hyper" parents="64 37463 37470"/>
    </justification>
  </clause>

  <clause id="37472">
    <literal><![CDATA[
      x \ ((K(y * x,x \ 1) / x) \ y) = y * (((x * y) \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27882,a(flip),b,37471,a)].">
      <j1 rule="hyper" parents="64 27882 37471"/>
    </justification>
  </clause>

  <clause id="37473">
    <literal><![CDATA[
      x * (((y * x) \ x) * y) = y \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(27879(a,1),37472(a,1,2)),flip(a)].">
      <j1 rule="para" parents="27879 37472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37474">
    <literal><![CDATA[
      x * (((y \ 1) * z) \ ((((1 / y) \ 1) \ z) * u)) = x * (((1 / y) \ z) * ((y * z) \ u))
    ]]></literal>
    <justification jstring="[para(82(a,1),37462(a,2,2,2,1,1))].">
      <j1 rule="para" parents="82 37462"/>
    </justification>
  </clause>

  <clause id="37476">
    <literal><![CDATA[
      x * (((y \ 1) * z) \ ((((1 / y) \ 1) \ z) * u)) = x * ((y \ z) * (((y \ 1) * z) \ u))
    ]]></literal>
    <justification jstring="[para(37460(a,1),37474(a,2,2))].">
      <j1 rule="para" parents="37460 37474"/>
    </justification>
  </clause>

  <clause id="37477">
    <literal><![CDATA[
      x * (((y \ 1) * z) \ ((y \ z) * u)) = x * ((y \ z) * (((y \ 1) * z) \ u))
    ]]></literal>
    <justification jstring="[para(82(a,1),37476(a,1,2,2,1,1))].">
      <j1 rule="para" parents="82 37476"/>
    </justification>
  </clause>

  <clause id="37479">
    <literal><![CDATA[
      x * ((y * z) \ (((1 / y) \ z) * u)) = x * ((y \ z) * (((y \ 1) * z) \ u))
    ]]></literal>
    <justification jstring="[para(1681(a,1),37477(a,1,2))].">
      <j1 rule="para" parents="1681 37477"/>
    </justification>
  </clause>

  <clause id="37480">
    <literal><![CDATA[
      (x / (y * (z / (z / x)))) * ((y * (z / (z / x))) / x) = (y * (z / (z / x))) \ ((K(x,x \ z) / y) \ x)
    ]]></literal>
    <justification jstring="[para(14507(a,1),31396(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14507 31396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37481">
    <literal><![CDATA[
      (x * (y / (y / z))) \ ((K(z,z \ y) / x) \ z) = (z / (x * (y / (y / z)))) * (x * K(z \ y,z))
    ]]></literal>
    <justification jstring="[para(6152(a,1),37480(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6152 37480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37482">
    <literal><![CDATA[
      (x * (y / (y / z))) \ ((K(z,z \ y) / x) \ z) = (z / (x * z)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,37121,a(flip),b,37481,a),flip(a)].">
      <j1 rule="hyper" parents="373 37121 37481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37484">
    <literal><![CDATA[
      (x * (y / (y / z))) \ ((K(z,z \ y) / x) \ z) = a(x,x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,30057,a(flip),b,37482,a),flip(a)].">
      <j1 rule="hyper" parents="373 30057 37482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37485">
    <literal><![CDATA[
      L(a(x,y,z) * u,L(u,u,a(x,y,z)),a(x,y,z)) = 1 / ((a(x,y,z) \ 1) * L(u \ 1,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29880,a(flip),b,31602,a)].">
      <j1 rule="hyper" parents="64 29880 31602"/>
    </justification>
  </clause>

  <clause id="37486">
    <literal><![CDATA[
      1 / ((a(x,y,z) \ 1) * L(u \ 1,u,a(x,y,z))) = L(a(x,y,z) * u,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,36825,a(flip),b,37485,a),flip(a)].">
      <j1 rule="hyper" parents="64 36825 37485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37487">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,x \ 1,(y * (z \ 1)) \ u) = L((x \ 1) \ 1,x,x * ((z * y) \ u)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(11794(a,1),31662(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11794 31662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37488">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,x \ 1,(y * (z \ 1)) \ u) = (a((z * y) \ u,x,x \ 1) \ x) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(33433(a,1),37487(a,2,1))].">
      <j1 rule="para" parents="33433 37487"/>
    </justification>
  </clause>

  <clause id="37489">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,x \ 1,(y * (x \ 1)) \ z) = (a(y \ (x \ z),x,x \ 1) \ x) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(33231(a,1),37488(a,2,1,1))].">
      <j1 rule="para" parents="33231 37488"/>
    </justification>
  </clause>

  <clause id="37490">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,x \ 1,(y * (x \ 1)) \ z) = x * (a(y \ (x \ z),x,x \ 1) \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,28807,a(flip),b,37489,a),flip(a)].">
      <j1 rule="hyper" parents="373 28807 37489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37491">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,x \ 1,(y * (x \ 1)) \ z) = x * L(x \ 1,x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(33375(a,1),37490(a,2,2))].">
      <j1 rule="para" parents="33375 37490"/>
    </justification>
  </clause>

  <clause id="37492">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,x \ 1,y \ ((x \ 1) * z)) = x * L(x \ 1,x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(35596(a,1),37491(a,1,2))].">
      <j1 rule="para" parents="35596 37491"/>
    </justification>
  </clause>

  <clause id="37493">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,x \ 1,y \ (x * z)) = x * L(x \ 1,x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(25698(a,1),37492(a,1,2))].">
      <j1 rule="para" parents="25698 37492"/>
    </justification>
  </clause>

  <clause id="37494">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,x,y \ (x * z)) = x * L(x \ 1,x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(11794(a,1),37493(a,1,2))].">
      <j1 rule="para" parents="11794 37493"/>
    </justification>
  </clause>

  <clause id="37495">
    <literal><![CDATA[
      L(x \ 1,x,y \ (x \ z)) = L(x \ 1,x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(39,a,5574,a,b,37494,a)].">
      <j1 rule="hyper" parents="39 5574 37494"/>
    </justification>
  </clause>

  <clause id="37496">
    <literal><![CDATA[
      L(x \ 1,x,(y * x) \ z) = L(x \ 1,x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33785,a,b,37495,a)].">
      <j1 rule="hyper" parents="64 33785 37495"/>
    </justification>
  </clause>

  <clause id="37497">
    <literal><![CDATA[
      L(x,x,((x \ y) \ y) * ((z * x) \ u)) = x * (L(x \ 1,x,z \ (x * u)) * x)
    ]]></literal>
    <justification jstring="[para(37496(a,1),29079(a,2,2,1))].">
      <j1 rule="para" parents="37496 29079"/>
    </justification>
  </clause>

  <clause id="37498">
    <literal><![CDATA[
      L(x,x,((x \ y) \ y) * ((z * x) \ u)) = L(x,x,x * (z \ (x * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,26664,a(flip),b,37497,a),flip(a)].">
      <j1 rule="hyper" parents="373 26664 37497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37499">
    <literal><![CDATA[
      L(x,x,x * ((y * x) \ z)) = L(x,x,x * (y \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,28981,a(flip),b,37498,a)].">
      <j1 rule="hyper" parents="64 28981 37498"/>
    </justification>
  </clause>

  <clause id="37500">
    <literal><![CDATA[
      L(x,x,x * (y \ (x \ z))) = L(x,x,x * (y \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,34436,a(flip),b,37499,a)].">
      <j1 rule="hyper" parents="64 34436 37499"/>
    </justification>
  </clause>

  <clause id="37501">
    <literal><![CDATA[
      L(x,x,x * (y \ (x * (z * y)))) = L(x,x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,36908,a(flip),b,37500,a),flip(a)].">
      <j1 rule="hyper" parents="64 36908 37500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37502">
    <literal><![CDATA[
      L(x,x,a(x,y,z) \ y) = L(x,x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33466,a,b,37501,a)].">
      <j1 rule="hyper" parents="64 33466 37501"/>
    </justification>
  </clause>

  <clause id="37503">
    <literal><![CDATA[
      L(x,x,L(y,x,z)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,34025,a(flip),b,37502,a),flip(a)].">
      <j1 rule="hyper" parents="64 34025 37502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37507">
    <literal><![CDATA[
      L(R(x,y,z),x,L(u,x,w)) = R(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(37503(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37503 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37508">
    <literal><![CDATA[
      L(L(x,y,z),x,L(u,x,w)) = L(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(37503(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37503 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37509">
    <literal><![CDATA[
      L(x,x,(y * x) \ z) = L(x,x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(346(a,1),37503(a,1,3))].">
      <j1 rule="para" parents="346 37503"/>
    </justification>
  </clause>

  <clause id="37511">
    <literal><![CDATA[
      L(x,x,y) \ L(R(x,z,u),x,L(y,x,w)) = L(x \ R(x,z,u),x,L(y,x,w))
    ]]></literal>
    <justification jstring="[para(37503(a,1),4243(a,1,1))].">
      <j1 rule="para" parents="37503 4243"/>
    </justification>
  </clause>

  <clause id="37512">
    <literal><![CDATA[
      a(L(x,y,z),y,y) = L(y,y,x) \ y
    ]]></literal>
    <justification jstring="[para(37503(a,1),30462(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37503 30462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37513">
    <literal><![CDATA[
      a(L(x,y,z),y,y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30462,a(flip),b,37512,a),flip(a)].">
      <j1 rule="hyper" parents="373 30462 37512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37515">
    <literal><![CDATA[
      L(a(x,y,y),y,z) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32607,a(flip),b,37513,a)].">
      <j1 rule="hyper" parents="64 32607 37513"/>
    </justification>
  </clause>

  <clause id="37516">
    <literal><![CDATA[
      a(x,y,y) * L(x,y,z) = R(L(x,y,z),y,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,37513,a(flip),b,15990,a)].">
      <j1 rule="hyper" parents="144 37513 15990"/>
    </justification>
  </clause>

  <clause id="37517">
    <literal><![CDATA[
      (x \ L(y,x,z)) / (1 / T(x,x \ L(y,x,z))) = a(y,x,x) \ L(y,x,z)
    ]]></literal>
    <justification jstring="[para(37513(a,1),30573(a,2,1))].">
      <j1 rule="para" parents="37513 30573"/>
    </justification>
  </clause>

  <clause id="37518">
    <literal><![CDATA[
      (a(x,y,y) * y) * z = a(x,y,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(37513(a,1),32609(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37513 32609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37519">
    <literal><![CDATA[
      (x * a(y,x,x)) * z = x * (z * a(y,x,x))
    ]]></literal>
    <justification jstring="[para(37513(a,1),33441(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="37513 33441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37520">
    <literal><![CDATA[
      a(x,y,a(z,y,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,37515,a)].">
      <j1 rule="hyper" parents="54 37515"/>
    </justification>
  </clause>

  <clause id="37521">
    <literal><![CDATA[
      (x / y) * (y * a(z,y,y)) = a(z,y,y) * x
    ]]></literal>
    <justification jstring="[para(37515(a,1),23576(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37515 23576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37522">
    <literal><![CDATA[
      (x * y) * a(z,y,y) = x * (a(z,y,y) * y)
    ]]></literal>
    <justification jstring="[para(37515(a,1),36318(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="37515 36318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37523">
    <literal><![CDATA[
      L(a(x,y,L(y,z,u)),L(y,z,u),u * z) = L(a(x,y,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(37515(a,1),36483(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37515 36483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37525">
    <literal><![CDATA[
      L(x,x,(y * x) \ z) = L(x,x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,25574,a(flip),b,37509,a),flip(a)].">
      <j1 rule="hyper" parents="373 25574 37509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37526">
    <literal><![CDATA[
      a(x,y,y) * L(x,y,z) = L(R(x,y,y),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29,a(flip),b,37516,a),flip(a)].">
      <j1 rule="hyper" parents="373 29 37516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37527">
    <literal><![CDATA[
      L(x,y,a(z,y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(606,a,37518,a)].">
      <j1 rule="hyper" parents="606 37518"/>
    </justification>
  </clause>

  <clause id="37528">
    <literal><![CDATA[
      (a(x,y,y) * y) * z = y * (a(x,y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,33249,a(flip),b,37518,a),flip(a)].">
      <j1 rule="hyper" parents="373 33249 37518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37529">
    <literal><![CDATA[
      (a(x,y,y) * y) \ z = y \ (a(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,75,a(flip),b,37518,a)].">
      <j1 rule="hyper" parents="139 75 37518"/>
    </justification>
  </clause>

  <clause id="37530">
    <literal><![CDATA[
      L(x,y \ z,a(z,z * y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,35690,a(flip),b,37527,a)].">
      <j1 rule="hyper" parents="64 35690 37527"/>
    </justification>
  </clause>

  <clause id="37531">
    <literal><![CDATA[
      L(x,y,a(y,L(y,z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,35424,a(flip),b,37527,a)].">
      <j1 rule="hyper" parents="64 35424 37527"/>
    </justification>
  </clause>

  <clause id="37532">
    <literal><![CDATA[
      L(x,L(y,z,u),a(y,y,w)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,35216,a(flip),b,37527,a)].">
      <j1 rule="hyper" parents="64 35216 37527"/>
    </justification>
  </clause>

  <clause id="37533">
    <literal><![CDATA[
      L(x,L(y,z,u),a(w,y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,35215,a(flip),b,37527,a)].">
      <j1 rule="hyper" parents="64 35215 37527"/>
    </justification>
  </clause>

  <clause id="37534">
    <literal><![CDATA[
      L(x,y,a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,30340,a(flip),b,37527,a)].">
      <j1 rule="hyper" parents="64 30340 37527"/>
    </justification>
  </clause>

  <clause id="37535">
    <literal><![CDATA[
      x * (a(x,x,y) * z) = R(x,x,y) * z
    ]]></literal>
    <justification jstring="[para(37527(a,1),30947(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37527 30947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37536">
    <literal><![CDATA[
      (a(x,y,y) \ 1) * (z * y) = z * L(y,y,x)
    ]]></literal>
    <justification jstring="[para(37527(a,1),31671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37527 31671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37537">
    <literal><![CDATA[
      L(x,y,a(y,y,z)) = u \ (u * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,9,a,b,37534,a),flip(a)].">
      <j1 rule="hyper" parents="373 9 37534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37539">
    <literal><![CDATA[
      L(x,y,z \ (y \ z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,36626,a(flip),b,37534,a),flip(a)].">
      <j1 rule="hyper" parents="64 36626 37534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37540">
    <literal><![CDATA[
      L(((x \ 1) * y) \ y,x,x) \ (x * z) = (((y / x) / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,36530,a(flip),b,37534,a)].">
      <j1 rule="hyper" parents="64 36530 37534"/>
    </justification>
  </clause>

  <clause id="37541">
    <literal><![CDATA[
      x * ((a(x,x,y) \ x) \ z) = (R(x,x,y) \ x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,34077,a(flip),b,37534,a)].">
      <j1 rule="hyper" parents="64 34077 37534"/>
    </justification>
  </clause>

  <clause id="37542">
    <literal><![CDATA[
      (x \ (y / (y * x))) \ z = (y / (y * x)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33657,a(flip),b,37534,a),flip(a)].">
      <j1 rule="hyper" parents="64 33657 37534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37543">
    <literal><![CDATA[
      (x \ (y \ (x \ y))) \ z = (y \ (x \ y)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31122,a(flip),b,37534,a),flip(a)].">
      <j1 rule="hyper" parents="64 31122 37534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37544">
    <literal><![CDATA[
      x * (R(x,x,y) \ z) = a(x,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,30920,a(flip),b,37534,a)].">
      <j1 rule="hyper" parents="64 30920 37534"/>
    </justification>
  </clause>

  <clause id="37546">
    <literal><![CDATA[
      R(x,x,y) * (x \ z) = a(x,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,37534,a(flip),b,30059,a)].">
      <j1 rule="hyper" parents="145 37534 30059"/>
    </justification>
  </clause>

  <clause id="37547">
    <literal><![CDATA[
      R(x,x,y) * (a(x,x,y) \ z) = x * z
    ]]></literal>
    <justification jstring="[hyper(145,a,37534,a(flip),b,30921,a(flip))].">
      <j1 rule="hyper" parents="145 37534 30921"/>
    </justification>
  </clause>

  <clause id="37548">
    <literal><![CDATA[
      (x / y) * R(y,y,z) = a(y,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(144,a,37534,a(flip),b,30076,a)].">
      <j1 rule="hyper" parents="144 37534 30076"/>
    </justification>
  </clause>

  <clause id="37549">
    <literal><![CDATA[
      a(x,x,y) \ (z / x) = z / R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(139,a,37534,a(flip),b,30911,a)].">
      <j1 rule="hyper" parents="139 37534 30911"/>
    </justification>
  </clause>

  <clause id="37550">
    <literal><![CDATA[
      x \ (a(x,x,y) \ z) = R(x,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,37534,a(flip),b,30920,a(flip))].">
      <j1 rule="hyper" parents="139 37534 30920"/>
    </justification>
  </clause>

  <clause id="37553">
    <literal><![CDATA[
      a(x,x,y) * (z * x) = z * R(x,x,y)
    ]]></literal>
    <justification jstring="[para(37534(a,1),30063(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37534 30063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37554">
    <literal><![CDATA[
      a(x,x,y) * (z * (1 / x)) = z * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(37534(a,1),31596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37534 31596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37555">
    <literal><![CDATA[
      x * ((x \ (y / (y * x))) * z) = (y / (y * x)) * z
    ]]></literal>
    <justification jstring="[para(37534(a,1),33656(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37534 33656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37556">
    <literal><![CDATA[
      x * ((x \ (y \ (y / x))) * z) = (y \ (y / x)) * z
    ]]></literal>
    <justification jstring="[para(37534(a,1),34247(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37534 34247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37557">
    <literal><![CDATA[
      L(x,y,L(y,y,z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(37534(a,1),34550(a,1,1))].">
      <j1 rule="para" parents="37534 34550"/>
    </justification>
  </clause>

  <clause id="37558">
    <literal><![CDATA[
      x * ((x \ ((y * x) \ y)) * z) = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[para(37534(a,1),35505(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37534 35505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37559">
    <literal><![CDATA[
      (a(x,L(x,y,z),u) * x) \ w = x \ (a(x,L(x,y,z),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(710,a,37531,a),flip(a)].">
      <j1 rule="hyper" parents="710 37531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37560">
    <literal><![CDATA[
      L(x,a(y,y,z),L(y,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,35514,a(flip),b,37532,a)].">
      <j1 rule="hyper" parents="64 35514 37532"/>
    </justification>
  </clause>

  <clause id="37561">
    <literal><![CDATA[
      a(x,y,y) * (y \ z) = L(y,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,31037,a(flip),b,37533,a)].">
      <j1 rule="hyper" parents="64 31037 37533"/>
    </justification>
  </clause>

  <clause id="37562">
    <literal><![CDATA[
      (x \ y) * a(z,x,x) = L(x,x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,31006,a(flip),b,37533,a)].">
      <j1 rule="hyper" parents="64 31006 37533"/>
    </justification>
  </clause>

  <clause id="37563">
    <literal><![CDATA[
      (x * a(y,z,z)) / z = x / L(z,z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30470,a(flip),b,37533,a)].">
      <j1 rule="hyper" parents="64 30470 37533"/>
    </justification>
  </clause>

  <clause id="37564">
    <literal><![CDATA[
      L(x,x,y) \ (a(y,x,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,30466,a(flip),b,37533,a),flip(a)].">
      <j1 rule="hyper" parents="64 30466 37533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37565">
    <literal><![CDATA[
      L(x,y \ (z \ y),a(u,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,29726,a(flip),b,37533,a)].">
      <j1 rule="hyper" parents="64 29726 37533"/>
    </justification>
  </clause>

  <clause id="37566">
    <literal><![CDATA[
      L(x,x,y) * (x \ z) = a(y,x,x) \ z
    ]]></literal>
    <justification jstring="[hyper(145,a,30466,a(flip),b,37533,a(flip))].">
      <j1 rule="hyper" parents="145 30466 37533"/>
    </justification>
  </clause>

  <clause id="37567">
    <literal><![CDATA[
      x * (L(x,x,y) \ z) = z * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,37533,a(flip),b,30467,a(flip))].">
      <j1 rule="hyper" parents="145 37533 30467"/>
    </justification>
  </clause>

  <clause id="37568">
    <literal><![CDATA[
      a(x,y,y) * (z * L(y,y,x)) = z * y
    ]]></literal>
    <justification jstring="[hyper(144,a,37533,a(flip),b,30469,a),flip(a)].">
      <j1 rule="hyper" parents="144 37533 30469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37569">
    <literal><![CDATA[
      (x / y) * L(y,y,z) = a(z,y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,37533,a(flip),b,31038,a),flip(a)].">
      <j1 rule="hyper" parents="139 37533 31038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37571">
    <literal><![CDATA[
      (x \ y) \ (L(x,x,z) \ y) = a(z,x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,37533,a(flip),b,31006,a(flip))].">
      <j1 rule="hyper" parents="139 37533 31006"/>
    </justification>
  </clause>

  <clause id="37572">
    <literal><![CDATA[
      a(x,y,y) * (L(y,y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(37533(a,1),30468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37533 30468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37573">
    <literal><![CDATA[
      x * ((x * (y \ (x \ y))) \ z) = L((y \ (x \ y)) \ z,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,36119,a(flip),b,37557,a)].">
      <j1 rule="hyper" parents="64 36119 37557"/>
    </justification>
  </clause>

  <clause id="37574">
    <literal><![CDATA[
      R(x,y,L(y,y,z)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,35353,a(flip),b,37557,a),flip(a)].">
      <j1 rule="hyper" parents="42 35353 37557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37575">
    <literal><![CDATA[
      (L(x,y,z) * a(x,x,u)) \ w = a(x,x,u) \ (L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(710,a,37560,a),flip(a)].">
      <j1 rule="hyper" parents="710 37560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37578">
    <literal><![CDATA[
      R(x,y \ (z \ y),z) = R(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29827,a,b,37574,a)].">
      <j1 rule="hyper" parents="64 29827 37574"/>
    </justification>
  </clause>

  <clause id="37580">
    <literal><![CDATA[
      (1 / (x / y)) * (((y / x) * (x / y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(37530(a,1),36381(a,2,2))].">
      <j1 rule="para" parents="37530 36381"/>
    </justification>
  </clause>

  <clause id="37581">
    <literal><![CDATA[
      L(x \ y,x,z \ (x \ z)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,569,a(flip),b,37539,a),flip(a)].">
      <j1 rule="hyper" parents="373 569 37539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37583">
    <literal><![CDATA[
      L(x,y \ (z \ y),z) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31369,a,b,37539,a)].">
      <j1 rule="hyper" parents="64 31369 37539"/>
    </justification>
  </clause>

  <clause id="37584">
    <literal><![CDATA[
      L((x \ 1) \ ((y \ (x \ y)) \ z),x,x) = ((y \ (x \ y)) * (x \ 1)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,11812,a(flip),b,37539,a),flip(a)].">
      <j1 rule="hyper" parents="64 11812 37539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37586">
    <literal><![CDATA[
      x * (((y * x) \ y) \ 1) = x / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(37565(a,1),34920(a,1,2))].">
      <j1 rule="para" parents="37565 34920"/>
    </justification>
  </clause>

  <clause id="37587">
    <literal><![CDATA[
      R(x,y \ ((z / u) \ y),u \ z) = R(x,z / u,z / u)
    ]]></literal>
    <justification jstring="[hyper(25233,a,37578,a)].">
      <j1 rule="hyper" parents="25233 37578"/>
    </justification>
  </clause>

  <clause id="37589">
    <literal><![CDATA[
      R(1 / ((x \ y) / y),x,x) = ((x \ y) / y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,26483,a(flip),b,37578,a),flip(a)].">
      <j1 rule="hyper" parents="64 26483 37578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37593">
    <literal><![CDATA[
      L(x,y \ z,z \ y) = L(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29553,a(flip),b,37583,a)].">
      <j1 rule="hyper" parents="64 29553 37583"/>
    </justification>
  </clause>

  <clause id="37594">
    <literal><![CDATA[
      x * (y * a(x,x,z)) = R(x,x,z) * y
    ]]></literal>
    <justification jstring="[hyper(23185,a,37535,a)].">
      <j1 rule="hyper" parents="23185 37535"/>
    </justification>
  </clause>

  <clause id="37597">
    <literal><![CDATA[
      a(x,x,y) * (x * z) = R(x,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,29956,a,b,37535,a)].">
      <j1 rule="hyper" parents="64 29956 37535"/>
    </justification>
  </clause>

  <clause id="37598">
    <literal><![CDATA[
      (x * y) \ (x * (R(y,y,z) * u)) = L(a(y,y,z) * u,y,x)
    ]]></literal>
    <justification jstring="[para(37535(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="37535 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37599">
    <literal><![CDATA[
      a(x,y,R(z,z,u) * ((a(w,v5,w) / z) \ v6)) = a(x,y,(z * R(z,z,u)) * v6)
    ]]></literal>
    <justification jstring="[para(37535(a,1),34628(a,1,3))].">
      <j1 rule="para" parents="37535 34628"/>
    </justification>
  </clause>

  <clause id="37601">
    <literal><![CDATA[
      x \ ((a(x,x,y) \ z) * (x * y)) = R(x,x,y) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(139,a,29994,a(flip),b,37544,a)].">
      <j1 rule="hyper" parents="139 29994 37544"/>
    </justification>
  </clause>

  <clause id="37603">
    <literal><![CDATA[
      a(x,x,y) \ (K(z,x) * u) = x * (R(T(x,z),x,y) \ u)
    ]]></literal>
    <justification jstring="[para(24599(a,1),37544(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24599 37544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37604">
    <literal><![CDATA[
      a(x,y,((R(z,z,u) \ w) * z) \ v5) = a(x,y,(a(z,z,u) \ w) \ v5)
    ]]></literal>
    <justification jstring="[para(37544(a,1),27394(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="37544 27394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37605">
    <literal><![CDATA[
      a(x,x,y) * ((1 / x) \ z) = (1 / R(x,x,y)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,35194,a(flip),b,37546,a),flip(a)].">
      <j1 rule="hyper" parents="64 35194 37546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37606">
    <literal><![CDATA[
      (x / (y * x)) * ((1 / y) \ z) = a(y,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,27926,a(flip),b,37546,a)].">
      <j1 rule="hyper" parents="64 27926 37546"/>
    </justification>
  </clause>

  <clause id="37607">
    <literal><![CDATA[
      L(x,y * ((z \ u) * R(z,z,w)),v5) = L(x,y * (a(z,z,w) * u),v5)
    ]]></literal>
    <justification jstring="[para(37546(a,1),29548(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="37546 29548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37609">
    <literal><![CDATA[
      a(x,x,y) \ (z / (x \ 1)) = z / R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,36673,a,b,37547,a),flip(a)].">
      <j1 rule="hyper" parents="35 36673 37547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37613">
    <literal><![CDATA[
      a(L(L(a(x,x,y),z / x,z / x),a(x,x,y),z / x),u,w) = a((z / x) * (z / R(x,x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(37549(a,1),32947(a,2,1,2))].">
      <j1 rule="para" parents="37549 32947"/>
    </justification>
  </clause>

  <clause id="37614">
    <literal><![CDATA[
      a(x,x,y) \ ((1 / x) \ z) = R(1 / x,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(39,a,2466,a(flip),b,37550,a),flip(a)].">
      <j1 rule="hyper" parents="39 2466 37550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37616">
    <literal><![CDATA[
      (x * R(y,y,z)) \ (a(y,y,z) * (x * (y * u))) = L(L(u,y,x),x * y,a(y,y,z))
    ]]></literal>
    <justification jstring="[para(37553(a,1),602(a,1,1))].">
      <j1 rule="para" parents="37553 602"/>
    </justification>
  </clause>

  <clause id="37617">
    <literal><![CDATA[
      a(x,x,y) * ((z * x) * y) = (z * R(x,x,y)) * y
    ]]></literal>
    <justification jstring="[para(37553(a,1),29319(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37553 29319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37618">
    <literal><![CDATA[
      a(x,x,y) * (a(x,z,u) * (w * x)) = a(x,z,u) * (w * R(x,x,y))
    ]]></literal>
    <justification jstring="[para(37553(a,1),31091(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37553 31091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37619">
    <literal><![CDATA[
      (x * R(y,y,z)) / ((x * (y * R(y,y,z))) / y) = a(x,y,y)
    ]]></literal>
    <justification jstring="[para(37553(a,1),34060(a,1,1))].">
      <j1 rule="para" parents="37553 34060"/>
    </justification>
  </clause>

  <clause id="37620">
    <literal><![CDATA[
      (x * R(y,y,z)) \ (a(y,y,z) * (y * (T(x,y) * u))) = L(L(u,x,y),x * y,a(z,y,y))
    ]]></literal>
    <justification jstring="[para(37553(a,1),29289(a,1,1))].">
      <j1 rule="para" parents="37553 29289"/>
    </justification>
  </clause>

  <clause id="37622">
    <literal><![CDATA[
      a(x,y \ K(z,u),y \ K(z,u)) * ((y \ K(z,u)) \ w) = K(u,z) * (L(y \ 1,y \ K(z,u),x) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26121,a,b,37561,a),flip(a)].">
      <j1 rule="hyper" parents="373 26121 37561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37623">
    <literal><![CDATA[
      L(x,x,y) * (a(y,x,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(1335,a,37561,a(flip))].">
      <j1 rule="hyper" parents="1335 37561"/>
    </justification>
  </clause>

  <clause id="37625">
    <literal><![CDATA[
      a(x,K(y,z) / u,K(y,z) / u) * (u * ((u \ K(y,z)) \ w)) = L(K(y,z) / u,K(y,z) / u,x) \ (u * w)
    ]]></literal>
    <justification jstring="[para(26127(a,1),37561(a,1,2))].">
      <j1 rule="para" parents="26127 37561"/>
    </justification>
  </clause>

  <clause id="37626">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * (x \ w) = L(x,x,a(y,z,u)) \ w
    ]]></literal>
    <justification jstring="[para(36326(a,1),37561(a,1,1))].">
      <j1 rule="para" parents="36326 37561"/>
    </justification>
  </clause>

  <clause id="37628">
    <literal><![CDATA[
      L(x,x,y) \ (x * z) = z * a(y,x,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),37562(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 37562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37630">
    <literal><![CDATA[
      a(x,y,y) * (z / y) = z / L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33298,a(flip),b,37563,a)].">
      <j1 rule="hyper" parents="64 33298 37563"/>
    </justification>
  </clause>

  <clause id="37631">
    <literal><![CDATA[
      a(x,y,y) \ (z / L(y,y,x)) = z / y
    ]]></literal>
    <justification jstring="[hyper(139,a,37563,a(flip),b,33298,a(flip))].">
      <j1 rule="hyper" parents="139 37563 33298"/>
    </justification>
  </clause>

  <clause id="37633">
    <literal><![CDATA[
      L(L(x,x,y),L(x,x,y),z) \ (a(z,L(x,x,y),L(x,x,y)) \ x) = a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,30462,a(flip),b,37564,a),flip(a)].">
      <j1 rule="hyper" parents="373 30462 37564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37635">
    <literal><![CDATA[
      L(x,y * ((z \ u) * L(z,z,w)),v5) = L(x,y * (a(w,z,z) \ u),v5)
    ]]></literal>
    <justification jstring="[para(37564(a,1),29549(a,1,2,2,1))].">
      <j1 rule="para" parents="37564 29549"/>
    </justification>
  </clause>

  <clause id="37636">
    <literal><![CDATA[
      L(x,x,y) \ L(x,x,z) = a(z,x,x) \ a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30476,a(flip),b,37566,a)].">
      <j1 rule="hyper" parents="64 30476 37566"/>
    </justification>
  </clause>

  <clause id="37637">
    <literal><![CDATA[
      (a(x,y,y) \ z) * y = z * L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,37566,a(flip),b,24378,a)].">
      <j1 rule="hyper" parents="144 37566 24378"/>
    </justification>
  </clause>

  <clause id="37638">
    <literal><![CDATA[
      (1 / x) \ (a(y,x,x) \ z) = (1 / L(x,x,y)) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,37566,a(flip),b,35193,a)].">
      <j1 rule="hyper" parents="139 37566 35193"/>
    </justification>
  </clause>

  <clause id="37639">
    <literal><![CDATA[
      T(x * a(y,z,z),z) = L(z,z,y) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(269,a,33196,a,b,37567,a)].">
      <j1 rule="hyper" parents="269 33196 37567"/>
    </justification>
  </clause>

  <clause id="37641">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,z \ 1,u) \ w,z,z)) = a(x,y,(w * a(u,z \ 1,z \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(37567(a,1),27368(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="37567 27368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37642">
    <literal><![CDATA[
      (x * x) * (y * a(x * z,x,x)) = x * (L(x \ 1,x,z) \ y)
    ]]></literal>
    <justification jstring="[para(37567(a,1),28048(a,1,2))].">
      <j1 rule="para" parents="37567 28048"/>
    </justification>
  </clause>

  <clause id="37644">
    <literal><![CDATA[
      (a(x,x,y) \ z) * x = z * (a(x,x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,36725,a(flip),b,37568,a),flip(a)].">
      <j1 rule="hyper" parents="64 36725 37568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37645">
    <literal><![CDATA[
      (a(x,y,y) * z) \ (z * y) = L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,37568,a(flip),b,33254,a)].">
      <j1 rule="hyper" parents="139 37568 33254"/>
    </justification>
  </clause>

  <clause id="37646">
    <literal><![CDATA[
      a(x,y \ ((1 / y) \ z),y \ ((1 / y) \ z)) * (y \ L(z,y \ ((1 / y) \ z),x)) = (y \ 1) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(1863(a,1),37568(a,1,2))].">
      <j1 rule="para" parents="1863 37568"/>
    </justification>
  </clause>

  <clause id="37648">
    <literal><![CDATA[
      (1 / x) \ ((a(y,x,x) \ 1) * z) = x \ ((x * L(x,x,y)) * z)
    ]]></literal>
    <justification jstring="[para(37569(a,1),27014(a,1,2,1))].">
      <j1 rule="para" parents="37569 27014"/>
    </justification>
  </clause>

  <clause id="37649">
    <literal><![CDATA[
      (1 / (1 / x)) \ ((a(y,x,x) \ 1) * z) = x \ ((L(x,x,y) * (1 / x)) * z)
    ]]></literal>
    <justification jstring="[para(37569(a,1),37110(a,1,2,1))].">
      <j1 rule="para" parents="37569 37110"/>
    </justification>
  </clause>

  <clause id="37650">
    <literal><![CDATA[
      (a(x,x,y) \ x) * z = x * (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,36721,a(flip),b,37572,a)].">
      <j1 rule="hyper" parents="64 36721 37572"/>
    </justification>
  </clause>

  <clause id="37651">
    <literal><![CDATA[
      L(x,x,L(y,y,x) * z) = L(x,x,y * z)
    ]]></literal>
    <justification jstring="[para(37572(a,1),34022(a,1,3)),flip(a)].">
      <j1 rule="para" parents="37572 34022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37652">
    <literal><![CDATA[
      (x * y) \ (x * (R(y,y,x) * z)) = L(z,y,x) * a(y,y,x)
    ]]></literal>
    <justification jstring="[para(37594(a,1),33516(a,1,2,2))].">
      <j1 rule="para" parents="37594 33516"/>
    </justification>
  </clause>

  <clause id="37653">
    <literal><![CDATA[
      L((x / y) / z,z,a(u,y,y)) = (x / L(y,y,u)) / (z * a(u,y,y))
    ]]></literal>
    <justification jstring="[para(37630(a,1),28811(a,2,1))].">
      <j1 rule="para" parents="37630 28811"/>
    </justification>
  </clause>

  <clause id="37654">
    <literal><![CDATA[
      T(a(x,y,y) \ K(z,y),y) = T(y,z) \ L(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(269,a,37637,a,b,5810,a)].">
      <j1 rule="hyper" parents="269 37637 5810"/>
    </justification>
  </clause>

  <clause id="37656">
    <literal><![CDATA[
      R(a(x,y,y),z,u) * L(y,y,x) = a((u * z) \ (a(x,y,y) \ (u * z)),z,u) * y
    ]]></literal>
    <justification jstring="[para(28073(a,2),37637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28073 37637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37657">
    <literal><![CDATA[
      L(x,a(y,x,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,30739,a,b,37645,a(flip))].">
      <j1 rule="hyper" parents="42 30739 37645"/>
    </justification>
  </clause>

  <clause id="37658">
    <literal><![CDATA[
      R(x,y,((z * (a(u,w,w) * w)) \ v5) * (a(u,w,w) * a(u,w,w))) = R(x,y,(z * L(w,w,u)) \ v5)
    ]]></literal>
    <justification jstring="[para(37645(a,1),31705(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="37645 31705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37659">
    <literal><![CDATA[
      L(x,a(x,x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,31821,a(flip),b,37657,a)].">
      <j1 rule="hyper" parents="64 31821 37657"/>
    </justification>
  </clause>

  <clause id="37660">
    <literal><![CDATA[
      L(R(x,y,z),a(u,x,x),w) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(37657(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37657 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37661">
    <literal><![CDATA[
      x * (y \ L(T(y,x),y,z)) = (L(y,y,z) * x) / y
    ]]></literal>
    <justification jstring="[para(37657(a,1),31658(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37657 31658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37662">
    <literal><![CDATA[
      L(a(x,x,y),a(z,x,x),u) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(37657(a,1),34877(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37657 34877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37663">
    <literal><![CDATA[
      a(x,a(x,x,y),z) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,37659,a(flip),b,34906,a),flip(a)].">
      <j1 rule="hyper" parents="140 37659 34906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37664">
    <literal><![CDATA[
      R(x * a(y,y,z),L(y,a(y,y,z),x),u) = ((x * (a(y,y,z) * y)) * u) / (y * u)
    ]]></literal>
    <justification jstring="[para(37659(a,1),603(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="37659 603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37665">
    <literal><![CDATA[
      L(a(x,x,y),a(x,x,z),u) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(37659(a,1),34877(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37659 34877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37666">
    <literal><![CDATA[
      a(x,a(y,z,z),R(z,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,37660,a)].">
      <j1 rule="hyper" parents="54 37660"/>
    </justification>
  </clause>

  <clause id="37667">
    <literal><![CDATA[
      a(x,a(y,z,z),L(z,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,27644,a(flip),b,37666,a)].">
      <j1 rule="hyper" parents="64 27644 37666"/>
    </justification>
  </clause>

  <clause id="37668">
    <literal><![CDATA[
      L(a(x,x,y * z),a(u,x,x),w) = a(x,x,z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,37662,a),flip(a)].">
      <j1 rule="hyper" parents="373 27298 37662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37669">
    <literal><![CDATA[
      (a(x,x,y) * a(z,x,x)) * u = a(x,x,y) * (a(z,x,x) * u)
    ]]></literal>
    <justification jstring="[para(37662(a,1),28784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37662 28784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37670">
    <literal><![CDATA[
      a(x,a(y,y,z),a(y,y,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,37665,a)].">
      <j1 rule="hyper" parents="54 37665"/>
    </justification>
  </clause>

  <clause id="37671">
    <literal><![CDATA[
      x * (a(y,y,z) \ 1) = a(y,y,z) \ x
    ]]></literal>
    <justification jstring="[para(37665(a,1),23106(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37665 23106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37672">
    <literal><![CDATA[
      (x \ L(x,y,y)) * z = a(y,y,x) \ z
    ]]></literal>
    <justification jstring="[para(37665(a,1),25663(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37665 25663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37673">
    <literal><![CDATA[
      (a(x,x,y) \ 1) \ z = a(x,x,y) * z
    ]]></literal>
    <justification jstring="[para(37665(a,1),28795(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37665 28795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37674">
    <literal><![CDATA[
      (a(x,x,y) \ 1) \ z = z * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(37665(a,1),28814(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37665 28814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37675">
    <literal><![CDATA[
      L(x,(a(y,y,z) \ u) * w,v5) = L(x,(a(y,y,z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(37665(a,1),31063(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="37665 31063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37676">
    <literal><![CDATA[
      a(a(x,x,y) \ z,u,w) = a(z * a(x,x,y),u,w)
    ]]></literal>
    <justification jstring="[para(37665(a,1),32532(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="37665 32532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37677">
    <literal><![CDATA[
      x \ (a(y,y,z) \ x) = a(y,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(149,a,37671,a)].">
      <j1 rule="hyper" parents="149 37671"/>
    </justification>
  </clause>

  <clause id="37678">
    <literal><![CDATA[
      (x * a(y,y,z)) \ x = a(y,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,23138,a(flip),b,37671,a)].">
      <j1 rule="hyper" parents="139 23138 37671"/>
    </justification>
  </clause>

  <clause id="37679">
    <literal><![CDATA[
      (R(x,x,y) \ x) * z = a(x,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,30145,a,b,37671,a)].">
      <j1 rule="hyper" parents="64 30145 37671"/>
    </justification>
  </clause>

  <clause id="37680">
    <literal><![CDATA[
      x * (R(y,y,z) \ y) = a(y,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,30142,a,b,37671,a)].">
      <j1 rule="hyper" parents="64 30142 37671"/>
    </justification>
  </clause>

  <clause id="37681">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * z = a(x,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,23736,a,b,37671,a)].">
      <j1 rule="hyper" parents="64 23736 37671"/>
    </justification>
  </clause>

  <clause id="37682">
    <literal><![CDATA[
      x * (y \ L(y,z,z)) = a(z,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,5667,a(flip),b,37671,a)].">
      <j1 rule="hyper" parents="64 5667 37671"/>
    </justification>
  </clause>

  <clause id="37683">
    <literal><![CDATA[
      (a(x,x,y) \ z) * K(u,w) = z * (a(x,x,y) \ K(u,w))
    ]]></literal>
    <justification jstring="[para(37671(a,1),24286(a,1,1))].">
      <j1 rule="para" parents="37671 24286"/>
    </justification>
  </clause>

  <clause id="37685">
    <literal><![CDATA[
      (x \ L(x,y,y)) \ z = z * a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,23138,a(flip),b,37672,a)].">
      <j1 rule="hyper" parents="139 23138 37672"/>
    </justification>
  </clause>

  <clause id="37686">
    <literal><![CDATA[
      (x \ L(x,y,y)) \ z = a(y,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,9,a(flip),b,37672,a)].">
      <j1 rule="hyper" parents="139 9 37672"/>
    </justification>
  </clause>

  <clause id="37689">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) * L(L(x \ L(x,y,y),z,u) \ 1,w,v5) = L(a(y,y,x) \ L((x \ L(x,y,y)) \ 1,w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(37672(a,1),4273(a,2,1))].">
      <j1 rule="para" parents="37672 4273"/>
    </justification>
  </clause>

  <clause id="37690">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) \ w = a(a(y,z,u),x,x) * w
    ]]></literal>
    <justification jstring="[para(28791(a,1),37672(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28791 37672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37694">
    <literal><![CDATA[
      a(x,a(y,z,u),a(y,z,u)) \ w = a(a(y,z,u),a(y,z,u),x) * w
    ]]></literal>
    <justification jstring="[para(27239(a,1),37673(a,1,1))].">
      <j1 rule="para" parents="27239 37673"/>
    </justification>
  </clause>

  <clause id="37695">
    <literal><![CDATA[
      (1 / x) * (a(y,y,x) * (L(x,y,y) * z)) = L(z,x,L(x,y,y))
    ]]></literal>
    <justification jstring="[para(37673(a,1),33619(a,1,2))].">
      <j1 rule="para" parents="37673 33619"/>
    </justification>
  </clause>

  <clause id="37696">
    <literal><![CDATA[
      (R(x,x,y) \ x) \ z = z * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(30090(a,2),37674(a,1,1))].">
      <j1 rule="para" parents="30090 37674"/>
    </justification>
  </clause>

  <clause id="37697">
    <literal><![CDATA[
      ((R(x,x,y) \ 1) * x) \ z = z * a(x,x,y * x)
    ]]></literal>
    <justification jstring="[para(30180(a,1),37674(a,1,1))].">
      <j1 rule="para" parents="30180 37674"/>
    </justification>
  </clause>

  <clause id="37699">
    <literal><![CDATA[
      L(a(x,x,y),z,z) \ z = (1 / z) \ (a(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(37677(a,1),34600(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37677 34600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37700">
    <literal><![CDATA[
      a(x,L(x,y,z),u) \ a(a(x,x,u) \ 1,y,z) = a(x,x,u) \ 1
    ]]></literal>
    <justification jstring="[para(37677(a,1),34886(a,1,2,1))].">
      <j1 rule="para" parents="37677 34886"/>
    </justification>
  </clause>

  <clause id="37701">
    <literal><![CDATA[
      (a(x,x,y) \ z) * L(u,R(x,x,y) \ x,z) = z * ((R(x,x,y) \ x) * u)
    ]]></literal>
    <justification jstring="[hyper(144,a,37680,a(flip),b,213,a)].">
      <j1 rule="hyper" parents="144 37680 213"/>
    </justification>
  </clause>

  <clause id="37702">
    <literal><![CDATA[
      (x \ (y * L(y \ x,z,z))) * u = a(z,z,(x \ y) \ 1) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,5687,a(flip),b,37681,a)].">
      <j1 rule="hyper" parents="64 5687 37681"/>
    </justification>
  </clause>

  <clause id="37705">
    <literal><![CDATA[
      (a(x,x,y) \ z) / L(x,L(x,x,y),z) = z * (1 / R(x,x,y))
    ]]></literal>
    <justification jstring="[para(37681(a,1),34813(a,1,1))].">
      <j1 rule="para" parents="37681 34813"/>
    </justification>
  </clause>

  <clause id="37706">
    <literal><![CDATA[
      a(L(x,x,L(R(x,y,y),z,z)),y,y) \ L(R(x,y,y),z,z) = a(z,z,R(x,y,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,36755,a,b,37682,a)].">
      <j1 rule="hyper" parents="64 36755 37682"/>
    </justification>
  </clause>

  <clause id="37707">
    <literal><![CDATA[
      L(x * a(y,y,z),z,a(z,y,y)) = z * (L(z,y,y) \ x)
    ]]></literal>
    <justification jstring="[para(37685(a,1),29373(a,1,1))].">
      <j1 rule="para" parents="37685 29373"/>
    </justification>
  </clause>

  <clause id="37708">
    <literal><![CDATA[
      a(x,x,y) * (a(x,x,y) * z) = y * (L(L(y,x,x),x,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30925,a(flip),b,37686,a),flip(a)].">
      <j1 rule="hyper" parents="64 30925 37686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37709">
    <literal><![CDATA[
      a(x \ 1,x,y) \ ((y / (x * y)) * z) = (1 / x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,31157,a,b,37581,a)].">
      <j1 rule="hyper" parents="64 31157 37581"/>
    </justification>
  </clause>

  <clause id="37710">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,y \ x) = (1 / (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,29106,a(flip),b,37581,a)].">
      <j1 rule="hyper" parents="64 29106 37581"/>
    </justification>
  </clause>

  <clause id="37711">
    <literal><![CDATA[
      (R(x,y,y) * y) \ (x * (y * (z * a(x,y,y)))) = L(z,L(y,y,x),x)
    ]]></literal>
    <justification jstring="[para(37519(a,1),36200(a,1,2,2))].">
      <j1 rule="para" parents="37519 36200"/>
    </justification>
  </clause>

  <clause id="37712">
    <literal><![CDATA[
      x * (y * a(a(z,u,w),x,x)) = L(x,x,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(36325(a,1),37519(a,1,1)),flip(a)].">
      <j1 rule="para" parents="36325 37519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37714">
    <literal><![CDATA[
      (x / y) * (a(z,y,y) * y) = a(z,y,y) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,23169,a,b,37521,a)].">
      <j1 rule="hyper" parents="64 23169 37521"/>
    </justification>
  </clause>

  <clause id="37715">
    <literal><![CDATA[
      L(R(x,y,y) \ R(R(x,y,y),y,z),R(x,y,y),y) = a(a(x,y,y) * L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(37526(a,2),33411(a,2,1))].">
      <j1 rule="para" parents="37526 33411"/>
    </justification>
  </clause>

  <clause id="37716">
    <literal><![CDATA[
      a(x,y,z * (a(u,z,z) * w)) = a(x,y,w * (z * a(u,z,z)))
    ]]></literal>
    <justification jstring="[para(37528(a,1),27462(a,1,3))].">
      <j1 rule="para" parents="37528 27462"/>
    </justification>
  </clause>

  <clause id="37717">
    <literal><![CDATA[
      K(x \ 1,y) * (x * (a(y,x,x) * z)) = (((y / x) / y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(37528(a,1),31409(a,1,2))].">
      <j1 rule="para" parents="37528 31409"/>
    </justification>
  </clause>

  <clause id="37718">
    <literal><![CDATA[
      R(x,y,(z \ (z / u)) * (u \ (a(z,u,u) \ w))) = R(x,y,((z \ (u \ z)) * (z \ (u \ z))) * w)
    ]]></literal>
    <justification jstring="[para(37529(a,1),37393(a,1,3,2))].">
      <j1 rule="para" parents="37529 37393"/>
    </justification>
  </clause>

  <clause id="37719">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) * y = y / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1238,a,b,37586,a)].">
      <j1 rule="hyper" parents="64 1238 37586"/>
    </justification>
  </clause>

  <clause id="37721">
    <literal><![CDATA[
      L(x,y \ z,z \ y) = L(x,y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,35219,a(flip),b,37593,a),flip(a)].">
      <j1 rule="hyper" parents="373 35219 37593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37723">
    <literal><![CDATA[
      (x \ (a(y,y,x) \ z)) * y = (x \ z) * (a(y,y,x) \ y)
    ]]></literal>
    <justification jstring="[para(33056(a,1),37644(a,1,1))].">
      <j1 rule="para" parents="33056 37644"/>
    </justification>
  </clause>

  <clause id="37725">
    <literal><![CDATA[
      (a(x,x,y) \ x) * (x \ z) = a(x,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(373,a,30269,a(flip),b,37650,a),flip(a)].">
      <j1 rule="hyper" parents="373 30269 37650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37727">
    <literal><![CDATA[
      a(x,y,(R(z \ 1,z,u) \ 1) * w) = a(x,y,z * (a(z,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(37650(a,1),30190(a,2,3))].">
      <j1 rule="para" parents="37650 30190"/>
    </justification>
  </clause>

  <clause id="37728">
    <literal><![CDATA[
      (x * x) * (x \ (((y * x) \ y) \ 1)) = x / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,37446,a,b,37719,a)].">
      <j1 rule="hyper" parents="64 37446 37719"/>
    </justification>
  </clause>

  <clause id="37729">
    <literal><![CDATA[
      ((x / (y * x)) \ 1) \ (a(y,y,x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,37725,a(flip),b,30160,a(flip))].">
      <j1 rule="hyper" parents="139 37725 30160"/>
    </justification>
  </clause>

  <clause id="37730">
    <literal><![CDATA[
      L(R(x,y,z),x,L(u,x,w)) = L(R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,29,a(flip),b,37507,a),flip(a)].">
      <j1 rule="hyper" parents="373 29 37507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37732">
    <literal><![CDATA[
      R((x / (y * x)) \ 1,y,y) = ((y \ x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(2032(a,1),37589(a,1,1))].">
      <j1 rule="para" parents="2032 37589"/>
    </justification>
  </clause>

  <clause id="37733">
    <literal><![CDATA[
      a(x,x,y) * (z * (x \ 1)) = z * R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31585,a(flip),b,37606,a),flip(a)].">
      <j1 rule="hyper" parents="64 31585 37606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37734">
    <literal><![CDATA[
      R(x / (y / (x * y)),x,x \ 1) = (((x \ y) / y) \ 1) * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(37732(a,1),25551(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37732 25551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37736">
    <literal><![CDATA[
      x * ((a(x,x,y) \ x) \ z) = z * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,37696,a(flip),b,37541,a),flip(a)].">
      <j1 rule="hyper" parents="373 37696 37541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37737">
    <literal><![CDATA[
      (a(x,x,y) \ x) \ z = (x \ z) * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,29909,a,b,37736,a),flip(a)].">
      <j1 rule="hyper" parents="35 29909 37736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37738">
    <literal><![CDATA[
      (x * a(y,y,z)) \ (x * y) = a(y,y,z) \ y
    ]]></literal>
    <justification jstring="[para(37736(a,1),34078(a,1,1))].">
      <j1 rule="para" parents="37736 34078"/>
    </justification>
  </clause>

  <clause id="37739">
    <literal><![CDATA[
      ((x / (y * x)) \ 1) \ z = (y \ z) * a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30161,a(flip),b,37737,a)].">
      <j1 rule="hyper" parents="64 30161 37737"/>
    </justification>
  </clause>

  <clause id="37740">
    <literal><![CDATA[
      x \ ((R(1 / y,y,z) \ 1) \ x) = x \ ((y \ x) * a(y,y,z))
    ]]></literal>
    <justification jstring="[para(37737(a,1),31766(a,2,2))].">
      <j1 rule="para" parents="37737 31766"/>
    </justification>
  </clause>

  <clause id="37741">
    <literal><![CDATA[
      a(x,y,(((z / (u * z)) \ 1) \ w) * v5) = a(x,y,v5 * (a(u,u,z) * (u \ w)))
    ]]></literal>
    <justification jstring="[para(37739(a,2),27462(a,1,3,1))].">
      <j1 rule="para" parents="37739 27462"/>
    </justification>
  </clause>

  <clause id="37742">
    <literal><![CDATA[
      T(x / (y / (y * x)),y / (y * x)) = (x \ (y / (y * x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,284,a,b,37542,a)].">
      <j1 rule="hyper" parents="373 284 37542"/>
    </justification>
  </clause>

  <clause id="37743">
    <literal><![CDATA[
      (x \ (y / (y * x))) \ 1 = (y / (y * x)) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,177,a(flip),b,37542,a),flip(a)].">
      <j1 rule="hyper" parents="373 177 37542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37744">
    <literal><![CDATA[
      (x \ y) / (y * x) = x \ (y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(225,a,343,a(flip),b,37542,a)].">
      <j1 rule="hyper" parents="225 343 37542"/>
    </justification>
  </clause>

  <clause id="37747">
    <literal><![CDATA[
      (x / y) \ (x / (x * (x / y))) = y / (x * (x / y))
    ]]></literal>
    <justification jstring="[para(82(a,1),37744(a,1,1)),flip(a)].">
      <j1 rule="para" parents="82 37744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37748">
    <literal><![CDATA[
      L(((x \ (y / (y * x))) \ 1) \ z,T(x \ y,u) / (y * x),(y * x) \ (x \ y)) = ((x \ y) / (y * x)) * z
    ]]></literal>
    <justification jstring="[para(37744(a,1),29788(a,1,1,1,1))].">
      <j1 rule="para" parents="37744 29788"/>
    </justification>
  </clause>

  <clause id="37750">
    <literal><![CDATA[
      ((1 / x) \ y) * a(x,x,z) = (1 / R(x,x,z)) \ y
    ]]></literal>
    <justification jstring="[hyper(23177,a,37605,a)].">
      <j1 rule="hyper" parents="23177 37605"/>
    </justification>
  </clause>

  <clause id="37751">
    <literal><![CDATA[
      R(1 / x,x,y) \ a(x,x,z) = a(x,x,y) \ R(x,x,z)
    ]]></literal>
    <justification jstring="[para(30066(a,1),37614(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30066 37614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37752">
    <literal><![CDATA[
      ((x * R(y,y,z)) * z) / (y * z) = a(y,y,z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(37617(a,1),29995(a,1,1))].">
      <j1 rule="para" parents="37617 29995"/>
    </justification>
  </clause>

  <clause id="37753">
    <literal><![CDATA[
      L(x,(a(y,y,z * y) \ u) * w,v5) = L(x,w * (u * a(y,y,y * z)),v5)
    ]]></literal>
    <justification jstring="[para(37668(a,1),31070(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="37668 31070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37754">
    <literal><![CDATA[
      a(a(x,x,y) \ z,u,w) = a(z * a(y,x,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32851,a,b,37676,a),flip(a)].">
      <j1 rule="hyper" parents="373 32851 37676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37755">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * (a(a(y,z,u),x,x) * w) = w
    ]]></literal>
    <justification jstring="[hyper(157,a,37690,a)].">
      <j1 rule="hyper" parents="157 37690"/>
    </justification>
  </clause>

  <clause id="37756">
    <literal><![CDATA[
      a(x,y,((z \ L(z,u,u)) \ w) * v5) = a(x,y,(w * a(u,u,z * u)) * v5)
    ]]></literal>
    <justification jstring="[para(37697(a,1),30178(a,2,3,1))].">
      <j1 rule="para" parents="37697 30178"/>
    </justification>
  </clause>

  <clause id="37757">
    <literal><![CDATA[
      (x * (y \ 1)) * a(y,y,z) = x * R(y \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(23177,a,37733,a)].">
      <j1 rule="hyper" parents="23177 37733"/>
    </justification>
  </clause>

  <clause id="37758">
    <literal><![CDATA[
      a((a(x,x,y) * z) * a(y,x,x),u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),37754(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 37754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37760">
    <literal><![CDATA[
      a((x / y) \ 1,x / y,y) \ ((y / x) * z) = (1 / (x / y)) * z
    ]]></literal>
    <justification jstring="[para(12(a,1),37709(a,1,2,1,2))].">
      <j1 rule="para" parents="12 37709"/>
    </justification>
  </clause>

  <clause id="37761">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) * ((1 / (y \ x)) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,37710,a(flip),b,31201,a)].">
      <j1 rule="hyper" parents="145 37710 31201"/>
    </justification>
  </clause>

  <clause id="37762">
    <literal><![CDATA[
      (x / y) \ ((1 / (y / x)) * z) = ((x / y) * (y / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(759,a,37580,a)].">
      <j1 rule="hyper" parents="759 37580"/>
    </justification>
  </clause>

  <clause id="37763">
    <literal><![CDATA[
      R(x,y \ ((z / (u / w)) \ y),(w \ u) \ z) = R(x,z / (u / w),z / (u / w))
    ]]></literal>
    <justification jstring="[hyper(64,a,26209,a(flip),b,37587,a)].">
      <j1 rule="hyper" parents="64 26209 37587"/>
    </justification>
  </clause>

  <clause id="37764">
    <literal><![CDATA[
      R(x,y / z,y / z) = R(x,y \ z,z \ y)
    ]]></literal>
    <justification jstring="[para(82(a,1),37587(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 37587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37765">
    <literal><![CDATA[
      R(x,y / z,z \ y) = R(x,y \ z,z \ y)
    ]]></literal>
    <justification jstring="[hyper(25233,a,37764,a)].">
      <j1 rule="hyper" parents="25233 37764"/>
    </justification>
  </clause>

  <clause id="37766">
    <literal><![CDATA[
      R(x,y \ z,z \ y) = R(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26410,a(flip),b,37765,a),flip(a)].">
      <j1 rule="hyper" parents="64 26410 37765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37767">
    <literal><![CDATA[
      R((x \ y) * x,y \ z,z \ y) = z * ((((x \ y) * x) \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,36948,a(flip),b,37766,a),flip(a)].">
      <j1 rule="hyper" parents="373 36948 37766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37768">
    <literal><![CDATA[
      K(x,y) * (a(y,y,z) \ u) = y * (R(T(y,x),y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,22774,a(flip),b,37603,a)].">
      <j1 rule="hyper" parents="64 22774 37603"/>
    </justification>
  </clause>

  <clause id="37769">
    <literal><![CDATA[
      x * (a(y,y,z) \ K(z,y \ 1)) = x / (y * (z \ (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,35637,a(flip),b,37683,a),flip(a)].">
      <j1 rule="hyper" parents="64 35637 37683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37770">
    <literal><![CDATA[
      L(L(x,y,y) * a(y,y,R(x,z,u)),R(x,z,u),a(R(x,z,u),y,y)) = R(x,z,u) * (L(x \ R(x,z,u),y,y) \ 1)
    ]]></literal>
    <justification jstring="[para(5386(a,1),37707(a,2,2))].">
      <j1 rule="para" parents="5386 37707"/>
    </justification>
  </clause>

  <clause id="37771">
    <literal><![CDATA[
      (x / ((y * y) / y)) \ (x * y) = y / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,31417,a(flip),b,37728,a)].">
      <j1 rule="hyper" parents="64 31417 37728"/>
    </justification>
  </clause>

  <clause id="37772">
    <literal><![CDATA[
      x / ((y * x) \ y) = (y / x) \ (y * x)
    ]]></literal>
    <justification jstring="[para(11(a,1),37771(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 37771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37773">
    <literal><![CDATA[
      (x \ y) / (((x \ 1) * (x \ y)) \ (x \ 1)) = (x * ((x \ 1) \ ((x \ 1) / (x \ y)))) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,1621,a,b,37772,a),flip(a)].">
      <j1 rule="hyper" parents="373 1621 37772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37774">
    <literal><![CDATA[
      K(x,y) * ((z / x) \ (z * x)) = T(x,y) / ((z * x) \ z)
    ]]></literal>
    <justification jstring="[para(37772(a,1),14825(a,1,2))].">
      <j1 rule="para" parents="37772 14825"/>
    </justification>
  </clause>

  <clause id="37775">
    <literal><![CDATA[
      (a(x,x,y) \ R(x,x,L(y,z,u))) \ L(y,z,u) = L(y,z,u) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(37751(a,1),36246(a,1,1))].">
      <j1 rule="para" parents="37751 36246"/>
    </justification>
  </clause>

  <clause id="37776">
    <literal><![CDATA[
      a(x,y,((z \ u) * (u \ z)) * ((1 / (u \ z)) * (w * v5))) = a(x,y,(v5 * w) * (z \ u))
    ]]></literal>
    <justification jstring="[para(37761(a,2),27462(a,2,3)),flip(a)].">
      <j1 rule="para" parents="37761 27462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37777">
    <literal><![CDATA[
      (x * R(K(x,y) / x,x,z)) \ u = x * (R(T(x,y),x,x * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31236,a,b,37768,a)].">
      <j1 rule="hyper" parents="64 31236 37768"/>
    </justification>
  </clause>

  <clause id="37778">
    <literal><![CDATA[
      T(x,y) / ((z * x) \ z) = (z / T(x,y)) \ (z * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24505,a(flip),b,37774,a),flip(a)].">
      <j1 rule="hyper" parents="64 24505 37774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37779">
    <literal><![CDATA[
      T(x,y) / ((z * x) \ z) = (z / x) \ (z * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,27826,a(flip),b,37778,a),flip(a)].">
      <j1 rule="hyper" parents="373 27826 37778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37780">
    <literal><![CDATA[
      (x / y) \ (x * T(y,x)) = y / ((y * x) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,15077,a(flip),b,37779,a),flip(a)].">
      <j1 rule="hyper" parents="64 15077 37779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37781">
    <literal><![CDATA[
      x / ((x * y) \ y) = (y / x) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,37780,a),flip(a)].">
      <j1 rule="hyper" parents="64 249 37780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37782">
    <literal><![CDATA[
      ((x / y) \ (y * x)) * (((y * x) \ x) / y) = 1
    ]]></literal>
    <justification jstring="[para(37781(a,1),35664(a,1,1))].">
      <j1 rule="para" parents="37781 35664"/>
    </justification>
  </clause>

  <clause id="37783">
    <literal><![CDATA[
      (((x * y) \ y) / x) * ((y / x) \ (x * y)) = 1
    ]]></literal>
    <justification jstring="[para(37781(a,1),35666(a,1,2))].">
      <j1 rule="para" parents="37781 35666"/>
    </justification>
  </clause>

  <clause id="37785">
    <literal><![CDATA[
      (x \ 1) * ((y \ (x \ y)) \ z) = (x * (y \ (x \ y))) \ z
    ]]></literal>
    <justification jstring="[hyper(35,a,1139,a,b,37573,a)].">
      <j1 rule="hyper" parents="35 1139 37573"/>
    </justification>
  </clause>

  <clause id="37786">
    <literal><![CDATA[
      (x \ 1) * ((y \ (x \ y)) \ 1) = y \ (x * (y * (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,30759,a(flip),b,37785,a),flip(a)].">
      <j1 rule="hyper" parents="373 30759 37785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37787">
    <literal><![CDATA[
      (x \ (y \ x)) \ (y \ 1) = x \ (y * (x * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,36163,a(flip),b,37786,a)].">
      <j1 rule="hyper" parents="64 36163 37786"/>
    </justification>
  </clause>

  <clause id="37788">
    <literal><![CDATA[
      a(x,y,L(y,y,z)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,33536,a(flip),b,37619,a)].">
      <j1 rule="hyper" parents="64 33536 37619"/>
    </justification>
  </clause>

  <clause id="37791">
    <literal><![CDATA[
      a(x,y \ (z \ y),z) = a(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32208,a,b,37788,a)].">
      <j1 rule="hyper" parents="64 32208 37788"/>
    </justification>
  </clause>

  <clause id="37794">
    <literal><![CDATA[
      a(x,y \ (z \ y),z \ 1) = a(x,z \ 1,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,32244,a(flip),b,37791,a)].">
      <j1 rule="hyper" parents="64 32244 37791"/>
    </justification>
  </clause>

  <clause id="37795">
    <literal><![CDATA[
      L(a(x,x,y) * z,x,y) = L(z,x,y) * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,37598,a(flip),b,37652,a)].">
      <j1 rule="hyper" parents="64 37598 37652"/>
    </justification>
  </clause>

  <clause id="37796">
    <literal><![CDATA[
      x * (y \ L(T(y,z \ 1),z,z)) = x / (z * (y \ (z \ y)))
    ]]></literal>
    <justification jstring="[para(25528(a,1),37769(a,1,2))].">
      <j1 rule="para" parents="25528 37769"/>
    </justification>
  </clause>

  <clause id="37797">
    <literal><![CDATA[
      x * (y \ (z * (y * (z \ 1)))) = x / (z * (y \ (z \ y)))
    ]]></literal>
    <justification jstring="[para(1140(a,1),37796(a,1,2,2))].">
      <j1 rule="para" parents="1140 37796"/>
    </justification>
  </clause>

  <clause id="37798">
    <literal><![CDATA[
      (L(1 / x,x,y) \ x) * z = x * (L(x \ 1,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,36453,a(flip),b,37642,a)].">
      <j1 rule="hyper" parents="64 36453 37642"/>
    </justification>
  </clause>

  <clause id="37799">
    <literal><![CDATA[
      ((x \ 1) \ y) * a(z,x,x \ 1) = L(x \ 1,x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,34820,a,b,37798,a(flip))].">
      <j1 rule="hyper" parents="35 34820 37798"/>
    </justification>
  </clause>

  <clause id="37800">
    <literal><![CDATA[
      L(x \ 1,x,y * x) \ y = (1 / x) \ R(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33354,a(flip),b,37799,a),flip(a)].">
      <j1 rule="hyper" parents="64 33354 37799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37801">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,x,y) \ z) = a(y,x,x \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,37799,a(flip),b,33243,a)].">
      <j1 rule="hyper" parents="145 37799 33243"/>
    </justification>
  </clause>

  <clause id="37802">
    <literal><![CDATA[
      a(x,y,L((1 / z) \ R(u,z,z),L(z \ 1,z,z * (u \ 1)),u)) = a(x,y,((u \ 1) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(37800(a,1),37143(a,1,3,1))].">
      <j1 rule="para" parents="37800 37143"/>
    </justification>
  </clause>

  <clause id="37803">
    <literal><![CDATA[
      L(x \ 1,x,y) * ((x \ 1) \ z) = a(y,x,x \ 1) \ z
    ]]></literal>
    <justification jstring="[hyper(756,a,37801,a),flip(a)].">
      <j1 rule="hyper" parents="756 37801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37804">
    <literal><![CDATA[
      L(L(x \ 1,x,y) \ z,x,x) = x * (a(y,x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(145,a,37801,a(flip),b,1148,a),flip(a)].">
      <j1 rule="hyper" parents="145 37801 1148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37805">
    <literal><![CDATA[
      a(x,y,y \ 1) \ (z * (y \ 1)) = z * L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,23886,a(flip),b,37801,a(flip))].">
      <j1 rule="hyper" parents="139 23886 37801"/>
    </justification>
  </clause>

  <clause id="37806">
    <literal><![CDATA[
      (x / y) * (z \ (z / (y \ 1))) = a(z,y,y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,30976,a(flip),b,37803,a)].">
      <j1 rule="hyper" parents="64 30976 37803"/>
    </justification>
  </clause>

  <clause id="37807">
    <literal><![CDATA[
      a(x,y,y) \ (z * (1 / y)) = z * L(y \ 1,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30718,a(flip),b,37805,a)].">
      <j1 rule="hyper" parents="64 30718 37805"/>
    </justification>
  </clause>

  <clause id="37808">
    <literal><![CDATA[
      (a(x,y,y \ 1) * y) * z = y * (a(x,y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35211,a(flip),b,37804,a)].">
      <j1 rule="hyper" parents="64 35211 37804"/>
    </justification>
  </clause>

  <clause id="37809">
    <literal><![CDATA[
      a(x,y,(L(z \ 1,z,u) \ 1) * w) = a(x,y,z * (a(u,z,z \ 1) * w))
    ]]></literal>
    <justification jstring="[para(37808(a,1),34154(a,2,3))].">
      <j1 rule="para" parents="37808 34154"/>
    </justification>
  </clause>

  <clause id="37810">
    <literal><![CDATA[
      L(x,a(y,z,z),a(z,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(606,a,37669,a)].">
      <j1 rule="hyper" parents="606 37669"/>
    </justification>
  </clause>

  <clause id="37811">
    <literal><![CDATA[
      L(x,a(y,y,z),a(y,y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,31827,a,b,37669,a)].">
      <j1 rule="hyper" parents="35 31827 37669"/>
    </justification>
  </clause>

  <clause id="37812">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (a(w,z,z) * v5)) = a(x,y,v5 * (a(z,z,u) * a(w,z,z)))
    ]]></literal>
    <justification jstring="[para(37669(a,1),27298(a,1,3))].">
      <j1 rule="para" parents="37669 27298"/>
    </justification>
  </clause>

  <clause id="37813">
    <literal><![CDATA[
      L(x,a(y,z,z),a(u,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,29287,a,b,37810,a)].">
      <j1 rule="hyper" parents="64 29287 37810"/>
    </justification>
  </clause>

  <clause id="37814">
    <literal><![CDATA[
      (x \ (1 / (y / (x * y)))) * z = (x * (y / (x * y))) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,35998,a(flip),b,37810,a)].">
      <j1 rule="hyper" parents="64 35998 37810"/>
    </justification>
  </clause>

  <clause id="37816">
    <literal><![CDATA[
      R(x,y,y) \ x = z \ (a(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,37810,a(flip),b,35393,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 37810 35393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37819">
    <literal><![CDATA[
      L(x,a(y,y,z),a(u,y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,29287,a,b,37811,a)].">
      <j1 rule="hyper" parents="64 29287 37811"/>
    </justification>
  </clause>

  <clause id="37820">
    <literal><![CDATA[
      x / (a(y,y,z) \ (a(y,y,u) \ x)) = a(y,y,u) * a(y,y,z)
    ]]></literal>
    <justification jstring="[hyper(225,a,37811,a(flip),b,346,a(flip))].">
      <j1 rule="hyper" parents="225 37811 346"/>
    </justification>
  </clause>

  <clause id="37823">
    <literal><![CDATA[
      (a(x,y,y) \ 1) \ z = z * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(34364,a,37813,a),flip(a)].">
      <j1 rule="hyper" parents="34364 37813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37824">
    <literal><![CDATA[
      (a(x,y,y) \ 1) * z = a(x,y,y) \ z
    ]]></literal>
    <justification jstring="[hyper(13952,a,37813,a)].">
      <j1 rule="hyper" parents="13952 37813"/>
    </justification>
  </clause>

  <clause id="37825">
    <literal><![CDATA[
      a(a(x,y,y),a(z,y,y),u) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,37813,a)].">
      <j1 rule="hyper" parents="54 37813"/>
    </justification>
  </clause>

  <clause id="37826">
    <literal><![CDATA[
      x * (a(y,z,z) \ 1) = a(y,z,z) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,37813,a(flip),b,23759,a),flip(a)].">
      <j1 rule="hyper" parents="139 37813 23759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37828">
    <literal><![CDATA[
      L(x,y,a(z,u,u) \ w) = L(x,y,w * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(37813(a,1),30388(a,1,3)),flip(a)].">
      <j1 rule="para" parents="37813 30388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37829">
    <literal><![CDATA[
      L(x,a(y,z,z) \ u,w) = L(x,u * a(y,z,z),w)
    ]]></literal>
    <justification jstring="[para(37813(a,1),31760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37813 31760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37830">
    <literal><![CDATA[
      a((a(x,y,y) \ z) * u,w,v5) = a((z * a(x,y,y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(37813(a,1),32824(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="37813 32824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37831">
    <literal><![CDATA[
      a(a(x,y,y),a(y,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,37819,a)].">
      <j1 rule="hyper" parents="54 37819"/>
    </justification>
  </clause>

  <clause id="37832">
    <literal><![CDATA[
      L(x,(y / z) * (z / y),a(u,y \ z,y \ z)) = x
    ]]></literal>
    <justification jstring="[para(30069(a,1),37819(a,1,2))].">
      <j1 rule="para" parents="30069 37819"/>
    </justification>
  </clause>

  <clause id="37833">
    <literal><![CDATA[
      a(a(x,y,y),a(z,y,y),u) = w \ w
    ]]></literal>
    <justification jstring="[hyper(373,a,68,a,b,37825,a),flip(a)].">
      <j1 rule="hyper" parents="373 68 37825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37835">
    <literal><![CDATA[
      a(a(x,L(x,y,z),u),a(x,x,w),v5) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,35558,a(flip),b,37831,a)].">
      <j1 rule="hyper" parents="64 35558 37831"/>
    </justification>
  </clause>

  <clause id="37837">
    <literal><![CDATA[
      (R(x,y,y) \ x) * z = a(x,y,y) \ z
    ]]></literal>
    <justification jstring="[hyper(144,a,37816,a,b,23767,a)].">
      <j1 rule="hyper" parents="144 37816 23767"/>
    </justification>
  </clause>

  <clause id="37838">
    <literal><![CDATA[
      x \ (a(y,z,z) \ x) = a(y,z,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,16007,a(flip),b,37816,a),flip(a)].">
      <j1 rule="hyper" parents="64 16007 37816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37839">
    <literal><![CDATA[
      x * (y \ L(y,y,z)) = a(z,y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,30494,a(flip),b,37816,a(flip))].">
      <j1 rule="hyper" parents="145 30494 37816"/>
    </justification>
  </clause>

  <clause id="37841">
    <literal><![CDATA[
      (x \ L(x,x,y)) \ z = z * a(y,x,x)
    ]]></literal>
    <justification jstring="[para(30465(a,1),37823(a,1,1))].">
      <j1 rule="para" parents="30465 37823"/>
    </justification>
  </clause>

  <clause id="37842">
    <literal><![CDATA[
      x * a(y,z \ y,z \ y) = ((y \ z) * (z \ y)) \ x
    ]]></literal>
    <justification jstring="[para(30492(a,1),37823(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30492 37823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37843">
    <literal><![CDATA[
      R(x,y,z * a(u * w,w,w)) = R(x,y,a(w,w,u) \ z)
    ]]></literal>
    <justification jstring="[para(37823(a,1),30935(a,1,3))].">
      <j1 rule="para" parents="37823 30935"/>
    </justification>
  </clause>

  <clause id="37844">
    <literal><![CDATA[
      a(x,y,a(z,z,u) \ w) = a(x,y,w * a(u,z,z))
    ]]></literal>
    <justification jstring="[para(37823(a,1),31011(a,1,3)),flip(a)].">
      <j1 rule="para" parents="37823 31011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37845">
    <literal><![CDATA[
      L(x * a(y,z,z),y,a(z,z,y)) = y * ((a(y,z,z) \ y) \ x)
    ]]></literal>
    <justification jstring="[para(37823(a,1),34067(a,1,1))].">
      <j1 rule="para" parents="37823 34067"/>
    </justification>
  </clause>

  <clause id="37846">
    <literal><![CDATA[
      a((x * y) \ ((x * y) * a(z,u,u)),y,x) = R(a(z,u,u) \ 1,y,x) * a(z,u,u)
    ]]></literal>
    <justification jstring="[para(37823(a,1),28080(a,1,1,2))].">
      <j1 rule="para" parents="37823 28080"/>
    </justification>
  </clause>

  <clause id="37847">
    <literal><![CDATA[
      a(x,y,(a(z,z,z \ u) \ w) \ v5) = a(x,y,(w * a(u,z,z)) \ v5)
    ]]></literal>
    <justification jstring="[para(37823(a,1),36463(a,2,3,1))].">
      <j1 rule="para" parents="37823 36463"/>
    </justification>
  </clause>

  <clause id="37849">
    <literal><![CDATA[
      L(x,(a(y,z,z) * u) * w,v5) = L(x,w * (a(y,z,z) \ u),v5)
    ]]></literal>
    <justification jstring="[para(37824(a,1),29519(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="37824 29519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37850">
    <literal><![CDATA[
      a(x,y \ x,y \ x) \ z = ((x \ y) * (y \ x)) * z
    ]]></literal>
    <justification jstring="[para(30492(a,1),37824(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30492 37824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37851">
    <literal><![CDATA[
      x * ((x \ (y \ (y / x))) * z) = (1 / x) * (a(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[para(37824(a,1),30548(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37824 30548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37852">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,w) \ v5)) = a(x,y,z \ (a(w,w,u) * v5))
    ]]></literal>
    <justification jstring="[para(37824(a,1),31437(a,1,3,2))].">
      <j1 rule="para" parents="37824 31437"/>
    </justification>
  </clause>

  <clause id="37853">
    <literal><![CDATA[
      a(x,x,(y \ ((y \ 1) \ x)) * z) = a(x,x,x * (a(x,y,y) \ z))
    ]]></literal>
    <justification jstring="[para(37824(a,1),33045(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="37824 33045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37854">
    <literal><![CDATA[
      a(x,y,a(z,u,u) \ w) = a(x,y,a(u,u,z) * w)
    ]]></literal>
    <justification jstring="[para(37824(a,1),35652(a,1,3))].">
      <j1 rule="para" parents="37824 35652"/>
    </justification>
  </clause>

  <clause id="37855">
    <literal><![CDATA[
      (1 / x) \ (a(y,x,x) \ z) = x \ ((x * L(x,x,y)) * z)
    ]]></literal>
    <justification jstring="[para(37824(a,1),37648(a,1,2))].">
      <j1 rule="para" parents="37824 37648"/>
    </justification>
  </clause>

  <clause id="37859">
    <literal><![CDATA[
      (R(x,L(y \ z,y \ z,z),L(y \ z,y \ z,z)) \ x) * u = a(x,z \ y,L(y \ z,y \ z,z)) \ u
    ]]></literal>
    <justification jstring="[para(26067(a,1),37837(a,2,1))].">
      <j1 rule="para" parents="26067 37837"/>
    </justification>
  </clause>

  <clause id="37861">
    <literal><![CDATA[
      a(x,y,y) \ (x * a(a(x,y,y) \ 1,z,u)) = ((x / y) / (1 / y)) * a(w \ (a(x,y,y) \ w),z,u)
    ]]></literal>
    <justification jstring="[para(37838(a,1),32928(a,1,2,2,1))].">
      <j1 rule="para" parents="37838 32928"/>
    </justification>
  </clause>

  <clause id="37865">
    <literal><![CDATA[
      (x * x) * (y * a(x * z,x,x)) = (x \ L(1 / x,x,z)) \ y
    ]]></literal>
    <justification jstring="[para(37841(a,1),33909(a,1,2))].">
      <j1 rule="para" parents="37841 33909"/>
    </justification>
  </clause>

  <clause id="37866">
    <literal><![CDATA[
      L(x,y,a(z,z,u) \ w) = L(x,y,w * a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,35885,a(flip),b,37828,a)].">
      <j1 rule="hyper" parents="64 35885 37828"/>
    </justification>
  </clause>

  <clause id="37867">
    <literal><![CDATA[
      L(x,(y / z) * (z / y),a(z,z * y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,35690,a(flip),b,37832,a)].">
      <j1 rule="hyper" parents="64 35690 37832"/>
    </justification>
  </clause>

  <clause id="37868">
    <literal><![CDATA[
      L(x,(y / z) * (y \ z),a(y,y * z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,29606,a(flip),b,37867,a)].">
      <j1 rule="hyper" parents="64 29606 37867"/>
    </justification>
  </clause>

  <clause id="37869">
    <literal><![CDATA[
      L(x,(y \ z) * (z \ y),a(y,y * z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,29606,a(flip),b,37868,a)].">
      <j1 rule="hyper" parents="64 29606 37868"/>
    </justification>
  </clause>

  <clause id="37870">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (a(u,z,z) * w)) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13875,a(flip),b,37854,a),flip(a)].">
      <j1 rule="hyper" parents="64 13875 37854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37871">
    <literal><![CDATA[
      L(x,y,(z * (u \ (z \ u))) \ w) = L(x,y,w * a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30113,a,b,37866,a)].">
      <j1 rule="hyper" parents="64 30113 37866"/>
    </justification>
  </clause>

  <clause id="37872">
    <literal><![CDATA[
      a(x,y \ x,y \ x) * z = ((x \ y) * (y \ x)) \ z
    ]]></literal>
    <justification jstring="[hyper(23777,a,37842,a)].">
      <j1 rule="hyper" parents="23777 37842"/>
    </justification>
  </clause>

  <clause id="37873">
    <literal><![CDATA[
      x * (((x \ y) * (y \ x)) \ ((y \ x) * (y \ x))) = (x * (y \ x)) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,37842,a(flip),b,29944,a)].">
      <j1 rule="hyper" parents="145 37842 29944"/>
    </justification>
  </clause>

  <clause id="37874">
    <literal><![CDATA[
      x * a(y,z * y,z \ y) = ((y \ z) * (z \ y)) \ x
    ]]></literal>
    <justification jstring="[para(35823(a,1),37842(a,1,2))].">
      <j1 rule="para" parents="35823 37842"/>
    </justification>
  </clause>

  <clause id="37875">
    <literal><![CDATA[
      (x \ (y * ((x \ y) \ 1))) \ z = ((x \ y) * (y \ x)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,30793,a(flip),b,37850,a)].">
      <j1 rule="hyper" parents="64 30793 37850"/>
    </justification>
  </clause>

  <clause id="37876">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (L(y \ x,y \ x,x) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,37572,a(flip),b,37872,a),flip(a)].">
      <j1 rule="hyper" parents="64 37572 37872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37877">
    <literal><![CDATA[
      a(x,y * x,y \ x) * z = ((x \ y) * (y \ x)) \ z
    ]]></literal>
    <justification jstring="[para(35823(a,1),37872(a,1,1))].">
      <j1 rule="para" parents="35823 37872"/>
    </justification>
  </clause>

  <clause id="37879">
    <literal><![CDATA[
      x * (y \ (1 / (z / (y * z)))) = (y * (z / (y * z))) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,35971,a(flip),b,37814,a)].">
      <j1 rule="hyper" parents="64 35971 37814"/>
    </justification>
  </clause>

  <clause id="37880">
    <literal><![CDATA[
      x \ ((x * L(x,x,y)) * z) = (1 / L(x,x,y)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,37638,a(flip),b,37855,a),flip(a)].">
      <j1 rule="hyper" parents="64 37638 37855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37881">
    <literal><![CDATA[
      x * ((1 / L(x,x,y)) \ z) = (x * L(x,x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,37638,a(flip),b,37855,a(flip))].">
      <j1 rule="hyper" parents="145 37638 37855"/>
    </justification>
  </clause>

  <clause id="37882">
    <literal><![CDATA[
      L(R(x,x,y),x,z) * y = (1 / L(x,x,z)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,34890,a(flip),b,37880,a)].">
      <j1 rule="hyper" parents="64 34890 37880"/>
    </justification>
  </clause>

  <clause id="37883">
    <literal><![CDATA[
      L(R(x,y \ (x \ y),z),x,y) = L(R(x,x,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,26564,a,b,37882,a)].">
      <j1 rule="hyper" parents="36 26564 37882"/>
    </justification>
  </clause>

  <clause id="37884">
    <literal><![CDATA[
      R(x,y \ (x \ y),z) = R(x,x,z)
    ]]></literal>
    <justification jstring="[hyper(51,a,37883,a)].">
      <j1 rule="hyper" parents="51 37883"/>
    </justification>
  </clause>

  <clause id="37885">
    <literal><![CDATA[
      R(T(x * y,z),(x \ T(x * y,z)) \ ((x * y) \ T(y,K(x,z))),u) = R(T(x * y,z),T(x * y,z),u)
    ]]></literal>
    <justification jstring="[para(16586(a,1),37884(a,1,2,2))].">
      <j1 rule="para" parents="16586 37884"/>
    </justification>
  </clause>

  <clause id="37887">
    <literal><![CDATA[
      (x / (y * x)) * (((x / (y * x)) \ 1) \ (z * (y \ ((x / (y * x)) \ 1)))) = ((x / (y * x)) * (x / (y * x))) * ((y * (x / (y * x))) \ z)
    ]]></literal>
    <justification jstring="[para(37879(a,1),28003(a,2,2))].">
      <j1 rule="para" parents="37879 28003"/>
    </justification>
  </clause>

  <clause id="37888">
    <literal><![CDATA[
      (x \ (x / y)) * z = (1 / y) * (a(x,y,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37556,a(flip),b,37851,a)].">
      <j1 rule="hyper" parents="64 37556 37851"/>
    </justification>
  </clause>

  <clause id="37889">
    <literal><![CDATA[
      L(x \ 1,x,x * y) * z = (1 / x) * (a(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[para(30659(a,2),37888(a,1,1))].">
      <j1 rule="para" parents="30659 37888"/>
    </justification>
  </clause>

  <clause id="37890">
    <literal><![CDATA[
      L(x \ 1,x,x * y) \ z = a(y,x,x) * ((1 / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,74,a(flip),b,37889,a)].">
      <j1 rule="hyper" parents="139 74 37889"/>
    </justification>
  </clause>

  <clause id="37891">
    <literal><![CDATA[
      L(x \ 1,x,x * y) \ x = x * ((x \ 1) \ a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,23932,a(flip),b,37890,a),flip(a)].">
      <j1 rule="hyper" parents="373 23932 37890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37892">
    <literal><![CDATA[
      a(a(x,y,z) * u,z,z) = a(u,z,z) * ((1 / z) \ (1 / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,34148,a,b,37890,a)].">
      <j1 rule="hyper" parents="64 34148 37890"/>
    </justification>
  </clause>

  <clause id="37893">
    <literal><![CDATA[
      a(a(x,y,z) * u,z,z) = a(u,z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,191,a(flip),b,37892,a),flip(a)].">
      <j1 rule="hyper" parents="373 191 37892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37894">
    <literal><![CDATA[
      a(x * a(y,z,u),u,u) = a(x,u,u)
    ]]></literal>
    <justification jstring="[hyper(26847,a,37893,a)].">
      <j1 rule="hyper" parents="26847 37893"/>
    </justification>
  </clause>

  <clause id="37896">
    <literal><![CDATA[
      a((x * y) * z,z,z) = a(x * (y * z),z,z)
    ]]></literal>
    <justification jstring="[para(15463(a,1),37893(a,1,1))].">
      <j1 rule="para" parents="15463 37893"/>
    </justification>
  </clause>

  <clause id="37897">
    <literal><![CDATA[
      a(x * (y * a(z,u,x)),x,x) = a(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(33200(a,1),37893(a,1,1))].">
      <j1 rule="para" parents="33200 37893"/>
    </justification>
  </clause>

  <clause id="37898">
    <literal><![CDATA[
      a(x * (y * z),z,z) = a(z * (x * y),z,z)
    ]]></literal>
    <justification jstring="[hyper(26847,a,37896,a),flip(a)].">
      <j1 rule="hyper" parents="26847 37896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37899">
    <literal><![CDATA[
      a((x * y) * z,z,z) = a(y * (x * z),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32388,a,b,37896,a)].">
      <j1 rule="hyper" parents="64 32388 37896"/>
    </justification>
  </clause>

  <clause id="37900">
    <literal><![CDATA[
      a((x \ 1) * (y * z),x,x) = a(y * (z * x),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26823,a,b,37896,a)].">
      <j1 rule="hyper" parents="64 26823 37896"/>
    </justification>
  </clause>

  <clause id="37901">
    <literal><![CDATA[
      a((x * y) * z,x,x) = a(x * (z * y),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32422,a,b,37898,a)].">
      <j1 rule="hyper" parents="64 32422 37898"/>
    </justification>
  </clause>

  <clause id="37902">
    <literal><![CDATA[
      a(x * (y * ((z * x) * u)),x,x) = a(y * (x * ((x * z) * u)),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32577,a(flip),b,37898,a),flip(a)].">
      <j1 rule="hyper" parents="64 32577 37898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37903">
    <literal><![CDATA[
      a(x * (y * z),z,z) = a(y * (x * z),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37896,a(flip),b,37899,a)].">
      <j1 rule="hyper" parents="64 37896 37899"/>
    </justification>
  </clause>

  <clause id="37904">
    <literal><![CDATA[
      a(x * (((x * y) * z) * y),y,y) = a(L(z,x * y,x * y),y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,26834,a(flip),b,37903,a),flip(a)].">
      <j1 rule="hyper" parents="373 26834 37903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37905">
    <literal><![CDATA[
      L(L(x,y,a(z,z,y)),L(y,z,z),L(y,z,z)) = L(x,y,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,35653,a,b,37695,a)].">
      <j1 rule="hyper" parents="64 35653 37695"/>
    </justification>
  </clause>

  <clause id="37906">
    <literal><![CDATA[
      L(L(x,a(y,y,z),L(z,y,y)),z,z) = L(x,z,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29402,a,b,37695,a)].">
      <j1 rule="hyper" parents="64 29402 37695"/>
    </justification>
  </clause>

  <clause id="37907">
    <literal><![CDATA[
      a(x,x,(y \ (z \ 1)) \ 1) \ u = (y \ (z \ L(z * y,x,x))) * u
    ]]></literal>
    <justification jstring="[para(1389(a,1),37702(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1389 37702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37908">
    <literal><![CDATA[
      x \ ((R(1 / y,y,z) \ 1) \ x) = R(x \ (y \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,30096,a(flip),b,37740,a),flip(a)].">
      <j1 rule="hyper" parents="373 30096 37740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37909">
    <literal><![CDATA[
      R(x,y,z) / R(a(u,u,w) \ (a(u,u,w) \ x),y,z) = a(u,u,w) * a(u,u,w)
    ]]></literal>
    <justification jstring="[para(2144(a,2),37820(a,1,2))].">
      <j1 rule="para" parents="2144 37820"/>
    </justification>
  </clause>

  <clause id="37910">
    <literal><![CDATA[
      a((a(x,y,y) \ z) * u,w,v5) = a((a(y,y,x) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,36064,a,b,37830,a),flip(a)].">
      <j1 rule="hyper" parents="373 36064 37830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37911">
    <literal><![CDATA[
      (x \ L(1 / x,x,y)) \ z = x * (L(x \ 1,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37642,a(flip),b,37865,a),flip(a)].">
      <j1 rule="hyper" parents="64 37642 37865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37912">
    <literal><![CDATA[
      (x \ 1) * (x \ (x * (L(x \ 1,x,x * y) \ z))) = T(L(x,x,y) * (1 / x),x * x) \ z
    ]]></literal>
    <justification jstring="[para(37911(a,1),36460(a,1,2,2))].">
      <j1 rule="para" parents="37911 36460"/>
    </justification>
  </clause>

  <clause id="37914">
    <literal><![CDATA[
      (((1 / x) * y) \ y) \ (x * z) = (((y / x) / y) * x) \ z
    ]]></literal>
    <justification jstring="[para(26364(a,1),37540(a,1,1))].">
      <j1 rule="para" parents="26364 37540"/>
    </justification>
  </clause>

  <clause id="37915">
    <literal><![CDATA[
      ((x / y) / x) \ ((1 / y) * z) = (((x / y) / x) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,35908,a(flip),b,37914,a)].">
      <j1 rule="hyper" parents="64 35908 37914"/>
    </justification>
  </clause>

  <clause id="37916">
    <literal><![CDATA[
      (((x / y) / x) * y) \ (y * z) = ((x / y) / x) \ L(z,y,y)
    ]]></literal>
    <justification jstring="[para(559(a,1),37915(a,1,2)),flip(a)].">
      <j1 rule="para" parents="559 37915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37917">
    <literal><![CDATA[
      (x \ ((y / (1 / (1 / x))) / y)) \ ((1 / x) * z) = ((y / x) / y) \ L(z,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,37045,a,b,37916,a)].">
      <j1 rule="hyper" parents="64 37045 37916"/>
    </justification>
  </clause>

  <clause id="37918">
    <literal><![CDATA[
      a(x,L(x,y,z),u) \ a(a(x,x,u),y,z) = a(x,x,u) \ 1
    ]]></literal>
    <justification jstring="[para(2653(a,1),37700(a,1,2))].">
      <j1 rule="para" parents="2653 37700"/>
    </justification>
  </clause>

  <clause id="37920">
    <literal><![CDATA[
      a(a(x,x,y),z,u) * a(x,x,y) = a(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(40,a,37678,a,b,37918,a)].">
      <j1 rule="hyper" parents="40 37678 37918"/>
    </justification>
  </clause>

  <clause id="37921">
    <literal><![CDATA[
      a(x,x,y) * a(a(x,x,y),z,u) = a(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(40,a,25064,a,b,37918,a)].">
      <j1 rule="hyper" parents="40 25064 37918"/>
    </justification>
  </clause>

  <clause id="37922">
    <literal><![CDATA[
      a(x,x,y) \ a(x,L(x,z,u),y) = a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,37677,a,b,37918,a)].">
      <j1 rule="hyper" parents="39 37677 37918"/>
    </justification>
  </clause>

  <clause id="37923">
    <literal><![CDATA[
      a(a(x,x,y),z,u) * a(x,x,y) = L(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,34877,a(flip),b,37920,a),flip(a)].">
      <j1 rule="hyper" parents="373 34877 37920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37924">
    <literal><![CDATA[
      a(a(x,y,y),z,u) * a(y,y,x) = a(y,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(32543(a,2),37920(a,1,1))].">
      <j1 rule="para" parents="32543 37920"/>
    </justification>
  </clause>

  <clause id="37925">
    <literal><![CDATA[
      a(x,x,y) \ L(a(x,x,y),z,u) = a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,34877,a(flip),b,37921,a)].">
      <j1 rule="hyper" parents="139 34877 37921"/>
    </justification>
  </clause>

  <clause id="37926">
    <literal><![CDATA[
      a(a(x,x,y),z,u) * a(x,x,y) = R(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,28787,a,b,37923,a),flip(a)].">
      <j1 rule="hyper" parents="373 28787 37923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37927">
    <literal><![CDATA[
      a(x,x,y) * L(a(x,x,y) \ 1,z,u) = a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,37299,a,b,37925,a)].">
      <j1 rule="hyper" parents="64 37299 37925"/>
    </justification>
  </clause>

  <clause id="37928">
    <literal><![CDATA[
      a(x,x,y) \ a(a(x,x,y),z,u) = L(a(x,x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,37925,a(flip),b,37299,a)].">
      <j1 rule="hyper" parents="139 37925 37299"/>
    </justification>
  </clause>

  <clause id="37929">
    <literal><![CDATA[
      a(x,x,y) * a(a(y,x,x),z,u) = R(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32545,a(flip),b,37926,a)].">
      <j1 rule="hyper" parents="64 32545 37926"/>
    </justification>
  </clause>

  <clause id="37930">
    <literal><![CDATA[
      a(x,x,y) \ a(a(y,x,x),z,u) = L(a(x,x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,32543,a,b,37927,a)].">
      <j1 rule="hyper" parents="139 32543 37927"/>
    </justification>
  </clause>

  <clause id="37931">
    <literal><![CDATA[
      a(x,x,y) * R(a(x,x,y) \ 1,z,u) = a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(37269(a,2),37927(a,1,2))].">
      <j1 rule="para" parents="37269 37927"/>
    </justification>
  </clause>

  <clause id="37932">
    <literal><![CDATA[
      R(x,x,y) * L(a(x,x,y) \ 1,z,u) = x * a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(37927(a,1),37535(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37927 37535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37933">
    <literal><![CDATA[
      x * (K(x \ 1,y) * (a(y,x,x) * z)) = (((y / x) / y) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,7038,a(flip),b,37717,a)].">
      <j1 rule="hyper" parents="64 7038 37717"/>
    </justification>
  </clause>

  <clause id="37934">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ ((x / y) * z) = (1 / (y / x)) * z
    ]]></literal>
    <justification jstring="[para(30157(a,1),37760(a,1,1))].">
      <j1 rule="para" parents="30157 37760"/>
    </justification>
  </clause>

  <clause id="37936">
    <literal><![CDATA[
      ((x / y) * (y / x)) * ((1 / (y / x)) * z) = (x / y) * z
    ]]></literal>
    <justification jstring="[hyper(157,a,37934,a)].">
      <j1 rule="hyper" parents="157 37934"/>
    </justification>
  </clause>

  <clause id="37937">
    <literal><![CDATA[
      ((x / y) * (y / x)) * (((x / y) \ 1) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,5274,a,b,37936,a)].">
      <j1 rule="hyper" parents="64 5274 37936"/>
    </justification>
  </clause>

  <clause id="37938">
    <literal><![CDATA[
      ((x / y) \ 1) \ (((x / y) * (y / x)) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[hyper(757,a,37937,a),flip(a)].">
      <j1 rule="hyper" parents="757 37937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37939">
    <literal><![CDATA[
      ((x / y) \ 1) * ((y / x) \ z) = ((x / y) * (y / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,10,a(flip),b,37937,a),flip(a)].">
      <j1 rule="hyper" parents="139 10 37937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37940">
    <literal><![CDATA[
      (x / ((y / x) * y)) \ z = (y / x) * ((x / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,37938,a(flip),b,32132,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 37938 32132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37941">
    <literal><![CDATA[
      (x / ((y / x) * y)) * z = (x / y) * ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(733,a,37940,a)].">
      <j1 rule="hyper" parents="733 37940"/>
    </justification>
  </clause>

  <clause id="37942">
    <literal><![CDATA[
      (x / y) * ((y / x) \ 1) = x / ((y / x) * y)
    ]]></literal>
    <justification jstring="[hyper(40,a,35582,a,b,37940,a)].">
      <j1 rule="hyper" parents="40 35582 37940"/>
    </justification>
  </clause>

  <clause id="37943">
    <literal><![CDATA[
      a((x / ((y / x) * y)) * z,u,w) = a(((y / x) * (x / y)) * z,u,w)
    ]]></literal>
    <justification jstring="[para(37942(a,1),4851(a,1,1,1))].">
      <j1 rule="para" parents="37942 4851"/>
    </justification>
  </clause>

  <clause id="37944">
    <literal><![CDATA[
      (x / ((y / x) * y)) * (((y / x) * (x / y)) \ ((y / x) * z)) = ((y / x) \ K(x / y,(y / x) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(37942(a,1),24953(a,1,1))].">
      <j1 rule="para" parents="37942 24953"/>
    </justification>
  </clause>

  <clause id="37945">
    <literal><![CDATA[
      (x * ((((x \ y) * x) \ x) \ 1)) \ y = (y \ x) * (y / x)
    ]]></literal>
    <justification jstring="[para(37767(a,1),26546(a,1,1))].">
      <j1 rule="para" parents="37767 26546"/>
    </justification>
  </clause>

  <clause id="37946">
    <literal><![CDATA[
      (x * T((y \ x) \ 1,x)) \ y = (y \ x) * (y / x)
    ]]></literal>
    <justification jstring="[para(7659(a,1),37945(a,1,1,2))].">
      <j1 rule="para" parents="7659 37945"/>
    </justification>
  </clause>

  <clause id="37947">
    <literal><![CDATA[
      (((x \ y) \ 1) * y) \ x = (x \ y) * (x / y)
    ]]></literal>
    <justification jstring="[para(115(a,1),37946(a,1,1))].">
      <j1 rule="para" parents="115 37946"/>
    </justification>
  </clause>

  <clause id="37948">
    <literal><![CDATA[
      ((1 / (1 / (x \ y))) * (x / y)) * (((x \ y) * (x \ y)) \ z) = ((((x \ y) \ 1) * y) \ x) * (((x \ y) \ 1) * ((x \ y) \ z))
    ]]></literal>
    <justification jstring="[para(37947(a,2),5273(a,2,1))].">
      <j1 rule="para" parents="37947 5273"/>
    </justification>
  </clause>

  <clause id="37949">
    <literal><![CDATA[
      a(x,x,(y \ ((y \ 1) \ x)) * z) = a(x,x,x * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32759,a(flip),b,37853,a),flip(a)].">
      <j1 rule="hyper" parents="373 32759 37853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37951">
    <literal><![CDATA[
      a(x * (y * ((y * x) * z)),y,y) = a(L(z,x * y,x * y),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32577,a(flip),b,37904,a)].">
      <j1 rule="hyper" parents="64 32577 37904"/>
    </justification>
  </clause>

  <clause id="37952">
    <literal><![CDATA[
      L(L(x,y,a(z,z,y)),y,y) = L(x,y,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,35161,a(flip),b,37905,a)].">
      <j1 rule="hyper" parents="64 35161 37905"/>
    </justification>
  </clause>

  <clause id="37954">
    <literal><![CDATA[
      L((x \ 1) \ y,x,L(x,z,z)) = L(x * y,x,a(z,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,1143,a(flip),b,37952,a),flip(a)].">
      <j1 rule="hyper" parents="64 1143 37952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37955">
    <literal><![CDATA[
      L(x,a(y,y,z),L(z,y,y)) = L(x,z,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(42,a,37906,a,b,37952,a)].">
      <j1 rule="hyper" parents="42 37906 37952"/>
    </justification>
  </clause>

  <clause id="37956">
    <literal><![CDATA[
      L(L(x,y,a(y,z,z)),y,y) = L(x,y,L(y,z,z))
    ]]></literal>
    <justification jstring="[para(29287(a,2),37952(a,1,1))].">
      <j1 rule="para" parents="29287 37952"/>
    </justification>
  </clause>

  <clause id="37957">
    <literal><![CDATA[
      a(x,x,y) * ((z / y) * L(y,x,x)) = L(z,y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29393,a,b,37955,a)].">
      <j1 rule="hyper" parents="64 29393 37955"/>
    </justification>
  </clause>

  <clause id="37958">
    <literal><![CDATA[
      L(x / L(y,z,z),y,a(z,z,y)) = a(z,z,y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29398,a(flip),b,37955,a),flip(a)].">
      <j1 rule="hyper" parents="64 29398 37955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37959">
    <literal><![CDATA[
      L(x,y,a(z,z,y)) / L(y,z,z) = a(z,z,y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(142,a,37955,a(flip),b,29329,a)].">
      <j1 rule="hyper" parents="142 37955 29329"/>
    </justification>
  </clause>

  <clause id="37960">
    <literal><![CDATA[
      L(R(x,y,y),y,a(y,z,z)) = R(x,y,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(42,a,35353,a,b,37956,a),flip(a)].">
      <j1 rule="hyper" parents="42 35353 37956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37961">
    <literal><![CDATA[
      L(x * ((y * (y * x)) \ z),x,a(y,y,x)) = ((y * (y * x)) / x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,36191,a(flip),b,37954,a),flip(a)].">
      <j1 rule="hyper" parents="64 36191 37954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37962">
    <literal><![CDATA[
      R(x / (1 / y),y,L(y,z,z)) = L(y * T(x,y),y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,33727,a(flip),b,37954,a)].">
      <j1 rule="hyper" parents="64 33727 37954"/>
    </justification>
  </clause>

  <clause id="37963">
    <literal><![CDATA[
      a(x,x,y) * (L(y,x,x) * (y \ z)) = L(z,y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,23900,a,b,37957,a)].">
      <j1 rule="hyper" parents="64 23900 37957"/>
    </justification>
  </clause>

  <clause id="37964">
    <literal><![CDATA[
      L(x / L(y,z,z),y,a(z,z,y)) = L(x,y,a(z,z,y)) / L(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,37958,a,b,37959,a)].">
      <j1 rule="hyper" parents="373 37958 37959"/>
    </justification>
  </clause>

  <clause id="37965">
    <literal><![CDATA[
      R(x / (1 / y),y,L(y,z,z)) = L(x * y,y,a(z,z,y))
    ]]></literal>
    <justification jstring="[para(115(a,1),37962(a,2,1))].">
      <j1 rule="para" parents="115 37962"/>
    </justification>
  </clause>

  <clause id="37966">
    <literal><![CDATA[
      a(x,x,y) \ (z * (y * a(x,x,y))) = L(z * y,y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,35612,a,b,37965,a)].">
      <j1 rule="hyper" parents="64 35612 37965"/>
    </justification>
  </clause>

  <clause id="37967">
    <literal><![CDATA[
      x * ((y \ (((1 / x) * y) * x)) * z) = (((y / x) / y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(24365(a,1),37933(a,1,2))].">
      <j1 rule="para" parents="24365 37933"/>
    </justification>
  </clause>

  <clause id="37969">
    <literal><![CDATA[
      L(x,y * ((z \ u) * L(z,z,w)),v5) = L(x,y * (a(z,z,w) * u),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,36278,a(flip),b,37607,a)].">
      <j1 rule="hyper" parents="64 36278 37607"/>
    </justification>
  </clause>

  <clause id="37970">
    <literal><![CDATA[
      L((x / y) / z,z,a(z,y,y)) = (x / L(y,y,z)) / R(z,y,y)
    ]]></literal>
    <justification jstring="[para(15984(a,1),37653(a,2,2))].">
      <j1 rule="para" parents="15984 37653"/>
    </justification>
  </clause>

  <clause id="37971">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(z,y,y)) = L(x,L(y,y,z),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35431,a(flip),b,37711,a)].">
      <j1 rule="hyper" parents="64 35431 37711"/>
    </justification>
  </clause>

  <clause id="37972">
    <literal><![CDATA[
      a(x,y,(L(z \ 1,z,u) \ 1) * w) = a(x,y,z * (a(z,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,34552,a(flip),b,37727,a)].">
      <j1 rule="hyper" parents="64 34552 37727"/>
    </justification>
  </clause>

  <clause id="37973">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) \ w) \ v5) = a(x,y,(w * a(u,z,z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,30187,a(flip),b,37847,a)].">
      <j1 rule="hyper" parents="64 30187 37847"/>
    </justification>
  </clause>

  <clause id="37974">
    <literal><![CDATA[
      a(x,y,((R(z,z,u) \ w) * z) \ v5) = a(x,y,(w * a(u,z,z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,37604,a,b,37973,a)].">
      <j1 rule="hyper" parents="64 37604 37973"/>
    </justification>
  </clause>

  <clause id="37975">
    <literal><![CDATA[
      a(x,x,(y \ (z \ 1)) \ 1) \ 1 = y \ (z \ L(z * y,x,x))
    ]]></literal>
    <justification jstring="[hyper(16068,a,37907,a)].">
      <j1 rule="hyper" parents="16068 37907"/>
    </justification>
  </clause>

  <clause id="37976">
    <literal><![CDATA[
      a(((x / y) * (y / x)) * z,u,w) = a((y / x) * ((x / y) \ z),u,w)
    ]]></literal>
    <justification jstring="[para(37941(a,1),37943(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37941 37943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37977">
    <literal><![CDATA[
      L(x / L(y,z,z),a(z,z,y),y) = L(x,y,a(z,z,y)) / L(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33832,a,b,37964,a)].">
      <j1 rule="hyper" parents="64 33832 37964"/>
    </justification>
  </clause>

  <clause id="37978">
    <literal><![CDATA[
      L(x,y * (a(z,u,u) \ w),v5) = L(x,y * (a(u,u,z) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,37635,a(flip),b,37969,a)].">
      <j1 rule="hyper" parents="64 37635 37969"/>
    </justification>
  </clause>

  <clause id="37979">
    <literal><![CDATA[
      L(x,(a(y,z,z) * u) * w,v5) = L(x,w * (a(z,z,y) * u),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,37849,a,b,37978,a)].">
      <j1 rule="hyper" parents="64 37849 37978"/>
    </justification>
  </clause>

  <clause id="37980">
    <literal><![CDATA[
      a(((x / y) * (y / x)) * z,u,w) = a((y / x) * ((y \ x) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32489,a(flip),b,37976,a),flip(a)].">
      <j1 rule="hyper" parents="373 32489 37976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37981">
    <literal><![CDATA[
      L(x / L(y,z,z),y * L(y,z,z),y) = L(x,y,a(z,z,y)) / L(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11916,a,b,37977,a)].">
      <j1 rule="hyper" parents="64 11916 37977"/>
    </justification>
  </clause>

  <clause id="37982">
    <literal><![CDATA[
      a(((x / y) * (y / x)) * z,u,w) = a((x \ y) * ((y \ x) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32367,a(flip),b,37980,a),flip(a)].">
      <j1 rule="hyper" parents="373 32367 37980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37983">
    <literal><![CDATA[
      a(((x / y) * (x \ y)) * z,u,w) = a((x \ y) * ((y \ x) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32560,a(flip),b,37982,a)].">
      <j1 rule="hyper" parents="64 32560 37982"/>
    </justification>
  </clause>

  <clause id="37984">
    <literal><![CDATA[
      a(((x \ y) * (y \ x)) * z,u,w) = a((y \ x) * ((x \ y) \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(32453,a,37983,a)].">
      <j1 rule="hyper" parents="32453 37983"/>
    </justification>
  </clause>

  <clause id="37985">
    <literal><![CDATA[
      (x \ L(y,x,z)) / (1 / T(x,x \ y)) = a(y,x,x) \ L(y,x,z)
    ]]></literal>
    <justification jstring="[para(28332(a,1),37517(a,1,2,2))].">
      <j1 rule="para" parents="28332 37517"/>
    </justification>
  </clause>

  <clause id="37986">
    <literal><![CDATA[
      (x \ L(y,x,z)) / (T(x,x * y) \ 1) = a(y,x,x) \ L(y,x,z)
    ]]></literal>
    <justification jstring="[para(8872(a,1),37985(a,1,2))].">
      <j1 rule="para" parents="8872 37985"/>
    </justification>
  </clause>

  <clause id="37988">
    <literal><![CDATA[
      (x \ L(y,x,z)) / (T(x,y * x) \ 1) = a(y,x,x) \ L(y,x,z)
    ]]></literal>
    <justification jstring="[para(4683(a,2),37986(a,1,2,1))].">
      <j1 rule="para" parents="4683 37986"/>
    </justification>
  </clause>

  <clause id="37989">
    <literal><![CDATA[
      L((x \ y) / (T(x,y * x) \ 1),x,z) = a(y,x,x) \ L(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34790,a,b,37988,a)].">
      <j1 rule="hyper" parents="64 34790 37988"/>
    </justification>
  </clause>

  <clause id="37990">
    <literal><![CDATA[
      L(a(x,y,y) \ x,y,z) = a(x,y,y) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(30572(a,1),37989(a,1,1))].">
      <j1 rule="para" parents="30572 37989"/>
    </justification>
  </clause>

  <clause id="37991">
    <literal><![CDATA[
      (1 / (1 / x)) \ (a(y,x,x) \ z) = x \ ((L(x,x,y) * (1 / x)) * z)
    ]]></literal>
    <justification jstring="[para(37824(a,1),37649(a,1,2))].">
      <j1 rule="para" parents="37824 37649"/>
    </justification>
  </clause>

  <clause id="37992">
    <literal><![CDATA[
      (a(x,x,y) \ z) * L(u,a(y,x,x),z) = z * ((R(x,x,y) \ x) * u)
    ]]></literal>
    <justification jstring="[para(31027(a,1),37701(a,1,2))].">
      <j1 rule="para" parents="31027 37701"/>
    </justification>
  </clause>

  <clause id="37993">
    <literal><![CDATA[
      (a(x,x,y) \ z) * L(u,a(y,x,x),z) = z * (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[para(37679(a,1),37992(a,2,2))].">
      <j1 rule="para" parents="37679 37992"/>
    </justification>
  </clause>

  <clause id="37994">
    <literal><![CDATA[
      (a(x,x,y) \ a(x,x,z)) * u = a(x,x,z) * (a(x,x,y) \ u)
    ]]></literal>
    <justification jstring="[para(37810(a,1),37993(a,1,2))].">
      <j1 rule="para" parents="37810 37993"/>
    </justification>
  </clause>

  <clause id="37995">
    <literal><![CDATA[
      a(x,x,y) \ (a(x,x,z) * u) = (a(x,x,y) \ a(x,x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,31096,a,b,37994,a)].">
      <j1 rule="hyper" parents="373 31096 37994"/>
    </justification>
  </clause>

  <clause id="37996">
    <literal><![CDATA[
      (a(x,x,y) \ a(x,x,z)) \ u = a(x,x,z) \ (a(x,x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(731,a,37995,a)].">
      <j1 rule="hyper" parents="731 37995"/>
    </justification>
  </clause>

  <clause id="37997">
    <literal><![CDATA[
      L(x,a(y,y,z) \ a(y,y,u),a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,598,a(flip),b,37995,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 598 37995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="37998">
    <literal><![CDATA[
      L(x,(a(y,y,z * y) * u) * w,v5) = L(x,w * (u * a(y,y,y * z)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,37675,a(flip),b,37753,a)].">
      <j1 rule="hyper" parents="64 37675 37753"/>
    </justification>
  </clause>

  <clause id="38000">
    <literal><![CDATA[
      a(x,y,(z * a(u,u,w * u)) * v5) = a(x,y,(z * a(u,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(37685(a,1),37756(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="37685 37756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38001">
    <literal><![CDATA[
      a(x,y,z * (a(u,u,w * u) * v5)) = a(x,y,(v5 * a(u,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27462,a(flip),b,38000,a)].">
      <j1 rule="hyper" parents="64 27462 38000"/>
    </justification>
  </clause>

  <clause id="38002">
    <literal><![CDATA[
      L(x / L(y,z,z),y \ L(y,z,z),y) = L(x,y,a(z,z,y)) / L(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11786,a,b,37981,a)].">
      <j1 rule="hyper" parents="64 11786 37981"/>
    </justification>
  </clause>

  <clause id="38003">
    <literal><![CDATA[
      L(x,y * (z * a(u,u,u * w)),v5) = L(x,y * (a(u,u,w) * z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,33649,a(flip),b,37998,a),flip(a)].">
      <j1 rule="hyper" parents="64 33649 37998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38004">
    <literal><![CDATA[
      x * ((x \ L(x,y,y)) * (L(x,y,y) \ z)) = L(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(38,a,1189,a,b,38002,a(flip))].">
      <j1 rule="hyper" parents="38 1189 38002"/>
    </justification>
  </clause>

  <clause id="38005">
    <literal><![CDATA[
      x * (a(y,y,x) \ (L(x,y,y) \ z)) = L(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(37672(a,1),38004(a,1,2))].">
      <j1 rule="para" parents="37672 38004"/>
    </justification>
  </clause>

  <clause id="38006">
    <literal><![CDATA[
      x * (a(y,y,x) \ (L(x,y,y) \ z)) = L(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,29287,a,b,38005,a),flip(a)].">
      <j1 rule="hyper" parents="373 29287 38005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38007">
    <literal><![CDATA[
      a(x,x,y) * L(z,y,a(y,x,x)) = y * (L(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,38006,a(flip),b,33206,a)].">
      <j1 rule="hyper" parents="145 38006 33206"/>
    </justification>
  </clause>

  <clause id="38008">
    <literal><![CDATA[
      a(x,x,y) * L(z,y,a(y,x,x)) = (a(x,x,y) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,37021,a,b,38007,a),flip(a)].">
      <j1 rule="hyper" parents="373 37021 38007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38009">
    <literal><![CDATA[
      x * a(y,a(y,z,z),x) = L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,34254,a,b,38008,a)].">
      <j1 rule="hyper" parents="35 34254 38008"/>
    </justification>
  </clause>

  <clause id="38010">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * x = L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,34967,a,b,38009,a)].">
      <j1 rule="hyper" parents="64 34967 38009"/>
    </justification>
  </clause>

  <clause id="38011">
    <literal><![CDATA[
      a(x,a(y,y,x),z) * z = L(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32890,a,b,38009,a)].">
      <j1 rule="hyper" parents="64 32890 38009"/>
    </justification>
  </clause>

  <clause id="38012">
    <literal><![CDATA[
      L(x,y * z,a(y * z,z,z)) = x * a(y * z,a(z,z,y),x)
    ]]></literal>
    <justification jstring="[para(32896(a,1),38009(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32896 38009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38013">
    <literal><![CDATA[
      x * a(x,y,a(y,z,z)) = L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(34966(a,1),38009(a,1,2))].">
      <j1 rule="para" parents="34966 38009"/>
    </justification>
  </clause>

  <clause id="38014">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * R(x,u,u) = a(x,u,u) * L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(38010(a,1),30914(a,1,2)),flip(a)].">
      <j1 rule="para" parents="38010 30914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38015">
    <literal><![CDATA[
      L(x,y \ z,a(y \ z,y,y)) = a(y \ z,a(y,y,z),x) * x
    ]]></literal>
    <justification jstring="[para(34970(a,1),38010(a,1,1)),flip(a)].">
      <j1 rule="para" parents="34970 38010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38016">
    <literal><![CDATA[
      L(x,y,(y * ((y \ z) * (y \ z))) \ (z * (y \ z))) = x * a(x,y,a(y,y \ z,y \ z))
    ]]></literal>
    <justification jstring="[para(90(a,2),38013(a,2,3)),flip(a)].">
      <j1 rule="para" parents="90 38013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38017">
    <literal><![CDATA[
      x * a(x,y \ z,a(z * y,z,z)) = L(x,y \ z,a(y \ z,z,z))
    ]]></literal>
    <justification jstring="[para(32537(a,1),38013(a,1,2,3))].">
      <j1 rule="para" parents="32537 38013"/>
    </justification>
  </clause>

  <clause id="38018">
    <literal><![CDATA[
      x * a(y * z,a(z,z,y),x) = L(x,y * z,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30336,a(flip),b,38012,a),flip(a)].">
      <j1 rule="hyper" parents="64 30336 38012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38019">
    <literal><![CDATA[
      L(x,y \ z,a(y * z,y,y)) = a(y \ z,a(y,y,z),x) * x
    ]]></literal>
    <justification jstring="[para(30543(a,1),38015(a,1,3))].">
      <j1 rule="para" parents="30543 38015"/>
    </justification>
  </clause>

  <clause id="38020">
    <literal><![CDATA[
      a(x \ y,a(x,x,y),z) * z = L(z,x \ y,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,30331,a(flip),b,38019,a),flip(a)].">
      <j1 rule="hyper" parents="64 30331 38019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38021">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * R(x,y,y) = L(R(x,y,y),y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,37526,a(flip),b,38014,a),flip(a)].">
      <j1 rule="hyper" parents="373 37526 38014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38022">
    <literal><![CDATA[
      a(x,y,y) * L(x,z,a(z,u,u)) = R(x,y,y) * a(z,a(z,u,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,34967,a(flip),b,38014,a),flip(a)].">
      <j1 rule="hyper" parents="64 34967 38014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38023">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * R(x,y,y) = R(x,y,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,37960,a(flip),b,38021,a),flip(a)].">
      <j1 rule="hyper" parents="373 37960 38021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38024">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,L(u,x,w)) = L(x,x,u) \ L(R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(37730(a,1),37511(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37730 37511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38025">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,L(u,x,w)) = L(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,4243,a(flip),b,38024,a),flip(a)].">
      <j1 rule="hyper" parents="373 4243 38024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38027">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),x,u),x,y * z) = L(a(x,y,z),x,L(u,x,w))
    ]]></literal>
    <justification jstring="[para(38025(a,1),16033(a,1,1))].">
      <j1 rule="para" parents="38025 16033"/>
    </justification>
  </clause>

  <clause id="38028">
    <literal><![CDATA[
      L(a(x,y,z),x,L(u,x,w)) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16033,a(flip),b,38027,a),flip(a)].">
      <j1 rule="hyper" parents="64 16033 38027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38029">
    <literal><![CDATA[
      a(x,y,R(z,z,u) * ((z \ a(w,v5,w)) \ v6)) = a(x,y,(z * R(z,z,u)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,27500,a(flip),b,37599,a)].">
      <j1 rule="hyper" parents="64 27500 37599"/>
    </justification>
  </clause>

  <clause id="38030">
    <literal><![CDATA[
      a(x,y,y) \ (a(z,L(y,y,x),L(y,y,x)) \ y) = L(L(y,y,x),L(y,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,37633,a)].">
      <j1 rule="hyper" parents="40 23134 37633"/>
    </justification>
  </clause>

  <clause id="38031">
    <literal><![CDATA[
      a(x,y,((((z * u) \ u) \ 1) \ w) * v5) = a(x,y,v5 * (a(z,z,u) * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27685,a(flip),b,37741,a)].">
      <j1 rule="hyper" parents="64 27685 37741"/>
    </justification>
  </clause>

  <clause id="38032">
    <literal><![CDATA[
      (x \ (1 / (1 / ((y / x) / y)))) \ ((1 / x) * z) = ((y / x) / y) \ L(z,x,x)
    ]]></literal>
    <justification jstring="[para(3946(a,1),37917(a,1,1,2))].">
      <j1 rule="para" parents="3946 37917"/>
    </justification>
  </clause>

  <clause id="38033">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * R(z,z,w)) = a(x,y,(z * R(z,z,w)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27597,a(flip),b,38029,a)].">
      <j1 rule="hyper" parents="64 27597 38029"/>
    </justification>
  </clause>

  <clause id="38034">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * L(z,z,w)) = a(x,y,(z * R(z,z,w)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31317,a(flip),b,38033,a)].">
      <j1 rule="hyper" parents="64 31317 38033"/>
    </justification>
  </clause>

  <clause id="38035">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * L(z,z,w)) = a(x,y,(z * L(z,z,w)) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,37060,a(flip),b,38034,a),flip(a)].">
      <j1 rule="hyper" parents="373 37060 38034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38036">
    <literal><![CDATA[
      a(x,y,((((z * u) \ u) \ 1) \ w) * a(z,z,u)) = a(x,y,u * (L(L(u,z,z),z,z) \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(37708(a,1),38031(a,2,3))].">
      <j1 rule="para" parents="37708 38031"/>
    </justification>
  </clause>

  <clause id="38037">
    <literal><![CDATA[
      R(x,y \ ((z / u) \ y),(u \ z) \ 1) = R(x,1 / (z / u),1 / (z / u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26711,a(flip),b,37763,a)].">
      <j1 rule="hyper" parents="64 26711 37763"/>
    </justification>
  </clause>

  <clause id="38038">
    <literal><![CDATA[
      R(x,1 / (y / z),1 / (y / z)) = R(x,y \ z,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(82(a,1),38037(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="82 38037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38039">
    <literal><![CDATA[
      R(x,1 / (y / z),1 / (y / z)) = R(x,z \ y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,35633,a(flip),b,38038,a),flip(a)].">
      <j1 rule="hyper" parents="373 35633 38038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38040">
    <literal><![CDATA[
      R(x,1 / (y / z),(y / z) \ 1) = R(x,z \ y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(25233,a,38039,a)].">
      <j1 rule="hyper" parents="25233 38039"/>
    </justification>
  </clause>

  <clause id="38041">
    <literal><![CDATA[
      R(x,(y / z) \ 1,(z \ y) \ 1) = R(x,z \ y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26480,a(flip),b,38040,a)].">
      <j1 rule="hyper" parents="64 26480 38040"/>
    </justification>
  </clause>

  <clause id="38042">
    <literal><![CDATA[
      R(x,y / z,(z \ y) \ 1) = R(x,z \ y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2975,a(flip),b,38041,a)].">
      <j1 rule="hyper" parents="64 2975 38041"/>
    </justification>
  </clause>

  <clause id="38043">
    <literal><![CDATA[
      R(x,y \ z,(y \ z) \ 1) = R(x,y \ z,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26410,a(flip),b,38042,a)].">
      <j1 rule="hyper" parents="64 26410 38042"/>
    </justification>
  </clause>

  <clause id="38046">
    <literal><![CDATA[
      a(x,y,z * (a(u,u,w) * a(w,u,u))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37870,a(flip),b,37812,a),flip(a)].">
      <j1 rule="hyper" parents="64 37870 37812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38047">
    <literal><![CDATA[
      R(x,y,z) / R(a(u,u,x) \ L(x,u,u),y,z) = a(u,u,x) * a(u,u,x)
    ]]></literal>
    <justification jstring="[para(5567(a,1),37909(a,1,2,1,2))].">
      <j1 rule="para" parents="5567 37909"/>
    </justification>
  </clause>

  <clause id="38048">
    <literal><![CDATA[
      R(x,y,z) / R(L(L(x,u,u),u,u),y,z) = a(u,u,x) * a(u,u,x)
    ]]></literal>
    <justification jstring="[para(30358(a,1),38047(a,1,2,1))].">
      <j1 rule="para" parents="30358 38047"/>
    </justification>
  </clause>

  <clause id="38049">
    <literal><![CDATA[
      R(x,y,z) / L(R(L(x,u,u),y,z),u,u) = a(u,u,x) * a(u,u,x)
    ]]></literal>
    <justification jstring="[para(29(a,1),38048(a,1,2))].">
      <j1 rule="para" parents="29 38048"/>
    </justification>
  </clause>

  <clause id="38050">
    <literal><![CDATA[
      R(x,y,z) / L(L(R(x,y,z),u,u),u,u) = a(u,u,x) * a(u,u,x)
    ]]></literal>
    <justification jstring="[para(29(a,1),38049(a,1,2,1))].">
      <j1 rule="para" parents="29 38049"/>
    </justification>
  </clause>

  <clause id="38051">
    <literal><![CDATA[
      L(L(R(x,y,z),u,u),u,u) \ R(x,y,z) = a(u,u,x) * a(u,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,10469,a(flip),b,38050,a)].">
      <j1 rule="hyper" parents="64 10469 38050"/>
    </justification>
  </clause>

  <clause id="38052">
    <literal><![CDATA[
      a(x,x,R(y,z,u)) * a(x,x,R(y,z,u)) = a(x,x,y) * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30926,a(flip),b,38051,a)].">
      <j1 rule="hyper" parents="64 30926 38051"/>
    </justification>
  </clause>

  <clause id="38053">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) * a(x,x,R(y,z,u)) = a(x,x,y) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(27644(a,1),38052(a,1,1))].">
      <j1 rule="para" parents="27644 38052"/>
    </justification>
  </clause>

  <clause id="38054">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) * a(x,x,L(y,z,u)) = a(x,x,y) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(27644(a,1),38053(a,1,2))].">
      <j1 rule="para" parents="27644 38053"/>
    </justification>
  </clause>

  <clause id="38055">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) * (a(x,x,y) \ a(x,x,L(y,z,u))) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,31106,a,b,38054,a(flip))].">
      <j1 rule="hyper" parents="35 31106 38054"/>
    </justification>
  </clause>

  <clause id="38056">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ a(x,x,y) = a(x,x,y) \ a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(149,a,38055,a)].">
      <j1 rule="hyper" parents="149 38055"/>
    </justification>
  </clause>

  <clause id="38057">
    <literal><![CDATA[
      L(x,y,z) = (z * R(y,y,x)) \ (a(y,y,x) * (z * (y * x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,33252,a(flip),b,37616,a)].">
      <j1 rule="hyper" parents="373 33252 37616"/>
    </justification>
  </clause>

  <clause id="38058">
    <literal><![CDATA[
      R(a(x,y,y),z,u) * L(y,y,x) = a(a(x,y,y) \ 1,z,u) * y
    ]]></literal>
    <justification jstring="[para(37838(a,1),37656(a,2,1,1))].">
      <j1 rule="para" parents="37838 37656"/>
    </justification>
  </clause>

  <clause id="38059">
    <literal><![CDATA[
      R(a(x,y,y),z,u) * L(y,y,x) = a(a(x,y,y),z,u) * y
    ]]></literal>
    <justification jstring="[para(2653(a,1),38058(a,2,1))].">
      <j1 rule="para" parents="2653 38058"/>
    </justification>
  </clause>

  <clause id="38062">
    <literal><![CDATA[
      a(L(x,y,z),u,u) * L(u,u,x) = a(a(x,u,u),y,z) * u
    ]]></literal>
    <justification jstring="[para(32595(a,2),38059(a,1,1))].">
      <j1 rule="para" parents="32595 38059"/>
    </justification>
  </clause>

  <clause id="38063">
    <literal><![CDATA[
      a(x,y,y) \ a(L(x,z,u),y,y) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(36,a,37637,a,b,38062,a(flip))].">
      <j1 rule="hyper" parents="36 37637 38062"/>
    </justification>
  </clause>

  <clause id="38064">
    <literal><![CDATA[
      a(a(x,y,y),z,u) * a(x,y,y) = a(L(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(23175,a,38063,a)].">
      <j1 rule="hyper" parents="23175 38063"/>
    </justification>
  </clause>

  <clause id="38066">
    <literal><![CDATA[
      L(a(a(x,y,y),z,u),a(y,y,x * y),z) = a(L(a(x,y,y),z,u),z,u)
    ]]></literal>
    <justification jstring="[para(38063(a,1),34921(a,1,1))].">
      <j1 rule="para" parents="38063 34921"/>
    </justification>
  </clause>

  <clause id="38067">
    <literal><![CDATA[
      (a(L(x,y,z),u,u) \ w) \ w = a(a(x,u,u),y,z) * a(x,u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23134,a,b,38064,a)].">
      <j1 rule="hyper" parents="373 23134 38064"/>
    </justification>
  </clause>

  <clause id="38068">
    <literal><![CDATA[
      a(L(x,y,z),u,u) \ a(x,u,u) = a(a(x,u,u),y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(40,a,29925,a,b,38067,a),flip(a)].">
      <j1 rule="hyper" parents="40 29925 38067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38069">
    <literal><![CDATA[
      L(x,x,y) \ L(x,x,L(y,z,u)) = a(a(y,x,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,37636,a,b,38068,a)].">
      <j1 rule="hyper" parents="64 37636 38068"/>
    </justification>
  </clause>

  <clause id="38070">
    <literal><![CDATA[
      L(a(a(x,y,y),z,u),a(x,y,y),z) = a(L(a(x,y,y),z,u),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30724,a(flip),b,38066,a)].">
      <j1 rule="hyper" parents="64 30724 38066"/>
    </justification>
  </clause>

  <clause id="38071">
    <literal><![CDATA[
      R(x * a(y,y,z),L(y,a(y,y,z),x),u) = ((x * R(y,y,z)) * u) / (y * u)
    ]]></literal>
    <justification jstring="[para(30053(a,1),37664(a,2,1,1,2))].">
      <j1 rule="para" parents="30053 37664"/>
    </justification>
  </clause>

  <clause id="38072">
    <literal><![CDATA[
      ((x * R(y,y,z)) * u) / (y * u) = R(x * a(y,y,z),y,u)
    ]]></literal>
    <justification jstring="[para(37659(a,1),38071(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37659 38071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38073">
    <literal><![CDATA[
      R(x * a(y,y,z),y,z) = a(y,y,z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37752,a(flip),b,38072,a),flip(a)].">
      <j1 rule="hyper" parents="64 37752 38072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38074">
    <literal><![CDATA[
      R(a(x,y,y) \ 1,z,u) * a(x,y,y) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),37846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 37846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38076">
    <literal><![CDATA[
      L(a(x,y,y) \ 1,z,u) * a(x,y,y) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[para(37269(a,1),38074(a,1,1))].">
      <j1 rule="para" parents="37269 38074"/>
    </justification>
  </clause>

  <clause id="38077">
    <literal><![CDATA[
      a(x,y,y) \ a(a(x,y,y),z,u) = L(a(x,y,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(23920,a,38076,a)].">
      <j1 rule="hyper" parents="23920 38076"/>
    </justification>
  </clause>

  <clause id="38078">
    <literal><![CDATA[
      a(x,y,y) \ a(a(y,y,x),z,u) = L(a(x,y,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32546,a(flip),b,38077,a)].">
      <j1 rule="hyper" parents="64 32546 38077"/>
    </justification>
  </clause>

  <clause id="38079">
    <literal><![CDATA[
      a(L(x,x,L(L(x,y,y),z,z)),y,y) \ L(R(x,y,y),z,z) = a(z,z,R(x,y,y)) \ x
    ]]></literal>
    <justification jstring="[para(29264(a,1),37706(a,1,1,1))].">
      <j1 rule="para" parents="29264 37706"/>
    </justification>
  </clause>

  <clause id="38080">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),y,y),R(x,y,y),y) = a(a(x,y,y) * L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(36889(a,1),37715(a,1,1))].">
      <j1 rule="para" parents="36889 37715"/>
    </justification>
  </clause>

  <clause id="38081">
    <literal><![CDATA[
      L(x \ R(x,y,z),R(x,y,y),y) = a(a(x,y,y) * L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(35753(a,1),38080(a,1,1))].">
      <j1 rule="para" parents="35753 38080"/>
    </justification>
  </clause>

  <clause id="38082">
    <literal><![CDATA[
      L(x \ R(x,y,z),L(x,y,y),y) = a(a(x,y,y) * L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(30986,a,38081,a)].">
      <j1 rule="hyper" parents="30986 38081"/>
    </justification>
  </clause>

  <clause id="38083">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,y) = a(a(x,y,y) * L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35542,a(flip),b,38082,a)].">
      <j1 rule="hyper" parents="64 35542 38082"/>
    </justification>
  </clause>

  <clause id="38084">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,y) = a(L(R(x,y,y),y,z),y,z)
    ]]></literal>
    <justification jstring="[para(37526(a,1),38083(a,2,1))].">
      <j1 rule="para" parents="37526 38083"/>
    </justification>
  </clause>

  <clause id="38085">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,y) = a(L(L(x,y,y),y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32711,a(flip),b,38084,a),flip(a)].">
      <j1 rule="hyper" parents="373 32711 38084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38086">
    <literal><![CDATA[
      (x \ y) / ((x * (x \ y)) \ ((1 / x) \ 1)) = (x * ((x \ 1) \ ((x \ 1) / (x \ y)))) \ y
    ]]></literal>
    <justification jstring="[para(1682(a,1),37773(a,1,2))].">
      <j1 rule="para" parents="1682 37773"/>
    </justification>
  </clause>

  <clause id="38087">
    <literal><![CDATA[
      a(x,y,((z \ u) * (u \ z)) * ((1 / (u \ z)) * (w * v5))) = a(x,y,(z \ u) * (w * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,27630,a,b,37776,a),flip(a)].">
      <j1 rule="hyper" parents="373 27630 37776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38088">
    <literal><![CDATA[
      a(L(x,x,x),y,y) \ L(R(x,y,y),z,z) = a(z,z,R(x,y,y)) \ x
    ]]></literal>
    <justification jstring="[para(36363(a,1),38079(a,1,1,1))].">
      <j1 rule="para" parents="36363 38079"/>
    </justification>
  </clause>

  <clause id="38089">
    <literal><![CDATA[
      a(x,y,y) \ L(R(x,y,y),z,z) = a(z,z,R(x,y,y)) \ x
    ]]></literal>
    <justification jstring="[para(11961(a,1),38088(a,1,1))].">
      <j1 rule="para" parents="11961 38088"/>
    </justification>
  </clause>

  <clause id="38091">
    <literal><![CDATA[
      a(x,y,y) \ L(R(x,y,y),z,z) = a(z,z,L(x,y,y)) \ x
    ]]></literal>
    <justification jstring="[para(27640(a,1),38089(a,2,1))].">
      <j1 rule="para" parents="27640 38089"/>
    </justification>
  </clause>

  <clause id="38092">
    <literal><![CDATA[
      a(x * a(y,y,x),z,z) \ R(x,z,z) = a(y,y,L(x * a(y,y,x),z,z)) \ (x * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(30234(a,1),38091(a,1,2))].">
      <j1 rule="para" parents="30234 38091"/>
    </justification>
  </clause>

  <clause id="38093">
    <literal><![CDATA[
      (x * ((x \ 1) \ ((x \ 1) / (x \ y)))) \ y = (x \ y) / (y \ ((1 / x) \ 1))
    ]]></literal>
    <justification jstring="[para(10(a,1),38086(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10 38086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38094">
    <literal><![CDATA[
      (x * ((x \ 1) \ ((x \ 1) / (x \ y)))) \ y = (x \ y) / (y \ x)
    ]]></literal>
    <justification jstring="[para(82(a,1),38093(a,2,2,2))].">
      <j1 rule="para" parents="82 38093"/>
    </justification>
  </clause>

  <clause id="38096">
    <literal><![CDATA[
      (x * (x \ (x / (x \ y)))) \ y = (x \ y) / (y \ x)
    ]]></literal>
    <justification jstring="[para(1215(a,1),38094(a,1,1,2))].">
      <j1 rule="para" parents="1215 38094"/>
    </justification>
  </clause>

  <clause id="38097">
    <literal><![CDATA[
      (x \ y) / (y \ x) = (x / (x \ y)) \ y
    ]]></literal>
    <justification jstring="[hyper(402,a,38096,a),flip(a)].">
      <j1 rule="hyper" parents="402 38096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38099">
    <literal><![CDATA[
      a(x,y,((z \ u) * (u \ z)) * ((z \ u) * ((1 / (u \ z)) * w))) = a(x,y,(z \ u) * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[para(34601(a,1),38087(a,1,3,2))].">
      <j1 rule="para" parents="34601 38087"/>
    </justification>
  </clause>

  <clause id="38101">
    <literal><![CDATA[
      (x * R(y,y,z)) \ (R(y,y,z) * (T(x,y) * u)) = L(L(u,x,y),x * y,a(z,y,y))
    ]]></literal>
    <justification jstring="[para(37597(a,1),37620(a,1,2))].">
      <j1 rule="para" parents="37597 37620"/>
    </justification>
  </clause>

  <clause id="38102">
    <literal><![CDATA[
      L(T(x,y) \ (T(x,y) * z),x,L(y,y,u)) = L(L(z,x,y),x * y,a(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29215,a,b,38101,a)].">
      <j1 rule="hyper" parents="64 29215 38101"/>
    </justification>
  </clause>

  <clause id="38103">
    <literal><![CDATA[
      L(L(x,y,z),y * z,a(u,z,z)) = L(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),38102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 38102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38104">
    <literal><![CDATA[
      L(a(x,y,z),u,L(w,w,x)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31094,a(flip),b,38103,a),flip(a)].">
      <j1 rule="hyper" parents="64 31094 38103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38105">
    <literal><![CDATA[
      L(x,y,L(z,z,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29972,a(flip),b,38103,a),flip(a)].">
      <j1 rule="hyper" parents="64 29972 38103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38107">
    <literal><![CDATA[
      L(x,y,x \ (z \ x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35048,a(flip),b,38105,a)].">
      <j1 rule="hyper" parents="64 35048 38105"/>
    </justification>
  </clause>

  <clause id="38108">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,z \ 1,u) \ w,z,z)) = a(x,y,(w * a(u,z,z \ 1)) * z)
    ]]></literal>
    <justification jstring="[para(11980(a,1),37641(a,2,3,1,2))].">
      <j1 rule="para" parents="11980 37641"/>
    </justification>
  </clause>

  <clause id="38109">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,z \ 1,u) \ w,z,z)) = a(x,y,a(u,z,z \ 1) * (w * z))
    ]]></literal>
    <justification jstring="[para(33225(a,1),38108(a,2,3))].">
      <j1 rule="para" parents="33225 38108"/>
    </justification>
  </clause>

  <clause id="38112">
    <literal><![CDATA[
      (x \ 1) * (x \ (x * (a(y,x,x) * ((1 / x) \ z)))) = T(L(x,x,y) * (1 / x),x * x) \ z
    ]]></literal>
    <justification jstring="[para(37890(a,1),37912(a,1,2,2,2))].">
      <j1 rule="para" parents="37890 37912"/>
    </justification>
  </clause>

  <clause id="38113">
    <literal><![CDATA[
      T(L(x,x,y) * (1 / x),x * x) \ z = (x \ 1) * (a(y,x,x) * ((1 / x) \ z))
    ]]></literal>
    <justification jstring="[hyper(739,a,38112,a),flip(a)].">
      <j1 rule="hyper" parents="739 38112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38115">
    <literal><![CDATA[
      T(L(x,x,y) * (1 / x),x * x) \ z = a(y * x,x,x \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,36458,a(flip),b,38113,a),flip(a)].">
      <j1 rule="hyper" parents="373 36458 38113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38116">
    <literal><![CDATA[
      (L(x,x,y) * (1 / x)) \ z = a(y * x,x,x \ 1) * z
    ]]></literal>
    <justification jstring="[para(23730(a,1),38115(a,1,1))].">
      <j1 rule="para" parents="23730 38115"/>
    </justification>
  </clause>

  <clause id="38118">
    <literal><![CDATA[
      a(x,y,L((1 / z) \ R(u,z,z),L(z \ 1,z,u * z),u)) = a(x,y,((u \ 1) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(23997(a,1),37802(a,1,3,2))].">
      <j1 rule="para" parents="23997 37802"/>
    </justification>
  </clause>

  <clause id="38119">
    <literal><![CDATA[
      a(x,y,L((1 / z) \ R(u,z,z),L(z,z,u * z),u)) = a(x,y,((u \ 1) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(29728(a,1),38118(a,1,3))].">
      <j1 rule="para" parents="29728 38118"/>
    </justification>
  </clause>

  <clause id="38120">
    <literal><![CDATA[
      a(x,y,L((1 / z) \ R(u,z,z),L(z,z,u),u)) = a(x,y,((u \ 1) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(29804(a,1),38119(a,1,3))].">
      <j1 rule="para" parents="29804 38119"/>
    </justification>
  </clause>

  <clause id="38121">
    <literal><![CDATA[
      a(x,y,L(z * u,L(z,z,u),u)) = a(x,y,((u \ 1) / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27991,a(flip),b,38120,a)].">
      <j1 rule="hyper" parents="64 27991 38120"/>
    </justification>
  </clause>

  <clause id="38122">
    <literal><![CDATA[
      a(x,y,L(z * u,z,u)) = a(x,y,((u \ 1) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(37230(a,1),38121(a,1,3))].">
      <j1 rule="para" parents="37230 38121"/>
    </justification>
  </clause>

  <clause id="38123">
    <literal><![CDATA[
      a(x,y,L(z * u,z,u)) = a(x,y,(z \ (u \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,27389,a(flip),b,38122,a),flip(a)].">
      <j1 rule="hyper" parents="373 27389 38122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38124">
    <literal><![CDATA[
      a(x,y,L(z * u,z,u)) \ w = a(x,y,(z \ (u \ 1)) \ 1) \ w
    ]]></literal>
    <justification jstring="[hyper(62,a,38123,a)].">
      <j1 rule="hyper" parents="62 38123"/>
    </justification>
  </clause>

  <clause id="38125">
    <literal><![CDATA[
      a(L(x,y,y),z,z) \ R(x,z,z) = a(y,y,L(x * a(y,y,x),z,z)) \ (x * a(y,y,x))
    ]]></literal>
    <justification jstring="[para(23949(a,1),38092(a,1,1))].">
      <j1 rule="para" parents="23949 38092"/>
    </justification>
  </clause>

  <clause id="38126">
    <literal><![CDATA[
      a(x,x,L(y * a(x,x,y),z,z)) \ (y * a(x,x,y)) = y * a(x,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,32647,a(flip),b,38125,a),flip(a)].">
      <j1 rule="hyper" parents="64 32647 38125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38127">
    <literal><![CDATA[
      a(L(L(a(x,x,y),x \ z,x \ z),a(x,x,y),z / x),u,w) = a((z / x) * (z / R(x,x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(29527(a,1),37613(a,1,1,1))].">
      <j1 rule="para" parents="29527 37613"/>
    </justification>
  </clause>

  <clause id="38128">
    <literal><![CDATA[
      a(x,y,y) \ (x * a(a(x,y,y),z,u)) = ((x / y) / (1 / y)) * a(w \ (a(x,y,y) \ w),z,u)
    ]]></literal>
    <justification jstring="[para(2653(a,1),37861(a,1,2,2))].">
      <j1 rule="para" parents="2653 37861"/>
    </justification>
  </clause>

  <clause id="38130">
    <literal><![CDATA[
      a(L(L(a(x,x,y),z * x,z * x),a(x,x,y),z / x),u,w) = a((z / x) * (z / R(x,x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(35219(a,1),38127(a,1,1,1))].">
      <j1 rule="para" parents="35219 38127"/>
    </justification>
  </clause>

  <clause id="38131">
    <literal><![CDATA[
      a(L(a(x,L(x,y * x,y * x),z),a(x,x,z),y / x),u,w) = a((y / x) * (y / R(x,x,z)),u,w)
    ]]></literal>
    <justification jstring="[para(34877(a,2),38130(a,1,1,1))].">
      <j1 rule="para" parents="34877 38130"/>
    </justification>
  </clause>

  <clause id="38132">
    <literal><![CDATA[
      a(L(a(x,(1 / (y / x)) * y,z),a(x,x,z),y / x),u,w) = a((y / x) * (y / R(x,x,z)),u,w)
    ]]></literal>
    <justification jstring="[para(34539(a,1),38131(a,1,1,1,2))].">
      <j1 rule="para" parents="34539 38131"/>
    </justification>
  </clause>

  <clause id="38133">
    <literal><![CDATA[
      a(L(a(x,(y / x) * y,z),a(x,x,z),y / x),u,w) = a((y / x) * (y / R(x,x,z)),u,w)
    ]]></literal>
    <justification jstring="[para(11967(a,1),38132(a,1,1,1))].">
      <j1 rule="para" parents="11967 38132"/>
    </justification>
  </clause>

  <clause id="38134">
    <literal><![CDATA[
      a(L(a(x,(x \ y) * y,z),a(x,x,z),y / x),u,w) = a((y / x) * (y / R(x,x,z)),u,w)
    ]]></literal>
    <justification jstring="[para(31904(a,1),38133(a,1,1,1))].">
      <j1 rule="para" parents="31904 38133"/>
    </justification>
  </clause>

  <clause id="38135">
    <literal><![CDATA[
      a(x,y \ K(z,u),y \ 1) * ((y \ K(z,u)) \ w) = K(u,z) * (L(y \ 1,y \ K(z,u),x) \ w)
    ]]></literal>
    <justification jstring="[para(27321(a,1),37622(a,1,1))].">
      <j1 rule="para" parents="27321 37622"/>
    </justification>
  </clause>

  <clause id="38137">
    <literal><![CDATA[
      K(x,y) * (L(z \ 1,z \ K(y,x),u) \ w) = a(u,z,z \ 1) * ((z \ K(y,x)) \ w)
    ]]></literal>
    <justification jstring="[para(32033(a,1),38135(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32033 38135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38138">
    <literal><![CDATA[
      a(x,y,y \ 1) * ((y \ K(z,u)) \ w) = K(u,z) * (L(y \ 1,y,x) \ w)
    ]]></literal>
    <justification jstring="[para(29653(a,1),38137(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="29653 38137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38140">
    <literal><![CDATA[
      a(x,y,y \ 1) * ((y \ K(z,u)) \ w) = L(y \ K(z,u),y,x) \ w
    ]]></literal>
    <justification jstring="[hyper(373,a,26121,a(flip),b,38138,a),flip(a)].">
      <j1 rule="hyper" parents="373 26121 38138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38142">
    <literal><![CDATA[
      R(T(x * y,z),(x \ T(x * y,z)) \ ((x * y) \ y),u) = R(T(x * y,z),T(x * y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26508,a(flip),b,37885,a)].">
      <j1 rule="hyper" parents="64 26508 37885"/>
    </justification>
  </clause>

  <clause id="38144">
    <literal><![CDATA[
      R(T(x * y,z),(x \ T(x * y,z)) \ (y \ (x \ y)),u) = R(T(x * y,z),T(x * y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26602,a(flip),b,38142,a)].">
      <j1 rule="hyper" parents="64 26602 38142"/>
    </justification>
  </clause>

  <clause id="38145">
    <literal><![CDATA[
      R(T(x * y,z),T(x * y,z),u) = R(T(x * y,z),(x \ (x * y)) \ (y \ (x \ y)),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26432,a(flip),b,38144,a),flip(a)].">
      <j1 rule="hyper" parents="64 26432 38144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38147">
    <literal><![CDATA[
      R(T(x * y,z),T(x * y,z),u) = R(T(x * y,z),y \ (y \ (x \ y)),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),38145(a,2,2,1))].">
      <j1 rule="para" parents="9 38145"/>
    </justification>
  </clause>

  <clause id="38148">
    <literal><![CDATA[
      R(T(x * y,z),T(x * y,z),u) = R(T(x * y,z),L(x \ y,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,30397,a(flip),b,38147,a),flip(a)].">
      <j1 rule="hyper" parents="373 30397 38147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38149">
    <literal><![CDATA[
      R(T(x * y,z),L(x \ y,y,y),u) = R(T(x * y,z),x * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26406,a(flip),b,38148,a),flip(a)].">
      <j1 rule="hyper" parents="64 26406 38148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38151">
    <literal><![CDATA[
      ((x / y) \ K(y / x,(x / y) \ 1)) * z = (y / ((x / y) * x)) * ((1 / (y / x)) * z)
    ]]></literal>
    <justification jstring="[para(37934(a,1),37944(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37934 37944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38152">
    <literal><![CDATA[
      ((x / y) \ K(y / x,(x / y) \ 1)) * z = (y / x) * ((x / y) \ ((1 / (y / x)) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,37941,a(flip),b,38151,a),flip(a)].">
      <j1 rule="hyper" parents="373 37941 38151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38153">
    <literal><![CDATA[
      ((x / y) \ K(y / x,(x / y) \ 1)) * z = (y / x) * (((x / y) * (y / x)) \ z)
    ]]></literal>
    <justification jstring="[para(37762(a,1),38152(a,2,2))].">
      <j1 rule="para" parents="37762 38152"/>
    </justification>
  </clause>

  <clause id="38154">
    <literal><![CDATA[
      ((x / y) \ K(y / x,(x / y) \ 1)) * z = (x \ y) * (((x / y) * (x \ y)) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,25740,a(flip),b,38153,a),flip(a)].">
      <j1 rule="hyper" parents="373 25740 38153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38155">
    <literal><![CDATA[
      ((x / y) \ K(y / x,y / x)) * z = (x \ y) * (((x / y) * (x \ y)) \ z)
    ]]></literal>
    <justification jstring="[para(6375(a,1),38154(a,1,1,2))].">
      <j1 rule="para" parents="6375 38154"/>
    </justification>
  </clause>

  <clause id="38156">
    <literal><![CDATA[
      (x \ y) * (((x / y) * (x \ y)) \ z) = ((x / y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(188(a,1),38155(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="188 38155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38158">
    <literal><![CDATA[
      L(((x / (x * y)) \ y) \ z,T(y \ x,u) / (x * y),(x * y) \ (y \ x)) = ((y \ x) / (x * y)) * z
    ]]></literal>
    <justification jstring="[para(37743(a,1),37748(a,1,1,1))].">
      <j1 rule="para" parents="37743 37748"/>
    </justification>
  </clause>

  <clause id="38159">
    <literal><![CDATA[
      L(((x / (x * y)) \ y) \ z,(x * y) \ (y \ x),(x * y) \ (y \ x)) = ((y \ x) / (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,29588,a(flip),b,38158,a)].">
      <j1 rule="hyper" parents="64 29588 38158"/>
    </justification>
  </clause>

  <clause id="38160">
    <literal><![CDATA[
      L(((x / (x * y)) \ y) \ z,(x * y) \ (y \ x),a(y,y,x)) = ((y \ x) / (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,30372,a(flip),b,38159,a)].">
      <j1 rule="hyper" parents="64 30372 38159"/>
    </justification>
  </clause>

  <clause id="38161">
    <literal><![CDATA[
      L(((x / (x * y)) \ y) \ z,a(y,y,x),a(y,y,x)) = ((y \ x) / (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,30401,a(flip),b,38160,a)].">
      <j1 rule="hyper" parents="64 30401 38160"/>
    </justification>
  </clause>

  <clause id="38162">
    <literal><![CDATA[
      ((x / (x * y)) \ y) \ z = ((y \ x) / (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,37811,a(flip),b,38161,a)].">
      <j1 rule="hyper" parents="64 37811 38161"/>
    </justification>
  </clause>

  <clause id="38164">
    <literal><![CDATA[
      ((x / (x * y)) \ y) \ z = (y \ (x / (x * y))) * z
    ]]></literal>
    <justification jstring="[para(37744(a,1),38162(a,2,1))].">
      <j1 rule="para" parents="37744 38162"/>
    </justification>
  </clause>

  <clause id="38165">
    <literal><![CDATA[
      ((x / (x * y)) \ y) * (y \ (x / (x * y))) = 1
    ]]></literal>
    <justification jstring="[hyper(734,a,38164,a)].">
      <j1 rule="hyper" parents="734 38164"/>
    </justification>
  </clause>

  <clause id="38166">
    <literal><![CDATA[
      x / (((y / (y * z)) \ z) * x) = z \ (y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(729,a,38164,a)].">
      <j1 rule="hyper" parents="729 38164"/>
    </justification>
  </clause>

  <clause id="38167">
    <literal><![CDATA[
      (x \ (y / (y * x))) * (((y / (y * x)) \ x) * z) = z
    ]]></literal>
    <justification jstring="[hyper(396,a,38164,a),flip(a)].">
      <j1 rule="hyper" parents="396 38164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38168">
    <literal><![CDATA[
      1 / (x \ (y / (y * x))) = (y / (y * x)) \ x
    ]]></literal>
    <justification jstring="[hyper(225,a,8,a(flip),b,38164,a)].">
      <j1 rule="hyper" parents="225 8 38164"/>
    </justification>
  </clause>

  <clause id="38169">
    <literal><![CDATA[
      ((x \ y) / x) / y = x \ (y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(35,a,36522,a,b,38165,a)].">
      <j1 rule="hyper" parents="35 36522 38165"/>
    </justification>
  </clause>

  <clause id="38170">
    <literal><![CDATA[
      (x / y) \ (x / (x * (x / y))) = (y / (x / y)) / x
    ]]></literal>
    <justification jstring="[para(82(a,1),38169(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="82 38169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38171">
    <literal><![CDATA[
      T(((x / (x * y)) / y) \ 1,x / (x * y)) = (y \ (x / (x * y))) \ 1
    ]]></literal>
    <justification jstring="[para(38166(a,1),7657(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38166 7657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38172">
    <literal><![CDATA[
      (x \ (y / (y * x))) * ((1 / (x \ (y / (y * x)))) * z) = z
    ]]></literal>
    <justification jstring="[para(38168(a,2),38167(a,1,2,1))].">
      <j1 rule="para" parents="38168 38167"/>
    </justification>
  </clause>

  <clause id="38173">
    <literal><![CDATA[
      (x / (y / x)) / y = x / (y * (y / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,37747,a(flip),b,38170,a),flip(a)].">
      <j1 rule="hyper" parents="64 37747 38170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38174">
    <literal><![CDATA[
      a(x,y,(((z \ u) * u) * (z \ 1)) * w) = a(x,y,(u / (z * (z / u))) * w)
    ]]></literal>
    <justification jstring="[para(38173(a,1),34332(a,2,3,1))].">
      <j1 rule="para" parents="38173 34332"/>
    </justification>
  </clause>

  <clause id="38175">
    <literal><![CDATA[
      ((x * y) \ T(x / y,y \ 1)) * ((1 / (y \ (x / (x * y)))) * z) = z
    ]]></literal>
    <justification jstring="[para(33873(a,2),38172(a,1,1))].">
      <j1 rule="para" parents="33873 38172"/>
    </justification>
  </clause>

  <clause id="38176">
    <literal><![CDATA[
      ((x / (x * y)) / y) \ 1 = y / (x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(41,a,37742,a,b,38171,a),flip(a)].">
      <j1 rule="hyper" parents="41 37742 38171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38177">
    <literal><![CDATA[
      1 / ((x / (x * y)) / y) = y / (x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,35982,a,b,38176,a)].">
      <j1 rule="hyper" parents="64 35982 38176"/>
    </justification>
  </clause>

  <clause id="38178">
    <literal><![CDATA[
      x * ((y / (z / (z * y))) \ 1) = x * ((z / (z * y)) / y)
    ]]></literal>
    <justification jstring="[para(38176(a,1),35983(a,1,2,1))].">
      <j1 rule="para" parents="38176 35983"/>
    </justification>
  </clause>

  <clause id="38179">
    <literal><![CDATA[
      (x / (y / (y * x))) \ K(z,u) = K(z,u) * ((y / (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,34732,a(flip),b,38178,a)].">
      <j1 rule="hyper" parents="64 34732 38178"/>
    </justification>
  </clause>

  <clause id="38180">
    <literal><![CDATA[
      ((x * y) \ T(x / y,y \ 1)) * ((1 / (y \ (x / (x * y)))) * z) = u * (w \ (w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,74,a,b,38175,a),flip(a)].">
      <j1 rule="hyper" parents="373 74 38175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38181">
    <literal><![CDATA[
      a(x,y,(((z \ u) * u) * (z \ 1)) * w) = a(x,y,((z * (u \ z)) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27975,a(flip),b,38174,a),flip(a)].">
      <j1 rule="hyper" parents="373 27975 38174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38182">
    <literal><![CDATA[
      a(x,y,((z * (u \ z)) \ u) * w) = a(x,y,(z \ (u / (z / u))) * w)
    ]]></literal>
    <justification jstring="[para(34329(a,1),38181(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="34329 38181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38183">
    <literal><![CDATA[
      a(x,y,((z * (u \ z)) \ u) * w) = a(x,y,(z \ ((z \ u) * u)) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,33715,a(flip),b,38182,a),flip(a)].">
      <j1 rule="hyper" parents="373 33715 38182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38184">
    <literal><![CDATA[
      a(x,(y * ((z * z) \ y)) * (u / ((((z * z) \ y) * w) / v5)),v6) = a(x,u / ((((1 / y) * (z * z)) * w) / v5),v6)
    ]]></literal>
    <justification jstring="[para(900(a,1),32210(a,2,2,2,1,1))].">
      <j1 rule="para" parents="900 32210"/>
    </justification>
  </clause>

  <clause id="38185">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u,L(R(z,w,v5),u,a(x,y,z))) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,11,a(flip),b,33271,a),flip(a)].">
      <j1 rule="hyper" parents="373 11 33271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38187">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u,R(z,w,v5)) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(33251(a,1),38185(a,1,3))].">
      <j1 rule="para" parents="33251 38185"/>
    </justification>
  </clause>

  <clause id="38188">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,u,L(z,w,v5)) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,26607,a(flip),b,38187,a)].">
      <j1 rule="hyper" parents="64 26607 38187"/>
    </justification>
  </clause>

  <clause id="38190">
    <literal><![CDATA[
      (x \ ((y / (y * z)) \ 1)) \ K(x \ ((y / (y * z)) \ 1),T(z,y) \ x) = 1 / (x \ ((y / (y * z)) \ 1))
    ]]></literal>
    <justification jstring="[para(24861(a,1),34714(a,1,2))].">
      <j1 rule="para" parents="24861 34714"/>
    </justification>
  </clause>

  <clause id="38191">
    <literal><![CDATA[
      (x \ ((y / (y * x)) \ 1)) \ K(x \ ((y / (y * x)) \ 1),K(y,x)) = 1 / (x \ ((y / (y * x)) \ 1))
    ]]></literal>
    <justification jstring="[para(5731(a,2),38190(a,1,2,2))].">
      <j1 rule="para" parents="5731 38190"/>
    </justification>
  </clause>

  <clause id="38192">
    <literal><![CDATA[
      (x \ ((y / (y * x)) \ 1)) \ K(y,K(x \ ((y / (y * x)) \ 1),x)) = 1 / (x \ ((y / (y * x)) \ 1))
    ]]></literal>
    <justification jstring="[para(8108(a,1),38191(a,1,2))].">
      <j1 rule="para" parents="8108 38191"/>
    </justification>
  </clause>

  <clause id="38193">
    <literal><![CDATA[
      (x \ ((y / (y * x)) \ 1)) \ K(y,K((x \ (y * x)) * (y \ 1),x)) = 1 / (x \ ((y / (y * x)) \ 1))
    ]]></literal>
    <justification jstring="[para(28498(a,1),38192(a,1,2,2))].">
      <j1 rule="para" parents="28498 38192"/>
    </justification>
  </clause>

  <clause id="38194">
    <literal><![CDATA[
      (x \ ((y / (y * x)) \ 1)) \ K(y,K(T(y,x) * (y \ 1),x)) = 1 / (x \ ((y / (y * x)) \ 1))
    ]]></literal>
    <justification jstring="[para(22(a,2),38193(a,1,2,2,1,1))].">
      <j1 rule="para" parents="22 38193"/>
    </justification>
  </clause>

  <clause id="38195">
    <literal><![CDATA[
      (x \ ((y / (y * x)) \ 1)) \ K(y,K(K(y,x),x)) = 1 / (x \ ((y / (y * x)) \ 1))
    ]]></literal>
    <justification jstring="[para(5740(a,2),38194(a,1,2,2,1))].">
      <j1 rule="para" parents="5740 38194"/>
    </justification>
  </clause>

  <clause id="38196">
    <literal><![CDATA[
      1 / (x \ ((y / (y * x)) \ 1)) = (x \ ((y / (y * x)) \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(8038(a,1),38195(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8038 38195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38199">
    <literal><![CDATA[
      1 / ((x \ ((y / (y * x)) \ 1)) \ 1) = (y / (y * x)) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(38196(a,1),37141(a,1,2))].">
      <j1 rule="para" parents="38196 37141"/>
    </justification>
  </clause>

  <clause id="38200">
    <literal><![CDATA[
      (x / (x * y)) \ (1 / y) = y \ ((x / (x * y)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(330,a,38199,a)].">
      <j1 rule="hyper" parents="330 38199"/>
    </justification>
  </clause>

  <clause id="38202">
    <literal><![CDATA[
      x * ((y \ ((1 / x) \ y)) \ 1) = x \ ((y / (y * x)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,31425,a,b,38200,a)].">
      <j1 rule="hyper" parents="64 31425 38200"/>
    </justification>
  </clause>

  <clause id="38203">
    <literal><![CDATA[
      ((1 / x) \ y) \ (y * x) = x \ ((y / (y * x)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,36768,a(flip),b,38202,a)].">
      <j1 rule="hyper" parents="64 36768 38202"/>
    </justification>
  </clause>

  <clause id="38204">
    <literal><![CDATA[
      L(x,y * (x \ ((1 / y) \ z)),y * (x \ ((y \ 1) \ z))) = (1 / ((a(y,y,z) * z) / x)) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29242,a(flip),b,35264,a)].">
      <j1 rule="hyper" parents="64 29242 35264"/>
    </justification>
  </clause>

  <clause id="38205">
    <literal><![CDATA[
      (K((x \ ((x * y) * y)) * z,x \ (x / (y * y))) / (x \ ((x * y) * y))) \ z = z / (1 / (x \ ((x * y) * y)))
    ]]></literal>
    <justification jstring="[para(28108(a,1),36089(a,1,1,1))].">
      <j1 rule="para" parents="28108 36089"/>
    </justification>
  </clause>

  <clause id="38206">
    <literal><![CDATA[
      L(x,y,(z \ (R(1 / u,w,v5) * v6)) * (v7 * v7)) = L(x,y,(R(u,w,v5) * v6) * L(z,z,L(1 / u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(33584(a,1),36445(a,2,3,2))].">
      <j1 rule="para" parents="33584 36445"/>
    </justification>
  </clause>

  <clause id="38207">
    <literal><![CDATA[
      R(T(a(x,y,z),u),a(x,y,z),T(x,w) * v5) = (T(x,w) * (v5 * a(x,y,z))) \ (T(x,w) * ((a(x,y,z) \ 1) \ (v5 * a(x,y,z))))
    ]]></literal>
    <justification jstring="[para(31641(a,1),37065(a,2,2))].">
      <j1 rule="para" parents="31641 37065"/>
    </justification>
  </clause>

  <clause id="38209">
    <literal><![CDATA[
      (((x \ (x \ y)) \ y) \ z) * K(x * x,(x \ y) / x) = T((y / (x \ (x \ y))) \ z,K(y,x * x))
    ]]></literal>
    <justification jstring="[para(79(a,1),37438(a,1,2,1,2))].">
      <j1 rule="para" parents="79 37438"/>
    </justification>
  </clause>

  <clause id="38211">
    <literal><![CDATA[
      (((x \ (x \ y)) \ y) \ z) * K(x * x,x \ (y / x)) = T((y / (x \ (x \ y))) \ z,K(y,x * x))
    ]]></literal>
    <justification jstring="[para(13331(a,1),38209(a,1,2))].">
      <j1 rule="para" parents="13331 38209"/>
    </justification>
  </clause>

  <clause id="38212">
    <literal><![CDATA[
      (((x \ (x \ y)) \ y) \ z) * K(x * x,(y / x) * x) = T((y / (x \ (x \ y))) \ z,K(y,x * x))
    ]]></literal>
    <justification jstring="[para(22812(a,1),38211(a,1,2))].">
      <j1 rule="para" parents="22812 38211"/>
    </justification>
  </clause>

  <clause id="38213">
    <literal><![CDATA[
      T((x / (y \ (y \ x))) \ z,K(x,y * y)) = (((y \ (y \ x)) \ x) \ z) * K(y * y,x)
    ]]></literal>
    <justification jstring="[para(12(a,1),38212(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 38212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38214">
    <literal><![CDATA[
      ((x \ (x \ y)) \ T(y,x * x)) \ z = (y / (x \ (x \ y))) \ z
    ]]></literal>
    <justification jstring="[hyper(41,a,24976,a,b,38213,a)].">
      <j1 rule="hyper" parents="41 24976 38213"/>
    </justification>
  </clause>

  <clause id="38215">
    <literal><![CDATA[
      ((x \ (x \ y)) \ y) \ K(x * x,y) = (y / (x \ (x \ y))) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,17062,a(flip),b,38214,a)].">
      <j1 rule="hyper" parents="64 17062 38214"/>
    </justification>
  </clause>

  <clause id="38216">
    <literal><![CDATA[
      ((x \ (x \ y)) \ y) \ K(x * x,y) = (((x \ y) / y) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(35865(a,1),38215(a,2,1))].">
      <j1 rule="para" parents="35865 38215"/>
    </justification>
  </clause>

  <clause id="38217">
    <literal><![CDATA[
      L(T(x \ a(y,z,u),x * w),x \ a(y,z,u),x \ a(y,z,u)) = T(x \ a(y,z,u),x \ w)
    ]]></literal>
    <justification jstring="[para(28641(a,1),37439(a,1,1))].">
      <j1 rule="para" parents="28641 37439"/>
    </justification>
  </clause>

  <clause id="38218">
    <literal><![CDATA[
      L(T(x \ a(y,z,u),x * w),x * a(y,z,u),x \ a(y,z,u)) = T(x \ a(y,z,u),x \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13758,a(flip),b,38217,a)].">
      <j1 rule="hyper" parents="64 13758 38217"/>
    </justification>
  </clause>

  <clause id="38220">
    <literal><![CDATA[
      L(T(x \ a(y,z,u),x * w),x,x \ a(y,z,u)) = T(x \ a(y,z,u),x \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33115,a(flip),b,38218,a)].">
      <j1 rule="hyper" parents="64 33115 38218"/>
    </justification>
  </clause>

  <clause id="38222">
    <literal><![CDATA[
      T(T(a(x,y,z) / u,u * w),a(x,y,z)) = T(u \ a(x,y,z),u \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,4809,a(flip),b,38220,a)].">
      <j1 rule="hyper" parents="64 4809 38220"/>
    </justification>
  </clause>

  <clause id="38223">
    <literal><![CDATA[
      T(a(x,y,z) / u,u * w) = T(u \ a(x,y,z),u \ w)
    ]]></literal>
    <justification jstring="[hyper(23173,a,38222,a)].">
      <j1 rule="hyper" parents="23173 38222"/>
    </justification>
  </clause>

  <clause id="38225">
    <literal><![CDATA[
      (x * (1 / (x * a(x,y,z)))) * (1 / (1 / x)) = 1 / T(x \ a(x,y,z),x \ x)
    ]]></literal>
    <justification jstring="[para(38223(a,1),37326(a,2,2))].">
      <j1 rule="para" parents="38223 37326"/>
    </justification>
  </clause>

  <clause id="38226">
    <literal><![CDATA[
      (x * (1 / (x * a(x,y,z)))) * (1 / (1 / x)) = 1 / (x \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(379(a,1),38225(a,2,2))].">
      <j1 rule="para" parents="379 38225"/>
    </justification>
  </clause>

  <clause id="38227">
    <literal><![CDATA[
      (x * (1 / (x * a(x,y,z)))) * (1 / (1 / x)) = (a(x,y,z) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,25195,a(flip),b,38226,a),flip(a)].">
      <j1 rule="hyper" parents="373 25195 38226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38229">
    <literal><![CDATA[
      (x \ R(T(x,y),z,z)) * (x * (T(R(x,z,z),y) \ (u * a(x,z,z)))) = (R(x,z,z) / x) * L(u,x,a(z,z,x))
    ]]></literal>
    <justification jstring="[para(4050(a,1),37440(a,1,1))].">
      <j1 rule="para" parents="4050 37440"/>
    </justification>
  </clause>

  <clause id="38230">
    <literal><![CDATA[
      (x * L(R(y,z,u),w,v5)) \ (x * L(R(R(y,x,y),z,u),w,v5)) = a(y,x,L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(4779(a,1),37441(a,1,1,2))].">
      <j1 rule="para" parents="4779 37441"/>
    </justification>
  </clause>

  <clause id="38232">
    <literal><![CDATA[
      (x * L(R(y,z,u),w,v5)) \ T(L(R(y,z,u),w,v5) * x,y) = a(y,x,L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(26161(a,1),38230(a,1,2))].">
      <j1 rule="para" parents="26161 38230"/>
    </justification>
  </clause>

  <clause id="38233">
    <literal><![CDATA[
      K(L(R(x,y,z),u,w),v5) * K(L(R(x,y,z),u,w) * v5,x) = a(x,v5,L(L(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,10827,a(flip),b,38232,a)].">
      <j1 rule="hyper" parents="64 10827 38232"/>
    </justification>
  </clause>

  <clause id="38234">
    <literal><![CDATA[
      K(R(x,y,z),u) * K(L(R(x,y,z),w,v5) * u,x) = a(x,u,L(L(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(23004(a,1),38233(a,1,1))].">
      <j1 rule="para" parents="23004 38233"/>
    </justification>
  </clause>

  <clause id="38236">
    <literal><![CDATA[
      K(x,y) * K(L(R(x,z,u),w,v5) * y,x) = a(x,y,L(L(x,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(23385(a,1),38234(a,1,1))].">
      <j1 rule="para" parents="23385 38234"/>
    </justification>
  </clause>

  <clause id="38238">
    <literal><![CDATA[
      a(x,y,L(L(x,z,u),w,v5)) = K(x,y) * K(R(x,z,u) * y,x)
    ]]></literal>
    <justification jstring="[para(28403(a,1),38236(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28403 38236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38239">
    <literal><![CDATA[
      a(x,y,L(L(x,z,u),w,v5)) = K(x,y) * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(28183(a,1),38238(a,2,2))].">
      <j1 rule="para" parents="28183 38238"/>
    </justification>
  </clause>

  <clause id="38241">
    <literal><![CDATA[
      a(x,y,L(L(x,z,u),w,v5)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10887,a(flip),b,38239,a),flip(a)].">
      <j1 rule="hyper" parents="373 10887 38239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38243">
    <literal><![CDATA[
      a(x,x,L(L(x,y,z),u,w)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,1853,a,b,38241,a),flip(a)].">
      <j1 rule="hyper" parents="373 1853 38241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38244">
    <literal><![CDATA[
      (K(x,x \ 1) / x) \ R(R(x,y,z),u,w) = R(R(x,y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(38243(a,1),34612(a,1,1,1))].">
      <j1 rule="para" parents="38243 34612"/>
    </justification>
  </clause>

  <clause id="38245">
    <literal><![CDATA[
      (x / (x * x)) \ R(R(x,y,z),u,w) = R(R(x,y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(1729(a,1),38244(a,1,1))].">
      <j1 rule="para" parents="1729 38244"/>
    </justification>
  </clause>

  <clause id="38247">
    <literal><![CDATA[
      R(R(x,y,z),u,w) / (1 / x) = R(R(x,y,z),u,w) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,33976,a(flip),b,38245,a)].">
      <j1 rule="hyper" parents="64 33976 38245"/>
    </justification>
  </clause>

  <clause id="38248">
    <literal><![CDATA[
      R(R(x,y,z),u,w) / (1 / x) = x * R(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,846,a(flip),b,38247,a),flip(a)].">
      <j1 rule="hyper" parents="373 846 38247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38249">
    <literal><![CDATA[
      R(x,y,y) * R(x,y,y) = x * R(R(x,y,y),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30592,a(flip),b,38248,a)].">
      <j1 rule="hyper" parents="64 30592 38248"/>
    </justification>
  </clause>

  <clause id="38250">
    <literal><![CDATA[
      L(x \ R(x,y,(z * R(R(z,u,u),u,u)) \ w),x,w * y) = a(x,y,(R(z,u,u) * R(z,u,u)) \ w)
    ]]></literal>
    <justification jstring="[para(38249(a,1),24739(a,1,1,2,3,1))].">
      <j1 rule="para" parents="38249 24739"/>
    </justification>
  </clause>

  <clause id="38251">
    <literal><![CDATA[
      a(x \ R(x,y,z),(u / x) \ u,u / x) = u \ ((x \ R(x,y,z)) \ (R(x,y,z) * (x \ u)))
    ]]></literal>
    <justification jstring="[para(5956(a,1),37442(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5956 37442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38252">
    <literal><![CDATA[
      a(x \ R(x,y,z),(u / x) \ u,u / x) = u \ L((x \ 1) \ (x \ u),x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(29209(a,1),38251(a,2,2))].">
      <j1 rule="para" parents="29209 38251"/>
    </justification>
  </clause>

  <clause id="38253">
    <literal><![CDATA[
      a(x \ R(x,y,z),(u / x) \ u,u / x) = u \ L(x \ ((1 / x) \ u),x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1166(a,1),38252(a,2,2,1))].">
      <j1 rule="para" parents="1166 38252"/>
    </justification>
  </clause>

  <clause id="38254">
    <literal><![CDATA[
      x \ L(y \ ((1 / y) \ x),y,L(y,z,u)) = a(y \ R(y,z,u),y,x / y)
    ]]></literal>
    <justification jstring="[para(82(a,1),38253(a,1,2)),flip(a)].">
      <j1 rule="para" parents="82 38253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38255">
    <literal><![CDATA[
      x \ L(y \ ((1 / y) \ x),y,L(y,z,u)) = a(y \ R(y,z,u),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,27308,a(flip),b,38254,a),flip(a)].">
      <j1 rule="hyper" parents="373 27308 38254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38256">
    <literal><![CDATA[
      x \ L(y \ ((1 / y) \ x),y,L(y,z,u)) = a(y \ L(y,z,u),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,34649,a(flip),b,38255,a),flip(a)].">
      <j1 rule="hyper" parents="373 34649 38255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38257">
    <literal><![CDATA[
      x \ L(y \ ((1 / y) \ x),y,L(y,z,u)) = a(y,y * L(y,z,u),y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,33572,a(flip),b,38256,a),flip(a)].">
      <j1 rule="hyper" parents="373 33572 38256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38258">
    <literal><![CDATA[
      x \ L(y \ ((1 / y) \ x),y,L(y,z,u)) = a(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,34290,a(flip),b,38257,a),flip(a)].">
      <j1 rule="hyper" parents="373 34290 38257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38259">
    <literal><![CDATA[
      R((1 / x) / (y \ a(y,y,L(x,z,u))),L(y,y,L(x,z,u)),R(x,z,u)) = (x \ R(x,z,u)) / (y \ R(x,z,u))
    ]]></literal>
    <justification jstring="[para(29203(a,1),37447(a,1,2))].">
      <j1 rule="para" parents="29203 37447"/>
    </justification>
  </clause>

  <clause id="38260">
    <literal><![CDATA[
      L(x,(y \ (R(1 / z,u,w) * v5)) * (z * z),v6) = L(x,(R(z,u,w) * v5) * L(y,y,L(z \ 1,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(29007(a,1),37448(a,2,2,2))].">
      <j1 rule="para" parents="29007 37448"/>
    </justification>
  </clause>

  <clause id="38261">
    <literal><![CDATA[
      a(x,K(y,z) / u,u \ K(y,z)) * (u * ((u \ K(y,z)) \ w)) = L(K(y,z) / u,K(y,z) / u,x) \ (u * w)
    ]]></literal>
    <justification jstring="[para(27308(a,1),37625(a,1,1))].">
      <j1 rule="para" parents="27308 37625"/>
    </justification>
  </clause>

  <clause id="38262">
    <literal><![CDATA[
      a(x,(y * ((z * z) \ y)) * (u / ((((z * z) \ y) * w) / v5)),v6) = a(x,u / (((1 / y) * ((z * z) * w)) / v5),v6)
    ]]></literal>
    <justification jstring="[para(34(a,1),38184(a,2,2,2,1))].">
      <j1 rule="para" parents="34 38184"/>
    </justification>
  </clause>

  <clause id="38263">
    <literal><![CDATA[
      L(x,y * (x \ ((1 / y) \ z)),y * (x \ (y \ z))) = (1 / ((a(y,y,z) * z) / x)) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,31741,a(flip),b,38204,a)].">
      <j1 rule="hyper" parents="64 31741 38204"/>
    </justification>
  </clause>

  <clause id="38264">
    <literal><![CDATA[
      L(x,(x \ (y \ z)) * y,y * (x \ (y \ z))) = (1 / ((a(y,y,z) * z) / x)) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,31073,a(flip),b,38263,a)].">
      <j1 rule="hyper" parents="64 31073 38263"/>
    </justification>
  </clause>

  <clause id="38265">
    <literal><![CDATA[
      L(x,(y \ z) * (x * y),(y \ z) * (x * y)) = (1 / ((a(y,y,z) * z) / x)) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,35246,a(flip),b,38264,a)].">
      <j1 rule="hyper" parents="64 35246 38264"/>
    </justification>
  </clause>

  <clause id="38266">
    <literal><![CDATA[
      (1 / ((a(x,x,y) * y) / z)) * (x \ ((1 / x) \ y)) = (1 / ((x \ (x \ y)) / z)) * (x \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,35265,a(flip),b,38265,a),flip(a)].">
      <j1 rule="hyper" parents="64 35265 38265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38267">
    <literal><![CDATA[
      (K((x \ ((x * y) * y)) * z,(y * y) \ 1) / (x \ ((x * y) * y))) \ z = z / (1 / (x \ ((x * y) * y)))
    ]]></literal>
    <justification jstring="[para(6709(a,1),38205(a,1,1,1))].">
      <j1 rule="para" parents="6709 38205"/>
    </justification>
  </clause>

  <clause id="38269">
    <literal><![CDATA[
      (K((x \ ((x * y) * y)) * z,y \ (y \ 1)) / (x \ ((x * y) * y))) \ z = z / (1 / (x \ ((x * y) * y)))
    ]]></literal>
    <justification jstring="[para(14419(a,1),38267(a,1,1,1))].">
      <j1 rule="para" parents="14419 38267"/>
    </justification>
  </clause>

  <clause id="38270">
    <literal><![CDATA[
      (K(x * x,(y \ ((y * x) * x)) * z) / (y \ ((y * x) * x))) \ z = z / (1 / (y \ ((y * x) * x)))
    ]]></literal>
    <justification jstring="[para(15871(a,1),38269(a,1,1,1))].">
      <j1 rule="para" parents="15871 38269"/>
    </justification>
  </clause>

  <clause id="38271">
    <literal><![CDATA[
      (K(x * x,(y \ (y * x)) * (x * z)) / (y \ ((y * x) * x))) \ z = z / (1 / (y \ ((y * x) * x)))
    ]]></literal>
    <justification jstring="[para(28461(a,1),38270(a,1,1,1))].">
      <j1 rule="para" parents="28461 38270"/>
    </justification>
  </clause>

  <clause id="38272">
    <literal><![CDATA[
      (K(x * x,x * (x * y)) / (z \ ((z * x) * x))) \ y = y / (1 / (z \ ((z * x) * x)))
    ]]></literal>
    <justification jstring="[para(9(a,1),38271(a,1,1,1,2,1))].">
      <j1 rule="para" parents="9 38271"/>
    </justification>
  </clause>

  <clause id="38273">
    <literal><![CDATA[
      (K(x * x,y) / (z \ ((z * x) * x))) \ y = y / (1 / (z \ ((z * x) * x)))
    ]]></literal>
    <justification jstring="[para(17275(a,1),38272(a,1,1,1))].">
      <j1 rule="para" parents="17275 38272"/>
    </justification>
  </clause>

  <clause id="38274">
    <literal><![CDATA[
      L(x,y,(z \ (R(1 / u,w,v5) * v6)) * (v7 * v7)) = L(x,y,(R(u,w,v5) * v6) * L(z,z,L(u \ 1,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(29007(a,1),38206(a,2,3,2))].">
      <j1 rule="para" parents="29007 38206"/>
    </justification>
  </clause>

  <clause id="38278">
    <literal><![CDATA[
      (K(x,y) * a(x,z,z)) * (x * (T(R(x,z,z),y) \ (u * a(x,z,z)))) = (R(x,z,z) / x) * L(u,x,a(z,z,x))
    ]]></literal>
    <justification jstring="[para(25348(a,1),38229(a,1,1))].">
      <j1 rule="para" parents="25348 38229"/>
    </justification>
  </clause>

  <clause id="38279">
    <literal><![CDATA[
      R((1 / x) / (y \ a(y,y,L(x,z,u))),L(y,y,L(x,z,u)),L(x,z,u)) = (x \ R(x,z,u)) / (y \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26360,a(flip),b,38259,a)].">
      <j1 rule="hyper" parents="64 26360 38259"/>
    </justification>
  </clause>

  <clause id="38280">
    <literal><![CDATA[
      L(x,(y \ (R(1 / z,u,w) * v5)) * (z * z),v6) = L(x,(R(z,u,w) * v5) * L(y,y,L(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(33601(a,1),38260(a,2,2,2))].">
      <j1 rule="para" parents="33601 38260"/>
    </justification>
  </clause>

  <clause id="38281">
    <literal><![CDATA[
      L(x,(y \ (R(1 / z,u,w) * v5)) * (z * z),v6) = L(x,(L(z,u,w) * v5) * L(y,y,L(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,36284,a(flip),b,38280,a),flip(a)].">
      <j1 rule="hyper" parents="373 36284 38280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38282">
    <literal><![CDATA[
      L(x,(y \ (R(1 / z,u,w) * v5)) * (z * z),v6) = L(x,y \ (L(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29779,a(flip),b,38281,a),flip(a)].">
      <j1 rule="hyper" parents="373 29779 38281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38283">
    <literal><![CDATA[
      L(x,y \ (R(1 / z,u,w) * v5),v6) = L(x,y \ (L(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29509,a(flip),b,38282,a)].">
      <j1 rule="hyper" parents="64 29509 38282"/>
    </justification>
  </clause>

  <clause id="38285">
    <literal><![CDATA[
      L(x,y \ (R(z,u,w) * v5),v6) = L(x,y \ (L(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,37044,a(flip),b,38283,a)].">
      <j1 rule="hyper" parents="64 37044 38283"/>
    </justification>
  </clause>

  <clause id="38286">
    <literal><![CDATA[
      L(x,y \ (L(z,z,z * u) * w),v5) = L(x,y \ (R(z,z,u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,37043,a(flip),b,38283,a),flip(a)].">
      <j1 rule="hyper" parents="64 37043 38283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38287">
    <literal><![CDATA[
      L(x,y \ (L(z,z,z * u) * w),v5) = L(x,y \ (L(z,z,u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,38285,a(flip),b,38286,a),flip(a)].">
      <j1 rule="hyper" parents="373 38285 38286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38288">
    <literal><![CDATA[
      a(x,K(y,z) / u,u \ 1) * (u * ((u \ K(y,z)) \ w)) = L(K(y,z) / u,K(y,z) / u,x) \ (u * w)
    ]]></literal>
    <justification jstring="[para(27321(a,1),38261(a,1,1))].">
      <j1 rule="para" parents="27321 38261"/>
    </justification>
  </clause>

  <clause id="38290">
    <literal><![CDATA[
      a(x,y \ K(z,u),y \ 1) * (y * ((y \ K(z,u)) \ w)) = L(K(z,u) / y,K(z,u) / y,x) \ (y * w)
    ]]></literal>
    <justification jstring="[para(31895(a,1),38288(a,1,1))].">
      <j1 rule="para" parents="31895 38288"/>
    </justification>
  </clause>

  <clause id="38291">
    <literal><![CDATA[
      L(K(x,y) / z,K(x,y) / z,u) \ (z * w) = a(u,z,z \ 1) * (z * ((z \ K(x,y)) \ w))
    ]]></literal>
    <justification jstring="[para(32033(a,1),38290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32033 38290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38292">
    <literal><![CDATA[
      L(K(x,y) / z,K(x,y) / z,u) \ (z * w) = z * (a(u,z,z \ 1) * ((z \ K(x,y)) \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,33455,a(flip),b,38291,a),flip(a)].">
      <j1 rule="hyper" parents="373 33455 38291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38294">
    <literal><![CDATA[
      L(K(x,y) / z,K(x,y) / z,u) \ (z * w) = z * (L(z \ K(x,y),z,u) \ w)
    ]]></literal>
    <justification jstring="[para(38140(a,1),38292(a,2,2))].">
      <j1 rule="para" parents="38140 38292"/>
    </justification>
  </clause>

  <clause id="38295">
    <literal><![CDATA[
      L(K(x,y) / z,z \ K(x,y),u) \ (z * w) = z * (L(z \ K(x,y),z,u) \ w)
    ]]></literal>
    <justification jstring="[para(29437(a,1),38294(a,1,1))].">
      <j1 rule="para" parents="29437 38294"/>
    </justification>
  </clause>

  <clause id="38296">
    <literal><![CDATA[
      L(K(x,y) / z,z,u) \ (z * w) = z * (L(z \ K(x,y),z,u) \ w)
    ]]></literal>
    <justification jstring="[para(29653(a,1),38295(a,1,1))].">
      <j1 rule="para" parents="29653 38295"/>
    </justification>
  </clause>

  <clause id="38298">
    <literal><![CDATA[
      a(x,(y * ((z * z) \ y)) * (u / ((((z * z) \ y) * w) / v5)),v6) = a(x,(((1 / y) * ((z * z) * w)) / v5) \ u,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,31895,a(flip),b,38262,a),flip(a)].">
      <j1 rule="hyper" parents="373 31895 38262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38299">
    <literal><![CDATA[
      L(x,y,(z \ (R(1 / u,w,v5) * v6)) * (v7 * v7)) = L(x,y,(R(u,w,v5) * v6) * L(z,z,L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(33601(a,1),38274(a,2,3,2))].">
      <j1 rule="para" parents="33601 38274"/>
    </justification>
  </clause>

  <clause id="38300">
    <literal><![CDATA[
      L(x,y,(z \ (R(1 / u,w,v5) * v6)) * (v7 * v7)) = L(x,y,(L(u,w,v5) * v6) * L(z,z,L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,33606,a(flip),b,38299,a),flip(a)].">
      <j1 rule="hyper" parents="373 33606 38299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38301">
    <literal><![CDATA[
      L(x,y,(z \ (R(1 / u,w,v5) * v6)) * (v7 * v7)) = L(x,y,z \ (L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,29158,a(flip),b,38300,a),flip(a)].">
      <j1 rule="hyper" parents="373 29158 38300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38302">
    <literal><![CDATA[
      L(x,y,z \ (R(1 / u,w,v5) * v6)) = L(x,y,z \ (L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(11866,a,38301,a)].">
      <j1 rule="hyper" parents="11866 38301"/>
    </justification>
  </clause>

  <clause id="38303">
    <literal><![CDATA[
      L(x,y,z \ (R(u,w,v5) * v6)) = L(x,y,z \ (L(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,36447,a(flip),b,38302,a)].">
      <j1 rule="hyper" parents="64 36447 38302"/>
    </justification>
  </clause>

  <clause id="38304">
    <literal><![CDATA[
      L(x,y,a(L(z,u,w),u,w)) = L(x,y,u \ (L(z,u,w) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,33427,a,b,38303,a)].">
      <j1 rule="hyper" parents="64 33427 38303"/>
    </justification>
  </clause>

  <clause id="38305">
    <literal><![CDATA[
      (K(x,y) * a(x,z,z)) * (x * (R(T(x,y),z,z) \ (u * a(x,z,z)))) = (R(x,z,z) / x) * L(u,x,a(z,z,x))
    ]]></literal>
    <justification jstring="[para(27(a,2),38278(a,1,2,2,1))].">
      <j1 rule="para" parents="27 38278"/>
    </justification>
  </clause>

  <clause id="38306">
    <literal><![CDATA[
      ((1 / x) * L(x,y,z)) / (u \ L(x,y,z)) = (x \ R(x,y,z)) / (u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30140,a(flip),b,38279,a)].">
      <j1 rule="hyper" parents="64 30140 38279"/>
    </justification>
  </clause>

  <clause id="38307">
    <literal><![CDATA[
      (x \ R(x,y,z)) / (u \ R(x,y,z)) = (x \ L(x,y,z)) / (u \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5590(a,1),38306(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5590 38306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38308">
    <literal><![CDATA[
      (x \ L(x,y,z)) / (u \ L(x,y,z)) = 1 / (u \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,31566,a(flip),b,38307,a),flip(a)].">
      <j1 rule="hyper" parents="64 31566 38307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38310">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ T((x \ L(x,y,z)) * (u \ L(x,y,z)),u \ L(x,y,z)) = T((x \ L(x,y,z)) / (1 / (u \ x)),L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(38308(a,1),25498(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="38308 25498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38311">
    <literal><![CDATA[
      a(x,(y * ((z * z) \ y)) * (u / ((((z * z) \ y) * w) / v5)),v6) = a(x,(v5 \ (y * ((z * z) * w))) \ u,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,33020,a(flip),b,38298,a),flip(a)].">
      <j1 rule="hyper" parents="373 33020 38298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38312">
    <literal><![CDATA[
      a(x,(y * ((z * z) \ y)) * (u / ((z * z) \ ((y * w) / v5))),v6) = a(x,(v5 \ (y * ((z * z) * w))) \ u,v6)
    ]]></literal>
    <justification jstring="[para(938(a,1),38311(a,1,2,2,2))].">
      <j1 rule="para" parents="938 38311"/>
    </justification>
  </clause>

  <clause id="38313">
    <literal><![CDATA[
      a(x,(y * ((z * z) \ y)) * ((u / ((y * w) / v5)) * (z * z)),v6) = a(x,(v5 \ (y * ((z * z) * w))) \ u,v6)
    ]]></literal>
    <justification jstring="[para(900(a,1),38312(a,1,2,2))].">
      <j1 rule="para" parents="900 38312"/>
    </justification>
  </clause>

  <clause id="38314">
    <literal><![CDATA[
      a(x,(y / ((z * u) / w)) * (z * ((v5 * v5) \ z)),v6) = a(x,(w \ (z * ((v5 * v5) * u))) \ y,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32211,a(flip),b,38313,a)].">
      <j1 rule="hyper" parents="64 32211 38313"/>
    </justification>
  </clause>

  <clause id="38316">
    <literal><![CDATA[
      a(x,(y \ (z * ((u * u) * w))) \ v5,v6) = a(x,(z * z) * (v5 / ((z * w) / y)),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32323,a(flip),b,38314,a),flip(a)].">
      <j1 rule="hyper" parents="64 32323 38314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38318">
    <literal><![CDATA[
      a(x,(y \ (z * ((u * u) * w))) \ v5,v6) = a(x,(z * z) * (((z * w) / y) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,31897,a(flip),b,38316,a),flip(a)].">
      <j1 rule="hyper" parents="373 31897 38316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38319">
    <literal><![CDATA[
      a(x,(y \ (z * ((u * u) * w))) \ v5,v6) = a(x,(z * z) * ((y \ (z * w)) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32074,a(flip),b,38318,a),flip(a)].">
      <j1 rule="hyper" parents="373 32074 38318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38320">
    <literal><![CDATA[
      a(x,(y \ (z * ((u * u) * w))) \ v5,v6) = a(x,(y \ (z * w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,11960,a(flip),b,38319,a),flip(a)].">
      <j1 rule="hyper" parents="373 11960 38319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38322">
    <literal><![CDATA[
      a(x,L(T(y * y,z) * u,z,w) \ v5,v6) = a(x,(T(w * z,v7) \ (w * (z * u))) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32170,a(flip),b,38320,a)].">
      <j1 rule="hyper" parents="64 32170 38320"/>
    </justification>
  </clause>

  <clause id="38324">
    <literal><![CDATA[
      a(x,L(T(y * y,z) * u,z,w) \ v5,v6) = a(x,L(K(v7,w * z) * u,z,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(26090(a,1),38322(a,2,2,1))].">
      <j1 rule="para" parents="26090 38322"/>
    </justification>
  </clause>

  <clause id="38325">
    <literal><![CDATA[
      a(x,L(T(y * y,z) * u,z,w) \ v5,v6) = a(x,L(u,z,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(23126(a,1),38324(a,2,2,1,1))].">
      <j1 rule="para" parents="23126 38324"/>
    </justification>
  </clause>

  <clause id="38326">
    <literal><![CDATA[
      a(x,L(y * (z * z),u,w) \ v5,v6) = a(x,L(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,34355,a(flip),b,38325,a)].">
      <j1 rule="hyper" parents="64 34355 38325"/>
    </justification>
  </clause>

  <clause id="38328">
    <literal><![CDATA[
      a(x,L((y * y) / z,u,w) \ v5,v6) = a(x,L(1 / z,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32250,a(flip),b,38326,a)].">
      <j1 rule="hyper" parents="64 32250 38326"/>
    </justification>
  </clause>

  <clause id="38330">
    <literal><![CDATA[
      a(x,L((y * y) / z,u,w) \ v5,v6) = a(x,L(z \ 1,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,31994,a(flip),b,38328,a),flip(a)].">
      <j1 rule="hyper" parents="373 31994 38328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38331">
    <literal><![CDATA[
      a(x,L(y \ 1,z,u) \ w,v5) = a(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[para(11(a,1),38330(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="11 38330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38332">
    <literal><![CDATA[
      K(x,y) * (a(x,z,z) * (x * (R(T(x,y),z,z) \ (u * a(x,z,z))))) = (R(x,z,z) / x) * L(u,x,a(z,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,23073,a(flip),b,38305,a)].">
      <j1 rule="hyper" parents="64 23073 38305"/>
    </justification>
  </clause>

  <clause id="38333">
    <literal><![CDATA[
      K(x,y) * (x * (a(x,z,z) * (R(T(x,y),z,z) \ (u * a(x,z,z))))) = (R(x,z,z) / x) * L(u,x,a(z,z,x))
    ]]></literal>
    <justification jstring="[para(29307(a,1),38332(a,1,2))].">
      <j1 rule="para" parents="29307 38332"/>
    </justification>
  </clause>

  <clause id="38334">
    <literal><![CDATA[
      T(x,y) * (a(x,z,z) * (R(T(x,y),z,z) \ (u * a(x,z,z)))) = (R(x,z,z) / x) * L(u,x,a(z,z,x))
    ]]></literal>
    <justification jstring="[hyper(5985,a,38333,a)].">
      <j1 rule="hyper" parents="5985 38333"/>
    </justification>
  </clause>

  <clause id="38335">
    <literal><![CDATA[
      (R(x,y,y) / x) * L(z,x,a(y,y,x)) = L(z * a(x,y,y),x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,34738,a(flip),b,38334,a),flip(a)].">
      <j1 rule="hyper" parents="64 34738 38334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38336">
    <literal><![CDATA[
      L(x * a(y,z,z),y,a(z,z,y)) = a(y,z,z) * L(x,y,a(z,z,y))
    ]]></literal>
    <justification jstring="[para(15990(a,1),38335(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15990 38335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38337">
    <literal><![CDATA[
      a(x,y,y) * L(z,x,a(y,y,x)) = x * ((a(x,y,y) \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37845,a(flip),b,38336,a),flip(a)].">
      <j1 rule="hyper" parents="64 37845 38336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38338">
    <literal><![CDATA[
      a(x,y,y) * L(z,x,a(y,y,x)) = R(x,y,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,35660,a(flip),b,38337,a),flip(a)].">
      <j1 rule="hyper" parents="373 35660 38337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38339">
    <literal><![CDATA[
      L(x / R(y,z,z),y,a(z,z,y)) = a(y,z,z) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(139,a,25148,a(flip),b,38338,a),flip(a)].">
      <j1 rule="hyper" parents="139 25148 38338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38340">
    <literal><![CDATA[
      a(x,y,y) * L(z,x,a(x,y,y)) = R(x,y,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29292,a,b,38338,a)].">
      <j1 rule="hyper" parents="64 29292 38338"/>
    </justification>
  </clause>

  <clause id="38341">
    <literal><![CDATA[
      L(x,(x \ y) / y,(x \ y) / y) / ((x \ y) / y) = (((x \ y) / y) \ 1) * (K(x \ 1,x) * x)
    ]]></literal>
    <justification jstring="[para(7358(a,1),24628(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7358 24628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38342">
    <literal><![CDATA[
      L(x,(x \ y) / y,(x \ y) / y) / ((x \ y) / y) = (((x \ y) / y) \ 1) * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(373,a,5983,a,b,38341,a),flip(a)].">
      <j1 rule="hyper" parents="373 5983 38341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38344">
    <literal><![CDATA[
      L(x,y \ (x \ y),y \ (x \ y)) / ((x \ y) / y) = (((x \ y) / y) \ 1) * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(29527(a,1),38342(a,1,1))].">
      <j1 rule="para" parents="29527 38342"/>
    </justification>
  </clause>

  <clause id="38345">
    <literal><![CDATA[
      (((x \ y) / y) \ 1) * (1 / (1 / x)) = (1 / (1 / x)) / ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(35027(a,1),38344(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35027 38344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38346">
    <literal><![CDATA[
      (((x \ y) / y) \ 1) * (1 / (1 / x)) = x / (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,26933,a(flip),b,38345,a),flip(a)].">
      <j1 rule="hyper" parents="373 26933 38345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38348">
    <literal><![CDATA[
      R(x / (y / (x * y)),x,x \ 1) = x / (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,37734,a,b,38346,a)].">
      <j1 rule="hyper" parents="64 37734 38346"/>
    </justification>
  </clause>

  <clause id="38349">
    <literal><![CDATA[
      L(x,(L(y \ z,K(y,y \ 1),K(y,y \ 1)) * u) * w,v5) = L(x,((((y \ 1) * (y * y)) \ z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(14692(a,1),25810(a,2,2,1,1,1))].">
      <j1 rule="para" parents="14692 25810"/>
    </justification>
  </clause>

  <clause id="38350">
    <literal><![CDATA[
      L(x,(L(y \ z,K(y,y \ 1),K(y,y \ 1)) * u) * w,v5) = L(x,(((y * y) \ ((y \ 1) \ z)) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(486(a,1),38349(a,2,2,1,1))].">
      <j1 rule="para" parents="486 38349"/>
    </justification>
  </clause>

  <clause id="38351">
    <literal><![CDATA[
      L(x,(L(y \ z,K(y,y \ 1),K(y,y \ 1)) * u) * w,v5) = L(x,(((y \ 1) \ z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,11781,a(flip),b,38350,a),flip(a)].">
      <j1 rule="hyper" parents="373 11781 38350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38353">
    <literal><![CDATA[
      L(x,(((y \ 1) \ z) * u) * w,v5) = L(x,((y \ z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[para(2217(a,1),38351(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2217 38351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38354">
    <literal><![CDATA[
      L(x,(L(y * z,y,y) * u) * w,v5) = L(x,((y \ z) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,36216,a,b,38353,a)].">
      <j1 rule="hyper" parents="64 36216 38353"/>
    </justification>
  </clause>

  <clause id="38355">
    <literal><![CDATA[
      L(x,(y * ((z \ 1) \ u)) * w,v5) = L(x,((z \ u) * y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29455,a,b,38353,a)].">
      <j1 rule="hyper" parents="64 29455 38353"/>
    </justification>
  </clause>

  <clause id="38361">
    <literal><![CDATA[
      L(x,(y * L(z * u,z,z)) * w,v5) = L(x,((z \ u) * y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29455,a,b,38354,a)].">
      <j1 rule="hyper" parents="64 29455 38354"/>
    </justification>
  </clause>

  <clause id="38362">
    <literal><![CDATA[
      L(x,((y \ (z / y)) * u) * w,v5) = L(x,(u * L(z,y,y)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29836,a(flip),b,38361,a),flip(a)].">
      <j1 rule="hyper" parents="64 29836 38361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38363">
    <literal><![CDATA[
      L(x,(y * L(z * u,u,u)) * w,v5) = L(x,((u \ z) * y) * w,v5)
    ]]></literal>
    <justification jstring="[para(11(a,1),38362(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11 38362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38364">
    <literal><![CDATA[
      K(R(x,x,x),x \ ((1 / x) \ y)) * ((x \ 1) \ (L(x,z,u) \ y)) = ((x \ 1) \ y) / L(R(x,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(1690(a,1),26983(a,1,1,2))].">
      <j1 rule="para" parents="1690 26983"/>
    </justification>
  </clause>

  <clause id="38365">
    <literal><![CDATA[
      K(R(x,x,x),y) * ((x \ 1) \ (L(x,z,u) \ y)) = ((x \ 1) \ y) / L(R(x,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(14475(a,1),38364(a,1,1))].">
      <j1 rule="para" parents="14475 38364"/>
    </justification>
  </clause>

  <clause id="38366">
    <literal><![CDATA[
      ((x \ 1) \ y) / L(R(x,x,x),z,u) = K(x,y) * ((x \ 1) \ (L(x,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(7388(a,1),38365(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7388 38365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38368">
    <literal><![CDATA[
      ((x \ 1) \ y) / L(R(x,x,x),z,u) = ((1 / x) \ y) / L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,36188,a(flip),b,38366,a),flip(a)].">
      <j1 rule="hyper" parents="373 36188 38366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38371">
    <literal><![CDATA[
      R(x \ R(x,y,z),u / (u / x),((u / x) \ u) \ w) * w = R(x * K(x \ u,x),y,z) * ((u / (u / x)) \ w)
    ]]></literal>
    <justification jstring="[para(26209(a,1),27058(a,1,1))].">
      <j1 rule="para" parents="26209 27058"/>
    </justification>
  </clause>

  <clause id="38372">
    <literal><![CDATA[
      (x \ (y * (x * (y \ 1)))) * R(z,y * (x \ (y \ x)),z) = T(z * (((y \ 1) * (y * (x \ (y \ x)))) \ (y \ 1)),z)
    ]]></literal>
    <justification jstring="[para(37787(a,1),27291(a,1,1))].">
      <j1 rule="para" parents="37787 27291"/>
    </justification>
  </clause>

  <clause id="38373">
    <literal><![CDATA[
      ((x * (1 / y)) * R(y,z,u)) / (y \ R(y,z,u)) = a(x,1 / y,R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(34868(a,1),27650(a,1,2))].">
      <j1 rule="para" parents="34868 27650"/>
    </justification>
  </clause>

  <clause id="38374">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ ((u * (1 / x)) * R(x,y,z)) = a(u,1 / x,R(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,23705,a(flip),b,38373,a)].">
      <j1 rule="hyper" parents="64 23705 38373"/>
    </justification>
  </clause>

  <clause id="38376">
    <literal><![CDATA[
      R((x * (1 / y)) / (1 / y),y,L(y,z,u)) = a(x,1 / y,R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,31537,a(flip),b,38374,a)].">
      <j1 rule="hyper" parents="64 31537 38374"/>
    </justification>
  </clause>

  <clause id="38377">
    <literal><![CDATA[
      a(x,1 / y,R(y,z,u)) * x = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),38376(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 38376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38378">
    <literal><![CDATA[
      a(x,1 / y,L(y,z,u)) * x = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(27644(a,1),38377(a,1,1))].">
      <j1 rule="para" parents="27644 38377"/>
    </justification>
  </clause>

  <clause id="38379">
    <literal><![CDATA[
      x * a(x,y,L(y,z,u)) = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,23953,a(flip),b,38378,a)].">
      <j1 rule="hyper" parents="64 23953 38378"/>
    </justification>
  </clause>

  <clause id="38380">
    <literal><![CDATA[
      x \ R(x,y,L(y,z,u)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,38378,a(flip),b,23953,a(flip))].">
      <j1 rule="hyper" parents="139 38378 23953"/>
    </justification>
  </clause>

  <clause id="38381">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) * x = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11966(a,1),38378(a,1,1))].">
      <j1 rule="para" parents="11966 38378"/>
    </justification>
  </clause>

  <clause id="38382">
    <literal><![CDATA[
      L(x,y,z) \ (T(x * x,x) * R(x \ (x \ L(x,y,z)),u,L(u,w,v5))) = a(x \ (x \ L(x,y,z)),u,L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,5655,a,b,38380,a)].">
      <j1 rule="hyper" parents="64 5655 38380"/>
    </justification>
  </clause>

  <clause id="38383">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,L(u,w,v5))) = a(x,y,a(z,u,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(38380(a,1),31322(a,1,3)),flip(a)].">
      <j1 rule="para" parents="38380 31322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38384">
    <literal><![CDATA[
      a(x,y,L(y,a(z,z,u),w)) \ R(x,y,L(y,a(u,z,z),w)) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,31822,a,b,38381,a)].">
      <j1 rule="hyper" parents="139 31822 38381"/>
    </justification>
  </clause>

  <clause id="38385">
    <literal><![CDATA[
      L(x \ R(x,y,((z \ (u \ w)) * (z \ (u \ w))) * v5),x,y * v5) = a(x,y,((z \ (w / u)) * (z \ (w / u))) * v5)
    ]]></literal>
    <justification jstring="[para(27192(a,1),28038(a,1,1,2))].">
      <j1 rule="para" parents="27192 28038"/>
    </justification>
  </clause>

  <clause id="38386">
    <literal><![CDATA[
      T(x \ a(x,x,y),x \ ((y / x) * L(x,z,u))) = (L(x,z,u) * y) \ ((y / x) * L(x,z,u))
    ]]></literal>
    <justification jstring="[para(35458(a,1),30213(a,1,1,2))].">
      <j1 rule="para" parents="35458 30213"/>
    </justification>
  </clause>

  <clause id="38387">
    <literal><![CDATA[
      T(x \ a(x,x,y),((x \ y) / x) * L(x,z,u)) = (L(x,z,u) * y) \ ((y / x) * L(x,z,u))
    ]]></literal>
    <justification jstring="[para(25126(a,1),38386(a,1,2))].">
      <j1 rule="para" parents="25126 38386"/>
    </justification>
  </clause>

  <clause id="38389">
    <literal><![CDATA[
      T(x \ a(x,x,y),x \ y) = (L(x,z,u) * y) \ ((y / x) * L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,28324,a(flip),b,38387,a)].">
      <j1 rule="hyper" parents="64 28324 38387"/>
    </justification>
  </clause>

  <clause id="38391">
    <literal><![CDATA[
      (L(x,y,z) * u) \ ((u / x) * L(x,y,z)) = (x * u) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,30125,a(flip),b,38389,a),flip(a)].">
      <j1 rule="hyper" parents="64 30125 38389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38392">
    <literal><![CDATA[
      a(x \ y,T(x,x * y) \ 1,x \ 1) \ (x \ y) = ((y / x) / (1 / x)) / (1 / (T(x,x * y) \ 1))
    ]]></literal>
    <justification jstring="[para(27316(a,1),30578(a,1,1))].">
      <j1 rule="para" parents="27316 30578"/>
    </justification>
  </clause>

  <clause id="38393">
    <literal><![CDATA[
      a(x \ y,T(x,x * y),x \ 1) \ (x \ y) = ((y / x) / (1 / x)) / (1 / (T(x,x * y) \ 1))
    ]]></literal>
    <justification jstring="[para(11980(a,1),38392(a,1,1))].">
      <j1 rule="para" parents="11980 38392"/>
    </justification>
  </clause>

  <clause id="38395">
    <literal><![CDATA[
      ((x / y) / (1 / y)) / (1 / (T(y,y * x) \ 1)) = a(y \ x,y,y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(31892(a,1),38393(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31892 38393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38396">
    <literal><![CDATA[
      ((x / y) / (1 / y)) / (1 / (T(y,y * x) \ 1)) = ((y \ x) / (y \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,33233,a(flip),b,38395,a),flip(a)].">
      <j1 rule="hyper" parents="373 33233 38395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38398">
    <literal><![CDATA[
      ((x / y) / (1 / y)) / T(y,y * x) = ((y \ x) / (y \ 1)) / y
    ]]></literal>
    <justification jstring="[para(79(a,1),38396(a,1,2))].">
      <j1 rule="para" parents="79 38396"/>
    </justification>
  </clause>

  <clause id="38399">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) / x = x \ ((y / x) / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,11607,a(flip),b,38398,a),flip(a)].">
      <j1 rule="hyper" parents="64 11607 38398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38401">
    <literal><![CDATA[
      (x \ y) * (x * (y \ (y / x))) = x \ ((y / x) / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,33438,a,b,38399,a)].">
      <j1 rule="hyper" parents="64 33438 38399"/>
    </justification>
  </clause>

  <clause id="38402">
    <literal><![CDATA[
      x \ ((y / x) / (x \ 1)) = (K(z,u) * y) / (1 / ((K(z,u) * y) \ (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,36123,a,b,38401,a),flip(a)].">
      <j1 rule="hyper" parents="64 36123 38401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38403">
    <literal><![CDATA[
      x \ ((y / x) / (x \ 1)) = (K(z,u) * y) / (1 / (y \ (K(u,z) * (x \ y))))
    ]]></literal>
    <justification jstring="[para(23199(a,1),38402(a,2,2,2))].">
      <j1 rule="para" parents="23199 38402"/>
    </justification>
  </clause>

  <clause id="38404">
    <literal><![CDATA[
      x \ ((y / x) / (x \ 1)) = K(z,u) * (y / (1 / (y \ (K(u,z) * (x \ y)))))
    ]]></literal>
    <justification jstring="[hyper(373,a,23224,a(flip),b,38403,a),flip(a)].">
      <j1 rule="hyper" parents="373 23224 38403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38405">
    <literal><![CDATA[
      x \ ((y / x) / (x \ 1)) = K(z,u) * (K(u,z) * (y / (1 / (y \ (x \ y)))))
    ]]></literal>
    <justification jstring="[para(25842(a,1),38404(a,2,2))].">
      <j1 rule="para" parents="25842 38404"/>
    </justification>
  </clause>

  <clause id="38406">
    <literal><![CDATA[
      x \ ((y / x) / (x \ 1)) = K(z,u) * (K(u,z) * ((1 / (y \ (y / x))) \ y))
    ]]></literal>
    <justification jstring="[para(35990(a,1),38405(a,2,2,2))].">
      <j1 rule="para" parents="35990 38405"/>
    </justification>
  </clause>

  <clause id="38407">
    <literal><![CDATA[
      K(x,y) * ((K(x,y) / (z \ (z / y))) \ z) = y \ ((z / y) / (y \ 1))
    ]]></literal>
    <justification jstring="[para(25746(a,1),38406(a,2,2)),flip(a)].">
      <j1 rule="para" parents="25746 38406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38408">
    <literal><![CDATA[
      K(x * y,x) * (((z \ (z / x)) \ K(x \ y,x)) \ z) = x \ ((z / x) / (x \ 1))
    ]]></literal>
    <justification jstring="[para(36966(a,1),38407(a,1,2,1))].">
      <j1 rule="para" parents="36966 38407"/>
    </justification>
  </clause>

  <clause id="38409">
    <literal><![CDATA[
      (L(x,y,z) * (a(x,x,u) * u)) * K(1 / x,L(x,y,z) * u) = (L(x,y,z) * (x \ u)) / (1 / x)
    ]]></literal>
    <justification jstring="[para(28690(a,1),30997(a,1,2))].">
      <j1 rule="para" parents="28690 30997"/>
    </justification>
  </clause>

  <clause id="38410">
    <literal><![CDATA[
      (L(x,y,z) * (a(x,x,u) * u)) * K(1 / x,x * u) = (L(x,y,z) * (x \ u)) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,28345,a(flip),b,38409,a)].">
      <j1 rule="hyper" parents="64 28345 38409"/>
    </justification>
  </clause>

  <clause id="38413">
    <literal><![CDATA[
      (L(x,y,z) * (a(x,x,u) * u)) * K(x \ 1,u * x) = (L(x,y,z) * (x \ u)) / (1 / x)
    ]]></literal>
    <justification jstring="[para(11114(a,1),38410(a,1,2))].">
      <j1 rule="para" parents="11114 38410"/>
    </justification>
  </clause>

  <clause id="38414">
    <literal><![CDATA[
      L(x,y,z) * ((a(x,x,u) * u) * K(x \ 1,u * x)) = (L(x,y,z) * (x \ u)) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(23059,a,38413,a)].">
      <j1 rule="hyper" parents="23059 38413"/>
    </justification>
  </clause>

  <clause id="38415">
    <literal><![CDATA[
      L(x,y,z) * (a(x,x,u) * (u * K(x \ 1,u * x))) = (L(x,y,z) * (x \ u)) / (1 / x)
    ]]></literal>
    <justification jstring="[para(23053(a,1),38414(a,1,2))].">
      <j1 rule="para" parents="23053 38414"/>
    </justification>
  </clause>

  <clause id="38416">
    <literal><![CDATA[
      L(x,y,z) * (u * ((u / T(x * u,x \ 1)) * x)) = (L(x,y,z) * (x \ u)) / (1 / x)
    ]]></literal>
    <justification jstring="[para(30442(a,1),38415(a,1,2))].">
      <j1 rule="para" parents="30442 38415"/>
    </justification>
  </clause>

  <clause id="38417">
    <literal><![CDATA[
      L(x,y,z) * (u * (((x * u) \ u) * x)) = (L(x,y,z) * (x \ u)) / (1 / x)
    ]]></literal>
    <justification jstring="[para(4591(a,1),38416(a,1,2,2,1))].">
      <j1 rule="para" parents="4591 38416"/>
    </justification>
  </clause>

  <clause id="38418">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) / (1 / x) = L(x,y,z) * (x \ (u / (1 / x)))
    ]]></literal>
    <justification jstring="[para(37473(a,1),38417(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37473 38417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38419">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u / (1 / x))) = u / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,35204,a(flip),b,38418,a),flip(a)].">
      <j1 rule="hyper" parents="64 35204 38418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38420">
    <literal><![CDATA[
      L(x,y,z) * (u / (1 / x)) = x * (u / (1 / L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(145,a,38419,a(flip),b,2325,a),flip(a)].">
      <j1 rule="hyper" parents="145 38419 2325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38421">
    <literal><![CDATA[
      a((x \ L(T(y * z,z),(y / z) / y,(y / z) / y)) * u,w,v5) = a((x \ (y / T(z,y))) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(6843(a,1),32862(a,2,1,1,2))].">
      <j1 rule="para" parents="6843 32862"/>
    </justification>
  </clause>

  <clause id="38422">
    <literal><![CDATA[
      a((x \ L(T(y * z,z),(y / z) / y,(y / z) / y)) * u,w,v5) = a((x \ (T(z,y) \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32492,a(flip),b,38421,a),flip(a)].">
      <j1 rule="hyper" parents="373 32492 38421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38423">
    <literal><![CDATA[
      a((x \ L(T(y * z,z),(y / z) / y,(y / z) / y)) * u,w,v5) = a((x \ (z \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32690,a(flip),b,38422,a),flip(a)].">
      <j1 rule="hyper" parents="373 32690 38422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38425">
    <literal><![CDATA[
      a((x \ L(T(y * z,z),(y / z) / y,y \ (y / z))) * u,w,v5) = a((x \ (z \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(23216(a,1),38423(a,1,1,1,2))].">
      <j1 rule="para" parents="23216 38423"/>
    </justification>
  </clause>

  <clause id="38426">
    <literal><![CDATA[
      a((x \ L(T(y * z,z),(y / z) / y,y \ (z \ y))) * u,w,v5) = a((x \ (z \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(29023(a,1),38425(a,1,1,1,2))].">
      <j1 rule="para" parents="29023 38425"/>
    </justification>
  </clause>

  <clause id="38427">
    <literal><![CDATA[
      a((x \ L(T(y * z,z),y \ (y / z),y \ (z \ y))) * u,w,v5) = a((x \ (z \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(29437(a,1),38426(a,1,1,1,2))].">
      <j1 rule="para" parents="29437 38426"/>
    </justification>
  </clause>

  <clause id="38428">
    <literal><![CDATA[
      a((x \ L(T(y * z,z),y \ (z \ y),y \ (z \ y))) * u,w,v5) = a((x \ (z \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(29552(a,1),38427(a,1,1,1,2))].">
      <j1 rule="para" parents="29552 38427"/>
    </justification>
  </clause>

  <clause id="38429">
    <literal><![CDATA[
      a((x \ L(T(y * z,z),z,z)) * u,w,v5) = a((x \ (z \ y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(35166(a,1),38428(a,1,1,1,2))].">
      <j1 rule="para" parents="35166 38428"/>
    </justification>
  </clause>

  <clause id="38430">
    <literal><![CDATA[
      a(x * (y \ L(z * u,u,u)),w,v5) = a((y \ (u \ z)) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32530,a(flip),b,38429,a)].">
      <j1 rule="hyper" parents="64 32530 38429"/>
    </justification>
  </clause>

  <clause id="38433">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((T(w,v5) * u) * z))) = a(x,y,R(T(w,T(v5,u)),u,w) * a(u,R(T(w,T(v5,u)),u,w),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27495,a(flip),b,33464,a)].">
      <j1 rule="hyper" parents="64 27495 33464"/>
    </justification>
  </clause>

  <clause id="38435">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((T(w,v5) * u) * z))) = a(x,y,R(T(w,T(v5,u)),u,w) * a(u,L(T(w,T(v5,u)),u,w),z))
    ]]></literal>
    <justification jstring="[para(32197(a,1),38433(a,2,3,2))].">
      <j1 rule="para" parents="32197 38433"/>
    </justification>
  </clause>

  <clause id="38436">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((T(w,v5) * u) * z))) = a(x,y,R(T(w,T(v5,u)),u,w) * a(u,L(w,u,w),z))
    ]]></literal>
    <justification jstring="[para(31912(a,1),38435(a,2,3,2))].">
      <j1 rule="para" parents="31912 38435"/>
    </justification>
  </clause>

  <clause id="38437">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((T(w,v5) * u) * z))) = a(x,y,R(T(w,T(v5,u)),u,w) * a(u,w,z))
    ]]></literal>
    <justification jstring="[para(13828(a,1),38436(a,2,3,2))].">
      <j1 rule="para" parents="13828 38436"/>
    </justification>
  </clause>

  <clause id="38439">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((T(w,v5) * u) * z))) = a(x,y,a(u,w,z) * R(w,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27529,a(flip),b,38437,a),flip(a)].">
      <j1 rule="hyper" parents="373 27529 38437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38442">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((T(w,v5) * u) * z))) = a(x,y,a(u,w,z) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,13870,a(flip),b,38439,a),flip(a)].">
      <j1 rule="hyper" parents="373 13870 38439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38444">
    <literal><![CDATA[
      L((1 / x) \ 1,1 / x,y * L(L(x,z,z) \ z,x,x)) = L(x,1 / x,R(z,z,x) * (y * (1 / x)))
    ]]></literal>
    <justification jstring="[para(82(a,1),34056(a,2,1))].">
      <j1 rule="para" parents="82 34056"/>
    </justification>
  </clause>

  <clause id="38445">
    <literal><![CDATA[
      L((1 / x) \ 1,1 / x,y * L(L(x,z,z) \ z,x,x)) = L(x,1 / x,R(z,z,x) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,29121,a(flip),b,38444,a),flip(a)].">
      <j1 rule="hyper" parents="373 29121 38444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38446">
    <literal><![CDATA[
      L((1 / x) \ 1,1 / x,y * L(L(x,z,z) \ z,x,x)) = L(x,1 / x,L(z,z,x) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,33584,a(flip),b,38445,a),flip(a)].">
      <j1 rule="hyper" parents="373 33584 38445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38447">
    <literal><![CDATA[
      L((1 / x) \ 1,1 / x,y * L(L(x,z,z) \ z,x,x)) = L(x,x,L(z,z,x) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,11776,a(flip),b,38446,a),flip(a)].">
      <j1 rule="hyper" parents="373 11776 38446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38448">
    <literal><![CDATA[
      L(x,1 / x,y * L(L(x,z,z) \ z,x,x)) = L(x,x,L(z,z,x) * (x * y))
    ]]></literal>
    <justification jstring="[para(82(a,1),38447(a,1,1))].">
      <j1 rule="para" parents="82 38447"/>
    </justification>
  </clause>

  <clause id="38449">
    <literal><![CDATA[
      L(x,1 / x,y * ((1 / x) * R(z,z,x))) = L(x,x,L(z,z,x) * (x * y))
    ]]></literal>
    <justification jstring="[para(25118(a,1),38448(a,1,3,2))].">
      <j1 rule="para" parents="25118 38448"/>
    </justification>
  </clause>

  <clause id="38450">
    <literal><![CDATA[
      L(x,1 / x,y * ((1 / x) * L(z,z,x))) = L(x,x,L(z,z,x) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,33615,a(flip),b,38449,a)].">
      <j1 rule="hyper" parents="64 33615 38449"/>
    </justification>
  </clause>

  <clause id="38451">
    <literal><![CDATA[
      L(x,1 / x,y * ((x \ 1) * L(z,z,x))) = L(x,x,L(z,z,x) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29089,a(flip),b,38450,a)].">
      <j1 rule="hyper" parents="64 29089 38450"/>
    </justification>
  </clause>

  <clause id="38452">
    <literal><![CDATA[
      L(x,1 / x,(x * L(y,y,x)) * z) = L(x,x,L(y,y,x) * (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,23995,a(flip),b,38451,a)].">
      <j1 rule="hyper" parents="64 23995 38451"/>
    </justification>
  </clause>

  <clause id="38453">
    <literal><![CDATA[
      L(x,x,L(y,y,x) * (x * z)) = L(x,1 / x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29375,a(flip),b,38452,a),flip(a)].">
      <j1 rule="hyper" parents="64 29375 38452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38454">
    <literal><![CDATA[
      L(x,x,L(y,y,x) * (x * z)) = L(x,x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,11776,a(flip),b,38453,a),flip(a)].">
      <j1 rule="hyper" parents="373 11776 38453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38455">
    <literal><![CDATA[
      L(x,x,(y \ x) * z) = L(x,x,y * (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,37651,a(flip),b,38454,a),flip(a)].">
      <j1 rule="hyper" parents="64 37651 38454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38456">
    <literal><![CDATA[
      R(x,y / R(T(R(z,u,w),y),R(z,u,w),R(z,u,w)),v5) = R(x,L(z,u,w) * (R(z,u,w) \ (R(z,u,w) \ y)),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26559,a(flip),b,34464,a),flip(a)].">
      <j1 rule="hyper" parents="373 26559 34464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38457">
    <literal><![CDATA[
      ((x \ 1) * y) \ (((1 / (x \ 1)) \ a(z,x,u)) * (a(z,x,u) \ y)) = a((x \ 1) \ 1,a(z,x,u),a(z,x,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1681,a(flip),b,35782,a)].">
      <j1 rule="hyper" parents="64 1681 35782"/>
    </justification>
  </clause>

  <clause id="38458">
    <literal><![CDATA[
      K(x,R(T(y / (z \ u),y * (z * (T(u,z) \ w))),z \ u,z) * v5) = K(x,T((y * z) / ((z \ u) * z),w) * v5)
    ]]></literal>
    <justification jstring="[para(25009(a,1),36147(a,1,2,1,1))].">
      <j1 rule="para" parents="25009 36147"/>
    </justification>
  </clause>

  <clause id="38459">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ L(a(y,z,u),a(y,z,u),x)),a(y,z,u)) = T(x * a(x,a(y,z,u),a(y,z,u)),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,37639,a,b,36307,a),flip(a)].">
      <j1 rule="hyper" parents="373 37639 36307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38460">
    <literal><![CDATA[
      R(x \ R(x,y,z),u / (u / x),x \ w) * w = R(x * K(x \ u,x),y,z) * ((u / (u / x)) \ w)
    ]]></literal>
    <justification jstring="[para(82(a,1),38371(a,1,1,3,1))].">
      <j1 rule="para" parents="82 38371"/>
    </justification>
  </clause>

  <clause id="38462">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,x \ u) * u = R(x * K(x \ w,x),y,z) * ((w / (w / x)) \ u)
    ]]></literal>
    <justification jstring="[para(26411(a,1),38460(a,1,1))].">
      <j1 rule="para" parents="26411 38460"/>
    </justification>
  </clause>

  <clause id="38463">
    <literal><![CDATA[
      R(x * K(x \ y,x),z,u) * ((y / (y / x)) \ w) = L(x \ R(x,z,u),x,x \ w) * w
    ]]></literal>
    <justification jstring="[para(25606(a,1),38462(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25606 38462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38465">
    <literal><![CDATA[
      R(x,y,z) * (K(x \ u,x) * ((u / (u / x)) \ w)) = L(x \ R(x,y,z),x,x \ w) * w
    ]]></literal>
    <justification jstring="[hyper(64,a,25983,a(flip),b,38463,a)].">
      <j1 rule="hyper" parents="64 25983 38463"/>
    </justification>
  </clause>

  <clause id="38466">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,x \ u) * u = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(6599(a,1),38465(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6599 38465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38467">
    <literal><![CDATA[
      T(x * (((y \ 1) * (y * (z \ (y \ z)))) \ (y \ 1)),x) = (z \ (y * (z * (y \ 1)))) * x
    ]]></literal>
    <justification jstring="[para(26630(a,1),38372(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26630 38372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38468">
    <literal><![CDATA[
      T(x * ((y \ (z \ y)) \ (z \ 1)),x) = (y \ (z * (y * (z \ 1)))) * x
    ]]></literal>
    <justification jstring="[para(26261(a,1),38467(a,1,1,2,1))].">
      <j1 rule="para" parents="26261 38467"/>
    </justification>
  </clause>

  <clause id="38469">
    <literal><![CDATA[
      T(x * (y \ (z * (y * (z \ 1)))),x) = (y \ (z * (y * (z \ 1)))) * x
    ]]></literal>
    <justification jstring="[para(37787(a,1),38468(a,1,1,2))].">
      <j1 rule="para" parents="37787 38468"/>
    </justification>
  </clause>

  <clause id="38470">
    <literal><![CDATA[
      T(x / (y * (z \ (y \ z))),x) = (z \ (y * (z * (y \ 1)))) * x
    ]]></literal>
    <justification jstring="[para(37797(a,1),38469(a,1,1))].">
      <j1 rule="para" parents="37797 38469"/>
    </justification>
  </clause>

  <clause id="38471">
    <literal><![CDATA[
      (x \ (y * (x * (y \ 1)))) * z = (y * (x \ (y \ x))) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,26631,a(flip),b,38470,a),flip(a)].">
      <j1 rule="hyper" parents="64 26631 38470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38472">
    <literal><![CDATA[
      (x \ (y * (x * (y \ 1)))) \ z = (y * (x \ (y \ x))) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,9,a(flip),b,38471,a)].">
      <j1 rule="hyper" parents="139 9 38471"/>
    </justification>
  </clause>

  <clause id="38473">
    <literal><![CDATA[
      (x * (y \ (x \ y))) \ ((x * x) * z) = (y \ (x * (y * x))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,37429,a(flip),b,38471,a),flip(a)].">
      <j1 rule="hyper" parents="64 37429 38471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38474">
    <literal><![CDATA[
      (x \ (y * (x * (y \ 1)))) \ z = ((y * (x * (y \ 1))) \ x) * z
    ]]></literal>
    <justification jstring="[para(30452(a,2),38472(a,2,1))].">
      <j1 rule="para" parents="30452 38472"/>
    </justification>
  </clause>

  <clause id="38475">
    <literal><![CDATA[
      ((1 / x) * (y \ (x \ y))) \ z = (y \ (x * (y * x))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,941,a(flip),b,38473,a)].">
      <j1 rule="hyper" parents="64 941 38473"/>
    </justification>
  </clause>

  <clause id="38476">
    <literal><![CDATA[
      ((1 / x) * (y \ (x \ y))) * z = (y \ (x * (y * x))) \ z
    ]]></literal>
    <justification jstring="[hyper(395,a,38475,a)].">
      <j1 rule="hyper" parents="395 38475"/>
    </justification>
  </clause>

  <clause id="38477">
    <literal><![CDATA[
      (x * x) * (((x * (y * x)) \ y) * z) = (y \ (x * (y * (x \ 1)))) \ z
    ]]></literal>
    <justification jstring="[hyper(373,a,15932,a,b,38474,a)].">
      <j1 rule="hyper" parents="373 15932 38474"/>
    </justification>
  </clause>

  <clause id="38478">
    <literal><![CDATA[
      (x \ (y * (x * y))) \ z = ((y * (x * y)) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(35,a,37430,a,b,38477,a)].">
      <j1 rule="hyper" parents="35 37430 38477"/>
    </justification>
  </clause>

  <clause id="38479">
    <literal><![CDATA[
      (x \ (y * (x * y))) \ 1 = (y * (x * y)) \ x
    ]]></literal>
    <justification jstring="[hyper(16068,a,38478,a)].">
      <j1 rule="hyper" parents="16068 38478"/>
    </justification>
  </clause>

  <clause id="38480">
    <literal><![CDATA[
      ((x * (y * x)) \ y) \ z = (y \ (x * (y * x))) * z
    ]]></literal>
    <justification jstring="[hyper(395,a,38478,a),flip(a)].">
      <j1 rule="hyper" parents="395 38478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38481">
    <literal><![CDATA[
      (1 / x) * (y \ (x \ y)) = (x * (y * x)) \ y
    ]]></literal>
    <justification jstring="[hyper(36,a,38476,a,b,38478,a(flip))].">
      <j1 rule="hyper" parents="36 38476 38478"/>
    </justification>
  </clause>

  <clause id="38482">
    <literal><![CDATA[
      (x \ (y * (x * y))) \ K(z,x) = K(z,x) * ((y * (x * y)) \ x)
    ]]></literal>
    <justification jstring="[para(38479(a,1),17040(a,1,2)),flip(a)].">
      <j1 rule="para" parents="38479 17040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38483">
    <literal><![CDATA[
      (x * (x * y)) \ ((x * y) / x) = (1 / x) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,25135,a,b,38481,a)].">
      <j1 rule="hyper" parents="373 25135 38481"/>
    </justification>
  </clause>

  <clause id="38484">
    <literal><![CDATA[
      K(x * y,y) * ((x \ (y * (x * y))) * z) = (x \ ((x / y) / y)) \ z
    ]]></literal>
    <justification jstring="[para(38480(a,1),36092(a,1,2))].">
      <j1 rule="para" parents="38480 36092"/>
    </justification>
  </clause>

  <clause id="38485">
    <literal><![CDATA[
      L(x,y,y) \ ((y * y) \ ((y * x) / y)) = (1 / y) * (x \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,881,a,b,38483,a)].">
      <j1 rule="hyper" parents="64 881 38483"/>
    </justification>
  </clause>

  <clause id="38486">
    <literal><![CDATA[
      (x \ ((x / y) / y)) \ z = (x \ ((x * y) * y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,30813,a(flip),b,38484,a),flip(a)].">
      <j1 rule="hyper" parents="64 30813 38484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38487">
    <literal><![CDATA[
      (x \ ((x / y) / y)) \ 1 = x \ ((x * y) * y)
    ]]></literal>
    <justification jstring="[hyper(141,a,30813,a(flip),b,38484,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="141 30813 38484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38488">
    <literal><![CDATA[
      1 / (x \ ((x * y) * y)) = x \ ((x / y) / y)
    ]]></literal>
    <justification jstring="[hyper(226,a,38487,a)].">
      <j1 rule="hyper" parents="226 38487"/>
    </justification>
  </clause>

  <clause id="38489">
    <literal><![CDATA[
      K(x,y) / (z \ ((z * u) * u)) = K(x,y) * (z \ ((z / u) / u))
    ]]></literal>
    <justification jstring="[hyper(225,a,38487,a(flip),b,14403,a)].">
      <j1 rule="hyper" parents="225 38487 14403"/>
    </justification>
  </clause>

  <clause id="38490">
    <literal><![CDATA[
      (x \ ((x * y) * y)) \ 1 = x \ ((x / y) / y)
    ]]></literal>
    <justification jstring="[para(38487(a,1),36082(a,1,1))].">
      <j1 rule="para" parents="38487 36082"/>
    </justification>
  </clause>

  <clause id="38491">
    <literal><![CDATA[
      x \ (((y \ ((y * z) * z)) \ K(y \ ((y * z) * z),x)) \ x) = ((y \ ((y / z) / z)) \ x) / x
    ]]></literal>
    <justification jstring="[para(38490(a,1),9507(a,2,1,1))].">
      <j1 rule="para" parents="38490 9507"/>
    </justification>
  </clause>

  <clause id="38492">
    <literal><![CDATA[
      (x \ ((x * y) * y)) \ K(z,u) = K(z,u) * (x \ ((x / y) / y))
    ]]></literal>
    <justification jstring="[para(38490(a,1),30812(a,1,2)),flip(a)].">
      <j1 rule="para" parents="38490 30812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38493">
    <literal><![CDATA[
      (K(x * x,y) * (z \ ((z / x) / x))) \ y = y / (1 / (z \ ((z * x) * x)))
    ]]></literal>
    <justification jstring="[para(38489(a,1),38273(a,1,1))].">
      <j1 rule="para" parents="38489 38273"/>
    </justification>
  </clause>

  <clause id="38494">
    <literal><![CDATA[
      (x \ ((x / y) / y)) \ T(z,y * y) = z / (1 / (x \ ((x * y) * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,14833,a(flip),b,38493,a)].">
      <j1 rule="hyper" parents="64 14833 38493"/>
    </justification>
  </clause>

  <clause id="38495">
    <literal><![CDATA[
      (x \ ((x / y) / y)) \ T(z,y * y) = z / (x \ ((x / y) / y))
    ]]></literal>
    <justification jstring="[para(38488(a,1),38494(a,2,2))].">
      <j1 rule="para" parents="38488 38494"/>
    </justification>
  </clause>

  <clause id="38496">
    <literal><![CDATA[
      (x \ ((x * y) * y)) * T(z,y * y) = z / (x \ ((x / y) / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,38486,a(flip),b,38495,a)].">
      <j1 rule="hyper" parents="64 38486 38495"/>
    </justification>
  </clause>

  <clause id="38497">
    <literal><![CDATA[
      x / (y \ ((y / z) / z)) = x * (y \ ((y * z) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,36398,a(flip),b,38496,a),flip(a)].">
      <j1 rule="hyper" parents="64 36398 38496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38499">
    <literal><![CDATA[
      x \ (((y \ ((y * z) * z)) \ K(z * z,x)) \ x) = ((y \ ((y / z) / z)) \ x) / x
    ]]></literal>
    <justification jstring="[para(28196(a,1),38491(a,1,2,1,2))].">
      <j1 rule="para" parents="28196 38491"/>
    </justification>
  </clause>

  <clause id="38501">
    <literal><![CDATA[
      x \ ((K(y * y,x) * (z \ ((z / y) / y))) \ x) = ((z \ ((z / y) / y)) \ x) / x
    ]]></literal>
    <justification jstring="[para(38492(a,1),38499(a,1,2,1))].">
      <j1 rule="para" parents="38492 38499"/>
    </justification>
  </clause>

  <clause id="38502">
    <literal><![CDATA[
      x \ ((y \ ((y / z) / z)) \ T(x,z * z)) = ((y \ ((y / z) / z)) \ x) / x
    ]]></literal>
    <justification jstring="[para(14833(a,1),38501(a,1,2))].">
      <j1 rule="para" parents="14833 38501"/>
    </justification>
  </clause>

  <clause id="38503">
    <literal><![CDATA[
      ((x \ ((x / y) / y)) \ z) / z = z \ (z / (x \ ((x / y) / y)))
    ]]></literal>
    <justification jstring="[para(38495(a,1),38502(a,1,2)),flip(a)].">
      <j1 rule="para" parents="38495 38502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38504">
    <literal><![CDATA[
      x / ((y \ ((y / z) / z)) * x) = x \ (x / (y \ ((y / z) / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,36085,a(flip),b,38503,a)].">
      <j1 rule="hyper" parents="64 36085 38503"/>
    </justification>
  </clause>

  <clause id="38505">
    <literal><![CDATA[
      (x \ (x / (y \ ((y / z) / z)))) \ x = (y \ ((y / z) / z)) * x
    ]]></literal>
    <justification jstring="[hyper(215,a,38504,a)].">
      <j1 rule="hyper" parents="215 38504"/>
    </justification>
  </clause>

  <clause id="38506">
    <literal><![CDATA[
      L(x,y,z) \ R(T(x * x,x) * (x \ (x \ L(x,y,z))),u,L(u,w,v5)) = a(x \ (x \ L(x,y,z)),u,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(26035(a,2),38382(a,1,2))].">
      <j1 rule="para" parents="26035 38382"/>
    </justification>
  </clause>

  <clause id="38507">
    <literal><![CDATA[
      R(x,y / R(T(R(z,u,w),y),R(z,u,w),R(z,u,w)),v5) = R(x,L(y,R(z,u,w),R(z,u,w)) * L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,30838,a(flip),b,38456,a),flip(a)].">
      <j1 rule="hyper" parents="373 30838 38456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38508">
    <literal><![CDATA[
      R(x,y / R(T(R(z,u,w),y),R(z,u,w),R(z,u,w)),v5) = R(x,L(y,R(z,u,w),L(z,u,w)) * L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(29203(a,1),38507(a,2,2,1))].">
      <j1 rule="para" parents="29203 38507"/>
    </justification>
  </clause>

  <clause id="38509">
    <literal><![CDATA[
      R(x,y / R(T(R(z,u,w),y),R(z,u,w),R(z,u,w)),v5) = R(x,L(y,L(z,u,w),L(z,u,w)) * L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[para(29794(a,1),38508(a,2,2,1))].">
      <j1 rule="para" parents="29794 38508"/>
    </justification>
  </clause>

  <clause id="38510">
    <literal><![CDATA[
      R(x,y / R(T(R(z,u,w),y),R(z,u,w),R(z,u,w)),v5) = R(x,L(z,u,w) \ y,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,30396,a(flip),b,38509,a),flip(a)].">
      <j1 rule="hyper" parents="373 30396 38509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38511">
    <literal><![CDATA[
      R(x,(y \ (z / R(y,u,w))) * y,v5) = R(x,L(y,u,w) \ z,v5)
    ]]></literal>
    <justification jstring="[para(25188(a,1),38510(a,1,2))].">
      <j1 rule="para" parents="25188 38510"/>
    </justification>
  </clause>

  <clause id="38512">
    <literal><![CDATA[
      R(x,y / R(z,u,w),v5) = R(x,L(z,u,w) \ y,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26415,a(flip),b,38511,a)].">
      <j1 rule="hyper" parents="64 26415 38511"/>
    </justification>
  </clause>

  <clause id="38514">
    <literal><![CDATA[
      R(x,R(y,z,u) \ w,v5) = R(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26410,a(flip),b,38512,a)].">
      <j1 rule="hyper" parents="64 26410 38512"/>
    </justification>
  </clause>

  <clause id="38515">
    <literal><![CDATA[
      R(x,R(T(y,z),u,w) \ v5,v6) = R(x,L(y,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26434,a,b,38514,a)].">
      <j1 rule="hyper" parents="64 26434 38514"/>
    </justification>
  </clause>

  <clause id="38516">
    <literal><![CDATA[
      ((x \ 1) * y) \ ((x \ a(z,x,u)) * (a(z,x,u) \ y)) = a((x \ 1) \ 1,a(z,x,u),a(z,x,u) \ y)
    ]]></literal>
    <justification jstring="[para(79(a,1),38457(a,1,2,1,1))].">
      <j1 rule="para" parents="79 38457"/>
    </justification>
  </clause>

  <clause id="38517">
    <literal><![CDATA[
      (x * y) \ (((1 / x) \ a(z,x,u)) * (a(z,x,u) \ y)) = a((x \ 1) \ 1,a(z,x,u),a(z,x,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,1681,a(flip),b,38516,a)].">
      <j1 rule="hyper" parents="64 1681 38516"/>
    </justification>
  </clause>

  <clause id="38519">
    <literal><![CDATA[
      (x * y) \ ((a(z,x,u) * x) * (a(z,x,u) \ y)) = a((x \ 1) \ 1,a(z,x,u),a(z,x,u) \ y)
    ]]></literal>
    <justification jstring="[para(35737(a,1),38517(a,1,2,1))].">
      <j1 rule="para" parents="35737 38517"/>
    </justification>
  </clause>

  <clause id="38520">
    <literal><![CDATA[
      K(x,R(T(y / (z \ u),y * ((u \ z) * w)),z \ u,z) * v5) = K(x,T((y * z) / ((z \ u) * z),w) * v5)
    ]]></literal>
    <justification jstring="[para(28593(a,1),38458(a,1,2,1,1))].">
      <j1 rule="para" parents="28593 38458"/>
    </justification>
  </clause>

  <clause id="38521">
    <literal><![CDATA[
      K(x,T((y * z) / ((z \ u) * z),w) * v5) = K(x,T(y / (z \ u),y * ((u \ z) * w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28103,a(flip),b,38520,a),flip(a)].">
      <j1 rule="hyper" parents="64 28103 38520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38523">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,(z \ y) * w) * v5) = K(x,T((u * y) / ((y \ z) * y),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,33740,a(flip),b,38521,a)].">
      <j1 rule="hyper" parents="373 33740 38521"/>
    </justification>
  </clause>

  <clause id="38524">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y * (w * z)) * v5) = K(x,T((u * y) / ((y \ z) * y),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,22409,a(flip),b,38523,a)].">
      <j1 rule="hyper" parents="64 22409 38523"/>
    </justification>
  </clause>

  <clause id="38525">
    <literal><![CDATA[
      K(x,T(y \ (z * u),z * (w * y)) * v5) = K(x,T((u * z) / ((z \ y) * z),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28351,a(flip),b,38524,a)].">
      <j1 rule="hyper" parents="64 28351 38524"/>
    </justification>
  </clause>

  <clause id="38526">
    <literal><![CDATA[
      K(x,T((y * z) / ((z \ u) * z),w) * v5) = K(x,T((z * y) / u,z * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28963,a(flip),b,38525,a),flip(a)].">
      <j1 rule="hyper" parents="64 28963 38525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38527">
    <literal><![CDATA[
      K(x,T((y * z) / ((z \ u) * z),w) * v5) = K(x,T(z / (u / y),z * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,28131,a(flip),b,38526,a),flip(a)].">
      <j1 rule="hyper" parents="373 28131 38526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38528">
    <literal><![CDATA[
      K(x,T((y * z) / ((z \ u) * z),w) * v5) = K(x,T((u / y) \ z,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,33740,a(flip),b,38527,a),flip(a)].">
      <j1 rule="hyper" parents="373 33740 38527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38529">
    <literal><![CDATA[
      K(x,T(y / (((z \ u) * z) / z),w) * v5) = K(x,T((u / y) \ z,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,28131,a(flip),b,38528,a)].">
      <j1 rule="hyper" parents="64 28131 38528"/>
    </justification>
  </clause>

  <clause id="38530">
    <literal><![CDATA[
      K(x,T(y / (z \ u),w) * v5) = K(x,T((u / y) \ z,w) * v5)
    ]]></literal>
    <justification jstring="[para(11(a,1),38529(a,1,2,1,1,2))].">
      <j1 rule="para" parents="11 38529"/>
    </justification>
  </clause>

  <clause id="38531">
    <literal><![CDATA[
      K(x,T(y / (z \ u),w) * v5) = K(x,T(y * (u \ z),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,33965,a(flip),b,38530,a),flip(a)].">
      <j1 rule="hyper" parents="373 33965 38530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38533">
    <literal><![CDATA[
      K(x,T((y / z) * u,w) * v5) = K(x,T(y * (z \ u),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,35346,a(flip),b,38531,a)].">
      <j1 rule="hyper" parents="64 35346 38531"/>
    </justification>
  </clause>

  <clause id="38534">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * (u \ (y \ z)),w) * v5) = K(x,T((u \ z) / y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,36548,a(flip),b,38533,a),flip(a)].">
      <j1 rule="hyper" parents="64 36548 38533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38535">
    <literal><![CDATA[
      K(x,T(T(y \ (z / u),K(z,u)),w) * v5) = K(x,T((y \ z) / u,w) * v5)
    ]]></literal>
    <justification jstring="[para(15107(a,1),38534(a,1,2,1,1))].">
      <j1 rule="para" parents="15107 38534"/>
    </justification>
  </clause>

  <clause id="38536">
    <literal><![CDATA[
      K(x,T((y \ z) / u,w) * v5) = K(x,T(y \ (z / u),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,17968,a(flip),b,38535,a),flip(a)].">
      <j1 rule="hyper" parents="64 17968 38535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38538">
    <literal><![CDATA[
      K(x,T(y \ (L(z,u,w) \ v5),K(z,z \ v5)) * v6) = K(x,T(L(z,u,w) \ (v5 / y),v5 * z) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,37187,a,b,38536,a)].">
      <j1 rule="hyper" parents="64 37187 38536"/>
    </justification>
  </clause>

  <clause id="38539">
    <literal><![CDATA[
      K(x,T(y \ (L(z,u,w) \ v5),K(z,z \ v5)) * v6) = K(x,T(z \ (v5 / y),v5 * z) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,33968,a(flip),b,38538,a),flip(a)].">
      <j1 rule="hyper" parents="373 33968 38538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38541">
    <literal><![CDATA[
      K(x,T(y \ (L(z,u,w) \ v5),K(z,z \ v5)) * v6) = K(x,T((v5 / y) / z,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,28958,a(flip),b,38539,a),flip(a)].">
      <j1 rule="hyper" parents="373 28958 38539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38542">
    <literal><![CDATA[
      K(x,T(y \ (L(z,u,w) \ v5),K(z,z \ v5)) * v6) = K(x,T(v5 / (z * y),v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,28129,a(flip),b,38541,a),flip(a)].">
      <j1 rule="hyper" parents="373 28129 38541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38543">
    <literal><![CDATA[
      K(x,T(y \ (L(z,u,w) \ v5),K(z,z \ v5)) * v6) = K(x,((z * y) \ v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,13443,a(flip),b,38542,a),flip(a)].">
      <j1 rule="hyper" parents="373 13443 38542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38544">
    <literal><![CDATA[
      K(x,T(y \ (L(z,u,w) \ v5),K(z,z \ v5)) * v6) = K(x,(y \ (z \ v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,28348,a(flip),b,38543,a),flip(a)].">
      <j1 rule="hyper" parents="373 28348 38543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38545">
    <literal><![CDATA[
      K(x,(y \ (L(z,u,w) \ v5)) * v6) = K(x,(y \ (z \ v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,17931,a(flip),b,38544,a)].">
      <j1 rule="hyper" parents="64 17931 38544"/>
    </justification>
  </clause>

  <clause id="38547">
    <literal><![CDATA[
      K(x,(y \ (T(z,y) \ u)) * w) = K(x,(z \ (y \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,34199,a(flip),b,38545,a)].">
      <j1 rule="hyper" parents="64 34199 38545"/>
    </justification>
  </clause>

  <clause id="38549">
    <literal><![CDATA[
      K(x,y \ T(z * (u / w),w)) = K(x,(y \ (w \ z)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31592,a,b,38547,a)].">
      <j1 rule="hyper" parents="64 31592 38547"/>
    </justification>
  </clause>

  <clause id="38550">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) * (w * z)) = K(x,y \ T(u * w,z))
    ]]></literal>
    <justification jstring="[para(11(a,1),38549(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 38549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38551">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ L(a(y,z,u),a(y,z,u),x)),a(y,z,u)) = T(R(x,a(y,z,u),a(y,z,u)),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(15984(a,1),38459(a,2,1))].">
      <j1 rule="para" parents="15984 38459"/>
    </justification>
  </clause>

  <clause id="38552">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ L(a(y,z,u),a(y,z,u),x)),a(y,z,u)) = T(L(x,a(y,z,u),a(y,z,u)),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(27237(a,1),38551(a,2,1))].">
      <j1 rule="para" parents="27237 38551"/>
    </justification>
  </clause>

  <clause id="38553">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ L(a(y,z,u),a(y,z,u),x)),a(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,23105,a(flip),b,38552,a),flip(a)].">
      <j1 rule="hyper" parents="373 23105 38552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38555">
    <literal><![CDATA[
      T(a(x,a(y,z,u),a(y,z,u)) \ x,a(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(30490(a,1),38553(a,1,1))].">
      <j1 rule="para" parents="30490 38553"/>
    </justification>
  </clause>

  <clause id="38556">
    <literal><![CDATA[
      T(a(a(x,y,z),a(x,y,z),u) * u,a(x,y,z)) = L(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(37694(a,1),38555(a,1,1))].">
      <j1 rule="para" parents="37694 38555"/>
    </justification>
  </clause>

  <clause id="38557">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z),u) * u = L(u,a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(23173,a,38556,a)].">
      <j1 rule="hyper" parents="23173 38556"/>
    </justification>
  </clause>

  <clause id="38559">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * L(u,a(x,y,z),a(x,y,z)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(38557(a,1),30238(a,1,2))].">
      <j1 rule="para" parents="38557 30238"/>
    </justification>
  </clause>

  <clause id="38560">
    <literal><![CDATA[
      L(x * a(y,z,u),a(y,z,u),a(y,z,u)) = (a(y,z,u) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(139,a,23138,a(flip),b,38559,a),flip(a)].">
      <j1 rule="hyper" parents="139 23138 38559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38561">
    <literal><![CDATA[
      L(L(x,a(y,z,u),a(y,z,u)),a(y,z,u),a(y,z,u) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(39,a,1640,a,b,38559,a(flip))].">
      <j1 rule="hyper" parents="39 1640 38559"/>
    </justification>
  </clause>

  <clause id="38562">
    <literal><![CDATA[
      R(L(x,a(y,z,u),a(y,z,u)),a(y,z,u),a(y,z,u) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,31802,a,b,38561,a)].">
      <j1 rule="hyper" parents="64 31802 38561"/>
    </justification>
  </clause>

  <clause id="38563">
    <literal><![CDATA[
      L(x * (a(y,z,u) \ 1),a(y,z,u),a(y,z,u)) = x / a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,780,a(flip),b,38562,a)].">
      <j1 rule="hyper" parents="64 780 38562"/>
    </justification>
  </clause>

  <clause id="38564">
    <literal><![CDATA[
      L(x * (a(y,z,u) \ 1),a(y,z,u),a(y,z,u)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,23133,a(flip),b,38563,a),flip(a)].">
      <j1 rule="hyper" parents="373 23133 38563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38565">
    <literal><![CDATA[
      L(x,y,z) \ R(x \ ((x * x) * (x \ L(x,y,z))),u,L(u,w,v5)) = a(x \ (x \ L(x,y,z)),u,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(6431(a,1),38506(a,1,2,1))].">
      <j1 rule="para" parents="6431 38506"/>
    </justification>
  </clause>

  <clause id="38566">
    <literal><![CDATA[
      L(x,y,z) \ R(x \ (x * L(x,y,z)),u,L(u,w,v5)) = a(x \ (x \ L(x,y,z)),u,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(5602(a,1),38565(a,1,2,1,2))].">
      <j1 rule="para" parents="5602 38565"/>
    </justification>
  </clause>

  <clause id="38567">
    <literal><![CDATA[
      a(x \ (x \ L(x,y,z)),u,L(u,w,v5)) = L(x,y,z) \ R(L(x,y,z),u,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(9(a,1),38566(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 38566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38568">
    <literal><![CDATA[
      a(x \ (x \ L(x,y,z)),u,L(u,w,v5)) = L(x \ R(x,u,L(u,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,4246,a(flip),b,38567,a),flip(a)].">
      <j1 rule="hyper" parents="373 4246 38567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38570">
    <literal><![CDATA[
      a(x \ (x \ L(x,y,z)),u,L(u,w,v5)) = L(a(x,u,L(u,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(38380(a,1),38568(a,2,1))].">
      <j1 rule="para" parents="38380 38568"/>
    </justification>
  </clause>

  <clause id="38571">
    <literal><![CDATA[
      a(L(L(x,y,z),x,x),u,L(u,w,v5)) = L(a(x,u,L(u,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30384,a(flip),b,38570,a)].">
      <j1 rule="hyper" parents="64 30384 38570"/>
    </justification>
  </clause>

  <clause id="38572">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,w,v5)) = L(a(x,u,L(u,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13131,a(flip),b,38571,a)].">
      <j1 rule="hyper" parents="64 13131 38571"/>
    </justification>
  </clause>

  <clause id="38575">
    <literal><![CDATA[
      L(x,y,y) * L(z,(y / (y / x)) * y,(x \ y) * x) = ((x \ y) * x) * (((((x \ y) * x) \ 1) * x) * z)
    ]]></literal>
    <justification jstring="[para(29441(a,1),24168(a,1,1))].">
      <j1 rule="para" parents="29441 24168"/>
    </justification>
  </clause>

  <clause id="38576">
    <literal><![CDATA[
      L(x,y,y) * L(z,(y / (y / x)) * y,y) = ((x \ y) * x) * (((((x \ y) * x) \ 1) * x) * z)
    ]]></literal>
    <justification jstring="[para(23833(a,1),38575(a,1,2))].">
      <j1 rule="para" parents="23833 38575"/>
    </justification>
  </clause>

  <clause id="38579">
    <literal><![CDATA[
      L(x,y,y) * L(z,((y / x) \ y) * y,y) = ((x \ y) * x) * (((((x \ y) * x) \ 1) * x) * z)
    ]]></literal>
    <justification jstring="[para(29443(a,1),38576(a,1,2))].">
      <j1 rule="para" parents="29443 38576"/>
    </justification>
  </clause>

  <clause id="38580">
    <literal><![CDATA[
      L(x,y,y) * L(z,x * y,y) = ((x \ y) * x) * (((((x \ y) * x) \ 1) * x) * z)
    ]]></literal>
    <justification jstring="[para(82(a,1),38579(a,1,2,2,1))].">
      <j1 rule="para" parents="82 38579"/>
    </justification>
  </clause>

  <clause id="38581">
    <literal><![CDATA[
      ((x \ y) * x) * (((((x \ y) * x) \ 1) * x) * z) = y * (((y \ 1) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14186,a(flip),b,38580,a),flip(a)].">
      <j1 rule="hyper" parents="64 14186 38580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38583">
    <literal><![CDATA[
      ((x * y) * (L(z,u,w) \ z)) / ((L(z,u,w) \ z) * y) = ((L(z,u,w) \ z) * y) \ ((L(z,u,w) \ z) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,28450,a(flip),b,24803,a),flip(a)].">
      <j1 rule="hyper" parents="64 28450 24803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38584">
    <literal><![CDATA[
      ((x * y) * (L(z,u,w) \ z)) / ((L(z,u,w) \ z) * y) = L(x,y,L(z,u,w) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,18,a,b,38583,a),flip(a)].">
      <j1 rule="hyper" parents="373 18 38583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38585">
    <literal><![CDATA[
      (x * y) * (L(x,z,u) \ x) = x * ((L(x,z,u) \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,33132,a(flip),b,38584,a),flip(a)].">
      <j1 rule="hyper" parents="144 33132 38584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38586">
    <literal><![CDATA[
      R(x * K(y,L(z,u,w) \ z),y,L(z,u,w) \ z) = L(x,y,L(z,u,w) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10304,a(flip),b,38584,a)].">
      <j1 rule="hyper" parents="64 10304 38584"/>
    </justification>
  </clause>

  <clause id="38587">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x * u) = x * ((L(x,y,z) \ x) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23581,a,b,38585,a)].">
      <j1 rule="hyper" parents="64 23581 38585"/>
    </justification>
  </clause>

  <clause id="38588">
    <literal><![CDATA[
      x \ ((L(x,y,z) \ x) * u) = (L(x,y,z) \ x) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(759,a,38587,a)].">
      <j1 rule="hyper" parents="759 38587"/>
    </justification>
  </clause>

  <clause id="38589">
    <literal><![CDATA[
      x * ((L(x,y,z) \ x) * (x \ u)) = (L(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(397,a,38587,a),flip(a)].">
      <j1 rule="hyper" parents="397 38587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38590">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ a(x,u,w)) = L(x,y,z) \ a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(35,a,30904,a(flip),b,38589,a),flip(a)].">
      <j1 rule="hyper" parents="35 30904 38589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38591">
    <literal><![CDATA[
      (x \ a(x,y,z)) \ (L(x,u,w) \ a(x,y,z)) = L(x,u,w) \ x
    ]]></literal>
    <justification jstring="[hyper(36,a,28544,a,b,38590,a)].">
      <j1 rule="hyper" parents="36 28544 38590"/>
    </justification>
  </clause>

  <clause id="38592">
    <literal><![CDATA[
      a(x,y,z) \ ((T(x,u) \ L(T(x,u),w,v5)) \ a(x,y,z)) = L(x,w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,36978,a,b,38591,a)].">
      <j1 rule="hyper" parents="64 36978 38591"/>
    </justification>
  </clause>

  <clause id="38594">
    <literal><![CDATA[
      a(x,y,z) \ ((x \ L(x,u,w)) \ a(x,y,z)) = L(x,u,w) \ x
    ]]></literal>
    <justification jstring="[para(24681(a,1),38592(a,1,2,1))].">
      <j1 rule="para" parents="24681 38592"/>
    </justification>
  </clause>

  <clause id="38595">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ a(x,u,w) = (L(x,y,z) \ x) * a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(23175,a,38594,a),flip(a)].">
      <j1 rule="hyper" parents="23175 38594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38596">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ a(x,u,w) = x * (L(x,y,z) \ a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,30904,a(flip),b,38595,a),flip(a)].">
      <j1 rule="hyper" parents="373 30904 38595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38597">
    <literal><![CDATA[
      R(x,y,L(z,u,w) \ z) = L(x,y,L(z,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(23538(a,1),38586(a,1,1))].">
      <j1 rule="para" parents="23538 38586"/>
    </justification>
  </clause>

  <clause id="38598">
    <literal><![CDATA[
      R(x,y,L(z,u,w) \ z) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,9385,a(flip),b,38597,a),flip(a)].">
      <j1 rule="hyper" parents="373 9385 38597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38599">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ x) * (x \ u)) = L(u,L(x,y,z),L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,36853,a,b,38597,a)].">
      <j1 rule="hyper" parents="64 36853 38597"/>
    </justification>
  </clause>

  <clause id="38600">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,L(y,z,u)) = L(x,L(y,z,u),L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,33857,a(flip),b,38597,a)].">
      <j1 rule="hyper" parents="64 33857 38597"/>
    </justification>
  </clause>

  <clause id="38601">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ x) * (x \ u)) = L(u,L(x,y,z),x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,36853,a,b,38598,a)].">
      <j1 rule="hyper" parents="64 36853 38598"/>
    </justification>
  </clause>

  <clause id="38602">
    <literal><![CDATA[
      R(x,y,(L(z,u,w) \ 1) * z) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,26169,a,b,38598,a)].">
      <j1 rule="hyper" parents="64 26169 38598"/>
    </justification>
  </clause>

  <clause id="38603">
    <literal><![CDATA[
      L(x,R(y,z,u),y * L(y,z,u)) * (x \ y) = x \ ((x * R(y,z,u)) * (R(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(38598(a,1),35625(a,1,1))].">
      <j1 rule="para" parents="38598 35625"/>
    </justification>
  </clause>

  <clause id="38604">
    <literal><![CDATA[
      x \ R(x,y,(L(z,u,w) \ 1) * z) = x * L(x \ 1,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,38602,a(flip),b,1990,a),flip(a)].">
      <j1 rule="hyper" parents="145 38602 1990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38605">
    <literal><![CDATA[
      L(x,y * L(y,z,u),L(y,z,u)) = L(x,L(y,z,u),L(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11874,a(flip),b,38600,a)].">
      <j1 rule="hyper" parents="64 11874 38600"/>
    </justification>
  </clause>

  <clause id="38606">
    <literal><![CDATA[
      L(x,y * L(y,z,u),L(y,z,u)) = L(x,L(y,z,u),y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,9385,a(flip),b,38605,a),flip(a)].">
      <j1 rule="hyper" parents="373 9385 38605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38607">
    <literal><![CDATA[
      x * L(x \ 1,y,z * L(z,u,w)) = x \ L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(38602(a,1),38604(a,1,2)),flip(a)].">
      <j1 rule="para" parents="38602 38604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38608">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),u,u * L(u,w,v5)) = L(x * L(x \ 1,u * L(u,w,v5),u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33156,a(flip),b,38607,a),flip(a)].">
      <j1 rule="hyper" parents="64 33156 38607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38609">
    <literal><![CDATA[
      L(x,L(y,z,u),y * L(y,z,u)) * (x \ y) = x \ ((x * R(y,z,u)) * (R(y,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(29794(a,1),38603(a,1,1))].">
      <j1 rule="para" parents="29794 38603"/>
    </justification>
  </clause>

  <clause id="38610">
    <literal><![CDATA[
      ((x * y) * (a(z,u,w) \ 1)) / ((a(z,u,w) \ 1) * y) = ((a(z,u,w) \ 1) * y) \ ((a(z,u,w) \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,28655,a(flip),b,24817,a),flip(a)].">
      <j1 rule="hyper" parents="64 28655 24817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38611">
    <literal><![CDATA[
      ((x * y) * (a(z,u,w) \ 1)) / ((a(z,u,w) \ 1) * y) = L(x,y,a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,18,a,b,38610,a),flip(a)].">
      <j1 rule="hyper" parents="373 18 38610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38612">
    <literal><![CDATA[
      ((x * y) * (a(z,u,w) \ 1)) / ((a(z,u,w) \ 1) * y) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,1631,a(flip),b,38611,a),flip(a)].">
      <j1 rule="hyper" parents="373 1631 38611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38613">
    <literal><![CDATA[
      R(x * K(y,a(z,u,w) \ 1),y,a(z,u,w) \ 1) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,10304,a(flip),b,38612,a)].">
      <j1 rule="hyper" parents="64 10304 38612"/>
    </justification>
  </clause>

  <clause id="38614">
    <literal><![CDATA[
      R(x * 1,y,a(z,u,w) \ 1) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(23696(a,1),38613(a,1,1,2))].">
      <j1 rule="para" parents="23696 38613"/>
    </justification>
  </clause>

  <clause id="38615">
    <literal><![CDATA[
      R(x,y,a(z,u,w) \ 1) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(8(a,1),38614(a,1,1))].">
      <j1 rule="para" parents="8 38614"/>
    </justification>
  </clause>

  <clause id="38618">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) * u,u,a(x,y,z)) = (a(x,y,z) / u) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,37234,a(flip),b,38615,a),flip(a)].">
      <j1 rule="hyper" parents="64 37234 38615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38619">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,a(z,u,w) * y) = a(x,y,a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(38615(a,1),24663(a,1,1,2))].">
      <j1 rule="para" parents="38615 24663"/>
    </justification>
  </clause>

  <clause id="38620">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * L(u \ 1,u,a(x,y,z)) = u \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(38615(a,1),23763(a,1,2))].">
      <j1 rule="para" parents="38615 23763"/>
    </justification>
  </clause>

  <clause id="38621">
    <literal><![CDATA[
      L(a(x,y,z) * u,u,a(x,y,z)) = 1 / (u \ (a(x,y,z) \ 1))
    ]]></literal>
    <justification jstring="[para(38620(a,1),37486(a,1,2)),flip(a)].">
      <j1 rule="para" parents="38620 37486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38622">
    <literal><![CDATA[
      L(a(x,y,z) * u,u,a(x,y,z)) = ((a(x,y,z) \ 1) / u) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,31788,a(flip),b,38621,a),flip(a)].">
      <j1 rule="hyper" parents="373 31788 38621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38623">
    <literal><![CDATA[
      L(a(x,y,z) * y,y,a(x,y,z)) = (a(x,y,z) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,36252,a(flip),b,38622,a),flip(a)].">
      <j1 rule="hyper" parents="373 36252 38622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38624">
    <literal><![CDATA[
      L(x * a(y,z,u),x,a(y,z,u)) = ((a(y,z,u) \ 1) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,23910,a(flip),b,38622,a)].">
      <j1 rule="hyper" parents="64 23910 38622"/>
    </justification>
  </clause>

  <clause id="38625">
    <literal><![CDATA[
      L((x \ ((x * y) * z)) / z,y,a(x,y,z)) = (a(x,y,z) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,33285,a,b,38623,a)].">
      <j1 rule="hyper" parents="64 33285 38623"/>
    </justification>
  </clause>

  <clause id="38626">
    <literal><![CDATA[
      x * (x * (((a(y,z,u) \ 1) * x) \ 1)) = ((a(y,z,u) \ 1) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,31600,a(flip),b,38624,a)].">
      <j1 rule="hyper" parents="64 31600 38624"/>
    </justification>
  </clause>

  <clause id="38627">
    <literal><![CDATA[
      x * (x * ((a(y,y,z) \ x) \ 1)) = ((a(y,y,z) \ 1) / x) \ 1
    ]]></literal>
    <justification jstring="[para(37681(a,1),38626(a,1,2,2,1))].">
      <j1 rule="para" parents="37681 38626"/>
    </justification>
  </clause>

  <clause id="38628">
    <literal><![CDATA[
      a(x,y,a(z,u,w) \ 1) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,28843,a(flip),b,38619,a),flip(a)].">
      <j1 rule="hyper" parents="64 28843 38619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38629">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (z \ u)) \ 1)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,30214,a,b,38628,a)].">
      <j1 rule="hyper" parents="64 30214 38628"/>
    </justification>
  </clause>

  <clause id="38630">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27731,a(flip),b,38628,a),flip(a)].">
      <j1 rule="hyper" parents="64 27731 38628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38631">
    <literal><![CDATA[
      a(x,y,a(L(z,z,u * w),u,w)) = a(x,y,(z \ R(z,u,w)) \ 1)
    ]]></literal>
    <justification jstring="[para(32467(a,1),38628(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="32467 38628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38632">
    <literal><![CDATA[
      a(x * y,z,a(u,w,w)) = a(y * x,z,a(w,w,u))
    ]]></literal>
    <justification jstring="[hyper(26847,a,38630,a)].">
      <j1 rule="hyper" parents="26847 38630"/>
    </justification>
  </clause>

  <clause id="38634">
    <literal><![CDATA[
      a(x * a(y,z,z),u,a(w,v5,v5)) = a(x * a(z,z,y),u,a(v5,v5,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,32851,a(flip),b,38630,a),flip(a)].">
      <j1 rule="hyper" parents="373 32851 38630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38635">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,a(w,v5,v5)) = a(z * a(y,y,x),u,a(v5,v5,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,32849,a(flip),b,38630,a),flip(a)].">
      <j1 rule="hyper" parents="373 32849 38630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38636">
    <literal><![CDATA[
      a(x,y,a(z * u,u,u)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,30310,a(flip),b,38630,a),flip(a)].">
      <j1 rule="hyper" parents="373 30310 38630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38637">
    <literal><![CDATA[
      a(x,y,a(z * u,z,z)) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,30189,a(flip),b,38630,a),flip(a)].">
      <j1 rule="hyper" parents="373 30189 38630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38638">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * w = w * a(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,38630,a,b,23174,a),flip(a)].">
      <j1 rule="hyper" parents="145 38630 23174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38639">
    <literal><![CDATA[
      x * a(y,z,a(u,w,w)) = x * a(y,z,a(w,w,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,38630,a,b,9,a)].">
      <j1 rule="hyper" parents="145 38630 9"/>
    </justification>
  </clause>

  <clause id="38640">
    <literal><![CDATA[
      a(x,y,a(y,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,37520,a(flip),b,38630,a),flip(a)].">
      <j1 rule="hyper" parents="64 37520 38630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38641">
    <literal><![CDATA[
      a(x,y,a(z,u \ 1,u \ 1)) = a(x,y,a(u,u \ 1,z))
    ]]></literal>
    <justification jstring="[para(2653(a,1),38630(a,2,3))].">
      <j1 rule="para" parents="2653 38630"/>
    </justification>
  </clause>

  <clause id="38642">
    <literal><![CDATA[
      a(x,y,a(z \ 1,u,u)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(2653(a,2),38630(a,1,3))].">
      <j1 rule="para" parents="2653 38630"/>
    </justification>
  </clause>

  <clause id="38643">
    <literal><![CDATA[
      a(x,y,a(z,u \ z,u \ z)) = a(x,y,(z / u) * (u / z))
    ]]></literal>
    <justification jstring="[para(30068(a,1),38630(a,2,3))].">
      <j1 rule="para" parents="30068 38630"/>
    </justification>
  </clause>

  <clause id="38644">
    <literal><![CDATA[
      a(x,y,a(z,z \ u,z \ u)) = a(x,y,(z / u) * (u / z))
    ]]></literal>
    <justification jstring="[para(30069(a,1),38630(a,2,3))].">
      <j1 rule="para" parents="30069 38630"/>
    </justification>
  </clause>

  <clause id="38645">
    <literal><![CDATA[
      a(x,y,a(z,u * z,u * z)) = a(x,y,(z / u) * (u / z))
    ]]></literal>
    <justification jstring="[para(34625(a,1),38630(a,2,3))].">
      <j1 rule="para" parents="34625 38630"/>
    </justification>
  </clause>

  <clause id="38646">
    <literal><![CDATA[
      L(a(x,x,y),x,z) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,38640,a)].">
      <j1 rule="hyper" parents="53 38640"/>
    </justification>
  </clause>

  <clause id="38647">
    <literal><![CDATA[
      a(x,L(y,z,u),a(y,y,w)) = 1
    ]]></literal>
    <justification jstring="[para(35139(a,1),38640(a,1,3))].">
      <j1 rule="para" parents="35139 38640"/>
    </justification>
  </clause>

  <clause id="38648">
    <literal><![CDATA[
      a(x,L(x,x,y),z) = a(x,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34877,a,b,38646,a)].">
      <j1 rule="hyper" parents="64 34877 38646"/>
    </justification>
  </clause>

  <clause id="38649">
    <literal><![CDATA[
      a(x \ (y \ x),y,z) = a(y,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34888,a(flip),b,38646,a)].">
      <j1 rule="hyper" parents="64 34888 38646"/>
    </justification>
  </clause>

  <clause id="38650">
    <literal><![CDATA[
      a(x,y \ (x \ y),z) = a(x,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34879,a(flip),b,38646,a)].">
      <j1 rule="hyper" parents="64 34879 38646"/>
    </justification>
  </clause>

  <clause id="38651">
    <literal><![CDATA[
      L(L(a(x,x,y),z,u),x,w) = L(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(38646(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38646 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38652">
    <literal><![CDATA[
      a(x,x,y) * L(x,x,z) = L(R(x,x,y),x,z)
    ]]></literal>
    <justification jstring="[para(38646(a,1),30088(a,1,1))].">
      <j1 rule="para" parents="38646 30088"/>
    </justification>
  </clause>

  <clause id="38653">
    <literal><![CDATA[
      L(a(x,x,y),z * x,z) = L(a(x,x,y),z,z)
    ]]></literal>
    <justification jstring="[para(38646(a,1),31111(a,1,1))].">
      <j1 rule="para" parents="38646 31111"/>
    </justification>
  </clause>

  <clause id="38654">
    <literal><![CDATA[
      L(L(a(x,x,y),z,u),L(R(x,x,w),z,u),x * y) = a(L(R(x,x,w),z,u),x,y)
    ]]></literal>
    <justification jstring="[para(38646(a,1),36909(a,1,1,1))].">
      <j1 rule="para" parents="38646 36909"/>
    </justification>
  </clause>

  <clause id="38655">
    <literal><![CDATA[
      L(a(x,x,y),L(x,z,u),w) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,38647,a)].">
      <j1 rule="hyper" parents="53 38647"/>
    </justification>
  </clause>

  <clause id="38657">
    <literal><![CDATA[
      a(R(x,y,y),L(x,R(x,y,y),y) * a(x,y,y),z) = a(R(x,y,y),R(x,y,y),z)
    ]]></literal>
    <justification jstring="[para(32623(a,2),38648(a,1,2))].">
      <j1 rule="para" parents="32623 38648"/>
    </justification>
  </clause>

  <clause id="38658">
    <literal><![CDATA[
      L(a(x,x,y) \ x,x,z) = a(x,x,y) \ L(x,x,z)
    ]]></literal>
    <justification jstring="[para(38648(a,1),36229(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38648 36229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38664">
    <literal><![CDATA[
      a((x / y) * x,x \ T(y / x,y),z) = a((x / y) * x,(x / y) * x,z)
    ]]></literal>
    <justification jstring="[para(5149(a,2),38650(a,1,2,2))].">
      <j1 rule="para" parents="5149 38650"/>
    </justification>
  </clause>

  <clause id="38665">
    <literal><![CDATA[
      a(x \ y,a(x,x,y),z) = a(z,x \ y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,34972,a(flip),b,38637,a)].">
      <j1 rule="hyper" parents="64 34972 38637"/>
    </justification>
  </clause>

  <clause id="38666">
    <literal><![CDATA[
      a(x * y,a(y,x,x),z) = a(z,x * y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,34971,a(flip),b,38637,a)].">
      <j1 rule="hyper" parents="64 34971 38637"/>
    </justification>
  </clause>

  <clause id="38667">
    <literal><![CDATA[
      a(x \ y,a(x,x,y),z) \ 1 = a(z,x \ y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,33558,a(flip),b,38637,a)].">
      <j1 rule="hyper" parents="64 33558 38637"/>
    </justification>
  </clause>

  <clause id="38668">
    <literal><![CDATA[
      a(x * y,a(x,x,y),z) \ 1 = a(z,x * y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,33552,a(flip),b,38637,a)].">
      <j1 rule="hyper" parents="64 33552 38637"/>
    </justification>
  </clause>

  <clause id="38669">
    <literal><![CDATA[
      L(x,y \ z,a(y \ z,z,z)) = x * a(x,y \ z,a(z,z,y))
    ]]></literal>
    <justification jstring="[para(38637(a,1),38017(a,1,2)),flip(a)].">
      <j1 rule="para" parents="38637 38017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38670">
    <literal><![CDATA[
      a(x,y,a(z \ (z \ L(z,u,w)),v5,v5)) = a(x,y,a(v5,v5,z * (L(z,u,w) \ z)))
    ]]></literal>
    <justification jstring="[para(24804(a,1),38642(a,1,3,1))].">
      <j1 rule="para" parents="24804 38642"/>
    </justification>
  </clause>

  <clause id="38671">
    <literal><![CDATA[
      L(x,x,y) * a(x,x,z) = L(R(x,x,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(23177,a,38652,a)].">
      <j1 rule="hyper" parents="23177 38652"/>
    </justification>
  </clause>

  <clause id="38673">
    <literal><![CDATA[
      L(a(x,L(x,y,z),u),x,w) = L(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(34877(a,2),38651(a,1,1))].">
      <j1 rule="para" parents="34877 38651"/>
    </justification>
  </clause>

  <clause id="38674">
    <literal><![CDATA[
      L(a(x,L(x,y,z),u),x,w) = a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,34877,a,b,38673,a),flip(a)].">
      <j1 rule="hyper" parents="373 34877 38673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38675">
    <literal><![CDATA[
      x * a(x,L(x,y,z),u) = R(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(145,a,38674,a(flip),b,36298,a(flip))].">
      <j1 rule="hyper" parents="145 38674 36298"/>
    </justification>
  </clause>

  <clause id="38676">
    <literal><![CDATA[
      L(L(a(x,L(x,y,z),u),w,v5),x,v6) = L(a(x,L(x,y,z),u),w,v5)
    ]]></literal>
    <justification jstring="[para(38674(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38674 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38677">
    <literal><![CDATA[
      a(x,L(x,y,z),u) * x = R(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(23777,a,38675,a)].">
      <j1 rule="hyper" parents="23777 38675"/>
    </justification>
  </clause>

  <clause id="38678">
    <literal><![CDATA[
      (1 / x) * (a(1 / x,L(1 / x,y,z),u) * T(w,x \ a(1 / x,L(1 / x,y,z),u))) = L(w,a(1 / x,L(1 / x,y,z),u),x) * R(1 / x,L(1 / x,y,z),u)
    ]]></literal>
    <justification jstring="[para(38675(a,1),15292(a,2,2))].">
      <j1 rule="para" parents="38675 15292"/>
    </justification>
  </clause>

  <clause id="38679">
    <literal><![CDATA[
      x \ (a(x,L(x,y,z),u) \ w) = R(x,L(x,y,z),u) \ w
    ]]></literal>
    <justification jstring="[para(38677(a,1),37559(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38677 37559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38680">
    <literal><![CDATA[
      L(x * y,a(x,y,y),z) \ (x * y) = a(z,x * y,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,34917,a(flip),b,38629,a)].">
      <j1 rule="hyper" parents="64 34917 38629"/>
    </justification>
  </clause>

  <clause id="38681">
    <literal><![CDATA[
      a(x \ (y \ x),y,a(y,y,x)) / T((x \ (y \ x)) * y,y) = 1 / (1 / (y \ ((x \ (y \ x)) \ 1)))
    ]]></literal>
    <justification jstring="[para(38629(a,1),25958(a,1,1))].">
      <j1 rule="para" parents="38629 25958"/>
    </justification>
  </clause>

  <clause id="38682">
    <literal><![CDATA[
      a(x,y,a(z,z \ 1,u)) = a(x,y,a(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(11980(a,1),38641(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11980 38641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38683">
    <literal><![CDATA[
      a(x,y,a(z,u,u \ 1)) = a(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(5598(a,1),38682(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5598 38682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38684">
    <literal><![CDATA[
      a(x,y \ z,a(y,y,z)) \ x = a(y \ z,a(y,y,z),x) * x
    ]]></literal>
    <justification jstring="[para(38667(a,1),33209(a,1,1))].">
      <j1 rule="para" parents="38667 33209"/>
    </justification>
  </clause>

  <clause id="38685">
    <literal><![CDATA[
      a(x * y,a(x,x,y),z) \ a(x,x,y) = a(z,x * y,a(x,x,y)) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(38668(a,1),31103(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38668 31103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38686">
    <literal><![CDATA[
      a(x,L(x,y,z),x * u) \ 1 = (R(x,L(x,y,z),u) \ 1) * x
    ]]></literal>
    <justification jstring="[para(38679(a,1),34902(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38679 34902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38687">
    <literal><![CDATA[
      a(x,y,a(z,u \ z,u \ z)) = a(x,y,(z / u) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27310,a(flip),b,38643,a),flip(a)].">
      <j1 rule="hyper" parents="373 27310 38643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38688">
    <literal><![CDATA[
      a(x,y,a(z,z \ u,z \ u)) = a(x,y,(z / u) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27310,a(flip),b,38644,a),flip(a)].">
      <j1 rule="hyper" parents="373 27310 38644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38689">
    <literal><![CDATA[
      a(x,y,a(z,u * z,u * z)) = a(x,y,(z / u) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27310,a(flip),b,38645,a),flip(a)].">
      <j1 rule="hyper" parents="373 27310 38645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38690">
    <literal><![CDATA[
      a(x,y,a(z,u \ z,u \ z)) = a(x,y,(u \ z) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27317,a(flip),b,38687,a),flip(a)].">
      <j1 rule="hyper" parents="373 27317 38687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38691">
    <literal><![CDATA[
      a(x,y,a(z,z \ u,z \ u)) = a(x,y,(u \ z) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27317,a(flip),b,38688,a),flip(a)].">
      <j1 rule="hyper" parents="373 27317 38688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38692">
    <literal><![CDATA[
      a(x,y,a(z,u * z,u * z)) = a(x,y,(u \ z) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27317,a(flip),b,38689,a),flip(a)].">
      <j1 rule="hyper" parents="373 27317 38689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38693">
    <literal><![CDATA[
      a(x,y,(z \ u) * (u \ z)) = a(x,y,a(z,z * u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,37029,a(flip),b,38690,a),flip(a)].">
      <j1 rule="hyper" parents="64 37029 38690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38694">
    <literal><![CDATA[
      a(x,y,a(z,z \ u,z \ u)) = a(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,38693,a(flip),b,38691,a),flip(a)].">
      <j1 rule="hyper" parents="373 38693 38691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38695">
    <literal><![CDATA[
      L(x,y,(y * ((y \ z) * (y \ z))) \ (z * (y \ z))) = x * a(x,y,a(z,z * y,y))
    ]]></literal>
    <justification jstring="[para(38694(a,1),38016(a,2,2))].">
      <j1 rule="para" parents="38694 38016"/>
    </justification>
  </clause>

  <clause id="38696">
    <literal><![CDATA[
      a(x,y,a(z,u * z,u * z)) = a(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,38693,a(flip),b,38692,a),flip(a)].">
      <j1 rule="hyper" parents="373 38693 38692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38697">
    <literal><![CDATA[
      a(x,y,a(z,z * u,z * u)) = a(x,y,a(u,u * z,z))
    ]]></literal>
    <justification jstring="[para(31938(a,1),38696(a,1,3))].">
      <j1 rule="para" parents="31938 38696"/>
    </justification>
  </clause>

  <clause id="38698">
    <literal><![CDATA[
      L(x,y \ z,a(z * y,z,z)) = x * a(x,y \ z,a(z,z,y))
    ]]></literal>
    <justification jstring="[para(32537(a,1),38669(a,1,3))].">
      <j1 rule="para" parents="32537 38669"/>
    </justification>
  </clause>

  <clause id="38699">
    <literal><![CDATA[
      x * ((y * z) \ L(y * z,a(z,z,y),x)) = a(x,y * z,a(z,z,y)) \ x
    ]]></literal>
    <justification jstring="[para(38680(a,1),35577(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38680 35577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38700">
    <literal><![CDATA[
      a(x,y \ z,a(y,y,z)) \ x = L(x,y \ z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,38020,a(flip),b,38684,a),flip(a)].">
      <j1 rule="hyper" parents="373 38020 38684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38701">
    <literal><![CDATA[
      x * R(1 / x,L(x,y,z),u) = a(x,L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(40,a,27046,a,b,38686,a)].">
      <j1 rule="hyper" parents="40 27046 38686"/>
    </justification>
  </clause>

  <clause id="38702">
    <literal><![CDATA[
      x * a(x,y \ z,a(z,z,y)) = L(x,y \ z,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30331,a(flip),b,38698,a),flip(a)].">
      <j1 rule="hyper" parents="64 30331 38698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38703">
    <literal><![CDATA[
      a(x,y,a(L(z,z,u * w),u,w)) = a(x,y,R(z,u,w) \ z)
    ]]></literal>
    <justification jstring="[para(5382(a,1),38631(a,2,3))].">
      <j1 rule="para" parents="5382 38631"/>
    </justification>
  </clause>

  <clause id="38704">
    <literal><![CDATA[
      a(x,y,a(L(z,z,u * w),u,w)) = a(x,y,L(z,u,w) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31334,a(flip),b,38703,a),flip(a)].">
      <j1 rule="hyper" parents="373 31334 38703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38705">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ z) = a(x,y,z \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(32467(a,1),38704(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32467 38704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38706">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ z) = a(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,31676,a(flip),b,38705,a),flip(a)].">
      <j1 rule="hyper" parents="373 31676 38705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38708">
    <literal><![CDATA[
      a((x / y) * x,x \ (y / x),z) = a((x / y) * x,(x / y) * x,z)
    ]]></literal>
    <justification jstring="[hyper(32041,a,38664,a)].">
      <j1 rule="hyper" parents="32041 38664"/>
    </justification>
  </clause>

  <clause id="38710">
    <literal><![CDATA[
      a((x / y) * x,x \ (x \ y),z) = a((x / y) * x,(x / y) * x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31908,a(flip),b,38708,a)].">
      <j1 rule="hyper" parents="64 31908 38708"/>
    </justification>
  </clause>

  <clause id="38711">
    <literal><![CDATA[
      a((x / y) * x,(x / y) * x,z) = a((x / y) * x,L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32142,a(flip),b,38710,a),flip(a)].">
      <j1 rule="hyper" parents="64 32142 38710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38712">
    <literal><![CDATA[
      a((x / y) * x,(x / y) * x,z) = a((y \ x) * x,L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32367,a(flip),b,38711,a),flip(a)].">
      <j1 rule="hyper" parents="373 32367 38711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38713">
    <literal><![CDATA[
      a(x,y * z,a(z,z,y)) \ x = x * a(y * z,a(z,z,y),x)
    ]]></literal>
    <justification jstring="[para(34915(a,1),38699(a,1,2)),flip(a)].">
      <j1 rule="para" parents="34915 38699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38714">
    <literal><![CDATA[
      a(x,y * z,a(z,z,y)) \ x = L(x,y * z,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,38018,a(flip),b,38713,a),flip(a)].">
      <j1 rule="hyper" parents="373 38018 38713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38715">
    <literal><![CDATA[
      L(a(x,L(x,y,z),u),L(R(x,x,w),y,z),x * u) = a(L(R(x,x,w),y,z),x,u)
    ]]></literal>
    <justification jstring="[para(34877(a,2),38654(a,1,1))].">
      <j1 rule="para" parents="34877 38654"/>
    </justification>
  </clause>

  <clause id="38716">
    <literal><![CDATA[
      a(R(x,y,y),L(x,L(x,y,y),y) * a(x,y,y),z) = a(R(x,y,y),R(x,y,y),z)
    ]]></literal>
    <justification jstring="[para(29794(a,1),38657(a,1,2,1))].">
      <j1 rule="para" parents="29794 38657"/>
    </justification>
  </clause>

  <clause id="38717">
    <literal><![CDATA[
      a(x,y,a(z,z,u * (L(u,w,v5) \ u))) = a(x,y,a(L(L(u,w,v5),u,u),z,z))
    ]]></literal>
    <justification jstring="[para(30384(a,1),38670(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30384 38670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38718">
    <literal><![CDATA[
      a(x,y,a(z,z,u * (L(u,w,v5) \ u))) = a(x,y,a(L(u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[para(13131(a,1),38717(a,2,3))].">
      <j1 rule="para" parents="13131 38717"/>
    </justification>
  </clause>

  <clause id="38720">
    <literal><![CDATA[
      a(L(R(x,x,y),z,u),x,w) = a(x,L(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,34894,a(flip),b,38715,a),flip(a)].">
      <j1 rule="hyper" parents="64 34894 38715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38722">
    <literal><![CDATA[
      a(L(L(x,x,y),z,u),x,w) = a(x,L(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32726,a(flip),b,38720,a)].">
      <j1 rule="hyper" parents="64 32726 38720"/>
    </justification>
  </clause>

  <clause id="38723">
    <literal><![CDATA[
      a(x,L(L(x,x,y),z,u),w) = a(x,L(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32734,a(flip),b,38722,a)].">
      <j1 rule="hyper" parents="64 32734 38722"/>
    </justification>
  </clause>

  <clause id="38724">
    <literal><![CDATA[
      a(R(x,y,y),L(x,x,y) * a(x,y,y),z) = a(R(x,y,y),R(x,y,y),z)
    ]]></literal>
    <justification jstring="[para(35531(a,1),38716(a,1,2,1))].">
      <j1 rule="para" parents="35531 38716"/>
    </justification>
  </clause>

  <clause id="38725">
    <literal><![CDATA[
      a(R(x,y,y),L(R(x,y,y),x,y),z) = a(R(x,y,y),R(x,y,y),z)
    ]]></literal>
    <justification jstring="[para(32623(a,1),38724(a,1,2))].">
      <j1 rule="para" parents="32623 38724"/>
    </justification>
  </clause>

  <clause id="38726">
    <literal><![CDATA[
      a(R(x,y,y),L(L(x,y,y),x,y),z) = a(R(x,y,y),R(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32281,a(flip),b,38725,a)].">
      <j1 rule="hyper" parents="64 32281 38725"/>
    </justification>
  </clause>

  <clause id="38727">
    <literal><![CDATA[
      a(R(x,y,y),(x \ y) * y,z) = a(R(x,y,y),R(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34095,a(flip),b,38726,a)].">
      <j1 rule="hyper" parents="64 34095 38726"/>
    </justification>
  </clause>

  <clause id="38728">
    <literal><![CDATA[
      a(L(x,y,y),(x \ y) * y,z) = a(R(x,y,y),R(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32590,a(flip),b,38727,a)].">
      <j1 rule="hyper" parents="64 32590 38727"/>
    </justification>
  </clause>

  <clause id="38729">
    <literal><![CDATA[
      a(L(x,y,y),(x \ y) * y,z) = a(R(x,y,y),L(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32197,a(flip),b,38728,a),flip(a)].">
      <j1 rule="hyper" parents="373 32197 38728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38730">
    <literal><![CDATA[
      a(L(x,y,y),(x \ y) * y,z) = a(L(x,y,y),L(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32590,a(flip),b,38729,a),flip(a)].">
      <j1 rule="hyper" parents="373 32590 38729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38731">
    <literal><![CDATA[
      a((x \ y) * y,L(x,y,y),z) = a(L(x,y,y),L(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,36863,a,b,38730,a)].">
      <j1 rule="hyper" parents="64 36863 38730"/>
    </justification>
  </clause>

  <clause id="38732">
    <literal><![CDATA[
      a((x / y) * x,(x / y) * x,z) = a(L(y,x,x),L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38712,a,b,38731,a)].">
      <j1 rule="hyper" parents="64 38712 38731"/>
    </justification>
  </clause>

  <clause id="38733">
    <literal><![CDATA[
      a(x * (y \ x),x * (y \ x),z) = a(L(y,x,x),L(y,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32517,a(flip),b,38732,a)].">
      <j1 rule="hyper" parents="64 32517 38732"/>
    </justification>
  </clause>

  <clause id="38734">
    <literal><![CDATA[
      a(x * (y \ x),x * (y \ x),z) = a(y,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,35139,a(flip),b,38733,a),flip(a)].">
      <j1 rule="hyper" parents="373 35139 38733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38736">
    <literal><![CDATA[
      a((x \ y) * y,(x \ y) * y,z) = a(x,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31940,a,b,38734,a)].">
      <j1 rule="hyper" parents="64 31940 38734"/>
    </justification>
  </clause>

  <clause id="38737">
    <literal><![CDATA[
      L(x,y,(z / (1 / (y \ z))) \ (z * (y \ z))) = x * a(x,y,a(z,z * y,y))
    ]]></literal>
    <justification jstring="[para(810(a,1),38695(a,1,3,1))].">
      <j1 rule="para" parents="810 38695"/>
    </justification>
  </clause>

  <clause id="38738">
    <literal><![CDATA[
      L(x,y,(y \ z) \ (((z * (y \ z)) \ z) \ 1)) = x * a(x,y,a(z,z * y,y))
    ]]></literal>
    <justification jstring="[para(31415(a,1),38737(a,1,3))].">
      <j1 rule="para" parents="31415 38737"/>
    </justification>
  </clause>

  <clause id="38739">
    <literal><![CDATA[
      L(x,y,(y \ z) \ ((z * (y \ z)) \ z)) = x * a(x,y,a(z,z * y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,25696,a(flip),b,38738,a)].">
      <j1 rule="hyper" parents="64 25696 38738"/>
    </justification>
  </clause>

  <clause id="38740">
    <literal><![CDATA[
      L(x,y,(y \ z) \ (z \ ((y \ z) \ z))) = x * a(x,y,a(z,z * y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29351,a(flip),b,38739,a)].">
      <j1 rule="hyper" parents="64 29351 38739"/>
    </justification>
  </clause>

  <clause id="38741">
    <literal><![CDATA[
      L(x,y,a(y \ z,y \ z,z)) = x * a(x,y,a(z,z * y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30374,a(flip),b,38740,a)].">
      <j1 rule="hyper" parents="64 30374 38740"/>
    </justification>
  </clause>

  <clause id="38742">
    <literal><![CDATA[
      x * a(x,y,a(z,z * y,y)) = L(x,y,(z / y) * (y / z))
    ]]></literal>
    <justification jstring="[para(30068(a,1),38741(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30068 38741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38743">
    <literal><![CDATA[
      x * a(x,y,a(z,z * y,y)) = L(x,y,(z / y) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,29018,a(flip),b,38742,a),flip(a)].">
      <j1 rule="hyper" parents="373 29018 38742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38744">
    <literal><![CDATA[
      x * a(x,y,a(z,z * y,y)) = L(x,y,(y \ z) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,28980,a(flip),b,38743,a),flip(a)].">
      <j1 rule="hyper" parents="373 28980 38743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38745">
    <literal><![CDATA[
      x * a(x,y,a(z,z * y,y)) = L(x,y,a(y,y * z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,35693,a(flip),b,38744,a),flip(a)].">
      <j1 rule="hyper" parents="373 35693 38744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38746">
    <literal><![CDATA[
      1 / T((x \ (y \ x)) * y,y) = 1 / (1 / (y \ ((x \ (y \ x)) \ 1)))
    ]]></literal>
    <justification jstring="[para(32465(a,1),38681(a,1,1))].">
      <j1 rule="para" parents="32465 38681"/>
    </justification>
  </clause>

  <clause id="38747">
    <literal><![CDATA[
      1 / (1 / (x \ ((y \ (x \ y)) \ 1))) = 1 / ((y \ (x \ y)) * x)
    ]]></literal>
    <justification jstring="[para(15653(a,1),38746(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15653 38746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38750">
    <literal><![CDATA[
      1 / (1 / (x \ ((y \ (x \ y)) \ 1))) = y \ (x * (y * (1 / x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,31134,a(flip),b,38747,a),flip(a)].">
      <j1 rule="hyper" parents="373 31134 38747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38751">
    <literal><![CDATA[
      1 / ((x \ ((y \ (x \ y)) \ 1)) \ 1) = y \ (x * (y * (1 / x)))
    ]]></literal>
    <justification jstring="[para(36437(a,1),38750(a,1,2))].">
      <j1 rule="para" parents="36437 38750"/>
    </justification>
  </clause>

  <clause id="38752">
    <literal><![CDATA[
      x \ ((y \ (x \ y)) \ 1) = y \ (x * (y * (1 / x)))
    ]]></literal>
    <justification jstring="[hyper(330,a,38751,a),flip(a)].">
      <j1 rule="hyper" parents="330 38751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38754">
    <literal><![CDATA[
      ((x * y) * (z \ L(z,u,w))) / ((z \ L(z,u,w)) * y) = ((z \ L(z,u,w)) * y) \ ((z \ L(z,u,w)) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,28396,a(flip),b,24824,a),flip(a)].">
      <j1 rule="hyper" parents="64 28396 24824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38755">
    <literal><![CDATA[
      ((x * y) * (z \ L(z,u,w))) / ((z \ L(z,u,w)) * y) = L(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,18,a,b,38754,a),flip(a)].">
      <j1 rule="hyper" parents="373 18 38754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38756">
    <literal><![CDATA[
      ((x * y) * (z \ L(z,u,w))) / ((z \ L(z,u,w)) * y) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,5608,a(flip),b,38755,a),flip(a)].">
      <j1 rule="hyper" parents="373 5608 38755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38757">
    <literal><![CDATA[
      R(x * K(y,z \ L(z,u,w)),y,z \ L(z,u,w)) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,10304,a(flip),b,38756,a)].">
      <j1 rule="hyper" parents="64 10304 38756"/>
    </justification>
  </clause>

  <clause id="38758">
    <literal><![CDATA[
      R(x,y,z \ L(z,u,w)) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(23693(a,1),38757(a,1,1))].">
      <j1 rule="para" parents="23693 38757"/>
    </justification>
  </clause>

  <clause id="38760">
    <literal><![CDATA[
      R(x,y,x \ L(x,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,33129,a(flip),b,38758,a),flip(a)].">
      <j1 rule="hyper" parents="373 33129 38758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38762">
    <literal><![CDATA[
      R(x,y,z \ R(z,u,w)) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,34424,a,b,38758,a)].">
      <j1 rule="hyper" parents="64 34424 38758"/>
    </justification>
  </clause>

  <clause id="38763">
    <literal><![CDATA[
      x \ L(x,x,y * L(y,z,u)) = a(x,x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,38758,a(flip),b,30054,a)].">
      <j1 rule="hyper" parents="139 38758 30054"/>
    </justification>
  </clause>

  <clause id="38764">
    <literal><![CDATA[
      x * (L(x,x,y * L(y,z,u)) * (y \ L(y,z,u))) = (x * x) * (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(38758(a,1),1903(a,1,2,1))].">
      <j1 rule="para" parents="38758 1903"/>
    </justification>
  </clause>

  <clause id="38765">
    <literal><![CDATA[
      L(x,y,(z \ 1) * L(z \ 1,u,w)) = R(x,y,z * L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(5574(a,1),38758(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5574 38758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38767">
    <literal><![CDATA[
      x * L(1 / x,x,y * L(y,z,u)) = a(x,x,x * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(38758(a,1),30137(a,1,2))].">
      <j1 rule="para" parents="38758 30137"/>
    </justification>
  </clause>

  <clause id="38768">
    <literal><![CDATA[
      R(R(x,y,z),u,x \ L(x,w,v5)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(38760(a,1),31(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38760 31"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38771">
    <literal><![CDATA[
      (x * R(R(y,z,u),x,y \ L(y,w,v5))) \ ((x * R(y,z,u)) * (y \ L(y,w,v5))) = L(y \ L(y,w,v5),x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(38768(a,1),11325(a,2,3))].">
      <j1 rule="para" parents="38768 11325"/>
    </justification>
  </clause>

  <clause id="38772">
    <literal><![CDATA[
      a(x * L(x,y,z),u,u) \ 1 = a(u,u,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30465,a,b,38763,a)].">
      <j1 rule="hyper" parents="64 30465 38763"/>
    </justification>
  </clause>

  <clause id="38773">
    <literal><![CDATA[
      a(x * L(x,y,z),u,u) \ 1 = a(u,u,x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,31676,a,b,38772,a),flip(a)].">
      <j1 rule="hyper" parents="373 31676 38772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38774">
    <literal><![CDATA[
      a(x,x,y \ L(y,z,u)) \ 1 = a(y * L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,38772,a)].">
      <j1 rule="hyper" parents="40 23134 38772"/>
    </justification>
  </clause>

  <clause id="38776">
    <literal><![CDATA[
      a(x * R(x,y,z),u,u \ 1) = a(x * L(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(40,a,36535,a,b,38773,a)].">
      <j1 rule="hyper" parents="40 36535 38773"/>
    </justification>
  </clause>

  <clause id="38778">
    <literal><![CDATA[
      a(x * L(x,y,z),u,u \ 1) = a(x * L(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34635,a(flip),b,38776,a)].">
      <j1 rule="hyper" parents="64 34635 38776"/>
    </justification>
  </clause>

  <clause id="38779">
    <literal><![CDATA[
      L(1 / x,x,y * L(y,z,u)) \ 1 = a(y * L(y,z,u),x,x) * x
    ]]></literal>
    <justification jstring="[para(38778(a,1),33359(a,2,1))].">
      <j1 rule="para" parents="38778 33359"/>
    </justification>
  </clause>

  <clause id="38780">
    <literal><![CDATA[
      R(x,y,z * L(z \ 1,u,w)) = L(x,y,z \ L(1 / z,u,w))
    ]]></literal>
    <justification jstring="[para(1391(a,1),38765(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1391 38765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38781">
    <literal><![CDATA[
      R(x,y,z * L(z \ 1,u,w)) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,33605,a(flip),b,38780,a),flip(a)].">
      <j1 rule="hyper" parents="373 33605 38780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38782">
    <literal><![CDATA[
      R(x,y,L(z \ 1,u,w) * z) = L(x,y,z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,26164,a,b,38781,a)].">
      <j1 rule="hyper" parents="64 26164 38781"/>
    </justification>
  </clause>

  <clause id="38783">
    <literal><![CDATA[
      R(1 / (1 / x),x,y * L((x \ y) \ 1,z,u)) = L(x,x,(x \ y) * L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,34682,a,b,38782,a)].">
      <j1 rule="hyper" parents="64 34682 38782"/>
    </justification>
  </clause>

  <clause id="38784">
    <literal><![CDATA[
      (K(x,y) * z) * T((z * K(x,y)) \ x,K(x,y) * z) = x * K((z * K(x,y)) \ x,T(z * K(x,y),y))
    ]]></literal>
    <justification jstring="[para(8164(a,1),25537(a,1,1))].">
      <j1 rule="para" parents="8164 25537"/>
    </justification>
  </clause>

  <clause id="38785">
    <literal><![CDATA[
      (K(x,y) * z) * T((z \ x) * K(y,x),z) = x * K((z * K(x,y)) \ x,T(z * K(x,y),y))
    ]]></literal>
    <justification jstring="[para(24524(a,1),38784(a,1,2))].">
      <j1 rule="para" parents="24524 38784"/>
    </justification>
  </clause>

  <clause id="38786">
    <literal><![CDATA[
      K(x,y) * (z * T((z \ x) * K(y,x),z)) = x * K((z * K(x,y)) \ x,T(z * K(x,y),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,23073,a(flip),b,38785,a)].">
      <j1 rule="hyper" parents="64 23073 38785"/>
    </justification>
  </clause>

  <clause id="38787">
    <literal><![CDATA[
      x * K((y * K(x,z)) \ x,T(y * K(x,z),z)) = K(x,z) * (((y \ x) * K(z,x)) * y)
    ]]></literal>
    <justification jstring="[hyper(737,a,38786,a),flip(a)].">
      <j1 rule="hyper" parents="737 38786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38788">
    <literal><![CDATA[
      x * K((y * K(x,z)) \ x,T(y * K(x,z),z)) = T(y \ x,K(x,z)) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,24354,a(flip),b,38787,a),flip(a)].">
      <j1 rule="hyper" parents="373 24354 38787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38789">
    <literal><![CDATA[
      x * K(K(y,x) * (z \ x),T(z * K(x,y),y)) = T(z \ x,K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(23272(a,1),38788(a,1,2,1))].">
      <j1 rule="para" parents="23272 38788"/>
    </justification>
  </clause>

  <clause id="38790">
    <literal><![CDATA[
      x * K(y \ T(x,z),T(y * K(x,z),z)) = T(y \ x,K(x,z)) * y
    ]]></literal>
    <justification jstring="[para(17361(a,1),38789(a,1,2))].">
      <j1 rule="para" parents="17361 38789"/>
    </justification>
  </clause>

  <clause id="38791">
    <literal><![CDATA[
      T(x \ y,K(y,z)) * x = y * K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[para(31485(a,1),38790(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31485 38790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38792">
    <literal><![CDATA[
      (L(x,x,y) \ y) * K(y \ (L(x,x,y) \ y),T(y,z)) = T(T(x,x * y) \ 1,K(L(x,x,y) \ y,z)) * y
    ]]></literal>
    <justification jstring="[para(14987(a,1),38791(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14987 38791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38793">
    <literal><![CDATA[
      T(1 / x,K(y,z)) * ((x \ y) * x) = (1 / x) * (y * K(x \ y,T(x,z)))
    ]]></literal>
    <justification jstring="[para(38791(a,1),26737(a,2,2))].">
      <j1 rule="para" parents="38791 26737"/>
    </justification>
  </clause>

  <clause id="38794">
    <literal><![CDATA[
      T(1 / x,K(y,z)) * ((x \ y) * x) = T((1 / x) * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,6815,a(flip),b,38793,a),flip(a)].">
      <j1 rule="hyper" parents="373 6815 38793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38795">
    <literal><![CDATA[
      T((1 / x) * ((x \ y) * x),K(y,z)) = T((1 / x) * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,22976,a,b,38794,a)].">
      <j1 rule="hyper" parents="64 22976 38794"/>
    </justification>
  </clause>

  <clause id="38796">
    <literal><![CDATA[
      T(T((1 / x) * y,x),K(y,z)) = T((1 / x) * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(1019(a,1),38795(a,1,1))].">
      <j1 rule="para" parents="1019 38795"/>
    </justification>
  </clause>

  <clause id="38797">
    <literal><![CDATA[
      T((1 / x) * y,K(y,z) * x) = T((1 / x) * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,22929,a(flip),b,38796,a)].">
      <j1 rule="hyper" parents="64 22929 38796"/>
    </justification>
  </clause>

  <clause id="38798">
    <literal><![CDATA[
      (L(x,x,y) \ y) * K(y \ (L(x,x,y) \ y),T(y,z)) = T(T(x,x * y) \ 1,K(x \ y,z)) * y
    ]]></literal>
    <justification jstring="[para(28404(a,1),38792(a,2,1,2))].">
      <j1 rule="para" parents="28404 38792"/>
    </justification>
  </clause>

  <clause id="38799">
    <literal><![CDATA[
      (L(x,x,y) \ y) * K(y \ (L(x,x,y) \ y),T(y,z)) = T(T(x,x * y) \ 1,K(z,x * y)) * y
    ]]></literal>
    <justification jstring="[para(17559(a,1),38798(a,2,1))].">
      <j1 rule="para" parents="17559 38798"/>
    </justification>
  </clause>

  <clause id="38801">
    <literal><![CDATA[
      (L(x,x,y) \ y) * K(y \ (L(x,x,y) \ y),T(y,z)) = (T(x,T(x * y,z)) \ 1) * y
    ]]></literal>
    <justification jstring="[para(9043(a,1),38799(a,2,1))].">
      <j1 rule="para" parents="9043 38799"/>
    </justification>
  </clause>

  <clause id="38802">
    <literal><![CDATA[
      (L(x,x,y) \ y) * K(T(x,x * y) \ 1,T(y,z)) = (T(x,T(x * y,z)) \ 1) * y
    ]]></literal>
    <justification jstring="[para(14987(a,1),38801(a,1,2,1))].">
      <j1 rule="para" parents="14987 38801"/>
    </justification>
  </clause>

  <clause id="38803">
    <literal><![CDATA[
      (L(x,x,y) \ y) * K(x \ 1,T(T(y,z),x * y)) = (T(x,T(x * y,z)) \ 1) * y
    ]]></literal>
    <justification jstring="[para(7872(a,1),38802(a,1,2))].">
      <j1 rule="para" parents="7872 38802"/>
    </justification>
  </clause>

  <clause id="38804">
    <literal><![CDATA[
      (L(x,x,y) \ y) * K(x \ 1,T(y,z * (x * y))) = (T(x,T(x * y,z)) \ 1) * y
    ]]></literal>
    <justification jstring="[para(25272(a,1),38803(a,1,2))].">
      <j1 rule="para" parents="25272 38803"/>
    </justification>
  </clause>

  <clause id="38805">
    <literal><![CDATA[
      (L(x,x,y) \ y) * K(x \ 1,T(y,z * x)) = (T(x,T(x * y,z)) \ 1) * y
    ]]></literal>
    <justification jstring="[para(9516(a,1),38804(a,1,2))].">
      <j1 rule="para" parents="9516 38804"/>
    </justification>
  </clause>

  <clause id="38806">
    <literal><![CDATA[
      (L(x,x,y) \ y) * K(1 / x,T(y,z)) = (T(x,T(x * y,z)) \ 1) * y
    ]]></literal>
    <justification jstring="[para(25280(a,1),38805(a,1,2))].">
      <j1 rule="para" parents="25280 38805"/>
    </justification>
  </clause>

  <clause id="38807">
    <literal><![CDATA[
      (L(x,x,y) \ y) * K(x \ 1,T(y,z)) = (T(x,T(x * y,z)) \ 1) * y
    ]]></literal>
    <justification jstring="[para(3776(a,1),38806(a,1,2))].">
      <j1 rule="para" parents="3776 38806"/>
    </justification>
  </clause>

  <clause id="38808">
    <literal><![CDATA[
      T(x * (K(y \ 1,T(x,z)) / y),y) = (T(y,T(y * x,z)) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,37103,a(flip),b,38807,a)].">
      <j1 rule="hyper" parents="64 37103 38807"/>
    </justification>
  </clause>

  <clause id="38809">
    <literal><![CDATA[
      T(x * T(1 / y,T(x,z)),y) = (T(y,T(y * x,z)) \ 1) * x
    ]]></literal>
    <justification jstring="[para(6001(a,1),38808(a,1,1,2))].">
      <j1 rule="para" parents="6001 38808"/>
    </justification>
  </clause>

  <clause id="38810">
    <literal><![CDATA[
      T(T((1 / x) * y,K(y,z)),x) = (T(x,T(x * y,z)) \ 1) * y
    ]]></literal>
    <justification jstring="[para(6998(a,2),38809(a,1,1))].">
      <j1 rule="para" parents="6998 38809"/>
    </justification>
  </clause>

  <clause id="38811">
    <literal><![CDATA[
      T((1 / x) * y,K(y,z) * x) = (T(x,T(x * y,z)) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,22924,a(flip),b,38810,a)].">
      <j1 rule="hyper" parents="64 22924 38810"/>
    </justification>
  </clause>

  <clause id="38812">
    <literal><![CDATA[
      (T(x,T(x * y,z)) \ 1) * y = T((1 / x) * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,38797,a(flip),b,38811,a),flip(a)].">
      <j1 rule="hyper" parents="64 38797 38811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38813">
    <literal><![CDATA[
      K(x,y) * (y / T((1 / z) * y,T(z,x))) = y / T((1 / z) * T(y,x),z)
    ]]></literal>
    <justification jstring="[para(38812(a,1),16450(a,1,2,2))].">
      <j1 rule="para" parents="38812 16450"/>
    </justification>
  </clause>

  <clause id="38814">
    <literal><![CDATA[
      K(x,y) * (((1 / z) * y) \ T(y,K(z,x))) = y / T((1 / z) * T(y,x),z)
    ]]></literal>
    <justification jstring="[para(33948(a,1),38813(a,1,2))].">
      <j1 rule="para" parents="33948 38813"/>
    </justification>
  </clause>

  <clause id="38815">
    <literal><![CDATA[
      K(x,y) * (((1 / z) * y) \ T(y,K(x,z))) = y / T((1 / z) * T(y,x),z)
    ]]></literal>
    <justification jstring="[para(8153(a,1),38814(a,1,2,2))].">
      <j1 rule="para" parents="8153 38814"/>
    </justification>
  </clause>

  <clause id="38816">
    <literal><![CDATA[
      K(x,T(y,z)) * (((1 / z) * y) \ y) = y / T((1 / z) * T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,17489,a(flip),b,38815,a)].">
      <j1 rule="hyper" parents="64 17489 38815"/>
    </justification>
  </clause>

  <clause id="38817">
    <literal><![CDATA[
      x / T((1 / y) * T(x,z),y) = ((1 / y) * T(x,T(z,y))) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,24965,a(flip),b,38816,a),flip(a)].">
      <j1 rule="hyper" parents="64 24965 38816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38818">
    <literal><![CDATA[
      (x * x) \ (((1 / x) * T(y,T(x,x))) \ y) = y / T(y * x,x)
    ]]></literal>
    <justification jstring="[para(38817(a,1),35275(a,1,2))].">
      <j1 rule="para" parents="38817 35275"/>
    </justification>
  </clause>

  <clause id="38819">
    <literal><![CDATA[
      (x * x) \ (((1 / x) * T(y,x)) \ y) = y / T(y * x,x)
    ]]></literal>
    <justification jstring="[para(114(a,1),38818(a,1,2,1,2,2))].">
      <j1 rule="para" parents="114 38818"/>
    </justification>
  </clause>

  <clause id="38820">
    <literal><![CDATA[
      T(x * T(y,x),x * x) \ y = y / T(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1456,a(flip),b,38819,a)].">
      <j1 rule="hyper" parents="64 1456 38819"/>
    </justification>
  </clause>

  <clause id="38821">
    <literal><![CDATA[
      T(x * y,y * y) \ x = x / T(x * y,y)
    ]]></literal>
    <justification jstring="[para(115(a,1),38820(a,1,1,1))].">
      <j1 rule="para" parents="115 38820"/>
    </justification>
  </clause>

  <clause id="38822">
    <literal><![CDATA[
      R(x \ (x \ y),z,u) * ((x \ (x \ y)) \ (y / x)) = ((x \ y) \ y) * R(((x \ y) \ y) \ (y / x),z,u)
    ]]></literal>
    <justification jstring="[para(4511(a,1),25750(a,1,2,1))].">
      <j1 rule="para" parents="4511 25750"/>
    </justification>
  </clause>

  <clause id="38823">
    <literal><![CDATA[
      ((x \ y) \ y) * R(((x \ y) \ y) \ (y / x),z,u) = R(y,z,u) / x
    ]]></literal>
    <justification jstring="[hyper(64,a,35951,a(flip),b,38822,a),flip(a)].">
      <j1 rule="hyper" parents="64 35951 38822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38824">
    <literal><![CDATA[
      ((x \ y) \ y) * R(x \ (x \ y),z,u) = R(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(4511(a,1),38823(a,1,2,1))].">
      <j1 rule="para" parents="4511 38823"/>
    </justification>
  </clause>

  <clause id="38825">
    <literal><![CDATA[
      (x \ (L(1 / x,y,z) \ 1)) / T(x \ 1,L(x \ 1,y,z)) = T((x \ 1) / (x \ L(1 / x,y,z)),L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(9392(a,1),25993(a,1,1))].">
      <j1 rule="para" parents="9392 25993"/>
    </justification>
  </clause>

  <clause id="38826">
    <literal><![CDATA[
      T(R(x,x,y) \ 1,x) \ R(T(R(x,x,y) \ 1,x),z,u) = R(x,x,y * x) \ (1 * R(1 \ R(x,x,y * x),z,u))
    ]]></literal>
    <justification jstring="[para(26229(a,2),26297(a,1,2,1))].">
      <j1 rule="para" parents="26229 26297"/>
    </justification>
  </clause>

  <clause id="38827">
    <literal><![CDATA[
      K((x * (y / (y / x))) \ 1,z) \ (x * (y / (y / x))) = 1 / T(1 / (x * (y / (y / x))),z)
    ]]></literal>
    <justification jstring="[para(5743(a,1),26599(a,1,1))].">
      <j1 rule="para" parents="5743 26599"/>
    </justification>
  </clause>

  <clause id="38828">
    <literal><![CDATA[
      K((x / (x / y)) \ (y \ 1),z) \ (y * (x / (x / y))) = 1 / T(1 / (y * (x / (x / y))),z)
    ]]></literal>
    <justification jstring="[para(23046(a,1),38827(a,1,1))].">
      <j1 rule="para" parents="23046 38827"/>
    </justification>
  </clause>

  <clause id="38829">
    <literal><![CDATA[
      K(x \ ((y / (y / x)) \ 1),z) \ (x * (y / (y / x))) = 1 / T(1 / (x * (y / (y / x))),z)
    ]]></literal>
    <justification jstring="[para(6620(a,1),38828(a,1,1,1))].">
      <j1 rule="para" parents="6620 38828"/>
    </justification>
  </clause>

  <clause id="38830">
    <literal><![CDATA[
      K(x \ (T(x,y) \ 1),z) \ (x * (y / (y / x))) = 1 / T(1 / (x * (y / (y / x))),z)
    ]]></literal>
    <justification jstring="[para(27150(a,1),38829(a,1,1))].">
      <j1 rule="para" parents="27150 38829"/>
    </justification>
  </clause>

  <clause id="38831">
    <literal><![CDATA[
      K(x \ T(x \ 1,y),z) \ (x * (y / (y / x))) = 1 / T(1 / (x * (y / (y / x))),z)
    ]]></literal>
    <justification jstring="[para(28271(a,2),38830(a,1,1))].">
      <j1 rule="para" parents="28271 38830"/>
    </justification>
  </clause>

  <clause id="38832">
    <literal><![CDATA[
      K(x,y * T(y,z)) \ (y * (z / (z / y))) = 1 / T(1 / (y * (z / (z / y))),x)
    ]]></literal>
    <justification jstring="[para(34602(a,1),38831(a,1,1))].">
      <j1 rule="para" parents="34602 38831"/>
    </justification>
  </clause>

  <clause id="38833">
    <literal><![CDATA[
      K(x \ ((y / (y / x)) \ 1),z) = K(z,x * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(40,a,38829,a,b,38832,a)].">
      <j1 rule="hyper" parents="40 38829 38832"/>
    </justification>
  </clause>

  <clause id="38834">
    <literal><![CDATA[
      K(x \ ((y / x) / y),z) = K(z,x * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,28178,a(flip),b,38833,a)].">
      <j1 rule="hyper" parents="64 28178 38833"/>
    </justification>
  </clause>

  <clause id="38835">
    <literal><![CDATA[
      K(x \ (y / (y * x)),z) = K(z,x * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,28176,a(flip),b,38834,a)].">
      <j1 rule="hyper" parents="64 28176 38834"/>
    </justification>
  </clause>

  <clause id="38836">
    <literal><![CDATA[
      K(x \ (y \ (x \ y)),z) = K(z,x * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,28468,a(flip),b,38835,a)].">
      <j1 rule="hyper" parents="64 28468 38835"/>
    </justification>
  </clause>

  <clause id="38837">
    <literal><![CDATA[
      R(x,y,((R(z,u,w) \ z) * (R(z,u,w) \ z)) * (1 \ v5)) = R(x,y,((z \ R(z,u,w)) * (z \ R(z,u,w))) \ v5)
    ]]></literal>
    <justification jstring="[para(24813(a,1),27190(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="24813 27190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38838">
    <literal><![CDATA[
      a(x,y,((1 / (z / u)) * (1 / (z / u))) * ((u / z) \ w)) = a(x,y,(((u / z) * (z / u)) * (z / u)) \ w)
    ]]></literal>
    <justification jstring="[para(82(a,1),27778(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="82 27778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38840">
    <literal><![CDATA[
      a(x,y,((1 / (z / u)) * (1 / (z / u))) * ((u / z) \ w)) = a(x,y,(u / (((z / u) \ 1) * u)) \ w)
    ]]></literal>
    <justification jstring="[para(31382(a,1),38838(a,2,3,1))].">
      <j1 rule="para" parents="31382 38838"/>
    </justification>
  </clause>

  <clause id="38841">
    <literal><![CDATA[
      a(x,y,((1 / (z / u)) * (1 / (z / u))) * ((u / z) \ w)) = a(x,y,((((z / u) \ 1) * u) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27389,a(flip),b,38840,a),flip(a)].">
      <j1 rule="hyper" parents="373 27389 38840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38842">
    <literal><![CDATA[
      a(x,y,((1 / (z / u)) * (1 / (z / u))) * ((u / z) \ w)) = a(x,y,(u \ (((z / u) \ 1) \ u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27680,a(flip),b,38841,a),flip(a)].">
      <j1 rule="hyper" parents="373 27680 38841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38843">
    <literal><![CDATA[
      a(x,y,((1 / (z / u)) * (1 / (z / u))) * ((z \ u) \ w)) = a(x,y,(u \ (((z / u) \ 1) \ u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27500,a(flip),b,38842,a)].">
      <j1 rule="hyper" parents="64 27500 38842"/>
    </justification>
  </clause>

  <clause id="38844">
    <literal><![CDATA[
      a(x,y,((1 / (z / u)) * ((z / u) \ 1)) * ((z \ u) \ w)) = a(x,y,(u \ (((z / u) \ 1) \ u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27469,a(flip),b,38843,a)].">
      <j1 rule="hyper" parents="64 27469 38843"/>
    </justification>
  </clause>

  <clause id="38845">
    <literal><![CDATA[
      a(x,y,(((z / u) * (z / u)) \ 1) * ((z \ u) \ w)) = a(x,y,(u \ (((z / u) \ 1) \ u)) \ w)
    ]]></literal>
    <justification jstring="[para(536(a,1),38844(a,1,3,1))].">
      <j1 rule="para" parents="536 38844"/>
    </justification>
  </clause>

  <clause id="38846">
    <literal><![CDATA[
      a(x,y,((z / u) * (z / u)) \ ((z \ u) \ w)) = a(x,y,(u \ (((z / u) \ 1) \ u)) \ w)
    ]]></literal>
    <justification jstring="[para(490(a,1),38845(a,1,3))].">
      <j1 rule="para" parents="490 38845"/>
    </justification>
  </clause>

  <clause id="38847">
    <literal><![CDATA[
      a(x,y,z \ ((u * L(u,u,u)) \ ((w \ ((u * u) * (u \ z))) * (u * w)))) = a(x,y,a(u,w,w \ ((u * u) * (u \ z))))
    ]]></literal>
    <justification jstring="[para(29340(a,1),27786(a,1,3))].">
      <j1 rule="para" parents="29340 27786"/>
    </justification>
  </clause>

  <clause id="38848">
    <literal><![CDATA[
      T(T((x \ (x \ y)) / y,x \ (x \ y)),T(z,x \ (x \ y))) = K(y,x * x) * T((x \ (x \ y)) / y,z)
    ]]></literal>
    <justification jstring="[para(14690(a,1),28472(a,2,1))].">
      <j1 rule="para" parents="14690 28472"/>
    </justification>
  </clause>

  <clause id="38849">
    <literal><![CDATA[
      T(T((x \ (x \ y)) / y,x \ (x \ y)),T(z,x \ (x \ y))) = T(((x \ (x \ y)) / y) * K(y,x * x),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,17826,a,b,38848,a),flip(a)].">
      <j1 rule="hyper" parents="373 17826 38848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38850">
    <literal><![CDATA[
      T(T((x \ (x \ y)) / y,x \ (x \ y)),T(z,x \ (x \ y))) = T(T((x \ (x \ y)) / y,y),z)
    ]]></literal>
    <justification jstring="[para(31739(a,1),38849(a,2,1))].">
      <j1 rule="para" parents="31739 38849"/>
    </justification>
  </clause>

  <clause id="38851">
    <literal><![CDATA[
      T(T((x \ (x \ y)) / y,x \ (x \ y)),T(z,x \ (x \ y))) = T(y \ (x \ (x \ y)),z)
    ]]></literal>
    <justification jstring="[para(117(a,1),38850(a,2,1))].">
      <j1 rule="para" parents="117 38850"/>
    </justification>
  </clause>

  <clause id="38852">
    <literal><![CDATA[
      T((x \ (x \ y)) / y,x \ (x \ y)) = y \ (x \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(41,a,33898,a,b,38851,a),flip(a)].">
      <j1 rule="hyper" parents="41 33898 38851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38853">
    <literal><![CDATA[
      T(((x \ (x \ y)) / y) \ 1,y) = (y \ (x \ (x \ y))) \ 1
    ]]></literal>
    <justification jstring="[para(38852(a,1),36543(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38852 36543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38854">
    <literal><![CDATA[
      R(T(1 / (1 / x),y \ L(y,z,u)),1 / x,y \ L(y,z,u)) \ x = a((1 / x) * (y \ L(y,z,u)),x,x)
    ]]></literal>
    <justification jstring="[para(25862(a,1),30514(a,1,1))].">
      <j1 rule="para" parents="25862 30514"/>
    </justification>
  </clause>

  <clause id="38855">
    <literal><![CDATA[
      R(1 / (1 / x),1 / x,y \ L(y,z,u)) \ x = a((1 / x) * (y \ L(y,z,u)),x,x)
    ]]></literal>
    <justification jstring="[para(23697(a,1),38854(a,1,1,1))].">
      <j1 rule="para" parents="23697 38854"/>
    </justification>
  </clause>

  <clause id="38857">
    <literal><![CDATA[
      L(1 / (1 / x),1 / x,y * L(y,z,u)) \ x = a((1 / x) * (y \ L(y,z,u)),x,x)
    ]]></literal>
    <justification jstring="[para(38758(a,1),38855(a,1,1))].">
      <j1 rule="para" parents="38758 38855"/>
    </justification>
  </clause>

  <clause id="38858">
    <literal><![CDATA[
      L(1 / (1 / x),x,y * L(y,z,u)) \ x = a((1 / x) * (y \ L(y,z,u)),x,x)
    ]]></literal>
    <justification jstring="[para(11776(a,1),38857(a,1,1))].">
      <j1 rule="para" parents="11776 38857"/>
    </justification>
  </clause>

  <clause id="38859">
    <literal><![CDATA[
      a((1 / x) * (y \ L(y,z,u)),x,x) = x * (1 / L(x,x,y * L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,25705,a(flip),b,38858,a),flip(a)].">
      <j1 rule="hyper" parents="64 25705 38858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38860">
    <literal><![CDATA[
      a(x * (y \ L(y,z,u)),T(x,w),x) \ (x * (y \ L(y,z,u))) = (K(w,x) * (y \ L(y,z,u))) / (1 / T(x,w))
    ]]></literal>
    <justification jstring="[para(27304(a,1),30581(a,1,1))].">
      <j1 rule="para" parents="27304 30581"/>
    </justification>
  </clause>

  <clause id="38862">
    <literal><![CDATA[
      a(x * (y \ L(y,z,u)),x,x) \ (x * (y \ L(y,z,u))) = (K(w,x) * (y \ L(y,z,u))) / (1 / T(x,w))
    ]]></literal>
    <justification jstring="[para(31892(a,1),38860(a,1,1))].">
      <j1 rule="para" parents="31892 38860"/>
    </justification>
  </clause>

  <clause id="38863">
    <literal><![CDATA[
      a(x * (y * L(y,z,u)),x,x) \ (x * (y \ L(y,z,u))) = (K(w,x) * (y \ L(y,z,u))) / (1 / T(x,w))
    ]]></literal>
    <justification jstring="[para(11989(a,1),38862(a,1,1))].">
      <j1 rule="para" parents="11989 38862"/>
    </justification>
  </clause>

  <clause id="38865">
    <literal><![CDATA[
      R(x,y,L(a(z,u,w) * a(z,u,w),y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,11,a(flip),b,33062,a),flip(a)].">
      <j1 rule="hyper" parents="373 11 33062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38867">
    <literal><![CDATA[
      R(x,y,a(z,u,w) * a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,26361,a(flip),b,38865,a)].">
      <j1 rule="hyper" parents="64 26361 38865"/>
    </justification>
  </clause>

  <clause id="38869">
    <literal><![CDATA[
      R(x,y,(a(z,u,w) * a(z,u,w)) * v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[para(38867(a,1),26512(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38867 26512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38870">
    <literal><![CDATA[
      R(x,y,z * (a(u,w,v5) * a(u,w,v5))) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26164,a,b,38869,a)].">
      <j1 rule="hyper" parents="64 26164 38869"/>
    </justification>
  </clause>

  <clause id="38871">
    <literal><![CDATA[
      R(x,y,(a(z,u,w) \ 1) \ v5) = R(x,y,a(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26331,a(flip),b,38869,a)].">
      <j1 rule="hyper" parents="64 26331 38869"/>
    </justification>
  </clause>

  <clause id="38872">
    <literal><![CDATA[
      R(x,y,(a(z,u,w) * a(z,u,w)) \ v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),38869(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 38869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38873">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,y * z) = a(x,y,(a(u,w,v5) * a(u,w,v5)) * z)
    ]]></literal>
    <justification jstring="[para(38869(a,1),25129(a,1,1,2))].">
      <j1 rule="para" parents="38869 25129"/>
    </justification>
  </clause>

  <clause id="38874">
    <literal><![CDATA[
      R(x,y,z \ (a(u,w,v5) \ 1)) = R(x,y,z \ a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(25312(a,1),38869(a,1,3)),flip(a)].">
      <j1 rule="para" parents="25312 38869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38875">
    <literal><![CDATA[
      R(x,y,(z * (a(u,w,w) * w)) \ v5) = R(x,y,(z * L(w,w,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,37658,a(flip),b,38870,a),flip(a)].">
      <j1 rule="hyper" parents="64 37658 38870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38876">
    <literal><![CDATA[
      R(x,y,z * ((a(u,w,v5) * a(u,w,v5)) * v6)) = R(x,y,v6 * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26284,a(flip),b,38870,a)].">
      <j1 rule="hyper" parents="64 26284 38870"/>
    </justification>
  </clause>

  <clause id="38877">
    <literal><![CDATA[
      R(x,y,z * a(u,z,z)) = R(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[para(37623(a,1),38870(a,1,3))].">
      <j1 rule="para" parents="37623 38870"/>
    </justification>
  </clause>

  <clause id="38878">
    <literal><![CDATA[
      R(x,y,(z \ (R(u,w,u) \ z)) \ 1) = R(x,y,L(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,34244,a,b,38877,a)].">
      <j1 rule="hyper" parents="64 34244 38877"/>
    </justification>
  </clause>

  <clause id="38879">
    <literal><![CDATA[
      R(x,y,L(a(z,u,w) \ v5,a(z,u,w),a(z,u,w))) = R(x,y,a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26293,a,b,38872,a)].">
      <j1 rule="hyper" parents="64 26293 38872"/>
    </justification>
  </clause>

  <clause id="38880">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,(a(x,y,z) \ 1) \ u,u \ a(x,y,z)) = u * (((a(x,y,z) \ 1) \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,30790,a(flip),b,38872,a),flip(a)].">
      <j1 rule="hyper" parents="64 30790 38872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38881">
    <literal><![CDATA[
      R(x,y,z \ L(L(u,w,w),w,w)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(31699(a,1),38872(a,1,3))].">
      <j1 rule="para" parents="31699 38872"/>
    </justification>
  </clause>

  <clause id="38882">
    <literal><![CDATA[
      R(x,y,((z \ R(z,u,w)) * a(L(z,z,u * w),u,w)) \ v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[para(32467(a,1),38872(a,1,3,1,1))].">
      <j1 rule="para" parents="32467 38872"/>
    </justification>
  </clause>

  <clause id="38883">
    <literal><![CDATA[
      R(x,y,(z \ 1) * L(u,z,z)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(1148(a,1),38881(a,1,3))].">
      <j1 rule="para" parents="1148 38881"/>
    </justification>
  </clause>

  <clause id="38884">
    <literal><![CDATA[
      R(x,y,L(z * (u \ 1),u,u)) = R(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26300,a,b,38883,a)].">
      <j1 rule="hyper" parents="64 26300 38883"/>
    </justification>
  </clause>

  <clause id="38885">
    <literal><![CDATA[
      R(x,y,z \ ((z \ 1) \ u)) = R(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26204,a(flip),b,38884,a),flip(a)].">
      <j1 rule="hyper" parents="64 26204 38884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38886">
    <literal><![CDATA[
      R(x,y,a(z,u,w) \ z) = R(x,y,z * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(29926(a,1),38871(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29926 38871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38887">
    <literal><![CDATA[
      R(x,y,a(z,z,u) \ w) = R(x,y,w * a(z,z,u))
    ]]></literal>
    <justification jstring="[para(37674(a,1),38871(a,1,3)),flip(a)].">
      <j1 rule="para" parents="37674 38871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38888">
    <literal><![CDATA[
      R(x,y,z * a(u * w,w,w)) = R(x,y,z * a(w,w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,37843,a,b,38887,a)].">
      <j1 rule="hyper" parents="64 37843 38887"/>
    </justification>
  </clause>

  <clause id="38889">
    <literal><![CDATA[
      R(x,y,z * a(u,u,z)) = R(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[para(5567(a,1),38887(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5567 38887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38890">
    <literal><![CDATA[
      R(x,y,L(z * u,z,z)) = R(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(30227(a,1),38889(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30227 38889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38891">
    <literal><![CDATA[
      R(x,y,L(z,z,u)) = R(x,y,(u \ (z \ u)) \ 1)
    ]]></literal>
    <justification jstring="[para(654(a,1),38878(a,1,3,1,2,1)),flip(a)].">
      <j1 rule="para" parents="654 38878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38892">
    <literal><![CDATA[
      R(x,y,L(z \ u,z \ u,u)) = R(x,y,(u \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,26223,a(flip),b,38891,a),flip(a)].">
      <j1 rule="hyper" parents="373 26223 38891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38893">
    <literal><![CDATA[
      R(x,y,(z \ (u \ z)) \ 1) = R(x,y,z \ ((u \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27178,a(flip),b,38891,a),flip(a)].">
      <j1 rule="hyper" parents="64 27178 38891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38894">
    <literal><![CDATA[
      (R(x,L(y \ z,y \ z,z),(z \ y) \ 1) \ x) * u = a(x,z \ y,L(y \ z,y \ z,z)) \ u
    ]]></literal>
    <justification jstring="[para(38892(a,1),37859(a,1,1,1))].">
      <j1 rule="para" parents="38892 37859"/>
    </justification>
  </clause>

  <clause id="38895">
    <literal><![CDATA[
      R(x,y,a(z,u,u \ 1) * w) = R(x,y,w * a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33377,a,b,38888,a)].">
      <j1 rule="hyper" parents="64 33377 38888"/>
    </justification>
  </clause>

  <clause id="38896">
    <literal><![CDATA[
      R(x,y,z * a(u,w,w \ 1)) = R(x,y,z * a(w,w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26164,a,b,38895,a)].">
      <j1 rule="hyper" parents="64 26164 38895"/>
    </justification>
  </clause>

  <clause id="38897">
    <literal><![CDATA[
      R(x,y,z * a(u,u,w * u)) = R(x,y,z * a(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,30719,a(flip),b,38896,a),flip(a)].">
      <j1 rule="hyper" parents="64 30719 38896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38898">
    <literal><![CDATA[
      R(x,y,z * a(u,w,w)) = R(x,y,z * a(w,w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,30731,a(flip),b,38897,a),flip(a)].">
      <j1 rule="hyper" parents="64 30731 38897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38899">
    <literal><![CDATA[
      R(x,y,a(z,u,u) * w) = R(x,y,w * a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26164,a,b,38898,a)].">
      <j1 rule="hyper" parents="64 26164 38898"/>
    </justification>
  </clause>

  <clause id="38900">
    <literal><![CDATA[
      R(x,y,z * (u * (a(w,v5,v6) * a(w,v5,v6)))) = R(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26178,a,b,38876,a)].">
      <j1 rule="hyper" parents="64 26178 38876"/>
    </justification>
  </clause>

  <clause id="38901">
    <literal><![CDATA[
      R(x,y,z * ((a(u,w,v5) \ 1) * v6)) = R(x,y,(a(u,w,v5) * v6) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27163,a(flip),b,38876,a),flip(a)].">
      <j1 rule="hyper" parents="64 27163 38876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38903">
    <literal><![CDATA[
      R(x,y,((z / u) * L(u,u,z)) \ w) = R(x,y,R(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[para(27055(a,1),38875(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="27055 38875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38904">
    <literal><![CDATA[
      R(x,y,(a(z,u,u) \ z) \ w) = R(x,y,R(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[para(30571(a,1),38903(a,1,3,1))].">
      <j1 rule="para" parents="30571 38903"/>
    </justification>
  </clause>

  <clause id="38905">
    <literal><![CDATA[
      R(x,y,(a(z,u,u) \ z) \ w) = R(x,y,L(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,35623,a(flip),b,38904,a),flip(a)].">
      <j1 rule="hyper" parents="373 35623 38904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38906">
    <literal><![CDATA[
      R(x,y,((1 / z) \ (u / z)) \ w) = R(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30580,a(flip),b,38905,a)].">
      <j1 rule="hyper" parents="64 30580 38905"/>
    </justification>
  </clause>

  <clause id="38907">
    <literal><![CDATA[
      R(x,y,((1 / z) \ (z \ u)) \ w) = R(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26222,a(flip),b,38906,a)].">
      <j1 rule="hyper" parents="64 26222 38906"/>
    </justification>
  </clause>

  <clause id="38908">
    <literal><![CDATA[
      R(x,y,((z \ 1) \ (z \ u)) \ w) = R(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26280,a(flip),b,38907,a)].">
      <j1 rule="hyper" parents="64 26280 38907"/>
    </justification>
  </clause>

  <clause id="38909">
    <literal><![CDATA[
      R(x,y,(z \ ((1 / z) \ u)) \ w) = R(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[para(1166(a,1),38908(a,1,3,1))].">
      <j1 rule="para" parents="1166 38908"/>
    </justification>
  </clause>

  <clause id="38910">
    <literal><![CDATA[
      R(x,y,L(z,z * u,z * u) \ w) = R(x,y,(((z / u) \ 1) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(34627(a,1),38909(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="34627 38909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38911">
    <literal><![CDATA[
      R(x,y,(z * (a(u,w,v5) \ 1)) * v6) = R(x,y,(a(u,w,v5) * z) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26247,a,b,38901,a)].">
      <j1 rule="hyper" parents="64 26247 38901"/>
    </justification>
  </clause>

  <clause id="38912">
    <literal><![CDATA[
      R(x,y,(a(z,u,u) \ w) * v5) = R(x,y,(a(z,u,u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(37826(a,1),38911(a,1,3,1))].">
      <j1 rule="para" parents="37826 38911"/>
    </justification>
  </clause>

  <clause id="38913">
    <literal><![CDATA[
      R(x,y,(a(z,u,u) \ (u \ w)) * v5) = R(x,y,(L(u,u,z) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(37561(a,1),38912(a,2,3,1))].">
      <j1 rule="para" parents="37561 38912"/>
    </justification>
  </clause>

  <clause id="38914">
    <literal><![CDATA[
      R(x,y,(z \ (a(u,z,z) \ w)) * v5) = R(x,y,(L(z,z,u) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(31039(a,1),38913(a,1,3,1))].">
      <j1 rule="para" parents="31039 38913"/>
    </justification>
  </clause>

  <clause id="38915">
    <literal><![CDATA[
      R(x,y,z * (u \ (a(w,u,u) \ v5))) = R(x,y,(L(u,u,w) \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26164,a,b,38914,a)].">
      <j1 rule="hyper" parents="64 26164 38914"/>
    </justification>
  </clause>

  <clause id="38916">
    <literal><![CDATA[
      R(x,y,(L(z,z,u) \ w) * (u \ (u / z))) = R(x,y,((u \ (z \ u)) * (u \ (z \ u))) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,37718,a(flip),b,38915,a),flip(a)].">
      <j1 rule="hyper" parents="64 37718 38915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38917">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) * a(z,u,w)) * v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,16031,a,b,38873,a),flip(a)].">
      <j1 rule="hyper" parents="64 16031 38873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38918">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,v5) * a(u,w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(27453,a,38917,a)].">
      <j1 rule="hyper" parents="27453 38917"/>
    </justification>
  </clause>

  <clause id="38919">
    <literal><![CDATA[
      a(x,y,z \ ((a(u,w,v5) \ 1) * v6)) = a(x,y,z \ (a(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,27784,a(flip),b,38917,a),flip(a)].">
      <j1 rule="hyper" parents="64 27784 38917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38920">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) \ 1) \ v5) = a(x,y,a(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27635,a(flip),b,38917,a)].">
      <j1 rule="hyper" parents="64 27635 38917"/>
    </justification>
  </clause>

  <clause id="38921">
    <literal><![CDATA[
      a(x,y,z * (u * (a(w,v5,v6) * a(w,v5,v6)))) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27571,a(flip),b,38917,a)].">
      <j1 rule="hyper" parents="64 27571 38917"/>
    </justification>
  </clause>

  <clause id="38922">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) * a(z,u,w)) \ v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),38917(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 38917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38923">
    <literal><![CDATA[
      a(x,y,R(z / a(u,w,v5),a(u,w,v5),a(u,w,v5)) \ v6) = a(x,y,(z * a(u,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(948(a,1),38917(a,1,3))].">
      <j1 rule="para" parents="948 38917"/>
    </justification>
  </clause>

  <clause id="38924">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * ((a(z,u,w) \ 1) \ v5)) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(13947(a,2),38917(a,1,3))].">
      <j1 rule="para" parents="13947 38917"/>
    </justification>
  </clause>

  <clause id="38925">
    <literal><![CDATA[
      a(x,y,z * (L(L(z,u,u),u,u) \ w)) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(30365(a,1),38917(a,1,3))].">
      <j1 rule="para" parents="30365 38917"/>
    </justification>
  </clause>

  <clause id="38926">
    <literal><![CDATA[
      a(x,y,((z \ R(z,u,w)) * a(L(z,z,u * w),u,w)) * v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(32467(a,1),38917(a,1,3,1,1))].">
      <j1 rule="para" parents="32467 38917"/>
    </justification>
  </clause>

  <clause id="38927">
    <literal><![CDATA[
      a(x,y,z * ((a(u,w,v5) \ 1) * v6)) = a(x,y,z * (a(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(34172(a,1),38917(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34172 38917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38928">
    <literal><![CDATA[
      a(x,y,L((a(z,u,w) * a(z,u,w)) * v5,v6,v7)) = a(x,y,L(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,34557,a,b,38918,a)].">
      <j1 rule="hyper" parents="64 34557 38918"/>
    </justification>
  </clause>

  <clause id="38929">
    <literal><![CDATA[
      a(x,y,z * a(u,z,z)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[para(37623(a,1),38918(a,1,3))].">
      <j1 rule="para" parents="37623 38918"/>
    </justification>
  </clause>

  <clause id="38930">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * u) = a(x,y,L(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(27453,a,38929,a)].">
      <j1 rule="hyper" parents="27453 38929"/>
    </justification>
  </clause>

  <clause id="38931">
    <literal><![CDATA[
      a(x,y,L(z \ 1,z,u) \ 1) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,31341,a,b,38929,a)].">
      <j1 rule="hyper" parents="64 31341 38929"/>
    </justification>
  </clause>

  <clause id="38932">
    <literal><![CDATA[
      L(x,a(y,z,L(u,u,w)),v5) = L(x,a(y,z,w \ (u \ w)),v5)
    ]]></literal>
    <justification jstring="[para(38929(a,1),34492(a,2,2)),flip(a)].">
      <j1 rule="para" parents="38929 34492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38933">
    <literal><![CDATA[
      a(x,y,L(z \ u,z \ u,u)) = a(x,y,(u \ z) \ 1)
    ]]></literal>
    <justification jstring="[para(30528(a,1),38930(a,1,3)),flip(a)].">
      <j1 rule="para" parents="30528 38930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38934">
    <literal><![CDATA[
      a(x,y,((a(z,u,w) \ 1) * v5) * v6) = a(x,y,(a(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,27628,a(flip),b,38922,a)].">
      <j1 rule="hyper" parents="64 27628 38922"/>
    </justification>
  </clause>

  <clause id="38935">
    <literal><![CDATA[
      a(x,y,((((z * u) \ u) \ 1) \ w) * a(z,z,u)) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,38036,a,b,38925,a)].">
      <j1 rule="hyper" parents="64 38036 38925"/>
    </justification>
  </clause>

  <clause id="38936">
    <literal><![CDATA[
      a(x,y,L(L(z,u,u),u,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(191(a,1),38925(a,1,3)),flip(a)].">
      <j1 rule="para" parents="191 38925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38937">
    <literal><![CDATA[
      a(x,y,z * a(u,u,z)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[para(30355(a,1),38925(a,1,3,2))].">
      <j1 rule="para" parents="30355 38925"/>
    </justification>
  </clause>

  <clause id="38938">
    <literal><![CDATA[
      a(x,y,L((z * z) \ u,z,z)) = a(x,y,z \ (z \ u))
    ]]></literal>
    <justification jstring="[para(346(a,1),38936(a,1,3,1))].">
      <j1 rule="para" parents="346 38936"/>
    </justification>
  </clause>

  <clause id="38939">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z)) = a(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1137(a,1),38936(a,1,3,1))].">
      <j1 rule="para" parents="1137 38936"/>
    </justification>
  </clause>

  <clause id="38940">
    <literal><![CDATA[
      a(x,y,L(L(z * u,w,v5),z,z)) = a(x,y,L((z \ 1) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(1143(a,1),38936(a,1,3,1))].">
      <j1 rule="para" parents="1143 38936"/>
    </justification>
  </clause>

  <clause id="38941">
    <literal><![CDATA[
      a(x,y,L(z * a(u,u,z),w,v5)) = a(x,y,L(L(z,w,v5),u,u))
    ]]></literal>
    <justification jstring="[para(30235(a,1),38936(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30235 38936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38942">
    <literal><![CDATA[
      a(x,y,z \ ((z \ 1) \ u)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30243,a,b,38937,a)].">
      <j1 rule="hyper" parents="64 30243 38937"/>
    </justification>
  </clause>

  <clause id="38943">
    <literal><![CDATA[
      a(x,y,z \ ((1 / z) \ u)) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30232,a,b,38937,a)].">
      <j1 rule="hyper" parents="64 30232 38937"/>
    </justification>
  </clause>

  <clause id="38944">
    <literal><![CDATA[
      a(x,y,L(z \ ((1 / z) \ u),w,v5)) = a(x,y,L(L(u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[para(30226(a,1),38937(a,1,3))].">
      <j1 rule="para" parents="30226 38937"/>
    </justification>
  </clause>

  <clause id="38945">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u)) = a(x,y,(u \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27377,a,b,38939,a)].">
      <j1 rule="hyper" parents="64 27377 38939"/>
    </justification>
  </clause>

  <clause id="38946">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,u)) = a(x,y,L(z,u,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,30851,a(flip),b,38942,a),flip(a)].">
      <j1 rule="hyper" parents="64 30851 38942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38947">
    <literal><![CDATA[
      a(x,y,L((z \ 1) * u,z,z)) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(9(a,1),38942(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="9 38942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38948">
    <literal><![CDATA[
      a(x,y,L(z \ ((z \ 1) \ u),w,v5)) = a(x,y,L(L(u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[para(5636(a,2),38942(a,1,3))].">
      <j1 rule="para" parents="5636 38942"/>
    </justification>
  </clause>

  <clause id="38949">
    <literal><![CDATA[
      a(x,y,((z \ u) \ 1) \ z) = a(x,y,(1 / (z / u)) * z)
    ]]></literal>
    <justification jstring="[para(34724(a,1),38945(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34724 38945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38950">
    <literal><![CDATA[
      a(x,y,L(z * L(u,w,v5),u,u)) = a(x,y,(L(u,w,v5) \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(35161(a,1),38945(a,1,3))].">
      <j1 rule="para" parents="35161 38945"/>
    </justification>
  </clause>

  <clause id="38951">
    <literal><![CDATA[
      a(x,y,L(z * (u \ 1),u,u)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27377,a,b,38947,a)].">
      <j1 rule="hyper" parents="64 27377 38947"/>
    </justification>
  </clause>

  <clause id="38952">
    <literal><![CDATA[
      a(x,y,(z \ (u * u)) * L(w,z,z)) = a(x,y,z \ ((u * u) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,34291,a(flip),b,38947,a)].">
      <j1 rule="hyper" parents="64 34291 38947"/>
    </justification>
  </clause>

  <clause id="38953">
    <literal><![CDATA[
      a(x,y,L(z \ u,z \ u,z)) = a(x,y,(u \ z) \ 1)
    ]]></literal>
    <justification jstring="[para(436(a,1),38931(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="436 38931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38954">
    <literal><![CDATA[
      a(x,y,L(z,(u * u) / w,(u * u) / w) \ (u * u)) = a(x,y,L(((u * u) \ z) \ 1,w,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,37125,a,b,38946,a)].">
      <j1 rule="hyper" parents="373 37125 38946"/>
    </justification>
  </clause>

  <clause id="38955">
    <literal><![CDATA[
      a(x,y,L((z \ u) \ 1,z,z)) = a(x,y,((z \ 1) * u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,27654,a(flip),b,38946,a),flip(a)].">
      <j1 rule="hyper" parents="373 27654 38946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38956">
    <literal><![CDATA[
      a(x,y \ z,(z \ y) \ 1) = a(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37788,a(flip),b,38933,a),flip(a)].">
      <j1 rule="hyper" parents="64 37788 38933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38957">
    <literal><![CDATA[
      a(x,y,z \ (((u \ z) \ 1) \ z)) = a(x,y,(z \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27692,a(flip),b,38933,a)].">
      <j1 rule="hyper" parents="64 27692 38933"/>
    </justification>
  </clause>

  <clause id="38958">
    <literal><![CDATA[
      a(x,(y * z) \ y,(y * z) \ y) = a(x,(y * z) \ y,z \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,1),38956(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="9 38956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38959">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (u * (z \ 1))) = a(x,y,z \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,31309,a(flip),b,38938,a)].">
      <j1 rule="hyper" parents="64 31309 38938"/>
    </justification>
  </clause>

  <clause id="38960">
    <literal><![CDATA[
      a(x,y,L(z \ (z \ u),z \ (z \ u),z)) = a(x,y,((u \ z) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,27790,a(flip),b,38953,a),flip(a)].">
      <j1 rule="hyper" parents="373 27790 38953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38961">
    <literal><![CDATA[
      a(x,y,((z \ u) \ 1) \ z) = a(x,y,((u \ z) \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27671,a(flip),b,38949,a),flip(a)].">
      <j1 rule="hyper" parents="373 27671 38949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38962">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) \ 1) = a(x,y,z \ ((u \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27660,a(flip),b,38957,a),flip(a)].">
      <j1 rule="hyper" parents="64 27660 38957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38963">
    <literal><![CDATA[
      a(x,y,(z \ 1) * ((z \ 1) * u)) = a(x,y,z \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27315,a,b,38959,a)].">
      <j1 rule="hyper" parents="64 27315 38959"/>
    </justification>
  </clause>

  <clause id="38964">
    <literal><![CDATA[
      a(x,y,(T(((z / u) \ 1) \ 1,w) \ 1) \ z) = a(x,y,((((u / z) \ z) \ z) \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27762,a,b,38961,a)].">
      <j1 rule="hyper" parents="64 27762 38961"/>
    </justification>
  </clause>

  <clause id="38965">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) = a(x,y,(u \ (z \ u)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,27692,a,b,38962,a)].">
      <j1 rule="hyper" parents="373 27692 38962"/>
    </justification>
  </clause>

  <clause id="38966">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,w,v5)) = a(x,a(y,z,u),v5 \ (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,36022,a(flip),b,38965,a),flip(a)].">
      <j1 rule="hyper" parents="373 36022 38965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38967">
    <literal><![CDATA[
      a(x,a(y,z,z),u \ (z \ u)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,37667,a(flip),b,38966,a),flip(a)].">
      <j1 rule="hyper" parents="64 37667 38966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38968">
    <literal><![CDATA[
      L(x \ (y \ x),a(z,y,y),u) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(53,a,38967,a)].">
      <j1 rule="hyper" parents="53 38967"/>
    </justification>
  </clause>

  <clause id="38969">
    <literal><![CDATA[
      (x \ (y \ x)) \ (y * z) = ((x \ (y \ x)) \ y) * z
    ]]></literal>
    <justification jstring="[para(38968(a,1),31813(a,1,1))].">
      <j1 rule="para" parents="38968 31813"/>
    </justification>
  </clause>

  <clause id="38970">
    <literal><![CDATA[
      (x \ (y \ (x \ y))) \ z = ((y \ (x \ y)) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,37543,a,b,38969,a)].">
      <j1 rule="hyper" parents="64 37543 38969"/>
    </justification>
  </clause>

  <clause id="38972">
    <literal><![CDATA[
      a(x,x,L(L(y,z,z),x,x)) \ (y * a(x,x,y)) = y * a(x,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(38941(a,1),38126(a,1,1))].">
      <j1 rule="para" parents="38941 38126"/>
    </justification>
  </clause>

  <clause id="38973">
    <literal><![CDATA[
      a(x,(y * z) \ y,(y * z) \ y) = a(x,y \ (z \ y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,32113,a(flip),b,38958,a),flip(a)].">
      <j1 rule="hyper" parents="373 32113 38958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38974">
    <literal><![CDATA[
      a(x,(y * z) \ y,(y * z) \ y) = a(x,z \ 1,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,37794,a(flip),b,38973,a),flip(a)].">
      <j1 rule="hyper" parents="373 37794 38973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38975">
    <literal><![CDATA[
      a(x,(y * z) \ y,(y * z) \ y) = a(x,z,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,33763,a(flip),b,38973,a),flip(a)].">
      <j1 rule="hyper" parents="373 33763 38973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38977">
    <literal><![CDATA[
      a(x,(y * z) \ y,(y * z) \ y) = a(x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,11980,a(flip),b,38974,a),flip(a)].">
      <j1 rule="hyper" parents="373 11980 38974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38978">
    <literal><![CDATA[
      a(x,(y * z) \ y,y \ (z \ y)) = a(x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27564,a(flip),b,38977,a)].">
      <j1 rule="hyper" parents="64 27564 38977"/>
    </justification>
  </clause>

  <clause id="38979">
    <literal><![CDATA[
      a(x,y \ (z \ y),y \ (z \ y)) = a(x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,32113,a(flip),b,38978,a)].">
      <j1 rule="hyper" parents="64 32113 38978"/>
    </justification>
  </clause>

  <clause id="38980">
    <literal><![CDATA[
      a(x,L(y,y,z),z \ (y \ z)) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,32205,a,b,38979,a)].">
      <j1 rule="hyper" parents="64 32205 38979"/>
    </justification>
  </clause>

  <clause id="38981">
    <literal><![CDATA[
      R(x,L(y,y,z),z \ (y \ z)) = x * a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(38980(a,1),35501(a,1,2)),flip(a)].">
      <j1 rule="para" parents="38980 35501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38982">
    <literal><![CDATA[
      R(x,L(y,y,z),z \ (y \ z)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,983,a(flip),b,38981,a),flip(a)].">
      <j1 rule="hyper" parents="373 983 38981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38984">
    <literal><![CDATA[
      R(x,y \ (z \ y),y \ (z \ y)) = R(x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,26561,a(flip),b,38982,a)].">
      <j1 rule="hyper" parents="64 26561 38982"/>
    </justification>
  </clause>

  <clause id="38985">
    <literal><![CDATA[
      a(x,y,z \ (y \ z)) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,38977,a(flip),b,38975,a),flip(a)].">
      <j1 rule="hyper" parents="64 38977 38975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38987">
    <literal><![CDATA[
      a(x,y \ z,(y \ z) \ 1) = a(x,y \ z,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27323,a(flip),b,38985,a),flip(a)].">
      <j1 rule="hyper" parents="64 27323 38985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38988">
    <literal><![CDATA[
      a(x,y \ z,z \ y) \ ((y \ z) \ 1) = L((y \ z) \ 1,y \ z,x)
    ]]></literal>
    <justification jstring="[para(38987(a,1),33375(a,1,1))].">
      <j1 rule="para" parents="38987 33375"/>
    </justification>
  </clause>

  <clause id="38990">
    <literal><![CDATA[
      a(x,y,L(L(z * u,z,z),w,v5)) = a(x,y,L((z \ 1) \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27702,a,b,38940,a)].">
      <j1 rule="hyper" parents="64 27702 38940"/>
    </justification>
  </clause>

  <clause id="38991">
    <literal><![CDATA[
      a(x,y \ 1,L(L(z,y,x),y,y)) * (y \ L(z,y \ 1,x)) = (y \ 1) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(38944(a,1),37142(a,1,1))].">
      <j1 rule="para" parents="38944 37142"/>
    </justification>
  </clause>

  <clause id="38992">
    <literal><![CDATA[
      a(x,y,L(R(z,z,z * (z * u)) * u,w,v5)) = a(x,y,L(L(u * z,w,v5),z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,36662,a,b,38948,a)].">
      <j1 rule="hyper" parents="64 36662 38948"/>
    </justification>
  </clause>

  <clause id="38993">
    <literal><![CDATA[
      a(x,y,L(L((z \ 1) * u,w,v5),z,z)) = a(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(9(a,1),38948(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="9 38948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38994">
    <literal><![CDATA[
      a(x,y,(z \ (u * u)) * L(w,z,z)) = a(x,y,(u * u) * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27392,a(flip),b,38952,a),flip(a)].">
      <j1 rule="hyper" parents="373 27392 38952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="38995">
    <literal><![CDATA[
      a(x,y,L(L((z \ 1) * u,z,z),w,v5)) = a(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27702,a,b,38993,a)].">
      <j1 rule="hyper" parents="64 27702 38993"/>
    </justification>
  </clause>

  <clause id="38996">
    <literal><![CDATA[
      a(x,y,L((1 / R(z,z,u)) * u,w,v5)) = a(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(30963(a,1),38995(a,1,3,1))].">
      <j1 rule="para" parents="30963 38995"/>
    </justification>
  </clause>

  <clause id="38997">
    <literal><![CDATA[
      a(x,y,L((R(z,z,u) \ 1) * u,w,v5)) = a(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27607,a(flip),b,38996,a)].">
      <j1 rule="hyper" parents="64 27607 38996"/>
    </justification>
  </clause>

  <clause id="38998">
    <literal><![CDATA[
      a(x,y,L((z \ 1) * L(u,z,z),w,v5)) = a(x,y,L(z \ u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,34816,a(flip),b,38997,a)].">
      <j1 rule="hyper" parents="64 34816 38997"/>
    </justification>
  </clause>

  <clause id="38999">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,z)) = a(x,y,z \ L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,38947,a(flip),b,38998,a),flip(a)].">
      <j1 rule="hyper" parents="64 38947 38998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39000">
    <literal><![CDATA[
      a(x,y,z \ (a(u,u,w) * w)) = a(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[para(5669(a,1),38919(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5669 38919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39001">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u \ 1) \ w))) = a(x,y,z \ L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,30250,a,b,39000,a)].">
      <j1 rule="hyper" parents="64 30250 39000"/>
    </justification>
  </clause>

  <clause id="39002">
    <literal><![CDATA[
      a(x,y,z \ (a(u,u,w / (w / (u \ v5))) * (w / (w / (u \ v5))))) = a(x,y,z \ (w / (w / ((1 / u) * v5))))
    ]]></literal>
    <justification jstring="[para(10475(a,1),39000(a,2,3,2))].">
      <j1 rule="para" parents="10475 39000"/>
    </justification>
  </clause>

  <clause id="39003">
    <literal><![CDATA[
      a(x,y,z * (a(u,u,w) \ v5)) = a(x,y,z * (a(u,u,w) * v5))
    ]]></literal>
    <justification jstring="[para(37681(a,1),38927(a,1,3,2))].">
      <j1 rule="para" parents="37681 38927"/>
    </justification>
  </clause>

  <clause id="39004">
    <literal><![CDATA[
      a(x,y,(z * (K(u,w) / z)) * (a(w,w,v5 * w) * v6)) = a(x,y,(w * R(K(w,u) / w,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,36464,a(flip),b,39003,a),flip(a)].">
      <j1 rule="hyper" parents="64 36464 39003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39005">
    <literal><![CDATA[
      a(x,y,L(1 / a(z,u,w),v5,v6)) = a(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(245(a,1),38928(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="245 38928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39006">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ 1,v5,v6)) = a(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,27344,a(flip),b,39005,a)].">
      <j1 rule="hyper" parents="64 27344 39005"/>
    </justification>
  </clause>

  <clause id="39007">
    <literal><![CDATA[
      a(x,y,L(a(z,u,u \ 1),w,v5)) = a(x,y,a(u,L(u,w,v5),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,34884,a(flip),b,39006,a),flip(a)].">
      <j1 rule="hyper" parents="64 34884 39006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39008">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),v5,v5 \ 1)) = a(x,y,a(v5,L(v5,u,w),z))
    ]]></literal>
    <justification jstring="[para(4248(a,2),39007(a,1,3))].">
      <j1 rule="para" parents="4248 39007"/>
    </justification>
  </clause>

  <clause id="39009">
    <literal><![CDATA[
      a(x,y,a(z,L(z,u,w),v5)) = a(x,y,a(z,z,L(v5,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,38683,a(flip),b,39008,a),flip(a)].">
      <j1 rule="hyper" parents="64 38683 39008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39010">
    <literal><![CDATA[
      a(x,a(y,y,z),a(y,L(y,u,w),v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,37670,a(flip),b,39009,a),flip(a)].">
      <j1 rule="hyper" parents="373 37670 39009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39011">
    <literal><![CDATA[
      a(x,a(y,L(y,z,u),w),a(y,L(y,v5,v6),v7)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,34885,a,b,39010,a)].">
      <j1 rule="hyper" parents="64 34885 39010"/>
    </justification>
  </clause>

  <clause id="39012">
    <literal><![CDATA[
      a(x,a(y,L(y,z,u),w),a(y,L(y,v5,v6),v7)) = v8 \ v8
    ]]></literal>
    <justification jstring="[hyper(373,a,68,a,b,39011,a),flip(a)].">
      <j1 rule="hyper" parents="373 68 39011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39013">
    <literal><![CDATA[
      L(x,a(y,L(y,z,u),w),a(y,L(y,z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,27238,a,b,39012,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 27238 39012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39014">
    <literal><![CDATA[
      (a(x,L(x,y,z),u) \ 1) \ w = w * a(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(34364,a,39013,a),flip(a)].">
      <j1 rule="hyper" parents="34364 39013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39015">
    <literal><![CDATA[
      x \ (a(y,L(y,z,u),w) \ x) = a(y,L(y,z,u),w) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,38564,a(flip),b,39013,a(flip))].">
      <j1 rule="hyper" parents="139 38564 39013"/>
    </justification>
  </clause>

  <clause id="39016">
    <literal><![CDATA[
      L(x,a(y,L(y,z,u),w),L(a(y,y,w),z,u)) = x
    ]]></literal>
    <justification jstring="[para(34877(a,1),39013(a,1,3))].">
      <j1 rule="para" parents="34877 39013"/>
    </justification>
  </clause>

  <clause id="39017">
    <literal><![CDATA[
      L(x,a(y,L(y,z,u),w),L(a(y,y,w) \ 1,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,34224,a,b,39016,a)].">
      <j1 rule="hyper" parents="64 34224 39016"/>
    </justification>
  </clause>

  <clause id="39018">
    <literal><![CDATA[
      R(x,a(y,L(y,z,u),w),L(a(y,y,w) \ 1,z,u) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,31805,a,b,39017,a)].">
      <j1 rule="hyper" parents="64 31805 39017"/>
    </justification>
  </clause>

  <clause id="39019">
    <literal><![CDATA[
      R(x,L(a(y,y,z),u,w),L(a(y,y,z) \ 1,u,w) \ 1) = x
    ]]></literal>
    <justification jstring="[para(34877(a,1),39018(a,1,2))].">
      <j1 rule="para" parents="34877 39018"/>
    </justification>
  </clause>

  <clause id="39020">
    <literal><![CDATA[
      R(x,L(a(y,y,z) \ 1,u,w),L(a(y,y,z) \ 1,u,w) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,26674,a,b,39019,a)].">
      <j1 rule="hyper" parents="64 26674 39019"/>
    </justification>
  </clause>

  <clause id="39021">
    <literal><![CDATA[
      T(x * L(a(y,y,z) \ 1,u,w),L(a(y,y,z) \ 1,u,w) \ 1) = (L(a(y,y,z) \ 1,u,w) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(493,a,39020,a(flip),b,297,a)].">
      <j1 rule="hyper" parents="493 39020 297"/>
    </justification>
  </clause>

  <clause id="39022">
    <literal><![CDATA[
      a(x,y,(a(z,u,u) * w) * v5) = a(x,y,(a(u,u,z) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31436,a(flip),b,38934,a),flip(a)].">
      <j1 rule="hyper" parents="64 31436 38934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39023">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) * u) * w) = a(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[para(5669(a,1),38934(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5669 38934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39024">
    <literal><![CDATA[
      a(x,y,(z \ ((1 / z) \ u)) * w) = a(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30242,a,b,39023,a)].">
      <j1 rule="hyper" parents="64 30242 39023"/>
    </justification>
  </clause>

  <clause id="39025">
    <literal><![CDATA[
      a(x,y,(z * a(u,u,z)) * w) = a(x,y,L(z,u,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27395,a,b,39023,a)].">
      <j1 rule="hyper" parents="64 27395 39023"/>
    </justification>
  </clause>

  <clause id="39026">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * (z \ w)) = a(x,y,z * (L(z,u,u) \ w))
    ]]></literal>
    <justification jstring="[para(37021(a,1),39023(a,1,3)),flip(a)].">
      <j1 rule="para" parents="37021 39023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39027">
    <literal><![CDATA[
      a(x,y,((T(z,u) * (w \ 1)) * a(w,w,T(z,u) * (w \ 1))) * v5) = a(x,y,((1 / w) * T(w * (z * (w \ 1)),u)) * v5)
    ]]></literal>
    <justification jstring="[para(1562(a,2),39025(a,2,3,1))].">
      <j1 rule="para" parents="1562 39025"/>
    </justification>
  </clause>

  <clause id="39028">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ (z \ u)) * w) = a(x,y,L(u,z,z) * w)
    ]]></literal>
    <justification jstring="[para(1166(a,2),39024(a,1,3,1))].">
      <j1 rule="para" parents="1166 39024"/>
    </justification>
  </clause>

  <clause id="39029">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ (T(u,w) \ v5))) = a(x,y,L(v5,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27715,a,b,39028,a)].">
      <j1 rule="hyper" parents="64 27715 39028"/>
    </justification>
  </clause>

  <clause id="39030">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(z,w,w)) = a(x,y,z * (L(z,w,w) \ u))
    ]]></literal>
    <justification jstring="[hyper(27453,a,39026,a)].">
      <j1 rule="hyper" parents="27453 39026"/>
    </justification>
  </clause>

  <clause id="39031">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ (w / T(u,v5)))) = a(x,y,L(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27482,a,b,39029,a)].">
      <j1 rule="hyper" parents="64 27482 39029"/>
    </justification>
  </clause>

  <clause id="39032">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z) * w) = a(x,y,w * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(214(a,1),39031(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="214 39031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39033">
    <literal><![CDATA[
      a(x,y,z * L(u * w,u,u)) = a(x,y,z * ((u \ 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(27453,a,39032,a)].">
      <j1 rule="hyper" parents="27453 39032"/>
    </justification>
  </clause>

  <clause id="39034">
    <literal><![CDATA[
      a(x,y,z * L(u * w,w,w)) = a(x,y,z * ((w \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27536,a(flip),b,39032,a)].">
      <j1 rule="hyper" parents="64 27536 39032"/>
    </justification>
  </clause>

  <clause id="39035">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ (u \ w))) = a(x,y,z * L(w,u,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),39033(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="10 39033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39036">
    <literal><![CDATA[
      a(x,y,z * (u \ ((u \ 1) \ w))) = a(x,y,z * L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27984,a(flip),b,39035,a)].">
      <j1 rule="hyper" parents="64 27984 39035"/>
    </justification>
  </clause>

  <clause id="39037">
    <literal><![CDATA[
      a(x,y,z * L((u \ 1) * w,u,u)) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[para(9(a,1),39036(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="9 39036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39038">
    <literal><![CDATA[
      a(x,y,L((z \ 1) * u,z,z) * w) = a(x,y,w * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(27453,a,39037,a)].">
      <j1 rule="hyper" parents="27453 39037"/>
    </justification>
  </clause>

  <clause id="39039">
    <literal><![CDATA[
      a(x,y,((1 / z) * L(u,z,z)) * w) = a(x,y,w * (z \ u))
    ]]></literal>
    <justification jstring="[para(1152(a,1),39038(a,1,3,1))].">
      <j1 rule="para" parents="1152 39038"/>
    </justification>
  </clause>

  <clause id="39040">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) * L(w,u,u))) = a(x,y,z * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27534,a(flip),b,39039,a)].">
      <j1 rule="hyper" parents="64 27534 39039"/>
    </justification>
  </clause>

  <clause id="39041">
    <literal><![CDATA[
      a(x,y,L(z,u \ 1,L(w,u,u)) * (u \ w)) = a(x,y,L(w,u,u) * ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27572,a(flip),b,39040,a),flip(a)].">
      <j1 rule="hyper" parents="64 27572 39040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39042">
    <literal><![CDATA[
      R(x,y,((z \ R(z,u,w)) * (z \ R(z,u,w))) \ v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[para(32467(a,1),38882(a,1,3,1,2))].">
      <j1 rule="para" parents="32467 38882"/>
    </justification>
  </clause>

  <clause id="39043">
    <literal><![CDATA[
      R(x,y,((R(z,u,w) \ z) * (R(z,u,w) \ z)) * (1 \ v5)) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,38837,a,b,39042,a)].">
      <j1 rule="hyper" parents="64 38837 39042"/>
    </justification>
  </clause>

  <clause id="39045">
    <literal><![CDATA[
      R(x,y,(z * (R(z,u,w) \ (R(z,u,w) \ z))) * (1 \ v5)) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[para(34573(a,1),39043(a,1,3,1))].">
      <j1 rule="para" parents="34573 39043"/>
    </justification>
  </clause>

  <clause id="39046">
    <literal><![CDATA[
      R(x,y,(z * (R(z,u,w) \ (R(z,u,w) \ z))) * v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[para(66(a,1),39045(a,1,3,2))].">
      <j1 rule="para" parents="66 39045"/>
    </justification>
  </clause>

  <clause id="39047">
    <literal><![CDATA[
      R(x,y,(((z / u) \ 1) \ u) \ w) = R(x,y,((1 / (u / z)) * u) \ w)
    ]]></literal>
    <justification jstring="[para(34540(a,1),38910(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="34540 38910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39048">
    <literal><![CDATA[
      R(x,y,(((z / u) \ 1) \ u) \ w) = R(x,y,(((z \ u) \ 1) * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27898,a(flip),b,39047,a),flip(a)].">
      <j1 rule="hyper" parents="373 27898 39047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39049">
    <literal><![CDATA[
      R(x,y,(((z \ u) \ 1) \ z) \ w) = R(x,y,(((u \ z) \ 1) * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,36577,a(flip),b,39048,a)].">
      <j1 rule="hyper" parents="64 36577 39048"/>
    </justification>
  </clause>

  <clause id="39050">
    <literal><![CDATA[
      R(x,y,(((z \ u) \ 1) * u) \ ((z \ u) * u)) = R(x,y,z \ (((u \ z) \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,36053,a(flip),b,39049,a),flip(a)].">
      <j1 rule="hyper" parents="64 36053 39049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39051">
    <literal><![CDATA[
      a(x,y,((z \ R(z,u,w)) * (z \ R(z,u,w))) * v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(32467(a,1),38926(a,1,3,1,2))].">
      <j1 rule="para" parents="32467 38926"/>
    </justification>
  </clause>

  <clause id="39052">
    <literal><![CDATA[
      a(x,y,((z \ R(z,u,w)) * (z \ R(z,u,w))) \ v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),39051(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 39051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39053">
    <literal><![CDATA[
      a(x,y,((z \ R(z,u,w)) * z) * (z \ R(T(z,v5),u,w))) = a(x,y,T(z,v5))
    ]]></literal>
    <justification jstring="[para(33905(a,1),39051(a,1,3))].">
      <j1 rule="para" parents="33905 39051"/>
    </justification>
  </clause>

  <clause id="39054">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) * R(z \ 1,u,w)) \ v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(28065(a,1),39052(a,1,3,1))].">
      <j1 rule="para" parents="28065 39052"/>
    </justification>
  </clause>

  <clause id="39055">
    <literal><![CDATA[
      a(x,(x * x) \ y,((y \ x) * x) \ 1) = a(x,x \ (x \ y),x \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,35716,a(flip),b,38960,a),flip(a)].">
      <j1 rule="hyper" parents="64 35716 38960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39056">
    <literal><![CDATA[
      a(x,x,L(y,z,z)) \ (y * a(x,x,y)) = y * a(x,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(30352(a,1),38972(a,1,1))].">
      <j1 rule="para" parents="30352 38972"/>
    </justification>
  </clause>

  <clause id="39057">
    <literal><![CDATA[
      a(x,y,((z \ R(z,u,w)) * z) * (z \ R(T(z,v5),u,w))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27304,a(flip),b,39053,a),flip(a)].">
      <j1 rule="hyper" parents="373 27304 39053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39059">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * (z \ R(T(z,v5),u,w))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27397,a(flip),b,39057,a)].">
      <j1 rule="hyper" parents="64 27397 39057"/>
    </justification>
  </clause>

  <clause id="39061">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * (z \ R(z,u,w))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27481,a(flip),b,39059,a)].">
      <j1 rule="hyper" parents="64 27481 39059"/>
    </justification>
  </clause>

  <clause id="39062">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * (z \ R(z,u,w))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31314,a(flip),b,39061,a)].">
      <j1 rule="hyper" parents="64 31314 39061"/>
    </justification>
  </clause>

  <clause id="39063">
    <literal><![CDATA[
      a(x,y,L(R(z,u,w),u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(33222(a,1),39062(a,1,3))].">
      <j1 rule="para" parents="33222 39062"/>
    </justification>
  </clause>

  <clause id="39064">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27703,a(flip),b,39063,a)].">
      <j1 rule="hyper" parents="64 27703 39063"/>
    </justification>
  </clause>

  <clause id="39065">
    <literal><![CDATA[
      a(x,y,L(L(L(z,u,w),v5,v6),u,w)) = a(x,y,L(z,v5,v6))
    ]]></literal>
    <justification jstring="[para(30(a,1),39064(a,1,3,1))].">
      <j1 rule="para" parents="30 39064"/>
    </justification>
  </clause>

  <clause id="39066">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,u,z)) = a(x,y,u \ (z \ w))
    ]]></literal>
    <justification jstring="[para(346(a,1),39064(a,1,3,1))].">
      <j1 rule="para" parents="346 39064"/>
    </justification>
  </clause>

  <clause id="39067">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((u * z) * w))) = a(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[para(596(a,1),39064(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="596 39064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39068">
    <literal><![CDATA[
      a(x,y,L(((z \ 1) * u) \ w,u,z)) = a(x,y,u \ ((z \ 1) \ w))
    ]]></literal>
    <justification jstring="[para(1633(a,1),39064(a,1,3,1))].">
      <j1 rule="para" parents="1633 39064"/>
    </justification>
  </clause>

  <clause id="39069">
    <literal><![CDATA[
      a(x,y,L((z * (u \ 1)) \ w,u,z)) = a(x,y,(u \ 1) \ (z \ w))
    ]]></literal>
    <justification jstring="[para(11812(a,1),39064(a,1,3,1))].">
      <j1 rule="para" parents="11812 39064"/>
    </justification>
  </clause>

  <clause id="39070">
    <literal><![CDATA[
      a(x,y,L((z * u) \ w,z,u)) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27626,a,b,39066,a)].">
      <j1 rule="hyper" parents="64 27626 39066"/>
    </justification>
  </clause>

  <clause id="39071">
    <literal><![CDATA[
      a(x,y,L(R(T(z,u * w),u,w),w,u)) = a(x,y,w \ (u \ ((z * u) * w)))
    ]]></literal>
    <justification jstring="[para(796(a,1),39066(a,1,3,1))].">
      <j1 rule="para" parents="796 39066"/>
    </justification>
  </clause>

  <clause id="39072">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * (u * z)))) = a(x,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27493,a,b,39067,a)].">
      <j1 rule="hyper" parents="64 27493 39067"/>
    </justification>
  </clause>

  <clause id="39073">
    <literal><![CDATA[
      a(x,y,L(L(z \ u,w,z),z,w)) = a(x,y,w \ (z \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27718,a,b,39070,a)].">
      <j1 rule="hyper" parents="64 27718 39070"/>
    </justification>
  </clause>

  <clause id="39074">
    <literal><![CDATA[
      a(x,y,L((z * (u \ 1)) \ w,z,u)) = a(x,y,z \ ((u \ 1) \ w))
    ]]></literal>
    <justification jstring="[para(1631(a,1),39070(a,1,3))].">
      <j1 rule="para" parents="1631 39070"/>
    </justification>
  </clause>

  <clause id="39075">
    <literal><![CDATA[
      a(x,y,T((z \ 1) \ (u \ w),v5)) = a(x,y,L((u * (z \ 1)) \ w,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27304,a,b,39069,a)].">
      <j1 rule="hyper" parents="373 27304 39069"/>
    </justification>
  </clause>

  <clause id="39076">
    <literal><![CDATA[
      a(x,x \ (x \ y),x \ (x \ y)) = a(x,y,((y \ x) * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,11965,a(flip),b,39055,a),flip(a)].">
      <j1 rule="hyper" parents="64 11965 39055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39078">
    <literal><![CDATA[
      L(x,y,a(z,u,((u \ z) * z) \ 1)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[para(39076(a,1),37151(a,1,3))].">
      <j1 rule="para" parents="39076 37151"/>
    </justification>
  </clause>

  <clause id="39079">
    <literal><![CDATA[
      L(x,y,a(z,u,(u \ z) * z)) = L(x,y,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33636,a(flip),b,39078,a)].">
      <j1 rule="hyper" parents="64 33636 39078"/>
    </justification>
  </clause>

  <clause id="39080">
    <literal><![CDATA[
      a(x,y,L(L(T(z,u * w),u,w),w,u)) = a(x,y,w \ (u \ ((z * u) * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27703,a(flip),b,39071,a)].">
      <j1 rule="hyper" parents="64 27703 39071"/>
    </justification>
  </clause>

  <clause id="39081">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((w * u) * z))) = a(x,y,L(L(w,u,z),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27497,a(flip),b,39080,a),flip(a)].">
      <j1 rule="hyper" parents="64 27497 39080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39083">
    <literal><![CDATA[
      a(x,y,L(L(z * u,w,v5),u,u)) = a(x,y,L((((u \ 1) \ 1) \ 1) \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(27897(a,1),38992(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="27897 38992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39084">
    <literal><![CDATA[
      a(x,y,L(L(z * u,w,v5),u,u)) = a(x,y,L((u \ 1) \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,27624,a(flip),b,39083,a),flip(a)].">
      <j1 rule="hyper" parents="373 27624 39083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39086">
    <literal><![CDATA[
      R(x,y,((z \ u) \ u) \ ((1 / (z \ u)) \ u)) = R(x,y,z \ (((u \ z) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(37459(a,1),39050(a,1,3))].">
      <j1 rule="para" parents="37459 39050"/>
    </justification>
  </clause>

  <clause id="39087">
    <literal><![CDATA[
      R(x,y,z \ (((u \ z) \ 1) * u)) = R(x,y,(z \ u) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26327,a(flip),b,39086,a),flip(a)].">
      <j1 rule="hyper" parents="64 26327 39086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39089">
    <literal><![CDATA[
      R(x,y,(z \ u) \ ((z \ u) \ 1)) = R(x,y,(u \ z) * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,31712,a,b,39087,a)].">
      <j1 rule="hyper" parents="64 31712 39087"/>
    </justification>
  </clause>

  <clause id="39090">
    <literal><![CDATA[
      R(R(x,y,(z \ u) * (z \ u)),y,w) = R(x,y,((u \ z) * (z / u)) \ w)
    ]]></literal>
    <justification jstring="[para(39089(a,1),27249(a,1,1))].">
      <j1 rule="para" parents="39089 27249"/>
    </justification>
  </clause>

  <clause id="39091">
    <literal><![CDATA[
      R(x,y,((z \ u) * (u / z)) \ w) = R(x,y,((u \ z) * (u \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26512,a(flip),b,39090,a),flip(a)].">
      <j1 rule="hyper" parents="64 26512 39090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39092">
    <literal><![CDATA[
      L(x \ R(x,y,((z \ u) * (z \ u)) * w),x,w * y) = a(x,y,((z / u) * (z / u)) \ w)
    ]]></literal>
    <justification jstring="[para(39091(a,1),27216(a,1,1,2))].">
      <j1 rule="para" parents="39091 27216"/>
    </justification>
  </clause>

  <clause id="39093">
    <literal><![CDATA[
      a(x,y,L(z,u,L(w,u,u)) * (u \ w)) = a(x,y,L(w,u,u) * ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[para(11794(a,1),39041(a,1,3,1))].">
      <j1 rule="para" parents="11794 39041"/>
    </justification>
  </clause>

  <clause id="39094">
    <literal><![CDATA[
      a(x,y,(T(((z / u) \ 1) \ 1,w) \ 1) \ z) = a(x,y,((u / z) \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27416,a(flip),b,38964,a),flip(a)].">
      <j1 rule="hyper" parents="373 27416 38964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39096">
    <literal><![CDATA[
      a(x,y,(T(((z / u) \ 1) \ 1,w) \ 1) \ z) = a(x,y,((z \ u) \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27412,a(flip),b,39094,a),flip(a)].">
      <j1 rule="hyper" parents="373 27412 39094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39097">
    <literal><![CDATA[
      a(x,y,((((z / u) \ 1) \ 1) \ 1) \ z) = a(x,y,((z \ u) \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27410,a(flip),b,39096,a)].">
      <j1 rule="hyper" parents="64 27410 39096"/>
    </justification>
  </clause>

  <clause id="39098">
    <literal><![CDATA[
      a(x,y,((z / u) \ 1) \ z) = a(x,y,((z \ u) \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27522,a(flip),b,39097,a)].">
      <j1 rule="hyper" parents="64 27522 39097"/>
    </justification>
  </clause>

  <clause id="39101">
    <literal><![CDATA[
      a(x,y,((z \ u) \ 1) \ u) = a(x,y,((u \ z) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27520,a(flip),b,39098,a)].">
      <j1 rule="hyper" parents="64 27520 39098"/>
    </justification>
  </clause>

  <clause id="39102">
    <literal><![CDATA[
      R(x,y,(L(z,z,u) \ w) * (u \ (z \ u))) = R(x,y,((u \ (z \ u)) * (u \ (z \ u))) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26254,a(flip),b,38916,a)].">
      <j1 rule="hyper" parents="64 26254 38916"/>
    </justification>
  </clause>

  <clause id="39103">
    <literal><![CDATA[
      a(x,y,((a(z,u,w) \ 1) * v5) \ v6) = a(x,y,(v5 * a(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,27746,a(flip),b,38923,a)].">
      <j1 rule="hyper" parents="64 27746 38923"/>
    </justification>
  </clause>

  <clause id="39104">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ v5,a(z,u,w),a(z,u,w)) \ v6) = a(x,y,(v5 * a(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,27654,a,b,39103,a)].">
      <j1 rule="hyper" parents="64 27654 39103"/>
    </justification>
  </clause>

  <clause id="39105">
    <literal><![CDATA[
      a(x,y,(z * a(u,u,z)) \ w) = a(x,y,L(z,u,u) \ w)
    ]]></literal>
    <justification jstring="[para(5669(a,1),39103(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="5669 39103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39106">
    <literal><![CDATA[
      a(x,y,(z \ ((z \ 1) \ u)) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30244,a,b,39105,a)].">
      <j1 rule="hyper" parents="64 30244 39105"/>
    </justification>
  </clause>

  <clause id="39107">
    <literal><![CDATA[
      a(x,y,L(z * u,z,z) \ w) = a(x,y,((z \ 1) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(30227(a,1),39105(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30227 39105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39108">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ (z \ u)) \ w) = a(x,y,L(u,z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27694,a,b,39106,a)].">
      <j1 rule="hyper" parents="64 27694 39106"/>
    </justification>
  </clause>

  <clause id="39109">
    <literal><![CDATA[
      a(x,y,L(z * u,u,u) \ w) = a(x,y,((u \ 1) \ z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31580,a(flip),b,39106,a),flip(a)].">
      <j1 rule="hyper" parents="64 31580 39106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39110">
    <literal><![CDATA[
      a(x,y,(L(z,u,u) * u) \ w) = a(x,y,((u \ 1) \ z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27729,a(flip),b,39107,a)].">
      <j1 rule="hyper" parents="64 27729 39107"/>
    </justification>
  </clause>

  <clause id="39111">
    <literal><![CDATA[
      a(x,y,L(z,u,u) \ (u \ z)) = a(x,y,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(27585,a,39108,a),flip(a)].">
      <j1 rule="hyper" parents="27585 39108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39112">
    <literal><![CDATA[
      a(x,y,L(z \ (u \ z),u,z)) = a(x,y,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,37185,a,b,39111,a)].">
      <j1 rule="hyper" parents="64 37185 39111"/>
    </justification>
  </clause>

  <clause id="39114">
    <literal><![CDATA[
      a(x,L(y \ (z \ y),z,y) * u,L(y \ (z \ y),z,y)) = a(x,L(y \ (z \ y),z,y) \ u,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,35684,a(flip),b,39112,a)].">
      <j1 rule="hyper" parents="64 35684 39112"/>
    </justification>
  </clause>

  <clause id="39115">
    <literal><![CDATA[
      a(x,y,((z / u) * (z / u)) \ w) = a(x,y,((z \ u) * (z \ u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24738,a(flip),b,39092,a),flip(a)].">
      <j1 rule="hyper" parents="64 24738 39092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39116">
    <literal><![CDATA[
      a(x,y,((z \ u) * (z \ u)) * ((z \ u) \ w)) = a(x,y,(u \ (((z / u) \ 1) \ u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,38846,a(flip),b,39115,a),flip(a)].">
      <j1 rule="hyper" parents="64 38846 39115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39117">
    <literal><![CDATA[
      a(x,y,(z \ (((u / z) \ 1) \ z)) \ w) = a(x,y,((u \ z) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27635,a(flip),b,39116,a),flip(a)].">
      <j1 rule="hyper" parents="64 27635 39116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39118">
    <literal><![CDATA[
      a(x,y,L(z \ u,u * z,z) \ w) = a(x,y,((u \ z) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,36109,a,b,39117,a)].">
      <j1 rule="hyper" parents="64 36109 39117"/>
    </justification>
  </clause>

  <clause id="39119">
    <literal><![CDATA[
      R(x,y,((z \ (u \ z)) * (z \ (u \ z))) * w) = R(x,y,(u * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,36177,a(flip),b,39102,a),flip(a)].">
      <j1 rule="hyper" parents="64 36177 39102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39121">
    <literal><![CDATA[
      L(x \ R(x,y,(z * z) \ u),x,y * u) = a(x,y,((w \ (w / z)) * (w \ (w / z))) * u)
    ]]></literal>
    <justification jstring="[para(39119(a,1),38385(a,1,1,2))].">
      <j1 rule="para" parents="39119 38385"/>
    </justification>
  </clause>

  <clause id="39122">
    <literal><![CDATA[
      a(x,y,((z \ (z / u)) * (z \ (z / u))) * w) = a(x,y,(u * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,25181,a(flip),b,39121,a),flip(a)].">
      <j1 rule="hyper" parents="64 25181 39121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39123">
    <literal><![CDATA[
      a(x,y,z * ((u \ (u / w)) * (u \ (u / w)))) = a(x,y,(w * w) \ z)
    ]]></literal>
    <justification jstring="[hyper(27453,a,39122,a)].">
      <j1 rule="hyper" parents="27453 39122"/>
    </justification>
  </clause>

  <clause id="39124">
    <literal><![CDATA[
      a(x,y,z * ((u \ (u / w)) * (u \ (w \ u)))) = a(x,y,(w * w) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27706,a(flip),b,39123,a)].">
      <j1 rule="hyper" parents="64 27706 39123"/>
    </justification>
  </clause>

  <clause id="39125">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w \ u)) * (u \ (w \ u)))) = a(x,y,(w * w) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27706,a(flip),b,39124,a)].">
      <j1 rule="hyper" parents="64 27706 39124"/>
    </justification>
  </clause>

  <clause id="39126">
    <literal><![CDATA[
      a(x,y,(z * z) \ (((u \ (z \ u)) \ 1) * w)) = a(x,y,((u \ (z \ u)) \ 1) \ L(w,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,35195,a(flip),b,39125,a),flip(a)].">
      <j1 rule="hyper" parents="64 35195 39125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39128">
    <literal><![CDATA[
      a(x,y,((z * z) \ ((u \ (z \ u)) \ 1)) * w) = a(x,y,((u \ (z \ u)) \ 1) \ L(w,z,z))
    ]]></literal>
    <justification jstring="[para(484(a,1),39126(a,1,3))].">
      <j1 rule="para" parents="484 39126"/>
    </justification>
  </clause>

  <clause id="39129">
    <literal><![CDATA[
      a(x,y,((z \ (u \ z)) \ 1) \ L(w,u,u)) = a(x,y,(1 / (z / (z * (1 / u)))) * w)
    ]]></literal>
    <justification jstring="[para(33081(a,1),39128(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="33081 39128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39130">
    <literal><![CDATA[
      a(x,y,((z \ (u \ z)) \ 1) \ L(w,u,u)) = a(x,y,(((z * (1 / u)) \ z) \ 1) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27671,a(flip),b,39129,a),flip(a)].">
      <j1 rule="hyper" parents="373 27671 39129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39131">
    <literal><![CDATA[
      a(x,y,((z \ (u \ z)) \ 1) \ L(w,u,u)) = a(x,y,((z \ ((1 / u) \ z)) \ 1) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,28084,a(flip),b,39130,a),flip(a)].">
      <j1 rule="hyper" parents="373 28084 39130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39132">
    <literal><![CDATA[
      a(x,y,((z \ ((1 / u) \ z)) \ 1) * w) = a(x,y,(z \ (((u \ 1) \ 1) \ z)) * w)
    ]]></literal>
    <justification jstring="[para(35217(a,1),39131(a,1,3)),flip(a)].">
      <j1 rule="para" parents="35217 39131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39133">
    <literal><![CDATA[
      a(x,y,((z \ ((1 / u) \ z)) \ 1) * w) = a(x,y,(z \ (u \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27683,a(flip),b,39132,a),flip(a)].">
      <j1 rule="hyper" parents="373 27683 39132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39135">
    <literal><![CDATA[
      a(x,y,((z \ (u \ z)) \ 1) * w) = a(x,y,(z \ ((u \ 1) \ z)) * w)
    ]]></literal>
    <justification jstring="[para(79(a,1),39133(a,1,3,1,1,2,1))].">
      <j1 rule="para" parents="79 39133"/>
    </justification>
  </clause>

  <clause id="39136">
    <literal><![CDATA[
      a(x,y,(z \ u) \ L(w,u \ z,u \ z)) = a(x,y,(z \ (((u \ z) \ 1) \ z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,35196,a,b,39135,a)].">
      <j1 rule="hyper" parents="64 35196 39135"/>
    </justification>
  </clause>

  <clause id="39137">
    <literal><![CDATA[
      a(x,y,(z \ (((u \ z) \ 1) \ z)) * w) = a(x,y,((z \ u) \ 1) * w)
    ]]></literal>
    <justification jstring="[para(35214(a,1),39136(a,1,3)),flip(a)].">
      <j1 rule="para" parents="35214 39136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39138">
    <literal><![CDATA[
      a(x,y,L(z,(u * u) / w,(u * u) / w) \ (u * u)) = a(x,y,L(z \ (u * u),w,w))
    ]]></literal>
    <justification jstring="[para(550(a,1),38954(a,2,3,1))].">
      <j1 rule="para" parents="550 38954"/>
    </justification>
  </clause>

  <clause id="39139">
    <literal><![CDATA[
      a(x,y,L(z,(u * u) / w,w) \ (u * u)) = a(x,y,L(z \ (u * u),w,w))
    ]]></literal>
    <justification jstring="[para(2197(a,1),39138(a,1,3,1))].">
      <j1 rule="para" parents="2197 39138"/>
    </justification>
  </clause>

  <clause id="39141">
    <literal><![CDATA[
      a(x,y,L(z \ (u * u),w,w)) = a(x,y,L(z,w,w) \ (u * u))
    ]]></literal>
    <justification jstring="[para(11870(a,1),39139(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="11870 39139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39142">
    <literal><![CDATA[
      a(x,y,L((z * T(u,u \ 1)) \ (w * w),u,u)) = a(x,y,(L(z,u,u) * u) \ (w * w))
    ]]></literal>
    <justification jstring="[para(3951(a,1),39141(a,2,3,1))].">
      <j1 rule="para" parents="3951 39141"/>
    </justification>
  </clause>

  <clause id="39144">
    <literal><![CDATA[
      a(x,y,L((z * T(u,u \ 1)) \ (w * w),u,u)) = a(x,y,((u \ 1) \ z) \ (w * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,39110,a(flip),b,39142,a),flip(a)].">
      <j1 rule="hyper" parents="373 39110 39142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39145">
    <literal><![CDATA[
      a(x,y,L(L(z,y,x),y,y)) * (y \ L(z,y \ 1,x)) = (y \ 1) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(11980(a,1),38991(a,1,1))].">
      <j1 rule="para" parents="11980 38991"/>
    </justification>
  </clause>

  <clause id="39146">
    <literal><![CDATA[
      a(x,y,L(L(z,y,x),y,y)) * (y \ L(z,y,x)) = (y \ 1) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(11794(a,1),39145(a,1,2,2))].">
      <j1 rule="para" parents="11794 39145"/>
    </justification>
  </clause>

  <clause id="39147">
    <literal><![CDATA[
      a(x,y,L(L(z,y,x),y,y)) * (y \ L(z,y,x)) = y \ z
    ]]></literal>
    <justification jstring="[hyper(373,a,1165,a(flip),b,39146,a),flip(a)].">
      <j1 rule="hyper" parents="373 1165 39146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39148">
    <literal><![CDATA[
      a(x,y,L(L(z,y,x),y,y)) = (y \ L(z,y,x)) \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,39147,a(flip),b,23136,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 39147 23136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39149">
    <literal><![CDATA[
      R(a(x,y,z) \ 1,a(x,y,z) \ u,u \ a(x,y,z)) = u * (((a(x,y,z) \ 1) \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,3028,a(flip),b,38880,a)].">
      <j1 rule="hyper" parents="64 3028 38880"/>
    </justification>
  </clause>

  <clause id="39150">
    <literal><![CDATA[
      (x / (1 / (x \ a(y,z,u)))) \ 1 = x * (((a(y,z,u) \ 1) \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,35976,a(flip),b,39149,a)].">
      <j1 rule="hyper" parents="64 35976 39149"/>
    </justification>
  </clause>

  <clause id="39151">
    <literal><![CDATA[
      (x / ((a(y,z,u) / x) \ 1)) \ 1 = x * (((a(y,z,u) \ 1) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(25195(a,1),39150(a,1,1,2))].">
      <j1 rule="para" parents="25195 39150"/>
    </justification>
  </clause>

  <clause id="39152">
    <literal><![CDATA[
      (((a(x,y,z) / u) \ 1) \ u) \ 1 = u * (((a(x,y,z) \ 1) \ u) \ 1)
    ]]></literal>
    <justification jstring="[para(23158(a,1),39151(a,1,1))].">
      <j1 rule="para" parents="23158 39151"/>
    </justification>
  </clause>

  <clause id="39153">
    <literal><![CDATA[
      ((a(x,y,z) / u) \ 1) \ u = u * ((a(x,y,z) \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(40,a,37318,a,b,39152,a),flip(a)].">
      <j1 rule="hyper" parents="40 37318 39152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39154">
    <literal><![CDATA[
      (x * ((a(y,z,u) \ x) \ 1)) \ x = (a(y,z,u) / x) \ 1
    ]]></literal>
    <justification jstring="[para(39153(a,1),23156(a,1,1))].">
      <j1 rule="para" parents="39153 23156"/>
    </justification>
  </clause>

  <clause id="39155">
    <literal><![CDATA[
      a(x,y \ z,L(z \ y,z \ y,y)) \ u = (R(x,y \ z,(y \ z) \ 1) \ x) * u
    ]]></literal>
    <justification jstring="[para(26063(a,1),38894(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="26063 38894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39156">
    <literal><![CDATA[
      a(x,y \ z,L(z \ y,z \ y,y)) \ u = (R(x,y \ z,z \ y) \ x) * u
    ]]></literal>
    <justification jstring="[para(38043(a,1),39155(a,2,1,1))].">
      <j1 rule="para" parents="38043 39155"/>
    </justification>
  </clause>

  <clause id="39157">
    <literal><![CDATA[
      a(x,y \ z,(y \ z) \ 1) \ u = (R(x,y \ z,z \ y) \ x) * u
    ]]></literal>
    <justification jstring="[para(38933(a,1),39156(a,1,1))].">
      <j1 rule="para" parents="38933 39156"/>
    </justification>
  </clause>

  <clause id="39158">
    <literal><![CDATA[
      (R(x,y \ z,z \ y) \ x) * u = a(x,y \ z,z \ y) \ u
    ]]></literal>
    <justification jstring="[para(38987(a,1),39157(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38987 39157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39159">
    <literal><![CDATA[
      a(x,y \ x,x \ y) \ ((y \ x) \ 1) = L((y \ x) \ 1,x * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,35540,a(flip),b,39158,a),flip(a)].">
      <j1 rule="hyper" parents="64 35540 39158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39160">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y) = L((x \ y) \ 1,y * x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,38988,a(flip),b,39159,a)].">
      <j1 rule="hyper" parents="64 38988 39159"/>
    </justification>
  </clause>

  <clause id="39161">
    <literal><![CDATA[
      L((x \ y) \ 1,y * x,y) = (y * (x \ y)) \ y
    ]]></literal>
    <justification jstring="[hyper(642,a,39160,a),flip(a)].">
      <j1 rule="hyper" parents="642 39160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39162">
    <literal><![CDATA[
      a(x,y,(z * R(K(z,u) / z,z,w)) \ v5) = a(x,y,(v5 * a(z,z,w)) * (v6 * (K(u,z) / v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,38001,a(flip),b,39004,a),flip(a)].">
      <j1 rule="hyper" parents="64 38001 39004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39163">
    <literal><![CDATA[
      a(x,y,(z * R(K(z,u) / z,z,w)) \ v5) = a(x,y,v5 * (a(z,z,w) * (v6 * (K(u,z) / v6))))
    ]]></literal>
    <justification jstring="[para(27793(a,1),39162(a,2,3))].">
      <j1 rule="para" parents="27793 39162"/>
    </justification>
  </clause>

  <clause id="39164">
    <literal><![CDATA[
      a(x,y,(z * R(K(z,u) / z,z,w)) \ v5) = a(x,y,v5 * (a(z,z,w) * K(u,z)))
    ]]></literal>
    <justification jstring="[para(193(a,1),39163(a,2,3,2,2))].">
      <j1 rule="para" parents="193 39163"/>
    </justification>
  </clause>

  <clause id="39165">
    <literal><![CDATA[
      a(x,y,(z * R(K(z,u) / z,z,w)) \ v5) = a(x,y,v5 * a(z,z,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27320,a(flip),b,39164,a),flip(a)].">
      <j1 rule="hyper" parents="373 27320 39164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39167">
    <literal><![CDATA[
      a(x,y,z * (R(T(z,u),z,z * w) \ v5)) = a(x,y,v5 * a(z,z,w))
    ]]></literal>
    <justification jstring="[para(37777(a,1),39165(a,1,3))].">
      <j1 rule="para" parents="37777 39165"/>
    </justification>
  </clause>

  <clause id="39168">
    <literal><![CDATA[
      a(x,y,z * (R(z,z,z * u) \ w)) = a(x,y,w * a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27507,a(flip),b,39167,a)].">
      <j1 rule="hyper" parents="64 27507 39167"/>
    </justification>
  </clause>

  <clause id="39169">
    <literal><![CDATA[
      a(x,y,a(z,z,z * u) \ w) = a(x,y,w * a(z,z,u))
    ]]></literal>
    <justification jstring="[para(37544(a,1),39168(a,1,3))].">
      <j1 rule="para" parents="37544 39168"/>
    </justification>
  </clause>

  <clause id="39170">
    <literal><![CDATA[
      a(x,y,z * a(u * w,u,u)) = a(x,y,z * a(u,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,37844,a(flip),b,39169,a)].">
      <j1 rule="hyper" parents="64 37844 39169"/>
    </justification>
  </clause>

  <clause id="39171">
    <literal><![CDATA[
      T(x * L(a(y,y,z) \ 1,u,w),a(y,y,z)) = (L(a(y,y,z) \ 1,u,w) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,24203,a(flip),b,39021,a)].">
      <j1 rule="hyper" parents="64 24203 39021"/>
    </justification>
  </clause>

  <clause id="39172">
    <literal><![CDATA[
      (L(a(x,x,y) \ 1,z,u) \ 1) \ w = w * L(a(x,x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(23173,a,39171,a),flip(a)].">
      <j1 rule="hyper" parents="23173 39171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39175">
    <literal><![CDATA[
      a(x,y,z \ (a(u,u,u \ w) * (v5 / (v5 / (u \ w))))) = a(x,y,z \ (v5 / (v5 / ((1 / u) * w))))
    ]]></literal>
    <justification jstring="[para(27306(a,1),39002(a,1,3,2,1))].">
      <j1 rule="para" parents="27306 39002"/>
    </justification>
  </clause>

  <clause id="39177">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (x * ((1 / (x \ L(x,y,z))) * (L(x,y,z) * u))) = (1 / x) * ((((x \ L(x,y,z)) \ 1) * x) * u)
    ]]></literal>
    <justification jstring="[para(5572(a,1),33171(a,1,2,2,1,2))].">
      <j1 rule="para" parents="5572 33171"/>
    </justification>
  </clause>

  <clause id="39178">
    <literal><![CDATA[
      L(L(L(x,y,z),u,w) \ L(R(L(x,y,z),x,v5),u,w),x,L(L(x,y,z),u,w)) = a(L(L(L(x,y,z),u,w),x,v5),x,v5)
    ]]></literal>
    <justification jstring="[para(29(a,1),33413(a,1,1,2))].">
      <j1 rule="para" parents="29 33413"/>
    </justification>
  </clause>

  <clause id="39179">
    <literal><![CDATA[
      L(x,y * a(L(z,y,u),y,u),w) = L(x,z * (R(z,y,u) \ y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,36025,a(flip),b,33473,a)].">
      <j1 rule="hyper" parents="64 36025 33473"/>
    </justification>
  </clause>

  <clause id="39181">
    <literal><![CDATA[
      x * (((y \ z) / z) \ K(((y \ z) / z) \ x,u * (y \ 1))) = T(x * (((y \ z) / z) \ 1),((y \ z) / z) * u)
    ]]></literal>
    <justification jstring="[para(76(a,1),34752(a,1,2,2,2,2,2))].">
      <j1 rule="para" parents="76 34752"/>
    </justification>
  </clause>

  <clause id="39182">
    <literal><![CDATA[
      x * (((y \ z) / z) \ K(((y \ z) / z) \ x,u / y)) = T(x * (((y \ z) / z) \ 1),((y \ z) / z) * u)
    ]]></literal>
    <justification jstring="[para(14406(a,1),39181(a,1,2,2))].">
      <j1 rule="para" parents="14406 39181"/>
    </justification>
  </clause>

  <clause id="39183">
    <literal><![CDATA[
      x * (((y \ z) / z) \ K(z * ((y \ z) \ x),u / y)) = T(x * (((y \ z) / z) \ 1),((y \ z) / z) * u)
    ]]></literal>
    <justification jstring="[para(28198(a,1),39182(a,1,2,2))].">
      <j1 rule="para" parents="28198 39182"/>
    </justification>
  </clause>

  <clause id="39184">
    <literal><![CDATA[
      T(x * (((y \ z) / z) \ 1),((y \ z) / z) * u) = x * (((y \ z) / z) \ K(y * x,u / y))
    ]]></literal>
    <justification jstring="[para(28205(a,1),39183(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28205 39183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39185">
    <literal><![CDATA[
      T(x * (((y \ z) / z) \ 1),((y \ z) / z) * u) = x * (((y \ z) / z) \ K(x * y,y \ u))
    ]]></literal>
    <justification jstring="[para(11179(a,2),39184(a,2,2,2))].">
      <j1 rule="para" parents="11179 39184"/>
    </justification>
  </clause>

  <clause id="39187">
    <literal><![CDATA[
      T(x * (((x \ y) / y) \ 1),((x \ y) / y) * z) = x * (((x \ y) / y) \ K(x * x,z * x))
    ]]></literal>
    <justification jstring="[para(22812(a,1),39185(a,2,2,2))].">
      <j1 rule="para" parents="22812 39185"/>
    </justification>
  </clause>

  <clause id="39188">
    <literal><![CDATA[
      T(x * (((x \ y) / y) \ 1),((x \ y) / y) * z) = x * (x \ T((y / (x * y)) \ x,z * x))
    ]]></literal>
    <justification jstring="[para(33973(a,1),39187(a,2,2))].">
      <j1 rule="para" parents="33973 39187"/>
    </justification>
  </clause>

  <clause id="39189">
    <literal><![CDATA[
      T(x * (((x \ y) / y) \ 1),((x \ y) / y) * z) = T((y / (x * y)) \ x,z * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,10,a(flip),b,39188,a),flip(a)].">
      <j1 rule="hyper" parents="373 10 39188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39191">
    <literal><![CDATA[
      T((x / (y * x)) \ y,((y \ x) / x) * z) = T((x / (y * x)) \ y,z * y)
    ]]></literal>
    <justification jstring="[para(25776(a,1),39189(a,1,1))].">
      <j1 rule="para" parents="25776 39189"/>
    </justification>
  </clause>

  <clause id="39192">
    <literal><![CDATA[
      T((x / (y * x)) \ y,y \ z) = T((x / (y * x)) \ y,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,24995,a(flip),b,39191,a)].">
      <j1 rule="hyper" parents="64 24995 39191"/>
    </justification>
  </clause>

  <clause id="39194">
    <literal><![CDATA[
      L(a(((x * (y * z)) / z) * x,a(x,y,z) * y,u),x,x) = a(((x * (y * z)) / z) * x,((x * (y * z)) / z) * x,u)
    ]]></literal>
    <justification jstring="[para(35816(a,1),35192(a,1,1))].">
      <j1 rule="para" parents="35816 35192"/>
    </justification>
  </clause>

  <clause id="39195">
    <literal><![CDATA[
      R(x,x,(1 / (K(y,z) / (x \ u))) * L((x \ u) \ 1,w,v5)) = R(1 / (1 / x),x,u * L((x \ u) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,26255,a(flip),b,35316,a),flip(a)].">
      <j1 rule="hyper" parents="373 26255 35316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39197">
    <literal><![CDATA[
      T(T(x,(y \ R(y,z,u)) \ 1) * ((y \ R(y,z,u)) \ 1),w) = x * ((y \ R(y,z,u)) \ K((R(y,z,u) \ y) * x,w))
    ]]></literal>
    <justification jstring="[para(28209(a,1),36073(a,2,2,2))].">
      <j1 rule="para" parents="28209 36073"/>
    </justification>
  </clause>

  <clause id="39198">
    <literal><![CDATA[
      L(x,T(y * R(y,z,u),y) * ((R(y,w,v5) * y) \ v6),v7) = L(x,(y * L(y,z,u)) * ((R(y,w,v5) \ y) \ v6),v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,35096,a(flip),b,37030,a)].">
      <j1 rule="hyper" parents="64 35096 37030"/>
    </justification>
  </clause>

  <clause id="39199">
    <literal><![CDATA[
      L(x,T(y * R(y,z,u),y) * ((y * R(y,w,v5)) \ v6),v7) = L(x,(y * L(y,z,u)) * ((R(y,w,v5) \ y) \ v6),v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,29628,a,b,39198,a)].">
      <j1 rule="hyper" parents="64 29628 39198"/>
    </justification>
  </clause>

  <clause id="39200">
    <literal><![CDATA[
      L(x,(y * L(y,z,u)) * ((R(y,z,u) \ y) \ w),v5) = L(x,K(y * R(y,z,u),y) * w,v5)
    ]]></literal>
    <justification jstring="[para(5778(a,1),39199(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5778 39199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39201">
    <literal><![CDATA[
      L(x,(y * L(y,z,u)) * ((R(y,z,u) \ y) \ w),v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29429,a(flip),b,39200,a),flip(a)].">
      <j1 rule="hyper" parents="373 29429 39200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39203">
    <literal><![CDATA[
      a(x,y \ ((1 / y) \ z),L(z,y,y)) * (y \ L(z,y \ ((1 / y) \ z),x)) = (y \ 1) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(38943(a,1),37646(a,1,1))].">
      <j1 rule="para" parents="38943 37646"/>
    </justification>
  </clause>

  <clause id="39204">
    <literal><![CDATA[
      a(x,y \ (y \ z),L(z,y,y)) * (y \ L(z,y \ ((1 / y) \ z),x)) = (y \ 1) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(32242(a,1),39203(a,1,1))].">
      <j1 rule="para" parents="32242 39203"/>
    </justification>
  </clause>

  <clause id="39205">
    <literal><![CDATA[
      a(x,L(y,z,z),L(y,z,z)) * (z \ L(y,z \ ((1 / z) \ y),x)) = (z \ 1) * (z \ ((1 / z) \ y))
    ]]></literal>
    <justification jstring="[para(32142(a,1),39204(a,1,1))].">
      <j1 rule="para" parents="32142 39204"/>
    </justification>
  </clause>

  <clause id="39206">
    <literal><![CDATA[
      a(x,L(y,z,z),L(y,z,z)) * (z \ L(y,z \ (z \ y),x)) = (z \ 1) * (z \ ((1 / z) \ y))
    ]]></literal>
    <justification jstring="[para(30872(a,1),39205(a,1,2,2))].">
      <j1 rule="para" parents="30872 39205"/>
    </justification>
  </clause>

  <clause id="39207">
    <literal><![CDATA[
      a(x,L(y,z,z),L(y,z,z)) * (z \ L(y,L(y,z,z),x)) = (z \ 1) * (z \ ((1 / z) \ y))
    ]]></literal>
    <justification jstring="[para(31756(a,1),39206(a,1,2,2))].">
      <j1 rule="para" parents="31756 39206"/>
    </justification>
  </clause>

  <clause id="39208">
    <literal><![CDATA[
      a(x,L(y,z,z),L(y,z,z)) * (z \ L(y,L(y,z,z),x)) = z \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,1165,a(flip),b,39207,a),flip(a)].">
      <j1 rule="hyper" parents="373 1165 39207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39209">
    <literal><![CDATA[
      L(L(x,y,y) * a(y,y,L(x,z,u)),R(x,z,u),a(R(x,z,u),y,y)) = R(x,z,u) * (L(x \ R(x,z,u),y,y) \ 1)
    ]]></literal>
    <justification jstring="[para(27644(a,1),37770(a,1,1,2))].">
      <j1 rule="para" parents="27644 37770"/>
    </justification>
  </clause>

  <clause id="39210">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * R(y,z,u)) * (y \ L(y,w,v5))) = L(y \ L(y,w,v5),x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(38768(a,1),38771(a,1,1,2))].">
      <j1 rule="para" parents="38768 38771"/>
    </justification>
  </clause>

  <clause id="39211">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,R(x,w,v5)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(396,a,39210,a),flip(a)].">
      <j1 rule="hyper" parents="396 39210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39214">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,L(x,w,v5)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29221,a(flip),b,39211,a)].">
      <j1 rule="hyper" parents="64 29221 39211"/>
    </justification>
  </clause>

  <clause id="39215">
    <literal><![CDATA[
      (L(x,y,z) * u) / (x \ L(x,w,v5)) = L(x,y,z) * (u / (x \ L(x,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(225,a,39214,a(flip),b,10262,a(flip))].">
      <j1 rule="hyper" parents="225 39214 10262"/>
    </justification>
  </clause>

  <clause id="39216">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,u,w) * v5) = L(x,u,w) * (v5 / (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,23740,a(flip),b,39215,a)].">
      <j1 rule="hyper" parents="64 23740 39215"/>
    </justification>
  </clause>

  <clause id="39217">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (L(x,u,w) * v5) = L(x,u,w) * ((x \ L(x,y,z)) \ v5)
    ]]></literal>
    <justification jstring="[para(23740(a,1),39216(a,2,2))].">
      <j1 rule="para" parents="23740 39216"/>
    </justification>
  </clause>

  <clause id="39218">
    <literal><![CDATA[
      L(x,y,z) * ((x \ L(x,y,z)) \ u) = L((x \ 1) \ u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11898,a(flip),b,39217,a),flip(a)].">
      <j1 rule="hyper" parents="64 11898 39217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39219">
    <literal><![CDATA[
      L(x,y,z) * ((x \ L(x,y,z)) \ u) = u * R(T(x,u),x \ L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,37155,a,b,39218,a),flip(a)].">
      <j1 rule="hyper" parents="373 37155 39218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39220">
    <literal><![CDATA[
      R(x,x \ L(x,y,z),u) * u = L(x,y,z) * ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,267,a(flip),b,39219,a)].">
      <j1 rule="hyper" parents="373 267 39219"/>
    </justification>
  </clause>

  <clause id="39221">
    <literal><![CDATA[
      L(x,x \ L(x,y,z),u) * u = L(x,y,z) * ((x \ L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(35115(a,1),39220(a,1,1))].">
      <j1 rule="para" parents="35115 39220"/>
    </justification>
  </clause>

  <clause id="39222">
    <literal><![CDATA[
      T((x \ 1) / (x \ L(1 / x,y,z)),L(x \ 1,y,z)) = (x \ (L(1 / x,y,z) \ 1)) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(198(a,1),38825(a,1,2)),flip(a)].">
      <j1 rule="para" parents="198 38825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39224">
    <literal><![CDATA[
      T(1 / L(1 / x,y,z),L(x \ 1,y,z)) = (x \ (L(1 / x,y,z) \ 1)) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(35064(a,1),39222(a,1,1))].">
      <j1 rule="para" parents="35064 39222"/>
    </justification>
  </clause>

  <clause id="39225">
    <literal><![CDATA[
      (x \ (L(1 / x,y,z) \ 1)) / (x \ 1) = T(1 / L(1 / x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,23153,a(flip),b,39224,a),flip(a)].">
      <j1 rule="hyper" parents="64 23153 39224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39227">
    <literal><![CDATA[
      (x \ (L(1 / x,y,z) \ 1)) / (x \ 1) = T(L(1 / x,y,z) \ 1,K(1,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,24387,a(flip),b,39225,a),flip(a)].">
      <j1 rule="hyper" parents="373 24387 39225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39228">
    <literal><![CDATA[
      (x \ (L(1 / x,y,z) \ 1)) / (x \ 1) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,28612,a(flip),b,39227,a),flip(a)].">
      <j1 rule="hyper" parents="373 28612 39227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39230">
    <literal><![CDATA[
      R(x,x,y * x) \ (1 * R(1 \ R(x,x,y * x),z,u)) = (R(x,x,y) \ 1) \ R(R(x,x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,24594,a(flip),b,38826,a),flip(a)].">
      <j1 rule="hyper" parents="64 24594 38826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39232">
    <literal><![CDATA[
      R(x,x,y * x) \ (1 * R(1 \ R(x,x,y * x),z,u)) = R(x,x,y) \ R(R(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2009,a(flip),b,39230,a),flip(a)].">
      <j1 rule="hyper" parents="373 2009 39230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39233">
    <literal><![CDATA[
      R(x,x,y * x) \ (1 * R(1 \ R(x,x,y * x),z,u)) = L(x \ R(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,36889,a(flip),b,39232,a),flip(a)].">
      <j1 rule="hyper" parents="373 36889 39232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39234">
    <literal><![CDATA[
      R(x,x,y * x) \ (1 * R(R(x,x,y * x),z,u)) = L(x \ R(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(66(a,1),39233(a,1,2,2,1))].">
      <j1 rule="para" parents="66 39233"/>
    </justification>
  </clause>

  <clause id="39235">
    <literal><![CDATA[
      R(x,x,y * x) \ R(R(x,x,y * x),z,u) = L(x \ R(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[hyper(342,a,39234,a)].">
      <j1 rule="hyper" parents="342 39234"/>
    </justification>
  </clause>

  <clause id="39236">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u * x) = L(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,36889,a(flip),b,39235,a)].">
      <j1 rule="hyper" parents="64 36889 39235"/>
    </justification>
  </clause>

  <clause id="39237">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,x \ u) = L(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23833,a(flip),b,39236,a),flip(a)].">
      <j1 rule="hyper" parents="64 23833 39236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39238">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u) = u \ ((u / x) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11070,a(flip),b,39237,a),flip(a)].">
      <j1 rule="hyper" parents="64 11070 39237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39239">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u) * u = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(39237(a,1),38466(a,1,1))].">
      <j1 rule="para" parents="39237 38466"/>
    </justification>
  </clause>

  <clause id="39240">
    <literal><![CDATA[
      L(x \ ((x / y) * R(y,z,u)),y,z * u) = L(a(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(39238(a,1),16033(a,1,1))].">
      <j1 rule="para" parents="39238 16033"/>
    </justification>
  </clause>

  <clause id="39241">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u) = u \ (R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[para(24603(a,2),39238(a,2,2))].">
      <j1 rule="para" parents="24603 39238"/>
    </justification>
  </clause>

  <clause id="39242">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,u) \ (R(x,y,z) * (x \ u)) = u
    ]]></literal>
    <justification jstring="[hyper(149,a,39239,a)].">
      <j1 rule="hyper" parents="149 39239"/>
    </justification>
  </clause>

  <clause id="39243">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,u)) = x \ (R(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,39241,a)].">
      <j1 rule="hyper" parents="64 102 39241"/>
    </justification>
  </clause>

  <clause id="39244">
    <literal><![CDATA[
      L(x \ (R(y,z,u) * (y \ x)),y,z * u) = L(a(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(39241(a,1),16033(a,1,1))].">
      <j1 rule="para" parents="39241 16033"/>
    </justification>
  </clause>

  <clause id="39245">
    <literal><![CDATA[
      x \ (R(y,y,z) * (y \ x)) = L(a(y,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(30058(a,1),39241(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30058 39241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39246">
    <literal><![CDATA[
      R(T(x / (y * x),z),y,y \ z) = L(a(y,y,x),y,z) * (z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(39245(a,1),35991(a,2,1))].">
      <j1 rule="para" parents="39245 35991"/>
    </justification>
  </clause>

  <clause id="39247">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (R(x,y,z) * (x \ a(u,x,w))) = a(u,x,w)
    ]]></literal>
    <justification jstring="[para(35836(a,1),39242(a,1,1))].">
      <j1 rule="para" parents="35836 39242"/>
    </justification>
  </clause>

  <clause id="39248">
    <literal><![CDATA[
      (x * R(y,z,u)) / (x * y) = x \ (R(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,23726,a,b,39243,a)].">
      <j1 rule="hyper" parents="64 23726 39243"/>
    </justification>
  </clause>

  <clause id="39249">
    <literal><![CDATA[
      K(x,y) * T(y \ (R(x,z,u) * (x \ y)),w) = (R(x,z,u) * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(39248(a,1),34439(a,1,2,1))].">
      <j1 rule="para" parents="39248 34439"/>
    </justification>
  </clause>

  <clause id="39250">
    <literal><![CDATA[
      L(a(x,y,z),x,x \ u) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16069,a(flip),b,39240,a)].">
      <j1 rule="hyper" parents="64 16069 39240"/>
    </justification>
  </clause>

  <clause id="39251">
    <literal><![CDATA[
      L(a(x,y,x \ z),x,z) = a(x,y,x \ z)
    ]]></literal>
    <justification jstring="[hyper(33227,a,39250,a),flip(a)].">
      <j1 rule="hyper" parents="33227 39250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39252">
    <literal><![CDATA[
      L(a(x,y,z),x,u * x) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(24199,a,39250,a),flip(a)].">
      <j1 rule="hyper" parents="24199 39250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39253">
    <literal><![CDATA[
      (x / y) * (y * a(y,z,u)) = x * L(a(y,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,39250,a(flip),b,11067,a),flip(a)].">
      <j1 rule="hyper" parents="145 39250 11067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39254">
    <literal><![CDATA[
      L(a(x,y,z),x,x * u) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),39250(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9 39250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39255">
    <literal><![CDATA[
      (x * ((y * x) * L(a(x,z,u),x,y))) \ (x * ((y * x) * a(x,z,u))) = a(y * x,x,L(a(x,z,u),y * x,x))
    ]]></literal>
    <justification jstring="[para(39252(a,1),27623(a,1,1,2,2))].">
      <j1 rule="para" parents="39252 27623"/>
    </justification>
  </clause>

  <clause id="39256">
    <literal><![CDATA[
      (x * y) * (T(y,x * y) * a(y,z,u)) = y * ((x * y) * L(a(y,z,u),y,x))
    ]]></literal>
    <justification jstring="[para(39252(a,1),29920(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="39252 29920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39257">
    <literal><![CDATA[
      L(a(x,y,x * z),x,z) = a(x,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(33227,a,39254,a),flip(a)].">
      <j1 rule="hyper" parents="33227 39254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39258">
    <literal><![CDATA[
      (x * a(x,y,x * z)) * z = x * (z * a(x,y,x * z))
    ]]></literal>
    <justification jstring="[para(39257(a,1),29927(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="39257 29927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39259">
    <literal><![CDATA[
      x * ((y / x) * (x * a(x,z,u))) = (a(x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[para(39253(a,2),30439(a,1,2))].">
      <j1 rule="para" parents="39253 30439"/>
    </justification>
  </clause>

  <clause id="39260">
    <literal><![CDATA[
      x \ ((x * a(x,y,z)) * u) = (u / x) * (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,23168,a(flip),b,39259,a)].">
      <j1 rule="hyper" parents="139 23168 39259"/>
    </justification>
  </clause>

  <clause id="39261">
    <literal><![CDATA[
      x * (y * (T(x,y) * a(x,z,u))) = (x * a(x,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,5022,a(flip),b,39260,a)].">
      <j1 rule="hyper" parents="145 5022 39260"/>
    </justification>
  </clause>

  <clause id="39262">
    <literal><![CDATA[
      x \ (L(x \ (R(L(y,y,x),z,u) * (L(y,y,x) \ x)),L(y,y,x),z * u) * (y \ x)) = (x \ (y \ x)) * T(a(L(y,y,x),z,u),y \ x)
    ]]></literal>
    <justification jstring="[para(39244(a,2),29729(a,1,2,1))].">
      <j1 rule="para" parents="39244 29729"/>
    </justification>
  </clause>

  <clause id="39263">
    <literal><![CDATA[
      L((x \ 1) \ (x \ a(y,x,z)),x,L(x,u,w)) = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29209,a(flip),b,39247,a)].">
      <j1 rule="hyper" parents="64 29209 39247"/>
    </justification>
  </clause>

  <clause id="39264">
    <literal><![CDATA[
      L(x \ ((1 / x) \ a(y,x,z)),x,L(x,u,w)) = a(y,x,z)
    ]]></literal>
    <justification jstring="[para(1166(a,1),39263(a,1,1))].">
      <j1 rule="para" parents="1166 39263"/>
    </justification>
  </clause>

  <clause id="39265">
    <literal><![CDATA[
      L(x \ (a(y,x,z) * x),x,L(x,u,w)) = a(y,x,z)
    ]]></literal>
    <justification jstring="[para(35737(a,1),39264(a,1,1,2))].">
      <j1 rule="para" parents="35737 39264"/>
    </justification>
  </clause>

  <clause id="39266">
    <literal><![CDATA[
      L(a(x,y,z),y,L(y,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(23174(a,1),39265(a,1,1))].">
      <j1 rule="para" parents="23174 39265"/>
    </justification>
  </clause>

  <clause id="39268">
    <literal><![CDATA[
      x * ((L(x,y,z) \ 1) * a(u,x,w)) = a(u,x,w) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(39266(a,1),24798(a,1,1)),flip(a)].">
      <j1 rule="para" parents="39266 24798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39269">
    <literal><![CDATA[
      x * (y * T(x * a(x,z,u),y)) = (x * a(x,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[para(28750(a,2),39261(a,1,2,2))].">
      <j1 rule="para" parents="28750 39261"/>
    </justification>
  </clause>

  <clause id="39270">
    <literal><![CDATA[
      (x * a(x,y,z)) * (x * u) = x * ((x * a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(737,a,39269,a),flip(a)].">
      <j1 rule="hyper" parents="737 39269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39271">
    <literal><![CDATA[
      (x * a(x,y,z)) \ (x * u) = x * ((x * a(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,39270,a)].">
      <j1 rule="hyper" parents="139 168 39270"/>
    </justification>
  </clause>

  <clause id="39272">
    <literal><![CDATA[
      (x * ((x * a(x,y,z)) * a(x,y,z))) \ (x * a(x,y,z)) = 1 / (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(39270(a,1),309(a,1,1))].">
      <j1 rule="para" parents="39270 309"/>
    </justification>
  </clause>

  <clause id="39273">
    <literal><![CDATA[
      (x * a(x,y,z)) \ (x * u) = x * ((a(x,y,z) * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,24797,a,b,39271,a),flip(a)].">
      <j1 rule="hyper" parents="373 24797 39271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39274">
    <literal><![CDATA[
      x * ((x * a(x,y,z)) \ (u * a(x,y,z))) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29955,a(flip),b,39271,a),flip(a)].">
      <j1 rule="hyper" parents="64 29955 39271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39275">
    <literal><![CDATA[
      L(a(x,y,z) \ u,x,a(x,y,z)) = x * ((a(x,y,z) * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30327,a,b,39273,a)].">
      <j1 rule="hyper" parents="64 30327 39273"/>
    </justification>
  </clause>

  <clause id="39276">
    <literal><![CDATA[
      L(x * y,x,a(x,z,u)) = x * L(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(26739(a,1),39274(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26739 39274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39277">
    <literal><![CDATA[
      L(x * T(y,x),x,a(x,z,u)) = L(y,x,a(x,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,266,a(flip),b,39276,a),flip(a)].">
      <j1 rule="hyper" parents="373 266 39276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39278">
    <literal><![CDATA[
      R(x * y,x,a(x,z,u)) = x * L(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,28832,a,b,39276,a)].">
      <j1 rule="hyper" parents="64 28832 39276"/>
    </justification>
  </clause>

  <clause id="39279">
    <literal><![CDATA[
      L(x / y,y,a(y,z,u)) = L(x,y,a(y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(35,a,5618,a(flip),b,39276,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 5618 39276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39280">
    <literal><![CDATA[
      L((x \ 1) \ y,x,a(x,z,u)) = (x \ 1) \ R(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,2146,a(flip),b,39278,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 2146 39278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39281">
    <literal><![CDATA[
      L(x \ y,x,a(x,z,u)) = x \ L(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(38,a,28864,a(flip),b,39279,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="38 28864 39279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39282">
    <literal><![CDATA[
      L(x * y,y,a(y,z,u)) = L(x,y,a(y,z,u)) * y
    ]]></literal>
    <justification jstring="[para(115(a,1),39277(a,1,1))].">
      <j1 rule="para" parents="115 39277"/>
    </justification>
  </clause>

  <clause id="39283">
    <literal><![CDATA[
      L((x \ 1) \ a(x,y,z),x,a(x,y,z)) = (x \ 1) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(24651(a,1),39280(a,2,2))].">
      <j1 rule="para" parents="24651 39280"/>
    </justification>
  </clause>

  <clause id="39284">
    <literal><![CDATA[
      (x \ (a(x,y,z) \ 1)) \ 1 = (x \ 1) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31586,a(flip),b,39283,a)].">
      <j1 rule="hyper" parents="64 31586 39283"/>
    </justification>
  </clause>

  <clause id="39285">
    <literal><![CDATA[
      (x * a(x,y,z)) \ 1 = x \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(40,a,25196,a,b,39284,a)].">
      <j1 rule="hyper" parents="40 25196 39284"/>
    </justification>
  </clause>

  <clause id="39286">
    <literal><![CDATA[
      a(x,x,y) \ (a(a(x,x,y),z,u) \ 1) = a(x,L(x,z,u),y) \ 1
    ]]></literal>
    <justification jstring="[para(37921(a,1),39285(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37921 39285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39287">
    <literal><![CDATA[
      a(x,L(x,y,z),u) \ a(x,x,u) = a(a(x,x,u),y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(39,a,39015,a,b,39286,a)].">
      <j1 rule="hyper" parents="39 39015 39286"/>
    </justification>
  </clause>

  <clause id="39288">
    <literal><![CDATA[
      L(a(x,x,y),x,z) * (z \ (x \ z)) = R(z \ (x \ z),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,28068,a(flip),b,39246,a),flip(a)].">
      <j1 rule="hyper" parents="64 28068 39246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39289">
    <literal><![CDATA[
      a(x,x,y) * (z \ (x \ z)) = R(z \ (x \ z),x,y)
    ]]></literal>
    <justification jstring="[para(38646(a,1),39288(a,1,1))].">
      <j1 rule="para" parents="38646 39288"/>
    </justification>
  </clause>

  <clause id="39291">
    <literal><![CDATA[
      K(x,y) * (y \ (R(x,z,u) * (x \ y))) = (R(x,z,u) * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(114(a,1),39249(a,1,2))].">
      <j1 rule="para" parents="114 39249"/>
    </justification>
  </clause>

  <clause id="39292">
    <literal><![CDATA[
      T(x,y) \ (R(y,z,u) * (y \ x)) = (R(y,z,u) * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(6301,a,39291,a)].">
      <j1 rule="hyper" parents="6301 39291"/>
    </justification>
  </clause>

  <clause id="39293">
    <literal><![CDATA[
      T(x,y) \ (R(y,z,u) * (y \ x)) = (x * y) \ (R(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,28940,a(flip),b,39292,a),flip(a)].">
      <j1 rule="hyper" parents="373 28940 39292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39294">
    <literal><![CDATA[
      (x * y) \ (R(y,z,u) * x) = x \ ((R(y,z,u) * x) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,25857,a(flip),b,39293,a),flip(a)].">
      <j1 rule="hyper" parents="64 25857 39293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39295">
    <literal><![CDATA[
      a((x * y) \ ((R(z,x,y * (u * u)) * (x * y)) / z),w,v5) = a(a(z,x,y * (u * u)),w,v5)
    ]]></literal>
    <justification jstring="[para(39294(a,1),35402(a,1,1))].">
      <j1 rule="para" parents="39294 35402"/>
    </justification>
  </clause>

  <clause id="39296">
    <literal><![CDATA[
      (x * y) * (T(y,x * y) * a(y,z,u)) = y * (x * (y * a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(100(a,1),39256(a,2,2))].">
      <j1 rule="para" parents="100 39256"/>
    </justification>
  </clause>

  <clause id="39297">
    <literal><![CDATA[
      (x * y) * (T(y,y * x) * a(y,z,u)) = y * (x * (y * a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(4683(a,1),39296(a,1,2,1))].">
      <j1 rule="para" parents="4683 39296"/>
    </justification>
  </clause>

  <clause id="39298">
    <literal><![CDATA[
      (x * y) * T(y * a(y,z,u),y * x) = y * (x * (y * a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(28750(a,2),39297(a,1,2))].">
      <j1 rule="para" parents="28750 39297"/>
    </justification>
  </clause>

  <clause id="39299">
    <literal><![CDATA[
      T((x * a(x,y,z)) * (u * x),K(u,x)) = x * (u * (x * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11061,a,b,39298,a)].">
      <j1 rule="hyper" parents="64 11061 39298"/>
    </justification>
  </clause>

  <clause id="39300">
    <literal><![CDATA[
      T((x * a(x,y,z)) * (u * x),K(x,u)) = x * (u * (x * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(8184,a,39299,a)].">
      <j1 rule="hyper" parents="8184 39299"/>
    </justification>
  </clause>

  <clause id="39301">
    <literal><![CDATA[
      (x * a(x,y,z)) * (u * x) = x * (u * (x * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,24829,a(flip),b,39300,a)].">
      <j1 rule="hyper" parents="64 24829 39300"/>
    </justification>
  </clause>

  <clause id="39302">
    <literal><![CDATA[
      (x * (x * (a(x,y,z) * a(x,y,z)))) \ (x * a(x,y,z)) = 1 / (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(29910(a,1),39272(a,1,1,2))].">
      <j1 rule="para" parents="29910 39272"/>
    </justification>
  </clause>

  <clause id="39303">
    <literal><![CDATA[
      L(a(x,y,z) * a(x,y,z),x,x) \ (a(x,y,z) / x) = 1 / (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,25237,a(flip),b,39302,a)].">
      <j1 rule="hyper" parents="64 25237 39302"/>
    </justification>
  </clause>

  <clause id="39304">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ (a(x,y,z) / x) = 1 / (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(33059(a,1),39303(a,1,1))].">
      <j1 rule="para" parents="33059 39303"/>
    </justification>
  </clause>

  <clause id="39305">
    <literal><![CDATA[
      (1 / a(x,y,z)) / x = 1 / (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,887,a(flip),b,39304,a)].">
      <j1 rule="hyper" parents="64 887 39304"/>
    </justification>
  </clause>

  <clause id="39307">
    <literal><![CDATA[
      (a(x,y,z) \ 1) / x = 1 / (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(13923(a,1),39305(a,1,1))].">
      <j1 rule="para" parents="13923 39305"/>
    </justification>
  </clause>

  <clause id="39308">
    <literal><![CDATA[
      1 / (x * a(x,y,z)) = a(x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30276,a(flip),b,39307,a),flip(a)].">
      <j1 rule="hyper" parents="64 30276 39307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39309">
    <literal><![CDATA[
      (x * (a(x,y,z) \ (1 / x))) * (1 / (1 / x)) = (a(x,y,z) / x) \ 1
    ]]></literal>
    <justification jstring="[para(39308(a,1),38227(a,1,1,2))].">
      <j1 rule="para" parents="39308 38227"/>
    </justification>
  </clause>

  <clause id="39310">
    <literal><![CDATA[
      (x * (a(x,y,z) \ (x \ 1))) * x = (a(x,y,z) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,37330,a(flip),b,39309,a)].">
      <j1 rule="hyper" parents="64 37330 39309"/>
    </justification>
  </clause>

  <clause id="39311">
    <literal><![CDATA[
      (a(x,y,z) / x) \ 1 = (a(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(30269(a,1),39310(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30269 39310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39312">
    <literal><![CDATA[
      (a(x,y,z) / x) \ 1 = a(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,29933,a(flip),b,39311,a),flip(a)].">
      <j1 rule="hyper" parents="373 29933 39311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39314">
    <literal><![CDATA[
      (a(x,y,z) \ a(a(x,y,z),u,w)) \ 1 = a(a(x,y,z),u,w) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(23133(a,1),39312(a,1,1))].">
      <j1 rule="para" parents="23133 39312"/>
    </justification>
  </clause>

  <clause id="39318">
    <literal><![CDATA[
      a(a(x,x,y),z,u) \ a(x,x,y) = L(a(x,x,y) \ 1,z,u) \ 1
    ]]></literal>
    <justification jstring="[para(37928(a,1),39314(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37928 39314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39319">
    <literal><![CDATA[
      a((x * y) \ (z \ (R(z,x,y * (u * u)) * (x * y))),w,v5) = a(a(z,x,y * (u * u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(32449,a,39295,a)].">
      <j1 rule="hyper" parents="32449 39295"/>
    </justification>
  </clause>

  <clause id="39320">
    <literal><![CDATA[
      a((x * y) \ (R(z,x,y * (u * u)) * (z \ (x * y))),w,v5) = a(a(z,x,y * (u * u)),w,v5)
    ]]></literal>
    <justification jstring="[para(1898(a,1),39319(a,1,1,2))].">
      <j1 rule="para" parents="1898 39319"/>
    </justification>
  </clause>

  <clause id="39321">
    <literal><![CDATA[
      a((x * y) \ (L(z,x,y * (u * u)) * (z \ (x * y))),w,v5) = a(a(z,x,y * (u * u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,35135,a(flip),b,39320,a)].">
      <j1 rule="hyper" parents="64 35135 39320"/>
    </justification>
  </clause>

  <clause id="39322">
    <literal><![CDATA[
      a(a(x,y,z * (u * u)),w,v5) = a((y * z) \ (L(x,y,z) * (x \ (y * z))),w,v5)
    ]]></literal>
    <justification jstring="[para(11774(a,1),39321(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11774 39321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39324">
    <literal><![CDATA[
      a(a(x,y,z * (u * u)),w,v5) = a((y * z) \ ((z * (T(y,z) * x)) / x),w,v5)
    ]]></literal>
    <justification jstring="[para(24911(a,1),39322(a,2,1,2))].">
      <j1 rule="para" parents="24911 39322"/>
    </justification>
  </clause>

  <clause id="39325">
    <literal><![CDATA[
      a(a(x,y,z * (u * u)),w,v5) = a((z * y) \ ((z * (y * x)) / x),w,v5)
    ]]></literal>
    <justification jstring="[para(25801(a,1),39324(a,2,1))].">
      <j1 rule="para" parents="25801 39324"/>
    </justification>
  </clause>

  <clause id="39326">
    <literal><![CDATA[
      (x * (y * (x * a(x,z,u)))) \ (x * ((y * x) * a(x,z,u))) = a(y * x,x,L(a(x,z,u),y * x,x))
    ]]></literal>
    <justification jstring="[para(100(a,1),39255(a,1,1,2))].">
      <j1 rule="para" parents="100 39255"/>
    </justification>
  </clause>

  <clause id="39327">
    <literal><![CDATA[
      L(a(x,y,a(y,z,u)),x * (y * a(y,z,u)),y) = a(x * y,y,L(a(y,z,u),x * y,y))
    ]]></literal>
    <justification jstring="[hyper(1082,a,39326,a)].">
      <j1 rule="hyper" parents="1082 39326"/>
    </justification>
  </clause>

  <clause id="39328">
    <literal><![CDATA[
      a(x * y,y,L(a(y,z,u),x * y,y)) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,33385,a(flip),b,39327,a),flip(a)].">
      <j1 rule="hyper" parents="64 33385 39327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39330">
    <literal><![CDATA[
      a(x * y,y,a(y,z,u)) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(29902(a,1),39328(a,1,3))].">
      <j1 rule="para" parents="29902 39328"/>
    </justification>
  </clause>

  <clause id="39331">
    <literal><![CDATA[
      a(x * y,x,a(x,z,u)) = a(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(26847,a,39330,a)].">
      <j1 rule="hyper" parents="26847 39330"/>
    </justification>
  </clause>

  <clause id="39332">
    <literal><![CDATA[
      a(x \ y,x,a(x,z,u)) = a(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26836,a(flip),b,39330,a),flip(a)].">
      <j1 rule="hyper" parents="64 26836 39330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39334">
    <literal><![CDATA[
      (x * y) \ (((x * y) * (x * a(x,z,u))) / a(x,z,u)) = a(y,x,a(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(39330(a,1),33339(a,1,1)),flip(a)].">
      <j1 rule="para" parents="39330 33339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39335">
    <literal><![CDATA[
      a(x,a(x,y,z),u * x) = a(u,x,a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(39330(a,1),33548(a,1,1)),flip(a)].">
      <j1 rule="para" parents="39330 33548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39337">
    <literal><![CDATA[
      (((x / y) * (y * a(y,z,u))) / a(y,z,u)) \ x = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,33399,a,b,39332,a)].">
      <j1 rule="hyper" parents="64 33399 39332"/>
    </justification>
  </clause>

  <clause id="39338">
    <literal><![CDATA[
      a(x,a(x,y,z),u * x) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,33548,a(flip),b,39335,a),flip(a)].">
      <j1 rule="hyper" parents="373 33548 39335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39339">
    <literal><![CDATA[
      a(x,a(x,y,z),x * u) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(27453,a,39338,a)].">
      <j1 rule="hyper" parents="27453 39338"/>
    </justification>
  </clause>

  <clause id="39340">
    <literal><![CDATA[
      a(x,y,z) \ ((x \ ((x * a(x,y,z)) * (u * x))) / (u * x)) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,33280,a(flip),b,39338,a)].">
      <j1 rule="hyper" parents="64 33280 39338"/>
    </justification>
  </clause>

  <clause id="39341">
    <literal><![CDATA[
      a(x,a(x,y,z),x \ u) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27299,a(flip),b,39338,a),flip(a)].">
      <j1 rule="hyper" parents="64 27299 39338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39343">
    <literal><![CDATA[
      (a(x,y,z) \ ((u / x) * (x * a(x,y,z)))) \ u = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(23133(a,1),39337(a,1,1))].">
      <j1 rule="para" parents="23133 39337"/>
    </justification>
  </clause>

  <clause id="39344">
    <literal><![CDATA[
      (x * y) \ (((x * y) * (x * a(x,z,u))) / a(x,z,u)) = L(x,a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,34904,a(flip),b,39334,a),flip(a)].">
      <j1 rule="hyper" parents="373 34904 39334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39345">
    <literal><![CDATA[
      (x * y) \ (a(x,z,u) \ ((x * y) * (x * a(x,z,u)))) = L(x,a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,23170,a(flip),b,39344,a)].">
      <j1 rule="hyper" parents="64 23170 39344"/>
    </justification>
  </clause>

  <clause id="39346">
    <literal><![CDATA[
      L(x,a(x,y,z),x * u) = L(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34907,a(flip),b,39345,a)].">
      <j1 rule="hyper" parents="64 34907 39345"/>
    </justification>
  </clause>

  <clause id="39347">
    <literal><![CDATA[
      L(x,a(x,y,z),x \ u) = L(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10(a,1),39346(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 39346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39348">
    <literal><![CDATA[
      L(x,a(x,y,z),u \ x) = L(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,38107,a(flip),b,39347,a),flip(a)].">
      <j1 rule="hyper" parents="64 38107 39347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39349">
    <literal><![CDATA[
      (x \ y) \ (a(y,z,u) \ ((x \ y) * (y * a(y,z,u)))) = L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,34907,a,b,39348,a)].">
      <j1 rule="hyper" parents="64 34907 39348"/>
    </justification>
  </clause>

  <clause id="39350">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * (y * a(y,z,u))) / a(y,z,u)) = L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,23170,a,b,39349,a)].">
      <j1 rule="hyper" parents="64 23170 39349"/>
    </justification>
  </clause>

  <clause id="39351">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * (y * a(y,z,u))) / a(y,z,u)) = a(x,y,a(y,z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,34904,a,b,39350,a),flip(a)].">
      <j1 rule="hyper" parents="373 34904 39350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39352">
    <literal><![CDATA[
      a(x,y,z) \ ((x \ (x * (u * (x * a(x,y,z))))) / (u * x)) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(39301(a,1),39340(a,1,2,1,2))].">
      <j1 rule="para" parents="39301 39340"/>
    </justification>
  </clause>

  <clause id="39353">
    <literal><![CDATA[
      a(x \ y,y,a(y,z,u)) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(40,a,33322,a,b,39351,a(flip))].">
      <j1 rule="hyper" parents="40 33322 39351"/>
    </justification>
  </clause>

  <clause id="39354">
    <literal><![CDATA[
      a(x,y,z) \ ((u * (x * a(x,y,z))) / (u * x)) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(9(a,1),39352(a,1,2,1))].">
      <j1 rule="para" parents="9 39352"/>
    </justification>
  </clause>

  <clause id="39356">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),x,u) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(23157(a,1),39354(a,1,2))].">
      <j1 rule="para" parents="23157 39354"/>
    </justification>
  </clause>

  <clause id="39357">
    <literal><![CDATA[
      a(x,a(x,y,z),u) * a(x,y,z) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(23175,a,39356,a)].">
      <j1 rule="hyper" parents="23175 39356"/>
    </justification>
  </clause>

  <clause id="39358">
    <literal><![CDATA[
      a(x,y,z) * a(x,a(x,y,z),u) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(157,a,39356,a)].">
      <j1 rule="hyper" parents="157 39356"/>
    </justification>
  </clause>

  <clause id="39359">
    <literal><![CDATA[
      a(L(a(x,y,z),x,u),x,u) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34265,a,b,39356,a)].">
      <j1 rule="hyper" parents="64 34265 39356"/>
    </justification>
  </clause>

  <clause id="39360">
    <literal><![CDATA[
      a(x,y,z) \ a(x,a(x,y,z),u) = L(a(x,y,z) \ 1,x,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,39356,a(flip),b,37299,a)].">
      <j1 rule="hyper" parents="139 39356 37299"/>
    </justification>
  </clause>

  <clause id="39361">
    <literal><![CDATA[
      L(a(x,y,z),x,u) \ a(x,y,z) = a(x,a(x,y,z),u) \ 1
    ]]></literal>
    <justification jstring="[para(39356(a,1),9374(a,1,1)),flip(a)].">
      <j1 rule="para" parents="39356 9374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39362">
    <literal><![CDATA[
      a(x,a(x,y,z),u) = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,36350,a(flip),b,39359,a),flip(a)].">
      <j1 rule="hyper" parents="64 36350 39359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39363">
    <literal><![CDATA[
      L(x,a(x,y,z),u) * a(x,a(x,y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,39362,a,b,34908,a)].">
      <j1 rule="hyper" parents="145 39362 34908"/>
    </justification>
  </clause>

  <clause id="39364">
    <literal><![CDATA[
      a(x,y,z) * a(x,a(x,y,z),y * z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,39362,a,b,34141,a)].">
      <j1 rule="hyper" parents="145 39362 34141"/>
    </justification>
  </clause>

  <clause id="39366">
    <literal><![CDATA[
      x * a(y,a(y,z,u),w) = x * a(w,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,39362,a,b,9,a)].">
      <j1 rule="hyper" parents="145 39362 9"/>
    </justification>
  </clause>

  <clause id="39367">
    <literal><![CDATA[
      x * a(y,x,a(x,z,u)) = L(x,a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(145,a,39362,a(flip),b,34910,a)].">
      <j1 rule="hyper" parents="145 39362 34910"/>
    </justification>
  </clause>

  <clause id="39368">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * y = L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(144,a,39362,a(flip),b,34909,a)].">
      <j1 rule="hyper" parents="144 39362 34909"/>
    </justification>
  </clause>

  <clause id="39370">
    <literal><![CDATA[
      (x * y) \ (x * L(y,a(y,z,u),w)) = L(a(w,y,a(y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[para(39362(a,1),34912(a,2,1))].">
      <j1 rule="para" parents="39362 34912"/>
    </justification>
  </clause>

  <clause id="39371">
    <literal><![CDATA[
      L(1 / x,a(x,y,z),u) \ 1 = L(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34913,a,b,39367,a)].">
      <j1 rule="hyper" parents="64 34913 39367"/>
    </justification>
  </clause>

  <clause id="39372">
    <literal><![CDATA[
      x \ (y * (T(x,y) * a(z,T(x \ 1,y),a(T(x \ 1,y),u,w)))) = (x \ 1) \ (y * L(T(x \ 1,y),a(T(x \ 1,y),u,w),z))
    ]]></literal>
    <justification jstring="[para(39367(a,1),12008(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="39367 12008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39373">
    <literal><![CDATA[
      a(x,L(y,y,z),a(L(y,y,z),u,w)) * (y \ L(T(y,a(x,L(y,y,z),a(L(y,y,z),u,w))),y,z)) = L(L(y,y,z),a(L(y,y,z),u,w),x) / y
    ]]></literal>
    <justification jstring="[para(39367(a,1),37661(a,2,1))].">
      <j1 rule="para" parents="39367 37661"/>
    </justification>
  </clause>

  <clause id="39374">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,x,z) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(37663(a,1),39360(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37663 39360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39376">
    <literal><![CDATA[
      L(a(x,y,z),x,u) \ a(x,y,z) = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,33546,a(flip),b,39361,a),flip(a)].">
      <j1 rule="hyper" parents="373 33546 39361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39377">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),x,u) \ u) = u * a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,39376,a(flip),b,35568,a),flip(a)].">
      <j1 rule="hyper" parents="145 39376 35568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39378">
    <literal><![CDATA[
      a(x,y,z) * a(u,x,a(x,y,z)) = L(a(x,y,z) \ 1,x,u) \ 1
    ]]></literal>
    <justification jstring="[para(39376(a,1),37297(a,1,2))].">
      <j1 rule="para" parents="39376 37297"/>
    </justification>
  </clause>

  <clause id="39379">
    <literal><![CDATA[
      x \ (L(y,a(y,z,u),w) * (y \ x)) = L(a(w,y,a(y,z,u)),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33811,a(flip),b,39370,a)].">
      <j1 rule="hyper" parents="64 33811 39370"/>
    </justification>
  </clause>

  <clause id="39380">
    <literal><![CDATA[
      a(x,y,z \ (((u * u) \ (w \ ((u * u) * (u \ z)))) * (R(u,u,u) * w))) = a(x,y,a(u,w,w \ ((u * u) * (u \ z))))
    ]]></literal>
    <justification jstring="[para(13654(a,1),38847(a,1,3,2))].">
      <j1 rule="para" parents="13654 38847"/>
    </justification>
  </clause>

  <clause id="39381">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (x * ((L(x,y,z) \ x) * (L(x,y,z) * u))) = (1 / x) * ((((x \ L(x,y,z)) \ 1) * x) * u)
    ]]></literal>
    <justification jstring="[para(5659(a,1),39177(a,1,2,2,1))].">
      <j1 rule="para" parents="5659 39177"/>
    </justification>
  </clause>

  <clause id="39382">
    <literal><![CDATA[
      (x * L(x,y,z)) \ (x * (L(x,y,z) * ((L(x,y,z) \ x) * u))) = (1 / x) * ((((x \ L(x,y,z)) \ 1) * x) * u)
    ]]></literal>
    <justification jstring="[para(36170(a,1),39381(a,1,2,2))].">
      <j1 rule="para" parents="36170 39381"/>
    </justification>
  </clause>

  <clause id="39383">
    <literal><![CDATA[
      L((L(x,y,z) \ x) * u,x,L(x,y,z)) = (1 / x) * ((((x \ L(x,y,z)) \ 1) * x) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2337,a(flip),b,39382,a)].">
      <j1 rule="hyper" parents="64 2337 39382"/>
    </justification>
  </clause>

  <clause id="39384">
    <literal><![CDATA[
      L((L(x,y,z) \ x) * u,x,L(x,y,z)) = (1 / x) * (((L(x,y,z) \ x) * x) * u)
    ]]></literal>
    <justification jstring="[para(9374(a,1),39383(a,2,2,1,1))].">
      <j1 rule="para" parents="9374 39383"/>
    </justification>
  </clause>

  <clause id="39385">
    <literal><![CDATA[
      L((L(x,y,z) \ x) * u,x,L(x,y,z)) = x * ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,33874,a(flip),b,39384,a),flip(a)].">
      <j1 rule="hyper" parents="373 33874 39384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39386">
    <literal><![CDATA[
      L(L(L(x,y,z),u,w) \ L(L(R(x,x,v5),y,z),u,w),x,L(L(x,y,z),u,w)) = a(L(L(L(x,y,z),u,w),x,v5),x,v5)
    ]]></literal>
    <justification jstring="[para(29(a,1),39178(a,1,1,2,1))].">
      <j1 rule="para" parents="29 39178"/>
    </justification>
  </clause>

  <clause id="39387">
    <literal><![CDATA[
      L(a((x \ (y * (z * x))) * y,a(y,z,x) * z,u),y,y) = a(((y * (z * x)) / x) * y,((y * (z * x)) / x) * y,u)
    ]]></literal>
    <justification jstring="[para(32367(a,1),39194(a,1,1))].">
      <j1 rule="para" parents="32367 39194"/>
    </justification>
  </clause>

  <clause id="39388">
    <literal><![CDATA[
      T(T(x,(y \ R(y,z,u)) \ 1) * ((y \ R(y,z,u)) \ 1),w) = x * ((y \ R(y,z,u)) \ K((y \ y) * x,w))
    ]]></literal>
    <justification jstring="[para(33983(a,1),39197(a,2,2,2))].">
      <j1 rule="para" parents="33983 39197"/>
    </justification>
  </clause>

  <clause id="39389">
    <literal><![CDATA[
      T(T(x,(y \ R(y,z,u)) \ 1) * ((y \ R(y,z,u)) \ 1),w) = x * ((y \ R(y,z,u)) \ K(x,w))
    ]]></literal>
    <justification jstring="[para(190(a,1),39388(a,2,2,2,1))].">
      <j1 rule="para" parents="190 39388"/>
    </justification>
  </clause>

  <clause id="39391">
    <literal><![CDATA[
      T(T(x,R(y,z,u) \ y) * ((y \ R(y,z,u)) \ 1),w) = x * ((y \ R(y,z,u)) \ K(x,w))
    ]]></literal>
    <justification jstring="[para(5382(a,1),39389(a,1,1,1,2))].">
      <j1 rule="para" parents="5382 39389"/>
    </justification>
  </clause>

  <clause id="39392">
    <literal><![CDATA[
      T(x * ((y \ R(y,z,u)) \ 1),w) = x * ((y \ R(y,z,u)) \ K(x,w))
    ]]></literal>
    <justification jstring="[para(25923(a,1),39391(a,1,1,1))].">
      <j1 rule="para" parents="25923 39391"/>
    </justification>
  </clause>

  <clause id="39393">
    <literal><![CDATA[
      T(x * (y * (R(y,z,u) \ 1)),w) = x * ((y \ R(y,z,u)) \ K(x,w))
    ]]></literal>
    <justification jstring="[para(5383(a,1),39392(a,1,1,2))].">
      <j1 rule="para" parents="5383 39392"/>
    </justification>
  </clause>

  <clause id="39394">
    <literal><![CDATA[
      T(x * (y * (R(y,z,u) \ 1)),w) = x * (y * (R(y,z,u) \ K(x,w)))
    ]]></literal>
    <justification jstring="[para(25720(a,1),39393(a,2,2))].">
      <j1 rule="para" parents="25720 39393"/>
    </justification>
  </clause>

  <clause id="39395">
    <literal><![CDATA[
      x * (y * (R(y,z,u) \ K(x,w))) = T(x * (R(y,z,u) \ y),w)
    ]]></literal>
    <justification jstring="[para(1909(a,1),39394(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1909 39394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39396">
    <literal><![CDATA[
      T(x * (R(y,z,u) \ y),w) = T(x,w) * (R(y,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,25945,a(flip),b,39395,a),flip(a)].">
      <j1 rule="hyper" parents="64 25945 39395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39397">
    <literal><![CDATA[
      (x * y) \ (y * T(x * (R(z,u,w) \ z),y)) = L(R(z,u,w) \ z,x,y)
    ]]></literal>
    <justification jstring="[para(39396(a,2),10980(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="39396 10980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39398">
    <literal><![CDATA[
      (x * y) \ ((x * (R(z,u,w) \ z)) * y) = L(R(z,u,w) \ z,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,39397,a)].">
      <j1 rule="hyper" parents="64 249 39397"/>
    </justification>
  </clause>

  <clause id="39399">
    <literal><![CDATA[
      R(T(R(x,y,z) \ x,u * w),u,w) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,25936,a(flip),b,39398,a)].">
      <j1 rule="hyper" parents="64 25936 39398"/>
    </justification>
  </clause>

  <clause id="39400">
    <literal><![CDATA[
      R(R(x,y,z) \ x,u,w) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(25921(a,1),39399(a,1,1))].">
      <j1 rule="para" parents="25921 39399"/>
    </justification>
  </clause>

  <clause id="39402">
    <literal><![CDATA[
      ((x \ R(x,y,z)) / u) / (1 / u) = L(R(x,y,z) \ x,u,u) \ 1
    ]]></literal>
    <justification jstring="[para(39400(a,1),30589(a,2,1))].">
      <j1 rule="para" parents="39400 30589"/>
    </justification>
  </clause>

  <clause id="39403">
    <literal><![CDATA[
      L(R(x,y,z) \ x,u,u) \ 1 = L(x \ R(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,36356,a(flip),b,39402,a),flip(a)].">
      <j1 rule="hyper" parents="64 36356 39402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39404">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,u) \ 1 = L(R(x,y,z) \ x,u,u)
    ]]></literal>
    <justification jstring="[hyper(40,a,24622,a,b,39403,a)].">
      <j1 rule="hyper" parents="40 24622 39403"/>
    </justification>
  </clause>

  <clause id="39405">
    <literal><![CDATA[
      L(L(x * a(y,y,L(x,z,u)),y,y),R(x,z,u),a(R(x,z,u),y,y)) = R(x,z,u) * (L(x \ R(x,z,u),y,y) \ 1)
    ]]></literal>
    <justification jstring="[para(30820(a,2),39209(a,1,1))].">
      <j1 rule="para" parents="30820 39209"/>
    </justification>
  </clause>

  <clause id="39406">
    <literal><![CDATA[
      a(x,y,z \ ((T(u,w * w) \ (w \ z)) * (R(w,w,w) * u))) = a(x,y,a(w,u,u \ ((w * w) * (w \ z))))
    ]]></literal>
    <justification jstring="[para(1458(a,1),39380(a,1,3,2,1))].">
      <j1 rule="para" parents="1458 39380"/>
    </justification>
  </clause>

  <clause id="39407">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * (T(w,u * u) \ (u \ z)))) = a(x,y,a(u,w,w \ ((u * u) * (u \ z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,27489,a(flip),b,39406,a)].">
      <j1 rule="hyper" parents="64 27489 39406"/>
    </justification>
  </clause>

  <clause id="39409">
    <literal><![CDATA[
      a(x,y,a(z,u,u \ ((z * z) * (z \ w)))) = a(x,y,w \ ((z * u) * (u \ (z \ w))))
    ]]></literal>
    <justification jstring="[hyper(64,a,27658,a(flip),b,39407,a),flip(a)].">
      <j1 rule="hyper" parents="64 27658 39407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39411">
    <literal><![CDATA[
      a(x,y,a(z,u,u \ ((z * z) * (z \ w)))) = a(x,y,a(z,u,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(345(a,1),39409(a,2,3))].">
      <j1 rule="para" parents="345 39409"/>
    </justification>
  </clause>

  <clause id="39412">
    <literal><![CDATA[
      L(L(L(x \ R(x,x,y),z,u),w,v5),x,L(L(x,z,u),w,v5)) = a(L(L(L(x,z,u),w,v5),x,y),x,y)
    ]]></literal>
    <justification jstring="[para(4252(a,1),39386(a,1,1))].">
      <j1 rule="para" parents="4252 39386"/>
    </justification>
  </clause>

  <clause id="39413">
    <literal><![CDATA[
      L(L(a(x,L(x,y,z),u),w,v5),x,L(L(x,y,z),w,v5)) = a(L(L(L(x,y,z),w,v5),x,u),x,u)
    ]]></literal>
    <justification jstring="[para(34874(a,1),39412(a,1,1,1))].">
      <j1 rule="para" parents="34874 39412"/>
    </justification>
  </clause>

  <clause id="39414">
    <literal><![CDATA[
      a(L(L(L(x,y,z),u,w),x,v5),x,v5) = L(a(x,L(x,y,z),v5),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,38676,a(flip),b,39413,a),flip(a)].">
      <j1 rule="hyper" parents="64 38676 39413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39416">
    <literal><![CDATA[
      L(a((x \ (y * (z * x))) * y,a(y,z,x) * z,u),y,y) = a(((y * (z * x)) / x) * y,(x \ (y * (z * x))) * y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,31904,a(flip),b,39387,a),flip(a)].">
      <j1 rule="hyper" parents="373 31904 39387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39417">
    <literal><![CDATA[
      L(a((x \ (y * (z * x))) * y,a(y,z,x) * z,u),y,y) = a((x \ (y * (z * x))) * y,(x \ (y * (z * x))) * y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32367,a(flip),b,39416,a),flip(a)].">
      <j1 rule="hyper" parents="373 32367 39416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39418">
    <literal><![CDATA[
      T(x / y,y * y) \ (a(x / y,y,y) \ T(x / y,y * y)) = ((y * y) \ (x * y)) \ T(x / y,y * y)
    ]]></literal>
    <justification jstring="[para(26779(a,1),25174(a,1,2,1))].">
      <j1 rule="para" parents="26779 25174"/>
    </justification>
  </clause>

  <clause id="39420">
    <literal><![CDATA[
      T(x / y,y * y) \ (a(y \ x,y,y) \ T(x / y,y * y)) = ((y * y) \ (x * y)) \ T(x / y,y * y)
    ]]></literal>
    <justification jstring="[para(26785(a,1),39418(a,1,2,1))].">
      <j1 rule="para" parents="26785 39418"/>
    </justification>
  </clause>

  <clause id="39421">
    <literal><![CDATA[
      ((x * x) \ (y * x)) \ T(y / x,x * x) = R(x \ y,x,x) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,37816,a,b,39420,a),flip(a)].">
      <j1 rule="hyper" parents="64 37816 39420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39424">
    <literal><![CDATA[
      (x * y) \ ((y * y) * T(x / y,y * y)) = R(y \ x,y,y) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,804,a(flip),b,39421,a)].">
      <j1 rule="hyper" parents="64 804 39421"/>
    </justification>
  </clause>

  <clause id="39425">
    <literal><![CDATA[
      (x * y) \ ((x / y) * (y * y)) = R(y \ x,y,y) \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,39424,a)].">
      <j1 rule="hyper" parents="64 249 39424"/>
    </justification>
  </clause>

  <clause id="39426">
    <literal><![CDATA[
      R(x \ y,x,x) \ (x \ y) = (y * x) \ (y / (1 / x))
    ]]></literal>
    <justification jstring="[para(809(a,1),39425(a,1,2)),flip(a)].">
      <j1 rule="para" parents="809 39425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39427">
    <literal><![CDATA[
      R(x \ y,x,x) \ (x \ y) = ((y * x) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,31418,a(flip),b,39426,a),flip(a)].">
      <j1 rule="hyper" parents="373 31418 39426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39428">
    <literal><![CDATA[
      (x * x) \ (((y * x) \ y) * x) = (y * x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(39427(a,1),31461(a,1,2))].">
      <j1 rule="para" parents="39427 31461"/>
    </justification>
  </clause>

  <clause id="39429">
    <literal><![CDATA[
      ((x * x) \ ((y * x) \ y)) * x = (y * x) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(806,a,39428,a)].">
      <j1 rule="hyper" parents="806 39428"/>
    </justification>
  </clause>

  <clause id="39431">
    <literal><![CDATA[
      1 \ (((1 / (x * y)) * x) * R(((1 / (x * y)) * x) \ 1,z,u)) = (((1 / (x * y)) * x) * L(R(y,z,u),x,x * y)) / 1
    ]]></literal>
    <justification jstring="[para(29(a,1),25713(a,2,1,2))].">
      <j1 rule="para" parents="29 25713"/>
    </justification>
  </clause>

  <clause id="39432">
    <literal><![CDATA[
      L((x \ y) * x,z,u) * L(K(x,x \ y) * (L(y,z,u) \ 1),w,w) = a(w,w,(L(y,z,u) * K(x \ y,x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6156(a,1),27088(a,1,2,1))].">
      <j1 rule="para" parents="6156 27088"/>
    </justification>
  </clause>

  <clause id="39433">
    <literal><![CDATA[
      R(x,R(T(y,z),u,w) \ (L(v5,R(T(y,z),u,w) \ v6,L(T(y,z),u,w)) * v6),v7) = R(x,(R(y,u,w) \ v6) * T(v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(29203(a,1),27904(a,1,2,2,1))].">
      <j1 rule="para" parents="29203 27904"/>
    </justification>
  </clause>

  <clause id="39434">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ ((y \ x) * (y \ R(y,z,u))) = R(T(y \ 1,x),y,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(28096(a,1),29857(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28096 29857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39435">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ ((y \ x) * (y \ R(y,z,u))) = R(T(y \ 1,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,35487,a(flip),b,39434,a),flip(a)].">
      <j1 rule="hyper" parents="373 35487 39434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39438">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ ((y \ x) * (y \ R(y,z,u))) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2985,a(flip),b,39435,a),flip(a)].">
      <j1 rule="hyper" parents="373 2985 39435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39439">
    <literal><![CDATA[
      a(x \ (y \ x),y \ R(y,z,u),x) = y \ R(y,y \ R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(39438(a,1),29858(a,1,1))].">
      <j1 rule="para" parents="39438 29858"/>
    </justification>
  </clause>

  <clause id="39440">
    <literal><![CDATA[
      a(x \ (y \ x),y \ L(y,z,u),x) = y \ R(y,y \ R(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,37374,a(flip),b,39439,a)].">
      <j1 rule="hyper" parents="64 37374 39439"/>
    </justification>
  </clause>

  <clause id="39442">
    <literal><![CDATA[
      a(x \ (y \ x),y * L(y,z,u),x) = y \ R(y,y \ R(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11978,a(flip),b,39440,a)].">
      <j1 rule="hyper" parents="64 11978 39440"/>
    </justification>
  </clause>

  <clause id="39443">
    <literal><![CDATA[
      L(x,y,z) * L(((z * y) \ (z * (y * x))) \ x,u,w) = (z * y) \ (z * ((y * x) * L(a(z,y,x),u,w)))
    ]]></literal>
    <justification jstring="[para(18(a,2),30203(a,1,1))].">
      <j1 rule="para" parents="18 30203"/>
    </justification>
  </clause>

  <clause id="39444">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L(a(x,y,z),u,w))) = L(z,y,x) * L(L(z,y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),39443(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="18 39443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39445">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(x,y,z)))) = L(z,y,x) * L(L(z,y,x) \ z,z,y)
    ]]></literal>
    <justification jstring="[para(100(a,1),39444(a,1,2,2))].">
      <j1 rule="para" parents="100 39444"/>
    </justification>
  </clause>

  <clause id="39446">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,x,y) = L(x * a(z,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(608,a,39445,a),flip(a)].">
      <j1 rule="hyper" parents="608 39445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39447">
    <literal><![CDATA[
      a(x,x,x \ ((1 / x) \ y)) \ ((((1 / x) \ y) \ z) \ z) = x * (y * K((1 / x) \ y,z * (y \ (1 / x))))
    ]]></literal>
    <justification jstring="[para(27323(a,1),30776(a,1,1))].">
      <j1 rule="para" parents="27323 30776"/>
    </justification>
  </clause>

  <clause id="39449">
    <literal><![CDATA[
      a(x,x,x \ ((x \ 1) \ y)) \ ((((1 / x) \ y) \ z) \ z) = x * (y * K((1 / x) \ y,z * (y \ (1 / x))))
    ]]></literal>
    <justification jstring="[para(27511(a,1),39447(a,1,1))].">
      <j1 rule="para" parents="27511 39447"/>
    </justification>
  </clause>

  <clause id="39450">
    <literal><![CDATA[
      a(x,x,y) \ ((((1 / x) \ y) \ z) \ z) = x * (y * K((1 / x) \ y,z * (y \ (1 / x))))
    ]]></literal>
    <justification jstring="[para(30361(a,1),39449(a,1,1))].">
      <j1 rule="para" parents="30361 39449"/>
    </justification>
  </clause>

  <clause id="39451">
    <literal><![CDATA[
      a(x,x,y) \ ((((1 / x) \ y) \ z) \ z) = x * (y * K((1 / x) \ y,z / (x * y)))
    ]]></literal>
    <justification jstring="[para(22640(a,1),39450(a,2,2,2))].">
      <j1 rule="para" parents="22640 39450"/>
    </justification>
  </clause>

  <clause id="39452">
    <literal><![CDATA[
      a(x,x,y) \ ((((1 / x) \ y) \ z) \ z) = x * (y * K(x * y,z / (x * y)))
    ]]></literal>
    <justification jstring="[para(14490(a,1),39451(a,2,2,2))].">
      <j1 rule="para" parents="14490 39451"/>
    </justification>
  </clause>

  <clause id="39453">
    <literal><![CDATA[
      a(x,x,y) \ ((((1 / x) \ y) \ z) \ z) = x * (y * K(x * y,(x * y) \ z))
    ]]></literal>
    <justification jstring="[para(5926(a,1),39452(a,2,2,2))].">
      <j1 rule="para" parents="5926 39452"/>
    </justification>
  </clause>

  <clause id="39454">
    <literal><![CDATA[
      a(x,x,y) \ ((((1 / x) \ y) \ z) \ z) = x * (y * K(x * y,y \ (x \ z)))
    ]]></literal>
    <justification jstring="[para(15358(a,1),39453(a,2,2,2))].">
      <j1 rule="para" parents="15358 39453"/>
    </justification>
  </clause>

  <clause id="39455">
    <literal><![CDATA[
      a(x,x,y) \ ((((1 / x) \ y) \ z) \ z) = T(x * y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,14495,a(flip),b,39454,a),flip(a)].">
      <j1 rule="hyper" parents="373 14495 39454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39456">
    <literal><![CDATA[
      (((1 / x) \ y) \ z) * T(x * y,y \ (x \ z)) = (z / ((1 / x) \ y)) * (x * y)
    ]]></literal>
    <justification jstring="[para(39455(a,1),30047(a,1,2))].">
      <j1 rule="para" parents="39455 30047"/>
    </justification>
  </clause>

  <clause id="39457">
    <literal><![CDATA[
      (x / ((1 / y) \ z)) * (y * z) = (y * z) * (((1 / y) \ z) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33890,a(flip),b,39456,a),flip(a)].">
      <j1 rule="hyper" parents="64 33890 39456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39458">
    <literal><![CDATA[
      (x / (y \ z)) * ((y \ 1) * z) = (y * z) * (((1 / y) \ z) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,35523,a(flip),b,39457,a)].">
      <j1 rule="hyper" parents="64 35523 39457"/>
    </justification>
  </clause>

  <clause id="39459">
    <literal><![CDATA[
      x / L(((y \ 1) * z) \ (y \ z),(y \ 1) * z,(y \ z) \ x) = (y * z) * (((1 / y) \ z) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,15003,a,b,39458,a)].">
      <j1 rule="hyper" parents="64 15003 39458"/>
    </justification>
  </clause>

  <clause id="39460">
    <literal><![CDATA[
      (x / ((1 / y) \ (a(z,y,y) \ z))) * (((1 / y) \ 1) * (a(z,y,y) \ z)) = ((z / y) * K(y \ 1,z)) * (((1 / (1 / y)) \ (a(z,y,y) \ z)) \ x)
    ]]></literal>
    <justification jstring="[para(31599(a,1),39458(a,2,1))].">
      <j1 rule="para" parents="31599 39458"/>
    </justification>
  </clause>

  <clause id="39461">
    <literal><![CDATA[
      x / L((y * z) \ ((1 / y) \ z),(y \ 1) * z,(y \ z) \ x) = (y * z) * (((1 / y) \ z) \ x)
    ]]></literal>
    <justification jstring="[para(1682(a,1),39459(a,1,2,1))].">
      <j1 rule="para" parents="1682 39459"/>
    </justification>
  </clause>

  <clause id="39462">
    <literal><![CDATA[
      x / L(a(y,y,z),(y \ 1) * z,(y \ z) \ x) = (y * z) * (((1 / y) \ z) \ x)
    ]]></literal>
    <justification jstring="[para(30034(a,1),39461(a,1,2,1))].">
      <j1 rule="para" parents="30034 39461"/>
    </justification>
  </clause>

  <clause id="39463">
    <literal><![CDATA[
      x / L(a(y,y,z),y * z,(y \ z) \ x) = (y * z) * (((1 / y) \ z) \ x)
    ]]></literal>
    <justification jstring="[para(11864(a,1),39462(a,1,2))].">
      <j1 rule="para" parents="11864 39462"/>
    </justification>
  </clause>

  <clause id="39464">
    <literal><![CDATA[
      L(x,R(y \ 1,z,u) \ (L(w,R(y \ 1,z,u) \ v5,L(y \ 1,z,u)) * v5),v6) = L(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(29203(a,1),31075(a,1,2,2,1))].">
      <j1 rule="para" parents="29203 31075"/>
    </justification>
  </clause>

  <clause id="39465">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) \ ((1 / (1 / a(x,y,y \ 1))) * z) = (y * a(x,y,y \ 1)) \ (a(x,y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(13931(a,1),33381(a,2,1,2))].">
      <j1 rule="para" parents="13931 33381"/>
    </justification>
  </clause>

  <clause id="39466">
    <literal><![CDATA[
      L(x \ y,x,a(z,x,x \ 1)) = (1 / ((z * x) \ z)) \ ((1 / (1 / a(z,x,x \ 1))) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,23190,a,b,39465,a)].">
      <j1 rule="hyper" parents="373 23190 39465"/>
    </justification>
  </clause>

  <clause id="39468">
    <literal><![CDATA[
      L(x \ y,x,a(z,x,x)) = (1 / ((z * x) \ z)) \ ((1 / (1 / a(z,x,x \ 1))) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,33636,a(flip),b,39466,a)].">
      <j1 rule="hyper" parents="64 33636 39466"/>
    </justification>
  </clause>

  <clause id="39469">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) \ ((1 / (1 / a(x,y,y \ 1))) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,37527,a(flip),b,39468,a),flip(a)].">
      <j1 rule="hyper" parents="64 37527 39468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39471">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) \ (a(x,y,y \ 1) * z) = y \ z
    ]]></literal>
    <justification jstring="[para(23160(a,1),39469(a,1,2,1))].">
      <j1 rule="para" parents="23160 39469"/>
    </justification>
  </clause>

  <clause id="39473">
    <literal><![CDATA[
      a(x,R(y \ 1,z,u) \ (L(w,R(y \ 1,z,u) \ v5,L(y \ 1,z,u)) * v5),v6) = a(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(29203(a,1),34116(a,1,2,2,1))].">
      <j1 rule="para" parents="29203 34116"/>
    </justification>
  </clause>

  <clause id="39474">
    <literal><![CDATA[
      ((x \ y) * (x \ y)) \ ((z / (x \ y)) * L(x \ y,x \ y,y)) = (x \ y) \ (((x \ y) * (1 / (x \ y))) * ((y \ x) * z))
    ]]></literal>
    <justification jstring="[para(24852(a,1),35271(a,1,2))].">
      <j1 rule="para" parents="24852 35271"/>
    </justification>
  </clause>

  <clause id="39475">
    <literal><![CDATA[
      R(x,y,z) \ L(R(x,y,z) * a(u,u,x),u,u) = x \ (L(x \ R(x,y,z),u,u) * ((x \ R(x,y,z)) \ x))
    ]]></literal>
    <justification jstring="[para(2069(a,1),36797(a,1,1))].">
      <j1 rule="para" parents="2069 36797"/>
    </justification>
  </clause>

  <clause id="39476">
    <literal><![CDATA[
      a(x,x,R(y,z,u)) \ a(x,x,y) = y \ (L(y \ R(y,z,u),x,x) * ((y \ R(y,z,u)) \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,31104,a(flip),b,39475,a)].">
      <j1 rule="hyper" parents="64 31104 39475"/>
    </justification>
  </clause>

  <clause id="39477">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ a(x,x,y) = y \ (L(y \ R(y,z,u),x,x) * ((y \ R(y,z,u)) \ y))
    ]]></literal>
    <justification jstring="[para(27644(a,1),39476(a,1,1))].">
      <j1 rule="para" parents="27644 39476"/>
    </justification>
  </clause>

  <clause id="39478">
    <literal><![CDATA[
      a(x,y,((T(z,u) * (w \ 1)) * a(w,w,w \ T(z,u))) * v5) = a(x,y,((1 / w) * T(w * (z * (w \ 1)),u)) * v5)
    ]]></literal>
    <justification jstring="[para(30356(a,1),39027(a,1,3,1,2))].">
      <j1 rule="para" parents="30356 39027"/>
    </justification>
  </clause>

  <clause id="39479">
    <literal><![CDATA[
      a(x,y,((T(z,u) * (w \ 1)) * a(w,w,w \ z)) * v5) = a(x,y,((1 / w) * T(w * (z * (w \ 1)),u)) * v5)
    ]]></literal>
    <justification jstring="[para(27301(a,1),39478(a,1,3,1,2))].">
      <j1 rule="para" parents="27301 39478"/>
    </justification>
  </clause>

  <clause id="39481">
    <literal><![CDATA[
      a(x,y,(T(z,u) * R(w \ 1,w,w \ z)) * v5) = a(x,y,((1 / w) * T(w * (z * (w \ 1)),u)) * v5)
    ]]></literal>
    <justification jstring="[para(37757(a,1),39479(a,1,3,1))].">
      <j1 rule="para" parents="37757 39479"/>
    </justification>
  </clause>

  <clause id="39482">
    <literal><![CDATA[
      a(x,y,((1 / z) * T(z * (u * (z \ 1)),w)) * v5) = a(x,y,(u * R(z \ 1,z,z \ u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27398,a(flip),b,39481,a),flip(a)].">
      <j1 rule="hyper" parents="64 27398 39481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39484">
    <literal><![CDATA[
      a(x,y,((1 / z) * T(z * (u * (z \ 1)),w)) * v5) = a(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,36514,a(flip),b,39482,a),flip(a)].">
      <j1 rule="hyper" parents="373 36514 39482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39485">
    <literal><![CDATA[
      a(x,y,L(T(z,u) * (w \ 1),w,w) * v5) = a(x,y,(w \ z) * v5)
    ]]></literal>
    <justification jstring="[para(1562(a,1),39484(a,1,3,1))].">
      <j1 rule="para" parents="1562 39484"/>
    </justification>
  </clause>

  <clause id="39486">
    <literal><![CDATA[
      a(x,y,z * L(u * (w \ 1),w,w)) = a(x,y,(w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27578,a(flip),b,39485,a)].">
      <j1 rule="hyper" parents="64 27578 39485"/>
    </justification>
  </clause>

  <clause id="39487">
    <literal><![CDATA[
      1 \ (((1 / (x * y)) * x) * R(((1 / (x * y)) * x) \ 1,z,u)) = ((1 / (x * y)) * (x * R(y,z,u))) / 1
    ]]></literal>
    <justification jstring="[para(1651(a,1),39431(a,2,1))].">
      <j1 rule="para" parents="1651 39431"/>
    </justification>
  </clause>

  <clause id="39488">
    <literal><![CDATA[
      1 \ (((1 / (x * y)) * x) * R(((1 / (x * y)) * x) \ 1,z,u)) = (1 / (x * y)) * (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,77,a(flip),b,39487,a),flip(a)].">
      <j1 rule="hyper" parents="373 77 39487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39489">
    <literal><![CDATA[
      1 \ (((1 / (x * y)) * x) \ R((1 / (x * y)) * x,z,u)) = (1 / (x * y)) * (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(1987(a,1),39488(a,1,2))].">
      <j1 rule="para" parents="1987 39488"/>
    </justification>
  </clause>

  <clause id="39490">
    <literal><![CDATA[
      1 \ ((((x * y) \ 1) * x) \ R(((x * y) \ 1) * x,z,u)) = (1 / (x * y)) * (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(36254(a,1),39489(a,1,2))].">
      <j1 rule="para" parents="36254 39489"/>
    </justification>
  </clause>

  <clause id="39491">
    <literal><![CDATA[
      1 \ (((x * y) * x) \ R((x * y) * x,z,u)) = (1 / (x * y)) * (x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(3144(a,1),39490(a,1,2))].">
      <j1 rule="para" parents="3144 39490"/>
    </justification>
  </clause>

  <clause id="39492">
    <literal><![CDATA[
      (1 / (x * y)) * (x * R(y,z,u)) = 1 \ L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(26014(a,1),39491(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26014 39491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39493">
    <literal><![CDATA[
      (1 / (x * y)) * (x * R(y,z,u)) = L(y \ R(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,66,a(flip),b,39492,a),flip(a)].">
      <j1 rule="hyper" parents="373 66 39492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39494">
    <literal><![CDATA[
      L(a(L(x,y,z),y,z),x * y,x * y) = L(x \ R(x,y,z),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,33415,a,b,39493,a)].">
      <j1 rule="hyper" parents="64 33415 39493"/>
    </justification>
  </clause>

  <clause id="39495">
    <literal><![CDATA[
      L(a(L(x,y,z),y,z),x * y,x * y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,35753,a(flip),b,39494,a),flip(a)].">
      <j1 rule="hyper" parents="373 35753 39494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39496">
    <literal><![CDATA[
      L(a(L(x,y,z),y,z),y * x,y * x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29507,a,b,39495,a)].">
      <j1 rule="hyper" parents="64 29507 39495"/>
    </justification>
  </clause>

  <clause id="39497">
    <literal><![CDATA[
      L(x \ R(x,y,z),y * x,y * x) = (y * R(x,y,z)) / (y * x)
    ]]></literal>
    <justification jstring="[para(39496(a,1),36481(a,1,1))].">
      <j1 rule="para" parents="39496 36481"/>
    </justification>
  </clause>

  <clause id="39498">
    <literal><![CDATA[
      (x * R(y,x,z)) / (x * y) = (x \ y) \ (x \ R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,35225,a(flip),b,39497,a),flip(a)].">
      <j1 rule="hyper" parents="64 35225 39497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39499">
    <literal><![CDATA[
      (x \ y) \ (x \ R(y,x,z)) = x \ (R(y,x,z) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,39248,a(flip),b,39498,a),flip(a)].">
      <j1 rule="hyper" parents="64 39248 39498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39500">
    <literal><![CDATA[
      L((x \ y) * x,z,u) * L(L((x \ y) * x,z,u) \ 1,w,w) = a(w,w,(L(y,z,u) * K(x \ y,x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(26138(a,1),39432(a,1,2,1))].">
      <j1 rule="para" parents="26138 39432"/>
    </justification>
  </clause>

  <clause id="39501">
    <literal><![CDATA[
      L(((x \ y) * x) * L(((x \ y) * x) \ 1,z,z),u,w) = a(z,z,(L(y,u,w) * K(x \ y,x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(4274,a,39500,a)].">
      <j1 rule="hyper" parents="4274 39500"/>
    </justification>
  </clause>

  <clause id="39502">
    <literal><![CDATA[
      a(x,x,(L(y,z,u) * K(w \ y,w)) \ 1) \ 1 = L(a(x,x,((w \ y) * w) \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(5666(a,2),39501(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5666 39501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39503">
    <literal><![CDATA[
      a(x,x,(L(y,z,u) * K(w \ y,w)) \ 1) \ 1 = L(a(x,x,y \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(27396(a,1),39502(a,2,1,1))].">
      <j1 rule="para" parents="27396 39502"/>
    </justification>
  </clause>

  <clause id="39504">
    <literal><![CDATA[
      L(a(x,x,y \ 1) \ 1,z,u) = a(x,x,L(y,z,u) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6841(a,1),39503(a,1,1,3,1)),flip(a)].">
      <j1 rule="para" parents="6841 39503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39506">
    <literal><![CDATA[
      a(x,x,L(y \ 1,z,u) \ 1) \ 1 = L(a(x,x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(5340(a,1),39504(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5340 39504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39508">
    <literal><![CDATA[
      a(x,x,y * (L(y,z,u) \ y)) \ 1 = L(a(x,x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(31340(a,1),39506(a,1,1))].">
      <j1 rule="para" parents="31340 39506"/>
    </justification>
  </clause>

  <clause id="39509">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,y,z) = a(x,x,L(y,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(38931(a,1),39506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38931 39506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39510">
    <literal><![CDATA[
      a(x,x,L((y \ 1) \ 1,z,z)) \ 1 = L(a(x,x,y) \ 1,z,z)
    ]]></literal>
    <justification jstring="[para(38946(a,2),39506(a,1,1))].">
      <j1 rule="para" parents="38946 39506"/>
    </justification>
  </clause>

  <clause id="39511">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,y,z) * u = a(x,x,L(y,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(39509(a,2),37681(a,1,1))].">
      <j1 rule="para" parents="39509 37681"/>
    </justification>
  </clause>

  <clause id="39512">
    <literal><![CDATA[
      a(x,x,L(y,y,z)) \ z = L(y,x,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33810,a(flip),b,39511,a),flip(a)].">
      <j1 rule="hyper" parents="64 33810 39511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39513">
    <literal><![CDATA[
      a(x,x,L((x \ 1) \ y,(x \ 1) \ y,z)) \ z = (x * y) * (((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(1137(a,1),39512(a,2,1))].">
      <j1 rule="para" parents="1137 39512"/>
    </justification>
  </clause>

  <clause id="39514">
    <literal><![CDATA[
      a(x,x,L((1 / x) \ y,(1 / x) \ y,z)) \ z = ((x * x) \ (x * ((x * x) * y))) * (((1 / x) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(583(a,2),39512(a,2,1))].">
      <j1 rule="para" parents="583 39512"/>
    </justification>
  </clause>

  <clause id="39515">
    <literal><![CDATA[
      a(x,y,a(z,z,u * (L(u,w,v5) \ u))) = a(x,y,L(a(z,z,u) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(39508(a,1),38628(a,1,3)),flip(a)].">
      <j1 rule="para" parents="39508 38628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39516">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,z) = a(x,x,L(y,z,z)) \ 1
    ]]></literal>
    <justification jstring="[para(27336(a,1),39510(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27336 39510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39517">
    <literal><![CDATA[
      a(x,x,L(y,z,z)) = L(a(x,x,y),z,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,36774,a(flip),b,39516,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 36774 39516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39519">
    <literal><![CDATA[
      L(a(x,x,y),z * x,z) = a(x,x,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,38653,a,b,39517,a)].">
      <j1 rule="hyper" parents="373 38653 39517"/>
    </justification>
  </clause>

  <clause id="39520">
    <literal><![CDATA[
      a(x,L(x,y,y),z) = a(x,x,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,34877,a,b,39517,a)].">
      <j1 rule="hyper" parents="373 34877 39517"/>
    </justification>
  </clause>

  <clause id="39521">
    <literal><![CDATA[
      x * a(y,y,L(z,x,x)) = (1 / x) \ a(y,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,39517,a,b,36310,a)].">
      <j1 rule="hyper" parents="145 39517 36310"/>
    </justification>
  </clause>

  <clause id="39522">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(y,z,z)) = a(a(x,x,y),z,z)
    ]]></literal>
    <justification jstring="[para(39517(a,2),28791(a,1,2))].">
      <j1 rule="para" parents="39517 28791"/>
    </justification>
  </clause>

  <clause id="39523">
    <literal><![CDATA[
      a(x,x,L(y,z,z)) \ z = (1 / z) \ (a(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(39517(a,2),37699(a,1,1))].">
      <j1 rule="para" parents="39517 37699"/>
    </justification>
  </clause>

  <clause id="39524">
    <literal><![CDATA[
      a(x,x,L(y,z \ x,z \ x)) = a(x,(1 / (z / x)) * z,y)
    ]]></literal>
    <justification jstring="[para(34721(a,1),39520(a,1,2)),flip(a)].">
      <j1 rule="para" parents="34721 39520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39525">
    <literal><![CDATA[
      a(x,L(x,y * x,y),z) = a(x,x,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,34877,a,b,39519,a)].">
      <j1 rule="hyper" parents="64 34877 39519"/>
    </justification>
  </clause>

  <clause id="39526">
    <literal><![CDATA[
      a(x,(x \ y) * y,z) = a(x,x,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,35810,a(flip),b,39525,a)].">
      <j1 rule="hyper" parents="64 35810 39525"/>
    </justification>
  </clause>

  <clause id="39527">
    <literal><![CDATA[
      a((x \ y) * y,x,z) = a(x,x,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32582,a,b,39526,a)].">
      <j1 rule="hyper" parents="64 32582 39526"/>
    </justification>
  </clause>

  <clause id="39528">
    <literal><![CDATA[
      a(L(a(x,x,L(y,z,z)),a(x,x,y),z / x),u,w) = a((z / x) * (z / R(x,x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(39526(a,1),38134(a,1,1,1))].">
      <j1 rule="para" parents="39526 38134"/>
    </justification>
  </clause>

  <clause id="39529">
    <literal><![CDATA[
      a(x * (y \ x),y,z) = a(y,y,L(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(26847,a,39527,a)].">
      <j1 rule="hyper" parents="26847 39527"/>
    </justification>
  </clause>

  <clause id="39530">
    <literal><![CDATA[
      (L(x,y,z) * ((x * x) \ u)) * a(L(x,y,z),L(x,y,z),L((x * x) \ u,x,x)) = ((x * x) / L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(39529(a,1),30448(a,1,2))].">
      <j1 rule="para" parents="39529 30448"/>
    </justification>
  </clause>

  <clause id="39531">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(y,z,z)) = a(z,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,36326,a(flip),b,39522,a),flip(a)].">
      <j1 rule="hyper" parents="373 36326 39522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39532">
    <literal><![CDATA[
      a(x,x,L(y,z \ x,z \ x)) = a(x,(z / x) * z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11967,a(flip),b,39524,a),flip(a)].">
      <j1 rule="hyper" parents="373 11967 39524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39533">
    <literal><![CDATA[
      a(x,x,L(y,z \ x,z \ x)) = a(x,(x \ z) * z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,31904,a(flip),b,39532,a),flip(a)].">
      <j1 rule="hyper" parents="373 31904 39532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39534">
    <literal><![CDATA[
      a(x,x,L(y,z \ x,z \ x)) = a(x,x,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,39526,a(flip),b,39533,a),flip(a)].">
      <j1 rule="hyper" parents="373 39526 39533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39535">
    <literal><![CDATA[
      a(x,x,L(y,z * x,z * x)) = a(x,x,L(y,z,z))
    ]]></literal>
    <justification jstring="[para(35222(a,1),39534(a,1,3))].">
      <j1 rule="para" parents="35222 39534"/>
    </justification>
  </clause>

  <clause id="39536">
    <literal><![CDATA[
      a(x,x,L(y,z * x,z * x)) = L(a(x,x,y),z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,39517,a(flip),b,39535,a),flip(a)].">
      <j1 rule="hyper" parents="373 39517 39535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39537">
    <literal><![CDATA[
      a(x,x,y) \ L(a(x,x,y),z,z) = a(a(x,x,y),z * x,z * x)
    ]]></literal>
    <justification jstring="[para(39536(a,1),39522(a,1,2))].">
      <j1 rule="para" parents="39536 39522"/>
    </justification>
  </clause>

  <clause id="39538">
    <literal><![CDATA[
      a(a(x,x,y),z * x,z * x) = a(a(x,x,y),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37925,a(flip),b,39537,a),flip(a)].">
      <j1 rule="hyper" parents="64 37925 39537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39539">
    <literal><![CDATA[
      a(x,y,L(a(z,z,u) \ 1,w,v5)) = a(x,y,a(L(u,w,v5),z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,38718,a(flip),b,39515,a),flip(a)].">
      <j1 rule="hyper" parents="64 38718 39515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39540">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,u),w,v5)) = a(x,y,a(L(z,w,v5),u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27977,a(flip),b,39539,a)].">
      <j1 rule="hyper" parents="64 27977 39539"/>
    </justification>
  </clause>

  <clause id="39541">
    <literal><![CDATA[
      a(x,x,L((x \ 1) \ y,x \ y,z)) \ z = (x * y) * (((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(29704(a,1),39513(a,1,1,3))].">
      <j1 rule="para" parents="29704 39513"/>
    </justification>
  </clause>

  <clause id="39542">
    <literal><![CDATA[
      a((x / y) * (x / R(y,y,z)),u,w) = a(a(y,y,L(z,x,x)),u,w)
    ]]></literal>
    <justification jstring="[para(37665(a,1),39528(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37665 39528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39543">
    <literal><![CDATA[
      a((x \ y) * (y / R(x,x,z)),u,w) = a(a(x,x,L(z,y,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32367,a(flip),b,39542,a)].">
      <j1 rule="hyper" parents="64 32367 39542"/>
    </justification>
  </clause>

  <clause id="39545">
    <literal><![CDATA[
      a((x \ y) * (R(x,x,z) \ y),u,w) = a(a(x,x,L(z,y,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32362,a(flip),b,39543,a)].">
      <j1 rule="hyper" parents="64 32362 39543"/>
    </justification>
  </clause>

  <clause id="39546">
    <literal><![CDATA[
      a(x,x,L((1 / x) \ y,x \ y,z)) \ z = ((x * x) \ (x * ((x * x) * y))) * (((1 / x) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(29694(a,1),39514(a,1,1,3))].">
      <j1 rule="para" parents="29694 39514"/>
    </justification>
  </clause>

  <clause id="39547">
    <literal><![CDATA[
      a(x,x,L((x \ 1) \ y,x \ y,z)) \ z = ((x * x) \ (x * ((x * x) * y))) * (((1 / x) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(27625(a,1),39546(a,1,1))].">
      <j1 rule="para" parents="27625 39546"/>
    </justification>
  </clause>

  <clause id="39548">
    <literal><![CDATA[
      (L(x,y,z) * ((x * x) \ u)) * a(L(x,y,z),L(x,y,z),x \ (x \ u)) = ((x * x) / L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(38938(a,1),39530(a,1,2))].">
      <j1 rule="para" parents="38938 39530"/>
    </justification>
  </clause>

  <clause id="39549">
    <literal><![CDATA[
      (L(x,y,z) * ((x * x) \ u)) * a(x,x,x \ (x \ u)) = ((x * x) / L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(35139(a,1),39548(a,1,2))].">
      <j1 rule="para" parents="35139 39548"/>
    </justification>
  </clause>

  <clause id="39550">
    <literal><![CDATA[
      L(x,y,z) * (((x * x) \ u) * a(x,x,x \ (x \ u))) = ((x * x) / L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,29959,a(flip),b,39549,a)].">
      <j1 rule="hyper" parents="64 29959 39549"/>
    </justification>
  </clause>

  <clause id="39552">
    <literal><![CDATA[
      ((x * x) / L(x,y,z)) \ u = L(x,y,z) * (x \ (x \ u))
    ]]></literal>
    <justification jstring="[para(1249(a,1),39550(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1249 39550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39553">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) \ u = L(x,y,z) * (x \ (x \ u))
    ]]></literal>
    <justification jstring="[para(24843(a,1),39552(a,1,1))].">
      <j1 rule="para" parents="24843 39552"/>
    </justification>
  </clause>

  <clause id="39554">
    <literal><![CDATA[
      ((L(x,y,z) \ x) * x) \ u = L(x,y,z) * (x \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,24799,a,b,39553,a)].">
      <j1 rule="hyper" parents="64 24799 39553"/>
    </justification>
  </clause>

  <clause id="39555">
    <literal><![CDATA[
      L(x * K(y * x,L(y,z,u) \ y),y,L(y,z,u) \ y) = L(y,z,u) * (y \ (y \ ((y * x) * (L(y,z,u) \ y))))
    ]]></literal>
    <justification jstring="[hyper(64,a,14648,a,b,39554,a)].">
      <j1 rule="hyper" parents="64 14648 39554"/>
    </justification>
  </clause>

  <clause id="39556">
    <literal><![CDATA[
      x * ((R(L(x \ 1,y,z) \ (x \ 1),x,x) / (x \ 1)) \ u) = (x \ 1) * (L(x \ 1,y,z) * ((x \ 1) \ ((x \ 1) \ u)))
    ]]></literal>
    <justification jstring="[para(39554(a,1),27017(a,2,2))].">
      <j1 rule="para" parents="39554 27017"/>
    </justification>
  </clause>

  <clause id="39557">
    <literal><![CDATA[
      L(x,y,z) * (x \ (x \ ((x * u) * (L(x,y,z) \ x)))) = L(u,x,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(23538(a,1),39555(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23538 39555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39558">
    <literal><![CDATA[
      L(x,y,z) * (x \ (x \ ((x * u) * (L(x,y,z) \ x)))) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,9385,a(flip),b,39557,a),flip(a)].">
      <j1 rule="hyper" parents="373 9385 39557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39559">
    <literal><![CDATA[
      L(x,y,z) * (x \ (x \ (x * ((L(x,y,z) \ x) * u)))) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(38585(a,1),39558(a,1,2,2,2))].">
      <j1 rule="para" parents="38585 39558"/>
    </justification>
  </clause>

  <clause id="39560">
    <literal><![CDATA[
      L(x,y,z) * (x \ ((L(x,y,z) \ x) * u)) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),39559(a,1,2,2))].">
      <j1 rule="para" parents="9 39559"/>
    </justification>
  </clause>

  <clause id="39562">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ x) * (x \ u)) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(38588(a,1),39560(a,1,2))].">
      <j1 rule="para" parents="38588 39560"/>
    </justification>
  </clause>

  <clause id="39563">
    <literal><![CDATA[
      L(x,L(y,z,u),y * L(y,z,u)) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,38601,a(flip),b,39562,a)].">
      <j1 rule="hyper" parents="64 38601 39562"/>
    </justification>
  </clause>

  <clause id="39564">
    <literal><![CDATA[
      L(x,y * L(y,z,u),L(y,z,u)) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,38606,a,b,39563,a)].">
      <j1 rule="hyper" parents="64 38606 39563"/>
    </justification>
  </clause>

  <clause id="39565">
    <literal><![CDATA[
      x \ ((x * R(y,z,u)) * (R(y,z,u) \ y)) = L(x,y,y * L(y,z,u)) * (x \ y)
    ]]></literal>
    <justification jstring="[para(39563(a,1),38609(a,1,1)),flip(a)].">
      <j1 rule="para" parents="39563 38609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39566">
    <literal><![CDATA[
      R(x,R(T(y,z),u,w) \ (L(v5,R(T(y,z),u,w) \ v6,L(y,u,w)) * v6),v7) = R(x,(R(y,u,w) \ v6) * T(v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(23843(a,1),39433(a,1,2,2,1))].">
      <j1 rule="para" parents="23843 39433"/>
    </justification>
  </clause>

  <clause id="39568">
    <literal><![CDATA[
      R(x,R(T(y,z),u,w) \ (L(v5,L(y,u,w) \ v6,L(y,u,w)) * v6),v7) = R(x,(R(y,u,w) \ v6) * T(v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(37354(a,1),39566(a,1,2,2,1))].">
      <j1 rule="para" parents="37354 39566"/>
    </justification>
  </clause>

  <clause id="39569">
    <literal><![CDATA[
      R(x,L(y,z,u) \ (L(w,L(y,z,u) \ v5,L(y,z,u)) * v5),v6) = R(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,38515,a(flip),b,39568,a)].">
      <j1 rule="hyper" parents="64 38515 39568"/>
    </justification>
  </clause>

  <clause id="39571">
    <literal><![CDATA[
      R(x,(R(y,z,u) \ w) * T(v5,w),v6) = R(x,(L(y,z,u) \ w) * T(v5,w),v6)
    ]]></literal>
    <justification jstring="[para(1010(a,1),39569(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1010 39569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39572">
    <literal><![CDATA[
      R(x,(R(y,z,u) \ w) * T(v5,w),v6) = R(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,26420,a(flip),b,39571,a),flip(a)].">
      <j1 rule="hyper" parents="373 26420 39571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39574">
    <literal><![CDATA[
      R(x,(R(y,z,u) \ w) * v5,v6) = R(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26420,a(flip),b,39572,a)].">
      <j1 rule="hyper" parents="64 26420 39572"/>
    </justification>
  </clause>

  <clause id="39576">
    <literal><![CDATA[
      R(x,a(L(y,z,u),z,u) * z,w) = R(x,(L(y,z,u) \ z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,35820,a,b,39574,a)].">
      <j1 rule="hyper" parents="64 35820 39574"/>
    </justification>
  </clause>

  <clause id="39577">
    <literal><![CDATA[
      L(x,R(y \ 1,z,u) \ (L(w,R(y \ 1,z,u) \ v5,L(y,z,u)) * v5),v6) = L(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(34224(a,1),39464(a,1,2,2,1))].">
      <j1 rule="para" parents="34224 39464"/>
    </justification>
  </clause>

  <clause id="39578">
    <literal><![CDATA[
      L(x,R(y \ 1,z,u) \ (L(w,L(y \ 1,z,u) \ v5,L(y,z,u)) * v5),v6) = L(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(37353(a,1),39577(a,1,2,2,1))].">
      <j1 rule="para" parents="37353 39577"/>
    </justification>
  </clause>

  <clause id="39579">
    <literal><![CDATA[
      L(x,R(y \ 1,z,u) \ (L(w,L(y,z,u) \ v5,L(y,z,u)) * v5),v6) = L(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(37356(a,1),39578(a,1,2,2,1))].">
      <j1 rule="para" parents="37356 39578"/>
    </justification>
  </clause>

  <clause id="39580">
    <literal><![CDATA[
      L(x,L(y \ 1,z,u) \ (L(w,L(y,z,u) \ v5,L(y,z,u)) * v5),v6) = L(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,37353,a(flip),b,39579,a)].">
      <j1 rule="hyper" parents="64 37353 39579"/>
    </justification>
  </clause>

  <clause id="39581">
    <literal><![CDATA[
      L(x,L(y,z,u) \ (L(w,L(y,z,u) \ v5,L(y,z,u)) * v5),v6) = L(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,37356,a(flip),b,39580,a)].">
      <j1 rule="hyper" parents="64 37356 39580"/>
    </justification>
  </clause>

  <clause id="39582">
    <literal><![CDATA[
      L(x,(R(y,z,u) \ w) * T(v5,w),v6) = L(x,(L(y,z,u) \ w) * T(v5,w),v6)
    ]]></literal>
    <justification jstring="[para(1010(a,1),39581(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1010 39581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39583">
    <literal><![CDATA[
      L(x,(R(y,z,u) \ w) * T(v5,w),v6) = L(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,29447,a(flip),b,39582,a),flip(a)].">
      <j1 rule="hyper" parents="373 29447 39582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39585">
    <literal><![CDATA[
      L(x,(R(y,z,u) \ w) * v5,v6) = L(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29447,a(flip),b,39583,a)].">
      <j1 rule="hyper" parents="64 29447 39583"/>
    </justification>
  </clause>

  <clause id="39586">
    <literal><![CDATA[
      L(x,(R(y,z,u) \ w) * (T(v5,v6) \ v7),v8) = L(x,(L(y,z,u) \ w) * (v5 \ v7),v8)
    ]]></literal>
    <justification jstring="[hyper(373,a,29625,a(flip),b,39585,a),flip(a)].">
      <j1 rule="hyper" parents="373 29625 39585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39588">
    <literal><![CDATA[
      L(x,(L(y,z,u) \ w) * L(v5,v5,L(y,z,u) \ w),v6) = L(x,v5 \ (R(y,z,u) \ w),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32987,a(flip),b,39585,a),flip(a)].">
      <j1 rule="hyper" parents="64 32987 39585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39589">
    <literal><![CDATA[
      L(x,(R(y,z,u) \ w) * (T(v5,v6) \ 1),v7) = L(x,v5 * (L(y,z,u) \ w),v7)
    ]]></literal>
    <justification jstring="[hyper(373,a,29520,a(flip),b,39586,a),flip(a)].">
      <j1 rule="hyper" parents="373 29520 39586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39590">
    <literal><![CDATA[
      L(x,T(y,z) * (R(u,w,v5) \ v6),v7) = L(x,y * (L(u,w,v5) \ v6),v7)
    ]]></literal>
    <justification jstring="[hyper(29616,a,39589,a)].">
      <j1 rule="hyper" parents="29616 39589"/>
    </justification>
  </clause>

  <clause id="39591">
    <literal><![CDATA[
      L(x,y * (R(z,u,w) \ v5),v6) = L(x,y * (L(z,u,w) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29438,a(flip),b,39590,a)].">
      <j1 rule="hyper" parents="64 29438 39590"/>
    </justification>
  </clause>

  <clause id="39592">
    <literal><![CDATA[
      L(x,y * a(L(z,y,u),y,u),w) = L(x,z * (L(z,y,u) \ y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,39179,a,b,39591,a)].">
      <j1 rule="hyper" parents="64 39179 39591"/>
    </justification>
  </clause>

  <clause id="39593">
    <literal><![CDATA[
      L(x,y \ (R(z,u,w) \ v5),v6) = L(x,y \ (L(z,u,w) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,29779,a(flip),b,39588,a),flip(a)].">
      <j1 rule="hyper" parents="64 29779 39588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39594">
    <literal><![CDATA[
      a(x,R(y \ 1,z,u) \ (L(w,R(y \ 1,z,u) \ v5,L(y,z,u)) * v5),v6) = a(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(34224(a,1),39473(a,1,2,2,1))].">
      <j1 rule="para" parents="34224 39473"/>
    </justification>
  </clause>

  <clause id="39595">
    <literal><![CDATA[
      a(x,R(y \ 1,z,u) \ (L(w,L(y \ 1,z,u) \ v5,L(y,z,u)) * v5),v6) = a(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(37353(a,1),39594(a,1,2,2,1))].">
      <j1 rule="para" parents="37353 39594"/>
    </justification>
  </clause>

  <clause id="39596">
    <literal><![CDATA[
      a(x,R(y \ 1,z,u) \ (L(w,L(y,z,u) \ v5,L(y,z,u)) * v5),v6) = a(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[para(37356(a,1),39595(a,1,2,2,1))].">
      <j1 rule="para" parents="37356 39595"/>
    </justification>
  </clause>

  <clause id="39597">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * (1 / (x \ y))) * ((y \ x) * z)) = ((x \ y) * (x \ y)) \ (a(y,x \ y,x \ y) \ z)
    ]]></literal>
    <justification jstring="[para(37569(a,1),39474(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37569 39474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39598">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * (1 / (x \ y))) * ((y \ x) * z)) = ((x \ y) * (x \ y)) \ (((y \ x) * (x \ y)) * z)
    ]]></literal>
    <justification jstring="[para(37850(a,1),39597(a,2,2))].">
      <j1 rule="para" parents="37850 39597"/>
    </justification>
  </clause>

  <clause id="39599">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * (1 / (x \ y))) * ((y \ x) * z)) = (((x \ y) * (x \ y)) \ ((y \ x) * (x \ y))) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,484,a(flip),b,39598,a),flip(a)].">
      <j1 rule="hyper" parents="373 484 39598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39600">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * (1 / (x \ y))) * ((y \ x) * z)) = ((((x \ y) * (x \ y)) \ (y \ x)) * (x \ y)) * z
    ]]></literal>
    <justification jstring="[para(484(a,1),39599(a,2,1))].">
      <j1 rule="para" parents="484 39599"/>
    </justification>
  </clause>

  <clause id="39601">
    <literal><![CDATA[
      x * ((R(x \ (L(1 / x,y,z) \ 1),x,x) / (x \ 1)) \ u) = (x \ 1) * (L(x \ 1,y,z) * ((x \ 1) \ ((x \ 1) \ u)))
    ]]></literal>
    <justification jstring="[para(9392(a,1),39556(a,1,2,1,1,1))].">
      <j1 rule="para" parents="9392 39556"/>
    </justification>
  </clause>

  <clause id="39602">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) * ((x \ 1) \ ((x \ 1) \ u))) = x * (((x \ (L(1 / x,y,z) \ 1)) / (x \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(31440(a,1),39601(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="31440 39601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39603">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,y,z) * ((x \ 1) \ ((x \ 1) \ u))) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(39228(a,1),39602(a,2,2,1))].">
      <j1 rule="para" parents="39228 39602"/>
    </justification>
  </clause>

  <clause id="39604">
    <literal><![CDATA[
      L(x \ 1,y,z) * ((x \ 1) \ u) = x * ((L(1 / x,y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(2334,a,39603,a)].">
      <j1 rule="hyper" parents="2334 39603"/>
    </justification>
  </clause>

  <clause id="39605">
    <literal><![CDATA[
      (x / (y \ 1)) * L(y \ 1,z,u) = y * ((L(1 / y,z,u) \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,23898,a(flip),b,39604,a)].">
      <j1 rule="hyper" parents="64 23898 39604"/>
    </justification>
  </clause>

  <clause id="39606">
    <literal><![CDATA[
      K(x \ 1,x) * (((1 / (1 / x)) \ ((1 / (1 / x)) \ y)) * x) = x \ T(y,1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(412(a,1),25147(a,1,1)),flip(a)].">
      <j1 rule="para" parents="412 25147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39607">
    <literal><![CDATA[
      K(x \ 1,x) * (((1 / (1 / x)) \ ((1 / (1 / x)) \ y)) * x) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3869(a,1),39606(a,2,2))].">
      <j1 rule="para" parents="3869 39606"/>
    </justification>
  </clause>

  <clause id="39608">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ ((1 / (1 / x)) \ y)) * ((x \ 1) \ 1)) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3920(a,1),39607(a,1,2))].">
      <j1 rule="para" parents="3920 39607"/>
    </justification>
  </clause>

  <clause id="39609">
    <literal><![CDATA[
      (T(x,x \ 1) \ ((1 / (1 / x)) \ y)) * ((x \ 1) \ 1) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24348,a(flip),b,39608,a)].">
      <j1 rule="hyper" parents="64 24348 39608"/>
    </justification>
  </clause>

  <clause id="39610">
    <literal><![CDATA[
      (x \ (T(1 / (1 / x),x \ 1) \ y)) * ((x \ 1) \ 1) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5305(a,1),39609(a,1,1))].">
      <j1 rule="para" parents="5305 39609"/>
    </justification>
  </clause>

  <clause id="39611">
    <literal><![CDATA[
      (x \ (x \ y)) * ((x \ 1) \ 1) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[para(1347(a,1),39610(a,1,1,2,1))].">
      <j1 rule="para" parents="1347 39610"/>
    </justification>
  </clause>

  <clause id="39612">
    <literal><![CDATA[
      a(x,(R((1 / y) \ z,u,w) \ (R((1 / y) \ z,u,w) \ v5)) * ((R((1 / y) \ z,u,w) \ 1) \ 1),v6) = a(x,R(y \ z,u,w) \ T(v5,R((1 / y) \ z,u,w)),v6)
    ]]></literal>
    <justification jstring="[para(39611(a,2),32912(a,1,2))].">
      <j1 rule="para" parents="39611 32912"/>
    </justification>
  </clause>

  <clause id="39613">
    <literal><![CDATA[
      R(x,y,((R(z,u,w) \ z) * (R(z,u,w) \ z)) * ((R(1 / z,u,w) \ 1) \ v5)) = R(x,y,(z * (z \ R(z,u,w))) \ v5)
    ]]></literal>
    <justification jstring="[para(24813(a,1),27191(a,2,3,1,2))].">
      <j1 rule="para" parents="24813 27191"/>
    </justification>
  </clause>

  <clause id="39614">
    <literal><![CDATA[
      R(x,y,((R(z,u,w) \ z) * (R(z,u,w) \ z)) * ((R(1 / z,u,w) \ 1) \ v5)) = R(x,y,R(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),39613(a,2,3,1))].">
      <j1 rule="para" parents="10 39613"/>
    </justification>
  </clause>

  <clause id="39615">
    <literal><![CDATA[
      R(x,y,((R(z,u,w) \ z) * (R(z,u,w) \ z)) * ((R(1 / z,u,w) \ 1) \ v5)) = R(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,35623,a(flip),b,39614,a),flip(a)].">
      <j1 rule="hyper" parents="373 35623 39614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39617">
    <literal><![CDATA[
      R(x,y,(z * (R(z,u,w) \ (R(z,u,w) \ z))) * ((R(1 / z,u,w) \ 1) \ v5)) = R(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[para(34573(a,1),39615(a,1,3,1))].">
      <j1 rule="para" parents="34573 39615"/>
    </justification>
  </clause>

  <clause id="39618">
    <literal><![CDATA[
      R(x,y,(R(1 / z,u,w) \ 1) \ v5) = R(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,39046,a(flip),b,39617,a)].">
      <j1 rule="hyper" parents="64 39046 39617"/>
    </justification>
  </clause>

  <clause id="39620">
    <literal><![CDATA[
      R(x,y,(L(1 / z,u,w) \ 1) \ v5) = R(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,36621,a(flip),b,39618,a)].">
      <j1 rule="hyper" parents="64 36621 39618"/>
    </justification>
  </clause>

  <clause id="39621">
    <literal><![CDATA[
      R(x,y,L(z \ 1,u,w)) = R(x,y,L(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(10466(a,1),39620(a,1,3))].">
      <j1 rule="para" parents="10466 39620"/>
    </justification>
  </clause>

  <clause id="39622">
    <literal><![CDATA[
      L(x \ R(x,y,L(z \ 1,u,w)),x,y * L(z,u,w)) = a(x,y,L(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(39621(a,2),24700(a,1,1,2))].">
      <j1 rule="para" parents="39621 24700"/>
    </justification>
  </clause>

  <clause id="39623">
    <literal><![CDATA[
      L(x \ R(x,y,L(a(z,u,w),v5,v6)),x,y * L(a(z,u,w) \ 1,v5,v6)) = a(x,y,L(a(z,u,w) \ 1,v5,v6) \ 1)
    ]]></literal>
    <justification jstring="[para(13931(a,1),39622(a,1,1,2,3,1))].">
      <j1 rule="para" parents="13931 39622"/>
    </justification>
  </clause>

  <clause id="39624">
    <literal><![CDATA[
      a(x,y,(R(1 / z,u,w) * R(z,u,w)) \ (R(1 / z,u,w) * v5)) = a(x,y,(z * z) \ ((R(1 / z,u,w) \ 1) * v5))
    ]]></literal>
    <justification jstring="[para(8(a,1),27976(a,2,3,1))].">
      <j1 rule="para" parents="8 27976"/>
    </justification>
  </clause>

  <clause id="39625">
    <literal><![CDATA[
      a(x,y,(R(1 / z,u,w) * R(z,u,w)) \ (R(1 / z,u,w) * v5)) = a(x,y,((z * z) \ (R(1 / z,u,w) \ 1)) * v5)
    ]]></literal>
    <justification jstring="[para(484(a,1),39624(a,2,3))].">
      <j1 rule="para" parents="484 39624"/>
    </justification>
  </clause>

  <clause id="39626">
    <literal><![CDATA[
      a(x,y,(R(1 / z,u,w) * R(z,u,w)) \ (R(1 / z,u,w) * v5)) = a(x,y,(R(1 / (1 / z),u,w) \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(2121(a,1),39625(a,2,3,1))].">
      <j1 rule="para" parents="2121 39625"/>
    </justification>
  </clause>

  <clause id="39627">
    <literal><![CDATA[
      a(x,y,(R(1 / z,u,w) * R(z,u,w)) \ (R(1 / z,u,w) * v5)) = a(x,y,(1 / R(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(11426(a,1),39626(a,2,3,1))].">
      <j1 rule="para" parents="11426 39626"/>
    </justification>
  </clause>

  <clause id="39628">
    <literal><![CDATA[
      a(x,y,(R(1 / z,u,w) * R(z,u,w)) \ (R(1 / z,u,w) * v5)) = a(x,y,(R(z,u,w) \ 1) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,27317,a(flip),b,39627,a),flip(a)].">
      <j1 rule="hyper" parents="373 27317 39627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39629">
    <literal><![CDATA[
      a(x,y,(R(1 / z,u,w) * R(z,u,w)) \ (R(1 / z,u,w) * v5)) = a(x,y,(L(z,u,w) \ 1) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,34552,a(flip),b,39628,a),flip(a)].">
      <j1 rule="hyper" parents="373 34552 39628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39630">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) * R(z \ 1,u,w)) \ (R(1 / z,u,w) * v5)) = a(x,y,(L(z,u,w) \ 1) * v5)
    ]]></literal>
    <justification jstring="[para(34188(a,1),39629(a,1,3,1))].">
      <j1 rule="para" parents="34188 39629"/>
    </justification>
  </clause>

  <clause id="39631">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) * R(z \ 1,u,w)) \ (L(1 / z,u,w) * v5)) = a(x,y,(L(z,u,w) \ 1) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,37062,a(flip),b,39630,a)].">
      <j1 rule="hyper" parents="64 37062 39630"/>
    </justification>
  </clause>

  <clause id="39632">
    <literal><![CDATA[
      a(x,y,L(1 / z,u,w) * v5) = a(x,y,(L(z,u,w) \ 1) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,39054,a(flip),b,39631,a)].">
      <j1 rule="hyper" parents="64 39054 39631"/>
    </justification>
  </clause>

  <clause id="39634">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) * v5) = a(x,y,(L(z,u,w) \ 1) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27429,a(flip),b,39632,a)].">
      <j1 rule="hyper" parents="64 27429 39632"/>
    </justification>
  </clause>

  <clause id="39635">
    <literal><![CDATA[
      a(x,y,(L(z \ 1,u,w) \ 1) * v5) = a(x,y,v5 * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27576,a(flip),b,39634,a),flip(a)].">
      <j1 rule="hyper" parents="64 27576 39634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39636">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) * ((L(z,u,w) \ 1) \ v5)) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),39634(a,2,3))].">
      <j1 rule="para" parents="10 39634"/>
    </justification>
  </clause>

  <clause id="39637">
    <literal><![CDATA[
      a(x,y,z * (a(z,z,u) \ w)) = a(x,y,w * L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,37972,a(flip),b,39635,a)].">
      <j1 rule="hyper" parents="64 37972 39635"/>
    </justification>
  </clause>

  <clause id="39638">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w)) = a(x,y,L(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(191(a,1),39636(a,1,3))].">
      <j1 rule="para" parents="191 39636"/>
    </justification>
  </clause>

  <clause id="39639">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) \ 1) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27336,a(flip),b,39638,a),flip(a)].">
      <j1 rule="hyper" parents="64 27336 39638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39641">
    <literal><![CDATA[
      a(x,y,L(z,u \ 1,w \ 1)) = a(x,y,L(z \ 1,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(11807(a,1),39639(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="11807 39639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39642">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) = a(x,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(39639(a,1),39506(a,1,1)),flip(a)].">
      <j1 rule="para" parents="39639 39506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39643">
    <literal><![CDATA[
      x \ (a(y,y,L(z,u,w)) \ x) = L(a(y,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,37677,a,b,39642,a)].">
      <j1 rule="hyper" parents="373 37677 39642"/>
    </justification>
  </clause>

  <clause id="39644">
    <literal><![CDATA[
      x * L(a(y,y,z) \ 1,u,w) = a(y,y,L(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,39642,a,b,37677,a)].">
      <j1 rule="hyper" parents="145 39642 37677"/>
    </justification>
  </clause>

  <clause id="39645">
    <literal><![CDATA[
      a(x,x,L(y,x,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,39374,a(flip),b,39642,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 39374 39642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39646">
    <literal><![CDATA[
      a(x,x,L(y,z,a(x,u,w))) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,31668,a(flip),b,39642,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 31668 39642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39647">
    <literal><![CDATA[
      a(x,x,L(y,z,x)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,31174,a(flip),b,39642,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 31174 39642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39649">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) \ w = w * a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(39642(a,2),37674(a,1,1))].">
      <j1 rule="para" parents="39642 37674"/>
    </justification>
  </clause>

  <clause id="39650">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,z,u) * w = a(x,x,L(y,z,u)) \ w
    ]]></literal>
    <justification jstring="[para(39642(a,2),37681(a,1,1))].">
      <j1 rule="para" parents="39642 37681"/>
    </justification>
  </clause>

  <clause id="39652">
    <literal><![CDATA[
      a(x,x,L(L(y,x,z),u,w)) = a(x,x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27702,a,b,39645,a)].">
      <j1 rule="hyper" parents="64 27702 39645"/>
    </justification>
  </clause>

  <clause id="39654">
    <literal><![CDATA[
      R(x,x,L(y,x,z)) = x * a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,39645,a(flip),b,30058,a),flip(a)].">
      <j1 rule="hyper" parents="145 39645 30058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39661">
    <literal><![CDATA[
      a(x,x,(x \ y) \ z) = a(x,x,y \ (x * z))
    ]]></literal>
    <justification jstring="[para(630(a,1),39647(a,1,3)),flip(a)].">
      <j1 rule="para" parents="630 39647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39666">
    <literal><![CDATA[
      R(x,x,L(y,x,z)) = R(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30054,a(flip),b,39654,a),flip(a)].">
      <j1 rule="hyper" parents="373 30054 39654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39667">
    <literal><![CDATA[
      R(x,x,(y * x) \ z) = R(x,x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(346(a,1),39666(a,1,3))].">
      <j1 rule="para" parents="346 39666"/>
    </justification>
  </clause>

  <clause id="39668">
    <literal><![CDATA[
      a(x,x,(a(x,y,z) * u) \ R(a(x,y,z) * w,v5,v6)) = a(x,x,u \ (a(x,y,z) * R(a(x,y,z) \ w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(2134(a,1),39646(a,1,3))].">
      <j1 rule="para" parents="2134 39646"/>
    </justification>
  </clause>

  <clause id="39669">
    <literal><![CDATA[
      R(x,x,y \ (y * ((z * x) \ u))) = R(x,x,x \ (z \ u))
    ]]></literal>
    <justification jstring="[para(9(a,2),39667(a,1,3))].">
      <j1 rule="para" parents="9 39667"/>
    </justification>
  </clause>

  <clause id="39670">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ a(x,x,y) = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,37930,a,b,39643,a),flip(a)].">
      <j1 rule="hyper" parents="39 37930 39643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39671">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(y,z,u)) = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,38056,a(flip),b,39670,a)].">
      <j1 rule="hyper" parents="64 38056 39670"/>
    </justification>
  </clause>

  <clause id="39672">
    <literal><![CDATA[
      a(x,x,y) * (a(x,x,L(y,z,u)) \ w) = a(a(y,x,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(39670(a,1),37994(a,1,1)),flip(a)].">
      <j1 rule="para" parents="39670 37994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39673">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(y,z,u)) = a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32543,a(flip),b,39671,a),flip(a)].">
      <j1 rule="hyper" parents="373 32543 39671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39675">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) = L(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,37925,a,b,39673,a),flip(a)].">
      <j1 rule="hyper" parents="39 37925 39673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39676">
    <literal><![CDATA[
      a(x,L(x,y,z),u) = a(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(39,a,37922,a,b,39673,a)].">
      <j1 rule="hyper" parents="39 37922 39673"/>
    </justification>
  </clause>

  <clause id="39677">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) * (a(x,x,y) \ w) = a(a(x,x,y),z,u) * w
    ]]></literal>
    <justification jstring="[para(39673(a,1),37994(a,1,1)),flip(a)].">
      <j1 rule="para" parents="39673 37994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39678">
    <literal><![CDATA[
      L(x,a(a(y,y,z),u,w),a(y,y,z)) = x
    ]]></literal>
    <justification jstring="[para(39673(a,1),37997(a,1,2))].">
      <j1 rule="para" parents="39673 37997"/>
    </justification>
  </clause>

  <clause id="39679">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ (a(x,x,y) * w) = a(a(x,x,y),z,u) \ w
    ]]></literal>
    <justification jstring="[para(39673(a,1),37996(a,1,1)),flip(a)].">
      <j1 rule="para" parents="39673 37996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39680">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) = R(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,28787,a,b,39675,a),flip(a)].">
      <j1 rule="hyper" parents="373 28787 39675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39681">
    <literal><![CDATA[
      a(x,x,L(y,L(x,z,u),w)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,38655,a(flip),b,39675,a),flip(a)].">
      <j1 rule="hyper" parents="373 38655 39675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39682">
    <literal><![CDATA[
      a(x,x,L(y \ z,y \ z,y)) = z \ (y * (x \ ((1 / x) \ (y \ z))))
    ]]></literal>
    <justification jstring="[hyper(373,a,30241,a(flip),b,39675,a),flip(a)].">
      <j1 rule="hyper" parents="373 30241 39675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39683">
    <literal><![CDATA[
      (x * y) * a(z,z,L(u,y,x)) = x * (y * a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,39675,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="145 39675 18"/>
    </justification>
  </clause>

  <clause id="39686">
    <literal><![CDATA[
      L(x * (y / (x * y)),z,u) = a(x,x,L(x * y,z,u))
    ]]></literal>
    <justification jstring="[para(30079(a,1),39675(a,2,1)),flip(a)].">
      <j1 rule="para" parents="30079 39675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39687">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) * L(x,z,u) = L(R(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(39675(a,2),30088(a,1,1))].">
      <j1 rule="para" parents="39675 30088"/>
    </justification>
  </clause>

  <clause id="39688">
    <literal><![CDATA[
      L(a(x,x,L(y,z,u)),w,x * y) = L(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(39675(a,2),30315(a,1,1))].">
      <j1 rule="para" parents="39675 30315"/>
    </justification>
  </clause>

  <clause id="39689">
    <literal><![CDATA[
      L(a(x * L(x,y,z),u,u) \ 1,w,v5) = a(u,u,L(x \ R(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(38773(a,2),39675(a,2,1)),flip(a)].">
      <j1 rule="para" parents="38773 39675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39690">
    <literal><![CDATA[
      x \ (y * (L(y,z,z) \ x)) = a(z,z,L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,37022,a,b,39676,a)].">
      <j1 rule="hyper" parents="64 37022 39676"/>
    </justification>
  </clause>

  <clause id="39691">
    <literal><![CDATA[
      a(L(x,y,z),x,u) = a(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,2784,a,b,39676,a)].">
      <j1 rule="hyper" parents="64 2784 39676"/>
    </justification>
  </clause>

  <clause id="39692">
    <literal><![CDATA[
      x * a(y,y,L(z,z,x)) = z * (L(z,y,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,39676,a(flip),b,37022,a)].">
      <j1 rule="hyper" parents="145 39676 37022"/>
    </justification>
  </clause>

  <clause id="39693">
    <literal><![CDATA[
      a(x,(y * ((y \ z) / x)) \ z,u) = a(x,x,L(u,x \ (y \ z),y))
    ]]></literal>
    <justification jstring="[para(10261(a,1),39676(a,1,2))].">
      <j1 rule="para" parents="10261 39676"/>
    </justification>
  </clause>

  <clause id="39694">
    <literal><![CDATA[
      (L(x,y,z) * a(x,x,L(L(u,x,L(x,y,z)),y,z))) \ (L(x,y,z) * u) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(39676(a,1),36047(a,1,1,2))].">
      <j1 rule="para" parents="39676 36047"/>
    </justification>
  </clause>

  <clause id="39695">
    <literal><![CDATA[
      (x \ y) * a(z,z,L(x,x,y)) = L(x,z,z) \ y
    ]]></literal>
    <justification jstring="[para(39676(a,1),37023(a,1,2))].">
      <j1 rule="para" parents="39676 37023"/>
    </justification>
  </clause>

  <clause id="39696">
    <literal><![CDATA[
      x * a(x,x,L(y,z,u)) = R(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(39676(a,1),38675(a,1,2))].">
      <j1 rule="para" parents="39676 38675"/>
    </justification>
  </clause>

  <clause id="39697">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ a(x,x,y) = a(a(x,x,y),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(39676(a,1),39287(a,1,1))].">
      <j1 rule="para" parents="39676 39287"/>
    </justification>
  </clause>

  <clause id="39698">
    <literal><![CDATA[
      L(x,a(y,y,z),a(a(y,y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,30415,a(flip),b,39678,a)].">
      <j1 rule="hyper" parents="64 30415 39678"/>
    </justification>
  </clause>

  <clause id="39699">
    <literal><![CDATA[
      a(x,x,L(a(x,y,z) * u,w,v5)) = R(a(x,x,u),w,v5)
    ]]></literal>
    <justification jstring="[para(32749(a,1),39680(a,2,1))].">
      <j1 rule="para" parents="32749 39680"/>
    </justification>
  </clause>

  <clause id="39700">
    <literal><![CDATA[
      (x \ a(x,x,y)) * L(y,L(x,z,u),w) = x \ L(y,L(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(39681(a,1),30104(a,1,1,2))].">
      <j1 rule="para" parents="39681 30104"/>
    </justification>
  </clause>

  <clause id="39701">
    <literal><![CDATA[
      a(x,x,y) * ((a(a(x,x,y),z,u) * a(x,x,y)) \ w) = a(a(x,x,y),z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(64,a,39275,a(flip),b,39698,a)].">
      <j1 rule="hyper" parents="64 39275 39698"/>
    </justification>
  </clause>

  <clause id="39702">
    <literal><![CDATA[
      L(x,a(y,y,z),a(a(z,y,y),u,w)) = x
    ]]></literal>
    <justification jstring="[para(32543(a,2),39698(a,1,3))].">
      <j1 rule="para" parents="32543 39698"/>
    </justification>
  </clause>

  <clause id="39703">
    <literal><![CDATA[
      L(x,a(y,z,z),a(a(y,z,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,31821,a,b,39702,a)].">
      <j1 rule="hyper" parents="64 31821 39702"/>
    </justification>
  </clause>

  <clause id="39704">
    <literal><![CDATA[
      a(x,y,y) * ((a(a(x,y,y),z,u) * a(x,y,y)) \ w) = a(a(x,y,y),z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(64,a,39275,a(flip),b,39703,a)].">
      <j1 rule="hyper" parents="64 39275 39703"/>
    </justification>
  </clause>

  <clause id="39705">
    <literal><![CDATA[
      R(x,L(x,y,z),u) = R(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30054,a(flip),b,39696,a),flip(a)].">
      <j1 rule="hyper" parents="64 30054 39696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39706">
    <literal><![CDATA[
      a(x,y,R(z,z,L(u,w,v5))) = a(x,y,L(z,L(z,w,v5),u))
    ]]></literal>
    <justification jstring="[para(39705(a,1),27644(a,1,3))].">
      <j1 rule="para" parents="39705 27644"/>
    </justification>
  </clause>

  <clause id="39707">
    <literal><![CDATA[
      a(x,x,L(y \ z,y \ z,y)) = (y * L(y \ z,x,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,34857,a(flip),b,39690,a),flip(a)].">
      <j1 rule="hyper" parents="64 34857 39690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39708">
    <literal><![CDATA[
      (x * y) \ (x * (z * (L(z,u,u) \ y))) = L(a(u,u,L(z,z,y)),y,x)
    ]]></literal>
    <justification jstring="[para(39690(a,1),102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="39690 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39709">
    <literal><![CDATA[
      (x * (y * a(z,z,u))) \ (x * y) = a(z,z,L(u,y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(39683(a,1),37678(a,1,1))].">
      <j1 rule="para" parents="39683 37678"/>
    </justification>
  </clause>

  <clause id="39710">
    <literal><![CDATA[
      a(x,x,L(x * R(y,z,y),u,w)) = L(x * (y / (x * y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,13883,a,b,39686,a)].">
      <j1 rule="hyper" parents="373 13883 39686"/>
    </justification>
  </clause>

  <clause id="39711">
    <literal><![CDATA[
      L(x * (R(T(y,K(x,z)),u,w) / T(x * R(y,u,w),K(x,z))),v5,v6) = a(x,x,L(x * R(T(y,K(x,z)),u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(8085(a,2),39686(a,1,1,2,2))].">
      <j1 rule="para" parents="8085 39686"/>
    </justification>
  </clause>

  <clause id="39712">
    <literal><![CDATA[
      L(x,y,z) * a(x,x,L(u,y,z)) = L(R(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(23177,a,39687,a)].">
      <j1 rule="hyper" parents="23177 39687"/>
    </justification>
  </clause>

  <clause id="39713">
    <literal><![CDATA[
      L(a(x,x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(39688(a,1),616(a,1))].">
      <j1 rule="para" parents="39688 616"/>
    </justification>
  </clause>

  <clause id="39714">
    <literal><![CDATA[
      a(x,x,L(a(x,y,z) * u,w,v5)) = a(x,x,L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,39680,a,b,39699,a),flip(a)].">
      <j1 rule="hyper" parents="373 39680 39699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39715">
    <literal><![CDATA[
      L(x,y,z) * a(x,x,a(u,y,y)) = L(R(x,x,a(u,y,y)),y,z)
    ]]></literal>
    <justification jstring="[para(37515(a,1),39712(a,1,2,3))].">
      <j1 rule="para" parents="37515 39712"/>
    </justification>
  </clause>

  <clause id="39716">
    <literal><![CDATA[
      a(x,x,L(y * a(x,z,u),w,v5)) = a(x,x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27377,a,b,39714,a)].">
      <j1 rule="hyper" parents="64 27377 39714"/>
    </justification>
  </clause>

  <clause id="39718">
    <literal><![CDATA[
      x * L(y \ L(y,z,z),u,w) = a(z,z,L(y,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(5665(a,1),39644(a,1,2,1))].">
      <j1 rule="para" parents="5665 39644"/>
    </justification>
  </clause>

  <clause id="39719">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) \ w = w * a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27169,a(flip),b,39649,a)].">
      <j1 rule="hyper" parents="64 27169 39649"/>
    </justification>
  </clause>

  <clause id="39720">
    <literal><![CDATA[
      (x * L(y,z,z)) * a(z,z,L(y,y,x)) = x * y
    ]]></literal>
    <justification jstring="[hyper(64,a,23758,a(flip),b,39649,a),flip(a)].">
      <j1 rule="hyper" parents="64 23758 39649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39721">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) * w = a(y,y,L(x,z,u)) \ w
    ]]></literal>
    <justification jstring="[hyper(64,a,27115,a(flip),b,39650,a)].">
      <j1 rule="hyper" parents="64 27115 39650"/>
    </justification>
  </clause>

  <clause id="39722">
    <literal><![CDATA[
      R(x,x,y \ (y * ((z * x) \ u))) = a(x,x,z \ u) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,30108,a,b,39669,a),flip(a)].">
      <j1 rule="hyper" parents="373 30108 39669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39723">
    <literal><![CDATA[
      a(x,y,L(z,L(z,u,w),v5)) = a(x,y,L(z,z,L(v5,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27644,a(flip),b,39706,a),flip(a)].">
      <j1 rule="hyper" parents="64 27644 39706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39724">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(y,y,L(z,u,w))) = a(a(x,x,y),L(y,u,w),z)
    ]]></literal>
    <justification jstring="[para(39723(a,1),39673(a,1,2))].">
      <j1 rule="para" parents="39723 39673"/>
    </justification>
  </clause>

  <clause id="39725">
    <literal><![CDATA[
      a(a(x,x,y),z,u) \ 1 = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,39670,a(flip),b,39697,a),flip(a)].">
      <j1 rule="hyper" parents="64 39670 39697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39726">
    <literal><![CDATA[
      (x * L(x \ y,z,z)) \ y = a(z,z,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,38953,a(flip),b,39707,a),flip(a)].">
      <j1 rule="hyper" parents="64 38953 39707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39727">
    <literal><![CDATA[
      (x * (y * a(z,z,u))) \ (x * y) = L(a(z,z,u) \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,39642,a,b,39709,a),flip(a)].">
      <j1 rule="hyper" parents="373 39642 39709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39728">
    <literal><![CDATA[
      (x * y) / (x * (z \ ((1 / z) \ y))) = L(a(z,z,y) \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33860,a(flip),b,39727,a)].">
      <j1 rule="hyper" parents="64 33860 39727"/>
    </justification>
  </clause>

  <clause id="39729">
    <literal><![CDATA[
      a(x,y,L(z,u \ 1,w \ 1)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,39639,a(flip),b,39641,a),flip(a)].">
      <j1 rule="hyper" parents="373 39639 39641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39730">
    <literal><![CDATA[
      a(x,y,L(z,u \ 1,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(1631(a,1),39729(a,1,3))].">
      <j1 rule="para" parents="1631 39729"/>
    </justification>
  </clause>

  <clause id="39731">
    <literal><![CDATA[
      a(x,y,L(z,u,w \ 1)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(11794(a,1),39729(a,1,3))].">
      <j1 rule="para" parents="11794 39729"/>
    </justification>
  </clause>

  <clause id="39732">
    <literal><![CDATA[
      L(x,y,z) * a(x,x,a(u,y,y)) = L(L(x,x,a(u,y,y)),y,z)
    ]]></literal>
    <justification jstring="[para(28832(a,1),39715(a,2,1))].">
      <j1 rule="para" parents="28832 39715"/>
    </justification>
  </clause>

  <clause id="39733">
    <literal><![CDATA[
      a(x,x,x * ((y * x) \ z)) = a(x,x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(38,a,30108,a,b,39722,a(flip))].">
      <j1 rule="hyper" parents="38 30108 39722"/>
    </justification>
  </clause>

  <clause id="39734">
    <literal><![CDATA[
      a(x,x,(x \ y) \ z) = a(x,x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27504,a(flip),b,39733,a),flip(a)].">
      <j1 rule="hyper" parents="64 27504 39733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39735">
    <literal><![CDATA[
      a(x,x,y \ (x * z)) = a(x,x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39661,a(flip),b,39734,a)].">
      <j1 rule="hyper" parents="64 39661 39734"/>
    </justification>
  </clause>

  <clause id="39736">
    <literal><![CDATA[
      a(x,L(x,y,z),(x \ u) \ w) = L(a(x,x,x * (u \ w)),y,z)
    ]]></literal>
    <justification jstring="[para(39734(a,1),34877(a,2,1))].">
      <j1 rule="para" parents="39734 34877"/>
    </justification>
  </clause>

  <clause id="39737">
    <literal><![CDATA[
      a((x \ 1) \ (y / x),(x \ 1) \ (y / x),((x \ 1) \ (y / x)) * (z \ (x \ 1))) = a((x \ 1) \ (y / x),(x \ 1) \ (y / x),z \ (T(y,x \ 1) / x))
    ]]></literal>
    <justification jstring="[para(5433(a,1),39735(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5433 39735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39738">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(x,z,u) = L(L(x,x,a(y,z,z)),z,u)
    ]]></literal>
    <justification jstring="[hyper(23777,a,39732,a)].">
      <j1 rule="hyper" parents="23777 39732"/>
    </justification>
  </clause>

  <clause id="39739">
    <literal><![CDATA[
      a(x,L(x,y,z),(x \ u) \ w) = a(x,L(x,y,z),x * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,34877,a,b,39736,a),flip(a)].">
      <j1 rule="hyper" parents="373 34877 39736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39740">
    <literal><![CDATA[
      a(x,L(x,y,z),x * (u \ w)) = a(x,x,L((x \ u) \ w,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39676,a(flip),b,39739,a),flip(a)].">
      <j1 rule="hyper" parents="64 39676 39739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39741">
    <literal><![CDATA[
      a(x,x,L((x \ y) \ z,u,w)) = a(x,x,L(x * (y \ z),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,39676,a(flip),b,39740,a),flip(a)].">
      <j1 rule="hyper" parents="64 39676 39740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39742">
    <literal><![CDATA[
      a(x,x,L(x * (1 \ y),x \ y,z)) \ z = (x * y) * (((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(39741(a,1),39541(a,1,1))].">
      <j1 rule="para" parents="39741 39541"/>
    </justification>
  </clause>

  <clause id="39743">
    <literal><![CDATA[
      a(x,x,L(x * (1 \ y),x \ y,z)) \ z = ((x * x) \ (x * ((x * x) * y))) * (((1 / x) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(39741(a,1),39547(a,1,1))].">
      <j1 rule="para" parents="39741 39547"/>
    </justification>
  </clause>

  <clause id="39744">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ (w * a(x,x,y)) = a(a(y,x,x),z,u) * w
    ]]></literal>
    <justification jstring="[hyper(64,a,31107,a,b,39672,a)].">
      <j1 rule="hyper" parents="64 31107 39672"/>
    </justification>
  </clause>

  <clause id="39745">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) * (a(x,x,y) \ w) = w * a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a(flip),b,39677,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 39677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39746">
    <literal><![CDATA[
      (a(x,x,L(y,z,u)) \ a(x,x,y)) * w = a(a(x,x,y),z,u) \ w
    ]]></literal>
    <justification jstring="[hyper(64,a,37995,a(flip),b,39679,a)].">
      <j1 rule="hyper" parents="64 37995 39679"/>
    </justification>
  </clause>

  <clause id="39747">
    <literal><![CDATA[
      a(x,(y * (x \ (y \ z))) \ z,u) = a(x,x,L(u,x \ (y \ z),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,31985,a(flip),b,39693,a)].">
      <j1 rule="hyper" parents="64 31985 39693"/>
    </justification>
  </clause>

  <clause id="39748">
    <literal><![CDATA[
      a(a(x,y,y),z,z) * x = x * a(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39056,a(flip),b,39744,a),flip(a)].">
      <j1 rule="hyper" parents="64 39056 39744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39749">
    <literal><![CDATA[
      a(a(x,y,y),z,z) = a(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(23176,a,39748,a)].">
      <j1 rule="hyper" parents="23176 39748"/>
    </justification>
  </clause>

  <clause id="39751">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) = a(z,z,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,36326,a(flip),b,39749,a)].">
      <j1 rule="hyper" parents="64 36326 39749"/>
    </justification>
  </clause>

  <clause id="39752">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * z = L(z,z,a(y,x,x))
    ]]></literal>
    <justification jstring="[para(39749(a,1),36324(a,1,1))].">
      <j1 rule="para" parents="39749 36324"/>
    </justification>
  </clause>

  <clause id="39753">
    <literal><![CDATA[
      x * (y * a(z,z,a(u,x,x))) = L(x,x,a(u,z,z)) * y
    ]]></literal>
    <justification jstring="[para(39749(a,1),37712(a,1,2,2))].">
      <j1 rule="para" parents="39749 37712"/>
    </justification>
  </clause>

  <clause id="39754">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) = a(z,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,38630,a(flip),b,39751,a),flip(a)].">
      <j1 rule="hyper" parents="373 38630 39751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39755">
    <literal><![CDATA[
      a(x,x,a(y * a(x,z,u),w,w)) = a(w,w,a(y,x,x))
    ]]></literal>
    <justification jstring="[para(34032(a,1),39751(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34032 39751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39756">
    <literal><![CDATA[
      a(x,x,a(y * a(z,u,x),w,w)) = a(w,w,a(y,x,x))
    ]]></literal>
    <justification jstring="[para(37894(a,1),39751(a,1,3)),flip(a)].">
      <j1 rule="para" parents="37894 39751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39757">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(z,x,u) = L(L(z,z,a(y,x,x)),x,u)
    ]]></literal>
    <justification jstring="[para(39751(a,1),39738(a,1,1))].">
      <j1 rule="para" parents="39751 39738"/>
    </justification>
  </clause>

  <clause id="39758">
    <literal><![CDATA[
      x \ a(y,y,a(z,u,u)) = x \ a(u,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,39754,a,b,10,a)].">
      <j1 rule="hyper" parents="139 39754 10"/>
    </justification>
  </clause>

  <clause id="39759">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) = a(y,y,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,38630,a(flip),b,39754,a)].">
      <j1 rule="hyper" parents="64 38630 39754"/>
    </justification>
  </clause>

  <clause id="39760">
    <literal><![CDATA[
      x * a(y,y,a(x,x,z)) = L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,39754,a(flip),b,30065,a)].">
      <j1 rule="hyper" parents="145 39754 30065"/>
    </justification>
  </clause>

  <clause id="39761">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * (a(z,u,w) \ 1) = a(z,u,w) \ a(z,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(39754(a,2),31093(a,1,1))].">
      <j1 rule="para" parents="39754 31093"/>
    </justification>
  </clause>

  <clause id="39762">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) * L(y,y,u) = L(R(y,y,a(z,x,x)),y,u)
    ]]></literal>
    <justification jstring="[para(39754(a,1),38652(a,1,1))].">
      <j1 rule="para" parents="39754 38652"/>
    </justification>
  </clause>

  <clause id="39763">
    <literal><![CDATA[
      (x * y) * a(z,z,a(u,y,y)) = x * L(y,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,24842,a(flip),b,39753,a),flip(a)].">
      <j1 rule="hyper" parents="35 24842 39753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39764">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) * L(y,y,u) = L(L(y,y,a(z,x,x)),y,u)
    ]]></literal>
    <justification jstring="[para(28832(a,1),39762(a,2,1))].">
      <j1 rule="para" parents="28832 39762"/>
    </justification>
  </clause>

  <clause id="39765">
    <literal><![CDATA[
      a(x,L(x,y,z),u) * (a(x,x,u) \ w) = w * a(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(39676(a,2),39745(a,1,1))].">
      <j1 rule="para" parents="39676 39745"/>
    </justification>
  </clause>

  <clause id="39766">
    <literal><![CDATA[
      (a(a(x,x,y),z,u) \ 1) * w = a(a(x,x,y),z,u) \ w
    ]]></literal>
    <justification jstring="[para(39697(a,1),39746(a,1,1))].">
      <j1 rule="para" parents="39697 39746"/>
    </justification>
  </clause>

  <clause id="39767">
    <literal><![CDATA[
      x * (a(a(y,y,z),u,w) \ 1) = a(a(y,y,z),u,w) \ x
    ]]></literal>
    <justification jstring="[hyper(23765,a,39766,a)].">
      <j1 rule="hyper" parents="23765 39766"/>
    </justification>
  </clause>

  <clause id="39768">
    <literal><![CDATA[
      x \ (a(a(y,y,z),u,w) \ x) = a(a(y,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,31522,a,b,39766,a)].">
      <j1 rule="hyper" parents="36 31522 39766"/>
    </justification>
  </clause>

  <clause id="39769">
    <literal><![CDATA[
      a(a(x,x,y),z,u) \ w = w * a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(39725(a,1),39767(a,1,2)),flip(a)].">
      <j1 rule="para" parents="39725 39767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39771">
    <literal><![CDATA[
      a(x,x,y) * (z * a(a(x,x,y),u,w)) = z * a(x,L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(145,a,39765,a(flip),b,31107,a)].">
      <j1 rule="hyper" parents="145 39765 31107"/>
    </justification>
  </clause>

  <clause id="39772">
    <literal><![CDATA[
      x * (a(y,y,z) * R(a(y,y,z) \ 1,u,w)) = a(y,L(y,u,w),z) * (a(y,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(37931(a,2),39765(a,2,2)),flip(a)].">
      <j1 rule="para" parents="37931 39765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39773">
    <literal><![CDATA[
      (a(x,x,y) * z) * a(a(y,x,x),u,w) = z * a(x,L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32548,a,b,39771,a)].">
      <j1 rule="hyper" parents="64 32548 39771"/>
    </justification>
  </clause>

  <clause id="39774">
    <literal><![CDATA[
      (x * a(y,y,z)) * a(a(z,y,y),u,w) = x * a(y,L(y,u,w),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23168,a(flip),b,39773,a)].">
      <j1 rule="hyper" parents="64 23168 39773"/>
    </justification>
  </clause>

  <clause id="39775">
    <literal><![CDATA[
      x \ (y * (z \ ((1 / z) \ (y \ x)))) = a(z,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,38953,a(flip),b,39682,a),flip(a)].">
      <j1 rule="hyper" parents="64 38953 39682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39776">
    <literal><![CDATA[
      (x * y) \ ((x * (z \ y)) * (u \ ((1 / u) \ L(T(z,z \ y),z \ y,x)))) = a(u,u,((x * y) \ (x * (z \ y))) \ 1)
    ]]></literal>
    <justification jstring="[para(409(a,2),39775(a,1,2,2,2,2))].">
      <j1 rule="para" parents="409 39775"/>
    </justification>
  </clause>

  <clause id="39777">
    <literal><![CDATA[
      (x * y) \ (x * (z * (L(z,u,u) \ y))) = a(u,u,L(L(z,z,y),y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,39675,a,b,39708,a),flip(a)].">
      <j1 rule="hyper" parents="373 39675 39708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39778">
    <literal><![CDATA[
      a(a(x,x,y),L(y,z,u),w) = a(a(x,x,y),y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39673,a(flip),b,39724,a),flip(a)].">
      <j1 rule="hyper" parents="64 39673 39724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39779">
    <literal><![CDATA[
      a(a(x,x,y),L(y,z,u),w) = a(y,a(x,x,y),L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,33522,a(flip),b,39778,a),flip(a)].">
      <j1 rule="hyper" parents="373 33522 39778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39780">
    <literal><![CDATA[
      a(x,x,L(x * y,x \ y,z)) \ z = (x * y) * (((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(66(a,1),39742(a,1,1,3,1,2))].">
      <j1 rule="para" parents="66 39742"/>
    </justification>
  </clause>

  <clause id="39781">
    <literal><![CDATA[
      a(x,x,y) * (a(x,L(x,z,u),y) \ w) = a(a(x,x,y),z,u) \ w
    ]]></literal>
    <justification jstring="[para(37920(a,1),39701(a,1,2,1))].">
      <j1 rule="para" parents="37920 39701"/>
    </justification>
  </clause>

  <clause id="39782">
    <literal><![CDATA[
      a(x,y,y) * (a(L(x,z,u),y,y) \ w) = a(a(x,y,y),z,u) \ w
    ]]></literal>
    <justification jstring="[para(38064(a,1),39704(a,1,2,1))].">
      <j1 rule="para" parents="38064 39704"/>
    </justification>
  </clause>

  <clause id="39783">
    <literal><![CDATA[
      (x \ y) * (a(x,x,y) * R(a(x,x,y) \ 1,z,u)) = a(x,L(x,z,u),y) * ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(30044(a,1),39772(a,2,2))].">
      <j1 rule="para" parents="30044 39772"/>
    </justification>
  </clause>

  <clause id="39784">
    <literal><![CDATA[
      (x \ y) * (a(x,x,y) * R(a(x,x,y) \ 1,z,u)) = (x \ a(x,L(x,z,u),y)) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,33310,a(flip),b,39783,a),flip(a)].">
      <j1 rule="hyper" parents="373 33310 39783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39785">
    <literal><![CDATA[
      (x \ a(x,L(x,y,z),u)) * u = (x \ u) * a(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(37931(a,1),39784(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37931 39784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39786">
    <literal><![CDATA[
      (x \ a(x,x,L(y,z,u))) * y = (x \ y) * a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(39676(a,1),39785(a,1,1,2))].">
      <j1 rule="para" parents="39676 39785"/>
    </justification>
  </clause>

  <clause id="39787">
    <literal><![CDATA[
      (x \ y) * a(a(x,x,y),z,u) = y * (L(y,z,u) \ (x \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,30122,a(flip),b,39786,a),flip(a)].">
      <j1 rule="hyper" parents="64 30122 39786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39788">
    <literal><![CDATA[
      a(a(x,x,y),z,u) * (x \ y) = y * (L(y,z,u) \ (x \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(23777,a,39787,a)].">
      <j1 rule="hyper" parents="23777 39787"/>
    </justification>
  </clause>

  <clause id="39789">
    <literal><![CDATA[
      (L(x,y,z) * a(x,x,L(u,y,z))) \ (L(x,y,z) * u) = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(39652(a,1),39694(a,1,1,2))].">
      <j1 rule="para" parents="39652 39694"/>
    </justification>
  </clause>

  <clause id="39790">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ (L(x,z,u) \ (L(x,z,u) * y)) = L(y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,37575,a(flip),b,39789,a)].">
      <j1 rule="hyper" parents="64 37575 39789"/>
    </justification>
  </clause>

  <clause id="39792">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ y = L(y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),39790(a,1,2))].">
      <j1 rule="para" parents="9 39790"/>
    </justification>
  </clause>

  <clause id="39793">
    <literal><![CDATA[
      L(x,y,L(y,z,u)) \ x = a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(40,a,5559,a,b,39792,a)].">
      <j1 rule="hyper" parents="40 5559 39792"/>
    </justification>
  </clause>

  <clause id="39794">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) = x \ L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,39792,a(flip),b,39718,a),flip(a)].">
      <j1 rule="hyper" parents="139 39792 39718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39795">
    <literal><![CDATA[
      a(x,L(x,y,z),u) \ u = L(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(39676(a,2),39792(a,1,1))].">
      <j1 rule="para" parents="39676 39792"/>
    </justification>
  </clause>

  <clause id="39796">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ (y * a(x,w,v5)) = L(y * a(x,w,v5),x,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(39716(a,1),39792(a,1,1))].">
      <j1 rule="para" parents="39716 39792"/>
    </justification>
  </clause>

  <clause id="39797">
    <literal><![CDATA[
      L(x,y,L(y,z,u)) \ x = a(y,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,39676,a,b,39793,a),flip(a)].">
      <j1 rule="hyper" parents="373 39676 39793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39798">
    <literal><![CDATA[
      a(x,L(x,y * x,y),z) \ z = L(z,x,(x \ y) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,35808,a(flip),b,39795,a),flip(a)].">
      <j1 rule="hyper" parents="373 35808 39795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39799">
    <literal><![CDATA[
      L(x,y,z * L(z,u,L(u,w,v5))) = L(x,y,a(u,L(u,w,v5),z))
    ]]></literal>
    <justification jstring="[para(39797(a,1),9385(a,1,3)),flip(a)].">
      <j1 rule="para" parents="39797 9385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39800">
    <literal><![CDATA[
      a(x,y,L(z \ L(z,u,u),w,v5)) = a(x,y,a(z,u,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(39794(a,2),38383(a,1,3))].">
      <j1 rule="para" parents="39794 38383"/>
    </justification>
  </clause>

  <clause id="39801">
    <literal><![CDATA[
      a(x,x,L(y,z,z)) \ y = L(y,x,(x \ z) * z)
    ]]></literal>
    <justification jstring="[para(39525(a,1),39798(a,1,1))].">
      <j1 rule="para" parents="39525 39798"/>
    </justification>
  </clause>

  <clause id="39802">
    <literal><![CDATA[
      L(x,y,(y \ z) * z) = L(x,y,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39792,a(flip),b,39801,a),flip(a)].">
      <j1 rule="hyper" parents="64 39792 39801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39803">
    <literal><![CDATA[
      L(x,y * z,L(y * z,z,z)) = L(x,y * z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29164,a(flip),b,39802,a),flip(a)].">
      <j1 rule="hyper" parents="64 29164 39802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39804">
    <literal><![CDATA[
      (((x \ y) * y) * (x \ 1)) \ (((x \ y) * y) * z) = L((x \ 1) \ z,x,L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,11813,a(flip),b,39802,a)].">
      <j1 rule="hyper" parents="64 11813 39802"/>
    </justification>
  </clause>

  <clause id="39805">
    <literal><![CDATA[
      L(x,y * z,z \ y) = L(x,y * z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30388,a(flip),b,39803,a)].">
      <j1 rule="hyper" parents="64 30388 39803"/>
    </justification>
  </clause>

  <clause id="39806">
    <literal><![CDATA[
      L(x,y,z * L(z,y,L(y,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,37531,a(flip),b,39799,a),flip(a)].">
      <j1 rule="hyper" parents="373 37531 39799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39807">
    <literal><![CDATA[
      L(x,y,z \ L(z,y,L(y,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,5608,a,b,39806,a)].">
      <j1 rule="hyper" parents="64 5608 39806"/>
    </justification>
  </clause>

  <clause id="39808">
    <literal><![CDATA[
      L(x,y,z \ R(z,y,L(y,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,33124,a,b,39807,a)].">
      <j1 rule="hyper" parents="64 33124 39807"/>
    </justification>
  </clause>

  <clause id="39809">
    <literal><![CDATA[
      L(x,y,a(z,y,L(y,u,w))) = x
    ]]></literal>
    <justification jstring="[para(38380(a,1),39808(a,1,3))].">
      <j1 rule="para" parents="38380 39808"/>
    </justification>
  </clause>

  <clause id="39810">
    <literal><![CDATA[
      (x * y) * a(z,y,L(y,u,w)) = x * (y * a(z,y,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(39809(a,1),28800(a,1,1)),flip(a)].">
      <j1 rule="para" parents="39809 28800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39811">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),v5,v5)) = a(x,y,a(z,v5,L(v5,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,39540,a(flip),b,39800,a)].">
      <j1 rule="hyper" parents="64 39540 39800"/>
    </justification>
  </clause>

  <clause id="39812">
    <literal><![CDATA[
      a(x,y,a(z,u,L(u,w,v5))) = a(x,y,a(u,u,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,38630,a(flip),b,39811,a),flip(a)].">
      <j1 rule="hyper" parents="64 38630 39811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39813">
    <literal><![CDATA[
      L(a(x,y,L(y,z,u)),y,w) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(606,a,39810,a)].">
      <j1 rule="hyper" parents="606 39810"/>
    </justification>
  </clause>

  <clause id="39814">
    <literal><![CDATA[
      L(a(x,L(y,z,u),y),y,w) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(16192(a,2),39813(a,1,1))].">
      <j1 rule="para" parents="16192 39813"/>
    </justification>
  </clause>

  <clause id="39815">
    <literal><![CDATA[
      x * (a(y,y,L(x,z,u)) \ a(y,w,v5)) = L(x * a(y,w,v5),y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,33489,a(flip),b,39796,a)].">
      <j1 rule="hyper" parents="64 33489 39796"/>
    </justification>
  </clause>

  <clause id="39816">
    <literal><![CDATA[
      L(x * a(y,y,x),y,L(y,z,u)) = x * a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[para(39670(a,1),39815(a,1,2)),flip(a)].">
      <j1 rule="para" parents="39670 39815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39817">
    <literal><![CDATA[
      L(x * a(a(x,y,y),z,u),y,y) = L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(39816(a,1),30235(a,1,1))].">
      <j1 rule="para" parents="39816 30235"/>
    </justification>
  </clause>

  <clause id="39818">
    <literal><![CDATA[
      (x \ (y / (x / y))) \ (((x \ y) * y) * z) = L((x \ 1) \ z,x,L(x,y,y))
    ]]></literal>
    <justification jstring="[para(34329(a,1),39804(a,1,1))].">
      <j1 rule="para" parents="34329 39804"/>
    </justification>
  </clause>

  <clause id="39819">
    <literal><![CDATA[
      L((x \ 1) \ (((x \ y) * y) \ z),x,L(x,y,y)) = (x \ (y / (x / y))) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),39818(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 39818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39820">
    <literal><![CDATA[
      a(x,x,L(x * y,x \ y,z)) \ z = ((x * x) \ (x * ((x * x) * y))) * (((1 / x) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(66(a,1),39743(a,1,1,3,1,2))].">
      <j1 rule="para" parents="66 39743"/>
    </justification>
  </clause>

  <clause id="39821">
    <literal><![CDATA[
      L(x * T(R(y,z,u) / (x * R(y,z,u)),K(x,w)),v5,v6) = a(x,x,L(x * R(T(y,K(x,w)),z,u),v5,v6))
    ]]></literal>
    <justification jstring="[para(26988(a,1),39711(a,1,1,2))].">
      <j1 rule="para" parents="26988 39711"/>
    </justification>
  </clause>

  <clause id="39822">
    <literal><![CDATA[
      a(x,x,L(x * R(T(y,K(x,z)),u,w),v5,v6)) = L(x * R(1 / x,x,R(y,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(2899(a,1),39821(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2899 39821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39824">
    <literal><![CDATA[
      a(x,x,L(x * R(T(y,K(x,z)),u,w),v5,v6)) = L(x * R(1 / x,x,L(y,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(26360(a,1),39822(a,2,1,2))].">
      <j1 rule="para" parents="26360 39822"/>
    </justification>
  </clause>

  <clause id="39825">
    <literal><![CDATA[
      a(x,x,L(x * R(T(y,K(x,z)),u,w),v5,v6)) = L(a(x,x,x * L(y,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(30137(a,1),39824(a,2,1))].">
      <j1 rule="para" parents="30137 39824"/>
    </justification>
  </clause>

  <clause id="39826">
    <literal><![CDATA[
      (x * y) \ ((x * (z \ y)) * L(u \ ((1 / u) \ T(z,z \ y)),z \ y,x)) = a(u,u,((x * y) \ (x * (z \ y))) \ 1)
    ]]></literal>
    <justification jstring="[para(1840(a,2),39776(a,1,2,2))].">
      <j1 rule="para" parents="1840 39776"/>
    </justification>
  </clause>

  <clause id="39827">
    <literal><![CDATA[
      (x * y) \ ((x * (z \ y)) * L(T(u \ ((1 / u) \ z),z \ y),z \ y,x)) = a(u,u,((x * y) \ (x * (z \ y))) \ 1)
    ]]></literal>
    <justification jstring="[para(1532(a,2),39826(a,1,2,2,1))].">
      <j1 rule="para" parents="1532 39826"/>
    </justification>
  </clause>

  <clause id="39828">
    <literal><![CDATA[
      (x * y) \ (x * ((z \ ((1 / z) \ u)) * (u \ y))) = a(z,z,((x * y) \ (x * (u \ y))) \ 1)
    ]]></literal>
    <justification jstring="[para(588(a,1),39827(a,1,2))].">
      <j1 rule="para" parents="588 39827"/>
    </justification>
  </clause>

  <clause id="39829">
    <literal><![CDATA[
      a(x,x,((y * z) \ (y * (u \ z))) \ 1) = (y * z) \ (y * (u * (L(u,x,x) \ z)))
    ]]></literal>
    <justification jstring="[para(37024(a,1),39828(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="37024 39828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39830">
    <literal><![CDATA[
      a(x,x,L(L(y,y,z),z,u)) = a(x,x,((u * z) \ (u * (y \ z))) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,39777,a(flip),b,39829,a)].">
      <j1 rule="hyper" parents="373 39777 39829"/>
    </justification>
  </clause>

  <clause id="39831">
    <literal><![CDATA[
      (x * (y / (y / z))) \ ((((z \ R(z,u,w)) / x) \ R(z,u,w)) * K(z \ y,z)) = a(x \ (z \ R(z,u,w)),x,y / (y / z))
    ]]></literal>
    <justification jstring="[para(25984(a,1),30350(a,1,2))].">
      <j1 rule="para" parents="25984 30350"/>
    </justification>
  </clause>

  <clause id="39832">
    <literal><![CDATA[
      L(x,y,(z \ L(u \ w,a(u,u,w) \ 1,a(u,u,w) \ 1)) * v5) = L(x,y,(z \ ((u \ 1) * ((a(u,u,w) \ 1) * w))) * v5)
    ]]></literal>
    <justification jstring="[para(35648(a,1),30429(a,2,3,1,2))].">
      <j1 rule="para" parents="35648 30429"/>
    </justification>
  </clause>

  <clause id="39833">
    <literal><![CDATA[
      L(x,(y * (z * u)) * (T(w,y * (((v5 * v5) \ z) * u)) * K(v6,v7)),v8) = L(x,w * (y * ((((v5 * v5) \ z) * u) * K(v6,v7))),v8)
    ]]></literal>
    <justification jstring="[para(23053(a,1),31077(a,2,2,2))].">
      <j1 rule="para" parents="23053 31077"/>
    </justification>
  </clause>

  <clause id="39834">
    <literal><![CDATA[
      (K(x,y) * (K(y,x) * (z / (z / ((a(u,w,v5) \ 1) * v6))))) \ z = z / ((K(y,x) \ 1) * ((a(u,w,v5) \ K(y,x)) * v6))
    ]]></literal>
    <justification jstring="[para(6092(a,1),31427(a,1,1,1))].">
      <j1 rule="para" parents="6092 31427"/>
    </justification>
  </clause>

  <clause id="39835">
    <literal><![CDATA[
      (K(x,y) * (K(y,x) * ((z / (z / u)) * (a(w,v5,v6) \ 1)))) \ z = z / ((K(y,x) \ 1) * ((a(w,v5,v6) \ K(y,x)) * u))
    ]]></literal>
    <justification jstring="[para(36427(a,1),39834(a,1,1,2,2))].">
      <j1 rule="para" parents="36427 39834"/>
    </justification>
  </clause>

  <clause id="39836">
    <literal><![CDATA[
      (K(x,y) * ((a(z,u,w) \ K(y,x)) * (v5 / (v5 / v6)))) \ v5 = v5 / ((K(y,x) \ 1) * ((a(z,u,w) \ K(y,x)) * v6))
    ]]></literal>
    <justification jstring="[para(26748(a,1),39835(a,1,1,2))].">
      <j1 rule="para" parents="26748 39835"/>
    </justification>
  </clause>

  <clause id="39837">
    <literal><![CDATA[
      (T(a(x,y,z) \ 1,K(u,w)) * (v5 / (v5 / v6))) \ v5 = v5 / ((K(u,w) \ 1) * ((a(x,y,z) \ K(u,w)) * v6))
    ]]></literal>
    <justification jstring="[para(24448(a,1),39836(a,1,1))].">
      <j1 rule="para" parents="24448 39836"/>
    </justification>
  </clause>

  <clause id="39838">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * (u / (u / w))) \ u = u / ((K(v5,v6) \ 1) * ((a(x,y,z) \ K(v5,v6)) * w))
    ]]></literal>
    <justification jstring="[para(23735(a,1),39837(a,1,1,1))].">
      <j1 rule="para" parents="23735 39837"/>
    </justification>
  </clause>

  <clause id="39839">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * (u / (u / w))) \ u = u / (K(v5,v6) * ((a(x,y,z) \ K(v6,v5)) * w))
    ]]></literal>
    <justification jstring="[para(6092(a,1),39838(a,2,2,1))].">
      <j1 rule="para" parents="6092 39838"/>
    </justification>
  </clause>

  <clause id="39841">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * (u / (u / w))) \ u = u / ((a(x,y,z) \ 1) * w)
    ]]></literal>
    <justification jstring="[para(24449(a,1),39839(a,2,2))].">
      <j1 rule="para" parents="24449 39839"/>
    </justification>
  </clause>

  <clause id="39842">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) \ 1) / T(u,(1 / ((a(x,y,z) \ 1) * u)) * u) = u \ (1 / ((a(x,y,z) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(39841(a,1),27019(a,2,2))].">
      <j1 rule="para" parents="39841 27019"/>
    </justification>
  </clause>

  <clause id="39843">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) \ 1) / T(u,u * (((a(x,y,z) \ 1) * u) \ 1)) = u \ (1 / ((a(x,y,z) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(28824(a,1),39842(a,1,2,2))].">
      <j1 rule="para" parents="28824 39842"/>
    </justification>
  </clause>

  <clause id="39844">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) \ 1) / T(u,(a(x,y,z) \ 1) \ 1) = u \ (1 / ((a(x,y,z) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(24706(a,1),39843(a,1,2))].">
      <j1 rule="para" parents="24706 39843"/>
    </justification>
  </clause>

  <clause id="39845">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) \ 1) / T(u,a(x,y,z)) = u \ (1 / ((a(x,y,z) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3871(a,1),39844(a,1,2))].">
      <j1 rule="para" parents="3871 39844"/>
    </justification>
  </clause>

  <clause id="39847">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) * u) \ 1) / u = u \ (1 / ((a(x,y,z) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(23105(a,1),39845(a,1,2))].">
      <j1 rule="para" parents="23105 39845"/>
    </justification>
  </clause>

  <clause id="39849">
    <literal><![CDATA[
      ((x * (x \ (1 / ((a(y,z,u) \ 1) * x)))) * x) * x = T(x * ((1 / ((a(y,z,u) \ 1) * x)) * x),x)
    ]]></literal>
    <justification jstring="[para(39847(a,1),28927(a,1,1,1,2))].">
      <j1 rule="para" parents="39847 28927"/>
    </justification>
  </clause>

  <clause id="39850">
    <literal><![CDATA[
      T(x * ((1 / ((a(y,z,u) \ 1) * x)) * x),x) = ((1 / ((a(y,z,u) \ 1) * x)) * x) * x
    ]]></literal>
    <justification jstring="[para(10(a,1),39849(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 39849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39852">
    <literal><![CDATA[
      T(x * ((1 / ((a(y,z,u) \ 1) * x)) * x),x) = (x * (((a(y,z,u) \ 1) * x) \ 1)) * x
    ]]></literal>
    <justification jstring="[para(28824(a,1),39850(a,2,1))].">
      <j1 rule="para" parents="28824 39850"/>
    </justification>
  </clause>

  <clause id="39853">
    <literal><![CDATA[
      T(x * (x * (((a(y,z,u) \ 1) * x) \ 1)),x) = (x * (((a(y,z,u) \ 1) * x) \ 1)) * x
    ]]></literal>
    <justification jstring="[para(28824(a,1),39852(a,1,1,2))].">
      <j1 rule="para" parents="28824 39852"/>
    </justification>
  </clause>

  <clause id="39854">
    <literal><![CDATA[
      (x * (((a(y,z,u) \ 1) * x) \ 1)) * x = T(((a(y,z,u) \ 1) / x) \ 1,x)
    ]]></literal>
    <justification jstring="[para(38626(a,1),39853(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38626 39853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39855">
    <literal><![CDATA[
      (x * (((a(y,z,u) \ 1) * x) \ 1)) * x = ((a(y,z,u) \ 1) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,25845,a(flip),b,39854,a),flip(a)].">
      <j1 rule="hyper" parents="373 25845 39854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39856">
    <literal><![CDATA[
      (x * x) * ((y \ R(y,z,u)) / (((y * R(y \ (x * x),z,u)) / (w \ 1)) / w)) = a(y * R(y,z,u),w,w \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,26877,a(flip),b,35007,a),flip(a)].">
      <j1 rule="hyper" parents="373 26877 35007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39858">
    <literal><![CDATA[
      (x * x) * ((y \ R(y,z,u)) / (((y * R(y \ (x * x),z,u)) / (w \ 1)) / w)) = a(y * L(y,z,u),w,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,38776,a(flip),b,39856,a),flip(a)].">
      <j1 rule="hyper" parents="373 38776 39856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39859">
    <literal><![CDATA[
      (x * x) * ((y \ R(y,z,u)) / (((x * x) * ((y \ R(y,z,u)) / (w \ 1))) / w)) = a(y * L(y,z,u),w,w)
    ]]></literal>
    <justification jstring="[para(35006(a,1),39858(a,1,2,2,1))].">
      <j1 rule="para" parents="35006 39858"/>
    </justification>
  </clause>

  <clause id="39860">
    <literal><![CDATA[
      (x * x) * ((y \ R(y,z,u)) / (((x * x) * ((y / w) \ R(y,z,u))) / w)) = a(y * L(y,z,u),w,w)
    ]]></literal>
    <justification jstring="[para(31560(a,1),39859(a,1,2,2,1,2))].">
      <j1 rule="para" parents="31560 39859"/>
    </justification>
  </clause>

  <clause id="39861">
    <literal><![CDATA[
      (x * x) * ((y \ R(y,z,u)) / ((x * x) * (((y / w) \ R(y,z,u)) / w))) = a(y * L(y,z,u),w,w)
    ]]></literal>
    <justification jstring="[para(807(a,1),39860(a,1,2,2))].">
      <j1 rule="para" parents="807 39860"/>
    </justification>
  </clause>

  <clause id="39862">
    <literal><![CDATA[
      (x * x) * ((y \ R(y,z,u)) / ((x * x) * L(y \ R(y,z,u),w,w))) = a(y * L(y,z,u),w,w)
    ]]></literal>
    <justification jstring="[para(36341(a,1),39861(a,1,2,2,2))].">
      <j1 rule="para" parents="36341 39861"/>
    </justification>
  </clause>

  <clause id="39863">
    <literal><![CDATA[
      (x * x) * ((x * x) \ (L(y \ R(y,z,u),w,w) \ (y \ R(y,z,u)))) = a(y * L(y,z,u),w,w)
    ]]></literal>
    <justification jstring="[para(24629(a,1),39862(a,1,2))].">
      <j1 rule="para" parents="24629 39862"/>
    </justification>
  </clause>

  <clause id="39864">
    <literal><![CDATA[
      (x * x) * ((x * x) \ a(y,y,z \ R(z,u,w))) = a(z * L(z,u,w),y,y)
    ]]></literal>
    <justification jstring="[para(1243(a,1),39863(a,1,2,2))].">
      <j1 rule="para" parents="1243 39863"/>
    </justification>
  </clause>

  <clause id="39865">
    <literal><![CDATA[
      (x * x) * ((x * x) \ a(y,y,z \ L(z,u,w))) = a(z * L(z,u,w),y,y)
    ]]></literal>
    <justification jstring="[para(31322(a,1),39864(a,1,2,2))].">
      <j1 rule="para" parents="31322 39864"/>
    </justification>
  </clause>

  <clause id="39866">
    <literal><![CDATA[
      a(x * L(x,y,z),u,u) = a(u,u,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(292,a,39865,a)].">
      <j1 rule="hyper" parents="292 39865"/>
    </justification>
  </clause>

  <clause id="39868">
    <literal><![CDATA[
      x * a(y * L(y,z,u),x,x) = L(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,39866,a,b,38763,a)].">
      <j1 rule="hyper" parents="145 39866 38763"/>
    </justification>
  </clause>

  <clause id="39869">
    <literal><![CDATA[
      a(x * L(x,y,z),u,u) * u = L(u,u,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(23777,a,39868,a)].">
      <j1 rule="hyper" parents="23777 39868"/>
    </justification>
  </clause>

  <clause id="39870">
    <literal><![CDATA[
      x * (y * a(z * L(z,u,w),x,x)) = L(x,x,z * L(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(39868(a,1),37519(a,1,1)),flip(a)].">
      <j1 rule="para" parents="39868 37519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39871">
    <literal><![CDATA[
      L(1 / x,x,y * L(y,z,u)) = 1 / L(x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(225,a,39869,a(flip),b,38779,a),flip(a)].">
      <j1 rule="hyper" parents="225 39869 38779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39872">
    <literal><![CDATA[
      a((1 / x) * (y \ L(y,z,u)),x,x) = x * L(1 / x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(39871(a,2),38859(a,2,2))].">
      <j1 rule="para" parents="39871 38859"/>
    </justification>
  </clause>

  <clause id="39873">
    <literal><![CDATA[
      a((1 / x) * (y * L(y,z,u)),x,x) = x * L(1 / x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11989,a(flip),b,39872,a)].">
      <j1 rule="hyper" parents="64 11989 39872"/>
    </justification>
  </clause>

  <clause id="39874">
    <literal><![CDATA[
      a((x \ 1) * (y * L(y,z,u)),x,x) = x * L(1 / x,x,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,32367,a(flip),b,39873,a)].">
      <j1 rule="hyper" parents="64 32367 39873"/>
    </justification>
  </clause>

  <clause id="39875">
    <literal><![CDATA[
      x * L(1 / x,x,y * L(y,z,u)) = a(y * (L(y,z,u) * x),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,37900,a(flip),b,39874,a),flip(a)].">
      <j1 rule="hyper" parents="64 37900 39874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39876">
    <literal><![CDATA[
      a(x * (L(x,y,z) * u),u,u) = a(u,u,u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,38767,a(flip),b,39875,a),flip(a)].">
      <j1 rule="hyper" parents="64 38767 39875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39877">
    <literal><![CDATA[
      a(x * (y * L(y,z,u)),x,x) = a(x,x,x * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,37898,a(flip),b,39876,a)].">
      <j1 rule="hyper" parents="64 37898 39876"/>
    </justification>
  </clause>

  <clause id="39878">
    <literal><![CDATA[
      a(x,x,x * (y \ L(y,z,u))) \ (x * (y \ L(y,z,u))) = (K(w,x) * (y \ L(y,z,u))) / (1 / T(x,w))
    ]]></literal>
    <justification jstring="[para(39877(a,1),38863(a,1,1))].">
      <j1 rule="para" parents="39877 38863"/>
    </justification>
  </clause>

  <clause id="39879">
    <literal><![CDATA[
      L(x * (y \ L(y,z,u)),x,x) = (K(w,x) * (y \ L(y,z,u))) / (1 / T(x,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,5567,a(flip),b,39878,a)].">
      <j1 rule="hyper" parents="64 5567 39878"/>
    </justification>
  </clause>

  <clause id="39880">
    <literal><![CDATA[
      L(x * (y \ L(y,z,u)),x,x) = K(w,x) * ((y \ L(y,z,u)) / (1 / T(x,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,23224,a(flip),b,39879,a),flip(a)].">
      <j1 rule="hyper" parents="373 23224 39879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39881">
    <literal><![CDATA[
      L(x * (y \ L(y,z,u)),x,x) = T(y \ L(y,z,u),K(w,x)) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25535,a(flip),b,39880,a),flip(a)].">
      <j1 rule="hyper" parents="373 25535 39880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39882">
    <literal><![CDATA[
      L(x * (y \ L(y,z,u)),x,x) = (y \ L(y,z,u)) / (1 / x)
    ]]></literal>
    <justification jstring="[para(2908(a,1),39881(a,2,1))].">
      <j1 rule="para" parents="2908 39881"/>
    </justification>
  </clause>

  <clause id="39883">
    <literal><![CDATA[
      T((x \ L(x,y,z)) / (1 / u),u \ (u \ 1)) = u * (u * ((u \ 1) * (x \ L(x,y,z))))
    ]]></literal>
    <justification jstring="[para(39882(a,1),36517(a,1,1))].">
      <j1 rule="para" parents="39882 36517"/>
    </justification>
  </clause>

  <clause id="39884">
    <literal><![CDATA[
      T((x * x) * ((y \ L(y,z,u)) / x),1) = x * (x * ((x \ 1) * (y \ L(y,z,u))))
    ]]></literal>
    <justification jstring="[hyper(64,a,18771,a(flip),b,39883,a)].">
      <j1 rule="hyper" parents="64 18771 39883"/>
    </justification>
  </clause>

  <clause id="39885">
    <literal><![CDATA[
      x * (x * ((x \ 1) * (y \ L(y,z,u)))) = T((1 / x) \ (y \ L(y,z,u)),1)
    ]]></literal>
    <justification jstring="[para(25892(a,1),39884(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25892 39884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39886">
    <literal><![CDATA[
      x * (x * ((x \ 1) * (y \ L(y,z,u)))) = (1 / x) \ (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,372,a(flip),b,39885,a),flip(a)].">
      <j1 rule="hyper" parents="373 372 39885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39887">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),x,x) = (1 / x) \ (y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1139(a,1),39886(a,1,2))].">
      <j1 rule="para" parents="1139 39886"/>
    </justification>
  </clause>

  <clause id="39888">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ (((1 / x) * (x * (y \ R(y,z,u)))) * x) = 1 / a(x,x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(30057(a,1),36225(a,2,2))].">
      <j1 rule="para" parents="30057 36225"/>
    </justification>
  </clause>

  <clause id="39889">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ (((1 / x) * (x * (y \ R(y,z,u)))) * x) = 1 / a(x,x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(31322(a,1),39888(a,2,2))].">
      <j1 rule="para" parents="31322 39888"/>
    </justification>
  </clause>

  <clause id="39890">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ (((1 / x) * (x * (y \ R(y,z,u)))) * x) = a(x,x,y \ L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,23133,a(flip),b,39889,a),flip(a)].">
      <j1 rule="hyper" parents="373 23133 39889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39891">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ (((1 / x) * (x * (y \ R(y,z,u)))) * x) = a(y * L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,38774,a(flip),b,39890,a),flip(a)].">
      <j1 rule="hyper" parents="373 38774 39890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39892">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ (L(y \ R(y,z,u),x,x) * x) = a(y * L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(559(a,1),39891(a,1,2,1))].">
      <j1 rule="para" parents="559 39891"/>
    </justification>
  </clause>

  <clause id="39893">
    <literal><![CDATA[
      (x * (y \ R(y,z,u))) \ ((y / x) \ R(y,z,u)) = a(y * L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(36340(a,1),39892(a,1,2))].">
      <j1 rule="para" parents="36340 39892"/>
    </justification>
  </clause>

  <clause id="39894">
    <literal><![CDATA[
      a(x \ y,x,y \ R(y,z,u)) = a(y * L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30349,a(flip),b,39893,a)].">
      <j1 rule="hyper" parents="64 30349 39893"/>
    </justification>
  </clause>

  <clause id="39895">
    <literal><![CDATA[
      a(x \ y,x,y \ L(y,z,u)) = a(y * L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,31676,a(flip),b,39894,a)].">
      <j1 rule="hyper" parents="64 31676 39894"/>
    </justification>
  </clause>

  <clause id="39896">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) * a(y * L(y,z,u),x,x) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,39895,a(flip),b,30349,a)].">
      <j1 rule="hyper" parents="145 39895 30349"/>
    </justification>
  </clause>

  <clause id="39897">
    <literal><![CDATA[
      x * ((y \ L(y,z,u)) * a(y * L(y,z,u),x,x)) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,33185,a(flip),b,39896,a)].">
      <j1 rule="hyper" parents="64 33185 39896"/>
    </justification>
  </clause>

  <clause id="39898">
    <literal><![CDATA[
      L(x,x,y * L(y,z,u)) * (y \ L(y,z,u)) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,39870,a(flip),b,39897,a)].">
      <j1 rule="hyper" parents="64 39870 39897"/>
    </justification>
  </clause>

  <clause id="39899">
    <literal><![CDATA[
      (x * x) * (y \ L(y,z,u)) = x * ((y / x) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(39898(a,1),38764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="39898 38764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39900">
    <literal><![CDATA[
      (1 / x) \ (y \ L(y,z,u)) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,538,a,b,39899,a(flip))].">
      <j1 rule="hyper" parents="35 538 39899"/>
    </justification>
  </clause>

  <clause id="39901">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),x,x) = (y / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,39887,a,b,39900,a)].">
      <j1 rule="hyper" parents="64 39887 39900"/>
    </justification>
  </clause>

  <clause id="39902">
    <literal><![CDATA[
      x \ ((y / x) \ L(y,z,u)) = L(y \ L(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,39900,a(flip),b,39887,a)].">
      <j1 rule="hyper" parents="139 39900 39887"/>
    </justification>
  </clause>

  <clause id="39903">
    <literal><![CDATA[
      a(x,x,L(y,z,z)) \ z = (y / z) \ L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,39718,a(flip),b,39901,a)].">
      <j1 rule="hyper" parents="64 39718 39901"/>
    </justification>
  </clause>

  <clause id="39904">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ x)) * (a(y,z,u) * T(a(y,z,u) \ w,v5)) = 1 * T(1 \ ((x \ (a(y,z,u) \ x)) * w),v5)
    ]]></literal>
    <justification jstring="[para(23134(a,1),36443(a,1,2,2,1,1))].">
      <j1 rule="para" parents="23134 36443"/>
    </justification>
  </clause>

  <clause id="39906">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ x)) * T((a(y,z,u) \ w) * a(y,z,u),v5) = 1 * T(1 \ ((x \ (a(y,z,u) \ x)) * w),v5)
    ]]></literal>
    <justification jstring="[para(28753(a,2),39904(a,1,2))].">
      <j1 rule="para" parents="28753 39904"/>
    </justification>
  </clause>

  <clause id="39907">
    <literal><![CDATA[
      1 * T(1 \ ((x \ (a(y,z,u) \ x)) * w),v5) = (x \ (a(y,z,u) \ x)) * T(w,v5)
    ]]></literal>
    <justification jstring="[para(23135(a,1),39906(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="23135 39906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39908">
    <literal><![CDATA[
      1 * T((x \ (a(y,z,u) \ x)) * w,v5) = (x \ (a(y,z,u) \ x)) * T(w,v5)
    ]]></literal>
    <justification jstring="[para(66(a,1),39907(a,1,2,1))].">
      <j1 rule="para" parents="66 39907"/>
    </justification>
  </clause>

  <clause id="39909">
    <literal><![CDATA[
      T((x \ (a(y,z,u) \ x)) * w,v5) = (x \ (a(y,z,u) \ x)) * T(w,v5)
    ]]></literal>
    <justification jstring="[hyper(147,a,39908,a)].">
      <j1 rule="hyper" parents="147 39908"/>
    </justification>
  </clause>

  <clause id="39910">
    <literal><![CDATA[
      (x * y) \ (y * T((z \ (a(u,w,v5) \ z)) * x,y)) = L(z \ (a(u,w,v5) \ z),x,y)
    ]]></literal>
    <justification jstring="[para(39909(a,2),25523(a,1,2,2))].">
      <j1 rule="para" parents="39909 25523"/>
    </justification>
  </clause>

  <clause id="39911">
    <literal><![CDATA[
      (x * y) \ (((z \ (a(u,w,v5) \ z)) * x) * y) = L(z \ (a(u,w,v5) \ z),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,39910,a)].">
      <j1 rule="hyper" parents="64 249 39910"/>
    </justification>
  </clause>

  <clause id="39912">
    <literal><![CDATA[
      R(T(x \ (a(y,z,u) \ x),w * v5),w,v5) = L(x \ (a(y,z,u) \ x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,796,a(flip),b,39911,a)].">
      <j1 rule="hyper" parents="64 796 39911"/>
    </justification>
  </clause>

  <clause id="39913">
    <literal><![CDATA[
      R(x \ (a(y,z,u) \ x),w,v5) = L(x \ (a(y,z,u) \ x),w,v5)
    ]]></literal>
    <justification jstring="[para(25308(a,1),39912(a,1,1))].">
      <j1 rule="para" parents="25308 39912"/>
    </justification>
  </clause>

  <clause id="39915">
    <literal><![CDATA[
      ((((x \ y) \ 1) * y) \ x) * (((x \ y) \ 1) * ((x \ y) \ z)) = ((x / y) * (x \ y)) * (((x \ y) * (x \ y)) \ z)
    ]]></literal>
    <justification jstring="[para(9415(a,1),37948(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9415 37948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39916">
    <literal><![CDATA[
      ((((x \ y) \ 1) * y) \ x) * (((x \ y) \ 1) * ((x \ y) \ z)) = R((x / y) / (x \ y),x \ y,x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,951,a(flip),b,39915,a),flip(a)].">
      <j1 rule="hyper" parents="373 951 39915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39917">
    <literal><![CDATA[
      a(x \ (y \ R(y,z,u)),x,w / (w / y)) = (x * (w / (w / y))) \ (((1 / x) \ y) * K(y \ w,y))
    ]]></literal>
    <justification jstring="[para(31561(a,1),39831(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="31561 39831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39918">
    <literal><![CDATA[
      a(x \ (y \ R(y,z,u)),x,w / (w / y)) = (x * (w / (w / y))) \ ((K(y,y \ w) / x) \ y)
    ]]></literal>
    <justification jstring="[para(15033(a,1),39917(a,2,2))].">
      <j1 rule="para" parents="15033 39917"/>
    </justification>
  </clause>

  <clause id="39920">
    <literal><![CDATA[
      a(x \ (y \ R(y,z,u)),x,w / (w / y)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,37484,a(flip),b,39918,a),flip(a)].">
      <j1 rule="hyper" parents="373 37484 39918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39922">
    <literal><![CDATA[
      a(x \ (y \ R(y,z,u)),x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27306,a(flip),b,39920,a)].">
      <j1 rule="hyper" parents="64 27306 39920"/>
    </justification>
  </clause>

  <clause id="39923">
    <literal><![CDATA[
      a(x \ (y \ L(y,z,u)),x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,37337,a(flip),b,39922,a)].">
      <j1 rule="hyper" parents="64 37337 39922"/>
    </justification>
  </clause>

  <clause id="39924">
    <literal><![CDATA[
      a(x \ (y * L(y,z,u)),x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26911,a(flip),b,39923,a)].">
      <j1 rule="hyper" parents="64 26911 39923"/>
    </justification>
  </clause>

  <clause id="39925">
    <literal><![CDATA[
      L(x,y,(z \ L(u \ w,a(u,u,w) \ 1,a(u,u,w) \ 1)) * v5) = L(x,y,(z \ ((u \ 1) * L(w,u,u))) * v5)
    ]]></literal>
    <justification jstring="[para(5669(a,1),39832(a,2,3,1,2,2))].">
      <j1 rule="para" parents="5669 39832"/>
    </justification>
  </clause>

  <clause id="39926">
    <literal><![CDATA[
      L(x,y,(z \ L(u \ w,a(u,u,w) \ 1,a(u,u,w) \ 1)) * v5) = L(x,y,(z \ (u * L(w,u,u))) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31623,a(flip),b,39925,a),flip(a)].">
      <j1 rule="hyper" parents="373 31623 39925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39927">
    <literal><![CDATA[
      L(x,y,(z \ L(u \ w,a(u,u,w),a(u,u,w))) * v5) = L(x,y,(z \ (u * L(w,u,u))) * v5)
    ]]></literal>
    <justification jstring="[para(1151(a,1),39926(a,1,3,1,2))].">
      <j1 rule="para" parents="1151 39926"/>
    </justification>
  </clause>

  <clause id="39928">
    <literal><![CDATA[
      L(x,y,(z \ (u * L(w,u,u))) * v5) = L(x,y,(z \ (u \ w)) * v5)
    ]]></literal>
    <justification jstring="[para(30298(a,1),39927(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="30298 39927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39931">
    <literal><![CDATA[
      L(x,(y * (z * u)) * (T(w,y * (((v5 * v5) \ z) * u)) * K(v6,v7)),v8) = L(x,w * (y * (((v5 * v5) \ z) * (u * K(v6,v7)))),v8)
    ]]></literal>
    <justification jstring="[para(23053(a,1),39833(a,2,2,2,2))].">
      <j1 rule="para" parents="23053 39833"/>
    </justification>
  </clause>

  <clause id="39932">
    <literal><![CDATA[
      L(x,(y * (z * u)) * (T(w,y * (((v5 * v5) \ z) * u)) * K(v6,v7)),v8) = L(x,w * (y * (u * ((v5 * v5) \ z))),v8)
    ]]></literal>
    <justification jstring="[hyper(373,a,36096,a(flip),b,39931,a),flip(a)].">
      <j1 rule="hyper" parents="373 36096 39931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39934">
    <literal><![CDATA[
      L(x,y * (z * (u * ((w * w) \ v5))),v6) = L(x,(z * (v5 * u)) * y,v6)
    ]]></literal>
    <justification jstring="[para(5748(a,1),39932(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5748 39932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39935">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) * (v5 * v6)) / T(v5 * L(a(x,y,z),u,w),v6) = R(K(v5,L(a(x,y,z),u,w)) * v6,v5,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(36373(a,2),26613(a,1,2))].">
      <j1 rule="para" parents="36373 26613"/>
    </justification>
  </clause>

  <clause id="39936">
    <literal><![CDATA[
      R(T(x / y,T(z * K(y,z),x * y)),y,y \ ((y \ z) * T(y,z))) = ((y \ z) * y) \ (x * (y \ T((y \ z) * T(y,z),y)))
    ]]></literal>
    <justification jstring="[para(30737(a,1),27276(a,1,1))].">
      <j1 rule="para" parents="30737 27276"/>
    </justification>
  </clause>

  <clause id="39937">
    <literal><![CDATA[
      a(x,y,(z \ u) * (((z \ a(w,v5,z)) * ((z * a(w,v5,z)) \ u)) \ 1)) = a(x,y,L(z \ 1,z \ u,z * (z \ u)) \ 1)
    ]]></literal>
    <justification jstring="[para(23997(a,1),27740(a,2,3,1))].">
      <j1 rule="para" parents="23997 27740"/>
    </justification>
  </clause>

  <clause id="39938">
    <literal><![CDATA[
      a(x,y,(z \ u) * (((z \ a(w,v5,z)) * ((z * a(w,v5,z)) \ u)) \ 1)) = a(x,y,L(z \ 1,z \ u,u) \ 1)
    ]]></literal>
    <justification jstring="[para(10(a,1),39937(a,2,3,1,3))].">
      <j1 rule="para" parents="10 39937"/>
    </justification>
  </clause>

  <clause id="39939">
    <literal><![CDATA[
      a(x,y,(z \ u) * (((z \ a(w,v5,z)) * ((z * a(w,v5,z)) \ u)) \ 1)) = a(x,y,L(z \ 1,z * u,u) \ 1)
    ]]></literal>
    <justification jstring="[para(37218(a,1),39938(a,2,3,1))].">
      <j1 rule="para" parents="37218 39938"/>
    </justification>
  </clause>

  <clause id="39940">
    <literal><![CDATA[
      a(x,y,(z \ u) * (((z \ a(w,v5,z)) * ((z * a(w,v5,z)) \ u)) \ 1)) = a(x,y,L(z,z * u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,39639,a(flip),b,39939,a),flip(a)].">
      <j1 rule="hyper" parents="373 39639 39939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39941">
    <literal><![CDATA[
      a(x,y,(z \ u) * (((z \ 1) * (z \ u)) \ 1)) = a(x,y,L(z,z * u,u))
    ]]></literal>
    <justification jstring="[para(9436(a,1),39940(a,1,3,2,1))].">
      <j1 rule="para" parents="9436 39940"/>
    </justification>
  </clause>

  <clause id="39942">
    <literal><![CDATA[
      a(x,y,(z \ u) * (u \ (z * ((z \ 1) \ 1)))) = a(x,y,L(z,z * u,u))
    ]]></literal>
    <justification jstring="[para(1660(a,1),39941(a,1,3,2))].">
      <j1 rule="para" parents="1660 39941"/>
    </justification>
  </clause>

  <clause id="39943">
    <literal><![CDATA[
      a(x,y,(z \ u) * (u \ ((1 / z) \ z))) = a(x,y,L(z,z * u,u))
    ]]></literal>
    <justification jstring="[para(1134(a,1),39942(a,1,3,2,2))].">
      <j1 rule="para" parents="1134 39942"/>
    </justification>
  </clause>

  <clause id="39944">
    <literal><![CDATA[
      a(x,y,(z \ u) * (u \ ((1 \ z) * z))) = a(x,y,L(z,z * u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,33684,a(flip),b,39943,a)].">
      <j1 rule="hyper" parents="64 33684 39943"/>
    </justification>
  </clause>

  <clause id="39945">
    <literal><![CDATA[
      a(x,y,(z \ u) * (u \ (z * z))) = a(x,y,L(z,z * u,u))
    ]]></literal>
    <justification jstring="[para(66(a,1),39944(a,1,3,2,2,1))].">
      <j1 rule="para" parents="66 39944"/>
    </justification>
  </clause>

  <clause id="39946">
    <literal><![CDATA[
      a(x,y,L(L(z,z,u),u,u)) = a(x,y,L(z,z * u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,33926,a,b,39945,a)].">
      <j1 rule="hyper" parents="64 33926 39945"/>
    </justification>
  </clause>

  <clause id="39947">
    <literal><![CDATA[
      a(x,y,L(L(z,u,u),z,u)) = a(x,y,L(z,z * u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27702,a,b,39946,a)].">
      <j1 rule="hyper" parents="64 27702 39946"/>
    </justification>
  </clause>

  <clause id="39948">
    <literal><![CDATA[
      (x * ((y \ z) \ (y \ u))) * a(x \ ((y \ 1) \ z),x,(y \ z) \ (y \ u)) = (((y \ 1) \ z) / x) \ ((y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1612(a,1),30447(a,1,2,3))].">
      <j1 rule="para" parents="1612 30447"/>
    </justification>
  </clause>

  <clause id="39949">
    <literal><![CDATA[
      (x * ((y \ z) \ (y \ u))) * a(x \ (y \ z),x,(y \ z) \ (y \ u)) = (((y \ 1) \ z) / x) \ ((y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(26925(a,1),39948(a,1,2))].">
      <j1 rule="para" parents="26925 39948"/>
    </justification>
  </clause>

  <clause id="39950">
    <literal><![CDATA[
      (((x \ 1) \ y) / z) \ ((x \ 1) \ u) = ((x \ y) / z) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30347,a(flip),b,39949,a),flip(a)].">
      <j1 rule="hyper" parents="64 30347 39949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39951">
    <literal><![CDATA[
      (((1 / x) \ y) / z) \ x = ((x \ y) / z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,16500,a(flip),b,39950,a)].">
      <j1 rule="hyper" parents="64 16500 39950"/>
    </justification>
  </clause>

  <clause id="39952">
    <literal><![CDATA[
      x \ ((x / (((1 / y) * z) \ 1)) * (((1 / y) * z) \ a(y,y,z))) = L(a(y,y,z),((1 / y) * z) \ 1,((1 / y) * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2234,a(flip),b,30927,a),flip(a)].">
      <j1 rule="hyper" parents="373 2234 30927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39953">
    <literal><![CDATA[
      x \ ((x / (((1 / y) * z) \ 1)) * (((1 / y) * z) \ a(y,y,z))) = L(a(y,y,z),((1 / y) * z) \ 1,(y * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25692,a(flip),b,39952,a),flip(a)].">
      <j1 rule="hyper" parents="373 25692 39952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39954">
    <literal><![CDATA[
      x \ ((x / (((1 / y) * z) \ 1)) * (((1 / y) * z) \ a(y,y,z))) = L(a(y,y,z),(1 / y) * z,(y * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,11794,a(flip),b,39953,a),flip(a)].">
      <j1 rule="hyper" parents="373 11794 39953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39955">
    <literal><![CDATA[
      x \ ((x / (((1 / y) * z) \ 1)) * (((1 / y) * z) \ a(y,y,z))) = L(a(y,y,z),y * z,(y * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,11777,a(flip),b,39954,a),flip(a)].">
      <j1 rule="hyper" parents="373 11777 39954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39956">
    <literal><![CDATA[
      x \ ((x / (((1 / y) * z) \ 1)) * (((1 / y) * z) \ a(y,y,z))) = a(y,L(y,y * z,(y * z) \ x),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,34877,a,b,39955,a),flip(a)].">
      <j1 rule="hyper" parents="373 34877 39955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39957">
    <literal><![CDATA[
      a(x,y,z * ((a(u,u,w) * a(w,u,u)) * L(v5,z,a(u,u,w) * a(w,u,u)))) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,38046,a(flip),b,31058,a),flip(a)].">
      <j1 rule="hyper" parents="373 38046 31058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39959">
    <literal><![CDATA[
      a(x,y,z * ((a(u,u,w) * a(w,u,u)) * v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(30834(a,1),39957(a,1,3,2,2))].">
      <j1 rule="para" parents="30834 39957"/>
    </justification>
  </clause>

  <clause id="39960">
    <literal><![CDATA[
      a(x,y,z * (a(u,u,w) * (a(w,u,u) * v5))) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(37669(a,1),39959(a,1,3,2))].">
      <j1 rule="para" parents="37669 39959"/>
    </justification>
  </clause>

  <clause id="39961">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * w) = a(x,y,w * a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,38921,a(flip),b,39960,a)].">
      <j1 rule="hyper" parents="64 38921 39960"/>
    </justification>
  </clause>

  <clause id="39962">
    <literal><![CDATA[
      a(x,y,z * a(u,w,w)) = a(x,y,z * a(w,w,u))
    ]]></literal>
    <justification jstring="[hyper(27453,a,39961,a),flip(a)].">
      <j1 rule="hyper" parents="27453 39961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39963">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * w) = a(x,y,w * a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(27453,a,39962,a)].">
      <j1 rule="hyper" parents="27453 39962"/>
    </justification>
  </clause>

  <clause id="39964">
    <literal><![CDATA[
      a(x,y,z * a(u * w,u,u)) = a(x,y,a(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,39170,a,b,39963,a)].">
      <j1 rule="hyper" parents="373 39170 39963"/>
    </justification>
  </clause>

  <clause id="39965">
    <literal><![CDATA[
      a(x,y,a(z,u,u \ 1) * w) = a(x,y,a(z,u,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33383,a,b,39964,a)].">
      <j1 rule="hyper" parents="64 33383 39964"/>
    </justification>
  </clause>

  <clause id="39966">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,z \ 1,u) \ w,z,z)) = a(x,y,a(u,z,z) * (w * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,38109,a,b,39965,a)].">
      <j1 rule="hyper" parents="64 38109 39965"/>
    </justification>
  </clause>

  <clause id="39967">
    <literal><![CDATA[
      a(x,y,a(z * u,u,u) * w) = a(x,y,w * a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,30720,a(flip),b,39965,a),flip(a)].">
      <j1 rule="hyper" parents="64 30720 39965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39968">
    <literal><![CDATA[
      a(x,y,z * a(u,w,w \ 1)) = a(x,y,z * a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,37312,a(flip),b,39967,a)].">
      <j1 rule="hyper" parents="64 37312 39967"/>
    </justification>
  </clause>

  <clause id="39969">
    <literal><![CDATA[
      a(x,y,(T(z,u) * w) * a(L(v5,w,z),v6,v6)) = a(x,y,z * (w * a(v5,v6,v6 \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27616,a(flip),b,39968,a),flip(a)].">
      <j1 rule="hyper" parents="64 27616 39968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39970">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,z \ 1,u) \ w,z,z)) = a(x,y,z * (a(u,z,z) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,33256,a(flip),b,39966,a),flip(a)].">
      <j1 rule="hyper" parents="373 33256 39966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39971">
    <literal><![CDATA[
      a(x,y,L(L(z \ 1,z,u) \ w,z,z)) = a(x,y,z * (a(u,z,z) * w))
    ]]></literal>
    <justification jstring="[para(11794(a,1),39970(a,1,3,1,1))].">
      <j1 rule="para" parents="11794 39970"/>
    </justification>
  </clause>

  <clause id="39972">
    <literal><![CDATA[
      a(x,y,z * (a(u,z,z \ 1) * w)) = a(x,y,z * (a(u,z,z) * w))
    ]]></literal>
    <justification jstring="[para(37804(a,1),39971(a,1,3))].">
      <j1 rule="para" parents="37804 39971"/>
    </justification>
  </clause>

  <clause id="39973">
    <literal><![CDATA[
      a(x,y,(L(z \ 1,z,u) \ 1) * w) = a(x,y,z * (a(u,z,z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,37809,a,b,39972,a)].">
      <j1 rule="hyper" parents="64 37809 39972"/>
    </justification>
  </clause>

  <clause id="39974">
    <literal><![CDATA[
      a(x,y,z * (a(u,z,z) * w)) = a(x,y,w * L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39635,a(flip),b,39973,a),flip(a)].">
      <j1 rule="hyper" parents="64 39635 39973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39975">
    <literal><![CDATA[
      a(x,y,z * (u * a(w,u,u))) = a(x,y,z * L(u,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,37716,a(flip),b,39974,a)].">
      <j1 rule="hyper" parents="64 37716 39974"/>
    </justification>
  </clause>

  <clause id="39976">
    <literal><![CDATA[
      a(x,y,T(z,u) * (w * a(v5,v6,v6))) = a(x,y,z * (w * a(v5,v6,v6 \ 1)))
    ]]></literal>
    <justification jstring="[para(32617(a,1),39969(a,1,3))].">
      <j1 rule="para" parents="32617 39969"/>
    </justification>
  </clause>

  <clause id="39977">
    <literal><![CDATA[
      a(x,y,z * (u * a(w,v5,v5 \ 1))) = a(x,y,z * (u * a(w,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27312,a(flip),b,39976,a),flip(a)].">
      <j1 rule="hyper" parents="64 27312 39976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39978">
    <literal><![CDATA[
      a(x,y,(a(z,u,u \ 1) * w) * v5) = a(x,y,v5 * (w * a(z,u,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27462,a,b,39977,a)].">
      <j1 rule="hyper" parents="64 27462 39977"/>
    </justification>
  </clause>

  <clause id="39979">
    <literal><![CDATA[
      a(x,y,((a(z,u,u \ 1) \ 1) * w) * v5) = a(x,y,v5 * (w * a(z,u,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,38934,a,b,39978,a)].">
      <j1 rule="hyper" parents="64 38934 39978"/>
    </justification>
  </clause>

  <clause id="39980">
    <literal><![CDATA[
      L(x,y,y) * a(L(y,z,u),y,y * (L(y,z,u) \ x)) = (L(y,z,u) * (y \ 1)) * ((y \ 1) \ (L(y,z,u) \ L(x,y,y)))
    ]]></literal>
    <justification jstring="[para(11980(a,1),31479(a,1,2))].">
      <j1 rule="para" parents="11980 31479"/>
    </justification>
  </clause>

  <clause id="39981">
    <literal><![CDATA[
      L(x,y,y) * a(y,L(y,z,u),y * (L(y,z,u) \ x)) = (L(y,z,u) * (y \ 1)) * ((y \ 1) \ (L(y,z,u) \ L(x,y,y)))
    ]]></literal>
    <justification jstring="[para(2784(a,1),39980(a,1,2))].">
      <j1 rule="para" parents="2784 39980"/>
    </justification>
  </clause>

  <clause id="39982">
    <literal><![CDATA[
      L(x,y,y) * a(y,L(y,z,u),x) = (L(y,z,u) * (y \ 1)) * ((y \ 1) \ (L(y,z,u) \ L(x,y,y)))
    ]]></literal>
    <justification jstring="[para(35492(a,1),39981(a,1,2))].">
      <j1 rule="para" parents="35492 39981"/>
    </justification>
  </clause>

  <clause id="39983">
    <literal><![CDATA[
      L(x * a(y,L(y,z,u),x),y,y) = (L(y,z,u) * (y \ 1)) * ((y \ 1) \ (L(y,z,u) \ L(x,y,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,30820,a,b,39982,a)].">
      <j1 rule="hyper" parents="64 30820 39982"/>
    </justification>
  </clause>

  <clause id="39985">
    <literal><![CDATA[
      L(x * a(y,L(y,z,u),x),y,y) = (y \ L(y,z,u)) * ((y \ 1) \ (L(y,z,u) \ L(x,y,y)))
    ]]></literal>
    <justification jstring="[para(1807(a,1),39983(a,2,1))].">
      <j1 rule="para" parents="1807 39983"/>
    </justification>
  </clause>

  <clause id="39986">
    <literal><![CDATA[
      L(x * a(y,L(y,z,u),x),y,y) = (y \ L(y,z,u)) * (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(31477(a,1),39985(a,2,2))].">
      <j1 rule="para" parents="31477 39985"/>
    </justification>
  </clause>

  <clause id="39987">
    <literal><![CDATA[
      L(x * a(y,L(y,z,u),x),y,y) = y * ((y \ L(y,z,u)) * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,33159,a(flip),b,39986,a),flip(a)].">
      <j1 rule="hyper" parents="373 33159 39986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39988">
    <literal><![CDATA[
      R(x,y,((z * (a(u,w,w) * R(u,w,w))) \ v5) * (a(u,w,w) * a(u,w,w))) = R(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(29309(a,1),31707(a,2,3,1,2))].">
      <j1 rule="para" parents="29309 31707"/>
    </justification>
  </clause>

  <clause id="39989">
    <literal><![CDATA[
      R(x,y,((z * R(R(u,w,w),w,w)) \ v5) * (a(u,w,w) * a(u,w,w))) = R(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[para(31175(a,1),39988(a,1,3,1,1,2))].">
      <j1 rule="para" parents="31175 39988"/>
    </justification>
  </clause>

  <clause id="39990">
    <literal><![CDATA[
      R(x,y,(z * R(R(u,w,w),w,w)) \ v5) = R(x,y,(z * u) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,38870,a(flip),b,39989,a)].">
      <j1 rule="hyper" parents="64 38870 39989"/>
    </justification>
  </clause>

  <clause id="39992">
    <literal><![CDATA[
      L(x \ R(x,y,(z * z) \ u),x,u * y) = a(x,y,(R(z,w,w) * R(z,w,w)) \ u)
    ]]></literal>
    <justification jstring="[para(39990(a,1),38250(a,1,1,2))].">
      <j1 rule="para" parents="39990 38250"/>
    </justification>
  </clause>

  <clause id="39993">
    <literal><![CDATA[
      a(x,y,(R(z,u,u) * R(z,u,u)) \ w) = a(x,y,(z * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,24739,a(flip),b,39992,a),flip(a)].">
      <j1 rule="hyper" parents="64 24739 39992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="39995">
    <literal><![CDATA[
      a(x,y,((z * z) \ R(u,z,z)) \ w) = a(x,y,(u * u) \ ((((u * z) * z) \ 1) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27981,a(flip),b,39993,a)].">
      <j1 rule="hyper" parents="64 27981 39993"/>
    </justification>
  </clause>

  <clause id="39997">
    <literal><![CDATA[
      a(x,y,(((z * u) * u) \ (z * z)) \ w) = a(x,y,((u * u) \ R(z,u,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27770,a(flip),b,39995,a)].">
      <j1 rule="hyper" parents="373 27770 39995"/>
    </justification>
  </clause>

  <clause id="39998">
    <literal><![CDATA[
      a(x,y,T((z / u) / u,z) \ w) = a(x,y,((u * u) \ R(z,u,u)) \ w)
    ]]></literal>
    <justification jstring="[para(36837(a,1),39997(a,1,3,1))].">
      <j1 rule="para" parents="36837 39997"/>
    </justification>
  </clause>

  <clause id="39999">
    <literal><![CDATA[
      a(x,y,((z * z) \ R(u,z,z)) \ w) = a(x,y,((u / z) / z) \ w)
    ]]></literal>
    <justification jstring="[hyper(27588,a,39998,a),flip(a)].">
      <j1 rule="hyper" parents="27588 39998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40001">
    <literal><![CDATA[
      a(x,y,((z * z) \ R(u,z,z)) \ w) = a(x,y,(z \ (z \ u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27673,a(flip),b,39999,a),flip(a)].">
      <j1 rule="hyper" parents="373 27673 39999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40002">
    <literal><![CDATA[
      a(x,y,(z * z) * (R(u,z,z) \ w)) = a(x,y,(z \ (z \ u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27541,a(flip),b,40001,a)].">
      <j1 rule="hyper" parents="64 27541 40001"/>
    </justification>
  </clause>

  <clause id="40003">
    <literal><![CDATA[
      a(x,y,(R(z,u,u) \ w) * (u * u)) = a(x,y,(u \ (u \ z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(27453,a,40002,a)].">
      <j1 rule="hyper" parents="27453 40002"/>
    </justification>
  </clause>

  <clause id="40004">
    <literal><![CDATA[
      a(x,y,((z \ 1) * ((z \ 1) * u)) \ w) = a(x,y,(z \ (z \ u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,35609,a,b,40003,a)].">
      <j1 rule="hyper" parents="64 35609 40003"/>
    </justification>
  </clause>

  <clause id="40005">
    <literal><![CDATA[
      a(x,L(y,T(z / (y * z),u),T(z / (y * z),u)) * w,v5) = a(x,((y * T((y \ z) / z,u)) * (z / (y * z))) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31978,a(flip),b,32191,a),flip(a)].">
      <j1 rule="hyper" parents="64 31978 32191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40007">
    <literal><![CDATA[
      a(x,L(y,T(z / (y * z),u),T(z / (y * z),u)) * w,v5) = a(x,((y * T((y \ z) / z,u)) * ((y * z) \ z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32167,a(flip),b,40005,a),flip(a)].">
      <j1 rule="hyper" parents="373 32167 40005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40008">
    <literal><![CDATA[
      a(x,L(y,T(z / (y * z),u),T(z / (y * z),u)) * w,v5) = a(x,((y * T((y \ z) / z,u)) * (z \ (y \ z))) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32880,a(flip),b,40007,a),flip(a)].">
      <j1 rule="hyper" parents="373 32880 40007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40009">
    <literal><![CDATA[
      a(x,L(y,T(z / (y * z),u),T(z / (y * z),u)) * w,v5) = a(x,((y * (z \ (y \ z))) * T((y \ z) / z,u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(33945(a,1),40008(a,2,2,1))].">
      <j1 rule="para" parents="33945 40008"/>
    </justification>
  </clause>

  <clause id="40010">
    <literal><![CDATA[
      a(x,L(y,T(z / (y * z),u),T(z / (y * z),u)) * w,v5) = a(x,((y * (z \ (y \ z))) * ((y \ z) / z)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31978,a(flip),b,40009,a),flip(a)].">
      <j1 rule="hyper" parents="373 31978 40009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40012">
    <literal><![CDATA[
      a(x,L(y,T(z / (y * z),u),T(z / (y * z),u)) * w,v5) = a(x,(a(y,y,z) * (z \ (y \ z))) * w,v5)
    ]]></literal>
    <justification jstring="[para(30106(a,1),40010(a,2,2,1))].">
      <j1 rule="para" parents="30106 40010"/>
    </justification>
  </clause>

  <clause id="40013">
    <literal><![CDATA[
      a(x,L(y,T(z / (y * z),u),(y * z) \ z) * w,v5) = a(x,(a(y,y,z) * (z \ (y \ z))) * w,v5)
    ]]></literal>
    <justification jstring="[para(23972(a,1),40012(a,1,2,1))].">
      <j1 rule="para" parents="23972 40012"/>
    </justification>
  </clause>

  <clause id="40015">
    <literal><![CDATA[
      a(x,L(y,T(z / (y * z),u),y) * w,v5) = a(x,(a(y,y,z) * (z \ (y \ z))) * w,v5)
    ]]></literal>
    <justification jstring="[para(35018(a,1),40013(a,1,2,1))].">
      <j1 rule="para" parents="35018 40013"/>
    </justification>
  </clause>

  <clause id="40016">
    <literal><![CDATA[
      a(x,(a(y,y,z) * (z \ (y \ z))) * u,w) = a(x,y * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,13830,a(flip),b,40015,a),flip(a)].">
      <j1 rule="hyper" parents="64 13830 40015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40019">
    <literal><![CDATA[
      a(x,R(y \ (z \ y),z,y) * u,w) = a(x,z * u,w)
    ]]></literal>
    <justification jstring="[para(39289(a,1),40016(a,1,2,1))].">
      <j1 rule="para" parents="39289 40016"/>
    </justification>
  </clause>

  <clause id="40020">
    <literal><![CDATA[
      a(x,L(y \ (z \ y),z,y) * u,w) = a(x,z * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33774,a(flip),b,40019,a)].">
      <j1 rule="hyper" parents="64 33774 40019"/>
    </justification>
  </clause>

  <clause id="40021">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) \ 1) * ((T(z,u) \ (1 / T(z,u))) \ w)) = a(x,y,(((z \ T(u,z)) / u) \ ((T(z,u) \ 1) \ 1)) * w)
    ]]></literal>
    <justification jstring="[para(1090(a,1),32864(a,1,3,2,1))].">
      <j1 rule="para" parents="1090 32864"/>
    </justification>
  </clause>

  <clause id="40022">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) \ 1) * ((z \ (1 / T(T(z,u),u))) \ w)) = a(x,y,(((z \ T(u,z)) / u) \ ((T(z,u) \ 1) \ 1)) * w)
    ]]></literal>
    <justification jstring="[para(6432(a,1),40021(a,1,3,2,1))].">
      <j1 rule="para" parents="6432 40021"/>
    </justification>
  </clause>

  <clause id="40023">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) \ 1) * (z * ((T(T(z,u),u) \ 1) \ w))) = a(x,y,(((z \ T(u,z)) / u) \ ((T(z,u) \ 1) \ 1)) * w)
    ]]></literal>
    <justification jstring="[para(34841(a,1),40022(a,1,3,2))].">
      <j1 rule="para" parents="34841 40022"/>
    </justification>
  </clause>

  <clause id="40024">
    <literal><![CDATA[
      a(x,y,a(z,z,u) \ (z * ((T(T(z,u),u) \ 1) \ w))) = a(x,y,(((z \ T(u,z)) / u) \ ((T(z,u) \ 1) \ 1)) * w)
    ]]></literal>
    <justification jstring="[para(37681(a,1),40023(a,1,3))].">
      <j1 rule="para" parents="37681 40023"/>
    </justification>
  </clause>

  <clause id="40025">
    <literal><![CDATA[
      a(x,y,(((z \ T(u,z)) / u) \ ((T(z,u) \ 1) \ 1)) * w) = a(x,y,z * (a(z,z,u) \ ((T(T(z,u),u) \ 1) \ w)))
    ]]></literal>
    <justification jstring="[para(29923(a,1),40024(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29923 40024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40026">
    <literal><![CDATA[
      a(x,y,(((z \ T(u,z)) / u) \ ((T(z,u) \ 1) \ 1)) * w) = a(x,y,((T(T(z,u),u) \ 1) \ w) * L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,39637,a(flip),b,40025,a),flip(a)].">
      <j1 rule="hyper" parents="373 39637 40025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40027">
    <literal><![CDATA[
      a(x,y,(((z \ T(u,z)) / u) \ ((T(z,u) \ 1) \ 1)) * w) = a(x,y,((T(z,u) \ 1) \ w) * L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27545,a(flip),b,40026,a),flip(a)].">
      <j1 rule="hyper" parents="373 27545 40026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40029">
    <literal><![CDATA[
      a(x,y,(((z \ T(u,z)) / u) \ ((T(z,u) \ 1) \ 1)) * w) = a(x,y,((z \ 1) \ w) * L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27545,a(flip),b,40027,a),flip(a)].">
      <j1 rule="hyper" parents="373 27545 40027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40031">
    <literal><![CDATA[
      a(x,y,(((z \ T(u,z)) / u) \ ((T(z,u) \ 1) \ 1)) * w) = a(x,y,(z * L(z,z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,38035,a(flip),b,40029,a),flip(a)].">
      <j1 rule="hyper" parents="373 38035 40029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40032">
    <literal><![CDATA[
      a(x,y,(((z \ T(u,z)) / u) \ T((z \ 1) \ 1,u)) * w) = a(x,y,(z * L(z,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(3568(a,2),40031(a,1,3,1,2))].">
      <j1 rule="para" parents="3568 40031"/>
    </justification>
  </clause>

  <clause id="40033">
    <literal><![CDATA[
      a(x,y,(((z \ T(u,z)) / u) \ ((z \ 1) \ 1)) * w) = a(x,y,(z * L(z,z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27468,a(flip),b,40032,a)].">
      <j1 rule="hyper" parents="64 27468 40032"/>
    </justification>
  </clause>

  <clause id="40035">
    <literal><![CDATA[
      a(x,y,(((z \ T(u,z)) / u) \ z) * w) = a(x,y,(z * L(z,z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27471,a(flip),b,40033,a)].">
      <j1 rule="hyper" parents="64 27471 40033"/>
    </justification>
  </clause>

  <clause id="40037">
    <literal><![CDATA[
      a(x,y,((z \ (u \ T(z,u))) \ u) * w) = a(x,y,(u * L(u,u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27412,a(flip),b,40035,a)].">
      <j1 rule="hyper" parents="64 27412 40035"/>
    </justification>
  </clause>

  <clause id="40038">
    <literal><![CDATA[
      R(x,y,z) * ((L(L(x,y,z),u * x,L(x,y,z)) \ u) * L(x,y,z)) = (R(x,y,z) * (L(x,y,z) \ u)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(33773(a,1),32929(a,1,2,1,1))].">
      <j1 rule="para" parents="33773 32929"/>
    </justification>
  </clause>

  <clause id="40040">
    <literal><![CDATA[
      R(x,y,z) * ((L(L(x,u * x,x),y,z) \ u) * L(x,y,z)) = (R(x,y,z) * (L(x,y,z) \ u)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(35023(a,1),40038(a,1,2,1,1))].">
      <j1 rule="para" parents="35023 40038"/>
    </justification>
  </clause>

  <clause id="40042">
    <literal><![CDATA[
      R(x,y,z) * ((u / L(T(x,u),y,z)) * L(x,y,z)) = (R(x,y,z) * (L(x,y,z) \ u)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(36387(a,1),40040(a,1,2,1))].">
      <j1 rule="para" parents="36387 40040"/>
    </justification>
  </clause>

  <clause id="40043">
    <literal><![CDATA[
      R(x,y,z) * (u * K(u,x)) = (R(x,y,z) * (L(x,y,z) \ u)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(24560(a,1),40042(a,1,2))].">
      <j1 rule="para" parents="24560 40042"/>
    </justification>
  </clause>

  <clause id="40044">
    <literal><![CDATA[
      (R(x,y,z) * (L(x,y,z) \ u)) * L(x,y,z) = R(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(5753(a,2),40043(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5753 40043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40046">
    <literal><![CDATA[
      (R(x,y,z) * (L(x,y,z) \ u)) * L(x,y,z) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,23681,a(flip),b,40044,a),flip(a)].">
      <j1 rule="hyper" parents="373 23681 40044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40047">
    <literal><![CDATA[
      a((x / R(T(R(y,z,u),x),R(y,z,u),R(y,z,u))) * w,v5,v6) = a((L(x,R(y,z,u),R(y,z,u)) * L(y,z,u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,34669,a(flip),b,34661,a),flip(a)].">
      <j1 rule="hyper" parents="373 34669 34661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40048">
    <literal><![CDATA[
      a((x / R(T(R(y,z,u),x),R(y,z,u),R(y,z,u))) * w,v5,v6) = a((L(x,R(y,z,u),L(y,z,u)) * L(y,z,u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(29203(a,1),40047(a,2,1,1,1))].">
      <j1 rule="para" parents="29203 40047"/>
    </justification>
  </clause>

  <clause id="40049">
    <literal><![CDATA[
      a((x / R(T(R(y,z,u),x),R(y,z,u),R(y,z,u))) * w,v5,v6) = a((L(x,L(y,z,u),L(y,z,u)) * L(y,z,u)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(29794(a,1),40048(a,2,1,1,1))].">
      <j1 rule="para" parents="29794 40048"/>
    </justification>
  </clause>

  <clause id="40050">
    <literal><![CDATA[
      a((x / R(T(R(y,z,u),x),R(y,z,u),R(y,z,u))) * w,v5,v6) = a((L(y,z,u) \ x) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32824,a(flip),b,40049,a),flip(a)].">
      <j1 rule="hyper" parents="373 32824 40049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40051">
    <literal><![CDATA[
      a(((x \ (y / R(x,z,u))) * x) * w,v5,v6) = a((L(x,z,u) \ y) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(25188(a,1),40050(a,1,1,1))].">
      <j1 rule="para" parents="25188 40050"/>
    </justification>
  </clause>

  <clause id="40052">
    <literal><![CDATA[
      a((x / R(y,z,u)) * w,v5,v6) = a((L(y,z,u) \ x) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32389,a(flip),b,40051,a)].">
      <j1 rule="hyper" parents="64 32389 40051"/>
    </justification>
  </clause>

  <clause id="40054">
    <literal><![CDATA[
      a((L(1 / x,y,z) \ u) * w,v5,v6) = a((R(x,y,z) \ u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,33015,a(flip),b,40052,a),flip(a)].">
      <j1 rule="hyper" parents="64 33015 40052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40055">
    <literal><![CDATA[
      a((R(x,y,z) \ u) * w,v5,v6) = a((L(x,y,z) \ u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32367,a(flip),b,40052,a)].">
      <j1 rule="hyper" parents="64 32367 40052"/>
    </justification>
  </clause>

  <clause id="40056">
    <literal><![CDATA[
      a((R(x,y,z) \ u) * (a(w,v5,w) * v6),v7,v8) = a(v6 * (L(x,y,z) \ u),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(373,a,26819,a(flip),b,40055,a),flip(a)].">
      <j1 rule="hyper" parents="373 26819 40055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40057">
    <literal><![CDATA[
      a((L(1 / x,y,z) \ u) * w,v5,v6) = a((L(x,y,z) \ u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,40055,a(flip),b,40054,a),flip(a)].">
      <j1 rule="hyper" parents="373 40055 40054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40058">
    <literal><![CDATA[
      a(x * (L(y \ 1,z,u) \ w),v5,v6) = a((L(y,z,u) \ w) * x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32531,a(flip),b,40057,a)].">
      <j1 rule="hyper" parents="64 32531 40057"/>
    </justification>
  </clause>

  <clause id="40059">
    <literal><![CDATA[
      a(x * (R(y,z,u) \ w),v5,v6) = a(x * (L(y,z,u) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,36467,a(flip),b,40056,a)].">
      <j1 rule="hyper" parents="64 36467 40056"/>
    </justification>
  </clause>

  <clause id="40060">
    <literal><![CDATA[
      a((x \ y) * (L(x,x,z) \ y),u,w) = a(a(x,x,L(z,y,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,39545,a(flip),b,40059,a),flip(a)].">
      <j1 rule="hyper" parents="64 39545 40059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40061">
    <literal><![CDATA[
      R((((x * y) \ x) / T(y,K(z,u))) * K(y,K(z,u)),T(y,K(z,u)),y) = ((T(y,K(z,u)) * T(y,K(z,u))) \ ((x * y) \ x)) * y
    ]]></literal>
    <justification jstring="[para(8108(a,1),34695(a,1,1,2))].">
      <j1 rule="para" parents="8108 34695"/>
    </justification>
  </clause>

  <clause id="40062">
    <literal><![CDATA[
      L((((x / y) / x) * y) \ z,y * (((y \ 1) * x) \ x),y * (x \ ((y \ 1) \ x))) = (1 / ((y \ 1) * (((y \ 1) * x) \ x))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,29186,a(flip),b,35375,a)].">
      <j1 rule="hyper" parents="64 29186 35375"/>
    </justification>
  </clause>

  <clause id="40063">
    <literal><![CDATA[
      a(x,y,(a(z,u,u) * a(z,u,u)) * (w \ (a(z,u,u) \ v5))) = a(x,y,w \ (v5 * a(L(z,a(z,u,u),a(z,u,u)),u,u)))
    ]]></literal>
    <justification jstring="[para(37826(a,1),35605(a,1,3,2,2))].">
      <j1 rule="para" parents="37826 35605"/>
    </justification>
  </clause>

  <clause id="40064">
    <literal><![CDATA[
      a(x,y,z \ (u * a(L(w,a(w,v5,v5),a(w,v5,v5)),v5,v5))) = a(x,y,z \ (a(w,v5,v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,38917,a(flip),b,40063,a),flip(a)].">
      <j1 rule="hyper" parents="64 38917 40063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40066">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,w) \ v5)) = a(x,y,z \ (v5 * a(u,w,w)))
    ]]></literal>
    <justification jstring="[para(29309(a,1),40064(a,1,3,2,2,1)),flip(a)].">
      <j1 rule="para" parents="29309 40064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40067">
    <literal><![CDATA[
      a(x,y,z \ (a(u,u,w) * v5)) = a(x,y,z \ (v5 * a(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,37852,a(flip),b,40066,a)].">
      <j1 rule="hyper" parents="64 37852 40066"/>
    </justification>
  </clause>

  <clause id="40069">
    <literal><![CDATA[
      (R(x,x,x) * (x * (L(x,y,z) \ a(u,x,w)))) / R(x,x,x) = ((x \ 1) \ a(u,x,w)) / L(R(x,x,x),y,z)
    ]]></literal>
    <justification jstring="[para(13575(a,1),35771(a,1,1,2))].">
      <j1 rule="para" parents="13575 35771"/>
    </justification>
  </clause>

  <clause id="40070">
    <literal><![CDATA[
      (x * (R(x,x,x) * (L(x,y,z) \ a(u,x,w)))) / R(x,x,x) = ((x \ 1) \ a(u,x,w)) / L(R(x,x,x),y,z)
    ]]></literal>
    <justification jstring="[para(1897(a,1),40069(a,1,1))].">
      <j1 rule="para" parents="1897 40069"/>
    </justification>
  </clause>

  <clause id="40072">
    <literal><![CDATA[
      (x * (x * (L(L(x,x,x),y,z) \ a(u,x,w)))) / R(x,x,x) = ((x \ 1) \ a(u,x,w)) / L(R(x,x,x),y,z)
    ]]></literal>
    <justification jstring="[para(13637(a,1),40070(a,1,1,2))].">
      <j1 rule="para" parents="13637 40070"/>
    </justification>
  </clause>

  <clause id="40073">
    <literal><![CDATA[
      (x * (x * (a(y,x,z) / L(x,u,w)))) / R(x,x,x) = ((x \ 1) \ a(y,x,z)) / L(R(x,x,x),u,w)
    ]]></literal>
    <justification jstring="[para(26944(a,1),40072(a,1,1,2,2))].">
      <j1 rule="para" parents="26944 40072"/>
    </justification>
  </clause>

  <clause id="40074">
    <literal><![CDATA[
      L((x * x) * ((a(y,x,z) / L(x,u,w)) / x),x,x) = ((x \ 1) \ a(y,x,z)) / L(R(x,x,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31209,a,b,40073,a)].">
      <j1 rule="hyper" parents="64 31209 40073"/>
    </justification>
  </clause>

  <clause id="40075">
    <literal><![CDATA[
      L((x * x) * ((a(y,x,z) / x) / L(x,u,w)),x,x) = ((x \ 1) \ a(y,x,z)) / L(R(x,x,x),u,w)
    ]]></literal>
    <justification jstring="[para(3201(a,1),40074(a,1,1,2))].">
      <j1 rule="para" parents="3201 40074"/>
    </justification>
  </clause>

  <clause id="40076">
    <literal><![CDATA[
      L(((1 / x) \ a(y,x,z)) / L(x,u,w),x,x) = ((x \ 1) \ a(y,x,z)) / L(R(x,x,x),u,w)
    ]]></literal>
    <justification jstring="[para(25505(a,1),40075(a,1,1))].">
      <j1 rule="para" parents="25505 40075"/>
    </justification>
  </clause>

  <clause id="40077">
    <literal><![CDATA[
      ((x \ 1) \ a(y,x,z)) / L(R(x,x,x),u,w) = L((a(y,x,z) * x) / L(x,u,w),x,x)
    ]]></literal>
    <justification jstring="[para(35737(a,1),40076(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="35737 40076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40078">
    <literal><![CDATA[
      ((x \ 1) \ a(y,x,z)) / L(R(x,x,x),u,w) = L(x * (L(x,u,w) \ a(y,x,z)),x,x)
    ]]></literal>
    <justification jstring="[para(24843(a,1),40077(a,2,1))].">
      <j1 rule="para" parents="24843 40077"/>
    </justification>
  </clause>

  <clause id="40079">
    <literal><![CDATA[
      ((x \ 1) \ a(y,x,z)) / L(R(x,x,x),u,w) = x * ((L(x,u,w) \ 1) * a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,35188,a(flip),b,40078,a),flip(a)].">
      <j1 rule="hyper" parents="373 35188 40078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40080">
    <literal><![CDATA[
      ((x \ 1) \ a(y,x,z)) / L(R(x,x,x),u,w) = a(y,x,z) * (L(x,u,w) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,39268,a(flip),b,40079,a),flip(a)].">
      <j1 rule="hyper" parents="373 39268 40079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40081">
    <literal><![CDATA[
      ((1 / x) \ a(y,x,z)) / L(x,u,w) = a(y,x,z) * (L(x,u,w) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,38368,a(flip),b,40080,a)].">
      <j1 rule="hyper" parents="64 38368 40080"/>
    </justification>
  </clause>

  <clause id="40082">
    <literal><![CDATA[
      (a(x,y,z) * y) / L(y,u,w) = a(x,y,z) * (L(y,u,w) \ y)
    ]]></literal>
    <justification jstring="[para(35737(a,1),40081(a,1,1))].">
      <j1 rule="para" parents="35737 40081"/>
    </justification>
  </clause>

  <clause id="40083">
    <literal><![CDATA[
      a(x,y,z) * (L(y,u,w) \ y) = y * (L(y,u,w) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,24843,a(flip),b,40082,a),flip(a)].">
      <j1 rule="hyper" parents="64 24843 40082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40084">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) * L(1 * a(y,y,L(x,z,u)),w,v5) = L(a(y,y,x) \ L((x \ L(x,y,y)) \ 1,w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(39719(a,1),37689(a,1,2,1))].">
      <j1 rule="para" parents="39719 37689"/>
    </justification>
  </clause>

  <clause id="40085">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) * L(a(y,y,L(x,z,u)),w,v5) = L(a(y,y,x) \ L((x \ L(x,y,y)) \ 1,w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),40084(a,1,2,1))].">
      <j1 rule="para" parents="7 40084"/>
    </justification>
  </clause>

  <clause id="40086">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,u) * a(y,y,L(L(x,z,u),w,v5)) = L(a(y,y,x) \ L((x \ L(x,y,y)) \ 1,w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(39675(a,2),40085(a,1,2))].">
      <j1 rule="para" parents="39675 40085"/>
    </justification>
  </clause>

  <clause id="40087">
    <literal><![CDATA[
      L(a(x,x,y) \ L((y \ L(y,x,x)) \ 1,z,u),w,v5) = a(x,x,L(y,w,v5)) \ a(x,x,L(L(y,w,v5),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39721,a(flip),b,40086,a),flip(a)].">
      <j1 rule="hyper" parents="64 39721 40086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40088">
    <literal><![CDATA[
      L(a(x,x,y) \ L((y \ L(y,x,x)) \ 1,z,u),w,v5) = a(a(L(y,w,v5),x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,39671,a(flip),b,40087,a),flip(a)].">
      <j1 rule="hyper" parents="373 39671 40087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40089">
    <literal><![CDATA[
      R(K(x,L(a(y,z,u),w,v5)) * v6,x,L(a(y,z,u),w,v5)) = L(K(L(a(y,z,u),w,v5),x) * v6,x,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,25847,a(flip),b,39935,a),flip(a)].">
      <j1 rule="hyper" parents="64 25847 39935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40090">
    <literal><![CDATA[
      R(K(x,L(a(y,z,u),w,v5)) * v6,x,L(a(y,z,u),w,v5)) = L(K(a(y,z,u),x) * v6,x,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(23004(a,1),40089(a,2,1,1))].">
      <j1 rule="para" parents="23004 40089"/>
    </justification>
  </clause>

  <clause id="40092">
    <literal><![CDATA[
      R(K(x,L(a(y,z,u),w,v5)) * v6,x,L(a(y,z,u),w,v5)) = L(v6,x,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(23126(a,1),40090(a,2,1))].">
      <j1 rule="para" parents="23126 40090"/>
    </justification>
  </clause>

  <clause id="40093">
    <literal><![CDATA[
      R(K(x,a(y,z,u)) * w,x,L(a(y,z,u),v5,v6)) = L(w,x,L(a(y,z,u),v5,v6))
    ]]></literal>
    <justification jstring="[para(23001(a,1),40092(a,1,1,1))].">
      <j1 rule="para" parents="23001 40092"/>
    </justification>
  </clause>

  <clause id="40095">
    <literal><![CDATA[
      R(x,y,L(a(z,u,w),v5,v6)) = L(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(23104(a,1),40093(a,1,1))].">
      <j1 rule="para" parents="23104 40093"/>
    </justification>
  </clause>

  <clause id="40096">
    <literal><![CDATA[
      L(x \ L(x,y,L(a(z,u,w),v5,v6)),x,y * L(a(z,u,w) \ 1,v5,v6)) = a(x,y,L(a(z,u,w) \ 1,v5,v6) \ 1)
    ]]></literal>
    <justification jstring="[para(40095(a,1),39623(a,1,1,2))].">
      <j1 rule="para" parents="40095 39623"/>
    </justification>
  </clause>

  <clause id="40097">
    <literal><![CDATA[
      L(x \ L(x,y,L(a(z,u,w),v5,v6)),x,L(a(z,u,w),v5,v6) * y) = a(x,y,L(a(z,u,w) \ 1,v5,v6) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,33602,a(flip),b,40096,a)].">
      <j1 rule="hyper" parents="64 33602 40096"/>
    </justification>
  </clause>

  <clause id="40098">
    <literal><![CDATA[
      R(T(x / y,T(z,y * (x * y))),y,y \ ((y \ z) * T(y,z))) = ((y \ z) * y) \ (x * (y \ T((y \ z) * T(y,z),y)))
    ]]></literal>
    <justification jstring="[para(25290(a,1),39936(a,1,1))].">
      <j1 rule="para" parents="25290 39936"/>
    </justification>
  </clause>

  <clause id="40099">
    <literal><![CDATA[
      R(T(x / y,T(z,x)),y,y \ ((y \ z) * T(y,z))) = ((y \ z) * y) \ (x * (y \ T((y \ z) * T(y,z),y)))
    ]]></literal>
    <justification jstring="[para(17396(a,1),40098(a,1,1))].">
      <j1 rule="para" parents="17396 40098"/>
    </justification>
  </clause>

  <clause id="40100">
    <literal><![CDATA[
      R(T(x / y,T(z,x)),y,T((y \ z) * K(y,z),y)) = ((y \ z) * y) \ (x * (y \ T((y \ z) * T(y,z),y)))
    ]]></literal>
    <justification jstring="[para(6853(a,2),40099(a,1,3))].">
      <j1 rule="para" parents="6853 40099"/>
    </justification>
  </clause>

  <clause id="40103">
    <literal><![CDATA[
      R(T(x / y,T(z,x)),y,T(K(y,z) * (y \ z),y)) = ((y \ z) * y) \ (x * (y \ T((y \ z) * T(y,z),y)))
    ]]></literal>
    <justification jstring="[para(7130(a,2),40100(a,1,3,1))].">
      <j1 rule="para" parents="7130 40100"/>
    </justification>
  </clause>

  <clause id="40105">
    <literal><![CDATA[
      R(T(x / y,T(z,x)),y,R(y,y * z,y) \ z) = ((y \ z) * y) \ (x * (y \ T((y \ z) * T(y,z),y)))
    ]]></literal>
    <justification jstring="[para(13739(a,1),40103(a,1,3))].">
      <j1 rule="para" parents="13739 40103"/>
    </justification>
  </clause>

  <clause id="40106">
    <literal><![CDATA[
      R(T(x / y,T(z,x)),y,y \ z) = ((y \ z) * y) \ (x * (y \ T((y \ z) * T(y,z),y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13902,a(flip),b,40105,a)].">
      <j1 rule="hyper" parents="64 13902 40105"/>
    </justification>
  </clause>

  <clause id="40108">
    <literal><![CDATA[
      ((x \ y) * x) \ (z * (x \ T((x \ y) * T(x,y),x))) = T(y,x) \ (z * (x \ T(y,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27236,a(flip),b,40106,a),flip(a)].">
      <j1 rule="hyper" parents="64 27236 40106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40109">
    <literal><![CDATA[
      ((x \ y) * x) \ (z * (x \ ((x \ y) * x))) = T(y,x) \ (z * (x \ T(y,x)))
    ]]></literal>
    <justification jstring="[para(4701(a,1),40108(a,1,2,2,2))].">
      <j1 rule="para" parents="4701 40108"/>
    </justification>
  </clause>

  <clause id="40110">
    <literal><![CDATA[
      ((x \ y) * x) \ (z * T(x \ y,x)) = T(y,x) \ (z * (x \ T(y,x)))
    ]]></literal>
    <justification jstring="[para(22(a,2),40109(a,1,2,2))].">
      <j1 rule="para" parents="22 40109"/>
    </justification>
  </clause>

  <clause id="40111">
    <literal><![CDATA[
      T(x,y) \ ((x * (y \ x)) * (y \ T(x,y))) = (y / (x / y)) \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,36977,a(flip),b,40110,a),flip(a)].">
      <j1 rule="hyper" parents="64 36977 40110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40112">
    <literal><![CDATA[
      (x / (y / x)) \ ((x \ y) * x) = (x / (x \ y)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,34251,a(flip),b,40111,a),flip(a)].">
      <j1 rule="hyper" parents="64 34251 40111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40114">
    <literal><![CDATA[
      ((T(x,K(y,z)) * T(x,K(y,z))) \ ((u * x) \ u)) * x = R(((u * x) \ u) / x,T(x,K(y,z)),x)
    ]]></literal>
    <justification jstring="[para(6848(a,1),40061(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6848 40061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40115">
    <literal><![CDATA[
      ((T(x,K(y,z)) * T(x,K(y,z))) \ ((u * x) \ u)) * x = R(((u * x) \ u) / x,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,26406,a(flip),b,40114,a),flip(a)].">
      <j1 rule="hyper" parents="373 26406 40114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40118">
    <literal><![CDATA[
      ((T(x,K(y,z)) * T(x,K(y,z))) \ ((u * x) \ u)) * x = ((u * x) \ u) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,31624,a(flip),b,40115,a),flip(a)].">
      <j1 rule="hyper" parents="373 31624 40115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40119">
    <literal><![CDATA[
      ((x * T(x,K(y,z * z))) \ ((u * x) \ u)) * x = ((u * x) \ u) / x
    ]]></literal>
    <justification jstring="[para(17041(a,1),40118(a,1,1,1,1))].">
      <j1 rule="para" parents="17041 40118"/>
    </justification>
  </clause>

  <clause id="40120">
    <literal><![CDATA[
      ((x * x) \ ((y * x) \ y)) * x = ((y * x) \ y) / x
    ]]></literal>
    <justification jstring="[para(3594(a,1),40119(a,1,1,1,2))].">
      <j1 rule="para" parents="3594 40119"/>
    </justification>
  </clause>

  <clause id="40121">
    <literal><![CDATA[
      ((x * y) \ x) / y = (x * y) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,39429,a(flip),b,40120,a),flip(a)].">
      <j1 rule="hyper" parents="64 39429 40120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40122">
    <literal><![CDATA[
      (x * y) \ (x / y) = y \ L(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27103,a,b,40121,a),flip(a)].">
      <j1 rule="hyper" parents="64 27103 40121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40123">
    <literal><![CDATA[
      (x * (x \ y)) \ (x / (x \ y)) = (y \ x) / (x \ y)
    ]]></literal>
    <justification jstring="[para(10(a,1),40121(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 40121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40124">
    <literal><![CDATA[
      ((x / y) * y) \ ((x / y) / y) = (x \ (x / y)) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),40121(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12 40121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40125">
    <literal><![CDATA[
      ((x * y) \ (x / y)) * (y * ((y \ 1) \ z)) = (((x * y) \ x) / (y \ 1)) * z
    ]]></literal>
    <justification jstring="[para(40121(a,1),1674(a,1,1))].">
      <j1 rule="para" parents="40121 1674"/>
    </justification>
  </clause>

  <clause id="40126">
    <literal><![CDATA[
      L(x \ y,x,x \ ((z * x) \ z)) = ((z * x) \ z) \ (((z * x) \ (z / x)) * y)
    ]]></literal>
    <justification jstring="[para(40121(a,1),11070(a,2,2,1))].">
      <j1 rule="para" parents="40121 11070"/>
    </justification>
  </clause>

  <clause id="40127">
    <literal><![CDATA[
      (x \ L(1 / x,x,y)) \ K((y * x) \ (y / x),y * x) = ((y / x) / (y * x)) \ 1
    ]]></literal>
    <justification jstring="[para(40122(a,1),6256(a,1,1))].">
      <j1 rule="para" parents="40122 6256"/>
    </justification>
  </clause>

  <clause id="40128">
    <literal><![CDATA[
      (x \ y) / (y \ x) = x \ (y / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(402,a,40123,a),flip(a)].">
      <j1 rule="hyper" parents="402 40123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40130">
    <literal><![CDATA[
      (((x \ y) * (x \ y)) \ (y \ x)) * (x \ y) = y \ (x / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30691,a,b,40128,a)].">
      <j1 rule="hyper" parents="64 30691 40128"/>
    </justification>
  </clause>

  <clause id="40131">
    <literal><![CDATA[
      (x \ y) * ((y \ x) \ 1) = x \ (y / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,30671,a,b,40128,a)].">
      <j1 rule="hyper" parents="64 30671 40128"/>
    </justification>
  </clause>

  <clause id="40132">
    <literal><![CDATA[
      (x / (x \ y)) \ y = x \ (y / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,38097,a(flip),b,40128,a)].">
      <j1 rule="hyper" parents="64 38097 40128"/>
    </justification>
  </clause>

  <clause id="40133">
    <literal><![CDATA[
      T(T(x \ (y / (y \ x)),z),y \ x) = T((y \ x) \ (x \ y),z)
    ]]></literal>
    <justification jstring="[para(40128(a,1),278(a,1,1,1))].">
      <j1 rule="para" parents="40128 278"/>
    </justification>
  </clause>

  <clause id="40134">
    <literal><![CDATA[
      K(x,x \ y) * (x \ (y / (y \ x))) = (y / x) / (y \ x)
    ]]></literal>
    <justification jstring="[para(40128(a,1),14696(a,1,2))].">
      <j1 rule="para" parents="40128 14696"/>
    </justification>
  </clause>

  <clause id="40135">
    <literal><![CDATA[
      ((x \ y) / (y \ x)) * x = T(y / (y \ x),x)
    ]]></literal>
    <justification jstring="[para(40128(a,2),31605(a,1,1))].">
      <j1 rule="para" parents="40128 31605"/>
    </justification>
  </clause>

  <clause id="40136">
    <literal><![CDATA[
      K(x,x \ y) * (x \ (y / (y \ x))) = (x / (y / x)) \ y
    ]]></literal>
    <justification jstring="[para(40132(a,1),24510(a,1,2))].">
      <j1 rule="para" parents="40132 24510"/>
    </justification>
  </clause>

  <clause id="40137">
    <literal><![CDATA[
      a(x * (y * (z \ (y / (y \ z)))),u,w) = a((z / (1 / (z \ y))) * x,u,w)
    ]]></literal>
    <justification jstring="[para(40131(a,1),32797(a,1,1,2,2))].">
      <j1 rule="para" parents="40131 32797"/>
    </justification>
  </clause>

  <clause id="40138">
    <literal><![CDATA[
      T(x / (((x \ y) * z) / z),y) = ((y \ x) / (x \ y)) * y
    ]]></literal>
    <justification jstring="[para(11(a,2),40135(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 40135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40139">
    <literal><![CDATA[
      (x \ (x / y)) / y = x \ ((x / y) / y)
    ]]></literal>
    <justification jstring="[para(12(a,1),40124(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 40124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40140">
    <literal><![CDATA[
      (x \ (x / y)) * L(z,y,y \ (x \ (x / y))) = (x \ ((x / y) / y)) * (y * z)
    ]]></literal>
    <justification jstring="[para(40139(a,1),11064(a,2,1))].">
      <j1 rule="para" parents="40139 11064"/>
    </justification>
  </clause>

  <clause id="40141">
    <literal><![CDATA[
      (x / y) / (x \ y) = (y / (x / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,40134,a(flip),b,40136,a)].">
      <j1 rule="hyper" parents="64 40134 40136"/>
    </justification>
  </clause>

  <clause id="40142">
    <literal><![CDATA[
      ((x \ y) \ 1) * (x / y) = (y / (x / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,30708,a,b,40141,a)].">
      <j1 rule="hyper" parents="64 30708 40141"/>
    </justification>
  </clause>

  <clause id="40143">
    <literal><![CDATA[
      R((x / (y / x)) \ y,y \ x,y \ x) = (y / x) / (y \ x)
    ]]></literal>
    <justification jstring="[para(40141(a,1),29248(a,1,1))].">
      <j1 rule="para" parents="40141 29248"/>
    </justification>
  </clause>

  <clause id="40144">
    <literal><![CDATA[
      ((((x \ y) \ 1) * y) \ x) * (((x \ y) \ 1) * ((x \ y) \ z)) = R((y / (x / y)) \ x,x \ y,x \ y) * z
    ]]></literal>
    <justification jstring="[para(40141(a,1),39916(a,2,1,1))].">
      <j1 rule="para" parents="40141 39916"/>
    </justification>
  </clause>

  <clause id="40145">
    <literal><![CDATA[
      L(((x / (y / x)) \ y) \ z,(y \ x) * (y / x),(y \ x) * (y / x)) = (1 / (((y \ x) \ 1) * (y / x))) * z
    ]]></literal>
    <justification jstring="[para(40142(a,1),35374(a,1,1,1))].">
      <j1 rule="para" parents="40142 35374"/>
    </justification>
  </clause>

  <clause id="40146">
    <literal><![CDATA[
      (x \ (y / (x / y))) * (y * (x / y)) = ((x \ y) / (y \ x)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,36487,a,b,40138,a)].">
      <j1 rule="hyper" parents="64 36487 40138"/>
    </justification>
  </clause>

  <clause id="40147">
    <literal><![CDATA[
      R((x / (y / x)) \ y,y \ x,y \ x) = (x / (y / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,40141,a(flip),b,40143,a),flip(a)].">
      <j1 rule="hyper" parents="373 40141 40143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40148">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * (1 / (x \ y))) * ((y \ x) * z)) = (y \ (x / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(40130(a,1),39600(a,2,1))].">
      <j1 rule="para" parents="40130 39600"/>
    </justification>
  </clause>

  <clause id="40149">
    <literal><![CDATA[
      (x \ y) / (x / y) = x \ (y / (x / y))
    ]]></literal>
    <justification jstring="[hyper(36,a,24943,a,b,40146,a)].">
      <j1 rule="hyper" parents="36 24943 40146"/>
    </justification>
  </clause>

  <clause id="40150">
    <literal><![CDATA[
      (x * y) \ (y / ((x * y) / y)) = ((x * y) \ y) / x
    ]]></literal>
    <justification jstring="[para(11(a,1),40149(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 40149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40151">
    <literal><![CDATA[
      K(x \ y,x) / (y \ (x / (y / x))) = 1 / ((y \ x) / (x \ y))
    ]]></literal>
    <justification jstring="[para(40149(a,1),14508(a,1,2))].">
      <j1 rule="para" parents="40149 14508"/>
    </justification>
  </clause>

  <clause id="40152">
    <literal><![CDATA[
      a(((x / y) \ (x \ y)) * z,u,w) = a((x \ (y / (x / y))) * z,u,w)
    ]]></literal>
    <justification jstring="[para(40149(a,1),32367(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="40149 32367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40153">
    <literal><![CDATA[
      ((x * y) \ y) / x = (x * y) \ (y / x)
    ]]></literal>
    <justification jstring="[para(11(a,1),40150(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11 40150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40154">
    <literal><![CDATA[
      L(x,y,y) \ ((y * y) \ ((y * x) / y)) = ((y * (y * x)) \ (y * x)) / y
    ]]></literal>
    <justification jstring="[hyper(373,a,881,a,b,40153,a)].">
      <j1 rule="hyper" parents="373 881 40153"/>
    </justification>
  </clause>

  <clause id="40155">
    <literal><![CDATA[
      (x \ 1) * ((x * y) \ y) = (x * y) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30688,a,b,40153,a)].">
      <j1 rule="hyper" parents="64 30688 40153"/>
    </justification>
  </clause>

  <clause id="40156">
    <literal><![CDATA[
      L(((x * y) \ (y / x)) \ z,((y / (x \ 1)) / y) / x,x) = R((x * y) \ y,x,x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(40153(a,1),36885(a,1,1,1))].">
      <j1 rule="para" parents="40153 36885"/>
    </justification>
  </clause>

  <clause id="40157">
    <literal><![CDATA[
      ((x / y) \ (y * x)) * ((y * x) \ (x / y)) = 1
    ]]></literal>
    <justification jstring="[para(40153(a,1),37782(a,1,2))].">
      <j1 rule="para" parents="40153 37782"/>
    </justification>
  </clause>

  <clause id="40158">
    <literal><![CDATA[
      ((x * y) \ (y / x)) * ((y / x) \ (x * y)) = 1
    ]]></literal>
    <justification jstring="[para(40153(a,1),37783(a,1,1))].">
      <j1 rule="para" parents="40153 37783"/>
    </justification>
  </clause>

  <clause id="40159">
    <literal><![CDATA[
      L(((x * y) \ (y / x)) \ z,x * ((x * y) \ y),x * ((x * y) \ y)) = (1 / ((x \ 1) * ((x * y) \ y))) * z
    ]]></literal>
    <justification jstring="[para(40155(a,1),35374(a,1,1,1))].">
      <j1 rule="para" parents="40155 35374"/>
    </justification>
  </clause>

  <clause id="40160">
    <literal><![CDATA[
      1 / ((x * y) \ (y / x)) = (y / x) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(154,a,40157,a)].">
      <j1 rule="hyper" parents="154 40157"/>
    </justification>
  </clause>

  <clause id="40161">
    <literal><![CDATA[
      1 / ((x \ y) \ (x * y)) = (x * y) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(142,a,40158,a(flip),b,25738,a(flip))].">
      <j1 rule="hyper" parents="142 40158 25738"/>
    </justification>
  </clause>

  <clause id="40162">
    <literal><![CDATA[
      L(((x \ y) \ (x * y)) \ z,(x \ y) \ (x * y),(x * y) \ (x \ y)) = ((x * y) \ (x \ y)) * z
    ]]></literal>
    <justification jstring="[para(40161(a,1),37710(a,2,1))].">
      <j1 rule="para" parents="40161 37710"/>
    </justification>
  </clause>

  <clause id="40163">
    <literal><![CDATA[
      ((x / (y / x)) \ y) * K(x \ y,x) = 1 / ((y \ x) / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,36072,a(flip),b,40151,a)].">
      <j1 rule="hyper" parents="64 36072 40151"/>
    </justification>
  </clause>

  <clause id="40164">
    <literal><![CDATA[
      (x / (y / x)) \ ((x \ y) * x) = 1 / ((y \ x) / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,15230,a(flip),b,40163,a)].">
      <j1 rule="hyper" parents="64 15230 40163"/>
    </justification>
  </clause>

  <clause id="40165">
    <literal><![CDATA[
      1 / ((x \ y) / (y \ x)) = (y / (y \ x)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,40112,a(flip),b,40164,a),flip(a)].">
      <j1 rule="hyper" parents="64 40112 40164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40166">
    <literal><![CDATA[
      1 / (x \ (y / (y \ x))) = (y / (y \ x)) \ x
    ]]></literal>
    <justification jstring="[para(40128(a,1),40165(a,1,2))].">
      <j1 rule="para" parents="40128 40165"/>
    </justification>
  </clause>

  <clause id="40167">
    <literal><![CDATA[
      1 / (x \ (y / (y \ x))) = y \ (x / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,40132,a(flip),b,40166,a),flip(a)].">
      <j1 rule="hyper" parents="373 40132 40166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40168">
    <literal><![CDATA[
      (x \ (y / (y \ x))) \ 1 = y \ (x / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(215,a,40167,a)].">
      <j1 rule="hyper" parents="215 40167"/>
    </justification>
  </clause>

  <clause id="40169">
    <literal><![CDATA[
      (x \ (y / (y \ x))) * R(z,y * ((x \ y) \ x),z) = T(z * (1 / (y \ (x / (x \ y)))),z)
    ]]></literal>
    <justification jstring="[para(40167(a,1),26553(a,1,1))].">
      <j1 rule="para" parents="40167 26553"/>
    </justification>
  </clause>

  <clause id="40170">
    <literal><![CDATA[
      (x \ (y / (y \ x))) * ((y \ (x / (x \ y))) \ (z * (T(y \ (x / (x \ y)),z) * u))) = z * (T((y \ (x / (x \ y))) \ 1,z) * u)
    ]]></literal>
    <justification jstring="[para(40168(a,1),12007(a,1,1))].">
      <j1 rule="para" parents="40168 12007"/>
    </justification>
  </clause>

  <clause id="40171">
    <literal><![CDATA[
      a(((x / y) \ (x \ y)) * z,u,w) = a((x \ ((x \ y) * y)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,33717,a(flip),b,40152,a),flip(a)].">
      <j1 rule="hyper" parents="373 33717 40152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40172">
    <literal><![CDATA[
      a(((x \ y) \ (y \ x)) * z,u,w) = a((y \ ((y \ x) * x)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32397,a(flip),b,40171,a)].">
      <j1 rule="hyper" parents="64 32397 40171"/>
    </justification>
  </clause>

  <clause id="40173">
    <literal><![CDATA[
      a((x \ ((x \ y) * y)) * z,u,w) = a(((x \ y) * (y \ x)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32431,a(flip),b,40172,a),flip(a)].">
      <j1 rule="hyper" parents="64 32431 40172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40174">
    <literal><![CDATA[
      a((x \ ((y \ x) \ y)) * z,u,w) = a(((x \ y) * (y \ x)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33718,a,b,40173,a)].">
      <j1 rule="hyper" parents="64 33718 40173"/>
    </justification>
  </clause>

  <clause id="40175">
    <literal><![CDATA[
      a(((x * ((y \ x) \ 1)) * y) * z,u,w) = a(((y \ x) * (x \ y)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,34343,a,b,40174,a)].">
      <j1 rule="hyper" parents="64 34343 40174"/>
    </justification>
  </clause>

  <clause id="40176">
    <literal><![CDATA[
      L(x,y,y) \ ((y * y) \ ((y * x) / y)) = R(T(1 / y,x),y,x) / y
    ]]></literal>
    <justification jstring="[para(25862(a,1),40154(a,2,1))].">
      <j1 rule="para" parents="25862 40154"/>
    </justification>
  </clause>

  <clause id="40177">
    <literal><![CDATA[
      R(T(1 / x,y),x,y) / x = (1 / x) * (y \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,38485,a(flip),b,40176,a),flip(a)].">
      <j1 rule="hyper" parents="64 38485 40176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40178">
    <literal><![CDATA[
      R(T(1 / x,y),x,y) / x = (x * (y * x)) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,38481,a(flip),b,40177,a),flip(a)].">
      <j1 rule="hyper" parents="373 38481 40177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40179">
    <literal><![CDATA[
      R(T(1 / x,y),x,y) / x = (y \ (x * (y * x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,38479,a,b,40178,a),flip(a)].">
      <j1 rule="hyper" parents="373 38479 40178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40180">
    <literal><![CDATA[
      (T(x,y * y) / (x * y)) / y = (x \ (y * (x * y))) \ 1
    ]]></literal>
    <justification jstring="[para(10203(a,2),40179(a,1,1))].">
      <j1 rule="para" parents="10203 40179"/>
    </justification>
  </clause>

  <clause id="40181">
    <literal><![CDATA[
      K(x,y * y) * ((x / (x * y)) / y) = (x \ (y * (x * y))) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,24432,a,b,40180,a)].">
      <j1 rule="hyper" parents="64 24432 40180"/>
    </justification>
  </clause>

  <clause id="40182">
    <literal><![CDATA[
      (x / (y / (y * x))) \ K(y,x * x) = (y \ (x * (y * x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,38179,a,b,40181,a)].">
      <j1 rule="hyper" parents="64 38179 40181"/>
    </justification>
  </clause>

  <clause id="40183">
    <literal><![CDATA[
      (x / (y / (y * x))) \ K(y,y \ (x * (y * x))) = (y \ (x * (y * x))) \ 1
    ]]></literal>
    <justification jstring="[para(10149(a,2),40182(a,1,2))].">
      <j1 rule="para" parents="10149 40182"/>
    </justification>
  </clause>

  <clause id="40184">
    <literal><![CDATA[
      ((x * y) \ (x / y)) * (y * ((y \ 1) \ z)) = (y * ((x * y) \ x)) * z
    ]]></literal>
    <justification jstring="[para(1875(a,1),40125(a,2,1))].">
      <j1 rule="para" parents="1875 40125"/>
    </justification>
  </clause>

  <clause id="40185">
    <literal><![CDATA[
      a(x * (y * (z \ ((y \ z) \ y))),u,w) = a((z / (1 / (z \ y))) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32653,a(flip),b,40137,a)].">
      <j1 rule="hyper" parents="64 32653 40137"/>
    </justification>
  </clause>

  <clause id="40186">
    <literal><![CDATA[
      a((((x \ y) * y) * x) * z,u,w) = a(((x \ y) * (y \ x)) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32658,a(flip),b,40175,a)].">
      <j1 rule="hyper" parents="64 32658 40175"/>
    </justification>
  </clause>

  <clause id="40187">
    <literal><![CDATA[
      a(((x \ y) * (y \ x)) * z,u,w) = a(z * a(x,x * y,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,35714,a(flip),b,40186,a),flip(a)].">
      <j1 rule="hyper" parents="64 35714 40186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40188">
    <literal><![CDATA[
      a(((x \ y) \ (y \ x)) * z,u,w) = a(z * a(y,y * x,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32431,a,b,40187,a)].">
      <j1 rule="hyper" parents="64 32431 40187"/>
    </justification>
  </clause>

  <clause id="40189">
    <literal><![CDATA[
      a((x \ y) * ((y \ x) \ z),u,w) = a(z * a(y,y * x,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,37984,a(flip),b,40187,a)].">
      <j1 rule="hyper" parents="64 37984 40187"/>
    </justification>
  </clause>

  <clause id="40190">
    <literal><![CDATA[
      (x * (y * x)) / y = x / (y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(40,a,6037,a,b,40183,a)].">
      <j1 rule="hyper" parents="40 6037 40183"/>
    </justification>
  </clause>

  <clause id="40191">
    <literal><![CDATA[
      T(x \ (y \ x),K(z,u)) / (x / (x * T(x \ (y \ x),K(z,u)))) = (T(x \ (y \ x),K(z,u)) * (T(y,K(z,u)) \ x)) / x
    ]]></literal>
    <justification jstring="[para(17704(a,1),40190(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="17704 40190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40192">
    <literal><![CDATA[
      ((x \ (y * (x * y))) \ z) * K(y * y,x) = (y / (x / (x * y))) \ z
    ]]></literal>
    <justification jstring="[para(40190(a,1),18836(a,2,1))].">
      <j1 rule="para" parents="40190 18836"/>
    </justification>
  </clause>

  <clause id="40193">
    <literal><![CDATA[
      (x \ (y * (x * y))) \ K(y * y,x) = (y / (x / (x * y))) \ 1
    ]]></literal>
    <justification jstring="[hyper(14603,a,40192,a)].">
      <j1 rule="hyper" parents="14603 40192"/>
    </justification>
  </clause>

  <clause id="40194">
    <literal><![CDATA[
      K(x * x,y) * ((x * (y * x)) \ y) = (x / (y / (y * x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,38482,a(flip),b,40193,a)].">
      <j1 rule="hyper" parents="64 38482 40193"/>
    </justification>
  </clause>

  <clause id="40195">
    <literal><![CDATA[
      (x / (y / (y * x))) \ 1 = y / (x * (y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,34764,a(flip),b,40194,a),flip(a)].">
      <j1 rule="hyper" parents="64 34764 40194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40196">
    <literal><![CDATA[
      x * ((y / (y * z)) / z) = x * (y / (z * (y * z)))
    ]]></literal>
    <justification jstring="[para(40195(a,1),38178(a,1,2)),flip(a)].">
      <j1 rule="para" parents="40195 38178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40197">
    <literal><![CDATA[
      (x / (x * y)) / y = x / (y * (x * y))
    ]]></literal>
    <justification jstring="[hyper(322,a,40196,a),flip(a)].">
      <j1 rule="hyper" parents="322 40196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40198">
    <literal><![CDATA[
      (x / (y * (x * y))) * K(z,y) = (x / (x * y)) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(144,a,40197,a(flip),b,6242,a)].">
      <j1 rule="hyper" parents="144 40197 6242"/>
    </justification>
  </clause>

  <clause id="40199">
    <literal><![CDATA[
      (x / y) / (y * ((x / y) * y)) = ((x / y) / x) / y
    ]]></literal>
    <justification jstring="[para(12(a,1),40197(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12 40197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40200">
    <literal><![CDATA[
      (x / (x * y)) * L(z,y,y \ (x / (x * y))) = (x / (y * (x * y))) * (y * z)
    ]]></literal>
    <justification jstring="[para(40197(a,1),11064(a,2,1))].">
      <j1 rule="para" parents="40197 11064"/>
    </justification>
  </clause>

  <clause id="40201">
    <literal><![CDATA[
      ((x * y) \ T(x / y,y \ 1)) * ((1 / (y \ (x / (x * y)))) * z) = (x / (y * (x * y))) * ((1 / ((x / (x * y)) / y)) * z)
    ]]></literal>
    <justification jstring="[para(40197(a,1),33916(a,2,1))].">
      <j1 rule="para" parents="40197 33916"/>
    </justification>
  </clause>

  <clause id="40202">
    <literal><![CDATA[
      ((x / y) / x) / y = (x / y) / (y * x)
    ]]></literal>
    <justification jstring="[para(12(a,1),40199(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12 40199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40203">
    <literal><![CDATA[
      (x / (x * y)) / T(y,z) = x / (T(y,z) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,24486,a(flip),b,40198,a),flip(a)].">
      <j1 rule="hyper" parents="64 24486 40198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40204">
    <literal><![CDATA[
      T(x / (T(y,x) * (x * y)),y) = y \ (x / (y * x))
    ]]></literal>
    <justification jstring="[para(40203(a,1),10605(a,1,1))].">
      <j1 rule="para" parents="40203 10605"/>
    </justification>
  </clause>

  <clause id="40205">
    <literal><![CDATA[
      T(x / (y * (y * x)),y) = y \ (x / (y * x))
    ]]></literal>
    <justification jstring="[para(4645(a,1),40204(a,1,1,2))].">
      <j1 rule="para" parents="4645 40204"/>
    </justification>
  </clause>

  <clause id="40206">
    <literal><![CDATA[
      (x / (y * x)) / y = x / (y * (y * x))
    ]]></literal>
    <justification jstring="[hyper(281,a,40205,a)].">
      <j1 rule="hyper" parents="281 40205"/>
    </justification>
  </clause>

  <clause id="40207">
    <literal><![CDATA[
      a((x * (x * y)) \ y,y \ (x * (x * y)),y) = ((y / (x * y)) / x) * ((x * (x * y)) / y)
    ]]></literal>
    <justification jstring="[para(40206(a,2),26894(a,2,1))].">
      <j1 rule="para" parents="40206 26894"/>
    </justification>
  </clause>

  <clause id="40208">
    <literal><![CDATA[
      a(x * (y * (z \ ((y \ z) \ y))),u,w) = a(((1 / (z \ y)) \ z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32367,a(flip),b,40185,a),flip(a)].">
      <j1 rule="hyper" parents="373 32367 40185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40209">
    <literal><![CDATA[
      a(x * (y * (z \ ((y \ z) \ y))),u,w) = a((((z \ y) \ 1) \ z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32397,a(flip),b,40208,a),flip(a)].">
      <j1 rule="hyper" parents="373 32397 40208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40210">
    <literal><![CDATA[
      a(x * (y * (z \ ((y \ z) \ y))),u,w) = a(((z \ y) \ z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32809,a(flip),b,40209,a),flip(a)].">
      <j1 rule="hyper" parents="373 32809 40209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40211">
    <literal><![CDATA[
      a(x * (y * (z \ ((y \ z) \ y))),u,w) = a(((y \ z) * z) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32871,a(flip),b,40210,a),flip(a)].">
      <j1 rule="hyper" parents="373 32871 40210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40212">
    <literal><![CDATA[
      L(x \ y,x,x \ (z \ (x \ z))) = ((z * x) \ z) \ (((z * x) \ (z / x)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29351,a(flip),b,40126,a)].">
      <j1 rule="hyper" parents="64 29351 40126"/>
    </justification>
  </clause>

  <clause id="40213">
    <literal><![CDATA[
      (x \ (x / y)) * L(z,y,y \ (x \ (y \ x))) = (x \ ((x / y) / y)) * (y * z)
    ]]></literal>
    <justification jstring="[para(29029(a,1),40140(a,1,2))].">
      <j1 rule="para" parents="29029 40140"/>
    </justification>
  </clause>

  <clause id="40214">
    <literal><![CDATA[
      (x / (x * y)) * L(z,y,y \ (x \ (y \ x))) = (x / (y * (x * y))) * (y * z)
    ]]></literal>
    <justification jstring="[para(29349(a,1),40200(a,1,2))].">
      <j1 rule="para" parents="29349 40200"/>
    </justification>
  </clause>

  <clause id="40215">
    <literal><![CDATA[
      L(x \ y,x,a(x,x,z)) = ((z * x) \ z) \ (((z * x) \ (z / x)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30374,a(flip),b,40212,a)].">
      <j1 rule="hyper" parents="64 30374 40212"/>
    </justification>
  </clause>

  <clause id="40216">
    <literal><![CDATA[
      ((x * y) \ (x / y)) * z = ((x * y) \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(145,a,37534,a(flip),b,40215,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 37534 40215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40218">
    <literal><![CDATA[
      ((x * y) \ (x / y)) * (y * z) = ((x * y) \ x) * L(z,u,a(u,u,w))
    ]]></literal>
    <justification jstring="[para(37537(a,2),40216(a,2,2))].">
      <j1 rule="para" parents="37537 40216"/>
    </justification>
  </clause>

  <clause id="40219">
    <literal><![CDATA[
      ((x * y) \ (x / y)) * (y * z) = y * ((y \ ((x * y) \ x)) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,35505,a(flip),b,40218,a),flip(a)].">
      <j1 rule="hyper" parents="373 35505 40218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40221">
    <literal><![CDATA[
      x * ((x \ ((y * x) \ y)) * ((x \ 1) \ z)) = (x * ((y * x) \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,40184,a(flip),b,40219,a),flip(a)].">
      <j1 rule="hyper" parents="64 40184 40219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40222">
    <literal><![CDATA[
      ((x * y) \ x) * ((y \ 1) \ z) = (y * ((x * y) \ x)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,37558,a(flip),b,40221,a)].">
      <j1 rule="hyper" parents="64 37558 40221"/>
    </justification>
  </clause>

  <clause id="40223">
    <literal><![CDATA[
      (x / y) * (z \ (z / (y \ 1))) = (y * ((z * y) \ z)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,30931,a(flip),b,40222,a)].">
      <j1 rule="hyper" parents="64 30931 40222"/>
    </justification>
  </clause>

  <clause id="40224">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * z = a(y,x,x \ 1) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,37806,a(flip),b,40223,a),flip(a)].">
      <j1 rule="hyper" parents="64 37806 40223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40225">
    <literal><![CDATA[
      (a(x,y,y \ 1) \ 1) * z = a(x,y,y \ 1) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,33363,a,b,40224,a)].">
      <j1 rule="hyper" parents="64 33363 40224"/>
    </justification>
  </clause>

  <clause id="40226">
    <literal><![CDATA[
      a(x,y,(a(z,u,u \ 1) \ w) * v5) = a(x,y,v5 * (w * a(z,u,u)))
    ]]></literal>
    <justification jstring="[para(40225(a,1),39979(a,1,3,1))].">
      <j1 rule="para" parents="40225 39979"/>
    </justification>
  </clause>

  <clause id="40227">
    <literal><![CDATA[
      a(x,y,(a(z,u,u \ 1) \ u) * w) = a(x,y,w * L(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,39975,a(flip),b,40226,a),flip(a)].">
      <j1 rule="hyper" parents="373 39975 40226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40228">
    <literal><![CDATA[
      (x \ (x / y)) * L(z,y,a(y,y,x)) = (x \ ((x / y) / y)) * (y * z)
    ]]></literal>
    <justification jstring="[para(30374(a,1),40213(a,1,2))].">
      <j1 rule="para" parents="30374 40213"/>
    </justification>
  </clause>

  <clause id="40229">
    <literal><![CDATA[
      (x \ ((x / y) / y)) * (y * z) = y * ((y \ (x \ (x / y))) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34247,a(flip),b,40228,a),flip(a)].">
      <j1 rule="hyper" parents="64 34247 40228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40230">
    <literal><![CDATA[
      x * ((x \ (y \ (y / x))) * (x \ z)) = (y \ ((y / x) / x)) * z
    ]]></literal>
    <justification jstring="[hyper(397,a,40229,a),flip(a)].">
      <j1 rule="hyper" parents="397 40229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40231">
    <literal><![CDATA[
      (x \ ((x / y) / y)) * z = (x \ (x / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37556,a(flip),b,40230,a),flip(a)].">
      <j1 rule="hyper" parents="64 37556 40230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40232">
    <literal><![CDATA[
      (x \ (x / (y \ ((y / z) / z)))) \ x = (y \ (y / z)) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,38505,a,b,40231,a)].">
      <j1 rule="hyper" parents="64 38505 40231"/>
    </justification>
  </clause>

  <clause id="40234">
    <literal><![CDATA[
      (x \ (x * (y \ ((y * z) * z)))) \ x = (y \ (y / z)) * (z \ x)
    ]]></literal>
    <justification jstring="[para(38497(a,1),40232(a,1,1,2))].">
      <j1 rule="para" parents="38497 40232"/>
    </justification>
  </clause>

  <clause id="40235">
    <literal><![CDATA[
      (x \ ((x * y) * y)) \ z = (x \ (x / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(9(a,1),40234(a,1,1))].">
      <j1 rule="para" parents="9 40234"/>
    </justification>
  </clause>

  <clause id="40237">
    <literal><![CDATA[
      a(x,y,(((z * u) * u) / z) \ w) = a(x,y,(z \ (z / u)) * (u \ w))
    ]]></literal>
    <justification jstring="[para(40235(a,1),27389(a,2,3))].">
      <j1 rule="para" parents="40235 27389"/>
    </justification>
  </clause>

  <clause id="40238">
    <literal><![CDATA[
      a(x,y,(z / ((z / u) / u)) \ w) = a(x,y,(z \ (z / u)) * (u \ w))
    ]]></literal>
    <justification jstring="[para(35282(a,1),40237(a,1,3,1))].">
      <j1 rule="para" parents="35282 40237"/>
    </justification>
  </clause>

  <clause id="40239">
    <literal><![CDATA[
      (x / (x * y)) * L(z,y,a(y,y,x)) = (x / (y * (x * y))) * (y * z)
    ]]></literal>
    <justification jstring="[para(30374(a,1),40214(a,1,2))].">
      <j1 rule="para" parents="30374 40214"/>
    </justification>
  </clause>

  <clause id="40240">
    <literal><![CDATA[
      (x / (y * (x * y))) * (y * z) = y * ((y \ (x / (x * y))) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33656,a(flip),b,40239,a),flip(a)].">
      <j1 rule="hyper" parents="64 33656 40239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40241">
    <literal><![CDATA[
      x * ((x \ (y / (y * x))) * (x \ z)) = (y / (x * (y * x))) * z
    ]]></literal>
    <justification jstring="[hyper(397,a,40240,a),flip(a)].">
      <j1 rule="hyper" parents="397 40240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40242">
    <literal><![CDATA[
      (x / (y * (x * y))) * z = (x / (x * y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37555,a(flip),b,40241,a),flip(a)].">
      <j1 rule="hyper" parents="64 37555 40241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40243">
    <literal><![CDATA[
      ((x * y) \ T(x / y,y \ 1)) * ((1 / (y \ (x / (x * y)))) * z) = (u / (w * (u * w))) * (w * ((u / (u * w)) \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,38180,a,b,40242,a)].">
      <j1 rule="hyper" parents="373 38180 40242"/>
    </justification>
  </clause>

  <clause id="40245">
    <literal><![CDATA[
      (x \ y) \ (K(x \ y,y \ x) * ((y \ x) * z)) = (y \ (x / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(4338(a,1),40148(a,1,2,1))].">
      <j1 rule="para" parents="4338 40148"/>
    </justification>
  </clause>

  <clause id="40246">
    <literal><![CDATA[
      (x \ y) \ ((y \ x) * (K(x \ y,y \ x) * z)) = (y \ (x / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(4534(a,1),40245(a,1,2))].">
      <j1 rule="para" parents="4534 40245"/>
    </justification>
  </clause>

  <clause id="40247">
    <literal><![CDATA[
      (x \ y) \ ((1 / (1 / (y \ x))) * z) = (y \ (x / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(4319(a,1),40246(a,1,2))].">
      <j1 rule="para" parents="4319 40246"/>
    </justification>
  </clause>

  <clause id="40248">
    <literal><![CDATA[
      (x \ (y / (y \ x))) * z = (x \ y) * ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33105,a(flip),b,40247,a),flip(a)].">
      <j1 rule="hyper" parents="64 33105 40247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40249">
    <literal><![CDATA[
      x \ ((y \ z) * ((z \ y) \ x)) = T(y \ (z / (z \ y)),x)
    ]]></literal>
    <justification jstring="[hyper(493,a,33105,a(flip),b,40247,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="493 33105 40247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40250">
    <literal><![CDATA[
      (x \ (y / (y \ x))) \ z = (y \ x) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,74,a(flip),b,40248,a)].">
      <j1 rule="hyper" parents="139 74 40248"/>
    </justification>
  </clause>

  <clause id="40251">
    <literal><![CDATA[
      a(x,y,(z \ ((z \ u) * u)) * w) = a(x,y,(z \ u) * ((u \ z) \ w))
    ]]></literal>
    <justification jstring="[para(40248(a,1),33714(a,1,3)),flip(a)].">
      <j1 rule="para" parents="40248 33714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40252">
    <literal><![CDATA[
      x * T(T(y \ (z / (z \ y)),x),z \ y) = T(y \ z,z \ y) * ((z \ y) \ x)
    ]]></literal>
    <justification jstring="[para(40249(a,1),26696(a,1,2,1))].">
      <j1 rule="para" parents="40249 26696"/>
    </justification>
  </clause>

  <clause id="40253">
    <literal><![CDATA[
      a(x,y,((z * (u \ z)) \ u) * w) = a(x,y,(z \ u) * ((u \ z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,38183,a,b,40251,a)].">
      <j1 rule="hyper" parents="64 38183 40251"/>
    </justification>
  </clause>

  <clause id="40254">
    <literal><![CDATA[
      T(x \ y,y \ x) * ((y \ x) \ z) = z * T((y \ x) \ (x \ y),z)
    ]]></literal>
    <justification jstring="[para(40133(a,1),40252(a,1,2)),flip(a)].">
      <j1 rule="para" parents="40133 40252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40255">
    <literal><![CDATA[
      T(x \ y,y \ x) * ((y \ x) \ z) = ((y \ x) \ (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,115,a(flip),b,40254,a),flip(a)].">
      <j1 rule="hyper" parents="373 115 40254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40256">
    <literal><![CDATA[
      (x \ L(1 / x,x,y)) \ K((y * x) \ (x \ y),y * x) = ((y / x) / (y * x)) \ 1
    ]]></literal>
    <justification jstring="[para(36134(a,1),40127(a,1,2))].">
      <j1 rule="para" parents="36134 40127"/>
    </justification>
  </clause>

  <clause id="40257">
    <literal><![CDATA[
      (x \ L(1 / x,x,y)) \ K(x \ (y \ (x \ y)),y * x) = ((y / x) / (y * x)) \ 1
    ]]></literal>
    <justification jstring="[para(14716(a,1),40256(a,1,2))].">
      <j1 rule="para" parents="14716 40256"/>
    </justification>
  </clause>

  <clause id="40258">
    <literal><![CDATA[
      (x \ L(1 / x,x,y)) \ K(y * x,x * T(x,y)) = ((y / x) / (y * x)) \ 1
    ]]></literal>
    <justification jstring="[para(38836(a,1),40257(a,1,2))].">
      <j1 rule="para" parents="38836 40257"/>
    </justification>
  </clause>

  <clause id="40259">
    <literal><![CDATA[
      (x \ L(1 / x,x,y)) \ K(x * y,x * x) = ((y / x) / (y * x)) \ 1
    ]]></literal>
    <justification jstring="[para(17606(a,1),40258(a,1,2))].">
      <j1 rule="para" parents="17606 40258"/>
    </justification>
  </clause>

  <clause id="40260">
    <literal><![CDATA[
      x * (L(x \ 1,x,y) \ K(x * y,x * x)) = ((y / x) / (y * x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,37911,a(flip),b,40259,a)].">
      <j1 rule="hyper" parents="64 37911 40259"/>
    </justification>
  </clause>

  <clause id="40261">
    <literal><![CDATA[
      (x \ (y / (y \ x))) * R(z,y * ((x \ y) * x),z) = T(z * (1 / (y \ (x / (x \ y)))),z)
    ]]></literal>
    <justification jstring="[para(28876(a,1),40169(a,1,2))].">
      <j1 rule="para" parents="28876 40169"/>
    </justification>
  </clause>

  <clause id="40262">
    <literal><![CDATA[
      a((x * (x * y)) \ y,y \ L(y,x,x),y) = ((y / (x * y)) / x) * ((x * (x * y)) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32221,a(flip),b,40207,a)].">
      <j1 rule="hyper" parents="64 32221 40207"/>
    </justification>
  </clause>

  <clause id="40263">
    <literal><![CDATA[
      a((x * (x * y)) \ y,y * L(y,x,x),y) = ((y / (x * y)) / x) * ((x * (x * y)) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35684,a(flip),b,40262,a)].">
      <j1 rule="hyper" parents="64 35684 40262"/>
    </justification>
  </clause>

  <clause id="40264">
    <literal><![CDATA[
      ((x / (y * x)) / y) * ((y * (y * x)) / x) = a((y * (y * x)) \ x,a(y,y,x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32040,a(flip),b,40263,a),flip(a)].">
      <j1 rule="hyper" parents="64 32040 40263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40265">
    <literal><![CDATA[
      ((x / (y * x)) / y) * ((y * (y * x)) / x) = a((y * (y * x)) \ x,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,32892,a(flip),b,40264,a),flip(a)].">
      <j1 rule="hyper" parents="373 32892 40264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40266">
    <literal><![CDATA[
      ((x / (y * x)) / y) * ((y * (y * x)) / x) = a(L(x,y,y) \ x,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,26914,a(flip),b,40265,a),flip(a)].">
      <j1 rule="hyper" parents="373 26914 40265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40267">
    <literal><![CDATA[
      ((x / (y * x)) / y) * ((y * (y * x)) / x) = a(a(y,y,x),x,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(1243(a,1),40266(a,2,1))].">
      <j1 rule="para" parents="1243 40266"/>
    </justification>
  </clause>

  <clause id="40268">
    <literal><![CDATA[
      (x \ (y / (y \ x))) * R(z,y * y,z) = T(z * (1 / (y \ (x / (x \ y)))),z)
    ]]></literal>
    <justification jstring="[para(26503(a,1),40261(a,1,2))].">
      <j1 rule="para" parents="26503 40261"/>
    </justification>
  </clause>

  <clause id="40269">
    <literal><![CDATA[
      T(x * (1 / (y \ (z / (z \ y)))),x) = (z \ (y / (y \ z))) * x
    ]]></literal>
    <justification jstring="[para(654(a,1),40268(a,1,2)),flip(a)].">
      <j1 rule="para" parents="654 40268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40271">
    <literal><![CDATA[
      T(x * (1 / (y \ (z / (z \ y)))),x) = (z \ y) * ((y \ z) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,40248,a(flip),b,40269,a),flip(a)].">
      <j1 rule="hyper" parents="373 40248 40269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40272">
    <literal><![CDATA[
      T(x * (y \ (z / (z \ y))),x) = (y \ z) * ((z \ y) \ x)
    ]]></literal>
    <justification jstring="[para(40167(a,1),40271(a,1,1,2))].">
      <j1 rule="para" parents="40167 40271"/>
    </justification>
  </clause>

  <clause id="40273">
    <literal><![CDATA[
      R(x,y \ (z / (z \ y)),x) * (T(y \ (z / (z \ y)),x) * u) = ((y \ z) * ((z \ y) \ x)) * L(u,y \ (z / (z \ y)),x)
    ]]></literal>
    <justification jstring="[para(40272(a,1),25959(a,1,1)),flip(a)].">
      <j1 rule="para" parents="40272 25959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40274">
    <literal><![CDATA[
      L(((x \ y) \ (x * y)) \ z,(x \ y) \ (x * y),a(x,x,y)) = ((x * y) \ (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,30045,a(flip),b,40162,a)].">
      <j1 rule="hyper" parents="64 30045 40162"/>
    </justification>
  </clause>

  <clause id="40275">
    <literal><![CDATA[
      L(((x \ y) \ (x * y)) \ z,a(x,x,y),a(x,x,y)) = ((x * y) \ (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,31048,a(flip),b,40274,a)].">
      <j1 rule="hyper" parents="64 31048 40274"/>
    </justification>
  </clause>

  <clause id="40276">
    <literal><![CDATA[
      ((x \ y) \ (x * y)) \ z = ((x * y) \ (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,37811,a(flip),b,40275,a)].">
      <j1 rule="hyper" parents="64 37811 40275"/>
    </justification>
  </clause>

  <clause id="40277">
    <literal><![CDATA[
      ((x * y) \ (x \ y)) \ z = ((x \ y) \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(395,a,40276,a),flip(a)].">
      <j1 rule="hyper" parents="395 40276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40279">
    <literal><![CDATA[
      (T(x \ y,x * x) / (x * y)) \ z = ((x \ y) \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(34761(a,2),40277(a,1,1))].">
      <j1 rule="para" parents="34761 40277"/>
    </justification>
  </clause>

  <clause id="40280">
    <literal><![CDATA[
      (T(x \ y,x * x) / (x * y)) \ z = ((x \ T(y,x)) \ (y * x)) * z
    ]]></literal>
    <justification jstring="[para(14906(a,2),40279(a,2,1))].">
      <j1 rule="para" parents="14906 40279"/>
    </justification>
  </clause>

  <clause id="40281">
    <literal><![CDATA[
      (T(x \ y,x * x) / (x * y)) \ z = K(x,y) * (((x \ y) \ (y * x)) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,24979,a,b,40280,a),flip(a)].">
      <j1 rule="hyper" parents="373 24979 40280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40282">
    <literal><![CDATA[
      ((x * y) \ (y \ x)) \ z = ((y \ x) \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(35,a,31704,a(flip),b,40281,a(flip))].">
      <j1 rule="hyper" parents="35 31704 40281"/>
    </justification>
  </clause>

  <clause id="40283">
    <literal><![CDATA[
      ((x \ y) \ (y * x)) \ z = ((y * x) \ (x \ y)) * z
    ]]></literal>
    <justification jstring="[hyper(395,a,40282,a),flip(a)].">
      <j1 rule="hyper" parents="395 40282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40284">
    <literal><![CDATA[
      ((((x \ y) \ 1) * y) \ x) * (((x \ y) \ 1) * ((x \ y) \ z)) = ((y / (x / y)) \ x) * z
    ]]></literal>
    <justification jstring="[para(40147(a,1),40144(a,2,1))].">
      <j1 rule="para" parents="40147 40144"/>
    </justification>
  </clause>

  <clause id="40285">
    <literal><![CDATA[
      ((x \ y) * (x / y)) * (((x \ y) \ 1) * ((x \ y) \ z)) = ((y / (x / y)) \ x) * z
    ]]></literal>
    <justification jstring="[para(37947(a,1),40284(a,1,1))].">
      <j1 rule="para" parents="37947 40284"/>
    </justification>
  </clause>

  <clause id="40286">
    <literal><![CDATA[
      L(((x / (y / x)) \ y) \ z,(y \ x) * (y / x),(y \ x) * (x \ y)) = (1 / (((y \ x) \ 1) * (y / x))) * z
    ]]></literal>
    <justification jstring="[hyper(29071,a,40145,a)].">
      <j1 rule="hyper" parents="29071 40145"/>
    </justification>
  </clause>

  <clause id="40287">
    <literal><![CDATA[
      L(((x * y) \ (y / x)) \ z,x * ((x * y) \ y),x * (y \ (x \ y))) = (1 / ((x \ 1) * ((x * y) \ y))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,29186,a(flip),b,40159,a)].">
      <j1 rule="hyper" parents="64 29186 40159"/>
    </justification>
  </clause>

  <clause id="40288">
    <literal><![CDATA[
      L(((x / (y / x)) \ y) \ z,(y \ x) * (y / x),a(y,y * x,x)) = (1 / (((y \ x) \ 1) * (y / x))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,35693,a(flip),b,40286,a)].">
      <j1 rule="hyper" parents="64 35693 40286"/>
    </justification>
  </clause>

  <clause id="40289">
    <literal><![CDATA[
      L(((x / (y / x)) \ y) \ z,(y \ x) * (x \ y),a(y,y * x,x)) = (1 / (((y \ x) \ 1) * (y / x))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,29547,a(flip),b,40288,a)].">
      <j1 rule="hyper" parents="64 29547 40288"/>
    </justification>
  </clause>

  <clause id="40290">
    <literal><![CDATA[
      (1 / (((x \ y) \ 1) * (x / y))) * z = ((y / (x / y)) \ x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,37869,a(flip),b,40289,a),flip(a)].">
      <j1 rule="hyper" parents="64 37869 40289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40292">
    <literal><![CDATA[
      (1 / ((x / (y / x)) \ y)) * z = ((x / (y / x)) \ y) \ z
    ]]></literal>
    <justification jstring="[para(40142(a,1),40290(a,1,1,2))].">
      <j1 rule="para" parents="40142 40290"/>
    </justification>
  </clause>

  <clause id="40293">
    <literal><![CDATA[
      1 / ((x / (y / x)) \ y) = y \ (x / (y / x))
    ]]></literal>
    <justification jstring="[hyper(141,a,40292,a,b,35941,a(flip))].">
      <j1 rule="hyper" parents="141 40292 35941"/>
    </justification>
  </clause>

  <clause id="40294">
    <literal><![CDATA[
      ((x / (y / x)) \ y) \ z = (y \ (x / (y / x))) * z
    ]]></literal>
    <justification jstring="[para(40293(a,1),40292(a,1,1)),flip(a)].">
      <j1 rule="para" parents="40293 40292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40295">
    <literal><![CDATA[
      (x \ (y / (x / y))) \ z = ((y / (x / y)) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(395,a,40294,a),flip(a)].">
      <j1 rule="hyper" parents="395 40294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40296">
    <literal><![CDATA[
      L(((x * y) \ (y / x)) \ z,x * ((x * y) \ y),a(x,x,y)) = (1 / ((x \ 1) * ((x * y) \ y))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,30112,a(flip),b,40287,a)].">
      <j1 rule="hyper" parents="64 30112 40287"/>
    </justification>
  </clause>

  <clause id="40297">
    <literal><![CDATA[
      L(((x * y) \ (y / x)) \ z,x * (y \ (x \ y)),a(x,x,y)) = (1 / ((x \ 1) * ((x * y) \ y))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,29764,a(flip),b,40296,a)].">
      <j1 rule="hyper" parents="64 29764 40296"/>
    </justification>
  </clause>

  <clause id="40298">
    <literal><![CDATA[
      L(((x * y) \ (y / x)) \ z,a(x,x,y),a(x,x,y)) = (1 / ((x \ 1) * ((x * y) \ y))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,30115,a(flip),b,40297,a)].">
      <j1 rule="hyper" parents="64 30115 40297"/>
    </justification>
  </clause>

  <clause id="40299">
    <literal><![CDATA[
      (1 / ((x \ 1) * ((x * y) \ y))) * z = ((x * y) \ (y / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,37811,a(flip),b,40298,a),flip(a)].">
      <j1 rule="hyper" parents="64 37811 40298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40301">
    <literal><![CDATA[
      (1 / ((x * y) \ (y / x))) * z = ((x * y) \ (y / x)) \ z
    ]]></literal>
    <justification jstring="[para(40155(a,1),40299(a,1,1,2))].">
      <j1 rule="para" parents="40155 40299"/>
    </justification>
  </clause>

  <clause id="40302">
    <literal><![CDATA[
      ((x * y) \ (y / x)) \ z = ((y / x) \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(40160(a,1),40301(a,1,1)),flip(a)].">
      <j1 rule="para" parents="40160 40301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40303">
    <literal><![CDATA[
      L(((x / y) \ (y * x)) * z,((x / (y \ 1)) / x) / y,y) = R((y * x) \ x,y,y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(40302(a,1),40156(a,1,1))].">
      <j1 rule="para" parents="40302 40156"/>
    </justification>
  </clause>

  <clause id="40304">
    <literal><![CDATA[
      L(((x / y) \ (y * x)) * z,y * ((y * x) \ x),y) = R((y * x) \ x,y,y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(36649(a,1),40303(a,1,2))].">
      <j1 rule="para" parents="36649 40303"/>
    </justification>
  </clause>

  <clause id="40305">
    <literal><![CDATA[
      L(((x / y) \ (y * x)) * z,y * (x \ (y \ x)),y) = R((y * x) \ x,y,y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29764,a(flip),b,40304,a)].">
      <j1 rule="hyper" parents="64 29764 40304"/>
    </justification>
  </clause>

  <clause id="40306">
    <literal><![CDATA[
      L(((x / y) \ (y * x)) * z,a(y,y,x),y) = R((y * x) \ x,y,y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30115,a(flip),b,40305,a)].">
      <j1 rule="hyper" parents="64 30115 40305"/>
    </justification>
  </clause>

  <clause id="40307">
    <literal><![CDATA[
      L(((x / y) \ (y * x)) * z,y,a(y,y,x)) = R((y * x) \ x,y,y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30415,a(flip),b,40306,a)].">
      <j1 rule="hyper" parents="64 30415 40306"/>
    </justification>
  </clause>

  <clause id="40308">
    <literal><![CDATA[
      R((x * y) \ y,x,x) \ (x * z) = ((y / x) \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,37534,a(flip),b,40307,a),flip(a)].">
      <j1 rule="hyper" parents="64 37534 40307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40310">
    <literal><![CDATA[
      L(K(x,y) / y,y,x) \ (y * z) = ((x / y) \ (y * x)) * z
    ]]></literal>
    <justification jstring="[para(25886(a,1),40308(a,1,1))].">
      <j1 rule="para" parents="25886 40308"/>
    </justification>
  </clause>

  <clause id="40311">
    <literal><![CDATA[
      x * (L(x \ K(y,x),x,y) \ z) = ((y / x) \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,38296,a(flip),b,40310,a)].">
      <j1 rule="hyper" parents="64 38296 40310"/>
    </justification>
  </clause>

  <clause id="40312">
    <literal><![CDATA[
      x * (((y * x) \ T(y,x)) \ z) = ((y / x) \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(5768(a,1),40311(a,1,2,1))].">
      <j1 rule="para" parents="5768 40311"/>
    </justification>
  </clause>

  <clause id="40313">
    <literal><![CDATA[
      ((x / y) \ (y * x)) * z = y * (((y * x) \ x) \ z)
    ]]></literal>
    <justification jstring="[para(6981(a,1),40312(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6981 40312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40314">
    <literal><![CDATA[
      ((x * y) \ (y / x)) \ z = x * (((x * y) \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40302,a,b,40313,a)].">
      <j1 rule="hyper" parents="64 40302 40313"/>
    </justification>
  </clause>

  <clause id="40315">
    <literal><![CDATA[
      L(x * (((x * y) \ y) \ z),(x * y) \ (x \ y),x * y) = (y / x) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(40314(a,1),29680(a,1,1))].">
      <j1 rule="para" parents="40314 29680"/>
    </justification>
  </clause>

  <clause id="40316">
    <literal><![CDATA[
      L(x * (((x * y) \ y) \ z),a(x,x,y),x * y) = (y / x) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30311,a(flip),b,40315,a)].">
      <j1 rule="hyper" parents="64 30311 40315"/>
    </justification>
  </clause>

  <clause id="40317">
    <literal><![CDATA[
      T(x \ (y \ x),K(z,u)) / (x / (x * T(x \ (y \ x),K(z,u)))) = T((y \ x) / y,x) / x
    ]]></literal>
    <justification jstring="[para(36065(a,1),40191(a,2,1))].">
      <j1 rule="para" parents="36065 40191"/>
    </justification>
  </clause>

  <clause id="40318">
    <literal><![CDATA[
      T(x \ (y \ x),K(z,u)) / (x / (x * T(x \ (y \ x),K(z,u)))) = x \ ((y \ x) / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,26690,a(flip),b,40317,a),flip(a)].">
      <j1 rule="hyper" parents="373 26690 40317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40320">
    <literal><![CDATA[
      T(x \ (y \ x),K(z,u)) / (x / (T(y,K(z,u)) \ x)) = x \ ((y \ x) / y)
    ]]></literal>
    <justification jstring="[para(17704(a,1),40318(a,1,2,2))].">
      <j1 rule="para" parents="17704 40318"/>
    </justification>
  </clause>

  <clause id="40321">
    <literal><![CDATA[
      T(x \ (y \ x),K(z,u)) / T(y,K(z,u)) = x \ ((y \ x) / y)
    ]]></literal>
    <justification jstring="[para(79(a,1),40320(a,1,2))].">
      <j1 rule="para" parents="79 40320"/>
    </justification>
  </clause>

  <clause id="40322">
    <literal><![CDATA[
      T((x \ (y \ x)) / y,K(z,u)) = x \ ((y \ x) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26987,a(flip),b,40321,a)].">
      <j1 rule="hyper" parents="64 26987 40321"/>
    </justification>
  </clause>

  <clause id="40324">
    <literal><![CDATA[
      (x \ (y \ x)) / y = x \ ((y \ x) / y)
    ]]></literal>
    <justification jstring="[hyper(19218,a,40322,a)].">
      <j1 rule="hyper" parents="19218 40322"/>
    </justification>
  </clause>

  <clause id="40325">
    <literal><![CDATA[
      (x \ (y \ x)) * (y \ 1) = x \ ((y \ x) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26766,a,b,40324,a)].">
      <j1 rule="hyper" parents="64 26766 40324"/>
    </justification>
  </clause>

  <clause id="40326">
    <literal><![CDATA[
      a(x,y,(z \ (u \ (z \ u))) \ w) = a(x,y,(u \ ((z \ u) / z)) \ w)
    ]]></literal>
    <justification jstring="[para(40324(a,1),27389(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="40324 27389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40327">
    <literal><![CDATA[
      K(x,y \ 1) * ((x \ ((y \ x) / y)) * z) = (y \ (x / (y * x))) * z
    ]]></literal>
    <justification jstring="[para(40324(a,1),31685(a,1,2,1))].">
      <j1 rule="para" parents="40324 31685"/>
    </justification>
  </clause>

  <clause id="40328">
    <literal><![CDATA[
      L((x \ 1) \ ((y \ (x \ y)) \ z),x,x) = (y \ ((x \ y) / x)) \ z
    ]]></literal>
    <justification jstring="[para(40325(a,1),37584(a,2,1))].">
      <j1 rule="para" parents="40325 37584"/>
    </justification>
  </clause>

  <clause id="40329">
    <literal><![CDATA[
      (x \ ((y \ x) / y)) \ z = y * ((x \ (y \ x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(1155,a,40328,a),flip(a)].">
      <j1 rule="hyper" parents="1155 40328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40330">
    <literal><![CDATA[
      (x \ ((y \ x) / y)) * z = (x \ (y \ x)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(733,a,40329,a)].">
      <j1 rule="hyper" parents="733 40329"/>
    </justification>
  </clause>

  <clause id="40331">
    <literal><![CDATA[
      a(x,y,(z \ ((u \ z) / u)) \ w) = a(x,y,((z \ (u \ z)) \ u) * w)
    ]]></literal>
    <justification jstring="[para(38970(a,1),40326(a,1,3)),flip(a)].">
      <j1 rule="para" parents="38970 40326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40332">
    <literal><![CDATA[
      K(x,y \ 1) * ((x \ (y \ x)) * (y \ z)) = (y \ (x / (y * x))) * z
    ]]></literal>
    <justification jstring="[para(40330(a,1),40327(a,1,2))].">
      <j1 rule="para" parents="40330 40327"/>
    </justification>
  </clause>

  <clause id="40333">
    <literal><![CDATA[
      a(x,y,((z \ (u \ z)) \ u) * w) = a(x,y,u * ((z \ (u \ z)) \ w))
    ]]></literal>
    <justification jstring="[para(40329(a,1),40331(a,1,3)),flip(a)].">
      <j1 rule="para" parents="40329 40331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40334">
    <literal><![CDATA[
      (x \ (y / (x * y))) * z = ((x \ y) / y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,6557,a(flip),b,40332,a),flip(a)].">
      <j1 rule="hyper" parents="64 6557 40332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40335">
    <literal><![CDATA[
      x \ ((x \ y) / (x * (x \ y))) = (x \ (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,12,a(flip),b,40334,a),flip(a)].">
      <j1 rule="hyper" parents="142 12 40334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40336">
    <literal><![CDATA[
      (x \ (x \ y)) / y = x \ ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(10(a,1),40335(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 40335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40337">
    <literal><![CDATA[
      T((x \ ((x \ y) / y)) \ 1,y) = (y \ (x \ (x \ y))) \ 1
    ]]></literal>
    <justification jstring="[para(40336(a,1),38853(a,1,1,1))].">
      <j1 rule="para" parents="40336 38853"/>
    </justification>
  </clause>

  <clause id="40338">
    <literal><![CDATA[
      a(x,y,((z \ (z \ u)) \ u) * w) = a(x,y,z * ((u \ (z \ u)) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,35881,a(flip),b,40333,a)].">
      <j1 rule="hyper" parents="64 35881 40333"/>
    </justification>
  </clause>

  <clause id="40339">
    <literal><![CDATA[
      ((x * y) \ T(x / y,y \ 1)) * ((1 / (y \ (x / (x * y)))) * z) = (x / (y * (x * y))) * ((y / (x / (x * y))) * z)
    ]]></literal>
    <justification jstring="[para(38177(a,1),40201(a,2,2,1))].">
      <j1 rule="para" parents="38177 40201"/>
    </justification>
  </clause>

  <clause id="40340">
    <literal><![CDATA[
      (x / (y / (y * x))) * z = x * ((y / (y * x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(35,a,40243,a(flip),b,40339,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 40243 40339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40341">
    <literal><![CDATA[
      x * (((x \ y) / ((x \ y) * x)) \ z) = (x / ((y / x) / y)) * z
    ]]></literal>
    <justification jstring="[para(10252(a,1),40340(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10252 40340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40343">
    <literal><![CDATA[
      (x / ((y / x) / y)) * z = x * (((y / x) / y) \ z)
    ]]></literal>
    <justification jstring="[para(10252(a,1),40341(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10252 40341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40344">
    <literal><![CDATA[
      R(x,y \ (z / (z \ y)),x) * (T(y \ (z / (z \ y)),x) * u) = ((y \ z) * ((z \ y) \ x)) * L(u,y \ ((z \ y) \ z),x)
    ]]></literal>
    <justification jstring="[para(29552(a,1),40273(a,2,2))].">
      <j1 rule="para" parents="29552 40273"/>
    </justification>
  </clause>

  <clause id="40345">
    <literal><![CDATA[
      R(x,y \ (z / (z \ y)),x) * (T(y \ (z / (z \ y)),x) * u) = ((y \ z) * ((z \ y) \ x)) * L(u,y \ ((y \ z) * z),x)
    ]]></literal>
    <justification jstring="[para(33700(a,1),40344(a,2,2))].">
      <j1 rule="para" parents="33700 40344"/>
    </justification>
  </clause>

  <clause id="40346">
    <literal><![CDATA[
      R(x,y \ (z / (z \ y)),x) * (T(y \ (z / (z \ y)),x) * u) = ((y \ z) * ((z \ y) \ x)) * L(u,a(z,z * y,y),x)
    ]]></literal>
    <justification jstring="[para(35700(a,1),40345(a,2,2))].">
      <j1 rule="para" parents="35700 40345"/>
    </justification>
  </clause>

  <clause id="40347">
    <literal><![CDATA[
      R(x,y \ (x / (x \ y)),x) * (T(y \ (x / (x \ y)),x) * z) = ((y \ x) * ((x \ y) \ x)) * L(z,x,a(x,x * y,y))
    ]]></literal>
    <justification jstring="[para(30415(a,1),40346(a,2,2))].">
      <j1 rule="para" parents="30415 40346"/>
    </justification>
  </clause>

  <clause id="40348">
    <literal><![CDATA[
      L((((x / y) / x) * y) \ z,y * (((y \ 1) * x) \ x),y * (x \ (y \ x))) = (1 / ((y \ 1) * (((y \ 1) * x) \ x))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,31741,a(flip),b,40062,a)].">
      <j1 rule="hyper" parents="64 31741 40062"/>
    </justification>
  </clause>

  <clause id="40349">
    <literal><![CDATA[
      L((((x / y) / x) * y) \ z,y * (((y \ 1) * x) \ x),a(y,y,x)) = (1 / ((y \ 1) * (((y \ 1) * x) \ x))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,30112,a(flip),b,40348,a)].">
      <j1 rule="hyper" parents="64 30112 40348"/>
    </justification>
  </clause>

  <clause id="40350">
    <literal><![CDATA[
      L((((x / y) / x) * y) \ z,y * (x \ ((y \ 1) \ x)),a(y,y,x)) = (1 / ((y \ 1) * (((y \ 1) * x) \ x))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,29764,a(flip),b,40349,a)].">
      <j1 rule="hyper" parents="64 29764 40349"/>
    </justification>
  </clause>

  <clause id="40351">
    <literal><![CDATA[
      L((((x / y) / x) * y) \ z,(x \ (y \ x)) * y,a(y,y,x)) = (1 / ((y \ 1) * (((y \ 1) * x) \ x))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,31147,a(flip),b,40350,a)].">
      <j1 rule="hyper" parents="64 31147 40350"/>
    </justification>
  </clause>

  <clause id="40352">
    <literal><![CDATA[
      L((((x / y) / x) * y) \ z,a(y,y,x),a(y,y,x)) = (1 / ((y \ 1) * (((y \ 1) * x) \ x))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,30116,a(flip),b,40351,a)].">
      <j1 rule="hyper" parents="64 30116 40351"/>
    </justification>
  </clause>

  <clause id="40353">
    <literal><![CDATA[
      (1 / ((x \ 1) * (((x \ 1) * y) \ y))) * z = (((y / x) / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,37811,a(flip),b,40352,a),flip(a)].">
      <j1 rule="hyper" parents="64 37811 40352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40355">
    <literal><![CDATA[
      (1 / (((x / y) / x) * y)) * z = (((x / y) / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(26380(a,1),40353(a,1,1,2))].">
      <j1 rule="para" parents="26380 40353"/>
    </justification>
  </clause>

  <clause id="40356">
    <literal><![CDATA[
      (x \ (((1 / y) * x) * y)) * z = (((x / y) / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(36224(a,1),40355(a,1,1))].">
      <j1 rule="para" parents="36224 40355"/>
    </justification>
  </clause>

  <clause id="40357">
    <literal><![CDATA[
      (x \ (((1 / y) * x) * y)) \ z = (((x / y) / x) * y) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,9,a(flip),b,40356,a)].">
      <j1 rule="hyper" parents="139 9 40356"/>
    </justification>
  </clause>

  <clause id="40358">
    <literal><![CDATA[
      x * ((((y / x) / y) * x) \ z) = (((y / x) / y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(40356(a,1),37967(a,1,2))].">
      <j1 rule="para" parents="40356 37967"/>
    </justification>
  </clause>

  <clause id="40359">
    <literal><![CDATA[
      L(x,y \ ((((z / u) / z) * u) * w),v5) = L(x,y \ (a(u,u,z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(40357(a,1),31632(a,1,2,2))].">
      <j1 rule="para" parents="40357 31632"/>
    </justification>
  </clause>

  <clause id="40360">
    <literal><![CDATA[
      L(x,y \ (((z \ (z / u)) * u) * w),v5) = L(x,y \ (a(u,u,z) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29659,a(flip),b,40359,a)].">
      <j1 rule="hyper" parents="64 29659 40359"/>
    </justification>
  </clause>

  <clause id="40361">
    <literal><![CDATA[
      L(x,y \ ((a(z,u,u) \ 1) * w),v5) = L(x,y \ (a(u,u,z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(30493(a,1),40360(a,1,2,2,1))].">
      <j1 rule="para" parents="30493 40360"/>
    </justification>
  </clause>

  <clause id="40362">
    <literal><![CDATA[
      L(x,y \ (a(z,u,u) \ w),v5) = L(x,y \ (a(u,u,z) \ w),v5)
    ]]></literal>
    <justification jstring="[para(37824(a,1),40361(a,1,2,2))].">
      <j1 rule="para" parents="37824 40361"/>
    </justification>
  </clause>

  <clause id="40363">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) \ a(z,u,w)),T(1 / (1 / y),a(z,u,w))) = x * (T(1 / (1 / y),x / y) \ a(z,u,w))
    ]]></literal>
    <justification jstring="[para(28851(a,1),25062(a,2,2,1))].">
      <j1 rule="para" parents="28851 25062"/>
    </justification>
  </clause>

  <clause id="40364">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) \ a(z,u,w)),T(1 / (1 / y),a(z,u,w))) = x * (T(1 / (1 / y),y \ x) \ a(z,u,w))
    ]]></literal>
    <justification jstring="[para(7505(a,1),40363(a,2,2,1))].">
      <j1 rule="para" parents="7505 40363"/>
    </justification>
  </clause>

  <clause id="40366">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) \ a(z,u,w)),T(1 / (1 / y),a(z,u,w))) = x * (T(y,x * y) \ a(z,u,w))
    ]]></literal>
    <justification jstring="[para(8865(a,1),40364(a,2,2,1))].">
      <j1 rule="para" parents="8865 40364"/>
    </justification>
  </clause>

  <clause id="40367">
    <literal><![CDATA[
      T(x * (a(y,z,u) / w),T(1 / (1 / w),a(y,z,u))) = x * (T(w,x * w) \ a(y,z,u))
    ]]></literal>
    <justification jstring="[para(24638(a,1),40366(a,1,1,2))].">
      <j1 rule="para" parents="24638 40366"/>
    </justification>
  </clause>

  <clause id="40368">
    <literal><![CDATA[
      T(x * (a(y,z,u) / w),1 / (1 / w)) = x * (T(w,x * w) \ a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,19214,a(flip),b,40367,a)].">
      <j1 rule="hyper" parents="64 19214 40367"/>
    </justification>
  </clause>

  <clause id="40370">
    <literal><![CDATA[
      x * (T(y,x * y) \ a(z,u,w)) = T(x * (a(z,u,w) / y),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,3869,a(flip),b,40368,a),flip(a)].">
      <j1 rule="hyper" parents="64 3869 40368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40371">
    <literal><![CDATA[
      K(R(x * (y * y),z,z),y \ (y \ 1)) * ((x * ((y * y) * a(x,z,z))) \ x) = x / (x * ((y * y) * a(x,z,z)))
    ]]></literal>
    <justification jstring="[para(28686(a,1),28484(a,1,1))].">
      <j1 rule="para" parents="28686 28484"/>
    </justification>
  </clause>

  <clause id="40372">
    <literal><![CDATA[
      K(x * x,R(y * (x * x),z,z)) * ((y * ((x * x) * a(y,z,z))) \ y) = y / (y * ((x * x) * a(y,z,z)))
    ]]></literal>
    <justification jstring="[para(15871(a,1),40371(a,1,1))].">
      <j1 rule="para" parents="15871 40371"/>
    </justification>
  </clause>

  <clause id="40374">
    <literal><![CDATA[
      K(x * x,y * (x * x)) * ((y * ((x * x) * a(y,z,z))) \ y) = y / (y * ((x * x) * a(y,z,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,23495,a(flip),b,40372,a)].">
      <j1 rule="hyper" parents="64 23495 40372"/>
    </justification>
  </clause>

  <clause id="40376">
    <literal><![CDATA[
      K(x * x,y) * ((y * ((x * x) * a(y,z,z))) \ y) = y / (y * ((x * x) * a(y,z,z)))
    ]]></literal>
    <justification jstring="[para(7727(a,1),40374(a,1,1))].">
      <j1 rule="para" parents="7727 40374"/>
    </justification>
  </clause>

  <clause id="40377">
    <literal><![CDATA[
      K(x * x,y) * (R(y * (x * x),z,z) \ y) = y / (y * ((x * x) * a(y,z,z)))
    ]]></literal>
    <justification jstring="[para(16050(a,1),40376(a,1,2,1))].">
      <j1 rule="para" parents="16050 40376"/>
    </justification>
  </clause>

  <clause id="40378">
    <literal><![CDATA[
      K(x * x,y) * ((x * x) \ (R(y,z,z) \ y)) = y / (y * ((x * x) * a(y,z,z)))
    ]]></literal>
    <justification jstring="[para(2105(a,1),40377(a,1,2))].">
      <j1 rule="para" parents="2105 40377"/>
    </justification>
  </clause>

  <clause id="40379">
    <literal><![CDATA[
      (x * x) \ (R(T(y,x * x),z,z) \ y) = y / (y * ((x * x) * a(y,z,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,25431,a(flip),b,40378,a)].">
      <j1 rule="hyper" parents="64 25431 40378"/>
    </justification>
  </clause>

  <clause id="40380">
    <literal><![CDATA[
      (x * x) \ (a(y,z,z) \ K(x * x,y)) = y / (y * ((x * x) * a(y,z,z)))
    ]]></literal>
    <justification jstring="[para(25940(a,1),40379(a,1,2))].">
      <j1 rule="para" parents="25940 40379"/>
    </justification>
  </clause>

  <clause id="40381">
    <literal><![CDATA[
      (x * x) \ (a(y,z,z) \ K(x * x,y)) = y / R(y * (x * x),z,z)
    ]]></literal>
    <justification jstring="[para(16050(a,1),40380(a,2,2))].">
      <j1 rule="para" parents="16050 40380"/>
    </justification>
  </clause>

  <clause id="40382">
    <literal><![CDATA[
      x / R(x * (y * y),y,y) = (((x * y) * y) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,28266,a(flip),b,40381,a),flip(a)].">
      <j1 rule="hyper" parents="64 28266 40381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40383">
    <literal><![CDATA[
      (((x * y) * y) / x) \ 1 = x / ((x * y) * y)
    ]]></literal>
    <justification jstring="[para(1403(a,1),40382(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1403 40382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40384">
    <literal><![CDATA[
      (x / ((x / y) / y)) \ 1 = x / ((x * y) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35283,a(flip),b,40383,a)].">
      <j1 rule="hyper" parents="64 35283 40383"/>
    </justification>
  </clause>

  <clause id="40385">
    <literal><![CDATA[
      1 / (x / ((x / y) / y)) = x / ((x * y) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35326,a,b,40384,a)].">
      <j1 rule="hyper" parents="64 35326 40384"/>
    </justification>
  </clause>

  <clause id="40386">
    <literal><![CDATA[
      (x / ((x * y) * y)) \ 1 = x / ((x / y) / y)
    ]]></literal>
    <justification jstring="[hyper(215,a,40385,a)].">
      <j1 rule="hyper" parents="215 40385"/>
    </justification>
  </clause>

  <clause id="40387">
    <literal><![CDATA[
      (1 / T(T(x,y),z)) * ((R(T(T(x,y),z),x,u \ 1) * (1 / u)) * u) = a(1 / T(T(x,y),z),(1 / T(T(x,y),z)) \ u,u) \ 1
    ]]></literal>
    <justification jstring="[para(5107(a,1),29791(a,1,2,1,1))].">
      <j1 rule="para" parents="5107 29791"/>
    </justification>
  </clause>

  <clause id="40388">
    <literal><![CDATA[
      (a(a(x,x,y),z,u) \ a(x,x,y)) \ ((1 / a(x,x,y)) \ x) = (a(x,L(x,z,u),y) \ 1) \ (R(1 / x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(39286(a,1),31121(a,2,1))].">
      <j1 rule="para" parents="39286 31121"/>
    </justification>
  </clause>

  <clause id="40389">
    <literal><![CDATA[
      (a(a(x,x,y),z,u) \ a(x,x,y)) \ ((1 / a(x,x,y)) \ x) = (R(1 / x,x,y) \ 1) * a(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,39014,a(flip),b,40388,a),flip(a)].">
      <j1 rule="hyper" parents="373 39014 40388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40390">
    <literal><![CDATA[
      (a(a(x,x,y),z,u) \ a(x,x,y)) \ ((1 / a(x,x,y)) \ x) = R(1 / x,x,y) \ a(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,31746,a(flip),b,40389,a),flip(a)].">
      <j1 rule="hyper" parents="373 31746 40389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40391">
    <literal><![CDATA[
      (L(a(x,x,y) \ 1,z,u) \ 1) \ ((1 / a(x,x,y)) \ x) = R(1 / x,x,y) \ a(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(39318(a,1),40390(a,1,1))].">
      <j1 rule="para" parents="39318 40390"/>
    </justification>
  </clause>

  <clause id="40392">
    <literal><![CDATA[
      (L(a(x,x,y) \ 1,z,u) \ 1) \ (a(x,x,y) * x) = R(1 / x,x,y) \ a(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(29938(a,1),40391(a,1,2))].">
      <j1 rule="para" parents="29938 40391"/>
    </justification>
  </clause>

  <clause id="40393">
    <literal><![CDATA[
      (L(a(x,x,y) \ 1,z,u) \ 1) \ R(x,x,y) = R(1 / x,x,y) \ a(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(30053(a,1),40392(a,1,2))].">
      <j1 rule="para" parents="30053 40392"/>
    </justification>
  </clause>

  <clause id="40394">
    <literal><![CDATA[
      R(1 / x,x,y) \ a(x,L(x,z,u),y) = R(x,x,y) * L(a(x,x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,39172,a(flip),b,40393,a),flip(a)].">
      <j1 rule="hyper" parents="64 39172 40393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40395">
    <literal><![CDATA[
      R(1 / x,x,y) \ a(x,L(x,z,u),y) = x * a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,37932,a(flip),b,40394,a),flip(a)].">
      <j1 rule="hyper" parents="373 37932 40394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40396">
    <literal><![CDATA[
      1 / L(L(x * ((y * x) \ y),z,u),w,x) = L(x * L(x \ 1,x,y),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(9475(a,1),31329(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9475 31329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40398">
    <literal><![CDATA[
      L(x \ (a(y,z,u) \ x),x,(a(y,z,u) \ (x \ 1)) \ w) \ w = (x \ 1) * ((((x \ 1) \ (a(y,z,u) \ (x \ 1))) * (x \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(39913(a,1),33070(a,1,1))].">
      <j1 rule="para" parents="39913 33070"/>
    </justification>
  </clause>

  <clause id="40399">
    <literal><![CDATA[
      a((1 / (x * R(y,z,u))) \ T(w,v5),v6,v7) = a((L(y,z,u) * x) * ((x * R(y,z,u)) \ ((1 / (x * R(y,z,u))) \ w)),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(32447,a,34660,a),flip(a)].">
      <j1 rule="hyper" parents="32447 34660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40401">
    <literal><![CDATA[
      a((1 / (x * R(y,z,u))) \ T(w,v5),v6,v7) = a((L(y,z,u) * x) * ((x * R(y,z,u)) \ (((x * R(y,z,u)) \ 1) \ w)),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(373,a,32675,a(flip),b,40399,a),flip(a)].">
      <j1 rule="hyper" parents="373 32675 40399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40402">
    <literal><![CDATA[
      a((1 / (x * R(y,z,u))) \ T(w,v5),v6,v7) = a(L(w,x * R(y,z,u),x * R(y,z,u)) * (L(y,z,u) * x),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(373,a,32932,a(flip),b,40401,a),flip(a)].">
      <j1 rule="hyper" parents="373 32932 40401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40403">
    <literal><![CDATA[
      a((1 / (x * R(y,z,u))) \ T(w,v5),v6,v7) = a(L(w,x * R(y,z,u),x * L(y,z,u)) * (L(y,z,u) * x),v6,v7)
    ]]></literal>
    <justification jstring="[para(33574(a,1),40402(a,2,1,1))].">
      <j1 rule="para" parents="33574 40402"/>
    </justification>
  </clause>

  <clause id="40404">
    <literal><![CDATA[
      a((1 / (x * R(y,z,u))) \ T(w,v5),v6,v7) = a(L(w,x * L(y,z,u),x * L(y,z,u)) * (L(y,z,u) * x),v6,v7)
    ]]></literal>
    <justification jstring="[para(36266(a,1),40403(a,2,1,1))].">
      <j1 rule="para" parents="36266 40403"/>
    </justification>
  </clause>

  <clause id="40405">
    <literal><![CDATA[
      a((1 / (x * R(y,z,u))) \ T(w,v5),v6,v7) = a((x * L(y,z,u)) \ w,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(373,a,32425,a(flip),b,40404,a),flip(a)].">
      <j1 rule="hyper" parents="373 32425 40404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40406">
    <literal><![CDATA[
      a((1 / (x * R(y,z,u))) \ w,v5,v6) = a((x * L(y,z,u)) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32360,a(flip),b,40405,a)].">
      <j1 rule="hyper" parents="64 32360 40405"/>
    </justification>
  </clause>

  <clause id="40407">
    <literal><![CDATA[
      a((x * R(y,z,u)) \ w,v5,v6) = a((x * L(y,z,u)) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,2671,a(flip),b,40406,a)].">
      <j1 rule="hyper" parents="64 2671 40406"/>
    </justification>
  </clause>

  <clause id="40408">
    <literal><![CDATA[
      R(x / (a(y,z,u) / ((1 / z) \ a(y,z,u))),z \ 1,((z \ 1) \ 1) * a(y,z,u)) = (x * (a(y,z,u) / (z \ 1))) / a(y,z,u)
    ]]></literal>
    <justification jstring="[para(24641(a,1),35783(a,1,1,2,2))].">
      <j1 rule="para" parents="24641 35783"/>
    </justification>
  </clause>

  <clause id="40409">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((T(1 / ((x \ y) * (y \ x)),z) \ (x \ y)) * u) = T(x \ (y * ((x \ y) \ 1)),z) \ ((1 / (y \ x)) * u)
    ]]></literal>
    <justification jstring="[para(30792(a,1),36989(a,2,1,1))].">
      <j1 rule="para" parents="30792 36989"/>
    </justification>
  </clause>

  <clause id="40410">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((T(1 / ((x \ y) * (y \ x)),z) \ (y \ x)) * u) = T(x \ (y * ((x \ y) \ 1)),z) \ (((x \ y) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(30792(a,1),36990(a,2,1,1))].">
      <j1 rule="para" parents="30792 36990"/>
    </justification>
  </clause>

  <clause id="40411">
    <literal><![CDATA[
      L((x \ a(y,x,z)) \ u,y \ ((y * (x * z)) / z),y \ (z \ (y * (x * z)))) = (1 / (x \ (x / (y \ ((y * (x * z)) / z))))) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,29023,a(flip),b,37343,a)].">
      <j1 rule="hyper" parents="64 29023 37343"/>
    </justification>
  </clause>

  <clause id="40412">
    <literal><![CDATA[
      R(T(a(x,y,z),u),a(x,y,z),T(x,w) * v5) = (T(x,w) * (v5 * a(x,y,z))) \ (T(x,w) * (v5 * (a(x,y,z) * a(x,y,z))))
    ]]></literal>
    <justification jstring="[para(27920(a,1),38207(a,2,2,2))].">
      <j1 rule="para" parents="27920 38207"/>
    </justification>
  </clause>

  <clause id="40413">
    <literal><![CDATA[
      R(T(a(x,y,z),u),a(x,y,z),T(x,w) * v5) = L(L(a(x,y,z),a(x,y,z),v5),v5 * a(x,y,z),T(x,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,602,a(flip),b,40412,a),flip(a)].">
      <j1 rule="hyper" parents="373 602 40412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40414">
    <literal><![CDATA[
      R(T(a(x,y,z),u),a(x,y,z),T(x,w) * v5) = L(L(a(x,y,z),a(x,y,z),v5),v5 * a(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,23215,a(flip),b,40413,a),flip(a)].">
      <j1 rule="hyper" parents="373 23215 40413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40416">
    <literal><![CDATA[
      R(T(a(x,y,z),u),a(x,y,z),T(x,w) * v5) = L(a(x,y,z),a(x,y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29913,a(flip),b,40414,a),flip(a)].">
      <j1 rule="hyper" parents="373 29913 40414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40418">
    <literal><![CDATA[
      R(a(x,y,z),a(x,y,z),T(x,u) * w) = L(a(x,y,z),a(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(114(a,1),40416(a,1,1))].">
      <j1 rule="para" parents="114 40416"/>
    </justification>
  </clause>

  <clause id="40419">
    <literal><![CDATA[
      R(a(x,y,z),a(x,y,z),x * u) = L(a(x,y,z),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26173,a(flip),b,40418,a)].">
      <j1 rule="hyper" parents="64 26173 40418"/>
    </justification>
  </clause>

  <clause id="40420">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),x * u) = L(a(x,y,z),a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31802,a(flip),b,40419,a)].">
      <j1 rule="hyper" parents="64 31802 40419"/>
    </justification>
  </clause>

  <clause id="40421">
    <literal><![CDATA[
      x \ (y * (T(x,y) * a(z,T(x \ 1,y),a(T(x \ 1,y),u,w)))) = (x \ 1) \ (y * L(T(x \ 1,y),a(x,u,w),z))
    ]]></literal>
    <justification jstring="[para(26783(a,1),39372(a,2,2,2,2))].">
      <j1 rule="para" parents="26783 39372"/>
    </justification>
  </clause>

  <clause id="40422">
    <literal><![CDATA[
      x \ (y * (T(x,y) * a(z,T(x \ 1,y),a(T(x \ 1,y),u,w)))) = (x \ 1) \ (L(x \ 1,a(x,u,w),z) * y)
    ]]></literal>
    <justification jstring="[para(266(a,1),40421(a,2,2))].">
      <j1 rule="para" parents="266 40421"/>
    </justification>
  </clause>

  <clause id="40424">
    <literal><![CDATA[
      x \ (y * (T(x,y) * a(z,T(x \ 1,y),a(T(x \ 1,y),u,w)))) = (y / (x \ 1)) * L(x \ 1,a(x,u,w),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,24852,a(flip),b,40422,a),flip(a)].">
      <j1 rule="hyper" parents="373 24852 40422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40425">
    <literal><![CDATA[
      x \ (y * (T(x,y) * a(z,T(x \ 1,y),a(T(x \ 1,y),u,w)))) = x * ((L(1 / x,a(x,u,w),z) \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,39605,a(flip),b,40424,a),flip(a)].">
      <j1 rule="hyper" parents="373 39605 40424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40426">
    <literal><![CDATA[
      x \ (y * (T(x,y) * a(z,T(x \ 1,y),a(T(x \ 1,y),u,w)))) = x * (L(x,a(x,u,w),z) \ y)
    ]]></literal>
    <justification jstring="[para(39371(a,1),40425(a,2,2,1))].">
      <j1 rule="para" parents="39371 40425"/>
    </justification>
  </clause>

  <clause id="40427">
    <literal><![CDATA[
      x \ (y * (T(x,y) * a(z,T(x \ 1,y),a(x,u,w)))) = x * (L(x,a(x,u,w),z) \ y)
    ]]></literal>
    <justification jstring="[para(26783(a,1),40426(a,1,2,2,2,3))].">
      <j1 rule="para" parents="26783 40426"/>
    </justification>
  </clause>

  <clause id="40429">
    <literal><![CDATA[
      x \ (y * (T(x,y) * a(z,x \ 1,a(x,u,w)))) = x * (L(x,a(x,u,w),z) \ y)
    ]]></literal>
    <justification jstring="[para(31892(a,1),40427(a,1,2,2,2))].">
      <j1 rule="para" parents="31892 40427"/>
    </justification>
  </clause>

  <clause id="40430">
    <literal><![CDATA[
      x \ (y * (T(x,y) * a(z,x,a(x,u,w)))) = x * (L(x,a(x,u,w),z) \ y)
    ]]></literal>
    <justification jstring="[para(11980(a,1),40429(a,1,2,2,2))].">
      <j1 rule="para" parents="11980 40429"/>
    </justification>
  </clause>

  <clause id="40432">
    <literal><![CDATA[
      x \ (y * T(x * a(z,x,a(x,u,w)),y)) = x * (L(x,a(x,u,w),z) \ y)
    ]]></literal>
    <justification jstring="[para(28750(a,2),40430(a,1,2,2))].">
      <j1 rule="para" parents="28750 40430"/>
    </justification>
  </clause>

  <clause id="40433">
    <literal><![CDATA[
      x \ (y * T(L(x,a(x,z,u),w),y)) = x * (L(x,a(x,z,u),w) \ y)
    ]]></literal>
    <justification jstring="[para(39367(a,1),40432(a,1,2,2,1))].">
      <j1 rule="para" parents="39367 40432"/>
    </justification>
  </clause>

  <clause id="40434">
    <literal><![CDATA[
      x \ (L(x,a(x,y,z),u) * w) = x * (L(x,a(x,y,z),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,249,a(flip),b,40433,a)].">
      <j1 rule="hyper" parents="64 249 40433"/>
    </justification>
  </clause>

  <clause id="40435">
    <literal><![CDATA[
      (x / y) * L(y,a(y,z,u),w) = y * (L(y,a(y,z,u),w) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24852,a(flip),b,40434,a)].">
      <j1 rule="hyper" parents="64 24852 40434"/>
    </justification>
  </clause>

  <clause id="40436">
    <literal><![CDATA[
      x \ (L(y,a(y,z,u),w) * (y \ v5)) = x \ (y * (L(y,a(y,z,u),w) \ v5))
    ]]></literal>
    <justification jstring="[para(40435(a,1),23899(a,2,2))].">
      <j1 rule="para" parents="40435 23899"/>
    </justification>
  </clause>

  <clause id="40437">
    <literal><![CDATA[
      (x \ (y / (y \ x))) * ((y \ (x / (x \ y))) \ (y * ((y \ T(x / (x \ y),y)) * z))) = y * (T((y \ (x / (x \ y))) \ 1,y) * z)
    ]]></literal>
    <justification jstring="[para(31606(a,1),40170(a,1,2,2,2,1))].">
      <j1 rule="para" parents="31606 40170"/>
    </justification>
  </clause>

  <clause id="40438">
    <literal><![CDATA[
      (1 / T(T(x,y),z)) * R(R(T(T(x,y),z),x,u \ 1),u,u) = a(1 / T(T(x,y),z),(1 / T(T(x,y),z)) \ u,u) \ 1
    ]]></literal>
    <justification jstring="[para(1405(a,1),40387(a,1,2))].">
      <j1 rule="para" parents="1405 40387"/>
    </justification>
  </clause>

  <clause id="40439">
    <literal><![CDATA[
      T(T(x,y),z) \ R(R(T(T(x,y),z),x,u \ 1),u,u) = a(1 / T(T(x,y),z),(1 / T(T(x,y),z)) \ u,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,26947,a(flip),b,40438,a)].">
      <j1 rule="hyper" parents="64 26947 40438"/>
    </justification>
  </clause>

  <clause id="40440">
    <literal><![CDATA[
      T(x,y) \ R(R(T(x,y),x,z \ 1),z,z) = a(1 / T(T(x,y),u),(1 / T(T(x,y),u)) \ z,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,25998,a(flip),b,40439,a)].">
      <j1 rule="hyper" parents="64 25998 40439"/>
    </justification>
  </clause>

  <clause id="40442">
    <literal><![CDATA[
      a(1 / T(T(x,y),z),(1 / T(T(x,y),z)) \ u,u) \ 1 = x \ R(R(x,x,u \ 1),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25998,a(flip),b,40440,a),flip(a)].">
      <j1 rule="hyper" parents="64 25998 40440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40444">
    <literal><![CDATA[
      a(1 / T(T(x,y),z),(1 / T(T(x,y),z)) \ u,u) \ 1 = ((1 / u) / (x / u)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,32780,a(flip),b,40442,a),flip(a)].">
      <j1 rule="hyper" parents="373 32780 40442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40445">
    <literal><![CDATA[
      a(1 / T(T(x,y),z),T(T(x,y),z) \ u,u) \ 1 = ((1 / u) / (x / u)) * x
    ]]></literal>
    <justification jstring="[para(32135(a,1),40444(a,1,1))].">
      <j1 rule="para" parents="32135 40444"/>
    </justification>
  </clause>

  <clause id="40446">
    <literal><![CDATA[
      a(1 / T(T(x,y),z),T(x,y) \ u,u) \ 1 = ((1 / u) / (x / u)) * x
    ]]></literal>
    <justification jstring="[para(31903(a,1),40445(a,1,1))].">
      <j1 rule="para" parents="31903 40445"/>
    </justification>
  </clause>

  <clause id="40447">
    <literal><![CDATA[
      a(1 / T(T(x,y),z),x \ u,u) \ 1 = ((1 / u) / (x / u)) * x
    ]]></literal>
    <justification jstring="[para(31903(a,1),40446(a,1,1))].">
      <j1 rule="para" parents="31903 40446"/>
    </justification>
  </clause>

  <clause id="40449">
    <literal><![CDATA[
      a(T(T(x,y),z),x \ u,u) \ 1 = ((1 / u) / (x / u)) * x
    ]]></literal>
    <justification jstring="[para(2641(a,1),40447(a,1,1))].">
      <j1 rule="para" parents="2641 40447"/>
    </justification>
  </clause>

  <clause id="40451">
    <literal><![CDATA[
      ((1 / x) / (y / x)) * y = a(y,y \ x,x) \ 1
    ]]></literal>
    <justification jstring="[para(374(a,1),40449(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="374 40449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40452">
    <literal><![CDATA[
      T((1 / x) / (y / x),y) = (y \ (1 / x)) * x
    ]]></literal>
    <justification jstring="[hyper(269,a,40451,a,b,29790,a)].">
      <j1 rule="hyper" parents="269 40451 29790"/>
    </justification>
  </clause>

  <clause id="40453">
    <literal><![CDATA[
      T((1 / x) / (y / x),T(y,x)) = (y \ (1 / x)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,34545,a,b,40452,a)].">
      <j1 rule="hyper" parents="64 34545 40452"/>
    </justification>
  </clause>

  <clause id="40454">
    <literal><![CDATA[
      1 / ((x \ (1 / y)) * y) = ((1 / y) / (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(40453(a,1),14954(a,1,2))].">
      <j1 rule="para" parents="40453 14954"/>
    </justification>
  </clause>

  <clause id="40455">
    <literal><![CDATA[
      1 / (((1 / x) / (y / x)) \ 1) = ((1 / (1 / y)) \ (1 / x)) * x
    ]]></literal>
    <justification jstring="[para(40454(a,1),31222(a,1,2))].">
      <j1 rule="para" parents="40454 31222"/>
    </justification>
  </clause>

  <clause id="40456">
    <literal><![CDATA[
      ((1 / (1 / x)) \ (1 / y)) * y = (1 / y) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(330,a,40455,a)].">
      <j1 rule="hyper" parents="330 40455"/>
    </justification>
  </clause>

  <clause id="40458">
    <literal><![CDATA[
      1 / R(x,x * y,y) = (1 / y) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35729,a,b,40456,a)].">
      <j1 rule="hyper" parents="64 35729 40456"/>
    </justification>
  </clause>

  <clause id="40459">
    <literal><![CDATA[
      1 / R(x * y,(x * y) * y,y) = (1 / y) / x
    ]]></literal>
    <justification jstring="[para(11(a,1),40458(a,2,2))].">
      <j1 rule="para" parents="11 40458"/>
    </justification>
  </clause>

  <clause id="40460">
    <literal><![CDATA[
      R(x,x * y,y) \ R(R(x,x * y,y),z,u) = ((1 / y) / (x / y)) \ (1 * R(1 \ (1 / R(x,x * y,y)),z,u))
    ]]></literal>
    <justification jstring="[para(40458(a,1),2471(a,1,1)),flip(a)].">
      <j1 rule="para" parents="40458 2471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40461">
    <literal><![CDATA[
      1 / R(x * y,x,y) = (1 / y) / x
    ]]></literal>
    <justification jstring="[para(35776(a,1),40459(a,1,2))].">
      <j1 rule="para" parents="35776 40459"/>
    </justification>
  </clause>

  <clause id="40462">
    <literal><![CDATA[
      1 / R(x,y,y \ x) = (1 / (y \ x)) / y
    ]]></literal>
    <justification jstring="[para(10(a,1),40461(a,1,2,1))].">
      <j1 rule="para" parents="10 40461"/>
    </justification>
  </clause>

  <clause id="40463">
    <literal><![CDATA[
      R(x,y,y \ x) \ R(R(x,y,y \ x),z,u) = ((1 / (y \ x)) / y) \ (1 * R(1 \ (1 / R(x,y,y \ x)),z,u))
    ]]></literal>
    <justification jstring="[para(40462(a,1),2471(a,1,1)),flip(a)].">
      <j1 rule="para" parents="40462 2471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40464">
    <literal><![CDATA[
      R(x,x * y,y) \ R(R(x,x * y,y),z,u) = ((1 / y) / (x / y)) \ (1 * R(1 \ ((1 / y) / (x / y)),z,u))
    ]]></literal>
    <justification jstring="[para(40458(a,1),40460(a,2,2,2,1,2))].">
      <j1 rule="para" parents="40458 40460"/>
    </justification>
  </clause>

  <clause id="40465">
    <literal><![CDATA[
      R(x,x * y,y) \ R(R(x,x * y,y),z,u) = ((1 / y) / (x / y)) \ (1 * R((1 / y) / (x / y),z,u))
    ]]></literal>
    <justification jstring="[para(66(a,1),40464(a,2,2,2,1))].">
      <j1 rule="para" parents="66 40464"/>
    </justification>
  </clause>

  <clause id="40466">
    <literal><![CDATA[
      R(x,x * y,y) \ R(R(x,x * y,y),z,u) = ((1 / y) / (x / y)) \ R((1 / y) / (x / y),z,u)
    ]]></literal>
    <justification jstring="[hyper(342,a,40465,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="342 40465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40467">
    <literal><![CDATA[
      R(x,x * y,y) \ R(R(x,x * y,y),z,u) = (x / y) \ ((1 / y) * R((1 / y) \ (x / y),z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,26012,a(flip),b,40466,a),flip(a)].">
      <j1 rule="hyper" parents="373 26012 40466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40468">
    <literal><![CDATA[
      R(x,x * y,y) \ R(R(x,x * y,y),z,u) = (x / y) \ ((1 * R(1 \ x,z,u)) / y)
    ]]></literal>
    <justification jstring="[para(2864(a,1),40467(a,2,2))].">
      <j1 rule="para" parents="2864 40467"/>
    </justification>
  </clause>

  <clause id="40469">
    <literal><![CDATA[
      R(x,x * y,y) \ R(R(x,x * y,y),z,u) = (x / y) \ ((1 * R(x,z,u)) / y)
    ]]></literal>
    <justification jstring="[para(66(a,1),40468(a,2,2,1,2,1))].">
      <j1 rule="para" parents="66 40468"/>
    </justification>
  </clause>

  <clause id="40470">
    <literal><![CDATA[
      R(x,x * y,y) \ R(R(x,x * y,y),z,u) = (x / y) \ (R(x,z,u) / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),40469(a,2,2,1))].">
      <j1 rule="para" parents="7 40469"/>
    </justification>
  </clause>

  <clause id="40471">
    <literal><![CDATA[
      R(x,x * y,y) \ R(R(x,x * y,y),z,u) = (y \ x) \ (y \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27064,a(flip),b,40470,a),flip(a)].">
      <j1 rule="hyper" parents="373 27064 40470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40472">
    <literal><![CDATA[
      L(x \ R(x,y,z),x * u,u) = (u \ x) \ (u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,36889,a(flip),b,40471,a)].">
      <j1 rule="hyper" parents="64 36889 40471"/>
    </justification>
  </clause>

  <clause id="40473">
    <literal><![CDATA[
      L(x \ R(x,y,z),u \ x,u) = (u \ x) \ (u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,37236,a,b,40472,a)].">
      <j1 rule="hyper" parents="64 37236 40472"/>
    </justification>
  </clause>

  <clause id="40474">
    <literal><![CDATA[
      L((x \ y) \ (x \ R(y,z,u)),y,z * u) = L(a(y,z,u),y * x,x)
    ]]></literal>
    <justification jstring="[para(40472(a,1),16033(a,1,1))].">
      <j1 rule="para" parents="40472 16033"/>
    </justification>
  </clause>

  <clause id="40475">
    <literal><![CDATA[
      L((x \ y) \ (x \ R(y,z,u)),y,z * u) = L(a(y,z,u),x \ y,x)
    ]]></literal>
    <justification jstring="[para(40473(a,1),16033(a,1,1))].">
      <j1 rule="para" parents="40473 16033"/>
    </justification>
  </clause>

  <clause id="40476">
    <literal><![CDATA[
      L(a(x,y,z),x \ u,u) = L(a(x,y,z),x * u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34942,a(flip),b,40474,a)].">
      <j1 rule="hyper" parents="64 34942 40474"/>
    </justification>
  </clause>

  <clause id="40477">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),x * u,u) = a(a(x,y,z),x \ u,u)
    ]]></literal>
    <justification jstring="[para(40476(a,1),32838(a,1,2))].">
      <j1 rule="para" parents="40476 32838"/>
    </justification>
  </clause>

  <clause id="40478">
    <literal><![CDATA[
      L(a(x,y,z),u \ x,u) = L(a(x,y,z),x * u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,40474,a(flip),b,40475,a),flip(a)].">
      <j1 rule="hyper" parents="64 40474 40475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40479">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),x * u,u) = a(a(x,y,z),u \ x,u)
    ]]></literal>
    <justification jstring="[para(40478(a,1),31770(a,1,2))].">
      <j1 rule="para" parents="40478 31770"/>
    </justification>
  </clause>

  <clause id="40480">
    <literal><![CDATA[
      a(a(x,y,z),u \ x,u) = a(a(x,y,z),x \ u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,40477,a(flip),b,40479,a),flip(a)].">
      <j1 rule="hyper" parents="64 40477 40479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40481">
    <literal><![CDATA[
      a(a(x,y,z),x \ u,u) = a(a(x,y,z),x * u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,35683,a(flip),b,40480,a),flip(a)].">
      <j1 rule="hyper" parents="64 35683 40480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40482">
    <literal><![CDATA[
      R(x,y,y \ x) \ R(R(x,y,y \ x),z,u) = ((1 / (y \ x)) / y) \ (1 * R(1 \ ((1 / (y \ x)) / y),z,u))
    ]]></literal>
    <justification jstring="[para(40462(a,1),40463(a,2,2,2,1,2))].">
      <j1 rule="para" parents="40462 40463"/>
    </justification>
  </clause>

  <clause id="40483">
    <literal><![CDATA[
      R(x,y,y \ x) \ R(R(x,y,y \ x),z,u) = ((1 / (y \ x)) / y) \ (1 * R((1 / (y \ x)) / y,z,u))
    ]]></literal>
    <justification jstring="[para(66(a,1),40482(a,2,2,2,1))].">
      <j1 rule="para" parents="66 40482"/>
    </justification>
  </clause>

  <clause id="40484">
    <literal><![CDATA[
      R(x,y,y \ x) \ R(R(x,y,y \ x),z,u) = ((1 / (y \ x)) / y) \ R((1 / (y \ x)) / y,z,u)
    ]]></literal>
    <justification jstring="[hyper(342,a,40483,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="342 40483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40485">
    <literal><![CDATA[
      R(x,y,y \ x) \ R(R(x,y,y \ x),z,u) = y \ ((1 / (y \ x)) * R((1 / (y \ x)) \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,26012,a(flip),b,40484,a),flip(a)].">
      <j1 rule="hyper" parents="373 26012 40484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40486">
    <literal><![CDATA[
      R(x,y,y \ x) \ R(R(x,y,y \ x),z,u) = y \ (((y \ x) \ 1) * R(((y \ x) \ 1) \ y,z,u))
    ]]></literal>
    <justification jstring="[para(27047(a,1),40485(a,2,2))].">
      <j1 rule="para" parents="27047 40485"/>
    </justification>
  </clause>

  <clause id="40487">
    <literal><![CDATA[
      R(x,y,y \ x) \ R(R(x,y,y \ x),z,u) = y \ ((y \ x) * R((y \ x) \ y,z,u))
    ]]></literal>
    <justification jstring="[para(2112(a,1),40486(a,2,2))].">
      <j1 rule="para" parents="2112 40486"/>
    </justification>
  </clause>

  <clause id="40488">
    <literal><![CDATA[
      R(x,y,y \ x) \ R(R(x,y,y \ x),z,u) = L(x \ R(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,36339,a(flip),b,40487,a),flip(a)].">
      <j1 rule="hyper" parents="373 36339 40487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40489">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,u \ x) = L(x \ R(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,36889,a(flip),b,40488,a)].">
      <j1 rule="hyper" parents="64 36889 40488"/>
    </justification>
  </clause>

  <clause id="40490">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,u),x,y * z) = L(a(x,y,z),u,u \ x)
    ]]></literal>
    <justification jstring="[para(40489(a,1),16033(a,1,1))].">
      <j1 rule="para" parents="40489 16033"/>
    </justification>
  </clause>

  <clause id="40491">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ x) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16033,a(flip),b,40490,a),flip(a)].">
      <j1 rule="hyper" parents="64 16033 40490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40492">
    <literal><![CDATA[
      (x / y) * (y * a(x,z,u)) = x * L(a(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,40491,a(flip),b,11067,a),flip(a)].">
      <j1 rule="hyper" parents="145 40491 11067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40493">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u,u) = a(a(x,y,z),u,u \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,40491,a(flip),b,31653,a)].">
      <j1 rule="hyper" parents="139 40491 31653"/>
    </justification>
  </clause>

  <clause id="40494">
    <literal><![CDATA[
      (a(x,y,z) * u) * (u \ x) = x * L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[para(40491(a,1),28776(a,1,2)),flip(a)].">
      <j1 rule="para" parents="40491 28776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40495">
    <literal><![CDATA[
      L(a(x,y,z) \ R(a(x,y,z),u,u \ x),a(x,y,z),u) = a(L(a(x,y,z),u,u),u,u \ x)
    ]]></literal>
    <justification jstring="[para(40491(a,1),33411(a,2,1))].">
      <j1 rule="para" parents="40491 33411"/>
    </justification>
  </clause>

  <clause id="40496">
    <literal><![CDATA[
      a(L(a(x,y,z),u,u),u,u \ x) = a(u \ x,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(40491(a,1),36350(a,1,1))].">
      <j1 rule="para" parents="40491 36350"/>
    </justification>
  </clause>

  <clause id="40497">
    <literal><![CDATA[
      L(a(x,y,z),x * u,L(u,u,x)) = L(a(x,y,z),x * u,x * u)
    ]]></literal>
    <justification jstring="[hyper(35,a,35054,a(flip),b,40492,a(flip))].">
      <j1 rule="hyper" parents="35 35054 40492"/>
    </justification>
  </clause>

  <clause id="40498">
    <literal><![CDATA[
      a(a(x,y,z),u,u \ x) = a(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28791,a(flip),b,40493,a),flip(a)].">
      <j1 rule="hyper" parents="64 28791 40493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40499">
    <literal><![CDATA[
      a(a(x * y,z,u),x,y) = a(a(x * y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13875,a(flip),b,40498,a)].">
      <j1 rule="hyper" parents="64 13875 40498"/>
    </justification>
  </clause>

  <clause id="40500">
    <literal><![CDATA[
      a(a(x * y,z,u),x,y) = a(x,x,a(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,36326,a(flip),b,40499,a),flip(a)].">
      <j1 rule="hyper" parents="373 36326 40499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40501">
    <literal><![CDATA[
      L(a(x,y,z),x * u,x * u) = L(a(x,y,z),x * u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,38104,a(flip),b,40497,a),flip(a)].">
      <j1 rule="hyper" parents="64 38104 40497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40502">
    <literal><![CDATA[
      L(a(x,y,z),x * u,x * u) = L(a(x,y,z),x \ u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,40476,a,b,40501,a),flip(a)].">
      <j1 rule="hyper" parents="373 40476 40501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40503">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),x \ u,u) = a(a(x,y,z),u * x,u * x)
    ]]></literal>
    <justification jstring="[para(40502(a,1),29665(a,1,2))].">
      <j1 rule="para" parents="40502 29665"/>
    </justification>
  </clause>

  <clause id="40504">
    <literal><![CDATA[
      a(a(x,y,z),u * x,u * x) = a(a(x,y,z),x \ u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32838,a(flip),b,40503,a),flip(a)].">
      <j1 rule="hyper" parents="64 32838 40503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40505">
    <literal><![CDATA[
      a(a(x,y,z),x * u,x * u) = a(a(x,y,z),x \ u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31938,a,b,40504,a)].">
      <j1 rule="hyper" parents="64 31938 40504"/>
    </justification>
  </clause>

  <clause id="40506">
    <literal><![CDATA[
      L(a(x,y,z) \ L(a(x,y,z),u,u \ x),a(x,y,z),u) = a(L(a(x,y,z),u,u),u,u \ x)
    ]]></literal>
    <justification jstring="[para(28787(a,1),40495(a,1,1,2))].">
      <j1 rule="para" parents="28787 40495"/>
    </justification>
  </clause>

  <clause id="40507">
    <literal><![CDATA[
      L(a(x,y,z) \ L(a(x,y,z),u,u),a(x,y,z),u) = a(L(a(x,y,z),u,u),u,u \ x)
    ]]></literal>
    <justification jstring="[para(40491(a,1),40506(a,1,1,2))].">
      <j1 rule="para" parents="40491 40506"/>
    </justification>
  </clause>

  <clause id="40508">
    <literal><![CDATA[
      L(a(a(x,y,z),u,u),a(x,y,z),u) = a(L(a(x,y,z),u,u),u,u \ x)
    ]]></literal>
    <justification jstring="[para(28791(a,1),40507(a,1,1))].">
      <j1 rule="para" parents="28791 40507"/>
    </justification>
  </clause>

  <clause id="40509">
    <literal><![CDATA[
      a(L(a(x,y,z),u,u),u,u \ x) = a(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(33227,a,40508,a),flip(a)].">
      <j1 rule="hyper" parents="33227 40508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40511">
    <literal><![CDATA[
      a(x \ y,x,a(y,z,u)) = a(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,40496,a(flip),b,40509,a)].">
      <j1 rule="hyper" parents="64 40496 40509"/>
    </justification>
  </clause>

  <clause id="40512">
    <literal><![CDATA[
      a(a(x * y,z,u),y,y) = a(x,y,a(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26791,a(flip),b,40511,a),flip(a)].">
      <j1 rule="hyper" parents="64 26791 40511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40513">
    <literal><![CDATA[
      L(x \ (a(y,z,u) \ x),x,(a(y,z,u) \ x) \ w) \ w = (x \ 1) * ((((x \ 1) \ (a(y,z,u) \ (x \ 1))) * (x \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(29355(a,1),40398(a,1,1))].">
      <j1 rule="para" parents="29355 40398"/>
    </justification>
  </clause>

  <clause id="40514">
    <literal><![CDATA[
      T((x / (a(y,z,u) \ w)) * w,w \ (a(y,z,u) \ w)) = (w \ 1) * ((((w \ 1) \ (a(y,z,u) \ (w \ 1))) * (w \ 1)) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,15117,a(flip),b,40513,a)].">
      <j1 rule="hyper" parents="64 15117 40513"/>
    </justification>
  </clause>

  <clause id="40515">
    <literal><![CDATA[
      T(x * ((a(y,z,u) \ x) \ w),x \ (a(y,z,u) \ x)) = (x \ 1) * ((((x \ 1) \ (a(y,z,u) \ (x \ 1))) * (x \ 1)) \ w)
    ]]></literal>
    <justification jstring="[para(28670(a,1),40514(a,1,1))].">
      <j1 rule="para" parents="28670 40514"/>
    </justification>
  </clause>

  <clause id="40516">
    <literal><![CDATA[
      (x \ 1) * ((((x \ 1) \ (a(y,z,u) \ (x \ 1))) * (x \ 1)) \ w) = x * ((a(y,z,u) \ x) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,25305,a(flip),b,40515,a),flip(a)].">
      <j1 rule="hyper" parents="64 25305 40515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40518">
    <literal><![CDATA[
      (x \ 1) * ((a(y,z,u) \ (x \ 1)) \ w) = x * ((a(y,z,u) \ x) \ w)
    ]]></literal>
    <justification jstring="[para(23768(a,1),40516(a,1,2,1))].">
      <j1 rule="para" parents="23768 40516"/>
    </justification>
  </clause>

  <clause id="40519">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,((y \ 1) \ 1) * a(z,y,u)) = (x * (a(z,y,u) / (y \ 1))) / a(z,y,u)
    ]]></literal>
    <justification jstring="[para(79(a,1),40408(a,1,1,2))].">
      <j1 rule="para" parents="79 40408"/>
    </justification>
  </clause>

  <clause id="40521">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,(y \ 1) \ a(z,y,u)) = (x * (a(z,y,u) / (y \ 1))) / a(z,y,u)
    ]]></literal>
    <justification jstring="[para(35741(a,1),40519(a,1,3))].">
      <j1 rule="para" parents="35741 40519"/>
    </justification>
  </clause>

  <clause id="40522">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y * a(z,y,u)) = (x * (a(z,y,u) / (y \ 1))) / a(z,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,35755,a(flip),b,40521,a)].">
      <j1 rule="hyper" parents="64 35755 40521"/>
    </justification>
  </clause>

  <clause id="40523">
    <literal><![CDATA[
      R(x / (1 / y),y,y * a(z,y,u)) = (x * (a(z,y,u) / (y \ 1))) / a(z,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2975,a(flip),b,40522,a)].">
      <j1 rule="hyper" parents="64 2975 40522"/>
    </justification>
  </clause>

  <clause id="40524">
    <literal><![CDATA[
      R(x / (1 / y),y,y * a(z,y,u)) = (x * ((1 / y) \ a(z,y,u))) / a(z,y,u)
    ]]></literal>
    <justification jstring="[para(24641(a,1),40523(a,2,1,2))].">
      <j1 rule="para" parents="24641 40523"/>
    </justification>
  </clause>

  <clause id="40525">
    <literal><![CDATA[
      R(x / (1 / y),y,y * a(z,y,u)) = (x * (a(z,y,u) * y)) / a(z,y,u)
    ]]></literal>
    <justification jstring="[para(35737(a,1),40524(a,2,1,2))].">
      <j1 rule="para" parents="35737 40524"/>
    </justification>
  </clause>

  <clause id="40526">
    <literal><![CDATA[
      R(x / (1 / y),y,y * a(z,y,u)) = a(z,y,u) \ (x * (a(z,y,u) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,23133,a(flip),b,40525,a),flip(a)].">
      <j1 rule="hyper" parents="373 23133 40525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40527">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((T(1 / ((x \ y) * (y \ x)),z) \ (x \ y)) * u) = (x \ (y * ((x \ y) \ 1))) \ ((1 / (y \ x)) * u)
    ]]></literal>
    <justification jstring="[para(13989(a,1),40409(a,2,1))].">
      <j1 rule="para" parents="13989 40409"/>
    </justification>
  </clause>

  <clause id="40528">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((T(1 / ((x \ y) * (y \ x)),z) \ (x \ y)) * u) = ((x \ y) * (y \ x)) * ((1 / (y \ x)) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,37875,a(flip),b,40527,a),flip(a)].">
      <j1 rule="hyper" parents="373 37875 40527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40530">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((T(((x \ y) * (y \ x)) \ 1,z) \ (x \ y)) * u) = ((x \ y) * (y \ x)) * ((1 / (y \ x)) * u)
    ]]></literal>
    <justification jstring="[para(5135(a,1),40528(a,1,2,1,1))].">
      <j1 rule="para" parents="5135 40528"/>
    </justification>
  </clause>

  <clause id="40531">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((T(x \ (y * ((x \ y) \ 1)),z) \ (x \ y)) * u) = ((x \ y) * (y \ x)) * ((1 / (y \ x)) * u)
    ]]></literal>
    <justification jstring="[para(30792(a,1),40530(a,1,2,1,1,1))].">
      <j1 rule="para" parents="30792 40530"/>
    </justification>
  </clause>

  <clause id="40532">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (((x \ (y * ((x \ y) \ 1))) \ (x \ y)) * z) = ((x \ y) * (y \ x)) * ((1 / (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(114(a,1),40531(a,1,2,1,1))].">
      <j1 rule="para" parents="114 40531"/>
    </justification>
  </clause>

  <clause id="40533">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (((y * ((x \ y) \ 1)) \ y) * z) = ((x \ y) * (y \ x)) * ((1 / (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(33494(a,1),40532(a,1,2,1))].">
      <j1 rule="para" parents="33494 40532"/>
    </justification>
  </clause>

  <clause id="40534">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) * ((x \ y) * z) = ((y * ((x \ y) \ 1)) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,37761,a(flip),b,40533,a)].">
      <j1 rule="hyper" parents="145 37761 40533"/>
    </justification>
  </clause>

  <clause id="40535">
    <literal><![CDATA[
      a(x,y,((z * ((u \ z) \ 1)) \ z) * ((1 / (z \ u)) * w)) = a(x,y,(u \ z) * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(40534(a,1),38099(a,1,3))].">
      <j1 rule="para" parents="40534 38099"/>
    </justification>
  </clause>

  <clause id="40536">
    <literal><![CDATA[
      a(x,y,((z * ((u \ z) \ 1)) \ z) * (((z \ u) \ 1) * w)) = a(x,y,(u \ z) * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27480,a(flip),b,40535,a)].">
      <j1 rule="hyper" parents="64 27480 40535"/>
    </justification>
  </clause>

  <clause id="40537">
    <literal><![CDATA[
      a(x,y,(z \ (((u \ z) \ 1) \ z)) * (((z \ u) \ 1) * w)) = a(x,y,(u \ z) * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27721,a(flip),b,40536,a)].">
      <j1 rule="hyper" parents="64 27721 40536"/>
    </justification>
  </clause>

  <clause id="40538">
    <literal><![CDATA[
      a(x,y,((z \ u) \ 1) * (((z \ u) \ 1) * w)) = a(x,y,(u \ z) * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,39137,a(flip),b,40537,a)].">
      <j1 rule="hyper" parents="64 39137 40537"/>
    </justification>
  </clause>

  <clause id="40539">
    <literal><![CDATA[
      a(x,y,(z \ u) \ ((z \ u) \ w)) = a(x,y,(u \ z) * ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,38963,a(flip),b,40538,a)].">
      <j1 rule="hyper" parents="64 38963 40538"/>
    </justification>
  </clause>

  <clause id="40540">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((T(1 / ((x \ y) * (y \ x)),z) \ (y \ x)) * u) = (x \ (y * ((x \ y) \ 1))) \ (((x \ y) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(13989(a,1),40410(a,2,1))].">
      <j1 rule="para" parents="13989 40410"/>
    </justification>
  </clause>

  <clause id="40541">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((T(1 / ((x \ y) * (y \ x)),z) \ (y \ x)) * u) = ((x \ y) * (y \ x)) * (((x \ y) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,37875,a(flip),b,40540,a),flip(a)].">
      <j1 rule="hyper" parents="373 37875 40540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40543">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((T(((x \ y) * (y \ x)) \ 1,z) \ (y \ x)) * u) = ((x \ y) * (y \ x)) * (((x \ y) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(5135(a,1),40541(a,1,2,1,1))].">
      <j1 rule="para" parents="5135 40541"/>
    </justification>
  </clause>

  <clause id="40544">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((T(x \ (y * ((x \ y) \ 1)),z) \ (y \ x)) * u) = ((x \ y) * (y \ x)) * (((x \ y) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(30792(a,1),40543(a,1,2,1,1,1))].">
      <j1 rule="para" parents="30792 40543"/>
    </justification>
  </clause>

  <clause id="40545">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (((x \ (y * ((x \ y) \ 1))) \ (y \ x)) * z) = ((x \ y) * (y \ x)) * (((x \ y) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(114(a,1),40544(a,1,2,1,1))].">
      <j1 rule="para" parents="114 40544"/>
    </justification>
  </clause>

  <clause id="40546">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((((x \ y) * (y \ x)) * (y \ x)) * z) = ((x \ y) * (y \ x)) * (((x \ y) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(37875(a,1),40545(a,1,2,1))].">
      <j1 rule="para" parents="37875 40545"/>
    </justification>
  </clause>

  <clause id="40547">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (L(y \ x,y \ x,x) * z) = ((x \ y) * (y \ x)) * (((x \ y) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(26665(a,1),40546(a,1,2,1))].">
      <j1 rule="para" parents="26665 40546"/>
    </justification>
  </clause>

  <clause id="40548">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((y \ x) * z) = ((x \ y) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(139,a,37876,a(flip),b,40547,a(flip))].">
      <j1 rule="hyper" parents="139 37876 40547"/>
    </justification>
  </clause>

  <clause id="40549">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ ((y \ x) * y) = ((x \ y) * (x / y)) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,32283,a,b,40548,a),flip(a)].">
      <j1 rule="hyper" parents="373 32283 40548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40550">
    <literal><![CDATA[
      a(x,y * x,y \ x) * ((y \ x) * z) = ((x \ y) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,37877,a,b,40548,a)].">
      <j1 rule="hyper" parents="64 37877 40548"/>
    </justification>
  </clause>

  <clause id="40551">
    <literal><![CDATA[
      (x \ y) * (z * a(y,x * y,x \ y)) = ((y \ x) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,33200,a(flip),b,40550,a)].">
      <j1 rule="hyper" parents="64 33200 40550"/>
    </justification>
  </clause>

  <clause id="40552">
    <literal><![CDATA[
      (x \ y) * (((y \ x) * (x \ y)) \ z) = ((y \ x) \ 1) * z
    ]]></literal>
    <justification jstring="[para(37874(a,1),40551(a,1,2))].">
      <j1 rule="para" parents="37874 40551"/>
    </justification>
  </clause>

  <clause id="40553">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (z * (y \ x)) = z * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,36209,a(flip),b,40552,a),flip(a)].">
      <j1 rule="hyper" parents="35 36209 40552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40554">
    <literal><![CDATA[
      x * ((y \ x) * ((x \ y) \ 1)) = (x * (y \ x)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(40553(a,1),37873(a,1,2))].">
      <j1 rule="para" parents="40553 37873"/>
    </justification>
  </clause>

  <clause id="40555">
    <literal><![CDATA[
      (x * (y \ x)) * (y \ x) = x * (y \ (x / (x \ y)))
    ]]></literal>
    <justification jstring="[para(40131(a,1),40554(a,1,2)),flip(a)].">
      <j1 rule="para" parents="40131 40554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40556">
    <literal><![CDATA[
      a(((x \ (y / (y \ x))) * y) * z,u,w) = a(z * ((y * (x \ y)) * (x \ y)),u,w)
    ]]></literal>
    <justification jstring="[para(40555(a,2),32422(a,2,1,2))].">
      <j1 rule="para" parents="40555 32422"/>
    </justification>
  </clause>

  <clause id="40557">
    <literal><![CDATA[
      R((x \ y) * x,((x \ y) * x) \ x,x \ ((x \ y) * x)) = ((y \ x) * (y / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,15071,a,b,40549,a)].">
      <j1 rule="hyper" parents="64 15071 40549"/>
    </justification>
  </clause>

  <clause id="40558">
    <literal><![CDATA[
      a(((x \ y) * ((y \ x) \ y)) * z,u,w) = a(z * ((y * (x \ y)) * (x \ y)),u,w)
    ]]></literal>
    <justification jstring="[para(40248(a,1),40556(a,1,1,1))].">
      <j1 rule="para" parents="40248 40556"/>
    </justification>
  </clause>

  <clause id="40559">
    <literal><![CDATA[
      R((x \ y) * x,((x \ y) * x) \ x,x \ y) = ((y \ x) * (y / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,26186,a(flip),b,40557,a)].">
      <j1 rule="hyper" parents="64 26186 40557"/>
    </justification>
  </clause>

  <clause id="40561">
    <literal><![CDATA[
      R((x \ y) * x,y \ x,x \ y) = ((y \ x) * (y / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,26426,a(flip),b,40559,a)].">
      <j1 rule="hyper" parents="64 26426 40559"/>
    </justification>
  </clause>

  <clause id="40563">
    <literal><![CDATA[
      R((x \ y) * x,x \ y,x \ y) = ((y \ x) * (y / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,37766,a(flip),b,40561,a)].">
      <j1 rule="hyper" parents="64 37766 40561"/>
    </justification>
  </clause>

  <clause id="40564">
    <literal><![CDATA[
      (x \ y) * (y * (1 / (x \ y))) = ((y \ x) * (y / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,2136,a(flip),b,40563,a)].">
      <j1 rule="hyper" parents="64 2136 40563"/>
    </justification>
  </clause>

  <clause id="40565">
    <literal><![CDATA[
      (x \ y) * (y * (1 / (x \ y))) = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,32283,a(flip),b,40564,a),flip(a)].">
      <j1 rule="hyper" parents="373 32283 40564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40566">
    <literal><![CDATA[
      (x \ y) \ ((y \ ((x \ y) \ y)) \ 1) = y \ (((y \ x) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(40565(a,1),38752(a,2,2))].">
      <j1 rule="para" parents="40565 38752"/>
    </justification>
  </clause>

  <clause id="40567">
    <literal><![CDATA[
      L((x \ a(y,x,z)) \ u,y \ (z \ (y * (x * z))),y \ (z \ (y * (x * z)))) = (1 / (x \ (x / (y \ ((y * (x * z)) / z))))) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,29552,a(flip),b,40411,a)].">
      <j1 rule="hyper" parents="64 29552 40411"/>
    </justification>
  </clause>

  <clause id="40568">
    <literal><![CDATA[
      (x \ (y / (y \ x))) \ (y * (T((y \ (x / (x \ y))) \ 1,y) * z)) = (y \ (x / (x \ y))) \ (y * ((y \ T(x / (x \ y),y)) * z))
    ]]></literal>
    <justification jstring="[hyper(149,a,40437,a)].">
      <j1 rule="hyper" parents="149 40437"/>
    </justification>
  </clause>

  <clause id="40569">
    <literal><![CDATA[
      L((x \ a(y,x,z)) \ u,(y * (x * z)) * (z * y),(y * (x * z)) * (z * y)) = (1 / (x \ (x / (y \ ((y * (x * z)) / z))))) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,35242,a(flip),b,40567,a)].">
      <j1 rule="hyper" parents="64 35242 40567"/>
    </justification>
  </clause>

  <clause id="40570">
    <literal><![CDATA[
      (x \ (y / (y \ x))) \ (y * (T(x \ (y / (y \ x)),y) * z)) = (y \ (x / (x \ y))) \ (y * ((y \ T(x / (x \ y),y)) * z))
    ]]></literal>
    <justification jstring="[para(40168(a,1),40568(a,1,2,2,1,1))].">
      <j1 rule="para" parents="40168 40568"/>
    </justification>
  </clause>

  <clause id="40571">
    <literal><![CDATA[
      (x \ (y / (y \ x))) \ (x * ((x \ T(y / (y \ x),x)) * z)) = (x \ y) * ((y \ x) \ (x * (T(y \ (x / (x \ y)),x) * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,40250,a(flip),b,40570,a),flip(a)].">
      <j1 rule="hyper" parents="64 40250 40570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40572">
    <literal><![CDATA[
      (x \ y) * ((y \ x) \ (x * (T(y \ (x / (x \ y)),x) * z))) = x * z
    ]]></literal>
    <justification jstring="[hyper(64,a,35855,a(flip),b,40571,a),flip(a)].">
      <j1 rule="hyper" parents="64 35855 40571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40574">
    <literal><![CDATA[
      x * (T(y \ (x / (x \ y)),x) * z) = (y \ x) * ((x \ y) \ (x * z))
    ]]></literal>
    <justification jstring="[para(40572(a,1),74(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="40572 74"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40575">
    <literal><![CDATA[
      L((x \ a(y,x,z)) \ u,(x * z) * (y \ (z * y)),(x * z) * (y \ (z * y))) = (1 / (x \ (x / (y \ ((y * (x * z)) / z))))) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,35254,a(flip),b,40569,a)].">
      <j1 rule="hyper" parents="64 35254 40569"/>
    </justification>
  </clause>

  <clause id="40576">
    <literal><![CDATA[
      L((x \ a(y,x,z)) \ u,(x * z) * T(z,y),(x * z) * (y \ (z * y))) = (1 / (x \ (x / (y \ ((y * (x * z)) / z))))) * u
    ]]></literal>
    <justification jstring="[para(22(a,2),40575(a,1,2,2))].">
      <j1 rule="para" parents="22 40575"/>
    </justification>
  </clause>

  <clause id="40577">
    <literal><![CDATA[
      L((x \ a(y,x,z)) \ u,(x * z) * T(z,y),(x * z) * T(z,y)) = (1 / (x \ (x / (y \ ((y * (x * z)) / z))))) * u
    ]]></literal>
    <justification jstring="[para(22(a,2),40576(a,1,3,2))].">
      <j1 rule="para" parents="22 40576"/>
    </justification>
  </clause>

  <clause id="40578">
    <literal><![CDATA[
      L((x \ a(y,x,z)) \ u,(x * z) * T(z,y),(x * z) * z) = (1 / (x \ (x / (y \ ((y * (x * z)) / z))))) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,28983,a(flip),b,40577,a)].">
      <j1 rule="hyper" parents="64 28983 40577"/>
    </justification>
  </clause>

  <clause id="40580">
    <literal><![CDATA[
      L((x \ a(y,x,z)) \ u,(x * z) * T(z,y),L(x,z,z)) = (1 / (x \ (x / (y \ ((y * (x * z)) / z))))) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,24838,a(flip),b,40578,a)].">
      <j1 rule="hyper" parents="64 24838 40578"/>
    </justification>
  </clause>

  <clause id="40581">
    <literal><![CDATA[
      L((x \ a(y,x,z)) \ u,L(x,z,z),L(x,z,z)) = (1 / (x \ (x / (y \ ((y * (x * z)) / z))))) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,29649,a(flip),b,40580,a)].">
      <j1 rule="hyper" parents="64 29649 40580"/>
    </justification>
  </clause>

  <clause id="40583">
    <literal><![CDATA[
      L((x \ a(y,x,z)) \ u,x,x) = (1 / (x \ (x / (y \ ((y * (x * z)) / z))))) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,35161,a(flip),b,40581,a)].">
      <j1 rule="hyper" parents="64 35161 40581"/>
    </justification>
  </clause>

  <clause id="40585">
    <literal><![CDATA[
      L((x \ a(y,x,z)) \ u,x,x) = (1 / (x \ a(y,x,z))) * u
    ]]></literal>
    <justification jstring="[para(33338(a,2),40583(a,2,1,2,2))].">
      <j1 rule="para" parents="33338 40583"/>
    </justification>
  </clause>

  <clause id="40586">
    <literal><![CDATA[
      L((x \ a(y,x,z)) \ u,x,x) = (a(y,x,z) \ x) * u
    ]]></literal>
    <justification jstring="[para(35789(a,1),40585(a,2,1))].">
      <j1 rule="para" parents="35789 40585"/>
    </justification>
  </clause>

  <clause id="40587">
    <literal><![CDATA[
      (a(x,y,z) \ y) * ((y \ a(x,y,z)) * u) = L(u,y,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),40586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 40586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40588">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ L(u,y,y) = (y \ a(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(149,a,40587,a)].">
      <j1 rule="hyper" parents="149 40587"/>
    </justification>
  </clause>

  <clause id="40589">
    <literal><![CDATA[
      (x \ a(y,x,z)) * (u * a(x,x,u)) = (a(y,x,z) \ x) \ u
    ]]></literal>
    <justification jstring="[hyper(139,a,30229,a(flip),b,40587,a),flip(a)].">
      <j1 rule="hyper" parents="139 30229 40587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40590">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ L((y \ 1) \ u,y,y) = (u / y) * (y * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,35760,a(flip),b,40588,a),flip(a)].">
      <j1 rule="hyper" parents="373 35760 40588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40591">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ L(u,y,y) = ((a(x,y,z) \ y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(35790(a,2),40588(a,2,1))].">
      <j1 rule="para" parents="35790 40588"/>
    </justification>
  </clause>

  <clause id="40592">
    <literal><![CDATA[
      L(a(x,y,z) \ y,a(x,y,z) \ y,u) \ u = u * ((y \ a(x,y,z)) * (K(u * y,y) * a(y,y,K(u * y,y))))
    ]]></literal>
    <justification jstring="[para(40589(a,2),36691(a,2,2))].">
      <j1 rule="para" parents="40589 36691"/>
    </justification>
  </clause>

  <clause id="40593">
    <literal><![CDATA[
      L(x,y * a(z,y,u),y * a(z,y,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(39,a,35226,a,b,40591,a)].">
      <j1 rule="hyper" parents="39 35226 40591"/>
    </justification>
  </clause>

  <clause id="40594">
    <literal><![CDATA[
      L(x,(y \ ((y * z) * u)) / u,z * a(y,z,u)) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33293,a,b,40593,a)].">
      <j1 rule="hyper" parents="64 33293 40593"/>
    </justification>
  </clause>

  <clause id="40595">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ (y * u) = (u / y) * (y * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(1137(a,1),40590(a,1,2))].">
      <j1 rule="para" parents="1137 40590"/>
    </justification>
  </clause>

  <clause id="40596">
    <literal><![CDATA[
      L(a(x,y,z) \ y,a(x,y,z) \ y,u) \ u = u * ((y \ a(x,y,z)) * K(u * y,y))
    ]]></literal>
    <justification jstring="[para(23081(a,1),40592(a,2,2,2))].">
      <j1 rule="para" parents="23081 40592"/>
    </justification>
  </clause>

  <clause id="40597">
    <literal><![CDATA[
      L(a(x,y,z) \ y,a(x,y,z) \ y,u) \ u = u * (T(y,u * y) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(19249(a,1),40596(a,2,2))].">
      <j1 rule="para" parents="19249 40596"/>
    </justification>
  </clause>

  <clause id="40599">
    <literal><![CDATA[
      L(a(x,y,z) \ y,a(x,y,z) \ y,u) \ u = T(u * (a(x,y,z) / y),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,40370,a(flip),b,40597,a),flip(a)].">
      <j1 rule="hyper" parents="373 40370 40597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40600">
    <literal><![CDATA[
      (((x * L(x,x,x)) \ y) * R(y \ ((x * L(x,x,x)) * x),z,u)) / x = (x * x) \ (x \ (y * R(((x * L(x,x,x)) \ y) \ x,z,u)))
    ]]></literal>
    <justification jstring="[para(13618(a,1),25712(a,1,1,2,1))].">
      <j1 rule="para" parents="13618 25712"/>
    </justification>
  </clause>

  <clause id="40601">
    <literal><![CDATA[
      R(x,y,(a(z,u,w) \ v5) * (v6 * (a(z,u,w) * a(z,u,w)))) = R(x,y,v6 * ((a(z,u,w) \ 1) \ v5))
    ]]></literal>
    <justification jstring="[para(593(a,1),26334(a,1,3,1))].">
      <j1 rule="para" parents="593 26334"/>
    </justification>
  </clause>

  <clause id="40603">
    <literal><![CDATA[
      R(x,y,z * ((a(u,w,v5) \ 1) \ v6)) = R(x,y,z * (a(u,w,v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,38900,a(flip),b,40601,a),flip(a)].">
      <j1 rule="hyper" parents="64 38900 40601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40605">
    <literal><![CDATA[
      L(x,y,z * (u \ (w * ((1 / w) * ((1 / (1 / w)) * v5))))) = L(x,y,z * (u \ ((w \ 1) * L(v5,1 / w,1 / w))))
    ]]></literal>
    <justification jstring="[para(848(a,1),29409(a,1,3,2,2,1)),flip(a)].">
      <j1 rule="para" parents="848 29409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40607">
    <literal><![CDATA[
      L(x,y,z * (u \ (w * ((1 / w) * ((1 / (1 / w)) * v5))))) = L(x,y,z * (u \ ((w \ 1) * L(v5,w,w))))
    ]]></literal>
    <justification jstring="[para(1158(a,1),40605(a,2,3,2,2,2))].">
      <j1 rule="para" parents="1158 40605"/>
    </justification>
  </clause>

  <clause id="40608">
    <literal><![CDATA[
      L(x,y,z * (u \ (w * ((1 / w) * ((1 / (1 / w)) * v5))))) = L(x,y,(u \ (w * L(v5,w,w))) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31622,a(flip),b,40607,a),flip(a)].">
      <j1 rule="hyper" parents="373 31622 40607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40609">
    <literal><![CDATA[
      L(x,y,z * (u \ (w * ((1 / w) * ((1 / (1 / w)) * v5))))) = L(x,y,(u \ (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,39928,a(flip),b,40608,a),flip(a)].">
      <j1 rule="hyper" parents="373 39928 40608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40610">
    <literal><![CDATA[
      L(x,y,z * (u \ (w * ((w \ 1) * (w * v5))))) = L(x,y,(u \ (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[para(6649(a,1),40609(a,1,3,2,2,2))].">
      <j1 rule="para" parents="6649 40609"/>
    </justification>
  </clause>

  <clause id="40611">
    <literal><![CDATA[
      L(x,y,z * (u \ L(w * v5,w,w))) = L(x,y,(u \ (w \ v5)) * z)
    ]]></literal>
    <justification jstring="[para(1139(a,1),40610(a,1,3,2,2))].">
      <j1 rule="para" parents="1139 40610"/>
    </justification>
  </clause>

  <clause id="40612">
    <literal><![CDATA[
      a(a(x,y,z),R(x,u,w),v5) * K(a(x,y,z),R(x,u,w) * v5) = a(R(x,u,w),a(x,y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,24647,a(flip),b,30883,a),flip(a)].">
      <j1 rule="hyper" parents="64 24647 30883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40613">
    <literal><![CDATA[
      a(a(x,y,z),R(x,u,w),v5) * K(a(x,y,z),R(x,u,w) * v5) = a(L(x,u,w),a(x,y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32590,a(flip),b,40612,a),flip(a)].">
      <j1 rule="hyper" parents="373 32590 40612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40614">
    <literal><![CDATA[
      a(a(x,y,z),L(x,u,w),v5) * K(a(x,y,z),R(x,u,w) * v5) = a(L(x,u,w),a(x,y,z),v5)
    ]]></literal>
    <justification jstring="[para(32197(a,1),40613(a,1,1))].">
      <j1 rule="para" parents="32197 40613"/>
    </justification>
  </clause>

  <clause id="40615">
    <literal><![CDATA[
      a(L(x,y,z),a(x,u,w),v5) = a(a(x,u,w),L(x,y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,23125,a(flip),b,40614,a),flip(a)].">
      <j1 rule="hyper" parents="64 23125 40614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40617">
    <literal><![CDATA[
      a(x * (((y * y) * ((z * u) * w)) * R(u,z,w)),R(u,z,w),R(u,z,w)) = a(x * (T((y * y) * z,u) * w),R(u,z,w),L(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27644,a(flip),b,34900,a),flip(a)].">
      <j1 rule="hyper" parents="373 27644 34900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40618">
    <literal><![CDATA[
      L((x \ ((y / (1 / (1 / x))) / y)) \ z,((y / x) / y) * x,(1 / x) \ ((y / x) / y)) = (1 / ((1 / (1 / x)) \ ((y / x) / y))) * z
    ]]></literal>
    <justification jstring="[para(3957(a,1),35234(a,1,1,1))].">
      <j1 rule="para" parents="3957 35234"/>
    </justification>
  </clause>

  <clause id="40619">
    <literal><![CDATA[
      (((x * L(x,x,x)) \ y) * R(y \ (x * (x * x)),z,u)) / x = (x * x) \ (x \ (y * R(((x * L(x,x,x)) \ y) \ x,z,u)))
    ]]></literal>
    <justification jstring="[para(2846(a,1),40600(a,1,1,2,1,2))].">
      <j1 rule="para" parents="2846 40600"/>
    </justification>
  </clause>

  <clause id="40620">
    <literal><![CDATA[
      (x * L(x,x,x)) \ ((y * R(y \ (x * (x * x)),z,u)) / x) = (x * x) \ (x \ (y * R(((x * L(x,x,x)) \ y) \ x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,13620,a(flip),b,40619,a)].">
      <j1 rule="hyper" parents="64 13620 40619"/>
    </justification>
  </clause>

  <clause id="40621">
    <literal><![CDATA[
      (x * x) \ ((y * R(y \ (x * (x * x)),z,u)) / L(x,x,x)) = (x * x) \ (x \ (y * R(((x * L(x,x,x)) \ y) \ x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,12931,a(flip),b,40620,a)].">
      <j1 rule="hyper" parents="64 12931 40620"/>
    </justification>
  </clause>

  <clause id="40622">
    <literal><![CDATA[
      L((x \ (x \ (y * R(y \ (x * (x * x)),z,u)))) / x,x,x) = (x * x) \ (x \ (y * R(((x * L(x,x,x)) \ y) \ x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,31210,a,b,40621,a)].">
      <j1 rule="hyper" parents="64 31210 40621"/>
    </justification>
  </clause>

  <clause id="40623">
    <literal><![CDATA[
      L((x \ ((x \ y) * R((x \ y) \ (x * x),z,u))) / x,x,x) = (x * x) \ (x \ (y * R(((x * L(x,x,x)) \ y) \ x,z,u)))
    ]]></literal>
    <justification jstring="[para(1956(a,1),40622(a,1,1,1,2))].">
      <j1 rule="para" parents="1956 40622"/>
    </justification>
  </clause>

  <clause id="40624">
    <literal><![CDATA[
      L(((x \ (x \ y)) * R((x \ (x \ y)) \ x,z,u)) / x,x,x) = (x * x) \ (x \ (y * R(((x * L(x,x,x)) \ y) \ x,z,u)))
    ]]></literal>
    <justification jstring="[para(1956(a,1),40623(a,1,1,1))].">
      <j1 rule="para" parents="1956 40623"/>
    </justification>
  </clause>

  <clause id="40625">
    <literal><![CDATA[
      (x * x) \ (x \ (y * R(((x * L(x,x,x)) \ y) \ x,z,u))) = L((((x \ y) / x) \ R(x \ y,z,u)) / x,x,x)
    ]]></literal>
    <justification jstring="[para(27049(a,1),40624(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="27049 40624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40626">
    <literal><![CDATA[
      (x * x) \ (x \ (y * R(((x * L(x,x,x)) \ y) \ x,z,u))) = L(L((x \ y) \ R(x \ y,z,u),x,x),x,x)
    ]]></literal>
    <justification jstring="[para(36341(a,1),40625(a,2,1))].">
      <j1 rule="para" parents="36341 40625"/>
    </justification>
  </clause>

  <clause id="40627">
    <literal><![CDATA[
      (x * x) \ (x \ (y * R(((x * L(x,x,x)) \ y) \ x,z,u))) = L(L(x \ (y * R(y \ x,z,u)),x,x),x,x)
    ]]></literal>
    <justification jstring="[para(2744(a,1),40626(a,2,1,1))].">
      <j1 rule="para" parents="2744 40626"/>
    </justification>
  </clause>

  <clause id="40628">
    <literal><![CDATA[
      (x * x) \ (x \ (y * R(((x * L(x,x,x)) \ y) \ x,z,u))) = L((1 / x) * (y * R(y \ x,z,u)),x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,580,a(flip),b,40627,a),flip(a)].">
      <j1 rule="hyper" parents="373 580 40627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40629">
    <literal><![CDATA[
      (x * x) \ (x \ (y * R(((x * L(x,x,x)) \ y) \ x,z,u))) = L((y * x) \ R(y * x,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(31776(a,1),40628(a,2,1))].">
      <j1 rule="para" parents="31776 40628"/>
    </justification>
  </clause>

  <clause id="40630">
    <literal><![CDATA[
      (x * x) \ (x \ (y * R(y \ ((x * L(x,x,x)) * x),z,u))) = L((y * x) \ R(y * x,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(13618(a,1),40629(a,1,2,2,2,1))].">
      <j1 rule="para" parents="13618 40629"/>
    </justification>
  </clause>

  <clause id="40631">
    <literal><![CDATA[
      (x * x) \ (x \ (y * R(y \ (x * (x * x)),z,u))) = L((y * x) \ R(y * x,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(2846(a,1),40630(a,1,2,2,2,1,2))].">
      <j1 rule="para" parents="2846 40630"/>
    </justification>
  </clause>

  <clause id="40632">
    <literal><![CDATA[
      (x * x) \ ((x \ y) * R((x \ y) \ (x * x),z,u)) = L((y * x) \ R(y * x,z,u),x,x)
    ]]></literal>
    <justification jstring="[para(1956(a,1),40631(a,1,2))].">
      <j1 rule="para" parents="1956 40631"/>
    </justification>
  </clause>

  <clause id="40633">
    <literal><![CDATA[
      ((x * x) \ (x \ y)) * R((x \ y) \ (x * x),z,u) = L((y * x) \ R(y * x,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(806,a,40632,a)].">
      <j1 rule="hyper" parents="806 40632"/>
    </justification>
  </clause>

  <clause id="40634">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ ((x * x) \ (x * x)),z,u) = L((y * x) \ R(y * x,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,2786,a(flip),b,40633,a)].">
      <j1 rule="hyper" parents="64 2786 40633"/>
    </justification>
  </clause>

  <clause id="40635">
    <literal><![CDATA[
      L((x * y) \ R(x * y,z,u),y,y) = (y \ x) * R((y \ x) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(68(a,1),40634(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="68 40634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40636">
    <literal><![CDATA[
      L((x * y) \ R(x * y,z,u),y,y) = y \ (x * R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,2743,a(flip),b,40635,a),flip(a)].">
      <j1 rule="hyper" parents="373 2743 40635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40638">
    <literal><![CDATA[
      L(x,x,L((y * z) * L(y * z,u,w),z,z)) = R(x,x,z \ (y * R(y \ z,u,w)))
    ]]></literal>
    <justification jstring="[para(40636(a,1),37086(a,1,3)),flip(a)].">
      <j1 rule="para" parents="40636 37086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40639">
    <literal><![CDATA[
      a(x * (((y * y) * ((z * u) * w)) * R(u,z,w)),R(u,z,w),R(u,z,w)) = a(x * (T((y * y) * z,u) * w),L(u,z,w),L(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,32197,a(flip),b,40617,a),flip(a)].">
      <j1 rule="hyper" parents="373 32197 40617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40640">
    <literal><![CDATA[
      L((x \ (1 / (1 / ((y / x) / y)))) \ z,((y / x) / y) * x,(1 / x) \ ((y / x) / y)) = (1 / ((1 / (1 / x)) \ ((y / x) / y))) * z
    ]]></literal>
    <justification jstring="[para(3946(a,1),40618(a,1,1,1,2))].">
      <j1 rule="para" parents="3946 40618"/>
    </justification>
  </clause>

  <clause id="40641">
    <literal><![CDATA[
      (1 / L(x,y,z)) * (T(x \ 1,L(x,y,z) \ (L(x,y,z) \ 1)) \ u) = (1 / x) \ ((1 / L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1127(a,1),27184(a,2,2))].">
      <j1 rule="para" parents="1127 27184"/>
    </justification>
  </clause>

  <clause id="40642">
    <literal><![CDATA[
      (1 / L(x,y,z)) * (T(x \ 1,L(x,y,z) \ (L(x,y,z) \ 1)) \ u) = (x \ 1) \ ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,33917,a(flip),b,40641,a),flip(a)].">
      <j1 rule="hyper" parents="373 33917 40641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40643">
    <literal><![CDATA[
      (1 / L(x,y,z)) * (T(x \ 1,x \ (x \ 1)) \ u) = (x \ 1) \ ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(28453(a,1),40642(a,1,2,1))].">
      <j1 rule="para" parents="28453 40642"/>
    </justification>
  </clause>

  <clause id="40644">
    <literal><![CDATA[
      (1 / L(x,y,z)) * (T(1 / x,x \ 1) \ u) = (x \ 1) \ ((L(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(14817(a,1),40643(a,1,2,1))].">
      <j1 rule="para" parents="14817 40643"/>
    </justification>
  </clause>

  <clause id="40646">
    <literal><![CDATA[
      (x \ 1) \ ((L(x,y,z) \ 1) * u) = (1 / L(x,y,z)) * ((1 / x) \ u)
    ]]></literal>
    <justification jstring="[para(282(a,1),40644(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="282 40644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40647">
    <literal><![CDATA[
      (x \ 1) \ ((L(x,y,z) \ 1) * u) = (L(x,y,z) \ 1) * ((x \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26980,a(flip),b,40646,a),flip(a)].">
      <j1 rule="hyper" parents="373 26980 40646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40648">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,35187,a(flip),b,40647,a),flip(a)].">
      <j1 rule="hyper" parents="64 35187 40647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40649">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * (1 / x))) = u * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,34453,a(flip),b,40648,a),flip(a)].">
      <j1 rule="hyper" parents="64 34453 40648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40650">
    <literal><![CDATA[
      (x / y) * (y * (L(y,z,u) \ y)) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,28903,a(flip),b,40648,a)].">
      <j1 rule="hyper" parents="64 28903 40648"/>
    </justification>
  </clause>

  <clause id="40651">
    <literal><![CDATA[
      (x / (y \ 1)) * (L(y,z,u) \ 1) = y * (L(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,28555,a(flip),b,40648,a)].">
      <j1 rule="hyper" parents="64 28555 40648"/>
    </justification>
  </clause>

  <clause id="40652">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * u = x * (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(40648(a,1),31554(a,1,2)),flip(a)].">
      <j1 rule="para" parents="40648 31554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40653">
    <literal><![CDATA[
      R(x,y,y) / L(y,z,u) = x * (1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,25111,a(flip),b,40649,a)].">
      <j1 rule="hyper" parents="64 25111 40649"/>
    </justification>
  </clause>

  <clause id="40654">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y,z,u)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(38,a,1408,a,b,40653,a)].">
      <j1 rule="hyper" parents="38 1408 40653"/>
    </justification>
  </clause>

  <clause id="40656">
    <literal><![CDATA[
      R(x,L(y,z,u),L(y,z,u)) = x * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,15984,a,b,40654,a),flip(a)].">
      <j1 rule="hyper" parents="373 15984 40654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40657">
    <literal><![CDATA[
      R(((1 / x) \ a(y,y,z)) \ 1,x,x) = (a(y,y,z) / (1 / L(x,x,a(z,y,y)))) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,30601,a(flip),b,40654,a),flip(a)].">
      <j1 rule="hyper" parents="64 30601 40654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40658">
    <literal><![CDATA[
      R(x,y \ (z \ y),y \ ((z \ 1) \ y)) = R(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27179,a(flip),b,40654,a)].">
      <j1 rule="hyper" parents="64 27179 40654"/>
    </justification>
  </clause>

  <clause id="40659">
    <literal><![CDATA[
      R(x,(1 / y) * z,L(y \ z,y,y)) = R(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[para(569(a,1),40654(a,1,2))].">
      <j1 rule="para" parents="569 40654"/>
    </justification>
  </clause>

  <clause id="40660">
    <literal><![CDATA[
      R(x,(y * z) \ u,L(z \ (y \ u),z,y)) = R(x,z \ (y \ u),z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(346(a,1),40654(a,1,2))].">
      <j1 rule="para" parents="346 40654"/>
    </justification>
  </clause>

  <clause id="40661">
    <literal><![CDATA[
      R(x,a(y,z,u),L(y \ R(y,z,u),y,z * u)) = R(x,y \ R(y,z,u),y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(16031(a,2),40654(a,1,2))].">
      <j1 rule="para" parents="16031 40654"/>
    </justification>
  </clause>

  <clause id="40663">
    <literal><![CDATA[
      R(x,y,y) / R(y,z,u) = x * (1 / R(y,z,u))
    ]]></literal>
    <justification jstring="[para(40654(a,1),26723(a,1,1))].">
      <j1 rule="para" parents="40654 26723"/>
    </justification>
  </clause>

  <clause id="40664">
    <literal><![CDATA[
      a(x,L(y,z,u),L(y,z,u)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,15984,a,b,40656,a(flip))].">
      <j1 rule="hyper" parents="35 15984 40656"/>
    </justification>
  </clause>

  <clause id="40665">
    <literal><![CDATA[
      a(x * (((y * y) * ((z * u) * w)) * R(u,z,w)),R(u,z,w),R(u,z,w)) = a(x * (T((y * y) * z,u) * w),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,40639,a,b,40664,a)].">
      <j1 rule="hyper" parents="64 40639 40664"/>
    </justification>
  </clause>

  <clause id="40666">
    <literal><![CDATA[
      a(x * (y * L(z,u,w)),L(z,u,w),L(z,u,w)) = a(L(z,u,w) * (x * y),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37898,a,b,40664,a)].">
      <j1 rule="hyper" parents="64 37898 40664"/>
    </justification>
  </clause>

  <clause id="40667">
    <literal><![CDATA[
      a(x,(y * z) \ u,L(z \ (y \ u),z,y)) = a(x,z \ (y \ u),z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(346(a,1),40664(a,1,2))].">
      <j1 rule="para" parents="346 40664"/>
    </justification>
  </clause>

  <clause id="40669">
    <literal><![CDATA[
      L(L(x,x,y),L(x,x,y),z) = a(y,x,x) \ (a(z,x,x) \ x)
    ]]></literal>
    <justification jstring="[para(40664(a,1),38030(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="40664 38030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40670">
    <literal><![CDATA[
      a(x,y,y) * (z \ L(y,L(y,z,z),x)) = z \ y
    ]]></literal>
    <justification jstring="[para(40664(a,1),39208(a,1,1))].">
      <j1 rule="para" parents="40664 39208"/>
    </justification>
  </clause>

  <clause id="40671">
    <literal><![CDATA[
      (x * (R(x,y,z) \ u)) * (1 / x) = u * (1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,36060,a,b,40663,a)].">
      <j1 rule="hyper" parents="64 36060 40663"/>
    </justification>
  </clause>

  <clause id="40674">
    <literal><![CDATA[
      (x * (L(x,y,z) \ x)) * (x \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31351,a(flip),b,40650,a)].">
      <j1 rule="hyper" parents="64 31351 40650"/>
    </justification>
  </clause>

  <clause id="40675">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * x)) = u * (x * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[para(11(a,1),40650(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 40650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40677">
    <literal><![CDATA[
      (x * y) \ (x * (x * (L(x,z,u) \ y))) = L(L(x,z,u) \ x,x,y)
    ]]></literal>
    <justification jstring="[para(40652(a,1),31856(a,1,2))].">
      <j1 rule="para" parents="40652 31856"/>
    </justification>
  </clause>

  <clause id="40678">
    <literal><![CDATA[
      (a(x,x,y) \ z) * (1 / x) = z * (1 / R(x,x,y))
    ]]></literal>
    <justification jstring="[para(37544(a,1),40671(a,1,1))].">
      <j1 rule="para" parents="37544 40671"/>
    </justification>
  </clause>

  <clause id="40679">
    <literal><![CDATA[
      (a(x,x,y) \ z) / L(x,x,z) = z * (1 / R(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,34029,a,b,40678,a)].">
      <j1 rule="hyper" parents="64 34029 40678"/>
    </justification>
  </clause>

  <clause id="40680">
    <literal><![CDATA[
      L(x,L(x,x,y),z) = L(x,x,z)
    ]]></literal>
    <justification jstring="[hyper(37,a,37705,a,b,40679,a)].">
      <j1 rule="hyper" parents="37 37705 40679"/>
    </justification>
  </clause>

  <clause id="40681">
    <literal><![CDATA[
      L(x,y \ (x \ y),z) = L(x,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29726,a(flip),b,40680,a)].">
      <j1 rule="hyper" parents="64 29726 40680"/>
    </justification>
  </clause>

  <clause id="40683">
    <literal><![CDATA[
      L(R(x,y,z),L(x,x,u),w) = R(L(x,x,w),y,z)
    ]]></literal>
    <justification jstring="[para(40680(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="40680 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40684">
    <literal><![CDATA[
      L(L(x,y,z),L(x,x,u),w) = L(L(x,x,w),y,z)
    ]]></literal>
    <justification jstring="[para(40680(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="40680 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40687">
    <literal><![CDATA[
      L(x,x,y) \ L(R(x,z,u),w \ (x \ w),y) = L(x \ R(x,z,u),w \ (x \ w),y)
    ]]></literal>
    <justification jstring="[para(40681(a,1),4243(a,1,1))].">
      <j1 rule="para" parents="40681 4243"/>
    </justification>
  </clause>

  <clause id="40688">
    <literal><![CDATA[
      L(R(x,y,z),L(x,x,u),w) = L(R(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29,a(flip),b,40683,a),flip(a)].">
      <j1 rule="hyper" parents="373 29 40683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40689">
    <literal><![CDATA[
      L(R(x,y,z),u \ (x \ u),w) = L(R(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29726,a(flip),b,40688,a)].">
      <j1 rule="hyper" parents="64 29726 40688"/>
    </justification>
  </clause>

  <clause id="40690">
    <literal><![CDATA[
      (x * y) \ (y * (L(y,z,u) \ (x * y))) = L(L(y,z,u) \ y,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,40675,a,b,100,a)].">
      <j1 rule="hyper" parents="139 40675 100"/>
    </justification>
  </clause>

  <clause id="40691">
    <literal><![CDATA[
      R(x,(1 / y) * z,(1 / y) * z) = R(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[para(569(a,1),40659(a,1,3))].">
      <j1 rule="para" parents="569 40659"/>
    </justification>
  </clause>

  <clause id="40692">
    <literal><![CDATA[
      R(x,(1 / y) * z,(y \ 1) * z) = R(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26180,a(flip),b,40691,a)].">
      <j1 rule="hyper" parents="64 26180 40691"/>
    </justification>
  </clause>

  <clause id="40693">
    <literal><![CDATA[
      R(x,y * z,(y \ 1) * z) = R(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2969,a(flip),b,40692,a)].">
      <j1 rule="hyper" parents="64 2969 40692"/>
    </justification>
  </clause>

  <clause id="40694">
    <literal><![CDATA[
      R(x,y * z,(z \ 1) * y) = R(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26409,a,b,40693,a)].">
      <j1 rule="hyper" parents="64 26409 40693"/>
    </justification>
  </clause>

  <clause id="40695">
    <literal><![CDATA[
      R(x,(y * z) * (u * ((y * z) / y)),((y * z) \ 1) * (u * ((y * z) / y))) = R(x,L(y \ T(u,T(z,y)),y,z),(y * z) \ (u * ((y * z) / y)))
    ]]></literal>
    <justification jstring="[para(11301(a,1),40693(a,2,2))].">
      <j1 rule="para" parents="11301 40693"/>
    </justification>
  </clause>

  <clause id="40696">
    <literal><![CDATA[
      a(x,y * z,(y \ 1) * z) = x \ R(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[para(40693(a,1),16185(a,1,2)),flip(a)].">
      <j1 rule="para" parents="40693 16185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40697">
    <literal><![CDATA[
      R(x,((y * y) * z) * (z * y),((z * y) \ 1) * ((y * y) * z)) = R(x,z \ ((y * y) * (z / y)),(z * y) \ ((y * y) * z))
    ]]></literal>
    <justification jstring="[para(26132(a,1),40694(a,2,2))].">
      <j1 rule="para" parents="26132 40694"/>
    </justification>
  </clause>

  <clause id="40698">
    <literal><![CDATA[
      a(x,y * z,(y \ 1) * z) = a(x,y \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,15987,a(flip),b,40696,a),flip(a)].">
      <j1 rule="hyper" parents="373 15987 40696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40699">
    <literal><![CDATA[
      a(x,y * z,(z \ 1) * y) = a(x,z \ y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(32008,a,40698,a)].">
      <j1 rule="hyper" parents="32008 40698"/>
    </justification>
  </clause>

  <clause id="40700">
    <literal><![CDATA[
      a(x,(y * ((z * u) / z)) * (z * u),((z * u) \ 1) * (y * ((z * u) / z))) = a(x,L(z \ T(y,T(u,z)),z,u),(z * u) \ (y * ((z * u) / z)))
    ]]></literal>
    <justification jstring="[para(11301(a,1),40699(a,2,2))].">
      <j1 rule="para" parents="11301 40699"/>
    </justification>
  </clause>

  <clause id="40701">
    <literal><![CDATA[
      L(L(x,x,y),L(x,x,y),z) = a(y,x,x) \ L(x,x,z)
    ]]></literal>
    <justification jstring="[para(30459(a,1),40669(a,2,2))].">
      <j1 rule="para" parents="30459 40669"/>
    </justification>
  </clause>

  <clause id="40705">
    <literal><![CDATA[
      a(x,y,y) \ L(y,y,z) = L(L(y,y,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,40684,a(flip),b,40701,a),flip(a)].">
      <j1 rule="hyper" parents="64 40684 40701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40707">
    <literal><![CDATA[
      a(x,y,y) \ L(y,y,z) = L(L(y,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,30,a,b,40705,a),flip(a)].">
      <j1 rule="hyper" parents="373 30 40705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40709">
    <literal><![CDATA[
      L(x \ (y * (L(y,z,u) \ x)),x,y) = L(L(y,z,u) \ y,y,x)
    ]]></literal>
    <justification jstring="[hyper(764,a,40677,a)].">
      <j1 rule="hyper" parents="764 40677"/>
    </justification>
  </clause>

  <clause id="40710">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(42,a,33181,a,b,40709,a)].">
      <j1 rule="hyper" parents="42 33181 40709"/>
    </justification>
  </clause>

  <clause id="40711">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,z,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,33484,a,b,40710,a)].">
      <j1 rule="hyper" parents="373 33484 40710"/>
    </justification>
  </clause>

  <clause id="40712">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,y) = a(z,y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,33406,a,b,40710,a),flip(a)].">
      <j1 rule="hyper" parents="373 33406 40710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40713">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) * u = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(144,a,40710,a,b,25456,a)].">
      <j1 rule="hyper" parents="144 40710 25456"/>
    </justification>
  </clause>

  <clause id="40714">
    <literal><![CDATA[
      L(L(x \ y,z,u) \ (x \ y),x \ y,x) = x \ (L(y / x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(25820(a,1),40710(a,2,2))].">
      <j1 rule="para" parents="25820 40710"/>
    </justification>
  </clause>

  <clause id="40716">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,40711,a),flip(a)].">
      <j1 rule="hyper" parents="373 23253 40711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40717">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,z,(x * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,1631,a,b,40711,a),flip(a)].">
      <j1 rule="hyper" parents="373 1631 40711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40718">
    <literal><![CDATA[
      L(a(x,y,z),z,x * y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(36303,a,40711,a(flip))].">
      <j1 rule="hyper" parents="36303 40711"/>
    </justification>
  </clause>

  <clause id="40719">
    <literal><![CDATA[
      L(a(x,y,z),z,y * x) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(36303,a,40716,a(flip))].">
      <j1 rule="hyper" parents="36303 40716"/>
    </justification>
  </clause>

  <clause id="40720">
    <literal><![CDATA[
      a(x * y,z,a(y,x,z)) * ((L(z,x,y) \ z) \ z) = L(L(z,x,y) \ z,z,x * y) \ z
    ]]></literal>
    <justification jstring="[para(40716(a,2),33496(a,1,1,3))].">
      <j1 rule="para" parents="40716 33496"/>
    </justification>
  </clause>

  <clause id="40721">
    <literal><![CDATA[
      L(x,y,z) \ (L(x / L(x,y,z),x,y * z) \ x) = a(y * z,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(40716(a,2),33520(a,1,3)),flip(a)].">
      <j1 rule="para" parents="40716 33520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40722">
    <literal><![CDATA[
      L(x,y,z) \ (L(x / L(x,y,z),x,y * z) \ x) = (L(x,y,z) * a(z,y,x)) \ x
    ]]></literal>
    <justification jstring="[para(40716(a,2),34866(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="40716 34866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40723">
    <literal><![CDATA[
      R(x,a(y,z,u),L(L(u,z,y) \ u,u,z * y)) = R(x,L(u,z,y) \ u,L(u,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(40716(a,2),40654(a,1,2))].">
      <j1 rule="para" parents="40716 40654"/>
    </justification>
  </clause>

  <clause id="40724">
    <literal><![CDATA[
      L(x,L(x,y,z),u) \ x = a(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39814,a(flip),b,40718,a),flip(a)].">
      <j1 rule="hyper" parents="64 39814 40718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40725">
    <literal><![CDATA[
      L(a(x \ y,x,z),z,y) = L(z,x,x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,23833,a(flip),b,40718,a)].">
      <j1 rule="hyper" parents="64 23833 40718"/>
    </justification>
  </clause>

  <clause id="40726">
    <literal><![CDATA[
      L(L(L(x,y,z),u,w) \ L(x,y,z),L(x,y,z),u) = a(w,u,L(L(x,u,w),y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27702,a,b,40712,a),flip(a)].">
      <j1 rule="hyper" parents="373 27702 40712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40727">
    <literal><![CDATA[
      L(L(x \ y,x,z) \ (x \ y),x \ y,x) = (x * ((z * x) \ (z * y))) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,30451,a(flip),b,40712,a),flip(a)].">
      <j1 rule="hyper" parents="373 30451 40712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40728">
    <literal><![CDATA[
      (L(L(x,y,z) \ x,x,y) * y) \ (y * x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(40712(a,2),33305(a,1,1,1))].">
      <j1 rule="para" parents="40712 33305"/>
    </justification>
  </clause>

  <clause id="40729">
    <literal><![CDATA[
      (L(L(x,y,z) \ x,x,y) \ y) * x = y * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(40712(a,2),33486(a,1,1,1))].">
      <j1 rule="para" parents="40712 33486"/>
    </justification>
  </clause>

  <clause id="40730">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,y) \ y = (y / x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(40712(a,2),33487(a,1,1))].">
      <j1 rule="para" parents="40712 33487"/>
    </justification>
  </clause>

  <clause id="40731">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,y) * (x \ y) = L(x,y,z) \ y
    ]]></literal>
    <justification jstring="[para(40712(a,2),33496(a,1,1))].">
      <j1 rule="para" parents="40712 33496"/>
    </justification>
  </clause>

  <clause id="40732">
    <literal><![CDATA[
      L(L(a(x,y,z),x,L(u,x,w)) \ a(x,y,z),a(x,y,z),x) = a(L(u,x,w),x,L(a(x,y,z),x,u))
    ]]></literal>
    <justification jstring="[para(38028(a,1),40712(a,2,3))].">
      <j1 rule="para" parents="38028 40712"/>
    </justification>
  </clause>

  <clause id="40733">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) \ y = L(y,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,40724,a)].">
      <j1 rule="hyper" parents="40 23134 40724"/>
    </justification>
  </clause>

  <clause id="40734">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,u,w),x,(z * y) \ 1) = L(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(40717(a,2),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="40717 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40736">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u * x) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,40710,a,b,40690,a)].">
      <j1 rule="hyper" parents="64 40710 40690"/>
    </justification>
  </clause>

  <clause id="40737">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,x \ u) = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23833,a(flip),b,40736,a),flip(a)].">
      <j1 rule="hyper" parents="64 23833 40736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40738">
    <literal><![CDATA[
      L(L(L(x,y,z) \ x,x,u),x,(z * y) \ 1) = L(a(z,y,x),x,x \ u)
    ]]></literal>
    <justification jstring="[para(40737(a,1),40734(a,1,1))].">
      <j1 rule="para" parents="40737 40734"/>
    </justification>
  </clause>

  <clause id="40739">
    <literal><![CDATA[
      L(a(x,y,z),z,z \ u) = L(a(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,40734,a(flip),b,40738,a),flip(a)].">
      <j1 rule="hyper" parents="64 40734 40738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40741">
    <literal><![CDATA[
      R(x,(y * z) \ u,(y * z) \ u) = R(x,z \ (y \ u),z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(346(a,1),40660(a,1,3))].">
      <j1 rule="para" parents="346 40660"/>
    </justification>
  </clause>

  <clause id="40742">
    <literal><![CDATA[
      a(x,(y * z) \ u,(y * z) \ u) = a(x,z \ (y \ u),z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(346(a,1),40667(a,1,3))].">
      <j1 rule="para" parents="346 40667"/>
    </justification>
  </clause>

  <clause id="40743">
    <literal><![CDATA[
      a(L(x,y,z) * (u * w),x,x) = a(u * (w * L(x,y,z)),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,40664,a(flip),b,40666,a),flip(a)].">
      <j1 rule="hyper" parents="64 40664 40666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40746">
    <literal><![CDATA[
      R(((1 / x) \ a(y,y,z)) \ 1,x,x) = (a(y,y,z) / L(1 / x,x,a(z,y,y))) \ 1
    ]]></literal>
    <justification jstring="[para(36333(a,2),40657(a,2,1,2))].">
      <j1 rule="para" parents="36333 40657"/>
    </justification>
  </clause>

  <clause id="40747">
    <literal><![CDATA[
      L(x \ R(x,y,z),u \ (x \ u),w) = L(x,x,w) \ L(R(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[para(40689(a,1),40687(a,1,2)),flip(a)].">
      <j1 rule="para" parents="40689 40687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40748">
    <literal><![CDATA[
      L(x \ R(x,y,z),u \ (x \ u),w) = L(x \ R(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,4243,a(flip),b,40747,a),flip(a)].">
      <j1 rule="hyper" parents="373 4243 40747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40750">
    <literal><![CDATA[
      L(x \ R(x,y,z),L(x,x,u),w) = L(x \ R(x,y,z),x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29731,a,b,40748,a)].">
      <j1 rule="hyper" parents="64 29731 40748"/>
    </justification>
  </clause>

  <clause id="40751">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),x,y * z),x,u) = a((x * u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(40748(a,1),31473(a,1,1))].">
      <j1 rule="para" parents="40748 31473"/>
    </justification>
  </clause>

  <clause id="40752">
    <literal><![CDATA[
      L(a(x,y,z),x,u) = a((x * u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(16031(a,2),40751(a,1,1))].">
      <j1 rule="para" parents="16031 40751"/>
    </justification>
  </clause>

  <clause id="40754">
    <literal><![CDATA[
      L(a(x,y,z),x,u) = a(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,13122,a(flip),b,40752,a),flip(a)].">
      <j1 rule="hyper" parents="373 13122 40752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40755">
    <literal><![CDATA[
      a(x \ (y \ x),z,x) = a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(33227,a,40754,a),flip(a)].">
      <j1 rule="hyper" parents="33227 40754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40756">
    <literal><![CDATA[
      a(L(x,x,y),z,u) = L(a(x,z,u),x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,32455,a,b,40754,a)].">
      <j1 rule="hyper" parents="373 32455 40754"/>
    </justification>
  </clause>

  <clause id="40757">
    <literal><![CDATA[
      x * a(y \ ((y \ x) \ y),z,u) = y * ((y \ x) * a(y \ x,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,40754,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="145 40754 101"/>
    </justification>
  </clause>

  <clause id="40759">
    <literal><![CDATA[
      x \ R(x,x \ R(x,y,z),u) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,39442,a(flip),b,40755,a)].">
      <j1 rule="hyper" parents="64 39442 40755"/>
    </justification>
  </clause>

  <clause id="40760">
    <literal><![CDATA[
      a(x \ y,z,y) = a(y \ x,z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32370,a(flip),b,40755,a),flip(a)].">
      <j1 rule="hyper" parents="64 32370 40755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40761">
    <literal><![CDATA[
      a((x * y) \ z,u,y * x) = a(z \ (x * y),u,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,40760,a)].">
      <j1 rule="hyper" parents="373 27298 40760"/>
    </justification>
  </clause>

  <clause id="40762">
    <literal><![CDATA[
      a(x,y,z) * a(x,a(x,y,z),u) = a(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,39358,a,b,40756,a)].">
      <j1 rule="hyper" parents="373 39358 40756"/>
    </justification>
  </clause>

  <clause id="40763">
    <literal><![CDATA[
      a(x,a(x,y,z),u) * a(x,y,z) = a(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,39357,a,b,40756,a)].">
      <j1 rule="hyper" parents="373 39357 40756"/>
    </justification>
  </clause>

  <clause id="40764">
    <literal><![CDATA[
      a(L(x,x,y),z,x * y) = a(x,z,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,39257,a(flip),b,40756,a),flip(a)].">
      <j1 rule="hyper" parents="373 39257 40756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40765">
    <literal><![CDATA[
      a(L(x,x,y),z,x \ y) = a(x,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,39251,a(flip),b,40756,a),flip(a)].">
      <j1 rule="hyper" parents="373 39251 40756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40766">
    <literal><![CDATA[
      a(L(x,x,y),L(x,z,u),w) = a(x,L(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,38674,a(flip),b,40756,a),flip(a)].">
      <j1 rule="hyper" parents="373 38674 40756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40767">
    <literal><![CDATA[
      a(x,y,z) \ a(L(x,x,u),y,z) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(139,a,40756,a,b,39358,a)].">
      <j1 rule="hyper" parents="139 40756 39358"/>
    </justification>
  </clause>

  <clause id="40768">
    <literal><![CDATA[
      a(x,y,z) * (x \ (a(L(x,x,L(u,x,a(x,y,z))),y,z) \ (x * u))) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(40756(a,2),35502(a,1,2,2,1))].">
      <j1 rule="para" parents="40756 35502"/>
    </justification>
  </clause>

  <clause id="40769">
    <literal><![CDATA[
      a(x,y,z) \ a(L(x,x,z * y),y,z) = a(x,x * L(x,y,z),z * y)
    ]]></literal>
    <justification jstring="[para(40756(a,2),36787(a,1,2))].">
      <j1 rule="para" parents="40756 36787"/>
    </justification>
  </clause>

  <clause id="40770">
    <literal><![CDATA[
      a(L(x,x,y),a(x,z,u),w) = L(a(w,x,a(x,z,u)),x,y)
    ]]></literal>
    <justification jstring="[para(39362(a,1),40756(a,2,1))].">
      <j1 rule="para" parents="39362 40756"/>
    </justification>
  </clause>

  <clause id="40771">
    <literal><![CDATA[
      a(x,y,z) * (a(L(x,x,u),y,z) \ u) = u * a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(40756(a,2),39377(a,1,2,1))].">
      <j1 rule="para" parents="40756 39377"/>
    </justification>
  </clause>

  <clause id="40772">
    <literal><![CDATA[
      a(L(x,x,y),L(x,x,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,38648,a(flip),b,40766,a),flip(a)].">
      <j1 rule="hyper" parents="373 38648 40766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40776">
    <literal><![CDATA[
      a(x,y,z) * a(u,x,a(x,y,z)) = a(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,39366,a(flip),b,40762,a)].">
      <j1 rule="hyper" parents="64 39366 40762"/>
    </justification>
  </clause>

  <clause id="40777">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,u) \ 1 = a(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,39378,a(flip),b,40776,a)].">
      <j1 rule="hyper" parents="64 39378 40776"/>
    </justification>
  </clause>

  <clause id="40778">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,u) = a(L(x,x,u),y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,40777,a),flip(a)].">
      <j1 rule="hyper" parents="40 23134 40777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40779">
    <literal><![CDATA[
      x \ R(x,x \ L(x,y,z),u) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(34465(a,1),40759(a,1,2))].">
      <j1 rule="para" parents="34465 40759"/>
    </justification>
  </clause>

  <clause id="40780">
    <literal><![CDATA[
      x \ (L(y,a(y,z,u),w) * (y \ x)) = a(L(y,y,x),a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,39379,a,b,40770,a)].">
      <j1 rule="hyper" parents="373 39379 40770"/>
    </justification>
  </clause>

  <clause id="40781">
    <literal><![CDATA[
      x \ L(x,x * L(x,y,z),u) = a(x,x * L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(35117(a,1),40779(a,1,2))].">
      <j1 rule="para" parents="35117 40779"/>
    </justification>
  </clause>

  <clause id="40782">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u * x) \ x = a(x,x * L(x,y,z),u) \ 1
    ]]></literal>
    <justification jstring="[para(40781(a,1),36046(a,2,1))].">
      <j1 rule="para" parents="40781 36046"/>
    </justification>
  </clause>

  <clause id="40783">
    <literal><![CDATA[
      x \ (y * (L(y,a(y,z,u),w) \ x)) = a(L(y,y,x),a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,40436,a(flip),b,40780,a)].">
      <j1 rule="hyper" parents="64 40436 40780"/>
    </justification>
  </clause>

  <clause id="40784">
    <literal><![CDATA[
      x * a(y \ ((x \ y) * y),z,u) = y * ((y \ x) * a(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(33702(a,1),40757(a,1,2))].">
      <j1 rule="para" parents="33702 40757"/>
    </justification>
  </clause>

  <clause id="40785">
    <literal><![CDATA[
      x * ((x \ y) * a(x \ y,z,u)) = y * a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(26791(a,1),40784(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26791 40784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40787">
    <literal><![CDATA[
      a(x,x * L(x,y,z),z * y) = a(x,y,z) \ (x \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(32463(a,1),40769(a,1,2)),flip(a)].">
      <j1 rule="para" parents="32463 40769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40788">
    <literal><![CDATA[
      a(x,x * L(x,y,z),z * y) = a(y * z,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,34141,a(flip),b,40787,a),flip(a)].">
      <j1 rule="hyper" parents="373 34141 40787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40789">
    <literal><![CDATA[
      L(x,y,z) \ (L(x / L(x,y,z),x,y * z) \ x) = (a(z,y,x) * L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,23560,a,b,40722,a),flip(a)].">
      <j1 rule="hyper" parents="373 23560 40722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40790">
    <literal><![CDATA[
      R(((1 / x) \ a(y,y,z)) \ 1,x,x) = (a(y,y,z) * (1 / (1 / x))) \ 1
    ]]></literal>
    <justification jstring="[para(29299(a,1),40746(a,2,1))].">
      <j1 rule="para" parents="29299 40746"/>
    </justification>
  </clause>

  <clause id="40791">
    <literal><![CDATA[
      R(((1 / x) \ a(y,y,z)) \ 1,x,x) = 1 / (x * a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,33939,a(flip),b,40790,a),flip(a)].">
      <j1 rule="hyper" parents="373 33939 40790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40792">
    <literal><![CDATA[
      (a(x,y,z) * L(z,y,x)) \ z = a(y * x,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,40721,a(flip),b,40789,a),flip(a)].">
      <j1 rule="hyper" parents="64 40721 40789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40793">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),y \ R(y,z,u)) = R(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(16031(a,2),40661(a,1,3)),flip(a)].">
      <j1 rule="para" parents="16031 40661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40794">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),y \ R(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,31802,a(flip),b,40793,a),flip(a)].">
      <j1 rule="hyper" parents="373 31802 40793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40795">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),y * L(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,38762,a(flip),b,40794,a)].">
      <j1 rule="hyper" parents="64 38762 40794"/>
    </justification>
  </clause>

  <clause id="40796">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),y * L(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,36271,a(flip),b,40795,a)].">
      <j1 rule="hyper" parents="64 36271 40795"/>
    </justification>
  </clause>

  <clause id="40797">
    <literal><![CDATA[
      L(x,y * L(y,z,u),y * L(y,z,u)) = L(x,a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11786,a(flip),b,40796,a)].">
      <j1 rule="hyper" parents="64 11786 40796"/>
    </justification>
  </clause>

  <clause id="40798">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,y * z) \ x = a(y * z,x,a(z,y,x)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(5559(a,1),40720(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5559 40720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40799">
    <literal><![CDATA[
      a(x * y,z,a(y,x,z)) * L(z,x,y) = a(y,x,z) \ z
    ]]></literal>
    <justification jstring="[para(40716(a,2),40798(a,1,1)),flip(a)].">
      <j1 rule="para" parents="40716 40798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40800">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,L(y,z,u) \ y) = R(x,a(u,z,y),a(u,z,y))
    ]]></literal>
    <justification jstring="[para(40716(a,2),40723(a,1,3)),flip(a)].">
      <j1 rule="para" parents="40716 40723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40801">
    <literal><![CDATA[
      R(x,L(y,z,u) \ y,L(y,z,u) \ y) = L(x,a(u,z,y),a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,31802,a(flip),b,40800,a),flip(a)].">
      <j1 rule="hyper" parents="373 31802 40800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40802">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,L(y,z,u) \ y) = L(x,a(u,z,y),a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,38597,a(flip),b,40801,a)].">
      <j1 rule="hyper" parents="64 38597 40801"/>
    </justification>
  </clause>

  <clause id="40803">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),L(y,z,u) \ y) = L(x,a(u,z,y),a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,37593,a,b,40802,a)].">
      <j1 rule="hyper" parents="64 37593 40802"/>
    </justification>
  </clause>

  <clause id="40804">
    <literal><![CDATA[
      a(x,y,z) * (x \ (a(L(x,x,u),y,z) \ (x * u))) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(37503(a,1),40768(a,1,2,2,1,1))].">
      <j1 rule="para" parents="37503 40768"/>
    </justification>
  </clause>

  <clause id="40805">
    <literal><![CDATA[
      a(x,y,z) * (x \ (x * (a(L(x,x,u),y,z) \ u))) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(30908(a,1),40804(a,1,2,2))].">
      <j1 rule="para" parents="30908 40804"/>
    </justification>
  </clause>

  <clause id="40807">
    <literal><![CDATA[
      a(x,y,z) * (a(L(x,x,u),y,z) \ u) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(739,a,40805,a)].">
      <j1 rule="hyper" parents="739 40805"/>
    </justification>
  </clause>

  <clause id="40809">
    <literal><![CDATA[
      x * a(x,y,a(y,z,u)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,40771,a(flip),b,40807,a)].">
      <j1 rule="hyper" parents="64 40771 40807"/>
    </justification>
  </clause>

  <clause id="40810">
    <literal><![CDATA[
      x \ L(x,y,a(y,z,u)) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,40807,a(flip),b,40771,a(flip))].">
      <j1 rule="hyper" parents="139 40807 40771"/>
    </justification>
  </clause>

  <clause id="40811">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * x = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(23777,a,40809,a)].">
      <j1 rule="hyper" parents="23777 40809"/>
    </justification>
  </clause>

  <clause id="40812">
    <literal><![CDATA[
      a(x,a(y,z,z),a(a(y,z,z),u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,39703,a(flip),b,40809,a),flip(a)].">
      <j1 rule="hyper" parents="138 39703 40809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40813">
    <literal><![CDATA[
      x * a(y,a(y,z,u),x) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39366,a,b,40809,a)].">
      <j1 rule="hyper" parents="64 39366 40809"/>
    </justification>
  </clause>

  <clause id="40815">
    <literal><![CDATA[
      L(x,y * (z \ (u \ 1)),a(y * (z \ (u \ 1)),w,v5)) = x * a(x,y * (z \ (u \ 1)),a((z \ u) * y,w,v5))
    ]]></literal>
    <justification jstring="[para(32689(a,1),40809(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="32689 40809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40816">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) \ (x * y) = L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(40809(a,1),35574(a,1,1))].">
      <j1 rule="para" parents="40809 35574"/>
    </justification>
  </clause>

  <clause id="40817">
    <literal><![CDATA[
      (x \ y) * a(x,y,a(y,z,u)) = L(x \ y,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(39353(a,1),40809(a,1,2))].">
      <j1 rule="para" parents="39353 40809"/>
    </justification>
  </clause>

  <clause id="40818">
    <literal><![CDATA[
      L(a(a(x,y,y),z,u),a(x,y,y),w) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(53,a,40812,a)].">
      <j1 rule="hyper" parents="53 40812"/>
    </justification>
  </clause>

  <clause id="40819">
    <literal><![CDATA[
      L(x \ L(x,y,a(y,z,u)),w,v5) = a(L(x,w,v5),y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,34495,a(flip),b,40810,a)].">
      <j1 rule="hyper" parents="64 34495 40810"/>
    </justification>
  </clause>

  <clause id="40820">
    <literal><![CDATA[
      a(x,a(x,y,z),u) \ u = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33554,a,b,40811,a)].">
      <j1 rule="hyper" parents="64 33554 40811"/>
    </justification>
  </clause>

  <clause id="40821">
    <literal><![CDATA[
      a(x,a(x,y,z),u) * L(u,x,a(x,y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(145,a,40811,a(flip),b,33554,a)].">
      <j1 rule="hyper" parents="145 40811 33554"/>
    </justification>
  </clause>

  <clause id="40823">
    <literal><![CDATA[
      a(x,a(x,y,z),u) * u = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(39362(a,2),40811(a,1,1))].">
      <j1 rule="para" parents="39362 40811"/>
    </justification>
  </clause>

  <clause id="40824">
    <literal><![CDATA[
      (x * y) * L(a(z,a(z,u,w),y),y,x) = x * L(y,z,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,40813,a(flip),b,344,a),flip(a)].">
      <j1 rule="hyper" parents="145 40813 344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40825">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) * a(y,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(23175,a,40820,a)].">
      <j1 rule="hyper" parents="23175 40820"/>
    </justification>
  </clause>

  <clause id="40826">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) \ x = a(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(40,a,5559,a,b,40820,a)].">
      <j1 rule="hyper" parents="40 5559 40820"/>
    </justification>
  </clause>

  <clause id="40828">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) \ x = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,40825,a(flip),b,39366,a(flip))].">
      <j1 rule="hyper" parents="139 40825 39366"/>
    </justification>
  </clause>

  <clause id="40829">
    <literal><![CDATA[
      T(x * (a(y,a(y,z,u),w) \ T(a(y,a(y,z,u),w) * L(w,y,a(y,z,u)),x)),a(y,a(y,z,u),w)) = L(a(y,a(y,z,u),w),L(w,y,a(y,z,u)),x) \ (w * x)
    ]]></literal>
    <justification jstring="[para(40825(a,1),30752(a,2,2,1))].">
      <j1 rule="para" parents="40825 30752"/>
    </justification>
  </clause>

  <clause id="40830">
    <literal><![CDATA[
      L(x / a(y,z,u),y,a(y,z,u)) \ x = a(y,z,u) * a(y,a(y,z,u),a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,40826,a(flip),b,35572,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 40826 35572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40831">
    <literal><![CDATA[
      a(x,y,z) \ ((u / x) * (x * a(x,y,z))) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(40,a,39343,a,b,40828,a)].">
      <j1 rule="hyper" parents="40 39343 40828"/>
    </justification>
  </clause>

  <clause id="40832">
    <literal><![CDATA[
      x * (L(x,y,a(y,z,u)) \ y) = L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(2342,a,40816,a)].">
      <j1 rule="hyper" parents="2342 40816"/>
    </justification>
  </clause>

  <clause id="40833">
    <literal><![CDATA[
      L(x,a(x,y,z),u) \ (x * u) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(40832(a,1),24847(a,1,1))].">
      <j1 rule="para" parents="40832 24847"/>
    </justification>
  </clause>

  <clause id="40834">
    <literal><![CDATA[
      (x * a(x,a(x,y,z),u)) \ (x * u) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(34905(a,2),40833(a,1,1))].">
      <j1 rule="para" parents="34905 40833"/>
    </justification>
  </clause>

  <clause id="40835">
    <literal><![CDATA[
      x * L(x \ y,y,a(y,z,u)) = a(x,y,a(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,40817,a(flip),b,29941,a)].">
      <j1 rule="hyper" parents="145 40817 29941"/>
    </justification>
  </clause>

  <clause id="40836">
    <literal><![CDATA[
      a(L(a(x,y,y),z,u),z,u) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,38070,a(flip),b,40818,a)].">
      <j1 rule="hyper" parents="64 38070 40818"/>
    </justification>
  </clause>

  <clause id="40838">
    <literal><![CDATA[
      a(a(x,y,y),z,u) = a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,36350,a(flip),b,40836,a),flip(a)].">
      <j1 rule="hyper" parents="64 36350 40836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40839">
    <literal><![CDATA[
      a(a(x,y,y),z,u) = a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,38630,a(flip),b,40838,a),flip(a)].">
      <j1 rule="hyper" parents="373 38630 40838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40840">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * w = w * a(a(z,u,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,40838,a,b,23174,a),flip(a)].">
      <j1 rule="hyper" parents="145 40838 23174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40841">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(y,z,u)) = a(u,z,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,39671,a,b,40838,a)].">
      <j1 rule="hyper" parents="64 39671 40838"/>
    </justification>
  </clause>

  <clause id="40842">
    <literal><![CDATA[
      a(a(x,x,y),z,u) = a(u,z,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,32543,a(flip),b,40838,a)].">
      <j1 rule="hyper" parents="64 32543 40838"/>
    </justification>
  </clause>

  <clause id="40843">
    <literal><![CDATA[
      a(a(x,x,y),z,u) * w = w * a(u,z,a(y,x,x))
    ]]></literal>
    <justification jstring="[para(40838(a,1),32545(a,2,2))].">
      <j1 rule="para" parents="40838 32545"/>
    </justification>
  </clause>

  <clause id="40844">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * w = w * a(a(u,z,z),y,x)
    ]]></literal>
    <justification jstring="[para(40838(a,2),38638(a,2,2))].">
      <j1 rule="para" parents="40838 38638"/>
    </justification>
  </clause>

  <clause id="40845">
    <literal><![CDATA[
      a(a(x,x,y),z,u) \ w = w * a(u,z,a(y,x,x))
    ]]></literal>
    <justification jstring="[para(40838(a,1),39769(a,2,2))].">
      <j1 rule="para" parents="40838 39769"/>
    </justification>
  </clause>

  <clause id="40846">
    <literal><![CDATA[
      (x / y) \ (x * a(z,z,u)) = (y * a(z,z,u)) * a(a(u,z,z),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,40839,a,b,30032,a),flip(a)].">
      <j1 rule="hyper" parents="145 40839 30032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40848">
    <literal><![CDATA[
      a(a(x,x,y),z,u) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32543,a(flip),b,40839,a)].">
      <j1 rule="hyper" parents="64 32543 40839"/>
    </justification>
  </clause>

  <clause id="40849">
    <literal><![CDATA[
      a(x,x,y) * a(z,u,a(x,x,y)) = a(x,x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,40839,a(flip),b,39671,a)].">
      <j1 rule="hyper" parents="145 40839 39671"/>
    </justification>
  </clause>

  <clause id="40850">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * a(z,z,u) = a(z,L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(40839(a,1),37924(a,1,1))].">
      <j1 rule="para" parents="40839 37924"/>
    </justification>
  </clause>

  <clause id="40851">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * a(u,z,z) = a(L(u,y,x),z,z)
    ]]></literal>
    <justification jstring="[para(40839(a,1),38064(a,1,1))].">
      <j1 rule="para" parents="40839 38064"/>
    </justification>
  </clause>

  <clause id="40852">
    <literal><![CDATA[
      a(a(x,x,y),z,u) \ w = w * a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(40839(a,1),39769(a,2,2))].">
      <j1 rule="para" parents="40839 39769"/>
    </justification>
  </clause>

  <clause id="40853">
    <literal><![CDATA[
      a(a(x,x,L(y,z,u)),w,v5) = a(v5,w,a(y,x,L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,39811,a(flip),b,40842,a),flip(a)].">
      <j1 rule="hyper" parents="373 39811 40842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40854">
    <literal><![CDATA[
      a(a(x,x,y),z,u * w) = a(w * u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,38632,a(flip),b,40842,a),flip(a)].">
      <j1 rule="hyper" parents="373 38632 40842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40855">
    <literal><![CDATA[
      a(x * y,x * y,a(z,y,y)) = a(a(y,y,z),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,39538,a(flip),b,40842,a),flip(a)].">
      <j1 rule="hyper" parents="64 39538 40842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40856">
    <literal><![CDATA[
      a(a(x,x,y),z,u) \ (a(u,z,a(y,x,x)) * w) = w
    ]]></literal>
    <justification jstring="[hyper(143,a,40842,a(flip),b,79,a),flip(a)].">
      <j1 rule="hyper" parents="143 40842 79"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40857">
    <literal><![CDATA[
      a(a(x,x,y),z,u) * w = a(u,z,a(x,x,y)) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,40848,a,b,11,a)].">
      <j1 rule="hyper" parents="144 40848 11"/>
    </justification>
  </clause>

  <clause id="40858">
    <literal><![CDATA[
      L(a(x,y,a(z,z,u)) * u,z,z) = L(u,z,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(40844(a,2),39817(a,1,1))].">
      <j1 rule="para" parents="40844 39817"/>
    </justification>
  </clause>

  <clause id="40859">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) \ w = w * a(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[para(40848(a,1),40845(a,1,1))].">
      <j1 rule="para" parents="40848 40845"/>
    </justification>
  </clause>

  <clause id="40860">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) \ w = w * a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[para(40848(a,1),40852(a,1,1))].">
      <j1 rule="para" parents="40848 40852"/>
    </justification>
  </clause>

  <clause id="40861">
    <literal><![CDATA[
      (a(x,y,a(z,u,u)) * w) * a(a(z,u,u),y,x) = w
    ]]></literal>
    <justification jstring="[hyper(64,a,39769,a(flip),b,40856,a)].">
      <j1 rule="hyper" parents="64 39769 40856"/>
    </justification>
  </clause>

  <clause id="40862">
    <literal><![CDATA[
      L(x,y,a(a(z,z,u),w,v5)) = L(x,y,a(v5,w,a(u,z,z)))
    ]]></literal>
    <justification jstring="[para(40856(a,1),2183(a,1,3)),flip(a)].">
      <j1 rule="para" parents="40856 2183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40863">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) \ w = a(x,y,a(z,z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(373,a,38638,a,b,40859,a),flip(a)].">
      <j1 rule="hyper" parents="373 38638 40859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40864">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) \ w = a(x,y,a(u,z,z)) * w
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a,b,40859,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 40859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40865">
    <literal><![CDATA[
      a(a(x,y,y),z,u) \ w = a(u,z,a(x,y,y)) * w
    ]]></literal>
    <justification jstring="[hyper(23920,a,40861,a)].">
      <j1 rule="hyper" parents="23920 40861"/>
    </justification>
  </clause>

  <clause id="40866">
    <literal><![CDATA[
      a(a(x,y,y),z,u) \ 1 = a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(143,a,40861,a(flip),b,499,a),flip(a)].">
      <j1 rule="hyper" parents="143 40861 499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40868">
    <literal><![CDATA[
      L(x,x,y) * a(z,u,a(y,x,x)) = L(x,x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,40866,a(flip),b,38069,a)].">
      <j1 rule="hyper" parents="145 40866 38069"/>
    </justification>
  </clause>

  <clause id="40869">
    <literal><![CDATA[
      a(x \ y,a(x,x,y),z) \ u = a(z,x \ y,a(x,x,y)) * u
    ]]></literal>
    <justification jstring="[para(38665(a,2),40863(a,1,1))].">
      <j1 rule="para" parents="38665 40863"/>
    </justification>
  </clause>

  <clause id="40871">
    <literal><![CDATA[
      a(x * y,a(y,x,x),z) \ u = a(z,x * y,a(x,x,y)) * u
    ]]></literal>
    <justification jstring="[para(38666(a,2),40863(a,1,1))].">
      <j1 rule="para" parents="38666 40863"/>
    </justification>
  </clause>

  <clause id="40872">
    <literal><![CDATA[
      a(a(x,y,y),z,u) \ w = a(a(x,y,y),z,u) * w
    ]]></literal>
    <justification jstring="[para(40838(a,2),40865(a,2,1))].">
      <j1 rule="para" parents="40838 40865"/>
    </justification>
  </clause>

  <clause id="40873">
    <literal><![CDATA[
      a(x,y,y) * (a(L(x,z,u),y,y) \ w) = a(a(x,y,y),z,u) * w
    ]]></literal>
    <justification jstring="[hyper(64,a,39782,a,b,40872,a)].">
      <j1 rule="hyper" parents="64 39782 40872"/>
    </justification>
  </clause>

  <clause id="40874">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * a(u,u,z) = a(u,u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(23175,a,40841,a)].">
      <j1 rule="hyper" parents="23175 40841"/>
    </justification>
  </clause>

  <clause id="40875">
    <literal><![CDATA[
      L(x * a(y,y,L(x,z,u)),y,y) = x * a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,40841,a(flip),b,31104,a),flip(a)].">
      <j1 rule="hyper" parents="145 40841 31104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40876">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * a(z,z,u) = a(z,z,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(23777,a,40849,a)].">
      <j1 rule="hyper" parents="23777 40849"/>
    </justification>
  </clause>

  <clause id="40877">
    <literal><![CDATA[
      a(x * y,a(x,x,y),z) \ a(x,x,y) = a(x,L(x,x * y,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,38685,a,b,40850,a)].">
      <j1 rule="hyper" parents="64 38685 40850"/>
    </justification>
  </clause>

  <clause id="40878">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) * z = L(z,y,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(42,a,37956,a,b,40858,a),flip(a)].">
      <j1 rule="hyper" parents="42 37956 40858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40879">
    <literal><![CDATA[
      x * a(y,y,a(x,z,z)) = L(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,38638,a(flip),b,40878,a)].">
      <j1 rule="hyper" parents="64 38638 40878"/>
    </justification>
  </clause>

  <clause id="40880">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) = a(z,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,40811,a,b,40878,a)].">
      <j1 rule="hyper" parents="36 40811 40878"/>
    </justification>
  </clause>

  <clause id="40881">
    <literal><![CDATA[
      a(x,a(y,y,x),z) = a(y,y,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,38011,a,b,40878,a)].">
      <j1 rule="hyper" parents="36 38011 40878"/>
    </justification>
  </clause>

  <clause id="40882">
    <literal><![CDATA[
      a(a(x,y,y),z,z) = a(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,40839,a,b,40880,a)].">
      <j1 rule="hyper" parents="373 40839 40880"/>
    </justification>
  </clause>

  <clause id="40883">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) = a(y,y,a(z,z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,39759,a,b,40880,a),flip(a)].">
      <j1 rule="hyper" parents="373 39759 40880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40884">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) = a(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,39754,a,b,40880,a),flip(a)].">
      <j1 rule="hyper" parents="373 39754 40880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40885">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) = a(z,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,38630,a,b,40880,a),flip(a)].">
      <j1 rule="hyper" parents="373 38630 40880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40886">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) = a(z,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,38630,a(flip),b,40880,a)].">
      <j1 rule="hyper" parents="64 38630 40880"/>
    </justification>
  </clause>

  <clause id="40887">
    <literal><![CDATA[
      ((1 / x) \ y) * a(z,u,a(u,x,x)) = (1 / R(x,x,a(u,u,z))) \ y
    ]]></literal>
    <justification jstring="[para(40880(a,2),37750(a,1,2))].">
      <j1 rule="para" parents="40880 37750"/>
    </justification>
  </clause>

  <clause id="40888">
    <literal><![CDATA[
      x * a(y,x,a(x,z,z)) = L(x,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(40880(a,2),39760(a,1,2))].">
      <j1 rule="para" parents="40880 39760"/>
    </justification>
  </clause>

  <clause id="40889">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * a(x,y,y) = a(L(x,z,z),y,y)
    ]]></literal>
    <justification jstring="[para(40880(a,2),40851(a,1,1))].">
      <j1 rule="para" parents="40880 40851"/>
    </justification>
  </clause>

  <clause id="40890">
    <literal><![CDATA[
      a(x,a(y,y,x),z) = a(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,39754,a,b,40881,a),flip(a)].">
      <j1 rule="hyper" parents="373 39754 40881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40891">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(u,x,x)) = L(x,x,a(z,u,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(145,a,40882,a(flip),b,37571,a)].">
      <j1 rule="hyper" parents="145 40882 37571"/>
    </justification>
  </clause>

  <clause id="40892">
    <literal><![CDATA[
      x * a(y,z,a(z,x,x)) = L(x,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,40882,a(flip),b,36328,a)].">
      <j1 rule="hyper" parents="145 40882 36328"/>
    </justification>
  </clause>

  <clause id="40893">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * (a(y,z,a(z,x,x)) * u) = u
    ]]></literal>
    <justification jstring="[para(40882(a,1),37755(a,1,2,1))].">
      <j1 rule="para" parents="40882 37755"/>
    </justification>
  </clause>

  <clause id="40894">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) = a(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,40880,a,b,40883,a)].">
      <j1 rule="hyper" parents="373 40880 40883"/>
    </justification>
  </clause>

  <clause id="40895">
    <literal><![CDATA[
      a(a(x,x,y),z,z) = a(y,z,a(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,40848,a,b,40883,a)].">
      <j1 rule="hyper" parents="373 40848 40883"/>
    </justification>
  </clause>

  <clause id="40896">
    <literal><![CDATA[
      a(x,x,y) * a(y,z,a(z,x,x)) = a(x,x,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,40883,a,b,39531,a)].">
      <j1 rule="hyper" parents="145 40883 39531"/>
    </justification>
  </clause>

  <clause id="40897">
    <literal><![CDATA[
      x * L(x \ 1,y,a(z,z,a(u,u,w))) = x \ L(x,y,a(w,z,a(z,u,u)))
    ]]></literal>
    <justification jstring="[para(40883(a,1),28848(a,1,2,3))].">
      <j1 rule="para" parents="40883 28848"/>
    </justification>
  </clause>

  <clause id="40898">
    <literal><![CDATA[
      x * a(y,z,a(z,u,u)) = x * a(z,z,a(y,u,u))
    ]]></literal>
    <justification jstring="[para(40883(a,2),38639(a,2,2)),flip(a)].">
      <j1 rule="para" parents="40883 38639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40899">
    <literal><![CDATA[
      x \ L(x,y,a(y,z,z)) = a(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,40810,a,b,40884,a)].">
      <j1 rule="hyper" parents="64 40810 40884"/>
    </justification>
  </clause>

  <clause id="40900">
    <literal><![CDATA[
      a(x,a(x,y,y),z) = a(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,39362,a,b,40884,a)].">
      <j1 rule="hyper" parents="64 39362 40884"/>
    </justification>
  </clause>

  <clause id="40901">
    <literal><![CDATA[
      a(x,x,a(x \ y,z,z)) = a(y,x,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39332,a(flip),b,40884,a),flip(a)].">
      <j1 rule="hyper" parents="64 39332 40884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40902">
    <literal><![CDATA[
      a(x,x,a(y * x,z,z)) = a(y,x,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39330,a(flip),b,40884,a),flip(a)].">
      <j1 rule="hyper" parents="64 39330 40884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40903">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) = a(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,38630,a(flip),b,40884,a)].">
      <j1 rule="hyper" parents="64 38630 40884"/>
    </justification>
  </clause>

  <clause id="40904">
    <literal><![CDATA[
      a(x,x,y) * a(y,y,a(z,x,x)) = a(x,x,L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,40884,a(flip),b,40841,a)].">
      <j1 rule="hyper" parents="145 40884 40841"/>
    </justification>
  </clause>

  <clause id="40905">
    <literal><![CDATA[
      x * a(y,y,a(x,z,z)) = L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,40884,a(flip),b,40810,a)].">
      <j1 rule="hyper" parents="145 40884 40810"/>
    </justification>
  </clause>

  <clause id="40906">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * y = L(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[para(40884(a,2),30055(a,1,1))].">
      <j1 rule="para" parents="40884 30055"/>
    </justification>
  </clause>

  <clause id="40907">
    <literal><![CDATA[
      a(x,y,(y \ z) \ (((z * (y \ z)) \ z) \ 1)) = a(y,y,a(x,y \ z,y \ z))
    ]]></literal>
    <justification jstring="[para(30554(a,1),40884(a,1,3))].">
      <j1 rule="para" parents="30554 40884"/>
    </justification>
  </clause>

  <clause id="40908">
    <literal><![CDATA[
      x * (y * a(z,x,a(x,u,u))) = L(x,x,a(z,u,u)) * y
    ]]></literal>
    <justification jstring="[para(40885(a,2),39753(a,1,2,2))].">
      <j1 rule="para" parents="40885 39753"/>
    </justification>
  </clause>

  <clause id="40909">
    <literal><![CDATA[
      (x * y) * a(z,y,a(y,u,u)) = x * L(y,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[para(40885(a,2),39763(a,1,2))].">
      <j1 rule="para" parents="40885 39763"/>
    </justification>
  </clause>

  <clause id="40910">
    <literal><![CDATA[
      a(x,y,a(z,z,y)) = a(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,40883,a,b,40886,a),flip(a)].">
      <j1 rule="hyper" parents="373 40883 40886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40911">
    <literal><![CDATA[
      a(a(x,x,y),L(y,z,u),w) = a(y,y,a(L(w,z,u),x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,39779,a,b,40890,a)].">
      <j1 rule="hyper" parents="64 39779 40890"/>
    </justification>
  </clause>

  <clause id="40912">
    <literal><![CDATA[
      a(x,x,y) * a(z,x,a(x,y,y)) = a(x,x,L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,40894,a,b,40841,a)].">
      <j1 rule="hyper" parents="145 40894 40841"/>
    </justification>
  </clause>

  <clause id="40913">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * u = u * a(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,40894,a,b,23174,a),flip(a)].">
      <j1 rule="hyper" parents="145 40894 23174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40914">
    <literal><![CDATA[
      a(x,y,y) * a(z,y,a(y,x,x)) = a(L(x,x,z),y,y)
    ]]></literal>
    <justification jstring="[para(40894(a,1),40776(a,1,2))].">
      <j1 rule="para" parents="40894 40776"/>
    </justification>
  </clause>

  <clause id="40915">
    <literal><![CDATA[
      a(x * y,x * y,a(z,y,y)) = a(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,40855,a,b,40895,a)].">
      <j1 rule="hyper" parents="64 40855 40895"/>
    </justification>
  </clause>

  <clause id="40916">
    <literal><![CDATA[
      (x * (((x * y) * y) \ z)) * a(x,x,a((y * (y * x)) \ z,y,y)) = (((x * y) * y) / x) \ z
    ]]></literal>
    <justification jstring="[para(40900(a,1),36733(a,1,2))].">
      <j1 rule="para" parents="40900 36733"/>
    </justification>
  </clause>

  <clause id="40917">
    <literal><![CDATA[
      a(x,y,y) * L(x,z,a(z,u,u)) = R(x,y,y) * a(z,z,a(x,u,u))
    ]]></literal>
    <justification jstring="[para(40900(a,1),38022(a,2,2))].">
      <j1 rule="para" parents="40900 38022"/>
    </justification>
  </clause>

  <clause id="40918">
    <literal><![CDATA[
      a(x \ y,x \ y,a(z,x,x)) = a(z,x \ y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30185,a(flip),b,40903,a),flip(a)].">
      <j1 rule="hyper" parents="64 30185 40903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40919">
    <literal><![CDATA[
      ((x * (y * a(z,z,y))) / a(z,z,y)) * a(x,z,a(z,y,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(145,a,40910,a(flip),b,33321,a(flip))].">
      <j1 rule="hyper" parents="145 40910 33321"/>
    </justification>
  </clause>

  <clause id="40920">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) \ u = u * a(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[para(40910(a,1),40859(a,1,1))].">
      <j1 rule="para" parents="40910 40859"/>
    </justification>
  </clause>

  <clause id="40921">
    <literal><![CDATA[
      L(x,a(x,y,y),z) = L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,39367,a(flip),b,40888,a)].">
      <j1 rule="hyper" parents="64 39367 40888"/>
    </justification>
  </clause>

  <clause id="40922">
    <literal><![CDATA[
      L(x,a(y,y,x),z) = L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,31821,a(flip),b,40921,a)].">
      <j1 rule="hyper" parents="64 31821 40921"/>
    </justification>
  </clause>

  <clause id="40923">
    <literal><![CDATA[
      R(L(x,x,a(y,z,z)),u,w) = L(R(x,u,w),a(x,z,z),y)
    ]]></literal>
    <justification jstring="[para(40921(a,1),29(a,1,1))].">
      <j1 rule="para" parents="40921 29"/>
    </justification>
  </clause>

  <clause id="40924">
    <literal><![CDATA[
      L(L(x,y,z),a(x,u,u),w) = L(L(x,x,a(w,u,u)),y,z)
    ]]></literal>
    <justification jstring="[para(40921(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="40921 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40925">
    <literal><![CDATA[
      (x * (a(y,z,z) \ 1)) * L(y,y,a(x,z,z)) = x * ((a(y,z,z) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(40921(a,1),11815(a,1,2))].">
      <j1 rule="para" parents="40921 11815"/>
    </justification>
  </clause>

  <clause id="40926">
    <literal><![CDATA[
      a(x * y,z,z) \ (y \ ((1 / y) \ a(x * y,z,z))) = a(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30230,a,b,40902,a)].">
      <j1 rule="hyper" parents="64 30230 40902"/>
    </justification>
  </clause>

  <clause id="40927">
    <literal><![CDATA[
      L(x,y,a(y,z,z)) = L(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,40879,a(flip),b,40905,a)].">
      <j1 rule="hyper" parents="64 40879 40905"/>
    </justification>
  </clause>

  <clause id="40928">
    <literal><![CDATA[
      a(x,y,z) * (u * a(x,x,a(u * a(x,y,z),w,w))) = L(u * a(x,y,z),x,a(x,w,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,31090,a(flip),b,40905,a)].">
      <j1 rule="hyper" parents="64 31090 40905"/>
    </justification>
  </clause>

  <clause id="40929">
    <literal><![CDATA[
      L(R(x,y,y),z,a(z,y,y)) = R(x,y,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,37960,a(flip),b,40927,a),flip(a)].">
      <j1 rule="hyper" parents="373 37960 40927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40930">
    <literal><![CDATA[
      L(x,y,a(z,z,y)) = L(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,29287,a(flip),b,40927,a)].">
      <j1 rule="hyper" parents="373 29287 40927"/>
    </justification>
  </clause>

  <clause id="40931">
    <literal><![CDATA[
      a(x,x,y) \ L(z,x,a(x,y,y)) = L(y,x,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,40930,a(flip),b,37963,a)].">
      <j1 rule="hyper" parents="139 40930 37963"/>
    </justification>
  </clause>

  <clause id="40932">
    <literal><![CDATA[
      a(x,y * z,a(y * z,z,z)) = a(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,40884,a,b,40915,a)].">
      <j1 rule="hyper" parents="64 40884 40915"/>
    </justification>
  </clause>

  <clause id="40933">
    <literal><![CDATA[
      a(x,y * z,a(z,z,y)) = a(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,38636,a(flip),b,40932,a)].">
      <j1 rule="hyper" parents="64 38636 40932"/>
    </justification>
  </clause>

  <clause id="40934">
    <literal><![CDATA[
      a(x * y,a(y,y,x),z) = a(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,34969,a(flip),b,40932,a)].">
      <j1 rule="hyper" parents="64 34969 40932"/>
    </justification>
  </clause>

  <clause id="40935">
    <literal><![CDATA[
      a(x,y * z,a(y,y,z)) = a(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(32008,a,40933,a)].">
      <j1 rule="hyper" parents="32008 40933"/>
    </justification>
  </clause>

  <clause id="40936">
    <literal><![CDATA[
      L(x,y * z,a(y,z,z)) = a(x,y,a(y,z,z)) \ x
    ]]></literal>
    <justification jstring="[para(40933(a,1),38714(a,1,1)),flip(a)].">
      <j1 rule="para" parents="40933 38714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40937">
    <literal><![CDATA[
      a(x * y,a(x,x,y),z) = a(z,y,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(26847,a,40934,a)].">
      <j1 rule="hyper" parents="26847 40934"/>
    </justification>
  </clause>

  <clause id="40938">
    <literal><![CDATA[
      a(x * y,a(y,x,x),z) = a(z,y,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,32888,a,b,40934,a)].">
      <j1 rule="hyper" parents="64 32888 40934"/>
    </justification>
  </clause>

  <clause id="40939">
    <literal><![CDATA[
      a(x * y,a(x,y,y),z) = a(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32887,a,b,40934,a)].">
      <j1 rule="hyper" parents="64 32887 40934"/>
    </justification>
  </clause>

  <clause id="40940">
    <literal><![CDATA[
      x * (((y * z) * a(y,y,z)) * a(x,z,a(z,y,y))) = (x * (y * z)) * a(y,y,z)
    ]]></literal>
    <justification jstring="[para(40935(a,1),29951(a,1,2,2))].">
      <j1 rule="para" parents="40935 29951"/>
    </justification>
  </clause>

  <clause id="40941">
    <literal><![CDATA[
      a(x * (y * L(x,z,u)),a(y * x,L(x,z,u),L(x,z,u)),w) = a(w,y * x,a(y * x,L(x,z,u),L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(24842(a,1),40938(a,1,1))].">
      <j1 rule="para" parents="24842 40938"/>
    </justification>
  </clause>

  <clause id="40942">
    <literal><![CDATA[
      a((x * ((y * y) \ z)) * L(z,u,w),a(x * ((y * y) \ L(z,u,w)),z,z),v5) = a(v5,x * ((y * y) \ L(z,u,w)),a(x * ((y * y) \ L(z,u,w)),z,z))
    ]]></literal>
    <justification jstring="[para(3212(a,1),40939(a,1,1))].">
      <j1 rule="para" parents="3212 40939"/>
    </justification>
  </clause>

  <clause id="40943">
    <literal><![CDATA[
      L(x,y * z,a(y,z,z)) = x * a(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,40920,a(flip),b,40936,a),flip(a)].">
      <j1 rule="hyper" parents="373 40920 40936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40944">
    <literal><![CDATA[
      L(x,y * z,a(y,z,z)) = L(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,40809,a(flip),b,40943,a),flip(a)].">
      <j1 rule="hyper" parents="373 40809 40943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40945">
    <literal><![CDATA[
      L(x,y * z,a(z,y,y)) = L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(29572,a,40944,a)].">
      <j1 rule="hyper" parents="29572 40944"/>
    </justification>
  </clause>

  <clause id="40946">
    <literal><![CDATA[
      L(x,a(y,z,z),y * z) = L(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,31825,a,b,40944,a)].">
      <j1 rule="hyper" parents="64 31825 40944"/>
    </justification>
  </clause>

  <clause id="40947">
    <literal><![CDATA[
      L(L(x,y,z),z,a(z,y,y)) = L(x,y,L(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,38103,a(flip),b,40944,a),flip(a)].">
      <j1 rule="hyper" parents="64 38103 40944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40948">
    <literal><![CDATA[
      L(L(x,y,z),y,a(y,z,z)) = L(x,L(y,y,z),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37971,a(flip),b,40944,a),flip(a)].">
      <j1 rule="hyper" parents="64 37971 40944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40949">
    <literal><![CDATA[
      L((x * y) \ ((((a(x,y,y) \ 1) \ 1) \ 1) \ z),y,a(y,x,x)) = (T(a(x,y,y) \ 1,a(x,y,y)) * (x * y)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,31200,a(flip),b,40944,a),flip(a)].">
      <j1 rule="hyper" parents="64 31200 40944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40950">
    <literal><![CDATA[
      (1 / a(x,y,y)) * ((x * y) * T(z,a(x,y,y) \ (x * y))) = L(z,y,a(y,x,x)) * ((1 / a(x,y,y)) * (x * y))
    ]]></literal>
    <justification jstring="[para(40944(a,1),15292(a,2,1))].">
      <j1 rule="para" parents="40944 15292"/>
    </justification>
  </clause>

  <clause id="40951">
    <literal><![CDATA[
      L(x,a(y,y,z),y * z) = L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,31823,a(flip),b,40946,a)].">
      <j1 rule="hyper" parents="64 31823 40946"/>
    </justification>
  </clause>

  <clause id="40952">
    <literal><![CDATA[
      L(a(x,y,y) \ z,y,a(y,x,x)) = (R(x,y,y) * y) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30020,a(flip),b,40946,a),flip(a)].">
      <j1 rule="hyper" parents="64 30020 40946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40953">
    <literal><![CDATA[
      L(x * (((x * y) \ y) \ z),x,a(x,y,y)) = (y / x) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40316,a(flip),b,40951,a),flip(a)].">
      <j1 rule="hyper" parents="64 40316 40951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40954">
    <literal><![CDATA[
      L(L(x,y,y * z),y,a(y,y * z,y * z)) = L(x,L(y,y,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29805,a(flip),b,40948,a),flip(a)].">
      <j1 rule="hyper" parents="373 29805 40948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40955">
    <literal><![CDATA[
      L(L(x,y,z),z,a(z,y,y)) = L(x,L(y,y,z),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40927,a,b,40948,a)].">
      <j1 rule="hyper" parents="64 40927 40948"/>
    </justification>
  </clause>

  <clause id="40956">
    <literal><![CDATA[
      L(L(x,y,L(z,u,w)),y,a(y,z,z)) = L(x,L(y,y,L(z,u,w)),L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,35215,a(flip),b,40948,a)].">
      <j1 rule="hyper" parents="64 35215 40948"/>
    </justification>
  </clause>

  <clause id="40957">
    <literal><![CDATA[
      L(L(x,y * z,z),y * z,a(y * z,z,z)) = L(x,L(y * z,z * y,z),z)
    ]]></literal>
    <justification jstring="[para(14181(a,1),40948(a,2,2))].">
      <j1 rule="para" parents="14181 40948"/>
    </justification>
  </clause>

  <clause id="40959">
    <literal><![CDATA[
      L(L(x,y * z,z),y * z,a(y * z,z,z)) = L(x,y \ (y / (1 / (y * z))),z)
    ]]></literal>
    <justification jstring="[para(31301(a,1),40948(a,2,2))].">
      <j1 rule="para" parents="31301 40948"/>
    </justification>
  </clause>

  <clause id="40960">
    <literal><![CDATA[
      L(x,L(y,y,z),z) = L(x,y,L(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,40947,a(flip),b,40955,a),flip(a)].">
      <j1 rule="hyper" parents="64 40947 40955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40961">
    <literal><![CDATA[
      L(x,y * z,L(y,y,y * z)) = L(x,L(z \ y,y,y),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31762,a(flip),b,40960,a),flip(a)].">
      <j1 rule="hyper" parents="64 31762 40960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40962">
    <literal><![CDATA[
      L(x,y,L(y * z,y * z,y)) = L(x,L(y,y,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29805,a(flip),b,40960,a),flip(a)].">
      <j1 rule="hyper" parents="64 29805 40960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40963">
    <literal><![CDATA[
      L(x,L(y,y,L(z,z,y)),L(z,z,y)) = L(x,y,L(L(z,z,y),z,y))
    ]]></literal>
    <justification jstring="[para(30633(a,1),40960(a,2,3))].">
      <j1 rule="para" parents="30633 40960"/>
    </justification>
  </clause>

  <clause id="40965">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * L(z,z,u) = L(z,z,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,38638,a,b,40868,a)].">
      <j1 rule="hyper" parents="64 38638 40868"/>
    </justification>
  </clause>

  <clause id="40966">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * (x \ R(x,y,y)) = a(L(x,z,z),y,y)
    ]]></literal>
    <justification jstring="[para(15987(a,2),40889(a,1,2))].">
      <j1 rule="para" parents="15987 40889"/>
    </justification>
  </clause>

  <clause id="40967">
    <literal><![CDATA[
      L(L(x,x,a(y,z,z)),x,y) = L(x,x,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39764,a(flip),b,40965,a)].">
      <j1 rule="hyper" parents="64 39764 40965"/>
    </justification>
  </clause>

  <clause id="40968">
    <literal><![CDATA[
      (x * a(x,a(x,y,z),z * y)) \ (x * (z * y)) = (x * a(x,y,z)) \ ((x * y) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,26742,a,b,40834,a),flip(a)].">
      <j1 rule="hyper" parents="373 26742 40834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40969">
    <literal><![CDATA[
      x * L(x \ y,y,a(y,z,u)) = L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,39368,a(flip),b,40835,a),flip(a)].">
      <j1 rule="hyper" parents="373 39368 40835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40970">
    <literal><![CDATA[
      L(x \ y,y,a(y,z,u)) = L(x,y,a(y,z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(35,a,40832,a,b,40969,a),flip(a)].">
      <j1 rule="hyper" parents="35 40832 40969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40971">
    <literal><![CDATA[
      L(x,y,a(a(z,z,u),w,v5)) = L(x,y,a(v5,w,a(z,z,u)))
    ]]></literal>
    <justification jstring="[para(38630(a,1),40862(a,2,3))].">
      <j1 rule="para" parents="38630 40862"/>
    </justification>
  </clause>

  <clause id="40972">
    <literal><![CDATA[
      a(a(x,x,y),L(y,z,u),w) = a(y,y,a(w,x,L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,39811,a(flip),b,40911,a),flip(a)].">
      <j1 rule="hyper" parents="373 39811 40911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40973">
    <literal><![CDATA[
      L(R(x,y,z),a(x,u,u),w) = L(R(x,y,z),x,a(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(25244,a,40923,a),flip(a)].">
      <j1 rule="hyper" parents="25244 40923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40974">
    <literal><![CDATA[
      L(x,L(y \ z,z,z),z) = L(x,z * y,L(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29223,a(flip),b,40961,a),flip(a)].">
      <j1 rule="hyper" parents="64 29223 40961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40975">
    <literal><![CDATA[
      L(x,L(y,y,z),y * z) = L(x,y,L(z \ y,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,35084,a(flip),b,40962,a),flip(a)].">
      <j1 rule="hyper" parents="64 35084 40962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40976">
    <literal><![CDATA[
      a(a(x,y,y),L(x,z,u),w) = a(x,x,a(w,y,L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,32543,a,b,40972,a)].">
      <j1 rule="hyper" parents="64 32543 40972"/>
    </justification>
  </clause>

  <clause id="40977">
    <literal><![CDATA[
      a(x,x,y) * a(y,y,a(z,x,L(x,u,w))) = R(a(x,x,y),L(y,u,w),z)
    ]]></literal>
    <justification jstring="[para(40976(a,1),37929(a,1,2))].">
      <j1 rule="para" parents="40976 37929"/>
    </justification>
  </clause>

  <clause id="40978">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * R(x,y,y) = x * a(L(x,z,z),y,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,40966,a(flip),b,30264,a),flip(a)].">
      <j1 rule="hyper" parents="145 40966 30264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40979">
    <literal><![CDATA[
      x * a(L(x,y,y),z,z) = R(x,z,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,38023,a(flip),b,40978,a),flip(a)].">
      <j1 rule="hyper" parents="64 38023 40978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40980">
    <literal><![CDATA[
      a(L(x,y,y),z,z) = a(x,z,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,38379,a,b,40979,a),flip(a)].">
      <j1 rule="hyper" parents="35 38379 40979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40981">
    <literal><![CDATA[
      a(x,y \ 1,L(y \ 1,z,z)) = a(L(x,z,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(32046,a,40980,a),flip(a)].">
      <j1 rule="hyper" parents="32046 40980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40982">
    <literal><![CDATA[
      a(L(x,y,y),z,L(z,y,y)) = a(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34954,a(flip),b,40980,a),flip(a)].">
      <j1 rule="hyper" parents="64 34954 40980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40983">
    <literal><![CDATA[
      a(x,y,L(y,z,z)) \ y = L(y,y,L(x,z,z))
    ]]></literal>
    <justification jstring="[para(40980(a,1),30459(a,1,1))].">
      <j1 rule="para" parents="40980 30459"/>
    </justification>
  </clause>

  <clause id="40984">
    <literal><![CDATA[
      a(x \ y,z,L(z,x,x)) = a(y * x,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30383,a(flip),b,40982,a)].">
      <j1 rule="hyper" parents="64 30383 40982"/>
    </justification>
  </clause>

  <clause id="40985">
    <literal><![CDATA[
      L(x,L(x,y,y),z) = L(x,x,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,40733,a(flip),b,40983,a)].">
      <j1 rule="hyper" parents="64 40733 40983"/>
    </justification>
  </clause>

  <clause id="40986">
    <literal><![CDATA[
      L(x,x,L(y,x \ z,x \ z)) = a(y,x,(1 / (z / x)) * z) \ x
    ]]></literal>
    <justification jstring="[para(10627(a,1),40983(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="10627 40983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40987">
    <literal><![CDATA[
      R(L(x,x,L(y,z,z)),u,w) = L(R(x,u,w),L(x,z,z),y)
    ]]></literal>
    <justification jstring="[para(40985(a,1),29(a,1,1))].">
      <j1 rule="para" parents="40985 29"/>
    </justification>
  </clause>

  <clause id="40988">
    <literal><![CDATA[
      L(x,x,L(y,z,z)) \ L(R(x,u,w),L(x,z,z),y) = L(x \ R(x,u,w),L(x,z,z),y)
    ]]></literal>
    <justification jstring="[para(40985(a,1),4243(a,1,1))].">
      <j1 rule="para" parents="40985 4243"/>
    </justification>
  </clause>

  <clause id="40989">
    <literal><![CDATA[
      a(x,y,y) * (z \ L(y,y,L(x,z,z))) = z \ y
    ]]></literal>
    <justification jstring="[para(40985(a,1),40670(a,1,2,2))].">
      <j1 rule="para" parents="40985 40670"/>
    </justification>
  </clause>

  <clause id="40990">
    <literal><![CDATA[
      a(L(x,y,y),z,z \ 1) = a(x,z,L(z \ 1,y,y))
    ]]></literal>
    <justification jstring="[hyper(32046,a,40981,a),flip(a)].">
      <j1 rule="hyper" parents="32046 40981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40991">
    <literal><![CDATA[
      x * a(y,z,L(z \ 1,x,x)) = (1 / x) \ a(y,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(40990(a,1),36313(a,1,2))].">
      <j1 rule="para" parents="40990 36313"/>
    </justification>
  </clause>

  <clause id="40992">
    <literal><![CDATA[
      L(R(x,y,z),L(x,u,u),w) = L(R(x,y,z),x,L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(25244,a,40987,a),flip(a)].">
      <j1 rule="hyper" parents="25244 40987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40993">
    <literal><![CDATA[
      a(L(x,y,z),u,a(u,w,v5)) = L(a(x,u,a(u,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(40810(a,1),40819(a,1,1)),flip(a)].">
      <j1 rule="para" parents="40810 40819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40994">
    <literal><![CDATA[
      a(L(x,y,z),u,a(u,w,v5)) = L(a(u,a(u,w,v5),x),y,z)
    ]]></literal>
    <justification jstring="[para(39362(a,2),40993(a,2,1))].">
      <j1 rule="para" parents="39362 40993"/>
    </justification>
  </clause>

  <clause id="40995">
    <literal><![CDATA[
      a(x,a(x,y,z),L(u,w,v5)) = L(a(x,a(x,y,z),u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,39362,a,b,40994,a)].">
      <j1 rule="hyper" parents="64 39362 40994"/>
    </justification>
  </clause>

  <clause id="40996">
    <literal><![CDATA[
      L(a(x,a(x,y,z),u),w,v5) = L(a(u,x,a(x,y,z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,40993,a(flip),b,40994,a),flip(a)].">
      <j1 rule="hyper" parents="64 40993 40994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="40997">
    <literal><![CDATA[
      a(L(x,x,y),a(x,z,u),w) = a(x,a(x,z,u),L(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,40756,a,b,40995,a)].">
      <j1 rule="hyper" parents="373 40756 40995"/>
    </justification>
  </clause>

  <clause id="40998">
    <literal><![CDATA[
      x \ (y * (L(y,a(y,z,u),w) \ x)) = a(y,a(y,z,u),L(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,40783,a,b,40997,a)].">
      <j1 rule="hyper" parents="64 40783 40997"/>
    </justification>
  </clause>

  <clause id="40999">
    <literal><![CDATA[
      a(x,y,z) * L(u,x,a(x,y,z)) = (u / x) * (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(157,a,40831,a)].">
      <j1 rule="hyper" parents="157 40831"/>
    </justification>
  </clause>

  <clause id="41000">
    <literal><![CDATA[
      a(x \ y,a(x,x,y),z) \ a(y,x,x) = a(L(y,x \ y,z),x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,40851,a(flip),b,40869,a),flip(a)].">
      <j1 rule="hyper" parents="373 40851 40869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41001">
    <literal><![CDATA[
      a(x * y,a(y,x,x),z) \ a(y,x,x) = a(L(y,x * y,z),x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,40851,a(flip),b,40871,a),flip(a)].">
      <j1 rule="hyper" parents="373 40851 40871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41003">
    <literal><![CDATA[
      a(x,y,y) \ a(a(x,y,y),z,u) = a(L(x,z,u),y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,8,a(flip),b,40873,a)].">
      <j1 rule="hyper" parents="139 8 40873"/>
    </justification>
  </clause>

  <clause id="41004">
    <literal><![CDATA[
      a(a(x,y,y),z,u) * (a(x,y,y) \ w) = a(L(x,z,u),y,y) \ w
    ]]></literal>
    <justification jstring="[hyper(35,a,30263,a,b,40873,a)].">
      <j1 rule="hyper" parents="35 30263 40873"/>
    </justification>
  </clause>

  <clause id="41005">
    <literal><![CDATA[
      (a(x,y,y) \ z) * a(a(x,y,y),u,w) = a(L(x,u,w),y,y) \ z
    ]]></literal>
    <justification jstring="[hyper(35,a,29922,a,b,40873,a)].">
      <j1 rule="hyper" parents="35 29922 40873"/>
    </justification>
  </clause>

  <clause id="41006">
    <literal><![CDATA[
      L(a(x,y,y) \ 1,z,u) = a(L(x,z,u),y,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,38077,a(flip),b,41003,a)].">
      <j1 rule="hyper" parents="64 38077 41003"/>
    </justification>
  </clause>

  <clause id="41007">
    <literal><![CDATA[
      L(a(x,y,y) \ 1,z,u) * w = a(L(x,z,u),y,y) \ w
    ]]></literal>
    <justification jstring="[para(41006(a,2),37824(a,1,1))].">
      <j1 rule="para" parents="41006 37824"/>
    </justification>
  </clause>

  <clause id="41008">
    <literal><![CDATA[
      L(a(x,y,y) \ K(z,u),w,v5) = a(L(x,w,v5),y,y) \ K(z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26080,a(flip),b,41007,a)].">
      <j1 rule="hyper" parents="64 26080 41007"/>
    </justification>
  </clause>

  <clause id="41009">
    <literal><![CDATA[
      L(L(x \ 1,x,y) * x,z,u) * w = a(L(x * y,z,u),x,x) \ w
    ]]></literal>
    <justification jstring="[para(30502(a,1),41007(a,1,1,1))].">
      <j1 rule="para" parents="30502 41007"/>
    </justification>
  </clause>

  <clause id="41010">
    <literal><![CDATA[
      T(L(a(x,y,y) \ K(z,y),u,w),y) = T(y,z) \ L(y,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(41008(a,2),37654(a,1,1))].">
      <j1 rule="para" parents="41008 37654"/>
    </justification>
  </clause>

  <clause id="41011">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) \ a(z,z,y) = a(z,L(z,z * y,x),y)
    ]]></literal>
    <justification jstring="[para(40937(a,1),40877(a,1,1))].">
      <j1 rule="para" parents="40937 40877"/>
    </justification>
  </clause>

  <clause id="41012">
    <literal><![CDATA[
      a(x,x,y) * a(z,x,a(x,y,y)) = a(x,L(x,x * y,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,40920,a(flip),b,41011,a)].">
      <j1 rule="hyper" parents="64 40920 41011"/>
    </justification>
  </clause>

  <clause id="41013">
    <literal><![CDATA[
      a(x,L(x,x * y,z),y) = a(x,x,L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,40912,a(flip),b,41012,a),flip(a)].">
      <j1 rule="hyper" parents="64 40912 41012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41014">
    <literal><![CDATA[
      x \ ((x / (((1 / y) * z) \ 1)) * (((1 / y) * z) \ a(y,y,z))) = a(y,y,L(z,z,(y * z) \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,39956,a,b,41013,a)].">
      <j1 rule="hyper" parents="64 39956 41013"/>
    </justification>
  </clause>

  <clause id="41015">
    <literal><![CDATA[
      a(x,L(L(x,x,y),L(x,x,y) * (x * y),z),x * y) = a(L(x,x,y),L(x,x,y),L(x * y,x * y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,40764,a(flip),b,41013,a)].">
      <j1 rule="hyper" parents="64 40764 41013"/>
    </justification>
  </clause>

  <clause id="41016">
    <literal><![CDATA[
      a(x,x,L(y,x * y,z)) = a(x,x,L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39676,a(flip),b,41013,a)].">
      <j1 rule="hyper" parents="64 39676 41013"/>
    </justification>
  </clause>

  <clause id="41017">
    <literal><![CDATA[
      (x * y) * (z * a(x,x,L(y,y,z))) = ((1 / x) \ y) * z
    ]]></literal>
    <justification jstring="[para(41013(a,1),34881(a,1,2,2))].">
      <j1 rule="para" parents="41013 34881"/>
    </justification>
  </clause>

  <clause id="41018">
    <literal><![CDATA[
      (x * y) * (y * (L(y,x,x) \ z)) = ((1 / x) \ y) * z
    ]]></literal>
    <justification jstring="[para(39692(a,1),41017(a,1,2))].">
      <j1 rule="para" parents="39692 41017"/>
    </justification>
  </clause>

  <clause id="41019">
    <literal><![CDATA[
      (x * y) \ (((1 / x) \ y) * z) = y * (L(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(149,a,41018,a)].">
      <j1 rule="hyper" parents="149 41018"/>
    </justification>
  </clause>

  <clause id="41020">
    <literal><![CDATA[
      x * ((y \ z) * (((y \ 1) * z) \ u)) = x * (z * (L(z,y,y) \ u))
    ]]></literal>
    <justification jstring="[para(41019(a,1),37479(a,1,2)),flip(a)].">
      <j1 rule="para" parents="41019 37479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41021">
    <literal><![CDATA[
      L(x,L(y,y,L(z,z,y)),L(z,z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,34162,a(flip),b,40963,a),flip(a)].">
      <j1 rule="hyper" parents="373 34162 40963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41023">
    <literal><![CDATA[
      L(x,L(y,y,z),L(z,z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(31286(a,1),41021(a,1,2))].">
      <j1 rule="para" parents="31286 41021"/>
    </justification>
  </clause>

  <clause id="41025">
    <literal><![CDATA[
      L(x,x,L(y,x \ z,x \ z)) = a(y,x,((x \ z) \ 1) * z) \ x
    ]]></literal>
    <justification jstring="[para(27671(a,1),40986(a,2,1))].">
      <j1 rule="para" parents="27671 40986"/>
    </justification>
  </clause>

  <clause id="41026">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) \ a(y,z,z) = a(L(y,z * y,x),z,z)
    ]]></literal>
    <justification jstring="[para(40938(a,1),41001(a,1,1))].">
      <j1 rule="para" parents="40938 41001"/>
    </justification>
  </clause>

  <clause id="41027">
    <literal><![CDATA[
      a(x,y,y) * a(z,y,a(y,x,x)) = a(L(x,y * x,z),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,40920,a(flip),b,41026,a)].">
      <j1 rule="hyper" parents="64 40920 41026"/>
    </justification>
  </clause>

  <clause id="41028">
    <literal><![CDATA[
      a(L(x,y * x,z),y,y) = a(L(x,x,z),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,40914,a(flip),b,41027,a),flip(a)].">
      <j1 rule="hyper" parents="64 40914 41027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41029">
    <literal><![CDATA[
      a(L(x,y,z),u,u) \ (w / L(u,u,x)) = a(a(x,u,u),y,z) * (w / u)
    ]]></literal>
    <justification jstring="[para(37631(a,1),41004(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37631 41004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41030">
    <literal><![CDATA[
      ((x / y) / (1 / y)) * a(a(x,y,y),z,u) = a(L(x,z,u),y,y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,30574,a(flip),b,41005,a)].">
      <j1 rule="hyper" parents="64 30574 41005"/>
    </justification>
  </clause>

  <clause id="41031">
    <literal><![CDATA[
      (x \ y) * (((x \ 1) * y) \ z) = y * (L(y,x,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(322,a,41020,a),flip(a)].">
      <j1 rule="hyper" parents="322 41020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41032">
    <literal><![CDATA[
      ((1 / x) \ y) * a(z,u,a(u,x,x)) = L(1 / x,x,a(u,u,z)) \ y
    ]]></literal>
    <justification jstring="[para(36335(a,2),40887(a,2,1))].">
      <j1 rule="para" parents="36335 40887"/>
    </justification>
  </clause>

  <clause id="41033">
    <literal><![CDATA[
      (x * a(y,z,z)) \ (a(y,z,z) * L(y,x,a(x,z,z))) = L(x \ y,x,a(y,z,z)) * a(x,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(40917(a,2),30735(a,1,2))].">
      <j1 rule="para" parents="40917 30735"/>
    </justification>
  </clause>

  <clause id="41034">
    <literal><![CDATA[
      (a(x,x,y) \ (z * (y * a(x,x,y)))) * a(z,x,a(x,y,y)) = z * y
    ]]></literal>
    <justification jstring="[para(23133(a,1),40919(a,1,1))].">
      <j1 rule="para" parents="23133 40919"/>
    </justification>
  </clause>

  <clause id="41035">
    <literal><![CDATA[
      L(L(x * ((y * x) \ y),z,x),u,w) * v5 = K(x,x \ 1) * (a(L(x * y,u,w),x,x) \ v5)
    ]]></literal>
    <justification jstring="[para(41009(a,1),37144(a,2,2))].">
      <j1 rule="para" parents="41009 37144"/>
    </justification>
  </clause>

  <clause id="41036">
    <literal><![CDATA[
      L(a(x,y,y) \ K(z,y),u,w) = T(y,z) \ L(y,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(41,a,8465,a,b,41010,a),flip(a)].">
      <j1 rule="hyper" parents="41 8465 41010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41037">
    <literal><![CDATA[
      L(x * y,y,a(z,z,y)) * a(x,z,a(z,y,y)) = x * y
    ]]></literal>
    <justification jstring="[para(37966(a,1),41034(a,1,1))].">
      <j1 rule="para" parents="37966 41034"/>
    </justification>
  </clause>

  <clause id="41038">
    <literal><![CDATA[
      L(x * y,y,a(y,z,z)) * a(x,z,a(z,y,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(64,a,29293,a,b,41037,a)].">
      <j1 rule="hyper" parents="64 29293 41037"/>
    </justification>
  </clause>

  <clause id="41039">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * L(x * y,y,a(y,z,z)) = x * y
    ]]></literal>
    <justification jstring="[hyper(64,a,40913,a,b,41038,a)].">
      <j1 rule="hyper" parents="64 40913 41038"/>
    </justification>
  </clause>

  <clause id="41040">
    <literal><![CDATA[
      a(x \ a(y,z,z),y,a(y,z,z)) * L((a(y,z,z) \ x) * y,y,a(y,z,z)) = (a(y,z,z) \ x) * y
    ]]></literal>
    <justification jstring="[para(40760(a,2),41039(a,1,1))].">
      <j1 rule="para" parents="40760 41039"/>
    </justification>
  </clause>

  <clause id="41041">
    <literal><![CDATA[
      L(L(x,y,y * z),y,a(z,z * y,y)) = L(x,L(y,y,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35699,a(flip),b,40954,a)].">
      <j1 rule="hyper" parents="64 35699 40954"/>
    </justification>
  </clause>

  <clause id="41042">
    <literal><![CDATA[
      R(a(x,x,y),L(y,x,z),u) = a(x,x,y) * a(y,y,a(u,x,x))
    ]]></literal>
    <justification jstring="[para(37788(a,1),40977(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="37788 40977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41043">
    <literal><![CDATA[
      R(a(x,x,y),L(y,x,z),u) = a(x,x,L(y,y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,40904,a(flip),b,41042,a),flip(a)].">
      <j1 rule="hyper" parents="373 40904 41042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41044">
    <literal><![CDATA[
      a(x,x,L(y,L(y,x,z),u)) = a(x,x,L(y,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39680,a,b,41043,a)].">
      <j1 rule="hyper" parents="64 39680 41043"/>
    </justification>
  </clause>

  <clause id="41045">
    <literal><![CDATA[
      a(x,x,L(y,y,L(z,x,u))) = a(x,x,L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39723,a(flip),b,41044,a)].">
      <j1 rule="hyper" parents="64 39723 41044"/>
    </justification>
  </clause>

  <clause id="41046">
    <literal><![CDATA[
      a(x,x,L(x * y,x \ y,z)) = a(x,x,L(x * y,x * y,z))
    ]]></literal>
    <justification jstring="[para(31759(a,1),41044(a,1,3))].">
      <j1 rule="para" parents="31759 41044"/>
    </justification>
  </clause>

  <clause id="41047">
    <literal><![CDATA[
      a(L(x,y,z),u,u) \ (x * (1 / u)) = a(a(x,u,u),y,z) * (x / u)
    ]]></literal>
    <justification jstring="[para(11795(a,1),41029(a,1,2))].">
      <j1 rule="para" parents="11795 41029"/>
    </justification>
  </clause>

  <clause id="41048">
    <literal><![CDATA[
      x * L(y \ 1,y,L(x,z,u) * y) = a(a(x,y,y),z,u) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,37807,a(flip),b,41047,a)].">
      <j1 rule="hyper" parents="64 37807 41047"/>
    </justification>
  </clause>

  <clause id="41049">
    <literal><![CDATA[
      a(a(x,y,y),z,u) * (x / y) = x * (L(x,z,u) \ (L(x,z,u) / y))
    ]]></literal>
    <justification jstring="[para(30662(a,1),41048(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30662 41048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41050">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * (x / y) = x * (L(x,z,z) \ (L(x,z,z) / y))
    ]]></literal>
    <justification jstring="[para(40882(a,1),41049(a,1,1))].">
      <j1 rule="para" parents="40882 41049"/>
    </justification>
  </clause>

  <clause id="41051">
    <literal><![CDATA[
      (x / y) \ (x * a(z,z,u)) = y * a(z,L(z,y,y \ x),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,39774,a(flip),b,40846,a),flip(a)].">
      <j1 rule="hyper" parents="373 39774 40846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41052">
    <literal><![CDATA[
      (x / y) \ (x * a(z,z,u)) = y * a(z,z,L(u,y,y \ x))
    ]]></literal>
    <justification jstring="[para(39676(a,1),41051(a,2,2))].">
      <j1 rule="para" parents="39676 41051"/>
    </justification>
  </clause>

  <clause id="41053">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,a(u,w,w))) = x \ L(x,y,a(u,u,a(w,w,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,28848,a(flip),b,40897,a),flip(a)].">
      <j1 rule="hyper" parents="64 28848 40897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41054">
    <literal><![CDATA[
      (a(x,y,y) \ z) * L(x,x,a(z,y,y)) = z * ((a(x,y,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(37826(a,1),40925(a,1,1))].">
      <j1 rule="para" parents="37826 40925"/>
    </justification>
  </clause>

  <clause id="41055">
    <literal><![CDATA[
      (a(x,y,y) \ z) * L(x,x,a(z,y,y)) = z * (a(x,y,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,29936,a(flip),b,41054,a),flip(a)].">
      <j1 rule="hyper" parents="373 29936 41054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41056">
    <literal><![CDATA[
      a(x * y,z,z) \ (y \ (a(y \ x,z,z) * y)) = a(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(35089(a,1),40926(a,1,2,2))].">
      <j1 rule="para" parents="35089 40926"/>
    </justification>
  </clause>

  <clause id="41057">
    <literal><![CDATA[
      a(x * y,z,z) \ a(y \ x,z,z) = a(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(23174(a,1),41056(a,1,2))].">
      <j1 rule="para" parents="23174 41056"/>
    </justification>
  </clause>

  <clause id="41058">
    <literal><![CDATA[
      a(a(x * y,z,z),y,x) = a(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,32989,a(flip),b,41057,a)].">
      <j1 rule="hyper" parents="64 32989 41057"/>
    </justification>
  </clause>

  <clause id="41060">
    <literal><![CDATA[
      (x / y) \ (x * a(z,z,(y \ x) * y)) = (y * a(z,z,(y \ x) * y)) * a(y \ x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(41058(a,1),40846(a,2,2))].">
      <j1 rule="para" parents="41058 40846"/>
    </justification>
  </clause>

  <clause id="41061">
    <literal><![CDATA[
      a(x,y,(y \ z) \ ((z \ ((y \ z) \ z)) \ 1)) = a(y,y,a(x,y \ z,y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,31584,a(flip),b,40907,a)].">
      <j1 rule="hyper" parents="64 31584 40907"/>
    </justification>
  </clause>

  <clause id="41062">
    <literal><![CDATA[
      L(L(x,y * z,z),y * z,a(y,z,z)) = L(x,L(y * z,z * y,z),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30336,a(flip),b,40957,a)].">
      <j1 rule="hyper" parents="64 30336 40957"/>
    </justification>
  </clause>

  <clause id="41063">
    <literal><![CDATA[
      L(L(x,y * z,z),z,a(z,y,y)) = L(x,L(y * z,z * y,z),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40944,a(flip),b,41062,a)].">
      <j1 rule="hyper" parents="64 40944 41062"/>
    </justification>
  </clause>

  <clause id="41064">
    <literal><![CDATA[
      L(L(x,y * z,z),z,a(z,y,y)) = L(x,L(y \ z,z,z),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31757,a(flip),b,41063,a),flip(a)].">
      <j1 rule="hyper" parents="373 31757 41063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41065">
    <literal><![CDATA[
      a(x,y,z \ (((z \ y) \ 1) * y)) = a(y,y,a(x,y \ z,y \ z))
    ]]></literal>
    <justification jstring="[para(40566(a,1),41061(a,1,3))].">
      <j1 rule="para" parents="40566 41061"/>
    </justification>
  </clause>

  <clause id="41066">
    <literal><![CDATA[
      a(x,x,a(y,x \ z,x \ z)) = a(y,x,a(x,x * z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,37028,a(flip),b,41065,a),flip(a)].">
      <j1 rule="hyper" parents="64 37028 41065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41067">
    <literal><![CDATA[
      x * ((y * (z * a(y,y,z))) * a(x,z,a(z,y,y))) = (x * (y * z)) * a(y,y,z)
    ]]></literal>
    <justification jstring="[para(29910(a,1),40940(a,1,2,1))].">
      <j1 rule="para" parents="29910 40940"/>
    </justification>
  </clause>

  <clause id="41068">
    <literal><![CDATA[
      L(L(x,y * z,z),y * z,a(y,z,z)) = L(x,y \ (y / (1 / (y * z))),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30336,a(flip),b,40959,a)].">
      <j1 rule="hyper" parents="64 30336 40959"/>
    </justification>
  </clause>

  <clause id="41069">
    <literal><![CDATA[
      L(L(x,y * z,z),z,a(z,y,y)) = L(x,y \ (y / (1 / (y * z))),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40944,a(flip),b,41068,a)].">
      <j1 rule="hyper" parents="64 40944 41068"/>
    </justification>
  </clause>

  <clause id="41070">
    <literal><![CDATA[
      L(x,L(y \ z,z,z),z) = L(x,y \ (y / (1 / (y * z))),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41064,a(flip),b,41069,a)].">
      <j1 rule="hyper" parents="64 41064 41069"/>
    </justification>
  </clause>

  <clause id="41071">
    <literal><![CDATA[
      x * (((1 / y) \ z) * a(x,z,a(z,y,y))) = (x * (y * z)) * a(y,y,z)
    ]]></literal>
    <justification jstring="[para(30219(a,1),41067(a,1,2,1))].">
      <j1 rule="para" parents="30219 41067"/>
    </justification>
  </clause>

  <clause id="41072">
    <literal><![CDATA[
      (x * (y * z)) * a(y,y,z) = x * (L(1 / y,y,a(z,z,x)) \ z)
    ]]></literal>
    <justification jstring="[para(41032(a,1),41071(a,1,2)),flip(a)].">
      <j1 rule="para" parents="41032 41071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41073">
    <literal><![CDATA[
      L(x,x,L(y,z,z)) \ L(R(x,u,w),x,L(y,z,z)) = L(x \ R(x,u,w),L(x,z,z),y)
    ]]></literal>
    <justification jstring="[para(40992(a,1),40988(a,1,2))].">
      <j1 rule="para" parents="40992 40988"/>
    </justification>
  </clause>

  <clause id="41074">
    <literal><![CDATA[
      L(x \ R(x,y,z),L(x,u,u),w) = L(x \ R(x,y,z),x,L(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,4243,a(flip),b,41073,a),flip(a)].">
      <j1 rule="hyper" parents="64 4243 41073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41075">
    <literal><![CDATA[
      L(a(x,y,z) \ u,x,a(x,y,z)) \ u = a(x,y,z) * a(x,a(x,y,z),a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(23133(a,1),40830(a,1,1,1))].">
      <j1 rule="para" parents="23133 40830"/>
    </justification>
  </clause>

  <clause id="41076">
    <literal><![CDATA[
      a(x,y,z) * (u * a(w,w,a(u,x,x))) = L(u * a(x,y,z),x,a(x,w,w))
    ]]></literal>
    <justification jstring="[para(39755(a,1),40928(a,1,2,2))].">
      <j1 rule="para" parents="39755 40928"/>
    </justification>
  </clause>

  <clause id="41078">
    <literal><![CDATA[
      L(x * a(y,z,u),y,a(y,w,w)) = a(y,z,u) * L(x,w,a(w,y,y))
    ]]></literal>
    <justification jstring="[para(40905(a,1),41076(a,1,2)),flip(a)].">
      <j1 rule="para" parents="40905 41076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41079">
    <literal><![CDATA[
      ((a(x,y,z) * x) \ (x * u)) \ u = a(x,y,z) * a(x,a(x,y,z),a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(30326(a,1),41075(a,1,1))].">
      <j1 rule="para" parents="30326 41075"/>
    </justification>
  </clause>

  <clause id="41080">
    <literal><![CDATA[
      (x * (((x * y) * y) \ z)) * a(x,x,a(y * ((y * x) \ z),y,y)) = (((x * y) * y) / x) \ z
    ]]></literal>
    <justification jstring="[para(36880(a,1),40916(a,1,2,3))].">
      <j1 rule="para" parents="36880 40916"/>
    </justification>
  </clause>

  <clause id="41081">
    <literal><![CDATA[
      ((x \ a(L(x * y,z,u),x,x)) * x) \ w = L(L(x * ((y * x) \ y),v5,x),z,u) * w
    ]]></literal>
    <justification jstring="[hyper(373,a,25208,a(flip),b,41035,a)].">
      <j1 rule="hyper" parents="373 25208 41035"/>
    </justification>
  </clause>

  <clause id="41082">
    <literal><![CDATA[
      L((x \ a(x * y,x,x)) * x,z,u) \ w = L(L(x * ((y * x) \ y),v5,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(32616(a,2),41081(a,1,1))].">
      <j1 rule="para" parents="32616 41081"/>
    </justification>
  </clause>

  <clause id="41083">
    <literal><![CDATA[
      L(L(x * ((y * x) \ y),z,x),u,w) * v5 = L(a(y,x,x \ 1),u,w) \ v5
    ]]></literal>
    <justification jstring="[para(33376(a,1),41082(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="33376 41082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41084">
    <literal><![CDATA[
      L(L(x * ((y * x) \ y),z,x),u,w) * v5 = a(L(y,u,w),x,x \ 1) \ v5
    ]]></literal>
    <justification jstring="[para(4248(a,2),41083(a,2,1))].">
      <j1 rule="para" parents="4248 41083"/>
    </justification>
  </clause>

  <clause id="41085">
    <literal><![CDATA[
      1 / L(L(x * ((y * x) \ y),z,x),u,w) = a(L(y,u,w),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(225,a,8,a(flip),b,41084,a(flip))].">
      <j1 rule="hyper" parents="225 8 41084"/>
    </justification>
  </clause>

  <clause id="41086">
    <literal><![CDATA[
      1 / L(x * L(x \ 1,x,y),z,u) = a(L(y,z,u),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(31327(a,1),41085(a,1,2,1))].">
      <j1 rule="para" parents="31327 41085"/>
    </justification>
  </clause>

  <clause id="41087">
    <literal><![CDATA[
      (x * (((x * y) * y) \ z)) * a(x,x,a(x \ z,y,y)) = (((x * y) * y) / x) \ z
    ]]></literal>
    <justification jstring="[para(36878(a,1),41080(a,1,2,3))].">
      <j1 rule="para" parents="36878 41080"/>
    </justification>
  </clause>

  <clause id="41088">
    <literal><![CDATA[
      (x * (((x * y) * y) \ z)) * a(z,x,a(x,y,y)) = (((x * y) * y) / x) \ z
    ]]></literal>
    <justification jstring="[para(40901(a,1),41087(a,1,2))].">
      <j1 rule="para" parents="40901 41087"/>
    </justification>
  </clause>

  <clause id="41089">
    <literal><![CDATA[
      x * ((((x * y) * y) \ z) * a(z,x,a(x,y,y))) = (((x * y) * y) / x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,33404,a(flip),b,41088,a)].">
      <j1 rule="hyper" parents="64 33404 41088"/>
    </justification>
  </clause>

  <clause id="41090">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) * (((x * z) * z) \ y) = (((x * z) * z) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,40908,a(flip),b,41089,a)].">
      <j1 rule="hyper" parents="64 40908 41089"/>
    </justification>
  </clause>

  <clause id="41091">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) * (((x * z) * z) \ y) = (x / ((x / z) / z)) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,35283,a(flip),b,41090,a),flip(a)].">
      <j1 rule="hyper" parents="373 35283 41090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41092">
    <literal><![CDATA[
      x \ ((x / (((1 / y) * z) \ 1)) * (((1 / y) * z) \ a(y,y,z))) = a(y,y,L(z,z,z * (y \ x)))
    ]]></literal>
    <justification jstring="[para(37525(a,1),41014(a,2,3))].">
      <j1 rule="para" parents="37525 41014"/>
    </justification>
  </clause>

  <clause id="41093">
    <literal><![CDATA[
      x \ ((x / (((1 / y) * z) \ 1)) * (((1 / y) * z) \ a(y,y,z))) = a(y,y,L(z,z,y \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,27599,a(flip),b,41092,a),flip(a)].">
      <j1 rule="hyper" parents="373 27599 41092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41094">
    <literal><![CDATA[
      x \ ((x / ((1 / y) * z)) * ((1 / ((1 / y) * z)) \ a(y,y,z))) = a(y,y,L(z,z,y \ x))
    ]]></literal>
    <justification jstring="[para(1689(a,1),41093(a,1,2))].">
      <j1 rule="para" parents="1689 41093"/>
    </justification>
  </clause>

  <clause id="41095">
    <literal><![CDATA[
      a(x,x,L(y,y,x \ z)) = z \ ((z / ((1 / x) * y)) * ((1 / (1 / x)) \ y))
    ]]></literal>
    <justification jstring="[para(35061(a,1),41094(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="35061 41094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41096">
    <literal><![CDATA[
      a(x,x,L(y,y,x \ z)) = z \ (((1 / x) \ y) * ((((1 / x) \ 1) * y) \ z))
    ]]></literal>
    <justification jstring="[para(37458(a,1),41095(a,2,2))].">
      <j1 rule="para" parents="37458 41095"/>
    </justification>
  </clause>

  <clause id="41097">
    <literal><![CDATA[
      a(x,x,L(y,y,x \ z)) = z \ (((1 / x) \ y) * ((x * y) \ z))
    ]]></literal>
    <justification jstring="[para(82(a,1),41096(a,2,2,2,1,1))].">
      <j1 rule="para" parents="82 41096"/>
    </justification>
  </clause>

  <clause id="41099">
    <literal><![CDATA[
      a(x,x,L(y,y,x \ z)) = z \ ((x \ y) * (((x \ 1) * y) \ z))
    ]]></literal>
    <justification jstring="[para(37460(a,1),41097(a,2,2))].">
      <j1 rule="para" parents="37460 41097"/>
    </justification>
  </clause>

  <clause id="41100">
    <literal><![CDATA[
      a(x,x,L(y,y,x \ z)) = z \ (y * (L(y,x,x) \ z))
    ]]></literal>
    <justification jstring="[para(41031(a,1),41099(a,2,2))].">
      <j1 rule="para" parents="41031 41099"/>
    </justification>
  </clause>

  <clause id="41101">
    <literal><![CDATA[
      a(x,x,L(y,y,x \ z)) = a(x,x,L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,39690,a(flip),b,41100,a),flip(a)].">
      <j1 rule="hyper" parents="373 39690 41100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41102">
    <literal><![CDATA[
      a(x,x,L(y,y,x * z)) = a(x,x,L(y,y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),41101(a,1,3,3)),flip(a)].">
      <j1 rule="para" parents="9 41101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41103">
    <literal><![CDATA[
      L(L(a(x,y,z),x,u) \ a(x,y,z),a(x,y,z),x) = a(L(u,x,w),x,L(a(x,y,z),x,u))
    ]]></literal>
    <justification jstring="[para(38028(a,1),40732(a,1,1,1))].">
      <j1 rule="para" parents="38028 40732"/>
    </justification>
  </clause>

  <clause id="41105">
    <literal><![CDATA[
      L(a(x,y,a(y,z,u)),a(y,z,u),y) = a(L(x,y,w),y,L(a(y,z,u),y,x))
    ]]></literal>
    <justification jstring="[para(39376(a,1),41103(a,1,1))].">
      <j1 rule="para" parents="39376 41103"/>
    </justification>
  </clause>

  <clause id="41106">
    <literal><![CDATA[
      a(L(x,y,z),y,L(a(y,u,w),y,x)) = a(x,y,a(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,33385,a(flip),b,41105,a),flip(a)].">
      <j1 rule="hyper" parents="64 33385 41105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41108">
    <literal><![CDATA[
      (x / y) \ (x * a(z,z,x)) = (y * a(z,z,(y \ x) * y)) * a(y \ x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(27299(a,1),41060(a,1,2,2))].">
      <j1 rule="para" parents="27299 41060"/>
    </justification>
  </clause>

  <clause id="41109">
    <literal><![CDATA[
      (x / y) \ (x * a(z,z,x)) = (y * a(z,z,x)) * a(y \ x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(27299(a,1),41108(a,2,1,2))].">
      <j1 rule="para" parents="27299 41108"/>
    </justification>
  </clause>

  <clause id="41112">
    <literal><![CDATA[
      (x / y) \ (x * a(z,z,x)) = (y * a(z,z,x)) * a(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(33501(a,1),41109(a,2,2))].">
      <j1 rule="para" parents="33501 41109"/>
    </justification>
  </clause>

  <clause id="41113">
    <literal><![CDATA[
      (x / y) \ (x * a(z,z,x)) = y * (a(z,z,x) * a(x,y,a(y,z,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,33404,a(flip),b,41112,a),flip(a)].">
      <j1 rule="hyper" parents="373 33404 41112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41114">
    <literal><![CDATA[
      (x / y) \ (x * a(z,z,x)) = y * a(z,z,L(x,y,y))
    ]]></literal>
    <justification jstring="[para(40896(a,1),41113(a,2,2))].">
      <j1 rule="para" parents="40896 41113"/>
    </justification>
  </clause>

  <clause id="41115">
    <literal><![CDATA[
      a(x,x,L(y,z,z \ y)) = a(x,x,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,41052,a(flip),b,41114,a(flip))].">
      <j1 rule="hyper" parents="35 41052 41114"/>
    </justification>
  </clause>

  <clause id="41116">
    <literal><![CDATA[
      a(x,x,L(y * z,z,z)) = a(x,x,L(y * z,z,y))
    ]]></literal>
    <justification jstring="[para(23842(a,1),41115(a,1,3)),flip(a)].">
      <j1 rule="para" parents="23842 41115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41117">
    <literal><![CDATA[
      a(x,x,L(y,z,y * z)) = a(x,x,L(y,z,z))
    ]]></literal>
    <justification jstring="[para(37224(a,1),41115(a,1,3))].">
      <j1 rule="para" parents="37224 41115"/>
    </justification>
  </clause>

  <clause id="41118">
    <literal><![CDATA[
      a(x,x,L(y \ z,y,z)) = a(x,x,L(y \ z,y,y))
    ]]></literal>
    <justification jstring="[para(23833(a,1),41117(a,1,3))].">
      <j1 rule="para" parents="23833 41117"/>
    </justification>
  </clause>

  <clause id="41119">
    <literal><![CDATA[
      a(x,x,L(y * z,z,y)) = a(x,x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,38945,a(flip),b,41116,a),flip(a)].">
      <j1 rule="hyper" parents="64 38945 41116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41120">
    <literal><![CDATA[
      a(x,x,L(y * z,y,z)) = a(x,x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27377,a,b,41119,a)].">
      <j1 rule="hyper" parents="64 27377 41119"/>
    </justification>
  </clause>

  <clause id="41121">
    <literal><![CDATA[
      a(x,x,(y \ (z \ 1)) \ 1) \ u = a(x,x,(y \ 1) \ z) \ u
    ]]></literal>
    <justification jstring="[para(41120(a,1),38124(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41120 38124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41122">
    <literal><![CDATA[
      a(x,x,L((y \ z) \ y,y \ z,y)) = a(x,x,((z / y) * (y \ z)) \ z)
    ]]></literal>
    <justification jstring="[para(15002(a,1),41118(a,2,3))].">
      <j1 rule="para" parents="15002 41118"/>
    </justification>
  </clause>

  <clause id="41123">
    <literal><![CDATA[
      a(x,x,(y \ 1) \ z) \ 1 = y \ (z \ L(z * y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,37975,a(flip),b,41121,a),flip(a)].">
      <j1 rule="hyper" parents="64 37975 41121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41124">
    <literal><![CDATA[
      a(x,x,((y / z) * (z \ y)) \ y) = a(x,x,y \ (z * z))
    ]]></literal>
    <justification jstring="[para(630(a,1),41122(a,1,3)),flip(a)].">
      <j1 rule="para" parents="630 41122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41125">
    <literal><![CDATA[
      a(x,x,((y \ z) * (z / y)) \ z) = a(x,x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(27591,a,41124,a)].">
      <j1 rule="hyper" parents="27591 41124"/>
    </justification>
  </clause>

  <clause id="41126">
    <literal><![CDATA[
      a(x,x,(1 / (y \ z)) * y) = a(x,x,z \ (y * y))
    ]]></literal>
    <justification jstring="[para(25894(a,1),41125(a,1,3))].">
      <j1 rule="para" parents="25894 41125"/>
    </justification>
  </clause>

  <clause id="41127">
    <literal><![CDATA[
      a(x,x,y * ((y \ z) \ 1)) = a(x,x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,27458,a(flip),b,41126,a)].">
      <j1 rule="hyper" parents="64 27458 41126"/>
    </justification>
  </clause>

  <clause id="41128">
    <literal><![CDATA[
      a(x,L(L(x,x,y),x * (L(x,x,y) * y),z),x * y) = a(L(x,x,y),L(x,x,y),L(x * y,x * y,z))
    ]]></literal>
    <justification jstring="[para(2323(a,1),41015(a,1,2,2))].">
      <j1 rule="para" parents="2323 41015"/>
    </justification>
  </clause>

  <clause id="41129">
    <literal><![CDATA[
      (x * a(y,z,z)) \ L(R(y,z,z),x,a(x,z,z)) = L(x \ y,x,a(y,z,z)) * a(x,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(32790(a,1),41033(a,1,2))].">
      <j1 rule="para" parents="32790 41033"/>
    </justification>
  </clause>

  <clause id="41130">
    <literal><![CDATA[
      L(x \ y,x,a(y,z,z)) * a(x,x,a(y,z,z)) = (x * a(y,z,z)) \ R(y,z,L(z,x,x))
    ]]></literal>
    <justification jstring="[para(40929(a,1),41129(a,1,2)),flip(a)].">
      <j1 rule="para" parents="40929 41129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41131">
    <literal><![CDATA[
      L(a(x,x,a(y,z,z)) * (x \ y),x,a(y,z,z)) = (x * a(y,z,z)) \ R(y,z,L(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,37795,a,b,41130,a)].">
      <j1 rule="hyper" parents="64 37795 41130"/>
    </justification>
  </clause>

  <clause id="41132">
    <literal><![CDATA[
      L(L(x,x,a(y,z,z)) \ y,x,a(y,z,z)) = (x * a(y,z,z)) \ R(y,z,L(z,x,x))
    ]]></literal>
    <justification jstring="[para(37626(a,1),41131(a,1,1))].">
      <j1 rule="para" parents="37626 41131"/>
    </justification>
  </clause>

  <clause id="41133">
    <literal><![CDATA[
      a(L(x,x,y),L(x,x,y),L(x * y,x * y,z)) = a(x,L(L(x,x,y),(x \ y) * x,z),x * y)
    ]]></literal>
    <justification jstring="[para(31062(a,1),41128(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31062 41128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41134">
    <literal><![CDATA[
      a(L(x,x,y),L(x,x,y),L(x * y,x * y,z)) = a(x,L(L(x,x,y),y,z),x * y)
    ]]></literal>
    <justification jstring="[para(29441(a,1),41133(a,2,2))].">
      <j1 rule="para" parents="29441 41133"/>
    </justification>
  </clause>

  <clause id="41135">
    <literal><![CDATA[
      a(L(x,x,y),L(x,x,y),L(x * y,x * y,z)) = a(x,L(x,y,z),x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,38723,a(flip),b,41134,a),flip(a)].">
      <j1 rule="hyper" parents="373 38723 41134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41138">
    <literal><![CDATA[
      a(x,x,L(x * y,x * y,z)) = a(x,L(x,y,z),x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,40772,a(flip),b,41135,a)].">
      <j1 rule="hyper" parents="64 40772 41135"/>
    </justification>
  </clause>

  <clause id="41139">
    <literal><![CDATA[
      a(x,x,L(x * y,x \ y,z)) = a(x,L(x,y,z),x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41046,a,b,41138,a)].">
      <j1 rule="hyper" parents="64 41046 41138"/>
    </justification>
  </clause>

  <clause id="41142">
    <literal><![CDATA[
      a(x,x,L(x * y,x \ y,z)) = a(x,x,L(x * y,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,39676,a(flip),b,41139,a),flip(a)].">
      <j1 rule="hyper" parents="373 39676 41139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41143">
    <literal><![CDATA[
      a(x,x,L(x * y,y,z)) \ z = (x * y) * (((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(41142(a,1),39780(a,1,1))].">
      <j1 rule="para" parents="41142 39780"/>
    </justification>
  </clause>

  <clause id="41144">
    <literal><![CDATA[
      a(x,x,L(x * y,y,z)) \ z = ((x * x) \ (x * ((x * x) * y))) * (((1 / x) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(41142(a,1),39820(a,1,1))].">
      <j1 rule="para" parents="41142 39820"/>
    </justification>
  </clause>

  <clause id="41145">
    <literal><![CDATA[
      a(x,x,L(x * y,y,z)) \ z = ((1 / x) * ((x * x) * y)) * (((1 / x) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(535(a,1),41144(a,2,1))].">
      <j1 rule="para" parents="535 41144"/>
    </justification>
  </clause>

  <clause id="41146">
    <literal><![CDATA[
      a(x,x,L(x * y,y,z)) \ z = ((1 / (1 / x)) * y) * (((1 / x) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(819(a,1),41145(a,2,1))].">
      <j1 rule="para" parents="819 41145"/>
    </justification>
  </clause>

  <clause id="41147">
    <literal><![CDATA[
      L(x,y * (z \ (u \ 1)),a(y * (z \ (u \ 1)),w,v5)) = x * a(x,(z \ u) * y,a((z \ u) * y,w,v5))
    ]]></literal>
    <justification jstring="[para(32269(a,1),40815(a,2,2))].">
      <j1 rule="para" parents="32269 40815"/>
    </justification>
  </clause>

  <clause id="41149">
    <literal><![CDATA[
      a(x * (((y * y) * ((z * u) * w)) * R(u,z,w)),R(u,z,w),R(u,z,w)) = a((((y * y) * z) * w) * x,u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32523,a(flip),b,40665,a),flip(a)].">
      <j1 rule="hyper" parents="373 32523 40665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41151">
    <literal><![CDATA[
      a(x * (((y * y) * ((z * u) * w)) * R(u,z,w)),R(u,z,w),R(u,z,w)) = a(((y * y) * (z * w)) * x,u,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),41149(a,2,1,1))].">
      <j1 rule="para" parents="33 41149"/>
    </justification>
  </clause>

  <clause id="41152">
    <literal><![CDATA[
      a(x * (((y * y) * ((z * u) * w)) * R(u,z,w)),R(u,z,w),R(u,z,w)) = a((z * w) * x,u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2655,a(flip),b,41151,a),flip(a)].">
      <j1 rule="hyper" parents="373 2655 41151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41154">
    <literal><![CDATA[
      a(x * ((y * y) * (((z * u) * w) * R(u,z,w))),R(u,z,w),R(u,z,w)) = a((z * w) * x,u,u)
    ]]></literal>
    <justification jstring="[para(33(a,1),41152(a,1,1,2))].">
      <j1 rule="para" parents="33 41152"/>
    </justification>
  </clause>

  <clause id="41155">
    <literal><![CDATA[
      a(x * ((y * y) * (((z * u) * w) * R(u,z,w))),R(u,z,w),L(u,z,w)) = a((z * w) * x,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27644,a(flip),b,41154,a)].">
      <j1 rule="hyper" parents="64 27644 41154"/>
    </justification>
  </clause>

  <clause id="41156">
    <literal><![CDATA[
      a(x * ((y * y) * (((z * u) * w) * R(u,z,w))),L(u,z,w),L(u,z,w)) = a((z * w) * x,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32197,a(flip),b,41155,a)].">
      <j1 rule="hyper" parents="64 32197 41155"/>
    </justification>
  </clause>

  <clause id="41157">
    <literal><![CDATA[
      a(x * ((y * y) * (((z * u) * w) * R(u,z,w))),u,u) = a((z * w) * x,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,40664,a(flip),b,41156,a)].">
      <j1 rule="hyper" parents="64 40664 41156"/>
    </justification>
  </clause>

  <clause id="41159">
    <literal><![CDATA[
      a(x * (((y * z) * u) * R(z,y,u)),z,z) = a((y * u) * x,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11957,a(flip),b,41157,a)].">
      <j1 rule="hyper" parents="64 11957 41157"/>
    </justification>
  </clause>

  <clause id="41160">
    <literal><![CDATA[
      a(x * (((y * z) * u) * L(z,y,u)),z,z) = a((y * u) * x,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34670,a(flip),b,41159,a)].">
      <j1 rule="hyper" parents="64 34670 41159"/>
    </justification>
  </clause>

  <clause id="41161">
    <literal><![CDATA[
      a(x * (y * L(x,z,u)),a(y * x,x,x),w) = a(w,y * x,a(y * x,L(x,z,u),L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(40664(a,1),40941(a,1,2))].">
      <j1 rule="para" parents="40664 40941"/>
    </justification>
  </clause>

  <clause id="41162">
    <literal><![CDATA[
      a(x,y * z,a(y * z,L(z,u,w),L(z,u,w))) = a(z * (y * L(z,u,w)),a(z,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32896,a(flip),b,41161,a),flip(a)].">
      <j1 rule="hyper" parents="64 32896 41161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41164">
    <literal><![CDATA[
      a(x * (y * L(x,z,u)),a(x,x,y),w) = a(w,y * x,a(y * x,x,x))
    ]]></literal>
    <justification jstring="[para(40664(a,1),41162(a,1,3)),flip(a)].">
      <j1 rule="para" parents="40664 41162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41165">
    <literal><![CDATA[
      a(x * (y * L(x,z,u)),a(x,x,y),w) = a(w,y,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,40932,a(flip),b,41164,a),flip(a)].">
      <j1 rule="hyper" parents="373 40932 41164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41167">
    <literal><![CDATA[
      L((x * y) \ ((((a(x,y,y) \ 1) \ 1) \ 1) \ z),y,a(y,x,x)) = ((a(x,y,y) \ 1) * (x * y)) \ z
    ]]></literal>
    <justification jstring="[para(13983(a,1),40949(a,2,1,1))].">
      <j1 rule="para" parents="13983 40949"/>
    </justification>
  </clause>

  <clause id="41171">
    <literal><![CDATA[
      L((x * y) \ ((((a(x,y,y) \ 1) \ 1) \ 1) \ z),y,a(y,x,x)) = (x * L(y,y,x)) \ z
    ]]></literal>
    <justification jstring="[para(37536(a,1),41167(a,2,1))].">
      <j1 rule="para" parents="37536 41167"/>
    </justification>
  </clause>

  <clause id="41172">
    <literal><![CDATA[
      L((x * y) \ ((a(x,y,y) \ 1) \ z),y,a(y,x,x)) = (x * L(y,y,x)) \ z
    ]]></literal>
    <justification jstring="[para(13931(a,1),41171(a,1,1,2,1,1))].">
      <j1 rule="para" parents="13931 41171"/>
    </justification>
  </clause>

  <clause id="41174">
    <literal><![CDATA[
      L((x * y) \ (z * a(x,y,y)),y,a(y,x,x)) = (x * L(y,y,x)) \ z
    ]]></literal>
    <justification jstring="[para(37823(a,1),41172(a,1,1,2))].">
      <j1 rule="para" parents="37823 41172"/>
    </justification>
  </clause>

  <clause id="41175">
    <literal><![CDATA[
      L(((x * y) \ z) * a(x,y,y),y,a(y,x,x)) = (x * L(y,y,x)) \ z
    ]]></literal>
    <justification jstring="[para(30714(a,1),41174(a,1,1))].">
      <j1 rule="para" parents="30714 41174"/>
    </justification>
  </clause>

  <clause id="41176">
    <literal><![CDATA[
      (a(x,y,y) \ 1) * ((x * y) * T(z,a(x,y,y) \ (x * y))) = L(z,y,a(y,x,x)) * ((1 / a(x,y,y)) * (x * y))
    ]]></literal>
    <justification jstring="[para(13923(a,1),40950(a,1,1))].">
      <j1 rule="para" parents="13923 40950"/>
    </justification>
  </clause>

  <clause id="41177">
    <literal><![CDATA[
      L(x,y,a(y,z,z)) * ((1 / a(z,y,y)) * (z * y)) = (a(z,y,y) \ 1) * ((z * y) * T(x,z * y))
    ]]></literal>
    <justification jstring="[para(28120(a,1),41176(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28120 41176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41178">
    <literal><![CDATA[
      L(x,y,a(y,z,z)) * ((1 / a(z,y,y)) * (z * y)) = (a(z,y,y) \ 1) * (x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,251,a(flip),b,41177,a),flip(a)].">
      <j1 rule="hyper" parents="373 251 41177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41181">
    <literal><![CDATA[
      L(x,y,a(y,z,z)) * ((1 / a(z,y,y)) * (z * y)) = a(z,y,y) \ (x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,37824,a(flip),b,41178,a),flip(a)].">
      <j1 rule="hyper" parents="373 37824 41178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41182">
    <literal><![CDATA[
      L(x,y,a(y,z,z)) * ((1 / a(z,y,y)) * (z * y)) = (a(z,y,y) \ x) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,29998,a(flip),b,41181,a),flip(a)].">
      <j1 rule="hyper" parents="373 29998 41181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41183">
    <literal><![CDATA[
      L(x,y,a(y,z,z)) * ((a(z,y,y) \ 1) * (z * y)) = (a(z,y,y) \ x) * (z * y)
    ]]></literal>
    <justification jstring="[para(13923(a,1),41182(a,1,2,1))].">
      <j1 rule="para" parents="13923 41182"/>
    </justification>
  </clause>

  <clause id="41184">
    <literal><![CDATA[
      L(x,y,a(y,z,z)) * (z * L(y,y,z)) = (a(z,y,y) \ x) * (z * y)
    ]]></literal>
    <justification jstring="[para(37536(a,1),41183(a,1,2))].">
      <j1 rule="para" parents="37536 41183"/>
    </justification>
  </clause>

  <clause id="41185">
    <literal><![CDATA[
      R(x,(y * y) * (z * (z * y)),((z * y) \ 1) * ((y * y) * z)) = R(x,z \ ((y * y) * (z / y)),(z * y) \ ((y * y) * z))
    ]]></literal>
    <justification jstring="[para(33(a,1),40697(a,1,2))].">
      <j1 rule="para" parents="33 40697"/>
    </justification>
  </clause>

  <clause id="41186">
    <literal><![CDATA[
      R(x,y \ ((z * z) * (y / z)),(y * z) \ ((z * z) * y)) = R(x,(z * z) * (y * (y * z)),((y * z) \ (z * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27174,a(flip),b,41185,a),flip(a)].">
      <j1 rule="hyper" parents="64 27174 41185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41187">
    <literal><![CDATA[
      R(x,y \ ((z * z) * (y / z)),(y * z) \ ((z * z) * y)) = R(x,(z * z) * (y * (y * z)),y * ((z * y) \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,26287,a(flip),b,41186,a),flip(a)].">
      <j1 rule="hyper" parents="373 26287 41186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41188">
    <literal><![CDATA[
      R(x,y \ ((z * z) * (y / z)),(y * z) \ ((z * z) * y)) = R(x,(z * z) * (y * (y * z)),a(z,y,y \ z) \ z)
    ]]></literal>
    <justification jstring="[para(35851(a,1),41187(a,2,3))].">
      <j1 rule="para" parents="35851 41187"/>
    </justification>
  </clause>

  <clause id="41189">
    <literal><![CDATA[
      R(x,y \ ((z * z) * (y / z)),(y * z) \ ((z * z) * y)) = R(x,(z * z) * (y * (y * z)),z * a(z,y,y \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,38886,a(flip),b,41188,a),flip(a)].">
      <j1 rule="hyper" parents="373 38886 41188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41190">
    <literal><![CDATA[
      R(x,y \ ((z * z) * (y / z)),(y * z) \ ((z * z) * y)) = R(x,(z * z) * (y * (y * z)),R(z,y,y \ z))
    ]]></literal>
    <justification jstring="[para(2091(a,1),41189(a,2,3))].">
      <j1 rule="para" parents="2091 41189"/>
    </justification>
  </clause>

  <clause id="41191">
    <literal><![CDATA[
      R(x,y \ ((z * z) * (y / z)),(y * z) \ ((z * z) * y)) = R(x,(z * z) * (y * (y * z)),L(z,y,y \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,26360,a(flip),b,41190,a),flip(a)].">
      <j1 rule="hyper" parents="373 26360 41190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41192">
    <literal><![CDATA[
      R(x,y \ ((z * z) * (y / z)),(y * z) \ ((z * z) * y)) = R(x,(z * z) * (y * (y * z)),L(z,y,z * y))
    ]]></literal>
    <justification jstring="[para(37224(a,1),41191(a,2,3))].">
      <j1 rule="para" parents="37224 41191"/>
    </justification>
  </clause>

  <clause id="41193">
    <literal><![CDATA[
      R(x,y \ ((z * z) * (y / z)),(y * z) \ ((z * z) * y)) = R(x,L(z,y,y) * (z * z),L(z,y,z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,26473,a(flip),b,41192,a),flip(a)].">
      <j1 rule="hyper" parents="373 26473 41192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41194">
    <literal><![CDATA[
      R(x,y \ ((z * z) * (y / z)),(y * z) \ ((z * z) * y)) = R(x,L(z,y,y),L(z,y,z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,26475,a(flip),b,41193,a),flip(a)].">
      <j1 rule="hyper" parents="373 26475 41193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41196">
    <literal><![CDATA[
      R(x,L(y,z,z),L(y,z,y * z)) = R(x,z \ ((y * y) * (z / y)),L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26359,a(flip),b,41194,a),flip(a)].">
      <j1 rule="hyper" parents="64 26359 41194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41197">
    <literal><![CDATA[
      R(x,L(y,z,z),L(y,z,y * z)) = R(x,z \ ((y * y) * (y \ z)),L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,26511,a(flip),b,41196,a),flip(a)].">
      <j1 rule="hyper" parents="373 26511 41196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41198">
    <literal><![CDATA[
      R(x,R(T(y,z),y,y \ z),L(y,y,z)) = R(x,L(y,z,z),L(y,z,y * z))
    ]]></literal>
    <justification jstring="[para(996(a,1),41197(a,2,2)),flip(a)].">
      <j1 rule="para" parents="996 41197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41199">
    <literal><![CDATA[
      R(x,L(T(y,z),y,y \ z),L(y,y,z)) = R(x,L(y,z,z),L(y,z,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26636,a(flip),b,41198,a)].">
      <j1 rule="hyper" parents="64 26636 41198"/>
    </justification>
  </clause>

  <clause id="41200">
    <literal><![CDATA[
      R(x,L(T(y,z),y,y * z),L(y,y,z)) = R(x,L(y,z,z),L(y,z,y * z))
    ]]></literal>
    <justification jstring="[para(29888(a,1),41199(a,1,2))].">
      <j1 rule="para" parents="29888 41199"/>
    </justification>
  </clause>

  <clause id="41201">
    <literal><![CDATA[
      R(x,L(y,z,z),L(y,z,y * z)) = R(x,L(y,y,y * z),L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26430,a(flip),b,41200,a),flip(a)].">
      <j1 rule="hyper" parents="64 26430 41200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41203">
    <literal><![CDATA[
      R(x,L(y,z,z),L(y,z,y * z)) = R(x,L(y,y,z),L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,26673,a(flip),b,41201,a),flip(a)].">
      <j1 rule="hyper" parents="373 26673 41201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41204">
    <literal><![CDATA[
      R(x,L(y,z,z),L(y,z,y * z)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,40654,a(flip),b,41203,a),flip(a)].">
      <j1 rule="hyper" parents="373 40654 41203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41206">
    <literal><![CDATA[
      L(x \ R(x,y,y),x,L(y,z,z) * L(y,z,y * z)) = a(x,L(y,z,z),L(y,z,y * z))
    ]]></literal>
    <justification jstring="[para(41204(a,1),16031(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="41204 16031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41207">
    <literal><![CDATA[
      R(x,L((y \ ((y * z) * u)) / u,z \ 1,z \ 1),L((y \ ((y * z) * u)) / u,z \ 1,a(y,z,u))) = R(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u)
    ]]></literal>
    <justification jstring="[para(35767(a,2),41204(a,1,3,3))].">
      <j1 rule="para" parents="35767 41204"/>
    </justification>
  </clause>

  <clause id="41208">
    <literal><![CDATA[
      L(a(x,y,y),x,L(y,z,z) * L(y,z,y * z)) = a(x,L(y,z,z),L(y,z,y * z))
    ]]></literal>
    <justification jstring="[para(15987(a,1),41206(a,1,1))].">
      <j1 rule="para" parents="15987 41206"/>
    </justification>
  </clause>

  <clause id="41209">
    <literal><![CDATA[
      L(a(x,y,y),x,(L(y,z,z) / z) * (z * y)) = a(x,L(y,z,z),L(y,z,y * z))
    ]]></literal>
    <justification jstring="[para(24007(a,1),41208(a,1,3))].">
      <j1 rule="para" parents="24007 41208"/>
    </justification>
  </clause>

  <clause id="41210">
    <literal><![CDATA[
      L(a(x,y,y),x,(z \ L(y,z,z)) * (z * y)) = a(x,L(y,z,z),L(y,z,y * z))
    ]]></literal>
    <justification jstring="[hyper(29066,a,41209,a)].">
      <j1 rule="hyper" parents="29066 41209"/>
    </justification>
  </clause>

  <clause id="41211">
    <literal><![CDATA[
      L(a(x,y,y),x,((z \ 1) * y) * (z * y)) = a(x,L(y,z,z),L(y,z,y * z))
    ]]></literal>
    <justification jstring="[para(1148(a,1),41210(a,1,3,1))].">
      <j1 rule="para" parents="1148 41210"/>
    </justification>
  </clause>

  <clause id="41212">
    <literal><![CDATA[
      L(a(x,y,y),x,(z * y) * (z * y)) = a(x,L(y,z,z),L(y,z,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,2271,a(flip),b,41211,a)].">
      <j1 rule="hyper" parents="64 2271 41211"/>
    </justification>
  </clause>

  <clause id="41213">
    <literal><![CDATA[
      a(x,L(y,z,z),L(y,z,y * z)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(622,a,41212,a),flip(a)].">
      <j1 rule="hyper" parents="622 41212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41215">
    <literal><![CDATA[
      a(x,L((y \ ((y * z) * u)) / u,z \ 1,z \ 1),L((y \ ((y * z) * u)) / u,z \ 1,a(y,z,u))) = a(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u)
    ]]></literal>
    <justification jstring="[para(35767(a,2),41213(a,1,3,3))].">
      <j1 rule="para" parents="35767 41213"/>
    </justification>
  </clause>

  <clause id="41216">
    <literal><![CDATA[
      L(((L(x,y,z) \ 1) * R((x \ 1) \ 1,y,z)) \ u,(R(x,y,z) \ 1) * L(x,y,z),L(x,y,z)) = (R(x,y,z) * 1) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(11415(a,2),31044(a,1,1,1,2))].">
      <j1 rule="para" parents="11415 31044"/>
    </justification>
  </clause>

  <clause id="41217">
    <literal><![CDATA[
      L(T(1 / ((x \ ((x * y) * z)) / z),y) \ u,(x \ ((x * y) * z)) / z,y * a(x,y,z)) = 1 \ ((y * a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(28644(a,1),33442(a,1,1,1))].">
      <j1 rule="para" parents="28644 33442"/>
    </justification>
  </clause>

  <clause id="41219">
    <literal><![CDATA[
      L(((a(x,y,z) * y) \ 1) \ u,(x \ ((x * y) * z)) / z,y * a(x,y,z)) = 1 \ ((y * a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(33289(a,1),41217(a,1,1,1))].">
      <j1 rule="para" parents="33289 41217"/>
    </justification>
  </clause>

  <clause id="41220">
    <literal><![CDATA[
      a(x,y,L(z \ (z \ R(z,u,w)),z,z * L(z,u,w)) \ v5) = a(x,y,(R(z,u,w) \ 1) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,39052,a(flip),b,33596,a),flip(a)].">
      <j1 rule="hyper" parents="373 39052 33596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41222">
    <literal><![CDATA[
      a(x,y,L(z \ (z \ R(z,u,w)),z,z * L(z,u,w)) \ v5) = a(x,y,(L(z,u,w) \ 1) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,36622,a(flip),b,41220,a),flip(a)].">
      <j1 rule="hyper" parents="373 36622 41220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41223">
    <literal><![CDATA[
      a(x,y,L(R(z \ 1,u,w),z,z * L(z,u,w)) \ v5) = a(x,y,(L(z,u,w) \ 1) \ v5)
    ]]></literal>
    <justification jstring="[para(1990(a,1),41222(a,1,3,1,1))].">
      <j1 rule="para" parents="1990 41222"/>
    </justification>
  </clause>

  <clause id="41224">
    <literal><![CDATA[
      a(x,y,R(z \ 1,u,w) \ v5) = a(x,y,(L(z,u,w) \ 1) \ v5)
    ]]></literal>
    <justification jstring="[para(33137(a,1),41223(a,1,3,1))].">
      <j1 rule="para" parents="33137 41223"/>
    </justification>
  </clause>

  <clause id="41225">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) \ v5) = a(x,y,(L(z,u,w) \ 1) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31334,a(flip),b,41224,a)].">
      <j1 rule="hyper" parents="64 31334 41224"/>
    </justification>
  </clause>

  <clause id="41227">
    <literal><![CDATA[
      a(x,y,L(z * L(u,w,v5),u,u)) = a(x,y,L(u \ 1,w,v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,38950,a,b,41225,a)].">
      <j1 rule="hyper" parents="373 38950 41225"/>
    </justification>
  </clause>

  <clause id="41228">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) \ v5) = a(x,y,(R(z,u,w) \ 1) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,36622,a,b,41225,a),flip(a)].">
      <j1 rule="hyper" parents="373 36622 41225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41229">
    <literal><![CDATA[
      a(x,y,L(T(z,u) \ 1,w,v5) \ L(z,w,v5)) = a(x,y,K(z,u) * (R(z,w,v5) * R(z,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,35977,a(flip),b,41228,a),flip(a)].">
      <j1 rule="hyper" parents="373 35977 41228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41230">
    <literal><![CDATA[
      a(x,y,K(z,u) * (R(z,w,v5) * R(z,w,v5))) = a(x,y,L(z \ 1,w,v5) \ L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27562,a(flip),b,41229,a),flip(a)].">
      <j1 rule="hyper" parents="64 27562 41229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41232">
    <literal><![CDATA[
      a(x,y,K(z,u) * (R(z,w,v5) * R(z,w,v5))) = a(x,y,z * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,36640,a(flip),b,41230,a),flip(a)].">
      <j1 rule="hyper" parents="373 36640 41230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41234">
    <literal><![CDATA[
      a(x,y,R(T(z,u),w,v5) * R(z,w,v5)) = a(x,y,z * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27454,a(flip),b,41232,a)].">
      <j1 rule="hyper" parents="64 27454 41232"/>
    </justification>
  </clause>

  <clause id="41235">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * L(T(z,v5),u,w)) = a(x,y,z * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31315,a(flip),b,41234,a)].">
      <j1 rule="hyper" parents="64 31315 41234"/>
    </justification>
  </clause>

  <clause id="41236">
    <literal><![CDATA[
      a(x,y,R(z,u,w) * L(z,u,w)) = a(x,y,z * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27342,a(flip),b,41235,a)].">
      <j1 rule="hyper" parents="64 27342 41235"/>
    </justification>
  </clause>

  <clause id="41237">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * L(z,u,w)) = a(x,y,z * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31315,a(flip),b,41236,a)].">
      <j1 rule="hyper" parents="64 31315 41236"/>
    </justification>
  </clause>

  <clause id="41238">
    <literal><![CDATA[
      R(x,y,L(L(z,u,z),w,v5) * L(L(z,u,z),w,v5)) = x * a(y,x,z * z)
    ]]></literal>
    <justification jstring="[para(41237(a,1),36830(a,2,2))].">
      <j1 rule="para" parents="41237 36830"/>
    </justification>
  </clause>

  <clause id="41239">
    <literal><![CDATA[
      R(x,y,L(L(z,u,z),w,v5) * L(L(z,u,z),w,v5)) = R(x,y,z * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,36423,a(flip),b,41238,a),flip(a)].">
      <j1 rule="hyper" parents="373 36423 41238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41241">
    <literal><![CDATA[
      R(x,y,L(L(z,u,z),w,v5) * L(z,w,v5)) = R(x,y,z * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35035,a(flip),b,41239,a)].">
      <j1 rule="hyper" parents="64 35035 41239"/>
    </justification>
  </clause>

  <clause id="41243">
    <literal><![CDATA[
      R(x,y,L(z,u,w) * L(z,u,w)) = R(x,y,z * z)
    ]]></literal>
    <justification jstring="[para(593(a,1),41241(a,1,3,1,1))].">
      <j1 rule="para" parents="593 41241"/>
    </justification>
  </clause>

  <clause id="41245">
    <literal><![CDATA[
      R(R(x,y,z * z),y,u) = R(x,y,(L(z,w,v5) * L(z,w,v5)) * u)
    ]]></literal>
    <justification jstring="[para(41243(a,1),26512(a,1,1))].">
      <j1 rule="para" parents="41243 26512"/>
    </justification>
  </clause>

  <clause id="41246">
    <literal><![CDATA[
      R(x,y,(L(z,u,w) * L(z,u,w)) * v5) = R(x,y,(z * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26512,a(flip),b,41245,a),flip(a)].">
      <j1 rule="hyper" parents="64 26512 41245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41247">
    <literal><![CDATA[
      L(x \ R(x,y,(z * z) * u),x,y * u) = a(x,y,(L(z,w,v5) * L(z,w,v5)) * u)
    ]]></literal>
    <justification jstring="[para(41246(a,1),25129(a,1,1,2))].">
      <j1 rule="para" parents="41246 25129"/>
    </justification>
  </clause>

  <clause id="41248">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * L(z,u,w)) * v5) = a(x,y,(z * z) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,25129,a(flip),b,41247,a),flip(a)].">
      <j1 rule="hyper" parents="64 25129 41247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41249">
    <literal><![CDATA[
      a(x,y,(z * z) * (u \ (L(z,w,v5) \ v6))) = a(x,y,u \ ((L(z,w,v5) \ 1) \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,27968,a(flip),b,41248,a),flip(a)].">
      <j1 rule="hyper" parents="64 27968 41248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41250">
    <literal><![CDATA[
      a(x,y,z \ (L(u,w,v5) \ (u * u))) = a(x,y,z \ ((L(u,w,v5) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,27766,a(flip),b,41249,a)].">
      <j1 rule="hyper" parents="64 27766 41249"/>
    </justification>
  </clause>

  <clause id="41251">
    <literal><![CDATA[
      a(x,y,z \ ((L(u,w,v5) \ 1) \ 1)) = a(x,y,z \ (u * (L(u,w,v5) \ u)))
    ]]></literal>
    <justification jstring="[para(2329(a,1),41250(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2329 41250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41252">
    <literal><![CDATA[
      a(x,y,z \ (u * (L(u,w,v5) \ u))) = a(x,y,z \ L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27323,a(flip),b,41251,a),flip(a)].">
      <j1 rule="hyper" parents="64 27323 41251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41254">
    <literal><![CDATA[
      (x / (y * x)) * (((x / (y * x)) \ 1) \ (z * (a(y,y,x) \ 1))) = ((x / (y * x)) * (x / (y * x))) * ((y * (x / (y * x))) \ z)
    ]]></literal>
    <justification jstring="[para(30162(a,1),37887(a,1,2,2,2))].">
      <j1 rule="para" parents="30162 37887"/>
    </justification>
  </clause>

  <clause id="41255">
    <literal><![CDATA[
      ((x / (y * x)) * (x / (y * x))) * ((y * (x / (y * x))) \ z) = (x / (y * x)) * (((x / (y * x)) \ 1) \ (a(y,y,x) \ z))
    ]]></literal>
    <justification jstring="[para(37671(a,1),41254(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="37671 41254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41256">
    <literal><![CDATA[
      ((x / (y * x)) * (x / (y * x))) * ((y * (x / (y * x))) \ z) = (x / (y * x)) * (y \ z)
    ]]></literal>
    <justification jstring="[para(37729(a,1),41255(a,2,2))].">
      <j1 rule="para" parents="37729 41255"/>
    </justification>
  </clause>

  <clause id="41257">
    <literal><![CDATA[
      R(x / (y / (x * y)),y / (x * y),y / (x * y)) \ z = (y / (x * y)) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,948,a(flip),b,41256,a)].">
      <j1 rule="hyper" parents="64 948 41256"/>
    </justification>
  </clause>

  <clause id="41259">
    <literal><![CDATA[
      R(x / (y / (x * y)),y / (x * y),(x * y) \ y) \ z = (y / (x * y)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(23813(a,1),41257(a,1,1))].">
      <j1 rule="para" parents="23813 41257"/>
    </justification>
  </clause>

  <clause id="41260">
    <literal><![CDATA[
      R(x / (y / (x * y)),y / (x * y),y \ (x \ y)) \ z = (y / (x * y)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(24667(a,1),41259(a,1,1))].">
      <j1 rule="para" parents="24667 41259"/>
    </justification>
  </clause>

  <clause id="41261">
    <literal><![CDATA[
      R(x / (y / (x * y)),(x * y) \ y,y \ (x \ y)) \ z = (y / (x * y)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(26410(a,1),41260(a,1,1))].">
      <j1 rule="para" parents="26410 41260"/>
    </justification>
  </clause>

  <clause id="41262">
    <literal><![CDATA[
      R(x / (y / (x * y)),y \ (x \ y),y \ (x \ y)) \ z = (y / (x * y)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(26609(a,1),41261(a,1,1))].">
      <j1 rule="para" parents="26609 41261"/>
    </justification>
  </clause>

  <clause id="41263">
    <literal><![CDATA[
      R(x / (y / (x * y)),x,x \ 1) \ z = (y / (x * y)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(38984(a,1),41262(a,1,1))].">
      <j1 rule="para" parents="38984 41262"/>
    </justification>
  </clause>

  <clause id="41264">
    <literal><![CDATA[
      (x / (y / (x * y))) \ z = (y / (x * y)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(38348(a,1),41263(a,1,1))].">
      <j1 rule="para" parents="38348 41263"/>
    </justification>
  </clause>

  <clause id="41266">
    <literal><![CDATA[
      L((L(x,y,z) \ R(x,y,z)) \ u,(R(x,y,z) \ 1) * L(x,y,z),L(x,y,z)) = (R(x,y,z) * 1) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(34778(a,1),41216(a,1,1,1))].">
      <j1 rule="para" parents="34778 41216"/>
    </justification>
  </clause>

  <clause id="41267">
    <literal><![CDATA[
      L((L(x,y,z) \ R(x,y,z)) \ u,R(x,y,z) * L(x,y,z),L(x,y,z)) = (R(x,y,z) * 1) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(29615,a,41266,a)].">
      <j1 rule="hyper" parents="29615 41266"/>
    </justification>
  </clause>

  <clause id="41268">
    <literal><![CDATA[
      L((L(x,y,z) \ R(x,y,z)) \ u,L(x,y,z) * L(x,y,z),L(x,y,z)) = (R(x,y,z) * 1) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,36264,a(flip),b,41267,a)].">
      <j1 rule="hyper" parents="64 36264 41267"/>
    </justification>
  </clause>

  <clause id="41269">
    <literal><![CDATA[
      (R(x,y,z) * 1) \ (L(x,y,z) * u) = (L(x,y,z) \ R(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(616,a,41268,a),flip(a)].">
      <j1 rule="hyper" parents="616 41268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41271">
    <literal><![CDATA[
      (L(x,y,z) \ R(x,y,z)) \ u = R(x,y,z) \ (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(8(a,1),41269(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8 41269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41272">
    <literal><![CDATA[
      ((((x / y) * L(y,z,u)) * y) \ ((x / y) * L(y,z,u))) * y = ((y * x) \ x) * T(y,(x / y) * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(38391(a,1),25128(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38391 25128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41273">
    <literal><![CDATA[
      ((((x / y) * L(y,z,u)) * y) \ ((x / y) * L(y,z,u))) * y = ((y * x) \ x) * T(y,x)
    ]]></literal>
    <justification jstring="[para(28324(a,1),41272(a,2,2))].">
      <j1 rule="para" parents="28324 41272"/>
    </justification>
  </clause>

  <clause id="41275">
    <literal><![CDATA[
      ((((x / y) * L(y,z,u)) * y) \ ((x / y) * L(y,z,u))) * y = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,15070,a(flip),b,41273,a),flip(a)].">
      <j1 rule="hyper" parents="373 15070 41273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41277">
    <literal><![CDATA[
      ((x * L(y,z,u)) \ ((x / y) * L(y,z,u))) * y = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[para(3194(a,1),41275(a,1,1,1))].">
      <j1 rule="para" parents="3194 41275"/>
    </justification>
  </clause>

  <clause id="41278">
    <literal><![CDATA[
      L(x,x,y * L(L(x,y * x,x),z,u)) = (((y * x) \ y) * x) * x
    ]]></literal>
    <justification jstring="[para(41277(a,1),37332(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41277 37332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41279">
    <literal><![CDATA[
      L(x,x,y * L(L(x,y * x,x),z,u)) = L(x,x,x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,26667,a(flip),b,41278,a),flip(a)].">
      <j1 rule="hyper" parents="373 26667 41278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41281">
    <literal><![CDATA[
      L(x,x,L(x,y,z) * u) = L(x,x,x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25219,a(flip),b,41279,a)].">
      <j1 rule="hyper" parents="64 25219 41279"/>
    </justification>
  </clause>

  <clause id="41283">
    <literal><![CDATA[
      a(L(x,y,z) * u,x,x) = L(x,x,x * u) \ x
    ]]></literal>
    <justification jstring="[para(41281(a,1),30462(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41281 30462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41284">
    <literal><![CDATA[
      a(L(x,y,z) * u,x,x) = a(x * u,x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,30462,a(flip),b,41283,a),flip(a)].">
      <j1 rule="hyper" parents="373 30462 41283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41285">
    <literal><![CDATA[
      a(x * (y * L(z,u,w)),z,z) = a(z * (x * y),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40743,a(flip),b,41284,a)].">
      <j1 rule="hyper" parents="64 40743 41284"/>
    </justification>
  </clause>

  <clause id="41287">
    <literal><![CDATA[
      a(x * (y * ((z * x) * u)),x,x) = a((z * u) * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,41160,a(flip),b,41285,a),flip(a)].">
      <j1 rule="hyper" parents="64 41160 41285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41289">
    <literal><![CDATA[
      a(x * (y * ((y * z) * u)),y,y) = a((z * u) * x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,37902,a(flip),b,41287,a)].">
      <j1 rule="hyper" parents="64 37902 41287"/>
    </justification>
  </clause>

  <clause id="41290">
    <literal><![CDATA[
      a(x * (y * ((y * x) * z)),y,y) = a(L(z,x,x),y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,26834,a(flip),b,41289,a),flip(a)].">
      <j1 rule="hyper" parents="373 26834 41289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41291">
    <literal><![CDATA[
      a(L(x,y * z,y * z),z,z) = a(L(x,y,y),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37951,a(flip),b,41290,a)].">
      <j1 rule="hyper" parents="64 37951 41290"/>
    </justification>
  </clause>

  <clause id="41292">
    <literal><![CDATA[
      a(L(x,y * z,y * z),y,y) = a(L(x,z,z),y,y)
    ]]></literal>
    <justification jstring="[para(29507(a,1),41291(a,1,1))].">
      <j1 rule="para" parents="29507 41291"/>
    </justification>
  </clause>

  <clause id="41293">
    <literal><![CDATA[
      a(x,y,y) \ a(L(x,z,z),y,y) = a(a(x,y,y),y * z,y * z)
    ]]></literal>
    <justification jstring="[para(41291(a,1),33642(a,1,2))].">
      <j1 rule="para" parents="41291 33642"/>
    </justification>
  </clause>

  <clause id="41294">
    <literal><![CDATA[
      a(x,y,L(y,y * z,y * z)) = a(L(x,z,z),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,40980,a(flip),b,41292,a)].">
      <j1 rule="hyper" parents="64 40980 41292"/>
    </justification>
  </clause>

  <clause id="41295">
    <literal><![CDATA[
      a(x,y,(1 / (z / y)) * z) = a(L(x,z,z),y,y)
    ]]></literal>
    <justification jstring="[para(34540(a,1),41294(a,1,3))].">
      <j1 rule="para" parents="34540 41294"/>
    </justification>
  </clause>

  <clause id="41296">
    <literal><![CDATA[
      a(x,(y \ z) * z,y) = a(L(x,z,z),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32188,a(flip),b,41295,a)].">
      <j1 rule="hyper" parents="64 32188 41295"/>
    </justification>
  </clause>

  <clause id="41297">
    <literal><![CDATA[
      a(x,(y \ z) * z,y) = a(x,y,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,40980,a(flip),b,41296,a),flip(a)].">
      <j1 rule="hyper" parents="373 40980 41296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41298">
    <literal><![CDATA[
      a(x,y,((y \ z) \ 1) * z) = a(x,y,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,32189,a,b,41297,a)].">
      <j1 rule="hyper" parents="64 32189 41297"/>
    </justification>
  </clause>

  <clause id="41299">
    <literal><![CDATA[
      a(x,((((1 / y) \ y) / z) \ y) * y,((1 / y) \ y) / z) = a(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(16553(a,1),41297(a,2,3))].">
      <j1 rule="para" parents="16553 41297"/>
    </justification>
  </clause>

  <clause id="41300">
    <literal><![CDATA[
      L(x,x,L(y,x \ z,x \ z)) = a(y,x,L(x,z,z)) \ x
    ]]></literal>
    <justification jstring="[para(41298(a,1),41025(a,2,1))].">
      <j1 rule="para" parents="41298 41025"/>
    </justification>
  </clause>

  <clause id="41301">
    <literal><![CDATA[
      L(x,x,L(y,x \ z,x \ z)) = L(x,x,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,40983,a(flip),b,41300,a),flip(a)].">
      <j1 rule="hyper" parents="373 40983 41300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41302">
    <literal><![CDATA[
      L(x,x,((x \ y) * z) * y) = L(x,x,L(x * z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,36913,a(flip),b,41301,a)].">
      <j1 rule="hyper" parents="64 36913 41301"/>
    </justification>
  </clause>

  <clause id="41303">
    <literal><![CDATA[
      a(a(x,y,y),y * z,y * z) = a(a(x,y,y),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38063,a(flip),b,41293,a),flip(a)].">
      <j1 rule="hyper" parents="64 38063 41293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41304">
    <literal><![CDATA[
      a(x,y,a(y,y * z,y * z)) = a(a(x,y,y),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40882,a(flip),b,41303,a)].">
      <j1 rule="hyper" parents="64 40882 41303"/>
    </justification>
  </clause>

  <clause id="41305">
    <literal><![CDATA[
      a(x,y,a(z,z * y,y)) = a(a(x,y,y),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38697,a(flip),b,41304,a)].">
      <j1 rule="hyper" parents="64 38697 41304"/>
    </justification>
  </clause>

  <clause id="41306">
    <literal><![CDATA[
      a(x,y,a(z,z * y,y)) = a(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,40882,a(flip),b,41305,a),flip(a)].">
      <j1 rule="hyper" parents="373 40882 41305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41307">
    <literal><![CDATA[
      L(x,y,a(y,y * z,z)) = x * a(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(41306(a,1),38745(a,1,2)),flip(a)].">
      <j1 rule="para" parents="41306 38745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41308">
    <literal><![CDATA[
      L(x,y,a(y,y * z,z)) = L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,40809,a(flip),b,41307,a),flip(a)].">
      <j1 rule="hyper" parents="373 40809 41307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41309">
    <literal><![CDATA[
      L(x,y,a(z,z * y,y)) = L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,35775,a,b,41308,a)].">
      <j1 rule="hyper" parents="64 35775 41308"/>
    </justification>
  </clause>

  <clause id="41310">
    <literal><![CDATA[
      a(x,y,a(y,y * z,z)) = x \ L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,41308,a(flip),b,40809,a),flip(a)].">
      <j1 rule="hyper" parents="139 41308 40809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41311">
    <literal><![CDATA[
      L(L(x,y,y * z),y,a(y,z,z)) = L(x,L(y,y,z),y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41041,a(flip),b,41309,a),flip(a)].">
      <j1 rule="hyper" parents="64 41041 41309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41312">
    <literal><![CDATA[
      a(x,y,a(y,y * z,z)) = a(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,40899,a(flip),b,41310,a),flip(a)].">
      <j1 rule="hyper" parents="373 40899 41310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41313">
    <literal><![CDATA[
      a(x,x,a(y,x \ z,x \ z)) = a(x,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41066,a,b,41312,a)].">
      <j1 rule="hyper" parents="64 41066 41312"/>
    </justification>
  </clause>

  <clause id="41314">
    <literal><![CDATA[
      a(x \ y,x \ y,a(z,x,x)) = a(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,39751,a,b,41313,a)].">
      <j1 rule="hyper" parents="64 39751 41313"/>
    </justification>
  </clause>

  <clause id="41315">
    <literal><![CDATA[
      a(x,y \ z,a(y,y,z)) = a(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,40918,a(flip),b,41314,a)].">
      <j1 rule="hyper" parents="64 40918 41314"/>
    </justification>
  </clause>

  <clause id="41316">
    <literal><![CDATA[
      a(x,y \ z,a(y,y,z)) = a(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,40885,a,b,41315,a),flip(a)].">
      <j1 rule="hyper" parents="373 40885 41315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41317">
    <literal><![CDATA[
      a(x \ y,a(x,x,y),z) = a(z,y,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,38665,a,b,41316,a)].">
      <j1 rule="hyper" parents="64 38665 41316"/>
    </justification>
  </clause>

  <clause id="41318">
    <literal><![CDATA[
      L(x,y \ z,a(z,y,y)) = a(x,z,a(z,y,y)) \ x
    ]]></literal>
    <justification jstring="[para(41316(a,1),38700(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41316 38700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41319">
    <literal><![CDATA[
      a(x \ y,a(x,x,y),z) \ a(y,x,x) = a(L(y,x * y,z),x,x)
    ]]></literal>
    <justification jstring="[para(41317(a,2),41026(a,1,1))].">
      <j1 rule="para" parents="41317 41026"/>
    </justification>
  </clause>

  <clause id="41320">
    <literal><![CDATA[
      L(x,y \ z,a(z,y,y)) = x * a(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,40920,a(flip),b,41318,a),flip(a)].">
      <j1 rule="hyper" parents="373 40920 41318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41321">
    <literal><![CDATA[
      L(x,y \ z,a(z,y,y)) = L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,40809,a(flip),b,41320,a),flip(a)].">
      <j1 rule="hyper" parents="373 40809 41320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41322">
    <literal><![CDATA[
      L(x,a(y,z,z),z \ y) = L(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,31841,a,b,41321,a)].">
      <j1 rule="hyper" parents="64 31841 41321"/>
    </justification>
  </clause>

  <clause id="41323">
    <literal><![CDATA[
      ((1 / (x \ y)) \ a(y,x,x)) * L(z,a(y,x,x),L(x \ y,x,a(x,y,y))) = R(x \ y,x \ y,a(y,x,x)) * (a(y,x,x) * z)
    ]]></literal>
    <justification jstring="[para(41321(a,1),29219(a,1,2,3))].">
      <j1 rule="para" parents="41321 29219"/>
    </justification>
  </clause>

  <clause id="41324">
    <literal><![CDATA[
      a(L(x,y \ x,z),y,y) = a(L(x,y * x,z),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41000,a(flip),b,41319,a)].">
      <j1 rule="hyper" parents="64 41000 41319"/>
    </justification>
  </clause>

  <clause id="41325">
    <literal><![CDATA[
      a(L(x,y \ x,z),y,y) = a(L(x,x,z),y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,41028,a(flip),b,41324,a),flip(a)].">
      <j1 rule="hyper" parents="373 41028 41324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41326">
    <literal><![CDATA[
      a(L(x,x,y),z,z) \ (y * (x * (1 / z))) = y * (x / z)
    ]]></literal>
    <justification jstring="[para(41325(a,1),32620(a,1,1))].">
      <j1 rule="para" parents="41325 32620"/>
    </justification>
  </clause>

  <clause id="41327">
    <literal><![CDATA[
      (x * (y \ z)) * a(L(z,z,x),y,y) = x * (y \ R(z,y,y))
    ]]></literal>
    <justification jstring="[para(41325(a,1),32642(a,1,2))].">
      <j1 rule="para" parents="41325 32642"/>
    </justification>
  </clause>

  <clause id="41328">
    <literal><![CDATA[
      (x * (y * (1 / z))) * L(z,z,L(y,y,x)) = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(41326(a,1),37637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41326 37637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41329">
    <literal><![CDATA[
      a(x,(((y \ y) / z) \ (y \ 1)) * y,((1 / y) \ y) / z) = a(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(39951(a,1),41299(a,1,2,1))].">
      <j1 rule="para" parents="39951 41299"/>
    </justification>
  </clause>

  <clause id="41330">
    <literal><![CDATA[
      a(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = a(x,((1 / z) \ (y \ 1)) * y,((1 / y) \ y) / z)
    ]]></literal>
    <justification jstring="[para(68(a,1),41329(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="68 41329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41331">
    <literal><![CDATA[
      a(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = a(x,((1 / z) \ (y \ 1)) * y,z \ ((1 / y) \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,27308,a(flip),b,41330,a),flip(a)].">
      <j1 rule="hyper" parents="373 27308 41330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41333">
    <literal><![CDATA[
      a(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = a(x,((1 / z) \ (y \ 1)) * y,z \ ((1 \ y) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,33682,a(flip),b,41331,a),flip(a)].">
      <j1 rule="hyper" parents="373 33682 41331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41334">
    <literal><![CDATA[
      a(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = a(x,((1 / z) \ (y \ 1)) * y,z \ (y * y))
    ]]></literal>
    <justification jstring="[para(66(a,1),41333(a,2,3,2,1))].">
      <j1 rule="para" parents="66 41333"/>
    </justification>
  </clause>

  <clause id="41335">
    <literal><![CDATA[
      a(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = a(x,((1 / z) \ y) * y,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,32268,a(flip),b,41334,a),flip(a)].">
      <j1 rule="hyper" parents="373 32268 41334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41336">
    <literal><![CDATA[
      a(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = a(x,((z \ 1) \ y) * y,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,31983,a(flip),b,41335,a),flip(a)].">
      <j1 rule="hyper" parents="373 31983 41335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41337">
    <literal><![CDATA[
      a(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = a(x,(z \ y) * y,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,32336,a(flip),b,41336,a),flip(a)].">
      <j1 rule="hyper" parents="373 32336 41336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41338">
    <literal><![CDATA[
      a(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = a(x,z,(z \ (y \ (y * y))) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,36845,a(flip),b,41337,a),flip(a)].">
      <j1 rule="hyper" parents="373 36845 41337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41339">
    <literal><![CDATA[
      a(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = a(x,z,(z \ y) * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),41338(a,2,3,1,2))].">
      <j1 rule="para" parents="9 41338"/>
    </justification>
  </clause>

  <clause id="41340">
    <literal><![CDATA[
      a(x,((1 / y) \ y) / z,L(((1 / y) \ y) / z,y,y)) = a(x,z,(z \ y) * y)
    ]]></literal>
    <justification jstring="[para(16553(a,2),41339(a,1,3))].">
      <j1 rule="para" parents="16553 41339"/>
    </justification>
  </clause>

  <clause id="41341">
    <literal><![CDATA[
      a(x,((1 / y) \ y) / z,L(z \ ((1 / y) \ y),y,y)) = a(x,z,(z \ y) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27344,a(flip),b,41340,a)].">
      <j1 rule="hyper" parents="64 27344 41340"/>
    </justification>
  </clause>

  <clause id="41342">
    <literal><![CDATA[
      a(x,((1 / y) \ y) / z,L(z \ (y * y),y,y)) = a(x,z,(z \ y) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27701,a(flip),b,41341,a)].">
      <j1 rule="hyper" parents="64 27701 41341"/>
    </justification>
  </clause>

  <clause id="41343">
    <literal><![CDATA[
      a(x,((1 / y) \ y) / z,y * (y * (z \ 1))) = a(x,z,(z \ y) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27742,a(flip),b,41342,a)].">
      <j1 rule="hyper" parents="64 27742 41342"/>
    </justification>
  </clause>

  <clause id="41344">
    <literal><![CDATA[
      a(x,y \ ((1 / z) \ z),z * (z * (y \ 1))) = a(x,y,(y \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(32042,a,41343,a)].">
      <j1 rule="hyper" parents="32042 41343"/>
    </justification>
  </clause>

  <clause id="41345">
    <literal><![CDATA[
      a(x,y \ ((1 \ z) * z),z * (z * (y \ 1))) = a(x,y,(y \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33690,a(flip),b,41344,a)].">
      <j1 rule="hyper" parents="64 33690 41344"/>
    </justification>
  </clause>

  <clause id="41346">
    <literal><![CDATA[
      a(x,y \ (z * z),z * (z * (y \ 1))) = a(x,y,(y \ z) * z)
    ]]></literal>
    <justification jstring="[para(66(a,1),41345(a,1,2,2,1))].">
      <j1 rule="para" parents="66 41345"/>
    </justification>
  </clause>

  <clause id="41347">
    <literal><![CDATA[
      a(x,y,z * (z * (y \ 1))) = a(x,y,(y \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32227,a(flip),b,41346,a)].">
      <j1 rule="hyper" parents="64 32227 41346"/>
    </justification>
  </clause>

  <clause id="41349">
    <literal><![CDATA[
      a(x,y,z * ((y \ 1) * z)) = a(x,y,(y \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27315,a,b,41347,a)].">
      <j1 rule="hyper" parents="64 27315 41347"/>
    </justification>
  </clause>

  <clause id="41350">
    <literal><![CDATA[
      L(x,x,a(y,z,(z \ u) * u)) \ a(y,z,u * ((z \ 1) * u)) = (x \ 1) * a(y,z,u * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(41349(a,1),25752(a,1,1,3))].">
      <j1 rule="para" parents="41349 25752"/>
    </justification>
  </clause>

  <clause id="41351">
    <literal><![CDATA[
      (x \ R(y,x,x)) * L(z,a(y,x,x),L(x \ y,x,a(x,y,y))) = R(x \ y,x \ y,a(y,x,x)) * (a(y,x,x) * z)
    ]]></literal>
    <justification jstring="[para(31570(a,1),41323(a,1,1))].">
      <j1 rule="para" parents="31570 41323"/>
    </justification>
  </clause>

  <clause id="41352">
    <literal><![CDATA[
      R(x \ y,x \ y,a(y,x,x)) * (a(y,x,x) * z) = (x \ R(y,x,x)) * L(z,a(y,x,x),x \ y)
    ]]></literal>
    <justification jstring="[para(31292(a,1),41351(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="31292 41351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41354">
    <literal><![CDATA[
      R(x \ y,x \ y,a(y,x,x)) * (a(y,x,x) * z) = (x \ R(y,x,x)) * L(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(41322(a,1),41352(a,2,2))].">
      <j1 rule="para" parents="41322 41352"/>
    </justification>
  </clause>

  <clause id="41355">
    <literal><![CDATA[
      L(x \ y,x \ y,a(y,x,x)) * (a(y,x,x) * z) = (x \ R(y,x,x)) * L(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(28832(a,1),41354(a,1,1))].">
      <j1 rule="para" parents="28832 41354"/>
    </justification>
  </clause>

  <clause id="41356">
    <literal><![CDATA[
      (x \ R(y,x,x)) * L(z,x,a(x,y,y)) = (x \ y) * (a(y,x,x) * z)
    ]]></literal>
    <justification jstring="[para(30299(a,1),41355(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30299 41355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41358">
    <literal><![CDATA[
      L(1 / x,y,y * x) \ (1 * R(1 \ L(1 / x,y,y * x),z,u)) = ((1 / (y * (x \ 1))) * y) \ R((1 / (y * (x \ 1))) * y,z,u)
    ]]></literal>
    <justification jstring="[para(24009(a,1),25582(a,2,2,1))].">
      <j1 rule="para" parents="24009 25582"/>
    </justification>
  </clause>

  <clause id="41359">
    <literal><![CDATA[
      L(1 / x,y,y * x) \ (1 * R(1 \ L(1 / x,y,y * x),z,u)) = (((y * (x \ 1)) \ 1) * y) \ R(((y * (x \ 1)) \ 1) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,36254,a(flip),b,41358,a),flip(a)].">
      <j1 rule="hyper" parents="373 36254 41358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41360">
    <literal><![CDATA[
      L(1 / x,y,y * x) \ (1 * R(1 \ L(1 / x,y,y * x),z,u)) = ((y * (x \ 1)) * y) \ R((y * (x \ 1)) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,3144,a(flip),b,41359,a),flip(a)].">
      <j1 rule="hyper" parents="373 3144 41359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41361">
    <literal><![CDATA[
      L(1 / x,y,y * x) \ (1 * R(1 \ L(1 / x,y,y * x),z,u)) = L((x \ 1) \ R(x \ 1,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,26014,a(flip),b,41360,a),flip(a)].">
      <j1 rule="hyper" parents="373 26014 41360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41362">
    <literal><![CDATA[
      L(1 / x,y,y * x) \ (1 * R(1 \ L(1 / x,y,y * x),z,u)) = L(x \ R(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[para(2009(a,1),41361(a,2,1))].">
      <j1 rule="para" parents="2009 41361"/>
    </justification>
  </clause>

  <clause id="41363">
    <literal><![CDATA[
      L(1 / x,y,y * x) \ (1 * R(L(1 / x,y,y * x),z,u)) = L(x \ R(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[para(66(a,1),41362(a,1,2,2,1))].">
      <j1 rule="para" parents="66 41362"/>
    </justification>
  </clause>

  <clause id="41364">
    <literal><![CDATA[
      L(1 / x,y,y * x) \ (1 * L(R(1 / x,z,u),y,y * x)) = L(x \ R(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[para(29(a,1),41363(a,1,2,2))].">
      <j1 rule="para" parents="29 41363"/>
    </justification>
  </clause>

  <clause id="41365">
    <literal><![CDATA[
      L(1 / x,y,y * x) \ L(R(1 / x,z,u),y,y * x) = L(x \ R(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(342,a,41364,a)].">
      <j1 rule="hyper" parents="342 41364"/>
    </justification>
  </clause>

  <clause id="41366">
    <literal><![CDATA[
      L((1 / x) \ R(1 / x,y,z),u,u * x) = L(x \ R(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,4243,a(flip),b,41365,a)].">
      <j1 rule="hyper" parents="64 4243 41365"/>
    </justification>
  </clause>

  <clause id="41367">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,u * x) = L(x \ R(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[para(1985(a,1),41366(a,1,1))].">
      <j1 rule="para" parents="1985 41366"/>
    </justification>
  </clause>

  <clause id="41368">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,u),x,y * z) = L(a(x,y,z),u,u * x)
    ]]></literal>
    <justification jstring="[para(41367(a,1),16033(a,1,1))].">
      <j1 rule="para" parents="41367 16033"/>
    </justification>
  </clause>

  <clause id="41369">
    <literal><![CDATA[
      L(a(x,y,z),u,u * x) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,16033,a(flip),b,41368,a),flip(a)].">
      <j1 rule="hyper" parents="64 16033 41368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41370">
    <literal><![CDATA[
      L(a(x,y,z) \ R(a(x,y,z),u,u * x),a(x,y,z),u) = a(L(a(x,y,z),u,u),u,u * x)
    ]]></literal>
    <justification jstring="[para(41369(a,1),33411(a,2,1))].">
      <j1 rule="para" parents="41369 33411"/>
    </justification>
  </clause>

  <clause id="41371">
    <literal><![CDATA[
      x \ (a(y,z,u) * (L(a(y,z,u),x,x * y) \ x)) = a(x * y,x,L(a(y,z,u),x,x))
    ]]></literal>
    <justification jstring="[para(41369(a,1),33406(a,1,3)),flip(a)].">
      <j1 rule="para" parents="41369 33406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41372">
    <literal><![CDATA[
      x \ (a(y,z,u) * (L(a(y,z,u),x,x) \ x)) = a(x * y,x,L(a(y,z,u),x,x))
    ]]></literal>
    <justification jstring="[para(41369(a,1),41371(a,1,2,2,1))].">
      <j1 rule="para" parents="41369 41371"/>
    </justification>
  </clause>

  <clause id="41373">
    <literal><![CDATA[
      a(x * y,x,L(a(y,z,u),x,x)) = x \ R(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(25114(a,1),41372(a,1,2)),flip(a)].">
      <j1 rule="para" parents="25114 41372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41374">
    <literal><![CDATA[
      a(x * y,x,L(a(y,z,u),x,x)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,30058,a(flip),b,41373,a),flip(a)].">
      <j1 rule="hyper" parents="373 30058 41373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41375">
    <literal><![CDATA[
      L(a(x,y,z) \ L(a(x,y,z),u,u * x),a(x,y,z),u) = a(L(a(x,y,z),u,u),u,u * x)
    ]]></literal>
    <justification jstring="[para(28787(a,1),41370(a,1,1,2))].">
      <j1 rule="para" parents="28787 41370"/>
    </justification>
  </clause>

  <clause id="41376">
    <literal><![CDATA[
      L(a(x,y,z) \ L(a(x,y,z),u,u),a(x,y,z),u) = a(L(a(x,y,z),u,u),u,u * x)
    ]]></literal>
    <justification jstring="[para(41369(a,1),41375(a,1,1,2))].">
      <j1 rule="para" parents="41369 41375"/>
    </justification>
  </clause>

  <clause id="41377">
    <literal><![CDATA[
      L(a(a(x,y,z),u,u),a(x,y,z),u) = a(L(a(x,y,z),u,u),u,u * x)
    ]]></literal>
    <justification jstring="[para(28791(a,1),41376(a,1,1))].">
      <j1 rule="para" parents="28791 41376"/>
    </justification>
  </clause>

  <clause id="41378">
    <literal><![CDATA[
      a(L(a(x,y,z),u,u),u,u * x) = a(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(33227,a,41377,a),flip(a)].">
      <j1 rule="hyper" parents="33227 41377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41380">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ L(a(x,y,z),a(x,y,z),(y * z) * L(x \ 1,y,z)) = L(a(x,y,z) \ 1,a(x,y,z),(y * z) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(33574(a,1),26961(a,1,2))].">
      <j1 rule="para" parents="33574 26961"/>
    </justification>
  </clause>

  <clause id="41381">
    <literal><![CDATA[
      a(x,L(x,x * y,z),y) \ a(a(x,L(x,x * y,z),y),a(x,x,L(y,x * y,z)),(x \ y) * z) = (((x \ 1) * y) * z) / ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(34885(a,1),34895(a,1,2))].">
      <j1 rule="para" parents="34885 34895"/>
    </justification>
  </clause>

  <clause id="41382">
    <literal><![CDATA[
      x \ (L(x \ (L(R(y,z,u),y,x) * (L(y,y,x) \ x)),L(y,y,x),z * u) * (y \ x)) = (x \ (y \ x)) * T(a(L(y,y,x),z,u),y \ x)
    ]]></literal>
    <justification jstring="[para(29(a,1),39262(a,1,2,1,1,2,1))].">
      <j1 rule="para" parents="29 39262"/>
    </justification>
  </clause>

  <clause id="41383">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ L(a(x,y,z),a(x,y,z),z * (T(y,z) * (x \ 1))) = L(a(x,y,z) \ 1,a(x,y,z),(y * z) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(10989(a,1),41380(a,1,2,3))].">
      <j1 rule="para" parents="10989 41380"/>
    </justification>
  </clause>

  <clause id="41384">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ L(a(x,y,z),a(x,y,z),z * (x * T(y,z))) = L(a(x,y,z) \ 1,a(x,y,z),(y * z) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(29120(a,1),41383(a,1,2))].">
      <j1 rule="para" parents="29120 41383"/>
    </justification>
  </clause>

  <clause id="41385">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ L(a(x,y,z),a(x,y,z),z * (x * y)) = L(a(x,y,z) \ 1,a(x,y,z),(y * z) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(29019(a,1),41384(a,1,2))].">
      <j1 rule="para" parents="29019 41384"/>
    </justification>
  </clause>

  <clause id="41387">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ L(a(x,y,z),a(x,y,z),x * y) = L(a(x,y,z) \ 1,a(x,y,z),(y * z) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(37083(a,1),41385(a,1,2))].">
      <j1 rule="para" parents="37083 41385"/>
    </justification>
  </clause>

  <clause id="41388">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ L(a(x,y,z),a(x,y,z),y) = L(a(x,y,z) \ 1,a(x,y,z),(y * z) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(40420(a,1),41387(a,1,2))].">
      <j1 rule="para" parents="40420 41387"/>
    </justification>
  </clause>

  <clause id="41389">
    <literal><![CDATA[
      L((a(x,y,z) * a(x,y,z)) \ a(x,y,z),a(x,y,z),y) = L(a(x,y,z) \ 1,a(x,y,z),(y * z) * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,35099,a,b,41388,a)].">
      <j1 rule="hyper" parents="64 35099 41388"/>
    </justification>
  </clause>

  <clause id="41390">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),(y * z) * (x \ 1)) = L(1 / a(x,y,z),a(x,y,z),y)
    ]]></literal>
    <justification jstring="[para(309(a,1),41389(a,1,1)),flip(a)].">
      <j1 rule="para" parents="309 41389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41391">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),(y * z) * (x \ 1)) = L(a(x,y,z) \ 1,a(x,y,z),y)
    ]]></literal>
    <justification jstring="[para(13923(a,1),41390(a,2,1))].">
      <j1 rule="para" parents="13923 41390"/>
    </justification>
  </clause>

  <clause id="41392">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),(y * z) * (x \ 1)) = y \ (x \ ((x * (y * z)) / z))
    ]]></literal>
    <justification jstring="[hyper(373,a,33340,a(flip),b,41391,a),flip(a)].">
      <j1 rule="hyper" parents="373 33340 41391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41393">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),x * (y * z)) = y \ (x \ ((x * (y * z)) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,23997,a(flip),b,41392,a)].">
      <j1 rule="hyper" parents="64 23997 41392"/>
    </justification>
  </clause>

  <clause id="41394">
    <literal><![CDATA[
      ((x * y) * z) \ ((x * (y * z)) * 1) = y \ (x \ ((x * (y * z)) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,961,a(flip),b,41393,a)].">
      <j1 rule="hyper" parents="64 961 41393"/>
    </justification>
  </clause>

  <clause id="41395">
    <literal><![CDATA[
      ((x * y) * z) \ (x * (y * z)) = y \ (x \ ((x * (y * z)) / z))
    ]]></literal>
    <justification jstring="[hyper(341,a,41394,a)].">
      <j1 rule="hyper" parents="341 41394"/>
    </justification>
  </clause>

  <clause id="41396">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,z * y) = y \ (z \ ((z * (y * x)) / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,646,a,b,41395,a)].">
      <j1 rule="hyper" parents="64 646 41395"/>
    </justification>
  </clause>

  <clause id="41397">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) / z) = y \ (x \ ((x * (y * z)) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33818,a(flip),b,41395,a)].">
      <j1 rule="hyper" parents="64 33818 41395"/>
    </justification>
  </clause>

  <clause id="41398">
    <literal><![CDATA[
      L(x,a(y,z,u * (w * w)),v5) = L(x,z \ (u \ ((u * (z * y)) / y)),v5)
    ]]></literal>
    <justification jstring="[para(41397(a,1),35455(a,2,2))].">
      <j1 rule="para" parents="41397 35455"/>
    </justification>
  </clause>

  <clause id="41399">
    <literal><![CDATA[
      a(a(x,y,z * (u * u)),w,v5) = a(y \ (z \ ((z * (y * x)) / x)),w,v5)
    ]]></literal>
    <justification jstring="[para(41397(a,1),39325(a,2,1))].">
      <j1 rule="para" parents="41397 39325"/>
    </justification>
  </clause>

  <clause id="41400">
    <literal><![CDATA[
      L(x,a(y,z,u * (w * w)),v5) = L(x,z \ (u \ (y \ (u * (z * y)))),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29559,a(flip),b,41398,a),flip(a)].">
      <j1 rule="hyper" parents="373 29559 41398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41401">
    <literal><![CDATA[
      a(a(x,y,z * (u * u)),w,v5) = a(y \ (z \ (x \ (z * (y * x)))),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32377,a(flip),b,41399,a),flip(a)].">
      <j1 rule="hyper" parents="373 32377 41399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41402">
    <literal><![CDATA[
      L(x,y \ (z \ (u \ (z * (y * u)))),w) = L(x,a(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,34487,a(flip),b,41400,a),flip(a)].">
      <j1 rule="hyper" parents="64 34487 41400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41403">
    <literal><![CDATA[
      L(x,a(y,z,u),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,37264,a(flip),b,41402,a)].">
      <j1 rule="hyper" parents="64 37264 41402"/>
    </justification>
  </clause>

  <clause id="41405">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),v5,v6) = L(L(x,v5,v6),a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(1435,a,41403,a)].">
      <j1 rule="hyper" parents="1435 41403"/>
    </justification>
  </clause>

  <clause id="41406">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * y = L(y,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,39368,a,b,41403,a)].">
      <j1 rule="hyper" parents="373 39368 41403"/>
    </justification>
  </clause>

  <clause id="41407">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * x = L(x,a(x,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,34929,a,b,41403,a)].">
      <j1 rule="hyper" parents="373 34929 41403"/>
    </justification>
  </clause>

  <clause id="41408">
    <literal><![CDATA[
      L(x,a(y * z,u,w),v5) = L(x,a(w,u,z * y),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,34493,a,b,41403,a)].">
      <j1 rule="hyper" parents="373 34493 41403"/>
    </justification>
  </clause>

  <clause id="41410">
    <literal><![CDATA[
      R(x,a(y,z,u),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31802,a,b,41403,a)].">
      <j1 rule="hyper" parents="373 31802 41403"/>
    </justification>
  </clause>

  <clause id="41411">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,v5,v5) * v6) = L(x,a(u,z,y),a(v5,v5,w) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,30833,a,b,41403,a)].">
      <j1 rule="hyper" parents="373 30833 41403"/>
    </justification>
  </clause>

  <clause id="41412">
    <literal><![CDATA[
      R(L(x,a(y,z,u),w),v5,v6) = L(R(x,v5,v6),a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29,a,b,41403,a)].">
      <j1 rule="hyper" parents="373 29 41403"/>
    </justification>
  </clause>

  <clause id="41413">
    <literal><![CDATA[
      L(x,a(y \ 1,z,u),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,34491,a(flip),b,41403,a),flip(a)].">
      <j1 rule="hyper" parents="373 34491 41403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41414">
    <literal><![CDATA[
      L(x,a(y,z,u),y) = L(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,33832,a(flip),b,41403,a),flip(a)].">
      <j1 rule="hyper" parents="373 33832 41403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41416">
    <literal><![CDATA[
      x * L(y,a(z,u,w),v5) = x * L(y,a(w,u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(145,a,41403,a,b,9,a)].">
      <j1 rule="hyper" parents="145 41403 9"/>
    </justification>
  </clause>

  <clause id="41417">
    <literal><![CDATA[
      (x * a(y,z,u)) * L(w,a(u,z,y),x) = x * (a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(145,a,41403,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="145 41403 18"/>
    </justification>
  </clause>

  <clause id="41418">
    <literal><![CDATA[
      L(x,a(y,z,u),w) \ v5 = L(x,a(u,z,y),w) \ v5
    ]]></literal>
    <justification jstring="[hyper(62,a,41403,a)].">
      <j1 rule="hyper" parents="62 41403"/>
    </justification>
  </clause>

  <clause id="41422">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (a(u,z,y) * w) = (x * a(u,z,y)) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,41410,a(flip),b,20,a(flip))].">
      <j1 rule="hyper" parents="144 41410 20"/>
    </justification>
  </clause>

  <clause id="41424">
    <literal><![CDATA[
      a(x,y,L(z,a(u,w,v5),v6)) = a(x,y,L(z,a(v5,w,u),v6))
    ]]></literal>
    <justification jstring="[para(41410(a,1),27644(a,1,3))].">
      <j1 rule="para" parents="41410 27644"/>
    </justification>
  </clause>

  <clause id="41425">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) = L(x,y,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30415,a(flip),b,41414,a),flip(a)].">
      <j1 rule="hyper" parents="64 30415 41414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41427">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,y)) = a(x,y,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,41425,a,b,40809,a)].">
      <j1 rule="hyper" parents="139 41425 40809"/>
    </justification>
  </clause>

  <clause id="41428">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) \ w = L(x,y,a(y,u,z)) \ w
    ]]></literal>
    <justification jstring="[hyper(62,a,41425,a)].">
      <j1 rule="hyper" parents="62 41425"/>
    </justification>
  </clause>

  <clause id="41429">
    <literal><![CDATA[
      L(x * y,x,a(x,z,u)) = x * L(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[para(41425(a,2),39276(a,2,2))].">
      <j1 rule="para" parents="41425 39276"/>
    </justification>
  </clause>

  <clause id="41430">
    <literal><![CDATA[
      L(x \ y,x,a(x,z,u)) = x \ L(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[para(41425(a,2),39281(a,2,2))].">
      <j1 rule="para" parents="41425 39281"/>
    </justification>
  </clause>

  <clause id="41431">
    <literal><![CDATA[
      L(x * y,y,a(y,z,u)) = L(x,y,a(u,z,y)) * y
    ]]></literal>
    <justification jstring="[para(41425(a,2),39282(a,2,1))].">
      <j1 rule="para" parents="41425 39282"/>
    </justification>
  </clause>

  <clause id="41432">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) \ x = a(y,a(y,u,z),x)
    ]]></literal>
    <justification jstring="[para(41425(a,2),40826(a,1,1))].">
      <j1 rule="para" parents="41425 40826"/>
    </justification>
  </clause>

  <clause id="41433">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(u,x,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,34929,a,b,41406,a)].">
      <j1 rule="hyper" parents="36 34929 41406"/>
    </justification>
  </clause>

  <clause id="41434">
    <literal><![CDATA[
      a(a(x,y,z),z,u) = a(u,z,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,34928,a,b,41406,a)].">
      <j1 rule="hyper" parents="36 34928 41406"/>
    </justification>
  </clause>

  <clause id="41435">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(x,a(x,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,39362,a,b,41433,a),flip(a)].">
      <j1 rule="hyper" parents="373 39362 41433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41436">
    <literal><![CDATA[
      a(x,a(y,z,x),u) \ 1 = a(x,a(x,z,y),u)
    ]]></literal>
    <justification jstring="[para(41433(a,2),33548(a,1,1))].">
      <j1 rule="para" parents="41433 33548"/>
    </justification>
  </clause>

  <clause id="41437">
    <literal><![CDATA[
      a(x,a(y,z,x),u) \ x = L(x,a(x,z,y),u)
    ]]></literal>
    <justification jstring="[para(41433(a,2),34904(a,1,1))].">
      <j1 rule="para" parents="41433 34904"/>
    </justification>
  </clause>

  <clause id="41439">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,z)),v5) = L(x,a(y,z,a(z,w,u)),v5)
    ]]></literal>
    <justification jstring="[para(41434(a,1),41403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="41434 41403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41440">
    <literal><![CDATA[
      a(x,a(y,z,x),x \ u) = a(x,a(x,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,39341,a(flip),b,41435,a),flip(a)].">
      <j1 rule="hyper" parents="373 39341 41435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41441">
    <literal><![CDATA[
      a(x,a(y,z,x),x * u) = a(x,a(x,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,39339,a(flip),b,41435,a),flip(a)].">
      <j1 rule="hyper" parents="373 39339 41435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41442">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * (a(x,z,y) * (u * x)) = u * (x * a(x,z,y))
    ]]></literal>
    <justification jstring="[para(41435(a,2),34815(a,1,1))].">
      <j1 rule="para" parents="41435 34815"/>
    </justification>
  </clause>

  <clause id="41443">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * a(x,z,y) = a(L(x,x,u),z,y)
    ]]></literal>
    <justification jstring="[para(41435(a,2),40763(a,1,1))].">
      <j1 rule="para" parents="41435 40763"/>
    </justification>
  </clause>

  <clause id="41444">
    <literal><![CDATA[
      a(x,y,a(y,z,L(u,u,z * y))) = x \ L(x,y,u \ R(u,z,y))
    ]]></literal>
    <justification jstring="[para(32467(a,1),41427(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="32467 41427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41445">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * y = L(y,a(y,u,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33933,a(flip),b,41437,a)].">
      <j1 rule="hyper" parents="64 33933 41437"/>
    </justification>
  </clause>

  <clause id="41446">
    <literal><![CDATA[
      a(x,y,z) * (L(u,z,z) * a(z,a(z,y,x),u)) = (a(x,y,z) / z) * (z * u)
    ]]></literal>
    <justification jstring="[para(41441(a,1),37407(a,1,2,2))].">
      <j1 rule="para" parents="41441 37407"/>
    </justification>
  </clause>

  <clause id="41447">
    <literal><![CDATA[
      x * a(y,x,a(z,u,x)) = L(x,a(x,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(23177,a,41445,a)].">
      <j1 rule="hyper" parents="23177 41445"/>
    </justification>
  </clause>

  <clause id="41448">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * y = y * a(x,y,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,39367,a,b,41445,a),flip(a)].">
      <j1 rule="hyper" parents="373 39367 41445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41449">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,41407,a,b,41445,a)].">
      <j1 rule="hyper" parents="36 41407 41445"/>
    </justification>
  </clause>

  <clause id="41450">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = a(x,y,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,39368,a,b,41445,a),flip(a)].">
      <j1 rule="hyper" parents="36 39368 41445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41451">
    <literal><![CDATA[
      a(x,a(x,y,z),u) = a(u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,34906,a,b,41445,a)].">
      <j1 rule="hyper" parents="36 34906 41445"/>
    </justification>
  </clause>

  <clause id="41452">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ 1 = a(y,a(y,u,z),x)
    ]]></literal>
    <justification jstring="[para(41449(a,1),41436(a,1,1))].">
      <j1 rule="para" parents="41449 41436"/>
    </justification>
  </clause>

  <clause id="41453">
    <literal><![CDATA[
      a(x,a(x,y,z),u) \ 1 = a(u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,33546,a,b,41450,a)].">
      <j1 rule="hyper" parents="373 33546 41450"/>
    </justification>
  </clause>

  <clause id="41454">
    <literal><![CDATA[
      a(x \ y,x,a(z,u,x)) = a(y,x,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,39332,a(flip),b,41450,a),flip(a)].">
      <j1 rule="hyper" parents="373 39332 41450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41455">
    <literal><![CDATA[
      x * a(x,y,a(z,u,y)) = L(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,41450,a,b,41427,a)].">
      <j1 rule="hyper" parents="145 41450 41427"/>
    </justification>
  </clause>

  <clause id="41456">
    <literal><![CDATA[
      x * a(x,y,a(z,u,y)) = L(x,y,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,41450,a,b,40810,a)].">
      <j1 rule="hyper" parents="145 41450 40810"/>
    </justification>
  </clause>

  <clause id="41458">
    <literal><![CDATA[
      a(x,a(y,z,u),u) = a(x,u,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,33531,a,b,41450,a)].">
      <j1 rule="hyper" parents="64 33531 41450"/>
    </justification>
  </clause>

  <clause id="41459">
    <literal><![CDATA[
      a(x,y,a(y,z,L(u,u,z * y))) = a(x,y,u \ R(u,z,y))
    ]]></literal>
    <justification jstring="[para(32467(a,1),41450(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32467 41450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41460">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * x = L(x,y,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(41450(a,2),40811(a,1,1))].">
      <j1 rule="para" parents="41450 40811"/>
    </justification>
  </clause>

  <clause id="41461">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) * a(x,y,a(z,u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,41451,a(flip),b,41432,a)].">
      <j1 rule="hyper" parents="145 41451 41432"/>
    </justification>
  </clause>

  <clause id="41462">
    <literal><![CDATA[
      a(x,a(x,y,z),u) * a(z,y,x) = L(a(z,y,x),x,u)
    ]]></literal>
    <justification jstring="[para(41451(a,2),36346(a,1,1))].">
      <j1 rule="para" parents="41451 36346"/>
    </justification>
  </clause>

  <clause id="41463">
    <literal><![CDATA[
      a(x,a(x,y,z),L(u,w,v5)) = L(a(u,x,a(z,y,x)),w,v5)
    ]]></literal>
    <justification jstring="[para(41451(a,1),40995(a,2,1))].">
      <j1 rule="para" parents="41451 40995"/>
    </justification>
  </clause>

  <clause id="41464">
    <literal><![CDATA[
      a(x,y,z) \ a(z,a(z,y,x),u) = L(a(x,y,z),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(41452(a,1),36351(a,1,2))].">
      <j1 rule="para" parents="41452 36351"/>
    </justification>
  </clause>

  <clause id="41465">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) \ x = ((x / (y \ 1)) * (y \ a(u,z,y))) / a(u,z,y)
    ]]></literal>
    <justification jstring="[para(41454(a,1),36049(a,1,1))].">
      <j1 rule="para" parents="41454 36049"/>
    </justification>
  </clause>

  <clause id="41467">
    <literal><![CDATA[
      x / L(a(y,z,a(u,w,z)),y,L(y,z,a(z,w,u)) \ x) = (x / (y * a(y,z,a(u,w,z)))) * y
    ]]></literal>
    <justification jstring="[para(41456(a,1),15007(a,1,2,3,1))].">
      <j1 rule="para" parents="41456 15007"/>
    </justification>
  </clause>

  <clause id="41468">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * L(x,y,a(z,u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(23777,a,41461,a)].">
      <j1 rule="hyper" parents="23777 41461"/>
    </justification>
  </clause>

  <clause id="41469">
    <literal><![CDATA[
      x * (L(y,z,a(u,w,z)) \ v5) = x * (L(y,z,a(z,w,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(145,a,41428,a,b,9,a)].">
      <j1 rule="hyper" parents="145 41428 9"/>
    </justification>
  </clause>

  <clause id="41472">
    <literal><![CDATA[
      L(x \ y,x,a(x,z,u)) = x \ R(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[para(28832(a,2),41430(a,2,2))].">
      <j1 rule="para" parents="28832 41430"/>
    </justification>
  </clause>

  <clause id="41473">
    <literal><![CDATA[
      a(x,y,a(y,z,L(u,u,z * y))) = a(x,y,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,31676,a(flip),b,41459,a),flip(a)].">
      <j1 rule="hyper" parents="373 31676 41459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41474">
    <literal><![CDATA[
      a(x,y,z) \ a(u,z,a(x,y,z)) = L(a(x,y,z),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(41451(a,1),41464(a,1,2))].">
      <j1 rule="para" parents="41451 41464"/>
    </justification>
  </clause>

  <clause id="41475">
    <literal><![CDATA[
      a(x,y,a(y,z,L(u,u,z * y))) = x \ L(x,y,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[para(33124(a,1),41444(a,2,2))].">
      <j1 rule="para" parents="33124 41444"/>
    </justification>
  </clause>

  <clause id="41476">
    <literal><![CDATA[
      a(x,y,a(y,z,L(u,u,z * y))) = x \ L(x,y,u * L(u,z,y))
    ]]></literal>
    <justification jstring="[para(5608(a,1),41475(a,2,2))].">
      <j1 rule="para" parents="5608 41475"/>
    </justification>
  </clause>

  <clause id="41477">
    <literal><![CDATA[
      x \ L(x,y,z * L(z,u,y)) = a(x,y,z \ L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41473,a(flip),b,41476,a),flip(a)].">
      <j1 rule="hyper" parents="64 41473 41476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41478">
    <literal><![CDATA[
      a(x \ (y \ (z \ (y * (x * z)))),u,w) = a(a(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,34579,a(flip),b,41401,a),flip(a)].">
      <j1 rule="hyper" parents="64 34579 41401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41479">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,37248,a(flip),b,41478,a)].">
      <j1 rule="hyper" parents="64 37248 41478"/>
    </justification>
  </clause>

  <clause id="41480">
    <literal><![CDATA[
      a(a(x,y,z),u,w \ 1) = a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,36144,a,b,41479,a)].">
      <j1 rule="hyper" parents="373 36144 41479"/>
    </justification>
  </clause>

  <clause id="41481">
    <literal><![CDATA[
      a(a(x,y,z \ 1),u,w) = a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,34584,a,b,41479,a)].">
      <j1 rule="hyper" parents="373 34584 41479"/>
    </justification>
  </clause>

  <clause id="41482">
    <literal><![CDATA[
      a(a(x,y * z,u),w,v5) = a(a(u,z * y,x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32089,a,b,41479,a)].">
      <j1 rule="hyper" parents="373 32089 41479"/>
    </justification>
  </clause>

  <clause id="41483">
    <literal><![CDATA[
      a(a(x,y,z),z * u,z * u) = a(a(z,y,x),z \ u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,40505,a(flip),b,41479,a),flip(a)].">
      <j1 rule="hyper" parents="373 40505 41479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41484">
    <literal><![CDATA[
      a(a(x,y,z * a(u,w,w)),v5,v5) = a(v5,v5,a(z * a(w,w,u),y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,36331,a(flip),b,41479,a),flip(a)].">
      <j1 rule="hyper" parents="373 36331 41479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41485">
    <literal><![CDATA[
      a(a(x,y,a(z,u,u) * w),v5,v5) = a(v5,v5,a(w * a(u,u,z),y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,36330,a(flip),b,41479,a),flip(a)].">
      <j1 rule="hyper" parents="373 36330 41479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41486">
    <literal><![CDATA[
      a(a(x,y,z),u,u) = a(u,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,36326,a(flip),b,41479,a),flip(a)].">
      <j1 rule="hyper" parents="373 36326 41479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41487">
    <literal><![CDATA[
      a(a(x,y,z),u,a(z,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,31089,a(flip),b,41479,a),flip(a)].">
      <j1 rule="hyper" parents="373 31089 41479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41489">
    <literal><![CDATA[
      x * a(a(y,z,u),w,v5) = x * a(a(u,z,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(145,a,41479,a,b,9,a)].">
      <j1 rule="hyper" parents="145 41479 9"/>
    </justification>
  </clause>

  <clause id="41490">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * v5 = a(a(z,y,x),u,w) * v5
    ]]></literal>
    <justification jstring="[hyper(144,a,41479,a,b,11,a)].">
      <j1 rule="hyper" parents="144 41479 11"/>
    </justification>
  </clause>

  <clause id="41492">
    <literal><![CDATA[
      a(a(x,y,z * (z * u)),w,v5) = a(a(L(u,z,z),y,x),w,v5)
    ]]></literal>
    <justification jstring="[para(2640(a,1),41479(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2640 41479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41493">
    <literal><![CDATA[
      a(a(x * y,z,u),w,v5) = a(a(u,z,y * x),w,v5)
    ]]></literal>
    <justification jstring="[para(26787(a,1),41479(a,1,1))].">
      <j1 rule="para" parents="26787 41479"/>
    </justification>
  </clause>

  <clause id="41494">
    <literal><![CDATA[
      a(a(x,y,z * (u * z)),w,v5) = a(a(L(u,z,z),y,x),w,v5)
    ]]></literal>
    <justification jstring="[para(26861(a,1),41479(a,1,1)),flip(a)].">
      <j1 rule="para" parents="26861 41479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41496">
    <literal><![CDATA[
      a(a(x,y,z),u,u) \ u = L(u,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(41479(a,1),30459(a,1,1))].">
      <j1 rule="para" parents="41479 30459"/>
    </justification>
  </clause>

  <clause id="41497">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(z,w,v5) = a(x,y,z) * (u * a(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(1432,a,41487,a)].">
      <j1 rule="hyper" parents="1432 41487"/>
    </justification>
  </clause>

  <clause id="41498">
    <literal><![CDATA[
      ((x / (y * x)) / y) * ((y * (y * x)) / x) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,40267,a,b,41487,a)].">
      <j1 rule="hyper" parents="64 40267 41487"/>
    </justification>
  </clause>

  <clause id="41500">
    <literal><![CDATA[
      a(x * y,x * y,a(z,u,x)) = a(a(x,u,z),x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,40505,a(flip),b,41486,a),flip(a)].">
      <j1 rule="hyper" parents="64 40505 41486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41502">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) \ x = L(x,x,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(41486(a,1),30459(a,1,1))].">
      <j1 rule="para" parents="41486 30459"/>
    </justification>
  </clause>

  <clause id="41503">
    <literal><![CDATA[
      a(a(x,y,z),u,u) * a(z,y,x) = L(a(z,y,x),u,u)
    ]]></literal>
    <justification jstring="[para(41486(a,2),36296(a,1,1))].">
      <j1 rule="para" parents="41486 36296"/>
    </justification>
  </clause>

  <clause id="41504">
    <literal><![CDATA[
      L(1 / x,x,a(y,z,u)) = a(x,x,a(u,z,y)) / x
    ]]></literal>
    <justification jstring="[para(41486(a,1),36336(a,2,1))].">
      <j1 rule="para" parents="41486 36336"/>
    </justification>
  </clause>

  <clause id="41505">
    <literal><![CDATA[
      a(x,y,z) \ (u \ a(x,y,z)) = u \ a(u,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(41486(a,1),36337(a,2,2))].">
      <j1 rule="para" parents="41486 36337"/>
    </justification>
  </clause>

  <clause id="41506">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) \ w = a(x,x,a(u,z,y)) * w
    ]]></literal>
    <justification jstring="[para(41486(a,1),37690(a,2,1))].">
      <j1 rule="para" parents="41486 37690"/>
    </justification>
  </clause>

  <clause id="41507">
    <literal><![CDATA[
      a(a(x,y,z),u,L(w,w,v5)) = a(a(z,y,x),u,v5 \ (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,38965,a,b,41480,a)].">
      <j1 rule="hyper" parents="64 38965 41480"/>
    </justification>
  </clause>

  <clause id="41508">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) = L(x,x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30459,a(flip),b,41496,a)].">
      <j1 rule="hyper" parents="64 30459 41496"/>
    </justification>
  </clause>

  <clause id="41509">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ a(u,z,y) = (x \ 1) * a(u,z,y)
    ]]></literal>
    <justification jstring="[para(41508(a,1),25752(a,1,1))].">
      <j1 rule="para" parents="41508 25752"/>
    </justification>
  </clause>

  <clause id="41511">
    <literal><![CDATA[
      a(L(x,x,a(y,z,u)),w,v5) = L(a(x,w,v5),x,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(41508(a,1),40756(a,1,1))].">
      <j1 rule="para" parents="41508 40756"/>
    </justification>
  </clause>

  <clause id="41513">
    <literal><![CDATA[
      (x * (x * y)) / y = x / (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(35,a,35665,a,b,41498,a),flip(a)].">
      <j1 rule="hyper" parents="35 35665 41498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41514">
    <literal><![CDATA[
      L(x * ((y * (y * x)) \ z),x,a(y,y,x)) = (y / (x / (y * x))) \ z
    ]]></literal>
    <justification jstring="[para(41513(a,1),37961(a,2,1))].">
      <j1 rule="para" parents="41513 37961"/>
    </justification>
  </clause>

  <clause id="41515">
    <literal><![CDATA[
      a(a(x,y,z),z * u,z * u) = a(a(z,y,x),z * u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,40481,a(flip),b,41483,a),flip(a)].">
      <j1 rule="hyper" parents="373 40481 41483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41516">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u * z,u * z) = a(a(z,y,x),z * u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29665,a,b,41515,a)].">
      <j1 rule="hyper" parents="64 29665 41515"/>
    </justification>
  </clause>

  <clause id="41517">
    <literal><![CDATA[
      a(x * y,x * y,a(z,u,x)) = a(a(x,u,z),x * y,y) \ 1
    ]]></literal>
    <justification jstring="[para(41515(a,1),28802(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41515 28802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41518">
    <literal><![CDATA[
      L(a(x,y,z),u,a(z,w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(28860,a,41497,a)].">
      <j1 rule="hyper" parents="28860 41497"/>
    </justification>
  </clause>

  <clause id="41519">
    <literal><![CDATA[
      (x * a(y,z,u)) * a(u,w,v5) = a(y,z,u) * (x * a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,23168,a(flip),b,41497,a)].">
      <j1 rule="hyper" parents="64 23168 41497"/>
    </justification>
  </clause>

  <clause id="41521">
    <literal><![CDATA[
      a(L(x,x,a(y,z,u)),w,u) = a(x,w,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,41511,a,b,41518,a)].">
      <j1 rule="hyper" parents="64 41511 41518"/>
    </justification>
  </clause>

  <clause id="41526">
    <literal><![CDATA[
      L(x * a(y,z,x),x,a(x,u,w)) = x * a(y,z,x)
    ]]></literal>
    <justification jstring="[para(41518(a,1),39276(a,2,2))].">
      <j1 rule="para" parents="41518 39276"/>
    </justification>
  </clause>

  <clause id="41527">
    <literal><![CDATA[
      L(x * a(y,z,x),x,a(u,w,x)) = x * a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,41425,a,b,41526,a)].">
      <j1 rule="hyper" parents="64 41425 41526"/>
    </justification>
  </clause>

  <clause id="41528">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) / z) \ 1 = z * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38624,a(flip),b,41527,a)].">
      <j1 rule="hyper" parents="64 38624 41527"/>
    </justification>
  </clause>

  <clause id="41529">
    <literal><![CDATA[
      1 / ((a(x,y,z) \ 1) \ z) = (a(x,y,z) \ 1) / z
    ]]></literal>
    <justification jstring="[hyper(225,a,33210,a,b,41528,a)].">
      <j1 rule="hyper" parents="225 33210 41528"/>
    </justification>
  </clause>

  <clause id="41530">
    <literal><![CDATA[
      1 / ((a(x,y,z) \ 1) \ z) = (1 / a(x,y,z)) / z
    ]]></literal>
    <justification jstring="[para(13923(a,2),41529(a,2,1))].">
      <j1 rule="para" parents="13923 41529"/>
    </justification>
  </clause>

  <clause id="41531">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ (a(x,y,z) / z) = 1 / ((a(x,y,z) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,887,a,b,41530,a)].">
      <j1 rule="hyper" parents="373 887 41530"/>
    </justification>
  </clause>

  <clause id="41532">
    <literal><![CDATA[
      a(x,y,z) * (u * a(z,z,a(u * a(x,y,z),w,w))) = L(u * a(x,y,z),z,a(z,w,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,40905,a(flip),b,41519,a),flip(a)].">
      <j1 rule="hyper" parents="64 40905 41519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41533">
    <literal><![CDATA[
      L(x * ((y * (y * x)) \ z),x,a(y,y,x)) = (x / (y * x)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,41264,a(flip),b,41514,a),flip(a)].">
      <j1 rule="hyper" parents="373 41264 41514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41534">
    <literal><![CDATA[
      ((x / (y \ 1)) * (y \ a(z,u,y))) / a(z,u,y) = a(y,a(y,u,z),x) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,33553,a(flip),b,41465,a),flip(a)].">
      <j1 rule="hyper" parents="64 33553 41465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41535">
    <literal><![CDATA[
      (a(x,y,z) / z) * (a(x,y,z) \ (a(x,y,z) \ 1)) = 1 / ((a(x,y,z) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26956,a,b,41531,a)].">
      <j1 rule="hyper" parents="64 26956 41531"/>
    </justification>
  </clause>

  <clause id="41536">
    <literal><![CDATA[
      ((x / y) * ((1 / y) \ a(z,u,y))) / a(z,u,y) = a(y,a(y,u,z),x) * x
    ]]></literal>
    <justification jstring="[para(1689(a,1),41534(a,1,1))].">
      <j1 rule="para" parents="1689 41534"/>
    </justification>
  </clause>

  <clause id="41537">
    <literal><![CDATA[
      ((x / y) * (y * a(z,u,y))) / a(z,u,y) = a(y,a(y,u,z),x) * x
    ]]></literal>
    <justification jstring="[para(9440(a,1),41536(a,1,1,2))].">
      <j1 rule="para" parents="9440 41536"/>
    </justification>
  </clause>

  <clause id="41538">
    <literal><![CDATA[
      a(x,y,z) \ ((u / z) * (z * a(x,y,z))) = a(z,a(z,y,x),u) * u
    ]]></literal>
    <justification jstring="[hyper(23179,a,41537,a)].">
      <j1 rule="hyper" parents="23179 41537"/>
    </justification>
  </clause>

  <clause id="41539">
    <literal><![CDATA[
      a(x,y,z) \ ((u / z) * (z * a(x,y,z))) = L(u,z,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,40823,a(flip),b,41538,a),flip(a)].">
      <j1 rule="hyper" parents="373 40823 41538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41540">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ a(z,u,x),x) = x * L(y,x,a(x,u,z))
    ]]></literal>
    <justification jstring="[para(41539(a,1),34795(a,1,2)),flip(a)].">
      <j1 rule="para" parents="41539 34795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41541">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ a(z,u,x),x) = L(x * y,x,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,39276,a,b,41540,a),flip(a)].">
      <j1 rule="hyper" parents="373 39276 41540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41542">
    <literal><![CDATA[
      L((x \ 1) \ y,x * a(z,u,x),x) = L(x * y,x,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,11879,a(flip),b,41541,a)].">
      <j1 rule="hyper" parents="64 11879 41541"/>
    </justification>
  </clause>

  <clause id="41543">
    <literal><![CDATA[
      L(x * ((x \ 1) * y),x,a(x,z,u)) = L(y,x * a(u,z,x),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),41542(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 41542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41544">
    <literal><![CDATA[
      L(L(x,y,y),y,a(y,z,u)) = L(x,y * a(u,z,y),y)
    ]]></literal>
    <justification jstring="[para(1139(a,1),41543(a,1,1))].">
      <j1 rule="para" parents="1139 41543"/>
    </justification>
  </clause>

  <clause id="41545">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),y,y) = L(x,y * a(u,z,y),y)
    ]]></literal>
    <justification jstring="[hyper(1435,a,41544,a)].">
      <j1 rule="hyper" parents="1435 41544"/>
    </justification>
  </clause>

  <clause id="41546">
    <literal><![CDATA[
      a(x,y,z) * L(u * a(z,a(z,y,x),u),z,z) = (a(x,y,z) / z) * (z * u)
    ]]></literal>
    <justification jstring="[para(30820(a,2),41446(a,1,2))].">
      <j1 rule="para" parents="30820 41446"/>
    </justification>
  </clause>

  <clause id="41547">
    <literal><![CDATA[
      a(x,y,z) * L(L(u,z,a(z,y,x)),z,z) = (a(x,y,z) / z) * (z * u)
    ]]></literal>
    <justification jstring="[para(40813(a,1),41546(a,1,2,1))].">
      <j1 rule="para" parents="40813 41546"/>
    </justification>
  </clause>

  <clause id="41548">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),y,y) = L(x,y,a(u,z,y) * y)
    ]]></literal>
    <justification jstring="[hyper(35,a,25445,a,b,41547,a),flip(a)].">
      <j1 rule="hyper" parents="35 25445 41547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41549">
    <literal><![CDATA[
      L(x,y * a(z,u,y),y) = L(x,y,a(z,u,y) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41545,a(flip),b,41548,a)].">
      <j1 rule="hyper" parents="64 41545 41548"/>
    </justification>
  </clause>

  <clause id="41550">
    <literal><![CDATA[
      (x \ L(y,x,a(z,u,x) * x)) * a(z,u,x) = (x \ a(z,u,x)) * y
    ]]></literal>
    <justification jstring="[para(41549(a,1),33530(a,1,1,2))].">
      <j1 rule="para" parents="41549 33530"/>
    </justification>
  </clause>

  <clause id="41551">
    <literal><![CDATA[
      1 / (a(x,y,z) \ z) = a(x,y,z) / z
    ]]></literal>
    <justification jstring="[hyper(36,a,1676,a,b,41535,a)].">
      <j1 rule="hyper" parents="36 1676 41535"/>
    </justification>
  </clause>

  <clause id="41552">
    <literal><![CDATA[
      (a(x,y,z) / z) \ 1 = a(x,y,z) \ z
    ]]></literal>
    <justification jstring="[hyper(215,a,41551,a)].">
      <j1 rule="hyper" parents="215 41551"/>
    </justification>
  </clause>

  <clause id="41553">
    <literal><![CDATA[
      a(x,y,z) * (u * a(w,w,a(u,z,z))) = L(u * a(x,y,z),z,a(z,w,w))
    ]]></literal>
    <justification jstring="[para(39756(a,1),41532(a,1,2,2))].">
      <j1 rule="para" parents="39756 41532"/>
    </justification>
  </clause>

  <clause id="41555">
    <literal><![CDATA[
      L(x * a(y,z,u),u,a(u,w,w)) = a(y,z,u) * L(x,w,a(w,u,u))
    ]]></literal>
    <justification jstring="[para(40905(a,1),41553(a,1,2)),flip(a)].">
      <j1 rule="para" parents="40905 41553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41556">
    <literal><![CDATA[
      L(x * a(y,z,z),z,a(z,y,y)) = R(y,z,z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,38340,a(flip),b,41555,a),flip(a)].">
      <j1 rule="hyper" parents="373 38340 41555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41557">
    <literal><![CDATA[
      x / a(L(y,y,L(y,z,a(z,u,w)) \ x),z,a(w,u,z)) = (x / (y * a(y,z,a(w,u,z)))) * y
    ]]></literal>
    <justification jstring="[para(40756(a,2),41467(a,1,2))].">
      <j1 rule="para" parents="40756 41467"/>
    </justification>
  </clause>

  <clause id="41558">
    <literal><![CDATA[
      x / a(L(y,y,x),z,a(u,w,z)) = (x / (y * a(y,z,a(u,w,z)))) * y
    ]]></literal>
    <justification jstring="[para(36753(a,1),41557(a,1,2))].">
      <j1 rule="para" parents="36753 41557"/>
    </justification>
  </clause>

  <clause id="41559">
    <literal><![CDATA[
      a(L(x,x,y),z,a(u,w,z)) \ y = (y / (x * a(x,z,a(u,w,z)))) * x
    ]]></literal>
    <justification jstring="[hyper(23179,a,41558,a)].">
      <j1 rule="hyper" parents="23179 41558"/>
    </justification>
  </clause>

  <clause id="41561">
    <literal><![CDATA[
      a(L(x,x,y),z,a(u,w,z)) \ y = (y / L(x,z,a(z,w,u))) * x
    ]]></literal>
    <justification jstring="[para(41456(a,1),41559(a,2,1,2))].">
      <j1 rule="para" parents="41456 41559"/>
    </justification>
  </clause>

  <clause id="41562">
    <literal><![CDATA[
      a(L(x,x,y),z,a(u,w,z)) \ y = x * (L(x,z,a(z,w,u)) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,23887,a(flip),b,41561,a),flip(a)].">
      <j1 rule="hyper" parents="373 23887 41561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41563">
    <literal><![CDATA[
      a(x,L(x,x * y,z),y) \ 1 = (((x \ 1) * y) * z) / ((x \ y) * z)
    ]]></literal>
    <justification jstring="[para(37835(a,1),41381(a,1,2))].">
      <j1 rule="para" parents="37835 41381"/>
    </justification>
  </clause>

  <clause id="41565">
    <literal><![CDATA[
      (((x \ 1) * y) * z) / ((x \ y) * z) = a(x,x,L(y,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(41013(a,1),41563(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41013 41563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41566">
    <literal><![CDATA[
      (((x \ 1) * y) * z) / ((x \ y) * z) = L(a(x,x,y) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,39642,a,b,41565,a),flip(a)].">
      <j1 rule="hyper" parents="373 39642 41565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41567">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,x \ y,z) = L(a(x,x,y) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37273,a,b,41566,a)].">
      <j1 rule="hyper" parents="64 37273 41566"/>
    </justification>
  </clause>

  <clause id="41568">
    <literal><![CDATA[
      (x * (y \ z)) \ (x * ((y \ 1) * z)) = L(a(y,y,z) \ 1,z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30424,a(flip),b,41567,a)].">
      <j1 rule="hyper" parents="64 30424 41567"/>
    </justification>
  </clause>

  <clause id="41569">
    <literal><![CDATA[
      (x \ y) \ (((x \ 1) * y) * z) = z * L(a(x,x,y) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(41567(a,1),37320(a,1,2)),flip(a)].">
      <j1 rule="para" parents="41567 37320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41570">
    <literal><![CDATA[
      a(x,x,L(y,y,z)) \ z = (x \ y) \ (((x \ 1) * y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,39644,a(flip),b,41569,a)].">
      <j1 rule="hyper" parents="373 39644 41569"/>
    </justification>
  </clause>

  <clause id="41571">
    <literal><![CDATA[
      (x \ y) \ (((x \ 1) * y) * z) = L(y,x,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,39512,a(flip),b,41570,a),flip(a)].">
      <j1 rule="hyper" parents="64 39512 41570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41572">
    <literal><![CDATA[
      x \ (L(x \ (x * (y \ R(y,z,u))),L(y,y,x),z * u) * (y \ x)) = (x \ (y \ x)) * T(a(L(y,y,x),z,u),y \ x)
    ]]></literal>
    <justification jstring="[para(33051(a,1),41382(a,1,2,1,1,2))].">
      <j1 rule="para" parents="33051 41382"/>
    </justification>
  </clause>

  <clause id="41573">
    <literal><![CDATA[
      x \ (L(y \ R(y,z,u),L(y,y,x),z * u) * (y \ x)) = (x \ (y \ x)) * T(a(L(y,y,x),z,u),y \ x)
    ]]></literal>
    <justification jstring="[para(9(a,1),41572(a,1,2,1,1))].">
      <j1 rule="para" parents="9 41572"/>
    </justification>
  </clause>

  <clause id="41575">
    <literal><![CDATA[
      x \ (L(y \ R(y,z,u),y,z * u) * (y \ x)) = (x \ (y \ x)) * T(a(L(y,y,x),z,u),y \ x)
    ]]></literal>
    <justification jstring="[para(40750(a,1),41573(a,1,2,1))].">
      <j1 rule="para" parents="40750 41573"/>
    </justification>
  </clause>

  <clause id="41576">
    <literal><![CDATA[
      (x \ (y \ x)) * T(a(L(y,y,x),z,u),y \ x) = x \ (a(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(16031(a,2),41575(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16031 41575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41578">
    <literal><![CDATA[
      (x \ (y \ x)) * a(L(y,y,x),z,u) = x \ (a(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[para(23127(a,1),41576(a,1,2))].">
      <j1 rule="para" parents="23127 41576"/>
    </justification>
  </clause>

  <clause id="41579">
    <literal><![CDATA[
      (x \ (y \ x)) * a(x \ (y \ x),z,u) = x \ (a(y,z,u) * (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,32464,a(flip),b,41578,a)].">
      <j1 rule="hyper" parents="64 32464 41578"/>
    </justification>
  </clause>

  <clause id="41581">
    <literal><![CDATA[
      R(T((T(x * y,z) \ x) \ 1,(x \ T(x * y,z)) * K(y * x,z)),T(x * y,z) \ x,K(y * x,z)) = L(y \ 1,y,x) \ K(y * x,z)
    ]]></literal>
    <justification jstring="[para(22657(a,1),25589(a,1,1))].">
      <j1 rule="para" parents="22657 25589"/>
    </justification>
  </clause>

  <clause id="41582">
    <literal><![CDATA[
      R(1 / (1 / (x / y)),1 / (y / x),z * ((y / x) \ 1)) * L(z,1 / (y / x),1 / (y / x)) = ((x / y) * (y / x)) * ((1 / (y / x)) * z)
    ]]></literal>
    <justification jstring="[para(26171(a,1),27106(a,1,1))].">
      <j1 rule="para" parents="26171 27106"/>
    </justification>
  </clause>

  <clause id="41583">
    <literal><![CDATA[
      1 * (x \ (a(y,y,y \ x) * (L(a(y,y,y \ x),z,u) \ x))) = x \ (L(a(y,y,y \ x),z,u) \ ((1 / y) \ (y \ x)))
    ]]></literal>
    <justification jstring="[para(23078(a,1),30204(a,1,1))].">
      <j1 rule="para" parents="23078 30204"/>
    </justification>
  </clause>

  <clause id="41585">
    <literal><![CDATA[
      1 * (x \ (a(y,y,y \ x) * (a(y,L(y,z,u),y \ x) \ x))) = x \ (L(a(y,y,y \ x),z,u) \ ((1 / y) \ (y \ x)))
    ]]></literal>
    <justification jstring="[para(34877(a,2),41583(a,1,2,2,2,1))].">
      <j1 rule="para" parents="34877 41583"/>
    </justification>
  </clause>

  <clause id="41586">
    <literal><![CDATA[
      x \ (L(a(y,y,y \ x),z,u) \ ((1 / y) \ (y \ x))) = 1 * (x \ (a(a(y,y,y \ x),z,u) \ x))
    ]]></literal>
    <justification jstring="[para(39781(a,1),41585(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="39781 41585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41587">
    <literal><![CDATA[
      x \ (L(a(y,y,y \ x),z,u) \ ((1 / y) \ (y \ x))) = 1 * (x \ (a(a(y,y,x),z,u) \ x))
    ]]></literal>
    <justification jstring="[para(30184(a,1),41586(a,2,2,2,1))].">
      <j1 rule="para" parents="30184 41586"/>
    </justification>
  </clause>

  <clause id="41588">
    <literal><![CDATA[
      x \ (L(a(y,y,y \ x),z,u) \ ((1 / y) \ (y \ x))) = 1 * (a(a(y,y,x),z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(39768(a,1),41587(a,2,2))].">
      <j1 rule="para" parents="39768 41587"/>
    </justification>
  </clause>

  <clause id="41589">
    <literal><![CDATA[
      x \ (L(a(y,y,y \ x),z,u) \ ((1 / y) \ (y \ x))) = a(a(y,y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,39767,a(flip),b,41588,a),flip(a)].">
      <j1 rule="hyper" parents="373 39767 41588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41591">
    <literal><![CDATA[
      x \ (a(y,L(y,z,u),y \ x) \ ((1 / y) \ (y \ x))) = a(a(y,y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(34877(a,2),41589(a,1,2,1))].">
      <j1 rule="para" parents="34877 41589"/>
    </justification>
  </clause>

  <clause id="41592">
    <literal><![CDATA[
      x \ ((1 / y) \ (a(y,L(y,z,u),y \ x) \ (y \ x))) = a(a(y,y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(33055(a,1),41591(a,1,2))].">
      <j1 rule="para" parents="33055 41591"/>
    </justification>
  </clause>

  <clause id="41593">
    <literal><![CDATA[
      x \ ((1 / y) \ L(y \ x,y,L(y,z,u))) = a(a(y,y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(39795(a,1),41592(a,1,2,2))].">
      <j1 rule="para" parents="39795 41592"/>
    </justification>
  </clause>

  <clause id="41594">
    <literal><![CDATA[
      x \ L((y \ 1) \ (y \ x),y,L(y,z,u)) = a(a(y,y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(37437(a,2),41593(a,1,2))].">
      <j1 rule="para" parents="37437 41593"/>
    </justification>
  </clause>

  <clause id="41595">
    <literal><![CDATA[
      x \ L(y \ ((1 / y) \ x),y,L(y,z,u)) = a(a(y,y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(1166(a,1),41594(a,1,2,1))].">
      <j1 rule="para" parents="1166 41594"/>
    </justification>
  </clause>

  <clause id="41596">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) = a(a(x,x,u),y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,38258,a(flip),b,41595,a)].">
      <j1 rule="hyper" parents="64 38258 41595"/>
    </justification>
  </clause>

  <clause id="41597">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) \ 1 = a(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(23919,a,41596,a)].">
      <j1 rule="hyper" parents="23919 41596"/>
    </justification>
  </clause>

  <clause id="41598">
    <literal><![CDATA[
      a(x,x * L(x,y,z),u) = a(a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,39725,a(flip),b,41596,a),flip(a)].">
      <j1 rule="hyper" parents="373 39725 41596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41599">
    <literal><![CDATA[
      a(x * L(x,y,z),x,u) = a(a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33573,a,b,41598,a)].">
      <j1 rule="hyper" parents="64 33573 41598"/>
    </justification>
  </clause>

  <clause id="41600">
    <literal><![CDATA[
      a(a(x * y,z,z),y,x) = a(y * x,z,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,40788,a(flip),b,41598,a),flip(a)].">
      <j1 rule="hyper" parents="64 40788 41598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41601">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u) = x * a(a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,41598,a(flip),b,40781,a),flip(a)].">
      <j1 rule="hyper" parents="145 41598 40781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41602">
    <literal><![CDATA[
      a(a(x,y,y),z,u) \ L(y,z,u) = (y * ((y \ L(y,z,u)) * x)) / x
    ]]></literal>
    <justification jstring="[para(41598(a,1),33398(a,1,1))].">
      <j1 rule="para" parents="41598 33398"/>
    </justification>
  </clause>

  <clause id="41603">
    <literal><![CDATA[
      a(L(x,y,z) \ x,x,u) = a(a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,9387,a,b,41599,a)].">
      <j1 rule="hyper" parents="64 9387 41599"/>
    </justification>
  </clause>

  <clause id="41604">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u * x) \ x = a(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40782,a,b,41597,a)].">
      <j1 rule="hyper" parents="64 40782 41597"/>
    </justification>
  </clause>

  <clause id="41605">
    <literal><![CDATA[
      a(x,x \ L(x,y,z),u) \ 1 = a(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(11978(a,2),41597(a,1,1))].">
      <j1 rule="para" parents="11978 41597"/>
    </justification>
  </clause>

  <clause id="41606">
    <literal><![CDATA[
      a(x * y,z,a(z,x,y)) = a(y,x,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41058,a(flip),b,41600,a),flip(a)].">
      <j1 rule="hyper" parents="64 41058 41600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41607">
    <literal><![CDATA[
      a(x * y,z,a(z,y,x)) = a(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(26847,a,41606,a)].">
      <j1 rule="hyper" parents="26847 41606"/>
    </justification>
  </clause>

  <clause id="41608">
    <literal><![CDATA[
      a(x * y,z,a(y,x,z)) = a(y,x,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41450,a,b,41606,a)].">
      <j1 rule="hyper" parents="64 41450 41606"/>
    </justification>
  </clause>

  <clause id="41609">
    <literal><![CDATA[
      a(x,y,z) \ R(x,y,z) = x * a(z,y,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,41606,a(flip),b,34139,a),flip(a)].">
      <j1 rule="hyper" parents="145 41606 34139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41610">
    <literal><![CDATA[
      a(x,a(x,y,z),z * y) = a(z,y,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,39362,a,b,41607,a)].">
      <j1 rule="hyper" parents="64 39362 41607"/>
    </justification>
  </clause>

  <clause id="41611">
    <literal><![CDATA[
      L(x,a(x,y,z),z * y) = x * a(z,y,a(y,x,x))
    ]]></literal>
    <justification jstring="[para(41607(a,1),39367(a,1,2)),flip(a)].">
      <j1 rule="para" parents="41607 39367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41612">
    <literal><![CDATA[
      a(x * y,z,a(y,x,z)) = a(a(y,x,x),z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,40882,a,b,41608,a),flip(a)].">
      <j1 rule="hyper" parents="373 40882 41608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41613">
    <literal><![CDATA[
      a(x * y,z,a(y,x,z)) = a(x,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,40884,a(flip),b,41608,a),flip(a)].">
      <j1 rule="hyper" parents="373 40884 41608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41614">
    <literal><![CDATA[
      (x * a(y,z,a(z,x,x))) \ (x * (y * z)) = (x * a(x,z,y)) \ ((x * z) * T(y,z))
    ]]></literal>
    <justification jstring="[para(41610(a,1),40968(a,1,1,2))].">
      <j1 rule="para" parents="41610 40968"/>
    </justification>
  </clause>

  <clause id="41615">
    <literal><![CDATA[
      a(x * y,z,a(y,x,z)) = L(z,z,a(y,x,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(373,a,30462,a,b,41612,a),flip(a)].">
      <j1 rule="hyper" parents="373 30462 41612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41616">
    <literal><![CDATA[
      a(x,a(x,y,z),y * z) = a(y,y,a(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41451,a,b,41613,a)].">
      <j1 rule="hyper" parents="64 41451 41613"/>
    </justification>
  </clause>

  <clause id="41617">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L(z,x,y) = a(y,x,z) \ z
    ]]></literal>
    <justification jstring="[para(41613(a,1),40799(a,1,1))].">
      <j1 rule="para" parents="41613 40799"/>
    </justification>
  </clause>

  <clause id="41618">
    <literal><![CDATA[
      x * (R(x,y,z) \ a(x,y,z)) = a(y,y,a(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,33567,a,b,41616,a)].">
      <j1 rule="hyper" parents="64 33567 41616"/>
    </justification>
  </clause>

  <clause id="41619">
    <literal><![CDATA[
      a(x,y,z) * a(y,y,a(z,x,x)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(41616(a,1),39364(a,1,2))].">
      <j1 rule="para" parents="41616 39364"/>
    </justification>
  </clause>

  <clause id="41620">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u) = x * a(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,41489,a,b,41601,a),flip(a)].">
      <j1 rule="hyper" parents="373 41489 41601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41621">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u) = a(z,y,a(x,x,u)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,40844,a,b,41601,a),flip(a)].">
      <j1 rule="hyper" parents="373 40844 41601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41622">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u) = a(z,y,a(u,x,x)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,40840,a,b,41601,a),flip(a)].">
      <j1 rule="hyper" parents="373 40840 41601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41623">
    <literal><![CDATA[
      L(x,y,z) \ (u \ ((x \ L(x,y,z)) * (u * x))) = a(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,36236,a,b,41605,a)].">
      <j1 rule="hyper" parents="64 36236 41605"/>
    </justification>
  </clause>

  <clause id="41624">
    <literal><![CDATA[
      a(x,y,z) \ R(x,y,z) = L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,40892,a(flip),b,41609,a),flip(a)].">
      <j1 rule="hyper" parents="373 40892 41609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41625">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,40892,a(flip),b,41609,a),flip(a)].">
      <j1 rule="hyper" parents="145 40892 41609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41626">
    <literal><![CDATA[
      R(x,y,z) = L(x,x,a(z,y,y)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(23175,a,41624,a),flip(a)].">
      <j1 rule="hyper" parents="23175 41624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41627">
    <literal><![CDATA[
      R(x,y,z) \ L(x,x,a(z,y,y)) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,41624,a(flip),b,30005,a)].">
      <j1 rule="hyper" parents="139 41624 30005"/>
    </justification>
  </clause>

  <clause id="41628">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) \ R(x,z,y) = a(x,z,y)
    ]]></literal>
    <justification jstring="[para(41624(a,1),23134(a,1,1))].">
      <j1 rule="para" parents="41624 23134"/>
    </justification>
  </clause>

  <clause id="41629">
    <literal><![CDATA[
      R(x,y,z) = L(x,x,a(y,y,z)) * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29293,a(flip),b,41626,a),flip(a)].">
      <j1 rule="hyper" parents="373 29293 41626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41630">
    <literal><![CDATA[
      L(x,x,a(y,y,z)) \ R(x,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,41626,a,b,29293,a(flip))].">
      <j1 rule="hyper" parents="139 41626 29293"/>
    </justification>
  </clause>

  <clause id="41631">
    <literal><![CDATA[
      L(x,x,1) * a(x,y \ (z \ y),a(z,u,w)) = R(x,y \ (z \ y),a(z,u,w))
    ]]></literal>
    <justification jstring="[para(32744(a,1),41626(a,2,1,3)),flip(a)].">
      <j1 rule="para" parents="32744 41626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41632">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(x \ R(x,y,z),x,u) = R(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(33525(a,1),41626(a,2,1)),flip(a)].">
      <j1 rule="para" parents="33525 41626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41633">
    <literal><![CDATA[
      L(x,x,a((L(y,z,u) * w) * v5,v6,v6)) * a(x,v6,(R(y,z,u) * w) * v5) = R(x,v6,(R(y,z,u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(34653(a,1),41626(a,2,1,3)),flip(a)].">
      <j1 rule="para" parents="34653 41626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41634">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(x \ L(x,y,z),x,u) = R(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(36997(a,1),41626(a,2,1)),flip(a)].">
      <j1 rule="para" parents="36997 41626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41635">
    <literal><![CDATA[
      L(x,x,1) \ R(x,L(y,z,u),a(w,v5,y)) = a(x,L(y,z,u),a(w,v5,y))
    ]]></literal>
    <justification jstring="[para(33272(a,1),41628(a,1,1,3))].">
      <j1 rule="para" parents="33272 41628"/>
    </justification>
  </clause>

  <clause id="41636">
    <literal><![CDATA[
      L(x,x,a(y * L(y,z,u),y * L(y,z,u),w)) \ R(x,L(y,z,u) \ y,w) = a(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(139,a,26595,a,b,41629,a(flip))].">
      <j1 rule="hyper" parents="139 26595 41629"/>
    </justification>
  </clause>

  <clause id="41637">
    <literal><![CDATA[
      (a(x,x,y) * (z * z)) \ ((a(x,x,y) * z) * R(z,x,y)) = L(a(z,x,y),L(z,z,a(x,x,y)),a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[para(41629(a,2),601(a,1,2,2))].">
      <j1 rule="para" parents="41629 601"/>
    </justification>
  </clause>

  <clause id="41638">
    <literal><![CDATA[
      L(x,x,1) \ R(x,y,L(a(y,z,u),w,v5)) = a(x,y,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(30341(a,1),41630(a,1,1,3))].">
      <j1 rule="para" parents="30341 41630"/>
    </justification>
  </clause>

  <clause id="41639">
    <literal><![CDATA[
      L(x,a(x,y,z),z * y) = L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,40892,a(flip),b,41611,a),flip(a)].">
      <j1 rule="hyper" parents="373 40892 41611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41640">
    <literal><![CDATA[
      a(x,y,z) * L(z,y,x) = L(z,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(40,a,40792,a,b,41615,a(flip))].">
      <j1 rule="hyper" parents="40 40792 41615"/>
    </justification>
  </clause>

  <clause id="41641">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,x) = L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(23177,a,41640,a)].">
      <j1 rule="hyper" parents="23177 41640"/>
    </justification>
  </clause>

  <clause id="41642">
    <literal><![CDATA[
      L(x,y,z) \ L(x,x,a(z,y,y)) = a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(36,a,5566,a,b,41640,a)].">
      <j1 rule="hyper" parents="36 5566 41640"/>
    </justification>
  </clause>

  <clause id="41643">
    <literal><![CDATA[
      L(x,y,z) \ L(x,x,a(y,y,z)) = a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,41508,a,b,41641,a)].">
      <j1 rule="hyper" parents="139 41508 41641"/>
    </justification>
  </clause>

  <clause id="41644">
    <literal><![CDATA[
      L(x,y,z) \ R(x,x,a(z,y,y)) = a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,28832,a,b,41641,a)].">
      <j1 rule="hyper" parents="139 28832 41641"/>
    </justification>
  </clause>

  <clause id="41645">
    <literal><![CDATA[
      L(L(x,y,z),x,u) \ L(x,y,z) = a(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,37533,a(flip),b,41641,a)].">
      <j1 rule="hyper" parents="139 37533 41641"/>
    </justification>
  </clause>

  <clause id="41646">
    <literal><![CDATA[
      L(x,y \ z,y) \ L(x,x,a(z,z * y,y)) = a(y,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,35690,a(flip),b,41641,a)].">
      <j1 rule="hyper" parents="139 35690 41641"/>
    </justification>
  </clause>

  <clause id="41647">
    <literal><![CDATA[
      L(L(x,y,z),L(x,u,w),v5) \ L(x,y,z) = a(v5,L(x,u,w),L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,33268,a(flip),b,41641,a)].">
      <j1 rule="hyper" parents="139 33268 41641"/>
    </justification>
  </clause>

  <clause id="41648">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (L(y,y,a(u,z,z)) * (a(u,z,y) \ x)) = x * R(L(y,z,u),a(u,z,y),a(u,z,y) \ x)
    ]]></literal>
    <justification jstring="[para(41641(a,1),24793(a,1,2,1))].">
      <j1 rule="para" parents="41641 24793"/>
    </justification>
  </clause>

  <clause id="41649">
    <literal><![CDATA[
      ((x * L(y,y,a(z,u,u))) / a(z,u,y)) \ (x * L(y,u,z)) = a(x,L(y,u,z),a(z,u,y))
    ]]></literal>
    <justification jstring="[para(41641(a,1),33321(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="41641 33321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41650">
    <literal><![CDATA[
      L(x,y * z,y) \ L(x,x,a(y,z * y,z * y)) = a(y,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,14185,a(flip),b,41642,a)].">
      <j1 rule="hyper" parents="64 14185 41642"/>
    </justification>
  </clause>

  <clause id="41652">
    <literal><![CDATA[
      L(x,y \ (R(z,u,w) \ L(z,z,a(w,u,u))),v5) = L(x,y \ a(w,u,z),v5)
    ]]></literal>
    <justification jstring="[para(41642(a,1),39593(a,2,2,2))].">
      <j1 rule="para" parents="41642 39593"/>
    </justification>
  </clause>

  <clause id="41653">
    <literal><![CDATA[
      a(x * (R(y,z,u) \ L(y,y,a(u,z,z))),w,v5) = a(x * a(u,z,y),w,v5)
    ]]></literal>
    <justification jstring="[para(41642(a,1),40059(a,2,1,2))].">
      <j1 rule="para" parents="41642 40059"/>
    </justification>
  </clause>

  <clause id="41654">
    <literal><![CDATA[
      L(x,y,L(z,z,y)) \ L(x,x,a(z,L(y,y,z),L(y,y,z))) = a(z,L(y,y,z),x)
    ]]></literal>
    <justification jstring="[para(40960(a,1),41642(a,1,1))].">
      <j1 rule="para" parents="40960 41642"/>
    </justification>
  </clause>

  <clause id="41655">
    <literal><![CDATA[
      L(x,y,z) \ L(x,x,a(y,y,z)) = (a(z,y,x) \ u) \ u
    ]]></literal>
    <justification jstring="[hyper(373,a,23134,a,b,41643,a),flip(a)].">
      <j1 rule="hyper" parents="373 23134 41643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41656">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * (L(x,z,y) \ x) = a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30942,a,b,41644,a)].">
      <j1 rule="hyper" parents="64 30942 41644"/>
    </justification>
  </clause>

  <clause id="41657">
    <literal><![CDATA[
      L(L(x,x,a(y,z,z)),z,y) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,39757,a(flip),b,41617,a)].">
      <j1 rule="hyper" parents="64 39757 41617"/>
    </justification>
  </clause>

  <clause id="41658">
    <literal><![CDATA[
      L(L(x,y,z),a(x,y,y),z) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,40924,a,b,41657,a)].">
      <j1 rule="hyper" parents="64 40924 41657"/>
    </justification>
  </clause>

  <clause id="41659">
    <literal><![CDATA[
      L(x,y,z) * a(x,x,a(z,y,y)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,39732,a,b,41657,a)].">
      <j1 rule="hyper" parents="64 39732 41657"/>
    </justification>
  </clause>

  <clause id="41660">
    <literal><![CDATA[
      L(L(x,x,a(y,y,z)),y,z) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[para(29287(a,1),41657(a,1,1))].">
      <j1 rule="para" parents="29287 41657"/>
    </justification>
  </clause>

  <clause id="41661">
    <literal><![CDATA[
      L(x,y,L(R(z,u,w),a(z,u,u),w)) = L(x,y,a(w,u,z) \ z)
    ]]></literal>
    <justification jstring="[para(41658(a,1),29264(a,2,3))].">
      <j1 rule="para" parents="41658 29264"/>
    </justification>
  </clause>

  <clause id="41662">
    <literal><![CDATA[
      L(x,L(R(y,z,u),a(y,z,z),u),w) = L(x,a(u,z,y) \ y,w)
    ]]></literal>
    <justification jstring="[para(41658(a,1),29856(a,2,2))].">
      <j1 rule="para" parents="41658 29856"/>
    </justification>
  </clause>

  <clause id="41663">
    <literal><![CDATA[
      a(x,a(y,z,u) \ u,L(L(u,z,y),a(u,z,z),y)) = a(x,L(u,z,y),L(u,z,y))
    ]]></literal>
    <justification jstring="[para(41658(a,1),40664(a,1,2))].">
      <j1 rule="para" parents="41658 40664"/>
    </justification>
  </clause>

  <clause id="41664">
    <literal><![CDATA[
      L(L(x,y,z),x,a(y,y,z)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(1435,a,41660,a)].">
      <j1 rule="hyper" parents="1435 41660"/>
    </justification>
  </clause>

  <clause id="41665">
    <literal><![CDATA[
      L(L(x,y,z),x,L(a(y,y,z),u,z)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[para(29331(a,2),41664(a,1,3))].">
      <j1 rule="para" parents="29331 41664"/>
    </justification>
  </clause>

  <clause id="41666">
    <literal><![CDATA[
      a(L(x,y,z),u,w) * a(u,u,a(w,L(x,y,z),L(x,y,z))) = L(R(x,u,w),y,z) / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2073,a,b,41619,a),flip(a)].">
      <j1 rule="hyper" parents="373 2073 41619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41667">
    <literal><![CDATA[
      R(1 / x,x,y) \ a(x,L(x,z,u),y) = L(x,x * L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,40395,a,b,41620,a)].">
      <j1 rule="hyper" parents="373 40395 41620"/>
    </justification>
  </clause>

  <clause id="41668">
    <literal><![CDATA[
      L(x,x \ L(x,y,z),u) = x * a(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11786,a,b,41620,a)].">
      <j1 rule="hyper" parents="64 11786 41620"/>
    </justification>
  </clause>

  <clause id="41669">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * a(x,y,z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(35,a,40893,a,b,41656,a)].">
      <j1 rule="hyper" parents="35 40893 41656"/>
    </justification>
  </clause>

  <clause id="41670">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) * a(z,y,x) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,41656,a(flip),b,41506,a)].">
      <j1 rule="hyper" parents="145 41656 41506"/>
    </justification>
  </clause>

  <clause id="41671">
    <literal><![CDATA[
      L(x,y,z) * a(x,x,a(z,y,y)) = (a(z,y,x) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,33213,a,b,41659,a),flip(a)].">
      <j1 rule="hyper" parents="373 33213 41659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41672">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ z) = a(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,41669,a(flip),b,40913,a(flip))].">
      <j1 rule="hyper" parents="139 41669 40913"/>
    </justification>
  </clause>

  <clause id="41673">
    <literal><![CDATA[
      a(x,y,z) \ (L(z,y,x) \ z) = a(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,40885,a(flip),b,41672,a),flip(a)].">
      <j1 rule="hyper" parents="373 40885 41672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41674">
    <literal><![CDATA[
      L(x,a(y,z,z),u) \ x = a(u,a(y,z,z),x)
    ]]></literal>
    <justification jstring="[hyper(40,a,37833,a(flip),b,41673,a)].">
      <j1 rule="hyper" parents="40 37833 41673"/>
    </justification>
  </clause>

  <clause id="41675">
    <literal><![CDATA[
      L(x,y,a(a(x,x,z),u,w)) = x
    ]]></literal>
    <justification jstring="[para(41604(a,1),33132(a,1,3))].">
      <j1 rule="para" parents="41604 33132"/>
    </justification>
  </clause>

  <clause id="41676">
    <literal><![CDATA[
      (x * y) * a(a(x,x,z),u,w) = x * (y * a(a(x,x,z),u,w))
    ]]></literal>
    <justification jstring="[para(41675(a,1),28800(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41675 28800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41677">
    <literal><![CDATA[
      L(x,y,z) \ R(x,x,a(y,y,z)) = (a(z,y,x) \ u) \ u
    ]]></literal>
    <justification jstring="[para(28832(a,2),41655(a,1,2))].">
      <j1 rule="para" parents="28832 41655"/>
    </justification>
  </clause>

  <clause id="41678">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(x,x,a(z,y,y))) = (a(z,y,x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(30065(a,2),41671(a,1,2))].">
      <j1 rule="para" parents="30065 41671"/>
    </justification>
  </clause>

  <clause id="41679">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ u = z * (L(z,y,x) \ a(z,z,a(y,y,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,30073,a,b,41677,a),flip(a)].">
      <j1 rule="hyper" parents="64 30073 41677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41680">
    <literal><![CDATA[
      L(x,y,L(R(z,u,w),z,a(w,u,u))) = L(x,y,a(w,u,z) \ z)
    ]]></literal>
    <justification jstring="[para(40973(a,1),41661(a,1,3))].">
      <j1 rule="para" parents="40973 41661"/>
    </justification>
  </clause>

  <clause id="41681">
    <literal><![CDATA[
      L(x,L(R(y,z,u),y,a(u,z,z)),w) = L(x,a(u,z,y) \ y,w)
    ]]></literal>
    <justification jstring="[para(40973(a,1),41662(a,1,2))].">
      <j1 rule="para" parents="40973 41662"/>
    </justification>
  </clause>

  <clause id="41682">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(x,x,a(z,y,y)) = (a(z,y,x) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,26936,a,b,41678,a)].">
      <j1 rule="hyper" parents="64 26936 41678"/>
    </justification>
  </clause>

  <clause id="41683">
    <literal><![CDATA[
      a(x,y,z) \ a(z,z,a(y,y,x)) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,38596,a,b,41679,a),flip(a)].">
      <j1 rule="hyper" parents="40 38596 41679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41684">
    <literal><![CDATA[
      a(x,y,z) \ a(y,y,a(x,z,z)) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,39758,a,b,41683,a)].">
      <j1 rule="hyper" parents="64 39758 41683"/>
    </justification>
  </clause>

  <clause id="41685">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,a(y,z,z)) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[para(40880(a,2),41683(a,1,2))].">
      <j1 rule="para" parents="40880 41683"/>
    </justification>
  </clause>

  <clause id="41686">
    <literal><![CDATA[
      a(x,y,z) \ a(x,z,a(z,y,y)) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[para(40883(a,2),41683(a,1,2))].">
      <j1 rule="para" parents="40883 41683"/>
    </justification>
  </clause>

  <clause id="41687">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) * (a(x,z,y) \ 1) = y \ L(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,31093,a,b,41686,a)].">
      <j1 rule="hyper" parents="64 31093 41686"/>
    </justification>
  </clause>

  <clause id="41688">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(x,a(y,y,x),z) = (a(z,y,x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(40922(a,2),41682(a,1,2))].">
      <j1 rule="para" parents="40922 41682"/>
    </justification>
  </clause>

  <clause id="41689">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(x,x * L(x,y,y),z) = (a(z,y,x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(11916(a,2),41688(a,1,2))].">
      <j1 rule="para" parents="11916 41688"/>
    </justification>
  </clause>

  <clause id="41690">
    <literal><![CDATA[
      R(1 / x,x,y) \ a(x,x,L(y,z,u)) = L(x,x * L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(39676(a,1),41667(a,1,2))].">
      <j1 rule="para" parents="39676 41667"/>
    </justification>
  </clause>

  <clause id="41691">
    <literal><![CDATA[
      a(x,x,y) \ R(x,x,L(y,z,u)) = L(x,x * L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,37751,a(flip),b,41690,a)].">
      <j1 rule="hyper" parents="64 37751 41690"/>
    </justification>
  </clause>

  <clause id="41692">
    <literal><![CDATA[
      (x * ((x \ L(x,y,z)) * u)) / u = a(z,y,a(u,x,x)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40865,a(flip),b,41602,a),flip(a)].">
      <j1 rule="hyper" parents="64 40865 41602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41693">
    <literal><![CDATA[
      a(x,y * L(y,z,u),y) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,36506,a(flip),b,41623,a)].">
      <j1 rule="hyper" parents="64 36506 41623"/>
    </justification>
  </clause>

  <clause id="41694">
    <literal><![CDATA[
      a(x,y,y \ L(y,z,u)) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,33570,a(flip),b,41693,a)].">
      <j1 rule="hyper" parents="64 33570 41693"/>
    </justification>
  </clause>

  <clause id="41695">
    <literal><![CDATA[
      (a(a(x,x,y),z,u) \ x) \ (a(y,x \ R(x,z,u),x) \ R(x,w,v5)) = x \ R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(41693(a,1),37382(a,1,1,1))].">
      <j1 rule="para" parents="41693 37382"/>
    </justification>
  </clause>

  <clause id="41696">
    <literal><![CDATA[
      a(x,y,y \ L(y,z,u)) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,41479,a,b,41694,a),flip(a)].">
      <j1 rule="hyper" parents="373 41479 41694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41697">
    <literal><![CDATA[
      a(x,y,y \ L(y,z,u)) = a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,40848,a(flip),b,41694,a),flip(a)].">
      <j1 rule="hyper" parents="373 40848 41694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41698">
    <literal><![CDATA[
      x \ L(x,y,y * L(y,z,u)) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,35119,a,b,41694,a)].">
      <j1 rule="hyper" parents="64 35119 41694"/>
    </justification>
  </clause>

  <clause id="41699">
    <literal><![CDATA[
      (x / y) \ (x * (y \ L(y,z,u))) = (y * (y \ L(y,z,u))) * a(a(y,y,y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,41694,a(flip),b,30032,a),flip(a)].">
      <j1 rule="hyper" parents="145 41694 30032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41700">
    <literal><![CDATA[
      a(a(x,y,L(y,z,L(y,u,w))),v5,v6) = a(x,y,y \ L(y,v5,v6))
    ]]></literal>
    <justification jstring="[para(27645(a,2),41696(a,2,1)),flip(a)].">
      <j1 rule="para" parents="27645 41696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41701">
    <literal><![CDATA[
      a(x,y,L(y,z,u) \ y) = a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,38706,a,b,41697,a)].">
      <j1 rule="hyper" parents="64 38706 41697"/>
    </justification>
  </clause>

  <clause id="41702">
    <literal><![CDATA[
      a(x,y,L(y,z,u) \ y) = a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,38630,a,b,41701,a),flip(a)].">
      <j1 rule="hyper" parents="373 38630 41701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41703">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,u,u)) = a(w,u,a(x,u,a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(34931(a,1),41702(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34931 41702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41704">
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) = x * a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,40842,a(flip),b,41698,a),flip(a)].">
      <j1 rule="hyper" parents="145 40842 41698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41705">
    <literal><![CDATA[
      L(x * L(x \ 1,y * L(y,z,u),y),w,v5) = a(a(y,y,L(x,w,v5)),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,38608,a(flip),b,41698,a)].">
      <j1 rule="hyper" parents="64 38608 41698"/>
    </justification>
  </clause>

  <clause id="41706">
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) * (x \ y) = y * a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(41698(a,1),33822(a,2,2))].">
      <j1 rule="para" parents="41698 33822"/>
    </justification>
  </clause>

  <clause id="41707">
    <literal><![CDATA[
      L(x * a(y,y,L(x,z,u)),y,y) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,40875,a,b,41704,a)].">
      <j1 rule="hyper" parents="373 40875 41704"/>
    </justification>
  </clause>

  <clause id="41708">
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) = a(u,z,a(x,y,y)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a,b,41704,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 41704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41709">
    <literal><![CDATA[
      L(x,y,y * L(y,x,z)) = L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,40888,a(flip),b,41704,a),flip(a)].">
      <j1 rule="hyper" parents="373 40888 41704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41710">
    <literal><![CDATA[
      L(x,y,y \ L(y,x,z)) = L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,5608,a,b,41709,a)].">
      <j1 rule="hyper" parents="64 5608 41709"/>
    </justification>
  </clause>

  <clause id="41711">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ x) * (x \ u)) = a(z,y,a(u,x,x)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,39562,a,b,41708,a)].">
      <j1 rule="hyper" parents="64 39562 41708"/>
    </justification>
  </clause>

  <clause id="41712">
    <literal><![CDATA[
      L(x * a(y,L(y,z,u),x),y,y) = L(x,y,y * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(39676(a,2),41707(a,1,1,2))].">
      <j1 rule="para" parents="39676 41707"/>
    </justification>
  </clause>

  <clause id="41713">
    <literal><![CDATA[
      x * ((x \ L(x,y,z)) * (L(x,y,z) \ u)) = L(u,x,x * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39987,a(flip),b,41712,a)].">
      <j1 rule="hyper" parents="64 39987 41712"/>
    </justification>
  </clause>

  <clause id="41714">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ L(u,x,x * L(x,y,z)) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,41712,a(flip),b,39986,a(flip))].">
      <j1 rule="hyper" parents="139 41712 39986"/>
    </justification>
  </clause>

  <clause id="41715">
    <literal><![CDATA[
      x \ ((x * R(y,z,u)) * (R(y,z,u) \ y)) = y * a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,39565,a,b,41706,a)].">
      <j1 rule="hyper" parents="64 39565 41706"/>
    </justification>
  </clause>

  <clause id="41716">
    <literal><![CDATA[
      L(x,y * z,y) \ L(x,x,a(z,z * y,y)) = a(y,z * y,x)
    ]]></literal>
    <justification jstring="[para(35698(a,1),41650(a,1,2))].">
      <j1 rule="para" parents="35698 41650"/>
    </justification>
  </clause>

  <clause id="41717">
    <literal><![CDATA[
      L(x,y * z,y) \ L(x,x,a(z,z * y,y)) = a(y,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,35687,a,b,41716,a),flip(a)].">
      <j1 rule="hyper" parents="373 35687 41716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41718">
    <literal><![CDATA[
      L(x,y \ z,y) = L(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,41646,a,b,41717,a)].">
      <j1 rule="hyper" parents="40 41646 41717"/>
    </justification>
  </clause>

  <clause id="41719">
    <literal><![CDATA[
      L((x \ y) \ z,x * y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(743,a,41718,a),flip(a)].">
      <j1 rule="hyper" parents="743 41718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41720">
    <literal><![CDATA[
      L(x,y \ z,y) = L(x,z * y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,29436,a,b,41718,a),flip(a)].">
      <j1 rule="hyper" parents="373 29436 41718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41721">
    <literal><![CDATA[
      x * L(y,z * x,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,41718,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="145 41718 101"/>
    </justification>
  </clause>

  <clause id="41722">
    <literal><![CDATA[
      x \ (L(y,x * z,x) * z) = (x \ z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(41718(a,1),1010(a,1,2,1))].">
      <j1 rule="para" parents="41718 1010"/>
    </justification>
  </clause>

  <clause id="41724">
    <literal><![CDATA[
      L(L(x \ 1,y * z,y),x,(y \ z) * x) = z \ (y * ((y \ z) / x))
    ]]></literal>
    <justification jstring="[para(41718(a,1),30711(a,1,1))].">
      <j1 rule="para" parents="41718 30711"/>
    </justification>
  </clause>

  <clause id="41726">
    <literal><![CDATA[
      a(L(x \ y,z * x,z),u,w) = a((x / z) \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(41718(a,1),34980(a,1,1))].">
      <j1 rule="para" parents="41718 34980"/>
    </justification>
  </clause>

  <clause id="41727">
    <literal><![CDATA[
      L((x \ y) \ z,y * x,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(743,a,41720,a),flip(a)].">
      <j1 rule="hyper" parents="743 41720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41730">
    <literal><![CDATA[
      x * L(y,x * z,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,41720,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="145 41720 101"/>
    </justification>
  </clause>

  <clause id="41734">
    <literal><![CDATA[
      a(x,y,L(z,u \ w,u)) = a(x,y,L(z,u * w,u))
    ]]></literal>
    <justification jstring="[para(41720(a,2),29739(a,1,3))].">
      <j1 rule="para" parents="41720 29739"/>
    </justification>
  </clause>

  <clause id="41737">
    <literal><![CDATA[
      L(((x * y) \ (y \ x)) * z,(y \ x) * (x * y),y \ x) = (x * y) \ ((y \ x) * z)
    ]]></literal>
    <justification jstring="[para(40283(a,1),41719(a,1,1))].">
      <j1 rule="para" parents="40283 41719"/>
    </justification>
  </clause>

  <clause id="41738">
    <literal><![CDATA[
      L(a(x \ y,z,u),x * y,x) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,40785,a(flip),b,41721,a),flip(a)].">
      <j1 rule="hyper" parents="35 40785 41721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41740">
    <literal><![CDATA[
      x * ((x \ y) * (T(y * x,x) \ z)) = y * (((y * x) * x) \ (x * z))
    ]]></literal>
    <justification jstring="[para(10979(a,1),41730(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10979 41730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41741">
    <literal><![CDATA[
      L(x,L(L(y,z * u,u),z,z),w) = L(x,z * (u * ((u \ z) * y)),w)
    ]]></literal>
    <justification jstring="[para(41730(a,1),11778(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="41730 11778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41743">
    <literal><![CDATA[
      (x \ 1) * L(y,x \ (a(z,x,u) / x),x \ a(z,x,u)) = (x \ a(z,x,u)) * (((x \ a(z,x,u)) \ (x \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(35768(a,1),41730(a,1,2,2))].">
      <j1 rule="para" parents="35768 41730"/>
    </justification>
  </clause>

  <clause id="41744">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ (L(v5,R(z,u,w) * v6,R(z,u,w)) * v6)) = a(x,y,(R(z,u,w) \ v6) * T(v5,v6))
    ]]></literal>
    <justification jstring="[para(41722(a,1),31334(a,1,3)),flip(a)].">
      <j1 rule="para" parents="41722 31334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41745">
    <literal><![CDATA[
      a(L(x \ y,z * x,z),u,w) = a((z \ x) \ (z \ y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32386,a(flip),b,41726,a),flip(a)].">
      <j1 rule="hyper" parents="373 32386 41726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41746">
    <literal><![CDATA[
      a(L((x \ y) \ z,y,x),u,w) = a((x \ (x \ y)) \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),41745(a,1,1,2))].">
      <j1 rule="para" parents="10 41745"/>
    </justification>
  </clause>

  <clause id="41747">
    <literal><![CDATA[
      a(L((x \ y) \ z,y,x),u,w) = a(L(y,x,x) \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,33711,a(flip),b,41746,a),flip(a)].">
      <j1 rule="hyper" parents="373 33711 41746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41748">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (a(y,y,a(x,x,z)) * x) = (a(z,y,x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(41621(a,1),41689(a,1,2))].">
      <j1 rule="para" parents="41621 41689"/>
    </justification>
  </clause>

  <clause id="41749">
    <literal><![CDATA[
      x \ ((y \ L(y,z,u)) * (x * y)) = a(u,z,a(x,y,y)) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,36235,a(flip),b,41692,a)].">
      <j1 rule="hyper" parents="64 36235 41692"/>
    </justification>
  </clause>

  <clause id="41750">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,z,u) \ y) = a(u,z,a(x,y,y)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,38599,a(flip),b,41711,a)].">
      <j1 rule="hyper" parents="64 38599 41711"/>
    </justification>
  </clause>

  <clause id="41751">
    <literal><![CDATA[
      L(x,L(y,z,u),L(y,z,u) \ y) = a(a(y,y,x),z,u) * x
    ]]></literal>
    <justification jstring="[para(40842(a,2),41750(a,2,1))].">
      <j1 rule="para" parents="40842 41750"/>
    </justification>
  </clause>

  <clause id="41752">
    <literal><![CDATA[
      x * L(y,L(z,u,w),L(z,u,w) \ z) = x * (y * a(a(z,z,y),u,w))
    ]]></literal>
    <justification jstring="[para(41751(a,2),23169(a,1,2))].">
      <j1 rule="para" parents="41751 23169"/>
    </justification>
  </clause>

  <clause id="41753">
    <literal><![CDATA[
      x * ((x \ L(x,y,z)) * (L(x,y,z) \ u)) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,5608,a,b,41713,a),flip(a)].">
      <j1 rule="hyper" parents="373 5608 41713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41754">
    <literal><![CDATA[
      a(x,R(y,z,u),R(y,z,u) \ y) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,29953,a(flip),b,41715,a(flip))].">
      <j1 rule="hyper" parents="35 29953 41715"/>
    </justification>
  </clause>

  <clause id="41755">
    <literal><![CDATA[
      a(L(R(x,y,z) \ x,u,x * L(x,y,z)),R(x,y,z),w) = (x * a(a(x,x,w),y,z)) \ x
    ]]></literal>
    <justification jstring="[para(41715(a,1),37357(a,2,1))].">
      <j1 rule="para" parents="41715 37357"/>
    </justification>
  </clause>

  <clause id="41756">
    <literal><![CDATA[
      a(x,R(y,z,u),L(y,z,u) \ y) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31334,a(flip),b,41754,a)].">
      <j1 rule="hyper" parents="64 31334 41754"/>
    </justification>
  </clause>

  <clause id="41757">
    <literal><![CDATA[
      a(x,R(y,z,u),y \ L(y,z,u)) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,38706,a(flip),b,41756,a)].">
      <j1 rule="hyper" parents="64 38706 41756"/>
    </justification>
  </clause>

  <clause id="41758">
    <literal><![CDATA[
      a(x,L(y,z,u),y \ L(y,z,u)) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32197,a(flip),b,41757,a)].">
      <j1 rule="hyper" parents="64 32197 41757"/>
    </justification>
  </clause>

  <clause id="41759">
    <literal><![CDATA[
      L((x / (1 / y)) \ ((x / (1 / y)) / z),y * x,y) = x \ (y * ((y \ x) / z))
    ]]></literal>
    <justification jstring="[hyper(64,a,31412,a(flip),b,41724,a)].">
      <j1 rule="hyper" parents="64 31412 41724"/>
    </justification>
  </clause>

  <clause id="41760">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (a(y,y,a(z,x,x)) \ x) = (a(z,y,x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(41506(a,2),41748(a,1,2))].">
      <j1 rule="para" parents="41506 41748"/>
    </justification>
  </clause>

  <clause id="41761">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * (L(x,y,z) \ u)) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33159,a,b,41753,a)].">
      <j1 rule="hyper" parents="64 33159 41753"/>
    </justification>
  </clause>

  <clause id="41762">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (a(y,a(x,x,y),z) \ x) = (a(z,y,x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(40890(a,2),41760(a,1,2,1))].">
      <j1 rule="para" parents="40890 41760"/>
    </justification>
  </clause>

  <clause id="41763">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (a(a(x,x,y),y,z) \ x) = (a(z,y,x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(32878(a,2),41762(a,1,2,1))].">
      <j1 rule="para" parents="32878 41762"/>
    </justification>
  </clause>

  <clause id="41764">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (a(y,x,x \ L(x,y,z)) \ x) = (a(z,y,x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(41694(a,2),41763(a,1,2,1))].">
      <j1 rule="para" parents="41694 41763"/>
    </justification>
  </clause>

  <clause id="41765">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(x * R(x,y,z),x,u) = R(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(2664(a,1),41632(a,1,2))].">
      <j1 rule="para" parents="2664 41632"/>
    </justification>
  </clause>

  <clause id="41766">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(x * L(x,y,z),x,u) = R(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(5609(a,1),41634(a,1,2))].">
      <j1 rule="para" parents="5609 41634"/>
    </justification>
  </clause>

  <clause id="41767">
    <literal><![CDATA[
      x \ R(x,L(y,z,u),a(w,v5,y)) = a(x,L(y,z,u),a(w,v5,y))
    ]]></literal>
    <justification jstring="[para(621(a,1),41635(a,1,1))].">
      <j1 rule="para" parents="621 41635"/>
    </justification>
  </clause>

  <clause id="41768">
    <literal><![CDATA[
      x \ L(x,L(y,z,u),a(w,v5,y)) = a(x,L(y,z,u),a(w,v5,y))
    ]]></literal>
    <justification jstring="[para(28832(a,1),41767(a,1,2))].">
      <j1 rule="para" parents="28832 41767"/>
    </justification>
  </clause>

  <clause id="41769">
    <literal><![CDATA[
      x \ R(x,y,L(a(y,z,u),w,v5)) = a(x,y,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(621(a,1),41638(a,1,1))].">
      <j1 rule="para" parents="621 41638"/>
    </justification>
  </clause>

  <clause id="41770">
    <literal><![CDATA[
      x \ L(x,y,L(a(y,z,u),w,v5)) = a(x,y,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(40095(a,1),41769(a,1,2))].">
      <j1 rule="para" parents="40095 41769"/>
    </justification>
  </clause>

  <clause id="41772">
    <literal><![CDATA[
      (x / L(x,y,z)) * (L(x,y,z) * u) = x * (u * a(a(x,x,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(11083,a,41752,a)].">
      <j1 rule="hyper" parents="11083 41752"/>
    </justification>
  </clause>

  <clause id="41773">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) * u) = x * (u * a(a(x,x,u),y,z))
    ]]></literal>
    <justification jstring="[para(5558(a,1),41772(a,1,1))].">
      <j1 rule="para" parents="5558 41772"/>
    </justification>
  </clause>

  <clause id="41774">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) \ x) * u) = x * (u * a(a(x,x,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,36170,a(flip),b,41773,a)].">
      <j1 rule="hyper" parents="64 36170 41773"/>
    </justification>
  </clause>

  <clause id="41775">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(x * L(x,y,z),x,u) = R(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(34635(a,1),41765(a,1,2))].">
      <j1 rule="para" parents="34635 41765"/>
    </justification>
  </clause>

  <clause id="41776">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(a(u,x,x),y,z) = R(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(41599(a,1),41766(a,1,2))].">
      <j1 rule="para" parents="41599 41766"/>
    </justification>
  </clause>

  <clause id="41777">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(a(u,x,x),y,z) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,35109,a(flip),b,41776,a),flip(a)].">
      <j1 rule="hyper" parents="373 35109 41776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41778">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(a(u,x,x),y,z) = R(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(41599(a,1),41775(a,1,2))].">
      <j1 rule="para" parents="41599 41775"/>
    </justification>
  </clause>

  <clause id="41779">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(a(u,x,x),y,z) = L(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,28821,a(flip),b,41778,a),flip(a)].">
      <j1 rule="hyper" parents="373 28821 41778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41780">
    <literal><![CDATA[
      (x \ R(x,y,z)) * a(z,y,a(u,x,x)) = L(x \ R(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[para(40838(a,1),41779(a,1,2))].">
      <j1 rule="para" parents="40838 41779"/>
    </justification>
  </clause>

  <clause id="41781">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) \ R(x,z,y) = L(x \ R(x,z,y),x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40891,a(flip),b,41780,a)].">
      <j1 rule="hyper" parents="64 40891 41780"/>
    </justification>
  </clause>

  <clause id="41782">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41628,a(flip),b,41781,a)].">
      <j1 rule="hyper" parents="64 41628 41781"/>
    </justification>
  </clause>

  <clause id="41783">
    <literal><![CDATA[
      a(L(x,y,z),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,34955,a,b,41782,a),flip(a)].">
      <j1 rule="hyper" parents="373 34955 41782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41784">
    <literal><![CDATA[
      a(x,y,z) = y \ ((y / x) * R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,39238,a(flip),b,41782,a),flip(a)].">
      <j1 rule="hyper" parents="373 39238 41782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41785">
    <literal><![CDATA[
      a(L(L(x,y,y),y,z),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,38085,a(flip),b,41782,a)].">
      <j1 rule="hyper" parents="373 38085 41782"/>
    </justification>
  </clause>

  <clause id="41786">
    <literal><![CDATA[
      x \ (y * R(y \ x,y,z)) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,630,a(flip),b,41782,a)].">
      <j1 rule="hyper" parents="373 630 41782"/>
    </justification>
  </clause>

  <clause id="41788">
    <literal><![CDATA[
      (x / y) * R(y,y \ x,z) = x * a(y,y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,41782,a,b,11070,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 41782 11070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41789">
    <literal><![CDATA[
      (x * y) * a(y,x,z) = x * R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,41782,a,b,102,a(flip))].">
      <j1 rule="hyper" parents="145 41782 102"/>
    </justification>
  </clause>

  <clause id="41790">
    <literal><![CDATA[
      L(a(x,y,z),x,y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36303,a,41782,a(flip))].">
      <j1 rule="hyper" parents="36303 41782"/>
    </justification>
  </clause>

  <clause id="41791">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,w)),x,y) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(28832(a,1),41782(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="28832 41782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41792">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,u),w),x,a(y,z,u)) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(31802(a,1),41782(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="31802 41782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41793">
    <literal><![CDATA[
      ((x * y) * z) * a(x,y,z) = (R(x,y,z) * y) * z
    ]]></literal>
    <justification jstring="[para(41782(a,2),33416(a,1,2))].">
      <j1 rule="para" parents="41782 33416"/>
    </justification>
  </clause>

  <clause id="41794">
    <literal><![CDATA[
      ((x * y) * z) * a(y,x,z) = (x * R(y,x,z)) * z
    ]]></literal>
    <justification jstring="[para(41782(a,2),33417(a,1,2))].">
      <j1 rule="para" parents="41782 33417"/>
    </justification>
  </clause>

  <clause id="41795">
    <literal><![CDATA[
      L(x \ L(x,y,z * L(z,u,w)),x,y) = a(x,y,z \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(38758(a,1),41782(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="38758 41782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41796">
    <literal><![CDATA[
      R(x,y,z) * (x \ y) = a(x,y,z) * y
    ]]></literal>
    <justification jstring="[para(41782(a,2),39239(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41782 39239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41797">
    <literal><![CDATA[
      L(a(x * L(x,y,z),u,u) \ 1,x,y) = a(u,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(41782(a,2),39689(a,2,3))].">
      <j1 rule="para" parents="41782 39689"/>
    </justification>
  </clause>

  <clause id="41798">
    <literal><![CDATA[
      a(L(L(x,y,z) \ x,x,u),x,u) = a(a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,41603,a(flip),b,41783,a),flip(a)].">
      <j1 rule="hyper" parents="373 41603 41783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41801">
    <literal><![CDATA[
      a(L(L(x,y,z),u,w),x,v5) = L(a(x,L(x,y,z),v5),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,39414,a(flip),b,41783,a),flip(a)].">
      <j1 rule="hyper" parents="64 39414 41783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41802">
    <literal><![CDATA[
      a(L(x,x,y),y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,36781,a(flip),b,41783,a),flip(a)].">
      <j1 rule="hyper" parents="64 36781 41783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41803">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,36350,a(flip),b,41783,a),flip(a)].">
      <j1 rule="hyper" parents="64 36350 41783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41804">
    <literal><![CDATA[
      a((x * y) \ z,x,y) = a(x \ (y \ z),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,34977,a(flip),b,41783,a),flip(a)].">
      <j1 rule="hyper" parents="64 34977 41783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41805">
    <literal><![CDATA[
      a((x * y) \ z,y,x) = a(y \ (x \ z),y,x)
    ]]></literal>
    <justification jstring="[para(346(a,1),41783(a,1,1))].">
      <j1 rule="para" parents="346 41783"/>
    </justification>
  </clause>

  <clause id="41806">
    <literal><![CDATA[
      a(x,y,z) * (y * x) = y * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(41783(a,1),33306(a,1,1))].">
      <j1 rule="para" parents="41783 33306"/>
    </justification>
  </clause>

  <clause id="41807">
    <literal><![CDATA[
      x * (a(x,y,z) * y) = R(x,y,z) * y
    ]]></literal>
    <justification jstring="[para(41783(a,1),33396(a,1,2,1))].">
      <j1 rule="para" parents="41783 33396"/>
    </justification>
  </clause>

  <clause id="41808">
    <literal><![CDATA[
      x * (y * a(x,y,z)) = R(x,y,z) * y
    ]]></literal>
    <justification jstring="[para(41783(a,1),33420(a,1,2,2))].">
      <j1 rule="para" parents="41783 33420"/>
    </justification>
  </clause>

  <clause id="41810">
    <literal><![CDATA[
      x * (R(x,y,z) \ y) = a(x,y,z) \ y
    ]]></literal>
    <justification jstring="[para(41783(a,1),33469(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41783 33469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41811">
    <literal><![CDATA[
      a(x,y,(z / u) * L(u,z,w)) = a(x,y,a(u,z,w) * z)
    ]]></literal>
    <justification jstring="[para(41783(a,1),33426(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="41783 33426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41812">
    <literal><![CDATA[
      R(x,y,z * (L(z,u,w) \ u)) = R(x,y,a(z,u,w) \ u)
    ]]></literal>
    <justification jstring="[para(41783(a,1),35627(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="41783 35627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41813">
    <literal><![CDATA[
      L(a(x,y,z),y * x,y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(41783(a,1),35769(a,1,1))].">
      <j1 rule="para" parents="41783 35769"/>
    </justification>
  </clause>

  <clause id="41814">
    <literal><![CDATA[
      L(x,y,z \ (L(u,z,w) * (u \ z))) = L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[para(41783(a,1),38304(a,1,3)),flip(a)].">
      <j1 rule="para" parents="41783 38304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41815">
    <literal><![CDATA[
      R(x,(L(y,z,u) \ z) * y,w) = R(x,a(y,z,u) * z,w)
    ]]></literal>
    <justification jstring="[para(41783(a,1),39576(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="41783 39576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41816">
    <literal><![CDATA[
      L(x,y * (L(y,z,u) \ z),w) = L(x,z * a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(41783(a,1),39592(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="41783 39592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41817">
    <literal><![CDATA[
      x * a(x,(y \ z) * z,y) = R(x,(y \ z) * z,y)
    ]]></literal>
    <justification jstring="[hyper(145,a,33481,a(flip),b,41790,a(flip))].">
      <j1 rule="hyper" parents="145 33481 41790"/>
    </justification>
  </clause>

  <clause id="41818">
    <literal><![CDATA[
      L(x,y,L(z,z,y)) \ L(x,x,a(L(z,z,y),y,y)) = z \ R(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,41642,a,b,41802,a)].">
      <j1 rule="hyper" parents="64 41642 41802"/>
    </justification>
  </clause>

  <clause id="41819">
    <literal><![CDATA[
      a(x,y,z) * a(y,x,a(x,y,z)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40776,a,b,41802,a)].">
      <j1 rule="hyper" parents="64 40776 41802"/>
    </justification>
  </clause>

  <clause id="41820">
    <literal><![CDATA[
      R(x,y,z) = (y / x) \ (y * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(41784(a,2),73(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="41784 73"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41821">
    <literal><![CDATA[
      a(L(x,y,y),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41783,a(flip),b,41785,a)].">
      <j1 rule="hyper" parents="64 41783 41785"/>
    </justification>
  </clause>

  <clause id="41822">
    <literal><![CDATA[
      a(x \ y,x,z) = a(x * y,x,z)
    ]]></literal>
    <justification jstring="[hyper(2694,a,41821,a),flip(a)].">
      <j1 rule="hyper" parents="2694 41821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41823">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),L(x,y,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35770,a,b,41821,a),flip(a)].">
      <j1 rule="hyper" parents="64 35770 41821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41826">
    <literal><![CDATA[
      a(a(x,y,z),u,u * x) = a(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,41378,a(flip),b,41821,a),flip(a)].">
      <j1 rule="hyper" parents="64 41378 41821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41827">
    <literal><![CDATA[
      a(x \ y,x,z) = a(y * x,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30383,a(flip),b,41821,a)].">
      <j1 rule="hyper" parents="64 30383 41821"/>
    </justification>
  </clause>

  <clause id="41828">
    <literal><![CDATA[
      a((1 / (x / y)) * x,x * y,z) = a(y,x * y,z)
    ]]></literal>
    <justification jstring="[para(34539(a,1),41821(a,1,1))].">
      <j1 rule="para" parents="34539 41821"/>
    </justification>
  </clause>

  <clause id="41830">
    <literal><![CDATA[
      a(x * (y * L(y,z,u)),x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,39924,a(flip),b,41822,a),flip(a)].">
      <j1 rule="hyper" parents="64 39924 41822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41831">
    <literal><![CDATA[
      (x / y) \ (x * z) = (y * z) * a(y * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,41822,a(flip),b,30032,a),flip(a)].">
      <j1 rule="hyper" parents="145 41822 30032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41833">
    <literal><![CDATA[
      a(x * (y \ z),x,y) \ z = ((z / y) / x) * (x * y)
    ]]></literal>
    <justification jstring="[para(41822(a,1),32458(a,1,1))].">
      <j1 rule="para" parents="41822 32458"/>
    </justification>
  </clause>

  <clause id="41834">
    <literal><![CDATA[
      a(x * y,x,z) \ y = ((y / x) * (x * z)) / z
    ]]></literal>
    <justification jstring="[para(41822(a,1),33423(a,1,1))].">
      <j1 rule="para" parents="41822 33423"/>
    </justification>
  </clause>

  <clause id="41835">
    <literal><![CDATA[
      a((x \ y) * (L(x,x,z) \ y),x \ y,u) = a(a(z,x,x),x \ y,u)
    ]]></literal>
    <justification jstring="[para(37571(a,1),41822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37571 41822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41836">
    <literal><![CDATA[
      L(x,a(y \ z,y,u),w) = L(x,a(u,y,z * y),w)
    ]]></literal>
    <justification jstring="[para(41822(a,2),41408(a,1,2))].">
      <j1 rule="para" parents="41822 41408"/>
    </justification>
  </clause>

  <clause id="41837">
    <literal><![CDATA[
      a(a(x \ y,x,z),u,w) = a(a(z,x,x * y),u,w)
    ]]></literal>
    <justification jstring="[para(41822(a,2),41479(a,1,1))].">
      <j1 rule="para" parents="41822 41479"/>
    </justification>
  </clause>

  <clause id="41838">
    <literal><![CDATA[
      a(x \ y,(x \ y) * y,z) = a(y * x,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35709,a,b,41827,a)].">
      <j1 rule="hyper" parents="64 35709 41827"/>
    </justification>
  </clause>

  <clause id="41840">
    <literal><![CDATA[
      L((x * y) * a(z * x,x,y),x \ z,x \ z) = (x \ z) * ((((x \ z) \ 1) * x) * y)
    ]]></literal>
    <justification jstring="[para(41827(a,1),30440(a,1,1,2))].">
      <j1 rule="para" parents="41827 30440"/>
    </justification>
  </clause>

  <clause id="41841">
    <literal><![CDATA[
      a(x * y,y,z) \ x = ((x / y) * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(41827(a,1),33423(a,1,1))].">
      <j1 rule="para" parents="41827 33423"/>
    </justification>
  </clause>

  <clause id="41842">
    <literal><![CDATA[
      a((x * y) \ ((y \ z) \ (x * z)),u,w) = a(a(z * y,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(41827(a,1),35563(a,2,1))].">
      <j1 rule="para" parents="41827 35563"/>
    </justification>
  </clause>

  <clause id="41843">
    <literal><![CDATA[
      L(a(x * y,y,z),z,x) = L(z,y,y \ x) \ z
    ]]></literal>
    <justification jstring="[para(41827(a,1),40725(a,1,1))].">
      <j1 rule="para" parents="41827 40725"/>
    </justification>
  </clause>

  <clause id="41844">
    <literal><![CDATA[
      x * (L(x,y,z) \ (y * z)) = y * R(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(34860,a,41789,a)].">
      <j1 rule="hyper" parents="34860 41789"/>
    </justification>
  </clause>

  <clause id="41845">
    <literal><![CDATA[
      (x \ y) \ (x \ R(y,x,z)) = x \ (a(y,x,z) * x)
    ]]></literal>
    <justification jstring="[para(41796(a,1),39499(a,2,2))].">
      <j1 rule="para" parents="41796 39499"/>
    </justification>
  </clause>

  <clause id="41847">
    <literal><![CDATA[
      a(a(x,y,z * u),w,v5) = a(v5,w,a(x,y,u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27752,a,b,41803,a),flip(a)].">
      <j1 rule="hyper" parents="373 27752 41803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41848">
    <literal><![CDATA[
      a(a(x * y,z,u),w,v5) = a(v5,w,a(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,26881,a,b,41803,a),flip(a)].">
      <j1 rule="hyper" parents="373 26881 41803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41849">
    <literal><![CDATA[
      a(a(x,y,z),u,L(w,w,u)) = w \ R(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,41802,a(flip),b,41803,a),flip(a)].">
      <j1 rule="hyper" parents="373 41802 41803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41850">
    <literal><![CDATA[
      a(a(x,y,L(y,z,u)),w,v5) = a(v5,w,a(y,y,L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,39812,a(flip),b,41803,a),flip(a)].">
      <j1 rule="hyper" parents="373 39812 41803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41851">
    <literal><![CDATA[
      a(a(x,y,z),u,L(L(w,w,v5),v5 * w,v6)) = a((v6 * (v5 * w)) \ (v6 * v5),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,34774,a(flip),b,41803,a),flip(a)].">
      <j1 rule="hyper" parents="373 34774 41803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41852">
    <literal><![CDATA[
      a(a(x,y,z),u,w \ 1) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,2653,a(flip),b,41803,a),flip(a)].">
      <j1 rule="hyper" parents="373 2653 41803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41853">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,41803,a,b,23174,a),flip(a)].">
      <j1 rule="hyper" parents="145 41803 23174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41854">
    <literal><![CDATA[
      x * a(a(y,z,u),w,v5) = x * a(v5,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,41803,a,b,9,a)].">
      <j1 rule="hyper" parents="145 41803 9"/>
    </justification>
  </clause>

  <clause id="41855">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * v5 = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(144,a,41803,a,b,23161,a)].">
      <j1 rule="hyper" parents="144 41803 23161"/>
    </justification>
  </clause>

  <clause id="41856">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * v5 = a(w,u,a(x,y,z)) * v5
    ]]></literal>
    <justification jstring="[hyper(144,a,41803,a,b,11,a)].">
      <j1 rule="hyper" parents="144 41803 11"/>
    </justification>
  </clause>

  <clause id="41858">
    <literal><![CDATA[
      a(a(x,y * z,u),w,v5) = a(v5,w,a(u,z * y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41482,a,b,41803,a)].">
      <j1 rule="hyper" parents="64 41482 41803"/>
    </justification>
  </clause>

  <clause id="41859">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41479,a,b,41803,a)].">
      <j1 rule="hyper" parents="64 41479 41803"/>
    </justification>
  </clause>

  <clause id="41860">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 * w))) = a(a(L(v5,w,w),u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,41494,a(flip),b,41803,a),flip(a)].">
      <j1 rule="hyper" parents="64 41494 41803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41861">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (w * v5))) = a(a(L(v5,w,w),u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,41492,a(flip),b,41803,a),flip(a)].">
      <j1 rule="hyper" parents="64 41492 41803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41862">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ (v5 * v5))) = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,34586,a(flip),b,41803,a),flip(a)].">
      <j1 rule="hyper" parents="64 34586 41803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41863">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ 1)) = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,34584,a(flip),b,41803,a),flip(a)].">
      <j1 rule="hyper" parents="64 34584 41803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41864">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 \ 1))) = a(a(z,u,v5 * w),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,34583,a(flip),b,41803,a),flip(a)].">
      <j1 rule="hyper" parents="64 34583 41803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41867">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),y,a(z,u,w)) = L(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(41803(a,1),34924(a,1,1,2))].">
      <j1 rule="para" parents="41803 34924"/>
    </justification>
  </clause>

  <clause id="41868">
    <literal><![CDATA[
      x * a(a(y,z,u),w,v5) = x * a(v5,w,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(41803(a,1),41489(a,1,2)),flip(a)].">
      <j1 rule="para" parents="41803 41489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41869">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * v5 = a(w,u,a(z,y,x)) * v5
    ]]></literal>
    <justification jstring="[para(41803(a,1),41490(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41803 41490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41871">
    <literal><![CDATA[
      a(a(x,y,z),L(x,u,w),v5) * a(x,y,z) = R(a(x,y,z),L(x,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(36,a,30012,a,b,41807,a(flip))].">
      <j1 rule="hyper" parents="36 30012 41807"/>
    </justification>
  </clause>

  <clause id="41872">
    <literal><![CDATA[
      ((x \ R(x,y,z)) / u) * (a((x \ R(x,y,z)) / u,u,x) * u) = (R(x,y,z) / (u * x)) * u
    ]]></literal>
    <justification jstring="[para(2078(a,1),41807(a,2,1))].">
      <j1 rule="para" parents="2078 41807"/>
    </justification>
  </clause>

  <clause id="41874">
    <literal><![CDATA[
      x * (L(x,y,z) \ (z * y)) = R(z,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,33485,a,b,41808,a)].">
      <j1 rule="hyper" parents="64 33485 41808"/>
    </justification>
  </clause>

  <clause id="41875">
    <literal><![CDATA[
      (x * a(y,x,z)) * K(y,x * a(y,x,z)) = (R(y,x,z) * x) / y
    ]]></literal>
    <justification jstring="[hyper(142,a,41808,a(flip),b,5722,a),flip(a)].">
      <j1 rule="hyper" parents="142 41808 5722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41877">
    <literal><![CDATA[
      x * (y * a(a(z,u,w),y,x)) = R(x,y,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(41803(a,2),41808(a,1,2,2))].">
      <j1 rule="para" parents="41803 41808"/>
    </justification>
  </clause>

  <clause id="41878">
    <literal><![CDATA[
      L(x,y * L(R(z,u,w) \ u,z,z),v5) = L(x,y * (z * (a(z,u,w) \ u)),v5)
    ]]></literal>
    <justification jstring="[para(41810(a,1),29717(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="41810 29717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41879">
    <literal><![CDATA[
      a(a(x,y,z),u,w * v5) = a(v5 * w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(27453,a,41859,a)].">
      <j1 rule="hyper" parents="27453 41859"/>
    </justification>
  </clause>

  <clause id="41881">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(a(w,u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,41859,a,b,23174,a),flip(a)].">
      <j1 rule="hyper" parents="145 41859 23174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41883">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41803,a(flip),b,41859,a)].">
      <j1 rule="hyper" parents="64 41803 41859"/>
    </justification>
  </clause>

  <clause id="41884">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ (a(w,u,a(z,y,x)) * v5) = v5
    ]]></literal>
    <justification jstring="[hyper(143,a,41859,a(flip),b,79,a),flip(a)].">
      <j1 rule="hyper" parents="143 41859 79"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41885">
    <literal><![CDATA[
      R(a(x,y,a(z,u,w)),v5,v6) = L(a(a(w,u,z),y,x),v5,v6)
    ]]></literal>
    <justification jstring="[para(41859(a,1),28787(a,1,1))].">
      <j1 rule="para" parents="41859 28787"/>
    </justification>
  </clause>

  <clause id="41888">
    <literal><![CDATA[
      L(a(a(x,y,z),u,w) \ v5,w,a(w,u,a(z,y,x))) = w * ((a(w,u,a(z,y,x)) * w) \ v5)
    ]]></literal>
    <justification jstring="[para(41859(a,2),39275(a,1,1,1))].">
      <j1 rule="para" parents="41859 39275"/>
    </justification>
  </clause>

  <clause id="41890">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(y * x,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(26847,a,41883,a)].">
      <j1 rule="hyper" parents="26847 41883"/>
    </justification>
  </clause>

  <clause id="41895">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,v6)) = a(x,y,a(v6,v5,z * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,32521,a,b,41883,a)].">
      <j1 rule="hyper" parents="373 32521 41883"/>
    </justification>
  </clause>

  <clause id="41896">
    <literal><![CDATA[
      a(x,y,a((z * u) * w,v5,v6)) = a(x,y,a(v6,v5,w * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,32429,a,b,41883,a)].">
      <j1 rule="hyper" parents="373 32429 41883"/>
    </justification>
  </clause>

  <clause id="41897">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) = a(x,y,a(v5,w,u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27752,a,b,41883,a),flip(a)].">
      <j1 rule="hyper" parents="373 27752 41883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41898">
    <literal><![CDATA[
      x \ (x * a(y,z,a(u,w,v5))) = a(y,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,9,a,b,41883,a)].">
      <j1 rule="hyper" parents="373 9 41883"/>
    </justification>
  </clause>

  <clause id="41899">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,v6)) = a(x,y,a(v6,v5,(w * u) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,32429,a(flip),b,41883,a)].">
      <j1 rule="hyper" parents="373 32429 41883"/>
    </justification>
  </clause>

  <clause id="41900">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,41883,a,b,23174,a),flip(a)].">
      <j1 rule="hyper" parents="145 41883 23174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41901">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) = x * a(y,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,41883,a,b,9,a)].">
      <j1 rule="hyper" parents="145 41883 9"/>
    </justification>
  </clause>

  <clause id="41902">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = a(x,y,a(w,u,z)) * v5
    ]]></literal>
    <justification jstring="[hyper(144,a,41883,a,b,11,a)].">
      <j1 rule="hyper" parents="144 41883 11"/>
    </justification>
  </clause>

  <clause id="41906">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * (v5 \ 1)) * v6)) = a(x,y,a((v5 * w) * v6,u,z))
    ]]></literal>
    <justification jstring="[para(32509(a,1),41883(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32509 41883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41907">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 \ (v6 \ 1)))) = a(x,y,a((v5 \ v6) * w,u,z))
    ]]></literal>
    <justification jstring="[para(32689(a,1),41883(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32689 41883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41908">
    <literal><![CDATA[
      a(x,y,a(z,u,w * ((v5 \ 1) \ v6))) = a(x,y,a((v5 \ v6) * w,u,z))
    ]]></literal>
    <justification jstring="[para(32810(a,1),41883(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32810 41883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41909">
    <literal><![CDATA[
      a(x,y,a(z,u,L(L(w,w,v5),v5,v5))) = a(x,y,a((w \ v5) * v5,u,z))
    ]]></literal>
    <justification jstring="[para(32816(a,1),41883(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32816 41883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41910">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),a(w,u,z),y) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(41883(a,1),34184(a,1,1,2))].">
      <j1 rule="para" parents="41883 34184"/>
    </justification>
  </clause>

  <clause id="41911">
    <literal><![CDATA[
      a(x,y,a(z * u,u,w)) = a(x,y,a(w,u,u \ z))
    ]]></literal>
    <justification jstring="[para(41827(a,1),41883(a,1,3))].">
      <j1 rule="para" parents="41827 41883"/>
    </justification>
  </clause>

  <clause id="41912">
    <literal><![CDATA[
      L(a(x,y,z),x * y,y) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29572,a,41813,a)].">
      <j1 rule="hyper" parents="29572 41813"/>
    </justification>
  </clause>

  <clause id="41913">
    <literal><![CDATA[
      a(x * (y * ((z * (1 / y)) \ z)),x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[para(246(a,1),41830(a,1,1,2,2))].">
      <j1 rule="para" parents="246 41830"/>
    </justification>
  </clause>

  <clause id="41914">
    <literal><![CDATA[
      x \ (y * R(y \ x,y,z)) = a(x * y,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,41827,a(flip),b,41786,a),flip(a)].">
      <j1 rule="hyper" parents="373 41827 41786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41915">
    <literal><![CDATA[
      a((x * y) \ z,x,y) = a((y \ z) * x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,41827,a(flip),b,41804,a),flip(a)].">
      <j1 rule="hyper" parents="373 41827 41804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41916">
    <literal><![CDATA[
      a((x * y) \ z,y,x) = a((x \ z) * y,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,41827,a(flip),b,41805,a),flip(a)].">
      <j1 rule="hyper" parents="373 41827 41805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41917">
    <literal><![CDATA[
      a(x \ (y \ (z \ (y * x))),x,y) = z \ R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,28073,a(flip),b,41805,a),flip(a)].">
      <j1 rule="hyper" parents="64 28073 41805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41918">
    <literal><![CDATA[
      a(x * y,x,a(z,u,y)) = a(a(y,u,z),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,41859,a(flip),b,41826,a)].">
      <j1 rule="hyper" parents="64 41859 41826"/>
    </justification>
  </clause>

  <clause id="41919">
    <literal><![CDATA[
      (a(x,y,z) * (u * (u * x))) / (u * x) = a(x,y,z) * (a(a(x,y,z),u,u) \ u)
    ]]></literal>
    <justification jstring="[para(41826(a,1),33320(a,2,2,1))].">
      <j1 rule="para" parents="41826 33320"/>
    </justification>
  </clause>

  <clause id="41920">
    <literal><![CDATA[
      L(x,y,z) = (y * R(z,y,x)) \ ((y * z) * x)
    ]]></literal>
    <justification jstring="[para(41844(a,1),24847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41844 24847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41921">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w) \ (u * w),z,z) * v5) = L(x,y,v5 * ((u * R(w,u,z)) * z))
    ]]></literal>
    <justification jstring="[para(41844(a,1),29154(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="41844 29154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41923">
    <literal><![CDATA[
      L(x,y,z) = (R(z,y,x) * y) \ ((z * y) * x)
    ]]></literal>
    <justification jstring="[para(41874(a,1),24847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41874 24847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41924">
    <literal><![CDATA[
      a((x \ y) * y,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,28060,a(flip),b,41914,a),flip(a)].">
      <j1 rule="hyper" parents="64 28060 41914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41925">
    <literal><![CDATA[
      (x \ y) * a(x * y,y,z) = R(x \ y,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,41914,a(flip),b,2744,a)].">
      <j1 rule="hyper" parents="145 41914 2744"/>
    </justification>
  </clause>

  <clause id="41926">
    <literal><![CDATA[
      R(x,y,z) = a((x \ y) * y,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(23776,a,41924,a),flip(a)].">
      <j1 rule="hyper" parents="23776 41924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41927">
    <literal><![CDATA[
      R(x,y,z) = x * a(y * (x \ y),y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,26787,a,b,41924,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 26787 41924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41929">
    <literal><![CDATA[
      a((x \ K(y,y \ 1)) * (y * ((x \ R(x,z,u)) / y)),y * ((x \ R(x,z,u)) / y),w) * R(x,z,u) = R(R(x,z,u),y * ((x \ R(x,z,u)) / y),w)
    ]]></literal>
    <justification jstring="[para(28878(a,1),41926(a,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="28878 41926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41931">
    <literal><![CDATA[
      a(x,x,y) * a((z / (x \ 1)) * (z / R(x \ 1,x,y)),z / (x \ 1),u) = R(a(x,x,y),z / (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(37609(a,1),41927(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="37609 41927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41932">
    <literal><![CDATA[
      a(x * (y \ (z \ y)),x,a(u,z,z \ 1)) = a(a(y \ (z \ y),z,u),x,x)
    ]]></literal>
    <justification jstring="[para(38985(a,1),41918(a,1,3))].">
      <j1 rule="para" parents="38985 41918"/>
    </justification>
  </clause>

  <clause id="41933">
    <literal><![CDATA[
      L(x,y,L(z,y,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29210,a(flip),b,41920,a)].">
      <j1 rule="hyper" parents="373 29210 41920"/>
    </justification>
  </clause>

  <clause id="41936">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = L(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,34235,a(flip),b,41933,a),flip(a)].">
      <j1 rule="hyper" parents="64 34235 41933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41937">
    <literal><![CDATA[
      L(x,y,(x * y) \ z) = L(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(346(a,1),41933(a,1,3))].">
      <j1 rule="para" parents="346 41933"/>
    </justification>
  </clause>

  <clause id="41940">
    <literal><![CDATA[
      L(x,y,y \ R(y,x,z)) = L(x,y,a(y,x,z))
    ]]></literal>
    <justification jstring="[para(41782(a,2),41933(a,1,3)),flip(a)].">
      <j1 rule="para" parents="41782 41933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41941">
    <literal><![CDATA[
      L(x,y,y \ L(y,x,z)) = L(x,y,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33124,a(flip),b,41940,a)].">
      <j1 rule="hyper" parents="64 33124 41940"/>
    </justification>
  </clause>

  <clause id="41942">
    <literal><![CDATA[
      L(x,y,a(y,x,z)) = L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41710,a(flip),b,41941,a),flip(a)].">
      <j1 rule="hyper" parents="64 41710 41941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41943">
    <literal><![CDATA[
      L(x,y,a(z,x,y)) = L(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41425,a,b,41942,a)].">
      <j1 rule="hyper" parents="64 41425 41942"/>
    </justification>
  </clause>

  <clause id="41944">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * z = L(z,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,39752,a,b,41943,a)].">
      <j1 rule="hyper" parents="373 39752 41943"/>
    </justification>
  </clause>

  <clause id="41945">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) * L(y,x,a(z,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(145,a,41944,a(flip),b,41506,a)].">
      <j1 rule="hyper" parents="145 41944 41506"/>
    </justification>
  </clause>

  <clause id="41946">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = a(y,y,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,41468,a,b,41945,a)].">
      <j1 rule="hyper" parents="36 41468 41945"/>
    </justification>
  </clause>

  <clause id="41947">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = a(y,y,a(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,41883,a,b,41946,a),flip(a)].">
      <j1 rule="hyper" parents="373 41883 41946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41948">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = a(z,y,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,40883,a,b,41946,a),flip(a)].">
      <j1 rule="hyper" parents="373 40883 41946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41949">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = a(z,x,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,40880,a,b,41946,a),flip(a)].">
      <j1 rule="hyper" parents="373 40880 41946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41950">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = a(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,39754,a,b,41946,a),flip(a)].">
      <j1 rule="hyper" parents="373 39754 41946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41951">
    <literal><![CDATA[
      a(x,y,a(y,x,z)) = a(y,y,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41883,a,b,41946,a)].">
      <j1 rule="hyper" parents="64 41883 41946"/>
    </justification>
  </clause>

  <clause id="41952">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) / T(a(x,x,z) * a(y,y,a(x,x,z)),u) = 1 / T(a(x,x,z),u)
    ]]></literal>
    <justification jstring="[para(41946(a,2),36959(a,1,1))].">
      <j1 rule="para" parents="41946 36959"/>
    </justification>
  </clause>

  <clause id="41953">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * a(z,x,y) = L(y,x,z) \ y
    ]]></literal>
    <justification jstring="[para(41946(a,2),41670(a,1,1))].">
      <j1 rule="para" parents="41946 41670"/>
    </justification>
  </clause>

  <clause id="41954">
    <literal><![CDATA[
      a(x,y,a(y,x,z)) = a(y,y,a(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41883,a,b,41947,a)].">
      <j1 rule="hyper" parents="64 41883 41947"/>
    </justification>
  </clause>

  <clause id="41955">
    <literal><![CDATA[
      x * a(y,z,a(u,y,z)) = x * a(u,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[para(41947(a,2),40898(a,2,2)),flip(a)].">
      <j1 rule="para" parents="41947 40898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41956">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,a(w,z,u))) = x \ L(x,y,a(u,u,a(z,z,w)))
    ]]></literal>
    <justification jstring="[para(41948(a,2),41053(a,1,2,3))].">
      <j1 rule="para" parents="41948 41053"/>
    </justification>
  </clause>

  <clause id="41957">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,a(y,z,z)) = L(a(x,y,z),z,y) \ 1
    ]]></literal>
    <justification jstring="[para(41949(a,1),41474(a,1,2))].">
      <j1 rule="para" parents="41949 41474"/>
    </justification>
  </clause>

  <clause id="41958">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * a(y,x,z) = L(a(y,x,z),z,x)
    ]]></literal>
    <justification jstring="[para(41950(a,1),36346(a,1,1))].">
      <j1 rule="para" parents="41950 36346"/>
    </justification>
  </clause>

  <clause id="41959">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * x = L(x,a(y,z,x),z)
    ]]></literal>
    <justification jstring="[para(41954(a,1),41406(a,1,1))].">
      <j1 rule="para" parents="41954 41406"/>
    </justification>
  </clause>

  <clause id="41960">
    <literal><![CDATA[
      L(x,a(y,z,x),z) = L(x,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30055,a(flip),b,41959,a),flip(a)].">
      <j1 rule="hyper" parents="64 30055 41959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41961">
    <literal><![CDATA[
      R(L(x,x,a(y,z,z)),u,w) = L(R(x,u,w),a(x,z,y),z)
    ]]></literal>
    <justification jstring="[para(41960(a,1),41412(a,1,1))].">
      <j1 rule="para" parents="41960 41412"/>
    </justification>
  </clause>

  <clause id="41962">
    <literal><![CDATA[
      (x * y) \ (((x * y) * y) * z) = (x / y) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,30039,a,b,41831,a)].">
      <j1 rule="hyper" parents="373 30039 41831"/>
    </justification>
  </clause>

  <clause id="41963">
    <literal><![CDATA[
      (x * y) \ (((x * y) * x) * z) = (y / x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29944,a,b,41831,a)].">
      <j1 rule="hyper" parents="373 29944 41831"/>
    </justification>
  </clause>

  <clause id="41964">
    <literal><![CDATA[
      x * L(y,z,z * x) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(145,a,30029,a(flip),b,41831,a),flip(a)].">
      <j1 rule="hyper" parents="145 30029 41831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41966">
    <literal><![CDATA[
      (x * a(y,z,z \ 1)) * a(x * ((y * z) \ y),x,a(y,z,z \ 1)) = (((y * z) \ y) / x) \ (z \ 1)
    ]]></literal>
    <justification jstring="[para(33373(a,1),41831(a,1,2)),flip(a)].">
      <j1 rule="para" parents="33373 41831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41967">
    <literal><![CDATA[
      (x * a(y,a(y,z,u),w)) * a(x * L(y,a(y,z,u),w),x,a(y,a(y,z,u),w)) = (L(y,a(y,z,u),w) / x) \ y
    ]]></literal>
    <justification jstring="[para(39363(a,1),41831(a,1,2)),flip(a)].">
      <j1 rule="para" parents="39363 41831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41968">
    <literal><![CDATA[
      (x / y) \ (x * a(z,u,x)) = (y * a(z,u,x)) * a(a(x,u,z),y,y)
    ]]></literal>
    <justification jstring="[para(41918(a,1),41831(a,2,2))].">
      <j1 rule="para" parents="41918 41831"/>
    </justification>
  </clause>

  <clause id="41969">
    <literal><![CDATA[
      L(x \ y,x,x * z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,41964,a),flip(a)].">
      <j1 rule="hyper" parents="139 168 41964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41970">
    <literal><![CDATA[
      x * L(y,z,x * z) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,24002,a,b,41964,a)].">
      <j1 rule="hyper" parents="64 24002 41964"/>
    </justification>
  </clause>

  <clause id="41971">
    <literal><![CDATA[
      L(x,y,y \ z) = L(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(35,a,11064,a,b,41964,a)].">
      <j1 rule="hyper" parents="35 11064 41964"/>
    </justification>
  </clause>

  <clause id="41972">
    <literal><![CDATA[
      x \ ((x / y) * (y * z)) = L(z,y,x * y)
    ]]></literal>
    <justification jstring="[hyper(139,a,41964,a(flip),b,24002,a)].">
      <j1 rule="hyper" parents="139 41964 24002"/>
    </justification>
  </clause>

  <clause id="41973">
    <literal><![CDATA[
      L((x * y) * (1 / x),z,z * x) = ((x / z) * (z * y)) * (1 / x)
    ]]></literal>
    <justification jstring="[para(41964(a,1),9448(a,2,1))].">
      <j1 rule="para" parents="41964 9448"/>
    </justification>
  </clause>

  <clause id="41974">
    <literal><![CDATA[
      (x \ 1) * L(y,z,x * z) = ((x \ 1) / z) * (z * y)
    ]]></literal>
    <justification jstring="[para(23997(a,1),41964(a,1,2))].">
      <j1 rule="para" parents="23997 41964"/>
    </justification>
  </clause>

  <clause id="41976">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) * z) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(24200,a,41971,a),flip(a)].">
      <j1 rule="hyper" parents="24200 41971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41977">
    <literal><![CDATA[
      L(x,y,y \ z) = L(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,23253,a,b,41971,a),flip(a)].">
      <j1 rule="hyper" parents="373 23253 41971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41979">
    <literal><![CDATA[
      R(x,a(y,z,u),a(y,z,u) \ w) = L(x,a(y,z,u),a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31802,a,b,41971,a)].">
      <j1 rule="hyper" parents="64 31802 41971"/>
    </justification>
  </clause>

  <clause id="41980">
    <literal><![CDATA[
      L(x,y,(y \ 1) \ z) = L(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2234,a,b,41971,a)].">
      <j1 rule="hyper" parents="64 2234 41971"/>
    </justification>
  </clause>

  <clause id="41981">
    <literal><![CDATA[
      L(x,y,y \ (y \ z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),41971(a,2,3))].">
      <j1 rule="para" parents="10 41971"/>
    </justification>
  </clause>

  <clause id="41984">
    <literal><![CDATA[
      L(x,y,(x * y) \ z) = L(x,y,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41937,a,b,41977,a)].">
      <j1 rule="hyper" parents="64 41937 41977"/>
    </justification>
  </clause>

  <clause id="41985">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = L(x,y,(x \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41936,a,b,41977,a)].">
      <j1 rule="hyper" parents="64 41936 41977"/>
    </justification>
  </clause>

  <clause id="41986">
    <literal><![CDATA[
      L(x,y,L(z,z,y)) = L(x,y,(z \ y) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35048,a,b,41977,a)].">
      <j1 rule="hyper" parents="64 35048 41977"/>
    </justification>
  </clause>

  <clause id="41987">
    <literal><![CDATA[
      x \ ((((x / y) / z) * (z * y)) * y) = L(y,z,(y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29126,a,b,41977,a)].">
      <j1 rule="hyper" parents="64 29126 41977"/>
    </justification>
  </clause>

  <clause id="41988">
    <literal><![CDATA[
      L(x,y,z / y) = L(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,23216,a,b,41977,a)].">
      <j1 rule="hyper" parents="64 23216 41977"/>
    </justification>
  </clause>

  <clause id="41989">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),w * a(x,y,z)) = w \ ((a(x,y,z) \ w) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23916,a(flip),b,41977,a),flip(a)].">
      <j1 rule="hyper" parents="64 23916 41977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41990">
    <literal><![CDATA[
      L(x \ y,x,z * x) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,11070,a(flip),b,41977,a),flip(a)].">
      <j1 rule="hyper" parents="64 11070 41977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41991">
    <literal><![CDATA[
      L(x,y \ z,((1 / y) \ (y \ z)) * (y \ z)) = L(x,y \ z,((1 / y) * z) \ z)
    ]]></literal>
    <justification jstring="[para(11447(a,1),41977(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11447 41977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41992">
    <literal><![CDATA[
      a(L(x \ y,z,x * z),u,w) = a(z \ ((z \ x) \ y),u,w)
    ]]></literal>
    <justification jstring="[para(41977(a,1),34963(a,1,1))].">
      <j1 rule="para" parents="41977 34963"/>
    </justification>
  </clause>

  <clause id="41993">
    <literal><![CDATA[
      L(x,y / z,L(z,z,y) * (y / z)) = L(x,y / z,(y * (1 / z)) \ z)
    ]]></literal>
    <justification jstring="[para(37001(a,1),41977(a,1,3)),flip(a)].">
      <j1 rule="para" parents="37001 41977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="41994">
    <literal><![CDATA[
      (x / y) \ (x * a(z,z,u)) = y * a(z,z,L(u,y,x * y))
    ]]></literal>
    <justification jstring="[para(41977(a,1),41052(a,2,2,3))].">
      <j1 rule="para" parents="41977 41052"/>
    </justification>
  </clause>

  <clause id="41995">
    <literal><![CDATA[
      L(x,y,L(z,y,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30390,a(flip),b,41981,a)].">
      <j1 rule="hyper" parents="64 30390 41981"/>
    </justification>
  </clause>

  <clause id="41998">
    <literal><![CDATA[
      L(x,L(y,y,z),y * z) = L(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,40975,a,b,41995,a)].">
      <j1 rule="hyper" parents="64 40975 41995"/>
    </justification>
  </clause>

  <clause id="42003">
    <literal><![CDATA[
      L(x,y \ z,(1 / (y / z)) * y) = L(x,y \ z,z)
    ]]></literal>
    <justification jstring="[para(34721(a,1),41995(a,1,3))].">
      <j1 rule="para" parents="34721 41995"/>
    </justification>
  </clause>

  <clause id="42004">
    <literal><![CDATA[
      L(x,L(y,z,u),L(w,y,y)) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(35161(a,1),41995(a,1,3))].">
      <j1 rule="para" parents="35161 41995"/>
    </justification>
  </clause>

  <clause id="42005">
    <literal><![CDATA[
      L(x,y * z,(1 / (y \ z)) * u) = L(x,y * z,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(35224(a,1),41995(a,1,3))].">
      <j1 rule="para" parents="35224 41995"/>
    </justification>
  </clause>

  <clause id="42006">
    <literal><![CDATA[
      x * (L(x,y,L(z,y,x)) \ (y \ z)) = y \ R(z,y,x)
    ]]></literal>
    <justification jstring="[para(41995(a,1),36410(a,1,2,1))].">
      <j1 rule="para" parents="41995 36410"/>
    </justification>
  </clause>

  <clause id="42007">
    <literal><![CDATA[
      a(x,y,L(z,u,w) * (u \ w)) = a(x,y,L(w,u,u) * ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[para(41995(a,1),39093(a,1,3,1))].">
      <j1 rule="para" parents="41995 39093"/>
    </justification>
  </clause>

  <clause id="42008">
    <literal><![CDATA[
      (x / y) * L(y \ z,y,x) = ((x / y) / y) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,24004,a(flip),b,41969,a(flip))].">
      <j1 rule="hyper" parents="145 24004 41969"/>
    </justification>
  </clause>

  <clause id="42009">
    <literal><![CDATA[
      L(x \ ((x / y) * z),(y * x) * y,(y * x) * y) = (1 / ((y * x) * y)) * ((y * x) * (y * (y \ z)))
    ]]></literal>
    <justification jstring="[para(41969(a,1),577(a,1,1))].">
      <j1 rule="para" parents="41969 577"/>
    </justification>
  </clause>

  <clause id="42010">
    <literal><![CDATA[
      a(L(x \ y,x,x * z),u,z) = a(((z / x) * y) \ z,u,z)
    ]]></literal>
    <justification jstring="[para(41969(a,2),40760(a,2,1)),flip(a)].">
      <j1 rule="para" parents="41969 40760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42011">
    <literal><![CDATA[
      L(x,y * z,L(z,z,y)) = L(x,y * z,y * (y * z))
    ]]></literal>
    <justification jstring="[hyper(35,a,35054,a(flip),b,41970,a)].">
      <j1 rule="hyper" parents="35 35054 41970"/>
    </justification>
  </clause>

  <clause id="42012">
    <literal><![CDATA[
      (((x * y) / z) * (z * y)) / y = x * L(y,z,(x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(142,a,41970,a(flip),b,3184,a)].">
      <j1 rule="hyper" parents="142 41970 3184"/>
    </justification>
  </clause>

  <clause id="42013">
    <literal><![CDATA[
      ((x * y) / (((x * y) \ x) * x)) * ((((x * y) \ x) * x) * z) = (x * y) * L(z,((x * y) \ x) * x,(x / y) * (y * x))
    ]]></literal>
    <justification jstring="[para(34313(a,1),41970(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="34313 41970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42015">
    <literal><![CDATA[
      L(L(x,y,(z \ y) * y),y,a(y,z,z)) = L(x,L(y,y,L(z,z,y)),L(z,z,y))
    ]]></literal>
    <justification jstring="[para(41986(a,1),40956(a,1,1))].">
      <j1 rule="para" parents="41986 40956"/>
    </justification>
  </clause>

  <clause id="42016">
    <literal><![CDATA[
      L(x,y,(z \ ((z / u) * w)) * ((z * u) * u)) = L(x,y,(z * u) * (u * (u \ w)))
    ]]></literal>
    <justification jstring="[para(41990(a,1),24005(a,1,3,1))].">
      <j1 rule="para" parents="41990 24005"/>
    </justification>
  </clause>

  <clause id="42017">
    <literal><![CDATA[
      a((x \ ((x / y) * z)) * ((x * y) * y),u,w) = a((x * y) * (y * (y \ z)),u,w)
    ]]></literal>
    <justification jstring="[para(41990(a,1),26837(a,1,1,1))].">
      <j1 rule="para" parents="41990 26837"/>
    </justification>
  </clause>

  <clause id="42018">
    <literal><![CDATA[
      L(x,L(y,y,z),z * y) = L(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(24201,a,41998,a)].">
      <j1 rule="hyper" parents="24201 41998"/>
    </justification>
  </clause>

  <clause id="42019">
    <literal><![CDATA[
      L(L(x,y,y * z),y,a(y,z,z)) = L(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41311,a,b,41998,a)].">
      <j1 rule="hyper" parents="64 41311 41998"/>
    </justification>
  </clause>

  <clause id="42020">
    <literal><![CDATA[
      (x * y) * (((x * y) \ x) * z) = x * L(z,y,x \ y)
    ]]></literal>
    <justification jstring="[para(42018(a,1),29727(a,2,2))].">
      <j1 rule="para" parents="42018 29727"/>
    </justification>
  </clause>

  <clause id="42021">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) * z) = L(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,41718,a(flip),b,41976,a),flip(a)].">
      <j1 rule="hyper" parents="373 41718 41976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42022">
    <literal><![CDATA[
      a(L(x,y,(x \ z) * y),u,w) = a((y * ((x * y) \ z)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(41984(a,1),32596(a,1,1))].">
      <j1 rule="para" parents="41984 32596"/>
    </justification>
  </clause>

  <clause id="42023">
    <literal><![CDATA[
      (a(x * (y * z),x,z) \ y) * z = (((y * z) / x) * (x * z)) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,33214,a(flip),b,41834,a)].">
      <j1 rule="hyper" parents="64 33214 41834"/>
    </justification>
  </clause>

  <clause id="42024">
    <literal><![CDATA[
      L(a(x * y,y,z),z,x) = L(z,y,x * y) \ z
    ]]></literal>
    <justification jstring="[para(41977(a,1),41843(a,2,1))].">
      <j1 rule="para" parents="41977 41843"/>
    </justification>
  </clause>

  <clause id="42025">
    <literal><![CDATA[
      L(x,L(y,z,u),y \ w) = L(x,L(y,z,u),w * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30388,a(flip),b,42004,a)].">
      <j1 rule="hyper" parents="64 30388 42004"/>
    </justification>
  </clause>

  <clause id="42026">
    <literal><![CDATA[
      (x / y) * a(L(y,y,x),z,a(z,u,w)) = ((x / y) / y) * L(y,z,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(40819(a,1),42008(a,1,2))].">
      <j1 rule="para" parents="40819 42008"/>
    </justification>
  </clause>

  <clause id="42027">
    <literal><![CDATA[
      L(a(x,y,z),z,y \ x) = L(z,y,(y \ x) * y) \ z
    ]]></literal>
    <justification jstring="[para(26836(a,1),42024(a,1,1))].">
      <j1 rule="para" parents="26836 42024"/>
    </justification>
  </clause>

  <clause id="42028">
    <literal><![CDATA[
      (x / y) \ (x * a(y,y \ x,z)) = R(y,y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(149,a,41788,a)].">
      <j1 rule="hyper" parents="149 41788"/>
    </justification>
  </clause>

  <clause id="42029">
    <literal><![CDATA[
      a(x,y,z) * ((x * y) * z) = (R(x,y,z) * y) * z
    ]]></literal>
    <justification jstring="[hyper(23777,a,41793,a)].">
      <j1 rule="hyper" parents="23777 41793"/>
    </justification>
  </clause>

  <clause id="42030">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w),(u * z) * w,(u * z) * w)) = L(x,y,((u * z) * w) * ((u * R(z,u,w)) * w))
    ]]></literal>
    <justification jstring="[para(41794(a,1),2185(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="41794 2185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42031">
    <literal><![CDATA[
      x * a(x,y,L(y,z,z)) = R(x,(y \ z) * z,y)
    ]]></literal>
    <justification jstring="[para(41297(a,1),41817(a,1,2))].">
      <j1 rule="para" parents="41297 41817"/>
    </justification>
  </clause>

  <clause id="42032">
    <literal><![CDATA[
      R(x,(y \ z) * z,y) = R(x,y,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,38379,a(flip),b,42031,a),flip(a)].">
      <j1 rule="hyper" parents="64 38379 42031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42033">
    <literal><![CDATA[
      R(x,((((1 / y) \ y) / z) \ y) * y,((1 / y) \ y) / z) = R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(16553(a,1),42032(a,2,3))].">
      <j1 rule="para" parents="16553 42032"/>
    </justification>
  </clause>

  <clause id="42034">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,L(y * z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,41074,a(flip),b,41823,a),flip(a)].">
      <j1 rule="hyper" parents="373 41074 41823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42035">
    <literal><![CDATA[
      a((x / y) * x,x * y,z) = a(y,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(2693,a,41828,a)].">
      <j1 rule="hyper" parents="2693 41828"/>
    </justification>
  </clause>

  <clause id="42036">
    <literal><![CDATA[
      a(x * (y \ x),x * y,z) = a(y,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32416,a(flip),b,42035,a)].">
      <j1 rule="hyper" parents="64 32416 42035"/>
    </justification>
  </clause>

  <clause id="42037">
    <literal><![CDATA[
      a((x \ y) * y,y * x,z) = a(x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32367,a(flip),b,42035,a)].">
      <j1 rule="hyper" parents="64 32367 42035"/>
    </justification>
  </clause>

  <clause id="42038">
    <literal><![CDATA[
      L(x,a(y,z,z \ u),w) = L(x,a(y,z,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,41403,a,b,41836,a)].">
      <j1 rule="hyper" parents="64 41403 41836"/>
    </justification>
  </clause>

  <clause id="42039">
    <literal><![CDATA[
      a(a(x,y,y \ z),u,w) = a(a(x,y,y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,41479,a,b,41837,a)].">
      <j1 rule="hyper" parents="64 41479 41837"/>
    </justification>
  </clause>

  <clause id="42040">
    <literal><![CDATA[
      a(x,y,z) = (y \ x) \ (y \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,23174,a(flip),b,41845,a)].">
      <j1 rule="hyper" parents="373 23174 41845"/>
    </justification>
  </clause>

  <clause id="42042">
    <literal><![CDATA[
      a(x,y,z) * (y \ x) = y \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(23776,a,42040,a)].">
      <j1 rule="hyper" parents="23776 42040"/>
    </justification>
  </clause>

  <clause id="42043">
    <literal><![CDATA[
      a(x,y,z) * (x / y) = R(x,y,z) / y
    ]]></literal>
    <justification jstring="[hyper(144,a,42040,a,b,27071,a)].">
      <j1 rule="hyper" parents="144 42040 27071"/>
    </justification>
  </clause>

  <clause id="42045">
    <literal><![CDATA[
      ((x \ y) * z) * a(y,x,z) = (x \ R(y,x,z)) * z
    ]]></literal>
    <justification jstring="[para(42042(a,1),33207(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42042 33207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42046">
    <literal><![CDATA[
      R(x,y,a(y,z,z)) / y = x * (L(x,z,z) \ (L(x,z,z) / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41050,a(flip),b,42043,a),flip(a)].">
      <j1 rule="hyper" parents="64 41050 42043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42047">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ y = y * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,34927,a,b,41855,a)].">
      <j1 rule="hyper" parents="64 34927 41855"/>
    </justification>
  </clause>

  <clause id="42048">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ (v5 * v5))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,41803,a(flip),b,41862,a),flip(a)].">
      <j1 rule="hyper" parents="373 41803 41862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42050">
    <literal><![CDATA[
      a(a(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(z,y,x)) = v5
    ]]></literal>
    <justification jstring="[para(41884(a,1),23178(a,1))].">
      <j1 rule="para" parents="41884 23178"/>
    </justification>
  </clause>

  <clause id="42051">
    <literal><![CDATA[
      a(x,y,a(z,u,u \ w)) = a(x,y,a(z,u,w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,41883,a,b,41911,a),flip(a)].">
      <j1 rule="hyper" parents="64 41883 41911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42052">
    <literal><![CDATA[
      a(x * a(y,y,z),x,y) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32872,a(flip),b,41913,a)].">
      <j1 rule="hyper" parents="64 32872 41913"/>
    </justification>
  </clause>

  <clause id="42053">
    <literal><![CDATA[
      a(x,y,a(z * a(y,y,u),z,y)) = a(z,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(42052(a,2),40886(a,1,3))].">
      <j1 rule="para" parents="42052 40886"/>
    </justification>
  </clause>

  <clause id="42054">
    <literal><![CDATA[
      a(x * (y \ (z \ (y * x))),x,y) = z \ R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41822,a(flip),b,41917,a)].">
      <j1 rule="hyper" parents="64 41822 41917"/>
    </justification>
  </clause>

  <clause id="42055">
    <literal><![CDATA[
      L(a(x,y,z),z,y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,36346,a(flip),b,41953,a)].">
      <j1 rule="hyper" parents="64 36346 41953"/>
    </justification>
  </clause>

  <clause id="42056">
    <literal><![CDATA[
      x \ (y \ ((y * x) * z)) = z * (L(z,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(41953(a,1),33518(a,1,2)),flip(a)].">
      <j1 rule="para" parents="41953 33518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42057">
    <literal><![CDATA[
      ((x * y) \ (x * (L(y,z,u) \ y))) \ (L(y,z,u) \ 1) = L(a(x,y,L(y,z,u) \ 1),L(y,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1859(a,2),42055(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1859 42055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42058">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,z,y)
    ]]></literal>
    <justification jstring="[para(42055(a,1),36294(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42055 36294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42059">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),x,y) = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(41803(a,1),42055(a,1,1))].">
      <j1 rule="para" parents="41803 42055"/>
    </justification>
  </clause>

  <clause id="42060">
    <literal><![CDATA[
      a(L(x,y,z),y,L(a(y,u,w),y,x)) = a(L(x,y,z),y,a(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,40732,a(flip),b,42058,a)].">
      <j1 rule="hyper" parents="373 40732 42058"/>
    </justification>
  </clause>

  <clause id="42061">
    <literal><![CDATA[
      (x * ((y * x) \ (y * z))) \ z = a(y,x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,40727,a(flip),b,42058,a)].">
      <j1 rule="hyper" parents="373 40727 42058"/>
    </justification>
  </clause>

  <clause id="42062">
    <literal><![CDATA[
      a(x,y,L(L(z,y,x),u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,40726,a(flip),b,42058,a)].">
      <j1 rule="hyper" parents="373 40726 42058"/>
    </justification>
  </clause>

  <clause id="42063">
    <literal><![CDATA[
      x \ (L(y / x,x,z) \ y) = a(z,x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,40714,a(flip),b,42058,a)].">
      <j1 rule="hyper" parents="373 40714 42058"/>
    </justification>
  </clause>

  <clause id="42064">
    <literal><![CDATA[
      a(x,y,L(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,40712,a(flip),b,42058,a)].">
      <j1 rule="hyper" parents="373 40712 42058"/>
    </justification>
  </clause>

  <clause id="42065">
    <literal><![CDATA[
      x * (L(x,y,z) \ y) = y * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,42058,a,b,40710,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 42058 40710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42066">
    <literal><![CDATA[
      L(L(x,y,(x \ z) * y) \ x,x,y) = a((x * y) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,41916,a,b,42058,a),flip(a)].">
      <j1 rule="hyper" parents="64 41916 42058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42067">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ L(x,y,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(42,a,30351,a,b,42058,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="42 30351 42058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42068">
    <literal><![CDATA[
      L(x * a(y,z,x),z,y) = L(x,z,y) * a(y,z,x)
    ]]></literal>
    <justification jstring="[para(42058(a,2),39446(a,1,2)),flip(a)].">
      <j1 rule="para" parents="42058 39446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42069">
    <literal><![CDATA[
      x * (L(x,y,z) \ y) = a(z,y,x) * y
    ]]></literal>
    <justification jstring="[para(42058(a,2),40713(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42058 40713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42070">
    <literal><![CDATA[
      L(x,y,z) = (a(z,y,x) * y) \ (y * x)
    ]]></literal>
    <justification jstring="[para(42058(a,2),40728(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="42058 40728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42071">
    <literal><![CDATA[
      (a(x,y,z) \ y) * z = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(42058(a,2),40729(a,1,1,1))].">
      <j1 rule="para" parents="42058 40729"/>
    </justification>
  </clause>

  <clause id="42072">
    <literal><![CDATA[
      (x / y) * L(y,x,z) = a(z,x,y) \ x
    ]]></literal>
    <justification jstring="[para(42058(a,2),40730(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42058 40730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42073">
    <literal><![CDATA[
      a(x,y,z) * (z \ y) = L(z,y,x) \ y
    ]]></literal>
    <justification jstring="[para(42058(a,2),40731(a,1,1))].">
      <j1 rule="para" parents="42058 40731"/>
    </justification>
  </clause>

  <clause id="42074">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w) \ x,x,a(u \ 1,z,y)) = a(w,a(u \ 1,z,y),x)
    ]]></literal>
    <justification jstring="[para(41413(a,1),42058(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="41413 42058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42075">
    <literal><![CDATA[
      L((x \ R(x,y,z)) \ a(x,y,z),a(x,y,z),x * y) = a(y,x * y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(41912(a,1),42058(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="41912 42058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42076">
    <literal><![CDATA[
      a(x,y,y \ (x \ (z * (x * y)))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,39072,a,b,42064,a)].">
      <j1 rule="hyper" parents="64 39072 42064"/>
    </justification>
  </clause>

  <clause id="42078">
    <literal><![CDATA[
      a(x,y,(x * y) \ z) = a(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39066,a(flip),b,42064,a),flip(a)].">
      <j1 rule="hyper" parents="64 39066 42064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42079">
    <literal><![CDATA[
      a(x,y,z * a(x,z,y)) = a(x,y,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,35681,a(flip),b,42064,a),flip(a)].">
      <j1 rule="hyper" parents="64 35681 42064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42081">
    <literal><![CDATA[
      a(x,y,z) \ (y * z) = y * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(42064(a,1),30196(a,1,1))].">
      <j1 rule="para" parents="42064 30196"/>
    </justification>
  </clause>

  <clause id="42082">
    <literal><![CDATA[
      a(x,y,z) \ (z * y) = L(z,y,x) * y
    ]]></literal>
    <justification jstring="[para(42064(a,1),30402(a,1,1))].">
      <j1 rule="para" parents="42064 30402"/>
    </justification>
  </clause>

  <clause id="42083">
    <literal><![CDATA[
      L(x,y,z) = (y * a(z,y,x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(42064(a,1),33277(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="42064 33277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42084">
    <literal><![CDATA[
      x \ (y * a(z,y,x)) = L(x,y,z) \ y
    ]]></literal>
    <justification jstring="[para(42064(a,1),33405(a,1,2,2))].">
      <j1 rule="para" parents="42064 33405"/>
    </justification>
  </clause>

  <clause id="42085">
    <literal><![CDATA[
      x * (a(y,z,x) \ z) = L(x,z,y) * z
    ]]></literal>
    <justification jstring="[para(42064(a,1),33488(a,1,2,1))].">
      <j1 rule="para" parents="42064 33488"/>
    </justification>
  </clause>

  <clause id="42086">
    <literal><![CDATA[
      L(x,y,z * (L(z,u,w) \ u)) = L(x,y,u * a(w,u,z))
    ]]></literal>
    <justification jstring="[para(42064(a,1),33419(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="42064 33419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42087">
    <literal><![CDATA[
      a(x,L(y,z,u),a(u,z,L(y,z,u))) = a(x,a(u,z,y),L(y,z,u))
    ]]></literal>
    <justification jstring="[para(42064(a,1),33531(a,1,2)),flip(a)].">
      <j1 rule="para" parents="42064 33531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42088">
    <literal><![CDATA[
      L(x,y,z \ (L(u,z,w) * (u \ z))) = L(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[para(42064(a,1),35239(a,1,3)),flip(a)].">
      <j1 rule="para" parents="42064 35239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42089">
    <literal><![CDATA[
      a(x * y,x,L(a(y,z,u),x,x)) = a(x * y,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(41369(a,1),42064(a,1,3))].">
      <j1 rule="para" parents="41369 42064"/>
    </justification>
  </clause>

  <clause id="42090">
    <literal><![CDATA[
      a(x,y,z) \ L(z,a(z,y,x),u) = L(a(x,y,z),z,u) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,41447,a(flip),b,42065,a)].">
      <j1 rule="hyper" parents="139 41447 42065"/>
    </justification>
  </clause>

  <clause id="42092">
    <literal><![CDATA[
      (a(x,y,y \ z) * y) \ z = L(y \ z,y,x)
    ]]></literal>
    <justification jstring="[para(10(a,1),42070(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10 42070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42093">
    <literal><![CDATA[
      (a(L(x,y,z) \ u,w,v5) * w) \ (w * v5) = L(v5,w,R(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(32982(a,1),42070(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="32982 42070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42094">
    <literal><![CDATA[
      (a(x,y \ 1,z * a(y,y,z)) \ (y \ 1)) * (z * a(y,y,z)) = y \ L(z,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,30236,a(flip),b,42071,a),flip(a)].">
      <j1 rule="hyper" parents="373 30236 42071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42095">
    <literal><![CDATA[
      L(x,y,z) * (x \ y) = a(z,y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(36,a,24376,a,b,42071,a)].">
      <j1 rule="hyper" parents="36 24376 42071"/>
    </justification>
  </clause>

  <clause id="42097">
    <literal><![CDATA[
      x \ (a(y,x,x \ z) \ z) = L(x \ z,x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,33053,a(flip),b,42082,a(flip))].">
      <j1 rule="hyper" parents="36 33053 42082"/>
    </justification>
  </clause>

  <clause id="42098">
    <literal><![CDATA[
      (x * (y \ R(y,x,z))) \ (x * z) = L(z,x,L(y,y,x * z))
    ]]></literal>
    <justification jstring="[para(32467(a,1),42083(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="32467 42083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42099">
    <literal><![CDATA[
      L(x,(y * z) * (y * a(u,y,z)),(y * z) * (y * a(u,y,z))) = L(x,L(z,y,u),(y * a(u,y,z)) \ (y * z))
    ]]></literal>
    <justification jstring="[para(42083(a,2),35219(a,1,2)),flip(a)].">
      <j1 rule="para" parents="42083 35219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42100">
    <literal><![CDATA[
      (x * a(y,x,y \ z)) \ (x * (y \ z)) = L(y \ z,x,L(y,y,z))
    ]]></literal>
    <justification jstring="[para(40765(a,1),42083(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="40765 42083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42101">
    <literal><![CDATA[
      (x * (y \ R(y,x,z))) \ (x * z) = L(z,x,L(y,y,x))
    ]]></literal>
    <justification jstring="[para(41802(a,1),42083(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="41802 42083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42102">
    <literal><![CDATA[
      (x * a(a(y,z,u),x,x)) \ (x * a(u,z,y)) = L(a(u,z,y),x,x * y)
    ]]></literal>
    <justification jstring="[para(41918(a,1),42083(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="41918 42083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42104">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (L(x,u,w) \ y) = a(z,y,L(x,u,w)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,164,a,b,42095,a)].">
      <j1 rule="hyper" parents="64 164 42095"/>
    </justification>
  </clause>

  <clause id="42105">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,y) = L(y \ (a(z,y,x) \ y),u,x)
    ]]></literal>
    <justification jstring="[para(42095(a,1),33816(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="42095 33816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42106">
    <literal><![CDATA[
      a(x,y,z) \ (L(u / a(x,y,z),a(x,y,z),x) \ u) = a(a(x,y,z) \ u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,41451,a(flip),b,42063,a),flip(a)].">
      <j1 rule="hyper" parents="373 41451 42063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42107">
    <literal><![CDATA[
      x / (y * (((z / x) * y) \ z)) = a(x \ z,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33462,a(flip),b,42063,a)].">
      <j1 rule="hyper" parents="64 33462 42063"/>
    </justification>
  </clause>

  <clause id="42108">
    <literal><![CDATA[
      a(x,y,y \ (R(x,x,y) \ (z * (x * y)))) = a(x,y,a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(37601(a,1),42076(a,1,3,2))].">
      <j1 rule="para" parents="37601 42076"/>
    </justification>
  </clause>

  <clause id="42109">
    <literal><![CDATA[
      a(R(x,x,y),y,y \ (R(x,x,y) \ z)) = a(R(x,x,y),y,((1 / x) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(1913(a,1),42078(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1913 42078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42110">
    <literal><![CDATA[
      a(1 / (a(x,x,y) / x),y,y \ ((1 / (a(x,x,y) / x)) \ z)) = a(1 / (a(x,x,y) / x),y,L(x * y,x,x) \ z)
    ]]></literal>
    <justification jstring="[para(30962(a,1),42078(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="30962 42078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42111">
    <literal><![CDATA[
      (x \ y) / ((x * z) \ y) = z * a(x,z,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(42078(a,1),33276(a,2,2))].">
      <j1 rule="para" parents="42078 33276"/>
    </justification>
  </clause>

  <clause id="42113">
    <literal><![CDATA[
      L(x \ y,x,a((x \ y) * x,z,z)) = (a(x \ y,x,a(x,z,z)) * x) \ y
    ]]></literal>
    <justification jstring="[para(41058(a,1),42092(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="41058 42092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42115">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ x),y,z) = x
    ]]></literal>
    <justification jstring="[para(42056(a,1),596(a,1,1))].">
      <j1 rule="para" parents="42056 596"/>
    </justification>
  </clause>

  <clause id="42116">
    <literal><![CDATA[
      x \ ((x \ y) \ (K(x \ y,x) * (z * y))) = T(z,y) * (L(T(z,y),x,x \ y) \ T(z,y))
    ]]></literal>
    <justification jstring="[para(10970(a,2),42056(a,1,2,2))].">
      <j1 rule="para" parents="10970 42056"/>
    </justification>
  </clause>

  <clause id="42117">
    <literal><![CDATA[
      L(x,y \ (L(z,z,(z * y) * u) * ((z * y) * u)),w) = L(x,u * (L(u,y,z) \ u),w)
    ]]></literal>
    <justification jstring="[para(42056(a,1),33644(a,2,2))].">
      <j1 rule="para" parents="42056 33644"/>
    </justification>
  </clause>

  <clause id="42118">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w \ ((w * u) * v5)))) = a(x,y,z \ L(v5,u,w))
    ]]></literal>
    <justification jstring="[para(42056(a,2),41252(a,1,3,2))].">
      <j1 rule="para" parents="42056 41252"/>
    </justification>
  </clause>

  <clause id="42119">
    <literal><![CDATA[
      L(L(x * (L(x,y,z) \ x),u,w),y,z) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(42115(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42115 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42120">
    <literal><![CDATA[
      a(L(L(x * (L(x,y,z) \ x),u,u),y,z),w,v5) = a(L(x,u,u * (x * (L(x,y,z) \ x))),w,v5)
    ]]></literal>
    <justification jstring="[para(42115(a,1),33795(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="42115 33795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42121">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w) \ 1,u,w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(37297(a,1),42115(a,1,1))].">
      <j1 rule="para" parents="37297 42115"/>
    </justification>
  </clause>

  <clause id="42122">
    <literal><![CDATA[
      ((x * (1 / y)) * ((z * (x * y)) \ (z * (x * (y * y))))) \ x = a(z,x * y,(x * y) \ (x * (y * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,25861,a(flip),b,42061,a)].">
      <j1 rule="hyper" parents="64 25861 42061"/>
    </justification>
  </clause>

  <clause id="42123">
    <literal><![CDATA[
      ((x \ a(x,x,y)) * ((z * (x \ a(x,x,y))) \ (z * (x \ y)))) \ (x \ y) = a(z,x \ a(x,x,y),y)
    ]]></literal>
    <justification jstring="[para(30123(a,1),42061(a,2,3))].">
      <j1 rule="para" parents="30123 42061"/>
    </justification>
  </clause>

  <clause id="42124">
    <literal><![CDATA[
      (x \ L(y,x,z)) \ (x \ y) = a(z,x,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,39148,a(flip),b,42062,a)].">
      <j1 rule="hyper" parents="64 39148 42062"/>
    </justification>
  </clause>

  <clause id="42125">
    <literal><![CDATA[
      a(x,y,L(z,y,y)) \ (y \ z) = y \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,42124,a)].">
      <j1 rule="hyper" parents="40 23134 42124"/>
    </justification>
  </clause>

  <clause id="42126">
    <literal><![CDATA[
      x \ ((y / x) \ (y * a(z,u,w))) = L(a(z,u,w),x,y * x)
    ]]></literal>
    <justification jstring="[hyper(139,a,41962,a(flip),b,36304,a(flip))].">
      <j1 rule="hyper" parents="139 41962 36304"/>
    </justification>
  </clause>

  <clause id="42127">
    <literal><![CDATA[
      L(x,y \ z,(y / z) * y) = L(x,y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,2186,a(flip),b,42003,a)].">
      <j1 rule="hyper" parents="64 2186 42003"/>
    </justification>
  </clause>

  <clause id="42128">
    <literal><![CDATA[
      L(x,y \ z,(z \ y) * y) = L(x,y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(29066,a,42127,a)].">
      <j1 rule="hyper" parents="29066 42127"/>
    </justification>
  </clause>

  <clause id="42129">
    <literal><![CDATA[
      ((((x \ y) * y) * (y \ x)) \ ((x \ y) * y)) \ z = L((y \ x) \ 1,y \ x,x) \ z
    ]]></literal>
    <justification jstring="[para(42128(a,1),437(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42128 437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42130">
    <literal><![CDATA[
      T((x / (y \ 1)) * (L(y,z,u) \ 1),L(y,z,u) * (y \ 1)) = L(y \ L(y,z,u),L(y,z,u),x * y) \ x
    ]]></literal>
    <justification jstring="[para(42025(a,1),16786(a,2,1))].">
      <j1 rule="para" parents="42025 16786"/>
    </justification>
  </clause>

  <clause id="42131">
    <literal><![CDATA[
      (x / y) \ (x * a(y,x * y,z)) = R(y,y \ x,z)
    ]]></literal>
    <justification jstring="[para(35687(a,1),42028(a,1,2,2))].">
      <j1 rule="para" parents="35687 42028"/>
    </justification>
  </clause>

  <clause id="42132">
    <literal><![CDATA[
      (((x * y) * z) * (a(x,y,z) \ 1)) * (((R(x,y,z) * y) * z) \ a(x,y,z)) = a(x,y,z) \ K((x * y) * z,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(42029(a,1),4038(a,1,2,1))].">
      <j1 rule="para" parents="42029 4038"/>
    </justification>
  </clause>

  <clause id="42133">
    <literal><![CDATA[
      ((R(x,y,z) * y) * z) \ ((1 / (a(x,y,z) * ((x * y) * z))) \ a(x,y,z)) = ((a(x,y,z) / ((x * y) * z)) \ 1) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(42029(a,1),34627(a,1,1))].">
      <j1 rule="para" parents="42029 34627"/>
    </justification>
  </clause>

  <clause id="42134">
    <literal><![CDATA[
      ((((x * y) * z) * a(x,y,z)) \ a(x,y,z)) * T(a(x,y,z),(x * y) * z) = T(a(x,y,z) / T((x * y) * z,a(x,y,z)),(R(x,y,z) * y) * z)
    ]]></literal>
    <justification jstring="[para(42029(a,1),34691(a,1,2)),flip(a)].">
      <j1 rule="para" parents="42029 34691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42135">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,30387,a(flip),b,42034,a),flip(a)].">
      <j1 rule="hyper" parents="373 30387 42034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42136">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),u,w),x,y \ z) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(42135(a,2),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42135 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42137">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ L(w,v5,v6))) = a(x,y,a(z,u,w * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(5654(a,1),42048(a,1,3,3))].">
      <j1 rule="para" parents="5654 42048"/>
    </justification>
  </clause>

  <clause id="42138">
    <literal><![CDATA[
      a(x,y,a(z,u,u \ ((z * z) * (z \ w)))) = a(x,y,a(z,u,(z \ w) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39411,a,b,42051,a)].">
      <j1 rule="hyper" parents="64 39411 42051"/>
    </justification>
  </clause>

  <clause id="42139">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(x,y,z)) = L(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,33148,a,b,42067,a)].">
      <j1 rule="hyper" parents="40 33148 42067"/>
    </justification>
  </clause>

  <clause id="42140">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(x,y,z) = L(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,23580,a,b,42067,a)].">
      <j1 rule="hyper" parents="40 23580 42067"/>
    </justification>
  </clause>

  <clause id="42141">
    <literal><![CDATA[
      L(L(L(x,y,z),y,z) \ L(x,y,z),L(x,y,z),u) = u \ (x * (L(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[para(42067(a,2),34855(a,1,1))].">
      <j1 rule="para" parents="42067 34855"/>
    </justification>
  </clause>

  <clause id="42142">
    <literal><![CDATA[
      L(x * a(y,z,x),z,y) = L(x,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,41641,a(flip),b,42068,a),flip(a)].">
      <j1 rule="hyper" parents="373 41641 42068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42143">
    <literal><![CDATA[
      L(a(x,y,z) * z,y,x) = L(z,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(24736,a,42142,a)].">
      <j1 rule="hyper" parents="24736 42142"/>
    </justification>
  </clause>

  <clause id="42144">
    <literal><![CDATA[
      L(x \ a(y,z,x \ 1),z,y) = L(x \ 1,x \ 1,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(9442(a,1),42142(a,1,1))].">
      <j1 rule="para" parents="9442 42142"/>
    </justification>
  </clause>

  <clause id="42145">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) \ 1 = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(36303,a,42121,a),flip(a)].">
      <j1 rule="hyper" parents="36303 42121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42147">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ L(x,y,z)) = x \ L(L(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,42139,a(flip),b,33161,a),flip(a)].">
      <j1 rule="hyper" parents="139 42139 33161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42148">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) = L(a(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(40,a,23792,a,b,42145,a),flip(a)].">
      <j1 rule="hyper" parents="40 23792 42145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42149">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,u * a(x,y,z)) = u * ((a(x,y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,28812,a(flip),b,42148,a),flip(a)].">
      <j1 rule="hyper" parents="373 28812 42148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42150">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(L(x,y,z) \ x,x,u)) = a(a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34155,a(flip),b,41798,a)].">
      <j1 rule="hyper" parents="64 34155 41798"/>
    </justification>
  </clause>

  <clause id="42151">
    <literal><![CDATA[
      a(a(x,y,z),u,L(w,w,u)) = w \ L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(28832(a,1),41849(a,2,2))].">
      <j1 rule="para" parents="28832 41849"/>
    </justification>
  </clause>

  <clause id="42152">
    <literal><![CDATA[
      ((x \ 1) / (x \ y)) * ((x \ y) * z) = (x \ 1) * L(z,x \ y,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),41974(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="10 41974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42153">
    <literal><![CDATA[
      x * (L(x,y,z) \ (y \ z)) = y \ R(z,y,x)
    ]]></literal>
    <justification jstring="[para(41933(a,1),42006(a,1,2,1))].">
      <j1 rule="para" parents="41933 42006"/>
    </justification>
  </clause>

  <clause id="42154">
    <literal><![CDATA[
      L(x,y,z) \ ((y \ z) * x) = T(y \ R(z,y,x),x)
    ]]></literal>
    <justification jstring="[para(42153(a,1),25113(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42153 25113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42155">
    <literal><![CDATA[
      L(x,a(y,z,u),w) \ ((a(u,z,y) \ w) * x) = T(a(u,z,y) \ R(w,a(u,z,y),x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,41418,a,b,42154,a)].">
      <j1 rule="hyper" parents="64 41418 42154"/>
    </justification>
  </clause>

  <clause id="42156">
    <literal><![CDATA[
      L(x,y * z,L(z,z,y)) = L(x,y * z,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,2185,a(flip),b,42011,a),flip(a)].">
      <j1 rule="hyper" parents="373 2185 42011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42157">
    <literal><![CDATA[
      L(x,(y * z) * y,y * z) = L(x,z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(35,a,41721,a,b,42020,a(flip))].">
      <j1 rule="hyper" parents="35 41721 42020"/>
    </justification>
  </clause>

  <clause id="42158">
    <literal><![CDATA[
      L(x,L(y,z,z),z * y) = L(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29508,a(flip),b,42157,a)].">
      <j1 rule="hyper" parents="64 29508 42157"/>
    </justification>
  </clause>

  <clause id="42159">
    <literal><![CDATA[
      L(a(x,y,z),z,y \ x) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[para(23833(a,1),42027(a,2,1))].">
      <j1 rule="para" parents="23833 42027"/>
    </justification>
  </clause>

  <clause id="42161">
    <literal><![CDATA[
      (x \ y) * (z * (L(z,x,y) \ z)) = ((x \ y) * z) * a(y,x,z)
    ]]></literal>
    <justification jstring="[para(42159(a,1),36300(a,1,2,2))].">
      <j1 rule="para" parents="42159 36300"/>
    </justification>
  </clause>

  <clause id="42162">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ x = x \ R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,41790,a(flip),b,42059,a),flip(a)].">
      <j1 rule="hyper" parents="64 41790 42059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42163">
    <literal><![CDATA[
      x * L(x \ 1,y,a(z,u,w)) = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,28837,a,b,42162,a)].">
      <j1 rule="hyper" parents="373 28837 42162"/>
    </justification>
  </clause>

  <clause id="42164">
    <literal><![CDATA[
      L(1 / x,y,a(z,u,w)) \ 1 = R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(39,a,28866,a,b,42162,a(flip))].">
      <j1 rule="hyper" parents="39 28866 42162"/>
    </justification>
  </clause>

  <clause id="42165">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ x = x \ L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(28832(a,1),42162(a,2,2))].">
      <j1 rule="para" parents="28832 42162"/>
    </justification>
  </clause>

  <clause id="42166">
    <literal><![CDATA[
      L(1 / x,y,a(z,u,w)) \ 1 = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,28832,a(flip),b,42164,a),flip(a)].">
      <j1 rule="hyper" parents="373 28832 42164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42168">
    <literal><![CDATA[
      L(1 / x,y,a(z,u,w)) = 1 / L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(225,a,28832,a(flip),b,42164,a),flip(a)].">
      <j1 rule="hyper" parents="225 28832 42164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42169">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (x \ L(x,y,a(z,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(157,a,42165,a)].">
      <j1 rule="hyper" parents="157 42165"/>
    </justification>
  </clause>

  <clause id="42170">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ x) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,42165,a,b,xx)].">
      <j1 rule="hyper" parents="145 42165"/>
    </justification>
  </clause>

  <clause id="42171">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,42067,a,b,42165,a(flip))].">
      <j1 rule="hyper" parents="40 42067 42165"/>
    </justification>
  </clause>

  <clause id="42174">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),w,a(y,z,u)) = x * a(a(y,z,u),x,w)
    ]]></literal>
    <justification jstring="[hyper(42,a,34924,a,b,42171,a),flip(a)].">
      <j1 rule="hyper" parents="42 34924 42171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42175">
    <literal><![CDATA[
      L((x * a(y,z,u)) \ w,x,a(y,z,u)) = x \ (a(y,z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(42,a,23941,a,b,42171,a),flip(a)].">
      <j1 rule="hyper" parents="42 23941 42171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42176">
    <literal><![CDATA[
      a(x,y,z) * (u * L(w,u,a(x,y,z))) = (u * a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(145,a,42171,a(flip),b,23191,a),flip(a)].">
      <j1 rule="hyper" parents="145 42171 23191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42177">
    <literal><![CDATA[
      a(x,y,z) * (L(u,w,a(x,y,z)) * w) = u * (a(x,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(144,a,42171,a(flip),b,28734,a),flip(a)].">
      <j1 rule="hyper" parents="144 42171 28734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42178">
    <literal><![CDATA[
      L(x \ 1,y,a(z,u,w)) = L(x,y,a(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[para(79(a,1),42166(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 42166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42179">
    <literal><![CDATA[
      (x / y) * L(y,z,a(u,w,v5)) = y * (L(y,z,a(u,w,v5)) \ x)
    ]]></literal>
    <justification jstring="[para(42170(a,1),40650(a,1,2))].">
      <j1 rule="para" parents="42170 40650"/>
    </justification>
  </clause>

  <clause id="42180">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (x \ v5) = x * (L(x,y,a(z,u,w)) \ v5)
    ]]></literal>
    <justification jstring="[para(42170(a,1),40674(a,1,1))].">
      <j1 rule="para" parents="42170 40674"/>
    </justification>
  </clause>

  <clause id="42181">
    <literal><![CDATA[
      a(x \ (y \ ((y * z) * x)),z \ 1,(z \ 1) \ x) = x / ((z \ 1) * (a(y,z,x) \ (y \ ((y * z) * x))))
    ]]></literal>
    <justification jstring="[para(35767(a,2),42107(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="35767 42107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42182">
    <literal><![CDATA[
      a(x,L(L(x,y,z),u,w),v5) = L(a(x,L(x,y,z),v5),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32734,a(flip),b,41801,a)].">
      <j1 rule="hyper" parents="64 32734 41801"/>
    </justification>
  </clause>

  <clause id="42183">
    <literal><![CDATA[
      a(x,y,a(z,u,w) \ u) = a(x,y,a(w,u,z) * u)
    ]]></literal>
    <justification jstring="[para(42072(a,1),41811(a,1,3))].">
      <j1 rule="para" parents="42072 41811"/>
    </justification>
  </clause>

  <clause id="42184">
    <literal><![CDATA[
      a(x,y,z \ (u \ (z * (w * u)))) = a(x,y,a(u,w,z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33345,a(flip),b,42183,a)].">
      <j1 rule="hyper" parents="64 33345 42183"/>
    </justification>
  </clause>

  <clause id="42185">
    <literal><![CDATA[
      R(x,y,a(z,u,w) \ u) = R(x,y,a(w,u,z) * u)
    ]]></literal>
    <justification jstring="[para(42069(a,1),41812(a,1,3)),flip(a)].">
      <j1 rule="para" parents="42069 41812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42186">
    <literal><![CDATA[
      R(x,y,(z \ a(u,z,w)) \ 1) = R(x,y,a(w,z,u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35795,a,b,42185,a)].">
      <j1 rule="hyper" parents="64 35795 42185"/>
    </justification>
  </clause>

  <clause id="42187">
    <literal><![CDATA[
      R(x,y * a(z,y,L(u,y,z)),w) = R(x,a(u,y,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33408,a(flip),b,41815,a)].">
      <j1 rule="hyper" parents="64 33408 41815"/>
    </justification>
  </clause>

  <clause id="42188">
    <literal><![CDATA[
      L(x,y * a(z,y,u),w) = L(x,y * a(u,y,z),w)
    ]]></literal>
    <justification jstring="[para(42065(a,1),41816(a,1,2))].">
      <j1 rule="para" parents="42065 41816"/>
    </justification>
  </clause>

  <clause id="42189">
    <literal><![CDATA[
      L(x,y * a(z,y,u),y * a(u,y,z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,40593,a(flip),b,42188,a),flip(a)].">
      <j1 rule="hyper" parents="373 40593 42188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42190">
    <literal><![CDATA[
      a(a(L(x,y,z),u,u),w,v5) = a(a(x,u,L(u,y,z)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,41859,a,b,41850,a)].">
      <j1 rule="hyper" parents="373 41859 41850"/>
    </justification>
  </clause>

  <clause id="42191">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 \ 1))) = a(x,y,a(z,u,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,41803,a(flip),b,41864,a),flip(a)].">
      <j1 rule="hyper" parents="373 41803 41864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42192">
    <literal><![CDATA[
      x * (y * a(a(z,u,w),y,x)) = L(x,y,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(28832(a,1),41877(a,2,1))].">
      <j1 rule="para" parents="28832 41877"/>
    </justification>
  </clause>

  <clause id="42193">
    <literal><![CDATA[
      L(a(a(x,y,z),u,w),v5,v6) = L(a(w,u,a(z,y,x)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,28787,a(flip),b,41885,a),flip(a)].">
      <j1 rule="hyper" parents="64 28787 41885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42194">
    <literal><![CDATA[
      L(R(x,y,z),a(x,u,w),u) = L(R(x,y,z),x,a(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(25244,a,41961,a),flip(a)].">
      <j1 rule="hyper" parents="25244 41961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42195">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41814,a(flip),b,42088,a)].">
      <j1 rule="hyper" parents="64 41814 42088"/>
    </justification>
  </clause>

  <clause id="42198">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ 1) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(2274,a,42195,a)].">
      <j1 rule="hyper" parents="2274 42195"/>
    </justification>
  </clause>

  <clause id="42199">
    <literal><![CDATA[
      L(x,y,a(z,u,w \ 1)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,33636,a,b,42195,a)].">
      <j1 rule="hyper" parents="373 33636 42195"/>
    </justification>
  </clause>

  <clause id="42202">
    <literal><![CDATA[
      L(x,y,a(z * u,w,v5)) = L(x,y,a(v5,w,u * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,28846,a,b,42195,a),flip(a)].">
      <j1 rule="hyper" parents="373 28846 42195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42205">
    <literal><![CDATA[
      L(x \ 1,y,a(z,u,w)) = L(x,y,a(w,u,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,42178,a(flip),b,42195,a),flip(a)].">
      <j1 rule="hyper" parents="373 42178 42195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42206">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,a(w,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,42171,a(flip),b,42195,a),flip(a)].">
      <j1 rule="hyper" parents="373 42171 42195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42208">
    <literal><![CDATA[
      L(x,y,a(z \ 1,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,33636,a(flip),b,42195,a),flip(a)].">
      <j1 rule="hyper" parents="373 33636 42195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42209">
    <literal><![CDATA[
      L(x \ (a(y,z,u) \ w),x,a(u,z,y)) = (a(y,z,u) * x) \ w
    ]]></literal>
    <justification jstring="[hyper(373,a,346,a(flip),b,42195,a),flip(a)].">
      <j1 rule="hyper" parents="373 346 42195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42211">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(w,u,z) * y) = a(w,u,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(144,a,42195,a,b,28734,a)].">
      <j1 rule="hyper" parents="144 42195 28734"/>
    </justification>
  </clause>

  <clause id="42212">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * v5 = L(x,y,a(w,u,z)) * v5
    ]]></literal>
    <justification jstring="[hyper(144,a,42195,a,b,11,a)].">
      <j1 rule="hyper" parents="144 42195 11"/>
    </justification>
  </clause>

  <clause id="42214">
    <literal><![CDATA[
      L(x,y,a(z,u,w * (w * v5))) = L(x,y,a(L(v5,w,w),u,z))
    ]]></literal>
    <justification jstring="[para(2640(a,1),42195(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2640 42195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42217">
    <literal><![CDATA[
      L(x,y,a(z,u,((w \ 1) \ v5) * v6)) = L(x,y,a((w \ v5) * v6,u,z))
    ]]></literal>
    <justification jstring="[para(32809(a,1),42195(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32809 42195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42219">
    <literal><![CDATA[
      L(x,y,a(z,u,L(u,w,v5))) = L(x,y,a(u,u,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[para(39691(a,1),42195(a,1,3)),flip(a)].">
      <j1 rule="para" parents="39691 42195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42220">
    <literal><![CDATA[
      a(x,y,z) * (u * L(w,u,a(z,y,x))) = (a(x,y,z) * u) * w
    ]]></literal>
    <justification jstring="[hyper(145,a,42206,a(flip),b,18,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 42206 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42221">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) * y) * a(w,u,z) = x * (y * a(w,u,z))
    ]]></literal>
    <justification jstring="[para(42206(a,1),28800(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42206 28800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42222">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(w,u,z)) = v5
    ]]></literal>
    <justification jstring="[para(42198(a,1),2275(a,1))].">
      <j1 rule="para" parents="42198 2275"/>
    </justification>
  </clause>

  <clause id="42224">
    <literal><![CDATA[
      a(x,L(L(x,y,z),u,w),v5) = L(a(x,x,L(v5,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(39676(a,1),42182(a,2,1))].">
      <j1 rule="para" parents="39676 42182"/>
    </justification>
  </clause>

  <clause id="42225">
    <literal><![CDATA[
      L(a(x,x,y) \ L((y \ L(y,x,x)) \ 1,z,u),w,v5) = a(a(y,x,L(x,w,v5)),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,40088,a,b,42190,a)].">
      <j1 rule="hyper" parents="64 40088 42190"/>
    </justification>
  </clause>

  <clause id="42226">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(a(z,u,w),y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,25106,a,b,42192,a)].">
      <j1 rule="hyper" parents="35 25106 42192"/>
    </justification>
  </clause>

  <clause id="42227">
    <literal><![CDATA[
      L(x,y,a(L(z,u,w),v5,v5)) = L(x,y,a(z,v5,L(v5,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,42195,a,b,42219,a)].">
      <j1 rule="hyper" parents="373 42195 42219"/>
    </justification>
  </clause>

  <clause id="42228">
    <literal><![CDATA[
      a(x,L(L(x,y,z),u,w),v5) = a(x,x,L(L(v5,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,39675,a,b,42224,a),flip(a)].">
      <j1 rule="hyper" parents="373 39675 42224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42229">
    <literal><![CDATA[
      a(L(L(x,y,z),u,w),x,v5) = a(x,x,L(L(v5,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,32734,a,b,42228,a)].">
      <j1 rule="hyper" parents="64 32734 42228"/>
    </justification>
  </clause>

  <clause id="42230">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,a(y,z,z)) = L(a(x,y,z) \ 1,z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,42148,a,b,41957,a),flip(a)].">
      <j1 rule="hyper" parents="373 42148 41957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42231">
    <literal><![CDATA[
      (x / y) \ (x * a(z,z,u)) = y * a(z,z,L(u,y,T(x,w) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,24922,a(flip),b,41994,a)].">
      <j1 rule="hyper" parents="64 24922 41994"/>
    </justification>
  </clause>

  <clause id="42232">
    <literal><![CDATA[
      a(L(x \ y,x,x * z),u,z) = a(((x \ z) * y) \ z,u,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32497,a(flip),b,42010,a),flip(a)].">
      <j1 rule="hyper" parents="373 32497 42010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42233">
    <literal><![CDATA[
      x \ ((((x * y) / z) * (z * y)) / y) = L(y,z,(x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(139,a,42012,a,b,xx)].">
      <j1 rule="hyper" parents="139 42012"/>
    </justification>
  </clause>

  <clause id="42234">
    <literal><![CDATA[
      a(x * y,x,a(y,z,u)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,41374,a(flip),b,42089,a),flip(a)].">
      <j1 rule="hyper" parents="64 41374 42089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42235">
    <literal><![CDATA[
      a(x * L(y,z,u),x,a(y,z,u)) = a(x,x,a(L(y,z,u),z,u))
    ]]></literal>
    <justification jstring="[para(41783(a,1),42234(a,1,3))].">
      <j1 rule="para" parents="41783 42234"/>
    </justification>
  </clause>

  <clause id="42236">
    <literal><![CDATA[
      L(x,y,L(z,z,y * x)) = L(x,y,L(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42101,a(flip),b,42098,a),flip(a)].">
      <j1 rule="hyper" parents="64 42101 42098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42237">
    <literal><![CDATA[
      a(a(x,x,y),z,L(u,u,z * x)) = a(y,x,x \ L(x,z,L(u,u,z)))
    ]]></literal>
    <justification jstring="[para(42236(a,1),41694(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="42236 41694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42238">
    <literal><![CDATA[
      (x / y) \ (x * a(y,x * y,z)) = R(y,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,41790,a(flip),b,42126,a),flip(a)].">
      <j1 rule="hyper" parents="39 41790 42126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42239">
    <literal><![CDATA[
      R(x,x \ y,z) = R(x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42131,a(flip),b,42238,a)].">
      <j1 rule="hyper" parents="64 42131 42238"/>
    </justification>
  </clause>

  <clause id="42241">
    <literal><![CDATA[
      R(x,a(y,z,u) * z,w) = R(x,z * a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(42064(a,1),42187(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="42064 42187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42242">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,z,y) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,41685,a(flip),b,42230,a),flip(a)].">
      <j1 rule="hyper" parents="64 41685 42230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42243">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),z,y) = L(z \ L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(42242(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42242 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42244">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ ((u * (w * (x \ R(x,y,z)))) / (u * w)) = L(a(u,w,x \ R(x,y,z)) \ 1,x \ R(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(23713(a,2),42242(a,2,2)),flip(a)].">
      <j1 rule="para" parents="23713 42242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42245">
    <literal><![CDATA[
      L(a(L(x,x,y),z,u) \ 1,u,z) = u \ L(u,z,L(x,x,x * y))
    ]]></literal>
    <justification jstring="[para(29223(a,2),42242(a,2,2))].">
      <j1 rule="para" parents="29223 42242"/>
    </justification>
  </clause>

  <clause id="42246">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),y,a(w,u,z)) = L(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(42222,a,41867,a)].">
      <j1 rule="hyper" parents="42222 41867"/>
    </justification>
  </clause>

  <clause id="42247">
    <literal><![CDATA[
      L(x,y * z,(y \ z) \ u) = L(x,y * z,(y \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2186,a(flip),b,42005,a),flip(a)].">
      <j1 rule="hyper" parents="64 2186 42005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42248">
    <literal><![CDATA[
      x / L(a(y,y,z),y * z,(y \ z) * x) = (y * z) * (((1 / y) \ z) \ x)
    ]]></literal>
    <justification jstring="[para(42247(a,1),39463(a,1,2))].">
      <j1 rule="para" parents="42247 39463"/>
    </justification>
  </clause>

  <clause id="42249">
    <literal><![CDATA[
      L(x,y,a(y,z,z)) / y = x * (L(x,z,z) \ (L(x,z,z) / y))
    ]]></literal>
    <justification jstring="[para(28832(a,1),42046(a,1,1))].">
      <j1 rule="para" parents="28832 42046"/>
    </justification>
  </clause>

  <clause id="42250">
    <literal><![CDATA[
      L(a(x,y,z) \ a(u,w,a(x,y,z)),w,u) = L(a(x,y,z) \ 1,a(x,y,z) \ 1,a(u,w,w))
    ]]></literal>
    <justification jstring="[para(38628(a,1),42144(a,1,1,2))].">
      <j1 rule="para" parents="38628 42144"/>
    </justification>
  </clause>

  <clause id="42251">
    <literal><![CDATA[
      (x \ y) * (z * (L(z,x,y) \ z)) = (x \ R(y,x,z)) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,42045,a(flip),b,42161,a),flip(a)].">
      <j1 rule="hyper" parents="373 42045 42161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42252">
    <literal><![CDATA[
      a(x,y,z) \ (u * (a(x,y,z) * w)) = L(u,w,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(149,a,42177,a)].">
      <j1 rule="hyper" parents="149 42177"/>
    </justification>
  </clause>

  <clause id="42253">
    <literal><![CDATA[
      a(x,y,z) * (u * L(w,u,a(z,y,x))) = (a(x \ 1,y,z) * u) * w
    ]]></literal>
    <justification jstring="[para(2653(a,2),42220(a,2,1,1))].">
      <j1 rule="para" parents="2653 42220"/>
    </justification>
  </clause>

  <clause id="42254">
    <literal><![CDATA[
      a(x * L(y,z,u),x,a(y,z,u)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(41783(a,1),42235(a,2,3))].">
      <j1 rule="para" parents="41783 42235"/>
    </justification>
  </clause>

  <clause id="42255">
    <literal><![CDATA[
      L(x / y,y,a(y,z,z)) = x * (L(x,z,z) \ (L(x,z,z) / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,39279,a,b,42249,a)].">
      <j1 rule="hyper" parents="64 39279 42249"/>
    </justification>
  </clause>

  <clause id="42256">
    <literal><![CDATA[
      R(x / (1 / y),y,y * a(z,y,u)) = L(x,y,a(z,y,u)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,40526,a,b,42252,a)].">
      <j1 rule="hyper" parents="64 40526 42252"/>
    </justification>
  </clause>

  <clause id="42257">
    <literal><![CDATA[
      L(x * (1 / y),y,a(z,y,u)) * y = R(x,y,y * a(z,y,u))
    ]]></literal>
    <justification jstring="[para(11(a,1),42256(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11 42256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42258">
    <literal><![CDATA[
      (x * a(y,x,z)) * K(y,x) = (R(y,x,z) * x) / y
    ]]></literal>
    <justification jstring="[para(28688(a,1),41875(a,1,2))].">
      <j1 rule="para" parents="28688 41875"/>
    </justification>
  </clause>

  <clause id="42259">
    <literal><![CDATA[
      x * (a(y,x,z) * K(y,x)) = (R(y,x,z) * x) / y
    ]]></literal>
    <justification jstring="[hyper(23059,a,42258,a)].">
      <j1 rule="hyper" parents="23059 42258"/>
    </justification>
  </clause>

  <clause id="42261">
    <literal><![CDATA[
      R(x,a(y,x,z) * K(y,x),(a(y,x,z) * K(y,x)) \ u) = (((R(y,x,z) * x) / y) * ((a(y,x,z) * K(y,x)) \ u)) / u
    ]]></literal>
    <justification jstring="[para(42259(a,1),110(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="42259 110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42262">
    <literal><![CDATA[
      a(L(x,y,z),y,a(y,u,w)) = a(x,y,a(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,41106,a(flip),b,42060,a),flip(a)].">
      <j1 rule="hyper" parents="64 41106 42060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42264">
    <literal><![CDATA[
      L(x,a(x,y,z),L(u,x,w)) = x * a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(42262(a,1),39367(a,1,2)),flip(a)].">
      <j1 rule="para" parents="42262 39367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42265">
    <literal><![CDATA[
      L(x,a(x,y,z),L(u,x,w)) = a(u,x,a(z,y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,41900,a,b,42264,a),flip(a)].">
      <j1 rule="hyper" parents="373 41900 42264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42266">
    <literal><![CDATA[
      a(L(x,y,z),y,a(u,w,y)) = a(x,y,a(u,w,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,41445,a,b,42265,a(flip))].">
      <j1 rule="hyper" parents="36 41445 42265"/>
    </justification>
  </clause>

  <clause id="42267">
    <literal><![CDATA[
      a(x,a(x,y,z),L(u,x,w)) = a(u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,34906,a,b,42265,a(flip))].">
      <j1 rule="hyper" parents="36 34906 42265"/>
    </justification>
  </clause>

  <clause id="42268">
    <literal><![CDATA[
      a(x,a(x,y,z),L(u,x,w)) = v5 \ (a(u,x,a(z,y,x)) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,23174,a,b,42267,a),flip(a)].">
      <j1 rule="hyper" parents="373 23174 42267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42269">
    <literal><![CDATA[
      L(a(x,y,a(z,u,y)),y,w) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41463,a(flip),b,42267,a)].">
      <j1 rule="hyper" parents="64 41463 42267"/>
    </justification>
  </clause>

  <clause id="42270">
    <literal><![CDATA[
      a(x,y,a(z,y,a(u,w,y))) = 1
    ]]></literal>
    <justification jstring="[hyper(54,a,42269,a)].">
      <j1 rule="hyper" parents="54 42269"/>
    </justification>
  </clause>

  <clause id="42271">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,u,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,41703,a,b,42270,a)].">
      <j1 rule="hyper" parents="64 41703 42270"/>
    </justification>
  </clause>

  <clause id="42273">
    <literal><![CDATA[
      a(a(x,y,y),a(z,u,y),w) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,41803,a,b,42271,a)].">
      <j1 rule="hyper" parents="64 41803 42271"/>
    </justification>
  </clause>

  <clause id="42275">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,u,u)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,42273,a)].">
      <j1 rule="hyper" parents="53 42273"/>
    </justification>
  </clause>

  <clause id="42276">
    <literal><![CDATA[
      L(x,a(y,z,u),a(u,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(42222,a,42275,a)].">
      <j1 rule="hyper" parents="42222 42275"/>
    </justification>
  </clause>

  <clause id="42284">
    <literal><![CDATA[
      x * (L(x,a(x,y,z),u) \ w) = a(u,x,a(z,y,x)) * w
    ]]></literal>
    <justification jstring="[hyper(39,a,40998,a,b,42268,a(flip))].">
      <j1 rule="hyper" parents="39 40998 42268"/>
    </justification>
  </clause>

  <clause id="42285">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * (y \ w) = L(y,a(y,u,z),x) \ w
    ]]></literal>
    <justification jstring="[hyper(2346,a,42284,a),flip(a)].">
      <j1 rule="hyper" parents="2346 42284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42287">
    <literal><![CDATA[
      (x \ y) * a(z,x,a(u,w,x)) = L(x,a(x,w,u),z) \ y
    ]]></literal>
    <justification jstring="[hyper(23177,a,42285,a)].">
      <j1 rule="hyper" parents="23177 42285"/>
    </justification>
  </clause>

  <clause id="42288">
    <literal><![CDATA[
      a(x,a(y,z,u),L(u,z,y)) = a(x,L(u,z,y),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(42064(a,1),42087(a,1,3)),flip(a)].">
      <j1 rule="para" parents="42064 42087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42289">
    <literal><![CDATA[
      L(x \ y,z,L(x,x,y)) = L(x \ y,z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42083,a,b,42100,a),flip(a)].">
      <j1 rule="hyper" parents="64 42083 42100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42290">
    <literal><![CDATA[
      L(L(x,y \ z,L(y,y,z)),y \ z,a(y \ z,y,y)) = L(x,L(y \ z,y \ z,y),L(y,y,z))
    ]]></literal>
    <justification jstring="[para(42289(a,1),40956(a,2,2))].">
      <j1 rule="para" parents="42289 40956"/>
    </justification>
  </clause>

  <clause id="42291">
    <literal><![CDATA[
      ((x \ 1) / (x \ a(x,y,z))) * ((x \ a(x,y,z)) * u) = (x \ 1) * L(u,x * a(x,y,z),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(16066(a,1),42152(a,2,2))].">
      <j1 rule="para" parents="16066 42152"/>
    </justification>
  </clause>

  <clause id="42292">
    <literal><![CDATA[
      (x / y) * a(z,z,L(u,x / y,T(x,w) * (x / y))) = (a(z,z,u) * x) / y
    ]]></literal>
    <justification jstring="[hyper(64,a,28818,a(flip),b,42231,a),flip(a)].">
      <j1 rule="hyper" parents="64 28818 42231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42293">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,x,u),z,y) = z \ L(z,y,L(x,x,x * u))
    ]]></literal>
    <justification jstring="[para(40778(a,2),42245(a,1,1))].">
      <j1 rule="para" parents="40778 42245"/>
    </justification>
  </clause>

  <clause id="42294">
    <literal><![CDATA[
      x \ L(x,y,L(z,z,z * u)) = L(x \ L(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42243,a(flip),b,42293,a),flip(a)].">
      <j1 rule="hyper" parents="64 42243 42293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42295">
    <literal><![CDATA[
      L(x \ L(x,y,z),z,u) = x \ L(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[para(29223(a,1),42294(a,1,2)),flip(a)].">
      <j1 rule="para" parents="29223 42294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42296">
    <literal><![CDATA[
      a(x,y,L(y \ L(y,z,u),u,w)) = a(a(y,y,x),z,L(u,u,w))
    ]]></literal>
    <justification jstring="[para(42295(a,2),41694(a,1,3))].">
      <j1 rule="para" parents="42295 41694"/>
    </justification>
  </clause>

  <clause id="42297">
    <literal><![CDATA[
      a(x,y,L(y \ L(y,z,u),u,z)) = u \ L(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,42151,a(flip),b,42296,a),flip(a)].">
      <j1 rule="hyper" parents="373 42151 42296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42298">
    <literal><![CDATA[
      L(x,y,L(z,z,y)) \ L(x,x,a(z,y,y)) = z \ R(z,y,x)
    ]]></literal>
    <justification jstring="[para(31288(a,1),41818(a,1,2,3))].">
      <j1 rule="para" parents="31288 41818"/>
    </justification>
  </clause>

  <clause id="42300">
    <literal><![CDATA[
      a(a(x,x,L(y,z,z)),x \ z,u) = a(a(y,x,x),x \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,40060,a(flip),b,41835,a)].">
      <j1 rule="hyper" parents="64 40060 41835"/>
    </justification>
  </clause>

  <clause id="42301">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * (v5 \ 1)) * v6)) = a(x,y,a(z,u,v6 * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,41896,a(flip),b,41906,a),flip(a)].">
      <j1 rule="hyper" parents="373 41896 41906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42302">
    <literal><![CDATA[
      a(x,y,a(z,u,w * ((v5 \ 1) \ v6))) = a(x,y,a(z,u,w * (v5 \ v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,41897,a(flip),b,41908,a),flip(a)].">
      <j1 rule="hyper" parents="373 41897 41908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42303">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,w * v5,v5))) = a(x,y,a((w \ v5) * v5,u,z))
    ]]></literal>
    <justification jstring="[para(39946(a,1),41909(a,1,3))].">
      <j1 rule="para" parents="39946 41909"/>
    </justification>
  </clause>

  <clause id="42304">
    <literal><![CDATA[
      (x / y) \ (x * a(z,u,x)) = y * (a(z,u,x) * a(a(x,u,z),y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,33185,a(flip),b,41968,a),flip(a)].">
      <j1 rule="hyper" parents="373 33185 41968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42305">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * ((u \ 1) * w)) = a(x,y,(u \ z) * L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(27453,a,42007,a),flip(a)].">
      <j1 rule="hyper" parents="27453 42007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42306">
    <literal><![CDATA[
      L(x,y,R(z,u,w) \ v5) = L(x,y,L(z,u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,42070,a,b,42093,a),flip(a)].">
      <j1 rule="hyper" parents="64 42070 42093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42308">
    <literal><![CDATA[
      L(x,y,R(z,u,w) \ (z * v5)) = L(x,y,z * (L(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(2329(a,1),42306(a,2,3))].">
      <j1 rule="para" parents="2329 42306"/>
    </justification>
  </clause>

  <clause id="42309">
    <literal><![CDATA[
      L(1 / L(x,y,z),1 / R(x,u,w),L(x,u,w) \ L(x,y,z)) \ 1 = (1 / ((1 / R(x,u,w)) * (L(x,y,z) \ 1))) * (1 / R(x,u,w))
    ]]></literal>
    <justification jstring="[para(42306(a,1),35074(a,1,1))].">
      <j1 rule="para" parents="42306 35074"/>
    </justification>
  </clause>

  <clause id="42310">
    <literal><![CDATA[
      L(x,y,z * (R(z,u,w) \ v5)) = L(x,y,z * (L(z,u,w) \ v5))
    ]]></literal>
    <justification jstring="[para(1907(a,1),42308(a,1,3))].">
      <j1 rule="para" parents="1907 42308"/>
    </justification>
  </clause>

  <clause id="42311">
    <literal><![CDATA[
      1 / (x * ((a(y,z,u) * x) \ 1)) = (1 / (x * (1 / a(y,z,u)))) * x
    ]]></literal>
    <justification jstring="[para(42149(a,1),29338(a,1,2))].">
      <j1 rule="para" parents="42149 29338"/>
    </justification>
  </clause>

  <clause id="42312">
    <literal><![CDATA[
      L(x,y,a(z,u,((w \ 1) \ v5) * v6)) = L(x,y,a(z,u,(w \ v5) * v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,42195,a,b,42217,a),flip(a)].">
      <j1 rule="hyper" parents="373 42195 42217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42313">
    <literal><![CDATA[
      a(a(x,x,y),z,L(u,u,z * x)) = a(y,x,L(x \ L(x,z,u),u,z))
    ]]></literal>
    <justification jstring="[para(42295(a,2),42237(a,2,3))].">
      <j1 rule="para" parents="42295 42237"/>
    </justification>
  </clause>

  <clause id="42314">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(w,z,u)) = a(x,y,((z \ 1) * w) * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(27453,a,42305,a),flip(a)].">
      <j1 rule="hyper" parents="27453 42305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42315">
    <literal><![CDATA[
      (x * ((a(y,z,u) * x) \ 1)) \ 1 = (1 / (x * (1 / a(y,z,u)))) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,34368,a(flip),b,42311,a)].">
      <j1 rule="hyper" parents="64 34368 42311"/>
    </justification>
  </clause>

  <clause id="42316">
    <literal><![CDATA[
      L(x,y,a(z,u,(w \ 1) * v5)) = L(x,y,a(z,u,w * v5))
    ]]></literal>
    <justification jstring="[para(5341(a,1),42312(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5341 42312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42317">
    <literal><![CDATA[
      L(x,y,a(z,u,(w \ 1) * v5)) = L(x,y,a(z,u,v5 * w))
    ]]></literal>
    <justification jstring="[para(27528(a,1),42312(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27528 42312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42318">
    <literal><![CDATA[
      L(x,y,a(z,u \ w,u \ w)) = L(x,y,a(z,u * w,u * w))
    ]]></literal>
    <justification jstring="[para(40698(a,1),42316(a,1,3))].">
      <j1 rule="para" parents="40698 42316"/>
    </justification>
  </clause>

  <clause id="42319">
    <literal><![CDATA[
      a(a(x,x,y),z,L(u,u,z * x)) = u \ L(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,42297,a(flip),b,42313,a),flip(a)].">
      <j1 rule="hyper" parents="373 42297 42313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42320">
    <literal><![CDATA[
      (x * ((a(y,z,u) * x) \ 1)) \ 1 = (1 / (x * (a(y,z,u) \ 1))) * x
    ]]></literal>
    <justification jstring="[para(13923(a,1),42315(a,2,1,2,2))].">
      <j1 rule="para" parents="13923 42315"/>
    </justification>
  </clause>

  <clause id="42321">
    <literal><![CDATA[
      (x * ((a(y,z,u) * x) \ 1)) \ 1 = x * (((a(y,z,u) \ 1) * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,28926,a(flip),b,42320,a),flip(a)].">
      <j1 rule="hyper" parents="373 28926 42320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42322">
    <literal><![CDATA[
      L(a(x,y,z),u,a(x,y,z) * u) = u * (((a(x,y,z) \ 1) * u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,28813,a,b,42321,a)].">
      <j1 rule="hyper" parents="64 28813 42321"/>
    </justification>
  </clause>

  <clause id="42323">
    <literal><![CDATA[
      L(a(x,y,z),u,u * a(x,y,z)) = u * (((a(x,y,z) \ 1) * u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(24201,a,42322,a)].">
      <j1 rule="hyper" parents="24201 42322"/>
    </justification>
  </clause>

  <clause id="42324">
    <literal><![CDATA[
      a(a(x,y,z),L(x,u,w),v5) * a(x,y,z) = L(a(x,y,z),L(x,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,28787,a(flip),b,41871,a),flip(a)].">
      <j1 rule="hyper" parents="373 28787 41871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42325">
    <literal><![CDATA[
      L(x,y / z,L(z,z,y) * (y / z)) = L(x,y / z,(y * (z \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29003,a(flip),b,41993,a),flip(a)].">
      <j1 rule="hyper" parents="373 29003 41993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42326">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ (x * a(u,z,y)) = L(a(u,z,y),x,x * y)
    ]]></literal>
    <justification jstring="[para(36325(a,1),42102(a,1,1))].">
      <j1 rule="para" parents="36325 42102"/>
    </justification>
  </clause>

  <clause id="42327">
    <literal><![CDATA[
      x * (L(x,x,a(y,z,u)) \ a(u,z,y)) = L(a(u,z,y),x,x * y)
    ]]></literal>
    <justification jstring="[hyper(2342,a,42326,a)].">
      <j1 rule="hyper" parents="2342 42326"/>
    </justification>
  </clause>

  <clause id="42328">
    <literal><![CDATA[
      L(a(x,y,z),u,u * z) = u * ((u \ 1) * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(41509(a,1),42327(a,1,2)),flip(a)].">
      <j1 rule="para" parents="41509 42327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42329">
    <literal><![CDATA[
      L(a(x,y,z),u,u * z) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,1139,a(flip),b,42328,a),flip(a)].">
      <j1 rule="hyper" parents="373 1139 42328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42330">
    <literal><![CDATA[
      L(x,y / z,L(z,z,y) * (y / z)) = L(x,y / z,(z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29100,a(flip),b,42325,a),flip(a)].">
      <j1 rule="hyper" parents="373 29100 42325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42331">
    <literal><![CDATA[
      L(x,y / z,L(z,z,y) * (y / z)) = L(x,y / z,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,29101,a(flip),b,42330,a),flip(a)].">
      <j1 rule="hyper" parents="373 29101 42330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42332">
    <literal><![CDATA[
      L(x,y / z,L(z,z,y) * (y / z)) = L(x,z \ y,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,29437,a(flip),b,42331,a),flip(a)].">
      <j1 rule="hyper" parents="373 29437 42331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42333">
    <literal><![CDATA[
      L(x,y / z,L(z,z,y) * (z \ y)) = L(x,z \ y,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(29071,a,42332,a)].">
      <j1 rule="hyper" parents="29071 42332"/>
    </justification>
  </clause>

  <clause id="42334">
    <literal><![CDATA[
      L(x,y / z,a(y,z,z) \ y) = L(x,z \ y,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(37566(a,1),42333(a,1,3))].">
      <j1 rule="para" parents="37566 42333"/>
    </justification>
  </clause>

  <clause id="42335">
    <literal><![CDATA[
      L(x,y \ z,y \ (z \ y)) = L(x,z / y,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29194,a(flip),b,42334,a),flip(a)].">
      <j1 rule="hyper" parents="64 29194 42334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42336">
    <literal><![CDATA[
      L(x,y \ z,y \ (z \ y)) = L(x,y \ z,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,29437,a(flip),b,42335,a),flip(a)].">
      <j1 rule="hyper" parents="373 29437 42335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42337">
    <literal><![CDATA[
      L(x,y \ z,L(z,z,y)) = L(x,y \ z,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,35048,a,b,42336,a)].">
      <j1 rule="hyper" parents="64 35048 42336"/>
    </justification>
  </clause>

  <clause id="42338">
    <literal><![CDATA[
      L(x,y \ z,L(z,z,y)) = L(x,y \ z,y \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,30390,a,b,42337,a),flip(a)].">
      <j1 rule="hyper" parents="373 30390 42337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42339">
    <literal><![CDATA[
      L(x,y \ (a(z,u,w) \ 1),v5) = L(x,y \ a(w,u,z),v5)
    ]]></literal>
    <justification jstring="[para(41627(a,1),41652(a,1,2,2))].">
      <j1 rule="para" parents="41627 41652"/>
    </justification>
  </clause>

  <clause id="42340">
    <literal><![CDATA[
      L(x,a(y,z,u) \ a(u,z,y),w) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,1607,a(flip),b,42339,a),flip(a)].">
      <j1 rule="hyper" parents="64 1607 42339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42341">
    <literal><![CDATA[
      a(x * (a(y,z,u) \ 1),w,v5) = a(x * a(u,z,y),w,v5)
    ]]></literal>
    <justification jstring="[para(41627(a,1),41653(a,1,1,2))].">
      <j1 rule="para" parents="41627 41653"/>
    </justification>
  </clause>

  <clause id="42342">
    <literal><![CDATA[
      a(x * a(y,z,u),w,v5) = a(x * a(u,z,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,26850,a(flip),b,42341,a)].">
      <j1 rule="hyper" parents="64 26850 42341"/>
    </justification>
  </clause>

  <clause id="42352">
    <literal><![CDATA[
      L(x * L(x \ 1,y,y * L(y,z,u)),w,v5) = a(a(y,y,L(x,w,v5)),z,u)
    ]]></literal>
    <justification jstring="[para(33155(a,1),41705(a,1,1,2))].">
      <j1 rule="para" parents="33155 41705"/>
    </justification>
  </clause>

  <clause id="42353">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,y) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,42085,a(flip),b,41764,a(flip))].">
      <j1 rule="hyper" parents="36 42085 41764"/>
    </justification>
  </clause>

  <clause id="42354">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,z) = L(z \ L(z,y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,33505,a,b,42353,a)].">
      <j1 rule="hyper" parents="373 33505 42353"/>
    </justification>
  </clause>

  <clause id="42355">
    <literal><![CDATA[
      L(L(x,y,z) \ L(L(x,y,z),x \ u,w),L(x,y,z),u * x) = a(w,x \ u,L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,42025,a(flip),b,42353,a)].">
      <j1 rule="hyper" parents="64 42025 42353"/>
    </justification>
  </clause>

  <clause id="42356">
    <literal><![CDATA[
      a(x * L(x,y,z),u,w) \ 1 = a(w,u,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41795,a(flip),b,42353,a),flip(a)].">
      <j1 rule="hyper" parents="64 41795 42353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42357">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ 1 = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,41792,a(flip),b,42353,a),flip(a)].">
      <j1 rule="hyper" parents="64 41792 42353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42358">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ 1 = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41791,a(flip),b,42353,a),flip(a)].">
      <j1 rule="hyper" parents="64 41791 42353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42360">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w),v5,v6) \ 1 = L(a(w,a(y,z,u),x),v5,v6)
    ]]></literal>
    <justification jstring="[para(42357(a,1),42145(a,1,1,1))].">
      <j1 rule="para" parents="42357 42145"/>
    </justification>
  </clause>

  <clause id="42361">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ 1 = a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,41859,a,b,42358,a),flip(a)].">
      <j1 rule="hyper" parents="373 41859 42358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42362">
    <literal><![CDATA[
      a(x * y,x * y,a(z,u,x)) = a(y,x * y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41517,a,b,42358,a)].">
      <j1 rule="hyper" parents="64 41517 42358"/>
    </justification>
  </clause>

  <clause id="42363">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ 1 = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,42358,a)].">
      <j1 rule="hyper" parents="40 23134 42358"/>
    </justification>
  </clause>

  <clause id="42365">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ 1 = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(41803(a,1),42358(a,1,1))].">
      <j1 rule="para" parents="41803 42358"/>
    </justification>
  </clause>

  <clause id="42366">
    <literal><![CDATA[
      x \ (a(y,x,z) \ x) = a(y,x,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(42,a,42105,a(flip),b,42354,a)].">
      <j1 rule="hyper" parents="42 42105 42354"/>
    </justification>
  </clause>

  <clause id="42367">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * y = a(x,y,z) \ y
    ]]></literal>
    <justification jstring="[hyper(144,a,42366,a(flip),b,23767,a)].">
      <j1 rule="hyper" parents="144 42366 23767"/>
    </justification>
  </clause>

  <clause id="42369">
    <literal><![CDATA[
      x \ (y \ ((y * (x * z)) / z)) = a(y,x,z) \ 1
    ]]></literal>
    <justification jstring="[para(33322(a,1),42366(a,1,2))].">
      <j1 rule="para" parents="33322 42366"/>
    </justification>
  </clause>

  <clause id="42370">
    <literal><![CDATA[
      x \ ((a(y,x,z) \ 1) \ x) = a(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,26386,a,b,42367,a(flip))].">
      <j1 rule="hyper" parents="40 26386 42367"/>
    </justification>
  </clause>

  <clause id="42372">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ ((a(x,y,z) \ 1) * u) = L(y \ u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(42367(a,1),1632(a,2,1)),flip(a)].">
      <j1 rule="para" parents="42367 1632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42373">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ y = a(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(39,a,23174,a,b,42370,a),flip(a)].">
      <j1 rule="hyper" parents="39 23174 42370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42374">
    <literal><![CDATA[
      L((x \ ((x * y) * z)) / z,y,a(x,y,z)) = a(x,y,z) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,38625,a,b,42373,a)].">
      <j1 rule="hyper" parents="64 38625 42373"/>
    </justification>
  </clause>

  <clause id="42375">
    <literal><![CDATA[
      (a(x,y,z) * y) \ 1 = y \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(42373(a,1),36251(a,1,1))].">
      <j1 rule="para" parents="42373 36251"/>
    </justification>
  </clause>

  <clause id="42376">
    <literal><![CDATA[
      a(x,y,z) \ (y \ 1) = y \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,35834,a(flip),b,42375,a)].">
      <j1 rule="hyper" parents="64 35834 42375"/>
    </justification>
  </clause>

  <clause id="42377">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ u,(y \ ((y * x) * z)) / z,x * a(y,x,z)) = 1 \ ((x * a(y,x,z)) * u)
    ]]></literal>
    <justification jstring="[para(42375(a,1),41219(a,1,1,1))].">
      <j1 rule="para" parents="42375 41219"/>
    </justification>
  </clause>

  <clause id="42378">
    <literal><![CDATA[
      R(x,y,L(z \ 1,u,z) \ (a(w,z \ 1,v5) \ 1)) = R(x,y,a(w,z \ 1,v5) \ ((z \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(42376(a,2),13904(a,2,3))].">
      <j1 rule="para" parents="42376 13904"/>
    </justification>
  </clause>

  <clause id="42379">
    <literal><![CDATA[
      (x \ 1) * ((x \ (a(y,x,z) \ 1)) \ u) = x * ((a(y,x,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[para(42376(a,1),40518(a,1,2,1))].">
      <j1 rule="para" parents="42376 40518"/>
    </justification>
  </clause>

  <clause id="42380">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,z * y) = a(z,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,41396,a,b,42369,a)].">
      <j1 rule="hyper" parents="64 41396 42369"/>
    </justification>
  </clause>

  <clause id="42381">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ 1,v5,v6) \ 1) = a(L(a(z,u,w),v5,v6),y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,40097,a(flip),b,42380,a)].">
      <j1 rule="hyper" parents="64 40097 42380"/>
    </justification>
  </clause>

  <clause id="42386">
    <literal><![CDATA[
      a(a(x,y,y),z,z * (u \ (y \ u))) = a(a(u \ (y \ u),y,x),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41863,a(flip),b,41932,a)].">
      <j1 rule="hyper" parents="64 41863 41932"/>
    </justification>
  </clause>

  <clause id="42387">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w) \ x,x,a(y,z,u)) = a(w,a(u \ 1,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42208,a(flip),b,42074,a)].">
      <j1 rule="hyper" parents="64 42208 42074"/>
    </justification>
  </clause>

  <clause id="42388">
    <literal><![CDATA[
      a(x,a(y \ 1,z,u),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42058,a,b,42387,a),flip(a)].">
      <j1 rule="hyper" parents="64 42058 42387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42391">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(2653(a,1),42388(a,1,2))].">
      <j1 rule="para" parents="2653 42388"/>
    </justification>
  </clause>

  <clause id="42393">
    <literal><![CDATA[
      a(a(x,y,z),a(u,w,v5),v6) = a(v6,a(v5,w,u),a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(42050,a,42391,a),flip(a)].">
      <j1 rule="hyper" parents="42050 42391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42394">
    <literal><![CDATA[
      a(x * y,a(z,u,w),v5) = a(y * x,a(w,u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(26847,a,42391,a)].">
      <j1 rule="hyper" parents="26847 42391"/>
    </justification>
  </clause>

  <clause id="42396">
    <literal><![CDATA[
      a(x,L(y,z,u),a(y,w,v5)) = a(x,a(v5,w,y),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,36212,a,b,42391,a)].">
      <j1 rule="hyper" parents="373 36212 42391"/>
    </justification>
  </clause>

  <clause id="42397">
    <literal><![CDATA[
      a(x,a(y,z,u),(w \ 1) \ v5) = a(x,a(u,z,y),w \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,36034,a,b,42391,a)].">
      <j1 rule="hyper" parents="373 36034 42391"/>
    </justification>
  </clause>

  <clause id="42398">
    <literal><![CDATA[
      a(L(x,x,a(y,z,u)),a(u,z,y),w) = x \ R(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,41802,a(flip),b,42391,a),flip(a)].">
      <j1 rule="hyper" parents="373 41802 42391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42400">
    <literal><![CDATA[
      x * a(y,a(z,u,w),v5) = x * a(y,a(w,u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(145,a,42391,a,b,9,a)].">
      <j1 rule="hyper" parents="145 42391 9"/>
    </justification>
  </clause>

  <clause id="42403">
    <literal><![CDATA[
      a(L(x,x,a(y,z,u)),a(u,z,y),w) = x \ L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(31802(a,1),42398(a,2,2))].">
      <j1 rule="para" parents="31802 42398"/>
    </justification>
  </clause>

  <clause id="42404">
    <literal><![CDATA[
      L(x \ y,x,a((x \ y) * x,z,z)) = (a(y,x,a(x,z,z)) * x) \ y
    ]]></literal>
    <justification jstring="[para(33501(a,1),42113(a,2,1,1))].">
      <j1 rule="para" parents="33501 42113"/>
    </justification>
  </clause>

  <clause id="42405">
    <literal><![CDATA[
      L(x \ y,x,a((x \ y) * x,z,z)) = L(x,x,a(y,z,z)) \ y
    ]]></literal>
    <justification jstring="[para(40906(a,1),42404(a,2,1))].">
      <j1 rule="para" parents="40906 42404"/>
    </justification>
  </clause>

  <clause id="42406">
    <literal><![CDATA[
      L(x \ y,x,a(y,z,z)) = L(x,x,a(y,z,z)) \ y
    ]]></literal>
    <justification jstring="[para(26836(a,1),42405(a,1,3))].">
      <j1 rule="para" parents="26836 42405"/>
    </justification>
  </clause>

  <clause id="42408">
    <literal><![CDATA[
      L(L(x \ y,x,a(y,z,z)),x,a(y,z,z)) = (x * a(y,z,z)) \ R(y,z,L(z,x,x))
    ]]></literal>
    <justification jstring="[para(42406(a,2),41132(a,1,1))].">
      <j1 rule="para" parents="42406 41132"/>
    </justification>
  </clause>

  <clause id="42409">
    <literal><![CDATA[
      a(x,y,a(z,u,(z * z) * (u \ (z \ w)))) = a(x,y,a(z,u,(z \ w) * u))
    ]]></literal>
    <justification jstring="[para(27392(a,1),42138(a,1,3))].">
      <j1 rule="para" parents="27392 42138"/>
    </justification>
  </clause>

  <clause id="42410">
    <literal><![CDATA[
      x / a(y,y,L(z,y * z,(y \ z) * x)) = (y * z) * (((1 / y) \ z) \ x)
    ]]></literal>
    <justification jstring="[para(39675(a,2),42248(a,1,2))].">
      <j1 rule="para" parents="39675 42248"/>
    </justification>
  </clause>

  <clause id="42411">
    <literal><![CDATA[
      L(x \ L(x,y,y * L(y,z,u)),w,v5) = a(a(y,y,L(x,w,v5)),z,u)
    ]]></literal>
    <justification jstring="[para(38607(a,1),42352(a,1,1))].">
      <j1 rule="para" parents="38607 42352"/>
    </justification>
  </clause>

  <clause id="42412">
    <literal><![CDATA[
      a(a(x,x,L(y,z,u)),w,v5) = L(a(a(x,x,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(41698(a,1),42411(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41698 42411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42413">
    <literal><![CDATA[
      L(a(a(x,x,y),z,u),x,w) = a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[para(39645(a,1),42412(a,1,1)),flip(a)].">
      <j1 rule="para" parents="39645 42412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42414">
    <literal><![CDATA[
      (x * a(a(x,x,y),z,u)) * w = (x * w) * a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,42413,a(flip),b,28783,a),flip(a)].">
      <j1 rule="hyper" parents="145 42413 28783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42415">
    <literal><![CDATA[
      (x * a(a(x,x,y),z,u)) * w = x * (w * a(a(x,x,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,41676,a(flip),b,42414,a),flip(a)].">
      <j1 rule="hyper" parents="373 41676 42414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42416">
    <literal><![CDATA[
      L(x,x \ L(x,y,z),u) * w = x * (w * a(a(x,x,u),y,z))
    ]]></literal>
    <justification jstring="[para(41668(a,2),42415(a,1,1))].">
      <j1 rule="para" parents="41668 42415"/>
    </justification>
  </clause>

  <clause id="42417">
    <literal><![CDATA[
      L(x,y,z) * ((x \ L(x,y,z)) \ u) = x * (u * a(a(x,x,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39221,a(flip),b,42416,a)].">
      <j1 rule="hyper" parents="64 39221 42416"/>
    </justification>
  </clause>

  <clause id="42418">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ u = (L(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(35,a,41774,a,b,42417,a),flip(a)].">
      <j1 rule="hyper" parents="35 41774 42417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42419">
    <literal><![CDATA[
      (L(x,y,z) \ x) * ((x \ L(x,y,z)) * u) = u
    ]]></literal>
    <justification jstring="[hyper(396,a,42418,a),flip(a)].">
      <j1 rule="hyper" parents="396 42418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42420">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ u = (x \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(395,a,42418,a),flip(a)].">
      <j1 rule="hyper" parents="395 42418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42423">
    <literal><![CDATA[
      x / (L(y,z,u) \ y) = (y \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,23588,a(flip),b,42418,a),flip(a)].">
      <j1 rule="hyper" parents="145 23588 42418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42426">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(u,x,x * L(x,y,z)) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,41714,a(flip),b,42418,a),flip(a)].">
      <j1 rule="hyper" parents="64 41714 42418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42427">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) * (L(x,y,z) \ x) = u
    ]]></literal>
    <justification jstring="[hyper(23589,a,42419,a)].">
      <j1 rule="hyper" parents="23589 42419"/>
    </justification>
  </clause>

  <clause id="42428">
    <literal><![CDATA[
      L(x,y \ L(y,z,u),L(y,z,u) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,7748,a(flip),b,42419,a)].">
      <j1 rule="hyper" parents="64 7748 42419"/>
    </justification>
  </clause>

  <clause id="42430">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,40803,a(flip),b,42428,a)].">
      <j1 rule="hyper" parents="64 40803 42428"/>
    </justification>
  </clause>

  <clause id="42431">
    <literal><![CDATA[
      L(x,y * L(y,z,u),y * L(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,37721,a(flip),b,42428,a)].">
      <j1 rule="hyper" parents="64 37721 42428"/>
    </justification>
  </clause>

  <clause id="42432">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(34364,a,42430,a),flip(a)].">
      <j1 rule="hyper" parents="34364 42430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42433">
    <literal><![CDATA[
      (a(x,y,z) \ 1) * u = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(13952,a,42430,a)].">
      <j1 rule="hyper" parents="13952 42430"/>
    </justification>
  </clause>

  <clause id="42435">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ u = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(1155,a,42430,a),flip(a)].">
      <j1 rule="hyper" parents="1155 42430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42436">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ u = a(x,y,z) \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(710,a,42430,a),flip(a)].">
      <j1 rule="hyper" parents="710 42430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42443">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,42430,a,b,25162,a),flip(a)].">
      <j1 rule="hyper" parents="140 42430 25162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42444">
    <literal><![CDATA[
      x * (a(y,z,u) \ 1) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,38564,a(flip),b,42430,a),flip(a)].">
      <j1 rule="hyper" parents="64 38564 42430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42446">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ 1) * v5 = L(a(x,y,z),u,w) \ v5
    ]]></literal>
    <justification jstring="[hyper(64,a,35185,a(flip),b,42430,a)].">
      <j1 rule="hyper" parents="64 35185 42430"/>
    </justification>
  </clause>

  <clause id="42448">
    <literal><![CDATA[
      x / (x * a(y,z,u)) = a(y,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(225,a,42430,a(flip),b,38560,a(flip))].">
      <j1 rule="hyper" parents="225 42430 38560"/>
    </justification>
  </clause>

  <clause id="42449">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) * u = a(x,y,z) * (u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,42430,a(flip),b,24645,a)].">
      <j1 rule="hyper" parents="145 42430 24645"/>
    </justification>
  </clause>

  <clause id="42450">
    <literal><![CDATA[
      x / (a(y,z,u) \ 1) = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(142,a,42430,a(flip),b,27215,a)].">
      <j1 rule="hyper" parents="142 42430 27215"/>
    </justification>
  </clause>

  <clause id="42452">
    <literal><![CDATA[
      x \ (a(y,z,u) \ x) = a(y,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,38564,a(flip),b,42430,a(flip))].">
      <j1 rule="hyper" parents="139 38564 42430"/>
    </justification>
  </clause>

  <clause id="42454">
    <literal><![CDATA[
      (x * a(y,z,u)) \ x = a(y,z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,42430,a(flip),b,27215,a)].">
      <j1 rule="hyper" parents="139 42430 27215"/>
    </justification>
  </clause>

  <clause id="42455">
    <literal><![CDATA[
      (a(x,y,z) * u) \ u = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(139,a,42430,a(flip),b,24623,a)].">
      <j1 rule="hyper" parents="139 42430 24623"/>
    </justification>
  </clause>

  <clause id="42456">
    <literal><![CDATA[
      (1 / a(x,y,z)) \ u = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(139,a,42430,a(flip),b,559,a)].">
      <j1 rule="hyper" parents="139 42430 559"/>
    </justification>
  </clause>

  <clause id="42458">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(42430(a,1),51(a,2))].">
      <j1 rule="para" parents="42430 51"/>
    </justification>
  </clause>

  <clause id="42459">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ v5) = L(x,y,a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(42430(a,1),2187(a,1,3))].">
      <j1 rule="para" parents="42430 2187"/>
    </justification>
  </clause>

  <clause id="42461">
    <literal><![CDATA[
      a(a(x,y,z) \ u,w,v5) = a(a(x,y,z) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(42430(a,1),2644(a,1,1))].">
      <j1 rule="para" parents="42430 2644"/>
    </justification>
  </clause>

  <clause id="42462">
    <literal><![CDATA[
      a((a(x,y,z) \ u) * w,v5,v6) = a((a(x,y,z) * u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(42430(a,1),2680(a,1,1,1))].">
      <j1 rule="para" parents="42430 2680"/>
    </justification>
  </clause>

  <clause id="42463">
    <literal><![CDATA[
      L(x,a(y,z,u) \ w,v5) = L(x,a(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(42430(a,1),11837(a,1,2))].">
      <j1 rule="para" parents="42430 11837"/>
    </justification>
  </clause>

  <clause id="42464">
    <literal><![CDATA[
      a(x,a(y,z,u) \ w,v5) = a(x,a(y,z,u) * w,v5)
    ]]></literal>
    <justification jstring="[para(42430(a,1),11982(a,1,2))].">
      <j1 rule="para" parents="42430 11982"/>
    </justification>
  </clause>

  <clause id="42465">
    <literal><![CDATA[
      a(x,(a(y,z,u) \ w) * v5,v6) = a(x,(a(y,z,u) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(42430(a,1),11992(a,1,2,1))].">
      <j1 rule="para" parents="42430 11992"/>
    </justification>
  </clause>

  <clause id="42467">
    <literal><![CDATA[
      a(a(x,y,z) \ u,w,v5) = a(u * a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[para(42430(a,1),30383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42430 30383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42468">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ v5) = L(x,y,v5 * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(42430(a,1),30388(a,1,3)),flip(a)].">
      <j1 rule="para" parents="42430 30388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42470">
    <literal><![CDATA[
      R(x,(a(y,z,u) \ w) * v5,v6) = R(x,(w * a(y,z,u)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(42430(a,1),30840(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="42430 30840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42471">
    <literal><![CDATA[
      L(x,y \ (a(z,u,w) \ v5),v6) = L(x,y \ (v5 * a(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[para(42430(a,1),31029(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="42430 31029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42472">
    <literal><![CDATA[
      L(x,a(y,z,u) \ w,v5) = L(x,w * a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[para(42430(a,1),31760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="42430 31760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42476">
    <literal><![CDATA[
      a((a(x,y,z) \ u) \ w,v5,v6) = a((a(x,y,z) * u) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(42430(a,1),33709(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="42430 33709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42478">
    <literal><![CDATA[
      L(x,(a(y,z,u) \ w) * v5,v6) = L(x,(w * a(y,z,u)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(42430(a,1),34383(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="42430 34383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42479">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),a(y,z,u) * y,a(y,z,u)) = y \ (y * x)
    ]]></literal>
    <justification jstring="[para(42430(a,1),29976(a,2,2))].">
      <j1 rule="para" parents="42430 29976"/>
    </justification>
  </clause>

  <clause id="42481">
    <literal><![CDATA[
      R(x,y,a(z,u,w) \ v5) = R(x,y,a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(42430(a,1),38879(a,1,3))].">
      <j1 rule="para" parents="42430 38879"/>
    </justification>
  </clause>

  <clause id="42482">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) \ v5) \ v6) = a(x,y,(v5 * a(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(42430(a,1),39104(a,1,3,1))].">
      <j1 rule="para" parents="42430 39104"/>
    </justification>
  </clause>

  <clause id="42484">
    <literal><![CDATA[
      (a(x,y,z) * a(z,y,x)) * u = a(x,y,z) * (a(z,y,x) * u)
    ]]></literal>
    <justification jstring="[para(42430(a,1),41417(a,1,2))].">
      <j1 rule="para" parents="42430 41417"/>
    </justification>
  </clause>

  <clause id="42485">
    <literal><![CDATA[
      a(x,a(y,z,u),a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,42393,a(flip),b,42443,a)].">
      <j1 rule="hyper" parents="64 42393 42443"/>
    </justification>
  </clause>

  <clause id="42490">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ 1 = w \ L(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(42443(a,1),41684(a,1,2))].">
      <j1 rule="para" parents="42443 41684"/>
    </justification>
  </clause>

  <clause id="42491">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,42485,a)].">
      <j1 rule="hyper" parents="53 42485"/>
    </justification>
  </clause>

  <clause id="42493">
    <literal><![CDATA[
      (R(x,y,z) \ x) / (x * (R(x,y,z) \ a(x,u,w))) = a(x,u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(225,a,30910,a(flip),b,42432,a)].">
      <j1 rule="hyper" parents="225 30910 42432"/>
    </justification>
  </clause>

  <clause id="42497">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * (v5 * a(z,u,w))) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[para(42432(a,1),38924(a,1,3,2))].">
      <j1 rule="para" parents="42432 38924"/>
    </justification>
  </clause>

  <clause id="42499">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ v5 = v5 * a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(42358(a,1),42432(a,1,1))].">
      <j1 rule="para" parents="42358 42432"/>
    </justification>
  </clause>

  <clause id="42501">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ v5 = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(42363(a,1),42432(a,1,1))].">
      <j1 rule="para" parents="42363 42432"/>
    </justification>
  </clause>

  <clause id="42502">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ v5 = v5 * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(42365(a,1),42432(a,1,1))].">
      <j1 rule="para" parents="42365 42432"/>
    </justification>
  </clause>

  <clause id="42507">
    <literal><![CDATA[
      a(x,y,z) \ L(u,u,a(x,y,z)) = (1 / u) \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,37296,a(flip),b,42433,a),flip(a)].">
      <j1 rule="hyper" parents="64 37296 42433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42510">
    <literal><![CDATA[
      (a(x,y,z) \ K(u,w)) * v5 = K(u,w) * (a(x,y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(42433(a,1),24366(a,1,2)),flip(a)].">
      <j1 rule="para" parents="42433 24366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42511">
    <literal><![CDATA[
      a(x * (a(y,z,u) \ w),v5,v6) = a(x * (a(y,z,u) * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(42433(a,1),26886(a,1,1,2))].">
      <j1 rule="para" parents="42433 26886"/>
    </justification>
  </clause>

  <clause id="42513">
    <literal><![CDATA[
      (a(x,y,z) \ x) \ (a(x,y,z) \ u) = L(x \ u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(42433(a,1),29939(a,1,2))].">
      <j1 rule="para" parents="42433 29939"/>
    </justification>
  </clause>

  <clause id="42516">
    <literal><![CDATA[
      (a(x,y,L(a(y,z,u),w,v5)) \ 1) * v6 = a(x,L(a(y,z,u),w,v5),y) \ v6
    ]]></literal>
    <justification jstring="[para(36394(a,1),42433(a,1,1,1))].">
      <j1 rule="para" parents="36394 42433"/>
    </justification>
  </clause>

  <clause id="42517">
    <literal><![CDATA[
      L(a(x,y,z) \ u,u,a(x,y,z)) = (a(x,y,z) / u) \ 1
    ]]></literal>
    <justification jstring="[para(42433(a,1),38618(a,1,1))].">
      <j1 rule="para" parents="42433 38618"/>
    </justification>
  </clause>

  <clause id="42519">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,v5) \ v6)) = a(x,y,z \ (a(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(42433(a,1),38919(a,1,3,2))].">
      <j1 rule="para" parents="42433 38919"/>
    </justification>
  </clause>

  <clause id="42520">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,v5) \ v6)) = a(x,y,z * (a(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(42433(a,1),38927(a,1,3,2))].">
      <j1 rule="para" parents="42433 38927"/>
    </justification>
  </clause>

  <clause id="42521">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) \ v5) * v6) = a(x,y,(a(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(42433(a,1),38934(a,1,3,1))].">
      <j1 rule="para" parents="42433 38934"/>
    </justification>
  </clause>

  <clause id="42522">
    <literal><![CDATA[
      (x * ((a(y,z,u) \ x) \ 1)) * x = ((a(y,z,u) \ 1) / x) \ 1
    ]]></literal>
    <justification jstring="[para(42433(a,1),39855(a,1,1,2,1))].">
      <j1 rule="para" parents="42433 39855"/>
    </justification>
  </clause>

  <clause id="42523">
    <literal><![CDATA[
      L(a(x,y,z),u,u * a(x,y,z)) = u * ((a(x,y,z) \ u) \ 1)
    ]]></literal>
    <justification jstring="[para(42433(a,1),42323(a,2,2,1))].">
      <j1 rule="para" parents="42433 42323"/>
    </justification>
  </clause>

  <clause id="42524">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ v5 = a(w,a(y,z,u),x) * v5
    ]]></literal>
    <justification jstring="[para(42357(a,1),42433(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42357 42433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42525">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ v5 = a(w,u,a(x,y,z)) * v5
    ]]></literal>
    <justification jstring="[para(42358(a,1),42433(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42358 42433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42526">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ v5 = a(a(z,u,w),y,x) * v5
    ]]></literal>
    <justification jstring="[para(42363(a,1),42433(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42363 42433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42528">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ (a(x,y,z) \ u) = L(y \ u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(42433(a,1),42372(a,1,2))].">
      <j1 rule="para" parents="42433 42372"/>
    </justification>
  </clause>

  <clause id="42529">
    <literal><![CDATA[
      L(x \ (a(y,z,u) * w),x,a(y,z,u)) = ((a(y,z,u) \ 1) * x) \ w
    ]]></literal>
    <justification jstring="[para(42435(a,1),1633(a,1,1,2))].">
      <j1 rule="para" parents="42435 1633"/>
    </justification>
  </clause>

  <clause id="42532">
    <literal><![CDATA[
      L(x,y * (a(z,u,w) \ v5),v6) = L(x,y * (a(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(42435(a,1),29866(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="42435 29866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42533">
    <literal><![CDATA[
      L(a(x,y,z) * u,x,a(x,y,z)) = (a(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(42435(a,1),31079(a,1,1))].">
      <j1 rule="para" parents="42435 31079"/>
    </justification>
  </clause>

  <clause id="42534">
    <literal><![CDATA[
      (a(x,y,z) * u) \ R(u,w,v5) = a(x,y,z) \ (u \ R(u,w,v5))
    ]]></literal>
    <justification jstring="[para(42435(a,1),31571(a,1,1))].">
      <j1 rule="para" parents="42435 31571"/>
    </justification>
  </clause>

  <clause id="42536">
    <literal><![CDATA[
      a(x,y * (a(z,u,w) \ v5),v6) = a(x,y * (a(z,u,w) * v5),v6)
    ]]></literal>
    <justification jstring="[para(42435(a,1),32111(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="42435 32111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42537">
    <literal><![CDATA[
      a(x,y,a(z,u,w) \ v5) = a(x,y,a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(42435(a,1),38920(a,1,3)),flip(a)].">
      <j1 rule="para" parents="42435 38920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42538">
    <literal><![CDATA[
      R(x,y,z * (a(u,w,v5) \ v6)) = R(x,y,z * (a(u,w,v5) * v6))
    ]]></literal>
    <justification jstring="[para(42435(a,1),40603(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="42435 40603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42539">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,w)) \ v5 = a(z * L(z,u,w),y,x) * v5
    ]]></literal>
    <justification jstring="[para(42356(a,1),42435(a,1,1))].">
      <j1 rule="para" parents="42356 42435"/>
    </justification>
  </clause>

  <clause id="42545">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,a(x,y,z),u) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(35,a,25198,a,b,42444,a)].">
      <j1 rule="hyper" parents="35 25198 42444"/>
    </justification>
  </clause>

  <clause id="42546">
    <literal><![CDATA[
      (1 / x) * (a(y,z,u) \ x) = L(a(y,z,u) \ 1,x,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,42444,a(flip),b,561,a)].">
      <j1 rule="hyper" parents="145 42444 561"/>
    </justification>
  </clause>

  <clause id="42547">
    <literal><![CDATA[
      x * (L(x,y,z) \ (a(u,w,v5) \ 1)) = L(x,y,z) \ (a(u,w,v5) \ x)
    ]]></literal>
    <justification jstring="[hyper(139,a,42444,a(flip),b,2328,a),flip(a)].">
      <j1 rule="hyper" parents="139 42444 2328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42548">
    <literal><![CDATA[
      R(x,y,z) * (x \ (a(u,w,v5) \ 1)) = x \ (a(u,w,v5) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,42444,a(flip),b,1902,a),flip(a)].">
      <j1 rule="hyper" parents="139 42444 1902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42549">
    <literal><![CDATA[
      (x * y) \ (x * (a(z,u,w) \ y)) = L(a(z,u,w) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(42444(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="42444 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42550">
    <literal><![CDATA[
      x * R(x \ (a(y,z,u) \ 1),w,v5) = x \ R(a(y,z,u) \ x,w,v5)
    ]]></literal>
    <justification jstring="[para(42444(a,1),2124(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="42444 2124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42552">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,a(x,y,z),u) = u * ((a(x,y,z) \ 1) * w)
    ]]></literal>
    <justification jstring="[para(42444(a,1),11815(a,1,1))].">
      <j1 rule="para" parents="42444 11815"/>
    </justification>
  </clause>

  <clause id="42554">
    <literal><![CDATA[
      (a(x,y,z) \ u) * K(w,v5) = u * (a(x,y,z) \ K(w,v5))
    ]]></literal>
    <justification jstring="[para(42444(a,1),24286(a,1,1))].">
      <j1 rule="para" parents="42444 24286"/>
    </justification>
  </clause>

  <clause id="42555">
    <literal><![CDATA[
      (x * (a(y,z,u) \ K(w,v5))) * v6 = (a(y,z,u) \ x) * (K(w,v5) * v6)
    ]]></literal>
    <justification jstring="[para(42444(a,1),24883(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42444 24883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42557">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,a(x,y,z),z) * z) = u \ ((a(x,y,z) \ u) * z)
    ]]></literal>
    <justification jstring="[para(42444(a,1),35805(a,2,2,1))].">
      <j1 rule="para" parents="42444 35805"/>
    </justification>
  </clause>

  <clause id="42559">
    <literal><![CDATA[
      a(a(x,y,z) \ u,w,v5) = a(u * a(z,y,x),w,v5)
    ]]></literal>
    <justification jstring="[para(42444(a,1),42341(a,1,1))].">
      <j1 rule="para" parents="42444 42341"/>
    </justification>
  </clause>

  <clause id="42561">
    <literal><![CDATA[
      (T(x,y) * a(z,u,w)) \ x = (a(z,u,w) \ 1) * K(y,x)
    ]]></literal>
    <justification jstring="[para(42450(a,1),15022(a,1,1))].">
      <j1 rule="para" parents="42450 15022"/>
    </justification>
  </clause>

  <clause id="42565">
    <literal><![CDATA[
      L(a(x,y,z),u,u) \ u = (1 / u) \ (a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(42452(a,1),34600(a,1,2)),flip(a)].">
      <j1 rule="para" parents="42452 34600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42568">
    <literal><![CDATA[
      (x \ (a(y,z,u) \ x)) * w = a(y,z,u) \ w
    ]]></literal>
    <justification jstring="[para(42452(a,2),42433(a,1,1))].">
      <j1 rule="para" parents="42452 42433"/>
    </justification>
  </clause>

  <clause id="42571">
    <literal><![CDATA[
      (x * a(y,z,a(u,w,v5))) \ x = a(a(u,w,v5),z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,42363,a(flip),b,42454,a),flip(a)].">
      <j1 rule="hyper" parents="373 42363 42454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42576">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z),u) = w \ (a(x,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,23174,a,b,42491,a),flip(a)].">
      <j1 rule="hyper" parents="373 23174 42491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42577">
    <literal><![CDATA[
      L(a(x,y,z) * a(u,w,a(x,y,z)),w,u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42142,a,b,42491,a)].">
      <j1 rule="hyper" parents="64 42142 42491"/>
    </justification>
  </clause>

  <clause id="42578">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * a(w,u,a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41641,a,b,42491,a)].">
      <j1 rule="hyper" parents="64 41641 42491"/>
    </justification>
  </clause>

  <clause id="42580">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ a(x,y,z) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,42491,a(flip),b,41641,a)].">
      <j1 rule="hyper" parents="139 42491 41641"/>
    </justification>
  </clause>

  <clause id="42581">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ a(z,u,w) = L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,42491,a(flip),b,41640,a)].">
      <j1 rule="hyper" parents="139 42491 41640"/>
    </justification>
  </clause>

  <clause id="42587">
    <literal><![CDATA[
      L(a(a(x,y,z),u,w),a(x,y,z),v5) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(42491(a,1),40756(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42491 40756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42592">
    <literal><![CDATA[
      a(x * L(x,y,z),x * L(x,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,42431,a,b,25162,a),flip(a)].">
      <j1 rule="hyper" parents="140 42431 25162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42593">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ u = (R(x,y,z) \ x) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,36357,a(flip),b,42431,a),flip(a)].">
      <j1 rule="hyper" parents="64 36357 42431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42597">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) \ (u * L(x,y,z)) = a(u,L(x,y,z),L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(42423(a,1),33334(a,1,1))].">
      <j1 rule="para" parents="42423 33334"/>
    </justification>
  </clause>

  <clause id="42598">
    <literal><![CDATA[
      (x * (y \ L(y,z,u))) \ x = L(y,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(139,a,42427,a(flip),b,23746,a(flip))].">
      <j1 rule="hyper" parents="139 42427 23746"/>
    </justification>
  </clause>

  <clause id="42603">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(u,w,v5) = u * (a(x,y,z) \ a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(145,a,42568,a(flip),b,29914,a),flip(a)].">
      <j1 rule="hyper" parents="145 42568 29914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42605">
    <literal><![CDATA[
      (R(x,y,z) \ x) * ((x \ R(x,y,z)) * u) = u
    ]]></literal>
    <justification jstring="[hyper(396,a,42593,a),flip(a)].">
      <j1 rule="hyper" parents="396 42593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42606">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ u = (x \ R(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(395,a,42593,a),flip(a)].">
      <j1 rule="hyper" parents="395 42593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42608">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ u = u * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,25926,a(flip),b,42593,a),flip(a)].">
      <j1 rule="hyper" parents="373 25926 42593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42611">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (u * (x \ R(x,y,z))) = u
    ]]></literal>
    <justification jstring="[para(23708(a,1),42605(a,1,2))].">
      <j1 rule="para" parents="23708 42605"/>
    </justification>
  </clause>

  <clause id="42612">
    <literal><![CDATA[
      L(x,(y * L(y,z,u)) * ((y \ R(y,z,u)) * w),v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[para(42606(a,1),39201(a,1,2,2))].">
      <j1 rule="para" parents="42606 39201"/>
    </justification>
  </clause>

  <clause id="42613">
    <literal><![CDATA[
      L(x \ R(x,y,z),x * L(x,y,z),u) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,36270,a,b,42608,a)].">
      <j1 rule="hyper" parents="40 36270 42608"/>
    </justification>
  </clause>

  <clause id="42616">
    <literal><![CDATA[
      L(x * (y \ R(y,z,u)),R(y,z,u) \ y,R(y,z,u)) = y \ (R(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(42611(a,1),101(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="42611 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42618">
    <literal><![CDATA[
      L(x,y,a(L(z,u,w),u,w) * u) = L(x,y,z * (R(z,u,w) \ u))
    ]]></literal>
    <justification jstring="[para(33469(a,1),42459(a,1,3)),flip(a)].">
      <j1 rule="para" parents="33469 42459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42619">
    <literal><![CDATA[
      L(x,a(y,z,u) * a(u,z,y),w) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,42340,a(flip),b,42463,a),flip(a)].">
      <j1 rule="hyper" parents="64 42340 42463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42621">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,v5) * a(v5,w,u))) \ v6) = a(x,y,(a(u,w,v5) * a(v5,w,u)) \ (z \ v6))
    ]]></literal>
    <justification jstring="[para(42619(a,1),39066(a,1,3))].">
      <j1 rule="para" parents="42619 39066"/>
    </justification>
  </clause>

  <clause id="42622">
    <literal><![CDATA[
      L(a(x,y,z) \ y,y * a(x,y,z),u) \ u = T(u * (a(x,y,z) / y),y)
    ]]></literal>
    <justification jstring="[para(42472(a,1),40599(a,1,1))].">
      <j1 rule="para" parents="42472 40599"/>
    </justification>
  </clause>

  <clause id="42625">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),w) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42357,a(flip),b,42490,a),flip(a)].">
      <j1 rule="hyper" parents="64 42357 42490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42626">
    <literal><![CDATA[
      L(x,a(y,z,u),w) \ x = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(40,a,5658,a,b,42490,a)].">
      <j1 rule="hyper" parents="40 5658 42490"/>
    </justification>
  </clause>

  <clause id="42627">
    <literal><![CDATA[
      x * a(x,a(y,z,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(145,a,42357,a(flip),b,42490,a(flip))].">
      <j1 rule="hyper" parents="145 42357 42490"/>
    </justification>
  </clause>

  <clause id="42628">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,42391,a,b,42625,a),flip(a)].">
      <j1 rule="hyper" parents="373 42391 42625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42632">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * x = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(39,a,23174,a,b,42625,a)].">
      <j1 rule="hyper" parents="39 23174 42625"/>
    </justification>
  </clause>

  <clause id="42634">
    <literal><![CDATA[
      L(x,a(y,z,u),w) \ x = a(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,42391,a,b,42626,a),flip(a)].">
      <j1 rule="hyper" parents="373 42391 42626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42636">
    <literal><![CDATA[
      x * L(x \ 1,a(y,z,u),w) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31832,a,b,42628,a)].">
      <j1 rule="hyper" parents="64 31832 42628"/>
    </justification>
  </clause>

  <clause id="42637">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,u),w),v5,v6) = a(L(x,v5,v6),a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,34562,a(flip),b,42628,a)].">
      <j1 rule="hyper" parents="64 34562 42628"/>
    </justification>
  </clause>

  <clause id="42638">
    <literal><![CDATA[
      x \ (y * L(y \ x,a(z,u,w),v5)) = a(x \ y,a(w,u,z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31834,a(flip),b,42628,a)].">
      <j1 rule="hyper" parents="64 31834 42628"/>
    </justification>
  </clause>

  <clause id="42640">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * x = R(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31802,a,b,42632,a),flip(a)].">
      <j1 rule="hyper" parents="373 31802 42632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42641">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),a(w,u,z),y) \ (x * a(y,x,a(z,u,w))) = a(y,a(z,u,w),L(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,42079,a(flip),b,42634,a),flip(a)].">
      <j1 rule="hyper" parents="373 42079 42634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42642">
    <literal><![CDATA[
      L(x * a(y,a(z,u,w),x),a(w,u,z),y) = x
    ]]></literal>
    <justification jstring="[para(42634(a,1),42115(a,1,1,2))].">
      <j1 rule="para" parents="42634 42115"/>
    </justification>
  </clause>

  <clause id="42643">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) * (a(z,u,w) * v5),v6,v7)) = a(x,y,L(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,34561,a,b,42497,a)].">
      <j1 rule="hyper" parents="64 34561 42497"/>
    </justification>
  </clause>

  <clause id="42644">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ v5 = a(x,y,a(w,u,z)) * v5
    ]]></literal>
    <justification jstring="[hyper(373,a,41881,a,b,42499,a),flip(a)].">
      <j1 rule="hyper" parents="373 41881 42499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42646">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(x,y,a(w,u,z)) * v5) = v5
    ]]></literal>
    <justification jstring="[hyper(145,a,41881,a,b,42499,a)].">
      <j1 rule="hyper" parents="145 41881 42499"/>
    </justification>
  </clause>

  <clause id="42650">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * (v5 * a(w,u,a(z,y,x))) = v5
    ]]></literal>
    <justification jstring="[hyper(145,a,41901,a,b,42501,a)].">
      <j1 rule="hyper" parents="145 41901 42501"/>
    </justification>
  </clause>

  <clause id="42651">
    <literal><![CDATA[
      L((x * a(y,z,a(u,w,v5))) \ v6,x * a(y,z,a(u,w,v5)),a(y,z,a(u,w,v5))) = x \ (a(y,z,a(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[para(42502(a,1),41727(a,1,1,1))].">
      <j1 rule="para" parents="42502 41727"/>
    </justification>
  </clause>

  <clause id="42653">
    <literal><![CDATA[
      ((x \ a(y,x,z)) * (((x \ a(y,x,z)) \ (x \ 1)) * u)) / u = a(u,a(y,x,z),x * a(y,x,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,35840,a,b,42524,a)].">
      <j1 rule="hyper" parents="64 35840 42524"/>
    </justification>
  </clause>

  <clause id="42656">
    <literal><![CDATA[
      a(x,y,y \ (R(x,x,y) \ (z * (x * y)))) = a(x,y,a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42108,a,b,42537,a)].">
      <j1 rule="hyper" parents="64 42108 42537"/>
    </justification>
  </clause>

  <clause id="42657">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * u) = a(x,y,a(w,u,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42183,a(flip),b,42537,a)].">
      <j1 rule="hyper" parents="64 42183 42537"/>
    </justification>
  </clause>

  <clause id="42658">
    <literal><![CDATA[
      ((a(x,y,z) * x) \ (x * u)) \ u = a(x,y,z) * a(x,a(x,y,z),a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(42537(a,1),41079(a,2,2))].">
      <j1 rule="para" parents="42537 41079"/>
    </justification>
  </clause>

  <clause id="42664">
    <literal><![CDATA[
      a(a(x,y,z) \ u,w,v5) = a(a(z,y,x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,42559,a),flip(a)].">
      <j1 rule="hyper" parents="373 26787 42559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42669">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * u) = a(x,y,u * a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(27453,a,42657,a),flip(a)].">
      <j1 rule="hyper" parents="27453 42657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42670">
    <literal><![CDATA[
      a(a(x,y,z) * u,w,v5) = a(a(z,y,x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,42461,a(flip),b,42664,a)].">
      <j1 rule="hyper" parents="64 42461 42664"/>
    </justification>
  </clause>

  <clause id="42671">
    <literal><![CDATA[
      a(x,y,z \ (u \ (z * (w * u)))) = a(x,y,w * a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,42184,a,b,42669,a)].">
      <j1 rule="hyper" parents="64 42184 42669"/>
    </justification>
  </clause>

  <clause id="42672">
    <literal><![CDATA[
      a(x,y,z \ (u \ ((T(w,v5) * u) * z))) = a(x,y,w * a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,38442,a,b,42669,a)].">
      <j1 rule="hyper" parents="64 38442 42669"/>
    </justification>
  </clause>

  <clause id="42673">
    <literal><![CDATA[
      (x \ a(y,z,u)) * L(a(y,z,u) \ 1,x,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(42546(a,1),27921(a,1,2))].">
      <j1 rule="para" parents="42546 27921"/>
    </justification>
  </clause>

  <clause id="42675">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(x,y,z)) = L(a(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[hyper(36303,a,42577,a),flip(a)].">
      <j1 rule="hyper" parents="36303 42577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42677">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,u,w) = L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,42578,a(flip),b,42502,a)].">
      <j1 rule="hyper" parents="145 42578 42502"/>
    </justification>
  </clause>

  <clause id="42678">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * a(x,y,z) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,42578,a(flip),b,42501,a)].">
      <j1 rule="hyper" parents="145 42578 42501"/>
    </justification>
  </clause>

  <clause id="42679">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u,w) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(42578(a,1),42571(a,1,1))].">
      <j1 rule="para" parents="42578 42571"/>
    </justification>
  </clause>

  <clause id="42683">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,u,z) = L(a(w,u,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42644,a(flip),b,42581,a)].">
      <j1 rule="hyper" parents="64 42644 42581"/>
    </justification>
  </clause>

  <clause id="42686">
    <literal><![CDATA[
      (x \ a(y,z,u)) \ (x \ 1) = L(a(y,z,u) \ 1,x,x)
    ]]></literal>
    <justification jstring="[hyper(149,a,42673,a)].">
      <j1 rule="hyper" parents="149 42673"/>
    </justification>
  </clause>

  <clause id="42687">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(z,y,x)) = L(a(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,41901,a,b,42675,a)].">
      <j1 rule="hyper" parents="64 41901 42675"/>
    </justification>
  </clause>

  <clause id="42688">
    <literal><![CDATA[
      a(x,y,z) * a(a(z,y,x),u,w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,41868,a,b,42675,a)].">
      <j1 rule="hyper" parents="64 41868 42675"/>
    </justification>
  </clause>

  <clause id="42689">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u,w) = a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,42675,a(flip),b,41868,a)].">
      <j1 rule="hyper" parents="139 42675 41868"/>
    </justification>
  </clause>

  <clause id="42694">
    <literal><![CDATA[
      a(x,y,z \ 1) * a(a(z,y,x),u,w) = L(a(x,y,z \ 1),u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,41481,a(flip),b,42679,a)].">
      <j1 rule="hyper" parents="145 41481 42679"/>
    </justification>
  </clause>

  <clause id="42695">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ 1,u,w) = a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,37299,a,b,42679,a)].">
      <j1 rule="hyper" parents="64 37299 42679"/>
    </justification>
  </clause>

  <clause id="42698">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u,w * u) = a(a(x,y,z),u,u \ w)
    ]]></literal>
    <justification jstring="[para(41977(a,1),42679(a,1,2))].">
      <j1 rule="para" parents="41977 42679"/>
    </justification>
  </clause>

  <clause id="42699">
    <literal><![CDATA[
      (x \ 1) / (x \ a(y,z,u)) = L(a(y,z,u) \ 1,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,23760,a,b,42686,a)].">
      <j1 rule="hyper" parents="64 23760 42686"/>
    </justification>
  </clause>

  <clause id="42701">
    <literal><![CDATA[
      (x / y) \ (x * a(z,u,x)) = y * L(a(z,u,x),y,y)
    ]]></literal>
    <justification jstring="[para(42688(a,1),42304(a,2,2))].">
      <j1 rule="para" parents="42688 42304"/>
    </justification>
  </clause>

  <clause id="42702">
    <literal><![CDATA[
      L(a(x,y,z),u * z,u * z) = L(a(x,y,z),z * u,u)
    ]]></literal>
    <justification jstring="[hyper(39,a,41516,a,b,42689,a)].">
      <j1 rule="hyper" parents="39 41516 42689"/>
    </justification>
  </clause>

  <clause id="42704">
    <literal><![CDATA[
      (x / y) \ (x * a(z,u,x)) = (1 / y) \ a(z,u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,36302,a(flip),b,42701,a),flip(a)].">
      <j1 rule="hyper" parents="373 36302 42701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42706">
    <literal><![CDATA[
      x * (L(a(y,z,u),w,v5) \ 1) = L(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,25714,a(flip),b,42446,a)].">
      <j1 rule="hyper" parents="64 25714 42446"/>
    </justification>
  </clause>

  <clause id="42707">
    <literal><![CDATA[
      x \ (L(a(y,z,u),w,v5) \ x) = L(a(y,z,u),w,v5) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,27010,a,b,42446,a)].">
      <j1 rule="hyper" parents="36 27010 42446"/>
    </justification>
  </clause>

  <clause id="42708">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * v5 = L(a(x,y,z),u,w) \ v5
    ]]></literal>
    <justification jstring="[para(42148(a,2),42446(a,1,1))].">
      <j1 rule="para" parents="42148 42446"/>
    </justification>
  </clause>

  <clause id="42709">
    <literal><![CDATA[
      x / (a(y,z,u) * K(w,v5)) = x * (a(y,z,u) \ K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,24938,a,b,42554,a)].">
      <j1 rule="hyper" parents="64 24938 42554"/>
    </justification>
  </clause>

  <clause id="42710">
    <literal><![CDATA[
      (T(L(x,y,z),u) * a(w,v5,v6)) \ L(x,y,z) = (a(w,v5,v6) \ 1) * K(u,x)
    ]]></literal>
    <justification jstring="[para(23001(a,1),42561(a,2,2))].">
      <j1 rule="para" parents="23001 42561"/>
    </justification>
  </clause>

  <clause id="42714">
    <literal><![CDATA[
      a(x,a(y,z,u),a(a(y,z,u),w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,42587,a,b,42578,a),flip(a)].">
      <j1 rule="hyper" parents="138 42587 42578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42715">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,v5,a(y,z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,42587,a(flip),b,42683,a),flip(a)].">
      <j1 rule="hyper" parents="140 42587 42683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42716">
    <literal><![CDATA[
      L(x,a(y,z,u),a(a(y,z,u),w,v5)) = x * 1
    ]]></literal>
    <justification jstring="[hyper(145,a,42714,a(flip),b,42625,a),flip(a)].">
      <j1 rule="hyper" parents="145 42714 42625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42717">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),a(z,u,w),v5) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(53,a,42715,a)].">
      <j1 rule="hyper" parents="53 42715"/>
    </justification>
  </clause>

  <clause id="42718">
    <literal><![CDATA[
      L(x,a(y,z,u),a(a(y,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a(flip),b,42716,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 42716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42722">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u) \ L(R(x,y,z),x * L(x,y,z),u) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,4243,a,b,42613,a)].">
      <j1 rule="hyper" parents="64 4243 42613"/>
    </justification>
  </clause>

  <clause id="42724">
    <literal><![CDATA[
      x * L(a(y,z,u) \ 1,w,v5) = L(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[para(42148(a,2),42706(a,1,2))].">
      <j1 rule="para" parents="42148 42706"/>
    </justification>
  </clause>

  <clause id="42725">
    <literal><![CDATA[
      x \ (L(a(y,z,u),w,v5) \ x) = L(a(y,z,u) \ 1,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,42148,a,b,42707,a),flip(a)].">
      <j1 rule="hyper" parents="373 42148 42707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42727">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) * v5 = v5 / L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,23785,a,b,42708,a),flip(a)].">
      <j1 rule="hyper" parents="373 23785 42708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42729">
    <literal><![CDATA[
      a(x,y,z) \ a(u,w,a(x,y,z)) = L(a(x,y,z) \ 1,w,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,42580,a(flip),b,42724,a)].">
      <j1 rule="hyper" parents="139 42580 42724"/>
    </justification>
  </clause>

  <clause id="42731">
    <literal><![CDATA[
      x * L(y \ (a(z,u,w) \ y),v5,v6) = L(a(z,u,w),v5,v6) \ x
    ]]></literal>
    <justification jstring="[para(42452(a,2),42724(a,1,2,1))].">
      <j1 rule="para" parents="42452 42724"/>
    </justification>
  </clause>

  <clause id="42732">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,u,w) \ v5 = v5 * L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,11,a(flip),b,42727,a)].">
      <j1 rule="hyper" parents="139 11 42727"/>
    </justification>
  </clause>

  <clause id="42733">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ (w * u) = w * (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(39,a,42725,a,b,42549,a)].">
      <j1 rule="hyper" parents="39 42725 42549"/>
    </justification>
  </clause>

  <clause id="42734">
    <literal><![CDATA[
      L(a(x,y,z),a(x,y,z) \ u,w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(40,a,27804,a,b,42733,a)].">
      <j1 rule="hyper" parents="40 27804 42733"/>
    </justification>
  </clause>

  <clause id="42735">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ (x * w) = L(a(y,z,u),w,x)
    ]]></literal>
    <justification jstring="[para(42733(a,1),23792(a,1,1))].">
      <j1 rule="para" parents="42733 23792"/>
    </justification>
  </clause>

  <clause id="42736">
    <literal><![CDATA[
      L(a(x,y,z),u * a(x,y,z),w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42472,a(flip),b,42734,a)].">
      <j1 rule="hyper" parents="64 42472 42734"/>
    </justification>
  </clause>

  <clause id="42737">
    <literal><![CDATA[
      (x * (a(y,z,u) \ w)) \ (x * w) = L(a(y,z,u) \ 1,w,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,42145,a,b,42735,a),flip(a)].">
      <j1 rule="hyper" parents="373 42145 42735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42742">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u * a(x,y,z),w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,42736,a,b,42675,a)].">
      <j1 rule="hyper" parents="139 42736 42675"/>
    </justification>
  </clause>

  <clause id="42743">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (z \ w)) \ (z * (u * (u \ (z \ w)))))) = a(x,y,(z \ w) / ((z * u) \ w))
    ]]></literal>
    <justification jstring="[para(42111(a,2),42671(a,2,3))].">
      <j1 rule="para" parents="42111 42671"/>
    </justification>
  </clause>

  <clause id="42745">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * (a(x,y,z) \ v5) = v5 * L(v5 \ (a(x,y,z) \ v5),u,w)
    ]]></literal>
    <justification jstring="[hyper(144,a,42695,a(flip),b,2624,a)].">
      <j1 rule="hyper" parents="144 42695 2624"/>
    </justification>
  </clause>

  <clause id="42748">
    <literal><![CDATA[
      L(x,y \ (a(z,z,u) \ w),v5) = L(x,y \ (w * a(u,z,z)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,40362,a(flip),b,42471,a)].">
      <j1 rule="hyper" parents="64 40362 42471"/>
    </justification>
  </clause>

  <clause id="42749">
    <literal><![CDATA[
      a((a(x,y,z) \ ((z * y) * x)) \ u,w,v5) = a(((z * y) * R(x,y,z)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(25682(a,1),42476(a,2,1,1))].">
      <j1 rule="para" parents="25682 42476"/>
    </justification>
  </clause>

  <clause id="42751">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) * (a(w,u,z) * v5)) \ v6) = a(x,y,(v5 * (a(z,u,w) * a(w,u,z))) \ v6)
    ]]></literal>
    <justification jstring="[para(42484(a,1),27394(a,1,3,1))].">
      <j1 rule="para" parents="42484 27394"/>
    </justification>
  </clause>

  <clause id="42752">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,a(w,v5,v6) * a(v6,v5,w))) = a(x,y,(z * (a(w,v5,v6) * a(v6,v5,w))) \ (a(w,v5,v6) * (a(v6,v5,w) * u)))
    ]]></literal>
    <justification jstring="[para(42484(a,1),27552(a,2,3,2))].">
      <j1 rule="para" parents="42484 27552"/>
    </justification>
  </clause>

  <clause id="42754">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,v5) * (a(v5,w,u) \ v6))) = a(x,y,z \ (a(v5,w,u) * (a(u,w,v5) * v6)))
    ]]></literal>
    <justification jstring="[para(36938(a,1),42519(a,1,3,2))].">
      <j1 rule="para" parents="36938 42519"/>
    </justification>
  </clause>

  <clause id="42755">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,v5) \ (v6 * (a(v6,v7,a(u,w,v5)) \ v7)))) = a(x,y,z * (L(a(u,w,v5),v7,v6) * (v6 * v7)))
    ]]></literal>
    <justification jstring="[para(33432(a,1),42520(a,2,3,2))].">
      <j1 rule="para" parents="33432 42520"/>
    </justification>
  </clause>

  <clause id="42756">
    <literal><![CDATA[
      L((a(x,y \ 1,z) \ (y \ 1)) \ (a(x,y \ 1,z) \ u),y,y) = L(y * u,y \ 1,a(x,y \ 1,z))
    ]]></literal>
    <justification jstring="[para(42528(a,2),1143(a,1,1))].">
      <j1 rule="para" parents="42528 1143"/>
    </justification>
  </clause>

  <clause id="42757">
    <literal><![CDATA[
      a(L(x,y,z),a(u,w,v5),v6) = L(a(x,a(u,w,v5),v6),y,z)
    ]]></literal>
    <justification jstring="[para(42628(a,1),42637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42628 42637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42758">
    <literal><![CDATA[
      a(L(x,y,z),a(x,u,w),v5) = a(x,a(x,u,w),L(v5,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,40995,a,b,42757,a),flip(a)].">
      <j1 rule="hyper" parents="373 40995 42757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42760">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,v6)) \ 1 = L(a(w,a(y,z,u),x),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,42357,a,b,42757,a)].">
      <j1 rule="hyper" parents="64 42357 42757"/>
    </justification>
  </clause>

  <clause id="42761">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w),v5,v6) \ 1 = a(w,a(y,z,u),L(x,v5,v6))
    ]]></literal>
    <justification jstring="[para(42757(a,1),42357(a,1,1))].">
      <j1 rule="para" parents="42757 42357"/>
    </justification>
  </clause>

  <clause id="42762">
    <literal><![CDATA[
      a(a(x,y,z),L(x,u,w),v5) = a(x,a(x,y,z),L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,40615,a(flip),b,42758,a)].">
      <j1 rule="hyper" parents="64 40615 42758"/>
    </justification>
  </clause>

  <clause id="42763">
    <literal><![CDATA[
      a(a(x,y,z),L(x,u,w),v5) = a(x,a(z,y,x),L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,42391,a,b,42762,a),flip(a)].">
      <j1 rule="hyper" parents="373 42391 42762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42764">
    <literal><![CDATA[
      a(a(x,y,z),L(z,u,w),v5) = a(z,a(z,y,x),L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,41479,a,b,42762,a)].">
      <j1 rule="hyper" parents="64 41479 42762"/>
    </justification>
  </clause>

  <clause id="42766">
    <literal><![CDATA[
      a(x,a(y,z,x),L(u,w,v5)) * a(x,z,y) = L(a(x,z,y),L(x,w,v5),u)
    ]]></literal>
    <justification jstring="[para(42763(a,1),42324(a,1,1))].">
      <j1 rule="para" parents="42763 42324"/>
    </justification>
  </clause>

  <clause id="42767">
    <literal><![CDATA[
      a(x,a(x,y,z),L(u,w,v5)) * a(z,y,x) = L(a(z,y,x),L(x,w,v5),u)
    ]]></literal>
    <justification jstring="[para(42764(a,1),42678(a,1,1))].">
      <j1 rule="para" parents="42764 42678"/>
    </justification>
  </clause>

  <clause id="42768">
    <literal><![CDATA[
      L(x,y \ (z * a(u,w,w)),v5) = L(x,y \ (z * a(w,w,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,42471,a(flip),b,42748,a),flip(a)].">
      <j1 rule="hyper" parents="64 42471 42748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42769">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,v6)) = L(a(x,a(y,z,u),w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(40,a,42360,a,b,42760,a),flip(a)].">
      <j1 rule="hyper" parents="40 42360 42760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42770">
    <literal><![CDATA[
      a(L(x,y,z),a(u,w,v5),v6) = a(x,a(u,w,v5),L(v6,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,42757,a,b,42769,a)].">
      <j1 rule="hyper" parents="373 42757 42769"/>
    </justification>
  </clause>

  <clause id="42771">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,x)) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29902,a(flip),b,42769,a),flip(a)].">
      <j1 rule="hyper" parents="373 29902 42769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42772">
    <literal><![CDATA[
      a(x,a(y,z,u),L(u,w,v5)) = L(a(x,u,a(u,z,y)),w,v5)
    ]]></literal>
    <justification jstring="[para(41458(a,1),42769(a,2,1))].">
      <j1 rule="para" parents="41458 42769"/>
    </justification>
  </clause>

  <clause id="42773">
    <literal><![CDATA[
      a(x,a(y,z,u),((x \ 1) * w) \ 1) = a(x,a(y,z,u),(x \ w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,38955,a(flip),b,42771,a)].">
      <j1 rule="hyper" parents="64 38955 42771"/>
    </justification>
  </clause>

  <clause id="42774">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,x,a(u,z,y))) = x \ L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42403,a(flip),b,42770,a),flip(a)].">
      <j1 rule="hyper" parents="64 42403 42770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42775">
    <literal><![CDATA[
      a(L(x,y,z),u,a(u,w,v5)) = a(x,a(v5,w,u),L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41458,a(flip),b,42770,a)].">
      <j1 rule="hyper" parents="64 41458 42770"/>
    </justification>
  </clause>

  <clause id="42776">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,u)) = a(x,a(w,v5,u),L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33531,a(flip),b,42770,a)].">
      <j1 rule="hyper" parents="64 33531 42770"/>
    </justification>
  </clause>

  <clause id="42777">
    <literal><![CDATA[
      a(x,a(y,z,u),L(u,w,v5)) = L(a(u,a(u,z,y),x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,40996,a,b,42772,a),flip(a)].">
      <j1 rule="hyper" parents="373 40996 42772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42778">
    <literal><![CDATA[
      a(L(x,y,z),u,a(u,w,v5)) = a(x,L(u,y,z),a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,42396,a,b,42775,a),flip(a)].">
      <j1 rule="hyper" parents="373 42396 42775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42779">
    <literal><![CDATA[
      (x * y) * a(y,a(z,u,w),L(w,y,x)) = x * L(y,w,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(42777(a,2),40824(a,1,2))].">
      <j1 rule="para" parents="42777 40824"/>
    </justification>
  </clause>

  <clause id="42780">
    <literal><![CDATA[
      a(x,L(y,y,z),a(y,u,w)) = a(x,y,a(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,42262,a(flip),b,42778,a),flip(a)].">
      <j1 rule="hyper" parents="64 42262 42778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42781">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w),v5,v6) \ 1 = a(w,a(u,z,y),L(x,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,42391,a,b,42761,a),flip(a)].">
      <j1 rule="hyper" parents="373 42391 42761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42782">
    <literal><![CDATA[
      a(x \ y,a(z,u,x),L(x,w,v5)) = L(a(x,a(x,u,z),y),w,v5) \ 1
    ]]></literal>
    <justification jstring="[para(41440(a,1),42761(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="41440 42761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42783">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,x,a(u,z,y))) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,42628,a(flip),b,42774,a),flip(a)].">
      <j1 rule="hyper" parents="373 42628 42774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42784">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,x,a(y,z,u))) = a(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42391,a,b,42783,a)].">
      <j1 rule="hyper" parents="64 42391 42783"/>
    </justification>
  </clause>

  <clause id="42785">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),a(y,z,u) * y,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,9,a(flip),b,42479,a),flip(a)].">
      <j1 rule="hyper" parents="373 9 42479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42788">
    <literal><![CDATA[
      L(x,a(y,z,u) * y,a(y,z,u)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(42,a,42171,a,b,42785,a)].">
      <j1 rule="hyper" parents="42 42171 42785"/>
    </justification>
  </clause>

  <clause id="42789">
    <literal><![CDATA[
      L(x,y * a(y,z,u),a(y,z,u)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(29572,a,42788,a)].">
      <j1 rule="hyper" parents="29572 42788"/>
    </justification>
  </clause>

  <clause id="42790">
    <literal><![CDATA[
      L(x,y,a(L(z,u,w),u,w) * u) = L(x,y,z * (L(z,u,w) \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,42310,a(flip),b,42618,a),flip(a)].">
      <j1 rule="hyper" parents="373 42310 42618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42791">
    <literal><![CDATA[
      a(x,y,L(L(T(z,u),w,v5),v5,w)) = a(x,y,z * a(v5,z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,39081,a(flip),b,42672,a)].">
      <j1 rule="hyper" parents="64 39081 42672"/>
    </justification>
  </clause>

  <clause id="42792">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),w,u)) = a(x,y,z * a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27497,a(flip),b,42791,a)].">
      <j1 rule="hyper" parents="64 27497 42791"/>
    </justification>
  </clause>

  <clause id="42793">
    <literal><![CDATA[
      a(a(x,y,z),u,u \ w) = a(a(z,y,x),u,w * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42689,a(flip),b,42698,a),flip(a)].">
      <j1 rule="hyper" parents="64 42689 42698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42794">
    <literal><![CDATA[
      a(a(x,y,z),u,u \ w) = a(a(x,y,z),u,w * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42679,a(flip),b,42698,a),flip(a)].">
      <j1 rule="hyper" parents="64 42679 42698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42795">
    <literal><![CDATA[
      a(a(x,y,z),u,(u \ w) \ 1) = a(a(x,y,z),u,w * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,41480,a,b,42793,a)].">
      <j1 rule="hyper" parents="64 41480 42793"/>
    </justification>
  </clause>

  <clause id="42796">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * w) \ (u * w) = L(a(x,y,z) \ 1,u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,28781,a,b,42737,a)].">
      <j1 rule="hyper" parents="64 28781 42737"/>
    </justification>
  </clause>

  <clause id="42797">
    <literal><![CDATA[
      L(x,y,z * (L(z,u,w) \ u)) = L(x,y,a(z,u,w) * u)
    ]]></literal>
    <justification jstring="[para(41783(a,1),42790(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="41783 42790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42798">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * u) = L(x,y,u * a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42086,a(flip),b,42797,a),flip(a)].">
      <j1 rule="hyper" parents="64 42086 42797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42799">
    <literal><![CDATA[
      L(x,y,z * a(u,z,w)) = L(x,y,z * a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(24201,a,42798,a)].">
      <j1 rule="hyper" parents="24201 42798"/>
    </justification>
  </clause>

  <clause id="42800">
    <literal><![CDATA[
      L(x,y \ a(z,y,u),w * a(v5,w,v6)) = L(x,y * a(z,y,u),w * a(v6,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,35747,a,b,42799,a)].">
      <j1 rule="hyper" parents="373 35747 42799"/>
    </justification>
  </clause>

  <clause id="42801">
    <literal><![CDATA[
      (R(x,y,z) \ x) / a(x,a(x,y,z),y * z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(33567(a,1),42493(a,1,2))].">
      <j1 rule="para" parents="33567 42493"/>
    </justification>
  </clause>

  <clause id="42802">
    <literal><![CDATA[
      a(x,a(x,y,z),y * z) \ (R(x,y,z) \ x) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(23179,a,42801,a)].">
      <j1 rule="hyper" parents="23179 42801"/>
    </justification>
  </clause>

  <clause id="42803">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) \ (R(z,x,y) \ z) = a(z,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(41616(a,1),42802(a,1,1))].">
      <j1 rule="para" parents="41616 42802"/>
    </justification>
  </clause>

  <clause id="42804">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * (a(z,x,y) \ 1) = R(z,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(157,a,42803,a)].">
      <j1 rule="hyper" parents="157 42803"/>
    </justification>
  </clause>

  <clause id="42805">
    <literal><![CDATA[
      a(x,y,z) \ a(x,x,a(y,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,39761,a(flip),b,42804,a)].">
      <j1 rule="hyper" parents="64 39761 42804"/>
    </justification>
  </clause>

  <clause id="42806">
    <literal><![CDATA[
      a(x,y,z) \ a(y,x,a(x,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(41951(a,2),42805(a,1,2))].">
      <j1 rule="para" parents="41951 42805"/>
    </justification>
  </clause>

  <clause id="42807">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,x,y) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,42729,a(flip),b,42806,a)].">
      <j1 rule="hyper" parents="64 42729 42806"/>
    </justification>
  </clause>

  <clause id="42808">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),x,y) = L(R(x,y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(42807(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42807 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42809">
    <literal><![CDATA[
      L(x \ (a(y,z,u) * w),x,a(y,z,u)) = (a(y,z,u) \ x) \ w
    ]]></literal>
    <justification jstring="[para(42433(a,1),42529(a,2,1))].">
      <j1 rule="para" parents="42433 42529"/>
    </justification>
  </clause>

  <clause id="42810">
    <literal><![CDATA[
      L((a(x,y,z) \ u) \ w,u,a(x,y,z)) = u \ (a(x,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(42,a,42171,a,b,42809,a)].">
      <j1 rule="hyper" parents="42 42171 42809"/>
    </justification>
  </clause>

  <clause id="42812">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (a(x,y,z) \ (u * w)) = L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(73(a,1),42809(a,1,1)),flip(a)].">
      <j1 rule="para" parents="73 42809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42813">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,u,a(x,y,z)) = a(x,y,z) \ (u * w)
    ]]></literal>
    <justification jstring="[hyper(157,a,42812,a)].">
      <j1 rule="hyper" parents="157 42812"/>
    </justification>
  </clause>

  <clause id="42814">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(w,u,a(z,y,x))) = (a(x,y,z) \ u) * w
    ]]></literal>
    <justification jstring="[hyper(145,a,42206,a(flip),b,42812,a),flip(a)].">
      <j1 rule="hyper" parents="145 42206 42812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42815">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(w,u,a(x,y,z))) = (a(x,y,z) \ u) * w
    ]]></literal>
    <justification jstring="[hyper(145,a,42171,a(flip),b,42812,a),flip(a)].">
      <j1 rule="hyper" parents="145 42171 42812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42816">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) \ y) = a(z,u,w) \ (y * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,28656,a(flip),b,42813,a)].">
      <j1 rule="hyper" parents="64 28656 42813"/>
    </justification>
  </clause>

  <clause id="42817">
    <literal><![CDATA[
      a(x,y,z) * ((a(x,y,z) \ u) * w) = u * L(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(157,a,42814,a)].">
      <j1 rule="hyper" parents="157 42814"/>
    </justification>
  </clause>

  <clause id="42818">
    <literal><![CDATA[
      (x \ a(y,z,u)) \ R(a(y,z,u) \ (x \ a(y,z,u)),w,v5) = R(x,w,v5) * (x \ (a(y,z,u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,2801,a(flip),b,42550,a),flip(a)].">
      <j1 rule="hyper" parents="64 2801 42550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42819">
    <literal><![CDATA[
      (a(x,y,z) \ (z * y)) * L(x,x,a(z,y,y)) = (z * y) * ((a(x,y,z) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(41639(a,1),42552(a,1,2))].">
      <j1 rule="para" parents="41639 42552"/>
    </justification>
  </clause>

  <clause id="42820">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,a(x,y,z),u) = u * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(42433(a,1),42552(a,2,2))].">
      <j1 rule="para" parents="42433 42552"/>
    </justification>
  </clause>

  <clause id="42821">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (u * (a(x,y,z) \ w)) = L(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(149,a,42820,a)].">
      <j1 rule="hyper" parents="149 42820"/>
    </justification>
  </clause>

  <clause id="42822">
    <literal><![CDATA[
      L(a(x,y,z) * (u \ w),a(x,y,z),u) = (a(x,y,z) \ u) \ w
    ]]></literal>
    <justification jstring="[hyper(139,a,74,a(flip),b,42820,a),flip(a)].">
      <j1 rule="hyper" parents="139 74 42820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42823">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,a(z,y,x),u) = u * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,41416,a,b,42820,a)].">
      <j1 rule="hyper" parents="64 41416 42820"/>
    </justification>
  </clause>

  <clause id="42824">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (u * (a(x,y,z) \ w)) = L(w,a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(139,a,42820,a(flip),b,41416,a)].">
      <j1 rule="hyper" parents="139 42820 41416"/>
    </justification>
  </clause>

  <clause id="42825">
    <literal><![CDATA[
      L(x,a(y,z,u),w) * (a(y,z,u) \ w) = (a(y,z,u) \ x) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,42821,a(flip),b,28857,a)].">
      <j1 rule="hyper" parents="144 42821 28857"/>
    </justification>
  </clause>

  <clause id="42826">
    <literal><![CDATA[
      x \ ((a(y,z,u) * x) * (a(y,z,u) \ w)) = L(w,a(y,z,u),a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),42821(a,1,1))].">
      <j1 rule="para" parents="9 42821"/>
    </justification>
  </clause>

  <clause id="42827">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ (u * (a(x,y,z) \ w)) = L(w,a(x \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(2653(a,2),42821(a,2,2))].">
      <j1 rule="para" parents="2653 42821"/>
    </justification>
  </clause>

  <clause id="42828">
    <literal><![CDATA[
      x \ (a(y,z,u) * (x * (a(y,z,u) \ w))) = L(L(w,a(y,z,u),x),x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(42821(a,1),42810(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42821 42810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42830">
    <literal><![CDATA[
      a(x,y,z) * (a(z,y,x) \ u) = u * (a(z,y,x) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(39,a,42576,a(flip),b,42824,a)].">
      <j1 rule="hyper" parents="39 42576 42824"/>
    </justification>
  </clause>

  <clause id="42831">
    <literal><![CDATA[
      a(a(x,y,z) \ u,a(x,y,z),a(x,y,z) \ w) = w \ L(w,a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(42824(a,1),30346(a,2,2))].">
      <j1 rule="para" parents="42824 30346"/>
    </justification>
  </clause>

  <clause id="42832">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,z,a(x,y,z)) * z) = u \ ((a(x,y,z) \ u) * z)
    ]]></literal>
    <justification jstring="[para(33531(a,1),42557(a,1,2,1))].">
      <j1 rule="para" parents="33531 42557"/>
    </justification>
  </clause>

  <clause id="42833">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) \ v5,v6,v7)) = a(x,y,L(v5 * a(z,u,w),v6,v7))
    ]]></literal>
    <justification jstring="[para(23182(a,1),42643(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="23182 42643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42834">
    <literal><![CDATA[
      a(a(x,y,z),u * a(x,y,z),w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42679,a(flip),b,42742,a)].">
      <j1 rule="hyper" parents="64 42679 42742"/>
    </justification>
  </clause>

  <clause id="42835">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z) * u,w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(32008,a,42834,a)].">
      <j1 rule="hyper" parents="32008 42834"/>
    </justification>
  </clause>

  <clause id="42836">
    <literal><![CDATA[
      a(a(x,y,z),a(x,y,z) \ u,w) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,35687,a,b,42834,a)].">
      <j1 rule="hyper" parents="64 35687 42834"/>
    </justification>
  </clause>

  <clause id="42837">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,a(y,z,u)) = a(a(y,z,u),w,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13838,a(flip),b,42836,a),flip(a)].">
      <j1 rule="hyper" parents="64 13838 42836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42838">
    <literal><![CDATA[
      a(x,a(y,z,u),(x \ w) \ 1) = a(x,a(y,z,u),x * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,36021,a(flip),b,42773,a),flip(a)].">
      <j1 rule="hyper" parents="64 36021 42773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42839">
    <literal><![CDATA[
      a(x,a(y,z,u),x \ w) = a(x,a(y,z,u),x * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,36022,a(flip),b,42838,a)].">
      <j1 rule="hyper" parents="64 36022 42838"/>
    </justification>
  </clause>

  <clause id="42840">
    <literal><![CDATA[
      a(x \ y,a(z,u,x),L(x,w,v5)) = a(y,a(z,u,x),L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,42781,a(flip),b,42782,a),flip(a)].">
      <j1 rule="hyper" parents="373 42781 42782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42841">
    <literal><![CDATA[
      a(x * y,a(z,u,x),L(x,w,v5)) = a(y,a(z,u,x),L(x,w,v5))
    ]]></literal>
    <justification jstring="[para(9(a,1),42840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 42840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42843">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,u,w) \ y) = a(z,u,w) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,249,a(flip),b,42816,a),flip(a)].">
      <j1 rule="hyper" parents="373 249 42816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42845">
    <literal><![CDATA[
      a(x,y,z) \ (L(u,w,a(x,y,z)) * w) = u * (a(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(42171(a,1),42843(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42171 42843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42846">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * y = a(z,u,w) * (x * (a(z,u,w) \ y))
    ]]></literal>
    <justification jstring="[hyper(157,a,42845,a),flip(a)].">
      <j1 rule="hyper" parents="157 42845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42847">
    <literal><![CDATA[
      a(x,y,z) \ (u * (a(x,y,z) * w)) = a(x,y,z) * (u * (a(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,42252,a,b,42846,a)].">
      <j1 rule="hyper" parents="64 42252 42846"/>
    </justification>
  </clause>

  <clause id="42848">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ x)) = L(u * x,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39282,a,b,42846,a),flip(a)].">
      <j1 rule="hyper" parents="64 39282 42846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42849">
    <literal><![CDATA[
      L(x,a(y,z,u) \ w,a(y,z,u)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,28764,a,b,42846,a)].">
      <j1 rule="hyper" parents="36 28764 42846"/>
    </justification>
  </clause>

  <clause id="42850">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * (u * (a(x,y,z) \ w))) = u * (a(x,y,z) * w)
    ]]></literal>
    <justification jstring="[hyper(145,a,42846,a(flip),b,42252,a)].">
      <j1 rule="hyper" parents="145 42846 42252"/>
    </justification>
  </clause>

  <clause id="42852">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,a(y,z,u)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,42463,a(flip),b,42849,a)].">
      <j1 rule="hyper" parents="64 42463 42849"/>
    </justification>
  </clause>

  <clause id="42853">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,a(u,z,y)) = L(x,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(42222,a,42852,a)].">
      <j1 rule="hyper" parents="42222 42852"/>
    </justification>
  </clause>

  <clause id="42855">
    <literal><![CDATA[
      a(x,y,z) \ L(z,a(z,y,x),u) = u \ ((a(x,y,z) \ u) * z)
    ]]></literal>
    <justification jstring="[para(41445(a,1),42832(a,1,2))].">
      <j1 rule="para" parents="41445 42832"/>
    </justification>
  </clause>

  <clause id="42856">
    <literal><![CDATA[
      L(a(x,y,z),z,u) \ z = u \ ((a(x,y,z) \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42090,a(flip),b,42855,a)].">
      <j1 rule="hyper" parents="64 42090 42855"/>
    </justification>
  </clause>

  <clause id="42857">
    <literal><![CDATA[
      a(L(x,x,L(y,z,u)),w,v5) = L(a(x,w,v5),L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41443,a(flip),b,42766,a)].">
      <j1 rule="hyper" parents="64 41443 42766"/>
    </justification>
  </clause>

  <clause id="42858">
    <literal><![CDATA[
      L(a(x,y,z),L(z,u,w),v5) = L(a(x,y,z),z,L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,41462,a(flip),b,42767,a),flip(a)].">
      <j1 rule="hyper" parents="64 41462 42767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42859">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) \ 1 = a(v6,v5,L(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,39639,a(flip),b,42381,a),flip(a)].">
      <j1 rule="hyper" parents="64 39639 42381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42860">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) \ 1 = a(L(a(z,u,w),v5,v6),y,x)
    ]]></literal>
    <justification jstring="[hyper(40,a,23134,a,b,42859,a)].">
      <j1 rule="hyper" parents="40 23134 42859"/>
    </justification>
  </clause>

  <clause id="42861">
    <literal><![CDATA[
      a(x,y,a(z,u,u \ ((z \ 1) \ w))) = a(x,y,a(z,u,(z \ w) * u))
    ]]></literal>
    <justification jstring="[para(27968(a,1),42409(a,1,3))].">
      <j1 rule="para" parents="27968 42409"/>
    </justification>
  </clause>

  <clause id="42862">
    <literal><![CDATA[
      x / a(y,y,L(z,z,(y \ z) * x)) = (y * z) * (((1 / y) \ z) \ x)
    ]]></literal>
    <justification jstring="[para(41016(a,1),42410(a,1,2))].">
      <j1 rule="para" parents="41016 42410"/>
    </justification>
  </clause>

  <clause id="42863">
    <literal><![CDATA[
      x / a(y,y,L(z,z,y * (z * x))) = (y * z) * (((1 / y) \ z) \ x)
    ]]></literal>
    <justification jstring="[para(38455(a,1),42862(a,1,2,3))].">
      <j1 rule="para" parents="38455 42862"/>
    </justification>
  </clause>

  <clause id="42864">
    <literal><![CDATA[
      x / a(y,y,L(z,z,z * x)) = (y * z) * (((1 / y) \ z) \ x)
    ]]></literal>
    <justification jstring="[para(41102(a,1),42863(a,1,2))].">
      <j1 rule="para" parents="41102 42863"/>
    </justification>
  </clause>

  <clause id="42865">
    <literal><![CDATA[
      x / a(y,y,L(z,z,x)) = (y * z) * (((1 / y) \ z) \ x)
    ]]></literal>
    <justification jstring="[para(27599(a,1),42864(a,1,2))].">
      <j1 rule="para" parents="27599 42864"/>
    </justification>
  </clause>

  <clause id="42866">
    <literal><![CDATA[
      a(x,x,L(y,y,z)) \ z = (x * y) * (((1 / x) \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(23179,a,42865,a)].">
      <j1 rule="hyper" parents="23179 42865"/>
    </justification>
  </clause>

  <clause id="42867">
    <literal><![CDATA[
      (x * y) * (((1 / x) \ y) \ z) = L(y,x,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,39512,a(flip),b,42866,a),flip(a)].">
      <j1 rule="hyper" parents="64 39512 42866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42868">
    <literal><![CDATA[
      x * (K(y,y \ x) * (((1 / y) \ (x / y)) \ z)) = L(x / y,y,y) * ((x / y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11849,a,b,42867,a)].">
      <j1 rule="hyper" parents="64 11849 42867"/>
    </justification>
  </clause>

  <clause id="42869">
    <literal><![CDATA[
      (L(x,y,y) * (x \ z)) / ((y \ 1) * x) = z / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(142,a,42867,a(flip),b,39458,a)].">
      <j1 rule="hyper" parents="142 42867 39458"/>
    </justification>
  </clause>

  <clause id="42870">
    <literal><![CDATA[
      (x * L(y,z,z)) / ((z \ 1) * y) = (x * y) / (z \ y)
    ]]></literal>
    <justification jstring="[para(23889(a,1),42869(a,1,1))].">
      <j1 rule="para" parents="23889 42869"/>
    </justification>
  </clause>

  <clause id="42871">
    <literal><![CDATA[
      (x * y) / ((x * z) / (y \ z)) = a(x,y,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(42870(a,1),33331(a,1,2))].">
      <j1 rule="para" parents="42870 33331"/>
    </justification>
  </clause>

  <clause id="42872">
    <literal><![CDATA[
      a(x,y,(y \ 1) * z) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33329,a(flip),b,42871,a),flip(a)].">
      <j1 rule="hyper" parents="64 33329 42871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42875">
    <literal><![CDATA[
      a(x,y,y \ ((y \ 1) \ z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(10(a,1),42872(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10 42872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42876">
    <literal><![CDATA[
      L(x,y,a(z,u,u \ w)) = L(x,y,a(z,u,w * u))
    ]]></literal>
    <justification jstring="[para(42872(a,1),42317(a,1,3))].">
      <j1 rule="para" parents="42872 42317"/>
    </justification>
  </clause>

  <clause id="42877">
    <literal><![CDATA[
      a(x,y,L(z,y,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38942,a(flip),b,42875,a)].">
      <j1 rule="hyper" parents="64 38942 42875"/>
    </justification>
  </clause>

  <clause id="42878">
    <literal><![CDATA[
      a(x,y,z) = (y \ L(z,y,x)) \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42124,a,b,42877,a),flip(a)].">
      <j1 rule="hyper" parents="64 42124 42877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42880">
    <literal><![CDATA[
      a(x,y,(y \ 1) \ z) = a(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38939,a(flip),b,42877,a)].">
      <j1 rule="hyper" parents="64 38939 42877"/>
    </justification>
  </clause>

  <clause id="42881">
    <literal><![CDATA[
      (x / y) \ (x * a(y,x,z)) = R(y,x,L(z,x,x))
    ]]></literal>
    <justification jstring="[para(42877(a,1),41820(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="42877 41820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42882">
    <literal><![CDATA[
      L(L(x,y,y),y,z) \ L(x,y,y) = L(a(z,y,x),L(x,y,y),y)
    ]]></literal>
    <justification jstring="[para(42877(a,1),42055(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42877 42055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42883">
    <literal><![CDATA[
      a(x,y,z) \ (y \ z) = y \ L(z,y,x)
    ]]></literal>
    <justification jstring="[para(42877(a,1),42125(a,1,1))].">
      <j1 rule="para" parents="42877 42125"/>
    </justification>
  </clause>

  <clause id="42884">
    <literal><![CDATA[
      a(x \ (y \ x),z,z * x) = y \ R(y,z,(z \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,36431,a(flip),b,42880,a),flip(a)].">
      <j1 rule="hyper" parents="64 36431 42880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42885">
    <literal><![CDATA[
      a(a(x,y,z),u,u * w) \ (u \ (u * w)) = u * L(u \ w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,28865,a(flip),b,42883,a),flip(a)].">
      <j1 rule="hyper" parents="373 28865 42883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42886">
    <literal><![CDATA[
      R(x,y,L(z,y,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41820,a,b,42881,a),flip(a)].">
      <j1 rule="hyper" parents="64 41820 42881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42887">
    <literal><![CDATA[
      R(x,y,(y \ 1) \ z) = R(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38890,a(flip),b,42886,a)].">
      <j1 rule="hyper" parents="64 38890 42886"/>
    </justification>
  </clause>

  <clause id="42890">
    <literal><![CDATA[
      a(x \ (y \ x),z,z * x) = y \ R(y,z,z * x)
    ]]></literal>
    <justification jstring="[para(42887(a,1),42884(a,2,2))].">
      <j1 rule="para" parents="42887 42884"/>
    </justification>
  </clause>

  <clause id="42891">
    <literal><![CDATA[
      L(L(x,y,y),y,z) \ L(x,y,y) = L(a(z,y,x),x,L(y,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,42858,a(flip),b,42882,a),flip(a)].">
      <j1 rule="hyper" parents="373 42858 42882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42892">
    <literal><![CDATA[
      L(L(x,y,y),y,z) \ L(x,y,y) = L(a(z,y,x),x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,12978,a(flip),b,42891,a),flip(a)].">
      <j1 rule="hyper" parents="373 12978 42891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42894">
    <literal><![CDATA[
      L(L(x,y,y),y,z) \ L(x,y,y) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,42055,a(flip),b,42892,a),flip(a)].">
      <j1 rule="hyper" parents="373 42055 42892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42895">
    <literal><![CDATA[
      a(x,L(a(y,z,u),w,v5),y) \ v6 = a(L(a(y,z,u),w,v5),y,x) * v6
    ]]></literal>
    <justification jstring="[para(42860(a,1),42516(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42860 42516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42896">
    <literal><![CDATA[
      (T(L(x,y,z),u) * a(w,v5,v6)) \ L(x,y,z) = a(w,v5,v6) \ K(u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,42433,a(flip),b,42710,a),flip(a)].">
      <j1 rule="hyper" parents="373 42433 42710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42897">
    <literal><![CDATA[
      T(a(x,y,z) * L(u,w,v5),v6) \ L(u,w,v5) = a(x,y,z) \ K(v6,u)
    ]]></literal>
    <justification jstring="[para(28744(a,2),42896(a,1,1))].">
      <j1 rule="para" parents="28744 42896"/>
    </justification>
  </clause>

  <clause id="42898">
    <literal><![CDATA[
      T(R(x,y,z),u) \ L(x,x,a(z,y,y)) = a(x,y,z) \ K(u,x)
    ]]></literal>
    <justification jstring="[para(41625(a,2),42897(a,1,1,1))].">
      <j1 rule="para" parents="41625 42897"/>
    </justification>
  </clause>

  <clause id="42899">
    <literal><![CDATA[
      R(T(x,y),z,u) \ L(x,x,a(u,z,z)) = a(x,z,u) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(27(a,2),42898(a,1,1))].">
      <j1 rule="para" parents="27 42898"/>
    </justification>
  </clause>

  <clause id="42900">
    <literal><![CDATA[
      a(a(x,y,z) \ u,a(x,y,z),a(x,y,z) \ w) = a(w,a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,42625,a(flip),b,42831,a),flip(a)].">
      <j1 rule="hyper" parents="373 42625 42831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42901">
    <literal><![CDATA[
      a(x,a(y,z,u),a(y,z,u) \ w) = a(w,a(u,z,y),a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(9(a,1),42900(a,1,1))].">
      <j1 rule="para" parents="9 42900"/>
    </justification>
  </clause>

  <clause id="42902">
    <literal><![CDATA[
      x \ L(x,a(y,z,u),a(y,z,u) * w) = a(w,a(y,z,u),a(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,42628,a,b,42901,a)].">
      <j1 rule="hyper" parents="373 42628 42901"/>
    </justification>
  </clause>

  <clause id="42903">
    <literal><![CDATA[
      a(x,a(y,z,u),(a(y,z,u) \ 1) * w) = a(w,a(u,z,y),a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42872,a,b,42901,a)].">
      <j1 rule="hyper" parents="64 42872 42901"/>
    </justification>
  </clause>

  <clause id="42904">
    <literal><![CDATA[
      (x * (y * a(z,u,w))) / a(z,u,w) = a(z,u,w) * (x * (a(z,u,w) \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,24760,a,b,42847,a)].">
      <j1 rule="hyper" parents="64 24760 42847"/>
    </justification>
  </clause>

  <clause id="42905">
    <literal><![CDATA[
      a(x,y,z) \ (u * (w * a(x,y,z))) = a(x,y,z) * (u * (a(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,24758,a(flip),b,42847,a)].">
      <j1 rule="hyper" parents="64 24758 42847"/>
    </justification>
  </clause>

  <clause id="42906">
    <literal><![CDATA[
      a(a(x,y,z),u,u * w) \ w = u * L(u \ w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(9(a,1),42885(a,1,2))].">
      <j1 rule="para" parents="9 42885"/>
    </justification>
  </clause>

  <clause id="42907">
    <literal><![CDATA[
      a(x * y,x,a(z,u,w)) * y = x * L(x \ y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,42525,a(flip),b,42906,a)].">
      <j1 rule="hyper" parents="64 42525 42906"/>
    </justification>
  </clause>

  <clause id="42908">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,w)) = y * a(x * y,x,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41900,a(flip),b,42907,a),flip(a)].">
      <j1 rule="hyper" parents="64 41900 42907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42909">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,w)) = y * a(a(z,u,w),x,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41853,a(flip),b,42907,a),flip(a)].">
      <j1 rule="hyper" parents="64 41853 42907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42910">
    <literal><![CDATA[
      L(x / y,y,a(z,u,w)) * y = x * a(a(z,u,w),y,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,836,a,b,42909,a)].">
      <j1 rule="hyper" parents="64 836 42909"/>
    </justification>
  </clause>

  <clause id="42911">
    <literal><![CDATA[
      a(x,y,z) * ((u / w) * (a(x,y,z) \ w)) = u * a(a(x,y,z),w,w * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42846,a(flip),b,42910,a)].">
      <j1 rule="hyper" parents="64 42846 42910"/>
    </justification>
  </clause>

  <clause id="42912">
    <literal><![CDATA[
      a(R(x,y,x),a(z,u,w),a(z,u,w) \ v5) = v5 \ L(v5,a(z,u,w),a(z,u,w) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,13103,a,b,42902,a)].">
      <j1 rule="hyper" parents="373 13103 42902"/>
    </justification>
  </clause>

  <clause id="42913">
    <literal><![CDATA[
      x \ ((x * a(y,z,u)) * (a(y,z,u) \ w)) = L(w,a(y,z,u),a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(39,a,30026,a,b,42902,a)].">
      <j1 rule="hyper" parents="39 30026 42902"/>
    </justification>
  </clause>

  <clause id="42914">
    <literal><![CDATA[
      a(x,a(y,z,u),(a(y,z,u) \ 1) * w) = a(w,a(y,z,u),a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,42391,a,b,42903,a),flip(a)].">
      <j1 rule="hyper" parents="373 42391 42903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42915">
    <literal><![CDATA[
      a(x,y,z) * ((u / w) * (a(x,y,z) \ w)) = u * a(a(x,y,z),w,u * w)
    ]]></literal>
    <justification jstring="[para(27298(a,1),42911(a,2,2))].">
      <j1 rule="para" parents="27298 42911"/>
    </justification>
  </clause>

  <clause id="42916">
    <literal><![CDATA[
      a(x,a(y,z,u),a(y,z,u) * w) = a(w,a(y,z,u),x * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,36029,a(flip),b,42914,a),flip(a)].">
      <j1 rule="hyper" parents="64 36029 42914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42917">
    <literal><![CDATA[
      a(x \ 1,a(y,z,u),w * a(y,z,u)) = a(w,a(y,z,u),a(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2653,a,b,42916,a)].">
      <j1 rule="hyper" parents="373 2653 42916"/>
    </justification>
  </clause>

  <clause id="42918">
    <literal><![CDATA[
      x * a(y,a(z,u,w),a(z,u,w) * x) = L(x,a(z,u,w),y * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,42916,a,b,42625,a)].">
      <j1 rule="hyper" parents="145 42916 42625"/>
    </justification>
  </clause>

  <clause id="42919">
    <literal><![CDATA[
      a(x \ 1,a(y,x,z),u * a(y,x,z)) = a(u,a(y,x,z),x * a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,42669,a(flip),b,42917,a),flip(a)].">
      <j1 rule="hyper" parents="373 42669 42917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42920">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(w,a(v5,v6,v7),a(v5,v6,v7) * (a(x,y,z) * u)) = L(a(x,y,z) \ u,a(v5,v6,v7),w * a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(42520(a,1),42918(a,1,2))].">
      <j1 rule="para" parents="42520 42918"/>
    </justification>
  </clause>

  <clause id="42921">
    <literal><![CDATA[
      x * a(x,y \ (z \ y),a(z,u,w)) = R(x,y \ (z \ y),a(z,u,w))
    ]]></literal>
    <justification jstring="[para(621(a,1),41631(a,1,1))].">
      <j1 rule="para" parents="621 41631"/>
    </justification>
  </clause>

  <clause id="42922">
    <literal><![CDATA[
      x * a(x,y \ (z \ y),a(z,u,w)) = L(x,y \ (z \ y),a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,28832,a(flip),b,42921,a),flip(a)].">
      <j1 rule="hyper" parents="373 28832 42921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42923">
    <literal><![CDATA[
      L(x,y * ((1 / R(z,u,w)) * u),v5) = L(x,y * (z * (a(z,u,w) \ u)),v5)
    ]]></literal>
    <justification jstring="[para(35169(a,1),41878(a,1,2,2))].">
      <j1 rule="para" parents="35169 41878"/>
    </justification>
  </clause>

  <clause id="42924">
    <literal><![CDATA[
      L(x,y * ((R(z,u,w) \ 1) * u),v5) = L(x,y * (z * (a(z,u,w) \ u)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29626,a(flip),b,42923,a)].">
      <j1 rule="hyper" parents="64 29626 42923"/>
    </justification>
  </clause>

  <clause id="42925">
    <literal><![CDATA[
      L(x,y * (z * (a(z,u,w) \ u)),v5) = L(x,(R(z,u,w) * u) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29519,a(flip),b,42924,a),flip(a)].">
      <j1 rule="hyper" parents="64 29519 42924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42926">
    <literal><![CDATA[
      L(x,y * (z * (a(z,u,w) \ u)),v5) = L(x,(L(z,u,w) * u) * y,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,36284,a(flip),b,42925,a),flip(a)].">
      <j1 rule="hyper" parents="373 36284 42925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42927">
    <literal><![CDATA[
      L(x,(L(y,z,u \ 1) * z) * u,w) = L(x,(u * z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33561,a(flip),b,42926,a),flip(a)].">
      <j1 rule="hyper" parents="64 33561 42926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42928">
    <literal><![CDATA[
      L(x,(L(y,z,u) * z) * u,w) = L(x,(u * z) * y,w)
    ]]></literal>
    <justification jstring="[para(1631(a,1),42927(a,1,2,1,1))].">
      <j1 rule="para" parents="1631 42927"/>
    </justification>
  </clause>

  <clause id="42929">
    <literal><![CDATA[
      L(L(x,y,(z \ y) * y),y,a(y,z,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,41021,a(flip),b,42015,a),flip(a)].">
      <j1 rule="hyper" parents="373 41021 42015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42930">
    <literal><![CDATA[
      a(R(x,x,y),y,y \ (R(x,x,y) \ z)) = a(R(x,x,y),y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27520,a(flip),b,42109,a),flip(a)].">
      <j1 rule="hyper" parents="373 27520 42109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42931">
    <literal><![CDATA[
      (x / y) * a(z,z,L(u,x / y,x * (T(x,w) / y))) = (a(z,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(14844(a,1),42292(a,1,2,3,3))].">
      <j1 rule="para" parents="14844 42292"/>
    </justification>
  </clause>

  <clause id="42932">
    <literal><![CDATA[
      L(x * (y \ R(y,z,u)),R(y,z,u) \ y,L(y,z,u)) = y \ (R(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29203,a(flip),b,42616,a)].">
      <j1 rule="hyper" parents="64 29203 42616"/>
    </justification>
  </clause>

  <clause id="42933">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * (a(x,y,z) \ v5) = L(a(x,y,z),u,w) \ v5
    ]]></literal>
    <justification jstring="[hyper(373,a,42731,a(flip),b,42745,a),flip(a)].">
      <j1 rule="hyper" parents="373 42731 42745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42936">
    <literal><![CDATA[
      a(x,y,z) \ (a(a(x,y,z),u,w) * v5) = L(a(x,y,z),u,w) \ v5
    ]]></literal>
    <justification jstring="[hyper(64,a,30264,a,b,42933,a)].">
      <j1 rule="hyper" parents="64 30264 42933"/>
    </justification>
  </clause>

  <clause id="42937">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(w,v5,a(x,y,z)) = L(a(x,y,z),v5,w) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,41855,a(flip),b,42933,a)].">
      <j1 rule="hyper" parents="64 41855 42933"/>
    </justification>
  </clause>

  <clause id="42938">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (L(a(z,u,w),y,x) \ v5) = a(z,u,w) \ v5
    ]]></literal>
    <justification jstring="[hyper(145,a,42933,a(flip),b,42526,a)].">
      <j1 rule="hyper" parents="145 42933 42526"/>
    </justification>
  </clause>

  <clause id="42939">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,w,a(z,y,x)) * v5) = L(a(x,y,z),w,u) \ v5
    ]]></literal>
    <justification jstring="[para(41859(a,1),42936(a,1,2,1))].">
      <j1 rule="para" parents="41859 42936"/>
    </justification>
  </clause>

  <clause id="42941">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(x,z,a(z,y,y)) = L(a(x,y,z),z,y) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,41955,a(flip),b,42937,a)].">
      <j1 rule="hyper" parents="64 41955 42937"/>
    </justification>
  </clause>

  <clause id="42942">
    <literal><![CDATA[
      a(x,y,z) * (L(a(x,y,z),u,w) \ v5) = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,42937,a(flip),b,33202,a)].">
      <j1 rule="hyper" parents="145 42937 33202"/>
    </justification>
  </clause>

  <clause id="42943">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (L(a(z,u,w) \ 1,y,x) * v5) = a(z,u,w) \ v5
    ]]></literal>
    <justification jstring="[para(42708(a,2),42938(a,1,2))].">
      <j1 rule="para" parents="42708 42938"/>
    </justification>
  </clause>

  <clause id="42944">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (x * (a(z,u,w) \ y)) = a(z,u,w) \ (x * y)
    ]]></literal>
    <justification jstring="[para(42733(a,1),42938(a,1,2))].">
      <j1 rule="para" parents="42733 42938"/>
    </justification>
  </clause>

  <clause id="42945">
    <literal><![CDATA[
      (L(a(x,y,z),u,w) \ v5) \ (a(w,u,a(z,y,x)) * v5) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(42939(a,1),23134(a,1,1))].">
      <j1 rule="para" parents="42939 23134"/>
    </justification>
  </clause>

  <clause id="42946">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(x,z,a(z,y,y)) = (L(z,y,x) \ z) \ u
    ]]></literal>
    <justification jstring="[para(42055(a,1),42941(a,2,1))].">
      <j1 rule="para" parents="42055 42941"/>
    </justification>
  </clause>

  <clause id="42947">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(x,z,a(z,y,y)) = (z \ L(z,y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,42420,a(flip),b,42946,a),flip(a)].">
      <j1 rule="hyper" parents="373 42420 42946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42948">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) * (a(y,z,x) \ u) = x * ((x \ L(x,z,y)) * u)
    ]]></literal>
    <justification jstring="[para(42947(a,1),40908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="42947 40908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42949">
    <literal><![CDATA[
      a(x,y,z) * (x * (L(a(x,y,z),u,w) \ v5)) = (x * v5) * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(30974(a,1),42942(a,1,2))].">
      <j1 rule="para" parents="30974 42942"/>
    </justification>
  </clause>

  <clause id="42951">
    <literal><![CDATA[
      x * (a(x,y,a(z,u,w)) * (a(z,u,w) \ y)) = a(z,u,w) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29956,a(flip),b,42944,a)].">
      <j1 rule="hyper" parents="64 29956 42944"/>
    </justification>
  </clause>

  <clause id="42952">
    <literal><![CDATA[
      x * ((a(y,z,u) \ w) * a(x,w,a(y,z,u))) = a(y,z,u) \ (x * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29912,a(flip),b,42944,a)].">
      <j1 rule="hyper" parents="64 29912 42944"/>
    </justification>
  </clause>

  <clause id="42953">
    <literal><![CDATA[
      x * (L(a(y,z,u),w,x) \ w) = a(y,z,u) \ (x * w)
    ]]></literal>
    <justification jstring="[para(42073(a,1),42951(a,1,2))].">
      <j1 rule="para" parents="42073 42951"/>
    </justification>
  </clause>

  <clause id="42954">
    <literal><![CDATA[
      a(x,y,z) \ (L(a(x,y,z) \ 1,u,w) \ v5) = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,23182,a(flip),b,42943,a),flip(a)].">
      <j1 rule="hyper" parents="64 23182 42943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42955">
    <literal><![CDATA[
      a(x,y,z) \ (u * L(a(x,y,z),w,v5)) = u * a(v5,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(42732(a,1),42954(a,1,2))].">
      <j1 rule="para" parents="42732 42954"/>
    </justification>
  </clause>

  <clause id="42956">
    <literal><![CDATA[
      a(x,y,z) * (u * a(w,v5,a(x,y,z))) = u * L(a(x,y,z),v5,w)
    ]]></literal>
    <justification jstring="[hyper(157,a,42955,a)].">
      <j1 rule="hyper" parents="157 42955"/>
    </justification>
  </clause>

  <clause id="42957">
    <literal><![CDATA[
      a(x,y,z) * (u * a(a(x,y,z),w,v5)) = u * L(a(x,y,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(145,a,41854,a,b,42955,a)].">
      <j1 rule="hyper" parents="145 41854 42955"/>
    </justification>
  </clause>

  <clause id="42958">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(a(x,y,z),w,v5) = u * a(v5,w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,25765,a(flip),b,42955,a)].">
      <j1 rule="hyper" parents="64 25765 42955"/>
    </justification>
  </clause>

  <clause id="42959">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(a(x,y,z),z,y) = u * a(x,z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,41955,a(flip),b,42958,a),flip(a)].">
      <j1 rule="hyper" parents="373 41955 42958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42960">
    <literal><![CDATA[
      (x * a(y,z,u)) * a(w,v5,a(y,z,u)) = x * L(a(y,z,u),v5,w)
    ]]></literal>
    <justification jstring="[para(23138(a,1),42958(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23138 42958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42961">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(a(x,y,z),z,y * x) = u * a(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[para(41613(a,1),42958(a,2,2))].">
      <j1 rule="para" parents="41613 42958"/>
    </justification>
  </clause>

  <clause id="42962">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(a(x,y,z),z,y) = a(x,z,a(z,y,y)) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a,b,42959,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 42959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42963">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * a(z,u,w)) = v5 * L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(23777,a,42960,a)].">
      <j1 rule="hyper" parents="23777 42960"/>
    </justification>
  </clause>

  <clause id="42965">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (L(z,y,x) \ z) = a(x,z,a(z,y,y)) * u
    ]]></literal>
    <justification jstring="[para(42055(a,1),42962(a,1,2))].">
      <j1 rule="para" parents="42055 42962"/>
    </justification>
  </clause>

  <clause id="42966">
    <literal><![CDATA[
      (a(x,y,z) \ (a(x,y,z) \ 1)) * (L(z,y,x) \ z) = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,41687,a(flip),b,42965,a),flip(a)].">
      <j1 rule="hyper" parents="373 41687 42965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42967">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * R(z,u,u) = z * L(a(z,u,u),y,x)
    ]]></literal>
    <justification jstring="[para(15984(a,1),42963(a,1,2))].">
      <j1 rule="para" parents="15984 42963"/>
    </justification>
  </clause>

  <clause id="42968">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * R(z,u,u) = z * a(L(z,y,x),u,u)
    ]]></literal>
    <justification jstring="[para(32607(a,2),42967(a,2,2))].">
      <j1 rule="para" parents="32607 42967"/>
    </justification>
  </clause>

  <clause id="42969">
    <literal><![CDATA[
      x * (a(x,y,y) * a(z,u,a(y,y,x))) = a(z,u,a(x,y,y)) * R(x,y,y)
    ]]></literal>
    <justification jstring="[para(42687(a,2),42967(a,2,2)),flip(a)].">
      <j1 rule="para" parents="42687 42967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42970">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x \ L(x,y,z)) = a(z,y,x) \ (a(z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(36,a,42427,a,b,42966,a)].">
      <j1 rule="hyper" parents="36 42427 42966"/>
    </justification>
  </clause>

  <clause id="42971">
    <literal><![CDATA[
      a(x,y,z) \ (a(x,y,z) \ 1) = z \ L(L(z,y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42147,a(flip),b,42970,a),flip(a)].">
      <j1 rule="hyper" parents="64 42147 42970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42972">
    <literal><![CDATA[
      (a(x,y,z) * a(x,y,z)) \ 1 = z \ L(L(z,y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42436,a,b,42971,a)].">
      <j1 rule="hyper" parents="64 42436 42971"/>
    </justification>
  </clause>

  <clause id="42973">
    <literal><![CDATA[
      L(L(x,y,z),y,z) * (a(z,y,x) * a(z,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,488,a,b,42972,a(flip))].">
      <j1 rule="hyper" parents="40 488 42972"/>
    </justification>
  </clause>

  <clause id="42974">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ x = a(z,y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(1433,a,42973,a)].">
      <j1 rule="hyper" parents="1433 42973"/>
    </justification>
  </clause>

  <clause id="42975">
    <literal><![CDATA[
      a(x,L(L(y,z,u),z,u),w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(42973(a,1),31939(a,1,2)),flip(a)].">
      <j1 rule="para" parents="42973 31939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42976">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),u,w) * v5) = a(x,y,v5 * z)
    ]]></literal>
    <justification jstring="[para(42973(a,1),38921(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="42973 38921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42977">
    <literal><![CDATA[
      a(x,L(T((y * (z \ 1)) \ u,w),z,y),v5) = a(x,T((z \ 1) \ (y \ u),w),v5)
    ]]></literal>
    <justification jstring="[para(11810(a,1),42975(a,1,2,1))].">
      <j1 rule="para" parents="11810 42975"/>
    </justification>
  </clause>

  <clause id="42978">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x,y,z))) \ x = a(z,y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(42139(a,2),42974(a,1,1))].">
      <j1 rule="para" parents="42139 42974"/>
    </justification>
  </clause>

  <clause id="42979">
    <literal><![CDATA[
      a(x,y,z * L(L(u,w,v5),w,v5)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(27453,a,42976,a)].">
      <j1 rule="hyper" parents="27453 42976"/>
    </justification>
  </clause>

  <clause id="42980">
    <literal><![CDATA[
      (T(L(x,y,z),x) * L(x \ L(x,y,z),x,L(x,y,z))) \ 1 = x \ (a(z,y,x) * a(z,y,x))
    ]]></literal>
    <justification jstring="[para(42978(a,1),37002(a,2,2))].">
      <j1 rule="para" parents="42978 37002"/>
    </justification>
  </clause>

  <clause id="42981">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (L(z,y,x) \ z) = u * a(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[para(40719(a,1),42961(a,1,2))].">
      <j1 rule="para" parents="40719 42961"/>
    </justification>
  </clause>

  <clause id="42982">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (u * a(y,y,a(z,x,x))) = a(z,y,x) \ u
    ]]></literal>
    <justification jstring="[hyper(36,a,42427,a,b,42981,a)].">
      <j1 rule="hyper" parents="36 42427 42981"/>
    </justification>
  </clause>

  <clause id="42983">
    <literal><![CDATA[
      L(x,y,(z \ R(z,u,w)) * (v5 * a(u,u,a(w,z,z)))) = L(x,y,a(w,u,z) \ v5)
    ]]></literal>
    <justification jstring="[para(42982(a,1),34157(a,2,3))].">
      <j1 rule="para" parents="42982 34157"/>
    </justification>
  </clause>

  <clause id="42984">
    <literal><![CDATA[
      a(R(x,x,y),y,y \ (R(x,x,y) \ z)) = a(L(x,x,y),y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32590,a(flip),b,42930,a),flip(a)].">
      <j1 rule="hyper" parents="373 32590 42930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42985">
    <literal><![CDATA[
      (x / y) * a(z,z,L(u,x / y,x * (y \ T(x,w)))) = (a(z,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(29018(a,1),42931(a,1,2,3))].">
      <j1 rule="para" parents="29018 42931"/>
    </justification>
  </clause>

  <clause id="42986">
    <literal><![CDATA[
      L(x * (y \ R(y,z,u)),y * L(y,z,u),L(y,z,u)) = y \ (R(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,36267,a(flip),b,42932,a)].">
      <j1 rule="hyper" parents="64 36267 42932"/>
    </justification>
  </clause>

  <clause id="42987">
    <literal><![CDATA[
      x * (a(x,y,z) * (L(a(x,y,z),u,w) \ v5)) = (x * v5) * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29956,a(flip),b,42949,a)].">
      <j1 rule="hyper" parents="64 29956 42949"/>
    </justification>
  </clause>

  <clause id="42988">
    <literal><![CDATA[
      a(x,T((y \ 1) \ (z \ u),w),v5) = a(x,L((z * (y \ 1)) \ u,y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31912,a(flip),b,42977,a),flip(a)].">
      <j1 rule="hyper" parents="64 31912 42977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42990">
    <literal><![CDATA[
      a(x,T((y \ 1) \ (z \ u),w),v5) = a(x,L((y * z) \ u,y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,36561,a(flip),b,42988,a),flip(a)].">
      <j1 rule="hyper" parents="373 36561 42988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42991">
    <literal><![CDATA[
      a(x,L((y * z) \ u,y,z),w) = a(x,y \ (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32140,a(flip),b,42990,a),flip(a)].">
      <j1 rule="hyper" parents="64 32140 42990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42992">
    <literal><![CDATA[
      a(x,L(L(y * K(y * z,u),z,u),u,T(z,y)),w) = a(x,u \ (T(z,y) \ ((T(z,y) * y) * u)),w)
    ]]></literal>
    <justification jstring="[para(29491(a,1),42991(a,1,2,1))].">
      <j1 rule="para" parents="29491 42991"/>
    </justification>
  </clause>

  <clause id="42993">
    <literal><![CDATA[
      a(R(x,x,y),y,y \ (R(x,x,y) \ z)) = x \ R(x,y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,41802,a(flip),b,42984,a),flip(a)].">
      <j1 rule="hyper" parents="373 41802 42984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42994">
    <literal><![CDATA[
      (x / y) * a(z,z,L(u,x / y,(y \ x) * x)) = (a(z,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(29146(a,1),42985(a,1,2,3))].">
      <j1 rule="para" parents="29146 42985"/>
    </justification>
  </clause>

  <clause id="42995">
    <literal><![CDATA[
      (x / y) * a(z,z,L(u,y \ x,(y \ x) * x)) = (a(z,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(29437(a,1),42994(a,1,2,3))].">
      <j1 rule="para" parents="29437 42994"/>
    </justification>
  </clause>

  <clause id="42996">
    <literal><![CDATA[
      (x / y) * a(z,z,L(u,y * x,y)) = (a(z,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(42021(a,1),42995(a,1,2,3))].">
      <j1 rule="para" parents="42021 42995"/>
    </justification>
  </clause>

  <clause id="42997">
    <literal><![CDATA[
      L(x * (y \ R(y,z,u)),y,y * L(y,z,u)) = y \ (R(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,39564,a(flip),b,42986,a)].">
      <j1 rule="hyper" parents="64 39564 42986"/>
    </justification>
  </clause>

  <clause id="42998">
    <literal><![CDATA[
      L(x * (y \ R(y,z,u)),y,y * L(y,z,u)) = R(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,1898,a(flip),b,42997,a),flip(a)].">
      <j1 rule="hyper" parents="373 1898 42997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="42999">
    <literal><![CDATA[
      (x * y) * a(z,u,a(x,w,v5)) = x * (y * a(z,u,a(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(42942(a,1),42987(a,1,2)),flip(a)].">
      <j1 rule="para" parents="42942 42987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43000">
    <literal><![CDATA[
      L(x,y,a(z,u,a(x,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(28860,a,42999,a)].">
      <j1 rule="hyper" parents="28860 42999"/>
    </justification>
  </clause>

  <clause id="43001">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (z * v5) = z * (v5 * a(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(23777,a,42999,a)].">
      <j1 rule="hyper" parents="23777 42999"/>
    </justification>
  </clause>

  <clause id="43004">
    <literal><![CDATA[
      L(x,y,a(a(z,u,x),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(41859(a,2),43000(a,1,3))].">
      <j1 rule="para" parents="41859 43000"/>
    </justification>
  </clause>

  <clause id="43008">
    <literal><![CDATA[
      (x * y) * a(z,u,a(w,v5,x)) = x * (y * a(z,u,a(w,v5,x)))
    ]]></literal>
    <justification jstring="[para(43004(a,1),42221(a,1,1,1))].">
      <j1 rule="para" parents="43004 42221"/>
    </justification>
  </clause>

  <clause id="43009">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),v5,w) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(14211,a,43008,a)].">
      <j1 rule="hyper" parents="14211 43008"/>
    </justification>
  </clause>

  <clause id="43010">
    <literal><![CDATA[
      L(x,y,L(z,z,y)) \ L(x,x,a(z,y,y)) = a(z,L(y,y,z),x)
    ]]></literal>
    <justification jstring="[para(33069(a,1),41654(a,1,2,3))].">
      <j1 rule="para" parents="33069 41654"/>
    </justification>
  </clause>

  <clause id="43011">
    <literal><![CDATA[
      a(x,L(y,y,x),z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42298,a(flip),b,43010,a),flip(a)].">
      <j1 rule="hyper" parents="64 42298 43010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43013">
    <literal><![CDATA[
      x \ R(x,x \ y,z) = a(x,y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32206,a(flip),b,43011,a),flip(a)].">
      <j1 rule="hyper" parents="64 32206 43011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43014">
    <literal><![CDATA[
      x \ R(x,y * x,z) = a(x,y \ x,z)
    ]]></literal>
    <justification jstring="[para(42239(a,1),43013(a,1,2))].">
      <j1 rule="para" parents="42239 43013"/>
    </justification>
  </clause>

  <clause id="43015">
    <literal><![CDATA[
      a(x,(x \ y) \ x,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(26415(a,1),43014(a,1,2)),flip(a)].">
      <j1 rule="para" parents="26415 43014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43016">
    <literal><![CDATA[
      a(x,(y \ x) * x,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32124,a(flip),b,43015,a)].">
      <j1 rule="hyper" parents="64 32124 43015"/>
    </justification>
  </clause>

  <clause id="43017">
    <literal><![CDATA[
      x * a(x,x * y,z) = R(x,y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,32091,a(flip),b,43016,a(flip))].">
      <j1 rule="hyper" parents="145 32091 43016"/>
    </justification>
  </clause>

  <clause id="43019">
    <literal><![CDATA[
      a(x,a(y,z,u) \ u,a(y,z,u) \ u) = a(x,L(u,z,y),L(u,z,y))
    ]]></literal>
    <justification jstring="[para(41658(a,1),41663(a,1,3))].">
      <j1 rule="para" parents="41658 41663"/>
    </justification>
  </clause>

  <clause id="43020">
    <literal><![CDATA[
      a(x,a(y,z,u) \ u,a(y,z,u) * u) = a(x,L(u,z,y),L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42537,a(flip),b,43019,a)].">
      <j1 rule="hyper" parents="64 42537 43019"/>
    </justification>
  </clause>

  <clause id="43021">
    <literal><![CDATA[
      a(x,a(y,z,u) * u,a(y,z,u) * u) = a(x,L(u,z,y),L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42464,a(flip),b,43020,a)].">
      <j1 rule="hyper" parents="64 42464 43020"/>
    </justification>
  </clause>

  <clause id="43022">
    <literal><![CDATA[
      a(x,a(y,z,u) * u,a(y,z,u) * u) = a(x,u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,40664,a(flip),b,43021,a),flip(a)].">
      <j1 rule="hyper" parents="373 40664 43021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43024">
    <literal><![CDATA[
      a(x,y * a(z,u,y),y * a(z,u,y)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31938,a,b,43022,a)].">
      <j1 rule="hyper" parents="64 31938 43022"/>
    </justification>
  </clause>

  <clause id="43025">
    <literal><![CDATA[
      a(a(x,y * a(z,u,y),y * a(z,u,y)),w,v5) = a(a(y,y,x),w,v5)
    ]]></literal>
    <justification jstring="[para(43024(a,2),32543(a,1,1))].">
      <j1 rule="para" parents="43024 32543"/>
    </justification>
  </clause>

  <clause id="43026">
    <literal><![CDATA[
      a(a(x * a(y,z,x),x * a(y,z,x),u),w,v5) = a(a(x,x,u),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,41479,a,b,43025,a)].">
      <j1 rule="hyper" parents="64 41479 43025"/>
    </justification>
  </clause>

  <clause id="43027">
    <literal><![CDATA[
      (x * y) \ (((x * y) * x) * a(y,z,u)) = a(y,z,u) * (a(a(y,z,u),x,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33931,a(flip),b,41919,a)].">
      <j1 rule="hyper" parents="64 33931 41919"/>
    </justification>
  </clause>

  <clause id="43028">
    <literal><![CDATA[
      L(x,y \ z,((1 / y) \ (y \ z)) * (y \ z)) = L(x,y \ z,z \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,13011,a(flip),b,41991,a),flip(a)].">
      <j1 rule="hyper" parents="373 13011 41991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43029">
    <literal><![CDATA[
      L(x,y,(z \ ((z / u) * w)) * L(z,u,u)) = L(x,y,(z * u) * (u * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29228,a(flip),b,42016,a)].">
      <j1 rule="hyper" parents="64 29228 42016"/>
    </justification>
  </clause>

  <clause id="43030">
    <literal><![CDATA[
      L(x,y,z * (L(z,u,u) \ ((z / u) * w))) = L(x,y,(z * u) * (u * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,36393,a(flip),b,43029,a)].">
      <j1 rule="hyper" parents="64 36393 43029"/>
    </justification>
  </clause>

  <clause id="43031">
    <literal><![CDATA[
      L(x,y,z * (L(z,u,u) \ ((u \ z) * w))) = L(x,y,(z * u) * (u * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29241,a(flip),b,43030,a)].">
      <j1 rule="hyper" parents="64 29241 43030"/>
    </justification>
  </clause>

  <clause id="43032">
    <literal><![CDATA[
      L(x,y,z * (L(z,u,u) \ ((u \ z) * w))) = L(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),43031(a,2,3,2))].">
      <j1 rule="para" parents="10 43031"/>
    </justification>
  </clause>

  <clause id="43034">
    <literal><![CDATA[
      a((x \ ((x / y) * z)) * L(x,y,y),u,w) = a((x * y) * (y * (y \ z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32720,a(flip),b,42017,a)].">
      <j1 rule="hyper" parents="64 32720 42017"/>
    </justification>
  </clause>

  <clause id="43035">
    <literal><![CDATA[
      a(x * (L(x,y,y) \ ((x / y) * z)),u,w) = a((x * y) * (y * (y \ z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,35237,a(flip),b,43034,a)].">
      <j1 rule="hyper" parents="64 35237 43034"/>
    </justification>
  </clause>

  <clause id="43036">
    <literal><![CDATA[
      a(x * (L(x,y,y) \ ((y \ x) * z)),u,w) = a((x * y) * (y * (y \ z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32674,a(flip),b,43035,a)].">
      <j1 rule="hyper" parents="64 32674 43035"/>
    </justification>
  </clause>

  <clause id="43037">
    <literal><![CDATA[
      a(x * (L(x,y,y) \ ((y \ x) * z)),u,w) = a((x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(10(a,1),43036(a,2,1,2))].">
      <j1 rule="para" parents="10 43036"/>
    </justification>
  </clause>

  <clause id="43039">
    <literal><![CDATA[
      L(x * (R(x,y,z) \ a(x,y,z)),a(x,y,z),x * y) = a(y,x * y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(34147(a,1),42075(a,1,1))].">
      <j1 rule="para" parents="34147 42075"/>
    </justification>
  </clause>

  <clause id="43040">
    <literal><![CDATA[
      L(x,y,z) * (L(L(x,y,z),y,z) \ u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(39,a,40710,a(flip),b,42141,a(flip))].">
      <j1 rule="hyper" parents="39 40710 42141"/>
    </justification>
  </clause>

  <clause id="43041">
    <literal><![CDATA[
      L(L(x,y,z),y,z) \ (u * L(x,y,z)) = L(x,y,z) \ (u * x)
    ]]></literal>
    <justification jstring="[hyper(139,a,23886,a(flip),b,43040,a),flip(a)].">
      <j1 rule="hyper" parents="139 23886 43040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43042">
    <literal><![CDATA[
      a(((a(x,y,z) \ (z * y)) * x) \ u,w,v5) = a(((z * y) * R(x,y,z)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(29973(a,1),42749(a,1,1,1))].">
      <j1 rule="para" parents="29973 42749"/>
    </justification>
  </clause>

  <clause id="43043">
    <literal><![CDATA[
      (L(x,y,z) * y) * L(z,z,a(x,y,y)) = (x * y) * ((a(z,y,x) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(42082(a,1),42819(a,1,1))].">
      <j1 rule="para" parents="42082 42819"/>
    </justification>
  </clause>

  <clause id="43044">
    <literal><![CDATA[
      (L(x,y,z) * y) * L(z,z,a(x,y,y)) = (x * y) * (a(z,y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29936,a(flip),b,43043,a),flip(a)].">
      <j1 rule="hyper" parents="373 29936 43043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43045">
    <literal><![CDATA[
      x \ (a(y,z,u) * (x * (a(y,z,u) \ w))) = L(L(w,x,a(y,z,u)),a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,30,a,b,42828,a),flip(a)].">
      <j1 rule="hyper" parents="373 30 42828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43046">
    <literal><![CDATA[
      (x / y) \ (x * a(x,z,u)) = a(x,z,u) * (a(a(x,z,u),y,y) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41963,a(flip),b,43027,a)].">
      <j1 rule="hyper" parents="64 41963 43027"/>
    </justification>
  </clause>

  <clause id="43047">
    <literal><![CDATA[
      (x / y) \ (x * a(x,z,u)) = a(x,z,u) * L(y,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(30459(a,1),43046(a,2,2))].">
      <j1 rule="para" parents="30459 43046"/>
    </justification>
  </clause>

  <clause id="43048">
    <literal><![CDATA[
      (x / y) \ (x * a(x,z,u)) = (1 / y) \ a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,27122,a(flip),b,43047,a),flip(a)].">
      <j1 rule="hyper" parents="373 27122 43047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43049">
    <literal><![CDATA[
      L(x,y \ z,((1 / y) \ (y \ z)) * (y \ z)) = L(x,y \ z,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,29357,a(flip),b,43028,a),flip(a)].">
      <j1 rule="hyper" parents="373 29357 43028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43050">
    <literal><![CDATA[
      L(x,y \ z,z * (y \ ((1 / y) \ (y \ z)))) = L(x,y \ z,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(31408(a,1),43049(a,1,3))].">
      <j1 rule="para" parents="31408 43049"/>
    </justification>
  </clause>

  <clause id="43051">
    <literal><![CDATA[
      L(x,y \ z,z * (y \ ((y \ 1) \ (y \ z)))) = L(x,y \ z,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29242,a(flip),b,43050,a)].">
      <j1 rule="hyper" parents="64 29242 43050"/>
    </justification>
  </clause>

  <clause id="43052">
    <literal><![CDATA[
      L(x,y \ z,z * (y \ (y \ ((1 / y) \ z)))) = L(x,y \ z,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(1166(a,1),43051(a,1,3,2,2))].">
      <j1 rule="para" parents="1166 43051"/>
    </justification>
  </clause>

  <clause id="43053">
    <literal><![CDATA[
      L(x,y \ z,L((1 / y) \ z,y,y) * z) = L(x,y \ z,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,34277,a(flip),b,43052,a)].">
      <j1 rule="hyper" parents="64 34277 43052"/>
    </justification>
  </clause>

  <clause id="43054">
    <literal><![CDATA[
      L(x,y \ z,(L(y,y,y) * z) * z) = L(x,y \ z,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(1256(a,1),43053(a,1,3,1))].">
      <j1 rule="para" parents="1256 43053"/>
    </justification>
  </clause>

  <clause id="43055">
    <literal><![CDATA[
      L(x,y \ z,L(L(y,y,y),z,z)) = L(x,y \ z,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,24838,a(flip),b,43054,a)].">
      <j1 rule="hyper" parents="64 24838 43054"/>
    </justification>
  </clause>

  <clause id="43056">
    <literal><![CDATA[
      L(x,y \ z,z \ (y \ z)) = L(x,y \ z,L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,13042,a(flip),b,43055,a),flip(a)].">
      <j1 rule="hyper" parents="64 13042 43055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43058">
    <literal><![CDATA[
      L(a(x,x,a(y,z,z)),a(z,x,y),z * x) = a(x,z * x,a(z,x,y))
    ]]></literal>
    <justification jstring="[para(41618(a,1),43039(a,1,1))].">
      <j1 rule="para" parents="41618 43039"/>
    </justification>
  </clause>

  <clause id="43059">
    <literal><![CDATA[
      a(x,y * x,a(y,x,z)) = a(x,x,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(42,a,42717,a,b,43058,a)].">
      <j1 rule="hyper" parents="42 42717 43058"/>
    </justification>
  </clause>

  <clause id="43060">
    <literal><![CDATA[
      a(x * y,x * y,a(z,y,x)) = a(y,y,a(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,42362,a,b,43059,a)].">
      <j1 rule="hyper" parents="64 42362 43059"/>
    </justification>
  </clause>

  <clause id="43062">
    <literal><![CDATA[
      a(a(x,y,z),x \ y,y) = a(y,y,a(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41500,a(flip),b,43060,a)].">
      <j1 rule="hyper" parents="64 41500 43060"/>
    </justification>
  </clause>

  <clause id="43063">
    <literal><![CDATA[
      a(a(x,y,z),y * x,y * x) = a(y,y,a(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,40504,a,b,43062,a)].">
      <j1 rule="hyper" parents="64 40504 43062"/>
    </justification>
  </clause>

  <clause id="43064">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * a(y,x,z) = L(a(y,x,z),x * z,x * z)
    ]]></literal>
    <justification jstring="[para(43063(a,1),41503(a,1,1))].">
      <j1 rule="para" parents="43063 41503"/>
    </justification>
  </clause>

  <clause id="43065">
    <literal><![CDATA[
      L(a(x,y,z),y * z,y * z) = L(a(x,y,z),z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41958,a(flip),b,43064,a),flip(a)].">
      <j1 rule="hyper" parents="64 41958 43064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43066">
    <literal><![CDATA[
      L(a(x,y,z),y * z,y * z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(373,a,42055,a(flip),b,43065,a),flip(a)].">
      <j1 rule="hyper" parents="373 42055 43065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43067">
    <literal><![CDATA[
      L(a(x,y,z),z * y,z * y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,29507,a,b,43066,a)].">
      <j1 rule="hyper" parents="64 29507 43066"/>
    </justification>
  </clause>

  <clause id="43068">
    <literal><![CDATA[
      L(a(x,y,z),z * y,y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,42702,a(flip),b,43066,a)].">
      <j1 rule="hyper" parents="64 42702 43066"/>
    </justification>
  </clause>

  <clause id="43069">
    <literal><![CDATA[
      a(a(x,y,z),u,L(u,y * z,y * z)) = a(L(z,y,x) \ z,u,u)
    ]]></literal>
    <justification jstring="[para(43066(a,1),40980(a,1,1)),flip(a)].">
      <j1 rule="para" parents="43066 40980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43070">
    <literal><![CDATA[
      L(a(x,y,z),y \ z,y) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,41720,a,b,43068,a)].">
      <j1 rule="hyper" parents="64 41720 43068"/>
    </justification>
  </clause>

  <clause id="43071">
    <literal><![CDATA[
      L(x \ y,x,z) \ (x \ y) = L(a(z,x,x \ y),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29441,a(flip),b,43068,a),flip(a)].">
      <j1 rule="hyper" parents="64 29441 43068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43072">
    <literal><![CDATA[
      L(a(x,y,L(1 / z,u,w) \ 1),L(L(z \ 1,u,w) \ y,z,z),y) = L(L(1 / z,u,w) \ 1,y,x) \ (L(1 / z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(35167(a,2),43068(a,1,2))].">
      <j1 rule="para" parents="35167 43068"/>
    </justification>
  </clause>

  <clause id="43073">
    <literal><![CDATA[
      L(a(x,y,y * z),((y \ 1) \ z) * y,y) = L((y \ 1) \ z,y,x) \ ((y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(42880(a,1),43068(a,1,1))].">
      <j1 rule="para" parents="42880 43068"/>
    </justification>
  </clause>

  <clause id="43074">
    <literal><![CDATA[
      L(x * y,y,z) \ (x * y) = L(a(z,y,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29493,a(flip),b,43070,a),flip(a)].">
      <j1 rule="hyper" parents="64 29493 43070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43075">
    <literal><![CDATA[
      L(a(x \ y,z,z \ x),x,z) = (((y / x) * z) \ y) \ (z \ x)
    ]]></literal>
    <justification jstring="[para(15002(a,1),43071(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15002 43071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43076">
    <literal><![CDATA[
      L(x \ y,x,L(z,z,x)) \ (x \ y) = L(z \ R(z,x,x \ y),y,x)
    ]]></literal>
    <justification jstring="[para(41802(a,1),43071(a,2,1))].">
      <j1 rule="para" parents="41802 43071"/>
    </justification>
  </clause>

  <clause id="43077">
    <literal><![CDATA[
      a(a(x,y,z),u,L(u,y * z,y * z)) = a(z * L(z,y,x),u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,9387,a(flip),b,43069,a),flip(a)].">
      <j1 rule="hyper" parents="373 9387 43069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43078">
    <literal><![CDATA[
      ((L(x,x,y) * y) \ (L(x,x,y) * z)) \ (y \ z) = L(x \ R(x,y,y \ z),z,y)
    ]]></literal>
    <justification jstring="[para(102(a,1),43076(a,1,1))].">
      <j1 rule="para" parents="102 43076"/>
    </justification>
  </clause>

  <clause id="43079">
    <literal><![CDATA[
      a(((L(x,y,z) * y) * z) \ u,w,v5) = a(((x * y) * R(z,y,x)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(42082(a,1),43042(a,1,1,1,1))].">
      <j1 rule="para" parents="42082 43042"/>
    </justification>
  </clause>

  <clause id="43080">
    <literal><![CDATA[
      a(((L(x,y,z) * y) * z) \ u,w,v5) = a(((x * y) * L(z,y,x)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,40407,a(flip),b,43079,a),flip(a)].">
      <j1 rule="hyper" parents="373 40407 43079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43081">
    <literal><![CDATA[
      a(((L(x,y,z) * y) * z) \ u,w,v5) = a((x * (y * z)) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(100(a,1),43080(a,2,1,1))].">
      <j1 rule="para" parents="100 43080"/>
    </justification>
  </clause>

  <clause id="43082">
    <literal><![CDATA[
      x \ (a(y,z,u) * (x * (a(y,z,u) \ (w * a(x,w,a(y,z,u)))))) = L(L(w,a(y,z,u),x),a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(41867(a,1),43045(a,2,1))].">
      <j1 rule="para" parents="41867 43045"/>
    </justification>
  </clause>

  <clause id="43083">
    <literal><![CDATA[
      (L(x,x,y) * y) \ (L(x,x,y) * z) = L(y \ z,y,L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(40,a,43076,a,b,43078,a),flip(a)].">
      <j1 rule="hyper" parents="40 43076 43078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43084">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(x,y,y),L(y \ x,y \ x,a(x,y,y))) = ((y \ x) * a(x,y,y)) \ (L(y \ x,y \ x,a(x,y,y)) * z)
    ]]></literal>
    <justification jstring="[para(30299(a,1),43083(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="30299 43083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43085">
    <literal><![CDATA[
      (x * a(x,y,z)) \ ((x * y) * T(z,y)) = L(x,x,a(z,y,y)) \ (x * (z * y))
    ]]></literal>
    <justification jstring="[para(40892(a,1),41614(a,1,1)),flip(a)].">
      <j1 rule="para" parents="40892 41614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43086">
    <literal><![CDATA[
      (x * a(x,y,z)) \ ((x * y) * T(z,y)) = (z * y) * a(a(z,y,y),x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,37628,a(flip),b,43085,a),flip(a)].">
      <j1 rule="hyper" parents="373 37628 43085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43087">
    <literal><![CDATA[
      (x * a(x,y,z)) \ ((x * y) * T(z,y)) = (z * y) * a(z,y,a(y,x,x))
    ]]></literal>
    <justification jstring="[para(40882(a,1),43086(a,2,2))].">
      <j1 rule="para" parents="40882 43086"/>
    </justification>
  </clause>

  <clause id="43088">
    <literal><![CDATA[
      (x * a(x,y,z)) \ ((x * y) * T(z,y)) = z * L(y,y,a(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,40909,a(flip),b,43087,a),flip(a)].">
      <j1 rule="hyper" parents="373 40909 43087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43089">
    <literal><![CDATA[
      L(x * y,z,a(z,y,x)) = x * L(y,y,a(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26742,a(flip),b,43088,a)].">
      <j1 rule="hyper" parents="64 26742 43088"/>
    </justification>
  </clause>

  <clause id="43090">
    <literal><![CDATA[
      L(((x * y) \ (y \ x)) * z,a(y,y,x),y \ x) = (x * y) \ ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30969,a(flip),b,41737,a)].">
      <j1 rule="hyper" parents="64 30969 41737"/>
    </justification>
  </clause>

  <clause id="43091">
    <literal><![CDATA[
      L(x,y,((1 / L(z,u,w)) * (u * w)) * v5) = L(x,y,v5 * ((u * R(w,u,z)) * z))
    ]]></literal>
    <justification jstring="[para(35163(a,1),41921(a,1,3,1))].">
      <j1 rule="para" parents="35163 41921"/>
    </justification>
  </clause>

  <clause id="43092">
    <literal><![CDATA[
      L(x,y,(L(z,u,w) * (u * w)) * v5) = L(x,y,v5 * ((u * R(w,u,z)) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,2238,a(flip),b,43091,a)].">
      <j1 rule="hyper" parents="64 2238 43091"/>
    </justification>
  </clause>

  <clause id="43093">
    <literal><![CDATA[
      L(x,y,z * ((u * R(w,u,v5)) * v5)) = L(x,y,(w * (u * v5)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33630,a(flip),b,43092,a),flip(a)].">
      <j1 rule="hyper" parents="64 33630 43092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43094">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y) \ z = (x \ (x / (x \ y))) \ z
    ]]></literal>
    <justification jstring="[para(29423(a,1),42129(a,1,1)),flip(a)].">
      <j1 rule="para" parents="29423 42129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43095">
    <literal><![CDATA[
      ((x * (y \ x)) \ x) \ z = (y \ (y / (y \ x))) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,437,a(flip),b,43094,a)].">
      <j1 rule="hyper" parents="64 437 43094"/>
    </justification>
  </clause>

  <clause id="43096">
    <literal><![CDATA[
      L(a(x,x,y) \ L(a(x,x,y) * 1,z,u),w,v5) = a(a(y,x,L(x,w,v5)),z,u)
    ]]></literal>
    <justification jstring="[para(37686(a,1),42225(a,1,1,2,1))].">
      <j1 rule="para" parents="37686 42225"/>
    </justification>
  </clause>

  <clause id="43097">
    <literal><![CDATA[
      L(a(x,x,y) \ L(a(x,x,y),z,u),w,v5) = a(a(y,x,L(x,w,v5)),z,u)
    ]]></literal>
    <justification jstring="[para(8(a,1),43096(a,1,1,2,1))].">
      <j1 rule="para" parents="8 43096"/>
    </justification>
  </clause>

  <clause id="43098">
    <literal><![CDATA[
      a(a(x,y,L(y,z,u)),w,v5) = L(a(a(x,y,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(42689(a,1),43097(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42689 43097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43099">
    <literal><![CDATA[
      L(a(a(x,y,y),z,u),w,L(y,v5,v6)) = a(x,y,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,41700,a(flip),b,43098,a),flip(a)].">
      <j1 rule="hyper" parents="64 41700 43098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43101">
    <literal><![CDATA[
      x \ L(x,y,y \ L(y,z,u)) = a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(42,a,27864,a,b,43099,a)].">
      <j1 rule="hyper" parents="42 27864 43099"/>
    </justification>
  </clause>

  <clause id="43103">
    <literal><![CDATA[
      (x * a(y,z,z)) \ R(y,z,L(z,x,x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,42171,a(flip),b,42408,a),flip(a)].">
      <j1 rule="hyper" parents="64 42171 42408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43104">
    <literal><![CDATA[
      (a(x,y,y) * z) \ R(x,y,L(y,z,z)) = z \ x
    ]]></literal>
    <justification jstring="[hyper(23968,a,43103,a)].">
      <j1 rule="hyper" parents="23968 43103"/>
    </justification>
  </clause>

  <clause id="43106">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) \ (u * L(x,y,z)) = a(u,L(x,y,z),x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,38706,a(flip),b,42597,a),flip(a)].">
      <j1 rule="hyper" parents="373 38706 42597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43107">
    <literal><![CDATA[
      a(L(x,x,a(x,y,z) * u),y,z) = ((a(x,y,z) * x) \ (x * u)) \ u
    ]]></literal>
    <justification jstring="[hyper(373,a,40762,a(flip),b,42658,a)].">
      <j1 rule="hyper" parents="373 40762 42658"/>
    </justification>
  </clause>

  <clause id="43108">
    <literal><![CDATA[
      ((a(x,y,z) * x) \ (x * u)) \ u = a(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(34022(a,1),43107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="34022 43107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43110">
    <literal><![CDATA[
      x * (K(y,y \ x) * (((1 / y) \ (x / y)) \ z)) = L(y \ x,y,y) * ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27082,a(flip),b,42868,a),flip(a)].">
      <j1 rule="hyper" parents="373 27082 42868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43111">
    <literal><![CDATA[
      a(R(x,y,x),a(z,x,u),a(z,x,u) \ w) = w \ L(w,a(z,x,u),x * a(u,x,z))
    ]]></literal>
    <justification jstring="[para(42798(a,1),42912(a,2,2))].">
      <j1 rule="para" parents="42798 42912"/>
    </justification>
  </clause>

  <clause id="43112">
    <literal><![CDATA[
      L(a(x,y,y * z),(y \ z) * y,y) = L((y \ 1) \ z,y,x) \ ((y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29865,a(flip),b,43073,a)].">
      <j1 rule="hyper" parents="64 29865 43073"/>
    </justification>
  </clause>

  <clause id="43113">
    <literal><![CDATA[
      L((x \ 1) \ y,x,z) \ ((x \ 1) \ y) = L(a(z,x,x * y),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29441,a(flip),b,43112,a),flip(a)].">
      <j1 rule="hyper" parents="64 29441 43112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43115">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) \ (u * L(x,y,z)) = a(a(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,41758,a(flip),b,43106,a),flip(a)].">
      <j1 rule="hyper" parents="373 41758 43106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43116">
    <literal><![CDATA[
      x * (K(y,y \ x) * (((1 / y) \ (x / y)) \ z)) = ((1 / y) * x) * ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[para(569(a,1),43110(a,2,1))].">
      <j1 rule="para" parents="569 43110"/>
    </justification>
  </clause>

  <clause id="43117">
    <literal><![CDATA[
      ((1 / x) * y) * ((x \ y) \ z) = y * (((1 / x) \ (x \ y)) \ z)
    ]]></literal>
    <justification jstring="[para(24522(a,1),43116(a,1,2)),flip(a)].">
      <j1 rule="para" parents="24522 43116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43118">
    <literal><![CDATA[
      a(x,x,L(x * y,y,z)) \ z = y * (((1 / (1 / x)) \ ((1 / x) \ y)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41146,a,b,43117,a)].">
      <j1 rule="hyper" parents="64 41146 43117"/>
    </justification>
  </clause>

  <clause id="43119">
    <literal><![CDATA[
      a(x,x,L(x * y,y,z)) \ z = y * ((x \ ((x \ 1) \ y)) \ z)
    ]]></literal>
    <justification jstring="[para(6617(a,1),43118(a,2,2,1))].">
      <j1 rule="para" parents="6617 43118"/>
    </justification>
  </clause>

  <clause id="43120">
    <literal><![CDATA[
      a(R(x,y,x),a(z,x,u),a(z,x,u) \ w) = a(w,a(u,x,z),x * a(u,x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,42628,a(flip),b,43111,a),flip(a)].">
      <j1 rule="hyper" parents="373 42628 43111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43121">
    <literal><![CDATA[
      a(R(x,y,x),a(z,x,u),a(z,x,u) * w) = a(w,a(u,x,z),x * a(u,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42537,a(flip),b,43120,a)].">
      <j1 rule="hyper" parents="64 42537 43120"/>
    </justification>
  </clause>

  <clause id="43122">
    <literal><![CDATA[
      a(x,a(y,z,u),z * a(y,z,u)) = a(z,a(u,z,y),a(u,z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,13103,a(flip),b,43121,a),flip(a)].">
      <j1 rule="hyper" parents="64 13103 43121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43123">
    <literal><![CDATA[
      (x * a(a(y,x,x),z,u)) \ (a(y,x \ R(x,z,u),x) \ R(x,w,v5)) = x \ R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(39769(a,1),41695(a,1,1))].">
      <j1 rule="para" parents="39769 41695"/>
    </justification>
  </clause>

  <clause id="43124">
    <literal><![CDATA[
      (x / y) \ (x * (y \ L(y,z,u))) = L(y,z,u) * a(a(y,y,y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,167,a(flip),b,41699,a),flip(a)].">
      <j1 rule="hyper" parents="373 167 41699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43126">
    <literal><![CDATA[
      (x / y) \ (x * (y \ L(y,z,u))) = L(y,z,u) * a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(30184(a,1),43124(a,2,2))].">
      <j1 rule="para" parents="30184 43124"/>
    </justification>
  </clause>

  <clause id="43127">
    <literal><![CDATA[
      L((x * y) * a(z * x,x,y),z * x,z * x) = (x \ z) * ((((x \ z) \ 1) * x) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35219,a(flip),b,41840,a)].">
      <j1 rule="hyper" parents="64 35219 41840"/>
    </justification>
  </clause>

  <clause id="43128">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) / T(a(x,x,L(z,y,y)),u) = 1 / T(a(x,x,z),u)
    ]]></literal>
    <justification jstring="[para(40849(a,1),41952(a,1,2,1))].">
      <j1 rule="para" parents="40849 41952"/>
    </justification>
  </clause>

  <clause id="43129">
    <literal><![CDATA[
      a(x,x,L(y,z,z)) \ a(x,z,a(y,x,z)) = 1 / T(a(x,x,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23918,a(flip),b,43128,a)].">
      <j1 rule="hyper" parents="64 23918 43128"/>
    </justification>
  </clause>

  <clause id="43130">
    <literal><![CDATA[
      a(x,x,L(y,z,z)) \ a(x,z,a(y,x,z)) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,23918,a(flip),b,43129,a),flip(a)].">
      <j1 rule="hyper" parents="373 23918 43129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43132">
    <literal><![CDATA[
      (a(x,y \ 1,L(z,y,y)) \ (y \ 1)) * (z * a(y,y,z)) = y \ L(z,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(38937(a,1),42094(a,1,1,1))].">
      <j1 rule="para" parents="38937 42094"/>
    </justification>
  </clause>

  <clause id="43133">
    <literal><![CDATA[
      (a(x,y,L(z,y,y)) \ (y \ 1)) * (z * a(y,y,z)) = y \ L(z,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(11980(a,1),43132(a,1,1,1))].">
      <j1 rule="para" parents="11980 43132"/>
    </justification>
  </clause>

  <clause id="43134">
    <literal><![CDATA[
      (a(x,y,L(z,y,y)) \ (y \ 1)) * (z * a(y,y,z)) = y \ L(z,y,x)
    ]]></literal>
    <justification jstring="[para(11794(a,1),43133(a,2,2))].">
      <j1 rule="para" parents="11794 43133"/>
    </justification>
  </clause>

  <clause id="43135">
    <literal><![CDATA[
      (x \ (a(y,x,L(z,x,x)) \ 1)) * (z * a(x,x,z)) = x \ L(z,x,y)
    ]]></literal>
    <justification jstring="[para(42376(a,1),43134(a,1,1))].">
      <j1 rule="para" parents="42376 43134"/>
    </justification>
  </clause>

  <clause id="43136">
    <literal><![CDATA[
      (x \ (a(y,x,z) \ 1)) * (z * a(x,x,z)) = x \ L(z,x,y)
    ]]></literal>
    <justification jstring="[para(42877(a,1),43135(a,1,1,2,1))].">
      <j1 rule="para" parents="42877 43135"/>
    </justification>
  </clause>

  <clause id="43137">
    <literal><![CDATA[
      L(x,y \ (L(z,z,z * (y * u)) * ((z * y) * u)),w) = L(x,u * (L(u,y,z) \ u),w)
    ]]></literal>
    <justification jstring="[para(34027(a,1),42117(a,1,2,2,1))].">
      <j1 rule="para" parents="34027 42117"/>
    </justification>
  </clause>

  <clause id="43138">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u) \ (a(u,x \ R(x,y,z),x) \ R(x,w,v5)) = x \ R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(41601(a,2),43123(a,1,1))].">
      <j1 rule="para" parents="41601 43123"/>
    </justification>
  </clause>

  <clause id="43139">
    <literal><![CDATA[
      (x \ y) * ((((x \ y) \ 1) * x) * z) = (y * x) * ((((y * x) \ 1) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30440,a(flip),b,43127,a),flip(a)].">
      <j1 rule="hyper" parents="64 30440 43127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43140">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ 1) * y) * z) = (1 / (x / y)) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27016,a(flip),b,43139,a),flip(a)].">
      <j1 rule="hyper" parents="64 27016 43139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43141">
    <literal><![CDATA[
      (1 / ((x \ y) / x)) * ((x \ y) * z) = y * (((y \ 1) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38581,a(flip),b,43140,a),flip(a)].">
      <j1 rule="hyper" parents="64 38581 43140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43142">
    <literal><![CDATA[
      L(x,y \ z,1 / ((y \ z) / y)) = (L(y,z,z) / x) \ ((z * (((z \ 1) * y) * x)) / x)
    ]]></literal>
    <justification jstring="[para(43141(a,1),35368(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="43141 35368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43143">
    <literal><![CDATA[
      L(x,y \ (L(z,z,y * u) * ((z * y) * u)),w) = L(x,u * (L(u,y,z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,38287,a(flip),b,43137,a)].">
      <j1 rule="hyper" parents="64 38287 43137"/>
    </justification>
  </clause>

  <clause id="43144">
    <literal><![CDATA[
      L(x,y \ (L(z,z,y * u) * ((z * y) * u)),w) = L(x,u * (u * L(u,y,z)),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,30864,a(flip),b,43143,a),flip(a)].">
      <j1 rule="hyper" parents="373 30864 43143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43145">
    <literal><![CDATA[
      L(x,L(L(y,z,u),y,y),w) = L(x,z \ (L(u,u,z * y) * ((u * z) * y)),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11778,a(flip),b,43144,a)].">
      <j1 rule="hyper" parents="373 11778 43144"/>
    </justification>
  </clause>

  <clause id="43146">
    <literal><![CDATA[
      L(x,y \ (L(z,z,y * u) * ((z * y) * u)),w) = L(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,35037,a(flip),b,43145,a),flip(a)].">
      <j1 rule="hyper" parents="64 35037 43145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43148">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u) \ (a(u,x \ L(x,y,z),x) \ R(x,w,v5)) = x \ R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(37374(a,1),43138(a,1,2,1))].">
      <j1 rule="para" parents="37374 43138"/>
    </justification>
  </clause>

  <clause id="43149">
    <literal><![CDATA[
      L(x,y \ z,1 / ((y \ z) / y)) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,36528,a(flip),b,43142,a),flip(a)].">
      <j1 rule="hyper" parents="373 36528 43142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43150">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) / y) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(2273,a,43149,a)].">
      <j1 rule="hyper" parents="2273 43149"/>
    </justification>
  </clause>

  <clause id="43151">
    <literal><![CDATA[
      L(x,y \ z,y \ (y \ z)) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(23857,a,43150,a)].">
      <j1 rule="hyper" parents="23857 43150"/>
    </justification>
  </clause>

  <clause id="43152">
    <literal><![CDATA[
      L(x,y \ z,L(z,z,y)) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42338,a,b,43151,a)].">
      <j1 rule="hyper" parents="64 42338 43151"/>
    </justification>
  </clause>

  <clause id="43153">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u) \ (a(u,x * L(x,y,z),x) \ R(x,w,v5)) = x \ R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(11978(a,1),43148(a,1,2,1))].">
      <j1 rule="para" parents="11978 43148"/>
    </justification>
  </clause>

  <clause id="43154">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u) \ (a(a(x,x,u),y,z) \ R(x,w,v5)) = x \ R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(41693(a,1),43153(a,1,2,1))].">
      <j1 rule="para" parents="41693 43153"/>
    </justification>
  </clause>

  <clause id="43155">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u) \ (R(x,w,v5) * a(a(u,x,x),y,z)) = x \ R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(39769(a,1),43154(a,1,2))].">
      <j1 rule="para" parents="39769 43154"/>
    </justification>
  </clause>

  <clause id="43156">
    <literal><![CDATA[
      L(R(x,y,z),x * L(x,y,z),u) = R(x,y,z) * a(a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,42722,a,b,43155,a)].">
      <j1 rule="hyper" parents="39 42722 43155"/>
    </justification>
  </clause>

  <clause id="43157">
    <literal><![CDATA[
      L(R(x,y,z),x * L(x,y,z),u) = a(a(u,x,x),y,z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a,b,43156,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 43156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43158">
    <literal><![CDATA[
      R(R(x,y,z),x \ L(x,y,z),u) = a(a(u,x,x),y,z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35117,a,b,43157,a)].">
      <j1 rule="hyper" parents="64 35117 43157"/>
    </justification>
  </clause>

  <clause id="43159">
    <literal><![CDATA[
      R(R(x,y,z),x \ R(x,y,z),u) = a(a(u,x,x),y,z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34465,a,b,43158,a)].">
      <j1 rule="hyper" parents="64 34465 43158"/>
    </justification>
  </clause>

  <clause id="43160">
    <literal><![CDATA[
      R(R(x,y,z),u * ((x \ R(x,y,z)) / u),w) = a(a(w,x,x),y,z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26413,a,b,43159,a)].">
      <j1 rule="hyper" parents="64 26413 43159"/>
    </justification>
  </clause>

  <clause id="43161">
    <literal><![CDATA[
      (a(x,y,z) \ (u * L(z,z,a(x,y,y)))) \ (u * L(z,y,x)) = a(u,L(z,y,x),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(23133(a,1),41649(a,1,1))].">
      <j1 rule="para" parents="23133 41649"/>
    </justification>
  </clause>

  <clause id="43162">
    <literal><![CDATA[
      a(L(R(x,y,z) \ x,u,x * L(x,y,z)),R(x,y,z),w) = a(a(x,x,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,42454,a(flip),b,41755,a),flip(a)].">
      <j1 rule="hyper" parents="373 42454 41755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43164">
    <literal><![CDATA[
      a(R(x,y,z) \ x,R(x,y,z),u) = a(a(x,x,u),y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,26802,a(flip),b,43162,a)].">
      <j1 rule="hyper" parents="64 26802 43162"/>
    </justification>
  </clause>

  <clause id="43165">
    <literal><![CDATA[
      a(R(x,y,z) \ x,L(x,y,z),u) = a(a(x,x,u),y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,32197,a(flip),b,43164,a)].">
      <j1 rule="hyper" parents="64 32197 43164"/>
    </justification>
  </clause>

  <clause id="43166">
    <literal><![CDATA[
      a(L(x,y,z) \ x,L(x,y,z),u) = a(a(x,x,u),y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,32982,a(flip),b,43165,a)].">
      <j1 rule="hyper" parents="64 32982 43165"/>
    </justification>
  </clause>

  <clause id="43167">
    <literal><![CDATA[
      a(x * L(x,y,z),L(x,y,z),u) = a(a(x,x,u),y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,41827,a(flip),b,43166,a)].">
      <j1 rule="hyper" parents="64 41827 43166"/>
    </justification>
  </clause>

  <clause id="43168">
    <literal><![CDATA[
      a(x * L(x,y,z),L(x,y,z),u) = a(a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,42361,a(flip),b,43167,a),flip(a)].">
      <j1 rule="hyper" parents="373 42361 43167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43169">
    <literal><![CDATA[
      (x \ L(x,y,z)) * a(a(u,x,x),y,z) = R(x \ L(x,y,z),L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(43168(a,1),41925(a,1,2))].">
      <j1 rule="para" parents="43168 41925"/>
    </justification>
  </clause>

  <clause id="43170">
    <literal><![CDATA[
      R(x \ L(x,y,z),L(x,y,z),u) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,41777,a(flip),b,43169,a),flip(a)].">
      <j1 rule="hyper" parents="64 41777 43169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43171">
    <literal><![CDATA[
      L(x \ L(x,y,z),L(x,y,z),u) = L(x \ L(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,35109,a(flip),b,43170,a)].">
      <j1 rule="hyper" parents="64 35109 43170"/>
    </justification>
  </clause>

  <clause id="43172">
    <literal><![CDATA[
      L(x * a(y,z,a(u,w,v5)),y,a(y,z,a(v5,w,u))) = y * ((a(y,z,a(v5,w,u)) * y) \ x)
    ]]></literal>
    <justification jstring="[para(42501(a,1),41888(a,1,1))].">
      <j1 rule="para" parents="42501 41888"/>
    </justification>
  </clause>

  <clause id="43173">
    <literal><![CDATA[
      a(x,y,z) \ (L(a(x,y,z) \ u,a(x,y,z),x) \ u) = a(a(x,y,z) \ u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(23133(a,1),42106(a,1,2,1,1))].">
      <j1 rule="para" parents="23133 42106"/>
    </justification>
  </clause>

  <clause id="43174">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,z \ y) \ T(x,y)) = z \ ((y / z) \ (x * y))
    ]]></literal>
    <justification jstring="[para(6593(a,1),42116(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6593 42116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43175">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,y * z) \ T(x,y)) = z \ ((y / z) \ (x * y))
    ]]></literal>
    <justification jstring="[para(41977(a,1),43174(a,1,2,1))].">
      <j1 rule="para" parents="41977 43174"/>
    </justification>
  </clause>

  <clause id="43176">
    <literal><![CDATA[
      T(x,y) * (L(x,z,y * z) \ x) = z \ ((y / z) \ (x * y))
    ]]></literal>
    <justification jstring="[para(24684(a,1),43175(a,1,2))].">
      <j1 rule="para" parents="24684 43175"/>
    </justification>
  </clause>

  <clause id="43177">
    <literal><![CDATA[
      T(x * (L(x,y,z * y) \ x),z) = y \ ((z / y) \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,31177,a,b,43176,a)].">
      <j1 rule="hyper" parents="64 31177 43176"/>
    </justification>
  </clause>

  <clause id="43179">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * L(z,z,a(x,y,y))) \ (u * L(z,y,x)) = a(u,L(z,y,x),a(x,y,z))
    ]]></literal>
    <justification jstring="[para(33274(a,1),43161(a,1,1))].">
      <j1 rule="para" parents="33274 43161"/>
    </justification>
  </clause>

  <clause id="43180">
    <literal><![CDATA[
      a(x,y,z) \ (((a(x,y,z) * x) \ (x * u)) \ u) = a(a(x,y,z) \ u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(23793(a,1),43173(a,1,2,1))].">
      <j1 rule="para" parents="23793 43173"/>
    </justification>
  </clause>

  <clause id="43181">
    <literal><![CDATA[
      a(a(x,y,z) \ u,x,a(z,y,x)) = a(x,y,z) \ a(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(43108(a,1),43180(a,1,2)),flip(a)].">
      <j1 rule="para" parents="43108 43180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43182">
    <literal><![CDATA[
      a(a(x,y,z) \ u,x,a(z,y,x)) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,40767,a(flip),b,43181,a),flip(a)].">
      <j1 rule="hyper" parents="373 40767 43181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43183">
    <literal><![CDATA[
      a(x * a(y,z,u),y,a(u,z,y)) = a(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42467,a(flip),b,43182,a)].">
      <j1 rule="hyper" parents="64 42467 43182"/>
    </justification>
  </clause>

  <clause id="43184">
    <literal><![CDATA[
      a(x,a(x,y,z),u * a(x,y,z)) = a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,41451,a,b,43183,a)].">
      <j1 rule="hyper" parents="64 41451 43183"/>
    </justification>
  </clause>

  <clause id="43185">
    <literal><![CDATA[
      a(x,a(y,z,u),a(y,z,u) * y) = a(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42916,a,b,43184,a)].">
      <j1 rule="hyper" parents="64 42916 43184"/>
    </justification>
  </clause>

  <clause id="43186">
    <literal><![CDATA[
      R(x,a(y,z,u),a(y,z,u) * y) = a(y,a(y,z,u),x) * x
    ]]></literal>
    <justification jstring="[para(43185(a,1),42640(a,1,1)),flip(a)].">
      <j1 rule="para" parents="43185 42640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43187">
    <literal><![CDATA[
      R(x,a(y,z,u),a(y,z,u) * y) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,40823,a(flip),b,43186,a),flip(a)].">
      <j1 rule="hyper" parents="373 40823 43186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43188">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u) * y) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,31802,a(flip),b,43187,a)].">
      <j1 rule="hyper" parents="64 31802 43187"/>
    </justification>
  </clause>

  <clause id="43189">
    <literal><![CDATA[
      ((x \ R(x,y,z)) / u) * (a(u \ (x \ R(x,y,z)),u,x) * u) = (R(x,y,z) / (u * x)) * u
    ]]></literal>
    <justification jstring="[para(26785(a,1),41872(a,1,2,1))].">
      <j1 rule="para" parents="26785 41872"/>
    </justification>
  </clause>

  <clause id="43190">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),u,w) = L(a(x,y,z) \ 1,a(x,y,z) \ 1,a(w,u,u))
    ]]></literal>
    <justification jstring="[para(42729(a,1),42250(a,1,1))].">
      <j1 rule="para" parents="42729 42250"/>
    </justification>
  </clause>

  <clause id="43191">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),u,w) = L(a(x,y,z) \ 1,a(x,y,z),a(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,11794,a(flip),b,43190,a),flip(a)].">
      <j1 rule="hyper" parents="373 11794 43190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43192">
    <literal><![CDATA[
      L(L(a(x,y,z) \ 1,u,w),u,w) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,42545,a(flip),b,43191,a),flip(a)].">
      <j1 rule="hyper" parents="373 42545 43191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43194">
    <literal><![CDATA[
      L(R(x,y,z) \ x,x,y) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,42808,a(flip),b,43192,a)].">
      <j1 rule="hyper" parents="64 42808 43192"/>
    </justification>
  </clause>

  <clause id="43195">
    <literal><![CDATA[
      a(x,y,R(y,x,z) \ y) * ((R(y,x,z) \ y) \ y) = (a(y,x,z) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(43194(a,1),42073(a,2,1))].">
      <j1 rule="para" parents="43194 42073"/>
    </justification>
  </clause>

  <clause id="43196">
    <literal><![CDATA[
      a(x,y,L(y,x,z) \ y) * ((R(y,x,z) \ y) \ y) = (a(y,x,z) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(31334(a,1),43195(a,1,1))].">
      <j1 rule="para" parents="31334 43195"/>
    </justification>
  </clause>

  <clause id="43197">
    <literal><![CDATA[
      a(x,y,y \ L(y,x,z)) * ((R(y,x,z) \ y) \ y) = (a(y,x,z) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(38706(a,1),43196(a,1,1))].">
      <j1 rule="para" parents="38706 43196"/>
    </justification>
  </clause>

  <clause id="43198">
    <literal><![CDATA[
      a(x,y,(z \ u) / ((z * w) \ u)) = a(x,y,z \ ((w \ (z \ u)) \ u))
    ]]></literal>
    <justification jstring="[para(75(a,1),42743(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="75 42743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43199">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) \ (z \ w)) = a(x,y,z \ ((u \ (z \ w)) \ w))
    ]]></literal>
    <justification jstring="[hyper(27586,a,43198,a)].">
      <j1 rule="hyper" parents="27586 43198"/>
    </justification>
  </clause>

  <clause id="43200">
    <literal><![CDATA[
      (T(L(x,y,z),x) * L(x \ L(x,y,z),x,L(x,y,z))) \ 1 = a(z,y,x) * (x \ a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,33308,a(flip),b,42980,a),flip(a)].">
      <j1 rule="hyper" parents="373 33308 42980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43201">
    <literal><![CDATA[
      ((x \ R(x,y,z)) / u) * (a(u,u,x) * u) = (R(x,y,z) / (u * x)) * u
    ]]></literal>
    <justification jstring="[para(39922(a,1),43189(a,1,2,1))].">
      <j1 rule="para" parents="39922 43189"/>
    </justification>
  </clause>

  <clause id="43202">
    <literal><![CDATA[
      ((x \ R(x,y,z)) / u) * R(u,u,x) = (R(x,y,z) / (u * x)) * u
    ]]></literal>
    <justification jstring="[para(30053(a,1),43201(a,1,2))].">
      <j1 rule="para" parents="30053 43201"/>
    </justification>
  </clause>

  <clause id="43204">
    <literal><![CDATA[
      a(x,x,y) * (y \ R(y,z,u)) = (R(y,z,u) / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,37548,a(flip),b,43202,a)].">
      <j1 rule="hyper" parents="64 37548 43202"/>
    </justification>
  </clause>

  <clause id="43205">
    <literal><![CDATA[
      (R(x,y,z) / (u * x)) * u = L(x,u,u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,28008,a(flip),b,43204,a),flip(a)].">
      <j1 rule="hyper" parents="64 28008 43204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43206">
    <literal><![CDATA[
      R(x * (y \ R(y,z,u)),x,y) = x * (L(y,x,x) \ R(y,z,u))
    ]]></literal>
    <justification jstring="[para(43205(a,1),2141(a,2,2))].">
      <j1 rule="para" parents="43205 2141"/>
    </justification>
  </clause>

  <clause id="43207">
    <literal><![CDATA[
      (x \ (x * (L(y,x,x) \ R(y,z,u)))) \ ((x \ (x * (y \ R(y,z,u)))) * y) = L(y,x,(x * y) \ ((x \ (x * (y \ R(y,z,u)))) * y))
    ]]></literal>
    <justification jstring="[para(43206(a,1),15008(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="43206 15008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43208">
    <literal><![CDATA[
      (L(x,y,z) * L(x \ L(x,y,z),x,L(x,y,z))) \ 1 = a(z,y,x) * (x \ a(z,y,x))
    ]]></literal>
    <justification jstring="[para(201(a,1),43200(a,1,1,1))].">
      <j1 rule="para" parents="201 43200"/>
    </justification>
  </clause>

  <clause id="43209">
    <literal><![CDATA[
      (L(x,y,z) * (x \ L(x,y,z))) \ 1 = a(z,y,x) * (x \ a(z,y,x))
    ]]></literal>
    <justification jstring="[para(5656(a,1),43208(a,1,1,2))].">
      <j1 rule="para" parents="5656 43208"/>
    </justification>
  </clause>

  <clause id="43210">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,z) \ x) = a(z,y,x) * (x \ a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,34848,a(flip),b,43209,a)].">
      <j1 rule="hyper" parents="64 34848 43209"/>
    </justification>
  </clause>

  <clause id="43213">
    <literal><![CDATA[
      x * (L(x,y,z) \ (L(x,y,z) \ x)) = a(z,y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,43210,a,b,33308,a)].">
      <j1 rule="hyper" parents="145 43210 33308"/>
    </justification>
  </clause>

  <clause id="43214">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (L(x,y,z) \ x) = a(z,y,x) * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,34136,a,b,43213,a)].">
      <j1 rule="hyper" parents="64 34136 43213"/>
    </justification>
  </clause>

  <clause id="43215">
    <literal><![CDATA[
      x * ((((x \ L(x,y,z)) \ 1) \ L(x,y,z)) \ u) = (a(z,y,x) * a(z,y,x)) * u
    ]]></literal>
    <justification jstring="[para(43214(a,1),31469(a,2,1))].">
      <j1 rule="para" parents="43214 31469"/>
    </justification>
  </clause>

  <clause id="43216">
    <literal><![CDATA[
      x * ((((x \ L(x,y,z)) \ 1) \ L(x,y,z)) \ u) = a(z,y,x) * (u * a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,42449,a(flip),b,43215,a),flip(a)].">
      <j1 rule="hyper" parents="373 42449 43215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43217">
    <literal><![CDATA[
      x * (((L(x,y,z) \ x) \ L(x,y,z)) \ u) = a(z,y,x) * (u * a(z,y,x))
    ]]></literal>
    <justification jstring="[para(9374(a,1),43216(a,1,2,1,1))].">
      <j1 rule="para" parents="9374 43216"/>
    </justification>
  </clause>

  <clause id="43218">
    <literal><![CDATA[
      a(x,y,z) * (u * a(x,y,z)) = z * (L(L(z,y,x),y,x) \ u)
    ]]></literal>
    <justification jstring="[para(42140(a,1),43217(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="42140 43217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43222">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) * a(v5,v5,a(v6,L(a(x,y,z),u,w),L(a(x,y,z),u,w))) = L(L(a(x,y,z),v5,v6),u,w) / L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(28787(a,1),41666(a,2,1,1))].">
      <j1 rule="para" parents="28787 41666"/>
    </justification>
  </clause>

  <clause id="43223">
    <literal><![CDATA[
      a(L(L(x * (L(x,y,z) \ x),u,u),y,z),w,v5) = a(L(x,u,L(x,y,z) * u),w,v5)
    ]]></literal>
    <justification jstring="[para(29142(a,1),42120(a,2,1))].">
      <j1 rule="para" parents="29142 42120"/>
    </justification>
  </clause>

  <clause id="43224">
    <literal><![CDATA[
      a(L(x,y,L(x,z,u) * y),w,v5) = a(L(x,y,y),w,v5)
    ]]></literal>
    <justification jstring="[para(42119(a,1),43223(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42119 43223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43226">
    <literal><![CDATA[
      L(L(x,y \ z,L(y,y,z)),y \ z,a(z * y,y,y)) = L(x,L(y \ z,y \ z,y),L(y,y,z))
    ]]></literal>
    <justification jstring="[para(30545(a,1),42290(a,1,3))].">
      <j1 rule="para" parents="30545 42290"/>
    </justification>
  </clause>

  <clause id="43227">
    <literal><![CDATA[
      (x * (y * y)) \ ((x * y) * L(L(y,y,x),y \ x,z)) = a(z,y \ x,L(y,y,x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,645,a(flip),b,42355,a)].">
      <j1 rule="hyper" parents="64 645 42355"/>
    </justification>
  </clause>

  <clause id="43228">
    <literal><![CDATA[
      (x * (y * y)) \ (x * (y * L(y,y \ x,z))) = a(z,y \ x,L(y,y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(513(a,1),43227(a,1,2))].">
      <j1 rule="para" parents="513 43227"/>
    </justification>
  </clause>

  <clause id="43229">
    <literal><![CDATA[
      (x * x) \ (y \ (y * (x * L(x,x \ y,z)))) = a(z,x \ y,L(x,x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(712,a,43228,a)].">
      <j1 rule="hyper" parents="712 43228"/>
    </justification>
  </clause>

  <clause id="43230">
    <literal><![CDATA[
      a(x,y \ z,L(y,y,z)) \ 1 = (y * y) \ (y * L(y,y \ z,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),43229(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 43229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43231">
    <literal><![CDATA[
      a(x,y \ z,L(y,y,z)) \ 1 = (1 / y) * L(y,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,535,a(flip),b,43230,a),flip(a)].">
      <j1 rule="hyper" parents="373 535 43230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43233">
    <literal><![CDATA[
      a(x,y \ z,L(y,y,z)) \ 1 = y \ L(y,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5590,a(flip),b,43231,a),flip(a)].">
      <j1 rule="hyper" parents="373 5590 43231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43234">
    <literal><![CDATA[
      a(x,y \ z,L(y,y,z)) = L(y,y \ z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(40,a,5658,a,b,43233,a),flip(a)].">
      <j1 rule="hyper" parents="40 5658 43233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43235">
    <literal><![CDATA[
      L(L(x,x,y),L(x,x,y),a(z,x \ y,x \ y)) = L(L(x,x,y),x \ y,z) * (L(x,x \ y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,43234,a(flip),b,41642,a),flip(a)].">
      <j1 rule="hyper" parents="145 43234 41642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43236">
    <literal><![CDATA[
      R(x,y,L(z \ 1,u,z) \ (a(w,z,v5) \ 1)) = R(x,y,a(w,z \ 1,v5) \ ((z \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(11980(a,1),42378(a,1,3,2,1))].">
      <j1 rule="para" parents="11980 42378"/>
    </justification>
  </clause>

  <clause id="43237">
    <literal><![CDATA[
      R(x,y,L(z \ 1,u,z) \ a(w,z,v5)) = R(x,y,a(w,z \ 1,v5) \ ((z \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,38874,a(flip),b,43236,a)].">
      <j1 rule="hyper" parents="64 38874 43236"/>
    </justification>
  </clause>

  <clause id="43238">
    <literal><![CDATA[
      R(x,y,a(z,u \ 1,w) \ ((u \ 1) \ 1)) = R(x,y,(u \ 1) \ a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,13904,a(flip),b,43237,a),flip(a)].">
      <j1 rule="hyper" parents="64 13904 43237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43239">
    <literal><![CDATA[
      R(x,y,a(z,u \ 1,w) \ ((u \ 1) \ 1)) = R(x,y,u * a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,35755,a(flip),b,43238,a),flip(a)].">
      <j1 rule="hyper" parents="373 35755 43238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43240">
    <literal><![CDATA[
      R(x,y,a(z,u,w) \ ((u \ 1) \ 1)) = R(x,y,u * a(z,u,w))
    ]]></literal>
    <justification jstring="[para(11980(a,1),43239(a,1,3,1))].">
      <j1 rule="para" parents="11980 43239"/>
    </justification>
  </clause>

  <clause id="43241">
    <literal><![CDATA[
      R(x,y,(z \ a(u,z,w)) \ 1) = R(x,y,z * a(u,z,w))
    ]]></literal>
    <justification jstring="[para(35803(a,1),43240(a,1,3))].">
      <j1 rule="para" parents="35803 43240"/>
    </justification>
  </clause>

  <clause id="43242">
    <literal><![CDATA[
      R(x,y,a(z,u,w) * u) = R(x,y,u * a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42186,a(flip),b,43241,a)].">
      <j1 rule="hyper" parents="64 42186 43241"/>
    </justification>
  </clause>

  <clause id="43243">
    <literal><![CDATA[
      L(L(x,y \ z,L(y,y,z)),y \ z,a(z,y,y)) = L(x,L(y \ z,y \ z,y),L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30336,a(flip),b,43226,a)].">
      <j1 rule="hyper" parents="64 30336 43226"/>
    </justification>
  </clause>

  <clause id="43244">
    <literal><![CDATA[
      L(L(x,y \ z,L(y,y,z)),y,a(y,z,z)) = L(x,L(y \ z,y \ z,y),L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41321,a(flip),b,43243,a)].">
      <j1 rule="hyper" parents="64 41321 43243"/>
    </justification>
  </clause>

  <clause id="43245">
    <literal><![CDATA[
      L(L(x,y \ z,L(y,y,z)),y,a(y,z,z)) = L(x,z \ y,L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,29725,a(flip),b,43244,a),flip(a)].">
      <j1 rule="hyper" parents="373 29725 43244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43246">
    <literal><![CDATA[
      L(L(x,y \ z,L(y,y,z)),y,a(y,z,z)) = L(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,43152,a(flip),b,43245,a),flip(a)].">
      <j1 rule="hyper" parents="373 43152 43245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43247">
    <literal><![CDATA[
      ((x \ a(x,x,y)) * L(y,L(x,x,y),z)) \ (x \ y) = a(z,x \ a(x,x,y),y)
    ]]></literal>
    <justification jstring="[para(31034(a,1),42123(a,1,1,2))].">
      <j1 rule="para" parents="31034 42123"/>
    </justification>
  </clause>

  <clause id="43248">
    <literal><![CDATA[
      (x \ L(y,L(x,x,y),z)) \ (x \ y) = a(z,x \ a(x,x,y),y)
    ]]></literal>
    <justification jstring="[para(39700(a,1),43247(a,1,1))].">
      <j1 rule="para" parents="39700 43247"/>
    </justification>
  </clause>

  <clause id="43249">
    <literal><![CDATA[
      (x \ L(y,L(x,x,y),z)) \ (x \ y) = a(z,x * a(x,x,y),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,35748,a(flip),b,43248,a),flip(a)].">
      <j1 rule="hyper" parents="373 35748 43248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43250">
    <literal><![CDATA[
      (x \ L(y,L(x,x,y),z)) \ (x \ y) = a(z,R(x,x,y),y)
    ]]></literal>
    <justification jstring="[para(30054(a,1),43249(a,2,2))].">
      <j1 rule="para" parents="30054 43249"/>
    </justification>
  </clause>

  <clause id="43251">
    <literal><![CDATA[
      (x \ L(y,L(x,x,y),z)) \ (x \ y) = a(z,L(x,x,y),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,32197,a(flip),b,43250,a),flip(a)].">
      <j1 rule="hyper" parents="373 32197 43250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43252">
    <literal><![CDATA[
      a(x,L(L(y * K(y * z,u),z,u),u,z),w) = a(x,u \ (T(z,y) \ ((T(z,y) * y) * u)),w)
    ]]></literal>
    <justification jstring="[para(23215(a,1),42992(a,1,2))].">
      <j1 rule="para" parents="23215 42992"/>
    </justification>
  </clause>

  <clause id="43253">
    <literal><![CDATA[
      a(x,y \ (T(z,u) \ ((T(z,u) * u) * y)),w) = a(x,L(L(u,z,y),y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32162,a(flip),b,43252,a),flip(a)].">
      <j1 rule="hyper" parents="64 32162 43252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43256">
    <literal><![CDATA[
      a(x,y \ (z \ ((z * u) * y)),w) = a(x,L(L(u,z,y),y,z),w)
    ]]></literal>
    <justification jstring="[para(24773(a,1),43253(a,1,2,2))].">
      <j1 rule="para" parents="24773 43253"/>
    </justification>
  </clause>

  <clause id="43258">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ (L(v5,R(z,u,w) * v6,R(z,u,w)) * v6)) = a(x,y,(R(z,u,w) \ v6) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,27309,a(flip),b,41744,a),flip(a)].">
      <j1 rule="hyper" parents="373 27309 41744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43260">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ (L(v5,R(z,u,w) * v6,L(z,u,w)) * v6)) = a(x,y,(R(z,u,w) \ v6) * v5)
    ]]></literal>
    <justification jstring="[para(29203(a,1),43258(a,1,3,2,1))].">
      <j1 rule="para" parents="29203 43258"/>
    </justification>
  </clause>

  <clause id="43261">
    <literal><![CDATA[
      a(x,y,L(z,u,w) \ (L(v5,L(z,u,w) * v6,L(z,u,w)) * v6)) = a(x,y,(R(z,u,w) \ v6) * v5)
    ]]></literal>
    <justification jstring="[para(36262(a,1),43260(a,1,3,2,1))].">
      <j1 rule="para" parents="36262 43260"/>
    </justification>
  </clause>

  <clause id="43262">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) \ v5) * T(v6,v5)) = a(x,y,(R(z,u,w) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(41722(a,1),43261(a,1,3))].">
      <j1 rule="para" parents="41722 43261"/>
    </justification>
  </clause>

  <clause id="43263">
    <literal><![CDATA[
      a(x,y,(R(z,u,w) \ v5) * v6) = a(x,y,(L(z,u,w) \ v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,27309,a(flip),b,43262,a),flip(a)].">
      <j1 rule="hyper" parents="64 27309 43262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43265">
    <literal><![CDATA[
      (x * a(y,z,z \ 1)) * a(a(y,z,z),x,x * ((y * z) \ y)) = (((y * z) \ y) / x) \ (z \ 1)
    ]]></literal>
    <justification jstring="[para(41863(a,1),41966(a,1,2))].">
      <j1 rule="para" parents="41863 41966"/>
    </justification>
  </clause>

  <clause id="43266">
    <literal><![CDATA[
      (x * a(y,z,z \ 1)) * a(a(y,z,z),x,x * (y \ (z \ y))) = (((y * z) \ y) / x) \ (z \ 1)
    ]]></literal>
    <justification jstring="[para(27714(a,1),43265(a,1,2))].">
      <j1 rule="para" parents="27714 43265"/>
    </justification>
  </clause>

  <clause id="43267">
    <literal><![CDATA[
      L(x \ ((x / y) * z),(y * x) * y,L(x,y,y)) = (1 / ((y * x) * y)) * ((y * x) * (y * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,24000,a(flip),b,42009,a)].">
      <j1 rule="hyper" parents="64 24000 42009"/>
    </justification>
  </clause>

  <clause id="43268">
    <literal><![CDATA[
      L(x \ ((x / y) * z),L(x,y,y),L(x,y,y)) = (1 / ((y * x) * y)) * ((y * x) * (y * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29508,a(flip),b,43267,a)].">
      <j1 rule="hyper" parents="64 29508 43267"/>
    </justification>
  </clause>

  <clause id="43269">
    <literal><![CDATA[
      L(x \ ((x / y) * z),x,x) = (1 / ((y * x) * y)) * ((y * x) * (y * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,35161,a(flip),b,43268,a)].">
      <j1 rule="hyper" parents="64 35161 43268"/>
    </justification>
  </clause>

  <clause id="43270">
    <literal><![CDATA[
      (1 / ((x * y) * x)) * ((x * y) * (x * (x \ z))) = (1 / y) * ((y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(742,a,43269,a),flip(a)].">
      <j1 rule="hyper" parents="742 43269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43272">
    <literal><![CDATA[
      (1 / ((x * y) * x)) * ((x * y) * (x * (x \ z))) = y * (((y \ 1) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1668,a(flip),b,43270,a),flip(a)].">
      <j1 rule="hyper" parents="373 1668 43270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43273">
    <literal><![CDATA[
      (1 / ((x * y) * x)) * ((x * y) * z) = y * (((y \ 1) / x) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),43272(a,1,2,2))].">
      <j1 rule="para" parents="10 43272"/>
    </justification>
  </clause>

  <clause id="43275">
    <literal><![CDATA[
      L(x,y * z,1 / ((y * z) * y)) = ((z * ((z \ 1) / y)) / x) \ ((z * (((z \ 1) / y) * x)) / x)
    ]]></literal>
    <justification jstring="[para(43273(a,1),31530(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="43273 31530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43276">
    <literal><![CDATA[
      L(x,y * z,1 / ((y * z) * y)) = L(x,(z \ 1) / y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,3209,a,b,43275,a),flip(a)].">
      <j1 rule="hyper" parents="373 3209 43275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43277">
    <literal><![CDATA[
      L(x,y * z,1 / ((y * z) * y)) = L(x,y \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29437,a(flip),b,43276,a),flip(a)].">
      <j1 rule="hyper" parents="373 29437 43276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43278">
    <literal><![CDATA[
      L(x,y * z,1 / ((y * z) * y)) = L(x,y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29701,a(flip),b,43277,a),flip(a)].">
      <j1 rule="hyper" parents="373 29701 43277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43279">
    <literal><![CDATA[
      L(x,y * z,(y * z) * y) = L(x,y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(2273,a,43278,a)].">
      <j1 rule="hyper" parents="2273 43278"/>
    </justification>
  </clause>

  <clause id="43280">
    <literal><![CDATA[
      L(x,y * z,L(z,y,y)) = L(x,y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,24000,a(flip),b,43279,a)].">
      <j1 rule="hyper" parents="64 24000 43279"/>
    </justification>
  </clause>

  <clause id="43281">
    <literal><![CDATA[
      (x / (x * y)) * ((x * y) * z) = x * L(z,x \ y,y)
    ]]></literal>
    <justification jstring="[para(43279(a,1),41964(a,1,2)),flip(a)].">
      <j1 rule="para" parents="43279 41964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43282">
    <literal><![CDATA[
      L(x,y * z,L(y,z,z)) = L(x,z \ y,y)
    ]]></literal>
    <justification jstring="[hyper(29572,a,43280,a)].">
      <j1 rule="hyper" parents="29572 43280"/>
    </justification>
  </clause>

  <clause id="43283">
    <literal><![CDATA[
      L(x,y * z,L(z,z,y)) = L(x,y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42156,a,b,43280,a)].">
      <j1 rule="hyper" parents="64 42156 43280"/>
    </justification>
  </clause>

  <clause id="43284">
    <literal><![CDATA[
      L(x,y * (y * (z * y)),L(y,y * (z * y),y * (z * y))) = L(x,z \ (z / (z * y)),y)
    ]]></literal>
    <justification jstring="[para(31188(a,1),43282(a,2,2))].">
      <j1 rule="para" parents="31188 43282"/>
    </justification>
  </clause>

  <clause id="43285">
    <literal><![CDATA[
      L(x,R(y \ 1,y,z) * (y \ z),L(R(y \ 1,y,z),y \ z,y \ z)) = L(x,L(z \ 1,z,y),R(y \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(31196(a,1),43282(a,2,2))].">
      <j1 rule="para" parents="31196 43282"/>
    </justification>
  </clause>

  <clause id="43286">
    <literal><![CDATA[
      L(x,y * z,L(y,y,z)) = L(x,z \ y,y)
    ]]></literal>
    <justification jstring="[hyper(29572,a,43283,a)].">
      <j1 rule="hyper" parents="29572 43283"/>
    </justification>
  </clause>

  <clause id="43287">
    <literal><![CDATA[
      L(x,L(y \ z,z,z),z) = L(x,y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40974,a,b,43286,a)].">
      <j1 rule="hyper" parents="64 40974 43286"/>
    </justification>
  </clause>

  <clause id="43288">
    <literal><![CDATA[
      L(x,y \ (y / (1 / (y * z))),z) = L(x,y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41070,a(flip),b,43287,a)].">
      <j1 rule="hyper" parents="64 41070 43287"/>
    </justification>
  </clause>

  <clause id="43289">
    <literal><![CDATA[
      L(x,y \ (((y * z) \ 1) \ y),z) = L(x,y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29828,a(flip),b,43288,a)].">
      <j1 rule="hyper" parents="64 29828 43288"/>
    </justification>
  </clause>

  <clause id="43290">
    <literal><![CDATA[
      L(x,y \ ((y * z) \ y),z) = L(x,y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30873,a(flip),b,43289,a)].">
      <j1 rule="hyper" parents="64 30873 43289"/>
    </justification>
  </clause>

  <clause id="43291">
    <literal><![CDATA[
      L(x,y \ (y \ (z \ y)),z) = L(x,y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30868,a(flip),b,43290,a)].">
      <j1 rule="hyper" parents="64 30868 43290"/>
    </justification>
  </clause>

  <clause id="43292">
    <literal><![CDATA[
      x * L(T(x * y,z) \ u,x \ y,y) = (x / (x * y)) * (K(z,x * y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,6154,a(flip),b,43281,a),flip(a)].">
      <j1 rule="hyper" parents="64 6154 43281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43293">
    <literal><![CDATA[
      x * L(T(x * y,z) \ u,x \ y,y) = (x / T(x * y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,24465,a(flip),b,43292,a),flip(a)].">
      <j1 rule="hyper" parents="373 24465 43292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43294">
    <literal><![CDATA[
      L(x,y * (y * (z * y)),L(y,y * (z * y),L(z,y,y))) = L(x,z \ (z / (z * y)),y)
    ]]></literal>
    <justification jstring="[para(24835(a,1),43284(a,1,3))].">
      <j1 rule="para" parents="24835 43284"/>
    </justification>
  </clause>

  <clause id="43295">
    <literal><![CDATA[
      L(x,y * (y * (z * y)),L(y,L(z,y,y),L(z,y,y))) = L(x,z \ (z / (z * y)),y)
    ]]></literal>
    <justification jstring="[para(29648(a,1),43294(a,1,3))].">
      <j1 rule="para" parents="29648 43294"/>
    </justification>
  </clause>

  <clause id="43296">
    <literal><![CDATA[
      L(x,y * (y * (z * y)),L(y,z,z)) = L(x,z \ (z / (z * y)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,34541,a(flip),b,43295,a)].">
      <j1 rule="hyper" parents="64 34541 43295"/>
    </justification>
  </clause>

  <clause id="43297">
    <literal><![CDATA[
      L(x,L(y * z,z,z),L(z,y,y)) = L(x,y \ (y / (y * z)),z)
    ]]></literal>
    <justification jstring="[hyper(11888,a,43296,a)].">
      <j1 rule="hyper" parents="11888 43296"/>
    </justification>
  </clause>

  <clause id="43299">
    <literal><![CDATA[
      L(x,y \ (y / (y * z)),z) = L(x,z \ y,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,31760,a(flip),b,43297,a),flip(a)].">
      <j1 rule="hyper" parents="64 31760 43297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43300">
    <literal><![CDATA[
      L(x,y \ (y \ (z \ y)),z) = L(x,z \ y,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30866,a(flip),b,43299,a)].">
      <j1 rule="hyper" parents="64 30866 43299"/>
    </justification>
  </clause>

  <clause id="43301">
    <literal><![CDATA[
      L(x,y \ z,L(y,z,z)) = L(x,z \ y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,43291,a(flip),b,43300,a),flip(a)].">
      <j1 rule="hyper" parents="64 43291 43300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43302">
    <literal><![CDATA[
      L(x,y \ z,z \ (y \ z)) = L(x,z \ y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,43056,a,b,43301,a)].">
      <j1 rule="hyper" parents="64 43056 43301"/>
    </justification>
  </clause>

  <clause id="43303">
    <literal><![CDATA[
      L(x,y \ z,L(y,y,z)) = L(x,z \ y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35048,a,b,43302,a)].">
      <j1 rule="hyper" parents="64 35048 43302"/>
    </justification>
  </clause>

  <clause id="43304">
    <literal><![CDATA[
      L(L(x,y \ z,z),z,a(z,y,y)) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[para(43303(a,1),43246(a,1,1))].">
      <j1 rule="para" parents="43303 43246"/>
    </justification>
  </clause>

  <clause id="43305">
    <literal><![CDATA[
      L(L(x,y \ z,z),y,a(y,z,z)) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40927,a,b,43304,a)].">
      <j1 rule="hyper" parents="64 40927 43304"/>
    </justification>
  </clause>

  <clause id="43306">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w),(u * z) * w,(u * z) * w)) = L(x,y,(z * (u * w)) * ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,43093,a(flip),b,42030,a),flip(a)].">
      <j1 rule="hyper" parents="373 43093 42030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43307">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w),z * (u \ w),z * (u \ w))) = L(x,y,(z * (u * w)) * ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(35254(a,1),43306(a,1,3))].">
      <j1 rule="para" parents="35254 43306"/>
    </justification>
  </clause>

  <clause id="43308">
    <literal><![CDATA[
      ((x * (1 / y)) * L(L(y,y,x),x * y,z)) \ x = a(z,x * y,(x * y) \ (x * (y * y)))
    ]]></literal>
    <justification jstring="[para(602(a,1),42122(a,1,1,2))].">
      <j1 rule="para" parents="602 42122"/>
    </justification>
  </clause>

  <clause id="43309">
    <literal><![CDATA[
      a(x,y * z,(y * z) \ (y * (z * z))) = (y * ((1 / z) * L(z,y * z,x))) \ y
    ]]></literal>
    <justification jstring="[para(11797(a,1),43308(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11797 43308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43310">
    <literal><![CDATA[
      a(x,y * z,(y * z) \ (y * (z * z))) = (y * (z \ L(z,y * z,x))) \ y
    ]]></literal>
    <justification jstring="[para(5590(a,1),43309(a,2,1,2))].">
      <j1 rule="para" parents="5590 43309"/>
    </justification>
  </clause>

  <clause id="43311">
    <literal><![CDATA[
      a(x,y * z,(y * z) \ (y * (z * z))) = L(z,y * z,x) \ z
    ]]></literal>
    <justification jstring="[hyper(373,a,42598,a(flip),b,43310,a),flip(a)].">
      <j1 rule="hyper" parents="373 42598 43310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43313">
    <literal><![CDATA[
      a(x,y * z,L(z,z,y)) = L(z,y * z,x) \ z
    ]]></literal>
    <justification jstring="[para(18(a,2),43311(a,1,3))].">
      <j1 rule="para" parents="18 43311"/>
    </justification>
  </clause>

  <clause id="43314">
    <literal><![CDATA[
      a(x,y,L(z,z,z \ y)) = L(z,(z \ y) * z,x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,31889,a(flip),b,43313,a)].">
      <j1 rule="hyper" parents="64 31889 43313"/>
    </justification>
  </clause>

  <clause id="43315">
    <literal><![CDATA[
      a(x,y,L(z,z,y)) = L(z,(z \ y) * z,x) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,27600,a(flip),b,43314,a)].">
      <j1 rule="hyper" parents="64 27600 43314"/>
    </justification>
  </clause>

  <clause id="43316">
    <literal><![CDATA[
      a(x,y,L(z,z,y)) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[para(29441(a,1),43315(a,2,1))].">
      <j1 rule="para" parents="29441 43315"/>
    </justification>
  </clause>

  <clause id="43317">
    <literal><![CDATA[
      L(x \ y,x,z) \ (x \ y) = a(z,x,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,38953,a(flip),b,43316,a),flip(a)].">
      <j1 rule="hyper" parents="64 38953 43316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43318">
    <literal><![CDATA[
      L(x \ y,y,z) \ (x \ y) = a(z,y,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,38933,a(flip),b,43316,a),flip(a)].">
      <j1 rule="hyper" parents="64 38933 43316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43320">
    <literal><![CDATA[
      L(x / y,y,z) \ (x / y) = a(z,y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,26945,a,b,43317,a)].">
      <j1 rule="hyper" parents="64 26945 43317"/>
    </justification>
  </clause>

  <clause id="43321">
    <literal><![CDATA[
      L(a(x,y,y \ z),z,y) = a(x,y,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,43071,a(flip),b,43317,a)].">
      <j1 rule="hyper" parents="64 43071 43317"/>
    </justification>
  </clause>

  <clause id="43322">
    <literal><![CDATA[
      L(a(x,y \ 1,(y \ 1) \ z),z,y \ 1) = a(x,y \ 1,L(z * y,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,38123,a,b,43321,a),flip(a)].">
      <j1 rule="hyper" parents="373 38123 43321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43323">
    <literal><![CDATA[
      L(a(x,y,(y \ 1) \ z),z,y \ 1) = a(x,y \ 1,L(z * y,z,y))
    ]]></literal>
    <justification jstring="[para(11980(a,1),43322(a,1,1))].">
      <j1 rule="para" parents="11980 43322"/>
    </justification>
  </clause>

  <clause id="43324">
    <literal><![CDATA[
      a(x,y \ 1,L(z * y,z,y)) = L(a(x,y,y * z),z,y \ 1)
    ]]></literal>
    <justification jstring="[para(42880(a,1),43323(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42880 43323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43325">
    <literal><![CDATA[
      a(x,y \ 1,L(z * y,z,y)) = L(a(x,y,y * z),z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,1631,a(flip),b,43324,a),flip(a)].">
      <j1 rule="hyper" parents="373 1631 43324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43326">
    <literal><![CDATA[
      a(x,y,L(z * y,z,y)) = L(a(x,y,y * z),z,y)
    ]]></literal>
    <justification jstring="[hyper(32046,a,43325,a)].">
      <j1 rule="hyper" parents="32046 43325"/>
    </justification>
  </clause>

  <clause id="43327">
    <literal><![CDATA[
      L((x \ 1) \ y,x,z) \ ((x \ 1) \ y) = a(z,x,L(y * x,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,43113,a,b,43326,a)].">
      <j1 rule="hyper" parents="373 43113 43326"/>
    </justification>
  </clause>

  <clause id="43328">
    <literal><![CDATA[
      ((x \ 1) / (x \ a(x,y,z))) * ((x \ a(x,y,z)) * u) = (x \ 1) * L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(42789(a,1),42291(a,2,2))].">
      <j1 rule="para" parents="42789 42291"/>
    </justification>
  </clause>

  <clause id="43329">
    <literal><![CDATA[
      L((x \ a(x,y,z)) \ u,x,a(x,y,z)) = (x \ 1) \ (((x \ 1) / (x \ a(x,y,z))) * u)
    ]]></literal>
    <justification jstring="[hyper(759,a,43328,a),flip(a)].">
      <j1 rule="hyper" parents="759 43328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43330">
    <literal><![CDATA[
      L((x \ a(x,y,z)) \ u,x,a(x,y,z)) = (x \ 1) \ (L(a(x,y,z) \ 1,x,x) * u)
    ]]></literal>
    <justification jstring="[para(42699(a,1),43329(a,2,2,1))].">
      <j1 rule="para" parents="42699 43329"/>
    </justification>
  </clause>

  <clause id="43331">
    <literal><![CDATA[
      L((x \ a(x,y,z)) \ u,x,a(x,y,z)) = (x \ 1) \ ((a(x,y,z) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(30826(a,1),43330(a,2,2,1))].">
      <j1 rule="para" parents="30826 43330"/>
    </justification>
  </clause>

  <clause id="43333">
    <literal><![CDATA[
      L((x \ a(x,y,z)) \ u,x,a(x,y,z)) = (x \ 1) \ (a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(42433(a,1),43331(a,2,2))].">
      <j1 rule="para" parents="42433 43331"/>
    </justification>
  </clause>

  <clause id="43334">
    <literal><![CDATA[
      L((a(x,y,z) \ (y \ 1)) \ (a(x,y \ 1,z) \ u),y,y) = L(y * u,y \ 1,a(x,y \ 1,z))
    ]]></literal>
    <justification jstring="[para(11980(a,1),42756(a,1,1,1,1))].">
      <j1 rule="para" parents="11980 42756"/>
    </justification>
  </clause>

  <clause id="43335">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ (a(y,x \ 1,z) \ u),x,x) = L(x * u,x \ 1,a(y,x \ 1,z))
    ]]></literal>
    <justification jstring="[para(42376(a,1),43334(a,1,1,1))].">
      <j1 rule="para" parents="42376 43334"/>
    </justification>
  </clause>

  <clause id="43336">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ (a(y,x,z) \ u),x,x) = L(x * u,x \ 1,a(y,x \ 1,z))
    ]]></literal>
    <justification jstring="[para(11980(a,1),43335(a,1,1,2,1))].">
      <j1 rule="para" parents="11980 43335"/>
    </justification>
  </clause>

  <clause id="43337">
    <literal><![CDATA[
      L(L(x,x,y),L(x,x,y),a(z,x \ y,x \ y)) = a(y,x,L(x,x \ y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,42104,a(flip),b,43235,a),flip(a)].">
      <j1 rule="hyper" parents="373 42104 43235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43338">
    <literal><![CDATA[
      L(x,x,1) \ R(x,L(y,z,u) \ y,w) = a(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(42592(a,1),41636(a,1,1,3))].">
      <j1 rule="para" parents="42592 41636"/>
    </justification>
  </clause>

  <clause id="43339">
    <literal><![CDATA[
      x \ R(x,L(y,z,u) \ y,w) = a(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(621(a,1),43338(a,1,1))].">
      <j1 rule="para" parents="621 43338"/>
    </justification>
  </clause>

  <clause id="43341">
    <literal><![CDATA[
      x \ L(x,y * L(y,z,u),w) = a(x,y * L(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(35116(a,1),43339(a,1,2))].">
      <j1 rule="para" parents="35116 43339"/>
    </justification>
  </clause>

  <clause id="43342">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z * L(z,u,w),v5) = a(x,z * L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,26779,a(flip),b,43341,a),flip(a)].">
      <j1 rule="hyper" parents="373 26779 43341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43344">
    <literal><![CDATA[
      a(x,y * L(y,z,u),y * L(y,z,u)) = T(x,w) \ L(T(x,w),a(y,z,u),a(y,z,u))
    ]]></literal>
    <justification jstring="[para(40797(a,1),43342(a,1,2)),flip(a)].">
      <j1 rule="para" parents="40797 43342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43345">
    <literal><![CDATA[
      a(T(x,y),a(z,u,w),a(z,u,w)) = a(x,z * L(z,u,w),z * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,42625,a(flip),b,43344,a)].">
      <j1 rule="hyper" parents="373 42625 43344"/>
    </justification>
  </clause>

  <clause id="43346">
    <literal><![CDATA[
      a(x,y * L(y,z,u),y * L(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,42485,a(flip),b,43345,a),flip(a)].">
      <j1 rule="hyper" parents="64 42485 43345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43348">
    <literal><![CDATA[
      L(x * L(x,y,z),x * L(x,y,z),u) = x * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,43346,a)].">
      <j1 rule="hyper" parents="53 43346"/>
    </justification>
  </clause>

  <clause id="43349">
    <literal><![CDATA[
      ((x * y) \ (x * (L(y,z,u) \ y))) \ (L(y,z,u) \ 1) = L(a(x,y,L(y \ 1,z,u)),L(y,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(39638(a,2),42057(a,2,1))].">
      <j1 rule="para" parents="39638 42057"/>
    </justification>
  </clause>

  <clause id="43350">
    <literal><![CDATA[
      a(x \ (y \ ((y * z) * x)),z \ 1,(z \ 1) \ x) = x / ((z \ 1) * (y \ (a(y,z,x) \ ((y * z) * x))))
    ]]></literal>
    <justification jstring="[para(30271(a,1),42181(a,2,2,2))].">
      <j1 rule="para" parents="30271 42181"/>
    </justification>
  </clause>

  <clause id="43351">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ u,x,x) = 1 \ ((x * a(y,x,z)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,40594,a(flip),b,42377,a)].">
      <j1 rule="hyper" parents="64 40594 42377"/>
    </justification>
  </clause>

  <clause id="43352">
    <literal><![CDATA[
      L((x \ (a(y,x,z) \ 1)) \ u,x,x) = (x * a(y,x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,66,a(flip),b,43351,a),flip(a)].">
      <j1 rule="hyper" parents="373 66 43351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43354">
    <literal><![CDATA[
      x * ((x \ 1) * ((x \ (a(y,x,z) \ 1)) \ u)) = (x * a(y,x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(1173,a,43352,a)].">
      <j1 rule="hyper" parents="1173 43352"/>
    </justification>
  </clause>

  <clause id="43355">
    <literal><![CDATA[
      L(x * y,x \ 1,a(z,x \ 1,u)) = (x * a(z,x,u)) * (a(z,x,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,43336,a(flip),b,43352,a)].">
      <j1 rule="hyper" parents="64 43336 43352"/>
    </justification>
  </clause>

  <clause id="43356">
    <literal><![CDATA[
      (x * a(y,x,z)) * ((x \ (a(y,x,z) \ 1)) * u) = L(u,x,x)
    ]]></literal>
    <justification jstring="[para(9(a,1),43352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 43352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43357">
    <literal><![CDATA[
      (x \ (a(y,x,z) \ 1)) * (u * a(x,x,u)) = (x * a(y,x,z)) \ u
    ]]></literal>
    <justification jstring="[hyper(139,a,30229,a(flip),b,43356,a),flip(a)].">
      <j1 rule="hyper" parents="139 30229 43356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43358">
    <literal><![CDATA[
      (x * a(y,x,z)) \ z = x \ L(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,43136,a(flip),b,43357,a),flip(a)].">
      <j1 rule="hyper" parents="64 43136 43357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43359">
    <literal><![CDATA[
      x * (x * ((a(y,x,z) \ x) \ u)) = (x * a(y,x,z)) * u
    ]]></literal>
    <justification jstring="[para(42379(a,1),43354(a,1,2))].">
      <j1 rule="para" parents="42379 43354"/>
    </justification>
  </clause>

  <clause id="43360">
    <literal><![CDATA[
      a(x,y,z) * (((a(u,a(x,y,z),w) \ a(x,y,z)) \ v5) * a(x,y,z)) = (a(x,y,z) * a(u,a(x,y,z),w)) * v5
    ]]></literal>
    <justification jstring="[hyper(23185,a,43359,a)].">
      <j1 rule="hyper" parents="23185 43359"/>
    </justification>
  </clause>

  <clause id="43361">
    <literal><![CDATA[
      x \ ((x * a(y,x,z)) * u) = x * ((a(y,x,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[hyper(149,a,43359,a)].">
      <j1 rule="hyper" parents="149 43359"/>
    </justification>
  </clause>

  <clause id="43362">
    <literal><![CDATA[
      (x * a(y,x,z)) * (a(y,x,z) \ u) = L(x * u,x \ 1,a(y,x,z))
    ]]></literal>
    <justification jstring="[para(11980(a,1),43355(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11980 43355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43363">
    <literal><![CDATA[
      (x * a(y,x,z)) * (a(y,x,z) \ u) = L(x * u,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,11794,a(flip),b,43362,a),flip(a)].">
      <j1 rule="hyper" parents="373 11794 43362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43364">
    <literal><![CDATA[
      (a(x,y,z) * y) * (a(x,y,z) \ u) = L(y * u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(23780,a,43363,a)].">
      <j1 rule="hyper" parents="23780 43363"/>
    </justification>
  </clause>

  <clause id="43365">
    <literal><![CDATA[
      (x \ L(x * y,x,a(z,x,u))) / (x \ (a(z,x,u) * (a(z,x,u) \ y))) = R(x,a(z,x,u),a(z,x,u) \ y)
    ]]></literal>
    <justification jstring="[para(43363(a,1),1939(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="43363 1939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43366">
    <literal><![CDATA[
      ((x \ y) * x) \ ((a(z,(x \ y) * x,u) * ((x \ y) * x)) * (a(z,(x \ y) * x,u) \ w)) = y \ L(y * w,(x \ y) * x,a(z,(x \ y) * x,u))
    ]]></literal>
    <justification jstring="[para(43364(a,2),27076(a,1,2))].">
      <j1 rule="para" parents="43364 27076"/>
    </justification>
  </clause>

  <clause id="43367">
    <literal><![CDATA[
      a((x \ 1) \ 1,a(y,x,z),a(y,x,z) \ u) = (x * u) \ L(x * u,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[para(43364(a,1),38519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="43364 38519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43368">
    <literal><![CDATA[
      x \ (a(y,z,u) * (x * ((a(y,z,u) \ w) * a(x,w,a(y,z,u))))) = L(L(w,a(y,z,u),x),a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(33202(a,1),43082(a,1,2,2,2))].">
      <j1 rule="para" parents="33202 43082"/>
    </justification>
  </clause>

  <clause id="43369">
    <literal><![CDATA[
      ((x * y) \ (x * (L(y,z,u) \ y))) \ (L(y,z,u) \ 1) = L(a(x,y,L(y \ 1,z,u)),L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,11794,a(flip),b,43349,a),flip(a)].">
      <j1 rule="hyper" parents="373 11794 43349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43370">
    <literal><![CDATA[
      ((x * y) \ (x * (L(y,z,u) \ y))) \ (L(y,z,u) \ 1) = L(a(x,y,L(y \ 1,z,u)),y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,2482,a(flip),b,43369,a),flip(a)].">
      <j1 rule="hyper" parents="373 2482 43369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43371">
    <literal><![CDATA[
      ((x * y) \ (x * (L(y,z,u) \ y))) \ (L(y,z,u) \ 1) = a(x,y,L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,39266,a(flip),b,43370,a),flip(a)].">
      <j1 rule="hyper" parents="373 39266 43370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43373">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,u) \ (L(x,y,z) \ 1) = a(u,x,L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(1859(a,1),43371(a,1,1))].">
      <j1 rule="para" parents="1859 43371"/>
    </justification>
  </clause>

  <clause id="43374">
    <literal><![CDATA[
      L(x * L(x \ 1,x,y),z,u) \ 1 = a(y,x,L(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,9394,a(flip),b,43373,a)].">
      <j1 rule="hyper" parents="64 9394 43373"/>
    </justification>
  </clause>

  <clause id="43375">
    <literal><![CDATA[
      1 / L(L(x * ((y * x) \ y),z,u),w,x) = a(y,x,L(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,40396,a,b,43374,a)].">
      <j1 rule="hyper" parents="64 40396 43374"/>
    </justification>
  </clause>

  <clause id="43376">
    <literal><![CDATA[
      1 / L(x * L(x \ 1,x,y),z,u) = a(y,x,L(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(31328(a,1),43375(a,1,2))].">
      <j1 rule="para" parents="31328 43375"/>
    </justification>
  </clause>

  <clause id="43377">
    <literal><![CDATA[
      a(L(x,y,z),u,u \ 1) = a(x,u,L(u \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41086,a(flip),b,43376,a)].">
      <j1 rule="hyper" parents="64 41086 43376"/>
    </justification>
  </clause>

  <clause id="43379">
    <literal><![CDATA[
      a(x,y,L(y \ 1,z,u)) = L(a(x,y,y \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,4248,a(flip),b,43377,a),flip(a)].">
      <j1 rule="hyper" parents="64 4248 43377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43380">
    <literal><![CDATA[
      a(x,y,y \ 1) * a(a(y,y,x),z,u) = a(x,y,L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,42694,a,b,43379,a)].">
      <j1 rule="hyper" parents="373 42694 43379"/>
    </justification>
  </clause>

  <clause id="43381">
    <literal><![CDATA[
      a(x \ (y \ ((y * z) * x)),z \ 1,(z \ 1) \ x) = x / ((z \ 1) * (y \ (y * (z * x))))
    ]]></literal>
    <justification jstring="[para(15467(a,1),43350(a,2,2,2,2))].">
      <j1 rule="para" parents="15467 43350"/>
    </justification>
  </clause>

  <clause id="43382">
    <literal><![CDATA[
      a(x \ (y \ ((y * z) * x)),z \ 1,(z \ 1) \ x) = x / ((z \ 1) * (z * x))
    ]]></literal>
    <justification jstring="[para(9(a,1),43381(a,2,2,2))].">
      <j1 rule="para" parents="9 43381"/>
    </justification>
  </clause>

  <clause id="43383">
    <literal><![CDATA[
      a(x \ (y \ ((y * z) * x)),z \ 1,(z \ 1) \ x) = z * (x / (z * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,30323,a(flip),b,43382,a),flip(a)].">
      <j1 rule="hyper" parents="373 30323 43382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43385">
    <literal><![CDATA[
      a(x \ (y \ ((y * z) * x)),z,(z \ 1) \ x) = z * (x / (z * x))
    ]]></literal>
    <justification jstring="[hyper(32046,a,43383,a)].">
      <j1 rule="hyper" parents="32046 43383"/>
    </justification>
  </clause>

  <clause id="43386">
    <literal><![CDATA[
      a(x \ (y \ ((y * z) * x)),z,z * x) = z * (x / (z * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,42880,a(flip),b,43385,a)].">
      <j1 rule="hyper" parents="64 42880 43385"/>
    </justification>
  </clause>

  <clause id="43387">
    <literal><![CDATA[
      a(L(L(x,y,z),z,y),x,x * z) = x * (z / (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,35835,a(flip),b,43386,a)].">
      <j1 rule="hyper" parents="64 35835 43386"/>
    </justification>
  </clause>

  <clause id="43388">
    <literal><![CDATA[
      a(x,x,L(L(x * y,z,y),y,z)) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42229,a(flip),b,43387,a)].">
      <j1 rule="hyper" parents="64 42229 43387"/>
    </justification>
  </clause>

  <clause id="43389">
    <literal><![CDATA[
      x \ (a(y,z,u) * (a(y,z,u) \ (x * w))) = L(L(w,a(y,z,u),x),a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(42952(a,1),43368(a,1,2,2))].">
      <j1 rule="para" parents="42952 43368"/>
    </justification>
  </clause>

  <clause id="43390">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),a(y,z,u),w) = x
    ]]></literal>
    <justification jstring="[hyper(398,a,43389,a),flip(a)].">
      <j1 rule="hyper" parents="398 43389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43393">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),a(u,z,y),w) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,41405,a,b,43390,a)].">
      <j1 rule="hyper" parents="64 41405 43390"/>
    </justification>
  </clause>

  <clause id="43395">
    <literal><![CDATA[
      L((a(x,y,z) \ u) \ w,a(x,y,z),u) = a(x,y,z) * (u \ w)
    ]]></literal>
    <justification jstring="[hyper(42,a,42822,a,b,43390,a),flip(a)].">
      <j1 rule="hyper" parents="42 42822 43390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43396">
    <literal><![CDATA[
      x * a(y,a(z,u,w),x) = L(x,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(42,a,42642,a,b,43390,a)].">
      <j1 rule="hyper" parents="42 42642 43390"/>
    </justification>
  </clause>

  <clause id="43397">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),a(z,u,w),y) = x * a(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(42,a,34184,a,b,43390,a),flip(a)].">
      <j1 rule="hyper" parents="42 34184 43390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43398">
    <literal><![CDATA[
      a(x,y,z) \ (u \ ((u * a(x,y,z)) * w)) = L(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(42,a,596,a,b,43390,a)].">
      <j1 rule="hyper" parents="42 596 43390"/>
    </justification>
  </clause>

  <clause id="43399">
    <literal><![CDATA[
      x * (a(y,z,u) \ L(w,a(y,z,u),x)) = (a(y,z,u) \ x) * w
    ]]></literal>
    <justification jstring="[hyper(145,a,43390,a(flip),b,42821,a),flip(a)].">
      <j1 rule="hyper" parents="145 43390 42821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43400">
    <literal><![CDATA[
      L(x,a(y,z,u),w) \ (v5 * x) = x \ (v5 * L(x,a(y,z,u),w))
    ]]></literal>
    <justification jstring="[para(43390(a,1),43041(a,1,1)),flip(a)].">
      <j1 rule="para" parents="43390 43041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43401">
    <literal><![CDATA[
      x * a(y,a(z,u,w),x) = L(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(42,a,42642,a,b,43393,a)].">
      <j1 rule="hyper" parents="42 42642 43393"/>
    </justification>
  </clause>

  <clause id="43402">
    <literal><![CDATA[
      a(x,y,z) \ (u \ ((u * a(x,y,z)) * w)) = L(w,a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(42,a,596,a,b,43393,a)].">
      <j1 rule="hyper" parents="42 596 43393"/>
    </justification>
  </clause>

  <clause id="43403">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * w = L(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(23777,a,43396,a)].">
      <j1 rule="hyper" parents="23777 43396"/>
    </justification>
  </clause>

  <clause id="43404">
    <literal><![CDATA[
      x * a(a(y,y,z) * u,a(w,v5,v6),x) = L(x,a(v6,v5,w),a(z,y,y) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,30833,a,b,43396,a),flip(a)].">
      <j1 rule="hyper" parents="373 30833 43396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43405">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(35,a,42627,a,b,43396,a)].">
      <j1 rule="hyper" parents="35 42627 43396"/>
    </justification>
  </clause>

  <clause id="43407">
    <literal><![CDATA[
      a(x * y,a(z,u,w),v5) = a(v5,a(w,u,z),y * x)
    ]]></literal>
    <justification jstring="[hyper(27453,a,43405,a),flip(a)].">
      <j1 rule="hyper" parents="27453 43405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43408">
    <literal><![CDATA[
      x \ (y * L(y \ x,a(z,u,w),v5)) = a(v5,a(z,u,w),x \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,42638,a,b,43405,a)].">
      <j1 rule="hyper" parents="373 42638 43405"/>
    </justification>
  </clause>

  <clause id="43409">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,42391,a,b,43405,a)].">
      <j1 rule="hyper" parents="373 42391 43405"/>
    </justification>
  </clause>

  <clause id="43413">
    <literal><![CDATA[
      a(x * a(y,z,u),a(y,z,u),w) = a(x,a(y,z,u),a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,42916,a,b,43409,a),flip(a)].">
      <j1 rule="hyper" parents="373 42916 43409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43414">
    <literal><![CDATA[
      a(a(x,y,z) * u,a(x,y,z),w) = a(u,a(x,y,z),w * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,42916,a(flip),b,43409,a),flip(a)].">
      <j1 rule="hyper" parents="373 42916 43409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43415">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * v5 = v5 * a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(145,a,43409,a,b,23174,a),flip(a)].">
      <j1 rule="hyper" parents="145 43409 23174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43418">
    <literal><![CDATA[
      (1 / x) \ a(y,a(z,u,w),v5) = (v5 / x) \ L(v5,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(43401(a,1),42704(a,1,2)),flip(a)].">
      <j1 rule="para" parents="43401 42704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43420">
    <literal><![CDATA[
      (a(x,y,z) * a(u,a(x,y,z),w)) \ T(a(x,y,z),a(v5,v6,v7)) = a(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(43415(a,1),33559(a,1,1))].">
      <j1 rule="para" parents="43415 33559"/>
    </justification>
  </clause>

  <clause id="43421">
    <literal><![CDATA[
      L(x / (y * a(z,u,w)),a(z,u,w),y) = a(z,u,w) \ (y \ (y * (x / y)))
    ]]></literal>
    <justification jstring="[para(31794(a,1),43398(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="31794 43398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43422">
    <literal><![CDATA[
      x \ ((a(y,z,u) \ w) * L(x,a(u,z,y),w)) = T(a(y,z,u) \ R(w,a(y,z,u),x),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42155,a(flip),b,43400,a),flip(a)].">
      <j1 rule="hyper" parents="64 42155 43400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43424">
    <literal><![CDATA[
      a(x,y,z) \ (y * ((a(x,y,z) \ y) \ u)) = L(u,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[para(43361(a,1),43402(a,1,2))].">
      <j1 rule="para" parents="43361 43402"/>
    </justification>
  </clause>

  <clause id="43425">
    <literal><![CDATA[
      x * L(x \ y,a(z,u,w),y) = L(y,a(w,u,z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(39,a,42628,a,b,43408,a),flip(a)].">
      <j1 rule="hyper" parents="39 42628 43408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43426">
    <literal><![CDATA[
      a(x,y,z) \ (y * (L(a(x,y,z) \ y,a(x,y,z) \ y,u) \ u)) = L(R(u,a(x,y,z) \ y,a(x,y,z) \ y),a(z,y,x),y)
    ]]></literal>
    <justification jstring="[para(11856(a,2),43424(a,1,2,2))].">
      <j1 rule="para" parents="11856 43424"/>
    </justification>
  </clause>

  <clause id="43427">
    <literal><![CDATA[
      a(x,y,z) \ (y * L(y \ u,y,a(x,y,z))) = L(a(x,y,z) \ u,a(z,y,x),y)
    ]]></literal>
    <justification jstring="[para(42528(a,1),43424(a,1,2,2))].">
      <j1 rule="para" parents="42528 43424"/>
    </justification>
  </clause>

  <clause id="43428">
    <literal><![CDATA[
      x * a(y,a(z,z,u),x * a(z,z,u)) = L(x,a(u,z,z),a(u,z,z) * y)
    ]]></literal>
    <justification jstring="[para(43414(a,1),43404(a,1,2))].">
      <j1 rule="para" parents="43414 43404"/>
    </justification>
  </clause>

  <clause id="43429">
    <literal><![CDATA[
      L(x / (y * a(z,u,w)),a(z,u,w),y) = a(z,u,w) \ (x / y)
    ]]></literal>
    <justification jstring="[para(9(a,1),43421(a,2,2))].">
      <j1 rule="para" parents="9 43421"/>
    </justification>
  </clause>

  <clause id="43431">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(z,y,x),y) = (a(x,y,z) \ y) * (y \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42815,a(flip),b,43427,a),flip(a)].">
      <j1 rule="hyper" parents="64 42815 43427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43432">
    <literal><![CDATA[
      T(a(x,y,z) \ R(u,a(x,y,z),w),w) = w \ (u * (a(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[para(42823(a,1),43422(a,1,2)),flip(a)].">
      <j1 rule="para" parents="42823 43422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43433">
    <literal><![CDATA[
      T(a(x,y,z) \ L(u,a(x,y,z),w),w) = w \ (u * (a(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[para(31802(a,1),43432(a,1,1,2))].">
      <j1 rule="para" parents="31802 43432"/>
    </justification>
  </clause>

  <clause id="43434">
    <literal><![CDATA[
      L(x,x,a((L(y,z,u) * w) * v5,v6,v6)) * a(x,v6,(L(y,z,u) * w) * v5) = R(x,v6,(R(y,z,u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(37054(a,1),41633(a,1,2))].">
      <j1 rule="para" parents="37054 41633"/>
    </justification>
  </clause>

  <clause id="43435">
    <literal><![CDATA[
      a(x,x,y) * a((z / (x \ 1)) * (z / R(x \ 1,x,y)),x \ z,u) = R(a(x,x,y),z / (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(32136(a,1),41931(a,1,2))].">
      <j1 rule="para" parents="32136 41931"/>
    </justification>
  </clause>

  <clause id="43436">
    <literal><![CDATA[
      a(x,x,y) * a((z / (x \ 1)) * (R(x \ 1,x,y) \ z),x \ z,u) = R(a(x,x,y),z / (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(32362(a,1),43435(a,1,2))].">
      <j1 rule="para" parents="32362 43435"/>
    </justification>
  </clause>

  <clause id="43437">
    <literal><![CDATA[
      a(x,x,y) * a(((x \ 1) \ z) * (R(x \ 1,x,y) \ z),x \ z,u) = R(a(x,x,y),z / (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(32367(a,1),43436(a,1,2))].">
      <j1 rule="para" parents="32367 43436"/>
    </justification>
  </clause>

  <clause id="43438">
    <literal><![CDATA[
      a(x,x,y) * a(((x \ 1) \ z) * (L(x \ 1,x,y) \ z),x \ z,u) = R(a(x,x,y),z / (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(40059(a,1),43437(a,1,2))].">
      <j1 rule="para" parents="40059 43437"/>
    </justification>
  </clause>

  <clause id="43439">
    <literal><![CDATA[
      a(x,x,y) * a((L(x,x,y) \ z) * ((x \ 1) \ z),x \ z,u) = R(a(x,x,y),z / (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(40058(a,1),43438(a,1,2))].">
      <j1 rule="para" parents="40058 43438"/>
    </justification>
  </clause>

  <clause id="43440">
    <literal><![CDATA[
      a(x,x,y) * a((x \ z) * (L(x,x,y) \ z),x \ z,u) = R(a(x,x,y),z / (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(32810(a,1),43439(a,1,2))].">
      <j1 rule="para" parents="32810 43439"/>
    </justification>
  </clause>

  <clause id="43441">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ u),L(x,y,z) * (x \ 1)) = L(x \ L(x,y,z),L(x,y,z),u * x) \ u
    ]]></literal>
    <justification jstring="[para(40651(a,1),42130(a,1,1))].">
      <j1 rule="para" parents="40651 42130"/>
    </justification>
  </clause>

  <clause id="43442">
    <literal><![CDATA[
      L(x \ L(x,y,z),L(x,y,z),u * x) \ u = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23749,a(flip),b,43441,a),flip(a)].">
      <j1 rule="hyper" parents="64 23749 43441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43444">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u * x) \ u = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(43171(a,1),43442(a,1,1))].">
      <j1 rule="para" parents="43171 43442"/>
    </justification>
  </clause>

  <clause id="43445">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) \ u = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(33817(a,1),43444(a,1,1))].">
      <j1 rule="para" parents="33817 43444"/>
    </justification>
  </clause>

  <clause id="43446">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) \ (x \ L(x,y,z)) = u \ ((x \ L(x,y,z)) * (x * (L(x,y,z) \ u)))
    ]]></literal>
    <justification jstring="[para(43445(a,1),35568(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="43445 35568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43447">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) \ (x \ L(x,y,z)) = u \ L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(41761(a,1),43446(a,2,2))].">
      <j1 rule="para" parents="41761 43446"/>
    </justification>
  </clause>

  <clause id="43448">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) \ (x \ L(x,y,z)) = a(a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,43101,a(flip),b,43447,a),flip(a)].">
      <j1 rule="hyper" parents="373 43101 43447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43449">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) \ (x \ L(x,y,z)) = L(x,y,z) * (x \ L(L(x,y,z) \ x,x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,42150,a,b,43448,a),flip(a)].">
      <j1 rule="hyper" parents="373 42150 43448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43450">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) \ (x \ L(x,y,z)) = (x \ L(x,y,z)) * L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,33183,a,b,43449,a),flip(a)].">
      <j1 rule="hyper" parents="373 33183 43449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43451">
    <literal><![CDATA[
      L(x \ L(x,y,z),x,u) \ 1 = L(L(x,y,z) \ x,x,u)
    ]]></literal>
    <justification jstring="[hyper(1860,a,43450,a)].">
      <j1 rule="hyper" parents="1860 43450"/>
    </justification>
  </clause>

  <clause id="43452">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,v5) \ (v6 * (v7 * a(v6,v7,a(u,w,v5)))))) = a(x,y,z * (L(a(u,w,v5),v7,v6) * (v6 * v7)))
    ]]></literal>
    <justification jstring="[para(42047(a,1),42755(a,1,3,2,2,2))].">
      <j1 rule="para" parents="42047 42755"/>
    </justification>
  </clause>

  <clause id="43453">
    <literal><![CDATA[
      (x * L(x \ y,x,a(z,x,u))) / (x \ (a(z,x,u) * (a(z,x,u) \ y))) = R(x,a(z,x,u),a(z,x,u) \ y)
    ]]></literal>
    <justification jstring="[para(28865(a,1),43365(a,1,1))].">
      <j1 rule="para" parents="28865 43365"/>
    </justification>
  </clause>

  <clause id="43454">
    <literal><![CDATA[
      R(x,y,(R(z,u,w) * v5) * v6) = R(x,y,(L(z,u,w) * v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,41626,a,b,43434,a),flip(a)].">
      <j1 rule="hyper" parents="64 41626 43434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43455">
    <literal><![CDATA[
      R(x,y,z * (R(T(u,w),v5,v6) * v7)) = R(x,y,(L(u,v5,v6) * v7) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26356,a,b,43454,a)].">
      <j1 rule="hyper" parents="64 26356 43454"/>
    </justification>
  </clause>

  <clause id="43456">
    <literal><![CDATA[
      R(x,y,(L(z * K(u,T(z,w)),v5,v6) * u) * v7) = R(x,y,(u * R(z,v5,v6)) * v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,37412,a(flip),b,43455,a),flip(a)].">
      <j1 rule="hyper" parents="64 37412 43455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43457">
    <literal><![CDATA[
      R(x,y,(L(z,u,w) * (K(v5,T(z,v6)) * v5)) * v7) = R(x,y,(v5 * R(z,u,w)) * v7)
    ]]></literal>
    <justification jstring="[para(26075(a,1),43456(a,1,3,1))].">
      <j1 rule="para" parents="26075 43456"/>
    </justification>
  </clause>

  <clause id="43458">
    <literal><![CDATA[
      R(x,y,(L(z,u,w) * T(v5,T(z,v6))) * v7) = R(x,y,(v5 * R(z,u,w)) * v7)
    ]]></literal>
    <justification jstring="[para(5756(a,2),43457(a,1,3,1,2))].">
      <j1 rule="para" parents="5756 43457"/>
    </justification>
  </clause>

  <clause id="43459">
    <literal><![CDATA[
      R(x,y,T(z * L(u,w,v5),K(u,v6)) * v7) = R(x,y,(z * R(u,w,v5)) * v7)
    ]]></literal>
    <justification jstring="[para(27208(a,2),43458(a,1,3,1))].">
      <j1 rule="para" parents="27208 43458"/>
    </justification>
  </clause>

  <clause id="43460">
    <literal><![CDATA[
      R(x,y,(z * R(u,w,v5)) * v6) = R(x,y,(z * L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,26173,a(flip),b,43459,a),flip(a)].">
      <j1 rule="hyper" parents="64 26173 43459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43462">
    <literal><![CDATA[
      R(x,y,z * (K(u,w) * (v5 * R(u,v6,v7)))) = R(x,y,(v5 * L(T(u,w),v6,v7)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26963,a,b,43460,a)].">
      <j1 rule="hyper" parents="64 26963 43460"/>
    </justification>
  </clause>

  <clause id="43463">
    <literal><![CDATA[
      R(x,y,z * (K(u,w) * (v5 * R(u,v6,v7)))) = R(x,y,z * (v5 * L(u,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(373,a,26301,a(flip),b,43462,a),flip(a)].">
      <j1 rule="hyper" parents="373 26301 43462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43465">
    <literal><![CDATA[
      R(x,y,z * (u * R(w,v5,v6))) = R(x,y,z * (u * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,26188,a(flip),b,43463,a)].">
      <j1 rule="hyper" parents="64 26188 43463"/>
    </justification>
  </clause>

  <clause id="43467">
    <literal><![CDATA[
      R(x,y,z * ((u \ 1) * L(u \ ((u \ 1) \ w),v5,v6))) = R(x,y,z * ((1 / (1 / u)) \ R(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(7058(a,1),43465(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="7058 43465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43468">
    <literal><![CDATA[
      R(x,y,z * ((1 / (1 / u)) \ R(w,v5,v6))) = R(x,y,z * ((1 / (1 / u)) \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(7059(a,1),43467(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="7059 43467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43469">
    <literal><![CDATA[
      R(x,y,z * ((1 / (1 / u)) \ R(w,v5,v6))) = R(x,y,z * (((1 / u) \ 1) \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,26275,a(flip),b,43468,a),flip(a)].">
      <j1 rule="hyper" parents="373 26275 43468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43470">
    <literal><![CDATA[
      R(x,y,z * ((1 / (1 / u)) \ R(w,v5,v6))) = R(x,y,z * (u \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(82(a,1),43469(a,2,3,2,1))].">
      <j1 rule="para" parents="82 43469"/>
    </justification>
  </clause>

  <clause id="43471">
    <literal><![CDATA[
      R(x,y,z * (((1 / u) \ 1) \ R(w,v5,v6))) = R(x,y,z * (u \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,26275,a(flip),b,43470,a)].">
      <j1 rule="hyper" parents="64 26275 43470"/>
    </justification>
  </clause>

  <clause id="43474">
    <literal><![CDATA[
      R(x,y,z * (u \ R(w,v5,v6))) = R(x,y,z * (u \ L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(82(a,1),43471(a,1,3,2,1))].">
      <j1 rule="para" parents="82 43471"/>
    </justification>
  </clause>

  <clause id="43477">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,v5) \ (R(v6,v7,a(u,w,v5)) * v7))) = a(x,y,z * (L(a(u,w,v5),v7,v6) * (v6 * v7)))
    ]]></literal>
    <justification jstring="[para(41808(a,1),43452(a,1,3,2,2))].">
      <j1 rule="para" parents="41808 43452"/>
    </justification>
  </clause>

  <clause id="43478">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,v5) \ (L(v6,v7,a(u,w,v5)) * v7))) = a(x,y,z * (L(a(u,w,v5),v7,v6) * (v6 * v7)))
    ]]></literal>
    <justification jstring="[para(28832(a,1),43477(a,1,3,2,2,1))].">
      <j1 rule="para" parents="28832 43477"/>
    </justification>
  </clause>

  <clause id="43479">
    <literal><![CDATA[
      a(x,y,z * (L(a(u,w,v5),v6,v7) * (v7 * v6))) = a(x,y,z * (v7 * (a(u,w,v5) \ v6)))
    ]]></literal>
    <justification jstring="[para(42845(a,1),43478(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="42845 43478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43480">
    <literal><![CDATA[
      a(x,y,z * (u * (a(w,v5,v6) \ v7))) = a(x,y,z * (u * (v7 * a(w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(23162(a,1),43479(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="23162 43479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43481">
    <literal><![CDATA[
      R(x,a(y,x,z),a(y,x,z) \ u) = (x * L(x \ u,x,a(y,x,z))) / (x \ u)
    ]]></literal>
    <justification jstring="[para(10(a,1),43453(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10 43453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43482">
    <literal><![CDATA[
      R(x,a(y,x,z),a(y,x,z) \ u) = (x / (x \ u)) * L(x \ u,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,3196,a(flip),b,43481,a),flip(a)].">
      <j1 rule="hyper" parents="373 3196 43481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43483">
    <literal><![CDATA[
      R(x,a(y,x,z),a(y,x,z) \ u) = a(a(y,x,z),x,x \ u) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,42072,a(flip),b,43482,a),flip(a)].">
      <j1 rule="hyper" parents="373 42072 43482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43484">
    <literal><![CDATA[
      R(x,a(y,x,z),a(y,x,z) \ u) = a(a(y,x,z),x,u * x) \ x
    ]]></literal>
    <justification jstring="[para(42794(a,1),43483(a,2,1))].">
      <j1 rule="para" parents="42794 43483"/>
    </justification>
  </clause>

  <clause id="43485">
    <literal><![CDATA[
      R(x,a(y,x,z),a(y,x,z) \ u) = a(u * x,x,a(y,x,z)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,42525,a(flip),b,43484,a),flip(a)].">
      <j1 rule="hyper" parents="373 42525 43484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43486">
    <literal><![CDATA[
      R(x,a(y,x,z),a(y,x,z) \ u) = x * a(u * x,x,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,41900,a(flip),b,43485,a),flip(a)].">
      <j1 rule="hyper" parents="373 41900 43485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43487">
    <literal><![CDATA[
      R(x,a(y,x,z),a(y,x,z) * u) = x * a(u * x,x,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42481,a(flip),b,43486,a)].">
      <j1 rule="hyper" parents="64 42481 43486"/>
    </justification>
  </clause>

  <clause id="43488">
    <literal><![CDATA[
      (a(x,x,y) * (z * z)) \ ((a(x,x,y) * z) * R(z,x,y)) = a(L(z,z,L(a(x,x,y) * z,z,a(x,x,y))),x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,42857,a,b,41637,a),flip(a)].">
      <j1 rule="hyper" parents="373 42857 41637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43489">
    <literal><![CDATA[
      K(x,y) * (L(y,y,a(z,u,u)) * (a(z,u,y) \ x)) = x * R(L(y,u,z),a(z,u,y),a(z,u,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,23383,a(flip),b,41648,a)].">
      <j1 rule="hyper" parents="64 23383 41648"/>
    </justification>
  </clause>

  <clause id="43491">
    <literal><![CDATA[
      K(x,y) * (y * ((y \ L(y,z,u)) * x)) = x * R(L(y,z,u),a(u,z,y),a(u,z,y) \ x)
    ]]></literal>
    <justification jstring="[para(42948(a,1),43489(a,1,2))].">
      <j1 rule="para" parents="42948 43489"/>
    </justification>
  </clause>

  <clause id="43492">
    <literal><![CDATA[
      x * R(L(y,z,u),a(u,z,y),a(u,z,y) \ x) = y * (K(x,y) * ((y \ L(y,z,u)) * x))
    ]]></literal>
    <justification jstring="[hyper(4556,a,43491,a),flip(a)].">
      <j1 rule="hyper" parents="4556 43491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43493">
    <literal><![CDATA[
      x * R(L(y,z,u),a(u,z,y),a(u,z,y) \ x) = y * ((T(y,x) \ L(y,z,u)) * x)
    ]]></literal>
    <justification jstring="[para(24348(a,1),43492(a,2,2))].">
      <j1 rule="para" parents="24348 43492"/>
    </justification>
  </clause>

  <clause id="43494">
    <literal><![CDATA[
      x * R(L(y,z,u),a(u,z,y),a(u,z,y) \ x) = (y \ L(y,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,34177,a(flip),b,43493,a),flip(a)].">
      <j1 rule="hyper" parents="373 34177 43493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43495">
    <literal><![CDATA[
      x * L(L(y,z,u),a(u,z,y),a(u,z,y) * x) = (y \ L(y,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[para(41979(a,1),43494(a,1,2))].">
      <j1 rule="para" parents="41979 43494"/>
    </justification>
  </clause>

  <clause id="43496">
    <literal><![CDATA[
      (x / a(y,z,u)) * (a(y,z,u) * L(u,z,y)) = (u \ L(u,z,y)) * (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,41964,a(flip),b,43495,a)].">
      <j1 rule="hyper" parents="64 41964 43495"/>
    </justification>
  </clause>

  <clause id="43497">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (a(x,y,z) * L(z,y,x)) = (z \ L(z,y,x)) * (u * z)
    ]]></literal>
    <justification jstring="[para(23133(a,1),43496(a,1,1))].">
      <j1 rule="para" parents="23133 43496"/>
    </justification>
  </clause>

  <clause id="43498">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(z,z,a(x,y,y)) = (z \ L(z,y,x)) * (u * z)
    ]]></literal>
    <justification jstring="[para(41640(a,1),43497(a,1,2))].">
      <j1 rule="para" parents="41640 43497"/>
    </justification>
  </clause>

  <clause id="43499">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * (u * x)) \ (u * L(x,y,z)) = a(u,L(x,y,z),a(z,y,x))
    ]]></literal>
    <justification jstring="[para(43498(a,1),43179(a,1,1))].">
      <j1 rule="para" parents="43498 43179"/>
    </justification>
  </clause>

  <clause id="43500">
    <literal><![CDATA[
      a(x,L(y,z,u),a(u,z,y)) = a(a(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,43115,a(flip),b,43499,a),flip(a)].">
      <j1 rule="hyper" parents="64 43115 43499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43501">
    <literal><![CDATA[
      a(x,a(y,z,u),L(u,z,y)) = a(a(u,u,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,42288,a,b,43500,a)].">
      <j1 rule="hyper" parents="64 42288 43500"/>
    </justification>
  </clause>

  <clause id="43502">
    <literal><![CDATA[
      L(x,(y * z) * (y * a(u,y,z)),(y * z) * (y * a(u,y,z))) = L(x,L(z,y,u),L(z,y,u))
    ]]></literal>
    <justification jstring="[para(42083(a,2),42099(a,2,3))].">
      <j1 rule="para" parents="42083 42099"/>
    </justification>
  </clause>

  <clause id="43503">
    <literal><![CDATA[
      L(x,(y * z) * (y * a(u,y,z)),(y * z) * (y * a(u,y,z))) = L(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,35161,a(flip),b,43502,a),flip(a)].">
      <j1 rule="hyper" parents="373 35161 43502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43505">
    <literal><![CDATA[
      L(x,y * (z \ (z * a(u,z,y))),y * (z \ (z * a(u,z,y)))) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35254,a(flip),b,43503,a)].">
      <j1 rule="hyper" parents="64 35254 43503"/>
    </justification>
  </clause>

  <clause id="43506">
    <literal><![CDATA[
      L(x,y * a(z,u,y),y * (u \ (u * a(z,u,y)))) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),43505(a,1,2,2))].">
      <j1 rule="para" parents="9 43505"/>
    </justification>
  </clause>

  <clause id="43507">
    <literal><![CDATA[
      L(x,y * a(z,u,y),y * a(z,u,y)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),43506(a,1,3,2))].">
      <j1 rule="para" parents="9 43506"/>
    </justification>
  </clause>

  <clause id="43509">
    <literal><![CDATA[
      L(x,y * a(z,u,y),a(z,u,y) * y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(23928(a,1),43506(a,1,3))].">
      <j1 rule="para" parents="23928 43506"/>
    </justification>
  </clause>

  <clause id="43510">
    <literal><![CDATA[
      L(x,a(y,z,u) * u,a(y,z,u) * u) = L(x,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29507,a,b,43507,a)].">
      <j1 rule="hyper" parents="64 29507 43507"/>
    </justification>
  </clause>

  <clause id="43512">
    <literal><![CDATA[
      L(L((x \ 1) \ y,x,a(z,u,x)),x,x) = (1 / (x \ a(z,u,x))) * (y * a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,35231,a(flip),b,43509,a),flip(a)].">
      <j1 rule="hyper" parents="64 35231 43509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43514">
    <literal><![CDATA[
      (1 / (x \ a(y,z,x))) * (u * a(y,z,x)) = L(x * u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,1143,a(flip),b,43512,a),flip(a)].">
      <j1 rule="hyper" parents="64 1143 43512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43515">
    <literal><![CDATA[
      ((a(x,y,z) / z) \ 1) * (u * a(x,y,z)) = L(z * u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(25195(a,1),43514(a,1,1))].">
      <j1 rule="para" parents="25195 43514"/>
    </justification>
  </clause>

  <clause id="43516">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ (x * a(y,x,a(w,u,z))) = a(y,a(w,u,z),L(x,y,a(w,u,z)))
    ]]></literal>
    <justification jstring="[para(41910(a,1),42641(a,1,1))].">
      <j1 rule="para" parents="41910 42641"/>
    </justification>
  </clause>

  <clause id="43517">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ a(y,x,a(w,u,z))) = a(y,a(w,u,z),L(x,y,a(w,u,z)))
    ]]></literal>
    <justification jstring="[hyper(2342,a,43516,a)].">
      <j1 rule="hyper" parents="2342 43516"/>
    </justification>
  </clause>

  <clause id="43518">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ a(y,x,a(w,u,z))) = a(y,a(z,u,w),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,42784,a(flip),b,43517,a),flip(a)].">
      <j1 rule="hyper" parents="373 42784 43517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43519">
    <literal><![CDATA[
      a(x,y,z) * (((a(u,a(x,y,z),w) * a(x,y,z)) \ v5) * a(x,y,z)) = (a(x,y,z) * a(w,a(x,y,z),u)) * v5
    ]]></literal>
    <justification jstring="[para(33544(a,1),43360(a,1,2,1,1))].">
      <j1 rule="para" parents="33544 43360"/>
    </justification>
  </clause>

  <clause id="43520">
    <literal><![CDATA[
      (a(x,x,y) * (z * z)) \ ((a(x,x,y) * z) * R(z,x,y)) = a(L(z,z,((a(x,x,y) \ 1) / z) \ 1),x,y)
    ]]></literal>
    <justification jstring="[para(38622(a,1),43488(a,2,1,3))].">
      <j1 rule="para" parents="38622 43488"/>
    </justification>
  </clause>

  <clause id="43521">
    <literal><![CDATA[
      (x \ 1) * L(y,x \ (a(z,x,u) / x),x * a(z,x,u)) = (x \ a(z,x,u)) * (((x \ a(z,x,u)) \ (x \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(35744(a,1),41743(a,1,2))].">
      <j1 rule="para" parents="35744 41743"/>
    </justification>
  </clause>

  <clause id="43522">
    <literal><![CDATA[
      (x * a(y,a(y,z,u),w)) * a(x,x,a(y,a(y,z,u),w)) = (L(y,a(y,z,u),w) / x) \ y
    ]]></literal>
    <justification jstring="[para(42254(a,1),41967(a,1,2))].">
      <j1 rule="para" parents="42254 41967"/>
    </justification>
  </clause>

  <clause id="43523">
    <literal><![CDATA[
      (L(x,a(x,y,z),u) / w) \ x = w * L(a(x,a(x,y,z),u),w,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42960,a(flip),b,43522,a),flip(a)].">
      <j1 rule="hyper" parents="64 42960 43522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43524">
    <literal><![CDATA[
      (L(x,a(x,y,z),u) / w) \ x = (1 / w) \ a(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,36302,a(flip),b,43523,a),flip(a)].">
      <j1 rule="hyper" parents="373 36302 43523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43525">
    <literal><![CDATA[
      R(x,(((y \ y) / z) \ (y \ 1)) * y,((1 / y) \ y) / z) = R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(39951(a,1),42033(a,1,2,1))].">
      <j1 rule="para" parents="39951 42033"/>
    </justification>
  </clause>

  <clause id="43526">
    <literal><![CDATA[
      L(x,(y \ z) / T(y,z),L(R(y \ 1,y,z),y \ z,y \ z)) = L(x,L(z \ 1,z,y),R(y \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(5155(a,1),43285(a,1,2))].">
      <j1 rule="para" parents="5155 43285"/>
    </justification>
  </clause>

  <clause id="43527">
    <literal><![CDATA[
      L(x,(y \ z) / T(y,z),L(R(y \ 1,y,z),z * y,z * y)) = L(x,L(z \ 1,z,y),R(y \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(35219(a,1),43526(a,1,3))].">
      <j1 rule="para" parents="35219 43526"/>
    </justification>
  </clause>

  <clause id="43528">
    <literal><![CDATA[
      L(x,(y \ z) / T(y,z),L(L(y \ 1,y,z),z * y,z * y)) = L(x,L(z \ 1,z,y),R(y \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29264,a(flip),b,43527,a)].">
      <j1 rule="hyper" parents="64 29264 43527"/>
    </justification>
  </clause>

  <clause id="43529">
    <literal><![CDATA[
      L(x,(y \ z) / T(y,z),(1 / (z * y)) * (z * 1)) = L(x,L(z \ 1,z,y),R(y \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(644(a,1),43528(a,1,3))].">
      <j1 rule="para" parents="644 43528"/>
    </justification>
  </clause>

  <clause id="43530">
    <literal><![CDATA[
      L(x,(y \ z) / T(y,z),(1 / (z * y)) * z) = L(x,L(z \ 1,z,y),R(y \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(8(a,1),43529(a,1,3,2))].">
      <j1 rule="para" parents="8 43529"/>
    </justification>
  </clause>

  <clause id="43531">
    <literal><![CDATA[
      L(x,L(y \ 1,y,z),R(z \ 1,z,y)) = L(x,(z \ y) / T(z,y),(y * z) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2186,a(flip),b,43530,a),flip(a)].">
      <j1 rule="hyper" parents="64 2186 43530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43532">
    <literal><![CDATA[
      L(x,L(y \ 1,y,z),R(z \ 1,z,y)) = L(x,(z \ y) / T(z,y),L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,24000,a(flip),b,43531,a),flip(a)].">
      <j1 rule="hyper" parents="373 24000 43531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43533">
    <literal><![CDATA[
      L(x,L(y \ 1,y,z),R(z \ 1,z,y)) = L(x,z \ (z \ y),L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,29581,a(flip),b,43532,a),flip(a)].">
      <j1 rule="hyper" parents="373 29581 43532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43535">
    <literal><![CDATA[
      L(x,L(y \ 1,y,z),R(z \ 1,z,y)) = L(x,L(y,z,z),L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,31756,a(flip),b,43533,a),flip(a)].">
      <j1 rule="hyper" parents="373 31756 43533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43536">
    <literal><![CDATA[
      L(x,L(y \ 1,y,z),R(z \ 1,z,y)) = L(x,L(y,z,z),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,42004,a(flip),b,43535,a),flip(a)].">
      <j1 rule="hyper" parents="373 42004 43535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43537">
    <literal><![CDATA[
      L(x,L(y \ 1,y,z),L(z \ 1,z,y)) = L(x,L(y,z,z),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29203,a(flip),b,43536,a)].">
      <j1 rule="hyper" parents="64 29203 43536"/>
    </justification>
  </clause>

  <clause id="43538">
    <literal><![CDATA[
      L(x,L(y \ 1,y,z),L(z,z,y)) = L(x,L(y,z,z),z)
    ]]></literal>
    <justification jstring="[hyper(34230,a,43537,a)].">
      <j1 rule="hyper" parents="34230 43537"/>
    </justification>
  </clause>

  <clause id="43539">
    <literal><![CDATA[
      L(x,L(y,y,z),L(z,z,y)) = L(x,L(y,z,z),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29880,a(flip),b,43538,a)].">
      <j1 rule="hyper" parents="64 29880 43538"/>
    </justification>
  </clause>

  <clause id="43540">
    <literal><![CDATA[
      L(x,L(y,z,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41023,a(flip),b,43539,a),flip(a)].">
      <j1 rule="hyper" parents="64 41023 43539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43547">
    <literal><![CDATA[
      L(L(x,y \ z,y \ z) \ R(L(x,y \ z,y \ z),y,z),x,y \ z) = a(L(x,y \ z,y \ z),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42135,a,b,43540,a),flip(a)].">
      <j1 rule="hyper" parents="64 42135 43540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43548">
    <literal><![CDATA[
      L((x \ ((1 / x) \ y)) \ z,y,x) = (x \ y) \ ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31400,a(flip),b,43540,a),flip(a)].">
      <j1 rule="hyper" parents="64 31400 43540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43550">
    <literal><![CDATA[
      a(x,L((y \ z) \ ((y \ 1) * u),z,y),w) = a(x,(y \ ((1 / y) \ z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(43548(a,1),42975(a,1,2,1))].">
      <j1 rule="para" parents="43548 42975"/>
    </justification>
  </clause>

  <clause id="43551">
    <literal><![CDATA[
      a(x,L((y \ z) \ (y * u),z,y),w) = a(x,(y \ ((1 / y) \ z)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32998,a(flip),b,43550,a)].">
      <j1 rule="hyper" parents="64 32998 43550"/>
    </justification>
  </clause>

  <clause id="43552">
    <literal><![CDATA[
      a(x,L((y \ z) \ (y * u),z,y),w) = a(x,(y \ ((y \ 1) \ z)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32261,a(flip),b,43551,a),flip(a)].">
      <j1 rule="hyper" parents="373 32261 43551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43553">
    <literal><![CDATA[
      a(x,L((y \ z) \ (y * u),z,y),w) = a(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,33033,a(flip),b,43552,a),flip(a)].">
      <j1 rule="hyper" parents="373 33033 43552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43554">
    <literal><![CDATA[
      L(L(x,y \ z,y \ z) \ R(L(x,y \ z,y \ z),y,z),x,y \ z) = a(L(x,z * y,z * y),y,z)
    ]]></literal>
    <justification jstring="[para(35219(a,1),43547(a,2,1))].">
      <j1 rule="para" parents="35219 43547"/>
    </justification>
  </clause>

  <clause id="43555">
    <literal><![CDATA[
      L(L(x,y * z,y * z) \ R(L(x,z \ y,z \ y),z,y),x,z \ y) = a(L(x,y * z,y * z),z,y)
    ]]></literal>
    <justification jstring="[para(35219(a,1),43554(a,1,1,1))].">
      <j1 rule="para" parents="35219 43554"/>
    </justification>
  </clause>

  <clause id="43556">
    <literal><![CDATA[
      L(L(x,y * z,y * z) \ R(L(x,y * z,y * z),z,y),x,z \ y) = a(L(x,y * z,y * z),z,y)
    ]]></literal>
    <justification jstring="[para(35219(a,1),43555(a,1,1,2,1))].">
      <j1 rule="para" parents="35219 43555"/>
    </justification>
  </clause>

  <clause id="43557">
    <literal><![CDATA[
      L(L(x \ R(x,y,z),z * y,z * y),x,y \ z) = a(L(x,z * y,z * y),y,z)
    ]]></literal>
    <justification jstring="[para(4246(a,1),43556(a,1,1))].">
      <j1 rule="para" parents="4246 43556"/>
    </justification>
  </clause>

  <clause id="43558">
    <literal><![CDATA[
      a(L(x,y * z,y * z),z,y) = L(a(x,z,y),y * z,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42136,a(flip),b,43557,a),flip(a)].">
      <j1 rule="hyper" parents="64 42136 43557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43559">
    <literal><![CDATA[
      a(L(x,y * z,y * z),z,y) = L(y,z,x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,43067,a(flip),b,43558,a),flip(a)].">
      <j1 rule="hyper" parents="373 43067 43558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43560">
    <literal><![CDATA[
      L(x,y,(x * y) * z) \ x = a((x * y) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30382,a(flip),b,43559,a),flip(a)].">
      <j1 rule="hyper" parents="64 30382 43559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43561">
    <literal><![CDATA[
      a(L(x \ y,z * (z \ x),z * (z \ x)),z \ x,z) = (((y / x) * (x / z)) \ y) \ z
    ]]></literal>
    <justification jstring="[para(15121(a,1),43559(a,2,1))].">
      <j1 rule="para" parents="15121 43559"/>
    </justification>
  </clause>

  <clause id="43562">
    <literal><![CDATA[
      a(L(x,y * z,y * z),y,z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[para(29507(a,1),43559(a,1,1))].">
      <j1 rule="para" parents="29507 43559"/>
    </justification>
  </clause>

  <clause id="43563">
    <literal><![CDATA[
      a(L(x,L(y,z,z) * (z \ 1),z \ y),z \ 1,L(y,z,z)) = L(L(y,z,z),z \ 1,x) \ L(y,z,z)
    ]]></literal>
    <justification jstring="[para(30392(a,1),43559(a,1,1))].">
      <j1 rule="para" parents="30392 43559"/>
    </justification>
  </clause>

  <clause id="43564">
    <literal><![CDATA[
      a((1 / (x \ y)) * z,y,x) = L(x,y,(x \ y) \ z) \ x
    ]]></literal>
    <justification jstring="[para(35224(a,1),43559(a,1,1))].">
      <j1 rule="para" parents="35224 43559"/>
    </justification>
  </clause>

  <clause id="43565">
    <literal><![CDATA[
      L(x,y,z * (y * x)) \ x = a((y * x) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30383,a(flip),b,43562,a),flip(a)].">
      <j1 rule="hyper" parents="64 30383 43562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43566">
    <literal><![CDATA[
      a(L(x,y * (z / y),z),y,z / y) = L(z / y,y,x) \ (z / y)
    ]]></literal>
    <justification jstring="[para(24004(a,1),43562(a,1,1))].">
      <j1 rule="para" parents="24004 43562"/>
    </justification>
  </clause>

  <clause id="43567">
    <literal><![CDATA[
      L(a((x * y) * z,y,x),x,y) = a((x * y) \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42055,a,b,43560,a)].">
      <j1 rule="hyper" parents="64 42055 43560"/>
    </justification>
  </clause>

  <clause id="43568">
    <literal><![CDATA[
      L(x,y,z * (y * x)) \ x = a((x \ z) * y,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,41915,a(flip),b,43565,a),flip(a)].">
      <j1 rule="hyper" parents="373 41915 43565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43569">
    <literal><![CDATA[
      L(x,y,(x \ z) * y) \ x = a((x * y) * z,y,x)
    ]]></literal>
    <justification jstring="[hyper(42,a,42066,a,b,43567,a)].">
      <j1 rule="hyper" parents="42 42066 43567"/>
    </justification>
  </clause>

  <clause id="43570">
    <literal><![CDATA[
      L(x,y,y * (x \ z)) \ x = a((x * y) * z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,24003,a,b,43569,a)].">
      <j1 rule="hyper" parents="64 24003 43569"/>
    </justification>
  </clause>

  <clause id="43571">
    <literal><![CDATA[
      L(x,y,(x \ y) \ z) \ x = a((x \ y) * z,y,x)
    ]]></literal>
    <justification jstring="[hyper(2693,a,43564,a),flip(a)].">
      <j1 rule="hyper" parents="2693 43564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43572">
    <literal><![CDATA[
      a(L(x,y,y),z,y / z) = L(y / z,z,x) \ (y / z)
    ]]></literal>
    <justification jstring="[para(29439(a,1),43566(a,1,1))].">
      <j1 rule="para" parents="29439 43566"/>
    </justification>
  </clause>

  <clause id="43573">
    <literal><![CDATA[
      a(L(x,y,y),z,z \ y) = L(y / z,z,x) \ (y / z)
    ]]></literal>
    <justification jstring="[hyper(27586,a,43572,a)].">
      <j1 rule="hyper" parents="27586 43572"/>
    </justification>
  </clause>

  <clause id="43575">
    <literal><![CDATA[
      a(L(x,y,y),z,z \ y) = a(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,43320,a(flip),b,43573,a),flip(a)].">
      <j1 rule="hyper" parents="373 43320 43573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43576">
    <literal><![CDATA[
      a(x \ y,z,(x \ z) \ 1) = a(x * y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(2694,a,43575,a),flip(a)].">
      <j1 rule="hyper" parents="2694 43575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43577">
    <literal><![CDATA[
      L(a(x \ y,z,z \ x),x,z) = a(x * y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,43321,a,b,43576,a)].">
      <j1 rule="hyper" parents="64 43321 43576"/>
    </justification>
  </clause>

  <clause id="43578">
    <literal><![CDATA[
      (((x / y) * z) \ x) \ (z \ y) = a(y * x,z,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,43075,a(flip),b,43577,a)].">
      <j1 rule="hyper" parents="64 43075 43577"/>
    </justification>
  </clause>

  <clause id="43579">
    <literal><![CDATA[
      a(L(x \ y,x,z * (z \ x)),z \ x,z) = (((y / x) * (x / z)) \ y) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),43561(a,1,1,2))].">
      <j1 rule="para" parents="10 43561"/>
    </justification>
  </clause>

  <clause id="43580">
    <literal><![CDATA[
      a(L(x \ y,x,x),z \ x,z) = (((y / x) * (x / z)) \ y) \ z
    ]]></literal>
    <justification jstring="[para(10(a,1),43579(a,1,1,3))].">
      <j1 rule="para" parents="10 43579"/>
    </justification>
  </clause>

  <clause id="43581">
    <literal><![CDATA[
      (((x / y) * (y / z)) \ x) \ z = a(y * x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(2694,a,43580,a),flip(a)].">
      <j1 rule="hyper" parents="2694 43580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43582">
    <literal><![CDATA[
      a(L(x,L(y * z,z,z) * (z \ 1),y),z \ 1,L(y * z,z,z)) = L(L(y * z,z,z),z \ 1,x) \ L(y * z,z,z)
    ]]></literal>
    <justification jstring="[para(23842(a,1),43563(a,1,1))].">
      <j1 rule="para" parents="23842 43563"/>
    </justification>
  </clause>

  <clause id="43583">
    <literal><![CDATA[
      (x \ 1) * L(y,x \ (x \ a(z,x,u)),x * a(z,x,u)) = (x \ a(z,x,u)) * (((x \ a(z,x,u)) \ (x \ 1)) * y)
    ]]></literal>
    <justification jstring="[para(29446(a,1),43521(a,1,2))].">
      <j1 rule="para" parents="29446 43521"/>
    </justification>
  </clause>

  <clause id="43584">
    <literal><![CDATA[
      R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = R(x,((1 / z) \ (y \ 1)) * y,((1 / y) \ y) / z)
    ]]></literal>
    <justification jstring="[para(68(a,1),43525(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="68 43525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43585">
    <literal><![CDATA[
      R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = R(x,((1 / z) \ (y \ 1)) * y,z \ ((1 / y) \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,23813,a(flip),b,43584,a),flip(a)].">
      <j1 rule="hyper" parents="373 23813 43584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43587">
    <literal><![CDATA[
      R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = R(x,((1 / z) \ (y \ 1)) * y,z \ ((1 \ y) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,33680,a(flip),b,43585,a),flip(a)].">
      <j1 rule="hyper" parents="373 33680 43585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43588">
    <literal><![CDATA[
      R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = R(x,((1 / z) \ (y \ 1)) * y,z \ (y * y))
    ]]></literal>
    <justification jstring="[para(66(a,1),43587(a,2,3,2,1))].">
      <j1 rule="para" parents="66 43587"/>
    </justification>
  </clause>

  <clause id="43589">
    <literal><![CDATA[
      R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = R(x,((1 / z) \ y) * y,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,26608,a(flip),b,43588,a),flip(a)].">
      <j1 rule="hyper" parents="373 26608 43588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43590">
    <literal><![CDATA[
      R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = R(x,((z \ 1) \ y) * y,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,26435,a(flip),b,43589,a),flip(a)].">
      <j1 rule="hyper" parents="373 26435 43589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43591">
    <literal><![CDATA[
      R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = R(x,(z \ y) * y,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,3029,a(flip),b,43590,a),flip(a)].">
      <j1 rule="hyper" parents="373 3029 43590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43592">
    <literal><![CDATA[
      (x \ a(y,x,z)) * (((x \ a(y,x,z)) \ (x \ 1)) * u) = (x \ 1) * L(u,L(a(y,x,z),x,x),x * a(y,x,z))
    ]]></literal>
    <justification jstring="[para(31756(a,1),43583(a,1,2)),flip(a)].">
      <j1 rule="para" parents="31756 43583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43593">
    <literal><![CDATA[
      (x \ a(y,x,z)) * (((x \ a(y,x,z)) \ (x \ 1)) * u) = (x \ 1) * L(u,a(y,x,z),x * a(y,x,z))
    ]]></literal>
    <justification jstring="[para(35734(a,1),43592(a,2,2,2))].">
      <j1 rule="para" parents="35734 43592"/>
    </justification>
  </clause>

  <clause id="43594">
    <literal><![CDATA[
      (x \ a(y,x,z)) * (((x \ a(y,x,z)) \ (x \ 1)) * u) = ((x \ 1) / a(y,x,z)) * (a(y,x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,41974,a(flip),b,43593,a),flip(a)].">
      <j1 rule="hyper" parents="373 41974 43593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43595">
    <literal><![CDATA[
      (x \ a(y,x,z)) * (((x \ a(y,x,z)) \ (x \ 1)) * u) = (a(y,x,z) \ (x \ 1)) * (a(y,x,z) * u)
    ]]></literal>
    <justification jstring="[para(23133(a,1),43594(a,2,1))].">
      <j1 rule="para" parents="23133 43594"/>
    </justification>
  </clause>

  <clause id="43596">
    <literal><![CDATA[
      a(1 / (a(x,x,y) / x),y,y \ ((1 / (a(x,x,y) / x)) \ z)) = a(1 / (a(x,x,y) / x),y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,39107,a(flip),b,42110,a),flip(a)].">
      <j1 rule="hyper" parents="373 39107 42110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43597">
    <literal><![CDATA[
      a(1 / (a(x,x,y) / x),y,y \ ((1 / (a(x,x,y) / x)) \ z)) = a((a(x,x,y) / x) \ 1,y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,26785,a(flip),b,43596,a),flip(a)].">
      <j1 rule="hyper" parents="373 26785 43596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43598">
    <literal><![CDATA[
      a(1 / (a(x,x,y) / x),y,y \ ((1 / (a(x,x,y) / x)) \ z)) = a(a(x,x,y) \ x,y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(30165(a,1),43597(a,2,1))].">
      <j1 rule="para" parents="30165 43597"/>
    </justification>
  </clause>

  <clause id="43599">
    <literal><![CDATA[
      a(1 / (a(x,x,y) / x),y,y \ ((1 / (a(x,x,y) / x)) \ z)) = a(L(x,x,y),y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32592,a(flip),b,43598,a),flip(a)].">
      <j1 rule="hyper" parents="373 32592 43598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43600">
    <literal><![CDATA[
      a(1 / (a(x,x,y) / x),y,y \ ((1 / (a(x,x,y) / x)) \ z)) = x \ R(x,y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,41802,a(flip),b,43599,a),flip(a)].">
      <j1 rule="hyper" parents="373 41802 43599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43601">
    <literal><![CDATA[
      a(1 / (a(x,x,y) / x),y,y \ (((a(x,x,y) / x) \ 1) \ z)) = x \ R(x,y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27511,a(flip),b,43600,a)].">
      <j1 rule="hyper" parents="64 27511 43600"/>
    </justification>
  </clause>

  <clause id="43602">
    <literal><![CDATA[
      a(1 / (a(x,x,y) / x),y,y \ ((a(x,x,y) \ x) \ z)) = x \ R(x,y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(30165(a,1),43601(a,1,3,2,1))].">
      <j1 rule="para" parents="30165 43601"/>
    </justification>
  </clause>

  <clause id="43603">
    <literal><![CDATA[
      a(1 / (a(x,x,y) / x),y,y \ ((x \ z) * a(x,x,y))) = x \ R(x,y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(37737(a,1),43602(a,1,3,2))].">
      <j1 rule="para" parents="37737 43602"/>
    </justification>
  </clause>

  <clause id="43604">
    <literal><![CDATA[
      a(1 / (a(x,x,y) / x),y,(y \ (x \ z)) * a(x,x,y)) = x \ R(x,y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(33202(a,1),43603(a,1,3))].">
      <j1 rule="para" parents="33202 43603"/>
    </justification>
  </clause>

  <clause id="43605">
    <literal><![CDATA[
      a((a(x,x,y) / x) \ 1,y,(y \ (x \ z)) * a(x,x,y)) = x \ R(x,y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(26880,a,43604,a)].">
      <j1 rule="hyper" parents="26880 43604"/>
    </justification>
  </clause>

  <clause id="43606">
    <literal><![CDATA[
      a(a(x,x,y) \ x,y,(y \ (x \ z)) * a(x,x,y)) = x \ R(x,y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[para(30165(a,1),43605(a,1,1))].">
      <j1 rule="para" parents="30165 43605"/>
    </justification>
  </clause>

  <clause id="43607">
    <literal><![CDATA[
      a(L(x,x,y),y,(y \ (x \ z)) * a(x,x,y)) = x \ R(x,y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32592,a(flip),b,43606,a)].">
      <j1 rule="hyper" parents="64 32592 43606"/>
    </justification>
  </clause>

  <clause id="43608">
    <literal><![CDATA[
      x \ R(x,y,(y \ (x \ z)) * a(x,x,y)) = x \ R(x,y,((x \ 1) \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41802,a(flip),b,43607,a)].">
      <j1 rule="hyper" parents="64 41802 43607"/>
    </justification>
  </clause>

  <clause id="43609">
    <literal><![CDATA[
      x \ R(x,y,((x \ 1) \ y) \ z) = x \ R(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(37035(a,1),43608(a,1,2)),flip(a)].">
      <j1 rule="para" parents="37035 43608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43610">
    <literal><![CDATA[
      a(R(x,x,y),y,y \ (R(x,x,y) \ z)) = x \ R(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42993,a,b,43609,a)].">
      <j1 rule="hyper" parents="64 42993 43609"/>
    </justification>
  </clause>

  <clause id="43611">
    <literal><![CDATA[
      a(L(x,x,y),y,y \ (R(x,x,y) \ z)) = x \ R(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,32590,a(flip),b,43610,a)].">
      <j1 rule="hyper" parents="64 32590 43610"/>
    </justification>
  </clause>

  <clause id="43612">
    <literal><![CDATA[
      x \ R(x,y,y \ (R(x,x,y) \ z)) = x \ R(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41802,a(flip),b,43611,a)].">
      <j1 rule="hyper" parents="64 41802 43611"/>
    </justification>
  </clause>

  <clause id="43613">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ ((u * (w * (x \ R(x,y,z)))) / (u * w)) = L(a(u,w,x \ L(x,y,z)) \ 1,x \ R(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(31322(a,1),42244(a,2,1,1))].">
      <j1 rule="para" parents="31322 42244"/>
    </justification>
  </clause>

  <clause id="43614">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ ((u * (w * (x \ R(x,y,z)))) / (u * w)) = L(a(x * L(x,y,z),w,u) * 1,x \ R(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(42539(a,1),43613(a,2,1))].">
      <j1 rule="para" parents="42539 43613"/>
    </justification>
  </clause>

  <clause id="43615">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ ((u * (w * (x \ R(x,y,z)))) / (u * w)) = L(a(x * L(x,y,z),w,u),x \ R(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(8(a,1),43614(a,2,1))].">
      <j1 rule="para" parents="8 43614"/>
    </justification>
  </clause>

  <clause id="43616">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ ((u * (w * (x \ R(x,y,z)))) / (u * w)) = L(a(x * L(x,y,z),w,u),x \ L(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,36271,a(flip),b,43615,a),flip(a)].">
      <j1 rule="hyper" parents="373 36271 43615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43617">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ ((u * (w * (x \ R(x,y,z)))) / (u * w)) = L(a(x * L(x,y,z),w,u),x * L(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11786,a(flip),b,43616,a),flip(a)].">
      <j1 rule="hyper" parents="373 11786 43616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43618">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ ((u * (w * (x \ R(x,y,z)))) / (u * w)) = a(L(x * L(x,y,z),x * L(x,y,z),w),w,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,40756,a,b,43617,a),flip(a)].">
      <j1 rule="hyper" parents="373 40756 43617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43619">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ ((u * (w * (x \ R(x,y,z)))) / (u * w)) = a(x * L(x,y,z),w,u)
    ]]></literal>
    <justification jstring="[para(43348(a,1),43618(a,2,1))].">
      <j1 rule="para" parents="43348 43618"/>
    </justification>
  </clause>

  <clause id="43620">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ L(x \ R(x,y,z),u,w) = a(x * L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(23713(a,1),43619(a,1,2))].">
      <j1 rule="para" parents="23713 43619"/>
    </justification>
  </clause>

  <clause id="43622">
    <literal><![CDATA[
      (R(x,y,z) \ x) * L(x \ R(x,y,z),u,w) = a(x * L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42593,a(flip),b,43620,a)].">
      <j1 rule="hyper" parents="64 42593 43620"/>
    </justification>
  </clause>

  <clause id="43623">
    <literal><![CDATA[
      ((x * y) / (((x * y) \ x) * x)) * ((((x * y) \ x) * x) * z) = (x * y) * L(z,((x * y) \ x) * x,(y \ x) * (y * x))
    ]]></literal>
    <justification jstring="[para(28980(a,1),42013(a,2,2))].">
      <j1 rule="para" parents="28980 42013"/>
    </justification>
  </clause>

  <clause id="43624">
    <literal><![CDATA[
      R(x,a(y,x,z) * K(y,x),(a(y,x,z) * K(y,x)) \ u) = (((R(y,x,z) * x) / y) * (K(x,y) * (a(y,x,z) \ u))) / u
    ]]></literal>
    <justification jstring="[para(23272(a,1),42261(a,2,1,2))].">
      <j1 rule="para" parents="23272 42261"/>
    </justification>
  </clause>

  <clause id="43625">
    <literal><![CDATA[
      a(L(x,y * L(z * y,y,y),z),y \ 1,L(z * y,y,y)) = L(L(z * y,y,y),y \ 1,x) \ L(z * y,y,y)
    ]]></literal>
    <justification jstring="[para(29520(a,1),43582(a,1,1))].">
      <j1 rule="para" parents="29520 43582"/>
    </justification>
  </clause>

  <clause id="43626">
    <literal><![CDATA[
      a(L(x,y \ (z * y),z),y \ 1,L(z * y,y,y)) = L(L(z * y,y,y),y \ 1,x) \ L(z * y,y,y)
    ]]></literal>
    <justification jstring="[para(31761(a,1),43625(a,1,1))].">
      <j1 rule="para" parents="31761 43625"/>
    </justification>
  </clause>

  <clause id="43627">
    <literal><![CDATA[
      a(L(x,y,y),z \ 1,L(y * z,z,z)) = L(L(y * z,z,z),z \ 1,x) \ L(y * z,z,z)
    ]]></literal>
    <justification jstring="[para(29493(a,1),43626(a,1,1))].">
      <j1 rule="para" parents="29493 43626"/>
    </justification>
  </clause>

  <clause id="43628">
    <literal><![CDATA[
      a(L(x,y,y),z \ 1,(z \ 1) \ y) = L(L(y * z,z,z),z \ 1,x) \ L(y * z,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38945,a(flip),b,43627,a)].">
      <j1 rule="hyper" parents="64 38945 43627"/>
    </justification>
  </clause>

  <clause id="43630">
    <literal><![CDATA[
      a(L(x,y,y),z,(z \ 1) \ y) = L(L(y * z,z,z),z \ 1,x) \ L(y * z,z,z)
    ]]></literal>
    <justification jstring="[hyper(32046,a,43628,a)].">
      <j1 rule="hyper" parents="32046 43628"/>
    </justification>
  </clause>

  <clause id="43631">
    <literal><![CDATA[
      a(L(x,y,y),z,z * y) = L(L(y * z,z,z),z \ 1,x) \ L(y * z,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42880,a(flip),b,43630,a)].">
      <j1 rule="hyper" parents="64 42880 43630"/>
    </justification>
  </clause>

  <clause id="43632">
    <literal><![CDATA[
      a(L(x,y,y),z,z * y) = L(L(y * z,z,z),z,x) \ L(y * z,z,z)
    ]]></literal>
    <justification jstring="[para(11794(a,1),43631(a,2,1))].">
      <j1 rule="para" parents="11794 43631"/>
    </justification>
  </clause>

  <clause id="43633">
    <literal><![CDATA[
      a(L(x,y,y),z,z * y) = L(y * z,z,x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,42894,a(flip),b,43632,a),flip(a)].">
      <j1 rule="hyper" parents="373 42894 43632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43634">
    <literal><![CDATA[
      L(a(x,y,z * y),z,y) = a(L(x,z,z),y,y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,43074,a(flip),b,43633,a)].">
      <j1 rule="hyper" parents="373 43074 43633"/>
    </justification>
  </clause>

  <clause id="43635">
    <literal><![CDATA[
      ((x * y) / (((x * y) \ x) * x)) * ((((x * y) \ x) * x) * z) = (x * y) * L(z,((x * y) \ x) * x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(30966(a,1),43623(a,2,2))].">
      <j1 rule="para" parents="30966 43623"/>
    </justification>
  </clause>

  <clause id="43636">
    <literal><![CDATA[
      ((x * y) / (((x * y) \ x) * x)) * ((((x * y) \ x) * x) * z) = (x * y) * L(z,(x \ (y \ x)) * x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(29854(a,1),43635(a,2,2))].">
      <j1 rule="para" parents="29854 43635"/>
    </justification>
  </clause>

  <clause id="43637">
    <literal><![CDATA[
      ((x * y) / (((x * y) \ x) * x)) * ((((x * y) \ x) * x) * z) = (x * y) * L(z,y \ x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(29441(a,1),43636(a,2,2))].">
      <j1 rule="para" parents="29441 43636"/>
    </justification>
  </clause>

  <clause id="43639">
    <literal><![CDATA[
      R(x,a(y,x,z) * K(y,x),(a(y,x,z) * K(y,x)) \ u) = (((R(y,x,z) * x) / T(y,x)) * (a(y,x,z) \ u)) / u
    ]]></literal>
    <justification jstring="[para(24465(a,1),43624(a,2,1))].">
      <j1 rule="para" parents="24465 43624"/>
    </justification>
  </clause>

  <clause id="43640">
    <literal><![CDATA[
      R(x,a(y,x,z) * K(y,x),(a(y,x,z) * K(y,x)) \ u) = ((R(y,x,z) * (y \ x)) * (a(y,x,z) \ u)) / u
    ]]></literal>
    <justification jstring="[para(25441(a,1),43639(a,2,1,1))].">
      <j1 rule="para" parents="25441 43639"/>
    </justification>
  </clause>

  <clause id="43641">
    <literal><![CDATA[
      R(x,a(y,x,z) * K(y,x),(a(y,x,z) * K(y,x)) \ u) = ((a(y,x,z) * x) * (a(y,x,z) \ u)) / u
    ]]></literal>
    <justification jstring="[para(41796(a,1),43640(a,2,1,1))].">
      <j1 rule="para" parents="41796 43640"/>
    </justification>
  </clause>

  <clause id="43642">
    <literal><![CDATA[
      R(x,a(y,x,z) * K(y,x),(a(y,x,z) * K(y,x)) \ u) = L(x * u,x,a(y,x,z)) / u
    ]]></literal>
    <justification jstring="[para(43364(a,1),43641(a,2,1))].">
      <j1 rule="para" parents="43364 43641"/>
    </justification>
  </clause>

  <clause id="43643">
    <literal><![CDATA[
      R(x,a(y,x,z) * K(y,x),(a(y,x,z) * K(y,x)) \ u) = u \ L(u * x,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,5543,a(flip),b,43642,a),flip(a)].">
      <j1 rule="hyper" parents="373 5543 43642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43644">
    <literal><![CDATA[
      R(x,a(y,x,z) * K(y,x),(a(y,x,z) * K(y,x)) \ u) = u * L(u \ x,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,28865,a(flip),b,43643,a),flip(a)].">
      <j1 rule="hyper" parents="373 28865 43643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43645">
    <literal><![CDATA[
      R(x,a(y,x,z) * K(y,x),K(x,y) * (a(y,x,z) \ u)) = u * L(u \ x,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[para(23272(a,1),43644(a,1,3))].">
      <j1 rule="para" parents="23272 43644"/>
    </justification>
  </clause>

  <clause id="43646">
    <literal><![CDATA[
      R(x,a(y,x,z) * K(y,x),K(x,y) * (a(y,x,z) * u)) = u * L(u \ x,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42538,a(flip),b,43645,a)].">
      <j1 rule="hyper" parents="64 42538 43645"/>
    </justification>
  </clause>

  <clause id="43647">
    <literal><![CDATA[
      R(x,a(y,x,z) * K(y,x),a(y,x,z) * u) = u * L(u \ x,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26172,a(flip),b,43646,a)].">
      <j1 rule="hyper" parents="64 26172 43646"/>
    </justification>
  </clause>

  <clause id="43649">
    <literal><![CDATA[
      R(x,a(y,x,z),a(y,x,z) * u) = u * L(u \ x,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26421,a(flip),b,43647,a)].">
      <j1 rule="hyper" parents="64 26421 43647"/>
    </justification>
  </clause>

  <clause id="43651">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,y,u)) = y * a(x * y,y,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,43487,a(flip),b,43649,a),flip(a)].">
      <j1 rule="hyper" parents="64 43487 43649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43652">
    <literal><![CDATA[
      (a(x,y,z) \ ((x * y) * z)) * (((R(x,y,z) * y) * z) \ a(x,y,z)) = a(x,y,z) \ K((x * y) * z,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(42444(a,1),42132(a,1,1))].">
      <j1 rule="para" parents="42444 42132"/>
    </justification>
  </clause>

  <clause id="43653">
    <literal><![CDATA[
      (x * (y * z)) * (((R(x,y,z) * y) * z) \ a(x,y,z)) = a(x,y,z) \ K((x * y) * z,a(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(15467(a,1),43652(a,1,1))].">
      <j1 rule="para" parents="15467 43652"/>
    </justification>
  </clause>

  <clause id="43654">
    <literal><![CDATA[
      L(R(x,a(y,z,u) \ z,a(y,z,u) \ z),a(u,z,y),z) = a(y,z,u) \ (z * T(x * (a(y,z,u) / z),z))
    ]]></literal>
    <justification jstring="[para(40599(a,1),43426(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="40599 43426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43655">
    <literal><![CDATA[
      L(R(x,a(y,z,u) \ z,a(y,z,u) \ z),a(u,z,y),z) = a(y,z,u) \ ((x * (a(y,z,u) / z)) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,249,a(flip),b,43654,a),flip(a)].">
      <j1 rule="hyper" parents="373 249 43654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43656">
    <literal><![CDATA[
      ((R(x,y,z) * y) * z) \ ((1 / ((R(x,y,z) * y) * z)) \ a(x,y,z)) = ((a(x,y,z) / ((x * y) * z)) \ 1) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(42029(a,1),42133(a,1,2,1,2))].">
      <j1 rule="para" parents="42029 42133"/>
    </justification>
  </clause>

  <clause id="43657">
    <literal><![CDATA[
      L(a(x,y,L((1 / z) \ 1,u,w)),L(L(z \ 1,u,w) \ y,z,z),y) = L(L(1 / z,u,w) \ 1,y,x) \ (L(1 / z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(39638(a,2),43072(a,1,1))].">
      <j1 rule="para" parents="39638 43072"/>
    </justification>
  </clause>

  <clause id="43658">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(x,y,y),L(y \ x,y \ x,a(x,y,y))) = (L(y,y,x) \ x) \ (L(y \ x,y \ x,a(x,y,y)) * z)
    ]]></literal>
    <justification jstring="[para(37562(a,1),43084(a,2,1))].">
      <j1 rule="para" parents="37562 43084"/>
    </justification>
  </clause>

  <clause id="43659">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(x,y,y),L(y \ x,y \ x,a(x,y,y))) = (L(y,y,x) \ x) \ ((y \ x) * z)
    ]]></literal>
    <justification jstring="[para(30299(a,1),43658(a,2,2,1))].">
      <j1 rule="para" parents="30299 43658"/>
    </justification>
  </clause>

  <clause id="43660">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(x,y,y),L(y \ x,y \ x,a(x,y,y))) = (x * (1 / y)) \ ((x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27948,a(flip),b,43659,a),flip(a)].">
      <j1 rule="hyper" parents="373 27948 43659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43662">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(x,y,y),y \ x) = (x * (1 / y)) \ ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(30299(a,1),43660(a,1,3))].">
      <j1 rule="para" parents="30299 43660"/>
    </justification>
  </clause>

  <clause id="43663">
    <literal><![CDATA[
      L(a(x,y,y) \ z,y,a(y,x,x)) = (x * (1 / y)) \ ((x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41322,a(flip),b,43662,a)].">
      <j1 rule="hyper" parents="64 41322 43662"/>
    </justification>
  </clause>

  <clause id="43665">
    <literal><![CDATA[
      (R(x,y,y) * y) \ ((x * y) * z) = (x * (1 / y)) \ ((x / y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40952,a(flip),b,43663,a)].">
      <j1 rule="hyper" parents="64 40952 43663"/>
    </justification>
  </clause>

  <clause id="43666">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),L(L(z \ 1,u,w) \ y,z,z),y) = L(L(1 / z,u,w) \ 1,y,x) \ (L(1 / z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(82(a,1),43657(a,1,1,3,1))].">
      <j1 rule="para" parents="82 43657"/>
    </justification>
  </clause>

  <clause id="43667">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),(L(1 / z,u,w) \ 1) * y,y) = L(L(1 / z,u,w) \ 1,y,x) \ (L(1 / z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(35167(a,1),43666(a,1,2))].">
      <j1 rule="para" parents="35167 43666"/>
    </justification>
  </clause>

  <clause id="43668">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),L(1 / z,u,w) * y,y) = L(L(1 / z,u,w) \ 1,y,x) \ (L(1 / z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(29615,a,43667,a)].">
      <j1 rule="hyper" parents="29615 43667"/>
    </justification>
  </clause>

  <clause id="43669">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),L(z,u,w) * y,y) = L(L(1 / z,u,w) \ 1,y,x) \ (L(1 / z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,36706,a(flip),b,43668,a)].">
      <j1 rule="hyper" parents="64 36706 43668"/>
    </justification>
  </clause>

  <clause id="43670">
    <literal><![CDATA[
      L(L(1 / x,y,z) \ 1,u,w) \ (L(1 / x,y,z) \ 1) = L(L(x,y,z),u,w) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,43068,a(flip),b,43669,a),flip(a)].">
      <j1 rule="hyper" parents="64 43068 43669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43671">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(x,y,z) = L((1 / x) * L((1 / x) \ 1,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,9394,a(flip),b,43670,a),flip(a)].">
      <j1 rule="hyper" parents="64 9394 43670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43672">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(x,y,z) = L((1 / x) * L(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),43671(a,2,1,1,2,1))].">
      <j1 rule="para" parents="82 43671"/>
    </justification>
  </clause>

  <clause id="43673">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(x,y,z) = L(x \ L(x,u,w),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(5590(a,1),43672(a,2,1,1))].">
      <j1 rule="para" parents="5590 43672"/>
    </justification>
  </clause>

  <clause id="43674">
    <literal><![CDATA[
      L(L(x,x,y),z,u) \ L(x,x,y) = L(L(x,z,u) \ x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,43451,a(flip),b,43673,a),flip(a)].">
      <j1 rule="hyper" parents="373 43451 43673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43675">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,y,z),u,w) = L(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,9374,a,b,43673,a(flip))].">
      <j1 rule="hyper" parents="40 9374 43673"/>
    </justification>
  </clause>

  <clause id="43676">
    <literal><![CDATA[
      L(x,y,z) * (x \ L(x,u,z)) = L(L(x,y,z),u,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,33190,a(flip),b,43675,a)].">
      <j1 rule="hyper" parents="145 33190 43675"/>
    </justification>
  </clause>

  <clause id="43677">
    <literal><![CDATA[
      L(x,y,z) \ L(L(x,u,w),y,z) = L(x \ L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,175,a,b,43675,a)].">
      <j1 rule="hyper" parents="64 175 43675"/>
    </justification>
  </clause>

  <clause id="43678">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(L(z,u,w),v5,v6)) = L(x,y,L(z \ L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(43675(a,1),5608(a,1,3)),flip(a)].">
      <j1 rule="para" parents="43675 5608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43679">
    <literal><![CDATA[
      (x * (L(x,y,z) \ 1)) * L(L(x,y,z),u,w) = L(x \ L(x,u,w),y,z) * x
    ]]></literal>
    <justification jstring="[para(43675(a,1),27958(a,2,1))].">
      <j1 rule="para" parents="43675 27958"/>
    </justification>
  </clause>

  <clause id="43688">
    <literal><![CDATA[
      L(x,y,L(z,u,w) * L(L(z,u,w),v5,v6)) = L(x,y,L(z * L(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,29421,a(flip),b,43678,a),flip(a)].">
      <j1 rule="hyper" parents="373 29421 43678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43689">
    <literal><![CDATA[
      (x \ (x * (L(y,x,x) \ R(y,z,u)))) \ ((x \ (x * (y \ R(y,z,u)))) * y) = L(y,x,(x * y) \ ((y \ R(y,z,u)) * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),43207(a,2,3,2,1))].">
      <j1 rule="para" parents="9 43207"/>
    </justification>
  </clause>

  <clause id="43690">
    <literal><![CDATA[
      (x \ (x * (L(y,x,x) \ R(y,z,u)))) \ ((x \ (x * (y \ R(y,z,u)))) * y) = L(y,x,(x * y) \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,29026,a(flip),b,43689,a),flip(a)].">
      <j1 rule="hyper" parents="373 29026 43689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43693">
    <literal><![CDATA[
      (x \ (x * (L(y,x,x) \ R(y,z,u)))) \ ((x \ (x * (y \ R(y,z,u)))) * y) = L(y,x,(x * y) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,33124,a(flip),b,43690,a),flip(a)].">
      <j1 rule="hyper" parents="373 33124 43690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43694">
    <literal><![CDATA[
      (L(x,y,y) \ R(x,z,u)) \ ((y \ (y * (x \ R(x,z,u)))) * x) = L(x,y,(y * x) \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),43693(a,1,1))].">
      <j1 rule="para" parents="9 43693"/>
    </justification>
  </clause>

  <clause id="43695">
    <literal><![CDATA[
      (L(x,y,y) \ R(x,z,u)) \ ((x \ R(x,z,u)) * x) = L(x,y,(y * x) \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(9(a,1),43694(a,1,2,1))].">
      <j1 rule="para" parents="9 43694"/>
    </justification>
  </clause>

  <clause id="43698">
    <literal><![CDATA[
      (L(x,y,y) \ R(x,z,u)) \ R(x,z,u) = L(x,y,(y * x) \ L(x,z,u))
    ]]></literal>
    <justification jstring="[para(2069(a,1),43695(a,1,2))].">
      <j1 rule="para" parents="2069 43695"/>
    </justification>
  </clause>

  <clause id="43699">
    <literal><![CDATA[
      L(x,y,(y * x) \ L(x,z,u)) = (L(x,y,y) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,27068,a(flip),b,43698,a),flip(a)].">
      <j1 rule="hyper" parents="64 27068 43698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43701">
    <literal><![CDATA[
      L(x,y,(y * x) \ L(x,z,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,5559,a(flip),b,43699,a),flip(a)].">
      <j1 rule="hyper" parents="373 5559 43699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43702">
    <literal><![CDATA[
      L(x,y,(x \ L(x,z,u)) * y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41985,a(flip),b,43701,a)].">
      <j1 rule="hyper" parents="64 41985 43701"/>
    </justification>
  </clause>

  <clause id="43703">
    <literal><![CDATA[
      L(1 / L(x,y,z),1 / R(x,u,w),L(x,u,w) * L(x,y,z)) \ 1 = (1 / ((1 / R(x,u,w)) * (L(x,y,z) \ 1))) * (1 / R(x,u,w))
    ]]></literal>
    <justification jstring="[para(24665(a,1),42309(a,1,1))].">
      <j1 rule="para" parents="24665 42309"/>
    </justification>
  </clause>

  <clause id="43704">
    <literal><![CDATA[
      L(1 / L(x,y,z),R(x,u,w),L(x,u,w) * L(x,y,z)) \ 1 = (1 / ((1 / R(x,u,w)) * (L(x,y,z) \ 1))) * (1 / R(x,u,w))
    ]]></literal>
    <justification jstring="[para(11776(a,1),43703(a,1,1))].">
      <j1 rule="para" parents="11776 43703"/>
    </justification>
  </clause>

  <clause id="43705">
    <literal><![CDATA[
      L(1 / L(x,y,z),L(x,u,w),L(x,u,w) * L(x,y,z)) \ 1 = (1 / ((1 / R(x,u,w)) * (L(x,y,z) \ 1))) * (1 / R(x,u,w))
    ]]></literal>
    <justification jstring="[para(29794(a,1),43704(a,1,1))].">
      <j1 rule="para" parents="29794 43704"/>
    </justification>
  </clause>

  <clause id="43706">
    <literal><![CDATA[
      (1 / ((1 / R(x,y,z)) * (L(x,u,w) \ 1))) * (1 / R(x,y,z)) = (1 / (L(x,y,z) * (L(x,u,w) \ 1))) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,24009,a(flip),b,43705,a),flip(a)].">
      <j1 rule="hyper" parents="64 24009 43705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43707">
    <literal><![CDATA[
      (1 / ((1 / R(x,y,z)) * (L(x,u,w) \ 1))) * (1 / R(x,y,z)) = (1 / (L(x,u,w) \ L(x,y,z))) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1850(a,1),43706(a,2,1,2))].">
      <j1 rule="para" parents="1850 43706"/>
    </justification>
  </clause>

  <clause id="43708">
    <literal><![CDATA[
      (1 / ((1 / R(x,y,z)) * (L(x,u,w) \ 1))) * (1 / R(x,y,z)) = ((L(x,u,w) \ L(x,y,z)) \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(28370(a,1),43707(a,2,1))].">
      <j1 rule="para" parents="28370 43707"/>
    </justification>
  </clause>

  <clause id="43709">
    <literal><![CDATA[
      x * ((y \ ((1 / y) \ z)) * R(a(y,y,z) \ 1,x,y \ ((1 / y) \ z))) = (L(a(y,y,z) \ 1,z,x) * x) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(39728(a,1),30259(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="39728 30259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43710">
    <literal><![CDATA[
      x * ((y \ ((1 / y) \ z)) * R(a(y,y,z) \ 1,x,y \ ((1 / y) \ z))) = (L(z,y,y) * (z \ x)) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(33810(a,1),43709(a,2,1))].">
      <j1 rule="para" parents="33810 43709"/>
    </justification>
  </clause>

  <clause id="43711">
    <literal><![CDATA[
      x * ((y \ ((1 / y) \ z)) * R(a(y,y,z) \ 1,x,y \ ((y \ 1) \ z))) = (L(z,y,y) * (z \ x)) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(26278(a,1),43710(a,1,2,2))].">
      <j1 rule="para" parents="26278 43710"/>
    </justification>
  </clause>

  <clause id="43712">
    <literal><![CDATA[
      x * ((y \ ((1 / y) \ z)) * R(a(y,y,z) \ 1,x,L(z,y,y))) = (L(z,y,y) * (z \ x)) * (y \ ((1 / y) \ z))
    ]]></literal>
    <justification jstring="[para(38885(a,1),43711(a,1,2,2))].">
      <j1 rule="para" parents="38885 43711"/>
    </justification>
  </clause>

  <clause id="43713">
    <literal><![CDATA[
      (L(x,y,y) * (x \ z)) * (y \ ((1 / y) \ x)) = z * ((y \ ((1 / y) \ x)) * (a(y,y,x) \ 1))
    ]]></literal>
    <justification jstring="[para(38188(a,1),43712(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="38188 43712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43714">
    <literal><![CDATA[
      (L(x,y,y) * (x \ z)) * (y \ ((1 / y) \ x)) = z * (a(y,y,x) \ (y \ ((1 / y) \ x)))
    ]]></literal>
    <justification jstring="[para(37671(a,1),43713(a,2,2))].">
      <j1 rule="para" parents="37671 43713"/>
    </justification>
  </clause>

  <clause id="43716">
    <literal><![CDATA[
      (L(x,y,y) * (x \ z)) * (y \ ((1 / y) \ x)) = z * x
    ]]></literal>
    <justification jstring="[para(30239(a,1),43714(a,2,2))].">
      <j1 rule="para" parents="30239 43714"/>
    </justification>
  </clause>

  <clause id="43717">
    <literal><![CDATA[
      a(x,x,y) \ (L(z,(1 / x) \ y,a(x,x,y)) * L(x * y,a(x,x,y),a(x,x,y))) = (a(x,x,y) \ (1 * (x * y))) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(30041(a,1),30457(a,1,2,1,2))].">
      <j1 rule="para" parents="30041 30457"/>
    </justification>
  </clause>

  <clause id="43718">
    <literal><![CDATA[
      a(x,x,y) \ (L(z,x \ y,a(x,x,y)) * L(x * y,a(x,x,y),a(x,x,y))) = (a(x,x,y) \ (1 * (x * y))) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(29694(a,1),43717(a,1,2,1))].">
      <j1 rule="para" parents="29694 43717"/>
    </justification>
  </clause>

  <clause id="43719">
    <literal><![CDATA[
      R(x,y \ (z * (T(T(z,u),u) \ w)),(z \ y) \ (T(T(z,u),u) \ w)) = R(x,(z \ y) \ (T(T(z,u),u) \ w),(T(z,u) \ (y \ w)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26286,a(flip),b,34432,a),flip(a)].">
      <j1 rule="hyper" parents="64 26286 34432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43721">
    <literal><![CDATA[
      R(x,y \ (z * (T(T(z,u),u) \ w)),(z \ y) \ (T(T(z,u),u) \ w)) = R(x,(z \ y) \ (T(T(z,u),u) \ w),(z \ (y \ w)) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,26216,a(flip),b,43719,a),flip(a)].">
      <j1 rule="hyper" parents="373 26216 43719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43723">
    <literal><![CDATA[
      R(x,y \ (z * (T(T(z,u),u) \ w)),(z \ y) \ (T(T(z,u),u) \ w)) = R(x,(z \ y) \ (T(T(z,u),u) \ w),y \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26165,a(flip),b,43721,a),flip(a)].">
      <j1 rule="hyper" parents="373 26165 43721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43725">
    <literal><![CDATA[
      R(x,y \ (z * (T(T(z,u),u) \ (w * w))),(z \ y) \ (T(T(z,u),u) \ (w * w))) = R(x,(z \ y) \ T(T(z,u),u),y \ (w * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,26710,a(flip),b,43723,a),flip(a)].">
      <j1 rule="hyper" parents="373 26710 43723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43726">
    <literal><![CDATA[
      R(x,y \ (z * (T(T(z,u),u) \ (w * w))),(z \ y) \ (T(T(z,u),u) \ (w * w))) = R(x,(z \ y) \ T(z,u),y \ (w * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,26422,a(flip),b,43725,a),flip(a)].">
      <j1 rule="hyper" parents="373 26422 43725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43728">
    <literal><![CDATA[
      R(x,y \ (z * (T(T(z,u),u) \ (w * w))),(z \ y) \ (T(T(z,u),u) \ (w * w))) = R(x,(z \ y) \ z,y \ (w * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,26422,a(flip),b,43726,a),flip(a)].">
      <j1 rule="hyper" parents="373 26422 43726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43730">
    <literal><![CDATA[
      R(x,y \ (z * (T(T(z,u),u) \ (w * w))),(z \ y) \ (T(T(z,u),u) \ (w * w))) = R(x,(y \ z) * z,y \ (w * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,26574,a(flip),b,43728,a),flip(a)].">
      <j1 rule="hyper" parents="373 26574 43728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43731">
    <literal><![CDATA[
      R(x,y * (T(T(y,z),z) \ (u \ (w * w))),(y \ u) \ (T(T(y,z),z) \ (w * w))) = R(x,(u \ y) * y,u \ (w * w))
    ]]></literal>
    <justification jstring="[para(22835(a,1),43730(a,1,2))].">
      <j1 rule="para" parents="22835 43730"/>
    </justification>
  </clause>

  <clause id="43732">
    <literal><![CDATA[
      R(x,y * (T(T(y,z),z) \ (u \ (w * w))),(y \ u) \ (T(y,z) \ (w * w))) = R(x,(u \ y) * y,u \ (w * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,26269,a(flip),b,43731,a)].">
      <j1 rule="hyper" parents="64 26269 43731"/>
    </justification>
  </clause>

  <clause id="43734">
    <literal><![CDATA[
      R(x,y * (T(T(y,z),z) \ (u \ (w * w))),(y \ u) \ (y \ (w * w))) = R(x,(u \ y) * y,u \ (w * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,26269,a(flip),b,43732,a)].">
      <j1 rule="hyper" parents="64 26269 43732"/>
    </justification>
  </clause>

  <clause id="43736">
    <literal><![CDATA[
      R(x,(T(y,z) \ (u \ (w * w))) * y,(y \ u) \ (y \ (w * w))) = R(x,(u \ y) * y,u \ (w * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,26550,a(flip),b,43734,a)].">
      <j1 rule="hyper" parents="64 26550 43734"/>
    </justification>
  </clause>

  <clause id="43738">
    <literal><![CDATA[
      R(x,(y \ (z \ (u * u))) * y,(y \ z) \ (y \ (u * u))) = R(x,(z \ y) * y,z \ (u * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,26431,a(flip),b,43736,a)].">
      <j1 rule="hyper" parents="64 26431 43736"/>
    </justification>
  </clause>

  <clause id="43739">
    <literal><![CDATA[
      R(x,y \ (z * z),(u \ y) \ (u \ (z * z))) = R(x,(y \ u) * u,y \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26415,a(flip),b,43738,a)].">
      <j1 rule="hyper" parents="64 26415 43738"/>
    </justification>
  </clause>

  <clause id="43741">
    <literal><![CDATA[
      R(x,(y \ z) * z,y \ (u * u)) = R(x,y,(z \ y) \ (z \ (u * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,26591,a(flip),b,43739,a),flip(a)].">
      <j1 rule="hyper" parents="64 26591 43739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43743">
    <literal><![CDATA[
      R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = R(x,z,(y \ z) \ (y \ (y * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,43591,a,b,43741,a)].">
      <j1 rule="hyper" parents="64 43591 43741"/>
    </justification>
  </clause>

  <clause id="43744">
    <literal><![CDATA[
      R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = R(x,z,(y \ z) \ y)
    ]]></literal>
    <justification jstring="[para(9(a,1),43743(a,2,3,2))].">
      <j1 rule="para" parents="9 43743"/>
    </justification>
  </clause>

  <clause id="43745">
    <literal><![CDATA[
      R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = R(x,z,(z \ y) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,26314,a(flip),b,43744,a),flip(a)].">
      <j1 rule="hyper" parents="373 26314 43744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43746">
    <literal><![CDATA[
      a((x * a(y,z,x)) * (u \ ((y \ a(y,z,x)) * x)),x,x) = a(u \ (y \ 1),x * a(y,z,x),x * a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,43024,a(flip),b,36882,a)].">
      <j1 rule="hyper" parents="64 43024 36882"/>
    </justification>
  </clause>

  <clause id="43748">
    <literal><![CDATA[
      a(x * ((y \ ((z \ a(z,u,x)) * x)) * a(z,u,x)),x,x) = a(y \ (z \ 1),x * a(z,u,x),x * a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,37901,a(flip),b,43746,a)].">
      <j1 rule="hyper" parents="64 37901 43746"/>
    </justification>
  </clause>

  <clause id="43749">
    <literal><![CDATA[
      a(x \ (y \ 1),z * a(y,u,z),z * a(y,u,z)) = a(z * (x \ ((y \ a(y,u,z)) * z)),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37897,a(flip),b,43748,a),flip(a)].">
      <j1 rule="hyper" parents="64 37897 43748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43751">
    <literal><![CDATA[
      a(x \ (y \ 1),z * a(y,u,z),z * a(y,u,z)) = a(x \ (y \ a(y,u,z)),z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,36881,a(flip),b,43749,a),flip(a)].">
      <j1 rule="hyper" parents="373 36881 43749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43752">
    <literal><![CDATA[
      a(x \ (y \ 1),z * a(y,u,z),z * a(y,u,z)) = a(x \ (y * a(y,u,z)),z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,26922,a(flip),b,43751,a),flip(a)].">
      <j1 rule="hyper" parents="373 26922 43751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43753">
    <literal><![CDATA[
      a(x \ (y * a(y,z,u)),u,u) = a(x \ (y \ 1),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,43024,a(flip),b,43752,a),flip(a)].">
      <j1 rule="hyper" parents="64 43024 43752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43755">
    <literal><![CDATA[
      a(x \ (y * a(y,z,u)),u,u) = a(x \ y,u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26855,a(flip),b,43753,a),flip(a)].">
      <j1 rule="hyper" parents="373 26855 43753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43756">
    <literal><![CDATA[
      R(T((T(x * y,z) \ x) \ 1,(x \ z) * ((x * y) / T(z,y * x))),T(x * y,z) \ x,K(y * x,z)) = L(y \ 1,y,x) \ K(y * x,z)
    ]]></literal>
    <justification jstring="[para(26964(a,1),41581(a,1,1))].">
      <j1 rule="para" parents="26964 41581"/>
    </justification>
  </clause>

  <clause id="43757">
    <literal><![CDATA[
      R(1 / (1 / (x / y)),1 / (y / x),z * ((x \ y) \ 1)) * L(z,1 / (y / x),1 / (y / x)) = ((x / y) * (y / x)) * ((1 / (y / x)) * z)
    ]]></literal>
    <justification jstring="[para(26275(a,1),41582(a,1,1))].">
      <j1 rule="para" parents="26275 41582"/>
    </justification>
  </clause>

  <clause id="43758">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) * a(v5,v5,a(v6,L(a(x,y,z),u,w),L(a(x,y,z),u,w))) = L(a(x,y,z),u,w) \ L(L(a(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,23785,a(flip),b,43222,a),flip(a)].">
      <j1 rule="hyper" parents="373 23785 43222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43759">
    <literal><![CDATA[
      R(T((T(x * y,z) \ x) \ 1,(x \ z) * (x * (T(z,x) \ y))),T(x * y,z) \ x,K(y * x,z)) = L(y \ 1,y,x) \ K(y * x,z)
    ]]></literal>
    <justification jstring="[para(36606(a,1),43756(a,1,1))].">
      <j1 rule="para" parents="36606 43756"/>
    </justification>
  </clause>

  <clause id="43760">
    <literal><![CDATA[
      R(T((T(x * y,z) \ x) \ 1,(x \ z) * ((z \ x) * y)),T(x * y,z) \ x,K(y * x,z)) = L(y \ 1,y,x) \ K(y * x,z)
    ]]></literal>
    <justification jstring="[para(28593(a,1),43759(a,1,1))].">
      <j1 rule="para" parents="28593 43759"/>
    </justification>
  </clause>

  <clause id="43761">
    <literal><![CDATA[
      R(T((T(x * y,z) \ x) \ 1,(x \ x) * y),T(x * y,z) \ x,K(y * x,z)) = L(y \ 1,y,x) \ K(y * x,z)
    ]]></literal>
    <justification jstring="[para(28457(a,1),43760(a,1,1))].">
      <j1 rule="para" parents="28457 43760"/>
    </justification>
  </clause>

  <clause id="43762">
    <literal><![CDATA[
      R(T((T(x * y,z) \ x) \ 1,y),T(x * y,z) \ x,K(y * x,z)) = L(y \ 1,y,x) \ K(y * x,z)
    ]]></literal>
    <justification jstring="[para(190(a,1),43761(a,1,1,2))].">
      <j1 rule="para" parents="190 43761"/>
    </justification>
  </clause>

  <clause id="43764">
    <literal><![CDATA[
      L(x \ 1,x,y) \ K(x * y,z) = T((T(y * x,z) \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(23316,a,43762,a),flip(a)].">
      <j1 rule="hyper" parents="23316 43762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43766">
    <literal><![CDATA[
      x * T((T(y * x,x * x) \ y) \ 1,x) = ((y / x) / (y * x)) \ 1
    ]]></literal>
    <justification jstring="[para(43764(a,1),40260(a,1,2))].">
      <j1 rule="para" parents="43764 40260"/>
    </justification>
  </clause>

  <clause id="43767">
    <literal><![CDATA[
      x * T((y / T(y * x,x)) \ 1,x) = ((y / x) / (y * x)) \ 1
    ]]></literal>
    <justification jstring="[para(38821(a,1),43766(a,1,2,1,1))].">
      <j1 rule="para" parents="38821 43766"/>
    </justification>
  </clause>

  <clause id="43768">
    <literal><![CDATA[
      x * ((y / T(y * x,x)) \ 1) = ((y / x) / (y * x)) \ 1
    ]]></literal>
    <justification jstring="[para(31577(a,1),43767(a,1,2))].">
      <j1 rule="para" parents="31577 43767"/>
    </justification>
  </clause>

  <clause id="43769">
    <literal><![CDATA[
      ((x / y) / (x * y)) \ 1 = x / ((x / y) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35312,a(flip),b,43768,a),flip(a)].">
      <j1 rule="hyper" parents="64 35312 43768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43770">
    <literal><![CDATA[
      (x / y) / (x * y) = x / ((x * y) * y)
    ]]></literal>
    <justification jstring="[hyper(40,a,40386,a,b,43769,a),flip(a)].">
      <j1 rule="hyper" parents="40 40386 43769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43771">
    <literal><![CDATA[
      ((x / y) / (x * y)) * K(x,y) = x / ((y * x) * y)
    ]]></literal>
    <justification jstring="[para(43770(a,2),24495(a,1,1))].">
      <j1 rule="para" parents="43770 24495"/>
    </justification>
  </clause>

  <clause id="43772">
    <literal><![CDATA[
      (x / y) / (y * x) = x / ((y * x) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,10595,a(flip),b,43771,a)].">
      <j1 rule="hyper" parents="64 10595 43771"/>
    </justification>
  </clause>

  <clause id="43773">
    <literal><![CDATA[
      ((x / y) / x) / y = x / ((y * x) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,40202,a,b,43772,a)].">
      <j1 rule="hyper" parents="64 40202 43772"/>
    </justification>
  </clause>

  <clause id="43774">
    <literal><![CDATA[
      x \ (1 / (1 / ((y / x) / y))) = y / ((x * y) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33790,a,b,43773,a)].">
      <j1 rule="hyper" parents="64 33790 43773"/>
    </justification>
  </clause>

  <clause id="43775">
    <literal><![CDATA[
      R(x / (y / ((z * y) * z)),z \ ((y / z) / y),z) = (x * z) / ((y / z) / y)
    ]]></literal>
    <justification jstring="[para(43773(a,1),10218(a,1,1,2))].">
      <j1 rule="para" parents="43773 10218"/>
    </justification>
  </clause>

  <clause id="43776">
    <literal><![CDATA[
      (x / ((y * x) * y)) \ ((1 / y) * z) = ((x / y) / x) \ L(z,y,y)
    ]]></literal>
    <justification jstring="[para(43774(a,1),38032(a,1,1))].">
      <j1 rule="para" parents="43774 38032"/>
    </justification>
  </clause>

  <clause id="43777">
    <literal><![CDATA[
      L((x / ((y * x) * y)) \ z,((x / y) / x) * y,(1 / y) \ ((x / y) / x)) = (1 / ((1 / (1 / y)) \ ((x / y) / x))) * z
    ]]></literal>
    <justification jstring="[para(43774(a,1),40640(a,1,1,1))].">
      <j1 rule="para" parents="43774 40640"/>
    </justification>
  </clause>

  <clause id="43778">
    <literal><![CDATA[
      R(x / (y / ((z * y) * z)),z \ (y \ (y / z)),z) = (x * z) / ((y / z) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26506,a(flip),b,43775,a)].">
      <j1 rule="hyper" parents="64 26506 43775"/>
    </justification>
  </clause>

  <clause id="43779">
    <literal><![CDATA[
      R(x / (y / ((z * y) * z)),z \ (y \ (z \ y)),z) = (x * z) / ((y / z) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26510,a(flip),b,43778,a)].">
      <j1 rule="hyper" parents="64 26510 43778"/>
    </justification>
  </clause>

  <clause id="43780">
    <literal><![CDATA[
      R(x / (y / ((z * y) * z)),a(y,z,z),z) = (x * z) / ((y / z) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,30609,a(flip),b,43779,a)].">
      <j1 rule="hyper" parents="64 30609 43779"/>
    </justification>
  </clause>

  <clause id="43781">
    <literal><![CDATA[
      L(x / (y / ((z * y) * z)),z,a(z,z,y)) = (x * z) / ((y / z) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31817,a(flip),b,43780,a)].">
      <j1 rule="hyper" parents="64 31817 43780"/>
    </justification>
  </clause>

  <clause id="43782">
    <literal><![CDATA[
      (x * y) / ((z / y) / z) = x / (z / ((y * z) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,37534,a(flip),b,43781,a),flip(a)].">
      <j1 rule="hyper" parents="64 37534 43781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43784">
    <literal><![CDATA[
      1 / (x / ((y * x) * y)) = y / ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(332,a,43782,a),flip(a)].">
      <j1 rule="hyper" parents="332 43782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43785">
    <literal><![CDATA[
      L((x / ((y * x) * y)) \ z,((x / y) / x) * y,((x / y) / x) * y) = (1 / ((1 / (1 / y)) \ ((x / y) / x))) * z
    ]]></literal>
    <justification jstring="[para(31492(a,1),43777(a,1,3))].">
      <j1 rule="para" parents="31492 43777"/>
    </justification>
  </clause>

  <clause id="43786">
    <literal><![CDATA[
      L((x / ((y * x) * y)) \ z,((x / y) / x) * y,(x \ (x / y)) * y) = (1 / ((1 / (1 / y)) \ ((x / y) / x))) * z
    ]]></literal>
    <justification jstring="[hyper(29066,a,43785,a)].">
      <j1 rule="hyper" parents="29066 43785"/>
    </justification>
  </clause>

  <clause id="43787">
    <literal><![CDATA[
      L((x / ((y * x) * y)) \ z,((x / y) / x) * y,a(x,y,y) \ 1) = (1 / ((1 / (1 / y)) \ ((x / y) / x))) * z
    ]]></literal>
    <justification jstring="[para(30493(a,1),43786(a,1,3))].">
      <j1 rule="para" parents="30493 43786"/>
    </justification>
  </clause>

  <clause id="43788">
    <literal><![CDATA[
      L((x / ((y * x) * y)) \ z,((x / y) / x) * y,a(x,y,y)) = (1 / ((1 / (1 / y)) \ ((x / y) / x))) * z
    ]]></literal>
    <justification jstring="[hyper(2275,a,43787,a)].">
      <j1 rule="hyper" parents="2275 43787"/>
    </justification>
  </clause>

  <clause id="43789">
    <literal><![CDATA[
      L((x / ((y * x) * y)) \ z,(x \ (x / y)) * y,a(x,y,y)) = (1 / ((1 / (1 / y)) \ ((x / y) / x))) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,29443,a(flip),b,43788,a)].">
      <j1 rule="hyper" parents="64 29443 43788"/>
    </justification>
  </clause>

  <clause id="43790">
    <literal><![CDATA[
      L((x / ((y * x) * y)) \ z,a(x,y,y) \ 1,a(x,y,y)) = (1 / ((1 / (1 / y)) \ ((x / y) / x))) * z
    ]]></literal>
    <justification jstring="[para(30493(a,1),43789(a,1,2))].">
      <j1 rule="para" parents="30493 43789"/>
    </justification>
  </clause>

  <clause id="43791">
    <literal><![CDATA[
      L((x / ((y * x) * y)) \ z,a(x,y,y),a(x,y,y)) = (1 / ((1 / (1 / y)) \ ((x / y) / x))) * z
    ]]></literal>
    <justification jstring="[hyper(11853,a,43790,a)].">
      <j1 rule="hyper" parents="11853 43790"/>
    </justification>
  </clause>

  <clause id="43792">
    <literal><![CDATA[
      (1 / ((1 / (1 / x)) \ ((y / x) / y))) * z = (y / ((x * y) * x)) \ z
    ]]></literal>
    <justification jstring="[hyper(42458,a,43791,a),flip(a)].">
      <j1 rule="hyper" parents="42458 43791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43795">
    <literal><![CDATA[
      (1 / (x \ ((y / (1 / (1 / x))) / y))) * z = (y / ((x * y) * x)) \ z
    ]]></literal>
    <justification jstring="[para(3957(a,1),43792(a,1,1,2))].">
      <j1 rule="para" parents="3957 43792"/>
    </justification>
  </clause>

  <clause id="43796">
    <literal><![CDATA[
      (1 / (x \ (1 / (1 / ((y / x) / y))))) * z = (y / ((x * y) * x)) \ z
    ]]></literal>
    <justification jstring="[para(3946(a,1),43795(a,1,1,2,2))].">
      <j1 rule="para" parents="3946 43795"/>
    </justification>
  </clause>

  <clause id="43797">
    <literal><![CDATA[
      (1 / (x / ((y * x) * y))) * z = (x / ((y * x) * y)) \ z
    ]]></literal>
    <justification jstring="[para(43774(a,1),43796(a,1,1,2))].">
      <j1 rule="para" parents="43774 43796"/>
    </justification>
  </clause>

  <clause id="43798">
    <literal><![CDATA[
      (x / ((y * x) * y)) \ z = (y / ((x / y) / x)) * z
    ]]></literal>
    <justification jstring="[para(43784(a,1),43797(a,1,1)),flip(a)].">
      <j1 rule="para" parents="43784 43797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43799">
    <literal><![CDATA[
      (x / ((y * x) * y)) \ z = y * (((x / y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,40343,a(flip),b,43798,a),flip(a)].">
      <j1 rule="hyper" parents="373 40343 43798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43800">
    <literal><![CDATA[
      x * (((y / x) / y) \ ((1 / x) * z)) = ((y / x) / y) \ L(z,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,43776,a(flip),b,43799,a),flip(a)].">
      <j1 rule="hyper" parents="64 43776 43799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43801">
    <literal><![CDATA[
      x * ((((y / x) / y) * x) \ z) = ((y / x) / y) \ L(z,x,x)
    ]]></literal>
    <justification jstring="[para(37915(a,1),43800(a,1,2))].">
      <j1 rule="para" parents="37915 43800"/>
    </justification>
  </clause>

  <clause id="43802">
    <literal><![CDATA[
      ((x / y) / x) \ L(z,y,y) = (((x / y) / x) \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,40358,a(flip),b,43801,a),flip(a)].">
      <j1 rule="hyper" parents="64 40358 43801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43803">
    <literal><![CDATA[
      (a(x,y,z) / y) \ L(u,x \ ((x * (y * z)) / z),x \ ((x * (y * z)) / z)) = (((y / (x \ ((x * (y * z)) / z))) / y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(33338(a,2),43802(a,1,1,1))].">
      <j1 rule="para" parents="33338 43802"/>
    </justification>
  </clause>

  <clause id="43804">
    <literal><![CDATA[
      (a(x,y,z) / y) \ L(u,x \ ((x * (y * z)) / z),x \ (z \ (x * (y * z)))) = (((y / (x \ ((x * (y * z)) / z))) / y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(29023(a,1),43803(a,1,2))].">
      <j1 rule="para" parents="29023 43803"/>
    </justification>
  </clause>

  <clause id="43805">
    <literal><![CDATA[
      (a(x,y,z) / y) \ L(u,x \ (z \ (x * (y * z))),x \ (z \ (x * (y * z)))) = (((y / (x \ ((x * (y * z)) / z))) / y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(29552(a,1),43804(a,1,2))].">
      <j1 rule="para" parents="29552 43804"/>
    </justification>
  </clause>

  <clause id="43806">
    <literal><![CDATA[
      (a(x,y,z) / y) \ L(u,(x * (y * z)) * (z * x),(x * (y * z)) * (z * x)) = (((y / (x \ ((x * (y * z)) / z))) / y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(35242(a,1),43805(a,1,2))].">
      <j1 rule="para" parents="35242 43805"/>
    </justification>
  </clause>

  <clause id="43807">
    <literal><![CDATA[
      (a(x,y,z) / y) \ L(u,(y * z) * (x \ (z * x)),(y * z) * (x \ (z * x))) = (((y / (x \ ((x * (y * z)) / z))) / y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(35254(a,1),43806(a,1,2))].">
      <j1 rule="para" parents="35254 43806"/>
    </justification>
  </clause>

  <clause id="43808">
    <literal><![CDATA[
      (a(x,y,z) / y) \ L(u,(y * z) * T(z,x),(y * z) * (x \ (z * x))) = (((y / (x \ ((x * (y * z)) / z))) / y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(22(a,2),43807(a,1,2,2,2))].">
      <j1 rule="para" parents="22 43807"/>
    </justification>
  </clause>

  <clause id="43809">
    <literal><![CDATA[
      (a(x,y,z) / y) \ L(u,(y * z) * T(z,x),(y * z) * T(z,x)) = (((y / (x \ ((x * (y * z)) / z))) / y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(22(a,2),43808(a,1,2,3,2))].">
      <j1 rule="para" parents="22 43808"/>
    </justification>
  </clause>

  <clause id="43810">
    <literal><![CDATA[
      (a(x,y,z) / y) \ L(u,(y * z) * T(z,x),(y * z) * z) = (((y / (x \ ((x * (y * z)) / z))) / y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(28983(a,1),43809(a,1,2))].">
      <j1 rule="para" parents="28983 43809"/>
    </justification>
  </clause>

  <clause id="43811">
    <literal><![CDATA[
      (a(x,y,z) / y) \ L(u,(y * z) * T(z,x),L(y,z,z)) = (((y / (x \ ((x * (y * z)) / z))) / y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(24838(a,1),43810(a,1,2))].">
      <j1 rule="para" parents="24838 43810"/>
    </justification>
  </clause>

  <clause id="43813">
    <literal><![CDATA[
      (a(x,y,z) / y) \ L(u,L(y,z,z),L(y,z,z)) = (((y / (x \ ((x * (y * z)) / z))) / y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(29649(a,1),43811(a,1,2))].">
      <j1 rule="para" parents="29649 43811"/>
    </justification>
  </clause>

  <clause id="43815">
    <literal><![CDATA[
      (a(x,y,z) / y) \ L(u,y,y) = (((y / (x \ ((x * (y * z)) / z))) / y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(35161(a,1),43813(a,1,2))].">
      <j1 rule="para" parents="35161 43813"/>
    </justification>
  </clause>

  <clause id="43816">
    <literal><![CDATA[
      (a(x,y,z) / y) \ L(u,y,y) = ((a(x,y,z) / y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(33338(a,2),43815(a,2,1,1,1))].">
      <j1 rule="para" parents="33338 43815"/>
    </justification>
  </clause>

  <clause id="43818">
    <literal><![CDATA[
      (a(x,y,z) / y) \ L(u,y,y) = (a(x,y,z) \ y) * u
    ]]></literal>
    <justification jstring="[para(35788(a,1),43816(a,2,1))].">
      <j1 rule="para" parents="35788 43816"/>
    </justification>
  </clause>

  <clause id="43819">
    <literal><![CDATA[
      (a(x,y,z) / y) \ ((1 / y) * u) = (a(x,y,z) \ y) * (y \ u)
    ]]></literal>
    <justification jstring="[para(569(a,1),43818(a,1,2))].">
      <j1 rule="para" parents="569 43818"/>
    </justification>
  </clause>

  <clause id="43820">
    <literal><![CDATA[
      (a(x,y,z) * ((a(x,y,z) / y) \ L(u,y,y))) / u = a(a(x,y,z),y * a(x,y,z),u) \ y
    ]]></literal>
    <justification jstring="[para(43818(a,2),35707(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="43818 35707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43821">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),y * a(x,y,z)) = y \ ((a(x,y,z) / y) \ L(u,y,y))
    ]]></literal>
    <justification jstring="[para(43818(a,2),41989(a,2,2))].">
      <j1 rule="para" parents="43818 41989"/>
    </justification>
  </clause>

  <clause id="43822">
    <literal><![CDATA[
      (x \ a(y,x,z)) \ ((x \ 1) * u) = (a(y,x,z) \ x) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26934,a(flip),b,43819,a)].">
      <j1 rule="hyper" parents="64 26934 43819"/>
    </justification>
  </clause>

  <clause id="43823">
    <literal><![CDATA[
      (x \ a(y,x,z)) \ ((x \ 1) * u) = (u / x) * (a(y,x,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,28765,a(flip),b,43822,a),flip(a)].">
      <j1 rule="hyper" parents="373 28765 43822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43824">
    <literal><![CDATA[
      (a(x,y,z) * y) \ (y * u) = (u / y) * (a(x,y,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35763,a(flip),b,43823,a)].">
      <j1 rule="hyper" parents="64 35763 43823"/>
    </justification>
  </clause>

  <clause id="43825">
    <literal><![CDATA[
      (x * a(y,x,z)) \ (x * u) = (u / x) * (a(y,x,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(23963,a,43824,a)].">
      <j1 rule="hyper" parents="23963 43824"/>
    </justification>
  </clause>

  <clause id="43826">
    <literal><![CDATA[
      (a(x,y,z) * ((a(x,y,z) / y) \ L(u,y,y))) / u = a(u,y,a(x,y,z)) \ y
    ]]></literal>
    <justification jstring="[para(42834(a,1),43820(a,2,1))].">
      <j1 rule="para" parents="42834 43820"/>
    </justification>
  </clause>

  <clause id="43827">
    <literal><![CDATA[
      (a(x,y,z) * ((a(x,y,z) / y) \ L(u,y,y))) / u = a(u,y,a(z,y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,42644,a(flip),b,43826,a),flip(a)].">
      <j1 rule="hyper" parents="373 42644 43826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43828">
    <literal><![CDATA[
      (a(x,y,z) * ((a(x,y,z) / y) \ L(u,y,y))) / u = y * a(u,y,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,23136,a(flip),b,43827,a),flip(a)].">
      <j1 rule="hyper" parents="373 23136 43827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43829">
    <literal><![CDATA[
      R(1 / (1 / (x / y)),y / x,z * ((x \ y) \ 1)) * L(z,1 / (y / x),1 / (y / x)) = ((x / y) * (y / x)) * ((1 / (y / x)) * z)
    ]]></literal>
    <justification jstring="[para(2968(a,1),43757(a,1,1))].">
      <j1 rule="para" parents="2968 43757"/>
    </justification>
  </clause>

  <clause id="43830">
    <literal><![CDATA[
      R(1 / (1 / (x / y)),x \ y,z * ((x \ y) \ 1)) * L(z,1 / (y / x),1 / (y / x)) = ((x / y) * (y / x)) * ((1 / (y / x)) * z)
    ]]></literal>
    <justification jstring="[para(26410(a,1),43829(a,1,1))].">
      <j1 rule="para" parents="26410 43829"/>
    </justification>
  </clause>

  <clause id="43831">
    <literal><![CDATA[
      R(1 / (1 / (x / y)),x \ y,z * ((x \ y) \ 1)) * L(z,1 / (y / x),y / x) = ((x / y) * (y / x)) * ((1 / (y / x)) * z)
    ]]></literal>
    <justification jstring="[para(1643(a,1),43830(a,1,2))].">
      <j1 rule="para" parents="1643 43830"/>
    </justification>
  </clause>

  <clause id="43832">
    <literal><![CDATA[
      R(1 / (1 / (x / y)),x \ y,z * ((x \ y) \ 1)) * L(z,1 / (y / x),x \ y) = ((x / y) * (y / x)) * ((1 / (y / x)) * z)
    ]]></literal>
    <justification jstring="[para(23216(a,1),43831(a,1,2))].">
      <j1 rule="para" parents="23216 43831"/>
    </justification>
  </clause>

  <clause id="43833">
    <literal><![CDATA[
      R(1 / (1 / (x / y)),x \ y,z * ((x \ y) \ 1)) * L(z,y / x,x \ y) = ((x / y) * (y / x)) * ((1 / (y / x)) * z)
    ]]></literal>
    <justification jstring="[para(11776(a,1),43832(a,1,2))].">
      <j1 rule="para" parents="11776 43832"/>
    </justification>
  </clause>

  <clause id="43834">
    <literal><![CDATA[
      R(1 / (1 / (x / y)),x \ y,z * ((x \ y) \ 1)) * L(z,x \ y,x \ y) = ((x / y) * (y / x)) * ((1 / (y / x)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29529,a(flip),b,43833,a)].">
      <j1 rule="hyper" parents="64 29529 43833"/>
    </justification>
  </clause>

  <clause id="43835">
    <literal><![CDATA[
      ((1 / (1 / (x / y))) * (x \ y)) * (((x \ y) \ 1) * z) = ((x / y) * (y / x)) * ((1 / (y / x)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26202,a(flip),b,43834,a)].">
      <j1 rule="hyper" parents="64 26202 43834"/>
    </justification>
  </clause>

  <clause id="43836">
    <literal><![CDATA[
      ((x / y) * (y / x)) * ((1 / (y / x)) * z) = ((x \ y) * (x / y)) * (((x \ y) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3822(a,1),43835(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3822 43835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43837">
    <literal><![CDATA[
      ((x \ y) * (x / y)) * (((x \ y) \ 1) * z) = (x / y) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,37936,a(flip),b,43836,a),flip(a)].">
      <j1 rule="hyper" parents="64 37936 43836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43838">
    <literal><![CDATA[
      ((x / (y / x)) \ y) * z = (y / x) * ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40285,a(flip),b,43837,a)].">
      <j1 rule="hyper" parents="64 40285 43837"/>
    </justification>
  </clause>

  <clause id="43839">
    <literal><![CDATA[
      (x \ (y / (x / y))) \ z = (x / y) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40295,a,b,43838,a)].">
      <j1 rule="hyper" parents="64 40295 43838"/>
    </justification>
  </clause>

  <clause id="43840">
    <literal><![CDATA[
      L((x \ 1) \ (((x \ y) * y) \ z),x,L(x,y,y)) = (x / y) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,39819,a,b,43839,a)].">
      <j1 rule="hyper" parents="64 39819 43839"/>
    </justification>
  </clause>

  <clause id="43841">
    <literal><![CDATA[
      L(x * (((x \ y) * y) \ z),x,a(y,y,x)) = (x / y) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37954,a(flip),b,43840,a)].">
      <j1 rule="hyper" parents="64 37954 43840"/>
    </justification>
  </clause>

  <clause id="43842">
    <literal><![CDATA[
      (x / y) * ((x \ y) \ (((x \ y) * y) * z)) = L(x * z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(9(a,1),43841(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 43841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43843">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) * a(v5,v5,a(v6,L(a(x,y,z),u,w),L(a(x,y,z),u,w))) = L(a(x,y,z) \ L(a(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,43677,a(flip),b,43758,a),flip(a)].">
      <j1 rule="hyper" parents="373 43677 43758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43844">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) * a(v5,v5,a(v6,L(a(x,y,z),u,w),L(a(x,y,z),u,w))) = L(a(a(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(42679(a,1),43843(a,2,1))].">
      <j1 rule="para" parents="42679 43843"/>
    </justification>
  </clause>

  <clause id="43845">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) * a(v5,v5,a(v6,a(x,y,z),a(x,y,z))) = L(a(a(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(40664(a,1),43844(a,1,2,3))].">
      <j1 rule="para" parents="40664 43844"/>
    </justification>
  </clause>

  <clause id="43847">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) * a(v5,v5,1) = L(a(a(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(42485(a,1),43845(a,1,2,3))].">
      <j1 rule="para" parents="42485 43845"/>
    </justification>
  </clause>

  <clause id="43848">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) * 1 = L(a(a(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[para(427(a,1),43847(a,1,2))].">
      <j1 rule="para" parents="427 43847"/>
    </justification>
  </clause>

  <clause id="43850">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) = L(a(a(x,y,z),v5,v6),u,w)
    ]]></literal>
    <justification jstring="[hyper(152,a,43848,a)].">
      <j1 rule="hyper" parents="152 43848"/>
    </justification>
  </clause>

  <clause id="43851">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) = L(a(v6,v5,a(z,y,x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(141,a,43848,a,b,42193,a(flip))].">
      <j1 rule="hyper" parents="141 43848 42193"/>
    </justification>
  </clause>

  <clause id="43854">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),z,v5) = L(a(z,a(x,y,z),v5),u,w)
    ]]></literal>
    <justification jstring="[para(33522(a,1),43850(a,2,1))].">
      <j1 rule="para" parents="33522 43850"/>
    </justification>
  </clause>

  <clause id="43855">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),v5,v6) = L(a(v6,v5,a(x,y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(41803(a,1),43850(a,2,1))].">
      <j1 rule="para" parents="41803 43850"/>
    </justification>
  </clause>

  <clause id="43856">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),x,v5) = a(x,a(x,y,z),L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,41463,a,b,43851,a),flip(a)].">
      <j1 rule="hyper" parents="373 41463 43851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43857">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),z,v5) = a(z,a(x,y,z),L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,42769,a,b,43854,a),flip(a)].">
      <j1 rule="hyper" parents="373 42769 43854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43858">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),z,v5) = a(z,a(z,y,x),L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,41463,a,b,43855,a),flip(a)].">
      <j1 rule="hyper" parents="373 41463 43855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43861">
    <literal><![CDATA[
      a(x,L(a(y,z,u),w,v5),y) \ v6 = a(y,a(y,z,u),L(x,w,v5)) * v6
    ]]></literal>
    <justification jstring="[para(43856(a,1),42895(a,2,1))].">
      <j1 rule="para" parents="43856 42895"/>
    </justification>
  </clause>

  <clause id="43862">
    <literal><![CDATA[
      a(x,a(x,y,z),L(u,w,v5)) \ 1 = a(u,x,L(a(z,y,x),w,v5))
    ]]></literal>
    <justification jstring="[para(43858(a,1),42859(a,1,1))].">
      <j1 rule="para" parents="43858 42859"/>
    </justification>
  </clause>

  <clause id="43863">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,u)) = a(x,u,L(a(w,v5,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41453,a(flip),b,43862,a)].">
      <j1 rule="hyper" parents="64 41453 43862"/>
    </justification>
  </clause>

  <clause id="43864">
    <literal><![CDATA[
      a(L(x,y,z),u,a(u,w,v5)) = a(x,u,L(a(v5,w,u),y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33546,a(flip),b,43862,a)].">
      <j1 rule="hyper" parents="64 33546 43862"/>
    </justification>
  </clause>

  <clause id="43865">
    <literal><![CDATA[
      a(x,a(y,z,u),L(u,w,v5)) = a(x,u,L(a(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,42776,a(flip),b,43863,a)].">
      <j1 rule="hyper" parents="64 42776 43863"/>
    </justification>
  </clause>

  <clause id="43866">
    <literal><![CDATA[
      a(x,y,L(a(z,u,y),y,w)) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42266,a(flip),b,43863,a),flip(a)].">
      <j1 rule="hyper" parents="64 42266 43863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43867">
    <literal><![CDATA[
      (x / y) * a(y,z,L(a(u,w,z),y,x)) = ((x / y) / y) * L(y,z,a(z,w,u))
    ]]></literal>
    <justification jstring="[para(43864(a,1),42026(a,1,2))].">
      <j1 rule="para" parents="43864 42026"/>
    </justification>
  </clause>

  <clause id="43868">
    <literal><![CDATA[
      a(x,a(y,z,u),L(y,w,v5)) = a(x,y,L(a(u,z,y),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,42391,a,b,43865,a)].">
      <j1 rule="hyper" parents="64 42391 43865"/>
    </justification>
  </clause>

  <clause id="43869">
    <literal><![CDATA[
      a(x,y,L(a(z,u,y),u,z)) = a(a(y,y,x),u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,43501,a(flip),b,43865,a),flip(a)].">
      <j1 rule="hyper" parents="64 43501 43865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43870">
    <literal><![CDATA[
      a(x * y,x,L(a(z,u,x),w,v5)) = a(y,a(z,u,x),L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,42841,a(flip),b,43865,a),flip(a)].">
      <j1 rule="hyper" parents="64 42841 43865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43871">
    <literal><![CDATA[
      (x * y) * a(y,z,L(a(u,w,z),y,x)) = x * L(y,z,a(z,w,u))
    ]]></literal>
    <justification jstring="[para(43865(a,1),42779(a,1,2))].">
      <j1 rule="para" parents="43865 42779"/>
    </justification>
  </clause>

  <clause id="43872">
    <literal><![CDATA[
      a(a(x,x,y),z,u) = a(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[para(29902(a,1),43869(a,1,3)),flip(a)].">
      <j1 rule="para" parents="29902 43869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43873">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(z,u,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(42050,a,43872,a)].">
      <j1 rule="hyper" parents="42050 43872"/>
    </justification>
  </clause>

  <clause id="43874">
    <literal><![CDATA[
      a(a(x,x,y),z,u) = a(x,a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,41451,a,b,43872,a),flip(a)].">
      <j1 rule="hyper" parents="373 41451 43872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43875">
    <literal><![CDATA[
      a(a(x,x,L(y,z,u)),w,v5) = a(y,x,L(a(v5,w,x),z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,43863,a(flip),b,43872,a),flip(a)].">
      <j1 rule="hyper" parents="373 43863 43872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43876">
    <literal><![CDATA[
      a(x,y,y \ L(y,z,u)) = a(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41694,a,b,43872,a)].">
      <j1 rule="hyper" parents="64 41694 43872"/>
    </justification>
  </clause>

  <clause id="43877">
    <literal><![CDATA[
      a(a(x,y,y),z,u) = a(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41479,a,b,43872,a)].">
      <j1 rule="hyper" parents="64 41479 43872"/>
    </justification>
  </clause>

  <clause id="43878">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(y,z,u)) = a(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,39673,a,b,43872,a)].">
      <j1 rule="hyper" parents="64 39673 43872"/>
    </justification>
  </clause>

  <clause id="43879">
    <literal><![CDATA[
      a(x,y * a(z,u,y),a(w,v5,y * a(z,u,y))) = a(a(y,y,x),v5,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,43026,a(flip),b,43872,a),flip(a)].">
      <j1 rule="hyper" parents="64 43026 43872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43880">
    <literal><![CDATA[
      a(x,y,a(L(z,z,u * y),u,y)) = z \ L(z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,42319,a(flip),b,43872,a),flip(a)].">
      <j1 rule="hyper" parents="64 42319 43872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43881">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = a(z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41803,a(flip),b,43872,a),flip(a)].">
      <j1 rule="hyper" parents="64 41803 43872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43882">
    <literal><![CDATA[
      a(x * y,z,a(u,u,w)) = a(w,u,a(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,40854,a(flip),b,43872,a)].">
      <j1 rule="hyper" parents="64 40854 43872"/>
    </justification>
  </clause>

  <clause id="43883">
    <literal><![CDATA[
      a(x,x,y) * a(y,x,a(z,u,x)) = a(x,x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,43872,a(flip),b,39673,a)].">
      <j1 rule="hyper" parents="145 43872 39673"/>
    </justification>
  </clause>

  <clause id="43885">
    <literal><![CDATA[
      a(x,y,y) \ a(x,y,a(z,u,y)) = L(a(x,y,y) \ 1,u,z)
    ]]></literal>
    <justification jstring="[para(43872(a,1),38078(a,1,2))].">
      <j1 rule="para" parents="43872 38078"/>
    </justification>
  </clause>

  <clause id="43886">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * (y \ x) = x * (L(x,u,z) \ (y \ L(x,u,z)))
    ]]></literal>
    <justification jstring="[para(43872(a,1),39788(a,1,1))].">
      <j1 rule="para" parents="43872 39788"/>
    </justification>
  </clause>

  <clause id="43887">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ w = w * a(z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(43872(a,1),40852(a,1,1))].">
      <j1 rule="para" parents="43872 40852"/>
    </justification>
  </clause>

  <clause id="43888">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * w = a(z,u,a(y,y,x)) * w
    ]]></literal>
    <justification jstring="[para(43872(a,1),40857(a,1,1))].">
      <j1 rule="para" parents="43872 40857"/>
    </justification>
  </clause>

  <clause id="43889">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,u))) = L(x,y,a(w,v5,a(u,u,z)))
    ]]></literal>
    <justification jstring="[para(43872(a,1),40971(a,1,3))].">
      <j1 rule="para" parents="43872 40971"/>
    </justification>
  </clause>

  <clause id="43890">
    <literal><![CDATA[
      a(L(x,y * x,z),y,a(u,w,y)) = a(a(y,y,L(x,x,z)),w,u)
    ]]></literal>
    <justification jstring="[para(41016(a,1),43872(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41016 43872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43891">
    <literal><![CDATA[
      x * a(x,y,a(z,u,a(y,w,u))) = L(x,y,a(y,w,a(u,u,z)))
    ]]></literal>
    <justification jstring="[para(43872(a,1),41456(a,1,2,3))].">
      <j1 rule="para" parents="43872 41456"/>
    </justification>
  </clause>

  <clause id="43892">
    <literal><![CDATA[
      x * a(y,z,a(u,w,z)) = x * a(u,w,a(z,z,y))
    ]]></literal>
    <justification jstring="[para(43872(a,1),41854(a,1,2))].">
      <j1 rule="para" parents="43872 41854"/>
    </justification>
  </clause>

  <clause id="43893">
    <literal><![CDATA[
      (x / y) \ (x * (y \ L(y,z,u))) = L(y,z,u) * a(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(43872(a,1),43126(a,2,2))].">
      <j1 rule="para" parents="43872 43126"/>
    </justification>
  </clause>

  <clause id="43894">
    <literal><![CDATA[
      a(x,y,y \ 1) * a(x,y,a(z,u,y)) = a(x,y,L(y \ 1,u,z))
    ]]></literal>
    <justification jstring="[para(43872(a,1),43380(a,1,2))].">
      <j1 rule="para" parents="43872 43380"/>
    </justification>
  </clause>

  <clause id="43895">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(z,u,a(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,41883,a,b,43873,a),flip(a)].">
      <j1 rule="hyper" parents="373 41883 43873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43896">
    <literal><![CDATA[
      a(x,a(x,y,z),u) = a(z,y,a(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,41451,a,b,43873,a)].">
      <j1 rule="hyper" parents="373 41451 43873"/>
    </justification>
  </clause>

  <clause id="43897">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(y,z,a(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,41449,a,b,43873,a)].">
      <j1 rule="hyper" parents="373 41449 43873"/>
    </justification>
  </clause>

  <clause id="43898">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * (z * w) = z * (a(z,u,a(x,y,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(144,a,43873,a,b,30218,a)].">
      <j1 rule="hyper" parents="144 43873 30218"/>
    </justification>
  </clause>

  <clause id="43899">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,L(y,z,u))) = a(w,v5,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(40664(a,1),43873(a,1,3)),flip(a)].">
      <j1 rule="para" parents="40664 43873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43900">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * u = L(u,a(u,y,x),z)
    ]]></literal>
    <justification jstring="[para(43873(a,2),41445(a,1,1))].">
      <j1 rule="para" parents="43873 41445"/>
    </justification>
  </clause>

  <clause id="43901">
    <literal><![CDATA[
      x * a(y,z,a(x,u,u)) = L(x,u,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(43873(a,2),41455(a,1,2))].">
      <j1 rule="para" parents="43873 41455"/>
    </justification>
  </clause>

  <clause id="43902">
    <literal><![CDATA[
      x * a(y,z,a(x,u,u)) = L(x,u,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(43873(a,2),41456(a,1,2))].">
      <j1 rule="para" parents="43873 41456"/>
    </justification>
  </clause>

  <clause id="43904">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * w = w * a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(43873(a,2),41900(a,2,2))].">
      <j1 rule="para" parents="43873 41900"/>
    </justification>
  </clause>

  <clause id="43907">
    <literal><![CDATA[
      a(x,a(x,y,z),u) = a(z,y,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,41803,a(flip),b,43874,a),flip(a)].">
      <j1 rule="hyper" parents="64 41803 43874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43908">
    <literal><![CDATA[
      a(x,a(x,y,z),L(u,w,v5)) = a(z,y,a(u,x,L(x,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,40853,a(flip),b,43874,a),flip(a)].">
      <j1 rule="hyper" parents="64 40853 43874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43910">
    <literal><![CDATA[
      a(a(x,y,y),z,u) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,41883,a,b,43877,a),flip(a)].">
      <j1 rule="hyper" parents="373 41883 43877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43911">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) \ a(x,x,y) = a(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,39670,a,b,43877,a)].">
      <j1 rule="hyper" parents="64 39670 43877"/>
    </justification>
  </clause>

  <clause id="43912">
    <literal><![CDATA[
      a(x,y,a(z * (u \ (y \ u)),z,y)) = a(a(u \ (y \ u),y,x),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42386,a(flip),b,43877,a),flip(a)].">
      <j1 rule="hyper" parents="64 42386 43877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43913">
    <literal><![CDATA[
      a(a(x,y * z,y * z),u,w) = a(x,y \ z,a(w,u,y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,35238,a(flip),b,43877,a)].">
      <j1 rule="hyper" parents="64 35238 43877"/>
    </justification>
  </clause>

  <clause id="43914">
    <literal><![CDATA[
      a(x,y,y) \ (x * a(x,y,a(z,u,y))) = ((x / y) / (1 / y)) * a(w \ (a(x,y,y) \ w),u,z)
    ]]></literal>
    <justification jstring="[para(43877(a,1),38128(a,1,2,2))].">
      <j1 rule="para" parents="43877 38128"/>
    </justification>
  </clause>

  <clause id="43915">
    <literal><![CDATA[
      L(R(x,y,z),x * L(x,y,z),u) = a(u,x,a(z,y,x)) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(43877(a,1),43157(a,2,1))].">
      <j1 rule="para" parents="43877 43157"/>
    </justification>
  </clause>

  <clause id="43916">
    <literal><![CDATA[
      (x * a(y,z,z \ 1)) * a(y,z,a(x * (y \ (z \ y)),x,z)) = (((y * z) \ y) / x) \ (z \ 1)
    ]]></literal>
    <justification jstring="[para(43877(a,1),43266(a,1,2))].">
      <j1 rule="para" parents="43877 43266"/>
    </justification>
  </clause>

  <clause id="43917">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) = a(u,z,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41883,a,b,43881,a),flip(a)].">
      <j1 rule="hyper" parents="64 41883 43881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43919">
    <literal><![CDATA[
      a(x * a(y,y,z),x,a(y,y,u)) = a(x,x,a(y,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,42053,a(flip),b,43881,a),flip(a)].">
      <j1 rule="hyper" parents="64 42053 43881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43920">
    <literal><![CDATA[
      x * a(y,z,a(u,u,w)) = x * a(w,u,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,43881,a(flip),b,41898,a)].">
      <j1 rule="hyper" parents="145 43881 41898"/>
    </justification>
  </clause>

  <clause id="43921">
    <literal><![CDATA[
      x * a(y,z,a(u,u,x)) = L(x,u,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(43881(a,1),41456(a,1,2))].">
      <j1 rule="para" parents="43881 41456"/>
    </justification>
  </clause>

  <clause id="43922">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * u = L(u,z,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(43881(a,1),41460(a,1,1))].">
      <j1 rule="para" parents="43881 41460"/>
    </justification>
  </clause>

  <clause id="43923">
    <literal><![CDATA[
      L(x,a(y,z,a(u,u,w)),v5) = L(x,a(w,u,a(u,z,y)),v5)
    ]]></literal>
    <justification jstring="[para(43881(a,1),41439(a,1,2))].">
      <j1 rule="para" parents="43881 41439"/>
    </justification>
  </clause>

  <clause id="43924">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(x,x,w)) = L(x,a(x,u,z),w) \ y
    ]]></literal>
    <justification jstring="[para(43881(a,1),42287(a,1,2))].">
      <j1 rule="para" parents="43881 42287"/>
    </justification>
  </clause>

  <clause id="43925">
    <literal><![CDATA[
      a(x \ a(y,z,u),y,a(y,w,v5)) = a(v5,w,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(34063(a,1),43895(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34063 43895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43926">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * a(y,y,x) = a(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(43895(a,1),40874(a,1,1))].">
      <j1 rule="para" parents="43895 40874"/>
    </justification>
  </clause>

  <clause id="43927">
    <literal><![CDATA[
      L(x,a(a(y,z,u),y,w),v5) = L(x,a(u,z,a(w,y,y)),v5)
    ]]></literal>
    <justification jstring="[para(43895(a,2),41403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="43895 41403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43929">
    <literal><![CDATA[
      a(x,a(L(x,y,z),u,w),L(v5,y,z)) = a(w,u,a(v5,L(x,y,z),L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,42770,a(flip),b,43896,a)].">
      <j1 rule="hyper" parents="64 42770 43896"/>
    </justification>
  </clause>

  <clause id="43930">
    <literal><![CDATA[
      a(x,a(y,z,x),u \ a(x,w,v5)) = a(y,z,a(u,x,x))
    ]]></literal>
    <justification jstring="[para(34063(a,1),43897(a,2,3))].">
      <j1 rule="para" parents="34063 43897"/>
    </justification>
  </clause>

  <clause id="43931">
    <literal><![CDATA[
      a(L(x,x,y),z,a(u,u,w)) = L(a(u,a(u,z,x),w),x,y)
    ]]></literal>
    <justification jstring="[para(43907(a,2),40756(a,2,1))].">
      <j1 rule="para" parents="43907 40756"/>
    </justification>
  </clause>

  <clause id="43932">
    <literal><![CDATA[
      a(x,a(x,y,z),L(u,u,L(w,x,v5))) = a(z,y,a(x,x,L(u,u,w)))
    ]]></literal>
    <justification jstring="[para(41045(a,1),43907(a,2,3))].">
      <j1 rule="para" parents="41045 43907"/>
    </justification>
  </clause>

  <clause id="43935">
    <literal><![CDATA[
      a(x * a(y,z,a(u,w,w)),v5,v6) = a(x * a(u,w,a(w,z,y)),v5,v6)
    ]]></literal>
    <justification jstring="[para(43910(a,1),42342(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="43910 42342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43936">
    <literal><![CDATA[
      a(x * a(y,z,u),y,a(y,w,v5)) = a(v5,w,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(32751(a,1),43917(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32751 43917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43937">
    <literal><![CDATA[
      R(x * y,L(z,y,x),a(u,w,a(w,v5,v6))) \ ((x * (y * z)) * a(u,w,a(w,v5,v6))) = a(v6,v5,a(w,w,u)) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(43917(a,2),23927(a,2,1))].">
      <j1 rule="para" parents="43917 23927"/>
    </justification>
  </clause>

  <clause id="43938">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * L(y,y,x) = L(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(43917(a,1),40965(a,1,1))].">
      <j1 rule="para" parents="43917 40965"/>
    </justification>
  </clause>

  <clause id="43939">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * ((R(y,x,z) \ y) \ y) = (a(y,x,z) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(43876(a,1),43197(a,1,1))].">
      <j1 rule="para" parents="43876 43197"/>
    </justification>
  </clause>

  <clause id="43940">
    <literal><![CDATA[
      L(x,x * L(x,y,z),u) = L(x,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,41622,a,b,43900,a)].">
      <j1 rule="hyper" parents="64 41622 43900"/>
    </justification>
  </clause>

  <clause id="43941">
    <literal><![CDATA[
      (x * a(y,z,u)) * a(w,v5,a(x,u,u)) = L(x * a(y,z,u),u,a(w,v5,u))
    ]]></literal>
    <justification jstring="[para(37894(a,1),43901(a,1,2,3))].">
      <j1 rule="para" parents="37894 43901"/>
    </justification>
  </clause>

  <clause id="43942">
    <literal><![CDATA[
      L(x,y,y * L(y,z,u)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,41704,a,b,43902,a)].">
      <j1 rule="hyper" parents="64 41704 43902"/>
    </justification>
  </clause>

  <clause id="43943">
    <literal><![CDATA[
      L(x * a(y,y,L(x,z,u)),y,y) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,40875,a,b,43902,a)].">
      <j1 rule="hyper" parents="64 40875 43902"/>
    </justification>
  </clause>

  <clause id="43944">
    <literal><![CDATA[
      R(x,y,y) * a(z,u,a(x,y,y)) = L(R(x,y,y),y,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(31176(a,1),43902(a,1,2,3))].">
      <j1 rule="para" parents="31176 43902"/>
    </justification>
  </clause>

  <clause id="43945">
    <literal><![CDATA[
      x * a(y,y,L(a(z,z,x),u,w)) = L(x,z,a(z,y,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(39691(a,1),43921(a,1,2))].">
      <j1 rule="para" parents="39691 43921"/>
    </justification>
  </clause>

  <clause id="43946">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),y,y) = L(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(43922(a,1),40858(a,1,1))].">
      <j1 rule="para" parents="43922 40858"/>
    </justification>
  </clause>

  <clause id="43947">
    <literal><![CDATA[
      a(x,x,y) \ R(x,x,L(y,z,u)) = L(x,a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41691,a,b,43940,a)].">
      <j1 rule="hyper" parents="64 41691 43940"/>
    </justification>
  </clause>

  <clause id="43948">
    <literal><![CDATA[
      L(R(x,y,z),x * L(x,u,w),v5) = R(L(x,a(x,u,w),v5),y,z)
    ]]></literal>
    <justification jstring="[para(43940(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="43940 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43949">
    <literal><![CDATA[
      L(L(x,y,z),x * L(x,u,w),v5) = L(L(x,a(x,u,w),v5),y,z)
    ]]></literal>
    <justification jstring="[para(43940(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="43940 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43952">
    <literal><![CDATA[
      L(x * (y \ R(y,z,u)),y,a(y,z,u)) = R(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42998,a(flip),b,43942,a),flip(a)].">
      <j1 rule="hyper" parents="64 42998 43942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43953">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(u,x,a(x,y,z)) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(43942(a,1),42426(a,1,2))].">
      <j1 rule="para" parents="43942 42426"/>
    </justification>
  </clause>

  <clause id="43954">
    <literal><![CDATA[
      L(x,y,a(z,u,y) * y) = L(x,y,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41548,a(flip),b,43946,a)].">
      <j1 rule="hyper" parents="64 41548 43946"/>
    </justification>
  </clause>

  <clause id="43955">
    <literal><![CDATA[
      L(R(x,y,y),y,a(y,z,u)) = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(42,a,35353,a,b,43946,a),flip(a)].">
      <j1 rule="hyper" parents="42 35353 43946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43958">
    <literal><![CDATA[
      (x \ L(y,x,L(x,z,u))) * a(u,z,x) = (x \ a(u,z,x)) * y
    ]]></literal>
    <justification jstring="[para(43954(a,1),41550(a,1,1,2))].">
      <j1 rule="para" parents="43954 41550"/>
    </justification>
  </clause>

  <clause id="43959">
    <literal><![CDATA[
      L(R(x,y,y),y,a(z,u,y)) = R(x,y,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(42222,a,43955,a)].">
      <j1 rule="hyper" parents="42222 43955"/>
    </justification>
  </clause>

  <clause id="43961">
    <literal><![CDATA[
      L(R(x,y,L(y,z,u)),y,a(y,z,u)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(42,a,42171,a,b,43955,a)].">
      <j1 rule="hyper" parents="42 42171 43955"/>
    </justification>
  </clause>

  <clause id="43963">
    <literal><![CDATA[
      L(R(x,((1 / y) \ y) / z,((1 / y) \ y) / z),((1 / y) \ y) / z,a(y,y,((1 / y) \ y) / z)) = R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(16553(a,1),43959(a,2,3))].">
      <j1 rule="para" parents="16553 43959"/>
    </justification>
  </clause>

  <clause id="43964">
    <literal><![CDATA[
      a(L(x * (y * T(x \ 1,z)),u,w),v5,a(v6,v6,v7)) = a(v7,v6,a((L(y,u,w) * T(x \ 1,z)) * x,v5,v6))
    ]]></literal>
    <justification jstring="[para(35618(a,2),43882(a,1,1))].">
      <j1 rule="para" parents="35618 43882"/>
    </justification>
  </clause>

  <clause id="43965">
    <literal><![CDATA[
      x * a(y,z,a(u,u,L(w,w,x))) = w * (L(w,u,a(u,z,y)) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,41562,a(flip),b,43887,a),flip(a)].">
      <j1 rule="hyper" parents="64 41562 43887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43966">
    <literal><![CDATA[
      L(L(a(x,y,a(z,z,u)),w,v5),v5 * w,v5) * L(w,v5,v5) = L(a(u,z,a(x,y,z)) * w,v5,v5)
    ]]></literal>
    <justification jstring="[para(43888(a,2),26948(a,2,1))].">
      <j1 rule="para" parents="43888 26948"/>
    </justification>
  </clause>

  <clause id="43967">
    <literal><![CDATA[
      L(L(a(x,y,a(y,z,u)),w,v5),v5 * w,v5) * L(w,v5,v5) = L(w * a(u,z,a(x,y,y)),v5,v5)
    ]]></literal>
    <justification jstring="[para(43904(a,1),26948(a,2,1))].">
      <j1 rule="para" parents="43904 26948"/>
    </justification>
  </clause>

  <clause id="43968">
    <literal><![CDATA[
      x \ (L(x \ R(x,y,z),u,u) * ((x \ R(x,y,z)) \ x)) = a(x,u,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39477,a(flip),b,43911,a)].">
      <j1 rule="hyper" parents="64 39477 43911"/>
    </justification>
  </clause>

  <clause id="43969">
    <literal><![CDATA[
      (a(x,x,y) \ z) * a(z,z,a(x,x,y)) = R(a(x,x,y) \ z,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(43919(a,1),35846(a,1,2))].">
      <j1 rule="para" parents="43919 35846"/>
    </justification>
  </clause>

  <clause id="43970">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) * L((a(z,x,x) \ y) * z,z,a(z,x,x)) = (a(z,x,x) \ y) * z
    ]]></literal>
    <justification jstring="[para(43925(a,1),41040(a,1,1))].">
      <j1 rule="para" parents="43925 41040"/>
    </justification>
  </clause>

  <clause id="43971">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),R(x,z,u),a(R(x,z,u),y,y)) = R(x,z,u) * (L(x \ R(x,z,u),y,y) \ 1)
    ]]></literal>
    <justification jstring="[para(43943(a,1),39405(a,1,1))].">
      <j1 rule="para" parents="43943 39405"/>
    </justification>
  </clause>

  <clause id="43972">
    <literal><![CDATA[
      L(x,a(x,y,z),u) \ L(u,y,z) = L(u,y,z) * (u \ (x \ u))
    ]]></literal>
    <justification jstring="[para(43947(a,1),37775(a,1,1))].">
      <j1 rule="para" parents="43947 37775"/>
    </justification>
  </clause>

  <clause id="43973">
    <literal><![CDATA[
      a(x,a(y,z,u),w \ (y \ w)) = a(x,y,L(a(u,z,y),y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,38966,a(flip),b,43868,a)].">
      <j1 rule="hyper" parents="64 38966 43868"/>
    </justification>
  </clause>

  <clause id="43974">
    <literal><![CDATA[
      a((x \ y) * (L(x,x,z) \ y),u,w) = a(z,x,L(a(w,u,x),y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,40060,a,b,43875,a)].">
      <j1 rule="hyper" parents="64 40060 43875"/>
    </justification>
  </clause>

  <clause id="43975">
    <literal><![CDATA[
      a(x,y,L(a(z,y \ u,y),u,u)) = a(a(x,y,y),y \ u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42300,a(flip),b,43875,a),flip(a)].">
      <j1 rule="hyper" parents="64 42300 43875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43976">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,L(y,z,u))) = a(x,y,a(w,v5,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,43873,a(flip),b,43899,a),flip(a)].">
      <j1 rule="hyper" parents="373 43873 43899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43977">
    <literal><![CDATA[
      a(L(x,x,y),z,a(u,u,w)) = a(u,a(u,z,x),L(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,42769,a,b,43931,a),flip(a)].">
      <j1 rule="hyper" parents="373 42769 43931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43978">
    <literal><![CDATA[
      a(x,L(y,z,u),a(L(y,z,u),w,v5)) = a(x,y,a(v5,w,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41883,a,b,43976,a)].">
      <j1 rule="hyper" parents="64 41883 43976"/>
    </justification>
  </clause>

  <clause id="43979">
    <literal><![CDATA[
      a(x,(y \ z) * z,a(u,w,L(y,y * z,z))) = a(x,y,a(u,w,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,35809,a(flip),b,43976,a)].">
      <j1 rule="hyper" parents="64 35809 43976"/>
    </justification>
  </clause>

  <clause id="43980">
    <literal><![CDATA[
      a(x,a(x,y,z),L(u,z,w)) = a(u,x,a(L(z,z,w),y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,43881,a,b,43977,a),flip(a)].">
      <j1 rule="hyper" parents="64 43881 43977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43981">
    <literal><![CDATA[
      a(x,y,a(L(z,z,u),w,y)) = a(z,w,a(x,y,L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,43908,a(flip),b,43980,a),flip(a)].">
      <j1 rule="hyper" parents="64 43908 43980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43982">
    <literal><![CDATA[
      a(x,y,z \ R(z,u,y)) = z \ L(z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(32467(a,1),43880(a,1,3))].">
      <j1 rule="para" parents="32467 43880"/>
    </justification>
  </clause>

  <clause id="43983">
    <literal><![CDATA[
      a(x,y,z \ L(z,u,y)) = z \ L(z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,31676,a(flip),b,43982,a)].">
      <j1 rule="hyper" parents="64 31676 43982"/>
    </justification>
  </clause>

  <clause id="43984">
    <literal><![CDATA[
      a(a(x,x,y),z,u \ L(u,w,z)) = u \ L(u,w,a(x,z,a(y,x,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,41956,a,b,43983,a),flip(a)].">
      <j1 rule="hyper" parents="373 41956 43983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43985">
    <literal><![CDATA[
      a(x * L(x,y,a(z,z,u)),w,w) = a(w,w,a(u,z,x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(43983(a,2),39866(a,2,3))].">
      <j1 rule="para" parents="43983 39866"/>
    </justification>
  </clause>

  <clause id="43986">
    <literal><![CDATA[
      a(x,a(y,z,u),w \ (y \ w)) = a(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,43866,a(flip),b,43973,a),flip(a)].">
      <j1 rule="hyper" parents="373 43866 43973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43988">
    <literal><![CDATA[
      a(x,y \ (z \ y),a(z,u,w)) = a(x,z,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,36992,a(flip),b,43986,a)].">
      <j1 rule="hyper" parents="64 36992 43986"/>
    </justification>
  </clause>

  <clause id="43990">
    <literal><![CDATA[
      L(x,y \ (z \ y),a(z,u,w)) = x * a(x,z,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(43988(a,1),42922(a,1,2)),flip(a)].">
      <j1 rule="para" parents="43988 42922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43991">
    <literal><![CDATA[
      L(x,y \ (z \ y),a(z,u,w)) = L(x,z,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,41456,a(flip),b,43990,a),flip(a)].">
      <j1 rule="hyper" parents="373 41456 43990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43993">
    <literal><![CDATA[
      a(x,y,L(a(z,y \ u,y),u,u)) = a(x,y,a(z,y \ u,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,43877,a(flip),b,43975,a),flip(a)].">
      <j1 rule="hyper" parents="373 43877 43975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43994">
    <literal><![CDATA[
      a(x,y,L(a(z,y \ u,y),u,u)) = a(x,y,a(z,u * y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,35705,a(flip),b,43993,a),flip(a)].">
      <j1 rule="hyper" parents="373 35705 43993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43995">
    <literal><![CDATA[
      a(x * y,x,L(a(z,u,x),w,v5)) = a(y,x,L(a(z,u,x),w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,43865,a(flip),b,43870,a),flip(a)].">
      <j1 rule="hyper" parents="373 43865 43870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43996">
    <literal><![CDATA[
      a(L(x,y * x,z),y,a(u,w,y)) = a(x,y,L(a(u,w,y),x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,43875,a(flip),b,43890,a),flip(a)].">
      <j1 rule="hyper" parents="373 43875 43890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43997">
    <literal><![CDATA[
      a(x,y \ z,a(u,w,y \ z)) = a(x,y * z,a(u,w,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,43877,a(flip),b,43913,a),flip(a)].">
      <j1 rule="hyper" parents="64 43877 43913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="43998">
    <literal><![CDATA[
      R(x,y,y) * a(z,u,a(x,y,y)) = R(x,y,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,43955,a(flip),b,43944,a),flip(a)].">
      <j1 rule="hyper" parents="373 43955 43944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44000">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * R(z,u,u) = R(z,u,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(23777,a,43998,a)].">
      <j1 rule="hyper" parents="23777 43998"/>
    </justification>
  </clause>

  <clause id="44002">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * R(z,u,u) = z * a(z,u,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,38379,a,b,44000,a),flip(a)].">
      <j1 rule="hyper" parents="373 38379 44000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44004">
    <literal><![CDATA[
      a(x,y,y) * a(z,u,a(y,y,x)) = a(x,y,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,42969,a,b,44002,a(flip))].">
      <j1 rule="hyper" parents="35 42969 44002"/>
    </justification>
  </clause>

  <clause id="44005">
    <literal><![CDATA[
      a(L(x,y,z),u,u) = a(x,u,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,42968,a(flip),b,44002,a(flip))].">
      <j1 rule="hyper" parents="35 42968 44002"/>
    </justification>
  </clause>

  <clause id="44006">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) = L(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(35,a,42967,a(flip),b,44002,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 42967 44002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44007">
    <literal><![CDATA[
      L(x,x,L(y,z,u)) \ x = a(y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,30462,a,b,44005,a)].">
      <j1 rule="hyper" parents="64 30462 44005"/>
    </justification>
  </clause>

  <clause id="44008">
    <literal><![CDATA[
      a((x * ((y * x) \ z)) \ z,u,u) = a(y,u,L(u,x,(y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,42022,a(flip),b,44005,a)].">
      <j1 rule="hyper" parents="64 42022 44005"/>
    </justification>
  </clause>

  <clause id="44009">
    <literal><![CDATA[
      a(x \ y,z,L(z,u,x * u)) = a(u \ ((u \ x) \ y),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41992,a(flip),b,44005,a),flip(a)].">
      <j1 rule="hyper" parents="64 41992 44005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44010">
    <literal><![CDATA[
      a(x,y,L(y,y \ x,z)) = a(L(x,x,z),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41325,a(flip),b,44005,a),flip(a)].">
      <j1 rule="hyper" parents="64 41325 44005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44011">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,z,u),w,v5)) = a(L(x,w,v5),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,40664,a(flip),b,44005,a),flip(a)].">
      <j1 rule="hyper" parents="64 40664 44005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44012">
    <literal><![CDATA[
      a(x * L(y,z,u),x,x) = a(x * y,x,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,36872,a(flip),b,44005,a)].">
      <j1 rule="hyper" parents="64 36872 44005"/>
    </justification>
  </clause>

  <clause id="44013">
    <literal><![CDATA[
      a((x * y) \ z,u,L(u,x,y)) = a(x \ (y \ z),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34977,a(flip),b,44005,a),flip(a)].">
      <j1 rule="hyper" parents="64 34977 44005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44015">
    <literal><![CDATA[
      a(x * (y \ 1),x,L(x,z,u)) = a(L(y \ x,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32716,a(flip),b,44005,a),flip(a)].">
      <j1 rule="hyper" parents="64 32716 44005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44016">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) = R(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32595,a(flip),b,44005,a),flip(a)].">
      <j1 rule="hyper" parents="64 32595 44005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44017">
    <literal><![CDATA[
      a((x * y) \ (x * z),u,u) = a(y \ z,u,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,32586,a(flip),b,44005,a)].">
      <j1 rule="hyper" parents="64 32586 44005"/>
    </justification>
  </clause>

  <clause id="44018">
    <literal><![CDATA[
      a((x * y) \ z,u,L(u,y * x,y)) = a((y * (x * y)) \ (y * z),u,u)
    ]]></literal>
    <justification jstring="[para(14184(a,1),44005(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14184 44005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44019">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) \ y = L(y,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(44005(a,1),30459(a,1,1))].">
      <j1 rule="para" parents="44005 30459"/>
    </justification>
  </clause>

  <clause id="44020">
    <literal><![CDATA[
      ((x / y) / (1 / y)) * a(a(x,y,y),z,u) = a(x,y,L(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(44005(a,1),41030(a,2,1))].">
      <j1 rule="para" parents="44005 41030"/>
    </justification>
  </clause>

  <clause id="44021">
    <literal><![CDATA[
      a((x \ y) \ z,u,L(u,x * y,x)) = a(y \ (x * z),u,u)
    ]]></literal>
    <justification jstring="[para(41719(a,1),44005(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41719 44005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44022">
    <literal><![CDATA[
      L(a(x,y,L(y,z,u)),L(y,z,u),u * z) = a(x,y,L(y,z * y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,37523,a,b,44006,a)].">
      <j1 rule="hyper" parents="373 37523 44006"/>
    </justification>
  </clause>

  <clause id="44024">
    <literal><![CDATA[
      L(x,L(x,y,z),u) = L(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(40,a,40724,a,b,44007,a)].">
      <j1 rule="hyper" parents="40 40724 44007"/>
    </justification>
  </clause>

  <clause id="44028">
    <literal><![CDATA[
      L(L(x,y,z),L(x,u,w),v5) = L(L(x,x,L(v5,u,w)),y,z)
    ]]></literal>
    <justification jstring="[para(44024(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="44024 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44030">
    <literal><![CDATA[
      T(x,x \ 1) \ L(x,x,L(y,z,u)) = (x \ 1) * L(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(44024(a,1),8894(a,1,2))].">
      <j1 rule="para" parents="44024 8894"/>
    </justification>
  </clause>

  <clause id="44031">
    <literal><![CDATA[
      a(x,y,L(y,y \ x,z)) = a(x,y,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,44005,a(flip),b,44010,a),flip(a)].">
      <j1 rule="hyper" parents="373 44005 44010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44032">
    <literal><![CDATA[
      L(L(x,x,y),L(x,x,y),a(z,x \ y,x \ y)) = a(y,x,L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[para(44031(a,1),43337(a,2,1))].">
      <j1 rule="para" parents="44031 43337"/>
    </justification>
  </clause>

  <clause id="44033">
    <literal><![CDATA[
      a(x * (y \ 1),x,L(x,z,u)) = a(R(y,z,u) \ x,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32985,a(flip),b,44012,a),flip(a)].">
      <j1 rule="hyper" parents="64 32985 44012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44034">
    <literal><![CDATA[
      a(x,y,y) * a(x,y,a(z,u,y)) = a(x,y,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,43892,a,b,44004,a)].">
      <j1 rule="hyper" parents="64 43892 44004"/>
    </justification>
  </clause>

  <clause id="44035">
    <literal><![CDATA[
      a(x,y,y) \ a(x,y,L(y,z,u)) = a(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(139,a,44004,a(flip),b,43892,a)].">
      <j1 rule="hyper" parents="139 44004 43892"/>
    </justification>
  </clause>

  <clause id="44036">
    <literal><![CDATA[
      a(x,y,y) \ a(x,y,L(y,z,u)) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,44004,a(flip),b,43920,a(flip))].">
      <j1 rule="hyper" parents="139 44004 43920"/>
    </justification>
  </clause>

  <clause id="44038">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,z,u),w,v5)) = a(x,y,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,44005,a(flip),b,44011,a),flip(a)].">
      <j1 rule="hyper" parents="373 44005 44011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44039">
    <literal><![CDATA[
      L(L(x,y,z),L(x,u,w),v5) = L(L(x,y,z),x,L(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,30,a,b,44028,a),flip(a)].">
      <j1 rule="hyper" parents="373 30 44028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44041">
    <literal><![CDATA[
      a(L(x \ y,z,u),y,y) = a(R(x,z,u) \ y,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,44015,a(flip),b,44033,a)].">
      <j1 rule="hyper" parents="64 44015 44033"/>
    </justification>
  </clause>

  <clause id="44042">
    <literal><![CDATA[
      a(L(x \ y,z,u),y,y) = a(L(x,z,u) \ y,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,32982,a(flip),b,44041,a),flip(a)].">
      <j1 rule="hyper" parents="373 32982 44041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44043">
    <literal><![CDATA[
      a(a(L(x \ y,z,u),y,y),w,v5) = a(a(y,y,L(x,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(44042(a,2),32779(a,1,1))].">
      <j1 rule="para" parents="44042 32779"/>
    </justification>
  </clause>

  <clause id="44044">
    <literal><![CDATA[
      L(L(x,y,z),L(x,u,z),a(y,y,z)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,41665,a(flip),b,44039,a),flip(a)].">
      <j1 rule="hyper" parents="373 41665 44039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44045">
    <literal><![CDATA[
      L(L(x,y,z),x,L(u,w,v5)) \ L(x,y,z) = a(u,L(x,w,v5),L(x,y,z))
    ]]></literal>
    <justification jstring="[para(44039(a,1),41647(a,1,1))].">
      <j1 rule="para" parents="44039 41647"/>
    </justification>
  </clause>

  <clause id="44046">
    <literal><![CDATA[
      L(L(x,y,z),L(x,u,z),a(z \ 1,y,y)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,42208,a,b,44044,a)].">
      <j1 rule="hyper" parents="64 42208 44044"/>
    </justification>
  </clause>

  <clause id="44047">
    <literal><![CDATA[
      x * a(y,y,a(z,z,L(x,u,w))) = L(x,z,a(z,y,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(39675(a,2),43945(a,1,2,3))].">
      <j1 rule="para" parents="39675 43945"/>
    </justification>
  </clause>

  <clause id="44048">
    <literal><![CDATA[
      L(R(x,y,z),x * L(x,u,w),v5) = L(R(x,y,z),a(x,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29,a(flip),b,43948,a),flip(a)].">
      <j1 rule="hyper" parents="373 29 43948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44049">
    <literal><![CDATA[
      (x \ L(L(x,L(x,y,z),u),x,L(x,x,x))) * a(x,x,x) = x \ L(x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,39700,a(flip),b,43958,a),flip(a)].">
      <j1 rule="hyper" parents="373 39700 43958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44050">
    <literal><![CDATA[
      a(x,y,L(a(z,u,y),y * x,w)) = a(x,y,L(a(z,u,y),x,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,43863,a(flip),b,43996,a)].">
      <j1 rule="hyper" parents="64 43863 43996"/>
    </justification>
  </clause>

  <clause id="44051">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u \ z,w,v5))) = a(a(z,z,L(u,w,v5)),y,x)
    ]]></literal>
    <justification jstring="[hyper(42050,a,44043,a)].">
      <j1 rule="hyper" parents="42050 44043"/>
    </justification>
  </clause>

  <clause id="44052">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u \ z,w,v5))) = a(u,z,L(a(x,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,43875,a(flip),b,44051,a),flip(a)].">
      <j1 rule="hyper" parents="373 43875 44051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44053">
    <literal><![CDATA[
      a(x,x,a(y,y,L(z \ x,u,w))) = a(z,x,L(a(y,y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,39759,a,b,44052,a)].">
      <j1 rule="hyper" parents="64 39759 44052"/>
    </justification>
  </clause>

  <clause id="44054">
    <literal><![CDATA[
      a(x,x,a(y,y,L(z \ x,u,w))) = a(z,x,a(y,y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(39675(a,2),44053(a,2,3))].">
      <j1 rule="para" parents="39675 44053"/>
    </justification>
  </clause>

  <clause id="44055">
    <literal><![CDATA[
      a(x,x,y) * a(y,x,L(a(z,x \ u,x),u,u)) = R(a(x,x,y),u / (x \ 1),z)
    ]]></literal>
    <justification jstring="[para(43974(a,1),43440(a,1,2))].">
      <j1 rule="para" parents="43974 43440"/>
    </justification>
  </clause>

  <clause id="44056">
    <literal><![CDATA[
      a(x,(y \ z) * z,a((y \ z) * z,u,w)) = a(x,y,a(w,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42303,a(flip),b,43979,a)].">
      <j1 rule="hyper" parents="64 42303 43979"/>
    </justification>
  </clause>

  <clause id="44057">
    <literal><![CDATA[
      L(x,y * (z \ (y \ 1)),a(y * (z \ (y \ 1)),u,w)) = x * a(x,z,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(44056(a,1),41147(a,2,2))].">
      <j1 rule="para" parents="44056 41147"/>
    </justification>
  </clause>

  <clause id="44058">
    <literal><![CDATA[
      a(x,y,L(a(y,z,u),w,v5)) \ v6 = a(y,a(y,z,u),L(x,w,v5)) * v6
    ]]></literal>
    <justification jstring="[para(36394(a,1),43861(a,1,1))].">
      <j1 rule="para" parents="36394 43861"/>
    </justification>
  </clause>

  <clause id="44059">
    <literal><![CDATA[
      a(x,y * a(z,u,y),a(w,v5,y * a(z,u,y))) = a(x,y,a(w,v5,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,43872,a(flip),b,43879,a),flip(a)].">
      <j1 rule="hyper" parents="373 43872 43879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44060">
    <literal><![CDATA[
      x \ R(y,x,a(z,u,x)) = y * (L(y,u,z) \ (x \ L(y,u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,42042,a(flip),b,43886,a)].">
      <j1 rule="hyper" parents="64 42042 43886"/>
    </justification>
  </clause>

  <clause id="44061">
    <literal><![CDATA[
      L(x \ y,x,a(x,z,u)) = y * (L(y,z,u) \ (x \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,41472,a,b,44060,a)].">
      <j1 rule="hyper" parents="64 41472 44060"/>
    </justification>
  </clause>

  <clause id="44062">
    <literal><![CDATA[
      L(x \ (a(y,y,z) * z),x,a(x,y,y)) = (a(y,y,z) * z) * (z \ (x \ L(a(y,y,z) * z,y,y)))
    ]]></literal>
    <justification jstring="[para(30233(a,1),44061(a,2,2,1))].">
      <j1 rule="para" parents="30233 44061"/>
    </justification>
  </clause>

  <clause id="44063">
    <literal><![CDATA[
      a(x,y,a(z * (u \ (y \ u)),z,y)) = a(a(y,y,x),z,z)
    ]]></literal>
    <justification jstring="[para(38649(a,1),43912(a,2,1))].">
      <j1 rule="para" parents="38649 43912"/>
    </justification>
  </clause>

  <clause id="44064">
    <literal><![CDATA[
      a(x,y,a(z * (u \ (y \ u)),z,y)) = a(x,y,a(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,43872,a(flip),b,44063,a),flip(a)].">
      <j1 rule="hyper" parents="373 43872 44063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44066">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) * R(y,x,z) = (a(y,x,z) \ 1) \ y
    ]]></literal>
    <justification jstring="[para(2157(a,1),43939(a,1,2))].">
      <j1 rule="para" parents="2157 43939"/>
    </justification>
  </clause>

  <clause id="44067">
    <literal><![CDATA[
      L(R(x,y,z),x * L(x,y,z),y) = (a(x,y,z) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,43915,a,b,44066,a)].">
      <j1 rule="hyper" parents="64 43915 44066"/>
    </justification>
  </clause>

  <clause id="44068">
    <literal><![CDATA[
      L(R(x,y,z),x * L(x,y,z),y) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,42435,a(flip),b,44067,a),flip(a)].">
      <j1 rule="hyper" parents="373 42435 44067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44069">
    <literal><![CDATA[
      L(R(x,y,z),a(x,y,z),y) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,44048,a(flip),b,44068,a)].">
      <j1 rule="hyper" parents="64 44048 44068"/>
    </justification>
  </clause>

  <clause id="44070">
    <literal><![CDATA[
      L(R(x,y,z),x,a(z,y,y)) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,42194,a(flip),b,44069,a)].">
      <j1 rule="hyper" parents="64 42194 44069"/>
    </justification>
  </clause>

  <clause id="44071">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ w) = L(x,y,a(w,u,z) * w)
    ]]></literal>
    <justification jstring="[para(44070(a,1),41680(a,1,3)),flip(a)].">
      <j1 rule="para" parents="44070 41680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44072">
    <literal><![CDATA[
      L(x,a(y,z,u) \ u,w) = L(x,a(u,z,y) * u,w)
    ]]></literal>
    <justification jstring="[para(44070(a,1),41681(a,1,2)),flip(a)].">
      <j1 rule="para" parents="44070 41681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44073">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * z) = L(x,y,z * a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42468,a(flip),b,44071,a),flip(a)].">
      <j1 rule="hyper" parents="64 42468 44071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44074">
    <literal><![CDATA[
      L(x,a(y,z,u) * y,w) = L(x,y * a(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42472,a(flip),b,44072,a),flip(a)].">
      <j1 rule="hyper" parents="64 42472 44072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44075">
    <literal><![CDATA[
      L(x,y,z \ a(z,u,w)) = L(x,y,z * a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,24662,a,b,44073,a)].">
      <j1 rule="hyper" parents="64 24662 44073"/>
    </justification>
  </clause>

  <clause id="44076">
    <literal><![CDATA[
      L(x,y * a(z,u,y),w) = L(x,y * a(y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(29572,a,44074,a),flip(a)].">
      <j1 rule="hyper" parents="29572 44074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44077">
    <literal><![CDATA[
      L(x,y * a(z,u,y),a(y,u,z) \ y) = L(x,y * a(y,u,z),y \ a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,39805,a(flip),b,44076,a),flip(a)].">
      <j1 rule="hyper" parents="373 39805 44076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44078">
    <literal><![CDATA[
      L(x,y * a(y,z,u),y * a(u,z,y)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,43507,a(flip),b,44076,a),flip(a)].">
      <j1 rule="hyper" parents="64 43507 44076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44079">
    <literal><![CDATA[
      L(x,y * a(z,u,y),y * a(y,u,z)) \ x = a(y * a(y,u,z),y * a(y,u,z),x)
    ]]></literal>
    <justification jstring="[para(44076(a,2),1243(a,1,1))].">
      <j1 rule="para" parents="44076 1243"/>
    </justification>
  </clause>

  <clause id="44080">
    <literal><![CDATA[
      a(x,y,a(z \ L(z,u,w),w,y)) = z \ L(z,u,a(y,w,a(x,y,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,43872,a(flip),b,43984,a)].">
      <j1 rule="hyper" parents="64 43872 43984"/>
    </justification>
  </clause>

  <clause id="44081">
    <literal><![CDATA[
      a(x * L(x,y,a(z,z,u)),w,w) = a(w,w,a(u,z,x * L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,42137,a(flip),b,43985,a),flip(a)].">
      <j1 rule="hyper" parents="373 42137 43985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44082">
    <literal><![CDATA[
      L(a(x,y,y) \ K(y \ 1,y),z,u) = (y \ 1) * L(y,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,41036,a,b,44030,a)].">
      <j1 rule="hyper" parents="64 41036 44030"/>
    </justification>
  </clause>

  <clause id="44083">
    <literal><![CDATA[
      a(x,y,L(a(y,z,u),w,v5)) \ a(u,z,y) = L(a(u,z,y),L(y,w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,42767,a(flip),b,44058,a),flip(a)].">
      <j1 rule="hyper" parents="373 42767 44058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44084">
    <literal><![CDATA[
      a(x * a(y,z,x),a(x * a(y,z,x),u,w),v5) = a(v5,x,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41451,a,b,44059,a)].">
      <j1 rule="hyper" parents="64 41451 44059"/>
    </justification>
  </clause>

  <clause id="44085">
    <literal><![CDATA[
      a(x,y,a(z * L(z,u,w),w,y)) = z \ L(z,u,a(y,w,a(x,y,w)))
    ]]></literal>
    <justification jstring="[para(5609(a,1),44080(a,1,3))].">
      <j1 rule="para" parents="5609 44080"/>
    </justification>
  </clause>

  <clause id="44086">
    <literal><![CDATA[
      L(T(1 / x,x) * L(x,x,y),z,u) = (x \ 1) * L(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(33541(a,1),44082(a,1,1))].">
      <j1 rule="para" parents="33541 44082"/>
    </justification>
  </clause>

  <clause id="44087">
    <literal><![CDATA[
      a(x,y,a(z,u * L(u,w,z),y)) = u \ L(u,w,a(y,z,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(37379(a,1),44085(a,1,3))].">
      <j1 rule="para" parents="37379 44085"/>
    </justification>
  </clause>

  <clause id="44088">
    <literal><![CDATA[
      L((x \ 1) * L(x,x,y),z,u) = (x \ 1) * L(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(117(a,1),44086(a,1,1,1))].">
      <j1 rule="para" parents="117 44086"/>
    </justification>
  </clause>

  <clause id="44089">
    <literal><![CDATA[
      L((x \ 1) * L(x,x,y),z,u) = (x \ 1) * L(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(44024(a,1),44088(a,2,2))].">
      <j1 rule="para" parents="44024 44088"/>
    </justification>
  </clause>

  <clause id="44090">
    <literal><![CDATA[
      a((x * y) \ z,u,L(u,y * x,y)) = a(L(x,y,y) \ (y * z),u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32693,a(flip),b,44018,a),flip(a)].">
      <j1 rule="hyper" parents="373 32693 44018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44091">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,w,v5)) = a(x,L(u,y,z),L(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,41645,a(flip),b,44045,a)].">
      <j1 rule="hyper" parents="64 41645 44045"/>
    </justification>
  </clause>

  <clause id="44092">
    <literal><![CDATA[
      a(x,L(y,z,u),L(y,w,v5)) = L(a(x,y,L(y,w,v5)),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,38572,a(flip),b,44091,a),flip(a)].">
      <j1 rule="hyper" parents="64 38572 44091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44093">
    <literal><![CDATA[
      a(x,L(y,z,u),a(w,v5,y)) = a(x,y,L(a(y,v5,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(40,a,42581,a,b,44083,a)].">
      <j1 rule="hyper" parents="40 42581 44083"/>
    </justification>
  </clause>

  <clause id="44094">
    <literal><![CDATA[
      x \ L(x,y,L(a(y,z,u),w,v5)) = a(x,L(y,w,v5),a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,41770,a,b,44093,a)].">
      <j1 rule="hyper" parents="373 41770 44093"/>
    </justification>
  </clause>

  <clause id="44095">
    <literal><![CDATA[
      L(x,L(y,z,u),a(w,v5,y)) = L(x,y,L(a(y,v5,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(39,a,41768,a,b,44094,a)].">
      <j1 rule="hyper" parents="39 41768 44094"/>
    </justification>
  </clause>

  <clause id="44096">
    <literal><![CDATA[
      L(x,L(y,z,u),a(y,w,v5)) = L(x,y,L(a(y,w,v5),z,u))
    ]]></literal>
    <justification jstring="[hyper(42222,a,44095,a)].">
      <j1 rule="hyper" parents="42222 44095"/>
    </justification>
  </clause>

  <clause id="44097">
    <literal><![CDATA[
      L(x,y \ (z \ y),a(z,u,w)) = L(x,z,L(a(z,u,w),z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29726,a(flip),b,44096,a)].">
      <j1 rule="hyper" parents="64 29726 44096"/>
    </justification>
  </clause>

  <clause id="44098">
    <literal><![CDATA[
      L(x,y \ (z \ y),a(z,u,w)) = L(x,z,a(L(z,z,y),u,w))
    ]]></literal>
    <justification jstring="[para(40756(a,2),44097(a,2,3))].">
      <j1 rule="para" parents="40756 44097"/>
    </justification>
  </clause>

  <clause id="44099">
    <literal><![CDATA[
      L(x,y,a(L(y,y,z),u,w)) = L(x,y,a(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,43991,a(flip),b,44098,a),flip(a)].">
      <j1 rule="hyper" parents="64 43991 44098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44102">
    <literal><![CDATA[
      a(x,a(L(x,y,z),u,w),L(v5,y,z)) = a(w,u,a(v5,x,x))
    ]]></literal>
    <justification jstring="[para(40664(a,1),43929(a,2,3))].">
      <j1 rule="para" parents="40664 43929"/>
    </justification>
  </clause>

  <clause id="44104">
    <literal><![CDATA[
      x * (a(y,z,u) * a(w,v5,a(x,u,u))) = L(x * a(y,z,u),u,a(w,v5,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,42999,a(flip),b,43941,a)].">
      <j1 rule="hyper" parents="64 42999 43941"/>
    </justification>
  </clause>

  <clause id="44105">
    <literal><![CDATA[
      R(a(x,x,y) \ z,z,a(x,x,y)) = a(x,x,y) \ R(z,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30064,a(flip),b,43969,a),flip(a)].">
      <j1 rule="hyper" parents="64 30064 43969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44106">
    <literal><![CDATA[
      R(a(x,x,y) \ z,z,a(x,x,y)) = a(x,x,y) \ L(z,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(28832(a,1),44105(a,2,2))].">
      <j1 rule="para" parents="28832 44105"/>
    </justification>
  </clause>

  <clause id="44107">
    <literal><![CDATA[
      R(a(x,x,y) \ z,z,a(x,x,y)) = (1 / z) \ (a(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,42507,a(flip),b,44106,a),flip(a)].">
      <j1 rule="hyper" parents="373 42507 44106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44108">
    <literal><![CDATA[
      L(a(x,x,y) \ z,z,a(x,x,y)) = (1 / z) \ (a(x,x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(28845,a,44107,a)].">
      <j1 rule="hyper" parents="28845 44107"/>
    </justification>
  </clause>

  <clause id="44109">
    <literal><![CDATA[
      (1 / x) \ (a(y,y,z) \ 1) = (a(y,y,z) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,42517,a(flip),b,44108,a),flip(a)].">
      <j1 rule="hyper" parents="64 42517 44108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44110">
    <literal><![CDATA[
      a(x,x,L(y,z,z)) \ z = (a(x,x,y) / z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,39523,a,b,44109,a)].">
      <j1 rule="hyper" parents="64 39523 44109"/>
    </justification>
  </clause>

  <clause id="44111">
    <literal><![CDATA[
      x * ((a(y,y,z) \ x) \ 1) = a(y,y,L(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(40,a,39154,a,b,44110,a)].">
      <j1 rule="hyper" parents="40 39154 44110"/>
    </justification>
  </clause>

  <clause id="44112">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) / z) \ 1 = z * a(x,x,L(y,z,z))
    ]]></literal>
    <justification jstring="[para(44111(a,1),38627(a,1,2)),flip(a)].">
      <j1 rule="para" parents="44111 38627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44113">
    <literal><![CDATA[
      ((a(x,x,y) \ 1) / z) \ 1 = (1 / z) \ a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,39521,a(flip),b,44112,a),flip(a)].">
      <j1 rule="hyper" parents="373 39521 44112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44114">
    <literal><![CDATA[
      ((1 / x) \ a(y,y,z)) \ 1 = x \ (a(y,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(44113(a,1),31786(a,1,1))].">
      <j1 rule="para" parents="44113 31786"/>
    </justification>
  </clause>

  <clause id="44115">
    <literal><![CDATA[
      (a(x,x,y) * (z * z)) \ ((a(x,x,y) * z) * R(z,x,y)) = a(L(z,z,(1 / z) \ a(x,x,y)),x,y)
    ]]></literal>
    <justification jstring="[para(44113(a,1),43520(a,2,1,3))].">
      <j1 rule="para" parents="44113 43520"/>
    </justification>
  </clause>

  <clause id="44116">
    <literal><![CDATA[
      R(x \ (a(y,y,z) \ 1),x,x) = 1 / (x * a(y,y,z))
    ]]></literal>
    <justification jstring="[para(44114(a,1),40791(a,1,1))].">
      <j1 rule="para" parents="44114 40791"/>
    </justification>
  </clause>

  <clause id="44117">
    <literal><![CDATA[
      (a(x,x,y) \ 1) * (1 / z) = 1 / (z * a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,27818,a(flip),b,44116,a)].">
      <j1 rule="hyper" parents="64 27818 44116"/>
    </justification>
  </clause>

  <clause id="44118">
    <literal><![CDATA[
      1 / (x * a(y,y,z)) = a(y,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42433,a(flip),b,44117,a),flip(a)].">
      <j1 rule="hyper" parents="64 42433 44117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44119">
    <literal><![CDATA[
      1 / (a(x,x,y) * z) = a(x,x,y) \ (1 / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23554,a,b,44118,a)].">
      <j1 rule="hyper" parents="64 23554 44118"/>
    </justification>
  </clause>

  <clause id="44120">
    <literal><![CDATA[
      L(L(x,x,y),L(x,x,y),a(z,x \ y,x \ y)) = L(x,x,L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,44019,a(flip),b,44032,a),flip(a)].">
      <j1 rule="hyper" parents="373 44019 44032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44121">
    <literal><![CDATA[
      L(L(x,x,y),L(x,x,y),a(z,x * y,x * y)) = L(x,x,L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42318,a(flip),b,44120,a)].">
      <j1 rule="hyper" parents="64 42318 44120"/>
    </justification>
  </clause>

  <clause id="44122">
    <literal><![CDATA[
      (x / y) * a(y,z,L(a(u,w,z),y,x)) = y * (L(y,z,a(z,w,u)) \ (x / y))
    ]]></literal>
    <justification jstring="[hyper(373,a,42179,a(flip),b,43867,a),flip(a)].">
      <j1 rule="hyper" parents="373 42179 43867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44123">
    <literal><![CDATA[
      x \ (L(x \ R(x,y,z),u,u) * (x * (R(x,y,z) \ x))) = a(x,u,a(z,y,u))
    ]]></literal>
    <justification jstring="[para(27841(a,1),43968(a,1,2,2))].">
      <j1 rule="para" parents="27841 43968"/>
    </justification>
  </clause>

  <clause id="44124">
    <literal><![CDATA[
      (x / y) * a(y,z,L(a(u,w,z),y,x)) = x / L(y,z,a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,24919,a(flip),b,44122,a),flip(a)].">
      <j1 rule="hyper" parents="373 24919 44122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44125">
    <literal><![CDATA[
      x \ (x * ((R(x,y,z) \ x) * L(x \ R(x,y,z),u,u))) = a(x,u,a(z,y,u))
    ]]></literal>
    <justification jstring="[para(31638(a,1),44123(a,1,2))].">
      <j1 rule="para" parents="31638 44123"/>
    </justification>
  </clause>

  <clause id="44126">
    <literal><![CDATA[
      x \ (x * a(x * L(x,y,z),u,u)) = a(x,u,a(z,y,u))
    ]]></literal>
    <justification jstring="[para(43622(a,1),44125(a,1,2,2))].">
      <j1 rule="para" parents="43622 44125"/>
    </justification>
  </clause>

  <clause id="44127">
    <literal><![CDATA[
      a(x * L(x,y,z),u,u) = a(x,u,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(396,a,44126,a)].">
      <j1 rule="hyper" parents="396 44126"/>
    </justification>
  </clause>

  <clause id="44128">
    <literal><![CDATA[
      a(a(x,y,z),u,L(u,y * z,y * z)) = a(z,u,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,43077,a,b,44127,a)].">
      <j1 rule="hyper" parents="64 43077 44127"/>
    </justification>
  </clause>

  <clause id="44130">
    <literal><![CDATA[
      a(x,x,a(y,z,u * L(u,w,z))) = a(u,x,a(a(z,z,y),w,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,44081,a(flip),b,44127,a)].">
      <j1 rule="hyper" parents="64 44081 44127"/>
    </justification>
  </clause>

  <clause id="44131">
    <literal><![CDATA[
      a(x,x,y \ L(y,z,u)) = a(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,39866,a(flip),b,44127,a)].">
      <j1 rule="hyper" parents="64 39866 44127"/>
    </justification>
  </clause>

  <clause id="44132">
    <literal><![CDATA[
      L(x,x,y * L(y,z,u)) = x * a(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[para(44127(a,1),39868(a,1,2)),flip(a)].">
      <j1 rule="para" parents="44127 39868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44133">
    <literal><![CDATA[
      a(x * L(x,y,(x \ z) * y),u,u) = a(x,u,a((x * y) \ z,y,u))
    ]]></literal>
    <justification jstring="[para(41984(a,1),44127(a,1,1,2))].">
      <j1 rule="para" parents="41984 44127"/>
    </justification>
  </clause>

  <clause id="44134">
    <literal><![CDATA[
      L(a(x,y,a(z,u,y)) \ 1,x,u) = a(y,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[para(44127(a,1),41797(a,1,1,1))].">
      <j1 rule="para" parents="44127 41797"/>
    </justification>
  </clause>

  <clause id="44135">
    <literal><![CDATA[
      a(x,x,y \ L(y,z,u)) = a(a(x,x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,43872,a,b,44131,a),flip(a)].">
      <j1 rule="hyper" parents="373 43872 44131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44136">
    <literal><![CDATA[
      a(x,x,y \ L(y,z,u * L(u,w,z))) = a(y,x,a(z,u * L(u,w,z),x))
    ]]></literal>
    <justification jstring="[para(36277(a,1),44131(a,1,3,2))].">
      <j1 rule="para" parents="36277 44131"/>
    </justification>
  </clause>

  <clause id="44137">
    <literal><![CDATA[
      a(x,x,L(y \ R(y,z,u),w,v5)) = a(a(x,x,L(y,w,v5)),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31323,a(flip),b,44135,a)].">
      <j1 rule="hyper" parents="64 31323 44135"/>
    </justification>
  </clause>

  <clause id="44139">
    <literal><![CDATA[
      L(x,x,y * L(y,z,u)) = L(x,a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,41447,a(flip),b,44132,a),flip(a)].">
      <j1 rule="hyper" parents="373 41447 44132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44140">
    <literal><![CDATA[
      R(1 / (1 / x),x,y * L((x \ y) \ 1,z,u)) = L(x,a(x,z,u),x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,38783,a,b,44139,a)].">
      <j1 rule="hyper" parents="64 38783 44139"/>
    </justification>
  </clause>

  <clause id="44141">
    <literal><![CDATA[
      L(L(x,L(x,x,y),z * L(z,u,w)),L(x,y,y),y) = L(L(x,x,y),a(L(x,x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35534,a,b,44139,a)].">
      <j1 rule="hyper" parents="64 35534 44139"/>
    </justification>
  </clause>

  <clause id="44142">
    <literal><![CDATA[
      L(x,x,y \ (z * L(z \ y,u,w))) = L(x,a(x,u,w),y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33621,a,b,44139,a)].">
      <j1 rule="hyper" parents="64 33621 44139"/>
    </justification>
  </clause>

  <clause id="44143">
    <literal><![CDATA[
      L(x,x,L(y * L(y,z,u),w,v5)) = L(x,a(x,z,u),L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,43688,a(flip),b,44139,a)].">
      <j1 rule="hyper" parents="64 43688 44139"/>
    </justification>
  </clause>

  <clause id="44144">
    <literal><![CDATA[
      L(x,x,(y * z) * L(L(z \ y,z,y),u,w)) = L(x,a(x,u,w),L(z \ y,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,2249,a(flip),b,44139,a)].">
      <j1 rule="hyper" parents="64 2249 44139"/>
    </justification>
  </clause>

  <clause id="44145">
    <literal><![CDATA[
      a(x * L(x,y,z),u,u) \ L(u,u,w) = L(L(u,a(u,y,z),x),u,w)
    ]]></literal>
    <justification jstring="[para(44139(a,1),40707(a,2,1))].">
      <j1 rule="para" parents="44139 40707"/>
    </justification>
  </clause>

  <clause id="44146">
    <literal><![CDATA[
      L(a(x,y,a(y,z,u)) * 1,x,z) = a(y,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(42644(a,1),44134(a,1,1))].">
      <j1 rule="para" parents="42644 44134"/>
    </justification>
  </clause>

  <clause id="44147">
    <literal><![CDATA[
      L(a(x,y,a(y,z,u)),x,z) = a(y,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(8(a,1),44146(a,1,1))].">
      <j1 rule="para" parents="8 44146"/>
    </justification>
  </clause>

  <clause id="44148">
    <literal><![CDATA[
      a(L(x,x,y),z,a(z,y,u)) = a(z,z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,40993,a,b,44147,a)].">
      <j1 rule="hyper" parents="64 40993 44147"/>
    </justification>
  </clause>

  <clause id="44149">
    <literal><![CDATA[
      a(x,y,L(a(z,u,y),x,u)) = a(y,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,43864,a(flip),b,44148,a)].">
      <j1 rule="hyper" parents="64 43864 44148"/>
    </justification>
  </clause>

  <clause id="44150">
    <literal><![CDATA[
      a(x,y,L(a(z,u,y),y * x,u)) = a(y,y,a(y * x,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,43995,a(flip),b,44149,a)].">
      <j1 rule="hyper" parents="64 43995 44149"/>
    </justification>
  </clause>

  <clause id="44151">
    <literal><![CDATA[
      a(x,y,L(a(z,u,y),x,u)) = a(y,y,a(y * x,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,44050,a(flip),b,44150,a)].">
      <j1 rule="hyper" parents="64 44050 44150"/>
    </justification>
  </clause>

  <clause id="44152">
    <literal><![CDATA[
      a(x,x,a(x * y,z,u)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,44149,a(flip),b,44151,a),flip(a)].">
      <j1 rule="hyper" parents="64 44149 44151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44153">
    <literal><![CDATA[
      a(a(x * y,z,u),y,y) = a(y,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,41848,a,b,44152,a)].">
      <j1 rule="hyper" parents="64 41848 44152"/>
    </justification>
  </clause>

  <clause id="44154">
    <literal><![CDATA[
      a(a(x * y,z,u),x,y) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,40500,a,b,44152,a)].">
      <j1 rule="hyper" parents="64 40500 44152"/>
    </justification>
  </clause>

  <clause id="44155">
    <literal><![CDATA[
      R(x,x,a(x * y,z,u)) = x * a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,44152,a(flip),b,30058,a),flip(a)].">
      <j1 rule="hyper" parents="145 44152 30058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44156">
    <literal><![CDATA[
      a(x,x,a(x \ y,z,u)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),44152(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 44152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44157">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z),a((x * y) * z,u,w)) = a(R(x,y,z),R(x,y,z),a(y * z,u,w))
    ]]></literal>
    <justification jstring="[para(111(a,1),44152(a,1,3,1))].">
      <j1 rule="para" parents="111 44152"/>
    </justification>
  </clause>

  <clause id="44158">
    <literal><![CDATA[
      a(x,x,a(y,z,L(u,u,z))) = a(x,x,L(u,z,x * y) \ u)
    ]]></literal>
    <justification jstring="[para(43316(a,1),44152(a,1,3)),flip(a)].">
      <j1 rule="para" parents="43316 44152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44159">
    <literal><![CDATA[
      a(x,y,a(x * y,z,u)) = a(y,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,40512,a(flip),b,44153,a)].">
      <j1 rule="hyper" parents="64 40512 44153"/>
    </justification>
  </clause>

  <clause id="44160">
    <literal><![CDATA[
      (x * a(x,x,a(y,z,u))) \ (x * y) = L(y,x,a(x * y,z,u))
    ]]></literal>
    <justification jstring="[para(44154(a,1),42083(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="44154 42083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44161">
    <literal><![CDATA[
      R(x,x,a(x * y,z,u)) = R(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,30054,a(flip),b,44155,a),flip(a)].">
      <j1 rule="hyper" parents="373 30054 44155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44162">
    <literal><![CDATA[
      R(x,x,a(x * y,z,u)) = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,28832,a(flip),b,44161,a),flip(a)].">
      <j1 rule="hyper" parents="373 28832 44161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44163">
    <literal><![CDATA[
      L(x,x,a(x * y,z,u)) = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(28845,a,44162,a)].">
      <j1 rule="hyper" parents="28845 44162"/>
    </justification>
  </clause>

  <clause id="44164">
    <literal><![CDATA[
      L(x,x,a(y,z,u * x)) = L(x,x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42202,a(flip),b,44163,a)].">
      <j1 rule="hyper" parents="64 42202 44163"/>
    </justification>
  </clause>

  <clause id="44165">
    <literal><![CDATA[
      L(x,x,a(y,z,u * x)) = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,42195,a,b,44164,a),flip(a)].">
      <j1 rule="hyper" parents="373 42195 44164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44166">
    <literal><![CDATA[
      a(x,x,a(y,z,L(u,u,z))) = a(x,x,u \ L(u,z,x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,38706,a(flip),b,44158,a),flip(a)].">
      <j1 rule="hyper" parents="373 38706 44158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44167">
    <literal><![CDATA[
      a(x,y,a(y * z,u,y)) = a(y,y,a(z,u,L(x,x,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,44131,a(flip),b,44166,a)].">
      <j1 rule="hyper" parents="373 44131 44166"/>
    </justification>
  </clause>

  <clause id="44168">
    <literal><![CDATA[
      a(x,y,a(y * z,u,y)) = a(y,y,L(x,u,z) \ x)
    ]]></literal>
    <justification jstring="[para(43316(a,1),44167(a,2,3))].">
      <j1 rule="para" parents="43316 44167"/>
    </justification>
  </clause>

  <clause id="44169">
    <literal><![CDATA[
      a(x,y,a(y * z,u,y)) = a(y,y,x \ L(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,38706,a(flip),b,44168,a),flip(a)].">
      <j1 rule="hyper" parents="373 38706 44168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44170">
    <literal><![CDATA[
      a(x,y,a(y * z,u,y)) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,44131,a(flip),b,44169,a),flip(a)].">
      <j1 rule="hyper" parents="373 44131 44169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44171">
    <literal><![CDATA[
      a(x,a(x,y,x * z),u) = a(u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41451,a,b,44170,a)].">
      <j1 rule="hyper" parents="64 41451 44170"/>
    </justification>
  </clause>

  <clause id="44172">
    <literal><![CDATA[
      a(x,y,a(y,z,u * y)) = a(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41897,a(flip),b,44170,a)].">
      <j1 rule="hyper" parents="64 41897 44170"/>
    </justification>
  </clause>

  <clause id="44173">
    <literal><![CDATA[
      a(x,y,a(y \ z,u,y)) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(10(a,1),44170(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 44170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44174">
    <literal><![CDATA[
      a(x * a(y,z,x),a(x \ a(y,z,x),u,(x \ a(y,z,x)) * w),v5) = a(v5,x \ a(y,z,x),a(w,u,x \ a(y,z,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,9437,a(flip),b,44171,a)].">
      <j1 rule="hyper" parents="64 9437 44171"/>
    </justification>
  </clause>

  <clause id="44175">
    <literal><![CDATA[
      (x * a(x,y,x * z)) * (a(x,y,x * z) \ (x \ u)) = u * a(a(x,y,x * z) \ (x \ u),x,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,44171,a(flip),b,345,a),flip(a)].">
      <j1 rule="hyper" parents="145 44171 345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44176">
    <literal><![CDATA[
      a(R(x,y,z),a(R(x,y,z),u,x \ ((x * y) * T(z,y))),w) = a(w,R(x,y,z),a(x \ (z * y),u,R(x,y,z)))
    ]]></literal>
    <justification jstring="[para(10238(a,1),44171(a,1,2,3))].">
      <j1 rule="para" parents="10238 44171"/>
    </justification>
  </clause>

  <clause id="44177">
    <literal><![CDATA[
      a(x \ y,z,a(u,x,x)) = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,43873,a,b,44173,a)].">
      <j1 rule="hyper" parents="64 43873 44173"/>
    </justification>
  </clause>

  <clause id="44178">
    <literal><![CDATA[
      a(x,y,y) * a(x,y,a(z,u,y)) = a(x,y,L(y,u,y \ z))
    ]]></literal>
    <justification jstring="[hyper(145,a,44173,a(flip),b,44035,a)].">
      <j1 rule="hyper" parents="145 44173 44035"/>
    </justification>
  </clause>

  <clause id="44179">
    <literal><![CDATA[
      a(x,y,L(y,z,y \ u)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,44034,a(flip),b,44178,a),flip(a)].">
      <j1 rule="hyper" parents="64 44034 44178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44180">
    <literal><![CDATA[
      a(x,y,L(y,z,u * y)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(23842(a,1),44179(a,1,3)),flip(a)].">
      <j1 rule="para" parents="23842 44179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44181">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,z,u),w,v5)) = a(x,y,L(y,w,v5 * L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,44038,a(flip),b,44180,a),flip(a)].">
      <j1 rule="hyper" parents="64 44038 44180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44182">
    <literal><![CDATA[
      a(x,x,a(y,z,u * L(u,w,z))) = a(u,x,a(y,z,a(x,w,z)))
    ]]></literal>
    <justification jstring="[para(43872(a,1),44130(a,2,3))].">
      <j1 rule="para" parents="43872 44130"/>
    </justification>
  </clause>

  <clause id="44183">
    <literal><![CDATA[
      a(x,x,L(y \ R(y,z,u),w,v5)) = a(x,a(x,z,u),L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,43874,a(flip),b,44137,a),flip(a)].">
      <j1 rule="hyper" parents="373 43874 44137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44184">
    <literal><![CDATA[
      a(a(x,x,L(y,y,z * u)),u,z) = a(x,x,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(23986(a,2),44137(a,1,3)),flip(a)].">
      <j1 rule="para" parents="23986 44137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44185">
    <literal><![CDATA[
      a(x,a(x,y,z),L(u,u,z * y)) = a(x,x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,43874,a(flip),b,44184,a)].">
      <j1 rule="hyper" parents="64 43874 44184"/>
    </justification>
  </clause>

  <clause id="44186">
    <literal><![CDATA[
      a(x,a(x,y,z),L(u,u,z * y)) = a(a(u,y,z),x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,41803,a,b,44185,a),flip(a)].">
      <j1 rule="hyper" parents="373 41803 44185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44187">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,u,x * y))) = a(a(u,y,x),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,43907,a(flip),b,44186,a)].">
      <j1 rule="hyper" parents="64 43907 44186"/>
    </justification>
  </clause>

  <clause id="44188">
    <literal><![CDATA[
      R(x,x,y \ (z * R(z \ y,u,w))) = L(x,a(x,u,w),L(z * y,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,40638,a(flip),b,44143,a)].">
      <j1 rule="hyper" parents="64 40638 44143"/>
    </justification>
  </clause>

  <clause id="44189">
    <literal><![CDATA[
      R(x,x,a(y,z,u)) \ (x * y) = L(y,x,a(x * y,z,u))
    ]]></literal>
    <justification jstring="[para(30054(a,1),44160(a,1,1))].">
      <j1 rule="para" parents="30054 44160"/>
    </justification>
  </clause>

  <clause id="44190">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ (x * y) = L(y,x,a(x * y,z,u))
    ]]></literal>
    <justification jstring="[para(28832(a,1),44189(a,1,1))].">
      <j1 rule="para" parents="28832 44189"/>
    </justification>
  </clause>

  <clause id="44191">
    <literal><![CDATA[
      L(x,y,a(y * x,z,u)) = x * a(a(x,z,u),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,37628,a(flip),b,44190,a),flip(a)].">
      <j1 rule="hyper" parents="64 37628 44190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44192">
    <literal><![CDATA[
      L(x,y,a(y * x,z,u)) = a(y,y,a(u,z,x)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,41881,a,b,44191,a),flip(a)].">
      <j1 rule="hyper" parents="373 41881 44191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44193">
    <literal><![CDATA[
      a(x,a(x,y,z),L(u * w,w,w)) = a(x,x,w \ (u * R(u \ w,y,z)))
    ]]></literal>
    <justification jstring="[para(40636(a,1),44183(a,1,3)),flip(a)].">
      <j1 rule="para" parents="40636 44183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44194">
    <literal><![CDATA[
      a(x,y,a((x * z) \ u,z,y)) = a(x,y,a((x \ u) * z,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,44127,a(flip),b,44133,a),flip(a)].">
      <j1 rule="hyper" parents="64 44127 44133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44195">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ L(y,y,w) = L(L(y,a(y,u,z),x),y,w)
    ]]></literal>
    <justification jstring="[para(44127(a,1),44145(a,1,1))].">
      <j1 rule="para" parents="44127 44145"/>
    </justification>
  </clause>

  <clause id="44196">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * L(y,y,w) = L(L(y,a(y,z,u),x),y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42644,a(flip),b,44195,a)].">
      <j1 rule="hyper" parents="64 42644 44195"/>
    </justification>
  </clause>

  <clause id="44197">
    <literal><![CDATA[
      L(L(x,a(x,y,z),u),x,u) = L(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,43938,a(flip),b,44196,a),flip(a)].">
      <j1 rule="hyper" parents="64 43938 44196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44198">
    <literal><![CDATA[
      a(x,y,L(y,z,u * L(y,w,v5))) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,44038,a(flip),b,44181,a),flip(a)].">
      <j1 rule="hyper" parents="64 44038 44181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44200">
    <literal><![CDATA[
      a(x,y,L(y,z,L(y,u,w) * v5)) = a(x,y,L(y,z,v5))
    ]]></literal>
    <justification jstring="[para(23253(a,1),44198(a,1,3))].">
      <j1 rule="para" parents="23253 44198"/>
    </justification>
  </clause>

  <clause id="44201">
    <literal><![CDATA[
      R(x,x,y \ (z * R(z \ y,u,w))) = L(x,a(x,u,w),y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,30388,a(flip),b,44188,a),flip(a)].">
      <j1 rule="hyper" parents="373 30388 44188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44202">
    <literal><![CDATA[
      R(x,x,x \ (y \ (z * R(z \ (y * x),u,w)))) = L(x,a(x,u,w),(y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,39667,a(flip),b,44201,a)].">
      <j1 rule="hyper" parents="64 39667 44201"/>
    </justification>
  </clause>

  <clause id="44203">
    <literal><![CDATA[
      a(x,x,y \ (z * R(z \ y,u,w))) = a(x,a(x,u,w),(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38945,a(flip),b,44193,a),flip(a)].">
      <j1 rule="hyper" parents="64 38945 44193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44204">
    <literal><![CDATA[
      a(x,x,y \ (z * R(z \ y,u,w))) = a(x,a(w,u,x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,42397,a(flip),b,44203,a),flip(a)].">
      <j1 rule="hyper" parents="373 42397 44203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44205">
    <literal><![CDATA[
      a(x,x,(a(x,y,z) * u) \ R(a(x,y,z) * u,w,v5)) = a(x,a(v5,w,x),u \ a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39668,a,b,44204,a)].">
      <j1 rule="hyper" parents="64 39668 44204"/>
    </justification>
  </clause>

  <clause id="44206">
    <literal><![CDATA[
      a(x,y,a(z,u * L(u,w,z),y)) = a(y,y,a(x,z,u \ L(u,w,z)))
    ]]></literal>
    <justification jstring="[para(41477(a,1),44136(a,1,3)),flip(a)].">
      <j1 rule="para" parents="41477 44136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44207">
    <literal><![CDATA[
      a(x,y,a(z,u * L(u,w,z),y)) = a(y,y,a(x,z,u * L(u,w,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,42137,a(flip),b,44206,a),flip(a)].">
      <j1 rule="hyper" parents="373 42137 44206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44208">
    <literal><![CDATA[
      a(x,y,a(z,u * L(u,w,z),y)) = a(u,y,a(x,z,a(y,w,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,44182,a(flip),b,44207,a),flip(a)].">
      <j1 rule="hyper" parents="373 44182 44207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44209">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,a(w,z,u))) = a(x,z,a(w,u,a(z,y,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,44087,a(flip),b,44208,a)].">
      <j1 rule="hyper" parents="64 44087 44208"/>
    </justification>
  </clause>

  <clause id="44210">
    <literal><![CDATA[
      x * a(x,y,a(z,u,a(y,w,u))) = R(x,w,a(y,u,a(z,y,u)))
    ]]></literal>
    <justification jstring="[para(44209(a,1),28834(a,1,2))].">
      <j1 rule="para" parents="44209 28834"/>
    </justification>
  </clause>

  <clause id="44211">
    <literal><![CDATA[
      R(x,y,a(z,u,a(w,z,u))) = L(x,z,a(z,y,a(u,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,43891,a(flip),b,44210,a),flip(a)].">
      <j1 rule="hyper" parents="64 43891 44210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44212">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,z,u))) = L(x,z,a(z,y,a(u,u,w)))
    ]]></literal>
    <justification jstring="[hyper(28845,a,44211,a)].">
      <j1 rule="hyper" parents="28845 44211"/>
    </justification>
  </clause>

  <clause id="44213">
    <literal><![CDATA[
      R(1 / (1 / x),x,y * L((x \ y) \ 1,z,u)) = L(x,a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,39347,a(flip),b,44140,a),flip(a)].">
      <j1 rule="hyper" parents="373 39347 44140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44214">
    <literal><![CDATA[
      R(x,x,(1 / (K(y,z) / (x \ u))) * L((x \ u) \ 1,w,v5)) = L(x,a(x,w,v5),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,39195,a,b,44213,a)].">
      <j1 rule="hyper" parents="64 39195 44213"/>
    </justification>
  </clause>

  <clause id="44215">
    <literal><![CDATA[
      a(x,x,y) * a(y,x,a(z,u * x,x)) = R(a(x,x,y),u / (x \ 1),z)
    ]]></literal>
    <justification jstring="[para(43994(a,1),44055(a,1,2))].">
      <j1 rule="para" parents="43994 44055"/>
    </justification>
  </clause>

  <clause id="44216">
    <literal><![CDATA[
      R(a(x,x,y),z / (x \ 1),u) = a(x,x,L(y,z * x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,43883,a(flip),b,44215,a),flip(a)].">
      <j1 rule="hyper" parents="64 43883 44215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44217">
    <literal><![CDATA[
      a(x,x,L(y,z * x,u)) = R(a(x,x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26481,a(flip),b,44216,a),flip(a)].">
      <j1 rule="hyper" parents="64 26481 44216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44218">
    <literal><![CDATA[
      a(x,x,L(y,x \ z,u)) = a(x,x,L(y,z * x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,39680,a,b,44217,a)].">
      <j1 rule="hyper" parents="373 39680 44217"/>
    </justification>
  </clause>

  <clause id="44220">
    <literal><![CDATA[
      a(x,(y * (x \ (y \ z))) \ z,u) = a(x,x,L(u,(y \ z) * x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,39747,a,b,44218,a)].">
      <j1 rule="hyper" parents="64 39747 44218"/>
    </justification>
  </clause>

  <clause id="44221">
    <literal><![CDATA[
      a(x,((y \ 1) * (x \ T((y \ z) * y,y \ 1))) \ T(z * (y \ 1),y),u) = a(x,x,L(u,((y \ 1) \ T(z * (y \ 1),y)) * x,y \ 1))
    ]]></literal>
    <justification jstring="[para(1041(a,1),44220(a,1,2,1,2,2))].">
      <j1 rule="para" parents="1041 44220"/>
    </justification>
  </clause>

  <clause id="44222">
    <literal><![CDATA[
      L(x,y * (z \ (y \ 1)),a(y * (z \ (y \ 1)),u,w)) = L(x,z,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,41456,a(flip),b,44057,a),flip(a)].">
      <j1 rule="hyper" parents="373 41456 44057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44223">
    <literal><![CDATA[
      L(x,y * (z \ (y \ 1)),a((z \ y) * y,u,w)) = L(x,z,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(32689(a,1),44222(a,1,3))].">
      <j1 rule="para" parents="32689 44222"/>
    </justification>
  </clause>

  <clause id="44224">
    <literal><![CDATA[
      L(x,(y \ z) * z,a((y \ z) * z,u,w)) = L(x,y,a(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,29835,a(flip),b,44223,a)].">
      <j1 rule="hyper" parents="64 29835 44223"/>
    </justification>
  </clause>

  <clause id="44225">
    <literal><![CDATA[
      L(L(x,(y \ z) * z,u),y,a(y,u,u)) = L(x,L((y \ z) * z,(y \ z) * z,u),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,40948,a(flip),b,44224,a),flip(a)].">
      <j1 rule="hyper" parents="64 40948 44224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44226">
    <literal><![CDATA[
      L(x,y * a(z,u,y),y * a(y,u,z)) = L(x,y * a(y,u,z),y \ a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42468,a(flip),b,44077,a)].">
      <j1 rule="hyper" parents="64 42468 44077"/>
    </justification>
  </clause>

  <clause id="44227">
    <literal><![CDATA[
      L(x,x,y * (z * L(z \ y,u,w))) = L(x,a(x,u,w),L(z \ y,z,y))
    ]]></literal>
    <justification jstring="[para(513(a,1),44144(a,1,3))].">
      <j1 rule="para" parents="513 44144"/>
    </justification>
  </clause>

  <clause id="44228">
    <literal><![CDATA[
      L(x,x,y * (z * L(z \ y,u,w))) = L(x,a(x,u,w),y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,2198,a(flip),b,44227,a),flip(a)].">
      <j1 rule="hyper" parents="373 2198 44227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44229">
    <literal><![CDATA[
      R(x,x,x \ ((y \ z) * R((y \ z) \ x,u,w))) = L(x,a(x,u,w),(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(1956(a,1),44202(a,1,3,2))].">
      <j1 rule="para" parents="1956 44202"/>
    </justification>
  </clause>

  <clause id="44230">
    <literal><![CDATA[
      R(x,x,L((x \ y) \ K(z,u),w,v5) * (x \ y)) = L(x,a(x,w,v5),y)
    ]]></literal>
    <justification jstring="[para(35315(a,1),44214(a,1,3))].">
      <j1 rule="para" parents="35315 44214"/>
    </justification>
  </clause>

  <clause id="44231">
    <literal><![CDATA[
      R(x,x,(x \ y) * L((x \ y) \ 1,z,u)) = L(x,a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26302,a(flip),b,44230,a)].">
      <j1 rule="hyper" parents="64 26302 44230"/>
    </justification>
  </clause>

  <clause id="44232">
    <literal><![CDATA[
      R(x,x,x \ (y * L(y \ x,z,u))) = L(x,a(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(2469(a,1),44231(a,1,3))].">
      <j1 rule="para" parents="2469 44231"/>
    </justification>
  </clause>

  <clause id="44233">
    <literal><![CDATA[
      R(x,x,y * (x \ L(y \ x,z,u))) = L(x,a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,34683,a(flip),b,44232,a)].">
      <j1 rule="hyper" parents="64 34683 44232"/>
    </justification>
  </clause>

  <clause id="44234">
    <literal><![CDATA[
      L(x,y * a(z,u,y),y * a(y,u,z)) = L(x,y * a(y,u,z),y * a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,44075,a(flip),b,44226,a),flip(a)].">
      <j1 rule="hyper" parents="373 44075 44226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44235">
    <literal><![CDATA[
      R(x,x,(y \ z) * (x \ R((y \ z) \ x,u,w))) = L(x,a(x,u,w),(y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34683,a(flip),b,44229,a)].">
      <j1 rule="hyper" parents="64 34683 44229"/>
    </justification>
  </clause>

  <clause id="44236">
    <literal><![CDATA[
      L(x,y * a(z,u,y),y * a(y,u,z)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,44078,a(flip),b,44234,a),flip(a)].">
      <j1 rule="hyper" parents="373 44078 44234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44238">
    <literal><![CDATA[
      R(x,x,(y \ z) * (x \ L((y \ z) \ x,u,w))) = L(x,a(x,u,w),(y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,43474,a(flip),b,44235,a)].">
      <j1 rule="hyper" parents="64 43474 44235"/>
    </justification>
  </clause>

  <clause id="44239">
    <literal><![CDATA[
      L(x,a(x,y,z),(u * x) \ w) = L(x,a(x,y,z),u \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,44233,a(flip),b,44238,a),flip(a)].">
      <j1 rule="hyper" parents="64 44233 44238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44240">
    <literal><![CDATA[
      (x \ L(L(x,x,L(y,z,u)),x,L(x,x,x))) * a(x,x,x) = x \ L(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(44024(a,1),44049(a,1,1,2,1))].">
      <j1 rule="para" parents="44024 44049"/>
    </justification>
  </clause>

  <clause id="44241">
    <literal><![CDATA[
      L(L(x,(y \ z) * z,z),y,a(y,z,z)) = L(x,L((y \ z) * z,y,z),z)
    ]]></literal>
    <justification jstring="[para(35547(a,1),44225(a,2,2))].">
      <j1 rule="para" parents="35547 44225"/>
    </justification>
  </clause>

  <clause id="44242">
    <literal><![CDATA[
      L(L(x,(y \ z) * z,z),y,a(y,z,z)) = L(x,L(y,z,z),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,34391,a(flip),b,44241,a),flip(a)].">
      <j1 rule="hyper" parents="373 34391 44241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44243">
    <literal><![CDATA[
      L(L(x,(y \ z) * z,z),y,a(y,z,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,43540,a(flip),b,44242,a),flip(a)].">
      <j1 rule="hyper" parents="373 43540 44242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44244">
    <literal><![CDATA[
      ((x \ 1) * L(x,x,L(y,z,u))) * a(x,x,x) = x \ L(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12990(a,1),44240(a,1,1))].">
      <j1 rule="para" parents="12990 44240"/>
    </justification>
  </clause>

  <clause id="44246">
    <literal><![CDATA[
      L((x \ 1) * L(x,x,y),z,u) * a(x,x,x) = x \ L(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(44089(a,2),44244(a,1,1))].">
      <j1 rule="para" parents="44089 44244"/>
    </justification>
  </clause>

  <clause id="44247">
    <literal><![CDATA[
      L(((x \ 1) * L(x,x,y)) * a(x,x,x),z,u) = x \ L(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,13623,a,b,44246,a)].">
      <j1 rule="hyper" parents="64 13623 44246"/>
    </justification>
  </clause>

  <clause id="44248">
    <literal><![CDATA[
      L((x \ 1) * (L(x,x,y) * a(x,x,x)),z,u) = x \ L(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(13196(a,1),44247(a,1,1))].">
      <j1 rule="para" parents="13196 44247"/>
    </justification>
  </clause>

  <clause id="44249">
    <literal><![CDATA[
      L((x \ 1) * L(R(x,x,x),x,y),z,u) = x \ L(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(13191(a,1),44248(a,1,1,2))].">
      <j1 rule="para" parents="13191 44248"/>
    </justification>
  </clause>

  <clause id="44250">
    <literal><![CDATA[
      L(x \ L(x,x,y),z,u) = x \ L(x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(1809(a,1),44249(a,1,1))].">
      <j1 rule="para" parents="1809 44249"/>
    </justification>
  </clause>

  <clause id="44251">
    <literal><![CDATA[
      L(x \ L(x,x,y),z,u) = x \ L(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(44024(a,1),44250(a,2,2))].">
      <j1 rule="para" parents="44024 44250"/>
    </justification>
  </clause>

  <clause id="44252">
    <literal><![CDATA[
      L(((a(x,y,y) \ z) * x) * a(y,y,a(z,x,x)),y,a(y,x,x)) = (a(x,y,y) \ z) * x
    ]]></literal>
    <justification jstring="[hyper(64,a,41078,a,b,43970,a)].">
      <j1 rule="hyper" parents="64 41078 43970"/>
    </justification>
  </clause>

  <clause id="44254">
    <literal><![CDATA[
      a(x * a(x,y,z),x * a(x,y,z),u) = L(u,x,x) \ u
    ]]></literal>
    <justification jstring="[para(44236(a,1),44079(a,1,1)),flip(a)].">
      <j1 rule="para" parents="44236 44079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44255">
    <literal><![CDATA[
      a(x * a(x,y,z),x * a(x,y,z),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,1243,a(flip),b,44254,a),flip(a)].">
      <j1 rule="hyper" parents="373 1243 44254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44257">
    <literal><![CDATA[
      a(a(x,y,z) * x,a(x,y,z) * x,u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31940,a,b,44255,a)].">
      <j1 rule="hyper" parents="64 31940 44255"/>
    </justification>
  </clause>

  <clause id="44258">
    <literal><![CDATA[
      a(a(x,y,z) * x,a(x,y,z) * x,a(u,w,v5)) = a(x,x,a((a(x,y,z) * x) * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,44152,a(flip),b,44257,a)].">
      <j1 rule="hyper" parents="64 44152 44257"/>
    </justification>
  </clause>

  <clause id="44259">
    <literal><![CDATA[
      L((a(x,y,y) \ z) * L(x,x,a(z,y,y)),y,a(y,x,x)) = (a(x,y,y) \ z) * x
    ]]></literal>
    <justification jstring="[para(39763(a,1),44252(a,1,1))].">
      <j1 rule="para" parents="39763 44252"/>
    </justification>
  </clause>

  <clause id="44260">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ y),z,a(z,y,y)) = (a(y,z,z) \ x) * y
    ]]></literal>
    <justification jstring="[para(41055(a,1),44259(a,1,1))].">
      <j1 rule="para" parents="41055 44259"/>
    </justification>
  </clause>

  <clause id="44261">
    <literal><![CDATA[
      L(L(x,x,y * L(y,z,u)),L(x,w,w),w) = L(L(x,x,w),a(L(x,x,w),z,u),y)
    ]]></literal>
    <justification jstring="[para(40680(a,1),44141(a,1,1))].">
      <j1 rule="para" parents="40680 44141"/>
    </justification>
  </clause>

  <clause id="44263">
    <literal><![CDATA[
      L(L(x,a(x,y,z),u),L(x,w,w),w) = L(L(x,x,w),a(L(x,x,w),y,z),u)
    ]]></literal>
    <justification jstring="[para(44139(a,1),44261(a,1,1))].">
      <j1 rule="para" parents="44139 44261"/>
    </justification>
  </clause>

  <clause id="44264">
    <literal><![CDATA[
      L(L(x,x,y),a(L(x,x,y),z,u),w) = L(L(x,x,y),a(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,35534,a(flip),b,44263,a),flip(a)].">
      <j1 rule="hyper" parents="64 35534 44263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44265">
    <literal><![CDATA[
      a(x,x,(a(x,y,z) * u) \ R(a(x,y,z) * u,w,v5)) = a(v5,w,a(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,43930,a(flip),b,44205,a),flip(a)].">
      <j1 rule="hyper" parents="373 43930 44205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44267">
    <literal><![CDATA[
      a(R(x,y,z),R(x,y,z),a((x * y) * z,u,w)) = a(x,x,a(y * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,35156,a(flip),b,44157,a),flip(a)].">
      <j1 rule="hyper" parents="373 35156 44157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44269">
    <literal><![CDATA[
      a(x,x,a((x * y) * z,u,w)) = a(x,x,a(y * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,35156,a(flip),b,44267,a)].">
      <j1 rule="hyper" parents="64 35156 44267"/>
    </justification>
  </clause>

  <clause id="44271">
    <literal><![CDATA[
      a(x,x,a((y * x) * z,u,w)) = a(x,x,a(y * z,u,w))
    ]]></literal>
    <justification jstring="[para(32388(a,1),44269(a,1,3))].">
      <j1 rule="para" parents="32388 44269"/>
    </justification>
  </clause>

  <clause id="44272">
    <literal><![CDATA[
      a(a(x,y,z) * x,a(x,y,z) * x,a(u,w,v5)) = a(x,x,a(a(x,y,z) * u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,44258,a,b,44271,a)].">
      <j1 rule="hyper" parents="64 44258 44271"/>
    </justification>
  </clause>

  <clause id="44273">
    <literal><![CDATA[
      a(x,x,a(a(x,y,z) * u,w,v5)) = a(x,x,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,44257,a(flip),b,44272,a),flip(a)].">
      <j1 rule="hyper" parents="64 44257 44272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44275">
    <literal><![CDATA[
      a(x,x,a(a(y,z,x) * u,w,v5)) = a(x,x,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(42670(a,1),44273(a,1,3))].">
      <j1 rule="para" parents="42670 44273"/>
    </justification>
  </clause>

  <clause id="44276">
    <literal><![CDATA[
      ((x / y) / (1 / y)) * a(z \ (a(x,y,y) \ z),u,w) = a(x,y,y) \ L(x,y,a(y,u,w))
    ]]></literal>
    <justification jstring="[para(41456(a,1),43914(a,1,2)),flip(a)].">
      <j1 rule="para" parents="41456 43914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44277">
    <literal><![CDATA[
      ((x / y) / (1 / y)) * a(z \ (a(x,y,y) \ z),u,w) = L(a(x,y,y) \ x,y,a(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,37990,a,b,44276,a),flip(a)].">
      <j1 rule="hyper" parents="373 37990 44276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44278">
    <literal><![CDATA[
      ((x / y) / (1 / y)) * a(a(x,y,y),z,u) = L(a(x,y,y) \ x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(40755(a,1),44277(a,1,2))].">
      <j1 rule="para" parents="40755 44277"/>
    </justification>
  </clause>

  <clause id="44279">
    <literal><![CDATA[
      L(a(x,y,y) \ x,y,a(y,z,u)) = a(x,y,L(y,z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,44020,a(flip),b,44278,a),flip(a)].">
      <j1 rule="hyper" parents="64 44020 44278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44280">
    <literal><![CDATA[
      (x * a(y,z,z \ 1)) * a(y,z,a(x,x,z)) = (((y * z) \ y) / x) \ (z \ 1)
    ]]></literal>
    <justification jstring="[para(44064(a,1),43916(a,1,2))].">
      <j1 rule="para" parents="44064 43916"/>
    </justification>
  </clause>

  <clause id="44281">
    <literal><![CDATA[
      x * (a(y,z,z \ 1) * a(y,z,a(x,x,z))) = (((y * z) \ y) / x) \ (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,42999,a(flip),b,44280,a)].">
      <j1 rule="hyper" parents="64 42999 44280"/>
    </justification>
  </clause>

  <clause id="44283">
    <literal><![CDATA[
      (((x * y) \ x) / z) \ (y \ 1) = z * a(x,y,L(y \ 1,z,z))
    ]]></literal>
    <justification jstring="[para(43894(a,1),44281(a,1,2)),flip(a)].">
      <j1 rule="para" parents="43894 44281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44284">
    <literal><![CDATA[
      (((x * y) \ x) / z) \ (y \ 1) = (1 / z) \ a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,40991,a(flip),b,44283,a),flip(a)].">
      <j1 rule="hyper" parents="373 40991 44283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44285">
    <literal><![CDATA[
      (L(x,x,y) / z) \ x = (1 / z) \ a(y,x \ 1,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27875,a,b,44284,a)].">
      <j1 rule="hyper" parents="64 27875 44284"/>
    </justification>
  </clause>

  <clause id="44286">
    <literal><![CDATA[
      (L(x,x,y) / z) \ x = (1 / z) \ a(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(5340(a,1),44285(a,2,2))].">
      <j1 rule="para" parents="5340 44285"/>
    </justification>
  </clause>

  <clause id="44287">
    <literal><![CDATA[
      (L(x,x,y) / z) \ x = (1 / z) \ a(y,x,x)
    ]]></literal>
    <justification jstring="[para(11980(a,1),44286(a,2,2))].">
      <j1 rule="para" parents="11980 44286"/>
    </justification>
  </clause>

  <clause id="44289">
    <literal><![CDATA[
      L(x \ (a(y,y,z) * z),x,a(x,y,y)) = (a(y,y,z) * z) * (z \ (x \ z))
    ]]></literal>
    <justification jstring="[para(30233(a,1),44062(a,2,2,2,2))].">
      <j1 rule="para" parents="30233 44062"/>
    </justification>
  </clause>

  <clause id="44290">
    <literal><![CDATA[
      L(x \ (a(y,y,z) * z),x,a(x,y,y)) = z * (L(z,y,y) \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,37021,a(flip),b,44289,a),flip(a)].">
      <j1 rule="hyper" parents="373 37021 44289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44291">
    <literal><![CDATA[
      (a(x,x,y) * (z * z)) \ ((a(x,x,y) * z) * R(z,x,y)) = a(L(z,z,(z \ 1) \ a(x,x,y)),x,y)
    ]]></literal>
    <justification jstring="[para(2236(a,1),44115(a,2,1))].">
      <j1 rule="para" parents="2236 44115"/>
    </justification>
  </clause>

  <clause id="44292">
    <literal><![CDATA[
      (a(x,x,y) * (z * z)) \ ((a(x,x,y) * z) * R(z,x,y)) = a(L(z,z,z * a(x,x,y)),x,y)
    ]]></literal>
    <justification jstring="[para(41980(a,1),44291(a,2,1))].">
      <j1 rule="para" parents="41980 44291"/>
    </justification>
  </clause>

  <clause id="44293">
    <literal><![CDATA[
      (a(x,x,y) * (z * z)) \ ((a(x,x,y) * z) * R(z,x,y)) = a(L(z,z,a(x,x,y)),x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,36752,a(flip),b,44292,a),flip(a)].">
      <j1 rule="hyper" parents="373 36752 44292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44294">
    <literal><![CDATA[
      (a(x,x,y) * (z * z)) \ ((a(x,x,y) * z) * R(z,x,y)) = a(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,41521,a(flip),b,44293,a),flip(a)].">
      <j1 rule="hyper" parents="373 41521 44293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44296">
    <literal><![CDATA[
      (a(x,x,y) * (z * z)) \ (z * (a(x,x,y) * R(z,x,y))) = a(z,x,y)
    ]]></literal>
    <justification jstring="[para(23955(a,1),44294(a,1,2))].">
      <j1 rule="para" parents="23955 44294"/>
    </justification>
  </clause>

  <clause id="44297">
    <literal><![CDATA[
      (a(x,x,y) * (z * z)) \ (z * R(z * a(x,x,y),x,y)) = a(z,x,y)
    ]]></literal>
    <justification jstring="[para(38073(a,2),44296(a,1,2,2))].">
      <j1 rule="para" parents="38073 44296"/>
    </justification>
  </clause>

  <clause id="44298">
    <literal><![CDATA[
      (x * x) \ (a(y,y,z) \ (x * R(x * a(y,y,z),y,z))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(712,a,44297,a)].">
      <j1 rule="hyper" parents="712 44297"/>
    </justification>
  </clause>

  <clause id="44299">
    <literal><![CDATA[
      a(x,x,y) \ ((1 / z) * R(z * a(x,x,y),x,y)) = a(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,23787,a(flip),b,44298,a)].">
      <j1 rule="hyper" parents="64 23787 44298"/>
    </justification>
  </clause>

  <clause id="44300">
    <literal><![CDATA[
      a(x,x,y) \ (z * R((z \ 1) * a(x,x,y),x,y)) = a(z,x,y)
    ]]></literal>
    <justification jstring="[para(2170(a,1),44299(a,1,2))].">
      <j1 rule="para" parents="2170 44299"/>
    </justification>
  </clause>

  <clause id="44301">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),R(x,z,u),a(L(x,z,u),y,y)) = R(x,z,u) * (L(x \ R(x,z,u),y,y) \ 1)
    ]]></literal>
    <justification jstring="[para(32590(a,1),43971(a,1,3))].">
      <j1 rule="para" parents="32590 43971"/>
    </justification>
  </clause>

  <clause id="44302">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),R(x,z,u),a(x,y,L(y,z,u))) = R(x,z,u) * (L(x \ R(x,z,u),y,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,42227,a(flip),b,44301,a)].">
      <j1 rule="hyper" parents="64 42227 44301"/>
    </justification>
  </clause>

  <clause id="44303">
    <literal><![CDATA[
      R(x,y,z) * (L(x \ R(x,y,z),u,u) \ 1) = L(x,u,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29972,a(flip),b,44302,a),flip(a)].">
      <j1 rule="hyper" parents="64 29972 44302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44305">
    <literal><![CDATA[
      R(x,y,z) * L(R(x,y,z) \ x,u,u) = L(x,u,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(39404(a,1),44303(a,1,2))].">
      <j1 rule="para" parents="39404 44303"/>
    </justification>
  </clause>

  <clause id="44306">
    <literal><![CDATA[
      R(x,y,z) * L(R(x,y,z) \ x,u,u) = x * a(z,y,a(x,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,43902,a,b,44305,a),flip(a)].">
      <j1 rule="hyper" parents="373 43902 44305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44307">
    <literal><![CDATA[
      a(x,x,(y \ R(y,z,u)) \ 1) = (y * a(u,z,a(y,x,x))) \ y
    ]]></literal>
    <justification jstring="[para(44306(a,1),39726(a,1,1)),flip(a)].">
      <j1 rule="para" parents="44306 39726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44308">
    <literal><![CDATA[
      a(x,x,(y \ R(y,z,u)) \ 1) = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,42571,a(flip),b,44307,a),flip(a)].">
      <j1 rule="hyper" parents="373 42571 44307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44310">
    <literal><![CDATA[
      a(x,x,R(y,z,u) \ y) = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[para(5382(a,1),44308(a,1,3))].">
      <j1 rule="para" parents="5382 44308"/>
    </justification>
  </clause>

  <clause id="44314">
    <literal><![CDATA[
      a(x,x,L(y,z,u) \ y) = a(a(y,x,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31334,a(flip),b,44310,a)].">
      <j1 rule="hyper" parents="64 31334 44310"/>
    </justification>
  </clause>

  <clause id="44315">
    <literal><![CDATA[
      a(x,x,L(y,z,u) \ y) = a(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,43910,a(flip),b,44314,a),flip(a)].">
      <j1 rule="hyper" parents="373 43910 44314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44316">
    <literal><![CDATA[
      (x * a(x,y,x * z)) * (a(x,y,x * z) \ (x \ u)) = u * a(x \ (a(x,y,x * z) \ u),x,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(30271(a,1),44175(a,2,2,1))].">
      <j1 rule="para" parents="30271 44175"/>
    </justification>
  </clause>

  <clause id="44317">
    <literal><![CDATA[
      (x * a(x,y,x * z)) * (a(x,y,x * z) \ (x \ u)) = u * a(a(x,y,x * z) \ u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(41454(a,1),44316(a,2,2))].">
      <j1 rule="para" parents="41454 44316"/>
    </justification>
  </clause>

  <clause id="44318">
    <literal><![CDATA[
      (x * a(x,y,x * z)) * (a(x,y,x * z) \ (x \ u)) = u * a(u * a(x,y,x * z),x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(42467(a,1),44317(a,2,2))].">
      <j1 rule="para" parents="42467 44317"/>
    </justification>
  </clause>

  <clause id="44319">
    <literal><![CDATA[
      (x * a(x,y,x * z)) * (a(x,y,x * z) \ (x \ u)) = u * a(z,y,a(x,x,u))
    ]]></literal>
    <justification jstring="[para(43936(a,1),44318(a,2,2))].">
      <j1 rule="para" parents="43936 44318"/>
    </justification>
  </clause>

  <clause id="44320">
    <literal><![CDATA[
      (x * a(x,y,x * z)) * (a(x,y,x * z) \ (x \ u)) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,43921,a(flip),b,44319,a),flip(a)].">
      <j1 rule="hyper" parents="373 43921 44319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44322">
    <literal><![CDATA[
      (x * a(x,y,x * z)) * (x \ (a(x,y,x * z) \ u)) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(30271(a,1),44320(a,1,2))].">
      <j1 rule="para" parents="30271 44320"/>
    </justification>
  </clause>

  <clause id="44323">
    <literal><![CDATA[
      a(R(x,y,z),a(R(x,y,z),u,x \ ((x * y) * z)),w) = a(w,R(x,y,z),a(x \ (z * y),u,R(x,y,z)))
    ]]></literal>
    <justification jstring="[para(27333(a,1),44176(a,1,2))].">
      <j1 rule="para" parents="27333 44176"/>
    </justification>
  </clause>

  <clause id="44325">
    <literal><![CDATA[
      a(R(x,y,z),a(L(x,y,z),u,x \ ((x * y) * z)),w) = a(w,R(x,y,z),a(x \ (z * y),u,R(x,y,z)))
    ]]></literal>
    <justification jstring="[para(32590(a,1),44323(a,1,2))].">
      <j1 rule="para" parents="32590 44323"/>
    </justification>
  </clause>

  <clause id="44326">
    <literal><![CDATA[
      a(L(x,y,z),a(L(x,y,z),u,x \ ((x * y) * z)),w) = a(w,R(x,y,z),a(x \ (z * y),u,R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,32590,a(flip),b,44325,a)].">
      <j1 rule="hyper" parents="64 32590 44325"/>
    </justification>
  </clause>

  <clause id="44327">
    <literal><![CDATA[
      a(x,a(L(x,y,z),u,x \ ((x * y) * z)),L(w,y,z)) = a(w,R(x,y,z),a(x \ (z * y),u,R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,42770,a(flip),b,44326,a)].">
      <j1 rule="hyper" parents="64 42770 44326"/>
    </justification>
  </clause>

  <clause id="44328">
    <literal><![CDATA[
      a(x \ ((x * y) * z),u,a(w,x,x)) = a(w,R(x,y,z),a(x \ (z * y),u,R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,44102,a(flip),b,44327,a)].">
      <j1 rule="hyper" parents="64 44102 44327"/>
    </justification>
  </clause>

  <clause id="44330">
    <literal><![CDATA[
      a(x,R(y,z,u),a(y \ (u * z),w,R(y,z,u))) = a(x,y,a((y * z) * u,w,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,44177,a(flip),b,44328,a),flip(a)].">
      <j1 rule="hyper" parents="64 44177 44328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44331">
    <literal><![CDATA[
      a(x,R(y,z,u),a(y \ (u * z),w,L(y,z,u))) = a(x,y,a((y * z) * u,w,y))
    ]]></literal>
    <justification jstring="[para(27644(a,1),44330(a,1,3))].">
      <j1 rule="para" parents="27644 44330"/>
    </justification>
  </clause>

  <clause id="44332">
    <literal><![CDATA[
      a(x,L(y,z,u),a(y \ (u * z),w,L(y,z,u))) = a(x,y,a((y * z) * u,w,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32197,a(flip),b,44331,a)].">
      <j1 rule="hyper" parents="64 32197 44331"/>
    </justification>
  </clause>

  <clause id="44333">
    <literal><![CDATA[
      a(x,y,a(y \ (z * u),w,y)) = a(x,y,a((y * u) * z,w,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,43976,a(flip),b,44332,a)].">
      <j1 rule="hyper" parents="64 43976 44332"/>
    </justification>
  </clause>

  <clause id="44335">
    <literal><![CDATA[
      a(x,y,a((y * z) * u,w,y)) = a(x,y,a(u * z,w,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,44173,a(flip),b,44333,a),flip(a)].">
      <j1 rule="hyper" parents="64 44173 44333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44336">
    <literal><![CDATA[
      L(x * y,L(z,y,x),a(u,w,a(w,v5,v6))) \ ((x * (y * z)) * a(u,w,a(w,v5,v6))) = a(v6,v5,a(w,w,u)) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(28832(a,1),43937(a,1,1))].">
      <j1 rule="para" parents="28832 43937"/>
    </justification>
  </clause>

  <clause id="44337">
    <literal><![CDATA[
      a(x * a(y,z,x),a(x \ a(y,z,x),u,(x \ a(y,z,x)) * w),v5) = a(v5,x * a(y,z,x),a(w,u,x * a(y,z,x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,43997,a(flip),b,44174,a),flip(a)].">
      <j1 rule="hyper" parents="373 43997 44174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44338">
    <literal><![CDATA[
      a(x * a(y,z,x),a(x \ a(y,z,x),u,(x \ a(y,z,x)) * w),v5) = a(v5,x,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,44059,a(flip),b,44337,a),flip(a)].">
      <j1 rule="hyper" parents="373 44059 44337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44340">
    <literal><![CDATA[
      a(x * a(y,z,x),a(x * a(y,z,x),u,(x \ a(y,z,x)) * w),v5) = a(v5,x,a(w,u,x))
    ]]></literal>
    <justification jstring="[para(9437(a,1),44338(a,1,2))].">
      <j1 rule="para" parents="9437 44338"/>
    </justification>
  </clause>

  <clause id="44341">
    <literal><![CDATA[
      a(x,y,a((y \ a(z,u,y)) * w,v5,y)) = a(x,y,a(w,v5,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,44084,a(flip),b,44340,a)].">
      <j1 rule="hyper" parents="64 44084 44340"/>
    </justification>
  </clause>

  <clause id="44343">
    <literal><![CDATA[
      a(x,y,a((y * a(z,u,y)) * w,v5,y)) = a(x,y,a(w,v5,y))
    ]]></literal>
    <justification jstring="[para(9438(a,1),44341(a,1,3))].">
      <j1 rule="para" parents="9438 44341"/>
    </justification>
  </clause>

  <clause id="44344">
    <literal><![CDATA[
      a(x,y,a(z * a(u,w,y),v5,y)) = a(x,y,a(z,v5,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,44335,a(flip),b,44343,a)].">
      <j1 rule="hyper" parents="64 44335 44343"/>
    </justification>
  </clause>

  <clause id="44345">
    <literal><![CDATA[
      a(x,((y \ 1) * (x \ T((y \ z) * y,y \ 1))) \ (z * (y \ 1)),u) = a(x,x,L(u,((y \ 1) \ T(z * (y \ 1),y)) * x,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(32041,a,44221,a)].">
      <j1 rule="hyper" parents="32041 44221"/>
    </justification>
  </clause>

  <clause id="44347">
    <literal><![CDATA[
      a(x,((y \ 1) * (x \ T((y \ z) * y,y \ 1))) \ (y * z),u) = a(x,x,L(u,((y \ 1) \ T(z * (y \ 1),y)) * x,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,32243,a(flip),b,44345,a)].">
      <j1 rule="hyper" parents="64 32243 44345"/>
    </justification>
  </clause>

  <clause id="44348">
    <literal><![CDATA[
      a(x,((y \ 1) * (x \ ((y \ z) * y))) \ (y * z),u) = a(x,x,L(u,((y \ 1) \ T(z * (y \ 1),y)) * x,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,32259,a(flip),b,44347,a)].">
      <j1 rule="hyper" parents="64 32259 44347"/>
    </justification>
  </clause>

  <clause id="44350">
    <literal><![CDATA[
      a(x,((y \ 1) * (x \ z)) \ (y * z),u) = a(x,x,L(u,((y \ 1) \ T(z * (y \ 1),y)) * x,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,32956,a(flip),b,44348,a)].">
      <j1 rule="hyper" parents="64 32956 44348"/>
    </justification>
  </clause>

  <clause id="44352">
    <literal><![CDATA[
      a(x,(y * (x \ z)) \ (y * z),u) = a(x,x,L(u,((y \ 1) \ T(z * (y \ 1),y)) * x,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,32239,a(flip),b,44350,a)].">
      <j1 rule="hyper" parents="64 32239 44350"/>
    </justification>
  </clause>

  <clause id="44353">
    <literal><![CDATA[
      a(x,(y * (x \ z)) \ (y * z),u) = a(x,x,L(u,T((y \ z) * y,y \ 1) * x,y \ 1))
    ]]></literal>
    <justification jstring="[para(1041(a,1),44352(a,2,3,2,1))].">
      <j1 rule="para" parents="1041 44352"/>
    </justification>
  </clause>

  <clause id="44354">
    <literal><![CDATA[
      a(x,(y * (x \ z)) \ (y * z),u) = a(x,x,L(u,T((y \ z) * y,y \ 1) * x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,39731,a(flip),b,44353,a),flip(a)].">
      <j1 rule="hyper" parents="373 39731 44353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44355">
    <literal><![CDATA[
      a(x,(y * (x \ z)) \ (y * z),u) = a(x,x,L(u,((y \ z) * y) * x,y))
    ]]></literal>
    <justification jstring="[para(29438(a,1),44354(a,2,3))].">
      <j1 rule="para" parents="29438 44354"/>
    </justification>
  </clause>

  <clause id="44357">
    <literal><![CDATA[
      a(x,(y * (x \ z)) \ (y * z),u) = a(x,x,L(u,x * z,y))
    ]]></literal>
    <justification jstring="[para(29666(a,1),44355(a,2,3))].">
      <j1 rule="para" parents="29666 44355"/>
    </justification>
  </clause>

  <clause id="44359">
    <literal><![CDATA[
      (T(x \ (y \ x),T(x,y)) \ z) * T((y * (x / y)) \ (x / y),y * (x / y)) = (R(1 / y,y,y \ x) \ z) * ((x / y) / (y * (x / y)))
    ]]></literal>
    <justification jstring="[para(11107(a,1),24928(a,1,1,1))].">
      <j1 rule="para" parents="11107 24928"/>
    </justification>
  </clause>

  <clause id="44360">
    <literal><![CDATA[
      (T(x \ (y \ x),x) \ z) * T((y * (x / y)) \ (x / y),y * (x / y)) = (R(1 / y,y,y \ x) \ z) * ((x / y) / (y * (x / y)))
    ]]></literal>
    <justification jstring="[para(7858(a,1),44359(a,1,1,1))].">
      <j1 rule="para" parents="7858 44359"/>
    </justification>
  </clause>

  <clause id="44361">
    <literal><![CDATA[
      (T(x \ (y \ x),x) \ z) * T(x \ (y \ x),y * (x / y)) = (R(1 / y,y,y \ x) \ z) * ((x / y) / (y * (x / y)))
    ]]></literal>
    <justification jstring="[para(24925(a,1),44360(a,1,2,1))].">
      <j1 rule="para" parents="24925 44360"/>
    </justification>
  </clause>

  <clause id="44362">
    <literal><![CDATA[
      (T(x \ (y \ x),x) \ z) * T(x \ (y \ x),T(x,y)) = (R(1 / y,y,y \ x) \ z) * ((x / y) / (y * (x / y)))
    ]]></literal>
    <justification jstring="[para(11107(a,1),44361(a,1,2))].">
      <j1 rule="para" parents="11107 44361"/>
    </justification>
  </clause>

  <clause id="44363">
    <literal><![CDATA[
      (T(x \ (y \ x),x) \ z) * T(x \ (y \ x),x) = (R(1 / y,y,y \ x) \ z) * ((x / y) / (y * (x / y)))
    ]]></literal>
    <justification jstring="[para(7858(a,1),44362(a,1,2))].">
      <j1 rule="para" parents="7858 44362"/>
    </justification>
  </clause>

  <clause id="44364">
    <literal><![CDATA[
      (R(1 / x,x,x \ y) \ z) * ((y / x) / (x * (y / x))) = (((x \ y) / y) \ z) * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,16183,a(flip),b,44363,a),flip(a)].">
      <j1 rule="hyper" parents="64 16183 44363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44365">
    <literal><![CDATA[
      (R(1 / x,x,x \ y) \ z) * R(1 / x,x,x \ y) = (((x \ y) / y) \ z) * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[para(15085(a,2),44364(a,1,2))].">
      <j1 rule="para" parents="15085 44364"/>
    </justification>
  </clause>

  <clause id="44366">
    <literal><![CDATA[
      (((x \ y) / y) \ z) * ((x \ y) / y) = ((1 / x) \ z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(64,a,25149,a(flip),b,44365,a),flip(a)].">
      <j1 rule="hyper" parents="64 25149 44365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44368">
    <literal><![CDATA[
      (((x \ y) / y) \ z) * ((x \ y) / y) = ((x \ 1) \ z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,3717,a(flip),b,44366,a),flip(a)].">
      <j1 rule="hyper" parents="373 3717 44366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44369">
    <literal><![CDATA[
      T((x \ (y / (x * y))) \ 1,(x \ y) / y) = (((x \ y) / y) / (((x \ 1) \ x) * (x \ 1))) \ 1
    ]]></literal>
    <justification jstring="[para(44368(a,1),31377(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="44368 31377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44370">
    <literal><![CDATA[
      T((x \ (y / (x * y))) \ 1,(x \ y) / y) = (((x \ y) / y) / ((x \ 1) \ 1)) \ 1
    ]]></literal>
    <justification jstring="[para(1131(a,1),44369(a,2,1,2))].">
      <j1 rule="para" parents="1131 44369"/>
    </justification>
  </clause>

  <clause id="44372">
    <literal><![CDATA[
      T((x \ (y / (x * y))) \ 1,(x \ y) / y) = (x \ ((x \ y) / y)) \ 1
    ]]></literal>
    <justification jstring="[para(31464(a,1),44370(a,2,1))].">
      <j1 rule="para" parents="31464 44370"/>
    </justification>
  </clause>

  <clause id="44373">
    <literal><![CDATA[
      T((x / (y * x)) \ y,(y \ x) / x) = (y \ ((y \ x) / x)) \ 1
    ]]></literal>
    <justification jstring="[para(35860(a,1),44372(a,1,1))].">
      <j1 rule="para" parents="35860 44372"/>
    </justification>
  </clause>

  <clause id="44374">
    <literal><![CDATA[
      T((x / (y * x)) \ y,y \ 1) = (y \ ((y \ x) / x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(4815,a,44373,a)].">
      <j1 rule="hyper" parents="4815 44373"/>
    </justification>
  </clause>

  <clause id="44376">
    <literal><![CDATA[
      T((x / (y * x)) \ y,1 * y) = (y \ ((y \ x) / x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,39192,a(flip),b,44374,a)].">
      <j1 rule="hyper" parents="64 39192 44374"/>
    </justification>
  </clause>

  <clause id="44377">
    <literal><![CDATA[
      T((x / (y * x)) \ y,y) = (y \ ((y \ x) / x)) \ 1
    ]]></literal>
    <justification jstring="[para(7(a,1),44376(a,1,2))].">
      <j1 rule="para" parents="7 44376"/>
    </justification>
  </clause>

  <clause id="44378">
    <literal><![CDATA[
      (x \ ((x \ y) / y)) \ 1 = ((x \ y) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,27143,a(flip),b,44377,a),flip(a)].">
      <j1 rule="hyper" parents="64 27143 44377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44379">
    <literal><![CDATA[
      (((x \ y) / y) \ x) \ 1 = x \ ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(40,a,31782,a,b,44378,a)].">
      <j1 rule="hyper" parents="40 31782 44378"/>
    </justification>
  </clause>

  <clause id="44380">
    <literal><![CDATA[
      (x \ ((x \ y) / y)) \ K(z,u) = (((x \ y) / y) \ x) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(144,a,44378,a(flip),b,14511,a),flip(a)].">
      <j1 rule="hyper" parents="144 44378 14511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44381">
    <literal><![CDATA[
      T(((x \ y) / y) \ x,y) = (y \ (x \ (x \ y))) \ 1
    ]]></literal>
    <justification jstring="[para(44378(a,1),40337(a,1,1))].">
      <j1 rule="para" parents="44378 40337"/>
    </justification>
  </clause>

  <clause id="44382">
    <literal><![CDATA[
      ((x \ (x \ y)) \ y) \ K(x * x,y) = x \ ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(64,a,38216,a,b,44379,a)].">
      <j1 rule="hyper" parents="64 38216 44379"/>
    </justification>
  </clause>

  <clause id="44383">
    <literal><![CDATA[
      (x \ (y \ (y \ x))) \ 1 = (y \ (y \ x)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,35899,a(flip),b,44381,a),flip(a)].">
      <j1 rule="hyper" parents="64 35899 44381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44384">
    <literal><![CDATA[
      (((x \ (x \ y)) \ y) \ K(x * x,y)) \ K(y,x \ (x \ y)) = T((y \ (x \ (x \ y))) \ 1,y \ (x \ (x \ y)))
    ]]></literal>
    <justification jstring="[para(44383(a,1),26736(a,1,1,1))].">
      <j1 rule="para" parents="44383 26736"/>
    </justification>
  </clause>

  <clause id="44385">
    <literal><![CDATA[
      T((x \ (y \ (y \ x))) \ 1,x \ (y \ (y \ x))) = (y \ ((y \ x) / x)) \ K(x,y \ (y \ x))
    ]]></literal>
    <justification jstring="[para(44382(a,1),44384(a,1,1)),flip(a)].">
      <j1 rule="para" parents="44382 44384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44386">
    <literal><![CDATA[
      T((x \ (y \ (y \ x))) \ 1,x \ (y \ (y \ x))) = (y \ ((y \ x) / x)) \ K(y * y,x)
    ]]></literal>
    <justification jstring="[para(17579(a,1),44385(a,2,2))].">
      <j1 rule="para" parents="17579 44385"/>
    </justification>
  </clause>

  <clause id="44387">
    <literal><![CDATA[
      T((x \ (y \ (y \ x))) \ 1,x \ (y \ (y \ x))) = (((y \ x) / x) \ y) * K(y * y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,44380,a(flip),b,44386,a),flip(a)].">
      <j1 rule="hyper" parents="373 44380 44386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44388">
    <literal><![CDATA[
      T((x \ (y \ (y \ x))) \ 1,x \ (y \ (y \ x))) = ((y \ T(x,y * y)) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,35894,a(flip),b,44387,a),flip(a)].">
      <j1 rule="hyper" parents="373 35894 44387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44389">
    <literal><![CDATA[
      T((x \ (y \ (y \ x))) \ 1,x \ (y \ (y \ x))) = (x \ (y \ T(x,y))) \ y
    ]]></literal>
    <justification jstring="[para(25793(a,1),44388(a,2,1))].">
      <j1 rule="para" parents="25793 44388"/>
    </justification>
  </clause>

  <clause id="44390">
    <literal><![CDATA[
      T((x \ (x \ y)) \ y,y \ (x \ (x \ y))) = (y \ (x \ T(y,x))) \ x
    ]]></literal>
    <justification jstring="[para(44383(a,1),44389(a,1,1))].">
      <j1 rule="para" parents="44383 44389"/>
    </justification>
  </clause>

  <clause id="44391">
    <literal><![CDATA[
      T((x \ (x \ y)) \ y,x \ (x \ 1)) = (y \ (x \ T(y,x))) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,28227,a(flip),b,44390,a)].">
      <j1 rule="hyper" parents="64 28227 44390"/>
    </justification>
  </clause>

  <clause id="44393">
    <literal><![CDATA[
      (x \ (y \ T(x,y))) \ y = (y \ (y \ x)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,35904,a(flip),b,44391,a),flip(a)].">
      <j1 rule="hyper" parents="64 35904 44391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44394">
    <literal><![CDATA[
      a(x,y,((z \ (z \ u)) \ u) * w) = a(x,y,(z * L(z,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(44393(a,1),40037(a,1,3,1))].">
      <j1 rule="para" parents="44393 40037"/>
    </justification>
  </clause>

  <clause id="44395">
    <literal><![CDATA[
      a(x,y,(z * L(z,z,u)) * w) = a(x,y,z * ((u \ (z \ u)) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,40338,a(flip),b,44394,a),flip(a)].">
      <j1 rule="hyper" parents="64 40338 44394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44396">
    <literal><![CDATA[
      L((a(x,y,z) \ 1) \ u,a(x,y,z) \ ((x \ 1) \ (x \ 1)),a(x,y,z) * (x \ 1)) = (x \ 1) \ ((a(x,y,z) * (x \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(42455(a,1),30989(a,1,1,1))].">
      <j1 rule="para" parents="42455 30989"/>
    </justification>
  </clause>

  <clause id="44397">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z) \ ((x \ 1) \ (x \ 1)),a(x,y,z) * (x \ 1)) = (x \ 1) \ ((a(x,y,z) * (x \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(42435(a,1),44396(a,1,1))].">
      <j1 rule="para" parents="42435 44396"/>
    </justification>
  </clause>

  <clause id="44399">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z) \ 1,a(x,y,z) * (x \ 1)) = (x \ 1) \ ((a(x,y,z) * (x \ 1)) * u)
    ]]></literal>
    <justification jstring="[para(68(a,1),44397(a,1,2,2))].">
      <j1 rule="para" parents="68 44397"/>
    </justification>
  </clause>

  <clause id="44400">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z) \ 1,a(x,y,z) * x) = (x \ 1) \ ((a(x,y,z) * (x \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(24743,a,44399,a)].">
      <j1 rule="hyper" parents="24743 44399"/>
    </justification>
  </clause>

  <clause id="44402">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),a(x,y,z) * x) = (x \ 1) \ ((a(x,y,z) * (x \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(11853,a,44400,a)].">
      <j1 rule="hyper" parents="11853 44400"/>
    </justification>
  </clause>

  <clause id="44403">
    <literal><![CDATA[
      L(a(x,y,z) * u,x,a(x,y,z)) = (x \ 1) \ ((a(x,y,z) * (x \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,43188,a(flip),b,44402,a)].">
      <j1 rule="hyper" parents="64 43188 44402"/>
    </justification>
  </clause>

  <clause id="44404">
    <literal><![CDATA[
      (x \ 1) \ ((a(x,y,z) * (x \ 1)) * u) = (a(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42533,a(flip),b,44403,a),flip(a)].">
      <j1 rule="hyper" parents="64 42533 44403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44405">
    <literal><![CDATA[
      (x \ 1) \ ((x \ a(x,y,z)) * u) = (a(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[para(23929(a,1),44404(a,1,2,1))].">
      <j1 rule="para" parents="23929 44404"/>
    </justification>
  </clause>

  <clause id="44406">
    <literal><![CDATA[
      x \ (((1 / x) \ a(x,y,z)) * u) = (a(x,y,z) \ x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,1601,a(flip),b,44405,a)].">
      <j1 rule="hyper" parents="64 1601 44405"/>
    </justification>
  </clause>

  <clause id="44407">
    <literal><![CDATA[
      (a(x,y,z) \ x) \ (x * u) = x \ ((x * a(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(16060(a,1),44406(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16060 44406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44408">
    <literal><![CDATA[
      (a(x,y,z) \ x) \ (x * u) = (u / x) * (x * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,39260,a(flip),b,44407,a),flip(a)].">
      <j1 rule="hyper" parents="373 39260 44407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44409">
    <literal><![CDATA[
      ((x \ y) / x) * (x * a(x,z,u)) = (a(x,z,u) \ x) \ y
    ]]></literal>
    <justification jstring="[para(10(a,1),44408(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10 44408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44410">
    <literal><![CDATA[
      a(x,y,z) * L(x \ u,x,a(x,y,z)) = (a(x,y,z) \ x) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,40999,a,b,44409,a)].">
      <j1 rule="hyper" parents="64 40999 44409"/>
    </justification>
  </clause>

  <clause id="44411">
    <literal><![CDATA[
      (x * a(x,y,z)) * (x \ u) = x * ((a(x,y,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[hyper(145,a,44409,a(flip),b,39260,a),flip(a)].">
      <j1 rule="hyper" parents="145 44409 39260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44412">
    <literal><![CDATA[
      x * ((a(x,y,x * z) \ x) \ (a(x,y,x * z) \ u)) = L(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,44322,a(flip),b,44411,a),flip(a)].">
      <j1 rule="hyper" parents="64 44322 44411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44413">
    <literal><![CDATA[
      x * L(x \ y,x,a(x,z,x * u)) = L(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(42513(a,1),44412(a,1,2))].">
      <j1 rule="para" parents="42513 44412"/>
    </justification>
  </clause>

  <clause id="44414">
    <literal><![CDATA[
      L(x * (x \ y),x,a(x,z,x * u)) = L(y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39276,a,b,44413,a)].">
      <j1 rule="hyper" parents="64 39276 44413"/>
    </justification>
  </clause>

  <clause id="44415">
    <literal><![CDATA[
      L(x,y,a(y,z,y * u)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),44414(a,1,1))].">
      <j1 rule="para" parents="10 44414"/>
    </justification>
  </clause>

  <clause id="44416">
    <literal><![CDATA[
      L((a(x * y,y,y \ 1) * y) \ z,y \ (L(y \ 1,y,y * x) \ y),L(y \ 1,y,y * x) * y) = y \ ((y * L(y \ 1,y,y * x)) * z)
    ]]></literal>
    <justification jstring="[para(38116(a,1),30991(a,1,1,1))].">
      <j1 rule="para" parents="38116 30991"/>
    </justification>
  </clause>

  <clause id="44417">
    <literal><![CDATA[
      ((x * y) \ (z \ (x * (y * z)))) * K(a(x,y,z) * K(z,x * y),((x * y) \ (z \ x)) * (y * z)) = 1 / (1 / ((x * y) \ (z \ (x * (y * z)))))
    ]]></literal>
    <justification jstring="[para(28460(a,1),31462(a,1,2))].">
      <j1 rule="para" parents="28460 31462"/>
    </justification>
  </clause>

  <clause id="44418">
    <literal><![CDATA[
      T(L(x \ L(x,y,z),x,u) \ u,x) / T(T(u,x),L(x \ L(x,y,z),x,u)) = T(T(u,x) / (x \ (u * L(x,y,z))),L(x \ L(x,y,z),x,u))
    ]]></literal>
    <justification jstring="[para(35105(a,2),33826(a,1,1))].">
      <j1 rule="para" parents="35105 33826"/>
    </justification>
  </clause>

  <clause id="44419">
    <literal><![CDATA[
      a(x,y,(z * z) \ (R(u / L(z,w,v5),L(z,w,v5),L(z,w,v5)) \ v6)) = a(x,y,L(z \ 1,w,v5) * ((L(z,w,v5) \ 1) \ ((u * L(z,w,v5)) \ v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27500,a(flip),b,33951,a),flip(a)].">
      <j1 rule="hyper" parents="373 27500 33951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44420">
    <literal><![CDATA[
      (((a(x,y,z) * K(z,x * y)) \ 1) * (z * (x * y))) \ ((x * (y * z)) * (1 / ((x * (y * z)) / (z * (x * y))))) = a(x,y,z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(15232(a,1),34727(a,1,1,1,1))].">
      <j1 rule="para" parents="15232 34727"/>
    </justification>
  </clause>

  <clause id="44421">
    <literal><![CDATA[
      ((a(x,y,z) \ K(x * y,z)) * (z * (x * y))) \ ((x * (y * z)) * (1 / ((x * (y * z)) / (z * (x * y))))) = a(x,y,z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(19398(a,1),44420(a,1,1,1))].">
      <j1 rule="para" parents="19398 44420"/>
    </justification>
  </clause>

  <clause id="44422">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) * ((x * y) * z)) \ ((x * (y * z)) * (1 / ((x * (y * z)) / (z * (x * y))))) = a(x,y,z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(14526(a,1),44421(a,1,1))].">
      <j1 rule="para" parents="14526 44421"/>
    </justification>
  </clause>

  <clause id="44423">
    <literal><![CDATA[
      (a(x,y,z) \ ((x * y) * z)) \ ((x * (y * z)) * (1 / ((x * (y * z)) / (z * (x * y))))) = a(x,y,z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(42433(a,1),44422(a,1,1))].">
      <j1 rule="para" parents="42433 44422"/>
    </justification>
  </clause>

  <clause id="44424">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * (y * z)) * (1 / ((x * (y * z)) / (z * (x * y))))) = a(x,y,z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(15467(a,1),44423(a,1,1))].">
      <j1 rule="para" parents="15467 44423"/>
    </justification>
  </clause>

  <clause id="44425">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * (y * z)) * (1 / ((z * (x * y)) \ (x * (y * z))))) = a(x,y,z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(31212(a,1),44424(a,1,2,2,2))].">
      <j1 rule="para" parents="31212 44424"/>
    </justification>
  </clause>

  <clause id="44426">
    <literal><![CDATA[
      1 / ((x * (y * z)) \ (y * (z * x))) = a(y,z,x) * K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(396,a,44425,a)].">
      <j1 rule="hyper" parents="396 44425"/>
    </justification>
  </clause>

  <clause id="44428">
    <literal><![CDATA[
      1 / ((x * y) \ (z \ (x * (y * z)))) = a(x,y,z) * K(z,x * y)
    ]]></literal>
    <justification jstring="[para(33829(a,1),44426(a,1,2))].">
      <j1 rule="para" parents="33829 44426"/>
    </justification>
  </clause>

  <clause id="44429">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * (y \ L(T(y,a(x,L(y,y,w),a(L(y,y,w),u,z))),y,w)) = L(L(y,y,w),a(L(y,y,w),u,z),x) / y
    ]]></literal>
    <justification jstring="[para(43978(a,1),39373(a,1,1))].">
      <j1 rule="para" parents="43978 39373"/>
    </justification>
  </clause>

  <clause id="44430">
    <literal><![CDATA[
      L(L(x,x,y),a(L(x,x,y),z,u),w) / x = a(w,x,a(u,z,x)) * (x \ L(x,x,y))
    ]]></literal>
    <justification jstring="[para(23105(a,1),44429(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="23105 44429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44432">
    <literal><![CDATA[
      L(L(x,x,y),a(L(x,x,y),z,u),w) / x = a(y,x,x) \ a(w,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,37839,a(flip),b,44430,a),flip(a)].">
      <j1 rule="hyper" parents="373 37839 44430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44433">
    <literal><![CDATA[
      L(L(x,x,y),a(x,z,u),w) / x = a(y,x,x) \ a(w,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[para(44264(a,1),44432(a,1,1))].">
      <j1 rule="para" parents="44264 44432"/>
    </justification>
  </clause>

  <clause id="44434">
    <literal><![CDATA[
      a(x,y,y) \ a(z,y,a(u,w,y)) = y \ L(L(y,y,x),a(y,w,u),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10463,a(flip),b,44433,a),flip(a)].">
      <j1 rule="hyper" parents="64 10463 44433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44435">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,x)) * (((1 / (1 / y)) \ (a(x,y,y) \ x)) \ z) = (z / ((1 / L(y,y,x)) \ x)) * (((1 / y) \ 1) * (a(x,y,y) \ x))
    ]]></literal>
    <justification jstring="[para(37638(a,1),39460(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="37638 39460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44436">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,x)) * (((1 / (1 / y)) \ (a(x,y,y) \ x)) \ z) = (z / ((1 / L(y,y,x)) \ x)) * (y * (a(x,y,y) \ x))
    ]]></literal>
    <justification jstring="[para(82(a,1),44435(a,2,2,1))].">
      <j1 rule="para" parents="82 44435"/>
    </justification>
  </clause>

  <clause id="44438">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,x)) * (((1 / (1 / y)) \ (a(x,y,y) \ x)) \ z) = (z / ((1 / L(y,y,x)) \ x)) * (L(y,y,x) * x)
    ]]></literal>
    <justification jstring="[para(30584(a,1),44436(a,2,2))].">
      <j1 rule="para" parents="30584 44436"/>
    </justification>
  </clause>

  <clause id="44439">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,x)) * (((1 / (1 / y)) \ (a(x,y,y) \ x)) \ z) = (L(y,y,x) * x) * (((1 / L(y,y,x)) \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,39457,a(flip),b,44438,a),flip(a)].">
      <j1 rule="hyper" parents="373 39457 44438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44440">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,x)) * (((1 / (1 / y)) \ (a(x,y,y) \ x)) \ z) = L(x,L(y,y,x),L(y,y,x)) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,42867,a(flip),b,44439,a),flip(a)].">
      <j1 rule="hyper" parents="373 42867 44439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44441">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,x)) * (((1 / (1 / y)) \ (a(x,y,y) \ x)) \ z) = L(x,y,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(31754(a,1),44440(a,2,1))].">
      <j1 rule="para" parents="31754 44440"/>
    </justification>
  </clause>

  <clause id="44443">
    <literal><![CDATA[
      R(x,(y * z) * (u * ((y * z) / y)),((y * z) \ 1) * (u * (y \ (y * z)))) = R(x,L(y \ T(u,T(z,y)),y,z),(y * z) \ (u * ((y * z) / y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,26253,a(flip),b,40695,a)].">
      <j1 rule="hyper" parents="64 26253 40695"/>
    </justification>
  </clause>

  <clause id="44444">
    <literal><![CDATA[
      a(x,(y * z) * (u * ((u * z) / u)),((u * z) \ 1) * (y * ((u * z) / u))) = a(x,L(u \ T(y,T(z,u)),u,z),(u * z) \ (y * ((u * z) / u)))
    ]]></literal>
    <justification jstring="[para(25490(a,1),40700(a,1,2))].">
      <j1 rule="para" parents="25490 40700"/>
    </justification>
  </clause>

  <clause id="44445">
    <literal><![CDATA[
      L((a(x,y,y) / (1 / y)) \ z,y \ (L(y \ 1,y,y * x) \ y),L(y \ 1,y,y * x) * y) = y \ ((y * L(y \ 1,y,y * x)) * z)
    ]]></literal>
    <justification jstring="[para(30743(a,1),44416(a,1,1,1))].">
      <j1 rule="para" parents="30743 44416"/>
    </justification>
  </clause>

  <clause id="44446">
    <literal><![CDATA[
      L((a(x,y,y) / (1 / y)) \ z,y \ (y * ((y \ 1) \ a(x,y,y))),L(y \ 1,y,y * x) * y) = y \ ((y * L(y \ 1,y,y * x)) * z)
    ]]></literal>
    <justification jstring="[para(37891(a,1),44445(a,1,2,2))].">
      <j1 rule="para" parents="37891 44445"/>
    </justification>
  </clause>

  <clause id="44447">
    <literal><![CDATA[
      L((a(x,y,y) / (1 / y)) \ z,(y \ 1) \ a(x,y,y),L(y \ 1,y,y * x) * y) = y \ ((y * L(y \ 1,y,y * x)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,11871,a(flip),b,44446,a)].">
      <j1 rule="hyper" parents="64 11871 44446"/>
    </justification>
  </clause>

  <clause id="44449">
    <literal><![CDATA[
      L((a(x,y,y) / (1 / y)) \ z,(y \ 1) \ a(x,y,y),(1 / y) * (a(x,y,y) \ y)) = y \ ((y * L(y \ 1,y,y * x)) * z)
    ]]></literal>
    <justification jstring="[para(37889(a,1),44447(a,1,3))].">
      <j1 rule="para" parents="37889 44447"/>
    </justification>
  </clause>

  <clause id="44450">
    <literal><![CDATA[
      L((a(x,y,y) / (1 / y)) \ z,(y \ 1) \ a(x,y,y),(1 / y) * L(y,y,x)) = y \ ((y * L(y \ 1,y,y * x)) * z)
    ]]></literal>
    <justification jstring="[para(30459(a,1),44449(a,1,3,2))].">
      <j1 rule="para" parents="30459 44449"/>
    </justification>
  </clause>

  <clause id="44451">
    <literal><![CDATA[
      L((a(x,y,y) / (1 / y)) \ z,(y \ 1) \ a(x,y,y),a(x,y,y) \ 1) = y \ ((y * L(y \ 1,y,y * x)) * z)
    ]]></literal>
    <justification jstring="[para(37569(a,1),44450(a,1,3))].">
      <j1 rule="para" parents="37569 44450"/>
    </justification>
  </clause>

  <clause id="44452">
    <literal><![CDATA[
      L((a(x,y,y) / (1 / y)) \ z,y \ a(x,y,y),a(x,y,y)) = y \ ((y * L(y \ 1,y,y * x)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29708,a(flip),b,44451,a)].">
      <j1 rule="hyper" parents="64 29708 44451"/>
    </justification>
  </clause>

  <clause id="44453">
    <literal><![CDATA[
      L((a(x,y,y) / (1 / y)) \ z,y * a(x,y,y),a(x,y,y)) = y \ ((y * L(y \ 1,y,y * x)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35747,a(flip),b,44452,a)].">
      <j1 rule="hyper" parents="64 35747 44452"/>
    </justification>
  </clause>

  <clause id="44454">
    <literal><![CDATA[
      L((a(x,y,y) / (1 / y)) \ z,L(y,y,x),a(x,y,y)) = y \ ((y * L(y \ 1,y,y * x)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30504,a(flip),b,44453,a)].">
      <j1 rule="hyper" parents="64 30504 44453"/>
    </justification>
  </clause>

  <clause id="44455">
    <literal><![CDATA[
      x \ ((x * L(x \ 1,x,x * y)) * z) = (a(y,x,x) / (1 / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,37533,a(flip),b,44454,a),flip(a)].">
      <j1 rule="hyper" parents="64 37533 44454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44457">
    <literal><![CDATA[
      x \ ((L(x,x,y) * (1 / x)) * z) = (a(y,x,x) / (1 / x)) \ z
    ]]></literal>
    <justification jstring="[para(30657(a,1),44455(a,1,2,1))].">
      <j1 rule="para" parents="30657 44455"/>
    </justification>
  </clause>

  <clause id="44458">
    <literal><![CDATA[
      (1 / (1 / x)) \ (a(y,x,x) \ z) = (a(y,x,x) / (1 / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,37991,a,b,44457,a)].">
      <j1 rule="hyper" parents="64 37991 44457"/>
    </justification>
  </clause>

  <clause id="44459">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,x)) * (((a(x,y,y) / (1 / y)) \ x) \ z) = L(x,y,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(44458(a,1),44441(a,1,2,1))].">
      <j1 rule="para" parents="44458 44441"/>
    </justification>
  </clause>

  <clause id="44460">
    <literal><![CDATA[
      ((x * y) \ (z \ (x * (y * z)))) * K(a(x,y,z) * K(z,x * y),(x * y) \ T(x * y,z)) = 1 / (1 / ((x * y) \ (z \ (x * (y * z)))))
    ]]></literal>
    <justification jstring="[para(38550(a,1),44417(a,1,2))].">
      <j1 rule="para" parents="38550 44417"/>
    </justification>
  </clause>

  <clause id="44461">
    <literal><![CDATA[
      ((x * y) \ (z \ (x * (y * z)))) * K(a(x,y,z) * K(z,x * y),K(x * y,z)) = 1 / (1 / ((x * y) \ (z \ (x * (y * z)))))
    ]]></literal>
    <justification jstring="[para(5726(a,2),44460(a,1,2,2))].">
      <j1 rule="para" parents="5726 44460"/>
    </justification>
  </clause>

  <clause id="44462">
    <literal><![CDATA[
      ((x * y) \ (z \ (x * (y * z)))) * K(x * y,K(a(x,y,z) * K(z,x * y),z)) = 1 / (1 / ((x * y) \ (z \ (x * (y * z)))))
    ]]></literal>
    <justification jstring="[para(8108(a,1),44461(a,1,2))].">
      <j1 rule="para" parents="8108 44461"/>
    </justification>
  </clause>

  <clause id="44463">
    <literal><![CDATA[
      ((x * y) \ (z \ (x * (y * z)))) * K(x * y,K(a(x,y,z),z)) = 1 / (1 / ((x * y) \ (z \ (x * (y * z)))))
    ]]></literal>
    <justification jstring="[para(8525(a,1),44462(a,1,2,2))].">
      <j1 rule="para" parents="8525 44462"/>
    </justification>
  </clause>

  <clause id="44466">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ (z \ (x * (y * z))))) = ((x * y) \ (z \ (x * (y * z)))) * 1
    ]]></literal>
    <justification jstring="[para(19217(a,1),44463(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19217 44463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44467">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ (z \ (x * (y * z))))) = (x * y) \ (z \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a(flip),b,44466,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 44466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44469">
    <literal><![CDATA[
      1 / (a(x,y,z) * K(z,x * y)) = (x * y) \ (z \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(44428(a,1),44467(a,1,2))].">
      <j1 rule="para" parents="44428 44467"/>
    </justification>
  </clause>

  <clause id="44470">
    <literal><![CDATA[
      (x * y) \ (z \ (x * (y * z))) = a(x,y,z) \ K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(137,a,42709,a(flip),b,44469,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 42709 44469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44471">
    <literal><![CDATA[
      a(x / y,y,z) \ K((x / y) * y,z) = x \ (z \ ((x / y) * (y * z)))
    ]]></literal>
    <justification jstring="[para(12(a,1),44470(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12 44470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44472">
    <literal><![CDATA[
      a(x / y,y,a(z,u,w)) \ K((x / y) * y,a(z,u,w)) = x \ (a(z,u,w) * ((x / y) * (a(z,u,w) \ y)))
    ]]></literal>
    <justification jstring="[para(42905(a,1),44471(a,2,2))].">
      <j1 rule="para" parents="42905 44471"/>
    </justification>
  </clause>

  <clause id="44473">
    <literal><![CDATA[
      a(x / y,y,a(z,u,w)) \ K((x / y) * y,a(z,u,w)) = x \ (L(x / y,y,a(z,u,w)) * y)
    ]]></literal>
    <justification jstring="[para(42846(a,2),44472(a,2,2))].">
      <j1 rule="para" parents="42846 44472"/>
    </justification>
  </clause>

  <clause id="44474">
    <literal><![CDATA[
      a(x / y,y,a(z,u,w)) \ K((x / y) * y,a(z,u,w)) = x \ (y * L(y \ x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(836(a,1),44473(a,2,2))].">
      <j1 rule="para" parents="836 44473"/>
    </justification>
  </clause>

  <clause id="44475">
    <literal><![CDATA[
      T(x * (L(x,y,z) \ u),x) / T(T(u,x),L(x \ L(x,y,z),x,u)) = T(T(u,x) / (x \ (u * L(x,y,z))),L(x \ L(x,y,z),x,u))
    ]]></literal>
    <justification jstring="[para(43445(a,1),44418(a,1,1,1))].">
      <j1 rule="para" parents="43445 44418"/>
    </justification>
  </clause>

  <clause id="44476">
    <literal><![CDATA[
      (L(x,y,z) \ (u * x)) / T(T(u,x),L(x \ L(x,y,z),x,u)) = T(T(u,x) / (x \ (u * L(x,y,z))),L(x \ L(x,y,z),x,u))
    ]]></literal>
    <justification jstring="[para(25113(a,1),44475(a,1,1))].">
      <j1 rule="para" parents="25113 44475"/>
    </justification>
  </clause>

  <clause id="44477">
    <literal><![CDATA[
      T(T(x,y) / (y \ (x * L(y,z,u))),L(y \ L(y,z,u),y,x)) = (L(y,z,u) \ (x * y)) / T(T(x,y),y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(23153(a,1),44476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23153 44476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44479">
    <literal><![CDATA[
      T(T(x,y) / (y \ (x * L(y,z,u))),L(y \ L(y,z,u),y,x)) = (L(y,z,u) \ (x * y)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(23697(a,1),44477(a,2,2))].">
      <j1 rule="para" parents="23697 44477"/>
    </justification>
  </clause>

  <clause id="44480">
    <literal><![CDATA[
      T(T(x,y) / (y \ (x * L(y,z,u))),L(y \ L(y,z,u),y,x)) = (L(y,z,u) \ (y * x)) / x
    ]]></literal>
    <justification jstring="[hyper(373,a,15229,a(flip),b,44479,a),flip(a)].">
      <j1 rule="hyper" parents="373 15229 44479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44482">
    <literal><![CDATA[
      T(T(x,y) / (y \ (x * L(y,z,u))),L(y \ L(y,z,u),y,x)) = (y * (L(y,z,u) \ x)) / x
    ]]></literal>
    <justification jstring="[para(2329(a,1),44480(a,2,1))].">
      <j1 rule="para" parents="2329 44480"/>
    </justification>
  </clause>

  <clause id="44483">
    <literal><![CDATA[
      T(T(x,y) / (y \ (x * L(y,z,u))),L(y \ L(y,z,u),y,x)) = x \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,25456,a(flip),b,44482,a),flip(a)].">
      <j1 rule="hyper" parents="373 25456 44482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44484">
    <literal><![CDATA[
      T(x / (y \ (L(y,z,u) * x)),L(y \ L(y,z,u),y,x)) = x \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(23637(a,1),44483(a,1,1))].">
      <j1 rule="para" parents="23637 44483"/>
    </justification>
  </clause>

  <clause id="44485">
    <literal><![CDATA[
      T(x / ((x / y) * L(y,z,u)),L(y \ L(y,z,u),y,x)) = x \ (y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(24852(a,1),44484(a,1,1,2))].">
      <j1 rule="para" parents="24852 44484"/>
    </justification>
  </clause>

  <clause id="44486">
    <literal><![CDATA[
      T((x \ y) \ (L(x,z,u) \ y),L(x \ L(x,z,u),x,y)) = y \ (x * (L(x,z,u) \ y))
    ]]></literal>
    <justification jstring="[para(34865(a,1),44485(a,1,1))].">
      <j1 rule="para" parents="34865 44485"/>
    </justification>
  </clause>

  <clause id="44487">
    <literal><![CDATA[
      (x \ y) \ (L(x,z,u) \ y) = y \ (x * (L(x,z,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(24117,a,44486,a)].">
      <j1 rule="hyper" parents="24117 44486"/>
    </justification>
  </clause>

  <clause id="44488">
    <literal><![CDATA[
      (x \ y) * L(L(x,z,u) \ x,x,y) = L(x,z,u) \ y
    ]]></literal>
    <justification jstring="[hyper(145,a,40710,a,b,44487,a)].">
      <j1 rule="hyper" parents="145 40710 44487"/>
    </justification>
  </clause>

  <clause id="44489">
    <literal><![CDATA[
      (x \ (y * (L(y,z,u) \ x))) * (y \ x) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(44487(a,1),28544(a,1,1))].">
      <j1 rule="para" parents="44487 28544"/>
    </justification>
  </clause>

  <clause id="44491">
    <literal><![CDATA[
      a(x,y,(z * z) \ (R(u / L(z,w,v5),L(z,w,v5),L(z,w,v5)) \ v6)) = a(x,y,(u * L(z,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,39636,a(flip),b,44419,a),flip(a)].">
      <j1 rule="hyper" parents="373 39636 44419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44493">
    <literal><![CDATA[
      a(x,y,(z * z) \ (R(u / L(z,w,v5),z,z) \ v6)) = a(x,y,(u * L(z,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(40654(a,1),44491(a,1,3,2,1))].">
      <j1 rule="para" parents="40654 44491"/>
    </justification>
  </clause>

  <clause id="44494">
    <literal><![CDATA[
      a(x,y,(((z / L(u,w,v5)) * u) * u) \ v6) = a(x,y,(z * L(u,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(875(a,1),44493(a,1,3))].">
      <j1 rule="para" parents="875 44493"/>
    </justification>
  </clause>

  <clause id="44496">
    <literal><![CDATA[
      a(x,y,((z * (L(z,u,w) \ v5)) * z) \ v6) = a(x,y,(v5 * L(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(23887(a,1),44494(a,1,3,1,1))].">
      <j1 rule="para" parents="23887 44494"/>
    </justification>
  </clause>

  <clause id="44497">
    <literal><![CDATA[
      R(x,L(y \ T(z,T(u,y)),y,u),(y * u) \ (z * ((y * u) / y))) = R(x,(y * u) * (z * ((y * u) / y)),((y * u) \ 1) * (z * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),44443(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="9 44443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44498">
    <literal><![CDATA[
      R(x,L(y \ T(z,T(u,y)),y,u),(y * u) \ (z * ((y * u) / y))) = R(x,(y * u) * (z * (y \ (y * u))),((y * u) \ 1) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,26557,a(flip),b,44497,a),flip(a)].">
      <j1 rule="hyper" parents="373 26557 44497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44500">
    <literal><![CDATA[
      R(x,L(y \ T(z,T(u,y)),y,u),(y * u) \ (z * ((y * u) / y))) = R(x,(y * u) * (z * u),((y * u) \ 1) * (z * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),44498(a,2,2,2,2))].">
      <j1 rule="para" parents="9 44498"/>
    </justification>
  </clause>

  <clause id="44501">
    <literal><![CDATA[
      R(x,L(y \ T(z,T(u,y)),y,u),(y * u) \ (z * ((y * u) / y))) = R(x,(y * u) \ (z * u),(y * u) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,40693,a(flip),b,44500,a),flip(a)].">
      <j1 rule="hyper" parents="373 40693 44500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44503">
    <literal><![CDATA[
      R(x,L(y \ T(z,T(u,y)),y,u),(y * u) \ (z * ((y * u) / y))) = R(x,u \ (y \ (z * u)),u \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,40741,a(flip),b,44501,a),flip(a)].">
      <j1 rule="hyper" parents="373 40741 44501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44504">
    <literal><![CDATA[
      R(x,L(y \ T(z,T(u,y)),y,u),L(y \ T(z,T(u,y)),y,u)) = R(x,u \ (y \ (z * u)),u \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[para(11301(a,1),44503(a,1,3))].">
      <j1 rule="para" parents="11301 44503"/>
    </justification>
  </clause>

  <clause id="44505">
    <literal><![CDATA[
      R(x,L(y \ T(z,T(u,y)),y,u),L(y \ z,y,u)) = R(x,u \ (y \ (z * u)),u \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,26321,a(flip),b,44504,a)].">
      <j1 rule="hyper" parents="64 26321 44504"/>
    </justification>
  </clause>

  <clause id="44507">
    <literal><![CDATA[
      R(x,L(y \ z,y,u),L(y \ z,y,u)) = R(x,u \ (y \ (z * u)),u \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,26588,a(flip),b,44505,a)].">
      <j1 rule="hyper" parents="64 26588 44505"/>
    </justification>
  </clause>

  <clause id="44509">
    <literal><![CDATA[
      R(x,y \ (z \ (u * y)),y \ (z \ (u * y))) = R(x,z \ u,z \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,40654,a(flip),b,44507,a),flip(a)].">
      <j1 rule="hyper" parents="64 40654 44507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44511">
    <literal><![CDATA[
      a(x,(y * z) * (u * ((u * z) / u)),((u * z) \ 1) * (y * (u \ (u * z)))) = a(x,L(u \ T(y,T(z,u)),u,z),(u * z) \ (y * ((u * z) / u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27478,a(flip),b,44444,a)].">
      <j1 rule="hyper" parents="64 27478 44444"/>
    </justification>
  </clause>

  <clause id="44512">
    <literal><![CDATA[
      a(x,L(y \ T(z,T(u,y)),y,u),(y * u) \ (z * ((y * u) / y))) = a(x,(z * u) * (y * ((y * u) / y)),((y * u) \ 1) * (z * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),44511(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="9 44511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44513">
    <literal><![CDATA[
      a(x,L(y \ T(z,T(u,y)),y,u),(y * u) \ (z * ((y * u) / y))) = a(x,(z * u) * (y * (y \ (y * u))),((y * u) \ 1) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,32057,a(flip),b,44512,a),flip(a)].">
      <j1 rule="hyper" parents="373 32057 44512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44515">
    <literal><![CDATA[
      a(x,L(y \ T(z,T(u,y)),y,u),(y * u) \ (z * ((y * u) / y))) = a(x,(z * u) * (y * u),((y * u) \ 1) * (z * u))
    ]]></literal>
    <justification jstring="[para(9(a,1),44513(a,2,2,2,2))].">
      <j1 rule="para" parents="9 44513"/>
    </justification>
  </clause>

  <clause id="44516">
    <literal><![CDATA[
      a(x,L(y \ T(z,T(u,y)),y,u),(y * u) \ (z * ((y * u) / y))) = a(x,(y * u) \ (z * u),(y * u) \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,40699,a(flip),b,44515,a),flip(a)].">
      <j1 rule="hyper" parents="373 40699 44515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44519">
    <literal><![CDATA[
      a(x,L(y \ T(z,T(u,y)),y,u),(y * u) \ (z * ((y * u) / y))) = a(x,u \ (y \ (z * u)),u \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,40742,a(flip),b,44516,a),flip(a)].">
      <j1 rule="hyper" parents="373 40742 44516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44520">
    <literal><![CDATA[
      a(x,L(y \ T(z,T(u,y)),y,u),L(y \ T(z,T(u,y)),y,u)) = a(x,u \ (y \ (z * u)),u \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[para(11301(a,1),44519(a,1,3))].">
      <j1 rule="para" parents="11301 44519"/>
    </justification>
  </clause>

  <clause id="44521">
    <literal><![CDATA[
      a(x,L(y \ T(z,T(u,y)),y,u),L(y \ z,y,u)) = a(x,u \ (y \ (z * u)),u \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27603,a(flip),b,44520,a)].">
      <j1 rule="hyper" parents="64 27603 44520"/>
    </justification>
  </clause>

  <clause id="44523">
    <literal><![CDATA[
      a(x,L(y \ z,y,u),L(y \ z,y,u)) = a(x,u \ (y \ (z * u)),u \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,32159,a(flip),b,44521,a)].">
      <j1 rule="hyper" parents="64 32159 44521"/>
    </justification>
  </clause>

  <clause id="44525">
    <literal><![CDATA[
      a(x,y \ (z \ (u * y)),y \ (z \ (u * y))) = a(x,z \ u,z \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,40664,a(flip),b,44523,a),flip(a)].">
      <j1 rule="hyper" parents="64 40664 44523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44529">
    <literal><![CDATA[
      R(T(x / y,x) * y,z,u) / T(T(x / y,x),(y \ x) * (y / (y \ x))) = R((y / x) * y,z,u) * T(x / y,x)
    ]]></literal>
    <justification jstring="[para(5148(a,1),31692(a,1,1,1,2))].">
      <j1 rule="para" parents="5148 31692"/>
    </justification>
  </clause>

  <clause id="44530">
    <literal><![CDATA[
      R(x * T(x \ y,y),z,u) / T(T(y / x,y),(x \ y) * (x / (x \ y))) = R((x / y) * x,z,u) * T(y / x,y)
    ]]></literal>
    <justification jstring="[para(525(a,1),44529(a,1,1,1))].">
      <j1 rule="para" parents="525 44529"/>
    </justification>
  </clause>

  <clause id="44531">
    <literal><![CDATA[
      R(x * T(x \ y,y),z,u) / T(T(y / x,y),T(x,x \ y)) = R((x / y) * x,z,u) * T(y / x,y)
    ]]></literal>
    <justification jstring="[para(11107(a,1),44530(a,1,2))].">
      <j1 rule="para" parents="11107 44530"/>
    </justification>
  </clause>

  <clause id="44532">
    <literal><![CDATA[
      R(x * T(x \ y,y),z,u) / T(T(y / x,y),T(x,y)) = R((x / y) * x,z,u) * T(y / x,y)
    ]]></literal>
    <justification jstring="[para(7410(a,1),44531(a,1,2))].">
      <j1 rule="para" parents="7410 44531"/>
    </justification>
  </clause>

  <clause id="44533">
    <literal><![CDATA[
      R(x * T(x \ y,y),z,u) / T(x \ y,y) = R((x / y) * x,z,u) * T(y / x,y)
    ]]></literal>
    <justification jstring="[para(4476(a,1),44532(a,1,2))].">
      <j1 rule="para" parents="4476 44532"/>
    </justification>
  </clause>

  <clause id="44534">
    <literal><![CDATA[
      T(x \ y,y) * R(T(x \ y,y) \ x,z,u) = R((x / y) * x,z,u) * T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,2111,a(flip),b,44533,a)].">
      <j1 rule="hyper" parents="64 2111 44533"/>
    </justification>
  </clause>

  <clause id="44535">
    <literal><![CDATA[
      R((x / y) * x,z,u) * T(y / x,y) = (x \ y) * R((x \ y) \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25995,a(flip),b,44534,a),flip(a)].">
      <j1 rule="hyper" parents="64 25995 44534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44537">
    <literal><![CDATA[
      R((x / y) * x,z,u) * T(y / x,y) = (y / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,27049,a(flip),b,44535,a),flip(a)].">
      <j1 rule="hyper" parents="373 27049 44535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44538">
    <literal><![CDATA[
      (x \ y) \ (T(1 / (1 / (y \ x)),(1 / (1 / (y \ x))) \ 1) * z) = K(1 / (1 / (y \ x)),1 / (y \ x)) * ((y \ x) * ((x \ y) \ z))
    ]]></literal>
    <justification jstring="[para(82(a,1),33106(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="82 33106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44540">
    <literal><![CDATA[
      (x \ y) \ (T(1 / (1 / (y \ x)),(1 / (1 / (y \ x))) \ 1) * z) = K(1 / (1 / (y \ x)),x \ y) * ((y \ x) * ((x \ y) \ z))
    ]]></literal>
    <justification jstring="[para(6699(a,1),44538(a,2,1))].">
      <j1 rule="para" parents="6699 44538"/>
    </justification>
  </clause>

  <clause id="44541">
    <literal><![CDATA[
      (x \ y) \ (T(1 / (1 / (y \ x)),(1 / (1 / (y \ x))) \ 1) * z) = K(y \ x,x \ y) * ((y \ x) * ((x \ y) \ z))
    ]]></literal>
    <justification jstring="[para(3778(a,1),44540(a,2,1))].">
      <j1 rule="para" parents="3778 44540"/>
    </justification>
  </clause>

  <clause id="44542">
    <literal><![CDATA[
      (x \ y) \ (T(1 / (1 / (y \ x)),(1 / (1 / (y \ x))) \ 1) * z) = T(y \ x,x \ y) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,5755,a(flip),b,44541,a),flip(a)].">
      <j1 rule="hyper" parents="373 5755 44541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44543">
    <literal><![CDATA[
      (x \ y) \ (T(1 / (1 / (y \ x)),(1 / (1 / (y \ x))) \ 1) * z) = ((x \ y) \ (y \ x)) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,40255,a(flip),b,44542,a),flip(a)].">
      <j1 rule="hyper" parents="373 40255 44542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44544">
    <literal><![CDATA[
      (x \ y) \ ((y \ x) * z) = ((x \ y) \ (y \ x)) * z
    ]]></literal>
    <justification jstring="[para(412(a,1),44543(a,1,2,1))].">
      <j1 rule="para" parents="412 44543"/>
    </justification>
  </clause>

  <clause id="44546">
    <literal><![CDATA[
      ((x / a(y,z,u)) * ((a(y,z,u) * (x / a(y,z,u))) \ (x * w))) \ (x * w) = (x * w) / ((a(y,z,u) \ x) * w)
    ]]></literal>
    <justification jstring="[para(6592(a,1),34369(a,2,2))].">
      <j1 rule="para" parents="6592 34369"/>
    </justification>
  </clause>

  <clause id="44547">
    <literal><![CDATA[
      ((a(x,y,z) \ u) * (u \ (u * w))) \ (u * w) = (u * w) / ((a(x,y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(11895(a,1),44546(a,1,1))].">
      <j1 rule="para" parents="11895 44546"/>
    </justification>
  </clause>

  <clause id="44548">
    <literal><![CDATA[
      (x * y) / ((a(z,u,w) \ x) * y) = ((a(z,u,w) \ x) * y) \ (x * y)
    ]]></literal>
    <justification jstring="[para(9(a,1),44547(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 44547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44549">
    <literal><![CDATA[
      (x * y) / ((a(z,u,w) \ x) * y) = L(a(z,u,w) \ 1,x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,42796,a(flip),b,44548,a),flip(a)].">
      <j1 rule="hyper" parents="373 42796 44548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44551">
    <literal><![CDATA[
      (x * y) / ((a(z,u,w) \ x) * y) = L(a(z,u,w),x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,42145,a(flip),b,44549,a),flip(a)].">
      <j1 rule="hyper" parents="373 42145 44549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44552">
    <literal><![CDATA[
      L(a(x,y,z),u,u \ w) \ w = (a(x,y,z) \ u) * (u \ w)
    ]]></literal>
    <justification jstring="[para(44551(a,1),349(a,1,1))].">
      <j1 rule="para" parents="44551 349"/>
    </justification>
  </clause>

  <clause id="44554">
    <literal><![CDATA[
      L(a(x,y,z),z,u) \ u = (a(x,y,z) \ z) * (z \ u)
    ]]></literal>
    <justification jstring="[para(40739(a,1),44552(a,1,1))].">
      <j1 rule="para" parents="40739 44552"/>
    </justification>
  </clause>

  <clause id="44555">
    <literal><![CDATA[
      (x * K(y * z,x)) * (T(x * K(y \ z,x),y * y) \ ((u \ K(y * y,x)) \ w)) = (u \ K(x * K(y * z,x),y * y)) \ w
    ]]></literal>
    <justification jstring="[para(22967(a,1),37096(a,1,2,2,1,2))].">
      <j1 rule="para" parents="22967 37096"/>
    </justification>
  </clause>

  <clause id="44557">
    <literal><![CDATA[
      (x * K(y * z,x)) * (K(x,y \ z) * (T(x,y * y) \ ((u \ K(y * y,x)) \ w))) = (u \ K(x * K(y * z,x),y * y)) \ w
    ]]></literal>
    <justification jstring="[para(25510(a,1),44555(a,1,2))].">
      <j1 rule="para" parents="25510 44555"/>
    </justification>
  </clause>

  <clause id="44558">
    <literal><![CDATA[
      (x \ K(y * K(z * u,y),z * z)) \ w = (y * K(z * u,y)) * (K(y,z \ u) * (y \ ((x \ 1) \ w)))
    ]]></literal>
    <justification jstring="[para(24971(a,1),44557(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="24971 44557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44560">
    <literal><![CDATA[
      (x \ K(y * K(z * u,y),z * z)) \ w = (y * K(z * u,y)) * (y \ ((x \ K(z \ u,y)) \ w))
    ]]></literal>
    <justification jstring="[para(24970(a,1),44558(a,2,2))].">
      <j1 rule="para" parents="24970 44558"/>
    </justification>
  </clause>

  <clause id="44561">
    <literal><![CDATA[
      (x \ K(y * K(z * u,y),z * z)) \ w = K(z * u,y) * ((x \ K(z \ u,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,4530,a(flip),b,44560,a),flip(a)].">
      <j1 rule="hyper" parents="373 4530 44560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44562">
    <literal><![CDATA[
      K(x * y,z) * ((u \ K(x \ y,z)) \ w) = (u \ K(z,x * x)) \ w
    ]]></literal>
    <justification jstring="[para(25893(a,1),44561(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="25893 44561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44563">
    <literal><![CDATA[
      ((x \ (x / y)) \ K(y,y * y)) \ x = y \ ((x / y) / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,38408,a(flip),b,44562,a),flip(a)].">
      <j1 rule="hyper" parents="64 38408 44562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44565">
    <literal><![CDATA[
      (a(x,y,y) / (1 / y)) \ x = y \ ((x / y) / (y \ 1))
    ]]></literal>
    <justification jstring="[para(33439(a,1),44563(a,1,1))].">
      <j1 rule="para" parents="33439 44563"/>
    </justification>
  </clause>

  <clause id="44566">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,x)) * ((y \ ((x / y) / (y \ 1))) \ z) = L(x,y,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(44565(a,1),44459(a,1,2,1))].">
      <j1 rule="para" parents="44565 44459"/>
    </justification>
  </clause>

  <clause id="44567">
    <literal><![CDATA[
      (x / y) * (K(y \ 1,x) * ((y \ ((x / y) / (y \ 1))) \ z)) = L(x,y,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(23285,a,44566,a)].">
      <j1 rule="hyper" parents="23285 44566"/>
    </justification>
  </clause>

  <clause id="44568">
    <literal><![CDATA[
      (x / y) * ((y \ ((x / y) / T(y \ 1,x))) \ z) = L(x,y,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(24894(a,1),44567(a,1,2))].">
      <j1 rule="para" parents="24894 44567"/>
    </justification>
  </clause>

  <clause id="44569">
    <literal><![CDATA[
      (x / y) * ((y \ ((y \ 1) \ (x / y))) \ z) = L(x,y,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(7236(a,1),44568(a,1,2,1,2))].">
      <j1 rule="para" parents="7236 44568"/>
    </justification>
  </clause>

  <clause id="44570">
    <literal><![CDATA[
      T(a(x,y,z) / T((x * y) * z,a(x,y,z)),(R(x,y,z) * y) * z) = (((R(x,y,z) * y) * z) \ a(x,y,z)) * T(a(x,y,z),(x * y) * z)
    ]]></literal>
    <justification jstring="[para(41793(a,1),42134(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="41793 42134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44571">
    <literal><![CDATA[
      ((x \ y) * x) \ ((a(z,y,u) * ((x \ y) * x)) * (a(z,(x \ y) * x,u) \ w)) = y \ L(y * w,(x \ y) * x,a(z,(x \ y) * x,u))
    ]]></literal>
    <justification jstring="[para(31889(a,1),43366(a,1,2,1,1))].">
      <j1 rule="para" parents="31889 43366"/>
    </justification>
  </clause>

  <clause id="44572">
    <literal><![CDATA[
      ((x \ y) * x) \ ((a(z,y,u) * ((x \ y) * x)) * (a(z,y,u) \ w)) = y \ L(y * w,(x \ y) * x,a(z,(x \ y) * x,u))
    ]]></literal>
    <justification jstring="[para(31889(a,1),44571(a,1,2,2,1))].">
      <j1 rule="para" parents="31889 44571"/>
    </justification>
  </clause>

  <clause id="44574">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u) * ((w \ z) * w)) = z \ L(z * x,(w \ z) * w,a(y,(w \ z) * w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,42826,a(flip),b,44572,a)].">
      <j1 rule="hyper" parents="64 42826 44572"/>
    </justification>
  </clause>

  <clause id="44576">
    <literal><![CDATA[
      L(x,a(y,z,u),z * a(y,z,u)) = z \ L(z * x,(w \ z) * w,a(y,(w \ z) * w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29143,a(flip),b,44574,a)].">
      <j1 rule="hyper" parents="64 29143 44574"/>
    </justification>
  </clause>

  <clause id="44578">
    <literal><![CDATA[
      L(x,a(y,z,u),z * a(y,z,u)) = z \ L(z * x,(w \ z) * w,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(31889(a,1),44576(a,2,2,3))].">
      <j1 rule="para" parents="31889 44576"/>
    </justification>
  </clause>

  <clause id="44579">
    <literal><![CDATA[
      L(x,a(y,z,u),z * a(y,z,u)) = z \ L(z * x,z,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(190(a,1),44578(a,2,2,2))].">
      <j1 rule="para" parents="190 44578"/>
    </justification>
  </clause>

  <clause id="44581">
    <literal><![CDATA[
      a(1 / L(x,y,z),L(x,u,w),L(x,u,w) \ L(x,y,z)) / (L(x,y,z) \ L(x,u,w)) = 1 / (1 / (L(x,u,w) \ ((1 / L(x,y,z)) \ 1)))
    ]]></literal>
    <justification jstring="[para(82(a,1),26751(a,1,1,3,2))].">
      <j1 rule="para" parents="82 26751"/>
    </justification>
  </clause>

  <clause id="44583">
    <literal><![CDATA[
      a(L(x,y,z),L(x,u,w),L(x,u,w) \ L(x,y,z)) / (L(x,y,z) \ L(x,u,w)) = 1 / (1 / (L(x,u,w) \ ((1 / L(x,y,z)) \ 1)))
    ]]></literal>
    <justification jstring="[para(2641(a,1),44581(a,1,1))].">
      <j1 rule="para" parents="2641 44581"/>
    </justification>
  </clause>

  <clause id="44584">
    <literal><![CDATA[
      1 / (1 / (L(x,y,z) \ ((1 / L(x,u,w)) \ 1))) = 1 / (L(x,u,w) \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(33089(a,1),44583(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33089 44583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44585">
    <literal><![CDATA[
      1 / (1 / (L(x,y,z) \ ((1 / L(x,u,w)) \ 1))) = (L(x,u,w) \ L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,28370,a(flip),b,44584,a),flip(a)].">
      <j1 rule="hyper" parents="373 28370 44584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44587">
    <literal><![CDATA[
      1 / (1 / (L(x,y,z) \ L(x,u,w))) = (L(x,u,w) \ L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(82(a,1),44585(a,1,2,2,2))].">
      <j1 rule="para" parents="82 44585"/>
    </justification>
  </clause>

  <clause id="44589">
    <literal><![CDATA[
      1 / ((L(x,y,z) \ L(x,u,w)) \ 1) = (L(x,u,w) \ L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(28370(a,1),44587(a,1,2))].">
      <j1 rule="para" parents="28370 44587"/>
    </justification>
  </clause>

  <clause id="44590">
    <literal><![CDATA[
      (L(x,y,z) \ L(x,u,w)) \ 1 = L(x,u,w) \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(330,a,44589,a)].">
      <j1 rule="hyper" parents="330 44589"/>
    </justification>
  </clause>

  <clause id="44593">
    <literal><![CDATA[
      (1 / ((1 / R(x,y,z)) * (L(x,u,w) \ 1))) * (1 / R(x,y,z)) = (L(x,y,z) \ L(x,u,w)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(44590(a,1),43708(a,2,1))].">
      <j1 rule="para" parents="44590 43708"/>
    </justification>
  </clause>

  <clause id="44594">
    <literal><![CDATA[
      (1 / ((1 / R(x,y,z)) * (L(x,u,w) \ 1))) * (1 / R(x,y,z)) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,5566,a(flip),b,44593,a),flip(a)].">
      <j1 rule="hyper" parents="373 5566 44593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44596">
    <literal><![CDATA[
      (1 / (R(x,y,z) * (L(x,u,w) \ 1))) * R(x,y,z) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,1233,a(flip),b,44594,a)].">
      <j1 rule="hyper" parents="64 1233 44594"/>
    </justification>
  </clause>

  <clause id="44597">
    <literal><![CDATA[
      (1 / (L(x,y,z) \ R(x,u,w))) * R(x,u,w) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1879(a,1),44596(a,1,1,2))].">
      <j1 rule="para" parents="1879 44596"/>
    </justification>
  </clause>

  <clause id="44598">
    <literal><![CDATA[
      R(x,y,z) * (1 / (R(x,y,z) / L(x,u,w))) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,35994,a(flip),b,44597,a)].">
      <j1 rule="hyper" parents="64 35994 44597"/>
    </justification>
  </clause>

  <clause id="44600">
    <literal><![CDATA[
      R(x,y,z) * (1 / (L(x,u,w) \ R(x,y,z))) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(5589(a,1),44598(a,1,2,2))].">
      <j1 rule="para" parents="5589 44598"/>
    </justification>
  </clause>

  <clause id="44601">
    <literal><![CDATA[
      R(x,y,z) * ((L(x,u,w) \ R(x,y,z)) \ 1) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(28435(a,1),44600(a,1,2))].">
      <j1 rule="para" parents="28435 44600"/>
    </justification>
  </clause>

  <clause id="44602">
    <literal><![CDATA[
      (L(x,y,z) \ L(x,y,z)) * (((L(x,y,z) \ R(x,u,w)) \ 1) \ 1) = ((1 / R(x,u,w)) * L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(44601(a,1),35075(a,1,1,2))].">
      <j1 rule="para" parents="44601 35075"/>
    </justification>
  </clause>

  <clause id="44603">
    <literal><![CDATA[
      1 * (((L(x,y,z) \ R(x,u,w)) \ 1) \ 1) = ((1 / R(x,u,w)) * L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(68(a,1),44602(a,1,1))].">
      <j1 rule="para" parents="68 44602"/>
    </justification>
  </clause>

  <clause id="44606">
    <literal><![CDATA[
      ((1 / R(x,y,z)) * L(x,u,w)) \ 1 = 1 * (L(x,u,w) \ R(x,y,z))
    ]]></literal>
    <justification jstring="[para(28607(a,1),44603(a,1,2)),flip(a)].">
      <j1 rule="para" parents="28607 44603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44607">
    <literal><![CDATA[
      ((1 / R(x,y,z)) * L(x,u,w)) \ 1 = L(x,u,w) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,7,a(flip),b,44606,a),flip(a)].">
      <j1 rule="hyper" parents="373 7 44606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44609">
    <literal><![CDATA[
      (R(x,y,z) \ L(x,u,w)) \ 1 = L(x,u,w) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(35073(a,1),44607(a,1,1))].">
      <j1 rule="para" parents="35073 44607"/>
    </justification>
  </clause>

  <clause id="44610">
    <literal><![CDATA[
      L(x,y * (x \ (y \ T(y * z,u))),(x \ (y \ (y * z))) * y) = (1 / (((y \ (y \ 1)) * T((y \ 1) \ z,u)) / x)) * (y \ (y \ T(y * z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29352,a(flip),b,35263,a)].">
      <j1 rule="hyper" parents="64 29352 35263"/>
    </justification>
  </clause>

  <clause id="44612">
    <literal><![CDATA[
      L(x,y * (x \ (y \ T(y * z,u))),(x \ z) * y) = (1 / (((y \ (y \ 1)) * T((y \ 1) \ z,u)) / x)) * (y \ (y \ T(y * z,u)))
    ]]></literal>
    <justification jstring="[para(9(a,1),44610(a,1,3,1,2))].">
      <j1 rule="para" parents="9 44610"/>
    </justification>
  </clause>

  <clause id="44613">
    <literal><![CDATA[
      L(x,y * (x \ (y \ (y * z))),(x \ z) * y) = (1 / (((y \ (y \ 1)) * T((y \ 1) \ z,u)) / x)) * (y \ (y \ T(y * z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,29677,a(flip),b,44612,a)].">
      <j1 rule="hyper" parents="64 29677 44612"/>
    </justification>
  </clause>

  <clause id="44615">
    <literal><![CDATA[
      L(x,y * (x \ z),(x \ z) * y) = (1 / (((y \ (y \ 1)) * T((y \ 1) \ z,u)) / x)) * (y \ (y \ T(y * z,u)))
    ]]></literal>
    <justification jstring="[para(9(a,1),44613(a,1,2,2,2))].">
      <j1 rule="para" parents="9 44613"/>
    </justification>
  </clause>

  <clause id="44616">
    <literal><![CDATA[
      (1 / (((x \ (x \ 1)) * T((x \ 1) \ y,z)) / u)) * (x \ (x \ T(x * y,z))) = (1 / ((x \ y) / u)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35261,a(flip),b,44615,a),flip(a)].">
      <j1 rule="hyper" parents="64 35261 44615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44617">
    <literal><![CDATA[
      (1 / ((x \ (x \ T(x * y,z))) / u)) * (x \ (x \ T(x * y,z))) = (1 / ((x \ y) / u)) * (x \ y)
    ]]></literal>
    <justification jstring="[para(1559(a,1),44616(a,1,1,2,1))].">
      <j1 rule="para" parents="1559 44616"/>
    </justification>
  </clause>

  <clause id="44618">
    <literal><![CDATA[
      ((x * y) \ (y \ (1 / (x / (y * x))))) \ (((x * y) \ (1 / (y * (x / (y * x))))) / z) = (L(x * y,y,y) \ 1) \ (((x * y) \ (y * (x / (y * x)))) / z)
    ]]></literal>
    <justification jstring="[para(35970(a,1),37079(a,1,1,2))].">
      <j1 rule="para" parents="35970 37079"/>
    </justification>
  </clause>

  <clause id="44619">
    <literal><![CDATA[
      a((x \ 1) * (R(y,y,y) * ((x \ R(x,z,u)) / y)),y * ((x \ R(x,z,u)) / y),w) * R(x,z,u) = R(R(x,z,u),y * ((x \ R(x,z,u)) / y),w)
    ]]></literal>
    <justification jstring="[para(25489(a,1),41929(a,1,1,1))].">
      <j1 rule="para" parents="25489 41929"/>
    </justification>
  </clause>

  <clause id="44620">
    <literal><![CDATA[
      a((x \ 1) * (y * ((x \ R(x,z,u)) / L(y,y,y))),y * ((x \ R(x,z,u)) / y),w) * R(x,z,u) = R(R(x,z,u),y * ((x \ R(x,z,u)) / y),w)
    ]]></literal>
    <justification jstring="[para(11374(a,1),44619(a,1,1,1,2))].">
      <j1 rule="para" parents="11374 44619"/>
    </justification>
  </clause>

  <clause id="44621">
    <literal><![CDATA[
      a((x \ 1) * (y * ((x \ R(x,z,u)) / L(y,y,y))),x \ R(x,z,u),w) * R(x,z,u) = R(R(x,z,u),y * ((x \ R(x,z,u)) / y),w)
    ]]></literal>
    <justification jstring="[para(31890(a,1),44620(a,1,1))].">
      <j1 rule="para" parents="31890 44620"/>
    </justification>
  </clause>

  <clause id="44623">
    <literal><![CDATA[
      a((x \ 1) * (y * ((x \ R(x,z,u)) / L(y,y,y))),x \ L(x,z,u),w) * R(x,z,u) = R(R(x,z,u),y * ((x \ R(x,z,u)) / y),w)
    ]]></literal>
    <justification jstring="[para(37374(a,1),44621(a,1,1))].">
      <j1 rule="para" parents="37374 44621"/>
    </justification>
  </clause>

  <clause id="44624">
    <literal><![CDATA[
      a((x \ 1) * (y * ((x \ R(x,z,u)) / L(y,y,y))),x * L(x,z,u),w) * R(x,z,u) = R(R(x,z,u),y * ((x \ R(x,z,u)) / y),w)
    ]]></literal>
    <justification jstring="[para(11978(a,1),44623(a,1,1))].">
      <j1 rule="para" parents="11978 44623"/>
    </justification>
  </clause>

  <clause id="44625">
    <literal><![CDATA[
      a((x \ 1) * (y * (L(y,y,y) \ (x \ R(x,z,u)))),x * L(x,z,u),w) * R(x,z,u) = R(R(x,z,u),y * ((x \ R(x,z,u)) / y),w)
    ]]></literal>
    <justification jstring="[para(32438(a,1),44624(a,1,1))].">
      <j1 rule="para" parents="32438 44624"/>
    </justification>
  </clause>

  <clause id="44626">
    <literal><![CDATA[
      a((x \ 1) * (y * ((x \ R(x,z,u)) / y)),x * L(x,z,u),w) * R(x,z,u) = R(R(x,z,u),y * ((x \ R(x,z,u)) / y),w)
    ]]></literal>
    <justification jstring="[para(31572(a,1),44625(a,1,1,1,2,2))].">
      <j1 rule="para" parents="31572 44625"/>
    </justification>
  </clause>

  <clause id="44627">
    <literal><![CDATA[
      a(R(x \ K(y,y \ 1),z,u),x * L(x,z,u),w) * R(x,z,u) = R(R(x,z,u),y * ((x \ R(x,z,u)) / y),w)
    ]]></literal>
    <justification jstring="[para(31603(a,1),44626(a,1,1,1))].">
      <j1 rule="para" parents="31603 44626"/>
    </justification>
  </clause>

  <clause id="44628">
    <literal><![CDATA[
      a(L(x \ K(y,y \ 1),z,u),x * L(x,z,u),w) * R(x,z,u) = R(R(x,z,u),y * ((x \ R(x,z,u)) / y),w)
    ]]></literal>
    <justification jstring="[para(32590(a,1),44627(a,1,1))].">
      <j1 rule="para" parents="32590 44627"/>
    </justification>
  </clause>

  <clause id="44629">
    <literal><![CDATA[
      R(R(x,y,z),u * ((x \ R(x,y,z)) / u),w) = a(L(x,y,z),x * L(x,y,z),w) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(32654(a,1),44628(a,1,1)),flip(a)].">
      <j1 rule="para" parents="32654 44628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44630">
    <literal><![CDATA[
      a(L(x,y,z),x * L(x,y,z),u) = a(a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,43160,a(flip),b,44629,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="36 43160 44629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44632">
    <literal><![CDATA[
      L(L(x,y,z),x * L(x,y,z),u) = L(x,y,z) * a(a(u,x,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,44630,a(flip),b,43341,a),flip(a)].">
      <j1 rule="hyper" parents="145 44630 43341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44633">
    <literal><![CDATA[
      L(L(x,y,z),x * L(x,y,z),u) = L(x,y,z) * a(u,x,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(43877(a,1),44632(a,2,2))].">
      <j1 rule="para" parents="43877 44632"/>
    </justification>
  </clause>

  <clause id="44634">
    <literal><![CDATA[
      L(L(x,y,z),x * L(x,y,z),u) = (u / x) \ (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,43893,a,b,44633,a),flip(a)].">
      <j1 rule="hyper" parents="373 43893 44633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44635">
    <literal><![CDATA[
      L(L(x,a(x,y,z),u),y,z) = (u / x) \ (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,43949,a(flip),b,44634,a)].">
      <j1 rule="hyper" parents="64 43949 44634"/>
    </justification>
  </clause>

  <clause id="44636">
    <literal><![CDATA[
      L(L(x,y,z),a(z,y,x),u) = (u / x) \ (u * (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,41405,a(flip),b,44635,a)].">
      <j1 rule="hyper" parents="64 41405 44635"/>
    </justification>
  </clause>

  <clause id="44637">
    <literal><![CDATA[
      (L(x * y,y,y) \ 1) \ (((x * y) \ (y * (x / (y * x)))) / z) = (((y \ 1) \ T(x,y)) \ 1) \ (((x * y) \ (1 / (y * (x / (y * x))))) / z)
    ]]></literal>
    <justification jstring="[para(35969(a,1),44618(a,1,1)),flip(a)].">
      <j1 rule="para" parents="35969 44618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44638">
    <literal><![CDATA[
      (L(x * y,y,y) \ 1) \ (((x * y) \ (y * (x / (y * x)))) / z) = (((y \ 1) \ T(x,y)) \ 1) \ (((x * y) \ (y \ (1 / (x / (y * x))))) / z)
    ]]></literal>
    <justification jstring="[para(35970(a,1),44637(a,2,2,1,2))].">
      <j1 rule="para" parents="35970 44637"/>
    </justification>
  </clause>

  <clause id="44639">
    <literal><![CDATA[
      (L(x * y,y,y) \ 1) \ (((x * y) \ (y * (x / (y * x)))) / z) = (((y \ 1) \ T(x,y)) \ 1) \ ((((y \ 1) \ T(x,y)) \ 1) / z)
    ]]></literal>
    <justification jstring="[para(35969(a,1),44638(a,2,2,1))].">
      <j1 rule="para" parents="35969 44638"/>
    </justification>
  </clause>

  <clause id="44640">
    <literal><![CDATA[
      (L(x * y,y,y) \ 1) \ (((x * y) \ (y * (x / (y * x)))) / z) = ((y \ 1) \ T(x,y)) \ (((y \ 1) \ T(x,y)) / z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1215,a(flip),b,44639,a),flip(a)].">
      <j1 rule="hyper" parents="373 1215 44639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44641">
    <literal><![CDATA[
      (L(x * y,y,y) \ 1) \ (((x * y) \ (y * (x / (y * x)))) / z) = ((y \ 1) \ x) \ (((y \ 1) \ x) / z)
    ]]></literal>
    <justification jstring="[hyper(373,a,31012,a(flip),b,44640,a),flip(a)].">
      <j1 rule="hyper" parents="373 31012 44640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44643">
    <literal><![CDATA[
      (L(x * y,y,y) \ 1) \ (((x * y) \ (y * (x / (y * x)))) / z) = (y \ x) \ ((y \ x) / z)
    ]]></literal>
    <justification jstring="[hyper(373,a,1613,a(flip),b,44641,a),flip(a)].">
      <j1 rule="hyper" parents="373 1613 44641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44644">
    <literal><![CDATA[
      (L(x * y,y,y) \ 1) \ ((L(x * y,y,y) \ 1) / z) = (y \ x) \ ((y \ x) / z)
    ]]></literal>
    <justification jstring="[para(30148(a,1),44643(a,1,2,1))].">
      <j1 rule="para" parents="30148 44643"/>
    </justification>
  </clause>

  <clause id="44645">
    <literal><![CDATA[
      L(x * y,y,y) \ (L(x * y,y,y) / z) = (y \ x) \ ((y \ x) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1215,a(flip),b,44644,a)].">
      <j1 rule="hyper" parents="64 1215 44644"/>
    </justification>
  </clause>

  <clause id="44646">
    <literal><![CDATA[
      (L(L(R(x,x,x),y,z),L(R(x,x,x),y,z),L(R(x,x,x),y,z)) \ u) \ 1 = (L(R(x,x,x),y,z) \ u) \ K(T(L(x,y,z) \ 1,x),R(x,x,x))
    ]]></literal>
    <justification jstring="[para(23001(a,1),25616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23001 25616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44647">
    <literal><![CDATA[
      (L(L(R(x,x,x),y,z),L(R(x,x,x),y,z),L(R(x,x,x),y,z)) \ u) \ 1 = (L(R(x,x,x),y,z) \ u) \ K(T(L(x,y,z) \ 1,x),x)
    ]]></literal>
    <justification jstring="[para(7402(a,1),44646(a,2,2))].">
      <j1 rule="para" parents="7402 44646"/>
    </justification>
  </clause>

  <clause id="44649">
    <literal><![CDATA[
      (L(L(R(x,x,x),y,z),L(R(x,x,x),y,z),L(R(x,x,x),y,z)) \ u) \ 1 = (L(R(x,x,x),y,z) \ u) \ K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6111(a,1),44647(a,2,2))].">
      <j1 rule="para" parents="6111 44647"/>
    </justification>
  </clause>

  <clause id="44653">
    <literal><![CDATA[
      (L(L(R(x,x,x),y,z),L(R(x,x,x),y,z),L(R(x,x,x),y,z)) \ u) \ 1 = (L(R(x,x,x),y,z) \ u) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(5204(a,1),44649(a,2,2))].">
      <j1 rule="para" parents="5204 44649"/>
    </justification>
  </clause>

  <clause id="44655">
    <literal><![CDATA[
      (L(L(R(x,x,x),y,z),L(R(x,x,x),y,z),L(x,y,z)) \ u) \ 1 = (L(R(x,x,x),y,z) \ u) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(12997(a,1),44653(a,1,1,1))].">
      <j1 rule="para" parents="12997 44653"/>
    </justification>
  </clause>

  <clause id="44657">
    <literal><![CDATA[
      (L(L(R(x,x,x),y,z),L(x,y,z),L(x,y,z)) \ u) \ 1 = (L(R(x,x,x),y,z) \ u) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(14176(a,1),44655(a,1,1,1))].">
      <j1 rule="para" parents="14176 44655"/>
    </justification>
  </clause>

  <clause id="44659">
    <literal><![CDATA[
      (L(R(x,x,x),y,z) \ u) \ K(x \ 1,x) = (L(x,y,z) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(34223(a,1),44657(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="34223 44657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44664">
    <literal><![CDATA[
      a((x \ 1) \ (y / x),(x \ 1) \ (y / x),((x \ 1) \ (y / x)) * (z \ (x \ 1))) = a((x \ 1) \ (y / x),(x \ 1) \ (y / x),z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,27602,a(flip),b,39737,a),flip(a)].">
      <j1 rule="hyper" parents="373 27602 39737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44666">
    <literal><![CDATA[
      a((x \ 1) \ (y / x),(x \ 1) \ (y / x),((x \ 1) \ (y / x)) * (z \ (x \ 1))) = a((x \ 1) \ (y / x),(x \ 1) \ (x \ y),z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,31908,a(flip),b,44664,a),flip(a)].">
      <j1 rule="hyper" parents="373 31908 44664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44667">
    <literal><![CDATA[
      a((x \ 1) \ (y / x),(x \ 1) \ (y / x),((x \ 1) \ (y / x)) * (z \ (x \ 1))) = a((x \ 1) \ (y / x),L(y,x,x),z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,30405,a(flip),b,44666,a),flip(a)].">
      <j1 rule="hyper" parents="373 30405 44666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44668">
    <literal><![CDATA[
      a((x \ 1) \ (y / x),(x \ 1) \ (y / x),((x \ 1) \ (y / x)) * (z \ (x \ 1))) = a(x \ (x \ y),L(y,x,x),z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,32454,a(flip),b,44667,a),flip(a)].">
      <j1 rule="hyper" parents="373 32454 44667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44669">
    <literal><![CDATA[
      a((x \ 1) \ (y / x),(x \ 1) \ (y / x),((x \ 1) \ (y / x)) * (z \ (x \ 1))) = a(L(y,x,x),L(y,x,x),z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,30384,a(flip),b,44668,a),flip(a)].">
      <j1 rule="hyper" parents="373 30384 44668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44670">
    <literal><![CDATA[
      a((x \ 1) \ (y / x),(x \ 1) \ (y / x),((x \ 1) \ (y / x)) * (z \ (x \ 1))) = a(y,y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(373,a,35139,a(flip),b,44669,a),flip(a)].">
      <j1 rule="hyper" parents="373 35139 44669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44672">
    <literal><![CDATA[
      a((x \ 1) \ (y / x),(x \ 1) \ (y / x),((x \ 1) \ (x \ y)) * (z \ (x \ 1))) = a(y,y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,27470,a(flip),b,44670,a)].">
      <j1 rule="hyper" parents="64 27470 44670"/>
    </justification>
  </clause>

  <clause id="44673">
    <literal><![CDATA[
      a((x \ 1) \ (y / x),(x \ 1) \ (y / x),(x \ ((1 / x) \ y)) * (z \ (x \ 1))) = a(y,y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(1166(a,1),44672(a,1,3,1))].">
      <j1 rule="para" parents="1166 44672"/>
    </justification>
  </clause>

  <clause id="44674">
    <literal><![CDATA[
      a((x \ 1) \ (y / x),(x \ 1) \ (y / x),(x \ ((x \ 1) \ y)) * (z \ (x \ 1))) = a(y,y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,27684,a(flip),b,44673,a)].">
      <j1 rule="hyper" parents="64 27684 44673"/>
    </justification>
  </clause>

  <clause id="44675">
    <literal><![CDATA[
      a((x \ 1) \ (y / x),(x \ 1) \ (x \ y),(x \ ((x \ 1) \ y)) * (z \ (x \ 1))) = a(y,y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,31908,a(flip),b,44674,a)].">
      <j1 rule="hyper" parents="64 31908 44674"/>
    </justification>
  </clause>

  <clause id="44676">
    <literal><![CDATA[
      a((x \ 1) \ (y / x),L(y,x,x),(x \ ((x \ 1) \ y)) * (z \ (x \ 1))) = a(y,y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30405,a(flip),b,44675,a)].">
      <j1 rule="hyper" parents="64 30405 44675"/>
    </justification>
  </clause>

  <clause id="44677">
    <literal><![CDATA[
      a(x \ (x \ y),L(y,x,x),(x \ ((x \ 1) \ y)) * (z \ (x \ 1))) = a(y,y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32454,a(flip),b,44676,a)].">
      <j1 rule="hyper" parents="64 32454 44676"/>
    </justification>
  </clause>

  <clause id="44678">
    <literal><![CDATA[
      a(L(x,y,y),L(x,y,y),(y \ ((y \ 1) \ x)) * (z \ (y \ 1))) = a(x,x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,30384,a(flip),b,44677,a)].">
      <j1 rule="hyper" parents="64 30384 44677"/>
    </justification>
  </clause>

  <clause id="44679">
    <literal><![CDATA[
      a(x,x,(y \ ((y \ 1) \ x)) * (z \ (y \ 1))) = a(x,x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,35139,a(flip),b,44678,a)].">
      <j1 rule="hyper" parents="64 35139 44678"/>
    </justification>
  </clause>

  <clause id="44681">
    <literal><![CDATA[
      a(x,x,x * (y \ (z \ 1))) = a(x,x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,37949,a(flip),b,44679,a)].">
      <j1 rule="hyper" parents="64 37949 44679"/>
    </justification>
  </clause>

  <clause id="44683">
    <literal><![CDATA[
      a(x,x,y \ ((1 / z) \ x)) = a(x,x,x * (y \ z))
    ]]></literal>
    <justification jstring="[para(82(a,1),44681(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="82 44681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44684">
    <literal><![CDATA[
      a((x * ((y * y) \ z)) * L(z,u,w),a(L(z,u,w) * x,z,z),v5) = a(v5,x * ((y * y) \ L(z,u,w)),a(x * ((y * y) \ L(z,u,w)),z,z))
    ]]></literal>
    <justification jstring="[para(26820(a,1),40942(a,1,2))].">
      <j1 rule="para" parents="26820 40942"/>
    </justification>
  </clause>

  <clause id="44686">
    <literal><![CDATA[
      a((x * ((y * y) \ z)) * L(z,u,w),a(z * x,z,z),v5) = a(v5,x * ((y * y) \ L(z,u,w)),a(x * ((y * y) \ L(z,u,w)),z,z))
    ]]></literal>
    <justification jstring="[para(41284(a,1),44684(a,1,2))].">
      <j1 rule="para" parents="41284 44684"/>
    </justification>
  </clause>

  <clause id="44687">
    <literal><![CDATA[
      a(x,y * ((z * z) \ L(u,w,v5)),a(y * ((z * z) \ L(u,w,v5)),u,u)) = a((y * ((z * z) \ u)) * L(u,w,v5),a(u,u,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32895,a(flip),b,44686,a),flip(a)].">
      <j1 rule="hyper" parents="64 32895 44686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44689">
    <literal><![CDATA[
      a(x,y * ((z * z) \ L(u,w,v5)),a(y * ((z * z) \ L(u,w,v5)),u,u)) = a((y * u) * L(u,w,v5),a(u,u,y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,32703,a(flip),b,44687,a),flip(a)].">
      <j1 rule="hyper" parents="373 32703 44687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44691">
    <literal><![CDATA[
      a(x,y * ((z * z) \ L(u,w,v5)),a(y * ((z * z) \ L(u,w,v5)),u,u)) = a(u * (y * L(u,w,v5)),a(u,u,y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,26838,a(flip),b,44689,a),flip(a)].">
      <j1 rule="hyper" parents="373 26838 44689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44692">
    <literal><![CDATA[
      a(x,y * ((z * z) \ L(u,w,v5)),a(y * ((z * z) \ L(u,w,v5)),u,u)) = a(x,y,a(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,41165,a(flip),b,44691,a),flip(a)].">
      <j1 rule="hyper" parents="373 41165 44691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44694">
    <literal><![CDATA[
      a(x,y * ((z * z) \ L(u,w,v5)),a(L(u,w,v5) * y,u,u)) = a(x,y,a(y,u,u))
    ]]></literal>
    <justification jstring="[para(26820(a,1),44692(a,1,3))].">
      <j1 rule="para" parents="26820 44692"/>
    </justification>
  </clause>

  <clause id="44696">
    <literal><![CDATA[
      a(x,y * ((z * z) \ L(u,w,v5)),a(u * y,u,u)) = a(x,y,a(y,u,u))
    ]]></literal>
    <justification jstring="[para(41284(a,1),44694(a,1,3))].">
      <j1 rule="para" parents="41284 44694"/>
    </justification>
  </clause>

  <clause id="44697">
    <literal><![CDATA[
      a(x,y * ((z * z) \ L(u,w,v5)),a(u,u,y)) = a(x,y,a(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,38637,a(flip),b,44696,a)].">
      <j1 rule="hyper" parents="64 38637 44696"/>
    </justification>
  </clause>

  <clause id="44699">
    <literal><![CDATA[
      a(x,L(y,z,u) * w,a(y,y,w)) = a(x,w,a(w,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,31947,a(flip),b,44697,a)].">
      <j1 rule="hyper" parents="64 31947 44697"/>
    </justification>
  </clause>

  <clause id="44700">
    <literal><![CDATA[
      a(x,y \ z,a(z,z,y)) = a(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,32152,a(flip),b,44699,a)].">
      <j1 rule="hyper" parents="64 32152 44699"/>
    </justification>
  </clause>

  <clause id="44701">
    <literal><![CDATA[
      L(x,y \ z,a(y,z,z)) = x * a(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(44700(a,1),38702(a,1,2)),flip(a)].">
      <j1 rule="para" parents="44700 38702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44702">
    <literal><![CDATA[
      L(x,y \ z,a(y,z,z)) = L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,40809,a(flip),b,44701,a),flip(a)].">
      <j1 rule="hyper" parents="373 40809 44701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44703">
    <literal><![CDATA[
      L(x,y \ z,a(z,z,y)) = L(x,y,a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(42222,a,44702,a)].">
      <j1 rule="hyper" parents="42222 44702"/>
    </justification>
  </clause>

  <clause id="44704">
    <literal><![CDATA[
      L(x,((y / z) \ z) \ z,a((z / y) \ y,(z / y) \ y,y)) = L(x,y,a(y,(z / y) \ y,(z / y) \ y))
    ]]></literal>
    <justification jstring="[para(33695(a,2),44703(a,1,2))].">
      <j1 rule="para" parents="33695 44703"/>
    </justification>
  </clause>

  <clause id="44705">
    <literal><![CDATA[
      L(x,((y / z) \ z) \ z,a((z / y) \ y,(y \ z) \ y,y)) = L(x,y,a(y,(z / y) \ y,(z / y) \ y))
    ]]></literal>
    <justification jstring="[para(31972(a,1),44704(a,1,3))].">
      <j1 rule="para" parents="31972 44704"/>
    </justification>
  </clause>

  <clause id="44706">
    <literal><![CDATA[
      L(x,((y / z) \ z) \ z,a((z / y) \ y,(z \ y) * y,y)) = L(x,y,a(y,(z / y) \ y,(z / y) \ y))
    ]]></literal>
    <justification jstring="[para(32124(a,1),44705(a,1,3))].">
      <j1 rule="para" parents="32124 44705"/>
    </justification>
  </clause>

  <clause id="44707">
    <literal><![CDATA[
      L(x,((y / z) \ z) \ z,a((y \ z) \ y,(z \ y) * y,y)) = L(x,y,a(y,(z / y) \ y,(z / y) \ y))
    ]]></literal>
    <justification jstring="[para(32386(a,1),44706(a,1,3))].">
      <j1 rule="para" parents="32386 44706"/>
    </justification>
  </clause>

  <clause id="44708">
    <literal><![CDATA[
      L(x,((y / z) \ z) \ z,a((z \ y) * y,(z \ y) * y,y)) = L(x,y,a(y,(z / y) \ y,(z / y) \ y))
    ]]></literal>
    <justification jstring="[para(32539(a,1),44707(a,1,3))].">
      <j1 rule="para" parents="32539 44707"/>
    </justification>
  </clause>

  <clause id="44709">
    <literal><![CDATA[
      L(x,((y / z) \ z) \ z,a(z,z,y)) = L(x,y,a(y,(z / y) \ y,(z / y) \ y))
    ]]></literal>
    <justification jstring="[para(38736(a,1),44708(a,1,3))].">
      <j1 rule="para" parents="38736 44708"/>
    </justification>
  </clause>

  <clause id="44710">
    <literal><![CDATA[
      L(x,y / z,a(z,z,y)) = L(x,y,a(y,(z / y) \ y,(z / y) \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29440,a(flip),b,44709,a)].">
      <j1 rule="hyper" parents="64 29440 44709"/>
    </justification>
  </clause>

  <clause id="44712">
    <literal><![CDATA[
      L(x,y \ z,a(y,y,z)) = L(x,z,a(z,(y / z) \ z,(y / z) \ z))
    ]]></literal>
    <justification jstring="[hyper(29617,a,44710,a)].">
      <j1 rule="hyper" parents="29617 44710"/>
    </justification>
  </clause>

  <clause id="44714">
    <literal><![CDATA[
      L(x,y \ z,a(y,y,z)) = L(x,z,a(z,(y / z) \ z,(z \ y) \ z))
    ]]></literal>
    <justification jstring="[para(27389(a,1),44712(a,2,3))].">
      <j1 rule="para" parents="27389 44712"/>
    </justification>
  </clause>

  <clause id="44715">
    <literal><![CDATA[
      L(x,y \ z,a(y,y,z)) = L(x,z,a(z,(y / z) \ z,(y \ z) * z))
    ]]></literal>
    <justification jstring="[para(27579(a,1),44714(a,2,3))].">
      <j1 rule="para" parents="27579 44714"/>
    </justification>
  </clause>

  <clause id="44716">
    <literal><![CDATA[
      L(x,y \ z,a(y,y,z)) = L(x,z,a(z,(z \ y) \ z,(y \ z) * z))
    ]]></literal>
    <justification jstring="[para(31972(a,1),44715(a,2,3))].">
      <j1 rule="para" parents="31972 44715"/>
    </justification>
  </clause>

  <clause id="44717">
    <literal><![CDATA[
      L(x,y \ z,a(y,y,z)) = L(x,z,a(z,(y \ z) * z,(y \ z) * z))
    ]]></literal>
    <justification jstring="[para(32124(a,1),44716(a,2,3))].">
      <j1 rule="para" parents="32124 44716"/>
    </justification>
  </clause>

  <clause id="44718">
    <literal><![CDATA[
      L(x,y \ z,a(y,y,z)) = L(x,z,a(z,y,(y \ z) * z))
    ]]></literal>
    <justification jstring="[para(37200(a,1),44717(a,2,3))].">
      <j1 rule="para" parents="37200 44717"/>
    </justification>
  </clause>

  <clause id="44719">
    <literal><![CDATA[
      L(x,y \ z,a(y,y,z)) = L(x,z,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,39079,a(flip),b,44718,a),flip(a)].">
      <j1 rule="hyper" parents="373 39079 44718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44720">
    <literal><![CDATA[
      L(x,a(y,y,z),y \ z) = L(x,z,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30749,a,b,44719,a)].">
      <j1 rule="hyper" parents="64 30749 44719"/>
    </justification>
  </clause>

  <clause id="44721">
    <literal><![CDATA[
      L((x \ y) \ ((((a(x,x,y) \ 1) \ 1) \ 1) \ z),y,a(x,x,y)) = (T(a(x,x,y) \ 1,a(x,x,y)) * (x \ y)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,31200,a(flip),b,44719,a),flip(a)].">
      <j1 rule="hyper" parents="64 31200 44719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44722">
    <literal><![CDATA[
      ((x * y) / (((x * y) \ x) * x)) * ((((x * y) \ x) * x) * z) = (x * y) * L(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(44719(a,1),43637(a,2,2))].">
      <j1 rule="para" parents="44719 43637"/>
    </justification>
  </clause>

  <clause id="44723">
    <literal><![CDATA[
      a(x,x,y) \ (L(z,y,a(x,x,y)) * L(x * y,a(x,x,y),a(x,x,y))) = (a(x,x,y) \ (1 * (x * y))) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(44719(a,1),43718(a,1,2,1))].">
      <j1 rule="para" parents="44719 43718"/>
    </justification>
  </clause>

  <clause id="44724">
    <literal><![CDATA[
      L(((x * y) \ (y \ x)) * z,x,a(y,y,x)) = (x * y) \ ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,43090,a(flip),b,44720,a),flip(a)].">
      <j1 rule="hyper" parents="64 43090 44720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44725">
    <literal><![CDATA[
      ((x / ((x * y) / x)) \ (x * y)) * ((((x * y) \ x) * x) * z) = (x * y) * L(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(35930(a,1),44722(a,1,1))].">
      <j1 rule="para" parents="35930 44722"/>
    </justification>
  </clause>

  <clause id="44726">
    <literal><![CDATA[
      ((x * y) / x) * (((x * y) \ x) \ ((((x * y) \ x) * x) * z)) = (x * y) * L(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,43838,a(flip),b,44725,a)].">
      <j1 rule="hyper" parents="64 43838 44725"/>
    </justification>
  </clause>

  <clause id="44727">
    <literal><![CDATA[
      L((x * y) * z,x * y,a(x,x,x * y)) = (x * y) * L(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,43842,a(flip),b,44726,a)].">
      <j1 rule="hyper" parents="64 43842 44726"/>
    </justification>
  </clause>

  <clause id="44728">
    <literal><![CDATA[
      L((x * y) * z,x * y,a(y,x,x)) = (x * y) * L(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,30294,a(flip),b,44727,a)].">
      <j1 rule="hyper" parents="64 30294 44727"/>
    </justification>
  </clause>

  <clause id="44729">
    <literal><![CDATA[
      L((x * y) * z,x,a(x,y,y)) = (x * y) * L(z,x,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,40945,a(flip),b,44728,a)].">
      <j1 rule="hyper" parents="64 40945 44728"/>
    </justification>
  </clause>

  <clause id="44730">
    <literal><![CDATA[
      L((x * y) * z,x,a(x,y,y)) = (x * y) * L(z,y,a(y,x,x))
    ]]></literal>
    <justification jstring="[para(40930(a,1),44729(a,2,2))].">
      <j1 rule="para" parents="40930 44729"/>
    </justification>
  </clause>

  <clause id="44731">
    <literal><![CDATA[
      L((x * y) * z,x,a(x,y,y)) = (x * y) * L(z,y,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,29292,a(flip),b,44730,a),flip(a)].">
      <j1 rule="hyper" parents="373 29292 44730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44732">
    <literal><![CDATA[
      L((x * y) * T(z,x * y),x,a(x,y,y)) = L(z,y,a(x,x,y)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,266,a(flip),b,44731,a),flip(a)].">
      <j1 rule="hyper" parents="373 266 44731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44733">
    <literal><![CDATA[
      L(x * (y * z),y,a(y,z,z)) = L(x,z,a(y,y,z)) * (y * z)
    ]]></literal>
    <justification jstring="[para(115(a,1),44732(a,1,1))].">
      <j1 rule="para" parents="115 44732"/>
    </justification>
  </clause>

  <clause id="44734">
    <literal><![CDATA[
      L((x \ y) \ ((((a(x,x,y) \ 1) \ 1) \ 1) \ z),y,a(x,x,y)) = ((a(x,x,y) \ 1) * (x \ y)) \ z
    ]]></literal>
    <justification jstring="[para(14433(a,1),44721(a,2,1,1))].">
      <j1 rule="para" parents="14433 44721"/>
    </justification>
  </clause>

  <clause id="44738">
    <literal><![CDATA[
      L((x \ y) \ ((((a(x,x,y) \ 1) \ 1) \ 1) \ z),y,a(x,x,y)) = ((x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(30425(a,1),44734(a,2,1))].">
      <j1 rule="para" parents="30425 44734"/>
    </justification>
  </clause>

  <clause id="44739">
    <literal><![CDATA[
      L((x \ y) \ ((a(x,x,y) \ 1) \ z),y,a(x,x,y)) = ((x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(13931(a,1),44738(a,1,1,2,1,1))].">
      <j1 rule="para" parents="13931 44738"/>
    </justification>
  </clause>

  <clause id="44741">
    <literal><![CDATA[
      L((x \ y) \ (a(x,x,y) * z),y,a(x,x,y)) = ((x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(37673(a,1),44739(a,1,1,2))].">
      <j1 rule="para" parents="37673 44739"/>
    </justification>
  </clause>

  <clause id="44742">
    <literal><![CDATA[
      L(((x \ y) \ z) * a(x,x,y),y,a(x,x,y)) = ((x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(31120(a,1),44741(a,1,1))].">
      <j1 rule="para" parents="31120 44741"/>
    </justification>
  </clause>

  <clause id="44743">
    <literal><![CDATA[
      a(x,x,y) \ (L(z,y,a(x,x,y)) * (x * y)) = (a(x,x,y) \ (1 * (x * y))) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(29963(a,1),44723(a,1,2,2))].">
      <j1 rule="para" parents="29963 44723"/>
    </justification>
  </clause>

  <clause id="44747">
    <literal><![CDATA[
      a(x,x,y) \ L(z * (x * y),x,a(x,y,y)) = (a(x,x,y) \ (1 * (x * y))) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(44733(a,2),44743(a,1,2))].">
      <j1 rule="para" parents="44733 44743"/>
    </justification>
  </clause>

  <clause id="44748">
    <literal><![CDATA[
      (a(x,x,y) \ (1 * (x * y))) * T(z,x * y) = L(y,x,x) * (y \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,40931,a(flip),b,44747,a),flip(a)].">
      <j1 rule="hyper" parents="64 40931 44747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44749">
    <literal><![CDATA[
      (a(x,x,y) \ (x * y)) * T(z,x * y) = L(y,x,x) * (y \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[para(7(a,1),44748(a,1,1,2))].">
      <j1 rule="para" parents="7 44748"/>
    </justification>
  </clause>

  <clause id="44750">
    <literal><![CDATA[
      L(x,y,y) * (x \ (z * (y * x))) = (y * L(x,y,y)) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(42081(a,1),44749(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42081 44749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44751">
    <literal><![CDATA[
      L(x,y,y) * (x \ (z * (y * x))) = z * (y * L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,28323,a(flip),b,44750,a),flip(a)].">
      <j1 rule="hyper" parents="373 28323 44750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44752">
    <literal><![CDATA[
      L(R(x,((1 / y) \ y) / z,z \ ((1 / y) \ y)),((1 / y) \ y) / z,a(y,y,((1 / y) \ y) / z)) = R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(23813(a,1),43963(a,1,1))].">
      <j1 rule="para" parents="23813 43963"/>
    </justification>
  </clause>

  <clause id="44753">
    <literal><![CDATA[
      L(R(x,((1 / y) \ y) / z,z \ ((1 \ y) * y)),((1 / y) \ y) / z,a(y,y,((1 / y) \ y) / z)) = R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(33680(a,1),44752(a,1,1))].">
      <j1 rule="para" parents="33680 44752"/>
    </justification>
  </clause>

  <clause id="44754">
    <literal><![CDATA[
      L(R(x,((1 / y) \ y) / z,z \ (y * y)),((1 / y) \ y) / z,a(y,y,((1 / y) \ y) / z)) = R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(66(a,1),44753(a,1,1,3,2,1))].">
      <j1 rule="para" parents="66 44753"/>
    </justification>
  </clause>

  <clause id="44755">
    <literal><![CDATA[
      L(R(x,y \ ((1 / z) \ z),y \ (z * z)),((1 / z) \ z) / y,a(z,z,((1 / z) \ z) / y)) = R(x,((1 / z) \ z) / y,z * (L(z,z,z) * (1 / y)))
    ]]></literal>
    <justification jstring="[para(26410(a,1),44754(a,1,1))].">
      <j1 rule="para" parents="26410 44754"/>
    </justification>
  </clause>

  <clause id="44756">
    <literal><![CDATA[
      L(R(x,y \ ((z \ 1) \ z),y \ (z * z)),((1 / z) \ z) / y,a(z,z,((1 / z) \ z) / y)) = R(x,((1 / z) \ z) / y,z * (L(z,z,z) * (1 / y)))
    ]]></literal>
    <justification jstring="[para(26547(a,1),44755(a,1,1))].">
      <j1 rule="para" parents="26547 44755"/>
    </justification>
  </clause>

  <clause id="44757">
    <literal><![CDATA[
      L(R(x,y,y \ (z * z)),((1 / z) \ z) / y,a(z,z,((1 / z) \ z) / y)) = R(x,((1 / z) \ z) / y,z * (L(z,z,z) * (1 / y)))
    ]]></literal>
    <justification jstring="[para(26722(a,1),44756(a,1,1))].">
      <j1 rule="para" parents="26722 44756"/>
    </justification>
  </clause>

  <clause id="44759">
    <literal><![CDATA[
      L(R(x,y,y \ (z * z)),((1 / z) \ z) / y,a(z,z,y \ ((1 / z) \ z))) = R(x,((1 / z) \ z) / y,z * (L(z,z,z) * (1 / y)))
    ]]></literal>
    <justification jstring="[para(27308(a,1),44757(a,1,3))].">
      <j1 rule="para" parents="27308 44757"/>
    </justification>
  </clause>

  <clause id="44760">
    <literal><![CDATA[
      L(R(x,y,y \ (z * z)),((1 / z) \ z) / y,a(z,z,z * (y \ z))) = R(x,((1 / z) \ z) / y,z * (L(z,z,z) * (1 / y)))
    ]]></literal>
    <justification jstring="[para(44683(a,1),44759(a,1,3))].">
      <j1 rule="para" parents="44683 44759"/>
    </justification>
  </clause>

  <clause id="44761">
    <literal><![CDATA[
      L(R(x,y,y \ (z * z)),((1 / z) \ z) / y,a(y \ z,z,z)) = R(x,((1 / z) \ z) / y,z * (L(z,z,z) * (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,30294,a(flip),b,44760,a)].">
      <j1 rule="hyper" parents="64 30294 44760"/>
    </justification>
  </clause>

  <clause id="44762">
    <literal><![CDATA[
      L(R(x,y,y \ (z * z)),((1 / z) \ z) / y,a(z * y,z,z)) = R(x,((1 / z) \ z) / y,z * (L(z,z,z) * (1 / y)))
    ]]></literal>
    <justification jstring="[para(32537(a,1),44761(a,1,3))].">
      <j1 rule="para" parents="32537 44761"/>
    </justification>
  </clause>

  <clause id="44763">
    <literal><![CDATA[
      L(R(x,y,y \ (z * z)),((1 / z) \ z) / y,a(y,z,z)) = R(x,((1 / z) \ z) / y,z * (L(z,z,z) * (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,30331,a(flip),b,44762,a)].">
      <j1 rule="hyper" parents="64 30331 44762"/>
    </justification>
  </clause>

  <clause id="44764">
    <literal><![CDATA[
      L(R(x,y,y \ (z * z)),y \ ((1 / z) \ z),a(y,z,z)) = R(x,((1 / z) \ z) / y,z * (L(z,z,z) * (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(29617,a,44763,a)].">
      <j1 rule="hyper" parents="29617 44763"/>
    </justification>
  </clause>

  <clause id="44765">
    <literal><![CDATA[
      L(R(x,y,y \ (z * z)),y \ ((1 \ z) * z),a(y,z,z)) = R(x,((1 / z) \ z) / y,z * (L(z,z,z) * (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,33687,a(flip),b,44764,a)].">
      <j1 rule="hyper" parents="64 33687 44764"/>
    </justification>
  </clause>

  <clause id="44766">
    <literal><![CDATA[
      R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = L(R(x,z,z \ (y * y)),z \ (y * y),a(z,y,y))
    ]]></literal>
    <justification jstring="[para(66(a,1),44765(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="66 44765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44767">
    <literal><![CDATA[
      R(x,((1 / y) \ y) / z,y * (L(y,y,y) * (1 / z))) = L(R(x,z,z \ (y * y)),z,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,11867,a(flip),b,44766,a),flip(a)].">
      <j1 rule="hyper" parents="373 11867 44766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44769">
    <literal><![CDATA[
      L(R(x,y,y \ (z * z)),y,a(y,z,z)) = R(x,y,(y \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,43745,a(flip),b,44767,a),flip(a)].">
      <j1 rule="hyper" parents="64 43745 44767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44770">
    <literal><![CDATA[
      ((1 / ((x / (y * x)) \ 1)) \ a(y,y,x)) / (((x / (y * x)) \ 1) * ((x / (y * x)) \ 1)) = ((1 / (x / (y * x))) \ a(y,y,x)) * K(y,((x / (y * x)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(24641(a,1),30166(a,2,1))].">
      <j1 rule="para" parents="24641 30166"/>
    </justification>
  </clause>

  <clause id="44771">
    <literal><![CDATA[
      ((1 / ((x / (y * x)) \ 1)) \ a(y,y,x)) / (((x / (y * x)) \ 1) * ((x / (y * x)) \ 1)) = (x / (y * L(x,y,y))) * K(y,((x / (y * x)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(33846(a,1),44770(a,2,1))].">
      <j1 rule="para" parents="33846 44770"/>
    </justification>
  </clause>

  <clause id="44772">
    <literal><![CDATA[
      ((1 / ((x / (y * x)) \ 1)) \ a(y,y,x)) / (((x / (y * x)) \ 1) * ((x / (y * x)) \ 1)) = (x / (y * L(x,y,y))) * K(y,(y \ x) / x)
    ]]></literal>
    <justification jstring="[para(2033(a,1),44771(a,2,2,2))].">
      <j1 rule="para" parents="2033 44771"/>
    </justification>
  </clause>

  <clause id="44773">
    <literal><![CDATA[
      ((1 / ((x / (y * x)) \ 1)) \ a(y,y,x)) / (((x / (y * x)) \ 1) * ((x / (y * x)) \ 1)) = (x / (y * L(x,y,y))) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(6379(a,1),44772(a,2,2))].">
      <j1 rule="para" parents="6379 44772"/>
    </justification>
  </clause>

  <clause id="44774">
    <literal><![CDATA[
      ((1 / ((x / (y * x)) \ 1)) \ a(y,y,x)) / (((x / (y * x)) \ 1) * ((x / (y * x)) \ 1)) = x / ((1 / (1 / y)) * L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,24488,a,b,44773,a),flip(a)].">
      <j1 rule="hyper" parents="373 24488 44773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44776">
    <literal><![CDATA[
      ((1 / ((x / (y * x)) \ 1)) \ a(y,y,x)) / (((x / (y * x)) \ 1) * ((x / (y * x)) \ 1)) = x / L(y * x,y,y)
    ]]></literal>
    <justification jstring="[para(1260(a,1),44774(a,2,2))].">
      <j1 rule="para" parents="1260 44774"/>
    </justification>
  </clause>

  <clause id="44777">
    <literal><![CDATA[
      ((x / (y * x)) \ a(y,y,x)) / (((x / (y * x)) \ 1) * ((x / (y * x)) \ 1)) = x / L(y * x,y,y)
    ]]></literal>
    <justification jstring="[para(79(a,1),44776(a,1,1,1))].">
      <j1 rule="para" parents="79 44776"/>
    </justification>
  </clause>

  <clause id="44779">
    <literal><![CDATA[
      x / (((y / (x * y)) \ 1) * ((y / (x * y)) \ 1)) = y / L(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(30086(a,1),44777(a,1,1))].">
      <j1 rule="para" parents="30086 44777"/>
    </justification>
  </clause>

  <clause id="44780">
    <literal><![CDATA[
      x / ((y / (x * y)) \ (1 / (y / (x * y)))) = y / L(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(1090(a,1),44779(a,1,2))].">
      <j1 rule="para" parents="1090 44779"/>
    </justification>
  </clause>

  <clause id="44781">
    <literal><![CDATA[
      x * ((1 / (y / (x * y))) \ (y / (x * y))) = y / L(x * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,1534,a(flip),b,44780,a)].">
      <j1 rule="hyper" parents="64 1534 44780"/>
    </justification>
  </clause>

  <clause id="44782">
    <literal><![CDATA[
      x * ((y / (x * y)) * ((x \ y) / y)) = y / L(x * y,x,x)
    ]]></literal>
    <justification jstring="[para(2038(a,1),44781(a,1,2))].">
      <j1 rule="para" parents="2038 44781"/>
    </justification>
  </clause>

  <clause id="44783">
    <literal><![CDATA[
      T(x / L(y * x,y,y),K(y,z)) = (y * (x / (y * x))) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(44782(a,1),35008(a,1,1))].">
      <j1 rule="para" parents="44782 35008"/>
    </justification>
  </clause>

  <clause id="44784">
    <literal><![CDATA[
      (x * (y / (x * y))) * (y / (x * y)) = y / L(x * y,x,x)
    ]]></literal>
    <justification jstring="[hyper(17166,a,44783,a),flip(a)].">
      <j1 rule="hyper" parents="17166 44783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44785">
    <literal><![CDATA[
      a(x,L(y \ 1,y * (z / (y * z)),y * (z / (y * z))) \ u,w) = a(x,(z / L(y * z,y,y)) \ u,w)
    ]]></literal>
    <justification jstring="[para(44784(a,1),32246(a,2,2,1))].">
      <j1 rule="para" parents="44784 32246"/>
    </justification>
  </clause>

  <clause id="44786">
    <literal><![CDATA[
      a(x,L(y \ 1,y * (z / (y * z)),y * (z / (y * z))) \ u,w) = a(x,(L(y * z,y,y) \ z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,31972,a(flip),b,44785,a),flip(a)].">
      <j1 rule="hyper" parents="373 31972 44785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44787">
    <literal><![CDATA[
      a(x,L(y \ 1,y * (z / (y * z)),y * ((y * z) \ z)) \ u,w) = a(x,(L(y * z,y,y) \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(29018(a,1),44786(a,1,2,1))].">
      <j1 rule="para" parents="29018 44786"/>
    </justification>
  </clause>

  <clause id="44788">
    <literal><![CDATA[
      a(x,(L(y * z,y,y) \ z) \ u,w) = a(x,(y \ 1) \ u,w)
    ]]></literal>
    <justification jstring="[para(30211(a,1),44787(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="30211 44787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44789">
    <literal><![CDATA[
      a(x,(L(y * z,y,y) \ z) \ u,w) = a(x,y \ u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32138,a(flip),b,44788,a),flip(a)].">
      <j1 rule="hyper" parents="373 32138 44788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44791">
    <literal><![CDATA[
      a(x,(y \ ((1 / R(1 / z,z,y)) \ y)) \ u,w) = a(x,z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32335,a(flip),b,44789,a)].">
      <j1 rule="hyper" parents="64 32335 44789"/>
    </justification>
  </clause>

  <clause id="44793">
    <literal><![CDATA[
      a(x,(y \ ((R(1 / z,z,y) \ 1) \ y)) \ u,w) = a(x,z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32261,a(flip),b,44791,a)].">
      <j1 rule="hyper" parents="64 32261 44791"/>
    </justification>
  </clause>

  <clause id="44794">
    <literal><![CDATA[
      a(x,R(y \ (z \ y),z,y) \ u,w) = a(x,z \ u,w)
    ]]></literal>
    <justification jstring="[para(37908(a,1),44793(a,1,2,1))].">
      <j1 rule="para" parents="37908 44793"/>
    </justification>
  </clause>

  <clause id="44795">
    <literal><![CDATA[
      L(L((x \ 1) \ y,x,a(z,u,x)),x \ (a(z,u,x) \ 1),(x \ 1) * (a(z,u,x) \ 1)) = (1 / ((a(z,u,x) \ 1) * (x \ 1))) * ((a(z,u,x) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(11807(a,1),33509(a,1,1))].">
      <j1 rule="para" parents="11807 33509"/>
    </justification>
  </clause>

  <clause id="44796">
    <literal><![CDATA[
      L(L((x \ 1) \ y,x,a(z,u,x)),x \ (a(z,u,x) \ 1),x \ (a(z,u,x) \ 1)) = (1 / ((a(z,u,x) \ 1) * (x \ 1))) * ((a(z,u,x) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(33507(a,1),44795(a,1,3))].">
      <j1 rule="para" parents="33507 44795"/>
    </justification>
  </clause>

  <clause id="44797">
    <literal><![CDATA[
      L(L((x \ 1) \ y,x,a(z,u,x)),a(z,u,x) * x,a(z,u,x) * x) = (1 / ((a(z,u,x) \ 1) * (x \ 1))) * ((a(z,u,x) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35243,a(flip),b,44796,a)].">
      <j1 rule="hyper" parents="64 35243 44796"/>
    </justification>
  </clause>

  <clause id="44798">
    <literal><![CDATA[
      L(L((x \ 1) \ y,x,a(z,u,x)),x,x) = (1 / ((a(z,u,x) \ 1) * (x \ 1))) * ((a(z,u,x) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,43510,a(flip),b,44797,a)].">
      <j1 rule="hyper" parents="64 43510 44797"/>
    </justification>
  </clause>

  <clause id="44800">
    <literal><![CDATA[
      (1 / ((a(x,y,z) \ 1) * (z \ 1))) * ((a(x,y,z) \ 1) * u) = L(z * u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1143,a(flip),b,44798,a),flip(a)].">
      <j1 rule="hyper" parents="64 1143 44798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44801">
    <literal><![CDATA[
      (1 / (x \ (a(y,z,x) \ 1))) * ((a(y,z,x) \ 1) * u) = L(x * u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(33508(a,1),44800(a,1,1,2))].">
      <j1 rule="para" parents="33508 44800"/>
    </justification>
  </clause>

  <clause id="44802">
    <literal><![CDATA[
      (((a(x,y,z) \ 1) / z) \ 1) * ((a(x,y,z) \ 1) * u) = L(z * u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(31788(a,1),44801(a,1,1))].">
      <j1 rule="para" parents="31788 44801"/>
    </justification>
  </clause>

  <clause id="44803">
    <literal><![CDATA[
      (x * a(y,z,x)) * ((a(y,z,x) \ 1) * u) = L(x * u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(41528(a,1),44802(a,1,1))].">
      <j1 rule="para" parents="41528 44802"/>
    </justification>
  </clause>

  <clause id="44804">
    <literal><![CDATA[
      (x * a(y,z,x)) * (a(y,z,x) \ u) = L(x * u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(42433(a,1),44803(a,1,2))].">
      <j1 rule="para" parents="42433 44803"/>
    </justification>
  </clause>

  <clause id="44805">
    <literal><![CDATA[
      (x * a(y,z,x)) * (a(y,z,x) \ u) = L(x * u,x,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,42195,a,b,44804,a),flip(a)].">
      <j1 rule="hyper" parents="373 42195 44804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44806">
    <literal><![CDATA[
      a(x,a(y,z,x),a(y,z,x) \ u) = (x * u) \ L(x * u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(139,a,44804,a(flip),b,957,a),flip(a)].">
      <j1 rule="hyper" parents="139 44804 957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44807">
    <literal><![CDATA[
      (a(x,y,z) * a(y,x,a(x,y,z))) * (a(x,x,a(y,y,z)) \ u) = L(a(x,y,z) * u,a(x,y,z),a(a(x,y,z),x,y))
    ]]></literal>
    <justification jstring="[para(41951(a,1),44805(a,1,2,1))].">
      <j1 rule="para" parents="41951 44805"/>
    </justification>
  </clause>

  <clause id="44808">
    <literal><![CDATA[
      a(x,a(y,z,x),a(y,z,x) \ u) = a(x * u,x,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,41427,a(flip),b,44806,a),flip(a)].">
      <j1 rule="hyper" parents="373 41427 44806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44809">
    <literal><![CDATA[
      a(x,a(y,z,x),a(y,z,x) \ u) = a(u,x,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,39331,a(flip),b,44808,a),flip(a)].">
      <j1 rule="hyper" parents="373 39331 44808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44810">
    <literal><![CDATA[
      a(x,a(x,y,z),a(z,y,x) \ u) = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42391,a,b,44809,a)].">
      <j1 rule="hyper" parents="64 42391 44809"/>
    </justification>
  </clause>

  <clause id="44811">
    <literal><![CDATA[
      a(x,a(x,y,z),a(z,y,x) * u) = a(u,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42537,a(flip),b,44810,a)].">
      <j1 rule="hyper" parents="64 42537 44810"/>
    </justification>
  </clause>

  <clause id="44812">
    <literal><![CDATA[
      a(x,a(y,z,u),a(y,z,u) \ u) = a(x,u,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42901,a,b,44811,a)].">
      <j1 rule="hyper" parents="64 42901 44811"/>
    </justification>
  </clause>

  <clause id="44813">
    <literal><![CDATA[
      a(x,y,z) \ (a(u,z,a(z,y,x)) \ z) = L(a(x,y,z) \ z,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(44812(a,1),42097(a,1,2,1))].">
      <j1 rule="para" parents="44812 42097"/>
    </justification>
  </clause>

  <clause id="44814">
    <literal><![CDATA[
      L(a(x,y,z) \ z,a(x,y,z),u) = a(x,y,z) \ L(z,a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(34904(a,1),44813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="34904 44813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44815">
    <literal><![CDATA[
      L(a(x,y,z) \ z,a(x,y,z),u) = L(a(x,y,z),z,u) \ z
    ]]></literal>
    <justification jstring="[hyper(373,a,42090,a(flip),b,44814,a),flip(a)].">
      <j1 rule="hyper" parents="373 42090 44814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44816">
    <literal><![CDATA[
      L(a(x,y,z),z,u) \ z = (a(x,y,z) * u) \ (u * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,23793,a(flip),b,44815,a),flip(a)].">
      <j1 rule="hyper" parents="64 23793 44815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44817">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),a(a(x,y,z),x,y)) = (x \ R(x,y,z)) * (a(x,x,a(y,y,z)) \ u)
    ]]></literal>
    <justification jstring="[para(41819(a,1),44807(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41819 44807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44818">
    <literal><![CDATA[
      L(L(((x \ 1) \ 1) \ y,x,a(z,x,u)),(x \ 1) \ a(z,x,u),((x \ 1) \ 1) * a(z,x,u)) = (1 / (a(z,x,u) * ((x \ 1) \ 1))) * (a(z,x,u) * y)
    ]]></literal>
    <justification jstring="[para(5325(a,1),35784(a,1,1))].">
      <j1 rule="para" parents="5325 35784"/>
    </justification>
  </clause>

  <clause id="44819">
    <literal><![CDATA[
      L(L(((x \ 1) \ 1) \ y,x,a(z,x,u)),(x \ 1) \ a(z,x,u),x * a(z,x,u)) = (1 / (a(z,x,u) * ((x \ 1) \ 1))) * (a(z,x,u) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,28981,a(flip),b,44818,a)].">
      <j1 rule="hyper" parents="64 28981 44818"/>
    </justification>
  </clause>

  <clause id="44822">
    <literal><![CDATA[
      L(L(((x \ 1) \ 1) \ y,x,a(z,x,u)),x \ a(z,x,u),x * a(z,x,u)) = (1 / (a(z,x,u) * ((x \ 1) \ 1))) * (a(z,x,u) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29704,a(flip),b,44819,a)].">
      <j1 rule="hyper" parents="64 29704 44819"/>
    </justification>
  </clause>

  <clause id="44823">
    <literal><![CDATA[
      L(L(((x \ 1) \ 1) \ y,x,a(z,x,u)),x * a(z,x,u),x * a(u,x,z)) = (1 / (a(z,x,u) * ((x \ 1) \ 1))) * (a(z,x,u) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,42800,a(flip),b,44822,a)].">
      <j1 rule="hyper" parents="64 42800 44822"/>
    </justification>
  </clause>

  <clause id="44824">
    <literal><![CDATA[
      L(L(((x \ 1) \ 1) \ y,x,a(z,x,u)),x,x) = (1 / (a(z,x,u) * ((x \ 1) \ 1))) * (a(z,x,u) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,42189,a(flip),b,44823,a)].">
      <j1 rule="hyper" parents="64 42189 44823"/>
    </justification>
  </clause>

  <clause id="44826">
    <literal><![CDATA[
      (1 / (a(x,y,z) * ((y \ 1) \ 1))) * (a(x,y,z) * u) = L((y \ 1) * u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,1388,a(flip),b,44824,a),flip(a)].">
      <j1 rule="hyper" parents="64 1388 44824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44827">
    <literal><![CDATA[
      (1 / ((x \ 1) \ a(y,x,z))) * (a(y,x,z) * u) = L((x \ 1) * u,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[para(35781(a,1),44826(a,1,1,2))].">
      <j1 rule="para" parents="35781 44826"/>
    </justification>
  </clause>

  <clause id="44828">
    <literal><![CDATA[
      ((a(x,y,z) / (y \ 1)) \ 1) * (a(x,y,z) * u) = L((y \ 1) * u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(25195(a,1),44827(a,1,1))].">
      <j1 rule="para" parents="25195 44827"/>
    </justification>
  </clause>

  <clause id="44829">
    <literal><![CDATA[
      (((1 / x) \ a(y,x,z)) \ 1) * (a(y,x,z) * u) = L((x \ 1) * u,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[para(24641(a,1),44828(a,1,1,1))].">
      <j1 rule="para" parents="24641 44828"/>
    </justification>
  </clause>

  <clause id="44830">
    <literal><![CDATA[
      ((a(x,y,z) * y) \ 1) * (a(x,y,z) * u) = L((y \ 1) * u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(35737(a,1),44829(a,1,1,1))].">
      <j1 rule="para" parents="35737 44829"/>
    </justification>
  </clause>

  <clause id="44831">
    <literal><![CDATA[
      (a(x,y,z) \ (y \ 1)) * (a(x,y,z) * u) = L((y \ 1) * u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(35834(a,1),44830(a,1,1))].">
      <j1 rule="para" parents="35834 44830"/>
    </justification>
  </clause>

  <clause id="44832">
    <literal><![CDATA[
      (x \ a(y,x,z)) * (((x \ a(y,x,z)) \ (x \ 1)) * u) = L((x \ 1) * u,x,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,43595,a,b,44831,a)].">
      <j1 rule="hyper" parents="64 43595 44831"/>
    </justification>
  </clause>

  <clause id="44833">
    <literal><![CDATA[
      a(x,(R((1 / y) \ z,u,w) \ (R((1 / y) \ z,u,w) \ v5)) * R((((1 / y) \ z) \ 1) \ 1,u,w),v6) = a(x,R(y \ z,u,w) \ T(v5,R((1 / y) \ z,u,w)),v6)
    ]]></literal>
    <justification jstring="[para(11415(a,2),39612(a,1,2,2))].">
      <j1 rule="para" parents="11415 39612"/>
    </justification>
  </clause>

  <clause id="44834">
    <literal><![CDATA[
      T(x * (a(y,a(y,z,u),w) \ T(w,x)),a(y,a(y,z,u),w)) = L(a(y,a(y,z,u),w),L(w,y,a(y,z,u)),x) \ (w * x)
    ]]></literal>
    <justification jstring="[para(40821(a,1),40829(a,1,1,2,2,1))].">
      <j1 rule="para" parents="40821 40829"/>
    </justification>
  </clause>

  <clause id="44835">
    <literal><![CDATA[
      T(x * T(a(y,a(y,z,u),w) \ w,x),a(y,a(y,z,u),w)) = L(a(y,a(y,z,u),w),L(w,y,a(y,z,u)),x) \ (w * x)
    ]]></literal>
    <justification jstring="[para(28757(a,2),44834(a,1,1,2))].">
      <j1 rule="para" parents="28757 44834"/>
    </justification>
  </clause>

  <clause id="44836">
    <literal><![CDATA[
      L(a(x,a(x,y,z),u),L(u,x,a(x,y,z)),w) \ (u * w) = T(w * T(L(u,x,a(x,y,z)),w),a(x,a(x,y,z),u))
    ]]></literal>
    <justification jstring="[para(40820(a,1),44835(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="40820 44835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44837">
    <literal><![CDATA[
      L(a(x,a(x,y,z),u),L(u,x,a(x,y,z)),w) \ (u * w) = T(L(u,x,a(x,y,z)) * w,a(x,a(x,y,z),u))
    ]]></literal>
    <justification jstring="[para(115(a,1),44836(a,2,1))].">
      <j1 rule="para" parents="115 44836"/>
    </justification>
  </clause>

  <clause id="44838">
    <literal><![CDATA[
      L(a(x,a(x,y,z),u),L(u,x,a(x,y,z)),w) \ (u * w) = L(u,x,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(373,a,23105,a(flip),b,44837,a),flip(a)].">
      <j1 rule="hyper" parents="373 23105 44837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44840">
    <literal><![CDATA[
      L(a(x,a(x,y,z),u),u,L(w,x,a(x,y,z))) \ (u * w) = L(u,x,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[para(42858(a,1),44838(a,1,1))].">
      <j1 rule="para" parents="42858 44838"/>
    </justification>
  </clause>

  <clause id="44841">
    <literal><![CDATA[
      a(x,a(x,y,z),L(u,u,L(w,x,a(x,y,z)))) \ (u * w) = L(u,x,a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[para(40995(a,2),44840(a,1,1))].">
      <j1 rule="para" parents="40995 44840"/>
    </justification>
  </clause>

  <clause id="44842">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,u,w))) \ (u * w) = L(u,z,a(z,y,x)) * w
    ]]></literal>
    <justification jstring="[para(43932(a,1),44841(a,1,1))].">
      <j1 rule="para" parents="43932 44841"/>
    </justification>
  </clause>

  <clause id="44843">
    <literal><![CDATA[
      a(x,y,a(L(z,z,u),w,w)) * (z * u) = L(z,w,a(w,y,x)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,42644,a(flip),b,44842,a)].">
      <j1 rule="hyper" parents="64 42644 44842"/>
    </justification>
  </clause>

  <clause id="44845">
    <literal><![CDATA[
      R(x,L((y \ ((y * z) * u)) / u,z,z),L((y \ ((y * z) * u)) / u,z \ 1,a(y,z,u))) = R(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u)
    ]]></literal>
    <justification jstring="[para(1151(a,1),41207(a,1,2))].">
      <j1 rule="para" parents="1151 41207"/>
    </justification>
  </clause>

  <clause id="44846">
    <literal><![CDATA[
      R(x,a(y,z,u) / (1 / z),L((y \ ((y * z) * u)) / u,z \ 1,a(y,z,u))) = R(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u)
    ]]></literal>
    <justification jstring="[para(36345(a,1),44845(a,1,2))].">
      <j1 rule="para" parents="36345 44845"/>
    </justification>
  </clause>

  <clause id="44847">
    <literal><![CDATA[
      R(x,a(y,z,u) / (1 / z),L((y \ ((y * z) * u)) / u,z,a(y,z,u))) = R(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u)
    ]]></literal>
    <justification jstring="[para(11794(a,1),44846(a,1,3))].">
      <j1 rule="para" parents="11794 44846"/>
    </justification>
  </clause>

  <clause id="44848">
    <literal><![CDATA[
      R(x,a(y,z,u) / (1 / z),a(y,z,u) * z) = R(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u)
    ]]></literal>
    <justification jstring="[para(42374(a,1),44847(a,1,3))].">
      <j1 rule="para" parents="42374 44847"/>
    </justification>
  </clause>

  <clause id="44849">
    <literal><![CDATA[
      R(x,a(y,z,u) / (1 / z),z * a(u,z,y)) = R(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,43242,a(flip),b,44848,a)].">
      <j1 rule="hyper" parents="64 43242 44848"/>
    </justification>
  </clause>

  <clause id="44850">
    <literal><![CDATA[
      R(x,(1 / y) \ a(z,y,u),y * a(u,y,z)) = R(x,(z \ ((z * y) * u)) / u,(z \ ((z * y) * u)) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,26410,a(flip),b,44849,a)].">
      <j1 rule="hyper" parents="64 26410 44849"/>
    </justification>
  </clause>

  <clause id="44851">
    <literal><![CDATA[
      R(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u) = R(x,a(y,z,u) * z,z * a(u,z,y))
    ]]></literal>
    <justification jstring="[para(35737(a,1),44850(a,1,2)),flip(a)].">
      <j1 rule="para" parents="35737 44850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44852">
    <literal><![CDATA[
      R(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u) = R(x,z * a(u,z,y),z * a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,42241,a(flip),b,44851,a),flip(a)].">
      <j1 rule="hyper" parents="373 42241 44851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44853">
    <literal><![CDATA[
      R(x,(y \ ((y * z) * u)) / u,u \ (y \ ((y * z) * u))) = R(x,z * a(u,z,y),z * a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(25233,a,44852,a)].">
      <j1 rule="hyper" parents="25233 44852"/>
    </justification>
  </clause>

  <clause id="44854">
    <literal><![CDATA[
      R(x,y \ (z \ ((z * u) * y)),y \ (z \ ((z * u) * y))) = R(x,u * a(y,u,z),u * a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26410,a(flip),b,44853,a)].">
      <j1 rule="hyper" parents="64 26410 44853"/>
    </justification>
  </clause>

  <clause id="44855">
    <literal><![CDATA[
      R(x,y \ (y * z),y \ (y * z)) = R(x,z * a(u,z,y),z * a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,44509,a(flip),b,44854,a)].">
      <j1 rule="hyper" parents="64 44509 44854"/>
    </justification>
  </clause>

  <clause id="44857">
    <literal><![CDATA[
      R(x,y * a(z,y,u),y * a(z,y,u)) = R(x,y,u \ (u * y))
    ]]></literal>
    <justification jstring="[para(9(a,1),44855(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 44855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44858">
    <literal><![CDATA[
      R(x,y * a(z,y,u),y * a(z,y,u)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),44857(a,2,3))].">
      <j1 rule="para" parents="9 44857"/>
    </justification>
  </clause>

  <clause id="44859">
    <literal><![CDATA[
      a(x,L((y \ ((y * z) * u)) / u,z,z),L((y \ ((y * z) * u)) / u,z \ 1,a(y,z,u))) = a(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u)
    ]]></literal>
    <justification jstring="[para(1151(a,1),41215(a,1,2))].">
      <j1 rule="para" parents="1151 41215"/>
    </justification>
  </clause>

  <clause id="44860">
    <literal><![CDATA[
      a(x,a(y,z,u) / (1 / z),L((y \ ((y * z) * u)) / u,z \ 1,a(y,z,u))) = a(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u)
    ]]></literal>
    <justification jstring="[para(36345(a,1),44859(a,1,2))].">
      <j1 rule="para" parents="36345 44859"/>
    </justification>
  </clause>

  <clause id="44861">
    <literal><![CDATA[
      a(x,a(y,z,u) / (1 / z),L((y \ ((y * z) * u)) / u,z,a(y,z,u))) = a(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,39730,a(flip),b,44860,a)].">
      <j1 rule="hyper" parents="64 39730 44860"/>
    </justification>
  </clause>

  <clause id="44862">
    <literal><![CDATA[
      a(x,a(y,z,u) / (1 / z),a(y,z,u) * z) = a(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u)
    ]]></literal>
    <justification jstring="[para(42374(a,1),44861(a,1,3))].">
      <j1 rule="para" parents="42374 44861"/>
    </justification>
  </clause>

  <clause id="44863">
    <literal><![CDATA[
      a(x,a(y,z,u) / (1 / z),z * a(u,z,y)) = a(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42669,a(flip),b,44862,a)].">
      <j1 rule="hyper" parents="64 42669 44862"/>
    </justification>
  </clause>

  <clause id="44864">
    <literal><![CDATA[
      a(x,(1 / y) \ a(z,y,u),y * a(u,y,z)) = a(x,(z \ ((z * y) * u)) / u,(z \ ((z * y) * u)) / u)
    ]]></literal>
    <justification jstring="[hyper(32042,a,44863,a)].">
      <j1 rule="hyper" parents="32042 44863"/>
    </justification>
  </clause>

  <clause id="44865">
    <literal><![CDATA[
      a(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u) = a(x,a(y,z,u) * z,z * a(u,z,y))
    ]]></literal>
    <justification jstring="[para(35737(a,1),44864(a,1,2)),flip(a)].">
      <j1 rule="para" parents="35737 44864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44866">
    <literal><![CDATA[
      a(x,(R((1 / y) \ z,u,w) \ (R((1 / y) \ z,u,w) \ v5)) * L((((1 / y) \ z) \ 1) \ 1,u,w),v6) = a(x,R(y \ z,u,w) \ T(v5,R((1 / y) \ z,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,33767,a(flip),b,44833,a)].">
      <j1 rule="hyper" parents="64 33767 44833"/>
    </justification>
  </clause>

  <clause id="44867">
    <literal><![CDATA[
      a(x,L(((1 / y) \ z) \ 1,u,w) * (R((1 / y) \ z,u,w) \ (R((1 / y) \ z,u,w) \ v5)),v6) = a(x,R(y \ z,u,w) \ T(v5,R((1 / y) \ z,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,37367,a(flip),b,44866,a)].">
      <j1 rule="hyper" parents="64 37367 44866"/>
    </justification>
  </clause>

  <clause id="44868">
    <literal><![CDATA[
      a(x,L(y,R((1 / z) \ u,w,v5),R((1 / z) \ u,w,v5)) * L(((1 / z) \ u) \ 1,w,v5),v6) = a(x,R(z \ u,w,v5) \ T(y,R((1 / z) \ u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32340,a(flip),b,44867,a)].">
      <j1 rule="hyper" parents="64 32340 44867"/>
    </justification>
  </clause>

  <clause id="44869">
    <literal><![CDATA[
      a(x,L(y,R((1 / z) \ u,w,v5),L((1 / z) \ u,w,v5)) * L(((1 / z) \ u) \ 1,w,v5),v6) = a(x,R(z \ u,w,v5) \ T(y,R((1 / z) \ u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(29203(a,1),44868(a,1,2,1))].">
      <j1 rule="para" parents="29203 44868"/>
    </justification>
  </clause>

  <clause id="44870">
    <literal><![CDATA[
      a(x,L(y,R((1 / z) \ u,w,v5),L((z \ 1) \ u,w,v5)) * L(((1 / z) \ u) \ 1,w,v5),v6) = a(x,R(z \ u,w,v5) \ T(y,R((1 / z) \ u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(29175(a,1),44869(a,1,2,1))].">
      <j1 rule="para" parents="29175 44869"/>
    </justification>
  </clause>

  <clause id="44871">
    <literal><![CDATA[
      a(x,L(y,R((1 / z) \ u,w,v5),L(z \ u,w,v5)) * L(((1 / z) \ u) \ 1,w,v5),v6) = a(x,R(z \ u,w,v5) \ T(y,R((1 / z) \ u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(34711(a,1),44870(a,1,2,1))].">
      <j1 rule="para" parents="34711 44870"/>
    </justification>
  </clause>

  <clause id="44872">
    <literal><![CDATA[
      a(x,L(y,L((1 / z) \ u,w,v5),L(z \ u,w,v5)) * L(((1 / z) \ u) \ 1,w,v5),v6) = a(x,R(z \ u,w,v5) \ T(y,R((1 / z) \ u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(29794(a,1),44871(a,1,2,1))].">
      <j1 rule="para" parents="29794 44871"/>
    </justification>
  </clause>

  <clause id="44873">
    <literal><![CDATA[
      a(x,L(y,L(z \ u,w,v5),L(z \ u,w,v5)) * L(((1 / z) \ u) \ 1,w,v5),v6) = a(x,R(z \ u,w,v5) \ T(y,R((1 / z) \ u,w,v5)),v6)
    ]]></literal>
    <justification jstring="[para(35442(a,1),44872(a,1,2,1))].">
      <j1 rule="para" parents="35442 44872"/>
    </justification>
  </clause>

  <clause id="44874">
    <literal><![CDATA[
      a(x,L((1 / y) \ z,u,w) * L(v5,L(y \ z,u,w),L(y \ z,u,w)),v6) = a(x,R(y \ z,u,w) \ T(v5,R((1 / y) \ z,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,37367,a(flip),b,44873,a)].">
      <j1 rule="hyper" parents="64 37367 44873"/>
    </justification>
  </clause>

  <clause id="44875">
    <literal><![CDATA[
      a(x,L(y \ z,u,w) * L(v5,L(y \ z,u,w),L(y \ z,u,w)),v6) = a(x,R(y \ z,u,w) \ T(v5,R((1 / y) \ z,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,37381,a(flip),b,44874,a)].">
      <j1 rule="hyper" parents="64 37381 44874"/>
    </justification>
  </clause>

  <clause id="44876">
    <literal><![CDATA[
      a(x,R(y \ z,u,w) \ T(v5,R((1 / y) \ z,u,w)),v6) = a(x,L(y \ z,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32145,a(flip),b,44875,a),flip(a)].">
      <j1 rule="hyper" parents="64 32145 44875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44877">
    <literal><![CDATA[
      a(x,R(y \ z,u,w) \ v5,v6) = a(x,L(y \ z,u,w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(32041,a,44876,a)].">
      <j1 rule="hyper" parents="32041 44876"/>
    </justification>
  </clause>

  <clause id="44879">
    <literal><![CDATA[
      a(x,L(y \ (z \ y),z,y) \ u,w) = a(x,z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,44794,a(flip),b,44877,a),flip(a)].">
      <j1 rule="hyper" parents="64 44794 44877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44880">
    <literal><![CDATA[
      a(x,L(y \ 1,z,u) \ (L(w,L(y,z,u) \ v5,L(y,z,u)) * v5),v6) = a(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,39596,a(flip),b,44877,a),flip(a)].">
      <j1 rule="hyper" parents="64 39596 44877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44881">
    <literal><![CDATA[
      a(x,L(y \ 1,z,u) \ w,v5) = a(x,R(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32236,a(flip),b,44877,a),flip(a)].">
      <j1 rule="hyper" parents="64 32236 44877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44882">
    <literal><![CDATA[
      a(x,L(y \ (z \ y),z,y) * u,L(y \ (z \ y),z,y)) = a(x,z \ u,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,39114,a,b,44879,a)].">
      <j1 rule="hyper" parents="64 39114 44879"/>
    </justification>
  </clause>

  <clause id="44883">
    <literal><![CDATA[
      a(x,R(y,z,u) \ w,v5) = a(x,L(y,z,u) \ w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,38331,a(flip),b,44881,a),flip(a)].">
      <j1 rule="hyper" parents="64 38331 44881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44887">
    <literal><![CDATA[
      a(x,L(y \ (z \ y),z,y) * u,z \ 1) = a(x,z \ u,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,39112,a(flip),b,44882,a)].">
      <j1 rule="hyper" parents="64 39112 44882"/>
    </justification>
  </clause>

  <clause id="44889">
    <literal><![CDATA[
      a(x,y \ z,y \ 1) = a(x,y * z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,40020,a(flip),b,44887,a),flip(a)].">
      <j1 rule="hyper" parents="64 40020 44887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44890">
    <literal><![CDATA[
      a(x,L(y,z,u) \ (L(w,L(y,z,u) \ v5,L(y,z,u)) * v5),v6) = a(x,(R(y,z,u) \ v5) * T(w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,38331,a(flip),b,44880,a)].">
      <j1 rule="hyper" parents="64 38331 44880"/>
    </justification>
  </clause>

  <clause id="44891">
    <literal><![CDATA[
      a(x,(R(y,z,u) \ w) * T(v5,w),v6) = a(x,(L(y,z,u) \ w) * T(v5,w),v6)
    ]]></literal>
    <justification jstring="[para(1010(a,1),44890(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1010 44890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44892">
    <literal><![CDATA[
      a(x,(R(y,z,u) \ w) * T(v5,w),v6) = a(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,31896,a(flip),b,44891,a),flip(a)].">
      <j1 rule="hyper" parents="373 31896 44891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44894">
    <literal><![CDATA[
      a(x,(R(y,z,u) \ w) * v5,v6) = a(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,31896,a(flip),b,44892,a)].">
      <j1 rule="hyper" parents="64 31896 44892"/>
    </justification>
  </clause>

  <clause id="44896">
    <literal><![CDATA[
      a(x,(R(1 / y,z,u) \ w) * v5,v6) = a(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,34101,a,b,44894,a)].">
      <j1 rule="hyper" parents="64 34101 44894"/>
    </justification>
  </clause>

  <clause id="44897">
    <literal><![CDATA[
      a(x,a(L(y,z,u),z,u) \ z,w) = a(x,(L(y,z,u) \ z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33474,a,b,44894,a)].">
      <j1 rule="hyper" parents="64 33474 44894"/>
    </justification>
  </clause>

  <clause id="44898">
    <literal><![CDATA[
      a(x,a(L(y,z,u),z,u) * z,w) = a(x,(L(y,z,u) \ z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42464,a(flip),b,44897,a)].">
      <j1 rule="hyper" parents="64 42464 44897"/>
    </justification>
  </clause>

  <clause id="44899">
    <literal><![CDATA[
      a(x,(L(y,z,u) \ z) * y,w) = a(x,a(y,z,u) * z,w)
    ]]></literal>
    <justification jstring="[para(41783(a,1),44898(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="41783 44898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44900">
    <literal><![CDATA[
      a(x,y * a(z,y,L(u,y,z)),w) = a(x,a(u,y,z) * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33409,a(flip),b,44899,a)].">
      <j1 rule="hyper" parents="64 33409 44899"/>
    </justification>
  </clause>

  <clause id="44901">
    <literal><![CDATA[
      a(x,a(y,z,u) * z,w) = a(x,z * a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(42064(a,1),44900(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="42064 44900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44902">
    <literal><![CDATA[
      a(x,y * a(z,y,u),w) = a(x,y * a(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(32008,a,44901,a)].">
      <j1 rule="hyper" parents="32008 44901"/>
    </justification>
  </clause>

  <clause id="44903">
    <literal><![CDATA[
      a(x,(y \ ((y * z) * u)) / u,(y \ ((y * z) * u)) / u) = a(x,z * a(u,z,y),z * a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,44865,a,b,44901,a)].">
      <j1 rule="hyper" parents="64 44865 44901"/>
    </justification>
  </clause>

  <clause id="44904">
    <literal><![CDATA[
      a(x,y * a(z,y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35819,a(flip),b,44901,a),flip(a)].">
      <j1 rule="hyper" parents="64 35819 44901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44905">
    <literal><![CDATA[
      a(x,(L(1 / y,z,u) \ w) * v5,v6) = a(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,44894,a(flip),b,44896,a)].">
      <j1 rule="hyper" parents="64 44894 44896"/>
    </justification>
  </clause>

  <clause id="44906">
    <literal><![CDATA[
      a(x,(L(y \ 1,z,u) \ w) * v5,v6) = a(x,(L(y,z,u) \ w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(79(a,1),44905(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="79 44905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44907">
    <literal><![CDATA[
      a(x,(y \ ((y * z) * u)) / u,u \ (y \ ((y * z) * u))) = a(x,z * a(u,z,y),z * a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(27586,a,44903,a)].">
      <j1 rule="hyper" parents="27586 44903"/>
    </justification>
  </clause>

  <clause id="44908">
    <literal><![CDATA[
      a(x,y \ (z \ ((z * u) * y)),y \ (z \ ((z * u) * y))) = a(x,u * a(y,u,z),u * a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(32042,a,44907,a)].">
      <j1 rule="hyper" parents="32042 44907"/>
    </justification>
  </clause>

  <clause id="44909">
    <literal><![CDATA[
      a(x,y \ (y * z),y \ (y * z)) = a(x,z * a(u,z,y),z * a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,44525,a(flip),b,44908,a)].">
      <j1 rule="hyper" parents="64 44525 44908"/>
    </justification>
  </clause>

  <clause id="44911">
    <literal><![CDATA[
      a(x,y * a(z,y,u),y * a(z,y,u)) = a(x,y,u \ (u * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,13838,a(flip),b,44909,a),flip(a)].">
      <j1 rule="hyper" parents="64 13838 44909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44913">
    <literal><![CDATA[
      a(x,y * a(z,y,u),y * a(z,y,u)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,13875,a(flip),b,44911,a),flip(a)].">
      <j1 rule="hyper" parents="373 13875 44911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44915">
    <literal><![CDATA[
      a(x,y * a(z,y,u),y * a(u,y,z)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,44902,a,b,44913,a)].">
      <j1 rule="hyper" parents="64 44902 44913"/>
    </justification>
  </clause>

  <clause id="44926">
    <literal><![CDATA[
      (1 / x) * (a(1 / x,L(x \ 1,y,z),u) * T(w,x \ a(1 / x,L(1 / x,y,z),u))) = L(w,a(1 / x,L(1 / x,y,z),u),x) * R(1 / x,L(1 / x,y,z),u)
    ]]></literal>
    <justification jstring="[para(31920(a,1),38678(a,1,2,1))].">
      <j1 rule="para" parents="31920 38678"/>
    </justification>
  </clause>

  <clause id="44927">
    <literal><![CDATA[
      (1 / x) * (a(1 / x,L(x,y,z),u) * T(w,x \ a(1 / x,L(1 / x,y,z),u))) = L(w,a(1 / x,L(1 / x,y,z),u),x) * R(1 / x,L(1 / x,y,z),u)
    ]]></literal>
    <justification jstring="[para(32203(a,1),44926(a,1,2,1))].">
      <j1 rule="para" parents="32203 44926"/>
    </justification>
  </clause>

  <clause id="44928">
    <literal><![CDATA[
      (1 / x) * (a(x,L(x,y,z),u) * T(w,x \ a(1 / x,L(1 / x,y,z),u))) = L(w,a(1 / x,L(1 / x,y,z),u),x) * R(1 / x,L(1 / x,y,z),u)
    ]]></literal>
    <justification jstring="[para(2641(a,1),44927(a,1,2,1))].">
      <j1 rule="para" parents="2641 44927"/>
    </justification>
  </clause>

  <clause id="44929">
    <literal><![CDATA[
      L(x,a(1 / y,L(1 / y,z,u),w),y) * R(1 / y,L(1 / y,z,u),w) = (1 / y) * (a(y,L(y,z,u),w) * T(x,y \ 1))
    ]]></literal>
    <justification jstring="[para(28658(a,1),44928(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="28658 44928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44931">
    <literal><![CDATA[
      L(x,a(1 / y,L(1 / y,z,u),w),y) * R(1 / y,L(1 / y,z,u),w) = (1 / y) * T(x * a(y,L(y,z,u),w),y \ 1)
    ]]></literal>
    <justification jstring="[para(28753(a,2),44929(a,2,2))].">
      <j1 rule="para" parents="28753 44929"/>
    </justification>
  </clause>

  <clause id="44932">
    <literal><![CDATA[
      L(x,a(1 / y,L(1 / y,z,u),w),y) * R(1 / y,L(1 / y,z,u),w) = T((x * a(y,L(y,z,u),w)) * (1 / y),K(1,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,8718,a,b,44931,a),flip(a)].">
      <j1 rule="hyper" parents="373 8718 44931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44933">
    <literal><![CDATA[
      L(x,a(1 / y,L(1 / y,z,u),w),y) * R(1 / y,L(1 / y,z,u),w) = T(a(y,L(y,z,u),w) * (x * (1 / y)),K(1,y))
    ]]></literal>
    <justification jstring="[para(30001(a,1),44932(a,2,1))].">
      <j1 rule="para" parents="30001 44932"/>
    </justification>
  </clause>

  <clause id="44934">
    <literal><![CDATA[
      L(x,a(1 / y,L(1 / y,z,u),w),y) * R(1 / y,L(1 / y,z,u),w) = T(a(y,L(y,z,u),w) * (x * (1 / y)),1)
    ]]></literal>
    <justification jstring="[para(381(a,1),44933(a,2,2))].">
      <j1 rule="para" parents="381 44933"/>
    </justification>
  </clause>

  <clause id="44935">
    <literal><![CDATA[
      L(x,a(1 / y,L(1 / y,z,u),w),y) * R(1 / y,L(1 / y,z,u),w) = a(y,L(y,z,u),w) * (x * (1 / y))
    ]]></literal>
    <justification jstring="[hyper(373,a,372,a(flip),b,44934,a),flip(a)].">
      <j1 rule="hyper" parents="373 372 44934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44937">
    <literal><![CDATA[
      L(x,a(1 / y,L(y \ 1,z,u),w),y) * R(1 / y,L(1 / y,z,u),w) = a(y,L(y,z,u),w) * (x * (1 / y))
    ]]></literal>
    <justification jstring="[para(31920(a,1),44935(a,1,1,2))].">
      <j1 rule="para" parents="31920 44935"/>
    </justification>
  </clause>

  <clause id="44938">
    <literal><![CDATA[
      L(x,a(1 / y,L(y,z,u),w),y) * R(1 / y,L(1 / y,z,u),w) = a(y,L(y,z,u),w) * (x * (1 / y))
    ]]></literal>
    <justification jstring="[para(32203(a,1),44937(a,1,1,2))].">
      <j1 rule="para" parents="32203 44937"/>
    </justification>
  </clause>

  <clause id="44939">
    <literal><![CDATA[
      L(x,a(y,L(y,z,u),w),y) * R(1 / y,L(1 / y,z,u),w) = a(y,L(y,z,u),w) * (x * (1 / y))
    ]]></literal>
    <justification jstring="[para(2641(a,1),44938(a,1,1,2))].">
      <j1 rule="para" parents="2641 44938"/>
    </justification>
  </clause>

  <clause id="44940">
    <literal><![CDATA[
      L(x,y,a(y,L(y,z,u),w)) * R(1 / y,L(1 / y,z,u),w) = a(y,L(y,z,u),w) * (x * (1 / y))
    ]]></literal>
    <justification jstring="[para(30415(a,1),44939(a,1,1))].">
      <j1 rule="para" parents="30415 44939"/>
    </justification>
  </clause>

  <clause id="44941">
    <literal><![CDATA[
      a(x,L(x,y,z),u) * (w * (1 / x)) = w * R(1 / x,L(1 / x,y,z),u)
    ]]></literal>
    <justification jstring="[para(37531(a,1),44940(a,1,1)),flip(a)].">
      <j1 rule="para" parents="37531 44940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44942">
    <literal><![CDATA[
      a(x,L(x,y,z),u) * (w * (1 / x)) = w * R(1 / x,L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(26652(a,1),44941(a,2,2))].">
      <j1 rule="para" parents="26652 44941"/>
    </justification>
  </clause>

  <clause id="44943">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) * (w * (1 / x)) = w * R(1 / x,L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(39676(a,1),44942(a,1,1))].">
      <j1 rule="para" parents="39676 44942"/>
    </justification>
  </clause>

  <clause id="44944">
    <literal><![CDATA[
      x * R(1 / y,L(y,z,u),w) = x * R(1 / y,y,L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,37554,a(flip),b,44943,a),flip(a)].">
      <j1 rule="hyper" parents="64 37554 44943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44945">
    <literal><![CDATA[
      x * R(1 / x,x,L(y,z,u)) = a(x,L(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,38701,a(flip),b,44944,a),flip(a)].">
      <j1 rule="hyper" parents="64 38701 44944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44946">
    <literal><![CDATA[
      a(x,L(x,y,z),x * u) = a(x,x,x * L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30137,a(flip),b,44945,a),flip(a)].">
      <j1 rule="hyper" parents="64 30137 44945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44947">
    <literal><![CDATA[
      a(x,x,L(x * y,z,u)) = a(x,x,x * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39676,a(flip),b,44946,a)].">
      <j1 rule="hyper" parents="64 39676 44946"/>
    </justification>
  </clause>

  <clause id="44948">
    <literal><![CDATA[
      a(x,x,L(x * y,z,u)) = a(x,x,L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,44947,a),flip(a)].">
      <j1 rule="hyper" parents="373 27298 44947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44949">
    <literal><![CDATA[
      a(x,x,L(x * R(T(y,K(x,z)),u,w),v5,v6)) = L(a(x,x,L(x * y,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(44947(a,2),39825(a,2,1))].">
      <j1 rule="para" parents="44947 39825"/>
    </justification>
  </clause>

  <clause id="44950">
    <literal><![CDATA[
      a(x,x,L(x * R(y,y,y),y,z * y)) = a(x,x,(a(z,y,y \ 1) \ y) * x)
    ]]></literal>
    <justification jstring="[para(33434(a,1),44948(a,2,3,1))].">
      <j1 rule="para" parents="33434 44948"/>
    </justification>
  </clause>

  <clause id="44951">
    <literal><![CDATA[
      a(x,x,L(x * R(y,y,y),y,z * y)) = a(x,x,x * L(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,40227,a(flip),b,44950,a),flip(a)].">
      <j1 rule="hyper" parents="373 40227 44950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44952">
    <literal><![CDATA[
      a(x,x,L(x * R(y,y,y),y,z * y)) = a(x,x,L(x * y,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,44947,a,b,44951,a),flip(a)].">
      <j1 rule="hyper" parents="373 44947 44951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44953">
    <literal><![CDATA[
      L(x * (y / (x * y)),y,z * y) = a(x,x,L(x * y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39710,a(flip),b,44952,a)].">
      <j1 rule="hyper" parents="64 39710 44952"/>
    </justification>
  </clause>

  <clause id="44955">
    <literal><![CDATA[
      a(x,x,L(x * R(T(y,K(x,z)),u,w),v5,v6)) = a(x,x,L(L(x * y,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,39675,a,b,44949,a),flip(a)].">
      <j1 rule="hyper" parents="373 39675 44949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44956">
    <literal><![CDATA[
      a(x,x,L(L(x * y,z,u),w,v5)) = a(x,x,L(x * R(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(3347(a,1),44955(a,1,3,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3347 44955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44957">
    <literal><![CDATA[
      a(x,x,L(L(x * y,z,y),u,w)) = L(x * (y / (x * y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,39710,a(flip),b,44956,a),flip(a)].">
      <j1 rule="hyper" parents="373 39710 44956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44958">
    <literal><![CDATA[
      L(x * (y / (x * y)),y,z) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,43388,a(flip),b,44957,a),flip(a)].">
      <j1 rule="hyper" parents="64 43388 44957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44960">
    <literal><![CDATA[
      a(x,x,L(x * y,y,z)) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,44953,a(flip),b,44958,a)].">
      <j1 rule="hyper" parents="64 44953 44958"/>
    </justification>
  </clause>

  <clause id="44962">
    <literal><![CDATA[
      (x * y) * (((x \ 1) \ y) \ z) = (x * (y / (x * y))) \ z
    ]]></literal>
    <justification jstring="[para(44960(a,1),41143(a,1,1)),flip(a)].">
      <j1 rule="para" parents="44960 41143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44963">
    <literal><![CDATA[
      x * ((y \ ((y \ 1) \ x)) \ z) = (y * (x / (y * x))) \ z
    ]]></literal>
    <justification jstring="[para(44960(a,1),43119(a,1,1)),flip(a)].">
      <j1 rule="para" parents="44960 43119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44964">
    <literal><![CDATA[
      ((x \ 1) \ y) \ ((x * y) * z) = (x * (y / (x * y))) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,3147,a,b,44962,a)].">
      <j1 rule="hyper" parents="64 3147 44962"/>
    </justification>
  </clause>

  <clause id="44966">
    <literal><![CDATA[
      (x * ((y / x) / (x * (y / x)))) \ z = L(y,x,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,44569,a(flip),b,44963,a),flip(a)].">
      <j1 rule="hyper" parents="64 44569 44963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44968">
    <literal><![CDATA[
      (x * ((x \ y) / y)) \ z = L(y,x,x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4811(a,1),44966(a,1,1,2))].">
      <j1 rule="para" parents="4811 44966"/>
    </justification>
  </clause>

  <clause id="44969">
    <literal><![CDATA[
      L(x,y,y) * (x \ z) = a(y,y,x) \ z
    ]]></literal>
    <justification jstring="[para(30070(a,1),44968(a,1,1)),flip(a)].">
      <j1 rule="para" parents="30070 44968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44970">
    <literal><![CDATA[
      a(x,x,y) \ (z * (x * y)) = z * (x * L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,44751,a(flip),b,44969,a),flip(a)].">
      <j1 rule="hyper" parents="64 44751 44969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44974">
    <literal><![CDATA[
      T(a(x,x,y) \ z,y) = y \ (z * L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(35,a,33491,a,b,44969,a)].">
      <j1 rule="hyper" parents="35 33491 44969"/>
    </justification>
  </clause>

  <clause id="44975">
    <literal><![CDATA[
      a(x,x,y) * (L(y,x,x) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(1335,a,44969,a(flip))].">
      <j1 rule="hyper" parents="1335 44969"/>
    </justification>
  </clause>

  <clause id="44976">
    <literal><![CDATA[
      x * (L(x,y,y) \ z) = a(y,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(733,a,44969,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="733 44969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44977">
    <literal><![CDATA[
      a(x,x,y) * (z * L(y,x,x)) = z * y
    ]]></literal>
    <justification jstring="[hyper(145,a,23889,a(flip),b,44969,a(flip))].">
      <j1 rule="hyper" parents="145 23889 44969"/>
    </justification>
  </clause>

  <clause id="44978">
    <literal><![CDATA[
      a(x,x,y) * (y \ z) = L(y,x,x) \ z
    ]]></literal>
    <justification jstring="[hyper(145,a,2326,a(flip),b,44969,a(flip))].">
      <j1 rule="hyper" parents="145 2326 44969"/>
    </justification>
  </clause>

  <clause id="44979">
    <literal><![CDATA[
      (x \ y) * (a(x,x,y) \ z) = ((x \ 1) * y) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,44969,a(flip),b,41571,a)].">
      <j1 rule="hyper" parents="145 44969 41571"/>
    </justification>
  </clause>

  <clause id="44981">
    <literal><![CDATA[
      (a(x,x,y) \ z) * y = z * L(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,44969,a(flip),b,24378,a)].">
      <j1 rule="hyper" parents="144 44969 24378"/>
    </justification>
  </clause>

  <clause id="44982">
    <literal><![CDATA[
      (a(x,x,y) * y) \ z = y \ (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(139,a,44969,a(flip),b,35203,a),flip(a)].">
      <j1 rule="hyper" parents="139 44969 35203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44983">
    <literal><![CDATA[
      a(x,x,L(y,y,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,39512,a,b,44969,a(flip))].">
      <j1 rule="hyper" parents="40 39512 44969"/>
    </justification>
  </clause>

  <clause id="44984">
    <literal><![CDATA[
      L(x,y,a(y,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(39,a,40931,a,b,44969,a(flip))].">
      <j1 rule="hyper" parents="39 40931 44969"/>
    </justification>
  </clause>

  <clause id="44985">
    <literal><![CDATA[
      (a(x,x,y) \ z) * (x \ ((1 / x) \ y)) = z * y
    ]]></literal>
    <justification jstring="[para(44969(a,1),43716(a,1,1))].">
      <j1 rule="para" parents="44969 43716"/>
    </justification>
  </clause>

  <clause id="44986">
    <literal><![CDATA[
      L(x,y,a(z,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(42222,a,44984,a)].">
      <j1 rule="hyper" parents="42222 44984"/>
    </justification>
  </clause>

  <clause id="44989">
    <literal><![CDATA[
      a(x,x,a(y,z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,44984,a,b,43970,a),flip(a)].">
      <j1 rule="hyper" parents="140 44984 43970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44990">
    <literal><![CDATA[
      a(x,y,a(y,z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,44984,a,b,41039,a),flip(a)].">
      <j1 rule="hyper" parents="140 44984 41039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44991">
    <literal><![CDATA[
      L(x,y,a(y,y * z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,41308,a,b,44984,a)].">
      <j1 rule="hyper" parents="64 41308 44984"/>
    </justification>
  </clause>

  <clause id="44992">
    <literal><![CDATA[
      R(x,y,y \ (z * z)) = R(x,y,(y \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,44769,a(flip),b,44984,a),flip(a)].">
      <j1 rule="hyper" parents="64 44769 44984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44993">
    <literal><![CDATA[
      x * (L(x,y,y) \ (z \ x)) = z \ (a(y,y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,44290,a(flip),b,44984,a)].">
      <j1 rule="hyper" parents="64 44290 44984"/>
    </justification>
  </clause>

  <clause id="44994">
    <literal><![CDATA[
      (a(x,y,y) \ z) * x = z * (a(x,y,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,44260,a(flip),b,44984,a)].">
      <j1 rule="hyper" parents="64 44260 44984"/>
    </justification>
  </clause>

  <clause id="44995">
    <literal><![CDATA[
      L(x,(y \ z) * z,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,44243,a(flip),b,44984,a),flip(a)].">
      <j1 rule="hyper" parents="64 44243 44984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44996">
    <literal><![CDATA[
      R(x,y,L(y,z,z)) = R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,43961,a(flip),b,44984,a),flip(a)].">
      <j1 rule="hyper" parents="64 43961 44984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44997">
    <literal><![CDATA[
      L(x,y \ z,z) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,43305,a(flip),b,44984,a),flip(a)].">
      <j1 rule="hyper" parents="64 43305 44984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44998">
    <literal><![CDATA[
      L(x,y,(z \ y) * y) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42929,a(flip),b,44984,a),flip(a)].">
      <j1 rule="hyper" parents="64 42929 44984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="44999">
    <literal><![CDATA[
      L(x,y,z \ y) = L(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42019,a(flip),b,44984,a)].">
      <j1 rule="hyper" parents="64 42019 44984"/>
    </justification>
  </clause>

  <clause id="45000">
    <literal><![CDATA[
      R(x,y,y) * (x \ z) = z * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41556,a(flip),b,44984,a)].">
      <j1 rule="hyper" parents="64 41556 44984"/>
    </justification>
  </clause>

  <clause id="45001">
    <literal><![CDATA[
      ((x * y) \ z) * a(x,y,y) = (x * L(y,y,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,41175,a(flip),b,44984,a),flip(a)].">
      <j1 rule="hyper" parents="64 41175 44984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45004">
    <literal><![CDATA[
      (x / y) \ ((y * x) * z) = y * (((y * x) \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40953,a(flip),b,44984,a)].">
      <j1 rule="hyper" parents="64 40953 44984"/>
    </justification>
  </clause>

  <clause id="45006">
    <literal><![CDATA[
      (x / L(y,y,z)) / R(z,y,y) = (x / y) / z
    ]]></literal>
    <justification jstring="[hyper(64,a,37970,a(flip),b,44984,a)].">
      <j1 rule="hyper" parents="64 37970 44984"/>
    </justification>
  </clause>

  <clause id="45007">
    <literal><![CDATA[
      x * (L(x,y,y) \ z) = z * a(y,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,37707,a(flip),b,44984,a)].">
      <j1 rule="hyper" parents="64 37707 44984"/>
    </justification>
  </clause>

  <clause id="45008">
    <literal><![CDATA[
      a(x,y,y) * (z * x) = z * R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(144,a,44984,a(flip),b,28833,a),flip(a)].">
      <j1 rule="hyper" parents="144 44984 28833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45009">
    <literal><![CDATA[
      a(x,x,a(y,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,44984,a(flip),b,43922,a),flip(a)].">
      <j1 rule="hyper" parents="140 44984 43922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45011">
    <literal><![CDATA[
      L(x,y,y) \ (L(x,y,y) / z) = x \ (x / z)
    ]]></literal>
    <justification jstring="[hyper(139,a,44984,a(flip),b,42255,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="139 44984 42255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45012">
    <literal><![CDATA[
      a(x,y,L(y,z,z)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,44279,a(flip),b,44984,a(flip))].">
      <j1 rule="hyper" parents="40 44279 44984"/>
    </justification>
  </clause>

  <clause id="45013">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,44259,a(flip),b,44984,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 44259 44984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45015">
    <literal><![CDATA[
      x * (a(x,y,y) * z) = R(x,y,y) * z
    ]]></literal>
    <justification jstring="[para(44984(a,1),29291(a,1,2)),flip(a)].">
      <j1 rule="para" parents="44984 29291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45016">
    <literal><![CDATA[
      (a(x,y,y) \ z) * (x * y) = z * (x * L(y,y,x))
    ]]></literal>
    <justification jstring="[para(44984(a,1),41184(a,1,1)),flip(a)].">
      <j1 rule="para" parents="44984 41184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45018">
    <literal><![CDATA[
      (x \ y) * (a(y,x,x) * z) = (x \ R(y,x,x)) * z
    ]]></literal>
    <justification jstring="[para(44984(a,1),41356(a,1,2)),flip(a)].">
      <j1 rule="para" parents="44984 41356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45021">
    <literal><![CDATA[
      ((x \ y) \ z) * a(x,x,y) = ((x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,44742,a(flip),b,44986,a),flip(a)].">
      <j1 rule="hyper" parents="64 44742 44986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45022">
    <literal><![CDATA[
      (x * y) \ ((y \ x) * z) = ((x * y) \ (y \ x)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,44724,a(flip),b,44986,a)].">
      <j1 rule="hyper" parents="64 44724 44986"/>
    </justification>
  </clause>

  <clause id="45023">
    <literal><![CDATA[
      (x / y) * ((x \ y) \ z) = x * (((x \ y) * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,43841,a(flip),b,44986,a)].">
      <j1 rule="hyper" parents="64 43841 44986"/>
    </justification>
  </clause>

  <clause id="45024">
    <literal><![CDATA[
      (x / (y * x)) * (y \ z) = x * ((y * (y * x)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41533,a(flip),b,44986,a)].">
      <j1 rule="hyper" parents="64 41533 44986"/>
    </justification>
  </clause>

  <clause id="45025">
    <literal><![CDATA[
      a(x,y,y) \ (z / x) = z / R(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,38339,a(flip),b,44986,a)].">
      <j1 rule="hyper" parents="64 38339 44986"/>
    </justification>
  </clause>

  <clause id="45028">
    <literal><![CDATA[
      (x * x) * a(y,z,z) = x * (x * a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(1432,a,44989,a)].">
      <j1 rule="hyper" parents="1432 44989"/>
    </justification>
  </clause>

  <clause id="45030">
    <literal><![CDATA[
      a(x,y,a(z,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,41950,a,b,44989,a)].">
      <j1 rule="hyper" parents="64 41950 44989"/>
    </justification>
  </clause>

  <clause id="45031">
    <literal><![CDATA[
      L(a(x,y,y),z,z) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,44989,a)].">
      <j1 rule="hyper" parents="53 44989"/>
    </justification>
  </clause>

  <clause id="45032">
    <literal><![CDATA[
      L(x,y,a(z,z,a(u,w,w))) = x
    ]]></literal>
    <justification jstring="[para(44989(a,2),621(a,1,3))].">
      <j1 rule="para" parents="44989 621"/>
    </justification>
  </clause>

  <clause id="45033">
    <literal><![CDATA[
      (x \ 1) * a(y,z,z) = x \ a(y,z,z)
    ]]></literal>
    <justification jstring="[para(44989(a,1),30104(a,1,1,2))].">
      <j1 rule="para" parents="44989 30104"/>
    </justification>
  </clause>

  <clause id="45034">
    <literal><![CDATA[
      (1 / x) \ a(y,z,z) = x * a(y,z,z)
    ]]></literal>
    <justification jstring="[para(44989(a,1),30118(a,1,1,1))].">
      <j1 rule="para" parents="44989 30118"/>
    </justification>
  </clause>

  <clause id="45035">
    <literal><![CDATA[
      L(1 / x,x,a(y,y,z)) = 1 / x
    ]]></literal>
    <justification jstring="[para(44989(a,1),41504(a,2,1))].">
      <j1 rule="para" parents="44989 41504"/>
    </justification>
  </clause>

  <clause id="45036">
    <literal><![CDATA[
      a(x,x,y) \ (z \ a(x,x,y)) = z \ 1
    ]]></literal>
    <justification jstring="[para(44989(a,1),41505(a,2,2))].">
      <j1 rule="para" parents="44989 41505"/>
    </justification>
  </clause>

  <clause id="45037">
    <literal><![CDATA[
      a(x,y,z) \ 1 = z \ L(z,y,x)
    ]]></literal>
    <justification jstring="[para(44989(a,1),41684(a,1,2))].">
      <j1 rule="para" parents="44989 41684"/>
    </justification>
  </clause>

  <clause id="45039">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,w,z))) = 1
    ]]></literal>
    <justification jstring="[para(44127(a,1),44989(a,1,3))].">
      <j1 rule="para" parents="44127 44989"/>
    </justification>
  </clause>

  <clause id="45044">
    <literal><![CDATA[
      L(a(x,y,y),x,z) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,44990,a)].">
      <j1 rule="hyper" parents="53 44990"/>
    </justification>
  </clause>

  <clause id="45045">
    <literal><![CDATA[
      L(a(x,y,z) \ 1,z,y) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(44990(a,1),42230(a,1,2)),flip(a)].">
      <j1 rule="para" parents="44990 42230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45049">
    <literal><![CDATA[
      a(x,y,a(z,z,L(y,u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,44054,a(flip),b,45009,a)].">
      <j1 rule="hyper" parents="64 44054 45009"/>
    </justification>
  </clause>

  <clause id="45050">
    <literal><![CDATA[
      L(a(x,x,y),z,z) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(53,a,45009,a)].">
      <j1 rule="hyper" parents="53 45009"/>
    </justification>
  </clause>

  <clause id="45051">
    <literal><![CDATA[
      (x \ 1) * a(y,y,z) = x \ a(y,y,z)
    ]]></literal>
    <justification jstring="[para(45009(a,1),30104(a,1,1,2))].">
      <j1 rule="para" parents="45009 30104"/>
    </justification>
  </clause>

  <clause id="45052">
    <literal><![CDATA[
      a(x,y,y) \ (z \ a(x,y,y)) = z \ 1
    ]]></literal>
    <justification jstring="[para(45009(a,1),41505(a,2,2))].">
      <j1 rule="para" parents="45009 41505"/>
    </justification>
  </clause>

  <clause id="45053">
    <literal><![CDATA[
      R(x,y,z) \ x = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(45009(a,1),42805(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45009 42805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45054">
    <literal><![CDATA[
      L(x,y,a(y,z,L(z,u,w))) = x * 1
    ]]></literal>
    <justification jstring="[para(45009(a,1),44047(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45009 44047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45055">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,w,w))) = 1
    ]]></literal>
    <justification jstring="[para(44265(a,1),45009(a,1,3))].">
      <j1 rule="para" parents="44265 45009"/>
    </justification>
  </clause>

  <clause id="45056">
    <literal><![CDATA[
      a(x,x,a(y,z,a(z,u,w))) = 1
    ]]></literal>
    <justification jstring="[para(44315(a,1),45009(a,1,3))].">
      <j1 rule="para" parents="44315 45009"/>
    </justification>
  </clause>

  <clause id="45058">
    <literal><![CDATA[
      L(a(x,y,z) * z,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(64,a,42143,a,b,45013,a)].">
      <j1 rule="hyper" parents="64 42143 45013"/>
    </justification>
  </clause>

  <clause id="45059">
    <literal><![CDATA[
      L(x * a(y,z,x),z,y) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,42142,a,b,45013,a)].">
      <j1 rule="hyper" parents="64 42142 45013"/>
    </justification>
  </clause>

  <clause id="45060">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,41641,a,b,45013,a)].">
      <j1 rule="hyper" parents="64 41641 45013"/>
    </justification>
  </clause>

  <clause id="45061">
    <literal><![CDATA[
      a(x,y,z) * L(z,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(64,a,41640,a,b,45013,a)].">
      <j1 rule="hyper" parents="64 41640 45013"/>
    </justification>
  </clause>

  <clause id="45062">
    <literal><![CDATA[
      a(x,y,z) \ R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,41624,a,b,45013,a)].">
      <j1 rule="hyper" parents="64 41624 45013"/>
    </justification>
  </clause>

  <clause id="45063">
    <literal><![CDATA[
      L(x,a(y,y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,40922,a,b,45013,a)].">
      <j1 rule="hyper" parents="64 40922 45013"/>
    </justification>
  </clause>

  <clause id="45064">
    <literal><![CDATA[
      L(x,x,L(y,y,z)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,44121,a(flip),b,45013,a)].">
      <j1 rule="hyper" parents="64 44121 45013"/>
    </justification>
  </clause>

  <clause id="45065">
    <literal><![CDATA[
      L(x,y,z) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,44046,a(flip),b,45013,a),flip(a)].">
      <j1 rule="hyper" parents="64 44046 45013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45066">
    <literal><![CDATA[
      R(x,y,z) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,45013,a(flip),b,41624,a),flip(a)].">
      <j1 rule="hyper" parents="145 45013 41624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45067">
    <literal><![CDATA[
      a(x,y,z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(139,a,45013,a(flip),b,41641,a),flip(a)].">
      <j1 rule="hyper" parents="139 45013 41641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45068">
    <literal><![CDATA[
      a(x,y,y) * (z \ 1) = z \ a(x,y,y)
    ]]></literal>
    <justification jstring="[para(45013(a,1),24639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45013 24639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45069">
    <literal><![CDATA[
      L(x,x,L(y,z,z)) = L(x,x,y)
    ]]></literal>
    <justification jstring="[para(45013(a,1),40967(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45013 40967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45070">
    <literal><![CDATA[
      (x / ((x / y) / y)) \ z = x * (((x * y) * y) \ z)
    ]]></literal>
    <justification jstring="[para(45013(a,1),41091(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45013 41091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45072">
    <literal><![CDATA[
      R(x,y,z) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(45013(a,1),41626(a,2,1))].">
      <j1 rule="para" parents="45013 41626"/>
    </justification>
  </clause>

  <clause id="45073">
    <literal><![CDATA[
      a(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(45013(a,1),41628(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45013 41628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45074">
    <literal><![CDATA[
      L(x \ y,x,a(y,z,z)) = x \ y
    ]]></literal>
    <justification jstring="[para(45013(a,1),42406(a,2,1))].">
      <j1 rule="para" parents="45013 42406"/>
    </justification>
  </clause>

  <clause id="45075">
    <literal><![CDATA[
      R(T(x,y),z,u) \ x = a(x,z,u) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(45013(a,1),42899(a,1,2))].">
      <j1 rule="para" parents="45013 42899"/>
    </justification>
  </clause>

  <clause id="45076">
    <literal><![CDATA[
      (x * y) * (a(z,y,x) \ z) = (L(x,y,z) * y) * z
    ]]></literal>
    <justification jstring="[para(45013(a,1),43044(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45013 43044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45078">
    <literal><![CDATA[
      L(x * y,z,a(z,y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(45013(a,1),43089(a,2,2))].">
      <j1 rule="para" parents="45013 43089"/>
    </justification>
  </clause>

  <clause id="45084">
    <literal><![CDATA[
      a(x,x,L(y,z,z)) \ 1 = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(45030(a,1),43130(a,1,2))].">
      <j1 rule="para" parents="45030 43130"/>
    </justification>
  </clause>

  <clause id="45085">
    <literal><![CDATA[
      L(x,y,a(y,z,a(u,u,w))) = L(x,z,1)
    ]]></literal>
    <justification jstring="[para(45030(a,1),44212(a,1,3)),flip(a)].">
      <j1 rule="para" parents="45030 44212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45090">
    <literal><![CDATA[
      R(x,y \ (x / (x \ y)),x) * (T(y \ (x / (x \ y)),x) * z) = ((y \ x) * ((x \ y) \ x)) * z
    ]]></literal>
    <justification jstring="[para(44991(a,1),40347(a,2,2))].">
      <j1 rule="para" parents="44991 40347"/>
    </justification>
  </clause>

  <clause id="45092">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * w = L(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(42,a,42206,a,b,45058,a),flip(a)].">
      <j1 rule="hyper" parents="42 42206 45058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45093">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * w = L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(42,a,42171,a,b,45058,a),flip(a)].">
      <j1 rule="hyper" parents="42 42171 45058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45094">
    <literal><![CDATA[
      L(L(a(x,y,z) * z,u,w),y,x) = L(z,u,w)
    ]]></literal>
    <justification jstring="[para(45058(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45058 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45100">
    <literal><![CDATA[
      a(x,a(y,z,u) * u,w) = a(x,L(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(45058(a,1),42975(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="45058 42975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45104">
    <literal><![CDATA[
      x * a(a(y,z,u),w,x) = L(x,w,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(42,a,42206,a,b,45059,a),flip(a)].">
      <j1 rule="hyper" parents="42 42206 45059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45113">
    <literal><![CDATA[
      a((x * a(y,z,x)) * u,w,v5) = a(L(x,z,y) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(45059(a,1),34666(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="45059 34666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45114">
    <literal><![CDATA[
      a(x * a(y,z,x),u,w) = a(L(x,z,y),u,w)
    ]]></literal>
    <justification jstring="[para(45059(a,1),34954(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="45059 34954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45115">
    <literal><![CDATA[
      L(x,y * a(z,u,y),w) = L(x,L(y,u,z),w)
    ]]></literal>
    <justification jstring="[para(45059(a,1),36290(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="45059 36290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45116">
    <literal><![CDATA[
      a(x,y,z * a(u,w,z)) = a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[para(45059(a,1),39064(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="45059 39064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45118">
    <literal><![CDATA[
      a(x,y * a(z,u,y),w) = a(x,L(y,u,z),w)
    ]]></literal>
    <justification jstring="[para(45059(a,1),42975(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="45059 42975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45119">
    <literal><![CDATA[
      a(x,y,z * (u * a(w,v5,u))) = a(x,y,L(u,v5,w) * z)
    ]]></literal>
    <justification jstring="[para(45059(a,1),42976(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="45059 42976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45128">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w)) = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(35,a,42169,a,b,45060,a)].">
      <j1 rule="hyper" parents="35 42169 45060"/>
    </justification>
  </clause>

  <clause id="45130">
    <literal><![CDATA[
      a(x,y,z) = z * (L(z,y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,1845,a,b,45060,a),flip(a)].">
      <j1 rule="hyper" parents="35 1845 45060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45132">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * x = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,45060,a(flip),b,42499,a)].">
      <j1 rule="hyper" parents="145 45060 42499"/>
    </justification>
  </clause>

  <clause id="45142">
    <literal><![CDATA[
      L(x,y,z) \ x != u
    ]]></literal>
    <literal><![CDATA[
      a(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(45060(a,1),335(a,1,2)),flip(b)].">
      <j1 rule="para" parents="45060 335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45147">
    <literal><![CDATA[
      a(x,y,z) \ z != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(45060(a,1),23797(a,1,2))].">
      <j1 rule="para" parents="45060 23797"/>
    </justification>
  </clause>

  <clause id="45148">
    <literal><![CDATA[
      L(x \ L(y,z,u),x,a(u,z,y)) = (a(u,z,y) * x) \ y
    ]]></literal>
    <justification jstring="[para(45060(a,1),23172(a,2,2))].">
      <j1 rule="para" parents="45060 23172"/>
    </justification>
  </clause>

  <clause id="45157">
    <literal><![CDATA[
      x * a(x,y,a(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,42650,a,b,45061,a)].">
      <j1 rule="hyper" parents="35 42650 45061"/>
    </justification>
  </clause>

  <clause id="45165">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * L(L(z,y,x),u,w) = L(z,u,w)
    ]]></literal>
    <justification jstring="[para(30(a,1),45061(a,1,2))].">
      <j1 rule="para" parents="30 45061"/>
    </justification>
  </clause>

  <clause id="45169">
    <literal><![CDATA[
      L(x,y,L(z,u,w) \ z) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(45061(a,1),23842(a,1,3,2))].">
      <j1 rule="para" parents="45061 23842"/>
    </justification>
  </clause>

  <clause id="45182">
    <literal><![CDATA[
      a(x,y,z) * (R(x,u,w) \ x) = R(x,u,w) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(45062(a,1),30979(a,1,2,2))].">
      <j1 rule="para" parents="45062 30979"/>
    </justification>
  </clause>

  <clause id="45187">
    <literal><![CDATA[
      (R(x,y,z) \ x) * u = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(45062(a,1),42568(a,1,1,2))].">
      <j1 rule="para" parents="45062 42568"/>
    </justification>
  </clause>

  <clause id="45189">
    <literal><![CDATA[
      L(x,y,z) = (a(z,y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,41552,a,b,45065,a),flip(a)].">
      <j1 rule="hyper" parents="373 41552 45065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45190">
    <literal><![CDATA[
      x * a(x,y,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,42501,a(flip),b,45065,a)].">
      <j1 rule="hyper" parents="373 42501 45065"/>
    </justification>
  </clause>

  <clause id="45193">
    <literal><![CDATA[
      (a(x,y,z) \ z) * a(u,w,v5) = a(u,w,v5) * L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,45065,a,b,23138,a),flip(a)].">
      <j1 rule="hyper" parents="145 45065 23138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45194">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,45065,a,b,42501,a(flip))].">
      <j1 rule="hyper" parents="139 45065 42501"/>
    </justification>
  </clause>

  <clause id="45209">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(45065(a,2),23911(a,1,1))].">
      <j1 rule="para" parents="45065 23911"/>
    </justification>
  </clause>

  <clause id="45213">
    <literal><![CDATA[
      (a(x,y,z) \ x) * z = x * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(45065(a,2),33312(a,2,2))].">
      <j1 rule="para" parents="45065 33312"/>
    </justification>
  </clause>

  <clause id="45215">
    <literal><![CDATA[
      L(x,L(y,x,x),z) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[para(35676(a,1),45065(a,2,1))].">
      <j1 rule="para" parents="35676 45065"/>
    </justification>
  </clause>

  <clause id="45221">
    <literal><![CDATA[
      (x \ L(x,y,z)) * u = a(z,y,x) \ u
    ]]></literal>
    <justification jstring="[para(45065(a,2),42568(a,1,1,2))].">
      <j1 rule="para" parents="45065 42568"/>
    </justification>
  </clause>

  <clause id="45227">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(z,a(z,y,x),u) = u * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(45065(a,2),42823(a,2,2))].">
      <j1 rule="para" parents="45065 42823"/>
    </justification>
  </clause>

  <clause id="45229">
    <literal><![CDATA[
      a(x,y,z * (u * (w * a(v5,v6,w)))) = a(x,y,z * (u * L(w,v6,v5)))
    ]]></literal>
    <justification jstring="[para(45065(a,2),43480(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="45065 43480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45231">
    <literal><![CDATA[
      L(a(x,y,z),z,u) \ u = L(z,y,x) * (z \ u)
    ]]></literal>
    <justification jstring="[para(45065(a,2),44554(a,2,1))].">
      <j1 rule="para" parents="45065 44554"/>
    </justification>
  </clause>

  <clause id="45232">
    <literal><![CDATA[
      L(L(x,y,z),a(z,y,x),u) = L(a(z,y,x),x,u) \ x
    ]]></literal>
    <justification jstring="[para(45065(a,2),44815(a,1,1))].">
      <j1 rule="para" parents="45065 44815"/>
    </justification>
  </clause>

  <clause id="45235">
    <literal><![CDATA[
      x * (y * a(x * y,z,x)) = R(x * y,z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,33200,a(flip),b,45066,a)].">
      <j1 rule="hyper" parents="373 33200 45066"/>
    </justification>
  </clause>

  <clause id="45241">
    <literal><![CDATA[
      x \ (y * R(y \ x,z,u)) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(36,a,2745,a,b,45066,a(flip))].">
      <j1 rule="hyper" parents="36 2745 45066"/>
    </justification>
  </clause>

  <clause id="45242">
    <literal><![CDATA[
      a((x \ y) * y,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,41926,a(flip),b,45066,a(flip))].">
      <j1 rule="hyper" parents="36 41926 45066"/>
    </justification>
  </clause>

  <clause id="45251">
    <literal><![CDATA[
      R(x,y,z) != x * u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(45066(a,2),23176(a,1))].">
      <j1 rule="para" parents="45066 23176"/>
    </justification>
  </clause>

  <clause id="45281">
    <literal><![CDATA[
      a(x,y,L(z,z,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,43316,a,b,45067,a)].">
      <j1 rule="hyper" parents="373 43316 45067"/>
    </justification>
  </clause>

  <clause id="45282">
    <literal><![CDATA[
      x * L(x \ 1,y,a(z,u,w)) = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,42163,a,b,45067,a)].">
      <j1 rule="hyper" parents="373 42163 45067"/>
    </justification>
  </clause>

  <clause id="45285">
    <literal><![CDATA[
      L(L(x,y,z) \ x,x,u) = a(z,y,L(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,43674,a(flip),b,45067,a)].">
      <j1 rule="hyper" parents="373 43674 45067"/>
    </justification>
  </clause>

  <clause id="45286">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ 1 = a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,43673,a(flip),b,45067,a)].">
      <j1 rule="hyper" parents="373 43673 45067"/>
    </justification>
  </clause>

  <clause id="45287">
    <literal><![CDATA[
      a((x \ y) \ z,y,x) = a((x \ y) * z,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,43571,a(flip),b,45067,a),flip(a)].">
      <j1 rule="hyper" parents="373 43571 45067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45288">
    <literal><![CDATA[
      a((x * y) * z,y,x) = a(y * (x \ z),y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,43570,a(flip),b,45067,a)].">
      <j1 rule="hyper" parents="373 43570 45067"/>
    </justification>
  </clause>

  <clause id="45289">
    <literal><![CDATA[
      a((x \ y) * z,z,x) = a(y * (z * x),z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,43568,a(flip),b,45067,a)].">
      <j1 rule="hyper" parents="373 43568 45067"/>
    </justification>
  </clause>

  <clause id="45290">
    <literal><![CDATA[
      a(x,y,L(z * y,z,y)) = a(x,y,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,43327,a(flip),b,45067,a)].">
      <j1 rule="hyper" parents="373 43327 45067"/>
    </justification>
  </clause>

  <clause id="45291">
    <literal><![CDATA[
      a(x,y,(y \ z) \ 1) = a(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,43318,a(flip),b,45067,a)].">
      <j1 rule="hyper" parents="373 43318 45067"/>
    </justification>
  </clause>

  <clause id="45292">
    <literal><![CDATA[
      a(x,y,(z \ y) \ 1) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,43317,a(flip),b,45067,a)].">
      <j1 rule="hyper" parents="373 43317 45067"/>
    </justification>
  </clause>

  <clause id="45300">
    <literal><![CDATA[
      L(a(x,y,z),x,u) = L(z,y,u \ (x \ u)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,40754,a,b,45067,a)].">
      <j1 rule="hyper" parents="64 40754 45067"/>
    </justification>
  </clause>

  <clause id="45311">
    <literal><![CDATA[
      L(x,x \ y,y * z) = ((z / y) * (y / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(40,a,43581,a,b,45067,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 43581 45067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45312">
    <literal><![CDATA[
      L(x \ y,x,y * z) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(40,a,43578,a,b,45067,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 43578 45067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45313">
    <literal><![CDATA[
      L(x,y,(x \ z) * y) = L(x,y,z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(40,a,43568,a,b,45067,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 43568 45067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45318">
    <literal><![CDATA[
      L(x,y,z * L(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(45067(a,2),9385(a,1,3)),flip(a)].">
      <j1 rule="para" parents="45067 9385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45319">
    <literal><![CDATA[
      a(x * L(x,y,z),u,w) = a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(45067(a,2),9387(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45067 9387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45321">
    <literal><![CDATA[
      L(x,y * L(y,z,u),w) = L(x,a(u,z,y),w)
    ]]></literal>
    <justification jstring="[para(45067(a,2),11874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45067 11874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45329">
    <literal><![CDATA[
      a(x,y,(L(z,u,w) * L(z,u,w)) * (v5 * a(w,u,z))) = a(x,y,((L(z,u,w) \ 1) \ z) * v5)
    ]]></literal>
    <justification jstring="[para(45067(a,2),27776(a,1,3,2,2))].">
      <j1 rule="para" parents="45067 27776"/>
    </justification>
  </clause>

  <clause id="45333">
    <literal><![CDATA[
      L(x,(y * L(y,z,u)) * w,v5) = L(x,a(u,z,y) * w,v5)
    ]]></literal>
    <justification jstring="[para(45067(a,2),29777(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="45067 29777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45343">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * a(w,u,x) = x * L(x \ R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(45067(a,2),37090(a,1,2))].">
      <j1 rule="para" parents="45067 37090"/>
    </justification>
  </clause>

  <clause id="45347">
    <literal><![CDATA[
      L(a(x,y,z) * u,z,L(z,y,x)) = z * ((L(z,y,x) \ 1) * u)
    ]]></literal>
    <justification jstring="[para(45067(a,2),39385(a,1,1,1))].">
      <j1 rule="para" parents="45067 39385"/>
    </justification>
  </clause>

  <clause id="45348">
    <literal><![CDATA[
      x * (L(x,y,z) \ a(u,x,w)) = a(u,x,w) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(45067(a,2),40083(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45067 40083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45350">
    <literal><![CDATA[
      x * (L(x,y,z) \ (u * x)) = u * (x * a(z,y,x))
    ]]></literal>
    <justification jstring="[para(45067(a,2),40675(a,2,2,2))].">
      <j1 rule="para" parents="45067 40675"/>
    </justification>
  </clause>

  <clause id="45351">
    <literal><![CDATA[
      L(a(x,y,z),z,u) * u = z * (L(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(45067(a,2),40713(a,1,1,1))].">
      <j1 rule="para" parents="45067 40713"/>
    </justification>
  </clause>

  <clause id="45352">
    <literal><![CDATA[
      (x \ y) * (z * a(y,x,z)) = (x \ R(y,x,z)) * z
    ]]></literal>
    <justification jstring="[para(45067(a,2),42251(a,1,2,2))].">
      <j1 rule="para" parents="45067 42251"/>
    </justification>
  </clause>

  <clause id="45354">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ u = a(z,y,x) * u
    ]]></literal>
    <justification jstring="[para(45067(a,2),42418(a,2,1))].">
      <j1 rule="para" parents="45067 42418"/>
    </justification>
  </clause>

  <clause id="45355">
    <literal><![CDATA[
      T(x * a(y * z,z,x),y) = z \ ((y / z) \ (x * y))
    ]]></literal>
    <justification jstring="[para(45067(a,2),43177(a,1,1,2))].">
      <j1 rule="para" parents="45067 43177"/>
    </justification>
  </clause>

  <clause id="45356">
    <literal><![CDATA[
      a(x,y,z) * L(u,z,a(z,y,x)) = z * (L(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(45067(a,2),43953(a,1,1))].">
      <j1 rule="para" parents="45067 43953"/>
    </justification>
  </clause>

  <clause id="45358">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) = a(y,y,a(u,z,x))
    ]]></literal>
    <justification jstring="[para(45067(a,2),44315(a,1,3)),flip(a)].">
      <j1 rule="para" parents="45067 44315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45359">
    <literal><![CDATA[
      (x \ y) * L(a(z,u,x),x,y) = L(x,u,z) \ y
    ]]></literal>
    <justification jstring="[para(45067(a,2),44488(a,1,2,1))].">
      <j1 rule="para" parents="45067 44488"/>
    </justification>
  </clause>

  <clause id="45361">
    <literal><![CDATA[
      x \ (a(y,z,u) * (y \ x)) = R(x \ (y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,41579,a(flip),b,45072,a)].">
      <j1 rule="hyper" parents="373 41579 45072"/>
    </justification>
  </clause>

  <clause id="45382">
    <literal><![CDATA[
      a(x,y \ x,z) = a(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,43017,a,b,45072,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 43017 45072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45383">
    <literal><![CDATA[
      a(x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,1988,a,b,45072,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="35 1988 45072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45392">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * R(L(z,y,x),u,w)) = L(a(L(z,y,x),u,w),L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(45072(a,2),601(a,1,2,2))].">
      <j1 rule="para" parents="45072 601"/>
    </justification>
  </clause>

  <clause id="45393">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * R(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(L(a(z,u,w),z,y),y * z,x) = v5
    ]]></literal>
    <justification jstring="[para(45072(a,2),1081(a,1,2,2,2))].">
      <j1 rule="para" parents="45072 1081"/>
    </justification>
  </clause>

  <clause id="45403">
    <literal><![CDATA[
      x * a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(45072(a,1),28845(a,1))].">
      <j1 rule="para" parents="45072 28845"/>
    </justification>
  </clause>

  <clause id="45406">
    <literal><![CDATA[
      x * (a(x,y,z) \ a(x,u,w)) = a(x,y,z) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[para(45072(a,2),29923(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45072 29923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45407">
    <literal><![CDATA[
      a(x,y,z) * (L(x,u,w) \ x) = L(x,u,w) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(45072(a,2),30905(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45072 30905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45412">
    <literal><![CDATA[
      x * (y * a(x,z,x * y)) = R(x,z,x * y) * y
    ]]></literal>
    <justification jstring="[para(45072(a,2),39258(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45072 39258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45416">
    <literal><![CDATA[
      x * R(x \ y,z,u) = y * a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(45072(a,2),40785(a,1,2))].">
      <j1 rule="para" parents="45072 40785"/>
    </justification>
  </clause>

  <clause id="45417">
    <literal><![CDATA[
      a(x,a(y,z,x),u) * (a(x,z,y) * (u * x)) = u * R(x,z,y)
    ]]></literal>
    <justification jstring="[para(45072(a,2),41442(a,2,2))].">
      <j1 rule="para" parents="45072 41442"/>
    </justification>
  </clause>

  <clause id="45421">
    <literal><![CDATA[
      (1 / x) \ a(y,z,u) = (y / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(45072(a,2),43048(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45072 43048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45422">
    <literal><![CDATA[
      a(x \ R(y,z,u),u,u) = a(x \ y,u,u)
    ]]></literal>
    <justification jstring="[para(45072(a,2),43755(a,1,1,2))].">
      <j1 rule="para" parents="45072 43755"/>
    </justification>
  </clause>

  <clause id="45426">
    <literal><![CDATA[
      a(x,(y \ x) * x,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,43016,a,b,45073,a)].">
      <j1 rule="hyper" parents="373 43016 45073"/>
    </justification>
  </clause>

  <clause id="45427">
    <literal><![CDATA[
      a(x \ (y \ x),z,z * x) = a(y,z,z * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,42890,a,b,45073,a)].">
      <j1 rule="hyper" parents="373 42890 45073"/>
    </justification>
  </clause>

  <clause id="45428">
    <literal><![CDATA[
      a(x * (y \ (z \ (y * x))),x,y) = a(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,42054,a,b,45073,a)].">
      <j1 rule="hyper" parents="373 42054 45073"/>
    </justification>
  </clause>

  <clause id="45430">
    <literal><![CDATA[
      L(a(x,y,z),x,y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,41790,a,b,45073,a)].">
      <j1 rule="hyper" parents="373 41790 45073"/>
    </justification>
  </clause>

  <clause id="45435">
    <literal><![CDATA[
      a(x,y,y \ (R(x,x,y) \ z)) = x \ R(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,43612,a(flip),b,45073,a),flip(a)].">
      <j1 rule="hyper" parents="373 43612 45073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45437">
    <literal><![CDATA[
      R(x \ R(x,y,z),u,w) = a(R(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,36890,a(flip),b,45073,a)].">
      <j1 rule="hyper" parents="373 36890 45073"/>
    </justification>
  </clause>

  <clause id="45440">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) = a(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,4246,a(flip),b,45073,a)].">
      <j1 rule="hyper" parents="373 4246 45073"/>
    </justification>
  </clause>

  <clause id="45443">
    <literal><![CDATA[
      (1 / (x \ y)) \ a(y,z,u) = x \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,45073,a,b,31567,a)].">
      <j1 rule="hyper" parents="139 45073 31567"/>
    </justification>
  </clause>

  <clause id="45444">
    <literal><![CDATA[
      R(1 / x,y,z) \ a(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(139,a,45073,a,b,2007,a)].">
      <j1 rule="hyper" parents="139 45073 2007"/>
    </justification>
  </clause>

  <clause id="45449">
    <literal><![CDATA[
      L(x,y,z) \ x = z \ R(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,45067,a(flip),b,45073,a)].">
      <j1 rule="hyper" parents="64 45067 45073"/>
    </justification>
  </clause>

  <clause id="45468">
    <literal><![CDATA[
      R(1 / x,y,z) \ 1 = a(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(45073(a,2),27842(a,2,1))].">
      <j1 rule="para" parents="45073 27842"/>
    </justification>
  </clause>

  <clause id="45470">
    <literal><![CDATA[
      L(x,y,z) * R(x \ 1,u,w) = (x \ L(x,y,z)) * a(x,u,w)
    ]]></literal>
    <justification jstring="[para(45073(a,2),28066(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45073 28066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45478">
    <literal><![CDATA[
      x \ (y * R(y \ x,z,u)) = L(a(y * x,z,u),x,y)
    ]]></literal>
    <justification jstring="[para(45073(a,2),36315(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45073 36315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45479">
    <literal><![CDATA[
      a(x,y,(z \ L(z,u,w)) * v5) = a(x,y,a(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(45073(a,2),36476(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="45073 36476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45481">
    <literal><![CDATA[
      a(((x * L(x,y,z)) * u) * w,v5,v6) = a((u * a(x,y,z)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(45073(a,2),37070(a,2,1,1,2))].">
      <j1 rule="para" parents="45073 37070"/>
    </justification>
  </clause>

  <clause id="45483">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ u = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(45073(a,2),42606(a,2,1))].">
      <j1 rule="para" parents="45073 42606"/>
    </justification>
  </clause>

  <clause id="45484">
    <literal><![CDATA[
      x * (R(y,z,u) \ y) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(45073(a,2),42608(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45073 42608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45485">
    <literal><![CDATA[
      (a(x,y,z) * u) \ R(u,w,v5) = a(x,y,z) \ a(u,w,v5)
    ]]></literal>
    <justification jstring="[para(45073(a,2),42534(a,2,2))].">
      <j1 rule="para" parents="45073 42534"/>
    </justification>
  </clause>

  <clause id="45486">
    <literal><![CDATA[
      L(x,(y * L(y,z,u)) * (a(y,z,u) * w),v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[para(45073(a,2),42612(a,1,2,2,1))].">
      <j1 rule="para" parents="45073 42612"/>
    </justification>
  </clause>

  <clause id="45488">
    <literal><![CDATA[
      L(x * a(y,z,u),y,a(y,z,u)) = R(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[para(45073(a,2),43952(a,1,1,2))].">
      <j1 rule="para" parents="45073 43952"/>
    </justification>
  </clause>

  <clause id="45492">
    <literal><![CDATA[
      a(x,x,(y \ z) \ 1) = a(x,x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,38953,a(flip),b,44983,a)].">
      <j1 rule="hyper" parents="64 38953 44983"/>
    </justification>
  </clause>

  <clause id="45494">
    <literal><![CDATA[
      L(a(x,x,y) \ 1,y,z) = a(x,x,y) \ 1
    ]]></literal>
    <justification jstring="[para(44983(a,1),39509(a,2,1))].">
      <j1 rule="para" parents="44983 39509"/>
    </justification>
  </clause>

  <clause id="45495">
    <literal><![CDATA[
      a(x,x,L(L(y,y,z),u,w)) = L(a(x,x,y),u,w)
    ]]></literal>
    <justification jstring="[para(44983(a,1),39675(a,2,1))].">
      <j1 rule="para" parents="44983 39675"/>
    </justification>
  </clause>

  <clause id="45498">
    <literal><![CDATA[
      a(x,y,L(a(z,u,y),x,w)) = a(a(y,y,x),u,z)
    ]]></literal>
    <justification jstring="[para(44983(a,1),43875(a,1,1)),flip(a)].">
      <j1 rule="para" parents="44983 43875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45499">
    <literal><![CDATA[
      x * (L(x,y,a(y,z,u)) \ w) = w * a(u,z,a(y,y,x))
    ]]></literal>
    <justification jstring="[para(44983(a,1),43965(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="44983 43965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45500">
    <literal><![CDATA[
      a(a(x,x,y),z,u) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(44983(a,1),44184(a,1,1))].">
      <j1 rule="para" parents="44983 44184"/>
    </justification>
  </clause>

  <clause id="45501">
    <literal><![CDATA[
      a(a(x,y,z),u,u) = a(z,y,a(u,u,x))
    ]]></literal>
    <justification jstring="[para(44983(a,1),44187(a,1,3)),flip(a)].">
      <j1 rule="para" parents="44983 44187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45504">
    <literal><![CDATA[
      (a(x,y,y) * z) \ R(x,y,y) = z \ x
    ]]></literal>
    <justification jstring="[para(44996(a,1),43104(a,1,2))].">
      <j1 rule="para" parents="44996 43104"/>
    </justification>
  </clause>

  <clause id="45505">
    <literal><![CDATA[
      a(a(x,y,z),u,u) = a(z,u,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,44128,a(flip),b,45012,a),flip(a)].">
      <j1 rule="hyper" parents="64 44128 45012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45506">
    <literal><![CDATA[
      a(x \ y,z,z) = a(y * x,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40984,a(flip),b,45012,a),flip(a)].">
      <j1 rule="hyper" parents="64 40984 45012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45507">
    <literal><![CDATA[
      a((x \ a(y,z,z)) \ u,w,v5) = a((a(y,z,z) * x) \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(45031(a,1),33712(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="45031 33712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45508">
    <literal><![CDATA[
      (1 / x) \ a(y,z,a(u,w,z)) = x * a(y,z,a(u,w,z))
    ]]></literal>
    <justification jstring="[para(45039(a,1),30118(a,1,1,1))].">
      <j1 rule="para" parents="45039 30118"/>
    </justification>
  </clause>

  <clause id="45509">
    <literal><![CDATA[
      a(L(x,x,y),z,z) = a(x,z,z)
    ]]></literal>
    <justification jstring="[hyper(32648,a,45044,a)].">
      <j1 rule="hyper" parents="32648 45044"/>
    </justification>
  </clause>

  <clause id="45511">
    <literal><![CDATA[
      (x * y) * a(x,z,z) = R(x,z,z) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,45044,a(flip),b,25607,a)].">
      <j1 rule="hyper" parents="145 45044 25607"/>
    </justification>
  </clause>

  <clause id="45514">
    <literal><![CDATA[
      a(x,x,L(y,z,z)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(39713,a,45050,a)].">
      <j1 rule="hyper" parents="39713 45050"/>
    </justification>
  </clause>

  <clause id="45520">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,w,a(v5,v6,w)))) = 1
    ]]></literal>
    <justification jstring="[para(44127(a,1),45055(a,1,3,3))].">
      <j1 rule="para" parents="44127 45055"/>
    </justification>
  </clause>

  <clause id="45527">
    <literal><![CDATA[
      (x * (y * (1 / z))) * L(z,z,y) = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(45064(a,1),41328(a,1,2))].">
      <j1 rule="para" parents="45064 41328"/>
    </justification>
  </clause>

  <clause id="45532">
    <literal><![CDATA[
      L(x,x,((x \ y) * z) * y) = L(x,x,x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41302,a,b,45069,a)].">
      <j1 rule="hyper" parents="64 41302 45069"/>
    </justification>
  </clause>

  <clause id="45537">
    <literal><![CDATA[
      L(x,x,y \ z) = L(x,x,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30387,a(flip),b,45069,a)].">
      <j1 rule="hyper" parents="64 30387 45069"/>
    </justification>
  </clause>

  <clause id="45539">
    <literal><![CDATA[
      a(x,y,y) * (z \ L(y,y,x)) = z \ y
    ]]></literal>
    <justification jstring="[para(45069(a,1),40989(a,1,2,2))].">
      <j1 rule="para" parents="45069 40989"/>
    </justification>
  </clause>

  <clause id="45545">
    <literal><![CDATA[
      R(x,y,L(z,z,y)) = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,45281,a(flip),b,45073,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 45281 45073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45547">
    <literal><![CDATA[
      a(x,y,y) \ (z * (x * (1 / y))) = z * (x / y)
    ]]></literal>
    <justification jstring="[para(45509(a,1),41326(a,1,1))].">
      <j1 rule="para" parents="45509 41326"/>
    </justification>
  </clause>

  <clause id="45548">
    <literal><![CDATA[
      (x * (y \ z)) * a(z,y,y) = x * (y \ R(z,y,y))
    ]]></literal>
    <justification jstring="[para(45509(a,1),41327(a,1,2))].">
      <j1 rule="para" parents="45509 41327"/>
    </justification>
  </clause>

  <clause id="45550">
    <literal><![CDATA[
      a(x,a(y,z,x),L(u,u,w)) = a(y,z,a(u,x,x))
    ]]></literal>
    <justification jstring="[para(45509(a,1),43897(a,2,3))].">
      <j1 rule="para" parents="45509 43897"/>
    </justification>
  </clause>

  <clause id="45551">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * (z * w) = L(z,u,a(u,y,x)) * w
    ]]></literal>
    <justification jstring="[para(45509(a,1),44843(a,1,1,3))].">
      <j1 rule="para" parents="45509 44843"/>
    </justification>
  </clause>

  <clause id="45557">
    <literal><![CDATA[
      a(x,x,L(y \ 1,z,u) \ w) = a(x,x,w * L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,41227,a(flip),b,45514,a)].">
      <j1 rule="hyper" parents="64 41227 45514"/>
    </justification>
  </clause>

  <clause id="45558">
    <literal><![CDATA[
      a(x,x,L((y \ 1) \ z,u,w)) = a(x,x,L(z * y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,39084,a(flip),b,45514,a)].">
      <j1 rule="hyper" parents="64 39084 45514"/>
    </justification>
  </clause>

  <clause id="45559">
    <literal><![CDATA[
      a(x,x,y * (z \ 1)) = a(x,x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,38951,a(flip),b,45514,a),flip(a)].">
      <j1 rule="hyper" parents="64 38951 45514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45560">
    <literal><![CDATA[
      a(x,x,(y \ 1) * z) = a(x,x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38947,a(flip),b,45514,a),flip(a)].">
      <j1 rule="hyper" parents="64 38947 45514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45561">
    <literal><![CDATA[
      a(x,x,(y \ 1) \ z) = a(x,x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,38945,a(flip),b,45514,a)].">
      <j1 rule="hyper" parents="64 38945 45514"/>
    </justification>
  </clause>

  <clause id="45567">
    <literal><![CDATA[
      a(x,x,L(y,z,z) * a(u,L(y,z,z),w)) = a(x,x,y * a(u,y,w))
    ]]></literal>
    <justification jstring="[para(35675(a,2),45514(a,1,3))].">
      <j1 rule="para" parents="35675 45514"/>
    </justification>
  </clause>

  <clause id="45570">
    <literal><![CDATA[
      (x / y) \ L(x,z,z) = a(z,z,x) \ y
    ]]></literal>
    <justification jstring="[para(45514(a,1),39903(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45514 39903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45574">
    <literal><![CDATA[
      L(x,y \ z,z) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29444,a(flip),b,44995,a),flip(a)].">
      <j1 rule="hyper" parents="64 29444 44995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45579">
    <literal><![CDATA[
      x * L(T(x * y,z) \ u,y * x,y) = (x / T(x * y,z)) * u
    ]]></literal>
    <justification jstring="[para(44997(a,1),43293(a,1,2))].">
      <j1 rule="para" parents="44997 43293"/>
    </justification>
  </clause>

  <clause id="45585">
    <literal><![CDATA[
      L(x,L(y,z,z),z * y) = L(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42158,a,b,44999,a)].">
      <j1 rule="hyper" parents="64 42158 44999"/>
    </justification>
  </clause>

  <clause id="45587">
    <literal><![CDATA[
      (x * (y * z)) * a(y,y,z) = x * ((1 / y) \ z)
    ]]></literal>
    <justification jstring="[para(45035(a,1),41072(a,2,2,1))].">
      <j1 rule="para" parents="45035 41072"/>
    </justification>
  </clause>

  <clause id="45589">
    <literal><![CDATA[
      a(x,y,z \ 1) \ 1 = z * L(z \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5574,a(flip),b,45037,a),flip(a)].">
      <j1 rule="hyper" parents="373 5574 45037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45592">
    <literal><![CDATA[
      a(x,y * z,u) \ 1 = u \ L(u,z * y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,31950,a,b,45037,a)].">
      <j1 rule="hyper" parents="64 31950 45037"/>
    </justification>
  </clause>

  <clause id="45594">
    <literal><![CDATA[
      a(x * y,z,u) \ 1 = u \ L(u,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,26835,a,b,45037,a)].">
      <j1 rule="hyper" parents="64 26835 45037"/>
    </justification>
  </clause>

  <clause id="45597">
    <literal><![CDATA[
      x * (y \ L(y,z,u)) = a(u,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(145,a,45037,a(flip),b,42452,a)].">
      <j1 rule="hyper" parents="145 45037 42452"/>
    </justification>
  </clause>

  <clause id="45616">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) \ v5 = v5 * L(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[para(45037(a,1),42732(a,1,1,1))].">
      <j1 rule="para" parents="45037 42732"/>
    </justification>
  </clause>

  <clause id="45617">
    <literal><![CDATA[
      ((x \ L(x,y,z)) / u) \ 1 = (u * ((a(z,y,x) \ u) \ 1)) * u
    ]]></literal>
    <justification jstring="[para(45037(a,1),42522(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="45037 42522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45634">
    <literal><![CDATA[
      L(x \ ((y \ z) * z),x,a(y,z * y,z * y)) = x \ ((y \ z) * z)
    ]]></literal>
    <justification jstring="[para(42037(a,1),45074(a,1,3))].">
      <j1 rule="para" parents="42037 45074"/>
    </justification>
  </clause>

  <clause id="45635">
    <literal><![CDATA[
      L(x \ (y * z),x,a(x,z,y)) = x \ (y * z)
    ]]></literal>
    <justification jstring="[para(45078(a,1),39281(a,2,2))].">
      <j1 rule="para" parents="45078 39281"/>
    </justification>
  </clause>

  <clause id="45644">
    <literal><![CDATA[
      a(((x * L(x,y,z)) * u) * w,v5,v6) = a((a(z,y,x) * u) * w,v5,v6)
    ]]></literal>
    <justification jstring="[para(45130(a,2),32792(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="45130 32792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45645">
    <literal><![CDATA[
      L(1 / x,y,a(z,u,w)) = a(a(z,u,w),y,x) / x
    ]]></literal>
    <justification jstring="[hyper(40,a,42166,a,b,45189,a(flip))].">
      <j1 rule="hyper" parents="40 42166 45189"/>
    </justification>
  </clause>

  <clause id="45647">
    <literal><![CDATA[
      L(x * y,x,a(z,u,x)) = L(x,u,z) * (y * a(z,u,x))
    ]]></literal>
    <justification jstring="[para(45189(a,2),43515(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45189 43515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45652">
    <literal><![CDATA[
      R(1 / x,y,z) \ u = (a(x,y,z) / x) \ u
    ]]></literal>
    <justification jstring="[para(45444(a,1),207(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="45444 207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45658">
    <literal><![CDATA[
      R(x,y,z) = z * (L(z,y,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(39,a,35568,a,b,45449,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 35568 45449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45663">
    <literal><![CDATA[
      a((x * y) \ z,u,L(u,y * x,y)) = a((y * z) * L(x,y,y),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,44090,a,b,45506,a)].">
      <j1 rule="hyper" parents="64 44090 45506"/>
    </justification>
  </clause>

  <clause id="45664">
    <literal><![CDATA[
      a((x \ y) \ z,u,L(u,x * y,x)) = a((x * z) * y,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,44021,a,b,45506,a)].">
      <j1 rule="hyper" parents="64 44021 45506"/>
    </justification>
  </clause>

  <clause id="45665">
    <literal><![CDATA[
      a((x * y) \ z,u,L(u,x,y)) = a((y \ z) * x,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,44013,a,b,45506,a)].">
      <j1 rule="hyper" parents="64 44013 45506"/>
    </justification>
  </clause>

  <clause id="45666">
    <literal><![CDATA[
      a(x \ y,z,L(z,u,x * u)) = a(((u \ x) \ y) * u,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,44009,a,b,45506,a)].">
      <j1 rule="hyper" parents="64 44009 45506"/>
    </justification>
  </clause>

  <clause id="45667">
    <literal><![CDATA[
      a(x \ y,z,L(z,x,u)) = a((u * y) * (u * x),z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,44017,a(flip),b,45506,a)].">
      <j1 rule="hyper" parents="64 44017 45506"/>
    </justification>
  </clause>

  <clause id="45668">
    <literal><![CDATA[
      a(x * (y * ((z * y) \ x)),u,u) = a(z,u,L(u,y,(z \ x) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,44008,a(flip),b,45506,a),flip(a)].">
      <j1 rule="hyper" parents="64 44008 45506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45669">
    <literal><![CDATA[
      a(x * (a(y,z,u) * w),y,y) = a(w \ x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35598,a(flip),b,45506,a),flip(a)].">
      <j1 rule="hyper" parents="64 35598 45506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45673">
    <literal><![CDATA[
      L(x,x,y * (z * L(z \ y,u,w))) = L(x,a(x,u,w),y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,44142,a(flip),b,45537,a),flip(a)].">
      <j1 rule="hyper" parents="64 44142 45537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45680">
    <literal><![CDATA[
      L(T(x,x \ y),x * y,y) = ((1 / y) * (x \ y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,921,a(flip),b,45574,a),flip(a)].">
      <j1 rule="hyper" parents="64 921 45574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45681">
    <literal><![CDATA[
      L((x \ y) \ z,x * y,y) = (y * (x \ y)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,102,a(flip),b,45574,a),flip(a)].">
      <j1 rule="hyper" parents="64 102 45574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45685">
    <literal><![CDATA[
      L(x,y,x \ z) \ z = R(x \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,2330,a(flip),b,45658,a)].">
      <j1 rule="hyper" parents="373 2330 45658"/>
    </justification>
  </clause>

  <clause id="45689">
    <literal><![CDATA[
      L(x,y,z) \ z = x \ R(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,45658,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="139 45658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45697">
    <literal><![CDATA[
      L(x,y,a(z,z,L(y,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(141,a,45054,a(flip),b,42219,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="141 45054 42219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45699">
    <literal><![CDATA[
      L(x,L(y,x,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,45065,a,b,45215,a),flip(a)].">
      <j1 rule="hyper" parents="373 45065 45215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45700">
    <literal><![CDATA[
      L(x,x \ y,z) = L(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(29742,a,45699,a),flip(a)].">
      <j1 rule="hyper" parents="29742 45699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45702">
    <literal><![CDATA[
      L(x,x \ y,z) = L(x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31760,a(flip),b,45699,a)].">
      <j1 rule="hyper" parents="64 31760 45699"/>
    </justification>
  </clause>

  <clause id="45704">
    <literal><![CDATA[
      L(x,L(y,y,x),z) = L(x,x * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29726,a,b,45700,a)].">
      <j1 rule="hyper" parents="64 29726 45700"/>
    </justification>
  </clause>

  <clause id="45707">
    <literal><![CDATA[
      L(x,(y \ z) * x,y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,10261,a(flip),b,45702,a),flip(a)].">
      <j1 rule="hyper" parents="64 10261 45702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45708">
    <literal><![CDATA[
      a(x,y,L(z,u * z,w)) = a(x,y,(w * (z \ u)) \ (w * u))
    ]]></literal>
    <justification jstring="[para(45702(a,1),27498(a,1,3))].">
      <j1 rule="para" parents="45702 27498"/>
    </justification>
  </clause>

  <clause id="45709">
    <literal><![CDATA[
      R(x,y,L(z,z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,45072,a,b,45545,a),flip(a)].">
      <j1 rule="hyper" parents="373 45072 45545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45711">
    <literal><![CDATA[
      R(x,y * z,z \ (z / (1 / y))) = R(x,y * z,y)
    ]]></literal>
    <justification jstring="[para(25566(a,1),45709(a,1,3))].">
      <j1 rule="para" parents="25566 45709"/>
    </justification>
  </clause>

  <clause id="45712">
    <literal><![CDATA[
      L(x,y,y) * (z * a(y,y,x)) = x * z
    ]]></literal>
    <justification jstring="[hyper(33299,a,44975,a),flip(a)].">
      <j1 rule="hyper" parents="33299 44975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45713">
    <literal><![CDATA[
      L(x,y,y) * (a(y,y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(64,a,29401,a(flip),b,44975,a)].">
      <j1 rule="hyper" parents="64 29401 44975"/>
    </justification>
  </clause>

  <clause id="45715">
    <literal><![CDATA[
      (x * y) * (a(x,x,y) * z) = ((1 / x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,44976,a(flip),b,41019,a)].">
      <j1 rule="hyper" parents="145 44976 41019"/>
    </justification>
  </clause>

  <clause id="45716">
    <literal><![CDATA[
      L(a(x,x,y) * z,y,y) = y * ((L(y,x,x) \ 1) * z)
    ]]></literal>
    <justification jstring="[para(44976(a,1),35188(a,1,1))].">
      <j1 rule="para" parents="44976 35188"/>
    </justification>
  </clause>

  <clause id="45719">
    <literal><![CDATA[
      a(x,y,(z \ u) * a(z,w,w)) = a(x,y,L(z,w,w) \ u)
    ]]></literal>
    <justification jstring="[para(44978(a,1),39961(a,1,3)),flip(a)].">
      <j1 rule="para" parents="44978 39961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45720">
    <literal><![CDATA[
      L(x,(y * ((a(z,z,y) \ 1) \ u)) * w,v5) = L(x,(u * L(y,z,z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(44981(a,1),38355(a,2,2,1))].">
      <j1 rule="para" parents="44981 38355"/>
    </justification>
  </clause>

  <clause id="45727">
    <literal><![CDATA[
      L(x,y,((z \ u) * w) * a(z,z,u)) = L(x,y,(u * z) * w)
    ]]></literal>
    <justification jstring="[para(45007(a,1),43032(a,1,3))].">
      <j1 rule="para" parents="45007 43032"/>
    </justification>
  </clause>

  <clause id="45728">
    <literal><![CDATA[
      a(((x \ y) * z) * a(x,x,y),u,w) = a((y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[para(45007(a,1),43037(a,1,1))].">
      <j1 rule="para" parents="45007 43037"/>
    </justification>
  </clause>

  <clause id="45730">
    <literal><![CDATA[
      (x * y) * a(y,z,z) = x * R(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(23177,a,45008,a)].">
      <j1 rule="hyper" parents="23177 45008"/>
    </justification>
  </clause>

  <clause id="45737">
    <literal><![CDATA[
      (x \ a(y,z,z)) \ ((x \ 1) * u) = (x * a(y,z,z)) \ (x * u)
    ]]></literal>
    <justification jstring="[para(45033(a,1),1658(a,1,1))].">
      <j1 rule="para" parents="45033 1658"/>
    </justification>
  </clause>

  <clause id="45738">
    <literal><![CDATA[
      (L(x,x,y) / z) \ x = z * a(y,x,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,44287,a,b,45034,a)].">
      <j1 rule="hyper" parents="64 44287 45034"/>
    </justification>
  </clause>

  <clause id="45740">
    <literal><![CDATA[
      a((x \ a(y,y,z)) * u,w,v5) = a((x * a(y,y,z)) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(45051(a,1),2690(a,1,1,1))].">
      <j1 rule="para" parents="45051 2690"/>
    </justification>
  </clause>

  <clause id="45742">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ a(u,u,w)) = a(x,y,a(u,u,w) * z)
    ]]></literal>
    <justification jstring="[para(45051(a,1),27528(a,1,3))].">
      <j1 rule="para" parents="45051 27528"/>
    </justification>
  </clause>

  <clause id="45744">
    <literal><![CDATA[
      a(x,x,y) \ (z * R(z \ a(x,x,y),x,y)) = a(z,x,y)
    ]]></literal>
    <justification jstring="[para(45051(a,1),44300(a,1,2,2,1))].">
      <j1 rule="para" parents="45051 44300"/>
    </justification>
  </clause>

  <clause id="45745">
    <literal><![CDATA[
      (x \ a(y,z,z)) \ R(x \ 1,u,w) = R(x,u,w) * (x \ (a(y,z,z) \ 1))
    ]]></literal>
    <justification jstring="[para(45052(a,1),42818(a,1,2,1))].">
      <j1 rule="para" parents="45052 42818"/>
    </justification>
  </clause>

  <clause id="45746">
    <literal><![CDATA[
      (a(x,y,y) * ((1 / z) \ 1)) \ R(z,u,w) = (z \ a(x,y,y)) \ R(z \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(45068(a,2),2756(a,1,1))].">
      <j1 rule="para" parents="45068 2756"/>
    </justification>
  </clause>

  <clause id="45747">
    <literal><![CDATA[
      L(x,y,a(y,z,a(u,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,621,a(flip),b,45085,a),flip(a)].">
      <j1 rule="hyper" parents="373 621 45085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45750">
    <literal><![CDATA[
      a(x,y,L(y,z,a(u,u,w))) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,44279,a(flip),b,45747,a(flip))].">
      <j1 rule="hyper" parents="40 44279 45747"/>
    </justification>
  </clause>

  <clause id="45770">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ T(a(z,y,x) \ (u \ L(x,y,z)),u \ L(x,y,z)) = T((x \ L(x,y,z)) / (1 / (u \ x)),L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(45221(a,1),38310(a,1,2,1))].">
      <j1 rule="para" parents="45221 38310"/>
    </justification>
  </clause>

  <clause id="45771">
    <literal><![CDATA[
      x \ (a(y,z,u) \ (x * u)) = a(y,z,a(x,u,u)) * L(u,z,y)
    ]]></literal>
    <justification jstring="[para(45221(a,1),41749(a,1,2))].">
      <j1 rule="para" parents="45221 41749"/>
    </justification>
  </clause>

  <clause id="45774">
    <literal><![CDATA[
      L(x,y,a(z,u,x) \ y) = L(x,y,y)
    ]]></literal>
    <justification jstring="[para(45221(a,1),43702(a,1,3))].">
      <j1 rule="para" parents="45221 43702"/>
    </justification>
  </clause>

  <clause id="45775">
    <literal><![CDATA[
      L(x,y,y * a(z,u,x)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,44999,a(flip),b,45774,a)].">
      <j1 rule="hyper" parents="64 44999 45774"/>
    </justification>
  </clause>

  <clause id="45776">
    <literal><![CDATA[
      a(a(x,y,z),u,w \ u) = a(a(x,y,z),u,w * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42795,a(flip),b,45291,a),flip(a)].">
      <j1 rule="hyper" parents="64 42795 45291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45778">
    <literal><![CDATA[
      a(x,y,y \ (z \ y)) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27388,a(flip),b,45292,a),flip(a)].">
      <j1 rule="hyper" parents="64 27388 45292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45780">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) = a(y,y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,41883,a,b,45358,a),flip(a)].">
      <j1 rule="hyper" parents="373 41883 45358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45783">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) = a(z,z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,43917,a,b,45358,a)].">
      <j1 rule="hyper" parents="64 43917 45358"/>
    </justification>
  </clause>

  <clause id="45784">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(u,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,43895,a,b,45358,a)].">
      <j1 rule="hyper" parents="64 43895 45358"/>
    </justification>
  </clause>

  <clause id="45785">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = a(y,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41883,a,b,45358,a)].">
      <j1 rule="hyper" parents="64 41883 45358"/>
    </justification>
  </clause>

  <clause id="45787">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * u = L(u,x,a(x,z,y))
    ]]></literal>
    <justification jstring="[para(45358(a,1),40811(a,1,1))].">
      <j1 rule="para" parents="45358 40811"/>
    </justification>
  </clause>

  <clause id="45789">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * w = a(y,y,a(z,u,x)) * w
    ]]></literal>
    <justification jstring="[para(45358(a,1),41902(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45358 41902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45790">
    <literal><![CDATA[
      x * a(y,z,a(u,u,w)) = x * a(u,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[para(45358(a,1),43920(a,2,2))].">
      <j1 rule="para" parents="45358 43920"/>
    </justification>
  </clause>

  <clause id="45791">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * a(x,x,u) = a(x,x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(45358(a,1),43926(a,1,1))].">
      <j1 rule="para" parents="45358 43926"/>
    </justification>
  </clause>

  <clause id="45794">
    <literal><![CDATA[
      L(x,(R(1 / y,z,u) * w) * v5,v6) = L(x,(w * (a(y,z,u) \ y)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(45468(a,1),29643(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="45468 29643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45803">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(u,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(42050,a,45500,a)].">
      <j1 rule="hyper" parents="42050 45500"/>
    </justification>
  </clause>

  <clause id="45806">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = a(y,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,43872,a(flip),b,45500,a)].">
      <j1 rule="hyper" parents="64 43872 45500"/>
    </justification>
  </clause>

  <clause id="45807">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) = a(z,z,a(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41803,a(flip),b,45500,a)].">
      <j1 rule="hyper" parents="64 41803 45500"/>
    </justification>
  </clause>

  <clause id="45808">
    <literal><![CDATA[
      a(x,y,a(z,u,L(u,w,v5))) = a(u,u,a(L(z,w,v5),y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,40853,a(flip),b,45500,a)].">
      <j1 rule="hyper" parents="64 40853 45500"/>
    </justification>
  </clause>

  <clause id="45809">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * w = w * a(u,z,a(y,x,x))
    ]]></literal>
    <justification jstring="[para(45500(a,1),40843(a,1,1))].">
      <j1 rule="para" parents="45500 40843"/>
    </justification>
  </clause>

  <clause id="45810">
    <literal><![CDATA[
      L(x,a(y,z,a(u,u,w)),v5) = L(x,a(u,u,a(w,z,y)),v5)
    ]]></literal>
    <justification jstring="[para(45500(a,1),41403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45500 41403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45811">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * w = w * a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[para(45500(a,1),41855(a,1,1))].">
      <j1 rule="para" parents="45500 41855"/>
    </justification>
  </clause>

  <clause id="45814">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,a(w,w,v5)) = a(w,w,a(z * a(y,y,x),u,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,41485,a(flip),b,45501,a),flip(a)].">
      <j1 rule="hyper" parents="64 41485 45501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45815">
    <literal><![CDATA[
      a(x * a(y,z,z),u,a(w,w,v5)) = a(w,w,a(x * a(z,z,y),u,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,41484,a(flip),b,45501,a),flip(a)].">
      <j1 rule="hyper" parents="64 41484 45501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45816">
    <literal><![CDATA[
      a(x,y,a(z,z,a(u,w,w) * v5)) = a(z,z,a(v5 * a(w,w,u),y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,36330,a(flip),b,45501,a),flip(a)].">
      <j1 rule="hyper" parents="64 36330 45501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45818">
    <literal><![CDATA[
      a(x,a(y,z,a(u,u,w)) * v5,v6) = a(x,a(u,u,a(w,z,y)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(45501(a,1),34112(a,1,2,1))].">
      <j1 rule="para" parents="45501 34112"/>
    </justification>
  </clause>

  <clause id="45821">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,w,a(v5,v5,v6)))) = 1
    ]]></literal>
    <justification jstring="[para(45501(a,1),45055(a,1,3,3))].">
      <j1 rule="para" parents="45501 45055"/>
    </justification>
  </clause>

  <clause id="45827">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = a(x,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,45501,a(flip),b,45505,a),flip(a)].">
      <j1 rule="hyper" parents="64 45501 45505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45828">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,a(w,v5,u)) = a(u,u,a(z * a(y,y,x),v5,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,41485,a(flip),b,45505,a),flip(a)].">
      <j1 rule="hyper" parents="64 41485 45505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45834">
    <literal><![CDATA[
      (x \ L(y,y,z)) \ z = (x \ y) \ R(z,y,y)
    ]]></literal>
    <justification jstring="[para(45539(a,1),45504(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45539 45504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45835">
    <literal><![CDATA[
      a(x,x,(y \ z) \ y) = a(x,x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41127,a(flip),b,45559,a),flip(a)].">
      <j1 rule="hyper" parents="64 41127 45559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45836">
    <literal><![CDATA[
      a(x,y,a(z,z,u \ w)) = a(x,y,a(z,z,u * w))
    ]]></literal>
    <justification jstring="[para(45559(a,1),42191(a,1,3))].">
      <j1 rule="para" parents="45559 42191"/>
    </justification>
  </clause>

  <clause id="45837">
    <literal><![CDATA[
      (x \ a(x,x,y \ z)) * (z * (1 / y)) = x \ (z * (1 / y))
    ]]></literal>
    <justification jstring="[para(45560(a,1),30132(a,1,1,2))].">
      <j1 rule="para" parents="45560 30132"/>
    </justification>
  </clause>

  <clause id="45838">
    <literal><![CDATA[
      T(x \ a(x,x,y * z),(z \ 1) \ y) = ((z \ 1) \ y) \ (x \ ((z \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(45561(a,1),30124(a,1,1,2))].">
      <j1 rule="para" parents="45561 30124"/>
    </justification>
  </clause>

  <clause id="45839">
    <literal><![CDATA[
      x \ (y \ L(y * x,z,z)) = a(z,z,y * x) \ 1
    ]]></literal>
    <justification jstring="[para(45561(a,1),41123(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45561 41123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45841">
    <literal><![CDATA[
      a(x,x,y) * (z \ L(y,x,x)) = z \ y
    ]]></literal>
    <justification jstring="[hyper(145,a,207,a(flip),b,45570,a(flip))].">
      <j1 rule="hyper" parents="145 207 45570"/>
    </justification>
  </clause>

  <clause id="45845">
    <literal><![CDATA[
      a(x,y,z) \ L(z,u,x) = L(L(z,u,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,43676,a(flip),b,45597,a),flip(a)].">
      <j1 rule="hyper" parents="64 43676 45597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45850">
    <literal><![CDATA[
      x * L(y \ L(y,z,u),w,v5) = a(u,z,L(y,w,v5)) \ x
    ]]></literal>
    <justification jstring="[para(43675(a,1),45597(a,1,2))].">
      <j1 rule="para" parents="43675 45597"/>
    </justification>
  </clause>

  <clause id="45851">
    <literal><![CDATA[
      L(L(x,y,z),a(z,y,x),u) = (u / x) \ (a(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(45597(a,1),44636(a,2,2))].">
      <j1 rule="para" parents="45597 44636"/>
    </justification>
  </clause>

  <clause id="45853">
    <literal><![CDATA[
      R(x \ (y \ x),z,x) = L(x,z,y) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(38107(a,1),45685(a,1,1)),flip(a)].">
      <j1 rule="para" parents="38107 45685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45854">
    <literal><![CDATA[
      L(x,(y \ z) * (u * a(y,y,y * z)),w) = L(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[para(45712(a,1),34381(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45712 34381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45856">
    <literal><![CDATA[
      a(x,y,z \ (a(u,u,w) * (v5 * w))) = a(x,y,z \ (v5 * R(w,u,u)))
    ]]></literal>
    <justification jstring="[para(45730(a,1),40067(a,2,3,2))].">
      <j1 rule="para" parents="45730 40067"/>
    </justification>
  </clause>

  <clause id="45858">
    <literal><![CDATA[
      a(x,y,L(y,z,a(u,w,w))) = a(x,y,y)
    ]]></literal>
    <justification jstring="[para(29287(a,2),45750(a,1,3))].">
      <j1 rule="para" parents="29287 45750"/>
    </justification>
  </clause>

  <clause id="45860">
    <literal><![CDATA[
      a(x,y,a(y,z,a(z,u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,45056,a(flip),b,45780,a),flip(a)].">
      <j1 rule="hyper" parents="373 45056 45780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45862">
    <literal><![CDATA[
      a(x,a(y,z,x),u) = a(x,x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41433,a,b,45780,a)].">
      <j1 rule="hyper" parents="64 41433 45780"/>
    </justification>
  </clause>

  <clause id="45866">
    <literal><![CDATA[
      a(x,y,z) * (u \ a(x,u,a(u,y,z))) = u \ T(a(x,y,z),u \ 1)
    ]]></literal>
    <justification jstring="[para(45780(a,2),30121(a,1,2,2))].">
      <j1 rule="para" parents="45780 30121"/>
    </justification>
  </clause>

  <clause id="45868">
    <literal><![CDATA[
      L(x,x,y) * a(z,x,a(x,u,w)) = L(R(x,x,a(z,u,w)),x,y)
    ]]></literal>
    <justification jstring="[para(45780(a,2),38671(a,1,2))].">
      <j1 rule="para" parents="45780 38671"/>
    </justification>
  </clause>

  <clause id="45870">
    <literal><![CDATA[
      a(x,x,L(y,z,a(z,u,w))) = 1 * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(45860(a,1),43926(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45860 43926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45871">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) = a(x,z,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,45780,a,b,45783,a),flip(a)].">
      <j1 rule="hyper" parents="373 45780 45783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45873">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,a(w,v5,v5)) = a(v5,v5,a(z * a(y,y,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,38635,a,b,45783,a)].">
      <j1 rule="hyper" parents="64 38635 45783"/>
    </justification>
  </clause>

  <clause id="45876">
    <literal><![CDATA[
      a(x,x,a(y,z,L(u,w,w))) = a(y,z,a(x,x,u))
    ]]></literal>
    <justification jstring="[para(45514(a,1),45783(a,1,3)),flip(a)].">
      <j1 rule="para" parents="45514 45783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45877">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(x,u,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,45780,a,b,45784,a),flip(a)].">
      <j1 rule="hyper" parents="373 45780 45784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45882">
    <literal><![CDATA[
      a(x,x,a(y,z,a(x,u,w) * v5)) = a(y,z,a(v5,x,x))
    ]]></literal>
    <justification jstring="[para(34031(a,1),45784(a,1,3)),flip(a)].">
      <j1 rule="para" parents="34031 45784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45883">
    <literal><![CDATA[
      L(x * a(y,y,a(z,x,u)),z,a(u,y,y)) = L(x,a(u,y,y),z)
    ]]></literal>
    <justification jstring="[para(45784(a,1),41867(a,1,1,2))].">
      <j1 rule="para" parents="45784 41867"/>
    </justification>
  </clause>

  <clause id="45884">
    <literal><![CDATA[
      a(x,y,a(z * u,w,w)) = a(w,w,a(x,y,u \ z))
    ]]></literal>
    <justification jstring="[para(45506(a,1),45784(a,1,3))].">
      <j1 rule="para" parents="45506 45784"/>
    </justification>
  </clause>

  <clause id="45886">
    <literal><![CDATA[
      a(a(x,y,z),u,a(w,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,45039,a(flip),b,45785,a),flip(a)].">
      <j1 rule="hyper" parents="373 45039 45785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45887">
    <literal><![CDATA[
      a(x,y * z,a(u,w,w)) = a(w,w,a(u,z * y,x))
    ]]></literal>
    <justification jstring="[hyper(32008,a,45803,a)].">
      <j1 rule="hyper" parents="32008 45803"/>
    </justification>
  </clause>

  <clause id="45889">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(z,y,a(x,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,45784,a,b,45803,a)].">
      <j1 rule="hyper" parents="373 45784 45803"/>
    </justification>
  </clause>

  <clause id="45890">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) = a(z,y,a(u,u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,45783,a,b,45803,a),flip(a)].">
      <j1 rule="hyper" parents="373 45783 45803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45896">
    <literal><![CDATA[
      L(L(x,y,a(z,u,u)),a(z,u,u),y) = x * a(u,u,a(z,x,y))
    ]]></literal>
    <justification jstring="[para(45803(a,1),43397(a,2,2))].">
      <j1 rule="para" parents="45803 43397"/>
    </justification>
  </clause>

  <clause id="45897">
    <literal><![CDATA[
      x * a(y,x,a(z,u,x)) = L(x,x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,45806,a,b,30065,a)].">
      <j1 rule="hyper" parents="145 45806 30065"/>
    </justification>
  </clause>

  <clause id="45898">
    <literal><![CDATA[
      a(x,x,a(y,z,u * a(w,v5,x))) = a(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,44344,a(flip),b,45806,a),flip(a)].">
      <j1 rule="hyper" parents="64 44344 45806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45902">
    <literal><![CDATA[
      a(x,y,a(z,u \ x,y)) = a(y,y,a(x,x * u,z))
    ]]></literal>
    <justification jstring="[para(45382(a,1),45806(a,2,3))].">
      <j1 rule="para" parents="45382 45806"/>
    </justification>
  </clause>

  <clause id="45903">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) = a(u,y,a(z,z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,45783,a,b,45807,a)].">
      <j1 rule="hyper" parents="373 45783 45807"/>
    </justification>
  </clause>

  <clause id="45905">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,a(v5,v5,v6)) = a(v5,v5,a(v6,w,u)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(45807(a,1),23183(a,2,1))].">
      <j1 rule="para" parents="45807 23183"/>
    </justification>
  </clause>

  <clause id="45908">
    <literal><![CDATA[
      L(x,x,y) * a(z,u,a(x,x,w)) = L(R(x,x,a(w,u,z)),x,y)
    ]]></literal>
    <justification jstring="[para(45807(a,2),38671(a,1,2))].">
      <j1 rule="para" parents="45807 38671"/>
    </justification>
  </clause>

  <clause id="45910">
    <literal><![CDATA[
      a(x * y,z,a(u,w,z)) = a(y * x,w,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(26847,a,45827,a)].">
      <j1 rule="hyper" parents="26847 45827"/>
    </justification>
  </clause>

  <clause id="45911">
    <literal><![CDATA[
      x * a(y,z,a(u,w,w)) = x * a(y,w,a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,45827,a,b,41898,a),flip(a)].">
      <j1 rule="hyper" parents="145 45827 41898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45912">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * w = w * a(x,z,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,45827,a,b,23174,a),flip(a)].">
      <j1 rule="hyper" parents="145 45827 23174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45914">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) * w) * v5 = (w * a(x,u,a(y,y,z))) * v5
    ]]></literal>
    <justification jstring="[para(45827(a,1),23168(a,2,1,2))].">
      <j1 rule="para" parents="45827 23168"/>
    </justification>
  </clause>

  <clause id="45915">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * a(y,y,z) = a(y,y,L(z,u,x))
    ]]></literal>
    <justification jstring="[para(45827(a,2),40876(a,1,1))].">
      <j1 rule="para" parents="45827 40876"/>
    </justification>
  </clause>

  <clause id="45916">
    <literal><![CDATA[
      x * a(x,y,a(z,z,u)) = L(x,z,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(45827(a,1),41455(a,1,2))].">
      <j1 rule="para" parents="45827 41455"/>
    </justification>
  </clause>

  <clause id="45918">
    <literal><![CDATA[
      a(x,y,y) * a(z,y,a(x,u,y)) = a(x,y,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(45827(a,2),44004(a,1,2))].">
      <j1 rule="para" parents="45827 44004"/>
    </justification>
  </clause>

  <clause id="45919">
    <literal><![CDATA[
      a(x,y,a(L(z,z,u),w,y)) = a(x,w,a(y,y,z))
    ]]></literal>
    <justification jstring="[para(44983(a,1),45827(a,2,3))].">
      <j1 rule="para" parents="44983 45827"/>
    </justification>
  </clause>

  <clause id="45921">
    <literal><![CDATA[
      L(x,y,a(z,z,u) * (w \ L(z * u,z,z))) = L(x,y,w \ (z * u))
    ]]></literal>
    <justification jstring="[para(45841(a,1),30182(a,1,3)),flip(a)].">
      <j1 rule="para" parents="45841 30182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45927">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,z)),v5) = L(x,a(y,w,a(z,z,u)),v5)
    ]]></literal>
    <justification jstring="[para(45871(a,2),41439(a,2,2))].">
      <j1 rule="para" parents="45871 41439"/>
    </justification>
  </clause>

  <clause id="45929">
    <literal><![CDATA[
      a(x,y,a(y,z,L(u,u,w))) = a(x,z,a(y,y,u))
    ]]></literal>
    <justification jstring="[para(44983(a,1),45871(a,1,3)),flip(a)].">
      <j1 rule="para" parents="44983 45871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45933">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,w)),v5) = L(x,a(u,z,a(w,w,y)),v5)
    ]]></literal>
    <justification jstring="[para(45877(a,2),43923(a,2,2)),flip(a)].">
      <j1 rule="para" parents="45877 43923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45939">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,z) = a(y,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(141,a,39721,a,b,45084,a(flip))].">
      <j1 rule="hyper" parents="141 39721 45084"/>
    </justification>
  </clause>

  <clause id="45941">
    <literal><![CDATA[
      L(x \ ((y \ z) * z),x,((y \ z) * z) * y) = (((z / (y / z)) \ y) * x) \ y
    ]]></literal>
    <justification jstring="[para(35930(a,1),45312(a,2,1,1))].">
      <j1 rule="para" parents="35930 45312"/>
    </justification>
  </clause>

  <clause id="45942">
    <literal><![CDATA[
      a(R(x,y,z) * u,z,z) = a(u \ x,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,45506,a(flip),b,45422,a)].">
      <j1 rule="hyper" parents="64 45506 45422"/>
    </justification>
  </clause>

  <clause id="45943">
    <literal><![CDATA[
      (x * (y \ z)) \ (x * ((y \ 1) * z)) = a(y,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,41568,a,b,45494,a)].">
      <j1 rule="hyper" parents="64 41568 45494"/>
    </justification>
  </clause>

  <clause id="45945">
    <literal><![CDATA[
      a(L(x,y,z) * u,z,z) = a(u \ x,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34634,a(flip),b,45942,a)].">
      <j1 rule="hyper" parents="64 34634 45942"/>
    </justification>
  </clause>

  <clause id="45946">
    <literal><![CDATA[
      a(L(x,y,z) * u,z,z) = a(x * u,z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,45506,a(flip),b,45945,a),flip(a)].">
      <j1 rule="hyper" parents="373 45506 45945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45947">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) \ z = y \ (a(x,x,y) \ z)
    ]]></literal>
    <justification jstring="[para(30228(a,2),44982(a,1,1))].">
      <j1 rule="para" parents="30228 44982"/>
    </justification>
  </clause>

  <clause id="45949">
    <literal><![CDATA[
      x \ R(x,y,(y \ z) * z) = a(x,y,y \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(139,a,44992,a(flip),b,45072,a(flip))].">
      <j1 rule="hyper" parents="139 44992 45072"/>
    </justification>
  </clause>

  <clause id="45952">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / z) = (y * x) \ ((y * x) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,44645,a(flip),b,45011,a)].">
      <j1 rule="hyper" parents="64 44645 45011"/>
    </justification>
  </clause>

  <clause id="45953">
    <literal><![CDATA[
      (x * (y * (y * a(z,u,u)))) \ w = (y * y) \ ((x * a(z,u,u)) \ w)
    ]]></literal>
    <justification jstring="[para(45028(a,1),28827(a,1,1,2))].">
      <j1 rule="para" parents="45028 28827"/>
    </justification>
  </clause>

  <clause id="45954">
    <literal><![CDATA[
      K(x,y) * (a(z,u,w) \ K(v5,z)) = z * (R(T(z,v5),u,w) \ K(x,y))
    ]]></literal>
    <justification jstring="[para(45075(a,1),27997(a,1,2))].">
      <j1 rule="para" parents="45075 27997"/>
    </justification>
  </clause>

  <clause id="45960">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * L(z,u,w) = L(a(x,y,z) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(42,a,45058,a,b,45094,a)].">
      <j1 rule="hyper" parents="42 45058 45094"/>
    </justification>
  </clause>

  <clause id="45961">
    <literal><![CDATA[
      a(x,a(y,z,u * w) * (w * u),v5) = a(x,L(u * w,z,y),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31902,a,b,45100,a)].">
      <j1 rule="hyper" parents="64 31902 45100"/>
    </justification>
  </clause>

  <clause id="45962">
    <literal><![CDATA[
      (1 / x) \ a(a(y,z,u),w,v5) = (v5 / x) \ L(v5,w,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(45104(a,1),42704(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45104 42704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45963">
    <literal><![CDATA[
      x * a(y,z,a(x,u,z)) = L(x,u,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(43872(a,1),45104(a,1,2))].">
      <j1 rule="para" parents="43872 45104"/>
    </justification>
  </clause>

  <clause id="45967">
    <literal><![CDATA[
      a((x \ 1) \ 1,a(y,x,z),a(y,x,z) \ u) = a(a(y,x,z),x,x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,43367,a,b,45128,a)].">
      <j1 rule="hyper" parents="64 43367 45128"/>
    </justification>
  </clause>

  <clause id="45969">
    <literal><![CDATA[
      L(x * a(y,z,a(u,w,v5)),y,a(y,z,a(v5,w,u))) = y * (L(y,z,a(v5,w,u)) \ x)
    ]]></literal>
    <justification jstring="[para(45132(a,1),43172(a,2,2,1))].">
      <j1 rule="para" parents="45132 43172"/>
    </justification>
  </clause>

  <clause id="45978">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (x \ v5) = v5 * L(v5 \ (x \ v5),y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,45190,a(flip),b,41579,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 45190 41579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45992">
    <literal><![CDATA[
      L(x,L(a(y \ z,u,w),y,y),v5) = L(x,y * (z * R(z \ y,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(45241(a,1),11837(a,1,2,1))].">
      <j1 rule="para" parents="45241 11837"/>
    </justification>
  </clause>

  <clause id="45994">
    <literal><![CDATA[
      L(x,y * (z * R(z \ y,u,w)),y) = L(x,a(y \ z,u,w),y)
    ]]></literal>
    <justification jstring="[para(45241(a,1),41718(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45241 41718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45995">
    <literal><![CDATA[
      a(x,y,L(z,z,x * y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,40711,a,b,45285,a),flip(a)].">
      <j1 rule="hyper" parents="64 40711 45285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="45996">
    <literal><![CDATA[
      x \ (y * (L(y,z,u) \ x)) = a(u,z,L(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,40710,a(flip),b,45285,a)].">
      <j1 rule="hyper" parents="64 40710 45285"/>
    </justification>
  </clause>

  <clause id="46000">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) = L(a(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[para(45067(a,2),45285(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45067 45285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46001">
    <literal><![CDATA[
      a(x,y,L(L(y,z,u),L(y,z,u),u * z)) = a(x,y,L(y,z * y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,44022,a(flip),b,46000,a),flip(a)].">
      <j1 rule="hyper" parents="373 44022 46000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46005">
    <literal><![CDATA[
      a((x \ y) * ((1 / (1 / (y \ x))) * z),y,x) = a((y \ x) * ((x \ y) \ z),y,x)
    ]]></literal>
    <justification jstring="[para(33105(a,1),45287(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33105 45287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46006">
    <literal><![CDATA[
      a(((x \ y) \ (y \ x)) * z,y,x) = a((x \ y) * ((y \ x) * z),y,x)
    ]]></literal>
    <justification jstring="[para(44544(a,1),45287(a,1,1))].">
      <j1 rule="para" parents="44544 45287"/>
    </justification>
  </clause>

  <clause id="46007">
    <literal><![CDATA[
      a((x * y) * z,x,y) = a(x * (y \ z),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32388,a,b,45288,a)].">
      <j1 rule="hyper" parents="64 32388 45288"/>
    </justification>
  </clause>

  <clause id="46008">
    <literal><![CDATA[
      a(x * (y \ z),x,y) = a(z * (x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32422,a(flip),b,45288,a),flip(a)].">
      <j1 rule="hyper" parents="64 32422 45288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46009">
    <literal><![CDATA[
      a((x \ (x / y)) * ((x \ 1) \ z),x \ (x / y),x \ 1) = a(((x \ 1) / y) * z,x \ (x / y),x \ 1)
    ]]></literal>
    <justification jstring="[para(1214(a,1),45288(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1214 45288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46010">
    <literal><![CDATA[
      a((x * y) * ((1 / z) \ x),y,x) = a(y * R(T(z,x),z,x),y,x)
    ]]></literal>
    <justification jstring="[para(1917(a,2),45288(a,2,1,2))].">
      <j1 rule="para" parents="1917 45288"/>
    </justification>
  </clause>

  <clause id="46011">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),T(x \ (x / y),y),1 / x) = a(((1 / x) / T(y,y \ 1)) * z,T(x \ (x / y),y),1 / x)
    ]]></literal>
    <justification jstring="[para(3930(a,1),45288(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3930 45288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46012">
    <literal><![CDATA[
      L(x,a(y * (z * u),z,u),w) = L(x,a(u,z,(u \ y) * z),w)
    ]]></literal>
    <justification jstring="[para(45289(a,1),41403(a,1,2))].">
      <j1 rule="para" parents="45289 41403"/>
    </justification>
  </clause>

  <clause id="46013">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),u,w)) = a(x,y,a(w,u,(w \ z) * u))
    ]]></literal>
    <justification jstring="[para(45289(a,1),41883(a,1,3))].">
      <j1 rule="para" parents="45289 41883"/>
    </justification>
  </clause>

  <clause id="46014">
    <literal><![CDATA[
      x \ ((((x / y) / z) * (z * y)) * y) = L(y,z,x * (z * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41987,a,b,45313,a)].">
      <j1 rule="hyper" parents="64 41987 45313"/>
    </justification>
  </clause>

  <clause id="46017">
    <literal><![CDATA[
      L(x,a(x,y,z),u) = L(x,x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,44139,a(flip),b,45318,a)].">
      <j1 rule="hyper" parents="64 44139 45318"/>
    </justification>
  </clause>

  <clause id="46019">
    <literal><![CDATA[
      L(x,a(x,y,z),u) = L(x,x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,42195,a,b,46017,a),flip(a)].">
      <j1 rule="hyper" parents="373 42195 46017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46020">
    <literal><![CDATA[
      L(x,x,y * (z * L(z \ y,u,w))) = L(x,x,a(w,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,44228,a,b,46017,a)].">
      <j1 rule="hyper" parents="64 44228 46017"/>
    </justification>
  </clause>

  <clause id="46022">
    <literal><![CDATA[
      x * L(x \ y,y,a(y,z,u)) = L(y,y,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,40969,a,b,46017,a)].">
      <j1 rule="hyper" parents="64 40969 46017"/>
    </justification>
  </clause>

  <clause id="46023">
    <literal><![CDATA[
      L(x,x,a(y,z,(u * x) \ w)) = L(x,a(x,z,y),u \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,44239,a(flip),b,46017,a),flip(a)].">
      <j1 rule="hyper" parents="64 44239 46017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46025">
    <literal><![CDATA[
      L(L(x,y,z),a(x,u,w),v5) = L(L(x,x,a(w,u,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(46017(a,1),30(a,1,1)),flip(a)].">
      <j1 rule="para" parents="46017 30"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46026">
    <literal><![CDATA[
      (L(x,x,a(y,z,u)) / w) \ x = (1 / w) \ a(x,a(x,z,y),u)
    ]]></literal>
    <justification jstring="[para(46017(a,1),43524(a,1,1,1))].">
      <j1 rule="para" parents="46017 43524"/>
    </justification>
  </clause>

  <clause id="46027">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(x,x,w)) = L(x,x,a(z,u,w)) \ y
    ]]></literal>
    <justification jstring="[para(46017(a,1),43924(a,2,1))].">
      <j1 rule="para" parents="46017 43924"/>
    </justification>
  </clause>

  <clause id="46028">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ L(u,z,y) = L(u,z,y) * (u \ (x \ u))
    ]]></literal>
    <justification jstring="[para(46017(a,1),43972(a,1,1))].">
      <j1 rule="para" parents="46017 43972"/>
    </justification>
  </clause>

  <clause id="46029">
    <literal><![CDATA[
      L(L(x,x,a(y,z,u)),x,u) = L(x,x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(46017(a,1),44197(a,1,1))].">
      <j1 rule="para" parents="46017 44197"/>
    </justification>
  </clause>

  <clause id="46035">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) * (a(u,z,x) * y) = (x * a(u,z,x)) * y
    ]]></literal>
    <justification jstring="[para(46019(a,1),41422(a,1,1))].">
      <j1 rule="para" parents="46019 41422"/>
    </justification>
  </clause>

  <clause id="46040">
    <literal><![CDATA[
      a((x \ T(y,T(z,u))) * ((T(z,u) * x) \ (y * T(z,u))),w,v5) = a(a(z,x,x \ T(y,T(z,u))),w,v5)
    ]]></literal>
    <justification jstring="[para(23838(a,1),45319(a,1,1,2))].">
      <j1 rule="para" parents="23838 45319"/>
    </justification>
  </clause>

  <clause id="46044">
    <literal><![CDATA[
      a(x,y,z * R(z \ u,w,u)) = a(x,y,L(u,w,u \ z))
    ]]></literal>
    <justification jstring="[para(45416(a,2),45116(a,1,3))].">
      <j1 rule="para" parents="45416 45116"/>
    </justification>
  </clause>

  <clause id="46047">
    <literal><![CDATA[
      (1 / L(x,x,y)) \ a(y,z,u) = (y * (1 / x)) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[para(11795(a,1),45421(a,2,1))].">
      <j1 rule="para" parents="11795 45421"/>
    </justification>
  </clause>

  <clause id="46048">
    <literal><![CDATA[
      a(x \ (L(y * y,z,u) \ (w \ x)),v5,v5 * x) = a(w,v5,v5 * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,36944,a,b,45427,a)].">
      <j1 rule="hyper" parents="64 36944 45427"/>
    </justification>
  </clause>

  <clause id="46049">
    <literal><![CDATA[
      a(x \ (y * z),z,y) = a(z * (y \ x),z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32442,a(flip),b,45428,a),flip(a)].">
      <j1 rule="hyper" parents="64 32442 45428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46050">
    <literal><![CDATA[
      a(R(x,y,z),u,w) = R(a(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(45073(a,2),45437(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45073 45437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46053">
    <literal><![CDATA[
      a(L(x,y,z),u,w) = R(a(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32590,a(flip),b,46050,a)].">
      <j1 rule="hyper" parents="64 32590 46050"/>
    </justification>
  </clause>

  <clause id="46055">
    <literal><![CDATA[
      a(L(x,y,L(z,u,w)),v5,z) = a(x,v5,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,33475,a(flip),b,46053,a),flip(a)].">
      <j1 rule="hyper" parents="373 33475 46053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46056">
    <literal><![CDATA[
      a(L(x,y,z),u,z) = a(x,u,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,33195,a(flip),b,46053,a),flip(a)].">
      <j1 rule="hyper" parents="373 33195 46053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46057">
    <literal><![CDATA[
      a(L(x,y,z),u,w) = L(a(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,28787,a(flip),b,46053,a),flip(a)].">
      <j1 rule="hyper" parents="373 28787 46053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46061">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),v5,v6)) = a(x,y,L(a(z,v5,v6),u,w))
    ]]></literal>
    <justification jstring="[para(46053(a,2),27644(a,1,3))].">
      <j1 rule="para" parents="46053 27644"/>
    </justification>
  </clause>

  <clause id="46081">
    <literal><![CDATA[
      a((x * y) \ z,u,y) = a(x \ (y \ z),u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,34977,a(flip),b,46056,a),flip(a)].">
      <j1 rule="hyper" parents="64 34977 46056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46083">
    <literal><![CDATA[
      a(x \ y,z,y) = a(x * y,z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32860,a(flip),b,46056,a)].">
      <j1 rule="hyper" parents="64 32860 46056"/>
    </justification>
  </clause>

  <clause id="46084">
    <literal><![CDATA[
      a(x \ y,z,x) = a(y * x,z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30383,a(flip),b,46056,a)].">
      <j1 rule="hyper" parents="64 30383 46056"/>
    </justification>
  </clause>

  <clause id="46086">
    <literal><![CDATA[
      a((x \ y) \ z,u,x) = a(y \ (x * z),u,x)
    ]]></literal>
    <justification jstring="[para(630(a,1),46056(a,1,1)),flip(a)].">
      <j1 rule="para" parents="630 46056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46110">
    <literal><![CDATA[
      L(x,y,L(z,u,x)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[para(46056(a,1),45065(a,2,1))].">
      <j1 rule="para" parents="46056 45065"/>
    </justification>
  </clause>

  <clause id="46112">
    <literal><![CDATA[
      a((x * y) \ z,u,y * x) = a(z * (x * y),u,x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,40761,a,b,46083,a)].">
      <j1 rule="hyper" parents="64 40761 46083"/>
    </justification>
  </clause>

  <clause id="46116">
    <literal><![CDATA[
      L(x * a(y * z,x,z),z,y / z) = y \ (((y / z) * x) * T(z,x))
    ]]></literal>
    <justification jstring="[para(46084(a,1),33537(a,1,1,2))].">
      <j1 rule="para" parents="46084 33537"/>
    </justification>
  </clause>

  <clause id="46117">
    <literal><![CDATA[
      L(x,y,L(z,u,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,45065,a,b,46110,a),flip(a)].">
      <j1 rule="hyper" parents="373 45065 46110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46133">
    <literal><![CDATA[
      L(x,y,x \ z) = L(x,y,z * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30388,a(flip),b,46117,a)].">
      <j1 rule="hyper" parents="64 30388 46117"/>
    </justification>
  </clause>

  <clause id="46137">
    <literal><![CDATA[
      L(R(x,y,z),u,L(w,v5,x)) = R(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(46117(a,1),29(a,1,1)),flip(a)].">
      <j1 rule="para" parents="46117 29"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46148">
    <literal><![CDATA[
      x * L(x \ y,a(z,u,w),y) = L(y,a(w,u,z),x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,43425,a,b,46133,a)].">
      <j1 rule="hyper" parents="64 43425 46133"/>
    </justification>
  </clause>

  <clause id="46149">
    <literal><![CDATA[
      a(L(x,y,z) \ u,w,x) = a(u * L(x,y,z),w,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,30383,a(flip),b,46055,a)].">
      <j1 rule="hyper" parents="64 30383 46055"/>
    </justification>
  </clause>

  <clause id="46156">
    <literal><![CDATA[
      a(L(x,y,y * z),u,z) = L(a(x,u,z),y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,42329,a(flip),b,46057,a),flip(a)].">
      <j1 rule="hyper" parents="373 42329 46057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46163">
    <literal><![CDATA[
      a(a(x,y,z),u,L(w,v5,v6)) = L(a(w,u,a(z,y,x)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,41859,a,b,46057,a)].">
      <j1 rule="hyper" parents="64 41859 46057"/>
    </justification>
  </clause>

  <clause id="46179">
    <literal><![CDATA[
      a(L(x,y,z),u,w) \ a(x,u,w) = a(z,y,a(x,u,w))
    ]]></literal>
    <justification jstring="[para(46057(a,2),42580(a,1,1))].">
      <j1 rule="para" parents="46057 42580"/>
    </justification>
  </clause>

  <clause id="46181">
    <literal><![CDATA[
      a(L(x,y,z),u,y) \ y = z \ ((a(x,u,y) \ z) * y)
    ]]></literal>
    <justification jstring="[para(46057(a,2),42856(a,1,1))].">
      <j1 rule="para" parents="46057 42856"/>
    </justification>
  </clause>

  <clause id="46183">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(w,v5,a(x,y,z)) = a(L(x,v5,w),y,z) \ u
    ]]></literal>
    <justification jstring="[para(46057(a,2),42937(a,2,1))].">
      <j1 rule="para" parents="46057 42937"/>
    </justification>
  </clause>

  <clause id="46186">
    <literal><![CDATA[
      a(L(x,y,z),u,y) \ y = (a(x,u,y) * z) \ (z * y)
    ]]></literal>
    <justification jstring="[para(46057(a,2),44816(a,1,1))].">
      <j1 rule="para" parents="46057 44816"/>
    </justification>
  </clause>

  <clause id="46188">
    <literal><![CDATA[
      x * a(L(y,y,x),z,u) = R(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(145,a,45440,a(flip),b,39241,a(flip))].">
      <j1 rule="hyper" parents="145 45440 39241"/>
    </justification>
  </clause>

  <clause id="46192">
    <literal><![CDATA[
      a((x \ y) * z,y,L(x,x,x * z)) = a((x \ y) * z,y,x)
    ]]></literal>
    <justification jstring="[para(45532(a,1),45995(a,1,3))].">
      <j1 rule="para" parents="45532 45995"/>
    </justification>
  </clause>

  <clause id="46194">
    <literal><![CDATA[
      x * (a(y,z,u \ 1) \ 1) = x * (u * L(u \ 1,z,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,45589,a,b,9,a)].">
      <j1 rule="hyper" parents="145 45589 9"/>
    </justification>
  </clause>

  <clause id="46196">
    <literal><![CDATA[
      R(x,y,z \ 1) \ x = z * L(z \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,45053,a,b,45589,a)].">
      <j1 rule="hyper" parents="64 45053 45589"/>
    </justification>
  </clause>

  <clause id="46201">
    <literal><![CDATA[
      (a(x,y,z) \ x) \ (z * y) = a(x,y,z) * (x \ (z * y))
    ]]></literal>
    <justification jstring="[para(45635(a,1),44410(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45635 44410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46202">
    <literal><![CDATA[
      a(x,y,L(1 / z,u,w) \ v5) = a(x,y,(a(z,u,w) / z) \ v5)
    ]]></literal>
    <justification jstring="[para(45652(a,1),31334(a,1,3)),flip(a)].">
      <j1 rule="para" parents="45652 31334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46203">
    <literal><![CDATA[
      L(x,y,a(y * x,z,u)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,44192,a,b,45787,a)].">
      <j1 rule="hyper" parents="64 44192 45787"/>
    </justification>
  </clause>

  <clause id="46204">
    <literal><![CDATA[
      (x \ L(y,y,z)) \ z = (x \ y) \ R(z,y * a(u,y,w),y * a(u,y,w))
    ]]></literal>
    <justification jstring="[para(44858(a,2),45834(a,2,2))].">
      <j1 rule="para" parents="44858 45834"/>
    </justification>
  </clause>

  <clause id="46205">
    <literal><![CDATA[
      a(x,x,y \ (z * z)) = a(x,x,(y \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27579,a(flip),b,45835,a),flip(a)].">
      <j1 rule="hyper" parents="64 27579 45835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46209">
    <literal><![CDATA[
      a(x,y,L(z,u,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,45065,a(flip),b,45845,a)].">
      <j1 rule="hyper" parents="40 45065 45845"/>
    </justification>
  </clause>

  <clause id="46219">
    <literal><![CDATA[
      a(x,y,L(L(z,u,x),w,v5)) = a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27702,a,b,46209,a)].">
      <j1 rule="hyper" parents="64 27702 46209"/>
    </justification>
  </clause>

  <clause id="46220">
    <literal><![CDATA[
      a(x,y,x \ (z \ x)) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,39112,a(flip),b,46209,a),flip(a)].">
      <j1 rule="hyper" parents="64 39112 46209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46221">
    <literal><![CDATA[
      a(x,y,(z * (x \ 1)) \ u) = a(x,y,z \ ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39074,a(flip),b,46209,a),flip(a)].">
      <j1 rule="hyper" parents="64 39074 46209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46222">
    <literal><![CDATA[
      a(x,y,(z * x) \ u) = a(x,y,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39070,a(flip),b,46209,a),flip(a)].">
      <j1 rule="hyper" parents="64 39070 46209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46223">
    <literal><![CDATA[
      a(x,y,((x \ 1) * z) \ u) = a(x,y,z \ ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39068,a(flip),b,46209,a),flip(a)].">
      <j1 rule="hyper" parents="64 39068 46209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46224">
    <literal><![CDATA[
      a(x,y,(x * z) \ u) = a(x,y,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39066,a(flip),b,46209,a),flip(a)].">
      <j1 rule="hyper" parents="64 39066 46209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46226">
    <literal><![CDATA[
      a(x,y,z * (x \ 1)) = a(x,y,x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38951,a(flip),b,46209,a),flip(a)].">
      <j1 rule="hyper" parents="64 38951 46209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46227">
    <literal><![CDATA[
      a(x,y,(x \ 1) \ z) = a(x,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38939,a(flip),b,46209,a)].">
      <j1 rule="hyper" parents="64 38939 46209"/>
    </justification>
  </clause>

  <clause id="46230">
    <literal><![CDATA[
      a(x,y,(x \ z) \ u) = a(x,y,z \ (x * u))
    ]]></literal>
    <justification jstring="[para(630(a,1),46209(a,1,3)),flip(a)].">
      <j1 rule="para" parents="630 46209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46231">
    <literal><![CDATA[
      a(x,y,L((x * z) \ u,w,v5)) = a(x,y,L(z \ (x \ u),w,v5))
    ]]></literal>
    <justification jstring="[para(709(a,1),46209(a,1,3))].">
      <j1 rule="para" parents="709 46209"/>
    </justification>
  </clause>

  <clause id="46232">
    <literal><![CDATA[
      a(x,y,L(z,x,x) \ (x * u)) = a(x,y,((x \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(1870(a,1),46209(a,1,3))].">
      <j1 rule="para" parents="1870 46209"/>
    </justification>
  </clause>

  <clause id="46233">
    <literal><![CDATA[
      a(x,y,L((x \ z) \ u,w,v5)) = a(x,y,L(z \ (x * u),w,v5))
    ]]></literal>
    <justification jstring="[para(1026(a,1),46209(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1026 46209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46254">
    <literal><![CDATA[
      a(x,y,z * ((x \ 1) * L(u,z,x \ 1))) = a(x,y,x \ (z * L(u,x \ 1,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27963,a(flip),b,46226,a)].">
      <j1 rule="hyper" parents="64 27963 46226"/>
    </justification>
  </clause>

  <clause id="46255">
    <literal><![CDATA[
      a(x,y,x \ L(z / (x \ 1),u,w)) = a(x,y,x \ L(x * z,u,w))
    ]]></literal>
    <justification jstring="[para(1801(a,1),46226(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1801 46226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46256">
    <literal><![CDATA[
      a(x,y,x \ (((z * (u * (x \ 1))) / (z * (x \ 1))) * z)) = a(x,y,z * (R(u,z,x \ 1) * (x \ 1)))
    ]]></literal>
    <justification jstring="[para(2738(a,1),46226(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2738 46226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46257">
    <literal><![CDATA[
      L(x,a(y,z,y \ u),w) = L(x,a(y,z,y * u),w)
    ]]></literal>
    <justification jstring="[para(46227(a,1),34489(a,1,2)),flip(a)].">
      <j1 rule="para" parents="46227 34489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46259">
    <literal><![CDATA[
      a(x,x,L(y,z,a(z,u,w))) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,7,a(flip),b,45870,a),flip(a)].">
      <j1 rule="hyper" parents="373 7 45870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46260">
    <literal><![CDATA[
      a(x,x,(y \ 1) \ (a(y,z,u) \ w)) = a(x,x,(y \ a(y,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(43333(a,1),46259(a,1,3))].">
      <j1 rule="para" parents="43333 46259"/>
    </justification>
  </clause>

  <clause id="46261">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) = L(x,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,45190,a(flip),b,45916,a),flip(a)].">
      <j1 rule="hyper" parents="64 45190 45916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46262">
    <literal><![CDATA[
      L(x,y,a(z,u,u)) = L(x,u,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,45157,a(flip),b,45916,a)].">
      <j1 rule="hyper" parents="64 45157 45916"/>
    </justification>
  </clause>

  <clause id="46263">
    <literal><![CDATA[
      L(x,y,a(z,z,u)) = L(x,z,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(42222,a,46261,a),flip(a)].">
      <j1 rule="hyper" parents="42222 46261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46265">
    <literal><![CDATA[
      L(x \ y,x,a(x,z,u)) = x \ L(y,z,a(x,x,u))
    ]]></literal>
    <justification jstring="[para(46261(a,1),41430(a,2,2))].">
      <j1 rule="para" parents="46261 41430"/>
    </justification>
  </clause>

  <clause id="46267">
    <literal><![CDATA[
      L(x,y,a(z,u,u)) = L(x,u,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,42195,a,b,46262,a),flip(a)].">
      <j1 rule="hyper" parents="373 42195 46262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46269">
    <literal><![CDATA[
      L(x * y,y,a(y,z,u)) = L(x,z,a(u,y,y)) * y
    ]]></literal>
    <justification jstring="[para(46262(a,2),41431(a,2,1))].">
      <j1 rule="para" parents="46262 41431"/>
    </justification>
  </clause>

  <clause id="46270">
    <literal><![CDATA[
      L(x \ y,y,a(y,z,u)) = L(x,z,a(y,y,u)) \ y
    ]]></literal>
    <justification jstring="[para(46263(a,2),40970(a,2,1))].">
      <j1 rule="para" parents="46263 40970"/>
    </justification>
  </clause>

  <clause id="46271">
    <literal><![CDATA[
      a(x,y,y) * ((a(x,y,y) \ z) * u) = z * L(u,y,a(y,z,x))
    ]]></literal>
    <justification jstring="[para(46263(a,1),42817(a,2,2))].">
      <j1 rule="para" parents="46263 42817"/>
    </justification>
  </clause>

  <clause id="46272">
    <literal><![CDATA[
      L(x,y,a(z * a(u,w,w),v5,v5)) = L(x,v5,a(v5,y,z * a(w,w,u)))
    ]]></literal>
    <justification jstring="[para(32851(a,2),46267(a,1,3))].">
      <j1 rule="para" parents="32851 46267"/>
    </justification>
  </clause>

  <clause id="46274">
    <literal><![CDATA[
      L(x,y \ z,a(u,z,z)) = L(x,z,a(z,z * y,u))
    ]]></literal>
    <justification jstring="[para(45382(a,1),46267(a,2,3))].">
      <j1 rule="para" parents="45382 46267"/>
    </justification>
  </clause>

  <clause id="46275">
    <literal><![CDATA[
      a(x * (y \ ((x * y) \ z)),x,y) = a(z,x,y)
    ]]></literal>
    <justification jstring="[para(10(a,1),46007(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 46007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46276">
    <literal><![CDATA[
      a(a(x * (y \ z),x,y),u,w) = a(a(y,x,z * (x * y)),u,w)
    ]]></literal>
    <justification jstring="[para(46007(a,1),41493(a,1,1))].">
      <j1 rule="para" parents="46007 41493"/>
    </justification>
  </clause>

  <clause id="46277">
    <literal><![CDATA[
      a(T(x,y * y) * ((1 / y) \ z),T(x,y * y),1 / y) = a(z * (((y * y) \ x) * y),T(x,y * y),1 / y)
    ]]></literal>
    <justification jstring="[para(929(a,1),46008(a,2,1,2))].">
      <j1 rule="para" parents="929 46008"/>
    </justification>
  </clause>

  <clause id="46278">
    <literal><![CDATA[
      a(x * (R(y,y,x) \ z),x,R(y,y,x)) = a(z * ((1 / y) \ T(x,y)),x,R(y,y,x))
    ]]></literal>
    <justification jstring="[para(24602(a,2),46008(a,2,1,2))].">
      <j1 rule="para" parents="24602 46008"/>
    </justification>
  </clause>

  <clause id="46279">
    <literal><![CDATA[
      a(x * (y \ (z \ (x * y))),x,y) = a(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32478,a(flip),b,46049,a),flip(a)].">
      <j1 rule="hyper" parents="64 32478 46049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46280">
    <literal><![CDATA[
      a(L(x,y,z * y),u,z) = L(a(x,u,z),y,y)
    ]]></literal>
    <justification jstring="[para(23253(a,1),46156(a,1,1))].">
      <j1 rule="para" parents="23253 46156"/>
    </justification>
  </clause>

  <clause id="46281">
    <literal><![CDATA[
      L(x,(R(y,z,((u * u) \ w) \ 1) \ y) * v5,v6) = L(x,(w * L(((u * u) \ w) \ 1,z,y)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(46196(a,2),11781(a,1,2,1))].">
      <j1 rule="para" parents="46196 11781"/>
    </justification>
  </clause>

  <clause id="46282">
    <literal><![CDATA[
      L(x \ y,x,a(y,z,u)) = L(x \ y,x,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),46203(a,1,3,1))].">
      <j1 rule="para" parents="10 46203"/>
    </justification>
  </clause>

  <clause id="46283">
    <literal><![CDATA[
      L(x,y,a(x * y,z,u)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(26787(a,1),46203(a,1,3))].">
      <j1 rule="para" parents="26787 46203"/>
    </justification>
  </clause>

  <clause id="46284">
    <literal><![CDATA[
      a(x,y,a(z,z,(u \ w) * w)) = a(a(z,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(46205(a,1),41862(a,1,3))].">
      <j1 rule="para" parents="46205 41862"/>
    </justification>
  </clause>

  <clause id="46286">
    <literal><![CDATA[
      a(x / T(y * y,z),u,((x / T(y * y,z)) * w) \ v5) = a(x / T(y * y,z),u,w \ (T(y * y,z) * (x \ v5)))
    ]]></literal>
    <justification jstring="[para(25542(a,1),46224(a,2,3,2))].">
      <j1 rule="para" parents="25542 46224"/>
    </justification>
  </clause>

  <clause id="46288">
    <literal><![CDATA[
      a(x * (y \ ((x / y) \ (x * z))),x,y) = a(((x * y) * y) * z,x,y)
    ]]></literal>
    <justification jstring="[para(41962(a,1),46275(a,1,1,2,2))].">
      <j1 rule="para" parents="41962 46275"/>
    </justification>
  </clause>

  <clause id="46289">
    <literal><![CDATA[
      (L(x,y,a(y,z,u)) * y) * a(u,z,x * y) = x * (y * a(u,z,x * y))
    ]]></literal>
    <justification jstring="[para(46283(a,1),42221(a,1,1,1))].">
      <j1 rule="para" parents="46283 42221"/>
    </justification>
  </clause>

  <clause id="46290">
    <literal><![CDATA[
      a(x,y,(z \ u) * (a(z,z,u) * w)) = a(x,y,((z \ 1) * u) * w)
    ]]></literal>
    <justification jstring="[para(44979(a,1),39003(a,1,3)),flip(a)].">
      <j1 rule="para" parents="44979 39003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46293">
    <literal><![CDATA[
      a(x,((y \ z) \ u) * a(z,y,y),w) = a(x,((y \ 1) * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(45021(a,1),34110(a,2,2))].">
      <j1 rule="para" parents="45021 34110"/>
    </justification>
  </clause>

  <clause id="46296">
    <literal><![CDATA[
      a(L(x,y,z),u,y) \ z = L(y,u,x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(46057(a,2),45231(a,1,1))].">
      <j1 rule="para" parents="46057 45231"/>
    </justification>
  </clause>

  <clause id="46297">
    <literal><![CDATA[
      a(x,y,L(z * y,z,y)) = a(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,42880,a(flip),b,45290,a),flip(a)].">
      <j1 rule="hyper" parents="373 42880 45290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46298">
    <literal><![CDATA[
      L(x,x \ (x * T(y,z)),(x * T(y,z)) * u) = ((u / (x * T(y,z))) * T((x * y) / x,z)) \ u
    ]]></literal>
    <justification jstring="[para(541(a,1),45311(a,2,1,2))].">
      <j1 rule="para" parents="541 45311"/>
    </justification>
  </clause>

  <clause id="46299">
    <literal><![CDATA[
      x * (L(x,y,z) \ (a(z,u,w) \ 1)) = a(z,y,x) * (a(z,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(31084(a,1),45351(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31084 45351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46300">
    <literal><![CDATA[
      a(x,x,L(L(y,y,z),u,w)) = a(x,x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,39675,a,b,45495,a),flip(a)].">
      <j1 rule="hyper" parents="373 39675 45495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46302">
    <literal><![CDATA[
      a(x,y,L(a(z,u,y),x,w)) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,43872,a(flip),b,45498,a),flip(a)].">
      <j1 rule="hyper" parents="373 43872 45498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46303">
    <literal><![CDATA[
      a(x,y,y) \ ((z \ a(z,z,y \ x)) * (x * (1 / y))) = z \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(373,a,30131,a(flip),b,45547,a),flip(a)].">
      <j1 rule="hyper" parents="373 30131 45547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46305">
    <literal><![CDATA[
      a(x,a(y,z,x),L(u,u,w)) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,45784,a(flip),b,45550,a),flip(a)].">
      <j1 rule="hyper" parents="373 45784 45550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46306">
    <literal><![CDATA[
      a(x,x,y) * (z * (x * y)) = z * ((1 / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(23777,a,45587,a)].">
      <j1 rule="hyper" parents="23777 45587"/>
    </justification>
  </clause>

  <clause id="46308">
    <literal><![CDATA[
      a(x * (a(y,z,u) * w),y,y) = a(x * w,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,45506,a(flip),b,45669,a),flip(a)].">
      <j1 rule="hyper" parents="373 45506 45669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46309">
    <literal><![CDATA[
      L(x,(y \ ((y * z) * x)) * x,y) = (y * (a(y,z,x) * z)) \ ((y * z) * x)
    ]]></literal>
    <justification jstring="[para(33279(a,1),45707(a,2,1,2))].">
      <j1 rule="para" parents="33279 45707"/>
    </justification>
  </clause>

  <clause id="46310">
    <literal><![CDATA[
      L(L(x,y,a(z,z,u)),a(z,z,u) * y,z * u) = (((1 / z) \ u) * y) \ ((z * u) * (a(z,z,u) * (y * x)))
    ]]></literal>
    <justification jstring="[para(45715(a,1),602(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45715 602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46311">
    <literal><![CDATA[
      a(x,x,a(y,z,L(u,w,w))) = a(u,x,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,43881,a,b,45876,a),flip(a)].">
      <j1 rule="hyper" parents="373 43881 45876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46312">
    <literal><![CDATA[
      a(x,x,a(y,z,L(u,w,w))) = a(u,x,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,43917,a(flip),b,45876,a),flip(a)].">
      <j1 rule="hyper" parents="373 43917 45876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46313">
    <literal><![CDATA[
      a(x,y,a(z,u,L(u,x,w))) = a(z,y,a(u,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,43981,a(flip),b,45919,a)].">
      <j1 rule="hyper" parents="64 43981 45919"/>
    </justification>
  </clause>

  <clause id="46317">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) * (z \ u) = L(z,y,x) \ u
    ]]></literal>
    <justification jstring="[para(45996(a,1),44489(a,1,1))].">
      <j1 rule="para" parents="45996 44489"/>
    </justification>
  </clause>

  <clause id="46318">
    <literal><![CDATA[
      L(R(x,y,z),u,L(w,v5,x)) = L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29,a(flip),b,46137,a),flip(a)].">
      <j1 rule="hyper" parents="373 29 46137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46320">
    <literal><![CDATA[
      R(x,y,z) * (x \ a(u,w,w)) = a(u,w,w) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(45013(a,1),46188(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="45013 46188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46323">
    <literal><![CDATA[
      L(x,y,L(z,x,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,42095,a,b,46296,a(flip))].">
      <j1 rule="hyper" parents="36 42095 46296"/>
    </justification>
  </clause>

  <clause id="46328">
    <literal><![CDATA[
      L(x * K(y,z),u,L(w,x,u)) = L(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(29449(a,1),46323(a,1,3))].">
      <j1 rule="para" parents="29449 46323"/>
    </justification>
  </clause>

  <clause id="46329">
    <literal><![CDATA[
      a(x,x,((y * z) \ (y * (u \ z))) \ 1) = a(x,x,L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,39830,a(flip),b,46300,a)].">
      <j1 rule="hyper" parents="64 39830 46300"/>
    </justification>
  </clause>

  <clause id="46330">
    <literal><![CDATA[
      (x * y) * a(y,z,a(u,w,z)) = x * L(y,z,a(z,w,u))
    ]]></literal>
    <justification jstring="[para(46302(a,1),43871(a,1,2))].">
      <j1 rule="para" parents="46302 43871"/>
    </justification>
  </clause>

  <clause id="46331">
    <literal><![CDATA[
      (x / y) * a(y,z,a(u,w,z)) = x / L(y,z,a(z,w,u))
    ]]></literal>
    <justification jstring="[para(46302(a,1),44124(a,1,2))].">
      <j1 rule="para" parents="46302 44124"/>
    </justification>
  </clause>

  <clause id="46332">
    <literal><![CDATA[
      a(L(a(x,y,z),u,w),z,u) = a(z,z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,43857,a,b,46305,a)].">
      <j1 rule="hyper" parents="64 43857 46305"/>
    </justification>
  </clause>

  <clause id="46333">
    <literal><![CDATA[
      L(x,y,z) = (z * R(y,y,x)) \ (z * ((1 / y) \ x))
    ]]></literal>
    <justification jstring="[para(46306(a,1),38057(a,2,2))].">
      <j1 rule="para" parents="46306 38057"/>
    </justification>
  </clause>

  <clause id="46336">
    <literal><![CDATA[
      a(x * (a(y,z,u) * w),v5,a(y,y,v6)) = a(v6,v5,a(x * w,y,y))
    ]]></literal>
    <justification jstring="[para(46308(a,1),45890(a,1,3)),flip(a)].">
      <j1 rule="para" parents="46308 45890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46338">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,x,w))) = a(u,y,a(z,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,39812,a(flip),b,46313,a)].">
      <j1 rule="hyper" parents="64 39812 46313"/>
    </justification>
  </clause>

  <clause id="46340">
    <literal><![CDATA[
      L(a(x,y,a(y,z,u)),x,w) = a(y,y,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,43851,a(flip),b,46332,a)].">
      <j1 rule="hyper" parents="64 43851 46332"/>
    </justification>
  </clause>

  <clause id="46341">
    <literal><![CDATA[
      a(T((x \ 1) \ (y \ z),u),w,a(v5,v5,x)) = a(x,w,a(v5,v5,T((y * (x \ 1)) \ z,u)))
    ]]></literal>
    <justification jstring="[para(11810(a,1),46338(a,1,3,3)),flip(a)].">
      <j1 rule="para" parents="11810 46338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46343">
    <literal><![CDATA[
      a(x,y,a(z,z,a(u,w,v5)) * v6) = a(x,y,v6 * a(v5,z,a(z,w,u)))
    ]]></literal>
    <justification jstring="[para(46340(a,1),27362(a,1,3,1))].">
      <j1 rule="para" parents="46340 27362"/>
    </justification>
  </clause>

  <clause id="46344">
    <literal><![CDATA[
      (a(x,x,y) \ z) * (x * y) = z * (x * L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,29994,a(flip),b,44970,a)].">
      <j1 rule="hyper" parents="64 29994 44970"/>
    </justification>
  </clause>

  <clause id="46346">
    <literal><![CDATA[
      x \ (a(y,y,z) * z) = (x \ z) * a(y,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,45007,a(flip),b,44993,a),flip(a)].">
      <j1 rule="hyper" parents="64 45007 44993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46347">
    <literal><![CDATA[
      a((x \ y) * a(z,z,y),u,w) = a(x \ L(y,z,z),u,w)
    ]]></literal>
    <justification jstring="[para(46346(a,1),26923(a,1,1))].">
      <j1 rule="para" parents="46346 26923"/>
    </justification>
  </clause>

  <clause id="46348">
    <literal><![CDATA[
      (x \ (y / (y / z))) * a(u,u,y / (y / z)) = x \ (a(u,u,z) * (y / (y / z)))
    ]]></literal>
    <justification jstring="[para(27306(a,1),46346(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="27306 46346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46351">
    <literal><![CDATA[
      a(x * (L(y,y,x) \ z),x,L(y,y,x)) \ z = (a(x,y,y) \ ((z / L(y,y,x)) / x)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,41833,a,b,45016,a)].">
      <j1 rule="hyper" parents="373 41833 45016"/>
    </justification>
  </clause>

  <clause id="46352">
    <literal><![CDATA[
      a(x,y,y) * ((y \ x) * z) = (y \ R(x,y,y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,30307,a,b,45018,a)].">
      <j1 rule="hyper" parents="64 30307 45018"/>
    </justification>
  </clause>

  <clause id="46354">
    <literal><![CDATA[
      (x * (y \ x)) \ (((y \ x) \ x) * (K(y \ x,y) * z)) = ((x * (y \ x)) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(373,a,24541,a(flip),b,45022,a),flip(a)].">
      <j1 rule="hyper" parents="373 24541 45022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46355">
    <literal><![CDATA[
      a(((x * y) \ (y \ x)) * (((y \ x) \ 1) \ z),u,w) = a((x * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(45022(a,1),26913(a,1,1))].">
      <j1 rule="para" parents="45022 26913"/>
    </justification>
  </clause>

  <clause id="46357">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((u \ z) \ w)) = a(x,y,u * (((u \ z) * z) \ w))
    ]]></literal>
    <justification jstring="[para(45023(a,1),27317(a,1,3)),flip(a)].">
      <j1 rule="para" parents="45023 27317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46359">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * (u \ w)) = a(x,y,z * ((u * (u * z)) \ w))
    ]]></literal>
    <justification jstring="[para(45024(a,1),27722(a,1,3)),flip(a)].">
      <j1 rule="para" parents="45024 27722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46360">
    <literal><![CDATA[
      a(x,y,(z \ (z / u)) * (u \ w)) = a(x,y,z * (((z * u) * u) \ w))
    ]]></literal>
    <justification jstring="[para(45070(a,1),40238(a,1,3)),flip(a)].">
      <j1 rule="para" parents="45070 40238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46361">
    <literal><![CDATA[
      L(x * K(y * x,a(z,x,y) \ z),y,a(z,x,y) \ z) = ((a(z,x,y) \ z) * y) \ ((L(y,x,z) * x) * z)
    ]]></literal>
    <justification jstring="[para(45076(a,1),14648(a,2,2))].">
      <j1 rule="para" parents="45076 14648"/>
    </justification>
  </clause>

  <clause id="46362">
    <literal><![CDATA[
      a((x * y) \ ((a(z,y,x) \ z) \ (x * y)),u,w) = a(((L(x,y,z) * y) * z) \ (x * y),u,w)
    ]]></literal>
    <justification jstring="[para(45076(a,1),32506(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="45076 32506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46363">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * (w \ v5) = v5 * L(v5 \ (w \ v5),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(144,a,45282,a(flip),b,2624,a)].">
      <j1 rule="hyper" parents="144 45282 2624"/>
    </justification>
  </clause>

  <clause id="46366">
    <literal><![CDATA[
      (x * (L(x,y,z) \ u)) * x = u * (x * a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,25110,a,b,45350,a)].">
      <j1 rule="hyper" parents="64 25110 45350"/>
    </justification>
  </clause>

  <clause id="46367">
    <literal><![CDATA[
      x * (y * a(x * y,a(z,u,w),x)) = R(x,a(w,u,z),x * y) * y
    ]]></literal>
    <justification jstring="[para(43405(a,1),45412(a,1,2,2))].">
      <j1 rule="para" parents="43405 45412"/>
    </justification>
  </clause>

  <clause id="46368">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (w * (z \ u))) = a(x,y,w * (z \ R(u,z,z)))
    ]]></literal>
    <justification jstring="[para(45548(a,1),39961(a,2,3))].">
      <j1 rule="para" parents="45548 39961"/>
    </justification>
  </clause>

  <clause id="46371">
    <literal><![CDATA[
      R(x,y * z,z \ ((1 / y) \ z)) = R(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26183,a(flip),b,45711,a)].">
      <j1 rule="hyper" parents="64 26183 45711"/>
    </justification>
  </clause>

  <clause id="46372">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(a(z,u,w),y,x * y)
    ]]></literal>
    <justification jstring="[para(45776(a,1),42226(a,2,2))].">
      <j1 rule="para" parents="45776 42226"/>
    </justification>
  </clause>

  <clause id="46373">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) * w) * v5 = (a(y,y,a(z,u,x)) * w) * v5
    ]]></literal>
    <justification jstring="[hyper(144,a,45789,a,b,11,a)].">
      <j1 rule="hyper" parents="144 45789 11"/>
    </justification>
  </clause>

  <clause id="46374">
    <literal><![CDATA[
      (x \ (y \ x)) * (T(x,y \ 1) * a(z,z,a(u,w,v5))) = ((y \ x) / x) * (x * a(u,w,a(z,z,v5)))
    ]]></literal>
    <justification jstring="[para(45790(a,1),5047(a,1,2))].">
      <j1 rule="para" parents="45790 5047"/>
    </justification>
  </clause>

  <clause id="46375">
    <literal><![CDATA[
      T(x,y) \ (y \ ((x * y) * a(z,z,a(u,w,v5)))) = x \ (y \ ((y * x) * a(u,w,a(z,z,v5))))
    ]]></literal>
    <justification jstring="[para(45790(a,1),10968(a,1,2,2))].">
      <j1 rule="para" parents="45790 10968"/>
    </justification>
  </clause>

  <clause id="46378">
    <literal><![CDATA[
      a(x,x,a(y,z,u \ w)) = a(x,x,a(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,45784,a(flip),b,45884,a),flip(a)].">
      <j1 rule="hyper" parents="64 45784 45884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46379">
    <literal><![CDATA[
      a(x * y,z,a(u,w,z)) = a(u,z,a(z,w,y * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,43917,a(flip),b,45910,a),flip(a)].">
      <j1 rule="hyper" parents="373 43917 45910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46380">
    <literal><![CDATA[
      x * (a(y,z,a(u,w,z)) * v5) = x * (v5 * a(y,w,a(u,z,z)))
    ]]></literal>
    <justification jstring="[para(45911(a,2),23169(a,2,2))].">
      <j1 rule="para" parents="45911 23169"/>
    </justification>
  </clause>

  <clause id="46381">
    <literal><![CDATA[
      a(x,y,y \ (z * z)) = a(x,y,(y \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,45073,a,b,45949,a),flip(a)].">
      <j1 rule="hyper" parents="64 45073 45949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46382">
    <literal><![CDATA[
      a(a(x,y,(y \ z) * z) * u,w,v5) = a(a(x,y,y) * u,w,v5)
    ]]></literal>
    <justification jstring="[para(46381(a,1),37165(a,1,1,1))].">
      <j1 rule="para" parents="46381 37165"/>
    </justification>
  </clause>

  <clause id="46383">
    <literal><![CDATA[
      a(x * a(y,z,(z \ u) * u),w,v5) = a(a(y,z,z) * x,w,v5)
    ]]></literal>
    <justification jstring="[para(46381(a,1),37171(a,1,1,2))].">
      <j1 rule="para" parents="46381 37171"/>
    </justification>
  </clause>

  <clause id="46385">
    <literal><![CDATA[
      (x / y) \ ((x / y) / z) = (x * y) \ ((x * y) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,14813,a,b,45952,a)].">
      <j1 rule="hyper" parents="64 14813 45952"/>
    </justification>
  </clause>

  <clause id="46386">
    <literal><![CDATA[
      L((x * y) \ ((x * y) / z),y * x,x * y) = (y \ x) * (((y \ x) \ 1) / z)
    ]]></literal>
    <justification jstring="[para(45952(a,1),35230(a,1,1))].">
      <j1 rule="para" parents="45952 35230"/>
    </justification>
  </clause>

  <clause id="46387">
    <literal><![CDATA[
      x * (L(x \ y,x,a(x,z,u)) * a(w,v5,x)) = L(y,z,a(x,x,u)) * a(w,v5,x)
    ]]></literal>
    <justification jstring="[para(46265(a,2),33197(a,1,2,1))].">
      <j1 rule="para" parents="46265 33197"/>
    </justification>
  </clause>

  <clause id="46388">
    <literal><![CDATA[
      (a(x,y,y) * (z * u)) \ ((a(x,y,y) * z) * L(u * y,y,a(y,z,x))) = L(y,L(u,z,a(x,y,y)),a(x,y,y) * z)
    ]]></literal>
    <justification jstring="[para(46269(a,2),601(a,1,2,2))].">
      <j1 rule="para" parents="46269 601"/>
    </justification>
  </clause>

  <clause id="46389">
    <literal><![CDATA[
      L(x \ y,x,a(z,u,x)) = L(x \ y,x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,42195,a,b,46282,a)].">
      <j1 rule="hyper" parents="373 42195 46282"/>
    </justification>
  </clause>

  <clause id="46390">
    <literal><![CDATA[
      a(x,y,a(z,z,(u \ w) * w)) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,43872,a(flip),b,46284,a),flip(a)].">
      <j1 rule="hyper" parents="373 43872 46284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46391">
    <literal><![CDATA[
      L(x,L(y,y,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,29795,a(flip),b,46333,a)].">
      <j1 rule="hyper" parents="373 29795 46333"/>
    </justification>
  </clause>

  <clause id="46394">
    <literal><![CDATA[
      L(x,x * (y \ x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,45704,a(flip),b,46391,a)].">
      <j1 rule="hyper" parents="64 45704 46391"/>
    </justification>
  </clause>

  <clause id="46397">
    <literal><![CDATA[
      (x \ L(y,x,z)) \ (x \ y) = a(z,L(x,x,y),y)
    ]]></literal>
    <justification jstring="[para(46391(a,1),43251(a,1,1,2))].">
      <j1 rule="para" parents="46391 43251"/>
    </justification>
  </clause>

  <clause id="46398">
    <literal><![CDATA[
      L(x,(y \ x) * x,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29572,a,46394,a)].">
      <j1 rule="hyper" parents="29572 46394"/>
    </justification>
  </clause>

  <clause id="46399">
    <literal><![CDATA[
      L(x,y \ x,z) = L(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29622,a(flip),b,46398,a),flip(a)].">
      <j1 rule="hyper" parents="64 29622 46398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46400">
    <literal><![CDATA[
      L(x,y \ x,a(z,u,w)) = L(x,x * y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(42222,a,46399,a)].">
      <j1 rule="hyper" parents="42222 46399"/>
    </justification>
  </clause>

  <clause id="46406">
    <literal><![CDATA[
      a(x,L(y,y,z),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42878,a,b,46397,a),flip(a)].">
      <j1 rule="hyper" parents="64 42878 46397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46408">
    <literal><![CDATA[
      a(x * (L(y,y,z) * z),L(y,y,z),z) = a(L(y,y,z) * (z \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46008,a(flip),b,46406,a)].">
      <j1 rule="hyper" parents="64 46008 46406"/>
    </justification>
  </clause>

  <clause id="46409">
    <literal><![CDATA[
      a(x,(y \ z) * z,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35682,a(flip),b,46406,a)].">
      <j1 rule="hyper" parents="64 35682 46406"/>
    </justification>
  </clause>

  <clause id="46411">
    <literal><![CDATA[
      a(x,y * (z \ y),y) = a(x,z,y)
    ]]></literal>
    <justification jstring="[hyper(32008,a,46409,a)].">
      <j1 rule="hyper" parents="32008 46409"/>
    </justification>
  </clause>

  <clause id="46412">
    <literal><![CDATA[
      a(x,y \ z,z) = a(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32091,a(flip),b,46409,a),flip(a)].">
      <j1 rule="hyper" parents="64 32091 46409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46414">
    <literal><![CDATA[
      a(x,y * (z \ y),y \ 1) = a(x,z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,32270,a(flip),b,46411,a)].">
      <j1 rule="hyper" parents="64 32270 46411"/>
    </justification>
  </clause>

  <clause id="46415">
    <literal><![CDATA[
      a(x,y,(z * (u * a(w,v5,u))) \ v6) = a(x,y,(z * L(u,v5,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(46366(a,1),44496(a,1,3,1))].">
      <j1 rule="para" parents="46366 44496"/>
    </justification>
  </clause>

  <clause id="46417">
    <literal><![CDATA[
      R(x,y * z,z \ ((y \ 1) \ z)) = R(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26278,a(flip),b,46371,a)].">
      <j1 rule="hyper" parents="64 26278 46371"/>
    </justification>
  </clause>

  <clause id="46418">
    <literal><![CDATA[
      a(x,x,a(y,z,u \ (y \ w))) = a(x,x,a(y,z,w * (y * u)))
    ]]></literal>
    <justification jstring="[para(46224(a,1),46378(a,1,3))].">
      <j1 rule="para" parents="46224 46378"/>
    </justification>
  </clause>

  <clause id="46419">
    <literal><![CDATA[
      L((x * (1 / y)) \ ((x * (1 / y)) / z),y * x,y) = x \ (y * ((y \ x) / z))
    ]]></literal>
    <justification jstring="[para(46385(a,1),41759(a,1,1))].">
      <j1 rule="para" parents="46385 41759"/>
    </justification>
  </clause>

  <clause id="46420">
    <literal><![CDATA[
      (a(x,y,z) * u) * L(u \ x,u,a(z,y,u)) = a(x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(145,a,46389,a,b,102,a(flip))].">
      <j1 rule="hyper" parents="145 46389 102"/>
    </justification>
  </clause>

  <clause id="46421">
    <literal><![CDATA[
      a((x \ y) * y,z,a(u,u,w)) = a(x,u,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,45903,a,b,46390,a)].">
      <j1 rule="hyper" parents="64 45903 46390"/>
    </justification>
  </clause>

  <clause id="46422">
    <literal><![CDATA[
      a((x \ y) * y,z,a(u,w,z)) = a(x,z,a(u,w,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,43881,a,b,46390,a)].">
      <j1 rule="hyper" parents="64 43881 46390"/>
    </justification>
  </clause>

  <clause id="46423">
    <literal><![CDATA[
      a(x * (y \ x),z,a(u,u,w)) = a(y,u,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(26847,a,46421,a)].">
      <j1 rule="hyper" parents="26847 46421"/>
    </justification>
  </clause>

  <clause id="46424">
    <literal><![CDATA[
      a(x \ y,z,a(u,u,w)) = a(x * y,u,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,32432,a(flip),b,46421,a)].">
      <j1 rule="hyper" parents="64 32432 46421"/>
    </justification>
  </clause>

  <clause id="46425">
    <literal><![CDATA[
      a(x \ y,z,a(u,w,z)) = a(x * y,z,a(u,w,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,32432,a(flip),b,46422,a)].">
      <j1 rule="hyper" parents="64 32432 46422"/>
    </justification>
  </clause>

  <clause id="46426">
    <literal><![CDATA[
      a(x \ y,z,a(u,u,w)) = a(y * x,u,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,46424,a),flip(a)].">
      <j1 rule="hyper" parents="373 26787 46424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46427">
    <literal><![CDATA[
      a(x \ y,z,a(u,w,a(v5,v5,v6))) = a(y * x,v5,a(a(v6,w,u),z,v5))
    ]]></literal>
    <justification jstring="[para(45807(a,2),46426(a,1,3))].">
      <j1 rule="para" parents="45807 46426"/>
    </justification>
  </clause>

  <clause id="46428">
    <literal><![CDATA[
      L(L(x,y,z),a(z,y,x),u) = a(L(z,x,u),y,x) \ x
    ]]></literal>
    <justification jstring="[para(46057(a,2),45232(a,2,1))].">
      <j1 rule="para" parents="46057 45232"/>
    </justification>
  </clause>

  <clause id="46429">
    <literal><![CDATA[
      (x / y) \ (a(z,u,w) * x) = y * (a(z,u,w) * a(x * y,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(145,a,28748,a(flip),b,45355,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 28748 45355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46431">
    <literal><![CDATA[
      R(x,y * z,L(y,y,z)) = ((x * (z / y)) * y) / z
    ]]></literal>
    <justification jstring="[hyper(142,a,45527,a(flip),b,26585,a),flip(a)].">
      <j1 rule="hyper" parents="142 45527 26585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46433">
    <literal><![CDATA[
      R(x,y * z,L(y,y,z)) = R(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,10215,a(flip),b,46431,a),flip(a)].">
      <j1 rule="hyper" parents="373 10215 46431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46434">
    <literal><![CDATA[
      R(x,y * z,z \ ((y \ 1) \ z)) = R(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27178,a(flip),b,46433,a)].">
      <j1 rule="hyper" parents="64 27178 46433"/>
    </justification>
  </clause>

  <clause id="46435">
    <literal><![CDATA[
      R(x,y \ z,y) = R(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46417,a(flip),b,46434,a),flip(a)].">
      <j1 rule="hyper" parents="64 46417 46434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46438">
    <literal><![CDATA[
      x \ ((y * (x / z)) * z) = R(T(y,x),z * x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,10214,a,b,46435,a)].">
      <j1 rule="hyper" parents="64 10214 46435"/>
    </justification>
  </clause>

  <clause id="46441">
    <literal><![CDATA[
      (x * (T(y,x) / z)) * z = y * R(x,z * y,z)
    ]]></literal>
    <justification jstring="[para(46435(a,1),26627(a,2,2))].">
      <j1 rule="para" parents="46435 26627"/>
    </justification>
  </clause>

  <clause id="46442">
    <literal><![CDATA[
      L(R(x,a(y,z,u) \ z,a(y,z,u) \ z),a(u,z,y),z) = R(T(x,a(y,z,u)),z * a(y,z,u),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,43655,a,b,46438,a)].">
      <j1 rule="hyper" parents="64 43655 46438"/>
    </justification>
  </clause>

  <clause id="46443">
    <literal><![CDATA[
      a((x * (y * z)) * (x * z),u,u) = a(y,u,L(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,26791,a(flip),b,45667,a),flip(a)].">
      <j1 rule="hyper" parents="64 26791 45667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46444">
    <literal><![CDATA[
      L(x,y,((z \ u) \ w) * ((u * (z \ u)) \ (u * w))) = L(x,y,a(u,z * u,(z \ u) \ w))
    ]]></literal>
    <justification jstring="[para(45681(a,1),45318(a,1,3,2))].">
      <j1 rule="para" parents="45681 45318"/>
    </justification>
  </clause>

  <clause id="46445">
    <literal><![CDATA[
      L(x,((y \ z) \ u) * ((z * (y \ z)) \ (z * u)),w) = L(x,a(z,y * z,(y \ z) \ u),w)
    ]]></literal>
    <justification jstring="[para(45681(a,1),45321(a,1,2,2))].">
      <j1 rule="para" parents="45681 45321"/>
    </justification>
  </clause>

  <clause id="46446">
    <literal><![CDATA[
      L(x,y,L(a(z,z,u) * w,u,u)) = L(x,y,u * (L(u,z,z) * w))
    ]]></literal>
    <justification jstring="[para(45716(a,2),25369(a,1,3))].">
      <j1 rule="para" parents="45716 25369"/>
    </justification>
  </clause>

  <clause id="46449">
    <literal><![CDATA[
      x \ ((a(y,z,u) \ x) * u) = L(u,z,L(y,u,x))
    ]]></literal>
    <justification jstring="[hyper(45147,a,46181,a),flip(a)].">
      <j1 rule="hyper" parents="45147 46181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46451">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (u * z) = L(z,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(45147,a,46186,a),flip(a)].">
      <j1 rule="hyper" parents="45147 46186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46452">
    <literal><![CDATA[
      (x * a(y,z,u)) \ (x * u) = L(u,z,L(y,u,x))
    ]]></literal>
    <justification jstring="[hyper(23963,a,46451,a)].">
      <j1 rule="hyper" parents="23963 46451"/>
    </justification>
  </clause>

  <clause id="46453">
    <literal><![CDATA[
      R(T(x / a(y,z,x),u),a(y,z,x),w) = T(L(x,z,L(y,x,w)),u)
    ]]></literal>
    <justification jstring="[para(46451(a,1),31799(a,1,1)),flip(a)].">
      <j1 rule="para" parents="46451 31799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46454">
    <literal><![CDATA[
      L(L(x,y,z),a(z,y,x),u) = L(x,y,L(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,45065,a,b,46428,a),flip(a)].">
      <j1 rule="hyper" parents="373 45065 46428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46455">
    <literal><![CDATA[
      a((x * y) * (x * (z * y)),u,u) = a(z,u,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(26847,a,46443,a)].">
      <j1 rule="hyper" parents="26847 46443"/>
    </justification>
  </clause>

  <clause id="46456">
    <literal><![CDATA[
      a(((x * y) * x) * ((y * x) * (z * T(x,y))),u,u) = a(z,u,L(u,T(x,y),y * x))
    ]]></literal>
    <justification jstring="[para(1296(a,1),46455(a,1,1,1))].">
      <j1 rule="para" parents="1296 46455"/>
    </justification>
  </clause>

  <clause id="46459">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * ((u \ 1) * w)) = a(x,y,(u \ z) * (w * a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,42007,a(flip),b,45119,a)].">
      <j1 rule="hyper" parents="373 42007 45119"/>
    </justification>
  </clause>

  <clause id="46460">
    <literal><![CDATA[
      (x \ L(y,z,u)) * a(a(y,z,u),x,x \ L(y,z,u)) = (a(u,z,y) * x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,45104,a,b,45148,a)].">
      <j1 rule="hyper" parents="64 45104 45148"/>
    </justification>
  </clause>

  <clause id="46462">
    <literal><![CDATA[
      a(x,y,z) \ a(x,u,w) = R(x,y,z) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,45484,a(flip),b,45182,a)].">
      <j1 rule="hyper" parents="64 45484 45182"/>
    </justification>
  </clause>

  <clause id="46463">
    <literal><![CDATA[
      (a(x,y,z) \ a(z,u,w)) * z = a(z,u,w) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(29954(a,1),45227(a,1,2))].">
      <j1 rule="para" parents="29954 45227"/>
    </justification>
  </clause>

  <clause id="46464">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(a(w,u,z),x,y) = a(x,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,43518,a(flip),b,45348,a),flip(a)].">
      <j1 rule="hyper" parents="64 43518 45348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46465">
    <literal><![CDATA[
      L(x,y,z) \ R(x,u,w) = a(x,u,w) * a(z,y,x)
    ]]></literal>
    <justification jstring="[para(45067(a,2),45407(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45067 45407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46466">
    <literal><![CDATA[
      (a(x,y,z) * a(z,y,x)) * u = R(x,y,z) * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(46465(a,1),32958(a,1,1))].">
      <j1 rule="para" parents="46465 32958"/>
    </justification>
  </clause>

  <clause id="46468">
    <literal><![CDATA[
      a(x,y,a(z,u,w) \ v5) = a(x,y,a(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[para(45221(a,1),45479(a,1,3))].">
      <j1 rule="para" parents="45221 45479"/>
    </justification>
  </clause>

  <clause id="46469">
    <literal><![CDATA[
      a(x,y,a(z,u,w) \ v5) = a(x,y,v5 * a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,46468,a),flip(a)].">
      <j1 rule="hyper" parents="373 27298 46468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46473">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * v5) = a(x,y,v5 * a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42537,a(flip),b,46469,a)].">
      <j1 rule="hyper" parents="64 42537 46469"/>
    </justification>
  </clause>

  <clause id="46474">
    <literal><![CDATA[
      a(x,y,z * a(u,w,v5)) = a(x,y,z * a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(27453,a,46473,a)].">
      <j1 rule="hyper" parents="27453 46473"/>
    </justification>
  </clause>

  <clause id="46479">
    <literal><![CDATA[
      L(x,a(y,z,u) * (a(u,z,y) * w),v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,45333,a(flip),b,45486,a)].">
      <j1 rule="hyper" parents="64 45333 45486"/>
    </justification>
  </clause>

  <clause id="46482">
    <literal><![CDATA[
      L(x * a(y,z,u),z,a(y,y,u)) = R(y,z,u) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,46263,a,b,45488,a)].">
      <j1 rule="hyper" parents="64 46263 45488"/>
    </justification>
  </clause>

  <clause id="46483">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(w,w,x)) = L(x,w,a(w,u,z)) \ y
    ]]></literal>
    <justification jstring="[hyper(2346,a,45499,a),flip(a)].">
      <j1 rule="hyper" parents="2346 45499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46484">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,y)) \ w) = w * a(z,u,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41469,a,b,45499,a)].">
      <j1 rule="hyper" parents="64 41469 45499"/>
    </justification>
  </clause>

  <clause id="46486">
    <literal><![CDATA[
      x * (a(x,y,a(z,u,y)) * w) = L(x,y,a(y,u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(64,a,43898,a(flip),b,45551,a)].">
      <j1 rule="hyper" parents="64 43898 45551"/>
    </justification>
  </clause>

  <clause id="46487">
    <literal><![CDATA[
      x * (y * a(z,u,a(x,w,w))) = L(x,w,a(w,u,z)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,43001,a(flip),b,45551,a)].">
      <j1 rule="hyper" parents="64 43001 45551"/>
    </justification>
  </clause>

  <clause id="46489">
    <literal><![CDATA[
      a(x,x,L(y \ 1,z,u) \ w) = a(x,x,L(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,45557,a),flip(a)].">
      <j1 rule="hyper" parents="373 27298 45557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46490">
    <literal><![CDATA[
      a(x,x,L(y * (z \ 1),u,w)) = a(x,x,L(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27624,a(flip),b,45558,a),flip(a)].">
      <j1 rule="hyper" parents="64 27624 45558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46493">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(137,a,45616,a(flip),b,45286,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 45616 45286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46495">
    <literal><![CDATA[
      a(L(x,y,z * y),u,z) = a(x,u,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,46280,a,b,46493,a)].">
      <j1 rule="hyper" parents="373 46280 46493"/>
    </justification>
  </clause>

  <clause id="46496">
    <literal><![CDATA[
      a(L(x,y,z),u,w) = a(x,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,46057,a,b,46493,a)].">
      <j1 rule="hyper" parents="373 46057 46493"/>
    </justification>
  </clause>

  <clause id="46497">
    <literal><![CDATA[
      x \ (y * R(y \ x,z,u)) = a(y * x,z,L(u,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,45478,a,b,46493,a)].">
      <j1 rule="hyper" parents="373 45478 46493"/>
    </justification>
  </clause>

  <clause id="46498">
    <literal><![CDATA[
      a(x,L(y,z,u),L(y,w,v5)) = a(x,y,L(L(y,w,v5),z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,44092,a,b,46493,a)].">
      <j1 rule="hyper" parents="373 44092 46493"/>
    </justification>
  </clause>

  <clause id="46500">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(z,y,x)) = a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,42687,a,b,46493,a)].">
      <j1 rule="hyper" parents="373 42687 46493"/>
    </justification>
  </clause>

  <clause id="46501">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,u,z) = a(w,u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,42683,a,b,46493,a)].">
      <j1 rule="hyper" parents="373 42683 46493"/>
    </justification>
  </clause>

  <clause id="46502">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,u,w) = a(z,u,L(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,42677,a,b,46493,a)].">
      <j1 rule="hyper" parents="373 42677 46493"/>
    </justification>
  </clause>

  <clause id="46503">
    <literal><![CDATA[
      a(x,y,z) * a(u,w,a(x,y,z)) = a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,42675,a,b,46493,a)].">
      <j1 rule="hyper" parents="373 42675 46493"/>
    </justification>
  </clause>

  <clause id="46504">
    <literal><![CDATA[
      x \ ((1 / x) \ a(y,z,u)) = a(y,z,L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,36310,a,b,46493,a)].">
      <j1 rule="hyper" parents="373 36310 46493"/>
    </justification>
  </clause>

  <clause id="46505">
    <literal><![CDATA[
      x \ (y \ ((y * x) * a(z,u,w))) = a(z,u,L(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,36297,a,b,46493,a)].">
      <j1 rule="hyper" parents="373 36297 46493"/>
    </justification>
  </clause>

  <clause id="46506">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) = R(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,28787,a,b,46493,a),flip(a)].">
      <j1 rule="hyper" parents="373 28787 46493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46507">
    <literal><![CDATA[
      x * (a(y,z,u) * (x \ 1)) = a(y,z,L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,23782,a,b,46493,a)].">
      <j1 rule="hyper" parents="373 23782 46493"/>
    </justification>
  </clause>

  <clause id="46508">
    <literal><![CDATA[
      a(x,y,L(z,x,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,45430,a(flip),b,46493,a),flip(a)].">
      <j1 rule="hyper" parents="373 45430 46493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46509">
    <literal><![CDATA[
      a(x,y,L(z,x,u)) = L(z,y,u \ (x \ u)) \ z
    ]]></literal>
    <justification jstring="[hyper(373,a,45300,a(flip),b,46493,a),flip(a)].">
      <j1 rule="hyper" parents="373 45300 46493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46510">
    <literal><![CDATA[
      a(L(x,y,y),z,z * y) = a(x,z,L(y * z,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,43634,a(flip),b,46493,a)].">
      <j1 rule="hyper" parents="373 43634 46493"/>
    </justification>
  </clause>

  <clause id="46511">
    <literal><![CDATA[
      a(x,y,L(z,u,u * a(x,y,z))) = u * ((a(x,y,z) \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,42523,a(flip),b,46493,a),flip(a)].">
      <j1 rule="hyper" parents="373 42523 46493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46512">
    <literal><![CDATA[
      a(x,y,L(z,u,u * z)) = L(a(x,y,z),u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,42329,a(flip),b,46493,a),flip(a)].">
      <j1 rule="hyper" parents="373 42329 46493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46513">
    <literal><![CDATA[
      a(x \ y,z,L(u,x * y,x)) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,41738,a(flip),b,46493,a),flip(a)].">
      <j1 rule="hyper" parents="373 41738 46493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46514">
    <literal><![CDATA[
      a(x \ (y \ x),z,u) = a(y,z,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,40754,a(flip),b,46493,a)].">
      <j1 rule="hyper" parents="373 40754 46493"/>
    </justification>
  </clause>

  <clause id="46515">
    <literal><![CDATA[
      a(x,y,L(L(y,z,u),y,w)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,39813,a(flip),b,46493,a),flip(a)].">
      <j1 rule="hyper" parents="373 39813 46493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46516">
    <literal><![CDATA[
      a(x,y,L(z,x,x * u)) = L(a(x,y,z),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,39254,a(flip),b,46493,a),flip(a)].">
      <j1 rule="hyper" parents="373 39254 46493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46517">
    <literal><![CDATA[
      a(x,y,L(z,x,y * z)) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,36298,a(flip),b,46493,a),flip(a)].">
      <j1 rule="hyper" parents="373 36298 46493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46519">
    <literal><![CDATA[
      a(x,y,L(z,u,L(x,w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,30884,a(flip),b,46493,a),flip(a)].">
      <j1 rule="hyper" parents="373 30884 46493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46521">
    <literal><![CDATA[
      x * a(y,z,L(u,x,x)) = (1 / x) \ a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,46493,a,b,36310,a)].">
      <j1 rule="hyper" parents="145 46493 36310"/>
    </justification>
  </clause>

  <clause id="46522">
    <literal><![CDATA[
      (x * y) * a(z,u,L(w,x,y)) = (x * a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(145,a,46493,a,b,28783,a)].">
      <j1 rule="hyper" parents="145 46493 28783"/>
    </justification>
  </clause>

  <clause id="46524">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * (u * w) = (u * a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[hyper(144,a,46493,a,b,28786,a)].">
      <j1 rule="hyper" parents="144 46493 28786"/>
    </justification>
  </clause>

  <clause id="46526">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,L(z,u,w)) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(139,a,46493,a,b,42687,a)].">
      <j1 rule="hyper" parents="139 46493 42687"/>
    </justification>
  </clause>

  <clause id="46527">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,L(z,u,w)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(139,a,46493,a,b,42675,a)].">
      <j1 rule="hyper" parents="139 46493 42675"/>
    </justification>
  </clause>

  <clause id="46528">
    <literal><![CDATA[
      (1 / x) \ a(y,z,L(u,x,x)) = x * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(139,a,46493,a,b,559,a)].">
      <j1 rule="hyper" parents="139 46493 559"/>
    </justification>
  </clause>

  <clause id="46529">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),v5,v6)) = L(a(x,y,L(z,v5,v6)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27702,a,b,46493,a)].">
      <j1 rule="hyper" parents="64 27702 46493"/>
    </justification>
  </clause>

  <clause id="46531">
    <literal><![CDATA[
      L(a(L(x,x,y),y,z),u,w) = x \ R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,41802,a(flip),b,46493,a),flip(a)].">
      <j1 rule="hyper" parents="64 41802 46493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46532">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),u,w) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,39064,a(flip),b,46493,a),flip(a)].">
      <j1 rule="hyper" parents="64 39064 46493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46534">
    <literal><![CDATA[
      L(a(x,y,L(z,y,u)),u * y,y) = L(a(x,y,z),L(y,u,y),y * u)
    ]]></literal>
    <justification jstring="[para(46493(a,2),35919(a,1,1))].">
      <j1 rule="para" parents="46493 35919"/>
    </justification>
  </clause>

  <clause id="46536">
    <literal><![CDATA[
      x \ (a(y,z,u) * (x * w)) = a(y,z,L(u,w,x)) * w
    ]]></literal>
    <justification jstring="[para(46493(a,2),36319(a,2,1))].">
      <j1 rule="para" parents="46493 36319"/>
    </justification>
  </clause>

  <clause id="46537">
    <literal><![CDATA[
      (a(x,y,L(z,u,w)) * u) * w = a(x,y,z) * (u * w)
    ]]></literal>
    <justification jstring="[para(46493(a,2),36321(a,1,1,1))].">
      <j1 rule="para" parents="46493 36321"/>
    </justification>
  </clause>

  <clause id="46538">
    <literal><![CDATA[
      (x * a(y,z,L(u,x,w))) * w = (x * w) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(46493(a,2),36376(a,1,1,2))].">
      <j1 rule="para" parents="46493 36376"/>
    </justification>
  </clause>

  <clause id="46540">
    <literal><![CDATA[
      (a(x,y,z) * u) * (u \ x) = x * a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[para(46493(a,2),40494(a,2,2))].">
      <j1 rule="para" parents="46493 40494"/>
    </justification>
  </clause>

  <clause id="46545">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,z) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(46493(a,2),42580(a,1,1))].">
      <j1 rule="para" parents="46493 42580"/>
    </justification>
  </clause>

  <clause id="46552">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,y,y))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(46493(a,2),42877(a,1,3))].">
      <j1 rule="para" parents="46493 42877"/>
    </justification>
  </clause>

  <clause id="46553">
    <literal><![CDATA[
      (a(x,y,L(z,u,w)) \ v5) \ (a(w,u,a(z,y,x)) * v5) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(46493(a,2),42945(a,1,1,1))].">
      <j1 rule="para" parents="46493 42945"/>
    </justification>
  </clause>

  <clause id="46554">
    <literal><![CDATA[
      x * (a(y,z,L(u,w,x)) \ w) = a(y,z,u) \ (x * w)
    ]]></literal>
    <justification jstring="[para(46493(a,2),42953(a,1,2,1))].">
      <j1 rule="para" parents="46493 42953"/>
    </justification>
  </clause>

  <clause id="46555">
    <literal><![CDATA[
      a(x,y,z) * (u * a(w,v5,a(x,y,z))) = u * a(x,y,L(z,v5,w))
    ]]></literal>
    <justification jstring="[para(46493(a,2),42956(a,2,2))].">
      <j1 rule="para" parents="46493 42956"/>
    </justification>
  </clause>

  <clause id="46556">
    <literal><![CDATA[
      a(x,y,z) * (u * a(a(x,y,z),w,v5)) = u * a(x,y,L(z,w,v5))
    ]]></literal>
    <justification jstring="[para(46493(a,2),42957(a,2,2))].">
      <j1 rule="para" parents="46493 42957"/>
    </justification>
  </clause>

  <clause id="46557">
    <literal><![CDATA[
      (x * a(y,z,u)) * a(w,v5,a(y,z,u)) = x * a(y,z,L(u,v5,w))
    ]]></literal>
    <justification jstring="[para(46493(a,2),42960(a,2,2))].">
      <j1 rule="para" parents="46493 42960"/>
    </justification>
  </clause>

  <clause id="46558">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * a(z,u,w)) = v5 * a(z,u,L(w,y,x))
    ]]></literal>
    <justification jstring="[para(46493(a,2),42963(a,2,2))].">
      <j1 rule="para" parents="46493 42963"/>
    </justification>
  </clause>

  <clause id="46559">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,z * (u \ w),z * (u \ w)))) = L(x,y,(z * (u * w)) * ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(46493(a,2),43307(a,1,3))].">
      <j1 rule="para" parents="46493 43307"/>
    </justification>
  </clause>

  <clause id="46561">
    <literal><![CDATA[
      L(x,L(y,z,u),a(y,w,v5)) = L(x,y,a(y,w,L(v5,z,u)))
    ]]></literal>
    <justification jstring="[para(46493(a,2),44096(a,2,3))].">
      <j1 rule="para" parents="46493 44096"/>
    </justification>
  </clause>

  <clause id="46562">
    <literal><![CDATA[
      L(L(x,y,z) \ x,u,w) = a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(45067(a,1),46493(a,2,1)),flip(a)].">
      <j1 rule="para" parents="45067 46493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46563">
    <literal><![CDATA[
      L(x,x,a(y,z,L(u,w,w))) = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(46493(a,2),45069(a,1,3))].">
      <j1 rule="para" parents="46493 45069"/>
    </justification>
  </clause>

  <clause id="46564">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,v5,x))) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(46493(a,2),46117(a,1,3))].">
      <j1 rule="para" parents="46493 46117"/>
    </justification>
  </clause>

  <clause id="46565">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,x))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(46493(a,2),46209(a,1,3))].">
      <j1 rule="para" parents="46493 46209"/>
    </justification>
  </clause>

  <clause id="46567">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) = L(a(x,y,a(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(46493(a,2),46493(a,1,3))].">
      <j1 rule="para" parents="46493 46493"/>
    </justification>
  </clause>

  <clause id="46568">
    <literal><![CDATA[
      a(x,y,T((x \ 1) \ (y \ z),u)) = a(x,y,(y * (x \ 1)) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,39075,a,b,46508,a)].">
      <j1 rule="hyper" parents="64 39075 46508"/>
    </justification>
  </clause>

  <clause id="46574">
    <literal><![CDATA[
      a(x * a(y,z,x),u,w) = a(x,u,L(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,45114,a,b,46496,a)].">
      <j1 rule="hyper" parents="64 45114 46496"/>
    </justification>
  </clause>

  <clause id="46576">
    <literal><![CDATA[
      a(R(x,y,z),u,w) = a(x,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,32590,a,b,46496,a)].">
      <j1 rule="hyper" parents="64 32590 46496"/>
    </justification>
  </clause>

  <clause id="46577">
    <literal><![CDATA[
      a((x * y) \ ((x * z) * y),u,w) = a(z,u,L(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32579,a,b,46496,a)].">
      <j1 rule="hyper" parents="64 32579 46496"/>
    </justification>
  </clause>

  <clause id="46578">
    <literal><![CDATA[
      a((x * (y \ 1)) * y,z,u) = a(x,z,L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,26878,a,b,46496,a)].">
      <j1 rule="hyper" parents="64 26878 46496"/>
    </justification>
  </clause>

  <clause id="46579">
    <literal><![CDATA[
      a((x * y) * y,z,u) = a(x,z,L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,26867,a,b,46496,a)].">
      <j1 rule="hyper" parents="64 26867 46496"/>
    </justification>
  </clause>

  <clause id="46580">
    <literal><![CDATA[
      a(x * (y * x),z,u) = a(y,z,L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,26861,a,b,46496,a)].">
      <j1 rule="hyper" parents="64 26861 46496"/>
    </justification>
  </clause>

  <clause id="46581">
    <literal><![CDATA[
      a((x * y) * x,z,u) = a(y,z,L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,26834,a,b,46496,a)].">
      <j1 rule="hyper" parents="64 26834 46496"/>
    </justification>
  </clause>

  <clause id="46582">
    <literal><![CDATA[
      a(x * (x * y),z,u) = a(y,z,L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,2640,a,b,46496,a)].">
      <j1 rule="hyper" parents="64 2640 46496"/>
    </justification>
  </clause>

  <clause id="46583">
    <literal><![CDATA[
      a(L(x,y,z),u,w * a(v5,v6,v7)) = a(x,u,L(a(v7,v6,v5) * w,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46473,a(flip),b,46496,a)].">
      <j1 rule="hyper" parents="64 46473 46496"/>
    </justification>
  </clause>

  <clause id="46585">
    <literal><![CDATA[
      a(x,y,L(z,u,L(x,w,v5) * u)) = a(L(x,u,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,43224,a(flip),b,46496,a),flip(a)].">
      <j1 rule="hyper" parents="64 43224 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46587">
    <literal><![CDATA[
      a(((x \ y) * z) \ y,u,y) = a(x \ z,u,L(y,x,x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42232,a(flip),b,46496,a)].">
      <j1 rule="hyper" parents="64 42232 46496"/>
    </justification>
  </clause>

  <clause id="46590">
    <literal><![CDATA[
      a(L(x,y,y) \ (y \ z),u,w) = a((y \ x) \ z,u,L(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41747,a(flip),b,46496,a)].">
      <j1 rule="hyper" parents="64 41747 46496"/>
    </justification>
  </clause>

  <clause id="46591">
    <literal><![CDATA[
      a(L(x,x,y),z,L(u,x * y,w)) = a((w * (x * y)) \ (w * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,36586,a(flip),b,46496,a),flip(a)].">
      <j1 rule="hyper" parents="64 36586 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46592">
    <literal><![CDATA[
      a(x * a(y,x,z),u,L(w,y,z)) = a(L(x,z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,35839,a(flip),b,46496,a),flip(a)].">
      <j1 rule="hyper" parents="64 35839 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46593">
    <literal><![CDATA[
      a(L(x,y,z),u,L(w,z,y)) = a(x * a(y,x,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,35829,a(flip),b,46496,a),flip(a)].">
      <j1 rule="hyper" parents="64 35829 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46594">
    <literal><![CDATA[
      a(L(x,y,z),u,L(w,z,y)) = a(x * a(z,x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,35828,a(flip),b,46496,a),flip(a)].">
      <j1 rule="hyper" parents="64 35828 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46595">
    <literal><![CDATA[
      a(x,y,L(z,u * x,u)) = a((x \ u) * u,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35814,a(flip),b,46496,a),flip(a)].">
      <j1 rule="hyper" parents="64 35814 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46596">
    <literal><![CDATA[
      a((x * y) \ z,u,L(w,x,y)) = a(x \ (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,34977,a(flip),b,46496,a),flip(a)].">
      <j1 rule="hyper" parents="64 34977 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46597">
    <literal><![CDATA[
      a(L(x * (y \ z),x,y),u,w) = a((x * y) \ z,u,L(w,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,34264,a(flip),b,46496,a)].">
      <j1 rule="hyper" parents="64 34264 46496"/>
    </justification>
  </clause>

  <clause id="46598">
    <literal><![CDATA[
      a(x * y,z,L(u,y,x)) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32861,a(flip),b,46496,a),flip(a)].">
      <j1 rule="hyper" parents="64 32861 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46599">
    <literal><![CDATA[
      a(x,y,L(z,x * u,x * u)) = a((x \ u) * u,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32736,a(flip),b,46496,a),flip(a)].">
      <j1 rule="hyper" parents="64 32736 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46600">
    <literal><![CDATA[
      a((x * y) \ z,u,L(w,x * y,y)) = a(L(x,y,y) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32695,a(flip),b,46496,a),flip(a)].">
      <j1 rule="hyper" parents="64 32695 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46601">
    <literal><![CDATA[
      a((x * y) \ L(z,x,x),u,w) = a(y \ (z * x),u,L(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,32682,a(flip),b,46496,a)].">
      <j1 rule="hyper" parents="64 32682 46496"/>
    </justification>
  </clause>

  <clause id="46603">
    <literal><![CDATA[
      a((x * y) \ (z * x),u,w) = a(y \ z,u,L(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,32480,a(flip),b,46496,a)].">
      <j1 rule="hyper" parents="64 32480 46496"/>
    </justification>
  </clause>

  <clause id="46604">
    <literal><![CDATA[
      a(x * y,z,L(u,y,y)) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30383,a(flip),b,46496,a),flip(a)].">
      <j1 rule="hyper" parents="64 30383 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46605">
    <literal><![CDATA[
      a(x * y,z,L(u,x,x)) = a(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,30382,a(flip),b,46496,a),flip(a)].">
      <j1 rule="hyper" parents="64 30382 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46607">
    <literal><![CDATA[
      a(x \ (y \ z),u,L(w,x,y)) = a((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(346(a,1),46496(a,1,1)),flip(a)].">
      <j1 rule="para" parents="346 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46608">
    <literal><![CDATA[
      a((x \ y) \ z,u,L(w,x \ y,x)) = a(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(630(a,1),46496(a,1,1)),flip(a)].">
      <j1 rule="para" parents="630 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46612">
    <literal><![CDATA[
      a(x,y,L(z,x,x * ((x \ u) * w))) = a(L(x,x,u * w),y,z)
    ]]></literal>
    <justification jstring="[para(34030(a,1),46496(a,1,1)),flip(a)].">
      <j1 rule="para" parents="34030 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46613">
    <literal><![CDATA[
      a((x \ y) \ z,u,L(w,x * y,x)) = a(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(41719(a,1),46496(a,1,1)),flip(a)].">
      <j1 rule="para" parents="41719 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46615">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) = a(x,y,a(w,u,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(46496(a,1),41883(a,1,3))].">
      <j1 rule="para" parents="46496 41883"/>
    </justification>
  </clause>

  <clause id="46617">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 * w))) = a(a(v5,u,L(z,w,w)),y,x)
    ]]></literal>
    <justification jstring="[para(46496(a,1),41860(a,2,1))].">
      <j1 rule="para" parents="46496 41860"/>
    </justification>
  </clause>

  <clause id="46618">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (w * v5))) = a(a(v5,u,L(z,w,w)),y,x)
    ]]></literal>
    <justification jstring="[para(46496(a,1),41861(a,2,1))].">
      <j1 rule="para" parents="46496 41861"/>
    </justification>
  </clause>

  <clause id="46619">
    <literal><![CDATA[
      L(x,y,a(z,u,w * (w * v5))) = L(x,y,a(v5,u,L(z,w,w)))
    ]]></literal>
    <justification jstring="[para(46496(a,1),42214(a,2,3))].">
      <j1 rule="para" parents="46496 42214"/>
    </justification>
  </clause>

  <clause id="46622">
    <literal><![CDATA[
      L(x,y,a(y,z,L(u,y,w))) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(46496(a,1),44099(a,1,3))].">
      <j1 rule="para" parents="46496 44099"/>
    </justification>
  </clause>

  <clause id="46623">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ z = L(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(46496(a,1),45065(a,2,1)),flip(a)].">
      <j1 rule="para" parents="46496 45065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46624">
    <literal><![CDATA[
      a(x,y,a(y,z,L(u,w,v5))) = a(y,y,a(u,z,L(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(46496(a,1),45358(a,2,3))].">
      <j1 rule="para" parents="46496 45358"/>
    </justification>
  </clause>

  <clause id="46625">
    <literal><![CDATA[
      a(x,y,a(y,z,L(u,w,v5))) = a(y,y,a(L(x,w,v5),z,u))
    ]]></literal>
    <justification jstring="[para(46496(a,2),45780(a,2,3))].">
      <j1 rule="para" parents="46496 45780"/>
    </justification>
  </clause>

  <clause id="46626">
    <literal><![CDATA[
      a(x,y,a(z,u,L(y,w,v5))) = a(x,u,a(y,y,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[para(46496(a,1),45827(a,1,3))].">
      <j1 rule="para" parents="46496 45827"/>
    </justification>
  </clause>

  <clause id="46627">
    <literal><![CDATA[
      a(x,y,L(z,u,L(w,v5,x))) = a(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(46117(a,1),46496(a,1,1)),flip(a)].">
      <j1 rule="para" parents="46117 46496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46628">
    <literal><![CDATA[
      a(a(L(x,y,z),u,w),v5,v6) = a(a(x,u,w),v5,L(v6,y,z))
    ]]></literal>
    <justification jstring="[para(46057(a,2),46496(a,1,1))].">
      <j1 rule="para" parents="46057 46496"/>
    </justification>
  </clause>

  <clause id="46629">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,v6)) = a(x,u,a(w,v5,L(v6,y,z)))
    ]]></literal>
    <justification jstring="[para(46493(a,2),46496(a,2,3))].">
      <j1 rule="para" parents="46493 46496"/>
    </justification>
  </clause>

  <clause id="46631">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) = a(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(46506(a,2),27644(a,1,3))].">
      <j1 rule="para" parents="46506 27644"/>
    </justification>
  </clause>

  <clause id="46632">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,v5,v6))) = L(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(46506(a,2),29203(a,1,3))].">
      <j1 rule="para" parents="46506 29203"/>
    </justification>
  </clause>

  <clause id="46637">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,L(x,v6,v7)))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(46493(a,2),46519(a,1,3))].">
      <j1 rule="para" parents="46493 46519"/>
    </justification>
  </clause>

  <clause id="46643">
    <literal><![CDATA[
      a(x \ (y \ x),z,(x * y) \ u) = a(y,z,y \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,39066,a(flip),b,46514,a),flip(a)].">
      <j1 rule="hyper" parents="373 39066 46514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46644">
    <literal><![CDATA[
      a(x,y,L(z,x,y * z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,45073,a,b,46517,a),flip(a)].">
      <j1 rule="hyper" parents="373 45073 46517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46645">
    <literal><![CDATA[
      a(x \ y,z,L(u,x,x)) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32389,a(flip),b,46579,a),flip(a)].">
      <j1 rule="hyper" parents="64 32389 46579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46646">
    <literal><![CDATA[
      a(x \ y,z,a(u,w,y)) = a(y * x,z,a(u,w,y))
    ]]></literal>
    <justification jstring="[para(33186(a,1),46598(a,1,3)),flip(a)].">
      <j1 rule="para" parents="33186 46598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46647">
    <literal><![CDATA[
      a(L(x,y,z) * u,w,L(R(x,v5,v6),u,x)) = a(u \ L(x,y,z),w,R(x,v5,v6))
    ]]></literal>
    <justification jstring="[para(35033(a,1),46598(a,1,3))].">
      <j1 rule="para" parents="35033 46598"/>
    </justification>
  </clause>

  <clause id="46648">
    <literal><![CDATA[
      a(x \ y,z,(x \ 1) \ u) = a(y * x,z,x * u)
    ]]></literal>
    <justification jstring="[para(1137(a,1),46604(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1137 46604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46649">
    <literal><![CDATA[
      a(x \ y,z,L(x,u,w)) = a(x * y,z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,34164,a(flip),b,46605,a),flip(a)].">
      <j1 rule="hyper" parents="64 34164 46605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46650">
    <literal><![CDATA[
      a(x \ y,z,a(u,w,x)) = a(x * y,z,a(u,w,x))
    ]]></literal>
    <justification jstring="[para(9435(a,1),46605(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9435 46605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46651">
    <literal><![CDATA[
      a(x * y,z,a(u,w,L(v5,x,x))) = a(x \ y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(46493(a,2),46605(a,1,3))].">
      <j1 rule="para" parents="46493 46605"/>
    </justification>
  </clause>

  <clause id="46652">
    <literal><![CDATA[
      a(x,y,L(L(z,u,u),x,u)) = a((x \ u) * u,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46514,a(flip),b,46645,a)].">
      <j1 rule="hyper" parents="64 46514 46645"/>
    </justification>
  </clause>

  <clause id="46653">
    <literal><![CDATA[
      a(x \ y,z,L(u,u * x,x)) = a(y * x,z,L(u,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,39946,a(flip),b,46645,a)].">
      <j1 rule="hyper" parents="64 39946 46645"/>
    </justification>
  </clause>

  <clause id="46654">
    <literal><![CDATA[
      a(x \ y,z,(x \ 1) \ u) = a(y * x,z,u * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,38945,a(flip),b,46645,a)].">
      <j1 rule="hyper" parents="64 38945 46645"/>
    </justification>
  </clause>

  <clause id="46655">
    <literal><![CDATA[
      a((x * y) \ z,u,(1 / (y / x)) * y) = a(z * (x * y),u,x)
    ]]></literal>
    <justification jstring="[para(34540(a,1),46645(a,1,3))].">
      <j1 rule="para" parents="34540 46645"/>
    </justification>
  </clause>

  <clause id="46657">
    <literal><![CDATA[
      a(x,y,L(z,u,u * z)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,46493,a,b,46512,a),flip(a)].">
      <j1 rule="hyper" parents="373 46493 46512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46658">
    <literal><![CDATA[
      a(x,y,L(z,x,x * u)) = a(x,y,L(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,46493,a,b,46516,a),flip(a)].">
      <j1 rule="hyper" parents="373 46493 46516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46662">
    <literal><![CDATA[
      a(x,y,L(z,z,L(u,w,v5))) \ z = L(z,y,L(x,L(z,w,v5),u))
    ]]></literal>
    <justification jstring="[para(39723(a,1),46623(a,1,1))].">
      <j1 rule="para" parents="39723 46623"/>
    </justification>
  </clause>

  <clause id="46664">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u)) = a(x,y,L(z \ u,z,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),46657(a,1,3,3))].">
      <j1 rule="para" parents="10 46657"/>
    </justification>
  </clause>

  <clause id="46666">
    <literal><![CDATA[
      a(x,y,L(z,(R(x,y,z) * y) * z,(R(x,y,z) * y) * z)) = ((a(x,y,z) / ((x * y) * z)) \ 1) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,43656,a(flip),b,46504,a),flip(a)].">
      <j1 rule="hyper" parents="64 43656 46504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46667">
    <literal><![CDATA[
      L(x,y,a(z \ (u \ z),w,v5)) = L(x,y,a(u,w,L(v5,u,z)))
    ]]></literal>
    <justification jstring="[para(46509(a,2),45169(a,1,3)),flip(a)].">
      <j1 rule="para" parents="46509 45169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46669">
    <literal><![CDATA[
      a(x,y,a(y \ z,u,w)) = a(x,y,a(z * y,u,w))
    ]]></literal>
    <justification jstring="[para(46604(a,1),46552(a,1,3))].">
      <j1 rule="para" parents="46604 46552"/>
    </justification>
  </clause>

  <clause id="46670">
    <literal><![CDATA[
      L(x,x,a(y \ z,u,w)) = L(x,x,a(y * z,u,w))
    ]]></literal>
    <justification jstring="[para(46605(a,1),46563(a,1,3))].">
      <j1 rule="para" parents="46605 46563"/>
    </justification>
  </clause>

  <clause id="46671">
    <literal><![CDATA[
      L(x,y,a(x \ z,u,w)) = L(x,y,a(x * z,u,w))
    ]]></literal>
    <justification jstring="[para(46605(a,1),46564(a,1,3))].">
      <j1 rule="para" parents="46605 46564"/>
    </justification>
  </clause>

  <clause id="46672">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * x) \ v5)) = a(x,y,a(z,u,w \ (x \ v5)))
    ]]></literal>
    <justification jstring="[para(39070(a,1),46565(a,1,3)),flip(a)].">
      <j1 rule="para" parents="39070 46565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46673">
    <literal><![CDATA[
      a(x,y,a(z \ x,u,w)) = a(x,y,a(x * z,u,w))
    ]]></literal>
    <justification jstring="[para(46598(a,1),46565(a,1,3))].">
      <j1 rule="para" parents="46598 46565"/>
    </justification>
  </clause>

  <clause id="46674">
    <literal><![CDATA[
      a((x \ y) * y,z,(y \ x) \ u) = a(x,z,x \ (y * u))
    ]]></literal>
    <justification jstring="[para(41719(a,1),46595(a,1,3)),flip(a)].">
      <j1 rule="para" parents="41719 46595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46675">
    <literal><![CDATA[
      a(x,y,L(z,u,L(w,v5,x))) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,46496,a(flip),b,46627,a),flip(a)].">
      <j1 rule="hyper" parents="373 46496 46627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46676">
    <literal><![CDATA[
      a(L(x,y,y),z,z * y) = a(x,z,z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,46297,a(flip),b,46510,a),flip(a)].">
      <j1 rule="hyper" parents="373 46297 46510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46677">
    <literal><![CDATA[
      a(x \ y,z,z * x) = a(x * y,z,z * x)
    ]]></literal>
    <justification jstring="[hyper(2694,a,46676,a),flip(a)].">
      <j1 rule="hyper" parents="2694 46676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46678">
    <literal><![CDATA[
      a(x,y,L(y * z,z,z)) = a(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46496,a(flip),b,46676,a)].">
      <j1 rule="hyper" parents="64 46496 46676"/>
    </justification>
  </clause>

  <clause id="46679">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ y) = a(x,y,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38945,a(flip),b,46678,a)].">
      <j1 rule="hyper" parents="64 38945 46678"/>
    </justification>
  </clause>

  <clause id="46680">
    <literal><![CDATA[
      a(x,y,y * (z \ 1)) = a(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27388,a(flip),b,46679,a),flip(a)].">
      <j1 rule="hyper" parents="64 27388 46679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46681">
    <literal><![CDATA[
      a(x,y,(z \ 1) * y) = a(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(27453,a,46680,a)].">
      <j1 rule="hyper" parents="27453 46680"/>
    </justification>
  </clause>

  <clause id="46682">
    <literal><![CDATA[
      a((x \ y) * y,z,L(u,x,y)) = a(x,z,L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,39065,a(flip),b,46652,a),flip(a)].">
      <j1 rule="hyper" parents="64 39065 46652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46684">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u)) = a(x,y,z \ L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,38999,a(flip),b,46664,a),flip(a)].">
      <j1 rule="hyper" parents="373 38999 46664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46686">
    <literal><![CDATA[
      a(x * (y \ x),z,L(u,y,x)) = a(y,z,L(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(26847,a,46682,a)].">
      <j1 rule="hyper" parents="26847 46682"/>
    </justification>
  </clause>

  <clause id="46687">
    <literal><![CDATA[
      a(x,y,L(z \ u,z,u)) = a(x,y,(z \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,13877,a(flip),b,46684,a),flip(a)].">
      <j1 rule="hyper" parents="373 13877 46684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46688">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) \ 1) = a(x,y,(u \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27656,a(flip),b,46687,a)].">
      <j1 rule="hyper" parents="64 27656 46687"/>
    </justification>
  </clause>

  <clause id="46689">
    <literal><![CDATA[
      a(x,y,((z \ u) \ 1) * z) = a(x,y,u \ (z * z))
    ]]></literal>
    <justification jstring="[para(630(a,1),46687(a,1,3)),flip(a)].">
      <j1 rule="para" parents="630 46687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46690">
    <literal><![CDATA[
      a(x * ((x * y) \ x),z,y \ (x * u)) = a(x * y,z,L((x \ y) \ u,x,x))
    ]]></literal>
    <justification jstring="[para(41719(a,1),46686(a,1,3))].">
      <j1 rule="para" parents="41719 46686"/>
    </justification>
  </clause>

  <clause id="46691">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (u \ (w * w))) = a(x,y,(u * z) \ (w * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,36197,a(flip),b,46688,a),flip(a)].">
      <j1 rule="hyper" parents="64 36197 46688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46693">
    <literal><![CDATA[
      a(x,y,((z \ u) \ 1) \ u) = a(x,y,z \ (u * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39101,a,b,46689,a)].">
      <j1 rule="hyper" parents="64 39101 46689"/>
    </justification>
  </clause>

  <clause id="46695">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (u * u)) = a(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27522,a(flip),b,46693,a),flip(a)].">
      <j1 rule="hyper" parents="64 27522 46693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46696">
    <literal><![CDATA[
      a(x,y,(z \ (u \ 1)) \ 1) = a(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27758,a,b,46695,a)].">
      <j1 rule="hyper" parents="64 27758 46695"/>
    </justification>
  </clause>

  <clause id="46697">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ (u \ 1)) = a(x,y,(z \ u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27622,a(flip),b,46695,a),flip(a)].">
      <j1 rule="hyper" parents="64 27622 46695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46700">
    <literal><![CDATA[
      a(x \ y,z,L((u \ 1) \ (w \ 1),x,x)) = a(y * x,z,(u \ w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,46645,a,b,46697,a)].">
      <j1 rule="hyper" parents="64 46645 46697"/>
    </justification>
  </clause>

  <clause id="46701">
    <literal><![CDATA[
      a(x \ y,z,(x \ u) \ 1) = a(y * x,z,(u \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,46654,a(flip),b,46697,a),flip(a)].">
      <j1 rule="hyper" parents="64 46654 46697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46702">
    <literal><![CDATA[
      a(x,y,((z \ (u * u)) \ w) \ 1) = a(x,y,(z \ (w \ 1)) * (u * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27763,a(flip),b,46697,a),flip(a)].">
      <j1 rule="hyper" parents="64 27763 46697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46708">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * a(v5,v6,a(z,y,L(x,u,w))) = a(x,y,L(L(z,u,w),v6,v5))
    ]]></literal>
    <justification jstring="[para(46496(a,1),46500(a,1,2,3))].">
      <j1 rule="para" parents="46496 46500"/>
    </justification>
  </clause>

  <clause id="46709">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * a(x,y,u) = a(x,y,L(u,z,z))
    ]]></literal>
    <justification jstring="[para(45807(a,2),46501(a,1,1))].">
      <j1 rule="para" parents="45807 46501"/>
    </justification>
  </clause>

  <clause id="46710">
    <literal><![CDATA[
      x \ (y \ ((y * a(z,u,w)) * x)) = a(z,u,L(L(w,y,x),x,y))
    ]]></literal>
    <justification jstring="[para(46522(a,1),46505(a,1,2,2))].">
      <j1 rule="para" parents="46522 46505"/>
    </justification>
  </clause>

  <clause id="46711">
    <literal><![CDATA[
      R(x,y,z) * a(u,w,a(z,y,x)) = R(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,46526,a(flip),b,46462,a(flip))].">
      <j1 rule="hyper" parents="145 46526 46462"/>
    </justification>
  </clause>

  <clause id="46712">
    <literal><![CDATA[
      a(x,y,z) \ R(x,y,L(z,u,w)) = x * a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(46526(a,1),45406(a,1,2)),flip(a)].">
      <j1 rule="para" parents="46526 45406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46714">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,w) = x \ R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(41802(a,1),46531(a,1,1))].">
      <j1 rule="para" parents="41802 46531"/>
    </justification>
  </clause>

  <clause id="46715">
    <literal><![CDATA[
      x * L(x \ R(x,y,z),u,w) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,46714,a,b,xx)].">
      <j1 rule="hyper" parents="145 46714"/>
    </justification>
  </clause>

  <clause id="46717">
    <literal><![CDATA[
      (x \ (a(y,z,u) * (x * w))) / w = a(y,z,L(u,w,x))
    ]]></literal>
    <justification jstring="[hyper(142,a,46536,a,b,xx)].">
      <j1 rule="hyper" parents="142 46536"/>
    </justification>
  </clause>

  <clause id="46718">
    <literal><![CDATA[
      (a(x,y,z) * u) * (u \ x) = R(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,45072,a,b,46540,a),flip(a)].">
      <j1 rule="hyper" parents="373 45072 46540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46723">
    <literal><![CDATA[
      R(x,y,L(z,u,w)) \ R(x,y,z) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46462,a(flip),b,46545,a)].">
      <j1 rule="hyper" parents="64 46462 46545"/>
    </justification>
  </clause>

  <clause id="46724">
    <literal><![CDATA[
      a(x,y,L(z,u,L(x,w,v5) * u)) = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,46496,a(flip),b,46585,a),flip(a)].">
      <j1 rule="hyper" parents="373 46496 46585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46725">
    <literal><![CDATA[
      a(x * a(y,x,z),u,L(w,y,z)) = a(x,u,L(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,46496,a(flip),b,46592,a),flip(a)].">
      <j1 rule="hyper" parents="373 46496 46592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46726">
    <literal><![CDATA[
      a(x * a(y,x,z),u,w) = a(x,u,L(L(w,z,y),y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46496,a(flip),b,46593,a),flip(a)].">
      <j1 rule="hyper" parents="64 46496 46593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46727">
    <literal><![CDATA[
      a(x * a(y,x,z),u,w) = a(x,u,L(L(w,y,z),z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46496,a(flip),b,46594,a),flip(a)].">
      <j1 rule="hyper" parents="64 46496 46594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46728">
    <literal><![CDATA[
      a((x * y) \ z,u,L(w,y,x)) = a(y \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(32451,a,46596,a)].">
      <j1 rule="hyper" parents="32451 46596"/>
    </justification>
  </clause>

  <clause id="46729">
    <literal><![CDATA[
      a((x * y) \ z,u,L(x,x * y,y)) = a(x \ (y \ z),u,L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,39947,a(flip),b,46596,a)].">
      <j1 rule="hyper" parents="64 39947 46596"/>
    </justification>
  </clause>

  <clause id="46730">
    <literal><![CDATA[
      a((x * y) \ z,u,L(y,w,v5)) = a(x \ (y \ z),u,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,34164,a(flip),b,46596,a)].">
      <j1 rule="hyper" parents="64 34164 46596"/>
    </justification>
  </clause>

  <clause id="46731">
    <literal><![CDATA[
      a((x * y) \ z,u,y \ ((x \ 1) \ y)) = a(x \ (y \ z),u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27692,a(flip),b,46596,a)].">
      <j1 rule="hyper" parents="64 27692 46596"/>
    </justification>
  </clause>

  <clause id="46732">
    <literal><![CDATA[
      a((x * y) \ z,u,(y * x) \ w) = a(x \ (y \ z),u,x \ (y \ w))
    ]]></literal>
    <justification jstring="[para(346(a,1),46596(a,1,3))].">
      <j1 rule="para" parents="346 46596"/>
    </justification>
  </clause>

  <clause id="46733">
    <literal><![CDATA[
      a(((x * y) * y) \ z,u,L(1 / x,y,y) \ 1) = a((x * y) \ (y \ z),u,L(x,x,y))
    ]]></literal>
    <justification jstring="[para(30856(a,1),46596(a,1,3))].">
      <j1 rule="para" parents="30856 46596"/>
    </justification>
  </clause>

  <clause id="46735">
    <literal><![CDATA[
      a(x,y,L(z,u * x,u * x)) = a((x \ u) * u,y,z)
    ]]></literal>
    <justification jstring="[para(29507(a,1),46599(a,1,3))].">
      <j1 rule="para" parents="29507 46599"/>
    </justification>
  </clause>

  <clause id="46736">
    <literal><![CDATA[
      a((x * (y * x)) \ (z * x),u,T(y,y \ x)) = a((y * x) \ z,u,((1 / x) * (y \ x)) \ 1)
    ]]></literal>
    <justification jstring="[para(45680(a,1),46603(a,2,3))].">
      <j1 rule="para" parents="45680 46603"/>
    </justification>
  </clause>

  <clause id="46737">
    <literal><![CDATA[
      a((x * y) \ z,u,L(x,w,v5)) = a(y \ (x \ z),u,L(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,34164,a(flip),b,46607,a),flip(a)].">
      <j1 rule="hyper" parents="64 34164 46607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46738">
    <literal><![CDATA[
      a(x,y,L(L(y,z,u),w,w)) = 1 * a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(45049(a,1),46709(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45049 46709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46740">
    <literal><![CDATA[
      a(x * a(y,x,z),u,L(w,z,y)) = a(x,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42342,a,b,46725,a)].">
      <j1 rule="hyper" parents="64 42342 46725"/>
    </justification>
  </clause>

  <clause id="46741">
    <literal><![CDATA[
      a(x * a(y,x,z),u,z) = a(x,u,L(z,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,13865,a(flip),b,46725,a)].">
      <j1 rule="hyper" parents="64 13865 46725"/>
    </justification>
  </clause>

  <clause id="46742">
    <literal><![CDATA[
      a(x * a(y,x,z),u,(z * y) \ w) = a(x,u,L(y \ (z \ w),z,y))
    ]]></literal>
    <justification jstring="[para(346(a,1),46725(a,1,3))].">
      <j1 rule="para" parents="346 46725"/>
    </justification>
  </clause>

  <clause id="46743">
    <literal><![CDATA[
      a(x \ (y \ ((y * z) * x)),u,w) = a(z,u,L(L(w,x,y),y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,33286,a,b,46726,a)].">
      <j1 rule="hyper" parents="64 33286 46726"/>
    </justification>
  </clause>

  <clause id="46744">
    <literal><![CDATA[
      a(x * a(y,x,a(z,u,w)),v5,v6) = a(x,v5,L(L(v6,y,a(z,u,w)),a(w,u,z),y))
    ]]></literal>
    <justification jstring="[para(41405(a,1),46726(a,2,3))].">
      <j1 rule="para" parents="41405 46726"/>
    </justification>
  </clause>

  <clause id="46745">
    <literal><![CDATA[
      a(x,a(y,x,z),L(L(u,y,z),z,y)) = a(x,a(y,x,z),a(y,x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,43413,a(flip),b,46727,a),flip(a)].">
      <j1 rule="hyper" parents="64 43413 46727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46746">
    <literal><![CDATA[
      a((x * y) \ z,u,x \ ((y \ 1) \ x)) = a(y \ (x \ z),u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27692,a(flip),b,46728,a)].">
      <j1 rule="hyper" parents="64 27692 46728"/>
    </justification>
  </clause>

  <clause id="46747">
    <literal><![CDATA[
      a((x \ y) * y,z,L(z,u,w)) = a(x,z,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(137,a,46738,a(flip),b,46735,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 46738 46735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46748">
    <literal><![CDATA[
      a(x \ y,z,L(z,u,w)) = a(y * x,z,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(137,a,46738,a(flip),b,46645,a(flip))].">
      <j1 rule="hyper" parents="137 46738 46645"/>
    </justification>
  </clause>

  <clause id="46749">
    <literal><![CDATA[
      a(x \ y,z,L(z,u,w)) = a(x * y,z,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(137,a,46738,a(flip),b,46605,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 46738 46605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46750">
    <literal><![CDATA[
      a(x,y * z,L((z \ 1) \ y,u,w)) = a(x,y * z,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(137,a,46738,a(flip),b,39084,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="137 46738 39084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46751">
    <literal><![CDATA[
      a((x * y) * (x * z),u,u) = a(y * z,u,L(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,45667,a(flip),b,46748,a)].">
      <j1 rule="hyper" parents="64 45667 46748"/>
    </justification>
  </clause>

  <clause id="46752">
    <literal><![CDATA[
      a((x * y) * (x * z),u,u) = a(z * y,u,L(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,45667,a(flip),b,46749,a)].">
      <j1 rule="hyper" parents="64 45667 46749"/>
    </justification>
  </clause>

  <clause id="46753">
    <literal><![CDATA[
      a((x * y) * z,u,L(u,x,y)) = a((y \ z) * x,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,45665,a(flip),b,46749,a),flip(a)].">
      <j1 rule="hyper" parents="64 45665 46749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46754">
    <literal><![CDATA[
      a(x * a(y,x,z),u,T((y * R(z,w,z)) \ v5,v6)) = a(x,u,L(T(R(z,w,z) \ (y \ v5),v6),y,z))
    ]]></literal>
    <justification jstring="[para(14174(a,1),46740(a,1,3))].">
      <j1 rule="para" parents="14174 46740"/>
    </justification>
  </clause>

  <clause id="46755">
    <literal><![CDATA[
      a((x * y) * (y * z),u,u) = a(x * z,u,L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32388,a,b,46751,a)].">
      <j1 rule="hyper" parents="64 32388 46751"/>
    </justification>
  </clause>

  <clause id="46756">
    <literal><![CDATA[
      a((a(x,y,y) \ z) * u,w,L(w,a(x,y,y) \ z,a(y,y,x))) = a(z * (a(y,y,x) * u),w,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,36061,a(flip),b,46752,a),flip(a)].">
      <j1 rule="hyper" parents="64 36061 46752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46757">
    <literal><![CDATA[
      a(((x \ y) * z) * (z * y),u,u) = a(x,u,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,46747,a(flip),b,46755,a),flip(a)].">
      <j1 rule="hyper" parents="373 46747 46755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46758">
    <literal><![CDATA[
      a(((x \ y) * z) * (y * z),u,u) = a(x,u,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(32448,a,46757,a)].">
      <j1 rule="hyper" parents="32448 46757"/>
    </justification>
  </clause>

  <clause id="46759">
    <literal><![CDATA[
      a(((x \ y) * z) * (y * z),u,u) = a(x,u * a(w,u,v5),L(u * a(w,u,v5),y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,44913,a(flip),b,46758,a)].">
      <j1 rule="hyper" parents="64 44913 46758"/>
    </justification>
  </clause>

  <clause id="46760">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ u),x,a(z,y,x)) = u * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,33478,a(flip),b,45647,a),flip(a)].">
      <j1 rule="hyper" parents="373 33478 45647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46761">
    <literal><![CDATA[
      a(x * a(y,y,z),y,L(z,a(y,y,z),x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46497,a(flip),b,45744,a)].">
      <j1 rule="hyper" parents="64 46497 45744"/>
    </justification>
  </clause>

  <clause id="46762">
    <literal><![CDATA[
      a(x * a(y,y,z),y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(45063(a,1),46761(a,1,3))].">
      <j1 rule="para" parents="45063 46761"/>
    </justification>
  </clause>

  <clause id="46763">
    <literal><![CDATA[
      a(x * (y * a(x,x,z)),x,z) = a(y * x,x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32511,a(flip),b,46762,a)].">
      <j1 rule="hyper" parents="64 32511 46762"/>
    </justification>
  </clause>

  <clause id="46764">
    <literal><![CDATA[
      L(x,y,z * a(y,y,x)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[para(46762(a,1),45065(a,2,1))].">
      <j1 rule="para" parents="46762 45065"/>
    </justification>
  </clause>

  <clause id="46765">
    <literal><![CDATA[
      L(x,y,z * a(y,y,x)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,45065,a,b,46764,a),flip(a)].">
      <j1 rule="hyper" parents="373 45065 46764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46766">
    <literal><![CDATA[
      a(R(x,x,y) * z,x,y) = a(z * x,x,y)
    ]]></literal>
    <justification jstring="[para(37594(a,1),46763(a,1,1))].">
      <j1 rule="para" parents="37594 46763"/>
    </justification>
  </clause>

  <clause id="46767">
    <literal><![CDATA[
      a(L(x,x,y) * z,x,y) = a(z * x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,34634,a(flip),b,46766,a)].">
      <j1 rule="hyper" parents="64 34634 46766"/>
    </justification>
  </clause>

  <clause id="46768">
    <literal><![CDATA[
      a(x * ((y * z) \ z),y,z) = a(x * y,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32737,a(flip),b,46766,a)].">
      <j1 rule="hyper" parents="64 32737 46766"/>
    </justification>
  </clause>

  <clause id="46769">
    <literal><![CDATA[
      a(x * (y \ (z \ y)),z,y) = a(x * z,z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32565,a(flip),b,46768,a)].">
      <j1 rule="hyper" parents="64 32565 46768"/>
    </justification>
  </clause>

  <clause id="46770">
    <literal><![CDATA[
      x * L(x \ L(x,y,z),u,w) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,46623,a(flip),b,45850,a),flip(a)].">
      <j1 rule="hyper" parents="373 46623 45850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46771">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) = x \ L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(139,a,46623,a(flip),b,45850,a),flip(a)].">
      <j1 rule="hyper" parents="139 46623 45850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46773">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,w) * x = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,23901,a,b,46770,a)].">
      <j1 rule="hyper" parents="64 23901 46770"/>
    </justification>
  </clause>

  <clause id="46775">
    <literal><![CDATA[
      L(x,y,L(z,u,L(x,w,v5))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,39214,a(flip),b,46771,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 39214 46771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46776">
    <literal><![CDATA[
      L(x,y,L(z,u,a(w,v5,x))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(39,a,36997,a(flip),b,46771,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="39 36997 46771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46778">
    <literal><![CDATA[
      L(x,y,z * a(u,z,a(w,v5,x))) = L(x,y,L(z,a(w,v5,x),u))
    ]]></literal>
    <justification jstring="[para(41867(a,1),46776(a,1,3)),flip(a)].">
      <j1 rule="para" parents="41867 46776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46779">
    <literal><![CDATA[
      (x * (L(x,y,z) \ 1)) * L(L(x,y,z),u,w) = L(x,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,43679,a,b,46773,a)].">
      <j1 rule="hyper" parents="64 43679 46773"/>
    </justification>
  </clause>

  <clause id="46780">
    <literal><![CDATA[
      (x / y) \ (a(z,u,y) \ x) = L(y,u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46454,a(flip),b,45851,a),flip(a)].">
      <j1 rule="hyper" parents="64 46454 45851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46782">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ (a(u,w,R(x,y,z)) \ x) = L(R(x,y,z),w,L(u,R(x,y,z),x))
    ]]></literal>
    <justification jstring="[para(2156(a,1),46780(a,1,1))].">
      <j1 rule="para" parents="2156 46780"/>
    </justification>
  </clause>

  <clause id="46783">
    <literal><![CDATA[
      L(x,x,a(y,z,(u * x) \ w)) = L(x,x,a(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,46017,a(flip),b,46023,a),flip(a)].">
      <j1 rule="hyper" parents="373 46017 46023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46784">
    <literal><![CDATA[
      L(L(x,y,z),a(x,u,w),v5) = L(L(x,y,z),x,a(w,u,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,30,a,b,46025,a),flip(a)].">
      <j1 rule="hyper" parents="373 30 46025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46786">
    <literal><![CDATA[
      a(x,y,z * L(z \ u,w,u)) = a(x,y,L(u,w,u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,31317,a(flip),b,46044,a)].">
      <j1 rule="hyper" parents="64 31317 46044"/>
    </justification>
  </clause>

  <clause id="46787">
    <literal><![CDATA[
      a(x,y,a(L(z,u,w),v5,v6)) = a(x,y,a(z,v5,L(v6,u,w)))
    ]]></literal>
    <justification jstring="[para(46493(a,2),46061(a,2,3))].">
      <j1 rule="para" parents="46493 46061"/>
    </justification>
  </clause>

  <clause id="46788">
    <literal><![CDATA[
      a(L((x * y) \ ((x * z) * y),u,w),v5,y * x) = a(((x * L(z,u,w)) * y) * (x * y),v5,x * y)
    ]]></literal>
    <justification jstring="[para(3182(a,2),46112(a,1,1))].">
      <j1 rule="para" parents="3182 46112"/>
    </justification>
  </clause>

  <clause id="46789">
    <literal><![CDATA[
      x * L(y,a(z,u,w),x * y) = L(x * y,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[hyper(145,a,46148,a(flip),b,31836,a)].">
      <j1 rule="hyper" parents="145 46148 31836"/>
    </justification>
  </clause>

  <clause id="46790">
    <literal><![CDATA[
      a(a(x,y,z),u,L(w,v5,x)) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,43009,a(flip),b,46163,a),flip(a)].">
      <j1 rule="hyper" parents="373 43009 46163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46791">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * L(x,v5,w) = L(L(x,v5,w),y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(46790(a,1),45092(a,1,1))].">
      <j1 rule="para" parents="46790 45092"/>
    </justification>
  </clause>

  <clause id="46792">
    <literal><![CDATA[
      x * (a(y,z,(u / w) \ 1) \ 1) = x * (w \ (u * L(u \ w,z,y)))
    ]]></literal>
    <justification jstring="[para(25708(a,1),46194(a,2,2))].">
      <j1 rule="para" parents="25708 46194"/>
    </justification>
  </clause>

  <clause id="46793">
    <literal><![CDATA[
      x * (a(y,z,z) * a(x,u,w)) = R(x,u,w) * a(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(145,a,46320,a(flip),b,1898,a)].">
      <j1 rule="hyper" parents="145 46320 1898"/>
    </justification>
  </clause>

  <clause id="46794">
    <literal><![CDATA[
      (x * y) * a(z,u,a(w,w,y)) = x * L(y,w,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,43892,a(flip),b,46330,a)].">
      <j1 rule="hyper" parents="64 43892 46330"/>
    </justification>
  </clause>

  <clause id="46797">
    <literal><![CDATA[
      (x / y) * a(z,z,a(y,u,w)) = x / L(y,z,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(45806(a,1),46331(a,1,2))].">
      <j1 rule="para" parents="45806 46331"/>
    </justification>
  </clause>

  <clause id="46799">
    <literal><![CDATA[
      a((x \ (y \ T(z,y))) * a(y,y,y \ T(z,y)),u,w) = a(x \ ((y * y) \ (z * y)),u,w)
    ]]></literal>
    <justification jstring="[para(521(a,1),46347(a,2,1,2))].">
      <j1 rule="para" parents="521 46347"/>
    </justification>
  </clause>

  <clause id="46800">
    <literal><![CDATA[
      a(x,y,z) \ ((a(u,w,x) \ a(x,y,z)) * x) = L(x,w,u)
    ]]></literal>
    <justification jstring="[hyper(720,a,46463,a)].">
      <j1 rule="hyper" parents="720 46463"/>
    </justification>
  </clause>

  <clause id="46801">
    <literal><![CDATA[
      L(x * a((x / y) * x,z,u),z,a((x / y) * x,(x / y) * x,u)) = R((x / y) * x,z,u) * T(y / x,y)
    ]]></literal>
    <justification jstring="[para(5149(a,2),46482(a,2,2))].">
      <j1 rule="para" parents="5149 46482"/>
    </justification>
  </clause>

  <clause id="46802">
    <literal><![CDATA[
      (x \ y) * a(z,z,a(x,u,w)) = L(x,z,a(z,u,w)) \ y
    ]]></literal>
    <justification jstring="[para(45807(a,1),46483(a,1,2))].">
      <j1 rule="para" parents="45807 46483"/>
    </justification>
  </clause>

  <clause id="46803">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(u,w,x)) = L(x,u,a(u,w,z)) \ y
    ]]></literal>
    <justification jstring="[para(45871(a,1),46483(a,1,2))].">
      <j1 rule="para" parents="45871 46483"/>
    </justification>
  </clause>

  <clause id="46804">
    <literal><![CDATA[
      x * (y * a(x,z,a(u,w,z))) = L(x,z,a(z,w,u)) * y
    ]]></literal>
    <justification jstring="[hyper(23185,a,46486,a)].">
      <j1 rule="hyper" parents="23185 46486"/>
    </justification>
  </clause>

  <clause id="46805">
    <literal><![CDATA[
      L(x * a(y,z,u),u,a(w,v5,u)) = L(x,u,a(u,v5,w)) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,44104,a(flip),b,46487,a)].">
      <j1 rule="hyper" parents="64 44104 46487"/>
    </justification>
  </clause>

  <clause id="46807">
    <literal><![CDATA[
      a(x,y * z,L(L(y * z,u,w),z,y)) = a(x,z \ y,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,32922,a(flip),b,46498,a),flip(a)].">
      <j1 rule="hyper" parents="64 32922 46498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46808">
    <literal><![CDATA[
      a(a(x,y,z),u,L(w,v5,v6)) = a(w,u,a(z,y,L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,46163,a,b,46567,a)].">
      <j1 rule="hyper" parents="373 46163 46567"/>
    </justification>
  </clause>

  <clause id="46809">
    <literal><![CDATA[
      L(a(x,y,a(z,z,L(u,w,v5))),v5 * w,v5) * L(w,v5,v5) = L(a(u,z,a(x,y,z)) * w,v5,v5)
    ]]></literal>
    <justification jstring="[para(46567(a,2),43966(a,1,1,1))].">
      <j1 rule="para" parents="46567 43966"/>
    </justification>
  </clause>

  <clause id="46810">
    <literal><![CDATA[
      L(a(x,y,a(y,z,L(u,w,v5))),v5 * w,v5) * L(w,v5,v5) = L(w * a(u,z,a(x,y,y)),v5,v5)
    ]]></literal>
    <justification jstring="[para(46567(a,2),43967(a,1,1,1))].">
      <j1 rule="para" parents="46567 43967"/>
    </justification>
  </clause>

  <clause id="46811">
    <literal><![CDATA[
      a(x,y,a(y,z,L(u,w,w))) = a(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,46311,a(flip),b,46624,a),flip(a)].">
      <j1 rule="hyper" parents="373 46311 46624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46812">
    <literal><![CDATA[
      a(x,y,a(z,u,L(y,w,w))) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46615,a,b,46811,a)].">
      <j1 rule="hyper" parents="64 46615 46811"/>
    </justification>
  </clause>

  <clause id="46813">
    <literal><![CDATA[
      a(x,y,L(y,z,L(u,w,w))) = a(x,y,y) * a(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,46811,a(flip),b,44036,a),flip(a)].">
      <j1 rule="hyper" parents="145 46811 44036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46814">
    <literal><![CDATA[
      a(x,y,a(z \ u,w,y)) = a(x,y,a(u * z,w,y))
    ]]></literal>
    <justification jstring="[para(46604(a,1),46812(a,1,3))].">
      <j1 rule="para" parents="46604 46812"/>
    </justification>
  </clause>

  <clause id="46815">
    <literal><![CDATA[
      a(x,y,a((x \ z) * u,u,y)) = a(x,y,a(z * (x * u),u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,44194,a(flip),b,46814,a)].">
      <j1 rule="hyper" parents="64 44194 46814"/>
    </justification>
  </clause>

  <clause id="46816">
    <literal><![CDATA[
      a(x,y,a(z,u,L(u,w,v5))) = a(z,u,a(u,y,L(x,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,45808,a,b,46625,a)].">
      <j1 rule="hyper" parents="373 45808 46625"/>
    </justification>
  </clause>

  <clause id="46817">
    <literal><![CDATA[
      a(a(x,y,L(z,u,w)),v5,v6) = a(a(z,y,x),v5,L(v6,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,41479,a,b,46628,a)].">
      <j1 rule="hyper" parents="64 41479 46628"/>
    </justification>
  </clause>

  <clause id="46819">
    <literal><![CDATA[
      a(x * (y * T(x \ 1,z)),u,a(w,w,L(v5,v6,v7))) = a(v5,w,a((L(y,v6,v7) * T(x \ 1,z)) * x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,43964,a(flip),b,46629,a),flip(a)].">
      <j1 rule="hyper" parents="64 43964 46629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46824">
    <literal><![CDATA[
      L(x,x,a(y,z,(x \ u) \ w)) = L(x,x,a(y,z,u \ w))
    ]]></literal>
    <justification jstring="[para(27396(a,1),46783(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27396 46783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46825">
    <literal><![CDATA[
      a(x,y,y) \ a(z,y,a(u,w,y)) = y \ L(L(y,y,x),y,a(u,w,z))
    ]]></literal>
    <justification jstring="[para(46784(a,1),44434(a,2,2))].">
      <j1 rule="para" parents="46784 44434"/>
    </justification>
  </clause>

  <clause id="46826">
    <literal><![CDATA[
      a(x,y,z * L(z \ u,w,u)) = a(x,y,L(u,w,z * u))
    ]]></literal>
    <justification jstring="[para(46133(a,1),46786(a,2,3))].">
      <j1 rule="para" parents="46133 46786"/>
    </justification>
  </clause>

  <clause id="46827">
    <literal><![CDATA[
      x * (a(x,y,z) * a(u,w,w)) = R(x,y,z) * a(u,w,w)
    ]]></literal>
    <justification jstring="[hyper(23185,a,46793,a)].">
      <j1 rule="hyper" parents="23185 46793"/>
    </justification>
  </clause>

  <clause id="46828">
    <literal><![CDATA[
      a(x,y,z) \ ((a(u * x,w,x) \ a(x,y,z)) * x) = L(x,w,x \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,46133,a,b,46800,a),flip(a)].">
      <j1 rule="hyper" parents="373 46133 46800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46830">
    <literal><![CDATA[
      a(a(x,y,z),u,w \ (v5 \ w)) = a(v5,u,a(x,y,L(z,v5,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,41507,a(flip),b,46808,a)].">
      <j1 rule="hyper" parents="64 41507 46808"/>
    </justification>
  </clause>

  <clause id="46831">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,x,v5))) * (x \ v5) = L(x,y,a(w,u,z)) \ v5
    ]]></literal>
    <justification jstring="[para(46808(a,1),46317(a,1,1))].">
      <j1 rule="para" parents="46808 46317"/>
    </justification>
  </clause>

  <clause id="46832">
    <literal><![CDATA[
      (1 / x) \ a(y,z,a(u,w,L(v5,x,x))) = x * a(a(v5,w,u),z,y)
    ]]></literal>
    <justification jstring="[para(46808(a,1),46528(a,1,2))].">
      <j1 rule="para" parents="46808 46528"/>
    </justification>
  </clause>

  <clause id="46833">
    <literal><![CDATA[
      a(x,x,a(L(y,z,u),w,L(v5,v6,v6))) = a(y,w,a(v5,x,L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,46312,a,b,46816,a)].">
      <j1 rule="hyper" parents="373 46312 46816"/>
    </justification>
  </clause>

  <clause id="46834">
    <literal><![CDATA[
      a(x,y,y \ (R(x,x,y) \ z)) = a(x,y,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,45073,a,b,45435,a),flip(a)].">
      <j1 rule="hyper" parents="373 45073 45435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46835">
    <literal><![CDATA[
      a(x,y,y \ (x \ (z * (x * y)))) = a(x,y,a(x,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42656,a(flip),b,46834,a),flip(a)].">
      <j1 rule="hyper" parents="64 42656 46834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46836">
    <literal><![CDATA[
      a((x \ y) * z,u,L(u,x * y,x)) = a((x * z) * y,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46749,a(flip),b,45664,a)].">
      <j1 rule="hyper" parents="64 46749 45664"/>
    </justification>
  </clause>

  <clause id="46837">
    <literal><![CDATA[
      a(x * y,z,L(z,u,x * u)) = a(((u \ x) \ y) * u,z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46749,a(flip),b,45666,a)].">
      <j1 rule="hyper" parents="64 46749 45666"/>
    </justification>
  </clause>

  <clause id="46838">
    <literal><![CDATA[
      L(x,y,(y \ x) * z) = L(x,y,(x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46765,a(flip),b,45727,a)].">
      <j1 rule="hyper" parents="64 46765 45727"/>
    </justification>
  </clause>

  <clause id="46839">
    <literal><![CDATA[
      L(x,y,(y \ x) * (z \ u)) = L(x,y,(u / z) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,29076,a,b,46838,a),flip(a)].">
      <j1 rule="hyper" parents="373 29076 46838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46840">
    <literal><![CDATA[
      a((x \ y) * z,x,y) = a((y * x) * z,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46762,a(flip),b,45728,a)].">
      <j1 rule="hyper" parents="64 46762 45728"/>
    </justification>
  </clause>

  <clause id="46841">
    <literal><![CDATA[
      a((x \ y) * z,x,y) = a(x * (y \ z),x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,45288,a(flip),b,46840,a),flip(a)].">
      <j1 rule="hyper" parents="373 45288 46840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46842">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * L(z,u,w) = L(z * a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,23910,a(flip),b,45960,a),flip(a)].">
      <j1 rule="hyper" parents="373 23910 45960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46843">
    <literal><![CDATA[
      a((x \ y) * z,y,L(x,x,z)) = a((x \ y) * z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27599,a(flip),b,46192,a)].">
      <j1 rule="hyper" parents="64 27599 46192"/>
    </justification>
  </clause>

  <clause id="46844">
    <literal><![CDATA[
      a(x,y,L(z,x,x) \ (x * u)) = a(x,y,z \ ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,46223,a(flip),b,46232,a),flip(a)].">
      <j1 rule="hyper" parents="373 46223 46232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46846">
    <literal><![CDATA[
      a(x,x,(y * (z \ u)) \ (y * u)) = a(x,x,L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,45492,a(flip),b,46329,a)].">
      <j1 rule="hyper" parents="64 45492 46329"/>
    </justification>
  </clause>

  <clause id="46847">
    <literal><![CDATA[
      a(x,x,L(y,z * y,u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,45708,a,b,46846,a)].">
      <j1 rule="hyper" parents="64 45708 46846"/>
    </justification>
  </clause>

  <clause id="46848">
    <literal><![CDATA[
      a(x,x,L(y,y * z,u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29739,a,b,46847,a)].">
      <j1 rule="hyper" parents="64 29739 46847"/>
    </justification>
  </clause>

  <clause id="46849">
    <literal><![CDATA[
      a(x,x,y) \ a(x,x,L(y,z,u)) = a(u,z * y,a(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(139,a,46847,a(flip),b,46500,a)].">
      <j1 rule="hyper" parents="139 46847 46500"/>
    </justification>
  </clause>

  <clause id="46850">
    <literal><![CDATA[
      (a(x,x,L(y,z,u)) * (y * z)) * u = a(x,x,y) * ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(46848(a,1),46537(a,1,1,1))].">
      <j1 rule="para" parents="46848 46537"/>
    </justification>
  </clause>

  <clause id="46851">
    <literal><![CDATA[
      a(((x \ y) * z) \ y,u,y) = a(x \ z,u,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,46657,a(flip),b,46587,a),flip(a)].">
      <j1 rule="hyper" parents="373 46657 46587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46852">
    <literal><![CDATA[
      a(((x \ y) * z) \ y,u,y) = a(z * x,u,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,46645,a(flip),b,46851,a),flip(a)].">
      <j1 rule="hyper" parents="373 46645 46851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46853">
    <literal><![CDATA[
      a(((x \ y) * z) * y,u,y) = a(z * x,u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46083,a(flip),b,46852,a)].">
      <j1 rule="hyper" parents="64 46083 46852"/>
    </justification>
  </clause>

  <clause id="46854">
    <literal><![CDATA[
      a(((x \ T(y,z)) * u) * T(y,z),w,y) = a(u * x,w,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(27584,a,46853,a)].">
      <j1 rule="hyper" parents="27584 46853"/>
    </justification>
  </clause>

  <clause id="46855">
    <literal><![CDATA[
      a(x * ((y \ x) * z),u,x) = a(z * y,u,x)
    ]]></literal>
    <justification jstring="[hyper(26847,a,46853,a)].">
      <j1 rule="hyper" parents="26847 46853"/>
    </justification>
  </clause>

  <clause id="46856">
    <literal><![CDATA[
      a(((x * K(y \ 1,y)) * z) * (y \ K(u,y)),w,y \ K(u,y)) = a(z * ((1 / T(y,u)) / x),w,y \ K(u,y))
    ]]></literal>
    <justification jstring="[para(24277(a,1),46853(a,1,1,1,1))].">
      <j1 rule="para" parents="24277 46853"/>
    </justification>
  </clause>

  <clause id="46857">
    <literal><![CDATA[
      a((T(x,y) * (z \ u)) * u,w,u) = a(x * z,w,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32552,a,b,46855,a)].">
      <j1 rule="hyper" parents="64 32552 46855"/>
    </justification>
  </clause>

  <clause id="46858">
    <literal><![CDATA[
      a((x * y) * z,u,z) = a(y * (x \ z),u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32575,a(flip),b,46855,a)].">
      <j1 rule="hyper" parents="64 32575 46855"/>
    </justification>
  </clause>

  <clause id="46859">
    <literal><![CDATA[
      a(x * (y \ z),u,z) = a(z * (y * x),u,z)
    ]]></literal>
    <justification jstring="[hyper(26847,a,46858,a),flip(a)].">
      <j1 rule="hyper" parents="26847 46858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46860">
    <literal><![CDATA[
      a(x * (y \ z),u,z) = a(z * (x * y),u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32422,a(flip),b,46858,a),flip(a)].">
      <j1 rule="hyper" parents="64 32422 46858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46861">
    <literal><![CDATA[
      a(((x \ 1) * y) * R(z,x,x \ 1),u,R(z,x,x \ 1)) = a(y * T(z * x,x \ 1),u,R(z,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(698(a,1),46858(a,2,1,2))].">
      <j1 rule="para" parents="698 46858"/>
    </justification>
  </clause>

  <clause id="46862">
    <literal><![CDATA[
      a(x,y,a(z * (u \ w),v5,w)) = a(x,y,a(w,v5,w * (u * z)))
    ]]></literal>
    <justification jstring="[para(46858(a,1),41897(a,1,3))].">
      <j1 rule="para" parents="46858 41897"/>
    </justification>
  </clause>

  <clause id="46863">
    <literal><![CDATA[
      a(x * (T(y \ z,y) \ ((y \ z) \ z)),u,(y \ z) \ z) = a(y * ((y \ z) * x),u,(y \ z) \ z)
    ]]></literal>
    <justification jstring="[para(5025(a,1),46859(a,2,1))].">
      <j1 rule="para" parents="5025 46859"/>
    </justification>
  </clause>

  <clause id="46864">
    <literal><![CDATA[
      a((x \ y) * (T(z,u) \ y),w,y) = a(z * x,w,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46858,a(flip),b,46857,a)].">
      <j1 rule="hyper" parents="64 46858 46857"/>
    </justification>
  </clause>

  <clause id="46865">
    <literal><![CDATA[
      a((x \ y) * (z \ y),u,y) = a(x * z,u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32524,a(flip),b,46864,a)].">
      <j1 rule="hyper" parents="64 32524 46864"/>
    </justification>
  </clause>

  <clause id="46866">
    <literal><![CDATA[
      a((x \ y) * z,u,y) = a(x * (z \ y),u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32384,a(flip),b,46865,a),flip(a)].">
      <j1 rule="hyper" parents="64 32384 46865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46867">
    <literal><![CDATA[
      a((x \ y) \ z,u,w \ (x \ w)) = a(y \ (x * z),u,w \ (x \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,35046,a(flip),b,46608,a)].">
      <j1 rule="hyper" parents="64 35046 46608"/>
    </justification>
  </clause>

  <clause id="46868">
    <literal><![CDATA[
      L(x,y,a((x \ z) \ u,w,v5)) = L(x,y,a(z \ (x * u),w,v5))
    ]]></literal>
    <justification jstring="[para(46608(a,1),46564(a,1,3)),flip(a)].">
      <j1 rule="para" parents="46608 46564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46869">
    <literal><![CDATA[
      a((x \ y) \ z,u,(x * (y \ x)) \ x) = a(y \ (x * z),u,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(39161(a,1),46613(a,1,3))].">
      <j1 rule="para" parents="39161 46613"/>
    </justification>
  </clause>

  <clause id="46870">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 * w))) = a(a(z,u,v5),y,L(x,w,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,46817,a(flip),b,46617,a),flip(a)].">
      <j1 rule="hyper" parents="373 46817 46617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46871">
    <literal><![CDATA[
      a(x,y,a(x,x,y) * z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42076,a(flip),b,46835,a),flip(a)].">
      <j1 rule="hyper" parents="64 42076 46835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46872">
    <literal><![CDATA[
      a(x,y,L(y,x,x) \ z) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(44978(a,1),46871(a,1,3))].">
      <j1 rule="para" parents="44978 46871"/>
    </justification>
  </clause>

  <clause id="46873">
    <literal><![CDATA[
      a(R(x \ 1,x,y) * z,u,L(u,y,x \ y)) = a(((y \ R(x \ 1,x,y)) \ z) * y,u,u)
    ]]></literal>
    <justification jstring="[para(2998(a,1),46837(a,1,3,3))].">
      <j1 rule="para" parents="2998 46837"/>
    </justification>
  </clause>

  <clause id="46874">
    <literal><![CDATA[
      a(T(x,y) * z,u,L(u,w,x * w)) = a(((w \ T(x,y)) \ z) * w,u,u)
    ]]></literal>
    <justification jstring="[para(28978(a,1),46837(a,1,3))].">
      <j1 rule="para" parents="28978 46837"/>
    </justification>
  </clause>

  <clause id="46875">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,(y / x) / (1 / x),L(x,x,y) * ((y / x) / (1 / x)))) = a(((y \ x) \ z) * ((y / x) / (1 / x)),u,u)
    ]]></literal>
    <justification jstring="[para(30705(a,1),46837(a,2,1,1,1))].">
      <j1 rule="para" parents="30705 46837"/>
    </justification>
  </clause>

  <clause id="46877">
    <literal><![CDATA[
      L(x * a(y,z,x),u,y) = a(y,z,x) * L(x,u,y)
    ]]></literal>
    <justification jstring="[para(46209(a,1),46842(a,1,1)),flip(a)].">
      <j1 rule="para" parents="46209 46842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46878">
    <literal><![CDATA[
      L(x * a(y,z,x),u,y) = L(x,u,y) * a(y,z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,23183,a,b,46877,a),flip(a)].">
      <j1 rule="hyper" parents="373 23183 46877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46879">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * L(z * a(x,u,z),y,x)) = L(a(x,u,z),L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(46878(a,2),601(a,1,2,2))].">
      <j1 rule="para" parents="46878 601"/>
    </justification>
  </clause>

  <clause id="46881">
    <literal><![CDATA[
      a(x,y,y \ ((x \ 1) \ z)) = a(x,y,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46872,a(flip),b,46844,a),flip(a)].">
      <j1 rule="hyper" parents="64 46872 46844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46882">
    <literal><![CDATA[
      a(x,y * z,a(z,u,u)) = a(z,u,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,43878,a(flip),b,46849,a),flip(a)].">
      <j1 rule="hyper" parents="64 43878 46849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46883">
    <literal><![CDATA[
      a(x,y * z,a(y,u,u)) = a(y,u,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(32008,a,46882,a)].">
      <j1 rule="hyper" parents="32008 46882"/>
    </justification>
  </clause>

  <clause id="46884">
    <literal><![CDATA[
      a(x,y * x,a(z,u,u)) = a(x,u,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,45889,a,b,46882,a)].">
      <j1 rule="hyper" parents="64 45889 46882"/>
    </justification>
  </clause>

  <clause id="46885">
    <literal><![CDATA[
      a(x,y * x,a(z,z,u)) = a(x,z,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,45890,a(flip),b,46882,a)].">
      <j1 rule="hyper" parents="64 45890 46882"/>
    </justification>
  </clause>

  <clause id="46886">
    <literal><![CDATA[
      a(x,x,a(y,y * z,u)) = a(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,45887,a(flip),b,46882,a)].">
      <j1 rule="hyper" parents="64 45887 46882"/>
    </justification>
  </clause>

  <clause id="46887">
    <literal><![CDATA[
      a(x,y,a(y,z * u,u)) = a(u,y,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,45877,a(flip),b,46882,a)].">
      <j1 rule="hyper" parents="64 45877 46882"/>
    </justification>
  </clause>

  <clause id="46888">
    <literal><![CDATA[
      a(x,x,a(y,z * y,u)) = a(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,45803,a(flip),b,46882,a)].">
      <j1 rule="hyper" parents="64 45803 46882"/>
    </justification>
  </clause>

  <clause id="46889">
    <literal><![CDATA[
      a(x,y,a(z,u * x,y)) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,43873,a(flip),b,46882,a)].">
      <j1 rule="hyper" parents="64 43873 46882"/>
    </justification>
  </clause>

  <clause id="46890">
    <literal><![CDATA[
      a(x,x,a(y,z * u,z)) = a(z,x,a(y,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,45784,a(flip),b,46883,a)].">
      <j1 rule="hyper" parents="64 45784 46883"/>
    </justification>
  </clause>

  <clause id="46891">
    <literal><![CDATA[
      a(x,y,a(y,x * z,u)) = a(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,43895,a(flip),b,46883,a)].">
      <j1 rule="hyper" parents="64 43895 46883"/>
    </justification>
  </clause>

  <clause id="46892">
    <literal><![CDATA[
      a(x,y,L(y,z * u,u)) = a(x,y,y) * a(u,y,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,46884,a(flip),b,46527,a),flip(a)].">
      <j1 rule="hyper" parents="145 46884 46527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46893">
    <literal><![CDATA[
      L(x,y * x,a(z,u,u)) = x * a(x,u,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,46884,a(flip),b,45194,a),flip(a)].">
      <j1 rule="hyper" parents="145 46884 45194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46894">
    <literal><![CDATA[
      a(L(x,y,z),(z * (y * x)) * x,a(u,w,w)) = a(L(x,y,z),w,a(u,(z * y) * x,w))
    ]]></literal>
    <justification jstring="[para(3198(a,1),46884(a,1,2))].">
      <j1 rule="para" parents="3198 46884"/>
    </justification>
  </clause>

  <clause id="46895">
    <literal><![CDATA[
      a(x,x,L(y,z * u,u)) = a(u,x,a(y,z,x)) * a(x,x,y)
    ]]></literal>
    <justification jstring="[para(46884(a,1),40874(a,1,1)),flip(a)].">
      <j1 rule="para" parents="46884 40874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46896">
    <literal><![CDATA[
      a(x,y,a(z,u * x,L(y,w,v5))) = a(x,y,a(L(z,w,v5),u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46626,a,b,46885,a)].">
      <j1 rule="hyper" parents="64 46626 46885"/>
    </justification>
  </clause>

  <clause id="46897">
    <literal><![CDATA[
      a(x,y,a(z,u \ x,y)) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,45902,a,b,46886,a)].">
      <j1 rule="hyper" parents="64 45902 46886"/>
    </justification>
  </clause>

  <clause id="46898">
    <literal><![CDATA[
      a(x,y,a(L((z \ 1) * (u * z),w,v5),v6,y)) = a(y,y,a(x,x * v6,L(L(u,z,z),w,v5)))
    ]]></literal>
    <justification jstring="[para(27792(a,1),46886(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27792 46886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46899">
    <literal><![CDATA[
      a(x \ y,z,a(u,y,z)) = a(z,z,a(y * x,x,u))
    ]]></literal>
    <justification jstring="[para(41838(a,1),46886(a,1,3)),flip(a)].">
      <j1 rule="para" parents="41838 46886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46900">
    <literal><![CDATA[
      a(x,x,a(y,z \ (u \ ((u * y) * z)),w)) = a(y,x,a(w,a(u,y,z),x))
    ]]></literal>
    <justification jstring="[para(33294(a,2),46888(a,1,3))].">
      <j1 rule="para" parents="33294 46888"/>
    </justification>
  </clause>

  <clause id="46901">
    <literal><![CDATA[
      L(x,y * x,a(z,u,u)) = L(x,u,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,45190,a(flip),b,46893,a),flip(a)].">
      <j1 rule="hyper" parents="373 45190 46893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46902">
    <literal><![CDATA[
      L(x,x * y,a(z,u,u)) = L(x,u,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(29572,a,46901,a)].">
      <j1 rule="hyper" parents="29572 46901"/>
    </justification>
  </clause>

  <clause id="46903">
    <literal><![CDATA[
      (a(x,y,y) * ((a(x,y,y) \ z) / u)) \ z = L(u,y,a(x,a(x,y,y) \ z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,45707,a(flip),b,46901,a)].">
      <j1 rule="hyper" parents="64 45707 46901"/>
    </justification>
  </clause>

  <clause id="46904">
    <literal><![CDATA[
      L(x,x * y,a(z,z,u)) = L(x,z,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29513,a(flip),b,46901,a)].">
      <j1 rule="hyper" parents="64 29513 46901"/>
    </justification>
  </clause>

  <clause id="46905">
    <literal><![CDATA[
      L(x,y,a(y,x * z,u)) = L(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46267,a(flip),b,46902,a)].">
      <j1 rule="hyper" parents="64 46267 46902"/>
    </justification>
  </clause>

  <clause id="46906">
    <literal><![CDATA[
      a(x * y,z,a(u,y,z)) = a(z,z,a(y * x,x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46425,a(flip),b,46899,a)].">
      <j1 rule="hyper" parents="64 46425 46899"/>
    </justification>
  </clause>

  <clause id="46907">
    <literal><![CDATA[
      a(x * y,z,a(u,x,z)) = a(z,z,a(x * y,y,u))
    ]]></literal>
    <justification jstring="[hyper(26847,a,46906,a)].">
      <j1 rule="hyper" parents="26847 46906"/>
    </justification>
  </clause>

  <clause id="46908">
    <literal><![CDATA[
      a(x * y,z,a(u,y,z)) = a(z,z,a(x * y,x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,26881,a,b,46906,a),flip(a)].">
      <j1 rule="hyper" parents="373 26881 46906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46909">
    <literal><![CDATA[
      a(x * y,z,a(z,x,u)) = a(z,z,a(x * y,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,41890,a,b,46906,a)].">
      <j1 rule="hyper" parents="64 41890 46906"/>
    </justification>
  </clause>

  <clause id="46910">
    <literal><![CDATA[
      a(x * y,x,a(z,z,u)) = a(z,z,a(x * y,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,45910,a(flip),b,46906,a)].">
      <j1 rule="hyper" parents="64 45910 46906"/>
    </justification>
  </clause>

  <clause id="46911">
    <literal><![CDATA[
      a(x * y,y,a(z,z,u)) = a(z,z,a(y * x,x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,45827,a(flip),b,46906,a)].">
      <j1 rule="hyper" parents="64 45827 46906"/>
    </justification>
  </clause>

  <clause id="46912">
    <literal><![CDATA[
      a(x,y,a(z,z,u * y)) = a(z,z,a(y * u,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,43881,a(flip),b,46906,a)].">
      <j1 rule="hyper" parents="64 43881 46906"/>
    </justification>
  </clause>

  <clause id="46913">
    <literal><![CDATA[
      a(x,x,a(y * z,z,u)) = a(x,x,a(y * z,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,45806,a(flip),b,46907,a),flip(a)].">
      <j1 rule="hyper" parents="64 45806 46907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46914">
    <literal><![CDATA[
      a(x,y,a(z,z,y * u)) = a(z,z,a(y * u,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,43881,a(flip),b,46907,a)].">
      <j1 rule="hyper" parents="64 43881 46907"/>
    </justification>
  </clause>

  <clause id="46915">
    <literal><![CDATA[
      a(x * y,z,a(u,y,z)) = a(u,x,a(z,z,x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,45807,a,b,46908,a),flip(a)].">
      <j1 rule="hyper" parents="373 45807 46908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46916">
    <literal><![CDATA[
      a(x * y,z,a(z,x,u)) = a(z,z,a(y * x,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,41890,a,b,46908,a)].">
      <j1 rule="hyper" parents="64 41890 46908"/>
    </justification>
  </clause>

  <clause id="46917">
    <literal><![CDATA[
      a(x * y,z,a(z,x,u)) = a(u,y,a(z,z,x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,45807,a,b,46909,a),flip(a)].">
      <j1 rule="hyper" parents="373 45807 46909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46918">
    <literal><![CDATA[
      a(x,y,a(z * u,z,y)) = a(y,y,a(z * u,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,43881,a,b,46910,a)].">
      <j1 rule="hyper" parents="64 43881 46910"/>
    </justification>
  </clause>

  <clause id="46919">
    <literal><![CDATA[
      a(x * y,z,a(z,y,u)) = a(u,x,a(z,z,x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,45780,a,b,46914,a)].">
      <j1 rule="hyper" parents="373 45780 46914"/>
    </justification>
  </clause>

  <clause id="46920">
    <literal><![CDATA[
      a(x,y,a(z,z,y * u)) = a(x,z,a(z,u,u * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46379,a(flip),b,46915,a),flip(a)].">
      <j1 rule="hyper" parents="64 46379 46915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46921">
    <literal><![CDATA[
      a(x,y,a(z,z,y * u)) \ w = w * a(y * u,z,a(z,u,x))
    ]]></literal>
    <justification jstring="[para(46919(a,2),40860(a,2,2))].">
      <j1 rule="para" parents="46919 40860"/>
    </justification>
  </clause>

  <clause id="46922">
    <literal><![CDATA[
      a(x,y \ z,a(u,u,(y \ z) * R(y,w,w))) = a(x,u,a(u,R(y,w,w),z * a(y,w,w)))
    ]]></literal>
    <justification jstring="[para(45000(a,1),46920(a,2,3,3))].">
      <j1 rule="para" parents="45000 46920"/>
    </justification>
  </clause>

  <clause id="46923">
    <literal><![CDATA[
      a(x,y,L(y,z * u,u)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,45918,a(flip),b,46892,a),flip(a)].">
      <j1 rule="hyper" parents="373 45918 46892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46924">
    <literal><![CDATA[
      a(x,y,L(y,z * u,z)) = a(x,y,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29739,a,b,46923,a)].">
      <j1 rule="hyper" parents="64 29739 46923"/>
    </justification>
  </clause>

  <clause id="46925">
    <literal><![CDATA[
      (a(x,y,L(y,z,u)) * (z * u)) * u = a(x,y,y) * ((z * u) * u)
    ]]></literal>
    <justification jstring="[para(46923(a,1),46537(a,1,1,1))].">
      <j1 rule="para" parents="46923 46537"/>
    </justification>
  </clause>

  <clause id="46926">
    <literal><![CDATA[
      a((x \ y) * z,u,L(u,y,x)) = a((x * z) * y,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46836,a(flip),b,46924,a),flip(a)].">
      <j1 rule="hyper" parents="64 46836 46924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46927">
    <literal><![CDATA[
      a(x,y,L(L(y,z,u),w * v5,w)) = L(a(x,y,L(y,v5,w)),z,u)
    ]]></literal>
    <justification jstring="[para(46924(a,1),46529(a,2,1))].">
      <j1 rule="para" parents="46924 46529"/>
    </justification>
  </clause>

  <clause id="46928">
    <literal><![CDATA[
      a(x,y,a(y,z,L(u,w * v5,w))) = a(u,z,a(x,y,L(y,v5,w)))
    ]]></literal>
    <justification jstring="[para(46924(a,1),46816(a,1,3)),flip(a)].">
      <j1 rule="para" parents="46924 46816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46929">
    <literal><![CDATA[
      a(x,x,L(y,z * u,u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,45915,a(flip),b,46895,a),flip(a)].">
      <j1 rule="hyper" parents="373 45915 46895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46930">
    <literal><![CDATA[
      a(x,x,L(y,z * u,z)) = a(x,x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,29739,a,b,46929,a)].">
      <j1 rule="hyper" parents="64 29739 46929"/>
    </justification>
  </clause>

  <clause id="46931">
    <literal><![CDATA[
      a(x * a(y * z,x,y),x,u) = a(x,x,L(L(u,y,y * z),z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46726,a,b,46930,a)].">
      <j1 rule="hyper" parents="64 46726 46930"/>
    </justification>
  </clause>

  <clause id="46932">
    <literal><![CDATA[
      a(x,x,L(L(y,z,z * u),u,z)) = a(x,x,y * a(z * u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42792,a(flip),b,46930,a),flip(a)].">
      <j1 rule="hyper" parents="64 42792 46930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46933">
    <literal><![CDATA[
      a(x,x,L((y * z) \ ((y \ 1) \ u),z,y)) = a(x,x,((y \ 1) * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(1633(a,1),46930(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1633 46930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46934">
    <literal><![CDATA[
      (x / y) * a(z,z,L(u,x,y)) = (a(z,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(46930(a,1),42996(a,1,2))].">
      <j1 rule="para" parents="46930 42996"/>
    </justification>
  </clause>

  <clause id="46935">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) * (z / u) = (a(x,x,y) * z) / u
    ]]></literal>
    <justification jstring="[hyper(23777,a,46934,a)].">
      <j1 rule="hyper" parents="23777 46934"/>
    </justification>
  </clause>

  <clause id="46936">
    <literal><![CDATA[
      a(x,(((y / z) \ u) \ u) * a(w,w,L(v5,y,z)),v6) = a(x,(a(w,w,v5) * y) / z,v6)
    ]]></literal>
    <justification jstring="[para(46934(a,1),31970(a,2,2))].">
      <j1 rule="para" parents="46934 31970"/>
    </justification>
  </clause>

  <clause id="46937">
    <literal><![CDATA[
      (a(x,x,y) * y) / z = a(x,x,y) * (y / z)
    ]]></literal>
    <justification jstring="[para(44983(a,1),46935(a,1,1)),flip(a)].">
      <j1 rule="para" parents="44983 46935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46939">
    <literal><![CDATA[
      (1 / (a(x,x,y) * (y / z))) * (x \ ((1 / x) \ y)) = (1 / ((x \ (x \ y)) / z)) * (x \ (x \ y))
    ]]></literal>
    <justification jstring="[para(46937(a,1),38266(a,1,1,2))].">
      <j1 rule="para" parents="46937 38266"/>
    </justification>
  </clause>

  <clause id="46940">
    <literal><![CDATA[
      L(x,y,x * ((L(x,z,u) \ 1) * w)) = L(x,y,a(u,z,x) * w)
    ]]></literal>
    <justification jstring="[para(45347(a,1),46775(a,1,3))].">
      <j1 rule="para" parents="45347 46775"/>
    </justification>
  </clause>

  <clause id="46941">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * (a(x,z,u) * (y * x)) = y * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(45862(a,1),45417(a,1,1))].">
      <j1 rule="para" parents="45862 45417"/>
    </justification>
  </clause>

  <clause id="46942">
    <literal><![CDATA[
      L(x,y,z) * R(x \ 1,u,w) = a(z,y,x) \ a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,45221,a(flip),b,45470,a),flip(a)].">
      <j1 rule="hyper" parents="373 45221 45470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46943">
    <literal><![CDATA[
      a(x,y,z) \ a(z,u,x) = z \ L(R(z,u,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,33623,a(flip),b,46942,a),flip(a)].">
      <j1 rule="hyper" parents="64 33623 46942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46944">
    <literal><![CDATA[
      a(x,y,z) * (a(z,y,x) \ u) = u * (x \ L(R(x,y,z),y,z))
    ]]></literal>
    <justification jstring="[para(46943(a,1),42830(a,2,2))].">
      <j1 rule="para" parents="46943 42830"/>
    </justification>
  </clause>

  <clause id="46945">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) / u) \ 1 = ((z \ L(z,y,x)) / u) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,42522,a(flip),b,45617,a)].">
      <j1 rule="hyper" parents="373 42522 45617"/>
    </justification>
  </clause>

  <clause id="46946">
    <literal><![CDATA[
      x \ ((a(y,z,u) \ x) * u) = a(y,z,a(x,u,u)) * L(u,z,y)
    ]]></literal>
    <justification jstring="[para(33214(a,1),45771(a,1,2))].">
      <j1 rule="para" parents="33214 45771"/>
    </justification>
  </clause>

  <clause id="46947">
    <literal><![CDATA[
      L(x,x,y) * a(z,x,a(x,u,w)) = L(L(x,x,a(z,u,w)),x,y)
    ]]></literal>
    <justification jstring="[para(28832(a,1),45868(a,2,1))].">
      <j1 rule="para" parents="28832 45868"/>
    </justification>
  </clause>

  <clause id="46948">
    <literal><![CDATA[
      L(x * a(y,y,a(z,x,u)),y \ z,a(u,y,y)) = L(x,a(u,y,y),y \ z)
    ]]></literal>
    <justification jstring="[para(44156(a,1),45883(a,1,1,2))].">
      <j1 rule="para" parents="44156 45883"/>
    </justification>
  </clause>

  <clause id="46949">
    <literal><![CDATA[
      L(x * a(y,y,a(z,x,u)),a(w,v5,y) * z,a(u,y,y)) = L(x,a(u,y,y),a(w,v5,y) * z)
    ]]></literal>
    <justification jstring="[para(44275(a,1),45883(a,1,1,2))].">
      <j1 rule="para" parents="44275 45883"/>
    </justification>
  </clause>

  <clause id="46950">
    <literal><![CDATA[
      (x \ ((a(y,z,z) \ 1) \ u)) * a(z,z,a(y,x \ ((a(y,z,z) \ 1) \ u),x)) = L(((a(y,z,z) \ 1) * x) \ u,a(y,z,z),x)
    ]]></literal>
    <justification jstring="[para(1633(a,1),45896(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1633 45896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46951">
    <literal><![CDATA[
      ((a(x,y,y) \ z) / u) * a(y,y,a(x,(a(x,y,y) \ z) / u,u)) = L(z / (u * a(x,y,y)),a(x,y,y),u)
    ]]></literal>
    <justification jstring="[para(28810(a,1),45896(a,1,1)),flip(a)].">
      <j1 rule="para" parents="28810 45896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46952">
    <literal><![CDATA[
      L(x,x,y) * a(z,u,a(x,x,w)) = L(L(x,x,a(w,u,z)),x,y)
    ]]></literal>
    <justification jstring="[para(28832(a,1),45908(a,2,1))].">
      <j1 rule="para" parents="28832 45908"/>
    </justification>
  </clause>

  <clause id="46953">
    <literal><![CDATA[
      (1 / x) \ a(y,z,a(u,w,z)) = (u / x) \ L(u,w,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(43872(a,1),45962(a,1,2))].">
      <j1 rule="para" parents="43872 45962"/>
    </justification>
  </clause>

  <clause id="46954">
    <literal><![CDATA[
      L(x,y * (z * L(z \ y,u,w)),y) = L(x,a(y \ z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,36278,a(flip),b,45994,a)].">
      <j1 rule="hyper" parents="64 36278 45994"/>
    </justification>
  </clause>

  <clause id="46955">
    <literal><![CDATA[
      L(x,a(y,z,(y \ u) * z),w) = L(x,a(y,z,u * (z * y)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,41403,a,b,46012,a),flip(a)].">
      <j1 rule="hyper" parents="64 41403 46012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46956">
    <literal><![CDATA[
      L(x,a(x,y,z),u \ w) = L(x,x,a(z,y,u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,45673,a(flip),b,46020,a)].">
      <j1 rule="hyper" parents="64 45673 46020"/>
    </justification>
  </clause>

  <clause id="46957">
    <literal><![CDATA[
      L(x,x,a(y,z,u \ w)) = L(x,x,a(y,z,u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46017,a(flip),b,46956,a)].">
      <j1 rule="hyper" parents="64 46017 46956"/>
    </justification>
  </clause>

  <clause id="46958">
    <literal><![CDATA[
      L(x,x,a(y,z,(x \ u) * w)) = L(x,x,a(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46824,a(flip),b,46957,a),flip(a)].">
      <j1 rule="hyper" parents="64 46824 46957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46959">
    <literal><![CDATA[
      L(x,x,a(y,z,(u \ w) * w)) = L(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(27307(a,1),46957(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27307 46957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46960">
    <literal><![CDATA[
      L(x,x,a(y,z,z)) \ a(y,z,u * ((z \ 1) * u)) = (x \ 1) * a(y,z,u * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(46959(a,1),41350(a,1,1))].">
      <j1 rule="para" parents="46959 41350"/>
    </justification>
  </clause>

  <clause id="46961">
    <literal><![CDATA[
      L(x,x,a(y,z,(x \ u) * w)) = L(x,x,a(y,z,u * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,46957,a(flip),b,46958,a),flip(a)].">
      <j1 rule="hyper" parents="373 46957 46958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46962">
    <literal><![CDATA[
      L(x,x,a((x \ y) * z,u,w)) = L(x,x,a(w,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(42222,a,46961,a)].">
      <j1 rule="hyper" parents="42222 46961"/>
    </justification>
  </clause>

  <clause id="46963">
    <literal><![CDATA[
      (1 / x) \ a(y,a(y,z,u),w) = x * a(a(u,z,w),y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,45738,a(flip),b,46026,a),flip(a)].">
      <j1 rule="hyper" parents="64 45738 46026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46964">
    <literal><![CDATA[
      (1 / x) \ a(y,a(y,z,u),w) = x * a(w,z,a(y,y,u))
    ]]></literal>
    <justification jstring="[para(45501(a,1),46963(a,2,2))].">
      <j1 rule="para" parents="45501 46963"/>
    </justification>
  </clause>

  <clause id="46965">
    <literal><![CDATA[
      (1 / x) \ a(y,z,a(z,u,w)) = x * a(y,u,a(z,z,w))
    ]]></literal>
    <justification jstring="[para(39362(a,1),46964(a,1,2))].">
      <j1 rule="para" parents="39362 46964"/>
    </justification>
  </clause>

  <clause id="46966">
    <literal><![CDATA[
      a(x,y,L(z \ 1,u,w) \ v5) = a(x,y,(a(z,u,w) / z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27431,a(flip),b,46202,a)].">
      <j1 rule="hyper" parents="64 27431 46202"/>
    </justification>
  </clause>

  <clause id="46967">
    <literal><![CDATA[
      a(x,y,L(z \ (x \ u),x,z)) = a(x,y,x \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39070,a(flip),b,46231,a),flip(a)].">
      <j1 rule="hyper" parents="64 39070 46231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46968">
    <literal><![CDATA[
      a(x \ (y \ x),z,x \ (y \ u)) = a(y,z,y \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46514,a,b,46967,a)].">
      <j1 rule="hyper" parents="64 46514 46967"/>
    </justification>
  </clause>

  <clause id="46969">
    <literal><![CDATA[
      a(x,y,y \ (x \ z)) = a(x,y,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46508,a(flip),b,46967,a)].">
      <j1 rule="hyper" parents="64 46508 46967"/>
    </justification>
  </clause>

  <clause id="46970">
    <literal><![CDATA[
      L(x,a(y,z,y \ (z \ u)),w) = L(x,a(y,z,(y \ u) * z),w)
    ]]></literal>
    <justification jstring="[para(46969(a,1),42038(a,1,2))].">
      <j1 rule="para" parents="46969 42038"/>
    </justification>
  </clause>

  <clause id="46971">
    <literal><![CDATA[
      a((x \ 1) \ (y \ x),z,(x \ 1) \ (y \ u)) = a(y,z,y \ ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,32651,a(flip),b,46968,a)].">
      <j1 rule="hyper" parents="64 32651 46968"/>
    </justification>
  </clause>

  <clause id="46972">
    <literal><![CDATA[
      a(x,y,L((x \ z) \ u,z,z)) = a(x,y,(1 / z) * (x * u))
    ]]></literal>
    <justification jstring="[para(569(a,1),46233(a,2,3))].">
      <j1 rule="para" parents="569 46233"/>
    </justification>
  </clause>

  <clause id="46973">
    <literal><![CDATA[
      a(x,y,L((x \ z) \ u,z,z)) = a(x,y,(z \ 1) * (x * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27317,a(flip),b,46972,a),flip(a)].">
      <j1 rule="hyper" parents="373 27317 46972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46974">
    <literal><![CDATA[
      a(x,y,y) * (z * (a(x,y,y) \ L(a(x,y,y) * (z \ u),z,a(x,y,y)))) = 1 * L(z * (((a(x,y,y) \ 1) * z) \ u),y,a(y,1,x))
    ]]></literal>
    <justification jstring="[para(11526(a,1),46271(a,1,2))].">
      <j1 rule="para" parents="11526 46271"/>
    </justification>
  </clause>

  <clause id="46975">
    <literal><![CDATA[
      a(a(x,y,(x \ z) * y),u,w) = a(a(x,y,z * (y * x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,41493,a(flip),b,46276,a)].">
      <j1 rule="hyper" parents="64 41493 46276"/>
    </justification>
  </clause>

  <clause id="46976">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(x * y,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,41868,a(flip),b,46372,a),flip(a)].">
      <j1 rule="hyper" parents="373 41868 46372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46977">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(y * x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(41879(a,1),46372(a,2,2))].">
      <j1 rule="para" parents="41879 46372"/>
    </justification>
  </clause>

  <clause id="46978">
    <literal><![CDATA[
      (a(x,y,z) * u) * L(u \ x,u,a(z,y,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,45066,a,b,46420,a),flip(a)].">
      <j1 rule="hyper" parents="373 45066 46420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46979">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(a(z,u,w),x,y) = a(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41902,a,b,46464,a)].">
      <j1 rule="hyper" parents="64 41902 46464"/>
    </justification>
  </clause>

  <clause id="46980">
    <literal><![CDATA[
      a(x,y,z) * (a(z,y,x) * u) = R(x,y,z) * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42484,a(flip),b,46466,a)].">
      <j1 rule="hyper" parents="64 42484 46466"/>
    </justification>
  </clause>

  <clause id="46981">
    <literal><![CDATA[
      x * ((a(y,z,u) \ x) \ 1) = a(y,z,L(u,x,x))
    ]]></literal>
    <justification jstring="[para(45775(a,1),46511(a,1,3)),flip(a)].">
      <j1 rule="para" parents="45775 46511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46982">
    <literal><![CDATA[
      ((a(x,y,z) / u) \ 1) \ u = a(x,y,L(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39153,a,b,46981,a)].">
      <j1 rule="hyper" parents="64 39153 46981"/>
    </justification>
  </clause>

  <clause id="46983">
    <literal><![CDATA[
      (a(x,y,z) \ u) \ 1 = a(x,y,z) * (u \ 1)
    ]]></literal>
    <justification jstring="[hyper(35,a,46507,a,b,46981,a),flip(a)].">
      <j1 rule="hyper" parents="35 46507 46981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46984">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) \ u = (a(x,y,z) / u) \ 1
    ]]></literal>
    <justification jstring="[para(46981(a,1),39154(a,1,1))].">
      <j1 rule="para" parents="46981 39154"/>
    </justification>
  </clause>

  <clause id="46988">
    <literal><![CDATA[
      x \ (a(y,z,u) * ((a(y,z,u) / x) \ 1)) = a(a(y,z,u),x,x)
    ]]></literal>
    <justification jstring="[hyper(139,a,46983,a(flip),b,30484,a(flip))].">
      <j1 rule="hyper" parents="139 46983 30484"/>
    </justification>
  </clause>

  <clause id="46989">
    <literal><![CDATA[
      a(x,y,z) * (((x * y) * z) \ 1) = (x * (y * z)) \ 1
    ]]></literal>
    <justification jstring="[para(15467(a,1),46983(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15467 46983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46990">
    <literal><![CDATA[
      L(a(x,y,z),u,u) \ u = (a(x,y,z) / u) \ 1
    ]]></literal>
    <justification jstring="[para(46493(a,1),46984(a,1,1))].">
      <j1 rule="para" parents="46493 46984"/>
    </justification>
  </clause>

  <clause id="46991">
    <literal><![CDATA[
      (1 / x) \ (a(y,z,u) \ 1) = (a(y,z,u) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,42565,a(flip),b,46990,a)].">
      <j1 rule="hyper" parents="64 42565 46990"/>
    </justification>
  </clause>

  <clause id="46992">
    <literal><![CDATA[
      a(x,y,z) \ L(u,u,a(x,y,z)) = (a(x,y,z) / u) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,28797,a(flip),b,46990,a)].">
      <j1 rule="hyper" parents="64 28797 46990"/>
    </justification>
  </clause>

  <clause id="46994">
    <literal><![CDATA[
      (a(x,y,z) / (1 / u)) \ 1 = (a(x,y,z) \ 1) / u
    ]]></literal>
    <justification jstring="[hyper(64,a,23702,a(flip),b,46991,a),flip(a)].">
      <j1 rule="hyper" parents="64 23702 46991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="46995">
    <literal><![CDATA[
      ((a(x,y,z) \ 1) / u) \ 1 = (1 / u) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(46994(a,1),25193(a,1,1))].">
      <j1 rule="para" parents="46994 25193"/>
    </justification>
  </clause>

  <clause id="46997">
    <literal><![CDATA[
      ((x \ L(x,y,z)) / u) \ 1 = (1 / u) \ a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,46945,a(flip),b,46995,a)].">
      <j1 rule="hyper" parents="64 46945 46995"/>
    </justification>
  </clause>

  <clause id="46999">
    <literal><![CDATA[
      (x \ L(x,y,z)) / (1 / u) = 1 / (a(z,y,x) / u)
    ]]></literal>
    <justification jstring="[hyper(225,a,24638,a(flip),b,46997,a),flip(a)].">
      <j1 rule="hyper" parents="225 24638 46997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47000">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) / v5) \ 1 = (1 / v5) \ a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(42689(a,1),46997(a,1,1,1))].">
      <j1 rule="para" parents="42689 46997"/>
    </justification>
  </clause>

  <clause id="47001">
    <literal><![CDATA[
      a(x,y,T((x \ 1) \ (y \ z),u)) = a(x,y,y \ ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,46221,a(flip),b,46568,a),flip(a)].">
      <j1 rule="hyper" parents="373 46221 46568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47002">
    <literal><![CDATA[
      a((x \ y) \ (x * z),u,L(w,y,x)) = a(L(y,x,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),46590(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 46590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47003">
    <literal><![CDATA[
      a((x * y) \ z,u,L(w,x,x)) = a(x * (y \ z),u,L(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46496,a(flip),b,46597,a),flip(a)].">
      <j1 rule="hyper" parents="64 46496 46597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47004">
    <literal><![CDATA[
      a((x * (y * x)) \ z,u,L(y,x,x)) = a(x * ((y * x) \ z),u,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46495,a(flip),b,46597,a),flip(a)].">
      <j1 rule="hyper" parents="64 46495 46597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47005">
    <literal><![CDATA[
      a((x * y) \ L(z,x,x),y,u) = a((z * x) * y,y,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,41827,a(flip),b,46601,a),flip(a)].">
      <j1 rule="hyper" parents="373 41827 46601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47006">
    <literal><![CDATA[
      a(x,y,L(z,x,x * ((x \ u) * w))) = a(x,y,L(z,x,u * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,46496,a(flip),b,46612,a),flip(a)].">
      <j1 rule="hyper" parents="373 46496 46612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47007">
    <literal><![CDATA[
      a((x * y) \ z,u,((x \ y) \ 1) * y) = a(z * (x * y),u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27671,a(flip),b,46655,a)].">
      <j1 rule="hyper" parents="64 27671 46655"/>
    </justification>
  </clause>

  <clause id="47008">
    <literal><![CDATA[
      L(x,y,L(z,L(x,u,w),v5)) = L(x,y,L(z,x,L(v5,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46623,a(flip),b,46662,a),flip(a)].">
      <j1 rule="hyper" parents="64 46623 46662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47009">
    <literal><![CDATA[
      a(x,y,(z \ (u * u)) * (w \ 1)) = a(x,y,(w * z) \ (u * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27781,a,b,46691,a)].">
      <j1 rule="hyper" parents="64 27781 46691"/>
    </justification>
  </clause>

  <clause id="47010">
    <literal><![CDATA[
      x * a(y,z,L(L(u,x,w),w,x)) = w \ ((w * a(y,z,u)) * x)
    ]]></literal>
    <justification jstring="[hyper(145,a,27702,a,b,46710,a)].">
      <j1 rule="hyper" parents="145 27702 46710"/>
    </justification>
  </clause>

  <clause id="47011">
    <literal><![CDATA[
      x \ ((x * a(y,z,u)) * w) = w * a(y,z,u * a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(145,a,42792,a(flip),b,46710,a),flip(a)].">
      <j1 rule="hyper" parents="145 42792 46710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47012">
    <literal><![CDATA[
      a(x,y,L(L(z,u,w),w,u)) = a(x,y,z) * a(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33242,a(flip),b,46710,a),flip(a)].">
      <j1 rule="hyper" parents="64 33242 46710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47013">
    <literal><![CDATA[
      a(x,y,z) * a(u,a(x,y,z),w) = a(x,y,z * a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,33239,a(flip),b,47011,a(flip))].">
      <j1 rule="hyper" parents="35 33239 47011"/>
    </justification>
  </clause>

  <clause id="47014">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,z * a(u,z,w)) = a(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(149,a,47013,a)].">
      <j1 rule="hyper" parents="149 47013"/>
    </justification>
  </clause>

  <clause id="47015">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * a(y,z,u) = a(y,z,u * a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,43415,a,b,47013,a)].">
      <j1 rule="hyper" parents="64 43415 47013"/>
    </justification>
  </clause>

  <clause id="47016">
    <literal><![CDATA[
      a(x,y,z) * a(u,a(z,y,x),w) = a(x,y,z * a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,42400,a,b,47013,a)].">
      <j1 rule="hyper" parents="64 42400 47013"/>
    </justification>
  </clause>

  <clause id="47017">
    <literal><![CDATA[
      a(x,y,z * a(u,z,w)) \ T(a(x,y,z),a(v5,v6,v7)) = a(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(47013(a,1),43420(a,1,1))].">
      <j1 rule="para" parents="47013 43420"/>
    </justification>
  </clause>

  <clause id="47018">
    <literal><![CDATA[
      a(x,y,z) * ((a(x,y,z * a(u,z,w)) \ v5) * a(x,y,z)) = (a(x,y,z) * a(w,a(x,y,z),u)) * v5
    ]]></literal>
    <justification jstring="[para(47015(a,1),43519(a,1,2,1,1))].">
      <j1 rule="para" parents="47015 43519"/>
    </justification>
  </clause>

  <clause id="47019">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) \ a(x,y,(y \ 1) * a(z,y \ 1,u)) = y \ a(u,a(y \ 1,y,x),z)
    ]]></literal>
    <justification jstring="[para(47016(a,1),39471(a,1,2))].">
      <j1 rule="para" parents="47016 39471"/>
    </justification>
  </clause>

  <clause id="47020">
    <literal><![CDATA[
      a(x,y \ z,z) * a(u,a(z,z * y,x),w) = a(x,y \ z,z * a(w,z,u))
    ]]></literal>
    <justification jstring="[para(45382(a,1),47016(a,1,2,2))].">
      <j1 rule="para" parents="45382 47016"/>
    </justification>
  </clause>

  <clause id="47021">
    <literal><![CDATA[
      a(x \ (y \ z),u,L(y,y,x)) = a(y \ (x \ z),u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46728,a(flip),b,46730,a),flip(a)].">
      <j1 rule="hyper" parents="64 46728 46730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47022">
    <literal><![CDATA[
      a(x \ (y \ z),u,L(y,y,x)) = a((x \ z) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,46084,a(flip),b,47021,a),flip(a)].">
      <j1 rule="hyper" parents="373 46084 47021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47023">
    <literal><![CDATA[
      a(x \ T(((y * y) \ z) * y,y),u,L(y,y,x)) = a((x \ R(T(z,y * y),y,y)) * y,u,y)
    ]]></literal>
    <justification jstring="[para(1400(a,1),47022(a,1,1,2))].">
      <j1 rule="para" parents="1400 47022"/>
    </justification>
  </clause>

  <clause id="47024">
    <literal><![CDATA[
      a((x * y) \ z,u,y \ ((x \ 1) \ y)) = a((y \ z) * x,u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,46084,a(flip),b,46731,a),flip(a)].">
      <j1 rule="hyper" parents="373 46084 46731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47025">
    <literal><![CDATA[
      a((x * y) \ z,u,x \ ((y \ 1) \ x)) = a((x \ z) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,46084,a(flip),b,46746,a),flip(a)].">
      <j1 rule="hyper" parents="373 46084 46746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47026">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * L(x,v5,w) = L(L(x,y,a(z,u,w)),v5,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,30,a,b,46791,a),flip(a)].">
      <j1 rule="hyper" parents="373 30 46791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47027">
    <literal><![CDATA[
      a(x,y,L(y,z,L(u,w,w))) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,44034,a(flip),b,46813,a),flip(a)].">
      <j1 rule="hyper" parents="373 44034 46813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47028">
    <literal><![CDATA[
      a(((x \ T(T(y,z) * u,w)) * v5) * T(T(y,z) * u,w),v6,y * u) = a(v5 * x,v6,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27312,a(flip),b,46854,a)].">
      <j1 rule="hyper" parents="64 27312 46854"/>
    </justification>
  </clause>

  <clause id="47029">
    <literal><![CDATA[
      L(x,x,a((x \ y) \ z,u,w)) = L(x,x,a(y * (x * z),u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,46670,a(flip),b,46868,a),flip(a)].">
      <j1 rule="hyper" parents="373 46670 46868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47030">
    <literal><![CDATA[
      a(x,y,a(z,u * x,L(y,w,v5))) = a(x,y,a(z,u,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,46787,a(flip),b,46896,a),flip(a)].">
      <j1 rule="hyper" parents="373 46787 46896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47031">
    <literal><![CDATA[
      a(x,y,L(L(y,z,u),w * v5,w)) = a(x,y,L(L(y,v5,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,46493,a,b,46927,a),flip(a)].">
      <j1 rule="hyper" parents="373 46493 46927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47032">
    <literal><![CDATA[
      L(x,y,x * (L(x,z,u) * w)) = L(x,y,a(u,z,x) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,25369,a(flip),b,46940,a)].">
      <j1 rule="hyper" parents="64 25369 46940"/>
    </justification>
  </clause>

  <clause id="47033">
    <literal><![CDATA[
      L(x,y,(L(x,z,u) * w) * x) = L(x,y,a(u,z,x) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,23995,a(flip),b,46940,a)].">
      <j1 rule="hyper" parents="64 23995 46940"/>
    </justification>
  </clause>

  <clause id="47034">
    <literal><![CDATA[
      L(x,y,a(z,u,x) * (w / L(x,u,z))) = L(x,y,w * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29115,a(flip),b,47032,a),flip(a)].">
      <j1 rule="hyper" parents="64 29115 47032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47035">
    <literal><![CDATA[
      L(x,y,a(z,u,x) * (L(x,u,z) \ w)) = L(x,y,x * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),47032(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="10 47032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47036">
    <literal><![CDATA[
      a(x,y,L(y,z,a(u,w,y) * v5)) = a(x,y,L(y,z,L(y,w,u) * v5))
    ]]></literal>
    <justification jstring="[para(47033(a,1),44180(a,1,3))].">
      <j1 rule="para" parents="47033 44180"/>
    </justification>
  </clause>

  <clause id="47037">
    <literal><![CDATA[
      L(x,y,a(z,u,x) * (w / L(x,u,z))) = L(x,y,x \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,46133,a,b,47034,a),flip(a)].">
      <j1 rule="hyper" parents="373 46133 47034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47038">
    <literal><![CDATA[
      a(x,y,z) * (u * R(x,x,a(u,y,z))) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,37618,a(flip),b,46941,a)].">
      <j1 rule="hyper" parents="64 37618 46941"/>
    </justification>
  </clause>

  <clause id="47039">
    <literal><![CDATA[
      a(x,y,z) * (u * L(x,x,a(u,y,z))) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(28832(a,1),47038(a,1,2,2))].">
      <j1 rule="para" parents="28832 47038"/>
    </justification>
  </clause>

  <clause id="47040">
    <literal><![CDATA[
      a(x,y,z \ (T(a(u,w,v5),v6) * (a(v5,w,u) \ v7))) = a(x,y,z \ (v7 * (u \ L(R(u,w,v5),w,v5))))
    ]]></literal>
    <justification jstring="[para(46944(a,1),27335(a,2,3,2))].">
      <j1 rule="para" parents="46944 27335"/>
    </justification>
  </clause>

  <clause id="47041">
    <literal><![CDATA[
      a(x,y,L(z \ (a(u,w,v5) \ v6),z,a(v5,w,u))) = a(x,y,(z * a(v5,w,u)) \ (v6 * (v5 \ L(R(v5,w,u),w,u))))
    ]]></literal>
    <justification jstring="[para(46944(a,1),27552(a,2,3,2))].">
      <j1 rule="para" parents="46944 27552"/>
    </justification>
  </clause>

  <clause id="47042">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * L(u,y,x) = L(u,y,L(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46449,a(flip),b,46946,a),flip(a)].">
      <j1 rule="hyper" parents="64 46449 46946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47043">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,a(x,x,u)) = L(x,y,L(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,41900,a(flip),b,47042,a)].">
      <j1 rule="hyper" parents="64 41900 47042"/>
    </justification>
  </clause>

  <clause id="47044">
    <literal><![CDATA[
      L(x,y,L(z,x,u)) * a(L(z,x,u),y,a(x,x,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,34162,a(flip),b,47043,a),flip(a)].">
      <j1 rule="hyper" parents="373 34162 47043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47046">
    <literal><![CDATA[
      (x / y) \ L(x,z,a(u,w,w)) = y * a(u,w,a(x,z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,45508,a(flip),b,46953,a),flip(a)].">
      <j1 rule="hyper" parents="64 45508 46953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47047">
    <literal><![CDATA[
      a(x,x,(a(y,z,u) / y) \ w) = a(x,x,L(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,46489,a(flip),b,46966,a),flip(a)].">
      <j1 rule="hyper" parents="64 46489 46966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47048">
    <literal><![CDATA[
      a(x,x,(y \ a(y,z,u)) \ w) = a(x,x,L(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27389,a(flip),b,47047,a)].">
      <j1 rule="hyper" parents="64 27389 47047"/>
    </justification>
  </clause>

  <clause id="47049">
    <literal><![CDATA[
      L(x,a(y,z,y \ (z \ u)),w) = L(x,a(y,z,u * (z * y)),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,46955,a(flip),b,46970,a),flip(a)].">
      <j1 rule="hyper" parents="373 46955 46970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47050">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(y * x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(41890(a,1),46976(a,2,2))].">
      <j1 rule="para" parents="41890 46976"/>
    </justification>
  </clause>

  <clause id="47051">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(y,x,a(z,u,w)) = a(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41854,a(flip),b,46979,a)].">
      <j1 rule="hyper" parents="64 41854 46979"/>
    </justification>
  </clause>

  <clause id="47052">
    <literal><![CDATA[
      (a(x,y,z) * (a(z,y,x) * u)) * L(x,y,z) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(46980(a,2),40046(a,1,1))].">
      <j1 rule="para" parents="46980 40046"/>
    </justification>
  </clause>

  <clause id="47053">
    <literal><![CDATA[
      x \ (a(y,z,u) * ((a(y,z,u) / x) \ 1)) = a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,45501,a(flip),b,46988,a),flip(a)].">
      <j1 rule="hyper" parents="373 45501 46988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47054">
    <literal><![CDATA[
      a(x,y,(x \ 1) \ (y \ z)) = a(x,y,y \ ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(27584,a,47001,a)].">
      <j1 rule="hyper" parents="27584 47001"/>
    </justification>
  </clause>

  <clause id="47055">
    <literal><![CDATA[
      a(x,y,y \ ((x \ 1) \ z)) = a(x,y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46227,a(flip),b,47054,a),flip(a)].">
      <j1 rule="hyper" parents="64 46227 47054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47056">
    <literal><![CDATA[
      a(x,y,y \ (x * z)) = a(x,y,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46881,a(flip),b,47055,a)].">
      <j1 rule="hyper" parents="64 46881 47055"/>
    </justification>
  </clause>

  <clause id="47057">
    <literal><![CDATA[
      a(x,y,a(z,u,(z \ w) * u)) = a(x,y,a(z,u,z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(47055(a,1),42861(a,1,3)),flip(a)].">
      <j1 rule="para" parents="47055 42861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47058">
    <literal><![CDATA[
      a(x,y,a((z * u) * w,w,z)) = a(x,y,a(z,w,z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(47056(a,1),41911(a,2,3))].">
      <j1 rule="para" parents="47056 41911"/>
    </justification>
  </clause>

  <clause id="47059">
    <literal><![CDATA[
      L(x,y,a(z,u,(z * w) * u)) = L(x,y,a(z,u,z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(47056(a,1),42876(a,1,3)),flip(a)].">
      <j1 rule="para" parents="47056 42876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47060">
    <literal><![CDATA[
      a((x \ (x * y)) \ (x * z),u,y \ (x * w)) = a(L(x * y,x,x) \ z,u,(x \ y) \ w)
    ]]></literal>
    <justification jstring="[para(41719(a,1),47002(a,1,3))].">
      <j1 rule="para" parents="41719 47002"/>
    </justification>
  </clause>

  <clause id="47061">
    <literal><![CDATA[
      a((x * y) \ z,u,L(w,y,y)) = a(y * (x \ z),u,L(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(32451,a,47003,a)].">
      <j1 rule="hyper" parents="32451 47003"/>
    </justification>
  </clause>

  <clause id="47062">
    <literal><![CDATA[
      a((x * y) \ z,u,L(L(w,x,y),x,x)) = a(x * (y \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,39064,a(flip),b,47003,a),flip(a)].">
      <j1 rule="hyper" parents="373 39064 47003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47063">
    <literal><![CDATA[
      a(x,y,L(z,x,(x \ u) * w)) = a(x,y,L(z,x,u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46658,a(flip),b,47006,a)].">
      <j1 rule="hyper" parents="64 46658 47006"/>
    </justification>
  </clause>

  <clause id="47064">
    <literal><![CDATA[
      a(((1 / x) \ (y * x)) \ z,u,((x \ 1) \ T(y,x)) \ ((x \ 1) \ ((x \ 1) \ T(y,x)))) = a((((x \ 1) \ T(y,x)) \ z) * x,u,x)
    ]]></literal>
    <justification jstring="[para(1136(a,1),47024(a,1,1,1))].">
      <j1 rule="para" parents="1136 47024"/>
    </justification>
  </clause>

  <clause id="47065">
    <literal><![CDATA[
      L(x,x,a((x \ y) * z,u,w)) = L(x,x,a(y * (x * z),u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46670,a(flip),b,47029,a)].">
      <j1 rule="hyper" parents="64 46670 47029"/>
    </justification>
  </clause>

  <clause id="47066">
    <literal><![CDATA[
      a(x,y,L(L(y,z * u,z),w,v5)) = a(x,y,L(L(y,u,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27702,a,b,47031,a)].">
      <j1 rule="hyper" parents="64 27702 47031"/>
    </justification>
  </clause>

  <clause id="47067">
    <literal><![CDATA[
      L(x,y,L(z,x,u)) * a(z,y,L(a(x,x,u),x,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(46496(a,1),47044(a,1,2))].">
      <j1 rule="para" parents="46496 47044"/>
    </justification>
  </clause>

  <clause id="47068">
    <literal><![CDATA[
      L(x,a(y,z,u * (z * y)),w) = L(x,a(y,z,y * (z \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,46257,a(flip),b,47049,a),flip(a)].">
      <j1 rule="hyper" parents="64 46257 47049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47069">
    <literal><![CDATA[
      a(x,y,z) * ((a(z,y,x) * u) * L(x,y,z)) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29974,a(flip),b,47052,a)].">
      <j1 rule="hyper" parents="64 29974 47052"/>
    </justification>
  </clause>

  <clause id="47070">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),u,w)) = a(x,y,a(w,u,w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46013,a,b,47057,a)].">
      <j1 rule="hyper" parents="64 46013 47057"/>
    </justification>
  </clause>

  <clause id="47071">
    <literal><![CDATA[
      a(x,y,a(z,u,u * (w * z))) = a(x,y,a(z,u,z * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,41896,a(flip),b,47058,a)].">
      <j1 rule="hyper" parents="64 41896 47058"/>
    </justification>
  </clause>

  <clause id="47072">
    <literal><![CDATA[
      a(a(x,y,x * (y \ z)),u,w) * w = L(w,u,a(x,y,(x * z) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,45093,a,b,47059,a)].">
      <j1 rule="hyper" parents="373 45093 47059"/>
    </justification>
  </clause>

  <clause id="47073">
    <literal><![CDATA[
      a((x * y) \ L(z,y,x),u,L(z,y,y)) = a((x * y) * L(z,y,x),u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,46858,a,b,47061,a),flip(a)].">
      <j1 rule="hyper" parents="373 46858 47061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47074">
    <literal><![CDATA[
      L(x,x,a(y * (x * z),u,w)) = L(x,x,a(w,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46962,a(flip),b,47065,a),flip(a)].">
      <j1 rule="hyper" parents="64 46962 47065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47075">
    <literal><![CDATA[
      L(x,x,a(y * (z * x),u,w)) = L(x,x,a(w,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,33639,a,b,47074,a)].">
      <j1 rule="hyper" parents="64 33639 47074"/>
    </justification>
  </clause>

  <clause id="47076">
    <literal><![CDATA[
      a(x,y,L(L(y,z * u,u),w,v5)) = a(x,y,L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(14181(a,2),47066(a,1,3,1))].">
      <j1 rule="para" parents="14181 47066"/>
    </justification>
  </clause>

  <clause id="47077">
    <literal><![CDATA[
      L(x,y,L(z,x,u)) * a(z,y,a(x,x,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(29331(a,1),47067(a,1,2,3))].">
      <j1 rule="para" parents="29331 47067"/>
    </justification>
  </clause>

  <clause id="47078">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * L(x,z,L(u,x,y)) = L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,45811,a,b,47077,a)].">
      <j1 rule="hyper" parents="64 45811 47077"/>
    </justification>
  </clause>

  <clause id="47081">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,w,a(v5,v5,v6)))) * L(x,z,L(a(u,w,a(v5,v5,v6)),x,y)) = L(x,z,a(v6,v5,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,43889,a,b,47078,a),flip(a)].">
      <j1 rule="hyper" parents="373 43889 47078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47082">
    <literal><![CDATA[
      a(x,x,a(y,z,a(x,u,y) \ u)) * L(x,z,K(y,u * x) * ((y * x) \ (x * (u * y)))) = L(x,z,a(x,u,y) \ u)
    ]]></literal>
    <justification jstring="[para(34594(a,2),47078(a,1,2,3))].">
      <j1 rule="para" parents="34594 47078"/>
    </justification>
  </clause>

  <clause id="47083">
    <literal><![CDATA[
      a(x,y,z) * (a(z,y,x) * (u * L(x,y,z))) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(33254(a,1),47069(a,1,2))].">
      <j1 rule="para" parents="33254 47069"/>
    </justification>
  </clause>

  <clause id="47084">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * a(w,u,x) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,46715,a(flip),b,45343,a),flip(a)].">
      <j1 rule="hyper" parents="373 46715 45343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47086">
    <literal><![CDATA[
      L(R(a(x,y,z),u,w),v5,a(x,v6,v7)) * 1 = R(a(x,y,z),u,L(w,v5,a(x,v6,v7)))
    ]]></literal>
    <justification jstring="[para(31089(a,1),47084(a,1,2))].">
      <j1 rule="para" parents="31089 47084"/>
    </justification>
  </clause>

  <clause id="47087">
    <literal><![CDATA[
      x * ((x \ y) * (T(y * x,z) \ u)) = (y / T(y * x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,41721,a(flip),b,45579,a)].">
      <j1 rule="hyper" parents="64 41721 45579"/>
    </justification>
  </clause>

  <clause id="47088">
    <literal><![CDATA[
      x * (((x * y) * y) \ (y * z)) = (x / T(x * y,y)) * z
    ]]></literal>
    <justification jstring="[hyper(64,a,41740,a(flip),b,47087,a)].">
      <j1 rule="hyper" parents="64 41740 47087"/>
    </justification>
  </clause>

  <clause id="47089">
    <literal><![CDATA[
      a(x * (y * ((z * y) \ x)),u,u) = a(z,u,u) * a(z,u,a((z \ x) * y,y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,44034,a,b,45668,a),flip(a)].">
      <j1 rule="hyper" parents="373 44034 45668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47090">
    <literal><![CDATA[
      L(x,(y \ z) * (a(y,y,z) * u),w) = L(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,38003,a(flip),b,45854,a)].">
      <j1 rule="hyper" parents="64 38003 45854"/>
    </justification>
  </clause>

  <clause id="47091">
    <literal><![CDATA[
      L(x,a(y,y,z) * ((y \ z) * u),w) = L(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[para(30302(a,2),47090(a,1,2))].">
      <j1 rule="para" parents="30302 47090"/>
    </justification>
  </clause>

  <clause id="47092">
    <literal><![CDATA[
      a(x * R(T(y,z),y,z),x,z) = a((y \ z) * (z * x),x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32812,a(flip),b,46010,a),flip(a)].">
      <j1 rule="hyper" parents="64 32812 46010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47093">
    <literal><![CDATA[
      a(x * L(T(y,z),y,z),x,z) = a((y \ z) * (z * x),x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34635,a(flip),b,47092,a)].">
      <j1 rule="hyper" parents="64 34635 47092"/>
    </justification>
  </clause>

  <clause id="47094">
    <literal><![CDATA[
      a((x \ y) * (y * z),z,y) = a(z * L(x,x,y),z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32380,a(flip),b,47093,a),flip(a)].">
      <j1 rule="hyper" parents="64 32380 47093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47096">
    <literal><![CDATA[
      a(x * L(y,y,z),x,z) = a(y * ((z * x) \ z),x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46866,a(flip),b,47094,a),flip(a)].">
      <j1 rule="hyper" parents="64 46866 47094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47097">
    <literal><![CDATA[
      a(x * L(y,y,z),x,z) = a(y * (z \ (x \ z)),x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32708,a(flip),b,47096,a),flip(a)].">
      <j1 rule="hyper" parents="373 32708 47096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47098">
    <literal><![CDATA[
      a(x * L(y,y,z),x,z) = a(y * x,x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,46769,a(flip),b,47097,a),flip(a)].">
      <j1 rule="hyper" parents="373 46769 47097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47099">
    <literal><![CDATA[
      L(x,y,y * L(z,z,x)) = a(z * y,y,x) \ x
    ]]></literal>
    <justification jstring="[para(47098(a,1),45065(a,2,1))].">
      <j1 rule="para" parents="47098 45065"/>
    </justification>
  </clause>

  <clause id="47100">
    <literal><![CDATA[
      L(x,y,y * L(z,z,x)) = L(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,45065,a,b,47099,a),flip(a)].">
      <j1 rule="hyper" parents="373 45065 47099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47101">
    <literal><![CDATA[
      L(x,y,(x \ (z \ x)) * y) = L(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31613,a,b,47100,a)].">
      <j1 rule="hyper" parents="64 31613 47100"/>
    </justification>
  </clause>

  <clause id="47102">
    <literal><![CDATA[
      L(x,y,(z \ x) * (y * x)) = L(x,y,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,45313,a(flip),b,47101,a)].">
      <j1 rule="hyper" parents="64 45313 47101"/>
    </justification>
  </clause>

  <clause id="47103">
    <literal><![CDATA[
      a(x * (L(y * y,z,u) \ (w \ x)),v5,v5 * x) = a(w,v5,v5 * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,46677,a(flip),b,46048,a)].">
      <j1 rule="hyper" parents="64 46677 46048"/>
    </justification>
  </clause>

  <clause id="47104">
    <literal><![CDATA[
      (a(x,y,z) \ z) * a(u,w,a(x,y,z)) = L(z,y,L(x,w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,45065,a,b,46183,a),flip(a)].">
      <j1 rule="hyper" parents="373 45065 46183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47107">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * L(w,u,z) = L(w,u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,45193,a(flip),b,47104,a)].">
      <j1 rule="hyper" parents="64 45193 47104"/>
    </justification>
  </clause>

  <clause id="47109">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * L(z,u,w) = L(z,u,L(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41902,a,b,47107,a)].">
      <j1 rule="hyper" parents="64 41902 47107"/>
    </justification>
  </clause>

  <clause id="47110">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * L(z,y,x) = L(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,41856,a,b,47107,a)].">
      <j1 rule="hyper" parents="64 41856 47107"/>
    </justification>
  </clause>

  <clause id="47111">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * ((z \ u) * w)) = a(x,y,((z \ 1) * u) * w)
    ]]></literal>
    <justification jstring="[para(30302(a,2),46290(a,1,3))].">
      <j1 rule="para" parents="30302 46290"/>
    </justification>
  </clause>

  <clause id="47112">
    <literal><![CDATA[
      a(x,((y \ z) \ u) * a(z,y,y),w) = a(x,(y * z) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32239,a(flip),b,46293,a),flip(a)].">
      <j1 rule="hyper" parents="373 32239 46293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47113">
    <literal><![CDATA[
      a(((x * y) \ z) * (a(u,w,v5) * a(x,y,y)),v6,a(u,u,v7)) = a(v7,v6,a((x * L(y,y,x)) \ z,u,u))
    ]]></literal>
    <justification jstring="[para(45001(a,1),46336(a,2,3,1))].">
      <j1 rule="para" parents="45001 46336"/>
    </justification>
  </clause>

  <clause id="47114">
    <literal><![CDATA[
      L(x,y,L(z * a(u,u,w),w,w)) = L(x,y,w * (L(w,u,u) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,24167,a,b,46446,a)].">
      <j1 rule="hyper" parents="64 24167 46446"/>
    </justification>
  </clause>

  <clause id="47115">
    <literal><![CDATA[
      R(T(x / a(y,z,x),u),a(y,z,x),w) = L(T(x,u),z,L(y,x,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,25,a,b,46453,a),flip(a)].">
      <j1 rule="hyper" parents="373 25 46453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47116">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ (a(z,y,a(x,u,w)) * L(x,y,z)) = a(w,u,x)
    ]]></literal>
    <justification jstring="[para(45065(a,2),46553(a,1,1))].">
      <j1 rule="para" parents="45065 46553"/>
    </justification>
  </clause>

  <clause id="47117">
    <literal><![CDATA[
      a(x,y,z) * (a(x,y,z) * ((u / w) * (a(x,y,z) \ w))) = u * a(x,y,L(z,w,w * u))
    ]]></literal>
    <justification jstring="[para(42911(a,2),46556(a,1,2))].">
      <j1 rule="para" parents="42911 46556"/>
    </justification>
  </clause>

  <clause id="47119">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,L(x,u,w)) = x * a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(45060(a,1),46557(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45060 46557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47120">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,L(x,u,w)) = x * a(a(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,41854,a,b,47119,a),flip(a)].">
      <j1 rule="hyper" parents="373 41854 47119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47121">
    <literal><![CDATA[
      L(x,y,z) * a(z,y,L(x,u,w)) = x * a(x * L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(45319(a,2),47120(a,2,2))].">
      <j1 rule="para" parents="45319 47120"/>
    </justification>
  </clause>

  <clause id="47123">
    <literal><![CDATA[
      a(x,y,z) * L(L(z,y,x),u,w) = L(z,u,L(w,y,x))
    ]]></literal>
    <justification jstring="[para(45130(a,2),46779(a,1,1))].">
      <j1 rule="para" parents="45130 46779"/>
    </justification>
  </clause>

  <clause id="47124">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * a(z,y,x) = L(x,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(23177,a,47123,a)].">
      <j1 rule="hyper" parents="23177 47123"/>
    </justification>
  </clause>

  <clause id="47125">
    <literal><![CDATA[
      a(x,y,z) \ L(z,u,L(w,y,x)) = L(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(149,a,47123,a)].">
      <j1 rule="hyper" parents="149 47123"/>
    </justification>
  </clause>

  <clause id="47129">
    <literal><![CDATA[
      L(L(x,y,z),u,w) \ L(x,y,L(z,u,w)) = a(w,u,x)
    ]]></literal>
    <justification jstring="[hyper(1433,a,47124,a)].">
      <j1 rule="hyper" parents="1433 47124"/>
    </justification>
  </clause>

  <clause id="47132">
    <literal><![CDATA[
      a(x,x,a(y,z,L(L(u,w,w),v5,v6))) = a(y,z,a(u,x,L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46787,a(flip),b,46833,a)].">
      <j1 rule="hyper" parents="64 46787 46833"/>
    </justification>
  </clause>

  <clause id="47133">
    <literal><![CDATA[
      (x * (a(y,y,L(x,z,u)) * z)) * u = a(y,y,x) * ((x * z) * u)
    ]]></literal>
    <justification jstring="[para(33266(a,1),46850(a,1,1))].">
      <j1 rule="para" parents="33266 46850"/>
    </justification>
  </clause>

  <clause id="47134">
    <literal><![CDATA[
      ((x * a(y,z,z)) * u) * u = a(y,z,z) * ((x * u) * u)
    ]]></literal>
    <justification jstring="[para(46524(a,1),46925(a,1,1))].">
      <j1 rule="para" parents="46524 46925"/>
    </justification>
  </clause>

  <clause id="47135">
    <literal><![CDATA[
      a(x,x,L(((y / z) * (z * u)) * (1 / y),y,z)) = a(x,x,((y * u) * (1 / y)) * a(z * y,(y * u) * (1 / y),z))
    ]]></literal>
    <justification jstring="[para(41973(a,1),46932(a,1,3,1))].">
      <j1 rule="para" parents="41973 46932"/>
    </justification>
  </clause>

  <clause id="47136">
    <literal><![CDATA[
      a((x \ y) * y,z,z * y) = a(x,z,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26827,a(flip),b,47103,a)].">
      <j1 rule="hyper" parents="64 26827 47103"/>
    </justification>
  </clause>

  <clause id="47137">
    <literal><![CDATA[
      a((((x / y) \ 1) / y) * ((x / y) \ K(y,x \ 1)),z,z * ((x / y) \ K(y,x \ 1))) = a(y,z,z * ((x / y) \ K(y,x \ 1)))
    ]]></literal>
    <justification jstring="[para(37194(a,1),47136(a,1,1,1))].">
      <j1 rule="para" parents="37194 47136"/>
    </justification>
  </clause>

  <clause id="47138">
    <literal><![CDATA[
      R(T(a(x,y,z) \ z,u),a(x,y,z),w) = L(T(z,u),y,L(x,z,w))
    ]]></literal>
    <justification jstring="[para(16647(a,1),47115(a,1,1,1))].">
      <j1 rule="para" parents="16647 47115"/>
    </justification>
  </clause>

  <clause id="47139">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ x,u,w) = x * a(x * L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(46562(a,2),47121(a,1,2))].">
      <j1 rule="para" parents="46562 47121"/>
    </justification>
  </clause>

  <clause id="47140">
    <literal><![CDATA[
      (a(x,y,z) * u) \ (z * u) = L(T(z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,31804,a(flip),b,47138,a)].">
      <j1 rule="hyper" parents="64 31804 47138"/>
    </justification>
  </clause>

  <clause id="47141">
    <literal><![CDATA[
      a(x,y,z * ((u * a(w,v5,u)) * v6)) = a(x,y,z * (v6 * L(u,v5,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27315,a,b,45229,a)].">
      <j1 rule="hyper" parents="64 27315 45229"/>
    </justification>
  </clause>

  <clause id="47142">
    <literal><![CDATA[
      L(x \ ((y \ z) * z),x,a(z,z * y,y)) = x \ ((y \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35698,a(flip),b,45634,a)].">
      <j1 rule="hyper" parents="64 35698 45634"/>
    </justification>
  </clause>

  <clause id="47143">
    <literal><![CDATA[
      a((a(x,y,z) * u) * w,v5,v6) = a((u * a(z,y,x)) * w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,45481,a(flip),b,45644,a),flip(a)].">
      <j1 rule="hyper" parents="64 45481 45644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47145">
    <literal><![CDATA[
      a((a(x,y,z) * u) * w,v5,v6) = a(w * (u * a(z,y,x)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,47143,a),flip(a)].">
      <j1 rule="hyper" parents="373 26787 47143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47146">
    <literal><![CDATA[
      a(x * (a(y,z,u) * w),v5,v6) = a(x * (w * a(u,z,y)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(26847,a,47145,a)].">
      <j1 rule="hyper" parents="26847 47145"/>
    </justification>
  </clause>

  <clause id="47149">
    <literal><![CDATA[
      a((x * y) * z,u,L(u,y * x,y)) = a((y * z) * L(x,y,y),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46749,a(flip),b,45663,a)].">
      <j1 rule="hyper" parents="64 46749 45663"/>
    </justification>
  </clause>

  <clause id="47150">
    <literal><![CDATA[
      a(x,y,z \ (a(u,u,w) * (v5 * w))) = a(x,y,z \ (v5 * L(w,u,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,37063,a(flip),b,45856,a),flip(a)].">
      <j1 rule="hyper" parents="373 37063 45856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47151">
    <literal><![CDATA[
      a(x,y,z) * (u \ a(x,u,a(u,y,z))) = u \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(23127(a,1),45866(a,2,2))].">
      <j1 rule="para" parents="23127 45866"/>
    </justification>
  </clause>

  <clause id="47152">
    <literal><![CDATA[
      a(x,y,z) * ((1 / L(u,u,x)) \ a(x,1 / L(u,u,x),a(1 / L(u,u,x),y,z))) = (x * (1 / u)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,46047,a(flip),b,47151,a),flip(a)].">
      <j1 rule="hyper" parents="373 46047 47151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47154">
    <literal><![CDATA[
      L(x,y,(z \ (u \ w)) * a(u,u,w)) = L(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,40611,a(flip),b,45921,a)].">
      <j1 rule="hyper" parents="64 40611 45921"/>
    </justification>
  </clause>

  <clause id="47155">
    <literal><![CDATA[
      L(x,((y \ (z * z)) * (R(T(y,u),w,v5) \ K(v6,v7))) * v8,v9) = L(x,(K(v6,v7) * (a(y,w,v5) \ K(u,y))) * v8,v9)
    ]]></literal>
    <justification jstring="[para(45954(a,2),11943(a,2,2,1))].">
      <j1 rule="para" parents="45954 11943"/>
    </justification>
  </clause>

  <clause id="47156">
    <literal><![CDATA[
      a(x,y,L(L(y,z,u),y,L(u * z,z,u))) = a(x,y,L(y,z * y,u))
    ]]></literal>
    <justification jstring="[para(44039(a,1),46001(a,1,3))].">
      <j1 rule="para" parents="44039 46001"/>
    </justification>
  </clause>

  <clause id="47157">
    <literal><![CDATA[
      a((x \ y) * ((y \ x) * z),y,x) = a(z * a(y,y * x,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,40188,a(flip),b,46006,a),flip(a)].">
      <j1 rule="hyper" parents="64 40188 46006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47158">
    <literal><![CDATA[
      L(x * a(y * z,x,z),z,y * z) = y \ (((y / z) * x) * T(z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41988,a(flip),b,46116,a)].">
      <j1 rule="hyper" parents="64 41988 46116"/>
    </justification>
  </clause>

  <clause id="47159">
    <literal><![CDATA[
      a(x,y,x \ L(z / (x \ 1),u,w)) = a(x,y,x * L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,31680,a(flip),b,46255,a),flip(a)].">
      <j1 rule="hyper" parents="373 31680 46255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47160">
    <literal><![CDATA[
      a(x,x,(y \ 1) \ (a(y,z,u) \ w)) = a(x,x,L(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,47048,a(flip),b,46260,a),flip(a)].">
      <j1 rule="hyper" parents="373 47048 46260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47161">
    <literal><![CDATA[
      a(x,x,(a(y,z,u) \ w) * y) = a(x,x,L(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,45561,a(flip),b,47160,a)].">
      <j1 rule="hyper" parents="64 45561 47160"/>
    </justification>
  </clause>

  <clause id="47162">
    <literal><![CDATA[
      a(x,x,(a(y,z,u) * w) * y) = a(x,x,L(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42521,a(flip),b,47161,a)].">
      <j1 rule="hyper" parents="64 42521 47161"/>
    </justification>
  </clause>

  <clause id="47163">
    <literal><![CDATA[
      a(x,x,a(y,z,u) * (w * y)) = a(x,x,L(y,z,u) * w)
    ]]></literal>
    <justification jstring="[para(29924(a,1),47162(a,1,3))].">
      <j1 rule="para" parents="29924 47162"/>
    </justification>
  </clause>

  <clause id="47164">
    <literal><![CDATA[
      L(x,y,((z * a(u,w,w)) * (v5 * v5)) \ (((z * a(u,w,w)) * v5) * v5)) = L(x,v5,a(v5,y,z * a(w,w,u)))
    ]]></literal>
    <justification jstring="[para(14(a,1),46272(a,1,3))].">
      <j1 rule="para" parents="14 46272"/>
    </justification>
  </clause>

  <clause id="47165">
    <literal><![CDATA[
      a(a(x * a(y,z,z),u,u),w * v5,v6) \ 1 = v6 \ L(v6,u,a(u,v5 * w,x * a(z,z,y)))
    ]]></literal>
    <justification jstring="[para(46272(a,1),45592(a,2,2))].">
      <j1 rule="para" parents="46272 45592"/>
    </justification>
  </clause>

  <clause id="47166">
    <literal><![CDATA[
      a(x * (y \ ((y \ x) \ (x * z))),x,y) = a(((x * y) * y) * z,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32675,a(flip),b,46288,a)].">
      <j1 rule="hyper" parents="64 32675 46288"/>
    </justification>
  </clause>

  <clause id="47167">
    <literal><![CDATA[
      x * (L(x,y,z) \ (a(z,u,w) \ 1)) = a(z,u,w) \ a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,42444,a(flip),b,46299,a),flip(a)].">
      <j1 rule="hyper" parents="373 42444 46299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47168">
    <literal><![CDATA[
      L(x,y,z) \ (a(z,u,w) \ x) = a(z,u,w) \ a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42547,a(flip),b,47167,a)].">
      <j1 rule="hyper" parents="64 42547 47167"/>
    </justification>
  </clause>

  <clause id="47169">
    <literal><![CDATA[
      a(x,y,y) \ (z \ (x * (1 / y))) = z \ (x / y)
    ]]></literal>
    <justification jstring="[para(45837(a,1),46303(a,1,2))].">
      <j1 rule="para" parents="45837 46303"/>
    </justification>
  </clause>

  <clause id="47170">
    <literal><![CDATA[
      (x \ (y / z)) \ (x \ (y * (1 / z))) = a(y,z,z)
    ]]></literal>
    <justification jstring="[para(47169(a,1),23134(a,1,1))].">
      <j1 rule="para" parents="47169 23134"/>
    </justification>
  </clause>

  <clause id="47171">
    <literal><![CDATA[
      a(x,y,((z * (u \ z)) \ u) * w) = a(x,y,u * (((u \ z) * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,40253,a,b,46357,a)].">
      <j1 rule="hyper" parents="64 40253 46357"/>
    </justification>
  </clause>

  <clause id="47172">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * (u \ w)) = a(x,y,z * (((z * u) * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27470,a(flip),b,46360,a)].">
      <j1 rule="hyper" parents="64 27470 46360"/>
    </justification>
  </clause>

  <clause id="47173">
    <literal><![CDATA[
      x * L(x \ (y \ x),x,a(z,u,w)) = L(y,x,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,42073,a(flip),b,46363,a),flip(a)].">
      <j1 rule="hyper" parents="64 42073 46363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47174">
    <literal><![CDATA[
      R(x,a(y,z,u),x * w) * w = R(x * w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,45235,a(flip),b,46367,a),flip(a)].">
      <j1 rule="hyper" parents="64 45235 46367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47175">
    <literal><![CDATA[
      R(x,a(y,z,u),x * w) * w = L(x * w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,31802,a(flip),b,47174,a),flip(a)].">
      <j1 rule="hyper" parents="373 31802 47174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47176">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (w * (z \ u))) = a(x,y,w * (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27726,a(flip),b,46368,a),flip(a)].">
      <j1 rule="hyper" parents="373 27726 46368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47177">
    <literal><![CDATA[
      a(x,y,L(L(z,y,u),u * y,y)) = L(a(x,y,z),L(y,u,y),y * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46493,a,b,46534,a)].">
      <j1 rule="hyper" parents="64 46493 46534"/>
    </justification>
  </clause>

  <clause id="47178">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w) * v5,v6,v7)) = a(x,y,L(v5 * a(w,u,z),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,46496,a(flip),b,46583,a),flip(a)].">
      <j1 rule="hyper" parents="64 46496 46583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47179">
    <literal><![CDATA[
      a((x * (y * z)) \ (x * z),u,w) = a(y,u,L(L(w,y * z,x),y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46496,a(flip),b,46591,a),flip(a)].">
      <j1 rule="hyper" parents="64 46496 46591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47181">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) \ (w * w)) = a(x,y,(z \ (u \ 1)) * (w * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,28081,a(flip),b,46702,a)].">
      <j1 rule="hyper" parents="64 28081 46702"/>
    </justification>
  </clause>

  <clause id="47182">
    <literal><![CDATA[
      a(x \ (y \ z),u,L(y,y * x,x)) = a(y \ (x \ z),u,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46737,a(flip),b,46729,a)].">
      <j1 rule="hyper" parents="64 46737 46729"/>
    </justification>
  </clause>

  <clause id="47183">
    <literal><![CDATA[
      a(L(x,y,y) \ (y * z),u,x) = a(x \ (y \ z),u,L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46600,a(flip),b,46729,a)].">
      <j1 rule="hyper" parents="64 46600 46729"/>
    </justification>
  </clause>

  <clause id="47184">
    <literal><![CDATA[
      a((x * y) * L(z,x,x),u,z) = a(z \ (x \ y),u,L(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46149,a(flip),b,47183,a)].">
      <j1 rule="hyper" parents="64 46149 47183"/>
    </justification>
  </clause>

  <clause id="47185">
    <literal><![CDATA[
      a((x * y) * L(z,x,x),u,z) = a(z * (x \ y),u,L(z,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,46649,a(flip),b,47184,a),flip(a)].">
      <j1 rule="hyper" parents="373 46649 47184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47186">
    <literal><![CDATA[
      a((x * y) * L(z,y,y),u,z) = a(z * (y \ x),u,L(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32388,a,b,47185,a)].">
      <j1 rule="hyper" parents="64 32388 47185"/>
    </justification>
  </clause>

  <clause id="47187">
    <literal><![CDATA[
      a((x * y) \ z,u,(x * y) \ w) = a(x \ (y \ z),u,x \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(27591,a,46732,a)].">
      <j1 rule="hyper" parents="27591 46732"/>
    </justification>
  </clause>

  <clause id="47188">
    <literal><![CDATA[
      x * (a(y,z,((u \ 1) / w) \ 1) \ 1) = x * (w \ (u \ L(u * w,z,y)))
    ]]></literal>
    <justification jstring="[para(1389(a,1),46792(a,2,2,2))].">
      <j1 rule="para" parents="1389 46792"/>
    </justification>
  </clause>

  <clause id="47189">
    <literal><![CDATA[
      a(x,y,z) \ ((a(u * (w \ x),v5,x) \ a(x,y,z)) * x) = L(x,v5,x \ (w * u))
    ]]></literal>
    <justification jstring="[para(46858(a,1),46828(a,1,2,1,1))].">
      <j1 rule="para" parents="46858 46828"/>
    </justification>
  </clause>

  <clause id="47190">
    <literal><![CDATA[
      a(x,y,L(y,z,a(u,w,y) * v5)) = a(x,y,L(y,z,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,44200,a(flip),b,47036,a),flip(a)].">
      <j1 rule="hyper" parents="373 44200 47036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47192">
    <literal><![CDATA[
      a(a((x * y) * z,z,x),u,w) = a(a(x,z,x * (z \ y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,45092,a,b,47072,a)].">
      <j1 rule="hyper" parents="36 45092 47072"/>
    </justification>
  </clause>

  <clause id="47193">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * L(z,y,x) = L(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(39,a,47129,a,b,47116,a),flip(a)].">
      <j1 rule="hyper" parents="39 47129 47116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47196">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(36,a,47110,a,b,47193,a)].">
      <j1 rule="hyper" parents="36 47110 47193"/>
    </justification>
  </clause>

  <clause id="47197">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(36,a,47109,a,b,47193,a)].">
      <j1 rule="hyper" parents="36 47109 47193"/>
    </justification>
  </clause>

  <clause id="47198">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,47107,a,b,47193,a),flip(a)].">
      <j1 rule="hyper" parents="36 47107 47193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47199">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * L(z,y,x) = L(z,y,L(x,u * x,y))
    ]]></literal>
    <justification jstring="[para(46889(a,1),47193(a,1,1))].">
      <j1 rule="para" parents="46889 47193"/>
    </justification>
  </clause>

  <clause id="47200">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,41883,a,b,47196,a),flip(a)].">
      <j1 rule="hyper" parents="373 41883 47196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47202">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(z,y,a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,41479,a,b,47196,a)].">
      <j1 rule="hyper" parents="64 41479 47196"/>
    </justification>
  </clause>

  <clause id="47203">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,x,v5))) = a(z,u,a(w,y,v5 \ (x \ v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46830,a(flip),b,47196,a)].">
      <j1 rule="hyper" parents="64 46830 47196"/>
    </justification>
  </clause>

  <clause id="47204">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) = a(w,u,a(z,y,L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46808,a(flip),b,47196,a)].">
      <j1 rule="hyper" parents="64 46808 47196"/>
    </justification>
  </clause>

  <clause id="47205">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(v5,w,a(u,z,y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41879,a(flip),b,47196,a)].">
      <j1 rule="hyper" parents="64 41879 47196"/>
    </justification>
  </clause>

  <clause id="47206">
    <literal><![CDATA[
      a(x,y * z,a(u,w,v5)) = a(v5,w,a(u,z * y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41858,a(flip),b,47196,a),flip(a)].">
      <j1 rule="hyper" parents="64 41858 47196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47207">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ 1)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41852,a(flip),b,47196,a),flip(a)].">
      <j1 rule="hyper" parents="64 41852 47196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47209">
    <literal><![CDATA[
      a(x,y,a(z * u,w,v5)) = a(v5,w,a(x,y,u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41847,a(flip),b,47196,a),flip(a)].">
      <j1 rule="hyper" parents="64 41847 47196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47211">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) * u,w,a(x,y,z)) = L(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(47196(a,1),34925(a,1,1,1))].">
      <j1 rule="para" parents="47196 34925"/>
    </justification>
  </clause>

  <clause id="47213">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) = x * a(v5,w,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(47196(a,1),41854(a,1,2))].">
      <j1 rule="para" parents="47196 41854"/>
    </justification>
  </clause>

  <clause id="47214">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(47196(a,1),41855(a,1,1))].">
      <j1 rule="para" parents="47196 41855"/>
    </justification>
  </clause>

  <clause id="47217">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = a(w,u,a(z,y,x)) * v5
    ]]></literal>
    <justification jstring="[para(47196(a,1),41869(a,1,1))].">
      <j1 rule="para" parents="47196 41869"/>
    </justification>
  </clause>

  <clause id="47221">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ v5 = v5 * a(z,u,a(w,y,x))
    ]]></literal>
    <justification jstring="[para(47196(a,1),42499(a,2,2))].">
      <j1 rule="para" parents="47196 42499"/>
    </justification>
  </clause>

  <clause id="47222">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * w = L(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(47196(a,1),45092(a,1,1))].">
      <j1 rule="para" parents="47196 45092"/>
    </justification>
  </clause>

  <clause id="47223">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) = L(x,w,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(47196(a,1),45104(a,1,2))].">
      <j1 rule="para" parents="47196 45104"/>
    </justification>
  </clause>

  <clause id="47228">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(u,w,a(v5,z,y * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,41890,a,b,47197,a)].">
      <j1 rule="hyper" parents="373 41890 47197"/>
    </justification>
  </clause>

  <clause id="47231">
    <literal><![CDATA[
      a(x,y,a(z,x,u)) = a(x,x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,45785,a(flip),b,47197,a),flip(a)].">
      <j1 rule="hyper" parents="373 45785 47197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47233">
    <literal><![CDATA[
      a(x,y,z) * a(x,y,a(z,u,w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,47197,a,b,46526,a)].">
      <j1 rule="hyper" parents="145 47197 46526"/>
    </justification>
  </clause>

  <clause id="47239">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(w,u,a(z,y,y * x))
    ]]></literal>
    <justification jstring="[para(47197(a,1),47050(a,2,2))].">
      <j1 rule="para" parents="47197 47050"/>
    </justification>
  </clause>

  <clause id="47240">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ (a(z,y,x) * v5) = L(T(a(z,y,x),v5),u,L(w,a(z,y,x),v5))
    ]]></literal>
    <justification jstring="[para(47197(a,1),47140(a,1,1,1))].">
      <j1 rule="para" parents="47197 47140"/>
    </justification>
  </clause>

  <clause id="47241">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(z,y,a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,47197,a,b,47198,a)].">
      <j1 rule="hyper" parents="373 47197 47198"/>
    </justification>
  </clause>

  <clause id="47242">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(z,u,a(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47196,a,b,47198,a)].">
      <j1 rule="hyper" parents="373 47196 47198"/>
    </justification>
  </clause>

  <clause id="47244">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,47198,a(flip),b,47198,a)].">
      <j1 rule="hyper" parents="373 47198 47198"/>
    </justification>
  </clause>

  <clause id="47245">
    <literal><![CDATA[
      a(x,y,a(y * (z * x),u,w)) = a(w,u,a(x,y,x * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47071,a(flip),b,47198,a),flip(a)].">
      <j1 rule="hyper" parents="373 47071 47198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47246">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) = a(w,u,a(x,y,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,46629,a(flip),b,47198,a),flip(a)].">
      <j1 rule="hyper" parents="373 46629 47198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47249">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,L(z,u,w)) = a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46527,a,b,47198,a)].">
      <j1 rule="hyper" parents="64 46527 47198"/>
    </justification>
  </clause>

  <clause id="47251">
    <literal><![CDATA[
      x \ L(x,y,a(z,u,w)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,45194,a,b,47198,a)].">
      <j1 rule="hyper" parents="64 45194 47198"/>
    </justification>
  </clause>

  <clause id="47252">
    <literal><![CDATA[
      a((x * y) * z,u,a(w,v5,v6)) = a(w,v5,a(z * (y * x),u,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,41899,a,b,47198,a),flip(a)].">
      <j1 rule="hyper" parents="64 41899 47198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47253">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,41883,a,b,47198,a)].">
      <j1 rule="hyper" parents="64 41883 47198"/>
    </justification>
  </clause>

  <clause id="47254">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41803,a,b,47198,a)].">
      <j1 rule="hyper" parents="64 41803 47198"/>
    </justification>
  </clause>

  <clause id="47258">
    <literal><![CDATA[
      x * a(y,z,a(x,u,w)) = L(x,u,a(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,47198,a(flip),b,45194,a)].">
      <j1 rule="hyper" parents="145 47198 45194"/>
    </justification>
  </clause>

  <clause id="47259">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) = x * a(u,w,a(y,z,v5))
    ]]></literal>
    <justification jstring="[hyper(145,a,47198,a(flip),b,41898,a)].">
      <j1 rule="hyper" parents="145 47198 41898"/>
    </justification>
  </clause>

  <clause id="47265">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(47198(a,1),41900(a,1,1))].">
      <j1 rule="para" parents="47198 41900"/>
    </justification>
  </clause>

  <clause id="47266">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = a(z,u,a(x,y,w)) * v5
    ]]></literal>
    <justification jstring="[para(47198(a,1),41902(a,1,1))].">
      <j1 rule="para" parents="47198 41902"/>
    </justification>
  </clause>

  <clause id="47267">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),u,a(w,z,y)) = L(x,a(w,z,y),u)
    ]]></literal>
    <justification jstring="[para(47198(a,1),41867(a,1,1,2))].">
      <j1 rule="para" parents="47198 41867"/>
    </justification>
  </clause>

  <clause id="47268">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),u,a(y,z,w)) = L(x,a(w,z,y),u)
    ]]></literal>
    <justification jstring="[para(47198(a,1),42246(a,1,1,2))].">
      <j1 rule="para" parents="47198 42246"/>
    </justification>
  </clause>

  <clause id="47270">
    <literal><![CDATA[
      a(x,y,a(z,u,a(y,w,v5))) = a(x,w,a(y,y,a(v5,u,z)))
    ]]></literal>
    <justification jstring="[para(47198(a,1),45871(a,2,3)),flip(a)].">
      <j1 rule="para" parents="47198 45871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47271">
    <literal><![CDATA[
      x * a(y,z,a(x,u,w)) = L(x,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[para(47198(a,1),45157(a,1,2))].">
      <j1 rule="para" parents="47198 45157"/>
    </justification>
  </clause>

  <clause id="47274">
    <literal><![CDATA[
      a(x \ (y \ x),z,a(u,w,v5)) = a(v5,w,a(y,z,L(u,y,x)))
    ]]></literal>
    <justification jstring="[para(46514(a,1),47198(a,2,3))].">
      <j1 rule="para" parents="46514 47198"/>
    </justification>
  </clause>

  <clause id="47276">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,y,x) = a(w,y,L(x,u,z))
    ]]></literal>
    <justification jstring="[para(47198(a,1),46502(a,1,1))].">
      <j1 rule="para" parents="47198 46502"/>
    </justification>
  </clause>

  <clause id="47277">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(w,u,a(y * x,y,z))
    ]]></literal>
    <justification jstring="[para(47198(a,1),47050(a,2,2))].">
      <j1 rule="para" parents="47198 47050"/>
    </justification>
  </clause>

  <clause id="47278">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,u,a(y,x,z)) = a(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(47198(a,1),47051(a,1,2))].">
      <j1 rule="para" parents="47198 47051"/>
    </justification>
  </clause>

  <clause id="47279">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * L(x,y,w) = L(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[para(47198(a,1),47107(a,1,1))].">
      <j1 rule="para" parents="47198 47107"/>
    </justification>
  </clause>

  <clause id="47280">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (z \ v5) = v5 * L(v5 \ (z \ v5),u,a(w,y,x))
    ]]></literal>
    <justification jstring="[para(47198(a,1),45978(a,1,1))].">
      <j1 rule="para" parents="47198 45978"/>
    </justification>
  </clause>

  <clause id="47281">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,47198,a(flip),b,47200,a),flip(a)].">
      <j1 rule="hyper" parents="373 47198 47200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47282">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (w * v5))) = a(v5,u,a(x,y,L(z,w,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46618,a,b,47200,a)].">
      <j1 rule="hyper" parents="64 46618 47200"/>
    </justification>
  </clause>

  <clause id="47285">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(x,y,a(w,v5,a(z,u,v6)))
    ]]></literal>
    <justification jstring="[para(47200(a,1),41883(a,1,3))].">
      <j1 rule="para" parents="47200 41883"/>
    </justification>
  </clause>

  <clause id="47286">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) = L(x,y,a(w,v5,a(z,u,v6)))
    ]]></literal>
    <justification jstring="[para(47200(a,1),42195(a,1,3))].">
      <j1 rule="para" parents="47200 42195"/>
    </justification>
  </clause>

  <clause id="47287">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * z = L(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(47200(a,1),45093(a,1,1))].">
      <j1 rule="para" parents="47200 45093"/>
    </justification>
  </clause>

  <clause id="47288">
    <literal><![CDATA[
      a(x * (y \ (z \ (x * y))),x,a(u,w,y)) = a(a(z,x,y),w,u)
    ]]></literal>
    <justification jstring="[para(46279(a,1),47200(a,1,1)),flip(a)].">
      <j1 rule="para" parents="46279 47200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47289">
    <literal><![CDATA[
      a(x * y,z,a(u,w,a(z,x,v5))) = a(z,z,a(x * y,y,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(47200(a,1),46907(a,1,3))].">
      <j1 rule="para" parents="47200 46907"/>
    </justification>
  </clause>

  <clause id="47290">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,47198,a,b,47202,a),flip(a)].">
      <j1 rule="hyper" parents="373 47198 47202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47291">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(a(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,41803,a,b,47202,a)].">
      <j1 rule="hyper" parents="373 41803 47202"/>
    </justification>
  </clause>

  <clause id="47292">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,x,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,45886,a(flip),b,47202,a),flip(a)].">
      <j1 rule="hyper" parents="64 45886 47202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47296">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(47202(a,1),42050(a,1))].">
      <j1 rule="para" parents="47202 42050"/>
    </justification>
  </clause>

  <clause id="47298">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,47198,a,b,47241,a)].">
      <j1 rule="hyper" parents="373 47198 47241"/>
    </justification>
  </clause>

  <clause id="47302">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(v5,z,a(y * x,w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,41890,a,b,47241,a)].">
      <j1 rule="hyper" parents="373 41890 47241"/>
    </justification>
  </clause>

  <clause id="47306">
    <literal><![CDATA[
      a(x,y,z) * a(x,u,a(w,y,z)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(145,a,47241,a,b,46527,a)].">
      <j1 rule="hyper" parents="145 47241 46527"/>
    </justification>
  </clause>

  <clause id="47309">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) = x * a(v5,z,a(y,w,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,47241,a,b,41898,a),flip(a)].">
      <j1 rule="hyper" parents="145 47241 41898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47311">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(w,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[para(47241(a,1),41900(a,2,2))].">
      <j1 rule="para" parents="47241 41900"/>
    </justification>
  </clause>

  <clause id="47312">
    <literal><![CDATA[
      L(L(x,y,a(z,u,a(w,v5,v6))),y,a(w,u,a(z,v5,v6))) = x
    ]]></literal>
    <justification jstring="[para(47241(a,1),42171(a,1,1,3))].">
      <j1 rule="para" parents="47241 42171"/>
    </justification>
  </clause>

  <clause id="47313">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),z,a(y,u,w)) = L(x,a(y,u,w),z)
    ]]></literal>
    <justification jstring="[para(47241(a,1),41867(a,1,1,2))].">
      <j1 rule="para" parents="47241 41867"/>
    </justification>
  </clause>

  <clause id="47316">
    <literal><![CDATA[
      x * a(y,z,a(x,u,w)) = L(x,z,a(w,u,y))
    ]]></literal>
    <justification jstring="[para(47241(a,1),45157(a,1,2))].">
      <j1 rule="para" parents="47241 45157"/>
    </justification>
  </clause>

  <clause id="47317">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(v6,y,a(x,v5,a(w,u,z)))
    ]]></literal>
    <justification jstring="[para(47197(a,1),47241(a,1,3))].">
      <j1 rule="para" parents="47197 47241"/>
    </justification>
  </clause>

  <clause id="47320">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(x,y,a(v6,u,a(z,v5,w)))
    ]]></literal>
    <justification jstring="[para(47242(a,1),41883(a,1,3)),flip(a)].">
      <j1 rule="para" parents="47242 41883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47322">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * z = L(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[para(47242(a,1),45093(a,1,1))].">
      <j1 rule="para" parents="47242 45093"/>
    </justification>
  </clause>

  <clause id="47324">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,47198,a,b,47244,a)].">
      <j1 rule="hyper" parents="373 47198 47244"/>
    </justification>
  </clause>

  <clause id="47325">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) \ a(x,y,z) = a(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,46545,a,b,47244,a)].">
      <j1 rule="hyper" parents="373 46545 47244"/>
    </justification>
  </clause>

  <clause id="47326">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(v5,z,a(u,w,y * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,41890,a,b,47244,a)].">
      <j1 rule="hyper" parents="373 41890 47244"/>
    </justification>
  </clause>

  <clause id="47327">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(w,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,41883,a,b,47244,a)].">
      <j1 rule="hyper" parents="373 41883 47244"/>
    </justification>
  </clause>

  <clause id="47328">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = a(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,41803,a,b,47244,a)].">
      <j1 rule="hyper" parents="373 41803 47244"/>
    </justification>
  </clause>

  <clause id="47329">
    <literal><![CDATA[
      a(x,y,a(z,u * w,v5)) = a(v5,y,a(x,w * u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,32311,a,b,47244,a),flip(a)].">
      <j1 rule="hyper" parents="373 32311 47244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47330">
    <literal><![CDATA[
      a(x * (y * z),u,a(w,v5,v6)) = a(v6,u,a(w,v5,x * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,41895,a(flip),b,47244,a),flip(a)].">
      <j1 rule="hyper" parents="373 41895 47244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47333">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,y,a(w,u,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(145,a,47244,a,b,42365,a)].">
      <j1 rule="hyper" parents="145 47244 42365"/>
    </justification>
  </clause>

  <clause id="47334">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) = x * a(v5,z,a(u,w,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,47244,a,b,41898,a)].">
      <j1 rule="hyper" parents="145 47244 41898"/>
    </justification>
  </clause>

  <clause id="47335">
    <literal><![CDATA[
      a(x * (y \ x),x * y,a(z,u,w)) = a(w,x * y,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42036,a,b,47244,a)].">
      <j1 rule="hyper" parents="64 42036 47244"/>
    </justification>
  </clause>

  <clause id="47341">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),w,a(y,u,z)) = L(x,a(y,u,z),w)
    ]]></literal>
    <justification jstring="[para(47244(a,2),41867(a,1,1,2))].">
      <j1 rule="para" parents="47244 41867"/>
    </justification>
  </clause>

  <clause id="47342">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),a(z,u,y),w) = L(x,w,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(47244(a,2),41910(a,1,1,2))].">
      <j1 rule="para" parents="47244 41910"/>
    </justification>
  </clause>

  <clause id="47343">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(z,y,a(x,u,w)) * v5) = v5
    ]]></literal>
    <justification jstring="[para(47244(a,1),42646(a,1,1))].">
      <j1 rule="para" parents="47244 42646"/>
    </justification>
  </clause>

  <clause id="47349">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) = L(x,z,a(u,w,y))
    ]]></literal>
    <justification jstring="[para(47244(a,2),45157(a,1,2))].">
      <j1 rule="para" parents="47244 45157"/>
    </justification>
  </clause>

  <clause id="47350">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,u,x) = a(z,u,L(x,y,w))
    ]]></literal>
    <justification jstring="[para(47244(a,2),46501(a,1,1))].">
      <j1 rule="para" parents="47244 46501"/>
    </justification>
  </clause>

  <clause id="47351">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(x,u,z) = a(x,u,L(z,y,w))
    ]]></literal>
    <justification jstring="[para(47244(a,2),46502(a,1,1))].">
      <j1 rule="para" parents="47244 46502"/>
    </justification>
  </clause>

  <clause id="47352">
    <literal><![CDATA[
      a(x,y * z,a(u,w,v5)) = a(u,w,a(x,z * y,v5))
    ]]></literal>
    <justification jstring="[hyper(32008,a,47253,a)].">
      <j1 rule="hyper" parents="32008 47253"/>
    </justification>
  </clause>

  <clause id="47358">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,w)) = y * a(w,u,a(x * y,x,z))
    ]]></literal>
    <justification jstring="[para(47253(a,1),42908(a,2,2))].">
      <j1 rule="para" parents="47253 42908"/>
    </justification>
  </clause>

  <clause id="47360">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(w,v5,a(x,y,a(v6,u,z)))
    ]]></literal>
    <justification jstring="[para(47198(a,1),47253(a,1,3))].">
      <j1 rule="para" parents="47198 47253"/>
    </justification>
  </clause>

  <clause id="47361">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(v6,u,a(x,y,a(z,v5,w)))
    ]]></literal>
    <justification jstring="[para(47244(a,2),47253(a,1,3))].">
      <j1 rule="para" parents="47244 47253"/>
    </justification>
  </clause>

  <clause id="47363">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 * w))) = a(v5,u,a(L(x,w,w),y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46870,a,b,47254,a)].">
      <j1 rule="hyper" parents="64 46870 47254"/>
    </justification>
  </clause>

  <clause id="47364">
    <literal><![CDATA[
      a(x,a(y,z,u) * w,a(y,z,u)) = a(u,z,a(x,w,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42837,a,b,47254,a)].">
      <j1 rule="hyper" parents="64 42837 47254"/>
    </justification>
  </clause>

  <clause id="47365">
    <literal><![CDATA[
      a((x * y) \ ((y \ z) \ (x * z)),u,w) = a(x,y,a(w,u,z * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41842,a,b,47254,a)].">
      <j1 rule="hyper" parents="64 41842 47254"/>
    </justification>
  </clause>

  <clause id="47366">
    <literal><![CDATA[
      a(a(x,y,x * (y \ z)),u,w) = a(x,y,a(w,u,(x * z) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47192,a(flip),b,47254,a)].">
      <j1 rule="hyper" parents="64 47192 47254"/>
    </justification>
  </clause>

  <clause id="47367">
    <literal><![CDATA[
      a(a(x,y,z * (y * x)),u,w) = a((x \ z) * y,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46975,a(flip),b,47254,a)].">
      <j1 rule="hyper" parents="64 46975 47254"/>
    </justification>
  </clause>

  <clause id="47369">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),w,a(y,z,u)) = x * a(u,z,a(w,x,y))
    ]]></literal>
    <justification jstring="[para(47254(a,1),42174(a,2,2))].">
      <j1 rule="para" parents="47254 42174"/>
    </justification>
  </clause>

  <clause id="47370">
    <literal><![CDATA[
      a(x,y,z) * ((u / w) * (a(x,y,z) \ w)) = u * a(z,y,a(u * w,w,x))
    ]]></literal>
    <justification jstring="[para(47254(a,1),42915(a,2,2))].">
      <j1 rule="para" parents="47254 42915"/>
    </justification>
  </clause>

  <clause id="47371">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ z = L(z,u,a(w,y,x))
    ]]></literal>
    <justification jstring="[para(47254(a,1),45065(a,2,1)),flip(a)].">
      <j1 rule="para" parents="47254 45065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47373">
    <literal><![CDATA[
      (x * a(y,z,a(u,w,v5))) \ (x * u) = L(u,w,L(a(v5,z,y),u,x))
    ]]></literal>
    <justification jstring="[para(47254(a,1),46452(a,1,1,2))].">
      <j1 rule="para" parents="47254 46452"/>
    </justification>
  </clause>

  <clause id="47374">
    <literal><![CDATA[
      a(a(x * (y \ z),u,z),w,v5) = a(z,u,a(v5,w,(y * x) * z))
    ]]></literal>
    <justification jstring="[para(46858(a,1),47254(a,1,1))].">
      <j1 rule="para" parents="46858 47254"/>
    </justification>
  </clause>

  <clause id="47375">
    <literal><![CDATA[
      a(a(x * (y \ z),u,z),w,v5) = a(z,u,a(v5,w,(x \ z) * y))
    ]]></literal>
    <justification jstring="[para(46866(a,1),47254(a,1,1))].">
      <j1 rule="para" parents="46866 47254"/>
    </justification>
  </clause>

  <clause id="47377">
    <literal><![CDATA[
      a(a(x,y,x \ (y \ z)),u,w) = a(y \ (x \ z),y,a(w,u,x))
    ]]></literal>
    <justification jstring="[para(46969(a,1),47254(a,1,1))].">
      <j1 rule="para" parents="46969 47254"/>
    </justification>
  </clause>

  <clause id="47378">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,u,a(y,x,w)) = a(x,a(w,u,z),y)
    ]]></literal>
    <justification jstring="[para(47254(a,1),46464(a,1,2))].">
      <j1 rule="para" parents="47254 46464"/>
    </justification>
  </clause>

  <clause id="47379">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) / v5) \ 1 = (1 / v5) \ a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(47254(a,1),47000(a,1,1,1))].">
      <j1 rule="para" parents="47254 47000"/>
    </justification>
  </clause>

  <clause id="47380">
    <literal><![CDATA[
      (1 / x) \ a(y,z,a(u,w,L(v5,x,x))) = x * a(u,w,a(y,z,v5))
    ]]></literal>
    <justification jstring="[para(47254(a,1),46832(a,2,2))].">
      <j1 rule="para" parents="47254 46832"/>
    </justification>
  </clause>

  <clause id="47381">
    <literal><![CDATA[
      a(x \ y,z,a(u,w,a(v5,v5,v6))) = a(y * x,v5,a(u,w,a(v5,z,v6)))
    ]]></literal>
    <justification jstring="[para(47254(a,1),46427(a,2,3))].">
      <j1 rule="para" parents="47254 46427"/>
    </justification>
  </clause>

  <clause id="47383">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),w,a(z,u,y)) = L(x,a(z,u,y),w)
    ]]></literal>
    <justification jstring="[para(47281(a,1),34924(a,1,1,2))].">
      <j1 rule="para" parents="47281 34924"/>
    </justification>
  </clause>

  <clause id="47384">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * w = L(w,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[para(47281(a,1),45093(a,1,1))].">
      <j1 rule="para" parents="47281 45093"/>
    </justification>
  </clause>

  <clause id="47385">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,x,a(z,u,y)) = a(x,a(z,u,w),y)
    ]]></literal>
    <justification jstring="[para(47281(a,1),46979(a,1,2))].">
      <j1 rule="para" parents="47281 46979"/>
    </justification>
  </clause>

  <clause id="47388">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) = L(x,y,a(w,u,a(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(47290(a,1),42195(a,1,3))].">
      <j1 rule="para" parents="47290 42195"/>
    </justification>
  </clause>

  <clause id="47389">
    <literal><![CDATA[
      x * (y * a(z,y,a(x,u,w))) = L(x,y,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(47290(a,1),42192(a,1,2,2))].">
      <j1 rule="para" parents="47290 42192"/>
    </justification>
  </clause>

  <clause id="47392">
    <literal><![CDATA[
      a(a(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,y,a(w,u,x)) = v5
    ]]></literal>
    <justification jstring="[para(47291(a,1),42050(a,1))].">
      <j1 rule="para" parents="47291 42050"/>
    </justification>
  </clause>

  <clause id="47393">
    <literal><![CDATA[
      a(x,y * z,a(u,w,v5)) = a(x,w,a(v5,z * y,u))
    ]]></literal>
    <justification jstring="[hyper(32008,a,47298,a)].">
      <j1 rule="hyper" parents="32008 47298"/>
    </justification>
  </clause>

  <clause id="47395">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(y * x,w,a(u,z,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,41890,a,b,47298,a)].">
      <j1 rule="hyper" parents="373 41890 47298"/>
    </justification>
  </clause>

  <clause id="47397">
    <literal><![CDATA[
      a(x,y,z) * a(u,y,a(x,w,z)) = a(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,47298,a,b,46526,a)].">
      <j1 rule="hyper" parents="145 47298 46526"/>
    </justification>
  </clause>

  <clause id="47398">
    <literal><![CDATA[
      x * a(x,y,a(z,u,w)) = L(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,47298,a,b,45194,a)].">
      <j1 rule="hyper" parents="145 47298 45194"/>
    </justification>
  </clause>

  <clause id="47402">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(w,y,z) * v5) = a(w,y,z) * (v5 * a(x,u,a(w,y,z)))
    ]]></literal>
    <justification jstring="[para(47298(a,1),33200(a,1,1))].">
      <j1 rule="para" parents="47298 33200"/>
    </justification>
  </clause>

  <clause id="47403">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[para(47298(a,1),41900(a,1,1))].">
      <j1 rule="para" parents="47298 41900"/>
    </justification>
  </clause>

  <clause id="47407">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,y,w) = a(z,y,L(w,u,x))
    ]]></literal>
    <justification jstring="[para(47298(a,1),46501(a,1,1))].">
      <j1 rule="para" parents="47298 46501"/>
    </justification>
  </clause>

  <clause id="47408">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,y,z) = a(w,y,L(z,u,x))
    ]]></literal>
    <justification jstring="[para(47298(a,1),46502(a,1,1))].">
      <j1 rule="para" parents="47298 46502"/>
    </justification>
  </clause>

  <clause id="47409">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w),v5,v6)) = a(x,v5,a(w,u,a(z,y,v6)))
    ]]></literal>
    <justification jstring="[para(47197(a,1),47298(a,1,3)),flip(a)].">
      <j1 rule="para" parents="47197 47298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47413">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),y,a(u,z,w)) = L(x,a(u,z,w),y)
    ]]></literal>
    <justification jstring="[para(47324(a,1),41867(a,1,1,2))].">
      <j1 rule="para" parents="47324 41867"/>
    </justification>
  </clause>

  <clause id="47415">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,z,a(u,w,y)) = v5
    ]]></literal>
    <justification jstring="[para(47327(a,1),45403(a,1,2))].">
      <j1 rule="para" parents="47327 45403"/>
    </justification>
  </clause>

  <clause id="47416">
    <literal><![CDATA[
      L(x,y,z * a(x,z,a(u,w,v5))) = L(x,y,L(z,a(u,w,x),v5))
    ]]></literal>
    <justification jstring="[para(47327(a,1),46778(a,1,3,2))].">
      <j1 rule="para" parents="47327 46778"/>
    </justification>
  </clause>

  <clause id="47417">
    <literal><![CDATA[
      L(1 / x,y,a(z,u,w)) = a(z,y,a(w,u,x)) / x
    ]]></literal>
    <justification jstring="[para(47328(a,1),45645(a,2,1))].">
      <j1 rule="para" parents="47328 45645"/>
    </justification>
  </clause>

  <clause id="47418">
    <literal><![CDATA[
      L(x,y,a(z,u,w \ 1)) = x * a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(145,a,47207,a(flip),b,45194,a),flip(a)].">
      <j1 rule="hyper" parents="145 47207 45194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47425">
    <literal><![CDATA[
      L(x,y,a(z * y,x,u)) = a(u,z,a(x,x,z * y)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,46921,a,b,47271,a),flip(a)].">
      <j1 rule="hyper" parents="64 46921 47271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47426">
    <literal><![CDATA[
      x * R(x \ y,z,a(y,u,w)) = L(y,u,a(y \ x,z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,45416,a,b,47271,a)].">
      <j1 rule="hyper" parents="64 45416 47271"/>
    </justification>
  </clause>

  <clause id="47427">
    <literal><![CDATA[
      x * a(y,z,a(x,u * w,u)) = L(x,u \ w,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(35684(a,1),47271(a,1,2,3))].">
      <j1 rule="para" parents="35684 47271"/>
    </justification>
  </clause>

  <clause id="47428">
    <literal><![CDATA[
      L(x,y,a(z,u,(w * (v5 \ 1)) * v6)) = x * a(z,u,a(x,y,v6 * (w * v5)))
    ]]></literal>
    <justification jstring="[para(42301(a,1),47271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="42301 47271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47429">
    <literal><![CDATA[
      x * a(y,z,a(u,w,L(x,v5,v6))) = L(x,w,a(y,z,L(u,v5,v6)))
    ]]></literal>
    <justification jstring="[para(46615(a,1),47271(a,1,2))].">
      <j1 rule="para" parents="46615 47271"/>
    </justification>
  </clause>

  <clause id="47431">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) * R(z,v5,v6) = L(R(z,v5,v6),u,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(46576(a,1),47287(a,1,1,3))].">
      <j1 rule="para" parents="46576 47287"/>
    </justification>
  </clause>

  <clause id="47432">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47271,a(flip),b,47316,a)].">
      <j1 rule="hyper" parents="64 47271 47316"/>
    </justification>
  </clause>

  <clause id="47433">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47258,a(flip),b,47316,a)].">
      <j1 rule="hyper" parents="64 47258 47316"/>
    </justification>
  </clause>

  <clause id="47434">
    <literal><![CDATA[
      R(x,y,a(z,u,w)) = L(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,28832,a,b,47432,a)].">
      <j1 rule="hyper" parents="373 28832 47432"/>
    </justification>
  </clause>

  <clause id="47435">
    <literal><![CDATA[
      L(x,y,a(z,a(z,y,u) * w,u)) = L(x,w,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,42853,a(flip),b,47432,a),flip(a)].">
      <j1 rule="hyper" parents="373 42853 47432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47436">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),u,a(z,y,w)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,42206,a(flip),b,47432,a),flip(a)].">
      <j1 rule="hyper" parents="373 42206 47432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47439">
    <literal><![CDATA[
      (a(x,y,z) \ u) * L(w,y,a(z,u,x)) = a(x,y,z) \ (u * w)
    ]]></literal>
    <justification jstring="[hyper(145,a,47432,a,b,42812,a)].">
      <j1 rule="hyper" parents="145 47432 42812"/>
    </justification>
  </clause>

  <clause id="47440">
    <literal><![CDATA[
      x * L(y,z,a(u,w,v5)) = x * L(y,w,a(v5,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,47432,a,b,9,a)].">
      <j1 rule="hyper" parents="145 47432 9"/>
    </justification>
  </clause>

  <clause id="47441">
    <literal><![CDATA[
      (a(x,y,z) * u) * L(w,y,a(z,u,x)) = a(x,y,z) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(145,a,47432,a,b,18,a(flip))].">
      <j1 rule="hyper" parents="145 47432 18"/>
    </justification>
  </clause>

  <clause id="47444">
    <literal><![CDATA[
      L(L(x,y,z),x,L(u,w,a(v5,x,v6))) = L(L(x,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(47432(a,1),37508(a,1,3))].">
      <j1 rule="para" parents="47432 37508"/>
    </justification>
  </clause>

  <clause id="47445">
    <literal><![CDATA[
      a(x,y,z) * (u * L(w,y,a(z,u,x))) = (u * a(x,y,z)) * w
    ]]></literal>
    <justification jstring="[para(47432(a,1),42176(a,1,2,2))].">
      <j1 rule="para" parents="47432 42176"/>
    </justification>
  </clause>

  <clause id="47446">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (a(z,y,w) * u) = a(z,y,w) * (x * u)
    ]]></literal>
    <justification jstring="[para(47432(a,1),42211(a,1,1))].">
      <j1 rule="para" parents="47432 42211"/>
    </justification>
  </clause>

  <clause id="47448">
    <literal><![CDATA[
      L(x,y * a(z,y,u),a(z,w,u)) = L(x,w,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(44904(a,1),47432(a,1,3)),flip(a)].">
      <j1 rule="para" parents="44904 47432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47450">
    <literal><![CDATA[
      L(x,y,a(y \ (z \ y),u,w)) = L(x,u,a(w,y,z \ 1))
    ]]></literal>
    <justification jstring="[para(45778(a,1),47432(a,1,3)),flip(a)].">
      <j1 rule="para" parents="45778 47432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47451">
    <literal><![CDATA[
      L(x,y,a(a(z,u,w),v5,v6)) = L(x,v5,a(w,u,a(z,y,v6)))
    ]]></literal>
    <justification jstring="[para(47197(a,1),47432(a,1,3)),flip(a)].">
      <j1 rule="para" parents="47197 47432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47452">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) = L(x,u,a(v6,y,a(z,v5,w)))
    ]]></literal>
    <justification jstring="[para(47242(a,1),47432(a,1,3)),flip(a)].">
      <j1 rule="para" parents="47242 47432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47453">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) = L(x,v5,a(w,y,a(v6,u,z)))
    ]]></literal>
    <justification jstring="[para(47254(a,1),47432(a,1,3))].">
      <j1 rule="para" parents="47254 47432"/>
    </justification>
  </clause>

  <clause id="47457">
    <literal><![CDATA[
      x * L(x \ y,z,a(u,y,w)) = y * a(x * y,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[para(47433(a,1),46976(a,1,2))].">
      <j1 rule="para" parents="47433 46976"/>
    </justification>
  </clause>

  <clause id="47458">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) = L(x,v5,a(z,y,a(v6,u,w)))
    ]]></literal>
    <justification jstring="[para(47298(a,1),47433(a,1,3))].">
      <j1 rule="para" parents="47298 47433"/>
    </justification>
  </clause>

  <clause id="47459">
    <literal><![CDATA[
      R(L(x,y,a(z,u,w)),u,a(z,y,w)) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,42206,a(flip),b,47434,a),flip(a)].">
      <j1 rule="hyper" parents="373 42206 47434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47463">
    <literal><![CDATA[
      a(x,y,z) \ R(x,y,L(z,u,w)) = L(x,u,a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46712,a,b,47349,a)].">
      <j1 rule="hyper" parents="64 46712 47349"/>
    </justification>
  </clause>

  <clause id="47464">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * a(v5,v6,a(w,y,a(z,u,x))) = x * a(w,y,L(a(z,u,x),v6,v5))
    ]]></literal>
    <justification jstring="[para(47349(a,1),46557(a,1,1))].">
      <j1 rule="para" parents="47349 46557"/>
    </justification>
  </clause>

  <clause id="47465">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(u,w,a(v5,z,x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41890,a,b,47205,a)].">
      <j1 rule="hyper" parents="64 41890 47205"/>
    </justification>
  </clause>

  <clause id="47466">
    <literal><![CDATA[
      x * a(y,z,a(a(u,w,v5),v6,v7)) = x * a(v7,v6,a(v5,z,a(y,w,u)))
    ]]></literal>
    <justification jstring="[para(47244(a,1),47213(a,2,2,3))].">
      <j1 rule="para" parents="47244 47213"/>
    </justification>
  </clause>

  <clause id="47469">
    <literal><![CDATA[
      x * a(y,z,a(u,x,w)) = x * a(u,x,a(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,13973,a(flip),b,47214,a),flip(a)].">
      <j1 rule="hyper" parents="64 13973 47214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47472">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(v5,v6,a(v7,v8,v9)) = a(w,u,a(z,y,x)) * a(v5,v6,a(v9,v8,v7))
    ]]></literal>
    <justification jstring="[hyper(373,a,41901,a,b,47217,a)].">
      <j1 rule="hyper" parents="373 41901 47217"/>
    </justification>
  </clause>

  <clause id="47473">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(x,y,z),a(a(x,y,z),x,y)) = (x \ R(x,y,z)) * (u * a(y,y,a(z,x,x)))
    ]]></literal>
    <justification jstring="[para(47221(a,1),44817(a,2,2))].">
      <j1 rule="para" parents="47221 44817"/>
    </justification>
  </clause>

  <clause id="47474">
    <literal><![CDATA[
      a(x,y,a(z,u,w * ((v5 * v5) * v6))) = a(v6 * w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,2655,a(flip),b,47228,a),flip(a)].">
      <j1 rule="hyper" parents="64 2655 47228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47477">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * R(w,y,x) = R(w,y,L(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,46711,a(flip),b,47265,a),flip(a)].">
      <j1 rule="hyper" parents="373 46711 47265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47479">
    <literal><![CDATA[
      L(L(x,y,a(z,u,a(w * v5,v6,v7))),u,a(v5 * w,y,a(v7,v6,z))) = x
    ]]></literal>
    <justification jstring="[para(47302(a,1),47436(a,1,1,3))].">
      <j1 rule="para" parents="47302 47436"/>
    </justification>
  </clause>

  <clause id="47481">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * a(x,u,a(w,y,z))) = v5
    ]]></literal>
    <justification jstring="[hyper(145,a,47334,a,b,47221,a)].">
      <j1 rule="hyper" parents="145 47334 47221"/>
    </justification>
  </clause>

  <clause id="47485">
    <literal><![CDATA[
      a(L(x,y,z),u,a(y,z,w)) * a(w,u,L(x,y,z)) = a(w,u,x * a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,42792,a(flip),b,47276,a),flip(a)].">
      <j1 rule="hyper" parents="373 42792 47276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47486">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,w) = L(x,y,L(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47026,a(flip),b,47279,a)].">
      <j1 rule="hyper" parents="64 47026 47279"/>
    </justification>
  </clause>

  <clause id="47487">
    <literal><![CDATA[
      L(L(x,y,z),y,a(u,w,z)) = L(x,y,L(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46791,a(flip),b,47279,a)].">
      <j1 rule="hyper" parents="64 46791 47279"/>
    </justification>
  </clause>

  <clause id="47491">
    <literal><![CDATA[
      L(L(x,y,a(z,z,u)),y,z * u) = L(x,y,L(z * u,z,z))
    ]]></literal>
    <justification jstring="[para(30181(a,1),47486(a,1,1))].">
      <j1 rule="para" parents="30181 47486"/>
    </justification>
  </clause>

  <clause id="47493">
    <literal><![CDATA[
      L(L(x,y,a(z,u,w)),y,z) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(42195(a,1),47486(a,1,1))].">
      <j1 rule="para" parents="42195 47486"/>
    </justification>
  </clause>

  <clause id="47495">
    <literal><![CDATA[
      L(L(x,y,z),y,a(z,u,w)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(42222,a,47487,a)].">
      <j1 rule="hyper" parents="42222 47487"/>
    </justification>
  </clause>

  <clause id="47496">
    <literal><![CDATA[
      L(L(x,y,z),u,a(w,y,z)) = L(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47433,a,b,47487,a)].">
      <j1 rule="hyper" parents="64 47433 47487"/>
    </justification>
  </clause>

  <clause id="47498">
    <literal><![CDATA[
      L(x * a(y,z,x),z,L(y,u,w)) = L(x,z,a(w,u,y))
    ]]></literal>
    <justification jstring="[para(45059(a,1),47487(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45059 47487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47504">
    <literal><![CDATA[
      a(x,y,a(z,a(z,y,u) * w,u)) = a(u,y,a(x,w,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47324,a,b,47364,a)].">
      <j1 rule="hyper" parents="64 47324 47364"/>
    </justification>
  </clause>

  <clause id="47508">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,L(v6,v7,v8)))) = L(x,y,a(v6,v5,a(z,u,L(w,v7,v8))))
    ]]></literal>
    <justification jstring="[para(46615(a,1),47286(a,1,3))].">
      <j1 rule="para" parents="46615 47286"/>
    </justification>
  </clause>

  <clause id="47509">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(v6,y,a(w,u,a(x,v5,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47285,a,b,47317,a),flip(a)].">
      <j1 rule="hyper" parents="373 47285 47317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47510">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(v6,y,a(z,u,a(w,v5,x)))
    ]]></literal>
    <justification jstring="[para(47197(a,1),47317(a,2,3))].">
      <j1 rule="para" parents="47197 47317"/>
    </justification>
  </clause>

  <clause id="47511">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(x,v5,a(z,u,a(v6,y,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47317,a,b,47360,a)].">
      <j1 rule="hyper" parents="373 47317 47360"/>
    </justification>
  </clause>

  <clause id="47512">
    <literal><![CDATA[
      a(x * y,y,a(z,u,a(w,v5,u))) = a(w,v5,a(u,u,a(y * x,x,z)))
    ]]></literal>
    <justification jstring="[para(46911(a,1),47360(a,2,3))].">
      <j1 rule="para" parents="46911 47360"/>
    </justification>
  </clause>

  <clause id="47513">
    <literal><![CDATA[
      a((x \ y) * y,z,a(u,w,a(z,v5,v6))) = a(v6,w,a(x,z,a(u,v5,z)))
    ]]></literal>
    <justification jstring="[para(46422(a,1),47361(a,2,3))].">
      <j1 rule="para" parents="46422 47361"/>
    </justification>
  </clause>

  <clause id="47514">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,w,a(v5,v6,v7)))) * L(x,w,L(a(v5,z,a(v7,v6,y)),x,u)) = L(x,w,a(v5,z,a(v7,v6,y)))
    ]]></literal>
    <justification jstring="[para(47361(a,1),47078(a,1,1,3))].">
      <j1 rule="para" parents="47361 47078"/>
    </justification>
  </clause>

  <clause id="47515">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = a(x,v5,a(v6,u,a(z,y,w)))
    ]]></literal>
    <justification jstring="[para(47200(a,1),47409(a,1,3))].">
      <j1 rule="para" parents="47200 47409"/>
    </justification>
  </clause>

  <clause id="47516">
    <literal><![CDATA[
      L(x,y,a(z * y,x,u)) = L(x,x,a(z * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,47371,a(flip),b,47425,a),flip(a)].">
      <j1 rule="hyper" parents="373 47371 47425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47517">
    <literal><![CDATA[
      x * L(x \ y,z,a(y,u,w)) = L(y,u,a(y \ x,z,w))
    ]]></literal>
    <justification jstring="[para(28832(a,1),47426(a,1,2))].">
      <j1 rule="para" parents="28832 47426"/>
    </justification>
  </clause>

  <clause id="47518">
    <literal><![CDATA[
      L(x,y \ z,a(u,w,y)) = L(x,y * z,a(u,w,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47271,a(flip),b,47427,a),flip(a)].">
      <j1 rule="hyper" parents="64 47271 47427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47519">
    <literal><![CDATA[
      L(x,y,a(y \ (z \ y),u,w)) = L(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,33636,a(flip),b,47450,a),flip(a)].">
      <j1 rule="hyper" parents="373 33636 47450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47520">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) = L(x,v5,a(z,u,a(v6,y,w)))
    ]]></literal>
    <justification jstring="[para(47254(a,1),47451(a,1,3))].">
      <j1 rule="para" parents="47254 47451"/>
    </justification>
  </clause>

  <clause id="47522">
    <literal><![CDATA[
      L(x,y * z,a(u,w,a(v5,v6,v7))) = L(x,v6,a(u,w,a(v5,z * y,v7)))
    ]]></literal>
    <justification jstring="[para(47393(a,1),47458(a,2,3))].">
      <j1 rule="para" parents="47393 47458"/>
    </justification>
  </clause>

  <clause id="47523">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,w,v5 * u))) = a(w,y,a(z,w,a(v5 * u,v5,x)))
    ]]></literal>
    <justification jstring="[para(46917(a,1),47509(a,2,3)),flip(a)].">
      <j1 rule="para" parents="46917 47509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47524">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,y,a(w,v5,a(x,u,v6))) = a(x,y,L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(47509(a,2),47397(a,1,2))].">
      <j1 rule="para" parents="47509 47397"/>
    </justification>
  </clause>

  <clause id="47525">
    <literal><![CDATA[
      a(x * y,z,a(z,x,a(u,w,v5))) = a(v5,z,a(y * x,y,a(u,w,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,46916,a,b,47510,a)].">
      <j1 rule="hyper" parents="373 46916 47510"/>
    </justification>
  </clause>

  <clause id="47526">
    <literal><![CDATA[
      x * L(x \ y,z,a(y,u,w)) = L(y,u,a(y * x,z,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,46671,a(flip),b,47517,a),flip(a)].">
      <j1 rule="hyper" parents="373 46671 47517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47527">
    <literal><![CDATA[
      L(x,y,L(z,u * z,y)) = L(x,y,L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47193,a(flip),b,47199,a),flip(a)].">
      <j1 rule="hyper" parents="64 47193 47199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47528">
    <literal><![CDATA[
      a(L(x,y * x,z),z,u) = L(u,z,L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(47527(a,1),45067(a,2,1))].">
      <j1 rule="para" parents="47527 45067"/>
    </justification>
  </clause>

  <clause id="47529">
    <literal><![CDATA[
      a(L(x,y * x,z),z,u) = a(L(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,45067,a,b,47528,a),flip(a)].">
      <j1 rule="hyper" parents="373 45067 47528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47530">
    <literal><![CDATA[
      a(L(x,y * x,z),z,u) = a(x,z,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,46496,a(flip),b,47529,a),flip(a)].">
      <j1 rule="hyper" parents="373 46496 47529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47531">
    <literal><![CDATA[
      a(x,y,L(z,u * x,y)) = a(x,y,L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46496,a(flip),b,47530,a)].">
      <j1 rule="hyper" parents="64 46496 47530"/>
    </justification>
  </clause>

  <clause id="47532">
    <literal><![CDATA[
      a(x,y,L(z,x * u,y)) = a(x,y,L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29739,a,b,47531,a)].">
      <j1 rule="hyper" parents="64 29739 47531"/>
    </justification>
  </clause>

  <clause id="47533">
    <literal><![CDATA[
      a(x \ (y \ z),y,L(u,(x \ (y \ z)) * x,y)) = a((y * x) \ z,y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,46607,a(flip),b,47532,a),flip(a)].">
      <j1 rule="hyper" parents="373 46607 47532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47534">
    <literal><![CDATA[
      a(a(x,y,z),x,a(u,w,L(y * v5,u,v6))) = a(v6 \ (u \ v6),w,a(z,v5,a(x,x,y * v5)))
    ]]></literal>
    <justification jstring="[para(46917(a,1),47274(a,1,3)),flip(a)].">
      <j1 rule="para" parents="46917 47274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47535">
    <literal><![CDATA[
      L(L(x,y,a(z,z,u)),y,z * u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,30387,a(flip),b,47491,a),flip(a)].">
      <j1 rule="hyper" parents="373 30387 47491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47536">
    <literal><![CDATA[
      L(L(x,y,a(z,z,u)),y,z * u) = L(x,y,(z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,30256,a(flip),b,47491,a),flip(a)].">
      <j1 rule="hyper" parents="373 30256 47491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47541">
    <literal><![CDATA[
      L(L(x,y,a(z,z,u)),y,z \ u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(42171(a,1),47535(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42171 47535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47542">
    <literal><![CDATA[
      L(x,a(y,z,u),u \ w) = L(x,a(y,z,u),u * w)
    ]]></literal>
    <justification jstring="[para(42276(a,1),47535(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42276 47535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47544">
    <literal><![CDATA[
      L(x,a(y,z,u),u \ w) = L(x,a(u,z,y),u * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,41403,a,b,47542,a),flip(a)].">
      <j1 rule="hyper" parents="373 41403 47542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47545">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),z,a(y,u,w)) = L(x,a(w,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,47432,a,b,47267,a)].">
      <j1 rule="hyper" parents="64 47432 47267"/>
    </justification>
  </clause>

  <clause id="47546">
    <literal><![CDATA[
      L(L(x,a(y,z,u),w),z,a(y,w,u)) = x * a(u,z,a(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(42,a,47436,a,b,47267,a)].">
      <j1 rule="hyper" parents="42 47436 47267"/>
    </justification>
  </clause>

  <clause id="47547">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w \ 1)),u,a(u \ (w \ u),z,y)) = L(x,a(u \ (w \ u),z,y),u)
    ]]></literal>
    <justification jstring="[para(46220(a,1),47267(a,1,1,2,3))].">
      <j1 rule="para" parents="46220 47267"/>
    </justification>
  </clause>

  <clause id="47548">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,a(w,v5,v6))) = y * a(v6,v5,a(y * x,y,a(w,u,z)))
    ]]></literal>
    <justification jstring="[para(47202(a,1),47277(a,1,2,3))].">
      <j1 rule="para" parents="47202 47277"/>
    </justification>
  </clause>

  <clause id="47549">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,y,a(u,z,x)) = a(z,a(x,y,w),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,47266,a,b,47278,a)].">
      <j1 rule="hyper" parents="64 47266 47278"/>
    </justification>
  </clause>

  <clause id="47550">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,u,a(y,z,x)) = a(z,a(x,u,w),y)
    ]]></literal>
    <justification jstring="[para(47241(a,1),47278(a,1,1))].">
      <j1 rule="para" parents="47241 47278"/>
    </justification>
  </clause>

  <clause id="47551">
    <literal><![CDATA[
      a(x * (y \ (z \ (x * y))),x,a(u,w,y)) = a(y,x,a(u,w,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,47254,a(flip),b,47288,a),flip(a)].">
      <j1 rule="hyper" parents="373 47254 47288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47552">
    <literal><![CDATA[
      a(x,y * z,a(z,u,w)) = a(z,y * z,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,42036,a(flip),b,47335,a),flip(a)].">
      <j1 rule="hyper" parents="64 42036 47335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47553">
    <literal><![CDATA[
      a(x,y * z,a(u,w,z)) = a(u,y * z,a(z,w,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47244,a,b,47552,a)].">
      <j1 rule="hyper" parents="373 47244 47552"/>
    </justification>
  </clause>

  <clause id="47554">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),u,a(z,w,y)) = L(x,a(y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,47432,a,b,47341,a)].">
      <j1 rule="hyper" parents="64 47432 47341"/>
    </justification>
  </clause>

  <clause id="47555">
    <literal><![CDATA[
      a(x * (y \ z),y,a(u,w,x)) = a(x,y,a(u,w,(x * z) * y))
    ]]></literal>
    <justification jstring="[hyper(47392,a,47366,a)].">
      <j1 rule="hyper" parents="47392 47366"/>
    </justification>
  </clause>

  <clause id="47556">
    <literal><![CDATA[
      a((x \ y) * z,z,a(u,w,x)) = a(y * (z * x),z,a(u,w,x))
    ]]></literal>
    <justification jstring="[hyper(47392,a,47367,a),flip(a)].">
      <j1 rule="hyper" parents="47392 47367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47557">
    <literal><![CDATA[
      L(L(x,a(y,x,z * x),u),u,a(y,x,z * x)) = z * L(z \ x,x,a(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,46976,a,b,47369,a),flip(a)].">
      <j1 rule="hyper" parents="373 46976 47369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47558">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * v5) * x)) = a(x,y,a(z,u,v5 * (w \ x)))
    ]]></literal>
    <justification jstring="[hyper(47392,a,47374,a),flip(a)].">
      <j1 rule="hyper" parents="47392 47374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47559">
    <literal><![CDATA[
      a(x,y,a(z,u,(w \ x) * v5)) = a(x,y,a(z,u,w * (v5 \ x)))
    ]]></literal>
    <justification jstring="[hyper(47392,a,47375,a),flip(a)].">
      <j1 rule="hyper" parents="47392 47375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47560">
    <literal><![CDATA[
      a(x \ (y \ z),y,a(u,w,x)) = a(y \ (x \ z),y,a(u,w,x))
    ]]></literal>
    <justification jstring="[hyper(47392,a,47377,a)].">
      <j1 rule="hyper" parents="47392 47377"/>
    </justification>
  </clause>

  <clause id="47561">
    <literal><![CDATA[
      L(x * a(y,z,a(u,x,w)),z,a(w,y,u)) = L(x,a(u,z,w),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47432,a,b,47413,a)].">
      <j1 rule="hyper" parents="64 47432 47413"/>
    </justification>
  </clause>

  <clause id="47564">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(u,z,a(w,y,x)) = a(z,a(x,y,w),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,47259,a,b,47549,a)].">
      <j1 rule="hyper" parents="64 47259 47549"/>
    </justification>
  </clause>

  <clause id="47565">
    <literal><![CDATA[
      a(x,a(y,z,z),u) \ (a(y,z,a(x,u,z)) * z) = a(z,z,a(u,x,y)) \ z
    ]]></literal>
    <justification jstring="[para(47549(a,1),37738(a,1,1))].">
      <j1 rule="para" parents="47549 37738"/>
    </justification>
  </clause>

  <clause id="47566">
    <literal><![CDATA[
      a((x \ y) * z,z,a(u,w,x)) = a(x,z,a(u,w,y * (x * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47330,a(flip),b,47556,a),flip(a)].">
      <j1 rule="hyper" parents="373 47330 47556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47567">
    <literal><![CDATA[
      a(x * (y \ z),u,a(w,v5,z)) = a(z,u,a(w,v5,y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47326,a,b,47559,a)].">
      <j1 rule="hyper" parents="64 47326 47559"/>
    </justification>
  </clause>

  <clause id="47568">
    <literal><![CDATA[
      a(x,y,a(z * (u \ x),w,v5)) = a(x,y,a(v5,w,u * (z \ x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,41897,a,b,47559,a)].">
      <j1 rule="hyper" parents="64 41897 47559"/>
    </justification>
  </clause>

  <clause id="47569">
    <literal><![CDATA[
      a(x \ (y \ z),x,a(u,w,y)) = a(y * (x \ z),x,a(u,w,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46650,a(flip),b,47560,a),flip(a)].">
      <j1 rule="hyper" parents="64 46650 47560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47570">
    <literal><![CDATA[
      a(x,y,a((z \ x) * u,w,v5)) = a(x,y,a(z * (u \ x),w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,41897,a,b,47568,a)].">
      <j1 rule="hyper" parents="373 41897 47568"/>
    </justification>
  </clause>

  <clause id="47571">
    <literal><![CDATA[
      a(x \ (y \ z),x,a(u,w,y)) = a((x \ z) * y,x,a(u,w,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,47569,a),flip(a)].">
      <j1 rule="hyper" parents="373 26787 47569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47572">
    <literal><![CDATA[
      a(x \ (y \ z),x,a(u,w,y)) = a(y,x,a(u,w,(y * z) * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47555,a(flip),b,47569,a),flip(a)].">
      <j1 rule="hyper" parents="373 47555 47569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47573">
    <literal><![CDATA[
      a(x,y,a(z * (u \ x),w,v5)) * x = L(x,y,a((z \ x) * u,w,v5))
    ]]></literal>
    <justification jstring="[para(47570(a,1),45132(a,1,1))].">
      <j1 rule="para" parents="47570 45132"/>
    </justification>
  </clause>

  <clause id="47574">
    <literal><![CDATA[
      a((x \ y) * z,z,a(u,w,x)) = a((z \ y) * x,z,a(u,w,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41827,a(flip),b,47571,a)].">
      <j1 rule="hyper" parents="64 41827 47571"/>
    </justification>
  </clause>

  <clause id="47575">
    <literal><![CDATA[
      a((x \ y) * z,z,a(u,w,x)) = a(x,z,a(u,w,(x * y) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41827,a(flip),b,47572,a)].">
      <j1 rule="hyper" parents="64 41827 47572"/>
    </justification>
  </clause>

  <clause id="47576">
    <literal><![CDATA[
      a((x \ y) * z,x,a(u,w,z)) = a(z,x,a(u,w,y * (z * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47566,a(flip),b,47574,a),flip(a)].">
      <j1 rule="hyper" parents="64 47566 47574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47577">
    <literal><![CDATA[
      a(x,y,a(z,u,(x * w) * y)) = a(x,y,a(z,u,w * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47566,a(flip),b,47575,a),flip(a)].">
      <j1 rule="hyper" parents="64 47566 47575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47578">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (x * y))) = a(x,y,a(z,u,x * (y \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47326,a(flip),b,47576,a),flip(a)].">
      <j1 rule="hyper" parents="64 47326 47576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47579">
    <literal><![CDATA[
      a(x,y,a(y * (z * x),u,w)) = a(x,y,a(w,u,z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,41899,a,b,47577,a)].">
      <j1 rule="hyper" parents="64 41899 47577"/>
    </justification>
  </clause>

  <clause id="47580">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * (x * y)) * T(y * x,v5))) = a(x,y,a(z,u,x * (y \ (w * T(y * x,v5)))))
    ]]></literal>
    <justification jstring="[para(35404(a,1),47578(a,1,3,3))].">
      <j1 rule="para" parents="35404 47578"/>
    </justification>
  </clause>

  <clause id="47581">
    <literal><![CDATA[
      (x * a(y,z,a(u,w,v5))) \ (x * u) = L(u,w,a(v5,z,L(y,u,x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,46632,a,b,47373,a),flip(a)].">
      <j1 rule="hyper" parents="373 46632 47373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47582">
    <literal><![CDATA[
      L(x,y,a(a(y,x * z,u),w,L(v5,x,v6))) = (v6 * a(v5,w,a(x,y,a(u,z,y)))) \ (v6 * x)
    ]]></literal>
    <justification jstring="[para(46891(a,1),47581(a,1,1,2,3)),flip(a)].">
      <j1 rule="para" parents="46891 47581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47583">
    <literal><![CDATA[
      a((x * y) * L(z,x,x),u,u) = a((z * x) * y,u,L(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46924,a(flip),b,47149,a),flip(a)].">
      <j1 rule="hyper" parents="64 46924 47149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47584">
    <literal><![CDATA[
      a((x * y) * L(z,x,x),u,u) = a((x \ y) * z,u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,46753,a(flip),b,47583,a),flip(a)].">
      <j1 rule="hyper" parents="373 46753 47583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47585">
    <literal><![CDATA[
      a((x \ (x \ y)) * z,u,u) = a(y * L(z,x,x),u,u)
    ]]></literal>
    <justification jstring="[para(10(a,1),47584(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 47584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47586">
    <literal><![CDATA[
      a(L(x,y,y) * z,u,u) = a(x * L(z,y,y),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32811,a(flip),b,47585,a)].">
      <j1 rule="hyper" parents="64 32811 47585"/>
    </justification>
  </clause>

  <clause id="47587">
    <literal><![CDATA[
      a(x,y,L(y,z * y,u)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46515,a(flip),b,47156,a),flip(a)].">
      <j1 rule="hyper" parents="64 46515 47156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47589">
    <literal><![CDATA[
      a(x,y,y) \ a(x,y,L(y,z,u)) = a(x,y,a(y,z * y,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,47587,a(flip),b,47233,a)].">
      <j1 rule="hyper" parents="139 47587 47233"/>
    </justification>
  </clause>

  <clause id="47591">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,z,u),u * (T(z / (w * w),u) * y),v5)) = a(x,L(y,z,u),L(L(y,z,u),z * ((w * w) \ u),v5))
    ]]></literal>
    <justification jstring="[para(29569(a,1),47587(a,1,3,2))].">
      <j1 rule="para" parents="29569 47587"/>
    </justification>
  </clause>

  <clause id="47592">
    <literal><![CDATA[
      a(x,y,a(y,z * y,u)) = a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,44036,a(flip),b,47589,a),flip(a)].">
      <j1 rule="hyper" parents="64 44036 47589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47594">
    <literal><![CDATA[
      L(x,y,a(y,z * y,u)) = x * a(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(145,a,47592,a(flip),b,45194,a),flip(a)].">
      <j1 rule="hyper" parents="145 47592 45194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47596">
    <literal><![CDATA[
      L(x,y,a(y,z * y,u)) = L(x,z,a(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,47398,a(flip),b,47594,a),flip(a)].">
      <j1 rule="hyper" parents="373 47398 47594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47597">
    <literal><![CDATA[
      L(x,y,a(y,z * y,u)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,45190,a(flip),b,47594,a),flip(a)].">
      <j1 rule="hyper" parents="373 45190 47594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47599">
    <literal><![CDATA[
      L(x,y,a(y,y * z,u)) = L(x,z,a(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32088,a,b,47596,a)].">
      <j1 rule="hyper" parents="64 32088 47596"/>
    </justification>
  </clause>

  <clause id="47600">
    <literal><![CDATA[
      L(x,y \ z,a(u,y,y)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(31889(a,1),47596(a,1,3)),flip(a)].">
      <j1 rule="para" parents="31889 47596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47604">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)),y,u) = L(x,y,L(u,z * y,y))
    ]]></literal>
    <justification jstring="[para(47597(a,1),47486(a,1,1))].">
      <j1 rule="para" parents="47597 47486"/>
    </justification>
  </clause>

  <clause id="47605">
    <literal><![CDATA[
      L(x,y \ z,a(u,z,z)) = L(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46274,a,b,47599,a)].">
      <j1 rule="hyper" parents="64 46274 47599"/>
    </justification>
  </clause>

  <clause id="47606">
    <literal><![CDATA[
      L(x,y \ z,a(u,y,y)) = x * a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,47258,a,b,47600,a),flip(a)].">
      <j1 rule="hyper" parents="373 47258 47600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47608">
    <literal><![CDATA[
      L(x,y * z,a(u,y,y)) = L(x,y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47518,a(flip),b,47600,a)].">
      <j1 rule="hyper" parents="64 47518 47600"/>
    </justification>
  </clause>

  <clause id="47613">
    <literal><![CDATA[
      L(x,R(y,z,u) * w,a(v5,R(y,z,u),L(y,z,u))) = L(x,R(y,z,u),a(R(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(27644(a,1),47608(a,1,3))].">
      <j1 rule="para" parents="27644 47608"/>
    </justification>
  </clause>

  <clause id="47614">
    <literal><![CDATA[
      a(x,y,a(z,y * u,y)) = a(x,u,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,47427,a,b,47606,a(flip))].">
      <j1 rule="hyper" parents="35 47427 47606"/>
    </justification>
  </clause>

  <clause id="47617">
    <literal><![CDATA[
      a(x,x,a(y,z * x,u)) = a(y,z,a(u,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47329,a(flip),b,47614,a)].">
      <j1 rule="hyper" parents="64 47329 47614"/>
    </justification>
  </clause>

  <clause id="47618">
    <literal><![CDATA[
      a(x,y,a(z,u,u)) * a(u,u,z) = a(u,u,L(z,y * u,x))
    ]]></literal>
    <justification jstring="[para(47617(a,1),45791(a,1,1))].">
      <j1 rule="para" parents="47617 45791"/>
    </justification>
  </clause>

  <clause id="47620">
    <literal><![CDATA[
      L(x,y,L(z,u * y,y)) = L(x,y,L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47486,a(flip),b,47604,a),flip(a)].">
      <j1 rule="hyper" parents="64 47486 47604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47621">
    <literal><![CDATA[
      a(L(x,y * z,z),z,u) = L(u,z,L(x,y,z)) \ u
    ]]></literal>
    <justification jstring="[para(47620(a,1),45067(a,2,1))].">
      <j1 rule="para" parents="47620 45067"/>
    </justification>
  </clause>

  <clause id="47622">
    <literal><![CDATA[
      a(L(x,y * z,z),z,u) = a(L(x,y,z),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,45067,a,b,47621,a),flip(a)].">
      <j1 rule="hyper" parents="373 45067 47621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47623">
    <literal><![CDATA[
      a(L(x,y * z,z),z,u) = a(x,z,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,46496,a(flip),b,47622,a),flip(a)].">
      <j1 rule="hyper" parents="373 46496 47622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47624">
    <literal><![CDATA[
      a(x,y,L(z,u * y,y)) = a(x,y,L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46496,a(flip),b,47623,a)].">
      <j1 rule="hyper" parents="64 46496 47623"/>
    </justification>
  </clause>

  <clause id="47625">
    <literal><![CDATA[
      a(x,y,L(z,y * u,y)) = a(x,y,L(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,29739,a,b,47624,a)].">
      <j1 rule="hyper" parents="64 29739 47624"/>
    </justification>
  </clause>

  <clause id="47626">
    <literal><![CDATA[
      a(x,(y * (x \ (y \ z))) \ z,u) = a(y,y \ z,a(u,x,x)) * a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,44220,a,b,47618,a)].">
      <j1 rule="hyper" parents="373 44220 47618"/>
    </justification>
  </clause>

  <clause id="47627">
    <literal><![CDATA[
      a(x,x,L(y,z * x,u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46501,a(flip),b,47618,a),flip(a)].">
      <j1 rule="hyper" parents="64 46501 47618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47630">
    <literal><![CDATA[
      a(x,x,L(y,x * z,u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,29739,a,b,47627,a)].">
      <j1 rule="hyper" parents="64 29739 47627"/>
    </justification>
  </clause>

  <clause id="47632">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * a(z,z,u) = a(z,z,L(u,z * y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,46502,a,b,47630,a)].">
      <j1 rule="hyper" parents="373 46502 47630"/>
    </justification>
  </clause>

  <clause id="47634">
    <literal><![CDATA[
      a(x,(y * (x \ z)) \ (y * z),u) = a(x,x,L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,44357,a,b,47630,a)].">
      <j1 rule="hyper" parents="64 44357 47630"/>
    </justification>
  </clause>

  <clause id="47637">
    <literal><![CDATA[
      x * a(y,((z * x) * (y \ x)) \ ((z * x) * x),u) = (z / x) \ (z * a(y,y,u))
    ]]></literal>
    <justification jstring="[para(47634(a,2),41994(a,2,2)),flip(a)].">
      <j1 rule="para" parents="47634 41994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47638">
    <literal><![CDATA[
      a(x,x,a(y,x * z,u)) = a(y,z,a(x,x,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,45791,a,b,47632,a)].">
      <j1 rule="hyper" parents="36 45791 47632"/>
    </justification>
  </clause>

  <clause id="47639">
    <literal><![CDATA[
      a(x,x,a(y,x * z,u * (y * w))) = a(y,z,a(x,x,w \ (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46418,a(flip),b,47638,a)].">
      <j1 rule="hyper" parents="64 46418 47638"/>
    </justification>
  </clause>

  <clause id="47641">
    <literal><![CDATA[
      a(x,y,a(y * z,u,y)) * a(u,z,a(y,y,x)) = a(y * z,a(x,y,y),u)
    ]]></literal>
    <justification jstring="[para(47638(a,1),47549(a,1,2))].">
      <j1 rule="para" parents="47638 47549"/>
    </justification>
  </clause>

  <clause id="47642">
    <literal><![CDATA[
      L(x * a(y,x,L(z * y,z,z)),z * y,z * (z * y)) = z \ (((z / (z * y)) * x) * T(z * y,x))
    ]]></literal>
    <justification jstring="[para(46582(a,1),47158(a,1,1,2))].">
      <j1 rule="para" parents="46582 47158"/>
    </justification>
  </clause>

  <clause id="47643">
    <literal><![CDATA[
      a(x,y,x \ L((x \ 1) \ z,u,w)) = a(x,y,x * L(x \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27345,a(flip),b,47159,a)].">
      <j1 rule="hyper" parents="64 27345 47159"/>
    </justification>
  </clause>

  <clause id="47644">
    <literal><![CDATA[
      a(x * (y \ ((y \ x) \ (x * z))),x,y) = a(z * L(x,y,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,32719,a(flip),b,47166,a),flip(a)].">
      <j1 rule="hyper" parents="373 32719 47166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47645">
    <literal><![CDATA[
      a(x,y,z * (((z * u) * u) \ w)) = a(x,y,z * ((u * (u * z)) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46359,a(flip),b,47172,a),flip(a)].">
      <j1 rule="hyper" parents="64 46359 47172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47646">
    <literal><![CDATA[
      a(x,y,L(L(z,y,u),u * y,y)) = L(a(x,y,z),y,y * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,14160,a(flip),b,47177,a),flip(a)].">
      <j1 rule="hyper" parents="373 14160 47177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47647">
    <literal><![CDATA[
      a(x,y,L(L(z,y,u),u * y,y)) = a(x,y,L(z,y,y * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,46493,a,b,47646,a),flip(a)].">
      <j1 rule="hyper" parents="373 46493 47646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47649">
    <literal><![CDATA[
      a(x,y,L(L(z,y,u),u,y)) = a(x,y,L(z,y,y * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47624,a(flip),b,47647,a)].">
      <j1 rule="hyper" parents="64 47624 47647"/>
    </justification>
  </clause>

  <clause id="47650">
    <literal><![CDATA[
      a(x,y,L(z \ u,y,y * z)) = a(x,y,y \ (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,39073,a(flip),b,47649,a),flip(a)].">
      <j1 rule="hyper" parents="64 39073 47649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47651">
    <literal><![CDATA[
      a(((x * y) * (x * y)) \ ((x * y) * y),z,(x * y) * u) = a(x,z,L(((x * y) \ 1) \ u,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,38990,a(flip),b,47179,a),flip(a)].">
      <j1 rule="hyper" parents="373 38990 47179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47652">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) \ (w * w)) = a(x,y,z \ (u \ (w * w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27765,a(flip),b,47181,a),flip(a)].">
      <j1 rule="hyper" parents="373 27765 47181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47653">
    <literal><![CDATA[
      a(x,y,L((z * T(u,u \ 1)) \ (w * w),u,u)) = a(x,y,u \ (z \ (w * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,39144,a,b,47652,a)].">
      <j1 rule="hyper" parents="64 39144 47652"/>
    </justification>
  </clause>

  <clause id="47654">
    <literal><![CDATA[
      a(x \ (y \ z),u,L(x,y,y)) = a((x \ z) * y,u,L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46653,a(flip),b,47182,a),flip(a)].">
      <j1 rule="hyper" parents="64 46653 47182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47655">
    <literal><![CDATA[
      a((x \ y) * z,u,L(x,x,z)) = a(x * (z \ y),u,L(x,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46649,a(flip),b,47654,a),flip(a)].">
      <j1 rule="hyper" parents="64 46649 47654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47656">
    <literal><![CDATA[
      a(x * (y \ z),u,L(y,y,x)) = a(y * (x \ z),u,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(26847,a,47655,a)].">
      <j1 rule="hyper" parents="26847 47655"/>
    </justification>
  </clause>

  <clause id="47657">
    <literal><![CDATA[
      a((x * y) \ (z * u),w,(y * x) \ v5) = a(y \ (x \ (u * z)),w,y \ (x \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,32504,a,b,47187,a)].">
      <j1 rule="hyper" parents="64 32504 47187"/>
    </justification>
  </clause>

  <clause id="47658">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(w,v5,x)) = y * L(y \ (x \ y),u,a(z,v5,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47214,a(flip),b,47280,a)].">
      <j1 rule="hyper" parents="64 47214 47280"/>
    </justification>
  </clause>

  <clause id="47659">
    <literal><![CDATA[
      x * a(y,z,a(u,w,a(v5,v6,v7))) = x * a(v7,v6,a(u,z,a(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(47202(a,1),47466(a,1,2,3))].">
      <j1 rule="para" parents="47202 47466"/>
    </justification>
  </clause>

  <clause id="47660">
    <literal><![CDATA[
      x * a(y,z,a(u,w,a(v5,v6,v7))) = x * a(v5,v6,a(u,z,a(y,w,v7)))
    ]]></literal>
    <justification jstring="[para(47254(a,1),47466(a,1,2,3))].">
      <j1 rule="para" parents="47254 47466"/>
    </justification>
  </clause>

  <clause id="47661">
    <literal><![CDATA[
      a(x * y,x,a(z,u,a(w,z,v5))) = a(w,u,a(v5,y,a(z,z,x * y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47360,a(flip),b,47523,a)].">
      <j1 rule="hyper" parents="373 47360 47523"/>
    </justification>
  </clause>

  <clause id="47662">
    <literal><![CDATA[
      L(x,y,a((z \ x) * u,w,v5)) = L(x,y,a(z * (u \ x),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,45132,a(flip),b,47573,a),flip(a)].">
      <j1 rule="hyper" parents="64 45132 47573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47663">
    <literal><![CDATA[
      a(x,y,a(z,z,u \ (x \ w))) = a(x,y,a(z,z,w * (x * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47638,a(flip),b,47639,a),flip(a)].">
      <j1 rule="hyper" parents="64 47638 47639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47664">
    <literal><![CDATA[
      a(x,y,a(z,z,u * (x \ w))) = a(x,y,a(z,z,w * (x * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,45836,a(flip),b,47663,a)].">
      <j1 rule="hyper" parents="64 45836 47663"/>
    </justification>
  </clause>

  <clause id="47665">
    <literal><![CDATA[
      a(x,y,z * L(L(u \ 1,w * z,w),u,(w * z) * u)) = a(x,y,z * (((z * w) * w) \ (w * ((w * z) / u))))
    ]]></literal>
    <justification jstring="[para(30712(a,2),47645(a,2,3,2)),flip(a)].">
      <j1 rule="para" parents="30712 47645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47666">
    <literal><![CDATA[
      a((x \ 1) \ 1,a(y,x,z),a(y,x,z) * u) = a(a(y,x,z),x,x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42537,a(flip),b,45967,a)].">
      <j1 rule="hyper" parents="64 42537 45967"/>
    </justification>
  </clause>

  <clause id="47667">
    <literal><![CDATA[
      L(x,L(a(y \ z,u,w),y,y),v5) = L(x,y * (z * L(z \ y,u,w)),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,36278,a(flip),b,45992,a),flip(a)].">
      <j1 rule="hyper" parents="373 36278 45992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47668">
    <literal><![CDATA[
      a(x * (L(y,y,z) * z),L(y,y,z),z) = a((z \ x) * y,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,46767,a(flip),b,46408,a),flip(a)].">
      <j1 rule="hyper" parents="373 46767 46408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47669">
    <literal><![CDATA[
      a(x * (L(y,y,z) * z),L(y,y,z),z) = a(x * (y * z),y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,45289,a(flip),b,47668,a),flip(a)].">
      <j1 rule="hyper" parents="373 45289 47668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47670">
    <literal><![CDATA[
      a(x * (L(y,y,z) * z),y,z) = a(x * (y * z),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46406,a(flip),b,47669,a)].">
      <j1 rule="hyper" parents="64 46406 47669"/>
    </justification>
  </clause>

  <clause id="47671">
    <literal><![CDATA[
      a(x * (y \ z),y,z) = a(x * (y * z),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32936,a(flip),b,47670,a)].">
      <j1 rule="hyper" parents="64 32936 47670"/>
    </justification>
  </clause>

  <clause id="47672">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),u,w)) = a(x,y,a(w,u,w * (u * z)))
    ]]></literal>
    <justification jstring="[para(47671(a,1),46862(a,1,3))].">
      <j1 rule="para" parents="47671 46862"/>
    </justification>
  </clause>

  <clause id="47673">
    <literal><![CDATA[
      a(x,y,a(z,u,z * (u \ w))) = a(x,y,a(z,u,z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47070,a(flip),b,47672,a)].">
      <j1 rule="hyper" parents="64 47070 47672"/>
    </justification>
  </clause>

  <clause id="47674">
    <literal><![CDATA[
      a(x,y,a(y * (z * x),u,w)) = a(w,u,a(x,y,x * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47245,a,b,47673,a)].">
      <j1 rule="hyper" parents="64 47245 47673"/>
    </justification>
  </clause>

  <clause id="47675">
    <literal><![CDATA[
      x * a(x,y,a(z,u,z * (u * w))) = R(x,y,a(z,u,z * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(145,a,47673,a(flip),b,45073,a(flip))].">
      <j1 rule="hyper" parents="145 47673 45073"/>
    </justification>
  </clause>

  <clause id="47676">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,z * (u * w))),y,a(z,u,z * (u \ w))) = L(x,a(z,u,z * (u \ w)),y)
    ]]></literal>
    <justification jstring="[para(47673(a,1),41867(a,1,1,2))].">
      <j1 rule="para" parents="47673 41867"/>
    </justification>
  </clause>

  <clause id="47677">
    <literal><![CDATA[
      a(x,y,a(y * (z * x),u,w)) = a(x,y,a(w,u,x * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47253,a,b,47674,a),flip(a)].">
      <j1 rule="hyper" parents="373 47253 47674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47678">
    <literal><![CDATA[
      a((x * y) * z,u,a(x,z,w)) = a(x,z,a(w,u,x * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47252,a,b,47677,a)].">
      <j1 rule="hyper" parents="64 47252 47677"/>
    </justification>
  </clause>

  <clause id="47679">
    <literal><![CDATA[
      a(x,y,a(y * (z * x),u,w)) = a(x,y,a(w,u,x * (z * y)))
    ]]></literal>
    <justification jstring="[para(27315(a,1),47677(a,2,3))].">
      <j1 rule="para" parents="27315 47677"/>
    </justification>
  </clause>

  <clause id="47680">
    <literal><![CDATA[
      a(x,y,a(z,u,y * (w * x))) = a(x,y,a(z,u,x * (w * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,41883,a,b,47679,a)].">
      <j1 rule="hyper" parents="64 41883 47679"/>
    </justification>
  </clause>

  <clause id="47681">
    <literal><![CDATA[
      R(x,y,a(z,u,z * (u \ w))) = L(x,y,a(z,u,z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(45403,a,47675,a),flip(a)].">
      <j1 rule="hyper" parents="45403 47675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47682">
    <literal><![CDATA[
      L(x,y,a(z,u,z * (u \ w))) = L(x,y,a(z,u,z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(28845,a,47681,a)].">
      <j1 rule="hyper" parents="28845 47681"/>
    </justification>
  </clause>

  <clause id="47683">
    <literal><![CDATA[
      a(x \ y,z,x * (u \ 1)) = a(y * x,z,(x \ u) \ 1)
    ]]></literal>
    <justification jstring="[para(1137(a,1),46700(a,1,3))].">
      <j1 rule="para" parents="1137 46700"/>
    </justification>
  </clause>

  <clause id="47684">
    <literal><![CDATA[
      a((x / y) \ z,u,(y \ x) * (w \ 1)) = a(z * (x / y),u,((x / y) \ w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27317,a(flip),b,47683,a)].">
      <j1 rule="hyper" parents="64 27317 47683"/>
    </justification>
  </clause>

  <clause id="47685">
    <literal><![CDATA[
      a(T(x / y,z) * u,w,L(w,v5,(y \ x) * v5)) = a(((v5 \ T(x / y,z)) \ u) * v5,w,w)
    ]]></literal>
    <justification jstring="[para(28980(a,1),46874(a,1,3))].">
      <j1 rule="para" parents="28980 46874"/>
    </justification>
  </clause>

  <clause id="47686">
    <literal><![CDATA[
      a(x,x,a(y,L(L(y,z,u),u,z),w)) = a(y,x,a(w,a(z,y,u),x))
    ]]></literal>
    <justification jstring="[para(43256(a,1),46900(a,1,3))].">
      <j1 rule="para" parents="43256 46900"/>
    </justification>
  </clause>

  <clause id="47687">
    <literal><![CDATA[
      a(x,x,a(y,y,L(L(z,u,w),w,u))) = a(y,x,a(z,a(u,y,w),x))
    ]]></literal>
    <justification jstring="[para(42228(a,1),47686(a,1,3))].">
      <j1 rule="para" parents="42228 47686"/>
    </justification>
  </clause>

  <clause id="47688">
    <literal><![CDATA[
      a(x,y,a(z,a(u,x,w),y)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,45009,a(flip),b,47687,a),flip(a)].">
      <j1 rule="hyper" parents="64 45009 47687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47690">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,w,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,47198,a,b,47688,a)].">
      <j1 rule="hyper" parents="64 47198 47688"/>
    </justification>
  </clause>

  <clause id="47691">
    <literal><![CDATA[
      a(x,y,L(y,a(z,u,w),u)) = a(x,y,y) * 1
    ]]></literal>
    <justification jstring="[para(47688(a,1),45918(a,1,2)),flip(a)].">
      <j1 rule="para" parents="47688 45918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47692">
    <literal><![CDATA[
      a(x,y,L(y,a(z,u,w),u)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a(flip),b,47691,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 47691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47693">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L(a(x,y,z),u,w))) = z * a(z * L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,39444,a,b,47139,a)].">
      <j1 rule="hyper" parents="64 39444 47139"/>
    </justification>
  </clause>

  <clause id="47694">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * R(z,v5,x) = L(R(z,v5,x),u,a(x,y,w))
    ]]></literal>
    <justification jstring="[para(46565(a,1),47431(a,1,1))].">
      <j1 rule="para" parents="46565 47431"/>
    </justification>
  </clause>

  <clause id="47696">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * R(w,v5,x) = L(R(w,v5,x),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41902,a,b,47694,a)].">
      <j1 rule="hyper" parents="64 41902 47694"/>
    </justification>
  </clause>

  <clause id="47697">
    <literal><![CDATA[
      L(R(x,y,z),u,a(z,y,w)) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47477,a(flip),b,47696,a),flip(a)].">
      <j1 rule="hyper" parents="64 47477 47696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47699">
    <literal><![CDATA[
      L(R(x,y,z),y,a(z,u,w)) = R(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47433,a,b,47697,a)].">
      <j1 rule="hyper" parents="64 47433 47697"/>
    </justification>
  </clause>

  <clause id="47702">
    <literal><![CDATA[
      L(R(x,y,L(z,u,w)),y,a(w,u,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(42,a,42206,a,b,47699,a)].">
      <j1 rule="hyper" parents="42 42206 47699"/>
    </justification>
  </clause>

  <clause id="47703">
    <literal><![CDATA[
      L(R(x,y,z \ 1),y,a(z,u,w)) = R(x,y,L(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(2653(a,1),47699(a,1,3))].">
      <j1 rule="para" parents="2653 47699"/>
    </justification>
  </clause>

  <clause id="47705">
    <literal><![CDATA[
      L(R(x,y,L(z,u,w)),y,L(z,u,w)) = L(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(47702(a,1),47486(a,1,1)),flip(a)].">
      <j1 rule="para" parents="47702 47486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47706">
    <literal><![CDATA[
      L(R(x,y,(z \ (u \ z)) \ 1),y,a(u,w,L(v5,u,z))) = R(x,y,L((z \ (u \ z)) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,46667,a(flip),b,47703,a)].">
      <j1 rule="hyper" parents="64 46667 47703"/>
    </justification>
  </clause>

  <clause id="47707">
    <literal><![CDATA[
      a(x \ (y \ z),y,L(u,y \ z,y)) = a((y * x) \ z,y,u)
    ]]></literal>
    <justification jstring="[para(29441(a,1),47533(a,1,3))].">
      <j1 rule="para" parents="29441 47533"/>
    </justification>
  </clause>

  <clause id="47708">
    <literal><![CDATA[
      a(x \ (y \ z),y,L(u,y * z,y)) = a((y * x) \ z,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,41734,a(flip),b,47707,a)].">
      <j1 rule="hyper" parents="64 41734 47707"/>
    </justification>
  </clause>

  <clause id="47710">
    <literal><![CDATA[
      a(x \ (y \ z),y,L(u,z,y)) = a((y * x) \ z,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,47625,a(flip),b,47708,a)].">
      <j1 rule="hyper" parents="64 47625 47708"/>
    </justification>
  </clause>

  <clause id="47711">
    <literal><![CDATA[
      a(x,a(y,x,z),a(y,x,z) * u) = a(a(y,x,z),x,x * u)
    ]]></literal>
    <justification jstring="[hyper(26846,a,47666,a)].">
      <j1 rule="hyper" parents="26846 47666"/>
    </justification>
  </clause>

  <clause id="47712">
    <literal><![CDATA[
      a(a(x,y,z),y,y * u) = a(y,a(x,y,z),L(L(u,x,z),z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46745,a,b,47711,a),flip(a)].">
      <j1 rule="hyper" parents="64 46745 47711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47713">
    <literal><![CDATA[
      a(x,a(y,z,u),z * a(y,z,u)) = a(a(u,z,y),z,z * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,43122,a,b,47711,a)].">
      <j1 rule="hyper" parents="64 43122 47711"/>
    </justification>
  </clause>

  <clause id="47715">
    <literal><![CDATA[
      a(x,a(y,z,u),z * a(u,z,y)) = a(a(u,z,y),z,z * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,46474,a,b,47713,a)].">
      <j1 rule="hyper" parents="64 46474 47713"/>
    </justification>
  </clause>

  <clause id="47716">
    <literal><![CDATA[
      ((x \ a(y,x,z)) * (((x \ a(y,x,z)) \ (x \ 1)) * u)) / u = a(a(z,x,y),x,x * u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(47713(a,1),42653(a,2,1))].">
      <j1 rule="para" parents="47713 42653"/>
    </justification>
  </clause>

  <clause id="47717">
    <literal><![CDATA[
      a(x \ 1,a(y,x,z),u * a(y,x,z)) = a(a(z,x,y),x,x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42919,a,b,47715,a)].">
      <j1 rule="hyper" parents="64 42919 47715"/>
    </justification>
  </clause>

  <clause id="47718">
    <literal><![CDATA[
      a(x,a(y,x,z),L(L(u,y,z),z,y)) = a(z,x,a(x * u,x,y))
    ]]></literal>
    <justification jstring="[hyper(47392,a,47712,a),flip(a)].">
      <j1 rule="hyper" parents="47392 47712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47719">
    <literal><![CDATA[
      a(x * y,y,a(z,y,u)) = a(y,a(u,y,z),L(L(x,u,z),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,41879,a(flip),b,47712,a)].">
      <j1 rule="hyper" parents="64 41879 47712"/>
    </justification>
  </clause>

  <clause id="47720">
    <literal><![CDATA[
      a(x,a(y,x,z),L(L(T((u * x) \ 1,x \ 1),y,z),z,y)) = a(z,x,a(((u / x) \ 1) / x,x,y))
    ]]></literal>
    <justification jstring="[para(30744(a,1),47718(a,2,3,1))].">
      <j1 rule="para" parents="30744 47718"/>
    </justification>
  </clause>

  <clause id="47721">
    <literal><![CDATA[
      a(x,a(y,x,z),u * a(y,x,z)) = a(a(z,x,y),x,x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2653,a(flip),b,47717,a)].">
      <j1 rule="hyper" parents="64 2653 47717"/>
    </justification>
  </clause>

  <clause id="47722">
    <literal><![CDATA[
      a(x * a(y,z,u),a(y,z,u),a(w,w,z)) = a(a(a(u,z,y),z,z * x),w,w)
    ]]></literal>
    <justification jstring="[para(47721(a,1),45501(a,1,1)),flip(a)].">
      <j1 rule="para" parents="47721 45501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47724">
    <literal><![CDATA[
      L(x,a(y \ z,u,L(w,y,y)),v5) = L(x,y * (z * L(z \ y,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(46493(a,2),47667(a,1,2))].">
      <j1 rule="para" parents="46493 47667"/>
    </justification>
  </clause>

  <clause id="47725">
    <literal><![CDATA[
      L(x,y * (z * L(z \ y,u,w)),v5) = L(x,a(z * y,u,w),v5)
    ]]></literal>
    <justification jstring="[para(46645(a,1),47724(a,1,2)),flip(a)].">
      <j1 rule="para" parents="46645 47724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47726">
    <literal><![CDATA[
      L(x,a(y \ z,u,w),y) = L(x,a(z * y,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46954,a(flip),b,47725,a)].">
      <j1 rule="hyper" parents="64 46954 47725"/>
    </justification>
  </clause>

  <clause id="47727">
    <literal><![CDATA[
      L(x,(y * (a(z,z,y) * u)) * w,v5) = L(x,(u * L(y,z,z)) * w,v5)
    ]]></literal>
    <justification jstring="[para(37673(a,1),45720(a,1,2,1,2))].">
      <j1 rule="para" parents="37673 45720"/>
    </justification>
  </clause>

  <clause id="47728">
    <literal><![CDATA[
      (x \ a(y,z,z)) \ R(x \ 1,u,w) = x \ (a(y,z,z) \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,42548,a(flip),b,45745,a),flip(a)].">
      <j1 rule="hyper" parents="373 42548 45745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47729">
    <literal><![CDATA[
      L(x,(L(1 / y,z,u) * w) * v5,v6) = L(x,(w * (a(y,z,u) \ y)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,36284,a(flip),b,45794,a)].">
      <j1 rule="hyper" parents="64 36284 45794"/>
    </justification>
  </clause>

  <clause id="47730">
    <literal><![CDATA[
      (x \ L(y,y,z)) \ z = (x \ y) \ R(z,y * a(u,y,w),a(w,y,u) * y)
    ]]></literal>
    <justification jstring="[para(43242(a,2),46204(a,2,2))].">
      <j1 rule="para" parents="43242 46204"/>
    </justification>
  </clause>

  <clause id="47731">
    <literal><![CDATA[
      L(x,(y \ ((y * z) * x)) * x,y) = (R(y,z,x) * z) \ ((y * z) * x)
    ]]></literal>
    <justification jstring="[para(41807(a,1),46309(a,2,1))].">
      <j1 rule="para" parents="41807 46309"/>
    </justification>
  </clause>

  <clause id="47732">
    <literal><![CDATA[
      L(x,(y \ ((y * z) * x)) * x,y) = L(x,z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,41923,a,b,47731,a),flip(a)].">
      <j1 rule="hyper" parents="373 41923 47731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47733">
    <literal><![CDATA[
      a(((x \ y) \ z) * ((y * x) \ (x \ y)),u,w) = a((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32810,a(flip),b,46355,a)].">
      <j1 rule="hyper" parents="64 32810 46355"/>
    </justification>
  </clause>

  <clause id="47734">
    <literal><![CDATA[
      a(a(x,y,y) * ((y \ x) \ z),u,w) = a((x * y) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,37170,a(flip),b,47733,a)].">
      <j1 rule="hyper" parents="64 37170 47733"/>
    </justification>
  </clause>

  <clause id="47735">
    <literal><![CDATA[
      a(a(x,y,y) * ((y \ x) \ z),u,a(w,v5,z)) = a(z * (x * y),u,a(w,v5,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,46646,a(flip),b,47734,a),flip(a)].">
      <j1 rule="hyper" parents="373 46646 47734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47736">
    <literal><![CDATA[
      (x / y) \ (a(z,u,w) * x) = y * a(z,u,L(w,y,x * y))
    ]]></literal>
    <justification jstring="[para(46503(a,1),46429(a,2,2))].">
      <j1 rule="para" parents="46503 46429"/>
    </justification>
  </clause>

  <clause id="47737">
    <literal><![CDATA[
      (L(x,y,z) / u) \ (a(x,w,v5) * L(x,y,z)) = u * a(x,w,L(v5,u,u))
    ]]></literal>
    <justification jstring="[para(46724(a,1),47736(a,2,2))].">
      <j1 rule="para" parents="46724 47736"/>
    </justification>
  </clause>

  <clause id="47738">
    <literal><![CDATA[
      (L(x,y,z) / u) \ (a(x,w,v5) * L(x,y,z)) = (1 / u) \ a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,46521,a(flip),b,47737,a),flip(a)].">
      <j1 rule="hyper" parents="373 46521 47737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47739">
    <literal><![CDATA[
      (L(x,y,z) / u) \ (L(x,y,z) * a(x,w,v5)) = (1 / u) \ a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,25322,a,b,47738,a)].">
      <j1 rule="hyper" parents="64 25322 47738"/>
    </justification>
  </clause>

  <clause id="47740">
    <literal><![CDATA[
      a(a(x,y,z),u,u \ L(x,w,v5)) = ((1 / u) \ a(x,y,z)) \ (a(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(47739(a,1),33336(a,1,1)),flip(a)].">
      <j1 rule="para" parents="47739 33336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47741">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * ((u \ 1) * w)) = a(x,y,(u \ R(z,u,w)) * w)
    ]]></literal>
    <justification jstring="[para(45352(a,1),46459(a,2,3))].">
      <j1 rule="para" parents="45352 46459"/>
    </justification>
  </clause>

  <clause id="47742">
    <literal><![CDATA[
      a(x,y,L(z,u,u) * ((u \ 1) * w)) = a(x,y,(u \ L(z,u,w)) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,36476,a(flip),b,47741,a),flip(a)].">
      <j1 rule="hyper" parents="373 36476 47741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47743">
    <literal><![CDATA[
      a((x \ y) \ z,u,x \ ((y \ x) \ x)) = a(y \ (x * z),u,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27564,a(flip),b,46869,a)].">
      <j1 rule="hyper" parents="64 27564 46869"/>
    </justification>
  </clause>

  <clause id="47744">
    <literal><![CDATA[
      L(x * a(y,y,a(z,x,u)),y,a(y,z,u)) = L(x,a(u,y,y),y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47600,a(flip),b,46948,a)].">
      <j1 rule="hyper" parents="64 47600 46948"/>
    </justification>
  </clause>

  <clause id="47745">
    <literal><![CDATA[
      L(x,a(y,z,z),z \ u) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,47545,a(flip),b,47744,a),flip(a)].">
      <j1 rule="hyper" parents="64 47545 47744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47746">
    <literal><![CDATA[
      L(x,a(y,y,z),y * u) = L(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,47544,a(flip),b,47745,a)].">
      <j1 rule="hyper" parents="64 47544 47745"/>
    </justification>
  </clause>

  <clause id="47747">
    <literal><![CDATA[
      L(x,a(y,z * a(u,z,w),z * a(u,z,w)),z \ L(w,z,u)) = L(x,a(y,z * a(u,z,w),z * a(u,z,w)),w)
    ]]></literal>
    <justification jstring="[para(43358(a,1),47745(a,1,3))].">
      <j1 rule="para" parents="43358 47745"/>
    </justification>
  </clause>

  <clause id="47748">
    <literal><![CDATA[
      L(x,a(R(y,z,u),R(y,z,u),w),(y * z) * u) = L(x,a(w,R(y,z,u),R(y,z,u)),z * u)
    ]]></literal>
    <justification jstring="[para(111(a,1),47746(a,1,3))].">
      <j1 rule="para" parents="111 47746"/>
    </justification>
  </clause>

  <clause id="47749">
    <literal><![CDATA[
      a(x * ((y * x) \ z),u,L(y,x,x)) = a(L(y,x,x) \ z,u,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,32693,a(flip),b,47004,a),flip(a)].">
      <j1 rule="hyper" parents="64 32693 47004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47750">
    <literal><![CDATA[
      a(x * ((y * x) \ z),u,L(y,x,x)) = a(z * L(y,x,x),u,L(y,x,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,46084,a(flip),b,47749,a),flip(a)].">
      <j1 rule="hyper" parents="373 46084 47749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47751">
    <literal><![CDATA[
      a(x * L(y,z,z),u,L(y,z,z)) = a(z \ ((y * z) \ x),u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46605,a(flip),b,47750,a),flip(a)].">
      <j1 rule="hyper" parents="64 46605 47750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47752">
    <literal><![CDATA[
      a(x,y,z * a(u,z,w)) \ a(x,y,z) = a(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(114(a,1),47017(a,1,2))].">
      <j1 rule="para" parents="114 47017"/>
    </justification>
  </clause>

  <clause id="47754">
    <literal><![CDATA[
      x * (a(y,z,(u \ (w \ 1)) \ 1) \ 1) = x * (u \ (w \ L(w * u,z,y)))
    ]]></literal>
    <justification jstring="[para(27389(a,1),47188(a,1,2,1))].">
      <j1 rule="para" parents="27389 47188"/>
    </justification>
  </clause>

  <clause id="47755">
    <literal><![CDATA[
      L(x,y,a(z,u,(w * (v5 \ 1)) * v6)) = L(x,y,a(z,u,v6 * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47271,a(flip),b,47428,a),flip(a)].">
      <j1 rule="hyper" parents="373 47271 47428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47756">
    <literal><![CDATA[
      a(x,a(y,z,z),u) \ (z * a(y,z,a(z,u,x))) = a(z,z,a(u,x,y)) \ z
    ]]></literal>
    <justification jstring="[para(41448(a,1),47565(a,1,2))].">
      <j1 rule="para" parents="41448 47565"/>
    </justification>
  </clause>

  <clause id="47757">
    <literal><![CDATA[
      a(x,(y * (x \ (y \ z))) \ z,u) = a(y,z * y,a(u,x,x)) * a(x,x,u)
    ]]></literal>
    <justification jstring="[para(35687(a,1),47626(a,2,1))].">
      <j1 rule="para" parents="35687 47626"/>
    </justification>
  </clause>

  <clause id="47758">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * a(u,z,a(y,y,x)) = a(y * z,a(x,y,y),u)
    ]]></literal>
    <justification jstring="[para(44170(a,1),47641(a,1,1))].">
      <j1 rule="para" parents="44170 47641"/>
    </justification>
  </clause>

  <clause id="47759">
    <literal><![CDATA[
      a(x * y,a(z,x,x),u) = a(y,a(z,x,x),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,47564,a(flip),b,47758,a),flip(a)].">
      <j1 rule="hyper" parents="64 47564 47758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47760">
    <literal><![CDATA[
      a((x \ a(y,x,z)) * u,a(w,x * a(y,x,z),x * a(y,x,z)),v5) = a(u,a(w,x * a(y,x,z),x * a(y,x,z)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,35761,a,b,47759,a)].">
      <j1 rule="hyper" parents="64 35761 47759"/>
    </justification>
  </clause>

  <clause id="47761">
    <literal><![CDATA[
      a(L(x,y,z) * u,a(w,x,x),v5) = a(u,a(w,L(x,y,z),L(x,y,z)),v5)
    ]]></literal>
    <justification jstring="[para(40664(a,1),47759(a,1,2))].">
      <j1 rule="para" parents="40664 47759"/>
    </justification>
  </clause>

  <clause id="47762">
    <literal><![CDATA[
      a(L(x,y,z) * u,a(w,x,x),v5) = a(u,a(w,x,x),v5)
    ]]></literal>
    <justification jstring="[para(40664(a,1),47761(a,2,2))].">
      <j1 rule="para" parents="40664 47761"/>
    </justification>
  </clause>

  <clause id="47764">
    <literal><![CDATA[
      a((x * y) * z,a(u,y,y),w) = a(x * z,a(u,y,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32574,a(flip),b,47762,a)].">
      <j1 rule="hyper" parents="64 32574 47762"/>
    </justification>
  </clause>

  <clause id="47766">
    <literal><![CDATA[
      a((x * y) * z,a(u,x,x),w) = a(y * z,a(u,x,x),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32388,a,b,47764,a)].">
      <j1 rule="hyper" parents="64 32388 47764"/>
    </justification>
  </clause>

  <clause id="47767">
    <literal><![CDATA[
      L(x,(y * (a(z,u,w) \ z)) * v5,v6) = L(x,(L(z,u,w) * y) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,36352,a(flip),b,47729,a),flip(a)].">
      <j1 rule="hyper" parents="64 36352 47729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47768">
    <literal><![CDATA[
      (x \ L(y,y,z)) \ z = (x \ y) \ R(z,y * a(u,y,w),a(w,y,u) \ y)
    ]]></literal>
    <justification jstring="[para(42481(a,2),47730(a,2,2))].">
      <j1 rule="para" parents="42481 47730"/>
    </justification>
  </clause>

  <clause id="47769">
    <literal><![CDATA[
      a(x \ (y * z),u,(x \ y) \ 1) = a((y \ x) \ z,u,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27323,a(flip),b,47743,a),flip(a)].">
      <j1 rule="hyper" parents="64 27323 47743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47771">
    <literal><![CDATA[
      a(x \ (y * z),u,(x \ y) \ 1) = a(z * (y \ x),u,y \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,46084,a(flip),b,47769,a),flip(a)].">
      <j1 rule="hyper" parents="373 46084 47769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47772">
    <literal><![CDATA[
      a((x * y) * z,u,(x \ 1) * z) = a(y * (x \ z),u,x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46701,a(flip),b,47771,a)].">
      <j1 rule="hyper" parents="64 46701 47771"/>
    </justification>
  </clause>

  <clause id="47773">
    <literal><![CDATA[
      a((x \ y) * (x \ z),u,x \ z) = a(y * z,u,(x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),47772(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10 47772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47775">
    <literal><![CDATA[
      x * (a(y,z,(u \ 1) \ w) \ 1) = x * (u \ (w \ L(w * u,z,y)))
    ]]></literal>
    <justification jstring="[para(46696(a,1),47754(a,1,2,1))].">
      <j1 rule="para" parents="46696 47754"/>
    </justification>
  </clause>

  <clause id="47777">
    <literal><![CDATA[
      x * (y \ (z \ L(z * y,u,w))) = a(w,u,(y \ 1) \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,42444,a(flip),b,47775,a),flip(a)].">
      <j1 rule="hyper" parents="64 42444 47775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47778">
    <literal><![CDATA[
      ((a(x,y,(z \ 1) \ u) \ (u \ L(u * z,y,x))) \ (u \ L(u * z,y,x))) \ w = (z \ (z / (z \ (u \ L(u * z,y,x))))) \ w
    ]]></literal>
    <justification jstring="[para(47777(a,1),43095(a,1,1,1))].">
      <j1 rule="para" parents="47777 43095"/>
    </justification>
  </clause>

  <clause id="47779">
    <literal><![CDATA[
      a(x,a(y,z,z),u) \ L(z,u,a(y,z,x)) = a(z,z,a(u,x,y)) \ z
    ]]></literal>
    <justification jstring="[para(47271(a,1),47756(a,1,2))].">
      <j1 rule="para" parents="47271 47756"/>
    </justification>
  </clause>

  <clause id="47780">
    <literal><![CDATA[
      a(x,a(y,z,z),u) * L(z,x,a(y,z,u)) = a(z,z,a(x,u,y)) \ z
    ]]></literal>
    <justification jstring="[hyper(64,a,42524,a(flip),b,47779,a)].">
      <j1 rule="hyper" parents="64 42524 47779"/>
    </justification>
  </clause>

  <clause id="47781">
    <literal><![CDATA[
      a(x,a(y,z,z),u) * L(z,x,a(y,z,u)) = L(z,z,a(y,u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,41502,a(flip),b,47780,a),flip(a)].">
      <j1 rule="hyper" parents="373 41502 47780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47782">
    <literal><![CDATA[
      a(x,(y * (x \ (y \ z))) \ z,u) = a(y,x,a(u,z,x)) * a(x,x,u)
    ]]></literal>
    <justification jstring="[para(46884(a,1),47757(a,2,1))].">
      <j1 rule="para" parents="46884 47757"/>
    </justification>
  </clause>

  <clause id="47783">
    <literal><![CDATA[
      a(x,(y * (x \ (y \ z))) \ z,u) = a(x,x,L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,47408,a(flip),b,47782,a),flip(a)].">
      <j1 rule="hyper" parents="373 47408 47782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47784">
    <literal><![CDATA[
      a(x,((y * (1 / z)) * (x \ z)) \ R(y,z,z),u) = a(x,x,L(u,R(y,z,z),y * (1 / z)))
    ]]></literal>
    <justification jstring="[para(1409(a,1),47783(a,1,2,1,2,2))].">
      <j1 rule="para" parents="1409 47783"/>
    </justification>
  </clause>

  <clause id="47785">
    <literal><![CDATA[
      L(a(x,y,z) \ y,y * a(z,y,x),u) = a(x,y,z) \ L(y,y,u)
    ]]></literal>
    <justification jstring="[hyper(40,a,45689,a,b,47768,a)].">
      <j1 rule="hyper" parents="40 45689 47768"/>
    </justification>
  </clause>

  <clause id="47786">
    <literal><![CDATA[
      L(a(x,y,z) \ y,y * a(x,y,z),u) = a(x,y,z) \ L(y,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42188,a,b,47785,a)].">
      <j1 rule="hyper" parents="64 42188 47785"/>
    </justification>
  </clause>

  <clause id="47787">
    <literal><![CDATA[
      L(a(x * y,z,a(z,x,u)) \ z,z * a(a(z,x,u),z,x * y),w) = a(z,z,a(y * x,y,u)) \ L(z,z,w)
    ]]></literal>
    <justification jstring="[para(46916(a,1),47785(a,2,1))].">
      <j1 rule="para" parents="46916 47785"/>
    </justification>
  </clause>

  <clause id="47788">
    <literal><![CDATA[
      (a(x,y,z) \ L(y,y,u)) \ u = T(u * (a(x,y,z) / y),y)
    ]]></literal>
    <justification jstring="[para(47786(a,1),42622(a,1,1))].">
      <j1 rule="para" parents="47786 42622"/>
    </justification>
  </clause>

  <clause id="47789">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ R(u,y,y) = T(u * (a(x,y,z) / y),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,45834,a(flip),b,47788,a)].">
      <j1 rule="hyper" parents="64 45834 47788"/>
    </justification>
  </clause>

  <clause id="47790">
    <literal><![CDATA[
      T(x \ a(x,x,y * z),z * y) = ((z \ 1) \ y) \ (x \ ((z \ 1) \ y))
    ]]></literal>
    <justification jstring="[hyper(14642,a,45838,a)].">
      <j1 rule="hyper" parents="14642 45838"/>
    </justification>
  </clause>

  <clause id="47791">
    <literal><![CDATA[
      ((x \ 1) \ y) \ (z \ ((x \ 1) \ y)) = (x * y) \ (z \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,30126,a(flip),b,47790,a),flip(a)].">
      <j1 rule="hyper" parents="64 30126 47790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47792">
    <literal><![CDATA[
      (x \ (x \ 1)) * (y \ ((x \ 1) \ z)) = (x \ z) * ((x * z) \ (y \ (x * z)))
    ]]></literal>
    <justification jstring="[para(47791(a,1),1615(a,1,2)),flip(a)].">
      <j1 rule="para" parents="47791 1615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47793">
    <literal><![CDATA[
      (x \ y) * ((x * y) \ (z \ (x * y))) = T(z,x * x) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,15286,a(flip),b,47792,a),flip(a)].">
      <j1 rule="hyper" parents="64 15286 47792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47794">
    <literal><![CDATA[
      L(x \ ((y \ z) * z),x,a(z,z * y,y)) = (((z / (y / z)) \ y) * x) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,35692,a(flip),b,45941,a)].">
      <j1 rule="hyper" parents="64 35692 45941"/>
    </justification>
  </clause>

  <clause id="47795">
    <literal><![CDATA[
      (((x / (y / x)) \ y) * z) \ y = z \ ((y \ x) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,47142,a(flip),b,47794,a),flip(a)].">
      <j1 rule="hyper" parents="64 47142 47794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47796">
    <literal><![CDATA[
      (1 / (x * y)) * ((x * y) / z) = (y \ x) * (((y \ x) \ 1) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29510,a(flip),b,46386,a)].">
      <j1 rule="hyper" parents="64 29510 46386"/>
    </justification>
  </clause>

  <clause id="47797">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ 1) / z) = (y * x) * (((y * x) \ 1) / z)
    ]]></literal>
    <justification jstring="[hyper(64,a,1217,a(flip),b,47796,a),flip(a)].">
      <j1 rule="hyper" parents="64 1217 47796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47798">
    <literal><![CDATA[
      L((x * y) \ ((x * y) / z),x * y,x) = y \ (x * ((x \ y) / z))
    ]]></literal>
    <justification jstring="[para(36918(a,1),46419(a,1,1))].">
      <j1 rule="para" parents="36918 46419"/>
    </justification>
  </clause>

  <clause id="47799">
    <literal><![CDATA[
      L(L(x \ 1,y * z,y),x,(y * z) * x) = z \ (y * ((y \ z) / x))
    ]]></literal>
    <justification jstring="[hyper(64,a,30677,a,b,47798,a)].">
      <j1 rule="hyper" parents="64 30677 47798"/>
    </justification>
  </clause>

  <clause id="47800">
    <literal><![CDATA[
      a(L(x,y,z) * u,w,L(L(x,v5,v6),u,x)) = a(u \ L(x,y,z),w,R(x,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,27703,a(flip),b,46647,a)].">
      <j1 rule="hyper" parents="64 27703 46647"/>
    </justification>
  </clause>

  <clause id="47801">
    <literal><![CDATA[
      a(x * (x \ (y \ x)),z,y \ (x * u)) = a(x * y,z,L((x \ y) \ u,x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,32708,a(flip),b,46690,a)].">
      <j1 rule="hyper" parents="64 32708 46690"/>
    </justification>
  </clause>

  <clause id="47802">
    <literal><![CDATA[
      (a(x,y,y) * ((a(x,y,y) \ z) / u)) \ z = L(u,y,a(x,a(x,y,y) * z,y))
    ]]></literal>
    <justification jstring="[para(42464(a,1),46903(a,2,3))].">
      <j1 rule="para" parents="42464 46903"/>
    </justification>
  </clause>

  <clause id="47803">
    <literal><![CDATA[
      a(x,x,L((y * z) \ ((y \ 1) \ u),z,y)) = a(x,x,L(z,y,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,27556,a(flip),b,46933,a),flip(a)].">
      <j1 rule="hyper" parents="373 27556 46933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47804">
    <literal><![CDATA[
      a(x,x,y \ (z \ ((z \ 1) \ u))) = a(x,x,L(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,39066,a(flip),b,47803,a)].">
      <j1 rule="hyper" parents="64 39066 47803"/>
    </justification>
  </clause>

  <clause id="47805">
    <literal><![CDATA[
      a(x,x,L(y,z,z) \ u) = a(x,x,y \ L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,39001,a(flip),b,47804,a),flip(a)].">
      <j1 rule="hyper" parents="64 39001 47804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47806">
    <literal><![CDATA[
      a(x,x,(y \ 1) \ L(z,u,u)) = a(x,x,z * L(y,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,45557,a(flip),b,47805,a),flip(a)].">
      <j1 rule="hyper" parents="64 45557 47805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47807">
    <literal><![CDATA[
      a(x,x,L(y,z,z) * u) = a(x,x,y * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,45561,a(flip),b,47806,a)].">
      <j1 rule="hyper" parents="64 45561 47806"/>
    </justification>
  </clause>

  <clause id="47808">
    <literal><![CDATA[
      a(x,x,y * L(a(z,L(y,u,u),w),u,u)) = a(x,x,y * a(z,y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,45567,a(flip),b,47807,a),flip(a)].">
      <j1 rule="hyper" parents="64 45567 47807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47809">
    <literal><![CDATA[
      a(x,x,y * a(z,L(y,u,u),L(w,u,u))) = a(x,x,y * a(z,y,w))
    ]]></literal>
    <justification jstring="[para(46493(a,2),47808(a,1,3,2))].">
      <j1 rule="para" parents="46493 47808"/>
    </justification>
  </clause>

  <clause id="47810">
    <literal><![CDATA[
      a(x,y * z,y) * a(u,a(y,y * z,x),w) = a(x,z \ y,y * a(w,y,u))
    ]]></literal>
    <justification jstring="[para(46412(a,1),47020(a,1,1))].">
      <j1 rule="para" parents="46412 47020"/>
    </justification>
  </clause>

  <clause id="47811">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),z,u)) * a(w,y,L(x,z,u)) = a(w,y,x * a(u,x,z))
    ]]></literal>
    <justification jstring="[para(46496(a,1),47485(a,1,1))].">
      <j1 rule="para" parents="46496 47485"/>
    </justification>
  </clause>

  <clause id="47812">
    <literal><![CDATA[
      a(x,y,L((z * u) \ (w * w),u,u)) = a(x,y,u \ (z \ (w * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27627,a(flip),b,47653,a)].">
      <j1 rule="hyper" parents="64 27627 47653"/>
    </justification>
  </clause>

  <clause id="47814">
    <literal><![CDATA[
      a(x * a(y,z,u),a(y,z,u),a(w,w,z)) = a(z * x,z,a(w,w,a(u,z,y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47254,a(flip),b,47722,a),flip(a)].">
      <j1 rule="hyper" parents="373 47254 47722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47815">
    <literal><![CDATA[
      a(x,y,a(z,u,(w \ v5) * (a(v5,w,w) \ x))) = a(x * (v5 * w),y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47567,a(flip),b,47735,a)].">
      <j1 rule="hyper" parents="64 47567 47735"/>
    </justification>
  </clause>

  <clause id="47816">
    <literal><![CDATA[
      a(a(x,y,z),u,u \ L(x,w,v5)) = u \ ((a(x,y,z) / (a(x,y,z) * u)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,38203,a(flip),b,47740,a),flip(a)].">
      <j1 rule="hyper" parents="373 38203 47740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47817">
    <literal><![CDATA[
      a(x \ L(y,z,u),w,R(y,v5,v6)) = a(L(y,z,u) * x,w,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,34164,a(flip),b,47800,a),flip(a)].">
      <j1 rule="hyper" parents="64 34164 47800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47819">
    <literal><![CDATA[
      a(x \ L(y,z,u),w,L(y,v5,v6)) = a(L(y,z,u) * x,w,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,27644,a(flip),b,47817,a)].">
      <j1 rule="hyper" parents="64 27644 47817"/>
    </justification>
  </clause>

  <clause id="47820">
    <literal><![CDATA[
      a(x * y,z,L((x \ y) \ u,x,x)) = a(y \ x,z,y \ (x * u))
    ]]></literal>
    <justification jstring="[para(10(a,1),47801(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 47801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47821">
    <literal><![CDATA[
      a(x \ y,z,(x \ y) \ u) = a(y \ x,z,y \ (x * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46605,a(flip),b,47820,a)].">
      <j1 rule="hyper" parents="64 46605 47820"/>
    </justification>
  </clause>

  <clause id="47823">
    <literal><![CDATA[
      a((x * (y * z)) \ (x * y),u,(x * (y * z)) \ ((x * y) * w)) = a(L(z,y,x),u,((x * y) \ (x * (y * z))) \ w)
    ]]></literal>
    <justification jstring="[para(18(a,2),47821(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18 47821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47824">
    <literal><![CDATA[
      a(R((x \ 1) \ 1,y,z) \ 1,u,T(R(x,y,z) \ 1,x) \ w) = a(1 \ R((x \ 1) \ 1,y,z),u,1 \ (R((x \ 1) \ 1,y,z) * w))
    ]]></literal>
    <justification jstring="[para(25605(a,2),47821(a,1,3,1))].">
      <j1 rule="para" parents="25605 47821"/>
    </justification>
  </clause>

  <clause id="47825">
    <literal><![CDATA[
      (a(x,y,y) * ((a(x,y,y) \ z) / u)) \ z = L(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,47435,a(flip),b,47802,a),flip(a)].">
      <j1 rule="hyper" parents="373 47435 47802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47826">
    <literal><![CDATA[
      L(x \ (a(y,z,z) \ u),u,a(y,z,z)) = (a(y,z,z) * x) \ u
    ]]></literal>
    <justification jstring="[para(79(a,1),47825(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="79 47825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47827">
    <literal><![CDATA[
      a(x,y \ z,z * a(u,z,w)) = a(x,z * y,z * a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47016,a(flip),b,47810,a),flip(a)].">
      <j1 rule="hyper" parents="64 47016 47810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47828">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,y,L(x,z,u)) = a(w,y,x * a(u,x,z))
    ]]></literal>
    <justification jstring="[para(45430(a,1),47811(a,1,1,3))].">
      <j1 rule="para" parents="45430 47811"/>
    </justification>
  </clause>

  <clause id="47829">
    <literal><![CDATA[
      a(x * y,x,a(z,z,a(u,x,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,47690,a(flip),b,47814,a),flip(a)].">
      <j1 rule="hyper" parents="64 47690 47814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47831">
    <literal><![CDATA[
      a(a(x,y,z),y,a(u,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,47551,a(flip),b,47829,a)].">
      <j1 rule="hyper" parents="64 47551 47829"/>
    </justification>
  </clause>

  <clause id="47832">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w),u,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,46423,a(flip),b,47829,a)].">
      <j1 rule="hyper" parents="64 46423 47829"/>
    </justification>
  </clause>

  <clause id="47834">
    <literal><![CDATA[
      a(x,y,L(y,z,a(u,z,w))) = a(x,y,y) * 1
    ]]></literal>
    <justification jstring="[hyper(145,a,47831,a(flip),b,46526,a),flip(a)].">
      <j1 rule="hyper" parents="145 47831 46526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47835">
    <literal><![CDATA[
      a(x,y,a(z,y,a(u,w,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,47409,a(flip),b,47832,a)].">
      <j1 rule="hyper" parents="64 47409 47832"/>
    </justification>
  </clause>

  <clause id="47836">
    <literal><![CDATA[
      R(x,y,a(z,y,a(u,w,w))) = x * 1
    ]]></literal>
    <justification jstring="[hyper(145,a,47835,a(flip),b,45073,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 47835 45073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47837">
    <literal><![CDATA[
      L(x,y,a(z,y,a(u,w,w))) = x
    ]]></literal>
    <justification jstring="[hyper(141,a,47836,a(flip),b,47459,a(flip))].">
      <j1 rule="hyper" parents="141 47836 47459"/>
    </justification>
  </clause>

  <clause id="47838">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,y,u))) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,47286,a,b,47837,a)].">
      <j1 rule="hyper" parents="64 47286 47837"/>
    </justification>
  </clause>

  <clause id="47839">
    <literal><![CDATA[
      R(x \ (a(y,z,a(u,w,w)) \ x),z,x) = x \ (a(y,z,a(u,w,w)) \ x)
    ]]></literal>
    <justification jstring="[para(47837(a,1),45853(a,2,1))].">
      <j1 rule="para" parents="47837 45853"/>
    </justification>
  </clause>

  <clause id="47840">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,x,u))) \ y = L(y,a(z,u,a(w,x,u)),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,34903,a(flip),b,47838,a),flip(a)].">
      <j1 rule="hyper" parents="64 34903 47838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47841">
    <literal><![CDATA[
      a(x * a(a(y,z,u),x,z),L(w,a(y,z,u),z),w) = a(x,L(w,a(y,z,u),z),L(w,a(y,z,u),z))
    ]]></literal>
    <justification jstring="[hyper(141,a,47834,a(flip),b,46727,a),flip(a)].">
      <j1 rule="hyper" parents="141 47834 46727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47842">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,z)),w) = 1 \ x
    ]]></literal>
    <justification jstring="[para(47292(a,1),47840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="47292 47840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47843">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,z)),w) = x
    ]]></literal>
    <justification jstring="[hyper(373,a,66,a(flip),b,47842,a),flip(a)].">
      <j1 rule="hyper" parents="373 66 47842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47845">
    <literal><![CDATA[
      ((x * (a(y,z,a(u,x,z)) * x)) / x) \ (L(x,a(y,z,a(u,x,z)),x) * w) = a(y,z,a(u,x,z)) \ w
    ]]></literal>
    <justification jstring="[hyper(64,a,13059,a,b,47843,a)].">
      <j1 rule="hyper" parents="64 13059 47843"/>
    </justification>
  </clause>

  <clause id="47846">
    <literal><![CDATA[
      R(x \ (a(y,z,a(u,u,w)) * x),z,x) = x \ (a(y,z,a(w,u,u)) \ x)
    ]]></literal>
    <justification jstring="[para(42644(a,1),47839(a,1,1,2))].">
      <j1 rule="para" parents="42644 47839"/>
    </justification>
  </clause>

  <clause id="47847">
    <literal><![CDATA[
      R(a(x,y,a(z,z,u)),y,w) = w \ (a(x,y,a(u,z,z)) \ w)
    ]]></literal>
    <justification jstring="[para(23174(a,1),47846(a,1,1))].">
      <j1 rule="para" parents="23174 47846"/>
    </justification>
  </clause>

  <clause id="47848">
    <literal><![CDATA[
      a(x,y,L(a(z,z,u),y,w)) = w \ (a(x,y,a(u,z,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,46506,a,b,47847,a)].">
      <j1 rule="hyper" parents="64 46506 47847"/>
    </justification>
  </clause>

  <clause id="47850">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,y,w))) = w \ (a(x,y,a(u,z,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,46631,a,b,47848,a)].">
      <j1 rule="hyper" parents="64 46631 47848"/>
    </justification>
  </clause>

  <clause id="47851">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,y,w))) = w \ (a(x,y,a(z,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(42644(a,1),47850(a,2,2))].">
      <j1 rule="para" parents="42644 47850"/>
    </justification>
  </clause>

  <clause id="47852">
    <literal><![CDATA[
      a(x,y,a(z,z,L(u,y,w))) = a(x,y,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,23174,a(flip),b,47851,a),flip(a)].">
      <j1 rule="hyper" parents="373 23174 47851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47854">
    <literal><![CDATA[
      a(x,y,a(z,u,(w \ v5) * (a(v5,w,w) * x))) = a(x * (v5 * w),y,a(z,u,x))
    ]]></literal>
    <justification jstring="[para(42520(a,1),47815(a,1,3))].">
      <j1 rule="para" parents="42520 47815"/>
    </justification>
  </clause>

  <clause id="47855">
    <literal><![CDATA[
      a(a(x,y,z),u,u \ L(x,w,v5)) = u \ ((a(x,y,z) \ (a(x,y,z) / u)) \ 1)
    ]]></literal>
    <justification jstring="[para(27098(a,1),47816(a,2,2,1))].">
      <j1 rule="para" parents="27098 47816"/>
    </justification>
  </clause>

  <clause id="47856">
    <literal><![CDATA[
      a(x,y,a(z,u,(w \ R(v5,w,w)) * x)) = a(x * (v5 * w),y,a(z,u,x))
    ]]></literal>
    <justification jstring="[para(45018(a,1),47854(a,1,3,3))].">
      <j1 rule="para" parents="45018 47854"/>
    </justification>
  </clause>

  <clause id="47857">
    <literal><![CDATA[
      a(x,y,a(z,u,(w \ L(v5,w,w)) * x)) = a(x * (v5 * w),y,a(z,u,x))
    ]]></literal>
    <justification jstring="[para(36476(a,1),47856(a,1,3))].">
      <j1 rule="para" parents="36476 47856"/>
    </justification>
  </clause>

  <clause id="47858">
    <literal><![CDATA[
      a(x,y,a(z,u,((w \ 1) * v5) * x)) = a(x * (v5 * w),y,a(z,u,x))
    ]]></literal>
    <justification jstring="[para(1148(a,1),47857(a,1,3,3,1))].">
      <j1 rule="para" parents="1148 47857"/>
    </justification>
  </clause>

  <clause id="47859">
    <literal><![CDATA[
      a(x,y,a(z,u,w * ((v5 \ 1) \ x))) = a(x * (w * v5),y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47558,a(flip),b,47858,a)].">
      <j1 rule="hyper" parents="64 47558 47858"/>
    </justification>
  </clause>

  <clause id="47860">
    <literal><![CDATA[
      a(x * (y * z),u,a(w,v5,x)) = a(x,u,a(w,v5,y * (z \ x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,42302,a(flip),b,47859,a),flip(a)].">
      <j1 rule="hyper" parents="64 42302 47859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47861">
    <literal><![CDATA[
      a(x * (y * z),u,a(w,v5,x)) = a(x,u,a(z * (y \ x),v5,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,47568,a,b,47860,a),flip(a)].">
      <j1 rule="hyper" parents="373 47568 47860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47862">
    <literal><![CDATA[
      a(x,y,a(z * (u \ x),w,v5)) = a(x,y,a(x * (u * z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,47244,a(flip),b,47861,a),flip(a)].">
      <j1 rule="hyper" parents="64 47244 47861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47863">
    <literal><![CDATA[
      a(a(x,y,z),u,u \ L(x,w,v5)) = u \ (a(x,y,z) * ((a(x,y,z) / u) \ 1))
    ]]></literal>
    <justification jstring="[para(46983(a,1),47855(a,2,2))].">
      <j1 rule="para" parents="46983 47855"/>
    </justification>
  </clause>

  <clause id="47864">
    <literal><![CDATA[
      a(a(x,y,z),u,u \ L(x,w,v5)) = a(z,y,a(u,u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47053,a(flip),b,47863,a),flip(a)].">
      <j1 rule="hyper" parents="373 47053 47863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47865">
    <literal><![CDATA[
      (x \ L(y,z,u)) * a(u,z,a(x,x,y)) = (a(u,z,y) * x) \ y
    ]]></literal>
    <justification jstring="[para(47864(a,1),46460(a,1,2))].">
      <j1 rule="para" parents="47864 46460"/>
    </justification>
  </clause>

  <clause id="47866">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) \ L(u,z,y) = (a(y,z,u) * x) \ u
    ]]></literal>
    <justification jstring="[hyper(64,a,46027,a(flip),b,47865,a)].">
      <j1 rule="hyper" parents="64 46027 47865"/>
    </justification>
  </clause>

  <clause id="47868">
    <literal><![CDATA[
      L(x,y,z) * (x \ (u \ x)) = (a(z,y,x) * u) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,46028,a(flip),b,47866,a)].">
      <j1 rule="hyper" parents="64 46028 47866"/>
    </justification>
  </clause>

  <clause id="47872">
    <literal><![CDATA[
      (x \ a(y,z,z)) \ R(x \ 1,u,w) = (a(y,z,z) * x) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[para(82(a,1),45746(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="82 45746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47873">
    <literal><![CDATA[
      (x \ a(y,z,z)) \ R(x \ 1,u,w) = a(y,z,z) \ a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,45485,a(flip),b,47872,a),flip(a)].">
      <j1 rule="hyper" parents="373 45485 47872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47875">
    <literal><![CDATA[
      x * (a(y,z,z) \ a(x,u,w)) = a(y,z,z) \ R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(145,a,47873,a(flip),b,47728,a(flip))].">
      <j1 rule="hyper" parents="145 47873 47728"/>
    </justification>
  </clause>

  <clause id="47876">
    <literal><![CDATA[
      a((x \ y) * ((1 / (1 / (y \ x))) * z),y,x) = a(y * (x \ ((x \ y) \ z)),y,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,46841,a(flip),b,46005,a),flip(a)].">
      <j1 rule="hyper" parents="373 46841 46005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47877">
    <literal><![CDATA[
      a(x,y,x \ (z * L(u,x \ 1,z))) = a(x,y,z * ((x \ 1) * L(u,z,x)))
    ]]></literal>
    <justification jstring="[para(1631(a,1),46254(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="1631 46254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47878">
    <literal><![CDATA[
      a(x,y,z * ((x \ 1) * L(u,z,x))) = a(x,y,x \ (z * L(u,x,z)))
    ]]></literal>
    <justification jstring="[para(11794(a,1),47877(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="11794 47877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47879">
    <literal><![CDATA[
      x \ (a(y,y,z) * (u / (u / z))) = (x \ (u / (u / z))) * a(y,y,z)
    ]]></literal>
    <justification jstring="[para(27306(a,1),46348(a,1,2)),flip(a)].">
      <j1 rule="para" parents="27306 46348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47881">
    <literal><![CDATA[
      a(x,y,(z \ (u / (u / (w \ v5)))) * a(w,w,w \ v5)) = a(x,y,z \ (u / (u / ((1 / w) * v5))))
    ]]></literal>
    <justification jstring="[para(47879(a,1),39175(a,1,3))].">
      <j1 rule="para" parents="47879 39175"/>
    </justification>
  </clause>

  <clause id="47882">
    <literal><![CDATA[
      (x * (y \ x)) \ (y * z) = ((x * (y \ x)) \ y) * z
    ]]></literal>
    <justification jstring="[para(6220(a,1),46354(a,1,2))].">
      <j1 rule="para" parents="6220 46354"/>
    </justification>
  </clause>

  <clause id="47884">
    <literal><![CDATA[
      a(x,y,(z * (u \ z)) \ (w * u)) = a(x,y,((z * (u \ z)) \ u) * w)
    ]]></literal>
    <justification jstring="[para(47882(a,1),27325(a,1,3)),flip(a)].">
      <j1 rule="para" parents="47882 27325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47885">
    <literal><![CDATA[
      a(x,y,(z * (u \ z)) \ (w * u)) = a(x,y,u * (((u \ z) * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,47171,a(flip),b,47884,a),flip(a)].">
      <j1 rule="hyper" parents="373 47171 47884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47886">
    <literal><![CDATA[
      x * L((x \ y) * a(z,u,x),x,a(w,v5,x)) = L(y,v5,a(x,x,w)) * a(z,u,x)
    ]]></literal>
    <justification jstring="[para(46805(a,2),46387(a,1,2))].">
      <j1 rule="para" parents="46805 46387"/>
    </justification>
  </clause>

  <clause id="47887">
    <literal><![CDATA[
      a(x * a(y,x,a(z,u,w)),v5,L(v5,v6,v7)) = a(x,L(v5,v6,v7),L(L(v5,y,a(z,u,w)),a(w,u,z),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,16192,a(flip),b,46744,a)].">
      <j1 rule="hyper" parents="64 16192 46744"/>
    </justification>
  </clause>

  <clause id="47888">
    <literal><![CDATA[
      a((x * y) \ L(z,y,x),u,L(z,y,y)) = a(x * (y * z),u,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(100(a,1),47073(a,2,1))].">
      <j1 rule="para" parents="100 47073"/>
    </justification>
  </clause>

  <clause id="47889">
    <literal><![CDATA[
      a(L(x,y,z) * (z * y),u,L(x,y,y)) = a(z * (y * x),u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47819,a(flip),b,47888,a)].">
      <j1 rule="hyper" parents="64 47819 47888"/>
    </justification>
  </clause>

  <clause id="47890">
    <literal><![CDATA[
      a(x * (y * z),u,L(z,y,y)) = a(x * (y * z),u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,26837,a(flip),b,47889,a)].">
      <j1 rule="hyper" parents="64 26837 47889"/>
    </justification>
  </clause>

  <clause id="47891">
    <literal><![CDATA[
      L(a(x,y,L(z,u,w)),v5,a(x,v6,v7)) * 1 = R(a(x,y,z),u,L(w,v5,a(x,v6,v7)))
    ]]></literal>
    <justification jstring="[para(46506(a,2),47086(a,1,1,1))].">
      <j1 rule="para" parents="46506 47086"/>
    </justification>
  </clause>

  <clause id="47892">
    <literal><![CDATA[
      a(x * (y * ((z * y) \ x)),u,u) = a(z,u,u) * a(z,u,a(x * (z * y),y,u))
    ]]></literal>
    <justification jstring="[para(46815(a,1),47089(a,2,2))].">
      <j1 rule="para" parents="46815 47089"/>
    </justification>
  </clause>

  <clause id="47893">
    <literal><![CDATA[
      L(x,y,x \ (z * u)) = L(x,y,u * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46800,a(flip),b,47189,a),flip(a)].">
      <j1 rule="hyper" parents="64 46800 47189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47894">
    <literal><![CDATA[
      L(x,y,a(z,u,x) * ((w * v5) / L(x,u,z))) = L(x,y,v5 * (w \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47037,a,b,47893,a)].">
      <j1 rule="hyper" parents="64 47037 47893"/>
    </justification>
  </clause>

  <clause id="47895">
    <literal><![CDATA[
      L(x,y,(z * u) * x) = L(x,y,u * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46133,a(flip),b,47893,a)].">
      <j1 rule="hyper" parents="64 46133 47893"/>
    </justification>
  </clause>

  <clause id="47896">
    <literal><![CDATA[
      L(x,y,a(z,u,x) * (((1 / w) * v5) / L(x,u,z))) = L(x,y,(w \ x) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,23996,a(flip),b,47894,a),flip(a)].">
      <j1 rule="hyper" parents="373 23996 47894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47897">
    <literal><![CDATA[
      L(x,y,a(z,u,x) * (L(x,u,z) \ (w * v5))) = L(x,y,(w \ x) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29406,a(flip),b,47896,a)].">
      <j1 rule="hyper" parents="64 29406 47896"/>
    </justification>
  </clause>

  <clause id="47898">
    <literal><![CDATA[
      L(x,y,(z \ x) * u) = L(x,y,x * (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47035,a(flip),b,47897,a),flip(a)].">
      <j1 rule="hyper" parents="64 47035 47897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47899">
    <literal><![CDATA[
      L(x,y,(z / u) * (x * y)) = L(x,y,x * (y * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46839,a(flip),b,47898,a)].">
      <j1 rule="hyper" parents="64 46839 47898"/>
    </justification>
  </clause>

  <clause id="47900">
    <literal><![CDATA[
      L(x,y,(z / y) * (x * y)) = L(x,y,x * z)
    ]]></literal>
    <justification jstring="[para(10(a,1),47899(a,2,3,2))].">
      <j1 rule="para" parents="10 47899"/>
    </justification>
  </clause>

  <clause id="47901">
    <literal><![CDATA[
      L(x,y,(y \ z) * (x * y)) = L(x,y,x * z)
    ]]></literal>
    <justification jstring="[hyper(29066,a,47900,a)].">
      <j1 rule="hyper" parents="29066 47900"/>
    </justification>
  </clause>

  <clause id="47902">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (a(w,y,z) * v5) = v5 * a(w,y,L(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,46555,a(flip),b,47402,a),flip(a)].">
      <j1 rule="hyper" parents="373 46555 47402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47903">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,y,a(w,v5,a(x,u,v6))) = a(x,y,a(z,u,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,46631,a,b,47524,a),flip(a)].">
      <j1 rule="hyper" parents="373 46631 47524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47904">
    <literal><![CDATA[
      x * a(y,((z * x) * (y \ x)) \ L(z,x,x),u) = (z / x) \ (z * a(y,y,u))
    ]]></literal>
    <justification jstring="[para(32265(a,1),47637(a,1,2))].">
      <j1 rule="para" parents="32265 47637"/>
    </justification>
  </clause>

  <clause id="47905">
    <literal><![CDATA[
      a((x * y) \ (x * z),u,(y * x) \ w) = a(y \ T(z,x),u,y \ (x \ w))
    ]]></literal>
    <justification jstring="[para(22(a,2),47657(a,2,1,2))].">
      <j1 rule="para" parents="22 47657"/>
    </justification>
  </clause>

  <clause id="47906">
    <literal><![CDATA[
      a((x * y) \ (x * z),u,(y * x) \ w) = a(y \ z,u,y \ (x \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,32360,a(flip),b,47905,a),flip(a)].">
      <j1 rule="hyper" parents="373 32360 47905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47908">
    <literal><![CDATA[
      a(x \ (y \ (x * z)),u,x \ (y \ w)) = a(y \ z,u,y \ (x \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46732,a(flip),b,47906,a)].">
      <j1 rule="hyper" parents="64 46732 47906"/>
    </justification>
  </clause>

  <clause id="47909">
    <literal><![CDATA[
      a((x / (y / (z * z))) \ u,w,((z * z) * (y \ x)) * (v5 \ 1)) = a(u * (x / (y / (z * z))),w,((x / (y / (z * z))) \ v5) \ 1)
    ]]></literal>
    <justification jstring="[para(890(a,1),47684(a,1,3,1))].">
      <j1 rule="para" parents="890 47684"/>
    </justification>
  </clause>

  <clause id="47910">
    <literal><![CDATA[
      (R(x,y,y) * y) \ (((x * y) * y) * L(a(R(x,y,y),y,y),z,u)) = y * a(y * L(y,y,R(x,y,y)),z,u)
    ]]></literal>
    <justification jstring="[para(662(a,1),47693(a,1,2))].">
      <j1 rule="para" parents="662 47693"/>
    </justification>
  </clause>

  <clause id="47911">
    <literal><![CDATA[
      a((x \ y) * (((1 / (y \ x)) \ 1) * z),y,x) = a(y * (x \ ((x \ y) \ z)),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32440,a(flip),b,47876,a)].">
      <j1 rule="hyper" parents="64 32440 47876"/>
    </justification>
  </clause>

  <clause id="47912">
    <literal><![CDATA[
      L(x * ((x \ y) * a(z,u,x)),x,a(x,w,v5)) = L(y,w,a(x,x,v5)) * a(z,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,41429,a,b,47886,a)].">
      <j1 rule="hyper" parents="64 41429 47886"/>
    </justification>
  </clause>

  <clause id="47913">
    <literal><![CDATA[
      R(a(x,y,z),u,L(w,v5,a(x,v6,v7))) = a(x,y,L(z,u,w)) * 1
    ]]></literal>
    <justification jstring="[para(31083(a,1),47891(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31083 47891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47914">
    <literal><![CDATA[
      a(x,y,L(z,u,L(w,v5,a(x,v6,v7)))) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(141,a,47913,a(flip),b,46506,a),flip(a)].">
      <j1 rule="hyper" parents="141 47913 46506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47916">
    <literal><![CDATA[
      a(x * (y * ((z * y) \ x)),u,u) = a(z,u,L(u,y,x * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,44034,a(flip),b,47892,a),flip(a)].">
      <j1 rule="hyper" parents="373 44034 47892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47917">
    <literal><![CDATA[
      a((x \ y) * ((y \ x) * z),y,x) = a(y * (x \ ((x \ y) \ z)),y,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),47911(a,1,1,2,1))].">
      <j1 rule="para" parents="82 47911"/>
    </justification>
  </clause>

  <clause id="47918">
    <literal><![CDATA[
      a(x * (y \ ((y \ x) \ z)),x,y) = a(z * a(x,x * y,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47157,a(flip),b,47917,a),flip(a)].">
      <j1 rule="hyper" parents="64 47157 47917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47920">
    <literal><![CDATA[
      a((x * y) * a(x,x * z,z),x,z) = a(y * L(x,z,z),x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47644,a(flip),b,47918,a),flip(a)].">
      <j1 rule="hyper" parents="64 47644 47918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47921">
    <literal><![CDATA[
      a(x * (y * a(x,x * z,z)),x,z) = a(y * L(x,z,z),x,z)
    ]]></literal>
    <justification jstring="[para(29910(a,1),47920(a,1,1))].">
      <j1 rule="para" parents="29910 47920"/>
    </justification>
  </clause>

  <clause id="47922">
    <literal><![CDATA[
      L(x * a(y,z,u),u,a(u,w,v5)) = L(x,w,a(u,u,v5)) * a(y,z,u)
    ]]></literal>
    <justification jstring="[para(33197(a,1),47912(a,1,1))].">
      <j1 rule="para" parents="33197 47912"/>
    </justification>
  </clause>

  <clause id="47923">
    <literal><![CDATA[
      L(x * a(y,z,u),u,a(u,w,v5)) = L(x,w,a(v5,u,u)) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,42212,a,b,47922,a),flip(a)].">
      <j1 rule="hyper" parents="373 42212 47922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47925">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) * v5,x,a(x,y,a(w,u,z))) = x * (L(x,y,a(w,u,z)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(24736,a,45969,a)].">
      <j1 rule="hyper" parents="24736 45969"/>
    </justification>
  </clause>

  <clause id="47926">
    <literal><![CDATA[
      a(x * (R(y,y,x) \ z),x,L(y,y,x)) = a(z * ((1 / y) \ T(x,y)),x,R(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,27644,a(flip),b,46278,a)].">
      <j1 rule="hyper" parents="64 27644 46278"/>
    </justification>
  </clause>

  <clause id="47927">
    <literal><![CDATA[
      a(((x * y) * x) * ((y * x) * (z * x)),u,u) = a(z,u,L(u,T(x,y),y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,32439,a(flip),b,46456,a)].">
      <j1 rule="hyper" parents="64 32439 46456"/>
    </justification>
  </clause>

  <clause id="47929">
    <literal><![CDATA[
      a(L(x,y,y) * ((x * y) * (z * y)),u,u) = a(z,u,L(u,T(y,x),x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32510,a(flip),b,47927,a)].">
      <j1 rule="hyper" parents="64 32510 47927"/>
    </justification>
  </clause>

  <clause id="47930">
    <literal><![CDATA[
      a(x * L((x * y) * (z * y),y,y),u,u) = a(z,u,L(u,T(y,x),x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47586,a(flip),b,47929,a)].">
      <j1 rule="hyper" parents="64 47586 47929"/>
    </justification>
  </clause>

  <clause id="47931">
    <literal><![CDATA[
      a(x * L((x * y) * (z * y),y,y),u,u) = a(z,u,L(u,y,x * y))
    ]]></literal>
    <justification jstring="[para(29434(a,1),47930(a,2,3))].">
      <j1 rule="para" parents="29434 47930"/>
    </justification>
  </clause>

  <clause id="47933">
    <literal><![CDATA[
      a(x,y * a(z,y,u),L(y * a(z,y,u),w,v5)) = a(x,y,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,46758,a(flip),b,46759,a),flip(a)].">
      <j1 rule="hyper" parents="64 46758 46759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47934">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ (a(u,w,L(x,y,z)) \ x) = L(R(x,y,z),w,L(u,R(x,y,z),x))
    ]]></literal>
    <justification jstring="[para(27644(a,1),46782(a,1,2,1))].">
      <j1 rule="para" parents="27644 46782"/>
    </justification>
  </clause>

  <clause id="47935">
    <literal><![CDATA[
      a(x * ((1 / y) \ T(z,y)),z,R(y,y,z)) = a(z * (R(y,y,z) \ x),z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,45281,a(flip),b,47926,a),flip(a)].">
      <j1 rule="hyper" parents="64 45281 47926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47936">
    <literal><![CDATA[
      a(x * ((1 / y) \ T(z,y)),z,R(y,y,z)) = a(z * (L(y,y,z) \ x),z,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,40059,a(flip),b,47935,a),flip(a)].">
      <j1 rule="hyper" parents="373 40059 47935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47937">
    <literal><![CDATA[
      a(x * ((1 / y) \ T(z,y)),z,L(y,y,z)) = a(z * (L(y,y,z) \ x),z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27644,a(flip),b,47936,a)].">
      <j1 rule="hyper" parents="64 27644 47936"/>
    </justification>
  </clause>

  <clause id="47938">
    <literal><![CDATA[
      a(x * (L(y,y,x) \ z),x,y) = a(z * ((1 / y) \ T(x,y)),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,45281,a(flip),b,47937,a),flip(a)].">
      <j1 rule="hyper" parents="64 45281 47937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47939">
    <literal><![CDATA[
      a(x * (L(y,y,x) \ z),x,y) = a(z * ((1 / y) \ x),x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,32437,a(flip),b,47938,a),flip(a)].">
      <j1 rule="hyper" parents="373 32437 47938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47941">
    <literal><![CDATA[
      a(x * (L(y,y,x) \ z),x,y) = a((y \ x) * z,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,32812,a(flip),b,47939,a),flip(a)].">
      <j1 rule="hyper" parents="373 32812 47939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47942">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ L(x,u,L(w,y,z)) = L(R(x,y,z),u,L(w,R(x,y,z),x))
    ]]></literal>
    <justification jstring="[para(46623(a,1),47934(a,1,2))].">
      <j1 rule="para" parents="46623 47934"/>
    </justification>
  </clause>

  <clause id="47943">
    <literal><![CDATA[
      L(R(x,y,z),u,L(w,R(x,y,z),x)) = a(x,y,z) * L(x,u,L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,45483,a(flip),b,47942,a),flip(a)].">
      <j1 rule="hyper" parents="64 45483 47942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47944">
    <literal><![CDATA[
      a(x,y,z) * L(x,u,L(w,y,z)) = L(R(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,46318,a(flip),b,47943,a),flip(a)].">
      <j1 rule="hyper" parents="64 46318 47943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47946">
    <literal><![CDATA[
      L(x,y,L(z,u,w)) \ L(R(x,u,w),y,z) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(139,a,47944,a(flip),b,23183,a)].">
      <j1 rule="hyper" parents="139 47944 23183"/>
    </justification>
  </clause>

  <clause id="47953">
    <literal><![CDATA[
      L(x,y,L(L(z,u,w),y,L(z,u,w))) \ L(R(x,y,z),y,z) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(47705(a,1),47946(a,1,2))].">
      <j1 rule="para" parents="47705 47946"/>
    </justification>
  </clause>

  <clause id="47954">
    <literal><![CDATA[
      L(x,y,L(z,u,w)) \ L(R(x,y,z),y,z) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(12978(a,1),47953(a,1,1))].">
      <j1 rule="para" parents="12978 47953"/>
    </justification>
  </clause>

  <clause id="47956">
    <literal><![CDATA[
      a(T((x \ 1) \ (y \ z),u),w,a(v5,v5,x)) = a(x,w,a(v5,v5,(y * (x \ 1)) \ z))
    ]]></literal>
    <justification jstring="[para(25163(a,1),46341(a,2,3))].">
      <j1 rule="para" parents="25163 46341"/>
    </justification>
  </clause>

  <clause id="47957">
    <literal><![CDATA[
      a(T((x \ 1) \ (y \ z),u),w,a(v5,v5,x)) = a(x,w,a(v5,v5,(y * (x \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,45836,a(flip),b,47956,a),flip(a)].">
      <j1 rule="hyper" parents="373 45836 47956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47959">
    <literal><![CDATA[
      a(T((x \ 1) \ (y \ z),u),w,a(v5,v5,x)) = a(x,w,a((x * y) * z,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,41906,a(flip),b,47957,a),flip(a)].">
      <j1 rule="hyper" parents="373 41906 47957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47960">
    <literal><![CDATA[
      a((x \ 1) \ (y \ z),u,a(w,w,x)) = a(x,u,a((x * y) * z,w,w))
    ]]></literal>
    <justification jstring="[hyper(26780,a,47959,a)].">
      <j1 rule="hyper" parents="26780 47959"/>
    </justification>
  </clause>

  <clause id="47961">
    <literal><![CDATA[
      a((x \ 1) * (y \ z),u,a(x,w,u)) = a(x,w,a((x * y) * z,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46424,a(flip),b,47960,a)].">
      <j1 rule="hyper" parents="64 46424 47960"/>
    </justification>
  </clause>

  <clause id="47962">
    <literal><![CDATA[
      a(x * (y \ z),u,a(x,w,u)) = a(x,w,a((x * y) * z,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,2662,a(flip),b,47961,a)].">
      <j1 rule="hyper" parents="64 2662 47961"/>
    </justification>
  </clause>

  <clause id="47963">
    <literal><![CDATA[
      a(x,y,a((x * z) * u,w,w)) = a(x,y,a(x * (z \ u),w,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47253,a,b,47962,a),flip(a)].">
      <j1 rule="hyper" parents="64 47253 47962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47964">
    <literal><![CDATA[
      a(x,y,a((z * x) * u,w,w)) = a(x,y,a(x * (z \ u),w,w))
    ]]></literal>
    <justification jstring="[para(32388(a,1),47963(a,1,3))].">
      <j1 rule="para" parents="32388 47963"/>
    </justification>
  </clause>

  <clause id="47965">
    <literal><![CDATA[
      a(((x * y) * y) \ z,u,L((1 / x) \ 1,y,y)) = a((x * y) \ (y \ z),u,L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,39638,a,b,46733,a)].">
      <j1 rule="hyper" parents="64 39638 46733"/>
    </justification>
  </clause>

  <clause id="47966">
    <literal><![CDATA[
      a(L(x,y,z),x * ((x * y) * z),a(u,w,w)) = a(L(x,y,z),w,a(u,(z * y) * x,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,32276,a(flip),b,46894,a)].">
      <j1 rule="hyper" parents="64 32276 46894"/>
    </justification>
  </clause>

  <clause id="47967">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * a(v5,v6,a(w,y,a(z,u,x))) = x * a(w,y,a(z,u,L(x,v6,v5)))
    ]]></literal>
    <justification jstring="[para(46493(a,2),47464(a,2,2,3))].">
      <j1 rule="para" parents="46493 47464"/>
    </justification>
  </clause>

  <clause id="47968">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(z,y,a(x,w,u)) = a(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,47378,a(flip),b,47472,a),flip(a)].">
      <j1 rule="hyper" parents="373 47378 47472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47969">
    <literal><![CDATA[
      R(x,x,a(y,z,u)) * a(y,x,a(x,u,z)) = x * a(u,a(x,x,y),z)
    ]]></literal>
    <justification jstring="[para(47968(a,1),37535(a,1,2)),flip(a)].">
      <j1 rule="para" parents="47968 37535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47970">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) * a(y,x,a(x,u,z)) = x * a(u,a(x,x,y),z)
    ]]></literal>
    <justification jstring="[para(28832(a,1),47969(a,1,1))].">
      <j1 rule="para" parents="28832 47969"/>
    </justification>
  </clause>

  <clause id="47971">
    <literal><![CDATA[
      L(L(x,x,a(y,z,u)),x,a(y,u,z)) = x * a(z,a(x,x,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46947,a(flip),b,47970,a)].">
      <j1 rule="hyper" parents="64 46947 47970"/>
    </justification>
  </clause>

  <clause id="47972">
    <literal><![CDATA[
      a(((x * y) * y) \ z,u,L(x,y,y)) = a((x * y) \ (y \ z),u,L(x,x,y))
    ]]></literal>
    <justification jstring="[para(82(a,1),47965(a,1,3,1))].">
      <j1 rule="para" parents="82 47965"/>
    </justification>
  </clause>

  <clause id="47973">
    <literal><![CDATA[
      a(L(x,y,y) \ z,u,L(x,y,y)) = a((x * y) \ (y \ z),u,L(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32694,a(flip),b,47972,a)].">
      <j1 rule="hyper" parents="64 32694 47972"/>
    </justification>
  </clause>

  <clause id="47974">
    <literal><![CDATA[
      a((x * y) \ (y \ z),u,L(x,x,y)) = a(z * L(x,y,y),u,L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46084,a(flip),b,47973,a),flip(a)].">
      <j1 rule="hyper" parents="64 46084 47973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47975">
    <literal><![CDATA[
      a((x * y) \ (y \ z),u,L(x,x,y)) = a(y \ ((x * y) \ z),u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,47751,a(flip),b,47974,a),flip(a)].">
      <j1 rule="hyper" parents="373 47751 47974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47976">
    <literal><![CDATA[
      a(x \ ((y * x) \ z),u,y) = a(y \ (x \ (x \ z)),u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46596,a(flip),b,47975,a),flip(a)].">
      <j1 rule="hyper" parents="64 46596 47975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47977">
    <literal><![CDATA[
      a(x \ ((y * x) \ z),u,y) = a((x \ (x \ z)) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,46084,a(flip),b,47976,a),flip(a)].">
      <j1 rule="hyper" parents="373 46084 47976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47978">
    <literal><![CDATA[
      a(x \ ((y * x) \ z),u,y) = a(L(z,x,x) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,32811,a(flip),b,47977,a),flip(a)].">
      <j1 rule="hyper" parents="373 32811 47977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47979">
    <literal><![CDATA[
      a(x * L(y,z,z),u,L(y,z,z)) = a(L(x,z,z) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47751,a,b,47978,a)].">
      <j1 rule="hyper" parents="64 47751 47978"/>
    </justification>
  </clause>

  <clause id="47980">
    <literal><![CDATA[
      a(x,x * ((x * y) * z),a(u,w,L(w,y,z))) = a(L(x,y,z),w,a(u,(z * y) * x,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46629,a(flip),b,47966,a)].">
      <j1 rule="hyper" parents="64 46629 47966"/>
    </justification>
  </clause>

  <clause id="47981">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * a(v5,v6,a(w,y,a(z,u,x))) = L(x,u,a(w,y,L(z,v6,v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47429,a(flip),b,47967,a),flip(a)].">
      <j1 rule="hyper" parents="373 47429 47967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47982">
    <literal><![CDATA[
      a((x \ (y \ T(z,y))) * a(y,y,y \ z),u,w) = a(x \ ((y * y) \ (z * y)),u,w)
    ]]></literal>
    <justification jstring="[para(27301(a,1),46799(a,1,1,2))].">
      <j1 rule="para" parents="27301 46799"/>
    </justification>
  </clause>

  <clause id="47983">
    <literal><![CDATA[
      a((x \ (y \ T(z,y))) * a(y,y,z),u,w) = a(x \ ((y * y) \ (z * y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32725,a(flip),b,47982,a)].">
      <j1 rule="hyper" parents="64 32725 47982"/>
    </justification>
  </clause>

  <clause id="47985">
    <literal><![CDATA[
      a(a(x,x,y) * (z \ (x \ y)),u,w) = a(z \ ((x * x) \ (y * x)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32529,a(flip),b,47983,a)].">
      <j1 rule="hyper" parents="64 32529 47983"/>
    </justification>
  </clause>

  <clause id="47986">
    <literal><![CDATA[
      a(a(x,x,y) * (z \ (x \ y)),u,w) = a(z \ (y * x),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26899,a(flip),b,47985,a),flip(a)].">
      <j1 rule="hyper" parents="373 26899 47985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47989">
    <literal><![CDATA[
      a(R(x \ 1,x,y) * z,u,L(u,y,y * x)) = a(((y \ R(x \ 1,x,y)) \ z) * y,u,u)
    ]]></literal>
    <justification jstring="[para(44999(a,1),46873(a,1,3))].">
      <j1 rule="para" parents="44999 46873"/>
    </justification>
  </clause>

  <clause id="47990">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (z * a(x,u,z)))) = L(a(x,u,z),L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(100(a,1),46879(a,1,2))].">
      <j1 rule="para" parents="100 46879"/>
    </justification>
  </clause>

  <clause id="47991">
    <literal><![CDATA[
      L(L(a(x,y,z),z,u),u * z,x) = L(a(x,y,z),L(z,u,x),x * u)
    ]]></literal>
    <justification jstring="[hyper(1081,a,47990,a)].">
      <j1 rule="hyper" parents="1081 47990"/>
    </justification>
  </clause>

  <clause id="47992">
    <literal><![CDATA[
      L(a(x,y,L(z,z,u)),u * z,x) = L(a(x,y,z),L(z,u,x),x * u)
    ]]></literal>
    <justification jstring="[para(46000(a,2),47991(a,1,1))].">
      <j1 rule="para" parents="46000 47991"/>
    </justification>
  </clause>

  <clause id="47993">
    <literal><![CDATA[
      L(a(x,y,z),L(z,u,x),x * u) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(30899,a,47992,a),flip(a)].">
      <j1 rule="hyper" parents="30899 47992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="47995">
    <literal><![CDATA[
      a(x,y,L(z,L(z,u,x),x * u)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46493,a,b,47993,a)].">
      <j1 rule="hyper" parents="64 46493 47993"/>
    </justification>
  </clause>

  <clause id="47996">
    <literal><![CDATA[
      a(x,y,L(z,z,L(x * u,u,x))) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39723,a(flip),b,47995,a)].">
      <j1 rule="hyper" parents="64 39723 47995"/>
    </justification>
  </clause>

  <clause id="47997">
    <literal><![CDATA[
      a(x,y,L(z,z,x * u)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46675,a(flip),b,47996,a)].">
      <j1 rule="hyper" parents="64 46675 47996"/>
    </justification>
  </clause>

  <clause id="48000">
    <literal><![CDATA[
      a(x,y,L(z,z,u * x)) = a(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[para(23253(a,1),47997(a,1,3))].">
      <j1 rule="para" parents="23253 47997"/>
    </justification>
  </clause>

  <clause id="48001">
    <literal><![CDATA[
      L(x,y,L(z,x,u * z)) = a(z,y,L(x,x,u)) \ x
    ]]></literal>
    <justification jstring="[para(48000(a,1),46623(a,1,1)),flip(a)].">
      <j1 rule="para" parents="48000 46623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48002">
    <literal><![CDATA[
      L(x,y,L(z,x,u * z)) = L(x,y,L(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,46623,a(flip),b,48001,a),flip(a)].">
      <j1 rule="hyper" parents="373 46623 48001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48003">
    <literal><![CDATA[
      a(x,x * y,a(z,u,L(u,w,v5))) = a(x,u,a(L((v6 \ 1) * (z * v6),w,v5),y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,47132,a(flip),b,46898,a)].">
      <j1 rule="hyper" parents="373 47132 46898"/>
    </justification>
  </clause>

  <clause id="48004">
    <literal><![CDATA[
      a(x,x * y,a(z,u,L(u,w,v5))) = a(x,u,a((v6 \ 1) * (z * v6),y,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,46787,a(flip),b,48003,a),flip(a)].">
      <j1 rule="hyper" parents="373 46787 48003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48006">
    <literal><![CDATA[
      a(x,x * y,a(z,u,L(u,w,v5))) = a(x,u,a(v6 * (z * v6),y,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(2662(a,1),48004(a,2,3))].">
      <j1 rule="para" parents="2662 48004"/>
    </justification>
  </clause>

  <clause id="48007">
    <literal><![CDATA[
      a(x,x * y,a(z,u,L(u,w,v5))) = a(x,u,a(z,y,L(L(u,w,v5),v6,v6)))
    ]]></literal>
    <justification jstring="[para(46580(a,1),48006(a,2,3))].">
      <j1 rule="para" parents="46580 48006"/>
    </justification>
  </clause>

  <clause id="48008">
    <literal><![CDATA[
      a(x,y \ z,a(u,u,(y \ z) * L(y,w,w))) = a(x,u,a(u,R(y,w,w),z * a(y,w,w)))
    ]]></literal>
    <justification jstring="[para(27987(a,1),46922(a,1,3))].">
      <j1 rule="para" parents="27987 46922"/>
    </justification>
  </clause>

  <clause id="48009">
    <literal><![CDATA[
      a(L(x * y,x,x) \ z,u,(x \ y) \ w) = a(y \ (x * z),u,y \ (x * w))
    ]]></literal>
    <justification jstring="[para(9(a,1),47060(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 47060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48010">
    <literal><![CDATA[
      a((x \ y) \ z,u,(x \ y) \ w) = a(y \ (x * z),u,y \ (x * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,33709,a(flip),b,48009,a)].">
      <j1 rule="hyper" parents="64 33709 48009"/>
    </justification>
  </clause>

  <clause id="48011">
    <literal><![CDATA[
      a(1 \ (x * (y \ x)),z,1 \ (x * (y \ u))) = a(y,z,y \ ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46971,a(flip),b,48010,a),flip(a)].">
      <j1 rule="hyper" parents="64 46971 48010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48012">
    <literal><![CDATA[
      a(x * (y \ x),z,1 \ (x * (y \ u))) = a(y,z,y \ ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(66(a,1),48011(a,1,1))].">
      <j1 rule="para" parents="66 48011"/>
    </justification>
  </clause>

  <clause id="48013">
    <literal><![CDATA[
      a(x * (y \ x),z,x * (y \ u)) = a(y,z,y \ ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(66(a,1),48012(a,1,3))].">
      <j1 rule="para" parents="66 48012"/>
    </justification>
  </clause>

  <clause id="48014">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z) \ ((x \ 1) \ z)) = a(x * (L(x,y,z) \ x),u,R(z,y,x))
    ]]></literal>
    <justification jstring="[para(45658(a,2),48013(a,1,3)),flip(a)].">
      <j1 rule="para" parents="45658 48013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48015">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z) \ ((x \ 1) \ z)) = a(x * a(z,y,x),u,R(z,y,x))
    ]]></literal>
    <justification jstring="[para(45067(a,2),48014(a,2,1,2))].">
      <j1 rule="para" parents="45067 48014"/>
    </justification>
  </clause>

  <clause id="48016">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z) \ ((x \ 1) \ z)) = a(x * a(z,y,x),u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,27644,a(flip),b,48015,a),flip(a)].">
      <j1 rule="hyper" parents="373 27644 48015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48017">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z) \ ((x \ 1) \ z)) = a(x,u,L(L(z,y,x),y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,46574,a(flip),b,48016,a),flip(a)].">
      <j1 rule="hyper" parents="373 46574 48016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48018">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z) \ ((x \ 1) \ z)) = a(x,u,L(z,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,46219,a(flip),b,48017,a),flip(a)].">
      <j1 rule="hyper" parents="373 46219 48017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48020">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z) \ ((x \ 1) \ z)) = a(x,u,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,13865,a(flip),b,48018,a),flip(a)].">
      <j1 rule="hyper" parents="373 13865 48018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48022">
    <literal><![CDATA[
      a(x,y,L(L(x,z,u) \ ((x \ 1) \ u),z,u)) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46496,a(flip),b,48020,a)].">
      <j1 rule="hyper" parents="64 46496 48020"/>
    </justification>
  </clause>

  <clause id="48023">
    <literal><![CDATA[
      x * a(y,z,L(u,w,w * x)) = (x / w) * (a(y,z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42850,a(flip),b,47117,a),flip(a)].">
      <j1 rule="hyper" parents="64 42850 47117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48024">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ (a(z,y,x) * v5) = L(a(z,y,x),u,L(w,a(z,y,x),v5))
    ]]></literal>
    <justification jstring="[para(23127(a,1),47240(a,2,1))].">
      <j1 rule="para" parents="23127 47240"/>
    </justification>
  </clause>

  <clause id="48025">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ (a(z,y,x) * v5) = a(z,y,L(x,u,L(w,a(z,y,x),v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,46493,a,b,48024,a),flip(a)].">
      <j1 rule="hyper" parents="373 46493 48024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48027">
    <literal><![CDATA[
      a(a(x,y,z),x,a(u,w,L(y * v5,u,v6))) = a((u \ v6) * v6,x,a(z,v5,a(x,w,y * v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47381,a(flip),b,47534,a),flip(a)].">
      <j1 rule="hyper" parents="373 47381 47534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48028">
    <literal><![CDATA[
      L(x,y,a(a(y,x * z,u),w,L(v5,x,v6))) = L(x,y,a(a(u,z,y),w,L(v5,x,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47581,a(flip),b,47582,a),flip(a)].">
      <j1 rule="hyper" parents="373 47581 47582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48029">
    <literal><![CDATA[
      L(x,y,a(a(y,x * z,u),w,L(v5,x,v6))) = L(x,y,a(y,z,a(L(v5,x,v6),w,u)))
    ]]></literal>
    <justification jstring="[para(47254(a,1),48028(a,2,3))].">
      <j1 rule="para" parents="47254 48028"/>
    </justification>
  </clause>

  <clause id="48030">
    <literal><![CDATA[
      L(x,y,a(a(y,x * z,u),w,L(v5,x,v6))) = L(x,y,a(y,z,a(v5,w,L(u,x,v6))))
    ]]></literal>
    <justification jstring="[para(46496(a,1),48029(a,2,3,3))].">
      <j1 rule="para" parents="46496 48029"/>
    </justification>
  </clause>

  <clause id="48031">
    <literal><![CDATA[
      L(x,R(y,z,u) * w,a(v5,L(y,z,u),L(y,z,u))) = L(x,R(y,z,u),a(R(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[para(32197(a,1),47613(a,1,3))].">
      <j1 rule="para" parents="32197 47613"/>
    </justification>
  </clause>

  <clause id="48032">
    <literal><![CDATA[
      a(T(x / y,z) * u,w,L(w,x,y)) = a(((x \ T(x / y,z)) \ u) * x,w,w)
    ]]></literal>
    <justification jstring="[para(44998(a,1),47685(a,1,3))].">
      <j1 rule="para" parents="44998 47685"/>
    </justification>
  </clause>

  <clause id="48033">
    <literal><![CDATA[
      a(((x \ T(x / y,z)) \ u) * x,w,w) = a((x / y) * u,w,L(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32363,a(flip),b,48032,a),flip(a)].">
      <j1 rule="hyper" parents="64 32363 48032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48035">
    <literal><![CDATA[
      a(((x \ T(x / y,z)) \ u) * x,w,w) = a((y \ x) * u,w,L(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,32367,a(flip),b,48033,a),flip(a)].">
      <j1 rule="hyper" parents="373 32367 48033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48036">
    <literal><![CDATA[
      a(((x \ T(x / y,z)) \ u) * x,w,w) = a((y * u) * x,w,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,46926,a(flip),b,48035,a),flip(a)].">
      <j1 rule="hyper" parents="373 46926 48035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48037">
    <literal><![CDATA[
      a(((x \ y) \ z) * x,u,u) = a(((y \ x) * z) * x,u,u)
    ]]></literal>
    <justification jstring="[para(23144(a,1),48036(a,1,1,1,1,2))].">
      <j1 rule="para" parents="23144 48036"/>
    </justification>
  </clause>

  <clause id="48038">
    <literal><![CDATA[
      a(((x \ y) \ z) * x,u,u) = a(x * (z * (y \ x)),u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32422,a(flip),b,48037,a),flip(a)].">
      <j1 rule="hyper" parents="373 32422 48037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48039">
    <literal><![CDATA[
      a(x,((y * (1 / z)) * (x \ z)) \ L(y,z,z),u) = a(x,x,L(u,R(y,z,z),y * (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,37374,a(flip),b,47784,a)].">
      <j1 rule="hyper" parents="64 37374 47784"/>
    </justification>
  </clause>

  <clause id="48040">
    <literal><![CDATA[
      a(L(x \ 1,x,y) * z,u,L(u,y,y * x)) = a(((y \ R(x \ 1,x,y)) \ z) * y,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34634,a(flip),b,47989,a)].">
      <j1 rule="hyper" parents="64 34634 47989"/>
    </justification>
  </clause>

  <clause id="48041">
    <literal><![CDATA[
      a(x,y \ z,a(u,u,y * (L(y,w,w) \ z))) = a(x,u,a(u,R(y,w,w),z * a(y,w,w)))
    ]]></literal>
    <justification jstring="[para(39030(a,1),48008(a,1,3))].">
      <j1 rule="para" parents="39030 48008"/>
    </justification>
  </clause>

  <clause id="48042">
    <literal><![CDATA[
      a(a(x,y,z),x,a(u,w,L(y * v5,u,v6))) = a(y * v5,v5,a(u,x,a(z,w,x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47513,a(flip),b,48027,a),flip(a)].">
      <j1 rule="hyper" parents="373 47513 48027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48043">
    <literal><![CDATA[
      a(x * y,y,a(z,u,a(w,v5,u))) = a(w,x,a(a(z,v5,L(x * y,z,v6)),u,u))
    ]]></literal>
    <justification jstring="[hyper(47392,a,48042,a),flip(a)].">
      <j1 rule="hyper" parents="47392 48042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48045">
    <literal><![CDATA[
      a(x * y,y,a(z,u,a(w,v5,u))) = a(w,x,a(L(x * y,z,v6),v5,a(u,u,z)))
    ]]></literal>
    <justification jstring="[para(45501(a,1),48043(a,2,3))].">
      <j1 rule="para" parents="45501 48043"/>
    </justification>
  </clause>

  <clause id="48046">
    <literal><![CDATA[
      a(x * y,y,a(z,u,a(w,v5,u))) = a(w,x,a(x * y,v5,a(u,u,z)))
    ]]></literal>
    <justification jstring="[para(594(a,1),48045(a,2,3,1))].">
      <j1 rule="para" parents="594 48045"/>
    </justification>
  </clause>

  <clause id="48047">
    <literal><![CDATA[
      L(x,R(y,z,u),a(R(y,z,u),w,v5)) = L(x,R(y,z,u) * w,a(v5,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,35215,a(flip),b,48031,a),flip(a)].">
      <j1 rule="hyper" parents="64 35215 48031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48049">
    <literal><![CDATA[
      L(x,R(y,z,u),a(R(y,z,u),w,v5)) = L(x,L(y,z,u) * w,a(v5,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,36262,a(flip),b,48047,a),flip(a)].">
      <j1 rule="hyper" parents="373 36262 48047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48050">
    <literal><![CDATA[
      L(x,R(y,z,u),a(R(y,z,u),y \ (w \ y),v5)) = L(x,(a(u,z,y) * w) \ y,a(v5,y,y))
    ]]></literal>
    <justification jstring="[para(47868(a,1),48049(a,2,2))].">
      <j1 rule="para" parents="47868 48049"/>
    </justification>
  </clause>

  <clause id="48051">
    <literal><![CDATA[
      a(x,((y * z) * (x \ z)) \ L(y,z,z),u) = a(x,x,L(u,R(y,z,z),y * (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,34844,a(flip),b,48039,a)].">
      <j1 rule="hyper" parents="64 34844 48039"/>
    </justification>
  </clause>

  <clause id="48052">
    <literal><![CDATA[
      a(x,((y * z) * (x \ z)) \ L(y,z,z),u) = a(x,x,L(u,R(y,z,z),z * y))
    ]]></literal>
    <justification jstring="[para(23999(a,1),48051(a,2,3))].">
      <j1 rule="para" parents="23999 48051"/>
    </justification>
  </clause>

  <clause id="48053">
    <literal><![CDATA[
      a(x,((y * z) * (x \ z)) \ L(y,z,z),u) = a(x,x,L(u,L(y,z,z),z * y))
    ]]></literal>
    <justification jstring="[para(29794(a,1),48052(a,2,3))].">
      <j1 rule="para" parents="29794 48052"/>
    </justification>
  </clause>

  <clause id="48054">
    <literal><![CDATA[
      a(x,((y * z) * (x \ z)) \ L(y,z,z),u) = a(x,x,L(u,y,y * z))
    ]]></literal>
    <justification jstring="[para(45585(a,1),48053(a,2,3))].">
      <j1 rule="para" parents="45585 48053"/>
    </justification>
  </clause>

  <clause id="48055">
    <literal><![CDATA[
      x * a(y,y,L(z,u,u * x)) = (u / x) \ (u * a(y,y,z))
    ]]></literal>
    <justification jstring="[para(48054(a,1),47904(a,1,2))].">
      <j1 rule="para" parents="48054 47904"/>
    </justification>
  </clause>

  <clause id="48056">
    <literal><![CDATA[
      (x / y) \ (x * a(z,z,u)) = (y / x) * (a(z,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,48023,a(flip),b,48055,a),flip(a)].">
      <j1 rule="hyper" parents="64 48023 48055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48057">
    <literal><![CDATA[
      (x / y) * (a(z,z,u) * y) = x * a(z,z,L(u,x,y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41994,a(flip),b,48056,a),flip(a)].">
      <j1 rule="hyper" parents="64 41994 48056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48058">
    <literal><![CDATA[
      x \ (y * a(z,z,L(u,y,(y / x) * y))) = K(x \ y,x) * (a(z,z,u) * (y / x))
    ]]></literal>
    <justification jstring="[hyper(139,a,48057,a(flip),b,6149,a(flip))].">
      <j1 rule="hyper" parents="139 48057 6149"/>
    </justification>
  </clause>

  <clause id="48059">
    <literal><![CDATA[
      (x \ y) * a(z,z,L(u,x \ y,T(y,x \ 1) * (x \ y))) = (y \ (x \ y)) * (a(z,z,u) * T(y,x \ 1))
    ]]></literal>
    <justification jstring="[para(4576(a,1),48057(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4576 48057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48060">
    <literal><![CDATA[
      x \ (y * a(z,z,L(u,y,(x \ y) * y))) = K(x \ y,x) * (a(z,z,u) * (y / x))
    ]]></literal>
    <justification jstring="[para(28980(a,1),48058(a,1,2,2,3))].">
      <j1 rule="para" parents="28980 48058"/>
    </justification>
  </clause>

  <clause id="48061">
    <literal><![CDATA[
      K(x \ y,x) * (a(z,z,u) * (y / x)) = x \ (y * a(z,z,L(u,y,x)))
    ]]></literal>
    <justification jstring="[para(44998(a,1),48060(a,1,2,2,3)),flip(a)].">
      <j1 rule="para" parents="44998 48060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48062">
    <literal><![CDATA[
      T(a(x,x,y) * (z \ u),K(z,u)) = z \ (u * a(x,x,L(y,u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,8905,a(flip),b,48061,a)].">
      <j1 rule="hyper" parents="64 8905 48061"/>
    </justification>
  </clause>

  <clause id="48063">
    <literal><![CDATA[
      x \ (y * a(z,z,L(u,y,x))) = (x \ y) * a(z,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,23791,a(flip),b,48062,a),flip(a)].">
      <j1 rule="hyper" parents="64 23791 48062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48064">
    <literal><![CDATA[
      (x \ y) * a(z,z,L(u,y,x)) = x \ (y * a(z,z,u))
    ]]></literal>
    <justification jstring="[para(39064(a,1),48063(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="39064 48063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48065">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,y,y * x)) = a(((y \ R(x \ 1,x,y)) \ z) * y,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34643,a(flip),b,48040,a)].">
      <j1 rule="hyper" parents="64 34643 48040"/>
    </justification>
  </clause>

  <clause id="48066">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,y,y * x)) = a(((R(x \ 1,x,y) \ y) * z) * y,u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,48037,a(flip),b,48065,a),flip(a)].">
      <j1 rule="hyper" parents="373 48037 48065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48067">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,y,y * x)) = a(((T(x,x \ 1) * y) * z) * y,u,u)
    ]]></literal>
    <justification jstring="[para(3033(a,1),48066(a,2,1,1,1))].">
      <j1 rule="para" parents="3033 48066"/>
    </justification>
  </clause>

  <clause id="48068">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,y,y * x)) = a(y * ((y * T(x,x \ 1)) * z),u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32655,a(flip),b,48067,a),flip(a)].">
      <j1 rule="hyper" parents="373 32655 48067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48069">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,y,y * x)) = a(y * (z * (y * x)),u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32718,a(flip),b,48068,a),flip(a)].">
      <j1 rule="hyper" parents="373 32718 48068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48071">
    <literal><![CDATA[
      a(x,y \ z,a(u,u,z * a(w,w,y))) = a(x,u,a(u,R(y,w,w),z * a(y,w,w)))
    ]]></literal>
    <justification jstring="[para(45007(a,1),48041(a,1,3,3))].">
      <j1 rule="para" parents="45007 48041"/>
    </justification>
  </clause>

  <clause id="48072">
    <literal><![CDATA[
      L(x,R(y,z,u),a(R(y,z,u),y \ (w \ y),v5)) = L(x,a(u,z,y) * w,a(v5,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,47605,a(flip),b,48050,a),flip(a)].">
      <j1 rule="hyper" parents="373 47605 48050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48073">
    <literal><![CDATA[
      L(x,R(y,z,u),a(y,y \ (w \ y),L(v5,z,u))) = L(x,a(u,z,y) * w,a(v5,y,y))
    ]]></literal>
    <justification jstring="[para(46576(a,1),48072(a,1,3))].">
      <j1 rule="para" parents="46576 48072"/>
    </justification>
  </clause>

  <clause id="48074">
    <literal><![CDATA[
      L(x,R(y,z,u),a(y,(w \ y) * y,L(v5,z,u))) = L(x,a(u,z,y) * w,a(v5,y,y))
    ]]></literal>
    <justification jstring="[para(35687(a,1),48073(a,1,3))].">
      <j1 rule="para" parents="35687 48073"/>
    </justification>
  </clause>

  <clause id="48075">
    <literal><![CDATA[
      L(x,R(y,z,u),a(y,w,L(v5,z,u))) = L(x,a(u,z,y) * w,a(v5,y,y))
    ]]></literal>
    <justification jstring="[para(45426(a,1),48074(a,1,3))].">
      <j1 rule="para" parents="45426 48074"/>
    </justification>
  </clause>

  <clause id="48076">
    <literal><![CDATA[
      L(x,L(y,z,u),a(y,w,L(v5,z,u))) = L(x,a(u,z,y) * w,a(v5,y,y))
    ]]></literal>
    <justification jstring="[hyper(30986,a,48075,a)].">
      <j1 rule="hyper" parents="30986 48075"/>
    </justification>
  </clause>

  <clause id="48077">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,a(v5,u,u)) = L(x,u,a(u,w,L(L(v5,z,y),z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46561,a(flip),b,48076,a),flip(a)].">
      <j1 rule="hyper" parents="64 46561 48076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48078">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,a(v5,u,u)) = L(x,u,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(39064(a,1),48077(a,2,3))].">
      <j1 rule="para" parents="39064 48077"/>
    </justification>
  </clause>

  <clause id="48080">
    <literal><![CDATA[
      a(x,y,((L(z,u,w) \ 1) \ z) * v5) = a(x,y,(z * z) * (v5 * a(w,u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,41248,a(flip),b,45329,a),flip(a)].">
      <j1 rule="hyper" parents="64 41248 45329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48082">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ L(z,u,w)) * v5) = a(x,y,(z * z) * (v5 * a(w,u,z)))
    ]]></literal>
    <justification jstring="[para(31878(a,1),48080(a,1,3,1))].">
      <j1 rule="para" parents="31878 48080"/>
    </justification>
  </clause>

  <clause id="48083">
    <literal><![CDATA[
      a(x,y,(z * z) * (u * a(w,v5,z))) = a(x,y,(z * L(z,v5,w)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,27803,a(flip),b,48082,a),flip(a)].">
      <j1 rule="hyper" parents="64 27803 48082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48084">
    <literal><![CDATA[
      a(x,y,(z * z) * (a(u,w,z) * v5)) = a(x,y,(z * L(z,w,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27554,a,b,48083,a)].">
      <j1 rule="hyper" parents="64 27554 48083"/>
    </justification>
  </clause>

  <clause id="48085">
    <literal><![CDATA[
      L(a(L(x,y,z),u,w),L(x,y,z),z * y) = (z * (y * x)) \ (z * (y * R(x,u,w)))
    ]]></literal>
    <justification jstring="[para(514(a,1),45392(a,1,2)),flip(a)].">
      <j1 rule="para" parents="514 45392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48086">
    <literal><![CDATA[
      a((x * y) \ ((a(z,y,x) \ z) \ (x * y)),u,w) = a((x * (y * z)) \ (x * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,43081,a(flip),b,46362,a),flip(a)].">
      <j1 rule="hyper" parents="373 43081 46362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48087">
    <literal><![CDATA[
      a((x * y) \ (a(z,y,x) * (z \ (x * y))),u,w) = a((x * (y * z)) \ (x * y),u,w)
    ]]></literal>
    <justification jstring="[para(46201(a,1),48086(a,1,1,2))].">
      <j1 rule="para" parents="46201 48086"/>
    </justification>
  </clause>

  <clause id="48088">
    <literal><![CDATA[
      a(R((x * y) \ (z \ (x * y)),y,x),u,w) = a((x * (y * z)) \ (x * y),u,w)
    ]]></literal>
    <justification jstring="[para(45361(a,1),48087(a,1,1))].">
      <j1 rule="para" parents="45361 48087"/>
    </justification>
  </clause>

  <clause id="48089">
    <literal><![CDATA[
      a((x * y) \ (z \ (x * y)),u,L(w,y,x)) = a((x * (y * z)) \ (x * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,46576,a(flip),b,48088,a)].">
      <j1 rule="hyper" parents="64 46576 48088"/>
    </justification>
  </clause>

  <clause id="48090">
    <literal><![CDATA[
      a((x * (y * z)) \ (x * y),u,w) = a(y \ (x \ (z \ (x * y))),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,46728,a(flip),b,48089,a),flip(a)].">
      <j1 rule="hyper" parents="64 46728 48089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48091">
    <literal><![CDATA[
      a(a(x,y,z),u,L(L(w,w,v5),v5 * w,v6)) = a(v5 \ (v6 \ (w \ (v6 * v5))),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,41851,a,b,48090,a)].">
      <j1 rule="hyper" parents="64 41851 48090"/>
    </justification>
  </clause>

  <clause id="48092">
    <literal><![CDATA[
      a(x \ (y \ (z \ (y * x))),u,a(w,v5,v6)) = a(v6,v5,a(L(L(z,z,x),x * z,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(47392,a,48091,a),flip(a)].">
      <j1 rule="hyper" parents="47392 48091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48093">
    <literal><![CDATA[
      a(x \ (y \ (z \ (y * x))),u,a(w,v5,v6)) = a(v6,v5,a(L(z,z,x),u,L(w,x * z,y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,46787,a(flip),b,48092,a),flip(a)].">
      <j1 rule="hyper" parents="373 46787 48092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48094">
    <literal><![CDATA[
      a(x \ (y \ (z \ (y * x))),u,a(w,v5,v6)) = a(v6,v5,a(z,u,L(L(w,x * z,y),z,x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,46787,a(flip),b,48093,a),flip(a)].">
      <j1 rule="hyper" parents="373 46787 48093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48095">
    <literal><![CDATA[
      L(x,y,a(z,u,(1 / ((u * z) / w)) * (u * z))) = L(x,y,(z * (u * w)) * ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(35256(a,1),46559(a,1,3,3))].">
      <j1 rule="para" parents="35256 46559"/>
    </justification>
  </clause>

  <clause id="48096">
    <literal><![CDATA[
      L(x,y,a(z,u,((w \ (u * z)) \ 1) * (u * z))) = L(x,y,(z * (u * w)) * ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(27671(a,1),48095(a,1,3))].">
      <j1 rule="para" parents="27671 48095"/>
    </justification>
  </clause>

  <clause id="48097">
    <literal><![CDATA[
      a((x * y) \ z,u,((1 / y) * (x \ y)) \ 1) = a((y * (x * y)) \ (z * y),u,x)
    ]]></literal>
    <justification jstring="[hyper(27584,a,46736,a),flip(a)].">
      <j1 rule="hyper" parents="27584 46736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48099">
    <literal><![CDATA[
      a((x * y) \ z,u,((1 / y) * (x \ y)) \ 1) = a(L(x,y,y) \ (z * y),u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,32693,a(flip),b,48097,a),flip(a)].">
      <j1 rule="hyper" parents="373 32693 48097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48100">
    <literal><![CDATA[
      a((x * y) \ z,u,((1 / y) * (x \ y)) \ 1) = a((z * y) * L(x,y,y),u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,46149,a(flip),b,48099,a),flip(a)].">
      <j1 rule="hyper" parents="373 46149 48099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48101">
    <literal><![CDATA[
      a((x * y) \ z,u,((1 / y) * (x \ y)) \ 1) = a(x * (y \ z),u,L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,47186,a(flip),b,48100,a),flip(a)].">
      <j1 rule="hyper" parents="373 47186 48100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48102">
    <literal><![CDATA[
      a((x * y) \ z,u,((y \ 1) * (x \ y)) \ 1) = a(x * (y \ z),u,L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,27519,a(flip),b,48101,a)].">
      <j1 rule="hyper" parents="64 27519 48101"/>
    </justification>
  </clause>

  <clause id="48103">
    <literal><![CDATA[
      a((x * y) \ z,u,((x \ y) \ 1) * y) = a(x * (y \ z),u,L(x,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46688,a(flip),b,48102,a)].">
      <j1 rule="hyper" parents="64 46688 48102"/>
    </justification>
  </clause>

  <clause id="48104">
    <literal><![CDATA[
      a(x * (y \ z),u,L(x,y,y)) = a(z * (x * y),u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,47007,a(flip),b,48103,a),flip(a)].">
      <j1 rule="hyper" parents="64 47007 48103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48105">
    <literal><![CDATA[
      a(x * (y \ z),u,L(y,y,x)) = a(z * (y * x),u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47656,a,b,48104,a)].">
      <j1 rule="hyper" parents="64 47656 48104"/>
    </justification>
  </clause>

  <clause id="48106">
    <literal><![CDATA[
      a((x \ y) * z,u,L(x,x,z)) = a(y * (x * z),u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,47655,a,b,48104,a)].">
      <j1 rule="hyper" parents="64 47655 48104"/>
    </justification>
  </clause>

  <clause id="48107">
    <literal><![CDATA[
      a((x \ y) * z,y,x) = a(y * (x * z),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,46843,a(flip),b,48106,a)].">
      <j1 rule="hyper" parents="64 46843 48106"/>
    </justification>
  </clause>

  <clause id="48108">
    <literal><![CDATA[
      a(x * (L(y,y,x) \ z),x,y) = a(x * (y * z),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47941,a,b,48107,a)].">
      <j1 rule="hyper" parents="64 47941 48107"/>
    </justification>
  </clause>

  <clause id="48109">
    <literal><![CDATA[
      a(x * ((x \ y) * z),y,x) = a(y * (x * (z \ x)),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,46860,a(flip),b,48107,a)].">
      <j1 rule="hyper" parents="64 46860 48107"/>
    </justification>
  </clause>

  <clause id="48110">
    <literal><![CDATA[
      a(x * (y * (z \ (u * u))),x,y) = a(z * (y \ x),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26875,a(flip),b,48107,a),flip(a)].">
      <j1 rule="hyper" parents="64 26875 48107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48111">
    <literal><![CDATA[
      a((x * y) * z,z,y) = a(x * (y \ z),z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32826,a(flip),b,48110,a)].">
      <j1 rule="hyper" parents="64 32826 48110"/>
    </justification>
  </clause>

  <clause id="48112">
    <literal><![CDATA[
      a(x * (y \ z),z,y) \ y = L(y,z,(x * y) * z)
    ]]></literal>
    <justification jstring="[para(48111(a,1),45065(a,2,1)),flip(a)].">
      <j1 rule="para" parents="48111 45065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48113">
    <literal><![CDATA[
      L(x,y,(z * x) * y) = L(x,y,z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(45147,a,48112,a),flip(a)].">
      <j1 rule="hyper" parents="45147 48112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48114">
    <literal><![CDATA[
      x \ ((((x * y) / z) * (z * y)) / y) = L(y,z,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42233,a,b,48113,a)].">
      <j1 rule="hyper" parents="64 42233 48113"/>
    </justification>
  </clause>

  <clause id="48115">
    <literal><![CDATA[
      a(x,y,a(z,z,L(L(u,w,v5),v5 * w,v5))) * L(w,v5,v5) = L(a(u,z,a(x,y,z)) * w,v5,v5)
    ]]></literal>
    <justification jstring="[para(46567(a,2),46809(a,1,1))].">
      <j1 rule="para" parents="46567 46809"/>
    </justification>
  </clause>

  <clause id="48116">
    <literal><![CDATA[
      a(x,y,a(y,z,L(L(u,w,v5),v5 * w,v5))) * L(w,v5,v5) = L(w * a(u,z,a(x,y,y)),v5,v5)
    ]]></literal>
    <justification jstring="[para(46567(a,2),46810(a,1,1))].">
      <j1 rule="para" parents="46567 46810"/>
    </justification>
  </clause>

  <clause id="48117">
    <literal><![CDATA[
      L(x * a(y,y,a(z,x,u)),y,a(y,z,u)) = L(x,a(u,y,y),a(w,v5,y) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,48078,a(flip),b,46949,a)].">
      <j1 rule="hyper" parents="64 48078 46949"/>
    </justification>
  </clause>

  <clause id="48119">
    <literal><![CDATA[
      L(x,a(y,z,z),a(u,w,z) * v5) = L(x,a(y,z,z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,47545,a(flip),b,48117,a),flip(a)].">
      <j1 rule="hyper" parents="64 47545 48117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48121">
    <literal><![CDATA[
      L(x,a(y,z,z),a(u,w,z) * v5) = x * a(x,a(y,z,z),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,42627,a,b,48119,a),flip(a)].">
      <j1 rule="hyper" parents="373 42627 48119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48122">
    <literal><![CDATA[
      a(x,a(y,y,z),u * a(y,y,z)) = a(u,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[hyper(35,a,43428,a,b,48121,a(flip))].">
      <j1 rule="hyper" parents="35 43428 48121"/>
    </justification>
  </clause>

  <clause id="48123">
    <literal><![CDATA[
      a(x,a(y,y,z),a(y,y,z) * u) = a(u,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[hyper(27453,a,48122,a)].">
      <j1 rule="hyper" parents="27453 48122"/>
    </justification>
  </clause>

  <clause id="48125">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(w,w,v5),v6 * a(w,w,v5)) = (a(x,y,z) \ u) * a(a(x,y,z) * u,a(v5,w,w),v6)
    ]]></literal>
    <justification jstring="[para(48123(a,1),42920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="48123 42920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48126">
    <literal><![CDATA[
      (x \ 1) * a(y,z,u * ((z \ 1) * u)) = x \ a(y,z,u * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(45013(a,1),46960(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45013 46960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48128">
    <literal><![CDATA[
      (x \ 1) * a(y,z,u * ((z \ 1) * u)) = x \ a(y,z,(z \ u) * u)
    ]]></literal>
    <justification jstring="[para(41349(a,1),48126(a,2,2))].">
      <j1 rule="para" parents="41349 48126"/>
    </justification>
  </clause>

  <clause id="48129">
    <literal><![CDATA[
      (x \ 1) * a(y,z,(z \ u) * u) = x \ a(y,z,(z \ u) * u)
    ]]></literal>
    <justification jstring="[para(41349(a,1),48128(a,1,2))].">
      <j1 rule="para" parents="41349 48128"/>
    </justification>
  </clause>

  <clause id="48130">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) \ a(x,y,(y \ 1) * a(z,y,u)) = y \ a(u,a(y \ 1,y,x),z)
    ]]></literal>
    <justification jstring="[para(11980(a,1),47019(a,1,2,3,2))].">
      <j1 rule="para" parents="11980 47019"/>
    </justification>
  </clause>

  <clause id="48131">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) \ a(x,y,y \ a(z,y,u)) = y \ a(u,a(y \ 1,y,x),z)
    ]]></literal>
    <justification jstring="[para(35739(a,1),48130(a,1,2,3))].">
      <j1 rule="para" parents="35739 48130"/>
    </justification>
  </clause>

  <clause id="48132">
    <literal><![CDATA[
      (x * y) \ R(x,y,y \ a(z,y,u)) = y \ a(u,a(y \ 1,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,45443,a(flip),b,48131,a)].">
      <j1 rule="hyper" parents="64 45443 48131"/>
    </justification>
  </clause>

  <clause id="48133">
    <literal><![CDATA[
      (x * y) \ R(x,y,y \ a(z,y,u)) = y \ a(u,a(y,y,x),z)
    ]]></literal>
    <justification jstring="[para(2653(a,1),48132(a,2,2,2))].">
      <j1 rule="para" parents="2653 48132"/>
    </justification>
  </clause>

  <clause id="48134">
    <literal><![CDATA[
      a(x \ (((y * y) \ z) * y),u,L(y,y,x)) = a((x \ R(T(z,y * y),y,y)) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32360,a(flip),b,47023,a)].">
      <j1 rule="hyper" parents="64 32360 47023"/>
    </justification>
  </clause>

  <clause id="48136">
    <literal><![CDATA[
      a(x \ (y * z),u,L(z,z,x)) = a((x \ R(T(y,z * z),z,z)) * z,u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26903,a(flip),b,48134,a)].">
      <j1 rule="hyper" parents="64 26903 48134"/>
    </justification>
  </clause>

  <clause id="48137">
    <literal><![CDATA[
      a(x \ (y * z),u,L(z,z,x)) = a((x \ L(T(y,z * z),z,z)) * z,u,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,34949,a(flip),b,48136,a),flip(a)].">
      <j1 rule="hyper" parents="373 34949 48136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48139">
    <literal><![CDATA[
      a(x \ (y * z),u,L(z,z,x)) = a(z * (x \ L(y,z,z)),u,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32530,a(flip),b,48137,a),flip(a)].">
      <j1 rule="hyper" parents="373 32530 48137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48141">
    <literal><![CDATA[
      a(x,x,a(y,z * u,w * a(v5,v6,v6))) \ 1 = y \ L(y,x,a(x,u * z,w * a(v6,v6,v5)))
    ]]></literal>
    <justification jstring="[para(47254(a,1),47165(a,1,1))].">
      <j1 rule="para" parents="47254 47165"/>
    </justification>
  </clause>

  <clause id="48142">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),w,a(w \ (y \ w),u,z)) = L(x,a(w \ (y \ w),u,z),w)
    ]]></literal>
    <justification jstring="[para(47207(a,1),47547(a,1,1,2))].">
      <j1 rule="para" parents="47207 47547"/>
    </justification>
  </clause>

  <clause id="48143">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),u,a(z,w,y)) = L(x,a(w \ (y \ w),u,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,47519,a(flip),b,48142,a)].">
      <j1 rule="hyper" parents="64 47519 48142"/>
    </justification>
  </clause>

  <clause id="48144">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,w)),u,a(z,w,y)) = L(x,a((y \ w) * w,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,47726,a(flip),b,48143,a),flip(a)].">
      <j1 rule="hyper" parents="373 47726 48143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48145">
    <literal><![CDATA[
      L(x,a((y \ z) * z,u,w),z) = L(x,a(y,u,w),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47554,a(flip),b,48144,a),flip(a)].">
      <j1 rule="hyper" parents="64 47554 48144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48146">
    <literal><![CDATA[
      L(x,a(y,z,u * (w \ u)),u) = L(x,a(w,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,41408,a(flip),b,48145,a)].">
      <j1 rule="hyper" parents="64 41408 48145"/>
    </justification>
  </clause>

  <clause id="48147">
    <literal><![CDATA[
      L(R(x,y,z \ ((u \ 1) \ z)),y,a(u,w,L(v5,u,z))) = R(x,y,L((z \ (u \ z)) \ 1,w,v5))
    ]]></literal>
    <justification jstring="[para(38893(a,1),47706(a,1,1))].">
      <j1 rule="para" parents="38893 47706"/>
    </justification>
  </clause>

  <clause id="48148">
    <literal><![CDATA[
      L(x,a(y,R(z,u,w),R(z,u,w)),u * w) = L(x,a(z,z,y),(z * u) * w)
    ]]></literal>
    <justification jstring="[para(35156(a,1),47748(a,1,2)),flip(a)].">
      <j1 rule="para" parents="35156 47748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48149">
    <literal><![CDATA[
      L(x,a(y,R(z,u,w),L(z,u,w)),u * w) = L(x,a(z,z,y),(z * u) * w)
    ]]></literal>
    <justification jstring="[para(27644(a,1),48148(a,1,2))].">
      <j1 rule="para" parents="27644 48148"/>
    </justification>
  </clause>

  <clause id="48151">
    <literal><![CDATA[
      L(x,a(y,L(z,u,w),L(z,u,w)),u * w) = L(x,a(z,z,y),(z * u) * w)
    ]]></literal>
    <justification jstring="[para(32197(a,1),48149(a,1,2))].">
      <j1 rule="para" parents="32197 48149"/>
    </justification>
  </clause>

  <clause id="48152">
    <literal><![CDATA[
      L(x,a(y,y,z),(y * u) * w) = L(x,a(z,y,y),u * w)
    ]]></literal>
    <justification jstring="[para(40664(a,1),48151(a,1,2)),flip(a)].">
      <j1 rule="para" parents="40664 48151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48153">
    <literal><![CDATA[
      L(x,a(y,z,z),(z * u) * w) = L(x,a(y,z,z),u * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,41403,a,b,48152,a)].">
      <j1 rule="hyper" parents="64 41403 48152"/>
    </justification>
  </clause>

  <clause id="48155">
    <literal><![CDATA[
      L(x,a(y,a(z,u,w) \ u,a(z,u,w) \ u),(u * L(w,u,z)) * v5) = L(x,a(y,a(z,u,w) \ u,a(z,u,w) \ u),w * v5)
    ]]></literal>
    <justification jstring="[para(42071(a,1),48153(a,1,3,1))].">
      <j1 rule="para" parents="42071 48153"/>
    </justification>
  </clause>

  <clause id="48156">
    <literal><![CDATA[
      a(x,y,a(z,z,L(L(u,w,v5),w,v5))) * L(w,v5,v5) = L(a(u,z,a(x,y,z)) * w,v5,v5)
    ]]></literal>
    <justification jstring="[para(46930(a,1),48115(a,1,1,3))].">
      <j1 rule="para" parents="46930 48115"/>
    </justification>
  </clause>

  <clause id="48157">
    <literal><![CDATA[
      L(a(x,y,a(z,u,y)) * w,v5,v5) = a(z,u,a(y,y,x)) * L(w,v5,v5)
    ]]></literal>
    <justification jstring="[para(39064(a,1),48156(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="39064 48156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48158">
    <literal><![CDATA[
      L(a(x,y,a(z,u,y)) * w,v5,v5) = L(w,v5,v5) * a(x,u,a(z,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,47311,a(flip),b,48157,a),flip(a)].">
      <j1 rule="hyper" parents="373 47311 48157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48160">
    <literal><![CDATA[
      L(x,y,y) \ (a(z,u,a(w,w,v5)) \ L(L(a(v5,w,a(z,u,w)) * x,y,y),v6,v6)) = a(v6,v6,a(z,u,a(w,w,v5)) * L(x,y,y)) \ 1
    ]]></literal>
    <justification jstring="[para(48157(a,2),45839(a,1,2,2,1))].">
      <j1 rule="para" parents="48157 45839"/>
    </justification>
  </clause>

  <clause id="48161">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,L(v5,y,z))) * L(y,z,z) = L(y * a(x,u,a(w,v5,v5)),z,z)
    ]]></literal>
    <justification jstring="[para(46928(a,1),48116(a,1,1))].">
      <j1 rule="para" parents="46928 48116"/>
    </justification>
  </clause>

  <clause id="48162">
    <literal><![CDATA[
      a(x,y,L(a(z,u,L(u,w,v5)),w,v5)) * L(w,v5,v5) = L(w * a(x,y,a(z,u,u)),v5,v5)
    ]]></literal>
    <justification jstring="[para(46496(a,1),48161(a,1,1))].">
      <j1 rule="para" parents="46496 48161"/>
    </justification>
  </clause>

  <clause id="48163">
    <literal><![CDATA[
      L(x * a(y,z,a(u,w,w)),v5,v5) = a(y,z,a(u,w,w)) * L(x,v5,v5)
    ]]></literal>
    <justification jstring="[para(46532(a,1),48162(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="46532 48162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48165">
    <literal><![CDATA[
      x \ L(x,y,a(y,x * z,u * a(w,w,v5))) = a(x,y,a(u * a(v5,w,w),z,y)) \ 1
    ]]></literal>
    <justification jstring="[para(46888(a,1),48141(a,1,1)),flip(a)].">
      <j1 rule="para" parents="46888 48141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48166">
    <literal><![CDATA[
      x \ L(x,y,a(y,x * z,u * a(w,w,v5))) = a(x,y,a(y,z,u * a(v5,w,w)))
    ]]></literal>
    <justification jstring="[hyper(141,a,42644,a(flip),b,48165,a),flip(a)].">
      <j1 rule="hyper" parents="141 42644 48165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48167">
    <literal><![CDATA[
      R(x,y \ (z \ y),L((y \ (z \ y)) \ 1,u,w)) = L(R(x,z,z),y \ (z \ y),a(z,u,L(w,z,y)))
    ]]></literal>
    <justification jstring="[para(40658(a,1),48147(a,1,1)),flip(a)].">
      <j1 rule="para" parents="40658 48147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48168">
    <literal><![CDATA[
      R(x,y * (x / (x \ y)),x) * (T(y \ (x / (x \ y)),x) * z) = ((y \ x) * ((x \ y) \ x)) * z
    ]]></literal>
    <justification jstring="[para(13733(a,1),45090(a,1,1))].">
      <j1 rule="para" parents="13733 45090"/>
    </justification>
  </clause>

  <clause id="48169">
    <literal><![CDATA[
      ((x / (y * T(z,u))) * T((y * z) / y,u)) \ x = L(y,T(z,u),(y * T(z,u)) * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,11871,a(flip),b,46298,a),flip(a)].">
      <j1 rule="hyper" parents="64 11871 46298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48171">
    <literal><![CDATA[
      ((x / (y * T(z,u))) * T((y * z) / y,u)) \ x = L(y,T(z,u),x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,29148,a(flip),b,48169,a),flip(a)].">
      <j1 rule="hyper" parents="373 29148 48169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48173">
    <literal><![CDATA[
      ((x / (y * T(z,u))) * T((y * z) / y,u)) \ x = L(y,z,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,29434,a(flip),b,48171,a),flip(a)].">
      <j1 rule="hyper" parents="373 29434 48171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48175">
    <literal><![CDATA[
      L(x,y,z * (x * y)) = ((z / (y * x)) * y) \ z
    ]]></literal>
    <justification jstring="[para(25500(a,1),48173(a,1,1)),flip(a)].">
      <j1 rule="para" parents="25500 48173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48176">
    <literal><![CDATA[
      a(x,y,L(z,x,(x \ u) * (z * x))) = a(x,y,((u / (x * z)) * x) \ u)
    ]]></literal>
    <justification jstring="[para(48175(a,1),47063(a,2,3))].">
      <j1 rule="para" parents="48175 47063"/>
    </justification>
  </clause>

  <clause id="48177">
    <literal><![CDATA[
      a(x,y,L(z,x,z * u)) = a(x,y,((u / (x * z)) * x) \ u)
    ]]></literal>
    <justification jstring="[para(47901(a,1),48176(a,1,3))].">
      <j1 rule="para" parents="47901 48176"/>
    </justification>
  </clause>

  <clause id="48178">
    <literal><![CDATA[
      a(x,y,L(z,x,z * u)) = a(x,y,(u / (x * z)) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,46222,a(flip),b,48177,a),flip(a)].">
      <j1 rule="hyper" parents="373 46222 48177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48179">
    <literal><![CDATA[
      a(x,y,L(z,x,z * u)) = a(x,y,((x * z) \ u) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27389,a(flip),b,48178,a),flip(a)].">
      <j1 rule="hyper" parents="373 27389 48178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48180">
    <literal><![CDATA[
      a(x,y,L(z,x,z * u)) = a(x,y,x \ ((z \ (x \ u)) \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,43199,a(flip),b,48179,a),flip(a)].">
      <j1 rule="hyper" parents="373 43199 48179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48181">
    <literal><![CDATA[
      a(x,y,L(z,x,u * z)) = a(x,y,x \ ((z \ (x \ u)) \ u))
    ]]></literal>
    <justification jstring="[para(23253(a,1),48180(a,1,3))].">
      <j1 rule="para" parents="23253 48180"/>
    </justification>
  </clause>

  <clause id="48182">
    <literal><![CDATA[
      a(x,y,x \ ((z \ (x \ u)) \ u)) \ z = L(z,y,L(x,x,z * u))
    ]]></literal>
    <justification jstring="[para(48180(a,1),46623(a,1,1))].">
      <j1 rule="para" parents="48180 46623"/>
    </justification>
  </clause>

  <clause id="48183">
    <literal><![CDATA[
      a(x,y,x \ ((z \ (x \ u)) \ u)) = L(x,y,L(z,x,u * z)) \ L(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47954,a,b,48181,a),flip(a)].">
      <j1 rule="hyper" parents="64 47954 48181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48184">
    <literal><![CDATA[
      a(x,y,x \ ((z \ (x \ y)) \ y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46644,a(flip),b,48181,a),flip(a)].">
      <j1 rule="hyper" parents="64 46644 48181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48185">
    <literal><![CDATA[
      a(x,y,z \ (x \ y)) = a(x,y,x \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,27510,a(flip),b,48184,a),flip(a)].">
      <j1 rule="hyper" parents="64 27510 48184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48186">
    <literal><![CDATA[
      a(x,y,x \ ((z \ (x \ u)) \ u)) = L(x,y,L(z,x,u)) \ L(R(x,y,z),y,z)
    ]]></literal>
    <justification jstring="[para(48002(a,1),48183(a,2,1))].">
      <j1 rule="para" parents="48002 48183"/>
    </justification>
  </clause>

  <clause id="48187">
    <literal><![CDATA[
      a(x,y,x \ ((z \ (x \ u)) \ u)) = a(x,y,L(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,47954,a(flip),b,48186,a),flip(a)].">
      <j1 rule="hyper" parents="373 47954 48186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48188">
    <literal><![CDATA[
      L(x,y,L(z,z,x * u)) = a(z,y,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(48187(a,1),48182(a,1,1)),flip(a)].">
      <j1 rule="para" parents="48187 48182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48189">
    <literal><![CDATA[
      L(x,y,L(z,z,x * u)) = L(x,y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,46623,a(flip),b,48188,a),flip(a)].">
      <j1 rule="hyper" parents="373 46623 48188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48190">
    <literal><![CDATA[
      L(x,y,a((x * a(z,y,x)) * u,z,z)) = L(x * a(z,y,x),y,L(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47498,a(flip),b,48189,a)].">
      <j1 rule="hyper" parents="64 47498 48189"/>
    </justification>
  </clause>

  <clause id="48192">
    <literal><![CDATA[
      L(x * a(y,z,x),z,L(y,y,u)) = L(x,z,a(L(x,z,y) * u,y,y))
    ]]></literal>
    <justification jstring="[para(45113(a,1),48190(a,1,3)),flip(a)].">
      <j1 rule="para" parents="45113 48190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48193">
    <literal><![CDATA[
      L(x * a(y,z,x),z,L(y,y,u)) = L(x,z,a(x * u,y,y))
    ]]></literal>
    <justification jstring="[para(45946(a,1),48192(a,2,3))].">
      <j1 rule="para" parents="45946 48192"/>
    </justification>
  </clause>

  <clause id="48194">
    <literal><![CDATA[
      L(x,y,a(x * z,u,u)) = L(x,y,a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47498,a(flip),b,48193,a),flip(a)].">
      <j1 rule="hyper" parents="64 47498 48193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48196">
    <literal><![CDATA[
      L(x,y,a(z,z,x * u)) = L(x,y,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(42222,a,48194,a)].">
      <j1 rule="hyper" parents="42222 48194"/>
    </justification>
  </clause>

  <clause id="48197">
    <literal><![CDATA[
      a(x * (L(y,y,x) \ z),x,L(y,y,x)) \ z = ((z / L(y,y,x)) / R(x,y,y)) * (x * y)
    ]]></literal>
    <justification jstring="[para(45025(a,1),46351(a,2,1))].">
      <j1 rule="para" parents="45025 46351"/>
    </justification>
  </clause>

  <clause id="48198">
    <literal><![CDATA[
      a(x * (L(y,y,x) \ z),x,L(y,y,x)) \ z = ((z / y) / x) * (x * y)
    ]]></literal>
    <justification jstring="[para(45006(a,1),48197(a,2,1))].">
      <j1 rule="para" parents="45006 48197"/>
    </justification>
  </clause>

  <clause id="48199">
    <literal><![CDATA[
      a(x * (L(y,y,x) \ z),x,y) \ z = ((z / y) / x) * (x * y)
    ]]></literal>
    <justification jstring="[para(45281(a,1),48198(a,1,1))].">
      <j1 rule="para" parents="45281 48198"/>
    </justification>
  </clause>

  <clause id="48200">
    <literal><![CDATA[
      a(x * (y * z),x,y) \ z = ((z / y) / x) * (x * y)
    ]]></literal>
    <justification jstring="[para(48108(a,1),48199(a,1,1))].">
      <j1 rule="para" parents="48108 48199"/>
    </justification>
  </clause>

  <clause id="48201">
    <literal><![CDATA[
      a(x * (y * z),x,z) \ y = ((y / z) / x) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32427,a,b,48200,a)].">
      <j1 rule="hyper" parents="64 32427 48200"/>
    </justification>
  </clause>

  <clause id="48202">
    <literal><![CDATA[
      (((x * y) / z) * (z * y)) / y = (((x / y) / z) * (z * y)) * y
    ]]></literal>
    <justification jstring="[para(48201(a,1),42023(a,1,1)),flip(a)].">
      <j1 rule="para" parents="48201 42023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48203">
    <literal><![CDATA[
      x \ ((((x / y) / z) * (z * y)) * y) = L(y,z,x * (y \ z))
    ]]></literal>
    <justification jstring="[para(48202(a,1),48114(a,1,2))].">
      <j1 rule="para" parents="48202 48114"/>
    </justification>
  </clause>

  <clause id="48204">
    <literal><![CDATA[
      L(x,y,z * (x \ y)) = L(x,y,z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46014,a(flip),b,48203,a),flip(a)].">
      <j1 rule="hyper" parents="64 46014 48203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48205">
    <literal><![CDATA[
      L(x,y,(z * x) * y) = L(x,y,z * (y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,48113,a,b,48204,a)].">
      <j1 rule="hyper" parents="64 48113 48204"/>
    </justification>
  </clause>

  <clause id="48206">
    <literal><![CDATA[
      a((a(x,y,y) \ z) * u,w,w) = a(z * (a(y,y,x) * u),w,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,45750,a(flip),b,46756,a)].">
      <j1 rule="hyper" parents="64 45750 46756"/>
    </justification>
  </clause>

  <clause id="48208">
    <literal><![CDATA[
      a((a(x,y,y) * z) * u,w,w) = a(z * (a(y,y,x) * u),w,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42462,a(flip),b,48206,a)].">
      <j1 rule="hyper" parents="64 42462 48206"/>
    </justification>
  </clause>

  <clause id="48209">
    <literal><![CDATA[
      a((a(x,x,y) * z) * u,w,w) = a(z * (a(x,x,y) * u),w,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,37910,a(flip),b,48206,a)].">
      <j1 rule="hyper" parents="64 37910 48206"/>
    </justification>
  </clause>

  <clause id="48210">
    <literal><![CDATA[
      a((x * a(y,z,z)) * u,w,w) = a(x * (a(z,z,y) * u),w,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,37830,a(flip),b,48206,a)].">
      <j1 rule="hyper" parents="64 37830 48206"/>
    </justification>
  </clause>

  <clause id="48211">
    <literal><![CDATA[
      a((x * a(y,y,z)) * u,w,w) = a(x * (a(y,y,z) * u),w,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,47143,a(flip),b,48208,a)].">
      <j1 rule="hyper" parents="64 47143 48208"/>
    </justification>
  </clause>

  <clause id="48212">
    <literal><![CDATA[
      a((x * L(y,z,z)) * (a(z,z,y) * u),w,w) = a((x * y) * u,w,w)
    ]]></literal>
    <justification jstring="[para(44977(a,1),48209(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="44977 48209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48213">
    <literal><![CDATA[
      (a(x,x,y) \ (1 / (y / z))) * (x \ ((1 / x) \ y)) = (1 / ((x \ (x \ y)) / z)) * (x \ (x \ y))
    ]]></literal>
    <justification jstring="[para(44119(a,1),46939(a,1,1))].">
      <j1 rule="para" parents="44119 46939"/>
    </justification>
  </clause>

  <clause id="48214">
    <literal><![CDATA[
      a((x * y) * y,z,(x * y) * u) = a(x,z,L(((x * y) \ 1) \ u,x,y))
    ]]></literal>
    <justification jstring="[hyper(2692,a,47651,a)].">
      <j1 rule="hyper" parents="2692 47651"/>
    </justification>
  </clause>

  <clause id="48216">
    <literal><![CDATA[
      a(x,y,L(((x * z) \ 1) \ u,x,z)) = a(x,y,L((x * z) * u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46579,a(flip),b,48214,a),flip(a)].">
      <j1 rule="hyper" parents="64 46579 48214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48217">
    <literal><![CDATA[
      a(x \ (y / z),u,L((((x \ (y / z)) * x) \ 1) \ z,x \ (y / z),x)) = a(x \ (y / z),u,L(z * ((x \ (z \ y)) * x),x,x))
    ]]></literal>
    <justification jstring="[para(5478(a,1),48216(a,2,3,1))].">
      <j1 rule="para" parents="5478 48216"/>
    </justification>
  </clause>

  <clause id="48218">
    <literal><![CDATA[
      a(x,y,(z \ (u / (u / (w \ v5)))) * a(w,w,v5)) = a(x,y,z \ (u / (u / ((1 / w) * v5))))
    ]]></literal>
    <justification jstring="[hyper(64,a,30186,a(flip),b,47881,a)].">
      <j1 rule="hyper" parents="64 30186 47881"/>
    </justification>
  </clause>

  <clause id="48219">
    <literal><![CDATA[
      a(x,y,(z \ ((u / (w \ v5)) \ u)) * a(w,w,v5)) = a(x,y,z \ (u / (u / ((1 / w) * v5))))
    ]]></literal>
    <justification jstring="[hyper(64,a,27470,a(flip),b,48218,a)].">
      <j1 rule="hyper" parents="64 27470 48218"/>
    </justification>
  </clause>

  <clause id="48220">
    <literal><![CDATA[
      a(x,y,z \ (u / (u / ((1 / w) * v5)))) = a(x,y,(z \ (w \ v5)) * a(w,w,v5))
    ]]></literal>
    <justification jstring="[para(82(a,1),48219(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="82 48219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48222">
    <literal><![CDATA[
      a(x,y,(z \ (u \ w)) * a(u,u,w)) = a(x,y,z \ ((1 / u) * w))
    ]]></literal>
    <justification jstring="[para(2085(a,1),48220(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2085 48220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48223">
    <literal><![CDATA[
      a(x,y,(z \ (u \ w)) * a(u,u,w)) = a(x,y,z \ ((u \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27492,a(flip),b,48222,a),flip(a)].">
      <j1 rule="hyper" parents="373 27492 48222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48224">
    <literal><![CDATA[
      R(x,y * ((x \ y) \ x),x) * (T(y \ (x / (x \ y)),x) * z) = ((y \ x) * ((x \ y) \ x)) * z
    ]]></literal>
    <justification jstring="[para(26500(a,1),48168(a,1,1))].">
      <j1 rule="para" parents="26500 48168"/>
    </justification>
  </clause>

  <clause id="48225">
    <literal><![CDATA[
      (1 / ((x \ (x \ y)) / z)) * (x \ (x \ y)) = (1 / (y / z)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,44985,a(flip),b,48213,a),flip(a)].">
      <j1 rule="hyper" parents="64 44985 48213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48227">
    <literal><![CDATA[
      (1 / (T(x * y,z) / u)) * T(x * y,z) = (1 / ((x \ y) / u)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,44617,a(flip),b,48225,a),flip(a)].">
      <j1 rule="hyper" parents="64 44617 48225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48229">
    <literal><![CDATA[
      (1 / ((x \ y) / z)) * (x \ y) = (1 / ((x * y) / z)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,24964,a(flip),b,48227,a),flip(a)].">
      <j1 rule="hyper" parents="64 24964 48227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48230">
    <literal><![CDATA[
      R(x,y * ((x \ y) * x),x) * (T(y \ (x / (x \ y)),x) * z) = ((y \ x) * ((x \ y) \ x)) * z
    ]]></literal>
    <justification jstring="[para(28876(a,1),48224(a,1,1))].">
      <j1 rule="para" parents="28876 48224"/>
    </justification>
  </clause>

  <clause id="48231">
    <literal><![CDATA[
      R(x,y * y,x) * (T(y \ (x / (x \ y)),x) * z) = ((y \ x) * ((x \ y) \ x)) * z
    ]]></literal>
    <justification jstring="[para(26503(a,1),48230(a,1,1))].">
      <j1 rule="para" parents="26503 48230"/>
    </justification>
  </clause>

  <clause id="48232">
    <literal><![CDATA[
      x * (T(y \ (x / (x \ y)),x) * z) = ((y \ x) * ((x \ y) \ x)) * z
    ]]></literal>
    <justification jstring="[para(654(a,1),48231(a,1,1))].">
      <j1 rule="para" parents="654 48231"/>
    </justification>
  </clause>

  <clause id="48234">
    <literal><![CDATA[
      ((x \ y) * ((y \ x) \ y)) * z = (x \ y) * ((y \ x) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,40574,a(flip),b,48232,a),flip(a)].">
      <j1 rule="hyper" parents="64 40574 48232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48235">
    <literal><![CDATA[
      a((x \ y) * ((y \ x) \ (y * z)),u,w) = a(z * ((y * (x \ y)) * (x \ y)),u,w)
    ]]></literal>
    <justification jstring="[para(48234(a,1),40558(a,1,1))].">
      <j1 rule="para" parents="48234 40558"/>
    </justification>
  </clause>

  <clause id="48236">
    <literal><![CDATA[
      a(x * ((y * (z \ y)) * (z \ y)),u,w) = a((y * x) * a(y,y * z,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,40189,a(flip),b,48235,a),flip(a)].">
      <j1 rule="hyper" parents="64 40189 48235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48237">
    <literal><![CDATA[
      a(x * ((y * (z \ y)) * (z \ y)),u,w) = a(y * (x * a(y,y * z,z)),u,w)
    ]]></literal>
    <justification jstring="[para(29910(a,1),48236(a,2,1))].">
      <j1 rule="para" parents="29910 48236"/>
    </justification>
  </clause>

  <clause id="48238">
    <literal><![CDATA[
      a(x * (y * (z \ (y / (y \ z)))),u,w) = a(y * (x * a(y,y * z,z)),u,w)
    ]]></literal>
    <justification jstring="[para(40555(a,1),48237(a,1,1,2))].">
      <j1 rule="para" parents="40555 48237"/>
    </justification>
  </clause>

  <clause id="48239">
    <literal><![CDATA[
      a(x * (y * (z \ ((y \ z) \ y))),u,w) = a(y * (x * a(y,y * z,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32653,a(flip),b,48238,a)].">
      <j1 rule="hyper" parents="64 32653 48238"/>
    </justification>
  </clause>

  <clause id="48240">
    <literal><![CDATA[
      a(x * (y * a(x,x * z,z)),u,w) = a(((x \ z) * z) * y,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,40211,a(flip),b,48239,a),flip(a)].">
      <j1 rule="hyper" parents="64 40211 48239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48241">
    <literal><![CDATA[
      a(((x \ y) * y) * z,x,y) = a(z * L(x,y,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47921,a(flip),b,48240,a),flip(a)].">
      <j1 rule="hyper" parents="64 47921 48240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48242">
    <literal><![CDATA[
      L(x,(R(y,z,u \ (w * w)) \ y) * v5,v6) = L(x,(u * L(((w * w) \ u) \ 1,z,y)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(550(a,1),46281(a,1,2,1,1,3))].">
      <j1 rule="para" parents="550 46281"/>
    </justification>
  </clause>

  <clause id="48243">
    <literal><![CDATA[
      L(x,(y * L(((z * z) \ y) \ 1,u,w)) * v5,v6) = L(x,a(w,u,y \ (z * z)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(45187(a,1),48242(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45187 48242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48244">
    <literal><![CDATA[
      L(x,(y * L(((z * z) \ y) \ 1,u,w)) * v5,v6) = L(x,v5 * a(w,u,y \ (z * z)),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,42472,a(flip),b,48243,a),flip(a)].">
      <j1 rule="hyper" parents="373 42472 48243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48245">
    <literal><![CDATA[
      L(x,(y * L(y \ (z * z),u,w)) * v5,v6) = L(x,v5 * a(w,u,y \ (z * z)),v6)
    ]]></literal>
    <justification jstring="[para(550(a,1),48244(a,1,2,1,2,1))].">
      <j1 rule="para" parents="550 48244"/>
    </justification>
  </clause>

  <clause id="48246">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x * a(z,z,a(u,w,v5)),y \ 1) = ((y \ x) / x) * (x * a(u,w,a(z,z,v5)))
    ]]></literal>
    <justification jstring="[para(28750(a,2),46374(a,1,2))].">
      <j1 rule="para" parents="28750 46374"/>
    </justification>
  </clause>

  <clause id="48247">
    <literal><![CDATA[
      L(R(x,a(y,z,u) \ z,a(y,z,u) \ z),a(u,z,y),z) = R(x,z * a(y,z,u),z)
    ]]></literal>
    <justification jstring="[para(23105(a,1),46442(a,2,1))].">
      <j1 rule="para" parents="23105 46442"/>
    </justification>
  </clause>

  <clause id="48248">
    <literal><![CDATA[
      L(R(x,a(y,z,u) \ z,a(y,z,u) * z),a(u,z,y),z) = R(x,z * a(y,z,u),z)
    ]]></literal>
    <justification jstring="[para(42481(a,1),48247(a,1,1))].">
      <j1 rule="para" parents="42481 48247"/>
    </justification>
  </clause>

  <clause id="48249">
    <literal><![CDATA[
      L(R(x,a(y,z,u) \ z,z * a(u,z,y)),a(u,z,y),z) = R(x,z * a(y,z,u),z)
    ]]></literal>
    <justification jstring="[para(43242(a,1),48248(a,1,1))].">
      <j1 rule="para" parents="43242 48248"/>
    </justification>
  </clause>

  <clause id="48250">
    <literal><![CDATA[
      L(R(x,a(y,z,u) * z,z * a(u,z,y)),a(u,z,y),z) = R(x,z * a(y,z,u),z)
    ]]></literal>
    <justification jstring="[para(35817(a,1),48249(a,1,1))].">
      <j1 rule="para" parents="35817 48249"/>
    </justification>
  </clause>

  <clause id="48251">
    <literal><![CDATA[
      L(R(x,y * a(z,y,u),y * a(z,y,u)),a(z,y,u),y) = R(x,y * a(u,y,z),y)
    ]]></literal>
    <justification jstring="[para(42241(a,1),48250(a,1,1))].">
      <j1 rule="para" parents="42241 48250"/>
    </justification>
  </clause>

  <clause id="48252">
    <literal><![CDATA[
      L(R(x,y,y),a(z,y,u),y) = R(x,y * a(u,y,z),y)
    ]]></literal>
    <justification jstring="[para(44858(a,1),48251(a,1,1))].">
      <j1 rule="para" parents="44858 48251"/>
    </justification>
  </clause>

  <clause id="48254">
    <literal><![CDATA[
      a(x * a(y,x,z),u,(y * R(z,w,z)) \ v5) = a(x,u,L(T(R(z,w,z) \ (y \ v5),v6),y,z))
    ]]></literal>
    <justification jstring="[hyper(27584,a,46754,a)].">
      <j1 rule="hyper" parents="27584 46754"/>
    </justification>
  </clause>

  <clause id="48256">
    <literal><![CDATA[
      a(x * a(y,x,z),u,(z * y) \ w) = a(x,u,L(T(R(z,v5,z) \ (y \ w),v6),y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27550,a(flip),b,48254,a)].">
      <j1 rule="hyper" parents="64 27550 48254"/>
    </justification>
  </clause>

  <clause id="48257">
    <literal><![CDATA[
      a(x * a(y,x,z),u,(z * y) \ w) = a(x,u,L(R(z,v5,z) \ (y \ w),y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27328,a(flip),b,48256,a),flip(a)].">
      <j1 rule="hyper" parents="373 27328 48256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48259">
    <literal><![CDATA[
      a(x * a(y,x,z),u,(z * y) \ w) = a(x,u,L(z \ (y \ w),y,z))
    ]]></literal>
    <justification jstring="[para(654(a,1),48257(a,2,3,1,1))].">
      <j1 rule="para" parents="654 48257"/>
    </justification>
  </clause>

  <clause id="48260">
    <literal><![CDATA[
      a(x,y,L(z \ (u \ w),u,z)) = a(x,y,L(u \ (z \ w),z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46742,a(flip),b,48259,a)].">
      <j1 rule="hyper" parents="64 46742 48259"/>
    </justification>
  </clause>

  <clause id="48261">
    <literal><![CDATA[
      a(((x * L(y,z,u)) * w) * (x * w),v5,x * w) = a((x * w) \ ((x * y) * w),v5,L(w * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46496,a(flip),b,46788,a),flip(a)].">
      <j1 rule="hyper" parents="64 46496 46788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48262">
    <literal><![CDATA[
      a(x * ((y \ z) \ (T(y \ z,y) \ z)),u,(y \ z) \ z) = a(y * ((y \ z) * x),u,(y \ z) \ z)
    ]]></literal>
    <justification jstring="[para(2415(a,1),46863(a,1,1,2))].">
      <j1 rule="para" parents="2415 46863"/>
    </justification>
  </clause>

  <clause id="48263">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,v5) * (a(v5,w,u) \ v6))) = a(x,y,z \ (v6 * (u \ L(R(u,w,v5),w,v5))))
    ]]></literal>
    <justification jstring="[hyper(64,a,27335,a(flip),b,47040,a)].">
      <j1 rule="hyper" parents="64 27335 47040"/>
    </justification>
  </clause>

  <clause id="48264">
    <literal><![CDATA[
      (x \ R(x,y,z)) * (u * a(y,y,a(z,x,x))) = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,42718,a(flip),b,47473,a),flip(a)].">
      <j1 rule="hyper" parents="64 42718 47473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48266">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ v5) = L(x,y,a(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[para(48264(a,1),42983(a,1,3)),flip(a)].">
      <j1 rule="para" parents="48264 42983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48270">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * v5) = L(x,y,v5 * a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42468,a(flip),b,48266,a),flip(a)].">
      <j1 rule="hyper" parents="64 42468 48266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48272">
    <literal><![CDATA[
      L(x,y,a(z,u,w) \ (v5 * L(v6,v5,a(z,u,w)))) = L(x,y,(a(w,u,z) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(42220(a,1),48266(a,2,3))].">
      <j1 rule="para" parents="42220 48266"/>
    </justification>
  </clause>

  <clause id="48275">
    <literal><![CDATA[
      L(x,y,a(z,u,w) * a(w,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(622,a,48270,a),flip(a)].">
      <j1 rule="hyper" parents="622 48270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48276">
    <literal><![CDATA[
      L(x,a(y,z,z),u * a(z,w,v5)) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,48119,a(flip),b,48270,a),flip(a)].">
      <j1 rule="hyper" parents="64 48119 48270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48279">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,v5) * a(v5,w,u))) \ (a(u,w,v5) * (a(v5,w,u) * v6))) = a(x,y,z \ v6)
    ]]></literal>
    <justification jstring="[para(48275(a,1),42752(a,1,3)),flip(a)].">
      <j1 rule="para" parents="48275 42752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48280">
    <literal><![CDATA[
      L(x,a(y,y,z),u * a(y,w,v5)) = L(x,a(z,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,41403,a,b,48276,a)].">
      <j1 rule="hyper" parents="64 41403 48276"/>
    </justification>
  </clause>

  <clause id="48281">
    <literal><![CDATA[
      L(x,y,(a(z,u,w) \ v5) * v6) = L(x,y,(a(w,u,z) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(42815(a,1),48272(a,1,3))].">
      <j1 rule="para" parents="42815 48272"/>
    </justification>
  </clause>

  <clause id="48283">
    <literal><![CDATA[
      a(x,y,a(z,u,x * (y \ (w * T(y * x,v5))))) = a(x,y,a(z,u,(w * (x * y)) * (y * x)))
    ]]></literal>
    <justification jstring="[para(27309(a,1),47580(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27309 47580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48285">
    <literal><![CDATA[
      a(x,y,a(z,u,x * (y \ (w * T(y * x,v5))))) = a(x,y,a(z,u,(x * y) * ((x * y) * w)))
    ]]></literal>
    <justification jstring="[para(27567(a,1),48283(a,2,3))].">
      <j1 rule="para" parents="27567 48283"/>
    </justification>
  </clause>

  <clause id="48286">
    <literal><![CDATA[
      a(x,y,a(z,u,x * (y \ (w * T(y * x,v5))))) = a(w,u,a(x,y,L(z,x * y,x * y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47282,a(flip),b,48285,a),flip(a)].">
      <j1 rule="hyper" parents="373 47282 48285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48287">
    <literal><![CDATA[
      a(x,y,a(z,u,x * (y \ (w * T(y * x,v5))))) = a(w,u,a((x \ y) * y,y,z))
    ]]></literal>
    <justification jstring="[para(46599(a,1),48286(a,2,3))].">
      <j1 rule="para" parents="46599 48286"/>
    </justification>
  </clause>

  <clause id="48288">
    <literal><![CDATA[
      a(x,y,a(z,u,x * (y \ (w * T(y * x,v5))))) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(45242(a,1),48287(a,2,3))].">
      <j1 rule="para" parents="45242 48287"/>
    </justification>
  </clause>

  <clause id="48289">
    <literal><![CDATA[
      a(x,y,a(z,u,x * (y \ (w * (y * x))))) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(114(a,1),48288(a,1,3,3,2,2,2))].">
      <j1 rule="para" parents="114 48288"/>
    </justification>
  </clause>

  <clause id="48290">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,z * (u * w))),y,a(z,u,z * (u * w))) = L(x,a(z,u,z * (u \ w)),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47682,a(flip),b,47676,a)].">
      <j1 rule="hyper" parents="64 47682 47676"/>
    </justification>
  </clause>

  <clause id="48291">
    <literal><![CDATA[
      ((x \ a(y,x,z)) * (((x \ a(y,x,z)) \ (x \ 1)) * u)) / u = x \ a(a(z,x,y),x,x * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,35736,a(flip),b,47716,a),flip(a)].">
      <j1 rule="hyper" parents="373 35736 47716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48292">
    <literal><![CDATA[
      x \ a(a(y,x,z),x,x * u) = L((x \ 1) * u,x,a(z,x,y)) / u
    ]]></literal>
    <justification jstring="[para(44832(a,1),48291(a,1,1)),flip(a)].">
      <j1 rule="para" parents="44832 48291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48293">
    <literal><![CDATA[
      x \ L(x * (y \ 1),y,a(z,y,u)) = y \ a(a(u,y,z),y,y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,5543,a(flip),b,48292,a)].">
      <j1 rule="hyper" parents="373 5543 48292"/>
    </justification>
  </clause>

  <clause id="48294">
    <literal><![CDATA[
      x \ a(a(y,x,z),x,x * u) = u * L(u \ (x \ 1),x,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,28865,a(flip),b,48293,a),flip(a)].">
      <j1 rule="hyper" parents="64 28865 48293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48295">
    <literal><![CDATA[
      x \ a(y,x,a(x * z,x,u)) = z * L(z \ (x \ 1),x,a(y,x,u))
    ]]></literal>
    <justification jstring="[para(47242(a,1),48294(a,1,2))].">
      <j1 rule="para" parents="47242 48294"/>
    </justification>
  </clause>

  <clause id="48296">
    <literal><![CDATA[
      a(x,a(y,x,z),L(L((u * x) \ 1,y,z),z,y)) = a(z,x,a(((u / x) \ 1) / x,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,27497,a(flip),b,47720,a)].">
      <j1 rule="hyper" parents="64 27497 47720"/>
    </justification>
  </clause>

  <clause id="48298">
    <literal><![CDATA[
      a(x,a(y,x,z),L(L((u * x) \ 1,y,z),z,y)) = a(z,x,a(x \ ((u / x) \ 1),x,y))
    ]]></literal>
    <justification jstring="[para(26785(a,1),48296(a,2,3))].">
      <j1 rule="para" parents="26785 48296"/>
    </justification>
  </clause>

  <clause id="48299">
    <literal><![CDATA[
      a(x,a(y,x,z),L(L((u * x) \ 1,y,z),z,y)) = a(z,x,a(((u / x) \ 1) * x,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,46669,a(flip),b,48298,a),flip(a)].">
      <j1 rule="hyper" parents="373 46669 48298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48300">
    <literal><![CDATA[
      a(x,a(y,x,z),L(L((u * x) \ 1,y,z),z,y)) = a(z,x,a((u / x) * x,x,y))
    ]]></literal>
    <justification jstring="[para(2662(a,1),48299(a,2,3))].">
      <j1 rule="para" parents="2662 48299"/>
    </justification>
  </clause>

  <clause id="48301">
    <literal><![CDATA[
      a(x,a(y,x,z),L(L((u * x) \ 1,y,z),z,y)) = a(z,x,a(u,x,y))
    ]]></literal>
    <justification jstring="[para(12(a,1),48300(a,2,3,1))].">
      <j1 rule="para" parents="12 48300"/>
    </justification>
  </clause>

  <clause id="48303">
    <literal><![CDATA[
      a(x * a(a(y,z,u),x,z),w,L(w,a(y,z,u),z)) = a(x,L(w,a(y,z,u),z),L(w,a(y,z,u),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,16192,a(flip),b,47841,a)].">
      <j1 rule="hyper" parents="64 16192 47841"/>
    </justification>
  </clause>

  <clause id="48304">
    <literal><![CDATA[
      a(x * a(y,x,a(z,u,w)),v5,v5) = a(x,L(v5,v6,a(v7,v8,v8)),L(L(v5,y,a(z,u,w)),a(w,u,z),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,45858,a(flip),b,47887,a)].">
      <j1 rule="hyper" parents="64 45858 47887"/>
    </justification>
  </clause>

  <clause id="48305">
    <literal><![CDATA[
      R(x,y \ (z \ y),L((y \ (z \ y)) \ 1,u,w)) = L(R(x,z,z),z,a(z,u,L(w,z,y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,43991,a(flip),b,48167,a),flip(a)].">
      <j1 rule="hyper" parents="373 43991 48167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48307">
    <literal><![CDATA[
      R(x,y \ (z \ y),L((y \ (z \ y)) \ 1,u,w)) = L(R(x,z,z),z,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,46622,a(flip),b,48305,a),flip(a)].">
      <j1 rule="hyper" parents="373 46622 48305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48309">
    <literal><![CDATA[
      R(x,y \ (z \ y),L((y \ (z \ y)) \ 1,u,w)) = R(x,z,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,47699,a(flip),b,48307,a),flip(a)].">
      <j1 rule="hyper" parents="373 47699 48307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48310">
    <literal><![CDATA[
      R(x,y \ (z \ y),L((y \ (z \ y)) \ 1,u,z * w)) = L(R(x,z,z),z,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,44415,a(flip),b,48307,a),flip(a)].">
      <j1 rule="hyper" parents="373 44415 48307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48311">
    <literal><![CDATA[
      R(x,y \ (z \ y),L((y \ (z \ y)) \ 1,u,z * w)) = R(x,z,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,47699,a(flip),b,48310,a),flip(a)].">
      <j1 rule="hyper" parents="373 47699 48310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48312">
    <literal><![CDATA[
      R(x,y,L(y,z,y * u)) = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,48309,a(flip),b,48311,a)].">
      <j1 rule="hyper" parents="64 48309 48311"/>
    </justification>
  </clause>

  <clause id="48313">
    <literal><![CDATA[
      a(((x * L(y,z,u)) * w) * (x * w),v5,x * w) = a(y,v5,L(L(w * x,z,u),x,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,46577,a(flip),b,48261,a),flip(a)].">
      <j1 rule="hyper" parents="373 46577 48261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48314">
    <literal><![CDATA[
      a(x * ((y * L(z,u,w)) \ (y * x)),v5,y * x) = a(z,v5,L(L(x * y,u,w),y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46858,a(flip),b,48313,a)].">
      <j1 rule="hyper" parents="64 46858 48313"/>
    </justification>
  </clause>

  <clause id="48315">
    <literal><![CDATA[
      a(x * ((y \ z) \ (T(y \ z,y) \ z)),u,y) = a(y * ((y \ z) * x),u,(y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(27585,a,48262,a)].">
      <j1 rule="hyper" parents="27585 48262"/>
    </justification>
  </clause>

  <clause id="48317">
    <literal><![CDATA[
      a(((x \ y) \ ((x \ y) \ y)) * z,u,x) = a(x * ((x \ y) * z),u,(x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32699,a(flip),b,48315,a)].">
      <j1 rule="hyper" parents="64 32699 48315"/>
    </justification>
  </clause>

  <clause id="48319">
    <literal><![CDATA[
      a(x * ((x \ y) * z),u,(x \ y) \ y) = a(L(y,x \ y,x \ y) * z,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32811,a(flip),b,48317,a),flip(a)].">
      <j1 rule="hyper" parents="64 32811 48317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48320">
    <literal><![CDATA[
      a(x * ((x \ y) * z),u,(x \ y) \ y) = a(((1 / (x / y)) * x) * z,u,x)
    ]]></literal>
    <justification jstring="[para(34721(a,1),48319(a,2,1,1))].">
      <j1 rule="para" parents="34721 48319"/>
    </justification>
  </clause>

  <clause id="48321">
    <literal><![CDATA[
      a(x * ((x \ y) * z),u,(x \ y) \ y) = a(((y \ x) * x) * z,u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,32662,a(flip),b,48320,a),flip(a)].">
      <j1 rule="hyper" parents="373 32662 48320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48322">
    <literal><![CDATA[
      a(((x \ y) * y) * z,u,y) = a(y * ((y \ x) * z),u,y)
    ]]></literal>
    <justification jstring="[hyper(27585,a,48321,a),flip(a)].">
      <j1 rule="hyper" parents="27585 48321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48324">
    <literal><![CDATA[
      a(x * ((x \ y) * z),y,x) = a(z * L(y,x,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,48241,a(flip),b,48322,a),flip(a)].">
      <j1 rule="hyper" parents="64 48241 48322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48325">
    <literal><![CDATA[
      a(x * (y * (z \ y)),x,y) = a(z * L(x,y,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,48109,a(flip),b,48324,a)].">
      <j1 rule="hyper" parents="64 48109 48324"/>
    </justification>
  </clause>

  <clause id="48326">
    <literal><![CDATA[
      a(x * ((y \ z) * z),x,z) = a(y * L(x,z,z),x,z)
    ]]></literal>
    <justification jstring="[hyper(32448,a,48325,a)].">
      <j1 rule="hyper" parents="32448 48325"/>
    </justification>
  </clause>

  <clause id="48327">
    <literal><![CDATA[
      a((x / y) * L(z,x,x),z,x) = a(z * (y * x),z,x)
    ]]></literal>
    <justification jstring="[para(82(a,1),48326(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="82 48326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48328">
    <literal><![CDATA[
      x \ L(x,y,((z \ x) * x) * y) = a(z * L(y,x,x),y,x) \ 1
    ]]></literal>
    <justification jstring="[para(48326(a,1),45594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="48326 45594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48329">
    <literal><![CDATA[
      x \ L(x,y,(z \ x) * (y * x)) = a(z * L(y,x,x),y,x) \ 1
    ]]></literal>
    <justification jstring="[para(48205(a,1),48328(a,1,2))].">
      <j1 rule="para" parents="48205 48328"/>
    </justification>
  </clause>

  <clause id="48330">
    <literal><![CDATA[
      a(x * L(y,z,z),y,z) \ 1 = z \ L(z,y,x * y)
    ]]></literal>
    <justification jstring="[para(47102(a,1),48329(a,1,2)),flip(a)].">
      <j1 rule="para" parents="47102 48329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48331">
    <literal><![CDATA[
      a(x * L(y,z,z),y,z) = a(x * y,y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,45037,a,b,48330,a),flip(a)].">
      <j1 rule="hyper" parents="40 45037 48330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48332">
    <literal><![CDATA[
      a((x / y) * z,z,x) = a(z * (y * x),z,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,48327,a(flip),b,48331,a),flip(a)].">
      <j1 rule="hyper" parents="64 48327 48331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48333">
    <literal><![CDATA[
      a(x * (L(x,y,y) \ z),x,y) = a((x \ z) * x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35237,a(flip),b,48331,a)].">
      <j1 rule="hyper" parents="64 35237 48331"/>
    </justification>
  </clause>

  <clause id="48334">
    <literal><![CDATA[
      a((x \ y) * z,z,y) = a(z * (x * y),z,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32367,a(flip),b,48332,a)].">
      <j1 rule="hyper" parents="64 32367 48332"/>
    </justification>
  </clause>

  <clause id="48335">
    <literal><![CDATA[
      a(x * (y \ z),y,z) = a(y * (x * z),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46866,a(flip),b,48334,a)].">
      <j1 rule="hyper" parents="64 46866 48334"/>
    </justification>
  </clause>

  <clause id="48336">
    <literal><![CDATA[
      a(x * (y * z),y,z) = a(y * (x * z),y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47671,a(flip),b,48335,a)].">
      <j1 rule="hyper" parents="64 47671 48335"/>
    </justification>
  </clause>

  <clause id="48337">
    <literal><![CDATA[
      x * a(y * (z * u),z,a(x,w,u)) = L(x,w,a(z * (y * u),z,u))
    ]]></literal>
    <justification jstring="[para(48336(a,1),47271(a,2,3))].">
      <j1 rule="para" parents="48336 47271"/>
    </justification>
  </clause>

  <clause id="48338">
    <literal><![CDATA[
      a(x * (L(x,y,y) \ z),x,y) = a(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,26836,a(flip),b,48333,a),flip(a)].">
      <j1 rule="hyper" parents="373 26836 48333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48340">
    <literal><![CDATA[
      a(x * a(y,y,z),z,y) = a(x,z,y)
    ]]></literal>
    <justification jstring="[para(45007(a,1),48338(a,1,1))].">
      <j1 rule="para" parents="45007 48338"/>
    </justification>
  </clause>

  <clause id="48341">
    <literal><![CDATA[
      L(x,y,z * a(x,x,y)) = a(z,y,x) \ x
    ]]></literal>
    <justification jstring="[para(48340(a,1),45065(a,2,1))].">
      <j1 rule="para" parents="48340 45065"/>
    </justification>
  </clause>

  <clause id="48342">
    <literal><![CDATA[
      L(x,y,z * a(x,x,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,45065,a,b,48341,a),flip(a)].">
      <j1 rule="hyper" parents="373 45065 48341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48343">
    <literal><![CDATA[
      L(x,a(y,z,y * (z \ u)),w) = L(x,a(y,z,y * (z * u)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,41867,a(flip),b,48290,a),flip(a)].">
      <j1 rule="hyper" parents="64 41867 48290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48344">
    <literal><![CDATA[
      L(x,a(y,z,u * (z * y)),w) = L(x,a(y,z,y * (z * u)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,47068,a,b,48343,a)].">
      <j1 rule="hyper" parents="64 47068 48343"/>
    </justification>
  </clause>

  <clause id="48345">
    <literal><![CDATA[
      a(x * a(a(y,z,u),x,z),w,w) = a(x,L(w,a(y,z,u),z),L(w,a(y,z,u),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47692,a(flip),b,48303,a)].">
      <j1 rule="hyper" parents="64 47692 48303"/>
    </justification>
  </clause>

  <clause id="48346">
    <literal><![CDATA[
      a(x * a(a(y,z,u),x,z),w,w) = a(x,w,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,40664,a(flip),b,48345,a),flip(a)].">
      <j1 rule="hyper" parents="373 40664 48345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48349">
    <literal><![CDATA[
      a(x * a(y,z,a(z,x,u)),w,w) = a(x,w,w)
    ]]></literal>
    <justification jstring="[para(47200(a,1),48346(a,1,1,2))].">
      <j1 rule="para" parents="47200 48346"/>
    </justification>
  </clause>

  <clause id="48350">
    <literal><![CDATA[
      a(x * a(y,x,a(z,u,u)),w,w) = a(x,w,L(w,a(u,u,z),y))
    ]]></literal>
    <justification jstring="[hyper(373,a,44038,a(flip),b,48304,a),flip(a)].">
      <j1 rule="hyper" parents="373 44038 48304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48351">
    <literal><![CDATA[
      a(x * a(y,z,a(z,x,u)),w,w) = a(x,w,L(w,a(z,z,y),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,43935,a(flip),b,48350,a)].">
      <j1 rule="hyper" parents="64 43935 48350"/>
    </justification>
  </clause>

  <clause id="48352">
    <literal><![CDATA[
      a(x,y,L(y,a(z,z,u),w)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,48349,a(flip),b,48351,a),flip(a)].">
      <j1 rule="hyper" parents="64 48349 48351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48354">
    <literal><![CDATA[
      a(x,y,L(y,a(z,u,u),w)) = a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41424,a,b,48352,a)].">
      <j1 rule="hyper" parents="64 41424 48352"/>
    </justification>
  </clause>

  <clause id="48355">
    <literal><![CDATA[
      a(((a(x,x,y) \ z) \ u) * a(x,x,y),w,w) = a(z * u,w,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,46837,a(flip),b,48352,a)].">
      <j1 rule="hyper" parents="64 46837 48352"/>
    </justification>
  </clause>

  <clause id="48357">
    <literal><![CDATA[
      a(x,a(y,y,z),a(u,x,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,48352,a(flip),b,47350,a),flip(a)].">
      <j1 rule="hyper" parents="140 48352 47350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48358">
    <literal><![CDATA[
      a(x,x,a(y,a(z,z,u),w)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,48352,a(flip),b,47276,a),flip(a)].">
      <j1 rule="hyper" parents="140 48352 47276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48360">
    <literal><![CDATA[
      a(x,y,y) \ R(x,y,L(y,a(z,u,u),w)) = x
    ]]></literal>
    <justification jstring="[para(48352(a,1),38384(a,1,1))].">
      <j1 rule="para" parents="48352 38384"/>
    </justification>
  </clause>

  <clause id="48362">
    <literal><![CDATA[
      L(a(x,y,z),a(u,u,w),y) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,48357,a)].">
      <j1 rule="hyper" parents="53 48357"/>
    </justification>
  </clause>

  <clause id="48363">
    <literal><![CDATA[
      L(a(x,a(y,y,z),u),w,w) = a(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(53,a,48358,a)].">
      <j1 rule="hyper" parents="53 48358"/>
    </justification>
  </clause>

  <clause id="48366">
    <literal><![CDATA[
      a(x,y,a(y,z,L(u,a(w,v5,v5),v6))) = a(u,z,a(x,y,y))
    ]]></literal>
    <justification jstring="[para(48354(a,1),46816(a,1,3)),flip(a)].">
      <j1 rule="para" parents="48354 46816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48368">
    <literal><![CDATA[
      a(x,y,L(z,a(u,u,w),y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46493,a,b,48362,a)].">
      <j1 rule="hyper" parents="64 46493 48362"/>
    </justification>
  </clause>

  <clause id="48369">
    <literal><![CDATA[
      a(x,y,L(z,a(u,w,w),y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41424,a,b,48368,a)].">
      <j1 rule="hyper" parents="64 41424 48368"/>
    </justification>
  </clause>

  <clause id="48370">
    <literal><![CDATA[
      L(x,a(y,z,z),a(u,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,47463,a(flip),b,48360,a)].">
      <j1 rule="hyper" parents="64 47463 48360"/>
    </justification>
  </clause>

  <clause id="48376">
    <literal><![CDATA[
      L(x,y,a(y,a(z,u,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,47433,a,b,48370,a)].">
      <j1 rule="hyper" parents="64 47433 48370"/>
    </justification>
  </clause>

  <clause id="48377">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,w),y)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,47432,a,b,48370,a)].">
      <j1 rule="hyper" parents="64 47432 48370"/>
    </justification>
  </clause>

  <clause id="48378">
    <literal><![CDATA[
      L(x,a(y,y,z),a(u,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,41403,a,b,48370,a)].">
      <j1 rule="hyper" parents="64 41403 48370"/>
    </justification>
  </clause>

  <clause id="48379">
    <literal><![CDATA[
      R(x,a(y,z,z),u) * (x \ w) = w * a(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46482,a(flip),b,48370,a)].">
      <j1 rule="hyper" parents="64 46482 48370"/>
    </justification>
  </clause>

  <clause id="48384">
    <literal><![CDATA[
      L(x,a(y,z,z),u \ w) = L(x,a(y,z,z),u * w)
    ]]></literal>
    <justification jstring="[para(48370(a,1),47535(a,1,1)),flip(a)].">
      <j1 rule="para" parents="48370 47535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48385">
    <literal><![CDATA[
      (a(x,a(y,z,z),u) * x) * w = a(x,a(y,z,z),u) * (x * w)
    ]]></literal>
    <justification jstring="[hyper(1960,a,48376,a),flip(a)].">
      <j1 rule="hyper" parents="1960 48376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48386">
    <literal><![CDATA[
      (x * y) * a(z,a(u,w,w),y) = x * (y * a(z,a(u,w,w),y))
    ]]></literal>
    <justification jstring="[para(48376(a,1),42221(a,1,1,1))].">
      <j1 rule="para" parents="48376 42221"/>
    </justification>
  </clause>

  <clause id="48387">
    <literal><![CDATA[
      x * (L(x,a(y,z,z),u) \ w) = w * a(u,a(y,z,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,46760,a(flip),b,48377,a),flip(a)].">
      <j1 rule="hyper" parents="64 46760 48377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48396">
    <literal><![CDATA[
      L(x,a(y,y,z),L(u,u,w)) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,47495,a(flip),b,48378,a)].">
      <j1 rule="hyper" parents="64 47495 48378"/>
    </justification>
  </clause>

  <clause id="48406">
    <literal><![CDATA[
      a(x,a(y,y,z),L(u,w,w)) = a(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46493,a,b,48363,a)].">
      <j1 rule="hyper" parents="64 46493 48363"/>
    </justification>
  </clause>

  <clause id="48407">
    <literal><![CDATA[
      R(x,a(y,y,z),L(u,u,w)) = L(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31802,a,b,48396,a)].">
      <j1 rule="hyper" parents="64 31802 48396"/>
    </justification>
  </clause>

  <clause id="48408">
    <literal><![CDATA[
      R(x,a(y,y,z),L(u,u,w)) = x * a(u,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,43396,a,b,48407,a),flip(a)].">
      <j1 rule="hyper" parents="373 43396 48407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48409">
    <literal><![CDATA[
      L(x,a(y,z,z),((u \ 1) \ w) \ ((u * w) * v5)) = L(x,a(y,z,z),(u * w) * (((u \ 1) \ w) * v5))
    ]]></literal>
    <justification jstring="[para(3146(a,1),48384(a,2,3))].">
      <j1 rule="para" parents="3146 48384"/>
    </justification>
  </clause>

  <clause id="48410">
    <literal><![CDATA[
      L(x,a(y,z,z),(u \ w) \ ((u * w) \ (v5 \ (u * w)))) = L(x,a(y,z,z),T(v5,u * u) \ (u \ w))
    ]]></literal>
    <justification jstring="[para(47793(a,1),48384(a,2,3))].">
      <j1 rule="para" parents="47793 48384"/>
    </justification>
  </clause>

  <clause id="48411">
    <literal><![CDATA[
      a(x,a(y,y,z),L(u,u,w)) = a(u,a(z,y,y),x)
    ]]></literal>
    <justification jstring="[hyper(45251,a,48408,a)].">
      <j1 rule="hyper" parents="45251 48408"/>
    </justification>
  </clause>

  <clause id="48412">
    <literal><![CDATA[
      a(x * y,a(z,z,u),L(L(w,w,v5),x,x)) = a(w,a(u,z,z),x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46605,a,b,48411,a)].">
      <j1 rule="hyper" parents="64 46605 48411"/>
    </justification>
  </clause>

  <clause id="48413">
    <literal><![CDATA[
      L(x,a(y,z,z),u) * (x \ w) = w * a(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(31802(a,1),48379(a,1,1))].">
      <j1 rule="para" parents="31802 48379"/>
    </justification>
  </clause>

  <clause id="48414">
    <literal><![CDATA[
      x * (L(x,a(y,z,z),u) \ w) = w * a(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(43409(a,1),48387(a,2,2))].">
      <j1 rule="para" parents="43409 48387"/>
    </justification>
  </clause>

  <clause id="48415">
    <literal><![CDATA[
      (x * y) * a(y,a(z,u,u),w) = x * L(y,a(z,u,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,23889,a(flip),b,48413,a),flip(a)].">
      <j1 rule="hyper" parents="64 23889 48413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48416">
    <literal><![CDATA[
      (x * y) * a(z,a(u,u,w),y) = x * L(y,a(w,u,u),z)
    ]]></literal>
    <justification jstring="[para(43405(a,1),48415(a,1,2))].">
      <j1 rule="para" parents="43405 48415"/>
    </justification>
  </clause>

  <clause id="48417">
    <literal><![CDATA[
      a(((x \ 1) \ y) * a(z,z,u),w,w) = a((x \ a(z,z,u)) * y,w,w)
    ]]></literal>
    <justification jstring="[para(45036(a,1),48355(a,1,1,1,1))].">
      <j1 rule="para" parents="45036 48355"/>
    </justification>
  </clause>

  <clause id="48418">
    <literal><![CDATA[
      (a(x,a(y,z,z),u) * x) * w = x * (a(x,a(y,z,z),u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,29956,a(flip),b,48385,a),flip(a)].">
      <j1 rule="hyper" parents="373 29956 48385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48419">
    <literal><![CDATA[
      (x * y) * a(z,a(u,w,w),y) = x * L(y,a(w,w,u),z)
    ]]></literal>
    <justification jstring="[para(43396(a,1),48386(a,2,2))].">
      <j1 rule="para" parents="43396 48386"/>
    </justification>
  </clause>

  <clause id="48420">
    <literal><![CDATA[
      x * (a(x,a(y,z,z),u) * w) = L(x,a(y,z,z),u) * w
    ]]></literal>
    <justification jstring="[para(42632(a,1),48418(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42632 48418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48421">
    <literal><![CDATA[
      a(x * y,a(z,z,u),L(w,w,v5)) = a(w,a(u,z,z),x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,48406,a(flip),b,48412,a)].">
      <j1 rule="hyper" parents="64 48406 48412"/>
    </justification>
  </clause>

  <clause id="48423">
    <literal><![CDATA[
      a(x,a(y,z,z),u \ w) = a(x,a(y,z,z),u * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,48411,a(flip),b,48421,a),flip(a)].">
      <j1 rule="hyper" parents="64 48411 48421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48424">
    <literal><![CDATA[
      a(((x \ 1) \ y) * a(z,z,u),w,w) = a((x * a(z,z,u)) * y,w,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,45740,a(flip),b,48417,a),flip(a)].">
      <j1 rule="hyper" parents="373 45740 48417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48425">
    <literal><![CDATA[
      a(((x \ 1) \ y) * a(z,z,u),w,w) = a(x * (a(z,z,u) * y),w,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,48211,a(flip),b,48424,a),flip(a)].">
      <j1 rule="hyper" parents="373 48211 48424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48426">
    <literal><![CDATA[
      a((x \ y) * a(z,z,u),w,w) = a(x * (a(z,z,u) * y),w,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32809,a(flip),b,48425,a)].">
      <j1 rule="hyper" parents="64 32809 48425"/>
    </justification>
  </clause>

  <clause id="48427">
    <literal><![CDATA[
      a((x \ y) * a(z,u,u),w,w) = a(x * (a(u,u,z) * y),w,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42342,a,b,48426,a)].">
      <j1 rule="hyper" parents="64 42342 48426"/>
    </justification>
  </clause>

  <clause id="48428">
    <literal><![CDATA[
      L(x,a(y,z,z),(u * w) * (((u \ 1) \ w) * v5)) = L(x,a(y,z,z),(u * (w / (u * w))) \ v5)
    ]]></literal>
    <justification jstring="[para(44964(a,1),48409(a,1,3)),flip(a)].">
      <j1 rule="para" parents="44964 48409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48429">
    <literal><![CDATA[
      L(x,a(y,z,z),(u * w) * (((u \ 1) \ w) * v5)) = L(x,a(y,z,z),(u * ((u * w) \ w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29003,a(flip),b,48428,a),flip(a)].">
      <j1 rule="hyper" parents="373 29003 48428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48430">
    <literal><![CDATA[
      L(x,a(y,z,z),(u * w) * (((u \ 1) \ w) * v5)) = L(x,a(y,z,z),(u * (w \ (u \ w))) \ v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,34170,a(flip),b,48429,a),flip(a)].">
      <j1 rule="hyper" parents="373 34170 48429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48431">
    <literal><![CDATA[
      L(x,a(y,z,z),(u * w) * (((u \ 1) \ w) * v5)) = L(x,a(y,z,z),v5 * a(w,u,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,37871,a(flip),b,48430,a),flip(a)].">
      <j1 rule="hyper" parents="373 37871 48430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48432">
    <literal><![CDATA[
      L(x,a(y,z,z),((u \ w) * (v5 \ (u * w))) * (u * w)) = L(x,a(y,z,z),T(v5,u * u) \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,36738,a(flip),b,48410,a)].">
      <j1 rule="hyper" parents="64 36738 48410"/>
    </justification>
  </clause>

  <clause id="48433">
    <literal><![CDATA[
      a((x \ T(y,T(z,u))) * ((T(z,u) * x) \ (y * z)),w,v5) = a(a(z,x,x \ T(y,T(z,u))),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32444,a(flip),b,46040,a)].">
      <j1 rule="hyper" parents="64 32444 46040"/>
    </justification>
  </clause>

  <clause id="48434">
    <literal><![CDATA[
      a(((x * y) \ (z * x)) * (y \ T(z,T(x,u))),w,v5) = a(a(x,y,y \ T(z,T(x,u))),w,v5)
    ]]></literal>
    <justification jstring="[hyper(32949,a,48433,a)].">
      <j1 rule="hyper" parents="32949 48433"/>
    </justification>
  </clause>

  <clause id="48437">
    <literal><![CDATA[
      a(a(x,y,y \ T(z,T(x,u))),w,v5) = a(((x * y) \ (z * x)) * (y \ z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32437,a(flip),b,48434,a),flip(a)].">
      <j1 rule="hyper" parents="64 32437 48434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48439">
    <literal><![CDATA[
      a(((x * y) \ (z * x)) * (y \ z),u,w) = a(a(x,y,y \ z),u,w)
    ]]></literal>
    <justification jstring="[para(27301(a,1),48437(a,1,1)),flip(a)].">
      <j1 rule="para" parents="27301 48437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48440">
    <literal><![CDATA[
      a(((x * y) \ (z * x)) * (y \ z),u,w) = a(a(x,y,y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,42039,a(flip),b,48439,a),flip(a)].">
      <j1 rule="hyper" parents="373 42039 48439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48442">
    <literal><![CDATA[
      a(((x * y) \ (z * x)) * (y \ z),u,w) = a(y * z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47254,a(flip),b,48440,a),flip(a)].">
      <j1 rule="hyper" parents="373 47254 48440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48443">
    <literal><![CDATA[
      a(x,y,x \ (((z * (u * (x \ 1))) / (z * (x \ 1))) * z)) = a(x,y,z * (L(u,z,x \ 1) * (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,37061,a(flip),b,46256,a),flip(a)].">
      <j1 rule="hyper" parents="373 37061 46256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48444">
    <literal><![CDATA[
      x * (L(L(x,y,z),y,z) \ (a(z,y,x * a(u,x,w)) \ v5)) = (a(z,y,x) * a(w,a(z,y,x),u)) * v5
    ]]></literal>
    <justification jstring="[hyper(64,a,43218,a(flip),b,47018,a)].">
      <j1 rule="hyper" parents="64 43218 47018"/>
    </justification>
  </clause>

  <clause id="48445">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,a(y,z,u) / (1 / w)),w * a(y,z,u),w * (w * a(y,z,u))) = w \ (((w / (w * a(y,z,u))) * x) * T(w * a(y,z,u),x))
    ]]></literal>
    <justification jstring="[para(36344(a,1),47642(a,1,1,2,3))].">
      <j1 rule="para" parents="36344 47642"/>
    </justification>
  </clause>

  <clause id="48446">
    <literal><![CDATA[
      ((x * (x * a(y,x,a(z,u,u)))) / x) \ (L(x,a(y,u,a(z,x,u)),x) * w) = a(y,u,a(z,x,u)) \ w
    ]]></literal>
    <justification jstring="[para(46380(a,1),47845(a,1,1,1))].">
      <j1 rule="para" parents="46380 47845"/>
    </justification>
  </clause>

  <clause id="48447">
    <literal><![CDATA[
      a(x,y,x \ (((z * (u * (x \ 1))) / (z * (x \ 1))) * z)) = a(x,y,z * (L(u,z,x) * (x \ 1)))
    ]]></literal>
    <justification jstring="[para(1631(a,1),48443(a,2,3,2,1))].">
      <j1 rule="para" parents="1631 48443"/>
    </justification>
  </clause>

  <clause id="48448">
    <literal><![CDATA[
      a(x,y,x \ (((z * (x \ 1)) \ (z * (u * (x \ 1)))) * z)) = a(x,y,z * (L(u,z,x) * (x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27492,a(flip),b,48447,a)].">
      <j1 rule="hyper" parents="64 27492 48447"/>
    </justification>
  </clause>

  <clause id="48449">
    <literal><![CDATA[
      a(x,y,x \ (L(T(z,x \ 1),x \ 1,u) * u)) = a(x,y,u * (L(z,u,x) * (x \ 1)))
    ]]></literal>
    <justification jstring="[para(262(a,1),48448(a,1,3,2,1))].">
      <j1 rule="para" parents="262 48448"/>
    </justification>
  </clause>

  <clause id="48450">
    <literal><![CDATA[
      a(x,y,x \ (L(T(z,x \ 1),x,u) * u)) = a(x,y,u * (L(z,u,x) * (x \ 1)))
    ]]></literal>
    <justification jstring="[para(11794(a,1),48449(a,1,3,2,1))].">
      <j1 rule="para" parents="11794 48449"/>
    </justification>
  </clause>

  <clause id="48451">
    <literal><![CDATA[
      a(x,y,z * (L(u,z,x) * (x \ 1))) = a(x,y,x \ (L(u,x,z) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27515,a(flip),b,48450,a),flip(a)].">
      <j1 rule="hyper" parents="64 27515 48450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48453">
    <literal><![CDATA[
      x * (a(y,z,x * a(u,x,w)) \ a(y,z,L(x,z,y))) = (a(y,z,x) * a(w,a(y,z,x),u)) * L(x,z,y)
    ]]></literal>
    <justification jstring="[para(47168(a,1),48444(a,1,2))].">
      <j1 rule="para" parents="47168 48444"/>
    </justification>
  </clause>

  <clause id="48454">
    <literal><![CDATA[
      ((x * x) * (a(y,x,a(z,u,u)) / x)) \ (L(x,a(y,u,a(z,x,u)),x) * w) = a(y,u,a(z,x,u)) \ w
    ]]></literal>
    <justification jstring="[para(35742(a,1),48446(a,1,1))].">
      <j1 rule="para" parents="35742 48446"/>
    </justification>
  </clause>

  <clause id="48455">
    <literal><![CDATA[
      ((1 / x) \ a(y,x,a(z,u,u))) \ (L(x,a(y,u,a(z,x,u)),x) * w) = a(y,u,a(z,x,u)) \ w
    ]]></literal>
    <justification jstring="[para(25057(a,1),48454(a,1,1))].">
      <j1 rule="para" parents="25057 48454"/>
    </justification>
  </clause>

  <clause id="48456">
    <literal><![CDATA[
      (a(x,y,a(z,u,u)) * y) \ (L(y,a(x,u,a(z,y,u)),y) * w) = a(x,u,a(z,y,u)) \ w
    ]]></literal>
    <justification jstring="[para(35737(a,1),48455(a,1,1))].">
      <j1 rule="para" parents="35737 48455"/>
    </justification>
  </clause>

  <clause id="48457">
    <literal><![CDATA[
      (x * a(y,x,a(z,z,u))) \ (L(x,a(y,z,a(u,x,z)),x) * w) = a(y,z,a(u,x,z)) \ w
    ]]></literal>
    <justification jstring="[para(41900(a,1),48456(a,1,1))].">
      <j1 rule="para" parents="41900 48456"/>
    </justification>
  </clause>

  <clause id="48458">
    <literal><![CDATA[
      (x * a(y,x,a(z,z,u))) \ (x * w) = a(y,z,a(u,x,z)) \ w
    ]]></literal>
    <justification jstring="[para(13919(a,1),48457(a,1,2,1))].">
      <j1 rule="para" parents="13919 48457"/>
    </justification>
  </clause>

  <clause id="48459">
    <literal><![CDATA[
      (x / y) * (a(z,y,a(u,u,w)) \ y) = a(z,u,a(w,y,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,43825,a(flip),b,48458,a)].">
      <j1 rule="hyper" parents="64 43825 48458"/>
    </justification>
  </clause>

  <clause id="48460">
    <literal><![CDATA[
      (x / y) * (y * a(z,y,a(u,u,w))) = a(z,u,a(w,y,u)) \ x
    ]]></literal>
    <justification jstring="[para(40860(a,1),48459(a,1,2))].">
      <j1 rule="para" parents="40860 48459"/>
    </justification>
  </clause>

  <clause id="48461">
    <literal><![CDATA[
      (x / y) * (y * a(z,y,a(u,u,w))) = a(z,u,a(u,y,w)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,42644,a(flip),b,48460,a),flip(a)].">
      <j1 rule="hyper" parents="373 42644 48460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48462">
    <literal><![CDATA[
      a((x \ (x / y)) * ((x \ 1) \ z),x \ (x / y),x \ 1) = a(((x \ 1) / y) * z,x * (x / y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,44889,a(flip),b,46009,a),flip(a)].">
      <j1 rule="hyper" parents="373 44889 46009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48463">
    <literal><![CDATA[
      a(x,y,a((L(z,u,w) * T(v5 \ 1,v6)) * v5,v7,y)) = a(v5 * (z * (v5 \ 1)),v7,a(y,y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,32364,a(flip),b,46819,a),flip(a)].">
      <j1 rule="hyper" parents="64 32364 46819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48465">
    <literal><![CDATA[
      a(x,y,a((L(z,u,w) * T(v5 \ 1,v6)) * v5,v7,y)) = a((v5 * z) * v5,v7,a(y,y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,32426,a(flip),b,48463,a),flip(a)].">
      <j1 rule="hyper" parents="373 32426 48463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48466">
    <literal><![CDATA[
      a(x,y,a((L(z,u,w) * T(v5 \ 1,v6)) * v5,v7,y)) = a(z,v7,L(a(y,y,L(x,u,w)),v5,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,46581,a(flip),b,48465,a),flip(a)].">
      <j1 rule="hyper" parents="373 46581 48465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48467">
    <literal><![CDATA[
      a(x,y,a((L(z,u,w) * T(v5 \ 1,v6)) * v5,v7,y)) = a(z,v7,a(y,y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(45050(a,1),48466(a,2,3))].">
      <j1 rule="para" parents="45050 48466"/>
    </justification>
  </clause>

  <clause id="48468">
    <literal><![CDATA[
      a(x,y,a(L((z * T(u \ 1,w)) * u,v5,v6),v7,y)) = a(z,v7,a(y,y,L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[para(33791(a,2),48467(a,1,3,1))].">
      <j1 rule="para" parents="33791 48467"/>
    </justification>
  </clause>

  <clause id="48470">
    <literal><![CDATA[
      a(x,y,a((z * T(u \ 1,w)) * u,v5,L(y,v6,v7))) = a(z,v5,a(y,y,L(x,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46787,a(flip),b,48468,a)].">
      <j1 rule="hyper" parents="64 46787 48468"/>
    </justification>
  </clause>

  <clause id="48471">
    <literal><![CDATA[
      a(x,y,a((z * (u \ 1)) * u,w,L(y,v5,v6))) = a(z,w,a(y,y,L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[para(114(a,1),48470(a,1,3,1,1,2))].">
      <j1 rule="para" parents="114 48470"/>
    </justification>
  </clause>

  <clause id="48472">
    <literal><![CDATA[
      a(x,y,a(z,u,L(L(y,w,v5),v6,v6))) = a(z,u,a(y,y,L(x,w,v5)))
    ]]></literal>
    <justification jstring="[para(46578(a,1),48471(a,1,3))].">
      <j1 rule="para" parents="46578 48471"/>
    </justification>
  </clause>

  <clause id="48473">
    <literal><![CDATA[
      a(x,x * y,a(z,u,L(u,w,v5))) = a(z,y,a(u,u,L(x,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,48007,a,b,48472,a)].">
      <j1 rule="hyper" parents="64 48007 48472"/>
    </justification>
  </clause>

  <clause id="48474">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,(z * y) * x,u)) = a(w,(x * y) * z,a(u,u,L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47980,a(flip),b,48473,a)].">
      <j1 rule="hyper" parents="64 47980 48473"/>
    </justification>
  </clause>

  <clause id="48475">
    <literal><![CDATA[
      a(x,(y * z) * u,a(w,w,L(y,z,u))) = a(y,w,a(x,(u * z) * y,L(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46629,a(flip),b,48474,a),flip(a)].">
      <j1 rule="hyper" parents="64 46629 48474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48476">
    <literal><![CDATA[
      a(x,(y * z) * u,a(w,w,L(y,z,u))) = a(y,w,a(x,u * z,L(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47030,a(flip),b,48475,a),flip(a)].">
      <j1 rule="hyper" parents="373 47030 48475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48477">
    <literal><![CDATA[
      a(((x \ T(T(y,z) * u,w)) * v5) * (T(y,z) * u),v6,y * u) = a(v5 * x,v6,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[hyper(32447,a,47028,a)].">
      <j1 rule="hyper" parents="32447 47028"/>
    </justification>
  </clause>

  <clause id="48479">
    <literal><![CDATA[
      a((x * y) * ((z \ T(T(x,u) * y,w)) * v5),v6,x * y) = a(v5 * z,v6,T(T(x,u) * y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,32523,a(flip),b,48477,a)].">
      <j1 rule="hyper" parents="64 32523 48477"/>
    </justification>
  </clause>

  <clause id="48481">
    <literal><![CDATA[
      a((x * y) * (z * (u \ (T(x,w) * y))),v5,x * y) = a(z * u,v5,T(T(x,w) * y,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,32717,a(flip),b,48479,a)].">
      <j1 rule="hyper" parents="64 32717 48479"/>
    </justification>
  </clause>

  <clause id="48483">
    <literal><![CDATA[
      a((x * y) * (z * (K(x,u) * y)),w,x * y) = a(z * x,w,T(T(x,u) * y,v5))
    ]]></literal>
    <justification jstring="[para(6071(a,1),48481(a,1,1,2,2))].">
      <j1 rule="para" parents="6071 48481"/>
    </justification>
  </clause>

  <clause id="48484">
    <literal><![CDATA[
      a((x * y) * (z * y),u,z * y) = a(x * z,u,T(T(z,w) * y,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,32527,a(flip),b,48483,a)].">
      <j1 rule="hyper" parents="64 32527 48483"/>
    </justification>
  </clause>

  <clause id="48486">
    <literal><![CDATA[
      a(x * (y \ (z * x)),u,z * x) = a(y * z,u,T(T(z,w) * x,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,46858,a(flip),b,48484,a)].">
      <j1 rule="hyper" parents="64 46858 48484"/>
    </justification>
  </clause>

  <clause id="48487">
    <literal><![CDATA[
      a(x * (y \ (z * x)),u,z * x) = a(y * z,u,z * x)
    ]]></literal>
    <justification jstring="[para(1501(a,1),48486(a,2,3))].">
      <j1 rule="para" parents="1501 48486"/>
    </justification>
  </clause>

  <clause id="48488">
    <literal><![CDATA[
      a((x * L(y,z,u)) * x,w,x * v5) = a(y,w,L(L(v5 * x,z,u),x,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,48314,a(flip),b,48487,a),flip(a)].">
      <j1 rule="hyper" parents="64 48314 48487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48489">
    <literal><![CDATA[
      a(L(x,y,z),u,L(w * v5,w,w)) = a(x,u,L(L(v5 * w,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,46581,a(flip),b,48488,a)].">
      <j1 rule="hyper" parents="64 46581 48488"/>
    </justification>
  </clause>

  <clause id="48490">
    <literal><![CDATA[
      a(x,y,L(L(z * u,w,v5),u,z)) = a(L(x,w,v5),y,(u \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38939,a(flip),b,48489,a),flip(a)].">
      <j1 rule="hyper" parents="64 38939 48489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48491">
    <literal><![CDATA[
      a(x,y,L(L(z * u,w,v5),u,z)) = a(x,y,L((u \ 1) \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,46496,a(flip),b,48490,a),flip(a)].">
      <j1 rule="hyper" parents="373 46496 48490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48492">
    <literal><![CDATA[
      a(x,y * z,L((z \ 1) \ y,u,w)) = a(x,z \ y,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46807,a(flip),b,48491,a),flip(a)].">
      <j1 rule="hyper" parents="64 46807 48491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48493">
    <literal><![CDATA[
      a(x,y \ z,L(z * y,u,w)) = a(x,z * y,L(z * y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46750,a(flip),b,48492,a),flip(a)].">
      <j1 rule="hyper" parents="64 46750 48492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48494">
    <literal><![CDATA[
      L(x,y,(z * ((u * u) * a(w,v5,v5))) \ (((z * a(w,v5,v5)) * u) * u)) = L(x,u,a(u,y,z * a(v5,v5,w)))
    ]]></literal>
    <justification jstring="[para(28825(a,1),47164(a,1,3,1))].">
      <j1 rule="para" parents="28825 47164"/>
    </justification>
  </clause>

  <clause id="48495">
    <literal><![CDATA[
      (a(x,y,z) * a(u,a(x,y,z),w)) * L(z,y,x) = z * (a(x,y,z * a(w,z,u)) \ a(x,y,z))
    ]]></literal>
    <justification jstring="[para(42064(a,1),48453(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="42064 48453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48497">
    <literal><![CDATA[
      (a(x,y,z) * a(u,a(x,y,z),w)) * L(z,y,x) = z * a(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(47752(a,1),48495(a,2,2))].">
      <j1 rule="para" parents="47752 48495"/>
    </justification>
  </clause>

  <clause id="48498">
    <literal><![CDATA[
      a(x,y,z * a(u,z,w)) * L(z,y,x) = z * a(w,a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(47013(a,1),48497(a,1,1))].">
      <j1 rule="para" parents="47013 48497"/>
    </justification>
  </clause>

  <clause id="48499">
    <literal><![CDATA[
      a((x \ (x / y)) * ((x \ 1) \ z),x \ (x / y),x \ 1) = a(((x \ 1) / y) * z,x * (y \ x),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,31897,a(flip),b,48462,a),flip(a)].">
      <j1 rule="hyper" parents="373 31897 48462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48500">
    <literal><![CDATA[
      L(x,y,(z * (u * (u * a(w,v5,v5)))) \ (((z * a(w,v5,v5)) * u) * u)) = L(x,u,a(u,y,z * a(v5,v5,w)))
    ]]></literal>
    <justification jstring="[para(45028(a,1),48494(a,1,3,1,2))].">
      <j1 rule="para" parents="45028 48494"/>
    </justification>
  </clause>

  <clause id="48501">
    <literal><![CDATA[
      a((x \ (x / y)) * ((x \ 1) \ z),x \ (x / y),x \ 1) = a(((x \ 1) / y) * z,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,46414,a(flip),b,48499,a),flip(a)].">
      <j1 rule="hyper" parents="373 46414 48499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48502">
    <literal><![CDATA[
      a((x \ (x / y)) * ((x \ 1) \ z),x \ (x / y),x \ 1) = a((y \ (x \ 1)) * z,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,32367,a(flip),b,48501,a),flip(a)].">
      <j1 rule="hyper" parents="373 32367 48501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48503">
    <literal><![CDATA[
      a((x \ (x / y)) * ((x \ 1) \ z),x \ (x / y),x \ 1) = a(y * ((x \ 1) \ z),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,46841,a(flip),b,48502,a),flip(a)].">
      <j1 rule="hyper" parents="373 46841 48502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48504">
    <literal><![CDATA[
      a((x \ (x / y)) * ((x \ 1) \ z),x \ (x / y),x \ 1) = a((x \ z) * y,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,32810,a(flip),b,48503,a),flip(a)].">
      <j1 rule="hyper" parents="373 32810 48503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48505">
    <literal><![CDATA[
      L(x,y,(z * (u * (u * a(w,v5,v5)))) \ (a(w,v5,v5) * ((z * u) * u))) = L(x,u,a(u,y,z * a(v5,v5,w)))
    ]]></literal>
    <justification jstring="[para(47134(a,1),48500(a,1,3,2))].">
      <j1 rule="para" parents="47134 48500"/>
    </justification>
  </clause>

  <clause id="48506">
    <literal><![CDATA[
      L(x,y,(z * z) \ ((u * a(w,v5,v5)) \ (a(w,v5,v5) * ((u * z) * z)))) = L(x,z,a(z,y,u * a(v5,v5,w)))
    ]]></literal>
    <justification jstring="[para(45953(a,1),48505(a,1,3))].">
      <j1 rule="para" parents="45953 48505"/>
    </justification>
  </clause>

  <clause id="48507">
    <literal><![CDATA[
      L(x,y,(z * a(u,w,w)) \ (a(u,w,w) * ((z * v5) * v5))) = L(x,v5,a(v5,y,z * a(w,w,u)))
    ]]></literal>
    <justification jstring="[hyper(2272,a,48506,a)].">
      <j1 rule="hyper" parents="2272 48506"/>
    </justification>
  </clause>

  <clause id="48509">
    <literal><![CDATA[
      L(x,y,(z * a(u,w,w)) \ (a(u,w,w) * L(z,v5,v5))) = L(x,v5,a(v5,y,z * a(w,w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,35134,a(flip),b,48507,a)].">
      <j1 rule="hyper" parents="64 35134 48507"/>
    </justification>
  </clause>

  <clause id="48510">
    <literal><![CDATA[
      L(x,y,a(z,u,u) \ (w \ (a(z,u,u) * L(w,v5,v5)))) = L(x,v5,a(v5,y,w * a(u,u,z)))
    ]]></literal>
    <justification jstring="[para(33825(a,1),48509(a,1,3))].">
      <j1 rule="para" parents="33825 48509"/>
    </justification>
  </clause>

  <clause id="48511">
    <literal><![CDATA[
      L(x,y,a(z,u,u) \ T(a(w,w,v5) \ a(z,u,u),v5)) = L(x,w,a(w,y,v5 * a(u,u,z)))
    ]]></literal>
    <justification jstring="[para(44974(a,2),48510(a,1,3,2))].">
      <j1 rule="para" parents="44974 48510"/>
    </justification>
  </clause>

  <clause id="48512">
    <literal><![CDATA[
      L(x,y,a(z,u,u) \ (a(w,w,v5) \ a(z,u,u))) = L(x,w,a(w,y,v5 * a(u,u,z)))
    ]]></literal>
    <justification jstring="[hyper(29068,a,48511,a)].">
      <j1 rule="hyper" parents="29068 48511"/>
    </justification>
  </clause>

  <clause id="48514">
    <literal><![CDATA[
      L(x,y,a(y,z,u * a(w,w,v5))) = L(x,z,a(y,y,u) \ 1)
    ]]></literal>
    <justification jstring="[para(37677(a,1),48512(a,1,3)),flip(a)].">
      <j1 rule="para" parents="37677 48512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48515">
    <literal><![CDATA[
      L(x,y,a(y,z,u * a(w,w,v5))) = L(x,z,a(y,y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,1631,a(flip),b,48514,a),flip(a)].">
      <j1 rule="hyper" parents="373 1631 48514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48517">
    <literal><![CDATA[
      a(a(x,y,z * a(u,u,w)),x,v5) \ x = (x / v5) * L(v5,y,a(x,x,z))
    ]]></literal>
    <justification jstring="[para(48515(a,1),42072(a,1,2)),flip(a)].">
      <j1 rule="para" parents="48515 42072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48518">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,z,u)),x,z) = a(a(z,y,u * a(w,w,v5)),z,x) \ 1
    ]]></literal>
    <justification jstring="[para(48515(a,1),42353(a,1,1,2))].">
      <j1 rule="para" parents="48515 42353"/>
    </justification>
  </clause>

  <clause id="48519">
    <literal><![CDATA[
      a(x,y,a(y,z,u * a(w,v5,v5))) = x \ L(x,x * z,a(y,y,u))
    ]]></literal>
    <justification jstring="[para(48515(a,1),48166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="48515 48166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48520">
    <literal><![CDATA[
      a(x,y,a(y,z,u * a(w,v5,v5))) = x \ L(x,y,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(46904(a,1),48519(a,2,2))].">
      <j1 rule="para" parents="46904 48519"/>
    </justification>
  </clause>

  <clause id="48522">
    <literal><![CDATA[
      a(x,y,a(y,z,u * a(w,v5,v5))) = a(y,z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,47251,a(flip),b,48520,a),flip(a)].">
      <j1 rule="hyper" parents="373 47251 48520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48523">
    <literal><![CDATA[
      a(a(x,y,z * a(u,u,w)),x,v5) \ x = v5 * (L(v5,y,a(x,x,z)) \ x)
    ]]></literal>
    <justification jstring="[hyper(373,a,42179,a(flip),b,48517,a),flip(a)].">
      <j1 rule="hyper" parents="373 42179 48517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48524">
    <literal><![CDATA[
      a(a(x,y,z * a(u,u,w)),x,v5) \ x = v5 * L(v5 \ x,x,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(46270(a,2),48523(a,2,2))].">
      <j1 rule="para" parents="46270 48523"/>
    </justification>
  </clause>

  <clause id="48525">
    <literal><![CDATA[
      a(a(x,y,z * a(u,u,w)),x,v5) \ x = L(x,x,a(z,y,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,46022,a(flip),b,48524,a),flip(a)].">
      <j1 rule="hyper" parents="373 46022 48524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48526">
    <literal><![CDATA[
      a(x * a(y,y,z),u,a(w,v5,v5)) \ v5 = L(v5,v5,a(x,u,w))
    ]]></literal>
    <justification jstring="[para(47254(a,1),48525(a,1,1))].">
      <j1 rule="para" parents="47254 48525"/>
    </justification>
  </clause>

  <clause id="48527">
    <literal><![CDATA[
      a(x * a(y,y,z),u,a(w,w,v5)) * w = L(w,w,a(x,u,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,42644,a(flip),b,48526,a)].">
      <j1 rule="hyper" parents="64 42644 48526"/>
    </justification>
  </clause>

  <clause id="48528">
    <literal><![CDATA[
      L(x,x,a(y * a(z,z,u),w,v5)) = L(x,x,a(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,47287,a(flip),b,48527,a)].">
      <j1 rule="hyper" parents="64 47287 48527"/>
    </justification>
  </clause>

  <clause id="48530">
    <literal><![CDATA[
      a(x,x,a(y * a(z,z,u),w,v5)) = L(x,x,a(y,w,v5)) \ x
    ]]></literal>
    <justification jstring="[para(48528(a,1),36327(a,1,1)),flip(a)].">
      <j1 rule="para" parents="48528 36327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48531">
    <literal><![CDATA[
      a(x,x,a(y * a(z,z,u),w,v5)) = a(a(y,w,v5),x,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,45067,a,b,48530,a),flip(a)].">
      <j1 rule="hyper" parents="373 45067 48530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48532">
    <literal><![CDATA[
      a(x,x,a(y * a(z,z,u),w,v5)) = a(v5,w,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,47254,a(flip),b,48531,a),flip(a)].">
      <j1 rule="hyper" parents="373 47254 48531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48533">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,a(w,v5,v5)) = a(w,u,a(v5,v5,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,45873,a,b,48532,a)].">
      <j1 rule="hyper" parents="64 45873 48532"/>
    </justification>
  </clause>

  <clause id="48534">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,a(w,v5,u)) = a(w,v5,a(u,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,45828,a,b,48532,a)].">
      <j1 rule="hyper" parents="64 45828 48532"/>
    </justification>
  </clause>

  <clause id="48535">
    <literal><![CDATA[
      a(x,y,a(z,z,a(u,w,w) * v5)) = a(x,y,a(z,z,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,45816,a,b,48532,a)].">
      <j1 rule="hyper" parents="64 45816 48532"/>
    </justification>
  </clause>

  <clause id="48536">
    <literal><![CDATA[
      a(x * a(y,z,z),u,a(w,w,v5)) = a(v5,u,a(w,w,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,45815,a,b,48532,a)].">
      <j1 rule="hyper" parents="64 45815 48532"/>
    </justification>
  </clause>

  <clause id="48537">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,a(w,w,v5)) = a(v5,u,a(w,w,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,45814,a,b,48532,a)].">
      <j1 rule="hyper" parents="64 45814 48532"/>
    </justification>
  </clause>

  <clause id="48539">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,a((w * a(v5,v6,v6)) * v7,v8,v8)) = a(v7 * (a(v6,v6,v5) * w),u,a(v8,v8,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,36063,a(flip),b,48533,a),flip(a)].">
      <j1 rule="hyper" parents="373 36063 48533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48542">
    <literal><![CDATA[
      a(x,y,a((z \ u) * a(w,v5,v5),v6,v6)) = a(x,y,a(v6,v6,z \ (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,41907,a(flip),b,48535,a)].">
      <j1 rule="hyper" parents="64 41907 48535"/>
    </justification>
  </clause>

  <clause id="48545">
    <literal><![CDATA[
      a(x,y,a(z * (a(u,u,w) * v5),v6,v6)) = a(x,y,a(v6,v6,z \ (v5 \ 1)))
    ]]></literal>
    <justification jstring="[para(48427(a,1),48542(a,1,3))].">
      <j1 rule="para" parents="48427 48542"/>
    </justification>
  </clause>

  <clause id="48546">
    <literal><![CDATA[
      a(x,y,a(z * (a(u,u,w) * v5),v6,v6)) = a(x,y,a(v6,v6,z * (v5 \ 1)))
    ]]></literal>
    <justification jstring="[hyper(373,a,45836,a(flip),b,48545,a),flip(a)].">
      <j1 rule="hyper" parents="373 45836 48545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48547">
    <literal><![CDATA[
      a(x,y,a(z * (a(u,u,w) * v5),v6,v6)) = a(x,y,a(v6,v6,v5 * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,42191,a(flip),b,48546,a),flip(a)].">
      <j1 rule="hyper" parents="373 42191 48546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48548">
    <literal><![CDATA[
      L(a(x,y,a(z,u,y)),z,y) = a(a(y,u,x * a(w,w,v5)),y,z) \ 1
    ]]></literal>
    <justification jstring="[para(47251(a,1),48518(a,1,1))].">
      <j1 rule="para" parents="47251 48518"/>
    </justification>
  </clause>

  <clause id="48549">
    <literal><![CDATA[
      a(a(x,y,z * a(u,u,w)),x,v5) \ 1 = a(z,x,a(v5,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,43009,a(flip),b,48548,a),flip(a)].">
      <j1 rule="hyper" parents="64 43009 48548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48551">
    <literal><![CDATA[
      a(x,y,a(y,z,u * a(w,w,v5))) = a(u,y,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42358,a(flip),b,48549,a)].">
      <j1 rule="hyper" parents="64 42358 48549"/>
    </justification>
  </clause>

  <clause id="48552">
    <literal><![CDATA[
      a(x,y,a(z,z,u * a(w,w,v5))) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47324,a,b,48551,a)].">
      <j1 rule="hyper" parents="64 47324 48551"/>
    </justification>
  </clause>

  <clause id="48553">
    <literal><![CDATA[
      a(x * a(y,y,z),u,a(w,w,v5)) = a(x,w,a(v5,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47197,a,b,48551,a)].">
      <j1 rule="hyper" parents="64 47197 48551"/>
    </justification>
  </clause>

  <clause id="48554">
    <literal><![CDATA[
      a(x,y,a(z,u \ x,y)) = a(z,y,a(y,R(u,w,w),x * a(u,w,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,48071,a(flip),b,48552,a),flip(a)].">
      <j1 rule="hyper" parents="64 48071 48552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48555">
    <literal><![CDATA[
      a(x * a(y,z,z),u,a(w,v5,v5)) = a(x,v5,a(w,u,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,38634,a,b,48553,a)].">
      <j1 rule="hyper" parents="64 38634 48553"/>
    </justification>
  </clause>

  <clause id="48558">
    <literal><![CDATA[
      a(x,y,a(y,R(z,u,u),w * a(z,u,u))) = a(w,y,a(x,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46897,a(flip),b,48554,a),flip(a)].">
      <j1 rule="hyper" parents="64 46897 48554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48559">
    <literal><![CDATA[
      a(x,y,a(y,L(z,u,u),w * a(z,u,u))) = a(w,y,a(x,z,y))
    ]]></literal>
    <justification jstring="[para(32187(a,1),48558(a,1,3))].">
      <j1 rule="para" parents="32187 48558"/>
    </justification>
  </clause>

  <clause id="48560">
    <literal><![CDATA[
      a(x,L(y,z,z),a(u,x,w)) = a(w,x,a(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,48522,a(flip),b,48559,a)].">
      <j1 rule="hyper" parents="64 48522 48559"/>
    </justification>
  </clause>

  <clause id="48562">
    <literal><![CDATA[
      a(x,L(y,z,z),a(u,u,w)) = a(w,u,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47241,a,b,48560,a)].">
      <j1 rule="hyper" parents="64 47241 48560"/>
    </justification>
  </clause>

  <clause id="48563">
    <literal><![CDATA[
      a(x,L(y,z,z),a(u,u,w)) = a(x,y,a(u,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,47198,a,b,48562,a),flip(a)].">
      <j1 rule="hyper" parents="373 47198 48562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48564">
    <literal><![CDATA[
      a(x,y \ z,a(u,u,w)) = a(x,y * z,a(u,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,32141,a(flip),b,48563,a)].">
      <j1 rule="hyper" parents="64 32141 48563"/>
    </justification>
  </clause>

  <clause id="48565">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,a(w * (a(v5,v5,v6) * v7),v8,v8)) = a(v7 * (a(v5,v5,v6) * w),u,a(v8,v8,z))
    ]]></literal>
    <justification jstring="[para(48210(a,1),48539(a,1,3))].">
      <j1 rule="para" parents="48210 48539"/>
    </justification>
  </clause>

  <clause id="48566">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,a(w,w,v5 * v6)) = a(v5 * (a(v7,v7,v8) * v6),u,a(w,w,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,48547,a(flip),b,48565,a)].">
      <j1 rule="hyper" parents="64 48547 48565"/>
    </justification>
  </clause>

  <clause id="48568">
    <literal><![CDATA[
      a(x * (a(y,y,z) * u),w,a(v5,v5,v6)) = a(x * u,w,a(v5,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,48537,a(flip),b,48566,a),flip(a)].">
      <j1 rule="hyper" parents="64 48537 48566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48569">
    <literal><![CDATA[
      a(x * (y * a(z,u,u)),w,a(v5,v5,v6)) = a(x * y,w,a(v5,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,47146,a(flip),b,48568,a)].">
      <j1 rule="hyper" parents="64 47146 48568"/>
    </justification>
  </clause>

  <clause id="48570">
    <literal><![CDATA[
      a(((x * y) \ z) * a(u,w,v5),v6,a(u,u,v7)) = a(v7,v6,a((x * L(y,y,x)) \ z,u,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47113,a(flip),b,48569,a),flip(a)].">
      <j1 rule="hyper" parents="64 47113 48569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48572">
    <literal><![CDATA[
      a(x,y,a((z * L(u,u,z)) \ w,v5,v5)) = a(v5,v5,a(x,y,a(v5,v6,v7) * ((z * u) \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47228,a(flip),b,48570,a),flip(a)].">
      <j1 rule="hyper" parents="64 47228 48570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48573">
    <literal><![CDATA[
      a(x,y,a((z * L(u,u,z)) \ w,v5,v5)) = a(x,y,a((z * u) \ w,v5,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,45882,a(flip),b,48572,a),flip(a)].">
      <j1 rule="hyper" parents="373 45882 48572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48574">
    <literal><![CDATA[
      a(x,y,a((z * L(u,u,z)) \ w,v5,v5)) = a(x,y,a(w * (z * u),v5,v5))
    ]]></literal>
    <justification jstring="[para(45506(a,1),48573(a,2,3))].">
      <j1 rule="para" parents="45506 48573"/>
    </justification>
  </clause>

  <clause id="48575">
    <literal><![CDATA[
      a(x,y,a(z * (u * L(w,w,u)),v5,v5)) = a(x,y,a(z * (u * w),v5,v5))
    ]]></literal>
    <justification jstring="[para(45506(a,1),48574(a,1,3))].">
      <j1 rule="para" parents="45506 48574"/>
    </justification>
  </clause>

  <clause id="48576">
    <literal><![CDATA[
      a(x,y,a(z * (u \ w),v5,v5)) = a(x,y,a(z * (w * u),v5,v5))
    ]]></literal>
    <justification jstring="[para(32937(a,1),48575(a,1,3))].">
      <j1 rule="para" parents="32937 48575"/>
    </justification>
  </clause>

  <clause id="48577">
    <literal><![CDATA[
      a(x,y,a((z * x) * u,w,w)) = a(x,y,a(x * (u * z),w,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47964,a,b,48576,a)].">
      <j1 rule="hyper" parents="64 47964 48576"/>
    </justification>
  </clause>

  <clause id="48578">
    <literal><![CDATA[
      a(x,y,a(z * (u * (w \ 1)),v5,v5)) = a(x,y,a((w \ u) * z,v5,v5))
    ]]></literal>
    <justification jstring="[para(32810(a,1),48576(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32810 48576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48579">
    <literal><![CDATA[
      a(x,y,a(x * (z * u),w,w)) = a(x,y,a(w,w,z * (u * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,41897,a(flip),b,48577,a),flip(a)].">
      <j1 rule="hyper" parents="64 41897 48577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48580">
    <literal><![CDATA[
      a(x,y,a(z,z,u * (w * x))) = a(x,y,a(z,z,x * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,41883,a,b,48579,a),flip(a)].">
      <j1 rule="hyper" parents="64 41883 48579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48581">
    <literal><![CDATA[
      a(x,y,a((z \ u) * w,v5,v5)) = a(x,y,a((z * u) * w,v5,v5))
    ]]></literal>
    <justification jstring="[para(32426(a,1),48578(a,1,3)),flip(a)].">
      <j1 rule="para" parents="32426 48578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48582">
    <literal><![CDATA[
      a(x,y,a((z \ u) * w,v5,v5)) = a(x,y,a(v5,v5,w * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,41896,a(flip),b,48581,a),flip(a)].">
      <j1 rule="hyper" parents="373 41896 48581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48583">
    <literal><![CDATA[
      a(x,y,a(z,z,u * (w \ v5))) = a(x,y,a(z,z,u * (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,41897,a(flip),b,48582,a)].">
      <j1 rule="hyper" parents="64 41897 48582"/>
    </justification>
  </clause>

  <clause id="48584">
    <literal><![CDATA[
      a(x,y,a(z,z,u * (w * x))) = a(x,y,a(z,z,w * (x * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47664,a(flip),b,48583,a),flip(a)].">
      <j1 rule="hyper" parents="64 47664 48583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48585">
    <literal><![CDATA[
      a(x,y,a(z,z,u * (x * w))) = a(x,y,a(z,z,x * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,48580,a(flip),b,48584,a),flip(a)].">
      <j1 rule="hyper" parents="64 48580 48584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48586">
    <literal><![CDATA[
      L(L(x,y,a(z,z,u)),a(z,z,u) * y,z * u) = (((1 / z) \ u) * y) \ (((1 / z) \ u) * (y * x))
    ]]></literal>
    <justification jstring="[para(45715(a,1),46310(a,2,2))].">
      <j1 rule="para" parents="45715 46310"/>
    </justification>
  </clause>

  <clause id="48587">
    <literal><![CDATA[
      L(L(x,y,a(z,z,u)),a(z,z,u) * y,z * u) = L(x,y,(1 / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,18,a,b,48586,a),flip(a)].">
      <j1 rule="hyper" parents="373 18 48586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48588">
    <literal><![CDATA[
      L(L(x,y,a(z,z,u)),a(z,z,u) * y,z * u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2230,a(flip),b,48587,a),flip(a)].">
      <j1 rule="hyper" parents="373 2230 48587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48589">
    <literal><![CDATA[
      L(L(x,a(y,y,z) * u,a(y,y,z)),L(u,a(y,y,z),a(y,y,z)),y * z) = L(x,a(y,y,z) * u,y \ z)
    ]]></literal>
    <justification jstring="[hyper(11888,a,48588,a)].">
      <j1 rule="hyper" parents="11888 48588"/>
    </justification>
  </clause>

  <clause id="48590">
    <literal><![CDATA[
      a(a(x,x,y),z,u) \ L(u,a(x,x,y) * z,L(x * y,z,a(x,x,y))) = L(u,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47125,a,b,48588,a)].">
      <j1 rule="hyper" parents="64 47125 48588"/>
    </justification>
  </clause>

  <clause id="48591">
    <literal><![CDATA[
      L(L(x,y,a(z,z,u)),y,z \ u) = L(x,a(z,z,u) * y,z * u)
    ]]></literal>
    <justification jstring="[para(42171(a,1),48588(a,1,1)),flip(a)].">
      <j1 rule="para" parents="42171 48588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48592">
    <literal><![CDATA[
      L(x,a(y,y,z) * u,y * z) = L(x,u,y * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47541,a(flip),b,48591,a),flip(a)].">
      <j1 rule="hyper" parents="64 47541 48591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48593">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ L(z,a(y,y,x) * u,L(y * x,u,a(y,y,x))) = L(z,u,y \ x)
    ]]></literal>
    <justification jstring="[para(43872(a,1),48590(a,1,1))].">
      <j1 rule="para" parents="43872 48590"/>
    </justification>
  </clause>

  <clause id="48594">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ L(z,a(y,y,x) * u,y * x) = L(z,u,y \ x)
    ]]></literal>
    <justification jstring="[para(29963(a,1),48593(a,1,2,3))].">
      <j1 rule="para" parents="29963 48593"/>
    </justification>
  </clause>

  <clause id="48596">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) \ L(z,u,y * x) = L(z,u,y \ x)
    ]]></literal>
    <justification jstring="[para(48592(a,1),48594(a,1,2))].">
      <j1 rule="para" parents="48592 48594"/>
    </justification>
  </clause>

  <clause id="48597">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) * L(u,z,y * x) = L(u,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42644,a(flip),b,48596,a)].">
      <j1 rule="hyper" parents="64 42644 48596"/>
    </justification>
  </clause>

  <clause id="48598">
    <literal><![CDATA[
      ((a(x,y,z) \ x) * z) \ ((L(z,y,x) * y) * x) = L(y * K(z * y,x),z,a(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(28686(a,1),46361(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="28686 46361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48599">
    <literal><![CDATA[
      ((a(x,y,z) \ x) * z) \ ((L(z,y,x) * y) * x) = L(y * K(z * y,x),z,x * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,42468,a(flip),b,48598,a),flip(a)].">
      <j1 rule="hyper" parents="373 42468 48598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48601">
    <literal><![CDATA[
      ((a(x,y,z) \ x) * z) \ ((L(z,y,x) * y) * x) = L(y * K(z * y,x),z,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(45072(a,2),48599(a,2,3))].">
      <j1 rule="para" parents="45072 48599"/>
    </justification>
  </clause>

  <clause id="48602">
    <literal><![CDATA[
      ((a(x,y,z) \ x) * z) \ ((L(z,y,x) * y) * x) = L(y * K(z * y,x),z,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,29203,a(flip),b,48601,a),flip(a)].">
      <j1 rule="hyper" parents="373 29203 48601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48603">
    <literal><![CDATA[
      ((a(x,y,z) \ x) * z) \ ((L(z,y,x) * y) * x) = L(y * K(z * y,x),z,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,46328,a(flip),b,48602,a),flip(a)].">
      <j1 rule="hyper" parents="373 46328 48602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48604">
    <literal><![CDATA[
      ((a(x,y,z) \ x) * z) \ ((L(z,y,x) * y) * x) = (x * z) \ ((z * y) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,14648,a(flip),b,48603,a),flip(a)].">
      <j1 rule="hyper" parents="373 14648 48603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48605">
    <literal><![CDATA[
      (x * L(y,z,x)) \ ((L(y,z,x) * z) * x) = (x * y) \ ((y * z) * x)
    ]]></literal>
    <justification jstring="[para(45213(a,1),48604(a,1,1))].">
      <j1 rule="para" parents="45213 48604"/>
    </justification>
  </clause>

  <clause id="48606">
    <literal><![CDATA[
      K(x,y * z) * ((x * z) \ ((z * y) * x)) = L(y,L(z,y,x),x)
    ]]></literal>
    <justification jstring="[para(48605(a,1),28319(a,1,2))].">
      <j1 rule="para" parents="48605 28319"/>
    </justification>
  </clause>

  <clause id="48607">
    <literal><![CDATA[
      L(x,L(y,x,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27292,a,b,48606,a),flip(a)].">
      <j1 rule="hyper" parents="64 27292 48606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48608">
    <literal><![CDATA[
      L(x,(x * y) \ z,y) = L(x,x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,36973,a(flip),b,48607,a),flip(a)].">
      <j1 rule="hyper" parents="64 36973 48607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48610">
    <literal><![CDATA[
      L(x,(y * x) \ z,y) = L(x,x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[para(346(a,1),48607(a,1,2))].">
      <j1 rule="para" parents="346 48607"/>
    </justification>
  </clause>

  <clause id="48612">
    <literal><![CDATA[
      L(x,(x * y) \ z,y) = L(x,(y \ z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,45702,a(flip),b,48608,a),flip(a)].">
      <j1 rule="hyper" parents="373 45702 48608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48613">
    <literal><![CDATA[
      L(x,(y * x) \ z,y) = L(x,(y \ z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,45702,a(flip),b,48610,a),flip(a)].">
      <j1 rule="hyper" parents="373 45702 48610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48614">
    <literal><![CDATA[
      L(x,(y \ ((y * z) * x)) * x,y) = L(x,L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,29476,a(flip),b,48612,a),flip(a)].">
      <j1 rule="hyper" parents="64 29476 48612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48615">
    <literal><![CDATA[
      L(x,(y \ z) * x,y) \ x = a(y,(x * y) \ z,x)
    ]]></literal>
    <justification jstring="[para(48612(a,1),45067(a,2,1)),flip(a)].">
      <j1 rule="para" parents="48612 45067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48616">
    <literal><![CDATA[
      a(x,(y * x) \ z,y) = a(x,(x \ z) * y,y)
    ]]></literal>
    <justification jstring="[hyper(45142,a,48615,a),flip(a)].">
      <j1 rule="hyper" parents="45142 48615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48617">
    <literal><![CDATA[
      L(x,L(y,z,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47732,a(flip),b,48614,a),flip(a)].">
      <j1 rule="hyper" parents="64 47732 48614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48619">
    <literal><![CDATA[
      L(x,(y * x) \ z,y) = L(x,y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,36973,a(flip),b,48617,a),flip(a)].">
      <j1 rule="hyper" parents="64 36973 48617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48620">
    <literal><![CDATA[
      a(x,y,L(L(L(z,u,w),v5,v6),u,w)) = a(x,y,L(z,L(v5,v6,L(z,u,w)),v6))
    ]]></literal>
    <justification jstring="[para(48617(a,1),39065(a,1,3,1))].">
      <j1 rule="para" parents="48617 39065"/>
    </justification>
  </clause>

  <clause id="48621">
    <literal><![CDATA[
      a(x,L(y,x,z),z) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[para(48617(a,1),45067(a,2,1))].">
      <j1 rule="para" parents="48617 45067"/>
    </justification>
  </clause>

  <clause id="48622">
    <literal><![CDATA[
      a(x,y,L(z,L(u,w,L(z,y,x)),w)) * L(L(z,y,x),u,w) = L(z,L(u,w,L(z,y,x)),w)
    ]]></literal>
    <justification jstring="[para(48617(a,1),45165(a,1,2))].">
      <j1 rule="para" parents="48617 45165"/>
    </justification>
  </clause>

  <clause id="48623">
    <literal><![CDATA[
      L(x,L(y,z,a(x,u,w)),z) = L(x,L(y,z,L(x,u,w)),z)
    ]]></literal>
    <justification jstring="[para(47493(a,1),48617(a,1,2)),flip(a)].">
      <j1 rule="para" parents="47493 48617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48624">
    <literal><![CDATA[
      a(x,L(y,x,z),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,45067,a,b,48621,a),flip(a)].">
      <j1 rule="hyper" parents="373 45067 48621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48626">
    <literal><![CDATA[
      a(x,T((y * R(x,z,x)) \ u,w),y) = a(x,T(R(x,z,x) \ (y \ u),w),y)
    ]]></literal>
    <justification jstring="[para(14174(a,1),48624(a,1,2))].">
      <j1 rule="para" parents="14174 48624"/>
    </justification>
  </clause>

  <clause id="48627">
    <literal><![CDATA[
      L(x,(y * x) \ z,y) = L(x,y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,41718,a(flip),b,48619,a),flip(a)].">
      <j1 rule="hyper" parents="373 41718 48619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48628">
    <literal><![CDATA[
      L(x,(y \ z) * x,y) = L(x,y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,48613,a(flip),b,48627,a)].">
      <j1 rule="hyper" parents="64 48613 48627"/>
    </justification>
  </clause>

  <clause id="48629">
    <literal><![CDATA[
      L(T(x,y),(z \ ((x * T(x,u)) * w)) * T(x,y),z) = L(T(x,y),z * ((K(x,y) / T(x,u)) \ w),z)
    ]]></literal>
    <justification jstring="[para(29180(a,1),48628(a,2,2,2))].">
      <j1 rule="para" parents="29180 48628"/>
    </justification>
  </clause>

  <clause id="48630">
    <literal><![CDATA[
      a(x,y,L(z,L(u,w,L(z,v5,v6)),w)) = a(x,y,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,39065,a(flip),b,48620,a),flip(a)].">
      <j1 rule="hyper" parents="64 39065 48620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48632">
    <literal><![CDATA[
      a(x,T(R(x,y,x) \ (z \ u),w),z) = a(x,(z * R(x,y,x)) \ u,z)
    ]]></literal>
    <justification jstring="[hyper(31997,a,48626,a),flip(a)].">
      <j1 rule="hyper" parents="31997 48626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48634">
    <literal><![CDATA[
      a(x,y,L(z,u,w)) * L(L(z,y,x),u,w) = L(z,L(u,w,L(z,y,x)),w)
    ]]></literal>
    <justification jstring="[para(48630(a,1),48622(a,1,1))].">
      <j1 rule="para" parents="48630 48622"/>
    </justification>
  </clause>

  <clause id="48635">
    <literal><![CDATA[
      L(x,L(y,z,L(x,u,w)),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,45165,a(flip),b,48634,a),flip(a)].">
      <j1 rule="hyper" parents="64 45165 48634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48638">
    <literal><![CDATA[
      L(x,L(y,z,a(x,u,w)),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,48623,a,b,48635,a)].">
      <j1 rule="hyper" parents="64 48623 48635"/>
    </justification>
  </clause>

  <clause id="48640">
    <literal><![CDATA[
      L(T(x,y),(z \ ((x * T(x,u)) * w)) * x,z) = L(T(x,y),z * ((K(x,y) / T(x,u)) \ w),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29447,a(flip),b,48629,a)].">
      <j1 rule="hyper" parents="64 29447 48629"/>
    </justification>
  </clause>

  <clause id="48642">
    <literal><![CDATA[
      L(T(x,y),z * ((K(x,y) / T(x,u)) \ w),z) = L(T(x,y),x * (z \ w),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34346,a(flip),b,48640,a),flip(a)].">
      <j1 rule="hyper" parents="64 34346 48640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48644">
    <literal><![CDATA[
      L(T(x,y),(T(x,z) \ u) * w,w) = L(T(x,y),x * (w \ u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,30857,a(flip),b,48642,a)].">
      <j1 rule="hyper" parents="64 30857 48642"/>
    </justification>
  </clause>

  <clause id="48646">
    <literal><![CDATA[
      L(T(x,y),(x \ z) * u,u) = L(T(x,y),x * (u \ z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,29460,a(flip),b,48644,a)].">
      <j1 rule="hyper" parents="64 29460 48644"/>
    </justification>
  </clause>

  <clause id="48647">
    <literal><![CDATA[
      a(x,(y \ z) * u,a(w,w,L(T(y,v5),y * (u \ z),u))) = a(x,(y \ z) * u,a(w,w,T(y,v5)))
    ]]></literal>
    <justification jstring="[para(48646(a,1),47852(a,1,3,3))].">
      <j1 rule="para" parents="48646 47852"/>
    </justification>
  </clause>

  <clause id="48648">
    <literal><![CDATA[
      a(x,(y \ z) * u,a(w,w,T(y,v5))) = a(x,(y \ z) * u,a(w,w,L(y,y * (u \ z),u)))
    ]]></literal>
    <justification jstring="[para(27328(a,1),48647(a,1,3)),flip(a)].">
      <j1 rule="para" parents="27328 48647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48650">
    <literal><![CDATA[
      a(x,(y \ z) * u,a(w,w,T(y,v5))) = a(x,(y \ z) * u,a(w,w,L(y,u \ z,u)))
    ]]></literal>
    <justification jstring="[para(46848(a,1),48648(a,2,3))].">
      <j1 rule="para" parents="46848 48648"/>
    </justification>
  </clause>

  <clause id="48651">
    <literal><![CDATA[
      a(x,(y \ z) * u,a(w,w,T(y,v5))) = a(x,(y \ z) * u,a(w,w,L(y,u * z,u)))
    ]]></literal>
    <justification jstring="[para(41718(a,1),48650(a,2,3,3))].">
      <j1 rule="para" parents="41718 48650"/>
    </justification>
  </clause>

  <clause id="48652">
    <literal><![CDATA[
      a(x,(y \ z) * u,a(w,w,T(y,v5))) = a(x,(y \ z) * u,a(w,w,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(46930(a,1),48651(a,2,3))].">
      <j1 rule="para" parents="46930 48651"/>
    </justification>
  </clause>

  <clause id="48653">
    <literal><![CDATA[
      a(((x \ 1) * y) * R(z,x,x \ 1),u,L(z,x,x)) = a(y * T(z * x,x \ 1),u,R(z,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,27596,a(flip),b,46861,a)].">
      <j1 rule="hyper" parents="64 27596 46861"/>
    </justification>
  </clause>

  <clause id="48654">
    <literal><![CDATA[
      a(((x \ 1) * y) * L(z,x,x \ 1),u,L(z,x,x)) = a(y * T(z * x,x \ 1),u,R(z,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(64,a,34635,a(flip),b,48653,a)].">
      <j1 rule="hyper" parents="64 34635 48653"/>
    </justification>
  </clause>

  <clause id="48655">
    <literal><![CDATA[
      a(((x \ 1) * y) * L(z,x,x),u,L(z,x,x)) = a(y * T(z * x,x \ 1),u,R(z,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1631(a,1),48654(a,1,1,2))].">
      <j1 rule="para" parents="1631 48654"/>
    </justification>
  </clause>

  <clause id="48656">
    <literal><![CDATA[
      a(x * T(y * z,z \ 1),u,R(y,z,z \ 1)) = a(L((z \ 1) * x,z,z) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47979,a(flip),b,48655,a),flip(a)].">
      <j1 rule="hyper" parents="64 47979 48655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48657">
    <literal><![CDATA[
      a(x * T(y * z,z \ 1),u,R(y,z,z \ 1)) = a(L(z * x,z,z) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,34644,a(flip),b,48656,a),flip(a)].">
      <j1 rule="hyper" parents="373 34644 48656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48658">
    <literal><![CDATA[
      a(x * T(y * z,z \ 1),u,R(y,z,z \ 1)) = a((z \ x) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,32818,a(flip),b,48657,a),flip(a)].">
      <j1 rule="hyper" parents="373 32818 48657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48659">
    <literal><![CDATA[
      a(x * T(y * z,z \ 1),u,L(y,z,z)) = a((z \ x) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,27596,a(flip),b,48658,a)].">
      <j1 rule="hyper" parents="64 27596 48658"/>
    </justification>
  </clause>

  <clause id="48660">
    <literal><![CDATA[
      a(x * (y * z),u,L(z,y,y)) = a((y \ x) * z,u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32423,a(flip),b,48659,a)].">
      <j1 rule="hyper" parents="64 32423 48659"/>
    </justification>
  </clause>

  <clause id="48662">
    <literal><![CDATA[
      a(x * (y * z),u,L(z,y,x)) = a((y \ x) * z,u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47890,a(flip),b,48660,a)].">
      <j1 rule="hyper" parents="64 47890 48660"/>
    </justification>
  </clause>

  <clause id="48663">
    <literal><![CDATA[
      a(x * (y * z),u,L(y,z,x)) = a((z \ x) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(32448,a,48662,a)].">
      <j1 rule="hyper" parents="32448 48662"/>
    </justification>
  </clause>

  <clause id="48664">
    <literal><![CDATA[
      a((x \ y) * (x \ (y \ z)),u,x \ (y \ z)) = a(y * (x * (x \ (y \ z))),u,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(346(a,1),48662(a,1,3)),flip(a)].">
      <j1 rule="para" parents="346 48662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48665">
    <literal><![CDATA[
      a((x \ y) * (z * ((z \ x) * K(y,u))),w,((y / x) * z) \ T(y,u)) = a((z \ (x \ y)) * ((z \ x) * K(y,u)),w,(z \ x) * K(y,u))
    ]]></literal>
    <justification jstring="[para(25947(a,1),48662(a,1,3))].">
      <j1 rule="para" parents="25947 48662"/>
    </justification>
  </clause>

  <clause id="48666">
    <literal><![CDATA[
      a(x * (y * L(z,y,y)),u,L(y,z,a(y,y,z) \ x)) = a((z \ (a(y,y,z) \ x)) * y,u,y)
    ]]></literal>
    <justification jstring="[para(46344(a,1),48663(a,1,1))].">
      <j1 rule="para" parents="46344 48663"/>
    </justification>
  </clause>

  <clause id="48667">
    <literal><![CDATA[
      a((x \ y) * (x \ (y \ z)),u,x \ (y \ z)) = a(z,u,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(75(a,1),48664(a,2,1))].">
      <j1 rule="para" parents="75 48664"/>
    </justification>
  </clause>

  <clause id="48668">
    <literal><![CDATA[
      a(x * (x \ y),z,(u \ 1) * (x \ y)) = a(y,z,(x * u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47773,a(flip),b,48667,a)].">
      <j1 rule="hyper" parents="64 47773 48667"/>
    </justification>
  </clause>

  <clause id="48669">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (u \ x)) = a(x,y,(u * z) \ x)
    ]]></literal>
    <justification jstring="[para(10(a,1),48668(a,1,1))].">
      <j1 rule="para" parents="10 48668"/>
    </justification>
  </clause>

  <clause id="48670">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ 1) * ((z \ u) \ x)) = a(x,y,(z * z) * (u \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,27771,a(flip),b,48669,a),flip(a)].">
      <j1 rule="hyper" parents="373 27771 48669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48671">
    <literal><![CDATA[
      a(x,y,(z * z) * (u \ x)) = a(x,y,z * ((z \ u) \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,27387,a(flip),b,48670,a),flip(a)].">
      <j1 rule="hyper" parents="64 27387 48670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48673">
    <literal><![CDATA[
      a(x * (y * L(z,y,y)),u,L(y,z,x * a(y,y,z))) = a((z \ (a(y,y,z) \ x)) * y,u,y)
    ]]></literal>
    <justification jstring="[para(42468(a,1),48666(a,1,3))].">
      <j1 rule="para" parents="42468 48666"/>
    </justification>
  </clause>

  <clause id="48674">
    <literal><![CDATA[
      a(x * (y * L(z,y,y)),u,L(y,z,x)) = a((z \ (a(y,y,z) \ x)) * y,u,y)
    ]]></literal>
    <justification jstring="[para(48342(a,1),48673(a,1,3))].">
      <j1 rule="para" parents="48342 48673"/>
    </justification>
  </clause>

  <clause id="48675">
    <literal><![CDATA[
      a((x \ (a(y,y,x) \ z)) * y,u,y) = a((y \ x) * z,u,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,32823,a(flip),b,48674,a),flip(a)].">
      <j1 rule="hyper" parents="64 32823 48674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48676">
    <literal><![CDATA[
      a((x \ y) * (a(z,z,x) \ z),u,z) = a((z \ x) * y,u,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(37723(a,1),48675(a,1,1))].">
      <j1 rule="para" parents="37723 48675"/>
    </justification>
  </clause>

  <clause id="48677">
    <literal><![CDATA[
      a(((x \ ((1 / x) \ y)) \ z) * x,u,x) = a((x \ y) * z,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(45947(a,2),48675(a,1,1,1))].">
      <j1 rule="para" parents="45947 48675"/>
    </justification>
  </clause>

  <clause id="48678">
    <literal><![CDATA[
      a((x \ y) * (a(z,z,x) * z),u,z) = a((z \ x) * y,u,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42511,a(flip),b,48676,a)].">
      <j1 rule="hyper" parents="64 42511 48676"/>
    </justification>
  </clause>

  <clause id="48679">
    <literal><![CDATA[
      a((x \ y) * R(z,z,x),u,z) = a((z \ x) * y,u,L(z,x,y))
    ]]></literal>
    <justification jstring="[para(30053(a,1),48678(a,1,1,2))].">
      <j1 rule="para" parents="30053 48678"/>
    </justification>
  </clause>

  <clause id="48680">
    <literal><![CDATA[
      a((x \ y) * L(z,z,x),u,z) = a((z \ x) * y,u,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,34635,a(flip),b,48679,a)].">
      <j1 rule="hyper" parents="64 34635 48679"/>
    </justification>
  </clause>

  <clause id="48681">
    <literal><![CDATA[
      ((a(x,y,y) \ z) / u) * a(y,y,a(x,(a(x,y,y) \ z) / u,u)) = a(x,y,y) \ (z / u)
    ]]></literal>
    <justification jstring="[hyper(373,a,43429,a(flip),b,46951,a),flip(a)].">
      <j1 rule="hyper" parents="373 43429 46951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48682">
    <literal><![CDATA[
      ((a(x,y,y) \ z) / u) * a(y,y,a(x,u \ (a(x,y,y) \ z),u)) = a(x,y,y) \ (z / u)
    ]]></literal>
    <justification jstring="[para(25642(a,1),48681(a,1,2,3))].">
      <j1 rule="para" parents="25642 48681"/>
    </justification>
  </clause>

  <clause id="48683">
    <literal><![CDATA[
      ((a(x,y,y) \ z) / u) * a(y,y,a(x,u * (a(x,y,y) \ z),u)) = a(x,y,y) \ (z / u)
    ]]></literal>
    <justification jstring="[para(35684(a,1),48682(a,1,2,3))].">
      <j1 rule="para" parents="35684 48682"/>
    </justification>
  </clause>

  <clause id="48684">
    <literal><![CDATA[
      ((a(x,y,y) \ z) / u) * a(y,y,a(x,u * (a(x,y,y) * z),u)) = a(x,y,y) \ (z / u)
    ]]></literal>
    <justification jstring="[para(42536(a,1),48683(a,1,2,3))].">
      <j1 rule="para" parents="42536 48683"/>
    </justification>
  </clause>

  <clause id="48685">
    <literal><![CDATA[
      ((a(x,y,y) \ z) / u) * a(u,y,a(x,a(x,y,y) * z,y)) = a(x,y,y) \ (z / u)
    ]]></literal>
    <justification jstring="[para(46890(a,1),48684(a,1,2))].">
      <j1 rule="para" parents="46890 48684"/>
    </justification>
  </clause>

  <clause id="48686">
    <literal><![CDATA[
      ((a(x,y,y) \ z) / u) * a(y,y,a(u,z,x)) = a(x,y,y) \ (z / u)
    ]]></literal>
    <justification jstring="[para(47504(a,1),48685(a,1,2))].">
      <j1 rule="para" parents="47504 48685"/>
    </justification>
  </clause>

  <clause id="48687">
    <literal><![CDATA[
      (a(x,y,y) \ z) / L(u,y,a(y,z,x)) = a(x,y,y) \ (z / u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46797,a(flip),b,48686,a)].">
      <j1 rule="hyper" parents="64 46797 48686"/>
    </justification>
  </clause>

  <clause id="48688">
    <literal><![CDATA[
      (a(x,y,y) \ (z / u)) \ ((a(x,y,y) \ z) * (1 / L(u,y,a(y,z,x)))) = a(a(x,y,y) \ z,L(u,y,a(y,z,x)),L(u,y,a(y,z,x)))
    ]]></literal>
    <justification jstring="[para(48687(a,1),30536(a,1,1))].">
      <j1 rule="para" parents="48687 30536"/>
    </justification>
  </clause>

  <clause id="48689">
    <literal><![CDATA[
      1 * L(x,y,L(a(z,u,a(w,w,v5)),x,v6)) = L(x,y,a(v5,w,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(45821(a,1),47081(a,1,1))].">
      <j1 rule="para" parents="45821 47081"/>
    </justification>
  </clause>

  <clause id="48691">
    <literal><![CDATA[
      1 * L(x,y,a(z,u,a(w,w,L(v5,x,v6)))) = L(x,y,a(v5,w,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(46567(a,2),48689(a,1,2,3))].">
      <j1 rule="para" parents="46567 48689"/>
    </justification>
  </clause>

  <clause id="48692">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,w,L(v5,x,v6)))) = L(x,y,a(v5,w,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(147,a,48691,a)].">
      <j1 rule="hyper" parents="147 48691"/>
    </justification>
  </clause>

  <clause id="48693">
    <literal><![CDATA[
      L(x,y,a(z,u,a(L(w,x,v5),v6,y))) = L(x,v6,a(w,y,a(z,u,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47520,a,b,48692,a)].">
      <j1 rule="hyper" parents="64 47520 48692"/>
    </justification>
  </clause>

  <clause id="48694">
    <literal><![CDATA[
      1 * L(x,y,L(a(z,u,a(y,w,v5)),x,v6)) = L(x,y,a(z,u,a(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(45520(a,1),47514(a,1,1))].">
      <j1 rule="para" parents="45520 47514"/>
    </justification>
  </clause>

  <clause id="48695">
    <literal><![CDATA[
      1 * L(x,y,a(z,u,a(y,w,L(v5,x,v6)))) = L(x,y,a(z,u,a(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(46567(a,2),48694(a,1,2,3))].">
      <j1 rule="para" parents="46567 48694"/>
    </justification>
  </clause>

  <clause id="48696">
    <literal><![CDATA[
      L(x,y,a(z,u,a(y,w,L(v5,x,v6)))) = L(x,y,a(z,u,a(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(147,a,48695,a)].">
      <j1 rule="hyper" parents="147 48695"/>
    </justification>
  </clause>

  <clause id="48697">
    <literal><![CDATA[
      L(x,y,a(y,z,a(u,w,L(v5,x,v6)))) = L(x,y,a(v5,w,a(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47508,a,b,48696,a)].">
      <j1 rule="hyper" parents="64 47508 48696"/>
    </justification>
  </clause>

  <clause id="48698">
    <literal><![CDATA[
      L(x,y,a(a(y,x * z,u),w,L(v5,x,v6))) = L(x,y,a(u,w,a(y,z,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,48030,a,b,48697,a)].">
      <j1 rule="hyper" parents="64 48030 48697"/>
    </justification>
  </clause>

  <clause id="48700">
    <literal><![CDATA[
      L(x,y,a(z,x * u,a(L(w,x,v5),v6,y))) = L(x,y,a(z,v6,a(y,u,w)))
    ]]></literal>
    <justification jstring="[para(47254(a,1),48698(a,1,3))].">
      <j1 rule="para" parents="47254 48698"/>
    </justification>
  </clause>

  <clause id="48701">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,x * v5,u))) = L(x,u,a(w,y,a(u,v5,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,48693,a(flip),b,48700,a)].">
      <j1 rule="hyper" parents="64 48693 48700"/>
    </justification>
  </clause>

  <clause id="48702">
    <literal><![CDATA[
      (R(x,y,y) * y) \ (((x * y) * y) * L(a(x,y,y),z,u)) = y * a(y * L(y,y,R(x,y,y)),z,u)
    ]]></literal>
    <justification jstring="[para(31176(a,1),47910(a,1,2,2,1))].">
      <j1 rule="para" parents="31176 47910"/>
    </justification>
  </clause>

  <clause id="48703">
    <literal><![CDATA[
      (R(x,y,y) * y) \ (((x * y) * y) * a(L(x,z,u),y,y)) = y * a(y * L(y,y,R(x,y,y)),z,u)
    ]]></literal>
    <justification jstring="[para(32607(a,2),48702(a,1,2,2))].">
      <j1 rule="para" parents="32607 48702"/>
    </justification>
  </clause>

  <clause id="48704">
    <literal><![CDATA[
      (R(x,y,y) * y) \ ((x * y) * (a(L(x,z,u),y,y) * y)) = y * a(y * L(y,y,R(x,y,y)),z,u)
    ]]></literal>
    <justification jstring="[para(37522(a,1),48703(a,1,2))].">
      <j1 rule="para" parents="37522 48703"/>
    </justification>
  </clause>

  <clause id="48705">
    <literal><![CDATA[
      (x * (1 / y)) \ ((x / y) * (a(L(x,z,u),y,y) * y)) = y * a(y * L(y,y,R(x,y,y)),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,43665,a(flip),b,48704,a)].">
      <j1 rule="hyper" parents="64 43665 48704"/>
    </justification>
  </clause>

  <clause id="48706">
    <literal><![CDATA[
      (x * (1 / y)) \ (a(L(x,z,u),y,y) * x) = y * a(y * L(y,y,R(x,y,y)),z,u)
    ]]></literal>
    <justification jstring="[para(37714(a,1),48705(a,1,2))].">
      <j1 rule="para" parents="37714 48705"/>
    </justification>
  </clause>

  <clause id="48707">
    <literal><![CDATA[
      (x * (1 / y)) \ (a(L(x,z,u),y,y) * x) = y * a(y * L(y,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(16076(a,1),48706(a,2,2,1,2))].">
      <j1 rule="para" parents="16076 48706"/>
    </justification>
  </clause>

  <clause id="48708">
    <literal><![CDATA[
      (x * (1 / y)) \ (a(L(x,z,u),y,y) * x) = y * a(a(x,y,y),z,u)
    ]]></literal>
    <justification jstring="[para(30478(a,1),48707(a,2,2))].">
      <j1 rule="para" parents="30478 48707"/>
    </justification>
  </clause>

  <clause id="48709">
    <literal><![CDATA[
      (x * (1 / y)) \ (a(L(x,z,u),y,y) * x) = L(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,41601,a,b,48708,a),flip(a)].">
      <j1 rule="hyper" parents="373 41601 48708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48710">
    <literal><![CDATA[
      (x * (1 / y)) \ (a(x,y,L(y,z,u)) * x) = L(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(44005(a,1),48709(a,1,2,1))].">
      <j1 rule="para" parents="44005 48709"/>
    </justification>
  </clause>

  <clause id="48711">
    <literal><![CDATA[
      (x * (1 / y)) \ R(x,y,L(y,z,u)) = L(y,y * L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(38381(a,1),48710(a,1,2))].">
      <j1 rule="para" parents="38381 48710"/>
    </justification>
  </clause>

  <clause id="48712">
    <literal><![CDATA[
      (x * (1 / y)) \ R(x,y,L(y,z,u)) = L(y,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,43940,a(flip),b,48711,a),flip(a)].">
      <j1 rule="hyper" parents="373 43940 48711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48713">
    <literal><![CDATA[
      (x * (1 / y)) \ R(x,y,L(y,z,u)) = L(y,y,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,46017,a(flip),b,48712,a),flip(a)].">
      <j1 rule="hyper" parents="373 46017 48712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48714">
    <literal><![CDATA[
      (x \ y) * a(z,z,L(u,x \ y,T(y,x \ 1) * (x \ y))) = (y \ (x \ y)) * T(y * a(z,z,u),x \ 1)
    ]]></literal>
    <justification jstring="[para(28753(a,2),48059(a,2,2))].">
      <j1 rule="para" parents="28753 48059"/>
    </justification>
  </clause>

  <clause id="48715">
    <literal><![CDATA[
      L(L(x,y,a(z,z,u)),L(y,a(z,z,u),a(z,z,u)),z * u) = L(x,a(z,z,u) * y,z \ u)
    ]]></literal>
    <justification jstring="[para(42852(a,1),48589(a,1,1))].">
      <j1 rule="para" parents="42852 48589"/>
    </justification>
  </clause>

  <clause id="48716">
    <literal><![CDATA[
      L(L(x,y,a(z,z,u)),y,z * u) = L(x,a(z,z,u) * y,z \ u)
    ]]></literal>
    <justification jstring="[para(37811(a,1),48715(a,1,2))].">
      <j1 rule="para" parents="37811 48715"/>
    </justification>
  </clause>

  <clause id="48717">
    <literal><![CDATA[
      L(x,a(y,y,z) * u,y \ z) = L(x,u,y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47535,a(flip),b,48716,a),flip(a)].">
      <j1 rule="hyper" parents="64 47535 48716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48718">
    <literal><![CDATA[
      L(x,a(y,z,z) * u,z \ y) = L(x,u,z \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31056,a,b,48717,a)].">
      <j1 rule="hyper" parents="64 31056 48717"/>
    </justification>
  </clause>

  <clause id="48719">
    <literal><![CDATA[
      x * L(y,a(z,u,u) * ((u \ z) * x),u \ z) = (u \ z) * (((u \ z) \ x) * y)
    ]]></literal>
    <justification jstring="[para(48718(a,2),41721(a,1,2))].">
      <j1 rule="para" parents="48718 41721"/>
    </justification>
  </clause>

  <clause id="48721">
    <literal><![CDATA[
      x * L(y,(z \ R(u,z,z)) * x,z \ u) = (z \ u) * (((z \ u) \ x) * y)
    ]]></literal>
    <justification jstring="[para(46352(a,1),48719(a,1,2,2))].">
      <j1 rule="para" parents="46352 48719"/>
    </justification>
  </clause>

  <clause id="48722">
    <literal><![CDATA[
      x * L(y,(z \ L(u,z,z)) * x,z \ u) = (z \ u) * (((z \ u) \ x) * y)
    ]]></literal>
    <justification jstring="[para(35320(a,1),48721(a,1,2))].">
      <j1 rule="para" parents="35320 48721"/>
    </justification>
  </clause>

  <clause id="48723">
    <literal><![CDATA[
      x * L(y,((z \ 1) * u) * x,z \ u) = (z \ u) * (((z \ u) \ x) * y)
    ]]></literal>
    <justification jstring="[para(1148(a,1),48722(a,1,2,2,1))].">
      <j1 rule="para" parents="1148 48722"/>
    </justification>
  </clause>

  <clause id="48724">
    <literal><![CDATA[
      x * L(y,(z * u) * x,z \ u) = (z \ u) * (((z \ u) \ x) * y)
    ]]></literal>
    <justification jstring="[para(11918(a,1),48723(a,1,2))].">
      <j1 rule="para" parents="11918 48723"/>
    </justification>
  </clause>

  <clause id="48725">
    <literal><![CDATA[
      (x \ y) * a(z,z,L(u,x \ y,(x \ y) * y)) = (y \ (x \ y)) * T(y * a(z,z,u),x \ 1)
    ]]></literal>
    <justification jstring="[para(29039(a,1),48714(a,1,2,3))].">
      <j1 rule="para" parents="29039 48714"/>
    </justification>
  </clause>

  <clause id="48727">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x * a(z,z,u),y \ 1) = (y \ x) * a(z,z,L(u,y * x,y))
    ]]></literal>
    <justification jstring="[para(42021(a,1),48725(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="42021 48725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48728">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x * a(z,z,u),y \ 1) = (y \ x) * a(z,z,L(u,x,y))
    ]]></literal>
    <justification jstring="[para(46930(a,1),48727(a,2,2))].">
      <j1 rule="para" parents="46930 48727"/>
    </justification>
  </clause>

  <clause id="48729">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x * a(z,z,u),y \ 1) = y \ (x * a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,48064,a(flip),b,48728,a),flip(a)].">
      <j1 rule="hyper" parents="373 48064 48728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48730">
    <literal><![CDATA[
      ((x \ y) / y) * (y * a(z,u,a(w,w,v5))) = x \ (y * a(w,w,a(z,u,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,48246,a(flip),b,48729,a)].">
      <j1 rule="hyper" parents="64 48246 48729"/>
    </justification>
  </clause>

  <clause id="48731">
    <literal><![CDATA[
      x \ (y * a(z,z,a(u,y,w))) = a(u,z,a(z,y,w)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,48461,a(flip),b,48730,a),flip(a)].">
      <j1 rule="hyper" parents="64 48461 48730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48732">
    <literal><![CDATA[
      x \ (y * a(z,y,a(u,z,w))) = a(u,z,a(z,y,w)) * (x \ y)
    ]]></literal>
    <justification jstring="[para(47231(a,2),48731(a,1,2,2))].">
      <j1 rule="para" parents="47231 48731"/>
    </justification>
  </clause>

  <clause id="48733">
    <literal><![CDATA[
      T(x,y) \ (a(z,u,a(u,x * y,w)) * (y \ (x * y))) = x \ (y \ ((y * x) * a(z,x * y,a(u,u,w))))
    ]]></literal>
    <justification jstring="[para(48731(a,1),46375(a,1,2))].">
      <j1 rule="para" parents="48731 46375"/>
    </justification>
  </clause>

  <clause id="48734">
    <literal><![CDATA[
      T(x,y) \ (a(z,u,a(u,x * y,w)) * T(x,y)) = x \ (y \ ((y * x) * a(z,x * y,a(u,u,w))))
    ]]></literal>
    <justification jstring="[para(22(a,2),48733(a,1,2,2))].">
      <j1 rule="para" parents="22 48733"/>
    </justification>
  </clause>

  <clause id="48735">
    <literal><![CDATA[
      x \ (y \ ((y * x) * a(z,x * y,a(u,u,w)))) = a(z,u,a(u,x * y,w))
    ]]></literal>
    <justification jstring="[hyper(23178,a,48734,a),flip(a)].">
      <j1 rule="hyper" parents="23178 48734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48737">
    <literal><![CDATA[
      a(x,y * z,L(a(u,u,w),y,z)) = a(x,u,a(u,y * z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46505,a(flip),b,48735,a)].">
      <j1 rule="hyper" parents="64 46505 48735"/>
    </justification>
  </clause>

  <clause id="48738">
    <literal><![CDATA[
      a(x,y * z,a(u,u,L(w,y,z))) = a(x,u,a(u,y * z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46631,a,b,48737,a)].">
      <j1 rule="hyper" parents="64 46631 48737"/>
    </justification>
  </clause>

  <clause id="48739">
    <literal><![CDATA[
      a(x,y,a(z,u * w,L(y,u,w))) = a(x,y,a(y,u * w,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46626,a,b,48738,a)].">
      <j1 rule="hyper" parents="64 46626 48738"/>
    </justification>
  </clause>

  <clause id="48740">
    <literal><![CDATA[
      a(x,y,a(z,u * w,L(y,w,u))) = a(x,y,a(y,w * u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,32311,a,b,48739,a)].">
      <j1 rule="hyper" parents="64 32311 48739"/>
    </justification>
  </clause>

  <clause id="48741">
    <literal><![CDATA[
      a(x,(y * z) * u,a(w,w,L(y,z,u))) = a(y,w,a(w,z * u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,48476,a,b,48740,a)].">
      <j1 rule="hyper" parents="64 48476 48740"/>
    </justification>
  </clause>

  <clause id="48742">
    <literal><![CDATA[
      a(T(x,y * y) * ((1 / y) \ z),T(x,y * y),y \ 1) = a(z * (((y * y) \ x) * y),T(x,y * y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(27586,a,46277,a)].">
      <j1 rule="hyper" parents="27586 46277"/>
    </justification>
  </clause>

  <clause id="48743">
    <literal><![CDATA[
      L(x * a((y \ x) * x,z,u),z,a((x / y) * x,(x / y) * x,u)) = R((x / y) * x,z,u) * T(y / x,y)
    ]]></literal>
    <justification jstring="[para(32367(a,1),46801(a,1,1,2))].">
      <j1 rule="para" parents="32367 46801"/>
    </justification>
  </clause>

  <clause id="48744">
    <literal><![CDATA[
      a((x * (K(y \ 1,y) * z)) * (y \ K(u,y)),w,y \ K(u,y)) = a(z * ((1 / T(y,u)) / x),w,y \ K(u,y))
    ]]></literal>
    <justification jstring="[para(5079(a,1),46856(a,1,1,1))].">
      <j1 rule="para" parents="5079 46856"/>
    </justification>
  </clause>

  <clause id="48745">
    <literal><![CDATA[
      a(x,y,(z * a(u,w,v5)) \ (v6 * (u \ L(R(u,w,v5),w,v5)))) = a(x,y,(a(v5,w,u) * z) \ v6)
    ]]></literal>
    <justification jstring="[para(42209(a,1),47041(a,1,3)),flip(a)].">
      <j1 rule="para" parents="42209 47041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48746">
    <literal><![CDATA[
      L(x,(R(T(y,z),u,w) * (y \ (v5 * v5))) * v6,v7) = L(x,(K(v8,v9) * (a(y,u,w) \ K(z,y))) * v6,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,33851,a(flip),b,47155,a)].">
      <j1 rule="hyper" parents="64 33851 47155"/>
    </justification>
  </clause>

  <clause id="48748">
    <literal><![CDATA[
      L(x,(T(y,z) * R(y \ (u * u),w,v5)) * v6,v7) = L(x,(K(v8,v9) * (a(y,w,v5) \ K(z,y))) * v6,v7)
    ]]></literal>
    <justification jstring="[para(27947(a,1),48746(a,1,2,1))].">
      <j1 rule="para" parents="27947 48746"/>
    </justification>
  </clause>

  <clause id="48749">
    <literal><![CDATA[
      L(x,(T(y,z) * L(y \ (u * u),w,v5)) * v6,v7) = L(x,(K(v8,v9) * (a(y,w,v5) \ K(z,y))) * v6,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,36280,a(flip),b,48748,a)].">
      <j1 rule="hyper" parents="64 36280 48748"/>
    </justification>
  </clause>

  <clause id="48750">
    <literal><![CDATA[
      L(x,(K(y,z) * (a(u,w,v5) \ K(v6,u))) * v7,v8) = L(x,(u * L(u \ (v9 * v9),w,v5)) * v7,v8)
    ]]></literal>
    <justification jstring="[hyper(64,a,29457,a(flip),b,48749,a),flip(a)].">
      <j1 rule="hyper" parents="64 29457 48749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48752">
    <literal><![CDATA[
      L(x,(a(y,z,u) \ K(w,v5)) * (K(v6,y) * v7),v8) = L(x,(y * L(y \ (v9 * v9),z,u)) * v7,v8)
    ]]></literal>
    <justification jstring="[para(42555(a,1),48750(a,1,2))].">
      <j1 rule="para" parents="42555 48750"/>
    </justification>
  </clause>

  <clause id="48753">
    <literal><![CDATA[
      L(x,K(y,z) * (a(u,w,v5) \ (K(v6,u) * v7)),v8) = L(x,(u * L(u \ (v9 * v9),w,v5)) * v7,v8)
    ]]></literal>
    <justification jstring="[para(42510(a,1),48752(a,1,2))].">
      <j1 rule="para" parents="42510 48752"/>
    </justification>
  </clause>

  <clause id="48754">
    <literal><![CDATA[
      L(x,K(y,z) * (a(u,w,v5) \ v6),v7) = L(x,(u * L(u \ (v8 * v8),w,v5)) * v6,v7)
    ]]></literal>
    <justification jstring="[para(23126(a,1),48753(a,1,2,2,2))].">
      <j1 rule="para" parents="23126 48753"/>
    </justification>
  </clause>

  <clause id="48756">
    <literal><![CDATA[
      L(x,K(y,z) * (a(u,w,v5) * v6),v7) = L(x,(u * L(u \ (v8 * v8),w,v5)) * v6,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,42532,a(flip),b,48754,a)].">
      <j1 rule="hyper" parents="64 42532 48754"/>
    </justification>
  </clause>

  <clause id="48757">
    <literal><![CDATA[
      L(x,(y * L(y \ (z * z),u,w)) * v5,v6) = L(x,a(y,u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(29576,a,48756,a),flip(a)].">
      <j1 rule="hyper" parents="29576 48756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48758">
    <literal><![CDATA[
      L(x,y * a(z,u,w \ (v5 * v5)),v6) = L(x,a(w,u,z) * y,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,48245,a(flip),b,48757,a)].">
      <j1 rule="hyper" parents="64 48245 48757"/>
    </justification>
  </clause>

  <clause id="48760">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,v5) = L(x,w * a(u,z,y),v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),48758(a,1,2,2,3)),flip(a)].">
      <j1 rule="para" parents="9 48758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48764">
    <literal><![CDATA[
      a(x,y,z * L(L(u \ 1,w * z,w),u,(w * z) * u)) = a(x,y,(z / T(z * w,w)) * ((w * z) / u))
    ]]></literal>
    <justification jstring="[para(47088(a,1),47665(a,2,3))].">
      <j1 rule="para" parents="47088 47665"/>
    </justification>
  </clause>

  <clause id="48765">
    <literal><![CDATA[
      a(x,y,z * L(L(u \ 1,w * z,w),u,(w * z) * u)) = a(x,y,(z / T(z * w,w)) * (u \ (w * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27310,a(flip),b,48764,a),flip(a)].">
      <j1 rule="hyper" parents="373 27310 48764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48766">
    <literal><![CDATA[
      a(x,y,z * L(L(u \ 1,w * z,w),u,(w * z) * u)) = a(x,y,(T(z * w,w) \ z) * (u \ (w * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27317,a(flip),b,48765,a),flip(a)].">
      <j1 rule="hyper" parents="373 27317 48765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48767">
    <literal><![CDATA[
      a(x,y,z * L(L(u \ 1,w * z,w),u,(w * z) * u)) = a(x,y,((z * w) \ z) * (u \ (w * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27401,a(flip),b,48766,a),flip(a)].">
      <j1 rule="hyper" parents="373 27401 48766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48769">
    <literal><![CDATA[
      a(x,y,z * L(L(u \ 1,w * z,w),u,(w * z) * u)) = a(x,y,(z \ (w \ z)) * (u \ (w * z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27721,a(flip),b,48767,a),flip(a)].">
      <j1 rule="hyper" parents="373 27721 48767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48770">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * (w \ (u * z))) = a(x,y,z * (z \ (u * ((u \ z) / w))))
    ]]></literal>
    <justification jstring="[para(47799(a,1),48769(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="47799 48769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48771">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * (w \ (u * z))) = a(x,y,u * ((u \ z) / w))
    ]]></literal>
    <justification jstring="[para(10(a,1),48770(a,2,3))].">
      <j1 rule="para" parents="10 48770"/>
    </justification>
  </clause>

  <clause id="48772">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * (w \ (u * z))) = a(x,y,u * (w \ (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27310,a(flip),b,48771,a),flip(a)].">
      <j1 rule="hyper" parents="373 27310 48771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48774">
    <literal><![CDATA[
      L(x * a(y * z,x,a(x,y,u)),x * a(a(x,y,u),x,y * z),w) = a(x,x,a(z * y,z,u)) \ L(x,x,w)
    ]]></literal>
    <justification jstring="[para(42047(a,1),47787(a,1,1))].">
      <j1 rule="para" parents="42047 47787"/>
    </justification>
  </clause>

  <clause id="48775">
    <literal><![CDATA[
      a(x * (((y * y) \ z) * y),T(z,y * y),1 / y) = a(T(z,y * y) * ((1 / y) \ x),z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(31997,a,48742,a),flip(a)].">
      <j1 rule="hyper" parents="31997 48742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48777">
    <literal><![CDATA[
      a(x * (((y * y) \ z) * y),T(z,y * y),1 / y) = a((y \ x) * T(z,y * y),z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,32812,a(flip),b,48775,a),flip(a)].">
      <j1 rule="hyper" parents="373 32812 48775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48778">
    <literal><![CDATA[
      a(x * (((y * y) \ z) * y),T(z,y * y),1 / y) = a((y \ x) * z,z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,32361,a(flip),b,48777,a),flip(a)].">
      <j1 rule="hyper" parents="373 32361 48777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48779">
    <literal><![CDATA[
      a(x * (((y * y) \ z) * y),T(z,y * y),y \ 1) = a((y \ x) * z,z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(27586,a,48778,a)].">
      <j1 rule="hyper" parents="27586 48778"/>
    </justification>
  </clause>

  <clause id="48781">
    <literal><![CDATA[
      a(x * (((y * y) \ z) * y),z,y \ 1) = a((y \ x) * z,z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(31997,a,48779,a)].">
      <j1 rule="hyper" parents="31997 48779"/>
    </justification>
  </clause>

  <clause id="48783">
    <literal><![CDATA[
      a((x \ y) * z,z,x \ 1) = a(y * (z * x),z,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,11959,a(flip),b,48781,a),flip(a)].">
      <j1 rule="hyper" parents="64 11959 48781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48785">
    <literal><![CDATA[
      a((x \ (x / y)) * ((x \ 1) \ z),x \ (x / y),x \ 1) = a(z * (y * x),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,48504,a,b,48783,a)].">
      <j1 rule="hyper" parents="64 48504 48783"/>
    </justification>
  </clause>

  <clause id="48786">
    <literal><![CDATA[
      a((x \ (x / y)) * ((x \ 1) \ z),x * (x / y),x \ 1) = a(z * (y * x),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,44889,a(flip),b,48785,a)].">
      <j1 rule="hyper" parents="64 44889 48785"/>
    </justification>
  </clause>

  <clause id="48787">
    <literal><![CDATA[
      a((x \ (x / y)) * ((x \ 1) \ z),x * (y \ x),x \ 1) = a(z * (y * x),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,31897,a(flip),b,48786,a)].">
      <j1 rule="hyper" parents="64 31897 48786"/>
    </justification>
  </clause>

  <clause id="48788">
    <literal><![CDATA[
      a((x \ (x / y)) * ((x \ 1) \ z),y,x \ 1) = a(z * (y * x),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,46414,a(flip),b,48787,a)].">
      <j1 rule="hyper" parents="64 46414 48787"/>
    </justification>
  </clause>

  <clause id="48789">
    <literal><![CDATA[
      a((x \ y) * (x \ (x / z)),z,x \ 1) = a(y * (z * x),z,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,32810,a(flip),b,48788,a)].">
      <j1 rule="hyper" parents="64 32810 48788"/>
    </justification>
  </clause>

  <clause id="48790">
    <literal><![CDATA[
      L(x * a((y \ x) * x,z,u),z,a((x / y) * x,(y \ x) * x,u)) = R((x / y) * x,z,u) * T(y / x,y)
    ]]></literal>
    <justification jstring="[para(31904(a,1),48743(a,1,3))].">
      <j1 rule="para" parents="31904 48743"/>
    </justification>
  </clause>

  <clause id="48791">
    <literal><![CDATA[
      a((x * y) * (K(z \ 1,z) * (z \ K(u,z))),w,z \ K(u,z)) = a(y * ((1 / T(z,u)) / x),w,z \ K(u,z))
    ]]></literal>
    <justification jstring="[para(5188(a,1),48744(a,1,1))].">
      <j1 rule="para" parents="5188 48744"/>
    </justification>
  </clause>

  <clause id="48792">
    <literal><![CDATA[
      L(L(x,y,a(y * z,x,u)),x * a(a(x,y,u),x,y * z),w) = a(x,x,a(z * y,z,u)) \ L(x,x,w)
    ]]></literal>
    <justification jstring="[para(47271(a,1),48774(a,1,1))].">
      <j1 rule="para" parents="47271 48774"/>
    </justification>
  </clause>

  <clause id="48793">
    <literal><![CDATA[
      L(L(x,y,a(y * z,x,u)),x * a(u,y,a(y * z,x,x)),w) = a(x,x,a(z * y,z,u)) \ L(x,x,w)
    ]]></literal>
    <justification jstring="[para(47254(a,1),48792(a,1,2,2))].">
      <j1 rule="para" parents="47254 48792"/>
    </justification>
  </clause>

  <clause id="48794">
    <literal><![CDATA[
      L(L(x,y,a(y * z,x,u)),L(x,y,a(y * z,x,u)),w) = a(x,x,a(z * y,z,u)) \ L(x,x,w)
    ]]></literal>
    <justification jstring="[para(47349(a,1),48793(a,1,2))].">
      <j1 rule="para" parents="47349 48793"/>
    </justification>
  </clause>

  <clause id="48795">
    <literal><![CDATA[
      L(L(x,y,a(y * z,x,u)),x,L(w,y,a(y * z,x,u))) = a(x,x,a(z * y,z,u)) \ L(x,x,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,44039,a(flip),b,48794,a)].">
      <j1 rule="hyper" parents="64 44039 48794"/>
    </justification>
  </clause>

  <clause id="48796">
    <literal><![CDATA[
      L(L(x,x,y),z,a(z * u,x,w)) = a(x,x,a(u * z,u,w)) \ L(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47444,a(flip),b,48795,a)].">
      <j1 rule="hyper" parents="64 47444 48795"/>
    </justification>
  </clause>

  <clause id="48797">
    <literal><![CDATA[
      L(L(x,x,y),z,a(z * u,x,w)) = L(a(x,x,a(u * z,u,w)) \ x,x,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,38658,a,b,48796,a),flip(a)].">
      <j1 rule="hyper" parents="373 38658 48796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48799">
    <literal><![CDATA[
      L(L(x,x,a(y,z,z * u)),x,w) = L(L(x,x,w),u,a(u * z,x,y))
    ]]></literal>
    <justification jstring="[para(41502(a,1),48797(a,2,1)),flip(a)].">
      <j1 rule="para" parents="41502 48797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48800">
    <literal><![CDATA[
      L(x * a((y \ x) * x,z,u),z,a((y \ x) * x,(y \ x) * x,u)) = R((x / y) * x,z,u) * T(y / x,y)
    ]]></literal>
    <justification jstring="[para(32367(a,1),48790(a,1,3))].">
      <j1 rule="para" parents="32367 48790"/>
    </justification>
  </clause>

  <clause id="48801">
    <literal><![CDATA[
      a((x * y) * (T(z,z \ 1) \ K(u,z)),w,z \ K(u,z)) = a(y * ((1 / T(z,u)) / x),w,z \ K(u,z))
    ]]></literal>
    <justification jstring="[para(6157(a,1),48791(a,1,1,2))].">
      <j1 rule="para" parents="6157 48791"/>
    </justification>
  </clause>

  <clause id="48802">
    <literal><![CDATA[
      a((x * y) * T(K(z,u) * (u \ 1),u),w,u \ K(z,u)) = a(y * ((1 / T(u,z)) / x),w,u \ K(z,u))
    ]]></literal>
    <justification jstring="[para(14767(a,2),48801(a,1,1,2))].">
      <j1 rule="para" parents="14767 48801"/>
    </justification>
  </clause>

  <clause id="48803">
    <literal><![CDATA[
      a((x * y) * T(T(z,u) \ 1,z),w,z \ K(u,z)) = a(y * ((1 / T(z,u)) / x),w,z \ K(u,z))
    ]]></literal>
    <justification jstring="[para(6157(a,1),48802(a,1,1,2,1))].">
      <j1 rule="para" parents="6157 48802"/>
    </justification>
  </clause>

  <clause id="48804">
    <literal><![CDATA[
      a((x * y) * T(T(z,u) \ 1,z),w,z \ 1) = a(y * ((1 / T(z,u)) / x),w,z \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27321,a(flip),b,48803,a)].">
      <j1 rule="hyper" parents="64 27321 48803"/>
    </justification>
  </clause>

  <clause id="48805">
    <literal><![CDATA[
      a(x * ((1 / T(y,z)) / u),w,y \ K(z,y)) = a((u * x) * (T(y,z) \ 1),w,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(32447,a,48804,a),flip(a)].">
      <j1 rule="hyper" parents="32447 48804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48808">
    <literal><![CDATA[
      a(x * ((1 / T(y,z)) / u),w,y \ K(z,y)) = a(T(y,z) * (u * x),w,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,26831,a(flip),b,48805,a),flip(a)].">
      <j1 rule="hyper" parents="373 26831 48805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48809">
    <literal><![CDATA[
      a(x * ((1 / T(y,z)) / u),w,y \ K(z,y)) = a(y * (u * x),w,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,32363,a(flip),b,48808,a),flip(a)].">
      <j1 rule="hyper" parents="373 32363 48808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48811">
    <literal><![CDATA[
      a(x * ((1 / T(y,z)) / u),w,y \ 1) = a(y * (u * x),w,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,27321,a(flip),b,48809,a)].">
      <j1 rule="hyper" parents="64 27321 48809"/>
    </justification>
  </clause>

  <clause id="48813">
    <literal><![CDATA[
      a(x * (y \ (1 / T(z,u))),w,z \ 1) = a(z * (y * x),w,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,32362,a(flip),b,48811,a)].">
      <j1 rule="hyper" parents="64 32362 48811"/>
    </justification>
  </clause>

  <clause id="48814">
    <literal><![CDATA[
      a(x * (y \ (T(z,u) \ 1)),w,z \ 1) = a(z * (y * x),w,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,32441,a(flip),b,48813,a)].">
      <j1 rule="hyper" parents="64 32441 48813"/>
    </justification>
  </clause>

  <clause id="48815">
    <literal><![CDATA[
      a((x \ T(y,z)) * u,w,y \ 1) = a(y * (x * u),w,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,32689,a(flip),b,48814,a)].">
      <j1 rule="hyper" parents="64 32689 48814"/>
    </justification>
  </clause>

  <clause id="48816">
    <literal><![CDATA[
      a((x \ y) * z,u,y \ 1) = a(y * (x * z),u,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(32583,a,48815,a)].">
      <j1 rule="hyper" parents="32583 48815"/>
    </justification>
  </clause>

  <clause id="48817">
    <literal><![CDATA[
      L(x * a((y \ x) * x,z,u),z,a(y,y,u)) = R((x / y) * x,z,u) * T(y / x,y)
    ]]></literal>
    <justification jstring="[para(38736(a,1),48800(a,1,3))].">
      <j1 rule="para" parents="38736 48800"/>
    </justification>
  </clause>

  <clause id="48818">
    <literal><![CDATA[
      L(x * a((y \ x) * x,z,u),z,a(y,y,u)) = (y / x) \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,44537,a(flip),b,48817,a),flip(a)].">
      <j1 rule="hyper" parents="373 44537 48817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48820">
    <literal><![CDATA[
      L(x * a((y \ x) * x,z,a(u,u,y * w)),z,a(y * w,u,a(y,w,u))) = (y / x) \ R(y,z,a(u,u,y * w))
    ]]></literal>
    <justification jstring="[para(46915(a,2),48818(a,1,3))].">
      <j1 rule="para" parents="46915 48818"/>
    </justification>
  </clause>

  <clause id="48821">
    <literal><![CDATA[
      a(x,y,L(z,(R(x,y,z) * y) * z,(L(x,y,z) * y) * z)) = ((a(x,y,z) / ((x * y) * z)) \ 1) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(33606(a,1),46666(a,1,3))].">
      <j1 rule="para" parents="33606 46666"/>
    </justification>
  </clause>

  <clause id="48822">
    <literal><![CDATA[
      a(x,y,z) * ((1 / L(u,u,x)) \ a(x,1 / L(u,u,x),a(L(u,u,x),y,z))) = (x * (1 / u)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2641(a,1),47152(a,1,2,2,3))].">
      <j1 rule="para" parents="2641 47152"/>
    </justification>
  </clause>

  <clause id="48823">
    <literal><![CDATA[
      a(x,y,z) * ((1 / L(u,u,x)) \ a(x,1 / L(u,u,x),a(u,y,L(z,u,x)))) = (x * (1 / u)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(46496(a,1),48822(a,1,2,2,3))].">
      <j1 rule="para" parents="46496 48822"/>
    </justification>
  </clause>

  <clause id="48824">
    <literal><![CDATA[
      a(x,y,z) * ((1 / L(u,u,x)) \ a(x,1 / L(u,u,x),a(u,y,z))) = (x * (1 / u)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(46565(a,1),48823(a,1,2,2))].">
      <j1 rule="para" parents="46565 48823"/>
    </justification>
  </clause>

  <clause id="48825">
    <literal><![CDATA[
      a(x,y,z) * ((1 / L(u,u,x)) \ a(x,L(u,u,x),a(u,y,z))) = (x * (1 / u)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(11966(a,1),48824(a,1,2,2))].">
      <j1 rule="para" parents="11966 48824"/>
    </justification>
  </clause>

  <clause id="48827">
    <literal><![CDATA[
      a(x,y,z) * ((1 / L(u,u,x)) \ a(x,u,a(u,y,z))) = (x * (1 / u)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(42780(a,1),48825(a,1,2,2))].">
      <j1 rule="para" parents="42780 48825"/>
    </justification>
  </clause>

  <clause id="48829">
    <literal><![CDATA[
      a(x,y,z) * (L(u,u,x) * a(x,y,a(u,u,z))) = (x * (1 / u)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(46965(a,1),48827(a,1,2))].">
      <j1 rule="para" parents="46965 48827"/>
    </justification>
  </clause>

  <clause id="48830">
    <literal><![CDATA[
      a(x,y,z) * L(L(u,u,a(z,y,x)),u,x) = (x * (1 / u)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(46952(a,1),48829(a,1,2))].">
      <j1 rule="para" parents="46952 48829"/>
    </justification>
  </clause>

  <clause id="48831">
    <literal><![CDATA[
      a(x,y,z) * L(u,u,L(x,y,z)) = (x * (1 / u)) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(46029(a,1),48830(a,1,2))].">
      <j1 rule="para" parents="46029 48830"/>
    </justification>
  </clause>

  <clause id="48832">
    <literal><![CDATA[
      L(x,a(y,z * a(u,z,w),z * a(u,z,w)),w) = L(x,a(y,z,z),z \ L(w,z,u))
    ]]></literal>
    <justification jstring="[para(44913(a,1),47747(a,1,2)),flip(a)].">
      <j1 rule="para" parents="44913 47747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48833">
    <literal><![CDATA[
      L(x,a(y,z * a(u,z,w),z * a(u,z,w)),w) = L(x,a(y,z,z),L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,47745,a(flip),b,48832,a),flip(a)].">
      <j1 rule="hyper" parents="373 47745 48832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48835">
    <literal><![CDATA[
      L(x,a(y,z,z),L(u,z,w)) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(44913(a,1),48833(a,1,2)),flip(a)].">
      <j1 rule="para" parents="44913 48833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48836">
    <literal><![CDATA[
      L(x,a(y,z,z),a(u,z,w)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,47493,a(flip),b,48835,a),flip(a)].">
      <j1 rule="hyper" parents="42 47493 48835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48846">
    <literal><![CDATA[
      (a(x,y,y) * a(z,y,u)) \ w = a(x,y,y) \ (a(z,y,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42175,a(flip),b,48836,a),flip(a)].">
      <j1 rule="hyper" parents="64 42175 48836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48850">
    <literal><![CDATA[
      (a(x,y,y) \ z) * a(u,y,w) = z * (a(x,y,y) \ a(u,y,w))
    ]]></literal>
    <justification jstring="[para(48836(a,1),42825(a,1,1)),flip(a)].">
      <j1 rule="para" parents="48836 42825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48854">
    <literal><![CDATA[
      a((x * (y * z)) \ (x * y),u,(x * (y * z)) \ ((x * y) * w)) = a(L(z,y,x),u,L(z,y,x) \ w)
    ]]></literal>
    <justification jstring="[para(18(a,2),47823(a,2,3,1))].">
      <j1 rule="para" parents="18 47823"/>
    </justification>
  </clause>

  <clause id="48855">
    <literal><![CDATA[
      a((x * (y * z)) \ (x * y),u,(x * (y * z)) \ ((x * y) * w)) = a(z,u,L(L(z,y,x) \ w,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,46496,a(flip),b,48854,a),flip(a)].">
      <j1 rule="hyper" parents="373 46496 48854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48856">
    <literal><![CDATA[
      a(x \ ((y * z) \ (x * y)),u,x \ ((y * z) \ ((x * y) * w))) = a(z,u,L(L(z,y,x) \ w,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47187,a(flip),b,48855,a)].">
      <j1 rule="hyper" parents="64 47187 48855"/>
    </justification>
  </clause>

  <clause id="48857">
    <literal><![CDATA[
      a((x * y) \ x,z,(x * y) \ (u \ ((u * x) * w))) = a(y,z,L(L(y,x,u) \ w,x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47908,a(flip),b,48856,a)].">
      <j1 rule="hyper" parents="64 47908 48856"/>
    </justification>
  </clause>

  <clause id="48858">
    <literal><![CDATA[
      a(x \ (y \ x),z,(x * y) \ (u \ ((u * x) * w))) = a(y,z,L(L(y,x,u) \ w,x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,32506,a(flip),b,48857,a)].">
      <j1 rule="hyper" parents="64 32506 48857"/>
    </justification>
  </clause>

  <clause id="48859">
    <literal><![CDATA[
      a(x,y,x \ (z \ (u \ ((u * z) * w)))) = a(x,y,L(L(x,z,u) \ w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46643,a(flip),b,48858,a)].">
      <j1 rule="hyper" parents="64 46643 48858"/>
    </justification>
  </clause>

  <clause id="48860">
    <literal><![CDATA[
      a(x,y,L(L(x,z,u) \ w,z,u)) = a(x,y,x \ L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,42118,a(flip),b,48859,a),flip(a)].">
      <j1 rule="hyper" parents="64 42118 48859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48861">
    <literal><![CDATA[
      a(x,y,x \ L((x \ 1) \ z,u,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,48022,a(flip),b,48860,a),flip(a)].">
      <j1 rule="hyper" parents="64 48022 48860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48862">
    <literal><![CDATA[
      a(x,y,x * L(x \ z,u,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47643,a(flip),b,48861,a)].">
      <j1 rule="hyper" parents="64 47643 48861"/>
    </justification>
  </clause>

  <clause id="48863">
    <literal><![CDATA[
      a(x,y,L(z,u,x * z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46826,a(flip),b,48862,a)].">
      <j1 rule="hyper" parents="64 46826 48862"/>
    </justification>
  </clause>

  <clause id="48865">
    <literal><![CDATA[
      a(x * y,z,a(x,u,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,48863,a(flip),b,47407,a),flip(a)].">
      <j1 rule="hyper" parents="140 48863 47407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48866">
    <literal><![CDATA[
      a(x * y,z,a(x,u,y)) = w \ w
    ]]></literal>
    <justification jstring="[hyper(373,a,68,a,b,48865,a),flip(a)].">
      <j1 rule="hyper" parents="373 68 48865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48867">
    <literal><![CDATA[
      R(x,y,L(z,u,x * z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,46723,a,b,48866,a(flip))].">
      <j1 rule="hyper" parents="40 46723 48866"/>
    </justification>
  </clause>

  <clause id="48871">
    <literal><![CDATA[
      L(x * a(y,z,a(y * u,w,z)),w,a(y * u,z,a(y,u,z))) = (y / x) \ R(y,w,a(z,z,y * u))
    ]]></literal>
    <justification jstring="[para(46421(a,1),48820(a,1,1,2))].">
      <j1 rule="para" parents="46421 48820"/>
    </justification>
  </clause>

  <clause id="48872">
    <literal><![CDATA[
      L(x * a(y,z,a(y * u,w,z)),w,a(y,u,a(y * u,z,z))) = (y / x) \ R(y,w,a(z,z,y * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47286,a,b,48871,a)].">
      <j1 rule="hyper" parents="64 47286 48871"/>
    </justification>
  </clause>

  <clause id="48874">
    <literal><![CDATA[
      L(x * a(y,z,a(y * u,w,z)),w,a(u,u,a(y,z,z))) = (y / x) \ R(y,w,a(z,z,y * u))
    ]]></literal>
    <justification jstring="[para(44159(a,1),48872(a,1,3))].">
      <j1 rule="para" parents="44159 48872"/>
    </justification>
  </clause>

  <clause id="48875">
    <literal><![CDATA[
      (x / y) \ R(x,z,a(u,u,x * w)) = y * a(x,u,a(x * w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,45032,a(flip),b,48874,a),flip(a)].">
      <j1 rule="hyper" parents="64 45032 48874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48877">
    <literal><![CDATA[
      (x / y) \ L(x,z,a(u,u,x * w)) = y * a(x,u,a(x * w,z,u))
    ]]></literal>
    <justification jstring="[para(28832(a,1),48875(a,1,2))].">
      <j1 rule="para" parents="28832 48875"/>
    </justification>
  </clause>

  <clause id="48878">
    <literal><![CDATA[
      (x / y) \ L(x,z,a(u,w,w)) = y * a(x,w,a(x * u,z,w))
    ]]></literal>
    <justification jstring="[para(48196(a,1),48877(a,1,2))].">
      <j1 rule="para" parents="48196 48877"/>
    </justification>
  </clause>

  <clause id="48879">
    <literal><![CDATA[
      x * a(y,z,a(y * u,w,z)) = x * a(u,z,a(y,w,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47046,a(flip),b,48878,a),flip(a)].">
      <j1 rule="hyper" parents="64 47046 48878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48880">
    <literal><![CDATA[
      a(x,y,a(z,z,x * u)) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(36,a,45912,a(flip),b,48879,a),flip(a)].">
      <j1 rule="hyper" parents="36 45912 48879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48881">
    <literal><![CDATA[
      a(x,y,a(z,z,u * (x * w))) = a(w * u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,48585,a,b,48880,a)].">
      <j1 rule="hyper" parents="64 48585 48880"/>
    </justification>
  </clause>

  <clause id="48882">
    <literal><![CDATA[
      a(x,y,a(z,z,u * x)) = a(u,z,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27752,a,b,48880,a)].">
      <j1 rule="hyper" parents="64 27752 48880"/>
    </justification>
  </clause>

  <clause id="48883">
    <literal><![CDATA[
      a(x,y,a(z,z,u * x)) = a(u,y,a(z,z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47298,a,b,48882,a),flip(a)].">
      <j1 rule="hyper" parents="373 47298 48882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48884">
    <literal><![CDATA[
      a(x,x,a(y * z,u,z)) = a(y,u,a(x,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47198,a,b,48883,a)].">
      <j1 rule="hyper" parents="64 47198 48883"/>
    </justification>
  </clause>

  <clause id="48885">
    <literal><![CDATA[
      a(x,y,a(z,u,a(y,w,v5 * z))) = a(x,w,a(v5,u,a(y,y,z)))
    ]]></literal>
    <justification jstring="[para(48884(a,1),47270(a,2,3))].">
      <j1 rule="para" parents="48884 47270"/>
    </justification>
  </clause>

  <clause id="48886">
    <literal><![CDATA[
      a(x * y,z,a(u,w,z)) * a(z,z,u) = a(z,z,L(u,w,y * (u * x)))
    ]]></literal>
    <justification jstring="[para(48881(a,1),47350(a,1,1))].">
      <j1 rule="para" parents="48881 47350"/>
    </justification>
  </clause>

  <clause id="48887">
    <literal><![CDATA[
      a(x * y,z,a(u,w,z)) * a(u,z,z) = a(u,z,L(z,w,y * (u * x)))
    ]]></literal>
    <justification jstring="[para(48881(a,1),47351(a,1,1))].">
      <j1 rule="para" parents="48881 47351"/>
    </justification>
  </clause>

  <clause id="48888">
    <literal><![CDATA[
      L(x * a(y * z,u,a(w,x,u)),z * (w * y),a(u,u,w)) = L(x,a(u,u,w),z * (w * y))
    ]]></literal>
    <justification jstring="[para(48881(a,1),47383(a,1,1,2))].">
      <j1 rule="para" parents="48881 47383"/>
    </justification>
  </clause>

  <clause id="48889">
    <literal><![CDATA[
      a(x,x,L(y,z,u * (y * w))) = a(x,x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47408,a(flip),b,48886,a),flip(a)].">
      <j1 rule="hyper" parents="64 47408 48886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48890">
    <literal><![CDATA[
      a(x,x,L(y,z,y * u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11774(a,1),48889(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11774 48889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48892">
    <literal><![CDATA[
      a(x,y,L(y,z,x * u)) * a(w,v5,a(y,y,L(x,z,u))) = a(x,y,L(L(y,z,x * u),v5,w))
    ]]></literal>
    <justification jstring="[para(48890(a,1),46708(a,1,2,3))].">
      <j1 rule="para" parents="48890 46708"/>
    </justification>
  </clause>

  <clause id="48893">
    <literal><![CDATA[
      a(x,y,L(y,z,u * (x * w))) = a(x,y,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47407,a(flip),b,48887,a),flip(a)].">
      <j1 rule="hyper" parents="64 47407 48887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48894">
    <literal><![CDATA[
      a(x,y,L(y,z,x * u)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11774(a,1),48893(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11774 48893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48895">
    <literal><![CDATA[
      a(x,y,L(y,z,u)) * a(w,v5,a(y,y,L(x,z,u))) = a(x,y,L(L(y,z,x * u),v5,w))
    ]]></literal>
    <justification jstring="[para(48894(a,1),48892(a,1,1))].">
      <j1 rule="para" parents="48894 48892"/>
    </justification>
  </clause>

  <clause id="48896">
    <literal><![CDATA[
      a(x,y,L(L(y,z,x * u),w,v5)) = a(x,y,L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,46708,a(flip),b,48895,a),flip(a)].">
      <j1 rule="hyper" parents="64 46708 48895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48897">
    <literal><![CDATA[
      a(x,y,L(L(y,z,u * x),w,v5)) = a(x,y,L(L(y,z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27719,a,b,48896,a)].">
      <j1 rule="hyper" parents="64 27719 48896"/>
    </justification>
  </clause>

  <clause id="48898">
    <literal><![CDATA[
      a(x,y,L(z,(R(x,y,z) * y) * z,x * (z * y))) = ((a(x,y,z) / ((x * y) * z)) \ 1) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(33614(a,1),48821(a,1,3))].">
      <j1 rule="para" parents="33614 48821"/>
    </justification>
  </clause>

  <clause id="48899">
    <literal><![CDATA[
      a(x,y,L(z,(L(x,y,z) * y) * z,x * (z * y))) = ((a(x,y,z) / ((x * y) * z)) \ 1) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(36284(a,1),48898(a,1,3))].">
      <j1 rule="para" parents="36284 48898"/>
    </justification>
  </clause>

  <clause id="48900">
    <literal><![CDATA[
      ((a(x,y,z) / ((x * y) * z)) \ 1) \ ((x * y) * z) = a(x,y,L(z,(z * y) * x,x * (z * y)))
    ]]></literal>
    <justification jstring="[para(42928(a,1),48899(a,1,3)),flip(a)].">
      <j1 rule="para" parents="42928 48899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48901">
    <literal><![CDATA[
      ((a(x,y,z) / ((x * y) * z)) \ 1) \ ((x * y) * z) = a(x,y,L(z,z * (y \ x),z * (y \ x)))
    ]]></literal>
    <justification jstring="[para(35257(a,1),48900(a,2,3))].">
      <j1 rule="para" parents="35257 48900"/>
    </justification>
  </clause>

  <clause id="48902">
    <literal><![CDATA[
      ((a(x,y,z) / ((x * y) * z)) \ 1) \ ((x * y) * z) = a(x,y,(1 / ((y \ x) / z)) * (y \ x))
    ]]></literal>
    <justification jstring="[para(34540(a,1),48901(a,2,3))].">
      <j1 rule="para" parents="34540 48901"/>
    </justification>
  </clause>

  <clause id="48903">
    <literal><![CDATA[
      ((a(x,y,z) / ((x * y) * z)) \ 1) \ ((x * y) * z) = a(x,y,(1 / ((y * x) / z)) * (y * x))
    ]]></literal>
    <justification jstring="[para(48229(a,1),48902(a,2,3))].">
      <j1 rule="para" parents="48229 48902"/>
    </justification>
  </clause>

  <clause id="48904">
    <literal><![CDATA[
      ((a(x,y,z) / ((x * y) * z)) \ 1) \ ((x * y) * z) = a(x,y,((z \ (y * x)) \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,27671,a(flip),b,48903,a),flip(a)].">
      <j1 rule="hyper" parents="373 27671 48903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48905">
    <literal><![CDATA[
      a(x,y,L(z,(x * y) * z,(x * y) * z)) = a(x,y,((z \ (y * x)) \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46982,a(flip),b,48904,a)].">
      <j1 rule="hyper" parents="64 46982 48904"/>
    </justification>
  </clause>

  <clause id="48906">
    <literal><![CDATA[
      a(x,y,(1 / ((x * y) / z)) * (x * y)) = a(x,y,((z \ (y * x)) \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[para(34539(a,1),48905(a,1,3))].">
      <j1 rule="para" parents="34539 48905"/>
    </justification>
  </clause>

  <clause id="48907">
    <literal><![CDATA[
      a(x,y,((z \ (y * x)) \ 1) * (y * x)) = a(x,y,((z \ (x * y)) \ 1) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,27671,a(flip),b,48906,a),flip(a)].">
      <j1 rule="hyper" parents="64 27671 48906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48908">
    <literal><![CDATA[
      a(x / T(y * y,z),u,(x * (T(y * y,z) \ w)) \ v5) = a(x / T(y * y,z),u,w \ (T(y * y,z) * (x \ v5)))
    ]]></literal>
    <justification jstring="[para(25553(a,1),46286(a,1,3,1))].">
      <j1 rule="para" parents="25553 46286"/>
    </justification>
  </clause>

  <clause id="48909">
    <literal><![CDATA[
      (a(x,y,y) * (z * u)) \ (a(x,y,y) * (z * (u * y))) = L(y,L(u,z,a(x,y,y)),a(x,y,y) * z)
    ]]></literal>
    <justification jstring="[para(47441(a,1),46388(a,1,2))].">
      <j1 rule="para" parents="47441 46388"/>
    </justification>
  </clause>

  <clause id="48910">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(u,x,x)) = L(x,L(y,z,a(u,x,x)),a(u,x,x) * z)
    ]]></literal>
    <justification jstring="[hyper(1081,a,48909,a)].">
      <j1 rule="hyper" parents="1081 48909"/>
    </justification>
  </clause>

  <clause id="48911">
    <literal><![CDATA[
      L(x,L(y,z,a(u,x,x)),a(u,x,x) * z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33252,a(flip),b,48910,a),flip(a)].">
      <j1 rule="hyper" parents="64 33252 48910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48913">
    <literal><![CDATA[
      L(x,L(y,L(a(z,x,x),u,u) * w,a(z,x,x)),L(w * a(u,u,a(z,x,x)),a(z,x,x),a(z,x,x))) = L(x,y,L(a(z,x,x),u,u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,47114,a,b,48911,a)].">
      <j1 rule="hyper" parents="64 47114 48911"/>
    </justification>
  </clause>

  <clause id="48914">
    <literal><![CDATA[
      a(x,x,a(y,z,u * a(y,u,x))) * L(x,z,K(y,u * x) * ((y * x) \ (x * (u * y)))) = L(x,z,a(x,u,y) \ u)
    ]]></literal>
    <justification jstring="[para(46469(a,1),47082(a,1,1,3))].">
      <j1 rule="para" parents="46469 47082"/>
    </justification>
  </clause>

  <clause id="48915">
    <literal><![CDATA[
      a(x,x,L(((y / z) * (z * u)) * (y \ 1),y,z)) = a(x,x,((y * u) * (1 / y)) * a(z * y,(y * u) * (1 / y),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27605,a(flip),b,47135,a)].">
      <j1 rule="hyper" parents="64 27605 47135"/>
    </justification>
  </clause>

  <clause id="48916">
    <literal><![CDATA[
      a(x / T(y * y,z),u,w \ (T(y * y,z) * (x \ v5))) = a(x / T(y * y,z),u,(((y * y) \ w) * x) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27699,a(flip),b,48908,a),flip(a)].">
      <j1 rule="hyper" parents="64 27699 48908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48918">
    <literal><![CDATA[
      a(x / T(y * y,z),u,w \ (T(y * y,z) * (x \ v5))) = a(x / T(y * y,z),u,(w * x) \ ((y * y) * v5))
    ]]></literal>
    <justification jstring="[para(942(a,1),48916(a,2,3))].">
      <j1 rule="para" parents="942 48916"/>
    </justification>
  </clause>

  <clause id="48919">
    <literal><![CDATA[
      a(x / T(y * y,z),u,w \ (T(y * y,z) * (x \ v5))) = a(x / T(y * y,z),u,(y * y) * ((w * x) \ v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,27392,a(flip),b,48918,a),flip(a)].">
      <j1 rule="hyper" parents="373 27392 48918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48920">
    <literal><![CDATA[
      a(x / T(y * y,z),u,w \ (T(y * y,z) * (x \ v5))) = a(T(y * y,z) \ x,u,(y * y) * ((w * x) \ v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,26785,a(flip),b,48919,a),flip(a)].">
      <j1 rule="hyper" parents="373 26785 48919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48921">
    <literal><![CDATA[
      a(x / T(y * y,z),u,w \ (T(y * y,z) * (x \ v5))) = a((y * y) \ x,u,(y * y) * ((w * x) \ v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,32366,a(flip),b,48920,a),flip(a)].">
      <j1 rule="hyper" parents="373 32366 48920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48923">
    <literal><![CDATA[
      a(x / T(y * y,z),u,w \ (T(y * y,z) * (x \ v5))) = a(x,u,(y * y) * ((w * x) \ v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,2637,a(flip),b,48921,a),flip(a)].">
      <j1 rule="hyper" parents="373 2637 48921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48925">
    <literal><![CDATA[
      a(x / T(y * y,z),u,w \ ((y * y) * (x \ v5))) = a(x,u,(y * y) * ((w * x) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27335,a(flip),b,48923,a)].">
      <j1 rule="hyper" parents="64 27335 48923"/>
    </justification>
  </clause>

  <clause id="48927">
    <literal><![CDATA[
      a(x / T(y * y,z),u,(y * y) * (w \ (x \ v5))) = a(x,u,(y * y) * ((w * x) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27392,a(flip),b,48925,a)].">
      <j1 rule="hyper" parents="64 27392 48925"/>
    </justification>
  </clause>

  <clause id="48928">
    <literal><![CDATA[
      a((x * x) \ y,z,(x * x) * (u \ (y \ w))) = a(y,z,(x * x) * ((u * y) \ w))
    ]]></literal>
    <justification jstring="[para(301(a,1),48927(a,1,1))].">
      <j1 rule="para" parents="301 48927"/>
    </justification>
  </clause>

  <clause id="48929">
    <literal><![CDATA[
      a(x,y,(z * z) * ((u * x) \ w)) = a(x,y,(z * z) * (u \ (x \ w)))
    ]]></literal>
    <justification jstring="[hyper(2692,a,48928,a),flip(a)].">
      <j1 rule="hyper" parents="2692 48928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48931">
    <literal><![CDATA[
      a(x \ 1,y,(z * z) * (u \ ((x \ 1) \ (x \ (1 / x))))) = a(x \ 1,y,(z * z) * ((x * T(u,x \ 1)) \ 1))
    ]]></literal>
    <justification jstring="[para(2319(a,1),48929(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="2319 48929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48932">
    <literal><![CDATA[
      a(x \ 1,y,(z * z) * (u \ ((x \ 1) \ (x \ (1 / x))))) = a(x \ 1,y,(z * z) * ((x * u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(373,a,27505,a(flip),b,48931,a),flip(a)].">
      <j1 rule="hyper" parents="373 27505 48931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48934">
    <literal><![CDATA[
      a(x \ 1,y,(z * z) * (u \ ((x \ 1) \ (x \ (1 / x))))) = a(x \ 1,y,(x * u) \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27390,a(flip),b,48932,a),flip(a)].">
      <j1 rule="hyper" parents="373 27390 48932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48935">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * L(y,u,K(x,z * y) * ((x * y) \ (y * (z * x)))) = L(y,u,a(y,z,x) \ z)
    ]]></literal>
    <justification jstring="[para(45898(a,1),48914(a,1,1))].">
      <j1 rule="para" parents="45898 48914"/>
    </justification>
  </clause>

  <clause id="48936">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * L(y,u,L(a(y,z,x) \ z,y,x)) = L(y,u,a(y,z,x) \ z)
    ]]></literal>
    <justification jstring="[para(34594(a,1),48935(a,1,2,3))].">
      <j1 rule="para" parents="34594 48935"/>
    </justification>
  </clause>

  <clause id="48938">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * L(y,u,L(z,x,y)) = L(y,u,a(y,z,x) \ z)
    ]]></literal>
    <justification jstring="[para(33534(a,1),48936(a,1,2))].">
      <j1 rule="para" parents="33534 48936"/>
    </justification>
  </clause>

  <clause id="48939">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * L(y,u,z) = L(y,u,a(y,z,x) \ z)
    ]]></literal>
    <justification jstring="[para(46117(a,1),48938(a,1,2))].">
      <j1 rule="para" parents="46117 48938"/>
    </justification>
  </clause>

  <clause id="48940">
    <literal><![CDATA[
      L(x,y,a(x,z,u) \ z) = L(x,y,L(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47107,a(flip),b,48939,a),flip(a)].">
      <j1 rule="hyper" parents="64 47107 48939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48942">
    <literal><![CDATA[
      L(x,y,z * a(x,z,u)) = L(x,y,L(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,42468,a(flip),b,48940,a)].">
      <j1 rule="hyper" parents="64 42468 48940"/>
    </justification>
  </clause>

  <clause id="48943">
    <literal><![CDATA[
      L(x,y,L(z,a(u,w,x),v5)) = L(x,y,L(z,x,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47416,a(flip),b,48942,a)].">
      <j1 rule="hyper" parents="64 47416 48942"/>
    </justification>
  </clause>

  <clause id="48944">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ (a(z,y,x) * v5) = a(z,y,L(x,u,L(w,x,a(z,y,v5))))
    ]]></literal>
    <justification jstring="[para(48943(a,1),48025(a,2,3))].">
      <j1 rule="para" parents="48943 48025"/>
    </justification>
  </clause>

  <clause id="48945">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ (a(z,y,x) * v5) = a(z,y,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,47914,a(flip),b,48944,a),flip(a)].">
      <j1 rule="hyper" parents="373 47914 48944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48947">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ (a(u,z,y) * a(u,z,a(y,x,w))) = a(u,z,L(y,w,x))
    ]]></literal>
    <justification jstring="[para(47968(a,1),48945(a,1,1))].">
      <j1 rule="para" parents="47968 48945"/>
    </justification>
  </clause>

  <clause id="48948">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ a(u,z,L(y,x,w)) = a(u,z,L(y,w,x))
    ]]></literal>
    <justification jstring="[para(47233(a,1),48947(a,1,2))].">
      <j1 rule="para" parents="47233 48947"/>
    </justification>
  </clause>

  <clause id="48949">
    <literal><![CDATA[
      a(x,a(y,z,u),w) * a(u,z,L(y,w,x)) = a(u,z,L(y,x,w))
    ]]></literal>
    <justification jstring="[hyper(157,a,48948,a)].">
      <j1 rule="hyper" parents="157 48948"/>
    </justification>
  </clause>

  <clause id="48950">
    <literal><![CDATA[
      a(x,x,L(y \ ((y / z) * (z * u)),y,z)) = a(x,x,((y * u) * (1 / y)) * a(z * y,(y * u) * (1 / y),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46490,a(flip),b,48915,a)].">
      <j1 rule="hyper" parents="64 46490 48915"/>
    </justification>
  </clause>

  <clause id="48951">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u * z),u,z)) = a(x,x,((u * y) * (1 / u)) * a(z * u,(u * y) * (1 / u),z))
    ]]></literal>
    <justification jstring="[para(41972(a,1),48950(a,1,3,1))].">
      <j1 rule="para" parents="41972 48950"/>
    </justification>
  </clause>

  <clause id="48952">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u * z),u,z)) = a(x,x,((u * y) * (1 / u)) * a(z * u,u * (u * y),z))
    ]]></literal>
    <justification jstring="[para(31948(a,1),48951(a,2,3,2))].">
      <j1 rule="para" parents="31948 48951"/>
    </justification>
  </clause>

  <clause id="48953">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u * z),u,z)) = a(x,x,((u * y) * (1 / u)) * a(z * u,L(y,u,u),z))
    ]]></literal>
    <justification jstring="[para(11968(a,1),48952(a,2,3,2))].">
      <j1 rule="para" parents="11968 48952"/>
    </justification>
  </clause>

  <clause id="48954">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u * z),u,z)) = a(x,x,((u * y) * (u \ 1)) * a(z * u,L(y,u,u),z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27469,a(flip),b,48953,a),flip(a)].">
      <j1 rule="hyper" parents="373 27469 48953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48955">
    <literal><![CDATA[
      a((x \ a(y,x,z)) * u,a(w,x * a(y,x,z),x * a(y,x,z)),v5) = a(u,a(w,x,x),v5)
    ]]></literal>
    <justification jstring="[para(44913(a,1),47760(a,2,2))].">
      <j1 rule="para" parents="44913 47760"/>
    </justification>
  </clause>

  <clause id="48956">
    <literal><![CDATA[
      a((x \ a(y,x,z)) * u,a(w,x,x),v5) = a(u,a(w,x,x),v5)
    ]]></literal>
    <justification jstring="[para(44913(a,1),48955(a,1,2))].">
      <j1 rule="para" parents="44913 48955"/>
    </justification>
  </clause>

  <clause id="48958">
    <literal><![CDATA[
      a((x * a(y,x,z)) * u,a(w,x,x),v5) = a(u,a(w,x,x),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,35761,a(flip),b,48956,a)].">
      <j1 rule="hyper" parents="64 35761 48956"/>
    </justification>
  </clause>

  <clause id="48960">
    <literal><![CDATA[
      a(a(x,y,z) * u,a(w,y,y),v5) = a(u,a(w,y,y),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,47766,a(flip),b,48958,a)].">
      <j1 rule="hyper" parents="64 47766 48958"/>
    </justification>
  </clause>

  <clause id="48963">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(y,y,w),v5 * a(y,y,w)) = (a(x,y,z) \ u) * a(u,a(w,y,y),v5)
    ]]></literal>
    <justification jstring="[para(48960(a,1),48125(a,2,2))].">
      <j1 rule="para" parents="48960 48125"/>
    </justification>
  </clause>

  <clause id="48964">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(y,y,w),v5 * a(y,y,w)) = u * (a(x,y,z) \ a(u,a(w,y,y),v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,42603,a(flip),b,48963,a),flip(a)].">
      <j1 rule="hyper" parents="373 42603 48963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48965">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(y,y,u),w * a(y,y,u)) = a(x,y,y) \ R(z,a(u,y,y),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,47875,a(flip),b,48964,a),flip(a)].">
      <j1 rule="hyper" parents="373 47875 48964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48966">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(y,y,u),w * a(y,y,u)) = a(x,y,y) \ L(z,a(u,y,y),w)
    ]]></literal>
    <justification jstring="[para(31802(a,1),48965(a,2,2))].">
      <j1 rule="para" parents="31802 48965"/>
    </justification>
  </clause>

  <clause id="48967">
    <literal><![CDATA[
      L(a(x,y,y) \ z,a(u,y,y),w) = a(x,y,y) \ L(z,a(u,y,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,48280,a(flip),b,48966,a)].">
      <j1 rule="hyper" parents="64 48280 48966"/>
    </justification>
  </clause>

  <clause id="48969">
    <literal><![CDATA[
      x * L(a(y,z,z) \ u,a(y,z,z),x) = (a(y,z,z) \ x) * u
    ]]></literal>
    <justification jstring="[para(48967(a,2),43399(a,1,2))].">
      <j1 rule="para" parents="48967 43399"/>
    </justification>
  </clause>

  <clause id="48970">
    <literal><![CDATA[
      T(L(a(x,y,y) \ z,a(x,y,y),u),u) = u \ (z * (a(x,y,y) \ u))
    ]]></literal>
    <justification jstring="[para(48967(a,2),43433(a,1,1))].">
      <j1 rule="para" parents="48967 43433"/>
    </justification>
  </clause>

  <clause id="48971">
    <literal><![CDATA[
      a(x,y,a(y,(a(z,u,u) \ w) * v5,L(a(z,u,u) \ v5,a(z,u,u),w))) = a(L(a(z,u,u) \ v5,a(z,u,u),w),y,a(x,w,y))
    ]]></literal>
    <justification jstring="[para(48969(a,1),46887(a,1,3,2))].">
      <j1 rule="para" parents="48969 46887"/>
    </justification>
  </clause>

  <clause id="48972">
    <literal><![CDATA[
      L(T(a(x,y,y) \ z,u),a(x,y,y),u) = u \ (z * (a(x,y,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(11860,a,48970,a)].">
      <j1 rule="hyper" parents="11860 48970"/>
    </justification>
  </clause>

  <clause id="48973">
    <literal><![CDATA[
      (a(x,y,y) * z) \ (u * z) = z \ (u * (a(x,y,y) \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,28763,a(flip),b,48972,a)].">
      <j1 rule="hyper" parents="64 28763 48972"/>
    </justification>
  </clause>

  <clause id="48974">
    <literal><![CDATA[
      x \ ((a(y,z,z) * u) * (a(y,z,z) \ x)) = L(T(u,x),a(y,z,z),x)
    ]]></literal>
    <justification jstring="[para(9(a,1),48972(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 48972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48975">
    <literal><![CDATA[
      x \ (y * R(a(z,u,u),(a(z,u,u) \ x) * y,a(z,u,u) \ x)) = L(T(T(y,a(z,u,u)) / (a(z,u,u) \ x),x),a(z,u,u),x)
    ]]></literal>
    <justification jstring="[para(46441(a,1),48974(a,1,2))].">
      <j1 rule="para" parents="46441 48974"/>
    </justification>
  </clause>

  <clause id="48976">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,z,u),u * ((z / (w * w)) * y),v5)) = a(x,L(y,z,u),L(L(y,z,u),z * ((w * w) \ u),v5))
    ]]></literal>
    <justification jstring="[para(29624(a,1),47591(a,1,3))].">
      <j1 rule="para" parents="29624 47591"/>
    </justification>
  </clause>

  <clause id="48977">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,z,u),u * (z * ((w * w) \ y)),v5)) = a(x,L(y,z,u),L(L(y,z,u),z * ((w * w) \ u),v5))
    ]]></literal>
    <justification jstring="[para(897(a,1),48976(a,1,3,2,2))].">
      <j1 rule="para" parents="897 48976"/>
    </justification>
  </clause>

  <clause id="48979">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,z,u),(y * z) * u,w)) = a(x,L(y,z,u),L(L(y,z,u),z * ((v5 * v5) \ u),w))
    ]]></literal>
    <justification jstring="[para(29714(a,1),48977(a,1,3))].">
      <j1 rule="para" parents="29714 48977"/>
    </justification>
  </clause>

  <clause id="48980">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,z,u),z * ((w * w) \ u),v5)) = a(x,y,L(y,(y * z) * u,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,44038,a(flip),b,48979,a),flip(a)].">
      <j1 rule="hyper" parents="64 44038 48979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48983">
    <literal><![CDATA[
      a(x,L(y,z,u),L(L(y,z,u),z * u,w)) = a(x,y,L(y,(y * z) * u,w))
    ]]></literal>
    <justification jstring="[para(29669(a,1),48980(a,1,3))].">
      <j1 rule="para" parents="29669 48980"/>
    </justification>
  </clause>

  <clause id="48984">
    <literal><![CDATA[
      a(x,y,L(y,(y * z) * u,w)) = a(x,y,L(y,z * u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,44038,a(flip),b,48983,a),flip(a)].">
      <j1 rule="hyper" parents="64 44038 48983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48986">
    <literal><![CDATA[
      a(x,a(y,z,u) \ z,L(a(y,z,u) \ z,(z * L(u,z,y)) * w,v5)) = a(x,a(y,z,u) \ z,L(a(y,z,u) \ z,u * w,v5))
    ]]></literal>
    <justification jstring="[para(42071(a,1),48984(a,1,3,2,1))].">
      <j1 rule="para" parents="42071 48984"/>
    </justification>
  </clause>

  <clause id="48987">
    <literal><![CDATA[
      a(x,a(y,z,u) * z,L(a(y,z,u) * z,L(z * w,z,a(y,z,u)) * v5,v6)) = a(x,a(y,z,u) * z,L(a(y,z,u) * z,(a(y,z,u) \ w) * v5,v6))
    ]]></literal>
    <justification jstring="[para(43364(a,1),48984(a,1,3,2,1))].">
      <j1 rule="para" parents="43364 48984"/>
    </justification>
  </clause>

  <clause id="48988">
    <literal><![CDATA[
      (x \ ((a(y,z,z) \ 1) \ u)) * a(z,z,a(y,x \ ((a(y,z,z) \ 1) \ u),x)) = L((a(y,z,z) \ x) \ u,a(y,z,z),x)
    ]]></literal>
    <justification jstring="[para(37824(a,1),46950(a,2,1,1))].">
      <j1 rule="para" parents="37824 46950"/>
    </justification>
  </clause>

  <clause id="48989">
    <literal><![CDATA[
      (x \ ((a(y,z,z) \ 1) \ u)) * a(z,z,a(y,x \ ((a(y,z,z) \ 1) \ u),x)) = a(y,z,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,43395,a(flip),b,48988,a),flip(a)].">
      <j1 rule="hyper" parents="373 43395 48988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48990">
    <literal><![CDATA[
      (x \ (a(y,z,z) * u)) * a(z,z,a(y,x \ ((a(y,z,z) \ 1) \ u),x)) = a(y,z,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(42435(a,1),48989(a,1,1,2))].">
      <j1 rule="para" parents="42435 48989"/>
    </justification>
  </clause>

  <clause id="48991">
    <literal><![CDATA[
      (x \ (a(y,z,z) * u)) * a(z,z,a(y,x \ (a(y,z,z) * u),x)) = a(y,z,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(42435(a,1),48990(a,1,2,3,2,2))].">
      <j1 rule="para" parents="42435 48990"/>
    </justification>
  </clause>

  <clause id="48992">
    <literal><![CDATA[
      (x \ (a(y,z,z) * u)) * a(z,z,a(y,x * (a(y,z,z) * u),x)) = a(y,z,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(35684(a,1),48991(a,1,2,3))].">
      <j1 rule="para" parents="35684 48991"/>
    </justification>
  </clause>

  <clause id="48993">
    <literal><![CDATA[
      (x \ (a(y,z,z) * u)) * a(x,z,a(y,a(y,z,z) * u,z)) = a(y,z,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(46890(a,1),48992(a,1,2))].">
      <j1 rule="para" parents="46890 48992"/>
    </justification>
  </clause>

  <clause id="48994">
    <literal><![CDATA[
      (x \ (a(y,z,z) * u)) * a(z,z,a(x,u,y)) = a(y,z,z) * (x \ u)
    ]]></literal>
    <justification jstring="[para(47504(a,1),48993(a,1,2))].">
      <j1 rule="para" parents="47504 48993"/>
    </justification>
  </clause>

  <clause id="48995">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) \ (a(u,y,y) * z) = a(u,y,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46802,a(flip),b,48994,a)].">
      <j1 rule="hyper" parents="64 46802 48994"/>
    </justification>
  </clause>

  <clause id="48996">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) * (a(u,y,y) * (x \ z)) = a(u,y,y) * z
    ]]></literal>
    <justification jstring="[hyper(145,a,48994,a(flip),b,46802,a(flip))].">
      <j1 rule="hyper" parents="145 48994 46802"/>
    </justification>
  </clause>

  <clause id="48997">
    <literal><![CDATA[
      (a(x,y,y) * (z \ u)) \ ((L(z,y,a(y,u,x)) \ 1) * (a(x,y,y) * u)) = a(L(z,y,a(y,u,x)),L(z,y,a(y,u,x)),a(x,y,y) * u) \ 1
    ]]></literal>
    <justification jstring="[para(48995(a,1),30422(a,1,1))].">
      <j1 rule="para" parents="48995 30422"/>
    </justification>
  </clause>

  <clause id="48998">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)) * (a(u,y,y) * (x \ z)),w,w) = L(L(a(u,y,y),z,w),w * z,w) * L(z,w,w)
    ]]></literal>
    <justification jstring="[para(48996(a,2),26948(a,2,1)),flip(a)].">
      <j1 rule="para" parents="48996 26948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="48999">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)) * (a(u,y,y) * (x \ z)),w,w) = L(a(u,y,L(y,z,w)),w * z,w) * L(z,w,w)
    ]]></literal>
    <justification jstring="[para(44006(a,2),48998(a,2,1,1))].">
      <j1 rule="para" parents="44006 48998"/>
    </justification>
  </clause>

  <clause id="49000">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)) * (a(u,y,y) * (x \ z)),w,w) = a(u,y,L(L(y,z,w),w * z,w)) * L(z,w,w)
    ]]></literal>
    <justification jstring="[para(46493(a,2),48999(a,2,1))].">
      <j1 rule="para" parents="46493 48999"/>
    </justification>
  </clause>

  <clause id="49001">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)) * (a(u,y,y) * (x \ z)),w,w) = a(u,y,L(L(y,z,w),z,w)) * L(z,w,w)
    ]]></literal>
    <justification jstring="[para(47031(a,1),49000(a,2,1))].">
      <j1 rule="para" parents="47031 49000"/>
    </justification>
  </clause>

  <clause id="49002">
    <literal><![CDATA[
      L(L(x,y,a(y,z,u)) * (a(u,y,y) * (x \ z)),w,w) = a(u,y,y) * L(z,w,w)
    ]]></literal>
    <justification jstring="[para(39064(a,1),49001(a,2,1))].">
      <j1 rule="para" parents="39064 49001"/>
    </justification>
  </clause>

  <clause id="49004">
    <literal><![CDATA[
      L(a(x,y,y) * z,u,u) = a(x,y,y) * L(z,u,u)
    ]]></literal>
    <justification jstring="[para(48996(a,1),49002(a,1,1))].">
      <j1 rule="para" parents="48996 49002"/>
    </justification>
  </clause>

  <clause id="49005">
    <literal><![CDATA[
      L(a(x,y,y) * z,u,u) = L(z,u,u) * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,23183,a,b,49004,a),flip(a)].">
      <j1 rule="hyper" parents="373 23183 49004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49006">
    <literal><![CDATA[
      L(x,a(y,a(z,u,w) \ u,u * a(w,u,z)),(u * L(w,u,z)) * v5) = L(x,a(y,a(z,u,w) \ u,a(z,u,w) \ u),w * v5)
    ]]></literal>
    <justification jstring="[para(46469(a,1),48155(a,1,2))].">
      <j1 rule="para" parents="46469 48155"/>
    </justification>
  </clause>

  <clause id="49007">
    <literal><![CDATA[
      a(x,y,a(y,(a(z,u,u) \ w) * v5,L(v5 * a(z,u,u),a(z,u,u),w))) = a(L(a(z,u,u) \ v5,a(z,u,u),w),y,a(x,w,y))
    ]]></literal>
    <justification jstring="[para(42833(a,1),48971(a,1,3))].">
      <j1 rule="para" parents="42833 48971"/>
    </justification>
  </clause>

  <clause id="49008">
    <literal><![CDATA[
      a(x,a(y,z,u) \ z,L(z * a(y,z,u),(z * L(u,z,y)) * w,v5)) = a(x,a(y,z,u) \ z,L(a(y,z,u) \ z,u * w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,42833,a(flip),b,48986,a)].">
      <j1 rule="hyper" parents="64 42833 48986"/>
    </justification>
  </clause>

  <clause id="49009">
    <literal><![CDATA[
      L(x,a(y,z * a(u,z,w),z * a(w,z,u)),(z * L(w,z,u)) * v5) = L(x,a(y,a(u,z,w) \ z,a(u,z,w) \ z),w * v5)
    ]]></literal>
    <justification jstring="[para(47827(a,1),49006(a,1,2))].">
      <j1 rule="para" parents="47827 49006"/>
    </justification>
  </clause>

  <clause id="49010">
    <literal><![CDATA[
      a(x,y,a(y,(a(z,u,u) * w) * v5,L(v5 * a(z,u,u),a(z,u,u),w))) = a(L(a(z,u,u) \ v5,a(z,u,u),w),y,a(x,w,y))
    ]]></literal>
    <justification jstring="[para(42465(a,1),49007(a,1,3))].">
      <j1 rule="para" parents="42465 49007"/>
    </justification>
  </clause>

  <clause id="49011">
    <literal><![CDATA[
      a(x,y * a(z,y,u),L(y * a(z,y,u),(y * L(u,y,z)) * w,v5)) = a(x,a(z,y,u) \ y,L(a(z,y,u) \ y,u * w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,48493,a(flip),b,49008,a)].">
      <j1 rule="hyper" parents="64 48493 49008"/>
    </justification>
  </clause>

  <clause id="49012">
    <literal><![CDATA[
      L(x,a(y,a(z,u,w) \ u,a(z,u,w) \ u),w * v5) = L(x,a(y,u,u),(u * L(w,u,z)) * v5)
    ]]></literal>
    <justification jstring="[para(44915(a,1),49009(a,1,2)),flip(a)].">
      <j1 rule="para" parents="44915 49009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49013">
    <literal><![CDATA[
      L(x,a(y,a(z,u,w) \ u,a(z,u,w) \ u),w * v5) = L(x,a(y,u,u),L(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,48153,a(flip),b,49012,a),flip(a)].">
      <j1 rule="hyper" parents="373 48153 49012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49015">
    <literal><![CDATA[
      L(x,a(y,a(z,u,w) \ u,u * a(w,u,z)),w * v5) = L(x,a(y,u,u),L(w,u,z) * v5)
    ]]></literal>
    <justification jstring="[para(46469(a,1),49013(a,1,2))].">
      <j1 rule="para" parents="46469 49013"/>
    </justification>
  </clause>

  <clause id="49016">
    <literal><![CDATA[
      L(x,a(y,z * a(u,z,w),z * a(w,z,u)),w * v5) = L(x,a(y,z,z),L(w,z,u) * v5)
    ]]></literal>
    <justification jstring="[para(47827(a,1),49015(a,1,2))].">
      <j1 rule="para" parents="47827 49015"/>
    </justification>
  </clause>

  <clause id="49017">
    <literal><![CDATA[
      L(x,a(y,z,z),L(u,z,w) * v5) = L(x,a(y,z,z),u * v5)
    ]]></literal>
    <justification jstring="[para(44915(a,1),49016(a,1,2)),flip(a)].">
      <j1 rule="para" parents="44915 49016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49018">
    <literal><![CDATA[
      L(x,a(y,z,z),u * L(w,z,v5)) = L(x,a(y,z,z),w * u)
    ]]></literal>
    <justification jstring="[hyper(24201,a,49017,a)].">
      <j1 rule="hyper" parents="24201 49017"/>
    </justification>
  </clause>

  <clause id="49020">
    <literal><![CDATA[
      a(L(a(x,y,y) \ z,a(x,y,y),u),w,a(v5,u,w)) = a(z * a(x,y,y),(a(x,y,y) * u) * z,a(v5,w,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,48366,a(flip),b,49010,a),flip(a)].">
      <j1 rule="hyper" parents="64 48366 49010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49022">
    <literal><![CDATA[
      a(L(a(x,y,y) \ z,a(x,y,y),u),w,a(v5,u,w)) = a(z,w,a(v5,(a(x,y,y) * u) * z,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,48555,a(flip),b,49020,a),flip(a)].">
      <j1 rule="hyper" parents="373 48555 49020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49024">
    <literal><![CDATA[
      a(L(a(x,y,y) \ z,a(x,y,y),u),w,a(v5,u,w)) = a(z,w,a(v5,a(x,y,y) * u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,46889,a(flip),b,49022,a),flip(a)].">
      <j1 rule="hyper" parents="373 46889 49022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49025">
    <literal><![CDATA[
      a(a(x,y,y) \ z,u,a(w,v5,L(u,a(x,y,y),v5))) = a(z,u,a(w,a(x,y,y) * v5,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46629,a(flip),b,49024,a)].">
      <j1 rule="hyper" parents="64 46629 49024"/>
    </justification>
  </clause>

  <clause id="49026">
    <literal><![CDATA[
      a(a(x,y,y) \ z,u,a(w,v5,u)) = a(z,u,a(w,a(x,y,y) * v5,u))
    ]]></literal>
    <justification jstring="[para(48369(a,1),49025(a,1,3))].">
      <j1 rule="para" parents="48369 49025"/>
    </justification>
  </clause>

  <clause id="49027">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,a(w,v5,u)) = a(z,u,a(w,a(x,y,y) * v5,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46425,a(flip),b,49026,a)].">
      <j1 rule="hyper" parents="64 46425 49026"/>
    </justification>
  </clause>

  <clause id="49029">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,w) * v5,y)) = a(z,v5,a(y,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,48534,a(flip),b,49027,a),flip(a)].">
      <j1 rule="hyper" parents="64 48534 49027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49031">
    <literal><![CDATA[
      a(x,y * a(z,u,u),a(w,v5,v5)) = a(x,y,a(v5,v5,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47352,a,b,49029,a)].">
      <j1 rule="hyper" parents="64 47352 49029"/>
    </justification>
  </clause>

  <clause id="49032">
    <literal><![CDATA[
      a(x,a(y,z,z) * u,a(w,v5,v5)) = a(w,u,a(v5,v5,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47324,a,b,49029,a)].">
      <j1 rule="hyper" parents="64 47324 49029"/>
    </justification>
  </clause>

  <clause id="49033">
    <literal><![CDATA[
      a(x,y * a(z,u,u),a(w,w,v5)) = a(x,y,a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,41883,a,b,49031,a)].">
      <j1 rule="hyper" parents="64 41883 49031"/>
    </justification>
  </clause>

  <clause id="49034">
    <literal><![CDATA[
      a(x,(y \ z) \ u,a(w,w,v5)) = a(x,(y * z) \ u,a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,47112,a(flip),b,49033,a),flip(a)].">
      <j1 rule="hyper" parents="64 47112 49033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49035">
    <literal><![CDATA[
      R(x,y * a(z,u,u),a(w,w,v5)) = x * a(x,y,a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(145,a,49033,a(flip),b,45073,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 49033 45073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49036">
    <literal><![CDATA[
      a(x,y,a(z,z,u)) * a(y * a(w,v5,v5),x,a(z,z,u)) = a(x,a(z,z,u),y * a(w,v5,v5))
    ]]></literal>
    <justification jstring="[para(49033(a,1),47051(a,1,1))].">
      <j1 rule="para" parents="49033 47051"/>
    </justification>
  </clause>

  <clause id="49037">
    <literal><![CDATA[
      a(x,L(L(y,y,z),u,w),a(v5,v5,v6)) = a(x,L(y,u,L(w,y,z)),a(v5,v5,v6))
    ]]></literal>
    <justification jstring="[para(47124(a,1),49033(a,1,2)),flip(a)].">
      <j1 rule="para" parents="47124 49033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49038">
    <literal><![CDATA[
      R(x,y * a(z,u,u),a(w,w,v5)) = L(x,y,a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,45190,a(flip),b,49035,a),flip(a)].">
      <j1 rule="hyper" parents="373 45190 49035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49039">
    <literal><![CDATA[
      L(x,y * a(z,u,u),a(w,w,v5)) = L(x,y,a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(28845,a,49038,a)].">
      <j1 rule="hyper" parents="28845 49038"/>
    </justification>
  </clause>

  <clause id="49040">
    <literal><![CDATA[
      L(x,y * a(z,u,u),a(w,v5,v5)) = L(x,y,a(v5,v5,w))
    ]]></literal>
    <justification jstring="[hyper(42222,a,49039,a)].">
      <j1 rule="hyper" parents="42222 49039"/>
    </justification>
  </clause>

  <clause id="49041">
    <literal><![CDATA[
      L(x,a(y,z,z) * u,a(w,v5,v5)) = L(x,u,a(v5,v5,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,29513,a,b,49039,a)].">
      <j1 rule="hyper" parents="64 29513 49039"/>
    </justification>
  </clause>

  <clause id="49042">
    <literal><![CDATA[
      L(x,L(y,y,z),a(u,u,w)) = L(x,y,a(w,u,u))
    ]]></literal>
    <justification jstring="[para(30460(a,1),49040(a,1,2)),flip(a)].">
      <j1 rule="para" parents="30460 49040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49043">
    <literal><![CDATA[
      L(x,L(y,y,z),a(u,w,w)) = L(x,y,a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(42222,a,49042,a)].">
      <j1 rule="hyper" parents="42222 49042"/>
    </justification>
  </clause>

  <clause id="49044">
    <literal><![CDATA[
      L(x \ L(x,y,a(z,u,u)),x,L(y,y,w)) = a(a(z,u,u),L(y,y,w),x) \ 1
    ]]></literal>
    <justification jstring="[para(49043(a,1),42353(a,1,1,2))].">
      <j1 rule="para" parents="49043 42353"/>
    </justification>
  </clause>

  <clause id="49045">
    <literal><![CDATA[
      a(x,(y * z) \ u,a(w,w,v5)) = a(x,(y \ z) * u,a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,48564,a(flip),b,49034,a),flip(a)].">
      <j1 rule="hyper" parents="64 48564 49034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49046">
    <literal><![CDATA[
      a(x,(y \ z) * u,a(w,w,v5)) = a(x,(y * z) * u,a(w,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,48564,a(flip),b,49045,a),flip(a)].">
      <j1 rule="hyper" parents="64 48564 49045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49047">
    <literal><![CDATA[
      a(x,(y \ z) * u,a(w,w,T(y,v5))) = a(x,(y * z) * u,a(w,w,L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,48652,a,b,49046,a)].">
      <j1 rule="hyper" parents="64 48652 49046"/>
    </justification>
  </clause>

  <clause id="49048">
    <literal><![CDATA[
      L(a(x,x,a(y,z,u)),y,L(z,z,w)) = a(a(u,x,x),L(z,z,w),y) \ 1
    ]]></literal>
    <justification jstring="[para(47251(a,1),49044(a,1,1))].">
      <j1 rule="para" parents="47251 49044"/>
    </justification>
  </clause>

  <clause id="49049">
    <literal><![CDATA[
      a(a(x,y,y),L(z,z,u),w) \ 1 = a(y,y,a(w,z,x))
    ]]></literal>
    <justification jstring="[hyper(42,a,45045,a,b,49048,a)].">
      <j1 rule="hyper" parents="42 45045 49048"/>
    </justification>
  </clause>

  <clause id="49050">
    <literal><![CDATA[
      a(x,x,a(y,L(z,z,u),w)) \ 1 = a(x,x,a(y,z,w))
    ]]></literal>
    <justification jstring="[para(47254(a,1),49049(a,1,1))].">
      <j1 rule="para" parents="47254 49049"/>
    </justification>
  </clause>

  <clause id="49052">
    <literal><![CDATA[
      a(x,x,a(y,L(z,z,u),w)) = a(x,x,a(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(141,a,42644,a(flip),b,49050,a(flip))].">
      <j1 rule="hyper" parents="141 42644 49050"/>
    </justification>
  </clause>

  <clause id="49053">
    <literal><![CDATA[
      a(x,L(y,y,z),a(u,u,w)) = a(u,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(47296,a,49052,a)].">
      <j1 rule="hyper" parents="47296 49052"/>
    </justification>
  </clause>

  <clause id="49054">
    <literal><![CDATA[
      a(x,y,a(z,L(u,u,w),y)) = a(y,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47244,a,b,49052,a)].">
      <j1 rule="hyper" parents="64 47244 49052"/>
    </justification>
  </clause>

  <clause id="49055">
    <literal><![CDATA[
      a(x,y,a(z,L(u,u,w),L(y,v5,v6))) = a(y,y,a(z,u,L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47246,a(flip),b,49053,a)].">
      <j1 rule="hyper" parents="64 47246 49053"/>
    </justification>
  </clause>

  <clause id="49056">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,L(v5,L(u,w,v5),v6)),y)) = a(y,y,a(z,L(u,w,v5),x))
    ]]></literal>
    <justification jstring="[para(47496(a,1),49054(a,1,3,2))].">
      <j1 rule="para" parents="47496 49054"/>
    </justification>
  </clause>

  <clause id="49057">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,L(v5,u,L(v6,w,v5))),y)) = a(y,y,a(z,L(u,w,v5),x))
    ]]></literal>
    <justification jstring="[para(47008(a,1),49056(a,1,3,2))].">
      <j1 rule="para" parents="47008 49056"/>
    </justification>
  </clause>

  <clause id="49058">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,L(v5,u,v6)),y)) = a(y,y,a(z,L(u,w,v5),x))
    ]]></literal>
    <justification jstring="[para(596(a,1),49057(a,1,3,2,3,3))].">
      <j1 rule="para" parents="596 49057"/>
    </justification>
  </clause>

  <clause id="49059">
    <literal><![CDATA[
      a(x,L(y,z,L(u,y,w)),a(v5,v5,v6)) = a(v5,v5,a(x,L(y,z,u),v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,47198,a,b,49058,a)].">
      <j1 rule="hyper" parents="64 47198 49058"/>
    </justification>
  </clause>

  <clause id="49061">
    <literal><![CDATA[
      a(x,L(L(y,y,z),u,w),a(v5,v5,v6)) = a(v5,v5,a(x,L(y,u,w),v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,49037,a,b,49059,a)].">
      <j1 rule="hyper" parents="64 49037 49059"/>
    </justification>
  </clause>

  <clause id="49062">
    <literal><![CDATA[
      a(x,y,a(z,L(L(u,u,w),v5,v6),y)) = a(y,y,a(z,L(u,v5,v6),x))
    ]]></literal>
    <justification jstring="[hyper(47296,a,49061,a)].">
      <j1 rule="hyper" parents="47296 49061"/>
    </justification>
  </clause>

  <clause id="49064">
    <literal><![CDATA[
      a(x,(y \ z) * u,a(w,w,T(y,v5))) = a(y,w,a(w,z * u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,48741,a(flip),b,49047,a),flip(a)].">
      <j1 rule="hyper" parents="373 48741 49047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49065">
    <literal><![CDATA[
      a(x,(y \ z) * u,a(w,w,y)) = a(y,w,a(w,z * u,x))
    ]]></literal>
    <justification jstring="[para(114(a,1),49064(a,1,3,3))].">
      <j1 rule="para" parents="114 49064"/>
    </justification>
  </clause>

  <clause id="49066">
    <literal><![CDATA[
      a(x,(y * z) * u,a(w,w,y)) = a(y,w,a(w,z * u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,49046,a(flip),b,49065,a)].">
      <j1 rule="hyper" parents="64 49046 49065"/>
    </justification>
  </clause>

  <clause id="49067">
    <literal><![CDATA[
      a(x,x,a(y,z * (u * w),u)) = a(u,x,a(x,w * z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47352,a(flip),b,49066,a)].">
      <j1 rule="hyper" parents="64 47352 49066"/>
    </justification>
  </clause>

  <clause id="49068">
    <literal><![CDATA[
      L(x,y * (z * u),a(w,w,z)) = x * a(z,w,a(w,u * y,x))
    ]]></literal>
    <justification jstring="[para(49067(a,1),47271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="49067 47271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49069">
    <literal><![CDATA[
      L(x,y * (z * u),a(w,w,z)) = L(x,w,a(w,u * y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,47349,a(flip),b,49068,a),flip(a)].">
      <j1 rule="hyper" parents="373 47349 49068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49070">
    <literal><![CDATA[
      L(x * a(y * z,u,a(w,x,u)),u,a(u,y * z,w)) = L(x,a(u,u,w),z * (w * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,48888,a(flip),b,49069,a),flip(a)].">
      <j1 rule="hyper" parents="64 48888 49069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49071">
    <literal><![CDATA[
      L(x,a(y,y,z),u * (z * w)) = L(x,a(z,y,y),w * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,47561,a(flip),b,49070,a),flip(a)].">
      <j1 rule="hyper" parents="64 47561 49070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49072">
    <literal><![CDATA[
      L(x,a(y,z,z),u * (y * w)) = L(x,a(y,z,z),w * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,41403,a,b,49071,a)].">
      <j1 rule="hyper" parents="64 41403 49071"/>
    </justification>
  </clause>

  <clause id="49073">
    <literal><![CDATA[
      L(x,a(y,z,z),y * u) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(11866,a,49072,a),flip(a)].">
      <j1 rule="hyper" parents="11866 49072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49074">
    <literal><![CDATA[
      a(x * y,a(x,z,z),u) = L(u,a(x,z,z),y) \ u
    ]]></literal>
    <justification jstring="[para(49073(a,1),41674(a,1,1)),flip(a)].">
      <j1 rule="para" parents="49073 41674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49075">
    <literal><![CDATA[
      a(x * y,a(x,z,z),u) = a(y,a(x,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,45067,a,b,49074,a),flip(a)].">
      <j1 rule="hyper" parents="373 45067 49074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49076">
    <literal><![CDATA[
      a(x * y,a(y,z,z),u) = a(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(26847,a,49075,a)].">
      <j1 rule="hyper" parents="26847 49075"/>
    </justification>
  </clause>

  <clause id="49077">
    <literal><![CDATA[
      a(x,a(y,y,z),u * a(w,v5,v5)) = a(x,u,a(y,y,z)) * a(z,x,a(y,y,u))
    ]]></literal>
    <justification jstring="[para(48536(a,1),49036(a,1,2)),flip(a)].">
      <j1 rule="para" parents="48536 49036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49078">
    <literal><![CDATA[
      a(x,a(y,y,z),u * a(w,v5,v5)) = a(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,47385,a(flip),b,49077,a),flip(a)].">
      <j1 rule="hyper" parents="373 47385 49077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49080">
    <literal><![CDATA[
      a(a(x,y,y) * z,a(u,w,w),v5) = a(v5,a(w,w,u),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,43407,a,b,49078,a)].">
      <j1 rule="hyper" parents="64 43407 49078"/>
    </justification>
  </clause>

  <clause id="49081">
    <literal><![CDATA[
      (a(x,y,y) * z) * a(u,a(w,w,v5),z) = R(a(x,y,y) * z,a(v5,w,w),u)
    ]]></literal>
    <justification jstring="[hyper(145,a,49080,a(flip),b,45073,a(flip))].">
      <j1 rule="hyper" parents="145 49080 45073"/>
    </justification>
  </clause>

  <clause id="49082">
    <literal><![CDATA[
      a(x * (y * a(z,u,u)),a(w,v5,v5),v6) = a(v6,a(v5,v5,w),x * y)
    ]]></literal>
    <justification jstring="[para(32614(a,1),49080(a,1,1))].">
      <j1 rule="para" parents="32614 49080"/>
    </justification>
  </clause>

  <clause id="49083">
    <literal><![CDATA[
      a(x * (y * a(z,u,u)),a(w,v5,v5),v6) = a(x * y,a(v5,v5,w),v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,43409,a,b,49082,a),flip(a)].">
      <j1 rule="hyper" parents="373 43409 49082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49084">
    <literal><![CDATA[
      a(x * (a(y,y,z) * u),a(w,v5,v5),v6) = a(x * u,a(v5,v5,w),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,47146,a,b,49083,a)].">
      <j1 rule="hyper" parents="64 47146 49083"/>
    </justification>
  </clause>

  <clause id="49085">
    <literal><![CDATA[
      a(x,a(y,z,z),u * (w * a(v5,v6,v6))) = a(u * w,a(z,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,43409,a,b,49083,a)].">
      <j1 rule="hyper" parents="64 43409 49083"/>
    </justification>
  </clause>

  <clause id="49086">
    <literal><![CDATA[
      a((a(x,x,y) * z) * u,a(w,w,v5),v6) = a(u * z,a(w,w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,42394,a,b,49084,a)].">
      <j1 rule="hyper" parents="64 42394 49084"/>
    </justification>
  </clause>

  <clause id="49087">
    <literal><![CDATA[
      a(x,a(y,z,z),u * R(w,v5,v5)) = a(u * w,a(z,z,y),x)
    ]]></literal>
    <justification jstring="[para(15984(a,1),49085(a,1,3,2))].">
      <j1 rule="para" parents="15984 49085"/>
    </justification>
  </clause>

  <clause id="49088">
    <literal><![CDATA[
      a(x,a(y,z,z),u * L(w,v5,v5)) = a(u * w,a(z,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,31317,a(flip),b,49087,a)].">
      <j1 rule="hyper" parents="64 31317 49087"/>
    </justification>
  </clause>

  <clause id="49089">
    <literal><![CDATA[
      a(x * L(y,z,z),a(u,u,w),v5) = a(v5,a(w,u,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,42979,a(flip),b,49088,a),flip(a)].">
      <j1 rule="hyper" parents="64 42979 49088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49090">
    <literal><![CDATA[
      a(a(x,y,y) * z,a(u,u,w),v5) = a(z,a(u,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,37758,a(flip),b,49086,a),flip(a)].">
      <j1 rule="hyper" parents="64 37758 49086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49091">
    <literal><![CDATA[
      a(x,a(y,z,z),a(u,w,w) * v5) = a(v5,a(z,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,43405,a,b,49090,a)].">
      <j1 rule="hyper" parents="64 43405 49090"/>
    </justification>
  </clause>

  <clause id="49092">
    <literal><![CDATA[
      R(x,a(y,z,z),a(u,w,w) * v5) = x * a(v5,a(z,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(145,a,49091,a(flip),b,45073,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 49091 45073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49093">
    <literal><![CDATA[
      R(x,a(y,z,z),a(u,w,w) * v5) = L(x,a(y,z,z),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,43396,a(flip),b,49092,a),flip(a)].">
      <j1 rule="hyper" parents="373 43396 49092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49094">
    <literal><![CDATA[
      L(x,a(y,z,z),a(u,w,w) * v5) = L(x,a(y,z,z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31802,a(flip),b,49093,a)].">
      <j1 rule="hyper" parents="64 31802 49093"/>
    </justification>
  </clause>

  <clause id="49095">
    <literal><![CDATA[
      L(x,a(y,z,z),u * a(w,v5,v5)) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(24201,a,49094,a)].">
      <j1 rule="hyper" parents="24201 49094"/>
    </justification>
  </clause>

  <clause id="49096">
    <literal><![CDATA[
      L(x,a(y,y,z),a(u,u,w) * v5) = L(x,a(z,y,y),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,41411,a(flip),b,49094,a)].">
      <j1 rule="hyper" parents="64 41411 49094"/>
    </justification>
  </clause>

  <clause id="49097">
    <literal><![CDATA[
      L(x,a(y,z,z),(u * w) * (((u \ 1) \ w) * v5)) = L(x,a(y,z,z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,48431,a,b,49095,a)].">
      <j1 rule="hyper" parents="64 48431 49095"/>
    </justification>
  </clause>

  <clause id="49098">
    <literal><![CDATA[
      x * (L(x,a(y,z,z),u) \ (a(w,w,v5) * u)) = R(a(w,w,v5) * u,a(z,z,y),x)
    ]]></literal>
    <justification jstring="[para(49096(a,1),45658(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="49096 45658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49100">
    <literal><![CDATA[
      L(x,a(y,z,z),((u \ w) * v5) * (u * w)) = L(x,a(y,z,z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,23994,a(flip),b,49097,a)].">
      <j1 rule="hyper" parents="64 23994 49097"/>
    </justification>
  </clause>

  <clause id="49101">
    <literal><![CDATA[
      L(x,a(y,z,z),T(u,w * w) \ (w \ v5)) = L(x,a(y,z,z),u \ (w * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,48432,a(flip),b,49100,a)].">
      <j1 rule="hyper" parents="64 48432 49100"/>
    </justification>
  </clause>

  <clause id="49102">
    <literal><![CDATA[
      R(a(x,y,y) * z,a(u,w,w),v5) = a(x,y,y) * L(z,a(u,w,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,48416,a(flip),b,49081,a),flip(a)].">
      <j1 rule="hyper" parents="64 48416 49081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49103">
    <literal><![CDATA[
      L(a(x,y,y) * z,a(u,w,w),v5) = a(x,y,y) * L(z,a(u,w,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31802,a(flip),b,49102,a)].">
      <j1 rule="hyper" parents="64 31802 49102"/>
    </justification>
  </clause>

  <clause id="49105">
    <literal><![CDATA[
      L(x,a(y,z,z),T(u,w * w) \ (w \ v5)) = L(x,a(y,z,z),u * (w * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,48384,a(flip),b,49101,a),flip(a)].">
      <j1 rule="hyper" parents="373 48384 49101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49106">
    <literal><![CDATA[
      L(x,a(y,z,z),u \ (w \ v5)) = L(x,a(y,z,z),u * (w * v5))
    ]]></literal>
    <justification jstring="[hyper(29065,a,49105,a)].">
      <j1 rule="hyper" parents="29065 49105"/>
    </justification>
  </clause>

  <clause id="49108">
    <literal><![CDATA[
      L(x,a(y,z,z),u * (w \ v5)) = L(x,a(y,z,z),u * (w * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,48384,a(flip),b,49106,a)].">
      <j1 rule="hyper" parents="64 48384 49106"/>
    </justification>
  </clause>

  <clause id="49109">
    <literal><![CDATA[
      (a(x,x,y) * z) * a(u,a(w,v5,v5),z) = R(a(x,x,y) * z,a(v5,v5,w),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,48414,a(flip),b,49098,a)].">
      <j1 rule="hyper" parents="64 48414 49098"/>
    </justification>
  </clause>

  <clause id="49110">
    <literal><![CDATA[
      R(a(x,x,y) * z,a(u,u,w),v5) = a(x,x,y) * L(z,a(u,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,48419,a(flip),b,49109,a),flip(a)].">
      <j1 rule="hyper" parents="64 48419 49109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49111">
    <literal><![CDATA[
      L(a(x,x,y) * z,a(u,u,w),v5) = a(x,x,y) * L(z,a(u,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31802,a(flip),b,49110,a)].">
      <j1 rule="hyper" parents="64 31802 49110"/>
    </justification>
  </clause>

  <clause id="49113">
    <literal><![CDATA[
      a(x,a(y,z,u) \ z,L(a(y,z,u) \ z,u * w,v5)) = a(x,z,L(z,(z * L(u,z,y)) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,47933,a(flip),b,49011,a),flip(a)].">
      <j1 rule="hyper" parents="64 47933 49011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49115">
    <literal><![CDATA[
      a(x,a(y,z,u) \ z,L(a(y,z,u) \ z,u * w,v5)) = a(x,z,L(z,L(u,z,y) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,48984,a(flip),b,49113,a),flip(a)].">
      <j1 rule="hyper" parents="373 48984 49113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49116">
    <literal><![CDATA[
      a(x,a(y,z,u) \ z,L(z * a(y,z,u),u * w,v5)) = a(x,z,L(z,L(u,z,y) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,42833,a(flip),b,49115,a)].">
      <j1 rule="hyper" parents="64 42833 49115"/>
    </justification>
  </clause>

  <clause id="49117">
    <literal><![CDATA[
      a(x,y * a(z,y,u),L(y * a(z,y,u),u * w,v5)) = a(x,y,L(y,L(u,y,z) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,48493,a(flip),b,49116,a)].">
      <j1 rule="hyper" parents="64 48493 49116"/>
    </justification>
  </clause>

  <clause id="49118">
    <literal><![CDATA[
      a(x,y,L(y,L(z,y,u) * w,v5)) = a(x,y,L(y,z * w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,47933,a(flip),b,49117,a),flip(a)].">
      <j1 rule="hyper" parents="64 47933 49117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49120">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ T(a(z,y,x) \ (u \ L(x,y,z)),u \ x) = T((x \ L(x,y,z)) / (1 / (u \ x)),L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(28332(a,1),45770(a,1,2))].">
      <j1 rule="para" parents="28332 45770"/>
    </justification>
  </clause>

  <clause id="49121">
    <literal><![CDATA[
      a(x,y,z) * T(a(x,y,z) \ (u \ L(z,y,x)),u \ z) = T((z \ L(z,y,x)) / (1 / (u \ z)),L(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,45354,a(flip),b,49120,a)].">
      <j1 rule="hyper" parents="64 45354 49120"/>
    </justification>
  </clause>

  <clause id="49123">
    <literal><![CDATA[
      T((a(x,y,z) \ (u \ L(z,y,x))) * a(x,y,z),u \ z) = T((z \ L(z,y,x)) / (1 / (u \ z)),L(z,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,28753,a,b,49121,a)].">
      <j1 rule="hyper" parents="64 28753 49121"/>
    </justification>
  </clause>

  <clause id="49124">
    <literal><![CDATA[
      T((x \ L(x,y,z)) / (1 / (u \ x)),L(x,y,z) \ u) = T(u \ L(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[para(23135(a,1),49123(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23135 49123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49125">
    <literal><![CDATA[
      T((x \ L(x,y,z)) / (1 / (u \ x)),L(x,y,z) \ u) = u \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,28368,a(flip),b,49124,a),flip(a)].">
      <j1 rule="hyper" parents="373 28368 49124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49127">
    <literal><![CDATA[
      T(1 / (a(x,y,z) / (u \ z)),L(z,y,x) \ u) = u \ L(z,y,x)
    ]]></literal>
    <justification jstring="[para(46999(a,1),49125(a,1,1))].">
      <j1 rule="para" parents="46999 49125"/>
    </justification>
  </clause>

  <clause id="49128">
    <literal><![CDATA[
      T(1 / (a(x,y,z) / (u \ z)),z \ u) = u \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(28399,a,49127,a)].">
      <j1 rule="hyper" parents="28399 49127"/>
    </justification>
  </clause>

  <clause id="49130">
    <literal><![CDATA[
      (a(x,y,z) / (u \ z)) \ 1 = u \ L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,28643,a(flip),b,49128,a)].">
      <j1 rule="hyper" parents="64 28643 49128"/>
    </justification>
  </clause>

  <clause id="49131">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) / (v5 \ w)) \ 1 = v5 \ L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(47196(a,1),49130(a,1,1,1))].">
      <j1 rule="para" parents="47196 49130"/>
    </justification>
  </clause>

  <clause id="49132">
    <literal><![CDATA[
      (1 / (x \ y)) \ a(z,u,a(w,v5,y)) = x \ L(y,u,a(w,v5,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47379,a(flip),b,49131,a)].">
      <j1 rule="hyper" parents="64 47379 49131"/>
    </justification>
  </clause>

  <clause id="49133">
    <literal><![CDATA[
      a(((1 / x) \ (y * x)) \ z,u,((x \ 1) \ T(y,x)) \ T((x \ 1) \ ((1 / x) \ y),x)) = a((((x \ 1) \ T(y,x)) \ z) * x,u,x)
    ]]></literal>
    <justification jstring="[para(31716(a,2),47064(a,1,3,2))].">
      <j1 rule="para" parents="31716 47064"/>
    </justification>
  </clause>

  <clause id="49134">
    <literal><![CDATA[
      a((((x / y) \ 1) / y) * ((x / y) \ K(y,x \ 1)),z,((x / y) \ 1) * z) = a(y,z,z * ((x / y) \ K(y,x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27574,a(flip),b,47137,a)].">
      <j1 rule="hyper" parents="64 27574 47137"/>
    </justification>
  </clause>

  <clause id="49136">
    <literal><![CDATA[
      a((((x / y) \ 1) / y) * ((x / y) \ K(y,x \ 1)),z,(x / y) \ z) = a(y,z,z * ((x / y) \ K(y,x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46681,a(flip),b,49134,a)].">
      <j1 rule="hyper" parents="64 46681 49134"/>
    </justification>
  </clause>

  <clause id="49137">
    <literal><![CDATA[
      a((((x / y) \ 1) / y) * ((x / y) \ K(y,x \ 1)),z,(y \ x) \ z) = a(y,z,z * ((x / y) \ K(y,x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27389,a(flip),b,49136,a)].">
      <j1 rule="hyper" parents="64 27389 49136"/>
    </justification>
  </clause>

  <clause id="49138">
    <literal><![CDATA[
      a((x / y) * (((x / y) \ 1) / y),z,(y \ x) \ z) = a(y,z,z * ((x / y) \ K(y,x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,32673,a(flip),b,49137,a)].">
      <j1 rule="hyper" parents="64 32673 49137"/>
    </justification>
  </clause>

  <clause id="49140">
    <literal><![CDATA[
      a((x \ y) * (((x \ y) \ 1) / x),z,(x \ y) \ z) = a(x,z,z * ((y / x) \ K(x,y \ 1)))
    ]]></literal>
    <justification jstring="[para(31387(a,1),49138(a,1,1))].">
      <j1 rule="para" parents="31387 49138"/>
    </justification>
  </clause>

  <clause id="49141">
    <literal><![CDATA[
      a((x * y) * (((x * y) \ 1) / y),z,(y \ x) \ z) = a(y,z,z * ((x / y) \ K(y,x \ 1)))
    ]]></literal>
    <justification jstring="[para(47797(a,1),49140(a,1,1))].">
      <j1 rule="para" parents="47797 49140"/>
    </justification>
  </clause>

  <clause id="49142">
    <literal><![CDATA[
      a((1 / (x * y)) * x,z,(y \ x) \ z) = a(y,z,z * ((x / y) \ K(y,x \ 1)))
    ]]></literal>
    <justification jstring="[para(1221(a,1),49141(a,1,1))].">
      <j1 rule="para" parents="1221 49141"/>
    </justification>
  </clause>

  <clause id="49143">
    <literal><![CDATA[
      a((x * y) * x,z,(y \ x) \ z) = a(y,z,z * ((x / y) \ K(y,x \ 1)))
    ]]></literal>
    <justification jstring="[hyper(2693,a,49142,a)].">
      <j1 rule="hyper" parents="2693 49142"/>
    </justification>
  </clause>

  <clause id="49144">
    <literal><![CDATA[
      a(x,y,L((x \ z) \ y,z,z)) = a(x,y,y * ((z / x) \ K(x,z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46581,a(flip),b,49143,a)].">
      <j1 rule="hyper" parents="64 46581 49143"/>
    </justification>
  </clause>

  <clause id="49145">
    <literal><![CDATA[
      a(x,y,y * ((z / x) \ K(x,z \ 1))) = a(x,y,(z \ 1) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46973,a(flip),b,49144,a),flip(a)].">
      <j1 rule="hyper" parents="64 46973 49144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49146">
    <literal><![CDATA[
      a(x,y,((z / x) \ 1) * y) = a(x,y,(z \ 1) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,27574,a(flip),b,49145,a)].">
      <j1 rule="hyper" parents="64 27574 49145"/>
    </justification>
  </clause>

  <clause id="49148">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (x * y)) = a(x,y,(z / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46681,a(flip),b,49146,a),flip(a)].">
      <j1 rule="hyper" parents="64 46681 49146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49149">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (x * y)) = a(x,y,(x \ z) \ y)
    ]]></literal>
    <justification jstring="[hyper(373,a,27389,a(flip),b,49148,a),flip(a)].">
      <j1 rule="hyper" parents="373 27389 49148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49150">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (x * y)) = a(x,y,z \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,46230,a(flip),b,49149,a),flip(a)].">
      <j1 rule="hyper" parents="373 46230 49149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49151">
    <literal><![CDATA[
      a(x,y,((z \ (x * y)) \ 1) * (x * y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27307,a(flip),b,49150,a),flip(a)].">
      <j1 rule="hyper" parents="373 27307 49150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49152">
    <literal><![CDATA[
      a(x,y,((z \ (y * x)) \ 1) * (y * x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,48907,a,b,49151,a)].">
      <j1 rule="hyper" parents="64 48907 49151"/>
    </justification>
  </clause>

  <clause id="49153">
    <literal><![CDATA[
      a(x,y,L(z,(x * y) * z,(x * y) * z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,48905,a,b,49152,a)].">
      <j1 rule="hyper" parents="64 48905 49152"/>
    </justification>
  </clause>

  <clause id="49154">
    <literal><![CDATA[
      L(x,y,(z * (u * w)) * ((u * z) * w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(49152(a,1),48096(a,1,3)),flip(a)].">
      <j1 rule="para" parents="49152 48096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49155">
    <literal><![CDATA[
      a(x,y,z) * (((x * y) * z) \ 1) = ((x * y) * z) \ a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(139,a,49153,a(flip),b,46507,a),flip(a)].">
      <j1 rule="hyper" parents="139 49153 46507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49156">
    <literal><![CDATA[
      T(a(x,y,z) / ((x * y) * z),x * (y * z)) = a(x,y,z) * (((x * y) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,25019,a,b,49155,a)].">
      <j1 rule="hyper" parents="373 25019 49155"/>
    </justification>
  </clause>

  <clause id="49157">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * z) * ((x * (y * z)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(145,a,46989,a(flip),b,49155,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="145 46989 49155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49158">
    <literal><![CDATA[
      L(x,((y * z) * u) * ((z * ((y \ 1) * u)) \ 1),w) = L(x,a(z,y \ 1,u),w)
    ]]></literal>
    <justification jstring="[para(49157(a,2),30852(a,1,2)),flip(a)].">
      <j1 rule="para" parents="49157 30852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49159">
    <literal><![CDATA[
      L(x,((y * z) * u) * ((z * ((y \ 1) * u)) \ 1),w) = L(x,a(z,y,u),w)
    ]]></literal>
    <justification jstring="[para(11980(a,1),49158(a,2,2))].">
      <j1 rule="para" parents="11980 49158"/>
    </justification>
  </clause>

  <clause id="49160">
    <literal><![CDATA[
      L(x,(y * ((z \ 1) * u)) * ((z * y) * u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(29616,a,49159,a)].">
      <j1 rule="hyper" parents="29616 49159"/>
    </justification>
  </clause>

  <clause id="49161">
    <literal><![CDATA[
      L(x,((y * z) * u) * ((y * u) * z),w) = L(x,a(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29642,a(flip),b,49160,a)].">
      <j1 rule="hyper" parents="64 29642 49160"/>
    </justification>
  </clause>

  <clause id="49162">
    <literal><![CDATA[
      T(a(x,y,z) / ((x * y) * z),R(x,u,w) * (y * z)) = a(x,y,z) * (((x * y) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,28124,a,b,49156,a)].">
      <j1 rule="hyper" parents="64 28124 49156"/>
    </justification>
  </clause>

  <clause id="49163">
    <literal><![CDATA[
      T(a(x,y,z) / ((x * y) * z),(R(x,u,w) * y) * z) = a(x,y,z) * (((x * y) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,25009,a,b,49162,a)].">
      <j1 rule="hyper" parents="64 25009 49162"/>
    </justification>
  </clause>

  <clause id="49164">
    <literal><![CDATA[
      T(a(x,y,z) / T((x * y) * z,a(u,w,v5)),(R(x,v6,v7) * y) * z) = a(x,y,z) * (((x * y) * z) \ 1)
    ]]></literal>
    <justification jstring="[para(23105(a,2),49163(a,1,1,2))].">
      <j1 rule="para" parents="23105 49163"/>
    </justification>
  </clause>

  <clause id="49165">
    <literal><![CDATA[
      T(a(x,y,z) / T((x * y) * z,a(u,w,v5)),(R(x,v6,v7) * y) * z) = (((x * y) * z) \ 1) * T(a(x,y,z),v8)
    ]]></literal>
    <justification jstring="[hyper(373,a,23961,a,b,49164,a),flip(a)].">
      <j1 rule="hyper" parents="373 23961 49164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49166">
    <literal><![CDATA[
      ((R(x,y,z) * y) * z) \ a(x,y,z) = ((x * y) * z) \ 1
    ]]></literal>
    <justification jstring="[hyper(36,a,44570,a(flip),b,49165,a(flip))].">
      <j1 rule="hyper" parents="36 44570 49165"/>
    </justification>
  </clause>

  <clause id="49167">
    <literal><![CDATA[
      a(x,y,z) \ K((x * y) * z,a(x,y,z) \ 1) = (x * (y * z)) * (((x * y) * z) \ 1)
    ]]></literal>
    <justification jstring="[para(49166(a,1),43653(a,1,2)),flip(a)].">
      <j1 rule="para" parents="49166 43653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49169">
    <literal><![CDATA[
      (x * (y * z)) * (((x * y) * z) \ 1) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(23696(a,1),49167(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23696 49167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49171">
    <literal><![CDATA[
      L(x,(y * (z * ((u * u) \ w))) * (((y * z) * w) \ 1),v5) = L(x,a(y,z,w) \ 1,v5)
    ]]></literal>
    <justification jstring="[para(49169(a,1),31152(a,2,2))].">
      <j1 rule="para" parents="49169 31152"/>
    </justification>
  </clause>

  <clause id="49172">
    <literal><![CDATA[
      L(x,((y * z) * u) * (y * (z * ((w * w) \ u))),v5) = L(x,a(y,z,u) \ 1,v5)
    ]]></literal>
    <justification jstring="[hyper(29616,a,49171,a)].">
      <j1 rule="hyper" parents="29616 49171"/>
    </justification>
  </clause>

  <clause id="49173">
    <literal><![CDATA[
      L(x,(y * (z * u)) * ((y * u) * z),w) = L(x,a(y,u,z) \ 1,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,39934,a(flip),b,49172,a)].">
      <j1 rule="hyper" parents="64 39934 49172"/>
    </justification>
  </clause>

  <clause id="49174">
    <literal><![CDATA[
      L(x,(y * (z * u)) * ((y * u) * z),w) = L(x,a(y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,11794,a(flip),b,49173,a),flip(a)].">
      <j1 rule="hyper" parents="373 11794 49173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49175">
    <literal><![CDATA[
      (x \ (x / (x \ (y \ L(y * x,z,u))))) \ w = a(u,z,(x \ 1) \ y) \ w
    ]]></literal>
    <justification jstring="[para(23134(a,1),47778(a,1,1)),flip(a)].">
      <j1 rule="para" parents="23134 47778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49177">
    <literal><![CDATA[
      (x \ ((x \ (y \ L(y * x,z,u))) \ x)) \ w = a(u,z,(x \ 1) \ y) \ w
    ]]></literal>
    <justification jstring="[para(24572(a,1),49175(a,1,1,2))].">
      <j1 rule="para" parents="24572 49175"/>
    </justification>
  </clause>

  <clause id="49178">
    <literal><![CDATA[
      (x \ (((y \ L(y * x,z,u)) \ x) * x)) \ w = a(u,z,(x \ 1) \ y) \ w
    ]]></literal>
    <justification jstring="[para(36054(a,1),49177(a,1,1,2))].">
      <j1 rule="para" parents="36054 49177"/>
    </justification>
  </clause>

  <clause id="49179">
    <literal><![CDATA[
      T((x \ L(x * y,z,u)) \ y,y) \ w = a(u,z,(y \ 1) \ x) \ w
    ]]></literal>
    <justification jstring="[para(22(a,2),49178(a,1,1))].">
      <j1 rule="para" parents="22 49178"/>
    </justification>
  </clause>

  <clause id="49180">
    <literal><![CDATA[
      ((x \ L(x * y,z,u)) \ y) \ w = a(u,z,(y \ 1) \ x) \ w
    ]]></literal>
    <justification jstring="[para(31555(a,1),49179(a,1,1))].">
      <j1 rule="para" parents="31555 49179"/>
    </justification>
  </clause>

  <clause id="49181">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) \ y = a(u,z,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[hyper(325,a,49180,a),flip(a)].">
      <j1 rule="hyper" parents="325 49180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49183">
    <literal><![CDATA[
      (a(x,x,a(y,z,u)) * L(a(x,x,a(u,z,y)) * w,v5,v6)) \ w = a(v6,v5,(w \ 1) \ a(x,x,a(u,z,y)))
    ]]></literal>
    <justification jstring="[para(41506(a,1),49181(a,1,1))].">
      <j1 rule="para" parents="41506 49181"/>
    </justification>
  </clause>

  <clause id="49185">
    <literal><![CDATA[
      a((x / (y / (z * z))) \ u,w,(z * z) * ((y \ x) * (v5 \ 1))) = a(u * (x / (y / (z * z))),w,((x / (y / (z * z))) \ v5) \ 1)
    ]]></literal>
    <justification jstring="[para(33(a,1),47909(a,1,3))].">
      <j1 rule="para" parents="33 47909"/>
    </justification>
  </clause>

  <clause id="49186">
    <literal><![CDATA[
      a(x \ (y / z),u,L((((x \ (y / z)) * x) \ 1) \ z,x * (y / z),x)) = a(x \ (y / z),u,L(z * ((x \ (z \ y)) * x),x,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,41734,a(flip),b,48217,a)].">
      <j1 rule="hyper" parents="64 41734 48217"/>
    </justification>
  </clause>

  <clause id="49187">
    <literal><![CDATA[
      x \ (y * R(a(z,u,u),(a(z,u,u) \ x) * y,a(z,u,u) * x)) = L(T(T(y,a(z,u,u)) / (a(z,u,u) \ x),x),a(z,u,u),x)
    ]]></literal>
    <justification jstring="[para(42481(a,1),48975(a,1,2,2))].">
      <j1 rule="para" parents="42481 48975"/>
    </justification>
  </clause>

  <clause id="49188">
    <literal><![CDATA[
      a(((1 / x) \ (y * x)) \ z,u,((x \ 1) \ T(y,x)) \ ((x \ 1) \ ((1 / x) \ y))) = a((((x \ 1) \ T(y,x)) \ z) * x,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27301,a(flip),b,49133,a)].">
      <j1 rule="hyper" parents="64 27301 49133"/>
    </justification>
  </clause>

  <clause id="49190">
    <literal><![CDATA[
      a(((1 / x) \ (y * x)) \ z,u,(x \ T(y,x)) \ (x \ ((1 / x) \ y))) = a((((x \ 1) \ T(y,x)) \ z) * x,u,x)
    ]]></literal>
    <justification jstring="[para(1612(a,1),49188(a,1,3))].">
      <j1 rule="para" parents="1612 49188"/>
    </justification>
  </clause>

  <clause id="49191">
    <literal><![CDATA[
      a(((1 / x) \ (y * x)) \ z,u,((x \ 1) * T(y,x)) \ y) = a((((x \ 1) \ T(y,x)) \ z) * x,u,x)
    ]]></literal>
    <justification jstring="[para(27830(a,1),49190(a,1,3))].">
      <j1 rule="para" parents="27830 49190"/>
    </justification>
  </clause>

  <clause id="49192">
    <literal><![CDATA[
      a(((1 / x) \ (y * x)) \ z,u,((x \ 1) * y) \ y) = a((((x \ 1) \ T(y,x)) \ z) * x,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27404,a(flip),b,49191,a)].">
      <j1 rule="hyper" parents="64 27404 49191"/>
    </justification>
  </clause>

  <clause id="49194">
    <literal><![CDATA[
      a(((1 / x) \ (y * x)) \ z,u,y \ ((x \ 1) \ y)) = a((((x \ 1) \ T(y,x)) \ z) * x,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,27457,a(flip),b,49192,a)].">
      <j1 rule="hyper" parents="64 27457 49192"/>
    </justification>
  </clause>

  <clause id="49195">
    <literal><![CDATA[
      a(((x \ 1) \ (y * x)) \ z,u,y \ ((x \ 1) \ y)) = a((((x \ 1) \ T(y,x)) \ z) * x,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32498,a(flip),b,49194,a)].">
      <j1 rule="hyper" parents="64 32498 49194"/>
    </justification>
  </clause>

  <clause id="49196">
    <literal><![CDATA[
      a((x * y) \ ((y \ 1) * z),u,x \ ((y \ 1) \ x)) = a((((y \ 1) \ T(x,y)) \ z) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46867,a(flip),b,49195,a)].">
      <j1 rule="hyper" parents="64 46867 49195"/>
    </justification>
  </clause>

  <clause id="49197">
    <literal><![CDATA[
      a((x * y) \ (y * z),u,x \ ((y \ 1) \ x)) = a((((y \ 1) \ T(x,y)) \ z) * y,u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,26916,a(flip),b,49196,a)].">
      <j1 rule="hyper" parents="64 26916 49196"/>
    </justification>
  </clause>

  <clause id="49198">
    <literal><![CDATA[
      a((((x \ 1) \ T(y,x)) \ z) * x,u,x) = a((y \ (x * z)) * x,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,47025,a(flip),b,49197,a),flip(a)].">
      <j1 rule="hyper" parents="64 47025 49197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49199">
    <literal><![CDATA[
      a((((x \ 1) \ y) \ z) * x,u,x) = a((y \ (x * z)) * x,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32402,a(flip),b,49198,a)].">
      <j1 rule="hyper" parents="64 32402 49198"/>
    </justification>
  </clause>

  <clause id="49201">
    <literal><![CDATA[
      a(((x \ y) \ z) * x,u,x) = a((y \ (x * z)) * x,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,32808,a(flip),b,49199,a)].">
      <j1 rule="hyper" parents="64 32808 49199"/>
    </justification>
  </clause>

  <clause id="49202">
    <literal><![CDATA[
      a(((x \ y) \ z) * x,u,x) = a(x * (y \ (z * x)),u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,32526,a(flip),b,49201,a),flip(a)].">
      <j1 rule="hyper" parents="373 32526 49201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49203">
    <literal><![CDATA[
      a((x \ y) * z,u,L(x,y,z)) = a(x * (((1 / x) \ y) \ (z * x)),u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,48677,a(flip),b,49202,a)].">
      <j1 rule="hyper" parents="64 48677 49202"/>
    </justification>
  </clause>

  <clause id="49204">
    <literal><![CDATA[
      a((x \ y) * z,u,L(x,y,z)) = a(x * (((x \ 1) \ y) \ (z * x)),u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,32677,a(flip),b,49203,a),flip(a)].">
      <j1 rule="hyper" parents="373 32677 49203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49205">
    <literal><![CDATA[
      a(((x \ y) \ (z * x)) * x,u,x) = a((x \ y) * z,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,32830,a(flip),b,49204,a)].">
      <j1 rule="hyper" parents="373 32830 49204"/>
    </justification>
  </clause>

  <clause id="49206">
    <literal><![CDATA[
      a((x \ y) * z,u,L(x,y,z)) = a(x * (y \ ((z * x) * x)),u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,49202,a(flip),b,49205,a),flip(a)].">
      <j1 rule="hyper" parents="64 49202 49205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49207">
    <literal><![CDATA[
      a((x \ y) * z,u,L(x,y,z)) = a(x * (y \ L(z,x,x)),u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,34951,a(flip),b,49206,a),flip(a)].">
      <j1 rule="hyper" parents="373 34951 49206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49208">
    <literal><![CDATA[
      a(x * (y / (z / (u * u))),w,((y / (z / (u * u))) \ v5) \ 1) = a((y / (z / (u * u))) \ x,w,(v5 \ (u * u)) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,27768,a(flip),b,49185,a),flip(a)].">
      <j1 rule="hyper" parents="64 27768 49185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49209">
    <literal><![CDATA[
      a(x * (1 / (y / (z * z))),u,((1 / (y / (z * z))) \ w) \ 1) = a((1 / (y / (z * z))) \ x,u,(y * w) \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,47009,a(flip),b,49208,a),flip(a)].">
      <j1 rule="hyper" parents="373 47009 49208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49210">
    <literal><![CDATA[
      a(x * (1 / (y / (z * z))),u,((1 / (y / (z * z))) \ w) \ 1) = a(y \ x,u,(y * w) \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,32502,a(flip),b,49209,a),flip(a)].">
      <j1 rule="hyper" parents="373 32502 49209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49212">
    <literal><![CDATA[
      a(x * (1 / (y / (z * z))),u,(((y / (z * z)) \ 1) \ w) \ 1) = a(y \ x,u,(y * w) \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27520,a(flip),b,49210,a)].">
      <j1 rule="hyper" parents="64 27520 49210"/>
    </justification>
  </clause>

  <clause id="49213">
    <literal><![CDATA[
      a(x * (1 / (y / (z * z))),u,(((z * z) * (y \ 1)) \ w) \ 1) = a(y \ x,u,(y * w) \ (z * z))
    ]]></literal>
    <justification jstring="[para(890(a,1),49212(a,1,3,1,1))].">
      <j1 rule="para" parents="890 49212"/>
    </justification>
  </clause>

  <clause id="49214">
    <literal><![CDATA[
      a(x * (1 / (y / (z * z))),u,((y \ 1) \ ((z * z) \ w)) \ 1) = a(y \ x,u,(y * w) \ (z * z))
    ]]></literal>
    <justification jstring="[para(487(a,1),49213(a,1,3,1))].">
      <j1 rule="para" parents="487 49213"/>
    </justification>
  </clause>

  <clause id="49215">
    <literal><![CDATA[
      a(x * (1 / (y / (z * z))),u,(z * z) * (((y \ 1) \ w) \ 1)) = a(y \ x,u,(y * w) \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,28039,a(flip),b,49214,a)].">
      <j1 rule="hyper" parents="64 28039 49214"/>
    </justification>
  </clause>

  <clause id="49216">
    <literal><![CDATA[
      a(x * (1 / (y / (z * z))),u,((y \ 1) \ w) \ (z * z)) = a(y \ x,u,(y * w) \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27390,a(flip),b,49215,a)].">
      <j1 rule="hyper" parents="64 27390 49215"/>
    </justification>
  </clause>

  <clause id="49217">
    <literal><![CDATA[
      a(x * (1 / (y / (z * z))),u,y \ (w \ (z * z))) = a(y \ x,u,(y * w) \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47652,a(flip),b,49216,a)].">
      <j1 rule="hyper" parents="64 47652 49216"/>
    </justification>
  </clause>

  <clause id="49218">
    <literal><![CDATA[
      a(x * ((y / (z * z)) \ 1),u,y \ (w \ (z * z))) = a(y \ x,u,(y * w) \ (z * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,32362,a(flip),b,49217,a)].">
      <j1 rule="hyper" parents="64 32362 49217"/>
    </justification>
  </clause>

  <clause id="49219">
    <literal><![CDATA[
      a(x * ((y * y) * (z \ 1)),u,z \ (w \ (y * y))) = a(z \ x,u,(z * w) \ (y * y))
    ]]></literal>
    <justification jstring="[para(890(a,1),49218(a,1,1,2))].">
      <j1 rule="para" parents="890 49218"/>
    </justification>
  </clause>

  <clause id="49220">
    <literal><![CDATA[
      a((x * (y * y)) * z,u,x \ (w \ (y * y))) = a(x \ z,u,(x * w) \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,32426,a(flip),b,49219,a)].">
      <j1 rule="hyper" parents="64 32426 49219"/>
    </justification>
  </clause>

  <clause id="49221">
    <literal><![CDATA[
      a(x * ((y * y) * z),u,x \ (w \ (y * y))) = a(x \ z,u,(x * w) \ (y * y))
    ]]></literal>
    <justification jstring="[para(34(a,1),49220(a,1,1))].">
      <j1 rule="para" parents="34 49220"/>
    </justification>
  </clause>

  <clause id="49222">
    <literal><![CDATA[
      a(x \ y,z,(x * u) \ (w * w)) = a(x * y,z,x \ (u \ (w * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,11957,a(flip),b,49221,a),flip(a)].">
      <j1 rule="hyper" parents="64 11957 49221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49224">
    <literal><![CDATA[
      a(x \ 1,y,(z * z) * (u \ ((x \ 1) \ (x \ (1 / x))))) = a(x * 1,y,x \ (u \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,48934,a,b,49222,a)].">
      <j1 rule="hyper" parents="64 48934 49222"/>
    </justification>
  </clause>

  <clause id="49225">
    <literal><![CDATA[
      a(x \ 1,y,(z * z) * (u \ ((x \ 1) \ (x \ (1 / x))))) = a(x,y,x \ (u \ (z * z)))
    ]]></literal>
    <justification jstring="[para(8(a,1),49224(a,2,1))].">
      <j1 rule="para" parents="8 49224"/>
    </justification>
  </clause>

  <clause id="49226">
    <literal><![CDATA[
      a(x \ 1,y,(z * z) * (u \ (x \ 1))) = a(x,y,x \ (u \ (z * z)))
    ]]></literal>
    <justification jstring="[para(1091(a,1),49225(a,1,3,2,2))].">
      <j1 rule="para" parents="1091 49225"/>
    </justification>
  </clause>

  <clause id="49227">
    <literal><![CDATA[
      a(x \ 1,y,z * ((z \ u) \ (x \ 1))) = a(x,y,x \ (u \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,48671,a(flip),b,49226,a)].">
      <j1 rule="hyper" parents="64 48671 49226"/>
    </justification>
  </clause>

  <clause id="49228">
    <literal><![CDATA[
      a(x,y,z * ((z \ u) \ (x \ 1))) = a(x,y,x \ (u \ (z * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,2653,a(flip),b,49227,a)].">
      <j1 rule="hyper" parents="64 2653 49227"/>
    </justification>
  </clause>

  <clause id="49229">
    <literal><![CDATA[
      a(x \ (y / z),u,L((((x \ (y / z)) * x) \ 1) \ z,x * (z \ y),x)) = a(x \ (y / z),u,L(z * ((x \ (z \ y)) * x),x,x))
    ]]></literal>
    <justification jstring="[para(29547(a,1),49186(a,1,3))].">
      <j1 rule="para" parents="29547 49186"/>
    </justification>
  </clause>

  <clause id="49230">
    <literal><![CDATA[
      x \ (y * R(a(z,u,u),(x * a(z,u,u)) * y,a(z,u,u) * x)) = L(T(T(y,a(z,u,u)) / (a(z,u,u) \ x),x),a(z,u,u),x)
    ]]></literal>
    <justification jstring="[para(42470(a,1),49187(a,1,2,2))].">
      <j1 rule="para" parents="42470 49187"/>
    </justification>
  </clause>

  <clause id="49231">
    <literal><![CDATA[
      a(x \ (y \ z),u,L((((x \ (z / y)) * x) \ 1) \ y,x * (y \ z),x)) = a(x \ (z / y),u,L(y * ((x \ (y \ z)) * x),x,x))
    ]]></literal>
    <justification jstring="[hyper(32449,a,49229,a)].">
      <j1 rule="hyper" parents="32449 49229"/>
    </justification>
  </clause>

  <clause id="49232">
    <literal><![CDATA[
      x \ (y * a(z,u,L(u,(x * a(z,u,u)) * y,a(z,u,u) * x))) = L(T(T(y,a(z,u,u)) / (a(z,u,u) \ x),x),a(z,u,u),x)
    ]]></literal>
    <justification jstring="[para(44016(a,2),49230(a,1,2,2))].">
      <j1 rule="para" parents="44016 49230"/>
    </justification>
  </clause>

  <clause id="49233">
    <literal><![CDATA[
      a(x \ (y / z),u,L(z * ((x \ (z \ y)) * x),x,x)) = a((z \ y) \ x,u,(((x \ (y / z)) * x) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46513,a(flip),b,49231,a),flip(a)].">
      <j1 rule="hyper" parents="64 46513 49231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49234">
    <literal><![CDATA[
      a(x \ (y / z),u,L(z * ((x \ (z \ y)) * x),x,x)) = a((z \ y) \ x,u,((y / z) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27521,a(flip),b,49233,a),flip(a)].">
      <j1 rule="hyper" parents="373 27521 49233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49236">
    <literal><![CDATA[
      a(x \ (y / z),u,L(z * ((x \ (z \ y)) * x),x,x)) = a((z \ y) \ x,u,((z \ y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27520,a(flip),b,49234,a),flip(a)].">
      <j1 rule="hyper" parents="373 27520 49234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49237">
    <literal><![CDATA[
      a(x \ (y / z),u,L(z * ((x \ (z \ y)) * x),x,x)) = a((z \ y) \ x,u,((y \ z) \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,38961,a(flip),b,49236,a),flip(a)].">
      <j1 rule="hyper" parents="373 38961 49236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49238">
    <literal><![CDATA[
      a(x \ (y / z),u,L(z * (z \ y),x,x)) = a((z \ y) \ x,u,((y \ z) \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27608,a(flip),b,49237,a)].">
      <j1 rule="hyper" parents="64 27608 49237"/>
    </justification>
  </clause>

  <clause id="49240">
    <literal><![CDATA[
      a((x \ y) \ z,u,((y \ x) \ 1) * x) = a(z \ (y / x),u,L(y,z,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),49238(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="10 49238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49241">
    <literal><![CDATA[
      a((x \ y) \ z,u,((y \ x) \ 1) * x) = a((y / x) * z,u,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,46645,a(flip),b,49240,a),flip(a)].">
      <j1 rule="hyper" parents="373 46645 49240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49242">
    <literal><![CDATA[
      a((x \ y) \ z,u,((y \ x) \ 1) * x) = a((x \ y) * z,u,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,32367,a(flip),b,49241,a),flip(a)].">
      <j1 rule="hyper" parents="373 32367 49241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49243">
    <literal><![CDATA[
      a((x \ y) \ z,u,((y \ x) \ 1) * x) = a(x * (z \ y),u,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,46866,a(flip),b,49242,a),flip(a)].">
      <j1 rule="hyper" parents="373 46866 49242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49244">
    <literal><![CDATA[
      a((a(x,y,(y \ z) * z) \ u) \ w,v5,((u \ a(x,y,(y \ z) * z)) \ 1) * a(x,y,(y \ z) * z)) = a(a(x,y,y) * (w \ u),v5,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,46382,a(flip),b,49243,a),flip(a)].">
      <j1 rule="hyper" parents="373 46382 49243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49245">
    <literal><![CDATA[
      L(T(T(x,a(y,z,z)) / (a(y,z,z) \ u),u),a(y,z,z),u) = u \ (x * a(y,z,L(z,(u * a(y,z,z)) * x,u)))
    ]]></literal>
    <justification jstring="[para(47190(a,1),49232(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="47190 49232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49247">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,(y / x) / (1 / x),x * ((y / x) / (1 / L(x,x,y))))) = a(((y \ x) \ z) * ((y / x) / (1 / x)),u,u)
    ]]></literal>
    <justification jstring="[para(38420(a,1),46875(a,1,3,3))].">
      <j1 rule="para" parents="38420 46875"/>
    </justification>
  </clause>

  <clause id="49248">
    <literal><![CDATA[
      L(x,y,y) \ (a(z,u,a(w,v5,v5)) * L(L(a(w,v5,a(z,u,v5)) * x,y,y),v6,v6)) = a(v6,v6,a(z,u,a(v5,v5,w)) * L(x,y,y)) \ 1
    ]]></literal>
    <justification jstring="[para(40864(a,1),48160(a,1,2))].">
      <j1 rule="para" parents="40864 48160"/>
    </justification>
  </clause>

  <clause id="49249">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,(y / x) / (1 / x),x * ((1 / L(x,x,y)) \ (y / x)))) = a(((y \ x) \ z) * ((y / x) / (1 / x)),u,u)
    ]]></literal>
    <justification jstring="[para(29018(a,1),49247(a,1,3))].">
      <j1 rule="para" parents="29018 49247"/>
    </justification>
  </clause>

  <clause id="49250">
    <literal><![CDATA[
      L(x,y,y) \ L(L(a(z,u,a(w,v5,u)) * x,y,y) * a(w,v5,a(z,u,u)),v6,v6) = a(v6,v6,a(w,v5,a(u,u,z)) * L(x,y,y)) \ 1
    ]]></literal>
    <justification jstring="[para(48163(a,2),49248(a,1,2))].">
      <j1 rule="para" parents="48163 49248"/>
    </justification>
  </clause>

  <clause id="49251">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,(y / x) / (1 / x),(x * L(x,x,y)) * (y / x))) = a(((y \ x) \ z) * ((y / x) / (1 / x)),u,u)
    ]]></literal>
    <justification jstring="[para(37881(a,1),49249(a,1,3,3))].">
      <j1 rule="para" parents="37881 49249"/>
    </justification>
  </clause>

  <clause id="49252">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,(y / x) / (1 / x),(x * L(x,x,y)) * (x \ y))) = a(((y \ x) \ z) * ((y / x) / (1 / x)),u,u)
    ]]></literal>
    <justification jstring="[para(29018(a,1),49251(a,1,3))].">
      <j1 rule="para" parents="29018 49251"/>
    </justification>
  </clause>

  <clause id="49253">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,(y / x) / (1 / x),a(y,x,x) * (x \ y))) = a(((y \ x) \ z) * ((y / x) / (1 / x)),u,u)
    ]]></literal>
    <justification jstring="[para(30489(a,1),49252(a,1,3))].">
      <j1 rule="para" parents="30489 49252"/>
    </justification>
  </clause>

  <clause id="49254">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,(y / x) / (1 / x),L(x,x,y) \ y)) = a(((y \ x) \ z) * ((y / x) / (1 / x)),u,u)
    ]]></literal>
    <justification jstring="[para(37561(a,1),49253(a,1,3,3))].">
      <j1 rule="para" parents="37561 49253"/>
    </justification>
  </clause>

  <clause id="49255">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,(y / x) / (1 / x),x * y)) = a(((y \ x) \ z) * ((y / x) / (1 / x)),u,u)
    ]]></literal>
    <justification jstring="[para(29136(a,1),49254(a,1,3))].">
      <j1 rule="para" parents="29136 49254"/>
    </justification>
  </clause>

  <clause id="49256">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,(1 / x) \ (y / x),x * y)) = a(((y \ x) \ z) * ((y / x) / (1 / x)),u,u)
    ]]></literal>
    <justification jstring="[para(29437(a,1),49255(a,1,3))].">
      <j1 rule="para" parents="29437 49255"/>
    </justification>
  </clause>

  <clause id="49257">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,(1 / x) \ (x \ y),x * y)) = a(((y \ x) \ z) * ((y / x) / (1 / x)),u,u)
    ]]></literal>
    <justification jstring="[para(29552(a,1),49256(a,1,3))].">
      <j1 rule="para" parents="29552 49256"/>
    </justification>
  </clause>

  <clause id="49258">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,x \ (x \ y),x * y)) = a(((y \ x) \ z) * ((y / x) / (1 / x)),u,u)
    ]]></literal>
    <justification jstring="[para(29694(a,1),49257(a,1,3))].">
      <j1 rule="para" parents="29694 49257"/>
    </justification>
  </clause>

  <clause id="49259">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,L(y,x,x),x * y)) = a(((y \ x) \ z) * ((y / x) / (1 / x)),u,u)
    ]]></literal>
    <justification jstring="[para(31756(a,1),49258(a,1,3))].">
      <j1 rule="para" parents="31756 49258"/>
    </justification>
  </clause>

  <clause id="49260">
    <literal><![CDATA[
      a(L(x,x,y) * z,u,L(u,y,y * x)) = a(((y \ x) \ z) * ((y / x) / (1 / x)),u,u)
    ]]></literal>
    <justification jstring="[para(45585(a,1),49259(a,1,3))].">
      <j1 rule="para" parents="45585 49259"/>
    </justification>
  </clause>

  <clause id="49261">
    <literal><![CDATA[
      a(((x \ y) \ z) * ((x / y) / (1 / y)),u,u) = a(x * (z * (x * y)),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,48069,a(flip),b,49260,a),flip(a)].">
      <j1 rule="hyper" parents="64 48069 49260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49262">
    <literal><![CDATA[
      a(((x \ y) \ z) * ((1 / y) \ (x / y)),u,u) = a(x * (z * (x * y)),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32362,a(flip),b,49261,a)].">
      <j1 rule="hyper" parents="64 32362 49261"/>
    </justification>
  </clause>

  <clause id="49263">
    <literal><![CDATA[
      a(((x \ y) \ z) * ((1 / y) \ (y \ x)),u,u) = a(x * (z * (x * y)),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32441,a(flip),b,49262,a)].">
      <j1 rule="hyper" parents="64 32441 49262"/>
    </justification>
  </clause>

  <clause id="49264">
    <literal><![CDATA[
      a((x \ (x \ y)) * ((y \ x) \ z),u,u) = a(y * (z * (y * x)),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32812,a(flip),b,49263,a)].">
      <j1 rule="hyper" parents="64 32812 49263"/>
    </justification>
  </clause>

  <clause id="49265">
    <literal><![CDATA[
      a(L(x,y,y) * ((x \ y) \ z),u,u) = a(x * (z * (x * y)),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32811,a(flip),b,49264,a)].">
      <j1 rule="hyper" parents="64 32811 49264"/>
    </justification>
  </clause>

  <clause id="49266">
    <literal><![CDATA[
      L(x,y,y) \ L(L(a(z,u,a(w,v5,u)) * (a(w,u,a(z,v5,u)) * x),y,y),v6,v6) = a(v6,v6,a(z,v5,a(u,u,w)) * L(x,y,y)) \ 1
    ]]></literal>
    <justification jstring="[para(48158(a,2),49250(a,1,2,1))].">
      <j1 rule="para" parents="48158 49250"/>
    </justification>
  </clause>

  <clause id="49267">
    <literal><![CDATA[
      L(x,y,y) \ L(L(x,y,y),z,z) = a(z,z,a(u,w,a(v5,v5,v6)) * L(x,y,y)) \ 1
    ]]></literal>
    <justification jstring="[para(47343(a,1),49266(a,1,2,1,1))].">
      <j1 rule="para" parents="47343 49266"/>
    </justification>
  </clause>

  <clause id="49268">
    <literal><![CDATA[
      L(x \ L(x,y,y),z,z) = a(y,y,a(u,w,a(v5,v5,v6)) * L(x,z,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,43675,a(flip),b,49267,a)].">
      <j1 rule="hyper" parents="64 43675 49267"/>
    </justification>
  </clause>

  <clause id="49269">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,u,w)) * L(v5,v6,v6)) \ 1 = a(x,x,v5) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,45939,a(flip),b,49268,a),flip(a)].">
      <j1 rule="hyper" parents="64 45939 49268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49271">
    <literal><![CDATA[
      a(x,x,L(a(y,z,a(u,w,z)) * v5,v6,v6)) \ 1 = a(x,x,v5) \ 1
    ]]></literal>
    <justification jstring="[para(48115(a,1),49269(a,1,1,3))].">
      <j1 rule="para" parents="48115 49269"/>
    </justification>
  </clause>

  <clause id="49272">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,w,z)) * v5) = a(x,x,v5)
    ]]></literal>
    <justification jstring="[hyper(40,a,45084,a(flip),b,49271,a(flip))].">
      <j1 rule="hyper" parents="40 45084 49271"/>
    </justification>
  </clause>

  <clause id="49273">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,y,w)) * v5) = a(x,x,v5)
    ]]></literal>
    <justification jstring="[para(47197(a,1),49272(a,1,3,1))].">
      <j1 rule="para" parents="47197 49272"/>
    </justification>
  </clause>

  <clause id="49274">
    <literal><![CDATA[
      a(x,x,y * a(z,u,L(w,v5,v5))) = a(x,x,a(z,u,w) * y)
    ]]></literal>
    <justification jstring="[para(47902(a,1),49273(a,1,3))].">
      <j1 rule="para" parents="47902 49273"/>
    </justification>
  </clause>

  <clause id="49275">
    <literal><![CDATA[
      a(x,x,a(y,L(z,u,u),w) * z) = a(x,x,z * a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47809,a(flip),b,49274,a),flip(a)].">
      <j1 rule="hyper" parents="64 47809 49274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49277">
    <literal><![CDATA[
      a(x,x,y * a(z,L(y,u,u),w)) = a(x,x,y * a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46473,a(flip),b,49275,a)].">
      <j1 rule="hyper" parents="64 46473 49275"/>
    </justification>
  </clause>

  <clause id="49278">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),T(x \ (x / y),y),1 / x) = a(((1 / x) / T(y,y \ 1)) * z,T(x \ (x / y),y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,27308,a(flip),b,46011,a),flip(a)].">
      <j1 rule="hyper" parents="373 27308 46011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49279">
    <literal><![CDATA[
      a(x,y,y) * (z * (a(x,y,y) * L(a(x,y,y) \ (z \ u),z,a(x,y,y)))) = 1 * L(z * (((a(x,y,y) \ 1) * z) \ u),y,a(y,1,x))
    ]]></literal>
    <justification jstring="[para(28865(a,1),46974(a,1,2,2))].">
      <j1 rule="para" parents="28865 46974"/>
    </justification>
  </clause>

  <clause id="49280">
    <literal><![CDATA[
      a(1 \ R((x \ 1) \ 1,y,z),u,1 \ (R((x \ 1) \ 1,y,z) * w)) = a(R((x \ 1) \ 1,y,z) \ 1,u,(R(x,y,z) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(27588,a,47824,a),flip(a)].">
      <j1 rule="hyper" parents="27588 47824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49281">
    <literal><![CDATA[
      a(1 \ R((x \ 1) \ 1,y,z),u,1 \ (R((x \ 1) \ 1,y,z) * w)) = a(R((x \ 1) \ 1,y,z) \ 1,u,L(x \ 1,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,41228,a,b,49280,a),flip(a)].">
      <j1 rule="hyper" parents="373 41228 49280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49283">
    <literal><![CDATA[
      a(1 \ R((x \ 1) \ 1,y,z),u,1 \ (R((x \ 1) \ 1,y,z) * w)) = a(R((x \ 1) \ 1,y,z),u,L(x \ 1,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(373,a,2653,a(flip),b,49281,a),flip(a)].">
      <j1 rule="hyper" parents="373 2653 49281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49284">
    <literal><![CDATA[
      a(1 \ R((x \ 1) \ 1,y,z),u,1 \ (R((x \ 1) \ 1,y,z) * w)) = a((x \ 1) \ 1,u,L(L(x \ 1,y,z) \ w,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,46576,a(flip),b,49283,a),flip(a)].">
      <j1 rule="hyper" parents="373 46576 49283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49285">
    <literal><![CDATA[
      a(1 \ R((x \ 1) \ 1,y,z),u,1 \ (R((x \ 1) \ 1,y,z) * w)) = a(x \ 1,u,L(L(x \ 1,y,z) \ w,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,2675,a(flip),b,49284,a),flip(a)].">
      <j1 rule="hyper" parents="373 2675 49284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49286">
    <literal><![CDATA[
      a(1 \ R((x \ 1) \ 1,y,z),u,1 \ (R((x \ 1) \ 1,y,z) * w)) = a(x \ 1,u,(x \ 1) \ L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,48860,a(flip),b,49285,a),flip(a)].">
      <j1 rule="hyper" parents="373 48860 49285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49287">
    <literal><![CDATA[
      a(1 \ R((x \ 1) \ 1,y,z),u,1 \ (R((x \ 1) \ 1,y,z) * w)) = a(1 * x,u,x * L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,46648,a(flip),b,49286,a),flip(a)].">
      <j1 rule="hyper" parents="373 46648 49286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49288">
    <literal><![CDATA[
      a(1 \ R((x \ 1) \ 1,y,z),u,1 \ (R((x \ 1) \ 1,y,z) * w)) = a(x,u,x * L(w,y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),49287(a,2,1))].">
      <j1 rule="para" parents="7 49287"/>
    </justification>
  </clause>

  <clause id="49289">
    <literal><![CDATA[
      a(R((x \ 1) \ 1,y,z),u,1 \ (R((x \ 1) \ 1,y,z) * w)) = a(x,u,x * L(w,y,z))
    ]]></literal>
    <justification jstring="[para(66(a,1),49288(a,1,1))].">
      <j1 rule="para" parents="66 49288"/>
    </justification>
  </clause>

  <clause id="49290">
    <literal><![CDATA[
      a(R((x \ 1) \ 1,y,z),u,R((x \ 1) \ 1,y,z) * w) = a(x,u,x * L(w,y,z))
    ]]></literal>
    <justification jstring="[para(66(a,1),49289(a,1,3))].">
      <j1 rule="para" parents="66 49289"/>
    </justification>
  </clause>

  <clause id="49291">
    <literal><![CDATA[
      a(R((x \ 1) \ 1,y,z),u,L((x \ 1) \ 1,y,z) * w) = a(x,u,x * L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,31314,a(flip),b,49290,a)].">
      <j1 rule="hyper" parents="64 31314 49290"/>
    </justification>
  </clause>

  <clause id="49292">
    <literal><![CDATA[
      a(R((x \ 1) \ 1,y,z),u,w * L(x,y,z)) = a(x,u,x * L(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27576,a(flip),b,49291,a)].">
      <j1 rule="hyper" parents="64 27576 49291"/>
    </justification>
  </clause>

  <clause id="49294">
    <literal><![CDATA[
      a((x \ 1) \ 1,y,L(z * L(x,u,w),u,w)) = a(x,y,x * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46576,a(flip),b,49292,a)].">
      <j1 rule="hyper" parents="64 46576 49292"/>
    </justification>
  </clause>

  <clause id="49295">
    <literal><![CDATA[
      a(x,y,L(z * L(x,u,w),u,w)) = a(x,y,x * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(26846,a,49294,a)].">
      <j1 rule="hyper" parents="26846 49294"/>
    </justification>
  </clause>

  <clause id="49296">
    <literal><![CDATA[
      a(x,y,L(L(x,z,u) * w,z,u)) = a(x,y,x * L(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27377,a,b,49295,a)].">
      <j1 rule="hyper" parents="64 27377 49295"/>
    </justification>
  </clause>

  <clause id="49298">
    <literal><![CDATA[
      a((x \ (y \ z)) * ((x \ y) * K(z,u)),w,(x \ y) * K(z,u)) = a((y \ z) * (y * K(z,u)),w,((z / y) * x) \ T(z,u))
    ]]></literal>
    <justification jstring="[para(23055(a,1),48665(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="23055 48665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49299">
    <literal><![CDATA[
      a((x \ (y \ z)) * ((x \ y) * K(z,u)),w,(x \ y) * K(z,u)) = a((y \ z) * (y * K(z,u)),w,((z / y) * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27301,a(flip),b,49298,a),flip(a)].">
      <j1 rule="hyper" parents="373 27301 49298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49302">
    <literal><![CDATA[
      a((x \ (y \ z)) * ((x \ y) * K(z,u)),w,(x \ y) * K(z,u)) = a((y \ z) * (y * K(z,u)),w,((y \ z) * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27519,a(flip),b,49299,a),flip(a)].">
      <j1 rule="hyper" parents="373 27519 49299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49303">
    <literal><![CDATA[
      a((x \ (y \ z)) * ((x \ y) * K(z,u)),w,(x \ y) * K(z,u)) = a((y \ z) * y,w,((y \ z) * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,32368,a(flip),b,49302,a),flip(a)].">
      <j1 rule="hyper" parents="373 32368 49302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49305">
    <literal><![CDATA[
      a((x \ (y \ z)) * ((x \ y) * K(z,u)),w,(x \ y) * K(z,u)) = a(z,w,((y \ z) * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,26836,a(flip),b,49303,a),flip(a)].">
      <j1 rule="hyper" parents="373 26836 49303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49306">
    <literal><![CDATA[
      a((x \ (y \ z)) * ((x \ y) * K(z,u)),w,x \ y) = a(z,w,((y \ z) * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(27583,a,49305,a)].">
      <j1 rule="hyper" parents="27583 49305"/>
    </justification>
  </clause>

  <clause id="49309">
    <literal><![CDATA[
      a((x \ (y \ z)) * (x \ y),u,x \ y) = a(z,u,((y \ z) * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32368,a(flip),b,49306,a)].">
      <j1 rule="hyper" parents="64 32368 49306"/>
    </justification>
  </clause>

  <clause id="49311">
    <literal><![CDATA[
      a((x \ y) * x,z,(u \ 1) * x) = a(y,z,((x \ y) * u) \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47773,a(flip),b,49309,a)].">
      <j1 rule="hyper" parents="64 47773 49309"/>
    </justification>
  </clause>

  <clause id="49312">
    <literal><![CDATA[
      a(x,y,((z \ x) * u) \ x) = a(x,y,(u \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26836,a(flip),b,49311,a),flip(a)].">
      <j1 rule="hyper" parents="64 26836 49311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49314">
    <literal><![CDATA[
      a(x,y,((z \ (x / (x \ z))) * u) \ x) = a(x,y,(u \ 1) * (z / (z \ x)))
    ]]></literal>
    <justification jstring="[para(40132(a,1),49312(a,1,3,1,1))].">
      <j1 rule="para" parents="40132 49312"/>
    </justification>
  </clause>

  <clause id="49315">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (u / (x / u))) = a(x,y,z \ ((x \ u) * u))
    ]]></literal>
    <justification jstring="[para(47795(a,1),49312(a,1,3)),flip(a)].">
      <j1 rule="para" parents="47795 49312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49316">
    <literal><![CDATA[
      a(x,y,(z \ 1) * ((x / u) \ u)) = a(x,y,z \ ((x \ u) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27310,a(flip),b,49315,a)].">
      <j1 rule="hyper" parents="64 27310 49315"/>
    </justification>
  </clause>

  <clause id="49317">
    <literal><![CDATA[
      a(x,y,(z \ 1) * ((u \ x) \ u)) = a(x,y,z \ ((x \ u) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27500,a(flip),b,49316,a)].">
      <j1 rule="hyper" parents="64 27500 49316"/>
    </justification>
  </clause>

  <clause id="49318">
    <literal><![CDATA[
      a(x,y,((z \ x) * ((x \ z) \ u)) \ x) = a(x,y,(u \ 1) * (z / (z \ x)))
    ]]></literal>
    <justification jstring="[para(40248(a,1),49314(a,1,3,1))].">
      <j1 rule="para" parents="40248 49314"/>
    </justification>
  </clause>

  <clause id="49319">
    <literal><![CDATA[
      a(x,y,(((x \ z) \ u) \ 1) * z) = a(x,y,(u \ 1) * (z / (z \ x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49312,a(flip),b,49318,a)].">
      <j1 rule="hyper" parents="64 49312 49318"/>
    </justification>
  </clause>

  <clause id="49320">
    <literal><![CDATA[
      a(x,y,(((x \ z) \ u) \ 1) * z) = a(x,y,(u \ 1) * ((z \ x) \ z))
    ]]></literal>
    <justification jstring="[hyper(373,a,27310,a(flip),b,49319,a),flip(a)].">
      <j1 rule="hyper" parents="373 27310 49319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49321">
    <literal><![CDATA[
      a(x,y,(((x \ z) \ u) \ 1) * z) = a(x,y,u \ ((x \ z) * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,49317,a(flip),b,49320,a),flip(a)].">
      <j1 rule="hyper" parents="373 49317 49320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49322">
    <literal><![CDATA[
      (a(x,y,y) \ (z / u)) \ ((a(x,y,y) \ z) * L(1 / u,y,a(y,z,x))) = a(a(x,y,y) \ z,L(u,y,a(y,z,x)),L(u,y,a(y,z,x)))
    ]]></literal>
    <justification jstring="[para(42168(a,2),48688(a,1,2,2))].">
      <j1 rule="para" parents="42168 48688"/>
    </justification>
  </clause>

  <clause id="49323">
    <literal><![CDATA[
      a((a(x,y,(y \ z) * z) \ u) \ w,v5,(u \ a(x,y,(y \ z) * z)) \ a(x,y,(y \ z) * z)) = a(a(x,y,y) * (w \ u),v5,u)
    ]]></literal>
    <justification jstring="[para(48129(a,1),49244(a,1,3))].">
      <j1 rule="para" parents="48129 49244"/>
    </justification>
  </clause>

  <clause id="49324">
    <literal><![CDATA[
      a((a(x,y,(y \ z) * z) \ u) \ w,v5,u) = a(a(x,y,y) * (w \ u),v5,u)
    ]]></literal>
    <justification jstring="[hyper(27585,a,49323,a)].">
      <j1 rule="hyper" parents="27585 49323"/>
    </justification>
  </clause>

  <clause id="49326">
    <literal><![CDATA[
      a((a(x,y,(y \ z) * z) * u) \ w,v5,u) = a(a(x,y,y) * (w \ u),v5,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42476,a(flip),b,49324,a)].">
      <j1 rule="hyper" parents="64 42476 49324"/>
    </justification>
  </clause>

  <clause id="49327">
    <literal><![CDATA[
      a(a(x,y,(y \ z) * z) \ (u \ w),v5,u) = a(a(x,y,y) * (w \ u),v5,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46081,a(flip),b,49326,a)].">
      <j1 rule="hyper" parents="64 46081 49326"/>
    </justification>
  </clause>

  <clause id="49328">
    <literal><![CDATA[
      a((x \ y) * a(z,u,(u \ w) * w),v5,x) = a(a(z,u,u) * (y \ x),v5,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42467,a(flip),b,49327,a)].">
      <j1 rule="hyper" parents="64 42467 49327"/>
    </justification>
  </clause>

  <clause id="49329">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ u),w,u) = a(a(x,y,y) * (u \ z),w,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46383,a(flip),b,49328,a),flip(a)].">
      <j1 rule="hyper" parents="64 46383 49328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49330">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ (u \ z)),w,z) = a(a(x,y,y) * (z \ (z * u)),w,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32708,a(flip),b,49329,a)].">
      <j1 rule="hyper" parents="64 32708 49329"/>
    </justification>
  </clause>

  <clause id="49331">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ (z \ (u \ z))),w,z) = a(a(x,y,y) * (z \ (z * (z * u))),w,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32957,a(flip),b,49330,a)].">
      <j1 rule="hyper" parents="64 32957 49330"/>
    </justification>
  </clause>

  <clause id="49332">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ (z * (z * u))),w,z) = a(L(u \ z,z,z) * a(x,y,y),w,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32817,a(flip),b,49331,a),flip(a)].">
      <j1 rule="hyper" parents="64 32817 49331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49333">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ (z * (z * u))),w,z) = a(L(a(x,y,y) * (u \ z),z,z),w,z)
    ]]></literal>
    <justification jstring="[para(49005(a,2),49332(a,2,1))].">
      <j1 rule="para" parents="49005 49332"/>
    </justification>
  </clause>

  <clause id="49334">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ (z * (z * u))),w,z) = a(a(x,y,y) * (u \ z),w,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,46056,a(flip),b,49333,a),flip(a)].">
      <j1 rule="hyper" parents="373 46056 49333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49336">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ u),w,u) = a(a(x,y,y) * (u * z),w,u)
    ]]></literal>
    <justification jstring="[para(9(a,1),49334(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9 49334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49337">
    <literal><![CDATA[
      a(a(x,y,y) * (z \ u),w,z) = a(a(x,y,y) * (z * u),w,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,49329,a(flip),b,49336,a)].">
      <j1 rule="hyper" parents="64 49329 49336"/>
    </justification>
  </clause>

  <clause id="49339">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),T(x \ (x / y),y),1 / x) = a(((1 / x) / T(y,y \ 1)) * z,x \ (x / y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,31892,a(flip),b,49278,a),flip(a)].">
      <j1 rule="hyper" parents="373 31892 49278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49341">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),T(x \ (x / y),y),1 / x) = a(((1 / x) / T(y,y \ 1)) * z,x * (x / y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,44889,a(flip),b,49339,a),flip(a)].">
      <j1 rule="hyper" parents="373 44889 49339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49342">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),T(x \ (x / y),y),1 / x) = a(((1 / x) / T(y,y \ 1)) * z,x * (y \ x),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,31897,a(flip),b,49341,a),flip(a)].">
      <j1 rule="hyper" parents="373 31897 49341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49343">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),T(x \ (x / y),y),1 / x) = a(((1 / x) / T(y,y \ 1)) * z,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,46414,a(flip),b,49342,a),flip(a)].">
      <j1 rule="hyper" parents="373 46414 49342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49344">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),T(x \ (x / y),y),1 / x) = a((T(y,y \ 1) \ (1 / x)) * z,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,32367,a(flip),b,49343,a),flip(a)].">
      <j1 rule="hyper" parents="373 32367 49343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49345">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),T(x \ (x / y),y),1 / x) = a((T(y,y \ 1) \ (x \ 1)) * z,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,32492,a(flip),b,49344,a),flip(a)].">
      <j1 rule="hyper" parents="373 32492 49344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49346">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),T(x \ (x / y),y),1 / x) = a((T(y,y \ 1) \ x) * z,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,32688,a(flip),b,49345,a),flip(a)].">
      <j1 rule="hyper" parents="373 32688 49345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49347">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),T(x \ (x / y),y),1 / x) = a((y \ x) * z,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,32391,a(flip),b,49346,a),flip(a)].">
      <j1 rule="hyper" parents="373 32391 49346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49348">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),T(x \ (x / y),y),x \ 1) = a((y \ x) * z,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(27586,a,49347,a)].">
      <j1 rule="hyper" parents="27586 49347"/>
    </justification>
  </clause>

  <clause id="49350">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),x \ (x / y),x \ 1) = a((y \ x) * z,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(31997,a,49348,a)].">
      <j1 rule="hyper" parents="31997 49348"/>
    </justification>
  </clause>

  <clause id="49352">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),x * (x / y),x \ 1) = a((y \ x) * z,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,44889,a(flip),b,49350,a)].">
      <j1 rule="hyper" parents="64 44889 49350"/>
    </justification>
  </clause>

  <clause id="49353">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),x * (y \ x),x \ 1) = a((y \ x) * z,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,31897,a(flip),b,49352,a)].">
      <j1 rule="hyper" parents="64 31897 49352"/>
    </justification>
  </clause>

  <clause id="49354">
    <literal><![CDATA[
      a(T(x \ (x / y),y) * ((1 / x) \ z),y,x \ 1) = a((y \ x) * z,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,46414,a(flip),b,49353,a)].">
      <j1 rule="hyper" parents="64 46414 49353"/>
    </justification>
  </clause>

  <clause id="49355">
    <literal><![CDATA[
      a((x \ y) * T(x \ (x / z),z),z,x \ 1) = a((z \ x) * y,z,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,32812,a(flip),b,49354,a)].">
      <j1 rule="hyper" parents="64 32812 49354"/>
    </justification>
  </clause>

  <clause id="49356">
    <literal><![CDATA[
      a((x \ y) * (x \ (x / z)),z,x \ 1) = a((z \ x) * y,z,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(32447,a,49355,a)].">
      <j1 rule="hyper" parents="32447 49355"/>
    </justification>
  </clause>

  <clause id="49358">
    <literal><![CDATA[
      a((x \ y) * z,x,y \ 1) = a(z * (x * y),x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,48789,a(flip),b,49356,a),flip(a)].">
      <j1 rule="hyper" parents="64 48789 49356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49359">
    <literal><![CDATA[
      a(x * (y * z),y,z \ 1) = a(z * (y * x),y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(64,a,48816,a(flip),b,49358,a),flip(a)].">
      <j1 rule="hyper" parents="64 48816 49358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49360">
    <literal><![CDATA[
      a(x * (y * z),y,a(z \ 1,u,w)) = a(w,u,a(z * (y * x),y,z \ 1))
    ]]></literal>
    <justification jstring="[para(49359(a,1),47198(a,2,3))].">
      <j1 rule="para" parents="49359 47198"/>
    </justification>
  </clause>

  <clause id="49361">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),u,z \ 1)) = a(w * (u * z),u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(2653(a,1),49360(a,1,3)),flip(a)].">
      <j1 rule="para" parents="2653 49360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49362">
    <literal><![CDATA[
      a(x * (y * z),y,a(z,u,w)) = a(z,y,a(w,u,z * (y * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47207,a(flip),b,49361,a),flip(a)].">
      <j1 rule="hyper" parents="64 47207 49361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49363">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (y * z))) = a(z,y,a(x,u,z * (y * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47327,a,b,49362,a)].">
      <j1 rule="hyper" parents="64 47327 49362"/>
    </justification>
  </clause>

  <clause id="49364">
    <literal><![CDATA[
      a(a(x,y,y) \ z,L(u,y,a(y,z,x)),L(u,y,a(y,z,x))) = (a(x,y,y) \ (z / u)) \ (a(x,y,y) \ (z * (1 / u)))
    ]]></literal>
    <justification jstring="[para(47439(a,1),49322(a,1,2)),flip(a)].">
      <j1 rule="para" parents="47439 49322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49365">
    <literal><![CDATA[
      a(a(x,y,y) \ z,L(u,y,a(y,z,x)),L(u,y,a(y,z,x))) = a(z,u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,47170,a(flip),b,49364,a),flip(a)].">
      <j1 rule="hyper" parents="373 47170 49364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49367">
    <literal><![CDATA[
      a(a(x,y,y) \ z,u,u) = a(z,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,40664,a(flip),b,49365,a)].">
      <j1 rule="hyper" parents="64 40664 49365"/>
    </justification>
  </clause>

  <clause id="49369">
    <literal><![CDATA[
      a(x * a(y,z,z),u,u) = a(x,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,45506,a(flip),b,49367,a)].">
      <j1 rule="hyper" parents="64 45506 49367"/>
    </justification>
  </clause>

  <clause id="49370">
    <literal><![CDATA[
      a(a(x,x,y) * z,u,u) = a(z,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42664,a(flip),b,49367,a)].">
      <j1 rule="hyper" parents="64 42664 49367"/>
    </justification>
  </clause>

  <clause id="49371">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,u) = a(z,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42461,a(flip),b,49367,a)].">
      <j1 rule="hyper" parents="64 42461 49367"/>
    </justification>
  </clause>

  <clause id="49373">
    <literal><![CDATA[
      a(x * (a(y,y,z) * u),w,w) = a(x \ u,w,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,48427,a(flip),b,49369,a)].">
      <j1 rule="hyper" parents="64 48427 49369"/>
    </justification>
  </clause>

  <clause id="49375">
    <literal><![CDATA[
      L(x,x,a(y,y,z) * u) = a(u,x,x) \ x
    ]]></literal>
    <justification jstring="[para(49370(a,1),30459(a,1,1)),flip(a)].">
      <j1 rule="para" parents="49370 30459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49378">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,u \ 1) = a(z,u \ 1,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(32046,a,49371,a)].">
      <j1 rule="hyper" parents="32046 49371"/>
    </justification>
  </clause>

  <clause id="49379">
    <literal><![CDATA[
      L(x,x,a(y,y,z) * u) = L(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,45065,a,b,49375,a),flip(a)].">
      <j1 rule="hyper" parents="373 45065 49375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49380">
    <literal><![CDATA[
      L(x \ 1,x,a(y,y,z) * u) = L(x \ 1,x \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(11853,a,49379,a)].">
      <j1 rule="hyper" parents="11853 49379"/>
    </justification>
  </clause>

  <clause id="49384">
    <literal><![CDATA[
      a(x * (a(y,y,z) * u),w,w) = a(u * x,w,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,45506,a(flip),b,49373,a),flip(a)].">
      <j1 rule="hyper" parents="373 45506 49373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49385">
    <literal><![CDATA[
      a(x * (y * L(z,u,u)),w,w) = a((y * z) * x,w,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,48212,a(flip),b,49384,a),flip(a)].">
      <j1 rule="hyper" parents="64 48212 49384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49386">
    <literal><![CDATA[
      a(L(x,y,y) * z,u,u) = a(z * x,u,u)
    ]]></literal>
    <justification jstring="[para(5563(a,1),49384(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5563 49384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49387">
    <literal><![CDATA[
      a(x * L(y,z,z),u,u) = a(y * x,u,u)
    ]]></literal>
    <justification jstring="[para(45713(a,1),49384(a,1,1)),flip(a)].">
      <j1 rule="para" parents="45713 49384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49388">
    <literal><![CDATA[
      a(((x \ y) \ z) * x,u,u) = a(x * (z * (x * y)),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,49265,a(flip),b,49386,a),flip(a)].">
      <j1 rule="hyper" parents="64 49265 49386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49390">
    <literal><![CDATA[
      a(((x * y) * (z * y)) * x,u,u) = a(z,u,L(u,y,x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47931,a(flip),b,49387,a),flip(a)].">
      <j1 rule="hyper" parents="64 47931 49387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49391">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,u \ 1) = a(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(373,a,11980,a(flip),b,49378,a),flip(a)].">
      <j1 rule="hyper" parents="373 11980 49378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49392">
    <literal><![CDATA[
      a(x,y,y \ 1) * ((y * (y \ 1)) * (a(z,u,u) * x)) = (y * (y \ 1)) * R(a(z,u,u) * x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(49391(a,1),23930(a,1,1))].">
      <j1 rule="para" parents="49391 23930"/>
    </justification>
  </clause>

  <clause id="49393">
    <literal><![CDATA[
      L(x \ 1,x,a(y,y,z) * u) = L(x \ 1,x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,11794,a(flip),b,49380,a),flip(a)].">
      <j1 rule="hyper" parents="373 11794 49380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49394">
    <literal><![CDATA[
      L(x \ 1,x,y * a(z,u,u)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,48270,a(flip),b,49393,a)].">
      <j1 rule="hyper" parents="64 48270 49393"/>
    </justification>
  </clause>

  <clause id="49397">
    <literal><![CDATA[
      a(x * (y * (z \ x)),u,u) = a(x * (y * (x * z)),u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,48038,a(flip),b,49388,a)].">
      <j1 rule="hyper" parents="64 48038 49388"/>
    </justification>
  </clause>

  <clause id="49398">
    <literal><![CDATA[
      a(x * (y * (x * (z * y))),u,u) = a(z,u,L(u,y,x * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47916,a(flip),b,49397,a),flip(a)].">
      <j1 rule="hyper" parents="64 47916 49397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49400">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,z * y,(1 / z) * (L(x,y,z) * (z * y)))) = a((1 / z) * ((z * y) * L(y * T(x,z * y),z,z)),u,u)
    ]]></literal>
    <justification jstring="[para(1341(a,1),49398(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1341 49398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49401">
    <literal><![CDATA[
      a(x,y,y \ 1) * (a(z,u,u) * x) = (y * (y \ 1)) * R(a(z,u,u) * x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(71(a,1),49392(a,1,2))].">
      <j1 rule="para" parents="71 49392"/>
    </justification>
  </clause>

  <clause id="49402">
    <literal><![CDATA[
      (x * (x \ 1)) * R(a(y,z,z) * u,x,x \ 1) = u * (a(u,x,x \ 1) * a(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,30266,a(flip),b,49401,a),flip(a)].">
      <j1 rule="hyper" parents="64 30266 49401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49404">
    <literal><![CDATA[
      (x * (x \ 1)) * R(a(y,z,z) * u,x,x \ 1) = R(u,x,x \ 1) * a(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,46827,a(flip),b,49402,a),flip(a)].">
      <j1 rule="hyper" parents="373 46827 49402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49405">
    <literal><![CDATA[
      R(a(x,y,y) * z,u,u \ 1) = R(z,u,u \ 1) * a(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(233,a,49404,a)].">
      <j1 rule="hyper" parents="233 49404"/>
    </justification>
  </clause>

  <clause id="49407">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,z * y,(1 / z) * (L(x,y,z) * (z * y)))) = a(z * (((z \ 1) * y) * L(y * T(x,z * y),z,z)),u,u)
    ]]></literal>
    <justification jstring="[para(1603(a,1),49400(a,2,1))].">
      <j1 rule="para" parents="1603 49400"/>
    </justification>
  </clause>

  <clause id="49408">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,z * y,(1 / z) * (L(x,y,z) * (z * y)))) = a((((z \ 1) * y) * (y * T(x,z * y))) * z,u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,49385,a(flip),b,49407,a),flip(a)].">
      <j1 rule="hyper" parents="373 49385 49407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49410">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,z * y,(1 / z) * (L(x,y,z) * (z * y)))) = a((((z \ 1) * y) * (x * y)) * z,u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32741,a(flip),b,49408,a),flip(a)].">
      <j1 rule="hyper" parents="373 32741 49408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49412">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,z * y,(1 / z) * (L(x,y,z) * (z * y)))) = a(((z * y) * (x * y)) * z,u,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,2706,a(flip),b,49410,a),flip(a)].">
      <j1 rule="hyper" parents="373 2706 49410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49413">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,z * y,(1 / z) * (L(x,y,z) * (z * y)))) = a(x,u,L(u,y,z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,49390,a(flip),b,49412,a),flip(a)].">
      <j1 rule="hyper" parents="373 49390 49412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49414">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,z * y,L(y * T(x,z * y),z,z))) = a(x,u,L(u,y,z * y))
    ]]></literal>
    <justification jstring="[para(1341(a,1),49413(a,1,3,3))].">
      <j1 rule="para" parents="1341 49413"/>
    </justification>
  </clause>

  <clause id="49415">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,z * y,L(y * x,z,z))) = a(x,u,L(u,y,z * y))
    ]]></literal>
    <justification jstring="[para(29035(a,1),49414(a,1,3))].">
      <j1 rule="para" parents="29035 49414"/>
    </justification>
  </clause>

  <clause id="49416">
    <literal><![CDATA[
      a(L(x,y,z),u,L(u,z * y,y * x)) = a(x,u,L(u,y,z * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47027,a(flip),b,49415,a)].">
      <j1 rule="hyper" parents="64 47027 49415"/>
    </justification>
  </clause>

  <clause id="49419">
    <literal><![CDATA[
      a(x,y,L(L(y,z * u,u * x),u,z)) = a(x,y,L(y,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46496,a(flip),b,49416,a)].">
      <j1 rule="hyper" parents="64 46496 49416"/>
    </justification>
  </clause>

  <clause id="49420">
    <literal><![CDATA[
      a(x,y,L(L(y,z * u,u),u,z)) = a(x,y,L(y,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,48897,a(flip),b,49419,a)].">
      <j1 rule="hyper" parents="64 48897 49419"/>
    </justification>
  </clause>

  <clause id="49421">
    <literal><![CDATA[
      a(x,y,L(L(y,z,u),u,z)) = a(x,y,L(y,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47076,a(flip),b,49420,a)].">
      <j1 rule="hyper" parents="64 47076 49420"/>
    </justification>
  </clause>

  <clause id="49422">
    <literal><![CDATA[
      a(x,y,y) \ a(x,y,L(y,z,u * z)) = a(u,a(x,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(139,a,49421,a(flip),b,47012,a(flip))].">
      <j1 rule="hyper" parents="139 49421 47012"/>
    </justification>
  </clause>

  <clause id="49423">
    <literal><![CDATA[
      a(x,x,a(y * z,z,u)) = a(y,a(u,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47249,a(flip),b,49422,a)].">
      <j1 rule="hyper" parents="64 47249 49422"/>
    </justification>
  </clause>

  <clause id="49424">
    <literal><![CDATA[
      a(x * y,z,a(u,w,a(z,x,v5))) = a(x,a(a(u,w,v5),z,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47289,a,b,49423,a)].">
      <j1 rule="hyper" parents="64 47289 49423"/>
    </justification>
  </clause>

  <clause id="49425">
    <literal><![CDATA[
      a(x,y,a(z * u,z,y)) = a(z,a(x,y,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46918,a,b,49423,a)].">
      <j1 rule="hyper" parents="64 46918 49423"/>
    </justification>
  </clause>

  <clause id="49426">
    <literal><![CDATA[
      a(x,y,a(z,z,y * u)) = a(y,a(x,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46914,a,b,49423,a)].">
      <j1 rule="hyper" parents="64 46914 49423"/>
    </justification>
  </clause>

  <clause id="49427">
    <literal><![CDATA[
      a(x,y,a(z,z,u * y)) = a(y,a(x,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46912,a,b,49423,a)].">
      <j1 rule="hyper" parents="64 46912 49423"/>
    </justification>
  </clause>

  <clause id="49428">
    <literal><![CDATA[
      a(x * y,y,a(z,z,u)) = a(y,a(u,z,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,46911,a,b,49423,a)].">
      <j1 rule="hyper" parents="64 46911 49423"/>
    </justification>
  </clause>

  <clause id="49429">
    <literal><![CDATA[
      a(x * y,z,a(z,x,u)) = a(x,a(u,z,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46909,a,b,49423,a)].">
      <j1 rule="hyper" parents="64 46909 49423"/>
    </justification>
  </clause>

  <clause id="49430">
    <literal><![CDATA[
      a(x * y,z,a(u,x,z)) = a(x,a(u,z,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46907,a,b,49423,a)].">
      <j1 rule="hyper" parents="64 46907 49423"/>
    </justification>
  </clause>

  <clause id="49431">
    <literal><![CDATA[
      a(x,x,a(y * z,y,u)) = a(y,a(u,x,x),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46913,a(flip),b,49423,a)].">
      <j1 rule="hyper" parents="64 46913 49423"/>
    </justification>
  </clause>

  <clause id="49432">
    <literal><![CDATA[
      a(x * y,y,a(z,u,a(w,v5,u))) = a(w,v5,a(y,a(z,u,u),x))
    ]]></literal>
    <justification jstring="[para(49423(a,1),47512(a,2,3))].">
      <j1 rule="para" parents="49423 47512"/>
    </justification>
  </clause>

  <clause id="49433">
    <literal><![CDATA[
      L(x,x,a(y,z,z * u)) = x * a(z,a(y,x,x),u)
    ]]></literal>
    <justification jstring="[para(49425(a,1),45897(a,1,2)),flip(a)].">
      <j1 rule="para" parents="49425 45897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49434">
    <literal><![CDATA[
      x * (y * a(z,u,a(x * (x * y),x,u))) = R(x,a(z,u,u),x * y) * y
    ]]></literal>
    <justification jstring="[para(49425(a,2),45412(a,1,2,2))].">
      <j1 rule="para" parents="49425 45412"/>
    </justification>
  </clause>

  <clause id="49435">
    <literal><![CDATA[
      a(x,a(y,z,z),u) * a(z,z,L(y,x * u,x)) = a(z,z,y * a(x,y,x * u))
    ]]></literal>
    <justification jstring="[para(49425(a,1),47828(a,1,1))].">
      <j1 rule="para" parents="49425 47828"/>
    </justification>
  </clause>

  <clause id="49436">
    <literal><![CDATA[
      a(x,y,a(z * u,z,a(w,v5,y))) = a(x,v5,a(z,a(w,y,y),u))
    ]]></literal>
    <justification jstring="[para(49426(a,1),47515(a,1,3)),flip(a)].">
      <j1 rule="para" parents="49426 47515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49437">
    <literal><![CDATA[
      a(x * y,x,a(z,u,a(w,z,v5))) = a(w,u,a(y,a(v5,z,z),x))
    ]]></literal>
    <justification jstring="[para(49427(a,1),47661(a,2,3))].">
      <j1 rule="para" parents="49427 47661"/>
    </justification>
  </clause>

  <clause id="49438">
    <literal><![CDATA[
      x * L(x \ y,z,a(u,y,z)) = y * a(y,a(u,z,z),x)
    ]]></literal>
    <justification jstring="[para(49428(a,1),47457(a,2,2))].">
      <j1 rule="para" parents="49428 47457"/>
    </justification>
  </clause>

  <clause id="49439">
    <literal><![CDATA[
      a(x,y,a(z * u,z,a(w,v5,y))) = a(u,a(a(w,v5,x),y,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47525,a(flip),b,49429,a)].">
      <j1 rule="hyper" parents="64 47525 49429"/>
    </justification>
  </clause>

  <clause id="49440">
    <literal><![CDATA[
      a(x,a(y,z,z),x \ u) = a(u,z,a(y,x,z))
    ]]></literal>
    <justification jstring="[para(10(a,1),49430(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 49430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49441">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,a(u,w,w),v5)) = y * a(a(z * v5,z,u),w,a(x * y,x,w))
    ]]></literal>
    <justification jstring="[para(49431(a,1),47358(a,1,2,3))].">
      <j1 rule="para" parents="49431 47358"/>
    </justification>
  </clause>

  <clause id="49442">
    <literal><![CDATA[
      x * a(y,z,a(z * u,w,a(v5,v5,v6))) = x * a(z,a(a(y,w,v6),v5,v5),u)
    ]]></literal>
    <justification jstring="[para(49431(a,1),47660(a,2,2))].">
      <j1 rule="para" parents="49431 47660"/>
    </justification>
  </clause>

  <clause id="49443">
    <literal><![CDATA[
      a(x,a(y,z,z),x * u) = a(u,z,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,48423,a(flip),b,49440,a)].">
      <j1 rule="hyper" parents="64 48423 49440"/>
    </justification>
  </clause>

  <clause id="49444">
    <literal><![CDATA[
      a(x,a(y,z,z),u * x) = a(u,z,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(27453,a,49443,a)].">
      <j1 rule="hyper" parents="27453 49443"/>
    </justification>
  </clause>

  <clause id="49445">
    <literal><![CDATA[
      a(x,a(y,y,z),x * u) = a(u,y,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42391,a,b,49443,a)].">
      <j1 rule="hyper" parents="64 42391 49443"/>
    </justification>
  </clause>

  <clause id="49446">
    <literal><![CDATA[
      a(x,a(y,z,z),L(L(x,u,w) * v5,u,w)) = a(v5,z,a(y,L(x,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46496,a(flip),b,49443,a)].">
      <j1 rule="hyper" parents="64 46496 49443"/>
    </justification>
  </clause>

  <clause id="49447">
    <literal><![CDATA[
      a(x * L(y,z,z),a(u,u,w),y) = a(x,u,a(w,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,49089,a,b,49444,a)].">
      <j1 rule="hyper" parents="64 49089 49444"/>
    </justification>
  </clause>

  <clause id="49448">
    <literal><![CDATA[
      a(x,y,y * a(z * u,y,u)) = a(x,y,y) * a(z,y,a(x,u,y))
    ]]></literal>
    <justification jstring="[hyper(145,a,49444,a(flip),b,47014,a),flip(a)].">
      <j1 rule="hyper" parents="145 49444 47014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49449">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ u,w,a(v5,u,w)) = u * a(z,a(v5,w,w),a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,47334,a,b,49438,a),flip(a)].">
      <j1 rule="hyper" parents="373 47334 49438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49450">
    <literal><![CDATA[
      x * L(x \ y,z,a(u,y,z)) = L(y,a(u,z,z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,42627,a(flip),b,49438,a),flip(a)].">
      <j1 rule="hyper" parents="373 42627 49438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49451">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) * (x \ u) = L(u,a(z,y,y),x \ u)
    ]]></literal>
    <justification jstring="[hyper(1072,a,49450,a)].">
      <j1 rule="hyper" parents="1072 49450"/>
    </justification>
  </clause>

  <clause id="49452">
    <literal><![CDATA[
      x * L(x \ ((x \ ((1 / x) \ a(y,z,z))) \ u),z,a(y,(x \ ((1 / x) \ a(y,z,z))) \ u,z)) = (x \ a(y,z,z)) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,43548,a(flip),b,49450,a),flip(a)].">
      <j1 rule="hyper" parents="373 43548 49450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49453">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(u,x \ y,x)) = L(x \ y,a(z,u,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47658,a,b,49450,a)].">
      <j1 rule="hyper" parents="64 47658 49450"/>
    </justification>
  </clause>

  <clause id="49454">
    <literal><![CDATA[
      a((x \ a(y,z,z)) \ u,w,x * L(x \ v5,z,a(y,v5,z))) = a(L(a(y,z,z),x,x) \ (x \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(49450(a,2),46590(a,2,3)),flip(a)].">
      <j1 rule="para" parents="49450 46590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49455">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,y)) \ u) = L(u,a(z,y,y),x \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42180,a(flip),b,49451,a)].">
      <j1 rule="hyper" parents="64 42180 49451"/>
    </justification>
  </clause>

  <clause id="49456">
    <literal><![CDATA[
      L(x,a(y,z,z),u \ x) = x * a(y,x,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46484,a(flip),b,49455,a),flip(a)].">
      <j1 rule="hyper" parents="64 46484 49455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49457">
    <literal><![CDATA[
      L(x,a(y,z,z),u * x) = x * a(y,x,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,48384,a(flip),b,49456,a)].">
      <j1 rule="hyper" parents="64 48384 49456"/>
    </justification>
  </clause>

  <clause id="49458">
    <literal><![CDATA[
      L(x,a(y,z,z),u * x) = x * a(z,x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,47309,a,b,49457,a),flip(a)].">
      <j1 rule="hyper" parents="373 47309 49457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49459">
    <literal><![CDATA[
      L(x,a(y,z,z),u * x) = x * a(z,z,a(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,47259,a,b,49457,a),flip(a)].">
      <j1 rule="hyper" parents="373 47259 49457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49460">
    <literal><![CDATA[
      L(x,a(y,z,z),u * x) = x * a(y,x,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,41901,a,b,49457,a),flip(a)].">
      <j1 rule="hyper" parents="373 41901 49457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49461">
    <literal><![CDATA[
      x \ L(y,a(z,u,u),w * y) = a(w,u,a(u,y,z)) * (x \ y)
    ]]></literal>
    <justification jstring="[para(49458(a,2),48732(a,1,2))].">
      <j1 rule="para" parents="49458 48732"/>
    </justification>
  </clause>

  <clause id="49462">
    <literal><![CDATA[
      L(L(x,y,a(z,u,u)),a(z,u,u),y) = L(x,a(z,u,u),y * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,45896,a,b,49459,a)].">
      <j1 rule="hyper" parents="373 45896 49459"/>
    </justification>
  </clause>

  <clause id="49463">
    <literal><![CDATA[
      L((1 / a(x,y,y)) \ z,a(u,y,y),x * ((1 / a(x,y,y)) \ z)) = (1 / a(x,y,y)) \ (a(u,(1 / a(x,y,y)) \ z,a(x,y,y)) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,33453,a,b,49460,a),flip(a)].">
      <j1 rule="hyper" parents="373 33453 49460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49464">
    <literal><![CDATA[
      L(x \ (T(a(y,z,z),u) * w),a(x,z,z),y * (x \ (T(a(y,z,z),u) * w))) = x \ (T(a(y,z,z),u) * (w * a(x,x \ (T(a(y,z,z),u) * w),a(y,z,z))))
    ]]></literal>
    <justification jstring="[hyper(373,a,33446,a,b,49460,a),flip(a)].">
      <j1 rule="hyper" parents="373 33446 49460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49465">
    <literal><![CDATA[
      L(T(a(x,y,y),z) * u,a(w,y,y),x * (T(a(x,y,y),z) * u)) = T(a(x,y,y),z) * (u * a(w,T(a(x,y,y),z) * u,a(x,y,y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,33198,a(flip),b,49460,a),flip(a)].">
      <j1 rule="hyper" parents="373 33198 49460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49466">
    <literal><![CDATA[
      L(x * L(y,z,u),a(w,v5,v5),L((x \ 1) * (x * y),z,u)) = (x * L(y,z,u)) * a(w,x * L(y,z,u),a(x \ 1,v5,v5))
    ]]></literal>
    <justification jstring="[para(5645(a,2),49460(a,1,3))].">
      <j1 rule="para" parents="5645 49460"/>
    </justification>
  </clause>

  <clause id="49467">
    <literal><![CDATA[
      a(x * y,z,a(u,w,a(z,x,v5))) = a(x,a(v5,w,a(z,z,u)),y)
    ]]></literal>
    <justification jstring="[para(45501(a,1),49424(a,2,2))].">
      <j1 rule="para" parents="45501 49424"/>
    </justification>
  </clause>

  <clause id="49468">
    <literal><![CDATA[
      a(x,y,a(y * z,u,a(w,w,v5))) = a(x,u,a(z,a(v5,w,w),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,48046,a(flip),b,49432,a)].">
      <j1 rule="hyper" parents="64 48046 49432"/>
    </justification>
  </clause>

  <clause id="49469">
    <literal><![CDATA[
      a(x,y,a(z * u,z,a(w,v5,y))) = a(u,a(x,v5,a(y,y,w)),z)
    ]]></literal>
    <justification jstring="[para(45501(a,1),49439(a,2,2))].">
      <j1 rule="para" parents="45501 49439"/>
    </justification>
  </clause>

  <clause id="49470">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(u,x * y,x)) = L(x \ y,a(z,u,u),y)
    ]]></literal>
    <justification jstring="[para(35684(a,1),49453(a,1,2,3))].">
      <j1 rule="para" parents="35684 49453"/>
    </justification>
  </clause>

  <clause id="49471">
    <literal><![CDATA[
      (L(x,y,a(z,u,u)) * a(z,u,u)) * (a(y,a(z,u,u),L(x,y,a(z,u,u))) \ y) = (L(x,a(z,u,u),y * x) * a(z,u,u)) * y
    ]]></literal>
    <justification jstring="[para(49462(a,1),45076(a,2,1,1))].">
      <j1 rule="para" parents="49462 45076"/>
    </justification>
  </clause>

  <clause id="49472">
    <literal><![CDATA[
      a(x,a(y,z,a(u,u,w)),v5) = a(y,z,a(v5,a(w,u,u),x))
    ]]></literal>
    <justification jstring="[hyper(64,a,49436,a(flip),b,49469,a),flip(a)].">
      <j1 rule="hyper" parents="64 49436 49469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49473">
    <literal><![CDATA[
      a(x,a(y,z,a(u,u,w)),v5) = a(x,a(w,u,u),a(v5,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,47197,a,b,49472,a),flip(a)].">
      <j1 rule="hyper" parents="373 47197 49472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49474">
    <literal><![CDATA[
      a(x * y,z,a(u,w,a(z,x,v5))) = a(x,a(u,z,z),a(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,49467,a,b,49473,a)].">
      <j1 rule="hyper" parents="64 49467 49473"/>
    </justification>
  </clause>

  <clause id="49475">
    <literal><![CDATA[
      L(x,y,a(y,x * z,u)) \ z = L(x \ z,a(u,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46803,a(flip),b,49470,a)].">
      <j1 rule="hyper" parents="64 46803 49470"/>
    </justification>
  </clause>

  <clause id="49476">
    <literal><![CDATA[
      L(x \ y,a(z,u,u),y) = L(x,u,a(z,y,u)) \ y
    ]]></literal>
    <justification jstring="[para(46905(a,1),49475(a,1,1)),flip(a)].">
      <j1 rule="para" parents="46905 49475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49477">
    <literal><![CDATA[
      L(x \ y,a(z,u,u),y) = L(x,y,a(u,u,z)) \ y
    ]]></literal>
    <justification jstring="[para(46261(a,1),49476(a,2,1))].">
      <j1 rule="para" parents="46261 49476"/>
    </justification>
  </clause>

  <clause id="49478">
    <literal><![CDATA[
      L(x,a(y,z,u),a(z,z,w)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,48836,a(flip),b,49477,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 48836 49477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49497">
    <literal><![CDATA[
      a(x,y,y) * (a(z,y,u) * ((a(x,y,y) * a(z,y,u)) \ w)) = w
    ]]></literal>
    <justification jstring="[hyper(38,a,29295,a,b,49478,a(flip))].">
      <j1 rule="hyper" parents="38 29295 49478"/>
    </justification>
  </clause>

  <clause id="49505">
    <literal><![CDATA[
      a(x,y,y) * (a(z,y,u) * (a(x,y,y) \ (a(z,y,u) \ w))) = w
    ]]></literal>
    <justification jstring="[para(48846(a,1),49497(a,1,2,2))].">
      <j1 rule="para" parents="48846 49497"/>
    </justification>
  </clause>

  <clause id="49506">
    <literal><![CDATA[
      a(x,y,y) * (a(z,y,u) * (a(x,y,y) \ w)) = a(z,y,u) * w
    ]]></literal>
    <justification jstring="[para(9(a,1),49505(a,1,2,2,2))].">
      <j1 rule="para" parents="9 49505"/>
    </justification>
  </clause>

  <clause id="49508">
    <literal><![CDATA[
      a(a(x,y,z) * (a(u,y,y) \ w),a(u,y,y),v5) * (a(x,y,z) * w) = a(u,y,y) * R(a(x,y,z) * (a(u,y,y) \ w),a(u,y,y),v5)
    ]]></literal>
    <justification jstring="[para(49506(a,1),41806(a,1,2))].">
      <j1 rule="para" parents="49506 41806"/>
    </justification>
  </clause>

  <clause id="49509">
    <literal><![CDATA[
      a(x,y,y * a(z * u,y,u)) = a(x,y,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,47397,a(flip),b,49448,a),flip(a)].">
      <j1 rule="hyper" parents="373 47397 49448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49510">
    <literal><![CDATA[
      a(x,a(y,z,z),x * L(u,w,v5)) = a(u,z,a(y,L(x,w,v5),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,49296,a(flip),b,49446,a)].">
      <j1 rule="hyper" parents="64 49296 49446"/>
    </justification>
  </clause>

  <clause id="49511">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,u)) = a(x,u,a(w,L(v5,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,49443,a(flip),b,49510,a)].">
      <j1 rule="hyper" parents="64 49443 49510"/>
    </justification>
  </clause>

  <clause id="49512">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5),y)) = a(x,y,a(z,u,L(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46629,a(flip),b,49511,a),flip(a)].">
      <j1 rule="hyper" parents="64 46629 49511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49513">
    <literal><![CDATA[
      a(x,y,a(z,L(u,u,w),L(y,v5,v6))) = a(y,y,a(z,L(u,v5,v6),x))
    ]]></literal>
    <justification jstring="[hyper(64,a,49062,a(flip),b,49512,a),flip(a)].">
      <j1 rule="hyper" parents="64 49062 49512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49514">
    <literal><![CDATA[
      a(x,x,a(y,L(z,u,w),v5)) = a(x,x,a(y,z,L(v5,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49055,a(flip),b,49513,a),flip(a)].">
      <j1 rule="hyper" parents="64 49055 49513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49515">
    <literal><![CDATA[
      x * (y * a(z,u,a(y,x,L(u,x,x)))) = R(x,a(z,u,u),x * y) * y
    ]]></literal>
    <justification jstring="[para(46582(a,1),49434(a,1,2,2,3))].">
      <j1 rule="para" parents="46582 49434"/>
    </justification>
  </clause>

  <clause id="49516">
    <literal><![CDATA[
      R(x,a(y,z,z),x * u) * u = x * (u * a(y,z,a(u,x,z)))
    ]]></literal>
    <justification jstring="[para(42877(a,1),49515(a,1,2,2,3)),flip(a)].">
      <j1 rule="para" parents="42877 49515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49517">
    <literal><![CDATA[
      R(x,a(y,z,z),x * u) * u = x * L(u,x,a(y,z,z))
    ]]></literal>
    <justification jstring="[para(45963(a,1),49516(a,2,2))].">
      <j1 rule="para" parents="45963 49516"/>
    </justification>
  </clause>

  <clause id="49519">
    <literal><![CDATA[
      L(x * y,a(z,z,u),x) = x * L(y,x,a(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47175,a(flip),b,49517,a)].">
      <j1 rule="hyper" parents="64 47175 49517"/>
    </justification>
  </clause>

  <clause id="49520">
    <literal><![CDATA[
      a(x,x,y) * L(z * u,a(x,x,y),z) = (a(x \ 1,x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(49519(a,2),42253(a,1,2))].">
      <j1 rule="para" parents="49519 42253"/>
    </justification>
  </clause>

  <clause id="49521">
    <literal><![CDATA[
      L(x * y,a(z,z,a(u,w,v5)),x) = x * L(y,x,a(v5,z,a(u,w,z)))
    ]]></literal>
    <justification jstring="[para(45505(a,1),49519(a,2,2,3))].">
      <j1 rule="para" parents="45505 49519"/>
    </justification>
  </clause>

  <clause id="49522">
    <literal><![CDATA[
      L(a(x,x,y) * (z * u),a(x,x,y),z) = (a(x \ 1,x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,49111,a,b,49520,a)].">
      <j1 rule="hyper" parents="64 49111 49520"/>
    </justification>
  </clause>

  <clause id="49523">
    <literal><![CDATA[
      L(a(x,x,y) * (z * u),a(x,x,y),z) = (a(x,x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(2653(a,1),49522(a,2,1,1))].">
      <j1 rule="para" parents="2653 49522"/>
    </justification>
  </clause>

  <clause id="49524">
    <literal><![CDATA[
      x * a(y,z,a(z * u,w,a(v5,v5,v6))) = x * a(z,a(v6,w,a(v5,v5,y)),u)
    ]]></literal>
    <justification jstring="[para(45501(a,1),49442(a,2,2,2))].">
      <j1 rule="para" parents="45501 49442"/>
    </justification>
  </clause>

  <clause id="49525">
    <literal><![CDATA[
      x * a(y,x,a(x * z,u,a(w,w,v5))) = L(x,a(v5,u,a(w,w,y)),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,42627,a(flip),b,49524,a),flip(a)].">
      <j1 rule="hyper" parents="373 42627 49524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49526">
    <literal><![CDATA[
      x * a(y,z,a(u,a(w,v5,v5),x)) = L(x,a(w,z,a(v5,v5,y)),u)
    ]]></literal>
    <justification jstring="[para(49468(a,1),49525(a,1,2))].">
      <j1 rule="para" parents="49468 49525"/>
    </justification>
  </clause>

  <clause id="49527">
    <literal><![CDATA[
      L(x,a(y,z,a(u,u,w)),v5) = L(x,z,a(v5,a(y,u,u),w))
    ]]></literal>
    <justification jstring="[hyper(47415,a,49526,a),flip(a)].">
      <j1 rule="hyper" parents="47415 49526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49528">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,w)),v5) = L(x,z,a(v5,a(u,w,w),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,45933,a,b,49527,a)].">
      <j1 rule="hyper" parents="64 45933 49527"/>
    </justification>
  </clause>

  <clause id="49529">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,z)),v5) = L(x,w,a(v5,a(y,z,z),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,45927,a,b,49527,a)].">
      <j1 rule="hyper" parents="64 45927 49527"/>
    </justification>
  </clause>

  <clause id="49530">
    <literal><![CDATA[
      L(x,a(y,y,a(z,u,w)),v5) = L(x,u,a(v5,a(w,y,y),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,45810,a(flip),b,49527,a)].">
      <j1 rule="hyper" parents="64 45810 49527"/>
    </justification>
  </clause>

  <clause id="49531">
    <literal><![CDATA[
      L(x,a(y,z,a(z,u,w)),v5) = L(x,u,a(v5,a(w,z,z),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,43923,a(flip),b,49527,a)].">
      <j1 rule="hyper" parents="64 43923 49527"/>
    </justification>
  </clause>

  <clause id="49532">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,w),v5 \ 1)) = L(x,a(v5,w,a(u,y,w)),z)
    ]]></literal>
    <justification jstring="[para(47207(a,1),49527(a,1,2)),flip(a)].">
      <j1 rule="para" parents="47207 49527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49533">
    <literal><![CDATA[
      L(x * y,z,a(x,a(u,w,w),v5)) = x * L(y,x,a(u,w,a(v5,z,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49521,a(flip),b,49530,a),flip(a)].">
      <j1 rule="hyper" parents="64 49521 49530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49534">
    <literal><![CDATA[
      x * L(x \ y,a(a(z,u,w),z,v5),y) = L(y,u,a(x * y,a(w,z,z),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,46148,a,b,49531,a)].">
      <j1 rule="hyper" parents="64 46148 49531"/>
    </justification>
  </clause>

  <clause id="49535">
    <literal><![CDATA[
      L(x,a(y,z,a(z,u,w * v5)),v6) = L(x,u,a(v6,a(v5 \ w,z,z),y))
    ]]></literal>
    <justification jstring="[para(45506(a,2),49531(a,2,3,2))].">
      <j1 rule="para" parents="45506 49531"/>
    </justification>
  </clause>

  <clause id="49536">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,w),v5 \ 1)) = L(x,y,a(z,a(v5,w,w),u))
    ]]></literal>
    <justification jstring="[hyper(373,a,49529,a(flip),b,49532,a),flip(a)].">
      <j1 rule="hyper" parents="373 49529 49532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49537">
    <literal><![CDATA[
      L(x,y,a(z * u,a(w,v5,v5),u \ 1)) = L(x,y,a(z,a(u,v5,v5),w))
    ]]></literal>
    <justification jstring="[para(49076(a,1),49536(a,2,3))].">
      <j1 rule="para" parents="49076 49536"/>
    </justification>
  </clause>

  <clause id="49538">
    <literal><![CDATA[
      L(x,y,a(z,a(u \ w,v5 \ 1,v5 \ 1),v6)) = L(x,a(v6,v5 \ 1,a(v5,y,w * u)),z)
    ]]></literal>
    <justification jstring="[para(2653(a,1),49535(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="2653 49535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49539">
    <literal><![CDATA[
      L(x,y,a(z * u,a(w,v5,v5),u)) = L(x,y,a(z,a(u,v5,v5),w))
    ]]></literal>
    <justification jstring="[hyper(64,a,33636,a(flip),b,49537,a)].">
      <j1 rule="hyper" parents="64 33636 49537"/>
    </justification>
  </clause>

  <clause id="49540">
    <literal><![CDATA[
      L(x,y,a(z,a(u,u,w),z * v5)) = L(x,y,a(v5,a(z,u,u),w))
    ]]></literal>
    <justification jstring="[para(43407(a,1),49539(a,1,3))].">
      <j1 rule="para" parents="43407 49539"/>
    </justification>
  </clause>

  <clause id="49541">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,w),v5)) = L(x,y,a(z,w,a(v5,u,w)))
    ]]></literal>
    <justification jstring="[para(49445(a,1),49540(a,1,3)),flip(a)].">
      <j1 rule="para" parents="49445 49540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49542">
    <literal><![CDATA[
      L(x * y,z,a(x,u,a(w,v5,u))) = x * L(y,x,a(v5,u,a(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49533,a(flip),b,49541,a),flip(a)].">
      <j1 rule="hyper" parents="64 49533 49541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49543">
    <literal><![CDATA[
      x * L(x \ y,a(z,u,a(w,v5,v5)),y) = L(y,u,a(x * y,a(z,v5,v5),w))
    ]]></literal>
    <justification jstring="[para(43927(a,1),49534(a,1,2))].">
      <j1 rule="para" parents="43927 49534"/>
    </justification>
  </clause>

  <clause id="49544">
    <literal><![CDATA[
      x * L(x \ y,z,a(y,a(u,w,w),v5)) = L(y,z,a(x * y,a(v5,w,w),u))
    ]]></literal>
    <justification jstring="[para(49528(a,1),49543(a,1,2))].">
      <j1 rule="para" parents="49528 49543"/>
    </justification>
  </clause>

  <clause id="49545">
    <literal><![CDATA[
      L(x,a(y,z,z),a(x * u,w,v5)) = L(x,w,a(u * x,a(v5,z,z),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47526,a(flip),b,49544,a)].">
      <j1 rule="hyper" parents="64 47526 49544"/>
    </justification>
  </clause>

  <clause id="49546">
    <literal><![CDATA[
      L(x,a(y,z,z),a(x * u,w,v5)) = L(x,w,a(u * x,z,a(y,v5,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,49541,a(flip),b,49545,a),flip(a)].">
      <j1 rule="hyper" parents="373 49541 49545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49547">
    <literal><![CDATA[
      a(x,a(y,z,z),u) * a(z,z,L(y,u,x)) = a(z,z,y * a(x,y,x * u))
    ]]></literal>
    <justification jstring="[para(46930(a,1),49435(a,1,2))].">
      <j1 rule="para" parents="46930 49435"/>
    </justification>
  </clause>

  <clause id="49548">
    <literal><![CDATA[
      a(x,x,y * a(z,y,z * u)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,48949,a(flip),b,49547,a),flip(a)].">
      <j1 rule="hyper" parents="64 48949 49547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49549">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,a(u,w,w),v5)) = y * a(x,a(a(z * v5,z,u),w,w),y)
    ]]></literal>
    <justification jstring="[para(49425(a,1),49441(a,2,2))].">
      <j1 rule="para" parents="49425 49441"/>
    </justification>
  </clause>

  <clause id="49550">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,a(u,w,w),v5)) = y * a(x,a(u,z,a(w,w,z * v5)),y)
    ]]></literal>
    <justification jstring="[para(45501(a,1),49549(a,2,2,2))].">
      <j1 rule="para" parents="45501 49549"/>
    </justification>
  </clause>

  <clause id="49551">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,a(u,w,w),v5)) = y * a(x,a(z,a(u,w,w),v5),y)
    ]]></literal>
    <justification jstring="[para(49426(a,1),49550(a,2,2,2))].">
      <j1 rule="para" parents="49426 49550"/>
    </justification>
  </clause>

  <clause id="49552">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,a(u,w,w),v5)) = L(y,a(z,a(u,w,w),v5),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,43401,a(flip),b,49551,a),flip(a)].">
      <j1 rule="hyper" parents="373 43401 49551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49553">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,a(u,w,w),v5)) = L(y,a(v5,a(u,w,w),z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,43396,a(flip),b,49551,a),flip(a)].">
      <j1 rule="hyper" parents="373 43396 49551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49554">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,a(w,v5,u))) = L(y,a(z,a(v5,u,u),w),x)
    ]]></literal>
    <justification jstring="[para(49541(a,1),49552(a,1,2))].">
      <j1 rule="para" parents="49541 49552"/>
    </justification>
  </clause>

  <clause id="49555">
    <literal><![CDATA[
      L(x \ y,a(z,a(u,w,w),v5),y) = L(x,y,a(v5,a(u,w,w),z)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,47173,a(flip),b,49553,a),flip(a)].">
      <j1 rule="hyper" parents="64 47173 49553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49556">
    <literal><![CDATA[
      L(x * (x \ y),z,a(x,a(u,w,w),v5)) = L(y,a(u,a(z,w,w),v5),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,49533,a,b,49554,a)].">
      <j1 rule="hyper" parents="64 49533 49554"/>
    </justification>
  </clause>

  <clause id="49557">
    <literal><![CDATA[
      x * L(x \ y,a(z,a(u,w,w),v5),y) = y * a(a(v5,a(u,w,w),z),y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,49555,a,b,42084,a)].">
      <j1 rule="hyper" parents="145 49555 42084"/>
    </justification>
  </clause>

  <clause id="49558">
    <literal><![CDATA[
      L(x,a(y,a(z,u,u),w),v5) = L(x,z,a(v5,a(y,u,u),w))
    ]]></literal>
    <justification jstring="[para(10(a,1),49556(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 49556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49559">
    <literal><![CDATA[
      L(x,a(y,a(z,u,u),w),v5) = L(x,z,a(v5,u,a(w,y,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,49541,a(flip),b,49558,a),flip(a)].">
      <j1 rule="hyper" parents="373 49541 49558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49560">
    <literal><![CDATA[
      L(L(x,y,a(z,u,a(w,v5,u))),a(y,u,u),a(v5,z,w)) = x * a(w,a(y,u,u),a(z,x,v5))
    ]]></literal>
    <justification jstring="[para(49559(a,1),47546(a,1,1))].">
      <j1 rule="para" parents="49559 47546"/>
    </justification>
  </clause>

  <clause id="49561">
    <literal><![CDATA[
      L(x,a(y,a(z,u,u),w),v5 * x) = x * a(a(y,a(z,u,u),w),x,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,46148,a(flip),b,49557,a)].">
      <j1 rule="hyper" parents="64 46148 49557"/>
    </justification>
  </clause>

  <clause id="49562">
    <literal><![CDATA[
      L(x,a(y,a(z,u,u),w),v5 * x) = x * a(w,a(z,u,u),a(v5,x,y))
    ]]></literal>
    <justification jstring="[para(47254(a,1),49561(a,2,2))].">
      <j1 rule="para" parents="47254 49561"/>
    </justification>
  </clause>

  <clause id="49563">
    <literal><![CDATA[
      L(x,y,a(z,a(u \ w,v5 \ 1,v5 \ 1),v6)) = L(x,a(v6,v5,a(v5,y,w * u)),z)
    ]]></literal>
    <justification jstring="[para(11980(a,1),49538(a,2,2))].">
      <j1 rule="para" parents="11980 49538"/>
    </justification>
  </clause>

  <clause id="49564">
    <literal><![CDATA[
      L(x,y,a(z,a(u \ w,u \ 1,u \ 1),v5)) = L(x,a(v5,u,a(w,y,u)),z)
    ]]></literal>
    <justification jstring="[para(44172(a,1),49563(a,2,2))].">
      <j1 rule="para" parents="44172 49563"/>
    </justification>
  </clause>

  <clause id="49565">
    <literal><![CDATA[
      L(x,y,a(z,a(u \ w,u \ 1,u \ 1),v5)) = L(x,y,a(z,a(v5,u,u),w))
    ]]></literal>
    <justification jstring="[hyper(373,a,49529,a(flip),b,49564,a),flip(a)].">
      <j1 rule="hyper" parents="373 49529 49564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49566">
    <literal><![CDATA[
      L(x,y,a(z,a(u \ w,u \ 1,u \ 1),v5)) = L(x,y,a(z,u,a(w,v5,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,49541,a(flip),b,49565,a),flip(a)].">
      <j1 rule="hyper" parents="373 49541 49565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49567">
    <literal><![CDATA[
      L(x,y,a(z,a(u \ w,u,u \ 1),v5)) = L(x,y,a(z,u,a(w,v5,u)))
    ]]></literal>
    <justification jstring="[para(11980(a,1),49566(a,1,3,2))].">
      <j1 rule="para" parents="11980 49566"/>
    </justification>
  </clause>

  <clause id="49568">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,w \ 1),v5)) = L(x,y,a(z,w,a(u,v5,w)))
    ]]></literal>
    <justification jstring="[para(34478(a,1),49567(a,1,3))].">
      <j1 rule="para" parents="34478 49567"/>
    </justification>
  </clause>

  <clause id="49569">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,w),v5)) = L(x,y,a(z,w,a(u,v5,w)))
    ]]></literal>
    <justification jstring="[para(34592(a,1),49568(a,1,3))].">
      <j1 rule="para" parents="34592 49568"/>
    </justification>
  </clause>

  <clause id="49570">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,u))) = L(x,y,a(z,u,a(v5,w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49541,a(flip),b,49569,a)].">
      <j1 rule="hyper" parents="64 49541 49569"/>
    </justification>
  </clause>

  <clause id="49571">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,u))) = L(x,y,a(z,u,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(41450(a,1),49570(a,1,3)),flip(a)].">
      <j1 rule="para" parents="41450 49570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49572">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,u,a(w,v5,u))) = y * a(x * y,x,a(a(v5,w,u),u,z))
    ]]></literal>
    <justification jstring="[para(49570(a,1),42908(a,1,2))].">
      <j1 rule="para" parents="49570 42908"/>
    </justification>
  </clause>

  <clause id="49573">
    <literal><![CDATA[
      L(x * (x \ y),z,a(x,u,a(w,v5,u))) = y * a(x * y,x,a(a(z,w,u),u,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,49542,a,b,49572,a)].">
      <j1 rule="hyper" parents="64 49542 49572"/>
    </justification>
  </clause>

  <clause id="49574">
    <literal><![CDATA[
      x * a(y * x,y,a(a(z,u,w),w,v5)) = L(x,z,a(y,w,a(u,v5,w)))
    ]]></literal>
    <justification jstring="[para(10(a,1),49573(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 49573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49575">
    <literal><![CDATA[
      x * a(y * x,y,a(z,u,a(w,z,v5))) = L(x,v5,a(y,z,a(u,w,z)))
    ]]></literal>
    <justification jstring="[para(47254(a,1),49574(a,1,2,3))].">
      <j1 rule="para" parents="47254 49574"/>
    </justification>
  </clause>

  <clause id="49576">
    <literal><![CDATA[
      x * a(y,z,a(x,a(u,w,w),v5)) = L(x,u,a(v5,w,a(z,y,w)))
    ]]></literal>
    <justification jstring="[para(49437(a,1),49575(a,1,2))].">
      <j1 rule="para" parents="49437 49575"/>
    </justification>
  </clause>

  <clause id="49577">
    <literal><![CDATA[
      L(x,a(y,z,z),a(u,w,v5)) = L(x,y,a(v5,z,a(w,u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47271,a(flip),b,49576,a)].">
      <j1 rule="hyper" parents="64 47271 49576"/>
    </justification>
  </clause>

  <clause id="49578">
    <literal><![CDATA[
      L(x,a(y,z,z),a(u,w,v5)) = L(x,y,a(v5,z,a(z,w,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,49571,a(flip),b,49577,a),flip(a)].">
      <j1 rule="hyper" parents="373 49571 49577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49579">
    <literal><![CDATA[
      L(x,y,a(z * x,u,a(w,v5,u))) = L(x,w,a(v5,u,a(y,x * z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49546,a(flip),b,49577,a)].">
      <j1 rule="hyper" parents="64 49546 49577"/>
    </justification>
  </clause>

  <clause id="49580">
    <literal><![CDATA[
      L(L(x,y,a(z,u,a(w,v5,u))),a(y,u,u),v5) = L(x,a(y,u,u),L(v5,w,z))
    ]]></literal>
    <justification jstring="[para(49577(a,1),47493(a,1,1))].">
      <j1 rule="para" parents="49577 47493"/>
    </justification>
  </clause>

  <clause id="49581">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ u,w,a(v5,u,w)) = L(u,v5,a(z,w,a(w,y,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49450,a,b,49578,a)].">
      <j1 rule="hyper" parents="64 49450 49578"/>
    </justification>
  </clause>

  <clause id="49582">
    <literal><![CDATA[
      L(x,y,a(z * x,u,a(w,v5,u))) = L(x,u,a(y,w,a(u,z,v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,48701,a(flip),b,49579,a),flip(a)].">
      <j1 rule="hyper" parents="373 48701 49579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49583">
    <literal><![CDATA[
      a(x,y,z) * L(a(x,y,z) \ u,w,a(v5,u,w)) = u * a(z,w,a(u,v5,a(w,y,x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47271,a,b,49581,a),flip(a)].">
      <j1 rule="hyper" parents="373 47271 49581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49584">
    <literal><![CDATA[
      a(x,a(y,z,z),a(u,w,v5)) = a(x,z,a(v5,y,a(z,w,u)))
    ]]></literal>
    <justification jstring="[hyper(35,a,49449,a(flip),b,49583,a(flip))].">
      <j1 rule="hyper" parents="35 49449 49583"/>
    </justification>
  </clause>

  <clause id="49585">
    <literal><![CDATA[
      L(x,a(y,a(z,u,u),w),v5 * x) = x * a(w,u,a(y,z,a(u,x,v5)))
    ]]></literal>
    <justification jstring="[para(49584(a,1),49562(a,2,2))].">
      <j1 rule="para" parents="49584 49562"/>
    </justification>
  </clause>

  <clause id="49586">
    <literal><![CDATA[
      L(x,y,a(z * x,u,a(w,v5,u))) = x * a(w,u,a(v5,y,a(u,x,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49559,a(flip),b,49585,a)].">
      <j1 rule="hyper" parents="64 49559 49585"/>
    </justification>
  </clause>

  <clause id="49587">
    <literal><![CDATA[
      x * a(y,z,a(u,w,a(z,x,v5))) = L(x,z,a(w,y,a(z,v5,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49582,a(flip),b,49586,a),flip(a)].">
      <j1 rule="hyper" parents="64 49582 49586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49588">
    <literal><![CDATA[
      L(L(x,y,a(z,u,a(w,v5,u))),y,a(w,u,a(z,v5,u))) = x * a(w,a(y,u,u),a(z,x,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,49577,a(flip),b,49560,a)].">
      <j1 rule="hyper" parents="64 49577 49560"/>
    </justification>
  </clause>

  <clause id="49589">
    <literal><![CDATA[
      x * a(y,a(z,u,u),a(w,x,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,47312,a(flip),b,49588,a),flip(a)].">
      <j1 rule="hyper" parents="64 47312 49588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49593">
    <literal><![CDATA[
      a(x,a(y,y,z),a(u,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,49589,a(flip),b,32890,a),flip(a)].">
      <j1 rule="hyper" parents="140 49589 32890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49594">
    <literal><![CDATA[
      x * a(y,z,a(u,w,a(z,x,v5))) = x
    ]]></literal>
    <justification jstring="[para(49584(a,1),49589(a,1,2))].">
      <j1 rule="para" parents="49584 49589"/>
    </justification>
  </clause>

  <clause id="49598">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),y)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,49447,a(flip),b,49593,a)].">
      <j1 rule="hyper" parents="64 49447 49593"/>
    </justification>
  </clause>

  <clause id="49604">
    <literal><![CDATA[
      a(x,y,a(y,a(z,u,w),v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,49598,a,b,47333,a),flip(a)].">
      <j1 rule="hyper" parents="138 49598 47333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49607">
    <literal><![CDATA[
      a(a(x,y,y),a(z,u,w),v5) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,47200,a,b,49598,a)].">
      <j1 rule="hyper" parents="64 47200 49598"/>
    </justification>
  </clause>

  <clause id="49609">
    <literal><![CDATA[
      L(1 / x,x,a(y,a(z,u,w),v5)) = 1 / x
    ]]></literal>
    <justification jstring="[para(49598(a,1),47417(a,2,1))].">
      <j1 rule="para" parents="49598 47417"/>
    </justification>
  </clause>

  <clause id="49613">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,v5,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,49607,a)].">
      <j1 rule="hyper" parents="53 49607"/>
    </justification>
  </clause>

  <clause id="49620">
    <literal><![CDATA[
      L(x,a(y,z,u),L(w,w,v5)) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,47487,a(flip),b,49613,a)].">
      <j1 rule="hyper" parents="64 47487 49613"/>
    </justification>
  </clause>

  <clause id="49629">
    <literal><![CDATA[
      a(x,y,a(z,u,a(y,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(148,a,49594,a),flip(a)].">
      <j1 rule="hyper" parents="148 49594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49630">
    <literal><![CDATA[
      L(x,y,a(z,u,a(y,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,49587,a(flip),b,49594,a)].">
      <j1 rule="hyper" parents="64 49587 49594"/>
    </justification>
  </clause>

  <clause id="49635">
    <literal><![CDATA[
      x * a(y,z,a(u,w,a(z,v5,v6))) = x
    ]]></literal>
    <justification jstring="[hyper(145,a,49629,a,b,68,a)].">
      <j1 rule="hyper" parents="145 49629 68"/>
    </justification>
  </clause>

  <clause id="49637">
    <literal><![CDATA[
      a(x,x,a(y,z,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,47509,a,b,49629,a)].">
      <j1 rule="hyper" parents="64 47509 49629"/>
    </justification>
  </clause>

  <clause id="49640">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,48885,a(flip),b,49629,a)].">
      <j1 rule="hyper" parents="64 48885 49629"/>
    </justification>
  </clause>

  <clause id="49646">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,47520,a,b,49630,a)].">
      <j1 rule="hyper" parents="64 47520 49630"/>
    </justification>
  </clause>

  <clause id="49647">
    <literal><![CDATA[
      L(x,y,a(z,z,a(u,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,47452,a,b,49630,a)].">
      <j1 rule="hyper" parents="64 47452 49630"/>
    </justification>
  </clause>

  <clause id="49648">
    <literal><![CDATA[
      L(x,y,a(z,u,a(u,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,47433,a,b,49630,a)].">
      <j1 rule="hyper" parents="64 47433 49630"/>
    </justification>
  </clause>

  <clause id="49649">
    <literal><![CDATA[
      L(x,y,a(y,z,a(u,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,47388,a,b,49630,a)].">
      <j1 rule="hyper" parents="64 47388 49630"/>
    </justification>
  </clause>

  <clause id="49650">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,u))) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,47458,a(flip),b,49630,a)].">
      <j1 rule="hyper" parents="64 47458 49630"/>
    </justification>
  </clause>

  <clause id="49654">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),v5,v5) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(53,a,49637,a)].">
      <j1 rule="hyper" parents="53 49637"/>
    </justification>
  </clause>

  <clause id="49658">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,y)) = a(x,y,a(z,u,w)) * 1
    ]]></literal>
    <justification jstring="[para(49637(a,1),47397(a,1,2)),flip(a)].">
      <j1 rule="para" parents="49637 47397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49659">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,v5,v5))) = L(x,u,a(w,y,z)) * 1
    ]]></literal>
    <justification jstring="[para(49637(a,1),47981(a,1,2)),flip(a)].">
      <j1 rule="para" parents="49637 47981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49670">
    <literal><![CDATA[
      (x * y) * a(z,u,a(w,v5,v5)) = x * (y * a(z,u,a(w,v5,v5)))
    ]]></literal>
    <justification jstring="[para(49646(a,1),28800(a,1,1)),flip(a)].">
      <j1 rule="para" parents="49646 28800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49673">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) * (w * v5) = w * (a(x,x,a(y,z,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(144,a,49647,a(flip),b,28734,a),flip(a)].">
      <j1 rule="hyper" parents="144 49647 28734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49678">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * a(u,w,a(w,v5,v6))) = a(v6,v5,a(w,w,u)) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(49648(a,1),44336(a,1,1))].">
      <j1 rule="para" parents="49648 44336"/>
    </justification>
  </clause>

  <clause id="49681">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ v5) = a(x,y,a(w,u,z)) * v5
    ]]></literal>
    <justification jstring="[hyper(64,a,47925,a(flip),b,49649,a)].">
      <j1 rule="hyper" parents="64 47925 49649"/>
    </justification>
  </clause>

  <clause id="49683">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) * w) * v5 = a(x,y,a(z,u,y)) * (w * v5)
    ]]></literal>
    <justification jstring="[hyper(1960,a,49650,a),flip(a)].">
      <j1 rule="hyper" parents="1960 49650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49693">
    <literal><![CDATA[
      (x * y) * a(z,u,a(w,v5,u)) = x * (y * a(z,u,a(w,v5,u)))
    ]]></literal>
    <justification jstring="[para(49650(a,1),28800(a,1,1)),flip(a)].">
      <j1 rule="para" parents="49650 28800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49694">
    <literal><![CDATA[
      L(x,a(y,z,z),L(u,w,v5)) = L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(49650(a,1),49580(a,1,1)),flip(a)].">
      <j1 rule="para" parents="49650 49580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49699">
    <literal><![CDATA[
      a(x,x,a(y,z,L(u,w,v5))) = a(x,x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47903,a(flip),b,49635,a)].">
      <j1 rule="hyper" parents="64 47903 49635"/>
    </justification>
  </clause>

  <clause id="49707">
    <literal><![CDATA[
      x * a(y,a(z,u,u),a(w,v5,v6)) = x
    ]]></literal>
    <justification jstring="[para(49474(a,1),49635(a,1,2))].">
      <j1 rule="para" parents="49474 49635"/>
    </justification>
  </clause>

  <clause id="49708">
    <literal><![CDATA[
      L(a(x,y,z),a(u,w,w),v5) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(45209,a,49707,a),flip(a)].">
      <j1 rule="hyper" parents="45209 49707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49712">
    <literal><![CDATA[
      a(x,y,L(z,a(u,w,w),v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47306,a(flip),b,49707,a)].">
      <j1 rule="hyper" parents="64 47306 49707"/>
    </justification>
  </clause>

  <clause id="49716">
    <literal><![CDATA[
      (a(x,y,y) \ z) * a(u,w,v5) = z * (a(x,y,y) \ a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(145,a,49708,a(flip),b,42827,a)].">
      <j1 rule="hyper" parents="145 49708 42827"/>
    </justification>
  </clause>

  <clause id="49718">
    <literal><![CDATA[
      a(x,y,L(z,a(u,u,w),v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,41424,a,b,49712,a)].">
      <j1 rule="hyper" parents="64 41424 49712"/>
    </justification>
  </clause>

  <clause id="49722">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) * w) * v5) = a(x,y,a(z,z,u) * (w * v5))
    ]]></literal>
    <justification jstring="[para(49523(a,1),49718(a,1,3))].">
      <j1 rule="para" parents="49523 49718"/>
    </justification>
  </clause>

  <clause id="49723">
    <literal><![CDATA[
      (1 / x) \ a(y,a(z,u,w),v5) = a(y,a(z,u,w),v5) * x
    ]]></literal>
    <justification jstring="[para(49609(a,1),25826(a,1,1))].">
      <j1 rule="para" parents="49609 25826"/>
    </justification>
  </clause>

  <clause id="49726">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,u),L(w,w,v5)),v6,v6) = v6 \ ((x / v6) \ L(x,a(y,z,u),w))
    ]]></literal>
    <justification jstring="[para(49620(a,1),39902(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="49620 39902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49727">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v5))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46567,a,b,49654,a)].">
      <j1 rule="hyper" parents="64 46567 49654"/>
    </justification>
  </clause>

  <clause id="49731">
    <literal><![CDATA[
      a(x,a(y,z,z),L(u,w,v5)) = x \ L(x,a(y,z,z),u)
    ]]></literal>
    <justification jstring="[hyper(139,a,49694,a(flip),b,42627,a),flip(a)].">
      <j1 rule="hyper" parents="139 49694 42627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49736">
    <literal><![CDATA[
      a(x,x,a(y,z,L(u,w,v5))) = a(y,x,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47244,a,b,49699,a),flip(a)].">
      <j1 rule="hyper" parents="373 47244 49699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49741">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v5))) = a(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,47298,a,b,49727,a),flip(a)].">
      <j1 rule="hyper" parents="373 47298 49727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49746">
    <literal><![CDATA[
      a(x,y,a(L(z,u,u),w,v5)) = a(x,w,a(v5,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47298,a,b,49727,a)].">
      <j1 rule="hyper" parents="64 47298 49727"/>
    </justification>
  </clause>

  <clause id="49748">
    <literal><![CDATA[
      a(x \ y,z,a(u,w,v5)) = a(x * y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,46651,a(flip),b,49727,a)].">
      <j1 rule="hyper" parents="64 46651 49727"/>
    </justification>
  </clause>

  <clause id="49750">
    <literal><![CDATA[
      a(x,x,a(y,L(z,u,w),v5)) = a(y,x,a(v5,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,49514,a,b,49736,a)].">
      <j1 rule="hyper" parents="64 49514 49736"/>
    </justification>
  </clause>

  <clause id="49754">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (w * v5))) = a(v5,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47282,a,b,49741,a)].">
      <j1 rule="hyper" parents="64 47282 49741"/>
    </justification>
  </clause>

  <clause id="49755">
    <literal><![CDATA[
      a(x,y,a(z,u,L(L(w,v5,v5),v6,v7))) = a(x,u,a(w,y,L(z,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46787,a(flip),b,49741,a)].">
      <j1 rule="hyper" parents="64 46787 49741"/>
    </justification>
  </clause>

  <clause id="49756">
    <literal><![CDATA[
      a(x \ y,z,a(u,w,v5)) = a(x * y,w,a(v5,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46651,a(flip),b,49741,a)].">
      <j1 rule="hyper" parents="64 46651 49741"/>
    </justification>
  </clause>

  <clause id="49757">
    <literal><![CDATA[
      (1 / x) \ a(y,z,a(u,w,v5)) = x * a(v5,z,a(y,w,u))
    ]]></literal>
    <justification jstring="[para(49741(a,1),47380(a,1,2))].">
      <j1 rule="para" parents="49741 47380"/>
    </justification>
  </clause>

  <clause id="49758">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 * w))) = a(v5,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47363,a,b,49746,a)].">
      <j1 rule="hyper" parents="64 47363 49746"/>
    </justification>
  </clause>

  <clause id="49763">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5),y)) = a(x,y,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47244,a,b,49750,a)].">
      <j1 rule="hyper" parents="64 47244 49750"/>
    </justification>
  </clause>

  <clause id="49771">
    <literal><![CDATA[
      a(x * y,z,a(u,w,v5)) = a(u,w,a(v5,z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47198,a,b,49748,a),flip(a)].">
      <j1 rule="hyper" parents="64 47198 49748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49772">
    <literal><![CDATA[
      L(x * a(y * z,u,a(w,x,v5)),w,a(y \ z,u,v5)) = L(x,a(v5,u,y \ z),w)
    ]]></literal>
    <justification jstring="[para(49748(a,1),47268(a,1,1,2))].">
      <j1 rule="para" parents="49748 47268"/>
    </justification>
  </clause>

  <clause id="49776">
    <literal><![CDATA[
      a(x * (y \ (z \ (y * x))),u,a(w,v5,v6)) = a(w,u,a(z,v5,L(L(v6,x * z,y),z,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,48094,a(flip),b,49756,a),flip(a)].">
      <j1 rule="hyper" parents="64 48094 49756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49778">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ v5)) = a(x,y,a(z,u,w * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,47198,a,b,49771,a),flip(a)].">
      <j1 rule="hyper" parents="64 47198 49771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49782">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(w,v5,x * y)) = L(x \ y,u,a(w,v5,z))
    ]]></literal>
    <justification jstring="[para(49778(a,1),47349(a,1,2))].">
      <j1 rule="para" parents="49778 47349"/>
    </justification>
  </clause>

  <clause id="49784">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,y))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(141,a,49658,a(flip),b,46631,a),flip(a)].">
      <j1 rule="hyper" parents="141 49658 46631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49786">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,u))) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47204,a,b,49784,a)].">
      <j1 rule="hyper" parents="64 47204 49784"/>
    </justification>
  </clause>

  <clause id="49787">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,v5,u))) = a(w,u,a(z,y,x)) * x
    ]]></literal>
    <justification jstring="[para(49786(a,1),45132(a,1,1)),flip(a)].">
      <j1 rule="para" parents="49786 45132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49788">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,v5,v5))) = L(x,u,a(w,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,8,a(flip),b,49659,a),flip(a)].">
      <j1 rule="hyper" parents="373 8 49659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49789">
    <literal><![CDATA[
      L(x,y,a(z,u,w * (w * v5))) = L(x,u,a(z,y,v5))
    ]]></literal>
    <justification jstring="[hyper(141,a,49659,a(flip),b,46619,a),flip(a)].">
      <j1 rule="hyper" parents="141 49659 46619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49790">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,v5,v5))) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,47432,a,b,49788,a),flip(a)].">
      <j1 rule="hyper" parents="373 47432 49788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49792">
    <literal><![CDATA[
      L(x,y,a(z \ u,w,v5)) = L(x,y,a(z * u,w,v5))
    ]]></literal>
    <justification jstring="[para(46605(a,1),49790(a,1,3))].">
      <j1 rule="para" parents="46605 49790"/>
    </justification>
  </clause>

  <clause id="49795">
    <literal><![CDATA[
      a(x,a(y,z,z),L(u,w,v5)) = a(x,a(z,z,y),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,42628,a(flip),b,49731,a),flip(a)].">
      <j1 rule="hyper" parents="373 42628 49731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49796">
    <literal><![CDATA[
      a(x,a(y,y,z),L(u,w,v5)) = a(x,a(y,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42391,a,b,49795,a)].">
      <j1 rule="hyper" parents="64 42391 49795"/>
    </justification>
  </clause>

  <clause id="49800">
    <literal><![CDATA[
      L(x,y,a(z,u,L(w,v5,u))) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,47222,a(flip),b,49787,a),flip(a)].">
      <j1 rule="hyper" parents="373 47222 49787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49801">
    <literal><![CDATA[
      L(a(x,y,a(L(z,u,y),w,v5)) * w,v5,a(x,y,z)) = L(w,a(x,y,L(z,u,y)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,47211,a(flip),b,49800,a),flip(a)].">
      <j1 rule="hyper" parents="64 47211 49800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49802">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (x \ v5) = L(x,y,a(w,u,z)) \ v5
    ]]></literal>
    <justification jstring="[hyper(2346,a,49681,a),flip(a)].">
      <j1 rule="hyper" parents="2346 49681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49804">
    <literal><![CDATA[
      (x / y) \ L(x,a(z,u,w),v5) = a(v5,a(z,u,w),x) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,43418,a(flip),b,49723,a)].">
      <j1 rule="hyper" parents="64 43418 49723"/>
    </justification>
  </clause>

  <clause id="49808">
    <literal><![CDATA[
      (x \ y) * a(y,z,a(u,w,v5)) = x \ L(y,z,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,49132,a(flip),b,49757,a),flip(a)].">
      <j1 rule="hyper" parents="64 49132 49757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49811">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(x,w,v5)) = L(x,u,a(z,w,v5)) \ y
    ]]></literal>
    <justification jstring="[hyper(64,a,47311,a(flip),b,49802,a)].">
      <j1 rule="hyper" parents="64 47311 49802"/>
    </justification>
  </clause>

  <clause id="49813">
    <literal><![CDATA[
      x * L(x \ (y \ x),z,a(u,w,v5)) = L(y,z,a(v5,w,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(64,a,45978,a(flip),b,49802,a)].">
      <j1 rule="hyper" parents="64 45978 49802"/>
    </justification>
  </clause>

  <clause id="49814">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,x,v5))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(36,a,46831,a,b,49802,a)].">
      <j1 rule="hyper" parents="36 46831 49802"/>
    </justification>
  </clause>

  <clause id="49817">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,x,v5))) = a(w,u,a(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47197,a,b,49814,a),flip(a)].">
      <j1 rule="hyper" parents="373 47197 49814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49818">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ (v5 \ w))) = a(v5,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47203,a(flip),b,49814,a)].">
      <j1 rule="hyper" parents="64 47203 49814"/>
    </justification>
  </clause>

  <clause id="49822">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,z,v5))) = a(w,y,a(x,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47253,a,b,49817,a)].">
      <j1 rule="hyper" parents="64 47253 49817"/>
    </justification>
  </clause>

  <clause id="49826">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ (v5 \ w))) = a(z,u,a(x,y,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,47327,a,b,49818,a),flip(a)].">
      <j1 rule="hyper" parents="373 47327 49818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49828">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 \ w))) = a(z,u,a(x,y,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,49778,a(flip),b,49826,a)].">
      <j1 rule="hyper" parents="64 49778 49826"/>
    </justification>
  </clause>

  <clause id="49831">
    <literal><![CDATA[
      a((x \ y) * y,z,a(u,w,v5)) = a(v5,z,a(u,w,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47228,a,b,49828,a)].">
      <j1 rule="hyper" parents="64 47228 49828"/>
    </justification>
  </clause>

  <clause id="49832">
    <literal><![CDATA[
      a((x * y) * (z \ (y * x)),u,a(w,v5,v6)) = a(v6,u,a(w,v5,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,32422,a,b,49831,a)].">
      <j1 rule="hyper" parents="64 32422 49831"/>
    </justification>
  </clause>

  <clause id="49833">
    <literal><![CDATA[
      (x \ y) * a(y,z,a(u,w,v5)) = x \ L(y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,41901,a,b,49808,a)].">
      <j1 rule="hyper" parents="64 41901 49808"/>
    </justification>
  </clause>

  <clause id="49836">
    <literal><![CDATA[
      a(x,y,((a(z,u,w) \ v5) \ v6) * a(z,v5 * a(z,u,w),a(a(z,u,w) \ v5,u,w))) = a(x,y,((v5 \ a(z,u,w)) \ 1) \ v6)
    ]]></literal>
    <justification jstring="[para(49811(a,2),39118(a,1,3))].">
      <j1 rule="para" parents="49811 39118"/>
    </justification>
  </clause>

  <clause id="49840">
    <literal><![CDATA[
      (x * y) * a(z,u,a(u,w,v5)) = x * (y * a(z,w,a(v5,u,u)))
    ]]></literal>
    <justification jstring="[para(45877(a,1),49670(a,1,2))].">
      <j1 rule="para" parents="45877 49670"/>
    </justification>
  </clause>

  <clause id="49842">
    <literal><![CDATA[
      ((a(x,x,a(y,z,u)) * w) * v5) \ (v6 \ ((a(x,x,a(y,z,u)) * (v6 * w)) * v5)) = a(v6,a(x,x,a(y,z,u)) * w,v5)
    ]]></literal>
    <justification jstring="[para(49673(a,2),30027(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="49673 30027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49843">
    <literal><![CDATA[
      (a(x,x,a(y,z,u)) * w) * v5 = a(u,x,a(y,z,x)) * (w * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,46373,a(flip),b,49683,a)].">
      <j1 rule="hyper" parents="64 46373 49683"/>
    </justification>
  </clause>

  <clause id="49844">
    <literal><![CDATA[
      (x * a(y,z,a(u,u,w))) * v5 = a(y,u,a(w,z,u)) * (x * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,45914,a(flip),b,49683,a)].">
      <j1 rule="hyper" parents="64 45914 49683"/>
    </justification>
  </clause>

  <clause id="49846">
    <literal><![CDATA[
      a(x,y,L((z * (a(u,w,w) \ a(v5,v6,v7))) \ v8,a(u,w,w) \ z,a(v5,v6,v7))) = a(x,y,(a(u,w,w) \ z) \ (a(v5,v6,v7) \ v8))
    ]]></literal>
    <justification jstring="[para(49716(a,1),39070(a,1,3,1,1))].">
      <j1 rule="para" parents="49716 39070"/>
    </justification>
  </clause>

  <clause id="49848">
    <literal><![CDATA[
      a(x,y,(a(z,u,u) * w) * v5) = a(x,y,a(u,u,z) * (w * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,39022,a,b,49722,a)].">
      <j1 rule="hyper" parents="64 39022 49722"/>
    </justification>
  </clause>

  <clause id="49849">
    <literal><![CDATA[
      a(x,y,(a(z,z,u) * w) * T(v5,w)) = a(x,y,a(z,z,u) * (v5 * w))
    ]]></literal>
    <justification jstring="[para(115(a,1),49722(a,2,3,2))].">
      <j1 rule="para" parents="115 49722"/>
    </justification>
  </clause>

  <clause id="49851">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * ((w \ v5) * a(w,w * v5,a(x,u,a(y,y,z)))) = w \ (v5 * a(x,u,a(y,y,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,35710,a(flip),b,49844,a),flip(a)].">
      <j1 rule="hyper" parents="64 35710 49844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49852">
    <literal><![CDATA[
      x \ (a(y,z,a(u,w,z)) * v5) = (x \ v5) * a(y,w,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(36,a,33049,a,b,49844,a)].">
      <j1 rule="hyper" parents="36 33049 49844"/>
    </justification>
  </clause>

  <clause id="49853">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (w * L(v5 \ 1,v5,w * a(u,z,z)))) = a(x,y,v5 \ (w * a(u,z,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27738,a(flip),b,49848,a),flip(a)].">
      <j1 rule="hyper" parents="64 27738 49848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49854">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * ((w \ L(z,z,u)) * v5)) = a(x,y,(w \ z) * v5)
    ]]></literal>
    <justification jstring="[para(45539(a,1),49848(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="45539 49848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49855">
    <literal><![CDATA[
      L((x * a(y,z,a(u,w,z))) \ v5,x * a(y,z,a(u,w,z)),a(y,z,a(u,w,z))) = (x \ v5) * a(y,w,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,42651,a,b,49852,a)].">
      <j1 rule="hyper" parents="64 42651 49852"/>
    </justification>
  </clause>

  <clause id="49857">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (w * v5)) = a(x,y,w * (a(z,z,u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27438,a(flip),b,49849,a),flip(a)].">
      <j1 rule="hyper" parents="64 27438 49849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49859">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,u),L(w,w,v5)),v6,v6) = v6 \ (a(w,a(y,z,u),x) * v6)
    ]]></literal>
    <justification jstring="[para(49804(a,1),49726(a,2,2))].">
      <j1 rule="para" parents="49804 49726"/>
    </justification>
  </clause>

  <clause id="49860">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,u),L(w,w,v5)),v6,v6) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,23174,a(flip),b,49859,a),flip(a)].">
      <j1 rule="hyper" parents="373 23174 49859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49862">
    <literal><![CDATA[
      L(x \ L(x,a(y,z,u),w),v5,v5) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(594(a,1),49860(a,1,1,2,3))].">
      <j1 rule="para" parents="594 49860"/>
    </justification>
  </clause>

  <clause id="49863">
    <literal><![CDATA[
      L(a(x,a(y,z,u),w),v5,v5) = a(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(42628(a,1),49862(a,1,1))].">
      <j1 rule="para" parents="42628 49862"/>
    </justification>
  </clause>

  <clause id="49864">
    <literal><![CDATA[
      a(x,a(y,z,u),L(w,v5,v5)) = a(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,46493,a,b,49863,a)].">
      <j1 rule="hyper" parents="64 46493 49863"/>
    </justification>
  </clause>

  <clause id="49866">
    <literal><![CDATA[
      a(x,a(y,z,u),w * (w * v5)) = a(v5,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,36028,a,b,49864,a)].">
      <j1 rule="hyper" parents="64 36028 49864"/>
    </justification>
  </clause>

  <clause id="49868">
    <literal><![CDATA[
      L(x * a(y * z,u,a(w,x,v5)),w,a(y * z,u,v5)) = L(x,a(v5,u,y \ z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,49792,a(flip),b,49772,a)].">
      <j1 rule="hyper" parents="64 49792 49772"/>
    </justification>
  </clause>

  <clause id="49869">
    <literal><![CDATA[
      L(a(x,y,a(z,u,L(w,v5,y))) * u,w,a(x,y,z)) = L(u,a(x,y,L(z,v5,y)),w)
    ]]></literal>
    <justification jstring="[para(46496(a,1),49801(a,1,1,1,3))].">
      <j1 rule="para" parents="46496 49801"/>
    </justification>
  </clause>

  <clause id="49870">
    <literal><![CDATA[
      L(x,a(y,z,u \ w),v5) = L(x,a(y,z,u * w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,47268,a(flip),b,49868,a),flip(a)].">
      <j1 rule="hyper" parents="64 47268 49868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49871">
    <literal><![CDATA[
      L(x,a(y,z,u \ w),v5) = L(x,a(y,z,w * u),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,33920,a,b,49870,a),flip(a)].">
      <j1 rule="hyper" parents="373 33920 49870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49872">
    <literal><![CDATA[
      L(x,a(y,z,L(u,u,w)),v5) = L(x,a(y,z,w * (u \ w)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,38932,a,b,49870,a)].">
      <j1 rule="hyper" parents="64 38932 49870"/>
    </justification>
  </clause>

  <clause id="49874">
    <literal><![CDATA[
      L(x,a(y,z,u * (w \ u)),v5) = L(x,a(y,z,w),v5)
    ]]></literal>
    <justification jstring="[para(27307(a,1),49871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="27307 49871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49876">
    <literal><![CDATA[
      a(x,y,a(y,a(z,u,L(w,w,v5)),v6)) * L(v6,a(z,u,L(w,w,v5)),y * x) = L(v6,a(z,u,v5 * (w \ v5)),y \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,48597,a,b,49872,a)].">
      <j1 rule="hyper" parents="64 48597 49872"/>
    </justification>
  </clause>

  <clause id="49877">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) * u,w,a(x,y,z)) = L(u,a(x,y,L(z,v5,y)),w)
    ]]></literal>
    <justification jstring="[para(49784(a,1),49869(a,1,1,1))].">
      <j1 rule="para" parents="49784 49869"/>
    </justification>
  </clause>

  <clause id="49878">
    <literal><![CDATA[
      L(x,a(y,z,L(u,w,z)),v5) = L(x,a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,47211,a(flip),b,49877,a),flip(a)].">
      <j1 rule="hyper" parents="64 47211 49877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49882">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * a(u,w,a(v5,v6,v6)))) = a(v5,w,a(v6,v6,u)) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(49840(a,1),49678(a,1,2))].">
      <j1 rule="para" parents="49840 49678"/>
    </justification>
  </clause>

  <clause id="49883">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(u,w,a(v5,v6,v6))))) = a(v5,w,a(v6,v6,u)) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(49670(a,1),49882(a,1,2,2))].">
      <j1 rule="para" parents="49670 49882"/>
    </justification>
  </clause>

  <clause id="49884">
    <literal><![CDATA[
      L(x * a(y,z,a(u,w,w)),v5,v6) = a(u,z,a(w,w,y)) * L(x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(608,a,49883,a)].">
      <j1 rule="hyper" parents="608 49883"/>
    </justification>
  </clause>

  <clause id="49885">
    <literal><![CDATA[
      L(x * a(y,z,a(u,w,w)),v5,v6) = a(w,w,a(u,z,y)) * L(x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,47266,a,b,49884,a),flip(a)].">
      <j1 rule="hyper" parents="373 47266 49884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49890">
    <literal><![CDATA[
      L(a(x,x,a(y,z,u)) * w,v5,v6) = a(x,x,a(y,z,u)) * L(w,v5,v6)
    ]]></literal>
    <justification jstring="[para(45809(a,2),49885(a,1,1))].">
      <j1 rule="para" parents="45809 49885"/>
    </justification>
  </clause>

  <clause id="49892">
    <literal><![CDATA[
      L(a(x,x,a(y,z,u)) * w,v5,v6) = L(w,v5,v6) * a(u,z,a(x,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,45905,a,b,49890,a),flip(a)].">
      <j1 rule="hyper" parents="373 45905 49890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49893">
    <literal><![CDATA[
      L(a(x,x,a(y,z,u)) * (a(x,x,a(u,z,y)) * w),v5,v6) \ w = a(v6,v5,(w \ 1) \ a(x,x,a(u,z,y)))
    ]]></literal>
    <justification jstring="[para(49890(a,2),49183(a,1,1))].">
      <j1 rule="para" parents="49890 49183"/>
    </justification>
  </clause>

  <clause id="49896">
    <literal><![CDATA[
      L(a(x,x,a(y * z,z,u)) * w,v5,v6) = L(w,v5,v6) * a(z,a(u,x,x),y)
    ]]></literal>
    <justification jstring="[para(49427(a,1),49892(a,2,2))].">
      <j1 rule="para" parents="49427 49892"/>
    </justification>
  </clause>

  <clause id="49897">
    <literal><![CDATA[
      L(a(x,a(y,z,z),u) * w,v5,v6) = L(w,v5,v6) * a(u,a(y,z,z),x)
    ]]></literal>
    <justification jstring="[para(49423(a,1),49896(a,1,1,1))].">
      <j1 rule="para" parents="49423 49896"/>
    </justification>
  </clause>

  <clause id="49898">
    <literal><![CDATA[
      L(a(x,a(y,z,z),u) * w,v5,v6) = a(x,a(y,z,z),u) * L(w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,43415,a,b,49897,a),flip(a)].">
      <j1 rule="hyper" parents="373 43415 49897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49899">
    <literal><![CDATA[
      L(a(x,a(y,z,z),u) * z,x,a(y,z,u)) = L(z,z,a(y,u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47781,a(flip),b,49898,a),flip(a)].">
      <j1 rule="hyper" parents="373 47781 49898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49900">
    <literal><![CDATA[
      a(L(x,y * z,u),w,a(v5,v6,z)) = a(y * (u \ (z \ (u * y))),w,a(v5,v6,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,49822,a(flip),b,49776,a)].">
      <j1 rule="hyper" parents="373 49822 49776"/>
    </justification>
  </clause>

  <clause id="49902">
    <literal><![CDATA[
      a(x * (y \ (z \ (y * x))),u,a(w,v5,v6)) = a(v6,u,a(w,v5,L(z,x * z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46629,a(flip),b,49900,a),flip(a)].">
      <j1 rule="hyper" parents="64 46629 49900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49903">
    <literal><![CDATA[
      a((x * y) \ (z \ (y * x)),u,L(L(a(w,v5,v6),x,y),x,x)) = a(v6,u,a(w,v5,L(z,x * z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47062,a,b,49902,a)].">
      <j1 rule="hyper" parents="64 47062 49902"/>
    </justification>
  </clause>

  <clause id="49904">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * (w * L(v5 \ 1,v5,w))) = a(x,y,v5 \ (w * a(u,z,z)))
    ]]></literal>
    <justification jstring="[para(49394(a,1),49853(a,1,3,2,2))].">
      <j1 rule="para" parents="49394 49853"/>
    </justification>
  </clause>

  <clause id="49905">
    <literal><![CDATA[
      a(x,y,z \ (u * a(w,v5,v5))) = a(x,y,(z \ u) * a(v5,v5,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,28944,a(flip),b,49904,a),flip(a)].">
      <j1 rule="hyper" parents="64 28944 49904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49907">
    <literal><![CDATA[
      a(x,y,z \ (a(u,u,w) * v5)) = a(x,y,(z \ v5) * a(u,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,40067,a,b,49905,a)].">
      <j1 rule="hyper" parents="64 40067 49905"/>
    </justification>
  </clause>

  <clause id="49908">
    <literal><![CDATA[
      a(x,y,(z \ (u * w)) * a(v5,v5,w)) = a(x,y,z \ (u * L(w,v5,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47150,a(flip),b,49907,a),flip(a)].">
      <j1 rule="hyper" parents="64 47150 49907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49909">
    <literal><![CDATA[
      a((x * y) \ (z \ (y * x)),u,L(a(w,v5,L(v6,x,y)),x,x)) = a(v6,u,a(w,v5,L(z,x * z,y)))
    ]]></literal>
    <justification jstring="[para(46493(a,2),49903(a,1,3,1))].">
      <j1 rule="para" parents="46493 49903"/>
    </justification>
  </clause>

  <clause id="49910">
    <literal><![CDATA[
      a((x * y) \ (z \ (y * x)),u,a(w,v5,L(L(v6,x,y),x,x))) = a(v6,u,a(w,v5,L(z,x * z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46631,a,b,49909,a)].">
      <j1 rule="hyper" parents="64 46631 49909"/>
    </justification>
  </clause>

  <clause id="49911">
    <literal><![CDATA[
      a((x * y) \ (z \ (y * x)),u,a(L(w,x,y),v5,v6)) = a(w,v5,a(v6,u,L(z,x * z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49741,a(flip),b,49910,a)].">
      <j1 rule="hyper" parents="64 49741 49910"/>
    </justification>
  </clause>

  <clause id="49913">
    <literal><![CDATA[
      a((x * y) * (z \ (y * x)),u,a(w,v5,L(v6,x,y))) = a(v6,u,a(w,v5,L(z,x * z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49756,a(flip),b,49911,a)].">
      <j1 rule="hyper" parents="64 49756 49911"/>
    </justification>
  </clause>

  <clause id="49914">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5 * w,v6))) = a(L(x,v5,v6),y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,49832,a(flip),b,49913,a),flip(a)].">
      <j1 rule="hyper" parents="64 49832 49913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49916">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5 * w,v6))) = a(x,y,a(z,u,L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,46629,a(flip),b,49914,a),flip(a)].">
      <j1 rule="hyper" parents="373 46629 49914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49917">
    <literal><![CDATA[
      a(x * (y \ (z \ (y * x))),u,a(w,v5,v6)) = a(v6,u,a(w,v5,L(z,x,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49902,a,b,49916,a)].">
      <j1 rule="hyper" parents="64 49902 49916"/>
    </justification>
  </clause>

  <clause id="49918">
    <literal><![CDATA[
      a(x * (((y * y) \ z) \ ((y * (y * u)) \ (z * x))),w,a(v5,v6,v7)) = a(v7,w,a(v5,v6,L(L(u,y,y),x,(y * y) \ z)))
    ]]></literal>
    <justification jstring="[para(1367(a,1),49917(a,1,1,2,2))].">
      <j1 rule="para" parents="1367 49917"/>
    </justification>
  </clause>

  <clause id="49919">
    <literal><![CDATA[
      a((x \ a(y,z,z)) \ u,w,x * L(x \ v5,z,a(y,v5,z))) = a(a(y,z,z) \ (x \ u),w,v5)
    ]]></literal>
    <justification jstring="[para(45031(a,1),49454(a,2,1,1))].">
      <j1 rule="para" parents="45031 49454"/>
    </justification>
  </clause>

  <clause id="49920">
    <literal><![CDATA[
      a((x \ a(y,z,z)) \ u,w,x * L(x \ v5,z,a(y,v5,z))) = a((x \ u) * a(y,z,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,42467,a(flip),b,49919,a),flip(a)].">
      <j1 rule="hyper" parents="373 42467 49919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49922">
    <literal><![CDATA[
      a((x \ a(y,z,z)) \ u,w,L(v5,a(y,z,z),x)) = a((x \ u) * a(y,z,z),w,v5)
    ]]></literal>
    <justification jstring="[para(49450(a,1),49920(a,1,3))].">
      <j1 rule="para" parents="49450 49920"/>
    </justification>
  </clause>

  <clause id="49923">
    <literal><![CDATA[
      a((x \ a(y,z,z)) \ u,w,v5) = a((x \ u) * a(y,z,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,49712,a(flip),b,49922,a)].">
      <j1 rule="hyper" parents="64 49712 49922"/>
    </justification>
  </clause>

  <clause id="49925">
    <literal><![CDATA[
      a((a(x,y,y) * z) \ u,w,v5) = a((z \ u) * a(x,y,y),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,45507,a(flip),b,49923,a)].">
      <j1 rule="hyper" parents="64 45507 49923"/>
    </justification>
  </clause>

  <clause id="49926">
    <literal><![CDATA[
      a((x * a(y,z,z)) \ u,w,v5) = a((x \ u) * a(y,z,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(32451,a,49925,a)].">
      <j1 rule="hyper" parents="32451 49925"/>
    </justification>
  </clause>

  <clause id="49927">
    <literal><![CDATA[
      a((T(x * (y * y),z) * (1 / y)) * a(u,w,w),v5,v6) = a((y * a(u,w,w)) \ T(y * (x * y),z),v5,v6)
    ]]></literal>
    <justification jstring="[para(5489(a,2),49926(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5489 49926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49928">
    <literal><![CDATA[
      a((x \ y) * a(z,u,u),w,v5) \ v5 = L(v5,w,(x * a(z,u,u)) \ y)
    ]]></literal>
    <justification jstring="[para(49926(a,1),45065(a,2,1)),flip(a)].">
      <j1 rule="para" parents="49926 45065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49929">
    <literal><![CDATA[
      L(x,y,(z * a(u,w,w)) \ v5) = L(x,y,(z \ v5) * a(u,w,w))
    ]]></literal>
    <justification jstring="[hyper(45147,a,49928,a),flip(a)].">
      <j1 rule="hyper" parents="45147 49928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49930">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ u) * a(w,v5,v5)) = L(x,y,(z \ a(w,v5,v5)) \ u)
    ]]></literal>
    <justification jstring="[para(45033(a,1),49929(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="45033 49929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49931">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * ((w \ v5) * 1) = w \ (v5 * a(x,u,a(y,y,z)))
    ]]></literal>
    <justification jstring="[para(49640(a,1),49851(a,1,2,2))].">
      <j1 rule="para" parents="49640 49851"/>
    </justification>
  </clause>

  <clause id="49932">
    <literal><![CDATA[
      x \ (y * a(z,u,a(w,w,v5))) = a(z,w,a(v5,u,w)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(738,a,49931,a),flip(a)].">
      <j1 rule="hyper" parents="738 49931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49934">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ a(u,u,a(w,v5,v6))) = L(z,y,x) \ z
    ]]></literal>
    <justification jstring="[para(42646(a,1),49893(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="42646 49893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49935">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ a(u,u,a(w,v5,v6))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,45067,a,b,49934,a),flip(a)].">
      <j1 rule="hyper" parents="373 45067 49934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49936">
    <literal><![CDATA[
      a(x,y,a(z,z,a(u,w,v5)) * v6) = a(x,y,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,45742,a(flip),b,49935,a)].">
      <j1 rule="hyper" parents="64 45742 49935"/>
    </justification>
  </clause>

  <clause id="49937">
    <literal><![CDATA[
      a(x,y,z * a(u,w,a(w,v5,v6))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46343,a(flip),b,49936,a)].">
      <j1 rule="hyper" parents="64 46343 49936"/>
    </justification>
  </clause>

  <clause id="49949">
    <literal><![CDATA[
      a((T(x * (y * y),z) * (1 / y)) * a(u,w,w),v5,v6) = a((y * a(u,w,w)) \ (y * (x * y)),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32360,a(flip),b,49927,a),flip(a)].">
      <j1 rule="hyper" parents="373 32360 49927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49951">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) * (w * v5)) \ (v6 \ ((a(y,y,a(z,u,x)) * (v6 * w)) * v5)) = a(v6,a(y,y,a(z,u,x)) * w,v5)
    ]]></literal>
    <justification jstring="[para(49843(a,1),49842(a,1,1))].">
      <j1 rule="para" parents="49843 49842"/>
    </justification>
  </clause>

  <clause id="49952">
    <literal><![CDATA[
      (x * a(y,z,a(u,w,z))) \ v5 = (x \ v5) * a(y,w,a(z,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,49650,a(flip),b,49855,a)].">
      <j1 rule="hyper" parents="64 49650 49855"/>
    </justification>
  </clause>

  <clause id="49953">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) * w) \ v5 = (w \ v5) * a(x,u,a(y,y,z))
    ]]></literal>
    <justification jstring="[hyper(23968,a,49952,a)].">
      <j1 rule="hyper" parents="23968 49952"/>
    </justification>
  </clause>

  <clause id="49955">
    <literal><![CDATA[
      L(x,a(y,z,u * (w \ u)),v5 \ v6) = 1 * L(x,a(y,z,L(w,w,u)),v5 * v6)
    ]]></literal>
    <justification jstring="[para(49604(a,1),49876(a,1,1)),flip(a)].">
      <j1 rule="para" parents="49604 49876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49956">
    <literal><![CDATA[
      L(x,a(y,z,L(u,u,w)),v5 * v6) = L(x,a(y,z,u),v5 \ v6)
    ]]></literal>
    <justification jstring="[hyper(137,a,49955,a(flip),b,49874,a(flip))].">
      <j1 rule="hyper" parents="137 49955 49874"/>
    </justification>
  </clause>

  <clause id="49958">
    <literal><![CDATA[
      L(x,a(y,z,u),w \ v5) = L(x,a(y,z,u),w * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,49878,a(flip),b,49956,a),flip(a)].">
      <j1 rule="hyper" parents="64 49878 49956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49964">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) * (w * v5)) \ (v6 \ (a(x,y,a(z,u,y)) * ((v6 * w) * v5))) = a(v6,a(y,y,a(z,u,x)) * w,v5)
    ]]></literal>
    <justification jstring="[para(49843(a,1),49951(a,1,2,2))].">
      <j1 rule="para" parents="49843 49951"/>
    </justification>
  </clause>

  <clause id="49965">
    <literal><![CDATA[
      (a(x,y,a(z,u,y)) * (w * v5)) \ ((v6 \ ((v6 * w) * v5)) * a(x,u,a(y,y,z))) = a(v6,a(y,y,a(z,u,x)) * w,v5)
    ]]></literal>
    <justification jstring="[para(49852(a,1),49964(a,1,2))].">
      <j1 rule="para" parents="49852 49964"/>
    </justification>
  </clause>

  <clause id="49966">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * ((a(x,y,a(z,u,y)) * (w * v5)) \ (v6 \ ((v6 * w) * v5))) = a(v6,a(y,y,a(z,u,x)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,49932,a(flip),b,49965,a)].">
      <j1 rule="hyper" parents="64 49932 49965"/>
    </justification>
  </clause>

  <clause id="49967">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * (((w * v5) \ (v6 \ ((v6 * w) * v5))) * a(x,u,a(y,y,z))) = a(v6,a(y,y,a(z,u,x)) * w,v5)
    ]]></literal>
    <justification jstring="[para(49953(a,1),49966(a,1,2))].">
      <j1 rule="para" parents="49953 49966"/>
    </justification>
  </clause>

  <clause id="49968">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) * (a(w,v5,v6) * a(x,u,a(y,y,z))) = a(w,a(y,y,a(z,u,x)) * v5,v6)
    ]]></literal>
    <justification jstring="[para(30027(a,2),49967(a,1,2,1))].">
      <j1 rule="para" parents="30027 49967"/>
    </justification>
  </clause>

  <clause id="49969">
    <literal><![CDATA[
      a(x,a(y,y,a(z,u,w)) * v5,v6) = a(x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,47481,a(flip),b,49968,a),flip(a)].">
      <j1 rule="hyper" parents="64 47481 49968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49971">
    <literal><![CDATA[
      a(x,a(y,z,a(u,u,w)) * v5,v6) = a(x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,45818,a,b,49969,a)].">
      <j1 rule="hyper" parents="64 45818 49969"/>
    </justification>
  </clause>

  <clause id="49973">
    <literal><![CDATA[
      a(x,y * a(z,z,L(u,w,v5)),v6) = a(x,y * a(z,z,u),v6)
    ]]></literal>
    <justification jstring="[para(46558(a,1),49971(a,1,2))].">
      <j1 rule="para" parents="46558 49971"/>
    </justification>
  </clause>

  <clause id="49974">
    <literal><![CDATA[
      a(x,(((y / z) \ u) \ u) * a(w,w,v5),v6) = a(x,(a(w,w,v5) * y) / z,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,46936,a(flip),b,49973,a),flip(a)].">
      <j1 rule="hyper" parents="64 46936 49973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49976">
    <literal><![CDATA[
      a(x,(a(y,y,z) * u) / w,v5) = a(x,a(y,y,z) * (u / w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32091,a(flip),b,49974,a),flip(a)].">
      <j1 rule="hyper" parents="64 32091 49974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49977">
    <literal><![CDATA[
      a(x,(a(y,y,z) * u) / w,v5) = a(x,a(y,y,z) * (w \ u),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31897,a(flip),b,49976,a),flip(a)].">
      <j1 rule="hyper" parents="373 31897 49976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49978">
    <literal><![CDATA[
      a(x,y \ (z * a(u,u,w)),v5) = a(x,a(u,u,w) * (y \ z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32063,a(flip),b,49977,a)].">
      <j1 rule="hyper" parents="64 32063 49977"/>
    </justification>
  </clause>

  <clause id="49979">
    <literal><![CDATA[
      a(x,a(y,y,z) * (u \ w),v5) \ v5 = L(v5,u \ (w * a(y,y,z)),x)
    ]]></literal>
    <justification jstring="[para(49978(a,1),45065(a,2,1)),flip(a)].">
      <j1 rule="para" parents="49978 45065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49980">
    <literal><![CDATA[
      L(x,y \ (z * a(u,u,w)),v5) = L(x,a(u,u,w) * (y \ z),v5)
    ]]></literal>
    <justification jstring="[hyper(45147,a,49979,a),flip(a)].">
      <j1 rule="hyper" parents="45147 49979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49981">
    <literal><![CDATA[
      L(x,y \ (z * a(u,w,w)),v5) = L(x,a(w,w,u) * (y \ z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,42768,a,b,49980,a)].">
      <j1 rule="hyper" parents="64 42768 49980"/>
    </justification>
  </clause>

  <clause id="49982">
    <literal><![CDATA[
      L(x,y \ (L(z,y,y) * a(u,w,w)),v5) = L(x,a(w,w,u) * ((y \ 1) * z),v5)
    ]]></literal>
    <justification jstring="[para(1148(a,1),49981(a,2,2,2))].">
      <j1 rule="para" parents="1148 49981"/>
    </justification>
  </clause>

  <clause id="49983">
    <literal><![CDATA[
      L(x,(y \ 1) \ (R(z,y,y \ 1) * a(u,w,w)),v5) = L(x,a(w,w,u) * T(z * y,y \ 1),v5)
    ]]></literal>
    <justification jstring="[para(698(a,1),49981(a,2,2,2))].">
      <j1 rule="para" parents="698 49981"/>
    </justification>
  </clause>

  <clause id="49984">
    <literal><![CDATA[
      L(x,y \ L(a(z,u,u) * w,y,y),v5) = L(x,a(u,u,z) * ((y \ 1) * w),v5)
    ]]></literal>
    <justification jstring="[para(49005(a,2),49982(a,1,2,2))].">
      <j1 rule="para" parents="49005 49982"/>
    </justification>
  </clause>

  <clause id="49985">
    <literal><![CDATA[
      L(x,a(y,y,z) * ((u \ 1) * w),v5) = L(x,(u \ 1) * (a(z,y,y) * w),v5)
    ]]></literal>
    <justification jstring="[para(1148(a,1),49984(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1148 49984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49986">
    <literal><![CDATA[
      L(x,a(y,y,z) * ((u \ 1) * w),v5) = L(x,u * (a(z,y,y) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,11864,a(flip),b,49985,a),flip(a)].">
      <j1 rule="hyper" parents="373 11864 49985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49987">
    <literal><![CDATA[
      L(x,(y * z) * a(u,u,w),v5) = L(x,y * (a(w,u,u) * z),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29519,a(flip),b,49986,a)].">
      <j1 rule="hyper" parents="64 29519 49986"/>
    </justification>
  </clause>

  <clause id="49989">
    <literal><![CDATA[
      L(x,(y \ 1) \ R(a(z,u,u) * w,y,y \ 1),v5) = L(x,a(u,u,z) * T(w * y,y \ 1),v5)
    ]]></literal>
    <justification jstring="[para(49405(a,2),49983(a,1,2,2))].">
      <j1 rule="para" parents="49405 49983"/>
    </justification>
  </clause>

  <clause id="49990">
    <literal><![CDATA[
      L(x,T((a(y,z,z) * u) * w,w \ 1),v5) = L(x,a(z,z,y) * T(u * w,w \ 1),v5)
    ]]></literal>
    <justification jstring="[para(698(a,1),49989(a,1,2))].">
      <j1 rule="para" parents="698 49989"/>
    </justification>
  </clause>

  <clause id="49991">
    <literal><![CDATA[
      L(x,a(y,y,z) * T(u * w,w \ 1),v5) = L(x,(a(z,y,y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(29565,a,49990,a),flip(a)].">
      <j1 rule="hyper" parents="29565 49990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49993">
    <literal><![CDATA[
      L(x,(a(y,z,z) * u) * w,v5) = L(x,(u * w) * a(z,z,y),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,29578,a(flip),b,49991,a),flip(a)].">
      <j1 rule="hyper" parents="64 29578 49991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49995">
    <literal><![CDATA[
      L(x,(a(y,z,z) * u) * w,v5) = L(x,u * (a(y,z,z) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,49987,a(flip),b,49993,a),flip(a)].">
      <j1 rule="hyper" parents="373 49987 49993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49996">
    <literal><![CDATA[
      L(x,y * (a(z,u,u) * w),v5) = L(x,w * (a(u,u,z) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,37979,a(flip),b,49995,a),flip(a)].">
      <j1 rule="hyper" parents="64 37979 49995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49997">
    <literal><![CDATA[
      L(x,((a(y,z,z) \ u) * y) * (a(z,z,y) * w),v5) = L(x,w * (u * y),v5)
    ]]></literal>
    <justification jstring="[para(29968(a,1),49996(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="29968 49996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="49998">
    <literal><![CDATA[
      L(x,(y * (a(z,u,u) \ z)) * (a(u,u,z) * w),v5) = L(x,w * (y * z),v5)
    ]]></literal>
    <justification jstring="[para(44994(a,1),49997(a,1,2,1))].">
      <j1 rule="para" parents="44994 49997"/>
    </justification>
  </clause>

  <clause id="49999">
    <literal><![CDATA[
      L(x,(L(y,z,z) * u) * (a(z,z,y) * w),v5) = L(x,w * (u * y),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,47767,a(flip),b,49998,a)].">
      <j1 rule="hyper" parents="64 47767 49998"/>
    </justification>
  </clause>

  <clause id="50000">
    <literal><![CDATA[
      a(x * (y \ ((z * z) * ((z * (z * u)) \ (y * x)))),w,a(v5,v6,v7)) = a(v7,w,a(v5,v6,L(L(u,z,z),x,(z * z) \ y)))
    ]]></literal>
    <justification jstring="[para(804(a,1),49918(a,1,1,2))].">
      <j1 rule="para" parents="804 49918"/>
    </justification>
  </clause>

  <clause id="50001">
    <literal><![CDATA[
      a(x * (y \ ((z * (z * u)) \ (y * x))),w,a(v5,v6,v7)) = a(v7,w,a(v5,v6,L(L(u,z,z),x,(z * z) \ y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,32705,a(flip),b,50000,a)].">
      <j1 rule="hyper" parents="64 32705 50000"/>
    </justification>
  </clause>

  <clause id="50003">
    <literal><![CDATA[
      a(x,y,a(z,u,L(L(w,v5,v5),v6,(v5 * v5) \ v7))) = a(x,y,a(z,u,L(v5 * (v5 * w),v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49917,a(flip),b,50001,a),flip(a)].">
      <j1 rule="hyper" parents="64 49917 50001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50004">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w * (w * v5),v6,v7))) = a(x,y,a(z,u,L(L(v5,w,w),v6,v7)))
    ]]></literal>
    <justification jstring="[para(2181(a,1),50003(a,1,3,3)),flip(a)].">
      <j1 rule="para" parents="2181 50003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50005">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w * (w * v5),v6,v7))) = a(x,u,a(v5,y,L(z,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(373,a,49755,a(flip),b,50004,a),flip(a)].">
      <j1 rule="hyper" parents="373 49755 50004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50008">
    <literal><![CDATA[
      L(x * L(y,z,u),a(w,v5,v5),L((x \ 1) * (x * y),z,u)) = (x * L(y,z,u)) * a(w,x * L(y,z,u),a(x,v5,v5))
    ]]></literal>
    <justification jstring="[para(2653(a,1),49466(a,2,2,3))].">
      <j1 rule="para" parents="2653 49466"/>
    </justification>
  </clause>

  <clause id="50009">
    <literal><![CDATA[
      L(x * L(y,z,u),a(w,v5,v5),L((x \ 1) * (x * y),z,u)) = (x * L(y,z,u)) * a(x,v5,a(w,L(y,z,u),v5))
    ]]></literal>
    <justification jstring="[para(46883(a,1),50008(a,2,2))].">
      <j1 rule="para" parents="46883 50008"/>
    </justification>
  </clause>

  <clause id="50010">
    <literal><![CDATA[
      L(x * L(y,z,u),a(w,v5,v5),L((x \ 1) * (x * y),z,u)) = (x * L(y,z,u)) * a(x,v5,a(w,y,v5))
    ]]></literal>
    <justification jstring="[para(49763(a,1),50009(a,2,2))].">
      <j1 rule="para" parents="49763 50009"/>
    </justification>
  </clause>

  <clause id="50011">
    <literal><![CDATA[
      L(x * L(y,z,u),a(w,v5,v5),L((x \ 1) * (x * y),z,u)) = x * (L(y,z,u) * a(x,v5,a(w,y,v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,49693,a(flip),b,50010,a),flip(a)].">
      <j1 rule="hyper" parents="373 49693 50010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50013">
    <literal><![CDATA[
      L(x * L(y,z,u),a(w,v5,v5),L((x \ 1) * (x * y),z,u)) = L(x,v5,a(v5,y,w)) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,46804,a(flip),b,50011,a),flip(a)].">
      <j1 rule="hyper" parents="373 46804 50011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50014">
    <literal><![CDATA[
      L(x * L(y,z,u),a(w,v5,v5),L(x * (x * y),z,u)) = L(x,v5,a(v5,y,w)) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34233,a(flip),b,50013,a)].">
      <j1 rule="hyper" parents="64 34233 50013"/>
    </justification>
  </clause>

  <clause id="50015">
    <literal><![CDATA[
      L(x * L(y,z,u),a(w,v5,v5),L(L(y,x,x),z,u)) = L(x,v5,a(v5,y,w)) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,34220,a(flip),b,50014,a)].">
      <j1 rule="hyper" parents="64 34220 50014"/>
    </justification>
  </clause>

  <clause id="50016">
    <literal><![CDATA[
      L(x * L(y,z,u),a(w,v5,v5),L(y,x,x)) = L(x,v5,a(v5,y,w)) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,49694,a(flip),b,50015,a)].">
      <j1 rule="hyper" parents="64 49694 50015"/>
    </justification>
  </clause>

  <clause id="50018">
    <literal><![CDATA[
      L(x * L(y,z,u),a(w,v5,v5),y) = L(x,v5,a(v5,y,w)) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,49694,a(flip),b,50016,a)].">
      <j1 rule="hyper" parents="64 49694 50016"/>
    </justification>
  </clause>

  <clause id="50020">
    <literal><![CDATA[
      a(x,y,((a(z,u,w) \ v5) \ v6) * a(z,v5 * a(z,u,w),a(v5 * a(z,u,w),u,w))) = a(x,y,((v5 \ a(z,u,w)) \ 1) \ v6)
    ]]></literal>
    <justification jstring="[para(42467(a,1),49836(a,1,3,2,3))].">
      <j1 rule="para" parents="42467 49836"/>
    </justification>
  </clause>

  <clause id="50021">
    <literal><![CDATA[
      a(x,y,((z \ a(u,w,v5)) \ 1) \ v6) = a(x,y,(a(u,w,v5) \ z) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,49937,a(flip),b,50020,a),flip(a)].">
      <j1 rule="hyper" parents="64 49937 50020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50023">
    <literal><![CDATA[
      a(x,y,((z \ a(u,w,v5)) \ 1) \ v6) = a(x,y,(z * a(u,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,42482,a(flip),b,50021,a),flip(a)].">
      <j1 rule="hyper" parents="373 42482 50021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50024">
    <literal><![CDATA[
      L(x * a(y,z,z),z,a(z,u,y)) * (a(u,a(y,z,z),L(x,u,a(y,z,z))) \ u) = (L(x,a(y,z,z),u * x) * a(y,z,z)) * u
    ]]></literal>
    <justification jstring="[para(47923(a,2),49471(a,1,1))].">
      <j1 rule="para" parents="47923 49471"/>
    </justification>
  </clause>

  <clause id="50025">
    <literal><![CDATA[
      L(x * a(y,z,z),z,a(z,u,y)) * (a(u,a(y,z,z),x) \ u) = (L(x,a(y,z,z),u * x) * a(y,z,z)) * u
    ]]></literal>
    <justification jstring="[para(46508(a,1),50024(a,1,2,1))].">
      <j1 rule="para" parents="46508 50024"/>
    </justification>
  </clause>

  <clause id="50026">
    <literal><![CDATA[
      L(x * a(y,z,z),z,a(z,u,y)) * (a(x,a(y,z,z),u) * u) = (L(x,a(y,z,z),u * x) * a(y,z,z)) * u
    ]]></literal>
    <justification jstring="[para(42524(a,1),50025(a,1,2))].">
      <j1 rule="para" parents="42524 50025"/>
    </justification>
  </clause>

  <clause id="50027">
    <literal><![CDATA[
      L(x * a(y,z,z),z,a(z,u,y)) * L(u,a(z,z,y),x) = (L(x,a(y,z,z),u * x) * a(y,z,z)) * u
    ]]></literal>
    <justification jstring="[para(43403(a,1),50026(a,1,2))].">
      <j1 rule="para" parents="43403 50026"/>
    </justification>
  </clause>

  <clause id="50028">
    <literal><![CDATA[
      L((x * a(y,z,z)) * L(u,a(z,z,y),x),a(y,z,z),u) = (L(x,a(y,z,z),u * x) * a(y,z,z)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,50018,a,b,50027,a)].">
      <j1 rule="hyper" parents="64 50018 50027"/>
    </justification>
  </clause>

  <clause id="50029">
    <literal><![CDATA[
      (L(x,a(y,z,z),u * x) * a(y,z,z)) * u = L(x * (a(y,z,z) * u),a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(31827(a,1),50028(a,1,1)),flip(a)].">
      <j1 rule="para" parents="31827 50028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50030">
    <literal><![CDATA[
      x * L(x \ ((x \ (x * a(y,z,z))) \ u),z,a(y,(x \ ((1 / x) \ a(y,z,z))) \ u,z)) = (x \ a(y,z,z)) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(45034(a,1),49452(a,1,2,1,2,1,2))].">
      <j1 rule="para" parents="45034 49452"/>
    </justification>
  </clause>

  <clause id="50031">
    <literal><![CDATA[
      x * L(x \ (a(y,z,z) \ u),z,a(y,(x \ ((1 / x) \ a(y,z,z))) \ u,z)) = (x \ a(y,z,z)) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),50030(a,1,2,1,2,1))].">
      <j1 rule="para" parents="9 50030"/>
    </justification>
  </clause>

  <clause id="50033">
    <literal><![CDATA[
      x * L(x \ (a(y,z,z) \ u),z,a(y,(x \ (x * a(y,z,z))) \ u,z)) = (x \ a(y,z,z)) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(45034(a,1),50031(a,1,2,3,2,1,2))].">
      <j1 rule="para" parents="45034 50031"/>
    </justification>
  </clause>

  <clause id="50034">
    <literal><![CDATA[
      x * L(x \ (a(y,z,z) \ u),z,a(y,a(y,z,z) \ u,z)) = (x \ a(y,z,z)) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(9(a,1),50033(a,1,2,3,2,1))].">
      <j1 rule="para" parents="9 50033"/>
    </justification>
  </clause>

  <clause id="50036">
    <literal><![CDATA[
      x * L(x \ (a(y,z,z) \ u),z,a(y,a(y,z,z) * u,z)) = (x \ a(y,z,z)) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(42464(a,1),50034(a,1,2,3))].">
      <j1 rule="para" parents="42464 50034"/>
    </justification>
  </clause>

  <clause id="50037">
    <literal><![CDATA[
      x * L(x \ (a(y,z,z) \ u),u,a(y,z,z)) = (x \ a(y,z,z)) \ ((x \ 1) * u)
    ]]></literal>
    <justification jstring="[para(47435(a,1),50036(a,1,2))].">
      <j1 rule="para" parents="47435 50036"/>
    </justification>
  </clause>

  <clause id="50038">
    <literal><![CDATA[
      (x \ a(y,z,z)) \ ((x \ 1) * u) = x * ((a(y,z,z) * x) \ u)
    ]]></literal>
    <justification jstring="[para(47826(a,1),50037(a,1,2)),flip(a)].">
      <j1 rule="para" parents="47826 50037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50039">
    <literal><![CDATA[
      (x * a(y,z,z)) \ (x * u) = x * ((a(y,z,z) * x) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,45737,a(flip),b,50038,a)].">
      <j1 rule="hyper" parents="64 45737 50038"/>
    </justification>
  </clause>

  <clause id="50040">
    <literal><![CDATA[
      a((T(x * (y * y),z) * (1 / y)) * a(u,w,w),v5,v6) = a(y * ((a(u,w,w) * y) \ (x * y)),v5,v6)
    ]]></literal>
    <justification jstring="[para(50039(a,1),49949(a,2,1))].">
      <j1 rule="para" parents="50039 49949"/>
    </justification>
  </clause>

  <clause id="50041">
    <literal><![CDATA[
      a((T(x * (y * y),z) * (1 / y)) * a(u,w,w),v5,v6) = a(y * (y \ (x * (a(u,w,w) \ y))),v5,v6)
    ]]></literal>
    <justification jstring="[para(48973(a,1),50040(a,2,1,2))].">
      <j1 rule="para" parents="48973 50040"/>
    </justification>
  </clause>

  <clause id="50042">
    <literal><![CDATA[
      a((T(x * (y * y),z) * (1 / y)) * a(u,w,w),v5,v6) = a(x * (a(u,w,w) \ y),v5,v6)
    ]]></literal>
    <justification jstring="[para(10(a,1),50041(a,2,1))].">
      <j1 rule="para" parents="10 50041"/>
    </justification>
  </clause>

  <clause id="50043">
    <literal><![CDATA[
      a((T(x * (y * y),z) * (1 / y)) * a(u,w,w),v5,v6) = a(x * (a(u,w,w) * y),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,42511,a(flip),b,50042,a),flip(a)].">
      <j1 rule="hyper" parents="373 42511 50042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50045">
    <literal><![CDATA[
      a((x \ T(x * (y * x),z)) * a(u,w,w),v5,v6) = a(y * (a(u,w,w) * x),v5,v6)
    ]]></literal>
    <justification jstring="[para(5489(a,1),50043(a,1,1,1))].">
      <j1 rule="para" parents="5489 50043"/>
    </justification>
  </clause>

  <clause id="50046">
    <literal><![CDATA[
      a((x \ (x * (y * x))) * a(z,u,u),w,v5) = a(y * (a(z,u,u) * x),w,v5)
    ]]></literal>
    <justification jstring="[hyper(32583,a,50045,a)].">
      <j1 rule="hyper" parents="32583 50045"/>
    </justification>
  </clause>

  <clause id="50047">
    <literal><![CDATA[
      a((x * y) * a(z,u,u),w,v5) = a(x * (a(z,u,u) * y),w,v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),50046(a,1,1,1))].">
      <j1 rule="para" parents="9 50046"/>
    </justification>
  </clause>

  <clause id="50048">
    <literal><![CDATA[
      a(a(x,x,y) * (z * u),w,v5) = a(u * (a(y,x,x) * z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32854,a,b,50047,a)].">
      <j1 rule="hyper" parents="64 32854 50047"/>
    </justification>
  </clause>

  <clause id="50050">
    <literal><![CDATA[
      a(a(x,x,y) * (z * u),w,v5) = a(u * (z * a(y,x,x)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,32365,a,b,50048,a),flip(a)].">
      <j1 rule="hyper" parents="373 32365 50048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50051">
    <literal><![CDATA[
      a(a(x,x,y) * ((y * z) * u),w,v5) = a(u * (R(y,x,x) * z),w,v5)
    ]]></literal>
    <justification jstring="[para(45511(a,1),50050(a,2,1,2))].">
      <j1 rule="para" parents="45511 50050"/>
    </justification>
  </clause>

  <clause id="50052">
    <literal><![CDATA[
      a(a(x,x,y) * ((y * z) * u),w,v5) = a(u * (L(y,x,x) * z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,34659,a(flip),b,50051,a),flip(a)].">
      <j1 rule="hyper" parents="373 34659 50051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50053">
    <literal><![CDATA[
      L((1 / a(x,y,y)) \ z,a(u,y,y),x * ((1 / a(x,y,y)) \ z)) = (a(x,y,y) \ 1) \ (a(u,(1 / a(x,y,y)) \ z,a(x,y,y)) * z)
    ]]></literal>
    <justification jstring="[para(13923(a,1),49463(a,2,1))].">
      <j1 rule="para" parents="13923 49463"/>
    </justification>
  </clause>

  <clause id="50054">
    <literal><![CDATA[
      L(T(a(x,y,y),z) * u,a(w,y,y),x * (T(a(x,y,y),z) * u)) = a(x,y,y) * (u * a(w,T(a(x,y,y),z) * u,a(x,y,y)))
    ]]></literal>
    <justification jstring="[para(13984(a,1),49465(a,2,1))].">
      <j1 rule="para" parents="13984 49465"/>
    </justification>
  </clause>

  <clause id="50055">
    <literal><![CDATA[
      L(T(a(x,y,y),z) * u,a(w,y,y),x * (T(a(x,y,y),z) * u)) = a(x,y,y) * (u * a(w,a(x,y,y) * u,a(x,y,y)))
    ]]></literal>
    <justification jstring="[para(13984(a,1),50054(a,2,2,2,2,1))].">
      <j1 rule="para" parents="13984 50054"/>
    </justification>
  </clause>

  <clause id="50058">
    <literal><![CDATA[
      L(T(a(x,y,y),z) * u,a(w,y,y),x * (T(a(x,y,y),z) * u)) = a(x,y,y) * (u * a(x,u,a(y,y,w)))
    ]]></literal>
    <justification jstring="[para(49032(a,1),50055(a,2,2,2))].">
      <j1 rule="para" parents="49032 50055"/>
    </justification>
  </clause>

  <clause id="50060">
    <literal><![CDATA[
      L(T(a(x,y,y),z) * u,a(w,y,y),x * (T(a(x,y,y),z) * u)) = a(x,y,y) * L(u,a(x,y,y),w * u)
    ]]></literal>
    <justification jstring="[para(49457(a,2),50058(a,2,2))].">
      <j1 rule="para" parents="49457 50058"/>
    </justification>
  </clause>

  <clause id="50061">
    <literal><![CDATA[
      L(T(a(x,y,y),z) * u,a(w,y,y),x * (T(a(x,y,y),z) * u)) = L(a(x,y,y) * u,a(x,y,y),w * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,49103,a,b,50060,a),flip(a)].">
      <j1 rule="hyper" parents="373 49103 50060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50062">
    <literal><![CDATA[
      L(a(x,y,y) * z,a(u,y,y),x * (T(a(x,y,y),w) * z)) = L(a(x,y,y) * z,a(x,y,y),u * z)
    ]]></literal>
    <justification jstring="[para(13984(a,1),50061(a,1,1,1))].">
      <j1 rule="para" parents="13984 50061"/>
    </justification>
  </clause>

  <clause id="50063">
    <literal><![CDATA[
      L(a(x,y,y) * z,a(u,y,y),x * (a(x,y,y) * z)) = L(a(x,y,y) * z,a(x,y,y),u * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29088,a(flip),b,50062,a)].">
      <j1 rule="hyper" parents="64 29088 50062"/>
    </justification>
  </clause>

  <clause id="50065">
    <literal><![CDATA[
      L(a(x,y,y) * z,a(u,y,y),R(x,y,y) * z) = L(a(x,y,y) * z,a(x,y,y),u * z)
    ]]></literal>
    <justification jstring="[para(45015(a,1),50063(a,1,3))].">
      <j1 rule="para" parents="45015 50063"/>
    </justification>
  </clause>

  <clause id="50066">
    <literal><![CDATA[
      L(a(x,y,y) * z,a(u,y,y),L(x,y,y) * z) = L(a(x,y,y) * z,a(x,y,y),u * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33584,a(flip),b,50065,a)].">
      <j1 rule="hyper" parents="64 33584 50065"/>
    </justification>
  </clause>

  <clause id="50067">
    <literal><![CDATA[
      L(a(x,y,y) * z,a(u,y,y),x * z) = L(a(x,y,y) * z,a(x,y,y),u * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,49017,a(flip),b,50066,a)].">
      <j1 rule="hyper" parents="64 49017 50066"/>
    </justification>
  </clause>

  <clause id="50069">
    <literal><![CDATA[
      a(a(x,y,z) * (a(u,y,y) * w),a(u,y,y),v5) * (a(x,y,z) * w) = a(u,y,y) * R(a(x,y,z) * (a(u,y,y) \ w),a(u,y,y),v5)
    ]]></literal>
    <justification jstring="[para(42511(a,1),49508(a,1,1))].">
      <j1 rule="para" parents="42511 49508"/>
    </justification>
  </clause>

  <clause id="50070">
    <literal><![CDATA[
      L((1 / a(x,y,y)) \ z,a(u,y,y),x * ((1 / a(x,y,y)) \ z)) = (a(x,y,y) \ 1) \ (a(u,a(x,y,y) * z,a(x,y,y)) * z)
    ]]></literal>
    <justification jstring="[para(42456(a,1),50053(a,2,2,1,2))].">
      <j1 rule="para" parents="42456 50053"/>
    </justification>
  </clause>

  <clause id="50071">
    <literal><![CDATA[
      L((1 / a(x,y,y)) \ z,a(u,y,y),x * ((1 / a(x,y,y)) \ z)) = (a(x,y,y) \ 1) \ (a(x,z,a(y,y,u)) * z)
    ]]></literal>
    <justification jstring="[para(49032(a,1),50070(a,2,2,1))].">
      <j1 rule="para" parents="49032 50070"/>
    </justification>
  </clause>

  <clause id="50072">
    <literal><![CDATA[
      L((1 / a(x,y,y)) \ z,a(u,y,y),x * ((1 / a(x,y,y)) \ z)) = (a(x,y,y) \ 1) \ (z * a(x,z,a(u,y,y)))
    ]]></literal>
    <justification jstring="[para(38638(a,1),50071(a,2,2))].">
      <j1 rule="para" parents="38638 50071"/>
    </justification>
  </clause>

  <clause id="50074">
    <literal><![CDATA[
      L((1 / a(x,y,y)) \ z,a(u,y,y),x * ((1 / a(x,y,y)) \ z)) = (a(x,y,y) \ 1) \ L(z,a(x,y,y),u * z)
    ]]></literal>
    <justification jstring="[para(49460(a,2),50072(a,2,2))].">
      <j1 rule="para" parents="49460 50072"/>
    </justification>
  </clause>

  <clause id="50075">
    <literal><![CDATA[
      L((1 / a(x,y,y)) \ z,a(u,y,y),x * ((1 / a(x,y,y)) \ z)) = a(u,y,a(y,z,x)) * ((a(x,y,y) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,49461,a(flip),b,50074,a),flip(a)].">
      <j1 rule="hyper" parents="373 49461 50074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50076">
    <literal><![CDATA[
      L((1 / a(x,y,y)) \ z,a(u,y,y),x * ((1 / a(x,y,y)) \ z)) = a(u,y,a(y,z,x)) * (a(x,y,y) * z)
    ]]></literal>
    <justification jstring="[para(42435(a,1),50075(a,2,2))].">
      <j1 rule="para" parents="42435 50075"/>
    </justification>
  </clause>

  <clause id="50077">
    <literal><![CDATA[
      L((1 / a(x,y,y)) \ z,a(u,y,y),x * ((1 / a(x,y,y)) \ z)) = z * a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,47902,a(flip),b,50076,a),flip(a)].">
      <j1 rule="hyper" parents="373 47902 50076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50078">
    <literal><![CDATA[
      L(a(x,y,y) * z,a(u,y,y),x * ((1 / a(x,y,y)) \ z)) = z * a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(42456(a,1),50077(a,1,1))].">
      <j1 rule="para" parents="42456 50077"/>
    </justification>
  </clause>

  <clause id="50079">
    <literal><![CDATA[
      L(a(x,y,y) * z,a(u,y,y),x * (a(x,y,y) * z)) = z * a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(42456(a,1),50078(a,1,3,2))].">
      <j1 rule="para" parents="42456 50078"/>
    </justification>
  </clause>

  <clause id="50080">
    <literal><![CDATA[
      L(a(x,y,y) * z,a(x,y,y),u * z) = z * a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,50063,a(flip),b,50079,a)].">
      <j1 rule="hyper" parents="64 50063 50079"/>
    </justification>
  </clause>

  <clause id="50081">
    <literal><![CDATA[
      L(a(x,y,y) * z,a(u,y,y),x * z) = z * a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,50067,a,b,50080,a)].">
      <j1 rule="hyper" parents="64 50067 50080"/>
    </justification>
  </clause>

  <clause id="50082">
    <literal><![CDATA[
      a(a(x,y,y) * z,a(x,y,y),u) * (a(w,y,v5) * z) = a(x,y,y) * R(a(w,y,v5) * (a(x,y,y) \ z),a(x,y,y),u)
    ]]></literal>
    <justification jstring="[para(48960(a,1),50069(a,1,1))].">
      <j1 rule="para" parents="48960 50069"/>
    </justification>
  </clause>

  <clause id="50083">
    <literal><![CDATA[
      a(x,a(y,z,z),u) * (a(w,z,v5) * x) = a(y,z,z) * R(a(w,z,v5) * (a(y,z,z) \ x),a(y,z,z),u)
    ]]></literal>
    <justification jstring="[para(48960(a,1),50082(a,1,1))].">
      <j1 rule="para" parents="48960 50082"/>
    </justification>
  </clause>

  <clause id="50085">
    <literal><![CDATA[
      a(x,y,y) * R(a(z,y,u) * (a(x,y,y) \ w),a(x,y,y),v5) = w * (a(w,a(x,y,y),v5) * a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,30266,a(flip),b,50083,a),flip(a)].">
      <j1 rule="hyper" parents="64 30266 50083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50087">
    <literal><![CDATA[
      a(x,y,y) * R(a(z,y,u) * (a(x,y,y) \ w),a(x,y,y),v5) = L(w,a(x,y,y),v5) * a(z,y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,48420,a(flip),b,50085,a),flip(a)].">
      <j1 rule="hyper" parents="373 48420 50085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50088">
    <literal><![CDATA[
      a(x,y,y) * L(a(z,y,u) * (a(x,y,y) \ w),a(x,y,y),v5) = L(w,a(x,y,y),v5) * a(z,y,u)
    ]]></literal>
    <justification jstring="[para(31802(a,1),50087(a,1,2))].">
      <j1 rule="para" parents="31802 50087"/>
    </justification>
  </clause>

  <clause id="50089">
    <literal><![CDATA[
      L(a(x,y,y) * (a(z,y,u) * (a(x,y,y) \ w)),a(x,y,y),v5) = L(w,a(x,y,y),v5) * a(z,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,49103,a,b,50088,a)].">
      <j1 rule="hyper" parents="64 49103 50088"/>
    </justification>
  </clause>

  <clause id="50090">
    <literal><![CDATA[
      L(a(x,y,z) * u,a(w,y,y),v5) = L(u,a(w,y,y),v5) * a(x,y,z)
    ]]></literal>
    <justification jstring="[para(49506(a,1),50089(a,1,1))].">
      <j1 rule="para" parents="49506 50089"/>
    </justification>
  </clause>

  <clause id="50092">
    <literal><![CDATA[
      L(a(x,y,y) * z,a(x,y,y),u * z) * u = L(z * (a(x,y,y) * u),a(x,y,y),u)
    ]]></literal>
    <justification jstring="[para(50090(a,2),50029(a,1,1))].">
      <j1 rule="para" parents="50090 50029"/>
    </justification>
  </clause>

  <clause id="50093">
    <literal><![CDATA[
      L(x * (a(y,z,z) * u),a(y,z,z),u) = (x * a(y,z,L(z,x,u))) * u
    ]]></literal>
    <justification jstring="[para(50080(a,1),50092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="50080 50092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50094">
    <literal><![CDATA[
      L(x * (a(y,z,z) * u),a(y,z,z),u) = (x * u) * a(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,46538,a(flip),b,50093,a),flip(a)].">
      <j1 rule="hyper" parents="373 46538 50093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50095">
    <literal><![CDATA[
      L(x,L(y,a(z,x,x) * u,a(z,x,x)),L(u * a(w,w,a(z,x,x)),a(z,x,x),a(z,x,x))) = L(x,y,L(a(z,x,x),w,w) * u)
    ]]></literal>
    <justification jstring="[para(45031(a,1),48913(a,1,2,2,1))].">
      <j1 rule="para" parents="45031 48913"/>
    </justification>
  </clause>

  <clause id="50097">
    <literal><![CDATA[
      L(x,L(y,z,a(x,x,u)),L(z * a(w,w,a(u,x,x)),a(u,x,x),a(u,x,x))) = L(x,y,L(a(u,x,x),w,w) * z)
    ]]></literal>
    <justification jstring="[para(49041(a,1),50095(a,1,2))].">
      <j1 rule="para" parents="49041 50095"/>
    </justification>
  </clause>

  <clause id="50098">
    <literal><![CDATA[
      L(x,L(y,z,a(x,x,u)),L(z * 1,a(u,x,x),a(u,x,x))) = L(x,y,L(a(u,x,x),w,w) * z)
    ]]></literal>
    <justification jstring="[para(44989(a,1),50097(a,1,3,1,2))].">
      <j1 rule="para" parents="44989 50097"/>
    </justification>
  </clause>

  <clause id="50100">
    <literal><![CDATA[
      L(x,L(y,z,a(x,x,u)),L(z,a(u,x,x),a(u,x,x))) = L(x,y,L(a(u,x,x),w,w) * z)
    ]]></literal>
    <justification jstring="[para(8(a,1),50098(a,1,3,1))].">
      <j1 rule="para" parents="8 50098"/>
    </justification>
  </clause>

  <clause id="50102">
    <literal><![CDATA[
      L(x,L(y,z,a(x,x,u)),z) = L(x,y,L(a(u,x,x),w,w) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46776,a(flip),b,50100,a)].">
      <j1 rule="hyper" parents="64 46776 50100"/>
    </justification>
  </clause>

  <clause id="50104">
    <literal><![CDATA[
      L(x,y,L(a(z,x,x),u,u) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,48638,a(flip),b,50102,a),flip(a)].">
      <j1 rule="hyper" parents="64 48638 50102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50106">
    <literal><![CDATA[
      L(x,y,a(z,x,x) * u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,12984,a(flip),b,50104,a)].">
      <j1 rule="hyper" parents="64 12984 50104"/>
    </justification>
  </clause>

  <clause id="50110">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,y) = L(y,u,z) \ y
    ]]></literal>
    <justification jstring="[para(50106(a,1),45067(a,2,1))].">
      <j1 rule="para" parents="50106 45067"/>
    </justification>
  </clause>

  <clause id="50111">
    <literal><![CDATA[
      a(a(x,y,y) * z,u,y) = a(z,u,y)
    ]]></literal>
    <justification jstring="[hyper(373,a,45067,a,b,50110,a),flip(a)].">
      <j1 rule="hyper" parents="373 45067 50110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50112">
    <literal><![CDATA[
      a(a(x,y,y) * (y \ z),u,y) = a(y * z,u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,49337,a,b,50111,a)].">
      <j1 rule="hyper" parents="64 49337 50111"/>
    </justification>
  </clause>

  <clause id="50113">
    <literal><![CDATA[
      a((x \ y) \ z,u,x) = a((y * x) \ z,u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,47734,a(flip),b,50111,a),flip(a)].">
      <j1 rule="hyper" parents="64 47734 50111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50116">
    <literal><![CDATA[
      a((x \ y) \ z,u,x) = a(y \ (x \ z),u,x)
    ]]></literal>
    <justification jstring="[hyper(373,a,46081,a(flip),b,50113,a),flip(a)].">
      <j1 rule="hyper" parents="373 46081 50113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50117">
    <literal><![CDATA[
      a(x \ (y \ z),u,y) = a(x \ (y * z),u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46086,a(flip),b,50116,a),flip(a)].">
      <j1 rule="hyper" parents="64 46086 50116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50118">
    <literal><![CDATA[
      a(L(x,x,y \ z) \ (y * z),u,y) = a(x * (y \ z),u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32679,a(flip),b,50117,a),flip(a)].">
      <j1 rule="hyper" parents="64 32679 50117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50119">
    <literal><![CDATA[
      a(a(x \ (y * z),u,y),w,v5) = a(y,u,a(v5,w,x \ (y \ z)))
    ]]></literal>
    <justification jstring="[para(50117(a,1),47254(a,1,1))].">
      <j1 rule="para" parents="50117 47254"/>
    </justification>
  </clause>

  <clause id="50120">
    <literal><![CDATA[
      a(L(x,x,y) \ z,u,x) = a(x * z,u,x)
    ]]></literal>
    <justification jstring="[para(37561(a,1),50112(a,1,1))].">
      <j1 rule="para" parents="37561 50112"/>
    </justification>
  </clause>

  <clause id="50121">
    <literal><![CDATA[
      a(x * L(y,y,z),u,y) = a(y * x,u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46149,a(flip),b,50120,a)].">
      <j1 rule="hyper" parents="64 46149 50120"/>
    </justification>
  </clause>

  <clause id="50122">
    <literal><![CDATA[
      a((x \ y) * z,u,L(x,y,z)) = a(x * (y \ z),u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,48680,a(flip),b,50121,a)].">
      <j1 rule="hyper" parents="64 48680 50121"/>
    </justification>
  </clause>

  <clause id="50124">
    <literal><![CDATA[
      a(x * (y \ L(z,x,x)),u,x) = a(x * (y \ z),u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,49207,a(flip),b,50122,a)].">
      <j1 rule="hyper" parents="64 49207 50122"/>
    </justification>
  </clause>

  <clause id="50125">
    <literal><![CDATA[
      a(x \ (y * z),u,L(z,z,x)) = a(z * (x \ y),u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,48139,a,b,50124,a)].">
      <j1 rule="hyper" parents="64 48139 50124"/>
    </justification>
  </clause>

  <clause id="50126">
    <literal><![CDATA[
      a(L(x,x,y * z) \ (y * z),u,y) = a(x * (y \ z),u,y)
    ]]></literal>
    <justification jstring="[para(45537(a,1),50118(a,1,1,1))].">
      <j1 rule="para" parents="45537 50118"/>
    </justification>
  </clause>

  <clause id="50127">
    <literal><![CDATA[
      a(x * (y \ z),u,y) = a(x * (y * z),u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,32679,a(flip),b,50126,a),flip(a)].">
      <j1 rule="hyper" parents="64 32679 50126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50130">
    <literal><![CDATA[
      (x \ (a(y * (z * u),w,z) * (x * v5))) / v5 = a(y * (z \ u),w,L(z,v5,x))
    ]]></literal>
    <justification jstring="[para(50127(a,1),46717(a,1,1,2,1))].">
      <j1 rule="para" parents="50127 46717"/>
    </justification>
  </clause>

  <clause id="50131">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ (x \ v5))) = a(x,y,a(z,u,w \ (x * v5)))
    ]]></literal>
    <justification jstring="[hyper(47392,a,50119,a),flip(a)].">
      <j1 rule="hyper" parents="47392 50119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50132">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * x) \ v5)) = a(x,y,a(z,u,w \ (x * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,46672,a,b,50131,a)].">
      <j1 rule="hyper" parents="64 46672 50131"/>
    </justification>
  </clause>

  <clause id="50133">
    <literal><![CDATA[
      a(x,y,a(z,u,w \ (x * v5))) = a(x,y,a(z,u,(w * x) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,49778,a(flip),b,50132,a),flip(a)].">
      <j1 rule="hyper" parents="64 49778 50132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50134">
    <literal><![CDATA[
      a(x,y,a(z,u,(w * x) * v5)) = a(x,y,a(z,u,w * (x * v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49778,a(flip),b,50133,a),flip(a)].">
      <j1 rule="hyper" parents="64 49778 50133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50135">
    <literal><![CDATA[
      a((x * y) * z,u,a(y,w,v5)) = a(y,w,a(v5,u,x * (y * z)))
    ]]></literal>
    <justification jstring="[hyper(47296,a,50134,a)].">
      <j1 rule="hyper" parents="47296 50134"/>
    </justification>
  </clause>

  <clause id="50136">
    <literal><![CDATA[
      a(x * (y * z),u,a(w,v5,z)) = a(z,u,a(w,v5,y * (z * x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47326,a,b,50134,a)].">
      <j1 rule="hyper" parents="64 47326 50134"/>
    </justification>
  </clause>

  <clause id="50140">
    <literal><![CDATA[
      a((x * y) * z,u,a(x,w,v5)) = a(x,w,a(v5,u,y * (x * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,32388,a,b,50135,a)].">
      <j1 rule="hyper" parents="64 32388 50135"/>
    </justification>
  </clause>

  <clause id="50141">
    <literal><![CDATA[
      a((x * y) * z,u,a(x,w,v5)) = a(y * (x * z),u,a(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,47465,a,b,50140,a),flip(a)].">
      <j1 rule="hyper" parents="373 47465 50140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50142">
    <literal><![CDATA[
      a(x * (y * z),u,a(y,w,v5)) = a(y,w,a(z * (x * y),u,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,47252,a(flip),b,50141,a),flip(a)].">
      <j1 rule="hyper" parents="64 47252 50141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50143">
    <literal><![CDATA[
      a(x * (y * z),u,a(w,v5,y)) = a(y,u,a(z * (x * y),v5,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47298,a,b,50142,a)].">
      <j1 rule="hyper" parents="64 47298 50142"/>
    </justification>
  </clause>

  <clause id="50144">
    <literal><![CDATA[
      a(x * (y \ z),u,L(y,w,v5)) = a(x * (y * z),u,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,46717,a(flip),b,50130,a),flip(a)].">
      <j1 rule="hyper" parents="64 46717 50130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50145">
    <literal><![CDATA[
      a(x * (y * z),u,L(y,y,x)) = a(z * (y * x),u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,48105,a(flip),b,50144,a),flip(a)].">
      <j1 rule="hyper" parents="64 48105 50144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50146">
    <literal><![CDATA[
      (a(x,y,y) * (z \ u)) \ (L(z \ 1,y,a(x,u,y)) * (a(x,y,y) * u)) = a(L(z,y,a(y,u,x)),L(z,y,a(y,u,x)),a(x,y,y) * u) \ 1
    ]]></literal>
    <justification jstring="[para(42205(a,2),48997(a,1,2,1))].">
      <j1 rule="para" parents="42205 48997"/>
    </justification>
  </clause>

  <clause id="50147">
    <literal><![CDATA[
      a(L(x,y,a(y,z,u)),L(x,y,a(y,z,u)),a(u,y,y) * z) \ 1 = (a(u,y,y) * (x \ z)) \ (a(u,y,y) * ((x \ 1) * z))
    ]]></literal>
    <justification jstring="[para(47446(a,1),50146(a,1,2)),flip(a)].">
      <j1 rule="para" parents="47446 50146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50148">
    <literal><![CDATA[
      a(L(x,y,a(y,z,u)),L(x,y,a(y,z,u)),a(u,y,y) * z) \ 1 = a(x,x,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(373,a,45943,a(flip),b,50147,a),flip(a)].">
      <j1 rule="hyper" parents="373 45943 50147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50150">
    <literal><![CDATA[
      a(x,x,a(y,z,z) * u) \ 1 = a(x,x,u) \ 1
    ]]></literal>
    <justification jstring="[para(35139(a,1),50148(a,1,1))].">
      <j1 rule="para" parents="35139 50148"/>
    </justification>
  </clause>

  <clause id="50151">
    <literal><![CDATA[
      a(x,x,a(y,z,z) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(325,a,50150,a),flip(a)].">
      <j1 rule="hyper" parents="325 50150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50153">
    <literal><![CDATA[
      a(x,x,L(y,z,z) * u) = a(x,x,u * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47163,a(flip),b,50151,a)].">
      <j1 rule="hyper" parents="64 47163 50151"/>
    </justification>
  </clause>

  <clause id="50156">
    <literal><![CDATA[
      a(x,x,y * L(z,u,u)) = a(x,x,z * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47807,a(flip),b,50153,a)].">
      <j1 rule="hyper" parents="64 47807 50153"/>
    </justification>
  </clause>

  <clause id="50159">
    <literal><![CDATA[
      a(x,x,(y * (z \ 1)) * u) = a(x,x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,39486,a(flip),b,50156,a),flip(a)].">
      <j1 rule="hyper" parents="64 39486 50156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50160">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u * z),u,z)) = a(x,x,(u \ (u * y)) * a(z * u,L(y,u,u),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,48954,a,b,50159,a)].">
      <j1 rule="hyper" parents="64 48954 50159"/>
    </justification>
  </clause>

  <clause id="50162">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u * z),u,z)) = a(x,x,y * a(z * u,L(y,u,u),z))
    ]]></literal>
    <justification jstring="[para(9(a,1),50160(a,2,3,1))].">
      <j1 rule="para" parents="9 50160"/>
    </justification>
  </clause>

  <clause id="50163">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u * z),u,z)) = a(x,x,y * a(z,y,z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,49277,a(flip),b,50162,a),flip(a)].">
      <j1 rule="hyper" parents="373 49277 50162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50165">
    <literal><![CDATA[
      a(x,x,L(L(y,z,u * z),u,z)) = a(x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,49548,a(flip),b,50163,a),flip(a)].">
      <j1 rule="hyper" parents="373 49548 50163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50166">
    <literal><![CDATA[
      a(x,a(y,z,u) * z,L(z * a(u,z,y),L(z * w,z,a(y,z,u)) * v5,v6)) = a(x,a(y,z,u) * z,L(a(y,z,u) * z,(a(y,z,u) \ w) * v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,47178,a(flip),b,48987,a)].">
      <j1 rule="hyper" parents="64 47178 48987"/>
    </justification>
  </clause>

  <clause id="50167">
    <literal><![CDATA[
      a(x,y * a(z,y,u),L(y * a(z,y,u),L(y * w,y,a(u,y,z)) * v5,v6)) = a(x,a(u,y,z) * y,L(a(u,y,z) * y,(a(u,y,z) \ w) * v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,44901,a(flip),b,50166,a)].">
      <j1 rule="hyper" parents="64 44901 50166"/>
    </justification>
  </clause>

  <clause id="50168">
    <literal><![CDATA[
      a(x,a(y,z,u) * z,L(a(y,z,u) * z,(a(y,z,u) \ w) * v5,v6)) = a(x,z,L(z,L(z * w,z,a(y,z,u)) * v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,47933,a(flip),b,50167,a),flip(a)].">
      <j1 rule="hyper" parents="64 47933 50167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50170">
    <literal><![CDATA[
      a(x,a(y,z,u) * z,L(a(y,z,u) * z,(a(y,z,u) \ w) * v5,v6)) = a(x,z,L(z,(z * w) * v5,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,49118,a(flip),b,50168,a),flip(a)].">
      <j1 rule="hyper" parents="373 49118 50168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50172">
    <literal><![CDATA[
      a(x,a(y,z,u) * z,L(a(y,z,u) * z,(a(y,z,u) \ w) * v5,v6)) = a(x,z,L(z,w * v5,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,48984,a(flip),b,50170,a),flip(a)].">
      <j1 rule="hyper" parents="373 48984 50170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50173">
    <literal><![CDATA[
      a(x,a(y,z,u) * z,L(a(y,z,u) * z,(w * a(y,z,u)) * v5,v6)) = a(x,z,L(z,w * v5,v6))
    ]]></literal>
    <justification jstring="[para(42478(a,1),50172(a,1,3))].">
      <j1 rule="para" parents="42478 50172"/>
    </justification>
  </clause>

  <clause id="50174">
    <literal><![CDATA[
      a(x,a(y,z,u) * z,L(z * a(u,z,y),(w * a(y,z,u)) * v5,v6)) = a(x,z,L(z,w * v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,47178,a(flip),b,50173,a)].">
      <j1 rule="hyper" parents="64 47178 50173"/>
    </justification>
  </clause>

  <clause id="50175">
    <literal><![CDATA[
      a(x,y * a(z,y,u),L(y * a(z,y,u),(w * a(u,y,z)) * v5,v6)) = a(x,y,L(y,w * v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,44901,a(flip),b,50174,a)].">
      <j1 rule="hyper" parents="64 44901 50174"/>
    </justification>
  </clause>

  <clause id="50176">
    <literal><![CDATA[
      a(x,y,L(y,(z * a(u,y,w)) * v5,v6)) = a(x,y,L(y,z * v5,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,47933,a(flip),b,50175,a)].">
      <j1 rule="hyper" parents="64 47933 50175"/>
    </justification>
  </clause>

  <clause id="50178">
    <literal><![CDATA[
      L(T(T(x,a(y,z,z)) / (a(y,z,z) \ u),u),a(y,z,z),u) = u \ (x * a(y,z,L(z,u * x,u)))
    ]]></literal>
    <justification jstring="[para(50176(a,1),49245(a,2,2,2))].">
      <j1 rule="para" parents="50176 49245"/>
    </justification>
  </clause>

  <clause id="50179">
    <literal><![CDATA[
      L(T(T(x,a(y,z,z)) / (a(y,z,z) \ u),u),a(y,z,z),u) = u \ (x * a(y,z,L(z,x,u)))
    ]]></literal>
    <justification jstring="[para(46924(a,1),50178(a,2,2,2))].">
      <j1 rule="para" parents="46924 50178"/>
    </justification>
  </clause>

  <clause id="50181">
    <literal><![CDATA[
      L(T(x / (a(y,z,z) \ u),u),a(y,z,z),u) = u \ (x * a(y,z,L(z,x,u)))
    ]]></literal>
    <justification jstring="[para(13983(a,1),50179(a,1,1,1,1))].">
      <j1 rule="para" parents="13983 50179"/>
    </justification>
  </clause>

  <clause id="50182">
    <literal><![CDATA[
      L((a(x,y,y) \ z) \ u,a(x,y,y),z) = z \ (u * a(x,y,L(y,u,z)))
    ]]></literal>
    <justification jstring="[para(28640(a,1),50181(a,1,1))].">
      <j1 rule="para" parents="28640 50181"/>
    </justification>
  </clause>

  <clause id="50183">
    <literal><![CDATA[
      x \ (y * a(z,u,L(u,y,x))) = a(z,u,u) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(64,a,43395,a(flip),b,50182,a),flip(a)].">
      <j1 rule="hyper" parents="64 43395 50182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50184">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,(1 / w) \ a(y,z,u)),w * a(y,z,u),w * (w * a(y,z,u))) = w \ (((w / (w * a(y,z,u))) * x) * T(w * a(y,z,u),x))
    ]]></literal>
    <justification jstring="[para(27308(a,1),48445(a,1,1,2))].">
      <j1 rule="para" parents="27308 48445"/>
    </justification>
  </clause>

  <clause id="50185">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,a(y,z,u) * z),z * a(y,z,u),z * (z * a(y,z,u))) = z \ (((z / (z * a(y,z,u))) * x) * T(z * a(y,z,u),x))
    ]]></literal>
    <justification jstring="[para(35737(a,1),50184(a,1,1,2,3))].">
      <j1 rule="para" parents="35737 50184"/>
    </justification>
  </clause>

  <clause id="50186">
    <literal><![CDATA[
      L(x * a(a(y,z,u),x,z * a(u,z,y)),z * a(y,z,u),z * (z * a(y,z,u))) = z \ (((z / (z * a(y,z,u))) * x) * T(z * a(y,z,u),x))
    ]]></literal>
    <justification jstring="[para(42669(a,1),50185(a,1,1,2))].">
      <j1 rule="para" parents="42669 50185"/>
    </justification>
  </clause>

  <clause id="50187">
    <literal><![CDATA[
      L(x * a(y,z,a(z * a(y,z,u),x,u)),z * a(u,z,y),z * (z * a(u,z,y))) = z \ (((z / (z * a(u,z,y))) * x) * T(z * a(u,z,y),x))
    ]]></literal>
    <justification jstring="[para(47254(a,1),50186(a,1,1,2))].">
      <j1 rule="para" parents="47254 50186"/>
    </justification>
  </clause>

  <clause id="50188">
    <literal><![CDATA[
      L(x * a(y,z,a(z,x,L(u,u,y))),z * a(u,z,y),z * (z * a(u,z,y))) = z \ (((z / (z * a(u,z,y))) * x) * T(z * a(u,z,y),x))
    ]]></literal>
    <justification jstring="[para(46741(a,1),50187(a,1,1,2,3))].">
      <j1 rule="para" parents="46741 50187"/>
    </justification>
  </clause>

  <clause id="50189">
    <literal><![CDATA[
      L(x * a(y,x,a(z,z,u)),z * a(u,z,y),z * (z * a(u,z,y))) = z \ (((z / (z * a(u,z,y))) * x) * T(z * a(u,z,y),x))
    ]]></literal>
    <justification jstring="[para(45929(a,1),50188(a,1,1,2))].">
      <j1 rule="para" parents="45929 50188"/>
    </justification>
  </clause>

  <clause id="50190">
    <literal><![CDATA[
      L(x * a(y,x,a(z,z,u)),z * a(u,z,y),L(a(u,z,y),z,z)) = z \ (((z / (z * a(u,z,y))) * x) * T(z * a(u,z,y),x))
    ]]></literal>
    <justification jstring="[hyper(64,a,2185,a(flip),b,50189,a)].">
      <j1 rule="hyper" parents="64 2185 50189"/>
    </justification>
  </clause>

  <clause id="50192">
    <literal><![CDATA[
      L(x * a(y,x,a(z,z,u)),z * a(u,z,y),a(u,z,y)) = z \ (((z / (z * a(u,z,y))) * x) * T(z * a(u,z,y),x))
    ]]></literal>
    <justification jstring="[para(35734(a,1),50190(a,1,3))].">
      <j1 rule="para" parents="35734 50190"/>
    </justification>
  </clause>

  <clause id="50193">
    <literal><![CDATA[
      x \ (((x / (x * a(y,x,z))) * u) * T(x * a(y,x,z),u)) = L(u * a(z,u,a(x,x,y)),x,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47448,a(flip),b,50192,a),flip(a)].">
      <j1 rule="hyper" parents="64 47448 50192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50194">
    <literal><![CDATA[
      x \ (((x / (x * a(y,x,z))) * u) * T(x * a(y,x,z),u)) = L(u,a(z,x,y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,47313,a(flip),b,50193,a),flip(a)].">
      <j1 rule="hyper" parents="373 47313 50193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50195">
    <literal><![CDATA[
      x \ (((a(y,x,z) \ 1) * u) * T(x * a(y,x,z),u)) = L(u,a(z,x,y),x)
    ]]></literal>
    <justification jstring="[para(42448(a,1),50194(a,1,2,1,1))].">
      <j1 rule="para" parents="42448 50194"/>
    </justification>
  </clause>

  <clause id="50196">
    <literal><![CDATA[
      x \ ((a(y,x,z) \ u) * T(x * a(y,x,z),u)) = L(u,a(z,x,y),x)
    ]]></literal>
    <justification jstring="[para(42433(a,1),50195(a,1,2,1))].">
      <j1 rule="para" parents="42433 50195"/>
    </justification>
  </clause>

  <clause id="50198">
    <literal><![CDATA[
      x \ ((x * a(y,x,z)) * (a(y,x,z) \ u)) = L(u,a(z,x,y),x)
    ]]></literal>
    <justification jstring="[para(28651(a,1),50196(a,1,2))].">
      <j1 rule="para" parents="28651 50196"/>
    </justification>
  </clause>

  <clause id="50199">
    <literal><![CDATA[
      x \ L(x * y,x,a(z,x,u)) = L(y,a(u,x,z),x)
    ]]></literal>
    <justification jstring="[para(43363(a,1),50198(a,1,2))].">
      <j1 rule="para" parents="43363 50198"/>
    </justification>
  </clause>

  <clause id="50200">
    <literal><![CDATA[
      L(x,a(y,z,u),z * a(y,z,u)) = L(x,a(u,z,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,44579,a,b,50199,a)].">
      <j1 rule="hyper" parents="64 44579 50199"/>
    </justification>
  </clause>

  <clause id="50201">
    <literal><![CDATA[
      x * L(x \ y,x,a(z,x,u)) = L(y,a(u,x,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,28865,a(flip),b,50199,a)].">
      <j1 rule="hyper" parents="64 28865 50199"/>
    </justification>
  </clause>

  <clause id="50202">
    <literal><![CDATA[
      a(x / y,y,a(z,y,u)) \ K((x / y) * y,a(z,y,u)) = x \ L(x,a(u,y,z),y)
    ]]></literal>
    <justification jstring="[para(50201(a,1),44474(a,2,2))].">
      <j1 rule="para" parents="50201 44474"/>
    </justification>
  </clause>

  <clause id="50203">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(z,y,x),y) = y \ ((a(x,y,z) / y) \ L(u,y,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,43821,a(flip),b,50200,a),flip(a)].">
      <j1 rule="hyper" parents="64 43821 50200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50204">
    <literal><![CDATA[
      x \ ((a(y,x,z) / x) \ L(u,x,x)) = (a(y,x,z) \ x) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,43431,a(flip),b,50203,a),flip(a)].">
      <j1 rule="hyper" parents="64 43431 50203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50205">
    <literal><![CDATA[
      x \ ((a(y,x,z) \ x) * u) = (a(y,x,z) \ x) * (x \ u)
    ]]></literal>
    <justification jstring="[para(43818(a,1),50204(a,1,2))].">
      <j1 rule="para" parents="43818 50204"/>
    </justification>
  </clause>

  <clause id="50206">
    <literal><![CDATA[
      (a(x,y,z) \ y) * (y * u) = y * ((a(x,y,z) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(1335,a,50205,a),flip(a)].">
      <j1 rule="hyper" parents="1335 50205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50207">
    <literal><![CDATA[
      (a(x,y,z) \ y) \ (y * u) = y * ((a(x,y,z) \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(139,a,168,a(flip),b,50206,a)].">
      <j1 rule="hyper" parents="139 168 50206"/>
    </justification>
  </clause>

  <clause id="50209">
    <literal><![CDATA[
      (x / y) * (y * a(z,y,u)) = y * ((a(z,y,u) \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(64,a,40595,a(flip),b,50207,a)].">
      <j1 rule="hyper" parents="64 40595 50207"/>
    </justification>
  </clause>

  <clause id="50211">
    <literal><![CDATA[
      x * ((a(y,x,z) \ x) \ R(u,x,x)) = (u * (1 / x)) * (x * a(y,x,z))
    ]]></literal>
    <justification jstring="[para(1408(a,1),50209(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1408 50209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50212">
    <literal><![CDATA[
      (x * (1 / y)) * (y * a(z,y,u)) = y * T(x * (a(z,y,u) / y),y)
    ]]></literal>
    <justification jstring="[para(47789(a,1),50211(a,1,2)),flip(a)].">
      <j1 rule="para" parents="47789 50211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50213">
    <literal><![CDATA[
      (x * (1 / y)) * (y * a(z,y,u)) = (x * (a(z,y,u) / y)) * y
    ]]></literal>
    <justification jstring="[hyper(373,a,115,a(flip),b,50212,a),flip(a)].">
      <j1 rule="hyper" parents="373 115 50212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50214">
    <literal><![CDATA[
      (x * ((1 / y) * (y * a(z,y,u)))) \ ((x * (a(z,y,u) / y)) * y) = a(x,1 / y,y * a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,50213,a(flip),b,88,a)].">
      <j1 rule="hyper" parents="139 50213 88"/>
    </justification>
  </clause>

  <clause id="50215">
    <literal><![CDATA[
      (x * (1 / y)) \ (((x * (a(z,y,u) / y)) * y) / a(z,y,u)) = a(x * (1 / y),y,a(z,y,u)) \ y
    ]]></literal>
    <justification jstring="[para(50213(a,1),33322(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="50213 33322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50216">
    <literal><![CDATA[
      a(x / y,y,a(z,y,u)) \ K((x / y) * y,a(z,y,u)) = a(x,a(z,y,u),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,42628,a(flip),b,50202,a),flip(a)].">
      <j1 rule="hyper" parents="373 42628 50202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50217">
    <literal><![CDATA[
      a(x \ y,x,a(z,x,u)) \ K((y / x) * x,a(z,x,u)) = a(y,a(z,x,u),x)
    ]]></literal>
    <justification jstring="[para(26785(a,1),50216(a,1,1))].">
      <j1 rule="para" parents="26785 50216"/>
    </justification>
  </clause>

  <clause id="50218">
    <literal><![CDATA[
      a(x * y,y,a(z,y,u)) \ K((x / y) * y,a(z,y,u)) = a(x,a(z,y,u),y)
    ]]></literal>
    <justification jstring="[para(41827(a,1),50217(a,1,1))].">
      <j1 rule="para" parents="41827 50217"/>
    </justification>
  </clause>

  <clause id="50219">
    <literal><![CDATA[
      a(x * y,y,a(z,y,u)) \ 1 = a(x,a(z,y,u),y)
    ]]></literal>
    <justification jstring="[para(23078(a,1),50218(a,1,2))].">
      <j1 rule="para" parents="23078 50218"/>
    </justification>
  </clause>

  <clause id="50220">
    <literal><![CDATA[
      a(x * y,y,a(z,y,u)) = a(x,a(u,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(141,a,42644,a(flip),b,50219,a(flip))].">
      <j1 rule="hyper" parents="141 42644 50219"/>
    </justification>
  </clause>

  <clause id="50222">
    <literal><![CDATA[
      a(x * y,x,a(z,x,u)) = a(y,a(z,x,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,41890,a,b,50220,a)].">
      <j1 rule="hyper" parents="64 41890 50220"/>
    </justification>
  </clause>

  <clause id="50223">
    <literal><![CDATA[
      a(x,a(y,x,z),L(L(u,y,z),z,y)) = a(u,a(y,x,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,47719,a(flip),b,50220,a)].">
      <j1 rule="hyper" parents="64 47719 50220"/>
    </justification>
  </clause>

  <clause id="50224">
    <literal><![CDATA[
      a(x,y,a(y * z,y,u)) = a(z,a(x,y,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47302,a(flip),b,50220,a)].">
      <j1 rule="hyper" parents="64 47302 50220"/>
    </justification>
  </clause>

  <clause id="50225">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,y,u)) = y * a(x,a(z,y,u),y)
    ]]></literal>
    <justification jstring="[para(50220(a,1),43651(a,2,2))].">
      <j1 rule="para" parents="50220 43651"/>
    </justification>
  </clause>

  <clause id="50226">
    <literal><![CDATA[
      x * L(x \ (y \ 1),y,a(z,y,u)) = y \ a(x,a(z,y,u),y)
    ]]></literal>
    <justification jstring="[para(50224(a,1),48295(a,1,2)),flip(a)].">
      <j1 rule="para" parents="50224 48295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50227">
    <literal><![CDATA[
      a((x * y) \ 1,a(z,y,u),y) = a(u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,48301,a(flip),b,50223,a),flip(a)].">
      <j1 rule="hyper" parents="64 48301 50223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50228">
    <literal><![CDATA[
      a(x * y,a(z,y,u),y) = a(u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,2653,a(flip),b,50227,a)].">
      <j1 rule="hyper" parents="64 2653 50227"/>
    </justification>
  </clause>

  <clause id="50229">
    <literal><![CDATA[
      a(x * (y \ 1),a(z,y,u),y) = a(u,y,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26850,a,b,50228,a)].">
      <j1 rule="hyper" parents="64 26850 50228"/>
    </justification>
  </clause>

  <clause id="50230">
    <literal><![CDATA[
      L(x,a(y,x,z),u * x) = x * a(z,x,a(u,x,y))
    ]]></literal>
    <justification jstring="[para(50228(a,1),43401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="50228 43401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50231">
    <literal><![CDATA[
      L(L(x,a(y,x,z),u),u,a(y,x,z)) = L(x,a(y,x,z),u * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,47369,a,b,50230,a)].">
      <j1 rule="hyper" parents="373 47369 50230"/>
    </justification>
  </clause>

  <clause id="50232">
    <literal><![CDATA[
      (a(x,y,z) * ((a(x,y,z) / y) \ L(u,y,y))) / u = L(y,a(x,y,u),z * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,43828,a,b,50230,a)].">
      <j1 rule="hyper" parents="373 43828 50230"/>
    </justification>
  </clause>

  <clause id="50233">
    <literal><![CDATA[
      x * L(y,a(z,y,u),x * y) = L(x,y,a(u,y,z)) * y
    ]]></literal>
    <justification jstring="[para(50230(a,2),47389(a,1,2))].">
      <j1 rule="para" parents="50230 47389"/>
    </justification>
  </clause>

  <clause id="50234">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,y,u)) = L(y,a(u,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,43396,a(flip),b,50225,a),flip(a)].">
      <j1 rule="hyper" parents="373 43396 50225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50235">
    <literal><![CDATA[
      L(L(x,a(y,x,z * x),u),u,a(y,x,z * x)) = L(x,a(u,x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47557,a,b,50234,a)].">
      <j1 rule="hyper" parents="64 47557 50234"/>
    </justification>
  </clause>

  <clause id="50236">
    <literal><![CDATA[
      x * L(x \ (y \ 1),y \ 1,a(z,y,u)) = L(y \ 1,a(u,y \ 1,z),x)
    ]]></literal>
    <justification jstring="[para(11980(a,1),50234(a,1,2,3))].">
      <j1 rule="para" parents="11980 50234"/>
    </justification>
  </clause>

  <clause id="50237">
    <literal><![CDATA[
      L(x * y,a(z,y,u),y) = L(x,y,a(z,y,u)) * y
    ]]></literal>
    <justification jstring="[hyper(64,a,46789,a(flip),b,50233,a)].">
      <j1 rule="hyper" parents="64 46789 50233"/>
    </justification>
  </clause>

  <clause id="50238">
    <literal><![CDATA[
      a(x,y,z) * (u * (a(x,y,z) \ y)) = L(u * y,a(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,42846,a(flip),b,50237,a)].">
      <j1 rule="hyper" parents="373 42846 50237"/>
    </justification>
  </clause>

  <clause id="50239">
    <literal><![CDATA[
      L((x * (1 / y)) * y,a(z,y,u),y) = R(x,y,y * a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,42257,a(flip),b,50237,a),flip(a)].">
      <j1 rule="hyper" parents="373 42257 50237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50240">
    <literal><![CDATA[
      L(L(x,a(y,x,z),u),u,a(z,x,y)) = L(x,a(y,x,z),u * x)
    ]]></literal>
    <justification jstring="[hyper(42222,a,50231,a)].">
      <j1 rule="hyper" parents="42222 50231"/>
    </justification>
  </clause>

  <clause id="50241">
    <literal><![CDATA[
      L(R(x,y,y),a(z,y,u),y) = R(x,y,y * a(z,y,u))
    ]]></literal>
    <justification jstring="[para(1405(a,1),50239(a,1,1))].">
      <j1 rule="para" parents="1405 50239"/>
    </justification>
  </clause>

  <clause id="50242">
    <literal><![CDATA[
      R(x,y * a(z,y,u),y) = R(x,y,y * a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,48252,a(flip),b,50241,a)].">
      <j1 rule="hyper" parents="64 48252 50241"/>
    </justification>
  </clause>

  <clause id="50243">
    <literal><![CDATA[
      L(x,a(y,x,z * x),u * x) = L(x,a(u,x,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,50231,a(flip),b,50235,a)].">
      <j1 rule="hyper" parents="64 50231 50235"/>
    </justification>
  </clause>

  <clause id="50244">
    <literal><![CDATA[
      L(x,a(x * y,x,z),u * x) = L(x,a(u,x,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,41408,a,b,50243,a)].">
      <j1 rule="hyper" parents="64 41408 50243"/>
    </justification>
  </clause>

  <clause id="50245">
    <literal><![CDATA[
      L(x,a(y,x,z * (x * y)),u * x) = L(x,a(u,x,y),y \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46955,a(flip),b,50243,a)].">
      <j1 rule="hyper" parents="64 46955 50243"/>
    </justification>
  </clause>

  <clause id="50246">
    <literal><![CDATA[
      L(x,a(y,x,z * (x * y)),u * x) = L(x,a(u,x,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,49958,a(flip),b,50245,a),flip(a)].">
      <j1 rule="hyper" parents="373 49958 50245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50247">
    <literal><![CDATA[
      x * L(x \ (y \ 1),y,a(z,y,u)) = L(y \ 1,a(u,y \ 1,z),x)
    ]]></literal>
    <justification jstring="[para(11794(a,1),50236(a,1,2))].">
      <j1 rule="para" parents="11794 50236"/>
    </justification>
  </clause>

  <clause id="50248">
    <literal><![CDATA[
      L(x \ 1,a(y,x \ 1,z),u) = x \ a(u,a(z,x,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,50226,a(flip),b,50247,a),flip(a)].">
      <j1 rule="hyper" parents="64 50226 50247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50249">
    <literal><![CDATA[
      L(x \ 1,a(y,x \ 1,z),u * (x \ 1)) = x \ a(y,x,a(u,x,z))
    ]]></literal>
    <justification jstring="[para(50229(a,1),50248(a,2,2))].">
      <j1 rule="para" parents="50229 50248"/>
    </justification>
  </clause>

  <clause id="50250">
    <literal><![CDATA[
      (a(x,y,z) * ((a(x,y,z) \ y) * u)) / u = L(y,a(x,y,u),z * y)
    ]]></literal>
    <justification jstring="[para(43818(a,1),50232(a,1,1,2))].">
      <j1 rule="para" parents="43818 50232"/>
    </justification>
  </clause>

  <clause id="50251">
    <literal><![CDATA[
      x \ (a(y,z,u) * (x * (a(y,z,u) \ z))) = L(z,a(y,z,x),u * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,33930,a(flip),b,50250,a)].">
      <j1 rule="hyper" parents="64 33930 50250"/>
    </justification>
  </clause>

  <clause id="50252">
    <literal><![CDATA[
      x \ L(x * y,a(z,y,u),y) = L(y,a(z,y,x),u * y)
    ]]></literal>
    <justification jstring="[para(50238(a,1),50251(a,1,2))].">
      <j1 rule="para" parents="50238 50251"/>
    </justification>
  </clause>

  <clause id="50253">
    <literal><![CDATA[
      x * L(x \ y,a(z,y,u),y) = L(y,a(z,y,x),u * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,31836,a(flip),b,50252,a)].">
      <j1 rule="hyper" parents="64 31836 50252"/>
    </justification>
  </clause>

  <clause id="50254">
    <literal><![CDATA[
      L(x,a(y,x,z),u * x) = L(x,a(u,x,y),z * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,46148,a(flip),b,50253,a),flip(a)].">
      <j1 rule="hyper" parents="64 46148 50253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50255">
    <literal><![CDATA[
      L(x,a(y,x,z),u * x) = L(x,a(y,x,u),z * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,41403,a,b,50254,a)].">
      <j1 rule="hyper" parents="373 41403 50254"/>
    </justification>
  </clause>

  <clause id="50256">
    <literal><![CDATA[
      L(x,a(y,x,z),((y * x) * (u \ (y * x))) * x) = L(x,a(u,x,z),y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,48146,a(flip),b,50254,a),flip(a)].">
      <j1 rule="hyper" parents="64 48146 50254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50257">
    <literal><![CDATA[
      L(x,a(x * (y \ z),x,y),u * x) = L(x,a(y,x,u),((x * y) * z) * x)
    ]]></literal>
    <justification jstring="[para(46007(a,1),50254(a,2,2)),flip(a)].">
      <j1 rule="para" parents="46007 50254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50258">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ 1,a(u,x \ 1,w),v5 * (x \ 1)) = L(x * L(x \ 1,a(u,x \ 1,v5),w * (x \ 1)),y,z)
    ]]></literal>
    <justification jstring="[para(50255(a,1),4273(a,2,1,2))].">
      <j1 rule="para" parents="50255 4273"/>
    </justification>
  </clause>

  <clause id="50259">
    <literal><![CDATA[
      L(x,a(y,x,z),(u \ (y * x)) * ((y * x) \ x)) = L(x,a(u,x,z),y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,47895,a(flip),b,50256,a)].">
      <j1 rule="hyper" parents="64 47895 50256"/>
    </justification>
  </clause>

  <clause id="50260">
    <literal><![CDATA[
      L(x,a(x * (y \ z),x,y),u * x) = L(x,a(y,x,u),z * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47895,a(flip),b,50257,a),flip(a)].">
      <j1 rule="hyper" parents="373 47895 50257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50261">
    <literal><![CDATA[
      L(x,a(y,x,z),(u \ (y * x)) * (x \ (y \ x))) = L(x,a(u,x,z),y * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,29186,a(flip),b,50259,a)].">
      <j1 rule="hyper" parents="64 29186 50259"/>
    </justification>
  </clause>

  <clause id="50262">
    <literal><![CDATA[
      L(x,a(x * (y \ z),x,y),u * x) = L(x,a(y,x,u),z * (x \ (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,29261,a(flip),b,50260,a),flip(a)].">
      <j1 rule="hyper" parents="373 29261 50260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50263">
    <literal><![CDATA[
      L(x,a(y,x,z),u * (x \ (y \ x))) = L(x,a(z,x,y),y \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,50244,a(flip),b,50262,a),flip(a)].">
      <j1 rule="hyper" parents="64 50244 50262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50264">
    <literal><![CDATA[
      L(x,a(y,x,z),u * (x \ (y \ x))) = L(x,a(z,x,y),y * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,49958,a(flip),b,50263,a),flip(a)].">
      <j1 rule="hyper" parents="373 49958 50263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50265">
    <literal><![CDATA[
      L(x,a(y,x,z),z * (u \ (z * x))) = L(x,a(u,x,y),z * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,50261,a(flip),b,50264,a),flip(a)].">
      <j1 rule="hyper" parents="64 50261 50264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50266">
    <literal><![CDATA[
      (x * (y * ((y \ 1) * a(z,y,u)))) \ ((x * (a(z,y,u) / y)) * y) = a(x,1 / y,y * a(z,y,u))
    ]]></literal>
    <justification jstring="[para(1135(a,1),50214(a,1,1,2))].">
      <j1 rule="para" parents="1135 50214"/>
    </justification>
  </clause>

  <clause id="50267">
    <literal><![CDATA[
      (x * (1 / y)) \ (((x * (a(z,y,u) / y)) * y) / a(z,y,u)) = a(x * (y \ 1),y,a(z,y,u)) \ y
    ]]></literal>
    <justification jstring="[para(32362(a,1),50215(a,2,1))].">
      <j1 rule="para" parents="32362 50215"/>
    </justification>
  </clause>

  <clause id="50268">
    <literal><![CDATA[
      (x * (y * (y \ a(z,y,u)))) \ ((x * (a(z,y,u) / y)) * y) = a(x,1 / y,y * a(z,y,u))
    ]]></literal>
    <justification jstring="[para(35739(a,1),50266(a,1,1,2,2))].">
      <j1 rule="para" parents="35739 50266"/>
    </justification>
  </clause>

  <clause id="50269">
    <literal><![CDATA[
      (x * a(y,z,u)) \ ((x * (a(y,z,u) / z)) * z) = a(x,1 / z,z * a(y,z,u))
    ]]></literal>
    <justification jstring="[para(10(a,1),50268(a,1,1,2))].">
      <j1 rule="para" parents="10 50268"/>
    </justification>
  </clause>

  <clause id="50270">
    <literal><![CDATA[
      a(x,1 / y,y * a(z,y,u)) = a(x,y * a(z,y,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,35702,a(flip),b,50269,a),flip(a)].">
      <j1 rule="hyper" parents="64 35702 50269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50272">
    <literal><![CDATA[
      a(x,y * a(z,y,u),y) = a(x,y,y * a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(32047,a,50270,a),flip(a)].">
      <j1 rule="hyper" parents="32047 50270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50273">
    <literal><![CDATA[
      (x * (1 / y)) \ (((x * (a(z,y,u) / y)) * y) / a(z,y,u)) = a(y * x,y,a(z,y,u)) \ y
    ]]></literal>
    <justification jstring="[para(26831(a,1),50267(a,2,1))].">
      <j1 rule="para" parents="26831 50267"/>
    </justification>
  </clause>

  <clause id="50274">
    <literal><![CDATA[
      (x * (1 / y)) \ (((x * (a(z,y,u) / y)) * y) / a(z,y,u)) = a(x,a(z,y,u),y) \ y
    ]]></literal>
    <justification jstring="[para(50222(a,1),50273(a,2,1))].">
      <j1 rule="para" parents="50222 50273"/>
    </justification>
  </clause>

  <clause id="50275">
    <literal><![CDATA[
      (x * (1 / y)) \ (((x * (a(z,y,u) / y)) * y) / a(z,y,u)) = L(y,a(z,y,u),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,45065,a,b,50274,a),flip(a)].">
      <j1 rule="hyper" parents="373 45065 50274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50276">
    <literal><![CDATA[
      (x * (1 / y)) \ (a(z,y,u) \ ((x * (a(z,y,u) / y)) * y)) = L(y,a(z,y,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,23170,a(flip),b,50275,a)].">
      <j1 rule="hyper" parents="64 23170 50275"/>
    </justification>
  </clause>

  <clause id="50277">
    <literal><![CDATA[
      (x * (1 / y)) \ R(T(x,a(z,y,u)),y * a(z,y,u),y) = L(y,a(z,y,u),x)
    ]]></literal>
    <justification jstring="[para(46438(a,1),50276(a,1,2))].">
      <j1 rule="para" parents="46438 50276"/>
    </justification>
  </clause>

  <clause id="50278">
    <literal><![CDATA[
      (x * (1 / y)) \ R(x,y * a(z,y,u),y) = L(y,a(z,y,u),x)
    ]]></literal>
    <justification jstring="[para(23105(a,1),50277(a,1,2,1))].">
      <j1 rule="para" parents="23105 50277"/>
    </justification>
  </clause>

  <clause id="50279">
    <literal><![CDATA[
      (x * (1 / y)) \ R(x,y,y * a(z,y,u)) = L(y,a(u,y,z),x)
    ]]></literal>
    <justification jstring="[para(50242(a,1),50278(a,1,2))].">
      <j1 rule="para" parents="50242 50278"/>
    </justification>
  </clause>

  <clause id="50280">
    <literal><![CDATA[
      (x * (1 / y)) \ R(x,y,y * a(z * (y * u),y,z)) = L(y,a(z,y,u * (y * z)),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,48344,a,b,50279,a),flip(a)].">
      <j1 rule="hyper" parents="373 48344 50279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50281">
    <literal><![CDATA[
      a(x,y,y * a(z,y,u)) * L(y,y,L(x,y,y * a(z,y,u))) = L(y,a(u,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,48831,a,b,50279,a)].">
      <j1 rule="hyper" parents="64 48831 50279"/>
    </justification>
  </clause>

  <clause id="50282">
    <literal><![CDATA[
      L(L(x * ((y * (1 / (x \ 1))) \ R(y,x \ 1,(x \ 1) * a(z,x \ 1,u))),w,v5),x,x) = L(x * L(x \ 1,a(u,x \ 1,z),y),w,v5)
    ]]></literal>
    <justification jstring="[para(50279(a,2),5626(a,1,1,1,2))].">
      <j1 rule="para" parents="50279 5626"/>
    </justification>
  </clause>

  <clause id="50283">
    <literal><![CDATA[
      a(x,y,y * a(z,y,u)) * L(y,y,x) = L(y,a(u,y,z),x)
    ]]></literal>
    <justification jstring="[para(37503(a,1),50281(a,1,2))].">
      <j1 rule="para" parents="37503 50281"/>
    </justification>
  </clause>

  <clause id="50284">
    <literal><![CDATA[
      x * a(y,a(z,x,x),u) = L(x,a(y,x,u),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,48498,a(flip),b,50283,a)].">
      <j1 rule="hyper" parents="64 48498 50283"/>
    </justification>
  </clause>

  <clause id="50286">
    <literal><![CDATA[
      L(x,x,a(y,z,z * u)) = L(x,a(z,x,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,49433,a,b,50284,a)].">
      <j1 rule="hyper" parents="64 49433 50284"/>
    </justification>
  </clause>

  <clause id="50287">
    <literal><![CDATA[
      x * a(y,a(x,x,z),u) = L(x,a(y,x,u),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,42400,a,b,50284,a)].">
      <j1 rule="hyper" parents="64 42400 50284"/>
    </justification>
  </clause>

  <clause id="50288">
    <literal><![CDATA[
      L(x,x,a(y * z,y,u)) = L(x,a(y,x,z),u)
    ]]></literal>
    <justification jstring="[hyper(42222,a,50286,a)].">
      <j1 rule="hyper" parents="42222 50286"/>
    </justification>
  </clause>

  <clause id="50289">
    <literal><![CDATA[
      L(L(x,x,y),z,a(z * u,x,w)) = L(L(x,a(u,x,z),w),x,y)
    ]]></literal>
    <justification jstring="[para(50286(a,1),48799(a,1,1)),flip(a)].">
      <j1 rule="para" parents="50286 48799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50290">
    <literal><![CDATA[
      L(L(x,x,a(y,z,u)),x,a(y,u,z)) = L(x,a(z,x,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47971,a,b,50287,a)].">
      <j1 rule="hyper" parents="64 47971 50287"/>
    </justification>
  </clause>

  <clause id="50291">
    <literal><![CDATA[
      L(x,y,a(z * y,x,u)) = L(x,a(z,x,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,47516,a,b,50288,a)].">
      <j1 rule="hyper" parents="64 47516 50288"/>
    </justification>
  </clause>

  <clause id="50292">
    <literal><![CDATA[
      L(L(x,a(y,x,z),u),y,a(y * z,x,u)) = x
    ]]></literal>
    <justification jstring="[hyper(42,a,47436,a,b,50288,a)].">
      <j1 rule="hyper" parents="42 47436 50288"/>
    </justification>
  </clause>

  <clause id="50293">
    <literal><![CDATA[
      L(x,x,a(y,z,u * z)) = L(x,a(u,x,z),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47432,a,b,50291,a)].">
      <j1 rule="hyper" parents="64 47432 50291"/>
    </justification>
  </clause>

  <clause id="50294">
    <literal><![CDATA[
      L(x,y,z) * L(L(x,y,z) \ 1,a(u,x,w),v5 * (x \ 1)) = L(x * L(x \ 1,a(u,x \ 1,v5),w * (x \ 1)),y,z)
    ]]></literal>
    <justification jstring="[para(11980(a,1),50258(a,1,2,2))].">
      <j1 rule="para" parents="11980 50258"/>
    </justification>
  </clause>

  <clause id="50295">
    <literal><![CDATA[
      L(x * L(x \ 1,a(y,x \ 1,z),u * (x \ 1)),w,v5) = L(x,w,v5) * L(L(x,w,v5) \ 1,a(y,x,u),x * z)
    ]]></literal>
    <justification jstring="[para(23997(a,1),50294(a,1,2)),flip(a)].">
      <j1 rule="para" parents="23997 50294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50296">
    <literal><![CDATA[
      L(x * L(x \ 1,a(y,x \ 1,z),u * (x \ 1)),w,v5) = a(L(x,w,v5),a(u,x,y),x * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,42636,a(flip),b,50295,a),flip(a)].">
      <j1 rule="hyper" parents="373 42636 50295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50297">
    <literal><![CDATA[
      L(x * L(x \ 1,a(y,x \ 1,z),u * (x \ 1)),w,v5) = a(x,a(u,x,y),L(x * z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,46496,a(flip),b,50296,a),flip(a)].">
      <j1 rule="hyper" parents="373 46496 50296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50298">
    <literal><![CDATA[
      L(x * (x \ a(y,x,a(z,x,u))),w,v5) = a(x,a(z,x,y),L(x * u,w,v5))
    ]]></literal>
    <justification jstring="[para(50249(a,1),50297(a,1,1,2))].">
      <j1 rule="para" parents="50249 50297"/>
    </justification>
  </clause>

  <clause id="50299">
    <literal><![CDATA[
      a(x,a(y,x,z),L(x * u,w,v5)) = L(a(z,x,a(y,x,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),50298(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10 50298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50300">
    <literal><![CDATA[
      a(x,a(y,x,z),L(x * u,w,v5)) = a(z,x,a(y,x,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,46567,a,b,50299,a),flip(a)].">
      <j1 rule="hyper" parents="373 46567 50299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50302">
    <literal><![CDATA[
      L(L(x * ((y * x) \ R(y,x \ 1,(x \ 1) * a(z,x \ 1,u))),w,v5),x,x) = L(x * L(x \ 1,a(u,x \ 1,z),y),w,v5)
    ]]></literal>
    <justification jstring="[para(79(a,1),50282(a,1,1,1,2,1,2))].">
      <j1 rule="para" parents="79 50282"/>
    </justification>
  </clause>

  <clause id="50304">
    <literal><![CDATA[
      L(L(x * ((y * x) \ R(y,x \ 1,(x \ 1) * a(z,x,u))),w,v5),x,x) = L(x * L(x \ 1,a(u,x \ 1,z),y),w,v5)
    ]]></literal>
    <justification jstring="[para(11980(a,1),50302(a,1,1,1,2,2,3,2))].">
      <j1 rule="para" parents="11980 50302"/>
    </justification>
  </clause>

  <clause id="50305">
    <literal><![CDATA[
      L(L(x * ((y * x) \ R(y,x \ 1,x \ a(z,x,u))),w,v5),x,x) = L(x * L(x \ 1,a(u,x \ 1,z),y),w,v5)
    ]]></literal>
    <justification jstring="[para(35739(a,1),50304(a,1,1,1,2,2,3))].">
      <j1 rule="para" parents="35739 50304"/>
    </justification>
  </clause>

  <clause id="50306">
    <literal><![CDATA[
      L(L(x * ((y * x) \ R(y,x,x \ a(z,x,u))),w,v5),x,x) = L(x * L(x \ 1,a(u,x \ 1,z),y),w,v5)
    ]]></literal>
    <justification jstring="[para(2975(a,1),50305(a,1,1,1,2,2))].">
      <j1 rule="para" parents="2975 50305"/>
    </justification>
  </clause>

  <clause id="50307">
    <literal><![CDATA[
      L(L(x * (x \ a(y,a(x,x,z),u)),w,v5),x,x) = L(x * L(x \ 1,a(y,x \ 1,u),z),w,v5)
    ]]></literal>
    <justification jstring="[para(48133(a,1),50306(a,1,1,1,2))].">
      <j1 rule="para" parents="48133 50306"/>
    </justification>
  </clause>

  <clause id="50308">
    <literal><![CDATA[
      L(L(a(x,a(y,y,z),u),w,v5),y,y) = L(y * L(y \ 1,a(x,y \ 1,u),z),w,v5)
    ]]></literal>
    <justification jstring="[para(10(a,1),50307(a,1,1,1))].">
      <j1 rule="para" parents="10 50307"/>
    </justification>
  </clause>

  <clause id="50310">
    <literal><![CDATA[
      L(a(x,a(y,y,z),L(u,w,v5)),y,y) = L(y * L(y \ 1,a(x,y \ 1,u),z),w,v5)
    ]]></literal>
    <justification jstring="[para(42769(a,2),50308(a,1,1))].">
      <j1 rule="para" parents="42769 50308"/>
    </justification>
  </clause>

  <clause id="50311">
    <literal><![CDATA[
      L(a(x,a(y,y,z),u),y,y) = L(y * L(y \ 1,a(x,y \ 1,u),z),w,v5)
    ]]></literal>
    <justification jstring="[para(49796(a,1),50310(a,1,1))].">
      <j1 rule="para" parents="49796 50310"/>
    </justification>
  </clause>

  <clause id="50312">
    <literal><![CDATA[
      L(x * L(x \ 1,a(y,x \ 1,z),u),w,v5) = a(y,a(x,x,u),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,48363,a(flip),b,50311,a),flip(a)].">
      <j1 rule="hyper" parents="64 48363 50311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50315">
    <literal><![CDATA[
      L(x * L(x \ 1,a(y,x,z),u),w,v5) = a(y,a(x,x,u),z)
    ]]></literal>
    <justification jstring="[para(11980(a,1),50312(a,1,1,2,2))].">
      <j1 rule="para" parents="11980 50312"/>
    </justification>
  </clause>

  <clause id="50316">
    <literal><![CDATA[
      L(a(x,a(y,x,z),u),w,v5) = a(z,a(x,x,u),y)
    ]]></literal>
    <justification jstring="[para(42636(a,1),50315(a,1,1))].">
      <j1 rule="para" parents="42636 50315"/>
    </justification>
  </clause>

  <clause id="50317">
    <literal><![CDATA[
      a(x,a(y,x,z),L(u,w,v5)) = a(z,a(x,x,u),y)
    ]]></literal>
    <justification jstring="[hyper(64,a,46493,a,b,50316,a)].">
      <j1 rule="hyper" parents="64 46493 50316"/>
    </justification>
  </clause>

  <clause id="50318">
    <literal><![CDATA[
      a(x,a(y,y,y * z),u) = a(x,y,a(u,y,L(z,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,50300,a(flip),b,50317,a),flip(a)].">
      <j1 rule="hyper" parents="64 50300 50317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50320">
    <literal><![CDATA[
      a(x,y,a(z,y,L(u,w,v5))) = a(x,a(u,y,y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32894,a(flip),b,50318,a),flip(a)].">
      <j1 rule="hyper" parents="64 32894 50318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50321">
    <literal><![CDATA[
      a(x,a(y,z,z),u) = a(x,z,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,49814,a(flip),b,50320,a),flip(a)].">
      <j1 rule="hyper" parents="64 49814 50320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50322">
    <literal><![CDATA[
      L(a(x,y,a(z,y,u)) * y,x,a(u,y,z)) = L(y,y,a(u,z,x))
    ]]></literal>
    <justification jstring="[para(50321(a,1),49899(a,1,1,1))].">
      <j1 rule="para" parents="50321 49899"/>
    </justification>
  </clause>

  <clause id="50323">
    <literal><![CDATA[
      L(x * a(y,x,a(z,x,u)),y,a(z,x,u)) = L(x,x,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(41900(a,1),50322(a,1,1))].">
      <j1 rule="para" parents="41900 50322"/>
    </justification>
  </clause>

  <clause id="50324">
    <literal><![CDATA[
      L(L(x,a(y,x,z),u * x),z,a(u,x,y)) = L(x,x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(50230(a,2),50323(a,1,1))].">
      <j1 rule="para" parents="50230 50323"/>
    </justification>
  </clause>

  <clause id="50325">
    <literal><![CDATA[
      x \ (T(a(y,z,z),u) * (w * a(x,x \ (T(a(y,z,z),u) * w),a(y,z,z)))) = L(x \ (a(y,z,z) * w),a(x,z,z),y * (x \ (T(a(y,z,z),u) * w)))
    ]]></literal>
    <justification jstring="[para(13984(a,1),49464(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13984 49464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50326">
    <literal><![CDATA[
      x \ (T(a(y,z,z),u) * (w * a(x,x \ (T(a(y,z,z),u) * w),a(y,z,z)))) = L(x \ (a(y,z,z) * w),a(x,z,z),y * (x \ (a(y,z,z) * w)))
    ]]></literal>
    <justification jstring="[para(13984(a,1),50325(a,2,3,2,2,1))].">
      <j1 rule="para" parents="13984 50325"/>
    </justification>
  </clause>

  <clause id="50328">
    <literal><![CDATA[
      x \ (T(a(y,z,z),u) * (w * a(x,x \ (T(a(y,z,z),u) * w),a(y,z,z)))) = L(x \ (a(y,z,z) * w),a(x,z,z),y * (x * (a(y,z,z) * w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,49108,a(flip),b,50326,a),flip(a)].">
      <j1 rule="hyper" parents="373 49108 50326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50330">
    <literal><![CDATA[
      x \ (T(a(y,z,z),u) * (w * a(x,x \ (T(a(y,z,z),u) * w),a(y,z,z)))) = L(x \ (a(y,z,z) * w),a(x,z,z),(a(y,z,z) * w) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,49072,a(flip),b,50328,a),flip(a)].">
      <j1 rule="hyper" parents="373 49072 50328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50331">
    <literal><![CDATA[
      x \ (T(a(y,z,z),u) * (w * a(x,x \ (T(a(y,z,z),u) * w),a(y,z,z)))) = L(x \ (a(y,z,z) * w),a(x,z,z),a(y,z,z) * (w * y))
    ]]></literal>
    <justification jstring="[para(29315(a,1),50330(a,2,3))].">
      <j1 rule="para" parents="29315 50330"/>
    </justification>
  </clause>

  <clause id="50332">
    <literal><![CDATA[
      x \ (T(a(y,z,z),u) * (w * a(x,x \ (T(a(y,z,z),u) * w),a(y,z,z)))) = L(x \ (a(y,z,z) * w),a(x,z,z),w * R(y,z,z))
    ]]></literal>
    <justification jstring="[para(45008(a,1),50331(a,2,3))].">
      <j1 rule="para" parents="45008 50331"/>
    </justification>
  </clause>

  <clause id="50333">
    <literal><![CDATA[
      x \ (T(a(y,z,z),u) * (w * a(x,x \ (T(a(y,z,z),u) * w),a(y,z,z)))) = L(x \ (a(y,z,z) * w),a(x,z,z),w * L(y,z,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,33574,a(flip),b,50332,a),flip(a)].">
      <j1 rule="hyper" parents="373 33574 50332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50334">
    <literal><![CDATA[
      x \ (T(a(y,z,z),u) * (w * a(x,x \ (T(a(y,z,z),u) * w),a(y,z,z)))) = L(x \ (a(y,z,z) * w),a(x,z,z),y * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,49018,a(flip),b,50333,a),flip(a)].">
      <j1 rule="hyper" parents="373 49018 50333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50336">
    <literal><![CDATA[
      x \ (a(y,z,z) * (u * a(x,x \ (T(a(y,z,z),w) * u),a(y,z,z)))) = L(x \ (a(y,z,z) * u),a(x,z,z),y * u)
    ]]></literal>
    <justification jstring="[para(13984(a,1),50334(a,1,2,1))].">
      <j1 rule="para" parents="13984 50334"/>
    </justification>
  </clause>

  <clause id="50337">
    <literal><![CDATA[
      x \ (a(y,z,z) * (u * a(x,x \ (a(y,z,z) * u),a(y,z,z)))) = L(x \ (a(y,z,z) * u),a(x,z,z),y * u)
    ]]></literal>
    <justification jstring="[para(114(a,1),50336(a,1,2,2,2,2,2,1))].">
      <j1 rule="para" parents="114 50336"/>
    </justification>
  </clause>

  <clause id="50339">
    <literal><![CDATA[
      x \ (a(y,z,z) * (u * a(x,(a(y,z,z) * u) * x,a(y,z,z)))) = L(x \ (a(y,z,z) * u),a(x,z,z),y * u)
    ]]></literal>
    <justification jstring="[para(35687(a,1),50337(a,1,2,2,2))].">
      <j1 rule="para" parents="35687 50337"/>
    </justification>
  </clause>

  <clause id="50340">
    <literal><![CDATA[
      x \ (a(y,z,z) * (u * a(x,z,a(y,a(y,z,z) * u,z)))) = L(x \ (a(y,z,z) * u),a(x,z,z),y * u)
    ]]></literal>
    <justification jstring="[para(46884(a,1),50339(a,1,2,2,2))].">
      <j1 rule="para" parents="46884 50339"/>
    </justification>
  </clause>

  <clause id="50341">
    <literal><![CDATA[
      L(x \ (a(y,z,z) * u),a(x,z,z),y * u) = x \ (a(y,z,z) * (u * a(z,z,a(x,u,y))))
    ]]></literal>
    <justification jstring="[para(47504(a,1),50340(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="47504 50340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50342">
    <literal><![CDATA[
      L(x \ (a(y,z,z) * u),a(x,z,z),y * u) = x \ (a(y,z,z) * L(u,a(x,z,z),y * u))
    ]]></literal>
    <justification jstring="[para(49459(a,2),50341(a,2,2,2))].">
      <j1 rule="para" parents="49459 50341"/>
    </justification>
  </clause>

  <clause id="50343">
    <literal><![CDATA[
      L(x \ (a(y,z,z) * u),a(x,z,z),y * u) = x \ L(a(y,z,z) * u,a(x,z,z),y * u)
    ]]></literal>
    <justification jstring="[para(49103(a,2),50342(a,2,2))].">
      <j1 rule="para" parents="49103 50342"/>
    </justification>
  </clause>

  <clause id="50344">
    <literal><![CDATA[
      L(x \ (a(y,z,z) * u),a(x,z,z),y * u) = x \ (u * a(y,z,L(z,u,x)))
    ]]></literal>
    <justification jstring="[para(50081(a,1),50343(a,2,2))].">
      <j1 rule="para" parents="50081 50343"/>
    </justification>
  </clause>

  <clause id="50345">
    <literal><![CDATA[
      L(x \ (a(y,z,z) * u),a(x,z,z),y * u) = a(y,z,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,50183,a(flip),b,50344,a),flip(a)].">
      <j1 rule="hyper" parents="373 50183 50344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50346">
    <literal><![CDATA[
      a(x,T(((R(y,z,u) * R(y,z,u)) \ w) * R(y,z,u),R(y,z,u)) * v5,v6) = a(x,(R(y \ 1,z,u) \ R(T(w,y * y),R(y,z,u),R(y,z,u))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(28135(a,1),34117(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="28135 34117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50347">
    <literal><![CDATA[
      a(x,T(((R(y,z,u) * R(y,z,u)) \ w) * R(y,z,u),R(y,z,u)) * v5,v6) = a(x,(R(y \ 1,z,u) \ R(T(w,y * y),L(y,z,u),L(y,z,u))) * v5,v6)
    ]]></literal>
    <justification jstring="[para(26637(a,1),50346(a,2,2,1,2))].">
      <j1 rule="para" parents="26637 50346"/>
    </justification>
  </clause>

  <clause id="50349">
    <literal><![CDATA[
      a(x,T(((R(y,z,u) * R(y,z,u)) \ w) * R(y,z,u),R(y,z,u)) * v5,v6) = a(x,(R(y \ 1,z,u) \ L(T(w,y * y),L(y,z,u),L(y,z,u))) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,37390,a(flip),b,50347,a),flip(a)].">
      <j1 rule="hyper" parents="373 37390 50347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50350">
    <literal><![CDATA[
      a(x,T(((R(y,z,u) * R(y,z,u)) \ w) * R(y,z,u),R(y,z,u)) * v5,v6) = a(x,(R(y \ 1,z,u) \ L(w,L(y,z,u),L(y,z,u))) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,32081,a(flip),b,50349,a),flip(a)].">
      <j1 rule="hyper" parents="373 32081 50349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50352">
    <literal><![CDATA[
      a(x,T(((R(y,z,u) * R(y,z,u)) \ w) * R(y,z,u),R(y,z,u)) * v5,v6) = a(x,(L(y \ 1,z,u) \ L(w,L(y,z,u),L(y,z,u))) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,44894,a(flip),b,50350,a),flip(a)].">
      <j1 rule="hyper" parents="373 44894 50350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50353">
    <literal><![CDATA[
      a(x,T(((R(y,z,u) * R(y,z,u)) \ w) * R(y,z,u),R(y,z,u)) * v5,v6) = a(x,(L(y,z,u) \ L(w,L(y,z,u),L(y,z,u))) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,44906,a(flip),b,50352,a),flip(a)].">
      <j1 rule="hyper" parents="373 44906 50352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50354">
    <literal><![CDATA[
      a(x,T(((R(y,z,u) * R(y,z,u)) \ w) * R(y,z,u),R(y,z,u)) * v5,v6) = a(x,((L(y,z,u) \ 1) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(1148(a,1),50353(a,2,2,1))].">
      <j1 rule="para" parents="1148 50353"/>
    </justification>
  </clause>

  <clause id="50355">
    <literal><![CDATA[
      a(x,T(((R(y,z,u) * R(y,z,u)) \ w) * R(y,z,u),R(y,z,u)) * v5,v6) = a(x,(L(y,z,u) * w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,11998,a(flip),b,50354,a),flip(a)].">
      <j1 rule="hyper" parents="373 11998 50354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50356">
    <literal><![CDATA[
      a(x,(L(y,z,u) * w) * v5,v6) = a(x,(w * R(y,z,u)) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32024,a(flip),b,50355,a),flip(a)].">
      <j1 rule="hyper" parents="64 32024 50355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50358">
    <literal><![CDATA[
      a(x,(L(y,z,u) * w) * T((w * R(y,z,u)) \ ((1 / (w * R(y,z,u))) \ v5),v6),v7) = a(x,(1 / (w * R(y,z,u))) \ T(v5,v6),v7)
    ]]></literal>
    <justification jstring="[para(1469(a,1),50356(a,2,2))].">
      <j1 rule="para" parents="1469 50356"/>
    </justification>
  </clause>

  <clause id="50360">
    <literal><![CDATA[
      a(x,(1 / (y * R(z,u,w))) \ T(v5,v6),v7) = a(x,(L(z,u,w) * y) * ((y * R(z,u,w)) \ ((1 / (y * R(z,u,w))) \ v5)),v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,31896,a(flip),b,50358,a),flip(a)].">
      <j1 rule="hyper" parents="64 31896 50358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50362">
    <literal><![CDATA[
      a(x,(1 / (y * R(z,u,w))) \ T(v5,v6),v7) = a(x,(L(z,u,w) * y) * ((y * R(z,u,w)) \ (((y * R(z,u,w)) \ 1) \ v5)),v7)
    ]]></literal>
    <justification jstring="[hyper(373,a,32954,a(flip),b,50360,a),flip(a)].">
      <j1 rule="hyper" parents="373 32954 50360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50363">
    <literal><![CDATA[
      a(x,(1 / (y * R(z,u,w))) \ T(v5,v6),v7) = a(x,((y * R(z,u,w)) \ ((y * R(z,u,w)) \ v5)) * (L(z,u,w) * y),v7)
    ]]></literal>
    <justification jstring="[hyper(373,a,34115,a(flip),b,50362,a),flip(a)].">
      <j1 rule="hyper" parents="373 34115 50362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50364">
    <literal><![CDATA[
      a(x,(1 / (y * R(z,u,w))) \ T(v5,v6),v7) = a(x,L(v5,y * R(z,u,w),y * R(z,u,w)) * (L(z,u,w) * y),v7)
    ]]></literal>
    <justification jstring="[hyper(373,a,32339,a(flip),b,50363,a),flip(a)].">
      <j1 rule="hyper" parents="373 32339 50363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50365">
    <literal><![CDATA[
      a(x,(1 / (y * R(z,u,w))) \ T(v5,v6),v7) = a(x,L(v5,y * R(z,u,w),y * L(z,u,w)) * (L(z,u,w) * y),v7)
    ]]></literal>
    <justification jstring="[para(33574(a,1),50364(a,2,2,1))].">
      <j1 rule="para" parents="33574 50364"/>
    </justification>
  </clause>

  <clause id="50366">
    <literal><![CDATA[
      a(x,(1 / (y * R(z,u,w))) \ T(v5,v6),v7) = a(x,L(v5,y * L(z,u,w),y * L(z,u,w)) * (L(z,u,w) * y),v7)
    ]]></literal>
    <justification jstring="[para(36266(a,1),50365(a,2,2,1))].">
      <j1 rule="para" parents="36266 50365"/>
    </justification>
  </clause>

  <clause id="50367">
    <literal><![CDATA[
      a(x,(1 / (y * R(z,u,w))) \ T(v5,v6),v7) = a(x,(y * L(z,u,w)) \ v5,v7)
    ]]></literal>
    <justification jstring="[hyper(373,a,32150,a(flip),b,50366,a),flip(a)].">
      <j1 rule="hyper" parents="373 32150 50366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50368">
    <literal><![CDATA[
      a(x,(1 / (y * R(z,u,w))) \ v5,v6) = a(x,(y * L(z,u,w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(32041,a,50367,a)].">
      <j1 rule="hyper" parents="32041 50367"/>
    </justification>
  </clause>

  <clause id="50369">
    <literal><![CDATA[
      a(x,(y * R(z,u,w)) \ v5,v6) = a(x,(y * L(z,u,w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32135,a(flip),b,50368,a)].">
      <j1 rule="hyper" parents="64 32135 50368"/>
    </justification>
  </clause>

  <clause id="50370">
    <literal><![CDATA[
      a(x,T(R(x,y,x) \ (z \ u),w),z) = a(x,(z * L(x,y,x)) \ u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,48632,a,b,50369,a)].">
      <j1 rule="hyper" parents="64 48632 50369"/>
    </justification>
  </clause>

  <clause id="50371">
    <literal><![CDATA[
      a(x,T(R(x,y,x) \ (z \ u),w),z) = a(x,(z * x) \ u,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,13837,a(flip),b,50370,a),flip(a)].">
      <j1 rule="hyper" parents="373 13837 50370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50373">
    <literal><![CDATA[
      a(x,T(R(x,y,x) \ (z \ u),w),z) = a(x,(x \ u) * z,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,48616,a(flip),b,50371,a),flip(a)].">
      <j1 rule="hyper" parents="373 48616 50371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50374">
    <literal><![CDATA[
      a(x,R(x,y,x) \ (z \ u),z) = a(x,(x \ u) * z,z)
    ]]></literal>
    <justification jstring="[hyper(31997,a,50373,a)].">
      <j1 rule="hyper" parents="31997 50373"/>
    </justification>
  </clause>

  <clause id="50375">
    <literal><![CDATA[
      a(x,L(x,y,x) \ (z \ u),z) = a(x,(x \ u) * z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,44883,a(flip),b,50374,a)].">
      <j1 rule="hyper" parents="64 44883 50374"/>
    </justification>
  </clause>

  <clause id="50376">
    <literal><![CDATA[
      a(x,L(x,y,x) * (z \ u),z) = a(x,(x \ u) * z,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35686,a(flip),b,50375,a)].">
      <j1 rule="hyper" parents="64 35686 50375"/>
    </justification>
  </clause>

  <clause id="50377">
    <literal><![CDATA[
      a(x,(x \ y) * z,z) = a(x,x * (z \ y),z)
    ]]></literal>
    <justification jstring="[hyper(64,a,13830,a(flip),b,50376,a),flip(a)].">
      <j1 rule="hyper" parents="64 13830 50376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50378">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),y * (x * (a(y,z,z) \ u))) = (x * (a(y,z,z) \ u)) * a(x,(x \ u) * a(y,z,z),a(y,z,z))
    ]]></literal>
    <justification jstring="[para(50377(a,2),49460(a,2,2))].">
      <j1 rule="para" parents="50377 49460"/>
    </justification>
  </clause>

  <clause id="50379">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),y * (x * (a(y,z,z) \ u))) = (x * (a(y,z,z) \ u)) * a(x,x \ u,a(z,z,y))
    ]]></literal>
    <justification jstring="[para(49031(a,1),50378(a,2,2))].">
      <j1 rule="para" parents="49031 50378"/>
    </justification>
  </clause>

  <clause id="50380">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),y * (x * (a(y,z,z) \ u))) = (x * (a(y,z,z) \ u)) * a(x,u * x,a(z,z,y))
    ]]></literal>
    <justification jstring="[para(35687(a,1),50379(a,2,2))].">
      <j1 rule="para" parents="35687 50379"/>
    </justification>
  </clause>

  <clause id="50382">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),y * (x * (a(y,z,z) \ u))) = (x * (a(y,z,z) \ u)) * a(x,z,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(46885(a,1),50380(a,2,2))].">
      <j1 rule="para" parents="46885 50380"/>
    </justification>
  </clause>

  <clause id="50383">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),y * (x * (a(y,z,z) \ u))) = x * ((a(y,z,z) \ u) * a(x,z,a(y,u,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,49693,a(flip),b,50382,a),flip(a)].">
      <j1 rule="hyper" parents="373 49693 50382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50384">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),y * (x * (a(y,z,z) \ u))) = x * (u * (a(y,z,z) \ a(x,z,a(y,u,z))))
    ]]></literal>
    <justification jstring="[para(48850(a,1),50383(a,2,2))].">
      <j1 rule="para" parents="48850 50383"/>
    </justification>
  </clause>

  <clause id="50385">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),y * (x * (a(y,z,z) \ u))) = x * (u * (z \ L(L(z,z,y),z,a(y,u,x))))
    ]]></literal>
    <justification jstring="[para(46825(a,1),50384(a,2,2,2))].">
      <j1 rule="para" parents="46825 50384"/>
    </justification>
  </clause>

  <clause id="50386">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),y * (x * (a(y,z,z) \ u))) = x * (u * (z \ L(z,z,L(y,u,x))))
    ]]></literal>
    <justification jstring="[para(47495(a,1),50385(a,2,2,2,2))].">
      <j1 rule="para" parents="47495 50385"/>
    </justification>
  </clause>

  <clause id="50387">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),y * (x * (a(y,z,z) \ u))) = x * (u * L(z \ L(z,z,y),u,x))
    ]]></literal>
    <justification jstring="[para(44251(a,2),50386(a,2,2,2))].">
      <j1 rule="para" parents="44251 50386"/>
    </justification>
  </clause>

  <clause id="50388">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),y * (x * (a(y,z,z) \ u))) = x * (a(y,z,L(z,u,x)) \ u)
    ]]></literal>
    <justification jstring="[para(45850(a,1),50387(a,2,2))].">
      <j1 rule="para" parents="45850 50387"/>
    </justification>
  </clause>

  <clause id="50389">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),y * (x * (a(y,z,z) \ u))) = a(y,z,z) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,46554,a(flip),b,50388,a),flip(a)].">
      <j1 rule="hyper" parents="373 46554 50388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50390">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),(a(y,z,z) \ u) * y) = a(y,z,z) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,49072,a(flip),b,50389,a)].">
      <j1 rule="hyper" parents="64 49072 50389"/>
    </justification>
  </clause>

  <clause id="50391">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),u * (a(y,z,z) \ y)) = a(y,z,z) \ (x * u)
    ]]></literal>
    <justification jstring="[para(44994(a,1),50390(a,1,3))].">
      <j1 rule="para" parents="44994 50390"/>
    </justification>
  </clause>

  <clause id="50392">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),u * (a(y,z,z) * y)) = a(y,z,z) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,49108,a(flip),b,50391,a)].">
      <j1 rule="hyper" parents="64 49108 50391"/>
    </justification>
  </clause>

  <clause id="50393">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),u * R(y,z,z)) = a(y,z,z) \ (x * u)
    ]]></literal>
    <justification jstring="[para(15998(a,1),50392(a,1,3,2))].">
      <j1 rule="para" parents="15998 50392"/>
    </justification>
  </clause>

  <clause id="50394">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),u * L(y,z,z)) = a(y,z,z) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(33586,a,50393,a)].">
      <j1 rule="hyper" parents="33586 50393"/>
    </justification>
  </clause>

  <clause id="50395">
    <literal><![CDATA[
      L(x * (a(y,z,z) \ u),a(x,z,z),y * u) = a(y,z,z) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,49018,a(flip),b,50394,a)].">
      <j1 rule="hyper" parents="64 49018 50394"/>
    </justification>
  </clause>

  <clause id="50397">
    <literal><![CDATA[
      a(x,y,T(((K(z,u) * w) * (v5 * (w \ K(u,z)))) * (w \ K(u,z)),w \ K(u,z)) \ v6) = a(x,y,(T(((1 / (w \ K(u,z))) * v5) * (w \ K(u,z)),w \ K(u,z)) * (w \ 1)) \ v6)
    ]]></literal>
    <justification jstring="[para(14445(a,1),27745(a,1,3,1,1,1,1))].">
      <j1 rule="para" parents="14445 27745"/>
    </justification>
  </clause>

  <clause id="50398">
    <literal><![CDATA[
      a(x,y,T((K(z,u) * (w * (v5 * (w \ K(u,z))))) * (w \ K(u,z)),w \ K(u,z)) \ v6) = a(x,y,(T(((1 / (w \ K(u,z))) * v5) * (w \ K(u,z)),w \ K(u,z)) * (w \ 1)) \ v6)
    ]]></literal>
    <justification jstring="[para(23073(a,1),50397(a,1,3,1,1,1))].">
      <j1 rule="para" parents="23073 50397"/>
    </justification>
  </clause>

  <clause id="50399">
    <literal><![CDATA[
      a(x,y,(T(((1 / (z \ K(u,w))) * v5) * (z \ K(u,w)),z \ K(u,w)) * (z \ 1)) \ v6) = a(x,y,T(T(z * (v5 * (z \ 1)),K(w,u)) * (z \ K(u,w)),z \ K(u,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(25385(a,1),50398(a,1,3,1,1,1)),flip(a)].">
      <j1 rule="para" parents="25385 50398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50400">
    <literal><![CDATA[
      a(x,y,(T(((1 / (z \ K(u,w))) * v5) * (z \ K(u,w)),z \ K(u,w)) * (z \ 1)) \ v6) = a(x,y,T(T(z * (v5 * (z \ 1)),K(u,w)) * (z \ K(u,w)),z \ K(u,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(8153(a,1),50399(a,2,3,1,1,1))].">
      <j1 rule="para" parents="8153 50399"/>
    </justification>
  </clause>

  <clause id="50401">
    <literal><![CDATA[
      a(x,y,(T(((1 / (z \ K(u,w))) * v5) * (z \ K(u,w)),z \ K(u,w)) * (z \ 1)) \ v6) = a(x,y,T((z * (K(u,w) * (v5 * (z \ 1)))) * (z \ 1),z \ K(u,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(35339(a,1),50400(a,2,3,1,1))].">
      <j1 rule="para" parents="35339 50400"/>
    </justification>
  </clause>

  <clause id="50402">
    <literal><![CDATA[
      a(x,y,(T(((1 / (z \ K(u,w))) * v5) * (z \ K(u,w)),z \ K(u,w)) * (z \ 1)) \ v6) = a(x,y,((z * (K(u,w) * (v5 * (z \ 1)))) * (z \ 1)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,27316,a(flip),b,50401,a),flip(a)].">
      <j1 rule="hyper" parents="373 27316 50401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50404">
    <literal><![CDATA[
      a(x,y,(T(((1 / (z \ K(u,w))) * v5) * (z \ K(u,w)),z \ K(u,w)) * (z \ 1)) \ v6) = a(x,y,L(K(u,w) * (v5 * (z \ 1)),z,z) \ v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,27618,a(flip),b,50402,a),flip(a)].">
      <j1 rule="hyper" parents="373 27618 50402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50405">
    <literal><![CDATA[
      a(x,y,(T(((1 / (z \ K(u,w))) * v5) * (z \ K(u,w)),z \ K(u,w)) * (z \ 1)) \ v6) = a(x,y,L(v5 * (z \ 1),z,z) \ (K(w,u) * v6))
    ]]></literal>
    <justification jstring="[para(26104(a,1),50404(a,2,3))].">
      <j1 rule="para" parents="26104 50404"/>
    </justification>
  </clause>

  <clause id="50406">
    <literal><![CDATA[
      a(x,y,(T(((1 / (z \ K(u,w))) * v5) * (z \ K(u,w)),z \ K(u,w)) * (z \ 1)) \ v6) = a(x,y,L(v5 * (z \ 1),z,z) \ v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,27331,a(flip),b,50405,a),flip(a)].">
      <j1 rule="hyper" parents="373 27331 50405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50408">
    <literal><![CDATA[
      a(x,y,(T(((K(z,u) * w) * v5) * (w \ K(u,z)),w \ K(u,z)) * (w \ 1)) \ v6) = a(x,y,L(v5 * (w \ 1),w,w) \ v6)
    ]]></literal>
    <justification jstring="[para(14445(a,1),50406(a,1,3,1,1,1,1,1))].">
      <j1 rule="para" parents="14445 50406"/>
    </justification>
  </clause>

  <clause id="50409">
    <literal><![CDATA[
      a(x,y,(T(K(z,u) * ((w * v5) * (w \ K(u,z))),w \ K(u,z)) * (w \ 1)) \ v6) = a(x,y,L(v5 * (w \ 1),w,w) \ v6)
    ]]></literal>
    <justification jstring="[para(24373(a,1),50408(a,1,3,1,1,1))].">
      <j1 rule="para" parents="24373 50408"/>
    </justification>
  </clause>

  <clause id="50410">
    <literal><![CDATA[
      a(x,y,(T(T((z * u) * (z \ 1),K(w,v5)),z \ K(w,v5)) * (z \ 1)) \ v6) = a(x,y,L(u * (z \ 1),z,z) \ v6)
    ]]></literal>
    <justification jstring="[para(24879(a,1),50409(a,1,3,1,1,1))].">
      <j1 rule="para" parents="24879 50409"/>
    </justification>
  </clause>

  <clause id="50411">
    <literal><![CDATA[
      a(x,y,(T((z * u) * (z \ 1),z \ K(w,v5 * v5)) * (z \ 1)) \ v6) = a(x,y,L(u * (z \ 1),z,z) \ v6)
    ]]></literal>
    <justification jstring="[para(17041(a,1),50410(a,1,3,1,1,1))].">
      <j1 rule="para" parents="17041 50410"/>
    </justification>
  </clause>

  <clause id="50412">
    <literal><![CDATA[
      a(x,y,(((z * u) * (z \ 1)) * (z \ 1)) \ w) = a(x,y,L(u * (z \ 1),z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27513,a(flip),b,50411,a)].">
      <j1 rule="hyper" parents="64 27513 50411"/>
    </justification>
  </clause>

  <clause id="50414">
    <literal><![CDATA[
      a(x,y,((z \ 1) * ((z \ 1) * (z * u))) \ w) = a(x,y,L(u * (z \ 1),z,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27698,a(flip),b,50412,a)].">
      <j1 rule="hyper" parents="64 27698 50412"/>
    </justification>
  </clause>

  <clause id="50415">
    <literal><![CDATA[
      a(x,y,L(z * (u \ 1),u,u) \ w) = a(x,y,(u \ (u \ (u * z))) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,40004,a(flip),b,50414,a),flip(a)].">
      <j1 rule="hyper" parents="64 40004 50414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50416">
    <literal><![CDATA[
      a(x,y,L(z * (u \ 1),u,u) \ w) = a(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(9(a,1),50415(a,2,3,1,2))].">
      <j1 rule="para" parents="9 50415"/>
    </justification>
  </clause>

  <clause id="50417">
    <literal><![CDATA[
      a(x,y,((z * (u \ 1)) \ w) * a(z * (u \ 1),u,u)) = a(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,45719,a,b,50416,a)].">
      <j1 rule="hyper" parents="64 45719 50416"/>
    </justification>
  </clause>

  <clause id="50418">
    <literal><![CDATA[
      a(x,y,((z * (u \ 1)) \ w) * a(z * (1 * u),u,u)) = a(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(34898(a,1),50417(a,1,3,2))].">
      <j1 rule="para" parents="34898 50417"/>
    </justification>
  </clause>

  <clause id="50419">
    <literal><![CDATA[
      a(L(T(x * y,x) \ 1,x * y,y \ (x \ y)),L(T(x * y,x) \ 1,x * y,y \ (x \ y)),z) = L((T(x * y,x) \ 1) \ R(T(x * y,x) \ 1,y \ (y \ (y / x)),z),x * y,y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(26506(a,1),33075(a,2,1,2))].">
      <j1 rule="para" parents="26506 33075"/>
    </justification>
  </clause>

  <clause id="50420">
    <literal><![CDATA[
      a(L(T(x * y,x) \ 1,x * y,y \ (x \ y)),L(T(x * y,x) \ 1,x * y,y \ (x \ y)),z) = L((T(x * y,x) \ 1) \ R(T(x * y,x) \ 1,L(y / x,y,y),z),x * y,y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(30397(a,1),50419(a,2,1,2))].">
      <j1 rule="para" parents="30397 50419"/>
    </justification>
  </clause>

  <clause id="50421">
    <literal><![CDATA[
      a(L(T(x * y,x) \ 1,x * y,y \ (x \ y)),L(T(x * y,x) \ 1,x * y,y \ (x \ y)),z) = L((T(x * y,x) \ 1) \ R(T(x * y,x) \ 1,L(x \ y,y,y),z),x * y,y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(26454(a,1),50420(a,2,1,2))].">
      <j1 rule="para" parents="26454 50420"/>
    </justification>
  </clause>

  <clause id="50422">
    <literal><![CDATA[
      a(L(T(x * y,x) \ 1,x * y,y \ (x \ y)),L(T(x * y,x) \ 1,x * y,y \ (x \ y)),z) = L(T(x * y,x) \ (1 * R(1 \ T(x * y,x),L(x \ y,y,y),z)),x * y,y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(2744(a,1),50421(a,2,1))].">
      <j1 rule="para" parents="2744 50421"/>
    </justification>
  </clause>

  <clause id="50423">
    <literal><![CDATA[
      a(L(T(x * y,x) \ 1,x * y,y \ (x \ y)),L(T(x * y,x) \ 1,x * y,y \ (x \ y)),z) = L(T(x * y,x) \ (1 * R(T(x * y,x),L(x \ y,y,y),z)),x * y,y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(66(a,1),50422(a,2,1,2,2,1))].">
      <j1 rule="para" parents="66 50422"/>
    </justification>
  </clause>

  <clause id="50424">
    <literal><![CDATA[
      a(L(T(x * y,x) \ 1,x * y,y \ (x \ y)),L(T(x * y,x) \ 1,x * y,y \ (x \ y)),z) = L(T(x * y,x) \ (1 * R(T(x * y,x),x * y,z)),x * y,y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(38149(a,1),50423(a,2,1,2,2))].">
      <j1 rule="para" parents="38149 50423"/>
    </justification>
  </clause>

  <clause id="50425">
    <literal><![CDATA[
      a(L(T(x * y,x) \ 1,x * y,y \ (x \ y)),L(T(x * y,x) \ 1,x * y,y \ (x \ y)),z) = L(T(x * y,x) \ R(T(x * y,x),x * y,z),x * y,y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(7(a,1),50424(a,2,1,2))].">
      <j1 rule="para" parents="7 50424"/>
    </justification>
  </clause>

  <clause id="50426">
    <literal><![CDATA[
      a(L(T(x * y,x) \ 1,x * y,y \ (x \ y)),L(T(x * y,x) \ 1,x * y,y \ (x \ y)),z) = L((x * y) \ R(x * y,x * y,z),x * y,y \ (x \ y))
    ]]></literal>
    <justification jstring="[para(24594(a,1),50425(a,2,1))].">
      <j1 rule="para" parents="24594 50425"/>
    </justification>
  </clause>

  <clause id="50427">
    <literal><![CDATA[
      a(L(T(x * y,x) \ 1,x * y,y \ (x \ y)),L(T(x * y,x) \ 1,x * y,y \ (x \ y)),z) = a(x * y,L(x * y,x * y,y \ (x \ y)),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,34874,a(flip),b,50426,a),flip(a)].">
      <j1 rule="hyper" parents="373 34874 50426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50429">
    <literal><![CDATA[
      a(L(T(x * y,x) \ 1,x * y,y \ (x \ y)),L(T(x * y,x) \ 1,x * y,y \ (x \ y)),z) = a(x * y,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,38648,a(flip),b,50427,a),flip(a)].">
      <j1 rule="hyper" parents="373 38648 50427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50431">
    <literal><![CDATA[
      a(x \ ((x / y) / x),L(T(y * x,y) \ 1,y * x,x \ (y \ x)),z) = a(y * x,y * x,z)
    ]]></literal>
    <justification jstring="[para(33072(a,1),50429(a,1,1))].">
      <j1 rule="para" parents="33072 50429"/>
    </justification>
  </clause>

  <clause id="50432">
    <literal><![CDATA[
      a(x \ ((x / y) / x),x \ ((x / y) / x),z) = a(y * x,y * x,z)
    ]]></literal>
    <justification jstring="[para(33072(a,1),50431(a,1,2))].">
      <j1 rule="para" parents="33072 50431"/>
    </justification>
  </clause>

  <clause id="50433">
    <literal><![CDATA[
      a(x \ ((x / y) / x),x \ (x \ (x / y)),z) = a(y * x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31908,a(flip),b,50432,a)].">
      <j1 rule="hyper" parents="64 31908 50432"/>
    </justification>
  </clause>

  <clause id="50434">
    <literal><![CDATA[
      a(x \ ((x / y) / x),L(x / y,x,x),z) = a(y * x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,32142,a(flip),b,50433,a)].">
      <j1 rule="hyper" parents="64 32142 50433"/>
    </justification>
  </clause>

  <clause id="50435">
    <literal><![CDATA[
      a(x \ ((x / y) / x),L(y \ x,x,x),z) = a(y * x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,31920,a(flip),b,50434,a)].">
      <j1 rule="hyper" parents="64 31920 50434"/>
    </justification>
  </clause>

  <clause id="50436">
    <literal><![CDATA[
      a(x \ (x \ (x / y)),L(y \ x,x,x),z) = a(y * x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(32449,a,50435,a)].">
      <j1 rule="hyper" parents="32449 50435"/>
    </justification>
  </clause>

  <clause id="50437">
    <literal><![CDATA[
      a(L(x / y,x,x),L(y \ x,x,x),z) = a(y * x,y * x,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30384,a(flip),b,50436,a)].">
      <j1 rule="hyper" parents="64 30384 50436"/>
    </justification>
  </clause>

  <clause id="50438">
    <literal><![CDATA[
      a(L(x \ y,y,y),L(x \ y,y,y),z) = a(x * y,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,26794,a(flip),b,50437,a)].">
      <j1 rule="hyper" parents="64 26794 50437"/>
    </justification>
  </clause>

  <clause id="50439">
    <literal><![CDATA[
      a(x \ y,x \ y,z) = a(x * y,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,35139,a(flip),b,50438,a)].">
      <j1 rule="hyper" parents="64 35139 50438"/>
    </justification>
  </clause>

  <clause id="50441">
    <literal><![CDATA[
      a((x \ y) \ z,(x \ y) \ z,u) = a(y * (x * z),y * (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,35250,a,b,50439,a)].">
      <j1 rule="hyper" parents="64 35250 50439"/>
    </justification>
  </clause>

  <clause id="50443">
    <literal><![CDATA[
      a((x * y) * (y * z),(x * y) * (y * z),u) = a(T(x,y) \ z,T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,35251,a(flip),b,50439,a),flip(a)].">
      <j1 rule="hyper" parents="64 35251 50439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50444">
    <literal><![CDATA[
      a(x \ (y \ z),x \ (y \ z),u) = a((y * x) * z,(y * x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,35240,a(flip),b,50439,a)].">
      <j1 rule="hyper" parents="64 35240 50439"/>
    </justification>
  </clause>

  <clause id="50445">
    <literal><![CDATA[
      a((x \ y) * z,(x \ y) * z,u) = a(y * (x * z),y * (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,50439,a(flip),b,50441,a)].">
      <j1 rule="hyper" parents="64 50439 50441"/>
    </justification>
  </clause>

  <clause id="50446">
    <literal><![CDATA[
      a((x * y) * z,(x * y) * z,u) = a(y * (x \ z),y * (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,50439,a(flip),b,50444,a),flip(a)].">
      <j1 rule="hyper" parents="64 50439 50444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50447">
    <literal><![CDATA[
      L(a((x \ (y * (z * x))) * y,a(y,z,x) * z,u),y,y) = a((y * (z * x)) * (x * y),(y * (z * x)) * (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,39417,a,b,50445,a)].">
      <j1 rule="hyper" parents="64 39417 50445"/>
    </justification>
  </clause>

  <clause id="50448">
    <literal><![CDATA[
      a((x * y) * (z * u),(x * T(y,w)) * (u * z),v5) = a(y * (x \ (u * z)),y * (x \ (u * z)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32424,a,b,50446,a)].">
      <j1 rule="hyper" parents="64 32424 50446"/>
    </justification>
  </clause>

  <clause id="50449">
    <literal><![CDATA[
      a(x * (y \ (x * z)),x * (y \ (x * z)),u) = a(T(y,x) \ z,T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,50446,a(flip),b,50443,a)].">
      <j1 rule="hyper" parents="64 50446 50443"/>
    </justification>
  </clause>

  <clause id="50450">
    <literal><![CDATA[
      a(x * (y \ (x * z)),x * (y \ (x * z)),u) = a(T(y,x) \ z,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,31903,a(flip),b,50449,a),flip(a)].">
      <j1 rule="hyper" parents="373 31903 50449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50452">
    <literal><![CDATA[
      a(x * (y \ (x * z)),x * (y \ (x * z)),u) = a(y \ z,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32366,a(flip),b,50450,a),flip(a)].">
      <j1 rule="hyper" parents="373 32366 50450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50454">
    <literal><![CDATA[
      a(x * (y \ (x * z)),x * (y \ (x * z)),u) = a(y * z,y * z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,50439,a(flip),b,50452,a),flip(a)].">
      <j1 rule="hyper" parents="373 50439 50452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50455">
    <literal><![CDATA[
      a((x * y) * (y * z),(x * y) * (y * z),u) = a(y * (x \ (z * y)),y * (x \ (z * y)),u)
    ]]></literal>
    <justification jstring="[para(10599(a,1),50448(a,1,2))].">
      <j1 rule="para" parents="10599 50448"/>
    </justification>
  </clause>

  <clause id="50456">
    <literal><![CDATA[
      a(x * (y \ (z * x)),x * (y \ (z * x)),u) = a(x * (y \ (x * z)),x * (y \ (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,50446,a(flip),b,50455,a),flip(a)].">
      <j1 rule="hyper" parents="64 50446 50455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50457">
    <literal><![CDATA[
      a(x * (y \ (z * x)),x * (y \ (z * x)),u) = a(y * z,y * z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,50454,a(flip),b,50456,a),flip(a)].">
      <j1 rule="hyper" parents="373 50454 50456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50459">
    <literal><![CDATA[
      L(a((x \ (y * (z * x))) * y,a(y,z,x) * z,u),y,y) = a((z * x) * (y \ (x * y)),(z * x) * (y \ (x * y)),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,50446,a(flip),b,50447,a),flip(a)].">
      <j1 rule="hyper" parents="373 50446 50447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50460">
    <literal><![CDATA[
      L(a((x \ (y * (z * x))) * y,a(y,z,x) * z,u),y,y) = a((z * x) * T(x,y),(z * x) * (y \ (x * y)),u)
    ]]></literal>
    <justification jstring="[para(22(a,2),50459(a,2,1,2))].">
      <j1 rule="para" parents="22 50459"/>
    </justification>
  </clause>

  <clause id="50461">
    <literal><![CDATA[
      L(a((x \ (y * (z * x))) * y,a(y,z,x) * z,u),y,y) = a((z * x) * T(x,y),(z * x) * T(x,y),u)
    ]]></literal>
    <justification jstring="[para(22(a,2),50460(a,2,2,2))].">
      <j1 rule="para" parents="22 50460"/>
    </justification>
  </clause>

  <clause id="50462">
    <literal><![CDATA[
      L(a((x \ (y * (z * x))) * y,a(y,z,x) * z,u),y,y) = a((z * x) * T(x,y),(z * x) * x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,31896,a(flip),b,50461,a),flip(a)].">
      <j1 rule="hyper" parents="373 31896 50461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50464">
    <literal><![CDATA[
      L(a((x \ (y * (z * x))) * y,a(y,z,x) * z,u),y,y) = a((z * x) * T(x,y),L(z,x,x),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32116,a(flip),b,50462,a),flip(a)].">
      <j1 rule="hyper" parents="373 32116 50462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50465">
    <literal><![CDATA[
      L(a((x \ (y * (z * x))) * y,a(y,z,x) * z,u),y,y) = a((z * x) * x,L(z,x,x),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32361,a(flip),b,50464,a),flip(a)].">
      <j1 rule="hyper" parents="373 32361 50464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50467">
    <literal><![CDATA[
      L(a((x \ (y * (z * x))) * y,a(y,z,x) * z,u),y,y) = a(L(z,x,x),L(z,x,x),u)
    ]]></literal>
    <justification jstring="[hyper(373,a,26867,a(flip),b,50465,a),flip(a)].">
      <j1 rule="hyper" parents="373 26867 50465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50468">
    <literal><![CDATA[
      L(a((x \ (y * (z * x))) * y,a(y,z,x) * z,u),y,y) = a(z,z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,35139,a(flip),b,50467,a),flip(a)].">
      <j1 rule="hyper" parents="373 35139 50467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50470">
    <literal><![CDATA[
      L(a((x \ (y * (z * x))) * y,z * a(x,z,y),u),y,y) = a(z,z,u)
    ]]></literal>
    <justification jstring="[para(44901(a,1),50468(a,1,1))].">
      <j1 rule="para" parents="44901 50468"/>
    </justification>
  </clause>

  <clause id="50471">
    <literal><![CDATA[
      a((x \ (y * (z * x))) * y,z * a(x,z,y),L(u,y,y)) = a(z,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46493,a,b,50470,a)].">
      <j1 rule="hyper" parents="64 46493 50470"/>
    </justification>
  </clause>

  <clause id="50472">
    <literal><![CDATA[
      a(x \ (y \ (x * (z * y))),z * a(y,z,x),u) = a(z,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46604,a(flip),b,50471,a)].">
      <j1 rule="hyper" parents="64 46604 50471"/>
    </justification>
  </clause>

  <clause id="50473">
    <literal><![CDATA[
      a(x * a(y,x,z),x * a(z,x,y),u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,35818,a(flip),b,50472,a)].">
      <j1 rule="hyper" parents="64 35818 50472"/>
    </justification>
  </clause>

  <clause id="50474">
    <literal><![CDATA[
      a(x,x * a(y,x,z),L(u,z,y)) = a(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46740,a(flip),b,50473,a)].">
      <j1 rule="hyper" parents="64 46740 50473"/>
    </justification>
  </clause>

  <clause id="50475">
    <literal><![CDATA[
      a(x,x * a(y,x,z),L(L(u,z,y),z,y)) = a(x * a(z,x,y),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,46727,a,b,50474,a),flip(a)].">
      <j1 rule="hyper" parents="373 46727 50474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50476">
    <literal><![CDATA[
      a(x * a(y,x,z),x,u) = a(x,x * a(z,x,y),u)
    ]]></literal>
    <justification jstring="[hyper(64,a,39064,a(flip),b,50475,a),flip(a)].">
      <j1 rule="hyper" parents="64 39064 50475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50478">
    <literal><![CDATA[
      a(x,x * a(y,x,y * z),u) = a(x,x,L(L(u,y,y * z),z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,46931,a(flip),b,50476,a),flip(a)].">
      <j1 rule="hyper" parents="64 46931 50476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50479">
    <literal><![CDATA[
      a(x,x * a(y,x,y * z),u) = a(x,x,L(L(u,y,z * y),z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,27719,a,b,50478,a),flip(a)].">
      <j1 rule="hyper" parents="373 27719 50478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50480">
    <literal><![CDATA[
      a(x,x * a(y,x,y * z),u) = a(x,x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,50165,a(flip),b,50479,a),flip(a)].">
      <j1 rule="hyper" parents="373 50165 50479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50481">
    <literal><![CDATA[
      (a(x,y * a(z,y,z * u),y) * w) * L(w \ x,w,a(y,y,L(w,z,u))) = R(x,y * a(z,y,z * u),y)
    ]]></literal>
    <justification jstring="[para(50480(a,1),46978(a,1,2,3))].">
      <j1 rule="para" parents="50480 46978"/>
    </justification>
  </clause>

  <clause id="50482">
    <literal><![CDATA[
      (a(x,y,y * a(z,y,z * u)) * w) * L(w \ x,w,a(y,y,L(w,z,u))) = R(x,y * a(z,y,z * u),y)
    ]]></literal>
    <justification jstring="[para(50272(a,1),50481(a,1,1,1))].">
      <j1 rule="para" parents="50272 50481"/>
    </justification>
  </clause>

  <clause id="50483">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) / z) \ a((x \ ((x * y) * z)) / z,z \ (x \ ((x * y) * z)),(y * u) * a(x,y,z))) * ((x \ ((x * y) * z)) / z) = a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(31895(a,1),33560(a,1,1,2))].">
      <j1 rule="para" parents="31895 33560"/>
    </justification>
  </clause>

  <clause id="50484">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) / z) \ a(z \ (x \ ((x * y) * z)),z \ (x \ ((x * y) * z)),(y * u) * a(x,y,z))) * ((x \ ((x * y) * z)) / z) = a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(26785(a,1),50483(a,1,1,2))].">
      <j1 rule="para" parents="26785 50483"/>
    </justification>
  </clause>

  <clause id="50485">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) / z) \ a(z * (x \ ((x * y) * z)),z * (x \ ((x * y) * z)),(y * u) * a(x,y,z))) * ((x \ ((x * y) * z)) / z) = a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(50439(a,1),50484(a,1,1,2))].">
      <j1 rule="para" parents="50439 50484"/>
    </justification>
  </clause>

  <clause id="50486">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) / z) \ a(x * (x * y),x * (x * y),(y * u) * a(x,y,z))) * ((x \ ((x * y) * z)) / z) = a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(50457(a,1),50485(a,1,1,2))].">
      <j1 rule="para" parents="50457 50485"/>
    </justification>
  </clause>

  <clause id="50487">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) / z) \ a(x * (x * y),L(y,x,x),(y * u) * a(x,y,z))) * ((x \ ((x * y) * z)) / z) = a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(11968(a,1),50486(a,1,1,2))].">
      <j1 rule="para" parents="11968 50486"/>
    </justification>
  </clause>

  <clause id="50489">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) / z) \ a(y,L(y,x,x),L((y * u) * a(x,y,z),x,x))) * ((x \ ((x * y) * z)) / z) = a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(46582(a,1),50487(a,1,1,2))].">
      <j1 rule="para" parents="46582 50487"/>
    </justification>
  </clause>

  <clause id="50490">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) / z) \ a(y,y,L(L((y * u) * a(x,y,z),x,x),x,x))) * ((x \ ((x * y) * z)) / z) = a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(39520(a,1),50489(a,1,1,2))].">
      <j1 rule="para" parents="39520 50489"/>
    </justification>
  </clause>

  <clause id="50491">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) / z) \ a(y,y,(y * u) * a(x,y,z))) * ((x \ ((x * y) * z)) / z) = a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(38936(a,1),50490(a,1,1,2))].">
      <j1 rule="para" parents="38936 50490"/>
    </justification>
  </clause>

  <clause id="50492">
    <literal><![CDATA[
      (((x \ ((x * y) * z)) / z) \ a(y,y,y * (u * a(x,y,z)))) * ((x \ ((x * y) * z)) / z) = a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(32753(a,1),50491(a,1,1,2))].">
      <j1 rule="para" parents="32753 50491"/>
    </justification>
  </clause>

  <clause id="50495">
    <literal><![CDATA[
      a(x,x,x * (y * a(z,x,u))) * K((z \ ((z * x) * u)) \ u,u \ (z \ ((z * x) * u))) = a((z \ ((z * x) * u)) / u,(z \ ((z * x) * u)) / u,L(y,x,a(z,x,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,26954,a(flip),b,50492,a)].">
      <j1 rule="hyper" parents="64 26954 50492"/>
    </justification>
  </clause>

  <clause id="50496">
    <literal><![CDATA[
      a(x,x,x * (y * a(z,x,u))) * K((z \ ((z * x) * u)) \ u,(u \ (z \ (z * x))) * u) = a((z \ ((z * x) * u)) / u,(z \ ((z * x) * u)) / u,L(y,x,a(z,x,u)))
    ]]></literal>
    <justification jstring="[para(28460(a,1),50495(a,1,2))].">
      <j1 rule="para" parents="28460 50495"/>
    </justification>
  </clause>

  <clause id="50497">
    <literal><![CDATA[
      a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z))) = a(y,y,y * (u * a(x,y,z))) * K((x \ ((x * y) * z)) \ z,(z \ y) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),50496(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="9 50496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50498">
    <literal><![CDATA[
      a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z))) = a(y,y,y * (u * a(x,y,z))) * K((x \ ((x * y) * z)) \ z,T(y,z))
    ]]></literal>
    <justification jstring="[para(11123(a,1),50497(a,2,2))].">
      <j1 rule="para" parents="11123 50497"/>
    </justification>
  </clause>

  <clause id="50499">
    <literal><![CDATA[
      a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z))) = a(y,y,y * (u * a(x,y,z))) * K(z / (x \ ((x * y) * z)),y)
    ]]></literal>
    <justification jstring="[para(8204(a,1),50498(a,2,2))].">
      <j1 rule="para" parents="8204 50498"/>
    </justification>
  </clause>

  <clause id="50500">
    <literal><![CDATA[
      a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z))) = a(y,y,y * (u * a(x,y,z))) * K((x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(28504(a,1),50499(a,2,2))].">
      <j1 rule="para" parents="28504 50499"/>
    </justification>
  </clause>

  <clause id="50501">
    <literal><![CDATA[
      a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z))) = a(y,y,y * (u * a(x,y,z))) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(4354(a,1),50500(a,2,2))].">
      <j1 rule="para" parents="4354 50500"/>
    </justification>
  </clause>

  <clause id="50503">
    <literal><![CDATA[
      a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z))) = y * R(K(y \ 1,y) / y,y,u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,30734,a(flip),b,50501,a),flip(a)].">
      <j1 rule="hyper" parents="373 30734 50501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50505">
    <literal><![CDATA[
      a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z))) = y * R(y \ 1,y,u * a(x,y,z))
    ]]></literal>
    <justification jstring="[para(415(a,1),50503(a,2,2,1))].">
      <j1 rule="para" parents="415 50503"/>
    </justification>
  </clause>

  <clause id="50506">
    <literal><![CDATA[
      a((x \ ((x * y) * z)) / z,(x \ ((x * y) * z)) / z,L(u,y,a(x,y,z))) = a(y,y,u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,45383,a,b,50505,a),flip(a)].">
      <j1 rule="hyper" parents="373 45383 50505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50507">
    <literal><![CDATA[
      a((x \ ((x * y) * z)) / z,z \ (x \ ((x * y) * z)),L(u,y,a(x,y,z))) = a(y,y,u * a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(32042,a,50506,a)].">
      <j1 rule="hyper" parents="32042 50506"/>
    </justification>
  </clause>

  <clause id="50508">
    <literal><![CDATA[
      a(x \ (y \ ((y * z) * x)),x \ (y \ ((y * z) * x)),L(u,z,a(y,z,x))) = a(z,z,u * a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(26880,a,50507,a)].">
      <j1 rule="hyper" parents="26880 50507"/>
    </justification>
  </clause>

  <clause id="50509">
    <literal><![CDATA[
      a(x * (y \ ((y * z) * x)),x * (y \ ((y * z) * x)),L(u,z,a(y,z,x))) = a(z,z,u * a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,50439,a(flip),b,50508,a)].">
      <j1 rule="hyper" parents="64 50439 50508"/>
    </justification>
  </clause>

  <clause id="50510">
    <literal><![CDATA[
      a(x * (x * y),x * (x * y),L(z,y,a(x,y,u))) = a(y,y,z * a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,50457,a(flip),b,50509,a)].">
      <j1 rule="hyper" parents="64 50457 50509"/>
    </justification>
  </clause>

  <clause id="50512">
    <literal><![CDATA[
      a(x * (x * y),L(y,x,x),L(z,y,a(x,y,u))) = a(y,y,z * a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,11968,a(flip),b,50510,a)].">
      <j1 rule="hyper" parents="64 11968 50510"/>
    </justification>
  </clause>

  <clause id="50513">
    <literal><![CDATA[
      a(x,L(x,y,y),L(L(z,x,a(y,x,u)),y,y)) = a(x,x,z * a(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46582,a(flip),b,50512,a)].">
      <j1 rule="hyper" parents="64 46582 50512"/>
    </justification>
  </clause>

  <clause id="50514">
    <literal><![CDATA[
      a(x,x,L(L(L(y,x,a(z,x,u)),z,z),z,z)) = a(x,x,y * a(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39676,a(flip),b,50513,a)].">
      <j1 rule="hyper" parents="64 39676 50513"/>
    </justification>
  </clause>

  <clause id="50515">
    <literal><![CDATA[
      a(x,x,L(y,x,a(z,x,u))) = a(x,x,y * a(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39064,a(flip),b,50514,a)].">
      <j1 rule="hyper" parents="64 39064 50514"/>
    </justification>
  </clause>

  <clause id="50517">
    <literal><![CDATA[
      a(x,x,y * a(z,x,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,39645,a(flip),b,50515,a),flip(a)].">
      <j1 rule="hyper" parents="64 39645 50515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50518">
    <literal><![CDATA[
      a(x,x,a(y,x,z) * u) = a(x,x,u)
    ]]></literal>
    <justification jstring="[hyper(27453,a,50517,a)].">
      <j1 rule="hyper" parents="27453 50517"/>
    </justification>
  </clause>

  <clause id="50520">
    <literal><![CDATA[
      (a(x,y,z) * u) * a(w,v5,a(y,y,u)) = L(a(x,y,z) * u,y,a(y,v5,w))
    ]]></literal>
    <justification jstring="[para(50518(a,1),43921(a,1,2,3))].">
      <j1 rule="para" parents="50518 43921"/>
    </justification>
  </clause>

  <clause id="50521">
    <literal><![CDATA[
      L(a(x,y,z) * u,y,a(y,w,v5)) = a(x,y,z) * L(u,y,a(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,46794,a(flip),b,50520,a),flip(a)].">
      <j1 rule="hyper" parents="64 46794 50520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50522">
    <literal><![CDATA[
      L(a(x,y,z) * u,y,a(y,w,v5)) = a(x,y,z) * L(u,w,a(v5,y,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,47440,a,b,50521,a),flip(a)].">
      <j1 rule="hyper" parents="373 47440 50521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50523">
    <literal><![CDATA[
      a(x,y,y) * (z * L(a(x,y,y) * (a(x,y,y) \ (z \ u)),y,a(y,z,x))) = 1 * L(z * (((a(x,y,y) \ 1) * z) \ u),y,a(y,1,x))
    ]]></literal>
    <justification jstring="[para(50522(a,2),49279(a,1,2,2))].">
      <j1 rule="para" parents="50522 49279"/>
    </justification>
  </clause>

  <clause id="50524">
    <literal><![CDATA[
      a(x,y,y) * (z * L(z \ u,y,a(y,z,x))) = 1 * L(z * (((a(x,y,y) \ 1) * z) \ u),y,a(y,1,x))
    ]]></literal>
    <justification jstring="[para(10(a,1),50523(a,1,2,2,1))].">
      <j1 rule="para" parents="10 50523"/>
    </justification>
  </clause>

  <clause id="50525">
    <literal><![CDATA[
      1 * L(x * (((a(y,z,z) \ 1) * x) \ u),z,a(z,1,y)) = (x * a(y,z,z)) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,47445,a(flip),b,50524,a),flip(a)].">
      <j1 rule="hyper" parents="64 47445 50524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50527">
    <literal><![CDATA[
      1 * L(x * ((a(y,z,z) \ x) \ u),z,a(z,1,y)) = (x * a(y,z,z)) * (x \ u)
    ]]></literal>
    <justification jstring="[para(37824(a,1),50525(a,1,2,1,2,1))].">
      <j1 rule="para" parents="37824 50525"/>
    </justification>
  </clause>

  <clause id="50528">
    <literal><![CDATA[
      1 * L(x * ((a(y,z,z) \ x) \ u),z,1) = (x * a(y,z,z)) * (x \ u)
    ]]></literal>
    <justification jstring="[para(618(a,1),50527(a,1,2,3))].">
      <j1 rule="para" parents="618 50527"/>
    </justification>
  </clause>

  <clause id="50530">
    <literal><![CDATA[
      1 * (x * ((a(y,z,z) \ x) \ u)) = (x * a(y,z,z)) * (x \ u)
    ]]></literal>
    <justification jstring="[para(621(a,1),50528(a,1,2))].">
      <j1 rule="para" parents="621 50528"/>
    </justification>
  </clause>

  <clause id="50531">
    <literal><![CDATA[
      (x * a(y,z,z)) * (x \ u) = x * ((a(y,z,z) \ x) \ u)
    ]]></literal>
    <justification jstring="[hyper(147,a,50530,a),flip(a)].">
      <j1 rule="hyper" parents="147 50530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50533">
    <literal><![CDATA[
      (x \ (x * ((a(y,z,z) \ x) \ u))) / (x \ u) = a(x,a(y,z,z),x \ u) * a(y,z,z)
    ]]></literal>
    <justification jstring="[para(50531(a,1),33279(a,1,1,2))].">
      <j1 rule="para" parents="50531 33279"/>
    </justification>
  </clause>

  <clause id="50534">
    <literal><![CDATA[
      (x \ y) * a(z,u,u * a(x \ y,u,x)) = x \ (x * ((a(z,u,u) \ x) \ y))
    ]]></literal>
    <justification jstring="[para(50531(a,1),47011(a,1,2)),flip(a)].">
      <j1 rule="para" parents="50531 47011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50535">
    <literal><![CDATA[
      (x \ y) * a(z,u,u * a(x \ y,u,x)) = (a(z,u,u) \ x) \ y
    ]]></literal>
    <justification jstring="[hyper(373,a,9,a(flip),b,50534,a),flip(a)].">
      <j1 rule="hyper" parents="373 9 50534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50537">
    <literal><![CDATA[
      (x \ y) * a(z,u,u * a(y * x,u,x)) = (a(z,u,u) \ x) \ y
    ]]></literal>
    <justification jstring="[para(46084(a,1),50535(a,1,2,3,2))].">
      <j1 rule="para" parents="46084 50535"/>
    </justification>
  </clause>

  <clause id="50538">
    <literal><![CDATA[
      (x \ y) * a(z,u,L(u,x,y)) = (a(z,u,u) \ x) \ y
    ]]></literal>
    <justification jstring="[para(49509(a,1),50537(a,1,2))].">
      <j1 rule="para" parents="49509 50537"/>
    </justification>
  </clause>

  <clause id="50539">
    <literal><![CDATA[
      (x \ y) \ ((a(z,u,u) \ x) \ y) = a(z,u,L(u,x,y))
    ]]></literal>
    <justification jstring="[hyper(149,a,50538,a)].">
      <j1 rule="hyper" parents="149 50538"/>
    </justification>
  </clause>

  <clause id="50540">
    <literal><![CDATA[
      ((a(x,y,y) \ z) \ u) / (z \ u) = a(z,a(x,y,y),z \ u) * a(x,y,y)
    ]]></literal>
    <justification jstring="[para(9(a,1),50533(a,1,1))].">
      <j1 rule="para" parents="9 50533"/>
    </justification>
  </clause>

  <clause id="50541">
    <literal><![CDATA[
      (x \ y) \ ((a(z,u,u) \ x) \ y) = a(x,a(z,u,u),x \ y) * a(z,u,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,36489,a(flip),b,50540,a)].">
      <j1 rule="hyper" parents="64 36489 50540"/>
    </justification>
  </clause>

  <clause id="50543">
    <literal><![CDATA[
      (x \ y) \ ((a(z,u,u) \ x) \ y) = a(x,a(z,u,u),x * y) * a(z,u,u)
    ]]></literal>
    <justification jstring="[para(42839(a,1),50541(a,2,1))].">
      <j1 rule="para" parents="42839 50541"/>
    </justification>
  </clause>

  <clause id="50544">
    <literal><![CDATA[
      a(x,y,y * a(z,y,z * u)) = (z \ u) \ ((a(x,y,y) \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(373,a,47015,a(flip),b,50543,a)].">
      <j1 rule="hyper" parents="373 47015 50543"/>
    </justification>
  </clause>

  <clause id="50545">
    <literal><![CDATA[
      a(x,y,y * a(z,y,z * u)) = a(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,50539,a(flip),b,50544,a),flip(a)].">
      <j1 rule="hyper" parents="373 50539 50544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50546">
    <literal><![CDATA[
      (a(x,y,L(y,z,u)) * w) * L(w \ x,w,a(y,y,L(w,z,u))) = R(x,y * a(z,y,z * u),y)
    ]]></literal>
    <justification jstring="[para(50545(a,1),50482(a,1,1,1))].">
      <j1 rule="para" parents="50545 50482"/>
    </justification>
  </clause>

  <clause id="50547">
    <literal><![CDATA[
      R(x,y * a(z,y,z * u),y) = (a(x,y,L(y,z,u)) * w) * (w \ x)
    ]]></literal>
    <justification jstring="[para(45697(a,1),50546(a,1,2)),flip(a)].">
      <j1 rule="para" parents="45697 50546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50548">
    <literal><![CDATA[
      R(x,y * a(z,y,z * u),y) = R(x,y,L(L(y,z,u),w,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,46718,a(flip),b,50547,a),flip(a)].">
      <j1 rule="hyper" parents="373 46718 50547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50550">
    <literal><![CDATA[
      R(x,y * a(z,y,z * u),y) = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,48867,a(flip),b,50548,a),flip(a)].">
      <j1 rule="hyper" parents="373 48867 50548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50551">
    <literal><![CDATA[
      R(x,y,y * a(z * u,y,z)) = R(x,y,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,50242,a(flip),b,50550,a)].">
      <j1 rule="hyper" parents="64 50242 50550"/>
    </justification>
  </clause>

  <clause id="50552">
    <literal><![CDATA[
      L(x,a(y,x,z * (x * y)),u) = (u * (1 / x)) \ R(u,x,L(x,y,x * z))
    ]]></literal>
    <justification jstring="[para(50551(a,1),50280(a,1,2)),flip(a)].">
      <j1 rule="para" parents="50551 50280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50553">
    <literal><![CDATA[
      L(x,a(y,x,z * (x * y)),u) = (u * (1 / x)) \ R(u,x,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(48312(a,1),50552(a,2,2))].">
      <j1 rule="para" parents="48312 50552"/>
    </justification>
  </clause>

  <clause id="50554">
    <literal><![CDATA[
      L(x,a(y,x,z * (x * y)),u) = L(x,x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,48713,a(flip),b,50553,a),flip(a)].">
      <j1 rule="hyper" parents="373 48713 50553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50555">
    <literal><![CDATA[
      L(x,a(y,x,z),z * u) = L(x,x,a(u,z,y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,50246,a(flip),b,50554,a)].">
      <j1 rule="hyper" parents="64 50246 50554"/>
    </justification>
  </clause>

  <clause id="50556">
    <literal><![CDATA[
      L(x,a(y,x,z),z * u) = L(x,x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,44165,a(flip),b,50555,a),flip(a)].">
      <j1 rule="hyper" parents="373 44165 50555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50557">
    <literal><![CDATA[
      L(x,x,a(y \ (z * x),z,u)) = L(x,a(y,x,u),z * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,50265,a(flip),b,50556,a),flip(a)].">
      <j1 rule="hyper" parents="64 50265 50556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50558">
    <literal><![CDATA[
      L(x,x,a(y * (z * x),z,u)) = L(x,a(y,x,u),z * x)
    ]]></literal>
    <justification jstring="[hyper(64,a,49792,a(flip),b,50557,a)].">
      <j1 rule="hyper" parents="64 49792 50557"/>
    </justification>
  </clause>

  <clause id="50559">
    <literal><![CDATA[
      L(x,a(y,x,z),u * x) = L(x,x,a(z,u,y * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47075,a(flip),b,50558,a),flip(a)].">
      <j1 rule="hyper" parents="64 47075 50558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50560">
    <literal><![CDATA[
      L(x,a(y,x,z),u * x) = L(x,a(y,x,u),z)
    ]]></literal>
    <justification jstring="[hyper(373,a,50293,a(flip),b,50559,a),flip(a)].">
      <j1 rule="hyper" parents="373 50293 50559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50561">
    <literal><![CDATA[
      L(L(x,a(y,x,z),u),u,a(z,x,y)) = L(x,x,a(z,y,u))
    ]]></literal>
    <justification jstring="[para(50560(a,1),50324(a,1,1))].">
      <j1 rule="para" parents="50560 50324"/>
    </justification>
  </clause>

  <clause id="50562">
    <literal><![CDATA[
      L(x,a(y,x,z),u * x) = L(x,x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,50240,a(flip),b,50561,a)].">
      <j1 rule="hyper" parents="64 50240 50561"/>
    </justification>
  </clause>

  <clause id="50563">
    <literal><![CDATA[
      L(x,a(y,x,z),u) = L(x,x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,50560,a(flip),b,50562,a)].">
      <j1 rule="hyper" parents="64 50560 50562"/>
    </justification>
  </clause>

  <clause id="50564">
    <literal><![CDATA[
      L(L(x,x,a(y,z,u)),z,a(z * u,x,y)) = x
    ]]></literal>
    <justification jstring="[para(50563(a,1),50292(a,1,1))].">
      <j1 rule="para" parents="50563 50292"/>
    </justification>
  </clause>

  <clause id="50565">
    <literal><![CDATA[
      L(L(x,a(y,x,z),u),x,a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,50289,a(flip),b,50564,a)].">
      <j1 rule="hyper" parents="64 50289 50564"/>
    </justification>
  </clause>

  <clause id="50566">
    <literal><![CDATA[
      L(L(x,x,a(y,z,u)),x,a(y,u,z)) = x
    ]]></literal>
    <justification jstring="[para(50563(a,1),50565(a,1,1))].">
      <j1 rule="para" parents="50563 50565"/>
    </justification>
  </clause>

  <clause id="50567">
    <literal><![CDATA[
      L(x,a(y,x,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,50290,a(flip),b,50566,a)].">
      <j1 rule="hyper" parents="64 50290 50566"/>
    </justification>
  </clause>

  <clause id="50569">
    <literal><![CDATA[
      a(x,a(y,y,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,50566,a(flip),b,47971,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="138 50566 47971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50572">
    <literal><![CDATA[
      L(x,x,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,50563,a(flip),b,50567,a)].">
      <j1 rule="hyper" parents="64 50563 50567"/>
    </justification>
  </clause>

  <clause id="50578">
    <literal><![CDATA[
      a(x,a(y,z,z),u) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,50567,a(flip),b,50284,a),flip(a)].">
      <j1 rule="hyper" parents="138 50567 50284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50580">
    <literal><![CDATA[
      a(x,y,a(z,y,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,50567,a(flip),b,50230,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="138 50567 50230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50599">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,49447,a(flip),b,50569,a)].">
      <j1 rule="hyper" parents="64 49447 50569"/>
    </justification>
  </clause>

  <clause id="50600">
    <literal><![CDATA[
      L(x,a(y,y,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,50569,a)].">
      <j1 rule="hyper" parents="53 50569"/>
    </justification>
  </clause>

  <clause id="50626">
    <literal><![CDATA[
      a(x,y,a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,50572,a(flip),b,47322,a),flip(a)].">
      <j1 rule="hyper" parents="140 50572 47322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50629">
    <literal><![CDATA[
      a(x,x,a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,50572,a(flip),b,45132,a),flip(a)].">
      <j1 rule="hyper" parents="140 50572 45132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50635">
    <literal><![CDATA[
      a(x,y,z) * (u \ 1) = u \ a(x,y,z)
    ]]></literal>
    <justification jstring="[para(50572(a,1),24639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="50572 24639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50660">
    <literal><![CDATA[
      (x * a(y,z,x)) * u = x * (a(y,z,x) * u)
    ]]></literal>
    <justification jstring="[para(50572(a,1),46035(a,1,1)),flip(a)].">
      <j1 rule="para" parents="50572 46035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50661">
    <literal><![CDATA[
      (a(x,y,z) / u) \ 1 = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(50572(a,1),46992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="50572 46992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50662">
    <literal><![CDATA[
      a(x,y,z) * (u * x) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(50572(a,1),47039(a,1,2,2))].">
      <j1 rule="para" parents="50572 47039"/>
    </justification>
  </clause>

  <clause id="50664">
    <literal><![CDATA[
      (x * a(y,z,u)) * z = a(y,z,u) * (x * z)
    ]]></literal>
    <justification jstring="[para(50572(a,1),47445(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="50572 47445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50667">
    <literal><![CDATA[
      (x * a(y,z,z)) * u = x * (a(y,z,z) * u)
    ]]></literal>
    <justification jstring="[hyper(1432,a,50578,a)].">
      <j1 rule="hyper" parents="1432 50578"/>
    </justification>
  </clause>

  <clause id="50675">
    <literal><![CDATA[
      L(x,a(y,z,z),u) = x
    ]]></literal>
    <justification jstring="[hyper(53,a,50578,a)].">
      <j1 rule="hyper" parents="53 50578"/>
    </justification>
  </clause>

  <clause id="50682">
    <literal><![CDATA[
      a(x,y,a(z,y,u)) * w = w
    ]]></literal>
    <justification jstring="[hyper(144,a,50580,a,b,76,a)].">
      <j1 rule="hyper" parents="144 50580 76"/>
    </justification>
  </clause>

  <clause id="50700">
    <literal><![CDATA[
      a(x,y,a(z,u,y)) = w \ w
    ]]></literal>
    <justification jstring="[hyper(373,a,68,a,b,50599,a),flip(a)].">
      <j1 rule="hyper" parents="373 68 50599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50706">
    <literal><![CDATA[
      L(a(x,y,z),z,u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,50599,a)].">
      <j1 rule="hyper" parents="53 50599"/>
    </justification>
  </clause>

  <clause id="50711">
    <literal><![CDATA[
      L(a(x,y,y) \ 1,z,u) = a(x,y,y) \ 1
    ]]></literal>
    <justification jstring="[para(50599(a,1),43885(a,1,2)),flip(a)].">
      <j1 rule="para" parents="50599 43885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50749">
    <literal><![CDATA[
      L(x,y,a(z,u,u)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,49519,a(flip),b,50600,a(flip))].">
      <j1 rule="hyper" parents="35 49519 50600"/>
    </justification>
  </clause>

  <clause id="50752">
    <literal><![CDATA[
      (a(x,x,y) * z) * u = z * (a(x,x,y) * u)
    ]]></literal>
    <justification jstring="[para(50600(a,1),31792(a,1,1)),flip(a)].">
      <j1 rule="para" parents="50600 31792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50785">
    <literal><![CDATA[
      L(a(x,y,z),x,u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,50626,a)].">
      <j1 rule="hyper" parents="53 50626"/>
    </justification>
  </clause>

  <clause id="50802">
    <literal><![CDATA[
      L(a(x,y,z),u,u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,50629,a)].">
      <j1 rule="hyper" parents="53 50629"/>
    </justification>
  </clause>

  <clause id="50816">
    <literal><![CDATA[
      (x * a(y,z,z)) \ u = a(y,z,z) \ (x \ u)
    ]]></literal>
    <justification jstring="[hyper(710,a,50675,a),flip(a)].">
      <j1 rule="hyper" parents="710 50675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50832">
    <literal><![CDATA[
      a(x,y,y) \ (z * u) = z * (a(x,y,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,50395,a(flip),b,50675,a)].">
      <j1 rule="hyper" parents="64 50395 50675"/>
    </justification>
  </clause>

  <clause id="50833">
    <literal><![CDATA[
      x \ (a(y,z,z) * u) = a(y,z,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,50345,a(flip),b,50675,a),flip(a)].">
      <j1 rule="hyper" parents="64 50345 50675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50834">
    <literal><![CDATA[
      (x * y) * a(z,u,u) = x * (a(z,u,u) * y)
    ]]></literal>
    <justification jstring="[hyper(64,a,50094,a(flip),b,50675,a)].">
      <j1 rule="hyper" parents="64 50094 50675"/>
    </justification>
  </clause>

  <clause id="50835">
    <literal><![CDATA[
      (a(x,y,y) \ z) \ u = a(x,y,y) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,43395,a(flip),b,50675,a),flip(a)].">
      <j1 rule="hyper" parents="64 43395 50675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50840">
    <literal><![CDATA[
      L(x,y,a(z,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,49477,a(flip),b,50675,a(flip))].">
      <j1 rule="hyper" parents="40 49477 50675"/>
    </justification>
  </clause>

  <clause id="50841">
    <literal><![CDATA[
      L(x,y,a(z,u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(40,a,49476,a(flip),b,50675,a(flip))].">
      <j1 rule="hyper" parents="40 49476 50675"/>
    </justification>
  </clause>

  <clause id="50842">
    <literal><![CDATA[
      L(x,y,a(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,50018,a(flip),b,50675,a(flip))].">
      <j1 rule="hyper" parents="36 50018 50675"/>
    </justification>
  </clause>

  <clause id="50843">
    <literal><![CDATA[
      (x * (a(y,z,z) * u)) \ ((x * a(y,z,z)) * (u * w)) = L(w,L(u,a(y,z,z),x),x * a(y,z,z))
    ]]></literal>
    <justification jstring="[para(50675(a,1),601(a,1,2,2,1))].">
      <j1 rule="para" parents="50675 601"/>
    </justification>
  </clause>

  <clause id="50845">
    <literal><![CDATA[
      (a(x,y,y) * z) * u = z * (a(x,y,y) * u)
    ]]></literal>
    <justification jstring="[para(50675(a,1),31792(a,1,1)),flip(a)].">
      <j1 rule="para" parents="50675 31792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50898">
    <literal><![CDATA[
      L(x,y,L(y,z,u)) = L(x,y,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,47496,a(flip),b,50749,a)].">
      <j1 rule="hyper" parents="64 47496 50749"/>
    </justification>
  </clause>

  <clause id="50899">
    <literal><![CDATA[
      L(x,y,L(z,u,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47495,a(flip),b,50749,a)].">
      <j1 rule="hyper" parents="64 47495 50749"/>
    </justification>
  </clause>

  <clause id="50900">
    <literal><![CDATA[
      L(x,y,L(z,z,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47487,a(flip),b,50749,a)].">
      <j1 rule="hyper" parents="64 47487 50749"/>
    </justification>
  </clause>

  <clause id="50903">
    <literal><![CDATA[
      (x * a(y,z,z)) \ u = x \ (a(y,z,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,42175,a(flip),b,50749,a),flip(a)].">
      <j1 rule="hyper" parents="64 42175 50749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50918">
    <literal><![CDATA[
      (x * y) * a(z,u,u) = x * (y * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(50749(a,1),28800(a,1,1)),flip(a)].">
      <j1 rule="para" parents="50749 28800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50922">
    <literal><![CDATA[
      a(x,x,y) * (z * u) = z * (a(x,x,y) * u)
    ]]></literal>
    <justification jstring="[para(50749(a,1),42211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="50749 42211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50987">
    <literal><![CDATA[
      L(x,y,z \ u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(50840(a,1),47535(a,1,1)),flip(a)].">
      <j1 rule="para" parents="50840 47535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="50988">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(50840(a,1),47536(a,1,1)),flip(a)].">
      <j1 rule="para" parents="50840 47536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51009">
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = u * a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,46760,a(flip),b,50841,a),flip(a)].">
      <j1 rule="hyper" parents="64 46760 50841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51072">
    <literal><![CDATA[
      (x * y) * a(z,u,x * y) = x * (y * a(z,u,x * y))
    ]]></literal>
    <justification jstring="[para(50842(a,1),46289(a,1,1,1))].">
      <j1 rule="para" parents="50842 46289"/>
    </justification>
  </clause>

  <clause id="51077">
    <literal><![CDATA[
      a(x,y,L(z,y,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47408,a(flip),b,50682,a)].">
      <j1 rule="hyper" parents="64 47408 50682"/>
    </justification>
  </clause>

  <clause id="51083">
    <literal><![CDATA[
      a(x,y,L(z,u,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,47325,a,b,50700,a(flip))].">
      <j1 rule="hyper" parents="40 47325 50700"/>
    </justification>
  </clause>

  <clause id="51084">
    <literal><![CDATA[
      a(x,x,L(y,z,u)) = a(x,x,y)
    ]]></literal>
    <justification jstring="[hyper(40,a,47249,a,b,50700,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="40 47249 50700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51085">
    <literal><![CDATA[
      a(x,y,L(z,z,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,46545,a,b,50700,a(flip))].">
      <j1 rule="hyper" parents="40 46545 50700"/>
    </justification>
  </clause>

  <clause id="51102">
    <literal><![CDATA[
      (x \ y) * a(z,u,x) = L(x,u,z) \ y
    ]]></literal>
    <justification jstring="[para(50706(a,1),45359(a,1,2))].">
      <j1 rule="para" parents="50706 45359"/>
    </justification>
  </clause>

  <clause id="51114">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * R(z,u,w))) = a(L(z,y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,48085,a(flip),b,50785,a)].">
      <j1 rule="hyper" parents="64 48085 50785"/>
    </justification>
  </clause>

  <clause id="51139">
    <literal><![CDATA[
      a(L(x,y,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46057,a,b,50802,a)].">
      <j1 rule="hyper" parents="64 46057 50802"/>
    </justification>
  </clause>

  <clause id="51154">
    <literal><![CDATA[
      (1 / x) * a(y,z,u) = a(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(50802(a,1),24637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="50802 24637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51176">
    <literal><![CDATA[
      L(x,y,L(y,z,u)) = L(x,y,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,50898,a,b,50898,a)].">
      <j1 rule="hyper" parents="373 50898 50898"/>
    </justification>
  </clause>

  <clause id="51209">
    <literal><![CDATA[
      L(x,y,(z \ 1) * u) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,2237,a(flip),b,50899,a)].">
      <j1 rule="hyper" parents="64 2237 50899"/>
    </justification>
  </clause>

  <clause id="51241">
    <literal><![CDATA[
      L(x,y,(z \ u) \ 1) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,34231,a(flip),b,50900,a)].">
      <j1 rule="hyper" parents="64 34231 50900"/>
    </justification>
  </clause>

  <clause id="51257">
    <literal><![CDATA[
      a(x,y,T((y \ 1) \ (z \ u),w)) = a(x,y,(z * (y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,39075,a,b,51077,a)].">
      <j1 rule="hyper" parents="64 39075 51077"/>
    </justification>
  </clause>

  <clause id="51263">
    <literal><![CDATA[
      a(x,y,y \ (z \ (y * u))) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,47650,a(flip),b,51077,a)].">
      <j1 rule="hyper" parents="64 47650 51077"/>
    </justification>
  </clause>

  <clause id="51303">
    <literal><![CDATA[
      a(x * (x * y),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46582,a,b,51083,a)].">
      <j1 rule="hyper" parents="64 46582 51083"/>
    </justification>
  </clause>

  <clause id="51304">
    <literal><![CDATA[
      a((x * y) * y,z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46579,a,b,51083,a)].">
      <j1 rule="hyper" parents="64 46579 51083"/>
    </justification>
  </clause>

  <clause id="51307">
    <literal><![CDATA[
      a(x,y,(z * u) \ (w * w)) = a(x,y,u \ (z \ (w * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47812,a(flip),b,51083,a),flip(a)].">
      <j1 rule="hyper" parents="64 47812 51083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51309">
    <literal><![CDATA[
      a((x \ y) * y,z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46735,a(flip),b,51083,a)].">
      <j1 rule="hyper" parents="64 46735 51083"/>
    </justification>
  </clause>

  <clause id="51310">
    <literal><![CDATA[
      a(x \ y,z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46645,a(flip),b,51083,a),flip(a)].">
      <j1 rule="hyper" parents="64 46645 51083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51311">
    <literal><![CDATA[
      a(x \ y,z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46605,a(flip),b,51083,a)].">
      <j1 rule="hyper" parents="64 46605 51083"/>
    </justification>
  </clause>

  <clause id="51315">
    <literal><![CDATA[
      a(x,y,z * (u \ 1)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38951,a(flip),b,51083,a),flip(a)].">
      <j1 rule="hyper" parents="64 38951 51083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51316">
    <literal><![CDATA[
      a(x,y,(z \ 1) * u) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,38947,a(flip),b,51083,a),flip(a)].">
      <j1 rule="hyper" parents="64 38947 51083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51317">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ u) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38945,a(flip),b,51083,a)].">
      <j1 rule="hyper" parents="64 38945 51083"/>
    </justification>
  </clause>

  <clause id="51318">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ u) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,38939,a(flip),b,51083,a)].">
      <j1 rule="hyper" parents="64 38939 51083"/>
    </justification>
  </clause>

  <clause id="51319">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * w)) = a(x,y,u * (u * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,33093,a(flip),b,51083,a),flip(a)].">
      <j1 rule="hyper" parents="64 33093 51083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51320">
    <literal><![CDATA[
      a(x,y,(z \ u) * (w * w)) = a(x,y,u * (z \ (w * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27798,a(flip),b,51083,a),flip(a)].">
      <j1 rule="hyper" parents="64 27798 51083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51321">
    <literal><![CDATA[
      a(x,y,(z * z) * u) = a(x,y,z * (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27651,a(flip),b,51083,a),flip(a)].">
      <j1 rule="hyper" parents="64 27651 51083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51370">
    <literal><![CDATA[
      (x * (a(y,y,x) * z)) * u = a(y,y,x) * ((x * z) * u)
    ]]></literal>
    <justification jstring="[para(51084(a,1),47133(a,1,1,2,1))].">
      <j1 rule="para" parents="51084 47133"/>
    </justification>
  </clause>

  <clause id="51384">
    <literal><![CDATA[
      a(x * (y * z),u,y) = a(z * (y * x),u,y)
    ]]></literal>
    <justification jstring="[hyper(64,a,50145,a(flip),b,51085,a)].">
      <j1 rule="hyper" parents="64 50145 51085"/>
    </justification>
  </clause>

  <clause id="51385">
    <literal><![CDATA[
      a(x \ (y * z),u,z) = a(z * (x \ y),u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,50125,a(flip),b,51085,a),flip(a)].">
      <j1 rule="hyper" parents="64 50125 51085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51433">
    <literal><![CDATA[
      L(x,y,(z \ (u \ w)) * a(u,u,w)) = L(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47154,a,b,50987,a)].">
      <j1 rule="hyper" parents="64 47154 50987"/>
    </justification>
  </clause>

  <clause id="51441">
    <literal><![CDATA[
      x * L(y,(z * u) * x,z * u) = (z \ u) * (((z \ u) \ x) * y)
    ]]></literal>
    <justification jstring="[para(50987(a,1),48724(a,1,2))].">
      <j1 rule="para" parents="50987 48724"/>
    </justification>
  </clause>

  <clause id="51444">
    <literal><![CDATA[
      a(x * (y \ x),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32512,a(flip),b,51303,a)].">
      <j1 rule="hyper" parents="64 32512 51303"/>
    </justification>
  </clause>

  <clause id="51445">
    <literal><![CDATA[
      a(x / y,z,u) = a(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32413,a(flip),b,51303,a),flip(a)].">
      <j1 rule="hyper" parents="64 32413 51303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51461">
    <literal><![CDATA[
      a(x,y,(z \ x) \ u) = a(x,y,x \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,46674,a(flip),b,51309,a),flip(a)].">
      <j1 rule="hyper" parents="64 46674 51309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51477">
    <literal><![CDATA[
      a(a(x,x,y) * (z \ (x \ y)),u,w) = a((y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,47986,a,b,51310,a)].">
      <j1 rule="hyper" parents="64 47986 51310"/>
    </justification>
  </clause>

  <clause id="51484">
    <literal><![CDATA[
      a(((x \ y) \ (z * y)) * (z * x),u,w) = a(z,x,a(w,u,y * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47365,a(flip),b,51310,a),flip(a)].">
      <j1 rule="hyper" parents="64 47365 51310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51485">
    <literal><![CDATA[
      a(x \ (y * z),u,L(w,x,z)) = a(L(y,z,z) * (z * x),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,46601,a(flip),b,51310,a)].">
      <j1 rule="hyper" parents="64 46601 51310"/>
    </justification>
  </clause>

  <clause id="51488">
    <literal><![CDATA[
      x * R(x \ y,z,u) = y * a(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(145,a,51310,a(flip),b,45241,a),flip(a)].">
      <j1 rule="hyper" parents="145 51310 45241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51549">
    <literal><![CDATA[
      L(x,y,((a(z,u,w) / v5) \ 1) * v6) = L(x,y,(a(w,u,z) * v5) * v6)
    ]]></literal>
    <justification jstring="[para(50661(a,2),48281(a,1,3,1))].">
      <j1 rule="para" parents="50661 48281"/>
    </justification>
  </clause>

  <clause id="51564">
    <literal><![CDATA[
      x * a(a(y,z,u),w * y,(w * y) \ (a(y,z,u) \ x)) = (w * R(y,z,u)) * ((w * y) \ (a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(50662(a,1),960(a,2,1))].">
      <j1 rule="para" parents="50662 960"/>
    </justification>
  </clause>

  <clause id="51581">
    <literal><![CDATA[
      (L(x,y,z) * u) \ (x * u) = a(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(34861,a,51009,a)].">
      <j1 rule="hyper" parents="34861 51009"/>
    </justification>
  </clause>

  <clause id="51639">
    <literal><![CDATA[
      (x \ (1 / x)) * a(y,z,u) = x \ (a(y,z,u) / x)
    ]]></literal>
    <justification jstring="[hyper(139,a,51154,a(flip),b,1104,a),flip(a)].">
      <j1 rule="hyper" parents="139 51154 1104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51749">
    <literal><![CDATA[
      L(x,y,L(y,z,u)) \ L(R(x,w,v5),y,y) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(51176(a,1),47946(a,1,1))].">
      <j1 rule="para" parents="51176 47946"/>
    </justification>
  </clause>

  <clause id="51766">
    <literal><![CDATA[
      a(x,y,((x \ z) \ u) \ z) = a(x,y,u \ ((x \ z) * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,49321,a(flip),b,51316,a),flip(a)].">
      <j1 rule="hyper" parents="64 49321 51316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51783">
    <literal><![CDATA[
      a(x,y,(z * a(u,w,v5)) \ v6) = a(x,y,(z \ a(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,50023,a(flip),b,51318,a)].">
      <j1 rule="hyper" parents="64 50023 51318"/>
    </justification>
  </clause>

  <clause id="51784">
    <literal><![CDATA[
      a(x,y,z \ (u * u)) = a(x,y,(z \ u) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46693,a(flip),b,51318,a)].">
      <j1 rule="hyper" parents="64 46693 51318"/>
    </justification>
  </clause>

  <clause id="51786">
    <literal><![CDATA[
      a(x,y,(z \ (u * u)) * w) = a(x,y,(u * u) * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27697,a(flip),b,51318,a),flip(a)].">
      <j1 rule="hyper" parents="64 27697 51318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51799">
    <literal><![CDATA[
      a(a(x,y,z) * (L(z,y,x) * u),w,v5) = a(z * u,w,v5)
    ]]></literal>
    <justification jstring="[para(51581(a,1),26836(a,1,1,1))].">
      <j1 rule="para" parents="51581 26836"/>
    </justification>
  </clause>

  <clause id="51803">
    <literal><![CDATA[
      L(x \ L(x,x,y),z,u) = a(y,x,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(64,a,33170,a(flip),b,50711,a)].">
      <j1 rule="hyper" parents="64 33170 50711"/>
    </justification>
  </clause>

  <clause id="51809">
    <literal><![CDATA[
      R(R(x,y,z),y * z,L(u \ L(u,u,w),z,x * y)) = ((x * y) * (z * (u \ L(u,u,w)))) / ((y * z) * (a(w,u,u) \ 1))
    ]]></literal>
    <justification jstring="[para(51803(a,1),2293(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="51803 2293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51812">
    <literal><![CDATA[
      a(x,y,z * (u * (a(w,v5,u) * v6))) = a(x,y,z * (v6 * L(u,v5,w)))
    ]]></literal>
    <justification jstring="[para(50660(a,1),47141(a,1,3,2))].">
      <j1 rule="para" parents="50660 47141"/>
    </justification>
  </clause>

  <clause id="51814">
    <literal><![CDATA[
      a(x,y,L(z,u,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(36,a,46524,a,b,50664,a(flip))].">
      <j1 rule="hyper" parents="36 46524 50664"/>
    </justification>
  </clause>

  <clause id="51831">
    <literal><![CDATA[
      a((x * y) \ z,x,u) = a(y \ (x \ z),x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,47710,a(flip),b,51814,a)].">
      <j1 rule="hyper" parents="64 47710 51814"/>
    </justification>
  </clause>

  <clause id="51833">
    <literal><![CDATA[
      a((x * y) \ z,y,u) = a(x \ (y \ z),y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,46596,a(flip),b,51814,a),flip(a)].">
      <j1 rule="hyper" parents="64 46596 51814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51836">
    <literal><![CDATA[
      a(x,y,(y \ z) \ u) = a(x,y,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(630(a,1),51814(a,1,3)),flip(a)].">
      <j1 rule="para" parents="630 51814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51862">
    <literal><![CDATA[
      (x * (a(y,z,z) * u)) \ w = a(y,z,z) \ ((x * u) \ w)
    ]]></literal>
    <justification jstring="[para(50834(a,1),50816(a,1,1))].">
      <j1 rule="para" parents="50834 50816"/>
    </justification>
  </clause>

  <clause id="51867">
    <literal><![CDATA[
      (x * (a(y,z,z) \ u)) \ w = a(y,z,z) * ((x * u) \ w)
    ]]></literal>
    <justification jstring="[para(50832(a,1),50835(a,1,1))].">
      <j1 rule="para" parents="50832 50835"/>
    </justification>
  </clause>

  <clause id="51868">
    <literal><![CDATA[
      (x * (a(y,z,z) * u)) \ (x * (u * (a(y,z,z) * w))) = L(w,a(y,z,z) * u,x)
    ]]></literal>
    <justification jstring="[para(50845(a,1),18(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="50845 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51870">
    <literal><![CDATA[
      a(x,y,((R(z,z,u) \ w) * z) \ v5) = a(x,y,w \ (a(u,z,z) \ v5))
    ]]></literal>
    <justification jstring="[para(50903(a,1),37974(a,2,3))].">
      <j1 rule="para" parents="50903 37974"/>
    </justification>
  </clause>

  <clause id="51872">
    <literal><![CDATA[
      x \ (y * a(z,u,u)) = (x \ y) * a(z,u,u)
    ]]></literal>
    <justification jstring="[hyper(783,a,50918,a)].">
      <j1 rule="hyper" parents="783 50918"/>
    </justification>
  </clause>

  <clause id="51879">
    <literal><![CDATA[
      a(x,y,z * (z * (a(u,w,z) * v5))) = a(x,y,(z * L(z,w,u)) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,48084,a(flip),b,51321,a),flip(a)].">
      <j1 rule="hyper" parents="64 48084 51321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51880">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * w)) = a(x,y,u * (u * (w * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27367,a(flip),b,51321,a)].">
      <j1 rule="hyper" parents="64 27367 51321"/>
    </justification>
  </clause>

  <clause id="51882">
    <literal><![CDATA[
      a(x * ((y \ ((y * z) * u)) / u),w,a(y,z,u)) = a(z * (a(y,z,u) * x),w,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(33279(a,2),51384(a,1,1,2))].">
      <j1 rule="para" parents="33279 51384"/>
    </justification>
  </clause>

  <clause id="51883">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,u)) = a(x,y,a(u,v5,w * (u * z)))
    ]]></literal>
    <justification jstring="[para(51384(a,1),41883(a,1,3))].">
      <j1 rule="para" parents="51384 41883"/>
    </justification>
  </clause>

  <clause id="51887">
    <literal><![CDATA[
      a(x * (y \ z),u,x) = a(y * (z * x),u,x)
    ]]></literal>
    <justification jstring="[hyper(64,a,51311,a(flip),b,51385,a),flip(a)].">
      <j1 rule="hyper" parents="64 51311 51385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51890">
    <literal><![CDATA[
      x * a((y * z) * x,u,w) = y * (z * R(z \ (y \ x),u,w))
    ]]></literal>
    <justification jstring="[hyper(2297,a,51488,a),flip(a)].">
      <j1 rule="hyper" parents="2297 51488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51897">
    <literal><![CDATA[
      a((x * y) \ z,x,u) = a((x \ z) * y,x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,51310,a(flip),b,51831,a),flip(a)].">
      <j1 rule="hyper" parents="373 51310 51831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51898">
    <literal><![CDATA[
      a(x \ (y \ L(z,x,x)),y,u) = a((z * x) * y,y,L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47005,a(flip),b,51833,a),flip(a)].">
      <j1 rule="hyper" parents="64 47005 51833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51899">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,w))) = (x \ (y * z)) * a(u,w,w)
    ]]></literal>
    <justification jstring="[para(50918(a,1),51872(a,1,2))].">
      <j1 rule="para" parents="50918 51872"/>
    </justification>
  </clause>

  <clause id="51900">
    <literal><![CDATA[
      a((x \ y) * z,x,u) = a(y * (x * z),x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,51310,a(flip),b,51897,a),flip(a)].">
      <j1 rule="hyper" parents="64 51310 51897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51903">
    <literal><![CDATA[
      a(x,y,z * u) * (u * z) = u * (z * a(x,y,u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27364,a,b,51072,a)].">
      <j1 rule="hyper" parents="64 27364 51072"/>
    </justification>
  </clause>

  <clause id="51905">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * w))) = a(x,y,((u * z) \ w) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,51784,a(flip),b,51307,a),flip(a)].">
      <j1 rule="hyper" parents="64 51784 51307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51908">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ (w * u))) = a(x,y,w * (z \ (u * u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27966,a,b,51320,a)].">
      <j1 rule="hyper" parents="64 27966 51320"/>
    </justification>
  </clause>

  <clause id="51909">
    <literal><![CDATA[
      L(x,a(y,y,z) * ((z * u) * w),v5) = L(x,(u * L(z,y,y)) * w,v5)
    ]]></literal>
    <justification jstring="[para(51370(a,1),47727(a,1,2))].">
      <j1 rule="para" parents="51370 47727"/>
    </justification>
  </clause>

  <clause id="51911">
    <literal><![CDATA[
      a(x,y,(z \ (u * u)) * w) = a(x,y,u * (u * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,51321,a(flip),b,51786,a),flip(a)].">
      <j1 rule="hyper" parents="373 51321 51786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51912">
    <literal><![CDATA[
      a(x,y,L(a(z,u,u) * ((w * a(v5,v6,v7)) \ v8),a(z,u,u) \ w,a(v5,v6,v7))) = a(x,y,(a(z,u,u) \ w) \ (a(v5,v6,v7) \ v8))
    ]]></literal>
    <justification jstring="[para(51867(a,1),49846(a,1,3,1))].">
      <j1 rule="para" parents="51867 49846"/>
    </justification>
  </clause>

  <clause id="51913">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * a(u,w,w))) = L(z,y,x) * a(u,w,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),51899(a,2,1))].">
      <j1 rule="para" parents="18 51899"/>
    </justification>
  </clause>

  <clause id="51914">
    <literal><![CDATA[
      a(x,y * (z * a(u,w,y * z)),v5) = a(x,L(z * y,w,u),v5)
    ]]></literal>
    <justification jstring="[para(51903(a,1),45961(a,1,2))].">
      <j1 rule="para" parents="51903 45961"/>
    </justification>
  </clause>

  <clause id="51915">
    <literal><![CDATA[
      a(x,y,z * ((z \ u) \ (x \ 1))) = a(x,y,((u * x) \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,49228,a,b,51905,a)].">
      <j1 rule="hyper" parents="64 49228 51905"/>
    </justification>
  </clause>

  <clause id="51916">
    <literal><![CDATA[
      a(x,y,z * (z * (u \ L(w,u,u)))) = a(x,y,(z * z) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,38994,a(flip),b,51911,a),flip(a)].">
      <j1 rule="hyper" parents="64 38994 51911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51917">
    <literal><![CDATA[
      L(L(a(x,y,z),x,u),u * x,w) = a(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(45393,a,51114,a)].">
      <j1 rule="hyper" parents="45393 51114"/>
    </justification>
  </clause>

  <clause id="51922">
    <literal><![CDATA[
      L(a(x,y,z),u * x,w) = a(L(x,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(50785(a,1),51917(a,1,1))].">
      <j1 rule="para" parents="50785 51917"/>
    </justification>
  </clause>

  <clause id="51927">
    <literal><![CDATA[
      a(L(x,y,z),u,w) \ a(x,u,w) = a(z,y * x,a(x,u,w))
    ]]></literal>
    <justification jstring="[para(51922(a,1),42580(a,1,1))].">
      <j1 rule="para" parents="51922 42580"/>
    </justification>
  </clause>

  <clause id="51929">
    <literal><![CDATA[
      a(x,y * z,a(z,u,w)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46179,a(flip),b,51927,a),flip(a)].">
      <j1 rule="hyper" parents="64 46179 51927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51930">
    <literal><![CDATA[
      a(x,y * z,a(y,u,w)) = a(x,z,a(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(32008,a,51929,a)].">
      <j1 rule="hyper" parents="32008 51929"/>
    </justification>
  </clause>

  <clause id="51932">
    <literal><![CDATA[
      a(x,y * z,a(z,u,w)) = a(z,y,a(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,47241,a,b,51929,a),flip(a)].">
      <j1 rule="hyper" parents="373 47241 51929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51935">
    <literal><![CDATA[
      a(x,y * z,a(u,w,z)) = a(u,y,a(z,w,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47553,a,b,51929,a)].">
      <j1 rule="hyper" parents="64 47553 51929"/>
    </justification>
  </clause>

  <clause id="51936">
    <literal><![CDATA[
      a(x,y,a(z,x * u,w)) = a(z,u,a(x,y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47352,a(flip),b,51929,a)].">
      <j1 rule="hyper" parents="64 47352 51929"/>
    </justification>
  </clause>

  <clause id="51939">
    <literal><![CDATA[
      a(x,y * z,a(u,w,y)) = a(x,z,a(y,w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,41883,a,b,51930,a)].">
      <j1 rule="hyper" parents="64 41883 51930"/>
    </justification>
  </clause>

  <clause id="51942">
    <literal><![CDATA[
      a(x,y * z,a(u,w,z)) = a(z,y,a(u,w,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47553,a,b,51932,a)].">
      <j1 rule="hyper" parents="64 47553 51932"/>
    </justification>
  </clause>

  <clause id="51943">
    <literal><![CDATA[
      a(x,y,a(z,u * w,w)) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47298,a,b,51932,a)].">
      <j1 rule="hyper" parents="64 47298 51932"/>
    </justification>
  </clause>

  <clause id="51944">
    <literal><![CDATA[
      a(x,y,a(z,z * u,w)) = a(z,u,a(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47206,a(flip),b,51932,a)].">
      <j1 rule="hyper" parents="64 47206 51932"/>
    </justification>
  </clause>

  <clause id="51945">
    <literal><![CDATA[
      a(x,y * z,a(u,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(373,a,50580,a(flip),b,51935,a),flip(a)].">
      <j1 rule="hyper" parents="373 50580 51935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51948">
    <literal><![CDATA[
      a(x,y * (z * u),a(y,z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,51930,a,b,51945,a)].">
      <j1 rule="hyper" parents="64 51930 51945"/>
    </justification>
  </clause>

  <clause id="51949">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,51948,a)].">
      <j1 rule="hyper" parents="53 51948"/>
    </justification>
  </clause>

  <clause id="51953">
    <literal><![CDATA[
      (x * (y * (z * u))) * a(y,z,u) = x * ((y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(145,a,51949,a(flip),b,635,a)].">
      <j1 rule="hyper" parents="145 51949 635"/>
    </justification>
  </clause>

  <clause id="51955">
    <literal><![CDATA[
      a(x,y,a(z,x * u,w)) = a(w,y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47198,a(flip),b,51936,a),flip(a)].">
      <j1 rule="hyper" parents="373 47198 51936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51958">
    <literal><![CDATA[
      a(x,y,a(z,u * L(x,w,v5),L(v6,w,v5))) = a(L(x,w,v5),u,a(z,y,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,47204,a,b,51942,a)].">
      <j1 rule="hyper" parents="64 47204 51942"/>
    </justification>
  </clause>

  <clause id="51962">
    <literal><![CDATA[
      a(x,y,a(z,u * (w \ (v5 / v6)),w \ (v6 \ v5))) = a(w \ (v5 / v6),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(27322(a,1),51943(a,1,3))].">
      <j1 rule="para" parents="27322 51943"/>
    </justification>
  </clause>

  <clause id="51965">
    <literal><![CDATA[
      a(x,x * y,a(z,u,w)) = a(z,u,a(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47298,a,b,51955,a)].">
      <j1 rule="hyper" parents="64 47298 51955"/>
    </justification>
  </clause>

  <clause id="51966">
    <literal><![CDATA[
      a(x,y,a(z,u * z,w)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47329,a(flip),b,51955,a)].">
      <j1 rule="hyper" parents="64 47329 51955"/>
    </justification>
  </clause>

  <clause id="51967">
    <literal><![CDATA[
      L(x,y,a(z,u * w,u \ 1)) = x * a(x,y,a(z,w,u))
    ]]></literal>
    <justification jstring="[para(51965(a,1),47418(a,2,2))].">
      <j1 rule="para" parents="51965 47418"/>
    </justification>
  </clause>

  <clause id="51970">
    <literal><![CDATA[
      L(x,y,a(z,u * w,u \ 1)) = L(x,y,a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,45190,a(flip),b,51967,a),flip(a)].">
      <j1 rule="hyper" parents="373 45190 51967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51971">
    <literal><![CDATA[
      L(x,y,a(z,u * w,w \ 1)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,32088,a,b,51970,a)].">
      <j1 rule="hyper" parents="64 32088 51970"/>
    </justification>
  </clause>

  <clause id="51974">
    <literal><![CDATA[
      L(x,y,a(z,u * z,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42199,a(flip),b,51971,a)].">
      <j1 rule="hyper" parents="64 42199 51971"/>
    </justification>
  </clause>

  <clause id="51978">
    <literal><![CDATA[
      a(L(x,y,y) * (y * z),u,w) = a((x * y) * z,u,L(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,51310,a(flip),b,51485,a),flip(a)].">
      <j1 rule="hyper" parents="64 51310 51485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51979">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) * v5) \ v6) = a(x,y,(v5 \ a(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(27591,a,51783,a)].">
      <j1 rule="hyper" parents="27591 51783"/>
    </justification>
  </clause>

  <clause id="51980">
    <literal><![CDATA[
      (x / y) * (z * R(z \ y,u,w)) = x * a(((x / y) * z) * x,u,w)
    ]]></literal>
    <justification jstring="[para(82(a,1),51890(a,2,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="82 51890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51982">
    <literal><![CDATA[
      a(x \ (y \ L(z,x,x)),y,u) = a((z * x) * y,y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,51077,a(flip),b,51898,a),flip(a)].">
      <j1 rule="hyper" parents="373 51077 51898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51984">
    <literal><![CDATA[
      a((x \ L(y,z,z)) * z,x,u) = a((y * z) * x,x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,51310,a(flip),b,51982,a)].">
      <j1 rule="hyper" parents="64 51310 51982"/>
    </justification>
  </clause>

  <clause id="51985">
    <literal><![CDATA[
      a(L(x,y,y) * (z * y),z,u) = a((x * y) * z,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,51900,a(flip),b,51984,a)].">
      <j1 rule="hyper" parents="64 51900 51984"/>
    </justification>
  </clause>

  <clause id="51986">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ z) * u) = (x * y) * (((x * y) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,41721,a(flip),b,51441,a),flip(a)].">
      <j1 rule="hyper" parents="64 41721 51441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51988">
    <literal><![CDATA[
      (x / y) * (((x / y) \ z) * u) = (y * x) * (((y * x) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,25723,a,b,51986,a)].">
      <j1 rule="hyper" parents="64 25723 51986"/>
    </justification>
  </clause>

  <clause id="51989">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(u,w,w)))) = L(z,y,x) * a(u,w,w)
    ]]></literal>
    <justification jstring="[para(50918(a,1),51913(a,1,2,2))].">
      <j1 rule="para" parents="50918 51913"/>
    </justification>
  </clause>

  <clause id="51990">
    <literal><![CDATA[
      a(x,y,z * (z * ((u \ 1) * w))) = a(x,y,(z * z) * (u \ w))
    ]]></literal>
    <justification jstring="[para(1148(a,1),51916(a,1,3,2,2))].">
      <j1 rule="para" parents="1148 51916"/>
    </justification>
  </clause>

  <clause id="51991">
    <literal><![CDATA[
      a(x,y,z * (z * ((u \ 1) * w))) = a(x,y,z * (z * (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,51321,a(flip),b,51990,a),flip(a)].">
      <j1 rule="hyper" parents="373 51321 51990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51992">
    <literal><![CDATA[
      a(x,y,z * (z * (u \ T((1 / u) \ w,v5)))) = a(x,y,z * (z * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27985,a(flip),b,51991,a),flip(a)].">
      <j1 rule="hyper" parents="64 27985 51991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="51993">
    <literal><![CDATA[
      L(x * a(y,z,z),u,w) = L(x,u,w) * a(y,z,z)
    ]]></literal>
    <justification jstring="[hyper(608,a,51989,a)].">
      <j1 rule="hyper" parents="608 51989"/>
    </justification>
  </clause>

  <clause id="51996">
    <literal><![CDATA[
      a(x,y,y) \ L(a(x,y,y) * z,u,w) = L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(36,a,5545,a,b,51993,a(flip))].">
      <j1 rule="hyper" parents="36 5545 51993"/>
    </justification>
  </clause>

  <clause id="52001">
    <literal><![CDATA[
      L(x,y,((z \ a(u,w,v5)) \ 1) * v6) = L(x,y,(a(v5,w,u) * z) * v6)
    ]]></literal>
    <justification jstring="[hyper(29069,a,51549,a)].">
      <j1 rule="hyper" parents="29069 51549"/>
    </justification>
  </clause>

  <clause id="52002">
    <literal><![CDATA[
      a(x,y,((R(z,z,u) \ w) * z) \ v5) = a(x,y,w \ (a(u,z,z) * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,42519,a(flip),b,51870,a),flip(a)].">
      <j1 rule="hyper" parents="373 42519 51870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52003">
    <literal><![CDATA[
      a(x,y,(z * L(z,u,w)) * v5) = a(x,y,z * (v5 * L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,51812,a(flip),b,51879,a),flip(a)].">
      <j1 rule="hyper" parents="64 51812 51879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52004">
    <literal><![CDATA[
      a(x,y,z * ((u \ (z \ u)) \ w)) = a(x,y,z * (w * L(z,z,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,44395,a(flip),b,52003,a)].">
      <j1 rule="hyper" parents="64 44395 52003"/>
    </justification>
  </clause>

  <clause id="52005">
    <literal><![CDATA[
      (x / (y * z)) * (y * R(z,u,w)) = x * a(((x / (y * z)) * y) * x,u,w)
    ]]></literal>
    <justification jstring="[para(9(a,1),51980(a,1,2,2,1))].">
      <j1 rule="para" parents="9 51980"/>
    </justification>
  </clause>

  <clause id="52006">
    <literal><![CDATA[
      a(x,y,z * (z * (u \ ((1 / u) \ w)))) = a(x,y,z * (z * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27662,a(flip),b,51992,a)].">
      <j1 rule="hyper" parents="64 27662 51992"/>
    </justification>
  </clause>

  <clause id="52007">
    <literal><![CDATA[
      L(x,y,(z \ a(u,w,v5)) \ v6) = L(x,y,(a(v5,w,u) * z) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,51209,a(flip),b,52001,a)].">
      <j1 rule="hyper" parents="64 51209 52001"/>
    </justification>
  </clause>

  <clause id="52008">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ u) * a(w,v5,v5)) = L(x,y,(a(v5,v5,w) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,49930,a,b,52007,a)].">
      <j1 rule="hyper" parents="64 49930 52007"/>
    </justification>
  </clause>

  <clause id="52009">
    <literal><![CDATA[
      a(x,y,((R(z,z,u) \ w) * z) \ v5) = a(x,y,a(u,z,z) * (w \ v5))
    ]]></literal>
    <justification jstring="[para(50833(a,1),52002(a,2,3))].">
      <j1 rule="para" parents="50833 52002"/>
    </justification>
  </clause>

  <clause id="52010">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ u) * a(w,v5,v5)) = L(x,y,z * (a(v5,v5,w) * u))
    ]]></literal>
    <justification jstring="[para(50752(a,1),52008(a,2,3))].">
      <j1 rule="para" parents="50752 52008"/>
    </justification>
  </clause>

  <clause id="52011">
    <literal><![CDATA[
      a(x,y,y) \ ((z * u) \ (z * (u * (a(x,y,y) * w)))) = L(w,a(x,y,y) * u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,51862,a(flip),b,51868,a)].">
      <j1 rule="hyper" parents="64 51862 51868"/>
    </justification>
  </clause>

  <clause id="52012">
    <literal><![CDATA[
      a(x,y,a(z,u * (w \ (v5 / v6)),w * (v6 \ v5))) = a(w \ (v5 / v6),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,49778,a(flip),b,51962,a)].">
      <j1 rule="hyper" parents="64 49778 51962"/>
    </justification>
  </clause>

  <clause id="52013">
    <literal><![CDATA[
      a(x,y,y) \ L(a(x,y,y) * z,u,w) = L(z,a(x,y,y) * u,w)
    ]]></literal>
    <justification jstring="[para(18(a,2),52011(a,1,2))].">
      <j1 rule="para" parents="18 52011"/>
    </justification>
  </clause>

  <clause id="52014">
    <literal><![CDATA[
      L(x,a(y,z,z) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,51996,a(flip),b,52013,a),flip(a)].">
      <j1 rule="hyper" parents="64 51996 52013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52016">
    <literal><![CDATA[
      L(x,y * a(z,u,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(29572,a,52014,a)].">
      <j1 rule="hyper" parents="29572 52014"/>
    </justification>
  </clause>

  <clause id="52018">
    <literal><![CDATA[
      L(x,y * a(z,z,u),w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,48760,a(flip),b,52014,a)].">
      <j1 rule="hyper" parents="64 48760 52014"/>
    </justification>
  </clause>

  <clause id="52019">
    <literal><![CDATA[
      L(x,a(y,y,z) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,46479,a(flip),b,52014,a),flip(a)].">
      <j1 rule="hyper" parents="64 46479 52014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52027">
    <literal><![CDATA[
      L(x,L(y,z,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,45115,a(flip),b,52018,a)].">
      <j1 rule="hyper" parents="64 45115 52018"/>
    </justification>
  </clause>

  <clause id="52028">
    <literal><![CDATA[
      L(x,y * L(z,u,u),w) = L(x,y * z,w)
    ]]></literal>
    <justification jstring="[para(39720(a,1),52018(a,1,2)),flip(a)].">
      <j1 rule="para" parents="39720 52018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52029">
    <literal><![CDATA[
      L(x,y \ z,u) = L(x,y * z,u)
    ]]></literal>
    <justification jstring="[hyper(29742,a,52027,a),flip(a)].">
      <j1 rule="hyper" parents="29742 52027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52054">
    <literal><![CDATA[
      L(x,L(y,z,z),u) = a(u,y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(373,a,45065,a(flip),b,52027,a),flip(a)].">
      <j1 rule="hyper" parents="373 45065 52027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52061">
    <literal><![CDATA[
      L(x,y * (z * ((z \ y) * u)),w) = L(x,L(u,y * z,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,41741,a(flip),b,52027,a)].">
      <j1 rule="hyper" parents="64 41741 52027"/>
    </justification>
  </clause>

  <clause id="52063">
    <literal><![CDATA[
      L(x,y \ z,u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,31760,a(flip),b,52027,a)].">
      <j1 rule="hyper" parents="64 31760 52027"/>
    </justification>
  </clause>

  <clause id="52112">
    <literal><![CDATA[
      L(x,(L(y,y,z * u) * ((y * z) * u)) * z,w) = L(x,L(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,43146,a(flip),b,52063,a),flip(a)].">
      <j1 rule="hyper" parents="64 43146 52063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52113">
    <literal><![CDATA[
      L(x,(y \ (z * u)) * ((y \ u) * z),w) = L(x,a(y,u * y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,35708,a(flip),b,52063,a),flip(a)].">
      <j1 rule="hyper" parents="64 35708 52063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52114">
    <literal><![CDATA[
      L(x,((y \ (z \ y)) * u) \ w,v5) = L(x,w * (((y * z) \ y) * u),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34241,a(flip),b,52063,a)].">
      <j1 rule="hyper" parents="64 34241 52063"/>
    </justification>
  </clause>

  <clause id="52115">
    <literal><![CDATA[
      L(x,y * (L(z * u,z,z) \ w),v5) = L(x,((z \ u) \ w) \ y,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34072,a(flip),b,52063,a),flip(a)].">
      <j1 rule="hyper" parents="64 34072 52063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52116">
    <literal><![CDATA[
      L(x,(y * ((z * y) * u)) * L(z,y,y),w) = L(x,L(u,z * y,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,31385,a(flip),b,52063,a),flip(a)].">
      <j1 rule="hyper" parents="64 31385 52063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52136">
    <literal><![CDATA[
      L(x,(y * L(z,u,u)) * w,v5) = L(x,(z * y) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,51909,a(flip),b,52019,a)].">
      <j1 rule="hyper" parents="64 51909 52019"/>
    </justification>
  </clause>

  <clause id="52137">
    <literal><![CDATA[
      L(x,(y \ z) * u,w) = L(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,47091,a(flip),b,52019,a),flip(a)].">
      <j1 rule="hyper" parents="64 47091 52019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52140">
    <literal><![CDATA[
      L(x,y * (a(z,z,u) * w),v5) = L(x,y * w,v5)
    ]]></literal>
    <justification jstring="[para(50922(a,1),52019(a,1,2))].">
      <j1 rule="para" parents="50922 52019"/>
    </justification>
  </clause>

  <clause id="52145">
    <literal><![CDATA[
      a(x,L(y,z,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(40,a,45065,a(flip),b,52054,a(flip))].">
      <j1 rule="hyper" parents="40 45065 52054"/>
    </justification>
  </clause>

  <clause id="52162">
    <literal><![CDATA[
      a(x,L((y * z) * y,u,w),v5) = a(x,L(z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,35334,a,b,52145,a)].">
      <j1 rule="hyper" parents="64 35334 52145"/>
    </justification>
  </clause>

  <clause id="52163">
    <literal><![CDATA[
      a(x,y * (y * z),u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,11968,a,b,52145,a)].">
      <j1 rule="hyper" parents="64 11968 52145"/>
    </justification>
  </clause>

  <clause id="52166">
    <literal><![CDATA[
      a(x,L(y \ z,u,w),v5) = a(x,L(y * z,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32300,a(flip),b,52145,a)].">
      <j1 rule="hyper" parents="64 32300 52145"/>
    </justification>
  </clause>

  <clause id="52168">
    <literal><![CDATA[
      a(x,y \ z,u) = a(x,y * z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,32141,a(flip),b,52145,a)].">
      <j1 rule="hyper" parents="64 32141 52145"/>
    </justification>
  </clause>

  <clause id="52174">
    <literal><![CDATA[
      a(x,y * (z * ((z \ y) * u)),w) = a(x,L(u,z * y,z),w)
    ]]></literal>
    <justification jstring="[para(41721(a,1),52163(a,1,2,2))].">
      <j1 rule="para" parents="41721 52163"/>
    </justification>
  </clause>

  <clause id="52198">
    <literal><![CDATA[
      L(x,y * (z * (z * u)),w) = L(x,y * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29717,a,b,52028,a)].">
      <j1 rule="hyper" parents="64 29717 52028"/>
    </justification>
  </clause>

  <clause id="52199">
    <literal><![CDATA[
      L(x,(y \ z) * u,w) = L(x,u * (y * z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,34382,a(flip),b,52028,a)].">
      <j1 rule="hyper" parents="64 34382 52028"/>
    </justification>
  </clause>

  <clause id="52205">
    <literal><![CDATA[
      L(x,y * (z \ u),w) = L(x,y * (z * u),w)
    ]]></literal>
    <justification jstring="[para(10(a,1),52198(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 52198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52207">
    <literal><![CDATA[
      L(x,y * (z / u),w) = L(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29619,a(flip),b,52199,a)].">
      <j1 rule="hyper" parents="64 29619 52199"/>
    </justification>
  </clause>

  <clause id="52210">
    <literal><![CDATA[
      L(x,((y \ z) \ u) * ((z * (y \ z)) * (z * u)),w) = L(x,a(z,y * z,(y \ z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,46445,a(flip),b,52205,a),flip(a)].">
      <j1 rule="hyper" parents="64 46445 52205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52213">
    <literal><![CDATA[
      L(x,(L(y,z,z) * u) * w,v5) = L(x,w * (u * y),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,49999,a(flip),b,52140,a),flip(a)].">
      <j1 rule="hyper" parents="64 49999 52140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52214">
    <literal><![CDATA[
      L(x,y * (L(z,u,u) * w),v5) = L(x,y * (z * w),v5)
    ]]></literal>
    <justification jstring="[para(44975(a,1),52140(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="44975 52140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52217">
    <literal><![CDATA[
      a(x,L(y / z,u,w),v5) = a(x,L(z * y,u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,31920,a,b,52166,a)].">
      <j1 rule="hyper" parents="64 31920 52166"/>
    </justification>
  </clause>

  <clause id="52218">
    <literal><![CDATA[
      a(x,L((y \ z) * (y * u),z,y),w) = a(x,L(z,y,y) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,43553,a(flip),b,52166,a),flip(a)].">
      <j1 rule="hyper" parents="64 43553 52166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52220">
    <literal><![CDATA[
      L(x,((y \ z) * u) * w,v5) = L(x,((z * y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,38363,a(flip),b,52136,a)].">
      <j1 rule="hyper" parents="64 38363 52136"/>
    </justification>
  </clause>

  <clause id="52226">
    <literal><![CDATA[
      a(x,y * (z * ((z \ y) * (u \ w))),v5) = a(x,L(w / u,z * y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,31920,a,b,52174,a),flip(a)].">
      <j1 rule="hyper" parents="373 31920 52174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52227">
    <literal><![CDATA[
      L(L(x,y,z),u * (w * ((w \ u) * v5)),v6) \ L(x,y,L(z,u * (w * ((w \ u) * v5)),v6)) = a(v6,L(v5,w * u,w),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,47129,a,b,52174,a)].">
      <j1 rule="hyper" parents="64 47129 52174"/>
    </justification>
  </clause>

  <clause id="52228">
    <literal><![CDATA[
      a(x,L((y \ z) * (y * u),z,y),w) = a(x,L(z,y,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,52168,a(flip),b,52218,a),flip(a)].">
      <j1 rule="hyper" parents="373 52168 52218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52229">
    <literal><![CDATA[
      L(x,y * (L(z * u,z,z) * w),v5) = L(x,((z \ u) \ w) \ y,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52205,a(flip),b,52115,a)].">
      <j1 rule="hyper" parents="64 52205 52115"/>
    </justification>
  </clause>

  <clause id="52230">
    <literal><![CDATA[
      L(x,((y \ z) \ u) \ w,v5) = L(x,w * ((y * z) * u),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52214,a(flip),b,52229,a),flip(a)].">
      <j1 rule="hyper" parents="64 52214 52229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52232">
    <literal><![CDATA[
      L(x,y * ((z \ u) \ w),v5) = L(x,y * ((z * u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52063,a(flip),b,52230,a)].">
      <j1 rule="hyper" parents="64 52063 52230"/>
    </justification>
  </clause>

  <clause id="52233">
    <literal><![CDATA[
      L(x,y * ((z \ u) * w),v5) = L(x,y * ((z * u) * w),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52205,a(flip),b,52232,a)].">
      <j1 rule="hyper" parents="64 52205 52232"/>
    </justification>
  </clause>

  <clause id="52234">
    <literal><![CDATA[
      L(x,(y \ (z * u)) * ((y * u) * z),w) = L(x,a(y,u * y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,52113,a(flip),b,52233,a),flip(a)].">
      <j1 rule="hyper" parents="64 52113 52233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52235">
    <literal><![CDATA[
      L(x,(y * (z * u)) * ((y * u) * z),w) = L(x,a(y,u * y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,52137,a(flip),b,52234,a)].">
      <j1 rule="hyper" parents="64 52137 52234"/>
    </justification>
  </clause>

  <clause id="52236">
    <literal><![CDATA[
      L(x,a(y,z * y,u),w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,49174,a(flip),b,52235,a),flip(a)].">
      <j1 rule="hyper" parents="64 49174 52235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52237">
    <literal><![CDATA[
      L(x,y * (((y * z) * u) * L(z,z,y * u)),w) = L(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29859,a(flip),b,52112,a)].">
      <j1 rule="hyper" parents="64 29859 52112"/>
    </justification>
  </clause>

  <clause id="52238">
    <literal><![CDATA[
      L(x,((y \ (z \ y)) * u) \ w,v5) = L(x,w * (((y * z) * y) * u),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,52233,a(flip),b,52114,a),flip(a)].">
      <j1 rule="hyper" parents="373 52233 52114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52239">
    <literal><![CDATA[
      L(x,(y * ((z * y) * u)) * z,w) = L(x,L(u,z * y,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,52028,a(flip),b,52116,a)].">
      <j1 rule="hyper" parents="64 52028 52116"/>
    </justification>
  </clause>

  <clause id="52241">
    <literal><![CDATA[
      L(x,y * (((y * z) * u) / (1 / z)),w) = L(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[para(34043(a,1),52237(a,1,2,2))].">
      <j1 rule="para" parents="34043 52237"/>
    </justification>
  </clause>

  <clause id="52242">
    <literal><![CDATA[
      L(x,y * ((1 / z) * ((y * z) * u)),w) = L(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,52207,a(flip),b,52241,a)].">
      <j1 rule="hyper" parents="64 52207 52241"/>
    </justification>
  </clause>

  <clause id="52243">
    <literal><![CDATA[
      L(x,y * ((z \ 1) * ((y * z) * u)),w) = L(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29626,a(flip),b,52242,a)].">
      <j1 rule="hyper" parents="64 29626 52242"/>
    </justification>
  </clause>

  <clause id="52244">
    <literal><![CDATA[
      L(x,(y * ((z * y) * u)) * z,w) = L(x,L(u,z,y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,29519,a(flip),b,52243,a)].">
      <j1 rule="hyper" parents="64 29519 52243"/>
    </justification>
  </clause>

  <clause id="52245">
    <literal><![CDATA[
      L(x,L(y,z * u,u),w) = L(x,L(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,52239,a(flip),b,52244,a)].">
      <j1 rule="hyper" parents="64 52239 52244"/>
    </justification>
  </clause>

  <clause id="52246">
    <literal><![CDATA[
      L(x,y * (z * ((z \ y) * u)),w) = L(x,L(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,52061,a,b,52245,a)].">
      <j1 rule="hyper" parents="64 52061 52245"/>
    </justification>
  </clause>

  <clause id="52248">
    <literal><![CDATA[
      L(x,((y \ (z \ y)) * u) \ w,v5) = L(x,(L(z,y,y) * u) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,29844,a(flip),b,52238,a),flip(a)].">
      <j1 rule="hyper" parents="373 29844 52238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52249">
    <literal><![CDATA[
      L(x,((y \ (z \ y)) * u) \ w,v5) = L(x,w * (u * z),v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,52213,a(flip),b,52248,a),flip(a)].">
      <j1 rule="hyper" parents="373 52213 52248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52251">
    <literal><![CDATA[
      L(x,y * ((z \ (u \ z)) * w),v5) = L(x,y * (w * u),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52063,a(flip),b,52249,a)].">
      <j1 rule="hyper" parents="64 52063 52249"/>
    </justification>
  </clause>

  <clause id="52252">
    <literal><![CDATA[
      L(x,y * ((z * (u \ z)) * w),v5) = L(x,y * (w * u),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52233,a(flip),b,52251,a)].">
      <j1 rule="hyper" parents="64 52233 52251"/>
    </justification>
  </clause>

  <clause id="52253">
    <literal><![CDATA[
      a(x,L(y / (z \ u),z * u,z),w) = a(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[para(10(a,1),52226(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10 52226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52254">
    <literal><![CDATA[
      a(x,y,a(z,u * (a(w,v5,v6) \ (1 / v7)),v7 \ a(w,v5,v6))) = a(a(w,v5,v6) \ (1 / v7),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(50635(a,1),52012(a,1,3,3))].">
      <j1 rule="para" parents="50635 52012"/>
    </justification>
  </clause>

  <clause id="52256">
    <literal><![CDATA[
      L(x,a(y,z * y,(z \ y) \ u),w) = L(x,((z \ y) \ u) * ((y * u) * z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,52252,a(flip),b,52210,a),flip(a)].">
      <j1 rule="hyper" parents="64 52252 52210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52258">
    <literal><![CDATA[
      L(x,a(y,z * y,(z \ y) \ u),w) = L(x,((z \ y) * u) * ((y * u) * z),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,52137,a(flip),b,52256,a),flip(a)].">
      <j1 rule="hyper" parents="373 52137 52256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52259">
    <literal><![CDATA[
      L(x,a(y,z * y,(z \ y) \ u),w) = L(x,((y * z) * u) * ((y * u) * z),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,52220,a(flip),b,52258,a),flip(a)].">
      <j1 rule="hyper" parents="373 52220 52258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52260">
    <literal><![CDATA[
      L(x,a(y,z * y,(z \ y) \ u),w) = L(x,a(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(373,a,49161,a(flip),b,52259,a),flip(a)].">
      <j1 rule="hyper" parents="373 49161 52259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52261">
    <literal><![CDATA[
      (x * (a(y,z,z) * u)) \ (x * (a(y,z,z) * (u * w))) = L(w,L(u,a(y,z,z),x),x * a(y,z,z))
    ]]></literal>
    <justification jstring="[para(50667(a,1),50843(a,1,2))].">
      <j1 rule="para" parents="50667 50843"/>
    </justification>
  </clause>

  <clause id="52262">
    <literal><![CDATA[
      L(L(x,y,a(z,u,u)),a(z,u,u) * y,w) = L(x,L(y,a(z,u,u),w),w * a(z,u,u))
    ]]></literal>
    <justification jstring="[hyper(1081,a,52261,a)].">
      <j1 rule="hyper" parents="1081 52261"/>
    </justification>
  </clause>

  <clause id="52263">
    <literal><![CDATA[
      L(L(x,y,a(z,u,u)),a(z,u,u) * y,w) = L(x,y,w * a(z,u,u))
    ]]></literal>
    <justification jstring="[para(50675(a,1),52262(a,2,2))].">
      <j1 rule="para" parents="50675 52262"/>
    </justification>
  </clause>

  <clause id="52264">
    <literal><![CDATA[
      L(x,a(y,z,z) * u,w) = L(x,u,w * a(y,z,z))
    ]]></literal>
    <justification jstring="[para(50749(a,1),52263(a,1,1))].">
      <j1 rule="para" parents="50749 52263"/>
    </justification>
  </clause>

  <clause id="52265">
    <literal><![CDATA[
      L(x,y,z * a(u,w,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,52014,a(flip),b,52264,a),flip(a)].">
      <j1 rule="hyper" parents="64 52014 52264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52271">
    <literal><![CDATA[
      L(x,y,z * (a(u,u,w) * v5)) = L(x,y,(z \ 1) \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52010,a(flip),b,52265,a)].">
      <j1 rule="hyper" parents="64 52010 52265"/>
    </justification>
  </clause>

  <clause id="52272">
    <literal><![CDATA[
      L(x,y,z * a(u,u,w)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,30832,a(flip),b,52265,a)].">
      <j1 rule="hyper" parents="64 30832 52265"/>
    </justification>
  </clause>

  <clause id="52273">
    <literal><![CDATA[
      L(x,y,z * a(u,w,w)) \ x = a(z,y,x)
    ]]></literal>
    <justification jstring="[para(52265(a,2),45067(a,2,1)),flip(a)].">
      <j1 rule="para" parents="52265 45067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52277">
    <literal><![CDATA[
      L(x,y,z \ (u \ w)) = L(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,51433,a(flip),b,52272,a),flip(a)].">
      <j1 rule="hyper" parents="64 51433 52272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52280">
    <literal><![CDATA[
      L(x,y,L(z,u,w)) \ L(R(x,u,w * a(v5,v5,v6)),y,z) = a(x,u,w * a(v5,v5,v6))
    ]]></literal>
    <justification jstring="[para(52272(a,1),47946(a,1,1,3))].">
      <j1 rule="para" parents="52272 47946"/>
    </justification>
  </clause>

  <clause id="52282">
    <literal><![CDATA[
      a(x * a(y,z,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(45142,a,52273,a)].">
      <j1 rule="hyper" parents="45142 52273"/>
    </justification>
  </clause>

  <clause id="52287">
    <literal><![CDATA[
      a(x * a(y,y,z),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42342,a,b,52282,a)].">
      <j1 rule="hyper" parents="64 42342 52282"/>
    </justification>
  </clause>

  <clause id="52288">
    <literal><![CDATA[
      a(a(x,x,y) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32852,a,b,52282,a)].">
      <j1 rule="hyper" parents="64 32852 52282"/>
    </justification>
  </clause>

  <clause id="52306">
    <literal><![CDATA[
      a((x \ y) * z,u,w) = a((y * x) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,45728,a(flip),b,52287,a),flip(a)].">
      <j1 rule="hyper" parents="64 45728 52287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52322">
    <literal><![CDATA[
      a(L(x,y,y) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,51799,a(flip),b,52288,a),flip(a)].">
      <j1 rule="hyper" parents="64 51799 52288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52323">
    <literal><![CDATA[
      a(x \ (y \ z),u,w) = a((z * y) * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,51477,a(flip),b,52288,a),flip(a)].">
      <j1 rule="hyper" parents="64 51477 52288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52324">
    <literal><![CDATA[
      a(x * (L(y,z,z) * u),w,v5) = a((y * u) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,50052,a(flip),b,52288,a)].">
      <j1 rule="hyper" parents="64 50052 52288"/>
    </justification>
  </clause>

  <clause id="52332">
    <literal><![CDATA[
      a((x * (y * x)) * z,u,w) = a(y * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32660,a,b,52322,a)].">
      <j1 rule="hyper" parents="64 32660 52322"/>
    </justification>
  </clause>

  <clause id="52333">
    <literal><![CDATA[
      a(x * (y * (y * z)),u,w) = a(z * x,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,26832,a,b,52322,a)].">
      <j1 rule="hyper" parents="64 26832 52322"/>
    </justification>
  </clause>

  <clause id="52334">
    <literal><![CDATA[
      a((x * y) * z,z,u) = a(x * (z * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,51985,a(flip),b,52322,a)].">
      <j1 rule="hyper" parents="64 51985 52322"/>
    </justification>
  </clause>

  <clause id="52335">
    <literal><![CDATA[
      a((x * y) * z,u,L(w,z,y)) = a(x * (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,51978,a(flip),b,52322,a)].">
      <j1 rule="hyper" parents="64 51978 52322"/>
    </justification>
  </clause>

  <clause id="52336">
    <literal><![CDATA[
      a((x \ y) * z,u,w) = a((x * y) * z,u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32818,a(flip),b,52322,a)].">
      <j1 rule="hyper" parents="64 32818 52322"/>
    </justification>
  </clause>

  <clause id="52341">
    <literal><![CDATA[
      L(x,y,z * (u \ w)) = L(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,50987,a(flip),b,52277,a)].">
      <j1 rule="hyper" parents="64 50987 52277"/>
    </justification>
  </clause>

  <clause id="52343">
    <literal><![CDATA[
      a((x \ y) * z,u,w) = a(z * (y * x),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,26787,a,b,52306,a),flip(a)].">
      <j1 rule="hyper" parents="373 26787 52306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52344">
    <literal><![CDATA[
      a((x \ y) * z,u,w) = a(z * (x * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32422,a(flip),b,52306,a),flip(a)].">
      <j1 rule="hyper" parents="373 32422 52306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52348">
    <literal><![CDATA[
      a((x * y) * z,y,u) = a(x * (y * z),y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,51900,a(flip),b,52306,a),flip(a)].">
      <j1 rule="hyper" parents="64 51900 52306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52349">
    <literal><![CDATA[
      a(((x * y) * (z \ y)) * (x * z),u,w) = a(x,z,a(w,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,51484,a(flip),b,52306,a),flip(a)].">
      <j1 rule="hyper" parents="64 51484 52306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52352">
    <literal><![CDATA[
      L(x,y,a((x * z) * u,w,v5)) = L(x,y,a(z * (u \ x),w,v5))
    ]]></literal>
    <justification jstring="[para(52306(a,1),47662(a,1,3))].">
      <j1 rule="para" parents="52306 47662"/>
    </justification>
  </clause>

  <clause id="52354">
    <literal><![CDATA[
      a(x \ (y \ z),u,w) = a(x * (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,32422,a(flip),b,52323,a),flip(a)].">
      <j1 rule="hyper" parents="373 32422 52323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52357">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 * (v6 * v5)))) = a(v6 * w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47228,a(flip),b,52332,a)].">
      <j1 rule="hyper" parents="64 47228 52332"/>
    </justification>
  </clause>

  <clause id="52359">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 * (v5 * v6)))) = a(v6 * w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47198,a,b,52333,a)].">
      <j1 rule="hyper" parents="64 47198 52333"/>
    </justification>
  </clause>

  <clause id="52360">
    <literal><![CDATA[
      a(x * (y * z),y,u) = a(y * (x * z),y,u)
    ]]></literal>
    <justification jstring="[hyper(26847,a,52334,a),flip(a)].">
      <j1 rule="hyper" parents="26847 52334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52362">
    <literal><![CDATA[
      a((x * y) * z,z,u) = a(x * (y * z),z,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32365,a,b,52334,a),flip(a)].">
      <j1 rule="hyper" parents="373 32365 52334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52367">
    <literal><![CDATA[
      a((x * y) * z,x,u) = a(y * (x * z),x,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,51900,a(flip),b,52336,a),flip(a)].">
      <j1 rule="hyper" parents="64 51900 52336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52370">
    <literal><![CDATA[
      L(x,y,((z \ u) \ w) * ((u * (z \ u)) * (u * w))) = L(x,y,a(u,z * u,(z \ u) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46444,a(flip),b,52341,a),flip(a)].">
      <j1 rule="hyper" parents="64 46444 52341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52371">
    <literal><![CDATA[
      L(x,y,z * (L(u * w,w,w) * v5)) = L(x,y,z * ((w \ u) \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,35520,a(flip),b,52341,a),flip(a)].">
      <j1 rule="hyper" parents="64 35520 52341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52373">
    <literal><![CDATA[
      a(x * (y \ z),u,w) = a(x * (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,52343,a)].">
      <j1 rule="hyper" parents="26847 52343"/>
    </justification>
  </clause>

  <clause id="52375">
    <literal><![CDATA[
      a(x * (y / z),u,w) = a(x * (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32417,a(flip),b,52343,a)].">
      <j1 rule="hyper" parents="64 32417 52343"/>
    </justification>
  </clause>

  <clause id="52378">
    <literal><![CDATA[
      a(x * (y \ z),u,w) = a(x * (y * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,52344,a)].">
      <j1 rule="hyper" parents="26847 52344"/>
    </justification>
  </clause>

  <clause id="52385">
    <literal><![CDATA[
      a((x * y) * z,y,u) = a(x * (z * y),y,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,32365,a,b,52348,a),flip(a)].">
      <j1 rule="hyper" parents="373 32365 52348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52390">
    <literal><![CDATA[
      a(x * (y * ((y * z) * x)),u,w) = a(z,u,L(L(w,x,y),y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46743,a(flip),b,52354,a),flip(a)].">
      <j1 rule="hyper" parents="64 46743 52354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52391">
    <literal><![CDATA[
      a(x * (y * z),z,u) = a(z * (x * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(32448,a,52360,a)].">
      <j1 rule="hyper" parents="32448 52360"/>
    </justification>
  </clause>

  <clause id="52396">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),w,v5)) = a(x,y,a(w * (u * z),w,v5))
    ]]></literal>
    <justification jstring="[para(52362(a,1),32429(a,1,3))].">
      <j1 rule="para" parents="52362 32429"/>
    </justification>
  </clause>

  <clause id="52397">
    <literal><![CDATA[
      a((x * y) * z,x,u) = a(x * (y * z),x,u)
    ]]></literal>
    <justification jstring="[hyper(373,a,52360,a(flip),b,52367,a),flip(a)].">
      <j1 rule="hyper" parents="373 52360 52367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52403">
    <literal><![CDATA[
      a(((x * y) \ (z * x)) * (z * y),u,w) = a(y * z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,48442,a(flip),b,52373,a),flip(a)].">
      <j1 rule="hyper" parents="64 48442 52373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52404">
    <literal><![CDATA[
      a(x * (L(y * z,z,z) * u),w,v5) = a((u \ (z \ y)) * x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,38430,a(flip),b,52373,a),flip(a)].">
      <j1 rule="hyper" parents="64 38430 52373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52407">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),w,v5)) = a(x,y,a(x * (u * z),w,v5))
    ]]></literal>
    <justification jstring="[para(52373(a,1),47862(a,1,3))].">
      <j1 rule="para" parents="52373 47862"/>
    </justification>
  </clause>

  <clause id="52408">
    <literal><![CDATA[
      a(x * (a(y,x,z) * u),w,a(y,x,z)) = a(u * ((y \ ((y * x) * z)) * z),w,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,51882,a(flip),b,52375,a)].">
      <j1 rule="hyper" parents="64 51882 52375"/>
    </justification>
  </clause>

  <clause id="52416">
    <literal><![CDATA[
      a(x * (y * z),u,z) = a(z * (x * y),u,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,51887,a(flip),b,52378,a)].">
      <j1 rule="hyper" parents="64 51887 52378"/>
    </justification>
  </clause>

  <clause id="52419">
    <literal><![CDATA[
      a(x,y,a(z * (u * x),w,v5)) = a(x,y,a(x * (u * z),w,v5))
    ]]></literal>
    <justification jstring="[para(52378(a,1),47862(a,1,3))].">
      <j1 rule="para" parents="52378 47862"/>
    </justification>
  </clause>

  <clause id="52421">
    <literal><![CDATA[
      a((x \ y) * z,y,u) = a(x * (z * y),y,u)
    ]]></literal>
    <justification jstring="[hyper(64,a,52336,a,b,52385,a)].">
      <j1 rule="hyper" parents="64 52336 52385"/>
    </justification>
  </clause>

  <clause id="52423">
    <literal><![CDATA[
      a(x * (y * z),u,a(w,z,v5)) = a(z * (x * y),z,a(w,u,v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,47324,a,b,52391,a)].">
      <j1 rule="hyper" parents="64 47324 52391"/>
    </justification>
  </clause>

  <clause id="52427">
    <literal><![CDATA[
      a(x * (y * z),y,a(u,w,v5)) = a(y * (z * x),y,a(v5,w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,41890,a,b,52397,a)].">
      <j1 rule="hyper" parents="64 41890 52397"/>
    </justification>
  </clause>

  <clause id="52428">
    <literal><![CDATA[
      a(x * (y * z),a(u,w,v5),z) = a(z,a(u,w,v5),z * (x * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,43409,a,b,52416,a),flip(a)].">
      <j1 rule="hyper" parents="373 43409 52416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52433">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),v5,z)) = a(x,y,a(z,v5,u * (z * w)))
    ]]></literal>
    <justification jstring="[para(52416(a,1),41895(a,1,3))].">
      <j1 rule="para" parents="52416 41895"/>
    </justification>
  </clause>

  <clause id="52435">
    <literal><![CDATA[
      L(x,y,z * (a(u,u,w) * v5)) = L(x,y,z * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,50988,a(flip),b,52271,a),flip(a)].">
      <j1 rule="hyper" parents="373 50988 52271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52436">
    <literal><![CDATA[
      L(x,y,z * (L(u,w,w) * v5)) = L(x,y,z * (u * v5))
    ]]></literal>
    <justification jstring="[para(44975(a,1),52435(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="44975 52435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52438">
    <literal><![CDATA[
      a(x * (y * z),u,L(w,x,z)) = a(y * (z * x),u,w)
    ]]></literal>
    <justification jstring="[hyper(26847,a,52335,a)].">
      <j1 rule="hyper" parents="26847 52335"/>
    </justification>
  </clause>

  <clause id="52440">
    <literal><![CDATA[
      a(x,y,a(z * (L(x,u,w) * v5),v6,v7)) = a(x,y,a(v5 * (z * L(x,u,w)),v6,v7))
    ]]></literal>
    <justification jstring="[para(52438(a,1),46637(a,1,3))].">
      <j1 rule="para" parents="52438 46637"/>
    </justification>
  </clause>

  <clause id="52441">
    <literal><![CDATA[
      L(x,y,a((x * z) * u,w,v5)) = L(x,y,a(z * (x * u),w,v5))
    ]]></literal>
    <justification jstring="[para(52373(a,1),52352(a,2,3))].">
      <j1 rule="para" parents="52373 52352"/>
    </justification>
  </clause>

  <clause id="52445">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (z * v5))) = a(x,y,a(z,u,z * (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,41895,a(flip),b,52433,a),flip(a)].">
      <j1 rule="hyper" parents="64 41895 52433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52447">
    <literal><![CDATA[
      L(x * a(y,x,a(z,u,a(w,v5,w * (v6 * v7)))),a(z,u,y),a(w,v5,v7 * (w * v6))) = L(x,a(w,v5,v7 * (w * v6)),a(z,u,y))
    ]]></literal>
    <justification jstring="[para(52445(a,1),47342(a,1,1,2,3))].">
      <j1 rule="para" parents="52445 47342"/>
    </justification>
  </clause>

  <clause id="52448">
    <literal><![CDATA[
      L(x,y,z * ((u \ w) \ v5)) = L(x,y,z * ((w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,52436,a(flip),b,52371,a),flip(a)].">
      <j1 rule="hyper" parents="64 52436 52371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52450">
    <literal><![CDATA[
      L(x,y,z * ((u \ w) * v5)) = L(x,y,z * ((w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,52341,a(flip),b,52448,a)].">
      <j1 rule="hyper" parents="64 52341 52448"/>
    </justification>
  </clause>

  <clause id="52451">
    <literal><![CDATA[
      L(x,y,z * ((u * (w \ u)) * v5)) = L(x,y,(w * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,29144,a(flip),b,52450,a),flip(a)].">
      <j1 rule="hyper" parents="64 29144 52450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52452">
    <literal><![CDATA[
      a(((x * y) * (y * z)) * (x * z),u,w) = a(z * x,z,a(w,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,52306,a(flip),b,52403,a)].">
      <j1 rule="hyper" parents="64 52306 52403"/>
    </justification>
  </clause>

  <clause id="52453">
    <literal><![CDATA[
      a((x \ (y \ z)) * u,w,v5) = a(((z * y) * x) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52324,a(flip),b,52404,a),flip(a)].">
      <j1 rule="hyper" parents="64 52324 52404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52456">
    <literal><![CDATA[
      a(((x * y) * z) * u,w,v5) = a((z * (y \ x)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52336,a(flip),b,52453,a),flip(a)].">
      <j1 rule="hyper" parents="64 52336 52453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52457">
    <literal><![CDATA[
      a(((x \ y) * z) * u,w,v5) = a(((y * x) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52306,a(flip),b,52453,a)].">
      <j1 rule="hyper" parents="64 52306 52453"/>
    </justification>
  </clause>

  <clause id="52458">
    <literal><![CDATA[
      a((x * (y \ z)) * u,w,v5) = a((x * (z * y)) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32388,a,b,52456,a),flip(a)].">
      <j1 rule="hyper" parents="64 32388 52456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52460">
    <literal><![CDATA[
      a(((x / y) * z) * u,w,v5) = a(((x * y) * z) * u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32396,a,b,52457,a)].">
      <j1 rule="hyper" parents="64 32396 52457"/>
    </justification>
  </clause>

  <clause id="52461">
    <literal><![CDATA[
      a(((x * y) * (y * z)) * (x * z),u,w) = a(x,z,a(w,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52349,a(flip),b,52458,a),flip(a)].">
      <j1 rule="hyper" parents="64 52349 52458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52462">
    <literal><![CDATA[
      (x / (y * z)) * (y * R(z,u,w)) = x * a(((x * (y * z)) * y) * x,u,w)
    ]]></literal>
    <justification jstring="[para(52460(a,1),52005(a,2,2))].">
      <j1 rule="para" parents="52460 52005"/>
    </justification>
  </clause>

  <clause id="52463">
    <literal><![CDATA[
      a(x * y,x,a(z,u,w)) = a(y,x,a(z,u,w * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,52452,a(flip),b,52461,a)].">
      <j1 rule="hyper" parents="64 52452 52461"/>
    </justification>
  </clause>

  <clause id="52464">
    <literal><![CDATA[
      a(x * y,y,a(z,u,w)) = a(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(26847,a,52463,a)].">
      <j1 rule="hyper" parents="26847 52463"/>
    </justification>
  </clause>

  <clause id="52465">
    <literal><![CDATA[
      a(x * (y * z),y,a(u,w,v5)) = a(z * x,y,a(v5,w,u * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,52427,a,b,52463,a)].">
      <j1 rule="hyper" parents="64 52427 52463"/>
    </justification>
  </clause>

  <clause id="52466">
    <literal><![CDATA[
      a(x * (y * z),u,a(w,z,v5)) = a(x * y,z,a(w,u,v5 * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52423,a,b,52463,a)].">
      <j1 rule="hyper" parents="64 52423 52463"/>
    </justification>
  </clause>

  <clause id="52467">
    <literal><![CDATA[
      a(x * (y * z),z,a(u,w,v5)) = a(x * y,z,a(u,w,v5 * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52391,a,b,52463,a)].">
      <j1 rule="hyper" parents="64 52391 52463"/>
    </justification>
  </clause>

  <clause id="52468">
    <literal><![CDATA[
      a(x * y,z,a(u,y,w)) = a(x,y,a(u,z,w * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47395,a,b,52463,a)].">
      <j1 rule="hyper" parents="64 47395 52463"/>
    </justification>
  </clause>

  <clause id="52469">
    <literal><![CDATA[
      a(x * y,z,a(u,x,w)) = a(y,x,a(u,z,w * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47324,a,b,52463,a)].">
      <j1 rule="hyper" parents="64 47324 52463"/>
    </justification>
  </clause>

  <clause id="52470">
    <literal><![CDATA[
      a(x * y,z,a(u,x,w)) = a(y,x,a(w,z,u * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,47298,a,b,52463,a)].">
      <j1 rule="hyper" parents="64 47298 52463"/>
    </justification>
  </clause>

  <clause id="52471">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(x,y,a(w,u,z * y))
    ]]></literal>
    <justification jstring="[para(52463(a,1),46977(a,2,2))].">
      <j1 rule="para" parents="52463 46977"/>
    </justification>
  </clause>

  <clause id="52472">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[para(52463(a,1),47050(a,2,2))].">
      <j1 rule="para" parents="52463 47050"/>
    </justification>
  </clause>

  <clause id="52473">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,a(w,v5,v6))) = y * a(v6,v5,a(x,y,a(w,u,z * y)))
    ]]></literal>
    <justification jstring="[para(52463(a,1),47548(a,2,2,3))].">
      <j1 rule="para" parents="52463 47548"/>
    </justification>
  </clause>

  <clause id="52474">
    <literal><![CDATA[
      a(a(x * y,y,z),u,w) = a(z * y,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47254,a,b,52464,a)].">
      <j1 rule="hyper" parents="373 47254 52464"/>
    </justification>
  </clause>

  <clause id="52475">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6 * u))) = L(x,u,a(w,y,a(v6,v5,z * u)))
    ]]></literal>
    <justification jstring="[para(52464(a,1),47452(a,2,3)),flip(a)].">
      <j1 rule="para" parents="52464 47452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52476">
    <literal><![CDATA[
      x * a(x * y,z,a(u,y,w)) = L(x,y,a(u,z,w * y))
    ]]></literal>
    <justification jstring="[hyper(145,a,52468,a,b,45194,a)].">
      <j1 rule="hyper" parents="145 52468 45194"/>
    </justification>
  </clause>

  <clause id="52477">
    <literal><![CDATA[
      a(x * y,z,a(x,u,w * z)) = a(x,z,a(w,u,x * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47678,a(flip),b,52468,a),flip(a)].">
      <j1 rule="hyper" parents="64 47678 52468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52478">
    <literal><![CDATA[
      a(x,y,a(z,u,w * y)) \ z = L(z,y,a(w,u,x * y))
    ]]></literal>
    <justification jstring="[para(52468(a,1),47371(a,1,1))].">
      <j1 rule="para" parents="52468 47371"/>
    </justification>
  </clause>

  <clause id="52480">
    <literal><![CDATA[
      a(x * y,z,a(u,x,u \ (w \ x))) = a(y,x,a(u,z,(w \ (u \ x)) * x))
    ]]></literal>
    <justification jstring="[para(48185(a,1),52469(a,1,3))].">
      <j1 rule="para" parents="48185 52469"/>
    </justification>
  </clause>

  <clause id="52482">
    <literal><![CDATA[
      a(x,y,a(z,u,w * y)) = a(x,y,a(w,u,z * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,52469,a(flip),b,52470,a)].">
      <j1 rule="hyper" parents="64 52469 52470"/>
    </justification>
  </clause>

  <clause id="52483">
    <literal><![CDATA[
      a(a(x * y,y,z),u,a(w,v5,v6)) = a(z * y,y,a(v6,v5,a(x,u,w)))
    ]]></literal>
    <justification jstring="[para(47254(a,1),52474(a,2,3))].">
      <j1 rule="para" parents="47254 52474"/>
    </justification>
  </clause>

  <clause id="52484">
    <literal><![CDATA[
      a(x,y,a(y * z,u,w)) = a(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,41897,a,b,52482,a)].">
      <j1 rule="hyper" parents="373 41897 52482"/>
    </justification>
  </clause>

  <clause id="52485">
    <literal><![CDATA[
      a(x,y,a(z * y,u,w)) = a(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,41883,a,b,52482,a)].">
      <j1 rule="hyper" parents="373 41883 52482"/>
    </justification>
  </clause>

  <clause id="52486">
    <literal><![CDATA[
      a(x,y,a(z * y,u,w)) = a(x,u,a(z,y,w * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,47324,a,b,52485,a),flip(a)].">
      <j1 rule="hyper" parents="373 47324 52485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52487">
    <literal><![CDATA[
      a(x,y,a(z * u,u,w)) = a(x,y,a(z,u,w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47324,a,b,52486,a)].">
      <j1 rule="hyper" parents="64 47324 52486"/>
    </justification>
  </clause>

  <clause id="52488">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6 * v5))) = L(x,v5,a(v6,u,a(z,y,w * v5)))
    ]]></literal>
    <justification jstring="[para(52486(a,1),47453(a,2,3)),flip(a)].">
      <j1 rule="para" parents="52486 47453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52489">
    <literal><![CDATA[
      a(x,y,a(z * u,u,w)) = a(x,y,a(z,u,u * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27752,a,b,52487,a),flip(a)].">
      <j1 rule="hyper" parents="373 27752 52487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52490">
    <literal><![CDATA[
      a(x,y,a(z * u,z,w)) = a(x,y,a(u,z,w * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,26881,a,b,52487,a)].">
      <j1 rule="hyper" parents="64 26881 52487"/>
    </justification>
  </clause>

  <clause id="52491">
    <literal><![CDATA[
      a(x,y,a(z \ 1,z \ (a(u,w,v5) \ 1),v6 * (z \ (a(u,w,v5) \ 1)))) = a(x,y,a(a(u,w,v5) \ (z \ (1 / z)),z \ (a(u,w,v5) \ 1),v6))
    ]]></literal>
    <justification jstring="[para(23909(a,1),52487(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="23909 52487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52492">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),u,v5)) = a(x,y,a(z * w,u,v5 * u))
    ]]></literal>
    <justification jstring="[para(52334(a,1),52487(a,1,3))].">
      <j1 rule="para" parents="52334 52487"/>
    </justification>
  </clause>

  <clause id="52493">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6 * u))) = a(x,y,a(z,u,u * a(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(52464(a,1),52489(a,1,3))].">
      <j1 rule="para" parents="52464 52489"/>
    </justification>
  </clause>

  <clause id="52494">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),w,v5)) = a(x,y,a(u * z,w,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,52396,a,b,52490,a)].">
      <j1 rule="hyper" parents="64 52396 52490"/>
    </justification>
  </clause>

  <clause id="52495">
    <literal><![CDATA[
      x * a(y,z,a(x * u,u,w)) = L(x,u,a(w,z,y * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47309,a(flip),b,52476,a)].">
      <j1 rule="hyper" parents="64 47309 52476"/>
    </justification>
  </clause>

  <clause id="52496">
    <literal><![CDATA[
      a(x,y,a(z * y,u,w)) * w = L(w,y,a(z,u,x * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,42644,a(flip),b,52478,a)].">
      <j1 rule="hyper" parents="64 42644 52478"/>
    </justification>
  </clause>

  <clause id="52497">
    <literal><![CDATA[
      a(x,y,z) * ((u / w) * (a(x,y,z) \ w)) = L(u,w,a(x,y,z * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47370,a,b,52495,a)].">
      <j1 rule="hyper" parents="64 47370 52495"/>
    </justification>
  </clause>

  <clause id="52498">
    <literal><![CDATA[
      L(x,y,a(z * y,u,w)) = L(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47384,a(flip),b,52496,a)].">
      <j1 rule="hyper" parents="64 47384 52496"/>
    </justification>
  </clause>

  <clause id="52499">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w * u,v5,v6))) = L(x,u,a(w,y,a(v6,v5,z) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47452,a(flip),b,52498,a)].">
      <j1 rule="hyper" parents="64 47452 52498"/>
    </justification>
  </clause>

  <clause id="52500">
    <literal><![CDATA[
      L(x,y,a(y * z,u,w)) = L(x,y,a(z,u,w * y))
    ]]></literal>
    <justification jstring="[para(26787(a,1),52498(a,1,3))].">
      <j1 rule="para" parents="26787 52498"/>
    </justification>
  </clause>

  <clause id="52501">
    <literal><![CDATA[
      a(x * y,z,a(u,w,x * z)) = a(x,z,a(u,w,x * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,49362,a(flip),b,52465,a),flip(a)].">
      <j1 rule="hyper" parents="64 49362 52465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52502">
    <literal><![CDATA[
      x * a(y * z,u,a(y,w,x * u)) = L(x,w,a(u * (z * y),u,y))
    ]]></literal>
    <justification jstring="[para(52465(a,1),48337(a,1,2))].">
      <j1 rule="para" parents="52465 48337"/>
    </justification>
  </clause>

  <clause id="52504">
    <literal><![CDATA[
      x \ ((x * y) * a(x \ 1,(x \ 1) * y,a(z,u,w * ((x \ 1) * y)))) = L((x \ 1) \ ((x \ 1) * y),(x \ 1) * y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,1596,a,b,52471,a)].">
      <j1 rule="hyper" parents="35 1596 52471"/>
    </justification>
  </clause>

  <clause id="52505">
    <literal><![CDATA[
      (x \ y) * a(z,x \ y,a(u,w,v5 * (x \ y))) = z * L(z \ (x \ y),y * x,a(v5,w,u))
    ]]></literal>
    <justification jstring="[para(52063(a,1),52471(a,1,2)),flip(a)].">
      <j1 rule="para" parents="52063 52471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52506">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w * v5)) = y * a(x,y,a(z,u,y * (v5 * w)))
    ]]></literal>
    <justification jstring="[para(27462(a,1),52472(a,2,2,3))].">
      <j1 rule="para" parents="27462 52472"/>
    </justification>
  </clause>

  <clause id="52507">
    <literal><![CDATA[
      a(x,y,a(x * z,u,w * u)) = a(x,u,a(w,y,x * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47253,a,b,52477,a)].">
      <j1 rule="hyper" parents="64 47253 52477"/>
    </justification>
  </clause>

  <clause id="52509">
    <literal><![CDATA[
      a(a(x * y,y,z),u,a(w,v5,v6)) = a(z,y,a(v6,v5,a(x,u,w) * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,52464,a(flip),b,52483,a),flip(a)].">
      <j1 rule="hyper" parents="373 52464 52483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52510">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6 * u))) = L(x,u,a(w,y,a(v6,v5,z) * u))
    ]]></literal>
    <justification jstring="[para(52485(a,1),52499(a,1,3))].">
      <j1 rule="para" parents="52485 52499"/>
    </justification>
  </clause>

  <clause id="52511">
    <literal><![CDATA[
      x * a(y,z,a(y * u,w,x * w)) = L(x,z,a(w * (u * y),w,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47259,a,b,52502,a)].">
      <j1 rule="hyper" parents="64 47259 52502"/>
    </justification>
  </clause>

  <clause id="52512">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w),v5,v6 * y)) = a(x,y,a(w,u,a(v6,v5,z) * y))
    ]]></literal>
    <justification jstring="[hyper(47392,a,52509,a)].">
      <j1 rule="hyper" parents="47392 52509"/>
    </justification>
  </clause>

  <clause id="52513">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6 * y))) = L(x,y,a(z,u,a(w,v5,v6) * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,52475,a(flip),b,52510,a)].">
      <j1 rule="hyper" parents="64 52475 52510"/>
    </justification>
  </clause>

  <clause id="52514">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w * y,v5,v6))) = a(x,y,a(z,u,a(w,v5,v6) * y))
    ]]></literal>
    <justification jstring="[para(47254(a,1),52512(a,1,3))].">
      <j1 rule="para" parents="47254 52512"/>
    </justification>
  </clause>

  <clause id="52515">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6 * y))) = L(x,y,a(z,u,y * a(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,28846,a,b,52513,a),flip(a)].">
      <j1 rule="hyper" parents="373 28846 52513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52516">
    <literal><![CDATA[
      (x / (y * z)) * (y * R(z,u,w)) = x * a(x * (y * ((y * z) * x)),u,w)
    ]]></literal>
    <justification jstring="[para(32657(a,1),52462(a,2,2))].">
      <j1 rule="para" parents="32657 52462"/>
    </justification>
  </clause>

  <clause id="52517">
    <literal><![CDATA[
      a(x * y,z,a(u,x,u * (w \ x))) = a(y,x,a(u,z,(w \ (u \ x)) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,49778,a(flip),b,52480,a)].">
      <j1 rule="hyper" parents="64 49778 52480"/>
    </justification>
  </clause>

  <clause id="52518">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,a(w,v5,v6 * y))) = y * a(x,y,a(z,u,y * (a(w,v5,v6) * y)))
    ]]></literal>
    <justification jstring="[para(52515(a,2),52506(a,1,2))].">
      <j1 rule="para" parents="52515 52506"/>
    </justification>
  </clause>

  <clause id="52519">
    <literal><![CDATA[
      (x / (y * z)) * (y * R(z,u,w)) = x * a(z,u,L(L(w,x,y),y,x))
    ]]></literal>
    <justification jstring="[para(52390(a,1),52516(a,2,2))].">
      <j1 rule="para" parents="52390 52516"/>
    </justification>
  </clause>

  <clause id="52520">
    <literal><![CDATA[
      (x / (y * z)) * (y * R(z,u,w)) = y \ ((y * a(z,u,w)) * x)
    ]]></literal>
    <justification jstring="[hyper(373,a,47010,a(flip),b,52519,a),flip(a)].">
      <j1 rule="hyper" parents="373 47010 52519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52521">
    <literal><![CDATA[
      (x * R(y,z,u)) * ((x * y) \ w) = x \ ((x * a(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,28547,a(flip),b,52520,a)].">
      <j1 rule="hyper" parents="64 28547 52520"/>
    </justification>
  </clause>

  <clause id="52522">
    <literal><![CDATA[
      a(x,y,a(z * (y * L(x,u,w)),v5,v6)) = a(x,y,a(L(x,u,w) * z,v5,v6 * y))
    ]]></literal>
    <justification jstring="[hyper(64,a,52484,a(flip),b,52440,a),flip(a)].">
      <j1 rule="hyper" parents="64 52484 52440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52523">
    <literal><![CDATA[
      L(x,y,a(z,u * z,(u \ z) \ w)) = L(x,y,(u * (z * w)) * ((u \ z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,52451,a(flip),b,52370,a),flip(a)].">
      <j1 rule="hyper" parents="64 52451 52370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52525">
    <literal><![CDATA[
      L(x,y,a(z,u * z,(u \ z) \ w)) = L(x,y,(u * (z * w)) * ((z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,52448,a(flip),b,52523,a),flip(a)].">
      <j1 rule="hyper" parents="373 52448 52523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52526">
    <literal><![CDATA[
      L(x,y,a(z,u * z,(u \ z) \ w)) = L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,49154,a(flip),b,52525,a),flip(a)].">
      <j1 rule="hyper" parents="373 49154 52525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52529">
    <literal><![CDATA[
      a(x * (a(y,x,z) * u),w,a(y,x,z)) = a(z,w,a(y,x,(y \ ((y * x) * z)) * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,50136,a(flip),b,52408,a),flip(a)].">
      <j1 rule="hyper" parents="373 50136 52408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52530">
    <literal><![CDATA[
      (x \ y) * a(z * u,x \ y,a(w,v5,v6 * (x \ y))) = z * (u * L(u \ (z \ (x \ y)),y * x,a(v6,v5,w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,1705,a(flip),b,52505,a),flip(a)].">
      <j1 rule="hyper" parents="373 1705 52505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52531">
    <literal><![CDATA[
      (x \ y) * a(z * (x \ y),x \ y,a(u,w,v5 * (x \ y))) = z * (L(z,y * x,a(u,w,v5)) \ (x \ y))
    ]]></literal>
    <justification jstring="[para(49813(a,1),52530(a,2,2))].">
      <j1 rule="para" parents="49813 52530"/>
    </justification>
  </clause>

  <clause id="52532">
    <literal><![CDATA[
      (x \ y) * a(z * (x \ y),x \ y,a(u,w,v5 * (x \ y))) = (x \ y) * a(a(u,w,v5),y * x,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,51009,a(flip),b,52531,a),flip(a)].">
      <j1 rule="hyper" parents="373 51009 52531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52533">
    <literal><![CDATA[
      (x \ y) * a(z * (x \ y),x \ y,a(u,w,v5 * (x \ y))) = (x \ y) * a(v5,w,a(z,y * x,u))
    ]]></literal>
    <justification jstring="[para(47254(a,1),52532(a,2,2))].">
      <j1 rule="para" parents="47254 52532"/>
    </justification>
  </clause>

  <clause id="52534">
    <literal><![CDATA[
      (x \ y) * a(y * (x \ y),x \ y,a(z,u,w * (x \ y))) = (x \ y) * a(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(51944(a,1),52533(a,2,2))].">
      <j1 rule="para" parents="51944 52533"/>
    </justification>
  </clause>

  <clause id="52535">
    <literal><![CDATA[
      (x \ y) * a(y * (x \ y),x \ y,a(z,u,w * (x \ y))) = x \ L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,49833,a(flip),b,52534,a),flip(a)].">
      <j1 rule="hyper" parents="373 49833 52534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52536">
    <literal><![CDATA[
      L(L(x,y,z),L(u,w,v5),v6) \ L(x,y,L(z,w * (v5 * ((v5 \ w) * u)),v6)) = a(v6,L(u,v5 * w,v5),x)
    ]]></literal>
    <justification jstring="[para(52246(a,1),52227(a,1,1))].">
      <j1 rule="para" parents="52246 52227"/>
    </justification>
  </clause>

  <clause id="52537">
    <literal><![CDATA[
      L(L(x,y,z),L(u,w,v5),v6) \ L(x,y,L(z,L(u,w,v5),v6)) = a(v6,L(u,v5 * w,v5),x)
    ]]></literal>
    <justification jstring="[para(52246(a,1),52536(a,1,2,3))].">
      <j1 rule="para" parents="52246 52536"/>
    </justification>
  </clause>

  <clause id="52538">
    <literal><![CDATA[
      a(x,L(y,z * u,z),w) = a(x,L(y,u,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,47129,a(flip),b,52537,a),flip(a)].">
      <j1 rule="hyper" parents="64 47129 52537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52539">
    <literal><![CDATA[
      a(x,L(y / (z \ u),u,z),w) = a(x,u * (z * y),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,52253,a(flip),b,52538,a),flip(a)].">
      <j1 rule="hyper" parents="64 52253 52538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52540">
    <literal><![CDATA[
      a(x,L((y \ z) * u,z,y),w) = a(x,z * (y * u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,52217,a(flip),b,52539,a)].">
      <j1 rule="hyper" parents="64 52217 52539"/>
    </justification>
  </clause>

  <clause id="52541">
    <literal><![CDATA[
      a(x,y * (z * (z * u)),w) = a(x,L(y,z,z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,52228,a(flip),b,52540,a),flip(a)].">
      <j1 rule="hyper" parents="64 52228 52540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52542">
    <literal><![CDATA[
      a(x,L(y,z,z) * u,w) = a(x,y * L(u,z,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32110,a(flip),b,52541,a),flip(a)].">
      <j1 rule="hyper" parents="64 32110 52541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52543">
    <literal><![CDATA[
      a(x,y * L(z,u,u),w) = a(x,z * L(y,u,u),w)
    ]]></literal>
    <justification jstring="[hyper(32008,a,52542,a)].">
      <j1 rule="hyper" parents="32008 52542"/>
    </justification>
  </clause>

  <clause id="52544">
    <literal><![CDATA[
      L(L(x,y,z),u * L(w,v5,v5),v6) \ L(x,y,L(z,u * L(w,v5,v5),v6)) = a(v6,w * L(u,v5,v5),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,47129,a,b,52543,a)].">
      <j1 rule="hyper" parents="373 47129 52543"/>
    </justification>
  </clause>

  <clause id="52545">
    <literal><![CDATA[
      a(x,L(y,z,u) * L(u * z,w,w),v5) = a(x,u * (z * L(y,w,w)),v5)
    ]]></literal>
    <justification jstring="[para(513(a,1),52543(a,1,2)),flip(a)].">
      <j1 rule="para" parents="513 52543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52546">
    <literal><![CDATA[
      L(L(x,y,z),u * w,v5) \ L(x,y,L(z,u * L(w,v6,v6),v5)) = a(v5,w * L(u,v6,v6),x)
    ]]></literal>
    <justification jstring="[para(52028(a,1),52544(a,1,1))].">
      <j1 rule="para" parents="52028 52544"/>
    </justification>
  </clause>

  <clause id="52547">
    <literal><![CDATA[
      a(x,y * L(z,u,u),w) = L(L(w,v5,v6),z * y,x) \ L(w,v5,L(v6,z * y,x))
    ]]></literal>
    <justification jstring="[para(52028(a,1),52546(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="52028 52546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52549">
    <literal><![CDATA[
      a(x,y * L(z,u,u),w) = a(x,z * y,w)
    ]]></literal>
    <justification jstring="[hyper(373,a,47129,a(flip),b,52547,a),flip(a)].">
      <j1 rule="hyper" parents="373 47129 52547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52551">
    <literal><![CDATA[
      a(x,(y * z) * L(u,z,y),w) = a(x,y * (z * L(u,v5,v5)),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,52545,a(flip),b,52549,a),flip(a)].">
      <j1 rule="hyper" parents="64 52545 52549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52552">
    <literal><![CDATA[
      a(x,(y \ z) * u,w) = a(x,(y * z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32338,a(flip),b,52549,a)].">
      <j1 rule="hyper" parents="64 32338 52549"/>
    </justification>
  </clause>

  <clause id="52557">
    <literal><![CDATA[
      a(x,(L(y * z,y,y) * u) * w,v5) = a(x,w * ((y \ z) \ u),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34128,a(flip),b,52552,a),flip(a)].">
      <j1 rule="hyper" parents="64 34128 52552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52558">
    <literal><![CDATA[
      a(x,((y \ z) * z) * u,w) = a(x,u * y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32091,a(flip),b,52552,a),flip(a)].">
      <j1 rule="hyper" parents="64 32091 52552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52559">
    <literal><![CDATA[
      a(x,((y \ (z \ y)) * y) * u,w) = a(x,u * (y * z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,33022,a(flip),b,52558,a)].">
      <j1 rule="hyper" parents="64 33022 52558"/>
    </justification>
  </clause>

  <clause id="52560">
    <literal><![CDATA[
      a(x,y * (z \ u),w) = a(x,y * (u * z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,32054,a(flip),b,52559,a)].">
      <j1 rule="hyper" parents="64 32054 52559"/>
    </justification>
  </clause>

  <clause id="52564">
    <literal><![CDATA[
      a(x,y,a(z,u * ((1 / w) * a(v5,v6,v7)),w \ a(v5,v6,v7))) = a(a(v5,v6,v7) \ (1 / w),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(52560(a,1),52254(a,1,3))].">
      <j1 rule="para" parents="52560 52254"/>
    </justification>
  </clause>

  <clause id="52566">
    <literal><![CDATA[
      a(x,y * (z * L(u,w,w)),v5) = a(x,y * (z * u),v5)
    ]]></literal>
    <justification jstring="[para(100(a,1),52551(a,1,2)),flip(a)].">
      <j1 rule="para" parents="100 52551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52567">
    <literal><![CDATA[
      a(x,(L(y,z,z) * u) * w,v5) = a(x,w * (u * y),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,32049,a,b,52566,a)].">
      <j1 rule="hyper" parents="64 32049 52566"/>
    </justification>
  </clause>

  <clause id="52568">
    <literal><![CDATA[
      a(x,y * ((z \ u) \ w),v5) = a(x,y * (w * (z * u)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52567,a(flip),b,52557,a),flip(a)].">
      <j1 rule="hyper" parents="64 52567 52557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52570">
    <literal><![CDATA[
      a(x,y * (z * (u \ w)),v5) = a(x,y * (z * (u * w)),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52560,a(flip),b,52568,a)].">
      <j1 rule="hyper" parents="64 52560 52568"/>
    </justification>
  </clause>

  <clause id="52571">
    <literal><![CDATA[
      a(x,y * (z * ((u \ K(w,v5)) * v6)),v7) = a(x,(z * (u \ v6)) * y,v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,33042,a(flip),b,52570,a),flip(a)].">
      <j1 rule="hyper" parents="64 33042 52570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52572">
    <literal><![CDATA[
      a(x,(y * (z \ u)) * w,v5) = a(x,(y * (z * u)) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,34134,a(flip),b,52571,a),flip(a)].">
      <j1 rule="hyper" parents="64 34134 52571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52573">
    <literal><![CDATA[
      a(x,y,a(z,u * (a(w,v5,v6) / v7),v7 \ a(w,v5,v6))) = a(a(w,v5,v6) \ (1 / v7),u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(51154(a,1),52564(a,1,3,2,2))].">
      <j1 rule="para" parents="51154 52564"/>
    </justification>
  </clause>

  <clause id="52574">
    <literal><![CDATA[
      a(a(x,y,z) \ (1 / u),u,a(w,v5,v6)) = a(w,v5,a(v6,a(x,y,z),u \ a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(31890(a,1),52573(a,1,3)),flip(a)].">
      <j1 rule="para" parents="31890 52573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52575">
    <literal><![CDATA[
      a(a(x,y,z) \ (1 / u),u,a(w,v5,v6)) = a(w,v5,a(v6,a(x,y,z),u * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,49778,a(flip),b,52574,a),flip(a)].">
      <j1 rule="hyper" parents="373 49778 52574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52576">
    <literal><![CDATA[
      R(R(x,y,z),y * z,L(u \ L(u,u,w),z,x * y)) = ((x * y) * (a(w,u,u) \ z)) / ((y * z) * (a(w,u,u) \ 1))
    ]]></literal>
    <justification jstring="[para(37839(a,1),51809(a,2,1,2))].">
      <j1 rule="para" parents="37839 51809"/>
    </justification>
  </clause>

  <clause id="52577">
    <literal><![CDATA[
      R(R(x,y,z),y * z,L(u \ L(u,u,w),z,x * y)) = ((x * y) * (a(w,u,u) \ z)) / (a(w,u,u) \ (y * z))
    ]]></literal>
    <justification jstring="[para(37826(a,1),52576(a,2,2))].">
      <j1 rule="para" parents="37826 52576"/>
    </justification>
  </clause>

  <clause id="52578">
    <literal><![CDATA[
      R(R(x,y,z),y * z,L(u \ L(u,u,w),z,x * y)) = ((x * y) * (a(w,u,u) \ z)) / (y * (a(w,u,u) \ z))
    ]]></literal>
    <justification jstring="[para(50832(a,1),52577(a,2,2))].">
      <j1 rule="para" parents="50832 52577"/>
    </justification>
  </clause>

  <clause id="52579">
    <literal><![CDATA[
      R(R(x,y,z),y * z,L(u \ L(u,u,w),z,x * y)) = R(x,y,a(w,u,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,20,a,b,52578,a),flip(a)].">
      <j1 rule="hyper" parents="373 20 52578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52580">
    <literal><![CDATA[
      R(R(x,y,z),y * z,L(u \ L(u,u,w),z,x * y)) = R(x,y,a(w,u,u) * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,42481,a(flip),b,52579,a),flip(a)].">
      <j1 rule="hyper" parents="373 42481 52579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52581">
    <literal><![CDATA[
      R(R(x,y,z),y * z,a(u,w,w) \ 1) = R(x,y,a(u,w,w) * z)
    ]]></literal>
    <justification jstring="[para(51803(a,1),52580(a,1,3))].">
      <j1 rule="para" parents="51803 52580"/>
    </justification>
  </clause>

  <clause id="52582">
    <literal><![CDATA[
      L(R(x,y,z),y * z,a(u,w,w)) = R(x,y,a(u,w,w) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38615,a(flip),b,52581,a)].">
      <j1 rule="hyper" parents="64 38615 52581"/>
    </justification>
  </clause>

  <clause id="52584">
    <literal><![CDATA[
      R(x,y,a(z,u,u) * w) = R(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,50749,a(flip),b,52582,a),flip(a)].">
      <j1 rule="hyper" parents="64 50749 52582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52588">
    <literal><![CDATA[
      R(x,y,z * a(u,u,w)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,38899,a(flip),b,52584,a)].">
      <j1 rule="hyper" parents="64 38899 52584"/>
    </justification>
  </clause>

  <clause id="52598">
    <literal><![CDATA[
      a(x,y,z * a(u,u,w)) = L(x,v5,L(v6,y,z)) \ L(R(x,y,z),v5,v6)
    ]]></literal>
    <justification jstring="[para(52588(a,1),52280(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="52588 52280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52600">
    <literal><![CDATA[
      a(x,y,z * a(u,u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(373,a,51749,a(flip),b,52598,a),flip(a)].">
      <j1 rule="hyper" parents="373 51749 52598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52602">
    <literal><![CDATA[
      a(x,y,a(z,z,u) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(27453,a,52600,a)].">
      <j1 rule="hyper" parents="27453 52600"/>
    </justification>
  </clause>

  <clause id="52605">
    <literal><![CDATA[
      a(x,y,z * a(u,w,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46474,a,b,52600,a)].">
      <j1 rule="hyper" parents="64 46474 52600"/>
    </justification>
  </clause>

  <clause id="52606">
    <literal><![CDATA[
      a(x,y,a(z,u,u) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(64,a,46473,a,b,52600,a)].">
      <j1 rule="hyper" parents="64 46473 52600"/>
    </justification>
  </clause>

  <clause id="52607">
    <literal><![CDATA[
      a(x,y,z \ (u * L(w,v5,v5))) = a(x,y,z \ (u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,49908,a(flip),b,52600,a)].">
      <j1 rule="hyper" parents="64 49908 52600"/>
    </justification>
  </clause>

  <clause id="52608">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) * w)) = a(x,y,z \ (u \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,48223,a(flip),b,52600,a)].">
      <j1 rule="hyper" parents="64 48223 52600"/>
    </justification>
  </clause>

  <clause id="52609">
    <literal><![CDATA[
      a(x,y,(((z * u) \ u) \ 1) \ w) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,38935,a(flip),b,52600,a),flip(a)].">
      <j1 rule="hyper" parents="64 38935 52600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52610">
    <literal><![CDATA[
      a(x,y,L(z,u,u) \ w) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(39695(a,1),52600(a,1,3))].">
      <j1 rule="para" parents="39695 52600"/>
    </justification>
  </clause>

  <clause id="52611">
    <literal><![CDATA[
      a(x,y,z * L(u,w,w)) = a(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(39720(a,1),52600(a,1,3)),flip(a)].">
      <j1 rule="para" parents="39720 52600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52613">
    <literal><![CDATA[
      a(x,y,(z * a(u,u,w)) * v5) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(46522(a,1),52600(a,1,3))].">
      <j1 rule="para" parents="46522 52600"/>
    </justification>
  </clause>

  <clause id="52615">
    <literal><![CDATA[
      a(x,y,z * ((u * u) * w)) = a(x,y,z * (u * (u * w)))
    ]]></literal>
    <justification jstring="[para(51953(a,1),52600(a,1,3))].">
      <j1 rule="para" parents="51953 52600"/>
    </justification>
  </clause>

  <clause id="52619">
    <literal><![CDATA[
      a(x,y,z * (a(u,u,w) * v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,49857,a(flip),b,52602,a)].">
      <j1 rule="hyper" parents="64 49857 52602"/>
    </justification>
  </clause>

  <clause id="52620">
    <literal><![CDATA[
      a(x,y,(z \ L(u,u,w)) * v5) = a(x,y,(z \ u) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,49854,a(flip),b,52602,a),flip(a)].">
      <j1 rule="hyper" parents="64 49854 52602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52621">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ 1))) = a(x,y,z * (w \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47176,a(flip),b,52602,a)].">
      <j1 rule="hyper" parents="64 47176 52602"/>
    </justification>
  </clause>

  <clause id="52622">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) * w) = a(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,47111,a(flip),b,52602,a)].">
      <j1 rule="hyper" parents="64 47111 52602"/>
    </justification>
  </clause>

  <clause id="52629">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) \ w) = a(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,50418,a(flip),b,52605,a),flip(a)].">
      <j1 rule="hyper" parents="64 50418 52605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52639">
    <literal><![CDATA[
      a(x,y,((R(z,z,u) \ w) * z) \ v5) = a(x,y,w \ v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52009,a,b,52606,a)].">
      <j1 rule="hyper" parents="64 52009 52606"/>
    </justification>
  </clause>

  <clause id="52648">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) \ w) = a(x,y,(u * z) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,39109,a(flip),b,52610,a)].">
      <j1 rule="hyper" parents="64 39109 52610"/>
    </justification>
  </clause>

  <clause id="52651">
    <literal><![CDATA[
      a(x,y,z * L(u,w,w)) = a(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,52611,a),flip(a)].">
      <j1 rule="hyper" parents="373 27298 52611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52655">
    <literal><![CDATA[
      a(x,y,z * (u * (w \ 1))) = a(x,y,(w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,39486,a(flip),b,52611,a),flip(a)].">
      <j1 rule="hyper" parents="64 39486 52611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52656">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ w)) = a(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,39034,a(flip),b,52611,a)].">
      <j1 rule="hyper" parents="64 39034 52611"/>
    </justification>
  </clause>

  <clause id="52657">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ w)) = a(x,y,z * (u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,39033,a(flip),b,52611,a)].">
      <j1 rule="hyper" parents="64 39033 52611"/>
    </justification>
  </clause>

  <clause id="52658">
    <literal><![CDATA[
      a(x,y,z * ((u * u) \ w)) = a(x,y,z * (u \ (u \ w)))
    ]]></literal>
    <justification jstring="[para(346(a,1),52611(a,1,3,2))].">
      <j1 rule="para" parents="346 52611"/>
    </justification>
  </clause>

  <clause id="52660">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(w,z,u)) = a(x,y,u * ((z \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,42314,a,b,52651,a)].">
      <j1 rule="hyper" parents="64 42314 52651"/>
    </justification>
  </clause>

  <clause id="52661">
    <literal><![CDATA[
      a(x,y,z * (u \ ((u \ 1) \ w))) = a(x,y,w * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,39036,a,b,52651,a)].">
      <j1 rule="hyper" parents="64 39036 52651"/>
    </justification>
  </clause>

  <clause id="52663">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ w)) = a(x,y,(w * u) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,39034,a(flip),b,52651,a)].">
      <j1 rule="hyper" parents="64 39034 52651"/>
    </justification>
  </clause>

  <clause id="52664">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ w)) = a(x,y,(u * w) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,39033,a(flip),b,52651,a)].">
      <j1 rule="hyper" parents="64 39033 52651"/>
    </justification>
  </clause>

  <clause id="52667">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * w) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[para(30227(a,1),52613(a,1,3,1))].">
      <j1 rule="para" parents="30227 52613"/>
    </justification>
  </clause>

  <clause id="52672">
    <literal><![CDATA[
      a(x,y,z * (R(u,u,w) * v5)) = a(x,y,z * (u * v5))
    ]]></literal>
    <justification jstring="[para(37597(a,1),52619(a,1,3,2))].">
      <j1 rule="para" parents="37597 52619"/>
    </justification>
  </clause>

  <clause id="52674">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ 1))) = a(x,y,z \ (w \ u))
    ]]></literal>
    <justification jstring="[hyper(27589,a,52608,a)].">
      <j1 rule="hyper" parents="27589 52608"/>
    </justification>
  </clause>

  <clause id="52678">
    <literal><![CDATA[
      a(x,y,((z * u) \ u) * w) = a(x,y,z \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,51318,a(flip),b,52609,a)].">
      <j1 rule="hyper" parents="64 51318 52609"/>
    </justification>
  </clause>

  <clause id="52679">
    <literal><![CDATA[
      a(x,y,z * ((u * w) \ w)) = a(x,y,u \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,51317,a(flip),b,52609,a)].">
      <j1 rule="hyper" parents="64 51317 52609"/>
    </justification>
  </clause>

  <clause id="52680">
    <literal><![CDATA[
      a(x,y,((z * u) \ z) * w) = a(x,y,u \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27406,a,b,52678,a)].">
      <j1 rule="hyper" parents="64 27406 52678"/>
    </justification>
  </clause>

  <clause id="52681">
    <literal><![CDATA[
      a(x,y,(z \ (u \ z)) * w) = a(x,y,u \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27723,a(flip),b,52678,a)].">
      <j1 rule="hyper" parents="64 27723 52678"/>
    </justification>
  </clause>

  <clause id="52682">
    <literal><![CDATA[
      a(x,y,(z \ u) \ w) = a(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27413,a(flip),b,52678,a),flip(a)].">
      <j1 rule="hyper" parents="64 27413 52678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52683">
    <literal><![CDATA[
      a(x,y,(z \ u) \ w) = a(x,y,w * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27504,a(flip),b,52679,a),flip(a)].">
      <j1 rule="hyper" parents="64 27504 52679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52688">
    <literal><![CDATA[
      a(x,y,z \ (u \ (z * w))) = a(x,y,z * (u \ (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,48772,a(flip),b,52681,a),flip(a)].">
      <j1 rule="hyper" parents="64 48772 52681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52692">
    <literal><![CDATA[
      a(x,y,z \ ((x \ u) * u)) = a(x,y,(z \ (x \ u)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,51766,a(flip),b,52682,a)].">
      <j1 rule="hyper" parents="64 51766 52682"/>
    </justification>
  </clause>

  <clause id="52693">
    <literal><![CDATA[
      a(x,y,x \ (z * u)) = a(x,y,(x \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,51461,a(flip),b,52682,a)].">
      <j1 rule="hyper" parents="64 51461 52682"/>
    </justification>
  </clause>

  <clause id="52694">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((u \ z) \ w)) = a(x,y,(z \ u) * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,40539,a(flip),b,52682,a),flip(a)].">
      <j1 rule="hyper" parents="64 40539 52682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52695">
    <literal><![CDATA[
      L(x,a(y,z * y,(y \ z) * u),w) = L(x,a(u,y,z),w)
    ]]></literal>
    <justification jstring="[para(52682(a,1),52260(a,1,2))].">
      <j1 rule="para" parents="52682 52260"/>
    </justification>
  </clause>

  <clause id="52696">
    <literal><![CDATA[
      L(x,y,a(z,u * z,(z \ u) * w)) = L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[para(52682(a,1),52526(a,1,3))].">
      <j1 rule="para" parents="52682 52526"/>
    </justification>
  </clause>

  <clause id="52697">
    <literal><![CDATA[
      a(x,y,z \ (y * u)) = a(x,y,u * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,51836,a(flip),b,52683,a)].">
      <j1 rule="hyper" parents="64 51836 52683"/>
    </justification>
  </clause>

  <clause id="52698">
    <literal><![CDATA[
      a(x,y,z \ (x * u)) = a(x,y,u * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(64,a,46230,a(flip),b,52683,a)].">
      <j1 rule="hyper" parents="64 46230 52683"/>
    </justification>
  </clause>

  <clause id="52699">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ x)) = a(x,y,u * (x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,51318,a(flip),b,52698,a),flip(a)].">
      <j1 rule="hyper" parents="64 51318 52698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52700">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) * w) = a(x,y,w * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(27453,a,52621,a)].">
      <j1 rule="hyper" parents="27453 52621"/>
    </justification>
  </clause>

  <clause id="52703">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) * w)) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(27453,a,52622,a)].">
      <j1 rule="hyper" parents="27453 52622"/>
    </justification>
  </clause>

  <clause id="52706">
    <literal><![CDATA[
      a(x,y,(z * u) * (w \ (z \ 1))) = a(x,y,(z \ u) * (w \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,28055,a(flip),b,52622,a)].">
      <j1 rule="hyper" parents="64 28055 52622"/>
    </justification>
  </clause>

  <clause id="52707">
    <literal><![CDATA[
      a(x,y,(z * (u \ 1)) \ w) = a(x,y,(z \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,52682,a(flip),b,52629,a),flip(a)].">
      <j1 rule="hyper" parents="373 52682 52629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52711">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ 1))) = a(x,y,(u * w) \ z)
    ]]></literal>
    <justification jstring="[hyper(64,a,52683,a(flip),b,52648,a)].">
      <j1 rule="hyper" parents="64 52683 52648"/>
    </justification>
  </clause>

  <clause id="52712">
    <literal><![CDATA[
      a(x,y,(z \ (u \ 1)) * w) = a(x,y,(z * u) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,52682,a(flip),b,52648,a)].">
      <j1 rule="hyper" parents="64 52682 52648"/>
    </justification>
  </clause>

  <clause id="52715">
    <literal><![CDATA[
      a(x,y,x \ (L(z,x,u) * u)) = a(x,y,(x \ L(z,u,x)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,48451,a(flip),b,52655,a)].">
      <j1 rule="hyper" parents="64 48451 52655"/>
    </justification>
  </clause>

  <clause id="52717">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 \ v6))) = a(x,y,a(z,u,w * (v6 * v5)))
    ]]></literal>
    <justification jstring="[para(52656(a,1),42302(a,1,3)),flip(a)].">
      <j1 rule="para" parents="52656 42302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52719">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (v5 \ v6))) = a(x,y,a(z,u,w * (v5 * v6)))
    ]]></literal>
    <justification jstring="[para(52657(a,1),42302(a,1,3)),flip(a)].">
      <j1 rule="para" parents="52657 42302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52722">
    <literal><![CDATA[
      a(x,y,T((z \ 1) \ (u / (w \ v5)),K(w,v5))) = a(x,y,(z * (u / (v5 / w))) * K(w,w \ v5))
    ]]></literal>
    <justification jstring="[para(35342(a,1),52664(a,1,3))].">
      <j1 rule="para" parents="35342 52664"/>
    </justification>
  </clause>

  <clause id="52723">
    <literal><![CDATA[
      a(x,(y * ((z \ 1) \ u)) * a(w,v5,(z * u) * y),v6) = a(x,L(y * ((z \ 1) \ u),v5,w),v6)
    ]]></literal>
    <justification jstring="[para(52664(a,1),45118(a,1,2,2))].">
      <j1 rule="para" parents="52664 45118"/>
    </justification>
  </clause>

  <clause id="52724">
    <literal><![CDATA[
      a(x,y,z \ ((u \ 1) \ w)) = a(x,y,z \ (w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27339,a(flip),b,52674,a),flip(a)].">
      <j1 rule="hyper" parents="64 27339 52674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52725">
    <literal><![CDATA[
      a(x,y,(z * x) * u) = a(x,y,z * (x * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,52664,a(flip),b,52699,a)].">
      <j1 rule="hyper" parents="64 52664 52699"/>
    </justification>
  </clause>

  <clause id="52726">
    <literal><![CDATA[
      a(x,y,(x * z) * u) = a(x,y,z * (x * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,52663,a(flip),b,52699,a)].">
      <j1 rule="hyper" parents="64 52663 52699"/>
    </justification>
  </clause>

  <clause id="52727">
    <literal><![CDATA[
      L(x,a(y,z,u * (w \ v5)),v6) = L(x,a(y,z,u * (w * v5)),v6)
    ]]></literal>
    <justification jstring="[para(52700(a,1),34490(a,1,2))].">
      <j1 rule="para" parents="52700 34490"/>
    </justification>
  </clause>

  <clause id="52728">
    <literal><![CDATA[
      L(x,y,a(z,u,w * (v5 \ v6))) = L(x,y,a(z,u,w * (v6 * v5)))
    ]]></literal>
    <justification jstring="[para(52700(a,1),47755(a,1,3))].">
      <j1 rule="para" parents="52700 47755"/>
    </justification>
  </clause>

  <clause id="52729">
    <literal><![CDATA[
      a(x,y,x \ (z * L(u,x,z))) = a(x,y,(x \ L(u,z,x)) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,47878,a(flip),b,52703,a)].">
      <j1 rule="hyper" parents="64 47878 52703"/>
    </justification>
  </clause>

  <clause id="52730">
    <literal><![CDATA[
      a(x,y,(z \ L(u,z,w)) * w) = a(x,y,(z \ w) * L(u,z,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47742,a(flip),b,52703,a)].">
      <j1 rule="hyper" parents="64 47742 52703"/>
    </justification>
  </clause>

  <clause id="52733">
    <literal><![CDATA[
      a(x,y,((z \ 1) * u) \ w) = a(x,y,(u \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(27591,a,52707,a)].">
      <j1 rule="hyper" parents="27591 52707"/>
    </justification>
  </clause>

  <clause id="52734">
    <literal><![CDATA[
      a(x,y,T((y \ 1) \ (z \ u),w)) = a(x,y,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,51257,a,b,52707,a)].">
      <j1 rule="hyper" parents="64 51257 52707"/>
    </justification>
  </clause>

  <clause id="52735">
    <literal><![CDATA[
      a(x,y,z * (u \ (w \ 1))) = a(x,y,(w * u) \ z)
    ]]></literal>
    <justification jstring="[hyper(373,a,27394,a,b,52711,a),flip(a)].">
      <j1 rule="hyper" parents="373 27394 52711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52738">
    <literal><![CDATA[
      a(x,y,z \ ((u * w) * w)) = a(x,y,u * (z \ (w * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,51908,a(flip),b,52724,a),flip(a)].">
      <j1 rule="hyper" parents="64 51908 52724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52739">
    <literal><![CDATA[
      a(x,y,(x * (z \ u)) \ z) = a(x,y,((u * x) \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,51915,a(flip),b,52735,a),flip(a)].">
      <j1 rule="hyper" parents="64 51915 52735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52740">
    <literal><![CDATA[
      a(x,y,(z * (u \ z)) \ w) = a(x,y,u * ((z * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27970,a(flip),b,52735,a),flip(a)].">
      <j1 rule="hyper" parents="64 27970 52735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52743">
    <literal><![CDATA[
      a(x,y,z \ (((u \ 1) * w) * w)) = a(x,y,z \ ((u \ w) * w))
    ]]></literal>
    <justification jstring="[para(25769(a,1),52607(a,1,3,2))].">
      <j1 rule="para" parents="25769 52607"/>
    </justification>
  </clause>

  <clause id="52744">
    <literal><![CDATA[
      a(x,y,z * (u \ L(w,w,v5))) = a(x,y,(u \ w) * z)
    ]]></literal>
    <justification jstring="[hyper(27453,a,52620,a)].">
      <j1 rule="hyper" parents="27453 52620"/>
    </justification>
  </clause>

  <clause id="52747">
    <literal><![CDATA[
      a(x,y,z * (L(u,u,w) * v5)) = a(x,y,z * (u * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,37061,a(flip),b,52672,a)].">
      <j1 rule="hyper" parents="64 37061 52672"/>
    </justification>
  </clause>

  <clause id="52749">
    <literal><![CDATA[
      a(x,y,z * (u * L(w,w,v5))) = a(x,y,z * (w * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27315,a,b,52747,a)].">
      <j1 rule="hyper" parents="64 27315 52747"/>
    </justification>
  </clause>

  <clause id="52750">
    <literal><![CDATA[
      a(x,y,z * ((u \ (z \ u)) \ w)) = a(x,y,z * (z * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,52004,a,b,52749,a)].">
      <j1 rule="hyper" parents="64 52004 52749"/>
    </justification>
  </clause>

  <clause id="52751">
    <literal><![CDATA[
      a(x,y,z * (u * (u * w))) = a(x,y,u * (u * (w * z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,51880,a(flip),b,52615,a),flip(a)].">
      <j1 rule="hyper" parents="64 51880 52615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52752">
    <literal><![CDATA[
      a(x,y,z * (u * (u * w))) = a(x,y,u * (u * (z * w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,51319,a(flip),b,52615,a),flip(a)].">
      <j1 rule="hyper" parents="64 51319 52615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52754">
    <literal><![CDATA[
      a(x,y,y * (z \ (y \ u))) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,51263,a(flip),b,52688,a),flip(a)].">
      <j1 rule="hyper" parents="64 51263 52688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52755">
    <literal><![CDATA[
      a(x,y,z \ (y * u)) = a(x,y,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(9(a,1),52754(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="9 52754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52756">
    <literal><![CDATA[
      a(x,y,z \ (y * u)) = a(x,y,(z \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(373,a,27298,a,b,52755,a),flip(a)].">
      <j1 rule="hyper" parents="373 27298 52755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52760">
    <literal><![CDATA[
      a(x,y,(z \ u) * y) = a(x,y,u * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(64,a,52697,a(flip),b,52756,a),flip(a)].">
      <j1 rule="hyper" parents="64 52697 52756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52761">
    <literal><![CDATA[
      a(x,y,(y \ 1) \ (z \ u)) = a(x,y,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(27584,a,52734,a)].">
      <j1 rule="hyper" parents="27584 52734"/>
    </justification>
  </clause>

  <clause id="52762">
    <literal><![CDATA[
      a(x,y,(z \ y) * u) = a(x,y,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,51318,a(flip),b,52761,a),flip(a)].">
      <j1 rule="hyper" parents="64 51318 52761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52763">
    <literal><![CDATA[
      a(x,y,((y \ 1) * z) \ u) = a(x,y,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,52733,a,b,52762,a)].">
      <j1 rule="hyper" parents="64 52733 52762"/>
    </justification>
  </clause>

  <clause id="52765">
    <literal><![CDATA[
      a(x,y,((y \ 1) * (z \ 1)) \ u) = a(x,y,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,52657,a(flip),b,52763,a),flip(a)].">
      <j1 rule="hyper" parents="373 52657 52763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52766">
    <literal><![CDATA[
      a(x,y,(z \ u) \ (x \ z)) = a(x,y,((u * x) \ z) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46224,a(flip),b,52739,a)].">
      <j1 rule="hyper" parents="64 46224 52739"/>
    </justification>
  </clause>

  <clause id="52767">
    <literal><![CDATA[
      a(x,y,(z * (u \ z)) \ w) = a(x,y,u * (z \ (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(373,a,52658,a(flip),b,52740,a),flip(a)].">
      <j1 rule="hyper" parents="373 52658 52740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52769">
    <literal><![CDATA[
      a(x,y,(z * (z * u)) * w) = a(x,y,z * (z * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(27453,a,52751,a)].">
      <j1 rule="hyper" parents="27453 52751"/>
    </justification>
  </clause>

  <clause id="52770">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * (((z \ 1) \ u) * ((z \ (1 / z)) * w))) = a(x,y,w * (((z \ 1) \ u) * (((1 / z) \ u) / (z * z))))
    ]]></literal>
    <justification jstring="[para(3771(a,1),52751(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="3771 52751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52771">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * (((z \ 1) \ u) * ((z \ (z \ 1)) * w))) = a(x,y,w * (((z \ 1) \ u) * T(u / z,z \ 1)))
    ]]></literal>
    <justification jstring="[para(7672(a,1),52751(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="7672 52751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52772">
    <literal><![CDATA[
      a(x,y,((z / u) \ 1) * (((z / u) \ 1) * ((w / ((z / u) \ 1)) * v5))) = a(x,y,v5 * (((z / u) \ 1) * ((u / z) * (w / (u / z)))))
    ]]></literal>
    <justification jstring="[para(27952(a,1),52751(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="27952 52751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52773">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * (v5 * (v5 * v6))) = a(x,y,v5 * (v5 * (((u * z) \ w) * v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27406,a,b,52752,a)].">
      <j1 rule="hyper" parents="64 27406 52752"/>
    </justification>
  </clause>

  <clause id="52774">
    <literal><![CDATA[
      a(x,y,((y \ 1) \ z) * u) = a(x,y,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,52707,a(flip),b,52765,a)].">
      <j1 rule="hyper" parents="64 52707 52765"/>
    </justification>
  </clause>

  <clause id="52775">
    <literal><![CDATA[
      a(x,y,(y * z) * u) = a(x,y,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,52667,a(flip),b,52774,a)].">
      <j1 rule="hyper" parents="64 52667 52774"/>
    </justification>
  </clause>

  <clause id="52776">
    <literal><![CDATA[
      a(x,y,z * (u * y)) = a(x,y,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,27462,a(flip),b,52775,a)].">
      <j1 rule="hyper" parents="64 27462 52775"/>
    </justification>
  </clause>

  <clause id="52779">
    <literal><![CDATA[
      a(x,y,z * (u * y)) = a(x,y,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27315,a,b,52776,a),flip(a)].">
      <j1 rule="hyper" parents="373 27315 52776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52780">
    <literal><![CDATA[
      a(x,y,((z * x) \ u) * u) = a(x,y,(z \ u) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,52682,a(flip),b,52766,a),flip(a)].">
      <j1 rule="hyper" parents="64 52682 52766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52781">
    <literal><![CDATA[
      a(x,y,z * (((z \ u) * u) \ w)) = a(x,y,z * (u \ (u \ (w * z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,47885,a(flip),b,52767,a)].">
      <j1 rule="hyper" parents="64 47885 52767"/>
    </justification>
  </clause>

  <clause id="52782">
    <literal><![CDATA[
      a(x,y,z * (z * ((z \ u) * w))) = a(x,y,(z * u) * w)
    ]]></literal>
    <justification jstring="[para(10(a,1),52769(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="10 52769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52783">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((z * u) * (((z * u) \ w) * v5))) = a(x,y,((z \ u) * w) * v5)
    ]]></literal>
    <justification jstring="[para(51986(a,1),52782(a,1,3,2))].">
      <j1 rule="para" parents="51986 52782"/>
    </justification>
  </clause>

  <clause id="52785">
    <literal><![CDATA[
      a(x,y,(z \ u) * L(w,z,u)) = a(x,y,(z \ w) * u)
    ]]></literal>
    <justification jstring="[hyper(373,a,52703,a(flip),b,52660,a),flip(a)].">
      <j1 rule="hyper" parents="373 52703 52660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52786">
    <literal><![CDATA[
      a(x,y,(z * u) \ (z * w)) = a(x,y,(z \ w) * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52735,a(flip),b,52706,a)].">
      <j1 rule="hyper" parents="64 52735 52706"/>
    </justification>
  </clause>

  <clause id="52787">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) \ w) * ((R(1 / u,u,z) \ v5) \ (z / (u * z)))) = a(x,y,v5 \ ((z / (u * z)) * w))
    ]]></literal>
    <justification jstring="[para(508(a,1),52786(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="508 52786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52788">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) \ w) * (T(v5,u \ 1) \ (z / (u * z)))) = a(x,y,(v5 * R(1 / u,u,z)) \ ((z / (u * z)) * w))
    ]]></literal>
    <justification jstring="[para(4850(a,1),52786(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4850 52786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52789">
    <literal><![CDATA[
      a(x,y,(L(z / (z / u),w,v5) \ v6) \ (K(u,u \ z) * v7)) = a(x,y,(K(u,u \ z) \ v7) * ((L(u,w,v5) \ v6) \ K(u,u \ z)))
    ]]></literal>
    <justification jstring="[para(26139(a,2),52786(a,1,3,1))].">
      <j1 rule="para" parents="26139 52786"/>
    </justification>
  </clause>

  <clause id="52790">
    <literal><![CDATA[
      a(x,y,(x \ L(z,u,x)) * u) = a(x,y,(x \ L(z,x,u)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,52693,a(flip),b,52715,a),flip(a)].">
      <j1 rule="hyper" parents="64 52693 52715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52791">
    <literal><![CDATA[
      a(x * y,z,a(u,x,u * (x * w))) = a(y,x,a(u,z,(w \ (u \ x)) * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,52517,a(flip),b,52717,a),flip(a)].">
      <j1 rule="hyper" parents="64 52517 52717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52792">
    <literal><![CDATA[
      a(x,y,a(z,u,x * ((w * (y * x)) * y))) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,48289,a(flip),b,52717,a),flip(a)].">
      <j1 rule="hyper" parents="64 48289 52717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52793">
    <literal><![CDATA[
      (x \ y) * a(y * (x \ y),x \ y,a(z,u,w * (y * x))) = x \ L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(52717(a,1),52535(a,1,2))].">
      <j1 rule="para" parents="52717 52535"/>
    </justification>
  </clause>

  <clause id="52799">
    <literal><![CDATA[
      a(x,y,(z \ L(u,z,w)) * w) = a(x,y,u * (z \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,52651,a(flip),b,52730,a),flip(a)].">
      <j1 rule="hyper" parents="373 52651 52730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52801">
    <literal><![CDATA[
      a(x,y,(z \ 1) * (u \ (w * w))) = a(x,y,u \ ((z \ w) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,52738,a(flip),b,52743,a)].">
      <j1 rule="hyper" parents="64 52738 52743"/>
    </justification>
  </clause>

  <clause id="52802">
    <literal><![CDATA[
      a(x,y,(x \ L(z,u,x)) * u) = a(x,y,z * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,52799,a(flip),b,52790,a),flip(a)].">
      <j1 rule="hyper" parents="373 52799 52790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52803">
    <literal><![CDATA[
      a(x,y,x \ (z * L(u,x,z))) = a(x,y,u * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52729,a,b,52802,a)].">
      <j1 rule="hyper" parents="64 52729 52802"/>
    </justification>
  </clause>

  <clause id="52804">
    <literal><![CDATA[
      a(x,y,(x \ z) * L(u,x,z)) = a(x,y,u * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52693,a(flip),b,52803,a)].">
      <j1 rule="hyper" parents="64 52693 52803"/>
    </justification>
  </clause>

  <clause id="52805">
    <literal><![CDATA[
      a(x,y,(x \ z) * u) = a(x,y,z * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,52785,a(flip),b,52804,a)].">
      <j1 rule="hyper" parents="64 52785 52804"/>
    </justification>
  </clause>

  <clause id="52807">
    <literal><![CDATA[
      a(x * (a(y,x,z) * u),w,a(y,x,z)) = a(z,w,a(y,x,((y * x) * z) * (y \ (z * u))))
    ]]></literal>
    <justification jstring="[para(52805(a,1),52529(a,2,3))].">
      <j1 rule="para" parents="52805 52529"/>
    </justification>
  </clause>

  <clause id="52808">
    <literal><![CDATA[
      L(x,a(y,z * y,z * (y \ u)),w) = L(x,a(u,y,z),w)
    ]]></literal>
    <justification jstring="[para(52805(a,1),52695(a,1,2))].">
      <j1 rule="para" parents="52805 52695"/>
    </justification>
  </clause>

  <clause id="52809">
    <literal><![CDATA[
      L(x,y,a(z,u * z,u * (z \ w))) = L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[para(52805(a,1),52696(a,1,3))].">
      <j1 rule="para" parents="52805 52696"/>
    </justification>
  </clause>

  <clause id="52810">
    <literal><![CDATA[
      L(x,a(y,z * y,z * (y * u)),w) = L(x,a(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,52727,a(flip),b,52808,a)].">
      <j1 rule="hyper" parents="64 52727 52808"/>
    </justification>
  </clause>

  <clause id="52811">
    <literal><![CDATA[
      L(x,y,a(z,u * z,u * (w * z))) = L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,52728,a(flip),b,52809,a)].">
      <j1 rule="hyper" parents="64 52728 52809"/>
    </justification>
  </clause>

  <clause id="52812">
    <literal><![CDATA[
      L(x,a(y,z,z * (y * u)),w) = L(x,a(u,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,52236,a(flip),b,52810,a)].">
      <j1 rule="hyper" parents="64 52236 52810"/>
    </justification>
  </clause>

  <clause id="52813">
    <literal><![CDATA[
      L(x,y,a(z * (u * w),z,w)) = L(x,y,a(z,w,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,51974,a(flip),b,52811,a)].">
      <j1 rule="hyper" parents="64 51974 52811"/>
    </justification>
  </clause>

  <clause id="52814">
    <literal><![CDATA[
      L(x,y,a(z * (u * w),z,w)) = x * a(x,y,a(u,w,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,45157,a,b,52813,a),flip(a)].">
      <j1 rule="hyper" parents="373 45157 52813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52815">
    <literal><![CDATA[
      a(x,y,a(x * z,u,w * u)) = a(w,y,a(z,x,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,52511,a,b,52814,a(flip))].">
      <j1 rule="hyper" parents="35 52511 52814"/>
    </justification>
  </clause>

  <clause id="52816">
    <literal><![CDATA[
      a(x,y,a(z * (u * x),z,w)) = a(w,y,a(u,x,z))
    ]]></literal>
    <justification jstring="[hyper(35,a,47349,a,b,52814,a(flip))].">
      <j1 rule="hyper" parents="35 47349 52814"/>
    </justification>
  </clause>

  <clause id="52817">
    <literal><![CDATA[
      a(x,y,a(z,u,u * (w * x))) = a(z,y,a(w,x,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,47316,a,b,52814,a(flip))].">
      <j1 rule="hyper" parents="35 47316 52814"/>
    </justification>
  </clause>

  <clause id="52818">
    <literal><![CDATA[
      a(x,y,a(z,u,y * (w * x))) = a(z,u,a(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,47258,a,b,52814,a(flip))].">
      <j1 rule="hyper" parents="35 47258 52814"/>
    </justification>
  </clause>

  <clause id="52819">
    <literal><![CDATA[
      a(x,y,a(y * (z * x),u,w)) = a(w,u,a(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,47223,a,b,52814,a(flip))].">
      <j1 rule="hyper" parents="35 47223 52814"/>
    </justification>
  </clause>

  <clause id="52820">
    <literal><![CDATA[
      a(x,y,a(z,u,u * (w * z))) = a(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,45157,a,b,52814,a(flip))].">
      <j1 rule="hyper" parents="35 45157 52814"/>
    </justification>
  </clause>

  <clause id="52821">
    <literal><![CDATA[
      a(x,y,a(z,u,x * (y * w))) = a(z,u,a(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,52507,a(flip),b,52815,a)].">
      <j1 rule="hyper" parents="64 52507 52815"/>
    </justification>
  </clause>

  <clause id="52823">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (x * u))) = a(z,y,a(w,x,u))
    ]]></literal>
    <justification jstring="[para(52779(a,2),52817(a,1,3))].">
      <j1 rule="para" parents="52779 52817"/>
    </justification>
  </clause>

  <clause id="52824">
    <literal><![CDATA[
      a(x,y,a(z,u,x * (w * y))) = a(z,u,a(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47680,a(flip),b,52818,a)].">
      <j1 rule="hyper" parents="64 47680 52818"/>
    </justification>
  </clause>

  <clause id="52825">
    <literal><![CDATA[
      a(L(T(x,y),z,u),w,a(v5,v6,w * (L(x,z,u) * y))) = a(v5,v6,a(y,L(T(x,y),z,u),w))
    ]]></literal>
    <justification jstring="[para(266(a,1),52818(a,1,3,3,2))].">
      <j1 rule="para" parents="266 52818"/>
    </justification>
  </clause>

  <clause id="52826">
    <literal><![CDATA[
      a(x,y,a(z,u,z * (u * w))) = a(x,y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47674,a(flip),b,52819,a)].">
      <j1 rule="hyper" parents="64 47674 52819"/>
    </justification>
  </clause>

  <clause id="52827">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (x * y))) = a(z,u,a(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47579,a(flip),b,52819,a)].">
      <j1 rule="hyper" parents="64 47579 52819"/>
    </justification>
  </clause>

  <clause id="52828">
    <literal><![CDATA[
      a(x,y,a(L(z \ (T(z \ 1,u) \ w),v5,v6),v7,v7 * (T(z \ 1,u) \ L(w,v5,v6)))) = a(x,y,a(z,L(z \ (T(z \ 1,u) \ w),v5,v6),v7))
    ]]></literal>
    <justification jstring="[para(26125(a,1),52820(a,1,3,3,2))].">
      <j1 rule="para" parents="26125 52820"/>
    </justification>
  </clause>

  <clause id="52829">
    <literal><![CDATA[
      x * a(y,z,a(x,x * u,(x * u) * (w * x))) = u * L(u \ x,x,a(w,z,y))
    ]]></literal>
    <justification jstring="[para(52820(a,2),47239(a,2,2)),flip(a)].">
      <j1 rule="para" parents="52820 47239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52830">
    <literal><![CDATA[
      a(x * y,z,a(u,w,x * z)) = a(u,w,a(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52501,a,b,52821,a)].">
      <j1 rule="hyper" parents="64 52501 52821"/>
    </justification>
  </clause>

  <clause id="52831">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (y * z))) = a(x,u,a(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,49363,a,b,52821,a)].">
      <j1 rule="hyper" parents="64 49363 52821"/>
    </justification>
  </clause>

  <clause id="52832">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (z * y))) = a(x,u,a(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47253,a,b,52823,a)].">
      <j1 rule="hyper" parents="64 47253 52823"/>
    </justification>
  </clause>

  <clause id="52833">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w * (z * y),v5,v6))) = L(x,v5,a(v6,u,a(w,z,y)))
    ]]></literal>
    <justification jstring="[para(52823(a,1),47520(a,1,3)),flip(a)].">
      <j1 rule="para" parents="52823 47520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52834">
    <literal><![CDATA[
      a(a(x,y,z),(u * u) * (a(x,y,z) \ w),a(v5,v6,v7 * ((u * u) * w))) = a(v5,v6,a(v7,a(x,y,z),(u * u) * (a(x,y,z) \ w)))
    ]]></literal>
    <justification jstring="[para(23578(a,1),52827(a,1,3,3,2))].">
      <j1 rule="para" parents="23578 52827"/>
    </justification>
  </clause>

  <clause id="52835">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6 * (z * y)))) = a(x,u,a(w,v5,a(v6,z,y)))
    ]]></literal>
    <justification jstring="[para(52827(a,1),47324(a,1,3)),flip(a)].">
      <j1 rule="para" parents="52827 47324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52836">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6 * (z * y)) * y)) = a(y * x,u,a(w,v5,a(v6,z,y)))
    ]]></literal>
    <justification jstring="[para(52827(a,1),52469(a,1,3)),flip(a)].">
      <j1 rule="para" parents="52827 52469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52837">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),w,u)) = a(z,y,a(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,52824,a(flip),b,52792,a)].">
      <j1 rule="hyper" parents="64 52824 52792"/>
    </justification>
  </clause>

  <clause id="52838">
    <literal><![CDATA[
      a(x,y,a(z * (u * w),w,u)) = a(z,u,a(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47324,a,b,52837,a),flip(a)].">
      <j1 rule="hyper" parents="373 47324 52837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52839">
    <literal><![CDATA[
      a(x,y,a(z,u,u * (z * w))) = a(w,y,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,51883,a(flip),b,52837,a)].">
      <j1 rule="hyper" parents="64 51883 52837"/>
    </justification>
  </clause>

  <clause id="52841">
    <literal><![CDATA[
      a(x,y,a(z * u,w,z * w)) = a(u,z,a(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,52494,a(flip),b,52838,a)].">
      <j1 rule="hyper" parents="64 52494 52838"/>
    </justification>
  </clause>

  <clause id="52842">
    <literal><![CDATA[
      a(x,y,z \ (u \ (w * w))) = a(x,y,u \ ((z \ w) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,51316,a(flip),b,52801,a)].">
      <j1 rule="hyper" parents="64 51316 52801"/>
    </justification>
  </clause>

  <clause id="52843">
    <literal><![CDATA[
      a(x,y,z \ ((u \ w) * w)) = a(x,y,((z * u) \ w) * w)
    ]]></literal>
    <justification jstring="[hyper(64,a,51905,a(flip),b,52842,a),flip(a)].">
      <j1 rule="hyper" parents="64 51905 52842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52844">
    <literal><![CDATA[
      a(x,y,((z * x) \ u) * u) = a(x,y,(z \ (x \ u)) * u)
    ]]></literal>
    <justification jstring="[hyper(64,a,52692,a(flip),b,52843,a),flip(a)].">
      <j1 rule="hyper" parents="64 52692 52843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52845">
    <literal><![CDATA[
      a(x,y,(z \ (x \ u)) * u) = a(x,y,(z \ u) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,52780,a(flip),b,52844,a),flip(a)].">
      <j1 rule="hyper" parents="64 52780 52844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52846">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((z \ u) * w)) = a(x,y,u * (((u \ z) * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46357,a(flip),b,52694,a),flip(a)].">
      <j1 rule="hyper" parents="64 46357 52694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52847">
    <literal><![CDATA[
      a(x,y,(z \ u) * ((z \ u) * w)) = a(x,y,u * (z \ (z \ (w * u))))
    ]]></literal>
    <justification jstring="[hyper(373,a,52781,a(flip),b,52846,a),flip(a)].">
      <j1 rule="hyper" parents="373 52781 52846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52848">
    <literal><![CDATA[
      a(x,y,a(z,u,(w \ (z \ y)) * y)) = a(y * x,u,a(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,52826,a(flip),b,52791,a),flip(a)].">
      <j1 rule="hyper" parents="64 52826 52791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52849">
    <literal><![CDATA[
      a(x,y,a(z,u,(w \ y) * (z \ y))) = a(y * x,u,a(w,z,y))
    ]]></literal>
    <justification jstring="[para(52845(a,1),52848(a,1,3))].">
      <j1 rule="para" parents="52845 52848"/>
    </justification>
  </clause>

  <clause id="52850">
    <literal><![CDATA[
      a(x,y,a(z,u,(w \ y) * (y * z))) = a(y * x,u,a(w,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,52717,a(flip),b,52849,a)].">
      <j1 rule="hyper" parents="64 52717 52849"/>
    </justification>
  </clause>

  <clause id="52851">
    <literal><![CDATA[
      a(x * y,z,a(u,w,x)) = a(y,z,a(u \ x,w,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,52831,a(flip),b,52850,a),flip(a)].">
      <j1 rule="hyper" parents="64 52831 52850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52852">
    <literal><![CDATA[
      a(x * y,z,a(u,w,x)) = a(y,z,a(x * u,w,x))
    ]]></literal>
    <justification jstring="[para(51310(a,1),52851(a,2,3))].">
      <j1 rule="para" parents="51310 52851"/>
    </justification>
  </clause>

  <clause id="52853">
    <literal><![CDATA[
      a(x,y,a(z * u,w,z)) = a(z,w,a(z * x,y,u))
    ]]></literal>
    <justification jstring="[hyper(47296,a,52852,a),flip(a)].">
      <j1 rule="hyper" parents="47296 52852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52854">
    <literal><![CDATA[
      a(x * y,z,a(u,w,y)) = a(x,w,a(y * u,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,47395,a,b,52852,a)].">
      <j1 rule="hyper" parents="64 47395 52852"/>
    </justification>
  </clause>

  <clause id="52855">
    <literal><![CDATA[
      a(x * y,z,a(u,w,a(x,v5,v6))) = a(y,z,a(x * a(v6,w,u),v5,x))
    ]]></literal>
    <justification jstring="[para(47254(a,1),52852(a,1,3))].">
      <j1 rule="para" parents="47254 52852"/>
    </justification>
  </clause>

  <clause id="52856">
    <literal><![CDATA[
      a(x,y,a(x * z,u,w)) = a(x,y,a(z,u,x * w))
    ]]></literal>
    <justification jstring="[hyper(47296,a,52853,a),flip(a)].">
      <j1 rule="hyper" parents="47296 52853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52857">
    <literal><![CDATA[
      a(x,y,a(z * a(u,w,v5),v6,z)) = a(z,w,a(z * x,y,a(v5,v6,u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47511,a,b,52853,a),flip(a)].">
      <j1 rule="hyper" parents="373 47511 52853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52858">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,z * a(a(u * w,v5,v6),z,u)) = a(w,v5,a(u * v6,a(x,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(373,a,47014,a,b,52853,a)].">
      <j1 rule="hyper" parents="373 47014 52853"/>
    </justification>
  </clause>

  <clause id="52859">
    <literal><![CDATA[
      a(x,y,a(z * a(u,w,v5),v6,z)) = a(v5,v6,a(u,y,a(z,w,z * x)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47509,a(flip),b,52853,a),flip(a)].">
      <j1 rule="hyper" parents="373 47509 52853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52860">
    <literal><![CDATA[
      a(x * ((y * y) * (z * z)),u,a((x * ((y * y) * (z * z))) * w,v5,v6)) = a(w,v5,a(x * ((y * y) * ((z * z) * v6)),u,x * ((y * y) * (z * z))))
    ]]></literal>
    <justification jstring="[para(2289(a,1),52853(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="2289 52853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52861">
    <literal><![CDATA[
      ((x / y) * (y * a((x * y) * z,u,w))) / a((x * y) * z,u,w) = a(z,u,a((x * y) * w,y,x * y)) \ x
    ]]></literal>
    <justification jstring="[para(52853(a,2),41841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="52853 41841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52862">
    <literal><![CDATA[
      x * a(y,z,a(x,u,a(w * v5,v6,w))) = L(x,u,a(w,v6,a(w * y,z,v5)))
    ]]></literal>
    <justification jstring="[para(52853(a,1),47271(a,2,3))].">
      <j1 rule="para" parents="52853 47271"/>
    </justification>
  </clause>

  <clause id="52863">
    <literal><![CDATA[
      a(x * y,z,a(y,u,w)) = a(x,u,a(y * w,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,41883,a,b,52854,a)].">
      <j1 rule="hyper" parents="64 41883 52854"/>
    </justification>
  </clause>

  <clause id="52864">
    <literal><![CDATA[
      a(x,y,a(z * (u * x),w,v5)) = a(x,y,a(u * z,w,x * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,52419,a,b,52856,a)].">
      <j1 rule="hyper" parents="64 52419 52856"/>
    </justification>
  </clause>

  <clause id="52865">
    <literal><![CDATA[
      a(x,y,a(z * (x * u),w,v5)) = a(x,y,a(u * z,w,x * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,52407,a,b,52856,a)].">
      <j1 rule="hyper" parents="64 52407 52856"/>
    </justification>
  </clause>

  <clause id="52866">
    <literal><![CDATA[
      a(x * y,z,a(x,u,w)) = a(x,u,a(y,z,x * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47253,a,b,52856,a)].">
      <j1 rule="hyper" parents="64 47253 52856"/>
    </justification>
  </clause>

  <clause id="52867">
    <literal><![CDATA[
      a(x * (y * z),u,a(w,v5,y)) = a(y,u,a(x * z,v5,y * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,50143,a,b,52864,a)].">
      <j1 rule="hyper" parents="64 50143 52864"/>
    </justification>
  </clause>

  <clause id="52868">
    <literal><![CDATA[
      L(x,y,a(z,u,a(y * w,v5,z * v6))) = L(x,v5,a(v6,u,a(w,z,y)))
    ]]></literal>
    <justification jstring="[para(52865(a,1),52833(a,1,3))].">
      <j1 rule="para" parents="52865 52833"/>
    </justification>
  </clause>

  <clause id="52869">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z \ u) * (((z * u) \ w) * v5))) = a(x,y,((z \ u) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,35415,a(flip),b,52783,a)].">
      <j1 rule="hyper" parents="64 35415 52783"/>
    </justification>
  </clause>

  <clause id="52870">
    <literal><![CDATA[
      x * a(y,z,a(x,x * u,u * (x * (w * x)))) = u * L(u \ x,x,a(w,z,y))
    ]]></literal>
    <justification jstring="[para(52726(a,1),52829(a,1,2,3))].">
      <j1 rule="para" parents="52726 52829"/>
    </justification>
  </clause>

  <clause id="52871">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w * y,v5,v6 * (z * y)))) = a(y * x,u,a(w,v5,a(v6,z,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52514,a,b,52836,a)].">
      <j1 rule="hyper" parents="64 52514 52836"/>
    </justification>
  </clause>

  <clause id="52872">
    <literal><![CDATA[
      x * a(y * z,x * z,a(u,w,x)) = z * L(z \ x,x,a(y,w,u))
    ]]></literal>
    <justification jstring="[para(52357(a,1),52870(a,1,2))].">
      <j1 rule="para" parents="52357 52870"/>
    </justification>
  </clause>

  <clause id="52873">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(z * x,x,a(y,u,w))
    ]]></literal>
    <justification jstring="[para(51939(a,1),52872(a,1,2)),flip(a)].">
      <j1 rule="para" parents="51939 52872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52875">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = y * a(z,x,a(y,u,w * x))
    ]]></literal>
    <justification jstring="[para(52464(a,1),52873(a,2,2))].">
      <j1 rule="para" parents="52464 52873"/>
    </justification>
  </clause>

  <clause id="52876">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,w)) = L(y,u,a(z,x,w * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47271,a(flip),b,52875,a),flip(a)].">
      <j1 rule="hyper" parents="373 47271 52875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52877">
    <literal><![CDATA[
      L(x,y,a(z,u,w * u)) = x * a(u,x,a(z,y,w * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,52472,a(flip),b,52876,a),flip(a)].">
      <j1 rule="hyper" parents="64 52472 52876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52878">
    <literal><![CDATA[
      L(x,y,a(z,u,w * u)) = x * a(z,x,a(u,y,w * x))
    ]]></literal>
    <justification jstring="[para(47241(a,1),52877(a,2,2))].">
      <j1 rule="para" parents="47241 52877"/>
    </justification>
  </clause>

  <clause id="52879">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w * v5,v5,v6))) = x * a(a(v6,u,z),x,a(v5,y,w * x))
    ]]></literal>
    <justification jstring="[para(47254(a,1),52878(a,1,3))].">
      <j1 rule="para" parents="47254 52878"/>
    </justification>
  </clause>

  <clause id="52880">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6 * v5))) = x * a(a(v6,u,z),x,a(v5,y,w * x))
    ]]></literal>
    <justification jstring="[para(52487(a,1),52879(a,1,3))].">
      <j1 rule="para" parents="52487 52879"/>
    </justification>
  </clause>

  <clause id="52881">
    <literal><![CDATA[
      a(x * y,z,a(u,w,a(v5,v6,x))) = a(y,z,a(u * x,w,a(v5,v6,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52835,a(flip),b,52871,a),flip(a)].">
      <j1 rule="hyper" parents="64 52835 52871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52882">
    <literal><![CDATA[
      a(x * y,z,a(u,w,a(x,v5,v6))) = a(y,z,a(v6 * x,w,a(u,v5,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47320,a,b,52881,a)].">
      <j1 rule="hyper" parents="64 47320 52881"/>
    </justification>
  </clause>

  <clause id="52883">
    <literal><![CDATA[
      a(x * y,z,a(u,w,a(x,v5,v6))) = a(y,z,a(v6,v5,a(x * u,w,x)))
    ]]></literal>
    <justification jstring="[para(52854(a,1),52882(a,2,3))].">
      <j1 rule="para" parents="52854 52882"/>
    </justification>
  </clause>

  <clause id="52884">
    <literal><![CDATA[
      (x \ y) * a(y * (x \ y),x * y,a(z,u,w * (y * x))) = x \ L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(52168(a,1),52793(a,1,2))].">
      <j1 rule="para" parents="52168 52793"/>
    </justification>
  </clause>

  <clause id="52885">
    <literal><![CDATA[
      (x \ y) * a(x,x * y,a(z,u,w * (y * x))) = x \ L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(51444(a,1),52884(a,1,2))].">
      <j1 rule="para" parents="51444 52884"/>
    </justification>
  </clause>

  <clause id="52887">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(w * (y * x),y,x)) = x \ L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(51965(a,1),52885(a,1,2))].">
      <j1 rule="para" parents="51965 52885"/>
    </justification>
  </clause>

  <clause id="52889">
    <literal><![CDATA[
      (x \ y) * a(z,u,a(w * x,y,x * y)) = x \ L(y,x,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(52492(a,1),52887(a,1,2))].">
      <j1 rule="para" parents="52492 52887"/>
    </justification>
  </clause>

  <clause id="52890">
    <literal><![CDATA[
      L(x \ y,z,a(u * x,y,w)) = x \ L(y,x,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(64,a,49782,a(flip),b,52889,a)].">
      <j1 rule="hyper" parents="64 49782 52889"/>
    </justification>
  </clause>

  <clause id="52891">
    <literal><![CDATA[
      a(x * (a(y,x,z) * u),w,a(y,x,z)) = a(z,w,a(y,x,((y * x) * z) * ((z * u) * y)))
    ]]></literal>
    <justification jstring="[hyper(373,a,52717,a(flip),b,52807,a),flip(a)].">
      <j1 rule="hyper" parents="373 52717 52807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52892">
    <literal><![CDATA[
      a(T(x,y),z,L(a(u,w,z * (L(x,v5,v6) * y)),v5,v6)) = a(u,w,a(y,L(T(x,y),v5,v6),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,46496,a(flip),b,52825,a)].">
      <j1 rule="hyper" parents="64 46496 52825"/>
    </justification>
  </clause>

  <clause id="52893">
    <literal><![CDATA[
      a(x * (a(y,x,z) * u),w,a(y,x,z)) = a(z,w,a(y,x,(y * x) * (z * ((z * u) * y))))
    ]]></literal>
    <justification jstring="[hyper(373,a,50134,a(flip),b,52891,a),flip(a)].">
      <j1 rule="hyper" parents="373 50134 52891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52894">
    <literal><![CDATA[
      a(x * (a(y,x,z) * u),w,a(y,x,z)) = a(z,w,a(y,x,x * (y * (z * ((z * u) * y)))))
    ]]></literal>
    <justification jstring="[para(52726(a,1),52893(a,2,3))].">
      <j1 rule="para" parents="52726 52893"/>
    </justification>
  </clause>

  <clause id="52895">
    <literal><![CDATA[
      a(x * (a(y,x,z) * u),w,a(y,x,z)) = a(z * ((z * u) * y),w,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,52839,a(flip),b,52894,a),flip(a)].">
      <j1 rule="hyper" parents="373 52839 52894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52896">
    <literal><![CDATA[
      a(x * (a(y,x,z) * u),w,a(y,x,z)) = a(z * (z * u),y,a(x,w,z * y))
    ]]></literal>
    <justification jstring="[hyper(373,a,52466,a(flip),b,52895,a),flip(a)].">
      <j1 rule="hyper" parents="373 52466 52895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52897">
    <literal><![CDATA[
      a(x * (a(y,x,z) * u),w,a(y,x,z)) = a(x,w,a(z * u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,52830,a(flip),b,52896,a),flip(a)].">
      <j1 rule="hyper" parents="373 52830 52896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52898">
    <literal><![CDATA[
      a(x * (a(y,x,z) * (u * x)),w,a(y,x,z)) = a(y,w,a(u,x,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,52816,a(flip),b,52897,a),flip(a)].">
      <j1 rule="hyper" parents="373 52816 52897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52899">
    <literal><![CDATA[
      a(a(x,y,z) * (u * y),y,a(x,w,z * y)) = a(x,w,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52469,a(flip),b,52898,a)].">
      <j1 rule="hyper" parents="64 52469 52898"/>
    </justification>
  </clause>

  <clause id="52900">
    <literal><![CDATA[
      a(a(x,y,z) * u,y,a(x,w,(z * y) * y)) = a(x,w,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52467,a(flip),b,52899,a)].">
      <j1 rule="hyper" parents="64 52467 52899"/>
    </justification>
  </clause>

  <clause id="52901">
    <literal><![CDATA[
      a(a(x,y,z) * u,y,a(x,w,y * (y * z))) = a(x,w,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(27462(a,1),52900(a,1,3))].">
      <j1 rule="para" parents="27462 52900"/>
    </justification>
  </clause>

  <clause id="52902">
    <literal><![CDATA[
      a(x,y,a(z,u,a(z,y,x) * w)) = a(z,u,a(w,y,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,49754,a(flip),b,52901,a)].">
      <j1 rule="hyper" parents="64 49754 52901"/>
    </justification>
  </clause>

  <clause id="52904">
    <literal><![CDATA[
      a(a(x,y,z) * u,w,a(x,y,z)) = a(x,w,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47197,a,b,52902,a)].">
      <j1 rule="hyper" parents="64 47197 52902"/>
    </justification>
  </clause>

  <clause id="52905">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(y,a(x,u,w) * z,a(x,u,w)) = a(a(x,u,w) * z,a(x,u,w),y)
    ]]></literal>
    <justification jstring="[para(52904(a,1),47051(a,1,1))].">
      <j1 rule="para" parents="52904 47051"/>
    </justification>
  </clause>

  <clause id="52906">
    <literal><![CDATA[
      a(x,y,(z * (u / (w / v5))) * K(v5,v5 \ w)) = a(x,y,(z \ 1) \ (u / (v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(27584,a,52722,a),flip(a)].">
      <j1 rule="hyper" parents="27584 52722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52908">
    <literal><![CDATA[
      a(x,y,(z * (u / (w / v5))) * K(v5,v5 \ w)) = a(x,y,(z \ 1) \ ((v5 \ w) \ u))
    ]]></literal>
    <justification jstring="[hyper(373,a,27322,a(flip),b,52906,a),flip(a)].">
      <j1 rule="hyper" parents="373 27322 52906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52909">
    <literal><![CDATA[
      a(x,(y * ((z \ 1) * u)) * a(w,v5,(z * u) * y),v6) = a(x,L(y * ((z \ 1) \ u),v5,w),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,52572,a(flip),b,52723,a)].">
      <j1 rule="hyper" parents="64 52572 52723"/>
    </justification>
  </clause>

  <clause id="52910">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * a(w,u,a(y,z,x)) = a(a(x,u,w) * z,a(x,u,w),y)
    ]]></literal>
    <justification jstring="[para(47364(a,1),52905(a,1,2))].">
      <j1 rule="para" parents="47364 52905"/>
    </justification>
  </clause>

  <clause id="52911">
    <literal><![CDATA[
      a(a(x,y,z) * u,a(x,y,z),w) = a(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,47550,a(flip),b,52910,a),flip(a)].">
      <j1 rule="hyper" parents="64 47550 52910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52913">
    <literal><![CDATA[
      a(x * (a(y,z,u) * w),a(y,z,u),v5) = a(x * w,a(y,z,u),v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52360,a,b,52911,a)].">
      <j1 rule="hyper" parents="64 52360 52911"/>
    </justification>
  </clause>

  <clause id="52914">
    <literal><![CDATA[
      a(x,a(y,z,u),a(y,z,u) * w) = a(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,43409,a,b,52911,a)].">
      <j1 rule="hyper" parents="64 43409 52911"/>
    </justification>
  </clause>

  <clause id="52915">
    <literal><![CDATA[
      a(a(x,y,z) * u,a(z,y,x),w) = a(u,a(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42391,a,b,52911,a)].">
      <j1 rule="hyper" parents="64 42391 52911"/>
    </justification>
  </clause>

  <clause id="52916">
    <literal><![CDATA[
      a(x,a(y,z,u),w * a(y,z,u)) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,43414,a(flip),b,52911,a)].">
      <j1 rule="hyper" parents="64 43414 52911"/>
    </justification>
  </clause>

  <clause id="52919">
    <literal><![CDATA[
      x * a(x,a(y,z,u),a(y,z,u) * w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[para(52914(a,2),43401(a,1,2))].">
      <j1 rule="para" parents="52914 43401"/>
    </justification>
  </clause>

  <clause id="52921">
    <literal><![CDATA[
      a(a(x,y,z) \ (1 / u),u,a(w,v5,v6)) = a(w,v5,a(v6,a(x,y,z),u))
    ]]></literal>
    <justification jstring="[para(52916(a,1),52575(a,2,3))].">
      <j1 rule="para" parents="52916 52575"/>
    </justification>
  </clause>

  <clause id="52922">
    <literal><![CDATA[
      L(x,a(y,z,u),a(y,z,u) * w) = L(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(64,a,42627,a(flip),b,52919,a)].">
      <j1 rule="hyper" parents="64 42627 52919"/>
    </justification>
  </clause>

  <clause id="52923">
    <literal><![CDATA[
      x \ ((x * a(y,z,u)) * (a(y,z,u) \ w)) = L(w,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,42913,a,b,52922,a)].">
      <j1 rule="hyper" parents="64 42913 52922"/>
    </justification>
  </clause>

  <clause id="52924">
    <literal><![CDATA[
      x \ ((x * a(y,z,u)) * (a(y,z,u) \ w)) = L(w,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(373,a,41403,a,b,52923,a),flip(a)].">
      <j1 rule="hyper" parents="373 41403 52923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52927">
    <literal><![CDATA[
      a(x,a(y,z,u),w * (a(u,z,y) * v5)) = a(w * v5,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(64,a,43405,a,b,52913,a)].">
      <j1 rule="hyper" parents="64 43405 52913"/>
    </justification>
  </clause>

  <clause id="52928">
    <literal><![CDATA[
      a((1 / x) * a(y,z,u),x,a(w,v5,v6)) = a(w,v5,a(v6,a(y,z,u),x))
    ]]></literal>
    <justification jstring="[hyper(64,a,51310,a(flip),b,52921,a)].">
      <j1 rule="hyper" parents="64 51310 52921"/>
    </justification>
  </clause>

  <clause id="52929">
    <literal><![CDATA[
      a(a(x,y,z) / u,u,a(w,v5,v6)) = a(w,v5,a(v6,a(x,y,z),u))
    ]]></literal>
    <justification jstring="[para(51154(a,1),52928(a,1,1))].">
      <j1 rule="para" parents="51154 52928"/>
    </justification>
  </clause>

  <clause id="52930">
    <literal><![CDATA[
      a(a(x,y,z) * u,u,a(w,v5,v6)) = a(w,v5,a(v6,a(x,y,z),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,51445,a(flip),b,52929,a)].">
      <j1 rule="hyper" parents="64 51445 52929"/>
    </justification>
  </clause>

  <clause id="52931">
    <literal><![CDATA[
      a(x,y,a(z,u,u * a(w,v5,v6))) = a(x,y,a(z,a(w,v5,v6),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47228,a(flip),b,52930,a)].">
      <j1 rule="hyper" parents="64 47228 52930"/>
    </justification>
  </clause>

  <clause id="52932">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6 * u))) = a(x,y,a(z,a(w,v5,v6),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,52493,a,b,52931,a)].">
      <j1 rule="hyper" parents="64 52493 52931"/>
    </justification>
  </clause>

  <clause id="52933">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,a(w,v5,v6))) = y * a(v6,v5,a(x,a(w,u,z),y))
    ]]></literal>
    <justification jstring="[para(52932(a,1),52473(a,2,2))].">
      <j1 rule="para" parents="52932 52473"/>
    </justification>
  </clause>

  <clause id="52934">
    <literal><![CDATA[
      x * L(x \ y,y,a(z,u,a(w,v5,v6))) = L(y,v5,a(x,a(w,u,z),v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,47349,a(flip),b,52933,a),flip(a)].">
      <j1 rule="hyper" parents="373 47349 52933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52935">
    <literal><![CDATA[
      x * a(y,x,a(z,u,x * (a(w,v5,v6) * x))) = L(x,v5,a(y,a(w,u,z),v6 * x))
    ]]></literal>
    <justification jstring="[hyper(64,a,52518,a(flip),b,52934,a)].">
      <j1 rule="hyper" parents="64 52518 52934"/>
    </justification>
  </clause>

  <clause id="52936">
    <literal><![CDATA[
      x * a(y,x,a(z,u,a(w,v5,v6) * x)) = L(x,v5,a(y,a(w,u,z),v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,52472,a(flip),b,52934,a)].">
      <j1 rule="hyper" parents="64 52472 52934"/>
    </justification>
  </clause>

  <clause id="52937">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6 * x)) = x * a(a(u,y,v6),x,a(v5,w,z))
    ]]></literal>
    <justification jstring="[para(49758(a,1),52935(a,1,2)),flip(a)].">
      <j1 rule="para" parents="49758 52935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52938">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6 * x)) = x * a(v6,y,a(a(v5,w,z),x,u))
    ]]></literal>
    <justification jstring="[para(47254(a,1),52937(a,2,2))].">
      <j1 rule="para" parents="47254 52937"/>
    </justification>
  </clause>

  <clause id="52940">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6 * x)) = x * a(v6,y,a(z,w,a(u,x,v5)))
    ]]></literal>
    <justification jstring="[para(47254(a,1),52938(a,2,2,3))].">
      <j1 rule="para" parents="47254 52938"/>
    </justification>
  </clause>

  <clause id="52941">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6 * x)) = x * a(u,w,a(z,x,a(v5,y,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47659,a,b,52940,a),flip(a)].">
      <j1 rule="hyper" parents="373 47659 52940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52943">
    <literal><![CDATA[
      a(x,((y * z) * u) * a(w,v5,(y * z) * u),v6) = a(x,L(u * ((y \ 1) \ z),v5,w),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,32908,a(flip),b,52909,a)].">
      <j1 rule="hyper" parents="64 32908 52909"/>
    </justification>
  </clause>

  <clause id="52944">
    <literal><![CDATA[
      a(x,(y * z) * (u * a(w,v5,(y * z) * u)),v6) = a(x,L(u * ((y \ 1) \ z),v5,w),v6)
    ]]></literal>
    <justification jstring="[para(51072(a,1),52943(a,1,2))].">
      <j1 rule="para" parents="51072 52943"/>
    </justification>
  </clause>

  <clause id="52945">
    <literal><![CDATA[
      a(x,L(y * ((z \ 1) \ u),w,v5),v6) = a(x,L(y * (z * u),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,51914,a(flip),b,52944,a),flip(a)].">
      <j1 rule="hyper" parents="64 51914 52944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52946">
    <literal><![CDATA[
      a(x,L(y * (z \ u),w,v5),v6) = a(x,L(y * (z * u),w,v5),v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,35330,a(flip),b,52945,a)].">
      <j1 rule="hyper" parents="64 35330 52945"/>
    </justification>
  </clause>

  <clause id="52947">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) \ w) * ((R(1 / u,u,z) \ v5) \ (z / (u * z)))) = a(x,y,v5 \ (((u * z) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27492,a(flip),b,52787,a),flip(a)].">
      <j1 rule="hyper" parents="373 27492 52787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52948">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) \ w) * ((R(1 / u,u,z) \ v5) \ (z / (u * z)))) = a(x,y,v5 \ ((z \ (u \ z)) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,28043,a(flip),b,52947,a),flip(a)].">
      <j1 rule="hyper" parents="373 28043 52947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52949">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) \ w) * ((R(1 / u,u,z) \ v5) \ ((u * z) \ z))) = a(x,y,v5 \ ((z \ (u \ z)) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27482,a(flip),b,52948,a)].">
      <j1 rule="hyper" parents="64 27482 52948"/>
    </justification>
  </clause>

  <clause id="52950">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) \ w) * ((R(1 / u,u,z) \ v5) \ (z \ (u \ z)))) = a(x,y,v5 \ ((z \ (u \ z)) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,36257,a(flip),b,52949,a)].">
      <j1 rule="hyper" parents="64 36257 52949"/>
    </justification>
  </clause>

  <clause id="52951">
    <literal><![CDATA[
      ((x / y) * (y * a((x * y) * z,u,w))) / a((x * y) * z,u,w) = a(z,u,a(x * (w * y),y,x * y)) \ x
    ]]></literal>
    <justification jstring="[para(52385(a,1),52861(a,2,1,3))].">
      <j1 rule="para" parents="52385 52861"/>
    </justification>
  </clause>

  <clause id="52952">
    <literal><![CDATA[
      ((x / y) * (y * a((x * y) * z,u,w))) / a((x * y) * z,u,w) = a(w * y,x,a(y,u,z)) \ x
    ]]></literal>
    <justification jstring="[para(52841(a,1),52951(a,2,1))].">
      <j1 rule="para" parents="52841 52951"/>
    </justification>
  </clause>

  <clause id="52953">
    <literal><![CDATA[
      ((x / y) * (y * a((x * y) * z,u,w))) / a((x * y) * z,u,w) = a(w,u,a(y * z,x,y)) \ x
    ]]></literal>
    <justification jstring="[para(52863(a,1),52952(a,2,1))].">
      <j1 rule="para" parents="52863 52952"/>
    </justification>
  </clause>

  <clause id="52954">
    <literal><![CDATA[
      ((x / y) * (y * a((x * y) * z,u,w))) / a((x * y) * z,u,w) = a(w,u,a(y,x,y * z)) * x
    ]]></literal>
    <justification jstring="[hyper(373,a,42644,a(flip),b,52953,a),flip(a)].">
      <j1 rule="hyper" parents="373 42644 52953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52955">
    <literal><![CDATA[
      ((x / y) * (y * a((x * y) * z,u,w))) / a((x * y) * z,u,w) = x * a(w,x,a(y,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,47403,a(flip),b,52954,a),flip(a)].">
      <j1 rule="hyper" parents="373 47403 52954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52956">
    <literal><![CDATA[
      a((x * y) * z,u,w) * ((x / y) * (a((x * y) * z,u,w) \ y)) = x * a(w,x,a(y,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,42904,a(flip),b,52955,a)].">
      <j1 rule="hyper" parents="64 42904 52955"/>
    </justification>
  </clause>

  <clause id="52957">
    <literal><![CDATA[
      L(x,y,a((x * y) * z,u,w * y)) = x * a(w,x,a(y,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52497,a(flip),b,52956,a)].">
      <j1 rule="hyper" parents="64 52497 52956"/>
    </justification>
  </clause>

  <clause id="52958">
    <literal><![CDATA[
      L(x,y,a(y * (x * z),u,w * y)) = x * a(w,x,a(y,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52441,a(flip),b,52957,a)].">
      <j1 rule="hyper" parents="64 52441 52957"/>
    </justification>
  </clause>

  <clause id="52959">
    <literal><![CDATA[
      L(x,y,a(x * z,u,(w * y) * y)) = x * a(w,x,a(y,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52500,a(flip),b,52958,a)].">
      <j1 rule="hyper" parents="64 52500 52958"/>
    </justification>
  </clause>

  <clause id="52960">
    <literal><![CDATA[
      L(x,y,a(x * z,u,y * (y * w))) = x * a(w,x,a(y,u,y * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,28847,a(flip),b,52959,a)].">
      <j1 rule="hyper" parents="64 28847 52959"/>
    </justification>
  </clause>

  <clause id="52961">
    <literal><![CDATA[
      x * a(y,x,a(z,u,z * w)) = L(x,u,a(x * w,z,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,49789,a(flip),b,52960,a),flip(a)].">
      <j1 rule="hyper" parents="64 49789 52960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52963">
    <literal><![CDATA[
      x * a(y,x,a(y * z,u,w)) = L(x,u,a(x * z,y,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47309,a,b,52961,a)].">
      <j1 rule="hyper" parents="64 47309 52961"/>
    </justification>
  </clause>

  <clause id="52964">
    <literal><![CDATA[
      x * a(y,x,a(y * z,u,w)) = L(x,y,a(w,u,x * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,47432,a,b,52963,a),flip(a)].">
      <j1 rule="hyper" parents="373 47432 52963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52965">
    <literal><![CDATA[
      x * a(y,z,a(u,x,u * w)) = L(x,u,a(y,z,x * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,47469,a,b,52964,a)].">
      <j1 rule="hyper" parents="64 47469 52964"/>
    </justification>
  </clause>

  <clause id="52966">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * (((z \ 1) \ u) * ((z \ (z \ 1)) * w))) = a(x,y,w * (((z \ 1) \ u) * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27314,a(flip),b,52771,a),flip(a)].">
      <j1 rule="hyper" parents="373 27314 52771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52968">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * (((z \ 1) \ u) * ((z \ (z \ 1)) * w))) = a(x,y,w * (((z \ 1) \ u) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27478,a(flip),b,52966,a),flip(a)].">
      <j1 rule="hyper" parents="373 27478 52966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52969">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) \ w) * (T(v5,u \ 1) \ (z / (u * z)))) = a(x,y,(v5 * R(1 / u,u,z)) \ (((u * z) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,27492,a(flip),b,52788,a),flip(a)].">
      <j1 rule="hyper" parents="373 27492 52788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52970">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) \ w) * (T(v5,u \ 1) \ (z / (u * z)))) = a(x,y,(v5 * R(1 / u,u,z)) \ ((z \ (u \ z)) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,28043,a(flip),b,52969,a),flip(a)].">
      <j1 rule="hyper" parents="373 28043 52969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52971">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * (((z \ 1) \ u) * ((z \ (1 / z)) * w))) = a(x,y,w * (((z \ 1) \ u) * ((z * z) \ ((1 / z) \ u))))
    ]]></literal>
    <justification jstring="[hyper(373,a,27478,a(flip),b,52770,a),flip(a)].">
      <j1 rule="hyper" parents="373 27478 52770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52972">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * (((z \ 1) \ u) * ((z \ (1 / z)) * w))) = a(x,y,w * (((z \ 1) \ u) * ((1 / (1 / z)) \ u)))
    ]]></literal>
    <justification jstring="[para(876(a,1),52971(a,2,3,2,2))].">
      <j1 rule="para" parents="876 52971"/>
    </justification>
  </clause>

  <clause id="52973">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * (((z \ 1) \ u) * ((z \ (1 / z)) * w))) = a(x,y,w * (((z \ 1) \ u) * (((1 / z) \ 1) \ u)))
    ]]></literal>
    <justification jstring="[hyper(373,a,27687,a(flip),b,52972,a),flip(a)].">
      <j1 rule="hyper" parents="373 27687 52972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52974">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * (((z \ 1) \ u) * ((z \ (1 / z)) * w))) = a(x,y,w * (((z \ 1) \ u) * (z \ u)))
    ]]></literal>
    <justification jstring="[para(82(a,1),52973(a,2,3,2,2,1))].">
      <j1 rule="para" parents="82 52973"/>
    </justification>
  </clause>

  <clause id="52976">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * (((z \ 1) \ u) * ((z \ 1) * (z \ w)))) = a(x,y,w * (((z \ 1) \ u) * (z \ u)))
    ]]></literal>
    <justification jstring="[para(1098(a,1),52974(a,1,3,2,2))].">
      <j1 rule="para" parents="1098 52974"/>
    </justification>
  </clause>

  <clause id="52977">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * (((z \ 1) \ u) * (z \ (z \ w)))) = a(x,y,w * (((z \ 1) \ u) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,51991,a(flip),b,52976,a)].">
      <j1 rule="hyper" parents="64 51991 52976"/>
    </justification>
  </clause>

  <clause id="52978">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ ((u \ 1) \ ((u \ (u \ w)) * z)))) = a(x,y,w * (((u \ 1) \ z) * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52847,a(flip),b,52977,a)].">
      <j1 rule="hyper" parents="64 52847 52977"/>
    </justification>
  </clause>

  <clause id="52979">
    <literal><![CDATA[
      a(x,y,z * ((u \ 1) \ (u \ (((1 / u) \ (u \ w)) * z)))) = a(x,y,w * (((u \ 1) \ z) * (u \ z)))
    ]]></literal>
    <justification jstring="[para(1601(a,1),52978(a,1,3,2,2))].">
      <j1 rule="para" parents="1601 52978"/>
    </justification>
  </clause>

  <clause id="52980">
    <literal><![CDATA[
      a(x,y,z * (u \ ((u \ 1) \ (((1 / u) \ (u \ w)) * z)))) = a(x,y,w * (((u \ 1) \ z) * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,27984,a(flip),b,52979,a)].">
      <j1 rule="hyper" parents="64 27984 52979"/>
    </justification>
  </clause>

  <clause id="52981">
    <literal><![CDATA[
      a(x,y,(((1 / z) \ (z \ u)) * w) * w) = a(x,y,u * (((z \ 1) \ w) * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52661,a(flip),b,52980,a)].">
      <j1 rule="hyper" parents="64 52661 52980"/>
    </justification>
  </clause>

  <clause id="52983">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) \ w) * (u \ w))) = a(x,y,w * (w * ((1 / u) \ (u \ z))))
    ]]></literal>
    <justification jstring="[hyper(64,a,27462,a(flip),b,52981,a),flip(a)].">
      <j1 rule="hyper" parents="64 27462 52981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52984">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) \ w) * (u \ w))) = a(x,y,w * (w * ((u \ 1) \ (u \ z))))
    ]]></literal>
    <justification jstring="[hyper(373,a,27687,a(flip),b,52983,a),flip(a)].">
      <j1 rule="hyper" parents="373 27687 52983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52985">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) \ w) * (u \ w))) = a(x,y,w * (w * (u \ ((1 / u) \ z))))
    ]]></literal>
    <justification jstring="[para(1166(a,1),52984(a,2,3,2,2))].">
      <j1 rule="para" parents="1166 52984"/>
    </justification>
  </clause>

  <clause id="52986">
    <literal><![CDATA[
      a(x,y,z * (((u \ 1) \ w) * (u \ w))) = a(x,y,w * (w * z))
    ]]></literal>
    <justification jstring="[hyper(373,a,52006,a(flip),b,52985,a),flip(a)].">
      <j1 rule="hyper" parents="373 52006 52985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52988">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * (((z \ 1) \ u) * ((z \ (z \ 1)) * w))) = a(x,y,u * (u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,52968,a,b,52986,a)].">
      <j1 rule="hyper" parents="64 52968 52986"/>
    </justification>
  </clause>

  <clause id="52990">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * (T(u / z,z \ 1) * w)) = a(x,y,u * (u * w))
    ]]></literal>
    <justification jstring="[para(7674(a,1),52988(a,1,3,2))].">
      <j1 rule="para" parents="7674 52988"/>
    </justification>
  </clause>

  <clause id="52991">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * ((u / z) * w)) = a(x,y,u * (u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27473,a(flip),b,52990,a)].">
      <j1 rule="hyper" parents="64 27473 52990"/>
    </justification>
  </clause>

  <clause id="52993">
    <literal><![CDATA[
      a(x,y,((z \ 1) \ u) * ((z \ u) * w)) = a(x,y,u * (u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27480,a(flip),b,52991,a)].">
      <j1 rule="hyper" parents="64 27480 52991"/>
    </justification>
  </clause>

  <clause id="52994">
    <literal><![CDATA[
      a(x,y,(z * u) * ((z \ u) * w)) = a(x,y,u * (u * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,52667,a(flip),b,52993,a)].">
      <j1 rule="hyper" parents="64 52667 52993"/>
    </justification>
  </clause>

  <clause id="52995">
    <literal><![CDATA[
      a(x,y,z * (z * (((u * z) \ w) * v5))) = a(x,y,((u \ z) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52869,a(flip),b,52994,a),flip(a)].">
      <j1 rule="hyper" parents="64 52869 52994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="52997">
    <literal><![CDATA[
      a(x,y,L(a(z,u,u) * ((w * a(v5,v6,v7)) \ v8),w * a(z,u,u),a(v5,v6,v7))) = a(x,y,(a(z,u,u) \ w) \ (a(v5,v6,v7) \ v8))
    ]]></literal>
    <justification jstring="[para(37829(a,1),51912(a,1,3))].">
      <j1 rule="para" parents="37829 51912"/>
    </justification>
  </clause>

  <clause id="52998">
    <literal><![CDATA[
      a(x,y,L(a(z,u,u) * ((w * a(v5,v6,v7)) \ v8),w,a(v5,v6,v7))) = a(x,y,(a(z,u,u) \ w) \ (a(v5,v6,v7) \ v8))
    ]]></literal>
    <justification jstring="[para(52016(a,1),52997(a,1,3))].">
      <j1 rule="para" parents="52016 52997"/>
    </justification>
  </clause>

  <clause id="53000">
    <literal><![CDATA[
      x \ ((x * y) * a(x \ 1,(x \ 1) * y,a(z,u,(x \ y) * w))) = L((x \ 1) \ ((x \ 1) * y),(x \ 1) * y,a(w,u,z))
    ]]></literal>
    <justification jstring="[para(52703(a,1),52504(a,1,2,2,3))].">
      <j1 rule="para" parents="52703 52504"/>
    </justification>
  </clause>

  <clause id="53001">
    <literal><![CDATA[
      L((x \ 1) \ ((x \ 1) * y),(x \ 1) * y,a(z,u,w)) = x \ ((x * y) * a(w,u,a((x \ y) * z,y,x \ 1)))
    ]]></literal>
    <justification jstring="[para(51965(a,1),53000(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="51965 53000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53002">
    <literal><![CDATA[
      L((x \ 1) \ ((x \ 1) * y),(x \ 1) * y,a(z,u,w)) = x \ ((x * y) * a(w,u,a(x * (z * y),y,x \ 1)))
    ]]></literal>
    <justification jstring="[para(52421(a,1),53001(a,2,2,2,3))].">
      <j1 rule="para" parents="52421 53001"/>
    </justification>
  </clause>

  <clause id="53003">
    <literal><![CDATA[
      L((x \ 1) \ ((x \ 1) * y),(x \ 1) * y,a(z,u,w)) = x \ ((x * y) * a(w,u,a(x * (z * y),y,x * 1)))
    ]]></literal>
    <justification jstring="[para(49778(a,1),53002(a,2,2,2))].">
      <j1 rule="para" parents="49778 53002"/>
    </justification>
  </clause>

  <clause id="53004">
    <literal><![CDATA[
      L((x \ 1) \ ((x \ 1) * y),(x \ 1) * y,a(z,u,w)) = x \ ((x * y) * a(w,u,a(x * (z * y),y,x)))
    ]]></literal>
    <justification jstring="[para(8(a,1),53003(a,2,2,2,3,3))].">
      <j1 rule="para" parents="8 53003"/>
    </justification>
  </clause>

  <clause id="53005">
    <literal><![CDATA[
      L((x \ 1) \ ((x \ 1) * y),(x \ 1) * y,a(z,u,w)) = x \ ((x * y) * a(w,u,a(z * x,y,x * y)))
    ]]></literal>
    <justification jstring="[para(52494(a,1),53004(a,2,2,2))].">
      <j1 rule="para" parents="52494 53004"/>
    </justification>
  </clause>

  <clause id="53006">
    <literal><![CDATA[
      L((x \ 1) \ ((x \ 1) * y),(x \ 1) * y,a(z,u,w)) = x \ L(x * y,u,a(z * x,y,w))
    ]]></literal>
    <justification jstring="[para(47349(a,1),53005(a,2,2))].">
      <j1 rule="para" parents="47349 53005"/>
    </justification>
  </clause>

  <clause id="53007">
    <literal><![CDATA[
      L((x \ 1) \ ((x \ 1) * y),(x \ 1) * y,a(z,u,w)) = x * L(x \ y,u,a(z * x,y,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,28865,a(flip),b,53006,a),flip(a)].">
      <j1 rule="hyper" parents="373 28865 53006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53008">
    <literal><![CDATA[
      x * L(x \ y,z,a(u * x,y,w)) = L(y,(x \ 1) * y,a(u,z,w))
    ]]></literal>
    <justification jstring="[para(9(a,1),53007(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 53007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53009">
    <literal><![CDATA[
      x * L(x \ y,z,a(u * x,y,w)) = L(y,x * y,a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(373,a,11864,a(flip),b,53008,a),flip(a)].">
      <j1 rule="hyper" parents="373 11864 53008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53010">
    <literal><![CDATA[
      L(x,y * x,a(z,u,w)) = y * (y \ L(x,y,a(w,u,z)))
    ]]></literal>
    <justification jstring="[para(52890(a,1),53009(a,1,2)),flip(a)].">
      <j1 rule="para" parents="52890 53009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53011">
    <literal><![CDATA[
      L(x,y * x,a(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,10,a(flip),b,53010,a),flip(a)].">
      <j1 rule="hyper" parents="373 10 53010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53015">
    <literal><![CDATA[
      L(x,y \ x,a(z,u,w)) = L(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52029,a,b,53011,a)].">
      <j1 rule="hyper" parents="64 52029 53011"/>
    </justification>
  </clause>

  <clause id="53016">
    <literal><![CDATA[
      L(x,x * y,a(z,u,w)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46400,a(flip),b,53015,a)].">
      <j1 rule="hyper" parents="64 46400 53015"/>
    </justification>
  </clause>

  <clause id="53020">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5 * x,v6))) = L(x,v5,a(z,u,a(w,y,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47522,a(flip),b,53016,a)].">
      <j1 rule="hyper" parents="64 47522 53016"/>
    </justification>
  </clause>

  <clause id="53021">
    <literal><![CDATA[
      a(x,y,((z / u) \ 1) * (((z / u) \ 1) * ((w / ((z / u) \ 1)) * v5))) = a(x,y,v5 * ((u / z) * (((z / u) \ 1) * (w / (u / z)))))
    ]]></literal>
    <justification jstring="[para(34430(a,1),52772(a,2,3,2))].">
      <j1 rule="para" parents="34430 52772"/>
    </justification>
  </clause>

  <clause id="53022">
    <literal><![CDATA[
      a(x,y,(K(z,z \ u) \ w) * ((L(z,v5,v6) \ v7) \ K(z,z \ u))) = a(x,y,(L(u / (u / z),v5,v6) \ v7) \ w)
    ]]></literal>
    <justification jstring="[hyper(64,a,27331,a(flip),b,52789,a),flip(a)].">
      <j1 rule="hyper" parents="64 27331 52789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53024">
    <literal><![CDATA[
      a(x,y,(K(z,z \ u) \ w) * ((L(z,v5,v6) \ v7) \ K(z,z \ u))) = a(x,y,(v7 \ L(u / (u / z),v5,v6)) * w)
    ]]></literal>
    <justification jstring="[hyper(373,a,52682,a(flip),b,53022,a),flip(a)].">
      <j1 rule="hyper" parents="373 52682 53022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53025">
    <literal><![CDATA[
      a(x * y,z,a(a(u,w,v5),(v6 * v6) * (a(u,w,v5) \ x),v7)) = a(v7,z,a(y,a(u,w,v5),(v6 * v6) * (a(u,w,v5) \ x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47474,a(flip),b,52834,a)].">
      <j1 rule="hyper" parents="64 47474 52834"/>
    </justification>
  </clause>

  <clause id="53027">
    <literal><![CDATA[
      a(x * y,z,a(a(u,w,v5),(v6 * v6) * (x * a(u,w,v5)),v7)) = a(v7,z,a(y,a(u,w,v5),(v6 * v6) * (a(u,w,v5) \ x)))
    ]]></literal>
    <justification jstring="[para(52560(a,1),53025(a,1,3))].">
      <j1 rule="para" parents="52560 53025"/>
    </justification>
  </clause>

  <clause id="53028">
    <literal><![CDATA[
      a(x * y,z,a(a(u,w,v5),x * a(u,w,v5),v6)) = a(v6,z,a(y,a(u,w,v5),(v7 * v7) * (a(u,w,v5) \ x)))
    ]]></literal>
    <justification jstring="[para(11960(a,1),53027(a,1,3))].">
      <j1 rule="para" parents="11960 53027"/>
    </justification>
  </clause>

  <clause id="53029">
    <literal><![CDATA[
      a(x * y,z,a(u,x,a(w,v5,v6))) = a(u,z,a(y,a(w,v5,v6),(v7 * v7) * (a(w,v5,v6) \ x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,51966,a(flip),b,53028,a)].">
      <j1 rule="hyper" parents="64 51966 53028"/>
    </justification>
  </clause>

  <clause id="53031">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),(v6 * v6) * (a(u,w,v5) \ v7))) = a(z,v7,a(x,y,a(u,w,v5) * v7))
    ]]></literal>
    <justification jstring="[hyper(64,a,52469,a(flip),b,53029,a),flip(a)].">
      <j1 rule="hyper" parents="64 52469 53029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53032">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),(v6 * v6) * (a(u,w,v5) \ v7))) = a(z,v7,a(x,y,a(u * v7,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(373,a,52514,a,b,53031,a),flip(a)].">
      <j1 rule="hyper" parents="373 52514 53031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53033">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),(v6 * v6) * (a(u,w,v5) * v7))) = a(z,v7,a(x,y,a(u * v7,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52719,a(flip),b,53032,a)].">
      <j1 rule="hyper" parents="64 52719 53032"/>
    </justification>
  </clause>

  <clause id="53034">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),v6 * (v6 * (a(u,w,v5) * v7)))) = a(z,v7,a(x,y,a(u * v7,w,v5)))
    ]]></literal>
    <justification jstring="[para(51321(a,1),53033(a,1,3))].">
      <j1 rule="para" parents="51321 53033"/>
    </justification>
  </clause>

  <clause id="53035">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w) * v5,a(w,u,z),v6)) = a(v6,v5,a(x,y,a(z * v5,u,w)))
    ]]></literal>
    <justification jstring="[para(49866(a,1),53034(a,1,3))].">
      <j1 rule="para" parents="49866 53034"/>
    </justification>
  </clause>

  <clause id="53036">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w * y,v5,v6))) = a(z,u,a(y,a(w,v5,v6),x))
    ]]></literal>
    <justification jstring="[para(52915(a,1),53035(a,1,3)),flip(a)].">
      <j1 rule="para" parents="52915 53035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53037">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6) * y)) = a(z,u,a(y,a(w,v5,v6),x))
    ]]></literal>
    <justification jstring="[hyper(64,a,52514,a(flip),b,53036,a)].">
      <j1 rule="hyper" parents="64 52514 53036"/>
    </justification>
  </clause>

  <clause id="53038">
    <literal><![CDATA[
      x * a(y,z,a(x,a(u,w,v5),v6)) = L(x,w,a(v6,a(u,z,y),v5))
    ]]></literal>
    <justification jstring="[para(53037(a,1),52936(a,1,2))].">
      <j1 rule="para" parents="53037 52936"/>
    </justification>
  </clause>

  <clause id="53039">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,v5,v6)) = L(x,z,a(v6,a(y,v5,w),u))
    ]]></literal>
    <justification jstring="[hyper(64,a,47271,a(flip),b,53038,a)].">
      <j1 rule="hyper" parents="64 47271 53038"/>
    </justification>
  </clause>

  <clause id="53044">
    <literal><![CDATA[
      a(x,y,((z / u) \ 1) * (((z / u) \ 1) * ((w / ((z / u) \ 1)) * v5))) = a(x,y,v5 * ((u / z) * (((z / u) \ 1) * ((u / z) \ w))))
    ]]></literal>
    <justification jstring="[hyper(373,a,27663,a(flip),b,53021,a),flip(a)].">
      <j1 rule="hyper" parents="373 27663 53021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53045">
    <literal><![CDATA[
      a(x,y,((z / u) \ 1) * (((z / u) \ 1) * ((w / ((z / u) \ 1)) * v5))) = a(x,y,v5 * ((u / z) * (((z / u) * (u / z)) \ w)))
    ]]></literal>
    <justification jstring="[para(37939(a,1),53044(a,2,3,2,2))].">
      <j1 rule="para" parents="37939 53044"/>
    </justification>
  </clause>

  <clause id="53046">
    <literal><![CDATA[
      a(x,y,((z / u) \ 1) * (((z / u) \ 1) * ((w / ((z / u) \ 1)) * v5))) = a(x,y,v5 * ((z \ u) * (((z / u) * (z \ u)) \ w)))
    ]]></literal>
    <justification jstring="[para(25740(a,1),53045(a,2,3,2))].">
      <j1 rule="para" parents="25740 53045"/>
    </justification>
  </clause>

  <clause id="53047">
    <literal><![CDATA[
      a(x,y,((z / u) \ 1) * (((z / u) \ 1) * ((w / ((z / u) \ 1)) * v5))) = a(x,y,v5 * (((z / u) \ 1) * w))
    ]]></literal>
    <justification jstring="[para(38156(a,1),53046(a,2,3,2))].">
      <j1 rule="para" parents="38156 53046"/>
    </justification>
  </clause>

  <clause id="53048">
    <literal><![CDATA[
      a(x,y,((z / u) \ 1) * (((z / u) \ 1) * ((w / ((z / u) \ 1)) * v5))) = a(x,y,((z / u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,52703,a(flip),b,53047,a),flip(a)].">
      <j1 rule="hyper" parents="373 52703 53047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53049">
    <literal><![CDATA[
      a(x,y,((z / u) \ 1) * (((z / u) \ 1) * ((w / ((z / u) \ 1)) * v5))) = a(x,y,((u \ z) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(373,a,27412,a(flip),b,53048,a),flip(a)].">
      <j1 rule="hyper" parents="373 27412 53048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53050">
    <literal><![CDATA[
      a(x,y,((z / u) \ 1) * (((z / u) \ 1) * ((((z / u) \ 1) \ w) * v5))) = a(x,y,((u \ z) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27664,a(flip),b,53049,a)].">
      <j1 rule="hyper" parents="64 27664 53049"/>
    </justification>
  </clause>

  <clause id="53051">
    <literal><![CDATA[
      a(x,y,((z / u) \ 1) * ((z / u) * (((z / u) \ w) * v5))) = a(x,y,((u \ z) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(1547(a,1),53050(a,1,3,2))].">
      <j1 rule="para" parents="1547 53050"/>
    </justification>
  </clause>

  <clause id="53052">
    <literal><![CDATA[
      a(x,y,((z / u) \ 1) * ((u * z) * (((u * z) \ w) * v5))) = a(x,y,((u \ z) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(51988(a,1),53051(a,1,3,2))].">
      <j1 rule="para" parents="51988 53051"/>
    </justification>
  </clause>

  <clause id="53053">
    <literal><![CDATA[
      a(x,y,(z / u) \ ((u * z) * (((u * z) \ w) * v5))) = a(x,y,((u \ z) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,51316,a(flip),b,53052,a)].">
      <j1 rule="hyper" parents="64 51316 53052"/>
    </justification>
  </clause>

  <clause id="53054">
    <literal><![CDATA[
      a(x,y,z * (((z * u) \ u) \ (((z * u) \ w) * v5))) = a(x,y,((z \ u) \ w) * v5)
    ]]></literal>
    <justification jstring="[para(45004(a,1),53053(a,1,3))].">
      <j1 rule="para" parents="45004 53053"/>
    </justification>
  </clause>

  <clause id="53055">
    <literal><![CDATA[
      a(x,y,z * ((u \ (z \ u)) \ (((z * u) \ w) * v5))) = a(x,y,((z \ u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27982,a(flip),b,53054,a)].">
      <j1 rule="hyper" parents="64 27982 53054"/>
    </justification>
  </clause>

  <clause id="53056">
    <literal><![CDATA[
      a(x,y,z * (z * (((z * u) \ w) * v5))) = a(x,y,((z \ u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52750,a(flip),b,53055,a)].">
      <j1 rule="hyper" parents="64 52750 53055"/>
    </justification>
  </clause>

  <clause id="53057">
    <literal><![CDATA[
      a(x,y,((z * u) \ w) * (u * (u * v5))) = a(x,y,((u \ z) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52773,a,b,53056,a)].">
      <j1 rule="hyper" parents="64 52773 53056"/>
    </justification>
  </clause>

  <clause id="53059">
    <literal><![CDATA[
      a(x,y,z * (z * (((u * z) \ w) * v5))) = a(x,y,((z \ u) \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52752,a(flip),b,53057,a)].">
      <j1 rule="hyper" parents="64 52752 53057"/>
    </justification>
  </clause>

  <clause id="53060">
    <literal><![CDATA[
      a(x,y,((z \ u) \ w) * v5) = a(x,y,((u \ z) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,52995,a(flip),b,53059,a),flip(a)].">
      <j1 rule="hyper" parents="64 52995 53059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53061">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) * (v5 \ v6)) \ v7) = a(x,y,((v6 \ v5) * a(z,u,w)) * v7)
    ]]></literal>
    <justification jstring="[hyper(64,a,51979,a,b,53060,a)].">
      <j1 rule="hyper" parents="64 51979 53060"/>
    </justification>
  </clause>

  <clause id="53062">
    <literal><![CDATA[
      a(x,y,((z / u) \ w) * v5) = a(x,y,((z \ u) * w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27412,a,b,53060,a)].">
      <j1 rule="hyper" parents="64 27412 53060"/>
    </justification>
  </clause>

  <clause id="53063">
    <literal><![CDATA[
      a(x,y,((z \ (z * u)) * w) * v5) = a(x,y,v5 * ((z \ (u \ z)) \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,28053,a(flip),b,53060,a),flip(a)].">
      <j1 rule="hyper" parents="64 28053 53060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53064">
    <literal><![CDATA[
      a(x,y,((z \ (u \ z)) * w) * v5) = a(x,y,(u \ w) * v5)
    ]]></literal>
    <justification jstring="[hyper(64,a,27416,a(flip),b,53060,a),flip(a)].">
      <j1 rule="hyper" parents="64 27416 53060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53065">
    <literal><![CDATA[
      a(x,y,(((z * u) \ z) * w) * v5) = a(x,y,(u \ w) * v5)
    ]]></literal>
    <justification jstring="[para(9(a,1),53060(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="9 53060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53066">
    <literal><![CDATA[
      a(x,y,((z \ (u * z)) * w) * ((R(1 / u,u,z) \ v5) \ (z \ (u \ z)))) = a(x,y,v5 \ ((z \ (u \ z)) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,52950,a(flip),b,53062,a),flip(a)].">
      <j1 rule="hyper" parents="64 52950 53062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53067">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w \ u)) * v5)) = a(x,y,(w \ v5) * z)
    ]]></literal>
    <justification jstring="[hyper(27453,a,53064,a)].">
      <j1 rule="hyper" parents="27453 53064"/>
    </justification>
  </clause>

  <clause id="53070">
    <literal><![CDATA[
      a(x,y,z * ((u \ (w \ u)) \ v5)) = a(x,y,(w * v5) * z)
    ]]></literal>
    <justification jstring="[para(9(a,1),53063(a,1,3,1,1)),flip(a)].">
      <j1 rule="para" parents="9 53063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53072">
    <literal><![CDATA[
      a(x,y,z * (((u * w) \ w) \ v5)) = a(x,y,(u * v5) * z)
    ]]></literal>
    <justification jstring="[hyper(64,a,27982,a,b,53070,a)].">
      <j1 rule="hyper" parents="64 27982 53070"/>
    </justification>
  </clause>

  <clause id="53074">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) * (v5 \ w)) \ v6) = a(x,y,(L(w,u,z) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(51102(a,1),53061(a,2,3,1))].">
      <j1 rule="para" parents="51102 53061"/>
    </justification>
  </clause>

  <clause id="53075">
    <literal><![CDATA[
      a(x,y,(T(z,u) * w) * ((R(1 / z,z,u) \ v5) \ (u \ (z \ u)))) = a(x,y,v5 \ ((u \ (z \ u)) * w))
    ]]></literal>
    <justification jstring="[para(22(a,2),53066(a,1,3,1,1))].">
      <j1 rule="para" parents="22 53066"/>
    </justification>
  </clause>

  <clause id="53076">
    <literal><![CDATA[
      a(x,y,(z * u) * ((R(1 / z,z,w) \ v5) \ (w \ (z \ w)))) = a(x,y,v5 \ ((w \ (z \ w)) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,27398,a(flip),b,53075,a)].">
      <j1 rule="hyper" parents="64 27398 53075"/>
    </justification>
  </clause>

  <clause id="53078">
    <literal><![CDATA[
      a(x,y,a(L(z \ (T(z \ 1,u) \ w),v5,v6),v7,((z \ 1) \ L(w,v5,v6)) * v7)) = a(x,y,a(z,L(z \ (T(z \ 1,u) \ w),v5,v6),v7))
    ]]></literal>
    <justification jstring="[para(27531(a,1),52828(a,1,3))].">
      <j1 rule="para" parents="27531 52828"/>
    </justification>
  </clause>

  <clause id="53080">
    <literal><![CDATA[
      a(x,y,a(L(z \ (T(z \ 1,u) \ w),v5,v6),v7,L(w,v5,v6) * ((z \ 1) \ v7))) = a(x,y,a(z,L(z \ (T(z \ 1,u) \ w),v5,v6),v7))
    ]]></literal>
    <justification jstring="[para(52760(a,1),53078(a,1,3))].">
      <j1 rule="para" parents="52760 53078"/>
    </justification>
  </clause>

  <clause id="53081">
    <literal><![CDATA[
      a(x,y,a(L(z \ (T(z \ 1,u) \ w),v5,v6),v7,L(w,v5,v6) * (z * v7))) = a(x,y,a(z,L(z \ (T(z \ 1,u) \ w),v5,v6),v7))
    ]]></literal>
    <justification jstring="[para(52657(a,1),53080(a,1,3))].">
      <j1 rule="para" parents="52657 53080"/>
    </justification>
  </clause>

  <clause id="53082">
    <literal><![CDATA[
      a(x,y,a(z \ (T(z \ 1,u) \ w),v5,L(L(w,v6,v7) * (z * v5),v6,v7))) = a(x,y,a(z,L(z \ (T(z \ 1,u) \ w),v6,v7),v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,46787,a(flip),b,53081,a)].">
      <j1 rule="hyper" parents="64 46787 53081"/>
    </justification>
  </clause>

  <clause id="53083">
    <literal><![CDATA[
      a(x,y,a((z * T(u \ 1,w)) * u,v5,L(L(z,v6,v7) * (u * v5),v6,v7))) = a(x,y,a(u,L(u \ (T(u \ 1,w) \ z),v6,v7),v5))
    ]]></literal>
    <justification jstring="[para(52323(a,1),53082(a,1,3))].">
      <j1 rule="para" parents="52323 53082"/>
    </justification>
  </clause>

  <clause id="53084">
    <literal><![CDATA[
      a(x,y,a((z * (u \ 1)) * u,w,L(L(z,v5,v6) * (u * w),v5,v6))) = a(x,y,a(u,L(u \ (T(u \ 1,v7) \ z),v5,v6),w))
    ]]></literal>
    <justification jstring="[para(32392(a,1),53083(a,1,3))].">
      <j1 rule="para" parents="32392 53083"/>
    </justification>
  </clause>

  <clause id="53086">
    <literal><![CDATA[
      a(x,y,a((z * u) * u,w,L(L(z,v5,v6) * (u * w),v5,v6))) = a(x,y,a(u,L(u \ (T(u \ 1,v7) \ z),v5,v6),w))
    ]]></literal>
    <justification jstring="[para(32573(a,1),53084(a,1,3))].">
      <j1 rule="para" parents="32573 53084"/>
    </justification>
  </clause>

  <clause id="53087">
    <literal><![CDATA[
      a(x,y,a(z,L(z \ (T(z \ 1,u) \ w),v5,v6),v7)) = a(x,y,a(w,v7,L(L(w,v5,v6) * (z * v7),v5,v6)))
    ]]></literal>
    <justification jstring="[para(51304(a,1),53086(a,1,3)),flip(a)].">
      <j1 rule="para" parents="51304 53086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53088">
    <literal><![CDATA[
      a(x,y,a(z,L(z \ (T(z \ 1,u) \ w),v5,v6),v7)) = a(x,y,a(w,v7,w * L(z * v7,v5,v6)))
    ]]></literal>
    <justification jstring="[para(49296(a,1),53087(a,2,3))].">
      <j1 rule="para" parents="49296 53087"/>
    </justification>
  </clause>

  <clause id="53090">
    <literal><![CDATA[
      a(x,y,a(z,L(z * (T(z \ 1,u) \ w),v5,v6),v7)) = a(x,y,a(w,v7,w * L(z * v7,v5,v6)))
    ]]></literal>
    <justification jstring="[para(52166(a,1),53088(a,1,3))].">
      <j1 rule="para" parents="52166 53088"/>
    </justification>
  </clause>

  <clause id="53091">
    <literal><![CDATA[
      a(x,y,a(z,L(z * (T(z \ 1,u) * w),v5,v6),v7)) = a(x,y,a(w,v7,w * L(z * v7,v5,v6)))
    ]]></literal>
    <justification jstring="[para(52946(a,1),53090(a,1,3))].">
      <j1 rule="para" parents="52946 53090"/>
    </justification>
  </clause>

  <clause id="53092">
    <literal><![CDATA[
      a(x,y,a(z,L(((z \ 1) * u) * z,w,v5),v6)) = a(x,y,a(u,v6,u * L(z * v6,w,v5)))
    ]]></literal>
    <justification jstring="[para(32321(a,1),53091(a,1,3))].">
      <j1 rule="para" parents="32321 53091"/>
    </justification>
  </clause>

  <clause id="53093">
    <literal><![CDATA[
      a(x,y,a(z,L((z * u) * z,w,v5),v6)) = a(x,y,a(u,v6,u * L(z * v6,w,v5)))
    ]]></literal>
    <justification jstring="[para(35335(a,1),53092(a,1,3))].">
      <j1 rule="para" parents="35335 53092"/>
    </justification>
  </clause>

  <clause id="53094">
    <literal><![CDATA[
      a(x,y,a(z,u,z * L(w * u,v5,v6))) = a(x,y,a(w,L(z,v5,v6),u))
    ]]></literal>
    <justification jstring="[para(52162(a,1),53093(a,1,3)),flip(a)].">
      <j1 rule="para" parents="52162 53093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53096">
    <literal><![CDATA[
      a(x,y,a(z \ 1,z \ (a(u,w,v5) \ 1),v6 * (z \ (a(u,w,v5) \ 1)))) = a(x,y,a(a(u,w,v5) \ (z \ (1 / z)),z * (a(u,w,v5) \ 1),v6))
    ]]></literal>
    <justification jstring="[para(52168(a,1),52491(a,2,3))].">
      <j1 rule="para" parents="52168 52491"/>
    </justification>
  </clause>

  <clause id="53097">
    <literal><![CDATA[
      a(x,y,a(z \ 1,z \ (a(u,w,v5) \ 1),v6 * (z \ (a(u,w,v5) \ 1)))) = a(x,y,a(a(u,w,v5) \ (z \ (1 / z)),a(u,w,v5) * z,v6))
    ]]></literal>
    <justification jstring="[para(31945(a,1),53096(a,2,3))].">
      <j1 rule="para" parents="31945 53096"/>
    </justification>
  </clause>

  <clause id="53098">
    <literal><![CDATA[
      a(x,y,a(z \ 1,z \ (a(u,w,v5) \ 1),v6 * (z \ (a(u,w,v5) \ 1)))) = a(x,y,a((z \ (1 / z)) * a(u,w,v5),a(u,w,v5) * z,v6))
    ]]></literal>
    <justification jstring="[para(42467(a,1),53097(a,2,3))].">
      <j1 rule="para" parents="42467 53097"/>
    </justification>
  </clause>

  <clause id="53099">
    <literal><![CDATA[
      a(x,y,a(z \ 1,z \ (a(u,w,v5) \ 1),v6 * (z \ (a(u,w,v5) \ 1)))) = a(x,y,a(z \ (a(u,w,v5) / z),a(u,w,v5) * z,v6))
    ]]></literal>
    <justification jstring="[para(51639(a,1),53098(a,2,3,1))].">
      <j1 rule="para" parents="51639 53098"/>
    </justification>
  </clause>

  <clause id="53100">
    <literal><![CDATA[
      a(x,y,a(z \ 1,z \ (a(u,w,v5) \ 1),v6 * (z \ (a(u,w,v5) \ 1)))) = a(x,y,a((a(u,w,v5) / z) * z,a(u,w,v5) * z,v6))
    ]]></literal>
    <justification jstring="[para(51310(a,1),53099(a,2,3))].">
      <j1 rule="para" parents="51310 53099"/>
    </justification>
  </clause>

  <clause id="53101">
    <literal><![CDATA[
      a(x,y,a(z \ 1,z \ (a(u,w,v5) \ 1),v6 * (z \ (a(u,w,v5) \ 1)))) = a(x,y,a(a(u,w,v5),a(u,w,v5) * z,v6))
    ]]></literal>
    <justification jstring="[para(12(a,1),53100(a,2,3,1))].">
      <j1 rule="para" parents="12 53100"/>
    </justification>
  </clause>

  <clause id="53103">
    <literal><![CDATA[
      a(x,y,a(z \ 1,z \ (a(u,w,v5) \ 1),v6 * (z \ (a(u,w,v5) \ 1)))) = a(x,y,a(v6,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(42835(a,1),53101(a,2,3))].">
      <j1 rule="para" parents="42835 53101"/>
    </justification>
  </clause>

  <clause id="53104">
    <literal><![CDATA[
      a(x,y,a(z \ 1,z \ (a(u,w,v5) \ 1),(a(u,w,v5) * z) \ v6)) = a(x,y,a(v6,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(52735(a,1),53103(a,1,3))].">
      <j1 rule="para" parents="52735 53103"/>
    </justification>
  </clause>

  <clause id="53105">
    <literal><![CDATA[
      a(x * ((y * y) * (z * z)),u,a((x * ((y * y) * (z * z))) * w,v5,v6)) = a(w,v5,a(x * ((y * y) * ((z * z) * v6)),u,x * (y * (y * (z * z)))))
    ]]></literal>
    <justification jstring="[para(52615(a,1),52860(a,2,3))].">
      <j1 rule="para" parents="52615 52860"/>
    </justification>
  </clause>

  <clause id="53106">
    <literal><![CDATA[
      a(x * ((y * y) * (z * z)),u,a((x * ((y * y) * (z * z))) * w,v5,v6)) = a(w,v5,a(((y * y) * v6) * x,u,x * (y * (y * (z * z)))))
    ]]></literal>
    <justification jstring="[para(32701(a,1),53105(a,2,3))].">
      <j1 rule="para" parents="32701 53105"/>
    </justification>
  </clause>

  <clause id="53107">
    <literal><![CDATA[
      a(x * ((y * y) * (z * z)),u,a((x * ((y * y) * (z * z))) * w,v5,v6)) = a(w,v5,a(v6 * x,u,x * (y * (y * (z * z)))))
    ]]></literal>
    <justification jstring="[para(2655(a,1),53106(a,2,3))].">
      <j1 rule="para" parents="2655 53106"/>
    </justification>
  </clause>

  <clause id="53109">
    <literal><![CDATA[
      a(x * ((y * y) * (z * z)),u,a((x * ((y * y) * (z * z))) * w,v5,v6)) = a((z * z) * x,u,a(w,v5,v6 * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,52359,a(flip),b,53107,a),flip(a)].">
      <j1 rule="hyper" parents="373 52359 53107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53112">
    <literal><![CDATA[
      a(x * ((y * y) * (z * z)),u,a((x * ((y * y) * (z * z))) * w,v5,v6)) = a(x,u,a(w,v5,v6 * x))
    ]]></literal>
    <justification jstring="[hyper(373,a,2639,a(flip),b,53109,a),flip(a)].">
      <j1 rule="hyper" parents="373 2639 53109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53114">
    <literal><![CDATA[
      a(x * ((y * y) * (z * z)),u,a(x * ((y * y) * ((z * z) * w)),v5,v6)) = a(x,u,a(w,v5,v6 * x))
    ]]></literal>
    <justification jstring="[para(2289(a,1),53112(a,1,3,1))].">
      <j1 rule="para" parents="2289 53112"/>
    </justification>
  </clause>

  <clause id="53115">
    <literal><![CDATA[
      a(x * ((y * y) * (z * z)),u,a(((y * y) * w) * x,v5,v6)) = a(x,u,a(w,v5,v6 * x))
    ]]></literal>
    <justification jstring="[para(32701(a,1),53114(a,1,3))].">
      <j1 rule="para" parents="32701 53114"/>
    </justification>
  </clause>

  <clause id="53116">
    <literal><![CDATA[
      a(x * ((y * y) * (z * z)),u,a(w * x,v5,v6)) = a(x,u,a(w,v5,v6 * x))
    ]]></literal>
    <justification jstring="[para(2655(a,1),53115(a,1,3))].">
      <j1 rule="para" parents="2655 53115"/>
    </justification>
  </clause>

  <clause id="53118">
    <literal><![CDATA[
      a(x,y,a(z * x,u,w)) = a(x,y,a(z,u,w * x))
    ]]></literal>
    <justification jstring="[hyper(26858,a,53116,a)].">
      <j1 rule="hyper" parents="26858 53116"/>
    </justification>
  </clause>

  <clause id="53120">
    <literal><![CDATA[
      a(x,y,a(z,u,w * x)) = a(w,u,a(x,y,x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,47209,a(flip),b,53118,a),flip(a)].">
      <j1 rule="hyper" parents="64 47209 53118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53121">
    <literal><![CDATA[
      a((x \ y) \ y,z,a(R(x \ (x \ y),u,w),v5,v6 * ((x \ y) \ y))) = a(v6,v5,a((x \ y) \ y,z,R(y,u,w) / x))
    ]]></literal>
    <justification jstring="[para(38824(a,1),53120(a,2,3,3))].">
      <j1 rule="para" parents="38824 53120"/>
    </justification>
  </clause>

  <clause id="53122">
    <literal><![CDATA[
      a(L(x,y,z),L(x,y,z),L(x,y,z) \ L(x,y,z)) \ (((R(x,y,z) \ L(x,y,z)) * a(L(x,y,z),L(x,y,z),R(x,y,z) \ L(x,y,z))) * u) = L(((R(x,y,z) \ L(x,y,z)) \ 1) \ u,R(x,y,z) \ L(x,y,z),((1 / L(x,y,z)) * R(x,y,z)) \ 1)
    ]]></literal>
    <justification jstring="[para(31334(a,1),35957(a,1,1))].">
      <j1 rule="para" parents="31334 35957"/>
    </justification>
  </clause>

  <clause id="53123">
    <literal><![CDATA[
      L(((R(x,y,z) \ L(x,y,z)) \ 1) \ u,R(x,y,z) \ L(x,y,z),((1 / L(x,y,z)) * R(x,y,z)) \ 1) = 1 \ (((R(x,y,z) \ L(x,y,z)) * a(L(x,y,z),L(x,y,z),R(x,y,z) \ L(x,y,z))) * u)
    ]]></literal>
    <justification jstring="[para(33089(a,1),53122(a,1,1)),flip(a)].">
      <j1 rule="para" parents="33089 53122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53124">
    <literal><![CDATA[
      L(((R(x,y,z) \ L(x,y,z)) \ 1) \ u,R(x,y,z) \ L(x,y,z),((1 / L(x,y,z)) * R(x,y,z)) \ 1) = 1 \ (((R(x,y,z) \ L(x,y,z)) * a(L(x,y,z),L(x,y,z),L(x,y,z) \ L(x,y,z))) * u)
    ]]></literal>
    <justification jstring="[para(31334(a,1),53123(a,2,2,1,2))].">
      <j1 rule="para" parents="31334 53123"/>
    </justification>
  </clause>

  <clause id="53126">
    <literal><![CDATA[
      L(((R(x,y,z) \ L(x,y,z)) \ 1) \ u,R(x,y,z) \ L(x,y,z),((1 / L(x,y,z)) * R(x,y,z)) \ 1) = 1 \ (((R(x,y,z) \ L(x,y,z)) * 1) * u)
    ]]></literal>
    <justification jstring="[para(33089(a,1),53124(a,2,2,1,2))].">
      <j1 rule="para" parents="33089 53124"/>
    </justification>
  </clause>

  <clause id="53127">
    <literal><![CDATA[
      L(((R(x,y,z) \ L(x,y,z)) \ 1) \ u,R(x,y,z) \ L(x,y,z),((1 / L(x,y,z)) * R(x,y,z)) \ 1) = 1 \ ((R(x,y,z) \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(8(a,1),53126(a,2,2,1))].">
      <j1 rule="para" parents="8 53126"/>
    </justification>
  </clause>

  <clause id="53129">
    <literal><![CDATA[
      L(((R(x,y,z) \ L(x,y,z)) \ 1) \ u,R(x,y,z) \ L(x,y,z),((1 / L(x,y,z)) * R(x,y,z)) \ 1) = (R(x,y,z) \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(373,a,66,a(flip),b,53127,a),flip(a)].">
      <j1 rule="hyper" parents="373 66 53127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53130">
    <literal><![CDATA[
      L((L(x,y,z) \ R(x,y,z)) \ u,R(x,y,z) \ L(x,y,z),((1 / L(x,y,z)) * R(x,y,z)) \ 1) = (R(x,y,z) \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(44609(a,1),53129(a,1,1,1))].">
      <j1 rule="para" parents="44609 53129"/>
    </justification>
  </clause>

  <clause id="53131">
    <literal><![CDATA[
      L(R(x,y,z) \ (L(x,y,z) * u),R(x,y,z) \ L(x,y,z),((1 / L(x,y,z)) * R(x,y,z)) \ 1) = (R(x,y,z) \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(41271(a,1),53130(a,1,1))].">
      <j1 rule="para" parents="41271 53130"/>
    </justification>
  </clause>

  <clause id="53132">
    <literal><![CDATA[
      L(R(x,y,z) \ (L(x,y,z) * u),R(x,y,z) \ L(x,y,z),(L(x,y,z) \ R(x,y,z)) \ 1) = (R(x,y,z) \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(26758(a,1),53131(a,1,3,1))].">
      <j1 rule="para" parents="26758 53131"/>
    </justification>
  </clause>

  <clause id="53133">
    <literal><![CDATA[
      L(R(x,y,z) \ (L(x,y,z) * u),R(x,y,z) \ L(x,y,z),R(x,y,z) \ L(x,y,z)) = (R(x,y,z) \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,51241,a(flip),b,53132,a)].">
      <j1 rule="hyper" parents="64 51241 53132"/>
    </justification>
  </clause>

  <clause id="53134">
    <literal><![CDATA[
      L(R(x,y,z) \ (L(x,y,z) * u),R(x,y,z) \ L(x,y,z),L(x,y,z) \ L(x,y,z)) = (R(x,y,z) \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,42306,a(flip),b,53133,a)].">
      <j1 rule="hyper" parents="64 42306 53133"/>
    </justification>
  </clause>

  <clause id="53135">
    <literal><![CDATA[
      L(R(x,y,z) \ (L(x,y,z) * u),R(x,y,z) \ L(x,y,z),1) = (R(x,y,z) \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(68(a,1),53134(a,1,3))].">
      <j1 rule="para" parents="68 53134"/>
    </justification>
  </clause>

  <clause id="53136">
    <literal><![CDATA[
      R(x,y,z) \ (L(x,y,z) * u) = (R(x,y,z) \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(624,a,53135,a)].">
      <j1 rule="hyper" parents="624 53135"/>
    </justification>
  </clause>

  <clause id="53138">
    <literal><![CDATA[
      (L(x,y,z) \ R(x,y,z)) \ u = (R(x,y,z) \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(64,a,41271,a,b,53136,a)].">
      <j1 rule="hyper" parents="64 41271 53136"/>
    </justification>
  </clause>

  <clause id="53140">
    <literal><![CDATA[
      (a(x,y,z) * a(z,y,x)) \ u = (R(x,y,z) \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(46465(a,1),53138(a,1,1))].">
      <j1 rule="para" parents="46465 53138"/>
    </justification>
  </clause>

  <clause id="53141">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,v5) * a(v5,w,u))) \ v6) = a(x,y,(R(u,w,v5) \ L(u,w,v5)) * (z \ v6))
    ]]></literal>
    <justification jstring="[para(53140(a,1),42621(a,2,3))].">
      <j1 rule="para" parents="53140 42621"/>
    </justification>
  </clause>

  <clause id="53142">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,v5) * a(v5,w,u))) \ v6) = a(x,y,(L(u,w,v5) \ L(u,w,v5)) * (z \ v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,43263,a(flip),b,53141,a),flip(a)].">
      <j1 rule="hyper" parents="373 43263 53141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53143">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,v5) * a(v5,w,u))) \ v6) = a(x,y,z \ v6)
    ]]></literal>
    <justification jstring="[para(190(a,1),53142(a,2,3))].">
      <j1 rule="para" parents="190 53142"/>
    </justification>
  </clause>

  <clause id="53144">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) * (a(w,u,z) * v5)) \ v6) = a(x,y,v5 \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,42751,a,b,53143,a)].">
      <j1 rule="hyper" parents="64 42751 53143"/>
    </justification>
  </clause>

  <clause id="53145">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,v5) * (a(v5,w,u) * v6))) = a(x,y,z \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,48279,a(flip),b,53143,a),flip(a)].">
      <j1 rule="hyper" parents="64 48279 53143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53149">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) * L(v5 * w,w,a(w,u,z))) \ v6) = a(x,y,(v5 * (a(w,u,z) \ w)) \ v6)
    ]]></literal>
    <justification jstring="[para(42848(a,1),53144(a,1,3,1,2))].">
      <j1 rule="para" parents="42848 53144"/>
    </justification>
  </clause>

  <clause id="53150">
    <literal><![CDATA[
      a(x,y,(z * R(u,w,v5)) \ v6) = a(x,y,(z * L(u,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(47083(a,1),53144(a,1,3,1))].">
      <j1 rule="para" parents="47083 53144"/>
    </justification>
  </clause>

  <clause id="53152">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,v5) * (a(v5,w,u) \ v6))) = a(x,y,z \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,42754,a,b,53145,a)].">
      <j1 rule="hyper" parents="64 42754 53145"/>
    </justification>
  </clause>

  <clause id="53154">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) \ w) * (T(v5,u \ 1) \ (z / (u * z)))) = a(x,y,(v5 * L(1 / u,u,z)) \ ((z \ (u \ z)) * w))
    ]]></literal>
    <justification jstring="[hyper(64,a,52970,a,b,53150,a)].">
      <j1 rule="hyper" parents="64 52970 53150"/>
    </justification>
  </clause>

  <clause id="53156">
    <literal><![CDATA[
      a(x,y,z \ (u * (w \ L(R(w,v5,v6),v5,v6)))) = a(x,y,z \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,48263,a(flip),b,53152,a)].">
      <j1 rule="hyper" parents="64 48263 53152"/>
    </justification>
  </clause>

  <clause id="53159">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) * v5) \ v6) = a(x,y,(v5 * a(w,u,z)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,48745,a(flip),b,53156,a)].">
      <j1 rule="hyper" parents="64 48745 53156"/>
    </justification>
  </clause>

  <clause id="53161">
    <literal><![CDATA[
      a(x,y,(a(z,u,w) * v5) \ v6) = a(x,y,(v5 \ a(w,u,z)) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,51783,a(flip),b,53159,a),flip(a)].">
      <j1 rule="hyper" parents="373 51783 53159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53162">
    <literal><![CDATA[
      a(x,y,((z \ u) \ a(u,w,v5)) * v6) = a(x,y,(L(u,w,v5) \ z) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,53074,a(flip),b,53161,a),flip(a)].">
      <j1 rule="hyper" parents="64 53074 53161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53163">
    <literal><![CDATA[
      a(x,y,a(z \ 1,z \ (a(u,w,v5) \ 1),(z \ a(v5,w,u)) * v6)) = a(x,y,a(v6,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(53161(a,1),53104(a,1,3))].">
      <j1 rule="para" parents="53161 53104"/>
    </justification>
  </clause>

  <clause id="53164">
    <literal><![CDATA[
      a(x,y,((z \ u) * a(z,w,v5)) * v6) = a(x,y,(L(z,w,v5) \ u) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,53060,a(flip),b,53162,a)].">
      <j1 rule="hyper" parents="64 53060 53162"/>
    </justification>
  </clause>

  <clause id="53165">
    <literal><![CDATA[
      a(x,y,(((z * (z * u)) \ z) * a(L(u,z,z),w,v5)) * v6) = a(x,y,(L(L(u,z,z),w,v5) \ (1 / z)) * v6)
    ]]></literal>
    <justification jstring="[para(886(a,1),53164(a,1,3,1,1))].">
      <j1 rule="para" parents="886 53164"/>
    </justification>
  </clause>

  <clause id="53166">
    <literal><![CDATA[
      a(x,y,(z * (L(z,u,w) \ (v5 * z))) \ v6) = a(x,y,(v5 * (a(z,u,w) \ z)) \ v6)
    ]]></literal>
    <justification jstring="[para(45356(a,1),53149(a,1,3,1))].">
      <j1 rule="para" parents="45356 53149"/>
    </justification>
  </clause>

  <clause id="53167">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,v5) \ u)) \ v6) = a(x,y,(z * (u * a(v5,w,u))) \ v6)
    ]]></literal>
    <justification jstring="[para(45350(a,1),53166(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="45350 53166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53168">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,v5) \ u)) \ v6) = a(x,y,(z * L(u,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,46415,a(flip),b,53167,a),flip(a)].">
      <j1 rule="hyper" parents="373 46415 53167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53169">
    <literal><![CDATA[
      a(x,y,(z * (R(1 / u,w,v5) \ 1)) \ v6) = a(x,y,(z * L(u,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(45468(a,2),53168(a,1,3,1,2))].">
      <j1 rule="para" parents="45468 53168"/>
    </justification>
  </clause>

  <clause id="53170">
    <literal><![CDATA[
      a(x,y,(z \ R(1 / u,w,v5)) * v6) = a(x,y,(z * L(u,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,52707,a(flip),b,53169,a)].">
      <j1 rule="hyper" parents="64 52707 53169"/>
    </justification>
  </clause>

  <clause id="53171">
    <literal><![CDATA[
      a(x,y,(z \ L(1 / u,w,v5)) * v6) = a(x,y,(z * L(u,w,v5)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,36476,a(flip),b,53170,a)].">
      <j1 rule="hyper" parents="64 36476 53170"/>
    </justification>
  </clause>

  <clause id="53172">
    <literal><![CDATA[
      a(x,y,(K(z,z \ 1) \ u) * ((L(z,w,v5) \ v6) \ K(z,z \ 1))) = a(x,y,(v6 * L(1 / z,w,v5)) \ u)
    ]]></literal>
    <justification jstring="[hyper(64,a,53024,a,b,53171,a)].">
      <j1 rule="hyper" parents="64 53024 53171"/>
    </justification>
  </clause>

  <clause id="53173">
    <literal><![CDATA[
      a(x,y,a(z \ 1,z * (a(u,w,v5) \ 1),(z \ a(v5,w,u)) * v6)) = a(x,y,a(v6,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(52168(a,1),53163(a,1,3))].">
      <j1 rule="para" parents="52168 53163"/>
    </justification>
  </clause>

  <clause id="53174">
    <literal><![CDATA[
      a(x,y,a(z \ 1,a(u,w,v5) * z,(z \ a(v5,w,u)) * v6)) = a(x,y,a(v6,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(31945(a,1),53173(a,1,3))].">
      <j1 rule="para" parents="31945 53173"/>
    </justification>
  </clause>

  <clause id="53175">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5) * z,(z \ a(v5,w,u)) * v6)) = a(x,y,a(v6,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(2653(a,1),53174(a,1,3))].">
      <j1 rule="para" parents="2653 53174"/>
    </justification>
  </clause>

  <clause id="53176">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5) * z,a(v5,w,u) * (z \ v6))) = a(x,y,a(v6,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(52805(a,1),53175(a,1,3))].">
      <j1 rule="para" parents="52805 53175"/>
    </justification>
  </clause>

  <clause id="53177">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5) * z,a(v5,w,u) * (v6 * z))) = a(x,y,a(v6,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52717,a(flip),b,53176,a)].">
      <j1 rule="hyper" parents="64 52717 53176"/>
    </justification>
  </clause>

  <clause id="53178">
    <literal><![CDATA[
      a(x,y,a(a(z,u,w) * (v5 * v6),a(w,u,z),v6)) = a(x,y,a(v5,v6,a(w,u,z)))
    ]]></literal>
    <justification jstring="[hyper(64,a,51966,a(flip),b,53177,a)].">
      <j1 rule="hyper" parents="64 51966 53177"/>
    </justification>
  </clause>

  <clause id="53179">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),z * (a(v5,w,u) * v6))) = a(x,y,a(v6,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(52428(a,1),53178(a,1,3))].">
      <j1 rule="para" parents="52428 53178"/>
    </justification>
  </clause>

  <clause id="53180">
    <literal><![CDATA[
      a(x,y,a(z * u,a(w,v5,v6),z)) = a(x,y,a(u,z,a(v6,v5,w)))
    ]]></literal>
    <justification jstring="[para(52927(a,1),53179(a,1,3))].">
      <j1 rule="para" parents="52927 53179"/>
    </justification>
  </clause>

  <clause id="53181">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,z * a(a(u * w,v5,v6),z,u)) = a(w,v5,a(v6,u,a(z,y,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52858,a,b,53180,a)].">
      <j1 rule="hyper" parents="64 52858 53180"/>
    </justification>
  </clause>

  <clause id="53182">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,z * a(u,w,a(v5,z,v5 * v6))) = a(v6,w,a(u,v5,a(z,y,x)))
    ]]></literal>
    <justification jstring="[para(47254(a,1),53181(a,1,2,3,2))].">
      <j1 rule="para" parents="47254 53181"/>
    </justification>
  </clause>

  <clause id="53183">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,L(z,u,a(w,v5,z * v6))) = a(v6,v5,a(w,u,a(z,y,x)))
    ]]></literal>
    <justification jstring="[para(52965(a,1),53182(a,1,2,3))].">
      <j1 rule="para" parents="52965 53182"/>
    </justification>
  </clause>

  <clause id="53184">
    <literal><![CDATA[
      a(x,y,a(a(z,u,x * w),v5,v6)) = a(w,u,a(z,v5,a(x,y,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,47249,a(flip),b,53183,a)].">
      <j1 rule="hyper" parents="64 47249 53183"/>
    </justification>
  </clause>

  <clause id="53185">
    <literal><![CDATA[
      a(x,y,a(x * z,u,a(w,v5,v6))) = a(z,u,a(v6,v5,a(x,y,w)))
    ]]></literal>
    <justification jstring="[para(47254(a,1),53184(a,1,3))].">
      <j1 rule="para" parents="47254 53184"/>
    </justification>
  </clause>

  <clause id="53186">
    <literal><![CDATA[
      a(x,y,a(z * a(u,w,v5),v6,z)) = a(x,y,a(u,v6,a(z,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52857,a,b,53185,a)].">
      <j1 rule="hyper" parents="64 52857 53185"/>
    </justification>
  </clause>

  <clause id="53187">
    <literal><![CDATA[
      a(x * y,z,a(u,w,a(x,v5,v6))) = a(y,z,a(v6,v5,a(x,w,u)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52855,a,b,53186,a)].">
      <j1 rule="hyper" parents="64 52855 53186"/>
    </justification>
  </clause>

  <clause id="53188">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,w * v6))) = a(v6,u,a(z,y,a(w,v5,x)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52859,a(flip),b,53186,a)].">
      <j1 rule="hyper" parents="64 52859 53186"/>
    </justification>
  </clause>

  <clause id="53189">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w * v5,v6,w))) = a(x,y,a(z,u,a(w,v6,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52883,a(flip),b,53187,a)].">
      <j1 rule="hyper" parents="64 52883 53187"/>
    </justification>
  </clause>

  <clause id="53190">
    <literal><![CDATA[
      L(x * a(y * z,u,a(w,x,a(v5,v6,v7))),a(w,u,v7),a(v5,v6,z * (v5 * y))) = L(x,a(v5,v6,z * (v5 * y)),a(w,u,v7))
    ]]></literal>
    <justification jstring="[para(53188(a,1),52447(a,1,1,2))].">
      <j1 rule="para" parents="53188 52447"/>
    </justification>
  </clause>

  <clause id="53191">
    <literal><![CDATA[
      L(x,y,a(z,u,a(z * w,v5,v6))) = x * a(w,v5,a(x,y,a(z,u,v6)))
    ]]></literal>
    <justification jstring="[para(53189(a,1),52862(a,1,2)),flip(a)].">
      <j1 rule="para" parents="53189 52862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53192">
    <literal><![CDATA[
      L(x,y,a(z,u,a(z * w,v5,v6))) = L(x,y,a(w,v5,a(z,u,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,47271,a(flip),b,53191,a),flip(a)].">
      <j1 rule="hyper" parents="373 47271 53191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53193">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,z * v6))) = L(x,y,a(w,v5,a(z,u,v6)))
    ]]></literal>
    <justification jstring="[para(52856(a,1),53192(a,1,3))].">
      <j1 rule="para" parents="52856 53192"/>
    </justification>
  </clause>

  <clause id="53194">
    <literal><![CDATA[
      L(x,y,a(y * z,u,a(w,v5,v6))) = L(x,u,a(v6,v5,a(z,w,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52868,a(flip),b,53193,a),flip(a)].">
      <j1 rule="hyper" parents="64 52868 53193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53195">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6) * y)) = L(x,u,a(v6,v5,a(z,w,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52500,a(flip),b,53194,a)].">
      <j1 rule="hyper" parents="64 52500 53194"/>
    </justification>
  </clause>

  <clause id="53196">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6 * y))) = L(x,u,a(v6,v5,a(z,w,y)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52513,a,b,53195,a)].">
      <j1 rule="hyper" parents="64 52513 53195"/>
    </justification>
  </clause>

  <clause id="53197">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6 * v5))) = L(x,u,a(w,y,a(v6,z,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52488,a,b,53196,a)].">
      <j1 rule="hyper" parents="64 52488 53196"/>
    </justification>
  </clause>

  <clause id="53198">
    <literal><![CDATA[
      x * a(a(y,z,u),x,a(w,v5,v6 * x)) = L(x,z,a(v6,v5,a(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52880,a(flip),b,53197,a)].">
      <j1 rule="hyper" parents="64 52880 53197"/>
    </justification>
  </clause>

  <clause id="53199">
    <literal><![CDATA[
      x * a(y,z,a(a(u,w,v5 * x),x,v6)) = L(x,z,a(v5,w,a(v6,y,u)))
    ]]></literal>
    <justification jstring="[para(47254(a,1),53198(a,1,2))].">
      <j1 rule="para" parents="47254 53198"/>
    </justification>
  </clause>

  <clause id="53200">
    <literal><![CDATA[
      x * a(y,z,a(u * x,w,a(v5,x,v6))) = L(x,z,a(u,w,a(v5,y,v6)))
    ]]></literal>
    <justification jstring="[para(47254(a,1),53199(a,1,2,3))].">
      <j1 rule="para" parents="47254 53199"/>
    </justification>
  </clause>

  <clause id="53201">
    <literal><![CDATA[
      x * a(y,z,a(u,x,a(w,v5,v6 * x))) = L(x,z,a(u,v5,a(w,y,v6)))
    ]]></literal>
    <justification jstring="[para(52468(a,1),53200(a,1,2,3))].">
      <j1 rule="para" parents="52468 53200"/>
    </justification>
  </clause>

  <clause id="53202">
    <literal><![CDATA[
      x * a(y,z,a(u,a(w,v5,v6),x)) = L(x,z,a(u,v5,a(w,y,v6)))
    ]]></literal>
    <justification jstring="[para(52932(a,1),53201(a,1,2))].">
      <j1 rule="para" parents="52932 53201"/>
    </justification>
  </clause>

  <clause id="53203">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6)) = L(x,y,a(z,w,a(u,v6,v5)))
    ]]></literal>
    <justification jstring="[hyper(47415,a,53202,a)].">
      <j1 rule="hyper" parents="47415 53202"/>
    </justification>
  </clause>

  <clause id="53204">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,v5,v6)) = L(x,z,a(v6,v5,a(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,53039,a,b,53203,a)].">
      <j1 rule="hyper" parents="64 53039 53203"/>
    </justification>
  </clause>

  <clause id="53205">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5 * x,v6))) = x * a(w,u,a(z,x,a(v6,y,v5)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52941,a(flip),b,53203,a),flip(a)].">
      <j1 rule="hyper" parents="64 52941 53203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53208">
    <literal><![CDATA[
      x * a(y,z,a(u,x,a(w,v5,v6))) = L(x,v6,a(u,z,a(y,v5,w)))
    ]]></literal>
    <justification jstring="[hyper(64,a,53020,a(flip),b,53205,a),flip(a)].">
      <j1 rule="hyper" parents="64 53020 53205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53209">
    <literal><![CDATA[
      a(x,y,(((z * (z * u)) \ z) * a(u,w,v5)) * v6) = a(x,y,(L(L(u,z,z),w,v5) \ (1 / z)) * v6)
    ]]></literal>
    <justification jstring="[para(51139(a,1),53165(a,1,3,1,2))].">
      <j1 rule="para" parents="51139 53165"/>
    </justification>
  </clause>

  <clause id="53210">
    <literal><![CDATA[
      a(x,y,(L(L(z,u,u),w,v5) \ (1 / u)) * v6) = a(x,y,((u * z) \ a(z,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,53065,a(flip),b,53209,a),flip(a)].">
      <j1 rule="hyper" parents="64 53065 53209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53213">
    <literal><![CDATA[
      a(x,y,(K(z \ 1,z) * u) * ((L(z,w,v5) \ v6) \ K(z,z \ 1))) = a(x,y,(v6 * L(1 / z,w,v5)) \ u)
    ]]></literal>
    <justification jstring="[para(2360(a,1),53172(a,1,3,1))].">
      <j1 rule="para" parents="2360 53172"/>
    </justification>
  </clause>

  <clause id="53214">
    <literal><![CDATA[
      a(x,y,(K(z \ 1,z) * u) * ((L(R(z,z,z),w,v5) \ v6) \ 1)) = a(x,y,(v6 * L(1 / z,w,v5)) \ u)
    ]]></literal>
    <justification jstring="[para(14728(a,1),53213(a,1,3,2))].">
      <j1 rule="para" parents="14728 53213"/>
    </justification>
  </clause>

  <clause id="53215">
    <literal><![CDATA[
      a(x,y,K(z \ 1,z) * (u * ((L(R(z,z,z),w,v5) \ v6) \ 1))) = a(x,y,(v6 * L(1 / z,w,v5)) \ u)
    ]]></literal>
    <justification jstring="[para(2227(a,1),53214(a,1,3))].">
      <j1 rule="para" parents="2227 53214"/>
    </justification>
  </clause>

  <clause id="53216">
    <literal><![CDATA[
      a(x,y,z * ((L(R(u,u,u),w,v5) \ v6) \ K(u \ 1,u))) = a(x,y,(v6 * L(1 / u,w,v5)) \ z)
    ]]></literal>
    <justification jstring="[para(5203(a,1),53215(a,1,3))].">
      <j1 rule="para" parents="5203 53215"/>
    </justification>
  </clause>

  <clause id="53217">
    <literal><![CDATA[
      a(x,y,(z * L(1 / u,w,v5)) \ v6) = a(x,y,v6 * ((L(u,w,v5) \ z) \ 1))
    ]]></literal>
    <justification jstring="[para(44659(a,1),53216(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="44659 53216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53218">
    <literal><![CDATA[
      a(x,y,(z * L(1 / u,w,v5)) \ v6) = a(x,y,(L(u,w,v5) \ z) \ v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,51315,a(flip),b,53217,a),flip(a)].">
      <j1 rule="hyper" parents="373 51315 53217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53219">
    <literal><![CDATA[
      a(x,y,(z * L(1 / u,w,v5)) \ v6) = a(x,y,(z \ L(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,52682,a(flip),b,53218,a),flip(a)].">
      <j1 rule="hyper" parents="373 52682 53218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53220">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) \ w) * (T(v5,u \ 1) \ (z / (u * z)))) = a(x,y,(v5 \ L(u,u,z)) * ((z \ (u \ z)) * w))
    ]]></literal>
    <justification jstring="[hyper(373,a,53219,a(flip),b,53154,a),flip(a)].">
      <j1 rule="hyper" parents="373 53219 53154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53221">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) \ w) * (T(v5,u \ 1) \ (z / (u * z)))) = a(x,y,(u \ w) * (v5 \ L(u,u,z)))
    ]]></literal>
    <justification jstring="[hyper(373,a,53067,a(flip),b,53220,a),flip(a)].">
      <j1 rule="hyper" parents="373 53067 53220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53223">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) \ w) * (T(v5,u \ 1) \ (z / (u * z)))) = a(x,y,(v5 \ u) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(373,a,52744,a(flip),b,53221,a),flip(a)].">
      <j1 rule="hyper" parents="373 52744 53221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53225">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) \ w) * (T(v5,u \ 1) \ ((u * z) \ z))) = a(x,y,(v5 \ u) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,27482,a(flip),b,53223,a)].">
      <j1 rule="hyper" parents="64 27482 53223"/>
    </justification>
  </clause>

  <clause id="53226">
    <literal><![CDATA[
      a(x,y,((z / (u * z)) \ w) * (T(v5,u \ 1) \ (z \ (u \ z)))) = a(x,y,(v5 \ u) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(64,a,36257,a(flip),b,53225,a)].">
      <j1 rule="hyper" parents="64 36257 53225"/>
    </justification>
  </clause>

  <clause id="53227">
    <literal><![CDATA[
      a(x,y,(z \ (u \ (w \ u))) * ((u / (w * u)) \ v5)) = a(x,y,(z \ w) * (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27531,a(flip),b,53226,a)].">
      <j1 rule="hyper" parents="64 27531 53226"/>
    </justification>
  </clause>

  <clause id="53229">
    <literal><![CDATA[
      a(x,y,(z \ (u \ (w \ u))) * (((w * u) \ u) \ v5)) = a(x,y,(z \ w) * (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27500,a(flip),b,53227,a)].">
      <j1 rule="hyper" parents="64 27500 53227"/>
    </justification>
  </clause>

  <clause id="53230">
    <literal><![CDATA[
      a(x,y,(z * u) * (w \ (v5 \ (z \ v5)))) = a(x,y,(w \ z) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(64,a,53072,a(flip),b,53229,a)].">
      <j1 rule="hyper" parents="64 53072 53229"/>
    </justification>
  </clause>

  <clause id="53232">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (w \ u)) * v5)) = a(x,y,((R(1 / w,w,u) \ z) \ w) * (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,53076,a(flip),b,53230,a)].">
      <j1 rule="hyper" parents="64 53076 53230"/>
    </justification>
  </clause>

  <clause id="53234">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (w \ u)) * v5)) = a(x,y,((R(w,w,u) \ z) \ (w \ 1)) * (w \ v5))
    ]]></literal>
    <justification jstring="[para(27114(a,1),53232(a,2,3,1))].">
      <j1 rule="para" parents="27114 53232"/>
    </justification>
  </clause>

  <clause id="53235">
    <literal><![CDATA[
      a(x,y,((R(z,z,u) \ w) * z) \ (z \ v5)) = a(x,y,w \ ((u \ (z \ u)) * v5))
    ]]></literal>
    <justification jstring="[hyper(373,a,52712,a(flip),b,53234,a)].">
      <j1 rule="hyper" parents="373 52712 53234"/>
    </justification>
  </clause>

  <clause id="53236">
    <literal><![CDATA[
      a(x,y,z \ ((u \ (w \ u)) * v5)) = a(x,y,z \ (w \ v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,52639,a(flip),b,53235,a),flip(a)].">
      <j1 rule="hyper" parents="64 52639 53235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53238">
    <literal><![CDATA[
      a(x,y,z \ ((u \ w) \ v5)) = a(x,y,z \ ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,28054,a(flip),b,53236,a),flip(a)].">
      <j1 rule="hyper" parents="64 28054 53236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53242">
    <literal><![CDATA[
      a(x,y,(z * (u / (w / v5))) * K(v5,v5 \ w)) = a(x,y,(z \ 1) \ ((w \ v5) * u))
    ]]></literal>
    <justification jstring="[hyper(64,a,52908,a,b,53238,a)].">
      <j1 rule="hyper" parents="64 52908 53238"/>
    </justification>
  </clause>

  <clause id="53244">
    <literal><![CDATA[
      a(x,y,(z * (u / (w / v5))) * K(v5,v5 \ w)) = a(x,y,z * ((w \ v5) * u))
    ]]></literal>
    <justification jstring="[hyper(373,a,51318,a(flip),b,53242,a),flip(a)].">
      <j1 rule="hyper" parents="373 51318 53242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53245">
    <literal><![CDATA[
      a(x,y,z * ((u / (w / v5)) * K(v5,v5 \ w))) = a(x,y,z * ((w \ v5) * u))
    ]]></literal>
    <justification jstring="[para(23053(a,1),53244(a,1,3))].">
      <j1 rule="para" parents="23053 53244"/>
    </justification>
  </clause>

  <clause id="53246">
    <literal><![CDATA[
      a(x,y,z * (u / (w \ v5))) = a(x,y,z * ((v5 \ w) * u))
    ]]></literal>
    <justification jstring="[para(6455(a,1),53245(a,1,3,2))].">
      <j1 rule="para" parents="6455 53245"/>
    </justification>
  </clause>

  <clause id="53247">
    <literal><![CDATA[
      a(x,y,z * ((u \ w) \ v5)) = a(x,y,z * ((w \ u) * v5))
    ]]></literal>
    <justification jstring="[hyper(64,a,27310,a(flip),b,53246,a)].">
      <j1 rule="hyper" parents="64 27310 53246"/>
    </justification>
  </clause>

  <clause id="53249">
    <literal><![CDATA[
      a((x \ y) \ y,z,a(R(x \ (x \ y),u,w),v5,v6 * ((y \ x) * y))) = a(v6,v5,a((x \ y) \ y,z,R(y,u,w) / x))
    ]]></literal>
    <justification jstring="[para(53247(a,1),53121(a,1,3))].">
      <j1 rule="para" parents="53247 53121"/>
    </justification>
  </clause>

  <clause id="53250">
    <literal><![CDATA[
      a((x \ y) \ y,z,a(R(x \ (x \ y),u,w),v5,v6 * x)) = a(v6,v5,a((x \ y) \ y,z,R(y,u,w) / x))
    ]]></literal>
    <justification jstring="[para(27319(a,1),53249(a,1,3))].">
      <j1 rule="para" parents="27319 53249"/>
    </justification>
  </clause>

  <clause id="53252">
    <literal><![CDATA[
      a((x \ y) \ y,z,a(x \ (x \ y),u,L(w * x,v5,v6))) = a(w,u,a((x \ y) \ y,z,R(y,v5,v6) / x))
    ]]></literal>
    <justification jstring="[para(46576(a,1),53250(a,1,3))].">
      <j1 rule="para" parents="46576 53250"/>
    </justification>
  </clause>

  <clause id="53253">
    <literal><![CDATA[
      a((x \ y) \ y,z,a((x \ y) * x,u,L(w * x,v5,v6))) = a(w,u,a((x \ y) \ y,z,R(y,v5,v6) / x))
    ]]></literal>
    <justification jstring="[para(51310(a,1),53252(a,1,3))].">
      <j1 rule="para" parents="51310 53252"/>
    </justification>
  </clause>

  <clause id="53254">
    <literal><![CDATA[
      a((x \ y) \ y,z,a(y,u,L(w * x,v5,v6))) = a(w,u,a((x \ y) \ y,z,R(y,v5,v6) / x))
    ]]></literal>
    <justification jstring="[para(26836(a,1),53253(a,1,3))].">
      <j1 rule="para" parents="26836 53253"/>
    </justification>
  </clause>

  <clause id="53255">
    <literal><![CDATA[
      a(x * (y \ x),z,a(x,u,L(w * y,v5,v6))) = a(w,u,a((y \ x) \ x,z,R(x,v5,v6) / y))
    ]]></literal>
    <justification jstring="[hyper(64,a,51310,a(flip),b,53254,a)].">
      <j1 rule="hyper" parents="64 51310 53254"/>
    </justification>
  </clause>

  <clause id="53257">
    <literal><![CDATA[
      a(x,y,a((z \ u) \ u,w,R(u,v5,v6) / z)) = a(u,y,a(z \ u,w,u * L(x * z,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(64,a,52866,a(flip),b,53255,a),flip(a)].">
      <j1 rule="hyper" parents="64 52866 53255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53258">
    <literal><![CDATA[
      a(x,y,a((z \ u) \ u,w,R(u,v5,v6) / z)) = a(u,y,a(u * z,w,u * L(x * z,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,46673,a(flip),b,53257,a),flip(a)].">
      <j1 rule="hyper" parents="373 46673 53257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53259">
    <literal><![CDATA[
      a(x,y,a((z \ u) \ u,w,R(u,v5,v6) / z)) = a(u,y,a(z,w,u * (u * L(x * z,v5,v6))))
    ]]></literal>
    <justification jstring="[hyper(373,a,52856,a(flip),b,53258,a),flip(a)].">
      <j1 rule="hyper" parents="373 52856 53258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53260">
    <literal><![CDATA[
      a(x,y,a((z \ u) \ u,w,R(u,v5,v6) / z)) = a(u,y,a(z,w,L(u * (u * (x * z)),v5,v6)))
    ]]></literal>
    <justification jstring="[para(34560(a,2),53259(a,2,3))].">
      <j1 rule="para" parents="34560 53259"/>
    </justification>
  </clause>

  <clause id="53261">
    <literal><![CDATA[
      a(x,y,a((z \ u) \ u,w,R(u,v5,v6) / z)) = a(u,w,a(x * z,y,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,50005,a(flip),b,53260,a),flip(a)].">
      <j1 rule="hyper" parents="373 50005 53260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53263">
    <literal><![CDATA[
      a(x,y,a((z \ u) \ u,w,z \ R(u,v5,v6))) = a(u,w,a(x * z,y,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(27308(a,1),53261(a,1,3))].">
      <j1 rule="para" parents="27308 53261"/>
    </justification>
  </clause>

  <clause id="53264">
    <literal><![CDATA[
      a(x,y,a((z \ u) \ u,w,z \ L(u,v5,v6))) = a(u,w,a(x * z,y,L(z,v5,v6)))
    ]]></literal>
    <justification jstring="[para(31676(a,1),53263(a,1,3))].">
      <j1 rule="para" parents="31676 53263"/>
    </justification>
  </clause>

  <clause id="53265">
    <literal><![CDATA[
      a(x,y,a(z * u,w,L(u,v5,v6))) = a(z,w,a(u,y,u \ L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[para(26784(a,1),53264(a,1,3)),flip(a)].">
      <j1 rule="para" parents="26784 53264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53266">
    <literal><![CDATA[
      a(x,y,a(z * u,w,L(u,v5,v6))) = a(z,w,a(u,y,u * L(x,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(373,a,49778,a(flip),b,53265,a),flip(a)].">
      <j1 rule="hyper" parents="373 49778 53265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53268">
    <literal><![CDATA[
      L(L(x,y,a(z,u,a(w * v5,v6,v7))),a(z,u,y),a(v7,v6,v5 * (v7 * w))) = L(x,a(v7,v6,v5 * (v7 * w)),a(z,u,y))
    ]]></literal>
    <justification jstring="[para(53208(a,1),53190(a,1,1))].">
      <j1 rule="para" parents="53208 53190"/>
    </justification>
  </clause>

  <clause id="53269">
    <literal><![CDATA[
      L(L(x,y,a(z,u,a(w * v5,v6,v7))),u,a(v5 * (v7 * w),v6,a(z,y,v7))) = L(x,a(v7,v6,v5 * (v7 * w)),a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,53204,a(flip),b,53268,a)].">
      <j1 rule="hyper" parents="64 53204 53268"/>
    </justification>
  </clause>

  <clause id="53270">
    <literal><![CDATA[
      L(L(x,y,a(z,u,a(w * v5,v6,v7))),u,a(v7,v6,a(v5 * w,y,v7 * z))) = L(x,a(v7,v6,v5 * (v7 * w)),a(z,u,y))
    ]]></literal>
    <justification jstring="[para(52867(a,1),53269(a,1,3))].">
      <j1 rule="para" parents="52867 53269"/>
    </justification>
  </clause>

  <clause id="53271">
    <literal><![CDATA[
      L(L(x,y,a(z,u,a(w * v5,v6,v7))),u,a(v5 * w,y,a(v7,v6,z))) = L(x,a(v7,v6,v5 * (v7 * w)),a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,53193,a(flip),b,53270,a)].">
      <j1 rule="hyper" parents="64 53193 53270"/>
    </justification>
  </clause>

  <clause id="53272">
    <literal><![CDATA[
      L(x,a(y,z,u * (y * w)),a(v5,v6,v7)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,47479,a(flip),b,53271,a),flip(a)].">
      <j1 rule="hyper" parents="64 47479 53271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53274">
    <literal><![CDATA[
      L(x,a(y,z,u),a(w,v5,v6)) = x
    ]]></literal>
    <justification jstring="[hyper(64,a,52812,a(flip),b,53272,a)].">
      <j1 rule="hyper" parents="64 52812 53272"/>
    </justification>
  </clause>

  <clause id="53316">
    <literal><![CDATA[
      a(x,a(y,z,u),a(w,v5,v6)) = 1
    ]]></literal>
    <justification jstring="[hyper(140,a,53274,a(flip),b,47384,a),flip(a)].">
      <j1 rule="hyper" parents="140 53274 47384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53339">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = 1
    ]]></literal>
    <justification jstring="[hyper(64,a,52832,a(flip),b,53316,a)].">
      <j1 rule="hyper" parents="64 52832 53316"/>
    </justification>
  </clause>

  <clause id="53340">
    <literal><![CDATA[
      L(a(x,y,z),a(u,w,v5),v6) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(53,a,53316,a)].">
      <j1 rule="hyper" parents="53 53316"/>
    </justification>
  </clause>

  <clause id="53351">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = v7 \ v7
    ]]></literal>
    <justification jstring="[hyper(373,a,68,a,b,53339,a),flip(a)].">
      <j1 rule="hyper" parents="373 68 53339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53354">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),v5,v6) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(53,a,53339,a)].">
      <j1 rule="hyper" parents="53 53339"/>
    </justification>
  </clause>

  <clause id="53365">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,v6)) = a(x,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(40,a,51927,a,b,53351,a(flip))].">
      <j1 rule="hyper" parents="40 51927 53351"/>
    </justification>
  </clause>

  <clause id="53366">
    <literal><![CDATA[
      a(x,y,L(z,u,a(w,v5,v6))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(40,a,47325,a,b,53351,a(flip))].">
      <j1 rule="hyper" parents="40 47325 53351"/>
    </justification>
  </clause>

  <clause id="53368">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(40,a,46545,a,b,53351,a(flip))].">
      <j1 rule="hyper" parents="40 46545 53351"/>
    </justification>
  </clause>

  <clause id="53379">
    <literal><![CDATA[
      a(x,y,L(z,a(u,w,v5),v6)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(64,a,46493,a,b,53340,a)].">
      <j1 rule="hyper" parents="64 46493 53340"/>
    </justification>
  </clause>

  <clause id="53396">
    <literal><![CDATA[
      a(x,y,L(z \ (a(u,w,v5) \ v6),a(u,w,v5),z)) = a(x,y,a(u,w,v5) \ (z \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,48260,a,b,53366,a)].">
      <j1 rule="hyper" parents="64 48260 53366"/>
    </justification>
  </clause>

  <clause id="53399">
    <literal><![CDATA[
      a(x,y,(a(z,u,u) \ w) \ (a(v5,v6,v7) \ v8)) = a(x,y,a(z,u,u) * ((w * a(v5,v6,v7)) \ v8))
    ]]></literal>
    <justification jstring="[hyper(64,a,52998,a(flip),b,53366,a)].">
      <j1 rule="hyper" parents="64 52998 53366"/>
    </justification>
  </clause>

  <clause id="53431">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,46567,a,b,53354,a)].">
      <j1 rule="hyper" parents="64 46567 53354"/>
    </justification>
  </clause>

  <clause id="53462">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,41883,a,b,53368,a),flip(a)].">
      <j1 rule="hyper" parents="373 41883 53368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53475">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,v6)) = a(x,u,a(w,v5,L(v6,v7,v8)))
    ]]></literal>
    <justification jstring="[hyper(373,a,53365,a,b,53431,a)].">
      <j1 rule="hyper" parents="373 53365 53431"/>
    </justification>
  </clause>

  <clause id="53488">
    <literal><![CDATA[
      a(x,y,a(z,u,L(w,v5,v6))) = a(x,y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,41883,a,b,53431,a),flip(a)].">
      <j1 rule="hyper" parents="373 41883 53431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53504">
    <literal><![CDATA[
      a(T(x,y),z,a(z * (L(x,u,w) * y),v5,v6)) = a(v6,v5,a(y,L(T(x,y),u,w),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52892,a(flip),b,53462,a),flip(a)].">
      <j1 rule="hyper" parents="64 52892 53462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53512">
    <literal><![CDATA[
      a(x,y,a(z,u,z * L(w,v5,v6))) = a(w,u,a(z,y,x * z))
    ]]></literal>
    <justification jstring="[hyper(64,a,53266,a(flip),b,53488,a)].">
      <j1 rule="hyper" parents="64 53266 53488"/>
    </justification>
  </clause>

  <clause id="53513">
    <literal><![CDATA[
      a(x,y,a(z,u * L(x,w,v5),v6)) = a(L(x,w,v5),u,a(v6,y,z))
    ]]></literal>
    <justification jstring="[hyper(64,a,51958,a(flip),b,53488,a),flip(a)].">
      <j1 rule="hyper" parents="64 51958 53488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53541">
    <literal><![CDATA[
      a(x * y,y,a(z,u,w * z)) = a(w,u,a(x,L(z,v5,v6),y))
    ]]></literal>
    <justification jstring="[hyper(64,a,53094,a(flip),b,53512,a),flip(a)].">
      <j1 rule="hyper" parents="64 53094 53512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53543">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5),v6)) = a(z,v6,a(u,y,(x * u) * v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,52464,a(flip),b,53541,a),flip(a)].">
      <j1 rule="hyper" parents="64 52464 53541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53545">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5),v6)) = a(z,v6,a(u,y,x * (u * v6)))
    ]]></literal>
    <justification jstring="[para(52725(a,1),53543(a,2,3))].">
      <j1 rule="para" parents="52725 53543"/>
    </justification>
  </clause>

  <clause id="53546">
    <literal><![CDATA[
      a(x,y,a(z,L(u,w,v5),v6)) = a(z,y,a(x,u,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,52832,a(flip),b,53545,a),flip(a)].">
      <j1 rule="hyper" parents="373 52832 53545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53555">
    <literal><![CDATA[
      a(x,y,a(z,u * L(x,w,v5),v6)) = a(x,u,a(v6,y,L(z,v7,v8)))
    ]]></literal>
    <justification jstring="[hyper(373,a,53475,a(flip),b,53513,a),flip(a)].">
      <j1 rule="hyper" parents="373 53475 53513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53558">
    <literal><![CDATA[
      a(x,y,a(z,u * L(x,w,v5),v6)) = a(x,u,a(z,y,v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,53488,a(flip),b,53555,a),flip(a)].">
      <j1 rule="hyper" parents="373 53488 53555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53561">
    <literal><![CDATA[
      a(x,y,a(z,u * L(x,w,v5),v6 * (u * L(x,w,v5)))) = a(x,u,a(z * (u * L(x,w,v5)),y,v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,52487,a(flip),b,53558,a)].">
      <j1 rule="hyper" parents="64 52487 53558"/>
    </justification>
  </clause>

  <clause id="53562">
    <literal><![CDATA[
      a(x,y,L(z \ (a(u,w,v5) \ v6),a(u,w,v5),z)) = a(x,y,a(u,w,v5) * (z \ v6))
    ]]></literal>
    <justification jstring="[hyper(373,a,42537,a(flip),b,53396,a),flip(a)].">
      <j1 rule="hyper" parents="373 42537 53396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53564">
    <literal><![CDATA[
      a(T(x,y),z,a(L(x,u,w) * y,v5,v6 * z)) = a(v6,v5,a(y,L(T(x,y),u,w),z))
    ]]></literal>
    <justification jstring="[hyper(64,a,52484,a(flip),b,53504,a)].">
      <j1 rule="hyper" parents="64 52484 53504"/>
    </justification>
  </clause>

  <clause id="53565">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,v5) \ v6)) = a(x,y,a(u,w,v5) * (z \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,53379,a(flip),b,53562,a)].">
      <j1 rule="hyper" parents="64 53379 53562"/>
    </justification>
  </clause>

  <clause id="53567">
    <literal><![CDATA[
      x * a(a(y,z,u),w * y,a(y,z,u) * ((w * y) \ x)) = (w * R(y,z,u)) * ((w * y) \ (a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(53565(a,1),51564(a,1,2))].">
      <j1 rule="para" parents="53565 51564"/>
    </justification>
  </clause>

  <clause id="53568">
    <literal><![CDATA[
      a(x,y,a(L(x,z,u) * w,v5,v6 * y)) = a(v6,v5,a(w,L(T(x,w),z,u),y))
    ]]></literal>
    <justification jstring="[hyper(26780,a,53564,a)].">
      <j1 rule="hyper" parents="26780 53564"/>
    </justification>
  </clause>

  <clause id="53570">
    <literal><![CDATA[
      a(x,y,a(L(x,z,u) * w,v5,v6 * y)) = a(v6,v5,a(w,L(x,z,u),y))
    ]]></literal>
    <justification jstring="[para(31912(a,1),53568(a,2,3))].">
      <j1 rule="para" parents="31912 53568"/>
    </justification>
  </clause>

  <clause id="53571">
    <literal><![CDATA[
      a(x,y,a(L(x,z,u) * w,v5,v6 * y)) = a(w,v5,a(v6,x,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,53546,a(flip),b,53570,a),flip(a)].">
      <j1 rule="hyper" parents="373 53546 53570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53575">
    <literal><![CDATA[
      a(x,y,a(z * (y * L(x,u,w)),v5,v6)) = a(z,v5,a(v6,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,52522,a,b,53571,a)].">
      <j1 rule="hyper" parents="64 52522 53571"/>
    </justification>
  </clause>

  <clause id="53578">
    <literal><![CDATA[
      a(x,y,(a(z,u,u) \ w) \ (a(v5,v6,v7) \ v8)) = a(x,y,(w * a(v5,v6,v7)) \ v8)
    ]]></literal>
    <justification jstring="[hyper(373,a,52606,a(flip),b,53399,a),flip(a)].">
      <j1 rule="hyper" parents="373 52606 53399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53580">
    <literal><![CDATA[
      a(x,y,(a(z,u,u) \ w) \ (a(v5,v6,v7) \ v8)) = a(x,y,(w \ a(v5,v6,v7)) * v8)
    ]]></literal>
    <justification jstring="[hyper(373,a,51783,a(flip),b,53578,a),flip(a)].">
      <j1 rule="hyper" parents="373 51783 53578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53581">
    <literal><![CDATA[
      a(x,y,z \ (a(u,w,v5) \ v6)) = a(x,y,(z \ a(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[para(13933(a,1),53580(a,1,3,1))].">
      <j1 rule="para" parents="13933 53580"/>
    </justification>
  </clause>

  <clause id="53582">
    <literal><![CDATA[
      a(x,y,(z \ a(u,w,v5)) * v6) = a(x,y,a(u,w,v5) * (z \ v6))
    ]]></literal>
    <justification jstring="[hyper(64,a,53565,a(flip),b,53581,a),flip(a)].">
      <j1 rule="hyper" parents="64 53565 53581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53583">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * ((v5 * z) \ v6)) = a(x,y,(L(L(z,v5,v5),u,w) \ (1 / v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(64,a,53210,a,b,53582,a),flip(a)].">
      <j1 rule="hyper" parents="64 53210 53582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53584">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * ((v5 * z) \ v6)) = a(x,y,((v5 * (v5 * L(z,u,w))) \ v5) * v6)
    ]]></literal>
    <justification jstring="[para(1048(a,1),53583(a,2,3,1))].">
      <j1 rule="para" parents="1048 53583"/>
    </justification>
  </clause>

  <clause id="53585">
    <literal><![CDATA[
      a(x,y,a(z,u,w) * ((v5 * z) \ v6)) = a(x,y,(v5 * L(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(373,a,52680,a(flip),b,53584,a),flip(a)].">
      <j1 rule="hyper" parents="373 52680 53584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53587">
    <literal><![CDATA[
      a(x,y,a(z,u * L(x,w,v5),v6 * (u * L(x,w,v5)))) = a(z,y,a(v6,x,u))
    ]]></literal>
    <justification jstring="[hyper(373,a,53575,a(flip),b,53561,a),flip(a)].">
      <j1 rule="hyper" parents="373 53575 53561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53589">
    <literal><![CDATA[
      a(x,y,a(z,u,w * (y * L(x,v5,v6)))) = a(z,u,a(w,x,y))
    ]]></literal>
    <justification jstring="[hyper(64,a,53558,a(flip),b,53587,a)].">
      <j1 rule="hyper" parents="64 53558 53587"/>
    </justification>
  </clause>

  <clause id="53591">
    <literal><![CDATA[
      x * a(a(y,z,u),w * y,(w * L(y,z,u)) \ x) = (w * R(y,z,u)) * ((w * y) \ (a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(53585(a,1),53567(a,1,2))].">
      <j1 rule="para" parents="53585 53567"/>
    </justification>
  </clause>

  <clause id="53592">
    <literal><![CDATA[
      x * a(y,z,a((u * L(w,z,y)) \ x,u * w,w)) = (u * R(w,z,y)) * ((u * w) \ (a(w,z,y) \ x))
    ]]></literal>
    <justification jstring="[para(47254(a,1),53591(a,1,2))].">
      <j1 rule="para" parents="47254 53591"/>
    </justification>
  </clause>

  <clause id="53593">
    <literal><![CDATA[
      x * a(y,z,a(x * (u * L(w,z,y)),u * w,w)) = (u * R(w,z,y)) * ((u * w) \ (a(w,z,y) \ x))
    ]]></literal>
    <justification jstring="[para(51310(a,1),53592(a,1,2,3))].">
      <j1 rule="para" parents="51310 53592"/>
    </justification>
  </clause>

  <clause id="53594">
    <literal><![CDATA[
      (x * R(y,z,u)) * ((x * y) \ (a(y,z,u) \ w)) = w * a(y,x,a(u,z,w * (x * L(y,z,u))))
    ]]></literal>
    <justification jstring="[para(51943(a,1),53593(a,1,2)),flip(a)].">
      <j1 rule="para" parents="51943 53593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53595">
    <literal><![CDATA[
      (x * R(y,z,u)) * ((x * y) \ (a(y,z,u) \ w)) = w * a(u,z,a(w,y,x))
    ]]></literal>
    <justification jstring="[para(53589(a,1),53594(a,2,2))].">
      <j1 rule="para" parents="53589 53594"/>
    </justification>
  </clause>

  <clause id="53596">
    <literal><![CDATA[
      (x * R(y,z,u)) * ((x * y) \ (a(y,z,u) \ w)) = L(w,y,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(373,a,47271,a(flip),b,53595,a),flip(a)].">
      <j1 rule="hyper" parents="373 47271 53595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53598">
    <literal><![CDATA[
      x \ ((x * a(y,z,u)) * (a(y,z,u) \ w)) = L(w,y,a(u,z,x))
    ]]></literal>
    <justification jstring="[hyper(64,a,52521,a(flip),b,53596,a)].">
      <j1 rule="hyper" parents="64 52521 53596"/>
    </justification>
  </clause>

  <clause id="53599">
    <literal><![CDATA[
      L(x,a(y,z,u),w) = L(x,u,a(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,52924,a(flip),b,53598,a)].">
      <j1 rule="hyper" parents="64 52924 53598"/>
    </justification>
  </clause>

  <clause id="53600">
    <literal><![CDATA[
      L(x,a(y,z,u),w) = L(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,52923,a(flip),b,53598,a)].">
      <j1 rule="hyper" parents="64 52923 53598"/>
    </justification>
  </clause>

  <clause id="53602">
    <literal><![CDATA[
      x * a(y,z,a(u,w,x)) = L(x,a(u,w,z),y)
    ]]></literal>
    <justification jstring="[hyper(373,a,47349,a,b,53599,a)].">
      <j1 rule="hyper" parents="373 47349 53599"/>
    </justification>
  </clause>

  <clause id="53631">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,z,a(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(64,a,53599,a(flip),b,53600,a)].">
      <j1 rule="hyper" parents="64 53599 53600"/>
    </justification>
  </clause>

  <clause id="53638">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) = L(x,w,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,47432,a,b,53631,a)].">
      <j1 rule="hyper" parents="373 47432 53631"/>
    </justification>
  </clause>

  <clause id="53660">
    <literal><![CDATA[
      x * a(y,z,a(x,u,w)) = L(x,u,a(y,w,z))
    ]]></literal>
    <justification jstring="[hyper(373,a,47316,a,b,53638,a)].">
      <j1 rule="hyper" parents="373 47316 53638"/>
    </justification>
  </clause>

  <clause id="53681">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(x,y,a(u,z,w))
    ]]></literal>
    <justification jstring="[hyper(35,a,43396,a,b,53602,a)].">
      <j1 rule="hyper" parents="35 43396 53602"/>
    </justification>
  </clause>

  <clause id="53706">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = a(x,w,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(35,a,47271,a,b,53660,a)].">
      <j1 rule="hyper" parents="35 47271 53660"/>
    </justification>
  </clause>

  <clause id="53713">
    <literal><![CDATA[
      a(x,a(y,z,u),w) = a(x,w,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(373,a,53681,a,b,53706,a)].">
      <j1 rule="hyper" parents="373 53681 53706"/>
    </justification>
  </clause>

  <clause id="53757">
    <literal><![CDATA[
      a(a(x,y,z),u,w) = 1
    ]]></literal>
    <justification jstring="[hyper(138,a,53713,a(flip),b,46464,a),flip(a)].">
      <j1 rule="hyper" parents="138 53713 46464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="53758">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("aa1")
    ]]></attribute>
    <justification jstring="[resolve(53757,a,65,a)].">
      <j1 rule="resolve" parents="53757 65"/>
    </justification>
  </clause>

</proof>

</proofs>
